diff --git a/-4C9-OgKLCY.txt b/-4C9-OgKLCY.txt new file mode 100644 index 0000000000000000000000000000000000000000..b5ed150ba53c74fe8026903c3e6076ed89abf135 --- /dev/null +++ b/-4C9-OgKLCY.txt @@ -0,0 +1,5475 @@ +align:start position:0% + +so with that I am going to turn it off + + align:start position:0% +so with that I am going to turn it off + + + align:start position:0% +so with that I am going to turn it off +to our first keynote speaker Chris Clark + + align:start position:0% +to our first keynote speaker Chris Clark + + + align:start position:0% +to our first keynote speaker Chris Clark +she also works at Lincoln laboratory + + align:start position:0% +she also works at Lincoln laboratory + + + align:start position:0% +she also works at Lincoln laboratory +with me but in a completely different + + align:start position:0% +with me but in a completely different + + + align:start position:0% +with me but in a completely different +field she's going to talk about space + + align:start position:0% +field she's going to talk about space + + + align:start position:0% +field she's going to talk about space +cameras um so as Kristen said I'm also a + + align:start position:0% +cameras um so as Kristen said I'm also a + + + align:start position:0% +cameras um so as Kristen said I'm also a +chrisan um but for I I go by Chris I + + align:start position:0% +chrisan um but for I I go by Chris I + + + align:start position:0% +chrisan um but for I I go by Chris I +work at Lincoln Laboratory um and I want + + align:start position:0% +work at Lincoln Laboratory um and I want + + + align:start position:0% +work at Lincoln Laboratory um and I want +to say that uh this is an amazing + + align:start position:0% +to say that uh this is an amazing + + + align:start position:0% +to say that uh this is an amazing +program so first how many of you have + + align:start position:0% +program so first how many of you have + + + align:start position:0% +program so first how many of you have +ever done a program like this like an + + align:start position:0% +ever done a program like this like an + + + align:start position:0% +ever done a program like this like an +engineering kind of thing for for girls + + align:start position:0% +engineering kind of thing for for girls + + + align:start position:0% +engineering kind of thing for for girls +come on way up I can't see that well + + align:start position:0% +come on way up I can't see that well + + + align:start position:0% +come on way up I can't see that well +okay cool now how many of you are + + align:start position:0% +okay cool now how many of you are + + + align:start position:0% +okay cool now how many of you are +freshmen + + align:start position:0% +freshmen + + + align:start position:0% +freshmen +sophomores juniors + + align:start position:0% +sophomores juniors + + + align:start position:0% +sophomores juniors +seniors all right no seniors they're all + + align:start position:0% +seniors all right no seniors they're all + + + align:start position:0% +seniors all right no seniors they're all +busy doing college applications all + + align:start position:0% +busy doing college applications all + + + align:start position:0% +busy doing college applications all +right so let's get started so today I'm + + align:start position:0% +right so let's get started so today I'm + + + align:start position:0% +right so let's get started so today I'm +going to talk a little bit about me just + + align:start position:0% +going to talk a little bit about me just + + + align:start position:0% +going to talk a little bit about me just +because we're kind of looking at what + + align:start position:0% +because we're kind of looking at what + + + align:start position:0% +because we're kind of looking at what +makes an engineer right they look + + align:start position:0% +makes an engineer right they look + + + align:start position:0% +makes an engineer right they look +they're it can be all over the map so + + align:start position:0% +they're it can be all over the map so + + + align:start position:0% +they're it can be all over the map so +there's no one key picture of what an + + align:start position:0% +there's no one key picture of what an + + + align:start position:0% +there's no one key picture of what an +engineer looks like or what a scientist + + align:start position:0% +engineer looks like or what a scientist + + + align:start position:0% +engineer looks like or what a scientist +looks like um then we'll go into a + + align:start position:0% +looks like um then we'll go into a + + + align:start position:0% +looks like um then we'll go into a +little bit about just really basic stuff + + align:start position:0% +little bit about just really basic stuff + + + align:start position:0% +little bit about just really basic stuff +like what is a camera what are the key + + align:start position:0% +like what is a camera what are the key + + + align:start position:0% +like what is a camera what are the key +components of a camera and then uh what + + align:start position:0% +components of a camera and then uh what + + + align:start position:0% +components of a camera and then uh what +can cameras do and then specifically I'm + + align:start position:0% +can cameras do and then specifically I'm + + + align:start position:0% +can cameras do and then specifically I'm +going to tell you about the program I'm + + align:start position:0% +going to tell you about the program I'm + + + align:start position:0% +going to tell you about the program I'm +currently working on it is a space + + align:start position:0% +currently working on it is a space + + + align:start position:0% +currently working on it is a space +camera looking for um exoplanets so I'll + + align:start position:0% +camera looking for um exoplanets so I'll + + + align:start position:0% +camera looking for um exoplanets so I'll +tell you a little bit about the + + align:start position:0% +tell you a little bit about the + + + align:start position:0% +tell you a little bit about the +specifics of that and I have some kind + + align:start position:0% +specifics of that and I have some kind + + + align:start position:0% +specifics of that and I have some kind +of cool animations that they did for me + + align:start position:0% +of cool animations that they did for me + + + align:start position:0% +of cool animations that they did for me +to show you the orbit and all that sort + + align:start position:0% +to show you the orbit and all that sort + + + align:start position:0% +to show you the orbit and all that sort +of + + align:start position:0% +of + + + align:start position:0% +of +stuff so stop me raise your hand + + align:start position:0% +stuff so stop me raise your hand + + + align:start position:0% +stuff so stop me raise your hand +questions you know you don't have to + + align:start position:0% +questions you know you don't have to + + + align:start position:0% +questions you know you don't have to +wait till the end or anything so um just + + align:start position:0% +wait till the end or anything so um just + + + align:start position:0% +wait till the end or anything so um just +speak up raise your hand get my + + align:start position:0% +speak up raise your hand get my + + + align:start position:0% +speak up raise your hand get my +attention so how I got here so you guys + + align:start position:0% +attention so how I got here so you guys + + + align:start position:0% +attention so how I got here so you guys +all this is Massachusetts right I did + + align:start position:0% +all this is Massachusetts right I did + + + align:start position:0% +all this is Massachusetts right I did +not stray very far I was born in + + align:start position:0% +not stray very far I was born in + + + align:start position:0% +not stray very far I was born in +Worcester in the center of the state I + + align:start position:0% +Worcester in the center of the state I + + + align:start position:0% +Worcester in the center of the state I +moved to Bill R Mass when I was two with + + align:start position:0% +moved to Bill R Mass when I was two with + + + align:start position:0% +moved to Bill R Mass when I was two with +my family I went to um Bill r Memorial + + align:start position:0% +my family I went to um Bill r Memorial + + + align:start position:0% +my family I went to um Bill r Memorial +High School + + align:start position:0% +High School + + + align:start position:0% +High School +then I went to MIT for undergraduate + + align:start position:0% +then I went to MIT for undergraduate + + + align:start position:0% +then I went to MIT for undergraduate +then to tus for graduate school so it's + + align:start position:0% +then to tus for graduate school so it's + + + align:start position:0% +then to tus for graduate school so it's +kind of this circle I never went more + + align:start position:0% +kind of this circle I never went more + + + align:start position:0% +kind of this circle I never went more +than 50 miles from home and ended up at + + align:start position:0% +than 50 miles from home and ended up at + + + align:start position:0% +than 50 miles from home and ended up at +Lincoln laboratory I've been there for + + align:start position:0% +Lincoln laboratory I've been there for + + + align:start position:0% +Lincoln laboratory I've been there for +the last 12 years working on um + + align:start position:0% +the last 12 years working on um + + + align:start position:0% +the last 12 years working on um +space-based uh Optical systems so I have + + align:start position:0% +space-based uh Optical systems so I have + + + align:start position:0% +space-based uh Optical systems so I have +three brothers two of them are also + + align:start position:0% +three brothers two of them are also + + + align:start position:0% +three brothers two of them are also +techie Geeks one's a lawyer so he's kind + + align:start position:0% +techie Geeks one's a lawyer so he's kind + + + align:start position:0% +techie Geeks one's a lawyer so he's kind +of the odd man out but um the only time + + align:start position:0% +of the odd man out but um the only time + + + align:start position:0% +of the odd man out but um the only time +really that I left the country was to be + + align:start position:0% +really that I left the country was to be + + + align:start position:0% +really that I left the country was to be +an exchange student for a year in high + + align:start position:0% +an exchange student for a year in high + + + align:start position:0% +an exchange student for a year in high +school and other than that stayed very + + align:start position:0% +school and other than that stayed very + + + align:start position:0% +school and other than that stayed very +close to hes so there's tons of + + align:start position:0% +close to hes so there's tons of + + + align:start position:0% +close to hes so there's tons of +opportunities right in your own backyard + + align:start position:0% +opportunities right in your own backyard + + + align:start position:0% +opportunities right in your own backyard +for being an + + align:start position:0% +for being an + + + align:start position:0% +for being an +engineer all right so now I need some + + align:start position:0% +engineer all right so now I need some + + + align:start position:0% +engineer all right so now I need some +audience participation what is a camera + + align:start position:0% +audience participation what is a camera + + + align:start position:0% +audience participation what is a camera +anyone want to take a stab at just kind + + align:start position:0% +anyone want to take a stab at just kind + + + align:start position:0% +anyone want to take a stab at just kind +of a general definition of a + + align:start position:0% + + + + align:start position:0% + +camera or even just if you're not really + + align:start position:0% +camera or even just if you're not really + + + align:start position:0% +camera or even just if you're not really +sure how to define it maybe just + + align:start position:0% +sure how to define it maybe just + + + align:start position:0% +sure how to define it maybe just +describe what it does that's a good way + + align:start position:0% +describe what it does that's a good way + + + align:start position:0% +describe what it does that's a good way +to + + align:start position:0% +to + + + align:start position:0% +to +start a device that takes photos good + + align:start position:0% +start a device that takes photos good + + + align:start position:0% +start a device that takes photos good +good device that takes photos anybody + + align:start position:0% +good device that takes photos anybody + + + align:start position:0% +good device that takes photos anybody +want to add to + + align:start position:0% +want to add to + + + align:start position:0% +want to add to +that any like key piece of information + + align:start position:0% +that any like key piece of information + + + align:start position:0% +that any like key piece of information +you can think of that might improve the + + align:start position:0% +you can think of that might improve the + + + align:start position:0% +you can think of that might improve the +definition for if you needed to describe + + align:start position:0% +definition for if you needed to describe + + + align:start position:0% +definition for if you needed to describe +a camera to + + align:start position:0% + + + + align:start position:0% + +somebody light affects how the photo + + align:start position:0% +somebody light affects how the photo + + + align:start position:0% +somebody light affects how the photo +taken is that what you said yep yep so + + align:start position:0% +taken is that what you said yep yep so + + + align:start position:0% +taken is that what you said yep yep so +light is very key right that's pretty + + align:start position:0% +light is very key right that's pretty + + + align:start position:0% +light is very key right that's pretty +much what we're trying to collect + + align:start position:0% +much what we're trying to collect + + + align:start position:0% +much what we're trying to collect +anybody else want to add to the + + align:start position:0% +anybody else want to add to the + + + align:start position:0% +anybody else want to add to the +definition all right well let's see this + + align:start position:0% +definition all right well let's see this + + + align:start position:0% +definition all right well let's see this +is kind of a generic definition camera + + align:start position:0% +is kind of a generic definition camera + + + align:start position:0% +is kind of a generic definition camera +is an optical instrument for recording + + align:start position:0% +is an optical instrument for recording + + + align:start position:0% +is an optical instrument for recording +or capturing images so if you look at + + align:start position:0% +or capturing images so if you look at + + + align:start position:0% +or capturing images so if you look at +that definition really there are two + + align:start position:0% +that definition really there are two + + + align:start position:0% +that definition really there are two +basic components you need to a camera + + align:start position:0% +basic components you need to a camera + + + align:start position:0% +basic components you need to a camera +does anyone want to take a guess at one + + align:start position:0% +does anyone want to take a guess at one + + + align:start position:0% +does anyone want to take a guess at one +or both of + + align:start position:0% +or both of + + + align:start position:0% +or both of +them what's the first thing you have to + + align:start position:0% +them what's the first thing you have to + + + align:start position:0% +them what's the first thing you have to +do when you want to take a + + align:start position:0% + + + + align:start position:0% + +picture all right I'll give you this + + align:start position:0% +picture all right I'll give you this + + + align:start position:0% +picture all right I'll give you this +one somehow you have to collect the + + align:start position:0% +one somehow you have to collect the + + + align:start position:0% +one somehow you have to collect the +light right so Focus your energy it can + + align:start position:0% +light right so Focus your energy it can + + + align:start position:0% +light right so Focus your energy it can +be visible light we'll talk a little bit + + align:start position:0% +be visible light we'll talk a little bit + + + align:start position:0% +be visible light we'll talk a little bit +more about other types of energy but + + align:start position:0% +more about other types of energy but + + + align:start position:0% +more about other types of energy but +once you have that light where you want + + align:start position:0% +once you have that light where you want + + + align:start position:0% +once you have that light where you want +it what's the next step it's there but + + align:start position:0% +it what's the next step it's there but + + + align:start position:0% +it what's the next step it's there but +what do you have to do to get a + + align:start position:0% +what do you have to do to get a + + + align:start position:0% +what do you have to do to get a +picture have something to record exactly + + align:start position:0% +picture have something to record exactly + + + align:start position:0% +picture have something to record exactly +so you need to detector right so + + align:start position:0% +so you need to detector right so + + + align:start position:0% +so you need to detector right so +basically two components you want to get + + align:start position:0% +basically two components you want to get + + + align:start position:0% +basically two components you want to get +the light for whatever you're trying to + + align:start position:0% +the light for whatever you're trying to + + + align:start position:0% +the light for whatever you're trying to +image to a particular place and then you + + align:start position:0% +image to a particular place and then you + + + align:start position:0% +image to a particular place and then you +need some sort of device old school if + + align:start position:0% +need some sort of device old school if + + + align:start position:0% +need some sort of device old school if +you're old school like me you've seen + + align:start position:0% +you're old school like me you've seen + + + align:start position:0% +you're old school like me you've seen +film cameras before you took some of + + align:start position:0% +film cameras before you took some of + + + align:start position:0% +film cameras before you took some of +those apart so film was the detector now + + align:start position:0% +those apart so film was the detector now + + + align:start position:0% +those apart so film was the detector now +it's much more the digital age right you + + align:start position:0% +it's much more the digital age right you + + + align:start position:0% +it's much more the digital age right you +get ccds and all sorts of digital + + align:start position:0% +get ccds and all sorts of digital + + + align:start position:0% +get ccds and all sorts of digital +imagers so so those are basically the + + align:start position:0% +imagers so so those are basically the + + + align:start position:0% +imagers so so those are basically the +two things that you have to do for a + + align:start position:0% +two things that you have to do for a + + + align:start position:0% +two things that you have to do for a +camera and then from there Sky limit + + align:start position:0% +camera and then from there Sky limit + + + align:start position:0% +camera and then from there Sky limit +there are so many different types that + + align:start position:0% +there are so many different types that + + + align:start position:0% +there are so many different types that +you can do so I thought I'd start really + + align:start position:0% +you can do so I thought I'd start really + + + align:start position:0% +you can do so I thought I'd start really +simply does that has anyone ever heard + + align:start position:0% +simply does that has anyone ever heard + + + align:start position:0% +simply does that has anyone ever heard +of a pinhole camera anyone ever built a + + align:start position:0% +of a pinhole camera anyone ever built a + + + align:start position:0% +of a pinhole camera anyone ever built a +pinhole camera all right so what's the + + align:start position:0% +pinhole camera all right so what's the + + + align:start position:0% +pinhole camera all right so what's the +basic premise do you remember what the + + align:start position:0% +basic premise do you remember what the + + + align:start position:0% +basic premise do you remember what the +the ideas behind a pinhole camera yeah + + align:start position:0% +the ideas behind a pinhole camera yeah + + + align:start position:0% +the ideas behind a pinhole camera yeah +you just put like a little like holes in + + align:start position:0% +you just put like a little like holes in + + + align:start position:0% +you just put like a little like holes in +a box yep so you have let see if I can + + align:start position:0% +a box yep so you have let see if I can + + + align:start position:0% +a box yep so you have let see if I can +get my little pointer thingy to work + + align:start position:0% +get my little pointer thingy to work + + + align:start position:0% +get my little pointer thingy to work +tiny tiny hole in a dark box so there's + + align:start position:0% +tiny tiny hole in a dark box so there's + + + align:start position:0% +tiny tiny hole in a dark box so there's +not even a lens in this camera that but + + align:start position:0% +not even a lens in this camera that but + + + align:start position:0% +not even a lens in this camera that but +that tiny tiny tiny hole is the the + + align:start position:0% +that tiny tiny tiny hole is the the + + + align:start position:0% +that tiny tiny tiny hole is the the +first half of what you need for a camera + + align:start position:0% +first half of what you need for a camera + + + align:start position:0% +first half of what you need for a camera +something to collect the light now the + + align:start position:0% +something to collect the light now the + + + align:start position:0% +something to collect the light now the +problem with a pinhole camera the tiny + + align:start position:0% +problem with a pinhole camera the tiny + + + align:start position:0% +problem with a pinhole camera the tiny +tiny hole you can't collect much light + + align:start position:0% +tiny hole you can't collect much light + + + align:start position:0% +tiny hole you can't collect much light +but it does limit very specifically that + + align:start position:0% +but it does limit very specifically that + + + align:start position:0% +but it does limit very specifically that +light from a particular point in what + + align:start position:0% +light from a particular point in what + + + align:start position:0% +light from a particular point in what +you're looking at can only get to a very + + align:start position:0% +you're looking at can only get to a very + + + align:start position:0% +you're looking at can only get to a very +specific point on the inside of the box + + align:start position:0% +specific point on the inside of the box + + + align:start position:0% +specific point on the inside of the box +and so basically that's your limiting + + align:start position:0% +and so basically that's your limiting + + + align:start position:0% +and so basically that's your limiting +light collection and the back surface of + + align:start position:0% +light collection and the back surface of + + + align:start position:0% +light collection and the back surface of +the box is your image plane now you + + align:start position:0% +the box is your image plane now you + + + align:start position:0% +the box is your image plane now you +can't really capture it because it's + + align:start position:0% +can't really capture it because it's + + + align:start position:0% +can't really capture it because it's +just the back of a box but you can look + + align:start position:0% +just the back of a box but you can look + + + align:start position:0% +just the back of a box but you can look +at it and it's there if you want to see + + align:start position:0% +at it and it's there if you want to see + + + align:start position:0% +at it and it's there if you want to see +it so very very primitive + + align:start position:0% +it so very very primitive + + + align:start position:0% +it so very very primitive +right so if we get into some things that + + align:start position:0% +right so if we get into some things that + + + align:start position:0% +right so if we get into some things that +you guys see every day and you probably + + align:start position:0% +you guys see every day and you probably + + + align:start position:0% +you guys see every day and you probably +don't really think a whole lot about how + + align:start position:0% +don't really think a whole lot about how + + + align:start position:0% +don't really think a whole lot about how +they work but um who would have guessed + + align:start position:0% +they work but um who would have guessed + + + align:start position:0% +they work but um who would have guessed +how many components are in that little + + align:start position:0% +how many components are in that little + + + align:start position:0% +how many components are in that little +tiny phone camera that's a lot of stuff + + align:start position:0% +tiny phone camera that's a lot of stuff + + + align:start position:0% +tiny phone camera that's a lot of stuff +right there's like six lenses before you + + align:start position:0% +right there's like six lenses before you + + + align:start position:0% +right there's like six lenses before you +even get to your detector image so lots + + align:start position:0% +even get to your detector image so lots + + + align:start position:0% +even get to your detector image so lots +of lenses are used and we won't talk + + align:start position:0% +of lenses are used and we won't talk + + + align:start position:0% +of lenses are used and we won't talk +specifically about lens design but + + align:start position:0% +specifically about lens design but + + + align:start position:0% +specifically about lens design but +basically the fancy your cameras have + + align:start position:0% +basically the fancy your cameras have + + + align:start position:0% +basically the fancy your cameras have +gotten you've noticed like iPhone + + align:start position:0% +gotten you've noticed like iPhone + + + align:start position:0% +gotten you've noticed like iPhone +cameras always tell you oh now we have + + align:start position:0% +cameras always tell you oh now we have + + + align:start position:0% +cameras always tell you oh now we have +you know that our image quality is + + align:start position:0% +you know that our image quality is + + + align:start position:0% +you know that our image quality is +improved from iPhone 4 to iPhone 6 by + + align:start position:0% +improved from iPhone 4 to iPhone 6 by + + + align:start position:0% +improved from iPhone 4 to iPhone 6 by +whatever percent it's all about how well + + align:start position:0% +whatever percent it's all about how well + + + align:start position:0% +whatever percent it's all about how well +you can correct the light that you're + + align:start position:0% +you can correct the light that you're + + + align:start position:0% +you can correct the light that you're +trying to collect and get it in the spot + + align:start position:0% +trying to collect and get it in the spot + + + align:start position:0% +trying to collect and get it in the spot +where you want it to be and that takes + + align:start position:0% +where you want it to be and that takes + + + align:start position:0% +where you want it to be and that takes +more and more lenses so that gets more + + align:start position:0% +more and more lenses so that gets more + + + align:start position:0% +more and more lenses so that gets more +sophisticated um now I like and then you + + align:start position:0% +sophisticated um now I like and then you + + + align:start position:0% +sophisticated um now I like and then you +have your software for image processing + + align:start position:0% +have your software for image processing + + + align:start position:0% +have your software for image processing +right so you can play around like when + + align:start position:0% +right so you can play around like when + + + align:start position:0% +right so you can play around like when +you post on and I'm way too old for this + + align:start position:0% +you post on and I'm way too old for this + + + align:start position:0% +you post on and I'm way too old for this +but Instagram and Twitter right you can + + align:start position:0% +but Instagram and Twitter right you can + + + align:start position:0% +but Instagram and Twitter right you can +do like color filters and and make it + + align:start position:0% +do like color filters and and make it + + + align:start position:0% +do like color filters and and make it +look kind of different that's all in the + + align:start position:0% +look kind of different that's all in the + + + align:start position:0% +look kind of different that's all in the +image processing you guys will get to do + + align:start position:0% +image processing you guys will get to do + + + align:start position:0% +image processing you guys will get to do +now I like the ey as an example because + + align:start position:0% +now I like the ey as an example because + + + align:start position:0% +now I like the ey as an example because +you've been using this camera since you + + align:start position:0% +you've been using this camera since you + + + align:start position:0% +you've been using this camera since you +were born and pretty much you have a + + align:start position:0% +were born and pretty much you have a + + + align:start position:0% +were born and pretty much you have a +lens it focuses the light on the back of + + align:start position:0% +lens it focuses the light on the back of + + + align:start position:0% +lens it focuses the light on the back of +your eye which is called the retina + + align:start position:0% +your eye which is called the retina + + + align:start position:0% +your eye which is called the retina +that's your detector and then your brain + + align:start position:0% +that's your detector and then your brain + + + align:start position:0% +that's your detector and then your brain +processes the information from the + + align:start position:0% +processes the information from the + + + align:start position:0% +processes the information from the +retina so your brain really is the image + + align:start position:0% +retina so your brain really is the image + + + align:start position:0% +retina so your brain really is the image +processing software and I don't know if + + align:start position:0% +processing software and I don't know if + + + align:start position:0% +processing software and I don't know if +you guys knew this but if we go back + + align:start position:0% +you guys knew this but if we go back + + + align:start position:0% +you guys knew this but if we go back +to what do you notice about the image of + + align:start position:0% +to what do you notice about the image of + + + align:start position:0% +to what do you notice about the image of +the tree in the pinhole camera upside + + align:start position:0% +the tree in the pinhole camera upside + + + align:start position:0% +the tree in the pinhole camera upside +down it's upside down right when your + + align:start position:0% +down it's upside down right when your + + + align:start position:0% +down it's upside down right when your +eye lens focuses on the back of your + + align:start position:0% +eye lens focuses on the back of your + + + align:start position:0% +eye lens focuses on the back of your +retina the image is actually inverted as + + align:start position:0% +retina the image is actually inverted as + + + align:start position:0% +retina the image is actually inverted as +well your brain fixes that for you so + + align:start position:0% +well your brain fixes that for you so + + + align:start position:0% +well your brain fixes that for you so +it's just kind of a funny thing like + + align:start position:0% +it's just kind of a funny thing like + + + align:start position:0% +it's just kind of a funny thing like +you're looking at it your lens actually + + align:start position:0% +you're looking at it your lens actually + + + align:start position:0% +you're looking at it your lens actually +focuses it upside down but your brain + + align:start position:0% +focuses it upside down but your brain + + + align:start position:0% +focuses it upside down but your brain +knows that up and down so kind of an + + align:start position:0% +knows that up and down so kind of an + + + align:start position:0% +knows that up and down so kind of an +interesting uh built-in image processing + + align:start position:0% +interesting uh built-in image processing + + + align:start position:0% +interesting uh built-in image processing +so can you guys think of any other + + align:start position:0% +so can you guys think of any other + + + align:start position:0% +so can you guys think of any other +examples of cameras that you use kind of + + align:start position:0% +examples of cameras that you use kind of + + + align:start position:0% +examples of cameras that you use kind of +every day + + align:start position:0% +every day + + + align:start position:0% +every day +or maybe not every day just specific + + align:start position:0% +or maybe not every day just specific + + + align:start position:0% +or maybe not every day just specific +ones you've heard of for other maybe for + + align:start position:0% +ones you've heard of for other maybe for + + + align:start position:0% +ones you've heard of for other maybe for +other + + align:start position:0% +other + + + align:start position:0% +other +applications you seen a camera somewhere + + align:start position:0% +applications you seen a camera somewhere + + + align:start position:0% +applications you seen a camera somewhere +else that you go during the day + + align:start position:0% +else that you go during the day + + + align:start position:0% +else that you go during the day +or H let's + + align:start position:0% + + + + align:start position:0% + +see I guess like C use like + + align:start position:0% +see I guess like C use like + + + align:start position:0% +see I guess like C use like +surgery what's + + align:start position:0% + + + + align:start position:0% + +inside yeah exactly so and you're you + + align:start position:0% +inside yeah exactly so and you're you + + + align:start position:0% +inside yeah exactly so and you're you +guys are going to hear about um a really + + align:start position:0% +guys are going to hear about um a really + + + align:start position:0% +guys are going to hear about um a really +cool Medical Imaging uh camera at + + align:start position:0% +cool Medical Imaging uh camera at + + + align:start position:0% +cool Medical Imaging uh camera at +lunchtime I think one that detects + + align:start position:0% +lunchtime I think one that detects + + + align:start position:0% +lunchtime I think one that detects +tumors in patients so very good example + + align:start position:0% +tumors in patients so very good example + + + align:start position:0% +tumors in patients so very good example +anybody got another different example of + + align:start position:0% +anybody got another different example of + + + align:start position:0% +anybody got another different example of +what cameras are used for infrar yep + + align:start position:0% +what cameras are used for infrar yep + + + align:start position:0% +what cameras are used for infrar yep +infrared cameras what do those + + align:start position:0% +infrared cameras what do those + + + align:start position:0% +infrared cameras what do those +do exactly and that brings us to our + + align:start position:0% +do exactly and that brings us to our + + + align:start position:0% +do exactly and that brings us to our +next portion so when we talk about light + + align:start position:0% +next portion so when we talk about light + + + align:start position:0% +next portion so when we talk about light +is anyone familiar with the term + + align:start position:0% +is anyone familiar with the term + + + align:start position:0% +is anyone familiar with the term +electromagnetic + + align:start position:0% +electromagnetic + + + align:start position:0% +electromagnetic +spectrum you know what that mean can you + + align:start position:0% +spectrum you know what that mean can you + + + align:start position:0% +spectrum you know what that mean can you +describe it a little bit um it's the + + align:start position:0% +describe it a little bit um it's the + + + align:start position:0% +describe it a little bit um it's the +it's the + + align:start position:0% +it's the + + + align:start position:0% +it's the +different scale for + + align:start position:0% +different scale for + + + align:start position:0% +different scale for +the exactly right so so light and other + + align:start position:0% +the exactly right so so light and other + + + align:start position:0% +the exactly right so so light and other +so we refer to light when most of the + + align:start position:0% +so we refer to light when most of the + + + align:start position:0% +so we refer to light when most of the +time when you say light you think of + + align:start position:0% +time when you say light you think of + + + align:start position:0% +time when you say light you think of +visible light right what we can see but + + align:start position:0% +visible light right what we can see but + + + align:start position:0% +visible light right what we can see but +really the electromagnetic spectrum + + align:start position:0% +really the electromagnetic spectrum + + + align:start position:0% +really the electromagnetic spectrum +defines an a really large range of + + align:start position:0% +defines an a really large range of + + + align:start position:0% +defines an a really large range of +basically electromagnetic waves and this + + align:start position:0% +basically electromagnetic waves and this + + + align:start position:0% +basically electromagnetic waves and this +very small region and we kind of Define + + align:start position:0% +very small region and we kind of Define + + + align:start position:0% +very small region and we kind of Define +this by wavelength right how long is the + + align:start position:0% +this by wavelength right how long is the + + + align:start position:0% +this by wavelength right how long is the +is the wavelength of the light most of + + align:start position:0% +is the wavelength of the light most of + + + align:start position:0% +is the wavelength of the light most of +the stuff we work with is in this very + + align:start position:0% +the stuff we work with is in this very + + + align:start position:0% +the stuff we work with is in this very +small Spectrum but it branches all the + + align:start position:0% +small Spectrum but it branches all the + + + align:start position:0% +small Spectrum but it branches all the +way out here to radio frequencies where + + align:start position:0% +way out here to radio frequencies where + + + align:start position:0% +way out here to radio frequencies where +you know a wavelength is the size of a + + align:start position:0% +you know a wavelength is the size of a + + + align:start position:0% +you know a wavelength is the size of a +building all the way out to like gamma + + align:start position:0% +building all the way out to like gamma + + + align:start position:0% +building all the way out to like gamma +rays where a wavelength is like atomic + + align:start position:0% +rays where a wavelength is like atomic + + + align:start position:0% +rays where a wavelength is like atomic +size right so the big reason probably + + align:start position:0% +size right so the big reason probably + + + align:start position:0% +size right so the big reason probably +that we focus so much on visible that's + + align:start position:0% +that we focus so much on visible that's + + + align:start position:0% +that we focus so much on visible that's +where our eyes work that's you know + + align:start position:0% +where our eyes work that's you know + + + align:start position:0% +where our eyes work that's you know +that's where we learned everything from + + align:start position:0% +that's where we learned everything from + + + align:start position:0% +that's where we learned everything from +the ground up of how Imaging Works cuz + + align:start position:0% +the ground up of how Imaging Works cuz + + + align:start position:0% +the ground up of how Imaging Works cuz +we didn't have ccds we didn't have film + + align:start position:0% +we didn't have ccds we didn't have film + + + align:start position:0% +we didn't have ccds we didn't have film +a long time ago we only had eyes and + + align:start position:0% +a long time ago we only had eyes and + + + align:start position:0% +a long time ago we only had eyes and +what we could see but now there are + + align:start position:0% +what we could see but now there are + + + align:start position:0% +what we could see but now there are +cameras available like you said infrared + + align:start position:0% +cameras available like you said infrared + + + align:start position:0% +cameras available like you said infrared +and I have a little picture of that + + align:start position:0% +and I have a little picture of that + + + align:start position:0% +and I have a little picture of that +right you can take a picture of your dog + + align:start position:0% +right you can take a picture of your dog + + + align:start position:0% +right you can take a picture of your dog +um so basically um it's a different type + + align:start position:0% +um so basically um it's a different type + + + align:start position:0% +um so basically um it's a different type +of camera it's collecting infrared light + + align:start position:0% +of camera it's collecting infrared light + + + align:start position:0% +of camera it's collecting infrared light +which your eyes cannot see but the + + align:start position:0% +which your eyes cannot see but the + + + align:start position:0% +which your eyes cannot see but the +particular lenses that are used to focus + + align:start position:0% +particular lenses that are used to focus + + + align:start position:0% +particular lenses that are used to focus +this light are specific materials that + + align:start position:0% +this light are specific materials that + + + align:start position:0% +this light are specific materials that +are used to focus infrared wavelengths + + align:start position:0% +are used to focus infrared wavelengths + + + align:start position:0% +are used to focus infrared wavelengths +and the detector is sensitive to that + + align:start position:0% +and the detector is sensitive to that + + + align:start position:0% +and the detector is sensitive to that +range of wavelengths as well so when we + + align:start position:0% +range of wavelengths as well so when we + + + align:start position:0% +range of wavelengths as well so when we +say we need a lens and a detector it's + + align:start position:0% +say we need a lens and a detector it's + + + align:start position:0% +say we need a lens and a detector it's +important to realize that the Mater + + align:start position:0% +important to realize that the Mater + + + align:start position:0% +important to realize that the Mater +materials that go into those are very um + + align:start position:0% +materials that go into those are very um + + + align:start position:0% +materials that go into those are very um +specific to whatever part of the + + align:start position:0% +specific to whatever part of the + + + align:start position:0% +specific to whatever part of the +spectrum you're trying to trying to + + align:start position:0% +spectrum you're trying to trying to + + + align:start position:0% +spectrum you're trying to trying to +image so there's an awful lot that goes + + align:start position:0% +image so there's an awful lot that goes + + + align:start position:0% +image so there's an awful lot that goes +into it some people spend their entire + + align:start position:0% +into it some people spend their entire + + + align:start position:0% +into it some people spend their entire +career on visible systems some people + + align:start position:0% +career on visible systems some people + + + align:start position:0% +career on visible systems some people +work entirely in the infrared there are + + align:start position:0% +work entirely in the infrared there are + + + align:start position:0% +work entirely in the infrared there are +whole companies Fleer system is all + + align:start position:0% +whole companies Fleer system is all + + + align:start position:0% +whole companies Fleer system is all +about forward looking infrared right so + + align:start position:0% +about forward looking infrared right so + + + align:start position:0% +about forward looking infrared right so +their whole business is built on + + align:start position:0% +their whole business is built on + + + align:start position:0% +their whole business is built on +infrared cameras certainly Medical + + align:start position:0% +infrared cameras certainly Medical + + + align:start position:0% +infrared cameras certainly Medical +Imaging right you got x-rays um so + + align:start position:0% +Imaging right you got x-rays um so + + + align:start position:0% +Imaging right you got x-rays um so +there's tons of fields and they can be + + align:start position:0% +there's tons of fields and they can be + + + align:start position:0% +there's tons of fields and they can be +very specific about what range they're + + align:start position:0% +very specific about what range they're + + + align:start position:0% +very specific about what range they're +looking at + + align:start position:0% +looking at + + + align:start position:0% +looking at +so I threw up some other examples some + + align:start position:0% +so I threw up some other examples some + + + align:start position:0% +so I threw up some other examples some +of them you guys already hid on right so + + align:start position:0% +of them you guys already hid on right so + + + align:start position:0% +of them you guys already hid on right so +here's that little tiny that's funny you + + align:start position:0% +here's that little tiny that's funny you + + + align:start position:0% +here's that little tiny that's funny you +mentioned that so little tiny camera + + align:start position:0% +mentioned that so little tiny camera + + + align:start position:0% +mentioned that so little tiny camera +that you can actually swallow and people + + align:start position:0% +that you can actually swallow and people + + + align:start position:0% +that you can actually swallow and people +you know they can image things in your + + align:start position:0% +you know they can image things in your + + + align:start position:0% +you know they can image things in your +digestive tract it's a little bit creepy + + align:start position:0% +digestive tract it's a little bit creepy + + + align:start position:0% +digestive tract it's a little bit creepy +to think about but it works um certainly + + align:start position:0% +to think about but it works um certainly + + + align:start position:0% +to think about but it works um certainly +if you've been to the airport anytime + + align:start position:0% +if you've been to the airport anytime + + + align:start position:0% +if you've been to the airport anytime +recently Homeland Security right um + + align:start position:0% +recently Homeland Security right um + + + align:start position:0% +recently Homeland Security right um +cameras everywhere does anybody know + + align:start position:0% +cameras everywhere does anybody know + + + align:start position:0% +cameras everywhere does anybody know +there's a specific kind of software that + + align:start position:0% +there's a specific kind of software that + + + align:start position:0% +there's a specific kind of software that +they can use um with cameras in the + + align:start position:0% +they can use um with cameras in the + + + align:start position:0% +they can use um with cameras in the +airport like that can do something very + + align:start position:0% +airport like that can do something very + + + align:start position:0% +airport like that can do something very +specific if you're looking for a + + align:start position:0% +specific if you're looking for a + + + align:start position:0% +specific if you're looking for a +particular + + align:start position:0% + + + + align:start position:0% + +person oh + + align:start position:0% +person oh + + + align:start position:0% +person oh +sorry face recognition right right so + + align:start position:0% +sorry face recognition right right so + + + align:start position:0% +sorry face recognition right right so +that's part of the image processing side + + align:start position:0% +that's part of the image processing side + + + align:start position:0% +that's part of the image processing side +of things right there are um cameras + + align:start position:0% +of things right there are um cameras + + + align:start position:0% +of things right there are um cameras +very sophisticated that are can scan + + align:start position:0% +very sophisticated that are can scan + + + align:start position:0% +very sophisticated that are can scan +whole crowds and based on a still image + + align:start position:0% +whole crowds and based on a still image + + + align:start position:0% +whole crowds and based on a still image +of a particular person they can try and + + align:start position:0% +of a particular person they can try and + + + align:start position:0% +of a particular person they can try and +pick out facial features by matching the + + align:start position:0% +pick out facial features by matching the + + + align:start position:0% +pick out facial features by matching the +images so it's it's pretty amazing stuff + + align:start position:0% +images so it's it's pretty amazing stuff + + + align:start position:0% +images so it's it's pretty amazing stuff +when you think about scanning through a + + align:start position:0% +when you think about scanning through a + + + align:start position:0% +when you think about scanning through a +crowd of hundreds of people and being + + align:start position:0% +crowd of hundreds of people and being + + + align:start position:0% +crowd of hundreds of people and being +able to pick out a specific person so um + + align:start position:0% +able to pick out a specific person so um + + + align:start position:0% +able to pick out a specific person so um +traffic regulation you know that's a + + align:start position:0% +traffic regulation you know that's a + + + align:start position:0% +traffic regulation you know that's a +little less exciting but they take a + + align:start position:0% +little less exciting but they take a + + + align:start position:0% +little less exciting but they take a +picture of you if you run a red light um + + align:start position:0% +picture of you if you run a red light um + + + align:start position:0% +picture of you if you run a red light um +certainly I've worked on oh sorry I've + + align:start position:0% +certainly I've worked on oh sorry I've + + + align:start position:0% +certainly I've worked on oh sorry I've +worked on a bunch of programs at Lincoln + + align:start position:0% +worked on a bunch of programs at Lincoln + + + align:start position:0% +worked on a bunch of programs at Lincoln +laboratory that are through um that work + + align:start position:0% +laboratory that are through um that work + + + align:start position:0% +laboratory that are through um that work +for to look at various aspects of + + align:start position:0% +for to look at various aspects of + + + align:start position:0% +for to look at various aspects of +weather sensing so anything I worked on + + align:start position:0% +weather sensing so anything I worked on + + + align:start position:0% +weather sensing so anything I worked on +one that was made to detect lightning + + align:start position:0% +one that was made to detect lightning + + + align:start position:0% +one that was made to detect lightning +because lightning causes Force fires and + + align:start position:0% +because lightning causes Force fires and + + + align:start position:0% +because lightning causes Force fires and +if you know where the lightning is going + + align:start position:0% +if you know where the lightning is going + + + align:start position:0% +if you know where the lightning is going +to strike you can kind of be prepared so + + align:start position:0% +to strike you can kind of be prepared so + + + align:start position:0% +to strike you can kind of be prepared so +very specific uses in weather sensing + + align:start position:0% +very specific uses in weather sensing + + + align:start position:0% +very specific uses in weather sensing +and then of course that brings us to my + + align:start position:0% +and then of course that brings us to my + + + align:start position:0% +and then of course that brings us to my +favorite space exploration which is what + + align:start position:0% +favorite space exploration which is what + + + align:start position:0% +favorite space exploration which is what +I'm working on + + align:start position:0% +I'm working on + + + align:start position:0% +I'm working on +now so now over broadreach of examples + + align:start position:0% +now so now over broadreach of examples + + + align:start position:0% +now so now over broadreach of examples +I'm going to talk about specifically the + + align:start position:0% +I'm going to talk about specifically the + + + align:start position:0% +I'm going to talk about specifically the +one for space applications and this is + + align:start position:0% +one for space applications and this is + + + align:start position:0% +one for space applications and this is +the current program that I'm working on + + align:start position:0% +the current program that I'm working on + + + align:start position:0% +the current program that I'm working on +I've been working on it for about four + + align:start position:0% +I've been working on it for about four + + + align:start position:0% +I've been working on it for about four +years right from the very beginning + + align:start position:0% +years right from the very beginning + + + align:start position:0% +years right from the very beginning +where we developed the first prototype + + align:start position:0% +where we developed the first prototype + + + align:start position:0% +where we developed the first prototype +camera and we've refined it since then + + align:start position:0% +camera and we've refined it since then + + + align:start position:0% +camera and we've refined it since then +so tell you a bit about that has anyone + + align:start position:0% +so tell you a bit about that has anyone + + + align:start position:0% +so tell you a bit about that has anyone +heard of it because it actually has its + + align:start position:0% +heard of it because it actually has its + + + align:start position:0% +heard of it because it actually has its +own Facebook page which is unusual for a + + align:start position:0% +own Facebook page which is unusual for a + + + align:start position:0% +own Facebook page which is unusual for a +lab program because it's completely + + align:start position:0% +lab program because it's completely + + + align:start position:0% +lab program because it's completely +unclassified and it has lots of + + align:start position:0% +unclassified and it has lots of + + + align:start position:0% +unclassified and it has lots of +followers it's um the science Community + + align:start position:0% +followers it's um the science Community + + + align:start position:0% +followers it's um the science Community +that's looking to use the data from Tess + + align:start position:0% +that's looking to use the data from Tess + + + align:start position:0% +that's looking to use the data from Tess +is all over the world like the Tess + + align:start position:0% +is all over the world like the Tess + + + align:start position:0% +is all over the world like the Tess +science Community actually meets down + + align:start position:0% +science Community actually meets down + + + align:start position:0% +science Community actually meets down +the road at at Harvard and uh they have + + align:start position:0% +the road at at Harvard and uh they have + + + align:start position:0% +the road at at Harvard and uh they have +people from all over Europe and nobody's + + align:start position:0% +people from all over Europe and nobody's + + + align:start position:0% +people from all over Europe and nobody's +heard of + + align:start position:0% +heard of + + + align:start position:0% +heard of +it um okay so I'm not really surprised + + align:start position:0% +it um okay so I'm not really surprised + + + align:start position:0% +it um okay so I'm not really surprised +but I figur Facebook you might have + + align:start position:0% +but I figur Facebook you might have + + + align:start position:0% +but I figur Facebook you might have +happened upon it um so basically the + + align:start position:0% +happened upon it um so basically the + + + align:start position:0% +happened upon it um so basically the +goal for tests is has anyone heard of + + align:start position:0% +goal for tests is has anyone heard of + + + align:start position:0% +goal for tests is has anyone heard of +Kepler here yeah so do you do you know + + align:start position:0% +Kepler here yeah so do you do you know + + + align:start position:0% +Kepler here yeah so do you do you know +what Kepler was looking for exop yep who + + align:start position:0% +what Kepler was looking for exop yep who + + + align:start position:0% +what Kepler was looking for exop yep who +knows what an exoplanet is + + align:start position:0% + + + + align:start position:0% + +anybody exactly sorry y it's any plant + + align:start position:0% +anybody exactly sorry y it's any plant + + + align:start position:0% +anybody exactly sorry y it's any plant +so it's that's pretty large field right + + align:start position:0% +so it's that's pretty large field right + + + align:start position:0% +so it's that's pretty large field right +because there only nine I still count + + align:start position:0% +because there only nine I still count + + + align:start position:0% +because there only nine I still count +Pluto um so any other planet that you + + align:start position:0% +Pluto um so any other planet that you + + + align:start position:0% +Pluto um so any other planet that you +can think of is called an exoplanet so + + align:start position:0% +can think of is called an exoplanet so + + + align:start position:0% +can think of is called an exoplanet so +something outside of our solar system so + + align:start position:0% +something outside of our solar system so + + + align:start position:0% +something outside of our solar system so +Kepler did look for um exoplanets and it + + align:start position:0% +Kepler did look for um exoplanets and it + + + align:start position:0% +Kepler did look for um exoplanets and it +was kind of the first one up there to + + align:start position:0% +was kind of the first one up there to + + + align:start position:0% +was kind of the first one up there to +look and see what we think there's a lot + + align:start position:0% +look and see what we think there's a lot + + + align:start position:0% +look and see what we think there's a lot +of exoplanets out there but let's go + + align:start position:0% +of exoplanets out there but let's go + + + align:start position:0% +of exoplanets out there but let's go +look at a specific section of the sky + + align:start position:0% +look at a specific section of the sky + + + align:start position:0% +look at a specific section of the sky +and make sure before we build lots of + + align:start position:0% +and make sure before we build lots of + + + align:start position:0% +and make sure before we build lots of +other missions to go look for exoplanets + + align:start position:0% +other missions to go look for exoplanets + + + align:start position:0% +other missions to go look for exoplanets +that that were kind of right and when + + align:start position:0% +that that were kind of right and when + + + align:start position:0% +that that were kind of right and when +Kepler did confirm there's an awful lot + + align:start position:0% +Kepler did confirm there's an awful lot + + + align:start position:0% +Kepler did confirm there's an awful lot +of exoplanets to look for so Along Came + + align:start position:0% +of exoplanets to look for so Along Came + + + align:start position:0% +of exoplanets to look for so Along Came +Tess Tess's goal is to go up and it's + + align:start position:0% +Tess Tess's goal is to go up and it's + + + align:start position:0% +Tess Tess's goal is to go up and it's +spent two years basically canvasing the + + align:start position:0% +spent two years basically canvasing the + + + align:start position:0% +spent two years basically canvasing the +entire sky looking at specific types of + + align:start position:0% +entire sky looking at specific types of + + + align:start position:0% +entire sky looking at specific types of +stars sort of red cooler stars to + + align:start position:0% +stars sort of red cooler stars to + + + align:start position:0% +stars sort of red cooler stars to +identify um where exoplanets might be + + align:start position:0% +identify um where exoplanets might be + + + align:start position:0% +identify um where exoplanets might be +and we do that it's pretty it's very + + align:start position:0% +and we do that it's pretty it's very + + + align:start position:0% +and we do that it's pretty it's very +simple actually if you have a star and + + align:start position:0% +simple actually if you have a star and + + + align:start position:0% +simple actually if you have a star and +and you happen to be looking at it in + + align:start position:0% +and you happen to be looking at it in + + + align:start position:0% +and you happen to be looking at it in +the planet's transiting is what it's + + align:start position:0% +the planet's transiting is what it's + + + align:start position:0% +the planet's transiting is what it's +called when it passes in front of the + + align:start position:0% +called when it passes in front of the + + + align:start position:0% +called when it passes in front of the +planet what do you think happens if + + align:start position:0% +planet what do you think happens if + + + align:start position:0% +planet what do you think happens if +you're looking at a star and you see the + + align:start position:0% +you're looking at a star and you see the + + + align:start position:0% +you're looking at a star and you see the +light from the star and the planet goes + + align:start position:0% +light from the star and the planet goes + + + align:start position:0% +light from the star and the planet goes +in front what do you think happens to + + align:start position:0% +in front what do you think happens to + + + align:start position:0% +in front what do you think happens to +the + + align:start position:0% +the + + + align:start position:0% +the +light there's a shadow right so the + + align:start position:0% +light there's a shadow right so the + + + align:start position:0% +light there's a shadow right so the +light is decreased and that's really the + + align:start position:0% +light is decreased and that's really the + + + align:start position:0% +light is decreased and that's really the +whole principle behind test is looking + + align:start position:0% +whole principle behind test is looking + + + align:start position:0% +whole principle behind test is looking +for those little decreases in the light + + align:start position:0% +for those little decreases in the light + + + align:start position:0% +for those little decreases in the light +from the Star now it's got some very + + align:start position:0% +from the Star now it's got some very + + + align:start position:0% +from the Star now it's got some very +specific things you you know you can + + align:start position:0% +specific things you you know you can + + + align:start position:0% +specific things you you know you can +only see it if the it is kind of + + align:start position:0% +only see it if the it is kind of + + + align:start position:0% +only see it if the it is kind of +orbiting in front of the star if it's + + align:start position:0% +orbiting in front of the star if it's + + + align:start position:0% +orbiting in front of the star if it's +going around this way you're not going + + align:start position:0% +going around this way you're not going + + + align:start position:0% +going around this way you're not going +to see that so it's a small percentage + + align:start position:0% +to see that so it's a small percentage + + + align:start position:0% +to see that so it's a small percentage +of you know chances to pick it up but + + align:start position:0% +of you know chances to pick it up but + + + align:start position:0% +of you know chances to pick it up but +that's how we're going to do it so I + + align:start position:0% +that's how we're going to do it so I + + + align:start position:0% +that's how we're going to do it so I +have kind of a cool movie let me see if + + align:start position:0% +have kind of a cool movie let me see if + + + align:start position:0% +have kind of a cool movie let me see if +I can get this started that shows we + + align:start position:0% +I can get this started that shows we + + + align:start position:0% +I can get this started that shows we +have some really good graphics people at + + align:start position:0% +have some really good graphics people at + + + align:start position:0% +have some really good graphics people at +the + + align:start position:0% +the + + + align:start position:0% +the +lab that put this movie together so this + + align:start position:0% +lab that put this movie together so this + + + align:start position:0% +lab that put this movie together so this +is the general idea the planet's going + + align:start position:0% +is the general idea the planet's going + + + align:start position:0% +is the general idea the planet's going +around the star and now at the bottom + + align:start position:0% +around the star and now at the bottom + + + align:start position:0% +around the star and now at the bottom +it'll start to trace out kind of the + + align:start position:0% +it'll start to trace out kind of the + + + align:start position:0% +it'll start to trace out kind of the +light signal so there's the star light + + align:start position:0% +light signal so there's the star light + + + align:start position:0% +light signal so there's the star light +and then as the planet pass passes in + + align:start position:0% +and then as the planet pass passes in + + + align:start position:0% +and then as the planet pass passes in +front of it there's a little dip now + + align:start position:0% +front of it there's a little dip now + + + align:start position:0% +front of it there's a little dip now +what do you notice when the planet + + align:start position:0% +what do you notice when the planet + + + align:start position:0% +what do you notice when the planet +passes behind the star you may notice + + align:start position:0% +passes behind the star you may notice + + + align:start position:0% +passes behind the star you may notice +anything interesting like when it passes + + align:start position:0% +anything interesting like when it passes + + + align:start position:0% +anything interesting like when it passes +in front the little the dip is pretty + + align:start position:0% +in front the little the dip is pretty + + + align:start position:0% +in front the little the dip is pretty +that's pretty obvious but what's the + + align:start position:0% +that's pretty obvious but what's the + + + align:start position:0% +that's pretty obvious but what's the +second dip anybody got any + + align:start position:0% + + + + align:start position:0% + +ideas I just as it + + align:start position:0% + + + + align:start position:0% + +around line go up little yep so somehow + + align:start position:0% +around line go up little yep so somehow + + + align:start position:0% +around line go up little yep so somehow +we're getting a little more light signal + + align:start position:0% +we're getting a little more light signal + + + align:start position:0% +we're getting a little more light signal +what do you think that is + + align:start position:0% + + + + align:start position:0% + +exactly exactly right so if you think of + + align:start position:0% +exactly exactly right so if you think of + + + align:start position:0% +exactly exactly right so if you think of +the Sun or a a star is emitting + + align:start position:0% +the Sun or a a star is emitting + + + align:start position:0% +the Sun or a a star is emitting +radiation in all directions we're seeing + + align:start position:0% +radiation in all directions we're seeing + + + align:start position:0% +radiation in all directions we're seeing +the stuff coming toward us right but as + + align:start position:0% +the stuff coming toward us right but as + + + align:start position:0% +the stuff coming toward us right but as +the planet passes behind the star some + + align:start position:0% +the planet passes behind the star some + + + align:start position:0% +the planet passes behind the star some +of the light that would be going kind of + + align:start position:0% +of the light that would be going kind of + + + align:start position:0% +of the light that would be going kind of +backwards gets reflected forwards and + + align:start position:0% +backwards gets reflected forwards and + + + align:start position:0% +backwards gets reflected forwards and +then you get this kind of increase in + + align:start position:0% +then you get this kind of increase in + + + align:start position:0% +then you get this kind of increase in +your light curve so this is called the + + align:start position:0% +your light curve so this is called the + + + align:start position:0% +your light curve so this is called the +characteristic light curve so if there + + align:start position:0% +characteristic light curve so if there + + + align:start position:0% +characteristic light curve so if there +were no Planet it would just be pretty + + align:start position:0% +were no Planet it would just be pretty + + + align:start position:0% +were no Planet it would just be pretty +much a constant line and what Tess is + + align:start position:0% +much a constant line and what Tess is + + + align:start position:0% +much a constant line and what Tess is +doing is looking for these little blips + + align:start position:0% +doing is looking for these little blips + + + align:start position:0% +doing is looking for these little blips +and they call it periodic because it + + align:start position:0% +and they call it periodic because it + + + align:start position:0% +and they call it periodic because it +happens kind of you know do everyone + + align:start position:0% +happens kind of you know do everyone + + + align:start position:0% +happens kind of you know do everyone +know what periodic means um and the + + align:start position:0% +know what periodic means um and the + + + align:start position:0% +know what periodic means um and the +problem is depending on what star you're + + align:start position:0% +problem is depending on what star you're + + + align:start position:0% +problem is depending on what star you're +looking at if it's a small planet what + + align:start position:0% +looking at if it's a small planet what + + + align:start position:0% +looking at if it's a small planet what +do you think happens to this if the + + align:start position:0% +do you think happens to this if the + + + align:start position:0% +do you think happens to this if the +planet gets + + align:start position:0% + + + + align:start position:0% + +bigger anybody the dip gets deeper the + + align:start position:0% +bigger anybody the dip gets deeper the + + + align:start position:0% +bigger anybody the dip gets deeper the +dip gets deeper right now we're trying + + align:start position:0% +dip gets deeper right now we're trying + + + align:start position:0% +dip gets deeper right now we're trying +to look for earthlike planets and if you + + align:start position:0% +to look for earthlike planets and if you + + + align:start position:0% +to look for earthlike planets and if you +think of Earth compared to other planets + + align:start position:0% +think of Earth compared to other planets + + + align:start position:0% +think of Earth compared to other planets +in our solar system what what size are + + align:start position:0% +in our solar system what what size are + + + align:start position:0% +in our solar system what what size are +we like compared to Jupiter we're small + + align:start position:0% +we like compared to Jupiter we're small + + + align:start position:0% +we like compared to Jupiter we're small +right so Jupiter is easy to find because + + align:start position:0% +right so Jupiter is easy to find because + + + align:start position:0% +right so Jupiter is easy to find because +reflects a lot of light it blocks a lot + + align:start position:0% +reflects a lot of light it blocks a lot + + + align:start position:0% +reflects a lot of light it blocks a lot +of light but the smaller you get and + + align:start position:0% +of light but the smaller you get and + + + align:start position:0% +of light but the smaller you get and +Earth is relatively small the smaller + + align:start position:0% +Earth is relatively small the smaller + + + align:start position:0% +Earth is relatively small the smaller +that dip is so Tess really needs to + + align:start position:0% +that dip is so Tess really needs to + + + align:start position:0% +that dip is so Tess really needs to +detect it's about 1% variation in this + + align:start position:0% +detect it's about 1% variation in this + + + align:start position:0% +detect it's about 1% variation in this +very bright signal from a star so that's + + align:start position:0% +very bright signal from a star so that's + + + align:start position:0% +very bright signal from a star so that's +the challenge for + + align:start position:0% +the challenge for + + + align:start position:0% +the challenge for +test just to show you a little bit about + + align:start position:0% +test just to show you a little bit about + + + align:start position:0% +test just to show you a little bit about +where Tess is orbiting and there's + + align:start position:0% +where Tess is orbiting and there's + + + align:start position:0% +where Tess is orbiting and there's +there's a movie so I won't spend too + + align:start position:0% +there's a movie so I won't spend too + + + align:start position:0% +there's a movie so I won't spend too +long in here but basically here's Earth + + align:start position:0% +long in here but basically here's Earth + + + align:start position:0% +long in here but basically here's Earth +Tess goes out really far like 60 earth + + align:start position:0% +Tess goes out really far like 60 earth + + + align:start position:0% +Tess goes out really far like 60 earth +radius far like beyond the moon so they + + align:start position:0% +radius far like beyond the moon so they + + + align:start position:0% +radius far like beyond the moon so they +call this highly + + align:start position:0% +call this highly + + + align:start position:0% +call this highly +elliptical um and that's for a lot of + + align:start position:0% +elliptical um and that's for a lot of + + + align:start position:0% +elliptical um and that's for a lot of +different reasons that um primarily um + + align:start position:0% +different reasons that um primarily um + + + align:start position:0% +different reasons that um primarily um +it's a very thermally stable orbit so + + align:start position:0% +it's a very thermally stable orbit so + + + align:start position:0% +it's a very thermally stable orbit so +the temperature stays the same and + + align:start position:0% +the temperature stays the same and + + + align:start position:0% +the temperature stays the same and +that's one of many variables that go + + align:start position:0% +that's one of many variables that go + + + align:start position:0% +that's one of many variables that go +into designing space cameras you have to + + align:start position:0% +into designing space cameras you have to + + + align:start position:0% +into designing space cameras you have to +be aware of the environment that your + + align:start position:0% +be aware of the environment that your + + + align:start position:0% +be aware of the environment that your +camera is going to live in right because + + align:start position:0% +camera is going to live in right because + + + align:start position:0% +camera is going to live in right because +you could have if you design a camera + + align:start position:0% +you could have if you design a camera + + + align:start position:0% +you could have if you design a camera +that works in your laboratory at like 20 + + align:start position:0% +that works in your laboratory at like 20 + + + align:start position:0% +that works in your laboratory at like 20 +degrees Celsius or 70 you know + + align:start position:0% +degrees Celsius or 70 you know + + + align:start position:0% +degrees Celsius or 70 you know +Fahrenheit then you try and send it into + + align:start position:0% +Fahrenheit then you try and send it into + + + align:start position:0% +Fahrenheit then you try and send it into +space where it's minus 80 might not work + + align:start position:0% +space where it's minus 80 might not work + + + align:start position:0% +space where it's minus 80 might not work +out so well so some of the important + + align:start position:0% +out so well so some of the important + + + align:start position:0% +out so well so some of the important +considerations and what test does is it + + align:start position:0% +considerations and what test does is it + + + align:start position:0% +considerations and what test does is it +has two orbits per month that it stares + + align:start position:0% +has two orbits per month that it stares + + + align:start position:0% +has two orbits per month that it stares +at a very particular section of the sky + + align:start position:0% +at a very particular section of the sky + + + align:start position:0% +at a very particular section of the sky +and we have four cameras aligned so we + + align:start position:0% +and we have four cameras aligned so we + + + align:start position:0% +and we have four cameras aligned so we +get a very wide field of view so we kind + + align:start position:0% +get a very wide field of view so we kind + + + align:start position:0% +get a very wide field of view so we kind +of go like this right there's four + + align:start position:0% +of go like this right there's four + + + align:start position:0% +of go like this right there's four +cameras and it's almost um almost 100° + + align:start position:0% +cameras and it's almost um almost 100° + + + align:start position:0% +cameras and it's almost um almost 100° +and it stares at a section of the sky + + align:start position:0% +and it stares at a section of the sky + + + align:start position:0% +and it stares at a section of the sky +and then after a month it moves and + + align:start position:0% +and then after a month it moves and + + + align:start position:0% +and then after a month it moves and +basically it scans out the entire sky so + + align:start position:0% +basically it scans out the entire sky so + + + align:start position:0% +basically it scans out the entire sky so +Tess is going to look at not 100% you + + align:start position:0% +Tess is going to look at not 100% you + + + align:start position:0% +Tess is going to look at not 100% you +can see we have a few a few open areas + + align:start position:0% +can see we have a few a few open areas + + + align:start position:0% +can see we have a few a few open areas +near the equator but about 95% of this + + align:start position:0% +near the equator but about 95% of this + + + align:start position:0% +near the equator but about 95% of this +guy will be looking and watching for + + align:start position:0% +guy will be looking and watching for + + + align:start position:0% +guy will be looking and watching for +exit planets so this movie shows it much + + align:start position:0% +exit planets so this movie shows it much + + + align:start position:0% +exit planets so this movie shows it much +better than I can describe + + align:start position:0% + + + + align:start position:0% + +it so you can see the moon orbiting the + + align:start position:0% +it so you can see the moon orbiting the + + + align:start position:0% +it so you can see the moon orbiting the +Earth and you can see Tess goes around + + align:start position:0% +Earth and you can see Tess goes around + + + align:start position:0% +Earth and you can see Tess goes around +the earth twice for every time the moon + + align:start position:0% +the earth twice for every time the moon + + + align:start position:0% +the earth twice for every time the moon +does + + align:start position:0% +does + + + align:start position:0% +does +and in fact the moon um I don't know a + + align:start position:0% +and in fact the moon um I don't know a + + + align:start position:0% +and in fact the moon um I don't know a +lot about orbital mechanics but I do + + align:start position:0% +lot about orbital mechanics but I do + + + align:start position:0% +lot about orbital mechanics but I do +know that in the process of getting to + + align:start position:0% +know that in the process of getting to + + + align:start position:0% +know that in the process of getting to +that final orbit there's about three + + align:start position:0% +that final orbit there's about three + + + align:start position:0% +that final orbit there's about three +different orbits that it gradually gets + + align:start position:0% +different orbits that it gradually gets + + + align:start position:0% +different orbits that it gradually gets +further and further out till it gets + + align:start position:0% +further and further out till it gets + + + align:start position:0% +further and further out till it gets +that final orbit and it uses the moon + + align:start position:0% +that final orbit and it uses the moon + + + align:start position:0% +that final orbit and it uses the moon +and gravitational pool from the Moon to + + align:start position:0% +and gravitational pool from the Moon to + + + align:start position:0% +and gravitational pool from the Moon to +hit to get out to that last highly + + align:start position:0% +hit to get out to that last highly + + + align:start position:0% +hit to get out to that last highly +elliptical orbit so there's a whole lot + + align:start position:0% +elliptical orbit so there's a whole lot + + + align:start position:0% +elliptical orbit so there's a whole lot +of interesting signs just to get Tess + + align:start position:0% +of interesting signs just to get Tess + + + align:start position:0% +of interesting signs just to get Tess +where it needs to go so now that Tess is + + align:start position:0% +where it needs to go so now that Tess is + + + align:start position:0% +where it needs to go so now that Tess is +on its orbit you'll watch and the + + align:start position:0% +on its orbit you'll watch and the + + + align:start position:0% +on its orbit you'll watch and the +outline here that's the field of view of + + align:start position:0% +outline here that's the field of view of + + + align:start position:0% +outline here that's the field of view of +each of the cam cameras so there's four + + align:start position:0% +each of the cam cameras so there's four + + + align:start position:0% +each of the cam cameras so there's four +cameras in a row and it scans out that's + + align:start position:0% +cameras in a row and it scans out that's + + + align:start position:0% +cameras in a row and it scans out that's +one month at a time that it's scanning + + align:start position:0% +one month at a time that it's scanning + + + align:start position:0% +one month at a time that it's scanning +out now what do you notice + + align:start position:0% +out now what do you notice + + + align:start position:0% +out now what do you notice +about this + + align:start position:0% + + + + align:start position:0% + +part + + align:start position:0% +part + + + align:start position:0% +part +sorry yeah so you this is what we call + + align:start position:0% +sorry yeah so you this is what we call + + + align:start position:0% +sorry yeah so you this is what we call +the continuous coverage zone right so in + + align:start position:0% +the continuous coverage zone right so in + + + align:start position:0% +the continuous coverage zone right so in +the attempt to see the entire Sky + + align:start position:0% +the attempt to see the entire Sky + + + align:start position:0% +the attempt to see the entire Sky +there's going to be some overlap so the + + align:start position:0% +there's going to be some overlap so the + + + align:start position:0% +there's going to be some overlap so the +basically at the + + align:start position:0% +basically at the + + + align:start position:0% +basically at the +poles we see almost full full year + + align:start position:0% +poles we see almost full full year + + + align:start position:0% +poles we see almost full full year +coverage + + align:start position:0% +coverage + + + align:start position:0% +coverage +now we're going to the southern + + align:start position:0% +now we're going to the southern + + + align:start position:0% +now we're going to the southern +hemisphere this is year two of the + + align:start position:0% +hemisphere this is year two of the + + + align:start position:0% +hemisphere this is year two of the +mission same thing we're going to scan + + align:start position:0% +mission same thing we're going to scan + + + align:start position:0% +mission same thing we're going to scan +out the entire sky and we got almost + + align:start position:0% +out the entire sky and we got almost + + + align:start position:0% +out the entire sky and we got almost +full um continuous coverage at the polls + + align:start position:0% +full um continuous coverage at the polls + + + align:start position:0% +full um continuous coverage at the polls +and so not by Chance the followon + + align:start position:0% +and so not by Chance the followon + + + align:start position:0% +and so not by Chance the followon +mission has anyone heard of James web + + align:start position:0% +mission has anyone heard of James web + + + align:start position:0% +mission has anyone heard of James web +Space + + align:start position:0% +Space + + + align:start position:0% +Space +Telescope yep it's looking up here so + + align:start position:0% +Telescope yep it's looking up here so + + + align:start position:0% +Telescope yep it's looking up here so +one of Tessa's goals is to provide + + align:start position:0% +one of Tessa's goals is to provide + + + align:start position:0% +one of Tessa's goals is to provide +basically a catalog of just thousands of + + align:start position:0% +basically a catalog of just thousands of + + + align:start position:0% +basically a catalog of just thousands of +places to go look say go look at the + + align:start position:0% +places to go look say go look at the + + + align:start position:0% +places to go look say go look at the +star we think there's an exoplanet there + + align:start position:0% +star we think there's an exoplanet there + + + align:start position:0% +star we think there's an exoplanet there +then James web doesn't have to spend a + + align:start position:0% +then James web doesn't have to spend a + + + align:start position:0% +then James web doesn't have to spend a +lot of time looking for them it knows + + align:start position:0% +lot of time looking for them it knows + + + align:start position:0% +lot of time looking for them it knows +exactly where to go look and James Webb + + align:start position:0% +exactly where to go look and James Webb + + + align:start position:0% +exactly where to go look and James Webb +is going up there too have the picture + + align:start position:0% +is going up there too have the picture + + + align:start position:0% +is going up there too have the picture +um it's a little bit further so James + + align:start position:0% +um it's a little bit further so James + + + align:start position:0% +um it's a little bit further so James +Webb is going up there and is going to + + align:start position:0% +Webb is going up there and is going to + + + align:start position:0% +Webb is going up there and is going to +have a Target planet and go look at the + + align:start position:0% +have a Target planet and go look at the + + + align:start position:0% +have a Target planet and go look at the +atmosphere of that planet so Tess is + + align:start position:0% +atmosphere of that planet so Tess is + + + align:start position:0% +atmosphere of that planet so Tess is +really just designed to find planets it + + align:start position:0% +really just designed to find planets it + + + align:start position:0% +really just designed to find planets it +can't really characterize planets James + + align:start position:0% +can't really characterize planets James + + + align:start position:0% +can't really characterize planets James +web can go up and look at the + + align:start position:0% +web can go up and look at the + + + align:start position:0% +web can go up and look at the +atmospherics of the planets in question + + align:start position:0% +atmospherics of the planets in question + + + align:start position:0% +atmospherics of the planets in question +and determine is it really like Earth is + + align:start position:0% +and determine is it really like Earth is + + + align:start position:0% +and determine is it really like Earth is +it hotter is it colder you know what's + + align:start position:0% +it hotter is it colder you know what's + + + align:start position:0% +it hotter is it colder you know what's +the + + align:start position:0% + + + + align:start position:0% + +atmosphere all right so since you guys + + align:start position:0% +atmosphere all right so since you guys + + + align:start position:0% +atmosphere all right so since you guys +are going to be have already ripped + + align:start position:0% +are going to be have already ripped + + + align:start position:0% +are going to be have already ripped +apart cameras and you're going to be + + align:start position:0% +apart cameras and you're going to be + + + align:start position:0% +apart cameras and you're going to be +building your own I figured I'd show you + + align:start position:0% +building your own I figured I'd show you + + + align:start position:0% +building your own I figured I'd show you +kind of the insides of the test camera + + align:start position:0% +kind of the insides of the test camera + + + align:start position:0% +kind of the insides of the test camera +so we identified our + + align:start position:0% +so we identified our + + + align:start position:0% +so we identified our +two key pieces now this is a cut a + + align:start position:0% +two key pieces now this is a cut a + + + align:start position:0% +two key pieces now this is a cut a +basically a section view so there's an + + align:start position:0% +basically a section view so there's an + + + align:start position:0% +basically a section view so there's an +awful lot of stuff going on in there but + + align:start position:0% +awful lot of stuff going on in there but + + + align:start position:0% +awful lot of stuff going on in there but +basically this whole backend section is + + align:start position:0% +basically this whole backend section is + + + align:start position:0% +basically this whole backend section is +our detector this front end section is + + align:start position:0% +our detector this front end section is + + + align:start position:0% +our detector this front end section is +our lens and anybody have any guesses + + align:start position:0% +our lens and anybody have any guesses + + + align:start position:0% +our lens and anybody have any guesses +that some of this stuff you can see in + + align:start position:0% +that some of this stuff you can see in + + + align:start position:0% +that some of this stuff you can see in +the back behind the detector anybody + + align:start position:0% +the back behind the detector anybody + + + align:start position:0% +the back behind the detector anybody +recognize + + align:start position:0% +recognize + + + align:start position:0% +recognize +anything back + + align:start position:0% + + + + align:start position:0% + +there cuz you're going to see some of + + align:start position:0% +there cuz you're going to see some of + + + align:start position:0% +there cuz you're going to see some of +this stuff a little bit later so + + align:start position:0% +this stuff a little bit later so + + + align:start position:0% +this stuff a little bit later so +detector pretty much made up you have + + align:start position:0% +detector pretty much made up you have + + + align:start position:0% +detector pretty much made up you have +your CCD right that's your silicon + + align:start position:0% +your CCD right that's your silicon + + + align:start position:0% +your CCD right that's your silicon +active area but you need some + + align:start position:0% +active area but you need some + + + align:start position:0% +active area but you need some +Electronics behind it too right so you + + align:start position:0% +Electronics behind it too right so you + + + align:start position:0% +Electronics behind it too right so you +guys are going to see that when you + + align:start position:0% +guys are going to see that when you + + + align:start position:0% +guys are going to see that when you +build your raspberry pie camera you can + + align:start position:0% +build your raspberry pie camera you can + + + align:start position:0% +build your raspberry pie camera you can +see the electronics that run that + + align:start position:0% +see the electronics that run that + + + align:start position:0% +see the electronics that run that +actually pull the image in and then + + align:start position:0% +actually pull the image in and then + + + align:start position:0% +actually pull the image in and then +you're going to do signal processing for + + align:start position:0% +you're going to do signal processing for + + + align:start position:0% +you're going to do signal processing for +tests that's all done on this back end + + align:start position:0% +tests that's all done on this back end + + + align:start position:0% +tests that's all done on this back end +now I am much more I'm + + align:start position:0% +now I am much more I'm + + + align:start position:0% +now I am much more I'm +a physicist by degree but my whole + + align:start position:0% +a physicist by degree but my whole + + + align:start position:0% +a physicist by degree but my whole +career has basically been on lens design + + align:start position:0% +career has basically been on lens design + + + align:start position:0% +career has basically been on lens design +and lens test so this is really more my + + align:start position:0% +and lens test so this is really more my + + + align:start position:0% +and lens test so this is really more my +sweet spot um this lens so we can + + align:start position:0% +sweet spot um this lens so we can + + + align:start position:0% +sweet spot um this lens so we can +characterize it a few different ways so + + align:start position:0% +characterize it a few different ways so + + + align:start position:0% +characterize it a few different ways so +there's seven different lenses so that + + align:start position:0% +there's seven different lenses so that + + + align:start position:0% +there's seven different lenses so that +tells you there's an awful lot that goes + + align:start position:0% +tells you there's an awful lot that goes + + + align:start position:0% +tells you there's an awful lot that goes +into this right because we're looking at + + align:start position:0% +into this right because we're looking at + + + align:start position:0% +into this right because we're looking at +a very specific um band and so that + + align:start position:0% +a very specific um band and so that + + + align:start position:0% +a very specific um band and so that +drives how many lenses we need and what + + align:start position:0% +drives how many lenses we need and what + + + align:start position:0% +drives how many lenses we need and what +materials they need to be made out of + + align:start position:0% +materials they need to be made out of + + + align:start position:0% +materials they need to be made out of +and we have to match our detector + + align:start position:0% +and we have to match our detector + + + align:start position:0% +and we have to match our detector +because if we image light that and then + + align:start position:0% +because if we image light that and then + + + align:start position:0% +because if we image light that and then +use a detector that isn't very sensitive + + align:start position:0% +use a detector that isn't very sensitive + + + align:start position:0% +use a detector that isn't very sensitive +to that particular um wavelength of + + align:start position:0% +to that particular um wavelength of + + + align:start position:0% +to that particular um wavelength of +light you're not going to get a very + + align:start position:0% +light you're not going to get a very + + + align:start position:0% +light you're not going to get a very +good image but there is one thing I + + align:start position:0% +good image but there is one thing I + + + align:start position:0% +good image but there is one thing I +wanted to stress about test so your + + align:start position:0% +wanted to stress about test so your + + + align:start position:0% +wanted to stress about test so your +phone takes really nice clear pictures + + align:start position:0% +phone takes really nice clear pictures + + + align:start position:0% +phone takes really nice clear pictures +right and you can take pictures of your + + align:start position:0% +right and you can take pictures of your + + + align:start position:0% +right and you can take pictures of your +friends and they're nice and clear test + + align:start position:0% +friends and they're nice and clear test + + + align:start position:0% +friends and they're nice and clear test +is not that kind of camera so if you + + align:start position:0% +is not that kind of camera so if you + + + align:start position:0% +is not that kind of camera so if you +think about what Tess is trying to do + + align:start position:0% +think about what Tess is trying to do + + + align:start position:0% +think about what Tess is trying to do +it's trying to look at a very wide field + + align:start position:0% +it's trying to look at a very wide field + + + align:start position:0% +it's trying to look at a very wide field +of view a huge area right and does + + align:start position:0% +of view a huge area right and does + + + align:start position:0% +of view a huge area right and does +anyone know what typically happens when + + align:start position:0% +anyone know what typically happens when + + + align:start position:0% +anyone know what typically happens when +you have a camera and you're trying to + + align:start position:0% +you have a camera and you're trying to + + + align:start position:0% +you have a camera and you're trying to +look at a very wide field of view with a + + align:start position:0% +look at a very wide field of view with a + + + align:start position:0% +look at a very wide field of view with a +camera what do you notice about the kind + + align:start position:0% +camera what do you notice about the kind + + + align:start position:0% +camera what do you notice about the kind +of the edges of the + + align:start position:0% +of the edges of the + + + align:start position:0% +of the edges of the +picture has anyone ever seen a very wide + + align:start position:0% +picture has anyone ever seen a very wide + + + align:start position:0% +picture has anyone ever seen a very wide +field view image maybe + + align:start position:0% +field view image maybe + + + align:start position:0% +field view image maybe +um try to think of a good example an old + + align:start position:0% +um try to think of a good example an old + + + align:start position:0% +um try to think of a good example an old +school camera an old school photo the + + align:start position:0% +school camera an old school photo the + + + align:start position:0% +school camera an old school photo the +image the edges of the image are not as + + align:start position:0% +image the edges of the image are not as + + + align:start position:0% +image the edges of the image are not as +good as the center okay so the if you + + align:start position:0% +good as the center okay so the if you + + + align:start position:0% +good as the center okay so the if you +are trying to + + align:start position:0% +are trying to + + + align:start position:0% +are trying to +optimize your camera to look at a very + + align:start position:0% +optimize your camera to look at a very + + + align:start position:0% +optimize your camera to look at a very +specific spot you can do really well in + + align:start position:0% +specific spot you can do really well in + + + align:start position:0% +specific spot you can do really well in +one place but the further you expand + + align:start position:0% +one place but the further you expand + + + align:start position:0% +one place but the further you expand +your field of view basically it's hard + + align:start position:0% +your field of view basically it's hard + + + align:start position:0% +your field of view basically it's hard +to keep the entire field of view in + + align:start position:0% +to keep the entire field of view in + + + align:start position:0% +to keep the entire field of view in +focus and so what Tess is not really + + align:start position:0% +focus and so what Tess is not really + + + align:start position:0% +focus and so what Tess is not really +concerned about taking really pretty + + align:start position:0% +concerned about taking really pretty + + + align:start position:0% +concerned about taking really pretty +Sharp Images all it needs to do is + + align:start position:0% +Sharp Images all it needs to do is + + + align:start position:0% +Sharp Images all it needs to do is +basically we call it a light bucket it's + + align:start position:0% +basically we call it a light bucket it's + + + align:start position:0% +basically we call it a light bucket it's +trying to collect the light from the + + align:start position:0% +trying to collect the light from the + + + align:start position:0% +trying to collect the light from the +stars in a small enough spot that we can + + align:start position:0% +stars in a small enough spot that we can + + + align:start position:0% +stars in a small enough spot that we can +notice that little change in the light + + align:start position:0% +notice that little change in the light + + + align:start position:0% +notice that little change in the light +curve so it's kind of a totally + + align:start position:0% +curve so it's kind of a totally + + + align:start position:0% +curve so it's kind of a totally +different type of camera it's not a + + align:start position:0% +different type of camera it's not a + + + align:start position:0% +different type of camera it's not a +pretty pictures camera it's a light + + align:start position:0% +pretty pictures camera it's a light + + + align:start position:0% +pretty pictures camera it's a light +collection camera and the other key + + align:start position:0% +collection camera and the other key + + + align:start position:0% +collection camera and the other key +thing to think about um when you're + + align:start position:0% +thing to think about um when you're + + + align:start position:0% +thing to think about um when you're +designing a camera so what are you + + align:start position:0% +designing a camera so what are you + + + align:start position:0% +designing a camera so what are you +trying to do with it but also where are + + align:start position:0% +trying to do with it but also where are + + + align:start position:0% +trying to do with it but also where are +you trying to do that right so Tess is + + align:start position:0% +you trying to do that right so Tess is + + + align:start position:0% +you trying to do that right so Tess is +going to operate we design it on the + + align:start position:0% +going to operate we design it on the + + + align:start position:0% +going to operate we design it on the +ground at a normal temperature for you + + align:start position:0% +ground at a normal temperature for you + + + align:start position:0% +ground at a normal temperature for you +and me but there's a lot of adjustments + + align:start position:0% +and me but there's a lot of adjustments + + + align:start position:0% +and me but there's a lot of adjustments +that have to go into the design to make + + align:start position:0% +that have to go into the design to make + + + align:start position:0% +that have to go into the design to make +sure that when it's up in space and + + align:start position:0% +sure that when it's up in space and + + + align:start position:0% +sure that when it's up in space and +really cold um that it will operate as + + align:start position:0% +really cold um that it will operate as + + + align:start position:0% +really cold um that it will operate as +intended so there's a lot that goes into + + align:start position:0% +intended so there's a lot that goes into + + + align:start position:0% +intended so there's a lot that goes into +the camera design it's not just what + + align:start position:0% +the camera design it's not just what + + + align:start position:0% +the camera design it's not just what +you're trying to do but where you're + + align:start position:0% +you're trying to do but where you're + + + align:start position:0% +you're trying to do but where you're +trying to do + + align:start position:0% + + + + align:start position:0% + +it and so this is where test fits into + + align:start position:0% +it and so this is where test fits into + + + align:start position:0% +it and so this is where test fits into +the exoplanet puzzle we talked a little + + align:start position:0% +the exoplanet puzzle we talked a little + + + align:start position:0% +the exoplanet puzzle we talked a little +bit about this before so and I wanted to + + align:start position:0% +bit about this before so and I wanted to + + + align:start position:0% +bit about this before so and I wanted to +put these pictures in because they look + + align:start position:0% +put these pictures in because they look + + + align:start position:0% +put these pictures in because they look +so different right so this is what + + align:start position:0% +so different right so this is what + + + align:start position:0% +so different right so this is what +Kepler looked like it was looking at a + + align:start position:0% +Kepler looked like it was looking at a + + + align:start position:0% +Kepler looked like it was looking at a +very specific section of sky so it was + + align:start position:0% +very specific section of sky so it was + + + align:start position:0% +very specific section of sky so it was +doing something different it was looking + + align:start position:0% +doing something different it was looking + + + align:start position:0% +doing something different it was looking +at a very narrow field of view and very + + align:start position:0% +at a very narrow field of view and very + + + align:start position:0% +at a very narrow field of view and very +specific planets test you've seen we've + + align:start position:0% +specific planets test you've seen we've + + + align:start position:0% +specific planets test you've seen we've +got four cameras and our goal is to just + + align:start position:0% +got four cameras and our goal is to just + + + align:start position:0% +got four cameras and our goal is to just +go up there and find planets but not + + align:start position:0% +go up there and find planets but not + + + align:start position:0% +go up there and find planets but not +really characterize them and then James + + align:start position:0% +really characterize them and then James + + + align:start position:0% +really characterize them and then James +web looks totally different than we do + + align:start position:0% +web looks totally different than we do + + + align:start position:0% +web looks totally different than we do +it's got multiple instruments on the + + align:start position:0% +it's got multiple instruments on the + + + align:start position:0% +it's got multiple instruments on the +same um on the same spacecraft and it's + + align:start position:0% +same um on the same spacecraft and it's + + + align:start position:0% +same um on the same spacecraft and it's +going up there and it can actually + + align:start position:0% +going up there and it can actually + + + align:start position:0% +going up there and it can actually +characterize the atmospheres of the + + align:start position:0% +characterize the atmospheres of the + + + align:start position:0% +characterize the atmospheres of the +planet so we get one step closer to + + align:start position:0% +planet so we get one step closer to + + + align:start position:0% +planet so we get one step closer to +finding out if there really is another + + align:start position:0% +finding out if there really is another + + + align:start position:0% +finding out if there really is another +earthlike planet up in + + align:start position:0% +earthlike planet up in + + + align:start position:0% +earthlike planet up in +space all right so just to kind of close + + align:start position:0% +space all right so just to kind of close + + + align:start position:0% +space all right so just to kind of close +out so we've talked about a bunch of + + align:start position:0% +out so we've talked about a bunch of + + + align:start position:0% +out so we've talked about a bunch of +different cameras and one thing I want + + align:start position:0% +different cameras and one thing I want + + + align:start position:0% +different cameras and one thing I want +to stress they're using so many + + align:start position:0% +to stress they're using so many + + + align:start position:0% +to stress they're using so many +different fields even if you don't want + + align:start position:0% +different fields even if you don't want + + + align:start position:0% +different fields even if you don't want +to be a camera designer just + + align:start position:0% +to be a camera designer just + + + align:start position:0% +to be a camera designer just +understanding how they work and and how + + align:start position:0% +understanding how they work and and how + + + align:start position:0% +understanding how they work and and how +you know different things affect them + + align:start position:0% +you know different things affect them + + + align:start position:0% +you know different things affect them +can be useful to you in so many + + align:start position:0% +can be useful to you in so many + + + align:start position:0% +can be useful to you in so many +different fields now right because no + + align:start position:0% +different fields now right because no + + + align:start position:0% +different fields now right because no +even if you're into something that's not + + align:start position:0% +even if you're into something that's not + + + align:start position:0% +even if you're into something that's not +really super technical you might end up + + align:start position:0% +really super technical you might end up + + + align:start position:0% +really super technical you might end up +using cameras right and so I think no + + align:start position:0% +using cameras right and so I think no + + + align:start position:0% +using cameras right and so I think no +matter what you choose to do it's nice + + align:start position:0% +matter what you choose to do it's nice + + + align:start position:0% +matter what you choose to do it's nice +to have that ability and to really + + align:start position:0% +to have that ability and to really + + + align:start position:0% +to have that ability and to really +understand how they function but if you + + align:start position:0% +understand how they function but if you + + + align:start position:0% +understand how they function but if you +do really get into it there's an awful + + align:start position:0% +do really get into it there's an awful + + + align:start position:0% +do really get into it there's an awful +lot of different areas that you could + + align:start position:0% +lot of different areas that you could + + + align:start position:0% +lot of different areas that you could +really focus on and I think make a make + + align:start position:0% +really focus on and I think make a make + + + align:start position:0% +really focus on and I think make a make +a huge difference difference in your + + align:start position:0% +a huge difference difference in your + + + align:start position:0% +a huge difference difference in your +field so what you can do with right + + align:start position:0% +field so what you can do with right + + + align:start position:0% +field so what you can do with right +cameras right + + align:start position:0% +cameras right + + + align:start position:0% +cameras right +now is have some fun so I hope you guys + + align:start position:0% +now is have some fun so I hope you guys + + + align:start position:0% +now is have some fun so I hope you guys +have a great day and um hope you have a + + align:start position:0% +have a great day and um hope you have a + + + align:start position:0% +have a great day and um hope you have a +fun building the cameras and and + + align:start position:0% +fun building the cameras and and + + + align:start position:0% +fun building the cameras and and +figuring out if you know maybe maybe + + align:start position:0% +figuring out if you know maybe maybe + + + align:start position:0% +figuring out if you know maybe maybe +Optical engineering or detector or + + align:start position:0% +Optical engineering or detector or + + + align:start position:0% +Optical engineering or detector or +signal processing is your passion so + + align:start position:0% +signal processing is your passion so + + + align:start position:0% +signal processing is your passion so +good luck with the rest of the + + align:start position:0% + + + + align:start position:0% + +day \ No newline at end of file diff --git a/0sKPkJME2Jw.txt b/0sKPkJME2Jw.txt new file mode 100644 index 0000000000000000000000000000000000000000..0ef5856d1aab3b7363329060fb2cd9730bcef981 --- /dev/null +++ b/0sKPkJME2Jw.txt @@ -0,0 +1,6659 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +all right welcome thank you so much for + + align:start position:0% +all right welcome thank you so much for + + + align:start position:0% +all right welcome thank you so much for +coming + + align:start position:0% +coming + + + align:start position:0% +coming +I'm Jeremy Kepner I'm a fellow at + + align:start position:0% +I'm Jeremy Kepner I'm a fellow at + + + align:start position:0% +I'm Jeremy Kepner I'm a fellow at +Lincoln Laboratory I lead the + + align:start position:0% +Lincoln Laboratory I lead the + + + align:start position:0% +Lincoln Laboratory I lead the +supercomputing Center there which means + + align:start position:0% +supercomputing Center there which means + + + align:start position:0% +supercomputing Center there which means +I have the privilege of working everyday + + align:start position:0% +I have the privilege of working everyday + + + align:start position:0% +I have the privilege of working everyday +with pretty much everyone at MIT I think + + align:start position:0% +with pretty much everyone at MIT I think + + + align:start position:0% +with pretty much everyone at MIT I think +I have the best job at MIT because I get + + align:start position:0% +I have the best job at MIT because I get + + + align:start position:0% +I have the best job at MIT because I get +to help me wall pursue your research + + align:start position:0% +to help me wall pursue your research + + + align:start position:0% +to help me wall pursue your research +research dreams and as a result of that + + align:start position:0% +research dreams and as a result of that + + + align:start position:0% +research dreams and as a result of that +I get an opportunity to sort of see what + + align:start position:0% +I get an opportunity to sort of see what + + + align:start position:0% +I get an opportunity to sort of see what +a really wide range of folks are doing + + align:start position:0% +a really wide range of folks are doing + + + align:start position:0% +a really wide range of folks are doing +and observe patterns between what + + align:start position:0% +and observe patterns between what + + + align:start position:0% +and observe patterns between what +different folks are doing so with that + + align:start position:0% +different folks are doing so with that + + + align:start position:0% +different folks are doing so with that +I'll get I'll get started this is meant + + align:start position:0% +I'll get I'll get started this is meant + + + align:start position:0% +I'll get I'll get started this is meant +to be some initial motivational material + + align:start position:0% +to be some initial motivational material + + + align:start position:0% +to be some initial motivational material +why you should be interested in learning + + align:start position:0% +why you should be interested in learning + + + align:start position:0% +why you should be interested in learning +about this mathematics this mathematics + + align:start position:0% +about this mathematics this mathematics + + + align:start position:0% +about this mathematics this mathematics +of big data and how it relates to + + align:start position:0% +of big data and how it relates to + + + align:start position:0% +of big data and how it relates to +machine learning and other really + + align:start position:0% +machine learning and other really + + + align:start position:0% +machine learning and other really +exciting topics it is a math course we + + align:start position:0% +exciting topics it is a math course we + + + align:start position:0% +exciting topics it is a math course we +will be going over a fair amount of math + + align:start position:0% +will be going over a fair amount of math + + + align:start position:0% +will be going over a fair amount of math +but we really work hard to make it very + + align:start position:0% +but we really work hard to make it very + + + align:start position:0% +but we really work hard to make it very +accessible to people so we start out + + align:start position:0% +accessible to people so we start out + + + align:start position:0% +accessible to people so we start out +with a really elementary mathematical + + align:start position:0% +with a really elementary mathematical + + + align:start position:0% +with a really elementary mathematical +concept here probably one that hopefully + + align:start position:0% +concept here probably one that hopefully + + + align:start position:0% +concept here probably one that hopefully +most of Lee most of you are familiar + + align:start position:0% +most of Lee most of you are familiar + + + align:start position:0% +most of Lee most of you are familiar +with it's sort of the basic concept of a + + align:start position:0% +with it's sort of the basic concept of a + + + align:start position:0% +with it's sort of the basic concept of a +circle right and I bring that up because + + align:start position:0% +circle right and I bring that up because + + + align:start position:0% +circle right and I bring that up because +many of us know you know many ways to + + align:start position:0% +many of us know you know many ways to + + + align:start position:0% +many of us know you know many ways to +state this mathematically right it's + + align:start position:0% +state this mathematically right it's + + + align:start position:0% +state this mathematically right it's +it's all the points that are equal + + align:start position:0% +it's all the points that are equal + + + align:start position:0% +it's all the points that are equal +distance from from a particular point + + align:start position:0% +distance from from a particular point + + + align:start position:0% +distance from from a particular point +there's other ways to describe it but + + align:start position:0% +there's other ways to describe it but + + + align:start position:0% +there's other ways to describe it but +this is sort of a basic mathematical + + align:start position:0% +this is sort of a basic mathematical + + + align:start position:0% +this is sort of a basic mathematical +concept of a circle that many of us have + + align:start position:0% +concept of a circle that many of us have + + + align:start position:0% +concept of a circle that many of us have +grown up with but of course the other + + align:start position:0% +grown up with but of course the other + + + align:start position:0% +grown up with but of course the other +thing we know is that right and this is + + align:start position:0% +thing we know is that right and this is + + + align:start position:0% +thing we know is that right and this is +sort of kind of the the big idea is that + + align:start position:0% +sort of kind of the the big idea is that + + + align:start position:0% +sort of kind of the the big idea is that +although I can write down an equation + + align:start position:0% +although I can write down an equation + + + align:start position:0% +although I can write down an equation +for a circle which is the equation for a + + align:start position:0% +for a circle which is the equation for a + + + align:start position:0% +for a circle which is the equation for a +perfect ideal circle we know that such + + align:start position:0% +perfect ideal circle we know that such + + + align:start position:0% +perfect ideal circle we know that such +things don't actually exist in nature + + align:start position:0% +things don't actually exist in nature + + + align:start position:0% +things don't actually exist in nature +there is no true perfect circle in + + align:start position:0% +there is no true perfect circle in + + + align:start position:0% +there is no true perfect circle in +nature even this circle that we've drawn + + align:start position:0% +nature even this circle that we've drawn + + + align:start position:0% +nature even this circle that we've drawn +here it has pixels if I zoomed in on it + + align:start position:0% +here it has pixels if I zoomed in on it + + + align:start position:0% +here it has pixels if I zoomed in on it +if I zoomed in on enough it wouldn't + + align:start position:0% +if I zoomed in on enough it wouldn't + + + align:start position:0% +if I zoomed in on enough it wouldn't +look like a circle at all it would look + + align:start position:0% +look like a circle at all it would look + + + align:start position:0% +look like a circle at all it would look +like a series of blocks it would look + + align:start position:0% +like a series of blocks it would look + + + align:start position:0% +like a series of blocks it would look +and so that approximation process right + + align:start position:0% +and so that approximation process right + + + align:start position:0% +and so that approximation process right +where we have a mathematical concept of + + align:start position:0% +where we have a mathematical concept of + + + align:start position:0% +where we have a mathematical concept of +an ideal circle right but we know that + + align:start position:0% +an ideal circle right but we know that + + + align:start position:0% +an ideal circle right but we know that +there are not really they don't really + + align:start position:0% +there are not really they don't really + + + align:start position:0% +there are not really they don't really +exist in nature but we understand that + + align:start position:0% +exist in nature but we understand that + + + align:start position:0% +exist in nature but we understand that +it is worthwhile to think about these + + align:start position:0% +it is worthwhile to think about these + + + align:start position:0% +it is worthwhile to think about these +mathematical ideals manipulate them and + + align:start position:0% +mathematical ideals manipulate them and + + + align:start position:0% +mathematical ideals manipulate them and +then take the results of those + + align:start position:0% +then take the results of those + + + align:start position:0% +then take the results of those +manipulation back into the real world + + align:start position:0% +manipulation back into the real world + + + align:start position:0% +manipulation back into the real world +that's a really productive way to think + + align:start position:0% +that's a really productive way to think + + + align:start position:0% +that's a really productive way to think +about things and really the basis for a + + align:start position:0% +about things and really the basis for a + + + align:start position:0% +about things and really the basis for a +lot of what we do here at MIT this + + align:start position:0% +lot of what we do here at MIT this + + + align:start position:0% +lot of what we do here at MIT this +concept you know is essentially the + + align:start position:0% +concept you know is essentially the + + + align:start position:0% +concept you know is essentially the +basis of sort of modern or not even or + + align:start position:0% +basis of sort of modern or not even or + + + align:start position:0% +basis of sort of modern or not even or +ancient Western thought on mathematics + + align:start position:0% +ancient Western thought on mathematics + + + align:start position:0% +ancient Western thought on mathematics +if you remember your history courses + + align:start position:0% +if you remember your history courses + + + align:start position:0% +if you remember your history courses +this concept of ideal shapes and ideal + + align:start position:0% +this concept of ideal shapes and ideal + + + align:start position:0% +this concept of ideal shapes and ideal +circles is sort of the foundation of + + align:start position:0% +circles is sort of the foundation of + + + align:start position:0% +circles is sort of the foundation of +platonic mathematics some 2500 years ago + + align:start position:0% +platonic mathematics some 2500 years ago + + + align:start position:0% +platonic mathematics some 2500 years ago +and at the time though that they were + + align:start position:0% +and at the time though that they were + + + align:start position:0% +and at the time though that they were +developing that concept this idea that + + align:start position:0% +developing that concept this idea that + + + align:start position:0% +developing that concept this idea that +that there are ideal shapes out there + + align:start position:0% +that there are ideal shapes out there + + + align:start position:0% +that there are ideal shapes out there +and that thinking about them and + + align:start position:0% +and that thinking about them and + + + align:start position:0% +and that thinking about them and +manipulate them was a more effective way + + align:start position:0% +manipulate them was a more effective way + + + align:start position:0% +manipulate them was a more effective way +to reason about the real world you know + + align:start position:0% +to reason about the real world you know + + + align:start position:0% +to reason about the real world you know +there was a lot of skepticism you could + + align:start position:0% +there was a lot of skepticism you could + + + align:start position:0% +there was a lot of skepticism you could +imagine 2,500 years ago someone's + + align:start position:0% +imagine 2,500 years ago someone's + + + align:start position:0% +imagine 2,500 years ago someone's +walking around saying I believe there's + + align:start position:0% +walking around saying I believe there's + + + align:start position:0% +walking around saying I believe there's +these things called ideal circles in + + align:start position:0% +these things called ideal circles in + + + align:start position:0% +these things called ideal circles in +ideal squares and ideal shapes but they + + align:start position:0% +ideal squares and ideal shapes but they + + + align:start position:0% +ideal squares and ideal shapes but they +don't actually exist in nature that + + align:start position:0% +don't actually exist in nature that + + + align:start position:0% +don't actually exist in nature that +would probably not be well-received in + + align:start position:0% +would probably not be well-received in + + + align:start position:0% +would probably not be well-received in +fact it was not well-received many of + + align:start position:0% +fact it was not well-received many of + + + align:start position:0% +fact it was not well-received many of +those those philosophers who were + + align:start position:0% +those those philosophers who were + + + align:start position:0% +those those philosophers who were +thinking about this were we're very + + align:start position:0% +thinking about this were we're very + + + align:start position:0% +thinking about this were we're very +negatively negatively received in fact + + align:start position:0% +negatively negatively received in fact + + + align:start position:0% +negatively negatively received in fact +if you want to learn about how negative + + align:start position:0% +if you want to learn about how negative + + + align:start position:0% +if you want to learn about how negative +the response was to this I encourage you + + align:start position:0% +the response was to this I encourage you + + + align:start position:0% +the response was to this I encourage you +to go and read the allegory of the cave + + align:start position:0% +to go and read the allegory of the cave + + + align:start position:0% +to go and read the allegory of the cave +which is essentially the story of these + + align:start position:0% +which is essentially the story of these + + + align:start position:0% +which is essentially the story of these +philosophers talking about how they're + + align:start position:0% +philosophers talking about how they're + + + align:start position:0% +philosophers talking about how they're +trying to bring the light of this + + align:start position:0% +trying to bring the light of this + + + align:start position:0% +trying to bring the light of this +knowledge to the broader world and how + + align:start position:0% +knowledge to the broader world and how + + + align:start position:0% +knowledge to the broader world and how +they essentially + + align:start position:0% +they essentially + + + align:start position:0% +they essentially +killed because of it because people + + align:start position:0% +killed because of it because people + + + align:start position:0% +killed because of it because people +don't want want to see it so that + + align:start position:0% +don't want want to see it so that + + + align:start position:0% +don't want want to see it so that +struggle that we they experience 2500 + + align:start position:0% +struggle that we they experience 2500 + + + align:start position:0% +struggle that we they experience 2500 +years ago it exists today you will you + + align:start position:0% +years ago it exists today you will you + + + align:start position:0% +years ago it exists today you will you +as as people at MIT will try and bring + + align:start position:0% +as as people at MIT will try and bring + + + align:start position:0% +as as people at MIT will try and bring +mathematical concepts into environments + + align:start position:0% +mathematical concepts into environments + + + align:start position:0% +mathematical concepts into environments +for people like I don't see why that's + + align:start position:0% +for people like I don't see why that's + + + align:start position:0% +for people like I don't see why that's +relevant and you will experience you + + align:start position:0% +relevant and you will experience you + + + align:start position:0% +relevant and you will experience you +know negative inputs but you should rest + + align:start position:0% +know negative inputs but you should rest + + + align:start position:0% +know negative inputs but you should rest +assured that this is a good bet it's + + align:start position:0% +assured that this is a good bet it's + + + align:start position:0% +assured that this is a good bet it's +worked well for thousands of years you + + align:start position:0% +worked well for thousands of years you + + + align:start position:0% +worked well for thousands of years you +know it's what I base my career on + + align:start position:0% +know it's what I base my career on + + + align:start position:0% +know it's what I base my career on +people ask well what's the basis of it + + align:start position:0% +people ask well what's the basis of it + + + align:start position:0% +people ask well what's the basis of it +well I'm just sort of betting on math + + align:start position:0% +well I'm just sort of betting on math + + + align:start position:0% +well I'm just sort of betting on math +here that's been a good it's been a good + + align:start position:0% +here that's been a good it's been a good + + + align:start position:0% +here that's been a good it's been a good +tool and so this is why we're beginning + + align:start position:0% +tool and so this is why we're beginning + + + align:start position:0% +tool and so this is why we're beginning +to think of this way when we talk about + + align:start position:0% +to think of this way when we talk about + + + align:start position:0% +to think of this way when we talk about +big data and machine learning sort of + + align:start position:0% +big data and machine learning sort of + + + align:start position:0% +big data and machine learning sort of +really looking at the fundamentals what + + align:start position:0% +really looking at the fundamentals what + + + align:start position:0% +really looking at the fundamentals what +are the ideals that we that we need in + + align:start position:0% +are the ideals that we that we need in + + + align:start position:0% +are the ideals that we that we need in +order to effectively reason about the + + align:start position:0% +order to effectively reason about the + + + align:start position:0% +order to effectively reason about the +problems that we're facing today in the + + align:start position:0% +problems that we're facing today in the + + + align:start position:0% +problems that we're facing today in the +virtual world right and the fact that + + align:start position:0% +virtual world right and the fact that + + + align:start position:0% +virtual world right and the fact that +you know this mathematical concepts you + + align:start position:0% +you know this mathematical concepts you + + + align:start position:0% +you know this mathematical concepts you +know describe the natural world so well + + align:start position:0% +know describe the natural world so well + + + align:start position:0% +know describe the natural world so well +and also described in you know in the + + align:start position:0% +and also described in you know in the + + + align:start position:0% +and also described in you know in the +virtual world is sometimes called the + + align:start position:0% +virtual world is sometimes called the + + + align:start position:0% +virtual world is sometimes called the +unreasonable effectiveness of + + align:start position:0% +unreasonable effectiveness of + + + align:start position:0% +unreasonable effectiveness of +mathematics you can look that up but + + align:start position:0% +mathematics you can look that up but + + + align:start position:0% +mathematics you can look that up but +people talk about math why does it doe + + align:start position:0% +people talk about math why does it doe + + + align:start position:0% +people talk about math why does it doe +do a such a good job of describing so + + align:start position:0% +do a such a good job of describing so + + + align:start position:0% +do a such a good job of describing so +many of things and people say well they + + align:start position:0% +many of things and people say well they + + + align:start position:0% +many of things and people say well they +don't really know but it's it seems to + + align:start position:0% +don't really know but it's it seems to + + + align:start position:0% +don't really know but it's it seems to +be a good bit of luck that it happens + + align:start position:0% +be a good bit of luck that it happens + + + align:start position:0% +be a good bit of luck that it happens +that way so you know this is circles and + + align:start position:0% +that way so you know this is circles and + + + align:start position:0% +that way so you know this is circles and +that gets us you know a certain way but + + align:start position:0% +that gets us you know a certain way but + + + align:start position:0% +that gets us you know a certain way but +in most of the fields that that we work + + align:start position:0% +in most of the fields that that we work + + + align:start position:0% +in most of the fields that that we work +with and I would say that in almost any + + align:start position:0% +with and I would say that in almost any + + + align:start position:0% +with and I would say that in almost any +introductory course that you take in + + align:start position:0% +introductory course that you take in + + + align:start position:0% +introductory course that you take in +college whatever the discipline is + + align:start position:0% +college whatever the discipline is + + + align:start position:0% +college whatever the discipline is +whether it be you know chemistry or + + align:start position:0% +whether it be you know chemistry or + + + align:start position:0% +whether it be you know chemistry or +mechanical engineering or Electrical + + align:start position:0% +mechanical engineering or Electrical + + + align:start position:0% +mechanical engineering or Electrical +Engineering or physics or biology the + + align:start position:0% +Engineering or physics or biology the + + + align:start position:0% +Engineering or physics or biology the +basic fundamental theoretical ideas that + + align:start position:0% +basic fundamental theoretical ideas that + + + align:start position:0% +basic fundamental theoretical ideas that +they will introduce to you will be the + + align:start position:0% +they will introduce to you will be the + + + align:start position:0% +they will introduce to you will be the +concept of a linear model so there we + + align:start position:0% +concept of a linear model so there we + + + align:start position:0% +concept of a linear model so there we +have a linear model right and why do we + + align:start position:0% +have a linear model right and why do we + + + align:start position:0% +have a linear model right and why do we +like linear models and again it can be + + align:start position:0% +like linear models and again it can be + + + align:start position:0% +like linear models and again it can be +physics it can be simple as F equals MA + + align:start position:0% +physics it can be simple as F equals MA + + + align:start position:0% +physics it can be simple as F equals MA +or in chemistry you can be some kind of + + align:start position:0% +or in chemistry you can be some kind of + + + align:start position:0% +or in chemistry you can be some kind of +chemical rate equation + + align:start position:0% +chemical rate equation + + + align:start position:0% +chemical rate equation +or in mechanical engineering there's you + + align:start position:0% +or in mechanical engineering there's you + + + align:start position:0% +or in mechanical engineering there's you +know it can be basic concepts of + + align:start position:0% +know it can be basic concepts of + + + align:start position:0% +know it can be basic concepts of +friction the reason we like these basic + + align:start position:0% +friction the reason we like these basic + + + align:start position:0% +friction the reason we like these basic +linear models is because we can project + + align:start position:0% +linear models is because we can project + + + align:start position:0% +linear models is because we can project +right I know that if that solid line + + align:start position:0% +right I know that if that solid line + + + align:start position:0% +right I know that if that solid line +represents what I believed you know I + + align:start position:0% +represents what I believed you know I + + + align:start position:0% +represents what I believed you know I +have evidence to support that that that + + align:start position:0% +have evidence to support that that that + + + align:start position:0% +have evidence to support that that that +is correct then I feel pretty good about + + align:start position:0% +is correct then I feel pretty good about + + + align:start position:0% +is correct then I feel pretty good about +projecting maybe where I don't have data + + align:start position:0% +projecting maybe where I don't have data + + + align:start position:0% +projecting maybe where I don't have data +or into a new domain so linear models + + align:start position:0% +or into a new domain so linear models + + + align:start position:0% +or into a new domain so linear models +allow us to do this this reasoning and + + align:start position:0% +allow us to do this this reasoning and + + + align:start position:0% +allow us to do this this reasoning and +that's why in almost every in the first + + align:start position:0% +that's why in almost every in the first + + + align:start position:0% +that's why in almost every in the first +few weeks of almost any introductory + + align:start position:0% +few weeks of almost any introductory + + + align:start position:0% +few weeks of almost any introductory +course they begin with these linear + + align:start position:0% +course they begin with these linear + + + align:start position:0% +course they begin with these linear +models because they have proven to be so + + align:start position:0% +models because they have proven to be so + + + align:start position:0% +models because they have proven to be so +effective now there are many nonlinear + + align:start position:0% +effective now there are many nonlinear + + + align:start position:0% +effective now there are many nonlinear +phenomena there tremendously important + + align:start position:0% +phenomena there tremendously important + + + align:start position:0% +phenomena there tremendously important +ok and and as a person who deals with + + align:start position:0% +ok and and as a person who deals with + + + align:start position:0% +ok and and as a person who deals with +large-scale computation you know those + + align:start position:0% +large-scale computation you know those + + + align:start position:0% +large-scale computation you know those +are a staple of what people do but in + + align:start position:0% +are a staple of what people do but in + + + align:start position:0% +are a staple of what people do but in +order to do nonlinear calculations or + + align:start position:0% +order to do nonlinear calculations or + + + align:start position:0% +order to do nonlinear calculations or +reason about things non linearly it + + align:start position:0% +reason about things non linearly it + + + align:start position:0% +reason about things non linearly it +usually requires a much more complicated + + align:start position:0% +usually requires a much more complicated + + + align:start position:0% +usually requires a much more complicated +analysis and much more computation much + + align:start position:0% +analysis and much more computation much + + + align:start position:0% +analysis and much more computation much +more data and so our ability to + + align:start position:0% +more data and so our ability to + + + align:start position:0% +more data and so our ability to +extrapolate is very limited ok it's very + + align:start position:0% +extrapolate is very limited ok it's very + + + align:start position:0% +extrapolate is very limited ok it's very +it's very limited so here I am talking + + align:start position:0% +it's very limited so here I am talking + + + align:start position:0% +it's very limited so here I am talking +about the benefits of ideal well + + align:start position:0% +about the benefits of ideal well + + + align:start position:0% +about the benefits of ideal well +thinking mathematically talking about + + align:start position:0% +thinking mathematically talking about + + + align:start position:0% +thinking mathematically talking about +you know linearity what does this have + + align:start position:0% +you know linearity what does this have + + + align:start position:0% +you know linearity what does this have +to do with big data well and and and + + align:start position:0% +to do with big data well and and and + + + align:start position:0% +to do with big data well and and and +machine learning so we would like to be + + align:start position:0% +machine learning so we would like to be + + + align:start position:0% +machine learning so we would like to be +able to do the same things that we've + + align:start position:0% +able to do the same things that we've + + + align:start position:0% +able to do the same things that we've +been able to do in other fields in this + + align:start position:0% +been able to do in other fields in this + + + align:start position:0% +been able to do in other fields in this +sort of new emerging field of big data + + align:start position:0% +sort of new emerging field of big data + + + align:start position:0% +sort of new emerging field of big data +and this often deals with data that + + align:start position:0% +and this often deals with data that + + + align:start position:0% +and this often deals with data that +doesn't look like the traditional you + + align:start position:0% +doesn't look like the traditional you + + + align:start position:0% +doesn't look like the traditional you +know measurements we see in in science + + align:start position:0% +know measurements we see in in science + + + align:start position:0% +know measurements we see in in science +this can be data that has to do with + + align:start position:0% +this can be data that has to do with + + + align:start position:0% +this can be data that has to do with +words or images pictures of people other + + align:start position:0% +words or images pictures of people other + + + align:start position:0% +words or images pictures of people other +types of things that don't feel like the + + align:start position:0% +types of things that don't feel like the + + + align:start position:0% +types of things that don't feel like the +kinds of data that we traditionally deal + + align:start position:0% +kinds of data that we traditionally deal + + + align:start position:0% +kinds of data that we traditionally deal +with in science and engineering but we + + align:start position:0% +with in science and engineering but we + + + align:start position:0% +with in science and engineering but we +know we want to use linear models so how + + align:start position:0% +know we want to use linear models so how + + + align:start position:0% +know we want to use linear models so how +are we going to do that how can we take + + align:start position:0% +are we going to do that how can we take + + + align:start position:0% +are we going to do that how can we take +this concept of Lin + + align:start position:0% +this concept of Lin + + + align:start position:0% +this concept of Lin +which has been so powerful across so + + align:start position:0% +which has been so powerful across so + + + align:start position:0% +which has been so powerful across so +many disciplines and bring them to this + + align:start position:0% +many disciplines and bring them to this + + + align:start position:0% +many disciplines and bring them to this +field that that just feels completely + + align:start position:0% +field that that just feels completely + + + align:start position:0% +field that that just feels completely +different in time the kinds of times of + + align:start position:0% +different in time the kinds of times of + + + align:start position:0% +different in time the kinds of times of +data that we have so to begin with I + + align:start position:0% +data that we have so to begin with I + + + align:start position:0% +data that we have so to begin with I +need to refresh for you what it really + + align:start position:0% +need to refresh for you what it really + + + align:start position:0% +need to refresh for you what it really +means to be linear before I showed you a + + align:start position:0% +means to be linear before I showed you a + + + align:start position:0% +means to be linear before I showed you a +line and hence line linear but + + align:start position:0% +line and hence line linear but + + + align:start position:0% +line and hence line linear but +mathematically linearity means something + + align:start position:0% +mathematically linearity means something + + + align:start position:0% +mathematically linearity means something +much deeper and so here's an equation + + align:start position:0% +much deeper and so here's an equation + + + align:start position:0% +much deeper and so here's an equation +that you may have first seen in + + align:start position:0% +that you may have first seen in + + + align:start position:0% +that you may have first seen in +elementary school we basically have 2 + + align:start position:0% +elementary school we basically have 2 + + + align:start position:0% +elementary school we basically have 2 +times 3 plus 4 is equal to 2 times 3 + + align:start position:0% +times 3 plus 4 is equal to 2 times 3 + + + align:start position:0% +times 3 plus 4 is equal to 2 times 3 +plus 2 times 4 that is called the + + align:start position:0% +plus 2 times 4 that is called the + + + align:start position:0% +plus 2 times 4 that is called the +distributive property + + align:start position:0% +distributive property + + + align:start position:0% +distributive property +it basically says multiplication + + align:start position:0% +it basically says multiplication + + + align:start position:0% +it basically says multiplication +distributes over addition and this is + + align:start position:0% +distributes over addition and this is + + + align:start position:0% +distributes over addition and this is +the fundamental reason why I would say + + align:start position:0% +the fundamental reason why I would say + + + align:start position:0% +the fundamental reason why I would say +mathematics works in our world right if + + align:start position:0% +mathematics works in our world right if + + + align:start position:0% +mathematics works in our world right if +this wasn't true very early on in the + + align:start position:0% +this wasn't true very early on in the + + + align:start position:0% +this wasn't true very early on in the +earliest days of inventing mathematics + + align:start position:0% +earliest days of inventing mathematics + + + align:start position:0% +earliest days of inventing mathematics +it would not have been very useful right + + align:start position:0% +it would not have been very useful right + + + align:start position:0% +it would not have been very useful right +you know they say that I have you know 2 + + align:start position:0% +you know they say that I have you know 2 + + + align:start position:0% +you know they say that I have you know 2 +of 3 plus 4 of something ok and then I + + align:start position:0% +of 3 plus 4 of something ok and then I + + + align:start position:0% +of 3 plus 4 of something ok and then I +can sort of change it and do in this + + align:start position:0% +can sort of change it and do in this + + + align:start position:0% +can sort of change it and do in this +other way that's really what makes + + align:start position:0% +other way that's really what makes + + + align:start position:0% +other way that's really what makes +mathematical mathematics useful and from + + align:start position:0% +mathematical mathematics useful and from + + + align:start position:0% +mathematical mathematics useful and from +a deeper perspective the distributive + + align:start position:0% +a deeper perspective the distributive + + + align:start position:0% +a deeper perspective the distributive +property is basically what makes math + + align:start position:0% +property is basically what makes math + + + align:start position:0% +property is basically what makes math +linear this is the property that if this + + align:start position:0% +linear this is the property that if this + + + align:start position:0% +linear this is the property that if this +property holds then we can reason about + + align:start position:0% +property holds then we can reason about + + + align:start position:0% +property holds then we can reason about +a system linearly now you're very + + align:start position:0% +a system linearly now you're very + + + align:start position:0% +a system linearly now you're very +familiar with this type of mathematics + + align:start position:0% +familiar with this type of mathematics + + + align:start position:0% +familiar with this type of mathematics +but there's other types of mathematics + + align:start position:0% +but there's other types of mathematics + + + align:start position:0% +but there's other types of mathematics +so if you will allow me hopefully you + + align:start position:0% +so if you will allow me hopefully you + + + align:start position:0% +so if you will allow me hopefully you +will let me just replace those + + align:start position:0% +will let me just replace those + + + align:start position:0% +will let me just replace those +multiplication symbols and addition + + align:start position:0% +multiplication symbols and addition + + + align:start position:0% +multiplication symbols and addition +symbols with the sort of funny circle + + align:start position:0% +symbols with the sort of funny circle + + + align:start position:0% +symbols with the sort of funny circle +times and circle plus and we'll get to + + align:start position:0% +times and circle plus and we'll get to + + + align:start position:0% +times and circle plus and we'll get to +why I'm going to do that because it + + align:start position:0% +why I'm going to do that because it + + + align:start position:0% +why I'm going to do that because it +turns out that while you have been done + + align:start position:0% +turns out that while you have been done + + + align:start position:0% +turns out that while you have been done +most of your careers with traditional + + align:start position:0% +most of your careers with traditional + + + align:start position:0% +most of your careers with traditional +arithmetic multiplication and addition + + align:start position:0% +arithmetic multiplication and addition + + + align:start position:0% +arithmetic multiplication and addition +the kind you would do on your calculator + + align:start position:0% +the kind you would do on your calculator + + + align:start position:0% +the kind you would do on your calculator +have done in in elementary school it + + align:start position:0% +have done in in elementary school it + + + align:start position:0% +have done in in elementary school it +turns out there's other pairs of + + align:start position:0% +turns out there's other pairs of + + + align:start position:0% +turns out there's other pairs of +operations that also obey + + align:start position:0% +operations that also obey + + + align:start position:0% +operations that also obey +property this distributive property and + + align:start position:0% +property this distributive property and + + + align:start position:0% +property this distributive property and +therefore allow us to potentially build + + align:start position:0% +therefore allow us to potentially build + + + align:start position:0% +therefore allow us to potentially build +linear models of very different types of + + align:start position:0% +linear models of very different types of + + + align:start position:0% +linear models of very different types of +data using this property so as I + + align:start position:0% +data using this property so as I + + + align:start position:0% +data using this property so as I +mentioned the sort of the classic two + + align:start position:0% +mentioned the sort of the classic two + + + align:start position:0% +mentioned the sort of the classic two +are you know circle plus is just equal + + align:start position:0% +are you know circle plus is just equal + + + align:start position:0% +are you know circle plus is just equal +to regular arithmetic addition as we + + align:start position:0% +to regular arithmetic addition as we + + + align:start position:0% +to regular arithmetic addition as we +show in the first line and circle x is + + align:start position:0% +show in the first line and circle x is + + + align:start position:0% +show in the first line and circle x is +equal to regular arithmetic + + align:start position:0% +equal to regular arithmetic + + + align:start position:0% +equal to regular arithmetic +multiplication so those are sort of the + + align:start position:0% +multiplication so those are sort of the + + + align:start position:0% +multiplication so those are sort of the +standard ones and by far this pair you + + align:start position:0% +standard ones and by far this pair you + + + align:start position:0% +standard ones and by far this pair you +know this is the most common pair that + + align:start position:0% +know this is the most common pair that + + + align:start position:0% +know this is the most common pair that +we use you know across the world today + + align:start position:0% +we use you know across the world today + + + align:start position:0% +we use you know across the world today +but there are others + + align:start position:0% +but there are others + + + align:start position:0% +but there are others +so for existence I can replace the plus + + align:start position:0% +so for existence I can replace the plus + + + align:start position:0% +so for existence I can replace the plus +operation with Max and the + + align:start position:0% +operation with Max and the + + + align:start position:0% +operation with Max and the +multiplication operation with addition + + align:start position:0% +multiplication operation with addition + + + align:start position:0% +multiplication operation with addition +okay and the above distributive equation + + align:start position:0% +okay and the above distributive equation + + + align:start position:0% +okay and the above distributive equation +will still hold right that's very little + + align:start position:0% +will still hold right that's very little + + + align:start position:0% +will still hold right that's very little +confusing and I often get confused that + + align:start position:0% +confusing and I often get confused that + + + align:start position:0% +confusing and I often get confused that +you know addition and you know the + + align:start position:0% +you know addition and you know the + + + align:start position:0% +you know addition and you know the +multiplication is no addition but this + + align:start position:0% +multiplication is no addition but this + + + align:start position:0% +multiplication is no addition but this +is this pair sometimes referred to as + + align:start position:0% +is this pair sometimes referred to as + + + align:start position:0% +is this pair sometimes referred to as +Max Plus you'll sometimes hear about as + + align:start position:0% +Max Plus you'll sometimes hear about as + + + align:start position:0% +Max Plus you'll sometimes hear about as +Max Plus algebra is actually very + + align:start position:0% +Max Plus algebra is actually very + + + align:start position:0% +Max Plus algebra is actually very +important in machine learning and neural + + align:start position:0% +important in machine learning and neural + + + align:start position:0% +important in machine learning and neural +networks this is actually sort of the + + align:start position:0% +networks this is actually sort of the + + + align:start position:0% +networks this is actually sort of the +the the back end of the rectified linear + + align:start position:0% +the the back end of the rectified linear + + + align:start position:0% +the the back end of the rectified linear +unit is essentially this this operation + + align:start position:0% +unit is essentially this this operation + + + align:start position:0% +unit is essentially this this operation +if you didn't understand what that meant + + align:start position:0% +if you didn't understand what that meant + + + align:start position:0% +if you didn't understand what that meant +that's okay we'll get to that later it's + + align:start position:0% +that's okay we'll get to that later it's + + + align:start position:0% +that's okay we'll get to that later it's +very important in finance there's + + align:start position:0% +very important in finance there's + + + align:start position:0% +very important in finance there's +certain finance operations that rely on + + align:start position:0% +certain finance operations that rely on + + + align:start position:0% +certain finance operations that rely on +this type of mathematics there are other + + align:start position:0% +this type of mathematics there are other + + + align:start position:0% +this type of mathematics there are other +pairs also so here's one I can replace + + align:start position:0% +pairs also so here's one I can replace + + + align:start position:0% +pairs also so here's one I can replace +addition with Union and multiplication + + align:start position:0% +addition with Union and multiplication + + + align:start position:0% +addition with Union and multiplication +with intersection right now this that + + align:start position:0% +with intersection right now this that + + + align:start position:0% +with intersection right now this that +also obeys that linear property this is + + align:start position:0% +also obeys that linear property this is + + + align:start position:0% +also obeys that linear property this is +essentially a pair of operations that + + align:start position:0% +essentially a pair of operations that + + + align:start position:0% +essentially a pair of operations that +you know anytime you make a transaction + + align:start position:0% +you know anytime you make a transaction + + + align:start position:0% +you know anytime you make a transaction +and work with what's called a relational + + align:start position:0% +and work with what's called a relational + + + align:start position:0% +and work with what's called a relational +database that's the mathematical + + align:start position:0% +database that's the mathematical + + + align:start position:0% +database that's the mathematical +operation a pair that's sitting inside + + align:start position:0% +operation a pair that's sitting inside + + + align:start position:0% +operation a pair that's sitting inside +it it's why those databases work it + + align:start position:0% +it it's why those databases work it + + + align:start position:0% +it it's why those databases work it +allows us to reason about queries which + + align:start position:0% +allows us to reason about queries which + + + align:start position:0% +allows us to reason about queries which +are just a series of intersections and + + align:start position:0% +are just a series of intersections and + + + align:start position:0% +are just a series of intersections and +using unions and and reorder them and + + align:start position:0% +using unions and and reorder them and + + + align:start position:0% +using unions and and reorder them and +Rianne + + align:start position:0% +Rianne + + + align:start position:0% +Rianne +in such a way well this isn't in + + align:start position:0% +in such a way well this isn't in + + + align:start position:0% +in such a way well this isn't in +databases is called query planning and + + align:start position:0% +databases is called query planning and + + + align:start position:0% +databases is called query planning and +if that property wasn't true we wouldn't + + align:start position:0% +if that property wasn't true we wouldn't + + + align:start position:0% +if that property wasn't true we wouldn't +be able to do that so this is a deep + + align:start position:0% +be able to do that so this is a deep + + + align:start position:0% +be able to do that so this is a deep +deep property of that so you know these + + align:start position:0% +deep property of that so you know these + + + align:start position:0% +deep property of that so you know these +these we can put all different types of + + align:start position:0% +these we can put all different types of + + + align:start position:0% +these we can put all different types of +pairs in here and and reason about them + + align:start position:0% +pairs in here and and reason about them + + + align:start position:0% +pairs in here and and reason about them +linearly and this is why that many many + + align:start position:0% +linearly and this is why that many many + + + align:start position:0% +linearly and this is why that many many +of the of the systems we use today work + + align:start position:0% +of the of the systems we use today work + + + align:start position:0% +of the of the systems we use today work +and so this class is about so really + + align:start position:0% +and so this class is about so really + + + align:start position:0% +and so this class is about so really +exposing that that really the + + align:start position:0% +exposing that that really the + + + align:start position:0% +exposing that that really the +mathematics that allows us to think + + align:start position:0% +mathematics that allows us to think + + + align:start position:0% +mathematics that allows us to think +linearly about data that we haven't + + align:start position:0% +linearly about data that we haven't + + + align:start position:0% +linearly about data that we haven't +really thought of as maybe obeying some + + align:start position:0% +really thought of as maybe obeying some + + + align:start position:0% +really thought of as maybe obeying some +kind of linear model this is essentially + + align:start position:0% +kind of linear model this is essentially + + + align:start position:0% +kind of linear model this is essentially +the critical point of this class so it + + align:start position:0% +the critical point of this class so it + + + align:start position:0% +the critical point of this class so it +goes beyond that though so hopefully + + align:start position:0% +goes beyond that though so hopefully + + + align:start position:0% +goes beyond that though so hopefully +you'll allow me to replace those numbers + + align:start position:0% +you'll allow me to replace those numbers + + + align:start position:0% +you'll allow me to replace those numbers +with letters right so that's sort of + + align:start position:0% +with letters right so that's sort of + + + align:start position:0% +with letters right so that's sort of +basic algebra there that just for + + align:start position:0% +basic algebra there that just for + + + align:start position:0% +basic algebra there that just for +refresher the previous equation you know + + align:start position:0% +refresher the previous equation you know + + + align:start position:0% +refresher the previous equation you know +we had a equals to B equals three C + + align:start position:0% +we had a equals to B equals three C + + + align:start position:0% +we had a equals to B equals three C +equals four but we're not limited to + + align:start position:0% +equals four but we're not limited to + + + align:start position:0% +equals four but we're not limited to +these variables or these these letters + + align:start position:0% +these variables or these these letters + + + align:start position:0% +these variables or these these letters +to being just simple scalar numbers in + + align:start position:0% +to being just simple scalar numbers in + + + align:start position:0% +to being just simple scalar numbers in +this case real numbers or integers or + + align:start position:0% +this case real numbers or integers or + + + align:start position:0% +this case real numbers or integers or +something like that they can be other + + align:start position:0% +something like that they can be other + + + align:start position:0% +something like that they can be other +things too so for instance a B and C + + align:start position:0% +things too so for instance a B and C + + + align:start position:0% +things too so for instance a B and C +could be spreadsheets and that's + + align:start position:0% +could be spreadsheets and that's + + + align:start position:0% +could be spreadsheets and that's +something we'll go over with extensively + + align:start position:0% +something we'll go over with extensively + + + align:start position:0% +something we'll go over with extensively +in a class so that I can basically have + + align:start position:0% +in a class so that I can basically have + + + align:start position:0% +in a class so that I can basically have +a B and C be whole spreadsheets of data + + align:start position:0% +a B and C be whole spreadsheets of data + + + align:start position:0% +a B and C be whole spreadsheets of data +and the linear equation will still hold + + align:start position:0% +and the linear equation will still hold + + + align:start position:0% +and the linear equation will still hold +in fact that's probably the key concept + + align:start position:0% +in fact that's probably the key concept + + + align:start position:0% +in fact that's probably the key concept +in big data is the necessity to reason + + align:start position:0% +in big data is the necessity to reason + + + align:start position:0% +in big data is the necessity to reason +about data as whole collections in + + align:start position:0% +about data as whole collections in + + + align:start position:0% +about data as whole collections in +transforming whole collections going and + + align:start position:0% +transforming whole collections going and + + + align:start position:0% +transforming whole collections going and +looking at things one element in time at + + align:start position:0% +looking at things one element in time at + + + align:start position:0% +looking at things one element in time at +a time is is essentially the thing that + + align:start position:0% +a time is is essentially the thing that + + + align:start position:0% +a time is is essentially the thing that +is extremely difficult to do when you + + align:start position:0% +is extremely difficult to do when you + + + align:start position:0% +is extremely difficult to do when you +have large amounts of data + + align:start position:0% + + + + align:start position:0% + +a B and C can be database tables right + + align:start position:0% +a B and C can be database tables right + + + align:start position:0% +a B and C can be database tables right +those doing differ too much from + + align:start position:0% +those doing differ too much from + + + align:start position:0% +those doing differ too much from +spreadsheets and as I talked to you you + + align:start position:0% +spreadsheets and as I talked to you you + + + align:start position:0% +spreadsheets and as I talked to you you +know in the previous slide you know that + + align:start position:0% +know in the previous slide you know that + + + align:start position:0% +know in the previous slide you know that +Union intersection pair naturally lines + + align:start position:0% +Union intersection pair naturally lines + + + align:start position:0% +Union intersection pair naturally lines +up and we can do reason about whole + + align:start position:0% +up and we can do reason about whole + + + align:start position:0% +up and we can do reason about whole +tables in a database using linear + + align:start position:0% +tables in a database using linear + + + align:start position:0% +tables in a database using linear +properties they can be matrices I think + + align:start position:0% +properties they can be matrices I think + + + align:start position:0% +properties they can be matrices I think +for those of you who have had linear + + align:start position:0% +for those of you who have had linear + + + align:start position:0% +for those of you who have had linear +algebra or matrix mathematics that would + + align:start position:0% +algebra or matrix mathematics that would + + + align:start position:0% +algebra or matrix mathematics that would +have been the first example right when I + + align:start position:0% +have been the first example right when I + + + align:start position:0% +have been the first example right when I +substituted the a B and C and had the + + align:start position:0% +substituted the a B and C and had the + + + align:start position:0% +substituted the a B and C and had the +these linear equations often in many of + + align:start position:0% +these linear equations often in many of + + + align:start position:0% +these linear equations often in many of +the sciences we think about you know + + align:start position:0% +the sciences we think about you know + + + align:start position:0% +the sciences we think about you know +matrix operations and linearity as sort + + align:start position:0% +matrix operations and linearity as sort + + + align:start position:0% +matrix operations and linearity as sort +of being a couple together and through + + align:start position:0% +of being a couple together and through + + + align:start position:0% +of being a couple together and through +the do allottee between matrices and and + + align:start position:0% +the do allottee between matrices and and + + + align:start position:0% +the do allottee between matrices and and +graphs and networks we can represent + + align:start position:0% +graphs and networks we can represent + + + align:start position:0% +graphs and networks we can represent +graphs and networks through matrices + + align:start position:0% +graphs and networks through matrices + + + align:start position:0% +graphs and networks through matrices +anytime you work with a neural network + + align:start position:0% +anytime you work with a neural network + + + align:start position:0% +anytime you work with a neural network +you're representing that network as a + + align:start position:0% +you're representing that network as a + + + align:start position:0% +you're representing that network as a +matrix and of course all these equations + + align:start position:0% +matrix and of course all these equations + + + align:start position:0% +matrix and of course all these equations +apply there as well and can reason about + + align:start position:0% +apply there as well and can reason about + + + align:start position:0% +apply there as well and can reason about +those systems linearly so that provides + + align:start position:0% +those systems linearly so that provides + + + align:start position:0% +those systems linearly so that provides +a little motivation there as it was we + + align:start position:0% +a little motivation there as it was we + + + align:start position:0% +a little motivation there as it was we +like to say enough about me let me tell + + align:start position:0% +like to say enough about me let me tell + + + align:start position:0% +like to say enough about me let me tell +you about my my book so this will be the + + align:start position:0% +you about my my book so this will be the + + + align:start position:0% +you about my my book so this will be the +text that will be use in the class we + + align:start position:0% +text that will be use in the class we + + + align:start position:0% +text that will be use in the class we +are not going to go through the full + + align:start position:0% +are not going to go through the full + + + align:start position:0% +are not going to go through the full +text but we have printed out copies of + + align:start position:0% +text but we have printed out copies of + + + align:start position:0% +text but we have printed out copies of +the first sort of seven chapters that we + + align:start position:0% +the first sort of seven chapters that we + + + align:start position:0% +the first sort of seven chapters that we +will go through and we will hand those + + align:start position:0% +will go through and we will hand those + + + align:start position:0% +will go through and we will hand those +out later when you when you when you do + + align:start position:0% +out later when you when you when you do + + + align:start position:0% +out later when you when you when you do +do the class so let me now switch gears + + align:start position:0% +do the class so let me now switch gears + + + align:start position:0% +do the class so let me now switch gears +a little bit and talk about how this + + align:start position:0% +a little bit and talk about how this + + + align:start position:0% +a little bit and talk about how this +relates to I think one of the most + + align:start position:0% +relates to I think one of the most + + + align:start position:0% +relates to I think one of the most +wonderful breakthroughs that we have + + align:start position:0% +wonderful breakthroughs that we have + + + align:start position:0% +wonderful breakthroughs that we have +seen where I've seen in my career and + + align:start position:0% +seen where I've seen in my career and + + + align:start position:0% +seen where I've seen in my career and +many of my colleagues here at MIT have + + align:start position:0% +many of my colleagues here at MIT have + + + align:start position:0% +many of my colleagues here at MIT have +seen which is what's been going on in + + align:start position:0% +seen which is what's been going on in + + + align:start position:0% +seen which is what's been going on in +machine learning right which is which is + + align:start position:0% +machine learning right which is which is + + + align:start position:0% +machine learning right which is which is +it's sort of beat it's not it's not hype + + align:start position:0% +it's sort of beat it's not it's not hype + + + align:start position:0% +it's sort of beat it's not it's not hype +there's a real real there there and it's + + align:start position:0% +there's a real real there there and it's + + + align:start position:0% +there's a real real there there and it's +tremendously exciting so + + align:start position:0% +tremendously exciting so + + + align:start position:0% +tremendously exciting so +give you a little history basic history + + align:start position:0% +give you a little history basic history + + + align:start position:0% +give you a little history basic history +of this field so in a certain sense + + align:start position:0% +of this field so in a certain sense + + + align:start position:0% +of this field so in a certain sense +before 2010 machine learning looked like + + align:start position:0% +before 2010 machine learning looked like + + + align:start position:0% +before 2010 machine learning looked like +this and then sort of after 2015 it kind + + align:start position:0% +this and then sort of after 2015 it kind + + + align:start position:0% +this and then sort of after 2015 it kind +of looks like this so when people talk + + align:start position:0% +of looks like this so when people talk + + + align:start position:0% +of looks like this so when people talk +about the hype in machine learning or AI + + align:start position:0% +about the hype in machine learning or AI + + + align:start position:0% +about the hype in machine learning or AI +really deep neural networks are the + + align:start position:0% +really deep neural networks are the + + + align:start position:0% +really deep neural networks are the +elephant inside the machine learning + + align:start position:0% +elephant inside the machine learning + + + align:start position:0% +elephant inside the machine learning +snake and they have that has stormed + + align:start position:0% +snake and they have that has stormed + + + align:start position:0% +snake and they have that has stormed +onto the scene in the last five years + + align:start position:0% +onto the scene in the last five years + + + align:start position:0% +onto the scene in the last five years +and basically allowed us to do things + + align:start position:0% +and basically allowed us to do things + + + align:start position:0% +and basically allowed us to do things +that you know we had almost taken for + + align:start position:0% +that you know we had almost taken for + + + align:start position:0% +that you know we had almost taken for +granted were a pop impossible in just + + align:start position:0% +granted were a pop impossible in just + + + align:start position:0% +granted were a pop impossible in just +the fact that you're able to talk to + + align:start position:0% +the fact that you're able to talk to + + + align:start position:0% +the fact that you're able to talk to +computers and they can understand you + + align:start position:0% +computers and they can understand you + + + align:start position:0% +computers and they can understand you +that we can have computers that can see + + align:start position:0% +that we can have computers that can see + + + align:start position:0% +that we can have computers that can see +in the way you know or at least in a way + + align:start position:0% +in the way you know or at least in a way + + + align:start position:0% +in the way you know or at least in a way +that approximate the way humans do these + + align:start position:0% +that approximate the way humans do these + + + align:start position:0% +that approximate the way humans do these +are really almost technological miracles + + align:start position:0% +are really almost technological miracles + + + align:start position:0% +are really almost technological miracles +that for those of us who've been working + + align:start position:0% +that for those of us who've been working + + + align:start position:0% +that for those of us who've been working +on this field for 50 years we get almost + + align:start position:0% +on this field for 50 years we get almost + + + align:start position:0% +on this field for 50 years we get almost +literally given up on and then all of a + + align:start position:0% +literally given up on and then all of a + + + align:start position:0% +literally given up on and then all of a +sudden it became possible so let me give + + align:start position:0% +sudden it became possible so let me give + + + align:start position:0% +sudden it became possible so let me give +you a little sense of a reprieve for + + align:start position:0% +you a little sense of a reprieve for + + + align:start position:0% +you a little sense of a reprieve for +this field and it's and its roots so + + align:start position:0% +this field and it's and its roots so + + + align:start position:0% +this field and it's and its roots so +machine learning like any field is + + align:start position:0% +machine learning like any field is + + + align:start position:0% +machine learning like any field is +defined as a set of techniques and + + align:start position:0% +defined as a set of techniques and + + + align:start position:0% +defined as a set of techniques and +problems when you ask what defines a + + align:start position:0% +problems when you ask what defines a + + + align:start position:0% +problems when you ask what defines a +field you ask well what are the problems + + align:start position:0% +field you ask well what are the problems + + + align:start position:0% +field you ask well what are the problems +that they work on that other fields + + align:start position:0% +that they work on that other fields + + + align:start position:0% +that they work on that other fields +don't really work on and what are the + + align:start position:0% +don't really work on and what are the + + + align:start position:0% +don't really work on and what are the +techniques they employ that really are + + align:start position:0% +techniques they employ that really are + + + align:start position:0% +techniques they employ that really are +not really you know be employed by + + align:start position:0% +not really you know be employed by + + + align:start position:0% +not really you know be employed by +others so you know the core techniques + + align:start position:0% +others so you know the core techniques + + + align:start position:0% +others so you know the core techniques +you know as I've mentioned earlier are + + align:start position:0% +you know as I've mentioned earlier are + + + align:start position:0% +you know as I've mentioned earlier are +these neural networks these are meant to + + align:start position:0% +these neural networks these are meant to + + + align:start position:0% +these neural networks these are meant to +crudely approximate maybe the way humans + + align:start position:0% +crudely approximate maybe the way humans + + + align:start position:0% +crudely approximate maybe the way humans +think about problems we have these + + align:start position:0% +think about problems we have these + + + align:start position:0% +think about problems we have these +circles which are neurons they have + + align:start position:0% +circles which are neurons they have + + + align:start position:0% +circles which are neurons they have +connections to other neurons + + align:start position:0% +connections to other neurons + + + align:start position:0% +connections to other neurons +you know those connections have + + align:start position:0% +you know those connections have + + + align:start position:0% +you know those connections have +different weights associated with them + + align:start position:0% +different weights associated with them + + + align:start position:0% +different weights associated with them +as information comes in they get + + align:start position:0% +as information comes in they get + + + align:start position:0% +as information comes in they get +multiplied by those weights they get + + align:start position:0% +multiplied by those weights they get + + + align:start position:0% +multiplied by those weights they get +some together and if they pass certain + + align:start position:0% +some together and if they pass certain + + + align:start position:0% +some together and if they pass certain +thresholds or criteria then they send a + + align:start position:0% +thresholds or criteria then they send a + + + align:start position:0% +thresholds or criteria then they send a +signal on to another neuron and this is + + align:start position:0% +signal on to another neuron and this is + + + align:start position:0% +signal on to another neuron and this is +to a certain degree how we believe the + + align:start position:0% +to a certain degree how we believe the + + + align:start position:0% +to a certain degree how we believe the +human the the brain works and is a sort + + align:start position:0% +human the the brain works and is a sort + + + align:start position:0% +human the the brain works and is a sort +of natural starting point for how do we + + align:start position:0% +of natural starting point for how do we + + + align:start position:0% +of natural starting point for how do we +think about how could we make + + align:start position:0% +think about how could we make + + + align:start position:0% +think about how could we make +do similar things sort of the big you + + align:start position:0% +do similar things sort of the big you + + + align:start position:0% +do similar things sort of the big you +know problems that people have worked on + + align:start position:0% +know problems that people have worked on + + + align:start position:0% +know problems that people have worked on +in in that are sort of kind of these + + align:start position:0% +in in that are sort of kind of these + + + align:start position:0% +in in that are sort of kind of these +sort of classic problems in machine + + align:start position:0% +sort of classic problems in machine + + + align:start position:0% +sort of classic problems in machine +learning our language how do we how do + + align:start position:0% +learning our language how do we how do + + + align:start position:0% +learning our language how do we how do +we make computers understand human human + + align:start position:0% +we make computers understand human human + + + align:start position:0% +we make computers understand human human +language vision how do we make computers + + align:start position:0% +language vision how do we make computers + + + align:start position:0% +language vision how do we make computers +see pictures or explain pictures back to + + align:start position:0% +see pictures or explain pictures back to + + + align:start position:0% +see pictures or explain pictures back to +us the way we would like and strategy + + align:start position:0% +us the way we would like and strategy + + + align:start position:0% +us the way we would like and strategy +and games and other types of things like + + align:start position:0% +and games and other types of things like + + + align:start position:0% +and games and other types of things like +that sort of how do we get them to solve + + align:start position:0% +that sort of how do we get them to solve + + + align:start position:0% +that sort of how do we get them to solve +problems this is not new these core + + align:start position:0% +problems this is not new these core + + + align:start position:0% +problems this is not new these core +concepts traced back to the earliest + + align:start position:0% +concepts traced back to the earliest + + + align:start position:0% +concepts traced back to the earliest +days of the field in fact these four + + align:start position:0% +days of the field in fact these four + + + align:start position:0% +days of the field in fact these four +figures here each one is taken from a + + align:start position:0% +figures here each one is taken from a + + + align:start position:0% +figures here each one is taken from a +paper that was presented at the very + + align:start position:0% +paper that was presented at the very + + + align:start position:0% +paper that was presented at the very +first machine learning conference in the + + align:start position:0% +first machine learning conference in the + + + align:start position:0% +first machine learning conference in the +mid-1950s so there was a machine + + align:start position:0% +mid-1950s so there was a machine + + + align:start position:0% +mid-1950s so there was a machine +learning conference in the mid-1950s it + + align:start position:0% +learning conference in the mid-1950s it + + + align:start position:0% +learning conference in the mid-1950s it +was in Los Angeles it had four papers + + align:start position:0% +was in Los Angeles it had four papers + + + align:start position:0% +was in Los Angeles it had four papers +presented these were the these were the + + align:start position:0% +presented these were the these were the + + + align:start position:0% +presented these were the these were the +four papers and I will say that three of + + align:start position:0% +four papers and I will say that three of + + + align:start position:0% +four papers and I will say that three of +them were done by folks at at MIT + + align:start position:0% +them were done by folks at at MIT + + + align:start position:0% +them were done by folks at at MIT +Lincoln Laboratory which is where I work + + align:start position:0% +Lincoln Laboratory which is where I work + + + align:start position:0% +Lincoln Laboratory which is where I work +and so that was the basically the neural + + align:start position:0% +and so that was the basically the neural + + + align:start position:0% +and so that was the basically the neural +networks the language and vision and we + + align:start position:0% +networks the language and vision and we + + + align:start position:0% +networks the language and vision and we +didn't play games so you know that was + + align:start position:0% +didn't play games so you know that was + + + align:start position:0% +didn't play games so you know that was +that was that was that so this is this + + align:start position:0% +that was that was that so this is this + + + align:start position:0% +that was that was that so this is this +was and you might say well why why is it + + align:start position:0% +was and you might say well why why is it + + + align:start position:0% +was and you might say well why why is it +why was there so much work going on in + + align:start position:0% +why was there so much work going on in + + + align:start position:0% +why was there so much work going on in +Lincoln Laboratory in the mid-1950s that + + align:start position:0% +Lincoln Laboratory in the mid-1950s that + + + align:start position:0% +Lincoln Laboratory in the mid-1950s that +they would they would want to sort of + + align:start position:0% +they would they would want to sort of + + + align:start position:0% +they would they would want to sort of +pioneer in these in these directions + + align:start position:0% + + + + align:start position:0% + +Lincoln lab you know at that time people + + align:start position:0% +Lincoln lab you know at that time people + + + align:start position:0% +Lincoln lab you know at that time people +were first building computers and + + align:start position:0% +were first building computers and + + + align:start position:0% +were first building computers and +computers were very special purpose so + + align:start position:0% +computers were very special purpose so + + + align:start position:0% +computers were very special purpose so +different organizations around the world + + align:start position:0% +different organizations around the world + + + align:start position:0% +different organizations around the world +we're building computers seduced + + align:start position:0% +we're building computers seduced + + + align:start position:0% +we're building computers seduced +different things some were doing them to + + align:start position:0% +different things some were doing them to + + + align:start position:0% +different things some were doing them to +simulate you know you know + + align:start position:0% + + + + align:start position:0% + +complex fluid dynamics systems you know + + align:start position:0% +complex fluid dynamics systems you know + + + align:start position:0% +complex fluid dynamics systems you know +think about designing ships or other + + align:start position:0% +think about designing ships or other + + + align:start position:0% +think about designing ships or other +types of things like that others or + + align:start position:0% +types of things like that others or + + + align:start position:0% +types of things like that others or +airplanes others were doing them to say + + align:start position:0% +airplanes others were doing them to say + + + align:start position:0% +airplanes others were doing them to say +like what Alan Turing was doing to break + + align:start position:0% +like what Alan Turing was doing to break + + + align:start position:0% +like what Alan Turing was doing to break +codes and our task was to help people + + align:start position:0% +codes and our task was to help people + + + align:start position:0% +codes and our task was to help people +who were watching radar scopes make + + align:start position:0% +who were watching radar scopes make + + + align:start position:0% +who were watching radar scopes make +decisions right how could we watch sent + + align:start position:0% +decisions right how could we watch sent + + + align:start position:0% +decisions right how could we watch sent +how could humans you know be innate + + align:start position:0% +how could humans you know be innate + + + align:start position:0% +how could humans you know be innate +could computers and able humans to watch + + align:start position:0% +could computers and able humans to watch + + + align:start position:0% +could computers and able humans to watch +more sensors to you know and see what + + align:start position:0% +more sensors to you know and see what + + + align:start position:0% +more sensors to you know and see what +their what they're going to how could we + + align:start position:0% +their what they're going to how could we + + + align:start position:0% +their what they're going to how could we +do that so at Lincoln Laboratory we were + + align:start position:0% +do that so at Lincoln Laboratory we were + + + align:start position:0% +do that so at Lincoln Laboratory we were +building special-purpose computers to do + + align:start position:0% +building special-purpose computers to do + + + align:start position:0% +building special-purpose computers to do +this and we built the first large + + align:start position:0% +this and we built the first large + + + align:start position:0% +this and we built the first large +computer with reliable fast memory this + + align:start position:0% +computer with reliable fast memory this + + + align:start position:0% +computer with reliable fast memory this +system had 4096 bytes of memory which at + + align:start position:0% +system had 4096 bytes of memory which at + + + align:start position:0% +system had 4096 bytes of memory which at +the time people thought was too much + + align:start position:0% +the time people thought was too much + + + align:start position:0% +the time people thought was too much +what could you possibly do with 4096 + + align:start position:0% +what could you possibly do with 4096 + + + align:start position:0% +what could you possibly do with 4096 +numbers the human brain of course right + + align:start position:0% +numbers the human brain of course right + + + align:start position:0% +numbers the human brain of course right +that's enough right most of us can + + align:start position:0% +that's enough right most of us can + + + align:start position:0% +that's enough right most of us can +remember five six seven digits right so + + align:start position:0% +remember five six seven digits right so + + + align:start position:0% +remember five six seven digits right so +a computer that can remember 4096 + + align:start position:0% +a computer that can remember 4096 + + + align:start position:0% +a computer that can remember 4096 +numbers should be able to do things like + + align:start position:0% +numbers should be able to do things like + + + align:start position:0% +numbers should be able to do things like +language and vision and strategy so why + + align:start position:0% +language and vision and strategy so why + + + align:start position:0% +language and vision and strategy so why +not so they went out and they started + + align:start position:0% +not so they went out and they started + + + align:start position:0% +not so they went out and they started +working on these problems okay and and + + align:start position:0% +working on these problems okay and and + + + align:start position:0% +working on these problems okay and and +but but Lincoln Laboratory being an + + align:start position:0% +but but Lincoln Laboratory being an + + + align:start position:0% +but but Lincoln Laboratory being an +Applied Research Laboratory it is we are + + align:start position:0% +Applied Research Laboratory it is we are + + + align:start position:0% +Applied Research Laboratory it is we are +required to get answers to our sponsors + + align:start position:0% +required to get answers to our sponsors + + + align:start position:0% +required to get answers to our sponsors +and you know a few years timeframe we if + + align:start position:0% +and you know a few years timeframe we if + + + align:start position:0% +and you know a few years timeframe we if +problems are going to take longer than + + align:start position:0% +problems are going to take longer than + + + align:start position:0% +problems are going to take longer than +that then they really are the are the + + align:start position:0% +that then they really are the are the + + + align:start position:0% +that then they really are the are the +purview of the basic research community + + align:start position:0% +purview of the basic research community + + + align:start position:0% +purview of the basic research community +universities and it became apparent + + align:start position:0% +universities and it became apparent + + + align:start position:0% +universities and it became apparent +pretty early on that this problem was + + align:start position:0% +pretty early on that this problem was + + + align:start position:0% +pretty early on that this problem was +going to be more difficult it was not + + align:start position:0% +going to be more difficult it was not + + + align:start position:0% +going to be more difficult it was not +going to be solved you know in in a few + + align:start position:0% +going to be solved you know in in a few + + + align:start position:0% +going to be solved you know in in a few +unit right away so we did what we often + + align:start position:0% +unit right away so we did what we often + + + align:start position:0% +unit right away so we did what we often +do is we partnered we found some bright + + align:start position:0% +do is we partnered we found some bright + + + align:start position:0% +do is we partnered we found some bright +young people at MIT people just like + + align:start position:0% +young people at MIT people just like + + + align:start position:0% +young people at MIT people just like +yourselves in this case we found a young + + align:start position:0% +yourselves in this case we found a young + + + align:start position:0% +yourselves in this case we found a young +young professor named Marvin Minsky who + + align:start position:0% +young professor named Marvin Minsky who + + + align:start position:0% +young professor named Marvin Minsky who +and we said why don't you go + + align:start position:0% +and we said why don't you go + + + align:start position:0% +and we said why don't you go +and get some of your friends together + + align:start position:0% +and get some of your friends together + + + align:start position:0% +and get some of your friends together +and create a meeting where you can lay + + align:start position:0% +and create a meeting where you can lay + + + align:start position:0% +and create a meeting where you can lay +out what the fundamental challenges are + + align:start position:0% +out what the fundamental challenges are + + + align:start position:0% +out what the fundamental challenges are +this field and then we will figure out + + align:start position:0% +this field and then we will figure out + + + align:start position:0% +this field and then we will figure out +how to get that funded so that you can + + align:start position:0% +how to get that funded so that you can + + + align:start position:0% +how to get that funded so that you can +go and do that research and that was the + + align:start position:0% +go and do that research and that was the + + + align:start position:0% +go and do that research and that was the +famous Dartmouth AI conference which + + align:start position:0% +famous Dartmouth AI conference which + + + align:start position:0% +famous Dartmouth AI conference which +kicked off the field and the the person + + align:start position:0% +kicked off the field and the the person + + + align:start position:0% +kicked off the field and the the person +leading this group Oliver Selfridge at + + align:start position:0% +leading this group Oliver Selfridge at + + + align:start position:0% +leading this group Oliver Selfridge at +Lincoln Laboratory basically arranged + + align:start position:0% +Lincoln Laboratory basically arranged + + + align:start position:0% +Lincoln Laboratory basically arranged +for that conference to happen and then + + align:start position:0% +for that conference to happen and then + + + align:start position:0% +for that conference to happen and then +subsequently arranged for the what would + + align:start position:0% +subsequently arranged for the what would + + + align:start position:0% +subsequently arranged for the what would +became the MIT AI lab that was founded + + align:start position:0% +became the MIT AI lab that was founded + + + align:start position:0% +became the MIT AI lab that was founded +by Professor Minsky and likewise + + align:start position:0% +by Professor Minsky and likewise + + + align:start position:0% +by Professor Minsky and likewise +professor Selfridge also realized that + + align:start position:0% +professor Selfridge also realized that + + + align:start position:0% +professor Selfridge also realized that +we would need more computing power so he + + align:start position:0% +we would need more computing power so he + + + align:start position:0% +we would need more computing power so he +he left Lincoln Laboratory informed what + + align:start position:0% +he left Lincoln Laboratory informed what + + + align:start position:0% +he left Lincoln Laboratory informed what +was called project Mac which became the + + align:start position:0% +was called project Mac which became the + + + align:start position:0% +was called project Mac which became the +laboratory for computer science and then + + align:start position:0% +laboratory for computer science and then + + + align:start position:0% +laboratory for computer science and then +those two entities later merged 30 years + + align:start position:0% +those two entities later merged 30 years + + + align:start position:0% +those two entities later merged 30 years +later to become csail so that was sort + + align:start position:0% +later to become csail so that was sort + + + align:start position:0% +later to become csail so that was sort +of the initial thing now it was pretty + + align:start position:0% +of the initial thing now it was pretty + + + align:start position:0% +of the initial thing now it was pretty +clear that when this problem was handed + + align:start position:0% +clear that when this problem was handed + + + align:start position:0% +clear that when this problem was handed +off to the basic research community that + + align:start position:0% +off to the basic research community that + + + align:start position:0% +off to the basic research community that +there was a feeling that this problem + + align:start position:0% +there was a feeling that this problem + + + align:start position:0% +there was a feeling that this problem +these problems would be solved in about + + align:start position:0% +these problems would be solved in about + + + align:start position:0% +these problems would be solved in about +a decade so we were really thinking by + + align:start position:0% +a decade so we were really thinking by + + + align:start position:0% +a decade so we were really thinking by +the mid 1960s is when these problems + + align:start position:0% +the mid 1960s is when these problems + + + align:start position:0% +the mid 1960s is when these problems +would be really solved so it's kind of + + align:start position:0% +would be really solved so it's kind of + + + align:start position:0% +would be really solved so it's kind of +like giving someone an assignment right + + align:start position:0% +like giving someone an assignment right + + + align:start position:0% +like giving someone an assignment right +you all are given assignments by + + align:start position:0% +you all are given assignments by + + + align:start position:0% +you all are given assignments by +professors and they give you a week to + + align:start position:0% +professors and they give you a week to + + + align:start position:0% +professors and they give you a week to +do it but it took a little longer in + + align:start position:0% +do it but it took a little longer in + + + align:start position:0% +do it but it took a little longer in +this case it took five weeks or in this + + align:start position:0% +this case it took five weeks or in this + + + align:start position:0% +this case it took five weeks or in this +case five decades to solve this problem + + align:start position:0% +case five decades to solve this problem + + + align:start position:0% +case five decades to solve this problem +and but we have we've we've now really + + align:start position:0% +and but we have we've we've now really + + + align:start position:0% +and but we have we've we've now really +using those techniques we've made + + align:start position:0% +using those techniques we've made + + + align:start position:0% +using those techniques we've made +tremendous progress on those problems + + align:start position:0% +tremendous progress on those problems + + + align:start position:0% +tremendous progress on those problems +but we don't know why it works so let me + + align:start position:0% +but we don't know why it works so let me + + + align:start position:0% +but we don't know why it works so let me +show you a little bit what we have + + align:start position:0% +show you a little bit what we have + + + align:start position:0% +show you a little bit what we have +learned and then this course will + + align:start position:0% +learned and then this course will + + + align:start position:0% +learned and then this course will +explore the deeper mathematics to help + + align:start position:0% +explore the deeper mathematics to help + + + align:start position:0% +explore the deeper mathematics to help +us gain insight we still don't know why + + align:start position:0% +us gain insight we still don't know why + + + align:start position:0% +us gain insight we still don't know why +it works at least we can lay the + + align:start position:0% +it works at least we can lay the + + + align:start position:0% +it works at least we can lay the +foundations and maybe you can figure it + + align:start position:0% +foundations and maybe you can figure it + + + align:start position:0% +foundations and maybe you can figure it +out so here I am 50 years later a person + + align:start position:0% +out so here I am 50 years later a person + + + align:start position:0% +out so here I am 50 years later a person +from Lincoln Laboratory saying + + align:start position:0% +from Lincoln Laboratory saying + + + align:start position:0% +from Lincoln Laboratory saying +alright question one has been answered + + align:start position:0% +alright question one has been answered + + + align:start position:0% +alright question one has been answered +here's question two ha why does this + + align:start position:0% +here's question two ha why does this + + + align:start position:0% +here's question two ha why does this +work and hopefully you can you can begin + + align:start position:0% +work and hopefully you can you can begin + + + align:start position:0% +work and hopefully you can you can begin +be the generation figures out hopefully + + align:start position:0% +be the generation figures out hopefully + + + align:start position:0% +be the generation figures out hopefully +it'll take less than 50 years + + align:start position:0% +it'll take less than 50 years + + + align:start position:0% +it'll take less than 50 years +historically this type once we know how + + align:start position:0% +historically this type once we know how + + + align:start position:0% +historically this type once we know how +it works + + align:start position:0% +it works + + + align:start position:0% +it works +it usually takes about 20 years to + + align:start position:0% +it usually takes about 20 years to + + + align:start position:0% +it usually takes about 20 years to +figure out why so I mean impasse but but + + align:start position:0% +figure out why so I mean impasse but but + + + align:start position:0% +figure out why so I mean impasse but but +maybe maybe you know some people are + + align:start position:0% +maybe maybe you know some people are + + + align:start position:0% +maybe maybe you know some people are +smarter and they'll figure it out faster + + align:start position:0% +smarter and they'll figure it out faster + + + align:start position:0% +smarter and they'll figure it out faster +so this is what a neural network looks + + align:start position:0% +so this is what a neural network looks + + + align:start position:0% +so this is what a neural network looks +like on the left you have your input in + + align:start position:0% +like on the left you have your input in + + + align:start position:0% +like on the left you have your input in +this case a vector Y 0 it's just these + + align:start position:0% +this case a vector Y 0 it's just these + + + align:start position:0% +this case a vector Y 0 it's just these +dots that are called features the you + + align:start position:0% +dots that are called features the you + + + align:start position:0% +dots that are called features the you +know what is a feature anything can be a + + align:start position:0% +know what is a feature anything can be a + + + align:start position:0% +know what is a feature anything can be a +feature that is the power of neural + + align:start position:0% +feature that is the power of neural + + + align:start position:0% +feature that is the power of neural +networks is they don't require you to + + align:start position:0% +networks is they don't require you to + + + align:start position:0% +networks is they don't require you to +sort of a priori state what the inputs + + align:start position:0% +sort of a priori state what the inputs + + + align:start position:0% +sort of a priori state what the inputs +can be they can be anything if people + + align:start position:0% +can be they can be anything if people + + + align:start position:0% +can be they can be anything if people +people have said well you know neural + + align:start position:0% +people have said well you know neural + + + align:start position:0% +people have said well you know neural +network to machine learn it's just curve + + align:start position:0% +network to machine learn it's just curve + + + align:start position:0% +network to machine learn it's just curve +fitting yeah but it's confer fitting + + align:start position:0% +fitting yeah but it's confer fitting + + + align:start position:0% +fitting yeah but it's confer fitting +without domain knowledge because the + + align:start position:0% +without domain knowledge because the + + + align:start position:0% +without domain knowledge because the +domain knowledge is so costly and + + align:start position:0% +domain knowledge is so costly and + + + align:start position:0% +domain knowledge is so costly and +expensive to create that having a + + align:start position:0% +expensive to create that having a + + + align:start position:0% +expensive to create that having a +general system that can do this is + + align:start position:0% +general system that can do this is + + + align:start position:0% +general system that can do this is +really what's so powerful so the inputs + + align:start position:0% +really what's so powerful so the inputs + + + align:start position:0% +really what's so powerful so the inputs +you know so we have an input feature it + + align:start position:0% +you know so we have an input feature it + + + align:start position:0% +you know so we have an input feature it +could be a vector which we call Y sub 0 + + align:start position:0% +could be a vector which we call Y sub 0 + + + align:start position:0% +could be a vector which we call Y sub 0 +and that can just be an image right the + + align:start position:0% +and that can just be an image right the + + + align:start position:0% +and that can just be an image right the +canonical thing being an image of a cat + + align:start position:0% +canonical thing being an image of a cat + + + align:start position:0% +canonical thing being an image of a cat +right and that can just be the the + + align:start position:0% +right and that can just be the the + + + align:start position:0% +right and that can just be the the +pixels values just sort of rolled out + + align:start position:0% +pixels values just sort of rolled out + + + align:start position:0% +pixels values just sort of rolled out +into a vector and there will be the + + align:start position:0% +into a vector and there will be the + + + align:start position:0% +into a vector and there will be the +inputs and then we have a series of + + align:start position:0% +inputs and then we have a series of + + + align:start position:0% +inputs and then we have a series of +layers these are called the hidden + + align:start position:0% +layers these are called the hidden + + + align:start position:0% +layers these are called the hidden +layers the circles are often referred to + + align:start position:0% +layers the circles are often referred to + + + align:start position:0% +layers the circles are often referred to +as neurons ok and each line connecting + + align:start position:0% +as neurons ok and each line connecting + + + align:start position:0% +as neurons ok and each line connecting +each dot has a value associated with it + + align:start position:0% +each dot has a value associated with it + + + align:start position:0% +each dot has a value associated with it +a weight and the strength of connection + + align:start position:0% +a weight and the strength of connection + + + align:start position:0% +a weight and the strength of connection +between any two neurons is given by that + + align:start position:0% +between any two neurons is given by that + + + align:start position:0% +between any two neurons is given by that +weight and then ultimately output in + + align:start position:0% +weight and then ultimately output in + + + align:start position:0% +weight and then ultimately output in +this case the the output classification + + align:start position:0% +this case the the output classification + + + align:start position:0% +this case the the output classification +the series of blue dots there are the + + align:start position:0% +the series of blue dots there are the + + + align:start position:0% +the series of blue dots there are the +different possible category + + align:start position:0% +different possible category + + + align:start position:0% +different possible category +so if I put in a cat picture one of + + align:start position:0% +so if I put in a cat picture one of + + + align:start position:0% +so if I put in a cat picture one of +those dots would be cat maybe one would + + align:start position:0% +those dots would be cat maybe one would + + + align:start position:0% +those dots would be cat maybe one would +be dog maybe one would be apple orange + + align:start position:0% +be dog maybe one would be apple orange + + + align:start position:0% +be dog maybe one would be apple orange +whatever whatever I whatever I desired + + align:start position:0% +whatever whatever I whatever I desired + + + align:start position:0% +whatever whatever I whatever I desired +and the whole idea is that if I put in a + + align:start position:0% +and the whole idea is that if I put in a + + + align:start position:0% +and the whole idea is that if I put in a +picture of a cat you know and I set all + + align:start position:0% +picture of a cat you know and I set all + + + align:start position:0% +picture of a cat you know and I set all +these values correctly then the the dot + + align:start position:0% +these values correctly then the the dot + + + align:start position:0% +these values correctly then the the dot +ass corresponding to cat will end up + + align:start position:0% +ass corresponding to cat will end up + + + align:start position:0% +ass corresponding to cat will end up +with the highest the highest score right + + align:start position:0% +with the highest the highest score right + + + align:start position:0% +with the highest the highest score right +and then I mentioned earlier that you + + align:start position:0% +and then I mentioned earlier that you + + + align:start position:0% +and then I mentioned earlier that you +know each one of these neurons collects + + align:start position:0% +know each one of these neurons collects + + + align:start position:0% +know each one of these neurons collects +inputs and if it's above a certain + + align:start position:0% +inputs and if it's above a certain + + + align:start position:0% +inputs and if it's above a certain +threshold it then chooses to pass on + + align:start position:0% +threshold it then chooses to pass on + + + align:start position:0% +threshold it then chooses to pass on +information to the next and that's where + + align:start position:0% +information to the next and that's where + + + align:start position:0% +information to the next and that's where +these B values which are vectors those + + align:start position:0% +these B values which are vectors those + + + align:start position:0% +these B values which are vectors those +are just the thresholds associated with + + align:start position:0% +are just the thresholds associated with + + + align:start position:0% +are just the thresholds associated with +each one of those it's a vector one + + align:start position:0% +each one of those it's a vector one + + + align:start position:0% +each one of those it's a vector one +value associated each one of those that + + align:start position:0% +value associated each one of those that + + + align:start position:0% +value associated each one of those that +does those this this entire system can + + align:start position:0% +does those this this entire system can + + + align:start position:0% +does those this this entire system can +be represented relatively simply with + + align:start position:0% +be represented relatively simply with + + + align:start position:0% +be represented relatively simply with +one equation which is that why I plus 1 + + align:start position:0% +one equation which is that why I plus 1 + + + align:start position:0% +one equation which is that why I plus 1 +which is the next vector in the layer ok + + align:start position:0% +which is the next vector in the layer ok + + + align:start position:0% +which is the next vector in the layer ok +can be computed by the previous vector Y + + align:start position:0% +can be computed by the previous vector Y + + + align:start position:0% +can be computed by the previous vector Y +I matrix multiplied by the weights W so + + align:start position:0% +I matrix multiplied by the weights W so + + + align:start position:0% +I matrix multiplied by the weights W so +whenever you see sort of transformations + + align:start position:0% +whenever you see sort of transformations + + + align:start position:0% +whenever you see sort of transformations +from one set of neurons to the next + + align:start position:0% +from one set of neurons to the next + + + align:start position:0% +from one set of neurons to the next +layer you should think oh I have a + + align:start position:0% +layer you should think oh I have a + + + align:start position:0% +layer you should think oh I have a +matrix that represent all those weights + + align:start position:0% +matrix that represent all those weights + + + align:start position:0% +matrix that represent all those weights +and I'm going to multiply it by the + + align:start position:0% +and I'm going to multiply it by the + + + align:start position:0% +and I'm going to multiply it by the +vector to give the next one then we + + align:start position:0% +vector to give the next one then we + + + align:start position:0% +vector to give the next one then we +apply these thresholds all right and + + align:start position:0% +apply these thresholds all right and + + + align:start position:0% +apply these thresholds all right and +then you know so we add these these the + + align:start position:0% +then you know so we add these these the + + + align:start position:0% +then you know so we add these these the +the B eyes and then we have a function + + align:start position:0% +the B eyes and then we have a function + + + align:start position:0% +the B eyes and then we have a function +that we pass it through + + align:start position:0% +that we pass it through + + + align:start position:0% +that we pass it through +typically the this h function has been + + align:start position:0% +typically the this h function has been + + + align:start position:0% +typically the this h function has been +given the name rectified linear unit it + + align:start position:0% +given the name rectified linear unit it + + + align:start position:0% +given the name rectified linear unit it +really just it's much simpler than that + + align:start position:0% +really just it's much simpler than that + + + align:start position:0% +really just it's much simpler than that +it's just if the value is greater than + + align:start position:0% +it's just if the value is greater than + + + align:start position:0% +it's just if the value is greater than +that comes out of this this matrix + + align:start position:0% +that comes out of this this matrix + + + align:start position:0% +that comes out of this this matrix +multiplying is if the value is greater + + align:start position:0% +multiplying is if the value is greater + + + align:start position:0% +multiplying is if the value is greater +than zero don't touch it just let it + + align:start position:0% +than zero don't touch it just let it + + + align:start position:0% +than zero don't touch it just let it +pass through if it's less than zero make + + align:start position:0% +pass through if it's less than zero make + + + align:start position:0% +pass through if it's less than zero make +it zero right you know it's pretty + + align:start position:0% +it zero right you know it's pretty + + + align:start position:0% +it zero right you know it's pretty +pretty complicated name for for for a + + align:start position:0% +pretty complicated name for for for a + + + align:start position:0% +pretty complicated name for for for a +very simple function that's actually + + align:start position:0% +very simple function that's actually + + + align:start position:0% +very simple function that's actually +critical if you didn't have that H + + align:start position:0% +critical if you didn't have that H + + + align:start position:0% +critical if you didn't have that H +function this nonlinear function there + + align:start position:0% +function this nonlinear function there + + + align:start position:0% +function this nonlinear function there +then we could roll up all of these + + align:start position:0% +then we could roll up all of these + + + align:start position:0% +then we could roll up all of these +together and we just have one big matrix + + align:start position:0% +together and we just have one big matrix + + + align:start position:0% +together and we just have one big matrix +equation right so that's really + + align:start position:0% +equation right so that's really + + + align:start position:0% +equation right so that's really +considered a pretty important part of it + + align:start position:0% +considered a pretty important part of it + + + align:start position:0% +considered a pretty important part of it +so that's pretty much what's going on + + align:start position:0% +so that's pretty much what's going on + + + align:start position:0% +so that's pretty much what's going on +when you want to know what the big deal + + align:start position:0% +when you want to know what the big deal + + + align:start position:0% +when you want to know what the big deal +is of neural networks that's all that's + + align:start position:0% +is of neural networks that's all that's + + + align:start position:0% +is of neural networks that's all that's +going on it's just that equation the + + align:start position:0% +going on it's just that equation the + + + align:start position:0% +going on it's just that equation the +challenge is we don't know what the W's + + align:start position:0% +challenge is we don't know what the W's + + + align:start position:0% +challenge is we don't know what the W's +and the B's are and we don't know how + + align:start position:0% +and the B's are and we don't know how + + + align:start position:0% +and the B's are and we don't know how +many layers there should be and we don't + + align:start position:0% +many layers there should be and we don't + + + align:start position:0% +many layers there should be and we don't +know how many you know neurons there + + align:start position:0% +know how many you know neurons there + + + align:start position:0% +know how many you know neurons there +should be in each layer and although the + + align:start position:0% +should be in each layer and although the + + + align:start position:0% +should be in each layer and although the +features can be arbitrary picking the + + align:start position:0% +features can be arbitrary picking the + + + align:start position:0% +features can be arbitrary picking the +right ones do matter and picking the + + align:start position:0% +right ones do matter and picking the + + + align:start position:0% +right ones do matter and picking the +right categories to matter so when + + align:start position:0% +right categories to matter so when + + + align:start position:0% +right categories to matter so when +people talk about I do machine learning + + align:start position:0% +people talk about I do machine learning + + + align:start position:0% +people talk about I do machine learning +or I'm off you know working on they're + + align:start position:0% +or I'm off you know working on they're + + + align:start position:0% +or I'm off you know working on they're +basically playing with all of these + + align:start position:0% +basically playing with all of these + + + align:start position:0% +basically playing with all of these +parameters to try and find the ones that + + align:start position:0% +parameters to try and find the ones that + + + align:start position:0% +parameters to try and find the ones that +will work best for their problem and + + align:start position:0% +will work best for their problem and + + + align:start position:0% +will work best for their problem and +there's a lot of trial there and you'll + + align:start position:0% +there's a lot of trial there and you'll + + + align:start position:0% +there's a lot of trial there and you'll +hear about there's now systems that try + + align:start position:0% +hear about there's now systems that try + + + align:start position:0% +hear about there's now systems that try +and use machine learning to do that + + align:start position:0% +and use machine learning to do that + + + align:start position:0% +and use machine learning to do that +process automatically you know this is + + align:start position:0% +process automatically you know this is + + + align:start position:0% +process automatically you know this is +from how do you make machines that learn + + align:start position:0% +from how do you make machines that learn + + + align:start position:0% +from how do you make machines that learn +how to do machine learning the basic + + align:start position:0% +how to do machine learning the basic + + + align:start position:0% +how to do machine learning the basic +approach is a trial and error approach I + + align:start position:0% +approach is a trial and error approach I + + + align:start position:0% +approach is a trial and error approach I +take a whole bunch of pictures of cats + + align:start position:0% +take a whole bunch of pictures of cats + + + align:start position:0% +take a whole bunch of pictures of cats +that I know have cats in them okay in + + align:start position:0% +that I know have cats in them okay in + + + align:start position:0% +that I know have cats in them okay in +other and other things right and I + + align:start position:0% +other and other things right and I + + + align:start position:0% +other and other things right and I +randomly set all those weights and + + align:start position:0% +randomly set all those weights and + + + align:start position:0% +randomly set all those weights and +thresholds and I put in the vector and I + + align:start position:0% +thresholds and I put in the vector and I + + + align:start position:0% +thresholds and I put in the vector and I +see what the system my guess what I + + align:start position:0% +see what the system my guess what I + + + align:start position:0% +see what the system my guess what I +think the number of layers and neurons + + align:start position:0% +think the number of layers and neurons + + + align:start position:0% +think the number of layers and neurons +and all it should be and I run it + + align:start position:0% +and all it should be and I run it + + + align:start position:0% +and all it should be and I run it +through the system and I get an estimate + + align:start position:0% +through the system and I get an estimate + + + align:start position:0% +through the system and I get an estimate +for what I think or a calculation for + + align:start position:0% +for what I think or a calculation for + + + align:start position:0% +for what I think or a calculation for +what I think the these final values + + align:start position:0% +what I think the these final values + + + align:start position:0% +what I think the these final values +should be and I compare it with the + + align:start position:0% +should be and I compare it with the + + + align:start position:0% +should be and I compare it with the +truth that is I just basically subtract + + align:start position:0% +truth that is I just basically subtract + + + align:start position:0% +truth that is I just basically subtract +it and then I use those Corrections to + + align:start position:0% +it and then I use those Corrections to + + + align:start position:0% +it and then I use those Corrections to +very carefully adjust the weights + + align:start position:0% +very carefully adjust the weights + + + align:start position:0% +very carefully adjust the weights +basically with the last weights first I + + align:start position:0% +basically with the last weights first I + + + align:start position:0% +basically with the last weights first I +what's called back propagate these + + align:start position:0% +what's called back propagate these + + + align:start position:0% +what's called back propagate these +little changes to try and make a better + + align:start position:0% +little changes to try and make a better + + + align:start position:0% +little changes to try and make a better +guess on what these weights should be so + + align:start position:0% +guess on what these weights should be so + + + align:start position:0% +guess on what these weights should be so +if you hear the term back propagation + + align:start position:0% +if you hear the term back propagation + + + align:start position:0% +if you hear the term back propagation +that's that process of taking those + + align:start position:0% +that's that process of taking those + + + align:start position:0% +that's that process of taking those +differences and using them to adjust + + align:start position:0% +differences and using them to adjust + + + align:start position:0% +differences and using them to adjust +these weights by about 0.01 percent at a + + align:start position:0% +these weights by about 0.01 percent at a + + + align:start position:0% +these weights by about 0.01 percent at a +time + + align:start position:0% +time + + + align:start position:0% +time +and so and then we just do this over and + + align:start position:0% +and so and then we just do this over and + + + align:start position:0% +and so and then we just do this over and +over again until eventually we get a set + + align:start position:0% +over again until eventually we get a set + + + align:start position:0% +over again until eventually we get a set +of weights that that we think does the + + align:start position:0% +of weights that that we think does the + + + align:start position:0% +of weights that that we think does the +problem well enough for our purpose so + + align:start position:0% +problem well enough for our purpose so + + + align:start position:0% +problem well enough for our purpose so +that's called back propagation right + + align:start position:0% +that's called back propagation right + + + align:start position:0% +that's called back propagation right +once we have the set of weights and we + + align:start position:0% +once we have the set of weights and we + + + align:start position:0% +once we have the set of weights and we +have a new picture that we want to know + + align:start position:0% +have a new picture that we want to know + + + align:start position:0% +have a new picture that we want to know +what it is we drop it in there and we + + align:start position:0% +what it is we drop it in there and we + + + align:start position:0% +what it is we drop it in there and we +get it tells us it's a cat or a dog + + align:start position:0% +get it tells us it's a cat or a dog + + + align:start position:0% +get it tells us it's a cat or a dog +whatever that forward step is called + + align:start position:0% +whatever that forward step is called + + + align:start position:0% +whatever that forward step is called +inference these are two words you'll + + align:start position:0% +inference these are two words you'll + + + align:start position:0% +inference these are two words you'll +hear you know frequently in machine + + align:start position:0% +hear you know frequently in machine + + + align:start position:0% +hear you know frequently in machine +learning back propagation and inference + + align:start position:0% +learning back propagation and inference + + + align:start position:0% +learning back propagation and inference +and that's all there is to it there's + + align:start position:0% +and that's all there is to it there's + + + align:start position:0% +and that's all there is to it there's +really no nothing else to that if you + + align:start position:0% +really no nothing else to that if you + + + align:start position:0% +really no nothing else to that if you +can understand this equation you'll be + + align:start position:0% +can understand this equation you'll be + + + align:start position:0% +can understand this equation you'll be +way ahead of most people and machine + + align:start position:0% +way ahead of most people and machine + + + align:start position:0% +way ahead of most people and machine +learning you know that's you know + + align:start position:0% +learning you know that's you know + + + align:start position:0% +learning you know that's you know +there's lots of people will understand + + align:start position:0% +there's lots of people will understand + + + align:start position:0% +there's lots of people will understand +about all the software and the packages + + align:start position:0% +about all the software and the packages + + + align:start position:0% +about all the software and the packages +and the data all of them are just doing + + align:start position:0% +and the data all of them are just doing + + + align:start position:0% +and the data all of them are just doing +that and I'd say this is one of the most + + align:start position:0% +that and I'd say this is one of the most + + + align:start position:0% +that and I'd say this is one of the most +powerful ways to be ahead in your field + + align:start position:0% +powerful ways to be ahead in your field + + + align:start position:0% +powerful ways to be ahead in your field +is to actually understand the + + align:start position:0% +is to actually understand the + + + align:start position:0% +is to actually understand the +mathematical principles because then the + + align:start position:0% +mathematical principles because then the + + + align:start position:0% +mathematical principles because then the +software and what it's doing is is is + + align:start position:0% +software and what it's doing is is is + + + align:start position:0% +software and what it's doing is is is +much clearer and other people who don't + + align:start position:0% +much clearer and other people who don't + + + align:start position:0% +much clearer and other people who don't +understand these mathematical principles + + align:start position:0% +understand these mathematical principles + + + align:start position:0% +understand these mathematical principles +they're really kind of guessing they're + + align:start position:0% +they're really kind of guessing they're + + + align:start position:0% +they're really kind of guessing they're +like oh well I I do this and I throw + + align:start position:0% +like oh well I I do this and I throw + + + align:start position:0% +like oh well I I do this and I throw +this module and they're like they don't + + align:start position:0% +this module and they're like they don't + + + align:start position:0% +this module and they're like they don't +really know that all that's doing is + + align:start position:0% +really know that all that's doing is + + + align:start position:0% +really know that all that's doing is +making adjustments to these various + + align:start position:0% +making adjustments to these various + + + align:start position:0% +making adjustments to these various +equations you know how many different + + align:start position:0% +equations you know how many different + + + align:start position:0% +equations you know how many different +layers they are and stuff like that now + + align:start position:0% +layers they are and stuff like that now + + + align:start position:0% +layers they are and stuff like that now +why is this important me like well what + + align:start position:0% +why is this important me like well what + + + align:start position:0% +why is this important me like well what +does it matter as I said before we have + + align:start position:0% +does it matter as I said before we have + + + align:start position:0% +does it matter as I said before we have +this system it works but we don't know + + align:start position:0% +this system it works but we don't know + + + align:start position:0% +this system it works but we don't know +why well why is it important to know why + + align:start position:0% +why well why is it important to know why + + + align:start position:0% +why well why is it important to know why +well there's two reasons one is that if + + align:start position:0% +well there's two reasons one is that if + + + align:start position:0% +well there's two reasons one is that if +we want to be able to apply this + + align:start position:0% +we want to be able to apply this + + + align:start position:0% +we want to be able to apply this +incredible innovation to other domains + + align:start position:0% +incredible innovation to other domains + + + align:start position:0% +incredible innovation to other domains +so many of you probably want to do that + + align:start position:0% +so many of you probably want to do that + + + align:start position:0% +so many of you probably want to do that +many of you want to see how can I apply + + align:start position:0% +many of you want to see how can I apply + + + align:start position:0% +many of you want to see how can I apply +machine learning to something else other + + align:start position:0% +machine learning to something else other + + + align:start position:0% +machine learning to something else other +than language or vision or some of these + + align:start position:0% +than language or vision or some of these + + + align:start position:0% +than language or vision or some of these +other sort of standard problems I kind + + align:start position:0% +other sort of standard problems I kind + + + align:start position:0% +other sort of standard problems I kind +of need some theory to know like okay if + + align:start position:0% +of need some theory to know like okay if + + + align:start position:0% +of need some theory to know like okay if +I have a problem it's kind of like this + + align:start position:0% +I have a problem it's kind of like this + + + align:start position:0% +I have a problem it's kind of like this +one over here and I change in this way + + align:start position:0% +one over here and I change in this way + + + align:start position:0% +one over here and I change in this way +you know you know it there's a good + + align:start position:0% +you know you know it there's a good + + + align:start position:0% +you know you know it there's a good +chance it'll work there's some basis for + + align:start position:0% +chance it'll work there's some basis for + + + align:start position:0% +chance it'll work there's some basis for +my for why I'm gonna try something right + + align:start position:0% +my for why I'm gonna try something right + + + align:start position:0% +my for why I'm gonna try something right +right now there's a lot of trial and + + align:start position:0% +right now there's a lot of trial and + + + align:start position:0% +right now there's a lot of trial and +error just like well it's an idea but if + + align:start position:0% +error just like well it's an idea but if + + + align:start position:0% +error just like well it's an idea but if +you can have some math that says you + + align:start position:0% +you can have some math that says you + + + align:start position:0% +you can have some math that says you +know I think that will probably work + + align:start position:0% +know I think that will probably work + + + align:start position:0% +know I think that will probably work +that really is a great way to guide + + align:start position:0% +that really is a great way to guide + + + align:start position:0% +that really is a great way to guide +guide your + + align:start position:0% +guide your + + + align:start position:0% +guide your +reasoning died your efforts another + + align:start position:0% +reasoning died your efforts another + + + align:start position:0% +reasoning died your efforts another +reason is that so here's a picture of a + + align:start position:0% +reason is that so here's a picture of a + + + align:start position:0% +reason is that so here's a picture of a +very cute poodle right and the machine + + align:start position:0% +very cute poodle right and the machine + + + align:start position:0% +very cute poodle right and the machine +learning system correctly identifies it + + align:start position:0% +learning system correctly identifies it + + + align:start position:0% +learning system correctly identifies it +as poodle one thing we realize is that + + align:start position:0% +as poodle one thing we realize is that + + + align:start position:0% +as poodle one thing we realize is that +the way you and I see that picture is + + align:start position:0% +the way you and I see that picture is + + + align:start position:0% +the way you and I see that picture is +actually very very different than the + + align:start position:0% +actually very very different than the + + + align:start position:0% +actually very very different than the +way the neural network sees that picture + + align:start position:0% +way the neural network sees that picture + + + align:start position:0% +way the neural network sees that picture +all right and in fact I can make changes + + align:start position:0% +all right and in fact I can make changes + + + align:start position:0% +all right and in fact I can make changes +to that picture that are imperceptible + + align:start position:0% +to that picture that are imperceptible + + + align:start position:0% +to that picture that are imperceptible +to you or me but will completely change + + align:start position:0% +to you or me but will completely change + + + align:start position:0% +to you or me but will completely change +how the neural network that is given a + + align:start position:0% +how the neural network that is given a + + + align:start position:0% +how the neural network that is given a +neural network I can basically make it + + align:start position:0% +neural network I can basically make it + + + align:start position:0% +neural network I can basically make it +think anything right and so for instance + + align:start position:0% +think anything right and so for instance + + + align:start position:0% +think anything right and so for instance +is a famous paper and they got the + + align:start position:0% +is a famous paper and they got the + + + align:start position:0% +is a famous paper and they got the +system to think that that was an ostrich + + align:start position:0% +system to think that that was an ostrich + + + align:start position:0% +system to think that that was an ostrich +right and you can you can basically show + + align:start position:0% +right and you can you can basically show + + + align:start position:0% +right and you can you can basically show +this for anything right + + align:start position:0% +this for anything right + + + align:start position:0% +this for anything right +so what's called robust AI a robust + + align:start position:0% +so what's called robust AI a robust + + + align:start position:0% +so what's called robust AI a robust +machine learning machine learning that + + align:start position:0% +machine learning machine learning that + + + align:start position:0% +machine learning machine learning that +can't be you know tricked it's gonna + + align:start position:0% +can't be you know tricked it's gonna + + + align:start position:0% +can't be you know tricked it's gonna +become more and more important and again + + align:start position:0% +become more and more important and again + + + align:start position:0% +become more and more important and again +having a deeper understanding of the + + align:start position:0% +having a deeper understanding of the + + + align:start position:0% +having a deeper understanding of the +theory is very very critical with that + + align:start position:0% +theory is very very critical with that + + + align:start position:0% +theory is very very critical with that +so how are we gonna do this what's + + align:start position:0% +so how are we gonna do this what's + + + align:start position:0% +so how are we gonna do this what's +what's that what's the main concept that + + align:start position:0% +what's that what's the main concept that + + + align:start position:0% +what's that what's the main concept that +we are going to go through in this class + + align:start position:0% +we are going to go through in this class + + + align:start position:0% +we are going to go through in this class +this has mostly been motivational but + + align:start position:0% +this has mostly been motivational but + + + align:start position:0% +this has mostly been motivational but +how are we gonna understand the data at + + align:start position:0% +how are we gonna understand the data at + + + align:start position:0% +how are we gonna understand the data at +a deeper level you know what's the + + align:start position:0% +a deeper level you know what's the + + + align:start position:0% +a deeper level you know what's the +what's the big idea and the big idea is + + align:start position:0% +what's the big idea and the big idea is + + + align:start position:0% +what's the big idea and the big idea is +sort of captured you know now in this + + align:start position:0% +sort of captured you know now in this + + + align:start position:0% +sort of captured you know now in this +should've won I apologized this I + + align:start position:0% +should've won I apologized this I + + + align:start position:0% +should've won I apologized this I +charged slide which is what we call it + + align:start position:0% +charged slide which is what we call it + + + align:start position:0% +charged slide which is what we call it +declarative mathematically rigorous data + + align:start position:0% +declarative mathematically rigorous data + + + align:start position:0% +declarative mathematically rigorous data +so we have this mathematical concept + + align:start position:0% +so we have this mathematical concept + + + align:start position:0% +so we have this mathematical concept +called an associative array and its + + align:start position:0% +called an associative array and its + + + align:start position:0% +called an associative array and its +course not bonding algebra that + + align:start position:0% +course not bonding algebra that + + + align:start position:0% +course not bonding algebra that +basically encompasses the data you would + + align:start position:0% +basically encompasses the data you would + + + align:start position:0% +basically encompasses the data you would +put in databases the data you would put + + align:start position:0% +put in databases the data you would put + + + align:start position:0% +put in databases the data you would put +in graphs the data you would put a + + align:start position:0% +in graphs the data you would put a + + + align:start position:0% +in graphs the data you would put a +matrices and it makes it all a linear + + align:start position:0% +matrices and it makes it all a linear + + + align:start position:0% +matrices and it makes it all a linear +system and the key operations are + + align:start position:0% +system and the key operations are + + + align:start position:0% +system and the key operations are +outlined there at the bottom if you + + align:start position:0% +outlined there at the bottom if you + + + align:start position:0% +outlined there at the bottom if you +recall we have our basic little addition + + align:start position:0% +recall we have our basic little addition + + + align:start position:0% +recall we have our basic little addition +or multiplication and then what's going + + align:start position:0% +or multiplication and then what's going + + + align:start position:0% +or multiplication and then what's going +to be very important probably the real + + align:start position:0% +to be very important probably the real + + + align:start position:0% +to be very important probably the real +sort of workhorse for this and I didn't + + align:start position:0% +sort of workhorse for this and I didn't + + + align:start position:0% +sort of workhorse for this and I didn't +show it before which is called + + align:start position:0% +show it before which is called + + + align:start position:0% +show it before which is called +essentially array multiplication or + + align:start position:0% +essentially array multiplication or + + + align:start position:0% +essentially array multiplication or +matrix multiplication and that's the LAT + + align:start position:0% +matrix multiplication and that's the LAT + + + align:start position:0% +matrix multiplication and that's the LAT +farm on the right there which we often + + align:start position:0% +farm on the right there which we often + + + align:start position:0% +farm on the right there which we often +abbreviate just with no symbol just a + + align:start position:0% +abbreviate just with no symbol just a + + + align:start position:0% +abbreviate just with no symbol just a +bee + + align:start position:0% +bee + + + align:start position:0% +bee +but if we really want to explicitly call + + align:start position:0% +but if we really want to explicitly call + + + align:start position:0% +but if we really want to explicitly call +out that it's matrix multiplication is a + + align:start position:0% +out that it's matrix multiplication is a + + + align:start position:0% +out that it's matrix multiplication is a +combination of both multiplication + + align:start position:0% +combination of both multiplication + + + align:start position:0% +combination of both multiplication +addition we put in what we call the + + align:start position:0% +addition we put in what we call the + + + align:start position:0% +addition we put in what we call the +punch-drunk emoji which is a + dot times + + align:start position:0% +punch-drunk emoji which is a + dot times + + + align:start position:0% +punch-drunk emoji which is a + dot times +you're probably all young enough that + + align:start position:0% +you're probably all young enough that + + + align:start position:0% +you're probably all young enough that +you don't even remember emojis when they + + align:start position:0% +you don't even remember emojis when they + + + align:start position:0% +you don't even remember emojis when they +had to type them out with just little + + align:start position:0% +had to type them out with just little + + + align:start position:0% +had to type them out with just little +characters and we didn't have icons + + align:start position:0% +characters and we didn't have icons + + + align:start position:0% +characters and we didn't have icons +right so that meant that meant you went + + align:start position:0% +right so that meant that meant you went + + + align:start position:0% +right so that meant that meant you went +to the bar and lost to the fight right + + align:start position:0% +to the bar and lost to the fight right + + + align:start position:0% +to the bar and lost to the fight right +so so so but anyway that's that's really + + align:start position:0% +so so so but anyway that's that's really + + + align:start position:0% +so so so but anyway that's that's really +going to be the workhorse of what we're + + align:start position:0% +going to be the workhorse of what we're + + + align:start position:0% +going to be the workhorse of what we're +doing here + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/12MkdZCr4iQ.txt b/12MkdZCr4iQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..36198ad0946f1d3a20686b91982b333985f6307d --- /dev/null +++ b/12MkdZCr4iQ.txt @@ -0,0 +1,531 @@ +align:start position:0% + +hello again i would now like to present + + align:start position:0% +hello again i would now like to present + + + align:start position:0% +hello again i would now like to present +the + + align:start position:0% +the + + + align:start position:0% +the +garage case + + align:start position:0% +garage case + + + align:start position:0% +garage case +the objective here is to provide a + + align:start position:0% +the objective here is to provide a + + + align:start position:0% +the objective here is to provide a +practical example of flexibility and + + align:start position:0% +practical example of flexibility and + + + align:start position:0% +practical example of flexibility and +design based upon a real situation + + align:start position:0% +design based upon a real situation + + + align:start position:0% +design based upon a real situation +the + + align:start position:0% +the + + + align:start position:0% +the +the value of this case which i'll be + + align:start position:0% +the value of this case which i'll be + + + align:start position:0% +the value of this case which i'll be +showing in the next presentation is that + + align:start position:0% +showing in the next presentation is that + + + align:start position:0% +showing in the next presentation is that +it shows how the proactive design avoids + + align:start position:0% +it shows how the proactive design avoids + + + align:start position:0% +it shows how the proactive design avoids +down side effects takes advantage of the + + align:start position:0% +down side effects takes advantage of the + + + align:start position:0% +down side effects takes advantage of the +upside + + align:start position:0% +upside + + + align:start position:0% +upside +possibilities and at the same time + + align:start position:0% +possibilities and at the same time + + + align:start position:0% +possibilities and at the same time +reducing the initial cost + + align:start position:0% +reducing the initial cost + + + align:start position:0% +reducing the initial cost +the + + align:start position:0% +the + + + align:start position:0% +the +case is a prototype example that is the + + align:start position:0% +case is a prototype example that is the + + + align:start position:0% +case is a prototype example that is the +mechanics of it and the design aspects + + align:start position:0% +mechanics of it and the design aspects + + + align:start position:0% +mechanics of it and the design aspects +of it is a model for a whole range of + + align:start position:0% +of it is a model for a whole range of + + + align:start position:0% +of it is a model for a whole range of +applications so it is based upon in this + + align:start position:0% +applications so it is based upon in this + + + align:start position:0% +applications so it is based upon in this +case this excel spreadsheet where you + + align:start position:0% +case this excel spreadsheet where you + + + align:start position:0% +case this excel spreadsheet where you +can relabel the columns and the rows and + + align:start position:0% +can relabel the columns and the rows and + + + align:start position:0% +can relabel the columns and the rows and +look at quite different situations so + + align:start position:0% +look at quite different situations so + + + align:start position:0% +look at quite different situations so +it's a useful as a + + align:start position:0% +it's a useful as a + + + align:start position:0% +it's a useful as a +model as a template for further analyses + + align:start position:0% +model as a template for further analyses + + + align:start position:0% +model as a template for further analyses +the technology in this case is simple + + align:start position:0% +the technology in this case is simple + + + align:start position:0% +the technology in this case is simple +enough so that when you see the results + + align:start position:0% +enough so that when you see the results + + + align:start position:0% +enough so that when you see the results +eventually you can understand how they + + align:start position:0% +eventually you can understand how they + + + align:start position:0% +eventually you can understand how they +occur because it's the technology is + + align:start position:0% +occur because it's the technology is + + + align:start position:0% +occur because it's the technology is +very easy to understand it's trivial to + + align:start position:0% +very easy to understand it's trivial to + + + align:start position:0% +very easy to understand it's trivial to +understand that's one of the values of + + align:start position:0% +understand that's one of the values of + + + align:start position:0% +understand that's one of the values of +this particular case + + align:start position:0% +this particular case + + + align:start position:0% +this particular case +and the specific value is the case + + align:start position:0% +and the specific value is the case + + + align:start position:0% +and the specific value is the case +represents the different ways it + + align:start position:0% +represents the different ways it + + + align:start position:0% +represents the different ways it +illustrates the different ways that the + + align:start position:0% +illustrates the different ways that the + + + align:start position:0% +illustrates the different ways that the +flexibility design can increase the + + align:start position:0% +flexibility design can increase the + + + align:start position:0% +flexibility design can increase the +value to it by reducing the cost + + align:start position:0% +value to it by reducing the cost + + + align:start position:0% +value to it by reducing the cost +increasing the opportunities getting rid + + align:start position:0% +increasing the opportunities getting rid + + + align:start position:0% +increasing the opportunities getting rid +of the downsides + + align:start position:0% +of the downsides + + + align:start position:0% +of the downsides +the case is based upon an actual example + + align:start position:0% +the case is based upon an actual example + + + align:start position:0% +the case is based upon an actual example +that i had the privilege of looking at + + align:start position:0% +that i had the privilege of looking at + + + align:start position:0% +that i had the privilege of looking at +in england it is the blue water shopping + + align:start position:0% +in england it is the blue water shopping + + + align:start position:0% +in england it is the blue water shopping +center near london in the united kingdom + + align:start position:0% +center near london in the united kingdom + + + align:start position:0% +center near london in the united kingdom +and it was built + + align:start position:0% +and it was built + + + align:start position:0% +and it was built +deliberately for the possible future + + align:start position:0% +deliberately for the possible future + + + align:start position:0% +deliberately for the possible future +edition of extra floors on this it was + + align:start position:0% +edition of extra floors on this it was + + + align:start position:0% +edition of extra floors on this it was +done + + align:start position:0% +done + + + align:start position:0% +done +by + + align:start position:0% +by + + + align:start position:0% +by +in a precast concrete kind of way so + + align:start position:0% +in a precast concrete kind of way so + + + align:start position:0% +in a precast concrete kind of way so +that the columns and the platforms and + + align:start position:0% +that the columns and the platforms and + + + align:start position:0% +that the columns and the platforms and +the floors could be created off-site and + + align:start position:0% +the floors could be created off-site and + + + align:start position:0% +the floors could be created off-site and +then brought to the garage and added on + + align:start position:0% +then brought to the garage and added on + + + align:start position:0% +then brought to the garage and added on +fairly quickly if that was the desired + + align:start position:0% +fairly quickly if that was the desired + + + align:start position:0% +fairly quickly if that was the desired +action to be taken + + align:start position:0% +action to be taken + + + align:start position:0% +action to be taken +and so that it was easily expandable it + + align:start position:0% +and so that it was easily expandable it + + + align:start position:0% +and so that it was easily expandable it +had been built for the flexibility + + align:start position:0% +had been built for the flexibility + + + align:start position:0% +had been built for the flexibility +should you wish to use it here is the + + align:start position:0% +should you wish to use it here is the + + + align:start position:0% +should you wish to use it here is the +image of the actual site an arrow view + + align:start position:0% +image of the actual site an arrow view + + + align:start position:0% +image of the actual site an arrow view +you may see that there is a wall behind + + align:start position:0% +you may see that there is a wall behind + + + align:start position:0% +you may see that there is a wall behind +here because this was built in an old + + align:start position:0% +here because this was built in an old + + + align:start position:0% +here because this was built in an old +quarry + + align:start position:0% +quarry + + + align:start position:0% +quarry +so when it will stop needing as a quarry + + align:start position:0% +so when it will stop needing as a quarry + + + align:start position:0% +so when it will stop needing as a quarry +they created a shopping center up here + + align:start position:0% +they created a shopping center up here + + + align:start position:0% +they created a shopping center up here +is where the + + align:start position:0% +is where the + + + align:start position:0% +is where the +shopping area itself is and + + align:start position:0% +shopping area itself is and + + + align:start position:0% +shopping area itself is and +the + + align:start position:0% +the + + + align:start position:0% +the +garage spaces are right along here + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/17VFTJvgBlY.txt b/17VFTJvgBlY.txt new file mode 100644 index 0000000000000000000000000000000000000000..30d69ee94e61ad72ae7384fb2d9e8c6ea496204e --- /dev/null +++ b/17VFTJvgBlY.txt @@ -0,0 +1,1475 @@ +align:start position:0% + +we have to talk about + + align:start position:0% +we have to talk about + + + align:start position:0% +we have to talk about +composition of your images but it's it's + + align:start position:0% +composition of your images but it's it's + + + align:start position:0% +composition of your images but it's it's +very difficult to separate the idea of + + align:start position:0% +very difficult to separate the idea of + + + align:start position:0% +very difficult to separate the idea of +composition and Point of View background + + align:start position:0% +composition and Point of View background + + + align:start position:0% +composition and Point of View background +and even lighting they all go together + + align:start position:0% +and even lighting they all go together + + + align:start position:0% +and even lighting they all go together +when you adjust your light you'll + + align:start position:0% +when you adjust your light you'll + + + align:start position:0% +when you adjust your light you'll +will'll see later you're going to get a + + align:start position:0% +will'll see later you're going to get a + + + align:start position:0% +will'll see later you're going to get a +different kind of Shadow and that shadow + + align:start position:0% +different kind of Shadow and that shadow + + + align:start position:0% +different kind of Shadow and that shadow +becomes part of the composition so we've + + align:start position:0% +becomes part of the composition so we've + + + align:start position:0% +becomes part of the composition so we've +Ed to separate them into three + + align:start position:0% +Ed to separate them into three + + + align:start position:0% +Ed to separate them into three +categories but really they are very + + align:start position:0% +categories but really they are very + + + align:start position:0% +categories but really they are very +closely connected and it's something to + + align:start position:0% +closely connected and it's something to + + + align:start position:0% +closely connected and it's something to +keep in mind so let's start with these + + align:start position:0% +keep in mind so let's start with these + + + align:start position:0% +keep in mind so let's start with these +leaves these autumn leaves that I put on + + align:start position:0% +leaves these autumn leaves that I put on + + + align:start position:0% +leaves these autumn leaves that I put on +a light box which you will see more of + + align:start position:0% +a light box which you will see more of + + + align:start position:0% +a light box which you will see more of +when we talk about light in fact the + + align:start position:0% +when we talk about light in fact the + + + align:start position:0% +when we talk about light in fact the +light box itself is an important + + align:start position:0% +light box itself is an important + + + align:start position:0% +light box itself is an important +compositional element in this image + + align:start position:0% +compositional element in this image + + + align:start position:0% +compositional element in this image +because it's giving us a very strong + + align:start position:0% +because it's giving us a very strong + + + align:start position:0% +because it's giving us a very strong +negative space between the leaves and it + + align:start position:0% +negative space between the leaves and it + + + align:start position:0% +negative space between the leaves and it +could be an interesting thing to play + + align:start position:0% +could be an interesting thing to play + + + align:start position:0% +could be an interesting thing to play +around with using the background as part + + align:start position:0% +around with using the background as part + + + align:start position:0% +around with using the background as part +of your composition something to think + + align:start position:0% +of your composition something to think + + + align:start position:0% +of your composition something to think +about taking a look at these crystals + + align:start position:0% +about taking a look at these crystals + + + align:start position:0% +about taking a look at these crystals +which I just randomly placed on a + + align:start position:0% +which I just randomly placed on a + + + align:start position:0% +which I just randomly placed on a +background just to show the ability of + + align:start position:0% +background just to show the ability of + + + align:start position:0% +background just to show the ability of +creating these crystals uh this is you + + align:start position:0% +creating these crystals uh this is you + + + align:start position:0% +creating these crystals uh this is you +know an okay image by the way notice how + + align:start position:0% +know an okay image by the way notice how + + + align:start position:0% +know an okay image by the way notice how +the shadows of these crystals become + + align:start position:0% +the shadows of these crystals become + + + align:start position:0% +the shadows of these crystals become +part of the + + align:start position:0% +part of the + + + align:start position:0% +part of the +composition what I finally decided to do + + align:start position:0% +composition what I finally decided to do + + + align:start position:0% +composition what I finally decided to do +was simplify the image and just selected + + align:start position:0% +was simplify the image and just selected + + + align:start position:0% +was simplify the image and just selected +four crystals and made a more close + + align:start position:0% +four crystals and made a more close + + + align:start position:0% +four crystals and made a more close +close-up shot of them they're both fine + + align:start position:0% +close-up shot of them they're both fine + + + align:start position:0% +close-up shot of them they're both fine +and and that's one of these issues about + + align:start position:0% +and and that's one of these issues about + + + align:start position:0% +and and that's one of these issues about +what's better I mean we could split + + align:start position:0% +what's better I mean we could split + + + align:start position:0% +what's better I mean we could split +hairs and I really don't think there's + + align:start position:0% +hairs and I really don't think there's + + + align:start position:0% +hairs and I really don't think there's +any we could argue either way that's the + + align:start position:0% +any we could argue either way that's the + + + align:start position:0% +any we could argue either way that's the +fun part about this once again there are + + align:start position:0% +fun part about this once again there are + + + align:start position:0% +fun part about this once again there are +no rules to any of these things one of + + align:start position:0% +no rules to any of these things one of + + + align:start position:0% +no rules to any of these things one of +my gut ideas which has no data + + align:start position:0% +my gut ideas which has no data + + + align:start position:0% +my gut ideas which has no data +associated with it is I think it's more + + align:start position:0% +associated with it is I think it's more + + + align:start position:0% +associated with it is I think it's more +interesting to show two of something + + align:start position:0% +interesting to show two of something + + + align:start position:0% +interesting to show two of something +rather than show one and I suppose I + + align:start position:0% +rather than show one and I suppose I + + + align:start position:0% +rather than show one and I suppose I +could speak to some psychologists and + + align:start position:0% +could speak to some psychologists and + + + align:start position:0% +could speak to some psychologists and +discuss whether we really do perceive it + + align:start position:0% +discuss whether we really do perceive it + + + align:start position:0% +discuss whether we really do perceive it +more I I don't know I just it's the way + + align:start position:0% +more I I don't know I just it's the way + + + align:start position:0% +more I I don't know I just it's the way +I do it and if I'm suggesting that if + + align:start position:0% +I do it and if I'm suggesting that if + + + align:start position:0% +I do it and if I'm suggesting that if +you like what I do then maybe you'll + + align:start position:0% +you like what I do then maybe you'll + + + align:start position:0% +you like what I do then maybe you'll +want to do it + + align:start position:0% +want to do it + + + align:start position:0% +want to do it +too I did take these two devices by the + + align:start position:0% +too I did take these two devices by the + + + align:start position:0% +too I did take these two devices by the +way it shows that you can do more than + + align:start position:0% +way it shows that you can do more than + + + align:start position:0% +way it shows that you can do more than +than one you can create more than one + + align:start position:0% +than one you can create more than one + + + align:start position:0% +than one you can create more than one +and I photographed it this way I + + align:start position:0% +and I photographed it this way I + + + align:start position:0% +and I photographed it this way I +photographed it in my studio with a + + align:start position:0% +photographed it in my studio with a + + + align:start position:0% +photographed it in my studio with a +skylight above and notice there's a + + align:start position:0% +skylight above and notice there's a + + + align:start position:0% +skylight above and notice there's a +little problem with depth of field the + + align:start position:0% +little problem with depth of field the + + + align:start position:0% +little problem with depth of field the +one above is not really as sharp as it + + align:start position:0% +one above is not really as sharp as it + + + align:start position:0% +one above is not really as sharp as it +should be and so I stopped down which + + align:start position:0% +should be and so I stopped down which + + + align:start position:0% +should be and so I stopped down which +you know what that means so that the + + align:start position:0% +you know what that means so that the + + + align:start position:0% +you know what that means so that the +aperture became smaller and we I gave + + align:start position:0% +aperture became smaller and we I gave + + + align:start position:0% +aperture became smaller and we I gave +myself more depth of field that is I got + + align:start position:0% +myself more depth of field that is I got + + + align:start position:0% +myself more depth of field that is I got +more in focus and what happened was it + + align:start position:0% +more in focus and what happened was it + + + align:start position:0% +more in focus and what happened was it +got so much in Focus that I could + + align:start position:0% +got so much in Focus that I could + + + align:start position:0% +got so much in Focus that I could +actually see the detail of the skylight + + align:start position:0% +actually see the detail of the skylight + + + align:start position:0% +actually see the detail of the skylight +with the clouds showing through this is + + align:start position:0% +with the clouds showing through this is + + + align:start position:0% +with the clouds showing through this is +tangential to the point but it's all + + align:start position:0% +tangential to the point but it's all + + + align:start position:0% +tangential to the point but it's all +connected and you have to really pay + + align:start position:0% +connected and you have to really pay + + + align:start position:0% +connected and you have to really pay +attention and learn to see what it is + + align:start position:0% +attention and learn to see what it is + + + align:start position:0% +attention and learn to see what it is +you're getting at eventually I wound up + + align:start position:0% +you're getting at eventually I wound up + + + align:start position:0% +you're getting at eventually I wound up +I thought that this next image was the + + align:start position:0% +I thought that this next image was the + + + align:start position:0% +I thought that this next image was the +best again using two and not necessarily + + align:start position:0% +best again using two and not necessarily + + + align:start position:0% +best again using two and not necessarily +showing exactly the edge of each I think + + align:start position:0% +showing exactly the edge of each I think + + + align:start position:0% +showing exactly the edge of each I think +it's an interesting idea to not + + align:start position:0% +it's an interesting idea to not + + + align:start position:0% +it's an interesting idea to not +completely finish the image let the + + align:start position:0% +completely finish the image let the + + + align:start position:0% +completely finish the image let the +viewer finish it more of a participatory + + align:start position:0% +viewer finish it more of a participatory + + + align:start position:0% +viewer finish it more of a participatory +involvement perhaps once again this idea + + align:start position:0% +involvement perhaps once again this idea + + + align:start position:0% +involvement perhaps once again this idea +of twos here are two balls that have so + + align:start position:0% +of twos here are two balls that have so + + + align:start position:0% +of twos here are two balls that have so +small a pattern that we're seeing light + + align:start position:0% +small a pattern that we're seeing light + + + align:start position:0% +small a pattern that we're seeing light +refracting and here are two silicon + + align:start position:0% +refracting and here are two silicon + + + align:start position:0% +refracting and here are two silicon +chips that have material embedded on it + + align:start position:0% +chips that have material embedded on it + + + align:start position:0% +chips that have material embedded on it +again I decided to do it in + + align:start position:0% +again I decided to do it in + + + align:start position:0% +again I decided to do it in +twos here's another two duet two Petri + + align:start position:0% +twos here's another two duet two Petri + + + align:start position:0% +twos here's another two duet two Petri +dishes of eoli growing by the way notice + + align:start position:0% +dishes of eoli growing by the way notice + + + align:start position:0% +dishes of eoli growing by the way notice +the composition it's not exactly equal + + align:start position:0% +the composition it's not exactly equal + + + align:start position:0% +the composition it's not exactly equal +equally divided I have one a little more + + align:start position:0% +equally divided I have one a little more + + + align:start position:0% +equally divided I have one a little more +than the other for our book no small + + align:start position:0% +than the other for our book no small + + + align:start position:0% +than the other for our book no small +matter we wanted to talk about self + + align:start position:0% +matter we wanted to talk about self + + + align:start position:0% +matter we wanted to talk about self +assembly actually these are two acrylic + + align:start position:0% +assembly actually these are two acrylic + + + align:start position:0% +assembly actually these are two acrylic +dishes with acrylic balls that literally + + align:start position:0% +dishes with acrylic balls that literally + + + align:start position:0% +dishes with acrylic balls that literally +line themselves up and I did it in twos + + align:start position:0% +line themselves up and I did it in twos + + + align:start position:0% +line themselves up and I did it in twos +as well you know again it's an idea that + + align:start position:0% +as well you know again it's an idea that + + + align:start position:0% +as well you know again it's an idea that +I'm comfortable with it's actually + + align:start position:0% +I'm comfortable with it's actually + + + align:start position:0% +I'm comfortable with it's actually +easier to compose when you have two + + align:start position:0% +easier to compose when you have two + + + align:start position:0% +easier to compose when you have two +things at least it is for me you might + + align:start position:0% +things at least it is for me you might + + + align:start position:0% +things at least it is for me you might +give it a shot you might think of using + + align:start position:0% +give it a shot you might think of using + + + align:start position:0% +give it a shot you might think of using +the process of composing your picture as + + align:start position:0% +the process of composing your picture as + + + align:start position:0% +the process of composing your picture as +a means of telling a story uh a visual + + align:start position:0% +a means of telling a story uh a visual + + + align:start position:0% +a means of telling a story uh a visual +story of what your devices are about + + align:start position:0% +story of what your devices are about + + + align:start position:0% +story of what your devices are about +what you're seeing here you're seeing + + align:start position:0% +what you're seeing here you're seeing + + + align:start position:0% +what you're seeing here you're seeing +basically three components of an image + + align:start position:0% +basically three components of an image + + + align:start position:0% +basically three components of an image +you're seeing the underside of a wafer + + align:start position:0% +you're seeing the underside of a wafer + + + align:start position:0% +you're seeing the underside of a wafer +on your upper left the green upper left + + align:start position:0% +on your upper left the green upper left + + + align:start position:0% +on your upper left the green upper left +and that wafer has fabricated on it + + align:start position:0% +and that wafer has fabricated on it + + + align:start position:0% +and that wafer has fabricated on it +small chips so the fuchsia color is what + + align:start position:0% +small chips so the fuchsia color is what + + + align:start position:0% +small chips so the fuchsia color is what +the wafer looks like as a whole and then + + align:start position:0% +the wafer looks like as a whole and then + + + align:start position:0% +the wafer looks like as a whole and then +we we have the individual uh chips on + + align:start position:0% +we we have the individual uh chips on + + + align:start position:0% +we we have the individual uh chips on +top of the larger wafer so you have see + + align:start position:0% +top of the larger wafer so you have see + + + align:start position:0% +top of the larger wafer so you have see +the individual ones as well so we're + + align:start position:0% +the individual ones as well so we're + + + align:start position:0% +the individual ones as well so we're +trying to sort of say this is a + + align:start position:0% +trying to sort of say this is a + + + align:start position:0% +trying to sort of say this is a +fabrication of these particular chips + + align:start position:0% +fabrication of these particular chips + + + align:start position:0% +fabrication of these particular chips +that deliver Drugs That's why we wanted + + align:start position:0% +that deliver Drugs That's why we wanted + + + align:start position:0% +that deliver Drugs That's why we wanted +to show the underside of the wafer by + + align:start position:0% +to show the underside of the wafer by + + + align:start position:0% +to show the underside of the wafer by +the way all this needs to be discussed + + align:start position:0% +the way all this needs to be discussed + + + align:start position:0% +the way all this needs to be discussed +in a caption none of this works without + + align:start position:0% +in a caption none of this works without + + + align:start position:0% +in a caption none of this works without +text but this is an attempt to visually + + align:start position:0% +text but this is an attempt to visually + + + align:start position:0% +text but this is an attempt to visually +describe what this is in this next one + + align:start position:0% +describe what this is in this next one + + + align:start position:0% +describe what this is in this next one +these are fibers that are constructed so + + align:start position:0% +these are fibers that are constructed so + + + align:start position:0% +these are fibers that are constructed so +that they have different Optical + + align:start position:0% +that they have different Optical + + + align:start position:0% +that they have different Optical +qualities and and I tried to weave them + + align:start position:0% +qualities and and I tried to weave them + + + align:start position:0% +qualities and and I tried to weave them +in a sort of a fabric because that's + + align:start position:0% +in a sort of a fabric because that's + + + align:start position:0% +in a sort of a fabric because that's +what they were thinking of making it + + align:start position:0% +what they were thinking of making it + + + align:start position:0% +what they were thinking of making it +work with they want they were imagining + + align:start position:0% +work with they want they were imagining + + + align:start position:0% +work with they want they were imagining +these fibers literally being woven into + + align:start position:0% +these fibers literally being woven into + + + align:start position:0% +these fibers literally being woven into +clothing don't know if it ever happened + + align:start position:0% +clothing don't know if it ever happened + + + align:start position:0% +clothing don't know if it ever happened +but this is a number of years ago once + + align:start position:0% +but this is a number of years ago once + + + align:start position:0% +but this is a number of years ago once +again telling suggesting the use of + + align:start position:0% +again telling suggesting the use of + + + align:start position:0% +again telling suggesting the use of +material in this next one I was just + + align:start position:0% +material in this next one I was just + + + align:start position:0% +material in this next one I was just +playing around with this was trying to + + align:start position:0% +playing around with this was trying to + + + align:start position:0% +playing around with this was trying to +show glass when it's treated properly + + align:start position:0% +show glass when it's treated properly + + + align:start position:0% +show glass when it's treated properly +you see on the upper right and the lower + + align:start position:0% +you see on the upper right and the lower + + + align:start position:0% +you see on the upper right and the lower +right when glass is treated in a certain + + align:start position:0% +right when glass is treated in a certain + + + align:start position:0% +right when glass is treated in a certain +way it shatters properly and safety wise + + align:start position:0% +way it shatters properly and safety wise + + + align:start position:0% +way it shatters properly and safety wise +whereas the other one in the more + + align:start position:0% +whereas the other one in the more + + + align:start position:0% +whereas the other one in the more +triangular area it's just not the way we + + align:start position:0% +triangular area it's just not the way we + + + align:start position:0% +triangular area it's just not the way we +want it it is a little too artsy + + align:start position:0% +want it it is a little too artsy + + + align:start position:0% +want it it is a little too artsy +probably for many of you but again I was + + align:start position:0% +probably for many of you but again I was + + + align:start position:0% +probably for many of you but again I was +just playing it and I do want you as I + + align:start position:0% +just playing it and I do want you as I + + + align:start position:0% +just playing it and I do want you as I +continue saying to play with this stuff + + align:start position:0% +continue saying to play with this stuff + + + align:start position:0% +continue saying to play with this stuff +the next one one it was about corn that + + align:start position:0% +the next one one it was about corn that + + + align:start position:0% +the next one one it was about corn that +was treated a particular way and I + + align:start position:0% +was treated a particular way and I + + + align:start position:0% +was treated a particular way and I +decided to use the containers the + + align:start position:0% +decided to use the containers the + + + align:start position:0% +decided to use the containers the +plastic material that it came in as a + + align:start position:0% +plastic material that it came in as a + + + align:start position:0% +plastic material that it came in as a +suggestion of how these are delivered + + align:start position:0% +suggestion of how these are delivered + + + align:start position:0% +suggestion of how these are delivered +and finally I'm going to just some + + align:start position:0% +and finally I'm going to just some + + + align:start position:0% +and finally I'm going to just some +devices that evolved over time these are + + align:start position:0% +devices that evolved over time these are + + + align:start position:0% +devices that evolved over time these are +various iterations of a particular idea + + align:start position:0% +various iterations of a particular idea + + + align:start position:0% +various iterations of a particular idea +and we see how they changed how they + + align:start position:0% +and we see how they changed how they + + + align:start position:0% +and we see how they changed how they +evolved telling sort of a chronology of + + align:start position:0% +evolved telling sort of a chronology of + + + align:start position:0% +evolved telling sort of a chronology of +these particular + + align:start position:0% +these particular + + + align:start position:0% +these particular +devices here's an example of really + + align:start position:0% +devices here's an example of really + + + align:start position:0% +devices here's an example of really +stretching our imagination it's the + + align:start position:0% +stretching our imagination it's the + + + align:start position:0% +stretching our imagination it's the +watch that we've seen before on my + + align:start position:0% +watch that we've seen before on my + + + align:start position:0% +watch that we've seen before on my +computer screen as well which I have + + align:start position:0% +computer screen as well which I have + + + align:start position:0% +computer screen as well which I have +focused in on and we're seeing a detail + + align:start position:0% +focused in on and we're seeing a detail + + + align:start position:0% +focused in on and we're seeing a detail +of the watch using the computer screen + + align:start position:0% +of the watch using the computer screen + + + align:start position:0% +of the watch using the computer screen +as um another light source but a + + align:start position:0% +as um another light source but a + + + align:start position:0% +as um another light source but a +compositional one as well so here I'm + + align:start position:0% +compositional one as well so here I'm + + + align:start position:0% +compositional one as well so here I'm +selecting um the image of the watch on + + align:start position:0% +selecting um the image of the watch on + + + align:start position:0% +selecting um the image of the watch on +the + + align:start position:0% +the + + + align:start position:0% +the +screen um I don't like the colors here + + align:start position:0% +screen um I don't like the colors here + + + align:start position:0% +screen um I don't like the colors here +that's what we're doing here we're we're + + align:start position:0% +that's what we're doing here we're we're + + + align:start position:0% +that's what we're doing here we're we're +basically going to be matching the + + align:start position:0% +basically going to be matching the + + + align:start position:0% +basically going to be matching the +colors so I selected the watch then + + align:start position:0% +colors so I selected the watch then + + + align:start position:0% +colors so I selected the watch then +inverted it selected the real watch as + + align:start position:0% +inverted it selected the real watch as + + + align:start position:0% +inverted it selected the real watch as +opposed to the screen and now we have an + + align:start position:0% +opposed to the screen and now we have an + + + align:start position:0% +opposed to the screen and now we have an +image that is balanced color-wise just + + align:start position:0% +image that is balanced color-wise just + + + align:start position:0% +image that is balanced color-wise just +imagine perhaps another kind of image on + + align:start position:0% +imagine perhaps another kind of image on + + + align:start position:0% +imagine perhaps another kind of image on +your screen with your device maybe to + + align:start position:0% +your screen with your device maybe to + + + align:start position:0% +your screen with your device maybe to +expand the explanation of how your image + + align:start position:0% +expand the explanation of how your image + + + align:start position:0% +expand the explanation of how your image +Works something that you might want to + + align:start position:0% +Works something that you might want to + + + align:start position:0% +Works something that you might want to +think of using your own + + align:start position:0% +think of using your own + + + align:start position:0% +think of using your own +imagination so this is just a hint of + + align:start position:0% +imagination so this is just a hint of + + + align:start position:0% +imagination so this is just a hint of +what you could do with + + align:start position:0% +what you could do with + + + align:start position:0% +what you could do with +composition and as I said before it's + + align:start position:0% +composition and as I said before it's + + + align:start position:0% +composition and as I said before it's +very difficult to separate this idea of + + align:start position:0% +very difficult to separate this idea of + + + align:start position:0% +very difficult to separate this idea of +composition with point of view and + + align:start position:0% +composition with point of view and + + + align:start position:0% +composition with point of view and +backgrounds which you'll see in very + + align:start position:0% +backgrounds which you'll see in very + + + align:start position:0% +backgrounds which you'll see in very +shortly so you know it's all connected + + align:start position:0% +shortly so you know it's all connected + + + align:start position:0% +shortly so you know it's all connected +and I could have very easily put some of + + align:start position:0% +and I could have very easily put some of + + + align:start position:0% +and I could have very easily put some of +these in other categories but thought it + + align:start position:0% +these in other categories but thought it + + + align:start position:0% +these in other categories but thought it +would be fun to just try for myself by + + align:start position:0% +would be fun to just try for myself by + + + align:start position:0% +would be fun to just try for myself by +the way in in separating them but they + + align:start position:0% +the way in in separating them but they + + + align:start position:0% +the way in in separating them but they +are truly very much + + align:start position:0% + + + + align:start position:0% + +connected \ No newline at end of file diff --git a/1UtJGRojmIg.txt b/1UtJGRojmIg.txt new file mode 100644 index 0000000000000000000000000000000000000000..d399d3b0b2acf242f4bd99654c790859fe9951d0 --- /dev/null +++ b/1UtJGRojmIg.txt @@ -0,0 +1,9323 @@ +align:start position:0% + +okay why don't we get started today + + align:start position:0% +okay why don't we get started today + + + align:start position:0% +okay why don't we get started today +we're gonna come full circle back to the + + align:start position:0% +we're gonna come full circle back to the + + + align:start position:0% +we're gonna come full circle back to the +first lecture so we in the first lecture + + align:start position:0% +first lecture so we in the first lecture + + + align:start position:0% +first lecture so we in the first lecture +we talked by we started by drawing a + + align:start position:0% +we talked by we started by drawing a + + + align:start position:0% +we talked by we started by drawing a +supply and demand graph we've now spent + + align:start position:0% +supply and demand graph we've now spent + + + align:start position:0% +supply and demand graph we've now spent +the last few weeks explaining where + + align:start position:0% +the last few weeks explaining where + + + align:start position:0% +the last few weeks explaining where +supply and demand curves come from and + + align:start position:0% +supply and demand curves come from and + + + align:start position:0% +supply and demand curves come from and +now we're gonna talk about the supply + + align:start position:0% +now we're gonna talk about the supply + + + align:start position:0% +now we're gonna talk about the supply +and demand curves you know what do they + + align:start position:0% +and demand curves you know what do they + + + align:start position:0% +and demand curves you know what do they +know did they know things let's find out + + align:start position:0% +know did they know things let's find out + + + align:start position:0% +know did they know things let's find out +so no one no one on that okay thank you + + align:start position:0% +so no one no one on that okay thank you + + + align:start position:0% +so no one no one on that okay thank you +alright so let's start by talking about + + align:start position:0% +alright so let's start by talking about + + + align:start position:0% +alright so let's start by talking about +shocking the supply and demand curves + + align:start position:0% + + + + align:start position:0% + +shocking the supply and demand curves + + align:start position:0% +shocking the supply and demand curves + + + align:start position:0% +shocking the supply and demand curves +that was a Bojack horseman reference for + + align:start position:0% +that was a Bojack horseman reference for + + + align:start position:0% +that was a Bojack horseman reference for +those who missed that okay let's let's + + align:start position:0% +those who missed that okay let's let's + + + align:start position:0% +those who missed that okay let's let's +talk about shocking the supply and + + align:start position:0% +talk about shocking the supply and + + + align:start position:0% +talk about shocking the supply and +demand curves so let's start with a + + align:start position:0% +demand curves so let's start with a + + + align:start position:0% +demand curves so let's start with a +review of the supply and demand + + align:start position:0% +review of the supply and demand + + + align:start position:0% +review of the supply and demand +framework that we introduced in the + + align:start position:0% +framework that we introduced in the + + + align:start position:0% +framework that we introduced in the +first lecture so let's go back to figure + + align:start position:0% +first lecture so let's go back to figure + + + align:start position:0% +first lecture so let's go back to figure +9 1 we've got the market for gasoline + + align:start position:0% +9 1 we've got the market for gasoline + + + align:start position:0% +9 1 we've got the market for gasoline +okay on the x-axis is big Q quantity of + + align:start position:0% +okay on the x-axis is big Q quantity of + + + align:start position:0% +okay on the x-axis is big Q quantity of +gases is a market level diagram on the + + align:start position:0% +gases is a market level diagram on the + + + align:start position:0% +gases is a market level diagram on the +y-axis the price of gas and as we said + + align:start position:0% +y-axis the price of gas and as we said + + + align:start position:0% +y-axis the price of gas and as we said +the first lecture to supply curve that's + + align:start position:0% +the first lecture to supply curve that's + + + align:start position:0% +the first lecture to supply curve that's +upward sloping representing the fact + + align:start position:0% +upward sloping representing the fact + + + align:start position:0% +upward sloping representing the fact +that higher prices call forth more + + align:start position:0% +that higher prices call forth more + + + align:start position:0% +that higher prices call forth more +supply we now know where that comes from + + align:start position:0% +supply we now know where that comes from + + + align:start position:0% +supply we now know where that comes from +we know that what happens is when + + align:start position:0% +we know that what happens is when + + + align:start position:0% +we know that what happens is when +there's a higher price firms can now + + align:start position:0% +there's a higher price firms can now + + + align:start position:0% +there's a higher price firms can now +afford to move up the marginal cost + + align:start position:0% +afford to move up the marginal cost + + + align:start position:0% +afford to move up the marginal cost +curve which is a supply curve so we know + + align:start position:0% +curve which is a supply curve so we know + + + align:start position:0% +curve which is a supply curve so we know +where that comes from + + align:start position:0% +where that comes from + + + align:start position:0% +where that comes from +we've demand curve which is downward + + align:start position:0% +we've demand curve which is downward + + + align:start position:0% +we've demand curve which is downward +sloping higher prices lead to less + + align:start position:0% +sloping higher prices lead to less + + + align:start position:0% +sloping higher prices lead to less +demand we know where that comes from + + align:start position:0% +demand we know where that comes from + + + align:start position:0% +demand we know where that comes from +we know that it's the price of a good + + align:start position:0% +we know that it's the price of a good + + + align:start position:0% +we know that it's the price of a good +Rises through both income and + + align:start position:0% +Rises through both income and + + + align:start position:0% +Rises through both income and +substitution effects for normal goods + + align:start position:0% +substitution effects for normal goods + + + align:start position:0% +substitution effects for normal goods +good sumers who want less of it so + + align:start position:0% +good sumers who want less of it so + + + align:start position:0% +good sumers who want less of it so +whenever that comes from so we now have + + align:start position:0% +whenever that comes from so we now have + + + align:start position:0% +whenever that comes from so we now have +derived these and we're back where we + + align:start position:0% +derived these and we're back where we + + + align:start position:0% +derived these and we're back where we +started in equilibrium so let's actually + + align:start position:0% +started in equilibrium so let's actually + + + align:start position:0% +started in equilibrium so let's actually +start by asking what happens let's say I + + align:start position:0% +start by asking what happens let's say I + + + align:start position:0% +start by asking what happens let's say I +start by asking as we move forward how + + align:start position:0% +start by asking as we move forward how + + + align:start position:0% +start by asking as we move forward how +do I want to think about these curves + + align:start position:0% +do I want to think about these curves + + + align:start position:0% +do I want to think about these curves +and the way I think about them is we + + align:start position:0% +and the way I think about them is we + + + align:start position:0% +and the way I think about them is we +want to think about the demand curve + + align:start position:0% +want to think about the demand curve + + + align:start position:0% +want to think about the demand curve +want to think about these as willingness + + align:start position:0% +want to think about these as willingness + + + align:start position:0% +want to think about these as willingness +to play pay and willingness to supply + + align:start position:0% +to play pay and willingness to supply + + + align:start position:0% +to play pay and willingness to supply +curse so think about the demand curve as + + align:start position:0% +curse so think about the demand curve as + + + align:start position:0% +curse so think about the demand curve as +a willingness to pay curve how much are + + align:start position:0% +a willingness to pay curve how much are + + + align:start position:0% +a willingness to pay curve how much are +you willing to pay to get the next unit + + align:start position:0% +you willing to pay to get the next unit + + + align:start position:0% +you willing to pay to get the next unit +of + + align:start position:0% +of + + + align:start position:0% +of +doors how much is the market willing to + + align:start position:0% +doors how much is the market willing to + + + align:start position:0% +doors how much is the market willing to +pay to get the next unit of the good + + align:start position:0% +pay to get the next unit of the good + + + align:start position:0% +pay to get the next unit of the good +okay and the supply curve is willing to + + align:start position:0% +okay and the supply curve is willing to + + + align:start position:0% +okay and the supply curve is willing to +supply okay an equilibrium is the point + + align:start position:0% +supply okay an equilibrium is the point + + + align:start position:0% +supply okay an equilibrium is the point +where consumers willingness to pay for + + align:start position:0% +where consumers willingness to pay for + + + align:start position:0% +where consumers willingness to pay for +the next unit of the good meets the + + align:start position:0% +the next unit of the good meets the + + + align:start position:0% +the next unit of the good meets the +suppliers willing to supply the next + + align:start position:0% +suppliers willing to supply the next + + + align:start position:0% +suppliers willing to supply the next +unit of the good when those are equal + + align:start position:0% +unit of the good when those are equal + + + align:start position:0% +unit of the good when those are equal +we're in equilibrium so that's kind of + + align:start position:0% +we're in equilibrium so that's kind of + + + align:start position:0% +we're in equilibrium so that's kind of +where we start now let's asking now + + align:start position:0% +where we start now let's asking now + + + align:start position:0% +where we start now let's asking now +let's ask what happens as these cars + + align:start position:0% +let's ask what happens as these cars + + + align:start position:0% +let's ask what happens as these cars +shift so for example let's take this + + align:start position:0% +shift so for example let's take this + + + align:start position:0% +shift so for example let's take this +market and imagine the tastes change + + align:start position:0% +market and imagine the tastes change + + + align:start position:0% +market and imagine the tastes change +suddenly everyone wants to drive big + + align:start position:0% +suddenly everyone wants to drive big + + + align:start position:0% +suddenly everyone wants to drive big +cars everyone's to drive SUVs okay what + + align:start position:0% +cars everyone's to drive SUVs okay what + + + align:start position:0% +cars everyone's to drive SUVs okay what +does this do to the market for gas well + + align:start position:0% +does this do to the market for gas well + + + align:start position:0% +does this do to the market for gas well +so what does this do well what it does + + align:start position:0% +so what does this do well what it does + + + align:start position:0% +so what does this do well what it does +yeah go ahead yes SUVs are what we call + + align:start position:0% +yeah go ahead yes SUVs are what we call + + + align:start position:0% +yeah go ahead yes SUVs are what we call +a complement a complement as opposed to + + align:start position:0% +a complement a complement as opposed to + + + align:start position:0% +a complement a complement as opposed to +substitute our complement for gasoline + + align:start position:0% +substitute our complement for gasoline + + + align:start position:0% +substitute our complement for gasoline +when demand for SUVs goes up demand for + + align:start position:0% +when demand for SUVs goes up demand for + + + align:start position:0% +when demand for SUVs goes up demand for +gas goes up so the demand curve would + + align:start position:0% +gas goes up so the demand curve would + + + align:start position:0% +gas goes up so the demand curve would +shift out so we would end up in a + + align:start position:0% +shift out so we would end up in a + + + align:start position:0% +shift out so we would end up in a +situation like figure 9 - but let's talk + + align:start position:0% +situation like figure 9 - but let's talk + + + align:start position:0% +situation like figure 9 - but let's talk +through the dynamics all you would see + + align:start position:0% +through the dynamics all you would see + + + align:start position:0% +through the dynamics all you would see +in the market is quantity of gas sold + + align:start position:0% +in the market is quantity of gas sold + + + align:start position:0% +in the market is quantity of gas sold +would go up from q1 to q2 and price of + + align:start position:0% +would go up from q1 to q2 and price of + + + align:start position:0% +would go up from q1 to q2 and price of +gas would go up from p1 to p2 well let's + + align:start position:0% +gas would go up from p1 to p2 well let's + + + align:start position:0% +gas would go up from p1 to p2 well let's +talk about underneath how we get there + + align:start position:0% +talk about underneath how we get there + + + align:start position:0% +talk about underneath how we get there +what happens is demand shifts up people + + align:start position:0% +what happens is demand shifts up people + + + align:start position:0% +what happens is demand shifts up people +want more gas because they want to drive + + align:start position:0% +want more gas because they want to drive + + + align:start position:0% +want more gas because they want to drive +these gas-guzzling cars so she demand + + align:start position:0% +these gas-guzzling cars so she demand + + + align:start position:0% +these gas-guzzling cars so she demand +shifts from d1 to d2 what does that mean + + align:start position:0% +shifts from d1 to d2 what does that mean + + + align:start position:0% +shifts from d1 to d2 what does that mean +that means that at the previous + + align:start position:0% +that means that at the previous + + + align:start position:0% +that means that at the previous +equilibrium price if the price didn't + + align:start position:0% +equilibrium price if the price didn't + + + align:start position:0% +equilibrium price if the price didn't +change if the price stayed at p1 what + + align:start position:0% +change if the price stayed at p1 what + + + align:start position:0% +change if the price stayed at p1 what +would happen + + align:start position:0% +would happen + + + align:start position:0% +would happen +well we'd no longer be in equilibrium + + align:start position:0% +well we'd no longer be in equilibrium + + + align:start position:0% +well we'd no longer be in equilibrium +because people firms would still be + + align:start position:0% +because people firms would still be + + + align:start position:0% +because people firms would still be +happy to supply q1 units of gas but + + align:start position:0% +happy to supply q1 units of gas but + + + align:start position:0% +happy to supply q1 units of gas but +people would want way more than that we + + align:start position:0% +people would want way more than that we + + + align:start position:0% +people would want way more than that we +would have excess demand if the price + + align:start position:0% +would have excess demand if the price + + + align:start position:0% +would have excess demand if the price +didn't change there would be excess + + align:start position:0% +didn't change there would be excess + + + align:start position:0% +didn't change there would be excess +demand people would want more than the + + align:start position:0% +demand people would want more than the + + + align:start position:0% +demand people would want more than the +q1 units of gas suppliers will recognize + + align:start position:0% +q1 units of gas suppliers will recognize + + + align:start position:0% +q1 units of gas suppliers will recognize +this and say well if people want more + + align:start position:0% +this and say well if people want more + + + align:start position:0% +this and say well if people want more +we're happy to produce more + + align:start position:0% +we're happy to produce more + + + align:start position:0% +we're happy to produce more +but remember we have to respect the + + align:start position:0% +but remember we have to respect the + + + align:start position:0% +but remember we have to respect the +marginal cost curve and marginal costs + + align:start position:0% +marginal cost curve and marginal costs + + + align:start position:0% +marginal cost curve and marginal costs +of rising if we're gonna produce more + + align:start position:0% +of rising if we're gonna produce more + + + align:start position:0% +of rising if we're gonna produce more +we're gonna have to charge more we're + + align:start position:0% +we're gonna have to charge more we're + + + align:start position:0% +we're gonna have to charge more we're +gonna have to move up the supply curve + + align:start position:0% +gonna have to move up the supply curve + + + align:start position:0% +gonna have to move up the supply curve +so a shift in the demand curve makes + + align:start position:0% +so a shift in the demand curve makes + + + align:start position:0% +so a shift in the demand curve makes +firms move along the supply curve we + + align:start position:0% +firms move along the supply curve we + + + align:start position:0% +firms move along the supply curve we +want to keep shifts and movement along + + align:start position:0% +want to keep shifts and movement along + + + align:start position:0% +want to keep shifts and movement along +curves separate a shift in the demand + + align:start position:0% +curves separate a shift in the demand + + + align:start position:0% +curves separate a shift in the demand +curve meaning people are saying to gas + + align:start position:0% +curve meaning people are saying to gas + + + align:start position:0% +curve meaning people are saying to gas +producers we want more gas gas firms + + align:start position:0% +producers we want more gas gas firms + + + align:start position:0% +producers we want more gas gas firms +like great we want to give you more gas + + align:start position:0% +like great we want to give you more gas + + + align:start position:0% +like great we want to give you more gas +but we're gonna have to charge you more + + align:start position:0% +but we're gonna have to charge you more + + + align:start position:0% +but we're gonna have to charge you more +to do it because our marginal cost curve + + align:start position:0% +to do it because our marginal cost curve + + + align:start position:0% +to do it because our marginal cost curve +is upward sloping which is our supply + + align:start position:0% +is upward sloping which is our supply + + + align:start position:0% +is upward sloping which is our supply +curve as we learned so the price rises + + align:start position:0% +curve as we learned so the price rises + + + align:start position:0% +curve as we learned so the price rises +and we need to reach a new equilibrium + + align:start position:0% +and we need to reach a new equilibrium + + + align:start position:0% +and we need to reach a new equilibrium +at e2 so we don't see these steps in + + align:start position:0% +at e2 so we don't see these steps in + + + align:start position:0% +at e2 so we don't see these steps in +practice in the end we just see the + + align:start position:0% +practice in the end we just see the + + + align:start position:0% +practice in the end we just see the +price change but think about it as two + + align:start position:0% +price change but think about it as two + + + align:start position:0% +price change but think about it as two +steps demand shifts out creating excess + + align:start position:0% +steps demand shifts out creating excess + + + align:start position:0% +steps demand shifts out creating excess +demand providers to meet that excess + + align:start position:0% +demand providers to meet that excess + + + align:start position:0% +demand providers to meet that excess +demand have to produce more and to + + align:start position:0% +demand have to produce more and to + + + align:start position:0% +demand have to produce more and to +produce more they're gonna charge a + + align:start position:0% +produce more they're gonna charge a + + + align:start position:0% +produce more they're gonna charge a +higher price and that moves you from e1 + + align:start position:0% +higher price and that moves you from e1 + + + align:start position:0% +higher price and that moves you from e1 +to e2 okay so we have a shift in demand + + align:start position:0% +to e2 okay so we have a shift in demand + + + align:start position:0% +to e2 okay so we have a shift in demand +which cause to slide up the supply curve + + align:start position:0% +which cause to slide up the supply curve + + + align:start position:0% +which cause to slide up the supply curve +okay now let's think about a different + + align:start position:0% +okay now let's think about a different + + + align:start position:0% +okay now let's think about a different +example imagine war breaks out in the + + align:start position:0% +example imagine war breaks out in the + + + align:start position:0% +example imagine war breaks out in the +Middle East not too hard to imagine + + align:start position:0% +Middle East not too hard to imagine + + + align:start position:0% +Middle East not too hard to imagine +unfortunately and as a result the + + align:start position:0% +unfortunately and as a result the + + + align:start position:0% +unfortunately and as a result the +quantity so suppliers need to pay more + + align:start position:0% +quantity so suppliers need to pay more + + + align:start position:0% +quantity so suppliers need to pay more +to get the oil that they used to make + + align:start position:0% +to get the oil that they used to make + + + align:start position:0% +to get the oil that they used to make +gasoline okay what does that do we see + + align:start position:0% +gasoline okay what does that do we see + + + align:start position:0% +gasoline okay what does that do we see +that in Figure 9 3 now what happens is + + align:start position:0% +that in Figure 9 3 now what happens is + + + align:start position:0% +that in Figure 9 3 now what happens is +for every you for every unit of gas + + align:start position:0% +for every you for every unit of gas + + + align:start position:0% +for every you for every unit of gas +suppliers need to charge more their + + align:start position:0% +suppliers need to charge more their + + + align:start position:0% +suppliers need to charge more their +underlying marginal costs have gone up + + align:start position:0% +underlying marginal costs have gone up + + + align:start position:0% +underlying marginal costs have gone up +because they have to pay more to get the + + align:start position:0% +because they have to pay more to get the + + + align:start position:0% +because they have to pay more to get the +oil that's a variable cost of production + + align:start position:0% +oil that's a variable cost of production + + + align:start position:0% +oil that's a variable cost of production +of gas so their marginal costs have gone + + align:start position:0% +of gas so their marginal costs have gone + + + align:start position:0% +of gas so their marginal costs have gone +up their marginal costs going up meaning + + align:start position:0% +up their marginal costs going up meaning + + + align:start position:0% +up their marginal costs going up meaning +their supply curve has shifted upwards + + align:start position:0% +their supply curve has shifted upwards + + + align:start position:0% +their supply curve has shifted upwards +okay for every unit of production their + + align:start position:0% +okay for every unit of production their + + + align:start position:0% +okay for every unit of production their +marginal cost is higher because they're + + align:start position:0% +marginal cost is higher because they're + + + align:start position:0% +marginal cost is higher because they're +variable costs have gone up therefore + + align:start position:0% +variable costs have gone up therefore + + + align:start position:0% +variable costs have gone up therefore +they're gonna need to charge a higher + + align:start position:0% +they're gonna need to charge a higher + + + align:start position:0% +they're gonna need to charge a higher +price to break-even okay we're still in + + align:start position:0% +price to break-even okay we're still in + + + align:start position:0% +price to break-even okay we're still in +perfectly competitive markets where + + align:start position:0% +perfectly competitive markets where + + + align:start position:0% +perfectly competitive markets where +nobody's making any profit okay they're + + align:start position:0% +nobody's making any profit okay they're + + + align:start position:0% +nobody's making any profit okay they're +gonna charge more to break-even + + align:start position:0% +gonna charge more to break-even + + + align:start position:0% +gonna charge more to break-even +so now let's once again talk with that + + align:start position:0% +so now let's once again talk with that + + + align:start position:0% +so now let's once again talk with that +dynamics of what's happening that I + + align:start position:0% +dynamics of what's happening that I + + + align:start position:0% +dynamics of what's happening that I +nameks are the cost of and the input to + + align:start position:0% +nameks are the cost of and the input to + + + align:start position:0% +nameks are the cost of and the input to +the suppliers went up Oh + + align:start position:0% +the suppliers went up Oh + + + align:start position:0% +the suppliers went up Oh +okay they're marginal cost serve shifts + + align:start position:0% +okay they're marginal cost serve shifts + + + align:start position:0% +okay they're marginal cost serve shifts +up to s2 so they want to charge a higher + + align:start position:0% +up to s2 so they want to charge a higher + + + align:start position:0% +up to s2 so they want to charge a higher +price so if we kept the price the same + + align:start position:0% +price so if we kept the price the same + + + align:start position:0% +price so if we kept the price the same +as it was before supplies would say we + + align:start position:0% +as it was before supplies would say we + + + align:start position:0% +as it was before supplies would say we +don't want to sell q1 anymore what I + + align:start position:0% +don't want to sell q1 anymore what I + + + align:start position:0% +don't want to sell q1 anymore what I +ain't shouldn't selling q1 anymore + + align:start position:0% +ain't shouldn't selling q1 anymore + + + align:start position:0% +ain't shouldn't selling q1 anymore +at that old price okay that doesn't + + align:start position:0% +at that old price okay that doesn't + + + align:start position:0% +at that old price okay that doesn't +interest us could sue there for + + align:start position:0% +interest us could sue there for + + + align:start position:0% +interest us could sue there for +consumers want more than providers are + + align:start position:0% +consumers want more than providers are + + + align:start position:0% +consumers want more than providers are +willing to sell and we once again have + + align:start position:0% +willing to sell and we once again have + + + align:start position:0% +willing to sell and we once again have +access to mant so we in both cases we + + align:start position:0% +access to mant so we in both cases we + + + align:start position:0% +access to mant so we in both cases we +get excess demand in the first case we + + align:start position:0% +get excess demand in the first case we + + + align:start position:0% +get excess demand in the first case we +got excess demand because consumers + + align:start position:0% +got excess demand because consumers + + + align:start position:0% +got excess demand because consumers +wanted more the lower the consumers + + align:start position:0% +wanted more the lower the consumers + + + align:start position:0% +wanted more the lower the consumers +taste shifted so they wanted more gas at + + align:start position:0% +taste shifted so they wanted more gas at + + + align:start position:0% +taste shifted so they wanted more gas at +every price now we have excess demand + + align:start position:0% +every price now we have excess demand + + + align:start position:0% +every price now we have excess demand +not cuz taste shift but because costs go + + align:start position:0% +not cuz taste shift but because costs go + + + align:start position:0% +not cuz taste shift but because costs go +up so providers don't wanna provide as + + align:start position:0% +up so providers don't wanna provide as + + + align:start position:0% +up so providers don't wanna provide as +much gas at every price so what happens + + align:start position:0% +much gas at every price so what happens + + + align:start position:0% +much gas at every price so what happens +is providers are gonna say fine we're + + align:start position:0% +is providers are gonna say fine we're + + + align:start position:0% +is providers are gonna say fine we're +gonna charge a higher price okay and + + align:start position:0% +gonna charge a higher price okay and + + + align:start position:0% +gonna charge a higher price okay and +we'll slide up the demand curve because + + align:start position:0% +we'll slide up the demand curve because + + + align:start position:0% +we'll slide up the demand curve because +as providers charge a higher price + + align:start position:0% +as providers charge a higher price + + + align:start position:0% +as providers charge a higher price +people want less gas at a higher price + + align:start position:0% +people want less gas at a higher price + + + align:start position:0% +people want less gas at a higher price +you want less gas through the + + align:start position:0% +you want less gas through the + + + align:start position:0% +you want less gas through the +substitution effect because you'll buy + + align:start position:0% +substitution effect because you'll buy + + + align:start position:0% +substitution effect because you'll buy +other things instead it's the income + + align:start position:0% +other things instead it's the income + + + align:start position:0% +other things instead it's the income +effect because you're effectively poorer + + align:start position:0% +effect because you're effectively poorer + + + align:start position:0% +effect because you're effectively poorer +because the price of gas went up for + + align:start position:0% +because the price of gas went up for + + + align:start position:0% +because the price of gas went up for +those reasons you're gonna shift up the + + align:start position:0% +those reasons you're gonna shift up the + + + align:start position:0% +those reasons you're gonna shift up the +demand curve and reach a new equilibrium + + align:start position:0% +demand curve and reach a new equilibrium + + + align:start position:0% +demand curve and reach a new equilibrium +and e2 so that's the underlying dynamics + + align:start position:0% +and e2 so that's the underlying dynamics + + + align:start position:0% +and e2 so that's the underlying dynamics +of how shifts in supply and demand lead + + align:start position:0% +of how shifts in supply and demand lead + + + align:start position:0% +of how shifts in supply and demand lead +to changes in quantity and price okay so + + align:start position:0% +to changes in quantity and price okay so + + + align:start position:0% +to changes in quantity and price okay so +that's basically what we're seeing + + align:start position:0% +that's basically what we're seeing + + + align:start position:0% +that's basically what we're seeing +questions about that yeah + + align:start position:0% + + + + align:start position:0% + +great great question so what's the + + align:start position:0% +great great question so what's the + + + align:start position:0% +great great question so what's the +answer how do you what's the + + align:start position:0% +answer how do you what's the + + + align:start position:0% +answer how do you what's the +substitution effect with gas well even + + align:start position:0% +substitution effect with gas well even + + + align:start position:0% +substitution effect with gas well even +it's yourself it's not driving it's + + align:start position:0% +it's yourself it's not driving it's + + + align:start position:0% +it's yourself it's not driving it's +taking the bus it's driving less it's + + align:start position:0% +taking the bus it's driving less it's + + + align:start position:0% +taking the bus it's driving less it's +walking or taking your bike so once + + align:start position:0% +walking or taking your bike so once + + + align:start position:0% +walking or taking your bike so once +again when everything about substitute + + align:start position:0% +again when everything about substitute + + + align:start position:0% +again when everything about substitute +eviction I think about the the + + align:start position:0% +eviction I think about the the + + + align:start position:0% +eviction I think about the the +opportunity the next opportunities you + + align:start position:0% +opportunity the next opportunities you + + + align:start position:0% +opportunity the next opportunities you +could use instead okay good question + + align:start position:0% +could use instead okay good question + + + align:start position:0% +could use instead okay good question +other questions okay so here's an + + align:start position:0% +other questions okay so here's an + + + align:start position:0% +other questions okay so here's an +interesting point look at figure 92 and + + align:start position:0% +interesting point look at figure 92 and + + + align:start position:0% +interesting point look at figure 92 and +93 in both cases the price went up okay + + align:start position:0% +93 in both cases the price went up okay + + + align:start position:0% +93 in both cases the price went up okay +in both case the price went up so we + + align:start position:0% +in both case the price went up so we + + + align:start position:0% +in both case the price went up so we +can't tell if a price goes up you can't + + align:start position:0% +can't tell if a price goes up you can't + + + align:start position:0% +can't tell if a price goes up you can't +tell from that alone whether there was a + + align:start position:0% +tell from that alone whether there was a + + + align:start position:0% +tell from that alone whether there was a +shift in demand or supply so if I for + + align:start position:0% +shift in demand or supply so if I for + + + align:start position:0% +shift in demand or supply so if I for +example asks you on an exam or your mom + + align:start position:0% +example asks you on an exam or your mom + + + align:start position:0% +example asks you on an exam or your mom +came home and your mom asks you hey umm + + align:start position:0% +came home and your mom asks you hey umm + + + align:start position:0% +came home and your mom asks you hey umm +if the price goes up does that mean + + align:start position:0% +if the price goes up does that mean + + + align:start position:0% +if the price goes up does that mean +demand shift or supply shifted you say + + align:start position:0% +demand shift or supply shifted you say + + + align:start position:0% +demand shift or supply shifted you say +to your mom I don't know I can't tell + + align:start position:0% +to your mom I don't know I can't tell + + + align:start position:0% +to your mom I don't know I can't tell +with just that information I knew what + + align:start position:0% +with just that information I knew what + + + align:start position:0% +with just that information I knew what +happened to quantity - okay and then you + + align:start position:0% +happened to quantity - okay and then you + + + align:start position:0% +happened to quantity - okay and then you +save your mom good question okay so + + align:start position:0% +save your mom good question okay so + + + align:start position:0% +save your mom good question okay so +let's go through the reasons why the + + align:start position:0% +let's go through the reasons why the + + + align:start position:0% +let's go through the reasons why the +supply and demand curve shift so why the + + align:start position:0% +supply and demand curve shift so why the + + + align:start position:0% +supply and demand curve shift so why the +curve shift okay + + align:start position:0% +curve shift okay + + + align:start position:0% +curve shift okay +well in the demand side there's at least + + align:start position:0% +well in the demand side there's at least + + + align:start position:0% +well in the demand side there's at least +six reasons why demand curves would + + align:start position:0% +six reasons why demand curves would + + + align:start position:0% +six reasons why demand curves would +shift so why do why do you demand curve + + align:start position:0% +shift so why do why do you demand curve + + + align:start position:0% +shift so why do why do you demand curve +shift okay one reason is taste change I + + align:start position:0% +shift okay one reason is taste change I + + + align:start position:0% +shift okay one reason is taste change I +just use that reason taste change + + align:start position:0% +just use that reason taste change + + + align:start position:0% +just use that reason taste change +okay people want different things + + align:start position:0% +okay people want different things + + + align:start position:0% +okay people want different things +okay a second reason is that income + + align:start position:0% +okay a second reason is that income + + + align:start position:0% +okay a second reason is that income +changes Zachary's could people are + + align:start position:0% +changes Zachary's could people are + + + align:start position:0% +changes Zachary's could people are +richer or poorer and so that makes them + + align:start position:0% +richer or poorer and so that makes them + + + align:start position:0% +richer or poorer and so that makes them +want different quantities even with the + + align:start position:0% +want different quantities even with the + + + align:start position:0% +want different quantities even with the +same tastes a third reason is the change + + align:start position:0% +same tastes a third reason is the change + + + align:start position:0% +same tastes a third reason is the change +the change in the price of a + + align:start position:0% +the change in the price of a + + + align:start position:0% +the change in the price of a +complimentary or substitutable good okay + + align:start position:0% +complimentary or substitutable good okay + + + align:start position:0% +complimentary or substitutable good okay +now that's different + + align:start position:0% +now that's different + + + align:start position:0% +now that's different +I should separate the actually example + + align:start position:0% +I should separate the actually example + + + align:start position:0% +I should separate the actually example +unifor was this taste change is slightly + + align:start position:0% +unifor was this taste change is slightly + + + align:start position:0% +unifor was this taste change is slightly +different so change in price so come buy + + align:start position:0% +different so change in price so come buy + + + align:start position:0% +different so change in price so come buy +substitute ago is what I talked about + + align:start position:0% +substitute ago is what I talked about + + + align:start position:0% +substitute ago is what I talked about +taste change would be literally for + + align:start position:0% +taste change would be literally for + + + align:start position:0% +taste change would be literally for +everything held in equal I just wake up + + align:start position:0% +everything held in equal I just wake up + + + align:start position:0% +everything held in equal I just wake up +on morning + + align:start position:0% +on morning + + + align:start position:0% +on morning +like to drive that be it takes change + + align:start position:0% +like to drive that be it takes change + + + align:start position:0% +like to drive that be it takes change +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so really this the example I used was to + + align:start position:0% +so really this the example I used was to + + + align:start position:0% +so really this the example I used was to +change the price of complementary no no + + align:start position:0% +change the price of complementary no no + + + align:start position:0% +change the price of complementary no no +please didn't change no I go back I go + + align:start position:0% +please didn't change no I go back I go + + + align:start position:0% +please didn't change no I go back I go +back the example I used was at exchange + + align:start position:0% +back the example I used was at exchange + + + align:start position:0% +back the example I used was at exchange +people wanted more you SUVs but at the + + align:start position:0% +people wanted more you SUVs but at the + + + align:start position:0% +people wanted more you SUVs but at the +same time imagine different a different + + align:start position:0% +same time imagine different a different + + + align:start position:0% +same time imagine different a different +change imagine that we're looking at the + + align:start position:0% +change imagine that we're looking at the + + + align:start position:0% +change imagine that we're looking at the +demand for babysitters and the price of + + align:start position:0% +demand for babysitters and the price of + + + align:start position:0% +demand for babysitters and the price of +movies goes up + + align:start position:0% +movies goes up + + + align:start position:0% +movies goes up +okay well movies are complementary with + + align:start position:0% +okay well movies are complementary with + + + align:start position:0% +okay well movies are complementary with +babysitters you guys know what about the + + align:start position:0% +babysitters you guys know what about the + + + align:start position:0% +babysitters you guys know what about the +scene of kids yet but trust me movies + + align:start position:0% +scene of kids yet but trust me movies + + + align:start position:0% +scene of kids yet but trust me movies +are complement babysitters that + + align:start position:0% +are complement babysitters that + + + align:start position:0% +are complement babysitters that +basically the more you go to the movies + + align:start position:0% +basically the more you go to the movies + + + align:start position:0% +basically the more you go to the movies +the more you need babysitters so if the + + align:start position:0% +the more you need babysitters so if the + + + align:start position:0% +the more you need babysitters so if the +price of movies goes up that's gonna + + align:start position:0% +price of movies goes up that's gonna + + + align:start position:0% +price of movies goes up that's gonna +lower my demand for babysitter's or + + align:start position:0% +lower my demand for babysitter's or + + + align:start position:0% +lower my demand for babysitter's or +vice-versa imagine that how the change + + align:start position:0% +vice-versa imagine that how the change + + + align:start position:0% +vice-versa imagine that how the change +in the price of movies affects the + + align:start position:0% +in the price of movies affects the + + + align:start position:0% +in the price of movies affects the +demand for Netflix well those are + + align:start position:0% +demand for Netflix well those are + + + align:start position:0% +demand for Netflix well those are +substitutable as the price of movies + + align:start position:0% +substitutable as the price of movies + + + align:start position:0% +substitutable as the price of movies +goes up I'm gonna want more Netflix and + + align:start position:0% +goes up I'm gonna want more Netflix and + + + align:start position:0% +goes up I'm gonna want more Netflix and +less babysitters so change in price of + + align:start position:0% +less babysitters so change in price of + + + align:start position:0% +less babysitters so change in price of +competent or substitutable goods will + + align:start position:0% +competent or substitutable goods will + + + align:start position:0% +competent or substitutable goods will +also affect my domain curve another + + align:start position:0% +also affect my domain curve another + + + align:start position:0% +also affect my domain curve another +thing that could affect the demand curve + + align:start position:0% +thing that could affect the demand curve + + + align:start position:0% +thing that could affect the demand curve +is a change in the market size so we + + align:start position:0% +is a change in the market size so we + + + align:start position:0% +is a change in the market size so we +will talk in a couple lectures about + + align:start position:0% +will talk in a couple lectures about + + + align:start position:0% +will talk in a couple lectures about +international trade if suddenly you're + + align:start position:0% +international trade if suddenly you're + + + align:start position:0% +international trade if suddenly you're +selling goods to a much larger market + + align:start position:0% +selling goods to a much larger market + + + align:start position:0% +selling goods to a much larger market +that will affect the demand for your + + align:start position:0% +that will affect the demand for your + + + align:start position:0% +that will affect the demand for your +good so preference I haven't changed + + align:start position:0% +good so preference I haven't changed + + + align:start position:0% +good so preference I haven't changed +price haven't change you just got to + + align:start position:0% +price haven't change you just got to + + + align:start position:0% +price haven't change you just got to +suddenly got a bunch of new customers + + align:start position:0% +suddenly got a bunch of new customers + + + align:start position:0% +suddenly got a bunch of new customers +that will affect demand for your good + + align:start position:0% +that will affect demand for your good + + + align:start position:0% +that will affect demand for your good +okay and the last thing that could + + align:start position:0% +okay and the last thing that could + + + align:start position:0% +okay and the last thing that could +change the most subtle way demand could + + align:start position:0% +change the most subtle way demand could + + + align:start position:0% +change the most subtle way demand could +change is expectations of the future so + + align:start position:0% +change is expectations of the future so + + + align:start position:0% +change is expectations of the future so +for example imagine you expect the price + + align:start position:0% +for example imagine you expect the price + + + align:start position:0% +for example imagine you expect the price +of gas to go up tomorrow you might buy + + align:start position:0% +of gas to go up tomorrow you might buy + + + align:start position:0% +of gas to go up tomorrow you might buy +more gas today and that'll be weird for + + align:start position:0% +more gas today and that'll be weird for + + + align:start position:0% +more gas today and that'll be weird for +the next day you say look nothing + + align:start position:0% +the next day you say look nothing + + + align:start position:0% +the next day you say look nothing +changed today your tastes didn't change + + align:start position:0% +changed today your tastes didn't change + + + align:start position:0% +changed today your tastes didn't change +prices nothing change but people buy + + align:start position:0% +prices nothing change but people buy + + + align:start position:0% +prices nothing change but people buy +more gas what's going on it's that they + + align:start position:0% +more gas what's going on it's that they + + + align:start position:0% +more gas what's going on it's that they +expect the price to change in the future + + align:start position:0% +expect the price to change in the future + + + align:start position:0% +expect the price to change in the future +so expectations the future can actually + + align:start position:0% +so expectations the future can actually + + + align:start position:0% +so expectations the future can actually +drive demand today okay we've all + + align:start position:0% +drive demand today okay we've all + + + align:start position:0% +drive demand today okay we've all +experienced this in very various aspects + + align:start position:0% +experienced this in very various aspects + + + align:start position:0% +experienced this in very various aspects +of our lives okay so those are the + + align:start position:0% +of our lives okay so those are the + + + align:start position:0% +of our lives okay so those are the +reasons why the demand curve can shift + + align:start position:0% +reasons why the demand curve can shift + + + align:start position:0% +reasons why the demand curve can shift +so a lot of reasons why the demand curve + + align:start position:0% +so a lot of reasons why the demand curve + + + align:start position:0% +so a lot of reasons why the demand curve +could shift for the supply curve wise + + align:start position:0% +could shift for the supply curve wise + + + align:start position:0% +could shift for the supply curve wise +supply curve shifts + + align:start position:0% +supply curve shifts + + + align:start position:0% +supply curve shifts +is sort of much simpler there's really + + align:start position:0% +is sort of much simpler there's really + + + align:start position:0% +is sort of much simpler there's really +only two reasons okay + + align:start position:0% +only two reasons okay + + + align:start position:0% +only two reasons okay +one reason is changes in input costs and + + align:start position:0% +one reason is changes in input costs and + + + align:start position:0% +one reason is changes in input costs and +the second reason changes in input costs + + align:start position:0% +the second reason changes in input costs + + + align:start position:0% +the second reason changes in input costs +and the second is a shift in the + + align:start position:0% +and the second is a shift in the + + + align:start position:0% +and the second is a shift in the +technology and production so the + + align:start position:0% +technology and production so the + + + align:start position:0% +technology and production so the +production function changes or input + + align:start position:0% +production function changes or input + + + align:start position:0% +production function changes or input +costs change that's pretty much why + + align:start position:0% +costs change that's pretty much why + + + align:start position:0% +costs change that's pretty much why +supply curve shift okay + + align:start position:0% +supply curve shift okay + + + align:start position:0% +supply curve shift okay +so that sort of gives you a catalog of + + align:start position:0% +so that sort of gives you a catalog of + + + align:start position:0% +so that sort of gives you a catalog of +how to think about these curve shifting + + align:start position:0% +how to think about these curve shifting + + + align:start position:0% +how to think about these curve shifting +I have a fun example in the videos that + + align:start position:0% +I have a fun example in the videos that + + + align:start position:0% +I have a fun example in the videos that +go with this class um which is that we + + align:start position:0% +go with this class um which is that we + + + align:start position:0% +go with this class um which is that we +all know Kim Kardashian is you may you + + align:start position:0% +all know Kim Kardashian is you may you + + + align:start position:0% +all know Kim Kardashian is you may you +may or may not know she has more + + align:start position:0% +may or may not know she has more + + + align:start position:0% +may or may not know she has more +Instagram followers and there are people + + align:start position:0% +Instagram followers and there are people + + + align:start position:0% +Instagram followers and there are people +in France + + align:start position:0% +in France + + + align:start position:0% +in France +she got eighty million about eight it's + + align:start position:0% +she got eighty million about eight it's + + + align:start position:0% +she got eighty million about eight it's +up to about a hundred and plus million + + align:start position:0% +up to about a hundred and plus million + + + align:start position:0% +up to about a hundred and plus million +Instagram followers Kim Kardashian a few + + align:start position:0% +Instagram followers Kim Kardashian a few + + + align:start position:0% +Instagram followers Kim Kardashian a few +years ago tweeted out a picture of + + align:start position:0% +years ago tweeted out a picture of + + + align:start position:0% +years ago tweeted out a picture of +herself in an exercise corset she called + + align:start position:0% +herself in an exercise corset she called + + + align:start position:0% +herself in an exercise corset she called +it she basically claimed of course it is + + align:start position:0% +it she basically claimed of course it is + + + align:start position:0% +it she basically claimed of course it is +this thing nice to wear like back like + + align:start position:0% +this thing nice to wear like back like + + + align:start position:0% +this thing nice to wear like back like +when we didn't care about women much at + + align:start position:0% +when we didn't care about women much at + + + align:start position:0% +when we didn't care about women much at +all and we just made them wear these + + align:start position:0% +all and we just made them wear these + + + align:start position:0% +all and we just made them wear these +incredibly constrictive things to make + + align:start position:0% +incredibly constrictive things to make + + + align:start position:0% +incredibly constrictive things to make +them look skinnier okay they're + + align:start position:0% +them look skinnier okay they're + + + align:start position:0% +them look skinnier okay they're +basically like a like a brace you'd wear + + align:start position:0% +basically like a like a brace you'd wear + + + align:start position:0% +basically like a like a brace you'd wear +to make you look skinnier back in the + + align:start position:0% +to make you look skinnier back in the + + + align:start position:0% +to make you look skinnier back in the +old days and Kim Kardashian said + + align:start position:0% +old days and Kim Kardashian said + + + align:start position:0% +old days and Kim Kardashian said +actually if you were a corset when you + + align:start position:0% +actually if you were a corset when you + + + align:start position:0% +actually if you were a corset when you +exercise it helps you lose weight well + + align:start position:0% +exercise it helps you lose weight well + + + align:start position:0% +exercise it helps you lose weight well +actually she's totally [ __ ] wrong + + align:start position:0% +actually she's totally [ __ ] wrong + + + align:start position:0% +actually she's totally [ __ ] wrong +okay it doesn't okay there is no it does + + align:start position:0% +okay it doesn't okay there is no it does + + + align:start position:0% +okay it doesn't okay there is no it does +not help you lose weight but she tweeted + + align:start position:0% +not help you lose weight but she tweeted + + + align:start position:0% +not help you lose weight but she tweeted +this out and there was a massive + + align:start position:0% +this out and there was a massive + + + align:start position:0% +this out and there was a massive +increase in demand for exercise corsets + + align:start position:0% +increase in demand for exercise corsets + + + align:start position:0% +increase in demand for exercise corsets +okay and the one company that made them + + align:start position:0% +okay and the one company that made them + + + align:start position:0% +okay and the one company that made them +made scads of money there was a huge + + align:start position:0% +made scads of money there was a huge + + + align:start position:0% +made scads of money there was a huge +demand shift based on this Kim + + align:start position:0% +demand shift based on this Kim + + + align:start position:0% +demand shift based on this Kim +Kardashian tweet okay so tell me what + + align:start position:0% +Kardashian tweet okay so tell me what + + + align:start position:0% +Kardashian tweet okay so tell me what +happened next yeah + + align:start position:0% +happened next yeah + + + align:start position:0% +happened next yeah +more companies entered okay so what + + align:start position:0% +more companies entered okay so what + + + align:start position:0% +more companies entered okay so what +happened was profits were being made on + + align:start position:0% +happened was profits were being made on + + + align:start position:0% +happened was profits were being made on +exercise corsets so more companies + + align:start position:0% +exercise corsets so more companies + + + align:start position:0% +exercise corsets so more companies +started making exercise corsets and they + + align:start position:0% +started making exercise corsets and they + + + align:start position:0% +started making exercise corsets and they +came in and drove those profits down + + align:start position:0% +came in and drove those profits down + + + align:start position:0% +came in and drove those profits down +okay so that's a classic example of how + + align:start position:0% +okay so that's a classic example of how + + + align:start position:0% +okay so that's a classic example of how +demand shift and how the market the + + align:start position:0% +demand shift and how the market the + + + align:start position:0% +demand shift and how the market the +long-run will respond to return us to + + align:start position:0% +long-run will respond to return us to + + + align:start position:0% +long-run will respond to return us to +zero profits see her profits the long + + align:start position:0% +zero profits see her profits the long + + + align:start position:0% +zero profits see her profits the long +when the short runs of course that money + + align:start position:0% +when the short runs of course that money + + + align:start position:0% +when the short runs of course that money +companies made a lot of money they + + align:start position:0% +companies made a lot of money they + + + align:start position:0% +companies made a lot of money they +should they owe Kim okay but in the long + + align:start position:0% +should they owe Kim okay but in the long + + + align:start position:0% +should they owe Kim okay but in the long +run profits go to zero yeah yeah + + align:start position:0% +run profits go to zero yeah yeah + + + align:start position:0% +run profits go to zero yeah yeah +anything where you basically well no but + + align:start position:0% +anything where you basically well no but + + + align:start position:0% +anything where you basically well no but +once that's on that's a price change a + + align:start position:0% +once that's on that's a price change a + + + align:start position:0% +once that's on that's a price change a +limited time sale for a good is + + align:start position:0% +limited time sale for a good is + + + align:start position:0% +limited time sale for a good is +literally just a standard the price + + align:start position:0% +literally just a standard the price + + + align:start position:0% +literally just a standard the price +changed okay it's sort of you think the + + align:start position:0% +changed okay it's sort of you think the + + + align:start position:0% +changed okay it's sort of you think the +sales go up in the future so you buy + + align:start position:0% +sales go up in the future so you buy + + + align:start position:0% +sales go up in the future so you buy +less today that's so the expectations + + align:start position:0% +less today that's so the expectations + + + align:start position:0% +less today that's so the expectations +okay so that's shifts in demand supply + + align:start position:0% +okay so that's shifts in demand supply + + + align:start position:0% +okay so that's shifts in demand supply +curse let's now talk about what + + align:start position:0% +curse let's now talk about what + + + align:start position:0% +curse let's now talk about what +determines the shapes of supply and + + align:start position:0% +determines the shapes of supply and + + + align:start position:0% +determines the shapes of supply and +demand curve then what determines the + + align:start position:0% +demand curve then what determines the + + + align:start position:0% +demand curve then what determines the +shapes of supply and demand curse okay + + align:start position:0% +shapes of supply and demand curse okay + + + align:start position:0% +shapes of supply and demand curse okay +so basically the effect not what term is + + align:start position:0% +so basically the effect not what term is + + + align:start position:0% +so basically the effect not what term is +the shape so we're talking about + + align:start position:0% +the shape so we're talking about + + + align:start position:0% +the shape so we're talking about +determines the shape so one talk about + + align:start position:0% +determines the shape so one talk about + + + align:start position:0% +determines the shape so one talk about +the role the shapes the supply demand + + align:start position:0% +the role the shapes the supply demand + + + align:start position:0% +the role the shapes the supply demand +curves play let me rephrase that we know + + align:start position:0% +curves play let me rephrase that we know + + + align:start position:0% +curves play let me rephrase that we know +what determines the shapes we covered + + align:start position:0% +what determines the shapes we covered + + + align:start position:0% +what determines the shapes we covered +that the last ten lectures or whatever + + align:start position:0% +that the last ten lectures or whatever + + + align:start position:0% +that the last ten lectures or whatever +now we're talking about the role that + + align:start position:0% +now we're talking about the role that + + + align:start position:0% +now we're talking about the role that +shapes play as demand curve shift so for + + align:start position:0% +shapes play as demand curve shift so for + + + align:start position:0% +shapes play as demand curve shift so for +example let's think about a Stan word + + align:start position:0% +example let's think about a Stan word + + + align:start position:0% +example let's think about a Stan word +figure nine three shows what happens + + align:start position:0% +figure nine three shows what happens + + + align:start position:0% +figure nine three shows what happens +with a supply the figure we're just + + align:start position:0% +with a supply the figure we're just + + + align:start position:0% +with a supply the figure we're just +looking at okay figure would just look + + align:start position:0% +looking at okay figure would just look + + + align:start position:0% +looking at okay figure would just look +at that figure nine three shows what + + align:start position:0% +at that figure nine three shows what + + + align:start position:0% +at that figure nine three shows what +happens when the supply shift with the + + align:start position:0% +happens when the supply shift with the + + + align:start position:0% +happens when the supply shift with the +standard downward sloping demand curve + + align:start position:0% +standard downward sloping demand curve + + + align:start position:0% +standard downward sloping demand curve +okay which is that the price goes up + + align:start position:0% +okay which is that the price goes up + + + align:start position:0% +okay which is that the price goes up +quantity Falls however imagine instead + + align:start position:0% +quantity Falls however imagine instead + + + align:start position:0% +quantity Falls however imagine instead +we had perfectly inelastic demand so for + + align:start position:0% +we had perfectly inelastic demand so for + + + align:start position:0% +we had perfectly inelastic demand so for +example for insulin then what would + + align:start position:0% +example for insulin then what would + + + align:start position:0% +example for insulin then what would +happen well figure nine four shows if + + align:start position:0% +happen well figure nine four shows if + + + align:start position:0% +happen well figure nine four shows if +demands perfectly inelastic quantity + + align:start position:0% +demands perfectly inelastic quantity + + + align:start position:0% +demands perfectly inelastic quantity +won't change so if there's a supply if + + align:start position:0% +won't change so if there's a supply if + + + align:start position:0% +won't change so if there's a supply if +there's a shock that shifts up the + + align:start position:0% +there's a shock that shifts up the + + + align:start position:0% +there's a shock that shifts up the +supply curve like war in the Middle East + + align:start position:0% +supply curve like war in the Middle East + + + align:start position:0% +supply curve like war in the Middle East +so this is the question here why + + align:start position:0% +so this is the question here why + + + align:start position:0% +so this is the question here why +wouldn't gas just be perfectly inelastic + + align:start position:0% +wouldn't gas just be perfectly inelastic + + + align:start position:0% +wouldn't gas just be perfectly inelastic +Allah demand in fact in the short-run + + align:start position:0% +Allah demand in fact in the short-run + + + align:start position:0% +Allah demand in fact in the short-run +gases + + align:start position:0% +gases + + + align:start position:0% +gases +actually pretty you know elastically + + align:start position:0% +actually pretty you know elastically + + + align:start position:0% +actually pretty you know elastically +demanded okay it's not perfectly + + align:start position:0% +demanded okay it's not perfectly + + + align:start position:0% +demanded okay it's not perfectly +inelastic but it's pretty inelastic okay + + align:start position:0% +inelastic but it's pretty inelastic okay + + + align:start position:0% +inelastic but it's pretty inelastic okay +so in that case you would see just + + align:start position:0% +so in that case you would see just + + + align:start position:0% +so in that case you would see just +prices going up and quantities wouldn't + + align:start position:0% +prices going up and quantities wouldn't + + + align:start position:0% +prices going up and quantities wouldn't +change now in the long run do we think + + align:start position:0% +change now in the long run do we think + + + align:start position:0% +change now in the long run do we think +the elasticity for gas will be higher or + + align:start position:0% +the elasticity for gas will be higher or + + + align:start position:0% +the elasticity for gas will be higher or +lower than the short-run the demand + + align:start position:0% +lower than the short-run the demand + + + align:start position:0% +lower than the short-run the demand +elasticity for gas hi somebody somebody + + align:start position:0% +elasticity for gas hi somebody somebody + + + align:start position:0% +elasticity for gas hi somebody somebody +graze their hand tell me why so every + + align:start position:0% +graze their hand tell me why so every + + + align:start position:0% +graze their hand tell me why so every +second tell me why somebody else besides + + align:start position:0% +second tell me why somebody else besides + + + align:start position:0% +second tell me why somebody else besides +people always answer questions yeah + + align:start position:0% +people always answer questions yeah + + + align:start position:0% +people always answer questions yeah +people can shift towards electric cars + + align:start position:0% +people can shift towards electric cars + + + align:start position:0% +people can shift towards electric cars +exactly in the short-run all you can do + + align:start position:0% +exactly in the short-run all you can do + + + align:start position:0% +exactly in the short-run all you can do +is drive less and we got to drive to + + align:start position:0% +is drive less and we got to drive to + + + align:start position:0% +is drive less and we got to drive to +work and stuff like that in the long run + + align:start position:0% +work and stuff like that in the long run + + + align:start position:0% +work and stuff like that in the long run +I can buy a different car so it's an + + align:start position:0% +I can buy a different car so it's an + + + align:start position:0% +I can buy a different car so it's an +example of long run versus short run how + + align:start position:0% +example of long run versus short run how + + + align:start position:0% +example of long run versus short run how +it can affect these elasticity's okay + + align:start position:0% +it can affect these elasticity's okay + + + align:start position:0% +it can affect these elasticity's okay +now let's think instead about a + + align:start position:0% +now let's think instead about a + + + align:start position:0% +now let's think instead about a +perfectly perfectly elastic demand the + + align:start position:0% +perfectly perfectly elastic demand the + + + align:start position:0% +perfectly perfectly elastic demand the +demand for I don't know you know + + align:start position:0% +demand for I don't know you know + + + align:start position:0% +demand for I don't know you know +tchotchkes in a market or something like + + align:start position:0% +tchotchkes in a market or something like + + + align:start position:0% +tchotchkes in a market or something like +that okay perfectly elastic demand in + + align:start position:0% +that okay perfectly elastic demand in + + + align:start position:0% +that okay perfectly elastic demand in +figure 9 it's always hard to think of + + align:start position:0% +figure 9 it's always hard to think of + + + align:start position:0% +figure 9 it's always hard to think of +markets with probably lasted man it's + + align:start position:0% +markets with probably lasted man it's + + + align:start position:0% +markets with probably lasted man it's +easy to think about firms having perfect + + align:start position:0% +easy to think about firms having perfect + + + align:start position:0% +easy to think about firms having perfect +elastic demand it's hard to think about + + align:start position:0% +elastic demand it's hard to think about + + + align:start position:0% +elastic demand it's hard to think about +markets but think about a market for a + + align:start position:0% +markets but think about a market for a + + + align:start position:0% +markets but think about a market for a +certain kind of candy okay well there's + + align:start position:0% +certain kind of candy okay well there's + + + align:start position:0% +certain kind of candy okay well there's +another kind of cane that's just as good + + align:start position:0% +another kind of cane that's just as good + + + align:start position:0% +another kind of cane that's just as good +okay so those are markets which are + + align:start position:0% +okay so those are markets which are + + + align:start position:0% +okay so those are markets which are +fairly elastically demanded okay there + + align:start position:0% +fairly elastically demanded okay there + + + align:start position:0% +fairly elastically demanded okay there +you see when the supply ships price + + align:start position:0% +you see when the supply ships price + + + align:start position:0% +you see when the supply ships price +doesn't change only quantity does and + + align:start position:0% +doesn't change only quantity does and + + + align:start position:0% +doesn't change only quantity does and +why is that that's when the demand is + + align:start position:0% +why is that that's when the demand is + + + align:start position:0% +why is that that's when the demand is +perfectly elastic you can't change the + + align:start position:0% +perfectly elastic you can't change the + + + align:start position:0% +perfectly elastic you can't change the +price if you try to raise price by one + + align:start position:0% +price if you try to raise price by one + + + align:start position:0% +price if you try to raise price by one +penny you'll lose the entire market if + + align:start position:0% +penny you'll lose the entire market if + + + align:start position:0% +penny you'll lose the entire market if +you lower the price by one penny you + + align:start position:0% +you lower the price by one penny you + + + align:start position:0% +you lower the price by one penny you +gain the entire market and then you'll + + align:start position:0% +gain the entire market and then you'll + + + align:start position:0% +gain the entire market and then you'll +your profits will go away because your + + align:start position:0% +your profits will go away because your + + + align:start position:0% +your profits will go away because your +marginal cost will be through the roof + + align:start position:0% +marginal cost will be through the roof + + + align:start position:0% +marginal cost will be through the roof +okay so with perfectly elastic demand + + align:start position:0% +okay so with perfectly elastic demand + + + align:start position:0% +okay so with perfectly elastic demand +okay you're gonna get prices fixed but + + align:start position:0% +okay you're gonna get prices fixed but + + + align:start position:0% +okay you're gonna get prices fixed but +only quantity changes okay so basically + + align:start position:0% +only quantity changes okay so basically + + + align:start position:0% +only quantity changes okay so basically +that's sort of how we think about these + + align:start position:0% +that's sort of how we think about these + + + align:start position:0% +that's sort of how we think about these +extremes the bottom line is that's how + + align:start position:0% +extremes the bottom line is that's how + + + align:start position:0% +extremes the bottom line is that's how +the shapes of supply and demand will + + align:start position:0% +the shapes of supply and demand will + + + align:start position:0% +the shapes of supply and demand will +affect the response to shocks okay the + + align:start position:0% +affect the response to shocks okay the + + + align:start position:0% +affect the response to shocks okay the +more elastically the more elastic is + + align:start position:0% +more elastically the more elastic is + + + align:start position:0% +more elastically the more elastic is +demand the more price shock will come + + align:start position:0% +demand the more price shock will come + + + align:start position:0% +demand the more price shock will come +through in quantity and lessen prices + + align:start position:0% +through in quantity and lessen prices + + + align:start position:0% +through in quantity and lessen prices +the more inelastic is demand the more + + align:start position:0% +the more inelastic is demand the more + + + align:start position:0% +the more inelastic is demand the more +supply shock will come through in prices + + align:start position:0% +supply shock will come through in prices + + + align:start position:0% +supply shock will come through in prices +in nom in quantity okay any questions + + align:start position:0% +in nom in quantity okay any questions + + + align:start position:0% +in nom in quantity okay any questions +about that okay so now let's go on to + + align:start position:0% +about that okay so now let's go on to + + + align:start position:0% +about that okay so now let's go on to +what we can do with the supply and + + align:start position:0% +what we can do with the supply and + + + align:start position:0% +what we can do with the supply and +demand curve so now we're where the + + align:start position:0% +demand curve so now we're where the + + + align:start position:0% +demand curve so now we're where the +Masters is applying two-man curves we + + align:start position:0% +Masters is applying two-man curves we + + + align:start position:0% +Masters is applying two-man curves we +know where they come from we know why + + align:start position:0% +know where they come from we know why + + + align:start position:0% +know where they come from we know why +they shape the way they do we + + align:start position:0% +they shape the way they do we + + + align:start position:0% +they shape the way they do we +what happens when they shift and we know + + align:start position:0% +what happens when they shift and we know + + + align:start position:0% +what happens when they shift and we know +what happens how that shift depends on + + align:start position:0% +what happens how that shift depends on + + + align:start position:0% +what happens how that shift depends on +their shapes so we own supply and demand + + align:start position:0% +their shapes so we own supply and demand + + + align:start position:0% +their shapes so we own supply and demand +curves now let's say what can we do with + + align:start position:0% +curves now let's say what can we do with + + + align:start position:0% +curves now let's say what can we do with +them and what we can do with them is use + + align:start position:0% +them and what we can do with them is use + + + align:start position:0% +them and what we can do with them is use +them to take the next step in this class + + align:start position:0% +them to take the next step in this class + + + align:start position:0% +them to take the next step in this class +from positive to normative economics so + + align:start position:0% +from positive to normative economics so + + + align:start position:0% +from positive to normative economics so +far this class has been completely + + align:start position:0% +far this class has been completely + + + align:start position:0% +far this class has been completely +focused on positive economics why do + + align:start position:0% +focused on positive economics why do + + + align:start position:0% +focused on positive economics why do +firms behave the way they do + + align:start position:0% +firms behave the way they do + + + align:start position:0% +firms behave the way they do +why do consumers behave the way they do + + align:start position:0% +why do consumers behave the way they do + + + align:start position:0% +why do consumers behave the way they do +and we haven't talked at all about + + align:start position:0% +and we haven't talked at all about + + + align:start position:0% +and we haven't talked at all about +whether it's a good thing or a bad thing + + align:start position:0% +whether it's a good thing or a bad thing + + + align:start position:0% +whether it's a good thing or a bad thing +well we need a new set of tools if we're + + align:start position:0% +well we need a new set of tools if we're + + + align:start position:0% +well we need a new set of tools if we're +gonna move from positive economics about + + align:start position:0% +gonna move from positive economics about + + + align:start position:0% +gonna move from positive economics about +why things the way things are turn or + + align:start position:0% +why things the way things are turn or + + + align:start position:0% +why things the way things are turn or +what if he connects about the way they + + align:start position:0% +what if he connects about the way they + + + align:start position:0% +what if he connects about the way they +should be okay and those set of tools + + align:start position:0% +should be okay and those set of tools + + + align:start position:0% +should be okay and those set of tools +were going to derive from supply and + + align:start position:0% +were going to derive from supply and + + + align:start position:0% +were going to derive from supply and +demand curves and this is critically + + align:start position:0% +demand curves and this is critically + + + align:start position:0% +demand curves and this is critically +important because for example let's take + + align:start position:0% +important because for example let's take + + + align:start position:0% +important because for example let's take +where we ended the last lecture or the + + align:start position:0% +where we ended the last lecture or the + + + align:start position:0% +where we ended the last lecture or the +lectures last lecture I think talking + + align:start position:0% +lectures last lecture I think talking + + + align:start position:0% +lectures last lecture I think talking +about how with perfectly or middle last + + align:start position:0% +about how with perfectly or middle last + + + align:start position:0% +about how with perfectly or middle last +lecture talking about on a perfectly + + align:start position:0% +lecture talking about on a perfectly + + + align:start position:0% +lecture talking about on a perfectly +competitive market under a set of + + align:start position:0% +competitive market under a set of + + + align:start position:0% +competitive market under a set of +assumptions all firms as you're a profit + + align:start position:0% +assumptions all firms as you're a profit + + + align:start position:0% +assumptions all firms as you're a profit +in the long run okay so we you buy that + + align:start position:0% +in the long run okay so we you buy that + + + align:start position:0% +in the long run okay so we you buy that +that's but you have to ask tough is that + + align:start position:0% +that's but you have to ask tough is that + + + align:start position:0% +that's but you have to ask tough is that +a good thing or a bad thing it's zero + + align:start position:0% +a good thing or a bad thing it's zero + + + align:start position:0% +a good thing or a bad thing it's zero +profits long run good or bad well on the + + align:start position:0% +profits long run good or bad well on the + + + align:start position:0% +profits long run good or bad well on the +one hand firms are cost minimizing + + align:start position:0% +one hand firms are cost minimizing + + + align:start position:0% +one hand firms are cost minimizing +that's good on the other hand why would + + align:start position:0% +that's good on the other hand why would + + + align:start position:0% +that's good on the other hand why would +anyone start a business in the long run + + align:start position:0% +anyone start a business in the long run + + + align:start position:0% +anyone start a business in the long run +they're gonna make no money that's bad + + align:start position:0% +they're gonna make no money that's bad + + + align:start position:0% +they're gonna make no money that's bad +so how do we think about trading those + + align:start position:0% +so how do we think about trading those + + + align:start position:0% +so how do we think about trading those +things off how do we think about whether + + align:start position:0% +things off how do we think about whether + + + align:start position:0% +things off how do we think about whether +it's a good idea or bad to have long run + + align:start position:0% +it's a good idea or bad to have long run + + + align:start position:0% +it's a good idea or bad to have long run +zero profits okay this is the question + + align:start position:0% +zero profits okay this is the question + + + align:start position:0% +zero profits okay this is the question +these this set of questions is what we + + align:start position:0% +these this set of questions is what we + + + align:start position:0% +these this set of questions is what we +turn to with with the notion of welfare + + align:start position:0% +turn to with with the notion of welfare + + + align:start position:0% +turn to with with the notion of welfare +economics welfare now welfare what's + + align:start position:0% +economics welfare now welfare what's + + + align:start position:0% +economics welfare now welfare what's +going to be used in two senses in this + + align:start position:0% +going to be used in two senses in this + + + align:start position:0% +going to be used in two senses in this +class mostly when I say welfare I'll + + align:start position:0% +class mostly when I say welfare I'll + + + align:start position:0% +class mostly when I say welfare I'll +mean as a measure of well-being most + + align:start position:0% +mean as a measure of well-being most + + + align:start position:0% +mean as a measure of well-being most +what I say welfare I mean welfare is + + align:start position:0% +what I say welfare I mean welfare is + + + align:start position:0% +what I say welfare I mean welfare is +well-being sometimes we say welfare we + + align:start position:0% +well-being sometimes we say welfare we + + + align:start position:0% +well-being sometimes we say welfare we +mean cash payments to poor people + + align:start position:0% +mean cash payments to poor people + + + align:start position:0% +mean cash payments to poor people +that's like welfare payments that's not + + align:start position:0% +that's like welfare payments that's not + + + align:start position:0% +that's like welfare payments that's not +what I mean usually when I say welfare + + align:start position:0% +what I mean usually when I say welfare + + + align:start position:0% +what I mean usually when I say welfare +I'll try to distinguish I mean the other + + align:start position:0% +I'll try to distinguish I mean the other + + + align:start position:0% +I'll try to distinguish I mean the other +thing when I say welfare I don't mean + + align:start position:0% +thing when I say welfare I don't mean + + + align:start position:0% +thing when I say welfare I don't mean +the way it's used in a political debate + + align:start position:0% +the way it's used in a political debate + + + align:start position:0% +the way it's used in a political debate +meaning cash payments to poor people + + align:start position:0% +meaning cash payments to poor people + + + align:start position:0% +meaning cash payments to poor people +I mean welfare is a measure of + + align:start position:0% +I mean welfare is a measure of + + + align:start position:0% +I mean welfare is a measure of +well-being and welfare economics is the + + align:start position:0% +well-being and welfare economics is the + + + align:start position:0% +well-being and welfare economics is the +tools of normative analysis the tools of + + align:start position:0% +tools of normative analysis the tools of + + + align:start position:0% +tools of normative analysis the tools of +well freakin dogs the tools of measuring + + align:start position:0% + + + + align:start position:0% + +well being and we're gonna start by + + align:start position:0% +well being and we're gonna start by + + + align:start position:0% +well being and we're gonna start by +talking about the concept of consumer + + align:start position:0% +talking about the concept of consumer + + + align:start position:0% +talking about the concept of consumer +surplus it's gonna be the first thing + + align:start position:0% +surplus it's gonna be the first thing + + + align:start position:0% +surplus it's gonna be the first thing +we're gonna use when we talk about + + align:start position:0% +we're gonna use when we talk about + + + align:start position:0% +we're gonna use when we talk about +welfare economics is consumer surplus + + align:start position:0% +welfare economics is consumer surplus + + + align:start position:0% +welfare economics is consumer surplus +okay now if we want to measure + + align:start position:0% +okay now if we want to measure + + + align:start position:0% +okay now if we want to measure +well-being however we have a problem + + align:start position:0% +well-being however we have a problem + + + align:start position:0% +well-being however we have a problem +which is how do you measure how happy I + + align:start position:0% +which is how do you measure how happy I + + + align:start position:0% +which is how do you measure how happy I +am my noodles but you don't exist so + + align:start position:0% +am my noodles but you don't exist so + + + align:start position:0% +am my noodles but you don't exist so +I've got a fundamental challenge here + + align:start position:0% +I've got a fundamental challenge here + + + align:start position:0% +I've got a fundamental challenge here +which is our indicator of well-being as + + align:start position:0% +which is our indicator of well-being as + + + align:start position:0% +which is our indicator of well-being as +utility function which isn't a real + + align:start position:0% +utility function which isn't a real + + + align:start position:0% +utility function which isn't a real +thing + + align:start position:0% +thing + + + align:start position:0% +thing +okay we use it to derive decisions but + + align:start position:0% +okay we use it to derive decisions but + + + align:start position:0% +okay we use it to derive decisions but +we don't actually have a measure of + + align:start position:0% +we don't actually have a measure of + + + align:start position:0% +we don't actually have a measure of +well-being that gives real meaningful + + align:start position:0% +well-being that gives real meaningful + + + align:start position:0% +well-being that gives real meaningful +inputs so what do we do we you a clever + + align:start position:0% +inputs so what do we do we you a clever + + + align:start position:0% +inputs so what do we do we you a clever +thing economists thought of a long time + + align:start position:0% +thing economists thought of a long time + + + align:start position:0% +thing economists thought of a long time +ago which is to use the concept of + + align:start position:0% +ago which is to use the concept of + + + align:start position:0% +ago which is to use the concept of +compensating variation the concept of + + align:start position:0% +compensating variation the concept of + + + align:start position:0% +compensating variation the concept of +compensating variation was that concept + + align:start position:0% +compensating variation was that concept + + + align:start position:0% +compensating variation was that concept +means that means that instead of asking + + align:start position:0% +means that means that instead of asking + + + align:start position:0% +means that means that instead of asking +you how happy you are I ask you how much + + align:start position:0% +you how happy you are I ask you how much + + + align:start position:0% +you how happy you are I ask you how much +would I have to pay you to become less + + align:start position:0% +would I have to pay you to become less + + + align:start position:0% +would I have to pay you to become less +set to become sadder or how much would + + align:start position:0% +set to become sadder or how much would + + + align:start position:0% +set to become sadder or how much would +you be willing to pay to be happier so I + + align:start position:0% +you be willing to pay to be happier so I + + + align:start position:0% +you be willing to pay to be happier so I +can't measure margin jillion dollars but + + align:start position:0% +can't measure margin jillion dollars but + + + align:start position:0% +can't measure margin jillion dollars but +I can measure how many dollars you would + + align:start position:0% +I can measure how many dollars you would + + + align:start position:0% +I can measure how many dollars you would +pay to buy the next good or how many + + align:start position:0% +pay to buy the next good or how many + + + align:start position:0% +pay to buy the next good or how many +dollars you pay me not to be punched or + + align:start position:0% +dollars you pay me not to be punched or + + + align:start position:0% +dollars you pay me not to be punched or +whatever okay I can basically measure + + align:start position:0% +whatever okay I can basically measure + + + align:start position:0% +whatever okay I can basically measure +those things by essentially ask asking + + align:start position:0% +those things by essentially ask asking + + + align:start position:0% +those things by essentially ask asking +you how much would you pay to be better + + align:start position:0% +you how much would you pay to be better + + + align:start position:0% +you how much would you pay to be better +off or how much would you be willing to + + align:start position:0% +off or how much would you be willing to + + + align:start position:0% +off or how much would you be willing to +pay not to be worse off and those are + + align:start position:0% +pay not to be worse off and those are + + + align:start position:0% +pay not to be worse off and those are +what we call dative compensating + + align:start position:0% +what we call dative compensating + + + align:start position:0% +what we call dative compensating +variation we measure your well-being by + + align:start position:0% +variation we measure your well-being by + + + align:start position:0% +variation we measure your well-being by +the money equivalent that you give to us + + align:start position:0% +the money equivalent that you give to us + + + align:start position:0% +the money equivalent that you give to us +okay in expressing your preferences and + + align:start position:0% +okay in expressing your preferences and + + + align:start position:0% +okay in expressing your preferences and +what we can then define consumer surplus + + align:start position:0% +what we can then define consumer surplus + + + align:start position:0% +what we can then define consumer surplus +will define consumer surplus which is + + align:start position:0% +will define consumer surplus which is + + + align:start position:0% +will define consumer surplus which is +our first measure of normative welfare + + align:start position:0% +our first measure of normative welfare + + + align:start position:0% +our first measure of normative welfare +economics as the benefit that it + + align:start position:0% +economics as the benefit that it + + + align:start position:0% +economics as the benefit that it +consumer gets from consuming a good + + align:start position:0% +consumer gets from consuming a good + + + align:start position:0% +consumer gets from consuming a good +above and beyond the price of that good + + align:start position:0% +above and beyond the price of that good + + + align:start position:0% +above and beyond the price of that good +the benefit that a consumer gets from + + align:start position:0% +the benefit that a consumer gets from + + + align:start position:0% +the benefit that a consumer gets from +consuming a good above and beyond what + + align:start position:0% +consuming a good above and beyond what + + + align:start position:0% +consuming a good above and beyond what +they + + align:start position:0% +they + + + align:start position:0% +they +for that good that's consumer surplus + + align:start position:0% +for that good that's consumer surplus + + + align:start position:0% +for that good that's consumer surplus +surplus means extra right so it's your + + align:start position:0% +surplus means extra right so it's your + + + align:start position:0% +surplus means extra right so it's your +extra it's how much more you get that + + align:start position:0% +extra it's how much more you get that + + + align:start position:0% +extra it's how much more you get that +when you had what you actually had to + + align:start position:0% +when you had what you actually had to + + + align:start position:0% +when you had what you actually had to +pay to get the good in the first place + + align:start position:0% +pay to get the good in the first place + + + align:start position:0% +pay to get the good in the first place +okay so basically um consider my + + align:start position:0% +okay so basically um consider my + + + align:start position:0% +okay so basically um consider my +daughter's demand for songs by Kendrick + + align:start position:0% +daughter's demand for songs by Kendrick + + + align:start position:0% +daughter's demand for songs by Kendrick +Lamar + + align:start position:0% +Lamar + + + align:start position:0% +Lamar +okay um let's and let's to make life + + align:start position:0% +okay um let's and let's to make life + + + align:start position:0% +okay um let's and let's to make life +easy let's say this is pre streaming and + + align:start position:0% +easy let's say this is pre streaming and + + + align:start position:0% +easy let's say this is pre streaming and +songs cost a dollar okay so she wants + + align:start position:0% +songs cost a dollar okay so she wants + + + align:start position:0% +songs cost a dollar okay so she wants +songs by Kendrick Lamar it's actually so + + align:start position:0% +songs by Kendrick Lamar it's actually so + + + align:start position:0% +songs by Kendrick Lamar it's actually so +let's actually yeah see what sort of + + align:start position:0% +let's actually yeah see what sort of + + + align:start position:0% +let's actually yeah see what sort of +icons Lamar and there's no streaming and + + align:start position:0% +icons Lamar and there's no streaming and + + + align:start position:0% +icons Lamar and there's no streaming and +she and the songs cost a dollar so if my + + align:start position:0% +she and the songs cost a dollar so if my + + + align:start position:0% +she and the songs cost a dollar so if my +daughter's willing to pay a dollar for + + align:start position:0% +daughter's willing to pay a dollar for + + + align:start position:0% +daughter's willing to pay a dollar for +Kendrick Lamar song and it costs a + + align:start position:0% +Kendrick Lamar song and it costs a + + + align:start position:0% +Kendrick Lamar song and it costs a +dollar then her consumer surplus is zero + + align:start position:0% +dollar then her consumer surplus is zero + + + align:start position:0% +dollar then her consumer surplus is zero +she's will heard the benefit she gets + + align:start position:0% +she's will heard the benefit she gets + + + align:start position:0% +she's will heard the benefit she gets +from the song as a dollar it costs a + + align:start position:0% +from the song as a dollar it costs a + + + align:start position:0% +from the song as a dollar it costs a +dollar her zero but if she was willing + + align:start position:0% +dollar her zero but if she was willing + + + align:start position:0% +dollar her zero but if she was willing +to pay two dollars for Kendrick Lamar + + align:start position:0% +to pay two dollars for Kendrick Lamar + + + align:start position:0% +to pay two dollars for Kendrick Lamar +song and all it cost a dollar then she's + + align:start position:0% +song and all it cost a dollar then she's + + + align:start position:0% +song and all it cost a dollar then she's +got a dollar in surplus okay so + + align:start position:0% +got a dollar in surplus okay so + + + align:start position:0% +got a dollar in surplus okay so +basically the key thing is to define + + align:start position:0% +basically the key thing is to define + + + align:start position:0% +basically the key thing is to define +consumer surplus we need two things the + + align:start position:0% +consumer surplus we need two things the + + + align:start position:0% +consumer surplus we need two things the +price and the willingness to pay well + + align:start position:0% +price and the willingness to pay well + + + align:start position:0% +price and the willingness to pay well +how the hell do we get willingness to + + align:start position:0% +how the hell do we get willingness to + + + align:start position:0% +how the hell do we get willingness to +pay where does that come from some raise + + align:start position:0% +pay where does that come from some raise + + + align:start position:0% +pay where does that come from some raise +their head and tell me yeah the demand + + align:start position:0% +their head and tell me yeah the demand + + + align:start position:0% +their head and tell me yeah the demand +curve we are defined it we are defined + + align:start position:0% +curve we are defined it we are defined + + + align:start position:0% +curve we are defined it we are defined +what will is toupees it's the demand + + align:start position:0% +what will is toupees it's the demand + + + align:start position:0% +what will is toupees it's the demand +curve so consumer surplus is simply + + align:start position:0% +curve so consumer surplus is simply + + + align:start position:0% +curve so consumer surplus is simply +defined as the area below the demand + + align:start position:0% +defined as the area below the demand + + + align:start position:0% +defined as the area below the demand +curve above the price because that tells + + align:start position:0% +curve above the price because that tells + + + align:start position:0% +curve above the price because that tells +you the demand curve tells you how much + + align:start position:0% +you the demand curve tells you how much + + + align:start position:0% +you the demand curve tells you how much +you're willing to pay for each unit the + + align:start position:0% +you're willing to pay for each unit the + + + align:start position:0% +you're willing to pay for each unit the +price new face tells you how much you + + align:start position:0% +price new face tells you how much you + + + align:start position:0% +price new face tells you how much you +had to pay so any gap between them is + + align:start position:0% +had to pay so any gap between them is + + + align:start position:0% +had to pay so any gap between them is +consumer surplus okay so let's go to + + align:start position:0% +consumer surplus okay so let's go to + + + align:start position:0% +consumer surplus okay so let's go to +figure nine six let's do my daughter's + + align:start position:0% +figure nine six let's do my daughter's + + + align:start position:0% +figure nine six let's do my daughter's +demand for Kendrick Lamar songs okay + + align:start position:0% + + + + align:start position:0% + +let's say that her demand is such that + + align:start position:0% +let's say that her demand is such that + + + align:start position:0% +let's say that her demand is such that +now once again the trick here is we've + + align:start position:0% +now once again the trick here is we've + + + align:start position:0% +now once again the trick here is we've +drawn a continuous demand curve it's a + + align:start position:0% +drawn a continuous demand curve it's a + + + align:start position:0% +drawn a continuous demand curve it's a +discrete decision so sort of bear with + + align:start position:0% +discrete decision so sort of bear with + + + align:start position:0% +discrete decision so sort of bear with +me the numbers you know bear with me as + + align:start position:0% +me the numbers you know bear with me as + + + align:start position:0% +me the numbers you know bear with me as +you think about this but roughly + + align:start position:0% +you think about this but roughly + + + align:start position:0% +you think about this but roughly +speaking she's willing to pay for the + + align:start position:0% +speaking she's willing to pay for the + + + align:start position:0% +speaking she's willing to pay for the +first Kendrick Lamar song + + align:start position:0% +first Kendrick Lamar song + + + align:start position:0% +first Kendrick Lamar song +between four and five dollars okay for + + align:start position:0% +between four and five dollars okay for + + + align:start position:0% +between four and five dollars okay for +the next Kendrick Lamar song's gonna pay + + align:start position:0% +the next Kendrick Lamar song's gonna pay + + + align:start position:0% +the next Kendrick Lamar song's gonna pay +between three and four dollars for the-- + + align:start position:0% +between three and four dollars for the-- + + + align:start position:0% +between three and four dollars for the-- +and so on + + align:start position:0% +and so on + + + align:start position:0% +and so on +so this gives you so let's to make life + + align:start position:0% +so this gives you so let's to make life + + + align:start position:0% +so this gives you so let's to make life +easy let's imagine willing to pay four + + align:start position:0% +easy let's imagine willing to pay four + + + align:start position:0% +easy let's imagine willing to pay four +dollars for the first Kendrick Lamar + + align:start position:0% +dollars for the first Kendrick Lamar + + + align:start position:0% +dollars for the first Kendrick Lamar +song three dollars for the second + + align:start position:0% +song three dollars for the second + + + align:start position:0% +song three dollars for the second +Kendrick Lamar song two dollars for the + + align:start position:0% +Kendrick Lamar song two dollars for the + + + align:start position:0% +Kendrick Lamar song two dollars for the +third Kendrick Lamar song and four + + align:start position:0% +third Kendrick Lamar song and four + + + align:start position:0% +third Kendrick Lamar song and four +dollars for the first country and four + + align:start position:0% +dollars for the first country and four + + + align:start position:0% +dollars for the first country and four +I'm sorry in one dollar for the fourth + + align:start position:0% +I'm sorry in one dollar for the fourth + + + align:start position:0% +I'm sorry in one dollar for the fourth +Kendrick Lamar song okay so imagine + + align:start position:0% +Kendrick Lamar song okay so imagine + + + align:start position:0% +Kendrick Lamar song okay so imagine +that's basically her demand curve it's + + align:start position:0% +that's basically her demand curve it's + + + align:start position:0% +that's basically her demand curve it's +not quite that discreet but we could + + align:start position:0% +not quite that discreet but we could + + + align:start position:0% +not quite that discreet but we could +make it stepwise if you want just be + + align:start position:0% +make it stepwise if you want just be + + + align:start position:0% +make it stepwise if you want just be +ugly-looking okay + + align:start position:0% +ugly-looking okay + + + align:start position:0% +ugly-looking okay +so that's her demand curve so what does + + align:start position:0% +so that's her demand curve so what does + + + align:start position:0% +so that's her demand curve so what does +that mean that means that when she buys + + align:start position:0% +that mean that means that when she buys + + + align:start position:0% +that mean that means that when she buys +the fourth Kendrick Lamar song okay when + + align:start position:0% +the fourth Kendrick Lamar song okay when + + + align:start position:0% +the fourth Kendrick Lamar song okay when +she buys King [ __ ] or whatever that is + + align:start position:0% +she buys King [ __ ] or whatever that is + + + align:start position:0% +she buys King [ __ ] or whatever that is +zero surplus okay zero surplus she was + + align:start position:0% +zero surplus okay zero surplus she was + + + align:start position:0% +zero surplus okay zero surplus she was +willing to pay a dollar for King Kunta + + align:start position:0% +willing to pay a dollar for King Kunta + + + align:start position:0% +willing to pay a dollar for King Kunta +and she and it cost a dollar so she's + + align:start position:0% +and she and it cost a dollar so she's + + + align:start position:0% +and she and it cost a dollar so she's +done okay however what does that mean + + align:start position:0% +done okay however what does that mean + + + align:start position:0% +done okay however what does that mean +that means when she bought Humble which + + align:start position:0% +that means when she bought Humble which + + + align:start position:0% +that means when she bought Humble which +was her first chor song okay she gained + + align:start position:0% +was her first chor song okay she gained + + + align:start position:0% +was her first chor song okay she gained +a surplus because she paid a dollar for + + align:start position:0% +a surplus because she paid a dollar for + + + align:start position:0% +a surplus because she paid a dollar for +that + + align:start position:0% +that + + + align:start position:0% +that +but she was willing to pay four dollars + + align:start position:0% +but she was willing to pay four dollars + + + align:start position:0% +but she was willing to pay four dollars +for it so she gained a surplus and the + + align:start position:0% +for it so she gained a surplus and the + + + align:start position:0% +for it so she gained a surplus and the +surplus is the difference between what + + align:start position:0% +surplus is the difference between what + + + align:start position:0% +surplus is the difference between what +she paid which is represented by the + + align:start position:0% +she paid which is represented by the + + + align:start position:0% +she paid which is represented by the +horizontal line and a dollar and what + + align:start position:0% +horizontal line and a dollar and what + + + align:start position:0% +horizontal line and a dollar and what +she was willing to pay which is a demand + + align:start position:0% +she was willing to pay which is a demand + + + align:start position:0% +she was willing to pay which is a demand +curve which is four dollars so she + + align:start position:0% +curve which is four dollars so she + + + align:start position:0% +curve which is four dollars so she +gained that surplus yeah it's a great + + align:start position:0% +gained that surplus yeah it's a great + + + align:start position:0% +gained that surplus yeah it's a great +question is a famous article about that + + align:start position:0% +question is a famous article about that + + + align:start position:0% +question is a famous article about that +I'll come back to that in one minute let + + align:start position:0% +I'll come back to that in one minute let + + + align:start position:0% +I'll come back to that in one minute let +me finish this the bottom line is the + + align:start position:0% +me finish this the bottom line is the + + + align:start position:0% +me finish this the bottom line is the +surplus there's been what she was + + align:start position:0% +surplus there's been what she was + + + align:start position:0% +surplus there's been what she was +willing to pay and what she had to pay + + align:start position:0% +willing to pay and what she had to pay + + + align:start position:0% +willing to pay and what she had to pay +which in the continuous example is this + + align:start position:0% +which in the continuous example is this + + + align:start position:0% +which in the continuous example is this +entire triangle think of by being able + + align:start position:0% +entire triangle think of by being able + + + align:start position:0% +entire triangle think of by being able +to buy fractions of songs + + align:start position:0% +to buy fractions of songs + + + align:start position:0% +to buy fractions of songs +okay little little bits ringtones or + + align:start position:0% +okay little little bits ringtones or + + + align:start position:0% +okay little little bits ringtones or +whatever okay fractions of songs okay + + align:start position:0% +whatever okay fractions of songs okay + + + align:start position:0% +whatever okay fractions of songs okay +then this entire area under the curve + + align:start position:0% +then this entire area under the curve + + + align:start position:0% +then this entire area under the curve +above the price is her surplus she was + + align:start position:0% +above the price is her surplus she was + + + align:start position:0% +above the price is her surplus she was +willing to pay the points on the curve + + align:start position:0% +willing to pay the points on the curve + + + align:start position:0% +willing to pay the points on the curve +she only had to pay the flat line at a + + align:start position:0% +she only had to pay the flat line at a + + + align:start position:0% +she only had to pay the flat line at a +dollar so the entire difference is her + + align:start position:0% +dollar so the entire difference is her + + + align:start position:0% +dollar so the entire difference is her +surplus + + align:start position:0% +surplus + + + align:start position:0% +surplus +okay the key point is this is all driven + + align:start position:0% +okay the key point is this is all driven + + + align:start position:0% +okay the key point is this is all driven +by diminishing marginal utility that is + + align:start position:0% +by diminishing marginal utility that is + + + align:start position:0% +by diminishing marginal utility that is +the reason her surplus goes to zero or + + align:start position:0% +the reason her surplus goes to zero or + + + align:start position:0% +the reason her surplus goes to zero or +eventually is because eventually gets + + align:start position:0% +eventually is because eventually gets + + + align:start position:0% +eventually is because eventually gets +tired of Kendrick Lamar songs so it goes + + align:start position:0% +tired of Kendrick Lamar songs so it goes + + + align:start position:0% +tired of Kendrick Lamar songs so it goes +down we have diminishing margin Chile + + align:start position:0% +down we have diminishing margin Chile + + + align:start position:0% +down we have diminishing margin Chile +for the songs and that's why we get + + align:start position:0% +for the songs and that's why we get + + + align:start position:0% +for the songs and that's why we get +consumer surplus as a triangle it's the + + align:start position:0% +consumer surplus as a triangle it's the + + + align:start position:0% +consumer surplus as a triangle it's the +difference between the downward sloping + + align:start position:0% +difference between the downward sloping + + + align:start position:0% +difference between the downward sloping +demand curve and the flat price line + + align:start position:0% +demand curve and the flat price line + + + align:start position:0% +demand curve and the flat price line +that the consumer faces okay so the + + align:start position:0% +that the consumer faces okay so the + + + align:start position:0% +that the consumer faces okay so the +individual consumer surplus individual + + align:start position:0% +individual consumer surplus individual + + + align:start position:0% +individual consumer surplus individual +consumer surplus okay it's hurt him as + + align:start position:0% +consumer surplus okay it's hurt him as + + + align:start position:0% +consumer surplus okay it's hurt him as +an individual graph okay individual + + align:start position:0% +an individual graph okay individual + + + align:start position:0% +an individual graph okay individual +graph per demand is downward sloping and + + align:start position:0% +graph per demand is downward sloping and + + + align:start position:0% +graph per demand is downward sloping and +therefore her surplus difference between + + align:start position:0% +therefore her surplus difference between + + + align:start position:0% +therefore her surplus difference between +is the area under the demand curve above + + align:start position:0% +is the area under the demand curve above + + + align:start position:0% +is the area under the demand curve above +the price line yeah let's talk about + + align:start position:0% +the price line yeah let's talk about + + + align:start position:0% +the price line yeah let's talk about +that let's let's talk about um actually + + align:start position:0% +that let's let's talk about um actually + + + align:start position:0% +that let's let's talk about um actually +I don't have it here if the man was + + align:start position:0% +I don't have it here if the man was + + + align:start position:0% +I don't have it here if the man was +Hurley inelastic you're absolutely right + + align:start position:0% +Hurley inelastic you're absolutely right + + + align:start position:0% +Hurley inelastic you're absolutely right +the consumer surplus would be infinite + + align:start position:0% +the consumer surplus would be infinite + + + align:start position:0% +the consumer surplus would be infinite +because the area under the demand curve + + align:start position:0% +because the area under the demand curve + + + align:start position:0% +because the area under the demand curve +above the price line would be infinity + + align:start position:0% +above the price line would be infinity + + + align:start position:0% +above the price line would be infinity +to be a rectangle go up to infinity why + + align:start position:0% +to be a rectangle go up to infinity why + + + align:start position:0% +to be a rectangle go up to infinity why +is that why is the consumer surplus + + align:start position:0% +is that why is the consumer surplus + + + align:start position:0% +is that why is the consumer surplus +infinite if demands inelastic because + + align:start position:0% +infinite if demands inelastic because + + + align:start position:0% +infinite if demands inelastic because +they pay anything for it + + align:start position:0% +they pay anything for it + + + align:start position:0% +they pay anything for it +so at any price it's a bargain in theory + + align:start position:0% +so at any price it's a bargain in theory + + + align:start position:0% +so at any price it's a bargain in theory +if you're if you're incredibly rich + + align:start position:0% +if you're if you're incredibly rich + + + align:start position:0% +if you're if you're incredibly rich +diabetic you would pay an infinite + + align:start position:0% +diabetic you would pay an infinite + + + align:start position:0% +diabetic you would pay an infinite +amount to have insulin so at any price + + align:start position:0% +amount to have insulin so at any price + + + align:start position:0% +amount to have insulin so at any price +you're getting huge surplus you're + + align:start position:0% +you're getting huge surplus you're + + + align:start position:0% +you're getting huge surplus you're +getting infinite circles infinity minus + + align:start position:0% +getting infinite circles infinity minus + + + align:start position:0% +getting infinite circles infinity minus +anything is infinity likewise what's the + + align:start position:0% +anything is infinity likewise what's the + + + align:start position:0% +anything is infinity likewise what's the +consumer surplus if demand is perfectly + + align:start position:0% +consumer surplus if demand is perfectly + + + align:start position:0% +consumer surplus if demand is perfectly +elastic same person what zero why that's + + align:start position:0% +elastic same person what zero why that's + + + align:start position:0% +elastic same person what zero why that's +graphically why but intuitively why why + + align:start position:0% +graphically why but intuitively why why + + + align:start position:0% +graphically why but intuitively why why +do you get no surplus from a good where + + align:start position:0% +do you get no surplus from a good where + + + align:start position:0% +do you get no surplus from a good where +demands fairly elastic + + align:start position:0% + + + + align:start position:0% + +what what makes a perfectly elastic + + align:start position:0% +what what makes a perfectly elastic + + + align:start position:0% +what what makes a perfectly elastic +demand curve because why as their + + align:start position:0% +demand curve because why as their + + + align:start position:0% +demand curve because why as their +substitutes that you're indifferent + + align:start position:0% +substitutes that you're indifferent + + + align:start position:0% +substitutes that you're indifferent +towards that's what gets a perfectly + + align:start position:0% +towards that's what gets a perfectly + + + align:start position:0% +towards that's what gets a perfectly +last demand + + align:start position:0% +last demand + + + align:start position:0% +last demand +so if I'm indifferent between jujyfruits + + align:start position:0% +so if I'm indifferent between jujyfruits + + + align:start position:0% +so if I'm indifferent between jujyfruits +god you got spot-on jujyfruits + + align:start position:0% +god you got spot-on jujyfruits + + + align:start position:0% +god you got spot-on jujyfruits +if I'm a different between god only know + + align:start position:0% +if I'm a different between god only know + + + align:start position:0% +if I'm a different between god only know +what candy is anymore + + align:start position:0% +what candy is anymore + + + align:start position:0% +what candy is anymore +whatever I mean everything candy and + + align:start position:0% +whatever I mean everything candy and + + + align:start position:0% +whatever I mean everything candy and +candy be okay and then I get no surplus + + align:start position:0% +candy be okay and then I get no surplus + + + align:start position:0% +candy be okay and then I get no surplus +from consuming candy a why because I'm + + align:start position:0% +from consuming candy a why because I'm + + + align:start position:0% +from consuming candy a why because I'm +equally happy with candy B so candy a + + align:start position:0% +equally happy with candy B so candy a + + + align:start position:0% +equally happy with candy B so candy a +gives me no surplus what is the candy + + align:start position:0% +gives me no surplus what is the candy + + + align:start position:0% +gives me no surplus what is the candy +people eat what do people eat what Jolly + + align:start position:0% +people eat what do people eat what Jolly + + + align:start position:0% +people eat what do people eat what Jolly +ranks I love Jolly Ranchers okay yeah + + align:start position:0% +ranks I love Jolly Ranchers okay yeah + + + align:start position:0% +ranks I love Jolly Ranchers okay yeah +well no but that's that's irrelevant cuz + + align:start position:0% +well no but that's that's irrelevant cuz + + + align:start position:0% +well no but that's that's irrelevant cuz +skittles are just disappointing M&Ms + + align:start position:0% +skittles are just disappointing M&Ms + + + align:start position:0% +skittles are just disappointing M&Ms +let's be honest when you get skittles + + align:start position:0% +let's be honest when you get skittles + + + align:start position:0% +let's be honest when you get skittles +you just pissed off the non M&Ms am i + + align:start position:0% +you just pissed off the non M&Ms am i + + + align:start position:0% +you just pissed off the non M&Ms am i +right I mean skittles is 220 M&Ms so we + + align:start position:0% +right I mean skittles is 220 M&Ms so we + + + align:start position:0% +right I mean skittles is 220 M&Ms so we +can't do that one let's do sort of you + + align:start position:0% +can't do that one let's do sort of you + + + align:start position:0% +can't do that one let's do sort of you +know Jolly Ranchers versus skittles + + align:start position:0% +know Jolly Ranchers versus skittles + + + align:start position:0% +know Jolly Ranchers versus skittles +maybe those are more comparable cuz M&Ms + + align:start position:0% +maybe those are more comparable cuz M&Ms + + + align:start position:0% +maybe those are more comparable cuz M&Ms +are better than everything so basically + + align:start position:0% +are better than everything so basically + + + align:start position:0% +are better than everything so basically +Jolly rationed skittles since I get + + align:start position:0% +Jolly rationed skittles since I get + + + align:start position:0% +Jolly rationed skittles since I get +since I'm indifferent Jolly Ranchers and + + align:start position:0% +since I'm indifferent Jolly Ranchers and + + + align:start position:0% +since I'm indifferent Jolly Ranchers and +skittles I get no surplus trimming the + + align:start position:0% +skittles I get no surplus trimming the + + + align:start position:0% +skittles I get no surplus trimming the +skittles cuz I would Etha happy having a + + align:start position:0% +skittles cuz I would Etha happy having a + + + align:start position:0% +skittles cuz I would Etha happy having a +jolly rancher so surplus is zero for a + + align:start position:0% +jolly rancher so surplus is zero for a + + + align:start position:0% +jolly rancher so surplus is zero for a +perfectly lastly demand good it's + + align:start position:0% +perfectly lastly demand good it's + + + align:start position:0% +perfectly lastly demand good it's +infinite for a perfectly inelastic they + + align:start position:0% +infinite for a perfectly inelastic they + + + align:start position:0% +infinite for a perfectly inelastic they +demand a good okay now let's go back to + + align:start position:0% +demand a good okay now let's go back to + + + align:start position:0% +demand a good okay now let's go back to +the question there's a famous article in + + align:start position:0% +the question there's a famous article in + + + align:start position:0% +the question there's a famous article in +economics called the deadweight loss of + + align:start position:0% +economics called the deadweight loss of + + + align:start position:0% +economics called the deadweight loss of +Christmas we're such an awful profession + + align:start position:0% +Christmas we're such an awful profession + + + align:start position:0% +Christmas we're such an awful profession +based about how terrible gift giving is + + align:start position:0% +based about how terrible gift giving is + + + align:start position:0% +based about how terrible gift giving is +and wise gift giving terrible because if + + align:start position:0% +and wise gift giving terrible because if + + + align:start position:0% +and wise gift giving terrible because if +you gave people cash they could get what + + align:start position:0% +you gave people cash they could get what + + + align:start position:0% +you gave people cash they could get what +they want the most but if you give them + + align:start position:0% +they want the most but if you give them + + + align:start position:0% +they want the most but if you give them +a gift it's by definition lower surplus + + align:start position:0% +a gift it's by definition lower surplus + + + align:start position:0% +a gift it's by definition lower surplus +than the cash because they could always + + align:start position:0% +than the cash because they could always + + + align:start position:0% +than the cash because they could always +go out and buy that good with the cash + + align:start position:0% +go out and buy that good with the cash + + + align:start position:0% +go out and buy that good with the cash +so by definition giving someone a gift + + align:start position:0% +so by definition giving someone a gift + + + align:start position:0% +so by definition giving someone a gift +makes them worse off they giving them + + align:start position:0% +makes them worse off they giving them + + + align:start position:0% +makes them worse off they giving them +that same amount of cash so this guy + + align:start position:0% +that same amount of cash so this guy + + + align:start position:0% +that same amount of cash so this guy +does the interview to all the students I + + align:start position:0% +does the interview to all the students I + + + align:start position:0% +does the interview to all the students I +think was at Penn State and he asked + + align:start position:0% +think was at Penn State and he asked + + + align:start position:0% +think was at Penn State and he asked +them how much their parents presents + + align:start position:0% +them how much their parents presents + + + align:start position:0% +them how much their parents presents +really worth to them and he found the + + align:start position:0% +really worth to them and he found the + + + align:start position:0% +really worth to them and he found the +deadweight loss of Christmas like + + align:start position:0% +deadweight loss of Christmas like + + + align:start position:0% +deadweight loss of Christmas like +hundreds of billions of dollars but like + + align:start position:0% +hundreds of billions of dollars but like + + + align:start position:0% +hundreds of billions of dollars but like +he would way rather have cash than the + + align:start position:0% +he would way rather have cash than the + + + align:start position:0% +he would way rather have cash than the +parents but what did he get wrong what + + align:start position:0% +parents but what did he get wrong what + + + align:start position:0% +parents but what did he get wrong what +did he get wrong why is that not why is + + align:start position:0% +did he get wrong why is that not why is + + + align:start position:0% +did he get wrong why is that not why is +that nicely a bad thing yeah you ask the + + align:start position:0% +that nicely a bad thing yeah you ask the + + + align:start position:0% +that nicely a bad thing yeah you ask the +first question so go ahead + + align:start position:0% + + + + align:start position:0% + +maybe but even ignoring that what else + + align:start position:0% +maybe but even ignoring that what else + + + align:start position:0% +maybe but even ignoring that what else +did he get wrong yeah that's um like the + + align:start position:0% +did he get wrong yeah that's um like the + + + align:start position:0% +did he get wrong yeah that's um like the +surprise there's emotional connections + + align:start position:0% +surprise there's emotional connections + + + align:start position:0% +surprise there's emotional connections +that's all well and good but that's not + + align:start position:0% +that's all well and good but that's not + + + align:start position:0% +that's all well and good but that's not +very big okay what's really big that he + + align:start position:0% +very big okay what's really big that he + + + align:start position:0% +very big okay what's really big that he +missed yeah he missed the fact the + + align:start position:0% +missed yeah he missed the fact the + + + align:start position:0% +missed yeah he missed the fact the +person who gave it gets utility from + + align:start position:0% +person who gave it gets utility from + + + align:start position:0% +person who gave it gets utility from +giving it so in fact the package may be + + align:start position:0% +giving it so in fact the package may be + + + align:start position:0% +giving it so in fact the package may be +efficient because you're like the + + align:start position:0% +efficient because you're like the + + + align:start position:0% +efficient because you're like the +surprising because the person gets + + align:start position:0% +surprising because the person gets + + + align:start position:0% +surprising because the person gets +utility but if you compared to dollars + + align:start position:0% +utility but if you compared to dollars + + + align:start position:0% +utility but if you compared to dollars +it's inefficient so it's kind of a + + align:start position:0% +it's inefficient so it's kind of a + + + align:start position:0% +it's inefficient so it's kind of a +clever clever little exercise he did um + + align:start position:0% +clever clever little exercise he did um + + + align:start position:0% +clever clever little exercise he did um +okay so basically that's individual + + align:start position:0% +okay so basically that's individual + + + align:start position:0% +okay so basically that's individual +consumer surplus but in this course we + + align:start position:0% +consumer surplus but in this course we + + + align:start position:0% +consumer surplus but in this course we +don't care about individual consumer + + align:start position:0% +don't care about individual consumer + + + align:start position:0% +don't care about individual consumer +surplus we care about market consumer + + align:start position:0% +surplus we care about market consumer + + + align:start position:0% +surplus we care about market consumer +surplus so let's turn to figure nine + + align:start position:0% +surplus so let's turn to figure nine + + + align:start position:0% +surplus so let's turn to figure nine +seven and think about a market listen + + align:start position:0% +seven and think about a market listen + + + align:start position:0% +seven and think about a market listen +about the market for gas + + align:start position:0% +about the market for gas + + + align:start position:0% +about the market for gas +now the mechanics is the same here but + + align:start position:0% +now the mechanics is the same here but + + + align:start position:0% +now the mechanics is the same here but +we're actually now thinking not about + + align:start position:0% +we're actually now thinking not about + + + align:start position:0% +we're actually now thinking not about +the individual buying one gallon versus + + align:start position:0% +the individual buying one gallon versus + + + align:start position:0% +the individual buying one gallon versus +two gallons but the market for gas how + + align:start position:0% +two gallons but the market for gas how + + + align:start position:0% +two gallons but the market for gas how +many gallons in aggregate will be bought + + align:start position:0% +many gallons in aggregate will be bought + + + align:start position:0% +many gallons in aggregate will be bought +but the analysis is the same okay that + + align:start position:0% +but the analysis is the same okay that + + + align:start position:0% +but the analysis is the same okay that +basically the willingness to pay for gas + + align:start position:0% +basically the willingness to pay for gas + + + align:start position:0% +basically the willingness to pay for gas +is the demand curve for gas the market + + align:start position:0% +is the demand curve for gas the market + + + align:start position:0% +is the demand curve for gas the market +demand curve for gas the price is the + + align:start position:0% +demand curve for gas the price is the + + + align:start position:0% +demand curve for gas the price is the +price so the difference is the area + + align:start position:0% +price so the difference is the area + + + align:start position:0% +price so the difference is the area +under the demand curve above the price + + align:start position:0% +under the demand curve above the price + + + align:start position:0% +under the demand curve above the price +the idea here is for consumers all the + + align:start position:0% +the idea here is for consumers all the + + + align:start position:0% +the idea here is for consumers all the +way to the left + + align:start position:0% +way to the left + + + align:start position:0% +way to the left +they have to drive to work they have to + + align:start position:0% +they have to drive to work they have to + + + align:start position:0% +they have to drive to work they have to +drive to have to drive a lot they're + + align:start position:0% +drive to have to drive a lot they're + + + align:start position:0% +drive to have to drive a lot they're +truck drivers or whatever they've drive + + align:start position:0% +truck drivers or whatever they've drive + + + align:start position:0% +truck drivers or whatever they've drive +a lot so for them they have a huge + + align:start position:0% +a lot so for them they have a huge + + + align:start position:0% +a lot so for them they have a huge +willingness to pay for gas so they make + + align:start position:0% +willingness to pay for gas so they make + + + align:start position:0% +willingness to pay for gas so they make +a huge surplus the more you want + + align:start position:0% +a huge surplus the more you want + + + align:start position:0% +a huge surplus the more you want +something you've given price the more + + align:start position:0% +something you've given price the more + + + align:start position:0% +something you've given price the more +circles you get where's you move to the + + align:start position:0% +circles you get where's you move to the + + + align:start position:0% +circles you get where's you move to the +right that's who will need to drive less + + align:start position:0% +right that's who will need to drive less + + + align:start position:0% +right that's who will need to drive less +and less + + align:start position:0% +and less + + + align:start position:0% +and less +once you pass point a why does surplus + + align:start position:0% +once you pass point a why does surplus + + + align:start position:0% +once you pass point a why does surplus +go away to the right of point a wise to + + align:start position:0% +go away to the right of point a wise to + + + align:start position:0% +go away to the right of point a wise to +know more consumer surplus yeah didn't + + align:start position:0% +know more consumer surplus yeah didn't + + + align:start position:0% +know more consumer surplus yeah didn't +happen because + + align:start position:0% + + + + align:start position:0% + +your willingness to pay is below the + + align:start position:0% +your willingness to pay is below the + + + align:start position:0% +your willingness to pay is below the +price right so transaction so consumer + + align:start position:0% +price right so transaction so consumer + + + align:start position:0% +price right so transaction so consumer +surplus can't go negative + + align:start position:0% +surplus can't go negative + + + align:start position:0% +surplus can't go negative +but when negative just wouldn't buy it + + align:start position:0% +but when negative just wouldn't buy it + + + align:start position:0% +but when negative just wouldn't buy it +so let's see his negative consumer + + align:start position:0% +so let's see his negative consumer + + + align:start position:0% +so let's see his negative consumer +surplus okay when negative you just + + align:start position:0% +surplus okay when negative you just + + + align:start position:0% +surplus okay when negative you just +wouldn't buy it okay but but as you get + + align:start position:0% +wouldn't buy it okay but but as you get + + + align:start position:0% +wouldn't buy it okay but but as you get +closer and closer to a then you actually + + align:start position:0% +closer and closer to a then you actually + + + align:start position:0% +closer and closer to a then you actually +do end up with consumer surplus going to + + align:start position:0% +do end up with consumer surplus going to + + + align:start position:0% +do end up with consumer surplus going to +zero okay so that's the UM that sort of + + align:start position:0% +zero okay so that's the UM that sort of + + + align:start position:0% +zero okay so that's the UM that sort of +mark consumer surplus so let's ask what + + align:start position:0% +mark consumer surplus so let's ask what + + + align:start position:0% +mark consumer surplus so let's ask what +let's let's talk about um a couple of + + align:start position:0% +let's let's talk about um a couple of + + + align:start position:0% +let's let's talk about um a couple of +aspects of our consumer surplus first + + align:start position:0% +aspects of our consumer surplus first + + + align:start position:0% +aspects of our consumer surplus first +question what happens to consumer + + align:start position:0% +question what happens to consumer + + + align:start position:0% +question what happens to consumer +surplus when the price changes let's + + align:start position:0% +surplus when the price changes let's + + + align:start position:0% +surplus when the price changes let's +show that in Figure nine eight + + align:start position:0% +show that in Figure nine eight + + + align:start position:0% +show that in Figure nine eight +let's say the price of gas goes up from + + align:start position:0% +let's say the price of gas goes up from + + + align:start position:0% +let's say the price of gas goes up from +$3 to 350 a gallon consumer surplus + + align:start position:0% +$3 to 350 a gallon consumer surplus + + + align:start position:0% +$3 to 350 a gallon consumer surplus +shrinks by consumer surplus shrinks by a + + align:start position:0% +shrinks by consumer surplus shrinks by a + + + align:start position:0% +shrinks by consumer surplus shrinks by a +trapezoid consumer surplus used to be + + align:start position:0% +trapezoid consumer surplus used to be + + + align:start position:0% +trapezoid consumer surplus used to be +the entire area below the demand curve + + align:start position:0% +the entire area below the demand curve + + + align:start position:0% +the entire area below the demand curve +it used to be the entire area below the + + align:start position:0% +it used to be the entire area below the + + + align:start position:0% +it used to be the entire area below the +demand curve and above $3 so used to be + + align:start position:0% +demand curve and above $3 so used to be + + + align:start position:0% +demand curve and above $3 so used to be +that whole triangle now it's just the + + align:start position:0% +that whole triangle now it's just the + + + align:start position:0% +that whole triangle now it's just the +empty triangle above the new price curve + + align:start position:0% +empty triangle above the new price curve + + + align:start position:0% +empty triangle above the new price curve +and below the demand curve so the new + + align:start position:0% +and below the demand curve so the new + + + align:start position:0% +and below the demand curve so the new +consumer surplus is just the area above + + align:start position:0% +consumer surplus is just the area above + + + align:start position:0% +consumer surplus is just the area above +350 on demand curves does the area not + + align:start position:0% +350 on demand curves does the area not + + + align:start position:0% +350 on demand curves does the area not +shaded in what you've lost is the + + align:start position:0% +shaded in what you've lost is the + + + align:start position:0% +shaded in what you've lost is the +trapezoid that goes that on the y-axis + + align:start position:0% +trapezoid that goes that on the y-axis + + + align:start position:0% +trapezoid that goes that on the y-axis +goes between 3 and 350 and then along + + align:start position:0% +goes between 3 and 350 and then along + + + align:start position:0% +goes between 3 and 350 and then along +the along the line goes from A to B + + align:start position:0% +the along the line goes from A to B + + + align:start position:0% +the along the line goes from A to B +you've lost that trapezoid why is it a + + align:start position:0% +you've lost that trapezoid why is it a + + + align:start position:0% +you've lost that trapezoid why is it a +trapezoid why have you lost why why is + + align:start position:0% +trapezoid why have you lost why why is + + + align:start position:0% +trapezoid why have you lost why why is +the lost consumer surplus a trapezoid + + align:start position:0% +the lost consumer surplus a trapezoid + + + align:start position:0% +the lost consumer surplus a trapezoid +because two things have happened what + + align:start position:0% +because two things have happened what + + + align:start position:0% +because two things have happened what +are the two things that have happened + + align:start position:0% +are the two things that have happened + + + align:start position:0% +are the two things that have happened +that have reduced your consumer surplus + + align:start position:0% +that have reduced your consumer surplus + + + align:start position:0% +that have reduced your consumer surplus +get some more folks involved folks you + + align:start position:0% +get some more folks involved folks you + + + align:start position:0% +get some more folks involved folks you +know good doctors quantity supplied + + align:start position:0% +know good doctors quantity supplied + + + align:start position:0% +know good doctors quantity supplied +quantity sold goes down because you want + + align:start position:0% +quantity sold goes down because you want + + + align:start position:0% +quantity sold goes down because you want +less supply because you are so the first + + align:start position:0% +less supply because you are so the first + + + align:start position:0% +less supply because you are so the first +thing is because the price gone up you + + align:start position:0% +thing is because the price gone up you + + + align:start position:0% +thing is because the price gone up you +want less that's the triangle you lost + + align:start position:0% +want less that's the triangle you lost + + + align:start position:0% +want less that's the triangle you lost +you have given up units that you used to + + align:start position:0% +you have given up units that you used to + + + align:start position:0% +you have given up units that you used to +get surplus on used to derive surplus on + + align:start position:0% +get surplus on used to derive surplus on + + + align:start position:0% +get surplus on used to derive surplus on +all the units from 900 to a thousand so + + align:start position:0% +all the units from 900 to a thousand so + + + align:start position:0% +all the units from 900 to a thousand so +what happened here is the price goes up + + align:start position:0% +what happened here is the price goes up + + + align:start position:0% +what happened here is the price goes up +and a hundred fewer people buy gas + + align:start position:0% +and a hundred fewer people buy gas + + + align:start position:0% +and a hundred fewer people buy gas +that's the way I've ladies that could be + + align:start position:0% +that's the way I've ladies that could be + + + align:start position:0% +that's the way I've ladies that could be +people buy less gas let's make it easy + + align:start position:0% +people buy less gas let's make it easy + + + align:start position:0% +people buy less gas let's make it easy +hundred people buy gas so hundred people + + align:start position:0% +hundred people buy gas so hundred people + + + align:start position:0% +hundred people buy gas so hundred people +used to buy gas no longer buy gas + + align:start position:0% +used to buy gas no longer buy gas + + + align:start position:0% +used to buy gas no longer buy gas +they're out of + + align:start position:0% +they're out of + + + align:start position:0% +they're out of +gasps market.they bike instead okay now + + align:start position:0% +gasps market.they bike instead okay now + + + align:start position:0% +gasps market.they bike instead okay now +they clearly were not that sad to bike + + align:start position:0% +they clearly were not that sad to bike + + + align:start position:0% +they clearly were not that sad to bike +or they would've had huge surplus from + + align:start position:0% +or they would've had huge surplus from + + + align:start position:0% +or they would've had huge surplus from +gas but they're little sad to bike gets + + align:start position:0% +gas but they're little sad to bike gets + + + align:start position:0% +gas but they're little sad to bike gets +crappy day out they ravage driving and + + align:start position:0% +crappy day out they ravage driving and + + + align:start position:0% +crappy day out they ravage driving and +so they lost surplus from the fact that + + align:start position:0% +so they lost surplus from the fact that + + + align:start position:0% +so they lost surplus from the fact that +now at the higher price they have to + + align:start position:0% +now at the higher price they have to + + + align:start position:0% +now at the higher price they have to +bike instead but it's a little bit of + + align:start position:0% +bike instead but it's a little bit of + + + align:start position:0% +bike instead but it's a little bit of +surplus it's just a little triangle okay + + align:start position:0% +surplus it's just a little triangle okay + + + align:start position:0% +surplus it's just a little triangle okay +so it's a little bit of surplus loss + + align:start position:0% +so it's a little bit of surplus loss + + + align:start position:0% +so it's a little bit of surplus loss +because some people who are close to and + + align:start position:0% +because some people who are close to and + + + align:start position:0% +because some people who are close to and +different now have to bike instead of + + align:start position:0% +different now have to bike instead of + + + align:start position:0% +different now have to bike instead of +driving but why the big what the big + + align:start position:0% +driving but why the big what the big + + + align:start position:0% +driving but why the big what the big +what's the big rectangle same person + + align:start position:0% +what's the big rectangle same person + + + align:start position:0% +what's the big rectangle same person +what caused a big rectangle increase in + + align:start position:0% +what caused a big rectangle increase in + + + align:start position:0% +what caused a big rectangle increase in +price for who for the people who are + + align:start position:0% +price for who for the people who are + + + align:start position:0% +price for who for the people who are +already buying it anyway + + align:start position:0% +already buying it anyway + + + align:start position:0% +already buying it anyway +so the big losers are the people are + + align:start position:0% +so the big losers are the people are + + + align:start position:0% +so the big losers are the people are +going to drive anyway and now just have + + align:start position:0% +going to drive anyway and now just have + + + align:start position:0% +going to drive anyway and now just have +to pay more for it because they because + + align:start position:0% +to pay more for it because they because + + + align:start position:0% +to pay more for it because they because +here's the key point the people between + + align:start position:0% +here's the key point the people between + + + align:start position:0% +here's the key point the people between +a and B people the last hundred people + + align:start position:0% +a and B people the last hundred people + + + align:start position:0% +a and B people the last hundred people +they were pretty close to indifferent + + align:start position:0% +they were pretty close to indifferent + + + align:start position:0% +they were pretty close to indifferent +they didn't lose that much surplus I'm + + align:start position:0% +they didn't lose that much surplus I'm + + + align:start position:0% +they didn't lose that much surplus I'm +not driving all the people to the left + + align:start position:0% +not driving all the people to the left + + + align:start position:0% +not driving all the people to the left +of person nine hundred they get big + + align:start position:0% +of person nine hundred they get big + + + align:start position:0% +of person nine hundred they get big +surplus from driving so their surplus + + align:start position:0% +surplus from driving so their surplus + + + align:start position:0% +surplus from driving so their surplus +simply went down by this rectangle they + + align:start position:0% +simply went down by this rectangle they + + + align:start position:0% +simply went down by this rectangle they +used to get the difference between the + + align:start position:0% +used to get the difference between the + + + align:start position:0% +used to get the difference between the +demand curve and three dollars not + + align:start position:0% +demand curve and three dollars not + + + align:start position:0% +demand curve and three dollars not +leaders to demand curve in 350 it's just + + align:start position:0% +leaders to demand curve in 350 it's just + + + align:start position:0% +leaders to demand curve in 350 it's just +a pure loss so when you raise a price + + align:start position:0% +a pure loss so when you raise a price + + + align:start position:0% +a pure loss so when you raise a price +the existing the people whose behavior + + align:start position:0% +the existing the people whose behavior + + + align:start position:0% +the existing the people whose behavior +doesn't change are worse off sometimes + + align:start position:0% +doesn't change are worse off sometimes + + + align:start position:0% +doesn't change are worse off sometimes +behavior change they're a little worse + + align:start position:0% +behavior change they're a little worse + + + align:start position:0% +behavior change they're a little worse +off but not that much so the triangle + + align:start position:0% +off but not that much so the triangle + + + align:start position:0% +off but not that much so the triangle +small the rectangles big the big loss is + + align:start position:0% +small the rectangles big the big loss is + + + align:start position:0% +small the rectangles big the big loss is +the people who like gas a lot but not to + + align:start position:0% +the people who like gas a lot but not to + + + align:start position:0% +the people who like gas a lot but not to +pay more for it okay point one point two + + align:start position:0% +pay more for it okay point one point two + + + align:start position:0% +pay more for it okay point one point two +what determines whether consumer surplus + + align:start position:0% +what determines whether consumer surplus + + + align:start position:0% +what determines whether consumer surplus +is large or small well we cover this + + align:start position:0% +is large or small well we cover this + + + align:start position:0% +is large or small well we cover this +it's elasticity of demand determines + + align:start position:0% +it's elasticity of demand determines + + + align:start position:0% +it's elasticity of demand determines +whether consumer surplus is large or + + align:start position:0% +whether consumer surplus is large or + + + align:start position:0% +whether consumer surplus is large or +small so for example figure nine nine + + align:start position:0% +small so for example figure nine nine + + + align:start position:0% +small so for example figure nine nine +takes the gas market with a price of + + align:start position:0% +takes the gas market with a price of + + + align:start position:0% +takes the gas market with a price of +three and a thousand people buying gas + + align:start position:0% +three and a thousand people buying gas + + + align:start position:0% +three and a thousand people buying gas +and uses two shows two different demand + + align:start position:0% +and uses two shows two different demand + + + align:start position:0% +and uses two shows two different demand +curves both of which go through point a + + align:start position:0% +curves both of which go through point a + + + align:start position:0% +curves both of which go through point a +so both demand curves yield the + + align:start position:0% +so both demand curves yield the + + + align:start position:0% +so both demand curves yield the +equilibrium price of three and the + + align:start position:0% +equilibrium price of three and the + + + align:start position:0% +equilibrium price of three and the +equilibrium quantity of a thousand okay + + align:start position:0% +equilibrium quantity of a thousand okay + + + align:start position:0% +equilibrium quantity of a thousand okay +so these two different Amman curves are + + align:start position:0% +so these two different Amman curves are + + + align:start position:0% +so these two different Amman curves are +just two different sets of preferences + + align:start position:0% +just two different sets of preferences + + + align:start position:0% +just two different sets of preferences +both of which yield the same equilibrium + + align:start position:0% +both of which yield the same equilibrium + + + align:start position:0% +both of which yield the same equilibrium +outcome and yet under the steeper demand + + align:start position:0% +outcome and yet under the steeper demand + + + align:start position:0% +outcome and yet under the steeper demand +curve the consumer surplus is larger + + align:start position:0% +curve the consumer surplus is larger + + + align:start position:0% +curve the consumer surplus is larger +that under the flatter cut + + align:start position:0% +that under the flatter cut + + + align:start position:0% +that under the flatter cut +man kerf and that's for the reason we + + align:start position:0% +man kerf and that's for the reason we + + + align:start position:0% +man kerf and that's for the reason we +talked about that's for the reason + + align:start position:0% +talked about that's for the reason + + + align:start position:0% +talked about that's for the reason +that's because with the steeper demand + + align:start position:0% +that's because with the steeper demand + + + align:start position:0% +that's because with the steeper demand +curve the more inelastic demand people + + align:start position:0% +curve the more inelastic demand people + + + align:start position:0% +curve the more inelastic demand people +want the good more they basically + + align:start position:0% +want the good more they basically + + + align:start position:0% +want the good more they basically +they're less willing to give it up as + + align:start position:0% +they're less willing to give it up as + + + align:start position:0% +they're less willing to give it up as +the price goes up therefore at any price + + align:start position:0% +the price goes up therefore at any price + + + align:start position:0% +the price goes up therefore at any price +they're making more surplus often with + + align:start position:0% +they're making more surplus often with + + + align:start position:0% +they're making more surplus often with +the flatter demand curve people are + + align:start position:0% +the flatter demand curve people are + + + align:start position:0% +the flatter demand curve people are +basically closer to indifferent with + + align:start position:0% +basically closer to indifferent with + + + align:start position:0% +basically closer to indifferent with +some other good so they're not so sad if + + align:start position:0% +some other good so they're not so sad if + + + align:start position:0% +some other good so they're not so sad if +the price goes up their surplus is + + align:start position:0% +the price goes up their surplus is + + + align:start position:0% +the price goes up their surplus is +smaller from getting this good there's + + align:start position:0% +smaller from getting this good there's + + + align:start position:0% +smaller from getting this good there's +even what that we're willing to pay and + + align:start position:0% +even what that we're willing to pay and + + + align:start position:0% +even what that we're willing to pay and +what they have to pay is smaller okay so + + align:start position:0% +what they have to pay is smaller okay so + + + align:start position:0% +what they have to pay is smaller okay so +that's how we think about consumer + + align:start position:0% +that's how we think about consumer + + + align:start position:0% +that's how we think about consumer +surplus it's basically the excess of + + align:start position:0% +surplus it's basically the excess of + + + align:start position:0% +surplus it's basically the excess of +your willingness to pay above what you + + align:start position:0% +your willingness to pay above what you + + + align:start position:0% +your willingness to pay above what you +have to pay so the price goes up your + + align:start position:0% +have to pay so the price goes up your + + + align:start position:0% +have to pay so the price goes up your +surplus goes down and surplus is larger + + align:start position:0% +surplus goes down and surplus is larger + + + align:start position:0% +surplus goes down and surplus is larger +the more inelastic is is the demand + + align:start position:0% +the more inelastic is is the demand + + + align:start position:0% +the more inelastic is is the demand +curve yeah great question when we talk + + align:start position:0% +curve yeah great question when we talk + + + align:start position:0% +curve yeah great question when we talk +about monopolies right now + + align:start position:0% +about monopolies right now + + + align:start position:0% +about monopolies right now +why can't producers do that why can't + + align:start position:0% +why can't producers do that why can't + + + align:start position:0% +why can't producers do that why can't +producers exploit that because perfectly + + align:start position:0% +producers exploit that because perfectly + + + align:start position:0% +producers exploit that because perfectly +yeah exactly + + align:start position:0% +yeah exactly + + + align:start position:0% +yeah exactly +cuz there that's a perfect answer to a + + align:start position:0% +cuz there that's a perfect answer to a + + + align:start position:0% +cuz there that's a perfect answer to a +perfectly competitive question cuz their + + align:start position:0% +perfectly competitive question cuz their + + + align:start position:0% +perfectly competitive question cuz their +price takers okay + + align:start position:0% +price takers okay + + + align:start position:0% +price takers okay +so they can't do an exploiting of + + align:start position:0% +so they can't do an exploiting of + + + align:start position:0% +so they can't do an exploiting of +consumers they don't have that choice + + align:start position:0% +consumers they don't have that choice + + + align:start position:0% +consumers they don't have that choice +mmm starting next lecture one lecture + + align:start position:0% +mmm starting next lecture one lecture + + + align:start position:0% +mmm starting next lecture one lecture +after we'll talk about monopolies then + + align:start position:0% +after we'll talk about monopolies then + + + align:start position:0% +after we'll talk about monopolies then +their price setters then they'll start + + align:start position:0% +their price setters then they'll start + + + align:start position:0% +their price setters then they'll start +thinking about that but right now they + + align:start position:0% +thinking about that but right now they + + + align:start position:0% +thinking about that but right now they +can't because the price takers I mean + + align:start position:0% +can't because the price takers I mean + + + align:start position:0% +can't because the price takers I mean +ultimately that's with it yeah + + align:start position:0% +ultimately that's with it yeah + + + align:start position:0% +ultimately that's with it yeah +ultimately they'd like the cert the + + align:start position:0% +ultimately they'd like the cert the + + + align:start position:0% +ultimately they'd like the cert the +surplus is just extra money somebody's + + align:start position:0% +surplus is just extra money somebody's + + + align:start position:0% +surplus is just extra money somebody's +got if you're a business owner why + + align:start position:0% +got if you're a business owner why + + + align:start position:0% +got if you're a business owner why +should consumers have it there you know + + align:start position:0% +should consumers have it there you know + + + align:start position:0% +should consumers have it there you know +you want it okay so that's um so that's + + align:start position:0% +you want it okay so that's um so that's + + + align:start position:0% +you want it okay so that's um so that's +consumer surplus any other questions + + align:start position:0% +consumer surplus any other questions + + + align:start position:0% +consumer surplus any other questions +about consumer surplus okay now let's + + align:start position:0% +about consumer surplus okay now let's + + + align:start position:0% +about consumer surplus okay now let's +move on and let's talk about producer + + align:start position:0% +move on and let's talk about producer + + + align:start position:0% +move on and let's talk about producer +surplus + + align:start position:0% + + + + align:start position:0% + +let's talk about producer surplus okay + + align:start position:0% +let's talk about producer surplus okay + + + align:start position:0% +let's talk about producer surplus okay +now the idea here is the same consumer + + align:start position:0% +now the idea here is the same consumer + + + align:start position:0% +now the idea here is the same consumer +surplus was the difference between the + + align:start position:0% +surplus was the difference between the + + + align:start position:0% +surplus was the difference between the +willingness to pay for a good and its + + align:start position:0% +willingness to pay for a good and its + + + align:start position:0% +willingness to pay for a good and its +price producer surplus is the difference + + align:start position:0% +price producer surplus is the difference + + + align:start position:0% +price producer surplus is the difference +between the willingness supply a good + + align:start position:0% +between the willingness supply a good + + + align:start position:0% +between the willingness supply a good +and its price and how do we measure + + align:start position:0% +and its price and how do we measure + + + align:start position:0% +and its price and how do we measure +willing to supply the supply curve so + + align:start position:0% +willing to supply the supply curve so + + + align:start position:0% +willing to supply the supply curve so +figure as figure 9/10 shows the producer + + align:start position:0% +figure as figure 9/10 shows the producer + + + align:start position:0% +figure as figure 9/10 shows the producer +surplus + + align:start position:0% +surplus + + + align:start position:0% +surplus +for any given firm for any given firm + + align:start position:0% +for any given firm for any given firm + + + align:start position:0% +for any given firm for any given firm +okay + + align:start position:0% +okay + + + align:start position:0% +okay +firms have an upward sloping supply + + align:start position:0% +firms have an upward sloping supply + + + align:start position:0% +firms have an upward sloping supply +curve and the market is delivering them + + align:start position:0% +curve and the market is delivering them + + + align:start position:0% +curve and the market is delivering them +some price so let's think about this + + align:start position:0% +some price so let's think about this + + + align:start position:0% +some price so let's think about this +firm when they produce the first unit + + align:start position:0% +firm when they produce the first unit + + + align:start position:0% +firm when they produce the first unit +this think this is a gas production firm + + align:start position:0% +this think this is a gas production firm + + + align:start position:0% +this think this is a gas production firm +okay a gas refiners say when they refine + + align:start position:0% +okay a gas refiners say when they refine + + + align:start position:0% +okay a gas refiners say when they refine +that first gallon of gas okay + + align:start position:0% +that first gallon of gas okay + + + align:start position:0% +that first gallon of gas okay +that costs them almost nothing because + + align:start position:0% +that costs them almost nothing because + + + align:start position:0% +that costs them almost nothing because +marginal costs upward sloping they've + + align:start position:0% +marginal costs upward sloping they've + + + align:start position:0% +marginal costs upward sloping they've +already paid the fixed costs they don't + + align:start position:0% +already paid the fixed costs they don't + + + align:start position:0% +already paid the fixed costs they don't +care in the short-run so I like ever + + align:start position:0% +care in the short-run so I like ever + + + align:start position:0% +care in the short-run so I like ever +this variable costs okay so in the end + + align:start position:0% +this variable costs okay so in the end + + + align:start position:0% +this variable costs okay so in the end +of the day this is not expensive they + + align:start position:0% +of the day this is not expensive they + + + align:start position:0% +of the day this is not expensive they +are willing to prove that first gallon + + align:start position:0% +are willing to prove that first gallon + + + align:start position:0% +are willing to prove that first gallon +really cheaply they've already invested + + align:start position:0% +really cheaply they've already invested + + + align:start position:0% +really cheaply they've already invested +in this giant refinery plant marginal + + align:start position:0% +in this giant refinery plant marginal + + + align:start position:0% +in this giant refinery plant marginal +costs are tiny so they get a huge but at + + align:start position:0% +costs are tiny so they get a huge but at + + + align:start position:0% +costs are tiny so they get a huge but at +the same time you pay them you don't + + align:start position:0% +the same time you pay them you don't + + + align:start position:0% +the same time you pay them you don't +differentiate what you pay per gallons + + align:start position:0% +differentiate what you pay per gallons + + + align:start position:0% +differentiate what you pay per gallons +you go to you plug the thing into your + + align:start position:0% +you go to you plug the thing into your + + + align:start position:0% +you go to you plug the thing into your +car and you get the gas okay so they're + + align:start position:0% +car and you get the gas okay so they're + + + align:start position:0% +car and you get the gas okay so they're +getting three bucks a gallon but they're + + align:start position:0% +getting three bucks a gallon but they're + + + align:start position:0% +getting three bucks a gallon but they're +not paying much to make that gallon + + align:start position:0% +not paying much to make that gallon + + + align:start position:0% +not paying much to make that gallon +however as they make more gallons their + + align:start position:0% +however as they make more gallons their + + + align:start position:0% +however as they make more gallons their +marginal cost increases so the surplus + + align:start position:0% +marginal cost increases so the surplus + + + align:start position:0% +marginal cost increases so the surplus +they earn on each gallon produced + + align:start position:0% +they earn on each gallon produced + + + align:start position:0% +they earn on each gallon produced +shrinks the surplus they earn at each + + align:start position:0% +shrinks the surplus they earn at each + + + align:start position:0% +shrinks the surplus they earn at each +gallon produced shrinks and so + + align:start position:0% +gallon produced shrinks and so + + + align:start position:0% +gallon produced shrinks and so +eventually they get to a point where + + align:start position:0% +eventually they get to a point where + + + align:start position:0% +eventually they get to a point where +they are essentially indifferent about + + align:start position:0% +they are essentially indifferent about + + + align:start position:0% +they are essentially indifferent about +producing the next unit of gasoline + + align:start position:0% +producing the next unit of gasoline + + + align:start position:0% +producing the next unit of gasoline +that's at a price of $3 and a quantity + + align:start position:0% +that's at a price of $3 and a quantity + + + align:start position:0% +that's at a price of $3 and a quantity +of should be little Q okay that's the + + align:start position:0% +of should be little Q okay that's the + + + align:start position:0% +of should be little Q okay that's the +point at which they are indifferent okay + + align:start position:0% +point at which they are indifferent okay + + + align:start position:0% +point at which they are indifferent okay +between producing producing gas and a + + align:start position:0% +between producing producing gas and a + + + align:start position:0% +between producing producing gas and a +producing gas therefore their surplus is + + align:start position:0% +producing gas therefore their surplus is + + + align:start position:0% +producing gas therefore their surplus is +zero so producer surplus is the + + align:start position:0% +zero so producer surplus is the + + + align:start position:0% +zero so producer surplus is the +difference between the price line and + + align:start position:0% +difference between the price line and + + + align:start position:0% +difference between the price line and +the upward sloping supply curve is + + align:start position:0% +the upward sloping supply curve is + + + align:start position:0% +the upward sloping supply curve is +pretty surplus now in the long run + + align:start position:0% +pretty surplus now in the long run + + + align:start position:0% +pretty surplus now in the long run +we have a name for that it's called + + align:start position:0% +we have a name for that it's called + + + align:start position:0% +we have a name for that it's called +profits + + align:start position:0% +profits + + + align:start position:0% +profits +okay so while consumer surplus is this + + align:start position:0% +okay so while consumer surplus is this + + + align:start position:0% +okay so while consumer surplus is this +sort of abstract weird theoretical + + align:start position:0% +sort of abstract weird theoretical + + + align:start position:0% +sort of abstract weird theoretical +concept pretty surplus you can get your + + align:start position:0% +concept pretty surplus you can get your + + + align:start position:0% +concept pretty surplus you can get your +hands around its profits basically in + + align:start position:0% +hands around its profits basically in + + + align:start position:0% +hands around its profits basically in +the long run remember in the long run + + align:start position:0% +the long run remember in the long run + + + align:start position:0% +the long run remember in the long run +marginal cost equals average cost right + + align:start position:0% +marginal cost equals average cost right + + + align:start position:0% +marginal cost equals average cost right +because in the long run you produce + + align:start position:0% +because in the long run you produce + + + align:start position:0% +because in the long run you produce +until marginal cost equals average cost + + align:start position:0% +until marginal cost equals average cost + + + align:start position:0% +until marginal cost equals average cost +therefore the supply curve is the + + align:start position:0% +therefore the supply curve is the + + + align:start position:0% +therefore the supply curve is the +average cost curve price minus average + + align:start position:0% +average cost curve price minus average + + + align:start position:0% +average cost curve price minus average +cost as profits + + align:start position:0% +cost as profits + + + align:start position:0% +cost as profits +therefore producer surpluses profits let + + align:start position:0% +therefore producer surpluses profits let + + + align:start position:0% +therefore producer surpluses profits let +me say it again little three line proof + + align:start position:0% +me say it again little three line proof + + + align:start position:0% +me say it again little three line proof +for you okay in the long run marginal + + align:start position:0% +for you okay in the long run marginal + + + align:start position:0% +for you okay in the long run marginal +cost equals average costs second the + + align:start position:0% +cost equals average costs second the + + + align:start position:0% +cost equals average costs second the +supply curve is the marginal cost curve + + align:start position:0% +supply curve is the marginal cost curve + + + align:start position:0% +supply curve is the marginal cost curve +therefore it's the average cost curve + + align:start position:0% +therefore it's the average cost curve + + + align:start position:0% +therefore it's the average cost curve +third profits is defined as price minus + + align:start position:0% +third profits is defined as price minus + + + align:start position:0% +third profits is defined as price minus +average cost fourth profits is the + + align:start position:0% +average cost fourth profits is the + + + align:start position:0% +average cost fourth profits is the +shaded area now in the short-run that's + + align:start position:0% +shaded area now in the short-run that's + + + align:start position:0% +shaded area now in the short-run that's +not quite right + + align:start position:0% +not quite right + + + align:start position:0% +not quite right +because there's the whole shutdown + + align:start position:0% +because there's the whole shutdown + + + align:start position:0% +because there's the whole shutdown +decision which makes things awkward but + + align:start position:0% +decision which makes things awkward but + + + align:start position:0% +decision which makes things awkward but +roughly speaking it's not terrible to + + align:start position:0% +roughly speaking it's not terrible to + + + align:start position:0% +roughly speaking it's not terrible to +think about producer surplus as being + + align:start position:0% +think about producer surplus as being + + + align:start position:0% +think about producer surplus as being +profits that's a shorthand that largely + + align:start position:0% +profits that's a shorthand that largely + + + align:start position:0% +profits that's a shorthand that largely +works if it ever doesn't work we'll let + + align:start position:0% +works if it ever doesn't work we'll let + + + align:start position:0% +works if it ever doesn't work we'll let +you know but that's a shorthand should + + align:start position:0% +you know but that's a shorthand should + + + align:start position:0% +you know but that's a shorthand should +largely work okay now of course once + + align:start position:0% +largely work okay now of course once + + + align:start position:0% +largely work okay now of course once +again we don't care about individual + + align:start position:0% +again we don't care about individual + + + align:start position:0% +again we don't care about individual +firms producer surplus we care about the + + align:start position:0% +firms producer surplus we care about the + + + align:start position:0% +firms producer surplus we care about the +market briefs or surplus so let's go to + + align:start position:0% +market briefs or surplus so let's go to + + + align:start position:0% +market briefs or surplus so let's go to +figure 911 figure 911 is basically the + + align:start position:0% +figure 911 figure 911 is basically the + + + align:start position:0% +figure 911 figure 911 is basically the +market surplus curve and the idea here + + align:start position:0% +market surplus curve and the idea here + + + align:start position:0% +market surplus curve and the idea here +is that essentially to the left you you + + align:start position:0% +is that essentially to the left you you + + + align:start position:0% +is that essentially to the left you you +have a market supply curve where + + align:start position:0% +have a market supply curve where + + + align:start position:0% +have a market supply curve where +basically remember the individual firms + + align:start position:0% +basically remember the individual firms + + + align:start position:0% +basically remember the individual firms +supply curve is always flat but the + + align:start position:0% +supply curve is always flat but the + + + align:start position:0% +supply curve is always flat but the +market supply curve doesn't have to be + + align:start position:0% +market supply curve doesn't have to be + + + align:start position:0% +market supply curve doesn't have to be +it doesn't have to be flat okay the + + align:start position:0% +it doesn't have to be flat okay the + + + align:start position:0% +it doesn't have to be flat okay the +market supply curve + + align:start position:0% +market supply curve + + + align:start position:0% +market supply curve +well note let me back up a market supply + + align:start position:0% +well note let me back up a market supply + + + align:start position:0% +well note let me back up a market supply +curve is flat under certain set of + + align:start position:0% +curve is flat under certain set of + + + align:start position:0% +curve is flat under certain set of +conditions but now let's imagine that + + align:start position:0% +conditions but now let's imagine that + + + align:start position:0% +conditions but now let's imagine that +those conditions aren't true for example + + align:start position:0% +those conditions aren't true for example + + + align:start position:0% +those conditions aren't true for example +let's go back to I talked at the end of + + align:start position:0% +let's go back to I talked at the end of + + + align:start position:0% +let's go back to I talked at the end of +last lecture about heterogeneous firms + + align:start position:0% +last lecture about heterogeneous firms + + + align:start position:0% +last lecture about heterogeneous firms +when we took the cotton example some + + align:start position:0% +when we took the cotton example some + + + align:start position:0% +when we took the cotton example some +firms are more efficient producers than + + align:start position:0% +firms are more efficient producers than + + + align:start position:0% +firms are more efficient producers than +others if all firms are identical it's + + align:start position:0% +others if all firms are identical it's + + + align:start position:0% +others if all firms are identical it's +hardly competitive of course the market + + align:start position:0% +hardly competitive of course the market + + + align:start position:0% +hardly competitive of course the market +supply curve is flat since this graph + + align:start position:0% +supply curve is flat since this graph + + + align:start position:0% +supply curve is flat since this graph +would be uninteresting but in fact + + align:start position:0% +would be uninteresting but in fact + + + align:start position:0% +would be uninteresting but in fact +imagine that firms aren't identical some + + align:start position:0% +imagine that firms aren't identical some + + + align:start position:0% +imagine that firms aren't identical some +firms are more efficient producers than + + align:start position:0% +firms are more efficient producers than + + + align:start position:0% +firms are more efficient producers than +others okay for example in that case + + align:start position:0% +others okay for example in that case + + + align:start position:0% +others okay for example in that case +what you'll see is the most efficient + + align:start position:0% +what you'll see is the most efficient + + + align:start position:0% +what you'll see is the most efficient +producer will earn the most surplus EE + + align:start position:0% +producer will earn the most surplus EE + + + align:start position:0% +producer will earn the most surplus EE +ie the most profit there all the way to + + align:start position:0% +ie the most profit there all the way to + + + align:start position:0% +ie the most profit there all the way to +the left + + align:start position:0% +the left + + + align:start position:0% +the left +as you move to the right you're getting + + align:start position:0% +as you move to the right you're getting + + + align:start position:0% +as you move to the right you're getting +to less and less efficient producers + + align:start position:0% +to less and less efficient producers + + + align:start position:0% +to less and less efficient producers +okay so profit is shrinking so under the + + align:start position:0% +okay so profit is shrinking so under the + + + align:start position:0% +okay so profit is shrinking so under the +conditions we started with last time + + align:start position:0% +conditions we started with last time + + + align:start position:0% +conditions we started with last time +then price would always equal supply be + + align:start position:0% +then price would always equal supply be + + + align:start position:0% +then price would always equal supply be +a flat supply curve at the price and + + align:start position:0% +a flat supply curve at the price and + + + align:start position:0% +a flat supply curve at the price and +therefore profits are zero that is + + align:start position:0% +therefore profits are zero that is + + + align:start position:0% +therefore profits are zero that is +producer surplus is zero so we we + + align:start position:0% +producer surplus is zero so we we + + + align:start position:0% +producer surplus is zero so we we +derived towards the end of the last + + align:start position:0% +derived towards the end of the last + + + align:start position:0% +derived towards the end of the last +election we said in the long run a + + align:start position:0% +election we said in the long run a + + + align:start position:0% +election we said in the long run a +perfectly competitive market profit is + + align:start position:0% +perfectly competitive market profit is + + + align:start position:0% +perfectly competitive market profit is +zero that's the same as saying producer + + align:start position:0% +zero that's the same as saying producer + + + align:start position:0% +zero that's the same as saying producer +surplus is zero and why is that + + align:start position:0% +surplus is zero and why is that + + + align:start position:0% +surplus is zero and why is that +that's because in that case the price + + align:start position:0% +that's because in that case the price + + + align:start position:0% +that's because in that case the price +line is on top of the supply curve + + align:start position:0% +line is on top of the supply curve + + + align:start position:0% +line is on top of the supply curve +therefore there's no gap between them so + + align:start position:0% +therefore there's no gap between them so + + + align:start position:0% +therefore there's no gap between them so +in the long run in a perfectly + + align:start position:0% +in the long run in a perfectly + + + align:start position:0% +in the long run in a perfectly +competitive market there's zero producer + + align:start position:0% +competitive market there's zero producer + + + align:start position:0% +competitive market there's zero producer +surplus means zero profit in reality we + + align:start position:0% +surplus means zero profit in reality we + + + align:start position:0% +surplus means zero profit in reality we +talked about conditions why there would + + align:start position:0% +talked about conditions why there would + + + align:start position:0% +talked about conditions why there would +be an upward sloping long run supply + + align:start position:0% +be an upward sloping long run supply + + + align:start position:0% +be an upward sloping long run supply +curve like firms different how efficient + + align:start position:0% +curve like firms different how efficient + + + align:start position:0% +curve like firms different how efficient +they are or where there's barriers to + + align:start position:0% +they are or where there's barriers to + + + align:start position:0% +they are or where there's barriers to +entry which means some firms can't come + + align:start position:0% +entry which means some firms can't come + + + align:start position:0% +entry which means some firms can't come +in and drive profits to zero or there's + + align:start position:0% +in and drive profits to zero or there's + + + align:start position:0% +in and drive profits to zero or there's +an upward sloping input price curve + + align:start position:0% +an upward sloping input price curve + + + align:start position:0% +an upward sloping input price curve +meaning that basically the more you want + + align:start position:0% +meaning that basically the more you want + + + align:start position:0% +meaning that basically the more you want +to produce the more you have to pay + + align:start position:0% +to produce the more you have to pay + + + align:start position:0% +to produce the more you have to pay +workers for all those reasons the supply + + align:start position:0% +workers for all those reasons the supply + + + align:start position:0% +workers for all those reasons the supply +curve slopes up and therefore you can + + align:start position:0% +curve slopes up and therefore you can + + + align:start position:0% +curve slopes up and therefore you can +get a producer surplus you can get some + + align:start position:0% +get a producer surplus you can get some + + + align:start position:0% +get a producer surplus you can get some +profits even the long-run okay so + + align:start position:0% +profits even the long-run okay so + + + align:start position:0% +profits even the long-run okay so +basically what we have here is a + + align:start position:0% +basically what we have here is a + + + align:start position:0% +basically what we have here is a +situation where as long as the supply + + align:start position:0% +situation where as long as the supply + + + align:start position:0% +situation where as long as the supply +curve slopes up you get a long-run + + align:start position:0% +curve slopes up you get a long-run + + + align:start position:0% +curve slopes up you get a long-run +producer surplus which is the difference + + align:start position:0% +producer surplus which is the difference + + + align:start position:0% +producer surplus which is the difference +between the price and the supply curve + + align:start position:0% +between the price and the supply curve + + + align:start position:0% +between the price and the supply curve +okay and that is the same as profits + + align:start position:0% +okay and that is the same as profits + + + align:start position:0% +okay and that is the same as profits +questions about that okay let me cover + + align:start position:0% +questions about that okay let me cover + + + align:start position:0% +questions about that okay let me cover +one last point going back to last + + align:start position:0% +one last point going back to last + + + align:start position:0% +one last point going back to last +lecture didn't have time to get to a + + align:start position:0% +lecture didn't have time to get to a + + + align:start position:0% +lecture didn't have time to get to a +last lecture remember we talked about + + align:start position:0% +last lecture remember we talked about + + + align:start position:0% +last lecture remember we talked about +three reasons why in the long run even + + align:start position:0% +three reasons why in the long run even + + + align:start position:0% +three reasons why in the long run even +even in a competitive market supply + + align:start position:0% +even in a competitive market supply + + + align:start position:0% +even in a competitive market supply +could give slope up we talked about + + align:start position:0% +could give slope up we talked about + + + align:start position:0% +could give slope up we talked about +heterogeneous firms that is firms with + + align:start position:0% +heterogeneous firms that is firms with + + + align:start position:0% +heterogeneous firms that is firms with +different levels of efficiency of + + align:start position:0% +different levels of efficiency of + + + align:start position:0% +different levels of efficiency of +production we talked about barriers to + + align:start position:0% +production we talked about barriers to + + + align:start position:0% +production we talked about barriers to +entry that is reasons why firms can't + + align:start position:0% +entry that is reasons why firms can't + + + align:start position:0% +entry that is reasons why firms can't +enter and drive profits to zero because + + align:start position:0% +enter and drive profits to zero because + + + align:start position:0% +enter and drive profits to zero because +it's not costless to enter and we talked + + align:start position:0% +it's not costless to enter and we talked + + + align:start position:0% +it's not costless to enter and we talked +about upward sloping input supply curves + + align:start position:0% +about upward sloping input supply curves + + + align:start position:0% +about upward sloping input supply curves +we talked about the fact that as you + + align:start position:0% +we talked about the fact that as you + + + align:start position:0% +we talked about the fact that as you +produce more you might have to pay more + + align:start position:0% +produce more you might have to pay more + + + align:start position:0% +produce more you might have to pay more +for your inputs and therefore you can't + + align:start position:0% +for your inputs and therefore you can't + + + align:start position:0% +for your inputs and therefore you can't +just charge one you have to charge the + + align:start position:0% +just charge one you have to charge the + + + align:start position:0% +just charge one you have to charge the +you have to charge higher prices as you + + align:start position:0% +you have to charge higher prices as you + + + align:start position:0% +you have to charge higher prices as you +produce more + + align:start position:0% +produce more + + + align:start position:0% +produce more +I want to highlight so they said quickly + + align:start position:0% +I want to highlight so they said quickly + + + align:start position:0% +I want to highlight so they said quickly +last time difference between these two + + align:start position:0% +last time difference between these two + + + align:start position:0% +last time difference between these two +and this one in these two there are + + align:start position:0% +and this one in these two there are + + + align:start position:0% +and this one in these two there are +profits and these two there are profits + + align:start position:0% +profits and these two there are profits + + + align:start position:0% +profits and these two there are profits +okay + + align:start position:0% +okay + + + align:start position:0% +okay +because then each of these their reasons + + align:start position:0% +because then each of these their reasons + + + align:start position:0% +because then each of these their reasons +why the market will not drive every firm + + align:start position:0% +why the market will not drive every firm + + + align:start position:0% +why the market will not drive every firm +to zero profit some furs will remain in + + align:start position:0% +to zero profit some furs will remain in + + + align:start position:0% +to zero profit some furs will remain in +much like Pakistan made profits on their + + align:start position:0% +much like Pakistan made profits on their + + + align:start position:0% +much like Pakistan made profits on their +cotton sales some froze Romanian + + align:start position:0% +cotton sales some froze Romanian + + + align:start position:0% +cotton sales some froze Romanian +likewise with the barriers to entry the + + align:start position:0% +likewise with the barriers to entry the + + + align:start position:0% +likewise with the barriers to entry the +firm's that have that are in the market + + align:start position:0% +firm's that have that are in the market + + + align:start position:0% +firm's that have that are in the market +that have gotten over those barriers + + align:start position:0% +that have gotten over those barriers + + + align:start position:0% +that have gotten over those barriers +will make money okay in this case the + + align:start position:0% +will make money okay in this case the + + + align:start position:0% +will make money okay in this case the +firm doesn't necessarily make money okay + + align:start position:0% +firm doesn't necessarily make money okay + + + align:start position:0% +firm doesn't necessarily make money okay +what it does here is it just pays it + + align:start position:0% +what it does here is it just pays it + + + align:start position:0% +what it does here is it just pays it +takes that extra money and pays it out + + align:start position:0% +takes that extra money and pays it out + + + align:start position:0% +takes that extra money and pays it out +to workers okay so whether or not an + + align:start position:0% +to workers okay so whether or not an + + + align:start position:0% +to workers okay so whether or not an +upward sloping supply curve doesn't + + align:start position:0% +upward sloping supply curve doesn't + + + align:start position:0% +upward sloping supply curve doesn't +necessarily mean the firm makes profit + + align:start position:0% +necessarily mean the firm makes profit + + + align:start position:0% +necessarily mean the firm makes profit +it could just be upward sloping because + + align:start position:0% +it could just be upward sloping because + + + align:start position:0% +it could just be upward sloping because +their input costs are rising okay so + + align:start position:0% +their input costs are rising okay so + + + align:start position:0% +their input costs are rising okay so +that's sort of an important distinction + + align:start position:0% +that's sort of an important distinction + + + align:start position:0% +that's sort of an important distinction +to keep in mind so let's stop there with + + align:start position:0% +to keep in mind so let's stop there with + + + align:start position:0% +to keep in mind so let's stop there with +that mind-blowing insight let's stop + + align:start position:0% +that mind-blowing insight let's stop + + + align:start position:0% +that mind-blowing insight let's stop +there and we will come back and we'll + + align:start position:0% +there and we will come back and we'll + + + align:start position:0% +there and we will come back and we'll +talk more about welfare economics \ No newline at end of file diff --git a/1v4uOjgrru4.txt b/1v4uOjgrru4.txt new file mode 100644 index 0000000000000000000000000000000000000000..b1fbab8cc25134d66cd8285f19426c7165a17f6a --- /dev/null +++ b/1v4uOjgrru4.txt @@ -0,0 +1,8443 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +I'm sure for the hydrogen and biofuels + + align:start position:0% +I'm sure for the hydrogen and biofuels + + + align:start position:0% +I'm sure for the hydrogen and biofuels +folks it might be a little hard which is + + align:start position:0% +folks it might be a little hard which is + + + align:start position:0% +folks it might be a little hard which is +why that's what I'm going to cover today + + align:start position:0% +why that's what I'm going to cover today + + + align:start position:0% +why that's what I'm going to cover today +so we all have sort of the same amount + + align:start position:0% +so we all have sort of the same amount + + + align:start position:0% +so we all have sort of the same amount +of of a head start + + align:start position:0% +of of a head start + + + align:start position:0% +of of a head start +to help go through this stuff does + + align:start position:0% +to help go through this stuff does + + + align:start position:0% +to help go through this stuff does +anyone have any questions on the design + + align:start position:0% +anyone have any questions on the design + + + align:start position:0% +anyone have any questions on the design +or what the groups are responsible for + + align:start position:0% +or what the groups are responsible for + + + align:start position:0% +or what the groups are responsible for +before I actually get into today's + + align:start position:0% +before I actually get into today's + + + align:start position:0% +before I actually get into today's +lectures okay great + + align:start position:0% +lectures okay great + + + align:start position:0% +lectures okay great +so I wanted to go through three things + + align:start position:0% +so I wanted to go through three things + + + align:start position:0% +so I wanted to go through three things +today through hydrogen production + + align:start position:0% +today through hydrogen production + + + align:start position:0% +today through hydrogen production +biofuel production and the design + + align:start position:0% +biofuel production and the design + + + align:start position:0% +biofuel production and the design +process and importance metrics because + + align:start position:0% +process and importance metrics because + + + align:start position:0% +process and importance metrics because +you guys are going to be coming up with + + align:start position:0% +you guys are going to be coming up with + + + align:start position:0% +you guys are going to be coming up with +a lot of design possibilities and in the + + align:start position:0% +a lot of design possibilities and in the + + + align:start position:0% +a lot of design possibilities and in the +end you're gonna have to pick one and + + align:start position:0% +end you're gonna have to pick one and + + + align:start position:0% +end you're gonna have to pick one and +I'll go over a couple of strategies + + align:start position:0% +I'll go over a couple of strategies + + + align:start position:0% +I'll go over a couple of strategies +where you can formally put down what + + align:start position:0% +where you can formally put down what + + + align:start position:0% +where you can formally put down what +sort of things are important what aren't + + align:start position:0% +sort of things are important what aren't + + + align:start position:0% +sort of things are important what aren't +important and actually have a numerical + + align:start position:0% +important and actually have a numerical + + + align:start position:0% +important and actually have a numerical +methodology to pick what's most + + align:start position:0% +methodology to pick what's most + + + align:start position:0% +methodology to pick what's most +important for you so when somebody comes + + align:start position:0% +important for you so when somebody comes + + + align:start position:0% +important for you so when somebody comes +back and says oh why did you pick this + + align:start position:0% +back and says oh why did you pick this + + + align:start position:0% +back and says oh why did you pick this +part of the design you can't just say + + align:start position:0% +part of the design you can't just say + + + align:start position:0% +part of the design you can't just say +because it's the best or because I + + align:start position:0% +because it's the best or because I + + + align:start position:0% +because it's the best or because I +rolled the dice you can say well we + + align:start position:0% +rolled the dice you can say well we + + + align:start position:0% +rolled the dice you can say well we +actually assign importances to different + + align:start position:0% +actually assign importances to different + + + align:start position:0% +actually assign importances to different +aspects and here's our chart if you do + + align:start position:0% +aspects and here's our chart if you do + + + align:start position:0% +aspects and here's our chart if you do +have some problems let's revise the + + align:start position:0% +have some problems let's revise the + + + align:start position:0% +have some problems let's revise the +chart and so this will help if you + + align:start position:0% +chart and so this will help if you + + + align:start position:0% +chart and so this will help if you +decide to switch design parameters later + + align:start position:0% +decide to switch design parameters later + + + align:start position:0% +decide to switch design parameters later +you'll already have a methodology where + + align:start position:0% +you'll already have a methodology where + + + align:start position:0% +you'll already have a methodology where +you can just change relative importance + + align:start position:0% +you can just change relative importance + + + align:start position:0% +you can just change relative importance +azan things come up with a with the the + + align:start position:0% +azan things come up with a with the the + + + align:start position:0% +azan things come up with a with the the +new optimal design pretty quickly so + + align:start position:0% +new optimal design pretty quickly so + + + align:start position:0% +new optimal design pretty quickly so +first I'll get into a survey of hydrogen + + align:start position:0% +first I'll get into a survey of hydrogen + + + align:start position:0% +first I'll get into a survey of hydrogen +production methods some of the major + + align:start position:0% +production methods some of the major + + + align:start position:0% +production methods some of the major +considerations to think about are what + + align:start position:0% +considerations to think about are what + + + align:start position:0% +considerations to think about are what +temperatures do you need to produce + + align:start position:0% +temperatures do you need to produce + + + align:start position:0% +temperatures do you need to produce +hydrogen and that helps determine what + + align:start position:0% +hydrogen and that helps determine what + + + align:start position:0% +hydrogen and that helps determine what +heat source to use which helps feed back + + align:start position:0% +heat source to use which helps feed back + + + align:start position:0% +heat source to use which helps feed back +and tell the core people I need to + + align:start position:0% +and tell the core people I need to + + + align:start position:0% +and tell the core people I need to +outlet temperature of roughly this so + + align:start position:0% +outlet temperature of roughly this so + + + align:start position:0% +outlet temperature of roughly this so +you may have noticed by now that sort of + + align:start position:0% +you may have noticed by now that sort of + + + align:start position:0% +you may have noticed by now that sort of +the flow of design parameters isn't + + align:start position:0% +the flow of design parameters isn't + + + align:start position:0% +the flow of design parameters isn't +moving from the core outwards to the + + align:start position:0% +moving from the core outwards to the + + + align:start position:0% +moving from the core outwards to the +hydrogen and biofuels folks it's moving + + align:start position:0% +hydrogen and biofuels folks it's moving + + + align:start position:0% +hydrogen and biofuels folks it's moving +from hydrogen and biofuels back in the + + align:start position:0% +from hydrogen and biofuels back in the + + + align:start position:0% +from hydrogen and biofuels back in the +core has a lot of different options you + + align:start position:0% +core has a lot of different options you + + + align:start position:0% +core has a lot of different options you +might not have as many viable options + + align:start position:0% +might not have as many viable options + + + align:start position:0% +might not have as many viable options +for hydrogen and biofuels production and + + align:start position:0% +for hydrogen and biofuels production and + + + align:start position:0% +for hydrogen and biofuels production and +so when you're more restricted on one + + align:start position:0% +so when you're more restricted on one + + + align:start position:0% +so when you're more restricted on one +end than the other that'll tend to say + + align:start position:0% +end than the other that'll tend to say + + + align:start position:0% +end than the other that'll tend to say +those folks with more restrictions might + + align:start position:0% +those folks with more restrictions might + + + align:start position:0% +those folks with more restrictions might +have a bigger say in the overall design + + align:start position:0% +have a bigger say in the overall design + + + align:start position:0% +have a bigger say in the overall design +parameters you'll want to consider your + + align:start position:0% +parameters you'll want to consider your + + + align:start position:0% +parameters you'll want to consider your +overall cost per G ger gallon of gas + + align:start position:0% +overall cost per G ger gallon of gas + + + align:start position:0% +overall cost per G ger gallon of gas +equivalent so how much does a certain + + align:start position:0% +equivalent so how much does a certain + + + align:start position:0% +equivalent so how much does a certain +amount of energy and hydrogen cost + + align:start position:0% +amount of energy and hydrogen cost + + + align:start position:0% +amount of energy and hydrogen cost +versus the same amount in gasoline + + align:start position:0% +versus the same amount in gasoline + + + align:start position:0% +versus the same amount in gasoline +that'll be a really good way for you to + + align:start position:0% +that'll be a really good way for you to + + + align:start position:0% +that'll be a really good way for you to +tell people quickly hydrogen is this + + align:start position:0% +tell people quickly hydrogen is this + + + align:start position:0% +tell people quickly hydrogen is this +much more expensive than gasoline for + + align:start position:0% +much more expensive than gasoline for + + + align:start position:0% +much more expensive than gasoline for +energy equivalent and then you can + + align:start position:0% +energy equivalent and then you can + + + align:start position:0% +energy equivalent and then you can +rationalize why it's a little more + + align:start position:0% +rationalize why it's a little more + + + align:start position:0% +rationalize why it's a little more +expensive or if it's less expensive + + align:start position:0% +expensive or if it's less expensive + + + align:start position:0% +expensive or if it's less expensive +that's a selling point for your + + align:start position:0% +that's a selling point for your + + + align:start position:0% +that's a selling point for your +technology + + align:start position:0% +technology + + + align:start position:0% +technology +are there any emissions to the process + + align:start position:0% +are there any emissions to the process + + + align:start position:0% +are there any emissions to the process +what new technologies can improve things + + align:start position:0% +what new technologies can improve things + + + align:start position:0% +what new technologies can improve things +so in the in the core and process heat + + align:start position:0% +so in the in the core and process heat + + + align:start position:0% +so in the in the core and process heat +folks as well as these lectures I've + + align:start position:0% +folks as well as these lectures I've + + + align:start position:0% +folks as well as these lectures I've +been going over some of the more + + align:start position:0% +been going over some of the more + + + align:start position:0% +been going over some of the more +tried-and-true methods for core design + + align:start position:0% +tried-and-true methods for core design + + + align:start position:0% +tried-and-true methods for core design +for a process heat transport storage + + align:start position:0% +for a process heat transport storage + + + align:start position:0% +for a process heat transport storage +don't let that limit you I think + + align:start position:0% +don't let that limit you I think + + + align:start position:0% +don't let that limit you I think +Matt you're talking about the inductor + + align:start position:0% +Matt you're talking about the inductor + + + align:start position:0% +Matt you're talking about the inductor +storage right yeah Matt came upon a + + align:start position:0% +storage right yeah Matt came upon a + + + align:start position:0% +storage right yeah Matt came upon a +strategy where you end up passing a + + align:start position:0% +strategy where you end up passing a + + + align:start position:0% +strategy where you end up passing a +large electric current through some + + align:start position:0% +large electric current through some + + + align:start position:0% +large electric current through some +inductors and when the load disappears + + align:start position:0% +inductors and when the load disappears + + + align:start position:0% +inductors and when the load disappears +you close the loop and the inductor + + align:start position:0% +you close the loop and the inductor + + + align:start position:0% +you close the loop and the inductor +keeps the current flowing so while those + + align:start position:0% +keeps the current flowing so while those + + + align:start position:0% +keeps the current flowing so while those +ideas might seem a little wacky they + + align:start position:0% +ideas might seem a little wacky they + + + align:start position:0% +ideas might seem a little wacky they +might not be they might end up being the + + align:start position:0% +might not be they might end up being the + + + align:start position:0% +might not be they might end up being the +best strategy when you balance off how + + align:start position:0% +best strategy when you balance off how + + + align:start position:0% +best strategy when you balance off how +far it's been developed versus what it + + align:start position:0% +far it's been developed versus what it + + + align:start position:0% +far it's been developed versus what it +can get you so don't let what I + + align:start position:0% +can get you so don't let what I + + + align:start position:0% +can get you so don't let what I +described here limit your choices and + + align:start position:0% +described here limit your choices and + + + align:start position:0% +described here limit your choices and +your research and one of the things I + + align:start position:0% +your research and one of the things I + + + align:start position:0% +your research and one of the things I +want the hydrogen folks to think about + + align:start position:0% +want the hydrogen folks to think about + + + align:start position:0% +want the hydrogen folks to think about +is how much do you actually want to make + + align:start position:0% +is how much do you actually want to make + + + align:start position:0% +is how much do you actually want to make +and if that's a small amount do you even + + align:start position:0% +and if that's a small amount do you even + + + align:start position:0% +and if that's a small amount do you even +care about the cost of production + + align:start position:0% +care about the cost of production + + + align:start position:0% +care about the cost of production +because if you're only making a small + + align:start position:0% +because if you're only making a small + + + align:start position:0% +because if you're only making a small +amount you can use an expensive process + + align:start position:0% +amount you can use an expensive process + + + align:start position:0% +amount you can use an expensive process +and the overall cost of the hydrogen + + align:start position:0% +and the overall cost of the hydrogen + + + align:start position:0% +and the overall cost of the hydrogen +production versus the overall plant + + align:start position:0% +production versus the overall plant + + + align:start position:0% +production versus the overall plant +could be negligible in which case that + + align:start position:0% +could be negligible in which case that + + + align:start position:0% +could be negligible in which case that +could open up more options for you guys + + align:start position:0% +could open up more options for you guys + + + align:start position:0% +could open up more options for you guys +to consider so the first process I'll + + align:start position:0% +to consider so the first process I'll + + + align:start position:0% +to consider so the first process I'll +talk about which I don't recommend using + + align:start position:0% +talk about which I don't recommend using + + + align:start position:0% +talk about which I don't recommend using +would be the Karner process which is + + align:start position:0% +would be the Karner process which is + + + align:start position:0% +would be the Karner process which is +pretty simple you take a fuel you zap it + + align:start position:0% +pretty simple you take a fuel you zap it + + + align:start position:0% +pretty simple you take a fuel you zap it +with a plasma arc at about 1600 Celsius + + align:start position:0% +with a plasma arc at about 1600 Celsius + + + align:start position:0% +with a plasma arc at about 1600 Celsius +and out comes carbon and hydrogen some + + align:start position:0% +and out comes carbon and hydrogen some + + + align:start position:0% +and out comes carbon and hydrogen some +problems with this is it burns fuel it + + align:start position:0% +problems with this is it burns fuel it + + + align:start position:0% +problems with this is it burns fuel it +requires 1600 sea temperatures which I + + align:start position:0% +requires 1600 sea temperatures which I + + + align:start position:0% +requires 1600 sea temperatures which I +don't think any of our designs can even + + align:start position:0% +don't think any of our designs can even + + + align:start position:0% +don't think any of our designs can even +come close and there are also other + + align:start position:0% +come close and there are also other + + + align:start position:0% +come close and there are also other +processes that gasify fuels + + align:start position:0% +processes that gasify fuels + + + align:start position:0% +processes that gasify fuels +I wouldn't take all those off the market + + align:start position:0% +I wouldn't take all those off the market + + + align:start position:0% +I wouldn't take all those off the market +yet but this is an example of one that's + + align:start position:0% +yet but this is an example of one that's + + + align:start position:0% +yet but this is an example of one that's +used + + align:start position:0% +used + + + align:start position:0% +used +but I wouldn't consider for you guys one + + align:start position:0% +but I wouldn't consider for you guys one + + + align:start position:0% +but I wouldn't consider for you guys one +solution that's been tried and true for + + align:start position:0% +solution that's been tried and true for + + + align:start position:0% +solution that's been tried and true for +over a hundred years is low-temperature + + align:start position:0% +over a hundred years is low-temperature + + + align:start position:0% +over a hundred years is low-temperature +electrolysis this is also pretty simple + + align:start position:0% +electrolysis this is also pretty simple + + + align:start position:0% +electrolysis this is also pretty simple +it works as low as room temperature all + + align:start position:0% +it works as low as room temperature all + + + align:start position:0% +it works as low as room temperature all +you do is you take some water and maybe + + align:start position:0% +you do is you take some water and maybe + + + align:start position:0% +you do is you take some water and maybe +a soluble salt to improve the + + align:start position:0% +a soluble salt to improve the + + + align:start position:0% +a soluble salt to improve the +conductivity hook up a battery or + + align:start position:0% +conductivity hook up a battery or + + + align:start position:0% +conductivity hook up a battery or +another electro-motive source to some + + align:start position:0% +another electro-motive source to some + + + align:start position:0% +another electro-motive source to some +electrodes oxygen comes out on one + + align:start position:0% +electrodes oxygen comes out on one + + + align:start position:0% +electrodes oxygen comes out on one +electrode and hydrogen comes out on the + + align:start position:0% +electrode and hydrogen comes out on the + + + align:start position:0% +electrode and hydrogen comes out on the +other now there are some problems with + + align:start position:0% +other now there are some problems with + + + align:start position:0% +other now there are some problems with +this it requires electricity and if you + + align:start position:0% +this it requires electricity and if you + + + align:start position:0% +this it requires electricity and if you +guys are in the process of making heat + + align:start position:0% +guys are in the process of making heat + + + align:start position:0% +guys are in the process of making heat +you have to go from heat convert to + + align:start position:0% +you have to go from heat convert to + + + align:start position:0% +you have to go from heat convert to +electricity where you lose about + + align:start position:0% +electricity where you lose about + + + align:start position:0% +electricity where you lose about +two-thirds of your energy then convert + + align:start position:0% +two-thirds of your energy then convert + + + align:start position:0% +two-thirds of your energy then convert +to hydrogen so it's a fairly inefficient + + align:start position:0% +to hydrogen so it's a fairly inefficient + + + align:start position:0% +to hydrogen so it's a fairly inefficient +process and it's expensive you need to + + align:start position:0% +process and it's expensive you need to + + + align:start position:0% +process and it's expensive you need to +use things like platinum electrodes and + + align:start position:0% +use things like platinum electrodes and + + + align:start position:0% +use things like platinum electrodes and +there's a fairly high cell voltage to + + align:start position:0% +there's a fairly high cell voltage to + + + align:start position:0% +there's a fairly high cell voltage to +overcome well that may not look like a + + align:start position:0% +overcome well that may not look like a + + + align:start position:0% +overcome well that may not look like a +high voltage compared to the wall and + + align:start position:0% +high voltage compared to the wall and + + + align:start position:0% +high voltage compared to the wall and +electrochemical terms it's pretty big + + align:start position:0% +electrochemical terms it's pretty big + + + align:start position:0% +electrochemical terms it's pretty big +now again you don't have to exclude this + + align:start position:0% +now again you don't have to exclude this + + + align:start position:0% +now again you don't have to exclude this +if you only want to make a small amount + + align:start position:0% +if you only want to make a small amount + + + align:start position:0% +if you only want to make a small amount +of hydrogen for whatever reason you + + align:start position:0% +of hydrogen for whatever reason you + + + align:start position:0% +of hydrogen for whatever reason you +choose you might go with this there are + + align:start position:0% +choose you might go with this there are + + + align:start position:0% +choose you might go with this there are +actually you know consumer devices + + align:start position:0% +actually you know consumer devices + + + align:start position:0% +actually you know consumer devices +hydrogen electrolysis machines that you + + align:start position:0% +hydrogen electrolysis machines that you + + + align:start position:0% +hydrogen electrolysis machines that you +plug into the wall and hydrogen comes + + align:start position:0% +plug into the wall and hydrogen comes + + + align:start position:0% +plug into the wall and hydrogen comes +out we in fact use one in our lab + + align:start position:0% +out we in fact use one in our lab + + + align:start position:0% +out we in fact use one in our lab +although it only makes about 20 cubic + + align:start position:0% +although it only makes about 20 cubic + + + align:start position:0% +although it only makes about 20 cubic +centimeters per minute so probably need + + align:start position:0% +centimeters per minute so probably need + + + align:start position:0% +centimeters per minute so probably need +a little more than that so what can we + + align:start position:0% +a little more than that so what can we + + + align:start position:0% +a little more than that so what can we +do to improve the situation we can + + align:start position:0% +do to improve the situation we can + + + align:start position:0% +do to improve the situation we can +increase the temperature drastically + + align:start position:0% +increase the temperature drastically + + + align:start position:0% +increase the temperature drastically +this plot over here shows the free + + align:start position:0% +this plot over here shows the free + + + align:start position:0% +this plot over here shows the free +energy of the electrolysis of water of + + align:start position:0% +energy of the electrolysis of water of + + + align:start position:0% +energy of the electrolysis of water of +basically of breaking apart water versus + + align:start position:0% +basically of breaking apart water versus + + + align:start position:0% +basically of breaking apart water versus +temperature and you can see it goes down + + align:start position:0% +temperature and you can see it goes down + + + align:start position:0% +temperature and you can see it goes down +pretty steep with temperature if you + + align:start position:0% +pretty steep with temperature if you + + + align:start position:0% +pretty steep with temperature if you +look at the equilibrium constant the + + align:start position:0% +look at the equilibrium constant the + + + align:start position:0% +look at the equilibrium constant the +dissociation constant it's going up by a + + align:start position:0% +dissociation constant it's going up by a + + + align:start position:0% +dissociation constant it's going up by a +you know 10 or 20 orders of magnitude + + align:start position:0% +you know 10 or 20 orders of magnitude + + + align:start position:0% +you know 10 or 20 orders of magnitude +every hundred or 200 see what happens + + align:start position:0% +every hundred or 200 see what happens + + + align:start position:0% +every hundred or 200 see what happens +when this k equals 1 what's going to + + align:start position:0% +when this k equals 1 what's going to + + + align:start position:0% +when this k equals 1 what's going to +start happening + + align:start position:0% + + + + align:start position:0% + +do you guys remember this at all from + + align:start position:0% +do you guys remember this at all from + + + align:start position:0% +do you guys remember this at all from +who took 3 or 91 no one took 4 unite on + + align:start position:0% +who took 3 or 91 no one took 4 unite on + + + align:start position:0% +who took 3 or 91 no one took 4 unite on +Wow ok once once you have a reaction + + align:start position:0% +Wow ok once once you have a reaction + + + align:start position:0% +Wow ok once once you have a reaction +constant of one products and the + + align:start position:0% +constant of one products and the + + + align:start position:0% +constant of one products and the +reactants are going to be in equal + + align:start position:0% +reactants are going to be in equal + + + align:start position:0% +reactants are going to be in equal +concentrations roughly so you know if we + + align:start position:0% +concentrations roughly so you know if we + + + align:start position:0% +concentrations roughly so you know if we +have if we extrapolate out to where K + + align:start position:0% +have if we extrapolate out to where K + + + align:start position:0% +have if we extrapolate out to where K +equals 1 the temperature is like off the + + align:start position:0% +equals 1 the temperature is like off the + + + align:start position:0% +equals 1 the temperature is like off the +chart so that's no good for us but we + + align:start position:0% +chart so that's no good for us but we + + + align:start position:0% +chart so that's no good for us but we +can make it easier and so by supplying a + + align:start position:0% +can make it easier and so by supplying a + + + align:start position:0% +can make it easier and so by supplying a +lot of the energy in the form of heat + + align:start position:0% +lot of the energy in the form of heat + + + align:start position:0% +lot of the energy in the form of heat +you can lower the amount of electric + + align:start position:0% +you can lower the amount of electric + + + align:start position:0% +you can lower the amount of electric +input that you need to electrolyze water + + align:start position:0% +input that you need to electrolyze water + + + align:start position:0% +input that you need to electrolyze water +there are three common cycles used that + + align:start position:0% +there are three common cycles used that + + + align:start position:0% +there are three common cycles used that +use high temperature we're talking you + + align:start position:0% +use high temperature we're talking you + + + align:start position:0% +use high temperature we're talking you +know 8 to 850 celsius heat that's not a + + align:start position:0% +know 8 to 850 celsius heat that's not a + + + align:start position:0% +know 8 to 850 celsius heat that's not a +hard requirement that's just the number + + align:start position:0% +hard requirement that's just the number + + + align:start position:0% +hard requirement that's just the number +at which folks have agreed it's + + align:start position:0% +at which folks have agreed it's + + + align:start position:0% +at which folks have agreed it's +efficient enough to pursue it works at + + align:start position:0% +efficient enough to pursue it works at + + + align:start position:0% +efficient enough to pursue it works at +lower temperatures not not that much + + align:start position:0% +lower temperatures not not that much + + + align:start position:0% +lower temperatures not not that much +lower maybe a couple hundred degrees but + + align:start position:0% +lower maybe a couple hundred degrees but + + + align:start position:0% +lower maybe a couple hundred degrees but +the efficiency is really low so the + + align:start position:0% +the efficiency is really low so the + + + align:start position:0% +the efficiency is really low so the +names of these cycles which I'm sure + + align:start position:0% +names of these cycles which I'm sure + + + align:start position:0% +names of these cycles which I'm sure +you'll see in the papers a lot are the + + align:start position:0% +you'll see in the papers a lot are the + + + align:start position:0% +you'll see in the papers a lot are the +espera mark 13 cycle the hybrid sulfur + + align:start position:0% +espera mark 13 cycle the hybrid sulfur + + + align:start position:0% +espera mark 13 cycle the hybrid sulfur +cycle which is also known as the + + align:start position:0% +cycle which is also known as the + + + align:start position:0% +cycle which is also known as the +Westinghouse sulfur process and GA 22 + + align:start position:0% +Westinghouse sulfur process and GA 22 + + + align:start position:0% +Westinghouse sulfur process and GA 22 +and it's per mark 11 they're all the + + align:start position:0% +and it's per mark 11 they're all the + + + align:start position:0% +and it's per mark 11 they're all the +same thing as well as the sulfur iodine + + align:start position:0% +same thing as well as the sulfur iodine + + + align:start position:0% +same thing as well as the sulfur iodine +process and I'll just explain these + + align:start position:0% +process and I'll just explain these + + + align:start position:0% +process and I'll just explain these +processes really quickly to you guys so + + align:start position:0% +processes really quickly to you guys so + + + align:start position:0% +processes really quickly to you guys so +the theory behind these all is very + + align:start position:0% +the theory behind these all is very + + + align:start position:0% +the theory behind these all is very +similar you raise the temperature you + + align:start position:0% +similar you raise the temperature you + + + align:start position:0% +similar you raise the temperature you +lower the activation energy to break + + align:start position:0% +lower the activation energy to break + + + align:start position:0% +lower the activation energy to break +apart that water molecule in addition + + align:start position:0% +apart that water molecule in addition + + + align:start position:0% +apart that water molecule in addition +you add sulfuric acid you lower the cell + + align:start position:0% +you add sulfuric acid you lower the cell + + + align:start position:0% +you add sulfuric acid you lower the cell +voltage so the lee lower the + + align:start position:0% +voltage so the lee lower the + + + align:start position:0% +voltage so the lee lower the +electrochemical force you need to break + + align:start position:0% +electrochemical force you need to break + + + align:start position:0% +electrochemical force you need to break +apart water all these three processes + + align:start position:0% +apart water all these three processes + + + align:start position:0% +apart water all these three processes +use the same first step where you start + + align:start position:0% +use the same first step where you start + + + align:start position:0% +use the same first step where you start +off with sulfuric acid and water and + + align:start position:0% +off with sulfuric acid and water and + + + align:start position:0% +off with sulfuric acid and water and +sulfur dioxide which is an equilibrium + + align:start position:0% +sulfur dioxide which is an equilibrium + + + align:start position:0% +sulfur dioxide which is an equilibrium +with h2 so4 and you break it apart into + + align:start position:0% +with h2 so4 and you break it apart into + + + align:start position:0% +with h2 so4 and you break it apart into +so2 h2o + o2 and i'll get back to this + + align:start position:0% +so2 h2o + o2 and i'll get back to this + + + align:start position:0% +so2 h2o + o2 and i'll get back to this +in a second i'll mention that maybe five + + align:start position:0% +in a second i'll mention that maybe five + + + align:start position:0% +in a second i'll mention that maybe five +minutes step two for the sulfur iodine + + align:start position:0% +minutes step two for the sulfur iodine + + + align:start position:0% +minutes step two for the sulfur iodine +and is pura thirteen processes which are + + align:start position:0% +and is pura thirteen processes which are + + + align:start position:0% +and is pura thirteen processes which are +very very similar is then you takes + + align:start position:0% +very very similar is then you takes + + + align:start position:0% +very very similar is then you takes +iodine for the sulfur iodine process or + + align:start position:0% +iodine for the sulfur iodine process or + + + align:start position:0% +iodine for the sulfur iodine process or +bromine for the espera 13 process either + + align:start position:0% +bromine for the espera 13 process either + + + align:start position:0% +bromine for the espera 13 process either +way it's a halogen add it and you end up + + align:start position:0% +way it's a halogen add it and you end up + + + align:start position:0% +way it's a halogen add it and you end up +with hydroiodic acid or hide + + align:start position:0% +with hydroiodic acid or hide + + + align:start position:0% +with hydroiodic acid or hide +Romek acid chemically they're very very + + align:start position:0% +Romek acid chemically they're very very + + + align:start position:0% +Romek acid chemically they're very very +similar and sulfuric acid + + align:start position:0% +similar and sulfuric acid + + + align:start position:0% +similar and sulfuric acid +step three is you break these apart in a + + align:start position:0% +step three is you break these apart in a + + + align:start position:0% +step three is you break these apart in a +lower temperature reaction like 400 or + + align:start position:0% +lower temperature reaction like 400 or + + + align:start position:0% +lower temperature reaction like 400 or +450 C into hydrogen and you get out your + + align:start position:0% +450 C into hydrogen and you get out your + + + align:start position:0% +450 C into hydrogen and you get out your +halogen again step two for the + + align:start position:0% +halogen again step two for the + + + align:start position:0% +halogen again step two for the +westinghouse sulfur process which is the + + align:start position:0% +westinghouse sulfur process which is the + + + align:start position:0% +westinghouse sulfur process which is the +only other step besides step one it's + + align:start position:0% +only other step besides step one it's + + + align:start position:0% +only other step besides step one it's +direct electrolysis from sulfur dioxide + + align:start position:0% +direct electrolysis from sulfur dioxide + + + align:start position:0% +direct electrolysis from sulfur dioxide +and water directly back to h2 so4 and + + align:start position:0% +and water directly back to h2 so4 and + + + align:start position:0% +and water directly back to h2 so4 and +hydrogen but all of these require input + + align:start position:0% +hydrogen but all of these require input + + + align:start position:0% +hydrogen but all of these require input +heat at 850 C or so in order to for most + + align:start position:0% +heat at 850 C or so in order to for most + + + align:start position:0% +heat at 850 C or so in order to for most +people to consider them efficient and + + align:start position:0% +people to consider them efficient and + + + align:start position:0% +people to consider them efficient and +that's not that doesn't leave the core a + + align:start position:0% +that's not that doesn't leave the core a + + + align:start position:0% +that's not that doesn't leave the core a +lot of options just to go through a + + align:start position:0% +lot of options just to go through a + + + align:start position:0% +lot of options just to go through a +diagram of the sulfur iodide process + + align:start position:0% +diagram of the sulfur iodide process + + + align:start position:0% +diagram of the sulfur iodide process +there's sort of a high temperature step + + align:start position:0% +there's sort of a high temperature step + + + align:start position:0% +there's sort of a high temperature step +where you end up splitting sulfuric acid + + align:start position:0% +where you end up splitting sulfuric acid + + + align:start position:0% +where you end up splitting sulfuric acid +and there's a low temperature step where + + align:start position:0% +and there's a low temperature step where + + + align:start position:0% +and there's a low temperature step where +you end up splitting up your halogen + + align:start position:0% +you end up splitting up your halogen + + + align:start position:0% +you end up splitting up your halogen +acid into actual hydrogen there is a + + align:start position:0% +acid into actual hydrogen there is a + + + align:start position:0% +acid into actual hydrogen there is a +little bit of heat rejection it needs a + + align:start position:0% +little bit of heat rejection it needs a + + + align:start position:0% +little bit of heat rejection it needs a +fair bit of water and oxygen is removed + + align:start position:0% +fair bit of water and oxygen is removed + + + align:start position:0% +fair bit of water and oxygen is removed +and you can actually remove more of it + + align:start position:0% +and you can actually remove more of it + + + align:start position:0% +and you can actually remove more of it +which I'll get into in a second + + align:start position:0% +which I'll get into in a second + + + align:start position:0% +which I'll get into in a second +the other two processes have the same + + align:start position:0% +the other two processes have the same + + + align:start position:0% +the other two processes have the same +high-temperature reactions and they just + + align:start position:0% +high-temperature reactions and they just + + + align:start position:0% +high-temperature reactions and they just +have slightly different low-temperature + + align:start position:0% +have slightly different low-temperature + + + align:start position:0% +have slightly different low-temperature +reactions now these aren't really the + + align:start position:0% +reactions now these aren't really the + + + align:start position:0% +reactions now these aren't really the +limiting factors here notice on this + + align:start position:0% +limiting factors here notice on this + + + align:start position:0% +limiting factors here notice on this +diagram well first of all notice this + + align:start position:0% +diagram well first of all notice this + + + align:start position:0% +diagram well first of all notice this +source this would be a good one to look + + align:start position:0% +source this would be a good one to look + + + align:start position:0% +source this would be a good one to look +up and go from there on this diagram + + align:start position:0% +up and go from there on this diagram + + + align:start position:0% +up and go from there on this diagram +it's indicated that with an inorganic + + align:start position:0% +it's indicated that with an inorganic + + + align:start position:0% +it's indicated that with an inorganic +membrane the process heat input is + + align:start position:0% +membrane the process heat input is + + + align:start position:0% +membrane the process heat input is +lowered to 700 C has anyone ever heard + + align:start position:0% +lowered to 700 C has anyone ever heard + + + align:start position:0% +lowered to 700 C has anyone ever heard +of this process of molecular sieving + + align:start position:0% +of this process of molecular sieving + + + align:start position:0% +of this process of molecular sieving +where you filter literally filter out + + align:start position:0% +where you filter literally filter out + + + align:start position:0% +where you filter literally filter out +the smaller molecules no okay well I'll + + align:start position:0% +the smaller molecules no okay well I'll + + + align:start position:0% +the smaller molecules no okay well I'll +go into that right now one of the ways + + align:start position:0% +go into that right now one of the ways + + + align:start position:0% +go into that right now one of the ways +that you can lower the temperature + + align:start position:0% +that you can lower the temperature + + + align:start position:0% +that you can lower the temperature +requirement for these hydrogen reactions + + align:start position:0% +requirement for these hydrogen reactions + + + align:start position:0% +requirement for these hydrogen reactions +is to remove the products from the + + align:start position:0% +is to remove the products from the + + + align:start position:0% +is to remove the products from the +reaction this reaction is going to have + + align:start position:0% +reaction this reaction is going to have + + + align:start position:0% +reaction this reaction is going to have +some sort of equilibrium constant and if + + align:start position:0% +some sort of equilibrium constant and if + + + align:start position:0% +some sort of equilibrium constant and if +you remove products from one side you + + align:start position:0% +you remove products from one side you + + + align:start position:0% +you remove products from one side you +shift the reaction in the direction of + + align:start position:0% +shift the reaction in the direction of + + + align:start position:0% +shift the reaction in the direction of +the removed products one way to two ways + + align:start position:0% +the removed products one way to two ways + + + align:start position:0% +the removed products one way to two ways +to remove the products are to have a + + align:start position:0% +to remove the products are to have a + + + align:start position:0% +to remove the products are to have a +membrane with different sized holes so + + align:start position:0% +membrane with different sized holes so + + + align:start position:0% +membrane with different sized holes so +this has taken from a similar but + + align:start position:0% +this has taken from a similar but + + + align:start position:0% +this has taken from a similar but +different application trying to separate + + align:start position:0% +different application trying to separate + + + align:start position:0% +different application trying to separate +hydrogen from nitrogen the nitrogen + + align:start position:0% +hydrogen from nitrogen the nitrogen + + + align:start position:0% +hydrogen from nitrogen the nitrogen +molecules of these big green while + + align:start position:0% +molecules of these big green while + + + align:start position:0% +molecules of these big green while +and the hydrogen ones are the small blue + + align:start position:0% +and the hydrogen ones are the small blue + + + align:start position:0% +and the hydrogen ones are the small blue +ones if you have a hole in the membrane + + align:start position:0% +ones if you have a hole in the membrane + + + align:start position:0% +ones if you have a hole in the membrane +big enough for them all to pass through + + align:start position:0% +big enough for them all to pass through + + + align:start position:0% +big enough for them all to pass through +pretty easily you don't end up + + align:start position:0% +pretty easily you don't end up + + + align:start position:0% +pretty easily you don't end up +separating them they all get through and + + align:start position:0% +separating them they all get through and + + + align:start position:0% +separating them they all get through and +it's just a leaky membrane if you have a + + align:start position:0% +it's just a leaky membrane if you have a + + + align:start position:0% +it's just a leaky membrane if you have a +membrane that's just slightly too big to + + align:start position:0% +membrane that's just slightly too big to + + + align:start position:0% +membrane that's just slightly too big to +stop the nitrogen molecules from going + + align:start position:0% +stop the nitrogen molecules from going + + + align:start position:0% +stop the nitrogen molecules from going +through you enter a regime what's known + + align:start position:0% +through you enter a regime what's known + + + align:start position:0% +through you enter a regime what's known +as Knudsen diffusion again going back to + + align:start position:0% +as Knudsen diffusion again going back to + + + align:start position:0% +as Knudsen diffusion again going back to +this 3:09 one knowledge if you have a + + align:start position:0% +this 3:09 one knowledge if you have a + + + align:start position:0% +this 3:09 one knowledge if you have a +bunch of different molecules at the same + + align:start position:0% +bunch of different molecules at the same + + + align:start position:0% +bunch of different molecules at the same +temperature + + align:start position:0% +temperature + + + align:start position:0% +temperature +they have different kinetic energies + + align:start position:0% +they have different kinetic energies + + + align:start position:0% +they have different kinetic energies +where the lighter molecules will have a + + align:start position:0% +where the lighter molecules will have a + + + align:start position:0% +where the lighter molecules will have a +higher kinetic energy than the lower + + align:start position:0% +higher kinetic energy than the lower + + + align:start position:0% +higher kinetic energy than the lower +than the sorry than the heavier ones + + align:start position:0% +than the sorry than the heavier ones + + + align:start position:0% +than the sorry than the heavier ones +from ke equals 1/2 MV squared something + + align:start position:0% +from ke equals 1/2 MV squared something + + + align:start position:0% +from ke equals 1/2 MV squared something +has a higher kinetic energy it has a + + align:start position:0% +has a higher kinetic energy it has a + + + align:start position:0% +has a higher kinetic energy it has a +higher velocity which means it's + + align:start position:0% +higher velocity which means it's + + + align:start position:0% +higher velocity which means it's +bouncing up and back against this + + align:start position:0% +bouncing up and back against this + + + align:start position:0% +bouncing up and back against this +membrane more frequently so more of the + + align:start position:0% +membrane more frequently so more of the + + + align:start position:0% +membrane more frequently so more of the +smaller molecules will make an attempt + + align:start position:0% +smaller molecules will make an attempt + + + align:start position:0% +smaller molecules will make an attempt +at getting through this hole than the + + align:start position:0% +at getting through this hole than the + + + align:start position:0% +at getting through this hole than the +larger ones you can also have what's + + align:start position:0% +larger ones you can also have what's + + + align:start position:0% +larger ones you can also have what's +called a molecular sieve which is where + + align:start position:0% +called a molecular sieve which is where + + + align:start position:0% +called a molecular sieve which is where +you have holes that are literally too + + align:start position:0% +you have holes that are literally too + + + align:start position:0% +you have holes that are literally too +small for the bigger molecules to get + + align:start position:0% +small for the bigger molecules to get + + + align:start position:0% +small for the bigger molecules to get +through so all that comes out here is + + align:start position:0% +through so all that comes out here is + + + align:start position:0% +through so all that comes out here is +hydrogen leaving the nitrogen behind but + + align:start position:0% +hydrogen leaving the nitrogen behind but + + + align:start position:0% +hydrogen leaving the nitrogen behind but +there are drawbacks to that the total + + align:start position:0% +there are drawbacks to that the total + + + align:start position:0% +there are drawbacks to that the total +mass throughput here could be lower so + + align:start position:0% +mass throughput here could be lower so + + + align:start position:0% +mass throughput here could be lower so +you have to think about how much do you + + align:start position:0% +you have to think about how much do you + + + align:start position:0% +you have to think about how much do you +want to purify the hydrogen in this step + + align:start position:0% +want to purify the hydrogen in this step + + + align:start position:0% +want to purify the hydrogen in this step +in terms of removing or you know not the + + align:start position:0% +in terms of removing or you know not the + + + align:start position:0% +in terms of removing or you know not the +huh sorry not the hydrogen the products + + align:start position:0% +huh sorry not the hydrogen the products + + + align:start position:0% +huh sorry not the hydrogen the products +in this step how much do you want to + + align:start position:0% +in this step how much do you want to + + + align:start position:0% +in this step how much do you want to +remove the products you know in terms of + + align:start position:0% +remove the products you know in terms of + + + align:start position:0% +remove the products you know in terms of +purity versus mass flow that's the big + + align:start position:0% +purity versus mass flow that's the big + + + align:start position:0% +purity versus mass flow that's the big +trade-off here there are plenty of new + + align:start position:0% +trade-off here there are plenty of new + + + align:start position:0% +trade-off here there are plenty of new +methods for producing hydrogen one of + + align:start position:0% +methods for producing hydrogen one of + + + align:start position:0% +methods for producing hydrogen one of +them is to use microbes some bacteria + + align:start position:0% +them is to use microbes some bacteria + + + align:start position:0% +them is to use microbes some bacteria +actually produce hydrogen when they are + + align:start position:0% +actually produce hydrogen when they are + + + align:start position:0% +actually produce hydrogen when they are +deprived of sulfur so there are a lot of + + align:start position:0% +deprived of sulfur so there are a lot of + + + align:start position:0% +deprived of sulfur so there are a lot of +bacteria that normally rely on a sulfur + + align:start position:0% +bacteria that normally rely on a sulfur + + + align:start position:0% +bacteria that normally rely on a sulfur +digestion cycle when you remove them + + align:start position:0% +digestion cycle when you remove them + + + align:start position:0% +digestion cycle when you remove them +they start metabolizing other things and + + align:start position:0% +they start metabolizing other things and + + + align:start position:0% +they start metabolizing other things and +one of the byproducts is hydrogen so + + align:start position:0% +one of the byproducts is hydrogen so + + + align:start position:0% +one of the byproducts is hydrogen so +another way you may consider making + + align:start position:0% +another way you may consider making + + + align:start position:0% +another way you may consider making +hydrogen in small to medium amounts is + + align:start position:0% +hydrogen in small to medium amounts is + + + align:start position:0% +hydrogen in small to medium amounts is +biologically with bacteria does not + + align:start position:0% +biologically with bacteria does not + + + align:start position:0% +biologically with bacteria does not +require much process heat that could + + align:start position:0% +require much process heat that could + + + align:start position:0% +require much process heat that could +simplify the process heat people's world + + align:start position:0% +simplify the process heat people's world + + + align:start position:0% +simplify the process heat people's world +by removing heat transport to the + + align:start position:0% +by removing heat transport to the + + + align:start position:0% +by removing heat transport to the +hydrogen plant all you really need is + + align:start position:0% +hydrogen plant all you really need is + + + align:start position:0% +hydrogen plant all you really need is +enough electricity to power the building + + align:start position:0% +enough electricity to power the building + + + align:start position:0% +enough electricity to power the building +and + + align:start position:0% +and + + + align:start position:0% +and +or ancillary stuff you need to keep the + + align:start position:0% +or ancillary stuff you need to keep the + + + align:start position:0% +or ancillary stuff you need to keep the +bacteria alive and there are lots of + + align:start position:0% +bacteria alive and there are lots of + + + align:start position:0% +bacteria alive and there are lots of +bacteria like e-coli and all these other + + align:start position:0% +bacteria like e-coli and all these other + + + align:start position:0% +bacteria like e-coli and all these other +ones that can produce hydrogen from + + align:start position:0% +ones that can produce hydrogen from + + + align:start position:0% +ones that can produce hydrogen from +organic materials there's also a new + + align:start position:0% +organic materials there's also a new + + + align:start position:0% +organic materials there's also a new +process coming out low temperature urine + + align:start position:0% +process coming out low temperature urine + + + align:start position:0% +process coming out low temperature urine +electrolysis believe it or not urea + + align:start position:0% +electrolysis believe it or not urea + + + align:start position:0% +electrolysis believe it or not urea +contains four very weakly bound hydrogen + + align:start position:0% +contains four very weakly bound hydrogen + + + align:start position:0% +contains four very weakly bound hydrogen +atoms compared to water and it has a + + align:start position:0% +atoms compared to water and it has a + + + align:start position:0% +atoms compared to water and it has a +much lower cell voltage than water so + + align:start position:0% +much lower cell voltage than water so + + + align:start position:0% +much lower cell voltage than water so +it's about three it's a little more than + + align:start position:0% +it's about three it's a little more than + + + align:start position:0% +it's about three it's a little more than +three times as efficient according to + + align:start position:0% +three times as efficient according to + + + align:start position:0% +three times as efficient according to +some preliminary research to electrolyze + + align:start position:0% +some preliminary research to electrolyze + + + align:start position:0% +some preliminary research to electrolyze +urine and water and urine is one of the + + align:start position:0% +urine and water and urine is one of the + + + align:start position:0% +urine and water and urine is one of the +largest waste streams on the planet so + + align:start position:0% +largest waste streams on the planet so + + + align:start position:0% +largest waste streams on the planet so +if you want to consider collecting + + align:start position:0% +if you want to consider collecting + + + align:start position:0% +if you want to consider collecting +transporting and using this valuable + + align:start position:0% +transporting and using this valuable + + + align:start position:0% +transporting and using this valuable +resource you might just make your lives + + align:start position:0% +resource you might just make your lives + + + align:start position:0% +resource you might just make your lives +easier not to mention that with a lower + + align:start position:0% +easier not to mention that with a lower + + + align:start position:0% +easier not to mention that with a lower +cell voltage you don't need these + + align:start position:0% +cell voltage you don't need these + + + align:start position:0% +cell voltage you don't need these +expensive platinum catalysts it can use + + align:start position:0% +expensive platinum catalysts it can use + + + align:start position:0% +expensive platinum catalysts it can use +nickel so that takes a lot of the cost + + align:start position:0% +nickel so that takes a lot of the cost + + + align:start position:0% +nickel so that takes a lot of the cost +out of these electrolysis cells and + + align:start position:0% +out of these electrolysis cells and + + + align:start position:0% +out of these electrolysis cells and +there are plenty more that exist I don't + + align:start position:0% +there are plenty more that exist I don't + + + align:start position:0% +there are plenty more that exist I don't +want to go through them all because I + + align:start position:0% +want to go through them all because I + + + align:start position:0% +want to go through them all because I +need to get through two other lectures + + align:start position:0% +need to get through two other lectures + + + align:start position:0% +need to get through two other lectures +in this hour so on to biofuels more than + + align:start position:0% +in this hour so on to biofuels more than + + + align:start position:0% +in this hour so on to biofuels more than +bovine emissions but it actually has + + align:start position:0% +bovine emissions but it actually has + + + align:start position:0% +bovine emissions but it actually has +some of the methods do have a lot in + + align:start position:0% +some of the methods do have a lot in + + + align:start position:0% +some of the methods do have a lot in +quality with bovine emissions as you'll + + align:start position:0% +quality with bovine emissions as you'll + + + align:start position:0% +quality with bovine emissions as you'll +see in a second the basic theory is to + + align:start position:0% +see in a second the basic theory is to + + + align:start position:0% +see in a second the basic theory is to +produce hydrocarbons from carbon and + + align:start position:0% +produce hydrocarbons from carbon and + + + align:start position:0% +produce hydrocarbons from carbon and +hydrogen bearing chemicals these + + align:start position:0% +hydrogen bearing chemicals these + + + align:start position:0% +hydrogen bearing chemicals these +hydrocarbons are used as fuel so you + + align:start position:0% +hydrocarbons are used as fuel so you + + + align:start position:0% +hydrocarbons are used as fuel so you +sort of burn in Reverse even even the + + align:start position:0% +sort of burn in Reverse even even the + + + align:start position:0% +sort of burn in Reverse even even the +word burn is a misnomer you run this + + align:start position:0% +word burn is a misnomer you run this + + + align:start position:0% +word burn is a misnomer you run this +combustion reaction in Reverse it + + align:start position:0% +combustion reaction in Reverse it + + + align:start position:0% +combustion reaction in Reverse it +consumes fairly large amounts of energy + + align:start position:0% +consumes fairly large amounts of energy + + + align:start position:0% +consumes fairly large amounts of energy +in terms of process heat and electricity + + align:start position:0% +in terms of process heat and electricity + + + align:start position:0% +in terms of process heat and electricity +but some major advantages are its + + align:start position:0% +but some major advantages are its + + + align:start position:0% +but some major advantages are its +sequester's carbon one of its inputs is + + align:start position:0% +sequester's carbon one of its inputs is + + + align:start position:0% +sequester's carbon one of its inputs is +carbon monoxide which can indirectly + + align:start position:0% +carbon monoxide which can indirectly + + + align:start position:0% +carbon monoxide which can indirectly +come carbon dioxide or from biological + + align:start position:0% +come carbon dioxide or from biological + + + align:start position:0% +come carbon dioxide or from biological +feedstock that use carbon dioxide as one + + align:start position:0% +feedstock that use carbon dioxide as one + + + align:start position:0% +feedstock that use carbon dioxide as one +of their inputs it can use waste from + + align:start position:0% +of their inputs it can use waste from + + + align:start position:0% +of their inputs it can use waste from +crop production so you can turn + + align:start position:0% +crop production so you can turn + + + align:start position:0% +crop production so you can turn +something that has been useless into + + align:start position:0% +something that has been useless into + + + align:start position:0% +something that has been useless into +something that is useful and really the + + align:start position:0% +something that is useful and really the + + + align:start position:0% +something that is useful and really the +reason I included on this project is it + + align:start position:0% +reason I included on this project is it + + + align:start position:0% +reason I included on this project is it +displaces fossil fuels so there's a lot + + align:start position:0% +displaces fossil fuels so there's a lot + + + align:start position:0% +displaces fossil fuels so there's a lot +of hype over domestic energy + + align:start position:0% +of hype over domestic energy + + + align:start position:0% +of hype over domestic energy +independence and producing these + + align:start position:0% +independence and producing these + + + align:start position:0% +independence and producing these +biofuels in this country is one of the + + align:start position:0% +biofuels in this country is one of the + + + align:start position:0% +biofuels in this country is one of the +best ways of doing that so one that + + align:start position:0% +best ways of doing that so one that + + + align:start position:0% +best ways of doing that so one that +you've + + align:start position:0% +you've + + + align:start position:0% +you've +probably seen if you own a car is + + align:start position:0% +probably seen if you own a car is + + + align:start position:0% +probably seen if you own a car is +producing ethanol from cellulose if you + + align:start position:0% +producing ethanol from cellulose if you + + + align:start position:0% +producing ethanol from cellulose if you +look at a lot of gas pumps today that + + align:start position:0% +look at a lot of gas pumps today that + + + align:start position:0% +look at a lot of gas pumps today that +they might not be this obvious but + + align:start position:0% +they might not be this obvious but + + + align:start position:0% +they might not be this obvious but +there'll be a sticker on it that says + + align:start position:0% +there'll be a sticker on it that says + + + align:start position:0% +there'll be a sticker on it that says +contains less than 10% ethanol which + + align:start position:0% +contains less than 10% ethanol which + + + align:start position:0% +contains less than 10% ethanol which +means it contains some ethanol a lot of + + align:start position:0% +means it contains some ethanol a lot of + + + align:start position:0% +means it contains some ethanol a lot of +that ethanol comes from corn corn + + align:start position:0% +that ethanol comes from corn corn + + + align:start position:0% +that ethanol comes from corn corn +produces a lot of sugar that sugar can + + align:start position:0% +produces a lot of sugar that sugar can + + + align:start position:0% +produces a lot of sugar that sugar can +be fermented into ethanol that ethanol + + align:start position:0% +be fermented into ethanol that ethanol + + + align:start position:0% +be fermented into ethanol that ethanol +can be burned into your car it's made + + align:start position:0% +can be burned into your car it's made + + + align:start position:0% +can be burned into your car it's made +from enzymatic decomposition of + + align:start position:0% +from enzymatic decomposition of + + + align:start position:0% +from enzymatic decomposition of +lignocellulose to go over those terms + + align:start position:0% +lignocellulose to go over those terms + + + align:start position:0% +lignocellulose to go over those terms +lignin is sort of the woody part of the + + align:start position:0% +lignin is sort of the woody part of the + + + align:start position:0% +lignin is sort of the woody part of the +plant and ana cellulose are the poly + + align:start position:0% +plant and ana cellulose are the poly + + + align:start position:0% +plant and ana cellulose are the poly +sugars so this process is surprisingly + + align:start position:0% +sugars so this process is surprisingly + + + align:start position:0% +sugars so this process is surprisingly +similar to bovine emissions what you + + align:start position:0% +similar to bovine emissions what you + + + align:start position:0% +similar to bovine emissions what you +essentially do is get a giant mechanical + + align:start position:0% +essentially do is get a giant mechanical + + + align:start position:0% +essentially do is get a giant mechanical +cow of sorts ferment these products and + + align:start position:0% +cow of sorts ferment these products and + + + align:start position:0% +cow of sorts ferment these products and +siphon off the ethanol and it does + + align:start position:0% +siphon off the ethanol and it does + + + align:start position:0% +siphon off the ethanol and it does +produce biogas just like natural + + align:start position:0% +produce biogas just like natural + + + align:start position:0% +produce biogas just like natural +reactors cows there is a concern about + + align:start position:0% +reactors cows there is a concern about + + + align:start position:0% +reactors cows there is a concern about +producing toxins these lignin this + + align:start position:0% +producing toxins these lignin this + + + align:start position:0% +producing toxins these lignin this +ligneous lignin fraction produces a lot + + align:start position:0% +ligneous lignin fraction produces a lot + + + align:start position:0% +ligneous lignin fraction produces a lot +of funny aromatic compounds that are + + align:start position:0% +of funny aromatic compounds that are + + + align:start position:0% +of funny aromatic compounds that are +considered toxic there is this concern + + align:start position:0% +considered toxic there is this concern + + + align:start position:0% +considered toxic there is this concern +however valid about we're burning our + + align:start position:0% +however valid about we're burning our + + + align:start position:0% +however valid about we're burning our +food + + align:start position:0% +food + + + align:start position:0% +food +you know we're growing corn and then + + align:start position:0% +you know we're growing corn and then + + + align:start position:0% +you know we're growing corn and then +we're burning it in our cars when + + align:start position:0% +we're burning it in our cars when + + + align:start position:0% +we're burning it in our cars when +there's all these hungry people out + + align:start position:0% +there's all these hungry people out + + + align:start position:0% +there's all these hungry people out +there but I'll leave the validity of + + align:start position:0% +there but I'll leave the validity of + + + align:start position:0% +there but I'll leave the validity of +that concern up to you guys and this + + align:start position:0% +that concern up to you guys and this + + + align:start position:0% +that concern up to you guys and this +lignin fraction is often burned it's + + align:start position:0% +lignin fraction is often burned it's + + + align:start position:0% +lignin fraction is often burned it's +very hard to convert this into something + + align:start position:0% +very hard to convert this into something + + + align:start position:0% +very hard to convert this into something +that's useful so you burn it to produce + + align:start position:0% +that's useful so you burn it to produce + + + align:start position:0% +that's useful so you burn it to produce +energy to power the cellulose + + align:start position:0% +energy to power the cellulose + + + align:start position:0% +energy to power the cellulose +decomposition reactions so enter nuclear + + align:start position:0% +decomposition reactions so enter nuclear + + + align:start position:0% +decomposition reactions so enter nuclear +heat if we don't want to burn our food + + align:start position:0% +heat if we don't want to burn our food + + + align:start position:0% +heat if we don't want to burn our food +in our cars using a high-temperature + + align:start position:0% +in our cars using a high-temperature + + + align:start position:0% +in our cars using a high-temperature +process heat opens up a lot of doors you + + align:start position:0% +process heat opens up a lot of doors you + + + align:start position:0% +process heat opens up a lot of doors you +can produce something called syngas + + align:start position:0% +can produce something called syngas + + + align:start position:0% +can produce something called syngas +synthetic gas it's essentially a mixture + + align:start position:0% +synthetic gas it's essentially a mixture + + + align:start position:0% +synthetic gas it's essentially a mixture +of carbon monoxide hydrogen and other + + align:start position:0% +of carbon monoxide hydrogen and other + + + align:start position:0% +of carbon monoxide hydrogen and other +hydrocarbons that with sufficiently high + + align:start position:0% +hydrocarbons that with sufficiently high + + + align:start position:0% +hydrocarbons that with sufficiently high +temperature you can produce from a lot + + align:start position:0% +temperature you can produce from a lot + + + align:start position:0% +temperature you can produce from a lot +of these biofuels you can then further + + align:start position:0% +of these biofuels you can then further + + + align:start position:0% +of these biofuels you can then further +refine it if you don't want a gaseous + + align:start position:0% +refine it if you don't want a gaseous + + + align:start position:0% +refine it if you don't want a gaseous +end product in what's called fischer + + align:start position:0% +end product in what's called fischer + + + align:start position:0% +end product in what's called fischer +tropsch synthesis where you take those + + align:start position:0% +tropsch synthesis where you take those + + + align:start position:0% +tropsch synthesis where you take those +gases and you combine them and you end + + align:start position:0% +gases and you combine them and you end + + + align:start position:0% +gases and you combine them and you end +up forming liquid fuels and one of the + + align:start position:0% +up forming liquid fuels and one of the + + + align:start position:0% +up forming liquid fuels and one of the +nice thing about these liquid fuels is + + align:start position:0% +nice thing about these liquid fuels is + + + align:start position:0% +nice thing about these liquid fuels is +if you start with really pure sin gas + + align:start position:0% +if you start with really pure sin gas + + + align:start position:0% +if you start with really pure sin gas +you end up with really pure fuel + + align:start position:0% +you end up with really pure fuel + + + align:start position:0% +you end up with really pure fuel +this here is a beaker of commercial + + align:start position:0% +this here is a beaker of commercial + + + align:start position:0% +this here is a beaker of commercial +diesel fuel over here is a beaker of + + align:start position:0% +diesel fuel over here is a beaker of + + + align:start position:0% +diesel fuel over here is a beaker of +fischer Tropes synthetic diesel fuel a + + align:start position:0% +fischer Tropes synthetic diesel fuel a + + + align:start position:0% +fischer Tropes synthetic diesel fuel a +lot of the yellow stuff can come from + + align:start position:0% +lot of the yellow stuff can come from + + + align:start position:0% +lot of the yellow stuff can come from +sulfur compounds which is one of the + + align:start position:0% +sulfur compounds which is one of the + + + align:start position:0% +sulfur compounds which is one of the +main really bad emissions coming out of + + align:start position:0% +main really bad emissions coming out of + + + align:start position:0% +main really bad emissions coming out of +oil fields especially when used when + + align:start position:0% +oil fields especially when used when + + + align:start position:0% +oil fields especially when used when +we're running out of oil we have to go + + align:start position:0% +we're running out of oil we have to go + + + align:start position:0% +we're running out of oil we have to go +to lower quality sources which are + + align:start position:0% +to lower quality sources which are + + + align:start position:0% +to lower quality sources which are +higher and sulfur if you can find a way + + align:start position:0% +higher and sulfur if you can find a way + + + align:start position:0% +higher and sulfur if you can find a way +to produce this same fuel without + + align:start position:0% +to produce this same fuel without + + + align:start position:0% +to produce this same fuel without +locking in all the sulfur which ends up + + align:start position:0% +locking in all the sulfur which ends up + + + align:start position:0% +locking in all the sulfur which ends up +going out of your cars that's a real big + + align:start position:0% +going out of your cars that's a real big + + + align:start position:0% +going out of your cars that's a real big +plus so for sin gas what you do is + + align:start position:0% +plus so for sin gas what you do is + + + align:start position:0% +plus so for sin gas what you do is +partially combust whatever feedstock you + + align:start position:0% +partially combust whatever feedstock you + + + align:start position:0% +partially combust whatever feedstock you +want whether it's corn silage or + + align:start position:0% +want whether it's corn silage or + + + align:start position:0% +want whether it's corn silage or +switchgrass or sugarcane or whatever you + + align:start position:0% +switchgrass or sugarcane or whatever you + + + align:start position:0% +switchgrass or sugarcane or whatever you +want with oxygen to create carbon + + align:start position:0% +want with oxygen to create carbon + + + align:start position:0% +want with oxygen to create carbon +monoxide and hydrogen + + align:start position:0% +monoxide and hydrogen + + + align:start position:0% +monoxide and hydrogen +now this gas mixture can actually be + + align:start position:0% +now this gas mixture can actually be + + + align:start position:0% +now this gas mixture can actually be +burned as a fuel it's often burned in + + align:start position:0% +burned as a fuel it's often burned in + + + align:start position:0% +burned as a fuel it's often burned in +biofuel plants to fuel further reactions + + align:start position:0% +biofuel plants to fuel further reactions + + + align:start position:0% +biofuel plants to fuel further reactions +that require a high temperature + + align:start position:0% +that require a high temperature + + + align:start position:0% +that require a high temperature +feedstocks can be clamped plants or they + + align:start position:0% +feedstocks can be clamped plants or they + + + align:start position:0% +feedstocks can be clamped plants or they +can actually be coal has anyone heard of + + align:start position:0% +can actually be coal has anyone heard of + + + align:start position:0% +can actually be coal has anyone heard of +coal liquification or coal gas + + align:start position:0% +coal liquification or coal gas + + + align:start position:0% +coal liquification or coal gas +liquification this is pretty much what + + align:start position:0% +liquification this is pretty much what + + + align:start position:0% +liquification this is pretty much what +happens traditional coal to liquid + + align:start position:0% +happens traditional coal to liquid + + + align:start position:0% +happens traditional coal to liquid +technologies get about one third of the + + align:start position:0% +technologies get about one third of the + + + align:start position:0% +technologies get about one third of the +carbon from the coal into the fuel the + + align:start position:0% +carbon from the coal into the fuel the + + + align:start position:0% +carbon from the coal into the fuel the +rest emitted but with enough hydrogen + + align:start position:0% +rest emitted but with enough hydrogen + + + align:start position:0% +rest emitted but with enough hydrogen +from the nuclear plant you can actually + + align:start position:0% +from the nuclear plant you can actually + + + align:start position:0% +from the nuclear plant you can actually +capture almost all of the carbon from + + align:start position:0% +capture almost all of the carbon from + + + align:start position:0% +capture almost all of the carbon from +coal + + align:start position:0% +coal + + + align:start position:0% +coal +so rather than losing two-thirds of the + + align:start position:0% +so rather than losing two-thirds of the + + + align:start position:0% +so rather than losing two-thirds of the +energy or not the energy but the carbon + + align:start position:0% +energy or not the energy but the carbon + + + align:start position:0% +energy or not the energy but the carbon +from the coal you can actually use it + + align:start position:0% +from the coal you can actually use it + + + align:start position:0% +from the coal you can actually use it +and need to get less of it in the end + + align:start position:0% +and need to get less of it in the end + + + align:start position:0% +and need to get less of it in the end +so whatever stocks of coal we have can + + align:start position:0% +so whatever stocks of coal we have can + + + align:start position:0% +so whatever stocks of coal we have can +last longer as I said syngas can be + + align:start position:0% +last longer as I said syngas can be + + + align:start position:0% +last longer as I said syngas can be +burned as fuel or fed as feedstock into + + align:start position:0% +burned as fuel or fed as feedstock into + + + align:start position:0% +burned as fuel or fed as feedstock into +fischer tropsch synthesis reactions now + + align:start position:0% +fischer tropsch synthesis reactions now + + + align:start position:0% +fischer tropsch synthesis reactions now +for a Fischer troph you'll synthesis you + + align:start position:0% +for a Fischer troph you'll synthesis you + + + align:start position:0% +for a Fischer troph you'll synthesis you +start off with a mixture ideally of pure + + align:start position:0% +start off with a mixture ideally of pure + + + align:start position:0% +start off with a mixture ideally of pure +hydrogen and carbon monoxide and you end + + align:start position:0% +hydrogen and carbon monoxide and you end + + + align:start position:0% +hydrogen and carbon monoxide and you end +up making nice hydrocarbons these carbon + + align:start position:0% +up making nice hydrocarbons these carbon + + + align:start position:0% +up making nice hydrocarbons these carbon +hydrogen chains with a carbon backbone + + align:start position:0% +hydrogen chains with a carbon backbone + + + align:start position:0% +hydrogen chains with a carbon backbone +and the hydrogen surrounding it + + align:start position:0% +and the hydrogen surrounding it + + + align:start position:0% +and the hydrogen surrounding it +better known as fuel and water is the + + align:start position:0% +better known as fuel and water is the + + + align:start position:0% +better known as fuel and water is the +other main by-product if you look at the + + align:start position:0% +other main by-product if you look at the + + + align:start position:0% +other main by-product if you look at the +exponents in this reaction you need + + align:start position:0% +exponents in this reaction you need + + + align:start position:0% +exponents in this reaction you need +about twice as much hydrogen as you do + + align:start position:0% +about twice as much hydrogen as you do + + + align:start position:0% +about twice as much hydrogen as you do +carbon monoxide but a lot of these + + align:start position:0% +carbon monoxide but a lot of these + + + align:start position:0% +carbon monoxide but a lot of these +feedstocks when you burn them they + + align:start position:0% +feedstocks when you burn them they + + + align:start position:0% +feedstocks when you burn them they +actually make less hydrogen than they do + + align:start position:0% +actually make less hydrogen than they do + + + align:start position:0% +actually make less hydrogen than they do +carbon monoxide so you can see that you + + align:start position:0% +carbon monoxide so you can see that you + + + align:start position:0% +carbon monoxide so you can see that you +need a ratio of about two hydrogen to + + align:start position:0% +need a ratio of about two hydrogen to + + + align:start position:0% +need a ratio of about two hydrogen to +carbon monoxide and you end up with + + align:start position:0% +carbon monoxide and you end up with + + + align:start position:0% +carbon monoxide and you end up with +about 0.7 from raw feedstock alone so + + align:start position:0% +about 0.7 from raw feedstock alone so + + + align:start position:0% +about 0.7 from raw feedstock alone so +this here is one of the best places + + align:start position:0% +this here is one of the best places + + + align:start position:0% +this here is one of the best places +where the hydrogen folks can make an + + align:start position:0% +where the hydrogen folks can make an + + + align:start position:0% +where the hydrogen folks can make an +impact if the biofuel folks say we + + align:start position:0% +impact if the biofuel folks say we + + + align:start position:0% +impact if the biofuel folks say we +intend to make this much fuel which + + align:start position:0% +intend to make this much fuel which + + + align:start position:0% +intend to make this much fuel which +means that we're going to have this much + + align:start position:0% +means that we're going to have this much + + + align:start position:0% +means that we're going to have this much +missing hydrogen there's your minimum + + align:start position:0% +missing hydrogen there's your minimum + + + align:start position:0% +missing hydrogen there's your minimum +hydrogen production number now you can + + align:start position:0% +hydrogen production number now you can + + + align:start position:0% +hydrogen production number now you can +choose to make more hydrogen if you want + + align:start position:0% +choose to make more hydrogen if you want + + + align:start position:0% +choose to make more hydrogen if you want +to sell it as fuel cells but you don't + + align:start position:0% +to sell it as fuel cells but you don't + + + align:start position:0% +to sell it as fuel cells but you don't +necessarily have to it's up to you guys + + align:start position:0% +necessarily have to it's up to you guys + + + align:start position:0% +necessarily have to it's up to you guys +to determine what this country can use + + align:start position:0% +to determine what this country can use + + + align:start position:0% +to determine what this country can use +in terms of fuels do you see synthetic + + align:start position:0% +in terms of fuels do you see synthetic + + + align:start position:0% +in terms of fuels do you see synthetic +biofuels being a bigger impact + + align:start position:0% +biofuels being a bigger impact + + + align:start position:0% +biofuels being a bigger impact +do you see hydrogen a hydrogen economy + + align:start position:0% +do you see hydrogen a hydrogen economy + + + align:start position:0% +do you see hydrogen a hydrogen economy +or fuel cells being a bigger impact that + + align:start position:0% +or fuel cells being a bigger impact that + + + align:start position:0% +or fuel cells being a bigger impact that +choice is up to you these require fairly + + align:start position:0% +choice is up to you these require fairly + + + align:start position:0% +choice is up to you these require fairly +low temperatures so temperatures of 150 + + align:start position:0% +low temperatures so temperatures of 150 + + + align:start position:0% +low temperatures so temperatures of 150 +to 300 Celsius so if you guys can find + + align:start position:0% +to 300 Celsius so if you guys can find + + + align:start position:0% +to 300 Celsius so if you guys can find +ways of bypassing the syngas step or + + align:start position:0% +ways of bypassing the syngas step or + + + align:start position:0% +ways of bypassing the syngas step or +otherwise producing hydrogen and carbon + + align:start position:0% +otherwise producing hydrogen and carbon + + + align:start position:0% +otherwise producing hydrogen and carbon +monoxide using a lower temperature + + align:start position:0% +monoxide using a lower temperature + + + align:start position:0% +monoxide using a lower temperature +process you may not have that high + + align:start position:0% +process you may not have that high + + + align:start position:0% +process you may not have that high +temperature requirement to produce your + + align:start position:0% +temperature requirement to produce your + + + align:start position:0% +temperature requirement to produce your +end products I already mentioned that I + + align:start position:0% +end products I already mentioned that I + + + align:start position:0% +end products I already mentioned that I +already mentioned that good so an + + align:start position:0% +already mentioned that good so an + + + align:start position:0% +already mentioned that good so an +example of one of these combined FinCEN + + align:start position:0% +example of one of these combined FinCEN + + + align:start position:0% +example of one of these combined FinCEN +gas Fisher tropes I khals if you want to + + align:start position:0% +gas Fisher tropes I khals if you want to + + + align:start position:0% +gas Fisher tropes I khals if you want to +see lots more I starred this for a + + align:start position:0% +see lots more I starred this for a + + + align:start position:0% +see lots more I starred this for a +reason check this source out this paper + + align:start position:0% +reason check this source out this paper + + + align:start position:0% +reason check this source out this paper +and actually this whole series of papers + + align:start position:0% +and actually this whole series of papers + + + align:start position:0% +and actually this whole series of papers +has a lot from introductory to technical + + align:start position:0% +has a lot from introductory to technical + + + align:start position:0% +has a lot from introductory to technical +detail on different ways methods and + + align:start position:0% +detail on different ways methods and + + + align:start position:0% +detail on different ways methods and +combinations of making biofuels and they + + align:start position:0% +combinations of making biofuels and they + + + align:start position:0% +combinations of making biofuels and they +actually go into economics and cost to + + align:start position:0% +actually go into economics and cost to + + + align:start position:0% +actually go into economics and cost to +which I'm not going to expect you guys + + align:start position:0% +which I'm not going to expect you guys + + + align:start position:0% +which I'm not going to expect you guys +to say give me a dollar amount to the + + align:start position:0% +to say give me a dollar amount to the + + + align:start position:0% +to say give me a dollar amount to the +nearest dollar but I will expect you to + + align:start position:0% +nearest dollar but I will expect you to + + + align:start position:0% +nearest dollar but I will expect you to +say we chose this because it's cheaper + + align:start position:0% +say we chose this because it's cheaper + + + align:start position:0% +say we chose this because it's cheaper +and we don't have an engineering + + align:start position:0% +and we don't have an engineering + + + align:start position:0% +and we don't have an engineering +trade-off or something like that in this + + align:start position:0% +trade-off or something like that in this + + + align:start position:0% +trade-off or something like that in this +you end up with biomass and ammonia + + align:start position:0% +you end up with biomass and ammonia + + + align:start position:0% +you end up with biomass and ammonia +whatever source of biomass you want and + + align:start position:0% +whatever source of biomass you want and + + + align:start position:0% +whatever source of biomass you want and +this here is essentially our giant + + align:start position:0% +this here is essentially our giant + + + align:start position:0% +this here is essentially our giant +mechanical synthetic cow that produces + + align:start position:0% +mechanical synthetic cow that produces + + + align:start position:0% +mechanical synthetic cow that produces +ethanol and biogas as well as solid + + align:start position:0% +ethanol and biogas as well as solid + + + align:start position:0% +ethanol and biogas as well as solid +residue this solid residue is still rich + + align:start position:0% +residue this solid residue is still rich + + + align:start position:0% +residue this solid residue is still rich +in carbon + + align:start position:0% +in carbon + + + align:start position:0% +in carbon +so you can gasify it like I said by + + align:start position:0% +so you can gasify it like I said by + + + align:start position:0% +so you can gasify it like I said by +partially combusting with oxygen remove + + align:start position:0% +partially combusting with oxygen remove + + + align:start position:0% +partially combusting with oxygen remove +the impurities that you don't want like + + align:start position:0% +the impurities that you don't want like + + + align:start position:0% +the impurities that you don't want like +hydrogen sulfide carbon dioxide and at + + align:start position:0% +hydrogen sulfide carbon dioxide and at + + + align:start position:0% +hydrogen sulfide carbon dioxide and at +this point it's clean sin gas which you + + align:start position:0% +this point it's clean sin gas which you + + + align:start position:0% +this point it's clean sin gas which you +can then feed into Fisher trough + + align:start position:0% +can then feed into Fisher trough + + + align:start position:0% +can then feed into Fisher trough +synthesis refine it just as you would in + + align:start position:0% +synthesis refine it just as you would in + + + align:start position:0% +synthesis refine it just as you would in +an oil refinery outcome Fisher troph + + align:start position:0% +an oil refinery outcome Fisher troph + + + align:start position:0% +an oil refinery outcome Fisher troph +liquids whatever sin gas you don't use + + align:start position:0% +liquids whatever sin gas you don't use + + + align:start position:0% +liquids whatever sin gas you don't use +you could burn as fuel and produce + + align:start position:0% +you could burn as fuel and produce + + + align:start position:0% +you could burn as fuel and produce +electricity or you can burn it and use + + align:start position:0% +electricity or you can burn it and use + + + align:start position:0% +electricity or you can burn it and use +that heat to fuel maybe the gasification + + align:start position:0% +that heat to fuel maybe the gasification + + + align:start position:0% +that heat to fuel maybe the gasification +reaction so maybe your process he + + align:start position:0% +reaction so maybe your process he + + + align:start position:0% +reaction so maybe your process he +doesn't have to come from the nuclear + + align:start position:0% +doesn't have to come from the nuclear + + + align:start position:0% +doesn't have to come from the nuclear +plant in its entirety maybe it can come + + align:start position:0% +plant in its entirety maybe it can come + + + align:start position:0% +plant in its entirety maybe it can come +from burning syngas or you can split it + + align:start position:0% +from burning syngas or you can split it + + + align:start position:0% +from burning syngas or you can split it +and do both and there are lots of other + + align:start position:0% +and do both and there are lots of other + + + align:start position:0% +and do both and there are lots of other +configurations but the end product of + + align:start position:0% +configurations but the end product of + + + align:start position:0% +configurations but the end product of +what I'd like the biofuels folks to give + + align:start position:0% +what I'd like the biofuels folks to give + + + align:start position:0% +what I'd like the biofuels folks to give +and I'm not I don't mean after week four + + align:start position:0% +and I'm not I don't mean after week four + + + align:start position:0% +and I'm not I don't mean after week four +I mean after week eight is a diagram + + align:start position:0% +I mean after week eight is a diagram + + + align:start position:0% +I mean after week eight is a diagram +like this where you know what your + + align:start position:0% +like this where you know what your + + + align:start position:0% +like this where you know what your +inputs and outputs are how much they are + + align:start position:0% +inputs and outputs are how much they are + + + align:start position:0% +inputs and outputs are how much they are +and really why you chose each one so you + + align:start position:0% +and really why you chose each one so you + + + align:start position:0% +and really why you chose each one so you +can say we chose this set of inputs and + + align:start position:0% +can say we chose this set of inputs and + + + align:start position:0% +can say we chose this set of inputs and +outputs because that and as you're + + align:start position:0% +outputs because that and as you're + + + align:start position:0% +outputs because that and as you're +choosing things think about what bought + + align:start position:0% +choosing things think about what bought + + + align:start position:0% +choosing things think about what bought +whatever biomass you choose is going to + + align:start position:0% +whatever biomass you choose is going to + + + align:start position:0% +whatever biomass you choose is going to +decide pretty much determine the rough + + align:start position:0% +decide pretty much determine the rough + + + align:start position:0% +decide pretty much determine the rough +region of the country where you're going + + align:start position:0% +region of the country where you're going + + + align:start position:0% +region of the country where you're going +to site this whole installation because + + align:start position:0% +to site this whole installation because + + + align:start position:0% +to site this whole installation because +you can put a nuclear plant in a lot of + + align:start position:0% +you can put a nuclear plant in a lot of + + + align:start position:0% +you can put a nuclear plant in a lot of +different places in this country you can + + align:start position:0% +different places in this country you can + + + align:start position:0% +different places in this country you can +make hydrogen pretty much anywhere but + + align:start position:0% +make hydrogen pretty much anywhere but + + + align:start position:0% +make hydrogen pretty much anywhere but +you can't grow certain crops in certain + + align:start position:0% +you can't grow certain crops in certain + + + align:start position:0% +you can't grow certain crops in certain +places you know you can grow potatoes in + + align:start position:0% +places you know you can grow potatoes in + + + align:start position:0% +places you know you can grow potatoes in +sandy soil you can grow corn in the soil + + align:start position:0% +sandy soil you can grow corn in the soil + + + align:start position:0% +sandy soil you can grow corn in the soil +all over the Midwest you know you can't + + align:start position:0% +all over the Midwest you know you can't + + + align:start position:0% +all over the Midwest you know you can't +really grow anything in the badlands you + + align:start position:0% +really grow anything in the badlands you + + + align:start position:0% +really grow anything in the badlands you +can grow lots of stuff near volcanic + + align:start position:0% +can grow lots of stuff near volcanic + + + align:start position:0% +can grow lots of stuff near volcanic +soil so that will your your choice of + + align:start position:0% +soil so that will your your choice of + + + align:start position:0% +soil so that will your your choice of +what feedstock to use will pretty much + + align:start position:0% +what feedstock to use will pretty much + + + align:start position:0% +what feedstock to use will pretty much +determine in what rough region of the + + align:start position:0% +determine in what rough region of the + + + align:start position:0% +determine in what rough region of the +country this plant will be sited and I + + align:start position:0% +country this plant will be sited and I + + + align:start position:0% +country this plant will be sited and I +don't really need you guys to tell me + + align:start position:0% +don't really need you guys to tell me + + + align:start position:0% +don't really need you guys to tell me +exactly what site it's going to be until + + align:start position:0% +exactly what site it's going to be until + + + align:start position:0% +exactly what site it's going to be until +the very end of the course so just keep + + align:start position:0% +the very end of the course so just keep + + + align:start position:0% +the very end of the course so just keep +it in mind but it's not a big factor + + align:start position:0% +it in mind but it's not a big factor + + + align:start position:0% +it in mind but it's not a big factor +right now so there are plenty of other + + align:start position:0% +right now so there are plenty of other + + + align:start position:0% +right now so there are plenty of other +methods being proposed or demonstrated + + align:start position:0% +methods being proposed or demonstrated + + + align:start position:0% +methods being proposed or demonstrated +on a research or R&D or prototype or + + align:start position:0% +on a research or R&D or prototype or + + + align:start position:0% +on a research or R&D or prototype or +commercials + + align:start position:0% +commercials + + + align:start position:0% +commercials +for making biofuels one of them that + + align:start position:0% +for making biofuels one of them that + + + align:start position:0% +for making biofuels one of them that +there's a lot of arpa-e energy grants + + align:start position:0% +there's a lot of arpa-e energy grants + + + align:start position:0% +there's a lot of arpa-e energy grants +out for is electrofuels it uses syngas + + align:start position:0% +out for is electrofuels it uses syngas + + + align:start position:0% +out for is electrofuels it uses syngas +as a feedstock and microbes act as + + align:start position:0% +as a feedstock and microbes act as + + + align:start position:0% +as a feedstock and microbes act as +catalysts sorry that should be a teeth + + align:start position:0% +catalysts sorry that should be a teeth + + + align:start position:0% +catalysts sorry that should be a teeth +micros acts as catalysts in fuel cells + + align:start position:0% +micros acts as catalysts in fuel cells + + + align:start position:0% +micros acts as catalysts in fuel cells +so you end up with microbes consuming + + align:start position:0% +so you end up with microbes consuming + + + align:start position:0% +so you end up with microbes consuming +syngas lowering the and then outputting + + align:start position:0% +syngas lowering the and then outputting + + + align:start position:0% +syngas lowering the and then outputting +things that lower the activation barrier + + align:start position:0% +things that lower the activation barrier + + + align:start position:0% +things that lower the activation barrier +- oh sorry - I think they create oil + + align:start position:0% +- oh sorry - I think they create oil + + + align:start position:0% +- oh sorry - I think they create oil +actually yeah that's right + + align:start position:0% +actually yeah that's right + + + align:start position:0% +actually yeah that's right +the microbes actually end up creating + + align:start position:0% +the microbes actually end up creating + + + align:start position:0% +the microbes actually end up creating +oil one of the arpa-e grants there that + + align:start position:0% +oil one of the arpa-e grants there that + + + align:start position:0% +oil one of the arpa-e grants there that +I was reading is geared specifically + + align:start position:0% +I was reading is geared specifically + + + align:start position:0% +I was reading is geared specifically +towards creating jet fuel so who said it + + align:start position:0% +towards creating jet fuel so who said it + + + align:start position:0% +towards creating jet fuel so who said it +has to be gasoline or diesel that you + + align:start position:0% +has to be gasoline or diesel that you + + + align:start position:0% +has to be gasoline or diesel that you +guys produce if you determine that the + + align:start position:0% +guys produce if you determine that the + + + align:start position:0% +guys produce if you determine that the +biggest deficiency in terms of supply + + align:start position:0% +biggest deficiency in terms of supply + + + align:start position:0% +biggest deficiency in terms of supply +versus demand is jet fuel which by the + + align:start position:0% +versus demand is jet fuel which by the + + + align:start position:0% +versus demand is jet fuel which by the +way is very expensive + + align:start position:0% +way is very expensive + + + align:start position:0% +way is very expensive +you could gear your biomass plant + + align:start position:0% +you could gear your biomass plant + + + align:start position:0% +you could gear your biomass plant +towards producing jet fuel so it'll be + + align:start position:0% +towards producing jet fuel so it'll be + + + align:start position:0% +towards producing jet fuel so it'll be +up to you guys to decide what are the + + align:start position:0% +up to you guys to decide what are the + + + align:start position:0% +up to you guys to decide what are the +energy stocks how much oil are we going + + align:start position:0% +energy stocks how much oil are we going + + + align:start position:0% +energy stocks how much oil are we going +to have how much jet fuel will that + + align:start position:0% +to have how much jet fuel will that + + + align:start position:0% +to have how much jet fuel will that +produce as years go on what's the demand + + align:start position:0% +produce as years go on what's the demand + + + align:start position:0% +produce as years go on what's the demand +going to look like and I would attack + + align:start position:0% +going to look like and I would attack + + + align:start position:0% +going to look like and I would attack +the largest difference in supply versus + + align:start position:0% +the largest difference in supply versus + + + align:start position:0% +the largest difference in supply versus +demand or possibly even weight that the + + align:start position:0% +demand or possibly even weight that the + + + align:start position:0% +demand or possibly even weight that the +largest sorry the largest difference + + align:start position:0% +largest sorry the largest difference + + + align:start position:0% +largest sorry the largest difference +between supply and demand times the + + align:start position:0% +between supply and demand times the + + + align:start position:0% +between supply and demand times the +amount of money you can make from each + + align:start position:0% +amount of money you can make from each + + + align:start position:0% +amount of money you can make from each +of those processes most of these are in + + align:start position:0% +of those processes most of these are in + + + align:start position:0% +of those processes most of these are in +early stages of R&D but it's up to you + + align:start position:0% +early stages of R&D but it's up to you + + + align:start position:0% +early stages of R&D but it's up to you +guys to decide at what point is the + + align:start position:0% +guys to decide at what point is the + + + align:start position:0% +guys to decide at what point is the +cutoff what's too much of an early phase + + align:start position:0% +cutoff what's too much of an early phase + + + align:start position:0% +cutoff what's too much of an early phase +for you to even consider and what can + + align:start position:0% +for you to even consider and what can + + + align:start position:0% +for you to even consider and what can +you say well that might be ready in five + + align:start position:0% +you say well that might be ready in five + + + align:start position:0% +you say well that might be ready in five +years and it's going to take years to + + align:start position:0% +years and it's going to take years to + + + align:start position:0% +years and it's going to take years to +license and approve this nuclear plant + + align:start position:0% +license and approve this nuclear plant + + + align:start position:0% +license and approve this nuclear plant +so by the time it comes time to build + + align:start position:0% +so by the time it comes time to build + + + align:start position:0% +so by the time it comes time to build +one of these this could be ready you + + align:start position:0% +one of these this could be ready you + + + align:start position:0% +one of these this could be ready you +could also grow algae and there are a + + align:start position:0% +could also grow algae and there are a + + + align:start position:0% +could also grow algae and there are a +number of companies even in Cambridge + + align:start position:0% +number of companies even in Cambridge + + + align:start position:0% +number of companies even in Cambridge +that are looking at growing algae to + + align:start position:0% +that are looking at growing algae to + + + align:start position:0% +that are looking at growing algae to +produce what's called veggie oil or bio + + align:start position:0% +produce what's called veggie oil or bio + + + align:start position:0% +produce what's called veggie oil or bio +lipids algae grows about 20 to 30 times + + align:start position:0% +lipids algae grows about 20 to 30 times + + + align:start position:0% +lipids algae grows about 20 to 30 times +faster than food crops you can have + + align:start position:0% +faster than food crops you can have + + + align:start position:0% +faster than food crops you can have +multiple harvests a year so instead of + + align:start position:0% +multiple harvests a year so instead of + + + align:start position:0% +multiple harvests a year so instead of +having one giant harvest once a year you + + align:start position:0% +having one giant harvest once a year you + + + align:start position:0% +having one giant harvest once a year you +can have continuous production of this + + align:start position:0% +can have continuous production of this + + + align:start position:0% +can have continuous production of this +feedstock and algae are very greasy when + + align:start position:0% +feedstock and algae are very greasy when + + + align:start position:0% +feedstock and algae are very greasy when +you dry algae you can have somewhere + + align:start position:0% +you dry algae you can have somewhere + + + align:start position:0% +you dry algae you can have somewhere +between 20 to 50 percent lipid content + + align:start position:0% +between 20 to 50 percent lipid content + + + align:start position:0% +between 20 to 50 percent lipid content +living as fat depending on which one you + + align:start position:0% +living as fat depending on which one you + + + align:start position:0% +living as fat depending on which one you +choose to use so in the lipid and + + align:start position:0% +choose to use so in the lipid and + + + align:start position:0% +choose to use so in the lipid and +carbohydrate content of the algae + + align:start position:0% +carbohydrate content of the algae + + + align:start position:0% +carbohydrate content of the algae +determines what kind of fuels you + + align:start position:0% +determines what kind of fuels you + + + align:start position:0% +determines what kind of fuels you +produce + + align:start position:0% +produce + + + align:start position:0% +produce +however algae are biological organisms + + align:start position:0% +however algae are biological organisms + + + align:start position:0% +however algae are biological organisms +they can be contaminated other strains + + align:start position:0% +they can be contaminated other strains + + + align:start position:0% +they can be contaminated other strains +can move in displace them they could be + + align:start position:0% +can move in displace them they could be + + + align:start position:0% +can move in displace them they could be +attacked by bacteria and at ten it tends + + align:start position:0% +attacked by bacteria and at ten it tends + + + align:start position:0% +attacked by bacteria and at ten it tends +to as all things the hardy or the algae + + align:start position:0% +to as all things the hardy or the algae + + + align:start position:0% +to as all things the hardy or the algae +the more resistant they are to attack + + align:start position:0% +the more resistant they are to attack + + + align:start position:0% +the more resistant they are to attack +the less lipids they tend to form so + + align:start position:0% +the less lipids they tend to form so + + + align:start position:0% +the less lipids they tend to form so +there is a trade-off between how much + + align:start position:0% +there is a trade-off between how much + + + align:start position:0% +there is a trade-off between how much +grease your algae can produce and how + + align:start position:0% +grease your algae can produce and how + + + align:start position:0% +grease your algae can produce and how +fragile it is and there is the problem + + align:start position:0% +fragile it is and there is the problem + + + align:start position:0% +fragile it is and there is the problem +of commercial viability if you start + + align:start position:0% +of commercial viability if you start + + + align:start position:0% +of commercial viability if you start +googling this you'll see these giant + + align:start position:0% +googling this you'll see these giant + + + align:start position:0% +googling this you'll see these giant +green tanks full of algae which are + + align:start position:0% +green tanks full of algae which are + + + align:start position:0% +green tanks full of algae which are +closed systems theory and they're a + + align:start position:0% +closed systems theory and they're a + + + align:start position:0% +closed systems theory and they're a +little harder and more expensive to + + align:start position:0% +little harder and more expensive to + + + align:start position:0% +little harder and more expensive to +produce the reason is if you have a big + + align:start position:0% +produce the reason is if you have a big + + + align:start position:0% +produce the reason is if you have a big +open pond + + align:start position:0% +open pond + + + align:start position:0% +open pond +it's open to whatever could happen to + + align:start position:0% +it's open to whatever could happen to + + + align:start position:0% +it's open to whatever could happen to +blow in and contaminate it but a big + + align:start position:0% +blow in and contaminate it but a big + + + align:start position:0% +blow in and contaminate it but a big +open pond certainly is a much cheaper + + align:start position:0% +open pond certainly is a much cheaper + + + align:start position:0% +open pond certainly is a much cheaper +way of producing algae so if you can + + align:start position:0% +way of producing algae so if you can + + + align:start position:0% +way of producing algae so if you can +find a strain that has a good trade-off + + align:start position:0% +find a strain that has a good trade-off + + + align:start position:0% +find a strain that has a good trade-off +between lipid production and hardiness + + align:start position:0% +between lipid production and hardiness + + + align:start position:0% +between lipid production and hardiness +then you might have a winner so with + + align:start position:0% +then you might have a winner so with + + + align:start position:0% +then you might have a winner so with +that I'll go over some major questions + + align:start position:0% +that I'll go over some major questions + + + align:start position:0% +that I'll go over some major questions +that the biofuels folks should be asking + + align:start position:0% +that the biofuels folks should be asking + + + align:start position:0% +that the biofuels folks should be asking +themselves what feedstock do you want to + + align:start position:0% +themselves what feedstock do you want to + + + align:start position:0% +themselves what feedstock do you want to +use do you want to use plants do you + + align:start position:0% +use do you want to use plants do you + + + align:start position:0% +use do you want to use plants do you +want to use coal do you want to use + + align:start position:0% +want to use coal do you want to use + + + align:start position:0% +want to use coal do you want to use +algae what and that'll help determine + + align:start position:0% +algae what and that'll help determine + + + align:start position:0% +algae what and that'll help determine +what products you produce so you may + + align:start position:0% +what products you produce so you may + + + align:start position:0% +what products you produce so you may +consider working backwards think of what + + align:start position:0% +consider working backwards think of what + + + align:start position:0% +consider working backwards think of what +products you want to use in order to + + align:start position:0% +products you want to use in order to + + + align:start position:0% +products you want to use in order to +maximize the usefulness of this plant + + align:start position:0% +maximize the usefulness of this plant + + + align:start position:0% +maximize the usefulness of this plant +and that will help narrow down what + + align:start position:0% +and that will help narrow down what + + + align:start position:0% +and that will help narrow down what +feedstocks are available to you what + + align:start position:0% +feedstocks are available to you what + + + align:start position:0% +feedstocks are available to you what +temperatures do you have to work with + + align:start position:0% +temperatures do you have to work with + + + align:start position:0% +temperatures do you have to work with +are the hydrogen folks going to require + + align:start position:0% +are the hydrogen folks going to require + + + align:start position:0% +are the hydrogen folks going to require +800c process heat in which case you'll + + align:start position:0% +800c process heat in which case you'll + + + align:start position:0% +800c process heat in which case you'll +have high-quality heat or are you going + + align:start position:0% +have high-quality heat or are you going + + + align:start position:0% +have high-quality heat or are you going +for a low temperature to open up + + align:start position:0% +for a low temperature to open up + + + align:start position:0% +for a low temperature to open up +possibilities for the core what + + align:start position:0% +possibilities for the core what + + + align:start position:0% +possibilities for the core what +processes will you use so what's the + + align:start position:0% +processes will you use so what's the + + + align:start position:0% +processes will you use so what's the +block diagram going to look like you'll + + align:start position:0% +block diagram going to look like you'll + + + align:start position:0% +block diagram going to look like you'll +have to choose if and how to use + + align:start position:0% +have to choose if and how to use + + + align:start position:0% +have to choose if and how to use +hydrogen and biofuel production for + + align:start position:0% +hydrogen and biofuel production for + + + align:start position:0% +hydrogen and biofuel production for +example you may not need it when it + + align:start position:0% +example you may not need it when it + + + align:start position:0% +example you may not need it when it +comes to algae you'll certainly need it + + align:start position:0% +comes to algae you'll certainly need it + + + align:start position:0% +comes to algae you'll certainly need it +to n do a fish and fish short rope + + align:start position:0% +to n do a fish and fish short rope + + + align:start position:0% +to n do a fish and fish short rope +synthesis how much do you want to + + align:start position:0% +synthesis how much do you want to + + + align:start position:0% +synthesis how much do you want to +produce so do you want all of the energy + + align:start position:0% +produce so do you want all of the energy + + + align:start position:0% +produce so do you want all of the energy +to go into biofuels maybe that's where + + align:start position:0% +to go into biofuels maybe that's where + + + align:start position:0% +to go into biofuels maybe that's where +the money is if not do you want to + + align:start position:0% +the money is if not do you want to + + + align:start position:0% +the money is if not do you want to +produce a certain amount of biofuels and + + align:start position:0% +produce a certain amount of biofuels and + + + align:start position:0% +produce a certain amount of biofuels and +the wrasses electricity or do you want + + align:start position:0% +the wrasses electricity or do you want + + + align:start position:0% +the wrasses electricity or do you want +to leave it all to hydrogen to sell the + + align:start position:0% +to leave it all to hydrogen to sell the + + + align:start position:0% +to leave it all to hydrogen to sell the +fuel cells and what are the economics of + + align:start position:0% +fuel cells and what are the economics of + + + align:start position:0% +fuel cells and what are the economics of +your choices this shouldn't be the major + + align:start position:0% +your choices this shouldn't be the major + + + align:start position:0% +your choices this shouldn't be the major +kill-all determining factor but it + + align:start position:0% +kill-all determining factor but it + + + align:start position:0% +kill-all determining factor but it +should be in the back of your mind so + + align:start position:0% +should be in the back of your mind so + + + align:start position:0% +should be in the back of your mind so +you don't end up doing what my class did + + align:start position:0% +you don't end up doing what my class did + + + align:start position:0% +you don't end up doing what my class did +and making the core out of solid rhenium + + align:start position:0% +and making the core out of solid rhenium + + + align:start position:0% +and making the core out of solid rhenium +so onto the design process all about + + align:start position:0% +so onto the design process all about + + + align:start position:0% +so onto the design process all about +decisions not just making them but why + + align:start position:0% +decisions not just making them but why + + + align:start position:0% +decisions not just making them but why +and how so I got this figure from one of + + align:start position:0% +and how so I got this figure from one of + + + align:start position:0% +and how so I got this figure from one of +these NASA design projects and I think + + align:start position:0% +these NASA design projects and I think + + + align:start position:0% +these NASA design projects and I think +it's a pretty good indication of how the + + align:start position:0% +it's a pretty good indication of how the + + + align:start position:0% +it's a pretty good indication of how the +design process goes overall first is + + align:start position:0% +design process goes overall first is + + + align:start position:0% +design process goes overall first is +I've taken care of this one for you + + align:start position:0% +I've taken care of this one for you + + + align:start position:0% +I've taken care of this one for you +identify the problem I've just given you + + align:start position:0% +identify the problem I've just given you + + + align:start position:0% +identify the problem I've just given you +the problem we'll be doing all this + + align:start position:0% +the problem we'll be doing all this + + + align:start position:0% +the problem we'll be doing all this +stuff in weeks 1 or 2 pretty much by the + + align:start position:0% +stuff in weeks 1 or 2 pretty much by the + + + align:start position:0% +stuff in weeks 1 or 2 pretty much by the +end of next Friday + + align:start position:0% +end of next Friday + + + align:start position:0% +end of next Friday +you'll guys will be about here halfway + + align:start position:0% +you'll guys will be about here halfway + + + align:start position:0% +you'll guys will be about here halfway +through pictorially halfway through the + + align:start position:0% +through pictorially halfway through the + + + align:start position:0% +through pictorially halfway through the +design cycle but not in terms of the + + align:start position:0% +design cycle but not in terms of the + + + align:start position:0% +design cycle but not in terms of the +amount of work + + align:start position:0% +amount of work + + + align:start position:0% +amount of work +step 2 is identify criteria and + + align:start position:0% +step 2 is identify criteria and + + + align:start position:0% +step 2 is identify criteria and +constraints and for you guys that pretty + + align:start position:0% +constraints and for you guys that pretty + + + align:start position:0% +constraints and for you guys that pretty +much means look at the problem statement + + align:start position:0% +much means look at the problem statement + + + align:start position:0% +much means look at the problem statement +and really understand how is it + + align:start position:0% +and really understand how is it + + + align:start position:0% +and really understand how is it +constraining you and where are there + + align:start position:0% +constraining you and where are there + + + align:start position:0% +constraining you and where are there +places where you have a lot of freedom + + align:start position:0% +places where you have a lot of freedom + + + align:start position:0% +places where you have a lot of freedom +these three steps are pretty much find + + align:start position:0% +these three steps are pretty much find + + + align:start position:0% +these three steps are pretty much find +out what's out there research research + + align:start position:0% +out what's out there research research + + + align:start position:0% +out what's out there research research +research and then iterate then meet with + + align:start position:0% +research and then iterate then meet with + + + align:start position:0% +research and then iterate then meet with +each other and tell each other what + + align:start position:0% +each other and tell each other what + + + align:start position:0% +each other and tell each other what +you've found and then go back and + + align:start position:0% +you've found and then go back and + + + align:start position:0% +you've found and then go back and +research and continue the cycle until + + align:start position:0% +research and continue the cycle until + + + align:start position:0% +research and continue the cycle until +you reach diminishing returns where you + + align:start position:0% +you reach diminishing returns where you + + + align:start position:0% +you reach diminishing returns where you +can research for an hour and you only + + align:start position:0% +can research for an hour and you only + + + align:start position:0% +can research for an hour and you only +find a tenth of what you're used to at + + align:start position:0% +find a tenth of what you're used to at + + + align:start position:0% +find a tenth of what you're used to at +some point and believe me you'll know + + align:start position:0% +some point and believe me you'll know + + + align:start position:0% +some point and believe me you'll know +when especially from experience it'll be + + align:start position:0% +when especially from experience it'll be + + + align:start position:0% +when especially from experience it'll be +time to just move on to the next step + + align:start position:0% +time to just move on to the next step + + + align:start position:0% +time to just move on to the next step +select an approach that's what you guys + + align:start position:0% +select an approach that's what you guys + + + align:start position:0% +select an approach that's what you guys +will be doing starting mid next week is + + align:start position:0% +will be doing starting mid next week is + + + align:start position:0% +will be doing starting mid next week is +using some official importance metrics + + align:start position:0% +using some official importance metrics + + + align:start position:0% +using some official importance metrics +to figure out what is the approach you + + align:start position:0% +to figure out what is the approach you + + + align:start position:0% +to figure out what is the approach you +want to take and after this you'll + + align:start position:0% +want to take and after this you'll + + + align:start position:0% +want to take and after this you'll +pretty much have one approach that + + align:start position:0% +pretty much have one approach that + + + align:start position:0% +pretty much have one approach that +you'll be doing and then you'll be able + + align:start position:0% +you'll be doing and then you'll be able + + + align:start position:0% +you'll be doing and then you'll be able +to start putting in numbers assembling + + align:start position:0% +to start putting in numbers assembling + + + align:start position:0% +to start putting in numbers assembling +block diagrams iterating improving until + + align:start position:0% +block diagrams iterating improving until + + + align:start position:0% +block diagrams iterating improving until +you reach diminishing returns and I'm + + align:start position:0% +you reach diminishing returns and I'm + + + align:start position:0% +you reach diminishing returns and I'm +not going to make you guys repeat + + align:start position:0% +not going to make you guys repeat + + + align:start position:0% +not going to make you guys repeat +because this is only one design problem + + align:start position:0% +because this is only one design problem + + + align:start position:0% +because this is only one design problem +so steps one and two identify key parts + + align:start position:0% +so steps one and two identify key parts + + + align:start position:0% +so steps one and two identify key parts +of the problem this whole problem + + align:start position:0% +of the problem this whole problem + + + align:start position:0% +of the problem this whole problem +statement was in the syllabus and I just + + align:start position:0% +statement was in the syllabus and I just + + + align:start position:0% +statement was in the syllabus and I just +want to point out a few things that I + + align:start position:0% +want to point out a few things that I + + + align:start position:0% +want to point out a few things that I +realize when you read them quickly it + + align:start position:0% +realize when you read them quickly it + + + align:start position:0% +realize when you read them quickly it +might seem a little + + align:start position:0% +might seem a little + + + align:start position:0% +might seem a little +different from when you read them very + + align:start position:0% +different from when you read them very + + + align:start position:0% +different from when you read them very +carefully so it was design a non PWR or + + align:start position:0% +carefully so it was design a non PWR or + + + align:start position:0% +carefully so it was design a non PWR or +BWR that produces hydrogen and biofuels + + align:start position:0% +BWR that produces hydrogen and biofuels + + + align:start position:0% +BWR that produces hydrogen and biofuels +that doesn't mean that light water is + + align:start position:0% +that doesn't mean that light water is + + + align:start position:0% +that doesn't mean that light water is +out so supercritical water is on the + + align:start position:0% +out so supercritical water is on the + + + align:start position:0% +out so supercritical water is on the +table it just means not a PWR or a BWR + + align:start position:0% +table it just means not a PWR or a BWR + + + align:start position:0% +table it just means not a PWR or a BWR +it must be able to produce at least a + + align:start position:0% +it must be able to produce at least a + + + align:start position:0% +it must be able to produce at least a +hundred megawatts electric I didn't say + + align:start position:0% +hundred megawatts electric I didn't say + + + align:start position:0% +hundred megawatts electric I didn't say +we have to sell at least a hundred + + align:start position:0% +we have to sell at least a hundred + + + align:start position:0% +we have to sell at least a hundred +megawatts electric I didn't say you have + + align:start position:0% +megawatts electric I didn't say you have + + + align:start position:0% +megawatts electric I didn't say you have +to produce any electricity at all but if + + align:start position:0% +to produce any electricity at all but if + + + align:start position:0% +to produce any electricity at all but if +you run some calculations your plant has + + align:start position:0% +you run some calculations your plant has + + + align:start position:0% +you run some calculations your plant has +to be of the correct size that if you + + align:start position:0% +to be of the correct size that if you + + + align:start position:0% +to be of the correct size that if you +chose to make electricity it would be + + align:start position:0% +chose to make electricity it would be + + + align:start position:0% +chose to make electricity it would be +possible to produce at least 100 + + align:start position:0% +possible to produce at least 100 + + + align:start position:0% +possible to produce at least 100 +megawatts electric it has to produce at + + align:start position:0% +megawatts electric it has to produce at + + + align:start position:0% +megawatts electric it has to produce at +least one alternative fuel source so + + align:start position:0% +least one alternative fuel source so + + + align:start position:0% +least one alternative fuel source so +like I said you don't have to sell + + align:start position:0% +like I said you don't have to sell + + + align:start position:0% +like I said you don't have to sell +hydrogen and biofuels and other stuff it + + align:start position:0% +hydrogen and biofuels and other stuff it + + + align:start position:0% +hydrogen and biofuels and other stuff it +can be just one if you choose to use one + + align:start position:0% +can be just one if you choose to use one + + + align:start position:0% +can be just one if you choose to use one +as some feedstock to the other and the + + align:start position:0% +as some feedstock to the other and the + + + align:start position:0% +as some feedstock to the other and the +h2 the hydrogen and biofuels processes + + align:start position:0% +h2 the hydrogen and biofuels processes + + + align:start position:0% +h2 the hydrogen and biofuels processes +must be somewhat demonstrated some what + + align:start position:0% +must be somewhat demonstrated some what + + + align:start position:0% +must be somewhat demonstrated some what +is up to you guys it doesn't have to be + + align:start position:0% +is up to you guys it doesn't have to be + + + align:start position:0% +is up to you guys it doesn't have to be +a commercial product it probably + + align:start position:0% +a commercial product it probably + + + align:start position:0% +a commercial product it probably +shouldn't be just an idea in someone's + + align:start position:0% +shouldn't be just an idea in someone's + + + align:start position:0% +shouldn't be just an idea in someone's +head in a conference paper but it is up + + align:start position:0% +head in a conference paper but it is up + + + align:start position:0% +head in a conference paper but it is up +to you guys to decide what determines + + align:start position:0% +to you guys to decide what determines + + + align:start position:0% +to you guys to decide what determines +when it's demonstrated enough is labs + + align:start position:0% +when it's demonstrated enough is labs + + + align:start position:0% +when it's demonstrated enough is labs +our lab scale experiments with a good + + align:start position:0% +our lab scale experiments with a good + + + align:start position:0% +our lab scale experiments with a good +promise of success good if they'll be + + align:start position:0% +promise of success good if they'll be + + + align:start position:0% +promise of success good if they'll be +realized in five years in 15 and 20 and + + align:start position:0% +realized in five years in 15 and 20 and + + + align:start position:0% +realized in five years in 15 and 20 and +that's up to you guys to decide how + + align:start position:0% +that's up to you guys to decide how + + + align:start position:0% +that's up to you guys to decide how +quickly do you think the design you're + + align:start position:0% +quickly do you think the design you're + + + align:start position:0% +quickly do you think the design you're +making could be licensed and built and + + align:start position:0% +making could be licensed and built and + + + align:start position:0% +making could be licensed and built and +in that case what would the turnaround + + align:start position:0% +in that case what would the turnaround + + + align:start position:0% +in that case what would the turnaround +time have to be for whatever these + + align:start position:0% +time have to be for whatever these + + + align:start position:0% +time have to be for whatever these +processes you use to actually make + + align:start position:0% +processes you use to actually make + + + align:start position:0% +processes you use to actually make +success steps 3 & 4 brainstorm solutions + + align:start position:0% +success steps 3 & 4 brainstorm solutions + + + align:start position:0% +success steps 3 & 4 brainstorm solutions +generate ideas I would start this based + + align:start position:0% +generate ideas I would start this based + + + align:start position:0% +generate ideas I would start this based +on what I've told you guys just in these + + align:start position:0% +on what I've told you guys just in these + + + align:start position:0% +on what I've told you guys just in these +lectures think of different ways to + + align:start position:0% +lectures think of different ways to + + + align:start position:0% +lectures think of different ways to +solve the problem there are different + + align:start position:0% +solve the problem there are different + + + align:start position:0% +solve the problem there are different +options for the core and in here I would + + align:start position:0% +options for the core and in here I would + + + align:start position:0% +options for the core and in here I would +sort of categorize them you can make a + + align:start position:0% +sort of categorize them you can make a + + + align:start position:0% +sort of categorize them you can make a +list of all of your options and then + + align:start position:0% +list of all of your options and then + + + align:start position:0% +list of all of your options and then +identify a key perfume a few key + + align:start position:0% +identify a key perfume a few key + + + align:start position:0% +identify a key perfume a few key +parameters like what's the size of the + + align:start position:0% +parameters like what's the size of the + + + align:start position:0% +parameters like what's the size of the +reactor what are the temperatures you + + align:start position:0% +reactor what are the temperatures you + + + align:start position:0% +reactor what are the temperatures you +can use what are some funny things about + + align:start position:0% +can use what are some funny things about + + + align:start position:0% +can use what are some funny things about +it each technology and I'd want all four + + align:start position:0% +it each technology and I'd want all four + + + align:start position:0% +it each technology and I'd want all four +of the groups to do that so you have + + align:start position:0% +of the groups to do that so you have + + + align:start position:0% +of the groups to do that so you have +some easily comparable parameters moving + + align:start position:0% + + + + align:start position:0% + +Step five is what you guys are doing + + align:start position:0% +Step five is what you guys are doing + + + align:start position:0% +Step five is what you guys are doing +right now + + align:start position:0% +right now + + + align:start position:0% +right now +lots of research learn what's out there + + align:start position:0% +lots of research learn what's out there + + + align:start position:0% +lots of research learn what's out there +the first step is usually learning the + + align:start position:0% +the first step is usually learning the + + + align:start position:0% +the first step is usually learning the +keywords and once you can start + + align:start position:0% +keywords and once you can start + + + align:start position:0% +keywords and once you can start +searching for the keywords like + + align:start position:0% +searching for the keywords like + + + align:start position:0% +searching for the keywords like +fischer tropsch synthesis heat storage + + align:start position:0% +fischer tropsch synthesis heat storage + + + align:start position:0% +fischer tropsch synthesis heat storage +latent heat sensible heat etc you'll + + align:start position:0% +latent heat sensible heat etc you'll + + + align:start position:0% +latent heat sensible heat etc you'll +really start to find a lot more of these + + align:start position:0% +really start to find a lot more of these + + + align:start position:0% +really start to find a lot more of these +papers and what I would say is whenever + + align:start position:0% +papers and what I would say is whenever + + + align:start position:0% +papers and what I would say is whenever +you find something share it with + + align:start position:0% +you find something share it with + + + align:start position:0% +you find something share it with +everyone share it with your team share + + align:start position:0% +everyone share it with your team share + + + align:start position:0% +everyone share it with your team share +it with the whole group because + + align:start position:0% +it with the whole group because + + + align:start position:0% +it with the whole group because +cross-pollination between these groups + + align:start position:0% +cross-pollination between these groups + + + align:start position:0% +cross-pollination between these groups +can sometimes lead to the best ideas and + + align:start position:0% +can sometimes lead to the best ideas and + + + align:start position:0% +can sometimes lead to the best ideas and +that way everyone's on the same field + + align:start position:0% +that way everyone's on the same field + + + align:start position:0% +that way everyone's on the same field +and everyone understands what's going on + + align:start position:0% +and everyone understands what's going on + + + align:start position:0% +and everyone understands what's going on +in each team so you collect your + + align:start position:0% +in each team so you collect your + + + align:start position:0% +in each team so you collect your +findings compared to your friends + + align:start position:0% +findings compared to your friends + + + align:start position:0% +findings compared to your friends +compared to your initial ideas and you + + align:start position:0% +compared to your initial ideas and you + + + align:start position:0% +compared to your initial ideas and you +may end up identifying oh there's sort + + align:start position:0% +may end up identifying oh there's sort + + + align:start position:0% +may end up identifying oh there's sort +of a hole here which means go back to + + align:start position:0% +of a hole here which means go back to + + + align:start position:0% +of a hole here which means go back to +step 3 do some more brainstorming do + + align:start position:0% +step 3 do some more brainstorming do + + + align:start position:0% +step 3 do some more brainstorming do +some more research until you reach them + + align:start position:0% +some more research until you reach them + + + align:start position:0% +some more research until you reach them +like I said diminishing returns or + + align:start position:0% +like I said diminishing returns or + + + align:start position:0% +like I said diminishing returns or +information saturation so you guys can + + align:start position:0% +information saturation so you guys can + + + align:start position:0% +information saturation so you guys can +come to a consensus to say okay I think + + align:start position:0% +come to a consensus to say okay I think + + + align:start position:0% +come to a consensus to say okay I think +we have enough to move forward let's + + align:start position:0% +we have enough to move forward let's + + + align:start position:0% +we have enough to move forward let's +just move on and start designing step + + align:start position:0% +just move on and start designing step + + + align:start position:0% +just move on and start designing step +six which we'll start to get into + + align:start position:0% +six which we'll start to get into + + + align:start position:0% +six which we'll start to get into +together next week down selection from + + align:start position:0% +together next week down selection from + + + align:start position:0% +together next week down selection from +all of your possible possibilities + + align:start position:0% +all of your possible possibilities + + + align:start position:0% +all of your possible possibilities +starting up here sort of the thickness + + align:start position:0% +starting up here sort of the thickness + + + align:start position:0% +starting up here sort of the thickness +of this graph as we go down tells you + + align:start position:0% +of this graph as we go down tells you + + + align:start position:0% +of this graph as we go down tells you +how many design choices you have up here + + align:start position:0% +how many design choices you have up here + + + align:start position:0% +how many design choices you have up here +is everything and you can probably + + align:start position:0% +is everything and you can probably + + + align:start position:0% +is everything and you can probably +eliminate a good number of them just by + + align:start position:0% +eliminate a good number of them just by + + + align:start position:0% +eliminate a good number of them just by +applying design criteria or let's say + + align:start position:0% +applying design criteria or let's say + + + align:start position:0% +applying design criteria or let's say +this isn't demonstrated yet and it's not + + align:start position:0% +this isn't demonstrated yet and it's not + + + align:start position:0% +this isn't demonstrated yet and it's not +going to be for 50 years throw it out + + align:start position:0% +going to be for 50 years throw it out + + + align:start position:0% +going to be for 50 years throw it out +the window and you reach this stage + + align:start position:0% +the window and you reach this stage + + + align:start position:0% +the window and you reach this stage +where you've narrowed down maybe half + + align:start position:0% +where you've narrowed down maybe half + + + align:start position:0% +where you've narrowed down maybe half +your ideas then in the team's you should + + align:start position:0% +your ideas then in the team's you should + + + align:start position:0% +your ideas then in the team's you should +start choosing what's most important to + + align:start position:0% +start choosing what's most important to + + + align:start position:0% +start choosing what's most important to +you in terms of outputs efficiency + + align:start position:0% +you in terms of outputs efficiency + + + align:start position:0% +you in terms of outputs efficiency +safety public appeal whatever you want + + align:start position:0% +safety public appeal whatever you want + + + align:start position:0% +safety public appeal whatever you want +and you'll be able to narrow it down in + + align:start position:0% +and you'll be able to narrow it down in + + + align:start position:0% +and you'll be able to narrow it down in +your sub teams to very few choices some + + align:start position:0% +your sub teams to very few choices some + + + align:start position:0% +your sub teams to very few choices some +very few possible contenders all of + + align:start position:0% +very few possible contenders all of + + + align:start position:0% +very few possible contenders all of +which would probably make a good design + + align:start position:0% +which would probably make a good design + + + align:start position:0% +which would probably make a good design +at this time which I think will be at + + align:start position:0% +at this time which I think will be at + + + align:start position:0% +at this time which I think will be at +near the end and next week the group + + align:start position:0% +near the end and next week the group + + + align:start position:0% +near the end and next week the group +will have to meet together and whether + + align:start position:0% +will have to meet together and whether + + + align:start position:0% +will have to meet together and whether +you decide to meet all together or just + + align:start position:0% +you decide to meet all together or just + + + align:start position:0% +you decide to meet all together or just +the focus area leads or pass the + + align:start position:0% +the focus area leads or pass the + + + align:start position:0% +the focus area leads or pass the +information up to the integrators and + + align:start position:0% +information up to the integrators and + + + align:start position:0% +information up to the integrators and +let them do the deciding is up to you + + align:start position:0% +let them do the deciding is up to you + + + align:start position:0% +let them do the deciding is up to you +you'll use some sort of official design + + align:start position:0% +you'll use some sort of official design + + + align:start position:0% +you'll use some sort of official design +metric for example the hoq the house of + + align:start position:0% +metric for example the hoq the house of + + + align:start position:0% +metric for example the hoq the house of +quality which + + align:start position:0% +quality which + + + align:start position:0% +quality which +get into on the next slide so you can + + align:start position:0% +get into on the next slide so you can + + + align:start position:0% +get into on the next slide so you can +actually say numerically here the + + align:start position:0% +actually say numerically here the + + + align:start position:0% +actually say numerically here the +importance as I ranked to different + + align:start position:0% +importance as I ranked to different + + + align:start position:0% +importance as I ranked to different +aspects of the design and here is why we + + align:start position:0% +aspects of the design and here is why we + + + align:start position:0% +aspects of the design and here is why we +chose this one as the best possible + + align:start position:0% +chose this one as the best possible + + + align:start position:0% +chose this one as the best possible +candidate and at that point at the end + + align:start position:0% +candidate and at that point at the end + + + align:start position:0% +candidate and at that point at the end +of week four you'll have a design path + + align:start position:0% +of week four you'll have a design path + + + align:start position:0% +of week four you'll have a design path +you'll know which way to go and you + + align:start position:0% +you'll know which way to go and you + + + align:start position:0% +you'll know which way to go and you +won't have to second-guess yourself all + + align:start position:0% +won't have to second-guess yourself all + + + align:start position:0% +won't have to second-guess yourself all +the time I didn't say never second-guess + + align:start position:0% +the time I didn't say never second-guess + + + align:start position:0% +the time I didn't say never second-guess +yourself because you've always got to be + + align:start position:0% +yourself because you've always got to be + + + align:start position:0% +yourself because you've always got to be +thinking is there something better but + + align:start position:0% +thinking is there something better but + + + align:start position:0% +thinking is there something better but +you won't you can shift your focus from + + align:start position:0% +you won't you can shift your focus from + + + align:start position:0% +you won't you can shift your focus from +research to design so the house of + + align:start position:0% +research to design so the house of + + + align:start position:0% +research to design so the house of +quality is one that we've actually used + + align:start position:0% +quality is one that we've actually used + + + align:start position:0% +quality is one that we've actually used +in this design course a couple times + + align:start position:0% +in this design course a couple times + + + align:start position:0% +in this design course a couple times +it's taken basically from the management + + align:start position:0% +it's taken basically from the management + + + align:start position:0% +it's taken basically from the management +world where you have to match the + + align:start position:0% +world where you have to match the + + + align:start position:0% +world where you have to match the +technical requirements which are what + + align:start position:0% +technical requirements which are what + + + align:start position:0% +technical requirements which are what +the engineers or you guys want to happen + + align:start position:0% +the engineers or you guys want to happen + + + align:start position:0% +the engineers or you guys want to happen +in this design with the customer + + align:start position:0% +in this design with the customer + + + align:start position:0% +in this design with the customer +requirements and in this case it's a + + align:start position:0% +requirements and in this case it's a + + + align:start position:0% +requirements and in this case it's a +little different from normal normally + + align:start position:0% +little different from normal normally + + + align:start position:0% +little different from normal normally +you can hand out a customer survey and + + align:start position:0% +you can hand out a customer survey and + + + align:start position:0% +you can hand out a customer survey and +say what's most important to you but you + + align:start position:0% +say what's most important to you but you + + + align:start position:0% +say what's most important to you but you +guys are going to have to estimate what + + align:start position:0% +guys are going to have to estimate what + + + align:start position:0% +guys are going to have to estimate what +the consumer public wants do they want + + align:start position:0% +the consumer public wants do they want + + + align:start position:0% +the consumer public wants do they want +more fueled are they gonna want more + + align:start position:0% +more fueled are they gonna want more + + + align:start position:0% +more fueled are they gonna want more +electricity and a lot of that you can + + align:start position:0% +electricity and a lot of that you can + + + align:start position:0% +electricity and a lot of that you can +look at supply and demand trends and see + + align:start position:0% +look at supply and demand trends and see + + + align:start position:0% +look at supply and demand trends and see +where is the biggest shortfall going to + + align:start position:0% +where is the biggest shortfall going to + + + align:start position:0% +where is the biggest shortfall going to +be in terms of supply versus demand what + + align:start position:0% +be in terms of supply versus demand what + + + align:start position:0% +be in terms of supply versus demand what +do you think the public cares about + + align:start position:0% +do you think the public cares about + + + align:start position:0% +do you think the public cares about +safety what do you think the public care + + align:start position:0% +safety what do you think the public care + + + align:start position:0% +safety what do you think the public care +is about citing are they all going to + + align:start position:0% +is about citing are they all going to + + + align:start position:0% +is about citing are they all going to +say not in my backyard are they all + + align:start position:0% +say not in my backyard are they all + + + align:start position:0% +say not in my backyard are they all +going to say no nuclear ever are they + + align:start position:0% +going to say no nuclear ever are they + + + align:start position:0% +going to say no nuclear ever are they +going to say go for it it's totally the + + align:start position:0% +going to say go for it it's totally the + + + align:start position:0% +going to say go for it it's totally the +way of the future + + align:start position:0% +way of the future + + + align:start position:0% +way of the future +you guys will have to choose what you + + align:start position:0% +you guys will have to choose what you + + + align:start position:0% +you guys will have to choose what you +think is most important I'd recommend + + align:start position:0% +think is most important I'd recommend + + + align:start position:0% +think is most important I'd recommend +doing this once inside your team's so + + align:start position:0% +doing this once inside your team's so + + + align:start position:0% +doing this once inside your team's so +that your team leaders can meet and + + align:start position:0% +that your team leaders can meet and + + + align:start position:0% +that your team leaders can meet and +compare what you think importances are + + align:start position:0% +compare what you think importances are + + + align:start position:0% +compare what you think importances are +for the customer because if after all + + align:start position:0% +for the customer because if after all + + + align:start position:0% +for the customer because if after all +you're estimating importance is for + + align:start position:0% +you're estimating importance is for + + + align:start position:0% +you're estimating importance is for +everyone in the country overall because + + align:start position:0% +everyone in the country overall because + + + align:start position:0% +everyone in the country overall because +this is a sort of a complex process + + align:start position:0% +this is a sort of a complex process + + + align:start position:0% +this is a sort of a complex process +there's a good online tutorial which is + + align:start position:0% +there's a good online tutorial which is + + + align:start position:0% +there's a good online tutorial which is +right here and there are templates so + + align:start position:0% +right here and there are templates so + + + align:start position:0% +right here and there are templates so +you don't have to build this entire + + align:start position:0% +you don't have to build this entire + + + align:start position:0% +you don't have to build this entire +thing you can just start filling in your + + align:start position:0% +thing you can just start filling in your + + + align:start position:0% +thing you can just start filling in your +importances get numbers out and + + align:start position:0% +importances get numbers out and + + + align:start position:0% +importances get numbers out and +understand it so I don't want you have + + align:start position:0% +understand it so I don't want you have + + + align:start position:0% +understand it so I don't want you have +to you guys to have to start from + + align:start position:0% +to you guys to have to start from + + + align:start position:0% +to you guys to have to start from +scratch and if people want if if you try + + align:start position:0% +scratch and if people want if if you try + + + align:start position:0% +scratch and if people want if if you try +and do this house a quality thing and it + + align:start position:0% +and do this house a quality thing and it + + + align:start position:0% +and do this house a quality thing and it +looks to be a little too difficult we + + align:start position:0% +looks to be a little too difficult we + + + align:start position:0% +looks to be a little too difficult we +can hold a recitation with an example + + align:start position:0% +can hold a recitation with an example + + + align:start position:0% +can hold a recitation with an example +this also isn't the only way to assign + + align:start position:0% +this also isn't the only way to assign + + + align:start position:0% +this also isn't the only way to assign +importances I'm just showing you one + + align:start position:0% +importances I'm just showing you one + + + align:start position:0% +importances I'm just showing you one +sort + + align:start position:0% +sort + + + align:start position:0% +sort +of example if you don't decide to use + + align:start position:0% +of example if you don't decide to use + + + align:start position:0% +of example if you don't decide to use +the house equality I would find a method + + align:start position:0% +the house equality I would find a method + + + align:start position:0% +the house equality I would find a method +that you can still numerically assign + + align:start position:0% +that you can still numerically assign + + + align:start position:0% +that you can still numerically assign +importances to things and come up with + + align:start position:0% +importances to things and come up with + + + align:start position:0% +importances to things and come up with +an answer that you can compare + + align:start position:0% +an answer that you can compare + + + align:start position:0% +an answer that you can compare +numerically not just it's clearly the + + align:start position:0% +numerically not just it's clearly the + + + align:start position:0% +numerically not just it's clearly the +best or I feel like it's the best step 7 + + align:start position:0% +best or I feel like it's the best step 7 + + + align:start position:0% +best or I feel like it's the best step 7 +start designing once you've chosen your + + align:start position:0% +start designing once you've chosen your + + + align:start position:0% +start designing once you've chosen your +design path and you have a house of + + align:start position:0% +design path and you have a house of + + + align:start position:0% +design path and you have a house of +quality or some other house of something + + align:start position:0% +quality or some other house of something + + + align:start position:0% +quality or some other house of something +to back it up you can start filling in + + align:start position:0% +to back it up you can start filling in + + + align:start position:0% +to back it up you can start filling in +parameters constructing block diagrams + + align:start position:0% +parameters constructing block diagrams + + + align:start position:0% +parameters constructing block diagrams +rearranging blocks that'll come later in + + align:start position:0% +rearranging blocks that'll come later in + + + align:start position:0% +rearranging blocks that'll come later in +week 4 and I'll have some more lectures + + align:start position:0% +week 4 and I'll have some more lectures + + + align:start position:0% +week 4 and I'll have some more lectures +on that so don't worry about that yet I + + align:start position:0% +on that so don't worry about that yet I + + + align:start position:0% +on that so don't worry about that yet I +just want to show you guys now the whole + + align:start position:0% +just want to show you guys now the whole + + + align:start position:0% +just want to show you guys now the whole +design process from start to finish and + + align:start position:0% +design process from start to finish and + + + align:start position:0% +design process from start to finish and +this is a good chance to see if anything + + align:start position:0% +this is a good chance to see if anything + + + align:start position:0% +this is a good chance to see if anything +totally doesn't work if you violated the + + align:start position:0% +totally doesn't work if you violated the + + + align:start position:0% +totally doesn't work if you violated the +laws of physics like you have certain + + align:start position:0% +laws of physics like you have certain + + + align:start position:0% +laws of physics like you have certain +amount of energy in and more energy out + + align:start position:0% +amount of energy in and more energy out + + + align:start position:0% +amount of energy in and more energy out +I know this from experience I ran I + + align:start position:0% +I know this from experience I ran I + + + align:start position:0% +I know this from experience I ran I +started an LED company like an LED + + align:start position:0% +started an LED company like an LED + + + align:start position:0% +started an LED company like an LED +lighting company for the movie industry + + align:start position:0% +lighting company for the movie industry + + + align:start position:0% +lighting company for the movie industry +and a lot of our customers knew what + + align:start position:0% +and a lot of our customers knew what + + + align:start position:0% +and a lot of our customers knew what +they were doing a couple did not I was + + align:start position:0% +they were doing a couple did not I was + + + align:start position:0% +they were doing a couple did not I was +asked to produce a fixture that would + + align:start position:0% +asked to produce a fixture that would + + + align:start position:0% +asked to produce a fixture that would +consume a hundred watts and put out a + + align:start position:0% +consume a hundred watts and put out a + + + align:start position:0% +consume a hundred watts and put out a +hundred and fifty because we'd be the + + align:start position:0% +hundred and fifty because we'd be the + + + align:start position:0% +hundred and fifty because we'd be the +first people on the market to do it we + + align:start position:0% +first people on the market to do it we + + + align:start position:0% +first people on the market to do it we +would blow the competition away well + + align:start position:0% +would blow the competition away well + + + align:start position:0% +would blow the competition away well +they're absolutely right but I don't + + align:start position:0% +they're absolutely right but I don't + + + align:start position:0% +they're absolutely right but I don't +need to say anymore you know I ended up + + align:start position:0% +need to say anymore you know I ended up + + + align:start position:0% +need to say anymore you know I ended up +quitting that company too + + align:start position:0% +quitting that company too + + + align:start position:0% +quitting that company too +for reasons exactly like that + + align:start position:0% +for reasons exactly like that + + + align:start position:0% +for reasons exactly like that +step eight step eight could be a + + align:start position:0% +step eight step eight could be a + + + align:start position:0% +step eight step eight could be a +never-ending cycle it's up to you to + + align:start position:0% +never-ending cycle it's up to you to + + + align:start position:0% +never-ending cycle it's up to you to +choose when to end the cycle this is the + + align:start position:0% +choose when to end the cycle this is the + + + align:start position:0% +choose when to end the cycle this is the +cycle of iteration where you design your + + align:start position:0% +cycle of iteration where you design your + + + align:start position:0% +cycle of iteration where you design your +team subpart you put it together in the + + align:start position:0% +team subpart you put it together in the + + + align:start position:0% +team subpart you put it together in the +whole scheme of things look to see where + + align:start position:0% +whole scheme of things look to see where + + + align:start position:0% +whole scheme of things look to see where +are the bottlenecks where are the pinch + + align:start position:0% +are the bottlenecks where are the pinch + + + align:start position:0% +are the bottlenecks where are the pinch +points what are the biggest restrictions + + align:start position:0% +points what are the biggest restrictions + + + align:start position:0% +points what are the biggest restrictions +in terms of output or input or energy + + align:start position:0% +in terms of output or input or energy + + + align:start position:0% +in terms of output or input or energy +flow go back and change things and see + + align:start position:0% +flow go back and change things and see + + + align:start position:0% +flow go back and change things and see +if a change to a parameter or a + + align:start position:0% +if a change to a parameter or a + + + align:start position:0% +if a change to a parameter or a +rearranging of your block diagram can + + align:start position:0% +rearranging of your block diagram can + + + align:start position:0% +rearranging of your block diagram can +improve the efficiency or the output or + + align:start position:0% +improve the efficiency or the output or + + + align:start position:0% +improve the efficiency or the output or +the total amount of production or the + + align:start position:0% +the total amount of production or the + + + align:start position:0% +the total amount of production or the +safety or the public appeal overall and + + align:start position:0% +safety or the public appeal overall and + + + align:start position:0% +safety or the public appeal overall and +at some point you guys all know after + + align:start position:0% +at some point you guys all know after + + + align:start position:0% +at some point you guys all know after +enough iteration we're done we could + + align:start position:0% +enough iteration we're done we could + + + align:start position:0% +enough iteration we're done we could +make tiny incremental changes but it's + + align:start position:0% +make tiny incremental changes but it's + + + align:start position:0% +make tiny incremental changes but it's +not worth our + + align:start position:0% +not worth our + + + align:start position:0% +not worth our +anymore and that's sort of one of the + + align:start position:0% +anymore and that's sort of one of the + + + align:start position:0% +anymore and that's sort of one of the +biggest things in the engineering design + + align:start position:0% +biggest things in the engineering design + + + align:start position:0% +biggest things in the engineering design +process when you give an engineer + + align:start position:0% +process when you give an engineer + + + align:start position:0% +process when you give an engineer +something and say make me a product that + + align:start position:0% +something and say make me a product that + + + align:start position:0% +something and say make me a product that +does this it's pretty common to take it + + align:start position:0% +does this it's pretty common to take it + + + align:start position:0% +does this it's pretty common to take it +to infinity to come up with lots of + + align:start position:0% +to infinity to come up with lots of + + + align:start position:0% +to infinity to come up with lots of +extra features to think I know what the + + align:start position:0% +extra features to think I know what the + + + align:start position:0% +extra features to think I know what the +customer wants don't tell me what the + + align:start position:0% +customer wants don't tell me what the + + + align:start position:0% +customer wants don't tell me what the +customer wants and perfect the + + align:start position:0% +customer wants and perfect the + + + align:start position:0% +customer wants and perfect the +efficiency possibly at the sacrifice of + + align:start position:0% +efficiency possibly at the sacrifice of + + + align:start position:0% +efficiency possibly at the sacrifice of +cost or deadlines or requirements and + + align:start position:0% +cost or deadlines or requirements and + + + align:start position:0% +cost or deadlines or requirements and +things and to be a really good + + align:start position:0% +things and to be a really good + + + align:start position:0% +things and to be a really good +engineering designer you have to know + + align:start position:0% +engineering designer you have to know + + + align:start position:0% +engineering designer you have to know +when to say enough is enough and that + + align:start position:0% +when to say enough is enough and that + + + align:start position:0% +when to say enough is enough and that +doesn't mean you do one design cycle and + + align:start position:0% +doesn't mean you do one design cycle and + + + align:start position:0% +doesn't mean you do one design cycle and +you're like I'm done that's it I've I'm + + align:start position:0% +you're like I'm done that's it I've I'm + + + align:start position:0% +you're like I'm done that's it I've I'm +tired but you will get to know through + + align:start position:0% +tired but you will get to know through + + + align:start position:0% +tired but you will get to know through +experience when enough is enough + + align:start position:0% +experience when enough is enough + + + align:start position:0% +experience when enough is enough +so in the last few minutes I'd like to + + align:start position:0% +so in the last few minutes I'd like to + + + align:start position:0% +so in the last few minutes I'd like to +hear from the focus area leaders how's + + align:start position:0% +hear from the focus area leaders how's + + + align:start position:0% +hear from the focus area leaders how's +the research process going or do you + + align:start position:0% +the research process going or do you + + + align:start position:0% +the research process going or do you +guys does everybody know what sort of + + align:start position:0% +guys does everybody know what sort of + + + align:start position:0% +guys does everybody know what sort of +amount of work you guys are doing have + + align:start position:0% +amount of work you guys are doing have + + + align:start position:0% +amount of work you guys are doing have +the groups split up the research process + + align:start position:0% +the groups split up the research process + + + align:start position:0% +the groups split up the research process +and does everyone have a little bit to + + align:start position:0% +and does everyone have a little bit to + + + align:start position:0% +and does everyone have a little bit to +do a fairly equal amount are you guys + + align:start position:0% +do a fairly equal amount are you guys + + + align:start position:0% +do a fairly equal amount are you guys +finding designs for example are you + + align:start position:0% +finding designs for example are you + + + align:start position:0% +finding designs for example are you +finding core designs in the core group + + align:start position:0% +finding core designs in the core group + + + align:start position:0% +finding core designs in the core group +or process heat ideas in terms of + + align:start position:0% +or process heat ideas in terms of + + + align:start position:0% +or process heat ideas in terms of +transport and storage for the process + + align:start position:0% +transport and storage for the process + + + align:start position:0% +transport and storage for the process +heat group or is anyone having trouble + + align:start position:0% +heat group or is anyone having trouble + + + align:start position:0% +heat group or is anyone having trouble +finding anything + + align:start position:0% + + + + align:start position:0% + +coming back so we have some like a + + align:start position:0% +coming back so we have some like a + + + align:start position:0% +coming back so we have some like a +couple paragraphs and like you know what + + align:start position:0% +couple paragraphs and like you know what + + + align:start position:0% +couple paragraphs and like you know what +that reactor design great well that's a + + align:start position:0% +that reactor design great well that's a + + + align:start position:0% +that reactor design great well that's a +great that's an excellent example how + + align:start position:0% +great that's an excellent example how + + + align:start position:0% +great that's an excellent example how +about the other groups what are you guys + + align:start position:0% +about the other groups what are you guys + + + align:start position:0% +about the other groups what are you guys +doing + + align:start position:0% + + + + align:start position:0% + +okay great how about biofuels folks + + align:start position:0% + + + + align:start position:0% + +okay okay oh great and process heat + + align:start position:0% +okay okay oh great and process heat + + + align:start position:0% +okay okay oh great and process heat +how's that going + + align:start position:0% + + + + align:start position:0% + +that's good yeah heat exchanges are + + align:start position:0% +that's good yeah heat exchanges are + + + align:start position:0% +that's good yeah heat exchanges are +definitely the the mathematically Meteor + + align:start position:0% +definitely the the mathematically Meteor + + + align:start position:0% +definitely the the mathematically Meteor +part of the design so what I'd like to + + align:start position:0% +part of the design so what I'd like to + + + align:start position:0% +part of the design so what I'd like to +do I guess everyone is free to go except + + align:start position:0% +do I guess everyone is free to go except + + + align:start position:0% +do I guess everyone is free to go except +the focus area leaders and the + + align:start position:0% +the focus area leaders and the + + + align:start position:0% +the focus area leaders and the +integrators I'd like to just go over a + + align:start position:0% +integrators I'd like to just go over a + + + align:start position:0% +integrators I'd like to just go over a +little bit of scheduling and reporting + + align:start position:0% +little bit of scheduling and reporting + + + align:start position:0% +little bit of scheduling and reporting +stuff and if anyone else has any + + align:start position:0% +stuff and if anyone else has any + + + align:start position:0% +stuff and if anyone else has any +questions that you want to come up and + + align:start position:0% +questions that you want to come up and + + + align:start position:0% +questions that you want to come up and +ask you're welcome to do so + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/2keGgDBJKGU.txt b/2keGgDBJKGU.txt new file mode 100644 index 0000000000000000000000000000000000000000..bf01e487c2531a9af853fc8ebc8797e288c7fd64 --- /dev/null +++ b/2keGgDBJKGU.txt @@ -0,0 +1,1787 @@ +align:start position:0% + +welcome back to recitation in this video + + align:start position:0% +welcome back to recitation in this video + + + align:start position:0% +welcome back to recitation in this video +we'd like to do another optimization + + align:start position:0% +we'd like to do another optimization + + + align:start position:0% +we'd like to do another optimization +problem this one's a little bit harder + + align:start position:0% +problem this one's a little bit harder + + + align:start position:0% +problem this one's a little bit harder +than the distance problem so the the + + align:start position:0% +than the distance problem so the the + + + align:start position:0% +than the distance problem so the the +question is the following consider + + align:start position:0% +question is the following consider + + + align:start position:0% +question is the following consider +triangles formed by lines passing + + align:start position:0% +triangles formed by lines passing + + + align:start position:0% +triangles formed by lines passing +through the point x 84 sorry the x axis + + align:start position:0% +through the point x 84 sorry the x axis + + + align:start position:0% +through the point x 84 sorry the x axis +and the y- axis find the dimensions that + + align:start position:0% +and the y- axis find the dimensions that + + + align:start position:0% +and the y- axis find the dimensions that +minimize area so what does this first + + align:start position:0% +minimize area so what does this first + + + align:start position:0% +minimize area so what does this first +sentence mean it really means use this + + align:start position:0% +sentence mean it really means use this + + + align:start position:0% +sentence mean it really means use this +point to draw a line through this point + + align:start position:0% +point to draw a line through this point + + + align:start position:0% +point to draw a line through this point +I'll give you an example it's kind of a + + align:start position:0% +I'll give you an example it's kind of a + + + align:start position:0% +I'll give you an example it's kind of a +wiggly line but hopefully it looks like + + align:start position:0% +wiggly line but hopefully it looks like + + + align:start position:0% +wiggly line but hopefully it looks like +a line to you and it makes a triangle + + align:start position:0% +a line to you and it makes a triangle + + + align:start position:0% +a line to you and it makes a triangle +with this line the X axxis and the y- + + align:start position:0% +with this line the X axxis and the y- + + + align:start position:0% +with this line the X axxis and the y- +AIS we can certainly calculate the area + + align:start position:0% +AIS we can certainly calculate the area + + + align:start position:0% +AIS we can certainly calculate the area +of that triangle so the problem is + + align:start position:0% +of that triangle so the problem is + + + align:start position:0% +of that triangle so the problem is +asking you to find the dimensions of the + + align:start position:0% +asking you to find the dimensions of the + + + align:start position:0% +asking you to find the dimensions of the +triangle that that minimize the area + + align:start position:0% +triangle that that minimize the area + + + align:start position:0% +triangle that that minimize the area +with the constraint that the line the + + align:start position:0% +with the constraint that the line the + + + align:start position:0% +with the constraint that the line the +hypotenuse goes through the0 84 I'm + + align:start position:0% +hypotenuse goes through the0 84 I'm + + + align:start position:0% +hypotenuse goes through the0 84 I'm +going to give you a couple minutes to + + align:start position:0% +going to give you a couple minutes to + + + align:start position:0% +going to give you a couple minutes to +work on it why don't you pause the video + + align:start position:0% +work on it why don't you pause the video + + + align:start position:0% +work on it why don't you pause the video +here and then uh when you're ready + + align:start position:0% +here and then uh when you're ready + + + align:start position:0% +here and then uh when you're ready +restart the video I'll come back and + + align:start position:0% +restart the video I'll come back and + + + align:start position:0% +restart the video I'll come back and +I'll help you solve the + + align:start position:0% + + + + align:start position:0% + +problem welcome back so again we're + + align:start position:0% +problem welcome back so again we're + + + align:start position:0% +problem welcome back so again we're +doing an optimization problem and we + + align:start position:0% +doing an optimization problem and we + + + align:start position:0% +doing an optimization problem and we +want to optimize because it says + + align:start position:0% +want to optimize because it says + + + align:start position:0% +want to optimize because it says +minimize area we know the optimizing + + align:start position:0% +minimize area we know the optimizing + + + align:start position:0% +minimize area we know the optimizing +equation is area so let's be very clear + + align:start position:0% +equation is area so let's be very clear + + + align:start position:0% +equation is area so let's be very clear +always when you're doing these problems + + align:start position:0% +always when you're doing these problems + + + align:start position:0% +always when you're doing these problems +you have again as we've said previously + + align:start position:0% +you have again as we've said previously + + + align:start position:0% +you have again as we've said previously +you have a constraint equation and you + + align:start position:0% +you have a constraint equation and you + + + align:start position:0% +you have a constraint equation and you +have an optimizing equation the + + align:start position:0% +have an optimizing equation the + + + align:start position:0% +have an optimizing equation the +optimizing equation now we've already + + align:start position:0% +optimizing equation now we've already + + + align:start position:0% +optimizing equation now we've already +said is area and area the easiest way to + + align:start position:0% +said is area and area the easiest way to + + + align:start position:0% +said is area and area the easiest way to +write + + align:start position:0% +write + + + align:start position:0% +write +area in this form is notice that this + + align:start position:0% +area in this form is notice that this + + + align:start position:0% +area in this form is notice that this +distance this we could write it as base + + align:start position:0% +distance this we could write it as base + + + align:start position:0% +distance this we could write it as base +times height or we could write it as x x + + align:start position:0% +times height or we could write it as x x + + + align:start position:0% +times height or we could write it as x x +y so the base here is X and the height + + align:start position:0% +y so the base here is X and the height + + + align:start position:0% +y so the base here is X and the height +here is y so the area of the triangle is + + align:start position:0% +here is y so the area of the triangle is + + + align:start position:0% +here is y so the area of the triangle is +12 base time + + align:start position:0% + + + + align:start position:0% + +height so the area is one half x x y + + align:start position:0% +height so the area is one half x x y + + + align:start position:0% +height so the area is one half x x y +that's the thing we want to optimize the + + align:start position:0% +that's the thing we want to optimize the + + + align:start position:0% +that's the thing we want to optimize the +problem is that we know when we're doing + + align:start position:0% +problem is that we know when we're doing + + + align:start position:0% +problem is that we know when we're doing +these optimization problems we want to + + align:start position:0% +these optimization problems we want to + + + align:start position:0% +these optimization problems we want to +take a derivative area with respect to a + + align:start position:0% +take a derivative area with respect to a + + + align:start position:0% +take a derivative area with respect to a +variable but right now we have two + + align:start position:0% +variable but right now we have two + + + align:start position:0% +variable but right now we have two +variables and so that's where the + + align:start position:0% +variables and so that's where the + + + align:start position:0% +variables and so that's where the +constraint equation comes in so now we + + align:start position:0% +constraint equation comes in so now we + + + align:start position:0% +constraint equation comes in so now we +have to figure + + align:start position:0% +have to figure + + + align:start position:0% +have to figure +out uh how we're going to use a + + align:start position:0% +out uh how we're going to use a + + + align:start position:0% +out uh how we're going to use a +constraint equation here the constraint + + align:start position:0% +constraint equation here the constraint + + + align:start position:0% +constraint equation here the constraint +is that it has to go through this this + + align:start position:0% +is that it has to go through this this + + + align:start position:0% +is that it has to go through this this +84 so what does our line have to look + + align:start position:0% +84 so what does our line have to look + + + align:start position:0% +84 so what does our line have to look +like well our line has to look like + + align:start position:0% +like well our line has to look like + + + align:start position:0% +like well our line has to look like +ultimately uh let's do maybe the point + + align:start position:0% +ultimately uh let's do maybe the point + + + align:start position:0% +ultimately uh let's do maybe the point +slope form Y is equal or sorry I said + + align:start position:0% +slope form Y is equal or sorry I said + + + align:start position:0% +slope form Y is equal or sorry I said +point slope form Yus 4 is equal to M + + align:start position:0% +point slope form Yus 4 is equal to M + + + align:start position:0% +point slope form Yus 4 is equal to M +time x - + + align:start position:0% +time x - + + + align:start position:0% +time x - +8 right notice I didn't I couldn't pick + + align:start position:0% +8 right notice I didn't I couldn't pick + + + align:start position:0% +8 right notice I didn't I couldn't pick +what M was because I don't the M + + align:start position:0% +what M was because I don't the M + + + align:start position:0% +what M was because I don't the M +completely determines the + + align:start position:0% +completely determines the + + + align:start position:0% +completely determines the +line so I hopefully that makes sense + + align:start position:0% +line so I hopefully that makes sense + + + align:start position:0% +line so I hopefully that makes sense +that you can see that now in fact let's + + align:start position:0% +that you can see that now in fact let's + + + align:start position:0% +that you can see that now in fact let's +look at how this problem will work the m + + align:start position:0% +look at how this problem will work the m + + + align:start position:0% +look at how this problem will work the m +is going to deter determine this point + + align:start position:0% +is going to deter determine this point + + + align:start position:0% +is going to deter determine this point +and it's going to determine this point + + align:start position:0% +and it's going to determine this point + + + align:start position:0% +and it's going to determine this point +if you can't see that well let's let's + + align:start position:0% +if you can't see that well let's let's + + + align:start position:0% +if you can't see that well let's let's +look back here this + + align:start position:0% +look back here this + + + align:start position:0% +look back here this +point is when y equals z right so I can + + align:start position:0% +point is when y equals z right so I can + + + align:start position:0% +point is when y equals z right so I can +put in y equals 0 and I get X in terms + + align:start position:0% +put in y equals 0 and I get X in terms + + + align:start position:0% +put in y equals 0 and I get X in terms +of + + align:start position:0% +of + + + align:start position:0% +of +M if I come back over here and look at + + align:start position:0% +M if I come back over here and look at + + + align:start position:0% +M if I come back over here and look at +this point this is when x equals + + align:start position:0% +this point this is when x equals + + + align:start position:0% +this point this is when x equals +z so if I put in zero for X I can find Y + + align:start position:0% +z so if I put in zero for X I can find Y + + + align:start position:0% +z so if I put in zero for X I can find Y +in terms of M so these two values the x + + align:start position:0% +in terms of M so these two values the x + + + align:start position:0% +in terms of M so these two values the x +value and and the Y value completely + + align:start position:0% +value and and the Y value completely + + + align:start position:0% +value and and the Y value completely +determin on the slope of this line that + + align:start position:0% +determin on the slope of this line that + + + align:start position:0% +determin on the slope of this line that +hopefully makes sense just even if you + + align:start position:0% +hopefully makes sense just even if you + + + align:start position:0% +hopefully makes sense just even if you +look geome at the geometric picture when + + align:start position:0% +look geome at the geometric picture when + + + align:start position:0% +look geome at the geometric picture when +I when I turn about this point at 84 + + align:start position:0% +I when I turn about this point at 84 + + + align:start position:0% +I when I turn about this point at 84 +these values change so the X and Y + + align:start position:0% +these values change so the X and Y + + + align:start position:0% +these values change so the X and Y +values are completely determined by the + + align:start position:0% +values are completely determined by the + + + align:start position:0% +values are completely determined by the +slope of the line in fact the area then + + align:start position:0% +slope of the line in fact the area then + + + align:start position:0% +slope of the line in fact the area then +is completely determined by the slope of + + align:start position:0% +is completely determined by the slope of + + + align:start position:0% +is completely determined by the slope of +the line so what we're going to do is + + align:start position:0% +the line so what we're going to do is + + + align:start position:0% +the line so what we're going to do is +we're going to use the constraint + + align:start position:0% +we're going to use the constraint + + + align:start position:0% +we're going to use the constraint +equation to find X and Y values all in + + align:start position:0% +equation to find X and Y values all in + + + align:start position:0% +equation to find X and Y values all in +terms of the slope so let's do that + + align:start position:0% +terms of the slope so let's do that + + + align:start position:0% +terms of the slope so let's do that +I said when Y is + + align:start position:0% + + + + align:start position:0% + +zero what do we get for X we + + align:start position:0% +zero what do we get for X we + + + align:start position:0% +zero what do we get for X we +get -4 over m + 8 is equal to X let me + + align:start position:0% +get -4 over m + 8 is equal to X let me + + + align:start position:0% +get -4 over m + 8 is equal to X let me +double check my math so I don't have to + + align:start position:0% +double check my math so I don't have to + + + align:start position:0% +double check my math so I don't have to +re-shoot this when Y is zero I divide by + + align:start position:0% +re-shoot this when Y is zero I divide by + + + align:start position:0% +re-shoot this when Y is zero I divide by +m I add eight I get + + align:start position:0% +m I add eight I get + + + align:start position:0% +m I add eight I get +X so that is the x value I'm interested + + align:start position:0% +X so that is the x value I'm interested + + + align:start position:0% +X so that is the x value I'm interested +in down + + align:start position:0% +in down + + + align:start position:0% +in down +here when X is zero + + align:start position:0% +here when X is zero + + + align:start position:0% +here when X is zero +let's see what I get when X is Zer I get + + align:start position:0% +let's see what I get when X is Zer I get + + + align:start position:0% +let's see what I get when X is Zer I get +8 m + 4 is + + align:start position:0% + + + + align:start position:0% + +y + + align:start position:0% +y + + + align:start position:0% +y +right X is 08 m + 4 so now what I'm + + align:start position:0% +right X is 08 m + 4 so now what I'm + + + align:start position:0% +right X is 08 m + 4 so now what I'm +going to do is plug these two things + + align:start position:0% +going to do is plug these two things + + + align:start position:0% +going to do is plug these two things +into the area + + align:start position:0% + + + + align:start position:0% + +equation area is now equal to 12 of x * + + align:start position:0% +equation area is now equal to 12 of x * + + + align:start position:0% +equation area is now equal to 12 of x * +y so 12 of a 8 - 4 + + align:start position:0% +y so 12 of a 8 - 4 + + + align:start position:0% +y so 12 of a 8 - 4 +M time you know what I'm going to do I'm + + align:start position:0% +M time you know what I'm going to do I'm + + + align:start position:0% +M time you know what I'm going to do I'm +going to take this one half and kill off + + align:start position:0% +going to take this one half and kill off + + + align:start position:0% +going to take this one half and kill off +terms in there so I don't have to worry + + align:start position:0% +terms in there so I don't have to worry + + + align:start position:0% +terms in there so I don't have to worry +about it anymore -4 m + 2 so this is X + + align:start position:0% +about it anymore -4 m + 2 so this is X + + + align:start position:0% +about it anymore -4 m + 2 so this is X +and this is half of Y so just to make it + + align:start position:0% +and this is half of Y so just to make it + + + align:start position:0% +and this is half of Y so just to make it +simpler I'm not carrying through the one + + align:start position:0% +simpler I'm not carrying through the one + + + align:start position:0% +simpler I'm not carrying through the one +half I'm killing off half of the things + + align:start position:0% +half I'm killing off half of the things + + + align:start position:0% +half I'm killing off half of the things +taking dividing every term in y by two + + align:start position:0% +taking dividing every term in y by two + + + align:start position:0% +taking dividing every term in y by two +and again what are we trying to do we're + + align:start position:0% +and again what are we trying to do we're + + + align:start position:0% +and again what are we trying to do we're +trying to optimize so now we want to + + align:start position:0% +trying to optimize so now we want to + + + align:start position:0% +trying to optimize so now we want to +take the derivative of area with respect + + align:start position:0% +take the derivative of area with respect + + + align:start position:0% +take the derivative of area with respect +to the + + align:start position:0% + + + + align:start position:0% + +slope so this is maybe to simplify first + + align:start position:0% +slope so this is maybe to simplify first + + + align:start position:0% +slope so this is maybe to simplify first +let's multiply + + align:start position:0% + + + + align:start position:0% + +through so this is just a little bit of + + align:start position:0% +through so this is just a little bit of + + + align:start position:0% +through so this is just a little bit of +algebra really quick 8 * 4 is 32 so I + + align:start position:0% +algebra really quick 8 * 4 is 32 so I + + + align:start position:0% +algebra really quick 8 * 4 is 32 so I +get - 32 m + + + align:start position:0% +get - 32 m + + + + align:start position:0% +get - 32 m + +16 and then here negative * the negative + + align:start position:0% +16 and then here negative * the negative + + + align:start position:0% +16 and then here negative * the negative +is a positive 4 * 4 is 16 m / m i just + + align:start position:0% +is a positive 4 * 4 is 16 m / m i just + + + align:start position:0% +is a positive 4 * 4 is 16 m / m i just +get + + align:start position:0% +get + + + align:start position:0% +get +16 and then here I + + align:start position:0% +16 and then here I + + + align:start position:0% +16 and then here I +get 8 + + align:start position:0% + + + + align:start position:0% + +m so I had to do a little bit of algebra + + align:start position:0% +m so I had to do a little bit of algebra + + + align:start position:0% +m so I had to do a little bit of algebra +first but this is much easier to take a + + align:start position:0% +first but this is much easier to take a + + + align:start position:0% +first but this is much easier to take a +derivative and not make mistakes than + + align:start position:0% +derivative and not make mistakes than + + + align:start position:0% +derivative and not make mistakes than +this one because you'd have a product + + align:start position:0% +this one because you'd have a product + + + align:start position:0% +this one because you'd have a product +rule and just you and then you'd still + + align:start position:0% +rule and just you and then you'd still + + + align:start position:0% +rule and just you and then you'd still +have to multiply so we might as well + + align:start position:0% +have to multiply so we might as well + + + align:start position:0% +have to multiply so we might as well +multiply out first oh so now let me just + + align:start position:0% +multiply out first oh so now let me just + + + align:start position:0% +multiply out first oh so now let me just +take the derivative of + + align:start position:0% +take the derivative of + + + align:start position:0% +take the derivative of +this and again I'm taking the derivative + + align:start position:0% +this and again I'm taking the derivative + + + align:start position:0% +this and again I'm taking the derivative +with respect to M so here I just get -32 + + align:start position:0% +with respect to M so here I just get -32 + + + align:start position:0% +with respect to M so here I just get -32 +0 0 and then what's the dtive of this is + + align:start position:0% +0 0 and then what's the dtive of this is + + + align:start position:0% +0 0 and then what's the dtive of this is +a - 8 m well the derivative of 1 M if + + align:start position:0% +a - 8 m well the derivative of 1 M if + + + align:start position:0% +a - 8 m well the derivative of 1 M if +you remember is- 1 m^ 2 I have another + + align:start position:0% +you remember is- 1 m^ 2 I have another + + + align:start position:0% +you remember is- 1 m^ 2 I have another +negative here so this is going to be + + align:start position:0% +negative here so this is going to be + + + align:start position:0% +negative here so this is going to be +plus 8 over + + align:start position:0% +plus 8 over + + + align:start position:0% +plus 8 over +m^2 right optimizing we want to set the + + align:start position:0% +m^2 right optimizing we want to set the + + + align:start position:0% +m^2 right optimizing we want to set the +derivative equal to zero so if I set the + + align:start position:0% +derivative equal to zero so if I set the + + + align:start position:0% +derivative equal to zero so if I set the +derivative equal to zero and + + align:start position:0% +derivative equal to zero and + + + align:start position:0% +derivative equal to zero and +solve I get + + align:start position:0% +solve I get + + + align:start position:0% +solve I get +32 m^2 = 8 or m^2 is equal to 8 over 32 + + align:start position:0% +32 m^2 = 8 or m^2 is equal to 8 over 32 + + + align:start position:0% +32 m^2 = 8 or m^2 is equal to 8 over 32 +which is 1/4 or M is equal + + align:start position:0% +which is 1/4 or M is equal + + + align:start position:0% +which is 1/4 or M is equal +to2 or I should say plus or minus a half + + align:start position:0% +to2 or I should say plus or minus a half + + + align:start position:0% +to2 or I should say plus or minus a half +we need to be aware I I would run into + + align:start position:0% +we need to be aware I I would run into + + + align:start position:0% +we need to be aware I I would run into +problems if I didn't put the minus so + + align:start position:0% +problems if I didn't put the minus so + + + align:start position:0% +problems if I didn't put the minus so +solving this problem I see that again + + align:start position:0% +solving this problem I see that again + + + align:start position:0% +solving this problem I see that again +what did I do I set area Prime equal to + + align:start position:0% +what did I do I set area Prime equal to + + + align:start position:0% +what did I do I set area Prime equal to +zero move the 32 over multiply by m^2 do + + align:start position:0% +zero move the 32 over multiply by m^2 do + + + align:start position:0% +zero move the 32 over multiply by m^2 do +some algebra and I get m is equal to + + align:start position:0% +some algebra and I get m is equal to + + + align:start position:0% +some algebra and I get m is equal to +plus or minus a half and now we need to + + align:start position:0% +plus or minus a half and now we need to + + + align:start position:0% +plus or minus a half and now we need to +see which of these things make sense and + + align:start position:0% +see which of these things make sense and + + + align:start position:0% +see which of these things make sense and +then we need to think about what happens + + align:start position:0% +then we need to think about what happens + + + align:start position:0% +then we need to think about what happens +as M goes to its extreme values + + align:start position:0% +as M goes to its extreme values + + + align:start position:0% +as M goes to its extreme values +so let's come back and look at the + + align:start position:0% +so let's come back and look at the + + + align:start position:0% +so let's come back and look at the +picture and from there we can probably + + align:start position:0% +picture and from there we can probably + + + align:start position:0% +picture and from there we can probably +tell which of these answers we + + align:start position:0% + + + + align:start position:0% + +need so it's m equal 12 or m equals + + align:start position:0% +need so it's m equal 12 or m equals + + + align:start position:0% +need so it's m equal 12 or m equals +minus one2 that we want to know which of + + align:start position:0% +minus one2 that we want to know which of + + + align:start position:0% +minus one2 that we want to know which of +these do we + + align:start position:0% +these do we + + + align:start position:0% +these do we +need so I'm going to use some some + + align:start position:0% +need so I'm going to use some some + + + align:start position:0% +need so I'm going to use some some +different colored chalk to draw What's + + align:start position:0% +different colored chalk to draw What's + + + align:start position:0% +different colored chalk to draw What's +Happening + + align:start position:0% +Happening + + + align:start position:0% +Happening +Here notice the slope of this line is + + align:start position:0% +Here notice the slope of this line is + + + align:start position:0% +Here notice the slope of this line is +negative right if I were going to do a + + align:start position:0% +negative right if I were going to do a + + + align:start position:0% +negative right if I were going to do a +positive sloping line which would be the + + align:start position:0% +positive sloping line which would be the + + + align:start position:0% +positive sloping line which would be the +case where m is equal to + + align:start position:0% +case where m is equal to + + + align:start position:0% +case where m is equal to +I would get something that's that's + + align:start position:0% +I would get something that's that's + + + align:start position:0% +I would get something that's that's +headed in this direction and notice that + + align:start position:0% +headed in this direction and notice that + + + align:start position:0% +headed in this direction and notice that +that's not going to make a triangle with + + align:start position:0% +that's not going to make a triangle with + + + align:start position:0% +that's not going to make a triangle with +the X and Y AIS and so immediately m + + align:start position:0% +the X and Y AIS and so immediately m + + + align:start position:0% +the X and Y AIS and so immediately m +equals 12 isn't even isn't even in this + + align:start position:0% +equals 12 isn't even isn't even in this + + + align:start position:0% +equals 12 isn't even isn't even in this +problem isn't allowed to work okay now + + align:start position:0% +problem isn't allowed to work okay now + + + align:start position:0% +problem isn't allowed to work okay now +where did it come from it came because + + align:start position:0% +where did it come from it came because + + + align:start position:0% +where did it come from it came because +somewhere I was multiplying M by itself + + align:start position:0% +somewhere I was multiplying M by itself + + + align:start position:0% +somewhere I was multiplying M by itself +which maybe isn't actually in the + + align:start position:0% +which maybe isn't actually in the + + + align:start position:0% +which maybe isn't actually in the +original part I was introducing a a a + + align:start position:0% +original part I was introducing a a a + + + align:start position:0% +original part I was introducing a a a +new thing happening there so I'm not + + align:start position:0% +new thing happening there so I'm not + + + align:start position:0% +new thing happening there so I'm not +going to get into it too much because we + + align:start position:0% +going to get into it too much because we + + + align:start position:0% +going to get into it too much because we +can immediately see that we don't have + + align:start position:0% +can immediately see that we don't have + + + align:start position:0% +can immediately see that we don't have +to worry about m equal 1/2 m equal minus + + align:start position:0% +to worry about m equal 1/2 m equal minus + + + align:start position:0% +to worry about m equal 1/2 m equal minus +1/2 looks good that's that's sloping in + + align:start position:0% +1/2 looks good that's that's sloping in + + + align:start position:0% +1/2 looks good that's that's sloping in +this direction and in fact that would + + align:start position:0% +this direction and in fact that would + + + align:start position:0% +this direction and in fact that would +give us a nice triangle the extreme + + align:start position:0% +give us a nice triangle the extreme + + + align:start position:0% +give us a nice triangle the extreme +values in this case are obviously when m + + align:start position:0% +values in this case are obviously when m + + + align:start position:0% +values in this case are obviously when m +is m is sloping all the way up to being + + align:start position:0% +is m is sloping all the way up to being + + + align:start position:0% +is m is sloping all the way up to being +vertical or when m is sloping to being + + align:start position:0% +vertical or when m is sloping to being + + + align:start position:0% +vertical or when m is sloping to being +horizontal and in both of those cases + + align:start position:0% +horizontal and in both of those cases + + + align:start position:0% +horizontal and in both of those cases +you notice that the area is getting + + align:start position:0% +you notice that the area is getting + + + align:start position:0% +you notice that the area is getting +arbitrarily large it's headed towards + + align:start position:0% +arbitrarily large it's headed towards + + + align:start position:0% +arbitrarily large it's headed towards +Infinity in both cases so I don't need + + align:start position:0% +Infinity in both cases so I don't need + + + align:start position:0% +Infinity in both cases so I don't need +to worry about looking at the extreme + + align:start position:0% +to worry about looking at the extreme + + + align:start position:0% +to worry about looking at the extreme +values there aren't end points really in + + align:start position:0% +values there aren't end points really in + + + align:start position:0% +values there aren't end points really in +this case but the extreme values they're + + align:start position:0% +this case but the extreme values they're + + + align:start position:0% +this case but the extreme values they're +both going to to positive Infinity the + + align:start position:0% +both going to to positive Infinity the + + + align:start position:0% +both going to to positive Infinity the +areas which convinces me even more that + + align:start position:0% +areas which convinces me even more that + + + align:start position:0% +areas which convinces me even more that +where m is equal to minus one2 is going + + align:start position:0% +where m is equal to minus one2 is going + + + align:start position:0% +where m is equal to minus one2 is going +to be a minimum you could also take the + + align:start position:0% +to be a minimum you could also take the + + + align:start position:0% +to be a minimum you could also take the +second derivative and run the second + + align:start position:0% +second derivative and run the second + + + align:start position:0% +second derivative and run the second +derivative test but even geometrically + + align:start position:0% +derivative test but even geometrically + + + align:start position:0% +derivative test but even geometrically +we can see in the picture that at m + + align:start position:0% +we can see in the picture that at m + + + align:start position:0% +we can see in the picture that at m +equals negative one2 we actually get a a + + align:start position:0% +equals negative one2 we actually get a a + + + align:start position:0% +equals negative one2 we actually get a a +negative sign for the or sorry a + + align:start position:0% +negative sign for the or sorry a + + + align:start position:0% +negative sign for the or sorry a +minimizer for the area and now the + + align:start position:0% +minimizer for the area and now the + + + align:start position:0% +minimizer for the area and now the +question asked to find the dimensions + + align:start position:0% +question asked to find the dimensions + + + align:start position:0% +question asked to find the dimensions +how do I go back and find the dimensions + + align:start position:0% +how do I go back and find the dimensions + + + align:start position:0% +how do I go back and find the dimensions +I'm not going to do any more on this + + align:start position:0% +I'm not going to do any more on this + + + align:start position:0% +I'm not going to do any more on this +problem but you can do it to finish it + + align:start position:0% +problem but you can do it to finish it + + + align:start position:0% +problem but you can do it to finish it +off finding the dimensions I know what m + + align:start position:0% +off finding the dimensions I know what m + + + align:start position:0% +off finding the dimensions I know what m +is I also know what x is in terms of M + + align:start position:0% +is I also know what x is in terms of M + + + align:start position:0% +is I also know what x is in terms of M +and what Y is in terms of M so I just + + align:start position:0% +and what Y is in terms of M so I just + + + align:start position:0% +and what Y is in terms of M so I just +evaluate X at that M and evaluate Y at + + align:start position:0% +evaluate X at that M and evaluate Y at + + + align:start position:0% +evaluate X at that M and evaluate Y at +that M that gives me the dimensions that + + align:start position:0% +that M that gives me the dimensions that + + + align:start position:0% +that M that gives me the dimensions that +will complete the problem but I think + + align:start position:0% +will complete the problem but I think + + + align:start position:0% +will complete the problem but I think +I'll stop there \ No newline at end of file diff --git a/2vHGYdepKLw.txt b/2vHGYdepKLw.txt new file mode 100644 index 0000000000000000000000000000000000000000..7d0b4fe15a4e1e6c8ea60be12778846ba4405bca --- /dev/null +++ b/2vHGYdepKLw.txt @@ -0,0 +1,1917 @@ +Good morning, +OK. + +Let's get started. +We have one handout today. + +That's your lecture notes. +There's some copies still + +outside for those who haven't +picked one up. + +In general, what I do is, +in the lecture notes, + +I leave out large amounts of +material. + +So, this will enable you to +keep your hands busy while I'm + +lecturing and take down some +notes and so on. + +So, don't assume that +everything that I talk about is + +on here. +Please follow along. + +OK, so as is my usual practice, +let me start with a quick + +review of what we covered so +far. + +So what we did primarily was +looked at this discipline that + +we call the lump matter +discipline, which was very + +similar, very reminiscent of the +point mass simplification in + +physics. +And this discipline, + +this set of constraints we +imposed on ourselves, + +allowed us to move from +Maxwell's equations to a very, + +very simple form of algebraic +equations. + +And specifically, +the discipline took two forms. + +One is, we said that we will +deal with elements for whom the + +rate of change of magnetic flux +is zero outside of the elements, + +and for whom the rate of change +of charge I want to charge + +inside the element was zero. +So, if I took any element, + +any element that I called a +lump circuit element, + +like a resistor or a voltage +source, and I put a black box + +around it, then what I'm saying +is that the net charge inside + +that is going to be zero. +And this is not true in + +general. +We will see examples where, + +if you choose some piece of an +element for example, + +there might be charge buildup, +but net inside the, + +if I put a box around the +entire element, + +I am going to assume that the +rate of change of charge is + +going to be zero. +So, what this did was it + +enabled us to create the lump +circuit abstraction, + +where I could take elements, +some element of the sort, + +this could be a resistor, +a voltage source, + +or whatever, +and I could now ascribe a + +voltage, some voltage across an +element, and also some current, + +"i," that was going into the +element. + +And as I go forward, +when I label the voltages and + +currents across and through +elements, I'm going to be + +following a convention. +OK, the convention is that I'm + +going to label, +if I label V in the following + +manner, then I'm going to label +"i" for that element as a + +current flowing into the +positive terminal. + +It's just a convention. +By doing this, + +it turns out that the power +consumed by the element is "vi" + +is positive. +OK, so by choosing I going in + +this way into the positive +terminal, the power consumed by + +the element is going to be +positive. + +OK, so in general of even +simply following this + +convention, when I label +voltages and currents, + +I'll be labeling the current +into an element entering in + +through the plus terminal. +Remember, of course, + +if the current is going this +way, let's have one amp of + +current flowing this way, +then when I compute the + +current, "i" will come out to be +negative. + +OK, so by making these +assumptions, the assumptions of + +the lumped matter discipline, +I said I was able to simplify + +my life tremendously. +And, in particular what it did + +was it allowed me to take +Maxwell's equations, + +OK, and simplify them into a +very simple algebraic form, + +which has both a voltage law +and a current law that I call + +Kirchhoff's voltage law, +and Kirchhoff's current law. + +KVL simply states that if I +have some circuit, + +and if I measured the voltages +in any loop in the circuit, + +so if I look at the voltages in +any loop, then the voltages in + +the loop would sum to zero. +OK, so I measure voltages in + +the loop, and they will sum to +zero. + +Similarly, for the current, +if I take a node of a circuit, + +if I build the circuit, +a node is a point in the + +circuit where multiple edges +connect. + +If I take a node, +then the current coming into + +that node, the net current +coming into a node is going to + +be zero. +OK, so if I take any node of + +the circuit and sum up all the +currents going into that node, + +they will all net sum to zero. +So, notice what I've done is by + +this discipline, +by this constraint I imposed on + +myself, I was able to make this +incredible leap from Maxwell's + +equations to these really, +really simple algebraic + +equations, KVL and KCL. +And I promise you, + +going forward to the rest of +6.002, if this is all you know, + +you can pretty much solve any +circuit using these two very + +simple relations. +It's actually really, + +really simple. +It's all very simple algebra, + +OK? +So, just to show you an + +example, let me do a little +demonstration. + +Let me build let me build a +small circuit and measure some + +voltages for you, +and show you that the voltages, + +indeed, add up to zero. +So, here's my little circuit. + +So, I'm going to show you a +simple circuit that looks like + +this, and let's go ahead and +measure some voltages and + +currents. +In terms of terminology to + +remember, this is called a loop. +So if I start from the point C + +and I travel through the voltage +source, come to the node A down + +through R1 and all the way down +through R2 back to C, + +that's a loop. +Similarly, this point A is a + +node where resistor R1 the +voltage source V0, + +and R4 are connected. +OK, just make sure your + +terminology is correct. +So, what I'll do is I'll make + +some quick measurements for you, +and show you that these KVL and + +KCL are indeed true. +So, the circuits up there, + +could I have a volunteer? +Any volunteer? + +All you have to do is write +things on the board. + +Come on over. +OK, so let me take some + +measurements, +and why don't you write down + +what I measure on the board? +What I'll do is, + +let me borrow another piece of +chalk here. + +What I'll do is focus on this +loop here, and focus on this + +node and make some measurements. + +All right, so you see the +circuit up there. + +OK, so I get 3 volts for the +voltage from C to A. + +so why don't you write down 3 +volts? + +OK, so the next one is -1.6. +And so that will be, + +I'm doing AB, +V_AB. + +OK, and then let me do the last +one. + +It is -1.37. +The measurements, + +I guess, have been this way. +So, what's written is V_AC. + +But it's OK for now. +Don't worry about it. + +So, well, thank you. +I appreciate your help here. + +OK, so within the bonds of +experimental error, + +noticed that if I add up these +three voltages, + +they nicely sum up to zero. +OK, next let me focus on this + +node here. +And at this node, + +let me go ahead and measure +some currents. + +What I'll do now is change to +an AC voltage so that I can go + +ahead and measure the current +without breaking my circuit. + +OK, this time around, +you'll get to see the + +measurements that I'm taking as +well. + +So, what I have here, +I guess you can see it this + +way. +What I have here is three wires + +that I have pulled out from D. +And this is the node D, + +OK? +So, I have three wires coming + +into the node D just to make it +a little bit easier for me to + +measure stuff. +OK, so everybody keep your + +fingers crossed so I don't look +like a fool here. + +I hope this works out. +So, you roughly get, + +what's that, +10 mV. + +OK, so it's about 10 mV peak to +peak out there, + +and let's say that if the +waveform raises on the left-hand + +side, it's positive. +So, it's positive 10 mV. + +And another positive 10 mV, +so that's 20 mV. + +And this time, +it's a negative, + +roughly 20, I guess, +-20. + +So, I'm getting, +in terms of currents, + +I have a -10, +-10, I'm sorry, + +positive 10, +positive 10, + +and a -20 that adds up to zero. +But more interestingly, + +I can show you the same thing +by holding this current + +measuring probe directly across +the node. + +And, notice that the net +current that is entering into + +this node here is zero. +OK, so that should just show + +you that KCL does indeed hold in +practice, and it is not just a + +figment of our imaginations. +So, before I go on, + +I wanted to point one other +thing out. + +Notice that I've written down +two assumptions of the lumped + +matter discipline, +OK? + +There is a total assumption of +the lump matter discipline, + +and that assumption is, +in spirit, at least, + +shared by the point mass +simplification in physics as + +well. +Can someone tell me what that + +assumption is? +A total assumption, + +which I did not mention, +which you can read in your + +notes in section 8.2 in the +appendix, what's a total + +assumption that is shared in +spirit with the point mass + +simplification? +Anybody? + +A total assumption to be made +here is that in all the signals + +that we will study in this +course, we've made the + +assumption that the signal +speeds of interest, + +transition speeds, +and so on, are much slower than + +the speed of light. +OK, that my signal transition + +speeds of interest are much +slower than the speed of light. + +Remember, the laws of motion, +the discrete laws of motion + +break down if your objects begin +moving at the speed of light. + +OK, the same token here, +our lump circuit abstraction + +breaks down if we approach the +speed of light. + +And there are follow on courses +that talk about waveguides and + +other distributed analysis +techniques that deal with + +signals that travel close to +speeds of light. + +OK, so with that, +let me go on to talking about + +method one of circuit analysis. +This is called the basic KVL + +KCL method. +So just based on those two + +simple algebraic relations, +I can analyze very interesting + +and complicated circuits. +The method goes as follows. + +So, let's say our goal is, +given a circuit like this, + +our goal is to solve it. +OK, in this course, + +we will do two kinds of things: +analysis and synthesis. + +Analysis says, +given a circuit, + +OK, what can you tell me about +the circuit? + +OK, so we'll solve existing +circuits for all the voltages + +and currents, +voltages across elements, + +and currents through those +elements. + +Synthesis says, +given a function, + +I may ask you to go and build +circuits. + +OK, so for analysis here, +we can apply this method that I + +want to show you. +And the idea here is that, + +given a circuit like this, +let us figure out all the + +voltages and currents that are a +function of the way these + +elements are connected. +So, the basic KVL and KCL + +method has the following steps. +The first step is to write down + +the element VI relationships. +OK, right down the element VI + +relationships for all the +elements. + +The second step is write KCL +for all the nodes, + +and the third step is to write +KVL for all the loops in the + +circuit. +That's it. + +Just go ahead and write down +element rules, + +KVL, and KCL, +and then go ahead and solve the + +circuit. +So, what we'll do, + +we'll do an example, +of course. + +But, just as a refresher, +we've looked at a bunch of + +elements so far, +and for the resistor, + +the element relation says that +V is pi R, where R is the + +resistance of the element here. +For a voltage source, + +V is equal to V nought. +That's the element + +relationship. +And for a current source, + +the element is the relation is, +"i" is simply the current + +flowing through the element. +OK, so these are some of the + +simple element rules for the +devices that the current source, + +voltage source, +and the resistor. + +So let's go ahead and solve +this simple circuit. + +And what I'll do is go ahead +and solve the circuit for you. + +OK, if you turn to page five of +your notes, I'm going to go + +ahead and edit the circuit here. +You can scribble the values on + +your notes on page five. +OK, so as a first step of my + +KVL KCL method, +I need to write down all my + +element VI relationships. +So, before I do that, + +let me go ahead and label all +the voltages and currents that + +are unknowns in the circuit. +So, let me label the voltages + +and currents associated with the +voltage source as here. + +Notice, I continue to follow +this convention where whenever I + +label voltages and currents for +an element, I will show the + +current going into the positive +terminal of the element + +variable, OK, +after element variable voltage. + +So here, I have V nought and I +nought. + +Let me pause here for five +seconds and show you a point of + +confusion that happens +sometimes. + +Often times, +people confuse between what is + +called the variable that is +associated with the element + +versus the element value. +OK, notice that here, + +capital V nought is the voltage +that this voltage source + +provides, while this name here, +v nought, is simply a variable + +that we've used to label the +voltage across that element. + +So, similarly, +I can label v1 as the voltage + +across the resistor, +and i1 is the current flowing + +through the resistor. +So this method of labeling, + +where I follow the convention, +that the current flows into the + +positive terminal is called the +associated variables discipline. + +I was trying to use the word +discipline in situations where + +you have a choice, +OK, and of a variety of + +possible choices, +you pick one as the convention. + +OK, so here, +as a convention, + +we use the associated variables +discipline, and use that method + +to consistently label the +unknown voltages and currents in + +our circuits. +OK, so let me continue the + +labeling here, +v4, i4, i3, v3 here, + +and v2 and i2, +v5, and i5. + +I think that's it. +So, I've gone ahead and labeled + +all my unknowns. +So each of these voltages and + +currents are the voltages and +currents associated with each of + +the elements. +And my goal is to solve for + +these. +OK, so in terms of our solution + +here, let's follow the method +that I outlined for you. + +So, as the first step I am +simply going to go ahead and + +write down all the element VI +relationships. + +OK, so as a first step, +I'm going to go ahead and write + +down all the VI relationships. +So, can someone yell out for me + +the VI relationship for the +voltage source? + +OK, good. +So, v0 is capital V nought, + +that is that the variable V +nought is simply equal to the + +voltage, v0. +Similarly, I can write the + +others. +v1 is i1, R1. + +v2 is i2, R2, +and so on. + +OK, and I have one, +two, three, four, + +five, six elements. +So, I will get six such + +equations. +Step two, I'm going to go ahead + +and write KCL for the nodes in +my system. + +So, let me start with node A. +So, for node A, + +let me take as positive the +currents going out of the node. + +So, I get i nought flowing out, +plus i1 flowing out, + +plus i4 flowing out, +and they must sum to zero for + +node A. +Then, I can go ahead and do the + +other nodes, let's say, +for example, + +I do node B. +For node B, I have i2 going + +out. +That's positive, + +i3, and i1 is coming in, +so I get -i1 equals zero. + +OK, so I have one, +two, three, four, + +I have four nodes. +OK, so I would get four + +equations. +It turns out that the fourth + +equation is not independent. +You can derive it from the + +others. +So, I get three independent + +equations out of this. +I can then write KVL. + +And for KVL, +I just go down my loops here. + +And let me go through this +first loop here in this manner. + +OK, and a simple trick that I +use, you have to be incredibly + +careful when you go through this +in keeping your minuses and + +pluses correct. +Otherwise you can get + +hopelessly muddled. +Once you label it, + +you need to be sure that you +get all your minuses and pluses + +correct. +So, for KVL, + +what I'd like to do is, +let's say I start at C, + +and from C I'm going to go to +A. + +For A I go to B, +and from B I'm going to come + +back to C. +OK, that's how I traverse my + +loop. +And, the trick that I'm going + +to follow is, +as my finger walks through that + +loop, I'm going to label the +voltage as the first sign that I + +see for that voltage. +OK, so I'm going to start with + +C, and I go up. +I start by punching into the + +voltage source element, +and then punch into it, + +I hit the minus sign for the V +nought. + +OK, so I'm just going to write +down minus V nought, + +plus then I go through and as I +come up to A and go down to B, + +I punch to the plus sign of the +V1. + +So, that's plus V1. +And then I punch into the plus + +sign of the V2, +and so I get plus V2, + +and that is zero. +OK, good. + +So, that matches what you have +in your notes as well. + +So, this is the first equation. +Similarly, I can go through my + +other loops and write down +equations for each of the loops. + +OK, and the convention that I +like to follow is as I go + +through the loop, +I write down as a sign for the + +voltage the first sign that I +counter for that element. + +OK, you can do the exact +opposite, if you want, + +just to be different. +But, as long as you stay + +consistent, you'll be OK. +All right, so in the same + +manner here, there are four +loops that I can have, + +so four equations. +Again, one of them turns out to + +be dependent on the others. +So I end up getting three + +independent equations. +So, I get a total of 12 + +equations. +I get 12 equations. + +There are six elements, +OK, voltage source, + +and five resistors. +So, there are six unknown + +voltages, and six unknown +currents. + +So, I have 12 equations, +and 12 unknowns. + +OK, I can take all of the +equations and put them through a + +big crank, and sit there and +grind. + +And if I was really cruel, +I'd give this as a homework + +problem, and have you grind, +and grind, and grind until you + +get your six voltages and six +currents. + +OK, it works. +OK, so you get 12 equations, + +and this method just works. +However, notice that this is + +quite a grubby method. +It's quite grungy. + +I get 12 equations, +and it's quite a pain even for + +a simple circuit like this. +However, suffice it to say that + +this fundamental method is one +step away from Maxwell's + +equations, simply works. +OK? + +So what you'll do is the rest +of this lecture, + +I'll introduce you to a couple +more methods. + +One is an intuitive method, +and another one called the node + +method is a little bit more +formal, but is much more, + +I guess, terse Than the KVL KCL +method. + +Method 2. +So the relevant section to read + +in the course notes is section +2.4. + +One of the things that I will +be stressing this semester is + +intuition. +What you'll find is that as you + +become EECS majors, +and so on, and go on, + +or if you talk to your TAs or +your professors and so on, + +you will find that very rarely +do they actually go ahead and + +apply the formal methods of +analysis. + +OK, by and large, +engineers are able to look at a + +circuit and simply by +observation write down an + +answer. +And usually in the past, + +what we have tried to do is +kind of ignore that process and + +told our students, +look, we teach you all the + +formal methods, +and you will develop your own + +intuition and be able to do it. +What we'll try to do this term + +is try to stress the intuitive +methods, and try to show you how + +the intuitive process goes, +so you can very quickly solve + +many of these circuits simply by +inspection. + +OK, so this method that I'm +going to show you here is one + +such an intuitive method. +And I'll call it element + +combination tools. +OK, for many simple circuits, + +you can solve them very quickly +by applying this method. + +The components of this method +are these. + +I learned about how to compose +a bunch of elements. + +So, let's say, +for example, + +I have a set of resistors, +R1 through RN, + +in series. +OK, you can use KVL and KCL to + +show that this is equivalent to +a single resistor whose value is + +given by the sum of the +resistances. + +OK, so if I have resistors in +series, then effectively it's + +the same as if there was a +single resistor whose value is + +the sum of all the resistances. +OK, you can look at the course + +notes for a proof for derivation +of this fact. + +Similarly, if I have +resistances in parallel, + +so let me call them +conductances. + +A conductance is the reciprocal +of a resistance. + +If resistance is measured in +ohms, conductance is measured in + +mhos, M-H-O-S. +OK, so that's the conductance + +is G1, G2, and G3. +And effectively, + +this is the same as having a +single conductance whose + +effective value is given by the +sum of the conductances. + +OK, the conductances in +parallel add, + +and resistances in series add. +Similarly, for voltage sources, + +if I have voltage sources in +series, then they are tantamount + +to the sum of the voltages. +And similarly, + +for currents, +if I have currents in parallel, + +then they can be viewed as a +single current source, + +whose currents are the sum of +the individual parallel + +currents. +So, let's do a quick example. + +So let's do this example. +So, let's say I have a circuit + +that looks like this, +and three resistances. + +And let's say all I care about +is the current, + +I, that flows through this +wire. + +All I care about is that +current. + +Of course, you can go ahead and +write KVL and KCL. + +You will get four equations, +and there are four unknowns. + +And you can solve it. +But, I can apply my element + +combination rules, +and very quickly figure out + +what the current I is, +using the following technique. + +So, what I can do is, +I can, first of all, + +take this circuit. +And, I can compose these two + +resistances and show that the +circuit is equivalent as far as + +this current, +I, is concerned to the + +following circuit, +R1. + +And I take the sum of the two +conductances, + +OK, and that comes out to be +R1, R2, R3, R2 plus R3. + +And then, I can further +simplify it, and I get a single + +resistance, whose value is given +by R1 plus R2, + +R3, R3. +OK, I'm just simplifying the + +circuit. +Now, from this circuit, + +I can get the answer that I +need. + +I is simply the voltage, +V, divided by R1 plus. + +OK, so in situations like this +where I'm looking for a single + +current, I can very quickly get +to the answer by applying some + +of these element combination +rules. + +And, I can get rid of having to +go through formal steps. + +So, in general, +whenever you encounter a + +circuit, by and large attempt to +use intuitive methods to solve + +it. +And go to a formal method only + +if some intuitive method fails. +Even in your homework, + +by and large, +the homeworks are not meant to + +be grungy. +OK, if you find a lot of grunge + +in your homework, +just remember you're probably + +not using some intuitive method. +OK, so just be cautious. + +All right, so let me go on to +the third method of circuit + +analysis, and the third method +is called the node method. + +So, the node method is simply a +specific application of the KVL + +KCL method and results in a +much, much more compact form of + +the final equations. +If there's one method that you + +have to remember for life, +then I would say just remember + +this method. +OK, the node method is a + +workhorse of the easiest +industry. + +OK, if there's one method that +you want to consistently apply, + +then this is the one to +remember. + +So, let me quickly outline for +you to method, + +and then work out an example +for you. + +The first step of the node +method will be to select a + +reference or a ground node. +This is the symbol for a ground + +node. +The ground node simply says + +that I'm going to denote +voltages at that point to be + +zero, and measure all my other +voltages with reference to that + +point. +So, I'm going to select a + +ground node in my circuit. +Second, I want to label the + +remaining voltages with respect +to the ground node. + +So, label voltages for all the +other nodes with respect to the + +ground node. +Next, write KCL for each of the + +nodes write KCL. +OK, but don't write KCL for the + +ground node. +Remember, if you have N nodes, + +the node equations will give +you N-1 independent equations. + +So, write KCL for the nodes, +but don't do so for the ground + +node. +Then, solve for the node + +voltages. +So, let's say when we label + +voltages. +I want to be labeling them as E + +something or the other. +So, solve for the unknown node + +voltages. +And then, once I know all the + +voltages associated with the +nodes, I can then back solve for + +all the branch voltages and +currents. + +OK, once I know all the node +voltages, I can then go ahead + +and figure out all the branch +voltages and the branch + +currents. +So, let's go ahead and apply + +this method, and work out an +example. + +Again, remember, +if there's one method that you + +should remember, +it's the node method. + +OK, and when in doubt, +consistently apply the node + +method and it will work whether +your circuit is linear or + +nonlinear, if the resistors are +built in the US or the USSR it + +doesn't matter. +OK, the node method will simply + +work, linear or nonlinear, +OK? + +So, what I'm going to do is I'm +going to build a circuit that's + +my old faithful. +It's our old faithful, + +plus I'll make it a little bit +more complicated by adding in + +the current source. +So, let's go have some fun. + +Let's do this. +So here's my voltage source, + +as before. +OK, what I'll do is for fun, + +add a current source out there. +And, you can convince + +yourselves that if you go ahead +and apply the KVL KCL method, + +it'll really be a mess of +equations. + +OK, so R1, R3, +R4, R2, R5. + +OK, so let's follow our method +and just plug and chug here. + +So let's apply the first step. +I select a ground node. + +It's a reference node from +which I'll measure all my other + +voltages. +OK, now without knowing + +anything about the node method, +try to use intuition as to + +which node you should choose as +a ground node. + +Remember, you want to label the +ground node with the voltage + +zero, and measure all the other +voltages with respect to that + +node. +OK, a usual trick is to pick a + +node which has the largest +number of elements connected to + +it as the ground node. +OK, and in particular, + +you will find out later it's +useful to pick a node in which + +all your voltage sources, +the maximum number of your + +voltage sources are also +connected. + +OK, so in this instance, +I'm going to choose this as my + +ground node. +OK, that's my first step. + +I chose that as my ground node. +And I'm going to label that as + +having a voltage zero. +Second step, + +I'll label voltages of the +other branches with respect to + +the ground node. +OK, so what I'll do is add this + +node here. +So I'm going to label that + +voltage E1. +These are my unknowns. + +Remember, node method, +because my node voltages are my + +unknowns. +So, I label this as E1. + +I label this one as my unknown +voltage, E2. + +What about this one here? +Is that voltage unknown? + +No. +I know what the voltage is + +because I know that this node is +at a voltage, + +V0, higher than the ground +node. + +OK, notice that to go from here +to here, I directly go through a + +voltage source. +And so, this node has voltage + +V0. +And I'll simply write down V0. + +OK, try to simplify the number +of steps that you have to go + +through, so directly go ahead +and write down the voltage, + +V0, for that node. +What I will also do, + +is for convenience, +I'm going to write down, + +I'm going to use conductances. +So I'm going to use GI in the + +place of one by RI, +and write down a bunch of node + +equations. +OK, so step one, + +I've chosen my ground node. +Step two, I've labeled my node + +voltages, E, OK? +I've done that with two of my + +steps. +Now, let me go ahead and -- + +OK, so let me go ahead and +apply step three. + +And, step three says go ahead +and apply KCL for each of the + +nodes at which you have an +unknown node voltage. + +And then that will give you +your equations. + +So let me start by applying KCL +at E1. + +So, let me write KCL at E1. +I do one more thing. + +Notice, I don't have any +currents there. + +OK, so how do I write KCL? +KCL simply says the sum of + +currents into a node is zero +again, remember, + +by the lump matter discipline. +So, if I don't have currents in + +there, so the trick that I adopt +is that to write KCL, + +I use the node voltages, +and implicitly substitute for + +the node voltages, +divide by the elemental the + +resistance, for instance, +so I take the node voltages, + +and divide by the resistance, +get the current. + +OK, so I implicitly apply +element relationships to get the + +node currents. +So, the example that make it + +clear, so I take node E1 and, +again, for currents going out + +I'm going to assume to have, +to be positive. + +So, the current going up is E1 +minus V nought, + +divide by R1, +so I multiplied by the G1. + +That's the current going up. +Plus, the current going down is + +E1 minus zero where the ground +node potential is zero, + +G2, OK, plus the current that +is going to resistor R3, + +which is simply E1 minus E2, +divide by R3. + +So, E1 minus E2, +divide by R3, + +or multiplied by G3 is equal to +zero. + +OK, see how I got this? +This is simply KCL, + +but to get my currents, +I simply take the differences + +of voltages across elements, +and divide by the element of + +resistance, and I get the +currents. + +OK, so I can similarly write +KCL at E2. + +So, at KCL at E2, +again, let me go outwards. + +So, the current going up is E2 +minus V nought multiplied by G4. + +The current going left is E2 +minus E1 divided by R3 or + +multiplied by G3. +The current going down is E2 + +minus zero multiplied by G5. +And, the current going down is + +-I1. +OK, you've got to be careful + +with your polarities here. +So all the currents going out + +sum to zero. +And here are the currents that + +are going out at this point. +So what I do next is I can move + +the constant terms to the +left-hand side and collect my + +unknowns. +So, let me write them out here. + +So, let's say I get E1 here, +OK, and from this equation, + +I have a V nought, +G1, which comes out here. + +So, minus V nought G1 comes +over to the other side. + +And, let me collect all the +values that multiply E1. + +So I get, G1 is one example. +I have G2, and I have G3. + +And then, for E2, +I have minus G3. + +OK, so I'll simply express this +as the element voltages + +multiplied by some terms in +parentheses, and I put my + +external sources on the right +hand side. + +Similarly, I go ahead and do +the same thing here. + +In this instance, +let me move my sources to the + +right. +So, I get I1 coming out there, + +and I get V nought G4 coming +out there. + +By the way, I just want to +mention to you that if you're + +looking to fall asleep, +this is a good time to do so + +because as soon as I write down +these two equations, + +OK, from now on it's nap time. +There's nothing new that you're + +going to learn from here on. +It's just Anant Agarwal having + +fun at the blackboard, +pushing symbols around. + +So, once you write down these +two node equations, + +the rest of it is just grubby +math. + +So, let me just have some fun. +So let me just go ahead and do + +that. +So, I moved my voltages and + +currents to the other side. +And let me collect all the + +coefficients for E1 here. +So, E1 minus G3, + +and that's it, +I guess. + +OK, and then I'll do the same +for E2. + +So, I get G4, +and I get G3, + +and I get G5. +OK, so notice here that I have + +two equations, +and two unknowns. + +OK, the two equations are on +the right hand side, + +I have some voltages and +currents which are my dry + +voltages and dry currents. +OK, so actually this is getting + +quite boring. +I'm going to pause here, + +and talk about something else. +So, you can take this and you + +can put it in matrix form, +so I've done that for you on + +page ten. +It's all matrix form. + +Yeah, I know that. +You can use any technique to + +solve it, use algebraic +techniques, use linear algebraic + +methods to solve it, +use a computer, + +whatever you want. +And, computers, + +when computers analyze +circuits, they write down these + +equations, and deal with solving +matrices. + +So, when you take the linear +algebra across, + +how many people here have taken +a linear algebra class? + +How many people here have heard +of Gaussian elimination? + +How can more people have heard +of Gaussian elimination than + +took a linear algebra class? +Well anyway, + +so now you know why you took +those linear algebra classes. + +And so, if I just collected +these into matrix form -- + +OK, so I just simply expressed +those two equations in linear + +algebraic form, +and here's my column vector of + +unknowns, and you can apply any +of the techniques you've learned + +in linear algebra to solve for +this. + +Gaussian elimination works. +OK, and in computer, + +people doing research in +computer techniques, + +or solving such equations +simply deals with huge equations + +like this, building computer +programs that, + +given equations like this, +can go ahead and solve them. + +OK, so let me stop here and +reemphasize that what you've + +done is made a huge leap from +Maxwell's equations to using the + +lump matter discipline to KVL +and KCL, which ended up giving a + +simple algebraic equation to +solve, and not having to worry + +about partial differential +equations that were the form of + +Maxwell's equations. \ No newline at end of file diff --git a/38ZN2IhWgOE.txt b/38ZN2IhWgOE.txt new file mode 100644 index 0000000000000000000000000000000000000000..a004d3a27c212a75ed5d2ff7d8d35bb0e60f3fa8 --- /dev/null +++ b/38ZN2IhWgOE.txt @@ -0,0 +1,10529 @@ +align:start position:0% + +so we're really moving now into the + + align:start position:0% +so we're really moving now into the + + + align:start position:0% +so we're really moving now into the +forier side uh Fier part of the course + + align:start position:0% +forier side uh Fier part of the course + + + align:start position:0% +forier side uh Fier part of the course +like we're about 2third through we've + + align:start position:0% +like we're about 2third through we've + + + align:start position:0% +like we're about 2third through we've +certainly seen Fier a little bit but now + + align:start position:0% +certainly seen Fier a little bit but now + + + align:start position:0% +certainly seen Fier a little bit but now +now quite a lot in this in these + + align:start position:0% +now quite a lot in this in these + + + align:start position:0% +now quite a lot in this in these +lectures today and in uh + + align:start position:0% +lectures today and in uh + + + align:start position:0% +lectures today and in uh +wavelengths there'll be a series of um + + align:start position:0% +wavelengths there'll be a series of um + + + align:start position:0% +wavelengths there'll be a series of um +lectures about signal processing and + + align:start position:0% +lectures about signal processing and + + + align:start position:0% +lectures about signal processing and +wavelets where fora methods are going to + + align:start position:0% +wavelets where fora methods are going to + + + align:start position:0% +wavelets where fora methods are going to +be crucial + + align:start position:0% +be crucial + + + align:start position:0% +be crucial +well this is something a topic called + + align:start position:0% +well this is something a topic called + + + align:start position:0% +well this is something a topic called +spectral + + align:start position:0% +spectral + + + align:start position:0% +spectral +methods and uh it's not an area I worked + + align:start position:0% +methods and uh it's not an area I worked + + + align:start position:0% +methods and uh it's not an area I worked +in so I was a little apprehensive about + + align:start position:0% +in so I was a little apprehensive about + + + align:start position:0% +in so I was a little apprehensive about +this lecture but I found a delightful + + align:start position:0% +this lecture but I found a delightful + + + align:start position:0% +this lecture but I found a delightful +book by my friend Nick tresan called + + align:start position:0% +book by my friend Nick tresan called + + + align:start position:0% +book by my friend Nick tresan called +spectral methods in mat lab the in mat + + align:start position:0% +spectral methods in mat lab the in mat + + + align:start position:0% +spectral methods in mat lab the in mat +lab part refers to the fact that in each + + align:start position:0% +lab part refers to the fact that in each + + + align:start position:0% +lab part refers to the fact that in each +section whatever he does he gives a mat + + align:start position:0% +section whatever he does he gives a mat + + + align:start position:0% +section whatever he does he gives a mat +lab a neat mat lab code to do it uh it's + + align:start position:0% +lab a neat mat lab code to do it uh it's + + + align:start position:0% +lab a neat mat lab code to do it uh it's +published by Cam and uh quite + + align:start position:0% +published by Cam and uh quite + + + align:start position:0% +published by Cam and uh quite +inexpensive and really uh he's a + + align:start position:0% +inexpensive and really uh he's a + + + align:start position:0% +inexpensive and really uh he's a +terrific author he's a he was at MIT and + + align:start position:0% +terrific author he's a he was at MIT and + + + align:start position:0% +terrific author he's a he was at MIT and +he's now at uh Oxford so I'm relying on + + align:start position:0% +he's now at uh Oxford so I'm relying on + + + align:start position:0% +he's now at uh Oxford so I'm relying on +this + + align:start position:0% +this + + + align:start position:0% +this +book + + align:start position:0% +book + + + align:start position:0% +book +um and maybe I start with the main + + align:start position:0% +um and maybe I start with the main + + + align:start position:0% +um and maybe I start with the main +question well so what what's the + + align:start position:0% +question well so what what's the + + + align:start position:0% +question well so what what's the +idea + + align:start position:0% +idea + + + align:start position:0% +idea +spectral methods are one more way to + + align:start position:0% +spectral methods are one more way to + + + align:start position:0% +spectral methods are one more way to +deal with differential equations to uh + + align:start position:0% +deal with differential equations to uh + + + align:start position:0% +deal with differential equations to uh +to make them discrete to make them + + align:start position:0% +to make them discrete to make them + + + align:start position:0% +to make them discrete to make them +solvable so the first most basic + + align:start position:0% +solvable so the first most basic + + + align:start position:0% +solvable so the first most basic +question is how do you discretize the + + align:start position:0% +question is how do you discretize the + + + align:start position:0% +question is how do you discretize the +derivative okay so let's just remember + + align:start position:0% +derivative okay so let's just remember + + + align:start position:0% +derivative okay so let's just remember +how we've done it so far because we've + + align:start position:0% +how we've done it so far because we've + + + align:start position:0% +how we've done it so far because we've +been doing it right but there are other + + align:start position:0% +been doing it right but there are other + + + align:start position:0% +been doing it right but there are other +ways ways to do it and the idea of + + align:start position:0% +ways ways to do it and the idea of + + + align:start position:0% +ways ways to do it and the idea of +spectral methods is going to be high + + align:start position:0% +spectral methods is going to be high + + + align:start position:0% +spectral methods is going to be high +high + + align:start position:0% +high + + + align:start position:0% +high +accuracy it it was just realize so so so + + align:start position:0% +accuracy it it was just realize so so so + + + align:start position:0% +accuracy it it was just realize so so so +this spectral methods goes back to I + + align:start position:0% +this spectral methods goes back to I + + + align:start position:0% +this spectral methods goes back to I +better put his name up here Steve + + align:start position:0% +better put his name up here Steve + + + align:start position:0% +better put his name up here Steve +orog was and and others and many others + + align:start position:0% +orog was and and others and many others + + + align:start position:0% +orog was and and others and many others +since Lots + + align:start position:0% +since Lots + + + align:start position:0% +since Lots +uh developed this idea that you didn't + + align:start position:0% +uh developed this idea that you didn't + + + align:start position:0% +uh developed this idea that you didn't +have to use just a three Point + + align:start position:0% +have to use just a three Point + + + align:start position:0% +have to use just a three Point +scheme you could use all the + + align:start position:0% +scheme you could use all the + + + align:start position:0% +scheme you could use all the +points and zip the accuracy way way + + align:start position:0% +points and zip the accuracy way way + + + align:start position:0% +points and zip the accuracy way way +up and uh so we need + + align:start position:0% +up and uh so we need + + + align:start position:0% +up and uh so we need +formulas how do how do we if we use + + align:start position:0% +formulas how do how do we if we use + + + align:start position:0% +formulas how do how do we if we use +three points suppose we're suppose we + + align:start position:0% +three points suppose we're suppose we + + + align:start position:0% +three points suppose we're suppose we +think about replacing the derivative + + align:start position:0% +think about replacing the derivative + + + align:start position:0% +think about replacing the derivative +dudx let's suppose we're on a + + align:start position:0% +dudx let's suppose we're on a + + + align:start position:0% +dudx let's suppose we're on a +practically have drawn here uh a let's + + align:start position:0% +practically have drawn here uh a let's + + + align:start position:0% +practically have drawn here uh a let's +say an equally spaced mesh + + align:start position:0% + + + + align:start position:0% + +start let's start with that spacing + + align:start position:0% +start let's start with that spacing + + + align:start position:0% +start let's start with that spacing +H typical Point + + align:start position:0% +H typical Point + + + align:start position:0% +H typical Point +J typical neighbors J + 1 and J minus + + align:start position:0% +J typical neighbors J + 1 and J minus + + + align:start position:0% +J typical neighbors J + 1 and J minus +one typical replacement of DX + + align:start position:0% +one typical replacement of DX + + + align:start position:0% +one typical replacement of DX +is what would be a reasonable reasonably + + align:start position:0% +is what would be a reasonable reasonably + + + align:start position:0% +is what would be a reasonable reasonably +good replacement the kind that we've uh + + align:start position:0% +good replacement the kind that we've uh + + + align:start position:0% +good replacement the kind that we've uh +done uh may be centered u j + 1 - U j- + + align:start position:0% +done uh may be centered u j + 1 - U j- + + + align:start position:0% +done uh may be centered u j + 1 - U j- +1/ + + align:start position:0% +1/ + + + align:start position:0% +1/ +2H so if we have a differential equation + + align:start position:0% +2H so if we have a differential equation + + + align:start position:0% +2H so if we have a differential equation +and we see a first derivative in + + align:start position:0% +and we see a first derivative in + + + align:start position:0% +and we see a first derivative in +it uh and we've got equally spaced mesh + + align:start position:0% +it uh and we've got equally spaced mesh + + + align:start position:0% +it uh and we've got equally spaced mesh +that's a + + align:start position:0% +that's a + + + align:start position:0% +that's a +natural replacement and it's a pretty + + align:start position:0% +natural replacement and it's a pretty + + + align:start position:0% +natural replacement and it's a pretty +decent it's the it's uh it's probably + + align:start position:0% +decent it's the it's uh it's probably + + + align:start position:0% +decent it's the it's uh it's probably +the best one we can create out of three + + align:start position:0% +the best one we can create out of three + + + align:start position:0% +the best one we can create out of three +points and what about second derivative + + align:start position:0% +points and what about second derivative + + + align:start position:0% +points and what about second derivative +because our equations often have a + + align:start position:0% +because our equations often have a + + + align:start position:0% +because our equations often have a +second derivative in it in them well + + align:start position:0% +second derivative in it in them well + + + align:start position:0% +second derivative in it in them well +then UJ + 1 - 2 UJ + UJ -1 / h^ 2 is our + + align:start position:0% +then UJ + 1 - 2 UJ + UJ -1 / h^ 2 is our + + + align:start position:0% +then UJ + 1 - 2 UJ + UJ -1 / h^ 2 is our +old friend good + + align:start position:0% +old friend good + + + align:start position:0% +old friend good +friend and it's certainly the the + + align:start position:0% +friend and it's certainly the the + + + align:start position:0% +friend and it's certainly the the +Natural Choice the right + + align:start position:0% +Natural Choice the right + + + align:start position:0% +Natural Choice the right +choice uh for uh three points okay now + + align:start position:0% +choice uh for uh three points okay now + + + align:start position:0% +choice uh for uh three points okay now +so my idea is to up the accuracy so I I + + align:start position:0% +so my idea is to up the accuracy so I I + + + align:start position:0% +so my idea is to up the accuracy so I I +need some principle to go on how how + + align:start position:0% +need some principle to go on how how + + + align:start position:0% +need some principle to go on how how +where did these come from and where + + align:start position:0% +where did these come from and where + + + align:start position:0% +where did these come from and where +could uh better methods better higher + + align:start position:0% +could uh better methods better higher + + + align:start position:0% +could uh better methods better higher +approximations and of course uh we can + + align:start position:0% +approximations and of course uh we can + + + align:start position:0% +approximations and of course uh we can +figure that to increase the so my first + + align:start position:0% +figure that to increase the so my first + + + align:start position:0% +figure that to increase the so my first +step up once I get the principle + + align:start position:0% +step up once I get the principle + + + align:start position:0% +step up once I get the principle +established will be to use uh not just + + align:start position:0% +established will be to use uh not just + + + align:start position:0% +established will be to use uh not just +the three points but maybe five + + align:start position:0% +the three points but maybe five + + + align:start position:0% +the three points but maybe five +points and it's natural to figure that + + align:start position:0% +points and it's natural to figure that + + + align:start position:0% +points and it's natural to figure that +if I choose the right formula + + align:start position:0% +if I choose the right formula + + + align:start position:0% +if I choose the right formula +I can represent + + align:start position:0% +I can represent + + + align:start position:0% +I can represent +dudx and the second derivative and other + + align:start position:0% +dudx and the second derivative and other + + + align:start position:0% +dudx and the second derivative and other +derivatives too uh with more accuracy if + + align:start position:0% +derivatives too uh with more accuracy if + + + align:start position:0% +derivatives too uh with more accuracy if +maybe these have sort of an accuracy of + + align:start position:0% +maybe these have sort of an accuracy of + + + align:start position:0% +maybe these have sort of an accuracy of +second + + align:start position:0% +second + + + align:start position:0% +second +order and very likely with uh going up + + align:start position:0% +order and very likely with uh going up + + + align:start position:0% +order and very likely with uh going up +to Five Points I can up the accuracy to + + align:start position:0% +to Five Points I can up the accuracy to + + + align:start position:0% +to Five Points I can up the accuracy to +fourth order that will I'm still in the + + align:start position:0% +fourth order that will I'm still in the + + + align:start position:0% +fourth order that will I'm still in the +world of polom accuracy here that is + + align:start position:0% +world of polom accuracy here that is + + + align:start position:0% +world of polom accuracy here that is +with this finite fixed set of + + align:start position:0% +with this finite fixed set of + + + align:start position:0% +with this finite fixed set of +points I'm not going to get Spectral + + align:start position:0% +points I'm not going to get Spectral + + + align:start position:0% +points I'm not going to get Spectral +accuracy + + align:start position:0% +accuracy + + + align:start position:0% +accuracy +infinite a you know in in well infinite + + align:start position:0% +infinite a you know in in well infinite + + + align:start position:0% +infinite a you know in in well infinite +is not quite what I mean infinite order + + align:start position:0% +is not quite what I mean infinite order + + + align:start position:0% +is not quite what I mean infinite order +accuracy but first of all the principle + + align:start position:0% +accuracy but first of all the principle + + + align:start position:0% +accuracy but first of all the principle +what's the principle where how do + + align:start position:0% +what's the principle where how do + + + align:start position:0% +what's the principle where how do +I so this is the governing principle of + + align:start position:0% +I so this is the governing principle of + + + align:start position:0% +I so this is the governing principle of +of of producing these + + align:start position:0% +of of producing these + + + align:start position:0% +of of producing these +formulas + + align:start position:0% +formulas + + + align:start position:0% +formulas +is what what's my problem I I'm given + + align:start position:0% +is what what's my problem I I'm given + + + align:start position:0% +is what what's my problem I I'm given +the + + align:start position:0% +the + + + align:start position:0% +the +values at mesh points + + align:start position:0% +values at mesh points + + + align:start position:0% +values at mesh points +right + + align:start position:0% +right + + + align:start position:0% +right +whatever I'm given values of U UJ at the + + align:start position:0% +whatever I'm given values of U UJ at the + + + align:start position:0% +whatever I'm given values of U UJ at the +mesh + + align:start position:0% + + + + align:start position:0% + +points + + align:start position:0% +points + + + align:start position:0% +points +so but what I know how to what calculus + + align:start position:0% +so but what I know how to what calculus + + + align:start position:0% +so but what I know how to what calculus +tells me how to take derivatives of is + + align:start position:0% +tells me how to take derivatives of is + + + align:start position:0% +tells me how to take derivatives of is +functions what I need is a function so + + align:start position:0% +functions what I need is a function so + + + align:start position:0% +functions what I need is a function so +the the principle is + + align:start position:0% +the the principle is + + + align:start position:0% +the the principle is +create or interpolate maybe I should say + + align:start position:0% +create or interpolate maybe I should say + + + align:start position:0% +create or interpolate maybe I should say +just + + align:start position:0% + + + + align:start position:0% + +interpolate the mesh + + align:start position:0% +interpolate the mesh + + + align:start position:0% +interpolate the mesh +values by F by a function or or some + + align:start position:0% +values by F by a function or or some + + + align:start position:0% +values by F by a function or or some +kind of pieces of functions or whatever + + align:start position:0% +kind of pieces of functions or whatever + + + align:start position:0% +kind of pieces of functions or whatever +by + + align:start position:0% + + + + align:start position:0% + +function and then then what let me call + + align:start position:0% +function and then then what let me call + + + align:start position:0% +function and then then what let me call +that P of + + align:start position:0% + + + + align:start position:0% + +X and then what + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +my + + align:start position:0% +my + + + align:start position:0% +my +Dux my approximation to D DX how am I + + align:start position:0% +Dux my approximation to D DX how am I + + + align:start position:0% +Dux my approximation to D DX how am I +how do I how am I going to come up with + + align:start position:0% +how do I how am I going to come up with + + + align:start position:0% +how do I how am I going to come up with +uh a derivative well take the derivative + + align:start position:0% +uh a derivative well take the derivative + + + align:start position:0% +uh a derivative well take the derivative +of P right I've got I've now got + + align:start position:0% +of P right I've got I've now got + + + align:start position:0% +of P right I've got I've now got +something I can so as a imately P Prim + + align:start position:0% +something I can so as a imately P Prim + + + align:start position:0% +something I can so as a imately P Prim +and the second + + align:start position:0% +and the second + + + align:start position:0% +and the second +derivative of U which doesn't really + + align:start position:0% +derivative of U which doesn't really + + + align:start position:0% +derivative of U which doesn't really +make sense because U is only defined on + + align:start position:0% +make sense because U is only defined on + + + align:start position:0% +make sense because U is only defined on +meshes so + + align:start position:0% +meshes so + + + align:start position:0% +meshes so +I'm but what but the good thing is that + + align:start position:0% +I'm but what but the good thing is that + + + align:start position:0% +I'm but what but the good thing is that +P is + + align:start position:0% +P is + + + align:start position:0% +P is +defined as a function and if it's a + + align:start position:0% +defined as a function and if it's a + + + align:start position:0% +defined as a function and if it's a +simple function as I would naturally + + align:start position:0% +simple function as I would naturally + + + align:start position:0% +simple function as I would naturally +choose I can take its second derivative + + align:start position:0% +choose I can take its second derivative + + + align:start position:0% +choose I can take its second derivative +to + + align:start position:0% +to + + + align:start position:0% +to +and I've got something okay now so I + + align:start position:0% +and I've got something okay now so I + + + align:start position:0% +and I've got something okay now so I +guess I hope that these + + align:start position:0% +guess I hope that these + + + align:start position:0% +guess I hope that these +formulas which + + align:start position:0% +formulas which + + + align:start position:0% +formulas which +we sort of just wrote up there and and + + align:start position:0% +we sort of just wrote up there and and + + + align:start position:0% +we sort of just wrote up there and and +we checked by Taylor series that this + + align:start position:0% +we checked by Taylor series that this + + + align:start position:0% +we checked by Taylor series that this +this is you know if I expand this in a + + align:start position:0% +this is you know if I expand this in a + + + align:start position:0% +this is you know if I expand this in a +Taylor series around UJ and this one and + + align:start position:0% +Taylor series around UJ and this one and + + + align:start position:0% +Taylor series around UJ and this one and +do the subtraction then sure enough the + + align:start position:0% +do the subtraction then sure enough the + + + align:start position:0% +do the subtraction then sure enough the +first term that'll pop out will be the + + align:start position:0% +first term that'll pop out will be the + + + align:start position:0% +first term that'll pop out will be the +udx and then there'll be a terms that I + + align:start position:0% +udx and then there'll be a terms that I + + + align:start position:0% +udx and then there'll be a terms that I +miss by and the first term I missed by + + align:start position:0% +miss by and the first term I missed by + + + align:start position:0% +miss by and the first term I missed by +Will will tell me the the uh order of + + align:start position:0% +Will will tell me the the uh order of + + + align:start position:0% +Will will tell me the the uh order of +accuracy okay so what function should I + + align:start position:0% +accuracy okay so what function should I + + + align:start position:0% +accuracy okay so what function should I +take to fit those to what function what + + align:start position:0% +take to fit those to what function what + + + align:start position:0% +take to fit those to what function what +inter what P of X should I take if I've + + align:start position:0% +inter what P of X should I take if I've + + + align:start position:0% +inter what P of X should I take if I've +got three + + align:start position:0% + + + + align:start position:0% + +points and I want to fit them by a + + align:start position:0% + + + + align:start position:0% + +function Natural Choice is a parabola + + align:start position:0% +function Natural Choice is a parabola + + + align:start position:0% +function Natural Choice is a parabola +second deegree function if if I'm going + + align:start position:0% +second deegree function if if I'm going + + + align:start position:0% +second deegree function if if I'm going +to use these three values jus1 J and J + + + align:start position:0% +to use these three values jus1 J and J + + + + align:start position:0% +to use these three values jus1 J and J + +1 and I fit those values by a parabola + + align:start position:0% +1 and I fit those values by a parabola + + + align:start position:0% +1 and I fit those values by a parabola +well I'm sorry I've made this look kind + + align:start position:0% +well I'm sorry I've made this look kind + + + align:start position:0% +well I'm sorry I've made this look kind +of goofy here let me let me L make let + + align:start position:0% +of goofy here let me let me L make let + + + align:start position:0% +of goofy here let me let me L make let +me make it a little uneven so now I fit + + align:start position:0% +me make it a little uneven so now I fit + + + align:start position:0% +me make it a little uneven so now I fit +it by some kind of + + align:start position:0% +it by some kind of + + + align:start position:0% +it by some kind of +Parabola and + + align:start position:0% +Parabola and + + + align:start position:0% +Parabola and +the derivative of the parabola the slope + + align:start position:0% +the derivative of the parabola the slope + + + align:start position:0% +the derivative of the parabola the slope +of the + + align:start position:0% +of the + + + align:start position:0% +of the +parabola is my gives me my formula + + align:start position:0% +parabola is my gives me my formula + + + align:start position:0% +parabola is my gives me my formula +because of course the parabola just + + align:start position:0% +because of course the parabola just + + + align:start position:0% +because of course the parabola just +depended on those three values UJ minus + + align:start position:0% +depended on those three values UJ minus + + + align:start position:0% +depended on those three values UJ minus +one UJ and UJ + 1 so I don't know if you + + align:start position:0% +one UJ and UJ + 1 so I don't know if you + + + align:start position:0% +one UJ and UJ + 1 so I don't know if you +want me to go through the + + align:start position:0% +want me to go through the + + + align:start position:0% +want me to go through the +step of figuring out the + + align:start position:0% +step of figuring out the + + + align:start position:0% +step of figuring out the +parabola taking its derivative well that + + align:start position:0% +parabola taking its derivative well that + + + align:start position:0% +parabola taking its derivative well that +we could sure do quick and then + + align:start position:0% +we could sure do quick and then + + + align:start position:0% +we could sure do quick and then +recognizing it this is what comes out + + align:start position:0% +recognizing it this is what comes out + + + align:start position:0% +recognizing it this is what comes out +well let me ask you suppose I only and + + align:start position:0% +well let me ask you suppose I only and + + + align:start position:0% +well let me ask you suppose I only and +so it would come + + align:start position:0% +so it would come + + + align:start position:0% +so it would come +out it would come out and let me let me + + align:start position:0% +out it would come out and let me let me + + + align:start position:0% +out it would come out and let me let me +think let me go up + + align:start position:0% +think let me go up + + + align:start position:0% +think let me go up +sorry I'll go up one to Five Points so + + align:start position:0% +sorry I'll go up one to Five Points so + + + align:start position:0% +sorry I'll go up one to Five Points so +so just let's think how would we get a + + align:start position:0% +so just let's think how would we get a + + + align:start position:0% +so just let's think how would we get a +five point + + align:start position:0% +five point + + + align:start position:0% +five point +formula for the first derivative let's + + align:start position:0% + + + + align:start position:0% + +say right polinomial x to the 4th + + align:start position:0% +say right polinomial x to the 4th + + + align:start position:0% +say right polinomial x to the 4th +exactly I mean it's neat to get this + + align:start position:0% +exactly I mean it's neat to get this + + + align:start position:0% +exactly I mean it's neat to get this +principle because this is what + + align:start position:0% +principle because this is what + + + align:start position:0% +principle because this is what +IO to trathan because once we got that + + align:start position:0% +IO to trathan because once we got that + + + align:start position:0% +IO to trathan because once we got that +principle we really got the idea here + + align:start position:0% +principle we really got the idea here + + + align:start position:0% +principle we really got the idea here +okay so we put a fourth degree + + align:start position:0% +okay so we put a fourth degree + + + align:start position:0% +okay so we put a fourth degree +polinomial so so so example one would be + + align:start position:0% +polinomial so so so example one would be + + + align:start position:0% +polinomial so so so example one would be +p is a + + align:start position:0% + + + + align:start position:0% + +parabola matching three + + align:start position:0% +parabola matching three + + + align:start position:0% +parabola matching three +values at a time and giving the point in + + align:start position:0% +values at a time and giving the point in + + + align:start position:0% +values at a time and giving the point in +the middle well of course actually yeah + + align:start position:0% +the middle well of course actually yeah + + + align:start position:0% +the middle well of course actually yeah +well all right anyway it's natural to + + align:start position:0% +well all right anyway it's natural to + + + align:start position:0% +well all right anyway it's natural to +take them take take just sort of + + align:start position:0% +take them take take just sort of + + + align:start position:0% +take them take take just sort of +symmetrically you figure okay it's + + align:start position:0% +symmetrically you figure okay it's + + + align:start position:0% +symmetrically you figure okay it's +smarter to use the three values one on + + align:start position:0% +smarter to use the three values one on + + + align:start position:0% +smarter to use the three values one on +one side the centered one and the one on + + align:start position:0% +one side the centered one and the one on + + + align:start position:0% +one side the centered one and the one on +the right okay so let's move it up to P + + align:start position:0% +the right okay so let's move it up to P + + + align:start position:0% +the right okay so let's move it up to P +equal 43 + + align:start position:0% + + + + align:start position:0% + +exactly use five + + align:start position:0% + + + + align:start position:0% + +values we're going to get some formula + + align:start position:0% +values we're going to get some formula + + + align:start position:0% +values we're going to get some formula +as I said that that got to be classical + + align:start position:0% +as I said that that got to be classical + + + align:start position:0% +as I said that that got to be classical +new Newton would have known it for sure + + align:start position:0% +new Newton would have known it for sure + + + align:start position:0% +new Newton would have known it for sure +uh so + + align:start position:0% +uh so + + + align:start position:0% +uh so +I can I I think I remember what those + + align:start position:0% +I can I I think I remember what those + + + align:start position:0% +I can I I think I remember what those +what those weights turn out to be here + + align:start position:0% +what those weights turn out to be here + + + align:start position:0% +what those weights turn out to be here +the weights were one 1 over 2H and and + + align:start position:0% +the weights were one 1 over 2H and and + + + align:start position:0% +the weights were one 1 over 2H and and +zero and minus one over 2H I think the + + align:start position:0% +zero and minus one over 2H I think the + + + align:start position:0% +zero and minus one over 2H I think the +the five values the when we fit with a + + align:start position:0% +the five values the when we fit with a + + + align:start position:0% +the five values the when we fit with a +fourth degree + + align:start position:0% +fourth degree + + + align:start position:0% +fourth degree +polinomial then we take the derivative + + align:start position:0% +polinomial then we take the derivative + + + align:start position:0% +polinomial then we take the derivative +as our little principle says I think the + + align:start position:0% +as our little principle says I think the + + + align:start position:0% +as our little principle says I think the +value that we would get I think it's + + align:start position:0% +value that we would get I think it's + + + align:start position:0% +value that we would get I think it's +minus a + + align:start position:0% +minus a + + + align:start position:0% +minus a +12th U J Min - 2 or maybe plus a 12 Min + + align:start position:0% +12th U J Min - 2 or maybe plus a 12 Min + + + align:start position:0% +12th U J Min - 2 or maybe plus a 12 Min +- 23 I think this is like a a nice + + align:start position:0% +- 23 I think this is like a a nice + + + align:start position:0% +- 23 I think this is like a a nice +exercise UJ minus one and because it's + + align:start position:0% +exercise UJ minus one and because it's + + + align:start position:0% +exercise UJ minus one and because it's +centered so centered and and anti- + + align:start position:0% +centered so centered and and anti- + + + align:start position:0% +centered so centered and and anti- +symmetric the first derivative of course + + align:start position:0% +symmetric the first derivative of course + + + align:start position:0% +symmetric the first derivative of course +we recognize is should like come out + + align:start position:0% +we recognize is should like come out + + + align:start position:0% +we recognize is should like come out +anti- symmetric then there we won't + + align:start position:0% +anti- symmetric then there we won't + + + align:start position:0% +anti- symmetric then there we won't +we'll use 2/3 with a plus sign u j + 1 + + align:start position:0% +we'll use 2/3 with a plus sign u j + 1 + + + align:start position:0% +we'll use 2/3 with a plus sign u j + 1 +and minus a 12th + + align:start position:0% +and minus a 12th + + + align:start position:0% +and minus a 12th +u j + 2 I think that's it's it's in + + align:start position:0% +u j + 2 I think that's it's it's in + + + align:start position:0% +u j + 2 I think that's it's it's in +numbers is 1 - 8 0 + 8 - one all over 12 + + align:start position:0% +numbers is 1 - 8 0 + 8 - one all over 12 + + + align:start position:0% +numbers is 1 - 8 0 + 8 - one all over 12 +oh all over 12 H 1/ H would of course + + align:start position:0% +oh all over 12 H 1/ H would of course + + + align:start position:0% +oh all over 12 H 1/ H would of course +show up here + + align:start position:0% +show up here + + + align:start position:0% +show up here +I'll in in this lecture I may forget + + align:start position:0% +I'll in in this lecture I may forget + + + align:start position:0% +I'll in in this lecture I may forget +various H's but they're they're uh okay + + align:start position:0% +various H's but they're they're uh okay + + + align:start position:0% +various H's but they're they're uh okay +you you see the idea and now here just + + align:start position:0% +you you see the idea and now here just + + + align:start position:0% +you you see the idea and now here just +to pin this idea down so this will be + + align:start position:0% +to pin this idea down so this will be + + + align:start position:0% +to pin this idea down so this will be +example + + align:start position:0% +example + + + align:start position:0% +example +zero how would I + + align:start position:0% +zero how would I + + + align:start position:0% +zero how would I +get uh just a simple forward difference + + align:start position:0% +get uh just a simple forward difference + + + align:start position:0% +get uh just a simple forward difference +like u j + 1 minus UJ over + + align:start position:0% +like u j + 1 minus UJ over + + + align:start position:0% +like u j + 1 minus UJ over +H which is the very very first uh + + align:start position:0% +H which is the very very first uh + + + align:start position:0% +H which is the very very first uh +approximation you you might think of to + + align:start position:0% +approximation you you might think of to + + + align:start position:0% +approximation you you might think of to +uh to the + + align:start position:0% +uh to the + + + align:start position:0% +uh to the +derivative so what would give me that + + align:start position:0% +derivative so what would give me that + + + align:start position:0% +derivative so what would give me that +one let's let's do one way down at the + + align:start position:0% +one let's let's do one way down at the + + + align:start position:0% +one let's let's do one way down at the +at the uh simplest level where we can + + align:start position:0% +at the uh simplest level where we can + + + align:start position:0% +at the uh simplest level where we can +where we can really think it through + + align:start position:0% +where we can really think it through + + + align:start position:0% +where we can really think it through +what + + align:start position:0% +what + + + align:start position:0% +what +what a line exactly I would I would I + + align:start position:0% +what a line exactly I would I would I + + + align:start position:0% +what a line exactly I would I would I +would just be using these two points + + align:start position:0% +would just be using these two points + + + align:start position:0% +would just be using these two points +well maybe I should improve the figure + + align:start position:0% +well maybe I should improve the figure + + + align:start position:0% +well maybe I should improve the figure +here so let let me squeeze knowing I'll + + align:start position:0% +here so let let me squeeze knowing I'll + + + align:start position:0% +here so let let me squeeze knowing I'll +need to space let me squeeze this figure + + align:start position:0% +need to space let me squeeze this figure + + + align:start position:0% +need to space let me squeeze this figure +in here so if I have UJ and UJ + one and + + align:start position:0% +in here so if I have UJ and UJ + one and + + + align:start position:0% +in here so if I have UJ and UJ + one and +I'm given + + align:start position:0% +I'm given + + + align:start position:0% +I'm given +values there if that height is UJ and + + align:start position:0% +values there if that height is UJ and + + + align:start position:0% +values there if that height is UJ and +this height is UJ + 1 I I fit it I've + + align:start position:0% +this height is UJ + 1 I I fit it I've + + + align:start position:0% +this height is UJ + 1 I I fit it I've +only got two points fit them by a + + align:start position:0% +only got two points fit them by a + + + align:start position:0% +only got two points fit them by a +straight + + align:start position:0% +straight + + + align:start position:0% +straight +line take the derivative of the straight + + align:start position:0% +line take the derivative of the straight + + + align:start position:0% +line take the derivative of the straight +line at at + + align:start position:0% +line at at + + + align:start position:0% +line at at +J and well it's the slope of the line + + align:start position:0% +J and well it's the slope of the line + + + align:start position:0% +J and well it's the slope of the line +and of course that's what it + + align:start position:0% + + + + align:start position:0% + +is so this is degree 1 this is degree 2 + + align:start position:0% +is so this is degree 1 this is degree 2 + + + align:start position:0% +is so this is degree 1 this is degree 2 +this is degree 4 four and so on all + + align:start position:0% + + + + align:start position:0% + +right now comes the spectral + + align:start position:0% +right now comes the spectral + + + align:start position:0% +right now comes the spectral +idea + + align:start position:0% +idea + + + align:start position:0% +idea +what instead of just staying with finite + + align:start position:0% +what instead of just staying with finite + + + align:start position:0% +what instead of just staying with finite +you know up to six or eight or so + + align:start position:0% +you know up to six or eight or so + + + align:start position:0% +you know up to six or eight or so +on what if I'm working on the whole line + + align:start position:0% +on what if I'm working on the whole line + + + align:start position:0% +on what if I'm working on the whole line +so so uh in my outline for the talk + + align:start position:0% +so so uh in my outline for the talk + + + align:start position:0% +so so uh in my outline for the talk +we've Now sort of covered polinomial + + align:start position:0% +we've Now sort of covered polinomial + + + align:start position:0% +we've Now sort of covered polinomial +accuracy that's oldfashioned + + align:start position:0% +accuracy that's oldfashioned + + + align:start position:0% +accuracy that's oldfashioned +as of today we're moving to spectral + + align:start position:0% +as of today we're moving to spectral + + + align:start position:0% +as of today we're moving to spectral +accuracy and I'm interested in + + align:start position:0% + + + + align:start position:0% + +three situations one where I'm on the + + align:start position:0% +three situations one where I'm on the + + + align:start position:0% +three situations one where I'm on the +whole line which is where I've been here + + align:start position:0% +whole line which is where I've been here + + + align:start position:0% +whole line which is where I've been here +I haven't worried about any + + align:start position:0% +I haven't worried about any + + + align:start position:0% +I haven't worried about any +boundaries then secondly will come a + + align:start position:0% +boundaries then secondly will come a + + + align:start position:0% +boundaries then secondly will come a +periodic case where the boundary + + align:start position:0% +periodic case where the boundary + + + align:start position:0% +periodic case where the boundary +condition there is a inter finite + + align:start position:0% +condition there is a inter finite + + + align:start position:0% +condition there is a inter finite +interval but periodicity makes life easy + + align:start position:0% +interval but periodicity makes life easy + + + align:start position:0% +interval but periodicity makes life easy +and then finally when there's a boundary + + align:start position:0% +and then finally when there's a boundary + + + align:start position:0% +and then finally when there's a boundary +condition other than periodic like U of0 + + align:start position:0% +condition other than periodic like U of0 + + + align:start position:0% +condition other than periodic like U of0 +equals 0 the boundary conditions that + + align:start position:0% +equals 0 the boundary conditions that + + + align:start position:0% +equals 0 the boundary conditions that +we've seen uh what happens there okay + + align:start position:0% +we've seen uh what happens there okay + + + align:start position:0% +we've seen uh what happens there okay +all right so we're on the whole line so + + align:start position:0% +all right so we're on the whole line so + + + align:start position:0% +all right so we're on the whole line so +this is part one whole + + align:start position:0% + + + + align:start position:0% + +line okay so now I've got the whole line + + align:start position:0% +line okay so now I've got the whole line + + + align:start position:0% +line okay so now I've got the whole line +with equally space mesh H I've got + + align:start position:0% +with equally space mesh H I've got + + + align:start position:0% +with equally space mesh H I've got +values of U at all points here + + align:start position:0% + + + + align:start position:0% + +and I'm looking for an interpolation + + align:start position:0% +and I'm looking for an interpolation + + + align:start position:0% +and I'm looking for an interpolation +function P of X let that's pinned down + + align:start position:0% +function P of X let that's pinned down + + + align:start position:0% +function P of X let that's pinned down +let's pin down J equals z here as a + + align:start position:0% +let's pin down J equals z here as a + + + align:start position:0% +let's pin down J equals z here as a +typical + + align:start position:0% + + + + align:start position:0% + +one I'm looking for an + + align:start position:0% + + + + align:start position:0% + +interpolation uh sort of the nicest + + align:start position:0% +interpolation uh sort of the nicest + + + align:start position:0% +interpolation uh sort of the nicest +function I can think + + align:start position:0% +function I can think + + + align:start position:0% +function I can think +of which will interpolate those values + + align:start position:0% +of which will interpolate those values + + + align:start position:0% +of which will interpolate those values +and I'll take its + + align:start position:0% +and I'll take its + + + align:start position:0% +and I'll take its +derivative and that will give me a + + align:start position:0% +derivative and that will give me a + + + align:start position:0% +derivative and that will give me a +formula that involves all the 's + + align:start position:0% +formula that involves all the 's + + + align:start position:0% +formula that involves all the 's +now so so it's this first step isn't + + align:start position:0% +now so so it's this first step isn't + + + align:start position:0% +now so so it's this first step isn't +completely practical because it's going + + align:start position:0% +completely practical because it's going + + + align:start position:0% +completely practical because it's going +to be a uh an infinitely long uh + + align:start position:0% +to be a uh an infinitely long uh + + + align:start position:0% +to be a uh an infinitely long uh +differentiation formula but also + + align:start position:0% +differentiation formula but also + + + align:start position:0% +differentiation formula but also +infinitely accurate and what what do you + + align:start position:0% +infinitely accurate and what what do you + + + align:start position:0% +infinitely accurate and what what do you +propose that I fit with I can't I can't + + align:start position:0% +propose that I fit with I can't I can't + + + align:start position:0% +propose that I fit with I can't I can't +very well take a polinomial of + + align:start position:0% +very well take a polinomial of + + + align:start position:0% +very well take a polinomial of +infinite degree I don't think doesn't + + align:start position:0% +infinite degree I don't think doesn't + + + align:start position:0% +infinite degree I don't think doesn't +sound like the right thing to + + align:start position:0% + + + + align:start position:0% + +do yeah that sync function is going to + + align:start position:0% +do yeah that sync function is going to + + + align:start position:0% +do yeah that sync function is going to +come in that sync function is going to + + align:start position:0% +come in that sync function is going to + + + align:start position:0% +come in that sync function is going to +come in so I'm going to + + align:start position:0% +come in so I'm going to + + + align:start position:0% +come in so I'm going to +use um and and what are some of the + + align:start position:0% +use um and and what are some of the + + + align:start position:0% +use um and and what are some of the +other words you you guys maybe know them + + align:start position:0% +other words you you guys maybe know them + + + align:start position:0% +other words you you guys maybe know them +so so who's whose formula am I going to + + align:start position:0% +so so who's whose formula am I going to + + + align:start position:0% +so so who's whose formula am I going to +use here for for producing out of these + + align:start position:0% +use here for for producing out of these + + + align:start position:0% +use here for for producing out of these +samples of function and uh what's the + + align:start position:0% +samples of function and uh what's the + + + align:start position:0% +samples of function and uh what's the +word that's associated with that type of + + align:start position:0% +word that's associated with that type of + + + align:start position:0% +word that's associated with that type of +a + + align:start position:0% +a + + + align:start position:0% +a +function band limit it is the word I'm + + align:start position:0% +function band limit it is the word I'm + + + align:start position:0% +function band limit it is the word I'm +going to look at right so so these are + + align:start position:0% +going to look at right so so these are + + + align:start position:0% +going to look at right so so these are +the right exactly the right words the + + align:start position:0% +the right exactly the right words the + + + align:start position:0% +the right exactly the right words the +sync + + align:start position:0% +sync + + + align:start position:0% +sync +function uh band limited my my so a + + align:start position:0% +function uh band limited my my so a + + + align:start position:0% +function uh band limited my my so a +combination of sync functions centered + + align:start position:0% +combination of sync functions centered + + + align:start position:0% +combination of sync functions centered +at different points they're they're band + + align:start position:0% +at different points they're they're band + + + align:start position:0% +at different points they're they're band +limited and who's the recently deceased + + align:start position:0% +limited and who's the recently deceased + + + align:start position:0% +limited and who's the recently deceased +uh Superstar of this world of of Shannon + + align:start position:0% +uh Superstar of this world of of Shannon + + + align:start position:0% +uh Superstar of this world of of Shannon +Shannon yeah so that + + align:start position:0% +Shannon yeah so that + + + align:start position:0% +Shannon yeah so that +and and earlier he wasn't of course the + + align:start position:0% +and and earlier he wasn't of course the + + + align:start position:0% +and and earlier he wasn't of course the +first I should mention + + align:start position:0% +first I should mention + + + align:start position:0% +first I should mention +Whitaker as another as a predecessor of + + align:start position:0% +Whitaker as another as a predecessor of + + + align:start position:0% +Whitaker as another as a predecessor of +Shannon and he may have Whitaker may + + align:start position:0% +Shannon and he may have Whitaker may + + + align:start position:0% +Shannon and he may have Whitaker may +have given the name the notation to sync + + align:start position:0% +have given the name the notation to sync + + + align:start position:0% +have given the name the notation to sync +functions I'm not sure okay so what is + + align:start position:0% +functions I'm not sure okay so what is + + + align:start position:0% +functions I'm not sure okay so what is +this um interpolate because that we have + + align:start position:0% +this um interpolate because that we have + + + align:start position:0% +this um interpolate because that we have +to know this interpolating function + + align:start position:0% +to know this interpolating function + + + align:start position:0% +to know this interpolating function +because we have to know that and then we + + align:start position:0% +because we have to know that and then we + + + align:start position:0% +because we have to know that and then we +take its derivative and we get all these + + align:start position:0% +take its derivative and we get all these + + + align:start position:0% +take its derivative and we get all these +wonderful numbers okay so the interp + + align:start position:0% +wonderful numbers okay so the interp + + + align:start position:0% +wonderful numbers okay so the interp +well let's since we've circled sync + + align:start position:0% +well let's since we've circled sync + + + align:start position:0% +well let's since we've circled sync +let's figure out the interpolate for + + align:start position:0% +let's figure out the interpolate for + + + align:start position:0% +let's figure out the interpolate for +suppose J at at zero this is always zero + + align:start position:0% +suppose J at at zero this is always zero + + + align:start position:0% +suppose J at at zero this is always zero +suppose it was one there and zero at all + + align:start position:0% +suppose it was one there and zero at all + + + align:start position:0% +suppose it was one there and zero at all +the other + + align:start position:0% +the other + + + align:start position:0% +the other +points then I'm looking for an + + align:start position:0% +points then I'm looking for an + + + align:start position:0% +points then I'm looking for an +interpolation function that'll fit those + + align:start position:0% +interpolation function that'll fit those + + + align:start position:0% +interpolation function that'll fit those +Val values and we hope it rather decays + + align:start position:0% +Val values and we hope it rather decays + + + align:start position:0% +Val values and we hope it rather decays +pretty pretty uh quickly but we can't + + align:start position:0% +pretty pretty uh quickly but we can't + + + align:start position:0% +pretty pretty uh quickly but we can't +control that and it doesn't actually + + align:start position:0% +control that and it doesn't actually + + + align:start position:0% +control that and it doesn't actually +Decay that + + align:start position:0% +Decay that + + + align:start position:0% +Decay that +fast and what is that function then well + + align:start position:0% +fast and what is that function then well + + + align:start position:0% +fast and what is that function then well +there are many functions of course that + + align:start position:0% +there are many functions of course that + + + align:start position:0% +there are many functions of course that +take + + align:start position:0% +take + + + align:start position:0% +take +these you know that are zero at all + + align:start position:0% +these you know that are zero at all + + + align:start position:0% +these you know that are zero at all +these points and one there I could call + + align:start position:0% +these points and one there I could call + + + align:start position:0% +these points and one there I could call +it the Cardinal function it's sometimes + + align:start position:0% +it the Cardinal function it's sometimes + + + align:start position:0% +it the Cardinal function it's sometimes +called Cardinal + + align:start position:0% +called Cardinal + + + align:start position:0% +called Cardinal +interpolation uh uh meaning there's one + + align:start position:0% +interpolation uh uh meaning there's one + + + align:start position:0% +interpolation uh uh meaning there's one +and all the rest zeros are like L + + align:start position:0% +and all the rest zeros are like L + + + align:start position:0% +and all the rest zeros are like L +gr + + align:start position:0% +gr + + + align:start position:0% +gr +uh well it's the sync + + align:start position:0% +uh well it's the sync + + + align:start position:0% +uh well it's the sync +function so this this P of X will be the + + align:start position:0% +function so this this P of X will be the + + + align:start position:0% +function so this this P of X will be the +sync function maybe I call it s + + align:start position:0% +sync function maybe I call it s + + + align:start position:0% +sync function maybe I call it s +ofx and what is it it's the sign of now + + align:start position:0% +ofx and what is it it's the sign of now + + + align:start position:0% +ofx and what is it it's the sign of now +we remember we've got to make the darn + + align:start position:0% +we remember we've got to make the darn + + + align:start position:0% +we remember we've got to make the darn +thing come to zero at x equal + + align:start position:0% +thing come to zero at x equal + + + align:start position:0% +thing come to zero at x equal +H so I guess maybe the S of Pi + + align:start position:0% +H so I guess maybe the S of Pi + + + align:start position:0% +H so I guess maybe the S of Pi +X over H would do the job right at xal H + + align:start position:0% +X over H would do the job right at xal H + + + align:start position:0% +X over H would do the job right at xal H +I'll have the S of pi x = 2 H I'll still + + align:start position:0% +I'll have the S of pi x = 2 H I'll still + + + align:start position:0% +I'll have the S of pi x = 2 H I'll still +have all sign of 2 pi and but I want to + + align:start position:0% +have all sign of 2 pi and but I want to + + + align:start position:0% +have all sign of 2 pi and but I want to +get a one at this point so I have to + + align:start position:0% +get a one at this point so I have to + + + align:start position:0% +get a one at this point so I have to +remembering that sin a over a approaches + + align:start position:0% +remembering that sin a over a approaches + + + align:start position:0% +remembering that sin a over a approaches +one I better put pix over H down there + + align:start position:0% +one I better put pix over H down there + + + align:start position:0% +one I better put pix over H down there +and that's my sync function that's the + + align:start position:0% +and that's my sync function that's the + + + align:start position:0% +and that's my sync function that's the +famous + + align:start position:0% + + + + align:start position:0% + +function + + align:start position:0% + + + + align:start position:0% + +okay known + + align:start position:0% + + + + align:start position:0% + +to everybody who works with fora stuff + + align:start position:0% +to everybody who works with fora stuff + + + align:start position:0% +to everybody who works with fora stuff +and now now what's the function that now + + align:start position:0% +and now now what's the function that now + + + align:start position:0% +and now now what's the function that now +now interpolate those + + align:start position:0% +now interpolate those + + + align:start position:0% +now interpolate those +values + + align:start position:0% +values + + + align:start position:0% +values +well these values I could think this I + + align:start position:0% +well these values I could think this I + + + align:start position:0% +well these values I could think this I +could think of as the + + align:start position:0% +could think of as the + + + align:start position:0% +could think of as the +values + + align:start position:0% +values + + + align:start position:0% +values +UJ well how should I think of this is as + + align:start position:0% +UJ well how should I think of this is as + + + align:start position:0% +UJ well how should I think of this is as +probably a sum of values UJ times the + + align:start position:0% +probably a sum of values UJ times the + + + align:start position:0% +probably a sum of values UJ times the +Delta function this was the Delta this + + align:start position:0% +Delta function this was the Delta this + + + align:start position:0% +Delta function this was the Delta this +is I am interpolating + + align:start position:0% + + + + align:start position:0% + +Delta Delta and now my more General case + + align:start position:0% +Delta Delta and now my more General case + + + align:start position:0% +Delta Delta and now my more General case +is some combination of Deltas that + + align:start position:0% +is some combination of Deltas that + + + align:start position:0% +is some combination of Deltas that +that's always the story right that's the + + align:start position:0% +that's always the story right that's the + + + align:start position:0% +that's always the story right that's the +beautiful thing about Delta functions is + + align:start position:0% +beautiful thing about Delta functions is + + + align:start position:0% +beautiful thing about Delta functions is +that they're like so basic one and the + + align:start position:0% +that they're like so basic one and the + + + align:start position:0% +that they're like so basic one and the +rest zero so now if I shift those + + align:start position:0% +rest zero so now if I shift those + + + align:start position:0% +rest zero so now if I shift those +Deltas + + align:start position:0% +Deltas + + + align:start position:0% +Deltas +over so is that is it am I doing this + + align:start position:0% +over so is that is it am I doing this + + + align:start position:0% +over so is that is it am I doing this +right well my I'm I guess it doesn't + + align:start position:0% +right well my I'm I guess it doesn't + + + align:start position:0% +right well my I'm I guess it doesn't +matter yeah it doesn't matter whether I + + align:start position:0% +matter yeah it doesn't matter whether I + + + align:start position:0% +matter yeah it doesn't matter whether I +write M minus J or this this should + + align:start position:0% +write M minus J or this this should + + + align:start position:0% +write M minus J or this this should +agree with what what what will that sum + + align:start position:0% +agree with what what what will that sum + + + align:start position:0% +agree with what what what will that sum +equal let me let me change the notation + + align:start position:0% +equal let me let me change the notation + + + align:start position:0% +equal let me let me change the notation +here to + + align:start position:0% + + + + align:start position:0% + +n suppose I take a sum from n equal + + align:start position:0% +n suppose I take a sum from n equal + + + align:start position:0% +n suppose I take a sum from n equal +minus in what I want to do you you see + + align:start position:0% +minus in what I want to do you you see + + + align:start position:0% +minus in what I want to do you you see +what I want to do I want to write this + + align:start position:0% +what I want to do I want to write this + + + align:start position:0% +what I want to do I want to write this +this series of disc this discrete + + align:start position:0% +this series of disc this discrete + + + align:start position:0% +this series of disc this discrete +function as a combination of Delta + + align:start position:0% +function as a combination of Delta + + + align:start position:0% +function as a combination of Delta +functions so and Delta functions are so + + align:start position:0% +functions so and Delta functions are so + + + align:start position:0% +functions so and Delta functions are so +beautiful do you see that what do I get + + align:start position:0% +beautiful do you see that what do I get + + + align:start position:0% +beautiful do you see that what do I get +if I if what do that sum + + align:start position:0% + + + + align:start position:0% + +equal well the only term that comes in + + align:start position:0% +equal well the only term that comes in + + + align:start position:0% +equal well the only term that comes in +is when m equal n right + + align:start position:0% +is when m equal n right + + + align:start position:0% +is when m equal n right +because Delta is zero at all the other + + align:start position:0% +because Delta is zero at all the other + + + align:start position:0% +because Delta is zero at all the other +points so the only term that comes in is + + align:start position:0% +points so the only term that comes in is + + + align:start position:0% +points so the only term that comes in is +so I get um M maybe I should if if the + + align:start position:0% +so I get um M maybe I should if if the + + + align:start position:0% +so I get um M maybe I should if if the +camera doesn't M since I've been using J + + align:start position:0% +camera doesn't M since I've been using J + + + align:start position:0% +camera doesn't M since I've been using J +why don't I yeah okay all right so I've + + align:start position:0% +why don't I yeah okay all right so I've + + + align:start position:0% +why don't I yeah okay all right so I've +written the data as a combination of + + align:start position:0% +written the data as a combination of + + + align:start position:0% +written the data as a combination of +Delta functions so what's my polinomial + + align:start position:0% +Delta functions so what's my polinomial + + + align:start position:0% +Delta functions so what's my polinomial +then + + align:start position:0% +then + + + align:start position:0% +then +so + + align:start position:0% +so + + + align:start position:0% +so +p is what what's P of X then what's my + + align:start position:0% +p is what what's P of X then what's my + + + align:start position:0% +p is what what's P of X then what's my +what's my card what's my band limited + + align:start position:0% +what's my card what's my band limited + + + align:start position:0% +what's my card what's my band limited +Shannon sync + + align:start position:0% +Shannon sync + + + align:start position:0% +Shannon sync +interpolating + + align:start position:0% +interpolating + + + align:start position:0% +interpolating +series + + align:start position:0% +series + + + align:start position:0% +series +that so for for Delta itself Delta zero + + align:start position:0% +that so for for Delta itself Delta zero + + + align:start position:0% +that so for for Delta itself Delta zero +we could say this was the + + align:start position:0% +we could say this was the + + + align:start position:0% +we could say this was the +guy but the process is going to be + + align:start position:0% +guy but the process is going to be + + + align:start position:0% +guy but the process is going to be +linear so if I have some + + align:start position:0% +linear so if I have some + + + align:start position:0% +linear so if I have some +combination with weights un what should + + align:start position:0% + + + + align:start position:0% + +I what should the function + + align:start position:0% +I what should the function + + + align:start position:0% +I what should the function +be shift it over right it should be S + + align:start position:0% +be shift it over right it should be S + + + align:start position:0% +be shift it over right it should be S +of pi x - n over H ided by the by pi x - + + align:start position:0% +of pi x - n over H ided by the by pi x - + + + align:start position:0% +of pi x - n over H ided by the by pi x - +n over H I guess that's got to be it I + + align:start position:0% +n over H I guess that's got to be it I + + + align:start position:0% +n over H I guess that's got to be it I +I'll put it there even without checking + + align:start position:0% +I'll put it there even without checking + + + align:start position:0% +I'll put it there even without checking +with Nick profan here so that's + + align:start position:0% +with Nick profan here so that's + + + align:start position:0% +with Nick profan here so that's +my + + align:start position:0% +my + + + align:start position:0% +my +do I want something a little + + align:start position:0% + + + + align:start position:0% + +different + + align:start position:0% +different + + + align:start position:0% +different +sorry oh the steps shouldn't yeah that's + + align:start position:0% +sorry oh the steps shouldn't yeah that's + + + align:start position:0% +sorry oh the steps shouldn't yeah that's +that's right the steps should be yeah + + align:start position:0% +that's right the steps should be yeah + + + align:start position:0% +that's right the steps should be yeah +thank you you can see I'm not really a + + align:start position:0% +thank you you can see I'm not really a + + + align:start position:0% +thank you you can see I'm not really a +pro at this at all NH yeah + + align:start position:0% +pro at this at all NH yeah + + + align:start position:0% +pro at this at all NH yeah +NH + + align:start position:0% +NH + + + align:start position:0% +NH +good + + align:start position:0% +good + + + align:start position:0% +good +okay now that looks better right + + align:start position:0% +okay now that looks better right + + + align:start position:0% +okay now that looks better right +so does this does this do what we want + + align:start position:0% +so does this does this do what we want + + + align:start position:0% +so does this does this do what we want +does it have this value at the point NH + + align:start position:0% +does it have this value at the point NH + + + align:start position:0% +does it have this value at the point NH +I I want I want and I hope I have P at + + align:start position:0% +I I want I want and I hope I have P at + + + align:start position:0% +I I want I want and I hope I have P at +the point NH should be + + align:start position:0% +the point NH should be + + + align:start position:0% +the point NH should be +what should be that should be un n that + + align:start position:0% +what should be that should be un n that + + + align:start position:0% +what should be that should be un n that +was my idea here is the + + align:start position:0% +was my idea here is the + + + align:start position:0% +was my idea here is the +point there's a point NH and it's got a + + align:start position:0% +point there's a point NH and it's got a + + + align:start position:0% +point there's a point NH and it's got a +height un so that's what I'm if I'm + + align:start position:0% +height un so that's what I'm if I'm + + + align:start position:0% +height un so that's what I'm if I'm +interpolating this is the interpolating + + align:start position:0% +interpolating this is the interpolating + + + align:start position:0% +interpolating this is the interpolating +condition hit hit all the discret points + + align:start position:0% +condition hit hit all the discret points + + + align:start position:0% +condition hit hit all the discret points +right and this is the function that + + align:start position:0% +right and this is the function that + + + align:start position:0% +right and this is the function that +fills in between those + + align:start position:0% +fills in between those + + + align:start position:0% +fills in between those +points in this band limited so what does + + align:start position:0% +points in this band limited so what does + + + align:start position:0% +points in this band limited so what does +band limited + + align:start position:0% +band limited + + + align:start position:0% +band limited +mean what's the band what's the what is + + align:start position:0% +mean what's the band what's the what is + + + align:start position:0% +mean what's the band what's the what is +it that's limited just to remember what + + align:start position:0% +it that's limited just to remember what + + + align:start position:0% +it that's limited just to remember what +we're talking about + + align:start position:0% +we're talking about + + + align:start position:0% +we're talking about +here what is it what what is does it + + align:start position:0% +here what is it what what is does it + + + align:start position:0% +here what is it what what is does it +mean to say that I've produced this band + + align:start position:0% +mean to say that I've produced this band + + + align:start position:0% +mean to say that I've produced this band +limited function and of course this sum + + align:start position:0% +limited function and of course this sum + + + align:start position:0% +limited function and of course this sum +is going from minus infinity to + + align:start position:0% +is going from minus infinity to + + + align:start position:0% +is going from minus infinity to +infinity and in a minute I'm supposed to + + align:start position:0% +infinity and in a minute I'm supposed to + + + align:start position:0% +infinity and in a minute I'm supposed to +take its derivative + + align:start position:0% +take its derivative + + + align:start position:0% +take its derivative +right and its second + + align:start position:0% +right and its second + + + align:start position:0% +right and its second +derivative and come up with magic + + align:start position:0% +derivative and come up with magic + + + align:start position:0% +derivative and come up with magic +numbers that's you see what's happening + + align:start position:0% +numbers that's you see what's happening + + + align:start position:0% +numbers that's you see what's happening +here see the the principle is so nice + + align:start position:0% +here see the the principle is so nice + + + align:start position:0% +here see the the principle is so nice +choose an + + align:start position:0% +choose an + + + align:start position:0% +choose an +intelligent p interpolating p of X and + + align:start position:0% +intelligent p interpolating p of X and + + + align:start position:0% +intelligent p interpolating p of X and +then take its derivative + + align:start position:0% +then take its derivative + + + align:start position:0% +then take its derivative +now what can I come back to that + + align:start position:0% +now what can I come back to that + + + align:start position:0% +now what can I come back to that +question I you'll have to give me some + + align:start position:0% +question I you'll have to give me some + + + align:start position:0% +question I you'll have to give me some +feedback on + + align:start position:0% +feedback on + + + align:start position:0% +feedback on +whether when I ask about band limited + + align:start position:0% +whether when I ask about band limited + + + align:start position:0% +whether when I ask about band limited +I'm asking about something you like + + align:start position:0% +I'm asking about something you like + + + align:start position:0% +I'm asking about something you like +dream about every evening so uh it's uh + + align:start position:0% +dream about every evening so uh it's uh + + + align:start position:0% +dream about every evening so uh it's uh +absurd or whether it helps to get that + + align:start position:0% +absurd or whether it helps to get that + + + align:start position:0% +absurd or whether it helps to get that +word out here so where is the maybe I + + align:start position:0% +word out here so where is the maybe I + + + align:start position:0% +word out here so where is the maybe I +need help actually so ban limited means + + align:start position:0% +need help actually so ban limited means + + + align:start position:0% +need help actually so ban limited means +that its 48 + + align:start position:0% +that its 48 + + + align:start position:0% +that its 48 +transform which is that word getting + + align:start position:0% +transform which is that word getting + + + align:start position:0% +transform which is that word getting +used here for the first moment + + align:start position:0% +used here for the first moment + + + align:start position:0% +used here for the first moment +is limited to a finite interval right + + align:start position:0% +is limited to a finite interval right + + + align:start position:0% +is limited to a finite interval right +the fora transform P hat of + + align:start position:0% +the fora transform P hat of + + + align:start position:0% +the fora transform P hat of +K is zero + + align:start position:0% +K is zero + + + align:start position:0% +K is zero +outside some interval of + + align:start position:0% +outside some interval of + + + align:start position:0% +outside some interval of +K that's what band limited means that + + align:start position:0% +K that's what band limited means that + + + align:start position:0% +K that's what band limited means that +that the the frequencies are all in this + + align:start position:0% +that the the frequencies are all in this + + + align:start position:0% +that the the frequencies are all in this +band and I I'm a little nervous about + + align:start position:0% +band and I I'm a little nervous about + + + align:start position:0% +band and I I'm a little nervous about +writing down what that band might + + align:start position:0% +writing down what that band might + + + align:start position:0% +writing down what that band might +be uh maybe I should be able to see it + + align:start position:0% +be uh maybe I should be able to see it + + + align:start position:0% +be uh maybe I should be able to see it +from here what's where are the + + align:start position:0% +from here what's where are the + + + align:start position:0% +from here what's where are the +frequencies + + align:start position:0% +frequencies + + + align:start position:0% +frequencies +here help help me + + align:start position:0% +here help help me + + + align:start position:0% +here help help me +out + + align:start position:0% +out + + + align:start position:0% +out +uh is it perhaps pi over + + align:start position:0% +uh is it perhaps pi over + + + align:start position:0% +uh is it perhaps pi over +h + + align:start position:0% +h + + + align:start position:0% +h +no h over + + align:start position:0% + + + + align:start position:0% + +Pi 1 over 2 H all right question minus + + align:start position:0% +Pi 1 over 2 H all right question minus + + + align:start position:0% +Pi 1 over 2 H all right question minus +all I know is it's it's it's all right + + align:start position:0% +all I know is it's it's it's all right + + + align:start position:0% +all I know is it's it's it's all right +we'll put that + + align:start position:0% +we'll put that + + + align:start position:0% +we'll put that +in yeah + + align:start position:0% +in yeah + + + align:start position:0% +in yeah +yeah okay yeah it be it'll have an H in + + align:start position:0% +yeah okay yeah it be it'll have an H in + + + align:start position:0% +yeah okay yeah it be it'll have an H in +the denominator and and uh possibly + + align:start position:0% +the denominator and and uh possibly + + + align:start position:0% +the denominator and and uh possibly +these pies that we'll get in our hair in + + align:start position:0% +these pies that we'll get in our hair in + + + align:start position:0% +these pies that we'll get in our hair in +all for8 formulas okay anyway what's + + align:start position:0% +all for8 formulas okay anyway what's + + + align:start position:0% +all for8 formulas okay anyway what's +important is it's a natural choice and + + align:start position:0% +important is it's a natural choice and + + + align:start position:0% +important is it's a natural choice and +we can take its derivative and we can + + align:start position:0% +we can take its derivative and we can + + + align:start position:0% +we can take its derivative and we can +replace this formula by by an infinitely + + align:start position:0% +replace this formula by by an infinitely + + + align:start position:0% +replace this formula by by an infinitely +accurate + + align:start position:0% +accurate + + + align:start position:0% +accurate +formula and what is that formula well + + align:start position:0% +formula and what is that formula well + + + align:start position:0% +formula and what is that formula well +let me just say thanks to tresan or of + + align:start position:0% +let me just say thanks to tresan or of + + + align:start position:0% +let me just say thanks to tresan or of +course he got it from predecessor what + + align:start position:0% +course he got it from predecessor what + + + align:start position:0% +course he got it from predecessor what +those numbers actually + + align:start position:0% + + + + align:start position:0% + +are yeah here they are they are oh well + + align:start position:0% +are yeah here they are they are oh well + + + align:start position:0% +are yeah here they are they are oh well +so the derivative + + align:start position:0% +so the derivative + + + align:start position:0% +so the derivative +DX can I just put down the coeffic and + + align:start position:0% +DX can I just put down the coeffic and + + + align:start position:0% +DX can I just put down the coeffic and +not the values so the coefficient of the + + align:start position:0% +not the values so the coefficient of the + + + align:start position:0% +not the values so the coefficient of the +center point is going to be zero as it + + align:start position:0% +center point is going to be zero as it + + + align:start position:0% +center point is going to be zero as it +was in here we had Z + + align:start position:0% +was in here we had Z + + + align:start position:0% +was in here we had Z +UJS here we had zero + + align:start position:0% +UJS here we had zero + + + align:start position:0% +UJS here we had zero +UJS we're everything's you know we're + + align:start position:0% +UJS we're everything's you know we're + + + align:start position:0% +UJS we're everything's you know we're +we're working antisymmetrically here so + + align:start position:0% +we're working antisymmetrically here so + + + align:start position:0% +we're working antisymmetrically here so +we'll have zero in the center of course + + align:start position:0% +we'll have zero in the center of course + + + align:start position:0% +we'll have zero in the center of course +we'll have a 1/h multiplying all these + + align:start position:0% +we'll have a 1/h multiplying all these + + + align:start position:0% +we'll have a 1/h multiplying all these +numbers and we have I think it's a + + align:start position:0% +numbers and we have I think it's a + + + align:start position:0% +numbers and we have I think it's a +minus1 one on the sides and then a 1/2 + + align:start position:0% +minus1 one on the sides and then a 1/2 + + + align:start position:0% +minus1 one on the sides and then a 1/2 +on a -2 next and a minus A3 and a thir + + align:start position:0% +on a -2 next and a minus A3 and a thir + + + align:start position:0% +on a -2 next and a minus A3 and a thir +next and so + + align:start position:0% +next and so + + + align:start position:0% +next and so +forth oh well sorry I've got the signs + + align:start position:0% +forth oh well sorry I've got the signs + + + align:start position:0% +forth oh well sorry I've got the signs +wrong because it ought to it ought to so + + align:start position:0% +wrong because it ought to it ought to so + + + align:start position:0% +wrong because it ought to it ought to so +it's plus there and minus here plus + + align:start position:0% +it's plus there and minus here plus + + + align:start position:0% +it's plus there and minus here plus +there and minus there + + align:start position:0% +there and minus there + + + align:start position:0% +there and minus there +so is that okay one I I'll erase that + + align:start position:0% +so is that okay one I I'll erase that + + + align:start position:0% +so is that okay one I I'll erase that +plus sign now to make it look + + align:start position:0% +plus sign now to make it look + + + align:start position:0% +plus sign now to make it look +clean yeah the numbers are 1- a half 1/3 + + align:start position:0% +clean yeah the numbers are 1- a half 1/3 + + + align:start position:0% +clean yeah the numbers are 1- a half 1/3 +minus A4 and so forth + + align:start position:0% +minus A4 and so forth + + + align:start position:0% +minus A4 and so forth +okay uh slowly decaying right slowly + + align:start position:0% +okay uh slowly decaying right slowly + + + align:start position:0% +okay uh slowly decaying right slowly +decaying the kind of Decay that we see + + align:start position:0% +decaying the kind of Decay that we see + + + align:start position:0% +decaying the kind of Decay that we see +in the sync function + + align:start position:0% +in the sync function + + + align:start position:0% +in the sync function +itself and I could figure out the second + + align:start position:0% +itself and I could figure out the second + + + align:start position:0% +itself and I could figure out the second +derivative why or I could better than + + align:start position:0% +derivative why or I could better than + + + align:start position:0% +derivative why or I could better than +that I could uh rely on uh Professor for + + align:start position:0% +that I could uh rely on uh Professor for + + + align:start position:0% +that I could uh rely on uh Professor for +the second derivative so but it's sort + + align:start position:0% +the second derivative so but it's sort + + + align:start position:0% +the second derivative so but it's sort +of interesting to know so here I'll have + + align:start position:0% +of interesting to know so here I'll have + + + align:start position:0% +of interesting to know so here I'll have +an H squared of + + align:start position:0% +an H squared of + + + align:start position:0% +an H squared of +course and if I do + + align:start position:0% +course and if I do + + + align:start position:0% +course and if I do +it he + + align:start position:0% +it he + + + align:start position:0% +it he +gets + + align:start position:0% +gets + + + align:start position:0% +gets +uh uh a one and a one now this is going + + align:start position:0% +uh uh a one and a one now this is going + + + align:start position:0% +uh uh a one and a one now this is going +to be the center here and then there's a + + align:start position:0% +to be the center here and then there's a + + + align:start position:0% +to be the center here and then there's a +minus a quar a minus oh of course this + + align:start position:0% +minus a quar a minus oh of course this + + + align:start position:0% +minus a quar a minus oh of course this +is symmetric right second derivative + + align:start position:0% +is symmetric right second derivative + + + align:start position:0% +is symmetric right second derivative +plus a 9th plus a + + align:start position:0% +plus a 9th plus a + + + align:start position:0% +plus a 9th plus a +9th and anybody want to tell me what + + align:start position:0% +9th and anybody want to tell me what + + + align:start position:0% +9th and anybody want to tell me what +number ought to go at the zero position + + align:start position:0% +number ought to go at the zero position + + + align:start position:0% +number ought to go at the zero position +well first tell me + + align:start position:0% +well first tell me + + + align:start position:0% +well first tell me +some way to what two ways to find it one + + align:start position:0% +some way to what two ways to find it one + + + align:start position:0% +some way to what two ways to find it one +way would + + align:start position:0% +way would + + + align:start position:0% +way would +be and I shouldn't be so cowardly as + + align:start position:0% +be and I shouldn't be so cowardly as + + + align:start position:0% +be and I shouldn't be so cowardly as +to Flint uh Flinch from this is would be + + align:start position:0% +to Flint uh Flinch from this is would be + + + align:start position:0% +to Flint uh Flinch from this is would be +to take the second + + align:start position:0% +to take the second + + + align:start position:0% +to take the second +derivative uh but you have a pretty + + align:start position:0% +derivative uh but you have a pretty + + + align:start position:0% +derivative uh but you have a pretty +shrewd idea of of another way to + + align:start position:0% +shrewd idea of of another way to + + + align:start position:0% +shrewd idea of of another way to +determine that number what what do you + + align:start position:0% + + + + align:start position:0% + +think the + + align:start position:0% +think the + + + align:start position:0% +think the +sum sum to zero yeah the sum has to be + + align:start position:0% +sum sum to zero yeah the sum has to be + + + align:start position:0% +sum sum to zero yeah the sum has to be +zero because if my function U was + + align:start position:0% +zero because if my function U was + + + align:start position:0% +zero because if my function U was +constant if all the values of U Were the + + align:start position:0% +constant if all the values of U Were the + + + align:start position:0% +constant if all the values of U Were the +same then I absolutely expect the + + align:start position:0% +same then I absolutely expect the + + + align:start position:0% +same then I absolutely expect the +derivatives to be zero here of course + + align:start position:0% +derivatives to be zero here of course + + + align:start position:0% +derivatives to be zero here of course +they summ to zero because there's a one + + align:start position:0% +they summ to zero because there's a one + + + align:start position:0% +they summ to zero because there's a one +and a Min - one and a minus a half and a + + align:start position:0% +and a Min - one and a minus a half and a + + + align:start position:0% +and a Min - one and a minus a half and a +half so the first derivative of the + + align:start position:0% +half so the first derivative of the + + + align:start position:0% +half so the first derivative of the +constant is zero here they'll sum to + + align:start position:0% +constant is zero here they'll sum to + + + align:start position:0% +constant is zero here they'll sum to +zero if I put the right number in there + + align:start position:0% +zero if I put the right number in there + + + align:start position:0% +zero if I put the right number in there +and that right number turns out to be + + align:start position:0% +and that right number turns out to be + + + align:start position:0% +and that right number turns out to be +minus < ^2 over + + align:start position:0% +minus < ^2 over + + + align:start position:0% +minus < ^2 over + + align:start position:0% + + + + align:start position:0% + +okay so I think that's right I think + + align:start position:0% +okay so I think that's right I think + + + align:start position:0% +okay so I think that's right I think +that's I think well at least I believing + + align:start position:0% +that's I think well at least I believing + + + align:start position:0% +that's I think well at least I believing +it's right okay so now + + align:start position:0% +it's right okay so now + + + align:start position:0% +it's right okay so now +um we've done it really for the whole + + align:start position:0% +um we've done it really for the whole + + + align:start position:0% +um we've done it really for the whole +line we found + + align:start position:0% +line we found + + + align:start position:0% +line we found +found an + + align:start position:0% +found an + + + align:start position:0% +found an +approximation with with infinite + + align:start position:0% +approximation with with infinite + + + align:start position:0% +approximation with with infinite +accuracy and now I just have to say what + + align:start position:0% +accuracy and now I just have to say what + + + align:start position:0% +accuracy and now I just have to say what +what does that accuracy mean what what + + align:start position:0% +what does that accuracy mean what what + + + align:start position:0% +what does that accuracy mean what what +what + + align:start position:0% +what + + + align:start position:0% +what +uh how is how do we see something with + + align:start position:0% +uh how is how do we see something with + + + align:start position:0% +uh how is how do we see something with +infinite accuracy infinite order of + + align:start position:0% +infinite accuracy infinite order of + + + align:start position:0% +infinite accuracy infinite order of +accuracy okay well certainly numerically + + align:start position:0% +accuracy okay well certainly numerically + + + align:start position:0% +accuracy okay well certainly numerically +you see it uh if you if you uh took a + + align:start position:0% +you see it uh if you if you uh took a + + + align:start position:0% +you see it uh if you if you uh took a +function + + align:start position:0% +function + + + align:start position:0% +function +you know some some reasonable + + align:start position:0% +you know some some reasonable + + + align:start position:0% +you know some some reasonable +function took its discrete + + align:start position:0% +function took its discrete + + + align:start position:0% +function took its discrete +values used the + + align:start position:0% +values used the + + + align:start position:0% +values used the +formulas you would see that this is + + align:start position:0% +formulas you would see that this is + + + align:start position:0% +formulas you would see that this is +second order accurate that as H went to + + align:start position:0% +second order accurate that as H went to + + + align:start position:0% +second order accurate that as H went to +zero you're you would see in a log plot + + align:start position:0% +zero you're you would see in a log plot + + + align:start position:0% +zero you're you would see in a log plot +You' you'd see it of + + align:start position:0% +You' you'd see it of + + + align:start position:0% +You' you'd see it of +course and this guy you would see as + + align:start position:0% +course and this guy you would see as + + + align:start position:0% +course and this guy you would see as +fourth order + + align:start position:0% +fourth order + + + align:start position:0% +fourth order +accurate again take a smooth + + align:start position:0% +accurate again take a smooth + + + align:start position:0% +accurate again take a smooth +function use its mesh + + align:start position:0% +function use its mesh + + + align:start position:0% +function use its mesh +values then the polinomial of course + + align:start position:0% +values then the polinomial of course + + + align:start position:0% +values then the polinomial of course +doesn't reconstruct the function exactly + + align:start position:0% +doesn't reconstruct the function exactly + + + align:start position:0% +doesn't reconstruct the function exactly +but + + align:start position:0% +but + + + align:start position:0% +but +it's H4 accurate and as H decreases on a + + align:start position:0% +it's H4 accurate and as H decreases on a + + + align:start position:0% +it's H4 accurate and as H decreases on a +log plot you see that slope of four fine + + align:start position:0% +log plot you see that slope of four fine + + + align:start position:0% +log plot you see that slope of four fine +well what do you see with one of these + + align:start position:0% +well what do you see with one of these + + + align:start position:0% +well what do you see with one of these +guys well of course now everything + + align:start position:0% +guys well of course now everything + + + align:start position:0% +guys well of course now everything +depends on the function so now I have to + + align:start position:0% +depends on the function so now I have to + + + align:start position:0% +depends on the function so now I have to +pause for a minute and talk about + + align:start position:0% +pause for a minute and talk about + + + align:start position:0% +pause for a minute and talk about +smoothness of functions right I have to + + align:start position:0% +smoothness of functions right I have to + + + align:start position:0% +smoothness of functions right I have to +talk say something about + + align:start position:0% + + + + align:start position:0% + +smoothness of the original function that + + align:start position:0% +smoothness of the original function that + + + align:start position:0% +smoothness of the original function that +I'm of the original function U of X that + + align:start position:0% +I'm of the original function U of X that + + + align:start position:0% +I'm of the original function U of X that +I'm uh + + align:start position:0% +I'm uh + + + align:start position:0% +I'm uh +working that's sort of behind the scenes + + align:start position:0% +working that's sort of behind the scenes + + + align:start position:0% +working that's sort of behind the scenes +that I'm that I'm uh approximating the + + align:start position:0% +that I'm that I'm uh approximating the + + + align:start position:0% +that I'm that I'm uh approximating the +derivative of + + align:start position:0% +derivative of + + + align:start position:0% +derivative of +okay suppose that original function U of + + align:start position:0% +okay suppose that original function U of + + + align:start position:0% +okay suppose that original function U of +X that I'm trying try to take the + + align:start position:0% +X that I'm trying try to take the + + + align:start position:0% +X that I'm trying try to take the +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +of hasn't got that many + + align:start position:0% +of hasn't got that many + + + align:start position:0% +of hasn't got that many +derivatives suppose it's like a hat + + align:start position:0% +derivatives suppose it's like a hat + + + align:start position:0% +derivatives suppose it's like a hat +function or + + align:start position:0% +function or + + + align:start position:0% +function or +something then can I then what can I + + align:start position:0% +something then can I then what can I + + + align:start position:0% +something then can I then what can I +expect so if my original + + align:start position:0% +expect so if my original + + + align:start position:0% +expect so if my original +function isn't that + + align:start position:0% +function isn't that + + + align:start position:0% +function isn't that +smooth then what could I expect from + + align:start position:0% +smooth then what could I expect from + + + align:start position:0% +smooth then what could I expect from +this these formulas this this + + align:start position:0% +this these formulas this this + + + align:start position:0% +this these formulas this this +formula then upgraded to this one and + + align:start position:0% +formula then upgraded to this one and + + + align:start position:0% +formula then upgraded to this one and +then hyper upgraded to this one what + + align:start position:0% +then hyper upgraded to this one what + + + align:start position:0% +then hyper upgraded to this one what +what would you expect to see if you + + align:start position:0% +what would you expect to see if you + + + align:start position:0% +what would you expect to see if you +compared those for if you looked at the + + align:start position:0% +compared those for if you looked at the + + + align:start position:0% +compared those for if you looked at the +if you let H get smaller and smaller use + + align:start position:0% +if you let H get smaller and smaller use + + + align:start position:0% +if you let H get smaller and smaller use +more and more V mesh values of the Hat + + align:start position:0% +more and more V mesh values of the Hat + + + align:start position:0% +more and more V mesh values of the Hat +function I just made up the Hat function + + align:start position:0% +function I just made up the Hat function + + + align:start position:0% +function I just made up the Hat function +as a as a typical function you know I'm + + align:start position:0% +as a as a typical function you know I'm + + + align:start position:0% +as a as a typical function you know I'm +I'm taking more and more finer and finer + + align:start position:0% +I'm taking more and more finer and finer + + + align:start position:0% +I'm taking more and more finer and finer +values of + + align:start position:0% + + + + align:start position:0% + +it but still the its problem isn't going + + align:start position:0% +it but still the its problem isn't going + + + align:start position:0% +it but still the its problem isn't going +away right so + + align:start position:0% +away right so + + + align:start position:0% +away right so +what I guess what I want to say is that + + align:start position:0% +what I guess what I want to say is that + + + align:start position:0% +what I guess what I want to say is that +the order + + align:start position:0% +the order + + + align:start position:0% +the order +of the that the Decay on my graph when I + + align:start position:0% +of the that the Decay on my graph when I + + + align:start position:0% +of the that the Decay on my graph when I +when I do this little numerical test by + + align:start position:0% +when I do this little numerical test by + + + align:start position:0% +when I do this little numerical test by +using professor's matlb + + align:start position:0% +using professor's matlb + + + align:start position:0% +using professor's matlb +program uh this can't really + + align:start position:0% +program uh this can't really + + + align:start position:0% +program uh this can't really +beat uh + + align:start position:0% +beat uh + + + align:start position:0% +beat uh +this because the function can't the + + align:start position:0% +this because the function can't the + + + align:start position:0% +this because the function can't the +function isn't good enough if the + + align:start position:0% +function isn't good enough if the + + + align:start position:0% +function isn't good enough if the +function isn't good enough to to to make + + align:start position:0% +function isn't good enough to to to make + + + align:start position:0% +function isn't good enough to to to make +higher accuracy possible then well + + align:start position:0% +higher accuracy possible then well + + + align:start position:0% +higher accuracy possible then well +that's its problem right we we can't our + + align:start position:0% +that's its problem right we we can't our + + + align:start position:0% +that's its problem right we we can't our +formula cannot + + align:start position:0% +formula cannot + + + align:start position:0% +formula cannot +uh uh achieve the impossible that is get + + align:start position:0% +uh uh achieve the impossible that is get + + + align:start position:0% +uh uh achieve the impossible that is get +terrific accuracy for a function that's + + align:start position:0% +terrific accuracy for a function that's + + + align:start position:0% +terrific accuracy for a function that's +uh that's who's uh who that hasn't got + + align:start position:0% +uh that's who's uh who that hasn't got + + + align:start position:0% +uh that's who's uh who that hasn't got +that many derivatives + + align:start position:0% +that many derivatives + + + align:start position:0% +that many derivatives +okay if the function were ban limited + + align:start position:0% +okay if the function were ban limited + + + align:start position:0% +okay if the function were ban limited +yes no so that's a good point suppose + + align:start position:0% +yes no so that's a good point suppose + + + align:start position:0% +yes no so that's a good point suppose +yeah now so let's let's here's + + align:start position:0% +yeah now so let's let's here's + + + align:start position:0% +yeah now so let's let's here's +a here's a non-s smooth example + + align:start position:0% +a here's a non-s smooth example + + + align:start position:0% +a here's a non-s smooth example +right now so let's just take a minute + + align:start position:0% +right now so let's just take a minute + + + align:start position:0% +right now so let's just take a minute +and and + + align:start position:0% +and and + + + align:start position:0% +and and +discuss infinitely smooth functions + + align:start position:0% +discuss infinitely smooth functions + + + align:start position:0% +discuss infinitely smooth functions +infinite + + align:start position:0% +infinite + + + align:start position:0% +infinite +smoothness cuz those are the ones which + + align:start position:0% +smoothness cuz those are the ones which + + + align:start position:0% +smoothness cuz those are the ones which +this guy is you know to totally take + + align:start position:0% +this guy is you know to totally take + + + align:start position:0% +this guy is you know to totally take +advantage of and the the graph you'll + + align:start position:0% +advantage of and the the graph you'll + + + align:start position:0% +advantage of and the the graph you'll +see the error just just you know it + + align:start position:0% +see the error just just you know it + + + align:start position:0% +see the error just just you know it +doesn't go down like some log deal on a + + align:start position:0% +doesn't go down like some log deal on a + + + align:start position:0% +doesn't go down like some log deal on a +log plot it's just boom and so what + + align:start position:0% +log plot it's just boom and so what + + + align:start position:0% +log plot it's just boom and so what +where would functions be infant smooth + + align:start position:0% +where would functions be infant smooth + + + align:start position:0% +where would functions be infant smooth +well your suggestion of suppose uh U of + + align:start position:0% +well your suggestion of suppose uh U of + + + align:start position:0% +well your suggestion of suppose uh U of +X might the original U of X might the + + align:start position:0% +X might the original U of X might the + + + align:start position:0% +X might the original U of X might the +shall I put orid just remember then that + + align:start position:0% +shall I put orid just remember then that + + + align:start position:0% +shall I put orid just remember then that +we're talking about this original + + align:start position:0% +we're talking about this original + + + align:start position:0% +we're talking about this original +function behind the scenes not talking + + align:start position:0% +function behind the scenes not talking + + + align:start position:0% +function behind the scenes not talking +about our our + + align:start position:0% +about our our + + + align:start position:0% +about our our +interpolation but if our original + + align:start position:0% +interpolation but if our original + + + align:start position:0% +interpolation but if our original +function U of X say is well so what are + + align:start position:0% +function U of X say is well so what are + + + align:start position:0% +function U of X say is well so what are +some + + align:start position:0% + + + + align:start position:0% + +yeah yeah + + align:start position:0% +yeah yeah + + + align:start position:0% +yeah yeah +uh maybe this is a moment this actually + + align:start position:0% +uh maybe this is a moment this actually + + + align:start position:0% +uh maybe this is a moment this actually +anticipates a little my next lecture + + align:start position:0% +anticipates a little my next lecture + + + align:start position:0% +anticipates a little my next lecture +about frea + + align:start position:0% +about frea + + + align:start position:0% +about frea +series + + align:start position:0% +series + + + align:start position:0% +series +what I want to connect and I'm going to + + align:start position:0% +what I want to connect and I'm going to + + + align:start position:0% +what I want to connect and I'm going to +use the idea of the forier transform of + + align:start position:0% +use the idea of the forier transform of + + + align:start position:0% +use the idea of the forier transform of +the + + align:start position:0% + + + + align:start position:0% + +function uh so if I have a function U of + + align:start position:0% +function uh so if I have a function U of + + + align:start position:0% +function uh so if I have a function U of +X it's got a fora transform uat of + + align:start position:0% +X it's got a fora transform uat of + + + align:start position:0% +X it's got a fora transform uat of +K and so I'm speaking now just + + align:start position:0% +K and so I'm speaking now just + + + align:start position:0% +K and so I'm speaking now just +informally about this topic + + align:start position:0% +informally about this topic + + + align:start position:0% +informally about this topic +of smoothness of a function and how it's + + align:start position:0% +of smoothness of a function and how it's + + + align:start position:0% +of smoothness of a function and how it's +reflected + + align:start position:0% +reflected + + + align:start position:0% +reflected +in its fora + + align:start position:0% +in its fora + + + align:start position:0% +in its fora +transform and how is it reflected + + align:start position:0% +transform and how is it reflected + + + align:start position:0% +transform and how is it reflected +generally speaking if I if I if I take + + align:start position:0% +generally speaking if I if I if I take + + + align:start position:0% +generally speaking if I if I if I take +this function which isn't very smooth + + align:start position:0% +this function which isn't very smooth + + + align:start position:0% +this function which isn't very smooth +what what's what's up with its 4A + + align:start position:0% +what what's what's up with its 4A + + + align:start position:0% +what what's what's up with its 4A +transform it + + align:start position:0% +transform it + + + align:start position:0% +transform it +sorry say again it's not band limited + + align:start position:0% +sorry say again it's not band limited + + + align:start position:0% +sorry say again it's not band limited +and so so it's it's + + align:start position:0% +and so so it's it's + + + align:start position:0% +and so so it's it's +not it's not zero outside some + + align:start position:0% +not it's not zero outside some + + + align:start position:0% +not it's not zero outside some +interval and more than that what does it + + align:start position:0% +interval and more than that what does it + + + align:start position:0% +interval and more than that what does it +do so outside you know as I approach + + align:start position:0% +do so outside you know as I approach + + + align:start position:0% +do so outside you know as I approach +Infinity it doesn't it's it doesn't chop + + align:start position:0% +Infinity it doesn't it's it doesn't chop + + + align:start position:0% +Infinity it doesn't it's it doesn't chop +off and it only decays po polinomial + + align:start position:0% +off and it only decays po polinomial + + + align:start position:0% +off and it only decays po polinomial +right in fact you know what the rate of + + align:start position:0% +right in fact you know what the rate of + + + align:start position:0% +right in fact you know what the rate of +decay of the of the so it's the Decay + + align:start position:0% +decay of the of the so it's the Decay + + + align:start position:0% +decay of the of the so it's the Decay +the smoothness of the function it + + align:start position:0% +the smoothness of the function it + + + align:start position:0% +the smoothness of the function it +connects with the Decay + + align:start position:0% +connects with the Decay + + + align:start position:0% +connects with the Decay +rate of the transform maybe we've noted + + align:start position:0% +rate of the transform maybe we've noted + + + align:start position:0% +rate of the transform maybe we've noted +this uh + + align:start position:0% +this uh + + + align:start position:0% +this uh +before but see it again so what's the + + align:start position:0% +before but see it again so what's the + + + align:start position:0% +before but see it again so what's the +Decay rate for this for U hat in that + + align:start position:0% +Decay rate for this for U hat in that + + + align:start position:0% +Decay rate for this for U hat in that +case U hat of K let's remember uh just I + + align:start position:0% +case U hat of K let's remember uh just I + + + align:start position:0% +case U hat of K let's remember uh just I +have to work from the Delta function so + + align:start position:0% +have to work from the Delta function so + + + align:start position:0% +have to work from the Delta function so +the Delta function doesn't the transform + + align:start position:0% +the Delta function doesn't the transform + + + align:start position:0% +the Delta function doesn't the transform +as a constant no Decay step function one + + align:start position:0% +as a constant no Decay step function one + + + align:start position:0% +as a constant no Decay step function one +one derivative better and the the U hat + + align:start position:0% +one derivative better and the the U hat + + + align:start position:0% +one derivative better and the the U hat +would Decay like first + + align:start position:0% +would Decay like first + + + align:start position:0% +would Decay like first +Power hat Function One derivative better + + align:start position:0% +Power hat Function One derivative better + + + align:start position:0% +Power hat Function One derivative better +better still so it'll Decay like 1/ + + align:start position:0% +better still so it'll Decay like 1/ + + + align:start position:0% +better still so it'll Decay like 1/ +K2 + + align:start position:0% +K2 + + + align:start position:0% +K2 +okay now if the band if theun ban + + align:start position:0% +okay now if the band if theun ban + + + align:start position:0% +okay now if the band if theun ban +limited well boy then the 4 transform + + align:start position:0% +limited well boy then the 4 transform + + + align:start position:0% +limited well boy then the 4 transform +decays as you know incredibly I mean + + align:start position:0% +decays as you know incredibly I mean + + + align:start position:0% +decays as you know incredibly I mean +it's actually zero outside the an so + + align:start position:0% +it's actually zero outside the an so + + + align:start position:0% +it's actually zero outside the an so +this is the other extreme this is this + + align:start position:0% +this is the other extreme this is this + + + align:start position:0% +this is the other extreme this is this +is great ter extreme smoothness so this + + align:start position:0% +is great ter extreme smoothness so this + + + align:start position:0% +is great ter extreme smoothness so this +is you hat is actually zero + + align:start position:0% +is you hat is actually zero + + + align:start position:0% +is you hat is actually zero +outside + + align:start position:0% +outside + + + align:start position:0% +outside +outside uh a finite + + align:start position:0% +outside uh a finite + + + align:start position:0% +outside uh a finite +interval now what about in between + + align:start position:0% +interval now what about in between + + + align:start position:0% +interval now what about in between +well I yeah so give me give me a a type + + align:start position:0% +well I yeah so give me give me a a type + + + align:start position:0% +well I yeah so give me give me a a type +of function yeah tell me a function here + + align:start position:0% +of function yeah tell me a function here + + + align:start position:0% +of function yeah tell me a function here +this is a good question tell me a + + align:start position:0% +this is a good question tell me a + + + align:start position:0% +this is a good question tell me a +function that's not band limited so it + + align:start position:0% +function that's not band limited so it + + + align:start position:0% +function that's not band limited so it +doesn't have this Superstar rate of + + align:start position:0% +doesn't have this Superstar rate of + + + align:start position:0% +doesn't have this Superstar rate of +decay in the + + align:start position:0% +decay in the + + + align:start position:0% +decay in the +transform but it's it decays faster than + + align:start position:0% +transform but it's it decays faster than + + + align:start position:0% +transform but it's it decays faster than +any polinomial so it hasn't got any any + + align:start position:0% +any polinomial so it hasn't got any any + + + align:start position:0% +any polinomial so it hasn't got any any +uh Delta functions even after you take + + align:start position:0% +uh Delta functions even after you take + + + align:start position:0% +uh Delta functions even after you take +its derivatives you still don't get get + + align:start position:0% +its derivatives you still don't get get + + + align:start position:0% +its derivatives you still don't get get +any so Galan thanks thanks if I took the + + align:start position:0% +any so Galan thanks thanks if I took the + + + align:start position:0% +any so Galan thanks thanks if I took the +Galan so Gan is a very good example + + align:start position:0% +Galan so Gan is a very good example + + + align:start position:0% +Galan so Gan is a very good example +because the function is is e- x^2 / 2 + + align:start position:0% +because the function is is e- x^2 / 2 + + + align:start position:0% +because the function is is e- x^2 / 2 +and we know its transform is eus k^ 2 + + align:start position:0% +and we know its transform is eus k^ 2 + + + align:start position:0% +and we know its transform is eus k^ 2 +over two modulo + + align:start position:0% + + + + align:start position:0% + +constants so there is an infinitely + + align:start position:0% +constants so there is an infinitely + + + align:start position:0% +constants so there is an infinitely +smooth function actually + + align:start position:0% +smooth function actually + + + align:start position:0% +smooth function actually +has yeah that e the minus what kind of a + + align:start position:0% +has yeah that e the minus what kind of a + + + align:start position:0% +has yeah that e the minus what kind of a +yeah what what do you how would I + + align:start position:0% +yeah what what do you how would I + + + align:start position:0% +yeah what what do you how would I +describe a function like e- x^2 over 2 I + + align:start position:0% +describe a function like e- x^2 over 2 I + + + align:start position:0% +describe a function like e- x^2 over 2 I +mean it hasn't got any singularities + + align:start position:0% +mean it hasn't got any singularities + + + align:start position:0% +mean it hasn't got any singularities +right in in the finite plane it never + + align:start position:0% +right in in the finite plane it never + + + align:start position:0% +right in in the finite plane it never +goes wrong and in fact I can extend it + + align:start position:0% +goes wrong and in fact I can extend it + + + align:start position:0% +goes wrong and in fact I can extend it +into the complex plane I can extend it + + align:start position:0% +into the complex plane I can extend it + + + align:start position:0% +into the complex plane I can extend it +into e Theus z^2 over + + align:start position:0% +into e Theus z^2 over + + + align:start position:0% +into e Theus z^2 over +2 so this this is defined on the real + + align:start position:0% +2 so this this is defined on the real + + + align:start position:0% +2 so this this is defined on the real +axis and you say that's where we are but + + align:start position:0% +axis and you say that's where we are but + + + align:start position:0% +axis and you say that's where we are but +but uh the properties of a function uh + + align:start position:0% +but uh the properties of a function uh + + + align:start position:0% +but uh the properties of a function uh +are get revealed also by what happens if + + align:start position:0% +are get revealed also by what happens if + + + align:start position:0% +are get revealed also by what happens if +you push them out to to and now still no + + align:start position:0% +you push them out to to and now still no + + + align:start position:0% +you push them out to to and now still no +still no + + align:start position:0% +still no + + + align:start position:0% +still no +singularities and that's what we see + + align:start position:0% +singularities and that's what we see + + + align:start position:0% +singularities and that's what we see +here this terrific rate of Decay okay so + + align:start position:0% +here this terrific rate of Decay okay so + + + align:start position:0% +here this terrific rate of Decay okay so +this would be I would call this thing an + + align:start position:0% +this would be I would call this thing an + + + align:start position:0% +this would be I would call this thing an +entire + + align:start position:0% + + + + align:start position:0% + +function an entire + + align:start position:0% +function an entire + + + align:start position:0% +function an entire +function and these band limited guys + + align:start position:0% +function and these band limited guys + + + align:start position:0% +function and these band limited guys +will be entire functions + + align:start position:0% +will be entire functions + + + align:start position:0% +will be entire functions +too they're they're even better than + + align:start position:0% +too they're they're even better than + + + align:start position:0% +too they're they're even better than +this right + + align:start position:0% +this right + + + align:start position:0% +this right +so an entire function is a function that + + align:start position:0% +so an entire function is a function that + + + align:start position:0% +so an entire function is a function that +you can extend out into the complex + + align:start position:0% +you can extend out into the complex + + + align:start position:0% +you can extend out into the complex +plane and it still doesn't have any + + align:start position:0% +plane and it still doesn't have any + + + align:start position:0% +plane and it still doesn't have any +singularities except at Infinity there + + align:start position:0% +singularities except at Infinity there + + + align:start position:0% +singularities except at Infinity there +are no poles nothing bad you you see + + align:start position:0% +are no poles nothing bad you you see + + + align:start position:0% +are no poles nothing bad you you see +there's some function Theory uh some + + align:start position:0% +there's some function Theory uh some + + + align:start position:0% +there's some function Theory uh some +some discussion of properties of + + align:start position:0% +some discussion of properties of + + + align:start position:0% +some discussion of properties of +functions hiding here and and it's the + + align:start position:0% +functions hiding here and and it's the + + + align:start position:0% +functions hiding here and and it's the +properties of the functions that control + + align:start position:0% +properties of the functions that control + + + align:start position:0% +properties of the functions that control +how terrific this infinite formula + + align:start position:0% +how terrific this infinite formula + + + align:start position:0% +how terrific this infinite formula +actually is okay okay so these are + + align:start position:0% +actually is okay okay so these are + + + align:start position:0% +actually is okay okay so these are +totally terrific and the pale weener + + align:start position:0% +totally terrific and the pale weener + + + align:start position:0% +totally terrific and the pale weener +theor enters to to describe uh it it + + align:start position:0% +theor enters to to describe uh it it + + + align:start position:0% +theor enters to to describe uh it it +pins down + + align:start position:0% +pins down + + + align:start position:0% +pins down +exactly um the property a connection + + align:start position:0% +exactly um the property a connection + + + align:start position:0% +exactly um the property a connection +between properties of functions and and + + align:start position:0% +between properties of functions and and + + + align:start position:0% +between properties of functions and and +properties of a + + align:start position:0% + + + + align:start position:0% + +transform rate of growth so this grows a + + align:start position:0% +transform rate of growth so this grows a + + + align:start position:0% +transform rate of growth so this grows a +bit fast so this wouldn't be pale and + + align:start position:0% +bit fast so this wouldn't be pale and + + + align:start position:0% +bit fast so this wouldn't be pale and +Weiner wouldn't be interested in this + + align:start position:0% +Weiner wouldn't be interested in this + + + align:start position:0% +Weiner wouldn't be interested in this +one we're naturally interested in it + + align:start position:0% +one we're naturally interested in it + + + align:start position:0% +one we're naturally interested in it +because we know it's transforming + + align:start position:0% +because we know it's transforming + + + align:start position:0% +because we know it's transforming +exactly and it's sort of in between the + + align:start position:0% +exactly and it's sort of in between the + + + align:start position:0% +exactly and it's sort of in between the +extreme I mean the you know the world's + + align:start position:0% +extreme I mean the you know the world's + + + align:start position:0% +extreme I mean the you know the world's +most perfect type of function and the + + align:start position:0% +most perfect type of function and the + + + align:start position:0% +most perfect type of function and the +world's nons smooth function and the + + align:start position:0% +world's nons smooth function and the + + + align:start position:0% +world's nons smooth function and the +non-s smooth right okay is that uh that + + align:start position:0% +non-s smooth right okay is that uh that + + + align:start position:0% +non-s smooth right okay is that uh that +little discussion helpful okay so I'm uh + + align:start position:0% +little discussion helpful okay so I'm uh + + + align:start position:0% +little discussion helpful okay so I'm uh +uh that's really what I wanted to say + + align:start position:0% +uh that's really what I wanted to say + + + align:start position:0% +uh that's really what I wanted to say +about the whole + + align:start position:0% + + + + align:start position:0% + +line uh + + align:start position:0% + + + + align:start position:0% + +yeah for which functions is it exact oh + + align:start position:0% +yeah for which functions is it exact oh + + + align:start position:0% +yeah for which functions is it exact oh +that's a good question it must be + + align:start position:0% +that's a good question it must be + + + align:start position:0% +that's a good question it must be +probably band limited yeah yeah because + + align:start position:0% +probably band limited yeah yeah because + + + align:start position:0% +probably band limited yeah yeah because +if the function was yeah so so if + + align:start position:0% +if the function was yeah so so if + + + align:start position:0% +if the function was yeah so so if +because if if the underlying function + + align:start position:0% +because if if the underlying function + + + align:start position:0% +because if if the underlying function +was band limited and our in + + align:start position:0% +was band limited and our in + + + align:start position:0% +was band limited and our in +to the same band and our then our as our + + align:start position:0% +to the same band and our then our as our + + + align:start position:0% +to the same band and our then our as our +interpolate they'd be the one and the + + align:start position:0% +interpolate they'd be the one and the + + + align:start position:0% +interpolate they'd be the one and the +same right yeah yeah so so I guess we + + align:start position:0% +same right yeah yeah so so I guess we + + + align:start position:0% +same right yeah yeah so so I guess we +get perfect accuracy on the functions + + align:start position:0% +get perfect accuracy on the functions + + + align:start position:0% +get perfect accuracy on the functions +where where where P of X is exactly the + + align:start position:0% +where where where P of X is exactly the + + + align:start position:0% +where where where P of X is exactly the +original U of it then then then of + + align:start position:0% +original U of it then then then of + + + align:start position:0% +original U of it then then then of +course when we take the + + align:start position:0% +course when we take the + + + align:start position:0% +course when we take the +derivative uh this becomes an equation + + align:start position:0% +derivative uh this becomes an equation + + + align:start position:0% +derivative uh this becomes an equation +if when p is exactly U so the functions + + align:start position:0% +if when p is exactly U so the functions + + + align:start position:0% +if when p is exactly U so the functions +who which fit perfectly our our uh our + + align:start position:0% +who which fit perfectly our our uh our + + + align:start position:0% +who which fit perfectly our our uh our +interpolation function then those are + + align:start position:0% +interpolation function then those are + + + align:start position:0% +interpolation function then those are +the ones we're going to get exactly + + align:start position:0% +the ones we're going to get exactly + + + align:start position:0% +the ones we're going to get exactly +right that's a very good point okay + + align:start position:0% +right that's a very good point okay + + + align:start position:0% +right that's a very good point okay +now what remains to do in these do in + + align:start position:0% +now what remains to do in these do in + + + align:start position:0% +now what remains to do in these do in +this discussion well I've got a ways to + + align:start position:0% +this discussion well I've got a ways to + + + align:start position:0% +this discussion well I've got a ways to +go here on this uh outline now I'm ready + + align:start position:0% +go here on this uh outline now I'm ready + + + align:start position:0% +go here on this uh outline now I'm ready +for + + align:start position:0% +for + + + align:start position:0% +for +periodic and then for non-p periodic + + align:start position:0% +periodic and then for non-p periodic + + + align:start position:0% +periodic and then for non-p periodic +okay so periodic what's up fora still + + align:start position:0% +okay so periodic what's up fora still + + + align:start position:0% +okay so periodic what's up fora still +going to + + align:start position:0% + + + + align:start position:0% + +operate but may be more realistic to + + align:start position:0% +operate but may be more realistic to + + + align:start position:0% +operate but may be more realistic to +think uh I'm going to have finite + + align:start position:0% +think uh I'm going to have finite + + + align:start position:0% +think uh I'm going to have finite +formulas my my formulas are not going to + + align:start position:0% +formulas my my formulas are not going to + + + align:start position:0% +formulas my my formulas are not going to +go infinitely + + align:start position:0% +go infinitely + + + align:start position:0% +go infinitely +long and + + align:start position:0% +long and + + + align:start position:0% +long and +uh I I'm going to deal with forier + + align:start position:0% +uh I I'm going to deal with forier + + + align:start position:0% +uh I I'm going to deal with forier +series somewhere instead of forier + + align:start position:0% +series somewhere instead of forier + + + align:start position:0% +series somewhere instead of forier +integrals you know I'm I'm and I'll I'll + + align:start position:0% +integrals you know I'm I'm and I'll I'll + + + align:start position:0% +integrals you know I'm I'm and I'll I'll +list at the uh at the beginning of the + + align:start position:0% +list at the uh at the beginning of the + + + align:start position:0% +list at the uh at the beginning of the +next like the these the different forier + + align:start position:0% +next like the these the different forier + + + align:start position:0% +next like the these the different forier +setups so this was the whole line setup + + align:start position:0% +setups so this was the whole line setup + + + align:start position:0% +setups so this was the whole line setup +and now I'm going to an interval + + align:start position:0% +and now I'm going to an interval + + + align:start position:0% +and now I'm going to an interval +periodic on an interval where 4A series + + align:start position:0% +periodic on an interval where 4A series + + + align:start position:0% +periodic on an interval where 4A series +operates okay uh our principle is going + + align:start position:0% +operates okay uh our principle is going + + + align:start position:0% +operates okay uh our principle is going +to be the + + align:start position:0% +to be the + + + align:start position:0% +to be the +same that we will now this interval will + + align:start position:0% +same that we will now this interval will + + + align:start position:0% +same that we will now this interval will +go from zero + + align:start position:0% +go from zero + + + align:start position:0% +go from zero +to or one to n 0 to n minus one would be + + align:start position:0% +to or one to n 0 to n minus one would be + + + align:start position:0% +to or one to n 0 to n minus one would be +uh + + align:start position:0% +uh + + + align:start position:0% +uh +tresan reveals himself as a + + align:start position:0% +tresan reveals himself as a + + + align:start position:0% +tresan reveals himself as a +mathematician by not choosing this + + align:start position:0% +mathematician by not choosing this + + + align:start position:0% +mathematician by not choosing this +County rule uh but uh so we now so n is + + align:start position:0% +County rule uh but uh so we now so n is + + + align:start position:0% +County rule uh but uh so we now so n is +going to be pretty large though so so + + align:start position:0% +going to be pretty large though so so + + + align:start position:0% +going to be pretty large though so so +what's our our differentiation + + align:start position:0% +what's our our differentiation + + + align:start position:0% +what's our our differentiation +formula is not going to be + + align:start position:0% + + + + align:start position:0% + +infinite where are we it's not going to + + align:start position:0% +infinite where are we it's not going to + + + align:start position:0% +infinite where are we it's not going to +be these infinite formulas anymore more + + align:start position:0% +be these infinite formulas anymore more + + + align:start position:0% +be these infinite formulas anymore more +but it will be quite long formulas it'll + + align:start position:0% +but it will be quite long formulas it'll + + + align:start position:0% +but it will be quite long formulas it'll +be formulas of length + + align:start position:0% +be formulas of length + + + align:start position:0% +be formulas of length +n and maybe I'll just write down what he + + align:start position:0% +n and maybe I'll just write down what he + + + align:start position:0% +n and maybe I'll just write down what he +get what he discovers just because it's + + align:start position:0% +get what he discovers just because it's + + + align:start position:0% +get what he discovers just because it's +just like curious to see what happens so + + align:start position:0% +just like curious to see what happens so + + + align:start position:0% +just like curious to see what happens so +you uh I'll I'll write them in just + + align:start position:0% +you uh I'll I'll write them in just + + + align:start position:0% +you uh I'll I'll write them in just +above the whole line + + align:start position:0% + + + + align:start position:0% + +case guess we I'm erasing this we never + + align:start position:0% +case guess we I'm erasing this we never + + + align:start position:0% +case guess we I'm erasing this we never +figured out or I I never figured out + + align:start position:0% +figured out or I I never figured out + + + align:start position:0% +figured out or I I never figured out +what that band was but it's within our + + align:start position:0% +what that band was but it's within our + + + align:start position:0% +what that band was but it's within our +powers okay so can I just just I hadn't + + align:start position:0% +powers okay so can I just just I hadn't + + + align:start position:0% +powers okay so can I just just I hadn't +learned this subject and so it was just + + align:start position:0% +learned this subject and so it was just + + + align:start position:0% +learned this subject and so it was just +naturally interesting to discover what + + align:start position:0% +naturally interesting to discover what + + + align:start position:0% +naturally interesting to discover what +these uh it's a one over two there's a + + align:start position:0% +these uh it's a one over two there's a + + + align:start position:0% +these uh it's a one over two there's a +two in that I can take + + align:start position:0% +two in that I can take + + + align:start position:0% +two in that I can take +out and I just want to look and and of + + align:start position:0% +out and I just want to look and and of + + + align:start position:0% +out and I just want to look and and of +course we're going to have a still a + + align:start position:0% +course we're going to have a still a + + + align:start position:0% +course we're going to have a still a +zero on that Center + + align:start position:0% +zero on that Center + + + align:start position:0% +zero on that Center +guy and it's it's periodic so uh um okay + + align:start position:0% +guy and it's it's periodic so uh um okay + + + align:start position:0% +guy and it's it's periodic so uh um okay +well it turns out to be a oh the H is + + align:start position:0% +well it turns out to be a oh the H is + + + align:start position:0% +well it turns out to be a oh the H is +not here it comes in + + align:start position:0% +not here it comes in + + + align:start position:0% +not here it comes in +this this H is one over + + align:start position:0% + + + + align:start position:0% + +n and uh n is affecting everything now + + align:start position:0% +n and uh n is affecting everything now + + + align:start position:0% +n and uh n is affecting everything now +so I can't expect H to just come out + + align:start position:0% +so I can't expect H to just come out + + + align:start position:0% +so I can't expect H to just come out +that way and what it turns out to be is + + align:start position:0% +that way and what it turns out to be is + + + align:start position:0% +that way and what it turns out to be is +a coent of H /2 and of course minus cent + + align:start position:0% +a coent of H /2 and of course minus cent + + + align:start position:0% +a coent of H /2 and of course minus cent +of h /2 and a minus cent of 2 h/ 2 and a + + align:start position:0% +of h /2 and a minus cent of 2 h/ 2 and a + + + align:start position:0% +of h /2 and a minus cent of 2 h/ 2 and a +plus that of course I won't I won't + + align:start position:0% +plus that of course I won't I won't + + + align:start position:0% +plus that of course I won't I won't +write it's anti-symmetric the next one + + align:start position:0% +write it's anti-symmetric the next one + + + align:start position:0% +write it's anti-symmetric the next one +would be plus cent of 3H over2 isn't + + align:start position:0% +would be plus cent of 3H over2 isn't + + + align:start position:0% +would be plus cent of 3H over2 isn't +that nice and so on and while I'm at it + + align:start position:0% +that nice and so on and while I'm at it + + + align:start position:0% +that nice and so on and while I'm at it +let me do the similar one for the second + + align:start position:0% +let me do the similar one for the second + + + align:start position:0% +let me do the similar one for the second +derivative uh that one well it'll have + + align:start position:0% +derivative uh that one well it'll have + + + align:start position:0% +derivative uh that one well it'll have +some messy expression in here to make + + align:start position:0% +some messy expression in here to make + + + align:start position:0% +some messy expression in here to make +the thing add to zero and it turns out + + align:start position:0% +the thing add to zero and it turns out + + + align:start position:0% +the thing add to zero and it turns out +to be it's symmetric of course now being + + align:start position:0% +to be it's symmetric of course now being + + + align:start position:0% +to be it's symmetric of course now being +the second derivative and it turns out + + align:start position:0% +the second derivative and it turns out + + + align:start position:0% +the second derivative and it turns out +to be cant + + align:start position:0% +to be cant + + + align:start position:0% +to be cant +squar of H + + align:start position:0% +squar of H + + + align:start position:0% +squar of H +over2 and symmetric and cosecant squar + + align:start position:0% +over2 and symmetric and cosecant squar + + + align:start position:0% +over2 and symmetric and cosecant squar +of 2 H over 2 and so forth symmetric so + + align:start position:0% +of 2 H over 2 and so forth symmetric so + + + align:start position:0% +of 2 H over 2 and so forth symmetric so +you got cosecant squar and + + align:start position:0% +you got cosecant squar and + + + align:start position:0% +you got cosecant squar and +coent in the uh in + + align:start position:0% +coent in the uh in + + + align:start position:0% +coent in the uh in +the in the + + align:start position:0% + + + + align:start position:0% + +formulas + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah ah then I better number again cuz + + align:start position:0% +yeah ah then I better number again cuz + + + align:start position:0% +yeah ah then I better number again cuz +he he says if there's one formula in + + align:start position:0% +he he says if there's one formula in + + + align:start position:0% +he he says if there's one formula in +this book to remember let me let me tell + + align:start position:0% +this book to remember let me let me tell + + + align:start position:0% +this book to remember let me let me tell +you the one he says remember this + + align:start position:0% +you the one he says remember this + + + align:start position:0% +you the one he says remember this +formula + + align:start position:0% +formula + + + align:start position:0% +formula +uh yeah it's quite + + align:start position:0% +uh yeah it's quite + + + align:start position:0% +uh yeah it's quite +memorable + + align:start position:0% +memorable + + + align:start position:0% +memorable +um pi over H is n + + align:start position:0% +um pi over H is n + + + align:start position:0% +um pi over H is n +/2 that's his he says remember that so I + + align:start position:0% +/2 that's his he says remember that so I + + + align:start position:0% +/2 that's his he says remember that so I +don't know how that helps but I'm sure + + align:start position:0% +don't know how that helps but I'm sure + + + align:start position:0% +don't know how that helps but I'm sure +it's + + align:start position:0% + + + + align:start position:0% + +relevant yeah so maybe it go goes from + + align:start position:0% +relevant yeah so maybe it go goes from + + + align:start position:0% +relevant yeah so maybe it go goes from +zero to n but maybe u u n is the same as + + align:start position:0% +zero to n but maybe u u n is the same as + + + align:start position:0% +zero to n but maybe u u n is the same as +U do you think where they're probably + + align:start position:0% +U do you think where they're probably + + + align:start position:0% +U do you think where they're probably +probably n yeah they're probably N in N + + align:start position:0% +probably n yeah they're probably N in N + + + align:start position:0% +probably n yeah they're probably N in N +independent guys and then un is the same + + align:start position:0% +independent guys and then un is the same + + + align:start position:0% +independent guys and then un is the same +as uo good good good yeah yeah you're + + align:start position:0% +as uo good good good yeah yeah you're + + + align:start position:0% +as uo good good good yeah yeah you're +totally right so un where so un n will + + align:start position:0% +totally right so un where so un n will + + + align:start position:0% +totally right so un where so un n will +be u in this periodic Cas okay and and + + align:start position:0% +be u in this periodic Cas okay and and + + + align:start position:0% +be u in this periodic Cas okay and and +then and then we have do you see what + + align:start position:0% +then and then we have do you see what + + + align:start position:0% +then and then we have do you see what +kind of what kind of a matrix are we + + align:start position:0% +kind of what kind of a matrix are we + + + align:start position:0% +kind of what kind of a matrix are we +going to what what would be our + + align:start position:0% +going to what what would be our + + + align:start position:0% +going to what what would be our +differentiation Matrix what what was our + + align:start position:0% +differentiation Matrix what what was our + + + align:start position:0% +differentiation Matrix what what was our +differentiation Matrix here yeah and our + + align:start position:0% +differentiation Matrix here yeah and our + + + align:start position:0% +differentiation Matrix here yeah and our +second differentiation oh well we've + + align:start position:0% +second differentiation oh well we've + + + align:start position:0% +second differentiation oh well we've +seen these matrices so so we + + align:start position:0% +seen these matrices so so we + + + align:start position:0% +seen these matrices so so we +certainly so what's the differentiation + + align:start position:0% +certainly so what's the differentiation + + + align:start position:0% +certainly so what's the differentiation +Matrix that I would that I would apply + + align:start position:0% +Matrix that I would that I would apply + + + align:start position:0% +Matrix that I would that I would apply +to the all the U list of U's there would + + align:start position:0% +to the all the U list of U's there would + + + align:start position:0% +to the all the U list of U's there would +be a 1 over + + align:start position:0% +be a 1 over + + + align:start position:0% +be a 1 over +2H and then there would be uh you know + + align:start position:0% +2H and then there would be uh you know + + + align:start position:0% +2H and then there would be uh you know +somehow + + align:start position:0% +somehow + + + align:start position:0% +somehow +a a one a zero and a minus one you + + align:start position:0% +a a one a zero and a minus one you + + + align:start position:0% +a a one a zero and a minus one you +right we we're good at that stuff and of + + align:start position:0% +right we we're good at that stuff and of + + + align:start position:0% +right we we're good at that stuff and of +course I don't have to say that in this + + align:start position:0% +course I don't have to say that in this + + + align:start position:0% +course I don't have to say that in this +one it would be a 1 minus 2 + + align:start position:0% +one it would be a 1 minus 2 + + + align:start position:0% +one it would be a 1 minus 2 +1 and if and now we're in the periodic + + align:start position:0% +1 and if and now we're in the periodic + + + align:start position:0% +1 and if and now we're in the periodic +case so what would happen in the + + align:start position:0% +case so what would happen in the + + + align:start position:0% +case so what would happen in the +periodic case + + align:start position:0% +periodic case + + + align:start position:0% +periodic case +here it would circle around this minus + + align:start position:0% +here it would circle around this minus + + + align:start position:0% +here it would circle around this minus +one would show up there and the one + + align:start position:0% +one would show up there and the one + + + align:start position:0% +one would show up there and the one +would show up there + + align:start position:0% +would show up there + + + align:start position:0% +would show up there +right a circul we'd have a circulent in + + align:start position:0% +right a circul we'd have a circulent in + + + align:start position:0% +right a circul we'd have a circulent in +the periodic case and we have the same + + align:start position:0% +the periodic case and we have the same + + + align:start position:0% +the periodic case and we have the same +circulent idea you know there's a + + align:start position:0% +circulent idea you know there's a + + + align:start position:0% +circulent idea you know there's a +typical row and the next row is shifted + + align:start position:0% +typical row and the next row is shifted + + + align:start position:0% +typical row and the next row is shifted +over because it's it's centered at J + + + align:start position:0% +over because it's it's centered at J + + + + align:start position:0% +over because it's it's centered at J + +one and the next row is shifted over but + + align:start position:0% +one and the next row is shifted over but + + + align:start position:0% +one and the next row is shifted over but +we loop around from period from + + align:start position:0% +we loop around from period from + + + align:start position:0% +we loop around from period from +periodicity so so we get a + + align:start position:0% +periodicity so so we get a + + + align:start position:0% +periodicity so so we get a +matrix with these + + align:start position:0% +matrix with these + + + align:start position:0% +matrix with these +diagonals and it's circulent looping + + align:start position:0% +diagonals and it's circulent looping + + + align:start position:0% +diagonals and it's circulent looping +around so it's n + + align:start position:0% +around so it's n + + + align:start position:0% +around so it's n +byn that's that's the differentiation + + align:start position:0% +byn that's that's the differentiation + + + align:start position:0% +byn that's that's the differentiation +Matrix you could say that's the Matrix + + align:start position:0% +Matrix you could say that's the Matrix + + + align:start position:0% +Matrix you could say that's the Matrix +that you would apply to the values to + + align:start position:0% +that you would apply to the values to + + + align:start position:0% +that you would apply to the values to +get values of the + + align:start position:0% +get values of the + + + align:start position:0% +get values of the +derivative that that's really what we're + + align:start position:0% +derivative that that's really what we're + + + align:start position:0% +derivative that that's really what we're +doing here we're constructing the + + align:start position:0% +doing here we're constructing the + + + align:start position:0% +doing here we're constructing the +differentiation Matrix the The Matrix + + align:start position:0% +differentiation Matrix the The Matrix + + + align:start position:0% +differentiation Matrix the The Matrix +that app that that you that you + + align:start position:0% +that app that that you that you + + + align:start position:0% +that app that that you that you +multiply by U1 U2 u3 Etc and get our + + align:start position:0% +multiply by U1 U2 u3 Etc and get our + + + align:start position:0% +multiply by U1 U2 u3 Etc and get our +here it is doing the job multiplying you + + align:start position:0% +here it is doing the job multiplying you + + + align:start position:0% +here it is doing the job multiplying you +1 U2 u3 so on and giving U1 Prime U2 + + align:start position:0% +1 U2 u3 so on and giving U1 Prime U2 + + + align:start position:0% +1 U2 u3 so on and giving U1 Prime U2 +prime u3 prime the derivative + + align:start position:0% +prime u3 prime the derivative + + + align:start position:0% +prime u3 prime the derivative +right so our Matrix is full that's the + + align:start position:0% +right so our Matrix is full that's the + + + align:start position:0% +right so our Matrix is full that's the +point Tri diagonal here Tri + + align:start position:0% +point Tri diagonal here Tri + + + align:start position:0% +point Tri diagonal here Tri +diagonal here pentad + + align:start position:0% +diagonal here pentad + + + align:start position:0% +diagonal here pentad +diagonal + + align:start position:0% +diagonal + + + align:start position:0% +diagonal +here and + + align:start position:0% +here and + + + align:start position:0% +here and +full here and here right it's a full + + align:start position:0% +full here and here right it's a full + + + align:start position:0% +full here and here right it's a full +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +so that's I guess what what + + align:start position:0% +so that's I guess what what + + + align:start position:0% +so that's I guess what what +orog that that's the essence of oro's + + align:start position:0% +orog that that's the essence of oro's + + + align:start position:0% +orog that that's the essence of oro's +proposal anybody really could have seen + + align:start position:0% +proposal anybody really could have seen + + + align:start position:0% +proposal anybody really could have seen +that + + align:start position:0% +that + + + align:start position:0% +that +hey + + align:start position:0% +hey + + + align:start position:0% +hey +um we can get infinite accuracy if we + + align:start position:0% +um we can get infinite accuracy if we + + + align:start position:0% +um we can get infinite accuracy if we +use infinitely many values right I + + align:start position:0% +use infinitely many values right I + + + align:start position:0% +use infinitely many values right I +that's not + + align:start position:0% +that's not + + + align:start position:0% +that's not +surprising but to say that you could + + align:start position:0% +surprising but to say that you could + + + align:start position:0% +surprising but to say that you could +actually work with the darn things + + align:start position:0% +actually work with the darn things + + + align:start position:0% +actually work with the darn things +that you could deal quite happily with + + align:start position:0% +that you could deal quite happily with + + + align:start position:0% +that you could deal quite happily with +these infinite very large and and + + align:start position:0% +these infinite very large and and + + + align:start position:0% +these infinite very large and and +totally full matrices is the whole + + align:start position:0% +totally full matrices is the whole + + + align:start position:0% +totally full matrices is the whole +point that that of course it isn't as + + align:start position:0% +point that that of course it isn't as + + + align:start position:0% +point that that of course it isn't as +simple as working with our tridiagonal + + align:start position:0% +simple as working with our tridiagonal + + + align:start position:0% +simple as working with our tridiagonal +matrices but the point is you can do it + + align:start position:0% +matrices but the point is you can do it + + + align:start position:0% +matrices but the point is you can do it +and and therefore the spectral methods + + align:start position:0% +and and therefore the spectral methods + + + align:start position:0% +and and therefore the spectral methods +have for problems that have got enough + + align:start position:0% +have for problems that have got enough + + + align:start position:0% +have for problems that have got enough +smoothness have uh become a really + + align:start position:0% +smoothness have uh become a really + + + align:start position:0% +smoothness have uh become a really +serious part of the of + + align:start position:0% + + + + align:start position:0% + +computations in real life that's right + + align:start position:0% +computations in real life that's right + + + align:start position:0% +computations in real life that's right +that's right maybe this guy I haven't + + align:start position:0% +that's right maybe this guy I haven't + + + align:start position:0% +that's right maybe this guy I haven't +figured it out but this is probably + + align:start position:0% +figured it out but this is probably + + + align:start position:0% +figured it out but this is probably +periodic is so I mean this this formula + + align:start position:0% +periodic is so I mean this this formula + + + align:start position:0% +periodic is so I mean this this formula +is suitably you know truncates itself so + + align:start position:0% +is suitably you know truncates itself so + + + align:start position:0% +is suitably you know truncates itself so +to + + align:start position:0% +to + + + align:start position:0% +to +speak swings around probably when I get + + align:start position:0% +speak swings around probably when I get + + + align:start position:0% +speak swings around probably when I get +to coent of you know when I've up this + + align:start position:0% +to coent of you know when I've up this + + + align:start position:0% +to coent of you know when I've up this +thing by pi I'm back to + + align:start position:0% + + + + align:start position:0% + +oh in the infinite line sure sure so + + align:start position:0% +oh in the infinite line sure sure so + + + align:start position:0% +oh in the infinite line sure sure so +when I did number one I was talking Blue + + align:start position:0% +when I did number one I was talking Blue + + + align:start position:0% +when I did number one I was talking Blue +Sky problem right now I'm + + align:start position:0% +Sky problem right now I'm + + + align:start position:0% +Sky problem right now I'm +talking cloudy Sky really but still + + align:start position:0% +talking cloudy Sky really but still + + + align:start position:0% +talking cloudy Sky really but still +periodic so that's still like I'm making + + align:start position:0% +periodic so that's still like I'm making + + + align:start position:0% +periodic so that's still like I'm making +life + + align:start position:0% +life + + + align:start position:0% +life +easy by saying okay periodic uh and and + + align:start position:0% +easy by saying okay periodic uh and and + + + align:start position:0% +easy by saying okay periodic uh and and +of + + align:start position:0% +of + + + align:start position:0% +of +course the idea would be use the f + + align:start position:0% +course the idea would be use the f + + + align:start position:0% +course the idea would be use the f +ft + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yes + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% +yes + + + align:start position:0% +yes +yes good point yeah what if I what if I + + align:start position:0% +yes good point yeah what if I what if I + + + align:start position:0% +yes good point yeah what if I what if I +used an nth order polom and compared it + + align:start position:0% +used an nth order polom and compared it + + + align:start position:0% +used an nth order polom and compared it +with this spectral method good good + + align:start position:0% +with this spectral method good good + + + align:start position:0% +with this spectral method good good +question and + + align:start position:0% +question and + + + align:start position:0% +question and +uh I guess I'm going to have to face + + align:start position:0% +uh I guess I'm going to have to face + + + align:start position:0% +uh I guess I'm going to have to face +that kind of question in the third case + + align:start position:0% +that kind of question in the third case + + + align:start position:0% +that kind of question in the third case +in the non-periodic case because I'm not + + align:start position:0% +in the non-periodic case because I'm not + + + align:start position:0% +in the non-periodic case because I'm not +I'm not really going to be entitled to + + align:start position:0% +I'm not really going to be entitled to + + + align:start position:0% +I'm not really going to be entitled to +do Fier stuff yeah so I'm ready I'm + + align:start position:0% +do Fier stuff yeah so I'm ready I'm + + + align:start position:0% +do Fier stuff yeah so I'm ready I'm +actually that that that your question is + + align:start position:0% +actually that that that your question is + + + align:start position:0% +actually that that that your question is +Right On + + align:start position:0% +Right On + + + align:start position:0% +Right On +Target particularly for this + + align:start position:0% +Target particularly for this + + + align:start position:0% +Target particularly for this +non-periodic case what if I fit so so + + align:start position:0% +non-periodic case what if I fit so so + + + align:start position:0% +non-periodic case what if I fit so so +your question would be what if I fit + + align:start position:0% +your question would be what if I fit + + + align:start position:0% +your question would be what if I fit +this thing by a polinomial of degree n + + align:start position:0% +this thing by a polinomial of degree n + + + align:start position:0% +this thing by a polinomial of degree n +okay can that that's just the right + + align:start position:0% +okay can that that's just the right + + + align:start position:0% +okay can that that's just the right +question so that's what we didn't do + + align:start position:0% +question so that's what we didn't do + + + align:start position:0% +question so that's what we didn't do +here right we didn't fit by a polinomial + + align:start position:0% +here right we didn't fit by a polinomial + + + align:start position:0% +here right we didn't fit by a polinomial +of degree n we fit by a band limited + + align:start position:0% +of degree n we fit by a band limited + + + align:start position:0% +of degree n we fit by a band limited +type guy periodic but b Periodic band + + align:start position:0% +type guy periodic but b Periodic band + + + align:start position:0% +type guy periodic but b Periodic band +limited and it gave us these numbers + + align:start position:0% +limited and it gave us these numbers + + + align:start position:0% +limited and it gave us these numbers +which are are winners in periodic + + align:start position:0% +which are are winners in periodic + + + align:start position:0% +which are are winners in periodic +problems if I use these this + + align:start position:0% +problems if I use these this + + + align:start position:0% +problems if I use these this +differentiation formula in periodic + + align:start position:0% +differentiation formula in periodic + + + align:start position:0% +differentiation formula in periodic +problems one I + + align:start position:0% +problems one I + + + align:start position:0% +problems one I +can I can live with it even though it's + + align:start position:0% +can I can live with it even though it's + + + align:start position:0% +can I can live with it even though it's +a full Matrix because the fft is is just + + align:start position:0% +a full Matrix because the fft is is just + + + align:start position:0% +a full Matrix because the fft is is just +happy to take matrices happy to work + + align:start position:0% +happy to take matrices happy to work + + + align:start position:0% +happy to take matrices happy to work +with a matrix like that + + align:start position:0% +with a matrix like that + + + align:start position:0% +with a matrix like that +now I got to go to the real to the the + + align:start position:0% +now I got to go to the real to the the + + + align:start position:0% +now I got to go to the real to the the +problem + + align:start position:0% +problem + + + align:start position:0% +problem +of + + align:start position:0% +of + + + align:start position:0% +of +non-periodic like our like our uh + + align:start position:0% +non-periodic like our like our uh + + + align:start position:0% +non-periodic like our like our uh +problem in lecture one so now I'm ready + + align:start position:0% +problem in lecture one so now I'm ready + + + align:start position:0% +problem in lecture one so now I'm ready +for part + + align:start position:0% +for part + + + align:start position:0% +for part +three nonp + + align:start position:0% +three nonp + + + align:start position:0% +three nonp +periodic n + + align:start position:0% +periodic n + + + align:start position:0% +periodic n +periodic boundary conditions for + + align:start position:0% +periodic boundary conditions for + + + align:start position:0% +periodic boundary conditions for +example U of 0 equal 0 and U of one + + align:start position:0% +example U of 0 equal 0 and U of one + + + align:start position:0% +example U of 0 equal 0 and U of one +equals z our our old + + align:start position:0% + + + + align:start position:0% + +friend what do we do + + align:start position:0% +friend what do we do + + + align:start position:0% +friend what do we do +now I could take that interval 01 I + + align:start position:0% +now I could take that interval 01 I + + + align:start position:0% +now I could take that interval 01 I +could chop it up into n equally spaced + + align:start position:0% +could chop it up into n equally spaced + + + align:start position:0% +could chop it up into n equally spaced +nodes I could fit by + + align:start position:0% +nodes I could fit by + + + align:start position:0% +nodes I could fit by +polinomial high degree I could create + + align:start position:0% +polinomial high degree I could create + + + align:start position:0% +polinomial high degree I could create +the difference for + + align:start position:0% +the difference for + + + align:start position:0% +the difference for +and it would be a + + align:start position:0% +and it would be a + + + align:start position:0% +and it would be a +disaster a total + + align:start position:0% +disaster a total + + + align:start position:0% +disaster a total +disaster and the reason is I started + + align:start position:0% +disaster and the reason is I started + + + align:start position:0% +disaster and the reason is I started +wrong I should never have taken equally + + align:start position:0% +wrong I should never have taken equally + + + align:start position:0% +wrong I should never have taken equally +spaced points if I'm going to do high + + align:start position:0% +spaced points if I'm going to do high + + + align:start position:0% +spaced points if I'm going to do high +deegree polom fitting so here's the this + + align:start position:0% +deegree polom fitting so here's the this + + + align:start position:0% +deegree polom fitting so here's the this +is the + + align:start position:0% +is the + + + align:start position:0% +is the +final + + align:start position:0% +final + + + align:start position:0% +final +message that if I have if I want to get + + align:start position:0% +message that if I have if I want to get + + + align:start position:0% +message that if I have if I want to get +this really high accuracy + + align:start position:0% +this really high accuracy + + + align:start position:0% +this really high accuracy +I better not use an equally spaced mesh + + align:start position:0% +I better not use an equally spaced mesh + + + align:start position:0% +I better not use an equally spaced mesh +if I'm on if I'm if I'm taking our our + + align:start position:0% +if I'm on if I'm if I'm taking our our + + + align:start position:0% +if I'm on if I'm if I'm taking our our +boundary value problem for a for a a rod + + align:start position:0% +boundary value problem for a for a a rod + + + align:start position:0% +boundary value problem for a for a a rod +second ordered simple second order + + align:start position:0% +second ordered simple second order + + + align:start position:0% +second ordered simple second order +differential equation from 0 to one well + + align:start position:0% +differential equation from 0 to one well + + + align:start position:0% +differential equation from 0 to one well +let me I should maybe turn it upside + + align:start position:0% +let me I should maybe turn it upside + + + align:start position:0% +let me I should maybe turn it upside +down and hang hang the rod for + + align:start position:0% +down and hang hang the rod for + + + align:start position:0% +down and hang hang the rod for +example uh or the elastic bar maybe I'll + + align:start position:0% +example uh or the elastic bar maybe I'll + + + align:start position:0% +example uh or the elastic bar maybe I'll +let it hang I'll have a theic l I zero + + align:start position:0% +let it hang I'll have a theic l I zero + + + align:start position:0% +let it hang I'll have a theic l I zero +value up here zero slope free end down + + align:start position:0% +value up here zero slope free end down + + + align:start position:0% +value up here zero slope free end down +here not periodic + + align:start position:0% +here not periodic + + + align:start position:0% +here not periodic +anyway and then the question is what are + + align:start position:0% +anyway and then the question is what are + + + align:start position:0% +anyway and then the question is what are +the right points to choose and maybe + + align:start position:0% +the right points to choose and maybe + + + align:start position:0% +the right points to choose and maybe +this is like it's it's the right ones + + align:start position:0% +this is like it's it's the right ones + + + align:start position:0% +this is like it's it's the right ones +are sufficiently memorable that that + + align:start position:0% +are sufficiently memorable that that + + + align:start position:0% +are sufficiently memorable that that +this is a + + align:start position:0% + + + + align:start position:0% + +good so the way we can remember the sync + + align:start position:0% +good so the way we can remember the sync + + + align:start position:0% +good so the way we can remember the sync +function for for equally SPAC points we + + align:start position:0% +function for for equally SPAC points we + + + align:start position:0% +function for for equally SPAC points we +got to remember what to do what what's a + + align:start position:0% +got to remember what to do what what's a + + + align:start position:0% +got to remember what to do what what's a +good spacing of points and here it + + align:start position:0% +good spacing of points and here it + + + align:start position:0% +good spacing of points and here it +is it's well let me draw the points and + + align:start position:0% +is it's well let me draw the points and + + + align:start position:0% +is it's well let me draw the points and +then we could figure out the formula + + align:start position:0% +then we could figure out the formula + + + align:start position:0% +then we could figure out the formula +imagine a + + align:start position:0% +imagine a + + + align:start position:0% +imagine a +circle take equally spaced points around + + align:start position:0% +circle take equally spaced points around + + + align:start position:0% +circle take equally spaced points around +the + + align:start position:0% + + + + align:start position:0% + +circle and project + + align:start position:0% +circle and project + + + align:start position:0% +circle and project +them onto the + + align:start position:0% + + + + align:start position:0% + +axis + + align:start position:0% + + + + align:start position:0% + +so they're cosiness right the these + + align:start position:0% +so they're cosiness right the these + + + align:start position:0% +so they're cosiness right the these +these the radius was one for all these + + align:start position:0% +these the radius was one for all these + + + align:start position:0% +these the radius was one for all these +points and we took the x component the + + align:start position:0% +points and we took the x component the + + + align:start position:0% +points and we took the x component the +projection on the x- axis so those + + align:start position:0% +projection on the x- axis so those + + + align:start position:0% +projection on the x- axis so those +values are cosiness that should I cheat + + align:start position:0% +values are cosiness that should I cheat + + + align:start position:0% +values are cosiness that should I cheat +and just be sure I'm expressing the + + align:start position:0% +and just be sure I'm expressing the + + + align:start position:0% +and just be sure I'm expressing the +right the cosine + + align:start position:0% +right the cosine + + + align:start position:0% +right the cosine +correctly these are the chbby CHF points + + align:start position:0% +correctly these are the chbby CHF points + + + align:start position:0% +correctly these are the chbby CHF points +so maybe I emphasize who who created + + align:start position:0% +so maybe I emphasize who who created + + + align:start position:0% +so maybe I emphasize who who created +these points and there are the the good + + align:start position:0% +these points and there are the the good + + + align:start position:0% +these points and there are the the good +points + + align:start position:0% + + + + align:start position:0% + +and math mathematical analysis has to + + align:start position:0% +and math mathematical analysis has to + + + align:start position:0% +and math mathematical analysis has to +explain why those points are good but + + align:start position:0% +explain why those points are good but + + + align:start position:0% +explain why those points are good but +they are they're they're way way better + + align:start position:0% +they are they're they're way way better + + + align:start position:0% +they are they're they're way way better +no comparison with u with um equally + + align:start position:0% +no comparison with u with um equally + + + align:start position:0% +no comparison with u with um equally +spaced points on non-periodic let's let + + align:start position:0% +spaced points on non-periodic let's let + + + align:start position:0% +spaced points on non-periodic let's let +me get to let me get to yeah if if you + + align:start position:0% +me get to let me get to yeah if if you + + + align:start position:0% +me get to let me get to yeah if if you +if you plot any + + align:start position:0% + + + + align:start position:0% + +graph I mean here I don't know if you + + align:start position:0% +graph I mean here I don't know if you + + + align:start position:0% +graph I mean here I don't know if you +can see this graph or if a camera can uh + + align:start position:0% +can see this graph or if a camera can uh + + + align:start position:0% +can see this graph or if a camera can uh +here is that you see how the chubby CHF + + align:start position:0% +here is that you see how the chubby CHF + + + align:start position:0% +here is that you see how the chubby CHF +points are of course you see them + + align:start position:0% +points are of course you see them + + + align:start position:0% +points are of course you see them +they're they're much they're bunched at + + align:start position:0% +they're they're much they're bunched at + + + align:start position:0% +they're they're much they're bunched at +the ends of the interval because it's + + align:start position:0% +the ends of the interval because it's + + + align:start position:0% +the ends of the interval because it's +the ends of the interval that where you + + align:start position:0% +the ends of the interval that where you + + + align:start position:0% +the ends of the interval that where you +got uh you know discontinuity the + + align:start position:0% +got uh you know discontinuity the + + + align:start position:0% +got uh you know discontinuity the +non-periodicity is is is killing you at + + align:start position:0% +non-periodicity is is is killing you at + + + align:start position:0% +non-periodicity is is is killing you at +that point but if you put the chubby + + align:start position:0% +that point but if you put the chubby + + + align:start position:0% +that point but if you put the chubby +Chev polinomial through those points + + align:start position:0% +Chev polinomial through those points + + + align:start position:0% +Chev polinomial through those points +they oscillate quite nicely they don't + + align:start position:0% +they oscillate quite nicely they don't + + + align:start position:0% +they oscillate quite nicely they don't +get out of hand if you take equally + + align:start position:0% +get out of hand if you take equally + + + align:start position:0% +get out of hand if you take equally +spaced points and fit with a polinomial + + align:start position:0% +spaced points and fit with a polinomial + + + align:start position:0% +spaced points and fit with a polinomial +it takes off at the end of the + + align:start position:0% +it takes off at the end of the + + + align:start position:0% +it takes off at the end of the +interval + + align:start position:0% +interval + + + align:start position:0% +interval +wildly and all any graph that you draw + + align:start position:0% +wildly and all any graph that you draw + + + align:start position:0% +wildly and all any graph that you draw +is is disaster and and any calculation + + align:start position:0% +is is disaster and and any calculation + + + align:start position:0% +is is disaster and and any calculation +you do is a disaster so uh so we see + + align:start position:0% +you do is a disaster so uh so we see + + + align:start position:0% +you do is a disaster so uh so we see +what those chibby CHF points are and + + align:start position:0% +what those chibby CHF points are and + + + align:start position:0% +what those chibby CHF points are and +then now finally me just write them down + + align:start position:0% +then now finally me just write them down + + + align:start position:0% +then now finally me just write them down +the cosine of j pi/ + + align:start position:0% +the cosine of j pi/ + + + align:start position:0% +the cosine of j pi/ +n these are the xjs that you should + + align:start position:0% +n these are the xjs that you should + + + align:start position:0% +n these are the xjs that you should +use uh + + align:start position:0% + + + + align:start position:0% + +for so so just to conclude this + + align:start position:0% +for so so just to conclude this + + + align:start position:0% +for so so just to conclude this +lecture + + align:start position:0% +lecture + + + align:start position:0% +lecture +without doing the analysis that says why + + align:start position:0% +without doing the analysis that says why + + + align:start position:0% +without doing the analysis that says why +those points are great maybe the graph + + align:start position:0% +those points are great maybe the graph + + + align:start position:0% +those points are great maybe the graph +helps to explain it that if I if I if I + + align:start position:0% +helps to explain it that if I if I if I + + + align:start position:0% +helps to explain it that if I if I if I +put polinomial if I if I put my my + + align:start position:0% +put polinomial if I if I put my my + + + align:start position:0% +put polinomial if I if I put my my +function P of + + align:start position:0% +function P of + + + align:start position:0% +function P of +X interpolating at those + + align:start position:0% +X interpolating at those + + + align:start position:0% +X interpolating at those +points then it stays reasonable as n + + align:start position:0% +points then it stays reasonable as n + + + align:start position:0% +points then it stays reasonable as n +gets large it doesn't blow Sky High and + + align:start position:0% +gets large it doesn't blow Sky High and + + + align:start position:0% +gets large it doesn't blow Sky High and +of course then I take the derivative and + + align:start position:0% +of course then I take the derivative and + + + align:start position:0% +of course then I take the derivative and +the second derivative so I'm doing chbby + + align:start position:0% +the second derivative so I'm doing chbby + + + align:start position:0% +the second derivative so I'm doing chbby +the I'm doing the chbby CHF spectral + + align:start position:0% +the I'm doing the chbby CHF spectral + + + align:start position:0% +the I'm doing the chbby CHF spectral +method and that's the right set of + + align:start position:0% +method and that's the right set of + + + align:start position:0% +method and that's the right set of +points for interpolation and for + + align:start position:0% +points for interpolation and for + + + align:start position:0% +points for interpolation and for +calculations on uh on a on a finite + + align:start position:0% +calculations on uh on a on a finite + + + align:start position:0% +calculations on uh on a on a finite +interval with uh without + + align:start position:0% +interval with uh without + + + align:start position:0% +interval with uh without +periodicity + + align:start position:0% +periodicity + + + align:start position:0% +periodicity +um so I I left here uh the + + align:start position:0% +um so I I left here uh the + + + align:start position:0% +um so I I left here uh the +applications I mean the + + align:start position:0% +applications I mean the + + + align:start position:0% +applications I mean the +applications are now straightforward + + align:start position:0% +applications are now straightforward + + + align:start position:0% +applications are now straightforward +once we know how to + + align:start position:0% +once we know how to + + + align:start position:0% +once we know how to +replace um a derivative by a discrete + + align:start position:0% +replace um a derivative by a discrete + + + align:start position:0% +replace um a derivative by a discrete +one that's what we that gives us the + + align:start position:0% +one that's what we that gives us the + + + align:start position:0% +one that's what we that gives us the +discrete equation that we work with if + + align:start position:0% +discrete equation that we work with if + + + align:start position:0% +discrete equation that we work with if +it's an igen value problem well so what + + align:start position:0% +it's an igen value problem well so what + + + align:start position:0% +it's an igen value problem well so what +are what are some examples here of let + + align:start position:0% +are what are some examples here of let + + + align:start position:0% +are what are some examples here of let +me we haven't spoken about an igen value + + align:start position:0% +me we haven't spoken about an igen value + + + align:start position:0% +me we haven't spoken about an igen value +problem before what would be a typical + + align:start position:0% +problem before what would be a typical + + + align:start position:0% +problem before what would be a typical +igen value problem we the I value + + align:start position:0% +igen value problem we the I value + + + align:start position:0% +igen value problem we the I value +problem uh uble + + align:start position:0% +problem uh uble + + + align:start position:0% +problem uh uble +prime uble prime equal Lambda + + align:start position:0% +prime uble prime equal Lambda + + + align:start position:0% +prime uble prime equal Lambda +U on an + + align:start position:0% +U on an + + + align:start position:0% +U on an +interval 0 to + + align:start position:0% +interval 0 to + + + align:start position:0% +interval 0 to +one well of course we could solve we + + align:start position:0% +one well of course we could solve we + + + align:start position:0% +one well of course we could solve we +could find those igen values + + align:start position:0% +could find those igen values + + + align:start position:0% +could find those igen values +exactly and then we could find + + align:start position:0% +exactly and then we could find + + + align:start position:0% +exactly and then we could find +them by CHF spectral methods and we + + align:start position:0% +them by CHF spectral methods and we + + + align:start position:0% +them by CHF spectral methods and we +could see are they any good and the + + align:start position:0% +could see are they any good and the + + + align:start position:0% +could see are they any good and the +answer would be yes they are + + align:start position:0% +answer would be yes they are + + + align:start position:0% +answer would be yes they are +good at least the igen values are good + + align:start position:0% +good at least the igen values are good + + + align:start position:0% +good at least the igen values are good +until you get up to + + align:start position:0% +until you get up to + + + align:start position:0% +until you get up to +a igen value which Al where the igen + + align:start position:0% +a igen value which Al where the igen + + + align:start position:0% +a igen value which Al where the igen +vector oscillates so fast that that your + + align:start position:0% +vector oscillates so fast that that your + + + align:start position:0% +vector oscillates so fast that that your +mesh can't see + + align:start position:0% +mesh can't see + + + align:start position:0% +mesh can't see +it so the answer is good and then uh + + align:start position:0% +it so the answer is good and then uh + + + align:start position:0% +it so the answer is good and then uh +what are other ones let's see I think + + align:start position:0% +what are other ones let's see I think + + + align:start position:0% +what are other ones let's see I think +the a the harmonic oscillator is that is + + align:start position:0% +the a the harmonic oscillator is that is + + + align:start position:0% +the a the harmonic oscillator is that is +that maybe satisfy that + + align:start position:0% +that maybe satisfy that + + + align:start position:0% +that maybe satisfy that +equation uh so that's a less trivial + + align:start position:0% +equation uh so that's a less trivial + + + align:start position:0% +equation uh so that's a less trivial +example than this one but a very famous + + align:start position:0% +example than this one but a very famous + + + align:start position:0% +example than this one but a very famous +and important one igen values are great + + align:start position:0% +and important one igen values are great + + + align:start position:0% +and important one igen values are great +using chbby CHF + + align:start position:0% +using chbby CHF + + + align:start position:0% +using chbby CHF +points and replacing the second + + align:start position:0% +points and replacing the second + + + align:start position:0% +points and replacing the second +derivative + + align:start position:0% +derivative + + + align:start position:0% +derivative +by the second difference Matrix yeah + + align:start position:0% +by the second difference Matrix yeah + + + align:start position:0% +by the second difference Matrix yeah +it's and these mat lab calculations just + + align:start position:0% +it's and these mat lab calculations just + + + align:start position:0% +it's and these mat lab calculations just +bring it all out and let me close by by + + align:start position:0% +bring it all out and let me close by by + + + align:start position:0% +bring it all out and let me close by by +referring to oro's + + align:start position:0% +referring to oro's + + + align:start position:0% +referring to oro's +original uh + + align:start position:0% +original uh + + + align:start position:0% +original uh +result which uh brought the brought this + + align:start position:0% +result which uh brought the brought this + + + align:start position:0% +result which uh brought the brought this +whole subject + + align:start position:0% +whole subject + + + align:start position:0% +whole subject +alive this was 1971 interesting H + + align:start position:0% + + + + align:start position:0% + +1971 he was Computing the instability of + + align:start position:0% +1971 he was Computing the instability of + + + align:start position:0% +1971 he was Computing the instability of +plain fluid + + align:start position:0% +plain fluid + + + align:start position:0% +plain fluid +flow P flow special simple + + align:start position:0% +flow P flow special simple + + + align:start position:0% +flow P flow special simple +flow and the question was what's the + + align:start position:0% +flow and the question was what's the + + + align:start position:0% +flow and the question was what's the +critical Reynolds + + align:start position:0% +critical Reynolds + + + align:start position:0% +critical Reynolds +number right between + + align:start position:0% +number right between + + + align:start position:0% +number right between +laminar I'm not an expert and you may + + align:start position:0% +laminar I'm not an expert and you may + + + align:start position:0% +laminar I'm not an expert and you may +not be or may not all be between laminar + + align:start position:0% +not be or may not all be between laminar + + + align:start position:0% +not be or may not all be between laminar +smooth flow and turbulence and the + + align:start position:0% +smooth flow and turbulence and the + + + align:start position:0% +smooth flow and turbulence and the +question is when does some operator of + + align:start position:0% +question is when does some operator of + + + align:start position:0% +question is when does some operator of +course the equation is nonlinear here so + + align:start position:0% +course the equation is nonlinear here so + + + align:start position:0% +course the equation is nonlinear here so +it'll be the + + align:start position:0% +it'll be the + + + align:start position:0% +it'll be the +linearization when does an igen + + align:start position:0% +linearization when does an igen + + + align:start position:0% +linearization when does an igen +value Go off into the in unstable half + + align:start position:0% +value Go off into the in unstable half + + + align:start position:0% +value Go off into the in unstable half +plane and he computed that the critical + + align:start position:0% +plane and he computed that the critical + + + align:start position:0% +plane and he computed that the critical +Reynolds number was r equal + + align:start position:0% +Reynolds number was r equal + + + align:start position:0% +Reynolds number was r equal + + align:start position:0% + + + + align:start position:0% + +2.22 okay that was the reyolds + + align:start position:0% +2.22 okay that was the reyolds + + + align:start position:0% +2.22 okay that was the reyolds +number and uh such uh accuracy had never + + align:start position:0% +number and uh such uh accuracy had never + + + align:start position:0% +number and uh such uh accuracy had never +been + + align:start position:0% +been + + + align:start position:0% +been +seen and uh brought this whole subject + + align:start position:0% +seen and uh brought this whole subject + + + align:start position:0% +seen and uh brought this whole subject +to + + align:start position:0% +to + + + align:start position:0% +to +life uh so that that's that's the kind + + align:start position:0% +life uh so that that's that's the kind + + + align:start position:0% +life uh so that that's that's the kind +of thing that real science can be done + + align:start position:0% +of thing that real science can be done + + + align:start position:0% +of thing that real science can be done +numerically when + + align:start position:0% +numerically when + + + align:start position:0% +numerically when +uh when you have a method as accurate as + + align:start position:0% +uh when you have a method as accurate as + + + align:start position:0% +uh when you have a method as accurate as +this I only have to add one more point + + align:start position:0% +this I only have to add one more point + + + align:start position:0% +this I only have to add one more point +before ending this + + align:start position:0% +before ending this + + + align:start position:0% +before ending this +lecture that the Matrix involved in + + align:start position:0% +lecture that the Matrix involved in + + + align:start position:0% +lecture that the Matrix involved in +this um example are not + + align:start position:0% +this um example are not + + + align:start position:0% +this um example are not +symmetric and Tran's whole work over the + + align:start position:0% +symmetric and Tran's whole work over the + + + align:start position:0% +symmetric and Tran's whole work over the +last 10 years or more has been to say if + + align:start position:0% +last 10 years or more has been to say if + + + align:start position:0% +last 10 years or more has been to say if +a matrix isn't symmetric its igen values + + align:start position:0% +a matrix isn't symmetric its igen values + + + align:start position:0% +a matrix isn't symmetric its igen values +are not the whole + + align:start position:0% +are not the whole + + + align:start position:0% +are not the whole +story so + + align:start position:0% +story so + + + align:start position:0% +story so +that you see that I'm hesitating to end + + align:start position:0% +that you see that I'm hesitating to end + + + align:start position:0% +that you see that I'm hesitating to end +a + + align:start position:0% +a + + + align:start position:0% +a +lecture which I owe to Tran's + + align:start position:0% +lecture which I owe to Tran's + + + align:start position:0% +lecture which I owe to Tran's +book without commenting that the this + + align:start position:0% +book without commenting that the this + + + align:start position:0% +book without commenting that the this +igen value critical igen value the + + align:start position:0% +igen value critical igen value the + + + align:start position:0% +igen value critical igen value the +critical value where an Igan value + + align:start position:0% +critical value where an Igan value + + + align:start position:0% +critical value where an Igan value +becomes + + align:start position:0% +becomes + + + align:start position:0% +becomes +unstable isn't the last word in a + + align:start position:0% +unstable isn't the last word in a + + + align:start position:0% +unstable isn't the last word in a +nonsymmetric + + align:start position:0% +nonsymmetric + + + align:start position:0% +nonsymmetric +problem um it's not just the igen values + + align:start position:0% +problem um it's not just the igen values + + + align:start position:0% +problem um it's not just the igen values +that matter uh the the um um the igen + + align:start position:0% +that matter uh the the um um the igen + + + align:start position:0% +that matter uh the the um um the igen +vectors play play role the the the the + + align:start position:0% +vectors play play role the the the the + + + align:start position:0% +vectors play play role the the the the +same the + + align:start position:0% +same the + + + align:start position:0% +same the +SVD comes in instead of just the the the + + align:start position:0% +SVD comes in instead of just the the the + + + align:start position:0% +SVD comes in instead of just the the the +igen vector + + align:start position:0% +igen vector + + + align:start position:0% +igen vector +decomposition igen vectors can run into + + align:start position:0% +decomposition igen vectors can run into + + + align:start position:0% +decomposition igen vectors can run into +each + + align:start position:0% +each + + + align:start position:0% +each +other uh and uh so the igen values don't + + align:start position:0% +other uh and uh so the igen values don't + + + align:start position:0% +other uh and uh so the igen values don't +tell you everything you have to know + + align:start position:0% +tell you everything you have to know + + + align:start position:0% +tell you everything you have to know +that the the conditioning of the igen + + align:start position:0% +that the the conditioning of the igen + + + align:start position:0% +that the the conditioning of the igen +vectors becomes all important anyway so + + align:start position:0% +vectors becomes all important anyway so + + + align:start position:0% +vectors becomes all important anyway so +Tans developed this uh theory of pseudo + + align:start position:0% + + + + align:start position:0% + +values to deal with the non symmetric or + + align:start position:0% +values to deal with the non symmetric or + + + align:start position:0% +values to deal with the non symmetric or +non-normal + + align:start position:0% +non-normal + + + align:start position:0% +non-normal +nonorthogonal when the Ian vectors when + + align:start position:0% +nonorthogonal when the Ian vectors when + + + align:start position:0% +nonorthogonal when the Ian vectors when +the igen vectors are not orthogonal then + + align:start position:0% +the igen vectors are not orthogonal then + + + align:start position:0% +the igen vectors are not orthogonal then +this this + + align:start position:0% +this this + + + align:start position:0% +this this +uh different approach + + align:start position:0% +uh different approach + + + align:start position:0% +uh different approach +um for for the people that are that are + + align:start position:0% +um for for the people that are that are + + + align:start position:0% +um for for the people that are that are +uh Believers in it promote and and and + + align:start position:0% +uh Believers in it promote and and and + + + align:start position:0% +uh Believers in it promote and and and +and promote develop the theory uh comes + + align:start position:0% +and promote develop the theory uh comes + + + align:start position:0% +and promote develop the theory uh comes +into its + + align:start position:0% +into its + + + align:start position:0% +into its +own okay is that uh that's pausing time + + align:start position:0% +own okay is that uh that's pausing time + + + align:start position:0% +own okay is that uh that's pausing time +certainly um you see that we use some of + + align:start position:0% +certainly um you see that we use some of + + + align:start position:0% +certainly um you see that we use some of +the ideas associated with 4A + + align:start position:0% +the ideas associated with 4A + + + align:start position:0% +the ideas associated with 4A +analysis that we ended up in this + + align:start position:0% +analysis that we ended up in this + + + align:start position:0% +analysis that we ended up in this +discussion of + + align:start position:0% +discussion of + + + align:start position:0% +discussion of +smoothness on about for analysis and now + + align:start position:0% +smoothness on about for analysis and now + + + align:start position:0% +smoothness on about for analysis and now +my second lecture this afternoon will + + align:start position:0% +my second lecture this afternoon will + + + align:start position:0% +my second lecture this afternoon will +will really focus on the the uh on what + + align:start position:0% +will really focus on the the uh on what + + + align:start position:0% +will really focus on the the uh on what +I think are the most useful tools that + + align:start position:0% +I think are the most useful tools that + + + align:start position:0% +I think are the most useful tools that +free analysis gives us so I I'll go from + + align:start position:0% +free analysis gives us so I I'll go from + + + align:start position:0% +free analysis gives us so I I'll go from +differential equations to to uh to the + + align:start position:0% +differential equations to to uh to the + + + align:start position:0% +differential equations to to uh to the +connections between U of + + align:start position:0% +connections between U of + + + align:start position:0% +connections between U of +X and U hat of + + align:start position:0% +X and U hat of + + + align:start position:0% +X and U hat of +K to other connections between you you + + align:start position:0% +K to other connections between you you + + + align:start position:0% +K to other connections between you you +you had of K and U ofx in the in the + + align:start position:0% +you had of K and U ofx in the in the + + + align:start position:0% +you had of K and U ofx in the in the +second lecture this afternoon so some + + align:start position:0% +second lecture this afternoon so some + + + align:start position:0% +second lecture this afternoon so some +some of that will be familiar it's it's + + align:start position:0% +some of that will be familiar it's it's + + + align:start position:0% +some of that will be familiar it's it's +for Theory and I'll try to pick out uh + + align:start position:0% +for Theory and I'll try to pick out uh + + + align:start position:0% +for Theory and I'll try to pick out uh +uh points that are really key for the + + align:start position:0% +uh points that are really key for the + + + align:start position:0% +uh points that are really key for the +applications okay so that's end of + + align:start position:0% +applications okay so that's end of + + + align:start position:0% +applications okay so that's end of +lecture 21 and 22 at at uh + + align:start position:0% +lecture 21 and 22 at at uh + + + align:start position:0% +lecture 21 and 22 at at uh +3:30 \ No newline at end of file diff --git a/3FVlVP5MKV4.txt b/3FVlVP5MKV4.txt new file mode 100644 index 0000000000000000000000000000000000000000..e6dd5970c77e893533ab7b9651df2e0ef80ccd07 --- /dev/null +++ b/3FVlVP5MKV4.txt @@ -0,0 +1,10552 @@ +align:start position:0% + +the following content is provided by mit + + align:start position:0% +the following content is provided by mit + + + align:start position:0% +the following content is provided by mit +open courseware under a creative commons + + align:start position:0% +open courseware under a creative commons + + + align:start position:0% +open courseware under a creative commons +license + + align:start position:0% +license + + + align:start position:0% +license +additional information about our license + + align:start position:0% +additional information about our license + + + align:start position:0% +additional information about our license +and mit open courseware in general is + + align:start position:0% +and mit open courseware in general is + + + align:start position:0% +and mit open courseware in general is +available at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay welcome back + + align:start position:0% +okay welcome back + + + align:start position:0% +okay welcome back +we're going to uh + + align:start position:0% +we're going to uh + + + align:start position:0% +we're going to uh +go through a very specific example of + + align:start position:0% +go through a very specific example of + + + align:start position:0% +go through a very specific example of +association studying illustrating this + + align:start position:0% +association studying illustrating this + + + align:start position:0% +association studying illustrating this +extremely important statistic the + + align:start position:0% +extremely important statistic the + + + align:start position:0% +extremely important statistic the +chi-squared statistic + + align:start position:0% +chi-squared statistic + + + align:start position:0% +chi-squared statistic +in the simplest case + + align:start position:0% +in the simplest case + + + align:start position:0% +in the simplest case +that simple case will be a single + + align:start position:0% +that simple case will be a single + + + align:start position:0% +that simple case will be a single +allele combination + + align:start position:0% +allele combination + + + align:start position:0% +allele combination +uh + + align:start position:0% +uh + + + align:start position:0% +uh +two alleles uh and two possible uh + + align:start position:0% +two alleles uh and two possible uh + + + align:start position:0% +two alleles uh and two possible uh +phenotypic outcomes + + align:start position:0% +phenotypic outcomes + + + align:start position:0% +phenotypic outcomes +hiv resistance and hiv uh non-resistance + + align:start position:0% +hiv resistance and hiv uh non-resistance + + + align:start position:0% +hiv resistance and hiv uh non-resistance +so to set up this association study + + align:start position:0% +so to set up this association study + + + align:start position:0% +so to set up this association study +which would be you know computational + + align:start position:0% +which would be you know computational + + + align:start position:0% +which would be you know computational +let's talk a little bit about the + + align:start position:0% +let's talk a little bit about the + + + align:start position:0% +let's talk a little bit about the +biology here we have + + align:start position:0% +biology here we have + + + align:start position:0% +biology here we have +uh + + align:start position:0% + + + + align:start position:0% + +all viruses need to get into your cells + + align:start position:0% +all viruses need to get into your cells + + + align:start position:0% +all viruses need to get into your cells +somehow + + align:start position:0% +somehow + + + align:start position:0% +somehow +hiv + + align:start position:0% +hiv + + + align:start position:0% +hiv +has a number of proteins to which it + + align:start position:0% +has a number of proteins to which it + + + align:start position:0% +has a number of proteins to which it +binds on the surface of your cell these + + align:start position:0% +binds on the surface of your cell these + + + align:start position:0% +binds on the surface of your cell these +proteins + + align:start position:0% +proteins + + + align:start position:0% +proteins +are not there not designed to bind hiv + + align:start position:0% +are not there not designed to bind hiv + + + align:start position:0% +are not there not designed to bind hiv +they do something else this is in a + + align:start position:0% +they do something else this is in a + + + align:start position:0% +they do something else this is in a +family of chemokine receptors is + + align:start position:0% +family of chemokine receptors is + + + align:start position:0% +family of chemokine receptors is +involved in intracellular signaling and + + align:start position:0% +involved in intracellular signaling and + + + align:start position:0% +involved in intracellular signaling and +so it's a receptor normally for these uh + + align:start position:0% +so it's a receptor normally for these uh + + + align:start position:0% +so it's a receptor normally for these uh +chemokines + + align:start position:0% +chemokines + + + align:start position:0% +chemokines +but it is also receptor for the for the + + align:start position:0% +but it is also receptor for the for the + + + align:start position:0% +but it is also receptor for the for the +virus + + align:start position:0% +virus + + + align:start position:0% +virus +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +in the human population as we alluded to + + align:start position:0% +in the human population as we alluded to + + + align:start position:0% +in the human population as we alluded to +earlier there are two at least two + + align:start position:0% +earlier there are two at least two + + + align:start position:0% +earlier there are two at least two +alleles two common alleles one of them + + align:start position:0% +alleles two common alleles one of them + + + align:start position:0% +alleles two common alleles one of them +the top one capital ccr5 + + align:start position:0% +the top one capital ccr5 + + + align:start position:0% +the top one capital ccr5 +is have this long open reading frame and + + align:start position:0% +is have this long open reading frame and + + + align:start position:0% +is have this long open reading frame and +this you could translate + + align:start position:0% +this you could translate + + + align:start position:0% +this you could translate +by your perl script that you wrote for + + align:start position:0% +by your perl script that you wrote for + + + align:start position:0% +by your perl script that you wrote for +the problem set and that's the dna + + align:start position:0% +the problem set and that's the dna + + + align:start position:0% +the problem set and that's the dna +sequence is in the middle here + + align:start position:0% +sequence is in the middle here + + + align:start position:0% +sequence is in the middle here +and the protein sequence derived from it + + align:start position:0% +and the protein sequence derived from it + + + align:start position:0% +and the protein sequence derived from it +is on the top + + align:start position:0% +is on the top + + + align:start position:0% +is on the top +strand and that's the capital ccr five + + align:start position:0% +strand and that's the capital ccr five + + + align:start position:0% +strand and that's the capital ccr five +and the little delta or deletion ccr5 is + + align:start position:0% +and the little delta or deletion ccr5 is + + + align:start position:0% +and the little delta or deletion ccr5 is +below it you've locked out 32 base pairs + + align:start position:0% +below it you've locked out 32 base pairs + + + align:start position:0% +below it you've locked out 32 base pairs +which is not an integral multiple of + + align:start position:0% +which is not an integral multiple of + + + align:start position:0% +which is not an integral multiple of +three and so as you know from last + + align:start position:0% +three and so as you know from last + + + align:start position:0% +three and so as you know from last +lecture + + align:start position:0% +lecture + + + align:start position:0% +lecture +that means it's going to be a different + + align:start position:0% +that means it's going to be a different + + + align:start position:0% +that means it's going to be a different +genetic code not only it every point + + align:start position:0% +genetic code not only it every point + + + align:start position:0% +genetic code not only it every point +downstream this can be frame shifted as + + align:start position:0% +downstream this can be frame shifted as + + + align:start position:0% +downstream this can be frame shifted as +you get a whole new set of amino acids + + align:start position:0% +you get a whole new set of amino acids + + + align:start position:0% +you get a whole new set of amino acids +for the entire for the entirety of + + align:start position:0% +for the entire for the entirety of + + + align:start position:0% +for the entire for the entirety of +the rest of the carboxy terminus + + align:start position:0% +the rest of the carboxy terminus + + + align:start position:0% +the rest of the carboxy terminus +so this in black here so if you're + + align:start position:0% +so this in black here so if you're + + + align:start position:0% +so this in black here so if you're +showing here in the single letter code a + + align:start position:0% +showing here in the single letter code a + + + align:start position:0% +showing here in the single letter code a +somewhat realistic folding of the + + align:start position:0% +somewhat realistic folding of the + + + align:start position:0% +somewhat realistic folding of the +schematic folding of the protein showing + + align:start position:0% +schematic folding of the protein showing + + + align:start position:0% +schematic folding of the protein showing +here disulfide between two cysteines you + + align:start position:0% +here disulfide between two cysteines you + + + align:start position:0% +here disulfide between two cysteines you +know transmembrane + + align:start position:0% +know transmembrane + + + align:start position:0% +know transmembrane +reason we have these hydrophobic uh + + align:start position:0% +reason we have these hydrophobic uh + + + align:start position:0% +reason we have these hydrophobic uh +alpha helices and finally in the black + + align:start position:0% +alpha helices and finally in the black + + + align:start position:0% +alpha helices and finally in the black +amino acids at the c-terminus that the + + align:start position:0% +amino acids at the c-terminus that the + + + align:start position:0% +amino acids at the c-terminus that the +the end of the protein are all + + align:start position:0% +the end of the protein are all + + + align:start position:0% +the end of the protein are all +substituted in this deletion mutant + + align:start position:0% +substituted in this deletion mutant + + + align:start position:0% +substituted in this deletion mutant +now + + align:start position:0% +now + + + align:start position:0% +now +that is sufficient sufficient to cause + + align:start position:0% +that is sufficient sufficient to cause + + + align:start position:0% +that is sufficient sufficient to cause +resistance to the virus it probably has + + align:start position:0% +resistance to the virus it probably has + + + align:start position:0% +resistance to the virus it probably has +some effect on its ability to bind + + align:start position:0% +some effect on its ability to bind + + + align:start position:0% +some effect on its ability to bind +chemokines or react to them or in some + + align:start position:0% +chemokines or react to them or in some + + + align:start position:0% +chemokines or react to them or in some +other way and presumably this is not uh + + align:start position:0% +other way and presumably this is not uh + + + align:start position:0% +other way and presumably this is not uh +that there is some deleterious effect we + + align:start position:0% +that there is some deleterious effect we + + + align:start position:0% +that there is some deleterious effect we +do not know about but in any case we can + + align:start position:0% +do not know about but in any case we can + + + align:start position:0% +do not know about but in any case we can +assess this we can determine we can make + + align:start position:0% +assess this we can determine we can make + + + align:start position:0% +assess this we can determine we can make +a genetic assay for this and we can look + + align:start position:0% +a genetic assay for this and we can look + + + align:start position:0% +a genetic assay for this and we can look +in uh human populations + + align:start position:0% +in uh human populations + + + align:start position:0% +in uh human populations +uh for the resistance to hiv and for the + + align:start position:0% +uh for the resistance to hiv and for the + + + align:start position:0% +uh for the resistance to hiv and for the +presence of + + align:start position:0% +presence of + + + align:start position:0% +presence of +either two alleles of uh + + align:start position:0% +either two alleles of uh + + + align:start position:0% +either two alleles of uh +the resistance or two alleles of the + + align:start position:0% +the resistance or two alleles of the + + + align:start position:0% +the resistance or two alleles of the +susceptible + + align:start position:0% +susceptible + + + align:start position:0% +susceptible +uh now i'm kind of biasing you here in + + align:start position:0% +uh now i'm kind of biasing you here in + + + align:start position:0% +uh now i'm kind of biasing you here in +this we haven't done the association + + align:start position:0% +this we haven't done the association + + + align:start position:0% +this we haven't done the association +study i really shouldn't be referring to + + align:start position:0% +study i really shouldn't be referring to + + + align:start position:0% +study i really shouldn't be referring to +it as resistant or not but it helps i + + align:start position:0% +it as resistant or not but it helps i + + + align:start position:0% +it as resistant or not but it helps i +think it helps you visualize it uh we'll + + align:start position:0% +think it helps you visualize it uh we'll + + + align:start position:0% +think it helps you visualize it uh we'll +be rigorous enough in the next slide so + + align:start position:0% +be rigorous enough in the next slide so + + + align:start position:0% +be rigorous enough in the next slide so +here is if you if you will the the big + + align:start position:0% +here is if you if you will the the big + + + align:start position:0% +here is if you if you will the the big +allele right it's it ha it's the + + align:start position:0% +allele right it's it ha it's the + + + align:start position:0% +allele right it's it ha it's the +original if it's the non-deleted allele + + align:start position:0% +original if it's the non-deleted allele + + + align:start position:0% +original if it's the non-deleted allele +so when you pcr do a pcr assay where + + align:start position:0% +so when you pcr do a pcr assay where + + + align:start position:0% +so when you pcr do a pcr assay where +you're amplifying with two primers + + align:start position:0% +you're amplifying with two primers + + + align:start position:0% +you're amplifying with two primers +across the region that could be deleted + + align:start position:0% +across the region that could be deleted + + + align:start position:0% +across the region that could be deleted +or not + + align:start position:0% +or not + + + align:start position:0% +or not +you'll tend to get a large amplification + + align:start position:0% +you'll tend to get a large amplification + + + align:start position:0% +you'll tend to get a large amplification +product you prime synthesis + + align:start position:0% +product you prime synthesis + + + align:start position:0% +product you prime synthesis +until you get + + align:start position:0% +until you get + + + align:start position:0% +until you get +something which is 403 base pairs and + + align:start position:0% +something which is 403 base pairs and + + + align:start position:0% +something which is 403 base pairs and +there's enough of it you can display it + + align:start position:0% +there's enough of it you can display it + + + align:start position:0% +there's enough of it you can display it +on electrophoretic gel and it migrates + + align:start position:0% +on electrophoretic gel and it migrates + + + align:start position:0% +on electrophoretic gel and it migrates +slowly because it's large + + align:start position:0% +slowly because it's large + + + align:start position:0% +slowly because it's large +the + + align:start position:0% +the + + + align:start position:0% +the +if you have a homozygote for the + + align:start position:0% +if you have a homozygote for the + + + align:start position:0% +if you have a homozygote for the +deletion allele we'll not call it the + + align:start position:0% +deletion allele we'll not call it the + + + align:start position:0% +deletion allele we'll not call it the +hiv resistance allele just yet + + align:start position:0% +hiv resistance allele just yet + + + align:start position:0% +hiv resistance allele just yet +um then you'll get a 371 base pair pcr + + align:start position:0% +um then you'll get a 371 base pair pcr + + + align:start position:0% +um then you'll get a 371 base pair pcr +product + + align:start position:0% +product + + + align:start position:0% +product +and if you have the heterozygote you'll + + align:start position:0% +and if you have the heterozygote you'll + + + align:start position:0% +and if you have the heterozygote you'll +get both the large and the small allele + + align:start position:0% +get both the large and the small allele + + + align:start position:0% +get both the large and the small allele +represented on this electrophoretic acid + + align:start position:0% +represented on this electrophoretic acid + + + align:start position:0% +represented on this electrophoretic acid +a very simple very robust dna pcr-based + + align:start position:0% +a very simple very robust dna pcr-based + + + align:start position:0% +a very simple very robust dna pcr-based +assay + + align:start position:0% + + + + align:start position:0% + +so now let's ask whether + + align:start position:0% +so now let's ask whether + + + align:start position:0% +so now let's ask whether +one allele or the other + + align:start position:0% +one allele or the other + + + align:start position:0% +one allele or the other +is more abundant in + + align:start position:0% +is more abundant in + + + align:start position:0% +is more abundant in +people which are observed to be + + align:start position:0% +people which are observed to be + + + align:start position:0% +people which are observed to be +sero-positive or serial negative + + align:start position:0% +sero-positive or serial negative + + + align:start position:0% +sero-positive or serial negative +sero-positive means that they have + + align:start position:0% +sero-positive means that they have + + + align:start position:0% +sero-positive means that they have +circulated antibodies in their + + align:start position:0% +circulated antibodies in their + + + align:start position:0% +circulated antibodies in their +serum + + align:start position:0% +serum + + + align:start position:0% +serum +which + + align:start position:0% +which + + + align:start position:0% +which +react positively to the hiv virus + + align:start position:0% +react positively to the hiv virus + + + align:start position:0% +react positively to the hiv virus +and so that's + + align:start position:0% +and so that's + + + align:start position:0% +and so that's +not necessarily but it's commonly + + align:start position:0% +not necessarily but it's commonly + + + align:start position:0% +not necessarily but it's commonly +associated with being heavily exposed to + + align:start position:0% +associated with being heavily exposed to + + + align:start position:0% +associated with being heavily exposed to +the hiv virus and therefore basically + + align:start position:0% +the hiv virus and therefore basically + + + align:start position:0% +the hiv virus and therefore basically +infected + + align:start position:0% +infected + + + align:start position:0% +infected +seronegative means that you um + + align:start position:0% +seronegative means that you um + + + align:start position:0% +seronegative means that you um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +are it's an indication that you're + + align:start position:0% +are it's an indication that you're + + + align:start position:0% +are it's an indication that you're +resistant now we could do this as a two + + align:start position:0% +resistant now we could do this as a two + + + align:start position:0% +resistant now we could do this as a two +by two matrix here of of alleles versus + + align:start position:0% +by two matrix here of of alleles versus + + + align:start position:0% +by two matrix here of of alleles versus +outcomes + + align:start position:0% +outcomes + + + align:start position:0% +outcomes +or we could do it as a three by two + + align:start position:0% +or we could do it as a three by two + + + align:start position:0% +or we could do it as a three by two +where we have genotypes versus outcomes + + align:start position:0% +where we have genotypes versus outcomes + + + align:start position:0% +where we have genotypes versus outcomes +the three genotypes are + + align:start position:0% +the three genotypes are + + + align:start position:0% +the three genotypes are +uh + + align:start position:0% +uh + + + align:start position:0% +uh +big big little little and big little + + align:start position:0% +big big little little and big little + + + align:start position:0% +big big little little and big little +heterozygote but let's just do it let's + + align:start position:0% +heterozygote but let's just do it let's + + + align:start position:0% +heterozygote but let's just do it let's +keep it simple in terms of alleles if + + align:start position:0% +keep it simple in terms of alleles if + + + align:start position:0% +keep it simple in terms of alleles if +there is a selective advance or that + + align:start position:0% +there is a selective advance or that + + + align:start position:0% +there is a selective advance or that +there's a uh + + align:start position:0% +there's a uh + + + align:start position:0% +there's a uh +a + + align:start position:0% +a + + + align:start position:0% +a +perceivable association between the + + align:start position:0% +perceivable association between the + + + align:start position:0% +perceivable association between the +serial po serial positive serial + + align:start position:0% +serial po serial positive serial + + + align:start position:0% +serial po serial positive serial +negative and the allele you should be + + align:start position:0% +negative and the allele you should be + + + align:start position:0% +negative and the allele you should be +able to see it in both the genotype or + + align:start position:0% +able to see it in both the genotype or + + + align:start position:0% +able to see it in both the genotype or +it's just the allele the allele is + + align:start position:0% +it's just the allele the allele is + + + align:start position:0% +it's just the allele the allele is +simpler it's a two by two matrix and so + + align:start position:0% +simpler it's a two by two matrix and so + + + align:start position:0% +simpler it's a two by two matrix and so +these are the data just these these four + + align:start position:0% +these are the data just these these four + + + align:start position:0% +these are the data just these these four +boxes here + + align:start position:0% +boxes here + + + align:start position:0% +boxes here +the the big allele + + align:start position:0% +the the big allele + + + align:start position:0% +the the big allele +uh is 12 78 observed negative and 1368 + + align:start position:0% +uh is 12 78 observed negative and 1368 + + + align:start position:0% +uh is 12 78 observed negative and 1368 +observed positive for a total of 26 46. + + align:start position:0% +observed positive for a total of 26 46. + + + align:start position:0% +observed positive for a total of 26 46. +you can see that there are fewer of + + align:start position:0% +you can see that there are fewer of + + + align:start position:0% +you can see that there are fewer of +total in the population surveyed of the + + align:start position:0% +total in the population surveyed of the + + + align:start position:0% +total in the population surveyed of the +uh deletion mutant this is consistent + + align:start position:0% +uh deletion mutant this is consistent + + + align:start position:0% +uh deletion mutant this is consistent +with the claim that i've made all along + + align:start position:0% +with the claim that i've made all along + + + align:start position:0% +with the claim that i've made all along +it's about nine percent in the general + + align:start position:0% +it's about nine percent in the general + + + align:start position:0% +it's about nine percent in the general +human population and it's nine percent + + align:start position:0% +human population and it's nine percent + + + align:start position:0% +human population and it's nine percent +of this population that's that's good + + align:start position:0% +of this population that's that's good + + + align:start position:0% +of this population that's that's good +um but now you have to correct for that + + align:start position:0% +um but now you have to correct for that + + + align:start position:0% +um but now you have to correct for that +you need to uh to + + align:start position:0% +you need to uh to + + + align:start position:0% +you need to uh to +you can't just ask is it more frequent + + align:start position:0% +you can't just ask is it more frequent + + + align:start position:0% +you can't just ask is it more frequent +here or not you have to correct for the + + align:start position:0% +here or not you have to correct for the + + + align:start position:0% +here or not you have to correct for the +actual frequencies in the population and + + align:start position:0% +actual frequencies in the population and + + + align:start position:0% +actual frequencies in the population and +the way that's done is you you calculate + + align:start position:0% +the way that's done is you you calculate + + + align:start position:0% +the way that's done is you you calculate +a + + align:start position:0% +a + + + align:start position:0% +a +a uh + + align:start position:0% +a uh + + + align:start position:0% +a uh +another table which is the expected + + align:start position:0% +another table which is the expected + + + align:start position:0% +another table which is the expected +uh + + align:start position:0% +uh + + + align:start position:0% +uh +number of each of these combinations of + + align:start position:0% +number of each of these combinations of + + + align:start position:0% +number of each of these combinations of +big with zero negative big with zero + + align:start position:0% +big with zero negative big with zero + + + align:start position:0% +big with zero negative big with zero +positive and so forth under the + + align:start position:0% +positive and so forth under the + + + align:start position:0% +positive and so forth under the +assumption that it's completely random + + align:start position:0% +assumption that it's completely random + + + align:start position:0% +assumption that it's completely random +there was you know the allele + + align:start position:0% +there was you know the allele + + + align:start position:0% +there was you know the allele +frequencies in the population but just + + align:start position:0% +frequencies in the population but just + + + align:start position:0% +frequencies in the population but just +say that they just randomly associated + + align:start position:0% +say that they just randomly associated + + + align:start position:0% +say that they just randomly associated +whether seropolis is zero negative you + + align:start position:0% +whether seropolis is zero negative you + + + align:start position:0% +whether seropolis is zero negative you +use these totals here and the + + align:start position:0% +use these totals here and the + + + align:start position:0% +use these totals here and the +frequencies in the population to + + align:start position:0% +frequencies in the population to + + + align:start position:0% +frequencies in the population to +generate this this expected under the + + align:start position:0% +generate this this expected under the + + + align:start position:0% +generate this this expected under the +random assumption and then you look for + + align:start position:0% +random assumption and then you look for + + + align:start position:0% +random assumption and then you look for +deviation of the real ones of the + + align:start position:0% +deviation of the real ones of the + + + align:start position:0% +deviation of the real ones of the +observed versus the expected now + + align:start position:0% +observed versus the expected now + + + align:start position:0% +observed versus the expected now +if uh + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +so any deviation between + + align:start position:0% +so any deviation between + + + align:start position:0% +so any deviation between +expected and the observed is going to be + + align:start position:0% +expected and the observed is going to be + + + align:start position:0% +expected and the observed is going to be +significant in this um + + align:start position:0% + + + + align:start position:0% + +so you want to do is take the difference + + align:start position:0% +so you want to do is take the difference + + + align:start position:0% +so you want to do is take the difference +between the observed and expected so + + align:start position:0% +between the observed and expected so + + + align:start position:0% +between the observed and expected so +we're working on a statistic here a type + + align:start position:0% +we're working on a statistic here a type + + + align:start position:0% +we're working on a statistic here a type +a a type of measure that will determine + + align:start position:0% +a a type of measure that will determine + + + align:start position:0% +a a type of measure that will determine +how far from expectation are the + + align:start position:0% +how far from expectation are the + + + align:start position:0% +how far from expectation are the +observations on the left-hand side of + + align:start position:0% +observations on the left-hand side of + + + align:start position:0% +observations on the left-hand side of +the in this uh two by two + + align:start position:0% +the in this uh two by two + + + align:start position:0% +the in this uh two by two +and so every for every + + align:start position:0% +and so every for every + + + align:start position:0% +and so every for every +square in the two by two you find the + + align:start position:0% +square in the two by two you find the + + + align:start position:0% +square in the two by two you find the +corresponding expected number and you + + align:start position:0% +corresponding expected number and you + + + align:start position:0% +corresponding expected number and you +subtract it that's the starting point + + align:start position:0% +subtract it that's the starting point + + + align:start position:0% +subtract it that's the starting point +but + + align:start position:0% +but + + + align:start position:0% +but +you you you don't care whether it's + + align:start position:0% +you you you don't care whether it's + + + align:start position:0% +you you you don't care whether it's +negative or positive you want it you + + align:start position:0% +negative or positive you want it you + + + align:start position:0% +negative or positive you want it you +want to make it positive so the trick + + align:start position:0% +want to make it positive so the trick + + + align:start position:0% +want to make it positive so the trick +we'll often use is to take the square of + + align:start position:0% +we'll often use is to take the square of + + + align:start position:0% +we'll often use is to take the square of +that so you can take the absolute value + + align:start position:0% +that so you can take the absolute value + + + align:start position:0% +that so you can take the absolute value +you take the square for the chi-square + + align:start position:0% +you take the square for the chi-square + + + align:start position:0% +you take the square for the chi-square +oddly enough and then you want to put on + + align:start position:0% +oddly enough and then you want to put on + + + align:start position:0% +oddly enough and then you want to put on +some kind of standard + + align:start position:0% +some kind of standard + + + align:start position:0% +some kind of standard +scale so that + + align:start position:0% +scale so that + + + align:start position:0% +scale so that +when you do a chi-square for any kind of + + align:start position:0% +when you do a chi-square for any kind of + + + align:start position:0% +when you do a chi-square for any kind of +phenomenon you'll be able to compare and + + align:start position:0% +phenomenon you'll be able to compare and + + + align:start position:0% +phenomenon you'll be able to compare and +the way you do that is you divide by the + + align:start position:0% +the way you do that is you divide by the + + + align:start position:0% +the way you do that is you divide by the +expected number or this puts it on you + + align:start position:0% +expected number or this puts it on you + + + align:start position:0% +expected number or this puts it on you +know if if these numbers were really + + align:start position:0% +know if if these numbers were really + + + align:start position:0% +know if if these numbers were really +huge this would uh bring them down + + align:start position:0% +huge this would uh bring them down + + + align:start position:0% +huge this would uh bring them down +very small it'll bring the same point + + align:start position:0% +very small it'll bring the same point + + + align:start position:0% +very small it'll bring the same point +and so you take the sum over all the + + align:start position:0% +and so you take the sum over all the + + + align:start position:0% +and so you take the sum over all the +squares in here and that's 15.6 + + align:start position:0% +squares in here and that's 15.6 + + + align:start position:0% +squares in here and that's 15.6 +and that's saying that it deviates um + + align:start position:0% +and that's saying that it deviates um + + + align:start position:0% +and that's saying that it deviates um +from the expectation by this amount it + + align:start position:0% +from the expectation by this amount it + + + align:start position:0% +from the expectation by this amount it +normalized you know as a sort of a + + align:start position:0% +normalized you know as a sort of a + + + align:start position:0% +normalized you know as a sort of a +fraction of the expected + + align:start position:0% +fraction of the expected + + + align:start position:0% +fraction of the expected +now + + align:start position:0% +now + + + align:start position:0% +now +to determine just a little uh + + align:start position:0% +to determine just a little uh + + + align:start position:0% +to determine just a little uh +side light on the chi-square in order to + + align:start position:0% +side light on the chi-square in order to + + + align:start position:0% +side light on the chi-square in order to +determine the probability of 15.6 being + + align:start position:0% +determine the probability of 15.6 being + + + align:start position:0% +determine the probability of 15.6 being +significant what does that mean what do + + align:start position:0% +significant what does that mean what do + + + align:start position:0% +significant what does that mean what do +you think is 0.6 you want to turn this + + align:start position:0% +you think is 0.6 you want to turn this + + + align:start position:0% +you think is 0.6 you want to turn this +into a probability because probabilities + + align:start position:0% +into a probability because probabilities + + + align:start position:0% +into a probability because probabilities +are sort of the common language that we + + align:start position:0% +are sort of the common language that we + + + align:start position:0% +are sort of the common language that we +can all share our surprise at this being + + align:start position:0% +can all share our surprise at this being + + + align:start position:0% +can all share our surprise at this being +different from expected the null + + align:start position:0% +different from expected the null + + + align:start position:0% +different from expected the null +hypothesis that this is the same as + + align:start position:0% +hypothesis that this is the same as + + + align:start position:0% +hypothesis that this is the same as +expected and so in order to evaluate you + + align:start position:0% +expected and so in order to evaluate you + + + align:start position:0% +expected and so in order to evaluate you +have to ask how much freedom there are + + align:start position:0% +have to ask how much freedom there are + + + align:start position:0% +have to ask how much freedom there are +degrees of freedom this is jargon for + + align:start position:0% +degrees of freedom this is jargon for + + + align:start position:0% +degrees of freedom this is jargon for +if + + align:start position:0% +if + + + align:start position:0% +if +uh how many different ways can uh can + + align:start position:0% +uh how many different ways can uh can + + + align:start position:0% +uh how many different ways can uh can +these two numbers vary well since we + + align:start position:0% +these two numbers vary well since we + + + align:start position:0% +these two numbers vary well since we +know the total number if we + + align:start position:0% +know the total number if we + + + align:start position:0% +know the total number if we +when we observe the number of ccr5 that + + align:start position:0% +when we observe the number of ccr5 that + + + align:start position:0% +when we observe the number of ccr5 that +fixes + + align:start position:0% +fixes + + + align:start position:0% +fixes +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in the columns uh the number of + + align:start position:0% +in the columns uh the number of + + + align:start position:0% +in the columns uh the number of +deletions right because it's just going + + align:start position:0% +deletions right because it's just going + + + align:start position:0% +deletions right because it's just going +to be the number of big alleles + + align:start position:0% +to be the number of big alleles + + + align:start position:0% +to be the number of big alleles +taken from the total + + align:start position:0% +taken from the total + + + align:start position:0% +taken from the total +so in a way the degrees of freedom is + + align:start position:0% +so in a way the degrees of freedom is + + + align:start position:0% +so in a way the degrees of freedom is +just one you fix this one number and the + + align:start position:0% +just one you fix this one number and the + + + align:start position:0% +just one you fix this one number and the +other one is is now known + + align:start position:0% +other one is is now known + + + align:start position:0% +other one is is now known +so and the same thing is true for rows + + align:start position:0% +so and the same thing is true for rows + + + align:start position:0% +so and the same thing is true for rows +and columns so the rows minus is just + + align:start position:0% +and columns so the rows minus is just + + + align:start position:0% +and columns so the rows minus is just +one and the columns is one + + align:start position:0% +one and the columns is one + + + align:start position:0% +one and the columns is one +and so the whole degrees of freedom is + + align:start position:0% +and so the whole degrees of freedom is + + + align:start position:0% +and so the whole degrees of freedom is +the product the rows and columns which + + align:start position:0% +the product the rows and columns which + + + align:start position:0% +the product the rows and columns which +is one + + align:start position:0% +is one + + + align:start position:0% +is one +so you plug this in if you look in your + + align:start position:0% +so you plug this in if you look in your + + + align:start position:0% +so you plug this in if you look in your +standard statistical your favorite + + align:start position:0% +standard statistical your favorite + + + align:start position:0% +standard statistical your favorite +statistical book or or software package + + align:start position:0% +statistical book or or software package + + + align:start position:0% +statistical book or or software package +excel or whatever you plug in this + + align:start position:0% +excel or whatever you plug in this + + + align:start position:0% +excel or whatever you plug in this +chi-square value and this degrees of + + align:start position:0% +chi-square value and this degrees of + + + align:start position:0% +chi-square value and this degrees of +freedom and you get this probability + + align:start position:0% +freedom and you get this probability + + + align:start position:0% +freedom and you get this probability +which is very significant generally + + align:start position:0% +which is very significant generally + + + align:start position:0% +which is very significant generally +better than + + align:start position:0% +better than + + + align:start position:0% +better than +uh five percent means that you will you + + align:start position:0% +uh five percent means that you will you + + + align:start position:0% +uh five percent means that you will you +will only be wrong twenty percent of the + + align:start position:0% +will only be wrong twenty percent of the + + + align:start position:0% +will only be wrong twenty percent of the +time + + align:start position:0% +time + + + align:start position:0% +time +some people would prefer to you know + + align:start position:0% +some people would prefer to you know + + + align:start position:0% +some people would prefer to you know +this this means you'll be wrong + + align:start position:0% +this this means you'll be wrong + + + align:start position:0% +this this means you'll be wrong +you know eight eight times in ten + + align:start position:0% +you know eight eight times in ten + + + align:start position:0% +you know eight eight times in ten +thousand + + align:start position:0% +thousand + + + align:start position:0% +thousand +very very infrequently + + align:start position:0% +very very infrequently + + + align:start position:0% +very very infrequently +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now this is great this is a two by two + + align:start position:0% +now this is great this is a two by two + + + align:start position:0% +now this is great this is a two by two +matrix we found an association we have a + + align:start position:0% +matrix we found an association we have a + + + align:start position:0% +matrix we found an association we have a +plausible uh molecular mechanism in the + + align:start position:0% +plausible uh molecular mechanism in the + + + align:start position:0% +plausible uh molecular mechanism in the +previous slide + + align:start position:0% +previous slide + + + align:start position:0% +previous slide +but how was it that we pulled ccr5 out + + align:start position:0% +but how was it that we pulled ccr5 out + + + align:start position:0% +but how was it that we pulled ccr5 out +of this rabbit out of the hat i mean why + + align:start position:0% +of this rabbit out of the hat i mean why + + + align:start position:0% +of this rabbit out of the hat i mean why +ccr5 + + align:start position:0% +ccr5 + + + align:start position:0% +ccr5 +there you know 40 000 some genes in the + + align:start position:0% +there you know 40 000 some genes in the + + + align:start position:0% +there you know 40 000 some genes in the +human genome yes + + align:start position:0% +human genome yes + + + align:start position:0% +human genome yes +i was + + align:start position:0% +i was + + + align:start position:0% +i was +curious as to what is what population is + + align:start position:0% +curious as to what is what population is + + + align:start position:0% +curious as to what is what population is +this + + align:start position:0% +this + + + align:start position:0% +this +i mean in which + + align:start position:0% +i mean in which + + + align:start position:0% +i mean in which +they're slightly more + + align:start position:0% +they're slightly more + + + align:start position:0% +they're slightly more +zero positive than zero negative people + + align:start position:0% +zero positive than zero negative people + + + align:start position:0% +zero positive than zero negative people +this must be a particular + + align:start position:0% +this must be a particular + + + align:start position:0% +this must be a particular +oh yeah these these are these this this + + align:start position:0% +oh yeah these these are these this this + + + align:start position:0% +oh yeah these these are these this this +is a case control study where you try to + + align:start position:0% +is a case control study where you try to + + + align:start position:0% +is a case control study where you try to +get roughly equal number of negatives + + align:start position:0% +get roughly equal number of negatives + + + align:start position:0% +get roughly equal number of negatives +and positives that are matched for + + align:start position:0% +and positives that are matched for + + + align:start position:0% +and positives that are matched for +socioeconomic group and race and gender + + align:start position:0% +socioeconomic group and race and gender + + + align:start position:0% +socioeconomic group and race and gender +and things like that so that's that's a + + align:start position:0% +and things like that so that's that's a + + + align:start position:0% +and things like that so that's that's a +setup but but then + + align:start position:0% +setup but but then + + + align:start position:0% +setup but but then +then if there's not a huge uh + + align:start position:0% +then if there's not a huge uh + + + align:start position:0% +then if there's not a huge uh +risk ratio for the two alleles then + + align:start position:0% +risk ratio for the two alleles then + + + align:start position:0% +risk ratio for the two alleles then +you'll expect them to be close to the + + align:start position:0% +you'll expect them to be close to the + + + align:start position:0% +you'll expect them to be close to the +population frequency which means you + + align:start position:0% +population frequency which means you + + + align:start position:0% +population frequency which means you +can't just look at it on inspection and + + align:start position:0% +can't just look at it on inspection and + + + align:start position:0% +can't just look at it on inspection and +say oh yeah + + align:start position:0% +say oh yeah + + + align:start position:0% +say oh yeah +all the zero positive or the big allele + + align:start position:0% +all the zero positive or the big allele + + + align:start position:0% +all the zero positive or the big allele +that would we would need a chi-square at + + align:start position:0% +that would we would need a chi-square at + + + align:start position:0% +that would we would need a chi-square at +that point but you know this is pretty + + align:start position:0% +that point but you know this is pretty + + + align:start position:0% +that point but you know this is pretty +close to the popular ratio population + + align:start position:0% +close to the popular ratio population + + + align:start position:0% +close to the popular ratio population +frequency and so that's why we had to do + + align:start position:0% +frequency and so that's why we had to do + + + align:start position:0% +frequency and so that's why we had to do +the chi square + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +the the the question that that + + align:start position:0% +the the the question that that + + + align:start position:0% +the the the question that that +that we're taking now is how did we pick + + align:start position:0% +that we're taking now is how did we pick + + + align:start position:0% +that we're taking now is how did we pick +ccr5 i mean i introduced this as being a + + align:start position:0% +ccr5 i mean i introduced this as being a + + + align:start position:0% +ccr5 i mean i introduced this as being a +putative receptor for the virus but one + + align:start position:0% +putative receptor for the virus but one + + + align:start position:0% +putative receptor for the virus but one +of the first pieces of evidence that + + align:start position:0% +of the first pieces of evidence that + + + align:start position:0% +of the first pieces of evidence that +this was a putative receptor for the + + align:start position:0% +this was a putative receptor for the + + + align:start position:0% +this was a putative receptor for the +virus was this sort of association study + + align:start position:0% +virus was this sort of association study + + + align:start position:0% +virus was this sort of association study +okay so how was it that they picked the + + align:start position:0% +okay so how was it that they picked the + + + align:start position:0% +okay so how was it that they picked the +chemokine receptor well you could say + + align:start position:0% +chemokine receptor well you could say + + + align:start position:0% +chemokine receptor well you could say +well some kind of hunch about chemicals + + align:start position:0% +well some kind of hunch about chemicals + + + align:start position:0% +well some kind of hunch about chemicals +being involved in immunology and + + align:start position:0% +being involved in immunology and + + + align:start position:0% +being involved in immunology and +immunology being important in in + + align:start position:0% +immunology being important in in + + + align:start position:0% +immunology being important in in +fighting viruses but that wouldn't + + align:start position:0% +fighting viruses but that wouldn't + + + align:start position:0% +fighting viruses but that wouldn't +suggest that it's the actual receptor + + align:start position:0% +suggest that it's the actual receptor + + + align:start position:0% +suggest that it's the actual receptor +um + + align:start position:0% +um + + + align:start position:0% +um +you know i think these are there's + + align:start position:0% +you know i think these are there's + + + align:start position:0% +you know i think these are there's +there's all kinds of inspired guesswork + + align:start position:0% +there's all kinds of inspired guesswork + + + align:start position:0% +there's all kinds of inspired guesswork +there's biochemistry happening behind + + align:start position:0% +there's biochemistry happening behind + + + align:start position:0% +there's biochemistry happening behind +the scene and so on but let's take let's + + align:start position:0% +the scene and so on but let's take let's + + + align:start position:0% +the scene and so on but let's take let's +just put that aside from home and take + + align:start position:0% +just put that aside from home and take + + + align:start position:0% +just put that aside from home and take +the more general case that you wanted to + + align:start position:0% +the more general case that you wanted to + + + align:start position:0% +the more general case that you wanted to +test not just this one hypothesis that + + align:start position:0% +test not just this one hypothesis that + + + align:start position:0% +test not just this one hypothesis that +ccr5 is involved but you've implicitly + + align:start position:0% +ccr5 is involved but you've implicitly + + + align:start position:0% +ccr5 is involved but you've implicitly +and tested or explicitly tested every + + align:start position:0% +and tested or explicitly tested every + + + align:start position:0% +and tested or explicitly tested every +gene + + align:start position:0% +gene + + + align:start position:0% +gene +you've gone through every gene and + + align:start position:0% +you've gone through every gene and + + + align:start position:0% +you've gone through every gene and +you've taken uh either the most common + + align:start position:0% +you've taken uh either the most common + + + align:start position:0% +you've taken uh either the most common +alleles or you've sequenced your own + + align:start position:0% +alleles or you've sequenced your own + + + align:start position:0% +alleles or you've sequenced your own +genome and you found the alleles that + + align:start position:0% +genome and you found the alleles that + + + align:start position:0% +genome and you found the alleles that +you have whether they're common or rare + + align:start position:0% +you have whether they're common or rare + + + align:start position:0% +you have whether they're common or rare +you don't care and you want to ask + + align:start position:0% +you don't care and you want to ask + + + align:start position:0% +you don't care and you want to ask +what's this what's the association + + align:start position:0% + + + + align:start position:0% + +this is uh + + align:start position:0% +this is uh + + + align:start position:0% +this is uh +let's consider the upper right hand + + align:start position:0% +let's consider the upper right hand + + + align:start position:0% +let's consider the upper right hand +panel here + + align:start position:0% +panel here + + + align:start position:0% +panel here +where we have some risk ratio + + align:start position:0% +where we have some risk ratio + + + align:start position:0% +where we have some risk ratio +a fairly subtle one 1.5 remember we were + + align:start position:0% +a fairly subtle one 1.5 remember we were + + + align:start position:0% +a fairly subtle one 1.5 remember we were +talking about risk ratios of 75 in the + + align:start position:0% +talking about risk ratios of 75 in the + + + align:start position:0% +talking about risk ratios of 75 in the +case of autism this is just 1.5 very + + align:start position:0% +case of autism this is just 1.5 very + + + align:start position:0% +case of autism this is just 1.5 very +subtle risk ratio just like you know i + + align:start position:0% +subtle risk ratio just like you know i + + + align:start position:0% +subtle risk ratio just like you know i +think in the last one could have been a + + align:start position:0% +think in the last one could have been a + + + align:start position:0% +think in the last one could have been a +a subtle risk ratio + + align:start position:0% +a subtle risk ratio + + + align:start position:0% +a subtle risk ratio +um uh what the x-axis is going to be the + + align:start position:0% +um uh what the x-axis is going to be the + + + align:start position:0% +um uh what the x-axis is going to be the +number of alleles that you that you're + + align:start position:0% +number of alleles that you that you're + + + align:start position:0% +number of alleles that you that you're +hypothetically testing this could be + + align:start position:0% +hypothetically testing this could be + + + align:start position:0% +hypothetically testing this could be +related to the number of genes that + + align:start position:0% +related to the number of genes that + + + align:start position:0% +related to the number of genes that +you're testing + + align:start position:0% +you're testing + + + align:start position:0% +you're testing +or it could be more than the number of + + align:start position:0% +or it could be more than the number of + + + align:start position:0% +or it could be more than the number of +genes that you're testing because you + + align:start position:0% +genes that you're testing because you + + + align:start position:0% +genes that you're testing because you +can have more than one allele for gene + + align:start position:0% +can have more than one allele for gene + + + align:start position:0% +can have more than one allele for gene +that you might want to test is this + + align:start position:0% +that you might want to test is this + + + align:start position:0% +that you might want to test is this +allele of this gene important in this + + align:start position:0% +allele of this gene important in this + + + align:start position:0% +allele of this gene important in this +disease or is this other one you know + + align:start position:0% +disease or is this other one you know + + + align:start position:0% +disease or is this other one you know +for example sickle cell is important but + + align:start position:0% +for example sickle cell is important but + + + align:start position:0% +for example sickle cell is important but +various other hemoglobin mutations are + + align:start position:0% +various other hemoglobin mutations are + + + align:start position:0% +various other hemoglobin mutations are +not + + align:start position:0% +not + + + align:start position:0% +not +this chemokine deletion is important + + align:start position:0% +this chemokine deletion is important + + + align:start position:0% +this chemokine deletion is important +maybe another one isn't many of the + + align:start position:0% +maybe another one isn't many of the + + + align:start position:0% +maybe another one isn't many of the +chemokine mutations will be neutral + + align:start position:0% +chemokine mutations will be neutral + + + align:start position:0% +chemokine mutations will be neutral +okay so as you increase the number of + + align:start position:0% +okay so as you increase the number of + + + align:start position:0% +okay so as you increase the number of +genes and alleles + + align:start position:0% +genes and alleles + + + align:start position:0% +genes and alleles +from here's 10 to the fourth + + align:start position:0% +from here's 10 to the fourth + + + align:start position:0% +from here's 10 to the fourth +on up then the number of + + align:start position:0% +on up then the number of + + + align:start position:0% +on up then the number of +sib pairs and so this is a simulation + + align:start position:0% +sib pairs and so this is a simulation + + + align:start position:0% +sib pairs and so this is a simulation +covering you know + + align:start position:0% +covering you know + + + align:start position:0% +covering you know +all kinds of experiments that you could + + align:start position:0% +all kinds of experiments that you could + + + align:start position:0% +all kinds of experiments that you could +do + + align:start position:0% +do + + + align:start position:0% +do +where you can apply you can use + + align:start position:0% +where you can apply you can use + + + align:start position:0% +where you can apply you can use +computational methods to help guide the + + align:start position:0% +computational methods to help guide the + + + align:start position:0% +computational methods to help guide the +design of experiments if you did if you + + align:start position:0% +design of experiments if you did if you + + + align:start position:0% +design of experiments if you did if you +did an expensive experiment you just + + align:start position:0% +did an expensive experiment you just + + + align:start position:0% +did an expensive experiment you just +happened to to use too few patients + + align:start position:0% +happened to to use too few patients + + + align:start position:0% +happened to to use too few patients +and too many alleles + + align:start position:0% +and too many alleles + + + align:start position:0% +and too many alleles +then you may have misused your resources + + align:start position:0% +then you may have misused your resources + + + align:start position:0% +then you may have misused your resources +you should have maybe done fewer alleles + + align:start position:0% +you should have maybe done fewer alleles + + + align:start position:0% +you should have maybe done fewer alleles +and more patients or + + align:start position:0% +and more patients or + + + align:start position:0% +and more patients or +something like that and this provides + + align:start position:0% +something like that and this provides + + + align:start position:0% +something like that and this provides +some guidance here but you can see that + + align:start position:0% +some guidance here but you can see that + + + align:start position:0% +some guidance here but you can see that +in order to get to a very large number + + align:start position:0% +in order to get to a very large number + + + align:start position:0% +in order to get to a very large number +of alleles you need a fairly modest + + align:start position:0% +of alleles you need a fairly modest + + + align:start position:0% +of alleles you need a fairly modest +increase in the number of patients and + + align:start position:0% +increase in the number of patients and + + + align:start position:0% +increase in the number of patients and +that's + + align:start position:0% +that's + + + align:start position:0% +that's +due to the + + align:start position:0% +due to the + + + align:start position:0% +due to the +sort of the exponential term that you + + align:start position:0% +sort of the exponential term that you + + + align:start position:0% +sort of the exponential term that you +have + + align:start position:0% +have + + + align:start position:0% +have +in + + align:start position:0% +in + + + align:start position:0% +in +in these probability distributions so + + align:start position:0% +in these probability distributions so + + + align:start position:0% +in these probability distributions so +you actually but nevertheless it's a big + + align:start position:0% +you actually but nevertheless it's a big + + + align:start position:0% +you actually but nevertheless it's a big +deal + + align:start position:0% +deal + + + align:start position:0% +deal +cost wise going up from say 400 patients + + align:start position:0% +cost wise going up from say 400 patients + + + align:start position:0% +cost wise going up from say 400 patients +to + + align:start position:0% +to + + + align:start position:0% +to + + align:start position:0% + + + align:start position:0% +nevertheless it's it's only linear in + + align:start position:0% +nevertheless it's it's only linear in + + + align:start position:0% +nevertheless it's it's only linear in +patients while it's it's exponential in + + align:start position:0% +patients while it's it's exponential in + + + align:start position:0% +patients while it's it's exponential in +the number of uh + + align:start position:0% +the number of uh + + + align:start position:0% +the number of uh +alleles you can test so that's the good + + align:start position:0% +alleles you can test so that's the good + + + align:start position:0% +alleles you can test so that's the good +news + + align:start position:0% +news + + + align:start position:0% +news +uh and you can see some of these other + + align:start position:0% +uh and you can see some of these other + + + align:start position:0% +uh and you can see some of these other +panels show the effect of other + + align:start position:0% +panels show the effect of other + + + align:start position:0% +panels show the effect of other +varying other parameters for example + + align:start position:0% +varying other parameters for example + + + align:start position:0% +varying other parameters for example +here on the left you've got varying the + + align:start position:0% +here on the left you've got varying the + + + align:start position:0% +here on the left you've got varying the +population frequency of the allele + + align:start position:0% +population frequency of the allele + + + align:start position:0% +population frequency of the allele +as you get to + + align:start position:0% +as you get to + + + align:start position:0% +as you get to +very very rare alleles on the right hand + + align:start position:0% +very very rare alleles on the right hand + + + align:start position:0% +very very rare alleles on the right hand +of the horizontal axis here + + align:start position:0% +of the horizontal axis here + + + align:start position:0% +of the horizontal axis here +then the number of uh + + align:start position:0% +then the number of uh + + + align:start position:0% +then the number of uh +sid pairs + + align:start position:0% +sid pairs + + + align:start position:0% +sid pairs +brothers sisters brother brothers that + + align:start position:0% +brothers sisters brother brothers that + + + align:start position:0% +brothers sisters brother brothers that +you need starts to go through the roof + + align:start position:0% +you need starts to go through the roof + + + align:start position:0% +you need starts to go through the roof +and now it's uh + + align:start position:0% +and now it's uh + + + align:start position:0% +and now it's uh +it's it's exponential on both axes or + + align:start position:0% +it's it's exponential on both axes or + + + align:start position:0% +it's it's exponential on both axes or +that is to say that it's a direct + + align:start position:0% +that is to say that it's a direct + + + align:start position:0% +that is to say that it's a direct +relationship + + align:start position:0% + + + + align:start position:0% + +that's the population + + align:start position:0% +that's the population + + + align:start position:0% +that's the population +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +that + + align:start position:0% +that + + + align:start position:0% +that +you're in on on the + + align:start position:0% +you're in on on the + + + align:start position:0% +you're in on on the +on + + align:start position:0% +on + + + align:start position:0% +on +the one we were just talking about on + + align:start position:0% +the one we were just talking about on + + + align:start position:0% +the one we were just talking about on +the left the the population frequency is + + align:start position:0% +the left the the population frequency is + + + align:start position:0% +the left the the population frequency is +the horizontal axis and it varies from + + align:start position:0% +the horizontal axis and it varies from + + + align:start position:0% +the horizontal axis and it varies from +um near unity to 10 to the minus nine as + + align:start position:0% +um near unity to 10 to the minus nine as + + + align:start position:0% +um near unity to 10 to the minus nine as +a very rare allele frequency + + align:start position:0% +a very rare allele frequency + + + align:start position:0% +a very rare allele frequency +on the right the one we started with top + + align:start position:0% +on the right the one we started with top + + + align:start position:0% +on the right the one we started with top +right + + align:start position:0% +right + + + align:start position:0% +right +we just picked 0.5 which would be very + + align:start position:0% +we just picked 0.5 which would be very + + + align:start position:0% +we just picked 0.5 which would be very +you know there out around here on the + + align:start position:0% +you know there out around here on the + + + align:start position:0% +you know there out around here on the +left hand end of this of the left hand + + align:start position:0% +left hand end of this of the left hand + + + align:start position:0% +left hand end of this of the left hand +quadrant so you pick one of these allele + + align:start position:0% +quadrant so you pick one of these allele + + + align:start position:0% +quadrant so you pick one of these allele +frequencies a fairly + + align:start position:0% +frequencies a fairly + + + align:start position:0% +frequencies a fairly +where it's equal frequency of the two + + align:start position:0% +where it's equal frequency of the two + + + align:start position:0% +where it's equal frequency of the two +alleles in the population as where you + + align:start position:0% +alleles in the population as where you + + + align:start position:0% +alleles in the population as where you +do the rest of the simulation you could + + align:start position:0% +do the rest of the simulation you could + + + align:start position:0% +do the rest of the simulation you could +think of all these these these panels + + align:start position:0% +think of all these these these panels + + + align:start position:0% +think of all these these these panels +could be some multi-dimensional display + + align:start position:0% +could be some multi-dimensional display + + + align:start position:0% +could be some multi-dimensional display +but i wanted to take them out one of the + + align:start position:0% +but i wanted to take them out one of the + + + align:start position:0% +but i wanted to take them out one of the +time + + align:start position:0% +time + + + align:start position:0% +time +and actually i i did all these you know + + align:start position:0% +and actually i i did all these you know + + + align:start position:0% +and actually i i did all these you know +in + + align:start position:0% +in + + + align:start position:0% +in +excel using the the equations that are + + align:start position:0% +excel using the the equations that are + + + align:start position:0% +excel using the the equations that are +present in this reference that's given + + align:start position:0% +present in this reference that's given + + + align:start position:0% +present in this reference that's given +on your + + align:start position:0% +on your + + + align:start position:0% +on your +in the slides here + + align:start position:0% +in the slides here + + + align:start position:0% +in the slides here +um + + align:start position:0% +um + + + align:start position:0% +um +a good sign of a well-written paper is + + align:start position:0% +a good sign of a well-written paper is + + + align:start position:0% +a good sign of a well-written paper is +for sort of average individual to be + + align:start position:0% +for sort of average individual to be + + + align:start position:0% +for sort of average individual to be +able to reproduce it + + align:start position:0% +able to reproduce it + + + align:start position:0% +able to reproduce it +so + + align:start position:0% +so + + + align:start position:0% +so +we have uh + + align:start position:0% +we have uh + + + align:start position:0% +we have uh +how many so we've been talking about + + align:start position:0% +how many so we've been talking about + + + align:start position:0% +how many so we've been talking about +new polymorphisms in fact the question + + align:start position:0% +new polymorphisms in fact the question + + + align:start position:0% +new polymorphisms in fact the question +that came up during the break was + + align:start position:0% +that came up during the break was + + + align:start position:0% +that came up during the break was +if you know if selection and drift cause + + align:start position:0% +if you know if selection and drift cause + + + align:start position:0% +if you know if selection and drift cause +allele frequencies to fix + + align:start position:0% +allele frequencies to fix + + + align:start position:0% +allele frequencies to fix +fairly rapidly drift in small + + align:start position:0% +fairly rapidly drift in small + + + align:start position:0% +fairly rapidly drift in small +populations sort of normal size + + align:start position:0% +populations sort of normal size + + + align:start position:0% +populations sort of normal size +populations will drift in and no you + + align:start position:0% +populations will drift in and no you + + + align:start position:0% +populations will drift in and no you +know + + align:start position:0% +know + + + align:start position:0% +know +fairly short evolutionary times and + + align:start position:0% +fairly short evolutionary times and + + + align:start position:0% +fairly short evolutionary times and +selection if you have a high selection + + align:start position:0% +selection if you have a high selection + + + align:start position:0% +selection if you have a high selection +coefficient of cost fixation why do we + + align:start position:0% +coefficient of cost fixation why do we + + + align:start position:0% +coefficient of cost fixation why do we +have any allele frequencies at all why + + align:start position:0% +have any allele frequencies at all why + + + align:start position:0% +have any allele frequencies at all why +isn't everything fixed at 100 percent + + align:start position:0% +isn't everything fixed at 100 percent + + + align:start position:0% +isn't everything fixed at 100 percent +for one particular allele and the answer + + align:start position:0% +for one particular allele and the answer + + + align:start position:0% +for one particular allele and the answer +is mutation and where all these new + + align:start position:0% +is mutation and where all these new + + + align:start position:0% +is mutation and where all these new +mutations or polymorphisms come from + + align:start position:0% +mutations or polymorphisms come from + + + align:start position:0% +mutations or polymorphisms come from +actually these should probably be called + + align:start position:0% +actually these should probably be called + + + align:start position:0% +actually these should probably be called +mutations because most of them have + + align:start position:0% +mutations because most of them have + + + align:start position:0% +mutations because most of them have +frequencies less than one percent + + align:start position:0% +frequencies less than one percent + + + align:start position:0% +frequencies less than one percent +well here's a specific model which + + align:start position:0% +well here's a specific model which + + + align:start position:0% +well here's a specific model which +doesn't follow all the assumptions we + + align:start position:0% +doesn't follow all the assumptions we + + + align:start position:0% +doesn't follow all the assumptions we +had before but we'll use a different + + align:start position:0% +had before but we'll use a different + + + align:start position:0% +had before but we'll use a different +we'll use the back of the envelope + + align:start position:0% +we'll use the back of the envelope + + + align:start position:0% +we'll use the back of the envelope +calculation to give you a feeling for + + align:start position:0% +calculation to give you a feeling for + + + align:start position:0% +calculation to give you a feeling for +for what is true for the the uh what is + + align:start position:0% +for what is true for the the uh what is + + + align:start position:0% +for what is true for the the uh what is +likely to be the case for the human + + align:start position:0% +likely to be the case for the human + + + align:start position:0% +likely to be the case for the human +population so human population there's a + + align:start position:0% +population so human population there's a + + + align:start position:0% +population so human population there's a +little bit of uh + + align:start position:0% +little bit of uh + + + align:start position:0% +little bit of uh +unknown in some of these parameters so + + align:start position:0% +unknown in some of these parameters so + + + align:start position:0% +unknown in some of these parameters so +you should take these all with a grain + + align:start position:0% +you should take these all with a grain + + + align:start position:0% +you should take these all with a grain +of salt actually everything i say you + + align:start position:0% +of salt actually everything i say you + + + align:start position:0% +of salt actually everything i say you +should take but uh + + align:start position:0% +should take but uh + + + align:start position:0% +should take but uh +this you know the number of populations + + align:start position:0% +this you know the number of populations + + + align:start position:0% +this you know the number of populations +that that we've had since a bottleneck + + align:start position:0% +that that we've had since a bottleneck + + + align:start position:0% +that that we've had since a bottleneck +in the human population maybe there were + + align:start position:0% +in the human population maybe there were + + + align:start position:0% +in the human population maybe there were +as few as 10 to the fourth humans at + + align:start position:0% +as few as 10 to the fourth humans at + + + align:start position:0% +as few as 10 to the fourth humans at +some point or another + + align:start position:0% +some point or another + + + align:start position:0% +some point or another +um maybe less + + align:start position:0% +um maybe less + + + align:start position:0% +um maybe less +but since that time there have been + + align:start position:0% +but since that time there have been + + + align:start position:0% +but since that time there have been +about 5 000 generations and during that + + align:start position:0% +about 5 000 generations and during that + + + align:start position:0% +about 5 000 generations and during that +time our population has now grown to 6 + + align:start position:0% +time our population has now grown to 6 + + + align:start position:0% +time our population has now grown to 6 +billion people that's the uh n prime and + + align:start position:0% +billion people that's the uh n prime and + + + align:start position:0% +billion people that's the uh n prime and +then + + align:start position:0% +then + + + align:start position:0% +then +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +the mutation rate is on as uh mentioned + + align:start position:0% +the mutation rate is on as uh mentioned + + + align:start position:0% +the mutation rate is on as uh mentioned +earlier in sponsored question is around + + align:start position:0% +earlier in sponsored question is around + + + align:start position:0% +earlier in sponsored question is around +ten to the minus eighth + + align:start position:0% +ten to the minus eighth + + + align:start position:0% +ten to the minus eighth +per base pair per genome + + align:start position:0% +per base pair per genome + + + align:start position:0% +per base pair per genome +per generation + + align:start position:0% +per generation + + + align:start position:0% +per generation +and so the genome size is about 6 + + align:start position:0% +and so the genome size is about 6 + + + align:start position:0% +and so the genome size is about 6 +billion coincidentally the same as the + + align:start position:0% +billion coincidentally the same as the + + + align:start position:0% +billion coincidentally the same as the +population size total coincidence + + align:start position:0% +population size total coincidence + + + align:start position:0% +population size total coincidence +then + + align:start position:0% +then + + + align:start position:0% +then +10 to the minus 8 times that number of + + align:start position:0% +10 to the minus 8 times that number of + + + align:start position:0% +10 to the minus 8 times that number of +base pairs means you have about 60 + + align:start position:0% +base pairs means you have about 60 + + + align:start position:0% +base pairs means you have about 60 +mutations or so + + align:start position:0% +mutations or so + + + align:start position:0% +mutations or so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +occurring in a generation so you've got + + align:start position:0% +occurring in a generation so you've got + + + align:start position:0% +occurring in a generation so you've got +a steady flow of new mutations now if + + align:start position:0% +a steady flow of new mutations now if + + + align:start position:0% +a steady flow of new mutations now if +you take that just roughly speaking if + + align:start position:0% +you take that just roughly speaking if + + + align:start position:0% +you take that just roughly speaking if +you take that over 5000 generations + + align:start position:0% +you take that over 5000 generations + + + align:start position:0% +you take that over 5000 generations +you've got sixty times five thousand + + align:start position:0% +you've got sixty times five thousand + + + align:start position:0% +you've got sixty times five thousand +you've got a very large number on the + + align:start position:0% +you've got a very large number on the + + + align:start position:0% +you've got a very large number on the +order of ten to the fourth + + align:start position:0% +order of ten to the fourth + + + align:start position:0% +order of ten to the fourth +uh mutations that have accumulated in + + align:start position:0% +uh mutations that have accumulated in + + + align:start position:0% +uh mutations that have accumulated in +our population assuming + + align:start position:0% +our population assuming + + + align:start position:0% +our population assuming +that uh relatively little drift because + + align:start position:0% +that uh relatively little drift because + + + align:start position:0% +that uh relatively little drift because +it's exponentially growing population + + align:start position:0% +it's exponentially growing population + + + align:start position:0% +it's exponentially growing population +and relatively little selection + + align:start position:0% +and relatively little selection + + + align:start position:0% +and relatively little selection +then this is the number that might have + + align:start position:0% +then this is the number that might have + + + align:start position:0% +then this is the number that might have +accumulated you can do subtle + + align:start position:0% +accumulated you can do subtle + + + align:start position:0% +accumulated you can do subtle +corrections for this + + align:start position:0% +corrections for this + + + align:start position:0% +corrections for this +exponential growth + + align:start position:0% +exponential growth + + + align:start position:0% +exponential growth +you know the number of mutations you got + + align:start position:0% +you know the number of mutations you got + + + align:start position:0% +you know the number of mutations you got +at the beginning + + align:start position:0% +at the beginning + + + align:start position:0% +at the beginning +will have higher frequency but there'll + + align:start position:0% +will have higher frequency but there'll + + + align:start position:0% +will have higher frequency but there'll +be fewer of them because population was + + align:start position:0% +be fewer of them because population was + + + align:start position:0% +be fewer of them because population was +smaller but anyway you get the picture + + align:start position:0% +smaller but anyway you get the picture + + + align:start position:0% +smaller but anyway you get the picture +is that the the total number of + + align:start position:0% +is that the the total number of + + + align:start position:0% +is that the the total number of +mutations in any one of this that are + + align:start position:0% +mutations in any one of this that are + + + align:start position:0% +mutations in any one of this that are +new since that knew since 5000 + + align:start position:0% +new since that knew since 5000 + + + align:start position:0% +new since that knew since 5000 +generations ago + + align:start position:0% +generations ago + + + align:start position:0% +generations ago +will be on the order of 10 to the 4th + + align:start position:0% +will be on the order of 10 to the 4th + + + align:start position:0% +will be on the order of 10 to the 4th +in your body + + align:start position:0% +in your body + + + align:start position:0% +in your body +not all of them doing good for you + + align:start position:0% +not all of them doing good for you + + + align:start position:0% +not all of them doing good for you +and + + align:start position:0% +and + + + align:start position:0% +and +for each of those rare mutations they + + align:start position:0% +for each of those rare mutations they + + + align:start position:0% +for each of those rare mutations they +might have a frequency about 10 to the + + align:start position:0% +might have a frequency about 10 to the + + + align:start position:0% +might have a frequency about 10 to the +minus 5. + + align:start position:0% +minus 5. + + + align:start position:0% +minus 5. +um + + align:start position:0% +um + + + align:start position:0% +um +there will be about uh + + align:start position:0% +there will be about uh + + + align:start position:0% +there will be about uh +10 to the fourth people on earth that + + align:start position:0% +10 to the fourth people on earth that + + + align:start position:0% +10 to the fourth people on earth that +will share that very rare mutation with + + align:start position:0% +will share that very rare mutation with + + + align:start position:0% +will share that very rare mutation with +you 10 to the minus 5 sounds like very + + align:start position:0% +you 10 to the minus 5 sounds like very + + + align:start position:0% +you 10 to the minus 5 sounds like very +rare but when you multiply it by 6 + + align:start position:0% +rare but when you multiply it by 6 + + + align:start position:0% +rare but when you multiply it by 6 +billion people there are a lot of people + + align:start position:0% +billion people there are a lot of people + + + align:start position:0% +billion people there are a lot of people +who share that with you okay it's a new + + align:start position:0% +who share that with you okay it's a new + + + align:start position:0% +who share that with you okay it's a new +mutation + + align:start position:0% +mutation + + + align:start position:0% +mutation +okay so the take home is and this is uh + + align:start position:0% +okay so the take home is and this is uh + + + align:start position:0% +okay so the take home is and this is uh +from this reference here um high genomic + + align:start position:0% +from this reference here um high genomic + + + align:start position:0% +from this reference here um high genomic +deleterious mutations uh accumulate over + + align:start position:0% +deleterious mutations uh accumulate over + + + align:start position:0% +deleterious mutations uh accumulate over +these four thousand uh by + + align:start position:0% +these four thousand uh by + + + align:start position:0% +these four thousand uh by +some large number of generations and + + align:start position:0% +some large number of generations and + + + align:start position:0% +some large number of generations and +they would confound linkage methods and + + align:start position:0% +they would confound linkage methods and + + + align:start position:0% +they would confound linkage methods and +they've confound assumptions that say + + align:start position:0% +they've confound assumptions that say + + + align:start position:0% +they've confound assumptions that say +that the common alleles uh common + + align:start position:0% +that the common alleles uh common + + + align:start position:0% +that the common alleles uh common +alleles uh + + align:start position:0% +alleles uh + + + align:start position:0% +alleles uh +are positive + + align:start position:0% +are positive + + + align:start position:0% +are positive +okay so let's say we've done an + + align:start position:0% +okay so let's say we've done an + + + align:start position:0% +okay so let's say we've done an +association study either we've done it + + align:start position:0% +association study either we've done it + + + align:start position:0% +association study either we've done it +on one gene picked one out of the hat + + align:start position:0% +on one gene picked one out of the hat + + + align:start position:0% +on one gene picked one out of the hat +like ccr5 we've done a full genome + + align:start position:0% +like ccr5 we've done a full genome + + + align:start position:0% +like ccr5 we've done a full genome +survey 40 000 genes all the alleles we + + align:start position:0% +survey 40 000 genes all the alleles we + + + align:start position:0% +survey 40 000 genes all the alleles we +know of + + align:start position:0% +know of + + + align:start position:0% +know of +in order to do the ladder we had to have + + align:start position:0% +in order to do the ladder we had to have + + + align:start position:0% +in order to do the ladder we had to have +a big + + align:start position:0% +a big + + + align:start position:0% +a big +patient population + + align:start position:0% +patient population + + + align:start position:0% +patient population +um but let's say we've done that now we + + align:start position:0% +um but let's say we've done that now we + + + align:start position:0% +um but let's say we've done that now we +want to prove that that association is + + align:start position:0% +want to prove that that association is + + + align:start position:0% +want to prove that that association is +that's + + align:start position:0% +that's + + + align:start position:0% +that's +that great statistic that we got out if + + align:start position:0% +that great statistic that we got out if + + + align:start position:0% +that great statistic that we got out if +we have a large enough patient + + align:start position:0% +we have a large enough patient + + + align:start position:0% +we have a large enough patient +population it's still just the statistic + + align:start position:0% +population it's still just the statistic + + + align:start position:0% +population it's still just the statistic +that what will constitute proof is after + + align:start position:0% +that what will constitute proof is after + + + align:start position:0% +that what will constitute proof is after +we find the association we make a copy + + align:start position:0% +we find the association we make a copy + + + align:start position:0% +we find the association we make a copy +of that mutation isolated away from the + + align:start position:0% +of that mutation isolated away from the + + + align:start position:0% +of that mutation isolated away from the +three three million other polymorphisms + + align:start position:0% +three three million other polymorphisms + + + align:start position:0% +three three million other polymorphisms +that are floating around in your body + + align:start position:0% +that are floating around in your body + + + align:start position:0% +that are floating around in your body +and we do some kind of test ideally we + + align:start position:0% +and we do some kind of test ideally we + + + align:start position:0% +and we do some kind of test ideally we +would make an isogenic uh pair of humans + + align:start position:0% +would make an isogenic uh pair of humans + + + align:start position:0% +would make an isogenic uh pair of humans +that only differ by this one mutation + + align:start position:0% +that only differ by this one mutation + + + align:start position:0% +that only differ by this one mutation +that is not generally considered + + align:start position:0% +that is not generally considered + + + align:start position:0% +that is not generally considered +medically feasible uh + + align:start position:0% +medically feasible uh + + + align:start position:0% +medically feasible uh +or or ethical + + align:start position:0% +or or ethical + + + align:start position:0% +or or ethical +um but somehow i know you can do it on + + align:start position:0% +um but somehow i know you can do it on + + + align:start position:0% +um but somehow i know you can do it on +human cells or you can do it in a uh + + align:start position:0% +human cells or you can do it in a uh + + + align:start position:0% +human cells or you can do it in a uh +mammalian + + align:start position:0% +mammalian + + + align:start position:0% +mammalian +uh model system but you have to make + + align:start position:0% +uh model system but you have to make + + + align:start position:0% +uh model system but you have to make +something that's close to isagenix a + + align:start position:0% +something that's close to isagenix a + + + align:start position:0% +something that's close to isagenix a +copy of this mutation and show that it + + align:start position:0% +copy of this mutation and show that it + + + align:start position:0% +copy of this mutation and show that it +has a phenotype that makes sense and + + align:start position:0% +has a phenotype that makes sense and + + + align:start position:0% +has a phenotype that makes sense and +then just to make sure you haven't + + align:start position:0% +then just to make sure you haven't + + + align:start position:0% +then just to make sure you haven't +introduced other mutations the really + + align:start position:0% +introduced other mutations the really + + + align:start position:0% +introduced other mutations the really +careful scientists will then revert that + + align:start position:0% +careful scientists will then revert that + + + align:start position:0% +careful scientists will then revert that +one polymorphism and show now you no + + align:start position:0% +one polymorphism and show now you no + + + align:start position:0% +one polymorphism and show now you no +longer have that phenotype okay + + align:start position:0% +longer have that phenotype okay + + + align:start position:0% +longer have that phenotype okay +so + + align:start position:0% +so + + + align:start position:0% +so +um let's + + align:start position:0% +um let's + + + align:start position:0% +um let's +walk through an example here's the third + + align:start position:0% +walk through an example here's the third + + + align:start position:0% +walk through an example here's the third +example in this lecture of a + + align:start position:0% +example in this lecture of a + + + align:start position:0% +example in this lecture of a +very specific allele where we've shown + + align:start position:0% +very specific allele where we've shown + + + align:start position:0% +very specific allele where we've shown +the molecular basis of it and it's the + + align:start position:0% +the molecular basis of it and it's the + + + align:start position:0% +the molecular basis of it and it's the +second example where it's not code it's + + align:start position:0% +second example where it's not code it's + + + align:start position:0% +second example where it's not code it's +not coding and it's the second example + + align:start position:0% +not coding and it's the second example + + + align:start position:0% +not coding and it's the second example +where it's in a repeat this is just to + + align:start position:0% +where it's in a repeat this is just to + + + align:start position:0% +where it's in a repeat this is just to +you know i'm not giving you a random + + align:start position:0% +you know i'm not giving you a random + + + align:start position:0% +you know i'm not giving you a random +sample here i'm specifically biasing + + align:start position:0% +sample here i'm specifically biasing + + + align:start position:0% +sample here i'm specifically biasing +this towards very interesting + + align:start position:0% +this towards very interesting + + + align:start position:0% +this towards very interesting +uh genes very interesting + + align:start position:0% +uh genes very interesting + + + align:start position:0% +uh genes very interesting +traits that are associated with + + align:start position:0% +traits that are associated with + + + align:start position:0% +traits that are associated with +non-coding repetitive uh alleles + + align:start position:0% +non-coding repetitive uh alleles + + + align:start position:0% +non-coding repetitive uh alleles +in this case the trait that got the + + align:start position:0% +in this case the trait that got the + + + align:start position:0% +in this case the trait that got the +attention of these researchers it isn't + + align:start position:0% +attention of these researchers it isn't + + + align:start position:0% +attention of these researchers it isn't +necessarily proven + + align:start position:0% +necessarily proven + + + align:start position:0% +necessarily proven +uh that this is the the relationship but + + align:start position:0% +uh that this is the the relationship but + + + align:start position:0% +uh that this is the the relationship but +the association was studied was between + + align:start position:0% +the association was studied was between + + + align:start position:0% +the association was studied was between +anxiety relation related traits anxiety + + align:start position:0% +anxiety relation related traits anxiety + + + align:start position:0% +anxiety relation related traits anxiety +and a polymorphism in the serotonin + + align:start position:0% +and a polymorphism in the serotonin + + + align:start position:0% +and a polymorphism in the serotonin +transporter oh this is a science paper + + align:start position:0% +transporter oh this is a science paper + + + align:start position:0% +transporter oh this is a science paper +um now the next step in this is this + + align:start position:0% +um now the next step in this is this + + + align:start position:0% +um now the next step in this is this +okay that was found associated there + + align:start position:0% +okay that was found associated there + + + align:start position:0% +okay that was found associated there +were lots of other alleles + + align:start position:0% +were lots of other alleles + + + align:start position:0% +were lots of other alleles +randomly uh + + align:start position:0% +randomly uh + + + align:start position:0% +randomly uh +being moved around because these are + + align:start position:0% +being moved around because these are + + + align:start position:0% +being moved around because these are +humans we have no control over + + align:start position:0% +humans we have no control over + + + align:start position:0% +humans we have no control over +who mates with who or very little and uh + + align:start position:0% +who mates with who or very little and uh + + + align:start position:0% +who mates with who or very little and uh +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +so so you you get what you're what + + align:start position:0% +so so you you get what you're what + + + align:start position:0% +so so you you get what you're what +you're given you can do the survey as + + align:start position:0% +you're given you can do the survey as + + + align:start position:0% +you're given you can do the survey as +best you can but now in order to move it + + align:start position:0% +best you can but now in order to move it + + + align:start position:0% +best you can but now in order to move it +towards a mechanistic + + align:start position:0% +towards a mechanistic + + + align:start position:0% +towards a mechanistic +basis + + align:start position:0% +basis + + + align:start position:0% +basis +and a proof of introducing just this one + + align:start position:0% +and a proof of introducing just this one + + + align:start position:0% +and a proof of introducing just this one +point mutation now + + align:start position:0% +point mutation now + + + align:start position:0% +point mutation now +what is the mutation found in this case + + align:start position:0% +what is the mutation found in this case + + + align:start position:0% +what is the mutation found in this case +of anxiety relationship in this + + align:start position:0% +of anxiety relationship in this + + + align:start position:0% +of anxiety relationship in this +serotonin transporter it's upstream of + + align:start position:0% +serotonin transporter it's upstream of + + + align:start position:0% +serotonin transporter it's upstream of +the first rna encoding exon one + + align:start position:0% +the first rna encoding exon one + + + align:start position:0% +the first rna encoding exon one +uh it is a 44 base pair deletion in a + + align:start position:0% +uh it is a 44 base pair deletion in a + + + align:start position:0% +uh it is a 44 base pair deletion in a +repetitive region in a few in a region + + align:start position:0% +repetitive region in a few in a region + + + align:start position:0% +repetitive region in a few in a region +which might be a responsible for promote + + align:start position:0% +which might be a responsible for promote + + + align:start position:0% +which might be a responsible for promote +promoting transcription + + align:start position:0% +promoting transcription + + + align:start position:0% +promoting transcription +uh you have the short and the long + + align:start position:0% +uh you have the short and the long + + + align:start position:0% +uh you have the short and the long +allele just like uh in the ccr5 but in + + align:start position:0% +allele just like uh in the ccr5 but in + + + align:start position:0% +allele just like uh in the ccr5 but in +this case it's in the it's in a puted + + align:start position:0% +this case it's in the it's in a puted + + + align:start position:0% +this case it's in the it's in a puted +promoter element and when you make this + + align:start position:0% +promoter element and when you make this + + + align:start position:0% +promoter element and when you make this +construct then you uh + + align:start position:0% +construct then you uh + + + align:start position:0% +construct then you uh +hook it up to a luciferase uh + + align:start position:0% +hook it up to a luciferase uh + + + align:start position:0% +hook it up to a luciferase uh +enzymatic activity in vitro in um in + + align:start position:0% +enzymatic activity in vitro in um in + + + align:start position:0% +enzymatic activity in vitro in um in +cultured cells so you don't actually + + align:start position:0% +cultured cells so you don't actually + + + align:start position:0% +cultured cells so you don't actually +have to construct a mutant human + + align:start position:0% +have to construct a mutant human + + + align:start position:0% +have to construct a mutant human +you you can now see the long allele + + align:start position:0% +you you can now see the long allele + + + align:start position:0% +you you can now see the long allele +always produces higher levels of + + align:start position:0% +always produces higher levels of + + + align:start position:0% +always produces higher levels of +expression than the short allele and + + align:start position:0% +expression than the short allele and + + + align:start position:0% +expression than the short allele and +these little error bars + + align:start position:0% +these little error bars + + + align:start position:0% +these little error bars +on top of each of the measures + + align:start position:0% + + + + align:start position:0% + +show your + + align:start position:0% +show your + + + align:start position:0% +show your +statistical measure of standard + + align:start position:0% +statistical measure of standard + + + align:start position:0% +statistical measure of standard +deviation as we did in the first lecture + + align:start position:0% +deviation as we did in the first lecture + + + align:start position:0% +deviation as we did in the first lecture +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +and if the black + + align:start position:0% +and if the black + + + align:start position:0% +and if the black +mean which is the height of the bar is + + align:start position:0% +mean which is the height of the bar is + + + align:start position:0% +mean which is the height of the bar is +different from the white mean + + align:start position:0% +different from the white mean + + + align:start position:0% +different from the white mean +by more than a couple of these standard + + align:start position:0% +by more than a couple of these standard + + + align:start position:0% +by more than a couple of these standard +deviations which is the root mean square + + align:start position:0% +deviations which is the root mean square + + + align:start position:0% +deviations which is the root mean square +of the standard deviations of each of + + align:start position:0% +of the standard deviations of each of + + + align:start position:0% +of the standard deviations of each of +the measures then you call it + + align:start position:0% +the measures then you call it + + + align:start position:0% +the measures then you call it +statistically significant + + align:start position:0% +statistically significant + + + align:start position:0% +statistically significant +and that's what these triple stars mean + + align:start position:0% +and that's what these triple stars mean + + + align:start position:0% +and that's what these triple stars mean +it's the statistical shorthand for this + + align:start position:0% +it's the statistical shorthand for this + + + align:start position:0% +it's the statistical shorthand for this +is statistically significant at the + + align:start position:0% +is statistically significant at the + + + align:start position:0% +is statistically significant at the +cutoff that we're using say five percent + + align:start position:0% +cutoff that we're using say five percent + + + align:start position:0% +cutoff that we're using say five percent +now in this case it's kind of showing + + align:start position:0% +now in this case it's kind of showing + + + align:start position:0% +now in this case it's kind of showing +off because every one of them is + + align:start position:0% +off because every one of them is + + + align:start position:0% +off because every one of them is +statistically significant um + + align:start position:0% +statistically significant um + + + align:start position:0% +statistically significant um +by two different uh + + align:start position:0% +by two different uh + + + align:start position:0% +by two different uh +completely different assays here but the + + align:start position:0% +completely different assays here but the + + + align:start position:0% +completely different assays here but the +point is this does not prove that + + align:start position:0% +point is this does not prove that + + + align:start position:0% +point is this does not prove that +anxiety + + align:start position:0% +anxiety + + + align:start position:0% +anxiety +uh + + align:start position:0% +uh + + + align:start position:0% +uh +is is uh meaningfully associated with + + align:start position:0% +is is uh meaningfully associated with + + + align:start position:0% +is is uh meaningfully associated with +this but it's uh but it does prove that + + align:start position:0% +this but it's uh but it does prove that + + + align:start position:0% +this but it's uh but it does prove that +this repetitive polymorphism is is uh + + align:start position:0% +this repetitive polymorphism is is uh + + + align:start position:0% +this repetitive polymorphism is is uh +causally in + + align:start position:0% +causally in + + + align:start position:0% +causally in +capable of + + align:start position:0% +capable of + + + align:start position:0% +capable of +differential transcription levels or + + align:start position:0% +differential transcription levels or + + + align:start position:0% +differential transcription levels or +reporter gene so you by introducing it + + align:start position:0% +reporter gene so you by introducing it + + + align:start position:0% +reporter gene so you by introducing it +um into a into a + + align:start position:0% +um into a into a + + + align:start position:0% +um into a into a +clean + + align:start position:0% +clean + + + align:start position:0% +clean +uh + + align:start position:0% +uh + + + align:start position:0% +uh +cellular system you can test + + align:start position:0% +cellular system you can test + + + align:start position:0% +cellular system you can test +uh at least part of the mechanism that + + align:start position:0% +uh at least part of the mechanism that + + + align:start position:0% +uh at least part of the mechanism that +might be involved in the association + + align:start position:0% +might be involved in the association + + + align:start position:0% +might be involved in the association +that originally got your attention + + align:start position:0% +that originally got your attention + + + align:start position:0% +that originally got your attention +now as you can see + + align:start position:0% +now as you can see + + + align:start position:0% +now as you can see +we're getting into a fairly mature + + align:start position:0% +we're getting into a fairly mature + + + align:start position:0% +we're getting into a fairly mature +and fairly new phase of + + align:start position:0% +and fairly new phase of + + + align:start position:0% +and fairly new phase of +human genetics + + align:start position:0% +human genetics + + + align:start position:0% +human genetics +some of the concepts are used here will + + align:start position:0% +some of the concepts are used here will + + + align:start position:0% +some of the concepts are used here will +be useful in a variety of other systems + + align:start position:0% +be useful in a variety of other systems + + + align:start position:0% +be useful in a variety of other systems +where we have relatively little control + + align:start position:0% +where we have relatively little control + + + align:start position:0% +where we have relatively little control +over the genetics but certainly in + + align:start position:0% +over the genetics but certainly in + + + align:start position:0% +over the genetics but certainly in +humans it's a very large + + align:start position:0% +humans it's a very large + + + align:start position:0% +humans it's a very large +um + + align:start position:0% +um + + + align:start position:0% +um +need + + align:start position:0% +need + + + align:start position:0% +need +and + + align:start position:0% +and + + + align:start position:0% +and +where this happened historically is with + + align:start position:0% +where this happened historically is with + + + align:start position:0% +where this happened historically is with +mendelian linkage which would involve + + align:start position:0% +mendelian linkage which would involve + + + align:start position:0% +mendelian linkage which would involve +very large + + align:start position:0% +very large + + + align:start position:0% +very large +home families with a complete pedigree + + align:start position:0% +home families with a complete pedigree + + + align:start position:0% +home families with a complete pedigree +multi-generation great grandfathers and + + align:start position:0% +multi-generation great grandfathers and + + + align:start position:0% +multi-generation great grandfathers and +mothers all the way down + + align:start position:0% +mothers all the way down + + + align:start position:0% +mothers all the way down +hundreds of people in a family and + + align:start position:0% +hundreds of people in a family and + + + align:start position:0% +hundreds of people in a family and +that's the problem because there aren't + + align:start position:0% +that's the problem because there aren't + + + align:start position:0% +that's the problem because there aren't +that many diseases for which you have + + align:start position:0% +that many diseases for which you have + + + align:start position:0% +that many diseases for which you have +large families with simple mendelian + + align:start position:0% +large families with simple mendelian + + + align:start position:0% +large families with simple mendelian +inheritance common diseases tend to be + + align:start position:0% +inheritance common diseases tend to be + + + align:start position:0% +inheritance common diseases tend to be +much more complicated involving + + align:start position:0% +much more complicated involving + + + align:start position:0% +much more complicated involving +multiple genes simultaneously and small + + align:start position:0% +multiple genes simultaneously and small + + + align:start position:0% +multiple genes simultaneously and small +families + + align:start position:0% + + + + align:start position:0% + +then there's lincoln's disequilibrium + + align:start position:0% +then there's lincoln's disequilibrium + + + align:start position:0% +then there's lincoln's disequilibrium +which + + align:start position:0% +which + + + align:start position:0% +which +uh + + align:start position:0% +uh + + + align:start position:0% +uh +which is uh depends on these uh common + + align:start position:0% +which is uh depends on these uh common + + + align:start position:0% +which is uh depends on these uh common +alleles + + align:start position:0% +alleles + + + align:start position:0% +alleles +um + + align:start position:0% +um + + + align:start position:0% +um +going where the population has gone + + align:start position:0% +going where the population has gone + + + align:start position:0% +going where the population has gone +through a particularly small bottleneck + + align:start position:0% +through a particularly small bottleneck + + + align:start position:0% +through a particularly small bottleneck +and where uh your common allele is a + + align:start position:0% +and where uh your common allele is a + + + align:start position:0% +and where uh your common allele is a +pretty good distance away from the + + align:start position:0% +pretty good distance away from the + + + align:start position:0% +pretty good distance away from the +causative one but it allows you to map + + align:start position:0% +causative one but it allows you to map + + + align:start position:0% +causative one but it allows you to map +it into a ballpark and then you then you + + align:start position:0% +it into a ballpark and then you then you + + + align:start position:0% +it into a ballpark and then you then you +hunker down and do the more expensive um + + align:start position:0% +hunker down and do the more expensive um + + + align:start position:0% +hunker down and do the more expensive um +uh testing of hypotheses for all and + + align:start position:0% +uh testing of hypotheses for all and + + + align:start position:0% +uh testing of hypotheses for all and +look in sequencing and looking for + + align:start position:0% +look in sequencing and looking for + + + align:start position:0% +look in sequencing and looking for +potentially causative alleles once you + + align:start position:0% +potentially causative alleles once you + + + align:start position:0% +potentially causative alleles once you +find a potentially cause of allele + + align:start position:0% +find a potentially cause of allele + + + align:start position:0% +find a potentially cause of allele +something that looks suspicious maybe + + align:start position:0% +something that looks suspicious maybe + + + align:start position:0% +something that looks suspicious maybe +something that's in a coding region that + + align:start position:0% +something that's in a coding region that + + + align:start position:0% +something that's in a coding region that +it's conserved that's the first priority + + align:start position:0% +it's conserved that's the first priority + + + align:start position:0% +it's conserved that's the first priority +despite all the counter examples i've + + align:start position:0% +despite all the counter examples i've + + + align:start position:0% +despite all the counter examples i've +given + + align:start position:0% +given + + + align:start position:0% +given +and then you go like that but the + + align:start position:0% +and then you go like that but the + + + align:start position:0% +and then you go like that but the +problem is that it's here at the mercy + + align:start position:0% +problem is that it's here at the mercy + + + align:start position:0% +problem is that it's here at the mercy +of the recombination that might have + + align:start position:0% +of the recombination that might have + + + align:start position:0% +of the recombination that might have +occurred in that population when you get + + align:start position:0% +occurred in that population when you get + + + align:start position:0% +occurred in that population when you get +the very interesting populations like uh + + align:start position:0% +the very interesting populations like uh + + + align:start position:0% +the very interesting populations like uh +you know + + align:start position:0% +you know + + + align:start position:0% +you know +people of african-american descent where + + align:start position:0% +people of african-american descent where + + + align:start position:0% +people of african-american descent where +where the population is is very old + + align:start position:0% +where the population is is very old + + + align:start position:0% +where the population is is very old +hasn't passed through a population + + align:start position:0% +hasn't passed through a population + + + align:start position:0% +hasn't passed through a population +bottleneck + + align:start position:0% +bottleneck + + + align:start position:0% +bottleneck +the link the useful linkage this + + align:start position:0% +the link the useful linkage this + + + align:start position:0% +the link the useful linkage this +equilibrium is on a few + + align:start position:0% +equilibrium is on a few + + + align:start position:0% +equilibrium is on a few +couple of kilobases rather than hundreds + + align:start position:0% +couple of kilobases rather than hundreds + + + align:start position:0% +couple of kilobases rather than hundreds +of kilobases so it actually is hard to + + align:start position:0% +of kilobases so it actually is hard to + + + align:start position:0% +of kilobases so it actually is hard to +find things that are linked as to say in + + align:start position:0% +find things that are linked as to say in + + + align:start position:0% +find things that are linked as to say in +cis but not causative insist the cause + + align:start position:0% +cis but not causative insist the cause + + + align:start position:0% +cis but not causative insist the cause +of the allele + + align:start position:0% +of the allele + + + align:start position:0% +of the allele +instead you have to look directly for + + align:start position:0% +instead you have to look directly for + + + align:start position:0% +instead you have to look directly for +cause of alleles and that's where now + + align:start position:0% +cause of alleles and that's where now + + + align:start position:0% +cause of alleles and that's where now +you look for common causative alleles + + align:start position:0% + + + + align:start position:0% + +this has the problem we've been talking + + align:start position:0% +this has the problem we've been talking + + + align:start position:0% +this has the problem we've been talking +about which is that maybe common alleles + + align:start position:0% +about which is that maybe common alleles + + + align:start position:0% +about which is that maybe common alleles +aren't uh + + align:start position:0% +aren't uh + + + align:start position:0% +aren't uh +often caused to they've been selected + + align:start position:0% +often caused to they've been selected + + + align:start position:0% +often caused to they've been selected +out + + align:start position:0% +out + + + align:start position:0% +out +so then you get into the scenario what + + align:start position:0% +so then you get into the scenario what + + + align:start position:0% +so then you get into the scenario what +if we wanted to look at all alleles well + + align:start position:0% +if we wanted to look at all alleles well + + + align:start position:0% +if we wanted to look at all alleles well +theoretically there's nothing wrong with + + align:start position:0% +theoretically there's nothing wrong with + + + align:start position:0% +theoretically there's nothing wrong with +that + + align:start position:0% +that + + + align:start position:0% +that +it'd be great + + align:start position:0% +it'd be great + + + align:start position:0% +it'd be great +we could do the association studies we'd + + align:start position:0% +we could do the association studies we'd + + + align:start position:0% +we could do the association studies we'd +have to have fairly large population you + + align:start position:0% +have to have fairly large population you + + + align:start position:0% +have to have fairly large population you +know populations but you saw it was + + align:start position:0% +know populations but you saw it was + + + align:start position:0% +know populations but you saw it was +linear with an exponential increase in + + align:start position:0% +linear with an exponential increase in + + + align:start position:0% +linear with an exponential increase in +number of hypotheses and you could rank + + align:start position:0% +number of hypotheses and you could rank + + + align:start position:0% +number of hypotheses and you could rank +those hypotheses by a priori likelihood + + align:start position:0% +those hypotheses by a priori likelihood + + + align:start position:0% +those hypotheses by a priori likelihood +and so forth but it's expensive and so + + align:start position:0% +and so forth but it's expensive and so + + + align:start position:0% +and so forth but it's expensive and so +now the discussion now + + align:start position:0% +now the discussion now + + + align:start position:0% +now the discussion now +has to include a little bit + + align:start position:0% +has to include a little bit + + + align:start position:0% +has to include a little bit +of uh discussion of the new technologies + + align:start position:0% +of uh discussion of the new technologies + + + align:start position:0% +of uh discussion of the new technologies +that might make this less expensive and + + align:start position:0% +that might make this less expensive and + + + align:start position:0% +that might make this less expensive and +a discussion of how we got the first + + align:start position:0% +a discussion of how we got the first + + + align:start position:0% +a discussion of how we got the first +genome and how the new technologies + + align:start position:0% +genome and how the new technologies + + + align:start position:0% +genome and how the new technologies +might be a little different + + align:start position:0% +might be a little different + + + align:start position:0% +might be a little different +but we're going to do this in the + + align:start position:0% +but we're going to do this in the + + + align:start position:0% +but we're going to do this in the +context of computation in the sense of + + align:start position:0% +context of computation in the sense of + + + align:start position:0% +context of computation in the sense of +how do we deal with random and + + align:start position:0% +how do we deal with random and + + + align:start position:0% +how do we deal with random and +systematic errors as we plan our + + align:start position:0% +systematic errors as we plan our + + + align:start position:0% +systematic errors as we plan our +strategy for getting each of our genomes + + align:start position:0% +strategy for getting each of our genomes + + + align:start position:0% +strategy for getting each of our genomes +personal genome sequence for a thousand + + align:start position:0% +personal genome sequence for a thousand + + + align:start position:0% +personal genome sequence for a thousand +dollars or so + + align:start position:0% +dollars or so + + + align:start position:0% +dollars or so +how do we choose which technology to + + align:start position:0% +how do we choose which technology to + + + align:start position:0% +how do we choose which technology to +pursue which ones have the lowest uh + + align:start position:0% +pursue which ones have the lowest uh + + + align:start position:0% +pursue which ones have the lowest uh +intrinsic random and systematic errors + + align:start position:0% +intrinsic random and systematic errors + + + align:start position:0% +intrinsic random and systematic errors +so we needed to study the first genome + + align:start position:0% +so we needed to study the first genome + + + align:start position:0% +so we needed to study the first genome +to see what what we mean by random and + + align:start position:0% +to see what what we mean by random and + + + align:start position:0% +to see what what we mean by random and +systematic errors + + align:start position:0% +systematic errors + + + align:start position:0% +systematic errors +how many people here + + align:start position:0% +how many people here + + + align:start position:0% +how many people here +know what the difference is + + align:start position:0% +know what the difference is + + + align:start position:0% +know what the difference is +already + + align:start position:0% + + + + align:start position:0% + +a few okay but anyway whether you do or + + align:start position:0% +a few okay but anyway whether you do or + + + align:start position:0% +a few okay but anyway whether you do or +not it's it it's good for the soul to go + + align:start position:0% +not it's it it's good for the soul to go + + + align:start position:0% +not it's it it's good for the soul to go +through some real examples of this a + + align:start position:0% +through some real examples of this a + + + align:start position:0% +through some real examples of this a +random mutation is something which + + align:start position:0% +random mutation is something which + + + align:start position:0% +random mutation is something which +occurs every time you do the uh + + align:start position:0% +occurs every time you do the uh + + + align:start position:0% +occurs every time you do the uh +experiment you get a different mutate + + align:start position:0% +experiment you get a different mutate + + + align:start position:0% +experiment you get a different mutate +different error + + align:start position:0% +different error + + + align:start position:0% +different error +and + + align:start position:0% + + + + align:start position:0% + +a systematic one is something where if + + align:start position:0% +a systematic one is something where if + + + align:start position:0% +a systematic one is something where if +you do it over and over the same way + + align:start position:0% +you do it over and over the same way + + + align:start position:0% +you do it over and over the same way +you'll get the same error or a simple + + align:start position:0% +you'll get the same error or a simple + + + align:start position:0% +you'll get the same error or a simple +class of errors occurring + + align:start position:0% +class of errors occurring + + + align:start position:0% +class of errors occurring +more than once + + align:start position:0% +more than once + + + align:start position:0% +more than once +uh over and over so for sequencing the + + align:start position:0% +uh over and over so for sequencing the + + + align:start position:0% +uh over and over so for sequencing the +process involves picking + + align:start position:0% +process involves picking + + + align:start position:0% +process involves picking +something that you want to sequence + + align:start position:0% +something that you want to sequence + + + align:start position:0% +something that you want to sequence +we'll call it a clone or template then + + align:start position:0% +we'll call it a clone or template then + + + align:start position:0% +we'll call it a clone or template then +actually doing the sequencing and then + + align:start position:0% +actually doing the sequencing and then + + + align:start position:0% +actually doing the sequencing and then +assembling this into a meaningful uh + + align:start position:0% +assembling this into a meaningful uh + + + align:start position:0% +assembling this into a meaningful uh +interpreted sequence and that's the this + + align:start position:0% +interpreted sequence and that's the this + + + align:start position:0% +interpreted sequence and that's the this +is + + align:start position:0% +is + + + align:start position:0% +is +an example where we might have + + align:start position:0% +an example where we might have + + + align:start position:0% +an example where we might have +chosen + + align:start position:0% +chosen + + + align:start position:0% +chosen +these + + align:start position:0% + + + + align:start position:0% + +big clones in other words you might + + align:start position:0% +big clones in other words you might + + + align:start position:0% +big clones in other words you might +fragment the genome up randomly into + + align:start position:0% +fragment the genome up randomly into + + + align:start position:0% +fragment the genome up randomly into +large clones of 100 kilobases called + + align:start position:0% +large clones of 100 kilobases called + + + align:start position:0% +large clones of 100 kilobases called +bacterial artificial chromosomes for + + align:start position:0% +bacterial artificial chromosomes for + + + align:start position:0% +bacterial artificial chromosomes for +example + + align:start position:0% +example + + + align:start position:0% +example +and then that's all random and so + + align:start position:0% +and then that's all random and so + + + align:start position:0% +and then that's all random and so +there's a shotgun of that scale and then + + align:start position:0% +there's a shotgun of that scale and then + + + align:start position:0% +there's a shotgun of that scale and then +we break it up randomly into smaller + + align:start position:0% +we break it up randomly into smaller + + + align:start position:0% +we break it up randomly into smaller +pieces which provide us with little + + align:start position:0% +pieces which provide us with little + + + align:start position:0% +pieces which provide us with little +sequences and then in the computer we + + align:start position:0% +sequences and then in the computer we + + + align:start position:0% +sequences and then in the computer we +assemble these by methods that we'll + + align:start position:0% +assemble these by methods that we'll + + + align:start position:0% +assemble these by methods that we'll +discuss in the next lecture um + + align:start position:0% +discuss in the next lecture um + + + align:start position:0% +discuss in the next lecture um +which can you which can take even fairly + + align:start position:0% +which can you which can take even fairly + + + align:start position:0% +which can you which can take even fairly +different sequences and assemble them in + + align:start position:0% +different sequences and assemble them in + + + align:start position:0% +different sequences and assemble them in +this case we're talking about very + + align:start position:0% +this case we're talking about very + + + align:start position:0% +this case we're talking about very +similar sequences + + align:start position:0% +similar sequences + + + align:start position:0% +similar sequences +um and then you assemble the little + + align:start position:0% +um and then you assemble the little + + + align:start position:0% +um and then you assemble the little +sequences into big sequences and you + + align:start position:0% +sequences into big sequences and you + + + align:start position:0% +sequences into big sequences and you +assemble the big sequences into even + + align:start position:0% +assemble the big sequences into even + + + align:start position:0% +assemble the big sequences into even +bigger sequences and then you have the + + align:start position:0% +bigger sequences and then you have the + + + align:start position:0% +bigger sequences and then you have the +whole thing but you can see there's a + + align:start position:0% +whole thing but you can see there's a + + + align:start position:0% +whole thing but you can see there's a +lot of opportunity for error here + + align:start position:0% +lot of opportunity for error here + + + align:start position:0% +lot of opportunity for error here +we make it look simple in this slide but + + align:start position:0% +we make it look simple in this slide but + + + align:start position:0% +we make it look simple in this slide but +we're going to talk about + + align:start position:0% +we're going to talk about + + + align:start position:0% +we're going to talk about +random and systematic errors in a moment + + align:start position:0% +random and systematic errors in a moment + + + align:start position:0% +random and systematic errors in a moment +where do we get those sequences those + + align:start position:0% +where do we get those sequences those + + + align:start position:0% +where do we get those sequences those +little sequences that we want to + + align:start position:0% +little sequences that we want to + + + align:start position:0% +little sequences that we want to +assemble we we we're going to go through + + align:start position:0% +assemble we we we're going to go through + + + align:start position:0% +assemble we we we're going to go through +a few methods in a moment but the most + + align:start position:0% +a few methods in a moment but the most + + + align:start position:0% +a few methods in a moment but the most +common one by far the thing that + + align:start position:0% +common one by far the thing that + + + align:start position:0% +common one by far the thing that +generated + + align:start position:0% +generated + + + align:start position:0% +generated +over 90 percent of the human genome + + align:start position:0% +over 90 percent of the human genome + + + align:start position:0% +over 90 percent of the human genome +sequence in the last couple years is + + align:start position:0% +sequence in the last couple years is + + + align:start position:0% +sequence in the last couple years is +capillary electrophoresis of + + align:start position:0% +capillary electrophoresis of + + + align:start position:0% +capillary electrophoresis of +fluorescently labeled + + align:start position:0% +fluorescently labeled + + + align:start position:0% +fluorescently labeled +polymerase terminated products when you + + align:start position:0% +polymerase terminated products when you + + + align:start position:0% +polymerase terminated products when you +electrophorese these things you're + + align:start position:0% +electrophorese these things you're + + + align:start position:0% +electrophorese these things you're +separating + + align:start position:0% +separating + + + align:start position:0% +separating +uh dna + + align:start position:0% +uh dna + + + align:start position:0% +uh dna +fragments which are in nucleotides long + + align:start position:0% +fragments which are in nucleotides long + + + align:start position:0% +fragments which are in nucleotides long +from the from a dna fragment which is n + + align:start position:0% +from the from a dna fragment which is n + + + align:start position:0% +from the from a dna fragment which is n +plus one nucleotides long that's a very + + align:start position:0% +plus one nucleotides long that's a very + + + align:start position:0% +plus one nucleotides long that's a very +subtle difference as n gets big as n + + align:start position:0% +subtle difference as n gets big as n + + + align:start position:0% +subtle difference as n gets big as n +gets big it gets harder and harder to + + align:start position:0% +gets big it gets harder and harder to + + + align:start position:0% +gets big it gets harder and harder to +separate in from n plus one as it does + + align:start position:0% +separate in from n plus one as it does + + + align:start position:0% +separate in from n plus one as it does +so you start getting all kinds of errors + + align:start position:0% +so you start getting all kinds of errors + + + align:start position:0% +so you start getting all kinds of errors +the total number of errors here in the + + align:start position:0% +the total number of errors here in the + + + align:start position:0% +the total number of errors here in the +uh lower left-hand corner is a number of + + align:start position:0% +uh lower left-hand corner is a number of + + + align:start position:0% +uh lower left-hand corner is a number of +insertions plus the number of deletions + + align:start position:0% +insertions plus the number of deletions + + + align:start position:0% +insertions plus the number of deletions +plus the number of substitutions plus n + + align:start position:0% +plus the number of substitutions plus n + + + align:start position:0% +plus the number of substitutions plus n +which is a uh + + align:start position:0% +which is a uh + + + align:start position:0% +which is a uh +abbreviation for no call it means the + + align:start position:0% +abbreviation for no call it means the + + + align:start position:0% +abbreviation for no call it means the +software + + align:start position:0% +software + + + align:start position:0% +software +felt that it was so close that it + + align:start position:0% +felt that it was so close that it + + + align:start position:0% +felt that it was so close that it +couldn't call it at all it just said + + align:start position:0% +couldn't call it at all it just said + + + align:start position:0% +couldn't call it at all it just said +it's in i don't know whether it's an acg + + align:start position:0% +it's in i don't know whether it's an acg + + + align:start position:0% +it's in i don't know whether it's an acg +it doesn't know whether it's an a c g or + + align:start position:0% +it doesn't know whether it's an a c g or + + + align:start position:0% +it doesn't know whether it's an a c g or +t calls it a no call + + align:start position:0% +t calls it a no call + + + align:start position:0% +t calls it a no call +and so if you look through this table it + + align:start position:0% +and so if you look through this table it + + + align:start position:0% +and so if you look through this table it +shows uh + + align:start position:0% +shows uh + + + align:start position:0% +shows uh +on the vertical axis for each of these + + align:start position:0% +on the vertical axis for each of these + + + align:start position:0% +on the vertical axis for each of these +six + + align:start position:0% +six + + + align:start position:0% +six +uh his uh hit + + align:start position:0% +uh his uh hit + + + align:start position:0% +uh his uh hit +bar charts is as you go up on the + + align:start position:0% +bar charts is as you go up on the + + + align:start position:0% +bar charts is as you go up on the +vertical axis you go from very short + + align:start position:0% +vertical axis you go from very short + + + align:start position:0% +vertical axis you go from very short +reads where it's easy to separate in + + align:start position:0% +reads where it's easy to separate in + + + align:start position:0% +reads where it's easy to separate in +from n plus one electrophoretically to + + align:start position:0% +from n plus one electrophoretically to + + + align:start position:0% +from n plus one electrophoretically to +very long ones where you start + + align:start position:0% +very long ones where you start + + + align:start position:0% +very long ones where you start +accumulating insertion deletion errors + + align:start position:0% +accumulating insertion deletion errors + + + align:start position:0% +accumulating insertion deletion errors +insertion deletion substitution and ends + + align:start position:0% +insertion deletion substitution and ends + + + align:start position:0% +insertion deletion substitution and ends +they all go up with length and so you + + align:start position:0% +they all go up with length and so you + + + align:start position:0% +they all go up with length and so you +can think of that as + + align:start position:0% +can think of that as + + + align:start position:0% +can think of that as +a random error superimposed on the + + align:start position:0% +a random error superimposed on the + + + align:start position:0% +a random error superimposed on the +systematic error of if you always do the + + align:start position:0% +systematic error of if you always do the + + + align:start position:0% +systematic error of if you always do the +experiment so the same base pair is + + align:start position:0% +experiment so the same base pair is + + + align:start position:0% +experiment so the same base pair is +always at the end of your run it's going + + align:start position:0% +always at the end of your run it's going + + + align:start position:0% +always at the end of your run it's going +to always have a higher random error + + align:start position:0% +to always have a higher random error + + + align:start position:0% +to always have a higher random error +rate so this is kind of a combination of + + align:start position:0% +rate so this is kind of a combination of + + + align:start position:0% +rate so this is kind of a combination of +random and systematic error so let's go + + align:start position:0% +random and systematic error so let's go + + + align:start position:0% +random and systematic error so let's go +through + + align:start position:0% +through + + + align:start position:0% +through +some examples here + + align:start position:0% +some examples here + + + align:start position:0% +some examples here +we have just isolating the template to + + align:start position:0% +we have just isolating the template to + + + align:start position:0% +we have just isolating the template to +prepare it for sequencing + + align:start position:0% +prepare it for sequencing + + + align:start position:0% +prepare it for sequencing +there are systematic errors + + align:start position:0% +there are systematic errors + + + align:start position:0% +there are systematic errors +if you have certain kinds of repeats + + align:start position:0% +if you have certain kinds of repeats + + + align:start position:0% +if you have certain kinds of repeats +long inverted repeats or certain kinds + + align:start position:0% +long inverted repeats or certain kinds + + + align:start position:0% +long inverted repeats or certain kinds +of restriction elements that the + + align:start position:0% +of restriction elements that the + + + align:start position:0% +of restriction elements that the +bacteria doesn't like or likes to chew + + align:start position:0% +bacteria doesn't like or likes to chew + + + align:start position:0% +bacteria doesn't like or likes to chew +up + + align:start position:0% +up + + + align:start position:0% +up +then you won't get that clone and that + + align:start position:0% +then you won't get that clone and that + + + align:start position:0% +then you won't get that clone and that +would play the early part of the genome + + align:start position:0% +would play the early part of the genome + + + align:start position:0% +would play the early part of the genome +project is + + align:start position:0% +project is + + + align:start position:0% +project is +you'd keep trying again and again the + + align:start position:0% +you'd keep trying again and again the + + + align:start position:0% +you'd keep trying again and again the +same way and you just wouldn't get + + align:start position:0% +same way and you just wouldn't get + + + align:start position:0% +same way and you just wouldn't get +certain clones it's as if there was a + + align:start position:0% +certain clones it's as if there was a + + + align:start position:0% +certain clones it's as if there was a +hole there you know that there's + + align:start position:0% +hole there you know that there's + + + align:start position:0% +hole there you know that there's +something there but you couldn't clone + + align:start position:0% +something there but you couldn't clone + + + align:start position:0% +something there but you couldn't clone +it + + align:start position:0% +it + + + align:start position:0% +it +um sequencing hairpins uh can form in + + align:start position:0% +um sequencing hairpins uh can form in + + + align:start position:0% +um sequencing hairpins uh can form in +the single strand of nucleic acids where + + align:start position:0% +the single strand of nucleic acids where + + + align:start position:0% +the single strand of nucleic acids where +you're trying to separate in from n plus + + align:start position:0% +you're trying to separate in from n plus + + + align:start position:0% +you're trying to separate in from n plus +one and those hairpins then fake out the + + align:start position:0% +one and those hairpins then fake out the + + + align:start position:0% +one and those hairpins then fake out the +the the gel electrophoresis and make it + + align:start position:0% +the the gel electrophoresis and make it + + + align:start position:0% +the the gel electrophoresis and make it +seem like it's much smaller than it + + align:start position:0% +seem like it's much smaller than it + + + align:start position:0% +seem like it's much smaller than it +actually is + + align:start position:0% +actually is + + + align:start position:0% +actually is +tandem repeats cause a problem in all + + align:start position:0% +tandem repeats cause a problem in all + + + align:start position:0% +tandem repeats cause a problem in all +three of these stages um + + align:start position:0% +three of these stages um + + + align:start position:0% +three of these stages um +in sequencing they get some polymerase + + align:start position:0% +in sequencing they get some polymerase + + + align:start position:0% +in sequencing they get some polymerase +stuttering and uh and you get a little + + align:start position:0% +stuttering and uh and you get a little + + + align:start position:0% +stuttering and uh and you get a little +artifacts an assembly repeats + + align:start position:0% +artifacts an assembly repeats + + + align:start position:0% +artifacts an assembly repeats +you're assembling by sequence homolog a + + align:start position:0% +you're assembling by sequence homolog a + + + align:start position:0% +you're assembling by sequence homolog a +sequence alignment if you have a repeat + + align:start position:0% +sequence alignment if you have a repeat + + + align:start position:0% +sequence alignment if you have a repeat +then the repeat's going to align just as + + align:start position:0% +then the repeat's going to align just as + + + align:start position:0% +then the repeat's going to align just as +well + + align:start position:0% +well + + + align:start position:0% +well +because it's a repeat within the genome + + align:start position:0% +because it's a repeat within the genome + + + align:start position:0% +because it's a repeat within the genome +as a repeat do experimental repeating + + align:start position:0% +as a repeat do experimental repeating + + + align:start position:0% +as a repeat do experimental repeating +and so the alignment can be off + + align:start position:0% +and so the alignment can be off + + + align:start position:0% +and so the alignment can be off +uh the errors that you got from these + + align:start position:0% +uh the errors that you got from these + + + align:start position:0% +uh the errors that you got from these +earlier steps make it hard to assemble + + align:start position:0% +earlier steps make it hard to assemble + + + align:start position:0% +earlier steps make it hard to assemble +polymorphisms look like errors chimeric + + align:start position:0% +polymorphisms look like errors chimeric + + + align:start position:0% +polymorphisms look like errors chimeric +clones means you've got things that have + + align:start position:0% +clones means you've got things that have + + + align:start position:0% +clones means you've got things that have +been disassembled + + align:start position:0% +been disassembled + + + align:start position:0% +been disassembled +early on here + + align:start position:0% +early on here + + + align:start position:0% +early on here +and so on + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +when we uh + + align:start position:0% +when we uh + + + align:start position:0% +when we uh +do this random selection of big clones + + align:start position:0% +do this random selection of big clones + + + align:start position:0% +do this random selection of big clones +and random selection of little phones + + align:start position:0% +and random selection of little phones + + + align:start position:0% +and random selection of little phones +for sequencing we want to know when to + + align:start position:0% +for sequencing we want to know when to + + + align:start position:0% +for sequencing we want to know when to +quit + + align:start position:0% +quit + + + align:start position:0% +quit +now you can you could say we're going to + + align:start position:0% +now you can you could say we're going to + + + align:start position:0% +now you can you could say we're going to +quit once we get it all assembled but + + align:start position:0% +quit once we get it all assembled but + + + align:start position:0% +quit once we get it all assembled but +you need to accumulate a certain amount + + align:start position:0% +you need to accumulate a certain amount + + + align:start position:0% +you need to accumulate a certain amount +of data + + align:start position:0% +of data + + + align:start position:0% +of data +in advance before you try to assemble it + + align:start position:0% +in advance before you try to assemble it + + + align:start position:0% +in advance before you try to assemble it +and so + + align:start position:0% +and so + + + align:start position:0% +and so +there were various + + align:start position:0% +there were various + + + align:start position:0% +there were various +it's the when to quit + + align:start position:0% +it's the when to quit + + + align:start position:0% +it's the when to quit +and this is related to the poisson + + align:start position:0% +and this is related to the poisson + + + align:start position:0% +and this is related to the poisson +distribution but it's not exactly and in + + align:start position:0% +distribution but it's not exactly and in + + + align:start position:0% +distribution but it's not exactly and in +fact + + align:start position:0% +fact + + + align:start position:0% +fact +one of the one of the studies done in + + align:start position:0% +one of the one of the studies done in + + + align:start position:0% +one of the one of the studies done in +1988 made some + + align:start position:0% +1988 made some + + + align:start position:0% +1988 made some +poor assumptions + + align:start position:0% +poor assumptions + + + align:start position:0% +poor assumptions +about the remember we we limit we + + align:start position:0% +about the remember we we limit we + + + align:start position:0% +about the remember we we limit we +mentioned it in the first lecture the + + align:start position:0% +mentioned it in the first lecture the + + + align:start position:0% +mentioned it in the first lecture the +assumptions of the poisson distribution + + align:start position:0% +assumptions of the poisson distribution + + + align:start position:0% +assumptions of the poisson distribution +um + + align:start position:0% +um + + + align:start position:0% +um +that make it an approximation when it + + align:start position:0% +that make it an approximation when it + + + align:start position:0% +that make it an approximation when it +becomes an approximation to a more uh + + align:start position:0% +becomes an approximation to a more uh + + + align:start position:0% +becomes an approximation to a more uh +formal distribution like the binomial + + align:start position:0% +formal distribution like the binomial + + + align:start position:0% +formal distribution like the binomial +anyway that approximation you should be + + align:start position:0% +anyway that approximation you should be + + + align:start position:0% +anyway that approximation you should be +getting as you get higher and higher + + align:start position:0% +getting as you get higher and higher + + + align:start position:0% +getting as you get higher and higher +coverage meaning + + align:start position:0% +coverage meaning + + + align:start position:0% +coverage meaning +more and more + + align:start position:0% +more and more + + + align:start position:0% +more and more +experimental repeats you'll eventually + + align:start position:0% +experimental repeats you'll eventually + + + align:start position:0% +experimental repeats you'll eventually +fill all the gaps + + align:start position:0% +fill all the gaps + + + align:start position:0% +fill all the gaps +and that means you'll get 100 percent + + align:start position:0% +and that means you'll get 100 percent + + + align:start position:0% +and that means you'll get 100 percent +complete coverage and it should + + align:start position:0% +complete coverage and it should + + + align:start position:0% +complete coverage and it should +asymptotically approach that well if you + + align:start position:0% +asymptotically approach that well if you + + + align:start position:0% +asymptotically approach that well if you +use the poisson incorrectly as authors + + align:start position:0% +use the poisson incorrectly as authors + + + align:start position:0% +use the poisson incorrectly as authors +did in 1988 you you basically go off to + + align:start position:0% +did in 1988 you you basically go off to + + + align:start position:0% +did in 1988 you you basically go off to +infinity you get you know 200 coverage + + align:start position:0% +infinity you get you know 200 coverage + + + align:start position:0% +infinity you get you know 200 coverage +which is physically impossible but both + + align:start position:0% +which is physically impossible but both + + + align:start position:0% +which is physically impossible but both +an earlier study which they ignored and + + align:start position:0% +an earlier study which they ignored and + + + align:start position:0% +an earlier study which they ignored and +a more recent study got it right and + + align:start position:0% +a more recent study got it right and + + + align:start position:0% +a more recent study got it right and +these are slightly different measures + + align:start position:0% +these are slightly different measures + + + align:start position:0% +these are slightly different measures +but they both converge on 100 + + align:start position:0% +but they both converge on 100 + + + align:start position:0% +but they both converge on 100 +and i urge you to look at that if you're + + align:start position:0% +and i urge you to look at that if you're + + + align:start position:0% +and i urge you to look at that if you're +designing an experiment um with simple + + align:start position:0% +designing an experiment um with simple + + + align:start position:0% +designing an experiment um with simple +formula on the other hand if you want to + + align:start position:0% +formula on the other hand if you want to + + + align:start position:0% +formula on the other hand if you want to +design the experiment that are more + + align:start position:0% +design the experiment that are more + + + align:start position:0% +design the experiment that are more +explicit you eventually get to a point + + align:start position:0% +explicit you eventually get to a point + + + align:start position:0% +explicit you eventually get to a point +where an a simple analytic formula won't + + align:start position:0% +where an a simple analytic formula won't + + + align:start position:0% +where an a simple analytic formula won't +do and you have to do monte carlo we + + align:start position:0% +do and you have to do monte carlo we + + + align:start position:0% +do and you have to do monte carlo we +treated this in the first class of uh + + align:start position:0% +treated this in the first class of uh + + + align:start position:0% +treated this in the first class of uh +you know analytic versus numeric + + align:start position:0% +you know analytic versus numeric + + + align:start position:0% +you know analytic versus numeric +differential equations and in many other + + align:start position:0% +differential equations and in many other + + + align:start position:0% +differential equations and in many other +cases the simulation you want to do is + + align:start position:0% +cases the simulation you want to do is + + + align:start position:0% +cases the simulation you want to do is +beyond it is too + + align:start position:0% +beyond it is too + + + align:start position:0% +beyond it is too +too hard to do analytically so gene + + align:start position:0% +too hard to do analytically so gene + + + align:start position:0% +too hard to do analytically so gene +myers uh set up just listed all the + + align:start position:0% +myers uh set up just listed all the + + + align:start position:0% +myers uh set up just listed all the +things he thought would be uh could + + align:start position:0% +things he thought would be uh could + + + align:start position:0% +things he thought would be uh could +affect the ability to assemble + + align:start position:0% +affect the ability to assemble + + + align:start position:0% +affect the ability to assemble +a genome sequence the read length and + + align:start position:0% +a genome sequence the read length and + + + align:start position:0% +a genome sequence the read length and +the + + align:start position:0% + + + + align:start position:0% + +types of repeats and all this stuff was + + align:start position:0% +types of repeats and all this stuff was + + + align:start position:0% +types of repeats and all this stuff was +simulated and he cranked from the + + align:start position:0% +simulated and he cranked from the + + + align:start position:0% +simulated and he cranked from the +simulation on real human genome size + + align:start position:0% +simulation on real human genome size + + + align:start position:0% +simulation on real human genome size +projects + + align:start position:0% +projects + + + align:start position:0% +projects +and came to the conclusion that you + + align:start position:0% +and came to the conclusion that you + + + align:start position:0% +and came to the conclusion that you +could do a shotgun assembly of a + + align:start position:0% +could do a shotgun assembly of a + + + align:start position:0% +could do a shotgun assembly of a +mammalian genome + + align:start position:0% +mammalian genome + + + align:start position:0% +mammalian genome +a company called solera was formed gene + + align:start position:0% +a company called solera was formed gene + + + align:start position:0% +a company called solera was formed gene +myers was hired + + align:start position:0% +myers was hired + + + align:start position:0% +myers was hired +as the computer guru they put together + + align:start position:0% +as the computer guru they put together + + + align:start position:0% +as the computer guru they put together +you know a large stable of computers and + + align:start position:0% +you know a large stable of computers and + + + align:start position:0% +you know a large stable of computers and +they started doing this on the human and + + align:start position:0% +they started doing this on the human and + + + align:start position:0% +they started doing this on the human and +the mouse genome + + align:start position:0% +the mouse genome + + + align:start position:0% +the mouse genome +the human genome was in the end not done + + align:start position:0% +the human genome was in the end not done + + + align:start position:0% +the human genome was in the end not done +by this method but the mouse genome was + + align:start position:0% +by this method but the mouse genome was + + + align:start position:0% +by this method but the mouse genome was +and it was a pretty good assembly the + + align:start position:0% +and it was a pretty good assembly the + + + align:start position:0% +and it was a pretty good assembly the +drosophila genome missing the drosophila + + align:start position:0% +drosophila genome missing the drosophila + + + align:start position:0% +drosophila genome missing the drosophila +repeats was also done by this method so + + align:start position:0% +repeats was also done by this method so + + + align:start position:0% +repeats was also done by this method so +this is scaled very gracefully from the + + align:start position:0% +this is scaled very gracefully from the + + + align:start position:0% +this is scaled very gracefully from the +first shotgun sequence which is on a 4kb + + align:start position:0% +first shotgun sequence which is on a 4kb + + + align:start position:0% +first shotgun sequence which is on a 4kb +plasmid to um + + align:start position:0% +plasmid to um + + + align:start position:0% +plasmid to um +to mammalian science genomes + + align:start position:0% +to mammalian science genomes + + + align:start position:0% +to mammalian science genomes +no mammalian genome is completely + + align:start position:0% +no mammalian genome is completely + + + align:start position:0% +no mammalian genome is completely +sequenced so we can't really declare + + align:start position:0% +sequenced so we can't really declare + + + align:start position:0% +sequenced so we can't really declare +victory but the sort of simulation that + + align:start position:0% +victory but the sort of simulation that + + + align:start position:0% +victory but the sort of simulation that +he did here + + align:start position:0% +he did here + + + align:start position:0% +he did here +has played out very nicely + + align:start position:0% +has played out very nicely + + + align:start position:0% +has played out very nicely +uh + + align:start position:0% +uh + + + align:start position:0% +uh +right here in boston there will be you + + align:start position:0% +right here in boston there will be you + + + align:start position:0% +right here in boston there will be you +know when we start thinking of the + + align:start position:0% +know when we start thinking of the + + + align:start position:0% +know when we start thinking of the +future of sequencing technology we would + + align:start position:0% +future of sequencing technology we would + + + align:start position:0% +future of sequencing technology we would +all like this is + + align:start position:0% +all like this is + + + align:start position:0% +all like this is +almost uncontroversial as to how much we + + align:start position:0% +almost uncontroversial as to how much we + + + align:start position:0% +almost uncontroversial as to how much we +desire that the genome not cost three + + align:start position:0% +desire that the genome not cost three + + + align:start position:0% +desire that the genome not cost three +billion dollars but it cost a thousand + + align:start position:0% +billion dollars but it cost a thousand + + + align:start position:0% +billion dollars but it cost a thousand +dollars and now there are a number of + + align:start position:0% +dollars and now there are a number of + + + align:start position:0% +dollars and now there are a number of +people who are uh + + align:start position:0% +people who are uh + + + align:start position:0% +people who are uh +making taking very definite steps to get + + align:start position:0% +making taking very definite steps to get + + + align:start position:0% +making taking very definite steps to get +us to that point + + align:start position:0% +us to that point + + + align:start position:0% +us to that point +uh + + align:start position:0% +uh + + + align:start position:0% +uh +to understand systematic and random + + align:start position:0% +to understand systematic and random + + + align:start position:0% +to understand systematic and random +errors that can occur in these steps + + align:start position:0% +errors that can occur in these steps + + + align:start position:0% +errors that can occur in these steps +let's take this dideoxy gel excretions + + align:start position:0% +let's take this dideoxy gel excretions + + + align:start position:0% +let's take this dideoxy gel excretions +we've been talking about here you have + + align:start position:0% +we've been talking about here you have + + + align:start position:0% +we've been talking about here you have +four different colored terminators this + + align:start position:0% +four different colored terminators this + + + align:start position:0% +four different colored terminators this +is where the the the polymerase can't go + + align:start position:0% +is where the the the polymerase can't go + + + align:start position:0% +is where the the the polymerase can't go +any further because + + align:start position:0% +any further because + + + align:start position:0% +any further because +there's no there's a blocking group here + + align:start position:0% +there's no there's a blocking group here + + + align:start position:0% +there's no there's a blocking group here +which is fluorescent labeled and if the + + align:start position:0% +which is fluorescent labeled and if the + + + align:start position:0% +which is fluorescent labeled and if the +template on the far left here + + align:start position:0% +template on the far left here + + + align:start position:0% +template on the far left here +is ready to accept an a you'll get an a + + align:start position:0% +is ready to accept an a you'll get an a + + + align:start position:0% +is ready to accept an a you'll get an a +and + + align:start position:0% +and + + + align:start position:0% +and +this in an n minus one will separate on + + align:start position:0% +this in an n minus one will separate on + + + align:start position:0% +this in an n minus one will separate on +this electrophoresis and the four colors + + align:start position:0% +this electrophoresis and the four colors + + + align:start position:0% +this electrophoresis and the four colors +will give you this four color pattern + + align:start position:0% +will give you this four color pattern + + + align:start position:0% +will give you this four color pattern +where the + + align:start position:0% +where the + + + align:start position:0% +where the +intensity reflects a good termination at + + align:start position:0% +intensity reflects a good termination at + + + align:start position:0% +intensity reflects a good termination at +that position + + align:start position:0% +that position + + + align:start position:0% +that position +and you can basically go along reading + + align:start position:0% +and you can basically go along reading + + + align:start position:0% +and you can basically go along reading +it g c g g a t now this is the + + align:start position:0% +it g c g g a t now this is the + + + align:start position:0% +it g c g g a t now this is the +well-behaved part an example of a + + align:start position:0% +well-behaved part an example of a + + + align:start position:0% +well-behaved part an example of a +systematic error that you get in this + + align:start position:0% +systematic error that you get in this + + + align:start position:0% +systematic error that you get in this +extension + + align:start position:0% +extension + + + align:start position:0% +extension +occurs here in the upper right hand + + align:start position:0% +occurs here in the upper right hand + + + align:start position:0% +occurs here in the upper right hand +corner of slide 40. + + align:start position:0% +corner of slide 40. + + + align:start position:0% +corner of slide 40. +now you've got because of one of these + + align:start position:0% +now you've got because of one of these + + + align:start position:0% +now you've got because of one of these +hairpins that i mentioned before you've + + align:start position:0% +hairpins that i mentioned before you've + + + align:start position:0% +hairpins that i mentioned before you've +got a pile up of + + align:start position:0% +got a pile up of + + + align:start position:0% +got a pile up of +seven nucleotides all at the same + + align:start position:0% +seven nucleotides all at the same + + + align:start position:0% +seven nucleotides all at the same +position + + align:start position:0% +position + + + align:start position:0% +position +a completely alternative method that + + align:start position:0% +a completely alternative method that + + + align:start position:0% +a completely alternative method that +doesn't involve gel phrases called + + align:start position:0% +doesn't involve gel phrases called + + + align:start position:0% +doesn't involve gel phrases called +pyrosequencing and this is an equivalent + + align:start position:0% +pyrosequencing and this is an equivalent + + + align:start position:0% +pyrosequencing and this is an equivalent +that you can be done + + align:start position:0% +that you can be done + + + align:start position:0% +that you can be done +with fluorescent addition + + align:start position:0% +with fluorescent addition + + + align:start position:0% +with fluorescent addition +instead of separate separating them in + + align:start position:0% +instead of separate separating them in + + + align:start position:0% +instead of separate separating them in +time by their size in electrophoresis + + align:start position:0% +time by their size in electrophoresis + + + align:start position:0% +time by their size in electrophoresis +you in time you ask serially do you want + + align:start position:0% +you in time you ask serially do you want + + + align:start position:0% +you in time you ask serially do you want +an a here if yes then you get a little + + align:start position:0% +an a here if yes then you get a little + + + align:start position:0% +an a here if yes then you get a little +green you get a little peak + + align:start position:0% +green you get a little peak + + + align:start position:0% +green you get a little peak +of um + + align:start position:0% +of um + + + align:start position:0% +of um +representing the release of + + align:start position:0% +representing the release of + + + align:start position:0% +representing the release of +pyrophosphate or the incorporation of + + align:start position:0% +pyrophosphate or the incorporation of + + + align:start position:0% +pyrophosphate or the incorporation of +fluorescent a + + align:start position:0% +fluorescent a + + + align:start position:0% +fluorescent a +and then you ask does you want a t and + + align:start position:0% +and then you ask does you want a t and + + + align:start position:0% +and then you ask does you want a t and +so forth and you go along and + + align:start position:0% +so forth and you go along and + + + align:start position:0% +so forth and you go along and +each signal means yes + + align:start position:0% +each signal means yes + + + align:start position:0% +each signal means yes +yes to the answer that it's ready for + + align:start position:0% +yes to the answer that it's ready for + + + align:start position:0% +yes to the answer that it's ready for +that particular base + + align:start position:0% +that particular base + + + align:start position:0% +that particular base +and you can see this doesn't have any + + align:start position:0% +and you can see this doesn't have any + + + align:start position:0% +and you can see this doesn't have any +problems with this hairpin region + + align:start position:0% +problems with this hairpin region + + + align:start position:0% +problems with this hairpin region +so it has a + + align:start position:0% +so it has a + + + align:start position:0% +so it has a +so when you have a systematic area you + + align:start position:0% +so when you have a systematic area you + + + align:start position:0% +so when you have a systematic area you +have to change the method that you're + + align:start position:0% +have to change the method that you're + + + align:start position:0% +have to change the method that you're +using fairly radically the opposite + + align:start position:0% +using fairly radically the opposite + + + align:start position:0% +using fairly radically the opposite +strand + + align:start position:0% +strand + + + align:start position:0% +strand +or a completely different method + + align:start position:0% + + + + align:start position:0% + +if you have + + align:start position:0% +if you have + + + align:start position:0% +if you have +early on we had huge differences in + + align:start position:0% +early on we had huge differences in + + + align:start position:0% +early on we had huge differences in +intensity of the fluorophores and + + align:start position:0% +intensity of the fluorophores and + + + align:start position:0% +intensity of the fluorophores and +different diff and new enzymes and new + + align:start position:0% +different diff and new enzymes and new + + + align:start position:0% +different diff and new enzymes and new +fluorophores were developed + + align:start position:0% +fluorophores were developed + + + align:start position:0% +fluorophores were developed +by tabor and matthews and glazer and so + + align:start position:0% +by tabor and matthews and glazer and so + + + align:start position:0% +by tabor and matthews and glazer and so +forth and this was a huge + + align:start position:0% +forth and this was a huge + + + align:start position:0% +forth and this was a huge +advance in making everything uniform and + + align:start position:0% +advance in making everything uniform and + + + align:start position:0% +advance in making everything uniform and +eliminating systematic errors + + align:start position:0% +eliminating systematic errors + + + align:start position:0% +eliminating systematic errors +so the sort of things that are on the + + align:start position:0% +so the sort of things that are on the + + + align:start position:0% +so the sort of things that are on the +horizon that hopefully will be discussed + + align:start position:0% +horizon that hopefully will be discussed + + + align:start position:0% +horizon that hopefully will be discussed +tomorrow in boston + + align:start position:0% +tomorrow in boston + + + align:start position:0% +tomorrow in boston +we've talked about + + align:start position:0% +we've talked about + + + align:start position:0% +we've talked about +this + + align:start position:0% +this + + + align:start position:0% +this +single + + align:start position:0% +single + + + align:start position:0% +single +short number of base extensions like + + align:start position:0% +short number of base extensions like + + + align:start position:0% +short number of base extensions like +power sequencing + + align:start position:0% +power sequencing + + + align:start position:0% +power sequencing +the longer extensions in capillary + + align:start position:0% +the longer extensions in capillary + + + align:start position:0% +the longer extensions in capillary +arrays which capillary arrays + + align:start position:0% +arrays which capillary arrays + + + align:start position:0% +arrays which capillary arrays +are changing from long capillaries into + + align:start position:0% +are changing from long capillaries into + + + align:start position:0% +are changing from long capillaries into +microfabricated uh chips + + align:start position:0% +microfabricated uh chips + + + align:start position:0% +microfabricated uh chips +i'll show an example of a mass spec in + + align:start position:0% +i'll show an example of a mass spec in + + + align:start position:0% +i'll show an example of a mass spec in +just a moment you've got + + align:start position:0% +just a moment you've got + + + align:start position:0% +just a moment you've got +a + + align:start position:0% +a + + + align:start position:0% +a +sequencing by hybridization on our + + align:start position:0% +sequencing by hybridization on our + + + align:start position:0% +sequencing by hybridization on our +arrays we'll illustrate + + align:start position:0% +arrays we'll illustrate + + + align:start position:0% +arrays we'll illustrate +as a prelude as an example of + + align:start position:0% +as a prelude as an example of + + + align:start position:0% +as a prelude as an example of +aphametrics technology + + align:start position:0% +aphametrics technology + + + align:start position:0% +aphametrics technology +in this slide + + align:start position:0% +in this slide + + + align:start position:0% +in this slide +okay so the idea here this is mainly for + + align:start position:0% +okay so the idea here this is mainly for + + + align:start position:0% +okay so the idea here this is mainly for +resequencing some of the some of the + + align:start position:0% +resequencing some of the some of the + + + align:start position:0% +resequencing some of the some of the +ways of reducing the cost of sequencing + + align:start position:0% +ways of reducing the cost of sequencing + + + align:start position:0% +ways of reducing the cost of sequencing +a human genome will not apply to + + align:start position:0% +a human genome will not apply to + + + align:start position:0% +a human genome will not apply to +sequencing brand new genomes but they + + align:start position:0% +sequencing brand new genomes but they + + + align:start position:0% +sequencing brand new genomes but they +still we need to pursue them because + + align:start position:0% +still we need to pursue them because + + + align:start position:0% +still we need to pursue them because +this may be the way that we get the + + align:start position:0% +this may be the way that we get the + + + align:start position:0% +this may be the way that we get the +thousand dollar human genome even if we + + align:start position:0% +thousand dollar human genome even if we + + + align:start position:0% +thousand dollar human genome even if we +don't get other ones + + align:start position:0% +don't get other ones + + + align:start position:0% +don't get other ones +um and here you know the sequence except + + align:start position:0% +um and here you know the sequence except + + + align:start position:0% +um and here you know the sequence except +there's some + + align:start position:0% +there's some + + + align:start position:0% +there's some +there's a possibility that could be a + + align:start position:0% +there's a possibility that could be a + + + align:start position:0% +there's a possibility that could be a +polymorphism at any base it could be any + + align:start position:0% +polymorphism at any base it could be any + + + align:start position:0% +polymorphism at any base it could be any +single base substitution at any base and + + align:start position:0% +single base substitution at any base and + + + align:start position:0% +single base substitution at any base and +so you you don't necessarily know in + + align:start position:0% +so you you don't necessarily know in + + + align:start position:0% +so you you don't necessarily know in +advance what the common ones are the + + align:start position:0% +advance what the common ones are the + + + align:start position:0% +advance what the common ones are the +rare ones but you do know the canonical + + align:start position:0% +rare ones but you do know the canonical + + + align:start position:0% +rare ones but you do know the canonical +sequence and so at every position you'll + + align:start position:0% +sequence and so at every position you'll + + + align:start position:0% +sequence and so at every position you'll +make uh + + align:start position:0% +make uh + + + align:start position:0% +make uh +you'll make a 25 mirror oligonucleotide + + align:start position:0% +you'll make a 25 mirror oligonucleotide + + + align:start position:0% +you'll make a 25 mirror oligonucleotide +which will bind to a fluorescently + + align:start position:0% +which will bind to a fluorescently + + + align:start position:0% +which will bind to a fluorescently +labeled version of your genome or a + + align:start position:0% +labeled version of your genome or a + + + align:start position:0% +labeled version of your genome or a +piece of your genome + + align:start position:0% +piece of your genome + + + align:start position:0% +piece of your genome +and this is actually developed for hiv + + align:start position:0% +and this is actually developed for hiv + + + align:start position:0% +and this is actually developed for hiv +resequencing by alphametrics + + align:start position:0% +resequencing by alphametrics + + + align:start position:0% +resequencing by alphametrics +and at this middle position + + align:start position:0% +and at this middle position + + + align:start position:0% +and at this middle position +you'll put in all four possible + + align:start position:0% +you'll put in all four possible + + + align:start position:0% +you'll put in all four possible +uh substitutions t g c or a + + align:start position:0% +uh substitutions t g c or a + + + align:start position:0% +uh substitutions t g c or a +and you'll you'll you'll consider each + + align:start position:0% +and you'll you'll you'll consider each + + + align:start position:0% +and you'll you'll you'll consider each +possible uh + + align:start position:0% +possible uh + + + align:start position:0% +possible uh +template + + align:start position:0% +template + + + align:start position:0% +template +um so if you have the template which is + + align:start position:0% +um so if you have the template which is + + + align:start position:0% +um so if you have the template which is +let's say these are the two alleles that + + align:start position:0% +let's say these are the two alleles that + + + align:start position:0% +let's say these are the two alleles that +occur in the human population or in your + + align:start position:0% +occur in the human population or in your + + + align:start position:0% +occur in the human population or in your +sample + + align:start position:0% +sample + + + align:start position:0% +sample +you can have this sequence and then all + + align:start position:0% +you can have this sequence and then all + + + align:start position:0% +you can have this sequence and then all +the variations on it stepping along + + align:start position:0% +the variations on it stepping along + + + align:start position:0% +the variations on it stepping along +changing a tc tgca for the first base + + align:start position:0% +changing a tc tgca for the first base + + + align:start position:0% +changing a tc tgca for the first base +the second base of third base and so + + align:start position:0% +the second base of third base and so + + + align:start position:0% +the second base of third base and so +forth until you hit this one and this is + + align:start position:0% +forth until you hit this one and this is + + + align:start position:0% +forth until you hit this one and this is +where the real polymorphism occurs + + align:start position:0% +where the real polymorphism occurs + + + align:start position:0% +where the real polymorphism occurs +and you could have either this as the + + align:start position:0% +and you could have either this as the + + + align:start position:0% +and you could have either this as the +context or this is the context + + align:start position:0% +context or this is the context + + + align:start position:0% +context or this is the context +and this is the this is schematic what + + align:start position:0% +and this is the this is schematic what + + + align:start position:0% +and this is the this is schematic what +happened this is the real data these are + + align:start position:0% +happened this is the real data these are + + + align:start position:0% +happened this is the real data these are +real data down here where you have the + + align:start position:0% +real data down here where you have the + + + align:start position:0% +real data down here where you have the +context of the a allele or the context + + align:start position:0% +context of the a allele or the context + + + align:start position:0% +context of the a allele or the context +of the c allele you can have the + + align:start position:0% +of the c allele you can have the + + + align:start position:0% +of the c allele you can have the +homozygotes or the heterozygote + + align:start position:0% +homozygotes or the heterozygote + + + align:start position:0% +homozygotes or the heterozygote +and in the homozygous a you can see it + + align:start position:0% +and in the homozygous a you can see it + + + align:start position:0% +and in the homozygous a you can see it +lights up the best the best + + align:start position:0% +lights up the best the best + + + align:start position:0% +lights up the best the best +hybridization when you have the a in the + + align:start position:0% +hybridization when you have the a in the + + + align:start position:0% +hybridization when you have the a in the +middle position middle position is most + + align:start position:0% +middle position middle position is most + + + align:start position:0% +middle position middle position is most +sensitive the hybridization changes + + align:start position:0% +sensitive the hybridization changes + + + align:start position:0% +sensitive the hybridization changes +and for the c you have it in the c + + align:start position:0% +and for the c you have it in the c + + + align:start position:0% +and for the c you have it in the c +uh + + align:start position:0% +uh + + + align:start position:0% +uh +row here + + align:start position:0% +row here + + + align:start position:0% +row here +and remember you've got all you're + + align:start position:0% +and remember you've got all you're + + + align:start position:0% +and remember you've got all you're +changing all the bases every position + + align:start position:0% +changing all the bases every position + + + align:start position:0% +changing all the bases every position +one two three four this is the one where + + align:start position:0% +one two three four this is the one where + + + align:start position:0% +one two three four this is the one where +the middle face of the middle position + + align:start position:0% +the middle face of the middle position + + + align:start position:0% +the middle face of the middle position +is in the right context + + align:start position:0% +is in the right context + + + align:start position:0% +is in the right context +this is in the a context of the c + + align:start position:0% +this is in the a context of the c + + + align:start position:0% +this is in the a context of the c +context and in the heterozygote you get + + align:start position:0% +context and in the heterozygote you get + + + align:start position:0% +context and in the heterozygote you get +both the a and the c + + align:start position:0% +both the a and the c + + + align:start position:0% +both the a and the c +and so this has been done on hiv it's + + align:start position:0% +and so this has been done on hiv it's + + + align:start position:0% +and so this has been done on hiv it's +been done on break one on mitochondria + + align:start position:0% +been done on break one on mitochondria + + + align:start position:0% +been done on break one on mitochondria +and now they've applied it with whole + + align:start position:0% +and now they've applied it with whole + + + align:start position:0% +and now they've applied it with whole +wafers to the entire human genome and + + align:start position:0% +wafers to the entire human genome and + + + align:start position:0% +wafers to the entire human genome and +this probably costs on the order of + + align:start position:0% +this probably costs on the order of + + + align:start position:0% +this probably costs on the order of +three million dollars + + align:start position:0% +three million dollars + + + align:start position:0% +three million dollars +or so + + align:start position:0% +or so + + + align:start position:0% +or so +mass spectrometry is another way that's + + align:start position:0% +mass spectrometry is another way that's + + + align:start position:0% +mass spectrometry is another way that's +used probably not for sequencing whole + + align:start position:0% +used probably not for sequencing whole + + + align:start position:0% +used probably not for sequencing whole +genome but it's used for single + + align:start position:0% +genome but it's used for single + + + align:start position:0% +genome but it's used for single +nucleotide polymorphisms this costs on + + align:start position:0% +nucleotide polymorphisms this costs on + + + align:start position:0% +nucleotide polymorphisms this costs on +the order of + + align:start position:0% +the order of + + + align:start position:0% +the order of +you know 50 cents + + align:start position:0% +you know 50 cents + + + align:start position:0% +you know 50 cents +per polymorphism if there's 3 million of + + align:start position:0% +per polymorphism if there's 3 million of + + + align:start position:0% +per polymorphism if there's 3 million of +them in your genome + + align:start position:0% + + + + align:start position:0% + +that's a lot of + + align:start position:0% +that's a lot of + + + align:start position:0% +that's a lot of +50 cents + + align:start position:0% + + + + align:start position:0% + +and here's what it looks like when you + + align:start position:0% +and here's what it looks like when you + + + align:start position:0% +and here's what it looks like when you +read it out just it's really just like + + align:start position:0% +read it out just it's really just like + + + align:start position:0% +read it out just it's really just like +electrophoresis you can now separate + + align:start position:0% +electrophoresis you can now separate + + + align:start position:0% +electrophoresis you can now separate +uh + + align:start position:0% + + + + align:start position:0% + +an addition of an a from an addition of + + align:start position:0% +an addition of an a from an addition of + + + align:start position:0% +an addition of an a from an addition of +a g + + align:start position:0% +a g + + + align:start position:0% +a g +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +and the difference in mass between an a + + align:start position:0% +and the difference in mass between an a + + + align:start position:0% +and the difference in mass between an a +and g this is even more subtle than the + + align:start position:0% +and g this is even more subtle than the + + + align:start position:0% +and g this is even more subtle than the +difference of an n and n plus one this + + align:start position:0% +difference of an n and n plus one this + + + align:start position:0% +difference of an n and n plus one this +is just the difference between a and a c + + align:start position:0% +is just the difference between a and a c + + + align:start position:0% +is just the difference between a and a c +is detectable in this in fact it's + + align:start position:0% +is detectable in this in fact it's + + + align:start position:0% +is detectable in this in fact it's +detectable and quantitative enough that + + align:start position:0% +detectable and quantitative enough that + + + align:start position:0% +detectable and quantitative enough that +you can pool samples this is a bit of a + + align:start position:0% +you can pool samples this is a bit of a + + + align:start position:0% +you can pool samples this is a bit of a +stunt but it's an important stunt to + + align:start position:0% +stunt but it's an important stunt to + + + align:start position:0% +stunt but it's an important stunt to +show that this is really a very precise + + align:start position:0% +show that this is really a very precise + + + align:start position:0% +show that this is really a very precise +method albeit still fairly expensive + + align:start position:0% +method albeit still fairly expensive + + + align:start position:0% +method albeit still fairly expensive +now just in closing i want to + + align:start position:0% +now just in closing i want to + + + align:start position:0% +now just in closing i want to +give you the simplest possible example + + align:start position:0% +give you the simplest possible example + + + align:start position:0% +give you the simplest possible example +of + + align:start position:0% +of + + + align:start position:0% +of +how we can search through sequences next + + align:start position:0% +how we can search through sequences next + + + align:start position:0% +how we can search through sequences next +week we'll give you a much more rigorous + + align:start position:0% +week we'll give you a much more rigorous + + + align:start position:0% +week we'll give you a much more rigorous +way that you can look through sequences + + align:start position:0% +way that you can look through sequences + + + align:start position:0% +way that you can look through sequences +with very extensive differences between + + align:start position:0% +with very extensive differences between + + + align:start position:0% +with very extensive differences between +the sequences but here where the theme + + align:start position:0% +the sequences but here where the theme + + + align:start position:0% +the sequences but here where the theme +of today's thought is the subtle + + align:start position:0% +of today's thought is the subtle + + + align:start position:0% +of today's thought is the subtle +polymorph differences that occur between + + align:start position:0% +polymorph differences that occur between + + + align:start position:0% +polymorph differences that occur between +you and me + + align:start position:0% +you and me + + + align:start position:0% +you and me +and here one different so some generally + + align:start position:0% +and here one different so some generally + + + align:start position:0% +and here one different so some generally +you're looking for exact matches and a + + align:start position:0% +you're looking for exact matches and a + + + align:start position:0% +you're looking for exact matches and a +good way to look for exact matches is + + align:start position:0% +good way to look for exact matches is + + + align:start position:0% +good way to look for exact matches is +good ways are hashing suffix arrays and + + align:start position:0% +good ways are hashing suffix arrays and + + + align:start position:0% +good ways are hashing suffix arrays and +suffix trees well you're basically in + + align:start position:0% +suffix trees well you're basically in + + + align:start position:0% +suffix trees well you're basically in +each of these you're looking for + + align:start position:0% +each of these you're looking for + + + align:start position:0% +each of these you're looking for +using a + + align:start position:0% +using a + + + align:start position:0% +using a +word + + align:start position:0% +word + + + align:start position:0% +word +a a word either that's built up and + + align:start position:0% +a a word either that's built up and + + + align:start position:0% +a a word either that's built up and +stored from the end the suffix + + align:start position:0% +stored from the end the suffix + + + align:start position:0% +stored from the end the suffix +one letter at a time or it's a chunk + + align:start position:0% +one letter at a time or it's a chunk + + + align:start position:0% +one letter at a time or it's a chunk +that you might have as a hash + + align:start position:0% +that you might have as a hash + + + align:start position:0% +that you might have as a hash +and + + align:start position:0% +and + + + align:start position:0% +and +you make up a lookup table and the size + + align:start position:0% +you make up a lookup table and the size + + + align:start position:0% +you make up a lookup table and the size +of that lookup table it's a trade-off + + align:start position:0% +of that lookup table it's a trade-off + + + align:start position:0% +of that lookup table it's a trade-off +between speed of searching and the size + + align:start position:0% +between speed of searching and the size + + + align:start position:0% +between speed of searching and the size +of the table the size is going to be if + + align:start position:0% +of the table the size is going to be if + + + align:start position:0% +of the table the size is going to be if +the word is in nucleotides long it's + + align:start position:0% +the word is in nucleotides long it's + + + align:start position:0% +the word is in nucleotides long it's +going to be 4 to the n it's going to be + + align:start position:0% +going to be 4 to the n it's going to be + + + align:start position:0% +going to be 4 to the n it's going to be +the storage space you have to put on + + align:start position:0% +the storage space you have to put on + + + align:start position:0% +the storage space you have to put on +disk or ram + + align:start position:0% +disk or ram + + + align:start position:0% +disk or ram +to do ram if you want to do a fast + + align:start position:0% +to do ram if you want to do a fast + + + align:start position:0% +to do ram if you want to do a fast +search and so 16 is a magic number sort + + align:start position:0% +search and so 16 is a magic number sort + + + align:start position:0% +search and so 16 is a magic number sort +of in the ballpark for a human genome + + align:start position:0% +of in the ballpark for a human genome + + + align:start position:0% +of in the ballpark for a human genome +because 4 to the 16th is 4 billion + + align:start position:0% +because 4 to the 16th is 4 billion + + + align:start position:0% +because 4 to the 16th is 4 billion +sequences you can represent but it's a + + align:start position:0% +sequences you can represent but it's a + + + align:start position:0% +sequences you can represent but it's a +huge table you have to have a table of 4 + + align:start position:0% +huge table you have to have a table of 4 + + + align:start position:0% +huge table you have to have a table of 4 +billion times however many bytes you + + align:start position:0% +billion times however many bytes you + + + align:start position:0% +billion times however many bytes you +need to store + + align:start position:0% +need to store + + + align:start position:0% +need to store +the positions + + align:start position:0% +the positions + + + align:start position:0% +the positions +typically about 4 bytes of storage + + align:start position:0% +typically about 4 bytes of storage + + + align:start position:0% +typically about 4 bytes of storage +if you cut back on this a little bit + + align:start position:0% +if you cut back on this a little bit + + + align:start position:0% +if you cut back on this a little bit +you'll end up with collisions where + + align:start position:0% +you'll end up with collisions where + + + align:start position:0% +you'll end up with collisions where +you'll have two things that have the + + align:start position:0% +you'll have two things that have the + + + align:start position:0% +you'll have two things that have the +same ash or suffix + + align:start position:0% +same ash or suffix + + + align:start position:0% +same ash or suffix +if you make it uh + + align:start position:0% +if you make it uh + + + align:start position:0% +if you make it uh +and it that's if you make it smaller + + align:start position:0% +and it that's if you make it smaller + + + align:start position:0% +and it that's if you make it smaller +it'll take less space if you make it + + align:start position:0% +it'll take less space if you make it + + + align:start position:0% +it'll take less space if you make it +bigger it'll take a ridiculous amount of + + align:start position:0% +bigger it'll take a ridiculous amount of + + + align:start position:0% +bigger it'll take a ridiculous amount of +ramp okay + + align:start position:0% +ramp okay + + + align:start position:0% +ramp okay +and then here's a kind of a uh + + align:start position:0% +and then here's a kind of a uh + + + align:start position:0% +and then here's a kind of a uh +whimsical + + align:start position:0% +whimsical + + + align:start position:0% +whimsical +uh another example of pearl where you + + align:start position:0% +uh another example of pearl where you + + + align:start position:0% +uh another example of pearl where you +not only want to find all the mutations + + align:start position:0% +not only want to find all the mutations + + + align:start position:0% +not only want to find all the mutations +here at a very high dens ridiculously + + align:start position:0% +here at a very high dens ridiculously + + + align:start position:0% +here at a very high dens ridiculously +high density you know not one per + + align:start position:0% +high density you know not one per + + + align:start position:0% +high density you know not one per +kilobase for one every few base pairs + + align:start position:0% +kilobase for one every few base pairs + + + align:start position:0% +kilobase for one every few base pairs +you're not going to find them but you + + align:start position:0% +you're not going to find them but you + + + align:start position:0% +you're not going to find them but you +want to correct them and here the pearl + + align:start position:0% +want to correct them and here the pearl + + + align:start position:0% +want to correct them and here the pearl +does the substitution + + align:start position:0% +does the substitution + + + align:start position:0% +does the substitution +and after gene therapy everybody walks + + align:start position:0% +and after gene therapy everybody walks + + + align:start position:0% +and after gene therapy everybody walks +out happy okay + + align:start position:0% +out happy okay + + + align:start position:0% +out happy okay +so \ No newline at end of file diff --git a/3eIzIJ6QncY.txt b/3eIzIJ6QncY.txt new file mode 100644 index 0000000000000000000000000000000000000000..71f773d340185195e23f89aab82e8988f0c0f409 --- /dev/null +++ b/3eIzIJ6QncY.txt @@ -0,0 +1,14754 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu today what we want to do is + + align:start position:0% +ocw.mit.edu today what we want to do is + + + align:start position:0% +ocw.mit.edu today what we want to do is +finish off our discussion of lotka + + align:start position:0% +finish off our discussion of lotka + + + align:start position:0% +finish off our discussion of lotka +voltera competition models right so + + align:start position:0% +voltera competition models right so + + + align:start position:0% +voltera competition models right so +starting with this idea of the two + + align:start position:0% +starting with this idea of the two + + + align:start position:0% +starting with this idea of the two +species interacting competitively but + + align:start position:0% +species interacting competitively but + + + align:start position:0% +species interacting competitively but +then moving on to try to think about the + + align:start position:0% +then moving on to try to think about the + + + align:start position:0% +then moving on to try to think about the +general properties of lock of voltera + + align:start position:0% +general properties of lock of voltera + + + align:start position:0% +general properties of lock of voltera +systems in particular when you have more + + align:start position:0% +systems in particular when you have more + + + align:start position:0% +systems in particular when you have more +species the kinds of dynamics that you + + align:start position:0% +species the kinds of dynamics that you + + + align:start position:0% +species the kinds of dynamics that you +can get also we're going to we're going + + align:start position:0% +can get also we're going to we're going + + + align:start position:0% +can get also we're going to we're going +to talk about these non-transitive + + align:start position:0% +to talk about these non-transitive + + + align:start position:0% +to talk about these non-transitive +interactions which are the rock paper + + align:start position:0% +interactions which are the rock paper + + + align:start position:0% +interactions which are the rock paper +scissors type interactions that may uh + + align:start position:0% +scissors type interactions that may uh + + + align:start position:0% +scissors type interactions that may uh +facilitate the maintenance of diversity + + align:start position:0% +facilitate the maintenance of diversity + + + align:start position:0% +facilitate the maintenance of diversity +in populations or ecosystems uh in + + align:start position:0% +in populations or ecosystems uh in + + + align:start position:0% +in populations or ecosystems uh in +particular in the presence of of some + + align:start position:0% +particular in the presence of of some + + + align:start position:0% +particular in the presence of of some +sort of spatial structure and so we'll + + align:start position:0% +sort of spatial structure and so we'll + + + align:start position:0% +sort of spatial structure and so we'll +talk both about this uh demonstration of + + align:start position:0% +talk both about this uh demonstration of + + + align:start position:0% +talk both about this uh demonstration of +rock paper scissors type interactions in + + align:start position:0% +rock paper scissors type interactions in + + + align:start position:0% +rock paper scissors type interactions in +the context of male mating strategies + + align:start position:0% +the context of male mating strategies + + + align:start position:0% +the context of male mating strategies +and lizards this paper uh that was by + + align:start position:0% +and lizards this paper uh that was by + + + align:start position:0% +and lizards this paper uh that was by +Kurt Lively and and then then we'll talk + + align:start position:0% +Kurt Lively and and then then we'll talk + + + align:start position:0% +Kurt Lively and and then then we'll talk +about another paper in the microbial + + align:start position:0% +about another paper in the microbial + + + align:start position:0% +about another paper in the microbial +realm where they showed that there are + + align:start position:0% +realm where they showed that there are + + + align:start position:0% +realm where they showed that there are +rock paper scissors type interactions in + + align:start position:0% +rock paper scissors type interactions in + + + align:start position:0% +rock paper scissors type interactions in +the context of cisin production so an + + align:start position:0% +the context of cisin production so an + + + align:start position:0% +the context of cisin production so an +toxin production in the context of + + align:start position:0% +toxin production in the context of + + + align:start position:0% +toxin production in the context of +bacteria then uh at the end we'll we'll + + align:start position:0% +bacteria then uh at the end we'll we'll + + + align:start position:0% +bacteria then uh at the end we'll we'll +talk about these population waves which + + align:start position:0% +talk about these population waves which + + + align:start position:0% +talk about these population waves which +is uh there was a rather mathematical + + align:start position:0% +is uh there was a rather mathematical + + + align:start position:0% +is uh there was a rather mathematical +reading in uh that I would originally + + align:start position:0% +reading in uh that I would originally + + + align:start position:0% +reading in uh that I would originally +proposed but then we kind of Switched + + align:start position:0% +proposed but then we kind of Switched + + + align:start position:0% +proposed but then we kind of Switched +things up a bit so that uh you could + + align:start position:0% +things up a bit so that uh you could + + + align:start position:0% +things up a bit so that uh you could +instead read that rock paper scissor + + align:start position:0% +instead read that rock paper scissor + + + align:start position:0% +instead read that rock paper scissor +paper that I rock paper scissors paper + + align:start position:0% +paper that I rock paper scissors paper + + + align:start position:0% +paper that I rock paper scissors paper +okay that is confusing um that I think + + align:start position:0% +okay that is confusing um that I think + + + align:start position:0% +okay that is confusing um that I think +is maybe more fun but I'll tell you kind + + align:start position:0% +is maybe more fun but I'll tell you kind + + + align:start position:0% +is maybe more fun but I'll tell you kind +of this this basic idea of the + + align:start position:0% +of this this basic idea of the + + + align:start position:0% +of this this basic idea of the +population waves what happens if you + + align:start position:0% +population waves what happens if you + + + align:start position:0% +population waves what happens if you +have a combination of kind of some + + align:start position:0% +have a combination of kind of some + + + align:start position:0% +have a combination of kind of some +growth process together with some + + align:start position:0% +growth process together with some + + + align:start position:0% +growth process together with some +effective diffusion you can get these + + align:start position:0% +effective diffusion you can get these + + + align:start position:0% +effective diffusion you can get these +population waves that correspond to uh + + align:start position:0% +population waves that correspond to uh + + + align:start position:0% +population waves that correspond to uh +this process of range expansion where a + + align:start position:0% +this process of range expansion where a + + + align:start position:0% +this process of range expansion where a +population expands into new territory + + align:start position:0% +population expands into new territory + + + align:start position:0% +population expands into new territory +okay right so I uh I wanted to I just + + align:start position:0% +okay right so I uh I wanted to I just + + + align:start position:0% +okay right so I uh I wanted to I just +started by uh putting up what we had + + align:start position:0% +started by uh putting up what we had + + + align:start position:0% +started by uh putting up what we had +from from last class so this is the two + + align:start position:0% +from from last class so this is the two + + + align:start position:0% +from from last class so this is the two +species Locka voltera competition model + + align:start position:0% +species Locka voltera competition model + + + align:start position:0% +species Locka voltera competition model +right so what we found was that for this + + align:start position:0% +right so what we found was that for this + + + align:start position:0% +right so what we found was that for this +to be competition right for the species + + align:start position:0% +to be competition right for the species + + + align:start position:0% +to be competition right for the species +to be kind of bad for each other that + + align:start position:0% +to be kind of bad for each other that + + + align:start position:0% +to be kind of bad for each other that +that corresponds to uh to the betas + + align:start position:0% +that corresponds to uh to the betas + + + align:start position:0% +that corresponds to uh to the betas +being positive + + align:start position:0% +being positive + + + align:start position:0% +being positive +right now U what what we what we found + + align:start position:0% +right now U what what we what we found + + + align:start position:0% +right now U what what we what we found +is there there + + align:start position:0% +is there there + + + align:start position:0% +is there there +are four uh there are four cases in + + align:start position:0% +are four uh there are four cases in + + + align:start position:0% +are four uh there are four cases in +terms of the outcome of this two species + + align:start position:0% +terms of the outcome of this two species + + + align:start position:0% +terms of the outcome of this two species +interaction and we wanted to at least + + align:start position:0% +interaction and we wanted to at least + + + align:start position:0% +interaction and we wanted to at least +try to get some sense of why that was + + align:start position:0% +try to get some sense of why that was + + + align:start position:0% +try to get some sense of why that was +and what this kind of um what the the + + align:start position:0% +and what this kind of um what the the + + + align:start position:0% +and what this kind of um what the the +trajectories might look like in terms of + + align:start position:0% +trajectories might look like in terms of + + + align:start position:0% +trajectories might look like in terms of +if you look at N1 and N2 we can draw + + align:start position:0% +if you look at N1 and N2 we can draw + + + align:start position:0% +if you look at N1 and N2 we can draw +these nullclines and then get a sense of + + align:start position:0% +these nullclines and then get a sense of + + + align:start position:0% +these nullclines and then get a sense of +where the trajectories are going to go + + align:start position:0% +where the trajectories are going to go + + + align:start position:0% +where the trajectories are going to go +now the basic outcome of this two + + align:start position:0% +now the basic outcome of this two + + + align:start position:0% +now the basic outcome of this two +species Lota voltera uh competition + + align:start position:0% +species Lota voltera uh competition + + + align:start position:0% +species Lota voltera uh competition +model are really exactly the same as the + + align:start position:0% +model are really exactly the same as the + + + align:start position:0% +model are really exactly the same as the +uh possible outcomes when we were + + align:start position:0% +uh possible outcomes when we were + + + align:start position:0% +uh possible outcomes when we were +thinking about frequency dependent + + align:start position:0% +thinking about frequency dependent + + + align:start position:0% +thinking about frequency dependent +selection right where we could get in + + align:start position:0% +selection right where we could get in + + + align:start position:0% +selection right where we could get in +this case that uh we could get that + + align:start position:0% +this case that uh we could get that + + + align:start position:0% +this case that uh we could get that +species one + + align:start position:0% +species one + + + align:start position:0% +species one +dominates or species two dominates right + + align:start position:0% +dominates or species two dominates right + + + align:start position:0% +dominates or species two dominates right +one or two but then we could also get + + align:start position:0% +one or two but then we could also get + + + align:start position:0% +one or two but then we could also get +coexistence or bability ility + + align:start position:0% + + + + align:start position:0% + +right and indeed there's uh in general a + + align:start position:0% +right and indeed there's uh in general a + + + align:start position:0% +right and indeed there's uh in general a +mapping + + align:start position:0% +mapping + + + align:start position:0% +mapping +from the the lot of voltera kind of + + align:start position:0% +from the the lot of voltera kind of + + + align:start position:0% +from the the lot of voltera kind of +approach here and uh and the general um + + align:start position:0% +approach here and uh and the general um + + + align:start position:0% +approach here and uh and the general um +the approach that was kind of in Martin + + align:start position:0% +the approach that was kind of in Martin + + + align:start position:0% +the approach that was kind of in Martin +noak's book of you can thinking about a + + align:start position:0% +noak's book of you can thinking about a + + + align:start position:0% +noak's book of you can thinking about a +frequency dependent selection in in this + + align:start position:0% +frequency dependent selection in in this + + + align:start position:0% +frequency dependent selection in in this +population okay so that there's uh and + + align:start position:0% +population okay so that there's uh and + + + align:start position:0% +population okay so that there's uh and +and so then there not a surprise that + + align:start position:0% +and so then there not a surprise that + + + align:start position:0% +and so then there not a surprise that +there you get the same four outcomes uh + + align:start position:0% +there you get the same four outcomes uh + + + align:start position:0% +there you get the same four outcomes uh +in between these two situations okay and + + align:start position:0% +in between these two situations okay and + + + align:start position:0% +in between these two situations okay and +I think that this is also highlighting + + align:start position:0% +I think that this is also highlighting + + + align:start position:0% +I think that this is also highlighting +some very interesting kind of deep + + align:start position:0% +some very interesting kind of deep + + + align:start position:0% +some very interesting kind of deep +connections between evolution which is + + align:start position:0% +connections between evolution which is + + + align:start position:0% +connections between evolution which is +changes in say a Leal frequency in a + + align:start position:0% +changes in say a Leal frequency in a + + + align:start position:0% +changes in say a Leal frequency in a +population of a single species over time + + align:start position:0% +population of a single species over time + + + align:start position:0% +population of a single species over time +and U and then some of these ecological + + align:start position:0% +and U and then some of these ecological + + + align:start position:0% +and U and then some of these ecological +kind of processes right where you're + + align:start position:0% +kind of processes right where you're + + + align:start position:0% +kind of processes right where you're +really thinking about these as different + + align:start position:0% +really thinking about these as different + + + align:start position:0% +really thinking about these as different +species + + align:start position:0% +species + + + align:start position:0% +species +right now of course in these uh in in + + align:start position:0% +right now of course in these uh in in + + + align:start position:0% +right now of course in these uh in in +the case of the evolutionary dynamics + + align:start position:0% +the case of the evolutionary dynamics + + + align:start position:0% +the case of the evolutionary dynamics +that we analyzed in Martin's book though + + align:start position:0% +that we analyzed in Martin's book though + + + align:start position:0% +that we analyzed in Martin's book though +those were the evolution of different uh + + align:start position:0% +those were the evolution of different uh + + + align:start position:0% +those were the evolution of different uh +different clonal populations and asexual + + align:start position:0% +different clonal populations and asexual + + + align:start position:0% +different clonal populations and asexual +uh asexually reproducing + + align:start position:0% +uh asexually reproducing + + + align:start position:0% +uh asexually reproducing +populations you guys remember what I'm + + align:start position:0% +populations you guys remember what I'm + + + align:start position:0% +populations you guys remember what I'm +talking + + align:start position:0% +talking + + + align:start position:0% +talking +about okay so I I just want to uh draw a + + align:start position:0% +about okay so I I just want to uh draw a + + + align:start position:0% +about okay so I I just want to uh draw a +couple of these sorts of diagrams uh I'm + + align:start position:0% +couple of these sorts of diagrams uh I'm + + + align:start position:0% +couple of these sorts of diagrams uh I'm +not going to draw out all four of them + + align:start position:0% +not going to draw out all four of them + + + align:start position:0% +not going to draw out all four of them +because it does take some time uh but uh + + align:start position:0% +because it does take some time uh but uh + + + align:start position:0% +because it does take some time uh but uh +but hopefully we can we can reconstruct + + align:start position:0% +but hopefully we can we can reconstruct + + + align:start position:0% +but hopefully we can we can reconstruct +where uh where we + + align:start position:0% +where uh where we + + + align:start position:0% +where uh where we +were all + + align:start position:0% +were all + + + align:start position:0% +were all +right the the case that we were we + + align:start position:0% +right the the case that we were we + + + align:start position:0% +right the the case that we were we +started out that we were analyzing + + align:start position:0% +started out that we were analyzing + + + align:start position:0% +started out that we were analyzing +before + + align:start position:0% +before + + + align:start position:0% +before +right so we might the N1 dot equal to + + align:start position:0% +right so we might the N1 dot equal to + + + align:start position:0% +right so we might the N1 dot equal to +zero we're going to have as a dash line + + align:start position:0% +zero we're going to have as a dash line + + + align:start position:0% +zero we're going to have as a dash line +and N2 is going to be although maybe + + align:start position:0% +and N2 is going to be although maybe + + + align:start position:0% +and N2 is going to be although maybe +we'll you try to use thick chalk oh wow + + align:start position:0% +we'll you try to use thick chalk oh wow + + + align:start position:0% +we'll you try to use thick chalk oh wow +I missed okay these are thick lines and + + align:start position:0% +I missed okay these are thick lines and + + + align:start position:0% +I missed okay these are thick lines and +right so we'll draw these uh these nines + + align:start position:0% +right so we'll draw these uh these nines + + + align:start position:0% +right so we'll draw these uh these nines +over here right so the N1 Dot and indeed + + align:start position:0% +over here right so the N1 Dot and indeed + + + align:start position:0% +over here right so the N1 Dot and indeed +one of the comments is that it would be + + align:start position:0% +one of the comments is that it would be + + + align:start position:0% +one of the comments is that it would be +nice to draw where the nines are on the + + align:start position:0% +nice to draw where the nines are on the + + + align:start position:0% +nice to draw where the nines are on the +axes as well and and and indeed we can + + align:start position:0% +axes as well and and and indeed we can + + + align:start position:0% +axes as well and and and indeed we can +we can do that we we aim to please all + + align:start position:0% +we can do that we we aim to please all + + + align:start position:0% +we can do that we we aim to please all +right so the dashed lines correspond to + + align:start position:0% +right so the dashed lines correspond to + + + align:start position:0% +right so the dashed lines correspond to +N1 dot being equal to zero so here's N1 + + align:start position:0% +N1 dot being equal to zero so here's N1 + + + align:start position:0% +N1 dot being equal to zero so here's N1 +N2 okay right so N1 equal to zero + + align:start position:0% +N2 okay right so N1 equal to zero + + + align:start position:0% +N2 okay right so N1 equal to zero +corresponds + + align:start position:0% +corresponds + + + align:start position:0% +corresponds +to this + + align:start position:0% +to this + + + align:start position:0% +to this +thing okay and then we have this other + + align:start position:0% +thing okay and then we have this other + + + align:start position:0% +thing okay and then we have this other +guy that's a line + + align:start position:0% +guy that's a line + + + align:start position:0% +guy that's a line +here + + align:start position:0% + + + + align:start position:0% + +um okay and what we found is that if N2 + + align:start position:0% +um okay and what we found is that if N2 + + + align:start position:0% +um okay and what we found is that if N2 +is equal to zero this intersects at uh + + align:start position:0% +is equal to zero this intersects at uh + + + align:start position:0% +is equal to zero this intersects at uh +K1 + + align:start position:0% + + + + align:start position:0% + +whereas the intersection over here is at + + align:start position:0% +whereas the intersection over here is at + + + align:start position:0% +whereas the intersection over here is at +K1 divid beta 1 + + align:start position:0% + + + + align:start position:0% + +2 okay now we have uh we have our other + + align:start position:0% +2 okay now we have uh we have our other + + + align:start position:0% +2 okay now we have uh we have our other +nines correspond to N2 do equal to Zer + + align:start position:0% +nines correspond to N2 do equal to Zer + + + align:start position:0% +nines correspond to N2 do equal to Zer +right now one of those lines is indeed + + align:start position:0% +right now one of those lines is indeed + + + align:start position:0% +right now one of those lines is indeed +going to be along + + align:start position:0% + + + + align:start position:0% + +here okay uh and the the other line uh + + align:start position:0% +here okay uh and the the other line uh + + + align:start position:0% +here okay uh and the the other line uh +can fall there are four different + + align:start position:0% +can fall there are four different + + + align:start position:0% +can fall there are four different +possibilities for how we might draw it + + align:start position:0% +possibilities for how we might draw it + + + align:start position:0% +possibilities for how we might draw it +in relation to this N1 do equal to zero + + align:start position:0% +in relation to this N1 do equal to zero + + + align:start position:0% +in relation to this N1 do equal to zero +kind of null Cline right and depending + + align:start position:0% +kind of null Cline right and depending + + + align:start position:0% +kind of null Cline right and depending +on the orientation of that you will will + + align:start position:0% +on the orientation of that you will will + + + align:start position:0% +on the orientation of that you will will +end up getting uh these four different + + align:start position:0% +end up getting uh these four different + + + align:start position:0% +end up getting uh these four different +possible outcomes of one dominating + + align:start position:0% +possible outcomes of one dominating + + + align:start position:0% +possible outcomes of one dominating +irrespective of the initial conditions + + align:start position:0% +irrespective of the initial conditions + + + align:start position:0% +irrespective of the initial conditions +two dominating irrespective of initial + + align:start position:0% +two dominating irrespective of initial + + + align:start position:0% +two dominating irrespective of initial +conditions or coexistence or bability so + + align:start position:0% +conditions or coexistence or bability so + + + align:start position:0% +conditions or coexistence or bability so +bability is the only you know so if you + + align:start position:0% +bability is the only you know so if you + + + align:start position:0% +bability is the only you know so if you +start with a finite number of each of + + align:start position:0% +start with a finite number of each of + + + align:start position:0% +start with a finite number of each of +these two species then BPI is the only + + align:start position:0% +these two species then BPI is the only + + + align:start position:0% +these two species then BPI is the only +case where the the outcome depends on + + align:start position:0% +case where the the outcome depends on + + + align:start position:0% +case where the the outcome depends on +the starting condition right so of + + align:start position:0% +the starting condition right so of + + + align:start position:0% +the starting condition right so of +course if you if you start out without + + align:start position:0% +course if you if you start out without + + + align:start position:0% +course if you if you start out without +one of the two species then you won't + + align:start position:0% +one of the two species then you won't + + + align:start position:0% +one of the two species then you won't +get creation of those species right + + align:start position:0% +get creation of those species right + + + align:start position:0% +get creation of those species right +because the only way to get creation of + + align:start position:0% +because the only way to get creation of + + + align:start position:0% +because the only way to get creation of +species one is by to have some species + + align:start position:0% +species one is by to have some species + + + align:start position:0% +species one is by to have some species +one individual in this model + + align:start position:0% + + + + align:start position:0% + +right right so we're going to get + + align:start position:0% +right right so we're going to get + + + align:start position:0% +right right so we're going to get +another line here corresponding to N2 do + + align:start position:0% +another line here corresponding to N2 do + + + align:start position:0% +another line here corresponding to N2 do +equal to zero and I think that the one + + align:start position:0% +equal to zero and I think that the one + + + align:start position:0% +equal to zero and I think that the one +that we were trying to analyze was was + + align:start position:0% +that we were trying to analyze was was + + + align:start position:0% +that we were trying to analyze was was +with the solid line underneath is that + + align:start position:0% +with the solid line underneath is that + + + align:start position:0% +with the solid line underneath is that +consistent with people's notes + + align:start position:0% +consistent with people's notes + + + align:start position:0% +consistent with people's notes +okay all right so we can uh we can draw + + align:start position:0% +okay all right so we can uh we can draw + + + align:start position:0% +okay all right so we can uh we can draw +some other line here it doesn't have to + + align:start position:0% +some other line here it doesn't have to + + + align:start position:0% +some other line here it doesn't have to +have the same slope right now it's good + + align:start position:0% +have the same slope right now it's good + + + align:start position:0% +have the same slope right now it's good +to be clear about where these things are + + align:start position:0% +to be clear about where these things are + + + align:start position:0% +to be clear about where these things are +going to fall so K2 is this point and + + align:start position:0% +going to fall so K2 is this point and + + + align:start position:0% +going to fall so K2 is this point and +now K2 / beta 21 is over here now recall + + align:start position:0% +now K2 / beta 21 is over here now recall + + + align:start position:0% +now K2 / beta 21 is over here now recall +that the betas are telling us beta one + + align:start position:0% +that the betas are telling us beta one + + + align:start position:0% +that the betas are telling us beta one +two is telling us about how much species + + align:start position:0% +two is telling us about how much species + + + align:start position:0% +two is telling us about how much species +2 is reducing the growth of species one + + align:start position:0% +2 is reducing the growth of species one + + + align:start position:0% +2 is reducing the growth of species one +whereas beta 21 is is the how much + + align:start position:0% +whereas beta 21 is is the how much + + + align:start position:0% +whereas beta 21 is is the how much +species one is producing growth of speci + + align:start position:0% + + + + align:start position:0% + +two right now everything comes down to + + align:start position:0% +two right now everything comes down to + + + align:start position:0% +two right now everything comes down to +the relative ordering of these two + + align:start position:0% +the relative ordering of these two + + + align:start position:0% +the relative ordering of these two +quantities and these two quantities and + + align:start position:0% +quantities and these two quantities and + + + align:start position:0% +quantities and these two quantities and +since there are two possibilities on + + align:start position:0% +since there are two possibilities on + + + align:start position:0% +since there are two possibilities on +each that gives us the four possible + + align:start position:0% +each that gives us the four possible + + + align:start position:0% +each that gives us the four possible +outcomes okay and broadly the idea here + + align:start position:0% +outcomes okay and broadly the idea here + + + align:start position:0% +outcomes okay and broadly the idea here +is just that if there if the species are + + align:start position:0% +is just that if there if the species are + + + align:start position:0% +is just that if there if the species are +weakly interfering with each other then + + align:start position:0% +weakly interfering with each other then + + + align:start position:0% +weakly interfering with each other then +what should + + align:start position:0% + + + + align:start position:0% + +happen yes so you should go coexistence + + align:start position:0% +happen yes so you should go coexistence + + + align:start position:0% +happen yes so you should go coexistence +right coexistence is when you know the + + align:start position:0% +right coexistence is when you know the + + + align:start position:0% +right coexistence is when you know the +beta the betas are betas are small of + + align:start position:0% +beta the betas are betas are small of + + + align:start position:0% +beta the betas are betas are small of +course you have to this is a concrete + + align:start position:0% +course you have to this is a concrete + + + align:start position:0% +course you have to this is a concrete +model so you have to Define what you + + align:start position:0% +model so you have to Define what you + + + align:start position:0% +model so you have to Define what you +mean by small and indeed small here ends + + align:start position:0% +mean by small and indeed small here ends + + + align:start position:0% +mean by small and indeed small here ends +up being relative to the ratios of these + + align:start position:0% +up being relative to the ratios of these + + + align:start position:0% +up being relative to the ratios of these +caring capacities okay if the caring + + align:start position:0% +caring capacities okay if the caring + + + align:start position:0% +caring capacities okay if the caring +capacities are just uh equal to say one + + align:start position:0% +capacities are just uh equal to say one + + + align:start position:0% +capacities are just uh equal to say one +then uh that's saying that the + + align:start position:0% +then uh that's saying that the + + + align:start position:0% +then uh that's saying that the +betas or in particular sorry if the + + align:start position:0% +betas or in particular sorry if the + + + align:start position:0% +betas or in particular sorry if the +caring capacities are the same then uh + + align:start position:0% +caring capacities are the same then uh + + + align:start position:0% +caring capacities are the same then uh +then the simple way to think about this + + align:start position:0% +then the simple way to think about this + + + align:start position:0% +then the simple way to think about this +is just whether the beta are larger or + + align:start position:0% +is just whether the beta are larger or + + + align:start position:0% +is just whether the beta are larger or +smaller than one right whether the uh + + align:start position:0% +smaller than one right whether the uh + + + align:start position:0% +smaller than one right whether the uh +whether each species interferes with the + + align:start position:0% +whether each species interferes with the + + + align:start position:0% +whether each species interferes with the +other species more than a member of that + + align:start position:0% +other species more than a member of that + + + align:start position:0% +other species more than a member of that +other species okay so that's kind of + + align:start position:0% +other species okay so that's kind of + + + align:start position:0% +other species okay so that's kind of +what so if the carrying capacitor is the + + align:start position:0% +what so if the carrying capacitor is the + + + align:start position:0% +what so if the carrying capacitor is the +same that's what that's what demarcates + + align:start position:0% +same that's what that's what demarcates + + + align:start position:0% +same that's what that's what demarcates +the different different zones okay so + + align:start position:0% +the different different zones okay so + + + align:start position:0% +the different different zones okay so +what we want to do is uh take this sort + + align:start position:0% +what we want to do is uh take this sort + + + align:start position:0% +what we want to do is uh take this sort +of diagram and try to figure out where + + align:start position:0% +of diagram and try to figure out where + + + align:start position:0% +of diagram and try to figure out where +will the trajectories be on this on this + + align:start position:0% +will the trajectories be on this on this + + + align:start position:0% +will the trajectories be on this on this +diagram right now it's always good to + + align:start position:0% +diagram right now it's always good to + + + align:start position:0% +diagram right now it's always good to +locate the fixed + + align:start position:0% +locate the fixed + + + align:start position:0% +locate the fixed +points right the fixed points of the + + align:start position:0% +points right the fixed points of the + + + align:start position:0% +points right the fixed points of the +system are you know somebody somebody + + align:start position:0% +system are you know somebody somebody + + + align:start position:0% +system are you know somebody somebody +words uh how would we Define fixed + + align:start position:0% +words uh how would we Define fixed + + + align:start position:0% +words uh how would we Define fixed +points in this + + align:start position:0% + + + + align:start position:0% + +system what's that both lines intersect + + align:start position:0% +system what's that both lines intersect + + + align:start position:0% +system what's that both lines intersect +right so when both the when the dash + + align:start position:0% +right so when both the when the dash + + + align:start position:0% +right so when both the when the dash +line intersects the solid lines right so + + align:start position:0% +line intersects the solid lines right so + + + align:start position:0% +line intersects the solid lines right so +uh we have one such fixed Point + + align:start position:0% +uh we have one such fixed Point + + + align:start position:0% +uh we have one such fixed Point +here right we have another fixed Point + + align:start position:0% +here right we have another fixed Point + + + align:start position:0% +here right we have another fixed Point +here and another fixed Point + + align:start position:0% +here and another fixed Point + + + align:start position:0% +here and another fixed Point +here right have we yet figured out the + + align:start position:0% +here right have we yet figured out the + + + align:start position:0% +here right have we yet figured out the +stability of those fixed points + + align:start position:0% +stability of those fixed points + + + align:start position:0% +stability of those fixed points +no okay but can somebody offer the + + align:start position:0% +no okay but can somebody offer the + + + align:start position:0% +no okay but can somebody offer the +stability what's the stability of this + + align:start position:0% +stability what's the stability of this + + + align:start position:0% +stability what's the stability of this +fix + + align:start position:0% + + + + align:start position:0% + +Point assuming that it's unstable right + + align:start position:0% +Point assuming that it's unstable right + + + align:start position:0% +Point assuming that it's unstable right +because we've already and previously + + align:start position:0% +because we've already and previously + + + align:start position:0% +because we've already and previously +assume that these + + align:start position:0% +assume that these + + + align:start position:0% +assume that these +RS uh are greater than zero right we're + + align:start position:0% +RS uh are greater than zero right we're + + + align:start position:0% +RS uh are greater than zero right we're +assuming that the species would be able + + align:start position:0% +assuming that the species would be able + + + align:start position:0% +assuming that the species would be able +to survive on their own right and that's + + align:start position:0% +to survive on their own right and that's + + + align:start position:0% +to survive on their own right and that's +actually true for both species right so + + align:start position:0% +actually true for both species right so + + + align:start position:0% +actually true for both species right so +this uh this thing is UN is unstable + + align:start position:0% +this uh this thing is UN is unstable + + + align:start position:0% +this uh this thing is UN is unstable +kind of in both directions right and and + + align:start position:0% +kind of in both directions right and and + + + align:start position:0% +kind of in both directions right and and +what what are the igen vectors + + align:start position:0% +what what are the igen vectors + + + align:start position:0% +what what are the igen vectors +associated with this fixed + + align:start position:0% +associated with this fixed + + + align:start position:0% +associated with this fixed +Point all right um on the count of three + + align:start position:0% +Point all right um on the count of three + + + align:start position:0% +Point all right um on the count of three +draw you know use your arms like the + + align:start position:0% +draw you know use your arms like the + + + align:start position:0% +draw you know use your arms like the +hands of a + + align:start position:0% +hands of a + + + align:start position:0% +hands of a +clock to indicate the directions of the + + align:start position:0% +clock to indicate the directions of the + + + align:start position:0% +clock to indicate the directions of the +the IG vectors all right ready three two + + align:start position:0% +the IG vectors all right ready three two + + + align:start position:0% +the IG vectors all right ready three two +one all right all right is every okay so + + align:start position:0% +one all right all right is every okay so + + + align:start position:0% +one all right all right is every okay so +but yeah there's no diagonals + + align:start position:0% +but yeah there's no diagonals + + + align:start position:0% +but yeah there's no diagonals +right right okay of course you could + + align:start position:0% +right right okay of course you could + + + align:start position:0% +right right okay of course you could +also you know I was waiting for somebody + + align:start position:0% +also you know I was waiting for somebody + + + align:start position:0% +also you know I was waiting for somebody +to be kind of obnoxious and point in the + + align:start position:0% +to be kind of obnoxious and point in the + + + align:start position:0% +to be kind of obnoxious and point in the +other direction but um yeah surp + + align:start position:0% +other direction but um yeah surp + + + align:start position:0% +other direction but um yeah surp +surprisingly non obnoxious class we have + + align:start position:0% +surprisingly non obnoxious class we have + + + align:start position:0% +surprisingly non obnoxious class we have +right and okay so this is just saying + + align:start position:0% +right and okay so this is just saying + + + align:start position:0% +right and okay so this is just saying +that if you start out with just a little + + align:start position:0% +that if you start out with just a little + + + align:start position:0% +that if you start out with just a little +bit of one species you'll just stay with + + align:start position:0% +bit of one species you'll just stay with + + + align:start position:0% +bit of one species you'll just stay with +that species right makes sense okay now + + align:start position:0% +that species right makes sense okay now + + + align:start position:0% +that species right makes sense okay now +what do these lines tell us about the + + align:start position:0% +what do these lines tell us about the + + + align:start position:0% +what do these lines tell us about the +directions of the + + align:start position:0% + + + + align:start position:0% + +trajectories or the orientations of the + + align:start position:0% + + + + align:start position:0% + +trajectories + + align:start position:0% + + + + align:start position:0% + +why did I draw + + align:start position:0% + + + + align:start position:0% + +them + + align:start position:0% +them + + + align:start position:0% +them +yes + + align:start position:0% +yes + + + align:start position:0% +yes +so so yeah these trajectories + + align:start position:0% + + + + align:start position:0% + +arein + + align:start position:0% + + + + align:start position:0% + +of all right one of the derivatives all + + align:start position:0% +of all right one of the derivatives all + + + align:start position:0% +of all right one of the derivatives all +right and in particular let's look + + align:start position:0% +right and in particular let's look + + + align:start position:0% +right and in particular let's look +at this line here do the are the + + align:start position:0% +at this line here do the are the + + + align:start position:0% +at this line here do the are the +trajectories again we're going to do the + + align:start position:0% +trajectories again we're going to do the + + + align:start position:0% +trajectories again we're going to do the +um we're going to do again our hand our + + align:start position:0% +um we're going to do again our hand our + + + align:start position:0% +um we're going to do again our hand our +arms to indicate the orientation of the + + align:start position:0% +arms to indicate the orientation of the + + + align:start position:0% +arms to indicate the orientation of the +trajectories okay in particular there's + + align:start position:0% +trajectories okay in particular there's + + + align:start position:0% +trajectories okay in particular there's +a trajectory right here what direction + + align:start position:0% +a trajectory right here what direction + + + align:start position:0% +a trajectory right here what direction +will that trajectory be pointing there's + + align:start position:0% +will that trajectory be pointing there's + + + align:start position:0% +will that trajectory be pointing there's +only going to be one arm okay ready + + align:start position:0% +only going to be one arm okay ready + + + align:start position:0% +only going to be one arm okay ready +three two + + align:start position:0% +three two + + + align:start position:0% +three two +one all right we're we got a lot of + + align:start position:0% +one all right we're we got a lot of + + + align:start position:0% +one all right we're we got a lot of +people not voting all right that means + + align:start position:0% +people not voting all right that means + + + align:start position:0% +people not voting all right that means +that we need to turn to our neighbors + + align:start position:0% +that we need to turn to our neighbors + + + align:start position:0% +that we need to turn to our neighbors +and discuss all right if if you didn't + + align:start position:0% +and discuss all right if if you didn't + + + align:start position:0% +and discuss all right if if you didn't +vote it means you're I think not + + align:start position:0% +vote it means you're I think not + + + align:start position:0% +vote it means you're I think not +following what we're talking about right + + align:start position:0% +following what we're talking about right + + + align:start position:0% +following what we're talking about right +yeah turn to somebody and + + align:start position:0% +yeah turn to somebody and + + + align:start position:0% +yeah turn to somebody and +and right and and another qu you know if + + align:start position:0% +and right and and another qu you know if + + + align:start position:0% +and right and and another qu you know if +your neighbor agrees with you about + + align:start position:0% +your neighbor agrees with you about + + + align:start position:0% +your neighbor agrees with you about +which direction you should be pointing + + align:start position:0% +which direction you should be pointing + + + align:start position:0% +which direction you should be pointing +your arm then try to figure out whether + + align:start position:0% +your arm then try to figure out whether + + + align:start position:0% +your arm then try to figure out whether +we all whether we know whether which + + align:start position:0% +we all whether we know whether which + + + align:start position:0% +we all whether we know whether which +orientation the uh the arrow should + + align:start position:0% +orientation the uh the arrow should + + + align:start position:0% +orientation the uh the arrow should +actually be in + + align:start position:0% +actually be in + + + align:start position:0% +actually be in +okay oh yeah yeah well + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +yeah + + align:start position:0% + + + + align:start position:0% + +is should be different on + + align:start position:0% + + + + align:start position:0% + +side and the question is whether that is + + align:start position:0% +side and the question is whether that is + + + align:start position:0% +side and the question is whether that is +like a stable + + align:start position:0% +like a stable + + + align:start position:0% +like a stable +line yeah we'll we'll figure this + + align:start position:0% + + + + align:start position:0% + +out + + align:start position:0% + + + + align:start position:0% + +all right let's go ahead and reconvene + + align:start position:0% +all right let's go ahead and reconvene + + + align:start position:0% +all right let's go ahead and reconvene +because it seems like some people are + + align:start position:0% +because it seems like some people are + + + align:start position:0% +because it seems like some people are +being quiet but I'm not sure if that's + + align:start position:0% +being quiet but I'm not sure if that's + + + align:start position:0% +being quiet but I'm not sure if that's +because they've figured they think they + + align:start position:0% +because they've figured they think they + + + align:start position:0% +because they've figured they think they +know what's going on or they're just + + align:start position:0% +know what's going on or they're just + + + align:start position:0% +know what's going on or they're just +very much unhappy with the situation all + + align:start position:0% +very much unhappy with the situation all + + + align:start position:0% +very much unhappy with the situation all +right but let let me see let me see a a + + align:start position:0% +right but let let me see let me see a a + + + align:start position:0% +right but let let me see let me see a a +fresh voting all right ready three two + + align:start position:0% +fresh voting all right ready three two + + + align:start position:0% +fresh voting all right ready three two +one okay definitely it's going to be up + + align:start position:0% +one okay definitely it's going to be up + + + align:start position:0% +one okay definitely it's going to be up +or down right because the definition of + + align:start position:0% +or down right because the definition of + + + align:start position:0% +or down right because the definition of +this dash line is that n one dot is + + align:start position:0% +this dash line is that n one dot is + + + align:start position:0% +this dash line is that n one dot is +equal to zero right we don't know what + + align:start position:0% +equal to zero right we don't know what + + + align:start position:0% +equal to zero right we don't know what +N2 dot is right we'll figure that out in + + align:start position:0% +N2 dot is right we'll figure that out in + + + align:start position:0% +N2 dot is right we'll figure that out in +a moment but what we know is that the + + align:start position:0% +a moment but what we know is that the + + + align:start position:0% +a moment but what we know is that the +trajectories which should be something + + align:start position:0% +trajectories which should be something + + + align:start position:0% +trajectories which should be something +lines here all right either up or down + + align:start position:0% +lines here all right either up or down + + + align:start position:0% +lines here all right either up or down +and we're going to find that they're + + align:start position:0% +and we're going to find that they're + + + align:start position:0% +and we're going to find that they're +down but here all right now on this + + align:start position:0% +down but here all right now on this + + + align:start position:0% +down but here all right now on this +solid line quickly the orientation of + + align:start position:0% +solid line quickly the orientation of + + + align:start position:0% +solid line quickly the orientation of +the trajectories ready 3 two one all + + align:start position:0% +the trajectories ready 3 two one all + + + align:start position:0% +the trajectories ready 3 two one all +right perfect okay so we know that N2 + + align:start position:0% +right perfect okay so we know that N2 + + + align:start position:0% +right perfect okay so we know that N2 +dot is is zero here + + align:start position:0% +dot is is zero here + + + align:start position:0% +dot is is zero here +okay now an actual direction of the + + align:start position:0% +okay now an actual direction of the + + + align:start position:0% +okay now an actual direction of the +trajectory at this point right here + + align:start position:0% +trajectory at this point right here + + + align:start position:0% +trajectory at this point right here +ready 3 2 + + align:start position:0% +ready 3 2 + + + align:start position:0% +ready 3 2 +1 okay good right because in the absence + + align:start position:0% +1 okay good right because in the absence + + + align:start position:0% +1 okay good right because in the absence +of + + align:start position:0% +of + + + align:start position:0% +of +N2 we know that species N1 should just + + align:start position:0% +N2 we know that species N1 should just + + + align:start position:0% +N2 we know that species N1 should just +come to carrying capacity + + align:start position:0% +come to carrying capacity + + + align:start position:0% +come to carrying capacity +K1 right same thing over here we should + + align:start position:0% +K1 right same thing over here we should + + + align:start position:0% +K1 right same thing over here we should +get arrows coming down right so indeed + + align:start position:0% +get arrows coming down right so indeed + + + align:start position:0% +get arrows coming down right so indeed +what you can see is that the arrows + + align:start position:0% +what you can see is that the arrows + + + align:start position:0% +what you can see is that the arrows +coming are coming down here that means + + align:start position:0% +coming are coming down here that means + + + align:start position:0% +coming are coming down here that means +they actually do have to come down + + align:start position:0% +they actually do have to come down + + + align:start position:0% +they actually do have to come down +immediately to the right of them okay + + align:start position:0% +immediately to the right of them okay + + + align:start position:0% +immediately to the right of them okay +whereas over here the trajectories + + align:start position:0% +whereas over here the trajectories + + + align:start position:0% +whereas over here the trajectories +pointing right here so um we can kind of + + align:start position:0% +pointing right here so um we can kind of + + + align:start position:0% +pointing right here so um we can kind of +figure out + + align:start position:0% +figure out + + + align:start position:0% +figure out +that all right so they're coming here + + align:start position:0% +that all right so they're coming here + + + align:start position:0% +that all right so they're coming here +and from far away they're coming here + + align:start position:0% +and from far away they're coming here + + + align:start position:0% +and from far away they're coming here +and you can see that they have to come + + align:start position:0% +and you can see that they have to come + + + align:start position:0% +and you can see that they have to come +across here and then they're going to + + align:start position:0% +across here and then they're going to + + + align:start position:0% +across here and then they're going to +come into this point right so this is + + align:start position:0% +come into this point right so this is + + + align:start position:0% +come into this point right so this is +going to be our stable fix point I'll + + align:start position:0% +going to be our stable fix point I'll + + + align:start position:0% +going to be our stable fix point I'll +color it in to indicate that from here + + align:start position:0% +color it in to indicate that from here + + + align:start position:0% +color it in to indicate that from here +they're going to curve around though so + + align:start position:0% +they're going to curve around though so + + + align:start position:0% +they're going to curve around though so +if you start out right here you kind of + + align:start position:0% +if you start out right here you kind of + + + align:start position:0% +if you start out right here you kind of +do this + + align:start position:0% +do this + + + align:start position:0% +do this +business + + align:start position:0% + + + + align:start position:0% + +okay whereas from here we come + + align:start position:0% + + + + align:start position:0% + +in right are these lines allowed to + + align:start position:0% +in right are these lines allowed to + + + align:start position:0% +in right are these lines allowed to +cross each + + align:start position:0% +cross each + + + align:start position:0% +cross each +other no + + align:start position:0% + + + + align:start position:0% + +okay now and indeed you can actually see + + align:start position:0% +okay now and indeed you can actually see + + + align:start position:0% +okay now and indeed you can actually see +here what is the direction of the other + + align:start position:0% +here what is the direction of the other + + + align:start position:0% +here what is the direction of the other +igen vector at this at this point using + + align:start position:0% +igen vector at this at this point using + + + align:start position:0% +igen vector at this at this point using +a hand arm okay ready three two + + align:start position:0% +a hand arm okay ready three two + + + align:start position:0% +a hand arm okay ready three two +one right it's kind of something in + + align:start position:0% +one right it's kind of something in + + + align:start position:0% +one right it's kind of something in +there right because there all these + + align:start position:0% +there right because there all these + + + align:start position:0% +there right because there all these +trajectories are coming here and then + + align:start position:0% +trajectories are coming here and then + + + align:start position:0% +trajectories are coming here and then +they they approach this fixed point from + + align:start position:0% +they they approach this fixed point from + + + align:start position:0% +they they approach this fixed point from +this point because there's here the + + align:start position:0% +this point because there's here the + + + align:start position:0% +this point because there's here the +other the other IG Vector is still + + align:start position:0% +other the other IG Vector is still + + + align:start position:0% +other the other IG Vector is still +horizontal right because we know if we + + align:start position:0% +horizontal right because we know if we + + + align:start position:0% +horizontal right because we know if we +don't have N2 then we just have N1 right + + align:start position:0% +don't have N2 then we just have N1 right + + + align:start position:0% +don't have N2 then we just have N1 right +but this other IG Vector is not purely + + align:start position:0% +but this other IG Vector is not purely + + + align:start position:0% +but this other IG Vector is not purely +straight up right the other one is along + + align:start position:0% +straight up right the other one is along + + + align:start position:0% +straight up right the other one is along +here because the trajectories are coming + + align:start position:0% +here because the trajectories are coming + + + align:start position:0% +here because the trajectories are coming +in along that + + align:start position:0% +in along that + + + align:start position:0% +in along that +okay does that make sense okay right so + + align:start position:0% +okay does that make sense okay right so + + + align:start position:0% +okay does that make sense okay right so +in this case and we should just be clear + + align:start position:0% +in this case and we should just be clear + + + align:start position:0% +in this case and we should just be clear +we are in the situation where K1 over + + align:start position:0% +we are in the situation where K1 over + + + align:start position:0% +we are in the situation where K1 over +beta 1 2 is greater than + + align:start position:0% +beta 1 2 is greater than + + + align:start position:0% +beta 1 2 is greater than +K2 right this is another another way of + + align:start position:0% +K2 right this is another another way of + + + align:start position:0% +K2 right this is another another way of +writing that is that beta one2 is less + + align:start position:0% +writing that is that beta one2 is less + + + align:start position:0% +writing that is that beta one2 is less +than K1 over K2 right so that mean + + align:start position:0% +than K1 over K2 right so that mean + + + align:start position:0% +than K1 over K2 right so that mean +species two does not strongly harm + + align:start position:0% +species two does not strongly harm + + + align:start position:0% +species two does not strongly harm +species one + + align:start position:0% +species one + + + align:start position:0% +species one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yet we know that K1 is greater than K2 / + + align:start position:0% +yet we know that K1 is greater than K2 / + + + align:start position:0% +yet we know that K1 is greater than K2 / +beta 21 right so that means that beta 21 + + align:start position:0% +beta 21 right so that means that beta 21 + + + align:start position:0% +beta 21 right so that means that beta 21 +is greater than K2 over + + align:start position:0% +is greater than K2 over + + + align:start position:0% +is greater than K2 over +K1 okay this is telling us that species + + align:start position:0% +K1 okay this is telling us that species + + + align:start position:0% +K1 okay this is telling us that species +one is strongly harming species 2 okay + + align:start position:0% +one is strongly harming species 2 okay + + + align:start position:0% +one is strongly harming species 2 okay +well all right that makes sense in that + + align:start position:0% +well all right that makes sense in that + + + align:start position:0% +well all right that makes sense in that +case species one + + align:start position:0% +case species one + + + align:start position:0% +case species one +wins + + align:start position:0% +wins + + + align:start position:0% +wins +right does that outcome change if we + + align:start position:0% +right does that outcome change if we + + + align:start position:0% +right does that outcome change if we +change the r + + align:start position:0% +change the r + + + align:start position:0% +change the r +values the division + + align:start position:0% + + + + align:start position:0% + +rates all right a is yes B is no I'm + + align:start position:0% +rates all right a is yes B is no I'm + + + align:start position:0% +rates all right a is yes B is no I'm +going to give you 10 seconds what I just + + align:start position:0% +going to give you 10 seconds what I just + + + align:start position:0% +going to give you 10 seconds what I just +said that if I change RS does that + + align:start position:0% +said that if I change RS does that + + + align:start position:0% +said that if I change RS does that +change the outcome + + align:start position:0% +change the outcome + + + align:start position:0% +change the outcome +ready three two + + align:start position:0% +ready three two + + + align:start position:0% +ready three two +one all right so we got a majority of B + + align:start position:0% +one all right so we got a majority of B + + + align:start position:0% +one all right so we got a majority of B +so the answer is no right this statement + + align:start position:0% +so the answer is no right this statement + + + align:start position:0% +so the answer is no right this statement +that in this + + align:start position:0% + + + + align:start position:0% + +situation species one do uh + + align:start position:0% +situation species one do uh + + + align:start position:0% +situation species one do uh +dominates that's independent of the + + align:start position:0% + + + + align:start position:0% + +RS the fixed points and and actually + + align:start position:0% +RS the fixed points and and actually + + + align:start position:0% +RS the fixed points and and actually +what you see is the conditions here only + + align:start position:0% +what you see is the conditions here only + + + align:start position:0% +what you see is the conditions here only +depend on the what's in here right so + + align:start position:0% +depend on the what's in here right so + + + align:start position:0% +depend on the what's in here right so +the actual shape of those trajectories + + align:start position:0% +the actual shape of those trajectories + + + align:start position:0% +the actual shape of those trajectories +will depend upon the + + align:start position:0% +will depend upon the + + + align:start position:0% +will depend upon the +RS right so if it's the case that + + align:start position:0% +RS right so if it's the case that + + + align:start position:0% +RS right so if it's the case that +species 2 divide is just a grow a faster + + align:start position:0% +species 2 divide is just a grow a faster + + + align:start position:0% +species 2 divide is just a grow a faster +grower than species one then you might + + align:start position:0% +grower than species one then you might + + + align:start position:0% +grower than species one then you might +end up with a situation where if you + + align:start position:0% +end up with a situation where if you + + + align:start position:0% +end up with a situation where if you +start with a little bit of each you + + align:start position:0% +start with a little bit of each you + + + align:start position:0% +start with a little bit of each you +might come clo way up here well no I + + align:start position:0% +might come clo way up here well no I + + + align:start position:0% +might come clo way up here well no I +guess you + + align:start position:0% +guess you + + + align:start position:0% +guess you +might come close to this fix point so + + align:start position:0% +might come close to this fix point so + + + align:start position:0% +might come close to this fix point so +you might think that it really looks + + align:start position:0% +you might think that it really looks + + + align:start position:0% +you might think that it really looks +like species 2 is about to win but + + align:start position:0% +like species 2 is about to win but + + + align:start position:0% +like species 2 is about to win but +eventually they'll curve over and come + + align:start position:0% +eventually they'll curve over and come + + + align:start position:0% +eventually they'll curve over and come +back right and uh and indeed uh in the + + align:start position:0% +back right and uh and indeed uh in the + + + align:start position:0% +back right and uh and indeed uh in the +stroots book The one of the chapters + + align:start position:0% +stroots book The one of the chapters + + + align:start position:0% +stroots book The one of the chapters +that I recommended they have he has an + + align:start position:0% +that I recommended they have he has an + + + align:start position:0% +that I recommended they have he has an +example of you know sheeps and rabbits + + align:start position:0% +example of you know sheeps and rabbits + + + align:start position:0% +example of you know sheeps and rabbits +the idea is that they are uh competing + + align:start position:0% +the idea is that they are uh competing + + + align:start position:0% +the idea is that they are uh competing +species maybe eating simil Foods I don't + + align:start position:0% +species maybe eating simil Foods I don't + + + align:start position:0% +species maybe eating simil Foods I don't +know if that's true but the rabbits can + + align:start position:0% +know if that's true but the rabbits can + + + align:start position:0% +know if that's true but the rabbits can +divide more rapidly right so that here + + align:start position:0% +divide more rapidly right so that here + + + align:start position:0% +divide more rapidly right so that here +the idea would be well if if the sheep + + align:start position:0% +the idea would be well if if the sheep + + + align:start position:0% +the idea would be well if if the sheep +can really displace the rabbits because + + align:start position:0% +can really displace the rabbits because + + + align:start position:0% +can really displace the rabbits because +it's just bigger and push them aside + + align:start position:0% +it's just bigger and push them aside + + + align:start position:0% +it's just bigger and push them aside +then what can happen is that the rabbits + + align:start position:0% +then what can happen is that the rabbits + + + align:start position:0% +then what can happen is that the rabbits +first divide rapidly it looks like + + align:start position:0% +first divide rapidly it looks like + + + align:start position:0% +first divide rapidly it looks like +they're going to take over but over time + + align:start position:0% +they're going to take over but over time + + + align:start position:0% +they're going to take over but over time +eventually the Sheep population uh kind + + align:start position:0% +eventually the Sheep population uh kind + + + align:start position:0% +eventually the Sheep population uh kind +of grow up and they start displacing the + + align:start position:0% +of grow up and they start displacing the + + + align:start position:0% +of grow up and they start displacing the +rabbits and then you end up excluding + + align:start position:0% +rabbits and then you end up excluding + + + align:start position:0% +rabbits and then you end up excluding +the rabbits okay this is this phenomenon + + align:start position:0% +the rabbits okay this is this phenomenon + + + align:start position:0% +the rabbits okay this is this phenomenon +of competitive + + align:start position:0% + + + + align:start position:0% + +exclusion + + align:start position:0% +exclusion + + + align:start position:0% +exclusion +right it's and depending upon the + + align:start position:0% +right it's and depending upon the + + + align:start position:0% +right it's and depending upon the +context X okay that's an e x depending + + align:start position:0% +context X okay that's an e x depending + + + align:start position:0% +context X okay that's an e x depending +on the context this is either more or + + align:start position:0% +on the context this is either more or + + + align:start position:0% +on the context this is either more or +less maybe formally phrased but the idea + + align:start position:0% +less maybe formally phrased but the idea + + + align:start position:0% +less maybe formally phrased but the idea +is that U that if there are two species + + align:start position:0% +is that U that if there are two species + + + align:start position:0% +is that U that if there are two species +that are per that are too similar and in + + align:start position:0% +that are per that are too similar and in + + + align:start position:0% +that are per that are too similar and in +particular if they're kind of somehow + + align:start position:0% +particular if they're kind of somehow + + + align:start position:0% +particular if they're kind of somehow +perfect competitors they're really just + + align:start position:0% +perfect competitors they're really just + + + align:start position:0% +perfect competitors they're really just +trying to eat the same thing then you + + align:start position:0% +trying to eat the same thing then you + + + align:start position:0% +trying to eat the same thing then you +should only uh end up with one of the + + align:start position:0% +should only uh end up with one of the + + + align:start position:0% +should only uh end up with one of the +two species surviving okay um and and + + align:start position:0% +two species surviving okay um and and + + + align:start position:0% +two species surviving okay um and and +that's that's the kind of idea here + + align:start position:0% +that's that's the kind of idea here + + + align:start position:0% +that's that's the kind of idea here +although I think you can argue about the + + align:start position:0% +although I think you can argue about the + + + align:start position:0% +although I think you can argue about the +mapping I think okay so this is one of + + align:start position:0% +mapping I think okay so this is one of + + + align:start position:0% +mapping I think okay so this is one of +the uh this is one of the four outcomes + + align:start position:0% +the uh this is one of the four outcomes + + + align:start position:0% +the uh this is one of the four outcomes +right it's um I don't it takes you know + + align:start position:0% +right it's um I don't it takes you know + + + align:start position:0% +right it's um I don't it takes you know +of course it takes 15 minutes to go + + align:start position:0% +of course it takes 15 minutes to go + + + align:start position:0% +of course it takes 15 minutes to go +through each of these examples so we're + + align:start position:0% +through each of these examples so we're + + + align:start position:0% +through each of these examples so we're +not going to go through all of them but + + align:start position:0% +not going to go through all of them but + + + align:start position:0% +not going to go through all of them but +um but you should be able + + align:start position:0% +um but you should be able + + + align:start position:0% +um but you should be able +to for a given combination of betas and + + align:start position:0% +to for a given combination of betas and + + + align:start position:0% +to for a given combination of betas and +K's right be able to figure out using + + align:start position:0% +K's right be able to figure out using + + + align:start position:0% +K's right be able to figure out using +some combination of algebra you know + + align:start position:0% +some combination of algebra you know + + + align:start position:0% +some combination of algebra you know +derivatives fix Point stability analyses + + align:start position:0% +derivatives fix Point stability analyses + + + align:start position:0% +derivatives fix Point stability analyses +and drawing of things uh well you should + + align:start position:0% +and drawing of things uh well you should + + + align:start position:0% +and drawing of things uh well you should +be able to do all of the above + + align:start position:0% +be able to do all of the above + + + align:start position:0% +be able to do all of the above +right + + align:start position:0% +right + + + align:start position:0% +right +okay are there any questions about where + + align:start position:0% +okay are there any questions about where + + + align:start position:0% +okay are there any questions about where +we are here what's + + align:start position:0% + + + + align:start position:0% + +the + + align:start position:0% +the + + + align:start position:0% +the +okay all right let's I guess none of + + align:start position:0% +okay all right let's I guess none of + + + align:start position:0% +okay all right let's I guess none of +thiss in + + align:start position:0% +thiss in + + + align:start position:0% +thiss in +theas very like yeah that's interesting + + align:start position:0% +theas very like yeah that's interesting + + + align:start position:0% +theas very like yeah that's interesting +question uh for example like in that + + align:start position:0% +question uh for example like in that + + + align:start position:0% +question uh for example like in that +case if R2 is much bigger then you're + + align:start position:0% +case if R2 is much bigger then you're + + + align:start position:0% +case if R2 is much bigger then you're +going to like get almost very close to + + align:start position:0% +going to like get almost very close to + + + align:start position:0% +going to like get almost very close to +like K2 and then maybe just the last + + align:start position:0% +like K2 and then maybe just the last + + + align:start position:0% +like K2 and then maybe just the last +individual that + + align:start position:0% +individual that + + + align:start position:0% +individual that +dies add that + + align:start position:0% +dies add that + + + align:start position:0% +dies add that +fix right um so yes so it's certainly + + align:start position:0% +fix right um so yes so it's certainly + + + align:start position:0% +fix right um so yes so it's certainly +the case that uh that once you have + + align:start position:0% +the case that uh that once you have + + + align:start position:0% +the case that uh that once you have +stochastic Extinction and and the thing + + align:start position:0% +stochastic Extinction and and the thing + + + align:start position:0% +stochastic Extinction and and the thing +is that you would probably be most + + align:start position:0% +is that you would probably be most + + + align:start position:0% +is that you would probably be most +susceptible to stochastic Extinction in + + align:start position:0% +susceptible to stochastic Extinction in + + + align:start position:0% +susceptible to stochastic Extinction in +the case in the case you were talking + + align:start position:0% +the case in the case you were talking + + + align:start position:0% +the case in the case you were talking +about you'd be most susceptible + + align:start position:0% +about you'd be most susceptible + + + align:start position:0% +about you'd be most susceptible +stochastic Extinction when you're around + + align:start position:0% +stochastic Extinction when you're around + + + align:start position:0% +stochastic Extinction when you're around +here actually because I think that these + + align:start position:0% +here actually because I think that these + + + align:start position:0% +here actually because I think that these +trajectories are are still always um + + align:start position:0% +trajectories are are still always um + + + align:start position:0% +trajectories are are still always um +moving up in K in N1 space right cuz I I + + align:start position:0% +moving up in K in N1 space right cuz I I + + + align:start position:0% +moving up in K in N1 space right cuz I I +just want to be I think I know what + + align:start position:0% +just want to be I think I know what + + + align:start position:0% +just want to be I think I know what +you're saying all right because we're + + align:start position:0% +you're saying all right because we're + + + align:start position:0% +you're saying all right because we're +going to maybe zoom in onto this N1 + + align:start position:0% +going to maybe zoom in onto this N1 + + + align:start position:0% +going to maybe zoom in onto this N1 +N2 right because we have this unstable + + align:start position:0% +N2 right because we have this unstable + + + align:start position:0% +N2 right because we have this unstable +fixed Point here and the claim was that + + align:start position:0% +fixed Point here and the claim was that + + + align:start position:0% +fixed Point here and the claim was that +if you start out over here + + align:start position:0% +if you start out over here + + + align:start position:0% +if you start out over here +uh then the trajectory might look + + align:start position:0% +uh then the trajectory might look + + + align:start position:0% +uh then the trajectory might look +something like this right and you'd say + + align:start position:0% +something like this right and you'd say + + + align:start position:0% +something like this right and you'd say +oh well you might go extinct here I + + align:start position:0% +oh well you might go extinct here I + + + align:start position:0% +oh well you might go extinct here I +guess the idea was just like the + + align:start position:0% +guess the idea was just like the + + + align:start position:0% +guess the idea was just like the +statement that it doesn't depend on R1 + + align:start position:0% +statement that it doesn't depend on R1 + + + align:start position:0% +statement that it doesn't depend on R1 +or R2 is like a very + + align:start position:0% +or R2 is like a very + + + align:start position:0% +or R2 is like a very +dynamical ah yes that hold it all + + align:start position:0% +dynamical ah yes that hold it all + + + align:start position:0% +dynamical ah yes that hold it all +yeah you know at all is always yeah it + + align:start position:0% +yeah you know at all is always yeah it + + + align:start position:0% +yeah you know at all is always yeah it +it's true that I guess things change + + align:start position:0% +it's true that I guess things change + + + align:start position:0% +it's true that I guess things change +uh there are a number of things you + + align:start position:0% +uh there are a number of things you + + + align:start position:0% +uh there are a number of things you +might want to say um first of all okay + + align:start position:0% +might want to say um first of all okay + + + align:start position:0% +might want to say um first of all okay +this is a purely well continuous and + + align:start position:0% +this is a purely well continuous and + + + align:start position:0% +this is a purely well continuous and +deterministic description of the of the + + align:start position:0% +deterministic description of the of the + + + align:start position:0% +deterministic description of the of the +setting uh it allows for fractional + + align:start position:0% +setting uh it allows for fractional + + + align:start position:0% +setting uh it allows for fractional +individuals right um there's no shocks + + align:start position:0% +individuals right um there's no shocks + + + align:start position:0% +individuals right um there's no shocks +or perturbations that you have to worry + + align:start position:0% +or perturbations that you have to worry + + + align:start position:0% +or perturbations that you have to worry +about uh I guess the only thing I wanted + + align:start position:0% +about uh I guess the only thing I wanted + + + align:start position:0% +about uh I guess the only thing I wanted +to say in regards to your question is + + align:start position:0% +to say in regards to your question is + + + align:start position:0% +to say in regards to your question is +that uh it's not I think the stochastic + + align:start position:0% +that uh it's not I think the stochastic + + + align:start position:0% +that uh it's not I think the stochastic +Extinction will not be dominated this + + align:start position:0% +Extinction will not be dominated this + + + align:start position:0% +Extinction will not be dominated this +you we're talking about stochastic + + align:start position:0% +you we're talking about stochastic + + + align:start position:0% +you we're talking about stochastic +Extinction of species one it will not be + + align:start position:0% +Extinction of species one it will not be + + + align:start position:0% +Extinction of species one it will not be +dominated due to stochastic Extinction + + align:start position:0% +dominated due to stochastic Extinction + + + align:start position:0% +dominated due to stochastic Extinction +here but stochastic Extinction at the + + align:start position:0% +here but stochastic Extinction at the + + + align:start position:0% +here but stochastic Extinction at the +beginning because I think although you + + align:start position:0% +beginning because I think although you + + + align:start position:0% +beginning because I think although you +know I haven't drawn this very well but + + align:start position:0% +know I haven't drawn this very well but + + + align:start position:0% +know I haven't drawn this very well but +uh in this case I think these + + align:start position:0% +uh in this case I think these + + + align:start position:0% +uh in this case I think these +trajectories always are going up in in + + align:start position:0% +trajectories always are going up in in + + + align:start position:0% +trajectories always are going up in in +numbers of one right in in numbers of + + align:start position:0% +numbers of one right in in numbers of + + + align:start position:0% +numbers of one right in in numbers of +the one species which means that you're + + align:start position:0% +the one species which means that you're + + + align:start position:0% +the one species which means that you're +most likely to experience stochastic + + align:start position:0% +most likely to experience stochastic + + + align:start position:0% +most likely to experience stochastic +Extinction at the beginning yeah R1 and + + align:start position:0% +Extinction at the beginning yeah R1 and + + + align:start position:0% +Extinction at the beginning yeah R1 and +R2 should still like really mess withas + + align:start position:0% +R2 should still like really mess withas + + + align:start position:0% +R2 should still like really mess withas +Extinction right because then + + align:start position:0% +Extinction right because then + + + align:start position:0% +Extinction right because then +well the larger R1 and R2 are the the + + align:start position:0% +well the larger R1 and R2 are the the + + + align:start position:0% +well the larger R1 and R2 are the the +quicker we get out of the regime + + align:start position:0% +quicker we get out of the regime + + + align:start position:0% +quicker we get out of the regime +ofas that that's all true + + align:start position:0% +ofas that that's all true + + + align:start position:0% +ofas that that's all true +um although I think we have to we have + + align:start position:0% +um although I think we have to we have + + + align:start position:0% +um although I think we have to we have +to be careful about many of these things + + align:start position:0% +to be careful about many of these things + + + align:start position:0% +to be careful about many of these things +um right so in particular if you go and + + align:start position:0% +um right so in particular if you go and + + + align:start position:0% +um right so in particular if you go and +you do a stochastic simulation of this + + align:start position:0% +you do a stochastic simulation of this + + + align:start position:0% +you do a stochastic simulation of this +so let's say you plug this thing into a + + align:start position:0% +so let's say you plug this thing into a + + + align:start position:0% +so let's say you plug this thing into a +Gillespie simulation right can you get + + align:start position:0% +Gillespie simulation right can you get + + + align:start position:0% +Gillespie simulation right can you get +stochastic + + align:start position:0% +stochastic + + + align:start position:0% +stochastic +Extinction a yes or B no ready three two + + align:start position:0% +Extinction a yes or B no ready three two + + + align:start position:0% +Extinction a yes or B no ready three two +one no all right yes so the answer is no + + align:start position:0% +one no all right yes so the answer is no + + + align:start position:0% +one no all right yes so the answer is no +but why I mean it depends like if you + + align:start position:0% +but why I mean it depends like if you + + + align:start position:0% +but why I mean it depends like if you +take combination per yeah exactly right + + align:start position:0% +take combination per yeah exactly right + + + align:start position:0% +take combination per yeah exactly right +so so right now as written there's no + + align:start position:0% +so so right now as written there's no + + + align:start position:0% +so so right now as written there's no +death right alth although I guess you + + align:start position:0% +death right alth although I guess you + + + align:start position:0% +death right alth although I guess you +could say that this is a dep well all + + align:start position:0% +could say that this is a dep well all + + + align:start position:0% +could say that this is a dep well all +right well we have it's just there's a + + align:start position:0% +right well we have it's just there's a + + + align:start position:0% +right well we have it's just there's a +question of how + + align:start position:0% +question of how + + + align:start position:0% +question of how +you partition things in your you know so + + align:start position:0% +you partition things in your you know so + + + align:start position:0% +you partition things in your you know so +in principle all these things this is + + align:start position:0% +in principle all these things this is + + + align:start position:0% +in principle all these things this is +the difference between the growth and + + align:start position:0% +the difference between the growth and + + + align:start position:0% +the difference between the growth and +the death rate right but the most + + align:start position:0% +the death rate right but the most + + + align:start position:0% +the death rate right but the most +straightforward way of doing such a + + align:start position:0% +straightforward way of doing such a + + + align:start position:0% +straightforward way of doing such a +simulation is that you put this whole + + align:start position:0% +simulation is that you put this whole + + + align:start position:0% +simulation is that you put this whole +thing in here as a rate for birth + + align:start position:0% + + + + align:start position:0% + +right all right you know somebody's say + + align:start position:0% +right all right you know somebody's say + + + align:start position:0% +right all right you know somebody's say +oh that's not how I was going to do the + + align:start position:0% +oh that's not how I was going to do the + + + align:start position:0% +oh that's not how I was going to do the +simulation right okay well that's + + align:start position:0% +simulation right okay well that's + + + align:start position:0% +simulation right okay well that's +probably how you were going to do it you + + align:start position:0% +probably how you were going to do it you + + + align:start position:0% +probably how you were going to do it you +know no but if you did that then that if + + align:start position:0% +know no but if you did that then that if + + + align:start position:0% +know no but if you did that then that if +there's only birth then you can't get + + align:start position:0% +there's only birth then you can't get + + + align:start position:0% +there's only birth then you can't get +stochastic Extinction obviously right + + align:start position:0% +stochastic Extinction obviously right + + + align:start position:0% +stochastic Extinction obviously right +but in in in general and this is one of + + align:start position:0% +but in in in general and this is one of + + + align:start position:0% +but in in in general and this is one of +the things we spend a lot of time kind + + align:start position:0% +the things we spend a lot of time kind + + + align:start position:0% +the things we spend a lot of time kind +of thinking about in this semester right + + align:start position:0% +of thinking about in this semester right + + + align:start position:0% +of thinking about in this semester right +is that there's a difference between uh + + align:start position:0% +is that there's a difference between uh + + + align:start position:0% +is that there's a difference between uh +there there are multiple ways of doing + + align:start position:0% +there there are multiple ways of doing + + + align:start position:0% +there there are multiple ways of doing +kind of a stochastic Sim simulation from + + align:start position:0% +kind of a stochastic Sim simulation from + + + align:start position:0% +kind of a stochastic Sim simulation from +a deterministic equation right and this + + align:start position:0% +a deterministic equation right and this + + + align:start position:0% +a deterministic equation right and this +thing could just you could be more + + align:start position:0% +thing could just you could be more + + + align:start position:0% +thing could just you could be more +explicit and say oh this thing is really + + align:start position:0% +explicit and say oh this thing is really + + + align:start position:0% +explicit and say oh this thing is really +a B2 minus a D2 so a birth rate minus a + + align:start position:0% +a B2 minus a D2 so a birth rate minus a + + + align:start position:0% +a B2 minus a D2 so a birth rate minus a +death rate for example right and from + + align:start position:0% +death rate for example right and from + + + align:start position:0% +death rate for example right and from +the standpoint of a differential + + align:start position:0% +the standpoint of a differential + + + align:start position:0% +the standpoint of a differential +equation it doesn't make any difference + + align:start position:0% +equation it doesn't make any difference + + + align:start position:0% +equation it doesn't make any difference +but if you if you calc if you do the + + align:start position:0% +but if you if you calc if you do the + + + align:start position:0% +but if you if you calc if you do the +fuer plank approximation or you do a + + align:start position:0% +fuer plank approximation or you do a + + + align:start position:0% +fuer plank approximation or you do a +simulation or whatnot then these these + + align:start position:0% +simulation or whatnot then these these + + + align:start position:0% +simulation or whatnot then these these +lead to different things right and in + + align:start position:0% +lead to different things right and in + + + align:start position:0% +lead to different things right and in +particular the rate of say stochastic + + align:start position:0% +particular the rate of say stochastic + + + align:start position:0% +particular the rate of say stochastic +Extinction here increases as B and D + + align:start position:0% +Extinction here increases as B and D + + + align:start position:0% +Extinction here increases as B and D +increase right because that leads to + + align:start position:0% +increase right because that leads to + + + align:start position:0% +increase right because that leads to +more of these + + align:start position:0% +more of these + + + align:start position:0% +more of these +fluctuations + + align:start position:0% +fluctuations + + + align:start position:0% +fluctuations +okay um yeah so there are many things + + align:start position:0% +okay um yeah so there are many things + + + align:start position:0% +okay um yeah so there are many things +that are different once you include uh + + align:start position:0% +that are different once you include uh + + + align:start position:0% +that are different once you include uh +once you include the stochastic Dynamics + + align:start position:0% +once you include the stochastic Dynamics + + + align:start position:0% +once you include the stochastic Dynamics +but I I think you I it's always good to + + align:start position:0% +but I I think you I it's always good to + + + align:start position:0% +but I I think you I it's always good to +get a base sense of the Dynamics you + + align:start position:0% +get a base sense of the Dynamics you + + + align:start position:0% +get a base sense of the Dynamics you +know from the standpoint of just + + align:start position:0% +know from the standpoint of just + + + align:start position:0% +know from the standpoint of just +deterministic differential equations + + align:start position:0% +deterministic differential equations + + + align:start position:0% +deterministic differential equations +before you think think too much about + + align:start position:0% +before you think think too much about + + + align:start position:0% +before you think think too much about +the stochastic Dynamics because + + align:start position:0% +the stochastic Dynamics because + + + align:start position:0% +the stochastic Dynamics because +otherwise you get you get overwhelmed + + align:start position:0% +otherwise you get you get overwhelmed + + + align:start position:0% +otherwise you get you get overwhelmed +quickly + + align:start position:0% + + + + align:start position:0% + +right any other questions about about + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +um okay what I want to do uh is just + + align:start position:0% +um okay what I want to do uh is just + + + align:start position:0% +um okay what I want to do uh is just +spend a little bit of time to think + + align:start position:0% +spend a little bit of time to think + + + align:start position:0% +spend a little bit of time to think +about the more generalized case of more + + align:start position:0% +about the more generalized case of more + + + align:start position:0% +about the more generalized case of more +species + + align:start position:0% + + + + align:start position:0% + +okay and in particular we could + + align:start position:0% +okay and in particular we could + + + align:start position:0% +okay and in particular we could +convert this set of equations we can + + align:start position:0% +convert this set of equations we can + + + align:start position:0% +convert this set of equations we can +normalize by each of their carrying + + align:start position:0% +normalize by each of their carrying + + + align:start position:0% +normalize by each of their carrying +capacities um and we can + + align:start position:0% +capacities um and we can + + + align:start position:0% +capacities um and we can +convert + + align:start position:0% +convert + + + align:start position:0% +convert +uh we can convert a set of equations to + + align:start position:0% +uh we can convert a set of equations to + + + align:start position:0% +uh we can convert a set of equations to +look something like this so now we just + + align:start position:0% +look something like this so now we just + + + align:start position:0% +look something like this so now we just +have XI Dot + + align:start position:0% +have XI Dot + + + align:start position:0% +have XI Dot +is equal to there some r + + align:start position:0% +is equal to there some r + + + align:start position:0% +is equal to there some r +ixi 1 minus what we can actually do is + + align:start position:0% +ixi 1 minus what we can actually do is + + + align:start position:0% +ixi 1 minus what we can actually do is +normalize everything so that it's just + + align:start position:0% +normalize everything so that it's just + + + align:start position:0% +normalize everything so that it's just +written like + + align:start position:0% + + + + align:start position:0% + +this okay and normally what we assume is + + align:start position:0% +this okay and normally what we assume is + + + align:start position:0% +this okay and normally what we assume is +that we've done things such that + + align:start position:0% +that we've done things such that + + + align:start position:0% +that we've done things such that +Alpha I I is equal to one for all for + + align:start position:0% +Alpha I I is equal to one for all for + + + align:start position:0% +Alpha I I is equal to one for all for +all I right so this is just saying that + + align:start position:0% +all I right so this is just saying that + + + align:start position:0% +all I right so this is just saying that +uh this is the normalization such that + + align:start position:0% +uh this is the normalization such that + + + align:start position:0% +uh this is the normalization such that +each species inhibits itself + + align:start position:0% +each species inhibits itself + + + align:start position:0% +each species inhibits itself +uh in a way that it's just going to give + + align:start position:0% +uh in a way that it's just going to give + + + align:start position:0% +uh in a way that it's just going to give +a simple logistic growth right and it's + + align:start position:0% +a simple logistic growth right and it's + + + align:start position:0% +a simple logistic growth right and it's +going to set and it's going to well it's + + align:start position:0% +going to set and it's going to well it's + + + align:start position:0% +going to set and it's going to well it's +going to be logistic growth with uh + + align:start position:0% +going to be logistic growth with uh + + + align:start position:0% +going to be logistic growth with uh +carrying capacity equal to + + align:start position:0% +carrying capacity equal to + + + align:start position:0% +carrying capacity equal to +one right and then once you've done that + + align:start position:0% +one right and then once you've done that + + + align:start position:0% +one right and then once you've done that +then the then a species inhibits itself + + align:start position:0% +then the then a species inhibits itself + + + align:start position:0% +then the then a species inhibits itself +U with Alpha I i1 and then everything + + align:start position:0% +U with Alpha I i1 and then everything + + + align:start position:0% +U with Alpha I i1 and then everything +comes down to what the uh what these + + align:start position:0% +comes down to what the uh what these + + + align:start position:0% +comes down to what the uh what these +various Al this Alpha Matrix + + align:start position:0% +various Al this Alpha Matrix + + + align:start position:0% +various Al this Alpha Matrix +is + + align:start position:0% +is + + + align:start position:0% +is +okay um and uh I would say that as + + align:start position:0% +okay um and uh I would say that as + + + align:start position:0% +okay um and uh I would say that as +always it's it's really very very + + align:start position:0% +always it's it's really very very + + + align:start position:0% +always it's it's really very very +important that you can go back and forth + + align:start position:0% +important that you can go back and forth + + + align:start position:0% +important that you can go back and forth +between the kind of non-dimensionalized + + align:start position:0% +between the kind of non-dimensionalized + + + align:start position:0% +between the kind of non-dimensionalized +versions of equations and the the base + + align:start position:0% +versions of equations and the the base + + + align:start position:0% +versions of equations and the the base +versions this was something that on on + + align:start position:0% +versions this was something that on on + + + align:start position:0% +versions this was something that on on +exam number two uh there was quite there + + align:start position:0% +exam number two uh there was quite there + + + align:start position:0% +exam number two uh there was quite there +were quite a lot of problems with uh + + align:start position:0% +were quite a lot of problems with uh + + + align:start position:0% +were quite a lot of problems with uh +this problem where you know we asked + + align:start position:0% +this problem where you know we asked + + + align:start position:0% +this problem where you know we asked +about you know what happened you know + + align:start position:0% +about you know what happened you know + + + align:start position:0% +about you know what happened you know +what you know how do you know what what + + align:start position:0% +what you know how do you know what what + + + align:start position:0% +what you know how do you know what what +what how does the parameter change when + + align:start position:0% +what how does the parameter change when + + + align:start position:0% +what how does the parameter change when +you change the strength of expression or + + align:start position:0% +you change the strength of expression or + + + align:start position:0% +you change the strength of expression or +this or that right U so this is + + align:start position:0% +this or that right U so this is + + + align:start position:0% +this or that right U so this is +something that I think is is very + + align:start position:0% +something that I think is is very + + + align:start position:0% +something that I think is is very +important because this comes up a lot + + align:start position:0% +important because this comes up a lot + + + align:start position:0% +important because this comes up a lot +okay all right so in this case the alpha + + align:start position:0% +okay all right so in this case the alpha + + + align:start position:0% +okay all right so in this case the alpha +Matrix tells you kind of + + align:start position:0% +Matrix tells you kind of + + + align:start position:0% +Matrix tells you kind of +everything and there are uh there are a + + align:start position:0% +everything and there are uh there are a + + + align:start position:0% +everything and there are uh there are a +number of things that you that well the + + align:start position:0% +number of things that you that well the + + + align:start position:0% +number of things that you that well the +mathematicians have proven about these + + align:start position:0% +mathematicians have proven about these + + + align:start position:0% +mathematicians have proven about these +sorts of equations and I just want to + + align:start position:0% +sorts of equations and I just want to + + + align:start position:0% +sorts of equations and I just want to +point you towards some of the things to + + align:start position:0% +point you towards some of the things to + + + align:start position:0% +point you towards some of the things to +think about so first uh all right and + + align:start position:0% +think about so first uh all right and + + + align:start position:0% +think about so first uh all right and +I'm I'm considering a case where uh + + align:start position:0% +I'm I'm considering a case where uh + + + align:start position:0% +I'm I'm considering a case where uh +again alpha alpha i j is greater than + + align:start position:0% +again alpha alpha i j is greater than + + + align:start position:0% +again alpha alpha i j is greater than +zero um again for all + + align:start position:0% +zero um again for all + + + align:start position:0% +zero um again for all +i j okay or greater than or equal to + + align:start position:0% +i j okay or greater than or equal to + + + align:start position:0% +i j okay or greater than or equal to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +well all right so some of them can be + + align:start position:0% +well all right so some of them can be + + + align:start position:0% +well all right so some of them can be +zero okay but the interactions when they + + align:start position:0% +zero okay but the interactions when they + + + align:start position:0% +zero okay but the interactions when they +exist are uh competitive + + align:start position:0% +exist are uh competitive + + + align:start position:0% +exist are uh competitive +okay so first um if you if you start out + + align:start position:0% +okay so first um if you if you start out + + + align:start position:0% +okay so first um if you if you start out +in the region uh where all of the + + align:start position:0% +in the region uh where all of the + + + align:start position:0% +in the region uh where all of the +species start between zero and one then + + align:start position:0% +species start between zero and one then + + + align:start position:0% +species start between zero and one then +you stay uh you stay in that region + + align:start position:0% + + + + align:start position:0% + +okay all right so if you start if this + + align:start position:0% +okay all right so if you start if this + + + align:start position:0% +okay all right so if you start if this +is true initially then it will be true + + align:start position:0% + + + + align:start position:0% + +forever + + align:start position:0% +forever + + + align:start position:0% +forever +okay that's good + + align:start position:0% +okay that's good + + + align:start position:0% +okay that's good +negative abundances you maybe were not + + align:start position:0% +negative abundances you maybe were not + + + align:start position:0% +negative abundances you maybe were not +so worried about but it's not as obvious + + align:start position:0% +so worried about but it's not as obvious + + + align:start position:0% +so worried about but it's not as obvious +that you can't get above one because + + align:start position:0% +that you can't get above one because + + + align:start position:0% +that you can't get above one because +there's nothing saying that in principle + + align:start position:0% +there's nothing saying that in principle + + + align:start position:0% +there's nothing saying that in principle +you couldn't have started there right or + + align:start position:0% +you couldn't have started there right or + + + align:start position:0% +you couldn't have started there right or +that in principle you couldn't have + + align:start position:0% +that in principle you couldn't have + + + align:start position:0% +that in principle you couldn't have +gotten + + align:start position:0% +gotten + + + align:start position:0% +gotten +there and certainly it's physical to + + align:start position:0% +there and certainly it's physical to + + + align:start position:0% +there and certainly it's physical to +think about start starting outside of + + align:start position:0% +think about start starting outside of + + + align:start position:0% +think about start starting outside of +that region because we often talk about + + align:start position:0% +that region because we often talk about + + + align:start position:0% +that region because we often talk about +carrying capacities as something it's + + align:start position:0% + + + + align:start position:0% + +like right if you think about this is an + + align:start position:0% +like right if you think about this is an + + + align:start position:0% +like right if you think about this is an +XI as a function of + + align:start position:0% +XI as a function of + + + align:start position:0% +XI as a function of +time right so in these in these in these + + align:start position:0% +time right so in these in these in these + + + align:start position:0% +time right so in these in these in these +situations it's not crazy to think about + + align:start position:0% +situations it's not crazy to think about + + + align:start position:0% +situations it's not crazy to think about +something above the carrying + + align:start position:0% +something above the carrying + + + align:start position:0% +something above the carrying +capacity right but this this + + align:start position:0% +capacity right but this this + + + align:start position:0% +capacity right but this this +mathematical statement about the lock of + + align:start position:0% +mathematical statement about the lock of + + + align:start position:0% +mathematical statement about the lock of +voltera framework is that if you start + + align:start position:0% +voltera framework is that if you start + + + align:start position:0% +voltera framework is that if you start +out with everything below its carrying + + align:start position:0% +out with everything below its carrying + + + align:start position:0% +out with everything below its carrying +capacity then everything will always + + align:start position:0% +capacity then everything will always + + + align:start position:0% +capacity then everything will always +stay there okay + + align:start position:0% +stay there okay + + + align:start position:0% +stay there okay +uh and it's all the + + align:start position:0% +uh and it's all the + + + align:start position:0% +uh and it's all the +Dynamics uh occur and this is this is + + align:start position:0% +Dynamics uh occur and this is this is + + + align:start position:0% +Dynamics uh occur and this is this is +for + + align:start position:0% +for + + + align:start position:0% +for +I equal to one to n do I want to use big + + align:start position:0% +I equal to one to n do I want to use big + + + align:start position:0% +I equal to one to n do I want to use big +n or little n does it + + align:start position:0% +n or little n does it + + + align:start position:0% +n or little n does it +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +matter + + align:start position:0% +matter + + + align:start position:0% +matter +um okay right so this is Big N different + + align:start position:0% +um okay right so this is Big N different + + + align:start position:0% +um okay right so this is Big N different +species the Dynamics occur on an N minus + + align:start position:0% +species the Dynamics occur on an N minus + + + align:start position:0% +species the Dynamics occur on an N minus +one manifold all right if we have any + + align:start position:0% +one manifold all right if we have any + + + align:start position:0% +one manifold all right if we have any +mathematicians they can explain what + + align:start position:0% +mathematicians they can explain what + + + align:start position:0% +mathematicians they can explain what +this technically means but um basically + + align:start position:0% +this technically means but um basically + + + align:start position:0% +this technically means but um basically +what it's saying is that there's going + + align:start position:0% +what it's saying is that there's going + + + align:start position:0% +what it's saying is that there's going +to be some n n minus one dimensional + + align:start position:0% +to be some n n minus one dimensional + + + align:start position:0% +to be some n n minus one dimensional +kind of surface or volume or what not + + align:start position:0% +kind of surface or volume or what not + + + align:start position:0% +kind of surface or volume or what not +where all the Dynamics are going to uh + + align:start position:0% +where all the Dynamics are going to uh + + + align:start position:0% +where all the Dynamics are going to uh +end up being on right and what that what + + align:start position:0% +end up being on right and what that what + + + align:start position:0% +end up being on right and what that what +that means is that in + + align:start position:0% +that means is that in + + + align:start position:0% +that means is that in +particular a limit cycle + + align:start position:0% +particular a limit cycle + + + align:start position:0% +particular a limit cycle +requires two two Dimensions + + align:start position:0% + + + + align:start position:0% + +right requires sorry requires 2D which + + align:start position:0% +right requires sorry requires 2D which + + + align:start position:0% +right requires sorry requires 2D which +means that to get a limit cycle + + align:start position:0% +means that to get a limit cycle + + + align:start position:0% +means that to get a limit cycle +requires um so that n has to be greater + + align:start position:0% +requires um so that n has to be greater + + + align:start position:0% +requires um so that n has to be greater +than equal to three to get a limit + + align:start position:0% +than equal to three to get a limit + + + align:start position:0% +than equal to three to get a limit +cycle do you you see what I'm saying + + align:start position:0% +cycle do you you see what I'm saying + + + align:start position:0% +cycle do you you see what I'm saying +right whereas uh chaos + + align:start position:0% +right whereas uh chaos + + + align:start position:0% +right whereas uh chaos +requires um requires + + align:start position:0% +requires um requires + + + align:start position:0% +requires um requires +3D okay and that means that n has to be + + align:start position:0% +3D okay and that means that n has to be + + + align:start position:0% +3D okay and that means that n has to be +greater than equal to + + align:start position:0% +greater than equal to + + + align:start position:0% +greater than equal to +four okay um and indeed you can get + + align:start position:0% +four okay um and indeed you can get + + + align:start position:0% +four okay um and indeed you can get +limit Cycles with n equal to 3 and you + + align:start position:0% +limit Cycles with n equal to 3 and you + + + align:start position:0% +limit Cycles with n equal to 3 and you +get chaos with n + + align:start position:0% +get chaos with n + + + align:start position:0% +get chaos with n +equal + + align:start position:0% +equal + + + align:start position:0% +equal +okay there's another theorem that says + + align:start position:0% +okay there's another theorem that says + + + align:start position:0% +okay there's another theorem that says +that any Dynamics are possible for n + + align:start position:0% +that any Dynamics are possible for n + + + align:start position:0% +that any Dynamics are possible for n +equal to five or larger um and I I know + + align:start position:0% +equal to five or larger um and I I know + + + align:start position:0% +equal to five or larger um and I I know +chaos seems as much as I would want to + + align:start position:0% +chaos seems as much as I would want to + + + align:start position:0% +chaos seems as much as I would want to +ask for but um there's + + align:start position:0% +ask for but um there's + + + align:start position:0% +ask for but um there's +apparently uh 4D Taurus something that + + align:start position:0% +apparently uh 4D Taurus something that + + + align:start position:0% +apparently uh 4D Taurus something that +is different all right this is something + + align:start position:0% +is different all right this is something + + + align:start position:0% +is different all right this is something +to think about in your spare time all + + align:start position:0% +to think about in your spare time all + + + align:start position:0% +to think about in your spare time all +right + + align:start position:0% +right + + + align:start position:0% +right +um + + align:start position:0% + + + + align:start position:0% + +yes uh well you know I like like a lot + + align:start position:0% +yes uh well you know I like like a lot + + + align:start position:0% +yes uh well you know I like like a lot +of things okay um yeah no and and um and + + align:start position:0% +of things okay um yeah no and and um and + + + align:start position:0% +of things okay um yeah no and and um and +this is worth spending a moment talking + + align:start position:0% +this is worth spending a moment talking + + + align:start position:0% +this is worth spending a moment talking +about because right um first of all okay + + align:start position:0% +about because right um first of all okay + + + align:start position:0% +about because right um first of all okay +so here's a two-dimensional thing right + + align:start position:0% +so here's a two-dimensional thing right + + + align:start position:0% +so here's a two-dimensional thing right +uh the special thing as you might + + align:start position:0% +uh the special thing as you might + + + align:start position:0% +uh the special thing as you might +remember about U continuous Dynamics is + + align:start position:0% +remember about U continuous Dynamics is + + + align:start position:0% +remember about U continuous Dynamics is +that these trajectories are not allowed + + align:start position:0% +that these trajectories are not allowed + + + align:start position:0% +that these trajectories are not allowed +to cross each other + + align:start position:0% +to cross each other + + + align:start position:0% +to cross each other +right which means that you just can't + + align:start position:0% +right which means that you just can't + + + align:start position:0% +right which means that you just can't +draw a cha iotic a chaotic trajectory + + align:start position:0% +draw a cha iotic a chaotic trajectory + + + align:start position:0% +draw a cha iotic a chaotic trajectory +because you're going to have to cross + + align:start position:0% +because you're going to have to cross + + + align:start position:0% +because you're going to have to cross +yourself again that's also why a limit + + align:start position:0% +yourself again that's also why a limit + + + align:start position:0% +yourself again that's also why a limit +cycle requires + + align:start position:0% +cycle requires + + + align:start position:0% +cycle requires +two right because we we originally tried + + align:start position:0% +two right because we we originally tried + + + align:start position:0% +two right because we we originally tried +to draw a limit cycle in one dimension + + align:start position:0% +to draw a limit cycle in one dimension + + + align:start position:0% +to draw a limit cycle in one dimension +and it didn't work do you remember this + + align:start position:0% +and it didn't work do you remember this + + + align:start position:0% +and it didn't work do you remember this +right and the same thing with you know + + align:start position:0% +right and the same thing with you know + + + align:start position:0% +right and the same thing with you know +you can imagine all right here's a nice + + align:start position:0% +you can imagine all right here's a nice + + + align:start position:0% +you can imagine all right here's a nice +limit cycle okay and that that could be + + align:start position:0% +limit cycle okay and that that could be + + + align:start position:0% +limit cycle okay and that that could be +stable um oh incidentally I uh I think + + align:start position:0% +stable um oh incidentally I uh I think + + + align:start position:0% +stable um oh incidentally I uh I think +you you were right about I I was getting + + align:start position:0% +you you were right about I I was getting + + + align:start position:0% +you you were right about I I was getting +confused about the point cray Ben Dixon + + align:start position:0% +confused about the point cray Ben Dixon + + + align:start position:0% +confused about the point cray Ben Dixon +theorem because I think there are these + + align:start position:0% +theorem because I think there are these + + + align:start position:0% +theorem because I think there are these +funny things wait no it wasn't you all + + align:start position:0% +funny things wait no it wasn't you all + + + align:start position:0% +funny things wait no it wasn't you all +right okay well you know all these + + align:start position:0% +right okay well you know all these + + + align:start position:0% +right okay well you know all these +people are complain about what I say all + + align:start position:0% +people are complain about what I say all + + + align:start position:0% +people are complain about what I say all +right yeah so right I think it was that + + align:start position:0% +right yeah so right I think it was that + + + align:start position:0% +right yeah so right I think it was that +because if you have this the + + align:start position:0% +because if you have this the + + + align:start position:0% +because if you have this the +trajectories are coming in um then what + + align:start position:0% +trajectories are coming in um then what + + + align:start position:0% +trajectories are coming in um then what +I said was that if you had an unstable + + align:start position:0% +I said was that if you had an unstable + + + align:start position:0% +I said was that if you had an unstable +fix Point coming out then you could draw + + align:start position:0% +fix Point coming out then you could draw + + + align:start position:0% +fix Point coming out then you could draw +this region and then you could be + + align:start position:0% +this region and then you could be + + + align:start position:0% +this region and then you could be +guaranteed that there was a limit cycle + + align:start position:0% +guaranteed that there was a limit cycle + + + align:start position:0% +guaranteed that there was a limit cycle +in there but you could you cannot just + + align:start position:0% +in there but you could you cannot just + + + align:start position:0% +in there but you could you cannot just +based on what I had said say that if + + align:start position:0% +based on what I had said say that if + + + align:start position:0% +based on what I had said say that if +it's a stable fix point then you won't + + align:start position:0% +it's a stable fix point then you won't + + + align:start position:0% +it's a stable fix point then you won't +get a limit cycle right I in some other + + align:start position:0% +get a limit cycle right I in some other + + + align:start position:0% +get a limit cycle right I in some other +other cases you can prove that that it + + align:start position:0% +other cases you can prove that that it + + + align:start position:0% +other cases you can prove that that it +doesn't work and particular like in the + + align:start position:0% +doesn't work and particular like in the + + + align:start position:0% +doesn't work and particular like in the +lock of voltera in the situation where + + align:start position:0% +lock of voltera in the situation where + + + align:start position:0% +lock of voltera in the situation where +you had uh there was there in one of the + + align:start position:0% +you had uh there was there in one of the + + + align:start position:0% +you had uh there was there in one of the +crossings you have + + align:start position:0% +crossings you have + + + align:start position:0% +crossings you have +a it's now going to be a stable fix + + align:start position:0% +a it's now going to be a stable fix + + + align:start position:0% +a it's now going to be a stable fix +point in that situation you can prove + + align:start position:0% +point in that situation you can prove + + + align:start position:0% +point in that situation you can prove +mathematically that you can never get a + + align:start position:0% +mathematically that you can never get a + + + align:start position:0% +mathematically that you can never get a +limit cycle oscillation because of some + + align:start position:0% +limit cycle oscillation because of some + + + align:start position:0% +limit cycle oscillation because of some +Divergence condition of some function + + align:start position:0% +Divergence condition of some function + + + align:start position:0% +Divergence condition of some function +and so forth but + + align:start position:0% +and so forth but + + + align:start position:0% +and so forth but +um but it you know in the example that I + + align:start position:0% +um but it you know in the example that I + + + align:start position:0% +um but it you know in the example that I +was telling you about in The Predator + + align:start position:0% +was telling you about in The Predator + + + align:start position:0% +was telling you about in The Predator +pre was also the it was true you know it + + align:start position:0% +pre was also the it was true you know it + + + align:start position:0% +pre was also the it was true you know it +was true in that particular case that + + align:start position:0% +was true in that particular case that + + + align:start position:0% +was true in that particular case that +when that thing is stable you don't get + + align:start position:0% +when that thing is stable you don't get + + + align:start position:0% +when that thing is stable you don't get +oscillations and when unstable do but it + + align:start position:0% +oscillations and when unstable do but it + + + align:start position:0% +oscillations and when unstable do but it +doesn't both directions do not follow + + align:start position:0% +doesn't both directions do not follow + + + align:start position:0% +doesn't both directions do not follow +from the P CR + + align:start position:0% +from the P CR + + + align:start position:0% +from the P CR +index okay um okay so this is this is a + + align:start position:0% +index okay um okay so this is this is a + + + align:start position:0% +index okay um okay so this is this is a +limit cycle all right now it's just that + + align:start position:0% +limit cycle all right now it's just that + + + align:start position:0% +limit cycle all right now it's just that +AA in a chaotic situation you have to be + + align:start position:0% +AA in a chaotic situation you have to be + + + align:start position:0% +AA in a chaotic situation you have to be +able to do something where you kind of + + align:start position:0% +able to do something where you kind of + + + align:start position:0% +able to do something where you kind of +come around and then you know every now + + align:start position:0% +come around and then you know every now + + + align:start position:0% +come around and then you know every now +and then you kind of go over here and + + align:start position:0% +and then you kind of go over here and + + + align:start position:0% +and then you kind of go over here and +then you go around and around and then + + align:start position:0% +then you go around and around and then + + + align:start position:0% +then you go around and around and then +every now and then you come you know + + align:start position:0% +every now and then you come you know + + + align:start position:0% +every now and then you come you know +some something crazy happens but um you + + align:start position:0% +some something crazy happens but um you + + + align:start position:0% +some something crazy happens but um you +can see that this situation doesn't work + + align:start position:0% +can see that this situation doesn't work + + + align:start position:0% +can see that this situation doesn't work +if it's only 2D + + align:start position:0% +if it's only 2D + + + align:start position:0% +if it's only 2D +right do do do you see why I'm saying + + align:start position:0% +right do do do you see why I'm saying + + + align:start position:0% +right do do do you see why I'm saying +that yeah no you don't that you don't + + align:start position:0% +that yeah no you don't that you don't + + + align:start position:0% +that yeah no you don't that you don't +you don't agree no it's just if it's 2D + + align:start position:0% +you don't agree no it's just if it's 2D + + + align:start position:0% +you don't agree no it's just if it's 2D +then these lines cannot cross so you + + align:start position:0% +then these lines cannot cross so you + + + align:start position:0% +then these lines cannot cross so you +need to have a third dimension so that + + align:start position:0% +need to have a third dimension so that + + + align:start position:0% +need to have a third dimension so that +they they can just shoot above each go + + align:start position:0% +they they can just shoot above each go + + + align:start position:0% +they they can just shoot above each go +above and below each other and what's + + align:start position:0% +above and below each other and what's + + + align:start position:0% +above and below each other and what's +the defition because you can come up + + align:start position:0% +the defition because you can come up + + + align:start position:0% +the defition because you can come up +with like trajectory like you can have + + align:start position:0% +with like trajectory like you can have + + + align:start position:0% +with like trajectory like you can have +trajectories that asically approach a + + align:start position:0% +trajectories that asically approach a + + + align:start position:0% +trajectories that asically approach a +limit cycle but that never cross + + align:start position:0% +limit cycle but that never cross + + + align:start position:0% +limit cycle but that never cross +themselves right and so I guess yeah no + + align:start position:0% +themselves right and so I guess yeah no + + + align:start position:0% +themselves right and so I guess yeah no +those are obviously not chaotic but the + + align:start position:0% +those are obviously not chaotic but the + + + align:start position:0% +those are obviously not chaotic but the +why right because okay those things + + align:start position:0% +why right because okay those things + + + align:start position:0% +why right because okay those things +right so then okay so yeah so this is + + align:start position:0% +right so then okay so yeah so this is + + + align:start position:0% +right so then okay so yeah so this is +not actually class in nonlinear Dynamics + + align:start position:0% +not actually class in nonlinear Dynamics + + + align:start position:0% +not actually class in nonlinear Dynamics +so we're not yeah so normally you you + + align:start position:0% +so we're not yeah so normally you you + + + align:start position:0% +so we're not yeah so normally you you +characterize this laav exponent which + + align:start position:0% +characterize this laav exponent which + + + align:start position:0% +characterize this laav exponent which +tells you about how the phase space is + + align:start position:0% +tells you about how the phase space is + + + align:start position:0% +tells you about how the phase space is +kind of growing or shrinking in the case + + align:start position:0% +kind of growing or shrinking in the case + + + align:start position:0% +kind of growing or shrinking in the case +that you were just talking about that's + + align:start position:0% +that you were just talking about that's + + + align:start position:0% +that you were just talking about that's +a case where all the trajectory they + + align:start position:0% +a case where all the trajectory they + + + align:start position:0% +a case where all the trajectory they +come together right so if you because in + + align:start position:0% +come together right so if you because in + + + align:start position:0% +come together right so if you because in +this case where this trajectory comes + + align:start position:0% +this case where this trajectory comes + + + align:start position:0% +this case where this trajectory comes +into the limit cycle if you draw like a + + align:start position:0% +into the limit cycle if you draw like a + + + align:start position:0% +into the limit cycle if you draw like a +blob of of phas space it's going to come + + align:start position:0% +blob of of phas space it's going to come + + + align:start position:0% +blob of of phas space it's going to come +together over time right whereas in a in + + align:start position:0% +together over time right whereas in a in + + + align:start position:0% +together over time right whereas in a in +a chaotic system if you have like a blob + + align:start position:0% +a chaotic system if you have like a blob + + + align:start position:0% +a chaotic system if you have like a blob +of face space it's going to diverge and + + align:start position:0% +of face space it's going to diverge and + + + align:start position:0% +of face space it's going to diverge and +fold and do kind of the all the + + align:start position:0% +fold and do kind of the all the + + + align:start position:0% +fold and do kind of the all the +craziness yeah okay + + align:start position:0% + + + + align:start position:0% + +yes yeah right so I yes so this is for + + align:start position:0% +yes yeah right so I yes so this is for + + + align:start position:0% +yes yeah right so I yes so this is for +the in this logal vola all right because + + align:start position:0% +the in this logal vola all right because + + + align:start position:0% +the in this logal vola all right because +in general you can get a limit cycle + + align:start position:0% +in general you can get a limit cycle + + + align:start position:0% +in general you can get a limit cycle +with two equations and in right and + + align:start position:0% +with two equations and in right and + + + align:start position:0% +with two equations and in right and +that's with a 2d and in general you can + + align:start position:0% +that's with a 2d and in general you can + + + align:start position:0% +that's with a 2d and in general you can +get AA you can get chaos with three + + align:start position:0% +get AA you can get chaos with three + + + align:start position:0% +get AA you can get chaos with three +equations or three variables right but + + align:start position:0% +equations or three variables right but + + + align:start position:0% +equations or three variables right but +the logic in The Logical vol Tera model + + align:start position:0% +the logic in The Logical vol Tera model + + + align:start position:0% +the logic in The Logical vol Tera model +it requires three and four respectively + + align:start position:0% +it requires three and four respectively + + + align:start position:0% +it requires three and four respectively +that doesn't mean that + + align:start position:0% +that doesn't mean that + + + align:start position:0% +that doesn't mean that +every four species logical Tera will + + align:start position:0% +every four species logical Tera will + + + align:start position:0% +every four species logical Tera will +have chaos but it means that it's + + align:start position:0% +have chaos but it means that it's + + + align:start position:0% +have chaos but it means that it's +possible to get one right yeah and I + + align:start position:0% +possible to get one right yeah and I + + + align:start position:0% +possible to get one right yeah and I +think one thing that's just rather + + align:start position:0% +think one thing that's just rather + + + align:start position:0% +think one thing that's just rather +striking is that this really is kind of + + align:start position:0% +striking is that this really is kind of + + + align:start position:0% +striking is that this really is kind of +the simplest possible model you can ever + + align:start position:0% +the simplest possible model you can ever + + + align:start position:0% +the simplest possible model you can ever +write down describing how species or how + + align:start position:0% +write down describing how species or how + + + align:start position:0% +write down describing how species or how +species might interact or you know + + align:start position:0% +species might interact or you know + + + align:start position:0% +species might interact or you know +variables might interact or whatnot and + + align:start position:0% +variables might interact or whatnot and + + + align:start position:0% +variables might interact or whatnot and +so it's really kind of incredible to me + + align:start position:0% +so it's really kind of incredible to me + + + align:start position:0% +so it's really kind of incredible to me +that you can get all all these crazy + + align:start position:0% +that you can get all all these crazy + + + align:start position:0% +that you can get all all these crazy +Dynamics + + align:start position:0% +Dynamics + + + align:start position:0% +Dynamics +um + + align:start position:0% + + + + align:start position:0% + +yes oh yeah so I think that this is um + + align:start position:0% +yes oh yeah so I think that this is um + + + align:start position:0% +yes oh yeah so I think that this is um +you know the the I think that the the + + align:start position:0% +you know the the I think that the the + + + align:start position:0% +you know the the I think that the the +transients or whatever can occur it + + align:start position:0% +transients or whatever can occur it + + + align:start position:0% +transients or whatever can occur it +requires the full end Dimensions to + + align:start position:0% +requires the full end Dimensions to + + + align:start position:0% +requires the full end Dimensions to +describe right because you can you + + align:start position:0% +describe right because you can you + + + align:start position:0% +describe right because you can you +because you can start any I mean to + + align:start position:0% +because you can start any I mean to + + + align:start position:0% +because you can start any I mean to +describe all of the trajectories clearly + + align:start position:0% +describe all of the trajectories clearly + + + align:start position:0% +describe all of the trajectories clearly +requires all Dimensions right because + + align:start position:0% +requires all Dimensions right because + + + align:start position:0% +requires all Dimensions right because +you know anywhere you start is you have + + align:start position:0% +you know anywhere you start is you have + + + align:start position:0% +you know anywhere you start is you have +to you have to specify it by five + + align:start position:0% +to you have to specify it by five + + + align:start position:0% +to you have to specify it by five +Dimensions right but um but the Dynamics + + align:start position:0% +Dimensions right but um but the Dynamics + + + align:start position:0% +Dimensions right but um but the Dynamics +as far as like um well and here there + + align:start position:0% +as far as like um well and here there + + + align:start position:0% +as far as like um well and here there +aren't even any Dynamics you know I + + align:start position:0% +aren't even any Dynamics you know I + + + align:start position:0% +aren't even any Dynamics you know I +think that you go to a point right so I + + align:start position:0% +think that you go to a point right so I + + + align:start position:0% +think that you go to a point right so I +think + + align:start position:0% +think + + + align:start position:0% +think +that's um what do you mean + + align:start position:0% +that's um what do you mean + + + align:start position:0% +that's um what do you mean +bynam yeah yeah no I agree that I that + + align:start position:0% +bynam yeah yeah no I agree that I that + + + align:start position:0% +bynam yeah yeah no I agree that I that +there's + + align:start position:0% +there's + + + align:start position:0% +there's +a um so in the case of the limit cycles + + align:start position:0% +a um so in the case of the limit cycles + + + align:start position:0% +a um so in the case of the limit cycles +and so farth this is really + + align:start position:0% +and so farth this is really + + + align:start position:0% +and so farth this is really +like at steady state it's doing + + align:start position:0% +like at steady state it's doing + + + align:start position:0% +like at steady state it's doing +something right so here I think steady + + align:start position:0% +something right so here I think steady + + + align:start position:0% +something right so here I think steady +state it only goes to the fixed points + + align:start position:0% +state it only goes to the fixed points + + + align:start position:0% +state it only goes to the fixed points +right so there's no yeah but in two but + + align:start position:0% +right so there's no yeah but in two but + + + align:start position:0% +right so there's no yeah but in two but +if you have a threedimensional system + + align:start position:0% +if you have a threedimensional system + + + align:start position:0% +if you have a threedimensional system +then you you can have it steady + + align:start position:0% +then you you can have it steady + + + align:start position:0% +then you you can have it steady +state uh the trajectories on a on like a + + align:start position:0% +state uh the trajectories on a on like a + + + align:start position:0% +state uh the trajectories on a on like a +plane you know uh and then + + align:start position:0% +plane you know uh and then + + + align:start position:0% +plane you know uh and then +yeah + + align:start position:0% + + + + align:start position:0% + +yeah uh I I don't think that + + align:start position:0% +yeah uh I I don't think that + + + align:start position:0% +yeah uh I I don't think that +that so I'm I'm not I'm not aware of + + align:start position:0% +that so I'm I'm not I'm not aware of + + + align:start position:0% +that so I'm I'm not I'm not aware of +that being the case + + align:start position:0% +that being the case + + + align:start position:0% +that being the case +but I'm hesitant to say that it's not + + align:start position:0% + + + + align:start position:0% + +true all right uh what I uh I want to + + align:start position:0% +true all right uh what I uh I want to + + + align:start position:0% +true all right uh what I uh I want to +switch gears a little bit and think + + align:start position:0% +switch gears a little bit and think + + + align:start position:0% +switch gears a little bit and think +about three species interactions and in + + align:start position:0% +about three species interactions and in + + + align:start position:0% +about three species interactions and in +particular the three species + + align:start position:0% +particular the three species + + + align:start position:0% +particular the three species +interactions when you have when they're + + align:start position:0% +interactions when you have when they're + + + align:start position:0% +interactions when you have when they're +non-transitive because this is thought + + align:start position:0% +non-transitive because this is thought + + + align:start position:0% +non-transitive because this is thought +to be potentially a significant uh + + align:start position:0% +to be potentially a significant uh + + + align:start position:0% +to be potentially a significant uh +stabilizer for uh for diversity in + + align:start position:0% + + + + align:start position:0% + +populations + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +all right so this is + + align:start position:0% + + + + align:start position:0% + +non-transitive interactions and and we + + align:start position:0% +non-transitive interactions and and we + + + align:start position:0% +non-transitive interactions and and we +we often just say rock paper + + align:start position:0% +we often just say rock paper + + + align:start position:0% +we often just say rock paper +scissors + + align:start position:0% + + + + align:start position:0% + +um all right has is is everybody from a + + align:start position:0% +um all right has is is everybody from a + + + align:start position:0% +um all right has is is everybody from a +culture that plays rock paper + + align:start position:0% + + + + align:start position:0% + +scissors yes all right so this is this + + align:start position:0% +scissors yes all right so this is this + + + align:start position:0% +scissors yes all right so this is this +is a true human Universal um although I + + align:start position:0% +is a true human Universal um although I + + + align:start position:0% +is a true human Universal um although I +think that what we call it does vary and + + align:start position:0% +think that what we call it does vary and + + + align:start position:0% +think that what we call it does vary and +so forth you know how you know how + + align:start position:0% +so forth you know how you know how + + + align:start position:0% +so forth you know how you know how +sometimes the linguists try to find this + + align:start position:0% +sometimes the linguists try to find this + + + align:start position:0% +sometimes the linguists try to find this +uru language that you know our ancestors + + align:start position:0% +uru language that you know our ancestors + + + align:start position:0% +uru language that you know our ancestors +spoke 50,000 years ago or whatever I + + align:start position:0% +spoke 50,000 years ago or whatever I + + + align:start position:0% +spoke 50,000 years ago or whatever I +think that you could probably do + + align:start position:0% +think that you could probably do + + + align:start position:0% +think that you could probably do +something similar with Rock Paper + + align:start position:0% +something similar with Rock Paper + + + align:start position:0% +something similar with Rock Paper +Scissors because it's seems to be a + + align:start position:0% +Scissors because it's seems to be a + + + align:start position:0% +Scissors because it's seems to be a +pretty common common theme um right so + + align:start position:0% +pretty common common theme um right so + + + align:start position:0% +pretty common common theme um right so +the the idea here is that you have wa + + align:start position:0% +the the idea here is that you have wa + + + align:start position:0% +the the idea here is that you have wa +which direction does it go all right + + align:start position:0% +which direction does it go all right + + + align:start position:0% +which direction does it go all right +paper beats Ro okay right so paper beats + + align:start position:0% +paper beats Ro okay right so paper beats + + + align:start position:0% +paper beats Ro okay right so paper beats +rock scissors beats paper but rock beats + + align:start position:0% +rock scissors beats paper but rock beats + + + align:start position:0% +rock scissors beats paper but rock beats +scissors yep + + align:start position:0% +scissors yep + + + align:start position:0% +scissors yep +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um right so so you can imagine that this + + align:start position:0% +um right so so you can imagine that this + + + align:start position:0% +um right so so you can imagine that this +this can be this kind of dynamic can be + + align:start position:0% +this can be this kind of dynamic can be + + + align:start position:0% +this can be this kind of dynamic can be +captured in the Locka volter type + + align:start position:0% +captured in the Locka volter type + + + align:start position:0% +captured in the Locka volter type +framework right so you just have to set + + align:start position:0% +framework right so you just have to set + + + align:start position:0% +framework right so you just have to set +up these betas or Alphas so that this + + align:start position:0% +up these betas or Alphas so that this + + + align:start position:0% +up these betas or Alphas so that this +this is true right and again dominance + + align:start position:0% +this is true right and again dominance + + + align:start position:0% +this is true right and again dominance +you know the this way to think about + + align:start position:0% +you know the this way to think about + + + align:start position:0% +you know the this way to think about +this would be simplest thing is think + + align:start position:0% +this would be simplest thing is think + + + align:start position:0% +this would be simplest thing is think +about is dominance right so that if you + + align:start position:0% +about is dominance right so that if you + + + align:start position:0% +about is dominance right so that if you +have the rock species and the scissor + + align:start position:0% +have the rock species and the scissor + + + align:start position:0% +have the rock species and the scissor +species together then the rock species + + align:start position:0% +species together then the rock species + + + align:start position:0% +species together then the rock species +will uh Drive the scissors species + + align:start position:0% +will uh Drive the scissors species + + + align:start position:0% +will uh Drive the scissors species +extinct right and so forth right now + + align:start position:0% +extinct right and so forth right now + + + align:start position:0% +extinct right and so forth right now +this is the kind of situation that in + + align:start position:0% +this is the kind of situation that in + + + align:start position:0% +this is the kind of situation that in +principle can lead to very complicated + + align:start position:0% +principle can lead to very complicated + + + align:start position:0% +principle can lead to very complicated +Dynamics and multispecies ecosystems + + align:start position:0% +Dynamics and multispecies ecosystems + + + align:start position:0% +Dynamics and multispecies ecosystems +that at least in many models can + + align:start position:0% +that at least in many models can + + + align:start position:0% +that at least in many models can +stabilize the uh the coexistence of of + + align:start position:0% +stabilize the uh the coexistence of of + + + align:start position:0% +stabilize the uh the coexistence of of +kind of multiple species via some of + + align:start position:0% +kind of multiple species via some of + + + align:start position:0% +kind of multiple species via some of +these complex crazy dynamics that um + + align:start position:0% +these complex crazy dynamics that um + + + align:start position:0% +these complex crazy dynamics that um +that we were just talking about I would + + align:start position:0% +that we were just talking about I would + + + align:start position:0% +that we were just talking about I would +say that as a mechanism for the + + align:start position:0% +say that as a mechanism for the + + + align:start position:0% +say that as a mechanism for the +stabilization of diversity I I don't + + align:start position:0% +stabilization of diversity I I don't + + + align:start position:0% +stabilization of diversity I I don't +know how convincing that that is in + + align:start position:0% +know how convincing that that is in + + + align:start position:0% +know how convincing that that is in +terms of being what explained why it is + + align:start position:0% +terms of being what explained why it is + + + align:start position:0% +terms of being what explained why it is +with there's so much diversity out + + align:start position:0% +with there's so much diversity out + + + align:start position:0% +with there's so much diversity out +outside when you know when you look + + align:start position:0% +outside when you know when you look + + + align:start position:0% +outside when you know when you look +outside the window but but at least it's + + align:start position:0% +outside the window but but at least it's + + + align:start position:0% +outside the window but but at least it's +it's it's in principle true and and one + + align:start position:0% +it's it's in principle true and and one + + + align:start position:0% +it's it's in principle true and and one +of the um one of the topics of these + + align:start position:0% +of the um one of the topics of these + + + align:start position:0% +of the um one of the topics of these +papers that um that well at least + + align:start position:0% +papers that um that well at least + + + align:start position:0% +papers that um that well at least +certainly the one that you just read is + + align:start position:0% +certainly the one that you just read is + + + align:start position:0% +certainly the one that you just read is +that rock paper scissors I.E + + align:start position:0% +that rock paper scissors I.E + + + align:start position:0% +that rock paper scissors I.E +non-transient interactions on their own + + align:start position:0% +non-transient interactions on their own + + + align:start position:0% +non-transient interactions on their own +uh may not be sufficient but in the + + align:start position:0% +uh may not be sufficient but in the + + + align:start position:0% +uh may not be sufficient but in the +presence of spatial structure maybe it + + align:start position:0% +presence of spatial structure maybe it + + + align:start position:0% +presence of spatial structure maybe it +does allow for uh long-term coexistence + + align:start position:0% +does allow for uh long-term coexistence + + + align:start position:0% +does allow for uh long-term coexistence +of these these species or or strategies + + align:start position:0% +of these these species or or strategies + + + align:start position:0% +of these these species or or strategies +and so forth and again it's not always + + align:start position:0% +and so forth and again it's not always + + + align:start position:0% +and so forth and again it's not always +clear in these situations ation whether + + align:start position:0% +clear in these situations ation whether + + + align:start position:0% +clear in these situations ation whether +you're thinking about ecology where + + align:start position:0% +you're thinking about ecology where + + + align:start position:0% +you're thinking about ecology where +these are different species or you're + + align:start position:0% +these are different species or you're + + + align:start position:0% +these are different species or you're +thinking about Evolution where these are + + align:start position:0% +thinking about Evolution where these are + + + align:start position:0% +thinking about Evolution where these are +different genotypes and indeed in the + + align:start position:0% +different genotypes and indeed in the + + + align:start position:0% +different genotypes and indeed in the +curve paper that you read these are all + + align:start position:0% +curve paper that you read these are all + + + align:start position:0% +curve paper that you read these are all +you know Eola you know so it's all one + + align:start position:0% +you know Eola you know so it's all one + + + align:start position:0% +you know Eola you know so it's all one +species it's just they have different uh + + align:start position:0% +species it's just they have different uh + + + align:start position:0% +species it's just they have different uh +different mutations so that was that's + + align:start position:0% +different mutations so that was that's + + + align:start position:0% +different mutations so that was that's +really uh rock paper scissors in the + + align:start position:0% +really uh rock paper scissors in the + + + align:start position:0% +really uh rock paper scissors in the +context of + + align:start position:0% +context of + + + align:start position:0% +context of +evolution right whereas in the the male + + align:start position:0% +evolution right whereas in the the male + + + align:start position:0% +evolution right whereas in the the male +mating strategies paper by by Kurt + + align:start position:0% +mating strategies paper by by Kurt + + + align:start position:0% +mating strategies paper by by Kurt +Lively uh so that's that's more of an + + align:start position:0% +Lively uh so that's that's more of an + + + align:start position:0% +Lively uh so that's that's more of an +ecological context but it still is + + align:start position:0% +ecological context but it still is + + + align:start position:0% +ecological context but it still is +evolution within the species right + + align:start position:0% +evolution within the species right + + + align:start position:0% +evolution within the species right +because uh because it is the these + + align:start position:0% +because uh because it is the these + + + align:start position:0% +because uh because it is the these +mating strategies are heritable okay so + + align:start position:0% +mating strategies are heritable okay so + + + align:start position:0% +mating strategies are heritable okay so +I I'll explain the + + align:start position:0% + + + + align:start position:0% + +um I I did tell you the base idea of + + align:start position:0% +um I I did tell you the base idea of + + + align:start position:0% +um I I did tell you the base idea of +this lizard mating strategy business or + + align:start position:0% +this lizard mating strategy business or + + + align:start position:0% +this lizard mating strategy business or +did I never say anything about that oh + + align:start position:0% +did I never say anything about that oh + + + align:start position:0% +did I never say anything about that oh +really okay uh for some reason I thought + + align:start position:0% +really okay uh for some reason I thought + + + align:start position:0% +really okay uh for some reason I thought +that I alluded to it okay well let me uh + + align:start position:0% +that I alluded to it okay well let me uh + + + align:start position:0% +that I alluded to it okay well let me uh +let me explain it to you it's uh I think + + align:start position:0% +let me explain it to you it's uh I think + + + align:start position:0% +let me explain it to you it's uh I think +it's kind of an incredible paper uh + + align:start position:0% +it's kind of an incredible paper uh + + + align:start position:0% +it's kind of an incredible paper uh +right so uh so this is a paper by by CT + + align:start position:0% +right so uh so this is a paper by by CT + + + align:start position:0% +right so uh so this is a paper by by CT +Lively so it's Cura curvo and + + align:start position:0% + + + + align:start position:0% + +Lively uh it was nature + + align:start position:0% + + + + align:start position:0% + +96 okay yeah it's it's called Uh the + + align:start position:0% +96 okay yeah it's it's called Uh the + + + align:start position:0% +96 okay yeah it's it's called Uh the +rock paper scissors game and the + + align:start position:0% +rock paper scissors game and the + + + align:start position:0% +rock paper scissors game and the +evolution of alternative male strategy + + align:start position:0% +evolution of alternative male strategy + + + align:start position:0% +evolution of alternative male strategy +so what uh what what was known is that + + align:start position:0% +so what uh what what was known is that + + + align:start position:0% +so what uh what what was known is that +there are many examples of um of + + align:start position:0% +there are many examples of um of + + + align:start position:0% +there are many examples of um of +alternative uh mating strategies in + + align:start position:0% +alternative uh mating strategies in + + + align:start position:0% +alternative uh mating strategies in +males in particular it's common that + + align:start position:0% +males in particular it's common that + + + align:start position:0% +males in particular it's common that +there are what you might call uh + + align:start position:0% +there are what you might call uh + + + align:start position:0% +there are what you might call uh +territorial + + align:start position:0% + + + + align:start position:0% + +males and and what what they often call + + align:start position:0% +males and and what what they often call + + + align:start position:0% +males and and what what they often call +sneaker + + align:start position:0% + + + + align:start position:0% + +males this is observed in in fish and + + align:start position:0% +males this is observed in in fish and + + + align:start position:0% +males this is observed in in fish and +various land animals and in many of the + + align:start position:0% +various land animals and in many of the + + + align:start position:0% +various land animals and in many of the +cases these sneaker males uh really do + + align:start position:0% +cases these sneaker males uh really do + + + align:start position:0% +cases these sneaker males uh really do +look phenotypically um like females okay + + align:start position:0% +look phenotypically um like females okay + + + align:start position:0% +look phenotypically um like females okay +uh + + align:start position:0% + + + + align:start position:0% + +and the idea that and this has been + + align:start position:0% +and the idea that and this has been + + + align:start position:0% +and the idea that and this has been +measured you know using various kinds of + + align:start position:0% +measured you know using various kinds of + + + align:start position:0% +measured you know using various kinds of +observational experimental approaches is + + align:start position:0% +observational experimental approaches is + + + align:start position:0% +observational experimental approaches is +that there's often what you call + + align:start position:0% +that there's often what you call + + + align:start position:0% +that there's often what you call +negative frequency dependent selection + + align:start position:0% +negative frequency dependent selection + + + align:start position:0% +negative frequency dependent selection +um between these these strategies in the + + align:start position:0% +um between these these strategies in the + + + align:start position:0% +um between these these strategies in the +sense that if um if there that the + + align:start position:0% +sense that if um if there that the + + + align:start position:0% +sense that if um if there that the +sneakers can often when rare can can + + align:start position:0% +sneakers can often when rare can can + + + align:start position:0% +sneakers can often when rare can can +spread in population of the Territorial + + align:start position:0% +spread in population of the Territorial + + + align:start position:0% +spread in population of the Territorial +and vice versa um but this was a at + + align:start position:0% +and vice versa um but this was a at + + + align:start position:0% +and vice versa um but this was a at +least the first case I'm aware of where + + align:start position:0% +least the first case I'm aware of where + + + align:start position:0% +least the first case I'm aware of where +um kind of these ideas had been + + align:start position:0% +um kind of these ideas had been + + + align:start position:0% +um kind of these ideas had been +demonstrated in as that there were + + align:start position:0% +demonstrated in as that there were + + + align:start position:0% +demonstrated in as that there were +really three strategies and the three + + align:start position:0% +really three strategies and the three + + + align:start position:0% +really three strategies and the three +strategies implemented one of these rock + + align:start position:0% +strategies implemented one of these rock + + + align:start position:0% +strategies implemented one of these rock +paper scissors interactions and um I + + align:start position:0% +paper scissors interactions and um I + + + align:start position:0% +paper scissors interactions and um I +want to uh maybe make a little more + + align:start position:0% +want to uh maybe make a little more + + + align:start position:0% +want to uh maybe make a little more +space uh if if you guys are available + + align:start position:0% +space uh if if you guys are available + + + align:start position:0% +space uh if if you guys are available +after class I encourage you to come up + + align:start position:0% +after class I encourage you to come up + + + align:start position:0% +after class I encourage you to come up +and look at the um look at the paper + + align:start position:0% +and look at the um look at the paper + + + align:start position:0% +and look at the um look at the paper +because they actually have pictures of + + align:start position:0% +because they actually have pictures of + + + align:start position:0% +because they actually have pictures of +them so you can identify the sneaker + + align:start position:0% +them so you can identify the sneaker + + + align:start position:0% +them so you can identify the sneaker +males um and and and because they + + align:start position:0% +males um and and and because they + + + align:start position:0% +males um and and and because they +because they actually look different on + + align:start position:0% +because they actually look different on + + + align:start position:0% +because they actually look different on +uh based on the coloring of their kind + + align:start position:0% +uh based on the coloring of their kind + + + align:start position:0% +uh based on the coloring of their kind +of throat okay so these are um right so + + align:start position:0% +of throat okay so these are um right so + + + align:start position:0% +of throat okay so these are um right so +these are lizards that live in the + + align:start position:0% +these are lizards that live in the + + + align:start position:0% +these are lizards that live in the +mountains up um outside of the Bay Area + + align:start position:0% +mountains up um outside of the Bay Area + + + align:start position:0% +mountains up um outside of the Bay Area +in California and Mer mered County + + align:start position:0% +in California and Mer mered County + + + align:start position:0% +in California and Mer mered County +they're they're side blotched lizards I + + align:start position:0% +they're they're side blotched lizards I + + + align:start position:0% +they're they're side blotched lizards I +don't know anything about that uh right + + align:start position:0% +don't know anything about that uh right + + + align:start position:0% +don't know anything about that uh right +and what what they showed was that + + align:start position:0% +and what what they showed was that + + + align:start position:0% +and what what they showed was that +there's um there these these guys with + + align:start position:0% +there's um there these these guys with + + + align:start position:0% +there's um there these these guys with +orange + + align:start position:0% + + + + align:start position:0% + +throats that are um kind of aggressive + + align:start position:0% +throats that are um kind of aggressive + + + align:start position:0% +throats that are um kind of aggressive +ter and they they they defend a very + + align:start position:0% +ter and they they they defend a very + + + align:start position:0% +ter and they they they defend a very +large territory uh with a large number + + align:start position:0% +large territory uh with a large number + + + align:start position:0% +large territory uh with a large number +of of females and they they fight off + + align:start position:0% +of of females and they they fight off + + + align:start position:0% +of of females and they they fight off +any males that that come then there are + + align:start position:0% +any males that that come then there are + + + align:start position:0% +any males that that come then there are +um the dark + + align:start position:0% + + + + align:start position:0% + +blue oh sorry I should have put that + + align:start position:0% +blue oh sorry I should have put that + + + align:start position:0% +blue oh sorry I should have put that +over here so there there are other + + align:start position:0% +over here so there there are other + + + align:start position:0% +over here so there there are other +lizards here that are that are dark + + align:start position:0% +lizards here that are that are dark + + + align:start position:0% +lizards here that are that are dark +blue um throats and these guys are um + + align:start position:0% +blue um throats and these guys are um + + + align:start position:0% +blue um throats and these guys are um +less aggressive with smaller territories + + align:start position:0% + + + + align:start position:0% + +all right so you can guess uh if it were + + align:start position:0% +all right so you can guess uh if it were + + + align:start position:0% +all right so you can guess uh if it were +just the orange throated guys in the + + align:start position:0% +just the orange throated guys in the + + + align:start position:0% +just the orange throated guys in the +dark and these are these are genetically + + align:start position:0% +dark and these are these are genetically + + + align:start position:0% +dark and these are these are genetically +encoded strategies in the sense that + + align:start position:0% +encoded strategies in the sense that + + + align:start position:0% +encoded strategies in the sense that +they do seem to be passed on and it's + + align:start position:0% +they do seem to be passed on and it's + + + align:start position:0% +they do seem to be passed on and it's +it's determined by the um the genes that + + align:start position:0% +it's determined by the um the genes that + + + align:start position:0% +it's determined by the um the genes that +this that the male inherits less + + align:start position:0% +this that the male inherits less + + + align:start position:0% +this that the male inherits less +aggressive and small uh territory all + + align:start position:0% +aggressive and small uh territory all + + + align:start position:0% +aggressive and small uh territory all +right can you imag can you guess which + + align:start position:0% +right can you imag can you guess which + + + align:start position:0% +right can you imag can you guess which +one wins between these two against each + + align:start position:0% + + + + align:start position:0% + +other what's that the two aggressive + + align:start position:0% +other what's that the two aggressive + + + align:start position:0% +other what's that the two aggressive +yeah but if you just have the two + + align:start position:0% +yeah but if you just have the two + + + align:start position:0% +yeah but if you just have the two +aggressive ones right then it's the this + + align:start position:0% +aggressive ones right then it's the this + + + align:start position:0% +aggressive ones right then it's the this +guy is going to beat this one right okay + + align:start position:0% +guy is going to beat this one right okay + + + align:start position:0% +guy is going to beat this one right okay +um that's just because the this + + align:start position:0% +um that's just because the this + + + align:start position:0% +um that's just because the this +aggressive male has a larger territory + + align:start position:0% +aggressive male has a larger territory + + + align:start position:0% +aggressive male has a larger territory +and you know passes on it they pass on + + align:start position:0% +and you know passes on it they pass on + + + align:start position:0% +and you know passes on it they pass on +more genes than the less aggressive ones + + align:start position:0% +more genes than the less aggressive ones + + + align:start position:0% +more genes than the less aggressive ones +okay um however what they found is that + + align:start position:0% +okay um however what they found is that + + + align:start position:0% +okay um however what they found is that +there's a third mating strategy here + + align:start position:0% +there's a third mating strategy here + + + align:start position:0% +there's a third mating strategy here +which are these um these sneaker males + + align:start position:0% +which are these um these sneaker males + + + align:start position:0% +which are these um these sneaker males +and they + + align:start position:0% +and they + + + align:start position:0% +and they +um they they indeed look like the + + align:start position:0% +um they they indeed look like the + + + align:start position:0% +um they they indeed look like the +females they have these yellow + + align:start position:0% +females they have these yellow + + + align:start position:0% +females they have these yellow +stripes on their + + align:start position:0% +stripes on their + + + align:start position:0% +stripes on their +throats they look like the female and + + align:start position:0% +throats they look like the female and + + + align:start position:0% +throats they look like the female and +they have no territory okay sneaker + + align:start position:0% +they have no territory okay sneaker + + + align:start position:0% +they have no territory okay sneaker +males um so they don't they don't defend + + align:start position:0% +males um so they don't they don't defend + + + align:start position:0% +males um so they don't they don't defend +any territory instead they just sneak + + align:start position:0% +any territory instead they just sneak + + + align:start position:0% +any territory instead they just sneak +onto the sneak into the the territory of + + align:start position:0% +onto the sneak into the the territory of + + + align:start position:0% +onto the sneak into the the territory of +these of the other males and try to try + + align:start position:0% +these of the other males and try to try + + + align:start position:0% +these of the other males and try to try +to mate with the females in that + + align:start position:0% +to mate with the females in that + + + align:start position:0% +to mate with the females in that +territory right and what what they show + + align:start position:0% +territory right and what what they show + + + align:start position:0% +territory right and what what they show +is that over the course of like seven + + align:start position:0% +is that over the course of like seven + + + align:start position:0% +is that over the course of like seven +years uh in this in the mountains of + + align:start position:0% +years uh in this in the mountains of + + + align:start position:0% +years uh in this in the mountains of +Merced they they see that the frequency + + align:start position:0% +Merced they they see that the frequency + + + align:start position:0% +Merced they they see that the frequency +of these things goes through an entire + + align:start position:0% +of these things goes through an entire + + + align:start position:0% +of these things goes through an entire +oscillation okay so they kind of they + + align:start position:0% +oscillation okay so they kind of they + + + align:start position:0% +oscillation okay so they kind of they +see just over one period of of this + + align:start position:0% +see just over one period of of this + + + align:start position:0% +see just over one period of of this +oscillation uh and and their argument is + + align:start position:0% +oscillation uh and and their argument is + + + align:start position:0% +oscillation uh and and their argument is +that although it's true that the + + align:start position:0% +that although it's true that the + + + align:start position:0% +that although it's true that the +aggressive males can out compete the + + align:start position:0% +aggressive males can out compete the + + + align:start position:0% +aggressive males can out compete the +less aggressive ones the sneakers + + align:start position:0% +less aggressive ones the sneakers + + + align:start position:0% +less aggressive ones the sneakers +actually out compete the these these + + align:start position:0% +actually out compete the these these + + + align:start position:0% +actually out compete the these these +aggressive ones basically + + align:start position:0% +aggressive ones basically + + + align:start position:0% +aggressive ones basically +because the these aggressive males uh + + align:start position:0% +because the these aggressive males uh + + + align:start position:0% +because the these aggressive males uh +it's just too large of a territory for + + align:start position:0% +it's just too large of a territory for + + + align:start position:0% +it's just too large of a territory for +them to effectively uh defend it okay so + + align:start position:0% +them to effectively uh defend it okay so + + + align:start position:0% +them to effectively uh defend it okay so +the sneakers can actually out compete uh + + align:start position:0% +the sneakers can actually out compete uh + + + align:start position:0% +the sneakers can actually out compete uh +the aggressive Mills yet the less + + align:start position:0% +the aggressive Mills yet the less + + + align:start position:0% +the aggressive Mills yet the less +aggressive ones can out compete the + + align:start position:0% +aggressive ones can out compete the + + + align:start position:0% +aggressive ones can out compete the +sneakers because they uh are trying to + + align:start position:0% +sneakers because they uh are trying to + + + align:start position:0% +sneakers because they uh are trying to +defend a smaller territory right so they + + align:start position:0% +defend a smaller territory right so they + + + align:start position:0% +defend a smaller territory right so they +they they went and they basically + + align:start position:0% +they they went and they basically + + + align:start position:0% +they they went and they basically +measured the uh frequency of these + + align:start position:0% +measured the uh frequency of these + + + align:start position:0% +measured the uh frequency of these +strategies and also the number of + + align:start position:0% +strategies and also the number of + + + align:start position:0% +strategies and also the number of +females in the different uh territories + + align:start position:0% +females in the different uh territories + + + align:start position:0% +females in the different uh territories +uh over over the time of the from 1990 + + align:start position:0% +uh over over the time of the from 1990 + + + align:start position:0% +uh over over the time of the from 1990 +to 96 or so and uh and saw that this + + align:start position:0% +to 96 or so and uh and saw that this + + + align:start position:0% +to 96 or so and uh and saw that this +thing kind of went around in some circle + + align:start position:0% +thing kind of went around in some circle + + + align:start position:0% +thing kind of went around in some circle +in this frequency space of of + + align:start position:0% +in this frequency space of of + + + align:start position:0% +in this frequency space of of +alternative male strategies okay um + + align:start position:0% + + + + align:start position:0% + +yeah kind of incredible uh an incredible + + align:start position:0% +yeah kind of incredible uh an incredible + + + align:start position:0% +yeah kind of incredible uh an incredible +paper + + align:start position:0% +paper + + + align:start position:0% +paper +uh so the so the the idea here is this + + align:start position:0% +uh so the so the the idea here is this + + + align:start position:0% +uh so the so the the idea here is this +is this is a situation where it is + + align:start position:0% +is this is a situation where it is + + + align:start position:0% +is this is a situation where it is +non-transitive right so there's this + + align:start position:0% +non-transitive right so there's this + + + align:start position:0% +non-transitive right so there's this +rock paper scissors type Dynamic and it + + align:start position:0% +rock paper scissors type Dynamic and it + + + align:start position:0% +rock paper scissors type Dynamic and it +is also spatial right because these + + align:start position:0% +is also spatial right because these + + + align:start position:0% +is also spatial right because these +lizards + + align:start position:0% +lizards + + + align:start position:0% +lizards +are they're they're in some particular + + align:start position:0% +are they're they're in some particular + + + align:start position:0% +are they're they're in some particular +place they have some territory and so + + align:start position:0% +place they have some territory and so + + + align:start position:0% +place they have some territory and so +forth and in this other paper by + + align:start position:0% +forth and in this other paper by + + + align:start position:0% +forth and in this other paper by +Benjamin Kerr what he wanted to do is + + align:start position:0% +Benjamin Kerr what he wanted to do is + + + align:start position:0% +Benjamin Kerr what he wanted to do is +try to understand something about how + + align:start position:0% +try to understand something about how + + + align:start position:0% +try to understand something about how +the what the role of that spatial + + align:start position:0% +the what the role of that spatial + + + align:start position:0% +the what the role of that spatial +structure might be in maintaining the + + align:start position:0% +structure might be in maintaining the + + + align:start position:0% +structure might be in maintaining the +diversity right so in this case the + + align:start position:0% +diversity right so in this case the + + + align:start position:0% +diversity right so in this case the +argument was that the reason that th + + align:start position:0% +argument was that the reason that th + + + align:start position:0% +argument was that the reason that th +that you if you go out and you look at + + align:start position:0% +that you if you go out and you look at + + + align:start position:0% +that you if you go out and you look at +these lizards the reason that you see + + align:start position:0% +these lizards the reason that you see + + + align:start position:0% +these lizards the reason that you see +all three of these strategies is because + + align:start position:0% +all three of these strategies is because + + + align:start position:0% +all three of these strategies is because +of this rock paper scissors Dynamic + + align:start position:0% +of this rock paper scissors Dynamic + + + align:start position:0% +of this rock paper scissors Dynamic +right so the rare if if one of the + + align:start position:0% +right so the rare if if one of the + + + align:start position:0% +right so the rare if if one of the +strategies becomes more rare it's going + + align:start position:0% +strategies becomes more rare it's going + + + align:start position:0% +strategies becomes more rare it's going +to have an advantage Rel to the others + + align:start position:0% +to have an advantage Rel to the others + + + align:start position:0% +to have an advantage Rel to the others +it's going to spread right and what + + align:start position:0% +it's going to spread right and what + + + align:start position:0% +it's going to spread right and what +Benjamin Kerr wanted to explore is + + align:start position:0% +Benjamin Kerr wanted to explore is + + + align:start position:0% +Benjamin Kerr wanted to explore is +whether that statement could be made in + + align:start position:0% +whether that statement could be made in + + + align:start position:0% +whether that statement could be made in +a um whether whether somehow you can + + align:start position:0% +a um whether whether somehow you can + + + align:start position:0% +a um whether whether somehow you can +distinguish between uh whether the + + align:start position:0% +distinguish between uh whether the + + + align:start position:0% +distinguish between uh whether the +spatial component is is important or not + + align:start position:0% +spatial component is is important or not + + + align:start position:0% +spatial component is is important or not +of course it's hard to do that in the + + align:start position:0% +of course it's hard to do that in the + + + align:start position:0% +of course it's hard to do that in the +case of the lizards but but he was able + + align:start position:0% +case of the lizards but but he was able + + + align:start position:0% +case of the lizards but but he was able +to implement this in the case of um some + + align:start position:0% +to implement this in the case of um some + + + align:start position:0% +to implement this in the case of um some +chemical warfare behavior in in bacteria + + align:start position:0% +chemical warfare behavior in in bacteria + + + align:start position:0% +chemical warfare behavior in in bacteria +right so in this paper by + + align:start position:0% +right so in this paper by + + + align:start position:0% +right so in this paper by +Kerr um and I it's also a nature paper + + align:start position:0% +Kerr um and I it's also a nature paper + + + align:start position:0% +Kerr um and I it's also a nature paper +um from + + align:start position:0% +um from + + + align:start position:0% +um from + + align:start position:0% + + + + align:start position:0% + +um right so this paper is called a local + + align:start position:0% +um right so this paper is called a local + + + align:start position:0% +um right so this paper is called a local +dispersal promotes biodiversity in a + + align:start position:0% +dispersal promotes biodiversity in a + + + align:start position:0% +dispersal promotes biodiversity in a +real life game of rock paper scissors uh + + align:start position:0% +real life game of rock paper scissors uh + + + align:start position:0% +real life game of rock paper scissors uh +can somebody so you guys read it so what + + align:start position:0% +can somebody so you guys read it so what + + + align:start position:0% +can somebody so you guys read it so what +what were the three + + align:start position:0% + + + + align:start position:0% + +strategies that's right so + + align:start position:0% +strategies that's right so + + + align:start position:0% +strategies that's right so +C is the cisin + + align:start position:0% + + + + align:start position:0% + +producers incidentally just uh this + + align:start position:0% +producers incidentally just uh this + + + align:start position:0% +producers incidentally just uh this +cison production is kind of an + + align:start position:0% +cison production is kind of an + + + align:start position:0% +cison production is kind of an +incredible uh phenomenon already so this + + align:start position:0% +incredible uh phenomenon already so this + + + align:start position:0% +incredible uh phenomenon already so this +is these are uh proteins that are + + align:start position:0% +is these are uh proteins that are + + + align:start position:0% +is these are uh proteins that are +produced that um they bind to other + + align:start position:0% +produced that um they bind to other + + + align:start position:0% +produced that um they bind to other +bacteria and kind of often make pores in + + align:start position:0% +bacteria and kind of often make pores in + + + align:start position:0% +bacteria and kind of often make pores in +the membrane and kill them but the + + align:start position:0% +the membrane and kill them but the + + + align:start position:0% +the membrane and kill them but the +amazing thing about the cisin production + + align:start position:0% +amazing thing about the cisin production + + + align:start position:0% +amazing thing about the cisin production +is that uh in eoli and other uh gram + + align:start position:0% +is that uh in eoli and other uh gram + + + align:start position:0% +is that uh in eoli and other uh gram +negative bacteria the only way that + + align:start position:0% +negative bacteria the only way that + + + align:start position:0% +negative bacteria the only way that +these cisin are released is by cell + + align:start position:0% +these cisin are released is by cell + + + align:start position:0% +these cisin are released is by cell +Lis okay so it's not just that the cell + + align:start position:0% +Lis okay so it's not just that the cell + + + align:start position:0% +Lis okay so it's not just that the cell +is engaging in some costly behavior in + + align:start position:0% +is engaging in some costly behavior in + + + align:start position:0% +is engaging in some costly behavior in +order to make this protein that will + + align:start position:0% +order to make this protein that will + + + align:start position:0% +order to make this protein that will +kill out the cells but the only way that + + align:start position:0% +kill out the cells but the only way that + + + align:start position:0% +kill out the cells but the only way that +the toxin is released is by the cell + + align:start position:0% +the toxin is released is by the cell + + + align:start position:0% +the toxin is released is by the cell +actually bursting open okay so it's + + align:start position:0% +actually bursting open okay so it's + + + align:start position:0% +actually bursting open okay so it's +clear then that this has to be uh + + align:start position:0% +clear then that this has to be uh + + + align:start position:0% +clear then that this has to be uh +supported by some kind of um group level + + align:start position:0% +supported by some kind of um group level + + + align:start position:0% +supported by some kind of um group level +or kin selection kind of argument in the + + align:start position:0% +or kin selection kind of argument in the + + + align:start position:0% +or kin selection kind of argument in the +sense that it can NE this can never be + + align:start position:0% +sense that it can NE this can never be + + + align:start position:0% +sense that it can NE this can never be +good for the + + align:start position:0% +good for the + + + align:start position:0% +good for the +individual right because the individual + + align:start position:0% +individual right because the individual + + + align:start position:0% +individual right because the individual +has had to you know spill its guts in + + align:start position:0% +has had to you know spill its guts in + + + align:start position:0% +has had to you know spill its guts in +order to harm harm other cells right so + + align:start position:0% +order to harm harm other cells right so + + + align:start position:0% +order to harm harm other cells right so +the only way that this can be supported + + align:start position:0% +the only way that this can be supported + + + align:start position:0% +the only way that this can be supported +is by um by inhibiting the growth of + + align:start position:0% +is by um by inhibiting the growth of + + + align:start position:0% +is by um by inhibiting the growth of +competitors and allowing um your kind of + + align:start position:0% +competitors and allowing um your kind of + + + align:start position:0% +competitors and allowing um your kind of +kinm mates or other cells that also have + + align:start position:0% +kinm mates or other cells that also have + + + align:start position:0% +kinm mates or other cells that also have +this plasmid and therefore also the + + align:start position:0% +this plasmid and therefore also the + + + align:start position:0% +this plasmid and therefore also the +immunity protein uh allowing them to to + + align:start position:0% +immunity protein uh allowing them to to + + + align:start position:0% +immunity protein uh allowing them to to +grow better right so this is a a very + + align:start position:0% +grow better right so this is a a very + + + align:start position:0% +grow better right so this is a a very +neat example of uh it's an + + align:start position:0% +neat example of uh it's an + + + align:start position:0% +neat example of uh it's an +altruistic kind of warlike Behavior + + align:start position:0% +altruistic kind of warlike Behavior + + + align:start position:0% +altruistic kind of warlike Behavior +right right so this is this is one of + + align:start position:0% +right right so this is this is one of + + + align:start position:0% +right right so this is this is one of +the strategies what was the other one or + + align:start position:0% +the strategies what was the other one or + + + align:start position:0% +the strategies what was the other one or +the other two + + align:start position:0% +the other two + + + align:start position:0% +the other two +rather + + align:start position:0% + + + + align:start position:0% + +resistant right so there's R which is + + align:start position:0% +resistant right so there's R which is + + + align:start position:0% +resistant right so there's R which is +resistant + + align:start position:0% + + + + align:start position:0% + +uh okay and between the C and the r who + + align:start position:0% +uh okay and between the C and the r who + + + align:start position:0% +uh okay and between the C and the r who +wins r r that's right because the you + + align:start position:0% +wins r r that's right because the you + + + align:start position:0% +wins r r that's right because the you +know there might be some cost associated + + align:start position:0% +know there might be some cost associated + + + align:start position:0% +know there might be some cost associated +with being resistant but the cost is not + + align:start position:0% +with being resistant but the cost is not + + + align:start position:0% +with being resistant but the cost is not +as large as actually bursting open right + + align:start position:0% +as large as actually bursting open right + + + align:start position:0% +as large as actually bursting open right +so + + align:start position:0% +so + + + align:start position:0% +so +the what what's the last + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% + + + + align:start position:0% + +sensitive perfect so this is just the + + align:start position:0% +sensitive perfect so this is just the + + + align:start position:0% +sensitive perfect so this is just the +normal bacteria + + align:start position:0% +normal bacteria + + + align:start position:0% +normal bacteria +right U and and the argument is that + + align:start position:0% +right U and and the argument is that + + + align:start position:0% +right U and and the argument is that +there's some often a cost to be + + align:start position:0% +there's some often a cost to be + + + align:start position:0% +there's some often a cost to be +resistant which means that sensitive + + align:start position:0% +resistant which means that sensitive + + + align:start position:0% +resistant which means that sensitive +bacteria will Al compete resistant yet + + align:start position:0% +bacteria will Al compete resistant yet + + + align:start position:0% +bacteria will Al compete resistant yet +if it's just the sensitive and the + + align:start position:0% +if it's just the sensitive and the + + + align:start position:0% +if it's just the sensitive and the +cogenic strains then this strain can + + align:start position:0% +cogenic strains then this strain can + + + align:start position:0% +cogenic strains then this strain can +beat this + + align:start position:0% +beat this + + + align:start position:0% +beat this +strain all right so this is the idea of + + align:start position:0% +strain all right so this is the idea of + + + align:start position:0% +strain all right so this is the idea of +the rock paper scissors game in this + + align:start position:0% +the rock paper scissors game in this + + + align:start position:0% +the rock paper scissors game in this +system they do say that in some + + align:start position:0% +system they do say that in some + + + align:start position:0% +system they do say that in some +situations the fitnesses are such that + + align:start position:0% +situations the fitnesses are such that + + + align:start position:0% +situations the fitnesses are such that +it's like this um and it's good to take + + align:start position:0% +it's like this um and it's good to take + + + align:start position:0% +it's like this um and it's good to take +these sentences seriously right because + + align:start position:0% +these sentences seriously right because + + + align:start position:0% +these sentences seriously right because +if if they thought that every time that + + align:start position:0% +if if they thought that every time that + + + align:start position:0% +if if they thought that every time that +you isolate a resistant + + align:start position:0% +you isolate a resistant + + + align:start position:0% +you isolate a resistant +bacterium that it would satisfy this + + align:start position:0% +bacterium that it would satisfy this + + + align:start position:0% +bacterium that it would satisfy this +they would have said when you do this + + align:start position:0% +they would have said when you do this + + + align:start position:0% +they would have said when you do this +this is what you see right their + + align:start position:0% +this is what you see right their + + + align:start position:0% +this is what you see right their +phrasing tells you that + + align:start position:0% +phrasing tells you that + + + align:start position:0% +phrasing tells you that +actually depending upon which strain you + + align:start position:0% +actually depending upon which strain you + + + align:start position:0% +actually depending upon which strain you +get here there you you may or may not + + align:start position:0% +get here there you you may or may not + + + align:start position:0% +get here there you you may or may not +see this so don't feel so you have to be + + align:start position:0% +see this so don't feel so you have to be + + + align:start position:0% +see this so don't feel so you have to be +careful just cuz there's a nice paper + + align:start position:0% +careful just cuz there's a nice paper + + + align:start position:0% +careful just cuz there's a nice paper +that's written about this doesn't mean + + align:start position:0% +that's written about this doesn't mean + + + align:start position:0% +that's written about this doesn't mean +that if you go out and you find + + align:start position:0% +that if you go out and you find + + + align:start position:0% +that if you go out and you find +particular strains like that have these + + align:start position:0% +particular strains like that have these + + + align:start position:0% +particular strains like that have these +properties that it will always yield + + align:start position:0% +properties that it will always yield + + + align:start position:0% +properties that it will always yield +this particular outcome + + align:start position:0% +this particular outcome + + + align:start position:0% +this particular outcome +right all right so they + + align:start position:0% +right all right so they + + + align:start position:0% +right all right so they +uh they argue that these strains just + + align:start position:0% +uh they argue that these strains just + + + align:start position:0% +uh they argue that these strains just +because they have a non-transitive + + align:start position:0% +because they have a non-transitive + + + align:start position:0% +because they have a non-transitive +interaction does not necessarily mean + + align:start position:0% +interaction does not necessarily mean + + + align:start position:0% +interaction does not necessarily mean +that they will be able to um to coexist + + align:start position:0% + + + + align:start position:0% + +right in a well mixed environment in + + align:start position:0% +right in a well mixed environment in + + + align:start position:0% +right in a well mixed environment in +particular um and in + + align:start position:0% +particular um and in + + + align:start position:0% +particular um and in +there in their simulations and the + + align:start position:0% +there in their simulations and the + + + align:start position:0% +there in their simulations and the +experiments where they did the + + align:start position:0% +experiments where they did the + + + align:start position:0% +experiments where they did the +experiments in a test tube which strain + + align:start position:0% +experiments in a test tube which strain + + + align:start position:0% +experiments in a test tube which strain +died + + align:start position:0% + + + + align:start position:0% + +first sensitive strain does that make + + align:start position:0% +first sensitive strain does that make + + + align:start position:0% +first sensitive strain does that make +sense yeah right I mean um and and the + + align:start position:0% +sense yeah right I mean um and and the + + + align:start position:0% +sense yeah right I mean um and and the +other thing to remember is that these + + align:start position:0% +other thing to remember is that these + + + align:start position:0% +other thing to remember is that these +strains there's no reason that they + + align:start position:0% +strains there's no reason that they + + + align:start position:0% +strains there's no reason that they +should be accurately described by a loot + + align:start position:0% +should be accurately described by a loot + + + align:start position:0% +should be accurately described by a loot +loot voltera type formulation + + align:start position:0% +loot voltera type formulation + + + align:start position:0% +loot voltera type formulation +right uh and in particular it could just + + align:start position:0% +right uh and in particular it could just + + + align:start position:0% +right uh and in particular it could just +be the case that if you have enough + + align:start position:0% +be the case that if you have enough + + + align:start position:0% +be the case that if you have enough +producers and they make enough of the + + align:start position:0% +producers and they make enough of the + + + align:start position:0% +producers and they make enough of the +cson then the Sens of cells are just all + + align:start position:0% +cson then the Sens of cells are just all + + + align:start position:0% +cson then the Sens of cells are just all +dead right uh and + + align:start position:0% +dead right uh and + + + align:start position:0% +dead right uh and +that will in general be hard to capture + + align:start position:0% +that will in general be hard to capture + + + align:start position:0% +that will in general be hard to capture +in this sort of + + align:start position:0% + + + + align:start position:0% + +framework um right so the idea is that + + align:start position:0% +framework um right so the idea is that + + + align:start position:0% +framework um right so the idea is that +if you start with a bunch of ends uh you + + align:start position:0% +if you start with a bunch of ends uh you + + + align:start position:0% +if you start with a bunch of ends uh you +know n for each of these three uh then + + align:start position:0% +know n for each of these three uh then + + + align:start position:0% +know n for each of these three uh then +first you see that the sensitive cells + + align:start position:0% +first you see that the sensitive cells + + + align:start position:0% +first you see that the sensitive cells +die right once the sensitive cells have + + align:start position:0% +die right once the sensitive cells have + + + align:start position:0% +die right once the sensitive cells have +died then you're really just playing an + + align:start position:0% +died then you're really just playing an + + + align:start position:0% +died then you're really just playing an +interaction between these two right in + + align:start position:0% +interaction between these two right in + + + align:start position:0% +interaction between these two right in +that case you get the col colonogenic + + align:start position:0% +that case you get the col colonogenic + + + align:start position:0% +that case you get the col colonogenic +strain dying and you're + + align:start position:0% +strain dying and you're + + + align:start position:0% +strain dying and you're +left with just the resistance + + align:start position:0% +left with just the resistance + + + align:start position:0% +left with just the resistance +trrain + + align:start position:0% +trrain + + + align:start position:0% +trrain +right right so the question then becomes + + align:start position:0% +right right so the question then becomes + + + align:start position:0% +right right so the question then becomes +um or one thing I want I want to caution + + align:start position:0% +um or one thing I want I want to caution + + + align:start position:0% +um or one thing I want I want to caution +you about those is that just because in + + align:start position:0% +you about those is that just because in + + + align:start position:0% +you about those is that just because in +this experiment they saw that + + align:start position:0% +this experiment they saw that + + + align:start position:0% +this experiment they saw that +coexistence of three rock paper scissors + + align:start position:0% +coexistence of three rock paper scissors + + + align:start position:0% +coexistence of three rock paper scissors +type strains was not possible in a well + + align:start position:0% +type strains was not possible in a well + + + align:start position:0% +type strains was not possible in a well +mixed environment does not mean that + + align:start position:0% +mixed environment does not mean that + + + align:start position:0% +mixed environment does not mean that +that will always be the case I think + + align:start position:0% +that will always be the case I think + + + align:start position:0% +that will always be the case I think +that um + + align:start position:0% +that um + + + align:start position:0% +that um +often this is a very well-known paper in + + align:start position:0% +often this is a very well-known paper in + + + align:start position:0% +often this is a very well-known paper in +the field and and the thing is that + + align:start position:0% +the field and and the thing is that + + + align:start position:0% +the field and and the thing is that +often people it's it's easy to forget + + align:start position:0% +often people it's it's easy to forget + + + align:start position:0% +often people it's it's easy to forget +what a paper shows and what it doesn't + + align:start position:0% +what a paper shows and what it doesn't + + + align:start position:0% +what a paper shows and what it doesn't +show right so what this shows is that um + + align:start position:0% +show right so what this shows is that um + + + align:start position:0% +show right so what this shows is that um +there is maybe a set of these three + + align:start position:0% +there is maybe a set of these three + + + align:start position:0% +there is maybe a set of these three +strains that have a rock paper scissors + + align:start position:0% +strains that have a rock paper scissors + + + align:start position:0% +strains that have a rock paper scissors +type interaction and in that those + + align:start position:0% +type interaction and in that those + + + align:start position:0% +type interaction and in that those +particular three strains that are + + align:start position:0% +particular three strains that are + + + align:start position:0% +particular three strains that are +interacting this particular way via + + align:start position:0% +interacting this particular way via + + + align:start position:0% +interacting this particular way via +cisin the killing then they don't + + align:start position:0% +cisin the killing then they don't + + + align:start position:0% +cisin the killing then they don't +coexist in this particular well mix you + + align:start position:0% +coexist in this particular well mix you + + + align:start position:0% +coexist in this particular well mix you +know but maybe and maybe other well + + align:start position:0% +know but maybe and maybe other well + + + align:start position:0% +know but maybe and maybe other well +mixed environments as well but this does + + align:start position:0% +mixed environments as well but this does + + + align:start position:0% +mixed environments as well but this does +not necessarily show that any rock paper + + align:start position:0% +not necessarily show that any rock paper + + + align:start position:0% +not necessarily show that any rock paper +scissors interaction in a well mixed + + align:start position:0% +scissors interaction in a well mixed + + + align:start position:0% +scissors interaction in a well mixed +environment will um not support + + align:start position:0% +environment will um not support + + + align:start position:0% +environment will um not support +coexistence right so uh and in + + align:start position:0% +coexistence right so uh and in + + + align:start position:0% +coexistence right so uh and in +particular you might remember in Martin + + align:start position:0% +particular you might remember in Martin + + + align:start position:0% +particular you might remember in Martin +Novak's book there are very reasonable + + align:start position:0% +Novak's book there are very reasonable + + + align:start position:0% +Novak's book there are very reasonable +equations that display rock paper + + align:start position:0% +equations that display rock paper + + + align:start position:0% +equations that display rock paper +scissors type interactions that can lead + + align:start position:0% +scissors type interactions that can lead + + + align:start position:0% +scissors type interactions that can lead +to coexist + + align:start position:0% +to coexist + + + align:start position:0% +to coexist +okay so you kind of can spiral in that + + align:start position:0% +okay so you kind of can spiral in that + + + align:start position:0% +okay so you kind of can spiral in that +space to a state of coexistence so it's + + align:start position:0% +space to a state of coexistence so it's + + + align:start position:0% +space to a state of coexistence so it's +possible but um but in this situation it + + align:start position:0% +possible but um but in this situation it + + + align:start position:0% +possible but um but in this situation it +doesn't happen + + align:start position:0% +doesn't happen + + + align:start position:0% +doesn't happen +okay all right can somebody remind us + + align:start position:0% +okay all right can somebody remind us + + + align:start position:0% +okay all right can somebody remind us +how the uh how they implemented a well + + align:start position:0% +how the uh how they implemented a well + + + align:start position:0% +how the uh how they implemented a well +or sorry the spatially structured + + align:start position:0% + + + + align:start position:0% + +environment yeah right so they used Ager + + align:start position:0% +environment yeah right so they used Ager + + + align:start position:0% +environment yeah right so they used Ager +plates they did this thing where + + align:start position:0% +plates they did this thing where + + + align:start position:0% +plates they did this thing where +they took this plate and they kind of + + align:start position:0% +they took this plate and they kind of + + + align:start position:0% +they took this plate and they kind of +used a hexagonal grid of some sort right + + align:start position:0% +used a hexagonal grid of some sort right + + + align:start position:0% +used a hexagonal grid of some sort right +is it actually yeah where they I don't + + align:start position:0% +is it actually yeah where they I don't + + + align:start position:0% +is it actually yeah where they I don't +know how they decided on the original + + align:start position:0% +know how they decided on the original + + + align:start position:0% +know how they decided on the original +order but they you know they said okay + + align:start position:0% +order but they you know they said okay + + + align:start position:0% +order but they you know they said okay +here's a sensitive sensitive + + align:start position:0% +here's a sensitive sensitive + + + align:start position:0% +here's a sensitive sensitive +resistant + + align:start position:0% +resistant + + + align:start position:0% +resistant +colicinogenic resistant I don't know + + align:start position:0% +colicinogenic resistant I don't know + + + align:start position:0% +colicinogenic resistant I don't know +whatever so + + align:start position:0% +whatever so + + + align:start position:0% +whatever so +they filled it up they put maybe 20 + + align:start position:0% +they filled it up they put maybe 20 + + + align:start position:0% +they filled it up they put maybe 20 +different kind of patches there and then + + align:start position:0% +different kind of patches there and then + + + align:start position:0% +different kind of patches there and then +they basically you know each each day + + align:start position:0% +they basically you know each each day + + + align:start position:0% +they basically you know each each day +they just used one of these velvets that + + align:start position:0% +they just used one of these velvets that + + + align:start position:0% +they just used one of these velvets that +we often we use to to do replica plating + + align:start position:0% +we often we use to to do replica plating + + + align:start position:0% +we often we use to to do replica plating +right and then they just kind of took + + align:start position:0% +right and then they just kind of took + + + align:start position:0% +right and then they just kind of took +off some of the cells and put it on a + + align:start position:0% +off some of the cells and put it on a + + + align:start position:0% +off some of the cells and put it on a +fresh plate and then they did this um + + align:start position:0% +fresh plate and then they did this um + + + align:start position:0% +fresh plate and then they did this um +for a week or so right and then they um + + align:start position:0% +for a week or so right and then they um + + + align:start position:0% +for a week or so right and then they um +and then they saw that there was some + + align:start position:0% +and then they saw that there was some + + + align:start position:0% +and then they saw that there was some +sense that these uh there was a spatial + + align:start position:0% +sense that these uh there was a spatial + + + align:start position:0% +sense that these uh there was a spatial +Dynamic taking place where you know + + align:start position:0% +Dynamic taking place where you know + + + align:start position:0% +Dynamic taking place where you know +where the spatial structure was kind of + + align:start position:0% +where the spatial structure was kind of + + + align:start position:0% +where the spatial structure was kind of +reminiscent of this right where the + + align:start position:0% +reminiscent of this right where the + + + align:start position:0% +reminiscent of this right where the +sensitive kind of moved into the + + align:start position:0% +sensitive kind of moved into the + + + align:start position:0% +sensitive kind of moved into the +resistant resistant kind of moved into + + align:start position:0% +resistant resistant kind of moved into + + + align:start position:0% +resistant resistant kind of moved into +the cogenic cogenic kind of moved into + + align:start position:0% +the cogenic cogenic kind of moved into + + + align:start position:0% +the cogenic cogenic kind of moved into +the sensitive but they couldn't actually + + align:start position:0% +the sensitive but they couldn't actually + + + align:start position:0% +the sensitive but they couldn't actually +see all of + + align:start position:0% +see all of + + + align:start position:0% +see all of +those right because two of the strains + + align:start position:0% +those right because two of the strains + + + align:start position:0% +those right because two of the strains +uh they said gr of similar density that + + align:start position:0% +uh they said gr of similar density that + + + align:start position:0% +uh they said gr of similar density that +was between the sensitive and the + + align:start position:0% +was between the sensitive and the + + + align:start position:0% +was between the sensitive and the +resistant right so visually they could + + align:start position:0% +resistant right so visually they could + + + align:start position:0% +resistant right so visually they could +only distinguish uh The colicinogenic + + align:start position:0% +only distinguish uh The colicinogenic + + + align:start position:0% +only distinguish uh The colicinogenic +Strain relative to the others right but + + align:start position:0% +Strain relative to the others right but + + + align:start position:0% +Strain relative to the others right but +um but what they found though is that + + align:start position:0% +um but what they found though is that + + + align:start position:0% +um but what they found though is that +over a similar amount of + + align:start position:0% +over a similar amount of + + + align:start position:0% +over a similar amount of +time they got coexistence of all three + + align:start position:0% +time they got coexistence of all three + + + align:start position:0% +time they got coexistence of all three +right so + + align:start position:0% +right so + + + align:start position:0% +right so +it's so R CS kind of all they the + + align:start position:0% +it's so R CS kind of all they the + + + align:start position:0% +it's so R CS kind of all they the +numbers is a function of time stuck + + align:start position:0% +numbers is a function of time stuck + + + align:start position:0% +numbers is a function of time stuck +around on in this spatially structured + + align:start position:0% +around on in this spatially structured + + + align:start position:0% +around on in this spatially structured +environment right so their argument is + + align:start position:0% +environment right so their argument is + + + align:start position:0% +environment right so their argument is +that in some cases maybe this + + align:start position:0% +that in some cases maybe this + + + align:start position:0% +that in some cases maybe this +non-transitive interaction is not + + align:start position:0% +non-transitive interaction is not + + + align:start position:0% +non-transitive interaction is not +sufficient to maintain uh diversity in a + + align:start position:0% +sufficient to maintain uh diversity in a + + + align:start position:0% +sufficient to maintain uh diversity in a +population whether it's genetic + + align:start position:0% +population whether it's genetic + + + align:start position:0% +population whether it's genetic +diversity or species diversity but that + + align:start position:0% +diversity or species diversity but that + + + align:start position:0% +diversity or species diversity but that +it may be that it's very important to + + align:start position:0% +it may be that it's very important to + + + align:start position:0% +it may be that it's very important to +have uh to have this spatial + + align:start position:0% +have uh to have this spatial + + + align:start position:0% +have uh to have this spatial +component + + align:start position:0% +component + + + align:start position:0% +component +okay if you're uh if you're curious + + align:start position:0% +okay if you're uh if you're curious + + + align:start position:0% +okay if you're uh if you're curious +about these things there's also a nice + + align:start position:0% +about these things there's also a nice + + + align:start position:0% +about these things there's also a nice +computational computational study done + + align:start position:0% +computational computational study done + + + align:start position:0% +computational computational study done +by Irwin + + align:start position:0% +by Irwin + + + align:start position:0% +by Irwin +fry + + align:start position:0% +fry + + + align:start position:0% +fry +uh uh who uh who studied kind of these + + align:start position:0% +uh uh who uh who studied kind of these + + + align:start position:0% +uh uh who uh who studied kind of these +rock paper scissors Dynamics as a + + align:start position:0% +rock paper scissors Dynamics as a + + + align:start position:0% +rock paper scissors Dynamics as a +function of the mobility of the + + align:start position:0% +function of the mobility of the + + + align:start position:0% +function of the mobility of the +individual kind of agents and uh in that + + align:start position:0% +individual kind of agents and uh in that + + + align:start position:0% +individual kind of agents and uh in that +study uh he found that there were there + + align:start position:0% +study uh he found that there were there + + + align:start position:0% +study uh he found that there were there +was sort of a critical level of Mobility + + align:start position:0% +was sort of a critical level of Mobility + + + align:start position:0% +was sort of a critical level of Mobility +at which you kind of um switch from it + + align:start position:0% +at which you kind of um switch from it + + + align:start position:0% +at which you kind of um switch from it +being a well- mixed thing with + + align:start position:0% +being a well- mixed thing with + + + align:start position:0% +being a well- mixed thing with +coexistence to um sorry from a from a + + align:start position:0% +coexistence to um sorry from a from a + + + align:start position:0% +coexistence to um sorry from a from a +spatially structured environment with + + align:start position:0% +spatially structured environment with + + + align:start position:0% +spatially structured environment with +coexistence to above some Mobility you + + align:start position:0% +coexistence to above some Mobility you + + + align:start position:0% +coexistence to above some Mobility you +end up with uh losing the diversity + + align:start position:0% +end up with uh losing the diversity + + + align:start position:0% +end up with uh losing the diversity +because it it kind of goes into this + + align:start position:0% +because it it kind of goes into this + + + align:start position:0% +because it it kind of goes into this +well mixed kind of regime so uh yeah so + + align:start position:0% +well mixed kind of regime so uh yeah so + + + align:start position:0% +well mixed kind of regime so uh yeah so +if you're curious about these things um + + align:start position:0% +if you're curious about these things um + + + align:start position:0% +if you're curious about these things um +I you can look up win's paper + + align:start position:0% + + + + align:start position:0% + +Okay are there any questions about what + + align:start position:0% +Okay are there any questions about what + + + align:start position:0% +Okay are there any questions about what +they did + + align:start position:0% +they did + + + align:start position:0% +they did +here what you think it + + align:start position:0% +here what you think it + + + align:start position:0% +here what you think it +means + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +know right because they can still uh + + align:start position:0% +know right because they can still uh + + + align:start position:0% +know right because they can still uh +they can just scrape off everything in + + align:start position:0% +they can just scrape off everything in + + + align:start position:0% +they can just scrape off everything in +plate uh and then right because well + + align:start position:0% +plate uh and then right because well + + + align:start position:0% +plate uh and then right because well +then you can you can ask oh were those + + align:start position:0% +then you can you can ask oh were those + + + align:start position:0% +then you can you can ask oh were those +guys sensitive to cisin or not right so + + align:start position:0% +guys sensitive to cisin or not right so + + + align:start position:0% +guys sensitive to cisin or not right so +there is so you + + align:start position:0% +there is so you + + + align:start position:0% +there is so you +can yeah or plate them on something with + + align:start position:0% +can yeah or plate them on something with + + + align:start position:0% +can yeah or plate them on something with +cisin or together yeah and I think this + + align:start position:0% +cisin or together yeah and I think this + + + align:start position:0% +cisin or together yeah and I think this +is a system that uh has been very + + align:start position:0% +is a system that uh has been very + + + align:start position:0% +is a system that uh has been very +influential but it's really not I think + + align:start position:0% +influential but it's really not I think + + + align:start position:0% +influential but it's really not I think +it's not yet or has not been a domestic + + align:start position:0% +it's not yet or has not been a domestic + + + align:start position:0% +it's not yet or has not been a domestic +iated kind of model system in the sense + + align:start position:0% +iated kind of model system in the sense + + + align:start position:0% +iated kind of model system in the sense +that you know there are not nice + + align:start position:0% +that you know there are not nice + + + align:start position:0% +that you know there are not nice +fluorescent proteins these cisin you + + align:start position:0% +fluorescent proteins these cisin you + + + align:start position:0% +fluorescent proteins these cisin you +know this is not on a nice cloning + + align:start position:0% +know this is not on a nice cloning + + + align:start position:0% +know this is not on a nice cloning +plasmid it's just kind of it was a a + + align:start position:0% +plasmid it's just kind of it was a a + + + align:start position:0% +plasmid it's just kind of it was a a +natural plasmid um and the this + + align:start position:0% +natural plasmid um and the this + + + align:start position:0% +natural plasmid um and the this +resistance strain it was just what they + + align:start position:0% +resistance strain it was just what they + + + align:start position:0% +resistance strain it was just what they +the way that they get it is they + + align:start position:0% +the way that they get it is they + + + align:start position:0% +the way that they get it is they +basically they + + align:start position:0% +basically they + + + align:start position:0% +basically they +they they take some sensitive cells and + + align:start position:0% +they they take some sensitive cells and + + + align:start position:0% +they they take some sensitive cells and +they add cisin you know they say the + + align:start position:0% +they add cisin you know they say the + + + align:start position:0% +they add cisin you know they say the +supernatent from here and they ask which + + align:start position:0% +supernatent from here and they ask which + + + align:start position:0% +supernatent from here and they ask which +cells grow and then that's a resistant + + align:start position:0% +cells grow and then that's a resistant + + + align:start position:0% +cells grow and then that's a resistant +cell and it's genetically resistant but + + align:start position:0% +cell and it's genetically resistant but + + + align:start position:0% +cell and it's genetically resistant but +then you know each one's going to be + + align:start position:0% +then you know each one's going to be + + + align:start position:0% +then you know each one's going to be +different often it can you know you know + + align:start position:0% +different often it can you know you know + + + align:start position:0% +different often it can you know you know +they have done sequencing it's say a + + align:start position:0% +they have done sequencing it's say a + + + align:start position:0% +they have done sequencing it's say a +Surface Pro it's a surface receptor that + + align:start position:0% +Surface Pro it's a surface receptor that + + + align:start position:0% +Surface Pro it's a surface receptor that +the cson maybe uses to go in or other + + align:start position:0% +the cson maybe uses to go in or other + + + align:start position:0% +the cson maybe uses to go in or other +things but I indeed we we actually did + + align:start position:0% +things but I indeed we we actually did + + + align:start position:0% +things but I indeed we we actually did +some experiments with some of the these + + align:start position:0% +some experiments with some of the these + + + align:start position:0% +some experiments with some of the these +uh these strains and it it it's a little + + align:start position:0% +uh these strains and it it it's a little + + + align:start position:0% +uh these strains and it it it's a little +bit messy you know I think that there's + + align:start position:0% +bit messy you know I think that there's + + + align:start position:0% +bit messy you know I think that there's +a sense that you have that the field + + align:start position:0% +a sense that you have that the field + + + align:start position:0% +a sense that you have that the field +maybe needs to um just make some nice + + align:start position:0% +maybe needs to um just make some nice + + + align:start position:0% +maybe needs to um just make some nice +plasmas with nice colors so we can + + align:start position:0% +plasmas with nice colors so we can + + + align:start position:0% +plasmas with nice colors so we can +really distinguish things because I + + align:start position:0% +really distinguish things because I + + + align:start position:0% +really distinguish things because I +think that this system despite I mean + + align:start position:0% +think that this system despite I mean + + + align:start position:0% +think that this system despite I mean +500 citations or so almost none of those + + align:start position:0% +500 citations or so almost none of those + + + align:start position:0% +500 citations or so almost none of those +citations are experimental papers really + + align:start position:0% +citations are experimental papers really + + + align:start position:0% +citations are experimental papers really +exploring this this thing you know + + align:start position:0% +exploring this this thing you know + + + align:start position:0% +exploring this this thing you know +because I think that it it still is it's + + align:start position:0% +because I think that it it still is it's + + + align:start position:0% +because I think that it it still is it's +just a little bit messy uh but I think + + align:start position:0% +just a little bit messy uh but I think + + + align:start position:0% +just a little bit messy uh but I think +that it's it's also you know it's also a + + align:start position:0% +that it's it's also you know it's also a + + + align:start position:0% +that it's it's also you know it's also a +very pretty uh system to explore these + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +ideas + + align:start position:0% + + + + align:start position:0% + +yeah oh oh right so the question is why + + align:start position:0% +yeah oh oh right so the question is why + + + align:start position:0% +yeah oh oh right so the question is why +why why can't you distinguish these and + + align:start position:0% +why why can't you distinguish these and + + + align:start position:0% +why why can't you distinguish these and +um you know they say it's because + + align:start position:0% +um you know they say it's because + + + align:start position:0% +um you know they say it's because +they're similar densities I I don't even + + align:start position:0% +they're similar densities I I don't even + + + align:start position:0% +they're similar densities I I don't even +know if that's even um you know of + + align:start position:0% +know if that's even um you know of + + + align:start position:0% +know if that's even um you know of +course if you just + + align:start position:0% +course if you just + + + align:start position:0% +course if you just +take well if you if you + + align:start position:0% +take well if you if you + + + align:start position:0% +take well if you if you +added sensitive cells here and sensitive + + align:start position:0% +added sensitive cells here and sensitive + + + align:start position:0% +added sensitive cells here and sensitive +cells here and they grew up it you know + + align:start position:0% +cells here and they grew up it you know + + + align:start position:0% +cells here and they grew up it you know +it's likely you're not going to see a + + align:start position:0% +it's likely you're not going to see a + + + align:start position:0% +it's likely you're not going to see a +boundary right and all just more + + align:start position:0% +boundary right and all just more + + + align:start position:0% +boundary right and all just more +generally if you take similar strains + + align:start position:0% +generally if you take similar strains + + + align:start position:0% +generally if you take similar strains +and these are rather similar strains + + align:start position:0% +and these are rather similar strains + + + align:start position:0% +and these are rather similar strains +this is just has some mutation relative + + align:start position:0% +this is just has some mutation relative + + + align:start position:0% +this is just has some mutation relative +to this then you won't often see a bound + + align:start position:0% +to this then you won't often see a bound + + + align:start position:0% +to this then you won't often see a bound +when they when the colonies kind of grow + + align:start position:0% +when they when the colonies kind of grow + + + align:start position:0% +when they when the colonies kind of grow +up + + align:start position:0% + + + + align:start position:0% + +um oh right so they they saw there were + + align:start position:0% +um oh right so they they saw there were + + + align:start position:0% +um oh right so they they saw there were +cells there but they they didn't know + + align:start position:0% +cells there but they they didn't know + + + align:start position:0% +cells there but they they didn't know +they they couldn't necessarily say that + + align:start position:0% +they they couldn't necessarily say that + + + align:start position:0% +they they couldn't necessarily say that +it was the it was true that the + + align:start position:0% +it was the it was true that the + + + align:start position:0% +it was the it was true that the +sensitive cells were kind of spreading + + align:start position:0% +sensitive cells were kind of spreading + + + align:start position:0% +sensitive cells were kind of spreading +into the resistance zone region because + + align:start position:0% +into the resistance zone region because + + + align:start position:0% +into the resistance zone region because +they couldn't see the + + align:start position:0% + + + + align:start position:0% + +boundary all right so uh in the last 20 + + align:start position:0% +boundary all right so uh in the last 20 + + + align:start position:0% +boundary all right so uh in the last 20 +minutes here 15 20 um I just want to say + + align:start position:0% +minutes here 15 20 um I just want to say + + + align:start position:0% +minutes here 15 20 um I just want to say +a few things about um these population + + align:start position:0% + + + + align:start position:0% + +waves so for many many purposes there's + + align:start position:0% +waves so for many many purposes there's + + + align:start position:0% +waves so for many many purposes there's +uh there are strong arguments to be made + + align:start position:0% +uh there are strong arguments to be made + + + align:start position:0% +uh there are strong arguments to be made +that in the context of evolution ecology + + align:start position:0% +that in the context of evolution ecology + + + align:start position:0% +that in the context of evolution ecology +you know spatial kind of Dynamics matter + + align:start position:0% +you know spatial kind of Dynamics matter + + + align:start position:0% +you know spatial kind of Dynamics matter +right and the way that we often think + + align:start position:0% +right and the way that we often think + + + align:start position:0% +right and the way that we often think +about the spatial Dynamics is um via + + align:start position:0% +about the spatial Dynamics is um via + + + align:start position:0% +about the spatial Dynamics is um via +some effective diffusive process right + + align:start position:0% +some effective diffusive process right + + + align:start position:0% +some effective diffusive process right +and that's convenient because we know a + + align:start position:0% +and that's convenient because we know a + + + align:start position:0% +and that's convenient because we know a +lot about how to model it but it's also + + align:start position:0% +lot about how to model it but it's also + + + align:start position:0% +lot about how to model it but it's also +maybe uh a reasonable description of the + + align:start position:0% +maybe uh a reasonable description of the + + + align:start position:0% +maybe uh a reasonable description of the +motion of animals and other other living + + align:start position:0% +motion of animals and other other living + + + align:start position:0% +motion of animals and other other living +things over over length scales that are + + align:start position:0% +things over over length scales that are + + + align:start position:0% +things over over length scales that are +large compared to the movements of the + + align:start position:0% +large compared to the movements of the + + + align:start position:0% +large compared to the movements of the +animals okay right so what we do is we + + align:start position:0% +animals okay right so what we do is we + + + align:start position:0% +animals okay right so what we do is we +take some equation such as well we often + + align:start position:0% +take some equation such as well we often + + + align:start position:0% +take some equation such as well we often +have say DN + + align:start position:0% +have say DN + + + align:start position:0% +have say DN +DT uh all right this is going to be + + align:start position:0% +DT uh all right this is going to be + + + align:start position:0% +DT uh all right this is going to be +about population + + align:start position:0% + + + + align:start position:0% + +waves uh right so we take our standard + + align:start position:0% +waves uh right so we take our standard + + + align:start position:0% +waves uh right so we take our standard +thing where we say oh here's + + align:start position:0% +thing where we say oh here's + + + align:start position:0% +thing where we say oh here's +R and n 1 - n / K okay and then we just + + align:start position:0% +R and n 1 - n / K okay and then we just + + + align:start position:0% +R and n 1 - n / K okay and then we just +want to add some spatial Dynamic so what + + align:start position:0% +want to add some spatial Dynamic so what + + + align:start position:0% +want to add some spatial Dynamic so what +we're going to do is we're going to say + + align:start position:0% +we're going to do is we're going to say + + + align:start position:0% +we're going to do is we're going to say +all right now the derivative now it's a + + align:start position:0% +all right now the derivative now it's a + + + align:start position:0% +all right now the derivative now it's a +density so we're going to use a little n + + align:start position:0% +density so we're going to use a little n + + + align:start position:0% +density so we're going to use a little n +just to for fun + + align:start position:0% + + + + align:start position:0% + +right and we might still use a k just + + align:start position:0% +right and we might still use a k just + + + align:start position:0% +right and we might still use a k just +for simple um but then we want we have + + align:start position:0% +for simple um but then we want we have + + + align:start position:0% +for simple um but then we want we have +to add some diffusive + + align:start position:0% + + + + align:start position:0% + +term + + align:start position:0% +term + + + align:start position:0% +term +okay right so there's still is going to + + align:start position:0% +okay right so there's still is going to + + + align:start position:0% +okay right so there's still is going to +be a local carrying capacit now this is + + align:start position:0% +be a local carrying capacit now this is + + + align:start position:0% +be a local carrying capacit now this is +in terms of density of the organism and + + align:start position:0% +in terms of density of the organism and + + + align:start position:0% +in terms of density of the organism and +we're going to assume that there is some + + align:start position:0% +we're going to assume that there is some + + + align:start position:0% +we're going to assume that there is some +diffusive type motion of the organism + + align:start position:0% +diffusive type motion of the organism + + + align:start position:0% +diffusive type motion of the organism +now this is saying this is course + + align:start position:0% +now this is saying this is course + + + align:start position:0% +now this is saying this is course +graining over the length scale over + + align:start position:0% +graining over the length scale over + + + align:start position:0% +graining over the length scale over +which the animals are actually doing + + align:start position:0% +which the animals are actually doing + + + align:start position:0% +which the animals are actually doing +things over their you know over shorter + + align:start position:0% +things over their you know over shorter + + + align:start position:0% +things over their you know over shorter +time scales right so it could be that uh + + align:start position:0% +time scales right so it could be that uh + + + align:start position:0% +time scales right so it could be that uh +different organisms have very different + + align:start position:0% +different organisms have very different + + + align:start position:0% +different organisms have very different +uh modes of motility in some cases they + + align:start position:0% +uh modes of motility in some cases they + + + align:start position:0% +uh modes of motility in some cases they +walk or Swim and some cases they just + + align:start position:0% +walk or Swim and some cases they just + + + align:start position:0% +walk or Swim and some cases they just +get picked up by a passing deer right so + + align:start position:0% +get picked up by a passing deer right so + + + align:start position:0% +get picked up by a passing deer right so +there are a wide range of of ways in + + align:start position:0% +there are a wide range of of ways in + + + align:start position:0% +there are a wide range of of ways in +which organisms move around but + + align:start position:0% +which organisms move around but + + + align:start position:0% +which organisms move around but +if you look at it over kind of longer + + align:start position:0% +if you look at it over kind of longer + + + align:start position:0% +if you look at it over kind of longer +length time scales then maybe it doesn't + + align:start position:0% +length time scales then maybe it doesn't + + + align:start position:0% +length time scales then maybe it doesn't +matter right and certainly if it's if + + align:start position:0% +matter right and certainly if it's if + + + align:start position:0% +matter right and certainly if it's if +it's an unbiased kind of motion with um + + align:start position:0% +it's an unbiased kind of motion with um + + + align:start position:0% +it's an unbiased kind of motion with um +motility uh having uh being well behaved + + align:start position:0% +motility uh having uh being well behaved + + + align:start position:0% +motility uh having uh being well behaved +right I.E if the probability + + align:start position:0% +right I.E if the probability + + + align:start position:0% +right I.E if the probability +distribution of these steps as long as + + align:start position:0% +distribution of these steps as long as + + + align:start position:0% +distribution of these steps as long as +it's not + + align:start position:0% +it's not + + + align:start position:0% +it's not +longtailed right inly Oscar hich over at + + align:start position:0% +longtailed right inly Oscar hich over at + + + align:start position:0% +longtailed right inly Oscar hich over at +Berkeley has been doing a lot of fun + + align:start position:0% +Berkeley has been doing a lot of fun + + + align:start position:0% +Berkeley has been doing a lot of fun +work looking at epidemic spread in cases + + align:start position:0% +work looking at epidemic spread in cases + + + align:start position:0% +work looking at epidemic spread in cases +where this kernel you know kind of Step + + align:start position:0% +where this kernel you know kind of Step + + + align:start position:0% +where this kernel you know kind of Step +size distribution has longtails um it + + align:start position:0% +size distribution has longtails um it + + + align:start position:0% +size distribution has longtails um it +leads to qualitatively different + + align:start position:0% +leads to qualitatively different + + + align:start position:0% +leads to qualitatively different +behaviors okay so if you're curious + + align:start position:0% +behaviors okay so if you're curious + + + align:start position:0% +behaviors okay so if you're curious +about such things check out Oscar's work + + align:start position:0% +about such things check out Oscar's work + + + align:start position:0% +about such things check out Oscar's work +but uh for for normal kind of Step siiz + + align:start position:0% +but uh for for normal kind of Step siiz + + + align:start position:0% +but uh for for normal kind of Step siiz +distributions then you the central limit + + align:start position:0% +distributions then you the central limit + + + align:start position:0% +distributions then you the central limit +theorem type considerations just tell + + align:start position:0% +theorem type considerations just tell + + + align:start position:0% +theorem type considerations just tell +you that you that you can maybe just + + align:start position:0% +you that you that you can maybe just + + + align:start position:0% +you that you that you can maybe just +look at it like this um over over time + + align:start position:0% +look at it like this um over over time + + + align:start position:0% +look at it like this um over over time +time spatial scales that are that are + + align:start position:0% +time spatial scales that are that are + + + align:start position:0% +time spatial scales that are that are +bigger yeah so but is it that you need + + align:start position:0% +bigger yeah so but is it that you need + + + align:start position:0% +bigger yeah so but is it that you need +correlation between your STS or I mean + + align:start position:0% +correlation between your STS or I mean + + + align:start position:0% +correlation between your STS or I mean +the + + align:start position:0% +the + + + align:start position:0% +the +centr as long as the + + align:start position:0% +centr as long as the + + + align:start position:0% +centr as long as the +variance I guess you're saying that's + + align:start position:0% +variance I guess you're saying that's + + + align:start position:0% +variance I guess you're saying that's +why I'm saying longtail VAR is infinite + + align:start position:0% +why I'm saying longtail VAR is infinite + + + align:start position:0% +why I'm saying longtail VAR is infinite +then exactly yeah so that's that's what + + align:start position:0% +then exactly yeah so that's that's what + + + align:start position:0% +then exactly yeah so that's that's what +I saying is that you know indeed people + + align:start position:0% +I saying is that you know indeed people + + + align:start position:0% +I saying is that you know indeed people +argue in the case of disease spread you + + align:start position:0% +argue in the case of disease spread you + + + align:start position:0% +argue in the case of disease spread you +know with modern air travel and so forth + + align:start position:0% +know with modern air travel and so forth + + + align:start position:0% +know with modern air travel and so forth +that the probability distribution of + + align:start position:0% +that the probability distribution of + + + align:start position:0% +that the probability distribution of +kind of Step sizes for infected + + align:start position:0% +kind of Step sizes for infected + + + align:start position:0% +kind of Step sizes for infected +individuals over the next you know week + + align:start position:0% +individuals over the next you know week + + + align:start position:0% +individuals over the next you know week +is longtailed right because you know + + align:start position:0% +is longtailed right because you know + + + align:start position:0% +is longtailed right because you know +there's a fair chance that you're just + + align:start position:0% +there's a fair chance that you're just + + + align:start position:0% +there's a fair chance that you're just +going to stay around your local + + align:start position:0% +going to stay around your local + + + align:start position:0% +going to stay around your local +neighborhood but there's a smaller + + align:start position:0% +neighborhood but there's a smaller + + + align:start position:0% +neighborhood but there's a smaller +chance you're going to go to the other + + align:start position:0% +chance you're going to go to the other + + + align:start position:0% +chance you're going to go to the other +side of town but you might go to + + align:start position:0% +side of town but you might go to + + + align:start position:0% +side of town but you might go to +you know a business trip over in DC at + + align:start position:0% +you know a business trip over in DC at + + + align:start position:0% +you know a business trip over in DC at +some small rate though you also fly to + + align:start position:0% +some small rate though you also fly to + + + align:start position:0% +some small rate though you also fly to +South Africa and go to a conference + + align:start position:0% +South Africa and go to a conference + + + align:start position:0% +South Africa and go to a conference +right so all of these things have + + align:start position:0% +right so all of these things have + + + align:start position:0% +right so all of these things have +reasonable probabilities and um and so + + align:start position:0% +reasonable probabilities and um and so + + + align:start position:0% +reasonable probabilities and um and so +there there are arguments that this is + + align:start position:0% +there there are arguments that this is + + + align:start position:0% +there there are arguments that this is +this is kind of some power LW type + + align:start position:0% +this is kind of some power LW type + + + align:start position:0% +this is kind of some power LW type +distribution and in those cases right + + align:start position:0% +distribution and in those cases right + + + align:start position:0% +distribution and in those cases right +they don't you don't necessarily have + + align:start position:0% +they don't you don't necessarily have + + + align:start position:0% +they don't you don't necessarily have +finite variance and so you so then you + + align:start position:0% +finite variance and so you so then you + + + align:start position:0% +finite variance and so you so then you +can't just Shuffle put everything under + + align:start position:0% +can't just Shuffle put everything under + + + align:start position:0% +can't just Shuffle put everything under +the rug right um + + align:start position:0% +the rug right um + + + align:start position:0% +the rug right um +yeah but we first want to understand + + align:start position:0% +yeah but we first want to understand + + + align:start position:0% +yeah but we first want to understand +what happens here and then we can well + + align:start position:0% +what happens here and then we can well + + + align:start position:0% +what happens here and then we can well +we're not going to but then other people + + align:start position:0% +we're not going to but then other people + + + align:start position:0% +we're not going to but then other people +can think more deeply about what happens + + align:start position:0% +can think more deeply about what happens + + + align:start position:0% +can think more deeply about what happens +in fancier situations + + align:start position:0% +in fancier situations + + + align:start position:0% +in fancier situations +right + + align:start position:0% +right + + + align:start position:0% +right +um it is worth saying though that this + + align:start position:0% +um it is worth saying though that this + + + align:start position:0% +um it is worth saying though that this +this approach I mean it looks very + + align:start position:0% + + + + align:start position:0% + +done by Fisher uh when he um so this was + + align:start position:0% +done by Fisher uh when he um so this was + + + align:start position:0% +done by Fisher uh when he um so this was +in the 20 1920s or so right so a long + + align:start position:0% +in the 20 1920s or so right so a long + + + align:start position:0% +in the 20 1920s or so right so a long +time ago originally to try to understand + + align:start position:0% +time ago originally to try to understand + + + align:start position:0% +time ago originally to try to understand +not the spread of a population but the + + align:start position:0% +not the spread of a population but the + + + align:start position:0% +not the spread of a population but the +spread of a beneficial Al in a spatial + + align:start position:0% +spread of a beneficial Al in a spatial + + + align:start position:0% +spread of a beneficial Al in a spatial +population right and once again this + + align:start position:0% +population right and once again this + + + align:start position:0% +population right and once again this +this highlights this deep connections + + align:start position:0% +this highlights this deep connections + + + align:start position:0% +this highlights this deep connections +between evolution and ecology right that + + align:start position:0% +between evolution and ecology right that + + + align:start position:0% +between evolution and ecology right that +you can have a genetic wave in space of + + align:start position:0% +you can have a genetic wave in space of + + + align:start position:0% +you can have a genetic wave in space of +a of a a beneficial mutant spreading or + + align:start position:0% +a of a a beneficial mutant spreading or + + + align:start position:0% +a of a a beneficial mutant spreading or +you can have a population wave of an + + align:start position:0% +you can have a population wave of an + + + align:start position:0% +you can have a population wave of an +invasive species or whatnot and and you + + align:start position:0% +invasive species or whatnot and and you + + + align:start position:0% +invasive species or whatnot and and you +end up getting very similar Dynamics + + align:start position:0% +end up getting very similar Dynamics + + + align:start position:0% +end up getting very similar Dynamics +okay + + align:start position:0% + + + + align:start position:0% + +um right so the the basic idea here is + + align:start position:0% +um right so the the basic idea here is + + + align:start position:0% +um right so the the basic idea here is +that if you look at the + + align:start position:0% + + + + align:start position:0% + +uh the density as a function of position + + align:start position:0% +uh the density as a function of position + + + align:start position:0% +uh the density as a function of position +right if you start with you know there's + + align:start position:0% +right if you start with you know there's + + + align:start position:0% +right if you start with you know there's +one + + align:start position:0% +one + + + align:start position:0% +one +individual all right what's going to + + align:start position:0% + + + + align:start position:0% + +happen all right it's going to start + + align:start position:0% +happen all right it's going to start + + + align:start position:0% +happen all right it's going to start +dividing right U all right so we kind of + + align:start position:0% +dividing right U all right so we kind of + + + align:start position:0% +dividing right U all right so we kind of +get you know and it's going to come up + + align:start position:0% +get you know and it's going to come up + + + align:start position:0% +get you know and it's going to come up +and eventually it's going to saturate + + align:start position:0% +and eventually it's going to saturate + + + align:start position:0% +and eventually it's going to saturate +right at at this at this carrying + + align:start position:0% +right at at this at this carrying + + + align:start position:0% +right at at this at this carrying +capacity + + align:start position:0% +capacity + + + align:start position:0% +capacity +K all right and then you end up getting + + align:start position:0% +K all right and then you end up getting + + + align:start position:0% +K all right and then you end up getting +these spreading population waves that + + align:start position:0% +these spreading population waves that + + + align:start position:0% +these spreading population waves that +look like this + + align:start position:0% +look like this + + + align:start position:0% +look like this +okay right and the reason we're calling + + align:start position:0% +okay right and the reason we're calling + + + align:start position:0% +okay right and the reason we're calling +it a wave is because the shape of this + + align:start position:0% +it a wave is because the shape of this + + + align:start position:0% +it a wave is because the shape of this +front is the same over + + align:start position:0% +front is the same over + + + align:start position:0% +front is the same over +time all right so it can really be + + align:start position:0% +time all right so it can really be + + + align:start position:0% +time all right so it can really be +described as some uh some function + + align:start position:0% +described as some uh some function + + + align:start position:0% +described as some uh some function +as a function of x minus uh + + align:start position:0% +as a function of x minus uh + + + align:start position:0% +as a function of x minus uh +VT okay and right we are going to maybe + + align:start position:0% +VT okay and right we are going to maybe + + + align:start position:0% +VT okay and right we are going to maybe +typically assume that we're in a + + align:start position:0% +typically assume that we're in a + + + align:start position:0% +typically assume that we're in a +situation where we don't have to think + + align:start position:0% +situation where we don't have to think + + + align:start position:0% +situation where we don't have to think +about the left and the right because + + align:start position:0% +about the left and the right because + + + align:start position:0% +about the left and the right because +it's just too complicated so we'll just + + align:start position:0% +it's just too complicated so we'll just + + + align:start position:0% +it's just too complicated so we'll just +think imagine being that it's at + + align:start position:0% +think imagine being that it's at + + + align:start position:0% +think imagine being that it's at +saturation here and then we're looking + + align:start position:0% +saturation here and then we're looking + + + align:start position:0% +saturation here and then we're looking +at at some front that's moving to the + + align:start position:0% +at at some front that's moving to the + + + align:start position:0% +at at some front that's moving to the +right okay + + align:start position:0% +right okay + + + align:start position:0% +right okay +now by dimensional analysis we should be + + align:start position:0% +now by dimensional analysis we should be + + + align:start position:0% +now by dimensional analysis we should be +able to figure out what the velocity is + + align:start position:0% +able to figure out what the velocity is + + + align:start position:0% +able to figure out what the velocity is +going to + + align:start position:0% + + + + align:start position:0% + +be remember how much like dimensional + + align:start position:0% +be remember how much like dimensional + + + align:start position:0% +be remember how much like dimensional +analysis in this + + align:start position:0% +analysis in this + + + align:start position:0% +analysis in this +class yes all right so what we're going + + align:start position:0% +class yes all right so what we're going + + + align:start position:0% +class yes all right so what we're going +to do is we're going + + align:start position:0% +to do is we're going + + + align:start position:0% +to do is we're going +to I'll give you some option you know + + align:start position:0% +to I'll give you some option you know + + + align:start position:0% +to I'll give you some option you know +characters that you're going to be able + + align:start position:0% +characters that you're going to be able + + + align:start position:0% +characters that you're going to be able +to use in your + + align:start position:0% + + + + align:start position:0% + +quest all right so we can use r k + + align:start position:0% +quest all right so we can use r k + + + align:start position:0% +quest all right so we can use r k +d I'll give you a square root in case + + align:start position:0% +d I'll give you a square root in case + + + align:start position:0% +d I'll give you a square root in case +you find it + + align:start position:0% +you find it + + + align:start position:0% +you find it +useful + + align:start position:0% +useful + + + align:start position:0% +useful +and to the you can raise something to + + align:start position:0% +and to the you can raise something to + + + align:start position:0% +and to the you can raise something to +the second power as + + align:start position:0% +the second power as + + + align:start position:0% +the second power as +well all right so what you can do is uh + + align:start position:0% +well all right so what you can do is uh + + + align:start position:0% +well all right so what you can do is uh +you're going to set up your card so that + + align:start position:0% +you're going to set up your card so that + + + align:start position:0% +you're going to set up your card so that +when I look at it from the left to the + + align:start position:0% +when I look at it from the left to the + + + align:start position:0% +when I look at it from the left to the +right it will describe the velocity of + + align:start position:0% +right it will describe the velocity of + + + align:start position:0% +right it will describe the velocity of +this + + align:start position:0% + + + + align:start position:0% + +wave yeah all right I'll give you 30 + + align:start position:0% +wave yeah all right I'll give you 30 + + + align:start position:0% +wave yeah all right I'll give you 30 +seconds + + align:start position:0% +seconds + + + align:start position:0% +seconds +to so this is dimensional + + align:start position:0% + + + + align:start position:0% + +analysis for um for this wave + + align:start position:0% + + + + align:start position:0% + +velocity + + align:start position:0% + + + + align:start position:0% + +all right do you need more time yes okay + + align:start position:0% +all right do you need more time yes okay + + + align:start position:0% +all right do you need more time yes okay +that's + + align:start position:0% + + + + align:start position:0% + +fine + + align:start position:0% + + + + align:start position:0% + +all right let's go ahead and uh go ahead + + align:start position:0% +all right let's go ahead and uh go ahead + + + align:start position:0% +all right let's go ahead and uh go ahead +and + + align:start position:0% + + + + align:start position:0% + +vote all right uh construct your answer + + align:start position:0% +vote all right uh construct your answer + + + align:start position:0% +vote all right uh construct your answer +remember from me from left to + + align:start position:0% + + + + align:start position:0% + +right ready three two one + + align:start position:0% + + + + align:start position:0% + +all right all right we have we have + + align:start position:0% +all right all right we have we have + + + align:start position:0% +all right all right we have we have +trouble you know a a key skill is being + + align:start position:0% +trouble you know a a key skill is being + + + align:start position:0% +trouble you know a a key skill is being +able to imagine yourself in someone + + align:start position:0% +able to imagine yourself in someone + + + align:start position:0% +able to imagine yourself in someone +else's shoes U so you know if I'm + + align:start position:0% +else's shoes U so you know if I'm + + + align:start position:0% +else's shoes U so you know if I'm +viewing okay but that's okay all right + + align:start position:0% +viewing okay but that's okay all right + + + align:start position:0% +viewing okay but that's okay all right +so uh right so we have here this is kind + + align:start position:0% +so uh right so we have here this is kind + + + align:start position:0% +so uh right so we have here this is kind +of units of one over + + align:start position:0% +of units of one over + + + align:start position:0% +of units of one over +time this is some length Square length + + align:start position:0% +time this is some length Square length + + + align:start position:0% +time this is some length Square length +squared over time right mean whereas + + align:start position:0% +squared over time right mean whereas + + + align:start position:0% +squared over time right mean whereas +this is uh a + + align:start position:0% +this is uh a + + + align:start position:0% +this is uh a +density right if we want something that + + align:start position:0% +density right if we want something that + + + align:start position:0% +density right if we want something that +is a length over + + align:start position:0% +is a length over + + + align:start position:0% +is a length over +time then we're going to end up having + + align:start position:0% +time then we're going to end up having + + + align:start position:0% +time then we're going to end up having +to take R time D and take a square root + + align:start position:0% +to take R time D and take a square root + + + align:start position:0% +to take R time D and take a square root +right so you should this should be a d a + + align:start position:0% +right so you should this should be a d a + + + align:start position:0% +right so you should this should be a d a +c which is a square + + align:start position:0% +c which is a square + + + align:start position:0% +c which is a square +root + + align:start position:0% +root + + + align:start position:0% +root +of um of course it depends on how you're + + align:start position:0% +of um of course it depends on how you're + + + align:start position:0% +of um of course it depends on how you're +entering into your calculator if you + + align:start position:0% +entering into your calculator if you + + + align:start position:0% +entering into your calculator if you +have a scientific calculator or + + align:start position:0% +have a scientific calculator or + + + align:start position:0% +have a scientific calculator or +something else maybe right but all right + + align:start position:0% +something else maybe right but all right + + + align:start position:0% +something else maybe right but all right +um and indeed it ends up there's a two + + align:start position:0% +um and indeed it ends up there's a two + + + align:start position:0% +um and indeed it ends up there's a two +here so the uh this is the + + align:start position:0% +here so the uh this is the + + + align:start position:0% +here so the uh this is the +velocity this + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +yes okay I see what you're saying but + + align:start position:0% +yes okay I see what you're saying but + + + align:start position:0% +yes okay I see what you're saying but +yeah but it ends up not being true right + + align:start position:0% +yeah but it ends up not being true right + + + align:start position:0% +yeah but it ends up not being true right +so these derivative signs don't have any + + align:start position:0% +so these derivative signs don't have any + + + align:start position:0% +so these derivative signs don't have any +um any units right so this is this is + + align:start position:0% +um any units right so this is this is + + + align:start position:0% +um any units right so this is this is +still has units of a density divided by + + align:start position:0% +still has units of a density divided by + + + align:start position:0% +still has units of a density divided by +a length squared right so for unit + + align:start position:0% +a length squared right so for unit + + + align:start position:0% +a length squared right so for unit +purposes you just look at this thing and + + align:start position:0% +purposes you just look at this thing and + + + align:start position:0% +purposes you just look at this thing and +this so + + align:start position:0% +this so + + + align:start position:0% +this so +This squar does mean mean there's a + + align:start position:0% +This squar does mean mean there's a + + + align:start position:0% +This squar does mean mean there's a +length Square in the denominator but + + align:start position:0% +length Square in the denominator but + + + align:start position:0% +length Square in the denominator but +this Square doesn't do anything okay um + + align:start position:0% +this Square doesn't do anything okay um + + + align:start position:0% +this Square doesn't do anything okay um +yeah okay so so D is still a length + + align:start position:0% +yeah okay so so D is still a length + + + align:start position:0% +yeah okay so so D is still a length +squared over + + align:start position:0% +squared over + + + align:start position:0% +squared over +time okay U right so this is the famous + + align:start position:0% +time okay U right so this is the famous + + + align:start position:0% +time okay U right so this is the famous +uh fer velocity + + align:start position:0% + + + + align:start position:0% + +there there are some mathematical + + align:start position:0% +there there are some mathematical + + + align:start position:0% +there there are some mathematical +subtleties to all this that we're not + + align:start position:0% +subtleties to all this that we're not + + + align:start position:0% +subtleties to all this that we're not +really going to get into H I don't know + + align:start position:0% +really going to get into H I don't know + + + align:start position:0% +really going to get into H I don't know +I'm trouble okay + + align:start position:0% + + + + align:start position:0% + +velocity but this there are few features + + align:start position:0% +velocity but this there are few features + + + align:start position:0% +velocity but this there are few features +to + + align:start position:0% +to + + + align:start position:0% +to +highlight if the organism grows + + align:start position:0% +highlight if the organism grows + + + align:start position:0% +highlight if the organism grows +faster the wave is going to spread + + align:start position:0% +faster the wave is going to spread + + + align:start position:0% +faster the wave is going to spread +faster that makes sense if it has a + + align:start position:0% +faster that makes sense if it has a + + + align:start position:0% +faster that makes sense if it has a +larger Mobility also moves faster that + + align:start position:0% +larger Mobility also moves faster that + + + align:start position:0% +larger Mobility also moves faster that +makes sense of course the velocity is + + align:start position:0% +makes sense of course the velocity is + + + align:start position:0% +makes sense of course the velocity is +given by both both of those things right + + align:start position:0% +given by both both of those things right + + + align:start position:0% +given by both both of those things right +so this this wave coming out really is a + + align:start position:0% +so this this wave coming out really is a + + + align:start position:0% +so this this wave coming out really is a +population level property okay because + + align:start position:0% +population level property okay because + + + align:start position:0% +population level property okay because +it's not just growth it's not just + + align:start position:0% +it's not just growth it's not just + + + align:start position:0% +it's not just growth it's not just +motion it's a result of the coupled + + align:start position:0% +motion it's a result of the coupled + + + align:start position:0% +motion it's a result of the coupled +Division and diffusion that leads to + + align:start position:0% +Division and diffusion that leads to + + + align:start position:0% +Division and diffusion that leads to +this population wave + + align:start position:0% +this population wave + + + align:start position:0% +this population wave +spreading + + align:start position:0% + + + + align:start position:0% + +okay importantly to first order it + + align:start position:0% +okay importantly to first order it + + + align:start position:0% +okay importantly to first order it +doesn't depend on the carrying + + align:start position:0% + + + + align:start position:0% + +capacity okay at least within the + + align:start position:0% +capacity okay at least within the + + + align:start position:0% +capacity okay at least within the +deterministic regime + + align:start position:0% + + + + align:start position:0% + +okay well it would + + align:start position:0% +okay well it would + + + align:start position:0% +okay well it would +be okay so okay so first of all you'd + + align:start position:0% +be okay so okay so first of all you'd + + + align:start position:0% +be okay so okay so first of all you'd +say oh it's it would be sort of + + align:start position:0% +say oh it's it would be sort of + + + align:start position:0% +say oh it's it would be sort of +surprising if it if it really kept on + + align:start position:0% +surprising if it if it really kept on + + + align:start position:0% +surprising if it if it really kept on +spreading in the absence of growth but + + align:start position:0% +spreading in the absence of growth but + + + align:start position:0% +spreading in the absence of growth but +what you're pointing out is that if you + + align:start position:0% +what you're pointing out is that if you + + + align:start position:0% +what you're pointing out is that if you +just at one moment turn off Division + + align:start position:0% +just at one moment turn off Division + + + align:start position:0% +just at one moment turn off Division +then there will still be diffusion and + + align:start position:0% +then there will still be diffusion and + + + align:start position:0% +then there will still be diffusion and +it'll still keep on going right but this + + align:start position:0% +it'll still keep on going right but this + + + align:start position:0% +it'll still keep on going right but this +is the velocity of a wave when it's a + + align:start position:0% +is the velocity of a wave when it's a + + + align:start position:0% +is the velocity of a wave when it's a +wave when it's described by a function + + align:start position:0% +wave when it's described by a function + + + align:start position:0% +wave when it's described by a function +like this right so it's true that you + + align:start position:0% +like this right so it's true that you + + + align:start position:0% +like this right so it's true that you +could turn off Division and it'll still + + align:start position:0% +could turn off Division and it'll still + + + align:start position:0% +could turn off Division and it'll still +diffuse but then the shape is changing + + align:start position:0% +diffuse but then the shape is changing + + + align:start position:0% +diffuse but then the shape is changing +as well + + align:start position:0% +as well + + + align:start position:0% +as well +yeah + + align:start position:0% + + + + align:start position:0% + +okay all right I'm going to draw a few + + align:start position:0% +okay all right I'm going to draw a few + + + align:start position:0% +okay all right I'm going to draw a few +lines + + align:start position:0% +lines + + + align:start position:0% +lines +describing + + align:start position:0% +describing + + + align:start position:0% +describing +possible populations now let's assume + + align:start position:0% +possible populations now let's assume + + + align:start position:0% +possible populations now let's assume +that have the same diff motion diffusion + + align:start position:0% +that have the same diff motion diffusion + + + align:start position:0% +that have the same diff motion diffusion +all right I want to know which one has + + align:start position:0% +all right I want to know which one has + + + align:start position:0% +all right I want to know which one has +the largest + + align:start position:0% + + + + align:start position:0% + +velocity is + + align:start position:0% + + + + align:start position:0% + +it a b c + + align:start position:0% +it a b c + + + align:start position:0% +it a b c +d + + align:start position:0% + + + + align:start position:0% + +so same + + align:start position:0% + + + + align:start position:0% + +diffusion per capita growth rate is a + + align:start position:0% +diffusion per capita growth rate is a + + + align:start position:0% +diffusion per capita growth rate is a +function of the density for three + + align:start position:0% +function of the density for three + + + align:start position:0% +function of the density for three +different + + align:start position:0% +different + + + align:start position:0% +different +organisms + + align:start position:0% + + + + align:start position:0% + +all right ready three two + + align:start position:0% + + + + align:start position:0% + +one all right so I'd say we have a fair + + align:start position:0% +one all right so I'd say we have a fair + + + align:start position:0% +one all right so I'd say we have a fair +number of B + + align:start position:0% +number of B + + + align:start position:0% +number of B +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +D's it seems like a b it's B versus D + + align:start position:0% +D's it seems like a b it's B versus D + + + align:start position:0% +D's it seems like a b it's B versus D +all right now this is tricky because D + + align:start position:0% +all right now this is tricky because D + + + align:start position:0% +all right now this is tricky because D +we have not explicitly considered here + + align:start position:0% +we have not explicitly considered here + + + align:start position:0% +we have not explicitly considered here +um but it turns out that the answer is + + align:start position:0% +um but it turns out that the answer is + + + align:start position:0% +um but it turns out that the answer is +B okay certainly between these three + + align:start position:0% +B okay certainly between these three + + + align:start position:0% +B okay certainly between these three +these are all really logistic growth + + align:start position:0% +these are all really logistic growth + + + align:start position:0% +these are all really logistic growth +functions and so from the standpoint of + + align:start position:0% +functions and so from the standpoint of + + + align:start position:0% +functions and so from the standpoint of +here it's just this R and R is the + + align:start position:0% +here it's just this R and R is the + + + align:start position:0% +here it's just this R and R is the +division rate at Z zero cell density + + align:start position:0% +division rate at Z zero cell density + + + align:start position:0% +division rate at Z zero cell density +right the growth rate at zero cell the + + align:start position:0% +right the growth rate at zero cell the + + + align:start position:0% +right the growth rate at zero cell the +per capita growth rate at zero cell + + align:start position:0% +per capita growth rate at zero cell + + + align:start position:0% +per capita growth rate at zero cell +density is what determines the Velocity + + align:start position:0% +density is what determines the Velocity + + + align:start position:0% +density is what determines the Velocity +in a Fisher wave right and indeed that's + + align:start position:0% +in a Fisher wave right and indeed that's + + + align:start position:0% +in a Fisher wave right and indeed that's +true even if there's no decrease in the + + align:start position:0% +true even if there's no decrease in the + + + align:start position:0% +true even if there's no decrease in the +um the growth up right until you get to + + align:start position:0% +um the growth up right until you get to + + + align:start position:0% +um the growth up right until you get to +some carrying capacity right and indeed + + align:start position:0% +some carrying capacity right and indeed + + + align:start position:0% +some carrying capacity right and indeed +all of these cases + + align:start position:0% +all of these cases + + + align:start position:0% +all of these cases +the division rate and the growth rate + + align:start position:0% +the division rate and the growth rate + + + align:start position:0% +the division rate and the growth rate +that's relevant for the velocity + + align:start position:0% +that's relevant for the velocity + + + align:start position:0% +that's relevant for the velocity +is when it hits this + + align:start position:0% +is when it hits this + + + align:start position:0% +is when it hits this +axis okay um and indeed all of these + + align:start position:0% +axis okay um and indeed all of these + + + align:start position:0% +axis okay um and indeed all of these +waves are described as Fisher or pulled + + align:start position:0% +waves are described as Fisher or pulled + + + align:start position:0% +waves are described as Fisher or pulled +waves because there's a sense that the + + align:start position:0% +waves because there's a sense that the + + + align:start position:0% +waves because there's a sense that the +entire wave is determined by the front + + align:start position:0% +entire wave is determined by the front + + + align:start position:0% +entire wave is determined by the front +of the wave right so we drew this + + align:start position:0% +of the wave right so we drew this + + + align:start position:0% +of the wave right so we drew this +profile okay I didn't do that very well + + align:start position:0% +profile okay I didn't do that very well + + + align:start position:0% +profile okay I didn't do that very well +here this is an + + align:start position:0% + + + + align:start position:0% + +exponential and the exponential actually + + align:start position:0% +exponential and the exponential actually + + + align:start position:0% +exponential and the exponential actually +is what's pulling this wave uh there + + align:start position:0% +is what's pulling this wave uh there + + + align:start position:0% +is what's pulling this wave uh there +actually there ends up being a + + align:start position:0% +actually there ends up being a + + + align:start position:0% +actually there ends up being a +characteristic length scale here that is + + align:start position:0% +characteristic length scale here that is + + + align:start position:0% +characteristic length scale here that is +uh the square root of D over r right so + + align:start position:0% +uh the square root of D over r right so + + + align:start position:0% +uh the square root of D over r right so +this is the length scale of the + + align:start position:0% +this is the length scale of the + + + align:start position:0% +this is the length scale of the +exponential right and the + + align:start position:0% +exponential right and the + + + align:start position:0% +exponential right and the +velocity and the length scale are only + + align:start position:0% +velocity and the length scale are only + + + align:start position:0% +velocity and the length scale are only +functions + + align:start position:0% +functions + + + align:start position:0% +functions +of the division rate at z um in the + + align:start position:0% +of the division rate at z um in the + + + align:start position:0% +of the division rate at z um in the +limit of low cell density or low density + + align:start position:0% +limit of low cell density or low density + + + align:start position:0% +limit of low cell density or low density +of + + align:start position:0% +of + + + align:start position:0% +of +organism okay + + align:start position:0% +organism okay + + + align:start position:0% +organism okay +um the shape of what goes on here + + align:start position:0% +um the shape of what goes on here + + + align:start position:0% +um the shape of what goes on here +changes indeed out this the bulk + + align:start position:0% +changes indeed out this the bulk + + + align:start position:0% +changes indeed out this the bulk +properties of the wave but doesn't + + align:start position:0% +properties of the wave but doesn't + + + align:start position:0% +properties of the wave but doesn't +change uh doesn't change the + + align:start position:0% +change uh doesn't change the + + + align:start position:0% +change uh doesn't change the +velocity okay I just want to make one + + align:start position:0% +velocity okay I just want to make one + + + align:start position:0% +velocity okay I just want to make one +comparison of all this to uh because + + align:start position:0% +comparison of all this to uh because + + + align:start position:0% +comparison of all this to uh because +there's another qualitatively different + + align:start position:0% +there's another qualitatively different + + + align:start position:0% +there's another qualitatively different +kind of wave which is a so-called uh + + align:start position:0% +kind of wave which is a so-called uh + + + align:start position:0% +kind of wave which is a so-called uh +pushed + + align:start position:0% + + + + align:start position:0% + +wave and that's what happens if you have + + align:start position:0% +wave and that's what happens if you have + + + align:start position:0% +wave and that's what happens if you have +this a an alley effect in particular + + align:start position:0% +this a an alley effect in particular + + + align:start position:0% +this a an alley effect in particular +like a strong alley effect if you're if + + align:start position:0% +like a strong alley effect if you're if + + + align:start position:0% +like a strong alley effect if you're if +this thing + + align:start position:0% + + + + align:start position:0% + +looks like this is certainly possible + + align:start position:0% +looks like this is certainly possible + + + align:start position:0% +looks like this is certainly possible +Right This is an alley effect + + align:start position:0% + + + + align:start position:0% + +now if you just said oh the only thing + + align:start position:0% +now if you just said oh the only thing + + + align:start position:0% +now if you just said oh the only thing +that matters is the growth rate at low + + align:start position:0% +that matters is the growth rate at low + + + align:start position:0% +that matters is the growth rate at low +cell density you would say oh this this + + align:start position:0% +cell density you would say oh this this + + + align:start position:0% +cell density you would say oh this this +thing cannot possibly expand although it + + align:start position:0% +thing cannot possibly expand although it + + + align:start position:0% +thing cannot possibly expand although it +turns out that it it still is possible + + align:start position:0% +turns out that it it still is possible + + + align:start position:0% +turns out that it it still is possible +and this in this situation it would be + + align:start position:0% +and this in this situation it would be + + + align:start position:0% +and this in this situation it would be +called a push wave where your profile + + align:start position:0% +called a push wave where your profile + + + align:start position:0% +called a push wave where your profile +somehow maybe looks kind of similar but + + align:start position:0% +somehow maybe looks kind of similar but + + + align:start position:0% +somehow maybe looks kind of similar but +instead of it being the front of the + + align:start position:0% +instead of it being the front of the + + + align:start position:0% +instead of it being the front of the +wave that's pulling the wave instead + + align:start position:0% +wave that's pulling the wave instead + + + align:start position:0% +wave that's pulling the wave instead +it's diffusion around the bulk because + + align:start position:0% +it's diffusion around the bulk because + + + align:start position:0% +it's diffusion around the bulk because +the bulk is the part that is actually + + align:start position:0% +the bulk is the part that is actually + + + align:start position:0% +the bulk is the part that is actually +happily growling right because the front + + align:start position:0% +happily growling right because the front + + + align:start position:0% +happily growling right because the front +here in this case is + + align:start position:0% +here in this case is + + + align:start position:0% +here in this case is +dying right yet it still is possible to + + align:start position:0% +dying right yet it still is possible to + + + align:start position:0% +dying right yet it still is possible to +have a positive + + align:start position:0% +have a positive + + + align:start position:0% +have a positive +velocity okay and so this this is a then + + align:start position:0% +velocity okay and so this this is a then + + + align:start position:0% +velocity okay and so this this is a then +a qualit qualitatively different kind of + + align:start position:0% +a qualit qualitatively different kind of + + + align:start position:0% +a qualit qualitatively different kind of +uh population expansion right so + + align:start position:0% +uh population expansion right so + + + align:start position:0% +uh population expansion right so +cooperatively growing populations expand + + align:start position:0% +cooperatively growing populations expand + + + align:start position:0% +cooperatively growing populations expand +uh very differently from logistically + + align:start position:0% +uh very differently from logistically + + + align:start position:0% +uh very differently from logistically +growing populations and one of the + + align:start position:0% +growing populations and one of the + + + align:start position:0% +growing populations and one of the +things that in in the reading of physics + + align:start position:0% +things that in in the reading of physics + + + align:start position:0% +things that in in the reading of physics +today talked about is these different + + align:start position:0% +today talked about is these different + + + align:start position:0% +today talked about is these different +rates of uh of loss of heterozygosity + + align:start position:0% +rates of uh of loss of heterozygosity + + + align:start position:0% +rates of uh of loss of heterozygosity +and so forth in different populations + + align:start position:0% +and so forth in different populations + + + align:start position:0% +and so forth in different populations +and as you might expect the pulled waves + + align:start position:0% +and as you might expect the pulled waves + + + align:start position:0% +and as you might expect the pulled waves +have uh a smaller effective population + + align:start position:0% +have uh a smaller effective population + + + align:start position:0% +have uh a smaller effective population +size than the pushed waves right because + + align:start position:0% +size than the pushed waves right because + + + align:start position:0% +size than the pushed waves right because +here the relevant population is at the + + align:start position:0% +here the relevant population is at the + + + align:start position:0% +here the relevant population is at the +front that's at low density whereas here + + align:start position:0% +front that's at low density whereas here + + + align:start position:0% +front that's at low density whereas here +the relevant population is the bulk + + align:start position:0% +the relevant population is the bulk + + + align:start position:0% +the relevant population is the bulk +that's at high + + align:start position:0% +that's at high + + + align:start position:0% +that's at high +density right with that I think that we + + align:start position:0% +density right with that I think that we + + + align:start position:0% +density right with that I think that we +should quit but I will see you on + + align:start position:0% +should quit but I will see you on + + + align:start position:0% +should quit but I will see you on +Tuesday and we'll talk about this + + align:start position:0% +Tuesday and we'll talk about this + + + align:start position:0% +Tuesday and we'll talk about this +neutral Theory and ecology right + + align:start position:0% + + + + align:start position:0% + +thanks \ No newline at end of file diff --git a/4fZPNSMiRvk.txt b/4fZPNSMiRvk.txt new file mode 100644 index 0000000000000000000000000000000000000000..77933ff309c223a0bc8242fadbcd3225b12ea697 --- /dev/null +++ b/4fZPNSMiRvk.txt @@ -0,0 +1,3342 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Good afternoon. + +Yes. + +Let's have an on time departure. + +The topic of last class +was the ac Stark effect. + +And I said what I've +been saying to you, + +was additional [INAUDIBLE] +of the ac Stark difference + +from perturbation theory. + +But then I have three +points for discussion. + +The first one was [INAUDIBLE] +for the [INAUDIBLE] problem, + +[INAUDIBLE]. + +The second one was the +oscillator strength, + +which we almost finished. + +And today, I want to say a +few words about [INAUDIBLE] + +in [INAUDIBLE]. + +And eventually how +the ac Stark effect + +leads to the absorption +coefficient, which many of you + +use [INAUDIBLE]. + +So I mentioned that the +oscillator strength is actually + +one way to parametrize +the matrix element. + +We'll actually talk +most of the lecture + +today about matrix +element, but I + +come to that in a few minutes. + +From here, the matrix +element is nothing, + +but you get on with [INAUDIBLE]. + +Sure, it's a dimension +of the Bohr radius + +but we don't really think +in terms of lengths. + +There are two ways how you +want to use a matrix element. + +One is the matrix +elements squared, + +having some other +effect with which + +to [INAUDIBLE] this +likeness, an actual likeness + +against a number you should +know how to [INAUDIBLE]. + +Or another way to +parametrize matrix elements + +is by this [INAUDIBLE] +number, which + +is what we will +see in this class. + +And that's, of +course, also related + +to semi-classical physics. + +And I mentioned that +in the last class, + +that the oscillator +strength allows + +us to connect the quantum +mechanical treatment of an atom + +to the response of a +classical harmonic oscillator + +through the charge of +an external [INAUDIBLE]. + +So I used this expression, +it was the end of class last. + +I used this expression +for the matrix element + +in terms of the +oscillator strengths + +to give you a nice relationship +for strong transition + +as in the alkaline E lines, +where the oscillator strength + +is close to 1. + +You see that the +matrix element is + +1 over square of 2 +times the geometric mean + +of the complete wave +lengths of the electron, + +and the wave lengths +of the transition. + +So that's actually important +for the dipole approximation, + +because the concurrent wave +lengths of the electron + +is very, very small. + +So therefore if +the matrix element + +is the geometric +mean of the two, + +that means that +the matrix element + +is smaller than the +optical wave lengths. + +And therefore, +the matrix element + +is the length scale, +the relevant length + +scale of the atom +for transition. + +It is smaller than the +optical wave lengths. + +And that means-- and we'll +talk about it today-- + +that in the expression E to +the IKR, KR is really small. + +So we can do the +dipole approximation. + +Now I have a question for you. + +I did it, frankly, +because we don't + +have many questions +to discuss with. + +But I mentioned that there is +a sum rule for the oscillator + +strengths. + +And the sum rule limits it to 1. + +And if there's a really +strong transition, + +it kind of exhausts +the sum rule, + +and this is what I +was talking about. + +But because the thought crossed +my mind after last lecture, + +if I don't add +something to it, you + +may actually use it as a +proof, which would be wrong. + +That the matrix element cannot +be larger than what you see + +on the right hand side. + +On the other hand, we discussed +in the context of Rydberg atoms + +that Rydberg atoms can +have huge matrix elements. + +Matrix elements +which [INAUDIBLE] + +but they can really become huge. + +So how do you reconcile +the fact that Rydberg atoms + +in large instates, in +states with large strengths + +of [INAUDIBLE] numbers can +have huge matrix elements. + +How do you reconcile +it with our discussion + +of oscillator strengths +and sum rules? + +The answer is simple but subtle. + +So is it a proof that the +matrix elements are impossible? + +Or if big matrix elements, +huge matrix elements, + +are possible, what property +of the oscillator strengths + +did I not emphasize? + +I mean, keep watching. + +So first, are there atoms which +have huge matrix elements? + +Yes. + +Rydberg atoms. + +So the left hand side +can be really huge. + +On the right hand side, +we have the wave lengths + +of the transition +which can get large. + +You have to count +the wave lengths. + +But then you have the +oscillator strengths. + +And the oscillator +strengths, the sum + +of all oscillator +strengths is 1. + +But you have to be careful +that not all oscillator + +strengths have to be possible. + +The definition of the +oscillator strengths + +involves frequency from +one state to the next. + +And depending whether +you go up or down, + +the frequency has +positive or negative side. + +So therefore we have a sum rule. + +For the ground state, +all frequencies + +are positive because +you can only go up. + +So therefore the +sum rule is only + +very useful for +the ground state, + +because all oscillator +strengths are positive. + +And if one oscillator +strength is 1, + +you know no other transition +has any strength at all. + +However when you +have an excited state + +and you find an oscillator +strength which is 1, + +you could still have a lot +of other strong transitions, + +but their oscillator strengths +are positive and negative + +and they compensate for +each other in the sum rule. + +So just be careful about that. + +For the ground state-- and +this is what I've proven to you + +here, I think +fairly rigorously-- + +if you are in the ground state, +the transition matrix element + +cannot be larger than +the geometric mean + +of the [INAUDIBLE] wave lengths +and the [INAUDIBLE] wave + +lengths. + +But for excited states, +you have to be careful, + +because the oscillator +strengths can have cosines. + +OK. + +Any questions about that? + +Then let's talk quickly +about the third point + +I wanted to discuss. + +And this is the relationship +to the index of refraction. + +The polarizability here is +responsible for the index + +of refraction. + +Well, the polarizability +determines [INAUDIBLE] + +evaluate the constant and use +whatever relation you want, + +but for a common +physics purpose, + +this is sort of the +useful relation. + +This is the index of refraction. + +It's related to +the polarizability. + +And assuming that the +polarizability is small, + +you get this, the +parallel extension. + +So roughly saying n minus 1. + +The difference of the index +of refraction from the vacuum + +is proportionate to +the atomic density + +times the polarizability. + +OK. + +And we know this is what we +derive from the perturbation + +theory, that the +polarizability depends + +on a matrix element squared +and 1 over the cube. + +Now I want to sort of show you +that by just using that concept + +and putting in +phenomenologically dissipation, + +we can get a full expression +what happens to a laser + +beam crossing an atomic medium, +like a [INAUDIBLE] condensate. + +How much of the laser +beam is absorbed? + +And what is the feature +of the laser beam. + +In order to get interesting +or simple formula, + +I want to now parametrize +the matrix element + +by this correlated gamma. + +This will turn out with +an actual [INAUDIBLE], + +but right now, since +we haven't talked + +about spontaneous +emission, just say + +I replace the matrix +element by gamma. + +And then I can write +the index of refraction + +in the following way. + +But the matrix element squared +is now parametrized by gamma. + +I have also introduced +the coordinate sigma + +0, which will later be +the lesson in absorption + +for section for atoms. + +But again here, just use +it as a parametrization. + +I mean, I've not introduced +any new concepts. + +I've just rewritten this +expression in this way, + +involved sigma 0, which is a +cross-section, and gamma, which + +is an actual light. + +OK. + +The polarizability depended-- +that was perturbation + +theory-- 1 over the +energy denominator, + +or 1 over the [INAUDIBLE]. + +Now we have used, with +the oscillator strengths, + +the analogy to a classical +harmonic oscillator. + +And at some level, you know +that every harmonic oscillator + +must have little bit of damping. + +And so the same applies +to atomic oscillators. + +And if you can account +for the damping + +by putting into the frequency +denominator of the [INAUDIBLE], + +1 over delta. + +Give it an imaginary part. + +So I'm just telling +you here, yes. + +Every oscillator +has some damping, + +and I can phenomenologically +accounting for the damping + +by making the resonant +frequency, or the tuning, + +slightly complex by +adding imaginary part. + +Later on I want to express +all the tunings normalized + +to this line which is parallel +to a normalized [INAUDIBLE] + +imaginary part. + +OK. + +So we have the situation +that this expression, gamma + +over delta-- this +was the expression + +for the polarizability-- +now acquires + +a small imaginary part, and that +means it's a complex number. + +And I can now take this +expression separate it + +into an imaginary +part and a real part. + +So why do I do that? + +Well, the index of +refraction appears + +in the propagation +of the plane wave. + +If you're a plane +wave, the key vector + +is no longer the key +vector in vacuum. + +It's multiplied with +the index of refraction, + +and that's what I do here. + +And now you see +that immediately, + +an imaginary part of +the index of refraction + +leads to absorption. + +And the real part +leads to [INAUDIBLE]. + +OK. + +So what we have now is we have +this expression for the plane + +wave after it is propagated +through the medium. + +And we see there is +exponential absorption. + +Exponential absorption. + +On resonance, we have +an optimal density + +which is given by +this expression. + +And the second term here +give us a phase shift. + +And it's clear since we +have one medium which + +has a certain thickness that the +optical density and the phase + +shift are related. + +Yes. + +If you're on resonance, you +have the maximum optical density + +and the maximum absorption. + +And the optical +density, of course, + +is 1 over the +[INAUDIBLE] squared. + +[INAUDIBLE] + +Whereas for large detuning, +the phase shift goes as 1 + +over delta. + +It's the dispersive +scaling with the tuning, + +and this is also what we +had when we started out. + +When we would have started out +with the polarizability and not + +a decaying dissipation, because +far away from resonance, + +you simply have a regional +of dispersive effect, + +and dissipation doesn't occur. + +So anyway, I +thought I would just + +show that to you because this +is a full understanding of what + +happens to optical views +when they pass the atomic + +[INAUDIBLE]. + +It's nothing else than +the polarizability + +or the harmonic +oscillator response + +of an atom to +electromagnetic radiation. + +The only thing which is +non-derivative here is-- + +and that's what we will +discuss later in this course-- + +is in order to get the +final result, which + +you may want to use in +analyzing your data, + +you have to set the +dissipative, the damping + +of the harmonic oscillator, +equal with this gamma + +parameter. + +And that's something I cannot +tell you without talking about + +spontaneous emission. + +So just to remind you, I +introduce big gamma just + +as a parametrization +of the matrix element. + +Then I introduce +phenomenologically little gamma + +as just the damping of +the harmonic oscillator + +of those two quantities +for two levels [INAUDIBLE] + +are identical. + +And that's something I +cannot show you here, + +because this requires discussion +of spontaneous emission + +and the other modes of +the electromagnetic field. + +This is not covered by +a discussion of the ac + +polarizability. + +OK. + +Any questions? + +But still-- I know +I'm repeating myself-- + +I always find it interesting +that the whole physics + +of absorption, the +beams are absorbed, + +you can pretty much pull +it out of the response + +of a harmonic oscillator. + +It's only the damping rate +of the harmonic oscillator + +that this is simply +spontaneous emission. + +That's the only +point where you have + +to go beyond the ac Stark shift +and bring in the [INAUDIBLE] + +nature of the +electromagnetic field + +and all the empty +modes of the vacuum. + +Any questions about waves, +or in general interactions + +of atoms with electric +and magnetic fields? + +Well, then let's move on. + +We have talked about +electric and magnetic fields + +intimately for +very good reasons, + +because low frequency fields +are either electric or magnetic + +in nature. + +But ultimately, we +want to understand + +what happens when atoms +interact with light. + +And this is our +discussion for today. + +The outline of this +chapter is as follows. + +Today, all I want to discuss is +the coupling matrix in an atom. + +In other words, when we have +a Hamiltonian between state A + +and B, we have an +off-diagonal matrix element. + +And this off-diagonal matrix +element causes transitions. + +Or when we calculate it, the +effect of electric field-- + +the ec Stark effect or +the ac Stark effect, + +we assume there was a +quantity, state 1, state 2, + +and we put some +operator in between. + +So this was a matrix element +which connects the two states. + +And so far, we +have always assumed + +using the classical +multiple expansion + +of electromagnetic field energy +that this matrix element has + +the form electric field +times dipole matrix element. + +And therefore, the +relevant matrix element + +was the position operator of +the electron connecting the two + +states. + +So in a way, we have +used it all the time. + +But in any more advanced +discussion of atomic physics, + +you have two states. + +And as long as they +are coupled, you + +have something +which you call H1 2 + +or you call it +matrix element N1 2, + +and you're not even asking +where it comes from. + +When two levels are coupled, +they undergo Rabi oscillations. + +You have transitions. + +If you're in the excited state +and you have a matrix element, + +you get spontaneous emission. + +So a lot of the things +we want to discuss + +about atomic physics, +all they require + +a number which is a matrix +element between state + +1 and state 2. + +And today, I want to talk to +you about different mechanisms + +which can lead to +matrix element. + +We talked about the +dipole operator, + +but you also talk about +higher order possibilities, + +magnetic dipole coupling, or +electric [INAUDIBLE] coupling. + +And a little bit later-- +this is an outlook-- + +we will talk about +twofold uncoupling. + +But in the end, even if +it's a twofold uncoupling, + +for a lot or phenomena, +all you need is a coupling. + +A coupling means +a Rabi frequency. + +A Rabi frequency means Rabi +oscillation, and so on. + +So today the focus is, +what is the structure, what + +are the principles +behind this number, which + +is a relevant matrix element. + +OK. + +So that's today. + +Next week is spring +break, but when we resume, + +we then want to talk about what +is the matrix element doing? + +And there are two cases +which we have to consider. + +One is we can see it's +narrow band and broad band. + +This matrix element +can couple just + +to one move of the +electromagnetic field. + +Everything is coherent. + +We have coherent +Rabi oscillation. + +Or you can couple to +many modes, and then you + +have a broad band situation, +which may be described + +[INAUDIBLE] and this +[INAUDIBLE] unit. + +Very, very different behavior. + +So that's what we +then want to discuss. + +When atoms interact +with light, we + +have two very different +limiting cases, narrow band + +and broad band. + +And eventually, we want to +go beyond the semi-classical + +formulation of the +electromagnetic field + +and we'll talk about the +quantized electromagnetic + +field. + +OK. + +So let's talk about the +coupling between atoms + +and electromagnetic fields. + +I want to give you +very brief derivation + +of the canonical coupling +between electromagnetic fields + +and atoms. + +I know this is covered +in many textbooks, + +and we have a very +deep discussion + +about it using the full +QED formulas in A422, + +but I feel this +course A421 would not + +be complete without a +discussion like that. + +And secondly-- this +is so important + +if you hear it twice from +two different angles, that's + +probably useful-- I +just want to remind you + +that if you use classical +electromagnetism + +and the Lagrangian +formalism, you find the very + +elegant result that the coupling +to the electromagnetic field + +can be introduced by +modifying the momentum. + +That the canonical momentum +which appears in the Lagrangian + +equation is no longer +the mechanical momentum + +which gives rise to +kinetic energy, But? + +It is modified by +the vector potential. + +So therefore the +Hamiltonian-- at this point + +it's the classical +Hamiltonian, but then we + +use the same expression +in quantum mechanics. + +The Hamiltonian has kinetic +energy and potential energy. + +But the kinetic energy +is no longer p square. + +Because by p, I mean now +the canonical momentum. + +We have to correct for +the vector potential + +to go from the +canonical momentum + +to the mechanical momentum. + +And if we squared it, this +gives the kinetic energy. + +If you worry about +this sign here, + +I will assume now that +the electron has a charge. + +The charge q f the +electron was minus e, + +so that's why we have a plus +sign here and not a minus sign. + +OK. + +So we will use this fact that we +have to substitute the momentum + +operator by the +canonical momentum, which + +is no longer the +mechanical momentum. + +We used it also in our +quantum mechanical Hamiltonian + +in the Schrodinger equation. + +If you ask me, can you prove it? + +No. + +Nobody can prove it. + +We can never prove what a +quantum mechanical equation is. + +We can just use +physical understanding, + +physical analogies. + +And that's how quantum mechanics +was developed in [INAUDIBLE]. + +Based on the classic quantum +mechanical correspondence, + +this seems to be a very +reasonable assumption. + +And ultimately, this very +reasonable assumption + +has now withstood the test of +time for many, many decades, + +over almost 100 years. + +So that's why we assume that +doing the same substitution + +in the Schrodinger equation +for the momentum operator + +gives the right result, +but there is no way + +how you can rigorously +derive fundamental equations + +in physics. + +You can observe +nature, postulate them, + +and verify them. + +So therefore, this line, which +was the classical Hamiltonian, + +by interpreting +p as an operator, + +is now our quantum +mechanical Hamiltonian. + +And the one thing we +have to consider now + +is that once we have +quantum mechanical operator, + +we have to be careful +about compute order. + +That certain quantities +have to be ordered. + +It matters which +one we put first. + +What is convenient now is +to use the Coulomb gauge. + +In the Coulomb gauge, +diversions of A is zero. + +But the del operator, the +deliberative operator, + +is the operator of the +canonical momentum. + +And therefore, if you +use the Coulomb gauge, + +then we have commutativity +between the canonical momentum, + +p, and the vector potential. + +And that's sort of nice, +because if you take this square + +and square it out, we +get p dot A plus A dot p, + +but they are the same +in the Coulomb gauge. + +So therefore our Hamiltonian +has now the following terms. + +We call it H naught. + +And we assume that the Coulomb +potential of the nucleus, + +which eventually gets +the electronic structure + +of the atom, is included here. + +So this is the +Hamiltonian part which + +describes the +structure of atoms. + +And then we have two +terms which couple + +to the electromagnetic field. + +So this is p dot A or A dot p. + +It doesn't matter in +the Coulomb gauge. + +We call this the +interaction Hamiltonian. + +And now we get a +second order term, + +which is the A square term. + +Well, since it's second +order, we designate it. + +We use the symbol H2. + +In the following, we neglect +the second order term. + +The argument is for weak fields. + +It doesn't matter. + +It's not so important +because it's higher order. + +However, in A422, we +look at it more carefully + +and we can actually do a +canonical transformation which + +eliminates the A square term. + +So to drop it is not necessary. + +You can actually show with +a canonical transformation + +that I'm doing is actually +more exact than just + +saying small and delineated. + +But anyway, I don't want to +spend too much time on it. + +All I wanted to remind you, what +are the steps to obtain-- just + +give me one second-- to obtain +the interaction Hamiltonian, + +and that's what I want +to use for the remainder + +of this class. + +That we have the +coupling of momentum + +to the vector potential. + +We assume that the vector +potential-- we are not + +quantizing the +electromagnetic field. + +It's a semi-classical field. + +It's therefore a +classical vector. + +And we will +investigate what is now + +the coupling between an +atom for this Hamiltonian + +to a plane wave of the +electromagnetic field. + +So therefore we are introducing +for the vector potential + +the expression that the vector +potential has an Hamiltonian + +naught. + +The polarization p hat, and +then the plane wave factor + +e to the ikr minus i omega t. + +So this can be divided in +a much more rigorous way, + +but this is now the starting +point of our discussion. + +[INAUDIBLE] + +OK. + +Any questions about that? + +Yes. + +Matt. + +AUDIENCE: Is it a +little bit weird + +that you're going to take the +divergence of its particular A + +that's not 0? + +Since it's divergence of e to +the ik dot r, just k dot A? + +PROFESSOR: Sorry. + +You said the divergence +of A-- so you're + +asking what is the +divergence of A, + +if A is a plane +wave e to the ikr? + +AUDIENCE: [INAUDIBLE] the +propagation of [INAUDIBLE]? + +PROFESSOR: Yeah. + +What happens is, +the polarization is + +A, and if you take the +divergence of the plane wave, + +you get a K vector, so you get +this [INAUDIBLE] product of e + +dot k. + +And electromagnetic +waves propagate. + +The polarizations +[INAUDIBLE] propagation. + +So ultimately what you +find is with Coulomb gauge + +and the radiation +field is transverse. + +It is only polarization +[INAUDIBLE] propagation. + +OK. + +So we want to talk +about matrix element. + +So the matrix element +between two states. + +Du to the interaction +Hamiltonian for one plane wave + +has the e to the minus i omega +t dependence, which is trivial. + +I mean, in terms +of we will assume + +that there is a +monochromatic wave. + +And what you want +to discuss now is + +this time independent +factor, H ba. + +Let me get the factors. + +Let me get the polarization. + +So your relevant operator which +connects the two states A and B + +is the momentum operator. + +And now for the +plane wave, we want + +to do an expansion +in orders of kr. + +And the leading term will +be the dipole approximation + +and the next order +term will give rise + +to magnetic dipole and electric +quadrupole transitions. + +So first, the fact that +I can do this expansion + +requires that k dot A +is much smaller than 1. + +So it's a long wave +length approximation, + +which you can say is valid as +long as the atom is smaller + +than the wave length +we are talking about. + +And I will show you later when +I discuss the next higher order + +term that for atoms +in the ground state, + +this is actually also +an expansion alpha. + +So again we retrieve the +fine-structure constant. + +So when we do this expansion +of this plane wave exponential, + +every term is smaller +than the previous term + +by the fine-structure constant +alpha, which is 1 over 137. + +OK. + +So the leading term is +the 1, and this gives rise + +to the dipole approximation. + +So what I want to show +you now in one or two + +minutes is that this is indeed +the dipole approximation. + +It leads to a +matrix element which + +is electric field times +r, the dipole moment. + +What we have right now is A +dot p, the vector potential, + +times the momentum. + +So in other words, +I want to show you + +that the A dot p matrix element +is equivalent to an e dot r + +matrix element. + +This can be done with a +canonical transformation, which + +we'll do in A422, but here +let me sort of just show you + +the elementary discussion. + +We want to replace +the vector potential + +by the electric field. + +So therefore, we use the +fact that the electric field + +is the derivative of +the vector potential. + +And the derivative of +the vector potential + +means since we have an E the +minus i omega t dependence, + +that we simply multiply +with a factor of omega + +of the frequency. + +And what we obtain here +is then the amplitude + +of the electric field, E naught. + +So with that, we +have a matrix element + +which now involves +the electric field. + +But still the matrix element +of the momentum operator. + +But we can easily go from +the momentum operator + +to the position operator +by taking the fact + +that the momentum +operator is nothing + +else than the commutator of r +with the Hamiltonian H naught. + +The kinetic energy in +H naught is p square, + +and the commutator of r +with p square is simply p. + +So this is what I'm using here. + +And these are the p factors. + +So therefore if you take the +momentum operator between two + +states, we have this relation +between the momentum operator + +and the position operator. + +But we have not the +momentum operator. + +We have the commutator. + +And r H naught gives us r. + +But when H naught acts on the +a, it gives the energy in a. + +For the other part of +the commutator, which + +is H naught r, we can have H +naught act on the left hand + +side on b, and this +gives us the energy ab. + +For dividing by H +bar, what we get + +is the energy +difference, eb minus ea. + +Or in frequency units, omega ba. + +So this is now how we have +implemented the commutator. + +So that by inserting +this into this equation, + +we now finally obtain our +result for the matrix element + +in the dipole approximation. + +We have e, the electric field +amplitude, the polarization, + +the matrix element +b r a, omega ba, + +and here we have an 1 over +omega in the denominator, which + +came from the derivative of +the vector potential da dt. + +This here is the matrix +element of the dipole operator. + +So in other words, I +have derived for you + +that the interaction +matrix element + +in the dipole approximation +is the dipole operator + +times the electric field as +long as I make the approximation + +that this frequency factor's +on the order of [INAUDIBLE]. + +Now this is clearly the +case in your resonance, + +so you should be safe. + +However, if you do the +more rigorous derivation + +of the dipole Hamiltonian +using canonical transformation, + +this factor of omega ba +over omega does not appear. + +So again, the dipole +approximations + +is better than I +presented today. + +The two approximations +topping the A squared term + +and approximating this +ratio of frequencies with 1 + +is not necessary if you +use the other methods using + +canonical transformation. + +Any questions about that? + +Let me make one comment. + +I've shown you in +this derivation + +that the A dot p term, +the A dot p interaction + +within the dipole approximation +is identical to the e dot r + +interaction. + +So these are the same operators, +and if you would exactly + +calculate them in atomic +structure calculation, + +you would get the same coupling, +the same matrix element. + +However, in practice, there +are important differences. + +Because the E dot r +operator, the r operator, + +has a lot of weight +where the electron is + +far away from the nucleus +because it's multiplied with r. + +Whereas the p operator +emphasizes the derivative + +of the wave function, +and this is usually + +strong at close distances. + +So in the end, the results +have to be the same. + +But if you make an approximation +to your wave function, + +one formulation may be +numerically much more accurate + +than the other one. + +But fundamentally, the +two terms are the same + +and they are related the way +how I derived it for you. + +Yes? + +AUDIENCE: So when we say it's +the dipole approximation, + +does it mean that it's +a long wave length, + +or be the small field +or everything together. + +So what's the absolute +fundamental assumption of this? + +PROFESSOR: The absolute +fundamental assumption + +of the dipole +approximation is that we + +assume-- let me just scroll up. + +In the equation above, +we had an expression + +for the vector potential. + +And the dipole +approximation means + +that we can neglect the position +dependence of the vector + +potential A of r, +so we approximate A + +of r as being A evaluated +at the origin of the atom. + +And over the extent, over +the size of the atom, + +we do not have to consider +a spacial dependence + +of the vector potential. + +So this is sufficient. + +The other things that +e square is small + +and that we're +near resonance-- I + +have to make those +assumptions if I + +want to use this +elementary derivation. + +But with a canonical +transformation, + +as is discussed in +atom-photon interactions, + +you do not need those +additional assumptions. + +The only assumption behind +the dipole approximation + +is that one, and this means +that the extent of the atom + +is much smaller than the +optical wave lengths. + +OK. + +But there are situations where +the leading approximation + +vanishes. + +For instance, if two levels +have the same parity, + +then the dipole operator +between the two of them is 0. + +And then if you want to +have a transition between, + +or if you want to consider a +transition between those two + +levels, it will come +from next order terms. + +So let's now discuss higher +order radiation processes. + +So the motivation why I want to +discuss higher order radiation + +processes is because +in some basic courses, + +you only need the +dipole approximation. + +And you think the +dipole coupling + +is the only coupling +which exists in the world. + +And by going to +higher order, I want + +to show you that +this is not the case. + +Also I want to sort of +give you an idea what + +it means if you +have leading order + +transitions are forbidden. + +I want to sort of show +you how other terms come + +in which can couple two levels. + +And also, actually, when +you drive transitions + +within the hyper-fine structure +using radio frequency fields, + +you are not driving them +with the electric dipole + +approximation. + +You're driving them +with a magnetic dipole, + +and this is actually +the next approximation. + +So there's a number +of reasons why + +I want to show you what +the next order terms are, + +and how they actually +lead to beautiful result, + +magnetic dipole, and electric +quadrupole transitions. + +So our coupling term-- let +me just rewrite the equation. + +Let me now simplify the +notation by assuming + +that the polarization +is in the z direction + +and the propagation +is in the x direction. + +So then the coupling +had the dipole term. + +And the next order +term is ikx, and this + +is what we want to +investigate now. + +So the term kx or kr is smaller. + +And now I want to +show you explicitly + +that it's smaller by alpha. + +The k vector of the photon is +related to the frequency H bar + +omega divided by H bar z. + +If I approximate for +r, the relevant r + +when we indicate over +the wave function + +will be the Bohr radius. + +The relevant frequency, H bar +omega, well, it's a Rydberg. + +And the Rydberg is e square +over the Bohr radius. + +So now if I insert it, the +Bohr radius cancels out. + +And what we find is, +well, kr is dimensionless. + +We have to find something +which is dimensionless, + +but expressed by the fundamental +constants of atomic physics. + +And the only quantity which is +available for that-- it's not + +a surprise-- is alpha. + +The fine-structure constant. + +So therefore the +dipole approximation + +is actually the result of an +expansion of the plane wave + +e the ikr factor in +units of expansion + +in the fine-structure constant. + +OK. + +We want to look now +at the second term. + +And well, sometimes if +you deal with a term, + +we first make it +more complicated + +and then we simplify it. + +I want to sort of symmetrize +and anti-symmetrize it + +in the following way. + +This is p z x. + +So let me subtract z p x. + +But then, of course, +I have to add it. + +So now we have two terms. + +1 has a minus sign, +one has a plus sign. + +And as will see +in just a minute, + +is the first one is +magnetic dipole transition. + +The second one is electric +quadrupole transition. + +And we see that the first +one can be regarded as-- p + +z x is like p dot r. + +Its the y component of +the vector product and + +is therefore the y component of +the orbital angular momentum. + +OK. + +So let's focus for +now on this part. + +The second term, which is +the electric quadrupole term, + +we'll do in a few moments. + +The relevant matrix element +is now the matrix element + +of the orbital +angular momentum Ly. + +The p factor-- let +me just collect + +all of the constant imaginary +unit ehr AK over 2 mc. + +That looks complicated, +but it immediately + +simplifies when we realize that +this here is the Bohr magneton. + +And well, we still have +the vector potential. + +But the magnetic field is the +curl of the vector potential, + +and that means we will +assume that we have a vector + +potential propagating +in x, polarized in z. + +That means that our +magnetic field is that. + +So therefore ka, which +appears in our expression + +for the coupling, is +just the magnetic field. + +So therefore we find the +result that the next order + +term in the coupling +of the atoms + +to the electromagnetic +field have the simple form + +to the electromagnetic field. + +That it is the +magnetic field part + +of the electromagnetic wave +times the Bohr magneton + +times the matrix element, due +to the orbital angular momentum + +operator. + +And actually, if you take +the orbital angular momentum + +and multiply it with +the Bohr magneton, + +this is actually the operator +of the magnetic moment. + +Well, with a minus sign because +the electron is negative + +charged. + +Remember we had +introduced the operator + +for the magnetic moment. + +And the magnetic +moment was the g factor + +times the Bohr magneton times +the orbital angular momentum. + +And the g factor for +the orbital motion is 1. + +So therefore the interaction +we are talking about + +is the Bohr magneton +times the magnetic field. + +And, of course, what we +realize is the operator-- maybe + +I should back up for a second +and say what we actually + +realize is that +operator which couples + +to the electromagnetic field +has actually the form u dot b. + +This is exactly what we use +for the Zeeman effect in a DC + +magnetic field. + +But now the same +form u dot b appears + +for time dependent +magnetic field. + +And time depending +magnetic fields + +are not only creating +level shifts. + +They can also use transitions +through the matrix element. + +So in other words, +this whole exercise + +show you that the form u dot +b, which appeared naturally + +in the formulation +for DC magnetic field, + +also applies to AC +magnetic fields. + +But with that, I can +say, wait a moment. + +There are now two sources +for the magnetic movement + +of the atom. + +One is due to orbital +angular momentum, + +and the other one is due +to spin angular momentum. + +But the spin +angular momentum has + +a g factor, which is different. + +The approximation of the +[INAUDIBLE] creation is 2. + +So therefore I +mean, we will never + +get spin out of a +semi-classical discussion. + +Remember, we started with a +classical canonical treatment + +of the electromagnetic +field, canonical momentum. + +And now we are +running with it and we + +find that there is a coupling +between the magnetic field + +and the magnetic +moment of the atom. + +But, of course, we only get the +magnetic moment to the extent + +that it comes from +orbital motion. + +But in a semi-classical way, +I'm waving my hands now and say, + +well, what is valid +for the coupling + +to orbit to the magnetic moment +of the orbital angular momentum + +also applies to the speed. + +And I'm simply +adding the spin here. + +And with that, I've +derived for you + +the expression for the +interaction matrix element + +called M1. + +M1 is the magnetic +dipole transitions. + +Let me just write it down here. + +So this is nothing +else than u dot b. + +Any questions? + +Let me just summarize. + +You may find it +sort of interesting, + +when we discussed static +electric and static magnetic + +fields. + +For the static +electric field, we + +had an electric field +times the dipole. + +And we find this now as +a time independent term + +which can drive transitions +for interactions with time + +dependent electromagnetic +field, but we find it + +in the dipole approximation. + +The magnetic part, +u dot b, we find + +when we go to the next order. + +We find it as a +magnetic dipole term. + +But there are more +terms, and I just + +want you to illustrate +that and then + +I'll stop with that +multiple expansion. + +We had the second term, +the kr term, was this one. + +But then we sort of +anti-symmetrized it + +and symmetrized it. + +The first one here, we could +relate to orbital angular + +momentum and to the +magnetic moment. + +And now I would want to +discuss the second term. + +So that term uses a mixture +of position and momentum + +operators. + +But we know already how we can +get rid of momentum operators, + +namely by expressing momentum +operators as commutators + +with the Hamiltonian. + +So this gives us the commutator +of z with H naught times x + +plus z times the commutator +of x with H naught. + +OK. + +So we have two commutators. + +Each of them has two terms. + +That means a total +of four terms. + +And if you write +them down, you see + +that two are opposite +but equal and cancel. + +So therefore we are left +with two terms, which + +are minus H naught zx +plus zx times H naught. + +So this term has now the +following contribution + +to the coupling between +the levels A and B. + +So we have this +coupling matrix element. + +We have b factor mc Am. + +OK. + +So using the same approach +we used for the dipole matrix + +element, the H naught can act on +the state A on the right side, + +and can act on the state +B on the left hand side. + +So this gives us simply +the energy difference. + +And what is left is +now a matrix element + +which only involves +position operators, + +but it uses a product of 2. + +And now, again, we express +the vector potential + +by the electric field, +as we had done before. + +And therefore we have now +expressed our coupling yes, + +by an electric field. + +And we assume that in the +near resonant approximation, + +as we had used for +the dipole coupling, + +that this is the +frequency omega. + +OK. + +So what we are +realizing is that we + +have one part of the +interaction Hamiltonian + +which couples levels +A and B, has-- + +we call it E2, this +electric quadrupole + +because it involves elements +of the quadrupole tensor, + +or products of coordinates +x, y, y, z, x, z. + +And for this geometry, which +we assume with our plane wave, + +it is z, x. + +It couples to the +electric field. + +And this is the p factor. + +For a more general +geometry of plane waves + +with different polarization +going in different directions, + +we would have obtained different +products of coordinates. + +So let me indicate that, that +what we have picked out here + +is one specific component +of a tensor, which + +is sort of the tensor form +by using the position vector + +r twice. + +So in this derivation, +we found when + +we go beyond the +dipole approximation, + +when we take the kr term +in leading order, that we + +have two contributions. + +One is M1, magnetic dipole. + +The other one was +electric quadrupole. + +We realized-- I tried to +keep of all the p factors-- + +that the electric quadrupole +matrix element is imaginary, + +whereas the magnetic +dipole was u dot b. + +There was no imaginary unit. + +It's real. + +That means that you will +never have any interference + +effect between magnetic dipole +and electric quadrupole. + +Or in other words, +when we have processes + +like spontaneous +emission where we + +take the square of +the matrix element, + +the square of the +matrix element will + +be the sum of the squares +of the matrix element + +for magnetic dipole and +electric quadrupole transitions. + +So let me summarize. + +We have discussed +three different ways + +how we can have coupling +matrix elements between two + +states, electric +dipole, magnetic dipole, + +electric quadrupole, E1, M1, E2. + +The operator was the +electric dipole operator. + +Here it was the operator of +the magnetic movement, which + +is orbital angular momentum +and spin angular momentum. + +And for the quadrupole, it +was the quadratic expression + +in the spatial coordinates. + +You can also ask +what is the parity? + +The electric dipole +operator connects + +states with opposite parity, +whereas both magnetic dipole + +and electric quadrupole +connect states + +even with the same parity. + +Magnetic dipole and electric +quadrupole transition + +are often called +forbidden transitions. + +Well, you would say it's +a misnomer because they + +are transitions, so they are +allowed, but they are weak. + +But this is the language we use. + +Weak transitions +are forbidden, which + +simply means they don't appear. + +They are forbidden +in leading order, + +but when you go to higher +order, they are allowed. + +You can, of course, say if +they were completely forbidden, + +there would be no +need to discuss them. + +But since they +are only forbidden + +at a certain level, +then, of course, + +it's interesting +to discuss them. + +And a lot of narrow +transitions which + +are relevant for atomic +clocks are highly forbidden + +transitions. + +The strength of them, which +usually scales with transitions + +with the square of +the matrix element, + +is on the order of 5 +times 10 to the minus 5. + +So those transitions +are four or five orders + +of magnitude weaker Yeah than +an allowed E1 transition. + +So that's what they are. + +Questions? + +AUDIENCE: When people talk about +highly forbidden transitions, + +does this mean that's like +a optical transition, or how + +do we distinguish it from +just regularly forbidden? + +PROFESSOR: Actually I would +say forbidden transitions + +are weaker by alpha +to the power n. + +Here we have situations +where the matrix + +element is just +smaller by alpha. + +But, yes. + +Sometimes, yes. + +Some transitions are +highly forbidden. + +For instance-- I +try to remember-- + +if you have hydrogen 1s and 2s. + +Because of s states-- +actually, you + +are asking question about the +next chapter, namely about + +selection rules. + +Let me give it in words. + +The s, if you +connect two s states, + +they have both 0 +angular momentum. + +AUDIENCE: Yeah. + +PROFESSOR: So you cannot have a +quadrupole operator connecting + +the two. + +It would violate +the triangle rule. + +You cannot have angular momentum +of 0 and angular momentum of 2 + +and get angular momentum of 0. + +So therefore you +have a transition + +between two states +of the same parity. + +There is no dipole operator. + +There is no quadrupole operator. + +So you soon run into a situation +where it's highly forbidden. + +Sometimes you have the situation +that something is forbidden + +in non-relativistic +physics, but they're + +a relativistic term, +which makes it allowed. + +Well, there's also +that relativistic terms + +are fine-structure terms is +also an expansion alpha squared. + +So the symmetry may +allow it, but only + +in connection with +relativistic terms. + +I'm not an expert on +forbidden transitions, + +but usually you have transitions +which are multiply forbidden. + +They are forbidden +by spacial symmetry. + +For instance, in +the helium atom, + +singular triplet are +forbidden by spin symmetry. + +So if you have multiple +layers of being forbidden, + +then you get extremely +weak transitions. + +And one example, actually, are +the singular triplet transition + +in helium, or the 1s to +2s transition in hydrogen. + +They are not allowed +by simply going + +to the next order in +a multiple expansion. + +Yes? + +AUDIENCE: In ordinary +situations when + +you do have to possibly do at +least even more [INAUDIBLE] + +for the other transitions? + +PROFESSOR: I'm not +an expert on that. + +I'm not sure if there +is an atom which + +has a relevant transition which +is a [INAUDIBLE] transition. + +I've not heard about that. + +At least relevant examples +which are the fundamental atoms, + +helium and hydrogen. + +For hydrogen, at the +2s to 1 transition, + +the leading order +is the emission, + +the simultaneous +emission of two photons. + +So you have not +just one photon, you + +have two photons which, +of course, requires + +in the perturbation +expansion the immediate step. + +We discuss two +photon transitions + +at the end of this course. + +So in that case, it's +not in higher order + +in the single photon +multiple expansion, + +it becomes a +multi-photon transition. + +So this is one relevant case. + +And for helium, +triplet to singlet, + +this involves +relativistic physics. + +Actually, I mentioned it in +the other class on helium. + +I tried to look it up +and I want to show here, + +you have to go to this +order to get a transition. + +But when I tried to look +into the literature, + +I couldn't find a clear answer. + +Ultimately, it was +a relativistic term + +in the fully +relativistic formulation + +of the coupling of +electromagnetic fields + +to the atom. + +I'm not sure if you can put a +label on it and it would say, + +this is this and +this order term. + +It may actually +involve-- and we know + +that this happens in the +[INAUDIBLE] creation-- + +that spin and spacial degrees +become treated together + +in the [INAUDIBLE] creation, and +maybe it's one of those terms. + +Yes? + +AUDIENCE: So what's +the actual meaning + +of interacting with +different Hamiltonians? + +Like, you wrote square root +of Hamiltonians and then-- + +PROFESSOR: No. + +I meant actually the square +of the matrix element. + +AUDIENCE: Oh. + +Sorry. + +PROFESSOR: If you have, +for instance-- actually + +I will talk about it in +the next lecture when + +we discuss Fermi's golden rule. + +The transition strength +in Fermi's golden rule + +is proportionate to the +square of the matrix element. + +But now you would ask +the question, well, + +could we have some +interference between the two + +different processes? + +And I wanted to point +out at this level + +that we don't, because one +matrix element is imaginary, + +the other one is real. + +And if you take the complex +matrix element between two + +states and calculate +the square, the square + +of the complex matrix element +is the square of the real part + +plus the square of +the imaginary part, + +and there's no interference +trend between the two. + +So in other words, if you have +an atom which has a weak decay + +through M1 and a weak +decay through quadrupole, + +the two parts cannot +destructively interfere, + +because one is real, +one is imaginary. + +They add up in quadrature, +That's what I wanted to say. + +OK. + +So these were examples of +higher order transitions. + +And as the questions +have shown, this + +leads us to a discussion +of selection rules. + +Selection rules is nothing +else than a classification + +of possible transitions +according to symmetry. + +And it's a way of using well, +[INAUDIBLE] coefficients, + +angular momentum coupling, +or using, you would say, + +symmetry to figure out +if matrix elements are + +non-vanishing or vanishing. + +And I gave you +already one example, + +and I want to formalize it now. + +If you go between two s states +which have 0 angular momentum, + +you cannot have an operator +which is a quadrupole operator + +because-- and this is what +I want to tell you now-- + +the quadrupole operator is a +spherical tensor with two units + +of angular momentum. + +And this would forbid +the triangle rule. + +This would forbid "conservation" +of angular momentum. + +So that's what I want to +discuss now in the next chapter, + +or at least get started +for the next five minutes + +by discussing selection rules. + +So the introduction +to selection rules + +is that we have +forbidden transitions. + +Forbidden transitions +are suppressed + +because we are forced +to go to higher order, + +and this is usually +higher order in alpha. + +So forbidden transitions are +weaker by some power of alpha. + +And that means they require +higher approximations. + +And, of course, the +comparison is always + +the dipole transition. + +This is the dominant transition. + +This is the industrial +strengths transition. + +And from there on, +it can get weaker. + +So if can get weaker +by multiple expansion. + +We've just discussed that. + +It can get weaker +because you have + +to have a cascade of +dipole transitions. + +This would be +multi-photon processes, + +as we discuss later +in the course. + +It can get weaker +because they are exactly + +0 in a non-relativistic +approximation + +and require +relativistic effects. + +The example we have +encountered in this course + +is the singlet to triplet +transition in helium. + +Or there are transitions which +would not be allowed just + +for the electron, but if we +invoke hyperfine interactions + +with a nucleus, then +they become allowed. + +So it's a rich subject, and I'm +not an expert and I cannot do + +full justice to it. + +But I want to at least give +you some general rules how + +we discussed matrix elements. + +So what is always a good +quantum number, what is always + +a label for our atomic +states is angular momentum. + +Because atoms [INAUDIBLE] +through space, + +and there is +rotation in variance. + +So we always categorize our +atoms with angular momentum + +with the quantum numbers JM. + +And we are asking, +are there transitions + +between a state JM to a +state J prime M prime? + +And all other +quantum numbers, we + +can now summarize +with a label n. + +And now we have an operator. + +I gave you examples +for the operator. + +The magnetic moment, +the electric dipole, + +the quadrupole operator. + +But in general, every +operator can be written, + +can be expanded, in a +sum of spherical tensors. + +So what is discussed +in the classification + +of matrix elements. + +Our matrix elements +involving components, + +the operator are components +of a spherical tensor. + +So T is a spherical +tensor of rank l. + +And if you want a +simple definition + +of what is a +spherical tensor, you + +try to write an operator-- +like the position operator + +r-- you try to write +it as a sum of terms, + +and each term transforms like +a spherical harmonic Ylm. + +So in other words, we +can write every operator + +as a sum of spherical tensors. + +And a spherical tensor +is characterized + +that it transforms +under rotations exactly + +as the spherical harmonics Ylm. + +so every operator is now a +sum of spherical tensors. + +I don't want to get too much +into symmetry classification, + +but the story is that you +know the Ylm functions are + +compensator functions. + +Every function can be expanded +and swell to harmonics. + +And similarly, if +you have an operator, + +you can decompose +it into objects + +which transform under +rotation, and it's the Ylms. + +So you have a part +which transforms + +according to an object. + +And Ylm is the classification +of wave functions + +with angular momentum. + +And so therefore each operator +may not have a specific angular + +momentum, but can be written +as the sum of operators, + +each of which has +the same symmetry, + +the same transformation +properties, + +as a state of angular momentum. + +And I think I should +stop here, but let + +me just give you +the final message. + +So by doing that, by +separating the operator + +into a sum of spherical tensors, +we are actually now back + +in angular momentum. + +If you have a matrix +element-- and just + +think how you calculate it in +the Schrodinger representation. + +You have a wave +function, operator, + +and a wave function +we indicate go by. + +So what you have is, you have +the product of the objects. + +And now we can classify +them by angular momentum. + +And this is what I will +show you in the next class, + +is that ultimately the question +whether this matrix element is + +0 or not will boil +down to the question + +whether J prime and M +prime angular momentum + +can be added to l and m. + +And there is overlap with +angular momentum of JM. + +So we are back to the rules +for adding angular momentum. + +We get the triangle rule. + +We get the [INAUDIBLE] +quote unquote [INAUDIBLE]. + +OK. + +Enjoy the spring break, +and we meet on Monday + +after the spring break. \ No newline at end of file diff --git a/4t_Fqd5Hd2c.txt b/4t_Fqd5Hd2c.txt new file mode 100644 index 0000000000000000000000000000000000000000..cb0fec02326ddca354810a7202fc97ca9cbeaba6 --- /dev/null +++ b/4t_Fqd5Hd2c.txt @@ -0,0 +1,8707 @@ +align:start position:0% + +problem so we're seeing Matrix equations + + align:start position:0% +problem so we're seeing Matrix equations + + + align:start position:0% +problem so we're seeing Matrix equations +rather than differential equations um + + align:start position:0% +rather than differential equations um + + + align:start position:0% +rather than differential equations um +Jeff uh has asked me to say uh after + + align:start position:0% +Jeff uh has asked me to say uh after + + + align:start position:0% +Jeff uh has asked me to say uh after +today's lectures then are three and four + + align:start position:0% +today's lectures then are three and four + + + align:start position:0% +today's lectures then are three and four +and after that uh he's going to make + + align:start position:0% +and after that uh he's going to make + + + align:start position:0% +and after that uh he's going to make +them available in a third way right now + + align:start position:0% +them available in a third way right now + + + align:start position:0% +them available in a third way right now +they're on the web and they're also on + + align:start position:0% +they're on the web and they're also on + + + align:start position:0% +they're on the web and they're also on +regular VHS in the library and now uh by + + align:start position:0% +regular VHS in the library and now uh by + + + align:start position:0% +regular VHS in the library and now uh by +next week uh CD ROMs in the library for + + align:start position:0% +next week uh CD ROMs in the library for + + + align:start position:0% +next week uh CD ROMs in the library for +the first four lectures so CD ROM is the + + align:start position:0% +the first four lectures so CD ROM is the + + + align:start position:0% +the first four lectures so CD ROM is the +new thing and then the web has a list of + + align:start position:0% +new thing and then the web has a list of + + + align:start position:0% +new thing and then the web has a list of +the dates for the Overflow room uh we'll + + align:start position:0% +the dates for the Overflow room uh we'll + + + align:start position:0% +the dates for the Overflow room uh we'll +keep that updated so + + align:start position:0% +keep that updated so + + + align:start position:0% +keep that updated so +today's uh lecture three then is + + align:start position:0% +today's uh lecture three then is + + + align:start position:0% +today's uh lecture three then is +another really a major application of + + align:start position:0% +another really a major application of + + + align:start position:0% +another really a major application of +the framework that we saw last time for + + align:start position:0% +the framework that we saw last time for + + + align:start position:0% +the framework that we saw last time for +a line of Springs so I have I'm going to + + align:start position:0% +a line of Springs so I have I'm going to + + + align:start position:0% +a line of Springs so I have I'm going to +have that same framework with a with a + + align:start position:0% +have that same framework with a with a + + + align:start position:0% +have that same framework with a with a +set of unknown owns you but now they'll + + align:start position:0% +set of unknown owns you but now they'll + + + align:start position:0% +set of unknown owns you but now they'll +be the potentials the voltages so we're + + align:start position:0% +be the potentials the voltages so we're + + + align:start position:0% +be the potentials the voltages so we're +moving sort of toward electrical + + align:start position:0% +moving sort of toward electrical + + + align:start position:0% +moving sort of toward electrical +engineering rather than mechanical + + align:start position:0% +engineering rather than mechanical + + + align:start position:0% +engineering rather than mechanical +engineering + + align:start position:0% +engineering + + + align:start position:0% +engineering +and their voltages at these nodes so + + align:start position:0% +and their voltages at these nodes so + + + align:start position:0% +and their voltages at these nodes so +these are the nodes of a network and I I + + align:start position:0% +these are the nodes of a network and I I + + + align:start position:0% +these are the nodes of a network and I I +really think that networks + + align:start position:0% +really think that networks + + + align:start position:0% +really think that networks +are uh the best discret model for so so + + align:start position:0% +are uh the best discret model for so so + + + align:start position:0% +are uh the best discret model for so so +many problems in Applied Mathematics so + + align:start position:0% +many problems in Applied Mathematics so + + + align:start position:0% +many problems in Applied Mathematics so +so what we do with networks is uh really + + align:start position:0% +so what we do with networks is uh really + + + align:start position:0% +so what we do with networks is uh really +I think valuable and uh and you'll see + + align:start position:0% +I think valuable and uh and you'll see + + + align:start position:0% +I think valuable and uh and you'll see +the framework uh sort of in all its + + align:start position:0% +the framework uh sort of in all its + + + align:start position:0% +the framework uh sort of in all its +Glory uh so again the framework you + + align:start position:0% +Glory uh so again the framework you + + + align:start position:0% +Glory uh so again the framework you +remember before these were displacements + + align:start position:0% +remember before these were displacements + + + align:start position:0% +remember before these were displacements +of masses and now there are potentials + + align:start position:0% +of masses and now there are potentials + + + align:start position:0% +of masses and now there are potentials +or voltages at nodes and then you + + align:start position:0% +or voltages at nodes and then you + + + align:start position:0% +or voltages at nodes and then you +remember there's a matrix + + align:start position:0% +remember there's a matrix + + + align:start position:0% +remember there's a matrix +a that connects those to the second set + + align:start position:0% +a that connects those to the second set + + + align:start position:0% +a that connects those to the second set +of unknowns which are at the on the + + align:start position:0% +of unknowns which are at the on the + + + align:start position:0% +of unknowns which are at the on the +edges so there'll be let's see in my + + align:start position:0% +edges so there'll be let's see in my + + + align:start position:0% +edges so there'll be let's see in my +picture I'm seeing n equal + + align:start position:0% +picture I'm seeing n equal + + + align:start position:0% +picture I'm seeing n equal +four nodes and m equal let's see maybe + + align:start position:0% +four nodes and m equal let's see maybe + + + align:start position:0% +four nodes and m equal let's see maybe +I'll number the edges one two three four + + align:start position:0% +I'll number the edges one two three four + + + align:start position:0% +I'll number the edges one two three four +and five edges so I'm going to see + + align:start position:0% +and five edges so I'm going to see + + + align:start position:0% +and five edges so I'm going to see +five uh I'm going to see uh I I just + + align:start position:0% +five uh I'm going to see uh I I just + + + align:start position:0% +five uh I'm going to see uh I I just +knocked out the six Edge so that we + + align:start position:0% +knocked out the six Edge so that we + + + align:start position:0% +knocked out the six Edge so that we +would have a slightly smaller Matrix to + + align:start position:0% +would have a slightly smaller Matrix to + + + align:start position:0% +would have a slightly smaller Matrix to +work + + align:start position:0% +work + + + align:start position:0% +work +with um okay so this is a a that's a + + align:start position:0% +with um okay so this is a a that's a + + + align:start position:0% +with um okay so this is a a that's a +directed + + align:start position:0% +directed + + + align:start position:0% +directed +graph a directed graph means a bunch of + + align:start position:0% +graph a directed graph means a bunch of + + + align:start position:0% +graph a directed graph means a bunch of +nodes and edges connecting some of the + + align:start position:0% +nodes and edges connecting some of the + + + align:start position:0% +nodes and edges connecting some of the +nodes and directed means that there's an + + align:start position:0% +nodes and directed means that there's an + + + align:start position:0% +nodes and directed means that there's an +arrow a direction on every Edge so that + + align:start position:0% +arrow a direction on every Edge so that + + + align:start position:0% +arrow a direction on every Edge so that +if we have a + + align:start position:0% +if we have a + + + align:start position:0% +if we have a +current and we say the value of that + + align:start position:0% +current and we say the value of that + + + align:start position:0% +current and we say the value of that +current is three that means it's three + + align:start position:0% +current is three that means it's three + + + align:start position:0% +current is three that means it's three +amps in the direction of the arrow if we + + align:start position:0% +amps in the direction of the arrow if we + + + align:start position:0% +amps in the direction of the arrow if we +say the value of the those are going to + + align:start position:0% +say the value of the those are going to + + + align:start position:0% +say the value of the those are going to +be the components of w if we say a + + align:start position:0% +be the components of w if we say a + + + align:start position:0% +be the components of w if we say a +component of w is negative all that + + align:start position:0% +component of w is negative all that + + + align:start position:0% +component of w is negative all that +means is the currents going against the + + align:start position:0% +means is the currents going against the + + + align:start position:0% +means is the currents going against the +arrow so the + + align:start position:0% +arrow so the + + + align:start position:0% +arrow so the +the the arrow directions are totally + + align:start position:0% +the the arrow directions are totally + + + align:start position:0% +the the arrow directions are totally +arbitrary we just have to assign a + + align:start position:0% +arbitrary we just have to assign a + + + align:start position:0% +arbitrary we just have to assign a +Direction so that we have a rule for + + align:start position:0% +Direction so that we have a rule for + + + align:start position:0% +Direction so that we have a rule for +plus and minus signs of currents okay so + + align:start position:0% +plus and minus signs of currents okay so + + + align:start position:0% +plus and minus signs of currents okay so +so our framework is begins with a a + + align:start position:0% +so our framework is begins with a a + + + align:start position:0% +so our framework is begins with a a +graph a network and then I'm interested + + align:start position:0% +graph a network and then I'm interested + + + align:start position:0% +graph a network and then I'm interested +in the potentials at the nodes so this + + align:start position:0% +in the potentials at the nodes so this + + + align:start position:0% +in the potentials at the nodes so this +is at the nodes so this is U1 to + + align:start position:0% +is at the nodes so this is U1 to + + + align:start position:0% +is at the nodes so this is U1 to +u4 and then potential differences on the + + align:start position:0% +u4 and then potential differences on the + + + align:start position:0% +u4 and then potential differences on the +edges emphasize that there there'll be + + align:start position:0% +edges emphasize that there there'll be + + + align:start position:0% +edges emphasize that there there'll be +five of them then M of them M potential + + align:start position:0% +five of them then M of them M potential + + + align:start position:0% +five of them then M of them M potential +differences on the edges then we're + + align:start position:0% +differences on the edges then we're + + + align:start position:0% +differences on the edges then we're +really our other key known as the + + align:start position:0% +really our other key known as the + + + align:start position:0% +really our other key known as the +currents the flows along those edges and + + align:start position:0% +currents the flows along those edges and + + + align:start position:0% +currents the flows along those edges and +so on each Edge there well so you + + align:start position:0% +so on each Edge there well so you + + + align:start position:0% +so on each Edge there well so you +remember there's a matrix capital + + align:start position:0% +remember there's a matrix capital + + + align:start position:0% +remember there's a matrix capital +c that expresses the physics of the + + align:start position:0% +c that expresses the physics of the + + + align:start position:0% +c that expresses the physics of the +problem the the relationship between how + + align:start position:0% +problem the the relationship between how + + + align:start position:0% +problem the the relationship between how +much current flows and this + + align:start position:0% +much current flows and this + + + align:start position:0% +much current flows and this +electromotive Force how much force is + + align:start position:0% +electromotive Force how much force is + + + align:start position:0% +electromotive Force how much force is +making it + + align:start position:0% +making it + + + align:start position:0% +making it +flow and then finally well you everybody + + align:start position:0% +flow and then finally well you everybody + + + align:start position:0% +flow and then finally well you everybody +I hope remembers the the beauty of this + + align:start position:0% +I hope remembers the the beauty of this + + + align:start position:0% +I hope remembers the the beauty of this +framework is that the third Matrix that + + align:start position:0% +framework is that the third Matrix that + + + align:start position:0% +framework is that the third Matrix that +connects things together is exactly a + + align:start position:0% +connects things together is exactly a + + + align:start position:0% +connects things together is exactly a +transpose of that one so the third + + align:start position:0% +transpose of that one so the third + + + align:start position:0% +transpose of that one so the third +Matrix is will be a transpose we hope I + + align:start position:0% +Matrix is will be a transpose we hope I + + + align:start position:0% +Matrix is will be a transpose we hope I +mean I can't just say it is I have to + + align:start position:0% +mean I can't just say it is I have to + + + align:start position:0% +mean I can't just say it is I have to +understand what this so there's some + + align:start position:0% +understand what this so there's some + + + align:start position:0% +understand what this so there's some +balance equation right there's always a + + align:start position:0% +balance equation right there's always a + + + align:start position:0% +balance equation right there's always a +equation of balance that will that will + + align:start position:0% +equation of balance that will that will + + + align:start position:0% +equation of balance that will that will +uh and it'll be Kirk off's current law + + align:start position:0% +uh and it'll be Kirk off's current law + + + align:start position:0% +uh and it'll be Kirk off's current law +in this case and we'll see it carefully + + align:start position:0% +in this case and we'll see it carefully + + + align:start position:0% +in this case and we'll see it carefully +so shall I go through the four the three + + align:start position:0% +so shall I go through the four the three + + + align:start position:0% +so shall I go through the four the three +uh steps of the + + align:start position:0% +uh steps of the + + + align:start position:0% +uh steps of the +framework uh for a network now instead + + align:start position:0% +framework uh for a network now instead + + + align:start position:0% +framework uh for a network now instead +of for a line of Springs okay so what's + + align:start position:0% +of for a line of Springs okay so what's + + + align:start position:0% +of for a line of Springs okay so what's +a what's the Matrix that connects + + align:start position:0% +a what's the Matrix that connects + + + align:start position:0% +a what's the Matrix that connects +potentials at + + align:start position:0% +potentials at + + + align:start position:0% +potentials at +nodes U1 U2 u3 u4 to potential + + align:start position:0% +nodes U1 U2 u3 u4 to potential + + + align:start position:0% +nodes U1 U2 u3 u4 to potential +differences well it's called the + + align:start position:0% +differences well it's called the + + + align:start position:0% +differences well it's called the +incidence Matrix + + align:start position:0% +incidence Matrix + + + align:start position:0% +incidence Matrix +so it's easy to write down this + + align:start position:0% +so it's easy to write down this + + + align:start position:0% +so it's easy to write down this +incidence Matrix so here here I'm going + + align:start position:0% +incidence Matrix so here here I'm going + + + align:start position:0% +incidence Matrix so here here I'm going +to fill in The Matrix and the size of it + + align:start position:0% +to fill in The Matrix and the size of it + + + align:start position:0% +to fill in The Matrix and the size of it +it's going to have a row for every edge + + align:start position:0% +it's going to have a row for every edge + + + align:start position:0% +it's going to have a row for every edge +of the graph the Matrix is going to tell + + align:start position:0% +of the graph the Matrix is going to tell + + + align:start position:0% +of the graph the Matrix is going to tell +us + + align:start position:0% +us + + + align:start position:0% +us +exactly what's the graph what the what + + align:start position:0% +exactly what's the graph what the what + + + align:start position:0% +exactly what's the graph what the what +the connections are in the graph it's + + align:start position:0% +the connections are in the graph it's + + + align:start position:0% +the connections are in the graph it's +the connection Matrix and after I write + + align:start position:0% +the connection Matrix and after I write + + + align:start position:0% +the connection Matrix and after I write +down the Matrix I could erase the graph + + align:start position:0% +down the Matrix I could erase the graph + + + align:start position:0% +down the Matrix I could erase the graph +because I could draw it again reading + + align:start position:0% +because I could draw it again reading + + + align:start position:0% +because I could draw it again reading +off the Matrix okay so there's a row + + align:start position:0% +off the Matrix okay so there's a row + + + align:start position:0% +off the Matrix okay so there's a row +this row corresponds to Edge + + align:start position:0% +this row corresponds to Edge + + + align:start position:0% +this row corresponds to Edge +one okay so we look at Edge one it goes + + align:start position:0% +one okay so we look at Edge one it goes + + + align:start position:0% +one okay so we look at Edge one it goes +from node one and enters node two the + + align:start position:0% +from node one and enters node two the + + + align:start position:0% +from node one and enters node two the +arrow having been that way so on this + + align:start position:0% +arrow having been that way so on this + + + align:start position:0% +arrow having been that way so on this +first row of the Matrix I'll give that + + align:start position:0% +first row of the Matrix I'll give that + + + align:start position:0% +first row of the Matrix I'll give that +information this way that a minus one + + align:start position:0% +information this way that a minus one + + + align:start position:0% +information this way that a minus one +for the node it Le leaves a plus one for + + align:start position:0% +for the node it Le leaves a plus one for + + + align:start position:0% +for the node it Le leaves a plus one for +the node it enters and nodes three and + + align:start position:0% +the node it enters and nodes three and + + + align:start position:0% +the node it enters and nodes three and +four + + align:start position:0% +four + + + align:start position:0% +four +aren't involved with Edge one okay can + + align:start position:0% +aren't involved with Edge one okay can + + + align:start position:0% +aren't involved with Edge one okay can +we fill in the second row so Edge two I + + align:start position:0% +we fill in the second row so Edge two I + + + align:start position:0% +we fill in the second row so Edge two I +look at Edge two it goes from one to + + align:start position:0% +look at Edge two it goes from one to + + + align:start position:0% +look at Edge two it goes from one to +three so I put a minus one there and a + + align:start position:0% +three so I put a minus one there and a + + + align:start position:0% +three so I put a minus one there and a +one there then Edge three goes from two + + align:start position:0% +one there then Edge three goes from two + + + align:start position:0% +one there then Edge three goes from two +to three so you see the kind of Matrix + + align:start position:0% +to three so you see the kind of Matrix + + + align:start position:0% +to three so you see the kind of Matrix +we're getting edge four goes from 1 to + + align:start position:0% +we're getting edge four goes from 1 to + + + align:start position:0% +we're getting edge four goes from 1 to +four Edge five goes from 2 to 4 and + + align:start position:0% +four Edge five goes from 2 to 4 and + + + align:start position:0% +four Edge five goes from 2 to 4 and +that's + + align:start position:0% +that's + + + align:start position:0% +that's +it so that's the + + align:start position:0% + + + + align:start position:0% + +Matrix that's the that Matrix then tells + + align:start position:0% +Matrix that's the that Matrix then tells + + + align:start position:0% +Matrix that's the that Matrix then tells +us everything about the + + align:start position:0% +us everything about the + + + align:start position:0% +us everything about the +graph okay and it's the Matrix that + + align:start position:0% +graph okay and it's the Matrix that + + + align:start position:0% +graph okay and it's the Matrix that +produces differences let's let me show + + align:start position:0% +produces differences let's let me show + + + align:start position:0% +produces differences let's let me show +you how it does that I I I claim is that + + align:start position:0% +you how it does that I I I claim is that + + + align:start position:0% +you how it does that I I I claim is that +if I multiply that + + align:start position:0% +if I multiply that + + + align:start position:0% +if I multiply that +Matrix let's just do it by U the vector + + align:start position:0% +Matrix let's just do it by U the vector + + + align:start position:0% +Matrix let's just do it by U the vector +of of potential so or voltages at the + + align:start position:0% +of of potential so or voltages at the + + + align:start position:0% +of of potential so or voltages at the +nodes so this is at the nodes and what + + align:start position:0% +nodes so this is at the nodes and what + + + align:start position:0% +nodes so this is at the nodes and what +do we get if I do this multiplication + + align:start position:0% +do we get if I do this multiplication + + + align:start position:0% +do we get if I do this multiplication +well the first row + + align:start position:0% +well the first row + + + align:start position:0% +well the first row +produces U2 minus + + align:start position:0% +produces U2 minus + + + align:start position:0% +produces U2 minus +U1 the second row produces you doing + + align:start position:0% +U1 the second row produces you doing + + + align:start position:0% +U1 the second row produces you doing +that multiplication u3 - + + align:start position:0% +that multiplication u3 - + + + align:start position:0% +that multiplication u3 - +U1 then u3 - + + align:start position:0% +U1 then u3 - + + + align:start position:0% +U1 then u3 - +U2 and u4 - U1 and U minus + + align:start position:0% +U2 and u4 - U1 and U minus + + + align:start position:0% +U2 and u4 - U1 and U minus +U2 so you see that that may + + align:start position:0% + + + + align:start position:0% + +starts with the potentials just like + + align:start position:0% +starts with the potentials just like + + + align:start position:0% +starts with the potentials just like +previously last time it started with the + + align:start position:0% +previously last time it started with the + + + align:start position:0% +previously last time it started with the +displacements and + + align:start position:0% +displacements and + + + align:start position:0% +displacements and +then multiplying by that Matrix produces + + align:start position:0% +then multiplying by that Matrix produces + + + align:start position:0% +then multiplying by that Matrix produces +potential differences + + align:start position:0% +potential differences + + + align:start position:0% +potential differences +okay so that Matrix is almost + + align:start position:0% +okay so that Matrix is almost + + + align:start position:0% +okay so that Matrix is almost +perfect but it's not quite + + align:start position:0% +perfect but it's not quite + + + align:start position:0% +perfect but it's not quite +perfect uh and that's why I've called it + + align:start position:0% +perfect uh and that's why I've called it + + + align:start position:0% +perfect uh and that's why I've called it +for the moment a + + align:start position:0% +for the moment a + + + align:start position:0% +for the moment a +zero because it's got a problem that we + + align:start position:0% +zero because it's got a problem that we + + + align:start position:0% +zero because it's got a problem that we +have to deal + + align:start position:0% + + + + align:start position:0% + +with I so like I'll often ask uh okay + + align:start position:0% +with I so like I'll often ask uh okay + + + align:start position:0% +with I so like I'll often ask uh okay +what's the null space What are the + + align:start position:0% +what's the null space What are the + + + align:start position:0% +what's the null space What are the +Solutions in this + + align:start position:0% +Solutions in this + + + align:start position:0% +Solutions in this +situation what 's would give all + + align:start position:0% +situation what 's would give all + + + align:start position:0% +situation what 's would give all +zeros so so the the null space are then + + align:start position:0% +zeros so so the the null space are then + + + align:start position:0% +zeros so so the the null space are then +the solutions to a u = 0 and + + align:start position:0% +the solutions to a u = 0 and + + + align:start position:0% +the solutions to a u = 0 and +and remember the situation if if there + + align:start position:0% +and remember the situation if if there + + + align:start position:0% +and remember the situation if if there +are solutions to that then we got a + + align:start position:0% +are solutions to that then we got a + + + align:start position:0% +are solutions to that then we got a +problem + + align:start position:0% +problem + + + align:start position:0% +problem +because our matrices won't be invertible + + align:start position:0% +because our matrices won't be invertible + + + align:start position:0% +because our matrices won't be invertible +you remember in the in the in the + + align:start position:0% +you remember in the in the in the + + + align:start position:0% +you remember in the in the in the +springs the the hanging Springs were + + align:start position:0% +springs the the hanging Springs were + + + align:start position:0% +springs the the hanging Springs were +fine The Matrix a was had had no uh + + align:start position:0% +fine The Matrix a was had had no uh + + + align:start position:0% +fine The Matrix a was had had no uh +there were no solutions to a u equals z + + align:start position:0% +there were no solutions to a u equals z + + + align:start position:0% +there were no solutions to a u equals z +except the zero solution but you + + align:start position:0% +except the zero solution but you + + + align:start position:0% +except the zero solution but you +remember there was that third + + align:start position:0% +remember there was that third + + + align:start position:0% +remember there was that third +possibility it had wasn't fixed at + + align:start position:0% +possibility it had wasn't fixed at + + + align:start position:0% +possibility it had wasn't fixed at +either end free free Springs and in that + + align:start position:0% +either end free free Springs and in that + + + align:start position:0% +either end free free Springs and in that +case there was a solution and in this + + align:start position:0% +case there was a solution and in this + + + align:start position:0% +case there was a solution and in this +case there is a solution and what is it + + align:start position:0% +case there is a solution and what is it + + + align:start position:0% +case there is a solution and what is it +all Conant all constant right and of + + align:start position:0% +all Conant all constant right and of + + + align:start position:0% +all Conant all constant right and of +course we see that in words if all the + + align:start position:0% +course we see that in words if all the + + + align:start position:0% +course we see that in words if all the +potentials are equal then all the + + align:start position:0% +potentials are equal then all the + + + align:start position:0% +potentials are equal then all the +potential differences are zero in other + + align:start position:0% +potential differences are zero in other + + + align:start position:0% +potential differences are zero in other +words the potentials can only be + + align:start position:0% +words the potentials can only be + + + align:start position:0% +words the potentials can only be +determined up to a constant we could add + + align:start position:0% +determined up to a constant we could add + + + align:start position:0% +determined up to a constant we could add +a constant to all the potenti poal it + + align:start position:0% +a constant to all the potenti poal it + + + align:start position:0% +a constant to all the potenti poal it +wouldn't change the potential + + align:start position:0% +wouldn't change the potential + + + align:start position:0% +wouldn't change the potential +differences it wouldn't change the + + align:start position:0% +differences it wouldn't change the + + + align:start position:0% +differences it wouldn't change the +currents it wouldn't change uh current + + align:start position:0% +currents it wouldn't change uh current + + + align:start position:0% +currents it wouldn't change uh current +balance and therefore we only know + + align:start position:0% +balance and therefore we only know + + + align:start position:0% +balance and therefore we only know +potentials up to a constant + + align:start position:0% +potentials up to a constant + + + align:start position:0% +potentials up to a constant +so one way to deal with that + + align:start position:0% + + + + align:start position:0% + +is okay let me let me see that same + + align:start position:0% +is okay let me let me see that same + + + align:start position:0% +is okay let me let me see that same +thing with respect to the Matrix before + + align:start position:0% +thing with respect to the Matrix before + + + align:start position:0% +thing with respect to the Matrix before +I before I remove that problem uh if you + + align:start position:0% +I before I remove that problem uh if you + + + align:start position:0% +I before I remove that problem uh if you +look at so I just want to we understand + + align:start position:0% +look at so I just want to we understand + + + align:start position:0% +look at so I just want to we understand +now that this Matrix has the vector one + + align:start position:0% +now that this Matrix has the vector one + + + align:start position:0% +now that this Matrix has the vector one +one one one that that Vector of ones + + align:start position:0% +one one one that that Vector of ones + + + align:start position:0% +one one one that that Vector of ones +again is the one that produces all + + align:start position:0% +again is the one that produces all + + + align:start position:0% +again is the one that produces all +zeros so with respect to the Matrix The + + align:start position:0% +zeros so with respect to the Matrix The + + + align:start position:0% +zeros so with respect to the Matrix The +Columns of the Matrix what what would + + align:start position:0% +Columns of the Matrix what what would + + + align:start position:0% +Columns of the Matrix what what would +you say about the columns I just want to + + align:start position:0% +you say about the columns I just want to + + + align:start position:0% +you say about the columns I just want to +translate the this + + align:start position:0% +translate the this + + + align:start position:0% +translate the this +um this uh Vector 1111 being being + + align:start position:0% +um this uh Vector 1111 being being + + + align:start position:0% +um this uh Vector 1111 being being +around and giving us trouble into a + + align:start position:0% +around and giving us trouble into a + + + align:start position:0% +around and giving us trouble into a +the same idea for the columns so what + + align:start position:0% +the same idea for the columns so what + + + align:start position:0% +the same idea for the columns so what +what do I say about the columns then + + align:start position:0% +what do I say about the columns then + + + align:start position:0% +what do I say about the columns then +they add to zero so the sum of that + + align:start position:0% +they add to zero so the sum of that + + + align:start position:0% +they add to zero so the sum of that +Vector plus that Vector plus that Vector + + align:start position:0% +Vector plus that Vector plus that Vector + + + align:start position:0% +Vector plus that Vector plus that Vector +plus that Vector all weighted by one in + + align:start position:0% +plus that Vector all weighted by one in + + + align:start position:0% +plus that Vector all weighted by one in +this nice case is the zero Vector you + + align:start position:0% +this nice case is the zero Vector you + + + align:start position:0% +this nice case is the zero Vector you +remember that's how I would do that + + align:start position:0% +remember that's how I would do that + + + align:start position:0% +remember that's how I would do that +multiplication if if this is all ones I + + align:start position:0% +multiplication if if this is all ones I + + + align:start position:0% +multiplication if if this is all ones I +think of it as one time that column one + + align:start position:0% +think of it as one time that column one + + + align:start position:0% +think of it as one time that column one +time that one time that one time that + + align:start position:0% +time that one time that one time that + + + align:start position:0% +time that one time that one time that +add up I would get all zeros + + align:start position:0% +add up I would get all zeros + + + align:start position:0% +add up I would get all zeros +so so now help me I'm looking for the + + align:start position:0% +so so now help me I'm looking for the + + + align:start position:0% +so so now help me I'm looking for the +word that says that these columns + + align:start position:0% +word that says that these columns + + + align:start position:0% +word that says that these columns +are dependent dependent they're not + + align:start position:0% +are dependent dependent they're not + + + align:start position:0% +are dependent dependent they're not +independent they're not independent + + align:start position:0% +independent they're not independent + + + align:start position:0% +independent they're not independent +because a combination of them gives zero + + align:start position:0% +because a combination of them gives zero + + + align:start position:0% +because a combination of them gives zero +there's some Vector in the null space + + align:start position:0% +there's some Vector in the null space + + + align:start position:0% +there's some Vector in the null space +other than just the zero Vector okay so + + align:start position:0% +other than just the zero Vector okay so + + + align:start position:0% +other than just the zero Vector okay so +I've got dependent columns my matrices + + align:start position:0% +I've got dependent columns my matrices + + + align:start position:0% +I've got dependent columns my matrices +that I create won't be invertible and of + + align:start position:0% +that I create won't be invertible and of + + + align:start position:0% +that I create won't be invertible and of +course they should shouldn't be because + + align:start position:0% +course they should shouldn't be because + + + align:start position:0% +course they should shouldn't be because +the potentials are not uniquely + + align:start position:0% +the potentials are not uniquely + + + align:start position:0% +the potentials are not uniquely +determined okay so how do you deal with + + align:start position:0% +determined okay so how do you deal with + + + align:start position:0% +determined okay so how do you deal with +that you set a potential say to zero let + + align:start position:0% +that you set a potential say to zero let + + + align:start position:0% +that you set a potential say to zero let +me set the fourth potential to zero so + + align:start position:0% +me set the fourth potential to zero so + + + align:start position:0% +me set the fourth potential to zero so +I'll I've forgotten the exact right way + + align:start position:0% +I'll I've forgotten the exact right way + + + align:start position:0% +I'll I've forgotten the exact right way +to draw it maybe maybe it's like that + + align:start position:0% +to draw it maybe maybe it's like that + + + align:start position:0% +to draw it maybe maybe it's like that +and what's the word for what I've just + + align:start position:0% +and what's the word for what I've just + + + align:start position:0% +and what's the word for what I've just +done I've grounded a node I've set so + + align:start position:0% +done I've grounded a node I've set so + + + align:start position:0% +done I've grounded a node I've set so +the ground is assumed to have potential + + align:start position:0% +the ground is assumed to have potential + + + align:start position:0% +the ground is assumed to have potential +zero the Earth and so I've + + align:start position:0% +zero the Earth and so I've + + + align:start position:0% +zero the Earth and so I've +set X4 equals + + align:start position:0% + + + + align:start position:0% + +0 I fixed a + + align:start position:0% +0 I fixed a + + + align:start position:0% +0 I fixed a +potential so by fixing a PO oh u4 sorry + + align:start position:0% +potential so by fixing a PO oh u4 sorry + + + align:start position:0% +potential so by fixing a PO oh u4 sorry +potentials are + + align:start position:0% +potentials are + + + align:start position:0% +potentials are +U u4 is set to zero so that's grounding + + align:start position:0% +U u4 is set to zero so that's grounding + + + align:start position:0% +U u4 is set to zero so that's grounding +a + + align:start position:0% +a + + + align:start position:0% +a +node + + align:start position:0% +node + + + align:start position:0% +node +ground node + + align:start position:0% +ground node + + + align:start position:0% +ground node +4 it wouldn't have to be zero but that's + + align:start position:0% +4 it wouldn't have to be zero but that's + + + align:start position:0% +4 it wouldn't have to be zero but that's +the Natural Choice to make okay so what + + align:start position:0% +the Natural Choice to make okay so what + + + align:start position:0% +the Natural Choice to make okay so what +happens now now um u4 is no longer an + + align:start position:0% +happens now now um u4 is no longer an + + + align:start position:0% +happens now now um u4 is no longer an +unknown it's zero we might as well take + + align:start position:0% +unknown it's zero we might as well take + + + align:start position:0% +unknown it's zero we might as well take +it out of + + align:start position:0% +it out of + + + align:start position:0% +it out of +there and the column it multiplies is + + align:start position:0% +there and the column it multiplies is + + + align:start position:0% +there and the column it multiplies is +gone so now I + + align:start position:0% +gone so now I + + + align:start position:0% +gone so now I +have really I have so I'm really the + + align:start position:0% +have really I have so I'm really the + + + align:start position:0% +have really I have so I'm really the +number n of + + align:start position:0% +number n of + + + align:start position:0% +number n of +independent unknown potentials is not + + align:start position:0% +independent unknown potentials is not + + + align:start position:0% +independent unknown potentials is not +four we one of them we know is zero it's + + align:start position:0% +four we one of them we know is zero it's + + + align:start position:0% +four we one of them we know is zero it's +really three so so really th this Matrix + + align:start position:0% +really three so so really th this Matrix + + + align:start position:0% +really three so so really th this Matrix +is + + align:start position:0% + + + + align:start position:0% + +5x3 five + + align:start position:0% +5x3 five + + + align:start position:0% +5x3 five +edges give five rows three nodes three + + align:start position:0% +edges give five rows three nodes three + + + align:start position:0% +edges give five rows three nodes three +unknown potentials give three columns + + align:start position:0% +unknown potentials give three columns + + + align:start position:0% +unknown potentials give three columns +three columns now not four and now I'm + + align:start position:0% +three columns now not four and now I'm + + + align:start position:0% +three columns now not four and now I'm +willing to call that thing that Matrix + + align:start position:0% +willing to call that thing that Matrix + + + align:start position:0% +willing to call that thing that Matrix +a so now I'm I'll use the name for that + + align:start position:0% +a so now I'm I'll use the name for that + + + align:start position:0% +a so now I'm I'll use the name for that +Matrix because why I mean what what so + + align:start position:0% +Matrix because why I mean what what so + + + align:start position:0% +Matrix because why I mean what what so +I'm now what's the unlike what I had + + align:start position:0% +I'm now what's the unlike what I had + + + align:start position:0% +I'm now what's the unlike what I had +before the what do you say about those + + align:start position:0% +before the what do you say about those + + + align:start position:0% +before the what do you say about those +columns the independent right I have + + align:start position:0% +columns the independent right I have + + + align:start position:0% +columns the independent right I have +independent columns independent columns + + align:start position:0% +independent columns independent columns + + + align:start position:0% +independent columns independent columns +and that's the of course it's a + + align:start position:0% +and that's the of course it's a + + + align:start position:0% +and that's the of course it's a +rectangular + + align:start position:0% +rectangular + + + align:start position:0% +rectangular +Matrix but when I combine it with a + + align:start position:0% +Matrix but when I combine it with a + + + align:start position:0% +Matrix but when I combine it with a +transpose which is going to show up then + + align:start position:0% +transpose which is going to show up then + + + align:start position:0% +transpose which is going to show up then +a transpose a will be invertible no + + align:start position:0% +a transpose a will be invertible no + + + align:start position:0% +a transpose a will be invertible no +problems so a transpose a has the same + + align:start position:0% +problems so a transpose a has the same + + + align:start position:0% +problems so a transpose a has the same +null space as a and in this case what is + + align:start position:0% +null space as a and in this case what is + + + align:start position:0% +null space as a and in this case what is +the null space of of this Matrix only + + align:start position:0% +the null space of of this Matrix only + + + align:start position:0% +the null space of of this Matrix only +the zero Vector that's that's + + align:start position:0% +the zero Vector that's that's + + + align:start position:0% +the zero Vector that's that's +independent columns is a is another way + + align:start position:0% +independent columns is a is another way + + + align:start position:0% +independent columns is a is another way +to say so let me I'll just put this + + align:start position:0% +to say so let me I'll just put this + + + align:start position:0% +to say so let me I'll just put this +little just because independent + + align:start position:0% +little just because independent + + + align:start position:0% +little just because independent +columns is exactly the same as saying + + align:start position:0% +columns is exactly the same as saying + + + align:start position:0% +columns is exactly the same as saying +that the null space + + align:start position:0% +that the null space + + + align:start position:0% +that the null space +is is only the zero + + align:start position:0% +is is only the zero + + + align:start position:0% +is is only the zero +vector + + align:start position:0% +vector + + + align:start position:0% +vector +that's just we're just saying it in + + align:start position:0% +that's just we're just saying it in + + + align:start position:0% +that's just we're just saying it in +different + + align:start position:0% +different + + + align:start position:0% +different +words okay and if you want I can remove + + align:start position:0% +words okay and if you want I can remove + + + align:start position:0% +words okay and if you want I can remove +these u4s from here because it's like a + + align:start position:0% +these u4s from here because it's like a + + + align:start position:0% +these u4s from here because it's like a +a boundary value we're assigning a value + + align:start position:0% +a boundary value we're assigning a value + + + align:start position:0% +a boundary value we're assigning a value +to uh to a + + align:start position:0% +to uh to a + + + align:start position:0% +to uh to a +potential okay now so in a way yeah I + + align:start position:0% +potential okay now so in a way yeah I + + + align:start position:0% +potential okay now so in a way yeah I +guess maybe maybe this is a moment to + + align:start position:0% +guess maybe maybe this is a moment to + + + align:start position:0% +guess maybe maybe this is a moment to +say a little more about this framework + + align:start position:0% +say a little more about this framework + + + align:start position:0% +say a little more about this framework +because uh the big picture of of a and c + + align:start position:0% +because uh the big picture of of a and c + + + align:start position:0% +because uh the big picture of of a and c +and a transpose oh well I better get + + align:start position:0% +and a transpose oh well I better get + + + align:start position:0% +and a transpose oh well I better get +around the framework before I change it + + align:start position:0% +around the framework before I change it + + + align:start position:0% +around the framework before I change it +okay so what's we got this far then we + + align:start position:0% +okay so what's we got this far then we + + + align:start position:0% +okay so what's we got this far then we +got the potential differences across the + + align:start position:0% +got the potential differences across the + + + align:start position:0% +got the potential differences across the +edges now what + + align:start position:0% +edges now what + + + align:start position:0% +edges now what +makes okay so what's happening what's + + align:start position:0% +makes okay so what's happening what's + + + align:start position:0% +makes okay so what's happening what's +what's C I'm right I'm at that point now + + align:start position:0% +what's C I'm right I'm at that point now + + + align:start position:0% +what's C I'm right I'm at that point now +what's the flow the current on the edge + + align:start position:0% +what's the flow the current on the edge + + + align:start position:0% +what's the flow the current on the edge +if the potential difference is whatever + + align:start position:0% +if the potential difference is whatever + + + align:start position:0% +if the potential difference is whatever +if the potent the potential difference + + align:start position:0% +if the potent the potential difference + + + align:start position:0% +if the potent the potential difference +here is u3 minus + + align:start position:0% +here is u3 minus + + + align:start position:0% +here is u3 minus +U1 and that's what makes current flow + + align:start position:0% +U1 and that's what makes current flow + + + align:start position:0% +U1 and that's what makes current flow +right it's the difference in potential + + align:start position:0% +right it's the difference in potential + + + align:start position:0% +right it's the difference in potential +the voltage drop and oh and that word + + align:start position:0% +the voltage drop and oh and that word + + + align:start position:0% +the voltage drop and oh and that word +drop comes in it's the it's a drop in + + align:start position:0% +drop comes in it's the it's a drop in + + + align:start position:0% +drop comes in it's the it's a drop in +voltage that sends current from high + + align:start position:0% +voltage that sends current from high + + + align:start position:0% +voltage that sends current from high +potential to low potential it's going to + + align:start position:0% +potential to low potential it's going to + + + align:start position:0% +potential to low potential it's going to +there's going to be a minus sign in in + + align:start position:0% +there's going to be a minus sign in in + + + align:start position:0% +there's going to be a minus sign in in +uh that appears in it's interesting half + + align:start position:0% +uh that appears in it's interesting half + + + align:start position:0% +uh that appears in it's interesting half +of Science and Engineering has got a + + align:start position:0% +of Science and Engineering has got a + + + align:start position:0% +of Science and Engineering has got a +plus sign this position and half a minus + + align:start position:0% +plus sign this position and half a minus + + + align:start position:0% +plus sign this position and half a minus +sign so this is electrical stuff uh + + align:start position:0% +sign so this is electrical stuff uh + + + align:start position:0% +sign so this is electrical stuff uh +estimation problems um physics actually + + align:start position:0% +estimation problems um physics actually + + + align:start position:0% +estimation problems um physics actually +probably Lincoln lab has the minus sign + + align:start position:0% +probably Lincoln lab has the minus sign + + + align:start position:0% +probably Lincoln lab has the minus sign +and uh and uh more people involved with + + align:start position:0% +and uh and uh more people involved with + + + align:start position:0% +and uh and uh more people involved with +mechanics and structures uh have a plus + + align:start position:0% +mechanics and structures uh have a plus + + + align:start position:0% +mechanics and structures uh have a plus +sign okay so you'll see the minus sign + + align:start position:0% +sign okay so you'll see the minus sign + + + align:start position:0% +sign okay so you'll see the minus sign +come in and the minus sign is + + align:start position:0% +come in and the minus sign is + + + align:start position:0% +come in and the minus sign is +because flow is from higher to lower + + align:start position:0% +because flow is from higher to lower + + + align:start position:0% +because flow is from higher to lower +potential that's okay so now let me so + + align:start position:0% +potential that's okay so now let me so + + + align:start position:0% +potential that's okay so now let me so +what governs the flow + + align:start position:0% +what governs the flow + + + align:start position:0% +what governs the flow +oh right now I haven't got any physics + + align:start position:0% +oh right now I haven't got any physics + + + align:start position:0% +oh right now I haven't got any physics +in the problem I haven't it's just like + + align:start position:0% +in the problem I haven't it's just like + + + align:start position:0% +in the problem I haven't it's just like +a an + + align:start position:0% +a an + + + align:start position:0% +a an +edge like the worldwide web or + + align:start position:0% +edge like the worldwide web or + + + align:start position:0% +edge like the worldwide web or +something I mean so this is a framework + + align:start position:0% +something I mean so this is a framework + + + align:start position:0% +something I mean so this is a framework +of graphs and and flows and so and + + align:start position:0% +of graphs and and flows and so and + + + align:start position:0% +of graphs and and flows and so and +connections that's uh highly important + + align:start position:0% +connections that's uh highly important + + + align:start position:0% +connections that's uh highly important +by itself to understand a graph of the + + align:start position:0% +by itself to understand a graph of the + + + align:start position:0% +by itself to understand a graph of the +web with millions of nodes and and uh + + align:start position:0% +web with millions of nodes and and uh + + + align:start position:0% +web with millions of nodes and and uh +links is uh highly important and we'll + + align:start position:0% +links is uh highly important and we'll + + + align:start position:0% +links is uh highly important and we'll +come back to that later in the in the + + align:start position:0% +come back to that later in the in the + + + align:start position:0% +come back to that later in the in the +lectures but here I'm speaking more + + align:start position:0% +lectures but here I'm speaking more + + + align:start position:0% +lectures but here I'm speaking more +about current and I have to make put + + align:start position:0% +about current and I have to make put + + + align:start position:0% +about current and I have to make put +some Physics in and let me just put a + + align:start position:0% +some Physics in and let me just put a + + + align:start position:0% +some Physics in and let me just put a +resistor in so I'll put a resistor on + + align:start position:0% +resistor in so I'll put a resistor on + + + align:start position:0% +resistor in so I'll put a resistor on +every every + + align:start position:0% +every every + + + align:start position:0% +every every +Edge and that resistor + + align:start position:0% +Edge and that resistor + + + align:start position:0% +Edge and that resistor +then uh has some conductance + + align:start position:0% +then uh has some conductance + + + align:start position:0% +then uh has some conductance +C2 it's number number two because that + + align:start position:0% +C2 it's number number two because that + + + align:start position:0% +C2 it's number number two because that +was Edge number two here's + + align:start position:0% +was Edge number two here's + + + align:start position:0% +was Edge number two here's +C1 on edge number + + align:start position:0% +C1 on edge number + + + align:start position:0% +C1 on edge number +one okay so I'm speaking then about so + + align:start position:0% +one okay so I'm speaking then about so + + + align:start position:0% +one okay so I'm speaking then about so +I'll have resistances on all five of the + + align:start position:0% +I'll have resistances on all five of the + + + align:start position:0% +I'll have resistances on all five of the +edges all five edges so there'll be a C1 + + align:start position:0% +edges all five edges so there'll be a C1 + + + align:start position:0% +edges all five edges so there'll be a C1 +C2 C3 C 4 and + + align:start position:0% +C2 C3 C 4 and + + + align:start position:0% +C2 C3 C 4 and +C5 so on each Edge there's a resist a + + align:start position:0% +C5 so on each Edge there's a resist a + + + align:start position:0% +C5 so on each Edge there's a resist a +conductance so the the resistance is + + align:start position:0% +conductance so the the resistance is + + + align:start position:0% +conductance so the the resistance is +it's sort of more convenient to use the + + align:start position:0% +it's sort of more convenient to use the + + + align:start position:0% +it's sort of more convenient to use the +conductance than the + + align:start position:0% +conductance than the + + + align:start position:0% +conductance than the +resistance and they're just reciprocals + + align:start position:0% +resistance and they're just reciprocals + + + align:start position:0% +resistance and they're just reciprocals +the conductance is one over the resist + + align:start position:0% +the conductance is one over the resist + + + align:start position:0% +the conductance is one over the resist +resistance okay now now I'm ready for + + align:start position:0% +resistance okay now now I'm ready for + + + align:start position:0% +resistance okay now now I'm ready for +who whose law is it that tells us what + + align:start position:0% +who whose law is it that tells us what + + + align:start position:0% +who whose law is it that tells us what +tells us this Matrix + + align:start position:0% + + + + align:start position:0% + +C oh oh fortunately we get a short guy + + align:start position:0% +C oh oh fortunately we get a short guy + + + align:start position:0% +C oh oh fortunately we get a short guy +with a short name for this for this one + + align:start position:0% +with a short name for this for this one + + + align:start position:0% +with a short name for this for this one +you may know what's coming whose name is + + align:start position:0% +you may know what's coming whose name is + + + align:start position:0% +you may know what's coming whose name is +coming for the next + + align:start position:0% +coming for the next + + + align:start position:0% +coming for the next +one longer okay so Ohm's law ohms law + + align:start position:0% +one longer okay so Ohm's law ohms law + + + align:start position:0% +one longer okay so Ohm's law ohms law +then is so what's ohms law let's just so + + align:start position:0% +then is so what's ohms law let's just so + + + align:start position:0% +then is so what's ohms law let's just so +that would be the next step maybe I + + align:start position:0% +that would be the next step maybe I + + + align:start position:0% +that would be the next step maybe I +write it here ohms + + align:start position:0% +write it here ohms + + + align:start position:0% +write it here ohms +law will be that the flow on an + + align:start position:0% +law will be that the flow on an + + + align:start position:0% +law will be that the flow on an +edge is the conductance times + + align:start position:0% +edge is the conductance times + + + align:start position:0% +edge is the conductance times +the electromotive force the the the + + align:start position:0% +the electromotive force the the the + + + align:start position:0% +the electromotive force the the the +voltage drop the across the resistance + + align:start position:0% +voltage drop the across the resistance + + + align:start position:0% +voltage drop the across the resistance +so that's this is each Edge separately + + align:start position:0% +so that's this is each Edge separately + + + align:start position:0% +so that's this is each Edge separately +just as + + align:start position:0% +just as + + + align:start position:0% +just as +before so our Matrix C is going to be a + + align:start position:0% +before so our Matrix C is going to be a + + + align:start position:0% +before so our Matrix C is going to be a +diagonal + + align:start position:0% +diagonal + + + align:start position:0% +diagonal +matrix so our Matrix C then is just + + align:start position:0% +matrix so our Matrix C then is just + + + align:start position:0% +matrix so our Matrix C then is just +going to + + align:start position:0% +going to + + + align:start position:0% +going to +be uh C1 C2 to C5 + + align:start position:0% +be uh C1 C2 to C5 + + + align:start position:0% +be uh C1 C2 to C5 +so it's of course it's m by m this is M + + align:start position:0% +so it's of course it's m by m this is M + + + align:start position:0% +so it's of course it's m by m this is M +by + + align:start position:0% + + + + align:start position:0% + +m + + align:start position:0% +m + + + align:start position:0% +m +and + + align:start position:0% +and + + + align:start position:0% +and +it's it tells us the the uh what's going + + align:start position:0% +it's it tells us the the uh what's going + + + align:start position:0% +it's it tells us the the uh what's going +on separately on every + + align:start position:0% +on separately on every + + + align:start position:0% +on separately on every +Edge Okay so we've got from the + + align:start position:0% +Edge Okay so we've got from the + + + align:start position:0% +Edge Okay so we've got from the +potentials to the potential differences + + align:start position:0% +potentials to the potential differences + + + align:start position:0% +potentials to the potential differences +to the + + align:start position:0% +to the + + + align:start position:0% +to the +currents and now what's the balance law + + align:start position:0% +currents and now what's the balance law + + + align:start position:0% +currents and now what's the balance law +cu as as always I emphasize there's some + + align:start position:0% +cu as as always I emphasize there's some + + + align:start position:0% +cu as as always I emphasize there's some +balance equation and there could + + align:start position:0% +balance equation and there could + + + align:start position:0% +balance equation and there could +be I have to deal in a minute with uh I + + align:start position:0% +be I have to deal in a minute with uh I + + + align:start position:0% +be I have to deal in a minute with uh I +need some external sources to make + + align:start position:0% +need some external sources to make + + + align:start position:0% +need some external sources to make +something + + align:start position:0% +something + + + align:start position:0% +something +happen but let let me first let's just + + align:start position:0% +happen but let let me first let's just + + + align:start position:0% +happen but let let me first let's just +take the balance law in its purest form + + align:start position:0% +take the balance law in its purest form + + + align:start position:0% +take the balance law in its purest form +where there's + + align:start position:0% +where there's + + + align:start position:0% +where there's +no in say in in node + + align:start position:0% +no in say in in node + + + align:start position:0% +no in say in in node +one what's the balance equation in node + + align:start position:0% +one what's the balance equation in node + + + align:start position:0% +one what's the balance equation in node +one so so now we're really coming to the + + align:start position:0% +one so so now we're really coming to the + + + align:start position:0% +one so so now we're really coming to the +the serious thing the the balance + + align:start position:0% +the serious thing the the balance + + + align:start position:0% +the serious thing the the balance +equations balance or conservation or or + + align:start position:0% +equations balance or conservation or or + + + align:start position:0% +equations balance or conservation or or +cons yeah conservation of charge + + align:start position:0% +cons yeah conservation of charge + + + align:start position:0% +cons yeah conservation of charge +continuity whatever there's always an + + align:start position:0% +continuity whatever there's always an + + + align:start position:0% +continuity whatever there's always an +equation like this and it's a balance + + align:start position:0% +equation like this and it's a balance + + + align:start position:0% +equation like this and it's a balance +equation at each + + align:start position:0% +equation at each + + + align:start position:0% +equation at each +node okay so tell me what it is at the + + align:start position:0% +node okay so tell me what it is at the + + + align:start position:0% +node okay so tell me what it is at the +first + + align:start position:0% +first + + + align:start position:0% +first +node at the first node so what what is + + align:start position:0% +node at the first node so what what is + + + align:start position:0% +node at the first node so what what is +it or in words what's this balance + + align:start position:0% +it or in words what's this balance + + + align:start position:0% +it or in words what's this balance +equation going to + + align:start position:0% +equation going to + + + align:start position:0% +equation going to +say total net current zero right current + + align:start position:0% +say total net current zero right current + + + align:start position:0% +say total net current zero right current +in equals current + + align:start position:0% +in equals current + + + align:start position:0% +in equals current +out that's just so + + align:start position:0% +out that's just so + + + align:start position:0% +out that's just so +fundamental and uh so well let's see uh + + align:start position:0% +fundamental and uh so well let's see uh + + + align:start position:0% +fundamental and uh so well let's see uh +we've got all the arrows going out of + + align:start position:0% +we've got all the arrows going out of + + + align:start position:0% +we've got all the arrows going out of +edge + + align:start position:0% +edge + + + align:start position:0% +edge +one out of node one so we've got a + + align:start position:0% +one out of node one so we've got a + + + align:start position:0% +one out of node one so we've got a +current a current W1 you you're + + align:start position:0% +current a current W1 you you're + + + align:start position:0% +current a current W1 you you're +remembering the lettering here those + + align:start position:0% +remembering the lettering here those + + + align:start position:0% +remembering the lettering here those +refer to the conductances + + align:start position:0% +refer to the conductances + + + align:start position:0% +refer to the conductances +and then we multiply by the E for that + + align:start position:0% +and then we multiply by the E for that + + + align:start position:0% +and then we multiply by the E for that +thing and those are the currents that + + align:start position:0% +thing and those are the currents that + + + align:start position:0% +thing and those are the currents that +let just be sure that we keep our + + align:start position:0% +let just be sure that we keep our + + + align:start position:0% +let just be sure that we keep our +letters straight okay so what's the + + align:start position:0% +letters straight okay so what's the + + + align:start position:0% +letters straight okay so what's the +balance equation at node one I would + + align:start position:0% +balance equation at node one I would + + + align:start position:0% +balance equation at node one I would +write it this way because those are + + align:start position:0% +write it this way because those are + + + align:start position:0% +write it this way because those are +going out there's a there's a flow W1 + + align:start position:0% +going out there's a there's a flow W1 + + + align:start position:0% +going out there's a there's a flow W1 +out a flow W2 out and a flow W4 Out and + + align:start position:0% +out a flow W2 out and a flow W4 Out and + + + align:start position:0% +out a flow W2 out and a flow W4 Out and +because they're out I'll let me + + align:start position:0% +because they're out I'll let me + + + align:start position:0% +because they're out I'll let me +consistently give them those minus signs + + align:start position:0% +consistently give them those minus signs + + + align:start position:0% +consistently give them those minus signs +maybe minus- W1 - W2 - W4 equal 0o + + align:start position:0% + + + + align:start position:0% + +right that's what's happening at the + + align:start position:0% +right that's what's happening at the + + + align:start position:0% +right that's what's happening at the +first + + align:start position:0% +first + + + align:start position:0% +first +node and I'm assuming for the moment no + + align:start position:0% +node and I'm assuming for the moment no + + + align:start position:0% +node and I'm assuming for the moment no +external current no current sources for + + align:start position:0% +external current no current sources for + + + align:start position:0% +external current no current sources for +the moment okay how about node + + align:start position:0% +the moment okay how about node + + + align:start position:0% +the moment okay how about node +two now W1 is coming in W3 and W4 are + + align:start position:0% +two now W1 is coming in W3 and W4 are + + + align:start position:0% +two now W1 is coming in W3 and W4 are +going out so there's a w + + align:start position:0% +going out so there's a w + + + align:start position:0% +going out so there's a w +is that + + align:start position:0% +is that + + + align:start position:0% +is that +right W1 in and a minus now + + align:start position:0% +right W1 in and a minus now + + + align:start position:0% +right W1 in and a minus now +right minus the W3 and the W4 going + + align:start position:0% +right minus the W3 and the W4 going + + + align:start position:0% +right minus the W3 and the W4 going +out is + + align:start position:0% +out is + + + align:start position:0% +out is +it ah it's it's five three and five good + + align:start position:0% +it ah it's it's five three and five good + + + align:start position:0% +it ah it's it's five three and five good +thanks three and + + align:start position:0% +thanks three and + + + align:start position:0% +thanks three and +five + + align:start position:0% +five + + + align:start position:0% +five +okay okay and now we can just carry on + + align:start position:0% +okay okay and now we can just carry on + + + align:start position:0% +okay okay and now we can just carry on +to node three say I since I + + align:start position:0% +to node three say I since I + + + align:start position:0% +to node three say I since I +took that edge out that's easy W2 in W + + align:start position:0% +took that edge out that's easy W2 in W + + + align:start position:0% +took that edge out that's easy W2 in W +no W2 in and W3 in right is that it W2 + + + align:start position:0% +no W2 in and W3 in right is that it W2 + + + + align:start position:0% +no W2 in and W3 in right is that it W2 + +W3 coming in and they have to + + align:start position:0% +W3 coming in and they have to + + + align:start position:0% +W3 coming in and they have to +balance then the next is oh we only have + + align:start position:0% +balance then the next is oh we only have + + + align:start position:0% +balance then the next is oh we only have +one more node to + + align:start position:0% +one more node to + + + align:start position:0% +one more node to +go and what's happening + + align:start position:0% +go and what's happening + + + align:start position:0% +go and what's happening +there four and five zero okay W4 + + + align:start position:0% +there four and five zero okay W4 + + + + align:start position:0% +there four and five zero okay W4 + +W5 is zero + + align:start position:0% + + + + align:start position:0% + +okay okay so this those so what equ what + + align:start position:0% +okay okay so this those so what equ what + + + align:start position:0% +okay okay so this those so what equ what +whose name do we associate with those + + align:start position:0% +whose name do we associate with those + + + align:start position:0% +whose name do we associate with those +with this with this current law kirkoff + + align:start position:0% +with this with this current law kirkoff + + + align:start position:0% +with this with this current law kirkoff +kirkoff and kirkoff has two hes uh in + + align:start position:0% +kirkoff and kirkoff has two hes uh in + + + align:start position:0% +kirkoff and kirkoff has two hes uh in +his name I this week I Was preparing the + + align:start position:0% +his name I this week I Was preparing the + + + align:start position:0% +his name I this week I Was preparing the +notes and spell Che thinks it only has + + align:start position:0% +notes and spell Che thinks it only has + + + align:start position:0% +notes and spell Che thinks it only has +one but is definitely two uh so uh so + + align:start position:0% +one but is definitely two uh so uh so + + + align:start position:0% +one but is definitely two uh so uh so +this is Kirk off's current law K so can + + align:start position:0% +this is Kirk off's current law K so can + + + align:start position:0% +this is Kirk off's current law K so can +I write + + align:start position:0% +I write + + + align:start position:0% +I write +KCl Kirk off's current law which is just + + align:start position:0% +KCl Kirk off's current law which is just + + + align:start position:0% +KCl Kirk off's current law which is just +the balance equation at every node and + + align:start position:0% +the balance equation at every node and + + + align:start position:0% +the balance equation at every node and +if we had current sources there would we + + align:start position:0% +if we had current sources there would we + + + align:start position:0% +if we had current sources there would we +we would have some right-and sides okay + + align:start position:0% +we would have some right-and sides okay + + + align:start position:0% +we would have some right-and sides okay +now I want to look at + + align:start position:0% + + + + align:start position:0% + +that of course I want to write that as a + + align:start position:0% + + + + align:start position:0% + +matrix and I've got zeros on the right + + align:start position:0% +matrix and I've got zeros on the right + + + align:start position:0% +matrix and I've got zeros on the right +side so there's some Matrix + + align:start position:0% +side so there's some Matrix + + + align:start position:0% +side so there's some Matrix +there multiplying the vector of WS + + align:start position:0% +there multiplying the vector of WS + + + align:start position:0% +there multiplying the vector of WS +should we should I just pull out that + + align:start position:0% +should we should I just pull out that + + + align:start position:0% +should we should I just pull out that +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +here so this so so if I go up to here + + align:start position:0% +here so this so so if I go up to here + + + align:start position:0% +here so this so so if I go up to here +the The Matrix I believe will be a + + align:start position:0% +the The Matrix I believe will be a + + + align:start position:0% +the The Matrix I believe will be a +transpose let's just pray that it is + + align:start position:0% +transpose let's just pray that it is + + + align:start position:0% +transpose let's just pray that it is +okay so a trans let me pull out the + + align:start position:0% +okay so a trans let me pull out the + + + align:start position:0% +okay so a trans let me pull out the +Matrix the The Matrix is so I want to + + align:start position:0% +Matrix the The Matrix is so I want to + + + align:start position:0% +Matrix the The Matrix is so I want to +rewrite this in Matrix form so I'm + + align:start position:0% +rewrite this in Matrix form so I'm + + + align:start position:0% +rewrite this in Matrix form so I'm +seeing minus1 + + align:start position:0% +seeing minus1 + + + align:start position:0% +seeing minus1 +-1 minus1 multiplying + + align:start position:0% + + + + align:start position:0% + +W and right now we have a w we do have a + + align:start position:0% +W and right now we have a w we do have a + + + align:start position:0% +W and right now we have a w we do have a +W5 for sure okay then there's a one and + + align:start position:0% +W5 for sure okay then there's a one and + + + align:start position:0% +W5 for sure okay then there's a one and +a minus1 and a minus + + align:start position:0% +a minus1 and a minus + + + align:start position:0% +a minus1 and a minus +one and then there's a two and a + + align:start position:0% +one and then there's a two and a + + + align:start position:0% +one and then there's a two and a +three and then there's a four and a five + + align:start position:0% +three and then there's a four and a five + + + align:start position:0% +three and then there's a four and a five +is that is that right two and three and + + align:start position:0% +is that is that right two and three and + + + align:start position:0% +is that is that right two and three and +four and five okay now wait a second + + align:start position:0% +four and five okay now wait a second + + + align:start position:0% +four and five okay now wait a second +so that is that the + + align:start position:0% +so that is that the + + + align:start position:0% +so that is that the +transpose of our incident + + align:start position:0% +transpose of our incident + + + align:start position:0% +transpose of our incident +Matrix well it was right that's right + + align:start position:0% +Matrix well it was right that's right + + + align:start position:0% +Matrix well it was right that's right +now I've got four so I I've got this if + + align:start position:0% +now I've got four so I I've got this if + + + align:start position:0% +now I've got four so I I've got this if +I put this fellow + + align:start position:0% +I put this fellow + + + align:start position:0% +I put this fellow +back then am I am I okay that that + + align:start position:0% +back then am I am I okay that that + + + align:start position:0% +back then am I am I okay that that +really is the transpose yeah let's let's + + align:start position:0% +really is the transpose yeah let's let's + + + align:start position:0% +really is the transpose yeah let's let's +just check one row right uh this column + + align:start position:0% +just check one row right uh this column + + + align:start position:0% +just check one row right uh this column +here is -1 -1 0 - one 0 and this row is + + align:start position:0% +here is -1 -1 0 - one 0 and this row is + + + align:start position:0% +here is -1 -1 0 - one 0 and this row is +the + + align:start position:0% + + + + align:start position:0% + +same and if one row comes out right + + align:start position:0% +same and if one row comes out right + + + align:start position:0% +same and if one row comes out right +that's proved right completely proved + + align:start position:0% +that's proved right completely proved + + + align:start position:0% +that's proved right completely proved +right but now what's up just just while + + align:start position:0% +right but now what's up just just while + + + align:start position:0% +right but now what's up just just while +we're cleaning up this uh the problems + + align:start position:0% +we're cleaning up this uh the problems + + + align:start position:0% +we're cleaning up this uh the problems +with this + + align:start position:0% +with this + + + align:start position:0% +with this +Matrix we + + align:start position:0% +Matrix we + + + align:start position:0% +Matrix we +we felt able to erase + + align:start position:0% +we felt able to erase + + + align:start position:0% +we felt able to erase +that column by setting u4 equals z by + + align:start position:0% +that column by setting u4 equals z by + + + align:start position:0% +that column by setting u4 equals z by +grounding a node because there was a + + align:start position:0% +grounding a node because there was a + + + align:start position:0% +grounding a node because there was a +null space we wanted to get rid of it we + + align:start position:0% +null space we wanted to get rid of it we + + + align:start position:0% +null space we wanted to get rid of it we +felt justified in erasing that column so + + align:start position:0% +felt justified in erasing that column so + + + align:start position:0% +felt justified in erasing that column so +how are we justified in erasing that row + + align:start position:0% +how are we justified in erasing that row + + + align:start position:0% +how are we justified in erasing that row +that's what I plan to do I plan to make + + align:start position:0% +that's what I plan to do I plan to make + + + align:start position:0% +that's what I plan to do I plan to make +that row go + + align:start position:0% +that row go + + + align:start position:0% +that row go +away so that I really do have the + + align:start position:0% +away so that I really do have the + + + align:start position:0% +away so that I really do have the +transpose so that row gave us this + + align:start position:0% +transpose so that row gave us this + + + align:start position:0% +transpose so that row gave us this +equation so why why can I ignore that + + align:start position:0% + + + + align:start position:0% + +equation why can I + + align:start position:0% + + + + align:start position:0% + +ignore well + + align:start position:0% +ignore well + + + align:start position:0% +ignore well +uh yeah node four is grounded so somehow + + align:start position:0% +uh yeah node four is grounded so somehow + + + align:start position:0% +uh yeah node four is grounded so somehow +it ought to come out right at that node + + align:start position:0% +it ought to come out right at that node + + + align:start position:0% +it ought to come out right at that node +right I mean whatever is happening it's + + align:start position:0% +right I mean whatever is happening it's + + + align:start position:0% +right I mean whatever is happening it's +just going into ground but now do you + + align:start position:0% +just going into ground but now do you + + + align:start position:0% +just going into ground but now do you +see how that equation + + align:start position:0% + + + + align:start position:0% + +it's not + + align:start position:0% + + + + align:start position:0% + +true let's see a current four coming in + + align:start position:0% +true let's see a current four coming in + + + align:start position:0% +true let's see a current four coming in +current five coming in and up you there + + align:start position:0% +current five coming in and up you there + + + align:start position:0% +current five coming in and up you there +might be a source okay but with with as + + align:start position:0% +might be a source okay but with with as + + + align:start position:0% +might be a source okay but with with as +it stands I just so here's my point that + + align:start position:0% +it stands I just so here's my point that + + + align:start position:0% +it stands I just so here's my point that +equation comes from these do you see how + + align:start position:0% +equation comes from these do you see how + + + align:start position:0% +equation comes from these do you see how +to get that equation from these three + + align:start position:0% + + + + align:start position:0% + +yeah I think + + align:start position:0% +yeah I think + + + align:start position:0% +yeah I think +that's yeah because they all all the if + + align:start position:0% +that's yeah because they all all the if + + + align:start position:0% +that's yeah because they all all the if +I what happens if I add up all four + + align:start position:0% +I what happens if I add up all four + + + align:start position:0% +I what happens if I add up all four +equations I I get Z equals z right + + align:start position:0% +equations I I get Z equals z right + + + align:start position:0% +equations I I get Z equals z right +that's what I got when I added up the + + align:start position:0% +that's what I got when I added up the + + + align:start position:0% +that's what I got when I added up the +columns so is what I ought to get when I + + align:start position:0% +columns so is what I ought to get when I + + + align:start position:0% +columns so is what I ought to get when I +add up rows so if I add up in other + + align:start position:0% +add up rows so if I add up in other + + + align:start position:0% +add up rows so if I add up in other +words to to find this one I would just + + align:start position:0% +words to to find this one I would just + + + align:start position:0% +words to to find this one I would just +like add up the first three what happens + + align:start position:0% +like add up the first three what happens + + + align:start position:0% +like add up the first three what happens +if I add up those first three + + align:start position:0% +if I add up those first three + + + align:start position:0% +if I add up those first three +equations that cancels that cancels this + + align:start position:0% +equations that cancels that cancels this + + + align:start position:0% +equations that cancels that cancels this +cancels I get minus W4 minus W5 right + + align:start position:0% +cancels I get minus W4 minus W5 right + + + align:start position:0% +cancels I get minus W4 minus W5 right +and therefore is zero and therefore + + align:start position:0% +and therefore is zero and therefore + + + align:start position:0% +and therefore is zero and therefore +that's so ultimately this last equation + + align:start position:0% +that's so ultimately this last equation + + + align:start position:0% +that's so ultimately this last equation +is a consequence of the others it's a + + align:start position:0% +is a consequence of the others it's a + + + align:start position:0% +is a consequence of the others it's a +it's sort of a con it's a consequence of + + align:start position:0% +it's sort of a con it's a consequence of + + + align:start position:0% +it's sort of a con it's a consequence of +overall balance of charge we haven't + + align:start position:0% +overall balance of charge we haven't + + + align:start position:0% +overall balance of charge we haven't +lost any anybody yeah so we really can + + align:start position:0% +lost any anybody yeah so we really can + + + align:start position:0% +lost any anybody yeah so we really can +remove that + + align:start position:0% +remove that + + + align:start position:0% +remove that +uh that uh last row that last equation + + align:start position:0% +uh that uh last row that last equation + + + align:start position:0% +uh that uh last row that last equation +okay now I've got to make something + + align:start position:0% +okay now I've got to make something + + + align:start position:0% +okay now I've got to make something +happen right now the right hand sides + + align:start position:0% +happen right now the right hand sides + + + align:start position:0% +happen right now the right hand sides +are + + align:start position:0% +are + + + align:start position:0% +are +zero and + + align:start position:0% +zero and + + + align:start position:0% +zero and +uh so for my present + + align:start position:0% +uh so for my present + + + align:start position:0% +uh so for my present +system for this system with no no + + align:start position:0% +system for this system with no no + + + align:start position:0% +system for this system with no no +external + + align:start position:0% +external + + + align:start position:0% +external +forces + + align:start position:0% +forces + + + align:start position:0% +forces +uh I'll I get the a transpose CA all + + align:start position:0% +uh I'll I get the a transpose CA all + + + align:start position:0% +uh I'll I get the a transpose CA all +right but I haven't got anything on the + + align:start position:0% +right but I haven't got anything on the + + + align:start position:0% +right but I haven't got anything on the +right hand side okay so where does the + + align:start position:0% +right hand side okay so where does the + + + align:start position:0% +right hand side okay so where does the +right right hand side come in okay well + + align:start position:0% +right right hand side come in okay well + + + align:start position:0% +right right hand side come in okay well +as you just said we could have current + + align:start position:0% + + + + align:start position:0% + +sources we could have we could be like a + + align:start position:0% +sources we could have we could be like a + + + align:start position:0% +sources we could have we could be like a +current coming out of here and into + + align:start position:0% +current coming out of here and into + + + align:start position:0% +current coming out of here and into +there right we could I now have to think + + align:start position:0% +there right we could I now have to think + + + align:start position:0% +there right we could I now have to think +okay what what are the external terms + + align:start position:0% +okay what what are the external terms + + + align:start position:0% +okay what what are the external terms +The Source terms that that make + + align:start position:0% +The Source terms that that make + + + align:start position:0% +The Source terms that that make +something happen and I guess I want to + + align:start position:0% +something happen and I guess I want to + + + align:start position:0% +something happen and I guess I want to +see even more possibilities than + + align:start position:0% + + + + align:start position:0% + +before in + + align:start position:0% +before in + + + align:start position:0% +before in +fact I want to see where the source + + align:start position:0% +fact I want to see where the source + + + align:start position:0% +fact I want to see where the source +terms enter so in a way that's a source + + align:start position:0% +terms enter so in a way that's a source + + + align:start position:0% +terms enter so in a way that's a source +term I would really be happier if I put + + align:start position:0% +term I would really be happier if I put + + + align:start position:0% +term I would really be happier if I put +zero there as the internal part and and + + align:start position:0% +zero there as the internal part and and + + + align:start position:0% +zero there as the internal part and and +then had a source term + + align:start position:0% +then had a source term + + + align:start position:0% +then had a source term +F coming in I that that's just + + align:start position:0% + + + + align:start position:0% + +picky that's just picky but I you'll see + + align:start position:0% +picky that's just picky but I you'll see + + + align:start position:0% +picky that's just picky but I you'll see +that it'll make the picture uh more + + align:start position:0% +that it'll make the picture uh more + + + align:start position:0% +that it'll make the picture uh more +symmetric okay so I I really the the + + align:start position:0% +symmetric okay so I I really the the + + + align:start position:0% +symmetric okay so I I really the the +true Kirk's current law would would have + + align:start position:0% +true Kirk's current law would would have + + + align:start position:0% +true Kirk's current law would would have +a source term suppose I suppose I + + align:start position:0% +a source term suppose I suppose I + + + align:start position:0% +a source term suppose I suppose I +run suppose I feed a + + align:start position:0% +run suppose I feed a + + + align:start position:0% +run suppose I feed a +current of + + align:start position:0% +current of + + + align:start position:0% +current of +F1 + + align:start position:0% +F1 + + + align:start position:0% +F1 +into + + align:start position:0% +into + + + align:start position:0% +into +um into node + + align:start position:0% +um into node + + + align:start position:0% +um into node +one and and uh don't touch the other nod + + align:start position:0% +one and and uh don't touch the other nod + + + align:start position:0% +one and and uh don't touch the other nod +so it'll be the grounded node that's + + align:start position:0% +so it'll be the grounded node that's + + + align:start position:0% +so it'll be the grounded node that's +affected so if I feed a current F1 into + + align:start position:0% +affected so if I feed a current F1 into + + + align:start position:0% +affected so if I feed a current F1 into +that then I I I guess I would have a + + align:start position:0% +that then I I I guess I would have a + + + align:start position:0% +that then I I I guess I would have a +that the balance at node one would + + align:start position:0% +that the balance at node one would + + + align:start position:0% +that the balance at node one would +include F1 and the balance at node four + + align:start position:0% +include F1 and the balance at node four + + + align:start position:0% +include F1 and the balance at node four +would include minus + + align:start position:0% + + + + align:start position:0% + +F1 you see I'm I'm putting the F into + + align:start position:0% +F1 you see I'm I'm putting the F into + + + align:start position:0% +F1 you see I'm I'm putting the F into +the equation and and and what FS am I + + align:start position:0% +the equation and and and what FS am I + + + align:start position:0% +the equation and and and what FS am I +allowing here I'm always because the + + align:start position:0% +allowing here I'm always because the + + + align:start position:0% +allowing here I'm always because the +left sides add to zero I better have the + + align:start position:0% +left sides add to zero I better have the + + + align:start position:0% +left sides add to zero I better have the +right sides add to zero whatever current + + align:start position:0% +right sides add to zero whatever current + + + align:start position:0% +right sides add to zero whatever current +goes into one node has to come out of + + align:start position:0% +goes into one node has to come out of + + + align:start position:0% +goes into one node has to come out of +another because I'm speaking here about + + align:start position:0% +another because I'm speaking here about + + + align:start position:0% +another because I'm speaking here about +steady + + align:start position:0% +steady + + + align:start position:0% +steady +state okay so I could in principle have + + align:start position:0% +state okay so I could in principle have + + + align:start position:0% +state okay so I could in principle have +let's see I've got four + + align:start position:0% +let's see I've got four + + + align:start position:0% +let's see I've got four +nodes I could have currents + + align:start position:0% +nodes I could have currents + + + align:start position:0% +nodes I could have currents +feeding uh into and out I could have + + align:start position:0% +feeding uh into and out I could have + + + align:start position:0% +feeding uh into and out I could have +currents I can have currents going into + + align:start position:0% +currents I can have currents going into + + + align:start position:0% +currents I can have currents going into +four nodes from outside but the total + + align:start position:0% +four nodes from outside but the total + + + align:start position:0% +four nodes from outside but the total +current has would have to add to zero so + + align:start position:0% +current has would have to add to zero so + + + align:start position:0% +current has would have to add to zero so +that would be an + + align:start position:0% +that would be an + + + align:start position:0% +that would be an +example right I as long as maybe just a + + align:start position:0% +example right I as long as maybe just a + + + align:start position:0% +example right I as long as maybe just a +moment of linear algebra I + + align:start position:0% +moment of linear algebra I + + + align:start position:0% +moment of linear algebra I +could I believe I could solve these + + align:start position:0% +could I believe I could solve these + + + align:start position:0% +could I believe I could solve these +equations with + + align:start position:0% + + + + align:start position:0% + +this with those right hand sides which I + + align:start position:0% +this with those right hand sides which I + + + align:start position:0% +this with those right hand sides which I +just invented now what what's special + + align:start position:0% +just invented now what what's special + + + align:start position:0% +just invented now what what's special +about those right hand sides + + align:start position:0% +about those right hand sides + + + align:start position:0% +about those right hand sides +they add to zero right and they have to + + align:start position:0% +they add to zero right and they have to + + + align:start position:0% +they add to zero right and they have to +because the left sides add to zero if I + + align:start position:0% +because the left sides add to zero if I + + + align:start position:0% +because the left sides add to zero if I +change that to some other number that + + align:start position:0% +change that to some other number that + + + align:start position:0% +change that to some other number that +minus + + align:start position:0% +minus + + + align:start position:0% +minus +8 or changed any one of those numbers I + + align:start position:0% +8 or changed any one of those numbers I + + + align:start position:0% +8 or changed any one of those numbers I +I I would I I wouldn't have a current + + align:start position:0% +I I would I I wouldn't have a current + + + align:start position:0% +I I would I I wouldn't have a current +balance any longer so the fs that I'm + + align:start position:0% +balance any longer so the fs that I'm + + + align:start position:0% +balance any longer so the fs that I'm +allowed are the ones that add to zero so + + align:start position:0% +allowed are the ones that add to zero so + + + align:start position:0% +allowed are the ones that add to zero so +so a a transpose w or in general a + + align:start position:0% +so a a transpose w or in general a + + + align:start position:0% +so a a transpose w or in general a +transpose W equaling an f and I need the + + align:start position:0% +transpose W equaling an f and I need the + + + align:start position:0% +transpose W equaling an f and I need the +sum of the + + align:start position:0% +sum of the + + + align:start position:0% +sum of the +fs better be zero okay I could I can see + + align:start position:0% +fs better be zero okay I could I can see + + + align:start position:0% +fs better be zero okay I could I can see +in every way I can see physically why + + align:start position:0% +in every way I can see physically why + + + align:start position:0% +in every way I can see physically why +that has to happen and I can see in + + align:start position:0% +that has to happen and I can see in + + + align:start position:0% +that has to happen and I can see in +linear algebra why that has to happen + + align:start position:0% +linear algebra why that has to happen + + + align:start position:0% +linear algebra why that has to happen +because it's necessary to make the + + align:start position:0% +because it's necessary to make the + + + align:start position:0% +because it's necessary to make the +equations + + align:start position:0% +equations + + + align:start position:0% +equations +consistent okay so I'm ready now to put + + align:start position:0% +consistent okay so I'm ready now to put + + + align:start position:0% +consistent okay so I'm ready now to put +oh no I've got + + align:start position:0% +oh no I've got + + + align:start position:0% +oh no I've got +another is it + + align:start position:0% +another is it + + + align:start position:0% +another is it +coming yeah that a is the one with the + + align:start position:0% +coming yeah that a is the one with the + + + align:start position:0% +coming yeah that a is the one with the +row stripped out right some of those FS + + align:start position:0% +row stripped out right some of those FS + + + align:start position:0% +row stripped out right some of those FS +isn't Zer that's true that's true good + + align:start position:0% +isn't Zer that's true that's true good + + + align:start position:0% +isn't Zer that's true that's true good +point so maybe I better emphasize the + + align:start position:0% +point so maybe I better emphasize the + + + align:start position:0% +point so maybe I better emphasize the +right how shall I say the sum from one + + align:start position:0% +right how shall I say the sum from one + + + align:start position:0% +right how shall I say the sum from one +to n oh no I've changed in ha what do I + + align:start position:0% +to n oh no I've changed in ha what do I + + + align:start position:0% +to n oh no I've changed in ha what do I +do + + align:start position:0% +do + + + align:start position:0% +do +now it was for a z wasn't it really okay + + align:start position:0% +now it was for a z wasn't it really okay + + + align:start position:0% +now it was for a z wasn't it really okay +should I make it a + + align:start position:0% +should I make it a + + + align:start position:0% +should I make it a +z okay that's the Kirk Hof's law at all + + align:start position:0% +z okay that's the Kirk Hof's law at all + + + align:start position:0% +z okay that's the Kirk Hof's law at all +the nodes and then I do need the sum of + + align:start position:0% +the nodes and then I do need the sum of + + + align:start position:0% +the nodes and then I do need the sum of +the F thanks that's great whereas once I + + align:start position:0% +the F thanks that's great whereas once I + + + align:start position:0% +the F thanks that's great whereas once I +knock out a column an equation which I + + align:start position:0% +knock out a column an equation which I + + + align:start position:0% +knock out a column an equation which I +plan to do then I can always recover it + + align:start position:0% +plan to do then I can always recover it + + + align:start position:0% +plan to do then I can always recover it +by adding up the + + align:start position:0% +by adding up the + + + align:start position:0% +by adding up the +others uh but now my right hand sides + + align:start position:0% +others uh but now my right hand sides + + + align:start position:0% +others uh but now my right hand sides +add to plus eight good was that the same + + align:start position:0% +add to plus eight good was that the same + + + align:start position:0% +add to plus eight good was that the same +thank for yeah I was going to say + + align:start position:0% +thank for yeah I was going to say + + + align:start position:0% +thank for yeah I was going to say +that current law yes also specifies + + align:start position:0% +that current law yes also specifies + + + align:start position:0% +that current law yes also specifies +that current will be zero right so I + + align:start position:0% +that current will be zero right so I + + + align:start position:0% +that current will be zero right so I +have a + + align:start position:0% + + + + align:start position:0% + +little well those + + align:start position:0% +little well those + + + align:start position:0% +little well those +are on each node let's see I'm so I'm + + align:start position:0% +are on each node let's see I'm so I'm + + + align:start position:0% +are on each node let's see I'm so I'm +imagining I'm feeding current into there + + align:start position:0% +imagining I'm feeding current into there + + + align:start position:0% +imagining I'm feeding current into there +I might have some current feeding along + + align:start position:0% +I might have some current feeding along + + + align:start position:0% +I might have some current feeding along +here some currents feeding so + + align:start position:0% +here some currents feeding so + + + align:start position:0% +here some currents feeding so +essentially you got current in equals + + align:start position:0% +essentially you got current in equals + + + align:start position:0% +essentially you got current in equals +current out again I I that's what I'm + + align:start position:0% +current out again I I that's what I'm + + + align:start position:0% +current out again I I that's what I'm +trying to say yeah I've got current in + + align:start position:0% +trying to say yeah I've got current in + + + align:start position:0% +trying to say yeah I've got current in +equal current out but now I'm + + align:start position:0% +equal current out but now I'm + + + align:start position:0% +equal current out but now I'm +including external current + + align:start position:0% + + + + align:start position:0% + +sources right we can come come back to + + align:start position:0% +sources right we can come come back to + + + align:start position:0% +sources right we can come come back to +that so there's current sources come + + align:start position:0% +that so there's current sources come + + + align:start position:0% +that so there's current sources come +into our framework here which is getting + + align:start position:0% +into our framework here which is getting + + + align:start position:0% +into our framework here which is getting +kind of hard to + + align:start position:0% +kind of hard to + + + align:start position:0% +kind of hard to +see and it's going to get + + align:start position:0% +see and it's going to get + + + align:start position:0% +see and it's going to get +worse because there's another kind of + + align:start position:0% +worse because there's another kind of + + + align:start position:0% +worse because there's another kind of +sources voltage sources we could also + + align:start position:0% +sources voltage sources we could also + + + align:start position:0% +sources voltage sources we could also +make things happen by putting a battery + + align:start position:0% +make things happen by putting a battery + + + align:start position:0% +make things happen by putting a battery +oh well you where the heck am I going to + + align:start position:0% +oh well you where the heck am I going to + + + align:start position:0% +oh well you where the heck am I going to +put a battery in this uh + + align:start position:0% +put a battery in this uh + + + align:start position:0% +put a battery in this uh +circuit let me put it between two and + + align:start position:0% +circuit let me put it between two and + + + align:start position:0% +circuit let me put it between two and +three as a little room okay there's a + + align:start position:0% +three as a little room okay there's a + + + align:start position:0% +three as a little room okay there's a +battery going in there I I'll write the + + align:start position:0% +battery going in there I I'll write the + + + align:start position:0% +battery going in there I I'll write the +equations here let me write all the + + align:start position:0% +equations here let me write all the + + + align:start position:0% +equations here let me write all the +equations here let me write all the + + align:start position:0% +equations here let me write all the + + + align:start position:0% +equations here let me write all the +equations + + align:start position:0% +equations + + + align:start position:0% +equations +here + + align:start position:0% +here + + + align:start position:0% +here +our our three fundamental + + align:start position:0% +our our three fundamental + + + align:start position:0% +our our three fundamental +equations okay and the last now is a + + align:start position:0% +equations okay and the last now is a + + + align:start position:0% +equations okay and the last now is a +transpose wal F and the middle one is w + + align:start position:0% +transpose wal F and the middle one is w + + + align:start position:0% +transpose wal F and the middle one is w += c e that's fine now it's this first + + align:start position:0% += c e that's fine now it's this first + + + align:start position:0% += c e that's fine now it's this first +equation that I want to get this first + + align:start position:0% + + + + align:start position:0% + +step and I I'm allow I want to allow now + + align:start position:0% +step and I I'm allow I want to allow now + + + align:start position:0% +step and I I'm allow I want to allow now +the possibility of + + align:start position:0% +the possibility of + + + align:start position:0% +the possibility of +a bunch of batteries entering there so + + align:start position:0% +a bunch of batteries entering there so + + + align:start position:0% +a bunch of batteries entering there so +here comes a + + align:start position:0% +here comes a + + + align:start position:0% +here comes a +new an external + + align:start position:0% +new an external + + + align:start position:0% +new an external +term a vector + + align:start position:0% +term a vector + + + align:start position:0% +term a vector +B one for every + + align:start position:0% +B one for every + + + align:start position:0% +B one for every +Edge so it's they batteries are on the + + align:start position:0% +Edge so it's they batteries are on the + + + align:start position:0% +Edge so it's they batteries are on the +edges and so it's entering the framework + + align:start position:0% +edges and so it's entering the framework + + + align:start position:0% +edges and so it's entering the framework +at this point you see what's new here up + + align:start position:0% +at this point you see what's new here up + + + align:start position:0% +at this point you see what's new here up +to now in the in the mechanics problem + + align:start position:0% +to now in the in the mechanics problem + + + align:start position:0% +to now in the in the mechanics problem +we only had external forces entering up + + align:start position:0% +we only had external forces entering up + + + align:start position:0% +we only had external forces entering up +there in the balance equation + + align:start position:0% +there in the balance equation + + + align:start position:0% +there in the balance equation +but now we have a b battery so let me + + align:start position:0% +but now we have a b battery so let me + + + align:start position:0% +but now we have a b battery so let me +draw a + + align:start position:0% +draw a + + + align:start position:0% +draw a +battery okay this is Edge number three + + align:start position:0% +battery okay this is Edge number three + + + align:start position:0% +battery okay this is Edge number three +it's got a resistor of course with or + + align:start position:0% +it's got a resistor of course with or + + + align:start position:0% +it's got a resistor of course with or +conductor with with C3 and then it's + + align:start position:0% +conductor with with C3 and then it's + + + align:start position:0% +conductor with with C3 and then it's +also got a + + align:start position:0% + + + + align:start position:0% + +battery and let me write down then the + + align:start position:0% +battery and let me write down then the + + + align:start position:0% +battery and let me write down then the +equation for e e the the force is the X + + align:start position:0% +equation for e e the the force is the X + + + align:start position:0% +equation for e e the the force is the X +external term coming from the + + align:start position:0% +external term coming from the + + + align:start position:0% +external term coming from the +battery minus the Au term the internal + + align:start position:0% +battery minus the Au term the internal + + + align:start position:0% +battery minus the Au term the internal +term coming + + align:start position:0% +term coming + + + align:start position:0% +term coming +from difference in potentials + + align:start position:0% + + + + align:start position:0% + +so this is this is now what we have to + + align:start position:0% +so this is this is now what we have to + + + align:start position:0% +so this is this is now what we have to +what we have to deal with these four equ + + align:start position:0% +what we have to deal with these four equ + + + align:start position:0% +what we have to deal with these four equ +these three equations those are our + + align:start position:0% +these three equations those are our + + + align:start position:0% +these three equations those are our +Central equations so what are my + + align:start position:0% +Central equations so what are my + + + align:start position:0% +Central equations so what are my +comments about them first the key fact + + align:start position:0% +comments about them first the key fact + + + align:start position:0% +comments about them first the key fact +that a and a transpose + + align:start position:0% +that a and a transpose + + + align:start position:0% +that a and a transpose +appear second the fact that we now have + + align:start position:0% +appear second the fact that we now have + + + align:start position:0% +appear second the fact that we now have +two Source terms F at the nodes and B on + + align:start position:0% +two Source terms F at the nodes and B on + + + align:start position:0% +two Source terms F at the nodes and B on +the + + align:start position:0% +the + + + align:start position:0% +the +edges third comment we now have this + + align:start position:0% +edges third comment we now have this + + + align:start position:0% +edges third comment we now have this +minus sign and you if we check we'll see + + align:start position:0% +minus sign and you if we check we'll see + + + align:start position:0% +minus sign and you if we check we'll see +that that's needed to make uh um + + align:start position:0% +that that's needed to make uh um + + + align:start position:0% +that that's needed to make uh um +current so if Au if this if U2 minus U1 + + align:start position:0% +current so if Au if this if U2 minus U1 + + + align:start position:0% +current so if Au if this if U2 minus U1 +was + + align:start position:0% + + + + align:start position:0% + +Zero so that the first component of au + + align:start position:0% +Zero so that the first component of au + + + align:start position:0% +Zero so that the first component of au +is zero then but there could still be a + + align:start position:0% +is zero then but there could still be a + + + align:start position:0% +is zero then but there could still be a +battery B1 that would make something + + align:start position:0% +battery B1 that would make something + + + align:start position:0% +battery B1 that would make something +happen right there's + + align:start position:0% +happen right there's + + + align:start position:0% +happen right there's +a uh do you see that the batteries the + + align:start position:0% +a uh do you see that the batteries the + + + align:start position:0% +a uh do you see that the batteries the +voltage sources enter at this point plus + + align:start position:0% +voltage sources enter at this point plus + + + align:start position:0% +voltage sources enter at this point plus +or minus the voltage differences now I + + align:start position:0% +or minus the voltage differences now I + + + align:start position:0% +or minus the voltage differences now I +refu I I frankly don't know which way + + align:start position:0% +refu I I frankly don't know which way + + + align:start position:0% +refu I I frankly don't know which way +the batter is + + align:start position:0% +the batter is + + + align:start position:0% +the batter is +installed either in my picture or in my + + align:start position:0% +installed either in my picture or in my + + + align:start position:0% +installed either in my picture or in my +uh + + align:start position:0% +uh + + + align:start position:0% +uh +camera uh and then the camera it's got + + align:start position:0% +camera uh and then the camera it's got + + + align:start position:0% +camera uh and then the camera it's got +that little plus and minus to uh guide + + align:start position:0% +that little plus and minus to uh guide + + + align:start position:0% +that little plus and minus to uh guide +you when you put in the battery uh I + + align:start position:0% +you when you put in the battery uh I + + + align:start position:0% +you when you put in the battery uh I +don't provide that here and I don't know + + align:start position:0% +don't provide that here and I don't know + + + align:start position:0% +don't provide that here and I don't know +which one way or the other uh I I always + + align:start position:0% +which one way or the other uh I I always + + + align:start position:0% +which one way or the other uh I I always +um so this is for my MIT class I tell + + align:start position:0% +um so this is for my MIT class I tell + + + align:start position:0% +um so this is for my MIT class I tell +them okay uh no penalty for getting the + + align:start position:0% +them okay uh no penalty for getting the + + + align:start position:0% +them okay uh no penalty for getting the +sign wrong because I generally get it + + align:start position:0% +sign wrong because I generally get it + + + align:start position:0% +sign wrong because I generally get it +wrong so uh the + + align:start position:0% +wrong so uh the + + + align:start position:0% +wrong so uh the +anyway with correct + + align:start position:0% +anyway with correct + + + align:start position:0% +anyway with correct +sign it'll be a vector B okay so those + + align:start position:0% +sign it'll be a vector B okay so those + + + align:start position:0% +sign it'll be a vector B okay so those +are our + + align:start position:0% +are our + + + align:start position:0% +are our +equations okay those are our equations + + align:start position:0% +equations okay those are our equations + + + align:start position:0% +equations okay those are our equations +and and in a so th I mean these are like + + align:start position:0% +and and in a so th I mean these are like + + + align:start position:0% +and and in a so th I mean these are like +the fundamental equations of linear + + align:start position:0% +the fundamental equations of linear + + + align:start position:0% +the fundamental equations of linear +resistive circuits I it's it's + + align:start position:0% +resistive circuits I it's it's + + + align:start position:0% +resistive circuits I it's it's +restricted now to resistors but um we + + align:start position:0% +restricted now to resistors but um we + + + align:start position:0% +restricted now to resistors but um we +can we can move to allow capacitors and + + align:start position:0% +can we can move to allow capacitors and + + + align:start position:0% +can we can move to allow capacitors and +inductors into the network + + align:start position:0% +inductors into the network + + + align:start position:0% +inductors into the network +and ultimately move to a nonlinear + + align:start position:0% +and ultimately move to a nonlinear + + + align:start position:0% +and ultimately move to a nonlinear +Network allow + + align:start position:0% +Network allow + + + align:start position:0% +Network allow +transistors diodes + + align:start position:0% +transistors diodes + + + align:start position:0% +transistors diodes +whatever okay but of course this is the + + align:start position:0% +whatever okay but of course this is the + + + align:start position:0% +whatever okay but of course this is the +the natural place to begin so I'm + + align:start position:0% +the natural place to begin so I'm + + + align:start position:0% +the natural place to begin so I'm +talking about linear steady state we + + align:start position:0% +talking about linear steady state we + + + align:start position:0% +talking about linear steady state we +we're not we don't have trents here we + + align:start position:0% +we're not we don't have trents here we + + + align:start position:0% +we're not we don't have trents here we +these currents are steady state + + align:start position:0% +these currents are steady state + + + align:start position:0% +these currents are steady state +currents DC we're direct currents and + + align:start position:0% +currents DC we're direct currents and + + + align:start position:0% +currents DC we're direct currents and +but we've got the three Central + + align:start position:0% +but we've got the three Central + + + align:start position:0% +but we've got the three Central +equations and they fit our framework + + align:start position:0% +equations and they fit our framework + + + align:start position:0% +equations and they fit our framework +okay and we we now see external sources + + align:start position:0% +okay and we we now see external sources + + + align:start position:0% +okay and we we now see external sources +B entering on the edges as + + align:start position:0% +B entering on the edges as + + + align:start position:0% +B entering on the edges as +batteries current sources entering at + + align:start position:0% +batteries current sources entering at + + + align:start position:0% +batteries current sources entering at +the + + align:start position:0% +the + + + align:start position:0% +the +nodes and we could + + align:start position:0% +nodes and we could + + + align:start position:0% +nodes and we could +fix just to see what are all the B what + + align:start position:0% +fix just to see what are all the B what + + + align:start position:0% +fix just to see what are all the B what +are all the external things we could fix + + align:start position:0% +are all the external things we could fix + + + align:start position:0% +are all the external things we could fix +potentials oh we already do fix the + + align:start position:0% +potentials oh we already do fix the + + + align:start position:0% +potentials oh we already do fix the +potential at node 4 and I could fix the + + align:start position:0% +potential at node 4 and I could fix the + + + align:start position:0% +potential at node 4 and I could fix the +potential at node two as 30 Vols + + align:start position:0% +potential at node two as 30 Vols + + + align:start position:0% +potential at node two as 30 Vols +so this would be another place where I + + align:start position:0% +so this would be another place where I + + + align:start position:0% +so this would be another place where I +could fixed potentials would be an + + align:start position:0% +could fixed potentials would be an + + + align:start position:0% +could fixed potentials would be an +external uh quantity or I could fix + + align:start position:0% +external uh quantity or I could fix + + + align:start position:0% +external uh quantity or I could fix +currents at certain places so now you're + + align:start position:0% +currents at certain places so now you're + + + align:start position:0% +currents at certain places so now you're +seeing really the full framework we've + + align:start position:0% +seeing really the full framework we've + + + align:start position:0% +seeing really the full framework we've +got the four pieces external Source + + align:start position:0% +got the four pieces external Source + + + align:start position:0% +got the four pieces external Source +terms entering here and here uh boundary + + align:start position:0% +terms entering here and here uh boundary + + + align:start position:0% +terms entering here and here uh boundary +terms you could say grounded nodes fixed + + align:start position:0% +terms you could say grounded nodes fixed + + + align:start position:0% +terms you could say grounded nodes fixed +potentials or fixed currents could enter + + align:start position:0% +potentials or fixed currents could enter + + + align:start position:0% +potentials or fixed currents could enter +there and there so at each of the four + + align:start position:0% +there and there so at each of the four + + + align:start position:0% +there and there so at each of the four +uh Corners uh there a possibility for uh + + align:start position:0% +uh Corners uh there a possibility for uh + + + align:start position:0% +uh Corners uh there a possibility for uh +specifying something okay but I'm happy + + align:start position:0% +specifying something okay but I'm happy + + + align:start position:0% +specifying something okay but I'm happy +to deal with these + + align:start position:0% +to deal with these + + + align:start position:0% +to deal with these +equations uh as they are all right okay + + align:start position:0% +equations uh as they are all right okay + + + align:start position:0% +equations uh as they are all right okay +now what do I what to do with them well + + align:start position:0% +now what do I what to do with them well + + + align:start position:0% +now what do I what to do with them well +I could put them together that's the + + align:start position:0% +I could put them together that's the + + + align:start position:0% +I could put them together that's the +most important thing if I combine those + + align:start position:0% +most important thing if I combine those + + + align:start position:0% +most important thing if I combine those +equations what do we get can I write + + align:start position:0% +equations what do we get can I write + + + align:start position:0% +equations what do we get can I write +them again maybe I'll maybe I'll copy + + align:start position:0% +them again maybe I'll maybe I'll copy + + + align:start position:0% +them again maybe I'll maybe I'll copy +them over here and because I'll I'll use + + align:start position:0% +them over here and because I'll I'll use + + + align:start position:0% +them over here and because I'll I'll use +that space again e is B minus Au + + align:start position:0% +that space again e is B minus Au + + + align:start position:0% +that space again e is B minus Au +U uh W is + + align:start position:0% +U uh W is + + + align:start position:0% +U uh W is +C and F is a transpose W + + align:start position:0% +C and F is a transpose W + + + align:start position:0% +C and F is a transpose W +okay right now so let me put those + + align:start position:0% +okay right now so let me put those + + + align:start position:0% +okay right now so let me put those +together let me oh let me first + + align:start position:0% +together let me oh let me first + + + align:start position:0% +together let me oh let me first +put take e out can I first first + + align:start position:0% +put take e out can I first first + + + align:start position:0% +put take e out can I first first +eliminate + + align:start position:0% +eliminate + + + align:start position:0% +eliminate +e and then I'll + + align:start position:0% +e and then I'll + + + align:start position:0% +e and then I'll +eliminate W so let me first eliminate e + + align:start position:0% +eliminate W so let me first eliminate e + + + align:start position:0% +eliminate W so let me first eliminate e +so e is C inverse W so I just write that + + align:start position:0% +so e is C inverse W so I just write that + + + align:start position:0% +so e is C inverse W so I just write that +e is C inverse W and let me put that in + + align:start position:0% +e is C inverse W and let me put that in + + + align:start position:0% +e is C inverse W and let me put that in +up + + align:start position:0% +up + + + align:start position:0% +up +here so so I have C inverse + + align:start position:0% + + + + align:start position:0% + +W that's e and I'll bring Au over on + + align:start position:0% +W that's e and I'll bring Au over on + + + align:start position:0% +W that's e and I'll bring Au over on +that side because it's involves unknowns + + align:start position:0% +that side because it's involves unknowns + + + align:start position:0% +that side because it's involves unknowns +equals B and then this equation uh I'll + + align:start position:0% +equals B and then this equation uh I'll + + + align:start position:0% +equals B and then this equation uh I'll +keep as a transpose W equal + + align:start position:0% +keep as a transpose W equal + + + align:start position:0% +keep as a transpose W equal +F + + align:start position:0% + + + + align:start position:0% + +okay so those are the two now I've got + + align:start position:0% +okay so those are the two now I've got + + + align:start position:0% +okay so those are the two now I've got +two equations actually here these this + + align:start position:0% +two equations actually here these this + + + align:start position:0% +two equations actually here these this +is a set let's see this was one for + + align:start position:0% +is a set let's see this was one for + + + align:start position:0% +is a set let's see this was one for +every Edge so I really have M equations + + align:start position:0% +every Edge so I really have M equations + + + align:start position:0% +every Edge so I really have M equations +there and here I have n equations so I + + align:start position:0% +there and here I have n equations so I + + + align:start position:0% +there and here I have n equations so I +have M plus n equations M plus n + + align:start position:0% +have M plus n equations M plus n + + + align:start position:0% +have M plus n equations M plus n +equations oh it's even worth pulling out + + align:start position:0% +equations oh it's even worth pulling out + + + align:start position:0% +equations oh it's even worth pulling out +that Matrix because it's so important C + + align:start position:0% +that Matrix because it's so important C + + + align:start position:0% +that Matrix because it's so important C +inverse a a + + align:start position:0% +inverse a a + + + align:start position:0% +inverse a a +transpose and zero + + align:start position:0% +transpose and zero + + + align:start position:0% +transpose and zero +multiply W and U the unknowns to + + align:start position:0% +multiply W and U the unknowns to + + + align:start position:0% +multiply W and U the unknowns to +give B and F The Source + + align:start position:0% +give B and F The Source + + + align:start position:0% +give B and F The Source +terms that I want to really put a star + + align:start position:0% +terms that I want to really put a star + + + align:start position:0% +terms that I want to really put a star +bide I need two stars beside that uh + + align:start position:0% +bide I need two stars beside that uh + + + align:start position:0% +bide I need two stars beside that uh +system of equations two stars maybe + + align:start position:0% +system of equations two stars maybe + + + align:start position:0% +system of equations two stars maybe +because it's two + + align:start position:0% +because it's two + + + align:start position:0% +because it's two +it's a two field we we're looking for + + align:start position:0% +it's a two field we we're looking for + + + align:start position:0% +it's a two field we we're looking for +currents and voltages both here I can + + align:start position:0% +currents and voltages both here I can + + + align:start position:0% +currents and voltages both here I can +eliminate one and get down to looking + + align:start position:0% +eliminate one and get down to looking + + + align:start position:0% +eliminate one and get down to looking +only for voltages and I will but for the + + align:start position:0% +only for voltages and I will but for the + + + align:start position:0% +only for voltages and I will but for the +moment this is I I see this type of + + align:start position:0% +moment this is I I see this type of + + + align:start position:0% +moment this is I I see this type of +Matrix so often that I want to talk + + align:start position:0% +Matrix so often that I want to talk + + + align:start position:0% +Matrix so often that I want to talk +about it uh + + align:start position:0% +about it uh + + + align:start position:0% +about it uh +here well tell me something about that + + align:start position:0% +here well tell me something about that + + + align:start position:0% +here well tell me something about that +Matrix is it well so we'll ask all the + + align:start position:0% +Matrix is it well so we'll ask all the + + + align:start position:0% +Matrix is it well so we'll ask all the +usual questions + + align:start position:0% +usual questions + + + align:start position:0% +usual questions +is it + + align:start position:0% +is it + + + align:start position:0% +is it +symmetric yes it is it is + + align:start position:0% +symmetric yes it is it is + + + align:start position:0% +symmetric yes it is it is +symmetric because if I because this C is + + align:start position:0% +symmetric because if I because this C is + + + align:start position:0% +symmetric because if I because this C is +symmetric up here in the corner and of + + align:start position:0% +symmetric up here in the corner and of + + + align:start position:0% +symmetric up here in the corner and of +course the zero M the this is a block + + align:start position:0% +course the zero M the this is a block + + + align:start position:0% +course the zero M the this is a block +Matrix of course so these are square + + align:start position:0% +Matrix of course so these are square + + + align:start position:0% +Matrix of course so these are square +blocks and yeah square + + align:start position:0% +blocks and yeah square + + + align:start position:0% +blocks and yeah square +blocks a is not Square true true a is + + align:start position:0% +blocks a is not Square true true a is + + + align:start position:0% +blocks a is not Square true true a is +not Square how do I so this is a square + + align:start position:0% +not Square how do I so this is a square + + + align:start position:0% +not Square how do I so this is a square +how do I well I guess I just say it so + + align:start position:0% +how do I well I guess I just say it so + + + align:start position:0% +how do I well I guess I just say it so +that's a square block and it's symmetric + + align:start position:0% +that's a square block and it's symmetric + + + align:start position:0% +that's a square block and it's symmetric +right oh in fact it's diagonal + + align:start position:0% +right oh in fact it's diagonal + + + align:start position:0% +right oh in fact it's diagonal +simple and of course the block of zeros + + align:start position:0% +simple and of course the block of zeros + + + align:start position:0% +simple and of course the block of zeros +is square and symmetric this is this is + + align:start position:0% +is square and symmetric this is this is + + + align:start position:0% +is square and symmetric this is this is +my M by M Block right and this is my n + + align:start position:0% +my M by M Block right and this is my n + + + align:start position:0% +my M by M Block right and this is my n +byn block + + align:start position:0% +byn block + + + align:start position:0% +byn block +fine but now a is not symmetric in fact + + align:start position:0% +fine but now a is not symmetric in fact + + + align:start position:0% +fine but now a is not symmetric in fact +it's not even square a is M by + + align:start position:0% +it's not even square a is M by + + + align:start position:0% +it's not even square a is M by +n n n columns so n columns are going + + align:start position:0% +n n n columns so n columns are going + + + align:start position:0% +n n n columns so n columns are going +down here and here's its transpose so it + + align:start position:0% +down here and here's its transpose so it + + + align:start position:0% +down here and here's its transpose so it +is + + align:start position:0% + + + + align:start position:0% + +symmetric this big + + align:start position:0% +symmetric this big + + + align:start position:0% +symmetric this big +Matrix what else would we want to know + + align:start position:0% +Matrix what else would we want to know + + + align:start position:0% +Matrix what else would we want to know +is it invertible of course that's of + + align:start position:0% +is it invertible of course that's of + + + align:start position:0% +is it invertible of course that's of +course that's the central + + align:start position:0% +course that's the central + + + align:start position:0% +course that's the central +question and we hope the answer is yes + + align:start position:0% +question and we hope the answer is yes + + + align:start position:0% +question and we hope the answer is yes +right because we we hope that by + + align:start position:0% +right because we we hope that by + + + align:start position:0% +right because we we hope that by +grounding the node making this so we + + align:start position:0% +grounding the node making this so we + + + align:start position:0% +grounding the node making this so we +knocked out that column let me erase it + + align:start position:0% +knocked out that column let me erase it + + + align:start position:0% +knocked out that column let me erase it +again we knocked out that column from + + align:start position:0% +again we knocked out that column from + + + align:start position:0% +again we knocked out that column from +a from a to give a so we it is + + align:start position:0% +a from a to give a so we it is + + + align:start position:0% +a from a to give a so we it is +invertible let me put invertible in + + align:start position:0% + + + + align:start position:0% + +there okay but I have to ask you + + align:start position:0% +there okay but I have to ask you + + + align:start position:0% +there okay but I have to ask you +about positive definite right that's the + + align:start position:0% +about positive definite right that's the + + + align:start position:0% +about positive definite right that's the +remaining property and that's the one + + align:start position:0% +remaining property and that's the one + + + align:start position:0% +remaining property and that's the one +that's less + + align:start position:0% +that's less + + + align:start position:0% +that's less +familiar so this gives us a chance to + + align:start position:0% +familiar so this gives us a chance to + + + align:start position:0% +familiar so this gives us a chance to +say is this Matrix positive definite or + + align:start position:0% +say is this Matrix positive definite or + + + align:start position:0% +say is this Matrix positive definite or +not so this question mark + + align:start position:0% +not so this question mark + + + align:start position:0% +not so this question mark +positive definite + + align:start position:0% + + + + align:start position:0% + +and well we're just learning about + + align:start position:0% +and well we're just learning about + + + align:start position:0% +and well we're just learning about +positive definite matrices so why don't + + align:start position:0% +positive definite matrices so why don't + + + align:start position:0% +positive definite matrices so why don't +we learn one why don't we spot the + + align:start position:0% +we learn one why don't we spot the + + + align:start position:0% +we learn one why don't we spot the +answer is no that Matrix is not positive + + align:start position:0% +answer is no that Matrix is not positive + + + align:start position:0% +answer is no that Matrix is not positive +definite it couldn't be with those zeros + + align:start position:0% +definite it couldn't be with those zeros + + + align:start position:0% +definite it couldn't be with those zeros +there positive definite matrixes + + align:start position:0% +there positive definite matrixes + + + align:start position:0% +there positive definite matrixes +positive definite matrices at a at a + + align:start position:0% +positive definite matrices at a at a + + + align:start position:0% +positive definite matrices at a at a +minimum have positive entries on the + + align:start position:0% +minimum have positive entries on the + + + align:start position:0% +minimum have positive entries on the +diagonal and and and also somehow those + + align:start position:0% +diagonal and and and also somehow those + + + align:start position:0% +diagonal and and and also somehow those +diagonal entries have to be big enough + + align:start position:0% +diagonal entries have to be big enough + + + align:start position:0% +diagonal entries have to be big enough +to to dominate what's off the diagonal + + align:start position:0% +to to dominate what's off the diagonal + + + align:start position:0% +to to dominate what's off the diagonal +here no luck no chance at all so the + + align:start position:0% +here no luck no chance at all so the + + + align:start position:0% +here no luck no chance at all so the +answer is not positive + + align:start position:0% + + + + align:start position:0% + +definite not positive definite in if I + + align:start position:0% +definite not positive definite in if I + + + align:start position:0% +definite not positive definite in if I +if I do elimination with that + + align:start position:0% +if I do elimination with that + + + align:start position:0% +if I do elimination with that +Matrix well well we can figure out what + + align:start position:0% +Matrix well well we can figure out what + + + align:start position:0% +Matrix well well we can figure out what +what will happen if I do + + align:start position:0% +what will happen if I do + + + align:start position:0% +what will happen if I do +elimination actually let's do + + align:start position:0% + + + + align:start position:0% + +elimination can so this is are you + + align:start position:0% +elimination can so this is are you + + + align:start position:0% +elimination can so this is are you +familiar with the sort of thinging about + + align:start position:0% +familiar with the sort of thinging about + + + align:start position:0% +familiar with the sort of thinging about +block + + align:start position:0% +block + + + align:start position:0% +block +matrices you're seeing here why they're + + align:start position:0% +matrices you're seeing here why they're + + + align:start position:0% +matrices you're seeing here why they're +so uh natural and come up so often I + + align:start position:0% +so uh natural and come up so often I + + + align:start position:0% +so uh natural and come up so often I +mean the the the natural way to to is to + + align:start position:0% +mean the the the natural way to to is to + + + align:start position:0% +mean the the the natural way to to is to +have these two sets of unknowns these + + align:start position:0% +have these two sets of unknowns these + + + align:start position:0% +have these two sets of unknowns these +two sets of sources and M they have to + + align:start position:0% +two sets of sources and M they have to + + + align:start position:0% +two sets of sources and M they have to +be matrices to multiply because that W + + align:start position:0% +be matrices to multiply because that W + + + align:start position:0% +be matrices to multiply because that W +is a vector no no problem it's just + + align:start position:0% +is a vector no no problem it's just + + + align:start position:0% +is a vector no no problem it's just +natural okay imagine doing elimination + + align:start position:0% +natural okay imagine doing elimination + + + align:start position:0% +natural okay imagine doing elimination +on this + + align:start position:0% +on this + + + align:start position:0% +on this +Matrix okay so you start what are the + + align:start position:0% +Matrix okay so you start what are the + + + align:start position:0% +Matrix okay so you start what are the +pivot what's the F so the numbers in so + + align:start position:0% +pivot what's the F so the numbers in so + + + align:start position:0% +pivot what's the F so the numbers in so +this C inverse is a diagonal matrix 1 + + align:start position:0% +this C inverse is a diagonal matrix 1 + + + align:start position:0% +this C inverse is a diagonal matrix 1 +over C1 1 over C2 1 over C3 right it's + + align:start position:0% +over C1 1 over C2 1 over C3 right it's + + + align:start position:0% +over C1 1 over C2 1 over C3 right it's +just C inverse will be C1 inverse C2 + + align:start position:0% +just C inverse will be C1 inverse C2 + + + align:start position:0% +just C inverse will be C1 inverse C2 +inverse C5 + + align:start position:0% +inverse C5 + + + align:start position:0% +inverse C5 +inverse just + + align:start position:0% +inverse just + + + align:start position:0% +inverse just +reciprocals so actually those will be + + align:start position:0% +reciprocals so actually those will be + + + align:start position:0% +reciprocals so actually those will be +the first pivots right so the first M + + align:start position:0% +the first pivots right so the first M + + + align:start position:0% +the first pivots right so the first M +pivots the first five pivots are + + align:start position:0% +pivots the first five pivots are + + + align:start position:0% +pivots the first five pivots are +positive no so we're like we're off to a + + align:start position:0% +positive no so we're like we're off to a + + + align:start position:0% +positive no so we're like we're off to a +good + + align:start position:0% +good + + + align:start position:0% +good +start but what are the what are the + + align:start position:0% +start but what are the what are the + + + align:start position:0% +start but what are the what are the +remaining pivots well they're not zeros + + align:start position:0% +remaining pivots well they're not zeros + + + align:start position:0% +remaining pivots well they're not zeros +right because so I I I want to ask you + + align:start position:0% +right because so I I I want to ask you + + + align:start position:0% +right because so I I I want to ask you +to imagine what elimination ordinary G + + align:start position:0% +to imagine what elimination ordinary G + + + align:start position:0% +to imagine what elimination ordinary G +elimination multiply rows by numbers to + + align:start position:0% +elimination multiply rows by numbers to + + + align:start position:0% +elimination multiply rows by numbers to +produce zeros below the pivots exactly + + align:start position:0% +produce zeros below the pivots exactly + + + align:start position:0% +produce zeros below the pivots exactly +the standard mat lab operation probably + + align:start position:0% +the standard mat lab operation probably + + + align:start position:0% +the standard mat lab operation probably +the most surely the + + align:start position:0% +the most surely the + + + align:start position:0% +the most surely the +most uh + + align:start position:0% +most uh + + + align:start position:0% +most uh +common + + align:start position:0% +common + + + align:start position:0% +common +um operation in scientific Computing + + align:start position:0% +um operation in scientific Computing + + + align:start position:0% +um operation in scientific Computing +I'll jump overboard here elim gaan + + align:start position:0% +I'll jump overboard here elim gaan + + + align:start position:0% +I'll jump overboard here elim gaan +elimination which was known to the + + align:start position:0% +elimination which was known to the + + + align:start position:0% +elimination which was known to the +Chinese but gaus uh uh didn't know that + + align:start position:0% +Chinese but gaus uh uh didn't know that + + + align:start position:0% +Chinese but gaus uh uh didn't know that +uh so anyway he he was a the greatest + + align:start position:0% +uh so anyway he he was a the greatest + + + align:start position:0% +uh so anyway he he was a the greatest +mathematician ever so fair if he gets + + align:start position:0% +mathematician ever so fair if he gets + + + align:start position:0% +mathematician ever so fair if he gets +credit occasionally for something he he + + align:start position:0% +credit occasionally for something he he + + + align:start position:0% +credit occasionally for something he he +wasn't first on uh uh that's that's the + + align:start position:0% +wasn't first on uh uh that's that's the + + + align:start position:0% +wasn't first on uh uh that's that's the +most important operation in in + + align:start position:0% +most important operation in in + + + align:start position:0% +most important operation in in +scientific Computing you're doing it all + + align:start position:0% +scientific Computing you're doing it all + + + align:start position:0% +scientific Computing you're doing it all +the time you're solving linear + + align:start position:0% +the time you're solving linear + + + align:start position:0% +the time you're solving linear +systems and how to do it faster is I + + align:start position:0% +systems and how to do it faster is I + + + align:start position:0% +systems and how to do it faster is I +mean like a a billion dollar + + align:start position:0% +mean like a a billion dollar + + + align:start position:0% +mean like a a billion dollar +question uh and uh we're imagining here + + align:start position:0% +question uh and uh we're imagining here + + + align:start position:0% +question uh and uh we're imagining here +that we just do it straight out the + + align:start position:0% +that we just do it straight out the + + + align:start position:0% +that we just do it straight out the +usual way and now what will happen if we + + align:start position:0% +usual way and now what will happen if we + + + align:start position:0% +usual way and now what will happen if we +do what will happen if we + + align:start position:0% + + + + align:start position:0% + +do right we'll get something here well + + align:start position:0% +do right we'll get something here well + + + align:start position:0% +do right we'll get something here well +yeah what we want to figure out what + + align:start position:0% +yeah what we want to figure out what + + + align:start position:0% +yeah what we want to figure out what +what will we get here when we do + + align:start position:0% +what will we get here when we do + + + align:start position:0% +what will we get here when we do +elimination the whole point to get zero + + align:start position:0% +elimination the whole point to get zero + + + align:start position:0% +elimination the whole point to get zero +so so let me do elimination let's do + + align:start position:0% +so so let me do elimination let's do + + + align:start position:0% +so so let me do elimination let's do +block we'll see the whole how valuable + + align:start position:0% +block we'll see the whole how valuable + + + align:start position:0% +block we'll see the whole how valuable +block matrices are so these row what + + align:start position:0% +block matrices are so these row what + + + align:start position:0% +block matrices are so these row what +happens at the these rows they were fine + + align:start position:0% +happens at the these rows they were fine + + + align:start position:0% +happens at the these rows they were fine +right C inverse was this diagonal matrix + + align:start position:0% +right C inverse was this diagonal matrix + + + align:start position:0% +right C inverse was this diagonal matrix +with zeros under it so there's no no + + align:start position:0% +with zeros under it so there's no no + + + align:start position:0% +with zeros under it so there's no no +multipliers no elimination to do at this + + align:start position:0% +multipliers no elimination to do at this + + + align:start position:0% +multipliers no elimination to do at this +for these first rows they're not + + align:start position:0% +for these first rows they're not + + + align:start position:0% +for these first rows they're not +changed but + + align:start position:0% +changed but + + + align:start position:0% +changed but +now below here is where we want to knock + + align:start position:0% +now below here is where we want to knock + + + align:start position:0% +now below here is where we want to knock +it out and then the question is what + + align:start position:0% +it out and then the question is what + + + align:start position:0% +it out and then the question is what +shows up there when we + + align:start position:0% +shows up there when we + + + align:start position:0% +shows up there when we +do so that that's + + align:start position:0% +do so that that's + + + align:start position:0% +do so that that's +really so this is still the unknown is + + align:start position:0% +really so this is still the unknown is + + + align:start position:0% +really so this is still the unknown is +still + + align:start position:0% +still + + + align:start position:0% +still +Wu and the right hand side is still B + + align:start position:0% +Wu and the right hand side is still B + + + align:start position:0% +Wu and the right hand side is still B +and then it's some new right hand side + + align:start position:0% +and then it's some new right hand side + + + align:start position:0% +and then it's some new right hand side +uh depending on our elimination steps + + align:start position:0% +uh depending on our elimination steps + + + align:start position:0% +uh depending on our elimination steps +okay do you see what's going to what is + + align:start position:0% +okay do you see what's going to what is + + + align:start position:0% +okay do you see what's going to what is +our eliminate what's our what are we + + align:start position:0% +our eliminate what's our what are we + + + align:start position:0% +our eliminate what's our what are we +doing here + + align:start position:0% +doing here + + + align:start position:0% +doing here +blockwise I'm multiplying this block row + + align:start position:0% +blockwise I'm multiplying this block row + + + align:start position:0% +blockwise I'm multiplying this block row +by some Matrix and + + align:start position:0% +by some Matrix and + + + align:start position:0% +by some Matrix and +subtracting from the row beneath just + + align:start position:0% +subtracting from the row beneath just + + + align:start position:0% +subtracting from the row beneath just +think in terms of blocks as numbers so + + align:start position:0% +think in terms of blocks as numbers so + + + align:start position:0% +think in terms of blocks as numbers so +what am I multiplying by let me let's + + align:start position:0% +what am I multiplying by let me let's + + + align:start position:0% +what am I multiplying by let me let's +see I'm multiplying I wan to I want to + + align:start position:0% +see I'm multiplying I wan to I want to + + + align:start position:0% +see I'm multiplying I wan to I want to +multiply this by something and subtract + + align:start position:0% +multiply this by something and subtract + + + align:start position:0% +multiply this by something and subtract +and kill + + align:start position:0% +and kill + + + align:start position:0% +and kill +it so what should have somebody + + align:start position:0% +it so what should have somebody + + + align:start position:0% +it so what should have somebody +said c a + + align:start position:0% +said c a + + + align:start position:0% +said c a +transpose but now I'm that's almost it + + align:start position:0% +transpose but now I'm that's almost it + + + align:start position:0% +transpose but now I'm that's almost it +but not + + align:start position:0% +but not + + + align:start position:0% +but not +quite If I multiply by C A + + align:start position:0% +quite If I multiply by C A + + + align:start position:0% +quite If I multiply by C A +transpose then this is C inverse what do + + align:start position:0% +transpose then this is C inverse what do + + + align:start position:0% +transpose then this is C inverse what do +I want to get I want to multiply it by + + align:start position:0% +I want to get I want to multiply it by + + + align:start position:0% +I want to get I want to multiply it by +something to give me a transpose right + + align:start position:0% +something to give me a transpose right + + + align:start position:0% +something to give me a transpose right +so so subtraction will give me the zero + + align:start position:0% +so so subtraction will give me the zero + + + align:start position:0% +so so subtraction will give me the zero +so what do I multiply this row by to + + align:start position:0% +so what do I multiply this row by to + + + align:start position:0% +so what do I multiply this row by to +give me a transpose aose C A transpose C + + align:start position:0% +give me a transpose aose C A transpose C + + + align:start position:0% +give me a transpose aose C A transpose C +I have to put them in the right order + + align:start position:0% +I have to put them in the right order + + + align:start position:0% +I have to put them in the right order +because these are matrices right so I'm + + align:start position:0% +because these are matrices right so I'm + + + align:start position:0% +because these are matrices right so I'm +multiplying the multiplier is a + + align:start position:0% +multiplying the multiplier is a + + + align:start position:0% +multiplying the multiplier is a +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +C I'm multiplying that M that row by a + + align:start position:0% +C I'm multiplying that M that row by a + + + align:start position:0% +C I'm multiplying that M that row by a +transpose C subtracting it knocks this + + align:start position:0% +transpose C subtracting it knocks this + + + align:start position:0% +transpose C subtracting it knocks this +out and what do I so now the key + + align:start position:0% +out and what do I so now the key + + + align:start position:0% +out and what do I so now the key +question is what do I get there + + align:start position:0% + + + + align:start position:0% + +there's a transpose C multiplies that a + + align:start position:0% +there's a transpose C multiplies that a + + + align:start position:0% +there's a transpose C multiplies that a +subtracts from zero + + align:start position:0% +subtracts from zero + + + align:start position:0% +subtracts from zero +right so it's + + align:start position:0% +right so it's + + + align:start position:0% +right so it's +negative minus now we're seeing what had + + align:start position:0% +negative minus now we're seeing what had + + + align:start position:0% +negative minus now we're seeing what had +to + + align:start position:0% + + + + align:start position:0% + +happen that's what's in there and and of + + align:start position:0% +happen that's what's in there and and of + + + align:start position:0% +happen that's what's in there and and of +course the right hand side was the F + + align:start position:0% +course the right hand side was the F + + + align:start position:0% +course the right hand side was the F +that was already there and then we took + + align:start position:0% +that was already there and then we took + + + align:start position:0% +that was already there and then we took +away let you have to do the same + + align:start position:0% +away let you have to do the same + + + align:start position:0% +away let you have to do the same +elimination on the right hand side we + + align:start position:0% +elimination on the right hand side we + + + align:start position:0% +elimination on the right hand side we +multiplied by a transpose C so we took + + align:start position:0% +multiplied by a transpose C so we took + + + align:start position:0% +multiplied by a transpose C so we took +away a transpose C + + align:start position:0% +away a transpose C + + + align:start position:0% +away a transpose C +B I never + + align:start position:0% + + + + align:start position:0% + +sure um right there this should be an a + + align:start position:0% +sure um right there this should be an a + + + align:start position:0% +sure um right there this should be an a +right thanks thanks especially because + + align:start position:0% +right thanks thanks especially because + + + align:start position:0% +right thanks thanks especially because +this is so permanent record of Errors uh + + align:start position:0% +this is so permanent record of Errors uh + + + align:start position:0% +this is so permanent record of Errors uh +and uh uh + + align:start position:0% +and uh uh + + + align:start position:0% +and uh uh +fixes fixes yes somebody sent me an + + align:start position:0% +fixes fixes yes somebody sent me an + + + align:start position:0% +fixes fixes yes somebody sent me an +email today this week an awful pun I had + + align:start position:0% +email today this week an awful pun I had + + + align:start position:0% +email today this week an awful pun I had +fixed up some equation he referred to it + + align:start position:0% +fixed up some equation he referred to it + + + align:start position:0% +fixed up some equation he referred to it +as a Strang fix I don't know if you know + + align:start position:0% +as a Strang fix I don't know if you know + + + align:start position:0% +as a Strang fix I don't know if you know +my book on finite elements my co-author + + align:start position:0% +my book on finite elements my co-author + + + align:start position:0% +my book on finite elements my co-author +was fix uh so that that's uh known that + + align:start position:0% +was fix uh so that that's uh known that + + + align:start position:0% +was fix uh so that that's uh known that +book is known by the two names anyway we + + align:start position:0% +book is known by the two names anyway we + + + align:start position:0% +book is known by the two names anyway we +just fixed it thank you right okay now I + + align:start position:0% +just fixed it thank you right okay now I + + + align:start position:0% +just fixed it thank you right okay now I +don't know whether you felt that was + + align:start position:0% +don't know whether you felt that was + + + align:start position:0% +don't know whether you felt that was +sort of + + align:start position:0% + + + + align:start position:0% + +mysterious if so let's just take the two + + align:start position:0% +mysterious if so let's just take the two + + + align:start position:0% +mysterious if so let's just take the two +equations and do something totally + + align:start position:0% +equations and do something totally + + + align:start position:0% +equations and do something totally +unmysterious + + align:start position:0% +unmysterious + + + align:start position:0% +unmysterious +uh remove + + align:start position:0% +uh remove + + + align:start position:0% +uh remove +W have I got space here here i' I I + + align:start position:0% +W have I got space here here i' I I + + + align:start position:0% +W have I got space here here i' I I +started with three + + align:start position:0% +started with three + + + align:start position:0% +started with three +equations I'm down to two and I liked I + + align:start position:0% +equations I'm down to two and I liked I + + + align:start position:0% +equations I'm down to two and I liked I +I I I didn't I paused it too because + + align:start position:0% +I I I didn't I paused it too because + + + align:start position:0% +I I I didn't I paused it too because +because it's that's an important + + align:start position:0% +because it's that's an important + + + align:start position:0% +because it's that's an important +Matrix but now if now I'm going to get + + align:start position:0% +Matrix but now if now I'm going to get + + + align:start position:0% +Matrix but now if now I'm going to get +down to one and what is my so what's my + + align:start position:0% +down to one and what is my so what's my + + + align:start position:0% +down to one and what is my so what's my +final equation + + align:start position:0% +final equation + + + align:start position:0% +final equation +here uh how do let's see what am I doing + + align:start position:0% +here uh how do let's see what am I doing + + + align:start position:0% +here uh how do let's see what am I doing +here I'm eliminating W from this + + align:start position:0% +here I'm eliminating W from this + + + align:start position:0% +here I'm eliminating W from this +equation and leaving only U right so how + + align:start position:0% +equation and leaving only U right so how + + + align:start position:0% +equation and leaving only U right so how +do I do that let's see can I just so + + align:start position:0% +do I do that let's see can I just so + + + align:start position:0% +do I do that let's see can I just so +this equation is a + + align:start position:0% +this equation is a + + + align:start position:0% +this equation is a +transpose but W is I want to eliminate W + + align:start position:0% +transpose but W is I want to eliminate W + + + align:start position:0% +transpose but W is I want to eliminate W +is C + + align:start position:0% +is C + + + align:start position:0% +is C +time b - Au + + align:start position:0% + + + + align:start position:0% + +U just made it in time equaling + + align:start position:0% + + + + align:start position:0% + +F that last when I combine these + + align:start position:0% +F that last when I combine these + + + align:start position:0% +F that last when I combine these +equations when I combine the three I got + + align:start position:0% +equations when I combine the three I got + + + align:start position:0% +equations when I combine the three I got +two when I combine the two I get one + + align:start position:0% +two when I combine the two I get one + + + align:start position:0% +two when I combine the two I get one +with only U left in it it's a + + align:start position:0% +with only U left in it it's a + + + align:start position:0% +with only U left in it it's a +transpose W is C * B minus Au U as we + + align:start position:0% +transpose W is C * B minus Au U as we + + + align:start position:0% +transpose W is C * B minus Au U as we +saw equaling F do you see that that's + + align:start position:0% +saw equaling F do you see that that's + + + align:start position:0% +saw equaling F do you see that that's +our final equation that's I'm sorry it's + + align:start position:0% +our final equation that's I'm sorry it's + + + align:start position:0% +our final equation that's I'm sorry it's +way in the corner because it's the + + align:start position:0% +way in the corner because it's the + + + align:start position:0% +way in the corner because it's the +equation we actually solve and do you + + align:start position:0% +equation we actually solve and do you + + + align:start position:0% +equation we actually solve and do you +see it here well with a minus sign oh no + + align:start position:0% +see it here well with a minus sign oh no + + + align:start position:0% +see it here well with a minus sign oh no +the minus sign is also there so just + + align:start position:0% +the minus sign is also there so just + + + align:start position:0% +the minus sign is also there so just +right you see the minus a transpose CA + + align:start position:0% +right you see the minus a transpose CA + + + align:start position:0% +right you see the minus a transpose CA +multiplying the U and then the right + + align:start position:0% +multiplying the U and then the right + + + align:start position:0% +multiplying the U and then the right +hand side is the B and minus a f and + + align:start position:0% +hand side is the B and minus a f and + + + align:start position:0% +hand side is the B and minus a f and +minus a transpose CB which is the the + + align:start position:0% +minus a transpose CB which is the the + + + align:start position:0% +minus a transpose CB which is the the +source term that really goes over hope + + align:start position:0% +source term that really goes over hope + + + align:start position:0% +source term that really goes over hope +you hope you see it I don't I I + + align:start position:0% +you hope you see it I don't I I + + + align:start position:0% +you hope you see it I don't I I +uh uh what we I guess what this + + align:start position:0% +uh uh what we I guess what this + + + align:start position:0% +uh uh what we I guess what this +illustrates is Guss elimination is + + align:start position:0% +illustrates is Guss elimination is + + + align:start position:0% +illustrates is Guss elimination is +totally common sense that that if we did + + align:start position:0% +totally common sense that that if we did + + + align:start position:0% +totally common sense that that if we did +Gus elimination by blocks we got the + + align:start position:0% +Gus elimination by blocks we got the + + + align:start position:0% +Gus elimination by blocks we got the +that's elimination is elimination in + + align:start position:0% +that's elimination is elimination in + + + align:start position:0% +that's elimination is elimination in +other words here is elimination done in + + align:start position:0% +other words here is elimination done in + + + align:start position:0% +other words here is elimination done in +Block Matrix form here is elimination + + align:start position:0% +Block Matrix form here is elimination + + + align:start position:0% +Block Matrix form here is elimination +done uh just saying well let's get W out + + align:start position:0% +done uh just saying well let's get W out + + + align:start position:0% +done uh just saying well let's get W out +of the system and that's what we have + + align:start position:0% +of the system and that's what we have + + + align:start position:0% +of the system and that's what we have +okay so that was our final + + align:start position:0% + + + + align:start position:0% + +system that was our final system I feel + + align:start position:0% +system that was our final system I feel + + + align:start position:0% +system that was our final system I feel +I should highlight that because that's + + align:start position:0% +I should highlight that because that's + + + align:start position:0% +I should highlight that because that's +the system that we finally solv so maybe + + align:start position:0% +the system that we finally solv so maybe + + + align:start position:0% +the system that we finally solv so maybe +I'll put it up here that we \ No newline at end of file diff --git a/58edfKe-LO8.txt b/58edfKe-LO8.txt new file mode 100644 index 0000000000000000000000000000000000000000..7b770a3bcccfbcf33eafc8a5da379a7c5efa609b --- /dev/null +++ b/58edfKe-LO8.txt @@ -0,0 +1,208 @@ +Here's a final logic implementation strategy +using read-only memories. + +This strategy is useful when you need to generate +many different outputs from the same set of + +inputs, a situation we'll see a lot when we +get to finite state machines later on in the + +course. + +Where MUXes are good for implementing truth +tables with one output column, read-only memories + +are good for implementing truth tables with +many output columns. + +One of the key components in a read-only memory +is the decoder which has K select inputs and + +2^K data outputs. + +Only one of the data outputs will be 1 (or +HIGH) at any given time, which one is determined + +by the value on the select inputs. + +The Jth output will be 1 when the select lines +are set to the binary representation of J. + +Here's a read-only memory implementation for +the 2-output truth table shown on the left. + +This particular 2-output device is a full +adder, which is used as a building block in + +addition circuits. + +The three inputs to the function (A, B, and +CI) are connected to the select lines of a + +3-to-8 decoder. + +The 8 outputs of the decoder run horizontally +in the schematic diagram and each is labeled + +with the input values for which that output +will be HIGH. + +So when the inputs are 000, the top decoder +output will be HIGH and all the other decoder + +outputs LOW. + +When the inputs are 001 - i.e., when A and +B are 0 and CI is 1 - the second decoder output + +will be HIGH. + +And so on. + +The decoder outputs control a matrix of NFET +pulldown switches. + +The matrix has one vertical column for each +output of the truth table. + +Each switch connects a particular vertical +column to ground, forcing it to a LOW value + +when the switch is on. + +The column circuitry is designed so that if +no pulldown switches force its value to 0, + +its value will be a 1. + +The value on each of the vertical columns +is inverted to produce the final output values. + +So how do we use all this circuitry to implement +the function described by the truth table? + +For any particular combination of input values, +exactly one of the decoder outputs will be + +HIGH, all the others will be low. + +Think of the decoder outputs as indicating +which row of the truth table has been selected + +by the input values. + +All of the pulldown switches controlled by +the HIGH decoder output will be turned ON, + +forcing the vertical column to which they +connect LOW. + +For example, if the inputs are 001, the decoder +output labeled 001 will be HIGH. + +This will turn on the circled pulldown switch, +forcing the S vertical column LOW. + +The COUT vertical column is not pulled down, +so it will be HIGH. + +After the output inverters, S will be 1 and +COUT will be 0, the desired output values. + +By changing the locations of the pulldown +switches, this read-only memory can be programmed + +to implement any 3-input, 2-output function. + +For read-only memories with many inputs, the +decoders have many outputs and the vertical + +columns in the switch matrix can become quite +long and slow. + +We can reconfigure the circuit slightly so +that some of the inputs control the decoder + +and the other inputs are used to select among +multiple shorter and faster vertical columns. + +This combination of smaller decoders and output +MUXes is quite common in these sorts of memory + +circuits. + +Read-only memories, ROMs for short, are an +implementation strategy that ignores the structure + +of the particular boolean expression to be +implemented. + +The ROM's size and overall layout are determined +only by the number of inputs and outputs. + +Typically the switch matrix is fully populated, +with all possible switch locations filled + +with an NFET pulldown. + +A separate physical or electrical programming +operation determines which switches are actually + +controlled by the decoder lines. + +The other switches are configured to be in +the permanently off state. + +If the ROM has N inputs and M outputs, then +the switch matrix will have 2^N rows and M + +output columns, corresponding exactly to the +size of the truth table. + +As the inputs to the ROM change, various decoder +outputs will turn off and on, but at slightly + +different times. + +As the decoder lines cycle, the output values +may change several times until the final configuration + +of the pulldown switches is stable. + +So ROMs are not lenient and the outputs may +show the glitchy behavior discussed earlier. + +Whew! + +This has been a whirlwind tour of various +circuits we can use to implement logic functions. + +The sum-of-products approach lends itself +nicely to implementation with inverting logic. + +Each circuit is custom-designed to implement +a particular function and as such can be made + +both fast and small. + +The design and manufacturing expense of creating +such circuits is worthwhile when you need + +high-end performance or are producing millions +of devices. + +MUX and ROM circuit implementations are mostly +independent of the specific function to be + +implemented. + +That's determined by a separate programming +step, which may be completed after the manufacture + +of the devices. + +They are particularly suited for prototyping, +low-volume production, or devices where the + +functionality may need to be updated after +the device is out in the field. \ No newline at end of file diff --git a/5sQRaJTogZw.txt b/5sQRaJTogZw.txt new file mode 100644 index 0000000000000000000000000000000000000000..f06427858a508d6fe3c4d447b40c6a120f8869be --- /dev/null +++ b/5sQRaJTogZw.txt @@ -0,0 +1,12947 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +we discussed the competent + + align:start position:0% +we discussed the competent + + + align:start position:0% +we discussed the competent +scattering + + align:start position:0% +scattering + + + align:start position:0% +scattering +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we set the example essentially we + + align:start position:0% +so we set the example essentially we + + + align:start position:0% +so we set the example essentially we +covered + + align:start position:0% +covered + + + align:start position:0% +covered +all the three level diagrams in QED + + align:start position:0% +all the three level diagrams in QED + + + align:start position:0% +all the three level diagrams in QED +so two level diagrams means those does + + align:start position:0% +so two level diagrams means those does + + + align:start position:0% +so two level diagrams means those does +not involve in Loops okay + + align:start position:0% +not involve in Loops okay + + + align:start position:0% +not involve in Loops okay +so so far + + align:start position:0% + + + + align:start position:0% + +encountered + + align:start position:0% + + + + align:start position:0% + +diagrams + + align:start position:0% + + + + align:start position:0% + +which are + + align:start position:0% + + + + align:start position:0% + +so which are called tree level without + + align:start position:0% + + + + align:start position:0% + +Loops okay so these are called the just + + align:start position:0% +Loops okay so these are called the just + + + align:start position:0% +Loops okay so these are called the just +a three level diagram + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and so so + + align:start position:0% +and so so + + + align:start position:0% +and so so +now you should be able to + + align:start position:0% +now you should be able to + + + align:start position:0% +now you should be able to +um + + align:start position:0% +um + + + align:start position:0% +um +actually treat all possible tree level + + align:start position:0% +actually treat all possible tree level + + + align:start position:0% +actually treat all possible tree level +diagrams okay you already have all the + + align:start position:0% +diagrams okay you already have all the + + + align:start position:0% +diagrams okay you already have all the +tools to treat all the opposable tree + + align:start position:0% +tools to treat all the opposable tree + + + align:start position:0% +tools to treat all the opposable tree +level diagrams + + align:start position:0% +level diagrams + + + align:start position:0% +level diagrams +but three level diagrams actually + + align:start position:0% +but three level diagrams actually + + + align:start position:0% +but three level diagrams actually +um there are many important things + + align:start position:0% +um there are many important things + + + align:start position:0% +um there are many important things +missing just in the three level diagrams + + align:start position:0% +missing just in the three level diagrams + + + align:start position:0% +missing just in the three level diagrams +okay so so now that's uh uh today we + + align:start position:0% +okay so so now that's uh uh today we + + + align:start position:0% +okay so so now that's uh uh today we +will talk about how to go beyond that + + align:start position:0% +will talk about how to go beyond that + + + align:start position:0% +will talk about how to go beyond that +so we talk about Quantum fluctuations + + align:start position:0% + + + + align:start position:0% + +so this is a very big subject + + align:start position:0% +so this is a very big subject + + + align:start position:0% +so this is a very big subject +and actually will consist + + align:start position:0% +and actually will consist + + + align:start position:0% +and actually will consist +s or a big chunk of + + align:start position:0% +s or a big chunk of + + + align:start position:0% +s or a big chunk of +um Quantum field series 2. so here it's + + align:start position:0% +um Quantum field series 2. so here it's + + + align:start position:0% +um Quantum field series 2. so here it's +more like just to give you a preview + + align:start position:0% +more like just to give you a preview + + + align:start position:0% +more like just to give you a preview +of the basic idea + + align:start position:0% +of the basic idea + + + align:start position:0% +of the basic idea +of the subject + + align:start position:0% +of the subject + + + align:start position:0% +of the subject +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so one feature of the three level + + align:start position:0% +so so one feature of the three level + + + align:start position:0% +so so one feature of the three level +diagram we have encountered + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +so if you want to summarize the say + + align:start position:0% +so if you want to summarize the say + + + align:start position:0% +so if you want to summarize the say +features of two level diagrams what + + align:start position:0% +features of two level diagrams what + + + align:start position:0% +features of two level diagrams what +would you say + + align:start position:0% + + + + align:start position:0% + +yeah other than the loops other than + + align:start position:0% +yeah other than the loops other than + + + align:start position:0% +yeah other than the loops other than +looks like a tree + + align:start position:0% +looks like a tree + + + align:start position:0% +looks like a tree +yes + + align:start position:0% + + + + align:start position:0% + +exactly so the key + + align:start position:0% +exactly so the key + + + align:start position:0% +exactly so the key +he said old + + align:start position:0% +he said old + + + align:start position:0% +he said old +intermediate momentum + + align:start position:0% + + + + align:start position:0% + +say in all propagators okay + + align:start position:0% +say in all propagators okay + + + align:start position:0% +say in all propagators okay +or intermediate + + align:start position:0% +or intermediate + + + align:start position:0% +or intermediate +intermediate momenta they are determined + + align:start position:0% + + + + align:start position:0% + +from external wires + + align:start position:0% +from external wires + + + align:start position:0% +from external wires +okay + + align:start position:0% + + + + align:start position:0% + +so so when you treat the tree level + + align:start position:0% +so so when you treat the tree level + + + align:start position:0% +so so when you treat the tree level +diagram + + align:start position:0% +diagram + + + align:start position:0% +diagram +there's no + + align:start position:0% + + + + align:start position:0% + +momentum integration + + align:start position:0% + + + + align:start position:0% + +okay so this looks like a very simple + + align:start position:0% +okay so this looks like a very simple + + + align:start position:0% +okay so this looks like a very simple +mathematical feature but actually uh it + + align:start position:0% +mathematical feature but actually uh it + + + align:start position:0% +mathematical feature but actually uh it +turns out actually there's a profound + + align:start position:0% +turns out actually there's a profound + + + align:start position:0% +turns out actually there's a profound +difference okay when you include both + + align:start position:0% +difference okay when you include both + + + align:start position:0% +difference okay when you include both +mathematically and physically when you + + align:start position:0% +mathematically and physically when you + + + align:start position:0% +mathematically and physically when you +include the loops and uh uh they are + + align:start position:0% +include the loops and uh uh they are + + + align:start position:0% +include the loops and uh uh they are +profound differences + + align:start position:0% + + + + align:start position:0% + +and also you can show + + align:start position:0% + + + + align:start position:0% + +that the uh yeah so loud now let me just + + align:start position:0% +that the uh yeah so loud now let me just + + + align:start position:0% +that the uh yeah so loud now let me just +summarize so now when you + + align:start position:0% +summarize so now when you + + + align:start position:0% +summarize so now when you +when including the loops + + align:start position:0% + + + + align:start position:0% + +okay there are many new features okay + + align:start position:0% +okay there are many new features okay + + + align:start position:0% +okay there are many new features okay +arises + + align:start position:0% +arises + + + align:start position:0% +arises +and so let me just first give you some + + align:start position:0% +and so let me just first give you some + + + align:start position:0% +and so let me just first give you some +simple examples of the including loops + + align:start position:0% +simple examples of the including loops + + + align:start position:0% +simple examples of the including loops +so let's just consider the uh say for + + align:start position:0% +so let's just consider the uh say for + + + align:start position:0% +so let's just consider the uh say for +example wine is the just you can see + + align:start position:0% +example wine is the just you can see + + + align:start position:0% +example wine is the just you can see +that the electron propagator + + align:start position:0% +that the electron propagator + + + align:start position:0% +that the electron propagator +and it's just a line okay but now you + + align:start position:0% +and it's just a line okay but now you + + + align:start position:0% +and it's just a line okay but now you +can consider adding a photon line here + + align:start position:0% + + + + align:start position:0% + +okay adding a photon line here + + align:start position:0% +okay adding a photon line here + + + align:start position:0% +okay adding a photon line here +so this is like the process and now you + + align:start position:0% +so this is like the process and now you + + + align:start position:0% +so this is like the process and now you +have a loop okay you can see so this + + align:start position:0% +have a loop okay you can see so this + + + align:start position:0% +have a loop okay you can see so this +Photon line and this electron line + + align:start position:0% +Photon line and this electron line + + + align:start position:0% +Photon line and this electron line +and so so you can consider this as a + + align:start position:0% +and so so you can consider this as a + + + align:start position:0% +and so so you can consider this as a +process like electron propagate + + align:start position:0% +process like electron propagate + + + align:start position:0% +process like electron propagate +and then can emit the photon and then it + + align:start position:0% +and then can emit the photon and then it + + + align:start position:0% +and then can emit the photon and then it +absorbs itself + + align:start position:0% +absorbs itself + + + align:start position:0% +absorbs itself +so this photon is purely virtual okay + + align:start position:0% +so this photon is purely virtual okay + + + align:start position:0% +so this photon is purely virtual okay +it's purely virtual does not uh uh it's + + align:start position:0% +it's purely virtual does not uh uh it's + + + align:start position:0% +it's purely virtual does not uh uh it's +probably a a virtual photo + + align:start position:0% +probably a a virtual photo + + + align:start position:0% +probably a a virtual photo +but such can process actually affect the + + align:start position:0% +but such can process actually affect the + + + align:start position:0% +but such can process actually affect the +propagation of electron + + align:start position:0% +propagation of electron + + + align:start position:0% +propagation of electron +okay uh so you can view these Photon as + + align:start position:0% +okay uh so you can view these Photon as + + + align:start position:0% +okay uh so you can view these Photon as +uh something fluctuate from the vacuum + + align:start position:0% +uh something fluctuate from the vacuum + + + align:start position:0% +uh something fluctuate from the vacuum +okay so uh so you can imagine this comes + + align:start position:0% +okay so uh so you can imagine this comes + + + align:start position:0% +okay so uh so you can imagine this comes +from the vacuum fluctuations + + align:start position:0% +from the vacuum fluctuations + + + align:start position:0% +from the vacuum fluctuations +oh + + align:start position:0% +oh + + + align:start position:0% +oh +so so this is one process and another + + align:start position:0% +so so this is one process and another + + + align:start position:0% +so so this is one process and another +simple process if you consider + + align:start position:0% +simple process if you consider + + + align:start position:0% +simple process if you consider +propagation of a photon + + align:start position:0% + + + + align:start position:0% + +and then the first one can actually + + align:start position:0% + + + + align:start position:0% + +break up say compare create electron + + align:start position:0% +break up say compare create electron + + + align:start position:0% +break up say compare create electron +pair + + align:start position:0% + + + + align:start position:0% + +okay and then this pair can allow it + + align:start position:0% +okay and then this pair can allow it + + + align:start position:0% +okay and then this pair can allow it +again + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% +and then + + + align:start position:0% +and then +and then to uh to form another photo + + align:start position:0% +and then to uh to form another photo + + + align:start position:0% +and then to uh to form another photo +so so this is just like + + align:start position:0% +so so this is just like + + + align:start position:0% +so so this is just like +again this is like a a a correction to + + align:start position:0% +again this is like a a a correction to + + + align:start position:0% +again this is like a a a correction to +just a simple propagation of a single + + align:start position:0% +just a simple propagation of a single + + + align:start position:0% +just a simple propagation of a single +Photon so initial state is still one + + align:start position:0% +Photon so initial state is still one + + + align:start position:0% +Photon so initial state is still one +Photon and the final state is still one + + align:start position:0% +Photon and the final state is still one + + + align:start position:0% +Photon and the final state is still one +Photon but something happens in between + + align:start position:0% +Photon but something happens in between + + + align:start position:0% +Photon but something happens in between +okay and again the Assumption happens in + + align:start position:0% +okay and again the Assumption happens in + + + align:start position:0% +okay and again the Assumption happens in +between + + align:start position:0% +between + + + align:start position:0% +between +you can interpret it as the some kind of + + align:start position:0% +you can interpret it as the some kind of + + + align:start position:0% +you can interpret it as the some kind of +vacuum fluctuations + + align:start position:0% +vacuum fluctuations + + + align:start position:0% +vacuum fluctuations +okay so so so about both reduction and + + align:start position:0% +okay so so so about both reduction and + + + align:start position:0% +okay so so so about both reduction and +the position here are completely virtual + + align:start position:0% +the position here are completely virtual + + + align:start position:0% +the position here are completely virtual +okay there's no real reductions you can + + align:start position:0% +okay there's no real reductions you can + + + align:start position:0% +okay there's no real reductions you can +detect + + align:start position:0% + + + + align:start position:0% + +so the third simple process + + align:start position:0% +so the third simple process + + + align:start position:0% +so the third simple process +is this when you remember we have the + + align:start position:0% +is this when you remember we have the + + + align:start position:0% +is this when you remember we have the +electron Photon interacting vertex + + align:start position:0% +electron Photon interacting vertex + + + align:start position:0% +electron Photon interacting vertex +okay so this is IE gamma mu + + align:start position:0% +okay so this is IE gamma mu + + + align:start position:0% +okay so this is IE gamma mu +okay so this is the electron Photon + + align:start position:0% +okay so this is the electron Photon + + + align:start position:0% +okay so this is the electron Photon +interacting vertex and this vertex can + + align:start position:0% +interacting vertex and this vertex can + + + align:start position:0% +interacting vertex and this vertex can +also be corrected so imagine you have a + + align:start position:0% +also be corrected so imagine you have a + + + align:start position:0% +also be corrected so imagine you have a +photon + + align:start position:0% +photon + + + align:start position:0% +photon +so imagine the electron when it comes to + + align:start position:0% +so imagine the electron when it comes to + + + align:start position:0% +so imagine the electron when it comes to +and the first emit the photon and then + + align:start position:0% +and the first emit the photon and then + + + align:start position:0% +and the first emit the photon and then +then get absorbed by the electron which + + align:start position:0% +then get absorbed by the electron which + + + align:start position:0% +then get absorbed by the electron which +comes out + + align:start position:0% +comes out + + + align:start position:0% +comes out +okay and and so these are uh will will + + align:start position:0% +okay and and so these are uh will will + + + align:start position:0% +okay and and so these are uh will will +correct the vertex and so this is called + + align:start position:0% +correct the vertex and so this is called + + + align:start position:0% +correct the vertex and so this is called +the vertex fractions so these two + + align:start position:0% +the vertex fractions so these two + + + align:start position:0% +the vertex fractions so these two +corrects the propagator and this one is + + align:start position:0% +corrects the propagator and this one is + + + align:start position:0% +corrects the propagator and this one is +the correct to the vertex + + align:start position:0% +the correct to the vertex + + + align:start position:0% +the correct to the vertex +so these are the simplest Loop diagrams + + align:start position:0% +so these are the simplest Loop diagrams + + + align:start position:0% +so these are the simplest Loop diagrams +okay these are the simplest Loop + + align:start position:0% +okay these are the simplest Loop + + + align:start position:0% +okay these are the simplest Loop +diagrams in each of them + + align:start position:0% +diagrams in each of them + + + align:start position:0% +diagrams in each of them +here just there's a single Loop + + align:start position:0% +here just there's a single Loop + + + align:start position:0% +here just there's a single Loop +and then there's a momentum a free + + align:start position:0% +and then there's a momentum a free + + + align:start position:0% +and then there's a momentum a free +momentum uh in the loop so you have to + + align:start position:0% +momentum uh in the loop so you have to + + + align:start position:0% +momentum uh in the loop so you have to +integrate over the momentum in this room + + align:start position:0% +integrate over the momentum in this room + + + align:start position:0% +integrate over the momentum in this room +because it's no longer determined by + + align:start position:0% +because it's no longer determined by + + + align:start position:0% +because it's no longer determined by +external moment + + align:start position:0% +external moment + + + align:start position:0% +external moment +it's no longer determined by extent + + align:start position:0% + + + + align:start position:0% + +so it turns out + + align:start position:0% +so it turns out + + + align:start position:0% +so it turns out +such kind of momentum integration so so + + align:start position:0% +such kind of momentum integration so so + + + align:start position:0% +such kind of momentum integration so so +if I call this say momentum k + + align:start position:0% +if I call this say momentum k + + + align:start position:0% +if I call this say momentum k +okay and then and then you will involve + + align:start position:0% +okay and then and then you will involve + + + align:start position:0% +okay and then and then you will involve +in so so a + + align:start position:0% +in so so a + + + align:start position:0% +in so so a +so let me first talk about the + + align:start position:0% +so let me first talk about the + + + align:start position:0% +so let me first talk about the +mathematical features + + align:start position:0% + + + + align:start position:0% + +mathematical new features + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +so so the mathematically now is you need + + align:start position:0% +so so the mathematically now is you need + + + align:start position:0% +so so the mathematically now is you need +to integrate + + align:start position:0% + + + + align:start position:0% + +over the internal momentum + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now you need to now you have some + + align:start position:0% +so now you need to now you have some + + + align:start position:0% +so now you need to now you have some +free momentum to integrate + + align:start position:0% +free momentum to integrate + + + align:start position:0% +free momentum to integrate +so so so this may look like something + + align:start position:0% +so so so this may look like something + + + align:start position:0% +so so so this may look like something +just uh varied + + align:start position:0% +just uh varied + + + align:start position:0% +just uh varied +yeah it may say this is not a big deal + + align:start position:0% +yeah it may say this is not a big deal + + + align:start position:0% +yeah it may say this is not a big deal +but actually this and that will be a + + align:start position:0% +but actually this and that will be a + + + align:start position:0% +but actually this and that will be a +very big deal + + align:start position:0% +very big deal + + + align:start position:0% +very big deal +because of the uh this momentum + + align:start position:0% +because of the uh this momentum + + + align:start position:0% +because of the uh this momentum +this integration just by definition is + + align:start position:0% +this integration just by definition is + + + align:start position:0% +this integration just by definition is +from the uh you integrate over all + + align:start position:0% +from the uh you integrate over all + + + align:start position:0% +from the uh you integrate over all +possible momentum + + align:start position:0% +possible momentum + + + align:start position:0% +possible momentum +so it's okay it's Integra so each case + + align:start position:0% +so it's okay it's Integra so each case + + + align:start position:0% +so it's okay it's Integra so each case +integrate from minus infinity to uh to + + align:start position:0% +integrate from minus infinity to uh to + + + align:start position:0% +integrate from minus infinity to uh to +plus infinity + + align:start position:0% +plus infinity + + + align:start position:0% +plus infinity +okay so in particular this includes the + + align:start position:0% +okay so in particular this includes the + + + align:start position:0% +okay so in particular this includes the +region + + align:start position:0% + + + + align:start position:0% + +if k0 can go to Infinity + + align:start position:0% +if k0 can go to Infinity + + + align:start position:0% +if k0 can go to Infinity +and the and the magnitude of K can also + + align:start position:0% +and the and the magnitude of K can also + + + align:start position:0% +and the and the magnitude of K can also +go to Infinity + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we include those regions + + align:start position:0% +so we include those regions + + + align:start position:0% +so we include those regions +some you have this kind of in infinite + + align:start position:0% +some you have this kind of in infinite + + + align:start position:0% +some you have this kind of in infinite +range of integrals + + align:start position:0% +range of integrals + + + align:start position:0% +range of integrals +then there's a possibility you get + + align:start position:0% +then there's a possibility you get + + + align:start position:0% +then there's a possibility you get +Divergence + + align:start position:0% +Divergence + + + align:start position:0% +Divergence +okay then of course where you get + + align:start position:0% +okay then of course where you get + + + align:start position:0% +okay then of course where you get +Divergence and in fact that Divergence + + align:start position:0% +Divergence and in fact that Divergence + + + align:start position:0% +Divergence and in fact that Divergence +to happen + + align:start position:0% +to happen + + + align:start position:0% +to happen +and uh happen almost everywhere + + align:start position:0% +and uh happen almost everywhere + + + align:start position:0% +and uh happen almost everywhere +okay whenever you look at Loop diagrams + + align:start position:0% +okay whenever you look at Loop diagrams + + + align:start position:0% +okay whenever you look at Loop diagrams +uh you always essentially always find + + align:start position:0% +uh you always essentially always find + + + align:start position:0% +uh you always essentially always find +the divergences okay + + align:start position:0% + + + + align:start position:0% + +so uh so this leads to + + align:start position:0% + + + + align:start position:0% + +divergences + + align:start position:0% + + + + align:start position:0% + +and such Divergence is + + align:start position:0% +and such Divergence is + + + align:start position:0% +and such Divergence is +a lot more complicated it's not like the + + align:start position:0% +a lot more complicated it's not like the + + + align:start position:0% +a lot more complicated it's not like the +simple divergences we can we already + + align:start position:0% +simple divergences we can we already + + + align:start position:0% +simple divergences we can we already +considered the worries that we already + + align:start position:0% +considered the worries that we already + + + align:start position:0% +considered the worries that we already +seen what is diverging the quantities + + align:start position:0% +seen what is diverging the quantities + + + align:start position:0% +seen what is diverging the quantities +and so far those diverging quantities + + align:start position:0% +and so far those diverging quantities + + + align:start position:0% +and so far those diverging quantities +can be treated in a more or less simple + + align:start position:0% +can be treated in a more or less simple + + + align:start position:0% +can be treated in a more or less simple +way so we add the subtract + + align:start position:0% +way so we add the subtract + + + align:start position:0% +way so we add the subtract +the infinite constant + + align:start position:0% +the infinite constant + + + align:start position:0% +the infinite constant +or you multiply it by Infinity constant + + align:start position:0% +or you multiply it by Infinity constant + + + align:start position:0% +or you multiply it by Infinity constant +okay and in the case when you multiply + + align:start position:0% +okay and in the case when you multiply + + + align:start position:0% +okay and in the case when you multiply +by input constant you can always take + + align:start position:0% +by input constant you can always take + + + align:start position:0% +by input constant you can always take +the ratio and then those infinite + + align:start position:0% +the ratio and then those infinite + + + align:start position:0% +the ratio and then those infinite +constants go away and or you can just + + align:start position:0% +constants go away and or you can just + + + align:start position:0% +constants go away and or you can just +subtracting constant redefine your + + align:start position:0% +subtracting constant redefine your + + + align:start position:0% +subtracting constant redefine your +energy redefine your charge + + align:start position:0% + + + + align:start position:0% + +but in those diagrams the Divergence is + + align:start position:0% +but in those diagrams the Divergence is + + + align:start position:0% +but in those diagrams the Divergence is +a much more complicated because they + + align:start position:0% +a much more complicated because they + + + align:start position:0% +a much more complicated because they +come from doing some + + align:start position:0% +come from doing some + + + align:start position:0% +come from doing some +integration of some complicated + + align:start position:0% +integration of some complicated + + + align:start position:0% +integration of some complicated +expression okay + + align:start position:0% +expression okay + + + align:start position:0% +expression okay +and so those Divergence cannot be simply + + align:start position:0% +and so those Divergence cannot be simply + + + align:start position:0% +and so those Divergence cannot be simply +removed but you just add the constant or + + align:start position:0% +removed but you just add the constant or + + + align:start position:0% +removed but you just add the constant or +removable constant or just multiply by + + align:start position:0% +removable constant or just multiply by + + + align:start position:0% +removable constant or just multiply by +Factor okay + + align:start position:0% +Factor okay + + + align:start position:0% +Factor okay +and and so um + + align:start position:0% +and and so um + + + align:start position:0% +and and so um +so they can actually cannot be removed + + align:start position:0% +so they can actually cannot be removed + + + align:start position:0% +so they can actually cannot be removed +in general cannot be removed simply + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +say subtractions + + align:start position:0% +say subtractions + + + align:start position:0% +say subtractions +remove the body + + align:start position:0% + + + + align:start position:0% + +simple + + align:start position:0% + + + + align:start position:0% + +abstractions + + align:start position:0% + + + + align:start position:0% + +or divisions okay + + align:start position:0% + + + + align:start position:0% + +so in other words the expression you get + + align:start position:0% +so in other words the expression you get + + + align:start position:0% +so in other words the expression you get +from doing such integration just doesn't + + align:start position:0% +from doing such integration just doesn't + + + align:start position:0% +from doing such integration just doesn't +make sense okay so the integration + + align:start position:0% +make sense okay so the integration + + + align:start position:0% +make sense okay so the integration +so the results + + align:start position:0% + + + + align:start position:0% + +from these diagrams + + align:start position:0% +from these diagrams + + + align:start position:0% +from these diagrams +okay + + align:start position:0% + + + + align:start position:0% + +not well defined + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +something's happening + + align:start position:0% +something's happening + + + align:start position:0% +something's happening +so uh uh uh so the result is not very + + align:start position:0% +so uh uh uh so the result is not very + + + align:start position:0% +so uh uh uh so the result is not very +defined + + align:start position:0% +defined + + + align:start position:0% +defined +so so normally when we encounter + + align:start position:0% +so so normally when we encounter + + + align:start position:0% +so so normally when we encounter +divergences + + align:start position:0% +divergences + + + align:start position:0% +divergences +so normally when we encounter Divergence + + align:start position:0% +so normally when we encounter Divergence + + + align:start position:0% +so normally when we encounter Divergence +is we always tell students we Encounter + + align:start position:0% +is we always tell students we Encounter + + + align:start position:0% +is we always tell students we Encounter +divergences of course the maybe one + + align:start position:0% +divergences of course the maybe one + + + align:start position:0% +divergences of course the maybe one +obvious reason is that you did something + + align:start position:0% +obvious reason is that you did something + + + align:start position:0% +obvious reason is that you did something +wrong okay you just made a mistake + + align:start position:0% +wrong okay you just made a mistake + + + align:start position:0% +wrong okay you just made a mistake +and about but but if you have done + + align:start position:0% +and about but but if you have done + + + align:start position:0% +and about but but if you have done +everything right when you encounter + + align:start position:0% +everything right when you encounter + + + align:start position:0% +everything right when you encounter +divergences actually that's opportunity + + align:start position:0% +divergences actually that's opportunity + + + align:start position:0% +divergences actually that's opportunity +because each time you see a Divergence + + align:start position:0% +because each time you see a Divergence + + + align:start position:0% +because each time you see a Divergence +then that means there's something you + + align:start position:0% +then that means there's something you + + + align:start position:0% +then that means there's something you +don't understand about physics + + align:start position:0% +don't understand about physics + + + align:start position:0% +don't understand about physics +okay if you understand a bad definition + + align:start position:0% +okay if you understand a bad definition + + + align:start position:0% +okay if you understand a bad definition +physics should not have divergences Okay + + align:start position:0% +physics should not have divergences Okay + + + align:start position:0% +physics should not have divergences Okay +so if you understand everything well and + + align:start position:0% +so if you understand everything well and + + + align:start position:0% +so if you understand everything well and +then and then so Divergence is it's a + + align:start position:0% +then and then so Divergence is it's a + + + align:start position:0% +then and then so Divergence is it's a +mathematics tell you there's something + + align:start position:0% +mathematics tell you there's something + + + align:start position:0% +mathematics tell you there's something +there's some important physics you are + + align:start position:0% +there's some important physics you are + + + align:start position:0% +there's some important physics you are +missing okay so indeed + + align:start position:0% +missing okay so indeed + + + align:start position:0% +missing okay so indeed +so here + + align:start position:0% +so here + + + align:start position:0% +so here +so when you look at those Divergence you + + align:start position:0% +so when you look at those Divergence you + + + align:start position:0% +so when you look at those Divergence you +can say oh what physics are we missing + + align:start position:0% +can say oh what physics are we missing + + + align:start position:0% +can say oh what physics are we missing +here + + align:start position:0% +here + + + align:start position:0% +here +so the physics missing here is very + + align:start position:0% +so the physics missing here is very + + + align:start position:0% +so the physics missing here is very +simple + + align:start position:0% +simple + + + align:start position:0% +simple +okay the physics missing here is very + + align:start position:0% +okay the physics missing here is very + + + align:start position:0% +okay the physics missing here is very +simple + + align:start position:0% +simple + + + align:start position:0% +simple +because this integrals + + align:start position:0% +because this integrals + + + align:start position:0% +because this integrals +because the diverge in the region + + align:start position:0% +because the diverge in the region + + + align:start position:0% +because the diverge in the region +corresponding to those quantities go to + + align:start position:0% +corresponding to those quantities go to + + + align:start position:0% +corresponding to those quantities go to +Infinity + + align:start position:0% +Infinity + + + align:start position:0% +Infinity +so those currently got Infinity because + + align:start position:0% +so those currently got Infinity because + + + align:start position:0% +so those currently got Infinity because +when it you have very high energy very + + align:start position:0% +when it you have very high energy very + + + align:start position:0% +when it you have very high energy very +light momentum + + align:start position:0% +light momentum + + + align:start position:0% +light momentum +okay and and the or in other words from + + align:start position:0% +okay and and the or in other words from + + + align:start position:0% +okay and and the or in other words from +very short distance + + align:start position:0% + + + + align:start position:0% + +but a very short + + align:start position:0% +but a very short + + + align:start position:0% +but a very short +that counts that comes from + + align:start position:0% +that counts that comes from + + + align:start position:0% +that counts that comes from +so this comes from divergences come from + + align:start position:0% + + + + align:start position:0% + +now here we extracted naive + + align:start position:0% +now here we extracted naive + + + align:start position:0% +now here we extracted naive +extrapolation + + align:start position:0% + + + + align:start position:0% + +say say they say consider QED + + align:start position:0% + + + + align:start position:0% + +to arbitrarily + + align:start position:0% + + + + align:start position:0% + +High + + align:start position:0% +High + + + align:start position:0% +High +energy scales + + align:start position:0% + + + + align:start position:0% + +yeah I think because we use the + + align:start position:0% +yeah I think because we use the + + + align:start position:0% +yeah I think because we use the +framework of QED + + align:start position:0% +framework of QED + + + align:start position:0% +framework of QED +but then when we do this integration + + align:start position:0% +but then when we do this integration + + + align:start position:0% +but then when we do this integration +involving very large momentum okay + + align:start position:0% +involving very large momentum okay + + + align:start position:0% +involving very large momentum okay +but nobody actually tells us that a + + align:start position:0% +but nobody actually tells us that a + + + align:start position:0% +but nobody actually tells us that a +community should be valid and not very + + align:start position:0% +community should be valid and not very + + + align:start position:0% +community should be valid and not very +high energies because the real + + align:start position:0% +high energies because the real + + + align:start position:0% +high energies because the real +experiment it don't uh you cannot probe + + align:start position:0% +experiment it don't uh you cannot probe + + + align:start position:0% +experiment it don't uh you cannot probe +very high energy process or or very + + align:start position:0% +very high energy process or or very + + + align:start position:0% +very high energy process or or very +short distance + + align:start position:0% +short distance + + + align:start position:0% +short distance +and because it's the limit of our energy + + align:start position:0% +and because it's the limit of our energy + + + align:start position:0% +and because it's the limit of our energy +resolution okay + + align:start position:0% +resolution okay + + + align:start position:0% +resolution okay +so so there's no reason to trust + + align:start position:0% +so so there's no reason to trust + + + align:start position:0% +so so there's no reason to trust +actually QED should be valid + + align:start position:0% +actually QED should be valid + + + align:start position:0% +actually QED should be valid +for k k zero and the K gold Infinity + + align:start position:0% +for k k zero and the K gold Infinity + + + align:start position:0% +for k k zero and the K gold Infinity +okay yes + + align:start position:0% + + + + align:start position:0% + +uh yeah it's not a feature of the + + align:start position:0% +uh yeah it's not a feature of the + + + align:start position:0% +uh yeah it's not a feature of the +potopic expansion yeah it's a it's a + + align:start position:0% +potopic expansion yeah it's a it's a + + + align:start position:0% +potopic expansion yeah it's a it's a +genuine + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so so this Divergence just come from + + align:start position:0% +so so so this Divergence just come from + + + align:start position:0% +so so so this Divergence just come from +we extrapolate credit to arbitrary high + + align:start position:0% +we extrapolate credit to arbitrary high + + + align:start position:0% +we extrapolate credit to arbitrary high +energy scales okay + + align:start position:0% +energy scales okay + + + align:start position:0% +energy scales okay +so uh so you say okay + + align:start position:0% +so uh so you say okay + + + align:start position:0% +so uh so you say okay +then then what do we do okay then what + + align:start position:0% +then then what do we do okay then what + + + align:start position:0% +then then what do we do okay then what +do we do so the simplest thing you can + + align:start position:0% +do we do so the simplest thing you can + + + align:start position:0% +do we do so the simplest thing you can +do + + align:start position:0% +do + + + align:start position:0% +do +you say only you can measure so suppose + + align:start position:0% +you say only you can measure so suppose + + + align:start position:0% +you say only you can measure so suppose +uh uh suppose in the say in the 30s in + + align:start position:0% +uh uh suppose in the say in the 30s in + + + align:start position:0% +uh uh suppose in the say in the 30s in +1930s when people first encountered this + + align:start position:0% +1930s when people first encountered this + + + align:start position:0% +1930s when people first encountered this +problem + + align:start position:0% +problem + + + align:start position:0% +problem +and uh uh uh you say okay + + align:start position:0% +and uh uh uh you say okay + + + align:start position:0% +and uh uh uh you say okay +and then let's put the cut off here + + align:start position:0% +and then let's put the cut off here + + + align:start position:0% +and then let's put the cut off here +let's only included the image regime + + align:start position:0% +let's only included the image regime + + + align:start position:0% +let's only included the image regime +which we can access + + align:start position:0% +which we can access + + + align:start position:0% +which we can access +okay + + align:start position:0% +okay + + + align:start position:0% +okay +but + + align:start position:0% +but + + + align:start position:0% +but +but again it was not a a was cut off you + + align:start position:0% +but again it was not a a was cut off you + + + align:start position:0% +but again it was not a a was cut off you +put there + + align:start position:0% +put there + + + align:start position:0% +put there +okay so it's not clear what kind of + + align:start position:0% +okay so it's not clear what kind of + + + align:start position:0% +okay so it's not clear what kind of +cattle we put there what is the validity + + align:start position:0% +cattle we put there what is the validity + + + align:start position:0% +cattle we put there what is the validity +of this series so so ideally you should + + align:start position:0% +of this series so so ideally you should + + + align:start position:0% +of this series so so ideally you should +put a cut off there to to add the uh the + + align:start position:0% +put a cut off there to to add the uh the + + + align:start position:0% +put a cut off there to to add the uh the +boundary over the validity of the uh uh + + align:start position:0% +boundary over the validity of the uh uh + + + align:start position:0% +boundary over the validity of the uh uh +Acuity okay + + align:start position:0% +Acuity okay + + + align:start position:0% +Acuity okay +before you actually can pour with the + + align:start position:0% +before you actually can pour with the + + + align:start position:0% +before you actually can pour with the +scale which really breaks down and yeah + + align:start position:0% +scale which really breaks down and yeah + + + align:start position:0% +scale which really breaks down and yeah +which scale should we put there so we + + align:start position:0% +which scale should we put there so we + + + align:start position:0% +which scale should we put there so we +don't know okay + + align:start position:0% +don't know okay + + + align:start position:0% +don't know okay +okay so so for 20 years + + align:start position:0% +okay so so for 20 years + + + align:start position:0% +okay so so for 20 years +people thought this it just + + align:start position:0% +people thought this it just + + + align:start position:0% +people thought this it just +doing this kind of diagrams just don't + + align:start position:0% +doing this kind of diagrams just don't + + + align:start position:0% +doing this kind of diagrams just don't +make physical sense okay because we + + align:start position:0% +make physical sense okay because we + + + align:start position:0% +make physical sense okay because we +don't know uh the short distance physics + + align:start position:0% +don't know uh the short distance physics + + + align:start position:0% +don't know uh the short distance physics +we don't know the short distance physics + + align:start position:0% +we don't know the short distance physics + + + align:start position:0% +we don't know the short distance physics +and indeed + + align:start position:0% +and indeed + + + align:start position:0% +and indeed +and uh and this point of view was + + align:start position:0% +and uh and this point of view was + + + align:start position:0% +and uh and this point of view was +justified so so for many years people + + align:start position:0% +justified so so for many years people + + + align:start position:0% +justified so so for many years people +just yeah for some years people just + + align:start position:0% +just yeah for some years people just + + + align:start position:0% +just yeah for some years people just +gave up on these ideas okay or they just + + align:start position:0% +gave up on these ideas okay or they just + + + align:start position:0% +gave up on these ideas okay or they just +say maybe this is does not make sense + + align:start position:0% +say maybe this is does not make sense + + + align:start position:0% +say maybe this is does not make sense +but then after the second World War uh + + align:start position:0% +but then after the second World War uh + + + align:start position:0% +but then after the second World War uh +in the in the late 40s and then a few + + align:start position:0% +in the in the late 40s and then a few + + + align:start position:0% +in the in the late 40s and then a few +young physicists at the time sharinger + + align:start position:0% +young physicists at the time sharinger + + + align:start position:0% +young physicists at the time sharinger +fireman in United States and topologa + + align:start position:0% +fireman in United States and topologa + + + align:start position:0% +fireman in United States and topologa +are in Japan + + align:start position:0% +are in Japan + + + align:start position:0% +are in Japan +they actually + + align:start position:0% +they actually + + + align:start position:0% +they actually +they say okay even though they're this + + align:start position:0% +they say okay even though they're this + + + align:start position:0% +they say okay even though they're this +kind of divergences and even though we + + align:start position:0% +kind of divergences and even though we + + + align:start position:0% +kind of divergences and even though we +don't understand the show distance + + align:start position:0% +don't understand the show distance + + + align:start position:0% +don't understand the show distance +physics let's see whether we can just + + align:start position:0% +physics let's see whether we can just + + + align:start position:0% +physics let's see whether we can just +use brute force + + align:start position:0% +use brute force + + + align:start position:0% +use brute force +try to design some mathematical way + + align:start position:0% +try to design some mathematical way + + + align:start position:0% +try to design some mathematical way +to get rid of those divergences and see + + align:start position:0% +to get rid of those divergences and see + + + align:start position:0% +to get rid of those divergences and see +whether I can get sensible results + + align:start position:0% +whether I can get sensible results + + + align:start position:0% +whether I can get sensible results +okay and so that was their starting + + align:start position:0% +okay and so that was their starting + + + align:start position:0% +okay and so that was their starting +point + + align:start position:0% +point + + + align:start position:0% +point +and that was the starting point + + align:start position:0% +and that was the starting point + + + align:start position:0% +and that was the starting point +and it was a crazy starting point + + align:start position:0% +and it was a crazy starting point + + + align:start position:0% +and it was a crazy starting point +because of the physical reason for those + + align:start position:0% +because of the physical reason for those + + + align:start position:0% +because of the physical reason for those +Divergence are very clear okay and but + + align:start position:0% +Divergence are very clear okay and but + + + align:start position:0% +Divergence are very clear okay and but +then it turned out to be actually + + align:start position:0% +then it turned out to be actually + + + align:start position:0% +then it turned out to be actually +success but they managed to be + + align:start position:0% +success but they managed to be + + + align:start position:0% +success but they managed to be +successful okay so so in in 1914 late + + align:start position:0% +successful okay so so in in 1914 late + + + align:start position:0% +successful okay so so in in 1914 late +1940s + + align:start position:0% + + + + align:start position:0% + +so you say people like uh people find + + align:start position:0% +so you say people like uh people find + + + align:start position:0% +so you say people like uh people find +the message yeah so so fireman + + align:start position:0% +the message yeah so so fireman + + + align:start position:0% +the message yeah so so fireman +schwinger and the topologa okay uh I + + align:start position:0% +schwinger and the topologa okay uh I + + + align:start position:0% +schwinger and the topologa okay uh I +manage it + + align:start position:0% + + + + align:start position:0% + +to find a way + + align:start position:0% + + + + align:start position:0% + +to remove the divergences + + align:start position:0% + + + + align:start position:0% + +and get a sensible + + align:start position:0% + + + + align:start position:0% + +get physically + + align:start position:0% + + + + align:start position:0% + +sensible answer + + align:start position:0% + + + + align:start position:0% + +from such diagrams + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and also uh uh uh at the beginning there + + align:start position:0% +and also uh uh uh at the beginning there + + + align:start position:0% +and also uh uh uh at the beginning there +work were very complicated and very few + + align:start position:0% +work were very complicated and very few + + + align:start position:0% +work were very complicated and very few +people actually understood them + + align:start position:0% +people actually understood them + + + align:start position:0% +people actually understood them +and their family used to find my + + align:start position:0% +and their family used to find my + + + align:start position:0% +and their family used to find my +diagrams okay so he invented the family + + align:start position:0% +diagrams okay so he invented the family + + + align:start position:0% +diagrams okay so he invented the family +diagrams to do this and because + + align:start position:0% +diagrams to do this and because + + + align:start position:0% +diagrams to do this and because +previously people do those calculations + + align:start position:0% +previously people do those calculations + + + align:start position:0% +previously people do those calculations +they don't use family diagrams and they + + align:start position:0% +they don't use family diagrams and they + + + align:start position:0% +they don't use family diagrams and they +use very complicated perturbation Theory + + align:start position:0% +use very complicated perturbation Theory + + + align:start position:0% +use very complicated perturbation Theory +as you do in the long relativistic + + align:start position:0% +as you do in the long relativistic + + + align:start position:0% +as you do in the long relativistic +physics it's very complicated and + + align:start position:0% +physics it's very complicated and + + + align:start position:0% +physics it's very complicated and +actually that's what the schwinger and + + align:start position:0% +actually that's what the schwinger and + + + align:start position:0% +actually that's what the schwinger and +the Tom Broker they were doing it okay + + align:start position:0% +the Tom Broker they were doing it okay + + + align:start position:0% +the Tom Broker they were doing it okay +so it's at the beginning the the thing + + align:start position:0% +so it's at the beginning the the thing + + + align:start position:0% +so it's at the beginning the the thing +was very complicated but then then the + + align:start position:0% +was very complicated but then then the + + + align:start position:0% +was very complicated but then then the +Freeman Dyson + + align:start position:0% +Freeman Dyson + + + align:start position:0% +Freeman Dyson +soon afterwards he understood all their + + align:start position:0% +soon afterwards he understood all their + + + align:start position:0% +soon afterwards he understood all their +work and actually greatly simplified the + + align:start position:0% +work and actually greatly simplified the + + + align:start position:0% +work and actually greatly simplified the +uh the process and actually the current + + align:start position:0% +uh the process and actually the current + + + align:start position:0% +uh the process and actually the current +understanding essentially came from from + + align:start position:0% +understanding essentially came from from + + + align:start position:0% +understanding essentially came from from +the simplification with the + + align:start position:0% +the simplification with the + + + align:start position:0% +the simplification with the +frigmentation + + align:start position:0% +frigmentation + + + align:start position:0% +frigmentation +and then Freeman dicing actually + + align:start position:0% +and then Freeman dicing actually + + + align:start position:0% +and then Freeman dicing actually +operated the assignment diagram in fact + + align:start position:0% +operated the assignment diagram in fact + + + align:start position:0% +operated the assignment diagram in fact +filament diagram a training + + align:start position:0% +filament diagram a training + + + align:start position:0% +filament diagram a training +essentially operated from a diagram + + align:start position:0% +essentially operated from a diagram + + + align:start position:0% +essentially operated from a diagram +chaining a camp at The Institute for the + + align:start position:0% +chaining a camp at The Institute for the + + + align:start position:0% +chaining a camp at The Institute for the +one study when he was a member so people + + align:start position:0% +one study when he was a member so people + + + align:start position:0% +one study when he was a member so people +went through there they all learned this + + align:start position:0% +went through there they all learned this + + + align:start position:0% +went through there they all learned this +family diagram techniques from Freeman + + align:start position:0% +family diagram techniques from Freeman + + + align:start position:0% +family diagram techniques from Freeman +Dyson and then they spread it out to all + + align:start position:0% +Dyson and then they spread it out to all + + + align:start position:0% +Dyson and then they spread it out to all +other places that's how family diagram a + + align:start position:0% +other places that's how family diagram a + + + align:start position:0% +other places that's how family diagram a +techniques could Spread spread out like + + align:start position:0% +techniques could Spread spread out like + + + align:start position:0% +techniques could Spread spread out like +in the physical Community okay and + + align:start position:0% +in the physical Community okay and + + + align:start position:0% +in the physical Community okay and +anyway so so so so so far he simplified + + align:start position:0% +anyway so so so so so far he simplified + + + align:start position:0% +anyway so so so so so far he simplified +the process and then and then then + + align:start position:0% +the process and then and then then + + + align:start position:0% +the process and then and then then +people eventually understood okay and + + align:start position:0% +people eventually understood okay and + + + align:start position:0% +people eventually understood okay and +there is a well-defined mathematical + + align:start position:0% +there is a well-defined mathematical + + + align:start position:0% +there is a well-defined mathematical +procedure + + align:start position:0% +procedure + + + align:start position:0% +procedure +you can actually get rid of those + + align:start position:0% +you can actually get rid of those + + + align:start position:0% +you can actually get rid of those +divergences and get sensible or + + align:start position:0% +divergences and get sensible or + + + align:start position:0% +divergences and get sensible or +physically sensible answer + + align:start position:0% +physically sensible answer + + + align:start position:0% +physically sensible answer +and so so it was a funny story because + + align:start position:0% +and so so it was a funny story because + + + align:start position:0% +and so so it was a funny story because +and so this is called the program of + + align:start position:0% +and so this is called the program of + + + align:start position:0% +and so this is called the program of +verbalization + + align:start position:0% + + + + align:start position:0% + +okay the process of getting rid of the + + align:start position:0% +okay the process of getting rid of the + + + align:start position:0% +okay the process of getting rid of the +divergences + + align:start position:0% + + + + align:start position:0% + +this is a funny story + + align:start position:0% +this is a funny story + + + align:start position:0% +this is a funny story +is because + + align:start position:0% +is because + + + align:start position:0% +is because +I said there's a very physical uh uh uh + + align:start position:0% +I said there's a very physical uh uh uh + + + align:start position:0% +I said there's a very physical uh uh uh +uh yeah this is a very funny story for + + align:start position:0% +uh yeah this is a very funny story for + + + align:start position:0% +uh yeah this is a very funny story for +the foreign reason as I mentioned that + + align:start position:0% +the foreign reason as I mentioned that + + + align:start position:0% +the foreign reason as I mentioned that +there's a we do know where the + + align:start position:0% +there's a we do know where the + + + align:start position:0% +there's a we do know where the +divergences come from okay Divergence + + align:start position:0% +divergences come from okay Divergence + + + align:start position:0% +divergences come from okay Divergence +come from our lack of understanding of + + align:start position:0% +come from our lack of understanding of + + + align:start position:0% +come from our lack of understanding of +Judaism physics + + align:start position:0% +Judaism physics + + + align:start position:0% +Judaism physics +and normally you believe + + align:start position:0% +and normally you believe + + + align:start position:0% +and normally you believe +you can only cure the Divergence if you + + align:start position:0% +you can only cure the Divergence if you + + + align:start position:0% +you can only cure the Divergence if you +understand that physics okay if you + + align:start position:0% +understand that physics okay if you + + + align:start position:0% +understand that physics okay if you +don't understand and feeding how you + + align:start position:0% +don't understand and feeding how you + + + align:start position:0% +don't understand and feeding how you +cure that Divergence okay + + align:start position:0% +cure that Divergence okay + + + align:start position:0% +cure that Divergence okay +so that's what most people thought at + + align:start position:0% +so that's what most people thought at + + + align:start position:0% +so that's what most people thought at +the time including all these quantum + + align:start position:0% +the time including all these quantum + + + align:start position:0% +the time including all these quantum +mechanics Big Shots okay all these old + + align:start position:0% +mechanics Big Shots okay all these old + + + align:start position:0% +mechanics Big Shots okay all these old +people like uh the rock party all those + + align:start position:0% +people like uh the rock party all those + + + align:start position:0% +people like uh the rock party all those +kinds of quantum mechanics they all + + align:start position:0% +kinds of quantum mechanics they all + + + align:start position:0% +kinds of quantum mechanics they all +believed you have to do something + + align:start position:0% +believed you have to do something + + + align:start position:0% +believed you have to do something +radical + + align:start position:0% +radical + + + align:start position:0% +radical +otherwise QD cannot be made sense you + + align:start position:0% +otherwise QD cannot be made sense you + + + align:start position:0% +otherwise QD cannot be made sense you +have to invent some completely + + align:start position:0% +have to invent some completely + + + align:start position:0% +have to invent some completely +reformalism and to uh to to circumvent + + align:start position:0% +reformalism and to uh to to circumvent + + + align:start position:0% +reformalism and to uh to to circumvent +those Divergence Etc + + align:start position:0% +those Divergence Etc + + + align:start position:0% +those Divergence Etc +but then the enticing a later commented + + align:start position:0% +but then the enticing a later commented + + + align:start position:0% +but then the enticing a later commented +that then then those young people + + align:start position:0% +that then then those young people + + + align:start position:0% +that then then those young people +at the time + + align:start position:0% +at the time + + + align:start position:0% +at the time +they say we will conservative we wanted + + align:start position:0% +they say we will conservative we wanted + + + align:start position:0% +they say we will conservative we wanted +just to look at those calculations just + + align:start position:0% +just to look at those calculations just + + + align:start position:0% +just to look at those calculations just +want to make sense of those calculations + + align:start position:0% +want to make sense of those calculations + + + align:start position:0% +want to make sense of those calculations +we don't think of those grand physics I + + align:start position:0% +we don't think of those grand physics I + + + align:start position:0% +we don't think of those grand physics I +just want to make sense of those + + align:start position:0% +just want to make sense of those + + + align:start position:0% +just want to make sense of those +calculations and then they succeeded + + align:start position:0% +calculations and then they succeeded + + + align:start position:0% +calculations and then they succeeded +okay so this is example which very old + + align:start position:0% +okay so this is example which very old + + + align:start position:0% +okay so this is example which very old +people they wanted to Grant new physics + + align:start position:0% +people they wanted to Grant new physics + + + align:start position:0% +people they wanted to Grant new physics +okay but young people want you very too + + align:start position:0% +okay but young people want you very too + + + align:start position:0% +okay but young people want you very too +conservative physics just do + + align:start position:0% +conservative physics just do + + + align:start position:0% +conservative physics just do +calculations uh one calculation at the + + align:start position:0% +calculations uh one calculation at the + + + align:start position:0% +calculations uh one calculation at the +time + + align:start position:0% +time + + + align:start position:0% +time +without clear physical motivation + + align:start position:0% +without clear physical motivation + + + align:start position:0% +without clear physical motivation +okay but for those young people tend not + + align:start position:0% +okay but for those young people tend not + + + align:start position:0% +okay but for those young people tend not +to be cracked okay and so they came up + + align:start position:0% +to be cracked okay and so they came up + + + align:start position:0% +to be cracked okay and so they came up +with this program yes + + align:start position:0% + + + + align:start position:0% + +no no it's not about the accuracy it's + + align:start position:0% +no no it's not about the accuracy it's + + + align:start position:0% +no no it's not about the accuracy it's +about to finding a sensible way to to to + + align:start position:0% +about to finding a sensible way to to to + + + align:start position:0% +about to finding a sensible way to to to +hide the divergences + + align:start position:0% + + + + align:start position:0% + +yeah yeah it's you can uh uh I'm because + + align:start position:0% +yeah yeah it's you can uh uh I'm because + + + align:start position:0% +yeah yeah it's you can uh uh I'm because +today will not be able to go into the + + align:start position:0% +today will not be able to go into the + + + align:start position:0% +today will not be able to go into the +detail I'm going to only tell you the + + align:start position:0% +detail I'm going to only tell you the + + + align:start position:0% +detail I'm going to only tell you the +result he said so that's why their + + align:start position:0% +result he said so that's why their + + + align:start position:0% +result he said so that's why their +results was actually a radical in some + + align:start position:0% +results was actually a radical in some + + + align:start position:0% +results was actually a radical in some +way because they realized there is some + + align:start position:0% +way because they realized there is some + + + align:start position:0% +way because they realized there is some +way + + align:start position:0% +way + + + align:start position:0% +way +somehow those divergences even they're + + align:start position:0% +somehow those divergences even they're + + + align:start position:0% +somehow those divergences even they're +there they do not affect those + + align:start position:0% +there they do not affect those + + + align:start position:0% +there they do not affect those +observable physics you can you can + + align:start position:0% +observable physics you can you can + + + align:start position:0% +observable physics you can you can +measure + + align:start position:0% +measure + + + align:start position:0% +measure +okay they don't affect those things so + + align:start position:0% +okay they don't affect those things so + + + align:start position:0% +okay they don't affect those things so +you can find some mathematical trick + + align:start position:0% +you can find some mathematical trick + + + align:start position:0% +you can find some mathematical trick +to to remove them + + align:start position:0% +to to remove them + + + align:start position:0% +to to remove them +okay and uh uh uh yeah + + align:start position:0% +okay and uh uh uh yeah + + + align:start position:0% +okay and uh uh uh yeah +so so so so so + + align:start position:0% +so so so so so + + + align:start position:0% +so so so so so +um + + align:start position:0% +um + + + align:start position:0% +um +but for many years + + align:start position:0% +but for many years + + + align:start position:0% +but for many years +so after they succeeded so so this is + + align:start position:0% +so after they succeeded so so this is + + + align:start position:0% +so after they succeeded so so this is +late 1940s and the Dyson was also later + + align:start position:0% +late 1940s and the Dyson was also later + + + align:start position:0% +late 1940s and the Dyson was also later +in 40s uh early 1950 even though this + + align:start position:0% +in 40s uh early 1950 even though this + + + align:start position:0% +in 40s uh early 1950 even though this +community achieved yeah and then as I'm + + align:start position:0% +community achieved yeah and then as I'm + + + align:start position:0% +community achieved yeah and then as I'm +going to mention at the end of the + + align:start position:0% +going to mention at the end of the + + + align:start position:0% +going to mention at the end of the +today's lecture and then the first + + align:start position:0% +today's lecture and then the first + + + align:start position:0% +today's lecture and then the first +calculated the quantity is this a + + align:start position:0% +calculated the quantity is this a + + + align:start position:0% +calculated the quantity is this a +aluminous Magnetic Moment + + align:start position:0% +aluminous Magnetic Moment + + + align:start position:0% +aluminous Magnetic Moment +uh which now uh require doing a + + align:start position:0% +uh which now uh require doing a + + + align:start position:0% +uh which now uh require doing a +calculation of this one + + align:start position:0% +calculation of this one + + + align:start position:0% +calculation of this one +uh doing a calculation of this one and + + align:start position:0% +uh doing a calculation of this one and + + + align:start position:0% +uh doing a calculation of this one and +Stringer uh did the first calculation + + align:start position:0% +Stringer uh did the first calculation + + + align:start position:0% +Stringer uh did the first calculation +and then he calculated okay the + + align:start position:0% +and then he calculated okay the + + + align:start position:0% +and then he calculated okay the +correction of this to the to the + + align:start position:0% +correction of this to the to the + + + align:start position:0% +correction of this to the to the +Magnetic Moment to of electron + + align:start position:0% +Magnetic Moment to of electron + + + align:start position:0% +Magnetic Moment to of electron +and that agreed very well with + + align:start position:0% +and that agreed very well with + + + align:start position:0% +and that agreed very well with +experiments so that was a chance at the + + align:start position:0% +experiments so that was a chance at the + + + align:start position:0% +experiments so that was a chance at the +time okay + + align:start position:0% +time okay + + + align:start position:0% +time okay +okay so so the experiment verified that + + align:start position:0% +okay so so the experiment verified that + + + align:start position:0% +okay so so the experiment verified that +the uh their success okay + + align:start position:0% +the uh their success okay + + + align:start position:0% +the uh their success okay +but still + + align:start position:0% +but still + + + align:start position:0% +but still +many people didn't believe this actually + + align:start position:0% +many people didn't believe this actually + + + align:start position:0% +many people didn't believe this actually +was something sensible it's many people + + align:start position:0% +was something sensible it's many people + + + align:start position:0% +was something sensible it's many people +for many years people saw this just a + + align:start position:0% +for many years people saw this just a + + + align:start position:0% +for many years people saw this just a +mathematical trick to to get some answer + + align:start position:0% +mathematical trick to to get some answer + + + align:start position:0% +mathematical trick to to get some answer +okay and so many people still uh for + + align:start position:0% +okay and so many people still uh for + + + align:start position:0% +okay and so many people still uh for +many years people was doubting this + + align:start position:0% +many years people was doubting this + + + align:start position:0% +many years people was doubting this +program of realization + + align:start position:0% +program of realization + + + align:start position:0% +program of realization +and then the only imaginator in in 1980 + + align:start position:0% +and then the only imaginator in in 1980 + + + align:start position:0% +and then the only imaginator in in 1980 +1960 so 1970s when we uh when when Ken + + align:start position:0% +1960 so 1970s when we uh when when Ken + + + align:start position:0% +1960 so 1970s when we uh when when Ken +Wilson came up with this idea a quote + + align:start position:0% +Wilson came up with this idea a quote + + + align:start position:0% +Wilson came up with this idea a quote +the realization group and then then + + align:start position:0% +the realization group and then then + + + align:start position:0% +the realization group and then then +people finally understood the physical + + align:start position:0% +people finally understood the physical + + + align:start position:0% +people finally understood the physical +reasoning and the physical basis behind + + align:start position:0% +reasoning and the physical basis behind + + + align:start position:0% +reasoning and the physical basis behind +this program of organization + + align:start position:0% +this program of organization + + + align:start position:0% +this program of organization +and so um yeah so so that was a + + align:start position:0% +and so um yeah so so that was a + + + align:start position:0% +and so um yeah so so that was a +revolutionary uh + + align:start position:0% +revolutionary uh + + + align:start position:0% +revolutionary uh +uh progress made by by Wilson yeah so so + + align:start position:0% +uh progress made by by Wilson yeah so so + + + align:start position:0% +uh progress made by by Wilson yeah so so +all this will be covered in detail uh uh + + align:start position:0% +all this will be covered in detail uh uh + + + align:start position:0% +all this will be covered in detail uh uh +in um + + align:start position:0% +in um + + + align:start position:0% +in um +uh uh in Quantum fields in with you okay + + align:start position:0% +uh uh in Quantum fields in with you okay + + + align:start position:0% +uh uh in Quantum fields in with you okay +and so so so today let me just very + + align:start position:0% +and so so so today let me just very + + + align:start position:0% +and so so so today let me just very +quickly tell you + + align:start position:0% +quickly tell you + + + align:start position:0% +quickly tell you +what this uh what this retire what this + + align:start position:0% +what this uh what this retire what this + + + align:start position:0% +what this uh what this retire what this +real roof diagrams do okay about this + + align:start position:0% +real roof diagrams do okay about this + + + align:start position:0% +real roof diagrams do okay about this +with a loop diagrams + + align:start position:0% +with a loop diagrams + + + align:start position:0% +with a loop diagrams +so first let me make some a general + + align:start position:0% +so first let me make some a general + + + align:start position:0% +so first let me make some a general +remark + + align:start position:0% +remark + + + align:start position:0% +remark +so mathematically you get divergences + + align:start position:0% +so mathematically you get divergences + + + align:start position:0% +so mathematically you get divergences +and then you have to find a way + + align:start position:0% +and then you have to find a way + + + align:start position:0% +and then you have to find a way +to to uh to uh to get rid of the + + align:start position:0% +to to uh to uh to get rid of the + + + align:start position:0% +to to uh to uh to get rid of the +divergences + + align:start position:0% +divergences + + + align:start position:0% +divergences +and physically there are also some new + + align:start position:0% +and physically there are also some new + + + align:start position:0% +and physically there are also some new +features + + align:start position:0% + + + + align:start position:0% + +a new important features okay + + align:start position:0% +a new important features okay + + + align:start position:0% +a new important features okay +any questions on this + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the first feature + + align:start position:0% + + + + align:start position:0% + +is that you already uh + + align:start position:0% + + + + align:start position:0% + +I already mentioned + + align:start position:0% +I already mentioned + + + align:start position:0% +I already mentioned +we include such loops + + align:start position:0% +we include such loops + + + align:start position:0% +we include such loops +you essentially uh include the quantum + + align:start position:0% +you essentially uh include the quantum + + + align:start position:0% +you essentially uh include the quantum +fluctuations + + align:start position:0% + + + + align:start position:0% + +of the vacuum + + align:start position:0% + + + + align:start position:0% + +okay so all this process + + align:start position:0% +okay so all this process + + + align:start position:0% +okay so all this process +so those electron pair that Photon that + + align:start position:0% +so those electron pair that Photon that + + + align:start position:0% +so those electron pair that Photon that +Photon they're all some virtual particle + + align:start position:0% +Photon they're all some virtual particle + + + align:start position:0% +Photon they're all some virtual particle +just come it just come from the vacuum + + align:start position:0% +just come it just come from the vacuum + + + align:start position:0% +just come it just come from the vacuum +okay it's just from the vacuum + + align:start position:0% +okay it's just from the vacuum + + + align:start position:0% +okay it's just from the vacuum +fluctuations + + align:start position:0% +fluctuations + + + align:start position:0% +fluctuations +so you can actually show mathematically + + align:start position:0% +so you can actually show mathematically + + + align:start position:0% +so you can actually show mathematically +rigorously + + align:start position:0% +rigorously + + + align:start position:0% +rigorously +okay that the three level diagrams + + align:start position:0% + + + + align:start position:0% + +and HP level diagrams + + align:start position:0% + + + + align:start position:0% + +can be obtained + + align:start position:0% + + + + align:start position:0% + +from + + align:start position:0% + + + + align:start position:0% + +solving + + align:start position:0% + + + + align:start position:0% + +your equation motion + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +so I just take your say take your own + + align:start position:0% +so I just take your say take your own + + + align:start position:0% +so I just take your say take your own +linear equation motion okay take the QD + + align:start position:0% +linear equation motion okay take the QD + + + align:start position:0% +linear equation motion okay take the QD +you write down the long linear equation + + align:start position:0% +you write down the long linear equation + + + align:start position:0% +you write down the long linear equation +motion and then you have this coupling e + + align:start position:0% +motion and then you have this coupling e + + + align:start position:0% +motion and then you have this coupling e +and then you just solve that equation + + align:start position:0% +and then you just solve that equation + + + align:start position:0% +and then you just solve that equation +perturbative order by order + + align:start position:0% +perturbative order by order + + + align:start position:0% +perturbative order by order +diagrams can be understood from that + + align:start position:0% +diagrams can be understood from that + + + align:start position:0% +diagrams can be understood from that +process + + align:start position:0% +process + + + align:start position:0% +process +okay essentially just come in from + + align:start position:0% +okay essentially just come in from + + + align:start position:0% +okay essentially just come in from +solving your a classical + + align:start position:0% +solving your a classical + + + align:start position:0% +solving your a classical +coming from solving that equation motion + + align:start position:0% +coming from solving that equation motion + + + align:start position:0% +coming from solving that equation motion +but then we know that Quantum nature + + align:start position:0% +but then we know that Quantum nature + + + align:start position:0% +but then we know that Quantum nature +come from doing the path integral okay + + align:start position:0% +come from doing the path integral okay + + + align:start position:0% +come from doing the path integral okay +equation motion uh uh uh uh uh capture + + align:start position:0% +equation motion uh uh uh uh uh capture + + + align:start position:0% +equation motion uh uh uh uh uh capture +some classical physics but but the + + align:start position:0% +some classical physics but but the + + + align:start position:0% +some classical physics but but the +gender and quantum physics come from + + align:start position:0% +gender and quantum physics come from + + + align:start position:0% +gender and quantum physics come from +doing the Classic Parts integral which + + align:start position:0% +doing the Classic Parts integral which + + + align:start position:0% +doing the Classic Parts integral which +integrate over all possible + + align:start position:0% +integrate over all possible + + + align:start position:0% +integrate over all possible +configurations + + align:start position:0% +configurations + + + align:start position:0% +configurations +and so that is not captured okay so + + align:start position:0% +and so that is not captured okay so + + + align:start position:0% +and so that is not captured okay so +those features of path indigo is not + + align:start position:0% +those features of path indigo is not + + + align:start position:0% +those features of path indigo is not +captured by the two level type + + align:start position:0% + + + + align:start position:0% + +but you may ask does true level diagram + + align:start position:0% +but you may ask does true level diagram + + + align:start position:0% +but you may ask does true level diagram +actually captures any quantum physics of + + align:start position:0% +actually captures any quantum physics of + + + align:start position:0% +actually captures any quantum physics of +course it does does capture quantum + + align:start position:0% +course it does does capture quantum + + + align:start position:0% +course it does does capture quantum +physics + + align:start position:0% +physics + + + align:start position:0% +physics +because the all this notion of the + + align:start position:0% +because the all this notion of the + + + align:start position:0% +because the all this notion of the +particles even the notion of the + + align:start position:0% +particles even the notion of the + + + align:start position:0% +particles even the notion of the +quantized in the particles + + align:start position:0% +quantized in the particles + + + align:start position:0% +quantized in the particles +that's already the including the economy + + align:start position:0% +that's already the including the economy + + + align:start position:0% +that's already the including the economy +fact + + align:start position:0% +fact + + + align:start position:0% +fact +okay it's just the three level diagram + + align:start position:0% +okay it's just the three level diagram + + + align:start position:0% +okay it's just the three level diagram +does not include the uh the fluctuations + + align:start position:0% +does not include the uh the fluctuations + + + align:start position:0% +does not include the uh the fluctuations +from the vaccine okay + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% +good + + + align:start position:0% +good +and so this is first feature okay so + + align:start position:0% +and so this is first feature okay so + + + align:start position:0% +and so this is first feature okay so +when you include the loops you uh you + + align:start position:0% +when you include the loops you uh you + + + align:start position:0% +when you include the loops you uh you +actually now finally include the quantum + + align:start position:0% +actually now finally include the quantum + + + align:start position:0% +actually now finally include the quantum +fluctuations + + align:start position:0% +fluctuations + + + align:start position:0% +fluctuations +and the second feature + + align:start position:0% + + + + align:start position:0% + +is very important it says the physical + + align:start position:0% +is very important it says the physical + + + align:start position:0% +is very important it says the physical +Mass + + align:start position:0% +Mass + + + align:start position:0% +Mass +charge + + align:start position:0% + + + + align:start position:0% + +and the field + + align:start position:0% + + + + align:start position:0% + +and the physical fields + + align:start position:0% + + + + align:start position:0% + +are not the same + + align:start position:0% + + + + align:start position:0% + +as that's appearing + + align:start position:0% + + + + align:start position:0% + +in the lagrangian + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so let me elaborate what this means + + align:start position:0% +so so let me elaborate what this means + + + align:start position:0% +so so let me elaborate what this means +so remember when you write down the + + align:start position:0% +so remember when you write down the + + + align:start position:0% +so remember when you write down the +LaGrange for QD + + align:start position:0% +LaGrange for QD + + + align:start position:0% +LaGrange for QD +we have I PSI bar + + align:start position:0% +we have I PSI bar + + + align:start position:0% +we have I PSI bar +menu mu + + align:start position:0% +menu mu + + + align:start position:0% +menu mu +minus + + align:start position:0% +minus + + + align:start position:0% +minus +PSI + + align:start position:0% + + + + align:start position:0% + +minus m + + align:start position:0% +minus m + + + align:start position:0% +minus m +PSI minus one half one quarter F squared + + align:start position:0% +PSI minus one half one quarter F squared + + + align:start position:0% +PSI minus one half one quarter F squared +okay so so that's not a long run and we + + align:start position:0% +okay so so that's not a long run and we + + + align:start position:0% +okay so so that's not a long run and we +say + + align:start position:0% +say + + + align:start position:0% +say +that this is the charge of the electron + + align:start position:0% +that this is the charge of the electron + + + align:start position:0% +that this is the charge of the electron +and this is the mass of the electron + + align:start position:0% +and this is the mass of the electron + + + align:start position:0% +and this is the mass of the electron +and and this side is the the loads of + + align:start position:0% +and and this side is the the loads of + + + align:start position:0% +and and this side is the the loads of +the electron Fields means that when you + + align:start position:0% +the electron Fields means that when you + + + align:start position:0% +the electron Fields means that when you +when you act it on the vacuum you can + + align:start position:0% +when you act it on the vacuum you can + + + align:start position:0% +when you act it on the vacuum you can +create the electron or anti-electron + + align:start position:0% +create the electron or anti-electron + + + align:start position:0% +create the electron or anti-electron +okay and similarly a mu equals one into + + align:start position:0% +okay and similarly a mu equals one into + + + align:start position:0% +okay and similarly a mu equals one into +the MU is messing is and and when a mu X + + align:start position:0% +the MU is messing is and and when a mu X + + + align:start position:0% +the MU is messing is and and when a mu X +and the vacuum can create the uh the + + align:start position:0% +and the vacuum can create the uh the + + + align:start position:0% +and the vacuum can create the uh the +photon okay + + align:start position:0% +photon okay + + + align:start position:0% +photon okay +I can create the photo + + align:start position:0% +I can create the photo + + + align:start position:0% +I can create the photo +when you include the loop effect + + align:start position:0% +when you include the loop effect + + + align:start position:0% +when you include the loop effect +the mass we we actually measure + + align:start position:0% +the mass we we actually measure + + + align:start position:0% +the mass we we actually measure +so by physical Mass means the the mass + + align:start position:0% +so by physical Mass means the the mass + + + align:start position:0% +so by physical Mass means the the mass +of the electron we actually measure in + + align:start position:0% +of the electron we actually measure in + + + align:start position:0% +of the electron we actually measure in +the lab + + align:start position:0% +the lab + + + align:start position:0% +the lab +and the charge will actually match in + + align:start position:0% +and the charge will actually match in + + + align:start position:0% +and the charge will actually match in +the lab + + align:start position:0% +the lab + + + align:start position:0% +the lab +they're no longer the same + + align:start position:0% +they're no longer the same + + + align:start position:0% +they're no longer the same +as the one appear in the lagrangian + + align:start position:0% +as the one appear in the lagrangian + + + align:start position:0% +as the one appear in the lagrangian +so the one in the LaGrange should be + + align:start position:0% +so the one in the LaGrange should be + + + align:start position:0% +so the one in the LaGrange should be +just viewed as some kind of parameter + + align:start position:0% +just viewed as some kind of parameter + + + align:start position:0% +just viewed as some kind of parameter +and so under your physical mass and the + + align:start position:0% +and so under your physical mass and the + + + align:start position:0% +and so under your physical mass and the +charge are functions of those parameters + + align:start position:0% +charge are functions of those parameters + + + align:start position:0% +charge are functions of those parameters +now there's some more complicated + + align:start position:0% +now there's some more complicated + + + align:start position:0% +now there's some more complicated +relation between those parameters and + + align:start position:0% +relation between those parameters and + + + align:start position:0% +relation between those parameters and +your physical mass and the charge + + align:start position:0% +your physical mass and the charge + + + align:start position:0% +your physical mass and the charge +and also the physical field which + + align:start position:0% +and also the physical field which + + + align:start position:0% +and also the physical field which +actually create the electron is no + + align:start position:0% +actually create the electron is no + + + align:start position:0% +actually create the electron is no +longer directly given by this sun + + align:start position:0% +longer directly given by this sun + + + align:start position:0% +longer directly given by this sun +okay it's related by side by some + + align:start position:0% +okay it's related by side by some + + + align:start position:0% +okay it's related by side by some +relation + + align:start position:0% + + + + align:start position:0% + +so so this difference okay so this is + + align:start position:0% +so so this difference okay so this is + + + align:start position:0% +so so this difference okay so this is +different it's also called the + + align:start position:0% +different it's also called the + + + align:start position:0% +different it's also called the +realization + + align:start position:0% + + + + align:start position:0% + +so here this + + align:start position:0% +so here this + + + align:start position:0% +so here this +two sense of validation + + align:start position:0% +two sense of validation + + + align:start position:0% +two sense of validation +which actually used for completely two + + align:start position:0% +which actually used for completely two + + + align:start position:0% +which actually used for completely two +different uh uh uh uh uh contexts + + align:start position:0% +different uh uh uh uh uh contexts + + + align:start position:0% +different uh uh uh uh uh contexts +so here so this realization just means + + align:start position:0% +so here so this realization just means + + + align:start position:0% +so here so this realization just means +the remove of the divergences + + align:start position:0% +the remove of the divergences + + + align:start position:0% +the remove of the divergences +and the risk of validation means + + align:start position:0% +and the risk of validation means + + + align:start position:0% +and the risk of validation means +that the parameters in your lagrangian + + align:start position:0% +that the parameters in your lagrangian + + + align:start position:0% +that the parameters in your lagrangian +may not be the same as the physical mass + + align:start position:0% +may not be the same as the physical mass + + + align:start position:0% +may not be the same as the physical mass +and the charge you measure + + align:start position:0% +and the charge you measure + + + align:start position:0% +and the charge you measure +okay so the thing you measure actually + + align:start position:0% +okay so the thing you measure actually + + + align:start position:0% +okay so the thing you measure actually +it's ready to the parameters in the + + align:start position:0% +it's ready to the parameters in the + + + align:start position:0% +it's ready to the parameters in the +logon in the non-trivial way + + align:start position:0% +logon in the non-trivial way + + + align:start position:0% +logon in the non-trivial way +okay in this supervisation + + align:start position:0% + + + + align:start position:0% + +is in principle a lot due to the + + align:start position:0% +is in principle a lot due to the + + + align:start position:0% +is in principle a lot due to the +Divergence it's just due to the + + align:start position:0% +Divergence it's just due to the + + + align:start position:0% +Divergence it's just due to the +interactions + + align:start position:0% + + + + align:start position:0% + +so so heuristically the physically is as + + align:start position:0% +so so heuristically the physically is as + + + align:start position:0% +so so heuristically the physically is as +follows just imagine you have a free + + align:start position:0% +follows just imagine you have a free + + + align:start position:0% +follows just imagine you have a free +electron + + align:start position:0% +electron + + + align:start position:0% +electron +so if you have a free electron + + align:start position:0% +so if you have a free electron + + + align:start position:0% +so if you have a free electron +and then the and then the and then the + + align:start position:0% +and then the and then the and then the + + + align:start position:0% +and then the and then the and then the +mass of the electron uh then it is what + + align:start position:0% +mass of the electron uh then it is what + + + align:start position:0% +mass of the electron uh then it is what +you measure + + align:start position:0% +you measure + + + align:start position:0% +you measure +okay but now if you include the + + align:start position:0% +okay but now if you include the + + + align:start position:0% +okay but now if you include the +interactions + + align:start position:0% +interactions + + + align:start position:0% +interactions +and now election can interact with the + + align:start position:0% +and now election can interact with the + + + align:start position:0% +and now election can interact with the +photon in a complicated way and that + + align:start position:0% +photon in a complicated way and that + + + align:start position:0% +photon in a complicated way and that +interaction + + align:start position:0% +interaction + + + align:start position:0% +interaction +then can change the mass of the electron + + align:start position:0% +then can change the mass of the electron + + + align:start position:0% +then can change the mass of the electron +okay so that's why + + align:start position:0% +okay so that's why + + + align:start position:0% +okay so that's why +so that's why uh uh uh in general for + + align:start position:0% +so that's why uh uh uh in general for + + + align:start position:0% +so that's why uh uh uh in general for +interacting Theory + + align:start position:0% +interacting Theory + + + align:start position:0% +interacting Theory +what appears in your lagrangian + + align:start position:0% +what appears in your lagrangian + + + align:start position:0% +what appears in your lagrangian +they they don't have to be the uh the + + align:start position:0% +they they don't have to be the uh the + + + align:start position:0% +they they don't have to be the uh the +quantity you actually measure + + align:start position:0% +quantity you actually measure + + + align:start position:0% +quantity you actually measure +okay because the uh the interactions can + + align:start position:0% +okay because the uh the interactions can + + + align:start position:0% +okay because the uh the interactions can +change how you translate those quantity + + align:start position:0% +change how you translate those quantity + + + align:start position:0% +change how you translate those quantity +into the physical quantities you measure + + align:start position:0% + + + + align:start position:0% + +and so uh uh uh yeah yeah so this + + align:start position:0% +and so uh uh uh yeah yeah so this + + + align:start position:0% +and so uh uh uh yeah yeah so this +organization just means the realization + + align:start position:0% +organization just means the realization + + + align:start position:0% +organization just means the realization +changes of the uh uh the value of your + + align:start position:0% +changes of the uh uh the value of your + + + align:start position:0% +changes of the uh uh the value of your +parameters okay + + align:start position:0% + + + + align:start position:0% + +so so now let me just make this a little + + align:start position:0% +so so now let me just make this a little + + + align:start position:0% +so so now let me just make this a little +bit more explicit and so before I do + + align:start position:0% +bit more explicit and so before I do + + + align:start position:0% +bit more explicit and so before I do +that do you have any questions yes + + align:start position:0% + + + + align:start position:0% + +parameter m + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +how this is I don't take mechanism and + + align:start position:0% +how this is I don't take mechanism and + + + align:start position:0% +how this is I don't take mechanism and +how we say get the message yeah but + + align:start position:0% +how we say get the message yeah but + + + align:start position:0% +how we say get the message yeah but +you're saying the QED at home has its + + align:start position:0% +you're saying the QED at home has its + + + align:start position:0% +you're saying the QED at home has its +way of explaining how the parameter + + align:start position:0% +way of explaining how the parameter + + + align:start position:0% +way of explaining how the parameter +emulates + + align:start position:0% +emulates + + + align:start position:0% +emulates +yeah yeah so this is the uh this is the + + align:start position:0% +yeah yeah so this is the uh this is the + + + align:start position:0% +yeah yeah so this is the uh this is the +so so when I write down this lagranging + + align:start position:0% +so so when I write down this lagranging + + + align:start position:0% +so so when I write down this lagranging +and then I have a parameters here called + + align:start position:0% +and then I have a parameters here called + + + align:start position:0% +and then I have a parameters here called +E and M + + align:start position:0% +E and M + + + align:start position:0% +E and M +and so if I ignore the interaction + + align:start position:0% +and so if I ignore the interaction + + + align:start position:0% +and so if I ignore the interaction +now you glow the interaction and then + + align:start position:0% +now you glow the interaction and then + + + align:start position:0% +now you glow the interaction and then +the M will be the mass of the particle + + align:start position:0% +the M will be the mass of the particle + + + align:start position:0% +the M will be the mass of the particle +you actually measure + + align:start position:0% +you actually measure + + + align:start position:0% +you actually measure +but now we include the action and the + + align:start position:0% +but now we include the action and the + + + align:start position:0% +but now we include the action and the +the interaction can change that Mass + + align:start position:0% +the interaction can change that Mass + + + align:start position:0% +the interaction can change that Mass +it's not related to that hicks or + + align:start position:0% +it's not related to that hicks or + + + align:start position:0% +it's not related to that hicks or +the kicks experience where this m come + + align:start position:0% +the kicks experience where this m come + + + align:start position:0% +the kicks experience where this m come +from + + align:start position:0% +from + + + align:start position:0% +from +yeah his experience where where this + + align:start position:0% +yeah his experience where where this + + + align:start position:0% +yeah his experience where where this +parameter come from yeah + + align:start position:0% + + + + align:start position:0% + +so this is organization on top of that + + align:start position:0% + + + + align:start position:0% + +good so now let me just elaborate what + + align:start position:0% +good so now let me just elaborate what + + + align:start position:0% +good so now let me just elaborate what +this means okay a level elaborate what + + align:start position:0% +this means okay a level elaborate what + + + align:start position:0% +this means okay a level elaborate what +this means + + align:start position:0% +this means + + + align:start position:0% +this means +so for this purpose now let me put + + align:start position:0% +so for this purpose now let me put + + + align:start position:0% +so for this purpose now let me put +a subscript B here + + align:start position:0% +a subscript B here + + + align:start position:0% +a subscript B here +on everything + + align:start position:0% +on everything + + + align:start position:0% +on everything +just to emphasize the no longer + + align:start position:0% + + + + align:start position:0% + +yeah it changes the energy you need to + + align:start position:0% +yeah it changes the energy you need to + + + align:start position:0% +yeah it changes the energy you need to +create the particle + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so now I now I reload everything to + + align:start position:0% +so so now I now I reload everything to + + + align:start position:0% +so so now I now I reload everything to +be with the B + + align:start position:0% +be with the B + + + align:start position:0% +be with the B +so those are called the back parameters + + align:start position:0% +so those are called the back parameters + + + align:start position:0% +so those are called the back parameters +so EB + + align:start position:0% +so EB + + + align:start position:0% +so EB +it's called The Bear charge + + align:start position:0% + + + + align:start position:0% + +an MB + + align:start position:0% +an MB + + + align:start position:0% +an MB +is called the bear + + align:start position:0% +is called the bear + + + align:start position:0% +is called the bear +Mass + + align:start position:0% +Mass + + + align:start position:0% +Mass +and this side B + + align:start position:0% +and this side B + + + align:start position:0% +and this side B +and a mu B + + align:start position:0% +and a mu B + + + align:start position:0% +and a mu B +is called the bare fields + + align:start position:0% + + + + align:start position:0% + +okay the code it + + align:start position:0% +okay the code it + + + align:start position:0% +okay the code it +and when I write this F Square b means + + align:start position:0% +and when I write this F Square b means + + + align:start position:0% +and when I write this F Square b means +that the F Square constructed out of a + + align:start position:0% +that the F Square constructed out of a + + + align:start position:0% +that the F Square constructed out of a +mu B + + align:start position:0% +mu B + + + align:start position:0% +mu B +a control of every + + align:start position:0% + + + + align:start position:0% + +so now let's just illustrate this thing + + align:start position:0% +so now let's just illustrate this thing + + + align:start position:0% +so now let's just illustrate this thing +using this three a simple diagrams + + align:start position:0% +using this three a simple diagrams + + + align:start position:0% +using this three a simple diagrams +okay so let's look at first that diagram + + align:start position:0% + + + + align:start position:0% + +the propagation of electron + + align:start position:0% +the propagation of electron + + + align:start position:0% +the propagation of electron +okay + + align:start position:0% + + + + align:start position:0% + +the progression of the electron + + align:start position:0% + + + + align:start position:0% + +so so we're not yeah uh you can just + + align:start position:0% +so so we're not yeah uh you can just + + + align:start position:0% +so so we're not yeah uh you can just +calculate what you need to do is you + + align:start position:0% +calculate what you need to do is you + + + align:start position:0% +calculate what you need to do is you +calculate this diagram + + align:start position:0% +calculate this diagram + + + align:start position:0% +calculate this diagram +and uh and then you find the correction + + align:start position:0% +and uh and then you find the correction + + + align:start position:0% +and uh and then you find the correction +to the propagator yeah so so this + + align:start position:0% +to the propagator yeah so so this + + + align:start position:0% +to the propagator yeah so so this +diagram will induce a fraction to the + + align:start position:0% +diagram will induce a fraction to the + + + align:start position:0% +diagram will induce a fraction to the +propagation to the propagate of the + + align:start position:0% +propagation to the propagate of the + + + align:start position:0% +propagation to the propagate of the +electron okay to the propagate of + + align:start position:0% +electron okay to the propagate of + + + align:start position:0% +electron okay to the propagate of +electron and from this correction and + + align:start position:0% +electron and from this correction and + + + align:start position:0% +electron and from this correction and +then you find that the uh + + align:start position:0% +then you find that the uh + + + align:start position:0% +then you find that the uh +yeah so yeah so let's first write down + + align:start position:0% +yeah so yeah so let's first write down + + + align:start position:0% +yeah so yeah so let's first write down +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +the tree level propagator + + align:start position:0% + + + + align:start position:0% + +so this is given by minus one + + align:start position:0% +so this is given by minus one + + + align:start position:0% +so this is given by minus one +ik slash + + align:start position:0% +ik slash + + + align:start position:0% +ik slash +minus n plus X + + align:start position:0% +minus n plus X + + + align:start position:0% +minus n plus X +okay so this is just MB + + align:start position:0% +okay so this is just MB + + + align:start position:0% +okay so this is just MB +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay + + align:start position:0% + + + + align:start position:0% + +so you can interpret the mass of + + align:start position:0% +so you can interpret the mass of + + + align:start position:0% +so you can interpret the mass of +electron as the pole of this K so when a + + align:start position:0% +electron as the pole of this K so when a + + + align:start position:0% +electron as the pole of this K so when a +k slash equal to MB and then and then + + align:start position:0% +k slash equal to MB and then and then + + + align:start position:0% +k slash equal to MB and then and then +that corresponding to the mass of the + + align:start position:0% +that corresponding to the mass of the + + + align:start position:0% +that corresponding to the mass of the +electron okay and the the mass of the + + align:start position:0% +electron okay and the the mass of the + + + align:start position:0% +electron okay and the the mass of the +electron corresponding to the pole of + + align:start position:0% +electron corresponding to the pole of + + + align:start position:0% +electron corresponding to the pole of +this propagate yes + + align:start position:0% + + + + align:start position:0% + +what I mean is just when when you invert + + align:start position:0% +what I mean is just when when you invert + + + align:start position:0% +what I mean is just when when you invert +it so this becomes K square plus M + + align:start position:0% +it so this becomes K square plus M + + + align:start position:0% +it so this becomes K square plus M +squared + + align:start position:0% +squared + + + align:start position:0% +squared +minus Epsilon yeah it just means K + + align:start position:0% +minus Epsilon yeah it just means K + + + align:start position:0% +minus Epsilon yeah it just means K +squared + + align:start position:0% +squared + + + align:start position:0% +squared +yeah so so upstairs + + align:start position:0% + + + + align:start position:0% + +yeah just means K square plus n is + + align:start position:0% +yeah just means K square plus n is + + + align:start position:0% +yeah just means K square plus n is +it + + align:start position:0% +it + + + align:start position:0% +it +the massive electron equals one into the + + align:start position:0% +the massive electron equals one into the + + + align:start position:0% +the massive electron equals one into the +pole of the pole + + align:start position:0% + + + + align:start position:0% + +so now when you include the such + + align:start position:0% +so now when you include the such + + + align:start position:0% +so now when you include the such +Corrections + + align:start position:0% +Corrections + + + align:start position:0% +Corrections +and then you find + + align:start position:0% +and then you find + + + align:start position:0% +and then you find +your propagator modified into the + + align:start position:0% +your propagator modified into the + + + align:start position:0% +your propagator modified into the +following scene Z + + align:start position:0% +following scene Z + + + align:start position:0% +following scene Z +divided by ik slash minus some other + + align:start position:0% +divided by ik slash minus some other + + + align:start position:0% +divided by ik slash minus some other +Mass plus Epsilon okay and now this m + + align:start position:0% +Mass plus Epsilon okay and now this m + + + align:start position:0% +Mass plus Epsilon okay and now this m +mass is no longer the same so this fit + + align:start position:0% +mass is no longer the same so this fit + + + align:start position:0% +mass is no longer the same so this fit +so this physical Mass + + align:start position:0% + + + + align:start position:0% + +is now just MB plus something else plus + + align:start position:0% +is now just MB plus something else plus + + + align:start position:0% +is now just MB plus something else plus +some corrections + + align:start position:0% +some corrections + + + align:start position:0% +some corrections +so so this is a physical Mass + + align:start position:0% + + + + align:start position:0% + +so so this tells you + + align:start position:0% +so so this tells you + + + align:start position:0% +so so this tells you +there's the mass of the electron we + + align:start position:0% +there's the mass of the electron we + + + align:start position:0% +there's the mass of the electron we +include such diagram actually get + + align:start position:0% +include such diagram actually get + + + align:start position:0% +include such diagram actually get +shifted + + align:start position:0% +shifted + + + align:start position:0% +shifted +okay get shifted from your bare Mass + + align:start position:0% +okay get shifted from your bare Mass + + + align:start position:0% +okay get shifted from your bare Mass +okay from the bare Mass + + align:start position:0% +okay from the bare Mass + + + align:start position:0% +okay from the bare Mass +so if you live recalculate it and then + + align:start position:0% +so if you live recalculate it and then + + + align:start position:0% +so if you live recalculate it and then +you find this cracking is infinite okay + + align:start position:0% +you find this cracking is infinite okay + + + align:start position:0% +you find this cracking is infinite okay +you find the contribution of this Diagon + + align:start position:0% +you find the contribution of this Diagon + + + align:start position:0% +you find the contribution of this Diagon +is infinite and so that's why you did + + align:start position:0% +is infinite and so that's why you did + + + align:start position:0% +is infinite and so that's why you did +include this validation such and then + + align:start position:0% +include this validation such and then + + + align:start position:0% +include this validation such and then +and then to calculate the finite + + align:start position:0% +and then to calculate the finite + + + align:start position:0% +and then to calculate the finite +quantity of this data + + align:start position:0% + + + + align:start position:0% + +so so you find that this uh the pole of + + align:start position:0% +so so you find that this uh the pole of + + + align:start position:0% +so so you find that this uh the pole of +the propaganda change + + align:start position:0% +the propaganda change + + + align:start position:0% +the propaganda change +you also find actually the the residue + + align:start position:0% +you also find actually the the residue + + + align:start position:0% +you also find actually the the residue +also change so here the residue just one + + align:start position:0% +also change so here the residue just one + + + align:start position:0% +also change so here the residue just one +okay here the relative becomes some + + align:start position:0% +okay here the relative becomes some + + + align:start position:0% +okay here the relative becomes some +other consonants d + + align:start position:0% + + + + align:start position:0% + +okay so so that means + + align:start position:0% +okay so so that means + + + align:start position:0% +okay so so that means +that when you create when you act side B + + align:start position:0% +that when you create when you act side B + + + align:start position:0% +that when you create when you act side B +on the vacuum + + align:start position:0% +on the vacuum + + + align:start position:0% +on the vacuum +you no longer create just the K okay + + align:start position:0% +you no longer create just the K okay + + + align:start position:0% +you no longer create just the K okay +here I'm just writing sigmatically + + align:start position:0% +here I'm just writing sigmatically + + + align:start position:0% +here I'm just writing sigmatically +you're actually creating square root Z + + align:start position:0% +you're actually creating square root Z + + + align:start position:0% +you're actually creating square root Z +times k + + align:start position:0% +times k + + + align:start position:0% +times k +okay because of the pre-factor okay so + + align:start position:0% +okay because of the pre-factor okay so + + + align:start position:0% +okay because of the pre-factor okay so +remember our previous episode B is equal + + align:start position:0% +remember our previous episode B is equal + + + align:start position:0% +remember our previous episode B is equal +to exactly exactly when you act on the + + align:start position:0% +to exactly exactly when you act on the + + + align:start position:0% +to exactly exactly when you act on the +Zero you will create a particle a long + + align:start position:0% +Zero you will create a particle a long + + + align:start position:0% +Zero you will create a particle a long +nice in a certain way but now with this + + align:start position:0% +nice in a certain way but now with this + + + align:start position:0% +nice in a certain way but now with this +Z Factor + + align:start position:0% +Z Factor + + + align:start position:0% +Z Factor +and then I create a a lot of the fact + + align:start position:0% +and then I create a a lot of the fact + + + align:start position:0% +and then I create a a lot of the fact +that + + align:start position:0% +that + + + align:start position:0% +that +now is a prefect Z okay + + align:start position:0% +now is a prefect Z okay + + + align:start position:0% +now is a prefect Z okay +okay so so we normally Define the + + align:start position:0% +okay so so we normally Define the + + + align:start position:0% +okay so so we normally Define the +physical field + + align:start position:0% + + + + align:start position:0% + +as the one which PSI + + align:start position:0% +as the one which PSI + + + align:start position:0% +as the one which PSI +when you act on the vacuum which just + + align:start position:0% +when you act on the vacuum which just + + + align:start position:0% +when you act on the vacuum which just +precisely created the states okay create + + align:start position:0% +precisely created the states okay create + + + align:start position:0% +precisely created the states okay create +the state + + align:start position:0% +the state + + + align:start position:0% +the state +and so and so now there's a relation + + align:start position:0% +and so and so now there's a relation + + + align:start position:0% +and so and so now there's a relation +between this barefield + + align:start position:0% +between this barefield + + + align:start position:0% +between this barefield +and the physical fields + + align:start position:0% + + + + align:start position:0% + +okay and that is a relation between the + + align:start position:0% +okay and that is a relation between the + + + align:start position:0% +okay and that is a relation between the +battlefield and the physical reals + + align:start position:0% +battlefield and the physical reals + + + align:start position:0% +battlefield and the physical reals +through this Factor + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so this tells you that the uh uh yeah + + align:start position:0% +so so this tells you that the uh uh yeah + + + align:start position:0% +so so this tells you that the uh uh yeah +uh the the field itself also gets uh the + + align:start position:0% +uh the the field itself also gets uh the + + + align:start position:0% +uh the the field itself also gets uh the +magnitude of the field instead of also + + align:start position:0% +magnitude of the field instead of also + + + align:start position:0% +magnitude of the field instead of also +getting low miles + + align:start position:0% + + + + align:start position:0% + +any questions on this + + align:start position:0% +any questions on this + + + align:start position:0% +any questions on this +so the similar thing is happening for + + align:start position:0% +so the similar thing is happening for + + + align:start position:0% +so the similar thing is happening for +the photon case + + align:start position:0% +the photon case + + + align:start position:0% +the photon case +so if you can see this process + + align:start position:0% + + + + align:start position:0% + +so this corresponds into a modification + + align:start position:0% +so this corresponds into a modification + + + align:start position:0% +so this corresponds into a modification +to the photon propagator + + align:start position:0% + + + + align:start position:0% + +that you create a program into the + + align:start position:0% +that you create a program into the + + + align:start position:0% +that you create a program into the +photon propagator + + align:start position:0% +photon propagator + + + align:start position:0% +photon propagator +so now you find + + align:start position:0% +so now you find + + + align:start position:0% +so now you find +that actually the photon mass is not + + align:start position:0% +that actually the photon mass is not + + + align:start position:0% +that actually the photon mass is not +changed + + align:start position:0% +changed + + + align:start position:0% +changed +so even we include such Corrections the + + align:start position:0% +so even we include such Corrections the + + + align:start position:0% +so even we include such Corrections the +photons still matches + + align:start position:0% +photons still matches + + + align:start position:0% +photons still matches +so so remember a previously we say why + + align:start position:0% +so so remember a previously we say why + + + align:start position:0% +so so remember a previously we say why +you cannot add a mask to the to a photon + + align:start position:0% +you cannot add a mask to the to a photon + + + align:start position:0% +you cannot add a mask to the to a photon +to remember why we cannot add the mass + + align:start position:0% +to remember why we cannot add the mass + + + align:start position:0% +to remember why we cannot add the mass +term to to the to the to the Maxwell + + align:start position:0% +term to to the to the to the Maxwell + + + align:start position:0% +term to to the to the to the Maxwell +field + + align:start position:0% +field + + + align:start position:0% +field +engaging varins so uh so the fact that + + align:start position:0% +engaging varins so uh so the fact that + + + align:start position:0% +engaging varins so uh so the fact that +the mass cannot uh be be generated by + + align:start position:0% +the mass cannot uh be be generated by + + + align:start position:0% +the mass cannot uh be be generated by +such correction just means that the + + align:start position:0% +such correction just means that the + + + align:start position:0% +such correction just means that the +gauge uh symmetry is uh is maintained + + align:start position:0% +gauge uh symmetry is uh is maintained + + + align:start position:0% +gauge uh symmetry is uh is maintained +okay so the photon remains mass please + + align:start position:0% + + + + align:start position:0% + +but but you do have similar memorization + + align:start position:0% +but but you do have similar memorization + + + align:start position:0% +but but you do have similar memorization +of the strains of the Maxwell field so + + align:start position:0% +of the strains of the Maxwell field so + + + align:start position:0% +of the strains of the Maxwell field so +now + + align:start position:0% + + + + align:start position:0% + +now the uh uh the the bar field is + + align:start position:0% +now the uh uh the the bar field is + + + align:start position:0% +now the uh uh the the bar field is +related to to your physical Fields + + align:start position:0% +related to to your physical Fields + + + align:start position:0% +related to to your physical Fields +through some Factor + + align:start position:0% +through some Factor + + + align:start position:0% +through some Factor +and called a yeah normally called D3 + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah it's just a constant yeah because + + align:start position:0% +yeah it's just a constant yeah because + + + align:start position:0% +yeah it's just a constant yeah because +we just calculated the uh yeah this just + + align:start position:0% +we just calculated the uh yeah this just + + + align:start position:0% +we just calculated the uh yeah this just +accounts + + align:start position:0% + + + + align:start position:0% + +so this is the defined to be the residue + + align:start position:0% +so this is the defined to be the residue + + + align:start position:0% +so this is the defined to be the residue +of the pope of the pole of the + + align:start position:0% +of the pope of the pole of the + + + align:start position:0% +of the pope of the pole of the +propaganda + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% +good + + + align:start position:0% +good +so so finally let me mention a little + + align:start position:0% +so so finally let me mention a little + + + align:start position:0% +so so finally let me mention a little +bit the the last diagram + + align:start position:0% + + + + align:start position:0% + +so so the last diagram + + align:start position:0% + + + + align:start position:0% + +so this last diagram which I mean we go + + align:start position:0% +so this last diagram which I mean we go + + + align:start position:0% +so this last diagram which I mean we go +in here + + align:start position:0% + + + + align:start position:0% + +so so remember if you just have the + + align:start position:0% +so so remember if you just have the + + + align:start position:0% +so so remember if you just have the +original one + + align:start position:0% + + + + align:start position:0% + +and then here just ieb + + align:start position:0% +and then here just ieb + + + align:start position:0% +and then here just ieb +gamma mu + + align:start position:0% +gamma mu + + + align:start position:0% +gamma mu +okay and now when you add such a + + align:start position:0% +okay and now when you add such a + + + align:start position:0% +okay and now when you add such a +correction so so this is the tree level + + align:start position:0% +correction so so this is the tree level + + + align:start position:0% +correction so so this is the tree level +one and then at one Loop level you can + + align:start position:0% +one and then at one Loop level you can + + + align:start position:0% +one and then at one Loop level you can +add such a thing okay when you add such + + align:start position:0% +add such a thing okay when you add such + + + align:start position:0% +add such a thing okay when you add such +a thing and then you uh you will + + align:start position:0% +a thing and then you uh you will + + + align:start position:0% +a thing and then you uh you will +normalize the charge + + align:start position:0% +normalize the charge + + + align:start position:0% +normalize the charge +okay then the charge gets changed + + align:start position:0% +okay then the charge gets changed + + + align:start position:0% +okay then the charge gets changed +okay so now you find interestingly + + align:start position:0% +okay so now you find interestingly + + + align:start position:0% +okay so now you find interestingly +you find another the the new electric + + align:start position:0% +you find another the the new electric + + + align:start position:0% +you find another the the new electric +charge + + align:start position:0% +charge + + + align:start position:0% +charge +is related so this is the reload the + + align:start position:0% +is related so this is the reload the + + + align:start position:0% +is related so this is the reload the +measured charge physical charge + + align:start position:0% + + + + align:start position:0% + +okay so a complicated calculation find + + align:start position:0% +okay so a complicated calculation find + + + align:start position:0% +okay so a complicated calculation find +this physical charge is related + + align:start position:0% +this physical charge is related + + + align:start position:0% +this physical charge is related +to the bad charge + + align:start position:0% + + + + align:start position:0% + +by the same factor D3 + + align:start position:0% +by the same factor D3 + + + align:start position:0% +by the same factor D3 +as in the case of the uh relation + + align:start position:0% +as in the case of the uh relation + + + align:start position:0% +as in the case of the uh relation +between the the the the the bare field + + align:start position:0% +between the the the the the bare field + + + align:start position:0% +between the the the the the bare field +and the denominized field + + align:start position:0% +and the denominized field + + + align:start position:0% +and the denominized field +okay you find the same number + + align:start position:0% +okay you find the same number + + + align:start position:0% +okay you find the same number +so appears in the relation between the + + align:start position:0% +so appears in the relation between the + + + align:start position:0% +so appears in the relation between the +physical elect charge and the bear + + align:start position:0% +physical elect charge and the bear + + + align:start position:0% +physical elect charge and the bear +charge + + align:start position:0% +charge + + + align:start position:0% +charge +okay as a bad charge + + align:start position:0% + + + + align:start position:0% + +so this is important + + align:start position:0% +so this is important + + + align:start position:0% +so this is important +for the following reason + + align:start position:0% +for the following reason + + + align:start position:0% +for the following reason +so now you observe because of these two + + align:start position:0% +so now you observe because of these two + + + align:start position:0% +so now you observe because of these two +relation + + align:start position:0% + + + + align:start position:0% + +okay because of this relation + + align:start position:0% +okay because of this relation + + + align:start position:0% +okay because of this relation +That You observe that EB + + align:start position:0% + + + + align:start position:0% + +a mub + + align:start position:0% +a mub + + + align:start position:0% +a mub +is actually equal to E A mu + + align:start position:0% +is actually equal to E A mu + + + align:start position:0% +is actually equal to E A mu +okay so the products are the same + + align:start position:0% +okay so the products are the same + + + align:start position:0% +okay so the products are the same +okay yeah because the square root three + + align:start position:0% +okay yeah because the square root three + + + align:start position:0% +okay yeah because the square root three +Factor cancel + + align:start position:0% +Factor cancel + + + align:start position:0% +Factor cancel +okay a square root should be Factor + + align:start position:0% +okay a square root should be Factor + + + align:start position:0% +okay a square root should be Factor +cancel + + align:start position:0% + + + + align:start position:0% + +right + + align:start position:0% +right + + + align:start position:0% +right +and this is important because because of + + align:start position:0% +and this is important because because of + + + align:start position:0% +and this is important because because of +this + + align:start position:0% +this + + + align:start position:0% +this +that means you can't covarian derivative + + align:start position:0% + + + + align:start position:0% + +does not change + + align:start position:0% + + + + align:start position:0% + +does not change + + align:start position:0% + + + + align:start position:0% + +so remember this uh the structure of + + align:start position:0% +so remember this uh the structure of + + + align:start position:0% +so remember this uh the structure of +this quadrant derivative + + align:start position:0% +this quadrant derivative + + + align:start position:0% +this quadrant derivative +is needed for the gate environments + + align:start position:0% +is needed for the gate environments + + + align:start position:0% +is needed for the gate environments +okay it's needed for the gating virus + + align:start position:0% +okay it's needed for the gating virus + + + align:start position:0% +okay it's needed for the gating virus +and so uh so that this is maintained + + align:start position:0% +and so uh so that this is maintained + + + align:start position:0% +and so uh so that this is maintained +again it's a it's an implication that + + align:start position:0% +again it's a it's an implication that + + + align:start position:0% +again it's a it's an implication that +the gauge symmetry is maintained + + align:start position:0% +the gauge symmetry is maintained + + + align:start position:0% +the gauge symmetry is maintained +right it's okay it's images + + align:start position:0% +right it's okay it's images + + + align:start position:0% +right it's okay it's images +in other words + + align:start position:0% +in other words + + + align:start position:0% +in other words +you want to say that if we want to + + align:start position:0% +you want to say that if we want to + + + align:start position:0% +you want to say that if we want to +maintain the gauge symmetry + + align:start position:0% +maintain the gauge symmetry + + + align:start position:0% +maintain the gauge symmetry +then then EB and a mu B they have to + + align:start position:0% +then then EB and a mu B they have to + + + align:start position:0% +then then EB and a mu B they have to +renormalize in the opposite way so that + + align:start position:0% +renormalize in the opposite way so that + + + align:start position:0% +renormalize in the opposite way so that +this is the same + + align:start position:0% +this is the same + + + align:start position:0% +this is the same +okay uh so this is the second + + align:start position:0% + + + + align:start position:0% + +so so this diagram + + align:start position:0% +so so this diagram + + + align:start position:0% +so so this diagram +have two effects + + align:start position:0% +have two effects + + + align:start position:0% +have two effects +so this diagram have two effects one in + + align:start position:0% +so this diagram have two effects one in + + + align:start position:0% +so this diagram have two effects one in +fact is cracked the electric charge + + align:start position:0% +fact is cracked the electric charge + + + align:start position:0% +fact is cracked the electric charge +and another effect is generate the + + align:start position:0% +and another effect is generate the + + + align:start position:0% +and another effect is generate the +Magnetic Moment generate the new uh + + align:start position:0% +Magnetic Moment generate the new uh + + + align:start position:0% +Magnetic Moment generate the new uh +aluminous Magnetic Moment so this has + + align:start position:0% +aluminous Magnetic Moment so this has + + + align:start position:0% +aluminous Magnetic Moment so this has +two effects the first effect is the to + + align:start position:0% +two effects the first effect is the to + + + align:start position:0% +two effects the first effect is the to +renormalize to change your charge + + align:start position:0% +renormalize to change your charge + + + align:start position:0% +renormalize to change your charge +and the second effect + + align:start position:0% +and the second effect + + + align:start position:0% +and the second effect +is generate + + align:start position:0% + + + + align:start position:0% + +an enormous Magnetic Moment + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you may have learned in your quantum + + align:start position:0% +so you may have learned in your quantum + + + align:start position:0% +so you may have learned in your quantum +mechanics + + align:start position:0% + + + + align:start position:0% + +so you may have learned in your quantum + + align:start position:0% +so you may have learned in your quantum + + + align:start position:0% +so you may have learned in your quantum +mechanics that it matters + + align:start position:0% +mechanics that it matters + + + align:start position:0% +mechanics that it matters +as a Magnetic Moment + + align:start position:0% + + + + align:start position:0% + +which is normally a written as following + + align:start position:0% +which is normally a written as following + + + align:start position:0% +which is normally a written as following +mu e equal to minus + + align:start position:0% +mu e equal to minus + + + align:start position:0% +mu e equal to minus +e divided by 2m + + align:start position:0% +e divided by 2m + + + align:start position:0% +e divided by 2m +G and the spin operator + + align:start position:0% +G and the spin operator + + + align:start position:0% +G and the spin operator +okay just because the electron has spin + + align:start position:0% +okay just because the electron has spin + + + align:start position:0% +okay just because the electron has spin +spin half + + align:start position:0% +spin half + + + align:start position:0% +spin half +and so has a magnetic moment and this + + align:start position:0% +and so has a magnetic moment and this + + + align:start position:0% +and so has a magnetic moment and this +being half of course is normally + + align:start position:0% +being half of course is normally + + + align:start position:0% +being half of course is normally +written the spring operator uh uh uh + + align:start position:0% +written the spring operator uh uh uh + + + align:start position:0% +written the spring operator uh uh uh +it's the in the spring half space then + + align:start position:0% +it's the in the spring half space then + + + align:start position:0% +it's the in the spring half space then +just a sigma Matrix + + align:start position:0% +just a sigma Matrix + + + align:start position:0% +just a sigma Matrix +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and this G Factor + + align:start position:0% +and this G Factor + + + align:start position:0% +and this G Factor +so this is a g factor which regulates + + align:start position:0% +so this is a g factor which regulates + + + align:start position:0% +so this is a g factor which regulates +the uh ERG just a longer + + align:start position:0% +the uh ERG just a longer + + + align:start position:0% +the uh ERG just a longer +Okay g is just a longer it's a long one + + align:start position:0% +Okay g is just a longer it's a long one + + + align:start position:0% +Okay g is just a longer it's a long one +equals g Factor yes + + align:start position:0% + + + + align:start position:0% + +yeah yeah the E can change itself yeah + + align:start position:0% +yeah yeah the E can change itself yeah + + + align:start position:0% +yeah yeah the E can change itself yeah +so so so uh + + align:start position:0% +so so so uh + + + align:start position:0% +so so so uh +you uh you just shift the value of e + + align:start position:0% +you uh you just shift the value of e + + + align:start position:0% +you uh you just shift the value of e +right + + align:start position:0% + + + + align:start position:0% + +yeah change is also small + + align:start position:0% +yeah change is also small + + + align:start position:0% +yeah change is also small +if the change is a higher order yeah + + align:start position:0% +if the change is a higher order yeah + + + align:start position:0% +if the change is a higher order yeah +yeah but this is a very good question + + align:start position:0% +yeah but this is a very good question + + + align:start position:0% +yeah but this is a very good question +uh this is a very good kind because + + align:start position:0% +uh this is a very good kind because + + + align:start position:0% +uh this is a very good kind because +naively as I mentioned naively if you + + align:start position:0% +naively as I mentioned naively if you + + + align:start position:0% +naively as I mentioned naively if you +look at those Corrections + + align:start position:0% +look at those Corrections + + + align:start position:0% +look at those Corrections +say this data m + + align:start position:0% +say this data m + + + align:start position:0% +say this data m +and this change + + align:start position:0% +and this change + + + align:start position:0% +and this change +between e and EB + + align:start position:0% +between e and EB + + + align:start position:0% +between e and EB +they're all Divergence okay so that's + + align:start position:0% +they're all Divergence okay so that's + + + align:start position:0% +they're all Divergence okay so that's +why uh they're all very complicated + + align:start position:0% +why uh they're all very complicated + + + align:start position:0% +why uh they're all very complicated +this is all Divergent so that's why it's + + align:start position:0% +this is all Divergent so that's why it's + + + align:start position:0% +this is all Divergent so that's why it's +it's non-trivial to find the scheme to + + align:start position:0% +it's non-trivial to find the scheme to + + + align:start position:0% +it's non-trivial to find the scheme to +make sense of those equations but if you + + align:start position:0% +make sense of those equations but if you + + + align:start position:0% +make sense of those equations but if you +have all those Divergence flying around + + align:start position:0% + + + + align:start position:0% + +other questions yes + + align:start position:0% + + + + align:start position:0% + +sorry + + align:start position:0% + + + + align:start position:0% + +oh they just different numbers + + align:start position:0% +oh they just different numbers + + + align:start position:0% +oh they just different numbers +yeah so this is some one number there's + + align:start position:0% +yeah so this is some one number there's + + + align:start position:0% +yeah so this is some one number there's +some other number yeah just say electron + + align:start position:0% +some other number yeah just say electron + + + align:start position:0% +some other number yeah just say electron +a field that will normalize in a + + align:start position:0% +a field that will normalize in a + + + align:start position:0% +a field that will normalize in a +different way from the from the photo + + align:start position:0% +different way from the from the photo + + + align:start position:0% +different way from the from the photo +but somehow the charge have to be uh + + align:start position:0% +but somehow the charge have to be uh + + + align:start position:0% +but somehow the charge have to be uh +normalized in the same + + align:start position:0% + + + + align:start position:0% + +thing + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah but but but uh but that's kind of a + + align:start position:0% +yeah but but but uh but that's kind of a + + + align:start position:0% +yeah but but but uh but that's kind of a +comma from a high uh uh uh uh yeah if it + + align:start position:0% +comma from a high uh uh uh uh yeah if it + + + align:start position:0% +comma from a high uh uh uh uh yeah if it +come out from that you may say just come + + align:start position:0% +come out from that you may say just come + + + align:start position:0% +come out from that you may say just come +up from the gauge symmetry + + align:start position:0% +up from the gauge symmetry + + + align:start position:0% +up from the gauge symmetry +from the requirements of great symmetry + + align:start position:0% + + + + align:start position:0% + +good + + align:start position:0% +good + + + align:start position:0% +good +so so this G Factor + + align:start position:0% +so so this G Factor + + + align:start position:0% +so so this G Factor +so if so the Iraq equation one of the + + align:start position:0% +so if so the Iraq equation one of the + + + align:start position:0% +so if so the Iraq equation one of the +chunks of the rock equation + + align:start position:0% +chunks of the rock equation + + + align:start position:0% +chunks of the rock equation +when you first uh when The Rock first + + align:start position:0% +when you first uh when The Rock first + + + align:start position:0% +when you first uh when The Rock first +written down he said the rock equations + + align:start position:0% + + + + align:start position:0% + +predict that g equal to two + + align:start position:0% + + + + align:start position:0% + +okay it's equal to two + + align:start position:0% +okay it's equal to two + + + align:start position:0% +okay it's equal to two +but in reality + + align:start position:0% +but in reality + + + align:start position:0% +but in reality +in the in the in the uh in the late 30s + + align:start position:0% +in the in the in the uh in the late 30s + + + align:start position:0% +in the in the in the uh in the late 30s +and early 40s the experiment were + + align:start position:0% +and early 40s the experiment were + + + align:start position:0% +and early 40s the experiment were +accurate enough at the beginning people + + align:start position:0% +accurate enough at the beginning people + + + align:start position:0% +accurate enough at the beginning people +saw the G equal to two Okay so that was + + align:start position:0% +saw the G equal to two Okay so that was + + + align:start position:0% +saw the G equal to two Okay so that was +considered to be chunk of the direct + + align:start position:0% +considered to be chunk of the direct + + + align:start position:0% +considered to be chunk of the direct +equation + + align:start position:0% +equation + + + align:start position:0% +equation +but then later when the experiment + + align:start position:0% +but then later when the experiment + + + align:start position:0% +but then later when the experiment +become more accurate + + align:start position:0% +become more accurate + + + align:start position:0% +become more accurate +they find that g is actually slightly + + align:start position:0% +they find that g is actually slightly + + + align:start position:0% +they find that g is actually slightly +greater than 2. + + align:start position:0% + + + + align:start position:0% + +okay of course this accuracy is Right a + + align:start position:0% +okay of course this accuracy is Right a + + + align:start position:0% +okay of course this accuracy is Right a +data at the beginning in the in the 40s + + align:start position:0% +data at the beginning in the in the 40s + + + align:start position:0% +data at the beginning in the in the 40s +they can already see that the G is no + + align:start position:0% +they can already see that the G is no + + + align:start position:0% +they can already see that the G is no +longer two okay there's some small + + align:start position:0% +longer two okay there's some small + + + align:start position:0% +longer two okay there's some small +Corrections + + align:start position:0% +Corrections + + + align:start position:0% +Corrections +so there was a big + + align:start position:0% +so there was a big + + + align:start position:0% +so there was a big +big question at the time how do you + + align:start position:0% +big question at the time how do you + + + align:start position:0% +big question at the time how do you +calculate this correction + + align:start position:0% +calculate this correction + + + align:start position:0% +calculate this correction +okay how do you calculate this + + align:start position:0% +okay how do you calculate this + + + align:start position:0% +okay how do you calculate this +correction + + align:start position:0% + + + + align:start position:0% + +so that amounts to calculate this + + align:start position:0% +so that amounts to calculate this + + + align:start position:0% +so that amounts to calculate this +diagram so that's what shringer did and + + align:start position:0% +diagram so that's what shringer did and + + + align:start position:0% +diagram so that's what shringer did and +so so you calculate this diagram he + + align:start position:0% +so so you calculate this diagram he + + + align:start position:0% +so so you calculate this diagram he +managed to get rid of the Divergence and + + align:start position:0% +managed to get rid of the Divergence and + + + align:start position:0% +managed to get rid of the Divergence and +he manages to reproduce these small + + align:start position:0% +he manages to reproduce these small + + + align:start position:0% +he manages to reproduce these small +Corrections + + align:start position:0% +Corrections + + + align:start position:0% +Corrections +so imagine a small crutches + + align:start position:0% +so imagine a small crutches + + + align:start position:0% +so imagine a small crutches +so now let me just very quickly tell you + + align:start position:0% + + + + align:start position:0% + +tell you where this result come from + + align:start position:0% +tell you where this result come from + + + align:start position:0% +tell you where this result come from +okay where this result come from why the + + align:start position:0% +okay where this result come from why the + + + align:start position:0% +okay where this result come from why the +rock equation predicts the G equal to + + align:start position:0% +rock equation predicts the G equal to + + + align:start position:0% +rock equation predicts the G equal to +two okay so this actually I had + + align:start position:0% +two okay so this actually I had + + + align:start position:0% +two okay so this actually I had +at some point was thinking as a homework + + align:start position:0% +at some point was thinking as a homework + + + align:start position:0% +at some point was thinking as a homework +exercise + + align:start position:0% +exercise + + + align:start position:0% +exercise +um yeah but but never got to put it in + + align:start position:0% +um yeah but but never got to put it in + + + align:start position:0% +um yeah but but never got to put it in +the homework but but this instructive + + align:start position:0% +the homework but but this instructive + + + align:start position:0% +the homework but but this instructive +exercise and so so during the uh uh uh + + align:start position:0% +exercise and so so during the uh uh uh + + + align:start position:0% +exercise and so so during the uh uh uh +analysis now let me try to explain uh + + align:start position:0% +analysis now let me try to explain uh + + + align:start position:0% +analysis now let me try to explain uh +where to come from + + align:start position:0% +where to come from + + + align:start position:0% +where to come from +foreign + + align:start position:0% + + + + align:start position:0% + +equation so now let's consider the rock + + align:start position:0% +equation so now let's consider the rock + + + align:start position:0% +equation so now let's consider the rock +equation + + align:start position:0% + + + + align:start position:0% + +of electron couple to say + + align:start position:0% +of electron couple to say + + + align:start position:0% +of electron couple to say +to some gauge field to to the + + align:start position:0% +to some gauge field to to the + + + align:start position:0% +to some gauge field to to the +electromagnetic field + + align:start position:0% +electromagnetic field + + + align:start position:0% +electromagnetic field +okay so let's consider this equation + + align:start position:0% + + + + align:start position:0% + +so the claim + + align:start position:0% +so the claim + + + align:start position:0% +so the claim +okay so the claim + + align:start position:0% +okay so the claim + + + align:start position:0% +okay so the claim +you say if you take this from this + + align:start position:0% +you say if you take this from this + + + align:start position:0% +you say if you take this from this +equation + + align:start position:0% +equation + + + align:start position:0% +equation +of course we don't see anything about + + align:start position:0% +of course we don't see anything about + + + align:start position:0% +of course we don't see anything about +the Magnetic Moment + + align:start position:0% +the Magnetic Moment + + + align:start position:0% +the Magnetic Moment +okay we don't see anything about + + align:start position:0% +okay we don't see anything about + + + align:start position:0% +okay we don't see anything about +magnetic moments so the claim is that if + + align:start position:0% +magnetic moments so the claim is that if + + + align:start position:0% +magnetic moments so the claim is that if +you take this equation + + align:start position:0% +you take this equation + + + align:start position:0% +you take this equation +and go to Long rativistic limits + + align:start position:0% +and go to Long rativistic limits + + + align:start position:0% +and go to Long rativistic limits +okay if you go to language realistic + + align:start position:0% +okay if you go to language realistic + + + align:start position:0% +okay if you go to language realistic +limits you will get the Schrodinger + + align:start position:0% +limits you will get the Schrodinger + + + align:start position:0% +limits you will get the Schrodinger +equation + + align:start position:0% +equation + + + align:start position:0% +equation +you get the so-called the power equation + + align:start position:0% +you get the so-called the power equation + + + align:start position:0% +you get the so-called the power equation +so you get the Schrodinger equation and + + align:start position:0% +so you get the Schrodinger equation and + + + align:start position:0% +so you get the Schrodinger equation and +this + + align:start position:0% +this + + + align:start position:0% +this +a spring half particle and this magnetic + + align:start position:0% +a spring half particle and this magnetic + + + align:start position:0% +a spring half particle and this magnetic +movement precisely given by G equal to + + align:start position:0% +movement precisely given by G equal to + + + align:start position:0% +movement precisely given by G equal to +two + + align:start position:0% +two + + + align:start position:0% +two +okay uh precisely giving back to you + + align:start position:0% +okay uh precisely giving back to you + + + align:start position:0% +okay uh precisely giving back to you +so now let's try to uh uh uh see this + + align:start position:0% +so now let's try to uh uh uh see this + + + align:start position:0% +so now let's try to uh uh uh see this +okay + + align:start position:0% + + + + align:start position:0% + +good do you have any questions + + align:start position:0% + + + + align:start position:0% + +so this is the just the drag equation + + align:start position:0% +so this is the just the drag equation + + + align:start position:0% +so this is the just the drag equation +itself but now if you include that + + align:start position:0% +itself but now if you include that + + + align:start position:0% +itself but now if you include that +vertex Corrections + + align:start position:0% +vertex Corrections + + + align:start position:0% +vertex Corrections +and then that will generate this uh uh + + align:start position:0% +and then that will generate this uh uh + + + align:start position:0% +and then that will generate this uh uh +additional + + align:start position:0% + + + + align:start position:0% + +so so yeah so so now let's look at this + + align:start position:0% +so so yeah so so now let's look at this + + + align:start position:0% +so so yeah so so now let's look at this +non-ratulations + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so so we want to so remember the + + align:start position:0% +so so we want to so remember the + + + align:start position:0% +so so we want to so remember the +the The Rock equation + + align:start position:0% + + + + align:start position:0% + +as well was originally convinced + + align:start position:0% +as well was originally convinced + + + align:start position:0% +as well was originally convinced +conceived + + align:start position:0% +conceived + + + align:start position:0% +conceived +was already a equation of the + + align:start position:0% +was already a equation of the + + + align:start position:0% +was already a equation of the +Schrodinger type + + align:start position:0% +Schrodinger type + + + align:start position:0% +Schrodinger type +say have the form of the + + align:start position:0% +say have the form of the + + + align:start position:0% +say have the form of the +iht PSI equal to H PSI + + align:start position:0% +iht PSI equal to H PSI + + + align:start position:0% +iht PSI equal to H PSI +so you just multiply the gamma zero + + align:start position:0% +so you just multiply the gamma zero + + + align:start position:0% +so you just multiply the gamma zero +I comma zero on both sides and then + + align:start position:0% +I comma zero on both sides and then + + + align:start position:0% +I comma zero on both sides and then +remove everything away okay so so so + + align:start position:0% +remove everything away okay so so so + + + align:start position:0% +remove everything away okay so so so +just this side keep only I particular t + + align:start position:0% +just this side keep only I particular t + + + align:start position:0% +just this side keep only I particular t +so through that procedure you have H + + align:start position:0% +so through that procedure you have H + + + align:start position:0% +so through that procedure you have H +is equal to M times beta plus Alpha + + align:start position:0% + + + + align:start position:0% + +p plus e a + + align:start position:0% +p plus e a + + + align:start position:0% +p plus e a +then plus e a zero okay here zero is + + align:start position:0% +then plus e a zero okay here zero is + + + align:start position:0% +then plus e a zero okay here zero is +zero component of a and then a e a is + + align:start position:0% +zero component of a and then a e a is + + + align:start position:0% +zero component of a and then a e a is +the vector component of a + + align:start position:0% +the vector component of a + + + align:start position:0% +the vector component of a +so so the beta is just the minus gamma I + + align:start position:0% +so so the beta is just the minus gamma I + + + align:start position:0% +so so the beta is just the minus gamma I +comma zero + + align:start position:0% + + + + align:start position:0% + +and Alpha I + + align:start position:0% +and Alpha I + + + align:start position:0% +and Alpha I +is equal to minus I gamma zero comma I + + align:start position:0% +is equal to minus I gamma zero comma I + + + align:start position:0% +is equal to minus I gamma zero comma I +and P + + align:start position:0% +and P + + + align:start position:0% +and P +equal to minus I + + align:start position:0% +equal to minus I + + + align:start position:0% +equal to minus I +just standard Grid in operator + + align:start position:0% + + + + align:start position:0% + +okay so so now the claim is that where I + + align:start position:0% +okay so so now the claim is that where I + + + align:start position:0% +okay so so now the claim is that where I +want to take the long relativistic limit + + align:start position:0% +want to take the long relativistic limit + + + align:start position:0% +want to take the long relativistic limit +this equation become ordinary showing + + align:start position:0% +this equation become ordinary showing + + + align:start position:0% +this equation become ordinary showing +equation + + align:start position:0% +equation + + + align:start position:0% +equation +and including the magnetic moments + + align:start position:0% +and including the magnetic moments + + + align:start position:0% +and including the magnetic moments +okay + + align:start position:0% + + + + align:start position:0% + +so it is clear what we want to do + + align:start position:0% +so it is clear what we want to do + + + align:start position:0% +so it is clear what we want to do +okay so so now let's choose the basis + + align:start position:0% +okay so so now let's choose the basis + + + align:start position:0% +okay so so now let's choose the basis +for the gamma matrices + + align:start position:0% +for the gamma matrices + + + align:start position:0% +for the gamma matrices +so for this purpose when you go to non + + align:start position:0% +so for this purpose when you go to non + + + align:start position:0% +so for this purpose when you go to non +rapid basic limits we should + + align:start position:0% +rapid basic limits we should + + + align:start position:0% +rapid basic limits we should +is convenient to use these spaces + + align:start position:0% +is convenient to use these spaces + + + align:start position:0% +is convenient to use these spaces +which actually I wrote down at the + + align:start position:0% +which actually I wrote down at the + + + align:start position:0% +which actually I wrote down at the +beginning when we talk about the Iraq + + align:start position:0% +beginning when we talk about the Iraq + + + align:start position:0% +beginning when we talk about the Iraq +equations + + align:start position:0% + + + + align:start position:0% + +okay again one is always two by two + + align:start position:0% +okay again one is always two by two + + + align:start position:0% +okay again one is always two by two +identity Matrix + + align:start position:0% + + + + align:start position:0% + +so from here + + align:start position:0% +so from here + + + align:start position:0% +so from here +you find the beta + + align:start position:0% +you find the beta + + + align:start position:0% +you find the beta +just equal to one zero zero minus one + + align:start position:0% +just equal to one zero zero minus one + + + align:start position:0% +just equal to one zero zero minus one +and the alpha just become zero Sigma + + align:start position:0% +and the alpha just become zero Sigma + + + align:start position:0% +and the alpha just become zero Sigma +Sigma zero + + align:start position:0% +Sigma zero + + + align:start position:0% +Sigma zero +okay + + align:start position:0% + + + + align:start position:0% + +so to reduce right now we just choose + + align:start position:0% +so to reduce right now we just choose + + + align:start position:0% +so to reduce right now we just choose +choose and then then also let's write + + align:start position:0% +choose and then then also let's write + + + align:start position:0% +choose and then then also let's write +PSI + + align:start position:0% +PSI + + + align:start position:0% +PSI +in terms of the + + align:start position:0% +in terms of the + + + align:start position:0% +in terms of the +Q components so each of five and the chi + + align:start position:0% +Q components so each of five and the chi + + + align:start position:0% +Q components so each of five and the chi +has two components all together four + + align:start position:0% +has two components all together four + + + align:start position:0% +has two components all together four +components okay so let's write PSI in + + align:start position:0% +components okay so let's write PSI in + + + align:start position:0% +components okay so let's write PSI in +terms of two upper component two lower + + align:start position:0% +terms of two upper component two lower + + + align:start position:0% +terms of two upper component two lower +components + + align:start position:0% + + + + align:start position:0% + +so now let's plug this all this into + + align:start position:0% +so now let's plug this all this into + + + align:start position:0% +so now let's plug this all this into +that equation + + align:start position:0% +that equation + + + align:start position:0% +that equation +okay all this into this equation + + align:start position:0% +okay all this into this equation + + + align:start position:0% +okay all this into this equation +and then you get + + align:start position:0% + + + + align:start position:0% + +partial T5 + + align:start position:0% +partial T5 + + + align:start position:0% +partial T5 +equal to M5 + + align:start position:0% +equal to M5 + + + align:start position:0% +equal to M5 +plus Sigma + + align:start position:0% +plus Sigma + + + align:start position:0% +plus Sigma +so it's p plus e a + + align:start position:0% +so it's p plus e a + + + align:start position:0% +so it's p plus e a +Chi + + align:start position:0% +Chi + + + align:start position:0% +Chi +then plus e a zero five + + align:start position:0% +then plus e a zero five + + + align:start position:0% +then plus e a zero five +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and then for the equation for Chi + + align:start position:0% +and then for the equation for Chi + + + align:start position:0% +and then for the equation for Chi +you get a similar equation + + align:start position:0% +you get a similar equation + + + align:start position:0% +you get a similar equation +because here is minus M Chi + + align:start position:0% +because here is minus M Chi + + + align:start position:0% +because here is minus M Chi +plus Sigma + + align:start position:0% +plus Sigma + + + align:start position:0% +plus Sigma +dot P plus e a + + align:start position:0% + + + + align:start position:0% + +Phi plus e a zero + + align:start position:0% +Phi plus e a zero + + + align:start position:0% +Phi plus e a zero +cut okay + + align:start position:0% + + + + align:start position:0% + +so you get these two equations + + align:start position:0% + + + + align:start position:0% + +okay so now so far we haven't done + + align:start position:0% +okay so now so far we haven't done + + + align:start position:0% +okay so now so far we haven't done +anything okay we just write this + + align:start position:0% +anything okay we just write this + + + align:start position:0% +anything okay we just write this +equation in a different form + + align:start position:0% +equation in a different form + + + align:start position:0% +equation in a different form +so now let's consider number activistic + + align:start position:0% +so now let's consider number activistic + + + align:start position:0% +so now let's consider number activistic +limits + + align:start position:0% + + + + align:start position:0% + +now consider now Write the basic limits + + align:start position:0% +now consider now Write the basic limits + + + align:start position:0% +now consider now Write the basic limits +so in the longest basic limit this p + + align:start position:0% + + + + align:start position:0% + +so this is essentially the momentum + + align:start position:0% +so this is essentially the momentum + + + align:start position:0% +so this is essentially the momentum +spatial momentum + + align:start position:0% +spatial momentum + + + align:start position:0% +spatial momentum +okay if you act on the wave + + align:start position:0% +okay if you act on the wave + + + align:start position:0% +okay if you act on the wave +and so so we take it to be MV + + align:start position:0% + + + + align:start position:0% + +and of course B to be much much smaller + + align:start position:0% +and of course B to be much much smaller + + + align:start position:0% +and of course B to be much much smaller +than one + + align:start position:0% +than one + + + align:start position:0% +than one +okay + + align:start position:0% + + + + align:start position:0% + +and then this ea0 + + align:start position:0% + + + + align:start position:0% + +which has unit of energy + + align:start position:0% +which has unit of energy + + + align:start position:0% +which has unit of energy +so it should be of all the MB Square + + align:start position:0% +so it should be of all the MB Square + + + align:start position:0% +so it should be of all the MB Square +okay should be other than b squared and + + align:start position:0% +okay should be other than b squared and + + + align:start position:0% +okay should be other than b squared and +this EA which should be the same order + + align:start position:0% +this EA which should be the same order + + + align:start position:0% +this EA which should be the same order +as p and then EA + + align:start position:0% +as p and then EA + + + align:start position:0% +as p and then EA +should also be of the same order + + align:start position:0% +should also be of the same order + + + align:start position:0% +should also be of the same order +as MV + + align:start position:0% +as MV + + + align:start position:0% +as MV +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay now let's look at this number limit + + align:start position:0% + + + + align:start position:0% + +s so so so far I have not done anything + + align:start position:0% +s so so so far I have not done anything + + + align:start position:0% +s so so so far I have not done anything +I just specified this + + align:start position:0% +I just specified this + + + align:start position:0% +I just specified this +and now let's + + align:start position:0% +and now let's + + + align:start position:0% +and now let's +consider us transformation + + align:start position:0% +consider us transformation + + + align:start position:0% +consider us transformation +limit + + align:start position:0% + + + + align:start position:0% + +we know that your total energy + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +is always the time dependence say always + + align:start position:0% +is always the time dependence say always + + + align:start position:0% +is always the time dependence say always +have something like IET okay + + align:start position:0% +have something like IET okay + + + align:start position:0% +have something like IET okay +and in the uh in the downloading basic + + align:start position:0% +and in the uh in the downloading basic + + + align:start position:0% +and in the uh in the downloading basic +limit e would be m + + align:start position:0% +limit e would be m + + + align:start position:0% +limit e would be m +plus one half MB squared Etc okay so + + align:start position:0% +plus one half MB squared Etc okay so + + + align:start position:0% +plus one half MB squared Etc okay so +this is much much larger than this term + + align:start position:0% +this is much much larger than this term + + + align:start position:0% +this is much much larger than this term +and this is much much larger than this + + align:start position:0% +and this is much much larger than this + + + align:start position:0% +and this is much much larger than this +term + + align:start position:0% +term + + + align:start position:0% +term +so so so in order to uh so + + align:start position:0% +so so so in order to uh so + + + align:start position:0% +so so so in order to uh so +so we can just isolate the speaker piece + + align:start position:0% +so we can just isolate the speaker piece + + + align:start position:0% +so we can just isolate the speaker piece +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we can try to isolate this big piece + + align:start position:0% +so we can try to isolate this big piece + + + align:start position:0% +so we can try to isolate this big piece +so we will make a slight transformation + + align:start position:0% +so we will make a slight transformation + + + align:start position:0% +so we will make a slight transformation +so we write 5 + + align:start position:0% +so we write 5 + + + align:start position:0% +so we write 5 +equal to expansion minus IMT + + align:start position:0% + + + + align:start position:0% + +Capital Phi + + align:start position:0% +Capital Phi + + + align:start position:0% +Capital Phi +and the chi equal to IMT + + align:start position:0% +and the chi equal to IMT + + + align:start position:0% +and the chi equal to IMT +X okay uh this or or Capital Chi okay + + align:start position:0% +X okay uh this or or Capital Chi okay + + + align:start position:0% +X okay uh this or or Capital Chi okay +so now + + align:start position:0% +so now + + + align:start position:0% +so now +this will only contain this low energy + + align:start position:0% +this will only contain this low energy + + + align:start position:0% +this will only contain this low energy +part okay those so those fields will + + align:start position:0% +part okay those so those fields will + + + align:start position:0% +part okay those so those fields will +only contain a low energy but they + + align:start position:0% +only contain a low energy but they + + + align:start position:0% +only contain a low energy but they +already isolate the Big scenes in here + + align:start position:0% +already isolate the Big scenes in here + + + align:start position:0% +already isolate the Big scenes in here +okay so the time dependence here we only + + align:start position:0% +okay so the time dependence here we only + + + align:start position:0% +okay so the time dependence here we only +include the low energy + + align:start position:0% +include the low energy + + + align:start position:0% +include the low energy +so so so so we assume that part of T5 + + align:start position:0% +so so so so we assume that part of T5 + + + align:start position:0% +so so so so we assume that part of T5 +say would be MV Square + + align:start position:0% +say would be MV Square + + + align:start position:0% +say would be MV Square +say Phi similarly with X okay + + align:start position:0% + + + + align:start position:0% + +similarly with x + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so this is the first + + align:start position:0% +so so this is the first + + + align:start position:0% +so so this is the first +oscillator part in time this is the slow + + align:start position:0% +oscillator part in time this is the slow + + + align:start position:0% +oscillator part in time this is the slow +part in time + + align:start position:0% +part in time + + + align:start position:0% +part in time +so now we plug this in + + align:start position:0% +so now we plug this in + + + align:start position:0% +so now we plug this in +to these two equations + + align:start position:0% + + + + align:start position:0% + +okay plugged into those equations + + align:start position:0% + + + + align:start position:0% + +then we find + + align:start position:0% + + + + align:start position:0% + +I partial t + + align:start position:0% + + + + align:start position:0% + +yeah I will also introduce yeah a iPad + + align:start position:0% +yeah I will also introduce yeah a iPad + + + align:start position:0% +yeah I will also introduce yeah a iPad +to T5 + + align:start position:0% +to T5 + + + align:start position:0% +to T5 +equal to Sigma dot pi + + align:start position:0% +equal to Sigma dot pi + + + align:start position:0% +equal to Sigma dot pi +X + + align:start position:0% +X + + + align:start position:0% +X +plus ea0 by + + align:start position:0% +plus ea0 by + + + align:start position:0% +plus ea0 by +and I partial t x + + align:start position:0% +and I partial t x + + + align:start position:0% +and I partial t x +equal to 2 minus + + align:start position:0% +equal to 2 minus + + + align:start position:0% +equal to 2 minus +m x + + align:start position:0% + + + + align:start position:0% + +we just called + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so I also have introduced the rotation + + align:start position:0% +so I also have introduced the rotation + + + align:start position:0% +so I also have introduced the rotation +that the pi + + align:start position:0% + + + + align:start position:0% + +is equal to P plus EA + + align:start position:0% +is equal to P plus EA + + + align:start position:0% +is equal to P plus EA +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay + + align:start position:0% + + + + align:start position:0% + +so now you see the difference between + + align:start position:0% +so now you see the difference between + + + align:start position:0% +so now you see the difference between +these two equations + + align:start position:0% + + + + align:start position:0% + +so they have the so smash term here have + + align:start position:0% +so they have the so smash term here have + + + align:start position:0% +so they have the so smash term here have +of this sign + + align:start position:0% + + + + align:start position:0% + +when I isolate that piece + + align:start position:0% + + + + align:start position:0% + +and then the math term for this equation + + align:start position:0% +and then the math term for this equation + + + align:start position:0% +and then the math term for this equation +canceled + + align:start position:0% +canceled + + + align:start position:0% +canceled +but in this equation they add together + + align:start position:0% +but in this equation they add together + + + align:start position:0% +but in this equation they add together +okay this minus 2m + + align:start position:0% +okay this minus 2m + + + align:start position:0% +okay this minus 2m +okay + + align:start position:0% +okay + + + align:start position:0% +okay +look at this minus 2m + + align:start position:0% +look at this minus 2m + + + align:start position:0% +look at this minus 2m +so now let's look at the magnitude of + + align:start position:0% +so now let's look at the magnitude of + + + align:start position:0% +so now let's look at the magnitude of +each term in this equation so this is + + align:start position:0% +each term in this equation so this is + + + align:start position:0% +each term in this equation so this is +like MV Square + + align:start position:0% +like MV Square + + + align:start position:0% +like MV Square +X + + align:start position:0% +X + + + align:start position:0% +X +so this is like M times x + + align:start position:0% + + + + align:start position:0% + +so this is just sometimes something five + + align:start position:0% +so this is just sometimes something five + + + align:start position:0% +so this is just sometimes something five +we don't need to work uh yeah we don't + + align:start position:0% +we don't need to work uh yeah we don't + + + align:start position:0% +we don't need to work uh yeah we don't +know the relative magnitude between X + + align:start position:0% +know the relative magnitude between X + + + align:start position:0% +know the relative magnitude between X +and Phi and so this is also MV Square + + align:start position:0% +and Phi and so this is also MV Square + + + align:start position:0% +and Phi and so this is also MV Square +X okay we said the a0 should be of order + + align:start position:0% +X okay we said the a0 should be of order + + + align:start position:0% +X okay we said the a0 should be of order +and V squared + + align:start position:0% +and V squared + + + align:start position:0% +and V squared +so so these three terms they're all + + align:start position:0% +so so these three terms they're all + + + align:start position:0% +so so these three terms they're all +related to X + + align:start position:0% + + + + align:start position:0% + +and this term dominates over these two + + align:start position:0% +and this term dominates over these two + + + align:start position:0% +and this term dominates over these two +okay so you can forget about these two + + align:start position:0% +okay so you can forget about these two + + + align:start position:0% +okay so you can forget about these two +terms + + align:start position:0% +terms + + + align:start position:0% +terms +okay in the non-registic limit + + align:start position:0% +okay in the non-registic limit + + + align:start position:0% +okay in the non-registic limit +and then we get + + align:start position:0% + + + + align:start position:0% + +so from here + + align:start position:0% +so from here + + + align:start position:0% +so from here +you could if I call this equation one + + align:start position:0% +you could if I call this equation one + + + align:start position:0% +you could if I call this equation one +and this equation 2 and from 2 + + align:start position:0% +and this equation 2 and from 2 + + + align:start position:0% +and this equation 2 and from 2 +we get in the language limit + + align:start position:0% + + + + align:start position:0% + +we just get 2mx + + align:start position:0% + + + + align:start position:0% + +plus Sigma Pi + + align:start position:0% +plus Sigma Pi + + + align:start position:0% +plus Sigma Pi +acting on Phi equal to zero + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so we now get now we find that X we can + + align:start position:0% +so we now get now we find that X we can + + + align:start position:0% +so we now get now we find that X we can +now solve x + + align:start position:0% +now solve x + + + align:start position:0% +now solve x +in terms of Phi + + align:start position:0% +in terms of Phi + + + align:start position:0% +in terms of Phi +1 over 2m Sigma dot pi + + align:start position:0% +1 over 2m Sigma dot pi + + + align:start position:0% +1 over 2m Sigma dot pi +Phi + + align:start position:0% + + + + align:start position:0% + +so now we can plug this back into this + + align:start position:0% +so now we can plug this back into this + + + align:start position:0% +so now we can plug this back into this +equation + + align:start position:0% + + + + align:start position:0% + +so this is equation three + + align:start position:0% +so this is equation three + + + align:start position:0% +so this is equation three +plug + + align:start position:0% +plug + + + align:start position:0% +plug +three into one again + + align:start position:0% + + + + align:start position:0% + +then we get a Schrodinger equation + + align:start position:0% +then we get a Schrodinger equation + + + align:start position:0% +then we get a Schrodinger equation +four five + + align:start position:0% +four five + + + align:start position:0% +four five +so X is no longer independent field it's + + align:start position:0% +so X is no longer independent field it's + + + align:start position:0% +so X is no longer independent field it's +just expressed in terms of Phi + + align:start position:0% +just expressed in terms of Phi + + + align:start position:0% +just expressed in terms of Phi +now we get the equation for Phi + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so now you see each term they are of the + + align:start position:0% +so now you see each term they are of the + + + align:start position:0% +so now you see each term they are of the +same order of magnitude so this is MV + + align:start position:0% +same order of magnitude so this is MV + + + align:start position:0% +same order of magnitude so this is MV +squared + + align:start position:0% +squared + + + align:start position:0% +squared +and this is mv's upstairs price of all + + align:start position:0% +and this is mv's upstairs price of all + + + align:start position:0% +and this is mv's upstairs price of all +the MB so this is M Square V squared + + align:start position:0% +the MB so this is M Square V squared + + + align:start position:0% +the MB so this is M Square V squared +divided by n so this again is MV square + + align:start position:0% +divided by n so this again is MV square + + + align:start position:0% +divided by n so this again is MV square +and ea0 is MB squared so so now + + align:start position:0% +and ea0 is MB squared so so now + + + align:start position:0% +and ea0 is MB squared so so now +everything is now activistic and of the + + align:start position:0% +everything is now activistic and of the + + + align:start position:0% +everything is now activistic and of the +same order + + align:start position:0% +same order + + + align:start position:0% +same order +okay so now let's look at the meaning of + + align:start position:0% +okay so now let's look at the meaning of + + + align:start position:0% +okay so now let's look at the meaning of +this term + + align:start position:0% + + + + align:start position:0% + +now let's look at the meaning of that + + align:start position:0% +now let's look at the meaning of that + + + align:start position:0% +now let's look at the meaning of that +term + + align:start position:0% + + + + align:start position:0% + +so so that term you can write it + + align:start position:0% +so so that term you can write it + + + align:start position:0% +so so that term you can write it +explicitly + + align:start position:0% + + + + align:start position:0% + +okay Sigma I Pi I Sigma J Pi J but + + align:start position:0% +okay Sigma I Pi I Sigma J Pi J but + + + align:start position:0% +okay Sigma I Pi I Sigma J Pi J but +remember Pi I and Pi J they are + + align:start position:0% +remember Pi I and Pi J they are + + + align:start position:0% +remember Pi I and Pi J they are +operators so you need to keep the keep + + align:start position:0% +operators so you need to keep the keep + + + align:start position:0% +operators so you need to keep the keep +the uh the the ordered in them okay + + align:start position:0% +the uh the the ordered in them okay + + + align:start position:0% +the uh the the ordered in them okay +yeah uh + + align:start position:0% +yeah uh + + + align:start position:0% +yeah uh +so so we can just write down so we just + + align:start position:0% +so so we can just write down so we just + + + align:start position:0% +so so we can just write down so we just +have Sigma I Sigma J + + align:start position:0% +have Sigma I Sigma J + + + align:start position:0% +have Sigma I Sigma J +just give me Delta i j + + align:start position:0% +just give me Delta i j + + + align:start position:0% +just give me Delta i j +plus I Epsilon i j k + + align:start position:0% + + + + align:start position:0% + +Sigma k + + align:start position:0% +Sigma k + + + align:start position:0% +Sigma k +and then Pi I Pi J + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +all right so the first term give me the + + align:start position:0% +all right so the first term give me the + + + align:start position:0% +all right so the first term give me the +pi Square + + align:start position:0% + + + + align:start position:0% + +and the second term I can just uh using + + align:start position:0% +and the second term I can just uh using + + + align:start position:0% +and the second term I can just uh using +the uh the anti-symmetric in i j + + align:start position:0% +the uh the anti-symmetric in i j + + + align:start position:0% +the uh the anti-symmetric in i j +I can write it as Epsilon i j k + + align:start position:0% +I can write it as Epsilon i j k + + + align:start position:0% +I can write it as Epsilon i j k +Sigma k + + align:start position:0% +Sigma k + + + align:start position:0% +Sigma k +and Pi I and Pi J + + align:start position:0% + + + + align:start position:0% + +okay so so just write the commutator in + + align:start position:0% +okay so so just write the commutator in + + + align:start position:0% +okay so so just write the commutator in +terms of them + + align:start position:0% +terms of them + + + align:start position:0% +terms of them +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now you can + + align:start position:0% + + + + align:start position:0% + +now it's easy to calculate + + align:start position:0% +now it's easy to calculate + + + align:start position:0% +now it's easy to calculate +J + + align:start position:0% +J + + + align:start position:0% +J +so this is just + + align:start position:0% +so this is just + + + align:start position:0% +so this is just +minus partial I + + align:start position:0% +minus partial I + + + align:start position:0% +minus partial I +plus e a i + + align:start position:0% + + + + align:start position:0% + +and the minus y to J + + align:start position:0% +and the minus y to J + + + align:start position:0% +and the minus y to J +minus I partial J plus e a j + + align:start position:0% +minus I partial J plus e a j + + + align:start position:0% +minus I partial J plus e a j +so if you calculate the commutator you + + align:start position:0% +so if you calculate the commutator you + + + align:start position:0% +so if you calculate the commutator you +just get minus e f i j + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and now if you plug this fij into here + + align:start position:0% +and now if you plug this fij into here + + + align:start position:0% +and now if you plug this fij into here +so Epsilon y j k times fij what do you + + align:start position:0% +so Epsilon y j k times fij what do you + + + align:start position:0% +so Epsilon y j k times fij what do you +get + + align:start position:0% + + + + align:start position:0% + +do you remember when Epsilon i j k + + align:start position:0% +do you remember when Epsilon i j k + + + align:start position:0% +do you remember when Epsilon i j k +multiply f i j what do you get + + align:start position:0% + + + + align:start position:0% + +you get B yeah so so now this equation + + align:start position:0% +you get B yeah so so now this equation + + + align:start position:0% +you get B yeah so so now this equation +when you plug this in here + + align:start position:0% +when you plug this in here + + + align:start position:0% +when you plug this in here +and then this just become + + align:start position:0% +and then this just become + + + align:start position:0% +and then this just become +High Square + + align:start position:0% +High Square + + + align:start position:0% +High Square +Plus + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +e + + align:start position:0% +e + + + align:start position:0% +e +Sigma dot b + + align:start position:0% +Sigma dot b + + + align:start position:0% +Sigma dot b +okay + + align:start position:0% + + + + align:start position:0% + +because f i j + + align:start position:0% +because f i j + + + align:start position:0% +because f i j +multiply the f i j k just get B K and B + + align:start position:0% +multiply the f i j k just get B K and B + + + align:start position:0% +multiply the f i j k just get B K and B +K A Sigma K the sigma dot b okay + + align:start position:0% + + + + align:start position:0% + +um yeah it's one half of ijk times Fiji + + align:start position:0% +um yeah it's one half of ijk times Fiji + + + align:start position:0% +um yeah it's one half of ijk times Fiji +will be + + align:start position:0% + + + + align:start position:0% + +yeah so if you use + + align:start position:0% +yeah so if you use + + + align:start position:0% +yeah so if you use +one half Epsilon ajk + + align:start position:0% +one half Epsilon ajk + + + align:start position:0% +one half Epsilon ajk +IJ + + align:start position:0% + + + + align:start position:0% + +okay good we are we're there + + align:start position:0% +okay good we are we're there + + + align:start position:0% +okay good we are we're there +so now we now we are done essentially + + align:start position:0% +so now we now we are done essentially + + + align:start position:0% +so now we now we are done essentially +so now the Schrodinger equation + + align:start position:0% +so now the Schrodinger equation + + + align:start position:0% +so now the Schrodinger equation +now we get the partial t five equal to + + align:start position:0% +now we get the partial t five equal to + + + align:start position:0% +now we get the partial t five equal to +H5 + + align:start position:0% +H5 + + + align:start position:0% +H5 +now H is equal to P Square + + align:start position:0% + + + + align:start position:0% + +you have Pi Square so Pi square if I + + align:start position:0% +you have Pi Square so Pi square if I + + + align:start position:0% +you have Pi Square so Pi square if I +write explicitly it's p plus EA + + align:start position:0% +write explicitly it's p plus EA + + + align:start position:0% +write explicitly it's p plus EA +squared divided by 2m + + align:start position:0% +squared divided by 2m + + + align:start position:0% +squared divided by 2m +then Plus + + align:start position:0% +then Plus + + + align:start position:0% +then Plus +e divided by 2m Sigma dot b + + align:start position:0% +e divided by 2m Sigma dot b + + + align:start position:0% +e divided by 2m Sigma dot b +come from this term + + align:start position:0% + + + + align:start position:0% + +and then the last term is ea0 + + align:start position:0% + + + + align:start position:0% + +so now if you recognize + + align:start position:0% +so now if you recognize + + + align:start position:0% +so now if you recognize +this part of the hamiltonian + + align:start position:0% +this part of the hamiltonian + + + align:start position:0% +this part of the hamiltonian +is precisely what you get when you + + align:start position:0% +is precisely what you get when you + + + align:start position:0% +is precisely what you get when you +couple shooting equation to + + align:start position:0% +couple shooting equation to + + + align:start position:0% +couple shooting equation to +electromagnetic field + + align:start position:0% +electromagnetic field + + + align:start position:0% +electromagnetic field +okay you have you just add P plus EA for + + align:start position:0% +okay you have you just add P plus EA for + + + align:start position:0% +okay you have you just add P plus EA for +the vector potential and here you get a + + align:start position:0% +the vector potential and here you get a + + + align:start position:0% +the vector potential and here you get a +zero + + align:start position:0% +zero + + + align:start position:0% +zero +but now here you get the additional + + align:start position:0% +but now here you get the additional + + + align:start position:0% +but now here you get the additional +terms so this is called the poly term + + align:start position:0% +terms so this is called the poly term + + + align:start position:0% +terms so this is called the poly term +okay when the particle have spin have my + + align:start position:0% +okay when the particle have spin have my + + + align:start position:0% +okay when the particle have spin have my +last moment then you have additional + + align:start position:0% +last moment then you have additional + + + align:start position:0% +last moment then you have additional +term so this term can be interpreted so + + align:start position:0% +term so this term can be interpreted so + + + align:start position:0% +term so this term can be interpreted so +remember + + align:start position:0% + + + + align:start position:0% + +have a Magnetic Moment + + align:start position:0% + + + + align:start position:0% + +so when a paragraph Magnetic Moment + + align:start position:0% +so when a paragraph Magnetic Moment + + + align:start position:0% +so when a paragraph Magnetic Moment +then you have the + + align:start position:0% +then you have the + + + align:start position:0% +then you have the +then you have a piece + + align:start position:0% +then you have a piece + + + align:start position:0% +then you have a piece +corresponding to Mu dot b + + align:start position:0% + + + + align:start position:0% + +okay so if you compare this with that + + align:start position:0% +okay so if you compare this with that + + + align:start position:0% +okay so if you compare this with that +term + + align:start position:0% +term + + + align:start position:0% +term +then we conclude that mu so in this case + + align:start position:0% +then we conclude that mu so in this case + + + align:start position:0% +then we conclude that mu so in this case +compare that term that term will be + + align:start position:0% +compare that term that term will be + + + align:start position:0% +compare that term that term will be +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +e q m Sigma dot b + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so now we conclude + + align:start position:0% +so so now we conclude + + + align:start position:0% +so so now we conclude +from here you can read what's the MU + + align:start position:0% +from here you can read what's the MU + + + align:start position:0% +from here you can read what's the MU +mu just minus E divided by 2m + + align:start position:0% +mu just minus E divided by 2m + + + align:start position:0% +mu just minus E divided by 2m +times 2 + + align:start position:0% +times 2 + + + align:start position:0% +times 2 +times Sigma divided by 2. okay so if you + + align:start position:0% +times Sigma divided by 2. okay so if you + + + align:start position:0% +times Sigma divided by 2. okay so if you +compare with this + + align:start position:0% +compare with this + + + align:start position:0% +compare with this +and you find that the G is exactly equal + + align:start position:0% +and you find that the G is exactly equal + + + align:start position:0% +and you find that the G is exactly equal +to 2. + + align:start position:0% + + + + align:start position:0% + +2 okay + + align:start position:0% +2 okay + + + align:start position:0% +2 okay +and so this way you see actually the + + align:start position:0% +and so this way you see actually the + + + align:start position:0% +and so this way you see actually the +debug equation contains the information + + align:start position:0% +debug equation contains the information + + + align:start position:0% +debug equation contains the information +the induction have magnetic moments + + align:start position:0% +the induction have magnetic moments + + + align:start position:0% +the induction have magnetic moments +okay I have magnetic moments yes + + align:start position:0% + + + + align:start position:0% + +uh yeah yeah yeah + + align:start position:0% + + + + align:start position:0% + +there's one plus 0.001 + + align:start position:0% +there's one plus 0.001 + + + align:start position:0% +there's one plus 0.001 +era as it applies no no no + + align:start position:0% +era as it applies no no no + + + align:start position:0% +era as it applies no no no +because the correction can be different + + align:start position:0% +because the correction can be different + + + align:start position:0% +because the correction can be different +for different formulas + + align:start position:0% +for different formulas + + + align:start position:0% +for different formulas +because different formulas they have + + align:start position:0% +because different formulas they have + + + align:start position:0% +because different formulas they have +different interactions + + align:start position:0% +different interactions + + + align:start position:0% +different interactions +and so that will change this vertex + + align:start position:0% +and so that will change this vertex + + + align:start position:0% +and so that will change this vertex +different + + align:start position:0% +different + + + align:start position:0% +different +for example muons and induction will be + + align:start position:0% +for example muons and induction will be + + + align:start position:0% +for example muons and induction will be +different + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yes yeah + + align:start position:0% + + + + align:start position:0% + +in the high speed you can no longer + + align:start position:0% +in the high speed you can no longer + + + align:start position:0% +in the high speed you can no longer +so so when you have high speeds all + + align:start position:0% +so so when you have high speeds all + + + align:start position:0% +so so when you have high speeds all +these effects + + align:start position:0% +these effects + + + align:start position:0% +these effects +they mix together + + align:start position:0% +they mix together + + + align:start position:0% +they mix together +so it's already basically you can no + + align:start position:0% +so it's already basically you can no + + + align:start position:0% +so it's already basically you can no +longer so isolate the contribution from + + align:start position:0% +longer so isolate the contribution from + + + align:start position:0% +longer so isolate the contribution from +that angle written from your orbital + + align:start position:0% +that angle written from your orbital + + + align:start position:0% +that angle written from your orbital +angle when I'm speaking language they + + align:start position:0% +angle when I'm speaking language they + + + align:start position:0% +angle when I'm speaking language they +all come together yeah so it's only in + + align:start position:0% +all come together yeah so it's only in + + + align:start position:0% +all come together yeah so it's only in +the long relatively case you can isolate + + align:start position:0% +the long relatively case you can isolate + + + align:start position:0% +the long relatively case you can isolate +like this and so so normally when we + + align:start position:0% +like this and so so normally when we + + + align:start position:0% +like this and so so normally when we +talk about magnetic lower moments we all + + align:start position:0% +talk about magnetic lower moments we all + + + align:start position:0% +talk about magnetic lower moments we all +think about in terms of non-rativistic + + align:start position:0% +think about in terms of non-rativistic + + + align:start position:0% +think about in terms of non-rativistic +situation + + align:start position:0% +situation + + + align:start position:0% +situation +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so now + + align:start position:0% +so so now + + + align:start position:0% +so so now +just some fellow words okay uh just + + align:start position:0% +just some fellow words okay uh just + + + align:start position:0% +just some fellow words okay uh just +erased that number + + align:start position:0% +erased that number + + + align:start position:0% +erased that number +so so schwinger then did this + + align:start position:0% +so so schwinger then did this + + + align:start position:0% +so so schwinger then did this +calculation + + align:start position:0% +calculation + + + align:start position:0% +calculation +so including this + + align:start position:0% + + + + align:start position:0% + +diagrams this calculation + + align:start position:0% +diagrams this calculation + + + align:start position:0% +diagrams this calculation +and then in fact then he found this + + align:start position:0% +and then in fact then he found this + + + align:start position:0% +and then in fact then he found this +small correction + + align:start position:0% +small correction + + + align:start position:0% +small correction +so normally put say say if I could one + + align:start position:0% +so normally put say say if I could one + + + align:start position:0% +so normally put say say if I could one +plus f + + align:start position:0% +plus f + + + align:start position:0% +plus f +and so this is a the correction okay + + align:start position:0% +and so this is a the correction okay + + + align:start position:0% +and so this is a the correction okay +and then the correction which means + + align:start position:0% +and then the correction which means + + + align:start position:0% +and then the correction which means +first calculated + + align:start position:0% +first calculated + + + align:start position:0% +first calculated +is given by Alpha just divided by two + + align:start position:0% +is given by Alpha just divided by two + + + align:start position:0% +is given by Alpha just divided by two +parts + + align:start position:0% +parts + + + align:start position:0% +parts +Okay the reason is Alpha is because the + + align:start position:0% +Okay the reason is Alpha is because the + + + align:start position:0% +Okay the reason is Alpha is because the +here there's a e here there's a e it's a + + align:start position:0% +here there's a e here there's a e it's a + + + align:start position:0% +here there's a e here there's a e it's a +e Square just Alpha okay and then so all + + align:start position:0% +e Square just Alpha okay and then so all + + + align:start position:0% +e Square just Alpha okay and then so all +these complicated calculation you do + + align:start position:0% +these complicated calculation you do + + + align:start position:0% +these complicated calculation you do +essentially you find this one over two + + align:start position:0% +essentially you find this one over two + + + align:start position:0% +essentially you find this one over two +pi okay because this correction has to + + align:start position:0% +pi okay because this correction has to + + + align:start position:0% +pi okay because this correction has to +be proportional to Alpha and the Nissan + + align:start position:0% +be proportional to Alpha and the Nissan + + + align:start position:0% +be proportional to Alpha and the Nissan +this number you to a very hard + + align:start position:0% +this number you to a very hard + + + align:start position:0% +this number you to a very hard +calculation you find this one over two + + align:start position:0% +calculation you find this one over two + + + align:start position:0% +calculation you find this one over two +Pi okay and then this actually agreed to + + align:start position:0% +Pi okay and then this actually agreed to + + + align:start position:0% +Pi okay and then this actually agreed to +be experiment very well okay so this is + + align:start position:0% +be experiment very well okay so this is + + + align:start position:0% +be experiment very well okay so this is +first calculated by schringer in 1948 + + align:start position:0% +first calculated by schringer in 1948 + + + align:start position:0% +first calculated by schringer in 1948 +okay so this was really a chunk a + + align:start position:0% +okay so this was really a chunk a + + + align:start position:0% +okay so this was really a chunk a +theoretical chunk at that time okay and + + align:start position:0% +theoretical chunk at that time okay and + + + align:start position:0% +theoretical chunk at that time okay and +the grease very well uh uh uh this + + align:start position:0% +the grease very well uh uh uh this + + + align:start position:0% +the grease very well uh uh uh this +experiments + + align:start position:0% +experiments + + + align:start position:0% +experiments +so then people then calculate to higher + + align:start position:0% +so then people then calculate to higher + + + align:start position:0% +so then people then calculate to higher +orders + + align:start position:0% +orders + + + align:start position:0% +orders +so say the last order + + align:start position:0% +so say the last order + + + align:start position:0% +so say the last order +so must be proportional to Alpha Square + + align:start position:0% +so must be proportional to Alpha Square + + + align:start position:0% +so must be proportional to Alpha Square +so we can mod so we can parameterize by + + align:start position:0% +so we can mod so we can parameterize by + + + align:start position:0% +so we can mod so we can parameterize by +Alpha divided by two Pi square and then + + align:start position:0% +Alpha divided by two Pi square and then + + + align:start position:0% +Alpha divided by two Pi square and then +we sum number A2 okay + + align:start position:0% +we sum number A2 okay + + + align:start position:0% +we sum number A2 okay +you you do an even more complicated + + align:start position:0% +you you do an even more complicated + + + align:start position:0% +you you do an even more complicated +calculation much much more complicated + + align:start position:0% +calculation much much more complicated + + + align:start position:0% +calculation much much more complicated +calculation you find this A2 this again + + align:start position:0% +calculation you find this A2 this again + + + align:start position:0% +calculation you find this A2 this again +it's a single longer + + align:start position:0% +it's a single longer + + + align:start position:0% +it's a single longer +and this contains seven diagrams + + align:start position:0% +and this contains seven diagrams + + + align:start position:0% +and this contains seven diagrams +so this is one diagram but when you go + + align:start position:0% +so this is one diagram but when you go + + + align:start position:0% +so this is one diagram but when you go +to the next order actually involving + + align:start position:0% +to the next order actually involving + + + align:start position:0% +to the next order actually involving +seven diagrams + + align:start position:0% +seven diagrams + + + align:start position:0% +seven diagrams +and that was calculated in 1957. okay + + align:start position:0% +and that was calculated in 1957. okay + + + align:start position:0% +and that was calculated in 1957. okay +again what's very important uh + + align:start position:0% +again what's very important uh + + + align:start position:0% +again what's very important uh +thing to do at that time because just to + + align:start position:0% +thing to do at that time because just to + + + align:start position:0% +thing to do at that time because just to +check whether QED uh because the + + align:start position:0% +check whether QED uh because the + + + align:start position:0% +check whether QED uh because the +experimental accuracy was at the level + + align:start position:0% +experimental accuracy was at the level + + + align:start position:0% +experimental accuracy was at the level +actually you can compare this number + + align:start position:0% + + + + align:start position:0% + +anyway so yeah actually this uh also + + align:start position:0% +anyway so yeah actually this uh also + + + align:start position:0% +anyway so yeah actually this uh also +there's some kind of story behind this + + align:start position:0% +there's some kind of story behind this + + + align:start position:0% +there's some kind of story behind this +number + + align:start position:0% +number + + + align:start position:0% +number +which at beginning the character is the + + align:start position:0% +which at beginning the character is the + + + align:start position:0% +which at beginning the character is the +wrong excited anyway so so now you can + + align:start position:0% +wrong excited anyway so so now you can + + + align:start position:0% +wrong excited anyway so so now you can +also calculate the last one + + align:start position:0% +also calculate the last one + + + align:start position:0% +also calculate the last one +A3 + + align:start position:0% +A3 + + + align:start position:0% +A3 +you can parameterize Again by cubes and + + align:start position:0% +you can parameterize Again by cubes and + + + align:start position:0% +you can parameterize Again by cubes and +now this concludes now include the 72 + + align:start position:0% +now this concludes now include the 72 + + + align:start position:0% +now this concludes now include the 72 +diagrams + + align:start position:0% + + + + align:start position:0% + +and then take two feet assist + + align:start position:0% +and then take two feet assist + + + align:start position:0% +and then take two feet assist +yeah I won't write down their names + + align:start position:0% +yeah I won't write down their names + + + align:start position:0% +yeah I won't write down their names +because + + align:start position:0% +because + + + align:start position:0% +because +took them 25 years to calculate it + + align:start position:0% +took them 25 years to calculate it + + + align:start position:0% +took them 25 years to calculate it +so actually they used it back + + align:start position:0% +so actually they used it back + + + align:start position:0% +so actually they used it back +someone + + align:start position:0% +someone + + + align:start position:0% +someone +so so so so so uh in 1996 okay the + + align:start position:0% +so so so so so uh in 1996 okay the + + + align:start position:0% +so so so so so uh in 1996 okay the +thyroid calculated this + + align:start position:0% +thyroid calculated this + + + align:start position:0% +thyroid calculated this +but now if you want to say oh let's try + + align:start position:0% +but now if you want to say oh let's try + + + align:start position:0% +but now if you want to say oh let's try +to calculate A4 + + align:start position:0% + + + + align:start position:0% + +so this includes 891 diagram just in QD + + align:start position:0% + + + + align:start position:0% + +and actually this also calculated using + + align:start position:0% +and actually this also calculated using + + + align:start position:0% +and actually this also calculated using +computer okay anyway + + align:start position:0% +computer okay anyway + + + align:start position:0% +computer okay anyway +so so uh and also you can calculate this + + align:start position:0% +so so uh and also you can calculate this + + + align:start position:0% +so so uh and also you can calculate this +from muang okay muon will have different + + align:start position:0% +from muang okay muon will have different + + + align:start position:0% +from muang okay muon will have different +a mule they receive yeah at a certain + + align:start position:0% +a mule they receive yeah at a certain + + + align:start position:0% +a mule they receive yeah at a certain +level you also need to include the + + align:start position:0% +level you also need to include the + + + align:start position:0% +level you also need to include the +contribution from other interactions not + + align:start position:0% +contribution from other interactions not + + + align:start position:0% +contribution from other interactions not +just Community okay weak interactions + + align:start position:0% +just Community okay weak interactions + + + align:start position:0% +just Community okay weak interactions +Etc anyway so so so the reason you want + + align:start position:0% +Etc anyway so so so the reason you want + + + align:start position:0% +Etc anyway so so so the reason you want +to calculate such number to very high + + align:start position:0% +to calculate such number to very high + + + align:start position:0% +to calculate such number to very high +accuracy is because this uh this F can + + align:start position:0% +accuracy is because this uh this F can + + + align:start position:0% +accuracy is because this uh this F can +be measured + + align:start position:0% +be measured + + + align:start position:0% +be measured +to very very high accuracy + + align:start position:0% +to very very high accuracy + + + align:start position:0% +to very very high accuracy +experimentally + + align:start position:0% +experimentally + + + align:start position:0% +experimentally +it's actually experimentally this is one + + align:start position:0% +it's actually experimentally this is one + + + align:start position:0% +it's actually experimentally this is one +of the most + + align:start position:0% +of the most + + + align:start position:0% +of the most +accurately match the number in physics + + align:start position:0% +accurately match the number in physics + + + align:start position:0% +accurately match the number in physics +okay they can measure this F + + align:start position:0% +okay they can measure this F + + + align:start position:0% +okay they can measure this F +so to order 10 to the minus 12. + + align:start position:0% +so to order 10 to the minus 12. + + + align:start position:0% +so to order 10 to the minus 12. +yourself + + align:start position:0% +yourself + + + align:start position:0% +yourself +and uh um yeah so so it's a it's a it's + + align:start position:0% +and uh um yeah so so it's a it's a it's + + + align:start position:0% +and uh um yeah so so it's a it's a it's +a yeah so so the uh I think the + + align:start position:0% +a yeah so so the uh I think the + + + align:start position:0% +a yeah so so the uh I think the +theoretical level you actually cannot + + align:start position:0% +theoretical level you actually cannot + + + align:start position:0% +theoretical level you actually cannot +calculate to this level accuracy but + + align:start position:0% +calculate to this level accuracy but + + + align:start position:0% +calculate to this level accuracy but +still you uh you can compare uh to very + + align:start position:0% +still you uh you can compare uh to very + + + align:start position:0% +still you uh you can compare uh to very +very good very very good uh agreements + + align:start position:0% +very good very very good uh agreements + + + align:start position:0% +very good very very good uh agreements +so so so uh so QED actually describes + + align:start position:0% +so so so uh so QED actually describes + + + align:start position:0% +so so so uh so QED actually describes +nature very very well okay very very + + align:start position:0% +nature very very well okay very very + + + align:start position:0% +nature very very well okay very very +well + + align:start position:0% +well + + + align:start position:0% +well +okay so I think that's the uh uh uh uh + + align:start position:0% +okay so I think that's the uh uh uh uh + + + align:start position:0% +okay so I think that's the uh uh uh uh +uh that's all + + align:start position:0% +uh that's all + + + align:start position:0% +uh that's all +and uh so + + align:start position:0% +and uh so + + + align:start position:0% +and uh so +um yeah + + align:start position:0% +um yeah + + + align:start position:0% +um yeah +um + + align:start position:0% +um + + + align:start position:0% +um +yeah I'm honored and very happy to have + + align:start position:0% +yeah I'm honored and very happy to have + + + align:start position:0% +yeah I'm honored and very happy to have +this opportunity to take you to this + + align:start position:0% +this opportunity to take you to this + + + align:start position:0% +this opportunity to take you to this +first part of the journey to to Quantum + + align:start position:0% +first part of the journey to to Quantum + + + align:start position:0% +first part of the journey to to Quantum +field Theory and uh + + align:start position:0% +field Theory and uh + + + align:start position:0% +field Theory and uh +um + + align:start position:0% +um + + + align:start position:0% +um +and I want to thank you all for making + + align:start position:0% +and I want to thank you all for making + + + align:start position:0% +and I want to thank you all for making +this uh uh a journey very uh + + align:start position:0% +this uh uh a journey very uh + + + align:start position:0% +this uh uh a journey very uh +are enjoyable and the rewarding for + + align:start position:0% +are enjoyable and the rewarding for + + + align:start position:0% +are enjoyable and the rewarding for +myself + + align:start position:0% +myself + + + align:start position:0% +myself +and I hope you have learned something + + align:start position:0% +and I hope you have learned something + + + align:start position:0% +and I hope you have learned something +from this class and whatever your career + + align:start position:0% +from this class and whatever your career + + + align:start position:0% +from this class and whatever your career +path takes you and I hope you will later + + align:start position:0% +path takes you and I hope you will later + + + align:start position:0% +path takes you and I hope you will later +find this course useful okay thank you + + align:start position:0% +find this course useful okay thank you + + + align:start position:0% +find this course useful okay thank you +thank you + + align:start position:0% +thank you + + + align:start position:0% +thank you +[Applause] \ No newline at end of file diff --git a/6EqHlKhGcc4.txt b/6EqHlKhGcc4.txt new file mode 100644 index 0000000000000000000000000000000000000000..230b83a32c63e64e8fd587c3033aa613c7596255 --- /dev/null +++ b/6EqHlKhGcc4.txt @@ -0,0 +1,3443 @@ +align:start position:0% + +this was more than just a listening + + align:start position:0% +this was more than just a listening + + + align:start position:0% +this was more than just a listening +experience these virtual labs take + + align:start position:0% +experience these virtual labs take + + + align:start position:0% +experience these virtual labs take +courses from being a listening + + align:start position:0% +courses from being a listening + + + align:start position:0% +courses from being a listening +experience with maybe some pencil p-sets + + align:start position:0% +experience with maybe some pencil p-sets + + + align:start position:0% +experience with maybe some pencil p-sets +to you know your hands are active so you + + align:start position:0% +to you know your hands are active so you + + + align:start position:0% +to you know your hands are active so you +know hands on brain on right and what + + align:start position:0% +know hands on brain on right and what + + + align:start position:0% +know hands on brain on right and what +people Rhaenys turn on it they remember + + align:start position:0% +people Rhaenys turn on it they remember + + + align:start position:0% +people Rhaenys turn on it they remember +it ever wonder how we go from the + + align:start position:0% +it ever wonder how we go from the + + + align:start position:0% +it ever wonder how we go from the +building blocks of atoms to creating + + align:start position:0% +building blocks of atoms to creating + + + align:start position:0% +building blocks of atoms to creating +things like Amazon Cloud and how + + align:start position:0% +things like Amazon Cloud and how + + + align:start position:0% +things like Amazon Cloud and how +educators introduced the architecture of + + align:start position:0% +educators introduced the architecture of + + + align:start position:0% +educators introduced the architecture of +digital systems to future engineers so + + align:start position:0% +digital systems to future engineers so + + + align:start position:0% +digital systems to future engineers so +here I was I was writing on the Hong + + align:start position:0% +here I was I was writing on the Hong + + + align:start position:0% +here I was I was writing on the Hong +Kong subway and some young adult comes + + align:start position:0% +Kong subway and some young adult comes + + + align:start position:0% +Kong subway and some young adult comes +up to me and says I took your MITx + + align:start position:0% +up to me and says I took your MITx + + + align:start position:0% +up to me and says I took your MITx +course I'm sorry going wow I mean this + + align:start position:0% +course I'm sorry going wow I mean this + + + align:start position:0% +course I'm sorry going wow I mean this +is you know welcome to chalk radio a + + align:start position:0% +is you know welcome to chalk radio a + + + align:start position:0% +is you know welcome to chalk radio a +podcast about inspired teaching at MIT + + align:start position:0% +podcast about inspired teaching at MIT + + + align:start position:0% +podcast about inspired teaching at MIT +I'm your host Sarah Hansen from MIT + + align:start position:0% +I'm your host Sarah Hansen from MIT + + + align:start position:0% +I'm your host Sarah Hansen from MIT +OpenCourseWare today on the podcast were + + align:start position:0% +OpenCourseWare today on the podcast were + + + align:start position:0% +OpenCourseWare today on the podcast were +diving into the world of six double O + + align:start position:0% +diving into the world of six double O + + + align:start position:0% +diving into the world of six double O +for computation structures this is an + + align:start position:0% +for computation structures this is an + + + align:start position:0% +for computation structures this is an +MIT course designed to teach + + align:start position:0% +MIT course designed to teach + + + align:start position:0% +MIT course designed to teach +undergraduate students how digital + + align:start position:0% +undergraduate students how digital + + + align:start position:0% +undergraduate students how digital +systems are engineered some students + + align:start position:0% +systems are engineered some students + + + align:start position:0% +systems are engineered some students +come to the class with prior experience + + align:start position:0% +come to the class with prior experience + + + align:start position:0% +come to the class with prior experience +in programming and some understanding of + + align:start position:0% +in programming and some understanding of + + + align:start position:0% +in programming and some understanding of +how computers are structured but others + + align:start position:0% +how computers are structured but others + + + align:start position:0% +how computers are structured but others +come knowing little more than how to use + + align:start position:0% +come knowing little more than how to use + + + align:start position:0% +come knowing little more than how to use +a browser through the iterative teaching + + align:start position:0% +a browser through the iterative teaching + + + align:start position:0% +a browser through the iterative teaching +practices of a team of instructors this + + align:start position:0% +practices of a team of instructors this + + + align:start position:0% +practices of a team of instructors this +course manages to engage all of these + + align:start position:0% +course manages to engage all of these + + + align:start position:0% +course manages to engage all of these +students in learning this cutting edge + + align:start position:0% +students in learning this cutting edge + + + align:start position:0% +students in learning this cutting edge +information today I'm speaking with one + + align:start position:0% +information today I'm speaking with one + + + align:start position:0% +information today I'm speaking with one +of the key educators in this course + + align:start position:0% +of the key educators in this course + + + align:start position:0% +of the key educators in this course +senior lecturer emeritus Christopher + + align:start position:0% +senior lecturer emeritus Christopher + + + align:start position:0% +senior lecturer emeritus Christopher +Turman will run through what it takes to + + align:start position:0% +Turman will run through what it takes to + + + align:start position:0% +Turman will run through what it takes to +connect and educate an audience whose + + align:start position:0% +connect and educate an audience whose + + + align:start position:0% +connect and educate an audience whose +experience might vary from complete + + align:start position:0% +experience might vary from complete + + + align:start position:0% +experience might vary from complete +novice to virtual professional in our + + align:start position:0% +novice to virtual professional in our + + + align:start position:0% +novice to virtual professional in our +conversation Turman shares his insights + + align:start position:0% +conversation Turman shares his insights + + + align:start position:0% +conversation Turman shares his insights +on the evolution of this course over the + + align:start position:0% +on the evolution of this course over the + + + align:start position:0% +on the evolution of this course over the +last twenty years and how its current + + align:start position:0% +last twenty years and how its current + + + align:start position:0% +last twenty years and how its current +design is so effective at engaging its + + align:start position:0% +design is so effective at engaging its + + + align:start position:0% +design is so effective at engaging its +broad student base we'll start off with + + align:start position:0% +broad student base we'll start off with + + + align:start position:0% +broad student base we'll start off with +Sherman's own story of getting engaged + + align:start position:0% +Sherman's own story of getting engaged + + + align:start position:0% +Sherman's own story of getting engaged +with computation structures so how did + + align:start position:0% +with computation structures so how did + + + align:start position:0% +with computation structures so how did +you become interested in computation + + align:start position:0% +you become interested in computation + + + align:start position:0% +you become interested in computation +structures well in the early 70s I was a + + align:start position:0% +structures well in the early 70s I was a + + + align:start position:0% +structures well in the early 70s I was a +college student trying to earn my way + + align:start position:0% +college student trying to earn my way + + + align:start position:0% +college student trying to earn my way +through college and so I was the + + align:start position:0% +through college and so I was the + + + align:start position:0% +through college and so I was the +computer operator on the third shift for + + align:start position:0% +computer operator on the third shift for + + + align:start position:0% +computer operator on the third shift for +the campus computer and I was in the era + + align:start position:0% +the campus computer and I was in the era + + + align:start position:0% +the campus computer and I was in the era +in which you + + align:start position:0% +in which you + + + align:start position:0% +in which you +only afford one and since watching the + + align:start position:0% +only afford one and since watching the + + + align:start position:0% +only afford one and since watching the +blinking lights was boring I pulled out + + align:start position:0% +blinking lights was boring I pulled out + + + align:start position:0% +blinking lights was boring I pulled out +the schematics for the computer I was + + align:start position:0% +the schematics for the computer I was + + + align:start position:0% +the schematics for the computer I was +running for the for the University and I + + align:start position:0% +running for the for the University and I + + + align:start position:0% +running for the for the University and I +started trying to figure out how the + + align:start position:0% +started trying to figure out how the + + + align:start position:0% +started trying to figure out how the +computer worked ever since then it's + + align:start position:0% +computer worked ever since then it's + + + align:start position:0% +computer worked ever since then it's +been sort of a lifelong interest in + + align:start position:0% +been sort of a lifelong interest in + + + align:start position:0% +been sort of a lifelong interest in +figuring out how do they actually put + + align:start position:0% +figuring out how do they actually put + + + align:start position:0% +figuring out how do they actually put +together these components to make a + + align:start position:0% +together these components to make a + + + align:start position:0% +together these components to make a +machine that can do computation what + + align:start position:0% +machine that can do computation what + + + align:start position:0% +machine that can do computation what +kind of background experiences so the + + align:start position:0% +kind of background experiences so the + + + align:start position:0% +kind of background experiences so the +students bring related to computation + + align:start position:0% +students bring related to computation + + + align:start position:0% +students bring related to computation +it's all over the map it's all over the + + align:start position:0% +it's all over the map it's all over the + + + align:start position:0% +it's all over the map it's all over the +map so some of them will come having you + + align:start position:0% +map so some of them will come having you + + + align:start position:0% +map so some of them will come having you +know programmed computers for a long + + align:start position:0% +know programmed computers for a long + + + align:start position:0% +know programmed computers for a long +time and maybe even know a little bit + + align:start position:0% +time and maybe even know a little bit + + + align:start position:0% +time and maybe even know a little bit +about how the computers are structured + + align:start position:0% +about how the computers are structured + + + align:start position:0% +about how the computers are structured +on the insides other people have not + + align:start position:0% +on the insides other people have not + + + align:start position:0% +on the insides other people have not +done beans and so they come with + + align:start position:0% +done beans and so they come with + + + align:start position:0% +done beans and so they come with +interests but no background at all so + + align:start position:0% +interests but no background at all so + + + align:start position:0% +interests but no background at all so +how do you structure a course to meet + + align:start position:0% +how do you structure a course to meet + + + align:start position:0% +how do you structure a course to meet +the needs of people with diverse + + align:start position:0% +the needs of people with diverse + + + align:start position:0% +the needs of people with diverse +backgrounds like that right so to handle + + align:start position:0% +backgrounds like that right so to handle + + + align:start position:0% +backgrounds like that right so to handle +really diverse backgrounds you have to + + align:start position:0% +really diverse backgrounds you have to + + + align:start position:0% +really diverse backgrounds you have to +have a huge range of materials so you + + align:start position:0% +have a huge range of materials so you + + + align:start position:0% +have a huge range of materials so you +need something that somebody who just I + + align:start position:0% +need something that somebody who just I + + + align:start position:0% +need something that somebody who just I +need to start at the beginning you need + + align:start position:0% +need to start at the beginning you need + + + align:start position:0% +need to start at the beginning you need +a beginning for them to start at and for + + align:start position:0% +a beginning for them to start at and for + + + align:start position:0% +a beginning for them to start at and for +somebody who sort of you know passed the + + align:start position:0% +somebody who sort of you know passed the + + + align:start position:0% +somebody who sort of you know passed the +first half of your material you need a + + align:start position:0% +first half of your material you need a + + + align:start position:0% +first half of your material you need a +second half which will engage their + + align:start position:0% +second half which will engage their + + + align:start position:0% +second half which will engage their +interest so I create a huge I think of + + align:start position:0% +interest so I create a huge I think of + + + align:start position:0% +interest so I create a huge I think of +it as a buffet there's lots of dishes + + align:start position:0% +it as a buffet there's lots of dishes + + + align:start position:0% +it as a buffet there's lots of dishes +and you can start at the beginning of + + align:start position:0% +and you can start at the beginning of + + + align:start position:0% +and you can start at the beginning of +the buffet and and sort of you know pick + + align:start position:0% +the buffet and and sort of you know pick + + + align:start position:0% +the buffet and and sort of you know pick +it up from scratch or you can say I skip + + align:start position:0% +it up from scratch or you can say I skip + + + align:start position:0% +it up from scratch or you can say I skip +the first couple courses and I'm ready + + align:start position:0% +the first couple courses and I'm ready + + + align:start position:0% +the first couple courses and I'm ready +to dive in you know sort of in the + + align:start position:0% +to dive in you know sort of in the + + + align:start position:0% +to dive in you know sort of in the +middle of the conversation somewhere so + + align:start position:0% +middle of the conversation somewhere so + + + align:start position:0% +middle of the conversation somewhere so +the I think the real key is having a + + align:start position:0% +the I think the real key is having a + + + align:start position:0% +the I think the real key is having a +huge selection of materials to draw from + + align:start position:0% +huge selection of materials to draw from + + + align:start position:0% +huge selection of materials to draw from +and that's I think one of the hallmarks + + align:start position:0% +and that's I think one of the hallmarks + + + align:start position:0% +and that's I think one of the hallmarks +of six double O 4 has been that you know + + align:start position:0% +of six double O 4 has been that you know + + + align:start position:0% +of six double O 4 has been that you know +we have every possible way of learning + + align:start position:0% +we have every possible way of learning + + + align:start position:0% +we have every possible way of learning +the materials so not only for different + + align:start position:0% +the materials so not only for different + + + align:start position:0% +the materials so not only for different +backgrounds but for different learning + + align:start position:0% +backgrounds but for different learning + + + align:start position:0% +backgrounds but for different learning +styles there's sort of an emerging best + + align:start position:0% +styles there's sort of an emerging best + + + align:start position:0% +styles there's sort of an emerging best +practices out how how to explain + + align:start position:0% +practices out how how to explain + + + align:start position:0% +practices out how how to explain +material to people for the first time so + + align:start position:0% +material to people for the first time so + + + align:start position:0% +material to people for the first time so +you know you want to do a short byte + + align:start position:0% +you know you want to do a short byte + + + align:start position:0% +you know you want to do a short byte +sound bytes video bytes you know those + + align:start position:0% +sound bytes video bytes you know those + + + align:start position:0% +sound bytes video bytes you know those +short segments of learning where you + + align:start position:0% +short segments of learning where you + + + align:start position:0% +short segments of learning where you +introduce a single skill or a single + + align:start position:0% +introduce a single skill or a single + + + align:start position:0% +introduce a single skill or a single +concept and then you take a moment to + + align:start position:0% +concept and then you take a moment to + + + align:start position:0% +concept and then you take a moment to +actually you know give them some checked + + align:start position:0% +actually you know give them some checked + + + align:start position:0% +actually you know give them some checked +yourself questions so the idea is well + + align:start position:0% +yourself questions so the idea is well + + + align:start position:0% +yourself questions so the idea is well +you in theory you just listen to this or + + align:start position:0% +you in theory you just listen to this or + + + align:start position:0% +you in theory you just listen to this or +watched it I'm going to ask you some + + align:start position:0% +watched it I'm going to ask you some + + + align:start position:0% +watched it I'm going to ask you some +simple question + + align:start position:0% +simple question + + + align:start position:0% +simple question +not puzzlers there does if you + + align:start position:0% +not puzzlers there does if you + + + align:start position:0% +not puzzlers there does if you +understood what I just told you on the + + align:start position:0% +understood what I just told you on the + + + align:start position:0% +understood what I just told you on the +video then you can answer them and I + + align:start position:0% +video then you can answer them and I + + + align:start position:0% +video then you can answer them and I +think the students appreciate it + + align:start position:0% +think the students appreciate it + + + align:start position:0% +think the students appreciate it +everything is much more bite-sized you + + align:start position:0% +everything is much more bite-sized you + + + align:start position:0% +everything is much more bite-sized you +know we both know is you can imagine + + align:start position:0% +know we both know is you can imagine + + + align:start position:0% +know we both know is you can imagine +pushing play on a 50 minute video you + + align:start position:0% +pushing play on a 50 minute video you + + + align:start position:0% +pushing play on a 50 minute video you +know long about minute while I'm gonna + + align:start position:0% +know long about minute while I'm gonna + + + align:start position:0% +know long about minute while I'm gonna +say 37 but I long about minute six + + align:start position:0% +say 37 but I long about minute six + + + align:start position:0% +say 37 but I long about minute six +you're going to be maybe I should check + + align:start position:0% +you're going to be maybe I should check + + + align:start position:0% +you're going to be maybe I should check +my email while I'm listening to this + + align:start position:0% +my email while I'm listening to this + + + align:start position:0% +my email while I'm listening to this +okay it's you know keeping things short + + align:start position:0% +okay it's you know keeping things short + + + align:start position:0% +okay it's you know keeping things short +and sweet plus is asynchronous another + + align:start position:0% +and sweet plus is asynchronous another + + + align:start position:0% +and sweet plus is asynchronous another +way of state they get to choose their + + align:start position:0% +way of state they get to choose their + + + align:start position:0% +way of state they get to choose their +time in place this must be just such an + + align:start position:0% +time in place this must be just such an + + + align:start position:0% +time in place this must be just such an +exciting time for you as someone who's + + align:start position:0% +exciting time for you as someone who's + + + align:start position:0% +exciting time for you as someone who's +really interested in the scholarship of + + align:start position:0% +really interested in the scholarship of + + + align:start position:0% +really interested in the scholarship of +teaching and learning and then the + + align:start position:0% +teaching and learning and then the + + + align:start position:0% +teaching and learning and then the +emergence of these digital tools to + + align:start position:0% +emergence of these digital tools to + + + align:start position:0% +emergence of these digital tools to +enable those that learning through best + + align:start position:0% +enable those that learning through best + + + align:start position:0% +enable those that learning through best +practices I can can feel your enthusiasm + + align:start position:0% +practices I can can feel your enthusiasm + + + align:start position:0% +practices I can can feel your enthusiasm +for kind of the era that we're in yeah + + align:start position:0% +for kind of the era that we're in yeah + + + align:start position:0% +for kind of the era that we're in yeah +well you know those of us who teach at + + align:start position:0% +well you know those of us who teach at + + + align:start position:0% +well you know those of us who teach at +the university level you know we get + + align:start position:0% +the university level you know we get + + + align:start position:0% +the university level you know we get +handed a piece of chalk and be told to + + align:start position:0% +handed a piece of chalk and be told to + + + align:start position:0% +handed a piece of chalk and be told to +teach you know unlike the teachers for + + align:start position:0% +teach you know unlike the teachers for + + + align:start position:0% +teach you know unlike the teachers for +your kids in elementary school who have + + align:start position:0% +your kids in elementary school who have + + + align:start position:0% +your kids in elementary school who have +actually gone through a program teaches + + align:start position:0% +actually gone through a program teaches + + + align:start position:0% +actually gone through a program teaches +them how to teach we're just said here + + align:start position:0% +them how to teach we're just said here + + + align:start position:0% +them how to teach we're just said here +at teach and so it's all anecdotal it's + + align:start position:0% +at teach and so it's all anecdotal it's + + + align:start position:0% +at teach and so it's all anecdotal it's +all trying to remember how people taught + + align:start position:0% +all trying to remember how people taught + + + align:start position:0% +all trying to remember how people taught +you + + align:start position:0% +you + + + align:start position:0% +you +finally we have you know the online + + align:start position:0% +finally we have you know the online + + + align:start position:0% +finally we have you know the online +courses are providing a real educational + + align:start position:0% +courses are providing a real educational + + + align:start position:0% +courses are providing a real educational +laboratory we're able to try out + + align:start position:0% +laboratory we're able to try out + + + align:start position:0% +laboratory we're able to try out +different techniques we're able to you + + align:start position:0% +different techniques we're able to you + + + align:start position:0% +different techniques we're able to you +know make fairly accurate assessments of + + align:start position:0% +know make fairly accurate assessments of + + + align:start position:0% +know make fairly accurate assessments of +how well did that just work you know + + align:start position:0% +how well did that just work you know + + + align:start position:0% +how well did that just work you know +whether it was an exercise or a video + + align:start position:0% +whether it was an exercise or a video + + + align:start position:0% +whether it was an exercise or a video +segment or a design problem and so we + + align:start position:0% +segment or a design problem and so we + + + align:start position:0% +segment or a design problem and so we +can actually you know do a/b tests + + align:start position:0% +can actually you know do a/b tests + + + align:start position:0% +can actually you know do a/b tests +within the same cadre so you know it's + + align:start position:0% +within the same cadre so you know it's + + + align:start position:0% +within the same cadre so you know it's +pretty neat having a lab I mean as a + + align:start position:0% +pretty neat having a lab I mean as a + + + align:start position:0% +pretty neat having a lab I mean as a +scientist and engineer even though + + align:start position:0% +scientist and engineer even though + + + align:start position:0% +scientist and engineer even though +hypothesis test it you know through a + + align:start position:0% +hypothesis test it you know through a + + + align:start position:0% +hypothesis test it you know through a +bunch of experiments we can really do + + align:start position:0% +bunch of experiments we can really do + + + align:start position:0% +bunch of experiments we can really do +the experiments with the MITx platform + + align:start position:0% +the experiments with the MITx platform + + + align:start position:0% +the experiments with the MITx platform +and so that's been great + + align:start position:0% +and so that's been great + + + align:start position:0% +and so that's been great +[Music] + + align:start position:0% + + + + align:start position:0% + +let's talk about learning in the + + align:start position:0% +let's talk about learning in the + + + align:start position:0% +let's talk about learning in the +classroom and teaching large lecture + + align:start position:0% +classroom and teaching large lecture + + + align:start position:0% +classroom and teaching large lecture +classes what strategies do you have for + + align:start position:0% +classes what strategies do you have for + + + align:start position:0% +classes what strategies do you have for +keeping students engaged well that's + + align:start position:0% +keeping students engaged well that's + + + align:start position:0% +keeping students engaged well that's +interesting because we have so many + + align:start position:0% +interesting because we have so many + + + align:start position:0% +interesting because we have so many +different materials really the only + + align:start position:0% +different materials really the only + + + align:start position:0% +different materials really the only +students who come to lecture are the + + align:start position:0% +students who come to lecture are the + + + align:start position:0% +students who come to lecture are the +ones who had you know for whom lecture + + align:start position:0% +ones who had you know for whom lecture + + + align:start position:0% +ones who had you know for whom lecture +is how they learn I was such a student + + align:start position:0% +is how they learn I was such a student + + + align:start position:0% +is how they learn I was such a student +so the people who were there are not a + + align:start position:0% +so the people who were there are not a + + + align:start position:0% +so the people who were there are not a +draft arm either so they're prepared to + + align:start position:0% +draft arm either so they're prepared to + + + align:start position:0% +draft arm either so they're prepared to +be someone engaged by a local + + align:start position:0% +be someone engaged by a local + + + align:start position:0% +be someone engaged by a local +presentation so I have a well-developed + + align:start position:0% +presentation so I have a well-developed + + + align:start position:0% +presentation so I have a well-developed +set of materials that I present in class + + align:start position:0% +set of materials that I present in class + + + align:start position:0% +set of materials that I present in class +that have sort of been debugged for + + align:start position:0% +that have sort of been debugged for + + + align:start position:0% +that have sort of been debugged for +having not too much or too little a + + align:start position:0% +having not too much or too little a + + + align:start position:0% +having not too much or too little a +progression that most people can follow + + align:start position:0% +progression that most people can follow + + + align:start position:0% +progression that most people can follow +this is a very relaxed sort of + + align:start position:0% +this is a very relaxed sort of + + + align:start position:0% +this is a very relaxed sort of +experience you know I tell jokes I tell + + align:start position:0% +experience you know I tell jokes I tell + + + align:start position:0% +experience you know I tell jokes I tell +stories from my career and it's + + align:start position:0% +stories from my career and it's + + + align:start position:0% +stories from my career and it's +interesting to me how you know when the + + align:start position:0% +interesting to me how you know when the + + + align:start position:0% +interesting to me how you know when the +P students are making comments at the + + align:start position:0% +P students are making comments at the + + + align:start position:0% +P students are making comments at the +end of the semester and the evaluations + + align:start position:0% +end of the semester and the evaluations + + + align:start position:0% +end of the semester and the evaluations +many of them say well I really like the + + align:start position:0% +many of them say well I really like the + + + align:start position:0% +many of them say well I really like the +story so it's you know after boring you + + align:start position:0% +story so it's you know after boring you + + + align:start position:0% +story so it's you know after boring you +with technical details that's fun to say + + align:start position:0% +with technical details that's fun to say + + + align:start position:0% +with technical details that's fun to say +and then when I tried to use that you + + align:start position:0% +and then when I tried to use that you + + + align:start position:0% +and then when I tried to use that you +know this following thing happened and + + align:start position:0% +know this following thing happened and + + + align:start position:0% +know this following thing happened and +all of a sudden they're sort of cooking + + align:start position:0% +all of a sudden they're sort of cooking + + + align:start position:0% +all of a sudden they're sort of cooking +up saying oh man you know and I think it + + align:start position:0% +up saying oh man you know and I think it + + + align:start position:0% +up saying oh man you know and I think it +helps them remember the related good it + + align:start position:0% +helps them remember the related good it + + + align:start position:0% +helps them remember the related good it +does not you think about what you + + align:start position:0% +does not you think about what you + + + align:start position:0% +does not you think about what you +remember from lectures is almost never a + + align:start position:0% +remember from lectures is almost never a + + + align:start position:0% +remember from lectures is almost never a +technical nugget it's no joke they told + + align:start position:0% +technical nugget it's no joke they told + + + align:start position:0% +technical nugget it's no joke they told +or an accident that happened or a + + align:start position:0% +or an accident that happened or a + + + align:start position:0% +or an accident that happened or a +mistake that was made and so it's faint + + align:start position:0% +mistake that was made and so it's faint + + + align:start position:0% +mistake that was made and so it's faint +if there's this concept called fluency + + align:start position:0% +if there's this concept called fluency + + + align:start position:0% +if there's this concept called fluency +mm-hmm which is basically how smoothly + + align:start position:0% +mm-hmm which is basically how smoothly + + + align:start position:0% +mm-hmm which is basically how smoothly +things are going and and and everybody's + + align:start position:0% +things are going and and and everybody's + + + align:start position:0% +things are going and and and everybody's +nodding but no you know your mind is + + align:start position:0% +nodding but no you know your mind is + + + align:start position:0% +nodding but no you know your mind is +starting to drift because it's all so + + align:start position:0% +starting to drift because it's all so + + + align:start position:0% +starting to drift because it's all so +it's actually good to try to put a + + align:start position:0% +it's actually good to try to put a + + + align:start position:0% +it's actually good to try to put a +little disfluency into your lecture to + + align:start position:0% +little disfluency into your lecture to + + + align:start position:0% +little disfluency into your lecture to +actually have a you know you stop and + + align:start position:0% +actually have a you know you stop and + + + align:start position:0% +actually have a you know you stop and +you tell a joke or you made you make a + + align:start position:0% +you tell a joke or you made you make a + + + align:start position:0% +you tell a joke or you made you make a +mistake or you drop the truck and say + + align:start position:0% +mistake or you drop the truck and say + + + align:start position:0% +mistake or you drop the truck and say +darn and you look at the floor or and + + align:start position:0% +darn and you look at the floor or and + + + align:start position:0% +darn and you look at the floor or and +here's what I like to do as you walk out + + align:start position:0% +here's what I like to do as you walk out + + + align:start position:0% +here's what I like to do as you walk out +from behind the lecture table or lectern + + align:start position:0% +from behind the lecture table or lectern + + + align:start position:0% +from behind the lecture table or lectern +and you approach the audience and you + + align:start position:0% +and you approach the audience and you + + + align:start position:0% +and you approach the audience and you +can see them sort of like wait his + + align:start position:0% +can see them sort of like wait his + + + align:start position:0% +can see them sort of like wait his +escape does anything that sort of + + align:start position:0% +escape does anything that sort of + + + align:start position:0% +escape does anything that sort of +switches up you know the sort of I'm + + align:start position:0% +switches up you know the sort of I'm + + + align:start position:0% +switches up you know the sort of I'm +just going along with the flow here so + + align:start position:0% +just going along with the flow here so + + + align:start position:0% +just going along with the flow here so +you know making you know little flows + + align:start position:0% +you know making you know little flows + + + align:start position:0% +you know making you know little flows +that have things that change make a lot + + align:start position:0% +that have things that change make a lot + + + align:start position:0% +that have things that change make a lot +of difference in keeping people sort of + + align:start position:0% +of difference in keeping people sort of + + + align:start position:0% +of difference in keeping people sort of +things I was curious about the teaching + + align:start position:0% +things I was curious about the teaching + + + align:start position:0% +things I was curious about the teaching +team behind a course like this so I + + align:start position:0% +team behind a course like this so I + + + align:start position:0% +team behind a course like this so I +asked Chris to tell me a little bit + + align:start position:0% +asked Chris to tell me a little bit + + + align:start position:0% +asked Chris to tell me a little bit +about the team of people that make a + + align:start position:0% +about the team of people that make a + + + align:start position:0% +about the team of people that make a +course like this work we have a little + + align:start position:0% +course like this work we have a little + + + align:start position:0% +course like this work we have a little +cadre of people who are instructors I've + + align:start position:0% +cadre of people who are instructors I've + + + align:start position:0% +cadre of people who are instructors I've +been sort of part of that cadre every + + align:start position:0% +been sort of part of that cadre every + + + align:start position:0% +been sort of part of that cadre every +semester for a very long time but we + + align:start position:0% +semester for a very long time but we + + + align:start position:0% +semester for a very long time but we +have other you know people who come in + + align:start position:0% +have other you know people who come in + + + align:start position:0% +have other you know people who come in +from the outside or in recent years the + + align:start position:0% +from the outside or in recent years the + + + align:start position:0% +from the outside or in recent years the +department is added election you know + + align:start position:0% +department is added election you know + + + align:start position:0% +department is added election you know +lecturer resources so there's another + + align:start position:0% +lecturer resources so there's another + + + align:start position:0% +lecturer resources so there's another +lecturer associated with it and then + + align:start position:0% +lecturer associated with it and then + + + align:start position:0% +lecturer associated with it and then +faculty come in so it's and though they + + align:start position:0% +faculty come in so it's and though they + + + align:start position:0% +faculty come in so it's and though they +provide a little depth to the gene pool + + align:start position:0% +provide a little depth to the gene pool + + + align:start position:0% +provide a little depth to the gene pool +but then we have graduate TAS who teach + + align:start position:0% +but then we have graduate TAS who teach + + + align:start position:0% +but then we have graduate TAS who teach +recitations okay and we have a student + + align:start position:0% +recitations okay and we have a student + + + align:start position:0% +recitations okay and we have a student +undergraduate TAS and then lab + + align:start position:0% +undergraduate TAS and then lab + + + align:start position:0% +undergraduate TAS and then lab +assistants so there sir we have this + + align:start position:0% +assistants so there sir we have this + + + align:start position:0% +assistants so there sir we have this +whole hierarchy they've all taken the + + align:start position:0% +whole hierarchy they've all taken the + + + align:start position:0% +whole hierarchy they've all taken the +course they've all loved it so you know + + align:start position:0% +course they've all loved it so you know + + + align:start position:0% +course they've all loved it so you know +sort of like me there's an enthusiasm a + + align:start position:0% +sort of like me there's an enthusiasm a + + + align:start position:0% +sort of like me there's an enthusiasm a +sort of bubbles out yeah and the + + align:start position:0% +sort of bubbles out yeah and the + + + align:start position:0% +sort of bubbles out yeah and the +students actually you know I sort of + + align:start position:0% +students actually you know I sort of + + + align:start position:0% +students actually you know I sort of +listed things sort of well I was going + + align:start position:0% +listed things sort of well I was going + + + align:start position:0% +listed things sort of well I was going +to say top down and I'm not sugar + + align:start position:0% +to say top down and I'm not sugar + + + align:start position:0% +to say top down and I'm not sugar +lecturers were at the top but their + + align:start position:0% +lecturers were at the top but their + + + align:start position:0% +lecturers were at the top but their +instructors are at the top but the + + align:start position:0% +instructors are at the top but the + + + align:start position:0% +instructors are at the top but the +students actually prefer the other thing + + align:start position:0% +students actually prefer the other thing + + + align:start position:0% +students actually prefer the other thing +which is they actually you know asking + + align:start position:0% +which is they actually you know asking + + + align:start position:0% +which is they actually you know asking +in LA it's not very intimidating and the + + align:start position:0% +in LA it's not very intimidating and the + + + align:start position:0% +in LA it's not very intimidating and the +students maybe they just took it last + + align:start position:0% +students maybe they just took it last + + + align:start position:0% +students maybe they just took it last +semester and so they have fresh in their + + align:start position:0% +semester and so they have fresh in their + + + align:start position:0% +semester and so they have fresh in their +minds what it is they needed to do in + + align:start position:0% +minds what it is they needed to do in + + + align:start position:0% +minds what it is they needed to do in +order to get whatever it is they're + + align:start position:0% +order to get whatever it is they're + + + align:start position:0% +order to get whatever it is they're +trying to get and then you sort of work + + align:start position:0% +trying to get and then you sort of work + + + align:start position:0% +trying to get and then you sort of work +up the hierarchy to you know get an + + align:start position:0% +up the hierarchy to you know get an + + + align:start position:0% +up the hierarchy to you know get an +answer if people below and that way + + align:start position:0% +answer if people below and that way + + + align:start position:0% +answer if people below and that way +you're only asking questions of the more + + align:start position:0% +you're only asking questions of the more + + + align:start position:0% +you're only asking questions of the more +intimidating people when you're pretty + + align:start position:0% +intimidating people when you're pretty + + + align:start position:0% +intimidating people when you're pretty +sure that no one else has the answers + + align:start position:0% +sure that no one else has the answers + + + align:start position:0% +sure that no one else has the answers +right what's the role of the online fora + + align:start position:0% +right what's the role of the online fora + + + align:start position:0% +right what's the role of the online fora +in the course for helping students feel + + align:start position:0% +in the course for helping students feel + + + align:start position:0% +in the course for helping students feel +comfortable asking questions and how do + + align:start position:0% +comfortable asking questions and how do + + + align:start position:0% +comfortable asking questions and how do +you monitor it how do you run it + + align:start position:0% +you monitor it how do you run it + + + align:start position:0% +you monitor it how do you run it +productively this is something that + + align:start position:0% +productively this is something that + + + align:start position:0% +productively this is something that +educators sometimes struggle with to me + + align:start position:0% +educators sometimes struggle with to me + + + align:start position:0% +educators sometimes struggle with to me +it's a it's a wonderful asset for the + + align:start position:0% +it's a it's a wonderful asset for the + + + align:start position:0% +it's a it's a wonderful asset for the +first time I'm able to make a thoughtful + + align:start position:0% +first time I'm able to make a thoughtful + + + align:start position:0% +first time I'm able to make a thoughtful +answer to a question and have a hundred + + align:start position:0% +answer to a question and have a hundred + + + align:start position:0% +answer to a question and have a hundred +and eighty people look at the answer + + align:start position:0% +and eighty people look at the answer + + + align:start position:0% +and eighty people look at the answer +instead of one and then the next person + + align:start position:0% +instead of one and then the next person + + + align:start position:0% +instead of one and then the next person +has the same question you say well I + + align:start position:0% +has the same question you say well I + + + align:start position:0% +has the same question you say well I +just + + align:start position:0% +just + + + align:start position:0% +just +I get up with a large class you can't + + align:start position:0% +I get up with a large class you can't + + + align:start position:0% +I get up with a large class you can't +spend 10 minutes for each of our you + + align:start position:0% +spend 10 minutes for each of our you + + + align:start position:0% +spend 10 minutes for each of our you +know 300 people so it's a great place to + + align:start position:0% +know 300 people so it's a great place to + + + align:start position:0% +know 300 people so it's a great place to +ask questions and so many of the + + align:start position:0% +ask questions and so many of the + + + align:start position:0% +ask questions and so many of the +questions are look I read the material + + align:start position:0% +questions are look I read the material + + + align:start position:0% +questions are look I read the material +I'm still not getting it I need an + + align:start position:0% +I'm still not getting it I need an + + + align:start position:0% +I'm still not getting it I need an +example so the students I try to make + + align:start position:0% +example so the students I try to make + + + align:start position:0% +example so the students I try to make +students feel very comfortable asking + + align:start position:0% +students feel very comfortable asking + + + align:start position:0% +students feel very comfortable asking +this never there's nothing no cost they + + align:start position:0% +this never there's nothing no cost they + + + align:start position:0% +this never there's nothing no cost they +can ask anonymously so that removes some + + align:start position:0% +can ask anonymously so that removes some + + + align:start position:0% +can ask anonymously so that removes some +of the barrier I see Paul 2017 we had + + align:start position:0% +of the barrier I see Paul 2017 we had + + + align:start position:0% +of the barrier I see Paul 2017 we had +about 2,500 contributions to power the + + align:start position:0% +about 2,500 contributions to power the + + + align:start position:0% +about 2,500 contributions to power the +average response time is about 20 + + align:start position:0% +average response time is about 20 + + + align:start position:0% +average response time is about 20 +minutes and so a lot of us who are + + align:start position:0% +minutes and so a lot of us who are + + + align:start position:0% +minutes and so a lot of us who are +involved in the core sort of have a we + + align:start position:0% +involved in the core sort of have a we + + + align:start position:0% +involved in the core sort of have a we +put the notification of postings on real + + align:start position:0% +put the notification of postings on real + + + align:start position:0% +put the notification of postings on real +time and so we get an email right away + + align:start position:0% +time and so we get an email right away + + + align:start position:0% +time and so we get an email right away +and I think the fast response time + + align:start position:0% +and I think the fast response time + + + align:start position:0% +and I think the fast response time +really reduces the frustration level of + + align:start position:0% +really reduces the frustration level of + + + align:start position:0% +really reduces the frustration level of +the students there's nothing like being + + align:start position:0% +the students there's nothing like being + + + align:start position:0% +the students there's nothing like being +stuck on something right and saying I I + + align:start position:0% +stuck on something right and saying I I + + + align:start position:0% +stuck on something right and saying I I +wish I could ask somebody + + align:start position:0% +wish I could ask somebody + + + align:start position:0% +wish I could ask somebody +well for the first time you can say wait + + align:start position:0% +well for the first time you can say wait + + + align:start position:0% +well for the first time you can say wait +I can't ask and I can get an answer and + + align:start position:0% +I can't ask and I can get an answer and + + + align:start position:0% +I can't ask and I can get an answer and +the students really really appreciate + + align:start position:0% +the students really really appreciate + + + align:start position:0% +the students really really appreciate +that so it the forum has really I think + + align:start position:0% +that so it the forum has really I think + + + align:start position:0% +that so it the forum has really I think +changed student's level of frustration + + align:start position:0% +changed student's level of frustration + + + align:start position:0% +changed student's level of frustration +when they get stuck they know it's being + + align:start position:0% +when they get stuck they know it's being + + + align:start position:0% +when they get stuck they know it's being +stuck it's just a 10-minute process not + + align:start position:0% +stuck it's just a 10-minute process not + + + align:start position:0% +stuck it's just a 10-minute process not +a two-day process + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +let's talk for a minute about the lab + + align:start position:0% +let's talk for a minute about the lab + + + align:start position:0% +let's talk for a minute about the lab +experiences in the course so students + + align:start position:0% +experiences in the course so students + + + align:start position:0% +experiences in the course so students +get hands-on experience doing digital + + align:start position:0% +get hands-on experience doing digital + + + align:start position:0% +get hands-on experience doing digital +design yes um could you talk about a few + + align:start position:0% +design yes um could you talk about a few + + + align:start position:0% +design yes um could you talk about a few +of those experiences and also does that + + align:start position:0% +of those experiences and also does that + + + align:start position:0% +of those experiences and also does that +take place here where we are right now + + align:start position:0% +take place here where we are right now + + + align:start position:0% +take place here where we are right now +well you can do it anywhere it's + + align:start position:0% +well you can do it anywhere it's + + + align:start position:0% +well you can do it anywhere it's +browser-based so there's no software to + + align:start position:0% +browser-based so there's no software to + + + align:start position:0% +browser-based so there's no software to +download you're just just on the web you + + align:start position:0% +download you're just just on the web you + + + align:start position:0% +download you're just just on the web you +go um you know 20 years ago I gave you + + align:start position:0% +go um you know 20 years ago I gave you + + + align:start position:0% +go um you know 20 years ago I gave you +software to download on your computer to + + align:start position:0% +software to download on your computer to + + + align:start position:0% +software to download on your computer to +do this stuff you know man mind that was + + align:start position:0% +do this stuff you know man mind that was + + + align:start position:0% +do this stuff you know man mind that was +everybody's environment was a little + + align:start position:0% +everybody's environment was a little + + + align:start position:0% +everybody's environment was a little +different oh you don't have the latest + + align:start position:0% +different oh you don't have the latest + + + align:start position:0% +different oh you don't have the latest +version of that library well you can't + + align:start position:0% +version of that library well you can't + + + align:start position:0% +version of that library well you can't +run this but if you update your library + + align:start position:0% +run this but if you update your library + + + align:start position:0% +run this but if you update your library +you can't run that and it was it was + + align:start position:0% +you can't run that and it was it was + + + align:start position:0% +you can't run that and it was it was +really a nightmare + + align:start position:0% +really a nightmare + + + align:start position:0% +really a nightmare +so yeah packaging up these lab + + align:start position:0% +so yeah packaging up these lab + + + align:start position:0% +so yeah packaging up these lab +experiences in a way that they can be + + align:start position:0% +experiences in a way that they can be + + + align:start position:0% +experiences in a way that they can be +used by people around the world + + align:start position:0% +used by people around the world + + + align:start position:0% +used by people around the world +you know I saw here I was I was writing + + align:start position:0% +you know I saw here I was I was writing + + + align:start position:0% +you know I saw here I was I was writing +on the Hong Kong subway some young adult + + align:start position:0% +on the Hong Kong subway some young adult + + + align:start position:0% +on the Hong Kong subway some young adult +comes up to me and says I took your mitx + + align:start position:0% +comes up to me and says I took your mitx + + + align:start position:0% +comes up to me and says I took your mitx +course yeah and I really love doing the + + align:start position:0% +course yeah and I really love doing the + + + align:start position:0% +course yeah and I really love doing the +circuit stuff and I didn't have to + + align:start position:0% +circuit stuff and I didn't have to + + + align:start position:0% +circuit stuff and I didn't have to +download anything and I'm sort of going + + align:start position:0% +download anything and I'm sort of going + + + align:start position:0% +download anything and I'm sort of going +wow I mean this is you know it is + + align:start position:0% +wow I mean this is you know it is + + + align:start position:0% +wow I mean this is you know it is +interesting to be stopped by people + + align:start position:0% +interesting to be stopped by people + + + align:start position:0% +interesting to be stopped by people +right and you know they start talking + + align:start position:0% +right and you know they start talking + + + align:start position:0% +right and you know they start talking +about how this was more than just a + + align:start position:0% +about how this was more than just a + + + align:start position:0% +about how this was more than just a +listening experience so these virtual + + align:start position:0% +listening experience so these virtual + + + align:start position:0% +listening experience so these virtual +labs are actually take horses from being + + align:start position:0% +labs are actually take horses from being + + + align:start position:0% +labs are actually take horses from being +a listening experience with maybe some + + align:start position:0% +a listening experience with maybe some + + + align:start position:0% +a listening experience with maybe some +pencil psets to you know your hands or + + align:start position:0% +pencil psets to you know your hands or + + + align:start position:0% +pencil psets to you know your hands or +active so you know hands on brain on + + align:start position:0% +active so you know hands on brain on + + + align:start position:0% +active so you know hands on brain on +right and what the old brains took on is + + align:start position:0% +right and what the old brains took on is + + + align:start position:0% +right and what the old brains took on is +amazing what they know remember it right + + align:start position:0% +amazing what they know remember it right + + + align:start position:0% +amazing what they know remember it right +one of the distinguishing and most + + align:start position:0% +one of the distinguishing and most + + + align:start position:0% +one of the distinguishing and most +interesting parts of this course is that + + align:start position:0% +interesting parts of this course is that + + + align:start position:0% +interesting parts of this course is that +the learning is greatly enhanced by + + align:start position:0% +the learning is greatly enhanced by + + + align:start position:0% +the learning is greatly enhanced by +deductive reasoning in fact the ability + + align:start position:0% +deductive reasoning in fact the ability + + + align:start position:0% +deductive reasoning in fact the ability +to apply prior knowledge to solve a + + align:start position:0% +to apply prior knowledge to solve a + + + align:start position:0% +to apply prior knowledge to solve a +problem in front of you is one of the + + align:start position:0% +problem in front of you is one of the + + + align:start position:0% +problem in front of you is one of the +main skills students come away with from + + align:start position:0% +main skills students come away with from + + + align:start position:0% +main skills students come away with from +this class lot of students aren't very + + align:start position:0% +this class lot of students aren't very + + + align:start position:0% +this class lot of students aren't very +good at taking the information they do + + align:start position:0% +good at taking the information they do + + + align:start position:0% +good at taking the information they do +know and using it to deduce the next + + align:start position:0% +know and using it to deduce the next + + + align:start position:0% +know and using it to deduce the next +thing to try or the next thing to test + + align:start position:0% +thing to try or the next thing to test + + + align:start position:0% +thing to try or the next thing to test +and sort narrow down where the problem + + align:start position:0% +and sort narrow down where the problem + + + align:start position:0% +and sort narrow down where the problem +is so something you have to learn how to + + align:start position:0% +is so something you have to learn how to + + + align:start position:0% +is so something you have to learn how to +do is to be organized about taking + + align:start position:0% +do is to be organized about taking + + + align:start position:0% +do is to be organized about taking +something that isn't working a + + align:start position:0% +something that isn't working a + + + align:start position:0% +something that isn't working a +complicated thing so parts of it are + + align:start position:0% +complicated thing so parts of it are + + + align:start position:0% +complicated thing so parts of it are +working but something isn't and trying + + align:start position:0% +working but something isn't and trying + + + align:start position:0% +working but something isn't and trying +to work back from both ends somewhere in + + align:start position:0% +to work back from both ends somewhere in + + + align:start position:0% +to work back from both ends somewhere in +the middle it does + + align:start position:0% +the middle it does + + + align:start position:0% +the middle it does +work and so that's a skill that you have + + align:start position:0% +work and so that's a skill that you have + + + align:start position:0% +work and so that's a skill that you have +to practice for a while and so I you + + align:start position:0% +to practice for a while and so I you + + + align:start position:0% +to practice for a while and so I you +know I we try to help with that steel + + align:start position:0% +know I we try to help with that steel + + + align:start position:0% +know I we try to help with that steel +it's sort of neat to watch them make the + + align:start position:0% +it's sort of neat to watch them make the + + + align:start position:0% +it's sort of neat to watch them make the +transition from coming in and sort of + + align:start position:0% +transition from coming in and sort of + + + align:start position:0% +transition from coming in and sort of +answer focused to leaving sort of like + + align:start position:0% +answer focused to leaving sort of like + + + align:start position:0% +answer focused to leaving sort of like +okay you can ask me anything because I + + align:start position:0% +okay you can ask me anything because I + + + align:start position:0% +okay you can ask me anything because I +actually know how to do things I mean I + + align:start position:0% +actually know how to do things I mean I + + + align:start position:0% +actually know how to do things I mean I +from scratch I can not only recognize + + align:start position:0% +from scratch I can not only recognize + + + align:start position:0% +from scratch I can not only recognize +the right answer when I see it I can + + align:start position:0% +the right answer when I see it I can + + + align:start position:0% +the right answer when I see it I can +actually make right answers that's a + + align:start position:0% +actually make right answers that's a + + + align:start position:0% +actually make right answers that's a +very but people feel empowered when they + + align:start position:0% +very but people feel empowered when they + + + align:start position:0% +very but people feel empowered when they +can do that + + align:start position:0% +can do that + + + align:start position:0% +can do that +we'll close out this episode with a + + align:start position:0% +we'll close out this episode with a + + + align:start position:0% +we'll close out this episode with a +moment from the interview that really + + align:start position:0% +moment from the interview that really + + + align:start position:0% +moment from the interview that really +struck me because it captured how chris + + align:start position:0% +struck me because it captured how chris + + + align:start position:0% +struck me because it captured how chris +strives to humanize the learning + + align:start position:0% +strives to humanize the learning + + + align:start position:0% +strives to humanize the learning +experience in six double-o for how he + + align:start position:0% +experience in six double-o for how he + + + align:start position:0% +experience in six double-o for how he +understands that students are whole + + align:start position:0% +understands that students are whole + + + align:start position:0% +understands that students are whole +people who bring their lives into + + align:start position:0% +people who bring their lives into + + + align:start position:0% +people who bring their lives into +classroom spaces doctors have this + + align:start position:0% +classroom spaces doctors have this + + + align:start position:0% +classroom spaces doctors have this +saying you know treat the patient not + + align:start position:0% +saying you know treat the patient not + + + align:start position:0% +saying you know treat the patient not +just the disease and so when students + + align:start position:0% +just the disease and so when students + + + align:start position:0% +just the disease and so when students +are struggling with material I find you + + align:start position:0% +are struggling with material I find you + + + align:start position:0% +are struggling with material I find you +know it's often the case that there's + + align:start position:0% +know it's often the case that there's + + + align:start position:0% +know it's often the case that there's +issues that are not just you know what's + + align:start position:0% +issues that are not just you know what's + + + align:start position:0% +issues that are not just you know what's +the technical concept or skill that + + align:start position:0% +the technical concept or skill that + + + align:start position:0% +the technical concept or skill that +we're talking about and so I learned + + align:start position:0% +we're talking about and so I learned + + + align:start position:0% +we're talking about and so I learned +over the years to make myself as best I + + align:start position:0% +over the years to make myself as best I + + + align:start position:0% +over the years to make myself as best I +can + + align:start position:0% +can + + + align:start position:0% +can +accessible to students who need to talk + + align:start position:0% +accessible to students who need to talk + + + align:start position:0% +accessible to students who need to talk +about their life as a student their life + + align:start position:0% +about their life as a student their life + + + align:start position:0% +about their life as a student their life +as a person here at MIT and you know + + align:start position:0% +as a person here at MIT and you know + + + align:start position:0% +as a person here at MIT and you know +everybody comes with a bit of imposter + + align:start position:0% +everybody comes with a bit of imposter + + + align:start position:0% +everybody comes with a bit of imposter +syndrome so you need to you know help + + align:start position:0% +syndrome so you need to you know help + + + align:start position:0% +syndrome so you need to you know help +students deal with that a little bit so + + align:start position:0% +students deal with that a little bit so + + + align:start position:0% +students deal with that a little bit so +there's a lot of issues that aren't on + + align:start position:0% +there's a lot of issues that aren't on + + + align:start position:0% +there's a lot of issues that aren't on +the syllabus and six double-o for that + + align:start position:0% +the syllabus and six double-o for that + + + align:start position:0% +the syllabus and six double-o for that +affect how they do in 1604 and I've + + align:start position:0% +affect how they do in 1604 and I've + + + align:start position:0% +affect how they do in 1604 and I've +learned that it's good for me to invest + + align:start position:0% +learned that it's good for me to invest + + + align:start position:0% +learned that it's good for me to invest +my time in helping them you know + + align:start position:0% +my time in helping them you know + + + align:start position:0% +my time in helping them you know +think about talk to their larger issues + + align:start position:0% +think about talk to their larger issues + + + align:start position:0% +think about talk to their larger issues +I'm not very good at writing + + align:start position:0% +I'm not very good at writing + + + align:start position:0% +I'm not very good at writing +prescriptions but you can sort of listen + + align:start position:0% +prescriptions but you can sort of listen + + + align:start position:0% +prescriptions but you can sort of listen +you try to offer a bit of perspective I + + align:start position:0% +you try to offer a bit of perspective I + + + align:start position:0% +you try to offer a bit of perspective I +think what's interesting is that over + + align:start position:0% +think what's interesting is that over + + + align:start position:0% +think what's interesting is that over +time you begin to appreciate it's going + + align:start position:0% +time you begin to appreciate it's going + + + align:start position:0% +time you begin to appreciate it's going +to put effort into something it might as + + align:start position:0% +to put effort into something it might as + + + align:start position:0% +to put effort into something it might as +well be the best it doesn't cost you any + + align:start position:0% +well be the best it doesn't cost you any + + + align:start position:0% +well be the best it doesn't cost you any +more even better and it's sort of + + align:start position:0% +more even better and it's sort of + + + align:start position:0% +more even better and it's sort of +interesting to me how many people say oh + + align:start position:0% +interesting to me how many people say oh + + + align:start position:0% +interesting to me how many people say oh +you know I'll go give that lecture but I + + align:start position:0% +you know I'll go give that lecture but I + + + align:start position:0% +you know I'll go give that lecture but I +won't really care no no you know that's + + align:start position:0% +won't really care no no you know that's + + + align:start position:0% +won't really care no no you know that's +that's not the right approach you may + + align:start position:0% +that's not the right approach you may + + + align:start position:0% +that's not the right approach you may +you should actually say look if I'm + + align:start position:0% +you should actually say look if I'm + + + align:start position:0% +you should actually say look if I'm +gonna spend 40 percent of my time each + + align:start position:0% +gonna spend 40 percent of my time each + + + align:start position:0% +gonna spend 40 percent of my time each +semester teaching students would it make + + align:start position:0% +semester teaching students would it make + + + align:start position:0% +semester teaching students would it make +sense to be proud how best right I think + + align:start position:0% +sense to be proud how best right I think + + + align:start position:0% +sense to be proud how best right I think +everybody comes to that you know the + + align:start position:0% +everybody comes to that you know the + + + align:start position:0% +everybody comes to that you know the +more you're here teaching the more you + + align:start position:0% +more you're here teaching the more you + + + align:start position:0% +more you're here teaching the more you +utilize that if you're interested in + + align:start position:0% +utilize that if you're interested in + + + align:start position:0% +utilize that if you're interested in +learning more about computation + + align:start position:0% +learning more about computation + + + align:start position:0% +learning more about computation +structures you can find the course + + align:start position:0% +structures you can find the course + + + align:start position:0% +structures you can find the course +materials on our website at ocw.mit.edu + + align:start position:0% +materials on our website at ocw.mit.edu + + + align:start position:0% +materials on our website at ocw.mit.edu +and if you're an educator check out our + + align:start position:0% +and if you're an educator check out our + + + align:start position:0% +and if you're an educator check out our +educator portal at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +you so much for listening if you enjoyed + + align:start position:0% +you so much for listening if you enjoyed + + + align:start position:0% +you so much for listening if you enjoyed +this podcast please consider subscribing + + align:start position:0% +this podcast please consider subscribing + + + align:start position:0% +this podcast please consider subscribing +and rating our show until next time I'm + + align:start position:0% +and rating our show until next time I'm + + + align:start position:0% +and rating our show until next time I'm +Sarah Hansen from MIT OpenCourseWare \ No newline at end of file diff --git a/6lZvF-CCXcA.txt b/6lZvF-CCXcA.txt new file mode 100644 index 0000000000000000000000000000000000000000..79a3e0941387e060b168dfc43284ca621b328f17 --- /dev/null +++ b/6lZvF-CCXcA.txt @@ -0,0 +1,14346 @@ +align:start position:0% + +so we're going to go on to a slightly + + align:start position:0% +so we're going to go on to a slightly + + + align:start position:0% +so we're going to go on to a slightly +new topic today we're going to be + + align:start position:0% +new topic today we're going to be + + + align:start position:0% +new topic today we're going to be +studying uh Aral inversion and then + + align:start position:0% +studying uh Aral inversion and then + + + align:start position:0% +studying uh Aral inversion and then +talking about paraday rotation Imaging + + align:start position:0% +talking about paraday rotation Imaging + + + align:start position:0% +talking about paraday rotation Imaging +does anyone have any questions on all + + align:start position:0% +does anyone have any questions on all + + + align:start position:0% +does anyone have any questions on all +the infmetry stuff we've covered so far + + align:start position:0% +the infmetry stuff we've covered so far + + + align:start position:0% +the infmetry stuff we've covered so far +before we leave the + + align:start position:0% + + + + align:start position:0% + +everyone seems very happy with in + + align:start position:0% +everyone seems very happy with in + + + align:start position:0% +everyone seems very happy with in +perometry all right so in the + + align:start position:0% +perometry all right so in the + + + align:start position:0% +perometry all right so in the +perometry this technique that we're + + align:start position:0% +perometry this technique that we're + + + align:start position:0% +perometry this technique that we're +going to be talking about today our + + align:start position:0% +going to be talking about today our + + + align:start position:0% +going to be talking about today our +inversion is actually quite General and + + align:start position:0% +inversion is actually quite General and + + + align:start position:0% +inversion is actually quite General and +I'm introducing in the context of + + align:start position:0% +I'm introducing in the context of + + + align:start position:0% +I'm introducing in the context of +interferometry because um we often use + + align:start position:0% +interferometry because um we often use + + + align:start position:0% +interferometry because um we often use +it with this technique but it could also + + align:start position:0% +it with this technique but it could also + + + align:start position:0% +it with this technique but it could also +be used with um you know ad mission to a + + align:start position:0% +be used with um you know ad mission to a + + + align:start position:0% +be used with um you know ad mission to a +plasma an image of we'll talk a little + + align:start position:0% +plasma an image of we'll talk a little + + + align:start position:0% +plasma an image of we'll talk a little +bit about you know what our inversion is + + align:start position:0% +bit about you know what our inversion is + + + align:start position:0% +bit about you know what our inversion is +and what symmetry requirements we have + + align:start position:0% +and what symmetry requirements we have + + + align:start position:0% +and what symmetry requirements we have +and you'll see quite quickly is actually + + align:start position:0% +and you'll see quite quickly is actually + + + align:start position:0% +and you'll see quite quickly is actually +quite General can be used in lots of + + align:start position:0% +quite General can be used in lots of + + + align:start position:0% +quite General can be used in lots of +different cases here so what we have + + align:start position:0% +different cases here so what we have + + + align:start position:0% +different cases here so what we have +from inry I'll just write as if like + + align:start position:0% +from inry I'll just write as if like + + + align:start position:0% +from inry I'll just write as if like +that is we've got some integration of + + align:start position:0% +that is we've got some integration of + + + align:start position:0% +that is we've got some integration of +any DL right so we have some line + + align:start position:0% +any DL right so we have some line + + + align:start position:0% +any DL right so we have some line +integrated quantity and we might have + + align:start position:0% +integrated quantity and we might have + + + align:start position:0% +integrated quantity and we might have +that line integrated quantity along a + + align:start position:0% +that line integrated quantity along a + + + align:start position:0% +that line integrated quantity along a +very specific chord so we might be + + align:start position:0% +very specific chord so we might be + + + align:start position:0% +very specific chord so we might be +integrating along the Z Direction and we + + align:start position:0% +integrating along the Z Direction and we + + + align:start position:0% +integrating along the Z Direction and we +might be at you know xal x0 + + align:start position:0% +might be at you know xal x0 + + + align:start position:0% +might be at you know xal x0 +yals y z and we might be resolving it as + + align:start position:0% +yals y z and we might be resolving it as + + + align:start position:0% +yals y z and we might be resolving it as +a function of time that would be our + + align:start position:0% +a function of time that would be our + + + align:start position:0% +a function of time that would be our +sort of temporary temporarily resolved + + align:start position:0% +sort of temporary temporarily resolved + + + align:start position:0% +sort of temporary temporarily resolved +in deometry or we might have an image of + + align:start position:0% +in deometry or we might have an image of + + + align:start position:0% +in deometry or we might have an image of +X and Y and we would have it at some + + align:start position:0% +X and Y and we would have it at some + + + align:start position:0% +X and Y and we would have it at some +specific time this would be our + + align:start position:0% +specific time this would be our + + + align:start position:0% +specific time this would be our +spatially resolved into perometry so + + align:start position:0% +spatially resolved into perometry so + + + align:start position:0% +spatially resolved into perometry so +this is what we + + align:start position:0% +this is what we + + + align:start position:0% +this is what we +have and of course what we + + align:start position:0% +have and of course what we + + + align:start position:0% +have and of course what we +want is what we can't have which is the + + align:start position:0% +want is what we can't have which is the + + + align:start position:0% +want is what we can't have which is the +electron density as a function of + + align:start position:0% +electron density as a function of + + + align:start position:0% +electron density as a function of +position everywhere in space preferably + + align:start position:0% +position everywhere in space preferably + + + align:start position:0% +position everywhere in space preferably +as a function of position in time this + + align:start position:0% +as a function of position in time this + + + align:start position:0% +as a function of position in time this +is what you'd like if you want to + + align:start position:0% +is what you'd like if you want to + + + align:start position:0% +is what you'd like if you want to +compare like a simulation or a theory or + + align:start position:0% +compare like a simulation or a theory or + + + align:start position:0% +compare like a simulation or a theory or +something like that and instead we have + + align:start position:0% +something like that and instead we have + + + align:start position:0% +something like that and instead we have +these line integrated measurements okay + + align:start position:0% +these line integrated measurements okay + + + align:start position:0% +these line integrated measurements okay +so if you want to calculate this density + + align:start position:0% +so if you want to calculate this density + + + align:start position:0% +so if you want to calculate this density +from some of these limited reduced uh + + align:start position:0% +from some of these limited reduced uh + + + align:start position:0% +from some of these limited reduced uh +data sets you could do a technique like + + align:start position:0% +data sets you could do a technique like + + + align:start position:0% +data sets you could do a technique like +to so if you youve ever gone for an MRI + + align:start position:0% +to so if you youve ever gone for an MRI + + + align:start position:0% +to so if you youve ever gone for an MRI +or something + + align:start position:0% + + + + align:start position:0% + +similar you'll know that what they do is + + align:start position:0% +similar you'll know that what they do is + + + align:start position:0% +similar you'll know that what they do is +they'll take lots and lots of different + + align:start position:0% +they'll take lots and lots of different + + + align:start position:0% +they'll take lots and lots of different +images slowly scanning around your head + + align:start position:0% +images slowly scanning around your head + + + align:start position:0% +images slowly scanning around your head +or other in part of your body and then + + align:start position:0% +or other in part of your body and then + + + align:start position:0% +or other in part of your body and then +they'll do some very fancy computer + + align:start position:0% +they'll do some very fancy computer + + + align:start position:0% +they'll do some very fancy computer +techniques to reconstruct the + + align:start position:0% +techniques to reconstruct the + + + align:start position:0% +techniques to reconstruct the +three-dimensional structure of whatever + + align:start position:0% +three-dimensional structure of whatever + + + align:start position:0% +three-dimensional structure of whatever +it is they're scanning right and this + + align:start position:0% +it is they're scanning right and this + + + align:start position:0% +it is they're scanning right and this +works extremely well because people have + + align:start position:0% +works extremely well because people have + + + align:start position:0% +works extremely well because people have +lifetimes of years but plasmas only have + + align:start position:0% +lifetimes of years but plasmas only have + + + align:start position:0% +lifetimes of years but plasmas only have +lifetimes of you know seconds or M + + align:start position:0% +lifetimes of you know seconds or M + + + align:start position:0% +lifetimes of you know seconds or M +millisecs or nanc and so it's very hard + + align:start position:0% +millisecs or nanc and so it's very hard + + + align:start position:0% +millisecs or nanc and so it's very hard +to just slowly rotate your Plasma in + + align:start position:0% +to just slowly rotate your Plasma in + + + align:start position:0% +to just slowly rotate your Plasma in +place while you take lots of pictures of + + align:start position:0% +place while you take lots of pictures of + + + align:start position:0% +place while you take lots of pictures of +it the alternative if you want to do + + align:start position:0% +it the alternative if you want to do + + + align:start position:0% +it the alternative if you want to do +single shot tomography will be to + + align:start position:0% +single shot tomography will be to + + + align:start position:0% +single shot tomography will be to +surround your plasma with lots and lots + + align:start position:0% +surround your plasma with lots and lots + + + align:start position:0% +surround your plasma with lots and lots +of cameras and look at it from lots of + + align:start position:0% +of cameras and look at it from lots of + + + align:start position:0% +of cameras and look at it from lots of +different angles so for example if we've + + align:start position:0% +different angles so for example if we've + + + align:start position:0% +different angles so for example if we've +got sort of a circular crosssection + + align:start position:0% +got sort of a circular crosssection + + + align:start position:0% +got sort of a circular crosssection +plasma like this maybe this is some sort + + align:start position:0% +plasma like this maybe this is some sort + + + align:start position:0% +plasma like this maybe this is some sort +of pokac type of thing we could just + + align:start position:0% +of pokac type of thing we could just + + + align:start position:0% +of pokac type of thing we could just +have lots of different lines of + + align:start position:0% +have lots of different lines of + + + align:start position:0% +have lots of different lines of +sight and we could do our tomographic + + align:start position:0% +sight and we could do our tomographic + + + align:start position:0% +sight and we could do our tomographic +reconstruction like this but of course + + align:start position:0% +reconstruction like this but of course + + + align:start position:0% +reconstruction like this but of course +lines of sight + + align:start position:0% +lines of sight + + + align:start position:0% +lines of sight +losos are expensive so we don't tend to + + align:start position:0% +losos are expensive so we don't tend to + + + align:start position:0% +losos are expensive so we don't tend to +be able to just have a very very large + + align:start position:0% +be able to just have a very very large + + + align:start position:0% +be able to just have a very very large +number of them but of course for some + + align:start position:0% +number of them but of course for some + + + align:start position:0% +number of them but of course for some +applications this might be justifiable + + align:start position:0% +applications this might be justifiable + + + align:start position:0% +applications this might be justifiable +on eter they've got 550 hometry lines of + + align:start position:0% +on eter they've got 550 hometry lines of + + + align:start position:0% +on eter they've got 550 hometry lines of +sight for reconstructing the emission + + align:start position:0% +sight for reconstructing the emission + + + align:start position:0% +sight for reconstructing the emission +prod so they made a choice to have a lot + + align:start position:0% +prod so they made a choice to have a lot + + + align:start position:0% +prod so they made a choice to have a lot +of Imaging lines of sight in general for + + align:start position:0% +of Imaging lines of sight in general for + + + align:start position:0% +of Imaging lines of sight in general for +deometry this is too expensive so we + + align:start position:0% +deometry this is too expensive so we + + + align:start position:0% +deometry this is too expensive so we +don't do it but what we can do is is a + + align:start position:0% +don't do it but what we can do is is a + + + align:start position:0% +don't do it but what we can do is is a +version of this where we make strong + + align:start position:0% +version of this where we make strong + + + align:start position:0% +version of this where we make strong +arguments about the symmetry of our + + align:start position:0% +arguments about the symmetry of our + + + align:start position:0% +arguments about the symmetry of our +plasma because if our plasma has some + + align:start position:0% +plasma because if our plasma has some + + + align:start position:0% +plasma because if our plasma has some +underlying symmetry it helps us have + + align:start position:0% +underlying symmetry it helps us have + + + align:start position:0% +underlying symmetry it helps us have +need fewer lines of sight and we can + + align:start position:0% +need fewer lines of sight and we can + + + align:start position:0% +need fewer lines of sight and we can +still start getting out an approximation + + align:start position:0% +still start getting out an approximation + + + align:start position:0% +still start getting out an approximation +of the the full density propile and the + + align:start position:0% +of the the full density propile and the + + + align:start position:0% +of the the full density propile and the +Symmetry we're going to talk about today + + align:start position:0% +Symmetry we're going to talk about today + + + align:start position:0% +Symmetry we're going to talk about today +with ar inversion is an assumption of + + align:start position:0% +with ar inversion is an assumption of + + + align:start position:0% +with ar inversion is an assumption of +cylindrical + + align:start position:0% +cylindrical + + + align:start position:0% +cylindrical +symmetry so we're going to + + align:start position:0% + + + + align:start position:0% + +assume cylindrical symmetry + + align:start position:0% + + + + align:start position:0% + +and so that could be again something + + align:start position:0% +and so that could be again something + + + align:start position:0% +and so that could be again something +like this plasma + + align:start position:0% +like this plasma + + + align:start position:0% +like this plasma +here with a circular + + align:start position:0% + + + + align:start position:0% + +cross-section and we're going to assume + + align:start position:0% +cross-section and we're going to assume + + + align:start position:0% +cross-section and we're going to assume +that there's maybe there's variation in + + align:start position:0% +that there's maybe there's variation in + + + align:start position:0% +that there's maybe there's variation in +this direction out of plane that doesn't + + align:start position:0% +this direction out of plane that doesn't + + + align:start position:0% +this direction out of plane that doesn't +matter we're only trying to measure it + + align:start position:0% +matter we're only trying to measure it + + + align:start position:0% +matter we're only trying to measure it +in one plane but we're going to assume + + align:start position:0% +in one plane but we're going to assume + + + align:start position:0% +in one plane but we're going to assume +that our electron density NE of x y and + + align:start position:0% +that our electron density NE of x y and + + + align:start position:0% +that our electron density NE of x y and +Zed is just a function NE of R in Z + + align:start position:0% +Zed is just a function NE of R in Z + + + align:start position:0% +Zed is just a function NE of R in Z +where r² isal X2 plus y^2 so that's the + + align:start position:0% +where r² isal X2 plus y^2 so that's the + + + align:start position:0% +where r² isal X2 plus y^2 so that's the +same as saying that the density is + + align:start position:0% +same as saying that the density is + + + align:start position:0% +same as saying that the density is +constant on sort of nested circular + + align:start position:0% +constant on sort of nested circular + + + align:start position:0% +constant on sort of nested circular +surfaces and of course if this is + + align:start position:0% +surfaces and of course if this is + + + align:start position:0% +surfaces and of course if this is +something like a + + align:start position:0% +something like a + + + align:start position:0% +something like a +toac that's quite nice because we know + + align:start position:0% +toac that's quite nice because we know + + + align:start position:0% +toac that's quite nice because we know +that on our flux surfaces quantities + + align:start position:0% +that on our flux surfaces quantities + + + align:start position:0% +that on our flux surfaces quantities +tend to be constant and this could also + + align:start position:0% +tend to be constant and this could also + + + align:start position:0% +tend to be constant and this could also +be true for like a cylindrical Z pinch + + align:start position:0% +be true for like a cylindrical Z pinch + + + align:start position:0% +be true for like a cylindrical Z pinch +plasma and experiments I do or other you + + align:start position:0% +plasma and experiments I do or other you + + + align:start position:0% +plasma and experiments I do or other you +can think of other situations where you + + align:start position:0% +can think of other situations where you + + + align:start position:0% +can think of other situations where you +think things are approximately symmetric + + align:start position:0% +think things are approximately symmetric + + + align:start position:0% +think things are approximately symmetric +right and if you have a system like this + + align:start position:0% +right and if you have a system like this + + + align:start position:0% +right and if you have a system like this +you could have a set of + + align:start position:0% +you could have a set of + + + align:start position:0% +you could have a set of +inders looking + + align:start position:0% +inders looking + + + align:start position:0% +inders looking +along parallel chords like this or if + + align:start position:0% +along parallel chords like this or if + + + align:start position:0% +along parallel chords like this or if +you aren't working with a toac and you + + align:start position:0% +you aren't working with a toac and you + + + align:start position:0% +you aren't working with a toac and you +can do like Imaging you could have a + + align:start position:0% +can do like Imaging you could have a + + + align:start position:0% +can do like Imaging you could have a +camera an expanded laser beam as we + + align:start position:0% +camera an expanded laser beam as we + + + align:start position:0% +camera an expanded laser beam as we +discussed before and that can camera is + + align:start position:0% +discussed before and that can camera is + + + align:start position:0% +discussed before and that can camera is +now measuring any of uh let's see x y t + + align:start position:0% +now measuring any of uh let's see x y t + + + align:start position:0% +now measuring any of uh let's see x y t +t0 or these could be a series of chords + + align:start position:0% +t0 or these could be a series of chords + + + align:start position:0% +t0 or these could be a series of chords +which are measuring any at xals + + align:start position:0% +which are measuring any at xals + + + align:start position:0% +which are measuring any at xals +X like that so this is just two + + align:start position:0% +X like that so this is just two + + + align:start position:0% +X like that so this is just two +different ways to look at this problem I + + align:start position:0% +different ways to look at this problem I + + + align:start position:0% +different ways to look at this problem I +can either build up my data from + + align:start position:0% +can either build up my data from + + + align:start position:0% +can either build up my data from +multiple time resolved into barometers + + align:start position:0% +multiple time resolved into barometers + + + align:start position:0% +multiple time resolved into barometers +looking along parallel chords or I could + + align:start position:0% +looking along parallel chords or I could + + + align:start position:0% +looking along parallel chords or I could +have an Imaging system looking at a + + align:start position:0% +have an Imaging system looking at a + + + align:start position:0% +have an Imaging system looking at a +single time in both these cases we can + + align:start position:0% +single time in both these cases we can + + + align:start position:0% +single time in both these cases we can +do this thing called the AR version I'll + + align:start position:0% +do this thing called the AR version I'll + + + align:start position:0% +do this thing called the AR version I'll +just write down oh I wrote it down okay + + align:start position:0% +just write down oh I wrote it down okay + + + align:start position:0% +just write down oh I wrote it down okay +good Al's one of these guys who's kind + + align:start position:0% +good Al's one of these guys who's kind + + + align:start position:0% +good Al's one of these guys who's kind +of depressing when you read his + + align:start position:0% +of depressing when you read his + + + align:start position:0% +of depressing when you read his +biography he was a Danish mathematician + + align:start position:0% +biography he was a Danish mathematician + + + align:start position:0% +biography he was a Danish mathematician +uh he invented all sorts of wonderful + + align:start position:0% +uh he invented all sorts of wonderful + + + align:start position:0% +uh he invented all sorts of wonderful +things in mathematics as well as the + + align:start position:0% +things in mathematics as well as the + + + align:start position:0% +things in mathematics as well as the +alha transformation and he died in + + align:start position:0% +alha transformation and he died in + + + align:start position:0% +alha transformation and he died in +consumption at the age of 26 so I don't + + align:start position:0% +consumption at the age of 26 so I don't + + + align:start position:0% +consumption at the age of 26 so I don't +know how many of you are still younger + + align:start position:0% +know how many of you are still younger + + + align:start position:0% +know how many of you are still younger +than 26 but you've still got maybe a + + align:start position:0% +than 26 but you've still got maybe a + + + align:start position:0% +than 26 but you've still got maybe a +couple of years to make such + + align:start position:0% +couple of years to make such + + + align:start position:0% +couple of years to make such +groundbreaking discoveries I'm already + + align:start position:0% +groundbreaking discoveries I'm already + + + align:start position:0% +groundbreaking discoveries I'm already +pass it I don't have a chance so you + + align:start position:0% +pass it I don't have a chance so you + + + align:start position:0% +pass it I don't have a chance so you +know look at his bi like damn a lot of + + align:start position:0% +know look at his bi like damn a lot of + + + align:start position:0% +know look at his bi like damn a lot of +work okay Co so what we have say from + + align:start position:0% +work okay Co so what we have say from + + + align:start position:0% +work okay Co so what we have say from +either of these two systems + + align:start position:0% + + + + align:start position:0% + +is a map of the line + + align:start position:0% +is a map of the line + + + align:start position:0% +is a map of the line +integrated electron density as a + + align:start position:0% +integrated electron density as a + + + align:start position:0% +integrated electron density as a +function of Y and I'm just going to draw + + align:start position:0% +function of Y and I'm just going to draw + + + align:start position:0% +function of Y and I'm just going to draw +this very suggestively as this sort of + + align:start position:0% +this very suggestively as this sort of + + + align:start position:0% +this very suggestively as this sort of +very blocky setup here so each of these + + align:start position:0% +very blocky setup here so each of these + + + align:start position:0% +very blocky setup here so each of these +densities could be + + align:start position:0% +densities could be + + + align:start position:0% +densities could be +the density that we've measured at a + + align:start position:0% +the density that we've measured at a + + + align:start position:0% +the density that we've measured at a +single Pixel on our image or it could be + + align:start position:0% +single Pixel on our image or it could be + + + align:start position:0% +single Pixel on our image or it could be +the density measured by our n time + + align:start position:0% +the density measured by our n time + + + align:start position:0% +the density measured by our n time +resolved inter thomet here so we've got + + align:start position:0% +resolved inter thomet here so we've got + + + align:start position:0% +resolved inter thomet here so we've got +some density value at each of these + + align:start position:0% + + + + align:start position:0% + +points like this here and what we + + align:start position:0% + + + + align:start position:0% + +want is of course + + align:start position:0% + + + + align:start position:0% + +our plasma density as a function of r + + align:start position:0% +our plasma density as a function of r + + + align:start position:0% +our plasma density as a function of r +not as a function of Y which is a + + align:start position:0% +not as a function of Y which is a + + + align:start position:0% +not as a function of Y which is a +coordinate for example could + + align:start position:0% +coordinate for example could + + + align:start position:0% +coordinate for example could +be one of these two I'm not really + + align:start position:0% +be one of these two I'm not really + + + align:start position:0% +be one of these two I'm not really +distinguish between Y and X here as long + + align:start position:0% +distinguish between Y and X here as long + + + align:start position:0% +distinguish between Y and X here as long +as it's perpendicular to the proing + + align:start position:0% +as it's perpendicular to the proing + + + align:start position:0% +as it's perpendicular to the proing +direction it doesn't really matter but + + align:start position:0% +direction it doesn't really matter but + + + align:start position:0% +direction it doesn't really matter but +what we want is this as a function of r + + align:start position:0% +what we want is this as a function of r + + + align:start position:0% +what we want is this as a function of r +and we' like to have some nice smooth + + align:start position:0% +and we' like to have some nice smooth + + + align:start position:0% +and we' like to have some nice smooth +function and it doesn't necessarily have + + align:start position:0% +function and it doesn't necessarily have + + + align:start position:0% +function and it doesn't necessarily have +to have the same shape of this of course + + align:start position:0% +to have the same shape of this of course + + + align:start position:0% +to have the same shape of this of course +because it's kind of clear if you look + + align:start position:0% +because it's kind of clear if you look + + + align:start position:0% +because it's kind of clear if you look +at this and you think about it for a + + align:start position:0% +at this and you think about it for a + + + align:start position:0% +at this and you think about it for a +little while that your profile in NL + + align:start position:0% +little while that your profile in NL + + + align:start position:0% +little while that your profile in NL +doesn't have to be the same as your + + align:start position:0% +doesn't have to be the same as your + + + align:start position:0% +doesn't have to be the same as your +profile in any like this so what we want + + align:start position:0% +profile in any like this so what we want + + + align:start position:0% +profile in any like this so what we want +is some mathematical formalism that + + align:start position:0% +is some mathematical formalism that + + + align:start position:0% +is some mathematical formalism that +allow us to take this data and produce + + align:start position:0% +allow us to take this data and produce + + + align:start position:0% +allow us to take this data and produce +this it's kind of clear how to go back + + align:start position:0% +this it's kind of clear how to go back + + + align:start position:0% +this it's kind of clear how to go back +the other way you can certainly do it + + align:start position:0% +the other way you can certainly do it + + + align:start position:0% +the other way you can certainly do it +numerically very easily you can just + + align:start position:0% +numerically very easily you can just + + + align:start position:0% +numerically very easily you can just +sort of make this up and then you can uh + + align:start position:0% +sort of make this up and then you can uh + + + align:start position:0% +sort of make this up and then you can uh +you can make up some profile like this + + align:start position:0% +you can make up some profile like this + + + align:start position:0% +you can make up some profile like this +and then you can just calculate the line + + align:start position:0% +and then you can just calculate the line + + + align:start position:0% +and then you can just calculate the line +integrating density along each line of + + align:start position:0% +integrating density along each line of + + + align:start position:0% +integrating density along each line of +site what's less Bally it is how to go + + align:start position:0% +site what's less Bally it is how to go + + + align:start position:0% +site what's less Bally it is how to go +back the other way from the data we have + + align:start position:0% +back the other way from the data we have + + + align:start position:0% +back the other way from the data we have +to the data we want so this is the setup + + align:start position:0% +to the data we want so this is the setup + + + align:start position:0% +to the data we want so this is the setup +of the problem does anyone have any + + align:start position:0% +of the problem does anyone have any + + + align:start position:0% +of the problem does anyone have any +questions about this so + + align:start position:0% + + + + align:start position:0% + +far any questions on + + align:start position:0% + + + + align:start position:0% + +that so + + align:start position:0% +that so + + + align:start position:0% +that so +this is what we measure and I'm going to + + align:start position:0% +this is what we measure and I'm going to + + + align:start position:0% +this is what we measure and I'm going to +call this some function capital F of Y + + align:start position:0% +call this some function capital F of Y + + + align:start position:0% +call this some function capital F of Y +and I'm going to call this some function + + align:start position:0% +and I'm going to call this some function + + + align:start position:0% +and I'm going to call this some function +lowercase f of R and the reason is + + align:start position:0% +lowercase f of R and the reason is + + + align:start position:0% +lowercase f of R and the reason is +because it doesn't actually matter + + align:start position:0% +because it doesn't actually matter + + + align:start position:0% +because it doesn't actually matter +whether this is density or brightness or + + align:start position:0% +whether this is density or brightness or + + + align:start position:0% +whether this is density or brightness or +whatever else the the mathematics are + + align:start position:0% +whatever else the the mathematics are + + + align:start position:0% +whatever else the the mathematics are +the same so I'm just going to refer to + + align:start position:0% +the same so I'm just going to refer to + + + align:start position:0% +the same so I'm just going to refer to +as these two different functions and + + align:start position:0% +as these two different functions and + + + align:start position:0% +as these two different functions and +we're trying to convert one to the + + align:start position:0% + + + + align:start position:0% + +other so mathematically we have our line + + align:start position:0% +other so mathematically we have our line + + + align:start position:0% +other so mathematically we have our line +integrated function F of Y which is + + align:start position:0% +integrated function F of Y which is + + + align:start position:0% +integrated function F of Y which is +equal to the integral of + + align:start position:0% + + + + align:start position:0% + +any Z like this and this is equal the + + align:start position:0% +any Z like this and this is equal the + + + align:start position:0% +any Z like this and this is equal the +integral from minus A2 - y^ 2 Ted to + + align:start position:0% +integral from minus A2 - y^ 2 Ted to + + + align:start position:0% +integral from minus A2 - y^ 2 Ted to +plus a 2 + y^ 2 + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +okay I had it right in my notes I decid + + align:start position:0% +okay I had it right in my notes I decid + + + align:start position:0% +okay I had it right in my notes I decid +to turn fly I hat it we're going back to + + align:start position:0% +to turn fly I hat it we're going back to + + + align:start position:0% +to turn fly I hat it we're going back to +the okay and I'll draw you a diagram of + + align:start position:0% +the okay and I'll draw you a diagram of + + + align:start position:0% +the okay and I'll draw you a diagram of +the geometry here might be slightly + + align:start position:0% +the geometry here might be slightly + + + align:start position:0% +the geometry here might be slightly +different the diagram of the geometry + + align:start position:0% +different the diagram of the geometry + + + align:start position:0% +different the diagram of the geometry +had just previously here so we have some + + align:start position:0% + + + + align:start position:0% + +plasma which has a approximately + + align:start position:0% +plasma which has a approximately + + + align:start position:0% +plasma which has a approximately +circular + + align:start position:0% +circular + + + align:start position:0% +circular +shape it's bounded at a so we can say + + align:start position:0% +shape it's bounded at a so we can say + + + align:start position:0% +shape it's bounded at a so we can say +that the pressure at a is equal to zero + + align:start position:0% +that the pressure at a is equal to zero + + + align:start position:0% +that the pressure at a is equal to zero +this just stops us having to cre out to + + align:start position:0% +this just stops us having to cre out to + + + align:start position:0% +this just stops us having to cre out to +Infinity which is very inconvenient when + + align:start position:0% +Infinity which is very inconvenient when + + + align:start position:0% +Infinity which is very inconvenient when +we try and do it in reality so we're + + align:start position:0% +we try and do it in reality so we're + + + align:start position:0% +we try and do it in reality so we're +going to stop our plasma at some + + align:start position:0% +going to stop our plasma at some + + + align:start position:0% +going to stop our plasma at some +distance since we only need to make + + align:start position:0% +distance since we only need to make + + + align:start position:0% +distance since we only need to make +measurements at to the boundary a in + + align:start position:0% +measurements at to the boundary a in + + + align:start position:0% +measurements at to the boundary a in +order to solve this problem we've got + + align:start position:0% +order to solve this problem we've got + + + align:start position:0% +order to solve this problem we've got +some cord going through the + + align:start position:0% +some cord going through the + + + align:start position:0% +some cord going through the +plasma we've got our coordinate + + align:start position:0% +plasma we've got our coordinate + + + align:start position:0% +plasma we've got our coordinate +system where Y is transverse to the + + align:start position:0% +system where Y is transverse to the + + + align:start position:0% +system where Y is transverse to the +direction that we're probing and X now + + align:start position:0% +direction that we're probing and X now + + + align:start position:0% +direction that we're probing and X now +is the direction that we're bring I was + + align:start position:0% +is the direction that we're bring I was + + + align:start position:0% +is the direction that we're bring I was +using Z previously but the way I've got + + align:start position:0% +using Z previously but the way I've got + + + align:start position:0% +using Z previously but the way I've got +it written is X thought myself + + align:start position:0% +it written is X thought myself + + + align:start position:0% +it written is X thought myself +that and so for any point inside the + + align:start position:0% +that and so for any point inside the + + + align:start position:0% +that and so for any point inside the +plasma we can say that there is some + + align:start position:0% +plasma we can say that there is some + + + align:start position:0% +plasma we can say that there is some +distance y that it sits at from the + + align:start position:0% +distance y that it sits at from the + + + align:start position:0% +distance y that it sits at from the +origin here and some + + align:start position:0% +origin here and some + + + align:start position:0% +origin here and some +distance X the long that it sits at and + + align:start position:0% +distance X the long that it sits at and + + + align:start position:0% +distance X the long that it sits at and +so there's some distance R and this is + + align:start position:0% +so there's some distance R and this is + + + align:start position:0% +so there's some distance R and this is +the radial coordinate we're assuming + + align:start position:0% +the radial coordinate we're assuming + + + align:start position:0% +the radial coordinate we're assuming +that we have symmetry it has a mutal + + align:start position:0% +that we have symmetry it has a mutal + + + align:start position:0% +that we have symmetry it has a mutal +direction in the angular Direction so + + align:start position:0% +direction in the angular Direction so + + + align:start position:0% +direction in the angular Direction so +we're only interested in the size of + + align:start position:0% +we're only interested in the size of + + + align:start position:0% +we're only interested in the size of +this radial coord here + + align:start position:0% +this radial coord here + + + align:start position:0% +this radial coord here +and then if you look at this and stare + + align:start position:0% +and then if you look at this and stare + + + align:start position:0% +and then if you look at this and stare +at it for long enough you can see that + + align:start position:0% +at it for long enough you can see that + + + align:start position:0% +at it for long enough you can see that +this is indeed the procedure I was + + align:start position:0% +this is indeed the procedure I was + + + align:start position:0% +this is indeed the procedure I was +talking about before where you can + + align:start position:0% +talking about before where you can + + + align:start position:0% +talking about before where you can +easily go from your if you come up with + + align:start position:0% +easily go from your if you come up with + + + align:start position:0% +easily go from your if you come up with +some calculated profile uh some guess of + + align:start position:0% +some calculated profile uh some guess of + + + align:start position:0% +some calculated profile uh some guess of +what you think the distribution is like + + align:start position:0% +what you think the distribution is like + + + align:start position:0% +what you think the distribution is like +the Gan how you go from that to your + + align:start position:0% +the Gan how you go from that to your + + + align:start position:0% +the Gan how you go from that to your +prediction of what you're actually going + + align:start position:0% +prediction of what you're actually going + + + align:start position:0% +prediction of what you're actually going +to get on the detector so this is the + + align:start position:0% +to get on the detector so this is the + + + align:start position:0% +to get on the detector so this is the +easy Direction This is actually the AR + + align:start position:0% +easy Direction This is actually the AR + + + align:start position:0% +easy Direction This is actually the AR +transformation and what we really + + align:start position:0% +transformation and what we really + + + align:start position:0% +transformation and what we really +interested in is the inverse trans + + align:start position:0% + + + + align:start position:0% + +now we're technically requiring this + + align:start position:0% +now we're technically requiring this + + + align:start position:0% +now we're technically requiring this +condition here I've written as pressure + + align:start position:0% +condition here I've written as pressure + + + align:start position:0% +condition here I've written as pressure +but why don't we now that we're talking + + align:start position:0% +but why don't we now that we're talking + + + align:start position:0% +but why don't we now that we're talking +in terms of these + + align:start position:0% +in terms of these + + + align:start position:0% +in terms of these +functions sort of written that I want F + + align:start position:0% +functions sort of written that I want F + + + align:start position:0% +functions sort of written that I want F +of a to be equal to zero this isn't + + align:start position:0% +of a to be equal to zero this isn't + + + align:start position:0% +of a to be equal to zero this isn't +actually quite true the rigorous + + align:start position:0% +actually quite true the rigorous + + + align:start position:0% +actually quite true the rigorous +requirement is that F of r as R tends to + + align:start position:0% +requirement is that F of r as R tends to + + + align:start position:0% +requirement is that F of r as R tends to +Infinity this needs to drop off + + align:start position:0% + + + + align:start position:0% + +or fall + + align:start position:0% +or fall + + + align:start position:0% +or fall +faster than one R so you can get away + + align:start position:0% +faster than one R so you can get away + + + align:start position:0% +faster than one R so you can get away +with like a gaan type function or + + align:start position:0% +with like a gaan type function or + + + align:start position:0% +with like a gaan type function or +something like that as long as it falls + + align:start position:0% +something like that as long as it falls + + + align:start position:0% +something like that as long as it falls +sufficiently fast you can't get away + + align:start position:0% +sufficiently fast you can't get away + + + align:start position:0% +sufficiently fast you can't get away +with something that's uniform across its + + align:start position:0% +with something that's uniform across its + + + align:start position:0% +with something that's uniform across its +space but as long as your function falls + + align:start position:0% +space but as long as your function falls + + + align:start position:0% +space but as long as your function falls +off nice and quickly uh you can use this + + align:start position:0% +off nice and quickly uh you can use this + + + align:start position:0% +off nice and quickly uh you can use this +technique here + + align:start position:0% +technique here + + + align:start position:0% +technique here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so so this is actually + + align:start position:0% + + + + align:start position:0% + +quite what we do with this point here is + + align:start position:0% +quite what we do with this point here is + + + align:start position:0% +quite what we do with this point here is +we realized that this is a horrific MTH + + align:start position:0% +we realized that this is a horrific MTH + + + align:start position:0% +we realized that this is a horrific MTH +of RS and y's and x's and things like + + align:start position:0% +of RS and y's and x's and things like + + + align:start position:0% +of RS and y's and x's and things like +that and we decid that we want to + + align:start position:0% +that and we decid that we want to + + + align:start position:0% +that and we decid that we want to +rewrite everything and we already said + + align:start position:0% +rewrite everything and we already said + + + align:start position:0% +rewrite everything and we already said +that R2 is equal to y^2 plus x^2 and so + + align:start position:0% +that R2 is equal to y^2 plus x^2 and so + + + align:start position:0% +that R2 is equal to y^2 plus x^2 and so +we want to have a go at substituting + + align:start position:0% +we want to have a go at substituting + + + align:start position:0% +we want to have a go at substituting +this X Out for something that's in terms + + align:start position:0% +this X Out for something that's in terms + + + align:start position:0% +this X Out for something that's in terms +of r instead and this gives us the real + + align:start position:0% +of r instead and this gives us the real + + + align:start position:0% +of r instead and this gives us the real +prop transformation which is f of Y is + + align:start position:0% +prop transformation which is f of Y is + + + align:start position:0% +prop transformation which is f of Y is +equal to 2 * the integral from y to + + align:start position:0% +equal to 2 * the integral from y to + + + align:start position:0% +equal to 2 * the integral from y to +a f of r + + align:start position:0% +a f of r + + + align:start position:0% +a f of r +r v + + align:start position:0% +r v + + + align:start position:0% +r v +r square otk of R + + align:start position:0% +r square otk of R + + + align:start position:0% +r square otk of R +2 Y + + align:start position:0% +2 Y + + + align:start position:0% +2 Y +squ and if you start this for long + + align:start position:0% +squ and if you start this for long + + + align:start position:0% +squ and if you start this for long +enough you can convince yourself of + + align:start position:0% +enough you can convince yourself of + + + align:start position:0% +enough you can convince yourself of +doing the substitution into the + + align:start position:0% +doing the substitution into the + + + align:start position:0% +doing the substitution into the +integration will work out and that we've + + align:start position:0% +integration will work out and that we've + + + align:start position:0% +integration will work out and that we've +correctly dealt with the here as well + + align:start position:0% +correctly dealt with the here as well + + + align:start position:0% +correctly dealt with the here as well +and so this is the thing which is called + + align:start position:0% +and so this is the thing which is called + + + align:start position:0% +and so this is the thing which is called +the trans + + align:start position:0% + + + + align:start position:0% + +okay but we as I mentioned don't want + + align:start position:0% +okay but we as I mentioned don't want + + + align:start position:0% +okay but we as I mentioned don't want +the AL transformation that's relatively + + align:start position:0% +the AL transformation that's relatively + + + align:start position:0% +the AL transformation that's relatively +easy to do what we have is f of Y and we + + align:start position:0% +easy to do what we have is f of Y and we + + + align:start position:0% +easy to do what we have is f of Y and we +want F of R so what we want to be able + + align:start position:0% +want F of R so what we want to be able + + + align:start position:0% +want F of R so what we want to be able +to do is the + + align:start position:0% + + + + align:start position:0% + +inverse and I'm not going to derive this + + align:start position:0% +inverse and I'm not going to derive this + + + align:start position:0% +inverse and I'm not going to derive this +um I'm not even sure I know how to um + + align:start position:0% +um I'm not even sure I know how to um + + + align:start position:0% +um I'm not even sure I know how to um +but if you stare at the what I'm about + + align:start position:0% +but if you stare at the what I'm about + + + align:start position:0% +but if you stare at the what I'm about +to write down in this for long enough + + align:start position:0% +to write down in this for long enough + + + align:start position:0% +to write down in this for long enough +you can convince yourself there is + + align:start position:0% +you can convince yourself there is + + + align:start position:0% +you can convince yourself there is +enough shared features to it that it's + + align:start position:0% +enough shared features to it that it's + + + align:start position:0% +enough shared features to it that it's +probably correct and you can go look it + + align:start position:0% +probably correct and you can go look it + + + align:start position:0% +probably correct and you can go look it +up if you want + + align:start position:0% +up if you want + + + align:start position:0% +up if you want +to so this gives us that F of R is equal + + align:start position:0% +to so this gives us that F of R is equal + + + align:start position:0% +to so this gives us that F of R is equal +to minus one upon pi times the integral + + align:start position:0% +to minus one upon pi times the integral + + + align:start position:0% +to minus one upon pi times the integral +from R to a of + + align:start position:0% +from R to a of + + + align:start position:0% +from R to a of +DF Dy that's our capital F + + align:start position:0% +DF Dy that's our capital F + + + align:start position:0% +DF Dy that's our capital F +here + + align:start position:0% +here + + + align:start position:0% +here +Dy y^ 2- r + + align:start position:0% + + + + align:start position:0% + +Square remember + + align:start position:0% +Square remember + + + align:start position:0% +Square remember +this capital F is something we have as a + + align:start position:0% +this capital F is something we have as a + + + align:start position:0% +this capital F is something we have as a +function of one so this is our line inte + + align:start position:0% +function of one so this is our line inte + + + align:start position:0% +function of one so this is our line inte +measurement and this is our as a + + align:start position:0% +measurement and this is our as a + + + align:start position:0% +measurement and this is our as a +movement symmetric R of depend me this + + align:start position:0% +movement symmetric R of depend me this + + + align:start position:0% +movement symmetric R of depend me this +is the thing we're actually trying to + + align:start position:0% +is the thing we're actually trying to + + + align:start position:0% +is the thing we're actually trying to +get + + align:start position:0% +get + + + align:start position:0% +get +out okay so this looks like a complete + + align:start position:0% +out okay so this looks like a complete + + + align:start position:0% +out okay so this looks like a complete +solution to the problem if I have some + + align:start position:0% +solution to the problem if I have some + + + align:start position:0% +solution to the problem if I have some +measurement from my detector which is l + + align:start position:0% +measurement from my detector which is l + + + align:start position:0% +measurement from my detector which is l +integrated and I have enough samples in + + align:start position:0% +integrated and I have enough samples in + + + align:start position:0% +integrated and I have enough samples in +y I should be able to work out what that + + align:start position:0% +y I should be able to work out what that + + + align:start position:0% +y I should be able to work out what that +is can anyone spot any limitations for + + align:start position:0% +is can anyone spot any limitations for + + + align:start position:0% +is can anyone spot any limitations for +this procedure there are + + align:start position:0% +this procedure there are + + + align:start position:0% +this procedure there are +two it's not clear where the plasma ends + + align:start position:0% +two it's not clear where the plasma ends + + + align:start position:0% +two it's not clear where the plasma ends +all the + + align:start position:0% +all the + + + align:start position:0% +all the +time can you just say that again please + + align:start position:0% +time can you just say that again please + + + align:start position:0% +time can you just say that again please +yeah it's not it's not always clear like + + align:start position:0% +yeah it's not it's not always clear like + + + align:start position:0% +yeah it's not it's not always clear like +what a you should choose okay so that's + + align:start position:0% +what a you should choose okay so that's + + + align:start position:0% +what a you should choose okay so that's +a reasonable one actually so uh where is + + align:start position:0% +a reasonable one actually so uh where is + + + align:start position:0% +a reasonable one actually so uh where is +a + + align:start position:0% + + + + align:start position:0% + +and that is actually a problem uh I will + + align:start position:0% +and that is actually a problem uh I will + + + align:start position:0% +and that is actually a problem uh I will +definitely agree it's a problem it's + + align:start position:0% +definitely agree it's a problem it's + + + align:start position:0% +definitely agree it's a problem it's +less of a problem as long as a drops off + + align:start position:0% +less of a problem as long as a drops off + + + align:start position:0% +less of a problem as long as a drops off +rapidly enough which is related to this + + align:start position:0% +rapidly enough which is related to this + + + align:start position:0% +rapidly enough which is related to this +but you're right you know the edge of + + align:start position:0% +but you're right you know the edge of + + + align:start position:0% +but you're right you know the edge of +our plasma is kind of fuzzy um I mean + + align:start position:0% +our plasma is kind of fuzzy um I mean + + + align:start position:0% +our plasma is kind of fuzzy um I mean +you know where the density definitely go + + align:start position:0% +you know where the density definitely go + + + align:start position:0% +you know where the density definitely go +to zero if you have a vacuum chamber + + align:start position:0% +to zero if you have a vacuum chamber + + + align:start position:0% +to zero if you have a vacuum chamber +right the hard metal walls of your + + align:start position:0% +right the hard metal walls of your + + + align:start position:0% +right the hard metal walls of your +vacuum chamber so maybe that would be + + align:start position:0% +vacuum chamber so maybe that would be + + + align:start position:0% +vacuum chamber so maybe that would be +good enough but yeah you certainly want + + align:start position:0% +good enough but yeah you certainly want + + + align:start position:0% +good enough but yeah you certainly want +to do this experiment to know where a is + + align:start position:0% +to do this experiment to know where a is + + + align:start position:0% +to do this experiment to know where a is +other + + align:start position:0% +other + + + align:start position:0% +other +limitations you need a derivative so + + align:start position:0% +limitations you need a derivative so + + + align:start position:0% +limitations you need a derivative so +that's going to be limited by detective + + align:start position:0% +that's going to be limited by detective + + + align:start position:0% +that's going to be limited by detective +resolution + + align:start position:0% +resolution + + + align:start position:0% +resolution +like experimental voice yeah so the f d + + align:start position:0% +like experimental voice yeah so the f d + + + align:start position:0% +like experimental voice yeah so the f d +y is noisy right if we go back + + align:start position:0% +y is noisy right if we go back + + + align:start position:0% +y is noisy right if we go back +to this very suggested picture that I + + align:start position:0% +to this very suggested picture that I + + + align:start position:0% +to this very suggested picture that I +put in here deliberately like this for + + align:start position:0% +put in here deliberately like this for + + + align:start position:0% +put in here deliberately like this for +any realistic system you have discrete + + align:start position:0% +any realistic system you have discrete + + + align:start position:0% +any realistic system you have discrete +measurements discrete locations and we + + align:start position:0% +measurements discrete locations and we + + + align:start position:0% +measurements discrete locations and we +all know that doing derivatives of + + align:start position:0% +all know that doing derivatives of + + + align:start position:0% +all know that doing derivatives of +discrete data is a nightmare because + + align:start position:0% +discrete data is a nightmare because + + + align:start position:0% +discrete data is a nightmare because +you're taking something that's noisy and + + align:start position:0% +you're taking something that's noisy and + + + align:start position:0% +you're taking something that's noisy and +you're dividing it by a small number so + + align:start position:0% +you're dividing it by a small number so + + + align:start position:0% +you're dividing it by a small number so +any noise here gets really Amplified up + + align:start position:0% +any noise here gets really Amplified up + + + align:start position:0% +any noise here gets really Amplified up +so this straight away looks + + align:start position:0% +so this straight away looks + + + align:start position:0% +so this straight away looks +problem uh third + + align:start position:0% +problem uh third + + + align:start position:0% +problem uh third +thing yes we want like once you start + + align:start position:0% +thing yes we want like once you start + + + align:start position:0% +thing yes we want like once you start +getting + + align:start position:0% + + + + align:start position:0% + +close + + align:start position:0% + + + + align:start position:0% + +muchar close to the + + align:start position:0% + + + + align:start position:0% + +edge you're close we + + align:start position:0% +edge you're close we + + + align:start position:0% +edge you're close we +right anyone else no so there what are + + align:start position:0% +right anyone else no so there what are + + + align:start position:0% +right anyone else no so there what are +we talking about here we're talking + + align:start position:0% +we talking about here we're talking + + + align:start position:0% +we talking about here we're talking +about the fact that there's something + + align:start position:0% +about the fact that there's something + + + align:start position:0% +about the fact that there's something +interesting going on here and your your + + align:start position:0% +interesting going on here and your your + + + align:start position:0% +interesting going on here and your your +physicist eyes have seen this and gone a + + align:start position:0% +physicist eyes have seen this and gone a + + + align:start position:0% +physicist eyes have seen this and gone a +hat you know whenever we start having + + align:start position:0% +hat you know whenever we start having + + + align:start position:0% +hat you know whenever we start having +numbers minus other numbers in the + + align:start position:0% +numbers minus other numbers in the + + + align:start position:0% +numbers minus other numbers in the +denominator here there's some chance + + align:start position:0% +denominator here there's some chance + + + align:start position:0% +denominator here there's some chance +that this thing will go to zero right + + align:start position:0% +that this thing will go to zero right + + + align:start position:0% +that this thing will go to zero right +and it will actually go to zero for Y + + align:start position:0% +and it will actually go to zero for Y + + + align:start position:0% +and it will actually go to zero for Y +close to R equals zero so near the + + align:start position:0% +close to R equals zero so near the + + + align:start position:0% +close to R equals zero so near the +center + + align:start position:0% +center + + + align:start position:0% +center +here this thing will have a singularity + + align:start position:0% +here this thing will have a singularity + + + align:start position:0% +here this thing will have a singularity +now in reality we won't have a + + align:start position:0% +now in reality we won't have a + + + align:start position:0% +now in reality we won't have a +singularity right because we'll never + + align:start position:0% +singularity right because we'll never + + + align:start position:0% +singularity right because we'll never +have a detector bin that's exactly in + + align:start position:0% +have a detector bin that's exactly in + + + align:start position:0% +have a detector bin that's exactly in +that position but what we will + + align:start position:0% +that position but what we will + + + align:start position:0% +that position but what we will +do is for the bins which are close to + + align:start position:0% +do is for the bins which are close to + + + align:start position:0% +do is for the bins which are close to +the center here will have a very small + + align:start position:0% +the center here will have a very small + + + align:start position:0% +the center here will have a very small +number on the bottom and so it will + + align:start position:0% +number on the bottom and so it will + + + align:start position:0% +number on the bottom and so it will +amplify the value of this big number so + + align:start position:0% +amplify the value of this big number so + + + align:start position:0% +amplify the value of this big number so +if this is noisy if there's some noise + + align:start position:0% +if this is noisy if there's some noise + + + align:start position:0% +if this is noisy if there's some noise +near the center here that noise will be + + align:start position:0% +near the center here that noise will be + + + align:start position:0% +near the center here that noise will be +massively Amplified and will appear + + align:start position:0% +massively Amplified and will appear + + + align:start position:0% +massively Amplified and will appear +everywhere else in our solution and it + + align:start position:0% +everywhere else in our solution and it + + + align:start position:0% +everywhere else in our solution and it +will cause problems the rest of our + + align:start position:0% +will cause problems the rest of our + + + align:start position:0% +will cause problems the rest of our +solution so I'll just write here that + + align:start position:0% +solution so I'll just write here that + + + align:start position:0% +solution so I'll just write here that +we've got a singularity + + align:start position:0% + + + + align:start position:0% + +near yal Z and this amplifies the + + align:start position:0% +near yal Z and this amplifies the + + + align:start position:0% +near yal Z and this amplifies the +noise of these + + align:start position:0% + + + + align:start position:0% + +points okay any questions on any of this + + align:start position:0% +points okay any questions on any of this + + + align:start position:0% +points okay any questions on any of this +why are we colleting the data where + + align:start position:0% +why are we colleting the data where + + + align:start position:0% +why are we colleting the data where +y you have y can only be positive this + + align:start position:0% + + + + align:start position:0% + +it's an excellent question does anyone + + align:start position:0% +it's an excellent question does anyone + + + align:start position:0% +it's an excellent question does anyone +know why we are neglecting the data that + + align:start position:0% +know why we are neglecting the data that + + + align:start position:0% +know why we are neglecting the data that +we have for y less than + + align:start position:0% + + + + align:start position:0% + +zero we've assumed symmetry right in + + align:start position:0% +zero we've assumed symmetry right in + + + align:start position:0% +zero we've assumed symmetry right in +order to do this + + align:start position:0% +order to do this + + + align:start position:0% +order to do this +calculation we have assumed as a mle + + align:start position:0% +calculation we have assumed as a mle + + + align:start position:0% +calculation we have assumed as a mle +symmetry and so the data must be + + align:start position:0% +symmetry and so the data must be + + + align:start position:0% +symmetry and so the data must be +identical for y less than zero the y + + align:start position:0% +identical for y less than zero the y + + + align:start position:0% +identical for y less than zero the y +greater than zero now in reality it + + align:start position:0% +greater than zero now in reality it + + + align:start position:0% +greater than zero now in reality it +won't be right we never have a system + + align:start position:0% +won't be right we never have a system + + + align:start position:0% +won't be right we never have a system +which is perfectly symmetric so the good + + align:start position:0% +which is perfectly symmetric so the good + + + align:start position:0% +which is perfectly symmetric so the good +way to present your data is to do the + + align:start position:0% +way to present your data is to do the + + + align:start position:0% +way to present your data is to do the +arble inversion on one half of your data + + align:start position:0% +arble inversion on one half of your data + + + align:start position:0% +arble inversion on one half of your data +and the arble inversion on the other + + align:start position:0% +and the arble inversion on the other + + + align:start position:0% +and the arble inversion on the other +half of your data separately and then + + align:start position:0% +half of your data separately and then + + + align:start position:0% +half of your data separately and then +see whether those two match and if they + + align:start position:0% +see whether those two match and if they + + + align:start position:0% +see whether those two match and if they +match close enough with an experimental + + align:start position:0% +match close enough with an experimental + + + align:start position:0% +match close enough with an experimental +error great you know like you you've got + + align:start position:0% +error great you know like you you've got + + + align:start position:0% +error great you know like you you've got +a good inversion if they don't match at + + align:start position:0% +a good inversion if they don't match at + + + align:start position:0% +a good inversion if they don't match at +all then like you shouldn't have used an + + align:start position:0% +all then like you shouldn't have used an + + + align:start position:0% +all then like you shouldn't have used an +Nal inversion in the first place your + + align:start position:0% +Nal inversion in the first place your + + + align:start position:0% +Nal inversion in the first place your +prior that you have the cylindrical + + align:start position:0% +prior that you have the cylindrical + + + align:start position:0% +prior that you have the cylindrical +symmetry is incorrect so you can't use + + align:start position:0% +symmetry is incorrect so you can't use + + + align:start position:0% +symmetry is incorrect so you can't use +this method so it's a good check + + align:start position:0% +this method so it's a good check + + + align:start position:0% +this method so it's a good check +actually on your data the other reason + + align:start position:0% +actually on your data the other reason + + + align:start position:0% +actually on your data the other reason +is because you know because of this + + align:start position:0% +is because you know because of this + + + align:start position:0% +is because you know because of this +symmetry if you're trying to save money + + align:start position:0% +symmetry if you're trying to save money + + + align:start position:0% +symmetry if you're trying to save money +you might only put detectors in one half + + align:start position:0% +you might only put detectors in one half + + + align:start position:0% +you might only put detectors in one half +okay if you're really sure that you've + + align:start position:0% +okay if you're really sure that you've + + + align:start position:0% +okay if you're really sure that you've +got symmetry then you don't need to + + align:start position:0% +got symmetry then you don't need to + + + align:start position:0% +got symmetry then you don't need to +check maybe you do the experiment a few + + align:start position:0% +check maybe you do the experiment a few + + + align:start position:0% +check maybe you do the experiment a few +times of all your detectors spread out + + align:start position:0% +times of all your detectors spread out + + + align:start position:0% +times of all your detectors spread out +and then you're like hey this is great + + align:start position:0% +and then you're like hey this is great + + + align:start position:0% +and then you're like hey this is great +now I can get higher resolution by + + align:start position:0% +now I can get higher resolution by + + + align:start position:0% +now I can get higher resolution by +moving half my detectors to the first + + align:start position:0% +moving half my detectors to the first + + + align:start position:0% +moving half my detectors to the first +half so you know there may be some + + align:start position:0% +half so you know there may be some + + + align:start position:0% +half so you know there may be some +reasons why you only need half the data + + align:start position:0% +reasons why you only need half the data + + + align:start position:0% +reasons why you only need half the data +here but yeah that's a really good + + align:start position:0% +here but yeah that's a really good + + + align:start position:0% +here but yeah that's a really good +point any other questions on this + + align:start position:0% +point any other questions on this + + + align:start position:0% +point any other questions on this +anything online + + align:start position:0% + + + + align:start position:0% + +Okay and like I said this is very + + align:start position:0% +Okay and like I said this is very + + + align:start position:0% +Okay and like I said this is very +generic um this could be interferometry + + align:start position:0% +generic um this could be interferometry + + + align:start position:0% +generic um this could be interferometry +on a toac this could be interferometry + + align:start position:0% +on a toac this could be interferometry + + + align:start position:0% +on a toac this could be interferometry +on the sorts of plasmas I work with this + + align:start position:0% +on the sorts of plasmas I work with this + + + align:start position:0% +on the sorts of plasmas I work with this +could be used for unfolding a mission on + + align:start position:0% +could be used for unfolding a mission on + + + align:start position:0% +could be used for unfolding a mission on +a nith hotspot from an x-ray image or + + align:start position:0% +a nith hotspot from an x-ray image or + + + align:start position:0% +a nith hotspot from an x-ray image or +something like that so we're just + + align:start position:0% +something like that so we're just + + + align:start position:0% +something like that so we're just +introducing it here because it's a + + align:start position:0% +introducing it here because it's a + + + align:start position:0% +introducing it here because it's a +useful technique you know okay how do we + + align:start position:0% +useful technique you know okay how do we + + + align:start position:0% +useful technique you know okay how do we +actually do this in practice + + align:start position:0% + + + + align:start position:0% + +any youone think of some way to overcome + + align:start position:0% +any youone think of some way to overcome + + + align:start position:0% +any youone think of some way to overcome +these some of these limitations + + align:start position:0% +these some of these limitations + + + align:start position:0% +these some of these limitations +particularly this one + + align:start position:0% + + + + align:start position:0% + +here so we've got + + align:start position:0% + + + + align:start position:0% + +again our data which is discreet and + + align:start position:0% +again our data which is discreet and + + + align:start position:0% +again our data which is discreet and +potentially + + align:start position:0% + + + + align:start position:0% + +noisy yeah mention + + align:start position:0% + + + + align:start position:0% + +sure that's so that that could be a + + align:start position:0% +sure that's so that that could be a + + + align:start position:0% +sure that's so that that could be a +problem yeah so you could you could + + align:start position:0% +problem yeah so you could you could + + + align:start position:0% +problem yeah so you could you could +deliberately shift your data so that y + + align:start position:0% +deliberately shift your data so that y + + + align:start position:0% +deliberately shift your data so that y +equals z is sort of on one side of one + + align:start position:0% +equals z is sort of on one side of one + + + align:start position:0% +equals z is sort of on one side of one +of your bins that too to close hard to + + align:start position:0% +of your bins that too to close hard to + + + align:start position:0% +of your bins that too to close hard to +get in practice because the plasma might + + align:start position:0% +get in practice because the plasma might + + + align:start position:0% +get in practice because the plasma might +move around so you're probably not gonna + + align:start position:0% +move around so you're probably not gonna + + + align:start position:0% +move around so you're probably not gonna +be able to do it yeah other ideas I + + align:start position:0% +be able to do it yeah other ideas I + + + align:start position:0% +be able to do it yeah other ideas I +guess that also means that this idea + + align:start position:0% +guess that also means that this idea + + + align:start position:0% +guess that also means that this idea +might have issues but if you know if you + + align:start position:0% +might have issues but if you know if you + + + align:start position:0% +might have issues but if you know if you +get information about where High gradi + + align:start position:0% +get information about where High gradi + + + align:start position:0% +get information about where High gradi +be in your plasma conate your measur + + align:start position:0% +be in your plasma conate your measur + + + align:start position:0% +be in your plasma conate your measur +regions that you're better resoling High + + align:start position:0% +regions that you're better resoling High + + + align:start position:0% +regions that you're better resoling High +gradi yeah so certainly these high + + align:start position:0% +gradi yeah so certainly these high + + + align:start position:0% +gradi yeah so certainly these high +gradients are going to be dominating + + align:start position:0% +gradients are going to be dominating + + + align:start position:0% +gradients are going to be dominating +this integral but of course also the + + align:start position:0% +this integral but of course also the + + + align:start position:0% +this integral but of course also the +grad any gradient near the center is + + align:start position:0% +grad any gradient near the center is + + + align:start position:0% +grad any gradient near the center is +going to be dominating so you might want + + align:start position:0% +going to be dominating so you might want + + + align:start position:0% +going to be dominating so you might want +to put more measurements near the middle + + align:start position:0% +to put more measurements near the middle + + + align:start position:0% +to put more measurements near the middle +so you'd have higher F other techniques + + align:start position:0% +so you'd have higher F other techniques + + + align:start position:0% +so you'd have higher F other techniques +is it possible to integrate by Parts + + align:start position:0% +is it possible to integrate by Parts + + + align:start position:0% +is it possible to integrate by Parts +therefore you + + align:start position:0% +therefore you + + + align:start position:0% +therefore you +don't inside + + align:start position:0% +don't inside + + + align:start position:0% +don't inside +different I I don't think you can do + + align:start position:0% +different I I don't think you can do + + + align:start position:0% +different I I don't think you can do +this by Parts but I haven't seen the + + align:start position:0% +this by Parts but I haven't seen the + + + align:start position:0% +this by Parts but I haven't seen the +analytical version of this which looks + + align:start position:0% +analytical version of this which looks + + + align:start position:0% +analytical version of this which looks +like it does that but I can't + + align:start position:0% +like it does that but I can't + + + align:start position:0% +like it does that but I can't +immediately check this and tell you that + + align:start position:0% +immediately check this and tell you that + + + align:start position:0% +immediately check this and tell you that +it doesn't I suspect it doesn't work + + align:start position:0% +it doesn't I suspect it doesn't work + + + align:start position:0% +it doesn't I suspect it doesn't work +yeah any other ideas might have some + + align:start position:0% +yeah any other ideas might have some + + + align:start position:0% +yeah any other ideas might have some +reasonable idea the distribution time + + align:start position:0% +reasonable idea the distribution time + + + align:start position:0% +reasonable idea the distribution time +form an expected interation okay yeah so + + align:start position:0% +form an expected interation okay yeah so + + + align:start position:0% +form an expected interation okay yeah so +maybe we've got some priers about the + + align:start position:0% +maybe we've got some priers about the + + + align:start position:0% +maybe we've got some priers about the +distribution and we fit to this that + + align:start position:0% +distribution and we fit to this that + + + align:start position:0% +distribution and we fit to this that +would be good a similar version is we + + align:start position:0% +would be good a similar version is we + + + align:start position:0% +would be good a similar version is we +could fit this noisy data with a set of + + align:start position:0% +could fit this noisy data with a set of + + + align:start position:0% +could fit this noisy data with a set of +basis functions that we think has the + + align:start position:0% +basis functions that we think has the + + + align:start position:0% +basis functions that we think has the +sort of information in it that describes + + align:start position:0% +sort of information in it that describes + + + align:start position:0% +sort of information in it that describes +this and those basis functions won't + + align:start position:0% +this and those basis functions won't + + + align:start position:0% +this and those basis functions won't +have any noes and they'll be like nice + + align:start position:0% +have any noes and they'll be like nice + + + align:start position:0% +have any noes and they'll be like nice +and differentiable because we we'll use + + align:start position:0% +and differentiable because we we'll use + + + align:start position:0% +and differentiable because we we'll use +some nice analytical basis functions + + align:start position:0% +some nice analytical basis functions + + + align:start position:0% +some nice analytical basis functions +right so we could have like a sum of M + + align:start position:0% +right so we could have like a sum of M + + + align:start position:0% +right so we could have like a sum of M +Gan functions right where the Gans have + + align:start position:0% +Gan functions right where the Gans have + + + align:start position:0% +Gan functions right where the Gans have +some position and sigma or width or + + align:start position:0% +some position and sigma or width or + + + align:start position:0% +some position and sigma or width or +something like that and then like we + + align:start position:0% +something like that and then like we + + + align:start position:0% +something like that and then like we +know what the derivative is for so yeah + + align:start position:0% +know what the derivative is for so yeah + + + align:start position:0% +know what the derivative is for so yeah +so is that that's fitting set of basis + + align:start position:0% +so is that that's fitting set of basis + + + align:start position:0% +so is that that's fitting set of basis +functions to the brightness of + + align:start position:0% +functions to the brightness of + + + align:start position:0% +functions to the brightness of +mity like big F or small we still be + + align:start position:0% +mity like big F or small we still be + + + align:start position:0% +mity like big F or small we still be +fitting to this this is the only thing + + align:start position:0% +fitting to this this is the only thing + + + align:start position:0% +fitting to this this is the only thing +we know okay yeah so you would you would + + align:start position:0% +we know okay yeah so you would you would + + + align:start position:0% +we know okay yeah so you would you would +you could say F of Y is equal for some + + align:start position:0% +you could say F of Y is equal for some + + + align:start position:0% +you could say F of Y is equal for some +weighted set of basis functions okay and + + align:start position:0% +weighted set of basis functions okay and + + + align:start position:0% +weighted set of basis functions okay and +there are some basis functions that work + + align:start position:0% +there are some basis functions that work + + + align:start position:0% +there are some basis functions that work +really well because they've got + + align:start position:0% +really well because they've got + + + align:start position:0% +really well because they've got +analytical Aral Transformations + + align:start position:0% +analytical Aral Transformations + + + align:start position:0% +analytical Aral Transformations +gaussians are one of them unsurprisingly + + align:start position:0% +gaussians are one of them unsurprisingly + + + align:start position:0% +gaussians are one of them unsurprisingly +but some functions have a nice + + align:start position:0% +but some functions have a nice + + + align:start position:0% +but some functions have a nice +analytical Aral inversion and some don't + + align:start position:0% +analytical Aral inversion and some don't + + + align:start position:0% +analytical Aral inversion and some don't +so you'd want to use a set of functions + + align:start position:0% +so you'd want to use a set of functions + + + align:start position:0% +so you'd want to use a set of functions +that have nice analytical verion so that + + align:start position:0% +that have nice analytical verion so that + + + align:start position:0% +that have nice analytical verion so that +works pretty well um and that's what + + align:start position:0% +works pretty well um and that's what + + + align:start position:0% +works pretty well um and that's what +most people do so if you go online + + align:start position:0% +most people do so if you go online + + + align:start position:0% +most people do so if you go online +python has a nice Al inversion package + + align:start position:0% +python has a nice Al inversion package + + + align:start position:0% +python has a nice Al inversion package +and theyve got like different basis + + align:start position:0% +and theyve got like different basis + + + align:start position:0% +and theyve got like different basis +functions and you depending on exact + + align:start position:0% +functions and you depending on exact + + + align:start position:0% +functions and you depending on exact +problem you might want basis functions + + align:start position:0% +problem you might want basis functions + + + align:start position:0% +problem you might want basis functions +that got more like spiky features at the + + align:start position:0% +that got more like spiky features at the + + + align:start position:0% +that got more like spiky features at the +edge or smooth features in the middle + + align:start position:0% +edge or smooth features in the middle + + + align:start position:0% +edge or smooth features in the middle +and so it's just like all of these sorts + + align:start position:0% +and so it's just like all of these sorts + + + align:start position:0% +and so it's just like all of these sorts +of problems there's no one siiz fit all + + align:start position:0% +of problems there's no one siiz fit all + + + align:start position:0% +of problems there's no one siiz fit all +you have to tailor to yeah did I see + + align:start position:0% +you have to tailor to yeah did I see + + + align:start position:0% +you have to tailor to yeah did I see +another + + align:start position:0% + + + + align:start position:0% + +question yeah so as always with our data + + align:start position:0% +question yeah so as always with our data + + + align:start position:0% +question yeah so as always with our data +we can smooth it out but then we lose + + align:start position:0% +we can smooth it out but then we lose + + + align:start position:0% +we can smooth it out but then we lose +spatial resolution so yeah so you know + + align:start position:0% +spatial resolution so yeah so you know + + + align:start position:0% +spatial resolution so yeah so you know +that that that could help us but you + + align:start position:0% +that that that could help us but you + + + align:start position:0% +that that that could help us but you +know at some cost and so you have to + + align:start position:0% +know at some cost and so you have to + + + align:start position:0% +know at some cost and so you have to +balance those things yeah yeah I mean my + + align:start position:0% +balance those things yeah yeah I mean my + + + align:start position:0% +balance those things yeah yeah I mean my +first thought I can't actually think how + + align:start position:0% +first thought I can't actually think how + + + align:start position:0% +first thought I can't actually think how +do this is the ideal would be get + + align:start position:0% +do this is the ideal would be get + + + align:start position:0% +do this is the ideal would be get +that right so the the idea was how to + + align:start position:0% +that right so the the idea was how to + + + align:start position:0% +that right so the the idea was how to +get this derivative in an directly yeah + + align:start position:0% +get this derivative in an directly yeah + + + align:start position:0% +get this derivative in an directly yeah +I don't know how to do it either um but + + align:start position:0% +I don't know how to do it either um but + + + align:start position:0% +I don't know how to do it either um but +I I think this is just a fundamental + + align:start position:0% +I I think this is just a fundamental + + + align:start position:0% +I I think this is just a fundamental +limitation when you're making one of + + align:start position:0% +limitation when you're making one of + + + align:start position:0% +limitation when you're making one of +these measurements that you can't can't + + align:start position:0% +these measurements that you can't can't + + + align:start position:0% +these measurements that you can't can't +overcome yeah there are some really + + align:start position:0% +overcome yeah there are some really + + + align:start position:0% +overcome yeah there are some really +interesting links between the Arin + + align:start position:0% +interesting links between the Arin + + + align:start position:0% +interesting links between the Arin +version the radon transform which is is + + align:start position:0% +version the radon transform which is is + + + align:start position:0% +version the radon transform which is is +also used in um tomography and Foria + + align:start position:0% +also used in um tomography and Foria + + + align:start position:0% +also used in um tomography and Foria +transforms they form like some sort of + + align:start position:0% +transforms they form like some sort of + + + align:start position:0% +transforms they form like some sort of +weird little cycle if you do all of them + + align:start position:0% +weird little cycle if you do all of them + + + align:start position:0% +weird little cycle if you do all of them +in a row you get back to where you + + align:start position:0% +in a row you get back to where you + + + align:start position:0% +in a row you get back to where you +started so there's like really fun + + align:start position:0% +started so there's like really fun + + + align:start position:0% +started so there's like really fun +mathematics going on inside this as well + + align:start position:0% +mathematics going on inside this as well + + + align:start position:0% +mathematics going on inside this as well +um which I am not intelligent enough to + + align:start position:0% +um which I am not intelligent enough to + + + align:start position:0% +um which I am not intelligent enough to +know about but if you like that sort + + align:start position:0% +know about but if you like that sort + + + align:start position:0% +know about but if you like that sort +thing you should go look on the + + align:start position:0% +thing you should go look on the + + + align:start position:0% +thing you should go look on the +Wikipedia page there's a lot of stuff so + + align:start position:0% +Wikipedia page there's a lot of stuff so + + + align:start position:0% +Wikipedia page there's a lot of stuff so +any other questions or thoughts on + + align:start position:0% +any other questions or thoughts on + + + align:start position:0% +any other questions or thoughts on +otherin verion this is just like a + + align:start position:0% +otherin verion this is just like a + + + align:start position:0% +otherin verion this is just like a +little aside we're going to go on and do + + align:start position:0% +little aside we're going to go on and do + + + align:start position:0% +little aside we're going to go on and do +Faraday rotation after this so + + align:start position:0% +Faraday rotation after this so + + + align:start position:0% +Faraday rotation after this so +completely changed topic so if you've + + align:start position:0% +completely changed topic so if you've + + + align:start position:0% +completely changed topic so if you've +got any more questions speak now so this + + align:start position:0% +got any more questions speak now so this + + + align:start position:0% +got any more questions speak now so this +condition of cylindrical symetry is is + + align:start position:0% +condition of cylindrical symetry is is + + + align:start position:0% +condition of cylindrical symetry is is +very strict so like for instance if we + + align:start position:0% +very strict so like for instance if we + + + align:start position:0% +very strict so like for instance if we +had a highly shaped par Plass with d Etc + + align:start position:0% +had a highly shaped par Plass with d Etc + + + align:start position:0% +had a highly shaped par Plass with d Etc +technically doesn't I mean it possesses + + align:start position:0% +technically doesn't I mean it possesses + + + align:start position:0% +technically doesn't I mean it possesses +a symmetry on Flex surfaces but those + + align:start position:0% +a symmetry on Flex surfaces but those + + + align:start position:0% +a symmetry on Flex surfaces but those +Flex surfaces aren't cylindrical so they + + align:start position:0% +Flex surfaces aren't cylindrical so they + + + align:start position:0% +Flex surfaces aren't cylindrical so they +there would be no way to incorporate + + align:start position:0% +there would be no way to incorporate + + + align:start position:0% +there would be no way to incorporate +that information yeah so the question + + align:start position:0% +that information yeah so the question + + + align:start position:0% +that information yeah so the question +was um how do we deal with like + + align:start position:0% +was um how do we deal with like + + + align:start position:0% +was um how do we deal with like +non-circular flux surfaces like in most + + align:start position:0% +non-circular flux surfaces like in most + + + align:start position:0% +non-circular flux surfaces like in most +modern top and yes you can no longer use + + align:start position:0% +modern top and yes you can no longer use + + + align:start position:0% +modern top and yes you can no longer use +an Aral inversion in that case but there + + align:start position:0% +an Aral inversion in that case but there + + + align:start position:0% +an Aral inversion in that case but there +is still sufficient Symmetry and there's + + align:start position:0% +is still sufficient Symmetry and there's + + + align:start position:0% +is still sufficient Symmetry and there's +a lot of symmetry but what you would do + + align:start position:0% +a lot of symmetry but what you would do + + + align:start position:0% +a lot of symmetry but what you would do +for a toac is I believe you do a granof + + align:start position:0% +for a toac is I believe you do a granof + + + align:start position:0% +for a toac is I believe you do a granof +reconstruction of the flux surfaces from + + align:start position:0% +reconstruction of the flux surfaces from + + + align:start position:0% +reconstruction of the flux surfaces from +your magnetic Diagnostics you would then + + align:start position:0% +your magnetic Diagnostics you would then + + + align:start position:0% +your magnetic Diagnostics you would then +know that the density is constant along + + align:start position:0% +know that the density is constant along + + + align:start position:0% +know that the density is constant along +a flux surface because they are surfaces + + align:start position:0% +a flux surface because they are surfaces + + + align:start position:0% +a flux surface because they are surfaces +of constant pressure and there's enough + + align:start position:0% +of constant pressure and there's enough + + + align:start position:0% +of constant pressure and there's enough +Motion in the toal direction to smooth + + align:start position:0% +Motion in the toal direction to smooth + + + align:start position:0% +Motion in the toal direction to smooth +out any density pertubations very + + align:start position:0% +out any density pertubations very + + + align:start position:0% +out any density pertubations very +quickly this is roughly obviously + + align:start position:0% +quickly this is roughly obviously + + + align:start position:0% +quickly this is roughly obviously +there's fluctuations and stuff like that + + align:start position:0% +there's fluctuations and stuff like that + + + align:start position:0% +there's fluctuations and stuff like that +in general den conent and then you would + + align:start position:0% +in general den conent and then you would + + + align:start position:0% +in general den conent and then you would +use that as a prior and you wouldn't do + + align:start position:0% +use that as a prior and you wouldn't do + + + align:start position:0% +use that as a prior and you wouldn't do +this Al inversion like analy Ally or + + align:start position:0% +this Al inversion like analy Ally or + + + align:start position:0% +this Al inversion like analy Ally or +even semianalytically but you would that + + align:start position:0% +even semianalytically but you would that + + + align:start position:0% +even semianalytically but you would that +would feed into your tomographic + + align:start position:0% +would feed into your tomographic + + + align:start position:0% +would feed into your tomographic +reconstruction algorithm and for any + + align:start position:0% +reconstruction algorithm and for any + + + align:start position:0% +reconstruction algorithm and for any +tomographic reconstruction algorithm the + + align:start position:0% +tomographic reconstruction algorithm the + + + align:start position:0% +tomographic reconstruction algorithm the +more data you have the better it is this + + align:start position:0% +more data you have the better it is this + + + align:start position:0% +more data you have the better it is this +is kind of obvious and it's sort of + + align:start position:0% +is kind of obvious and it's sort of + + + align:start position:0% +is kind of obvious and it's sort of +obvious here as well if I only have four + + align:start position:0% +obvious here as well if I only have four + + + align:start position:0% +obvious here as well if I only have four +chords of in perometry my data is so + + align:start position:0% +chords of in perometry my data is so + + + align:start position:0% +chords of in perometry my data is so +sparse I'm gonna have a bad Al version + + align:start position:0% +sparse I'm gonna have a bad Al version + + + align:start position:0% +sparse I'm gonna have a bad Al version +and so you can have four chords + + align:start position:0% +and so you can have four chords + + + align:start position:0% +and so you can have four chords +of you could have your chords of + + align:start position:0% +of you could have your chords of + + + align:start position:0% +of you could have your chords of +infmetry crisscrossing the plasma like + + align:start position:0% +infmetry crisscrossing the plasma like + + + align:start position:0% +infmetry crisscrossing the plasma like +this or you could still have them + + align:start position:0% +this or you could still have them + + + align:start position:0% +this or you could still have them +crossing the plasma like this and even + + align:start position:0% +crossing the plasma like this and even + + + align:start position:0% +crossing the plasma like this and even +if your plasma was strongly shaped so if + + align:start position:0% +if your plasma was strongly shaped so if + + + align:start position:0% +if your plasma was strongly shaped so if +you know some + + align:start position:0% + + + + align:start position:0% + +classic single null low Expo type thing + + align:start position:0% +classic single null low Expo type thing + + + align:start position:0% +classic single null low Expo type thing +like this you could have your cords + + align:start position:0% +like this you could have your cords + + + align:start position:0% +like this you could have your cords +proing in this fashion and that would be + + align:start position:0% +proing in this fashion and that would be + + + align:start position:0% +proing in this fashion and that would be +good enough to get an invers to be able + + align:start position:0% +good enough to get an invers to be able + + + align:start position:0% +good enough to get an invers to be able +to do some sort of inversion in the + + align:start position:0% +to do some sort of inversion in the + + + align:start position:0% +to do some sort of inversion in the +middle here yeah and there's actually I + + align:start position:0% +middle here yeah and there's actually I + + + align:start position:0% +middle here yeah and there's actually I +think one of an White's students who's + + align:start position:0% +think one of an White's students who's + + + align:start position:0% +think one of an White's students who's +about to graduate has been working on + + align:start position:0% +about to graduate has been working on + + + align:start position:0% +about to graduate has been working on +this for X-rays and he came up with some + + align:start position:0% +this for X-rays and he came up with some + + + align:start position:0% +this for X-rays and he came up with some +cool ideas about like what if you have + + align:start position:0% +cool ideas about like what if you have + + + align:start position:0% +cool ideas about like what if you have +some sparse cords of uh data and then in + + align:start position:0% +some sparse cords of uh data and then in + + + align:start position:0% +some sparse cords of uh data and then in +some section here you have like really + + align:start position:0% +some section here you have like really + + + align:start position:0% +some section here you have like really +really fine cords can you combine those + + align:start position:0% +really fine cords can you combine those + + + align:start position:0% +really fine cords can you combine those +and measure like very small turbant + + align:start position:0% +and measure like very small turbant + + + align:start position:0% +and measure like very small turbant +fluctuations with this apparently is yes + + align:start position:0% +fluctuations with this apparently is yes + + + align:start position:0% +fluctuations with this apparently is yes +so there's lot of cool + + align:start position:0% +so there's lot of cool + + + align:start position:0% +so there's lot of cool +things + + align:start position:0% +things + + + align:start position:0% +things +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +commonly formation of Al or is it more + + align:start position:0% +commonly formation of Al or is it more + + + align:start position:0% +commonly formation of Al or is it more +common to do like mat where + + align:start position:0% +common to do like mat where + + + align:start position:0% +common to do like mat where +you the length of your sideline all of + + align:start position:0% +you the length of your sideline all of + + + align:start position:0% +you the length of your sideline all of +your like thins in space and then you + + align:start position:0% +your like thins in space and then you + + + align:start position:0% +your like thins in space and then you +can take the iners Matrix with some you + + align:start position:0% +can take the iners Matrix with some you + + + align:start position:0% +can take the iners Matrix with some you +know MTH + + align:start position:0% +know MTH + + + align:start position:0% +know MTH +massaging I I don't know what technique + + align:start position:0% +massaging I I don't know what technique + + + align:start position:0% +massaging I I don't know what technique +is more popular when when I've done this + + align:start position:0% +is more popular when when I've done this + + + align:start position:0% +is more popular when when I've done this +I tended to use uh fitting with sort of + + align:start position:0% +I tended to use uh fitting with sort of + + + align:start position:0% +I tended to use uh fitting with sort of +basis functions and then do the um AR + + align:start position:0% +basis functions and then do the um AR + + + align:start position:0% +basis functions and then do the um AR +inv version analytically to the fits of + + align:start position:0% +inv version analytically to the fits of + + + align:start position:0% +inv version analytically to the fits of +the basis function but I imagine there + + align:start position:0% +the basis function but I imagine there + + + align:start position:0% +the basis function but I imagine there +might be good reasons for doing like a + + align:start position:0% +might be good reasons for doing like a + + + align:start position:0% +might be good reasons for doing like a +matrix formation so especially if you're + + align:start position:0% +matrix formation so especially if you're + + + align:start position:0% +matrix formation so especially if you're +trying to use this for like real time + + align:start position:0% +trying to use this for like real time + + + align:start position:0% +trying to use this for like real time +control so on eer the bomet are going to + + align:start position:0% +control so on eer the bomet are going to + + + align:start position:0% +control so on eer the bomet are going to +be used for showing where the glowy pit + + align:start position:0% +be used for showing where the glowy pit + + + align:start position:0% +be used for showing where the glowy pit +of the plasma is and we want that to + + align:start position:0% +of the plasma is and we want that to + + + align:start position:0% +of the plasma is and we want that to +stay in the middle if it starts going + + align:start position:0% +stay in the middle if it starts going + + + align:start position:0% +stay in the middle if it starts going +somewhere else then you want to feedback + + align:start position:0% +somewhere else then you want to feedback + + + align:start position:0% +somewhere else then you want to feedback +on that and so then you need to do it + + align:start position:0% +on that and so then you need to do it + + + align:start position:0% +on that and so then you need to do it +quickly and so it's having some sort of + + align:start position:0% +quickly and so it's having some sort of + + + align:start position:0% +quickly and so it's having some sort of +Matrix technique would be beneficial + + align:start position:0% +Matrix technique would be beneficial + + + align:start position:0% +Matrix technique would be beneficial +compared to like oh I'll carefully chew + + align:start position:0% +compared to like oh I'll carefully chew + + + align:start position:0% +compared to like oh I'll carefully chew +my fitting functions you know you don't + + align:start position:0% +my fitting functions you know you don't + + + align:start position:0% +my fitting functions you know you don't +have time to + + align:start position:0% +have time to + + + align:start position:0% +have time to +do okay any questions + + align:start position:0% + + + + align:start position:0% + +online all right let's do some far are + + align:start position:0% +online all right let's do some far are + + + align:start position:0% +online all right let's do some far are +there ways of handling systems are there + + align:start position:0% +there ways of handling systems are there + + + align:start position:0% +there ways of handling systems are there +ways of Handling Systems that don't have + + align:start position:0% +ways of Handling Systems that don't have + + + align:start position:0% +ways of Handling Systems that don't have +like um I mean I guess you already + + align:start position:0% +like um I mean I guess you already + + + align:start position:0% +like um I mean I guess you already +talked about this but like are there are + + align:start position:0% +talked about this but like are there are + + + align:start position:0% +talked about this but like are there are +there ways of Handling Systems that like + + align:start position:0% +there ways of Handling Systems that like + + + align:start position:0% +there ways of Handling Systems that like +don't have any symmetry um priors if you + + align:start position:0% +don't have any symmetry um priors if you + + + align:start position:0% +don't have any symmetry um priors if you +yeah actually I have a gr student of + + align:start position:0% +yeah actually I have a gr student of + + + align:start position:0% +yeah actually I have a gr student of +mine who's been working on this recently + + align:start position:0% +mine who's been working on this recently + + + align:start position:0% +mine who's been working on this recently +for tomographic reconstruction so like + + align:start position:0% +for tomographic reconstruction so like + + + align:start position:0% +for tomographic reconstruction so like +you can always do a reconstruction but + + align:start position:0% +you can always do a reconstruction but + + + align:start position:0% +you can always do a reconstruction but +it's always poorly posed right I mean + + align:start position:0% +it's always poorly posed right I mean + + + align:start position:0% +it's always poorly posed right I mean +you you don't have enough information to + + align:start position:0% +you you don't have enough information to + + + align:start position:0% +you you don't have enough information to +fully + + align:start position:0% +fully + + + align:start position:0% +fully +reconstruct the dense signal points in + + align:start position:0% +reconstruct the dense signal points in + + + align:start position:0% +reconstruct the dense signal points in +space right but like if you have some + + align:start position:0% +space right but like if you have some + + + align:start position:0% +space right but like if you have some +priors you can make some guesses even + + align:start position:0% +priors you can make some guesses even + + + align:start position:0% +priors you can make some guesses even +with just a single line of sight right + + align:start position:0% +with just a single line of sight right + + + align:start position:0% +with just a single line of sight right +you can make some guesses and the more + + align:start position:0% +you can make some guesses and the more + + + align:start position:0% +you can make some guesses and the more +lines of sight you add the more you can + + align:start position:0% +lines of sight you add the more you can + + + align:start position:0% +lines of sight you add the more you can +constrain it and he was working on a + + align:start position:0% +constrain it and he was working on a + + + align:start position:0% +constrain it and he was working on a +technique uh which I can't remember the + + align:start position:0% +technique uh which I can't remember the + + + align:start position:0% +technique uh which I can't remember the +acronym is Art and I can't remember what + + align:start position:0% +acronym is Art and I can't remember what + + + align:start position:0% +acronym is Art and I can't remember what +it stands for um but with two orthogonal + + align:start position:0% +it stands for um but with two orthogonal + + + align:start position:0% +it stands for um but with two orthogonal +lines of sight and just a flat uniform + + align:start position:0% +lines of sight and just a flat uniform + + + align:start position:0% +lines of sight and just a flat uniform +prior so like no information about what + + align:start position:0% +prior so like no information about what + + + align:start position:0% +prior so like no information about what +it looks like to start with he was able + + align:start position:0% +it looks like to start with he was able + + + align:start position:0% +it looks like to start with he was able +to reconstruct some relatively + + align:start position:0% +to reconstruct some relatively + + + align:start position:0% +to reconstruct some relatively +complicated shapes out of this uh so you + + align:start position:0% +complicated shapes out of this uh so you + + + align:start position:0% +complicated shapes out of this uh so you +know there are there are some clever + + align:start position:0% +know there are there are some clever + + + align:start position:0% +know there are there are some clever +things that you can do and I think + + align:start position:0% +things that you can do and I think + + + align:start position:0% +things that you can do and I think +there's a lot of cool stuff that we can + + align:start position:0% +there's a lot of cool stuff that we can + + + align:start position:0% +there's a lot of cool stuff that we can +take in plas physics from other fields + + align:start position:0% +take in plas physics from other fields + + + align:start position:0% +take in plas physics from other fields +so a lot of stuff from computer vision + + align:start position:0% +so a lot of stuff from computer vision + + + align:start position:0% +so a lot of stuff from computer vision +from tomography from Medical Imaging uh + + align:start position:0% +from tomography from Medical Imaging uh + + + align:start position:0% +from tomography from Medical Imaging uh +which can be used for understanding this + + align:start position:0% +which can be used for understanding this + + + align:start position:0% +which can be used for understanding this +stuff and people do already so there's + + align:start position:0% +stuff and people do already so there's + + + align:start position:0% +stuff and people do already so there's +lots of uh nice things out there that + + align:start position:0% +lots of uh nice things out there that + + + align:start position:0% +lots of uh nice things out there that +you can do at the end of the day the + + align:start position:0% +you can do at the end of the day the + + + align:start position:0% +you can do at the end of the day the +more data you have the easier this sit + + align:start position:0% +more data you have the easier this sit + + + align:start position:0% +more data you have the easier this sit +right so if you have very little data + + align:start position:0% +right so if you have very little data + + + align:start position:0% +right so if you have very little data +you have to provide that information + + align:start position:0% +you have to provide that information + + + align:start position:0% +you have to provide that information +from somewhere else which is like your + + align:start position:0% +from somewhere else which is like your + + + align:start position:0% +from somewhere else which is like your +intuition your guesses about so you + + align:start position:0% +intuition your guesses about so you + + + align:start position:0% +intuition your guesses about so you +can't win you you can't get just get + + align:start position:0% +can't win you you can't get just get + + + align:start position:0% +can't win you you can't get just get +this information for + + align:start position:0% +this information for + + + align:start position:0% +this information for +free okay I'm GNA go on now so you have + + align:start position:0% +free okay I'm GNA go on now so you have + + + align:start position:0% +free okay I'm GNA go on now so you have +time to cover all of this + + align:start position:0% + + + + align:start position:0% + +we're going to be looking at farad + + align:start position:0% + + + + align:start position:0% + +rotation but we're actually just going + + align:start position:0% +rotation but we're actually just going + + + align:start position:0% +rotation but we're actually just going +to take a little Sid track for maybe + + align:start position:0% +to take a little Sid track for maybe + + + align:start position:0% +to take a little Sid track for maybe +most of the rest of this lecture to look + + align:start position:0% +most of the rest of this lecture to look + + + align:start position:0% +most of the rest of this lecture to look +again at waves in magnetized + + align:start position:0% +again at waves in magnetized + + + align:start position:0% +again at waves in magnetized +plas of which Faraday rotation is one + + align:start position:0% +plas of which Faraday rotation is one + + + align:start position:0% +plas of which Faraday rotation is one +the reason is although you hopefully + + align:start position:0% +the reason is although you hopefully + + + align:start position:0% +the reason is although you hopefully +have seen some of this in earlier plasma + + align:start position:0% +have seen some of this in earlier plasma + + + align:start position:0% +have seen some of this in earlier plasma +classes I think there are lots of + + align:start position:0% +classes I think there are lots of + + + align:start position:0% +classes I think there are lots of +different ways of looking it and I think + + align:start position:0% +different ways of looking it and I think + + + align:start position:0% +different ways of looking it and I think +the way that Hutchinson has and that + + align:start position:0% +the way that Hutchinson has and that + + + align:start position:0% +the way that Hutchinson has and that +I've adapted is quite a nice way of + + align:start position:0% +I've adapted is quite a nice way of + + + align:start position:0% +I've adapted is quite a nice way of +looking at it and we're also going to + + align:start position:0% +looking at it and we're also going to + + + align:start position:0% +looking at it and we're also going to +need lots of these results not only for + + align:start position:0% +need lots of these results not only for + + + align:start position:0% +need lots of these results not only for +farad rotation uh but also for + + align:start position:0% +farad rotation uh but also for + + + align:start position:0% +farad rotation uh but also for +reflectometry and electron C from + + align:start position:0% +reflectometry and electron C from + + + align:start position:0% +reflectometry and electron C from +emission so we need to know how waves + + align:start position:0% +emission so we need to know how waves + + + align:start position:0% +emission so we need to know how waves +propagate in a magnetized plasma and so + + align:start position:0% +propagate in a magnetized plasma and so + + + align:start position:0% +propagate in a magnetized plasma and so +we may as well just review this quickly + + align:start position:0% +we may as well just review this quickly + + + align:start position:0% +we may as well just review this quickly +so if you've seen this before and you're + + align:start position:0% +so if you've seen this before and you're + + + align:start position:0% +so if you've seen this before and you're +very confident you know feel free to + + align:start position:0% +very confident you know feel free to + + + align:start position:0% +very confident you know feel free to +relax and if you haven't seen it maybe + + align:start position:0% +relax and if you haven't seen it maybe + + + align:start position:0% +relax and if you haven't seen it maybe +pay attention Okay so remember we had + + align:start position:0% +pay attention Okay so remember we had + + + align:start position:0% +pay attention Okay so remember we had +before some assumptions that are plasma + + align:start position:0% +before some assumptions that are plasma + + + align:start position:0% +before some assumptions that are plasma +was cold and we Quantified that by + + align:start position:0% +was cold and we Quantified that by + + + align:start position:0% +was cold and we Quantified that by +saying that the thermal velocity of the + + align:start position:0% +saying that the thermal velocity of the + + + align:start position:0% +saying that the thermal velocity of the +electrons is much less than the speed + + align:start position:0% +electrons is much less than the speed + + + align:start position:0% +electrons is much less than the speed +right um we said that our frequency was + + align:start position:0% +right um we said that our frequency was + + + align:start position:0% +right um we said that our frequency was +high and we Quantified that by saying + + align:start position:0% +high and we Quantified that by saying + + + align:start position:0% +high and we Quantified that by saying +that our ion plasma frequency was much + + align:start position:0% +that our ion plasma frequency was much + + + align:start position:0% +that our ion plasma frequency was much +less than the um + + align:start position:0% +less than the um + + + align:start position:0% +less than the um +uh frequency of the waves of ascending + + align:start position:0% +uh frequency of the waves of ascending + + + align:start position:0% +uh frequency of the waves of ascending +through the plasma and that meant the + + align:start position:0% +through the plasma and that meant the + + + align:start position:0% +through the plasma and that meant the +ions effectively stationary so we can + + align:start position:0% +ions effectively stationary so we can + + + align:start position:0% +ions effectively stationary so we can +just neglect them and just deal with the + + align:start position:0% +just neglect them and just deal with the + + + align:start position:0% +just neglect them and just deal with the +electrons that made life much um easier + + align:start position:0% +electrons that made life much um easier + + + align:start position:0% +electrons that made life much um easier +and we also made this following + + align:start position:0% +and we also made this following + + + align:start position:0% +and we also made this following +restriction that K do + + align:start position:0% +restriction that K do + + + align:start position:0% +restriction that K do +e was equal to zero and this was the + + align:start position:0% +e was equal to zero and this was the + + + align:start position:0% +e was equal to zero and this was the +Restriction that the waves were + + align:start position:0% + + + + align:start position:0% + +transverse now this restriction the + + align:start position:0% +transverse now this restriction the + + + align:start position:0% +transverse now this restriction the +final one the transverse waves made our + + align:start position:0% +final one the transverse waves made our + + + align:start position:0% +final one the transverse waves made our +life very simple algebraically + + align:start position:0% +life very simple algebraically + + + align:start position:0% +life very simple algebraically +but it turns out that if you try and + + align:start position:0% +but it turns out that if you try and + + + align:start position:0% +but it turns out that if you try and +find the waves in a magnetized plasma + + align:start position:0% +find the waves in a magnetized plasma + + + align:start position:0% +find the waves in a magnetized plasma +while keeping this restriction you don't + + align:start position:0% +while keeping this restriction you don't + + + align:start position:0% +while keeping this restriction you don't +get all of the Waves you in fact have + + align:start position:0% +get all of the Waves you in fact have + + + align:start position:0% +get all of the Waves you in fact have +explicitly ruled out one of the most + + align:start position:0% +explicitly ruled out one of the most + + + align:start position:0% +explicitly ruled out one of the most +important waves the extraordinary mode + + align:start position:0% +important waves the extraordinary mode + + + align:start position:0% +important waves the extraordinary mode +which is extraordinarily useful and so + + align:start position:0% +which is extraordinarily useful and so + + + align:start position:0% +which is extraordinarily useful and so +we have to drop this restriction here + + align:start position:0% +we have to drop this restriction here + + + align:start position:0% +we have to drop this restriction here +and then deal with all the horrible + + align:start position:0% +and then deal with all the horrible + + + align:start position:0% +and then deal with all the horrible +consequences of that right so now we + + align:start position:0% +consequences of that right so now we + + + align:start position:0% +consequences of that right so now we +have k. + + align:start position:0% + + + + align:start position:0% + +e not equal to zero and if you go back + + align:start position:0% +e not equal to zero and if you go back + + + align:start position:0% +e not equal to zero and if you go back +and you look through the derivation and + + align:start position:0% +and you look through the derivation and + + + align:start position:0% +and you look through the derivation and +you start rederiving bits you end up + + align:start position:0% +you start rederiving bits you end up + + + align:start position:0% +you start rederiving bits you end up +with an equation now that looks like + + align:start position:0% +with an equation now that looks like + + + align:start position:0% +with an equation now that looks like +Omega 2 minus + + align:start position:0% +Omega 2 minus + + + align:start position:0% +Omega 2 minus +c² k + + align:start position:0% +c² k + + + align:start position:0% +c² k +s we had something like this before but + + align:start position:0% +s we had something like this before but + + + align:start position:0% +s we had something like this before but +our equation previously was a scalar + + align:start position:0% +our equation previously was a scalar + + + align:start position:0% +our equation previously was a scalar +equation our equation now is going to + + align:start position:0% +equation our equation now is going to + + + align:start position:0% +equation our equation now is going to +be a matrix equation with these 3x3 + + align:start position:0% +be a matrix equation with these 3x3 + + + align:start position:0% +be a matrix equation with these 3x3 +matrices and this is just the identity + + align:start position:0% + + + + align:start position:0% + +Matrix and this is my + + align:start position:0% +Matrix and this is my + + + align:start position:0% +Matrix and this is my +an even more odd looking object which is + + align:start position:0% +an even more odd looking object which is + + + align:start position:0% +an even more odd looking object which is +KK which is a diad which is also a 3X3 + + align:start position:0% +KK which is a diad which is also a 3X3 + + + align:start position:0% +KK which is a diad which is also a 3X3 +Matrix here um you can look up more of + + align:start position:0% +Matrix here um you can look up more of + + + align:start position:0% +Matrix here um you can look up more of +the details of this and + + align:start position:0% + + + + align:start position:0% + +how all of this is now dotted with the + + align:start position:0% +how all of this is now dotted with the + + + align:start position:0% +how all of this is now dotted with the +electric field and that is equal to + + align:start position:0% +electric field and that is equal to + + + align:start position:0% +electric field and that is equal to +minus I Omega + + align:start position:0% +minus I Omega + + + align:start position:0% +minus I Omega +J over + + align:start position:0% +J over + + + align:start position:0% +J over +epon now once again we realized that + + align:start position:0% +epon now once again we realized that + + + align:start position:0% +epon now once again we realized that +is equal to minus e + + align:start position:0% +is equal to minus e + + + align:start position:0% +is equal to minus e +ne and what we want to try and do is + + align:start position:0% +ne and what we want to try and do is + + + align:start position:0% +ne and what we want to try and do is +write this entire equation in terms of e + + align:start position:0% +write this entire equation in terms of e + + + align:start position:0% +write this entire equation in terms of e +we want to get rid of J completely and + + align:start position:0% +we want to get rid of J completely and + + + align:start position:0% +we want to get rid of J completely and +then of course this is an equation that + + align:start position:0% +then of course this is an equation that + + + align:start position:0% +then of course this is an equation that +looks like a matrix times a vector zero + + align:start position:0% +looks like a matrix times a vector zero + + + align:start position:0% +looks like a matrix times a vector zero +and we know how to do this it's what we + + align:start position:0% +and we know how to do this it's what we + + + align:start position:0% +and we know how to do this it's what we +trained our whole lives for we take the + + align:start position:0% +trained our whole lives for we take the + + + align:start position:0% +trained our whole lives for we take the +determinant of this find the mode + + align:start position:0% +determinant of this find the mode + + + align:start position:0% +determinant of this find the mode +of That's great so right we really love + + align:start position:0% +of That's great so right we really love + + + align:start position:0% +of That's great so right we really love +these sorts of equations and so we're + + align:start position:0% +these sorts of equations and so we're + + + align:start position:0% +these sorts of equations and so we're +trying to make this equation look like + + align:start position:0% +trying to make this equation look like + + + align:start position:0% +trying to make this equation look like +one of those + + align:start position:0% +one of those + + + align:start position:0% +one of those +so now we need an equation of motion for + + align:start position:0% +so now we need an equation of motion for + + + align:start position:0% +so now we need an equation of motion for +the previously remember we just looked + + align:start position:0% +the previously remember we just looked + + + align:start position:0% +the previously remember we just looked +at the response of the electrons to the + + align:start position:0% +at the response of the electrons to the + + + align:start position:0% +at the response of the electrons to the +electric field but now we want to have a + + align:start position:0% +electric field but now we want to have a + + + align:start position:0% +electric field but now we want to have a +magnetic field as well so we have me d v + + align:start position:0% +magnetic field as well so we have me d v + + + align:start position:0% +magnetic field as well so we have me d v +DT is equal to minus E + + align:start position:0% +DT is equal to minus E + + + align:start position:0% +DT is equal to minus E +* the electric field plus b cross B so + + align:start position:0% +* the electric field plus b cross B so + + + align:start position:0% +* the electric field plus b cross B so +this is just the Loren's Force but we've + + align:start position:0% +this is just the Loren's Force but we've + + + align:start position:0% +this is just the Loren's Force but we've +now got the magnetic field here and + + align:start position:0% +now got the magnetic field here and + + + align:start position:0% +now got the magnetic field here and +we're going to assume that our magnetic + + align:start position:0% +we're going to assume that our magnetic + + + align:start position:0% +we're going to assume that our magnetic +field at least the first order is just + + align:start position:0% +field at least the first order is just + + + align:start position:0% +field at least the first order is just +some static field and we're going to + + align:start position:0% +some static field and we're going to + + + align:start position:0% +some static field and we're going to +point it in the Z direction of course I + + align:start position:0% +point it in the Z direction of course I + + + align:start position:0% +point it in the Z direction of course I +can point in any direction want I've + + align:start position:0% +can point in any direction want I've + + + align:start position:0% +can point in any direction want I've +chosen set in this case + + align:start position:0% +chosen set in this case + + + align:start position:0% +chosen set in this case +here and then from this you get out a + + align:start position:0% +here and then from this you get out a + + + align:start position:0% +here and then from this you get out a +series of equations for the velocity and + + align:start position:0% +series of equations for the velocity and + + + align:start position:0% +series of equations for the velocity and +I think you've all seen this so I'm + + align:start position:0% +I think you've all seen this so I'm + + + align:start position:0% +I think you've all seen this so I'm +actually not going to go through this + + align:start position:0% +actually not going to go through this + + + align:start position:0% +actually not going to go through this +line by + + align:start position:0% +line by + + + align:start position:0% +line by +line + + align:start position:0% +line + + + align:start position:0% +line +um well I might go through okay + + align:start position:0% +um well I might go through okay + + + align:start position:0% +um well I might go through okay +I'm not going to write uh this equation + + align:start position:0% +I'm not going to write uh this equation + + + align:start position:0% +I'm not going to write uh this equation +out in terms of its Vector components + + align:start position:0% +out in terms of its Vector components + + + align:start position:0% +out in terms of its Vector components +like I had in the notes I will make the + + align:start position:0% +like I had in the notes I will make the + + + align:start position:0% +like I had in the notes I will make the +point that as before we're going to say + + align:start position:0% +point that as before we're going to say + + + align:start position:0% +point that as before we're going to say +that we're going to assume that V equals + + align:start position:0% +that we're going to assume that V equals + + + align:start position:0% +that we're going to assume that V equals +v0 exponential of + + align:start position:0% +v0 exponential of + + + align:start position:0% +v0 exponential of +i k do + + align:start position:0% +i k do + + + align:start position:0% +i k do +xus Omega T and that allows us to + + align:start position:0% +xus Omega T and that allows us to + + + align:start position:0% +xus Omega T and that allows us to +replace D + + align:start position:0% +replace D + + + align:start position:0% +replace D +DT with minus I Omega like that so + + align:start position:0% +DT with minus I Omega like that so + + + align:start position:0% +DT with minus I Omega like that so +returns this differential equation into + + align:start position:0% +returns this differential equation into + + + align:start position:0% +returns this differential equation into +an and then we find that the + + align:start position:0% +an and then we find that the + + + align:start position:0% +an and then we find that the +velocity of our single electron here is + + align:start position:0% +velocity of our single electron here is + + + align:start position:0% +velocity of our single electron here is +going to have a structure with some nice + + align:start position:0% +going to have a structure with some nice + + + align:start position:0% +going to have a structure with some nice +symmetry due to the magnetic field so VX + + align:start position:0% +symmetry due to the magnetic field so VX + + + align:start position:0% +symmetry due to the magnetic field so VX +and v y are going to look very similar + + align:start position:0% +and v y are going to look very similar + + + align:start position:0% +and v y are going to look very similar +they're going to look likeus i e over + + align:start position:0% +they're going to look likeus i e over + + + align:start position:0% +they're going to look likeus i e over +Omega e Time 1 over + + align:start position:0% +Omega e Time 1 over + + + align:start position:0% +Omega e Time 1 over +1us Omega 2 over Omega s doesn't work so + + align:start position:0% +1us Omega 2 over Omega s doesn't work so + + + align:start position:0% +1us Omega 2 over Omega s doesn't work so +when I said that's capital Omega lowas + + align:start position:0% +when I said that's capital Omega lowas + + + align:start position:0% +when I said that's capital Omega lowas +Omega and this is going to be equal + + align:start position:0% +Omega and this is going to be equal + + + align:start position:0% +Omega and this is going to be equal +to the electric field in the X Direction + + align:start position:0% +to the electric field in the X Direction + + + align:start position:0% +to the electric field in the X Direction +minus I Capital Omega over lowercase + + align:start position:0% +minus I Capital Omega over lowercase + + + align:start position:0% +minus I Capital Omega over lowercase +Omega electric field in the y direction + + align:start position:0% +Omega electric field in the y direction + + + align:start position:0% +Omega electric field in the y direction +where we've defined + + align:start position:0% +where we've defined + + + align:start position:0% +where we've defined +here Omega + + align:start position:0% +here Omega + + + align:start position:0% +here Omega +toyy + + align:start position:0% + + + + align:start position:0% + +e for VY we + + align:start position:0% +e for VY we + + + align:start position:0% +e for VY we +have all of these terms + + align:start position:0% +have all of these terms + + + align:start position:0% +have all of these terms +again but in the bracket we have + + align:start position:0% +again but in the bracket we have + + + align:start position:0% +again but in the bracket we have +something that look similar but slightly + + align:start position:0% +something that look similar but slightly + + + align:start position:0% +something that look similar but slightly +different I Capal Omega + + align:start position:0% + + + + align:start position:0% + +Omega when you look at this and you + + align:start position:0% +Omega when you look at this and you + + + align:start position:0% +Omega when you look at this and you +squint you calate BX S Plus b y^ 2 you + + align:start position:0% +squint you calate BX S Plus b y^ 2 you + + + align:start position:0% +squint you calate BX S Plus b y^ 2 you +find out that this is just when you when + + align:start position:0% +find out that this is just when you when + + + align:start position:0% +find out that this is just when you when +you just look at how these work this is + + align:start position:0% +you just look at how these work this is + + + align:start position:0% +you just look at how these work this is +of course are particles circulating + + align:start position:0% +of course are particles circulating + + + align:start position:0% +of course are particles circulating +around the magnetic field line remember + + align:start position:0% +around the magnetic field line remember + + + align:start position:0% +around the magnetic field line remember +the field line going in the direction + + align:start position:0% +the field line going in the direction + + + align:start position:0% +the field line going in the direction +these two components are just the + + align:start position:0% +these two components are just the + + + align:start position:0% +these two components are just the +spiraling VX and V here finally we have + + align:start position:0% +spiraling VX and V here finally we have + + + align:start position:0% +spiraling VX and V here finally we have +the Z + + align:start position:0% +the Z + + + align:start position:0% +the Z +components and that's very simple that's + + align:start position:0% +components and that's very simple that's + + + align:start position:0% +components and that's very simple that's +minus I over + + align:start position:0% + + + + align:start position:0% + +Omega okay you've seen all this before + + align:start position:0% +Omega okay you've seen all this before + + + align:start position:0% +Omega okay you've seen all this before +you can then take this make it into a + + align:start position:0% +you can then take this make it into a + + + align:start position:0% +you can then take this make it into a +nice vector substitute it back into this + + align:start position:0% +nice vector substitute it back into this + + + align:start position:0% +nice vector substitute it back into this +equation for J substitute J back into + + align:start position:0% +equation for J substitute J back into + + + align:start position:0% +equation for J substitute J back into +here and you see very quickly that all + + align:start position:0% +here and you see very quickly that all + + + align:start position:0% +here and you see very quickly that all +you're going to have left of things like + + align:start position:0% +you're going to have left of things like + + + align:start position:0% +you're going to have left of things like +omegas C's and K's and capital omegas + + align:start position:0% +omegas C's and K's and capital omegas + + + align:start position:0% +omegas C's and K's and capital omegas +and this electric field so we're going + + align:start position:0% +and this electric field so we're going + + + align:start position:0% +and this electric field so we're going +to have sub Matrix equation E is + + align:start position:0% + + + + align:start position:0% + +equal and that Matrix well we can + + align:start position:0% +equal and that Matrix well we can + + + align:start position:0% +equal and that Matrix well we can +write J is equal to minus e n + + align:start position:0% +write J is equal to minus e n + + + align:start position:0% +write J is equal to minus e n +e time the velocity and we can write + + align:start position:0% +e time the velocity and we can write + + + align:start position:0% +e time the velocity and we can write +that in terms of some sort of + + align:start position:0% +that in terms of some sort of + + + align:start position:0% +that in terms of some sort of +conductivity tens times the electric + + align:start position:0% +conductivity tens times the electric + + + align:start position:0% +conductivity tens times the electric +field where that + + align:start position:0% +field where that + + + align:start position:0% +field where that +conductivity is this monster I ne + + align:start position:0% +conductivity is this monster I ne + + + align:start position:0% +conductivity is this monster I ne +e over NE + + align:start position:0% +e over NE + + + align:start position:0% +e over NE +Omega + + align:start position:0% +Omega + + + align:start position:0% +Omega +1 1us Omega lowas + + align:start position:0% +1 1us Omega lowas + + + align:start position:0% +1 1us Omega lowas +Omega by being + + align:start position:0% +Omega by being + + + align:start position:0% +Omega by being +Matrix got few ones down the diagonal + + align:start position:0% + + + + align:start position:0% + +here on these two off diang elements + + align:start position:0% +here on these two off diang elements + + + align:start position:0% +here on these two off diang elements +then + + align:start position:0% +then + + + align:start position:0% +then +Zer if you're surprised that seeing + + align:start position:0% +Zer if you're surprised that seeing + + + align:start position:0% +Zer if you're surprised that seeing +something interesting involving the + + align:start position:0% +something interesting involving the + + + align:start position:0% +something interesting involving the +magnetic field show up in the z z + + align:start position:0% +magnetic field show up in the z z + + + align:start position:0% +magnetic field show up in the z z +component this tensor it's literally + + align:start position:0% +component this tensor it's literally + + + align:start position:0% +component this tensor it's literally +only there to cancel it out here so in + + align:start position:0% +only there to cancel it out here so in + + + align:start position:0% +only there to cancel it out here so in +fact it doesn't exist at all it's just + + align:start position:0% +fact it doesn't exist at all it's just + + + align:start position:0% +fact it doesn't exist at all it's just +it's more convenient writing this Factor + + align:start position:0% +it's more convenient writing this Factor + + + align:start position:0% +it's more convenient writing this Factor +underneath four of these CS so you know + + align:start position:0% +underneath four of these CS so you know + + + align:start position:0% +underneath four of these CS so you know +this is just + + align:start position:0% +this is just + + + align:start position:0% +this is just +a so this is the + + align:start position:0% + + + + align:start position:0% + +condu which means we can then write out + + align:start position:0% +condu which means we can then write out + + + align:start position:0% +condu which means we can then write out +in short form that Omega squ + + align:start position:0% +in short form that Omega squ + + + align:start position:0% +in short form that Omega squ +C + + align:start position:0% +C + + + align:start position:0% +C +k^ identity + + align:start position:0% +k^ identity + + + align:start position:0% +k^ identity +Matrix minus this + + align:start position:0% +Matrix minus this + + + align:start position:0% +Matrix minus this +D + + align:start position:0% +D + + + align:start position:0% +D +A plus I Omega + + align:start position:0% +A plus I Omega + + + align:start position:0% +A plus I Omega +epon + + align:start position:0% + + + + align:start position:0% + +Sigma and I like writing things in terms + + align:start position:0% +Sigma and I like writing things in terms + + + align:start position:0% +Sigma and I like writing things in terms +of this conductivity term but if you + + align:start position:0% +of this conductivity term but if you + + + align:start position:0% +of this conductivity term but if you +like things in terms of e I'm sorry in + + align:start position:0% +like things in terms of e I'm sorry in + + + align:start position:0% +like things in terms of e I'm sorry in +terms of Epsilon the dialectric + + align:start position:0% +terms of Epsilon the dialectric + + + align:start position:0% +terms of Epsilon the dialectric +tensor you can rewrite this and you'll + + align:start position:0% +tensor you can rewrite this and you'll + + + align:start position:0% +tensor you can rewrite this and you'll +get hutson's equation + + align:start position:0% +get hutson's equation + + + align:start position:0% +get hutson's equation +4.1.2 one + + align:start position:0% +4.1.2 one + + + align:start position:0% +4.1.2 one +okay so the magnetic field in this + + align:start position:0% +okay so the magnetic field in this + + + align:start position:0% +okay so the magnetic field in this +system breaks the Symmetry right so we + + align:start position:0% +system breaks the Symmetry right so we + + + align:start position:0% +system breaks the Symmetry right so we +have to treat Z differently from VX and + + align:start position:0% +have to treat Z differently from VX and + + + align:start position:0% +have to treat Z differently from VX and +Vy but we don't have to treat VX and v y + + align:start position:0% +Vy but we don't have to treat VX and v y + + + align:start position:0% +Vy but we don't have to treat VX and v y +the same we can pick our orientation of + + align:start position:0% +the same we can pick our orientation of + + + align:start position:0% +the same we can pick our orientation of +X and Y AIS to make our life simple in + + align:start position:0% +X and Y AIS to make our life simple in + + + align:start position:0% +X and Y AIS to make our life simple in +what's going to follow and we're going + + align:start position:0% +what's going to follow and we're going + + + align:start position:0% +what's going to follow and we're going +to do that + + align:start position:0% +to do that + + + align:start position:0% +to do that +now just go space here + + align:start position:0% + + + + align:start position:0% + +so we're going to have a coordinate + + align:start position:0% +so we're going to have a coordinate + + + align:start position:0% +so we're going to have a coordinate +system like this with zed pointing + + align:start position:0% +system like this with zed pointing + + + align:start position:0% +system like this with zed pointing +upwards and that's the direction of the + + align:start position:0% +upwards and that's the direction of the + + + align:start position:0% +upwards and that's the direction of the +magnetic field we're going to have this + + align:start position:0% +magnetic field we're going to have this + + + align:start position:0% +magnetic field we're going to have this +coordinate Y and a + + align:start position:0% +coordinate Y and a + + + align:start position:0% +coordinate Y and a +coordinate X like this and I'm going to + + align:start position:0% +coordinate X like this and I'm going to + + + align:start position:0% +coordinate X like this and I'm going to +choose our K + + align:start position:0% +choose our K + + + align:start position:0% +choose our K +Vector to always be in the Y Z plane + + align:start position:0% +Vector to always be in the Y Z plane + + + align:start position:0% +Vector to always be in the Y Z plane +with some angle of theta to The Zed AIS + + align:start position:0% +with some angle of theta to The Zed AIS + + + align:start position:0% +with some angle of theta to The Zed AIS +here so effectively choosing our + + align:start position:0% +here so effectively choosing our + + + align:start position:0% +here so effectively choosing our +coordinate system such that we can write + + align:start position:0% +coordinate system such that we can write + + + align:start position:0% +coordinate system such that we can write +K is equal to the size of the vector k + + align:start position:0% +K is equal to the size of the vector k + + + align:start position:0% +K is equal to the size of the vector k +times + + align:start position:0% +times + + + align:start position:0% +times +Z sin + + align:start position:0% +Z sin + + + align:start position:0% +Z sin +Theta cosine + + align:start position:0% +Theta cosine + + + align:start position:0% +Theta cosine +Theta this makes our life much much + + align:start position:0% +Theta this makes our life much much + + + align:start position:0% +Theta this makes our life much much +easier in more follows but even if you + + align:start position:0% +easier in more follows but even if you + + + align:start position:0% +easier in more follows but even if you +do that when you go to solve this + + align:start position:0% +do that when you go to solve this + + + align:start position:0% +do that when you go to solve this +equation in full generality with all + + align:start position:0% +equation in full generality with all + + + align:start position:0% +equation in full generality with all +these signs and cosiness it's an ungodly + + align:start position:0% +these signs and cosiness it's an ungodly + + + align:start position:0% +these signs and cosiness it's an ungodly +mess right so this is absolutely + + align:start position:0% +mess right so this is absolutely + + + align:start position:0% +mess right so this is absolutely +horrible so you still get something + + align:start position:0% +horrible so you still get something + + + align:start position:0% +horrible so you still get something +terrible which is equation + + align:start position:0% +terrible which is equation + + + align:start position:0% +terrible which is equation +4.1.2 for which I think is called the + + align:start position:0% +4.1.2 for which I think is called the + + + align:start position:0% +4.1.2 for which I think is called the +Appleton partry dispersion relationship + + align:start position:0% +Appleton partry dispersion relationship + + + align:start position:0% +Appleton partry dispersion relationship +and it's a mess right so it's very very + + align:start position:0% +and it's a mess right so it's very very + + + align:start position:0% +and it's a mess right so it's very very +hard to work with and this trick is that + + align:start position:0% +hard to work with and this trick is that + + + align:start position:0% +hard to work with and this trick is that +no one actually works with it most of + + align:start position:0% +no one actually works with it most of + + + align:start position:0% +no one actually works with it most of +the time we just work in the case where + + align:start position:0% +the time we just work in the case where + + + align:start position:0% +the time we just work in the case where +we + + align:start position:0% +we + + + align:start position:0% +we +have Theta equal to zero or Theta equ Al + + align:start position:0% +have Theta equal to zero or Theta equ Al + + + align:start position:0% +have Theta equal to zero or Theta equ Al +to Pi two so those are the two cases + + align:start position:0% +to Pi two so those are the two cases + + + align:start position:0% +to Pi two so those are the two cases +that I'm going to tell you about when + + align:start position:0% +that I'm going to tell you about when + + + align:start position:0% +that I'm going to tell you about when +we've got waves propagating along the + + align:start position:0% +we've got waves propagating along the + + + align:start position:0% +we've got waves propagating along the +magnetic field or perpendicular to the + + align:start position:0% +magnetic field or perpendicular to the + + + align:start position:0% +magnetic field or perpendicular to the +magnetic field if you ever in the + + align:start position:0% +magnetic field if you ever in the + + + align:start position:0% +magnetic field if you ever in the +unfortunate case of having to do + + align:start position:0% +unfortunate case of having to do + + + align:start position:0% +unfortunate case of having to do +something between you'll have to go back + + align:start position:0% +something between you'll have to go back + + + align:start position:0% +something between you'll have to go back +to this equation and work it out + + align:start position:0% +to this equation and work it out + + + align:start position:0% +to this equation and work it out +yourself but at least in the limiting + + align:start position:0% +yourself but at least in the limiting + + + align:start position:0% +yourself but at least in the limiting +cases the behavior is slightly easier to + + align:start position:0% +cases the behavior is slightly easier to + + + align:start position:0% +cases the behavior is slightly easier to +understand so those are the cases that + + align:start position:0% +understand so those are the cases that + + + align:start position:0% +understand so those are the cases that +I'm going to go through now so that was + + align:start position:0% +I'm going to go through now so that was + + + align:start position:0% +I'm going to go through now so that was +a bit of a wish stop tour any questions + + align:start position:0% + + + + align:start position:0% + +good everyone loves waves + + align:start position:0% + + + + align:start position:0% + +so we're going to start with + + align:start position:0% +so we're going to start with + + + align:start position:0% +so we're going to start with +the beta equals zero + + align:start position:0% + + + + align:start position:0% + +that so this case is maybe particularly + + align:start position:0% +that so this case is maybe particularly + + + align:start position:0% +that so this case is maybe particularly +relevant if you're trying to diagnose + + align:start position:0% +relevant if you're trying to diagnose + + + align:start position:0% +relevant if you're trying to diagnose +something like poac which many of you + + align:start position:0% +something like poac which many of you + + + align:start position:0% +something like poac which many of you +are if we draw our poac looking from + + align:start position:0% +are if we draw our poac looking from + + + align:start position:0% +are if we draw our poac looking from +above we have magnetic field lines going + + align:start position:0% +above we have magnetic field lines going + + + align:start position:0% +above we have magnetic field lines going +around like this and remember the thidal + + align:start position:0% +around like this and remember the thidal + + + align:start position:0% +around like this and remember the thidal +magnetic field on the top m is very + + align:start position:0% +magnetic field on the top m is very + + + align:start position:0% +magnetic field on the top m is very +strong and so really although the + + align:start position:0% +strong and so really although the + + + align:start position:0% +strong and so really although the +magnetic field lines are slightly not + + align:start position:0% +magnetic field lines are slightly not + + + align:start position:0% +magnetic field lines are slightly not +like this they really are very much just + + align:start position:0% +like this they really are very much just + + + align:start position:0% +like this they really are very much just +circles around the top and where do we + + align:start position:0% +circles around the top and where do we + + + align:start position:0% +circles around the top and where do we +put our Diagnostics well we can't put + + align:start position:0% +put our Diagnostics well we can't put + + + align:start position:0% +put our Diagnostics well we can't put +them on the inside usually um we don't + + align:start position:0% +them on the inside usually um we don't + + + align:start position:0% +them on the inside usually um we don't +want to put them at some weird line of + + align:start position:0% +want to put them at some weird line of + + + align:start position:0% +want to put them at some weird line of +sight like this because that would be + + align:start position:0% +sight like this because that would be + + + align:start position:0% +sight like this because that would be +integrating through things where we're + + align:start position:0% +integrating through things where we're + + + align:start position:0% +integrating through things where we're +not really sure about the + + align:start position:0% +not really sure about the + + + align:start position:0% +not really sure about the +Symmetry we're very likely to put our + + align:start position:0% +Symmetry we're very likely to put our + + + align:start position:0% +Symmetry we're very likely to put our +Diagnostics like this on a line of s + + align:start position:0% +Diagnostics like this on a line of s + + + align:start position:0% +Diagnostics like this on a line of s +which is indeed perpendicular at 90 + + align:start position:0% +which is indeed perpendicular at 90 + + + align:start position:0% +which is indeed perpendicular at 90 +degrees the local magnetic field that + + align:start position:0% +degrees the local magnetic field that + + + align:start position:0% +degrees the local magnetic field that +might be because you've got to fit + + align:start position:0% +might be because you've got to fit + + + align:start position:0% +might be because you've got to fit +through some gaps between the magnets or + + align:start position:0% +through some gaps between the magnets or + + + align:start position:0% +through some gaps between the magnets or +simply because it's very easy and almost + + align:start position:0% +simply because it's very easy and almost + + + align:start position:0% +simply because it's very easy and almost +every toac I've seen has diagnostic + + align:start position:0% +every toac I've seen has diagnostic + + + align:start position:0% +every toac I've seen has diagnostic +design look on this line of sight if you + + align:start position:0% +design look on this line of sight if you + + + align:start position:0% +design look on this line of sight if you +have something you'll looked at a weird + + align:start position:0% +have something you'll looked at a weird + + + align:start position:0% +have something you'll looked at a weird +angle that's very unusual so it's very + + align:start position:0% +angle that's very unusual so it's very + + + align:start position:0% +angle that's very unusual so it's very +relevant to ask how the waves propagate + + align:start position:0% +relevant to ask how the waves propagate + + + align:start position:0% +relevant to ask how the waves propagate +in a magnetized plasma like a toac + + align:start position:0% +in a magnetized plasma like a toac + + + align:start position:0% +in a magnetized plasma like a toac +perpendicular to the magnetic field and + + align:start position:0% +perpendicular to the magnetic field and + + + align:start position:0% +perpendicular to the magnetic field and +what you get are two different modes + + align:start position:0% +what you get are two different modes + + + align:start position:0% +what you get are two different modes +here we have one mode where the + + align:start position:0% +here we have one mode where the + + + align:start position:0% +here we have one mode where the +dispersion relationship is very familiar + + align:start position:0% +dispersion relationship is very familiar + + + align:start position:0% +dispersion relationship is very familiar +n² is equal to + + align:start position:0% +n² is equal to + + + align:start position:0% +n² is equal to +1us Omega p^ + + align:start position:0% +1us Omega p^ + + + align:start position:0% +1us Omega p^ +2 upon + + align:start position:0% +2 upon + + + align:start position:0% +2 upon +ceg s + + align:start position:0% + + + + align:start position:0% + +so this is just the wave that we found + + align:start position:0% +so this is just the wave that we found + + + align:start position:0% +so this is just the wave that we found +in unmagnetized plasmas what's + + align:start position:0% +in unmagnetized plasmas what's + + + align:start position:0% +in unmagnetized plasmas what's +interesting is that although we've done + + align:start position:0% +interesting is that although we've done + + + align:start position:0% +interesting is that although we've done +all of that mathematics there is one + + align:start position:0% +all of that mathematics there is one + + + align:start position:0% +all of that mathematics there is one +wave which propagates perpendicular + + align:start position:0% +wave which propagates perpendicular + + + align:start position:0% +wave which propagates perpendicular +magnetic field which looks like the + + align:start position:0% +magnetic field which looks like the + + + align:start position:0% +magnetic field which looks like the +magnetic field doesn't matter at all and + + align:start position:0% +magnetic field doesn't matter at all and + + + align:start position:0% +magnetic field doesn't matter at all and +so we call this wave the O + + align:start position:0% +so we call this wave the O + + + align:start position:0% +so we call this wave the O +mode where o stands + + align:start position:0% + + + + align:start position:0% + +for all right so in the ordinary mode + + align:start position:0% +for all right so in the ordinary mode + + + align:start position:0% +for all right so in the ordinary mode +remember we can then go back this is our + + align:start position:0% +remember we can then go back this is our + + + align:start position:0% +remember we can then go back this is our +igen value we can work out what the igen + + align:start position:0% +igen value we can work out what the igen + + + align:start position:0% +igen value we can work out what the igen +mode is in terms of EX and ey and e z + + align:start position:0% +mode is in terms of EX and ey and e z + + + align:start position:0% +mode is in terms of EX and ey and e z +and we find that ex is equal to e is + + align:start position:0% +and we find that ex is equal to e is + + + align:start position:0% +and we find that ex is equal to e is +equal to zero here and so all of our + + align:start position:0% +equal to zero here and so all of our + + + align:start position:0% +equal to zero here and so all of our +electric field is in the Z Direction + + align:start position:0% +electric field is in the Z Direction + + + align:start position:0% +electric field is in the Z Direction +just remember we have this diagram where + + align:start position:0% +just remember we have this diagram where + + + align:start position:0% +just remember we have this diagram where +we have Z like + + align:start position:0% +we have Z like + + + align:start position:0% +we have Z like +this y like this and X like this + + align:start position:0% +this y like this and X like this + + + align:start position:0% +this y like this and X like this +I've restricted my K Vector to be in the + + align:start position:0% +I've restricted my K Vector to be in the + + + align:start position:0% +I've restricted my K Vector to be in the +y z plane I now set Theta Pi 2 and so + + align:start position:0% +y z plane I now set Theta Pi 2 and so + + + align:start position:0% +y z plane I now set Theta Pi 2 and so +therefore K is pointing in this + + align:start position:0% +therefore K is pointing in this + + + align:start position:0% +therefore K is pointing in this +direction which means that our electric + + align:start position:0% +direction which means that our electric + + + align:start position:0% +direction which means that our electric +field is pointing purely in Z + + align:start position:0% + + + + align:start position:0% + +Direction and this actually gives us a + + align:start position:0% +Direction and this actually gives us a + + + align:start position:0% +Direction and this actually gives us a +hint why the O mode dispersion + + align:start position:0% +hint why the O mode dispersion + + + align:start position:0% +hint why the O mode dispersion +relationship doesn't seem to know + + align:start position:0% +relationship doesn't seem to know + + + align:start position:0% +relationship doesn't seem to know +anything about the magnetic field and + + align:start position:0% +anything about the magnetic field and + + + align:start position:0% +anything about the magnetic field and +that's because the electrons are + + align:start position:0% +that's because the electrons are + + + align:start position:0% +that's because the electrons are +traveling along in the Z Direction and + + align:start position:0% +traveling along in the Z Direction and + + + align:start position:0% +traveling along in the Z Direction and +the electric field as it oscillates up + + align:start position:0% +the electric field as it oscillates up + + + align:start position:0% +the electric field as it oscillates up +and down is simply accelerating or + + align:start position:0% +and down is simply accelerating or + + + align:start position:0% +and down is simply accelerating or +decelerating them along the magnetic + + align:start position:0% +decelerating them along the magnetic + + + align:start position:0% +decelerating them along the magnetic +field and so it doesn't have any effect + + align:start position:0% +field and so it doesn't have any effect + + + align:start position:0% +field and so it doesn't have any effect +from the gting particle orbits you just + + align:start position:0% +from the gting particle orbits you just + + + align:start position:0% +from the gting particle orbits you just +have particles which are + + align:start position:0% +have particles which are + + + align:start position:0% +have particles which are +going like this and maybe they're being + + align:start position:0% +going like this and maybe they're being + + + align:start position:0% +going like this and maybe they're being +slightly accelerated or slightly + + align:start position:0% +slightly accelerated or slightly + + + align:start position:0% +slightly accelerated or slightly +decelerated but it's all in the B + + align:start position:0% +decelerated but it's all in the B + + + align:start position:0% +decelerated but it's all in the B +Direction so it doesn't have an + + align:start position:0% +Direction so it doesn't have an + + + align:start position:0% +Direction so it doesn't have an +interaction with magn field + + align:start position:0% + + + + align:start position:0% + +whatsoever so these are nice and easy + + align:start position:0% +whatsoever so these are nice and easy + + + align:start position:0% +whatsoever so these are nice and easy +and the nice thing about these modes + + align:start position:0% +and the nice thing about these modes + + + align:start position:0% +and the nice thing about these modes +actually is that they are transverse so + + align:start position:0% +actually is that they are transverse so + + + align:start position:0% +actually is that they are transverse so +k. e is equal to zero so although we + + align:start position:0% +k. e is equal to zero so although we + + + align:start position:0% +k. e is equal to zero so although we +relax that condition we obviously didn't + + align:start position:0% +relax that condition we obviously didn't + + + align:start position:0% +relax that condition we obviously didn't +need it in order to get this mode as you + + align:start position:0% +need it in order to get this mode as you + + + align:start position:0% +need it in order to get this mode as you +can see because we already got the mode + + align:start position:0% +can see because we already got the mode + + + align:start position:0% +can see because we already got the mode +as before when we did have the + + align:start position:0% +as before when we did have the + + + align:start position:0% +as before when we did have the +transverse condition so this is our nice + + align:start position:0% +transverse condition so this is our nice + + + align:start position:0% +transverse condition so this is our nice +easy way the next one is + + align:start position:0% +easy way the next one is + + + align:start position:0% +easy way the next one is +not so the next + + align:start position:0% + + + + align:start position:0% + +one has dispersion relationship that + + align:start position:0% +one has dispersion relationship that + + + align:start position:0% +one has dispersion relationship that +looks like this now + + align:start position:0% +looks like this now + + + align:start position:0% +looks like this now +in hutson's book he rewrites several of + + align:start position:0% +in hutson's book he rewrites several of + + + align:start position:0% +in hutson's book he rewrites several of +these terms as like X and Y and things + + align:start position:0% +these terms as like X and Y and things + + + align:start position:0% +these terms as like X and Y and things +like that to make it more compact which + + align:start position:0% +like that to make it more compact which + + + align:start position:0% +like that to make it more compact which +I think is great if you're going to + + align:start position:0% +I think is great if you're going to + + + align:start position:0% +I think is great if you're going to +write it a lot but just in this case I + + align:start position:0% +write it a lot but just in this case I + + + align:start position:0% +write it a lot but just in this case I +want to write it out in its full + + align:start position:0% +want to write it out in its full + + + align:start position:0% +want to write it out in its full +generality in terms of things like + + align:start position:0% +generality in terms of things like + + + align:start position:0% +generality in terms of things like +plasma frequency and stuff like that so + + align:start position:0% +plasma frequency and stuff like that so + + + align:start position:0% +plasma frequency and stuff like that so +that you can see where all of those + + align:start position:0% +that you can see where all of those + + + align:start position:0% +that you can see where all of those +terms come from so it's going to look a + + align:start position:0% +terms come from so it's going to look a + + + align:start position:0% +terms come from so it's going to look a +little bit more complicated than what + + align:start position:0% +little bit more complicated than what + + + align:start position:0% +little bit more complicated than what +you're get H in this book but I think + + align:start position:0% +you're get H in this book but I think + + + align:start position:0% +you're get H in this book but I think +it's more useful so it's oneus Omega p^ + + align:start position:0% +it's more useful so it's oneus Omega p^ + + + align:start position:0% +it's more useful so it's oneus Omega p^ +2 over Omega + + align:start position:0% +2 over Omega + + + align:start position:0% +2 over Omega +2 oh good but then it's actually times + + align:start position:0% +2 oh good but then it's actually times + + + align:start position:0% +2 oh good but then it's actually times +1us Omega + + align:start position:0% + + + + align:start position:0% + +Pega and all of + + align:start position:0% +Pega and all of + + + align:start position:0% +Pega and all of +those not the one all the rest of these + + align:start position:0% +those not the one all the rest of these + + + align:start position:0% +those not the one all the rest of these +are over one minus Omega p 2 + + align:start position:0% +are over one minus Omega p 2 + + + align:start position:0% +are over one minus Omega p 2 +omegaus Capital Omega over lowercase + + align:start position:0% +omegaus Capital Omega over lowercase + + + align:start position:0% +omegaus Capital Omega over lowercase +omeg s so this is a little bit eres + + align:start position:0% +omeg s so this is a little bit eres + + + align:start position:0% +omeg s so this is a little bit eres +there sort of bits of the same thing + + align:start position:0% +there sort of bits of the same thing + + + align:start position:0% +there sort of bits of the same thing +repeated in a fractal pattern and the + + align:start position:0% +repeated in a fractal pattern and the + + + align:start position:0% +repeated in a fractal pattern and the +more you stare at it the more you think + + align:start position:0% +more you stare at it the more you think + + + align:start position:0% +more you stare at it the more you think +whatas is playing it seems very + + align:start position:0% +whatas is playing it seems very + + + align:start position:0% +whatas is playing it seems very +complicated remember this is the + + align:start position:0% +complicated remember this is the + + + align:start position:0% +complicated remember this is the +simplified version where we've already + + align:start position:0% +simplified version where we've already + + + align:start position:0% +simplified version where we've already +taken they Pon too if you want to put in + + align:start position:0% +taken they Pon too if you want to put in + + + align:start position:0% +taken they Pon too if you want to put in +all of the cosiness and signs becomes + + align:start position:0% +all of the cosiness and signs becomes + + + align:start position:0% +all of the cosiness and signs becomes +much more complicated so straight away + + align:start position:0% +much more complicated so straight away + + + align:start position:0% +much more complicated so straight away +we can see that this is more than + + align:start position:0% +we can see that this is more than + + + align:start position:0% +we can see that this is more than +ordinary and so this is of course the X + + align:start position:0% +ordinary and so this is of course the X + + + align:start position:0% +ordinary and so this is of course the X +mode and it is the extraordinary + + align:start position:0% + + + + align:start position:0% + +now you can probably guess just by + + align:start position:0% +now you can probably guess just by + + + align:start position:0% +now you can probably guess just by +looking at this that when we substitute + + align:start position:0% +looking at this that when we substitute + + + align:start position:0% +looking at this that when we substitute +this back in uh to our equation and we + + align:start position:0% +this back in uh to our equation and we + + + align:start position:0% +this back in uh to our equation and we +try and get out the igen modes of the + + align:start position:0% +try and get out the igen modes of the + + + align:start position:0% +try and get out the igen modes of the +system they're not going to be quite as + + align:start position:0% +system they're not going to be quite as + + + align:start position:0% +system they're not going to be quite as +simple as this you are quite right so + + align:start position:0% +simple as this you are quite right so + + + align:start position:0% +simple as this you are quite right so +what we find out is that e x over e + + align:start position:0% +what we find out is that e x over e + + + align:start position:0% +what we find out is that e x over e +y so the X and the Y components of the + + align:start position:0% +y so the X and the Y components of the + + + align:start position:0% +y so the X and the Y components of the +electric field are related to each other + + align:start position:0% +electric field are related to each other + + + align:start position:0% +electric field are related to each other +and the relationship between them is + + align:start position:0% +and the relationship between them is + + + align:start position:0% +and the relationship between them is +minus itimes + + align:start position:0% +minus itimes + + + align:start position:0% +minus itimes +1us Omega + + align:start position:0% + + + + align:start position:0% + +pegaus Capal + + align:start position:0% + + + + align:start position:0% + +omaa all of that is + + align:start position:0% +omaa all of that is + + + align:start position:0% +omaa all of that is +over Omega p^2 over Omega + + align:start position:0% + + + + align:start position:0% + +s although that looks complicated + + align:start position:0% +s although that looks complicated + + + align:start position:0% +s although that looks complicated +fortunately for us the Z + + align:start position:0% +fortunately for us the Z + + + align:start position:0% +fortunately for us the Z +component is in fact + + align:start position:0% +component is in fact + + + align:start position:0% +component is in fact +zero that saves us a little bit + + align:start position:0% +zero that saves us a little bit + + + align:start position:0% +zero that saves us a little bit +of so if I plot out + + align:start position:0% + + + + align:start position:0% + +now y and z x like this I still got my + + align:start position:0% +now y and z x like this I still got my + + + align:start position:0% +now y and z x like this I still got my +magnetic field in this direction and + + align:start position:0% +magnetic field in this direction and + + + align:start position:0% +magnetic field in this direction and +I've still got my K Vector in this + + align:start position:0% +I've still got my K Vector in this + + + align:start position:0% +I've still got my K Vector in this +direction it's got exactly the same + + align:start position:0% + + + + align:start position:0% + +K anyone tell me what the electric field + + align:start position:0% +K anyone tell me what the electric field + + + align:start position:0% +K anyone tell me what the electric field +looks like here previously we said the + + align:start position:0% +looks like here previously we said the + + + align:start position:0% +looks like here previously we said the +electric field was just point in the Z + + align:start position:0% +electric field was just point in the Z + + + align:start position:0% +electric field was just point in the Z +Direction it was um but now it looks a + + align:start position:0% +Direction it was um but now it looks a + + + align:start position:0% +Direction it was um but now it looks a +little bit more complicated + + align:start position:0% + + + + align:start position:0% + +anyone + + align:start position:0% +anyone + + + align:start position:0% +anyone +yes so the answer was an ellipse yes do + + align:start position:0% +yes so the answer was an ellipse yes do + + + align:start position:0% +yes so the answer was an ellipse yes do +you want to be more specific the XY + + align:start position:0% +you want to be more specific the XY + + + align:start position:0% +you want to be more specific the XY +plane be + + align:start position:0% +plane be + + + align:start position:0% +plane be +out okay so we're talking about an + + align:start position:0% +out okay so we're talking about an + + + align:start position:0% +out okay so we're talking about an +ellipse in the XY plane when we have an + + align:start position:0% +ellipse in the XY plane when we have an + + + align:start position:0% +ellipse in the XY plane when we have an +ellipse we have a minor axis and a major + + align:start position:0% +ellipse we have a minor axis and a major + + + align:start position:0% +ellipse we have a minor axis and a major +axis so do you know where which uh what + + align:start position:0% +axis so do you know where which uh what + + + align:start position:0% +axis so do you know where which uh what +is the orientation of the major axis + + align:start position:0% +is the orientation of the major axis + + + align:start position:0% +is the orientation of the major axis +with respect to this XY C + + align:start position:0% +with respect to this XY C + + + align:start position:0% +with respect to this XY C +system that's effectively asking you is + + align:start position:0% +system that's effectively asking you is + + + align:start position:0% +system that's effectively asking you is +ex bigger than ey or is ey bigger than + + align:start position:0% +ex bigger than ey or is ey bigger than + + + align:start position:0% +ex bigger than ey or is ey bigger than +ex and we made some very strong + + align:start position:0% +ex and we made some very strong + + + align:start position:0% +ex and we made some very strong +assumptions in deriving this will help + + align:start position:0% +assumptions in deriving this will help + + + align:start position:0% +assumptions in deriving this will help +you what that + + align:start position:0% +you what that + + + align:start position:0% +you what that +about in particular we assumed that this + + align:start position:0% +about in particular we assumed that this + + + align:start position:0% +about in particular we assumed that this +was a high frequency + + align:start position:0% + + + + align:start position:0% + +work any answers + + align:start position:0% + + + + align:start position:0% + +online youve got a 50/50 chance of being + + align:start position:0% +online youve got a 50/50 chance of being + + + align:start position:0% +online youve got a 50/50 chance of being +right yeah I hope everyone realizes that + + align:start position:0% +right yeah I hope everyone realizes that + + + align:start position:0% +right yeah I hope everyone realizes that +it's not going to be like wildly at some + + align:start position:0% +it's not going to be like wildly at some + + + align:start position:0% +it's not going to be like wildly at some +random + + align:start position:0% +random + + + align:start position:0% +random +angle make the frequency really large in + + align:start position:0% +angle make the frequency really large in + + + align:start position:0% +angle make the frequency really large in +there right basically one divided + + align:start position:0% +there right basically one divided + + + align:start position:0% +there right basically one divided +by ex way bigger yeah ex is way bigger + + align:start position:0% +by ex way bigger yeah ex is way bigger + + + align:start position:0% +by ex way bigger yeah ex is way bigger +so if we have a high frequency this term + + align:start position:0% +so if we have a high frequency this term + + + align:start position:0% +so if we have a high frequency this term +is going to be very very small which + + align:start position:0% +is going to be very very small which + + + align:start position:0% +is going to be very very small which +means ex is much bigger than ey right + + align:start position:0% +means ex is much bigger than ey right + + + align:start position:0% +means ex is much bigger than ey right +and so we have an + + align:start position:0% +and so we have an + + + align:start position:0% +and so we have an +ellipse sort of is extended like this so + + align:start position:0% +ellipse sort of is extended like this so + + + align:start position:0% +ellipse sort of is extended like this so +X much much bigger than e and because + + align:start position:0% +X much much bigger than e and because + + + align:start position:0% +X much much bigger than e and because +there's this uh I inside here they're + + align:start position:0% +there's this uh I inside here they're + + + align:start position:0% +there's this uh I inside here they're +actually related to each other in a + + align:start position:0% +actually related to each other in a + + + align:start position:0% +actually related to each other in a +complex fashion so it means the electric + + align:start position:0% +complex fashion so it means the electric + + + align:start position:0% +complex fashion so it means the electric +field Vector is going to be sweeping out + + align:start position:0% +field Vector is going to be sweeping out + + + align:start position:0% +field Vector is going to be sweeping out +this ellipse as the wave propagates okay + + align:start position:0% +this ellipse as the wave propagates okay + + + align:start position:0% +this ellipse as the wave propagates okay +now the main thing to note here is that + + align:start position:0% +now the main thing to note here is that + + + align:start position:0% +now the main thing to note here is that +this wave is not transverse so K do e is + + align:start position:0% +this wave is not transverse so K do e is + + + align:start position:0% +this wave is not transverse so K do e is +not equal to zero because of course k y + + align:start position:0% +not equal to zero because of course k y + + + align:start position:0% +not equal to zero because of course k y +is parallel to our small but existent ey + + align:start position:0% +is parallel to our small but existent ey + + + align:start position:0% +is parallel to our small but existent ey +so this is the wave we would not have + + align:start position:0% +so this is the wave we would not have + + + align:start position:0% +so this is the wave we would not have +got if we insisted on only looking at + + align:start position:0% +got if we insisted on only looking at + + + align:start position:0% +got if we insisted on only looking at +transverse waves which is why you have + + align:start position:0% +transverse waves which is why you have + + + align:start position:0% +transverse waves which is why you have +to go back and rederive it all with this + + align:start position:0% +to go back and rederive it all with this + + + align:start position:0% +to go back and rederive it all with this +of course we also put in the equation of + + align:start position:0% +of course we also put in the equation of + + + align:start position:0% +of course we also put in the equation of +motion for particles in magnetic field + + align:start position:0% +motion for particles in magnetic field + + + align:start position:0% +motion for particles in magnetic field +but you can see why it's much easier to + + align:start position:0% +but you can see why it's much easier to + + + align:start position:0% +but you can see why it's much easier to +go and drive the ordinary mode in an + + align:start position:0% +go and drive the ordinary mode in an + + + align:start position:0% +go and drive the ordinary mode in an +unmagnetized plasma than it is to get + + align:start position:0% +unmagnetized plasma than it is to get + + + align:start position:0% +unmagnetized plasma than it is to get +these two modes in a magnetized plasma + + align:start position:0% +these two modes in a magnetized plasma + + + align:start position:0% +these two modes in a magnetized plasma +straight away um so this is a very fun + + align:start position:0% +straight away um so this is a very fun + + + align:start position:0% +straight away um so this is a very fun +way indeed now + + align:start position:0% + + + + align:start position:0% + +there is a question in Hutchinson's + + align:start position:0% +there is a question in Hutchinson's + + + align:start position:0% +there is a question in Hutchinson's +book which caused me a lot of thought as + + align:start position:0% +book which caused me a lot of thought as + + + align:start position:0% +book which caused me a lot of thought as +a gr student because I didn't understand + + align:start position:0% +a gr student because I didn't understand + + + align:start position:0% +a gr student because I didn't understand +what the hell he was getting at and so I + + align:start position:0% +what the hell he was getting at and so I + + + align:start position:0% +what the hell he was getting at and so I +will put it to you now and we shall see + + align:start position:0% +will put it to you now and we shall see + + + align:start position:0% +will put it to you now and we shall see +whether you can spot it straight or not + + align:start position:0% +whether you can spot it straight or not + + + align:start position:0% +whether you can spot it straight or not +the question in B you have set up an + + align:start position:0% +the question in B you have set up an + + + align:start position:0% +the question in B you have set up an +interferometer looking across the plasma + + align:start position:0% +interferometer looking across the plasma + + + align:start position:0% +interferometer looking across the plasma +like this if you have accidentally set + + align:start position:0% +like this if you have accidentally set + + + align:start position:0% +like this if you have accidentally set +up your perometer to measure the X mode + + align:start position:0% +up your perometer to measure the X mode + + + align:start position:0% +up your perometer to measure the X mode +rather than the O mode what would the + + align:start position:0% +rather than the O mode what would the + + + align:start position:0% +rather than the O mode what would the +error be in your measurements and you + + align:start position:0% +error be in your measurements and you + + + align:start position:0% +error be in your measurements and you +give some plasma parameters so you can + + align:start position:0% +give some plasma parameters so you can + + + align:start position:0% +give some plasma parameters so you can +calculate so remember in our + + align:start position:0% +calculate so remember in our + + + align:start position:0% +calculate so remember in our +interferometer what we measure is not + + align:start position:0% +interferometer what we measure is not + + + align:start position:0% +interferometer what we measure is not +density but we measure changes in + + align:start position:0% +density but we measure changes in + + + align:start position:0% +density but we measure changes in +refractive index and so he's saying if + + align:start position:0% +refractive index and so he's saying if + + + align:start position:0% +refractive index and so he's saying if +you set up your infometer such it + + align:start position:0% +you set up your infometer such it + + + align:start position:0% +you set up your infometer such it +measures this refractive index how + + align:start position:0% +measures this refractive index how + + + align:start position:0% +measures this refractive index how +different would your result be than if + + align:start position:0% +different would your result be than if + + + align:start position:0% +different would your result be than if +you were measuring this refractive index + + align:start position:0% +you were measuring this refractive index + + + align:start position:0% +you were measuring this refractive index +and my question I was always asking was + + align:start position:0% +and my question I was always asking was + + + align:start position:0% +and my question I was always asking was +like how the hell do you even set it up + + align:start position:0% +like how the hell do you even set it up + + + align:start position:0% +like how the hell do you even set it up +to do one or the other so perhaps we can + + align:start position:0% +to do one or the other so perhaps we can + + + align:start position:0% +to do one or the other so perhaps we can +work it out together how do I get to + + align:start position:0% +work it out together how do I get to + + + align:start position:0% +work it out together how do I get to +choose whether I'm using the O mode or + + align:start position:0% +choose whether I'm using the O mode or + + + align:start position:0% +choose whether I'm using the O mode or +the + + align:start position:0% + + + + align:start position:0% + +X well for o mode right you have a z you + + align:start position:0% +X well for o mode right you have a z you + + + align:start position:0% +X well for o mode right you have a z you +could polarize + + align:start position:0% +could polarize + + + align:start position:0% +could polarize +your light coming yeah so if I'm + + align:start position:0% +your light coming yeah so if I'm + + + align:start position:0% +your light coming yeah so if I'm +injecting Li in for my + + align:start position:0% +injecting Li in for my + + + align:start position:0% +injecting Li in for my +ineter right and maybe it's collected + + align:start position:0% +ineter right and maybe it's collected + + + align:start position:0% +ineter right and maybe it's collected +here or about that doesn't that so if I + + align:start position:0% +here or about that doesn't that so if I + + + align:start position:0% +here or about that doesn't that so if I +have + + align:start position:0% +have + + + align:start position:0% +have +this + + align:start position:0% +this + + + align:start position:0% +this +polarization that's theote because the + + align:start position:0% +polarization that's theote because the + + + align:start position:0% +polarization that's theote because the +polarization e is parallel to B right + + align:start position:0% +polarization e is parallel to B right + + + align:start position:0% +polarization e is parallel to B right +and if I + + align:start position:0% + + + + align:start position:0% + +have this polarization out of the page + + align:start position:0% +have this polarization out of the page + + + align:start position:0% +have this polarization out of the page +like that that's the + + align:start position:0% +like that that's the + + + align:start position:0% +like that that's the +Expo so you get to choose which + + align:start position:0% +Expo so you get to choose which + + + align:start position:0% +Expo so you get to choose which +refractive index you prone by your + + align:start position:0% +refractive index you prone by your + + + align:start position:0% +refractive index you prone by your +choice of um the polarization that + + align:start position:0% +choice of um the polarization that + + + align:start position:0% +choice of um the polarization that +you're injecting and that was the bit + + align:start position:0% +you're injecting and that was the bit + + + align:start position:0% +you're injecting and that was the bit +that I missed as a grad student and it + + align:start position:0% +that I missed as a grad student and it + + + align:start position:0% +that I missed as a grad student and it +took me until I was teaching this class + + align:start position:0% +took me until I was teaching this class + + + align:start position:0% +took me until I was teaching this class +for the first time to finally work out + + align:start position:0% +for the first time to finally work out + + + align:start position:0% +for the first time to finally work out +what was going on is that you actually + + align:start position:0% +what was going on is that you actually + + + align:start position:0% +what was going on is that you actually +do have a choice it's not like the + + align:start position:0% +do have a choice it's not like the + + + align:start position:0% +do have a choice it's not like the +plasma decides for you which is why I + + align:start position:0% +plasma decides for you which is why I + + + align:start position:0% +plasma decides for you which is why I +was like what will the plasma want to do + + align:start position:0% +was like what will the plasma want to do + + + align:start position:0% +was like what will the plasma want to do +but that doesn't matter in this case in + + align:start position:0% +but that doesn't matter in this case in + + + align:start position:0% +but that doesn't matter in this case in +this case you have a choice the plasma + + align:start position:0% +this case you have a choice the plasma + + + align:start position:0% +this case you have a choice the plasma +is not in control of you okay so and in + + align:start position:0% +is not in control of you okay so and in + + + align:start position:0% +is not in control of you okay so and in +general you could launch a wave through + + align:start position:0% +general you could launch a wave through + + + align:start position:0% +general you could launch a wave through +the plasma at some arbitrary + + align:start position:0% +the plasma at some arbitrary + + + align:start position:0% +the plasma at some arbitrary +polarization of 45 degrees and then + + align:start position:0% +polarization of 45 degrees and then + + + align:start position:0% +polarization of 45 degrees and then +because you can always decompose uh your + + align:start position:0% +because you can always decompose uh your + + + align:start position:0% +because you can always decompose uh your +wave into various sets of modes but this + + align:start position:0% +wave into various sets of modes but this + + + align:start position:0% +wave into various sets of modes but this +is a good set of modes which is valid + + align:start position:0% +is a good set of modes which is valid + + + align:start position:0% +is a good set of modes which is valid +for V Pi upon two then you would see + + align:start position:0% +for V Pi upon two then you would see + + + align:start position:0% +for V Pi upon two then you would see +that one of your polarizations would + + align:start position:0% +that one of your polarizations would + + + align:start position:0% +that one of your polarizations would +travel faster than the other + + align:start position:0% +travel faster than the other + + + align:start position:0% +travel faster than the other +polarization right because it would have + + align:start position:0% +polarization right because it would have + + + align:start position:0% +polarization right because it would have +a different refractive index and so + + align:start position:0% +a different refractive index and so + + + align:start position:0% +a different refractive index and so +you'd see all sorts of funky effects + + align:start position:0% +you'd see all sorts of funky effects + + + align:start position:0% +you'd see all sorts of funky effects +going on that may be very hard to + + align:start position:0% +going on that may be very hard to + + + align:start position:0% +going on that may be very hard to +interpret so it's definitely worth + + align:start position:0% +interpret so it's definitely worth + + + align:start position:0% +interpret so it's definitely worth +thinking about uh the polarization and + + align:start position:0% +thinking about uh the polarization and + + + align:start position:0% +thinking about uh the polarization and +when I went looking recently for some + + align:start position:0% +when I went looking recently for some + + + align:start position:0% +when I went looking recently for some +papers on how people actually do this in + + align:start position:0% +papers on how people actually do this in + + + align:start position:0% +papers on how people actually do this in +toax um they spend an awful lot of time + + align:start position:0% +toax um they spend an awful lot of time + + + align:start position:0% +toax um they spend an awful lot of time +thinking about the polarization often + + align:start position:0% +thinking about the polarization often + + + align:start position:0% +thinking about the polarization often +they have the ability to switch it + + align:start position:0% +they have the ability to switch it + + + align:start position:0% +they have the ability to switch it +between X mode and O mode so they can do + + align:start position:0% +between X mode and O mode so they can do + + + align:start position:0% +between X mode and O mode so they can do +different meurs + + align:start position:0% + + + + align:start position:0% + +yes the X mode should be polarized + + align:start position:0% +yes the X mode should be polarized + + + align:start position:0% +yes the X mode should be polarized +so yeah out of the page yeah yes because + + align:start position:0% +so yeah out of the page yeah yes because + + + align:start position:0% +so yeah out of the page yeah yes because +you're primarily going to be exciting + + align:start position:0% +you're primarily going to be exciting + + + align:start position:0% +you're primarily going to be exciting +this large ex and the plasma will do the + + align:start position:0% +this large ex and the plasma will do the + + + align:start position:0% +this large ex and the plasma will do the +work of giving you the ey and it will do + + align:start position:0% +work of giving you the ey and it will do + + + align:start position:0% +work of giving you the ey and it will do +that because of the uh electrons + + align:start position:0% +that because of the uh electrons + + + align:start position:0% +that because of the uh electrons +generating around the field line so you + + align:start position:0% +generating around the field line so you + + + align:start position:0% +generating around the field line so you +don't have to worry about it the ey is + + align:start position:0% +don't have to worry about it the ey is + + + align:start position:0% +don't have to worry about it the ey is +truly fantastically small here so it's + + align:start position:0% +truly fantastically small here so it's + + + align:start position:0% +truly fantastically small here so it's +it's okay like you don't have to give it + + align:start position:0% +it's okay like you don't have to give it + + + align:start position:0% +it's okay like you don't have to give it +that yourself which would be impossible + + align:start position:0% +that yourself which would be impossible + + + align:start position:0% +that yourself which would be impossible +because in free space waves are only + + align:start position:0% +because in free space waves are only + + + align:start position:0% +because in free space waves are only +transverse you can't launch a wave in + + align:start position:0% +transverse you can't launch a wave in + + + align:start position:0% +transverse you can't launch a wave in +free space that has a polarization along + + align:start position:0% +free space that has a polarization along + + + align:start position:0% +free space that has a polarization along +the direction of propagation but it's + + align:start position:0% +the direction of propagation but it's + + + align:start position:0% +the direction of propagation but it's +okay the plasmas has got your back there + + align:start position:0% +okay the plasmas has got your back there + + + align:start position:0% +okay the plasmas has got your back there +yeah and these are the only two waves + + align:start position:0% +yeah and these are the only two waves + + + align:start position:0% +yeah and these are the only two waves +the only two electromagnetic high + + align:start position:0% +the only two electromagnetic high + + + align:start position:0% +the only two electromagnetic high +frequency coals magnetize waves which + + align:start position:0% +frequency coals magnetize waves which + + + align:start position:0% +frequency coals magnetize waves which +can propagate in a plasma so if you hit + + align:start position:0% +can propagate in a plasma so if you hit + + + align:start position:0% +can propagate in a plasma so if you hit +the plasma with some wave it will + + align:start position:0% +the plasma with some wave it will + + + align:start position:0% +the plasma with some wave it will +instantly convert into some mixture of + + align:start position:0% +instantly convert into some mixture of + + + align:start position:0% +instantly convert into some mixture of +these two because they're the only modes + + align:start position:0% +these two because they're the only modes + + + align:start position:0% +these two because they're the only modes +which are supported by the plasma medium + + align:start position:0% +which are supported by the plasma medium + + + align:start position:0% +which are supported by the plasma medium +so + + align:start position:0% +so + + + align:start position:0% +so +yeah um when that conver that is + + align:start position:0% +yeah um when that conver that is + + + align:start position:0% +yeah um when that conver that is +happening are we at all worried about + + align:start position:0% +happening are we at all worried about + + + align:start position:0% +happening are we at all worried about +reflective power then you know being + + align:start position:0% +reflective power then you know being + + + align:start position:0% +reflective power then you know being +like + + align:start position:0% +like + + + align:start position:0% +like +different because like if you're + + align:start position:0% +different because like if you're + + + align:start position:0% +different because like if you're +rejecting the wave to the plasma vacuum + + align:start position:0% +rejecting the wave to the plasma vacuum + + + align:start position:0% +rejecting the wave to the plasma vacuum +wave it's from onx you I imagine there's + + align:start position:0% +wave it's from onx you I imagine there's + + + align:start position:0% +wave it's from onx you I imagine there's +some chance of that vacuum wave + + align:start position:0% +some chance of that vacuum wave + + + align:start position:0% +some chance of that vacuum wave +reflecting back in you could that you + + align:start position:0% +reflecting back in you could that you + + + align:start position:0% +reflecting back in you could that you +know hurt your s ratio in some way or is + + align:start position:0% +know hurt your s ratio in some way or is + + + align:start position:0% +know hurt your s ratio in some way or is +there very a very small amount + + align:start position:0% +there very a very small amount + + + align:start position:0% +there very a very small amount +doesn't so the question is when you have + + align:start position:0% +doesn't so the question is when you have + + + align:start position:0% +doesn't so the question is when you have +this conversion from the vacuum wave + + align:start position:0% +this conversion from the vacuum wave + + + align:start position:0% +this conversion from the vacuum wave +into to the plasma waves is there any + + align:start position:0% +into to the plasma waves is there any + + + align:start position:0% +into to the plasma waves is there any +power which is reflected and the answer + + align:start position:0% +power which is reflected and the answer + + + align:start position:0% +power which is reflected and the answer +is I don't know I would imagine that + + align:start position:0% +is I don't know I would imagine that + + + align:start position:0% +is I don't know I would imagine that +there could be some power reflected in + + align:start position:0% +there could be some power reflected in + + + align:start position:0% +there could be some power reflected in +that interface there um and yeah also an + + align:start position:0% +that interface there um and yeah also an + + + align:start position:0% +that interface there um and yeah also an +important thing to notice is that on a + + align:start position:0% +important thing to notice is that on a + + + align:start position:0% +important thing to notice is that on a +toap the magnetic field stays in the + + align:start position:0% +toap the magnetic field stays in the + + + align:start position:0% +toap the magnetic field stays in the +same direction but if you're in + + align:start position:0% +same direction but if you're in + + + align:start position:0% +same direction but if you're in +something like an RFP reverse field + + align:start position:0% +something like an RFP reverse field + + + align:start position:0% +something like an RFP reverse field +pinch where the magnetic field rotates + + align:start position:0% +pinch where the magnetic field rotates + + + align:start position:0% +pinch where the magnetic field rotates +your wave will convert between you may + + align:start position:0% +your wave will convert between you may + + + align:start position:0% +your wave will convert between you may +launch an O mode in it may convert + + align:start position:0% +launch an O mode in it may convert + + + align:start position:0% +launch an O mode in it may convert +itself to an X mode so and and + + align:start position:0% +itself to an X mode so and and + + + align:start position:0% +itself to an X mode so and and +intermediate you'll have all those + + align:start position:0% +intermediate you'll have all those + + + align:start position:0% +intermediate you'll have all those +intermediate polarizations and K vectors + + align:start position:0% +intermediate polarizations and K vectors + + + align:start position:0% +intermediate polarizations and K vectors +respect to magnetic field and you'll + + align:start position:0% +respect to magnetic field and you'll + + + align:start position:0% +respect to magnetic field and you'll +have to go back and do the Apple Harry + + align:start position:0% +have to go back and do the Apple Harry + + + align:start position:0% +have to go back and do the Apple Harry +formalism and that's probably why people + + align:start position:0% +formalism and that's probably why people + + + align:start position:0% +formalism and that's probably why people +don't work on rfps anymore they're + + align:start position:0% +don't work on rfps anymore they're + + + align:start position:0% +don't work on rfps anymore they're +extremely difficult to work now one + + align:start position:0% +extremely difficult to work now one + + + align:start position:0% +extremely difficult to work now one +thing I will note is you might ask you + + align:start position:0% +thing I will note is you might ask you + + + align:start position:0% +thing I will note is you might ask you +know Jack you work on Z pinches right + + align:start position:0% +know Jack you work on Z pinches right + + + align:start position:0% +know Jack you work on Z pinches right +and they've got strong magnetic fields + + align:start position:0% +and they've got strong magnetic fields + + + align:start position:0% +and they've got strong magnetic fields +and yet you don't seem to be worried at + + align:start position:0% +and yet you don't seem to be worried at + + + align:start position:0% +and yet you don't seem to be worried at +all about the magnetic field or or + + align:start position:0% +all about the magnetic field or or + + + align:start position:0% +all about the magnetic field or or +polarizing your beam or anything like + + align:start position:0% +polarizing your beam or anything like + + + align:start position:0% +polarizing your beam or anything like +that and the reason for that is when you + + align:start position:0% +that and the reason for that is when you + + + align:start position:0% +that and the reason for that is when you +start looking at the frequency orderings + + align:start position:0% +start looking at the frequency orderings + + + align:start position:0% +start looking at the frequency orderings +uh in the sorts of plasmas I work with + + align:start position:0% +uh in the sorts of plasmas I work with + + + align:start position:0% +uh in the sorts of plasmas I work with +this term here is very very very very + + align:start position:0% +this term here is very very very very + + + align:start position:0% +this term here is very very very very +very very very very small and so this + + align:start position:0% +very very very very small and so this + + + align:start position:0% +very very very very small and so this +cancels out that and huzzah you just + + align:start position:0% +cancels out that and huzzah you just + + + align:start position:0% +cancels out that and huzzah you just +have two oh modes so you're basically + + align:start position:0% +have two oh modes so you're basically + + + align:start position:0% +have two oh modes so you're basically +Bly unmagnetized plasma so depending on + + align:start position:0% +Bly unmagnetized plasma so depending on + + + align:start position:0% +Bly unmagnetized plasma so depending on +your plasma regime you may not be + + align:start position:0% +your plasma regime you may not be + + + align:start position:0% +your plasma regime you may not be +sensitive to the magne field anyway and + + align:start position:0% +sensitive to the magne field anyway and + + + align:start position:0% +sensitive to the magne field anyway and +basically that's the requirement that + + align:start position:0% +basically that's the requirement that + + + align:start position:0% +basically that's the requirement that +the probing frequency of your wave is + + align:start position:0% +the probing frequency of your wave is + + + align:start position:0% +the probing frequency of your wave is +much much higher than the uh gyro + + align:start position:0% +much much higher than the uh gyro + + + align:start position:0% +much much higher than the uh gyro +frequency which is the unmagnetized + + align:start position:0% +frequency which is the unmagnetized + + + align:start position:0% +frequency which is the unmagnetized +condition we wrote down um all the way + + align:start position:0% +condition we wrote down um all the way + + + align:start position:0% +condition we wrote down um all the way +back when we derve the unified we so you + + align:start position:0% +back when we derve the unified we so you + + + align:start position:0% +back when we derve the unified we so you +may not be sensitive to this it just + + align:start position:0% +may not be sensitive to this it just + + + align:start position:0% +may not be sensitive to this it just +turns out to the toat you tend to be in + + align:start position:0% +turns out to the toat you tend to be in + + + align:start position:0% +turns out to the toat you tend to be in +a regime where this is important so + + align:start position:0% +a regime where this is important so + + + align:start position:0% +a regime where this is important so +we'll talk a little bit about that when + + align:start position:0% +we'll talk a little bit about that when + + + align:start position:0% +we'll talk a little bit about that when +we talk about electron + + align:start position:0% +we talk about electron + + + align:start position:0% +we talk about electron +Cy + + align:start position:0% +Cy + + + align:start position:0% +Cy +okay any questions on + + align:start position:0% + + + + align:start position:0% + +this if you noted just a minute ago + + align:start position:0% +this if you noted just a minute ago + + + align:start position:0% +this if you noted just a minute ago +there's a number of assumptions that + + align:start position:0% +there's a number of assumptions that + + + align:start position:0% +there's a number of assumptions that +I've got derivation cheap among them + + align:start position:0% +I've got derivation cheap among them + + + align:start position:0% +I've got derivation cheap among them +being low temperature most of today's + + align:start position:0% +being low temperature most of today's + + + align:start position:0% +being low temperature most of today's +modern toax operating one to 10 K the + + align:start position:0% +modern toax operating one to 10 K the + + + align:start position:0% +modern toax operating one to 10 K the +ion temperatures does not me like + + align:start position:0% +ion temperatures does not me like + + + align:start position:0% +ion temperatures does not me like +something thats a low temperature + + align:start position:0% + + + + align:start position:0% + +requ applied to a diagnostic system but + + align:start position:0% +requ applied to a diagnostic system but + + + align:start position:0% +requ applied to a diagnostic system but +I mean is this valid + + align:start position:0% +I mean is this valid + + + align:start position:0% +I mean is this valid +or we still need the thermal yeah so + + align:start position:0% +or we still need the thermal yeah so + + + align:start position:0% +or we still need the thermal yeah so +when we say cold we're just talking + + align:start position:0% +when we say cold we're just talking + + + align:start position:0% +when we say cold we're just talking +about compared to the speed of light and + + align:start position:0% +about compared to the speed of light and + + + align:start position:0% +about compared to the speed of light and +that's pretty fast so even when you've + + align:start position:0% +that's pretty fast so even when you've + + + align:start position:0% +that's pretty fast so even when you've +got like so you can't neglect relativist + + align:start position:0% +got like so you can't neglect relativist + + + align:start position:0% +got like so you can't neglect relativist +relativistic effects completely for + + align:start position:0% +relativistic effects completely for + + + align:start position:0% +relativistic effects completely for +electrons at 10kv right they've got one + + align:start position:0% +electrons at 10kv right they've got one + + + align:start position:0% +electrons at 10kv right they've got one +of 20 perent some decent fraction of + + align:start position:0% +of 20 perent some decent fraction of + + + align:start position:0% +of 20 perent some decent fraction of +their rest mass at 500k it's not less + + align:start position:0% +their rest mass at 500k it's not less + + + align:start position:0% +their rest mass at 500k it's not less +than so in some cases relatively effects + + align:start position:0% +than so in some cases relatively effects + + + align:start position:0% +than so in some cases relatively effects +will be important and we'll come across + + align:start position:0% +will be important and we'll come across + + + align:start position:0% +will be important and we'll come across +those when we do cyc transmission I + + align:start position:0% +those when we do cyc transmission I + + + align:start position:0% +those when we do cyc transmission I +believe that for inter perometry we + + align:start position:0% +believe that for inter perometry we + + + align:start position:0% +believe that for inter perometry we +don't have to worry about relatively + + align:start position:0% +don't have to worry about relatively + + + align:start position:0% +don't have to worry about relatively +stick effects here and this holds well + + align:start position:0% +stick effects here and this holds well + + + align:start position:0% +stick effects here and this holds well +enough and the corrections that you get + + align:start position:0% +enough and the corrections that you get + + + align:start position:0% +enough and the corrections that you get +will be on the order of the ratio + + align:start position:0% +will be on the order of the ratio + + + align:start position:0% +will be on the order of the ratio +between the thermal velocity and speed + + align:start position:0% +between the thermal velocity and speed + + + align:start position:0% +between the thermal velocity and speed +of light and that is a small number so I + + align:start position:0% +of light and that is a small number so I + + + align:start position:0% +of light and that is a small number so I +think this a really good point but this + + align:start position:0% +think this a really good point but this + + + align:start position:0% +think this a really good point but this +is actually this holds very very well so + + align:start position:0% +is actually this holds very very well so + + + align:start position:0% +is actually this holds very very well so +we're not dealing with with we're not + + align:start position:0% +we're not dealing with with we're not + + + align:start position:0% +we're not dealing with with we're not +dealing with like plasma waves the waves + + align:start position:0% +dealing with like plasma waves the waves + + + align:start position:0% +dealing with like plasma waves the waves +inside of plasma which are being + + align:start position:0% +inside of plasma which are being + + + align:start position:0% +inside of plasma which are being +generated where thermal effects are + + align:start position:0% +generated where thermal effects are + + + align:start position:0% +generated where thermal effects are +important like langma waves we're + + align:start position:0% +important like langma waves we're + + + align:start position:0% +important like langma waves we're +dealing with these high frequency + + align:start position:0% +dealing with these high frequency + + + align:start position:0% +dealing with these high frequency +electromagnetic waves which are + + align:start position:0% +electromagnetic waves which are + + + align:start position:0% +electromagnetic waves which are +traveling so fast at their phase + + align:start position:0% +traveling so fast at their phase + + + align:start position:0% +traveling so fast at their phase +velocity is close to the speed of light + + align:start position:0% +velocity is close to the speed of light + + + align:start position:0% +velocity is close to the speed of light +really sorry I shouldn't say C here I + + align:start position:0% +really sorry I shouldn't say C here I + + + align:start position:0% +really sorry I shouldn't say C here I +mean this is the phase velocity it's + + align:start position:0% +mean this is the phase velocity it's + + + align:start position:0% +mean this is the phase velocity it's +just the phase velocity is very close to + + align:start position:0% +just the phase velocity is very close to + + + align:start position:0% +just the phase velocity is very close to +the speed of light for these + + align:start position:0% +the speed of light for these + + + align:start position:0% +the speed of light for these +electromagnetic waves so C is is close + + align:start position:0% +electromagnetic waves so C is is close + + + align:start position:0% +electromagnetic waves so C is is close +enough so this is the actual condition + + align:start position:0% +enough so this is the actual condition + + + align:start position:0% +enough so this is the actual condition +for the waves inside your plasma where + + align:start position:0% +for the waves inside your plasma where + + + align:start position:0% +for the waves inside your plasma where +you deal with hot plasma effects and + + align:start position:0% +you deal with hot plasma effects and + + + align:start position:0% +you deal with hot plasma effects and +like damping and all sorts of fun things + + align:start position:0% +like damping and all sorts of fun things + + + align:start position:0% +like damping and all sorts of fun things +like that that phase velocity is much + + align:start position:0% +like that that phase velocity is much + + + align:start position:0% +like that that phase velocity is much +lower and so the phase velocity is close + + align:start position:0% +lower and so the phase velocity is close + + + align:start position:0% +lower and so the phase velocity is close +to the thermal velocity and then you + + align:start position:0% +to the thermal velocity and then you + + + align:start position:0% +to the thermal velocity and then you +have the interaction between the wave + + align:start position:0% +have the interaction between the wave + + + align:start position:0% +have the interaction between the wave +and the distribution function of plasma + + align:start position:0% +and the distribution function of plasma + + + align:start position:0% +and the distribution function of plasma +that gives you Lal damping all we're + + align:start position:0% +that gives you Lal damping all we're + + + align:start position:0% +that gives you Lal damping all we're +nowhere near that that's a really good + + align:start position:0% +nowhere near that that's a really good + + + align:start position:0% +nowhere near that that's a really good +question okay any other + + align:start position:0% + + + + align:start position:0% + +questions okay now we'll do the other + + align:start position:0% + + + + align:start position:0% + +this has nothing to do with + + align:start position:0% +this has nothing to do with + + + align:start position:0% +this has nothing to do with +the but it's interesting and we will use + + align:start position:0% +the but it's interesting and we will use + + + align:start position:0% +the but it's interesting and we will use +it twice again so so now we're going to + + align:start position:0% +it twice again so so now we're going to + + + align:start position:0% +it twice again so so now we're going to +do the case where the wave is + + align:start position:0% +do the case where the wave is + + + align:start position:0% +do the case where the wave is +propagating along the magnetic field + + align:start position:0% +propagating along the magnetic field + + + align:start position:0% +propagating along the magnetic field +here okay so this is maybe a harder case + + align:start position:0% +here okay so this is maybe a harder case + + + align:start position:0% +here okay so this is maybe a harder case +to get inside a toap but it's a very + + align:start position:0% +to get inside a toap but it's a very + + + align:start position:0% +to get inside a toap but it's a very +easy case to get inside for example a z + + align:start position:0% +easy case to get inside for example a z + + + align:start position:0% +easy case to get inside for example a z +pinch or many other systems like that so + + align:start position:0% +pinch or many other systems like that so + + + align:start position:0% +pinch or many other systems like that so +for example if you have a z + + align:start position:0% +for example if you have a z + + + align:start position:0% +for example if you have a z +pinch some wobbly plasma like this it's + + align:start position:0% +pinch some wobbly plasma like this it's + + + align:start position:0% +pinch some wobbly plasma like this it's +got current like this and then it's + + align:start position:0% +got current like this and then it's + + + align:start position:0% +got current like this and then it's +got magnetic + + align:start position:0% +got magnetic + + + align:start position:0% +got magnetic +field like this if I power a laser beam + + align:start position:0% +field like this if I power a laser beam + + + align:start position:0% +field like this if I power a laser beam +through this there's going to be at + + align:start position:0% +through this there's going to be at + + + align:start position:0% +through this there's going to be at +least parts of a laser beam which are + + align:start position:0% + + + + align:start position:0% + +parallel or rounding parallel you get + + align:start position:0% +parallel or rounding parallel you get + + + align:start position:0% +parallel or rounding parallel you get +the same result to the magnetic field + + align:start position:0% +the same result to the magnetic field + + + align:start position:0% +the same result to the magnetic field +and in fact we'll show that this result + + align:start position:0% +and in fact we'll show that this result + + + align:start position:0% +and in fact we'll show that this result +that we deriv for Theta equal Z applies + + align:start position:0% +that we deriv for Theta equal Z applies + + + align:start position:0% +that we deriv for Theta equal Z applies +to almost every angle between + + align:start position:0% +to almost every angle between + + + align:start position:0% +to almost every angle between +zero and pi over two and the theory only + + align:start position:0% +zero and pi over two and the theory only + + + align:start position:0% +zero and pi over two and the theory only +breaks down very very close to Pi two so + + align:start position:0% +breaks down very very close to Pi two so + + + align:start position:0% +breaks down very very close to Pi two so +in fact this still works even when for + + align:start position:0% +in fact this still works even when for + + + align:start position:0% +in fact this still works even when for +example here my K is in the same + + align:start position:0% +example here my K is in the same + + + align:start position:0% +example here my K is in the same +direction but my magnetic field is bent + + align:start position:0% +direction but my magnetic field is bent + + + align:start position:0% +direction but my magnetic field is bent +there's quite a largea between here so + + align:start position:0% +there's quite a largea between here so + + + align:start position:0% +there's quite a largea between here so +this is the very + + align:start position:0% +this is the very + + + align:start position:0% +this is the very +useful okay so we go and uh we plug + + align:start position:0% +useful okay so we go and uh we plug + + + align:start position:0% +useful okay so we go and uh we plug +theta equals z into the up hatry + + align:start position:0% +theta equals z into the up hatry + + + align:start position:0% +theta equals z into the up hatry +relationship and then uh we solve the + + align:start position:0% +relationship and then uh we solve the + + + align:start position:0% +relationship and then uh we solve the +determinant and we get out of our + + align:start position:0% +determinant and we get out of our + + + align:start position:0% +determinant and we get out of our +and we get first of + + align:start position:0% + + + + align:start position:0% + +all well we get two modes and these + + align:start position:0% +all well we get two modes and these + + + align:start position:0% +all well we get two modes and these +modes I tend to write with a plus and a + + align:start position:0% +modes I tend to write with a plus and a + + + align:start position:0% +modes I tend to write with a plus and a +minus and write the two of them together + + align:start position:0% +minus and write the two of them together + + + align:start position:0% +minus and write the two of them together +because they're very very similar and so + + align:start position:0% +because they're very very similar and so + + + align:start position:0% +because they're very very similar and so +this mode plus and minus that's the + + align:start position:0% +this mode plus and minus that's the + + + align:start position:0% +this mode plus and minus that's the +names of the two modes is equal to 1 + + align:start position:0% +names of the two modes is equal to 1 + + + align:start position:0% +names of the two modes is equal to 1 +minus Omega p^ 2 on Omega s over one + + align:start position:0% +minus Omega p^ 2 on Omega s over one + + + align:start position:0% +minus Omega p^ 2 on Omega s over one +plus and minus this is the difference + + align:start position:0% +plus and minus this is the difference + + + align:start position:0% +plus and minus this is the difference +between the two Capital Omega over + + align:start position:0% +between the two Capital Omega over + + + align:start position:0% +between the two Capital Omega over +lower so the first thing that we notice + + align:start position:0% +lower so the first thing that we notice + + + align:start position:0% +lower so the first thing that we notice +of course is that + + align:start position:0% +of course is that + + + align:start position:0% +of course is that +for Capital Omega over lowas Omega much + + align:start position:0% +for Capital Omega over lowas Omega much + + + align:start position:0% +for Capital Omega over lowas Omega much +less than one which was our unmagnetized + + align:start position:0% +less than one which was our unmagnetized + + + align:start position:0% +less than one which was our unmagnetized +addition we just reduced back to our + + align:start position:0% +addition we just reduced back to our + + + align:start position:0% +addition we just reduced back to our +magnetized dispers relationship so + + align:start position:0% +magnetized dispers relationship so + + + align:start position:0% +magnetized dispers relationship so +that's good we haven't introduced + + align:start position:0% +that's good we haven't introduced + + + align:start position:0% +that's good we haven't introduced +anything funky in the + + align:start position:0% + + + + align:start position:0% + +mag okay and then when we solve to get + + align:start position:0% +mag okay and then when we solve to get + + + align:start position:0% +mag okay and then when we solve to get +the I modes we find out that we have e x + + align:start position:0% +the I modes we find out that we have e x + + + align:start position:0% +the I modes we find out that we have e x +e y isal to plus orus I here let me just + + align:start position:0% +e y isal to plus orus I here let me just + + + align:start position:0% +e y isal to plus orus I here let me just +draw again the geometry + + align:start position:0% +draw again the geometry + + + align:start position:0% +draw again the geometry +existing Z upwards y like this x like + + align:start position:0% +existing Z upwards y like this x like + + + align:start position:0% +existing Z upwards y like this x like +this our magnetic field is in a z + + align:start position:0% +this our magnetic field is in a z + + + align:start position:0% +this our magnetic field is in a z +Direction and now our k + + align:start position:0% +Direction and now our k + + + align:start position:0% +Direction and now our k +vectoral z is also in the Z Direction + + align:start position:0% +vectoral z is also in the Z Direction + + + align:start position:0% +vectoral z is also in the Z Direction +and now we have X and e y + + align:start position:0% + + + + align:start position:0% + +L is equal to zero so this is again a + + align:start position:0% +L is equal to zero so this is again a + + + align:start position:0% +L is equal to zero so this is again a +transverse + + align:start position:0% + + + + align:start position:0% + +wave so does anyone know what this wave + + align:start position:0% +wave so does anyone know what this wave + + + align:start position:0% +wave so does anyone know what this wave +is the electric and the two components + + align:start position:0% +is the electric and the two components + + + align:start position:0% +is the electric and the two components +of the electric field appear to be out + + align:start position:0% +of the electric field appear to be out + + + align:start position:0% +of the electric field appear to be out +of phase from each other by a factor of + + align:start position:0% +of phase from each other by a factor of + + + align:start position:0% +of phase from each other by a factor of + + align:start position:0% + + + + align:start position:0% + +circly polarized yes everyone in the + + align:start position:0% +circly polarized yes everyone in the + + + align:start position:0% +circly polarized yes everyone in the +room is doing + + align:start position:0% +room is doing + + + align:start position:0% +room is doing +this I I I guess that I want to say + + align:start position:0% +this I I I guess that I want to say + + + align:start position:0% +this I I I guess that I want to say +second okay so what we can do is we can + + align:start position:0% +second okay so what we can do is we can + + + align:start position:0% +second okay so what we can do is we can +say you know ex is g to go like + + align:start position:0% +say you know ex is g to go like + + + align:start position:0% +say you know ex is g to go like +exponential of + + align:start position:0% +exponential of + + + align:start position:0% +exponential of +i k dot X in reality this is just right + + align:start position:0% + + + + align:start position:0% + +T and e y is exactly the same plus an + + align:start position:0% +T and e y is exactly the same plus an + + + align:start position:0% +T and e y is exactly the same plus an +extra factor of I upon 2 inside the + + align:start position:0% + + + + align:start position:0% + +brackets okay so if we + + align:start position:0% + + + + align:start position:0% + +plot either space or time it doesn't + + align:start position:0% +plot either space or time it doesn't + + + align:start position:0% +plot either space or time it doesn't +matter we can either fix ourselves in + + align:start position:0% +matter we can either fix ourselves in + + + align:start position:0% +matter we can either fix ourselves in +one place and watch a wave go by or we + + align:start position:0% +one place and watch a wave go by or we + + + align:start position:0% +one place and watch a wave go by or we +can attach ourselves the wave and see + + align:start position:0% +can attach ourselves the wave and see + + + align:start position:0% +can attach ourselves the wave and see +how it changes in space we're going to + + align:start position:0% +how it changes in space we're going to + + + align:start position:0% +how it changes in space we're going to +get at uh two oscillating Fields the + + align:start position:0% +get at uh two oscillating Fields the + + + align:start position:0% +get at uh two oscillating Fields the +electric field X will look like this the + + align:start position:0% +electric field X will look like this the + + + align:start position:0% +electric field X will look like this the +electric field in y will look + + align:start position:0% + + + + align:start position:0% + +like trying very hard to draw this + + align:start position:0% +like trying very hard to draw this + + + align:start position:0% +like trying very hard to draw this +properly + + align:start position:0% + + + + align:start position:0% + +that and if you then look at what in the + + align:start position:0% +that and if you then look at what in the + + + align:start position:0% +that and if you then look at what in the +XY plane the electric field is + + align:start position:0% +XY plane the electric field is + + + align:start position:0% +XY plane the electric field is +doing and you stop at this Point here + + align:start position:0% +doing and you stop at this Point here + + + align:start position:0% +doing and you stop at this Point here +and then at this point here and then at + + align:start position:0% +and then at this point here and then at + + + align:start position:0% +and then at this point here and then at +this point here and then at this point + + align:start position:0% +this point here and then at this point + + + align:start position:0% +this point here and then at this point +here and ask which direction is the + + align:start position:0% +here and ask which direction is the + + + align:start position:0% +here and ask which direction is the +electric field pointing well first of + + align:start position:0% +electric field pointing well first of + + + align:start position:0% +electric field pointing well first of +all it's going to be + + align:start position:0% +all it's going to be + + + align:start position:0% +all it's going to be +pointing entirely in the y direction and + + align:start position:0% +pointing entirely in the y direction and + + + align:start position:0% +pointing entirely in the y direction and +then it's going to be pointing entirely + + align:start position:0% +then it's going to be pointing entirely + + + align:start position:0% +then it's going to be pointing entirely +in the X + + align:start position:0% + + + + align:start position:0% + +Direction and so we can see the electric + + align:start position:0% +Direction and so we can see the electric + + + align:start position:0% +Direction and so we can see the electric +field VOR traces out a circle this is + + align:start position:0% +field VOR traces out a circle this is + + + align:start position:0% +field VOR traces out a circle this is +what we call circular polarization + + align:start position:0% +what we call circular polarization + + + align:start position:0% +what we call circular polarization +and often these two waves which I've + + align:start position:0% +and often these two waves which I've + + + align:start position:0% +and often these two waves which I've +been calling plus or minus + + align:start position:0% +been calling plus or minus + + + align:start position:0% +been calling plus or minus +here we might call them the right hand + + align:start position:0% +here we might call them the right hand + + + align:start position:0% +here we might call them the right hand +and the left hand circularly trailerized + + align:start position:0% +and the left hand circularly trailerized + + + align:start position:0% +and the left hand circularly trailerized +wave I can never remember the convention + + align:start position:0% +wave I can never remember the convention + + + align:start position:0% +wave I can never remember the convention +but I think it's like right hand + + align:start position:0% +but I think it's like right hand + + + align:start position:0% +but I think it's like right hand +rule vector and it's like is it going + + align:start position:0% +rule vector and it's like is it going + + + align:start position:0% +rule vector and it's like is it going +this way or is it going the other way + + align:start position:0% +this way or is it going the other way + + + align:start position:0% +this way or is it going the other way +like that um I never really mind too + + align:start position:0% +like that um I never really mind too + + + align:start position:0% +like that um I never really mind too +much about which way around it is but + + align:start position:0% +much about which way around it is but + + + align:start position:0% +much about which way around it is but +there is a convention about whether it's + + align:start position:0% +there is a convention about whether it's + + + align:start position:0% +there is a convention about whether it's +right or left and that's what this plus + + align:start position:0% +right or left and that's what this plus + + + align:start position:0% +right or left and that's what this plus +and negative sign really mean here we've + + align:start position:0% +and negative sign really mean here we've + + + align:start position:0% +and negative sign really mean here we've +got two modes one of which is going + + align:start position:0% +got two modes one of which is going + + + align:start position:0% +got two modes one of which is going +clockwise and one of is going + + align:start position:0% +clockwise and one of is going + + + align:start position:0% +clockwise and one of is going +counterclockwise okay any questions on + + align:start position:0% +counterclockwise okay any questions on + + + align:start position:0% +counterclockwise okay any questions on +that we're going to use that in a moment + + align:start position:0% +that we're going to use that in a moment + + + align:start position:0% +that we're going to use that in a moment +there there's not really anything + + align:start position:0% +there there's not really anything + + + align:start position:0% +there there's not really anything +particular profound at this point we + + align:start position:0% +particular profound at this point we + + + align:start position:0% +particular profound at this point we +will get on to something profound in a + + align:start position:0% +will get on to something profound in a + + + align:start position:0% +will get on to something profound in a +moment any questions on Act + + align:start position:0% + + + + align:start position:0% + +okay just so I can keep that up on the + + align:start position:0% +okay just so I can keep that up on the + + + align:start position:0% +okay just so I can keep that up on the +board I'm get this stuff forget about + + align:start position:0% +board I'm get this stuff forget about + + + align:start position:0% +board I'm get this stuff forget about +that until we get on to + + align:start position:0% + + + + align:start position:0% + +so now finally we fulfilling promis and + + align:start position:0% +so now finally we fulfilling promis and + + + align:start position:0% +so now finally we fulfilling promis and +we're going to talk about + + align:start position:0% + + + + align:start position:0% + +paration and the main point about ration + + align:start position:0% +paration and the main point about ration + + + align:start position:0% +paration and the main point about ration +is that your magnetic fields cause a + + align:start position:0% +is that your magnetic fields cause a + + + align:start position:0% +is that your magnetic fields cause a +phenomena called by + + align:start position:0% + + + + align:start position:0% + +refringent does anyone come across + + align:start position:0% +refringent does anyone come across + + + align:start position:0% +refringent does anyone come across +refringence studying Optics before and + + align:start position:0% +refringence studying Optics before and + + + align:start position:0% +refringence studying Optics before and +can give us a concise + + align:start position:0% + + + + align:start position:0% + +definition yes either one of you you can + + align:start position:0% +definition yes either one of you you can + + + align:start position:0% +definition yes either one of you you can +sort of say it in + + align:start position:0% + + + + align:start position:0% + +unison it's object index ofaction is + + align:start position:0% +unison it's object index ofaction is + + + align:start position:0% +unison it's object index ofaction is +different depending on the direction of + + align:start position:0% +different depending on the direction of + + + align:start position:0% +different depending on the direction of +propagation yeah + + align:start position:0% + + + + align:start position:0% + +no is that your guess too my that that + + align:start position:0% +no is that your guess too my that that + + + align:start position:0% +no is that your guess too my that that +is a really interesting phenomena and it + + align:start position:0% +is a really interesting phenomena and it + + + align:start position:0% +is a really interesting phenomena and it +definitely happens but it's not this + + align:start position:0% + + + + align:start position:0% + +yeah angle reflection depends + + align:start position:0% +yeah angle reflection depends + + + align:start position:0% +yeah angle reflection depends +on okay so that was the angle of + + align:start position:0% +on okay so that was the angle of + + + align:start position:0% +on okay so that was the angle of +reflection depends on the frequency no + + align:start position:0% +reflection depends on the frequency no + + + align:start position:0% +reflection depends on the frequency no +that's also not true but that's not a + + align:start position:0% +that's also not true but that's not a + + + align:start position:0% +that's also not true but that's not a +good definition of + + align:start position:0% + + + + align:start position:0% + +Hance anyone got any thoughts about what + + align:start position:0% +Hance anyone got any thoughts about what + + + align:start position:0% +Hance anyone got any thoughts about what +V refringence could be related to + + align:start position:0% +V refringence could be related to + + + align:start position:0% +V refringence could be related to +anything on this board here that makes + + align:start position:0% +anything on this board here that makes + + + align:start position:0% +anything on this board here that makes +you think anyone online um I'll give it + + align:start position:0% +you think anyone online um I'll give it + + + align:start position:0% +you think anyone online um I'll give it +a try sorry I'll give it a try yeah + + align:start position:0% +a try sorry I'll give it a try yeah + + + align:start position:0% +a try sorry I'll give it a try yeah +please um B refringence is that there + + align:start position:0% +please um B refringence is that there + + + align:start position:0% +please um B refringence is that there +are different refractive indexes for + + align:start position:0% +are different refractive indexes for + + + align:start position:0% +are different refractive indexes for +different directions not different + + align:start position:0% +different directions not different + + + align:start position:0% +different directions not different +directions different components of the + + align:start position:0% +directions different components of the + + + align:start position:0% +directions different components of the +uh material so it's like a tensor and + + align:start position:0% +uh material so it's like a tensor and + + + align:start position:0% +uh material so it's like a tensor and +then the different components have + + align:start position:0% +then the different components have + + + align:start position:0% +then the different components have +different refractive indexes yeah this + + align:start position:0% +different refractive indexes yeah this + + + align:start position:0% +different refractive indexes yeah this +is very very close so it's different + + align:start position:0% +is very very close so it's different + + + align:start position:0% +is very very close so it's different +refractive indexes for different + + align:start position:0% +refractive indexes for different + + + align:start position:0% +refractive indexes for different +polarizations for different directions + + align:start position:0% +polarizations for different directions + + + align:start position:0% +polarizations for different directions +of the electric field so everyone had + + align:start position:0% +of the electric field so everyone had + + + align:start position:0% +of the electric field so everyone had +some thought about Direction in there + + align:start position:0% +some thought about Direction in there + + + align:start position:0% +some thought about Direction in there +and that was all good it's not to do + + align:start position:0% +and that was all good it's not to do + + + align:start position:0% +and that was all good it's not to do +with frequency though of course this is + + align:start position:0% +with frequency though of course this is + + + align:start position:0% +with frequency though of course this is +frequency dependent but of course the + + align:start position:0% +frequency dependent but of course the + + + align:start position:0% +frequency dependent but of course the +refractive index for plasma is always + + align:start position:0% +refractive index for plasma is always + + + align:start position:0% +refractive index for plasma is always +frequency dependent so that's that's not + + align:start position:0% +frequency dependent so that's that's not + + + align:start position:0% +frequency dependent so that's that's not +a unique thing for this solution here + + align:start position:0% +a unique thing for this solution here + + + align:start position:0% +a unique thing for this solution here +the unique thing about it is that these + + align:start position:0% +the unique thing about it is that these + + + align:start position:0% +the unique thing about it is that these +waves have got different speed so the + + align:start position:0% +waves have got different speed so the + + + align:start position:0% +waves have got different speed so the +other thing the X mode and the O mode + + align:start position:0% +other thing the X mode and the O mode + + + align:start position:0% +other thing the X mode and the O mode +those are also b refringent as well + + align:start position:0% +those are also b refringent as well + + + align:start position:0% +those are also b refringent as well +they're just not b refringent in a + + align:start position:0% +they're just not b refringent in a + + + align:start position:0% +they're just not b refringent in a +particularly useful way this is b + + align:start position:0% +particularly useful way this is b + + + align:start position:0% +particularly useful way this is b +refringent in a way that we can + + align:start position:0% +refringent in a way that we can + + + align:start position:0% +refringent in a way that we can +exploit okay and um if you ever want to + + align:start position:0% +exploit okay and um if you ever want to + + + align:start position:0% +exploit okay and um if you ever want to +go down a rabit ho of interesting stuff + + align:start position:0% +go down a rabit ho of interesting stuff + + + align:start position:0% +go down a rabit ho of interesting stuff +there were several Viking vars where + + align:start position:0% +there were several Viking vars where + + + align:start position:0% +there were several Viking vars where +they found from these Viking Warlords + + align:start position:0% +they found from these Viking Warlords + + + align:start position:0% +they found from these Viking Warlords +buried with lumps of calite and people + + align:start position:0% +buried with lumps of calite and people + + + align:start position:0% +buried with lumps of calite and people +are like why have they got calite it's + + align:start position:0% +are like why have they got calite it's + + + align:start position:0% +are like why have they got calite it's +not a particularly pretty Crystal it's + + align:start position:0% +not a particularly pretty Crystal it's + + + align:start position:0% +not a particularly pretty Crystal it's +kind of transparent and you can't really + + align:start position:0% +kind of transparent and you can't really + + + align:start position:0% +kind of transparent and you can't really +make jewelry out of it it's it's sort of + + align:start position:0% +make jewelry out of it it's it's sort of + + + align:start position:0% +make jewelry out of it it's it's sort of +you know quarty and it wasn't carved in + + align:start position:0% +you know quarty and it wasn't carved in + + + align:start position:0% +you know quarty and it wasn't carved in +any case it was just this lump of Cal + + align:start position:0% +any case it was just this lump of Cal + + + align:start position:0% +any case it was just this lump of Cal +and there is a belief unproven amongst + + align:start position:0% +and there is a belief unproven amongst + + + align:start position:0% +and there is a belief unproven amongst +archaeologists that this calite which is + + align:start position:0% +archaeologists that this calite which is + + + align:start position:0% +archaeologists that this calite which is +a b refringent material could be used to + + align:start position:0% +a b refringent material could be used to + + + align:start position:0% +a b refringent material could be used to +navigate on a cloudy day so when you're + + align:start position:0% +navigate on a cloudy day so when you're + + + align:start position:0% +navigate on a cloudy day so when you're +sailing across the Atlantic or the North + + align:start position:0% +sailing across the Atlantic or the North + + + align:start position:0% +sailing across the Atlantic or the North +Sea to ra some Monastery um and it's all + + align:start position:0% +Sea to ra some Monastery um and it's all + + + align:start position:0% +Sea to ra some Monastery um and it's all +cloudy like Dam you know I don't know + + align:start position:0% +cloudy like Dam you know I don't know + + + align:start position:0% +cloudy like Dam you know I don't know +how to get to this Monastery and they + + align:start position:0% +how to get to this Monastery and they + + + align:start position:0% +how to get to this Monastery and they +didn't have compasses in those days at + + align:start position:0% +didn't have compasses in those days at + + + align:start position:0% +didn't have compasses in those days at +least the Vikings didn't the Chinese did + + align:start position:0% +least the Vikings didn't the Chinese did + + + align:start position:0% +least the Vikings didn't the Chinese did +um the compasses this IR crystal is very + + align:start position:0% +um the compasses this IR crystal is very + + + align:start position:0% +um the compasses this IR crystal is very +interesting because you might know that + + align:start position:0% +interesting because you might know that + + + align:start position:0% +interesting because you might know that +the light from the sun is polarized by + + align:start position:0% +the light from the sun is polarized by + + + align:start position:0% +the light from the sun is polarized by +scattering and so although that light + + align:start position:0% +scattering and so although that light + + + align:start position:0% +scattering and so although that light +isn't directly hitting your ship in the + + align:start position:0% +isn't directly hitting your ship in the + + + align:start position:0% +isn't directly hitting your ship in the +fog some of that light is getting + + align:start position:0% +fog some of that light is getting + + + align:start position:0% +fog some of that light is getting +through and although the fog is messing + + align:start position:0% +through and although the fog is messing + + + align:start position:0% +through and although the fog is messing +with that polarization there's still + + align:start position:0% +with that polarization there's still + + + align:start position:0% +with that polarization there's still +going to be some overall polarization + + align:start position:0% +going to be some overall polarization + + + align:start position:0% +going to be some overall polarization +there and by rotating this bi + + align:start position:0% +there and by rotating this bi + + + align:start position:0% +there and by rotating this bi +refrigerant crystal in the lights that + + align:start position:0% +refrigerant crystal in the lights that + + + align:start position:0% +refrigerant crystal in the lights that +you're getting that's slightly polarized + + align:start position:0% +you're getting that's slightly polarized + + + align:start position:0% +you're getting that's slightly polarized +from the Sun and looking at markings on + + align:start position:0% +from the Sun and looking at markings on + + + align:start position:0% +from the Sun and looking at markings on +a bit of stone when you rotate the + + align:start position:0% +a bit of stone when you rotate the + + + align:start position:0% +a bit of stone when you rotate the +crystal just so the light is going to + + align:start position:0% +crystal just so the light is going to + + + align:start position:0% +crystal just so the light is going to +come through and the two markings will + + align:start position:0% +come through and the two markings will + + + align:start position:0% +come through and the two markings will +line up and then you will know roughly + + align:start position:0% +line up and then you will know roughly + + + align:start position:0% +line up and then you will know roughly +where North is and then you can go and + + align:start position:0% +where North is and then you can go and + + + align:start position:0% +where North is and then you can go and +sail and ra so not saying it's true you + + align:start position:0% +sail and ra so not saying it's true you + + + align:start position:0% +sail and ra so not saying it's true you +go read some really cool papers on + + align:start position:0% +go read some really cool papers on + + + align:start position:0% +go read some really cool papers on +people trying to do this like people + + align:start position:0% +people trying to do this like people + + + align:start position:0% +people trying to do this like people +have tried to go out in a boat on a + + align:start position:0% +have tried to go out in a boat on a + + + align:start position:0% +have tried to go out in a boat on a +cloudy day and navigate like this it did + + align:start position:0% +cloudy day and navigate like this it did + + + align:start position:0% +cloudy day and navigate like this it did +not go + + align:start position:0% +not go + + + align:start position:0% +not go +well but you know they didn't have as + + align:start position:0% +well but you know they didn't have as + + + align:start position:0% +well but you know they didn't have as +much practice as the Vikings thing + + align:start position:0% +much practice as the Vikings thing + + + align:start position:0% +much practice as the Vikings thing +because we have GPS these days and so we + + align:start position:0% +because we have GPS these days and so we + + + align:start position:0% +because we have GPS these days and so we +don't worry about such things but it's + + align:start position:0% +don't worry about such things but it's + + + align:start position:0% +don't worry about such things but it's +really cool so if you like Optics go + + align:start position:0% +really cool so if you like Optics go + + + align:start position:0% +really cool so if you like Optics go +look up Viking sunstones + + align:start position:0% + + + + align:start position:0% + +they I always like + + align:start position:0% +they I always like + + + align:start position:0% +they I always like +R okay back to + + align:start position:0% +R okay back to + + + align:start position:0% +R okay back to +plasmas so we said we have these two + + align:start position:0% +plasmas so we said we have these two + + + align:start position:0% +plasmas so we said we have these two +modes inside the plasma uh these are the + + align:start position:0% +modes inside the plasma uh these are the + + + align:start position:0% +modes inside the plasma uh these are the +right hand and left hand circly polarize + + align:start position:0% +right hand and left hand circly polarize + + + align:start position:0% +right hand and left hand circly polarize +modes which I'm going to refer to as + + align:start position:0% +modes which I'm going to refer to as + + + align:start position:0% +modes which I'm going to refer to as +plus and minus like this so plus is the + + align:start position:0% +plus and minus like this so plus is the + + + align:start position:0% +plus and minus like this so plus is the +clockwise going mode and minus is the + + align:start position:0% +clockwise going mode and minus is the + + + align:start position:0% +clockwise going mode and minus is the +anticlockwise going if you're confused + + align:start position:0% +anticlockwise going if you're confused + + + align:start position:0% +anticlockwise going if you're confused +about why I'm confused about this + + align:start position:0% +about why I'm confused about this + + + align:start position:0% +about why I'm confused about this +convention it's because like is it + + align:start position:0% +convention it's because like is it + + + align:start position:0% +convention it's because like is it +clockwise as you look down the ray of + + align:start position:0% +clockwise as you look down the ray of + + + align:start position:0% +clockwise as you look down the ray of +light or is it clockwise as you look + + align:start position:0% +light or is it clockwise as you look + + + align:start position:0% +light or is it clockwise as you look +towards the ray of light those are + + align:start position:0% +towards the ray of light those are + + + align:start position:0% +towards the ray of light those are +different and I can never remember which + + align:start position:0% +different and I can never remember which + + + align:start position:0% +different and I can never remember which +one the convention is for okay I think + + align:start position:0% +one the convention is for okay I think + + + align:start position:0% +one the convention is for okay I think +it probably should be as you look down + + align:start position:0% +it probably should be as you look down + + + align:start position:0% +it probably should be as you look down +the ray of L but who knows and so maybe + + align:start position:0% +the ray of L but who knows and so maybe + + + align:start position:0% +the ray of L but who knows and so maybe +I've got this the wrong way around if I + + align:start position:0% +I've got this the wrong way around if I + + + align:start position:0% +I've got this the wrong way around if I +got the wrong way around you just swap + + align:start position:0% +got the wrong way around you just swap + + + align:start position:0% +got the wrong way around you just swap +whether I'm looking down the r of light + + align:start position:0% +whether I'm looking down the r of light + + + align:start position:0% +whether I'm looking down the r of light +or at the r of light where I'm looking + + align:start position:0% +or at the r of light where I'm looking + + + align:start position:0% +or at the r of light where I'm looking +down the r of light and then I'll be + + align:start position:0% +down the r of light and then I'll be + + + align:start position:0% +down the r of light and then I'll be +writing again so it's um oh note by the + + align:start position:0% +writing again so it's um oh note by the + + + align:start position:0% +writing again so it's um oh note by the +way that this does depend on the + + align:start position:0% +way that this does depend on the + + + align:start position:0% +way that this does depend on the +direction the magnetic field this is not + + align:start position:0% +direction the magnetic field this is not + + + align:start position:0% +direction the magnetic field this is not +omega squar Capital Omega squ it's just + + align:start position:0% +omega squar Capital Omega squ it's just + + + align:start position:0% +omega squar Capital Omega squ it's just +Omega so the direction of the magnetic + + align:start position:0% +Omega so the direction of the magnetic + + + align:start position:0% +Omega so the direction of the magnetic +field changes which of these modes + + align:start position:0% +field changes which of these modes + + + align:start position:0% +field changes which of these modes +propagates faster if you're propagating + + align:start position:0% +propagates faster if you're propagating + + + align:start position:0% +propagates faster if you're propagating +along the magnetic field one of your + + align:start position:0% +along the magnetic field one of your + + + align:start position:0% +along the magnetic field one of your +modes is faster than the other if you're + + align:start position:0% +modes is faster than the other if you're + + + align:start position:0% +modes is faster than the other if you're +propagating against magnet field the + + align:start position:0% +propagating against magnet field the + + + align:start position:0% +propagating against magnet field the +other mode is faster that's very + + align:start position:0% +other mode is faster that's very + + + align:start position:0% +other mode is faster that's very +important that's going to be what we use + + align:start position:0% +important that's going to be what we use + + + align:start position:0% +important that's going to be what we use +to measure both the magnetic Field's + + align:start position:0% +to measure both the magnetic Field's + + + align:start position:0% +to measure both the magnetic Field's +amplitude and its + + align:start position:0% +amplitude and its + + + align:start position:0% +amplitude and its +direction and we can use this neat uh + + align:start position:0% +direction and we can use this neat uh + + + align:start position:0% +direction and we can use this neat uh +technique called Stokes + + align:start position:0% +technique called Stokes + + + align:start position:0% +technique called Stokes +vectors uh where a Stokes Vector is uh + + align:start position:0% +vectors uh where a Stokes Vector is uh + + + align:start position:0% +vectors uh where a Stokes Vector is uh +just a vector of + + align:start position:0% +just a vector of + + + align:start position:0% +just a vector of +e e normalized by the sum of E2 plus e y + + align:start position:0% +e e normalized by the sum of E2 plus e y + + + align:start position:0% +e e normalized by the sum of E2 plus e y +squ these Stokes vectors make our life + + align:start position:0% +squ these Stokes vectors make our life + + + align:start position:0% +squ these Stokes vectors make our life +very easy when we want to calculations + + align:start position:0% + + + + align:start position:0% + +same guy as stok theorem um and we can + + align:start position:0% +same guy as stok theorem um and we can + + + align:start position:0% +same guy as stok theorem um and we can +say looking at this relation between + + align:start position:0% +say looking at this relation between + + + align:start position:0% +say looking at this relation between +these two that the e+ is going to have + + align:start position:0% +these two that the e+ is going to have + + + align:start position:0% +these two that the e+ is going to have +something I'm going to call the vector R + + align:start position:0% +something I'm going to call the vector R + + + align:start position:0% +something I'm going to call the vector R +and that's going to be one over I oh I + + align:start position:0% +and that's going to be one over I oh I + + + align:start position:0% +and that's going to be one over I oh I +lied I'm not going to normalize all of + + align:start position:0% +lied I'm not going to normalize all of + + + align:start position:0% +lied I'm not going to normalize all of +them I can't be bothered to put a square + + align:start position:0% +them I can't be bothered to put a square + + + align:start position:0% +them I can't be bothered to put a square +root in front of this so just remember + + align:start position:0% +root in front of this so just remember + + + align:start position:0% +root in front of this so just remember +there should be a square2 matter and + + align:start position:0% +there should be a square2 matter and + + + align:start position:0% +there should be a square2 matter and +then the left Vector is going to be + + align:start position:0% +then the left Vector is going to be + + + align:start position:0% +then the left Vector is going to be +oneus R and you can see that these have + + align:start position:0% +oneus R and you can see that these have + + + align:start position:0% +oneus R and you can see that these have +the same relationships between ex and e + + align:start position:0% +the same relationships between ex and e + + + align:start position:0% +the same relationships between ex and e +um and so these are the Stoke spectors + + align:start position:0% +um and so these are the Stoke spectors + + + align:start position:0% +um and so these are the Stoke spectors +from right and left so light we also can + + align:start position:0% +from right and left so light we also can + + + align:start position:0% +from right and left so light we also can +write some other polarizations in this + + align:start position:0% +write some other polarizations in this + + + align:start position:0% +write some other polarizations in this +Stoke Spector notation so if we were + + align:start position:0% +Stoke Spector notation so if we were + + + align:start position:0% +Stoke Spector notation so if we were +polarized entirely in the X Direction + + align:start position:0% +polarized entirely in the X Direction + + + align:start position:0% +polarized entirely in the X Direction +here so ey equals z this would be the + + align:start position:0% +here so ey equals z this would be the + + + align:start position:0% +here so ey equals z this would be the +vector X and that would be equal to one + + align:start position:0% +vector X and that would be equal to one + + + align:start position:0% +vector X and that would be equal to one +Z and if we have x equal to Z this will + + align:start position:0% +Z and if we have x equal to Z this will + + + align:start position:0% +Z and if we have x equal to Z this will +be the vector capital Y this will be + + align:start position:0% +be the vector capital Y this will be + + + align:start position:0% +be the vector capital Y this will be +equal to Z one like that now there are + + align:start position:0% +equal to Z one like that now there are + + + align:start position:0% +equal to Z one like that now there are +two modes inside the plasma we can write + + align:start position:0% +two modes inside the plasma we can write + + + align:start position:0% +two modes inside the plasma we can write +any arbitrary polarization of our wave + + align:start position:0% +any arbitrary polarization of our wave + + + align:start position:0% +any arbitrary polarization of our wave +as a sum of these two basis vectors + + align:start position:0% +as a sum of these two basis vectors + + + align:start position:0% +as a sum of these two basis vectors +effectively and so we can switch basis + + align:start position:0% +effectively and so we can switch basis + + + align:start position:0% +effectively and so we can switch basis +vectors if we want to so generally when + + align:start position:0% +vectors if we want to so generally when + + + align:start position:0% +vectors if we want to so generally when +we're launching lights we don't launch + + align:start position:0% +we're launching lights we don't launch + + + align:start position:0% +we're launching lights we don't launch +it with a circular polarization that's + + align:start position:0% +it with a circular polarization that's + + + align:start position:0% +it with a circular polarization that's +quite hard to come by we launch it with + + align:start position:0% +quite hard to come by we launch it with + + + align:start position:0% +quite hard to come by we launch it with +some linear polarization but this linear + + align:start position:0% +some linear polarization but this linear + + + align:start position:0% +some linear polarization but this linear +polarization is made up of these two + + align:start position:0% +polarization is made up of these two + + + align:start position:0% +polarization is made up of these two +circular polarizations so for example + + align:start position:0% +circular polarizations so for example + + + align:start position:0% +circular polarizations so for example +this x linear polarization is + + align:start position:0% +this x linear polarization is + + + align:start position:0% +this x linear polarization is +R plus + + align:start position:0% +R plus + + + align:start position:0% +R plus +l two the Y polarization is R minus + + align:start position:0% +l two the Y polarization is R minus + + + align:start position:0% +l two the Y polarization is R minus +L over + + align:start position:0% + + + + align:start position:0% + +two don't know why + + align:start position:0% + + + + align:start position:0% + +I oh well okay maybe it's a good point + + align:start position:0% +I oh well okay maybe it's a good point + + + align:start position:0% +I oh well okay maybe it's a good point +so just to draw our geometry another + + align:start position:0% +so just to draw our geometry another + + + align:start position:0% +so just to draw our geometry another +time like this we've got some K Vector + + align:start position:0% +time like this we've got some K Vector + + + align:start position:0% +time like this we've got some K Vector +which is an angle Theta to the magnetic + + align:start position:0% +which is an angle Theta to the magnetic + + + align:start position:0% +which is an angle Theta to the magnetic +field B like that and again for theta + + align:start position:0% +field B like that and again for theta + + + align:start position:0% +field B like that and again for theta +equals + + align:start position:0% +equals + + + align:start position:0% +equals +zero this is our dispersion relationship + + align:start position:0% +zero this is our dispersion relationship + + + align:start position:0% +zero this is our dispersion relationship +I just want to point out one slightly + + align:start position:0% +I just want to point out one slightly + + + align:start position:0% +I just want to point out one slightly +funny I think it's funny thing about + + align:start position:0% +funny I think it's funny thing about + + + align:start position:0% +funny I think it's funny thing about +this so if we have K in this + + align:start position:0% +this so if we have K in this + + + align:start position:0% +this so if we have K in this +direction that means that this wave is a + + align:start position:0% +direction that means that this wave is a + + + align:start position:0% +direction that means that this wave is a +parallel + + align:start position:0% +parallel + + + align:start position:0% +parallel +propagation but of course it's still a + + align:start position:0% +propagation but of course it's still a + + + align:start position:0% +propagation but of course it's still a +transverse wave I think people often get + + align:start position:0% +transverse wave I think people often get + + + align:start position:0% +transverse wave I think people often get +this very confused because the words + + align:start position:0% +this very confused because the words + + + align:start position:0% +this very confused because the words +parallel and perpendicular and + + align:start position:0% +parallel and perpendicular and + + + align:start position:0% +parallel and perpendicular and +transverse and longitudinal have similar + + align:start position:0% +transverse and longitudinal have similar + + + align:start position:0% +transverse and longitudinal have similar +meanings so this is a parallel and + + align:start position:0% +meanings so this is a parallel and + + + align:start position:0% +meanings so this is a parallel and +transverse + + align:start position:0% + + + + align:start position:0% + +W and there's one more word as well + + align:start position:0% +W and there's one more word as well + + + align:start position:0% +W and there's one more word as well +which means something similar I can't + + align:start position:0% +which means something similar I can't + + + align:start position:0% +which means something similar I can't +remember which one it is but yeah there + + align:start position:0% +remember which one it is but yeah there + + + align:start position:0% +remember which one it is but yeah there +lot of yeah for the Rus L what + + align:start position:0% +lot of yeah for the Rus L what + + + align:start position:0% +lot of yeah for the Rus L what +that oh yeah I meant to there + + align:start position:0% +that oh yeah I meant to there + + + align:start position:0% +that oh yeah I meant to there +here + + align:start position:0% + + + + align:start position:0% + +looking or maybe that + + align:start position:0% +looking or maybe that + + + align:start position:0% +looking or maybe that +but no it's + + align:start position:0% +but no it's + + + align:start position:0% +but no it's +not cool okay it turns out you know we I + + align:start position:0% +not cool okay it turns out you know we I + + + align:start position:0% +not cool okay it turns out you know we I +derive this for Theta Pi 2 I didn't dve + + align:start position:0% +derive this for Theta Pi 2 I didn't dve + + + align:start position:0% +derive this for Theta Pi 2 I didn't dve +it I showed you it for pi 2 and Theta + + align:start position:0% +it I showed you it for pi 2 and Theta + + + align:start position:0% +it I showed you it for pi 2 and Theta +equal Z and but it actually turns out + + align:start position:0% +equal Z and but it actually turns out + + + align:start position:0% +equal Z and but it actually turns out +that the theta equals z case applies + + align:start position:0% +that the theta equals z case applies + + + align:start position:0% +that the theta equals z case applies +over a huge range of different uh + + align:start position:0% +over a huge range of different uh + + + align:start position:0% +over a huge range of different uh +conditions here so in fact this beta + + align:start position:0% +conditions here so in fact this beta + + + align:start position:0% +conditions here so in fact this beta +equals zero which we call the POS + + align:start position:0% +equals zero which we call the POS + + + align:start position:0% +equals zero which we call the POS +parallel + + align:start position:0% +parallel + + + align:start position:0% +parallel +case it isn't good simply for theta + + align:start position:0% +case it isn't good simply for theta + + + align:start position:0% +case it isn't good simply for theta +equals z it's good for Capital Omega + + align:start position:0% +equals z it's good for Capital Omega + + + align:start position:0% +equals z it's good for Capital Omega +over Omega the cant of data is much much + + align:start position:0% +over Omega the cant of data is much much + + + align:start position:0% +over Omega the cant of data is much much +less than + + align:start position:0% +less than + + + align:start position:0% +less than +one and it turns out that uh for some + + align:start position:0% +one and it turns out that uh for some + + + align:start position:0% +one and it turns out that uh for some +reasonable values of Omega here and here + + align:start position:0% +reasonable values of Omega here and here + + + align:start position:0% +reasonable values of Omega here and here +this can apply for for Theta almost the + + align:start position:0% +this can apply for for Theta almost the + + + align:start position:0% +this can apply for for Theta almost the +pi upon 2 so you can use this dispersion + + align:start position:0% +pi upon 2 so you can use this dispersion + + + align:start position:0% +pi upon 2 so you can use this dispersion +relationship as I set up here even for + + align:start position:0% +relationship as I set up here even for + + + align:start position:0% +relationship as I set up here even for +relatively large angles the waves will + + align:start position:0% +relatively large angles the waves will + + + align:start position:0% +relatively large angles the waves will +propagate as if they had this dispersion + + align:start position:0% +propagate as if they had this dispersion + + + align:start position:0% +propagate as if they had this dispersion +relationship or at least extremely close + + align:start position:0% +relationship or at least extremely close + + + align:start position:0% +relationship or at least extremely close +to and that's very very + + align:start position:0% +to and that's very very + + + align:start position:0% +to and that's very very +convenient they they will propagate with + + align:start position:0% +convenient they they will propagate with + + + align:start position:0% +convenient they they will propagate with +that dispersion relationship as long as + + align:start position:0% +that dispersion relationship as long as + + + align:start position:0% +that dispersion relationship as long as +you write your e to be the component + + align:start position:0% +you write your e to be the component + + + align:start position:0% +you write your e to be the component +parallel to propagation so you replace B + + align:start position:0% +parallel to propagation so you replace B + + + align:start position:0% +parallel to propagation so you replace B +with B zero + + align:start position:0% +with B zero + + + align:start position:0% +with B zero +cosine of theta so now the dispersion + + align:start position:0% +cosine of theta so now the dispersion + + + align:start position:0% +cosine of theta so now the dispersion +relationship here which has Capital + + align:start position:0% +relationship here which has Capital + + + align:start position:0% +relationship here which has Capital +Omega in is to do with the projection of + + align:start position:0% +Omega in is to do with the projection of + + + align:start position:0% +Omega in is to do with the projection of +the magnetic field along your wave so + + align:start position:0% +the magnetic field along your wave so + + + align:start position:0% +the magnetic field along your wave so +effectively the wave feels the component + + align:start position:0% +effectively the wave feels the component + + + align:start position:0% +effectively the wave feels the component +of the magnetic field in the direction + + align:start position:0% +of the magnetic field in the direction + + + align:start position:0% +of the magnetic field in the direction +it's traveling and ignores that other + + align:start position:0% +it's traveling and ignores that other + + + align:start position:0% +it's traveling and ignores that other +component until it gets very very close + + align:start position:0% +component until it gets very very close + + + align:start position:0% +component until it gets very very close +to Pi upon two when the component along + + align:start position:0% +to Pi upon two when the component along + + + align:start position:0% +to Pi upon two when the component along +the direction of travel is almost zero + + align:start position:0% +the direction of travel is almost zero + + + align:start position:0% +the direction of travel is almost zero +and then we suddenly see this pi over + + align:start position:0% +and then we suddenly see this pi over + + + align:start position:0% +and then we suddenly see this pi over +two condition so this is very very + + align:start position:0% +two condition so this is very very + + + align:start position:0% +two condition so this is very very +useful because it means that we only + + align:start position:0% +useful because it means that we only + + + align:start position:0% +useful because it means that we only +need to have for some cylindrical object + + align:start position:0% +need to have for some cylindrical object + + + align:start position:0% +need to have for some cylindrical object +like this we can use this um uh + + align:start position:0% +like this we can use this um uh + + + align:start position:0% +like this we can use this um uh +dispersion relationship for almost the + + align:start position:0% +dispersion relationship for almost the + + + align:start position:0% +dispersion relationship for almost the +entire region that we're programed for + + align:start position:0% +entire region that we're programed for + + + align:start position:0% +entire region that we're programed for +farad rotation okay I'm well aware that + + align:start position:0% +farad rotation okay I'm well aware that + + + align:start position:0% +farad rotation okay I'm well aware that +I've G time so I'm going to leave it + + align:start position:0% +I've G time so I'm going to leave it + + + align:start position:0% +I've G time so I'm going to leave it +here and we will get on to exactly how + + align:start position:0% +here and we will get on to exactly how + + + align:start position:0% +here and we will get on to exactly how +we exploit this interesting mathematics + + align:start position:0% +we exploit this interesting mathematics + + + align:start position:0% +we exploit this interesting mathematics +and these Scopes vectors in order to + + align:start position:0% +and these Scopes vectors in order to + + + align:start position:0% +and these Scopes vectors in order to +measure magnetic fields in the next + + align:start position:0% +measure magnetic fields in the next + + + align:start position:0% +measure magnetic fields in the next +lecture so thank you very much I'll see + + align:start position:0% +lecture so thank you very much I'll see + + + align:start position:0% +lecture so thank you very much I'll see +you oh not on Tuesday because you all + + align:start position:0% +you oh not on Tuesday because you all + + + align:start position:0% +you oh not on Tuesday because you all +have a student holiday so for the people + + align:start position:0% +have a student holiday so for the people + + + align:start position:0% +have a student holiday so for the people +in Columbia who are unfamiliar with this + + align:start position:0% +in Columbia who are unfamiliar with this + + + align:start position:0% +in Columbia who are unfamiliar with this +idea we have Monday off and then to + + align:start position:0% +idea we have Monday off and then to + + + align:start position:0% +idea we have Monday off and then to +recover from the three-day + + align:start position:0% +recover from the three-day + + + align:start position:0% +recover from the three-day +weekend the students have a second day + + align:start position:0% +weekend the students have a second day + + + align:start position:0% +weekend the students have a second day +off for the classes so I will see you on + + align:start position:0% +off for the classes so I will see you on + + + align:start position:0% +off for the classes so I will see you on +Thursday okay \ No newline at end of file diff --git a/73wmLvud_O8.txt b/73wmLvud_O8.txt new file mode 100644 index 0000000000000000000000000000000000000000..70fa62ea3a928d251ad24bc70c181c9dc57b7734 --- /dev/null +++ b/73wmLvud_O8.txt @@ -0,0 +1,17315 @@ +align:start position:0% + +foreign + + align:start position:0% + + + + align:start position:0% + +talk about in the last week in terms of + + align:start position:0% +talk about in the last week in terms of + + + align:start position:0% +talk about in the last week in terms of +credit I'm not quite done with the labor + + align:start position:0% +credit I'm not quite done with the labor + + + align:start position:0% +credit I'm not quite done with the labor +section so what I'm going to do is just + + align:start position:0% +section so what I'm going to do is just + + + align:start position:0% +section so what I'm going to do is just +spend about 10 minutes just sort of + + align:start position:0% +spend about 10 minutes just sort of + + + align:start position:0% +spend about 10 minutes just sort of +giving a couple of highlights of some of + + align:start position:0% +giving a couple of highlights of some of + + + align:start position:0% +giving a couple of highlights of some of +the last like a little overview of + + align:start position:0% +the last like a little overview of + + + align:start position:0% +the last like a little overview of +coming to the topics that that are in + + align:start position:0% +coming to the topics that that are in + + + align:start position:0% +coming to the topics that that are in +the labor notes you're welcome to sort + + align:start position:0% +the labor notes you're welcome to sort + + + align:start position:0% +the labor notes you're welcome to sort +of review them in detail and then I kind + + align:start position:0% +of review them in detail and then I kind + + + align:start position:0% +of review them in detail and then I kind +of want to get into the credit stuff in + + align:start position:0% +of want to get into the credit stuff in + + + align:start position:0% +of want to get into the credit stuff in +uh in detail + + align:start position:0% +uh in detail + + + align:start position:0% +uh in detail +okay so there were two other + + align:start position:0% +okay so there were two other + + + align:start position:0% +okay so there were two other +um kind of two other + + align:start position:0% +um kind of two other + + + align:start position:0% +um kind of two other +topics that I just wanted to give you a + + align:start position:0% +topics that I just wanted to give you a + + + align:start position:0% +topics that I just wanted to give you a +the first is there's been some + + align:start position:0% +the first is there's been some + + + align:start position:0% +the first is there's been some +additional attention and these are all + + align:start position:0% +additional attention and these are all + + + align:start position:0% +additional attention and these are all +sort of what's happening in kind of the + + align:start position:0% +sort of what's happening in kind of the + + + align:start position:0% +sort of what's happening in kind of the +urban labor markets so there's been some + + align:start position:0% +urban labor markets so there's been some + + + align:start position:0% +urban labor markets so there's been some +work recently on understanding kind of + + align:start position:0% +work recently on understanding kind of + + + align:start position:0% +work recently on understanding kind of +matching frictions and in particular you + + align:start position:0% +matching frictions and in particular you + + + align:start position:0% +matching frictions and in particular you +know a big issue in labor markets is the + + align:start position:0% +know a big issue in labor markets is the + + + align:start position:0% +know a big issue in labor markets is the +fact that + + align:start position:0% +fact that + + + align:start position:0% +fact that +um you know not all jobs are the same + + align:start position:0% +um you know not all jobs are the same + + + align:start position:0% +um you know not all jobs are the same +not all people are the same so we want + + align:start position:0% +not all people are the same so we want + + + align:start position:0% +not all people are the same so we want +to kind of match people to jobs right + + align:start position:0% +to kind of match people to jobs right + + + align:start position:0% +to kind of match people to jobs right +that's that's a big a big issue that + + align:start position:0% +that's that's a big a big issue that + + + align:start position:0% +that's that's a big a big issue that +differentiates labor markets from mother + + align:start position:0% +differentiates labor markets from mother + + + align:start position:0% +differentiates labor markets from mother +markets is kind of the rich + + align:start position:0% +markets is kind of the rich + + + align:start position:0% +markets is kind of the rich +heterogeneity both in the employer aside + + align:start position:0% +heterogeneity both in the employer aside + + + align:start position:0% +heterogeneity both in the employer aside +and on the on the other side and so you + + align:start position:0% +and on the on the other side and so you + + + align:start position:0% +and on the on the other side and so you +and so job search is a big issue and how + + align:start position:0% +and so job search is a big issue and how + + + align:start position:0% +and so job search is a big issue and how +do you sort of um and this question is + + align:start position:0% +do you sort of um and this question is + + + align:start position:0% +do you sort of um and this question is +sort of a big a big one in kind of + + align:start position:0% +sort of a big a big one in kind of + + + align:start position:0% +sort of a big a big one in kind of +developed country labor markets and I + + align:start position:0% +developed country labor markets and I + + + align:start position:0% +developed country labor markets and I +think people are just starting to + + align:start position:0% +think people are just starting to + + + align:start position:0% +think people are just starting to +understand how those issues may be + + align:start position:0% +understand how those issues may be + + + align:start position:0% +understand how those issues may be +different in in developing country + + align:start position:0% +different in in developing country + + + align:start position:0% +different in in developing country +contexts and um + + align:start position:0% +contexts and um + + + align:start position:0% +contexts and um +you know one issue that people have + + align:start position:0% +you know one issue that people have + + + align:start position:0% +you know one issue that people have +started to think about is that we may + + align:start position:0% +started to think about is that we may + + + align:start position:0% +started to think about is that we may +you know part of how we sort of help + + align:start position:0% +you know part of how we sort of help + + + align:start position:0% +you know part of how we sort of help +solve these problems is we have + + align:start position:0% +solve these problems is we have + + + align:start position:0% +solve these problems is we have +um uh various signals that help us sort + + align:start position:0% +um uh various signals that help us sort + + + align:start position:0% +um uh various signals that help us sort +of signal in the market kind of what our + + align:start position:0% +of signal in the market kind of what our + + + align:start position:0% +of signal in the market kind of what our +skills are right so you know you you + + align:start position:0% +skills are right so you know you you + + + align:start position:0% +skills are right so you know you you +know are get a PhD from MIT that like is + + align:start position:0% +know are get a PhD from MIT that like is + + + align:start position:0% +know are get a PhD from MIT that like is +a signal that you could take to Future + + align:start position:0% +a signal that you could take to Future + + + align:start position:0% +a signal that you could take to Future +employers and say like you know I know + + align:start position:0% +employers and say like you know I know + + + align:start position:0% +employers and say like you know I know +it's in economics for example right at + + align:start position:0% +it's in economics for example right at + + + align:start position:0% +it's in economics for example right at +least we hope that that's a useful + + align:start position:0% +least we hope that that's a useful + + + align:start position:0% +least we hope that that's a useful +signal + + align:start position:0% +signal + + + align:start position:0% +signal +but if those signals are sort of weak + + align:start position:0% +but if those signals are sort of weak + + + align:start position:0% +but if those signals are sort of weak +and the the quality of the signals is + + align:start position:0% +and the the quality of the signals is + + + align:start position:0% +and the the quality of the signals is +not as good like it there may be some + + align:start position:0% +not as good like it there may be some + + + align:start position:0% +not as good like it there may be some +challenges so one paper is sort of um + + align:start position:0% +challenges so one paper is sort of um + + + align:start position:0% +challenges so one paper is sort of um +uh trying to understand these issues + + align:start position:0% +uh trying to understand these issues + + + align:start position:0% +uh trying to understand these issues +looking in the South African labor + + align:start position:0% +looking in the South African labor + + + align:start position:0% +looking in the South African labor +market and + + align:start position:0% +market and + + + align:start position:0% +market and +um they basically uh they do some + + align:start position:0% +um they basically uh they do some + + + align:start position:0% +um they basically uh they do some +interesting things on this they sort of + + align:start position:0% +interesting things on this they sort of + + + align:start position:0% +interesting things on this they sort of +look at sort of uh giving people + + align:start position:0% +look at sort of uh giving people + + + align:start position:0% +look at sort of uh giving people +information about + + align:start position:0% +information about + + + align:start position:0% +information about +and they sort of knew that sort of these + + align:start position:0% +and they sort of knew that sort of these + + + align:start position:0% +and they sort of knew that sort of these +skill assessments tell you multiple + + align:start position:0% +skill assessments tell you multiple + + + align:start position:0% +skill assessments tell you multiple +things right in the MIT example right if + + align:start position:0% +things right in the MIT example right if + + + align:start position:0% +things right in the MIT example right if +you get a PhD from MIT like that's a + + align:start position:0% +you get a PhD from MIT like that's a + + + align:start position:0% +you get a PhD from MIT like that's a +valuable signal in labor market it's + + align:start position:0% +valuable signal in labor market it's + + + align:start position:0% +valuable signal in labor market it's +also essential to you that actually like + + align:start position:0% +also essential to you that actually like + + + align:start position:0% +also essential to you that actually like +you're pretty good at economics because + + align:start position:0% +you're pretty good at economics because + + + align:start position:0% +you're pretty good at economics because +like you managed to get a PhD you know + + align:start position:0% +like you managed to get a PhD you know + + + align:start position:0% +like you managed to get a PhD you know +in economics so those those information + + align:start position:0% +in economics so those those information + + + align:start position:0% +in economics so those those information +they provide information both to the job + + align:start position:0% +they provide information both to the job + + + align:start position:0% +they provide information both to the job +seeker and to potential employers so + + align:start position:0% +seeker and to potential employers so + + + align:start position:0% +seeker and to potential employers so +they they um to get at this idea so not + + align:start position:0% +they they um to get at this idea so not + + + align:start position:0% +they they um to get at this idea so not +within not with phds for example they + + align:start position:0% +within not with phds for example they + + + align:start position:0% +within not with phds for example they +they basically help people they do a + + align:start position:0% +they basically help people they do a + + + align:start position:0% +they basically help people they do a +skill assessments of people + + align:start position:0% +skill assessments of people + + + align:start position:0% +skill assessments of people +um and they give them a certificate with + + align:start position:0% +um and they give them a certificate with + + + align:start position:0% +um and they give them a certificate with +a world Bank sort of brand like a + + align:start position:0% +a world Bank sort of brand like a + + + align:start position:0% +a world Bank sort of brand like a +credible brand saying you here's your + + align:start position:0% +credible brand saying you here's your + + + align:start position:0% +credible brand saying you here's your +skill set your skills assessment or + + align:start position:0% +skill set your skills assessment or + + + align:start position:0% +skill set your skills assessment or +whatever then they also do sort of a + + align:start position:0% +whatever then they also do sort of a + + + align:start position:0% +whatever then they also do sort of a +second arm where they give the same + + align:start position:0% +second arm where they give the same + + + align:start position:0% +second arm where they give the same +information but kind of privately the + + align:start position:0% +information but kind of privately the + + + align:start position:0% +information but kind of privately the +job Seekers they sort of show it to them + + align:start position:0% +job Seekers they sort of show it to them + + + align:start position:0% +job Seekers they sort of show it to them +but they don't sort of give them a + + align:start position:0% +but they don't sort of give them a + + + align:start position:0% +but they don't sort of give them a +certificate they can sort of bring out + + align:start position:0% +certificate they can sort of bring out + + + align:start position:0% +certificate they can sort of bring out +people and they sort of in order to + + align:start position:0% +people and they sort of in order to + + + align:start position:0% +people and they sort of in order to +decompose kind of what is the role of + + align:start position:0% +decompose kind of what is the role of + + + align:start position:0% +decompose kind of what is the role of +the job Seekers from the sort of the uh + + align:start position:0% +the job Seekers from the sort of the uh + + + align:start position:0% +the job Seekers from the sort of the uh +the information of the job Seekers from + + align:start position:0% +the information of the job Seekers from + + + align:start position:0% +the information of the job Seekers from +the information to and potential + + align:start position:0% +the information to and potential + + + align:start position:0% +the information to and potential +employers + + align:start position:0% +employers + + + align:start position:0% +employers +um + + align:start position:0% +um + + + align:start position:0% +um +that's right this is without + + align:start position:0% +that's right this is without + + + align:start position:0% +that's right this is without +certificates and so they basically and + + align:start position:0% +certificates and so they basically and + + + align:start position:0% +certificates and so they basically and +so they basically sort of decompose this + + align:start position:0% +so they basically sort of decompose this + + + align:start position:0% +so they basically sort of decompose this +so I'm not going to go through this + + align:start position:0% +so I'm not going to go through this + + + align:start position:0% +so I'm not going to go through this +analogy so I just wanted to sort of + + align:start position:0% +analogy so I just wanted to sort of + + + align:start position:0% +analogy so I just wanted to sort of +highlight + + align:start position:0% +highlight + + + align:start position:0% +highlight +that this area of sort of how do we + + align:start position:0% +that this area of sort of how do we + + + align:start position:0% +that this area of sort of how do we +think about the job job search in + + align:start position:0% +think about the job job search in + + + align:start position:0% +think about the job job search in +general is an area people are starting + + align:start position:0% +general is an area people are starting + + + align:start position:0% +general is an area people are starting +to think through and this is one this + + align:start position:0% +to think through and this is one this + + + align:start position:0% +to think through and this is one this +question about sort of um + + align:start position:0% +question about sort of um + + + align:start position:0% +question about sort of um +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +understanding kind of the role of + + align:start position:0% +understanding kind of the role of + + + align:start position:0% +understanding kind of the role of +credible signals for Employers in that + + align:start position:0% +credible signals for Employers in that + + + align:start position:0% +credible signals for Employers in that +is one it was when we look at this and + + align:start position:0% +is one it was when we look at this and + + + align:start position:0% +is one it was when we look at this and +it's a very nice paper so I'm not going + + align:start position:0% +it's a very nice paper so I'm not going + + + align:start position:0% +it's a very nice paper so I'm not going +to go through in detail but I encourage + + align:start position:0% +to go through in detail but I encourage + + + align:start position:0% +to go through in detail but I encourage +you to look at it + + align:start position:0% +you to look at it + + + align:start position:0% +you to look at it +um + + align:start position:0% +um + + + align:start position:0% +um +the other thing people are starting + + align:start position:0% +the other thing people are starting + + + align:start position:0% +the other thing people are starting +people are starting to look at sort of + + align:start position:0% +people are starting to look at sort of + + + align:start position:0% +people are starting to look at sort of +job search and online platforms so + + align:start position:0% +job search and online platforms so + + + align:start position:0% +job search and online platforms so +um you know this has been a big move in + + align:start position:0% +um you know this has been a big move in + + + align:start position:0% +um you know this has been a big move in +kind of the the developed country is + + align:start position:0% +kind of the the developed country is + + + align:start position:0% +kind of the the developed country is +that it really markets is the world of + + align:start position:0% +that it really markets is the world of + + + align:start position:0% +that it really markets is the world of +these online job matching programs is + + align:start position:0% +these online job matching programs is + + + align:start position:0% +these online job matching programs is +that actually relevant in sort of these + + align:start position:0% +that actually relevant in sort of these + + + align:start position:0% +that actually relevant in sort of these +you know in lower middle income + + align:start position:0% +you know in lower middle income + + + align:start position:0% +you know in lower middle income +countries I think people are starting to + + align:start position:0% +countries I think people are starting to + + + align:start position:0% +countries I think people are starting to +think maybe it is but you know so that's + + align:start position:0% +think maybe it is but you know so that's + + + align:start position:0% +think maybe it is but you know so that's +something people are working on + + align:start position:0% +something people are working on + + + align:start position:0% +something people are working on +um job training there's a lot of work on + + align:start position:0% +um job training there's a lot of work on + + + align:start position:0% +um job training there's a lot of work on +this question of sort of how do we + + align:start position:0% +this question of sort of how do we + + + align:start position:0% +this question of sort of how do we +teach people jobs et cetera you know is + + align:start position:0% +teach people jobs et cetera you know is + + + align:start position:0% +teach people jobs et cetera you know is +there general purpose training Civic + + align:start position:0% +there general purpose training Civic + + + align:start position:0% +there general purpose training Civic +training you know again I'm not going to + + align:start position:0% +training you know again I'm not going to + + + align:start position:0% +training you know again I'm not going to +go through this in detail but I just + + align:start position:0% +go through this in detail but I just + + + align:start position:0% +go through this in detail but I just +want to sort of give you a pointer that + + align:start position:0% +want to sort of give you a pointer that + + + align:start position:0% +want to sort of give you a pointer that +sort of some of this work exists and if + + align:start position:0% +sort of some of this work exists and if + + + align:start position:0% +sort of some of this work exists and if +you're interested in these questions you + + align:start position:0% +you're interested in these questions you + + + align:start position:0% +you're interested in these questions you +should have a look at it + + align:start position:0% +should have a look at it + + + align:start position:0% +should have a look at it +um the second issue in labor market in + + align:start position:0% +um the second issue in labor market in + + + align:start position:0% +um the second issue in labor market in +urban labor markets I also wanted to + + align:start position:0% +urban labor markets I also wanted to + + + align:start position:0% +urban labor markets I also wanted to +highlight is the role of working + + align:start position:0% +highlight is the role of working + + + align:start position:0% +highlight is the role of working +conditions and + + align:start position:0% +conditions and + + + align:start position:0% +conditions and +um + + align:start position:0% +um + + + align:start position:0% +um +you know there's this is an issue + + align:start position:0% +you know there's this is an issue + + + align:start position:0% +you know there's this is an issue +I think if we think both about sort of + + align:start position:0% +I think if we think both about sort of + + + align:start position:0% +I think if we think both about sort of +the development you know the Industrial + + align:start position:0% +the development you know the Industrial + + + align:start position:0% +the development you know the Industrial +Revolution and sort of the area in the + + align:start position:0% +Revolution and sort of the area in the + + + align:start position:0% +Revolution and sort of the area in the +post right post-industrial revolution in + + align:start position:0% +post right post-industrial revolution in + + + align:start position:0% +post right post-industrial revolution in +uh you know in a lot of in countries + + align:start position:0% +uh you know in a lot of in countries + + + align:start position:0% +uh you know in a lot of in countries +like the us or the UK + + align:start position:0% +like the us or the UK + + + align:start position:0% +like the us or the UK +um or other kind of you know richer + + align:start position:0% +um or other kind of you know richer + + + align:start position:0% +um or other kind of you know richer +countries today or in a lot of kind of + + align:start position:0% +countries today or in a lot of kind of + + + align:start position:0% +countries today or in a lot of kind of +lower middle income countries today like + + align:start position:0% +lower middle income countries today like + + + align:start position:0% +lower middle income countries today like +how do you think about you know are work + + align:start position:0% +how do you think about you know are work + + + align:start position:0% +how do you think about you know are work +what are working conditions like + + align:start position:0% +what are working conditions like + + + align:start position:0% +what are working conditions like +um in a lot of these industrial uh + + align:start position:0% +um in a lot of these industrial uh + + + align:start position:0% +um in a lot of these industrial uh +factories + + align:start position:0% +factories + + + align:start position:0% +factories +um + + align:start position:0% +um + + + align:start position:0% +um +they're still not perfect everywhere of + + align:start position:0% +they're still not perfect everywhere of + + + align:start position:0% +they're still not perfect everywhere of +course but there's a lot of regulation + + align:start position:0% +course but there's a lot of regulation + + + align:start position:0% +course but there's a lot of regulation +for example in in more developed + + align:start position:0% +for example in in more developed + + + align:start position:0% +for example in in more developed +countries it sort of helps make you know + + align:start position:0% +countries it sort of helps make you know + + + align:start position:0% +countries it sort of helps make you know +I think about worker safety and things + + align:start position:0% +I think about worker safety and things + + + align:start position:0% +I think about worker safety and things +like that if you have large informal + + align:start position:0% +like that if you have large informal + + + align:start position:0% +like that if you have large informal +sectors you know that aren't sort of uh + + align:start position:0% +sectors you know that aren't sort of uh + + + align:start position:0% +sectors you know that aren't sort of uh +subject to those regulations you know + + align:start position:0% +subject to those regulations you know + + + align:start position:0% +subject to those regulations you know +what's what's kind of happening in this + + align:start position:0% +what's what's kind of happening in this + + + align:start position:0% +what's what's kind of happening in this +in in the in these lower metrics I think + + align:start position:0% +in in the in these lower metrics I think + + + align:start position:0% +in in the in these lower metrics I think +to me this is a really interesting and + + align:start position:0% +to me this is a really interesting and + + + align:start position:0% +to me this is a really interesting and +really important issue and one that I + + align:start position:0% +really important issue and one that I + + + align:start position:0% +really important issue and one that I +feel like is is not particularly + + align:start position:0% +feel like is is not particularly + + + align:start position:0% +feel like is is not particularly +um studied it probably should be in the + + align:start position:0% +um studied it probably should be in the + + + align:start position:0% +um studied it probably should be in the +economics literature so I think it's a + + align:start position:0% +economics literature so I think it's a + + + align:start position:0% +economics literature so I think it's a +really important area + + align:start position:0% +really important area + + + align:start position:0% +really important area +um + + align:start position:0% +um + + + align:start position:0% +um +so you know as I mentioned like you know + + align:start position:0% +so you know as I mentioned like you know + + + align:start position:0% +so you know as I mentioned like you know +this was a you know there were huge sort + + align:start position:0% +this was a you know there were huge sort + + + align:start position:0% +this was a you know there were huge sort +of uproares about this kind of you know + + align:start position:0% +of uproares about this kind of you know + + + align:start position:0% +of uproares about this kind of you know +100 years ago in the U.S for example + + align:start position:0% +100 years ago in the U.S for example + + + align:start position:0% +100 years ago in the U.S for example +um about some of these sort of workplace + + align:start position:0% +um about some of these sort of workplace + + + align:start position:0% +um about some of these sort of workplace +tragedies + + align:start position:0% +tragedies + + + align:start position:0% +tragedies +um you know there have been similar sort + + align:start position:0% +um you know there have been similar sort + + + align:start position:0% +um you know there have been similar sort +of tragic incidents + + align:start position:0% +of tragic incidents + + + align:start position:0% +of tragic incidents +um in you know there were a couple of + + align:start position:0% +um in you know there were a couple of + + + align:start position:0% +um in you know there were a couple of +very famous ones in Bangladesh about 10 + + align:start position:0% +very famous ones in Bangladesh about 10 + + + align:start position:0% +very famous ones in Bangladesh about 10 +years ago there was a this collapse of + + align:start position:0% +years ago there was a this collapse of + + + align:start position:0% +years ago there was a this collapse of +this this Factory that had many textile + + align:start position:0% +this this Factory that had many textile + + + align:start position:0% +this this Factory that had many textile +shops you know hundreds or actually over + + align:start position:0% +shops you know hundreds or actually over + + + align:start position:0% +shops you know hundreds or actually over +a thousand people were killed + + align:start position:0% +a thousand people were killed + + + align:start position:0% +a thousand people were killed +um so you know how do we think about + + align:start position:0% +um so you know how do we think about + + + align:start position:0% +um so you know how do we think about +some of these kind of workplace issues + + align:start position:0% +some of these kind of workplace issues + + + align:start position:0% +some of these kind of workplace issues +again particularly when you have a large + + align:start position:0% +again particularly when you have a large + + + align:start position:0% +again particularly when you have a large +and why is this kind of why is this kind + + align:start position:0% +and why is this kind of why is this kind + + + align:start position:0% +and why is this kind of why is this kind +of a development issue or or it's + + align:start position:0% +of a development issue or or it's + + + align:start position:0% +of a development issue or or it's +because you know we think that sort of + + align:start position:0% +because you know we think that sort of + + + align:start position:0% +because you know we think that sort of +Regulation actually is sort of what + + align:start position:0% +Regulation actually is sort of what + + + align:start position:0% +Regulation actually is sort of what +helps solve some of these problems in in + + align:start position:0% +helps solve some of these problems in in + + + align:start position:0% +helps solve some of these problems in in +uh in more in more developed countries + + align:start position:0% +uh in more in more developed countries + + + align:start position:0% +uh in more in more developed countries +um but with these large informal sectors + + align:start position:0% +um but with these large informal sectors + + + align:start position:0% +um but with these large informal sectors +kind of you know the regulatory issues + + align:start position:0% +kind of you know the regulatory issues + + + align:start position:0% +kind of you know the regulatory issues +maybe maybe not so may not work + + align:start position:0% +maybe maybe not so may not work + + + align:start position:0% +maybe maybe not so may not work +regulatory Solutions may not work so + + align:start position:0% +regulatory Solutions may not work so + + + align:start position:0% +regulatory Solutions may not work so +well + + align:start position:0% +well + + + align:start position:0% +well +um so I just think I just wanted to sort + + align:start position:0% +um so I just think I just wanted to sort + + + align:start position:0% +um so I just think I just wanted to sort +of flag that as something I think is a + + align:start position:0% +of flag that as something I think is a + + + align:start position:0% +of flag that as something I think is a +really important area there's one paper + + align:start position:0% +really important area there's one paper + + + align:start position:0% +really important area there's one paper +uh recently by Laura beaudreau which I + + align:start position:0% +uh recently by Laura beaudreau which I + + + align:start position:0% +uh recently by Laura beaudreau which I +thought was a very nice one about sort + + align:start position:0% +thought was a very nice one about sort + + + align:start position:0% +thought was a very nice one about sort +of looking at + + align:start position:0% +of looking at + + + align:start position:0% +of looking at +um uh + + align:start position:0% +um uh + + + align:start position:0% +um uh +um + + align:start position:0% +um + + + align:start position:0% +um +these kind of worker safety worker + + align:start position:0% +these kind of worker safety worker + + + align:start position:0% +these kind of worker safety worker +management safety committees and + + align:start position:0% +management safety committees and + + + align:start position:0% +management safety committees and +actually sort of randomizing the + + align:start position:0% +actually sort of randomizing the + + + align:start position:0% +actually sort of randomizing the +creation of these in the Bangladeshi + + align:start position:0% +creation of these in the Bangladeshi + + + align:start position:0% +creation of these in the Bangladeshi +factories and kind of looking at some + + align:start position:0% +factories and kind of looking at some + + + align:start position:0% +factories and kind of looking at some +issues here I think sort of what is more + + align:start position:0% +issues here I think sort of what is more + + + align:start position:0% +issues here I think sort of what is more +generally I think what is the role of + + align:start position:0% +generally I think what is the role of + + + align:start position:0% +generally I think what is the role of +multinationals actually and are they + + align:start position:0% +multinationals actually and are they + + + align:start position:0% +multinationals actually and are they +playing a role in sort of disciplining + + align:start position:0% +playing a role in sort of disciplining + + + align:start position:0% +playing a role in sort of disciplining +kind of the working conditions in kind + + align:start position:0% +kind of the working conditions in kind + + + align:start position:0% +kind of the working conditions in kind +of the factories in lower middle + + align:start position:0% +of the factories in lower middle + + + align:start position:0% +of the factories in lower middle +countries that are sort of producing + + align:start position:0% +countries that are sort of producing + + + align:start position:0% +countries that are sort of producing +their stuff I think is another is a + + align:start position:0% +their stuff I think is another is a + + + align:start position:0% +their stuff I think is another is a +really interesting area + + align:start position:0% +really interesting area + + + align:start position:0% +really interesting area +um again I'm not going to go through + + align:start position:0% +um again I'm not going to go through + + + align:start position:0% +um again I'm not going to go through +this in detail given sort of the the + + align:start position:0% +this in detail given sort of the the + + + align:start position:0% +this in detail given sort of the the +limited time I have but I kind of wanted + + align:start position:0% +limited time I have but I kind of wanted + + + align:start position:0% +limited time I have but I kind of wanted +to just uh flag this paper if you're + + align:start position:0% +to just uh flag this paper if you're + + + align:start position:0% +to just uh flag this paper if you're +interested in it and um + + align:start position:0% +interested in it and um + + + align:start position:0% +interested in it and um +um uh just more generally sort of say + + align:start position:0% +um uh just more generally sort of say + + + align:start position:0% +um uh just more generally sort of say +that I think that sort of this this + + align:start position:0% +that I think that sort of this this + + + align:start position:0% +that I think that sort of this this +issue about multinational issue of + + align:start position:0% +issue about multinational issue of + + + align:start position:0% +issue about multinational issue of +working conditions in general + + align:start position:0% +working conditions in general + + + align:start position:0% +working conditions in general +multinationals in particular and what + + align:start position:0% +multinationals in particular and what + + + align:start position:0% +multinationals in particular and what +role they play is an important one and + + align:start position:0% +role they play is an important one and + + + align:start position:0% +role they play is an important one and +one that's a good area for future + + align:start position:0% +one that's a good area for future + + + align:start position:0% +one that's a good area for future +research + + align:start position:0% +research + + + align:start position:0% +research +okay so that's all I'm going to say and + + align:start position:0% +okay so that's all I'm going to say and + + + align:start position:0% +okay so that's all I'm going to say and +then I'm going to switch gears + + align:start position:0% +then I'm going to switch gears + + + align:start position:0% +then I'm going to switch gears +um do people have any other comments or + + align:start position:0% +um do people have any other comments or + + + align:start position:0% +um do people have any other comments or +questions before we switch to the last + + align:start position:0% +questions before we switch to the last + + + align:start position:0% +questions before we switch to the last +topic + + align:start position:0% + + + + align:start position:0% + +so sorry I didn't get to go through + + align:start position:0% +so sorry I didn't get to go through + + + align:start position:0% +so sorry I didn't get to go through +those papers in detail but there's a lot + + align:start position:0% +those papers in detail but there's a lot + + + align:start position:0% +those papers in detail but there's a lot +to talk about in credit too + + align:start position:0% +to talk about in credit too + + + align:start position:0% +to talk about in credit too +I want to make sure I get to it + + align:start position:0% +I want to make sure I get to it + + + align:start position:0% +I want to make sure I get to it +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so um + + align:start position:0% +so um + + + align:start position:0% +so um +credit is sort of obviously a hugely + + align:start position:0% +credit is sort of obviously a hugely + + + align:start position:0% +credit is sort of obviously a hugely +important + + align:start position:0% +important + + + align:start position:0% +important +um you know issue if you think about + + align:start position:0% +um you know issue if you think about + + + align:start position:0% +um you know issue if you think about +kind of like what we've talked about + + align:start position:0% +kind of like what we've talked about + + + align:start position:0% +kind of like what we've talked about +um you know if you think about sort of + + align:start position:0% +um you know if you think about sort of + + + align:start position:0% +um you know if you think about sort of +the overall production function right + + align:start position:0% +the overall production function right + + + align:start position:0% +the overall production function right +there's like you know + + align:start position:0% + + + + align:start position:0% + +if we think about a production function + + align:start position:0% +if we think about a production function + + + align:start position:0% +if we think about a production function +that looks like this right we have you + + align:start position:0% +that looks like this right we have you + + + align:start position:0% +that looks like this right we have you +know labor which I just talked about + + align:start position:0% +know labor which I just talked about + + + align:start position:0% +know labor which I just talked about +human capital + + align:start position:0% + + + + align:start position:0% + +which Ezra talked about in sort of + + align:start position:0% +which Ezra talked about in sort of + + + align:start position:0% +which Ezra talked about in sort of +extensive detail there's some other + + align:start position:0% +extensive detail there's some other + + + align:start position:0% +extensive detail there's some other +components of this one is like + + align:start position:0% +components of this one is like + + + align:start position:0% +components of this one is like +productivity + + align:start position:0% + + + + align:start position:0% + +and the other is capital + + align:start position:0% + + + + align:start position:0% + +right so understanding kind of you know + + align:start position:0% +right so understanding kind of you know + + + align:start position:0% +right so understanding kind of you know +what are the sort of the the challenges + + align:start position:0% +what are the sort of the the challenges + + + align:start position:0% +what are the sort of the the challenges +and sort of overall production in kind + + align:start position:0% +and sort of overall production in kind + + + align:start position:0% +and sort of overall production in kind +of lower middle income countries + + align:start position:0% +of lower middle income countries + + + align:start position:0% +of lower middle income countries +compared to sort of developed world you + + align:start position:0% +compared to sort of developed world you + + + align:start position:0% +compared to sort of developed world you +want to sort of understand kind of all + + align:start position:0% +want to sort of understand kind of all + + + align:start position:0% +want to sort of understand kind of all +four of these components right so we've + + align:start position:0% +four of these components right so we've + + + align:start position:0% +four of these components right so we've +talked a lot about Labor we've talked a + + align:start position:0% +talked a lot about Labor we've talked a + + + align:start position:0% +talked a lot about Labor we've talked a +lot about human capital + + align:start position:0% +lot about human capital + + + align:start position:0% +lot about human capital +um we're going to talk next semester + + align:start position:0% +um we're going to talk next semester + + + align:start position:0% +um we're going to talk next semester +much more about uh productivity there's + + align:start position:0% +much more about uh productivity there's + + + align:start position:0% +much more about uh productivity there's +going to be a lot of discussion about + + align:start position:0% +going to be a lot of discussion about + + + align:start position:0% +going to be a lot of discussion about +sort of you know how do we think about + + align:start position:0% +sort of you know how do we think about + + + align:start position:0% +sort of you know how do we think about +productivity and how do we think about + + align:start position:0% +productivity and how do we think about + + + align:start position:0% +productivity and how do we think about +heterogeneity and productivity across + + align:start position:0% +heterogeneity and productivity across + + + align:start position:0% +heterogeneity and productivity across +firms and the final piece is we should + + align:start position:0% +firms and the final piece is we should + + + align:start position:0% +firms and the final piece is we should +take about Capital right and + + align:start position:0% +take about Capital right and + + + align:start position:0% +take about Capital right and +um and when you think and we're going to + + align:start position:0% +um and when you think and we're going to + + + align:start position:0% +um and when you think and we're going to +sort of split our discussion of capital + + align:start position:0% +sort of split our discussion of capital + + + align:start position:0% +sort of split our discussion of capital +across kind of what I'm going to talk + + align:start position:0% +across kind of what I'm going to talk + + + align:start position:0% +across kind of what I'm going to talk +about uh today and and next time and + + align:start position:0% +about uh today and and next time and + + + align:start position:0% +about uh today and and next time and +we're going to talk about in 14772 next + + align:start position:0% +we're going to talk about in 14772 next + + + align:start position:0% +we're going to talk about in 14772 next +semester + + align:start position:0% +semester + + + align:start position:0% +semester +and um in particular what we're going to + + align:start position:0% +and um in particular what we're going to + + + align:start position:0% +and um in particular what we're going to +talk about is credit constraints and so + + align:start position:0% +talk about is credit constraints and so + + + align:start position:0% +talk about is credit constraints and so +you know normally right if you just you + + align:start position:0% +you know normally right if you just you + + + align:start position:0% +you know normally right if you just you +know we're maximizing this production + + align:start position:0% +know we're maximizing this production + + + align:start position:0% +know we're maximizing this production +function right you know minus if you + + align:start position:0% +function right you know minus if you + + + align:start position:0% +function right you know minus if you +were maximizing something like this + + align:start position:0% + + + + align:start position:0% + +over you know L H and K you know minus + + align:start position:0% +over you know L H and K you know minus + + + align:start position:0% +over you know L H and K you know minus +whatever + + align:start position:0% +whatever + + + align:start position:0% +whatever +w l minus whatever I'll call it w h of H + + align:start position:0% +w l minus whatever I'll call it w h of H + + + align:start position:0% +w l minus whatever I'll call it w h of H +right you would you would choose the + + align:start position:0% +right you would you would choose the + + + align:start position:0% +right you would you would choose the +amount of capital such that a prime + + align:start position:0% +amount of capital such that a prime + + + align:start position:0% +amount of capital such that a prime +sorry a + + align:start position:0% +sorry a + + + align:start position:0% +sorry a +um f Prime sub K is equal to R right you + + align:start position:0% +um f Prime sub K is equal to R right you + + + align:start position:0% +um f Prime sub K is equal to R right you +would just sort of you know maximize + + align:start position:0% +would just sort of you know maximize + + + align:start position:0% +would just sort of you know maximize +choose your level of capital such that + + align:start position:0% +choose your level of capital such that + + + align:start position:0% +choose your level of capital such that +the marginal return to the capital was + + align:start position:0% +the marginal return to the capital was + + + align:start position:0% +the marginal return to the capital was +equal to the interest rate or the or the + + align:start position:0% +equal to the interest rate or the or the + + + align:start position:0% +equal to the interest rate or the or the +rate of return to Capital or which is we + + align:start position:0% +rate of return to Capital or which is we + + + align:start position:0% +rate of return to Capital or which is we +think of as the interest rate + + align:start position:0% +think of as the interest rate + + + align:start position:0% +think of as the interest rate +so we're going to talk about today are + + align:start position:0% +so we're going to talk about today are + + + align:start position:0% +so we're going to talk about today are +are reasons why you may not be able to + + align:start position:0% +are reasons why you may not be able to + + + align:start position:0% +are reasons why you may not be able to +do that and in particular we want to + + align:start position:0% +do that and in particular we want to + + + align:start position:0% +do that and in particular we want to +understand kind of how does kind of the + + align:start position:0% +understand kind of how does kind of the + + + align:start position:0% +understand kind of how does kind of the +market for capital or the market for + + align:start position:0% +market for capital or the market for + + + align:start position:0% +market for capital or the market for +credit kind of work and are there + + align:start position:0% +credit kind of work and are there + + + align:start position:0% +credit kind of work and are there +reasons why firms might not be able to + + align:start position:0% +reasons why firms might not be able to + + + align:start position:0% +reasons why firms might not be able to +get this much capital + + align:start position:0% +get this much capital + + + align:start position:0% +get this much capital +firms businesses anybody who needs + + align:start position:0% +firms businesses anybody who needs + + + align:start position:0% +firms businesses anybody who needs +Capital might not be able to get this + + align:start position:0% +Capital might not be able to get this + + + align:start position:0% +Capital might not be able to get this +much Capital it might be sort of limited + + align:start position:0% +much Capital it might be sort of limited + + + align:start position:0% +much Capital it might be sort of limited +in sort of their capital + + align:start position:0% +in sort of their capital + + + align:start position:0% +in sort of their capital +so today I want to talk about sort of + + align:start position:0% +so today I want to talk about sort of + + + align:start position:0% +so today I want to talk about sort of +the basic sort of theory of credit + + align:start position:0% +the basic sort of theory of credit + + + align:start position:0% +the basic sort of theory of credit +constraints and that's going to + + align:start position:0% +constraints and that's going to + + + align:start position:0% +constraints and that's going to +basically take me kind of all of today + + align:start position:0% +basically take me kind of all of today + + + align:start position:0% +basically take me kind of all of today +so how do we think about why might + + align:start position:0% +so how do we think about why might + + + align:start position:0% +so how do we think about why might +people not be able to get this much + + align:start position:0% +people not be able to get this much + + + align:start position:0% +people not be able to get this much +capital + + align:start position:0% +capital + + + align:start position:0% +capital +and I'll talk about more Hazard reasons + + align:start position:0% +and I'll talk about more Hazard reasons + + + align:start position:0% +and I'll talk about more Hazard reasons +I have reflection reasons and monitoring + + align:start position:0% +I have reflection reasons and monitoring + + + align:start position:0% +I have reflection reasons and monitoring +reasons + + align:start position:0% +reasons + + + align:start position:0% +reasons +um + + align:start position:0% +um + + + align:start position:0% +um +and we'll think about sort of what is + + align:start position:0% +and we'll think about sort of what is + + + align:start position:0% +and we'll think about sort of what is +that what does that all mean and then + + align:start position:0% +that what does that all mean and then + + + align:start position:0% +that what does that all mean and then +and then I'm going to talk + + align:start position:0% +and then I'm going to talk + + + align:start position:0% +and then I'm going to talk +um on Wednesday about the rule of + + align:start position:0% +um on Wednesday about the rule of + + + align:start position:0% +um on Wednesday about the rule of +microfinance and and how we think about + + align:start position:0% +microfinance and and how we think about + + + align:start position:0% +microfinance and and how we think about +microfinance as sort of you know one way + + align:start position:0% +microfinance as sort of you know one way + + + align:start position:0% +microfinance as sort of you know one way +of solving these kind of credits or a + + align:start position:0% +of solving these kind of credits or a + + + align:start position:0% +of solving these kind of credits or a +mute not solving but ameliorating some + + align:start position:0% +mute not solving but ameliorating some + + + align:start position:0% +mute not solving but ameliorating some +of these credit constraints for a really + + align:start position:0% +of these credit constraints for a really + + + align:start position:0% +of these credit constraints for a really +poor uh not poor but small very you know + + align:start position:0% +poor uh not poor but small very you know + + + align:start position:0% +poor uh not poor but small very you know +typically for very small kind of micro + + align:start position:0% +typically for very small kind of micro + + + align:start position:0% +typically for very small kind of micro +Enterprises okay and there's been sort + + align:start position:0% +Enterprises okay and there's been sort + + + align:start position:0% +Enterprises okay and there's been sort +of an explosion of work sort of + + align:start position:0% +of an explosion of work sort of + + + align:start position:0% +of an explosion of work sort of +understanding you know both whether or + + align:start position:0% +understanding you know both whether or + + + align:start position:0% +understanding you know both whether or +not microfinance does or does not + + align:start position:0% +not microfinance does or does not + + + align:start position:0% +not microfinance does or does not +ameliorate credit constraints and + + align:start position:0% +ameliorate credit constraints and + + + align:start position:0% +ameliorate credit constraints and +understanding all the many different + + align:start position:0% +understanding all the many different + + + align:start position:0% +understanding all the many different +features that happen in microfinance and + + align:start position:0% +features that happen in microfinance and + + + align:start position:0% +features that happen in microfinance and +understanding whether those are + + align:start position:0% +understanding whether those are + + + align:start position:0% +understanding whether those are +important + + align:start position:0% +important + + + align:start position:0% +important +so that's what I'm going to do this week + + align:start position:0% +so that's what I'm going to do this week + + + align:start position:0% +so that's what I'm going to do this week +what we're then going to sort of think + + align:start position:0% +what we're then going to sort of think + + + align:start position:0% +what we're then going to sort of think +about is + + align:start position:0% +about is + + + align:start position:0% +about is +in 14772 we'll think about the role of + + align:start position:0% +in 14772 we'll think about the role of + + + align:start position:0% +in 14772 we'll think about the role of +banks as sort of intermediaries and how + + align:start position:0% +banks as sort of intermediaries and how + + + align:start position:0% +banks as sort of intermediaries and how +what are what are banks doing how are + + align:start position:0% +what are what are banks doing how are + + + align:start position:0% +what are what are banks doing how are +they allocating Capital what are they + + align:start position:0% +they allocating Capital what are they + + + align:start position:0% +they allocating Capital what are they +doing in sort of credit constraints and + + align:start position:0% +doing in sort of credit constraints and + + + align:start position:0% +doing in sort of credit constraints and +more generally sort of understanding + + align:start position:0% +more generally sort of understanding + + + align:start position:0% +more generally sort of understanding +kind of firm's demand for credit and + + align:start position:0% +kind of firm's demand for credit and + + + align:start position:0% +kind of firm's demand for credit and +sort of the impact of credit on firms + + align:start position:0% +sort of the impact of credit on firms + + + align:start position:0% +sort of the impact of credit on firms +you can think of in some ways it's like + + align:start position:0% +you can think of in some ways it's like + + + align:start position:0% +you can think of in some ways it's like +estimating that FK thing right what is + + align:start position:0% +estimating that FK thing right what is + + + align:start position:0% +estimating that FK thing right what is +the impact of of additional capital and + + align:start position:0% +the impact of of additional capital and + + + align:start position:0% +the impact of of additional capital and +kind of the firm sector so we sort of + + align:start position:0% +kind of the firm sector so we sort of + + + align:start position:0% +kind of the firm sector so we sort of +split this topic kind of you know the + + align:start position:0% +split this topic kind of you know the + + + align:start position:0% +split this topic kind of you know the +stuff that we think of is kind of more a + + align:start position:0% +stuff that we think of is kind of more a + + + align:start position:0% +stuff that we think of is kind of more a +little more this is mostly about you + + align:start position:0% +little more this is mostly about you + + + align:start position:0% +little more this is mostly about you +know people and sort of the basics of + + align:start position:0% +know people and sort of the basics of + + + align:start position:0% +know people and sort of the basics of +understanding these models I'm going to + + align:start position:0% +understanding these models I'm going to + + + align:start position:0% +understanding these models I'm going to +do now the stuff about really sort of + + align:start position:0% +do now the stuff about really sort of + + + align:start position:0% +do now the stuff about really sort of +getting into how this effect firms will + + align:start position:0% +getting into how this effect firms will + + + align:start position:0% +getting into how this effect firms will +do next semester + + align:start position:0% +do next semester + + + align:start position:0% +do next semester +okay that's the the plan + + align:start position:0% +okay that's the the plan + + + align:start position:0% +okay that's the the plan +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so here's the neoclassical model of the + + align:start position:0% +so here's the neoclassical model of the + + + align:start position:0% +so here's the neoclassical model of the +Capital Market + + align:start position:0% +Capital Market + + + align:start position:0% +Capital Market +imagine that everyone faces the same + + align:start position:0% +imagine that everyone faces the same + + + align:start position:0% +imagine that everyone faces the same +interest rate adjusted for risk + + align:start position:0% +interest rate adjusted for risk + + + align:start position:0% +interest rate adjusted for risk +and so what that means is now what that + + align:start position:0% +and so what that means is now what that + + + align:start position:0% +and so what that means is now what that +means by the way is if there's a d + + align:start position:0% +means by the way is if there's a d + + + align:start position:0% +means by the way is if there's a d +percent risk of default + + align:start position:0% +percent risk of default + + + align:start position:0% +percent risk of default +um then uh + + align:start position:0% +um then uh + + + align:start position:0% +um then uh +so we're also gonna we're gonna work + + align:start position:0% +so we're also gonna we're gonna work + + + align:start position:0% +so we're also gonna we're gonna work +with What's called the gross interest + + align:start position:0% +with What's called the gross interest + + + align:start position:0% +with What's called the gross interest +rate uh which is how much so you repay + + align:start position:0% +rate uh which is how much so you repay + + + align:start position:0% +rate uh which is how much so you repay +the growth which is often more + + align:start position:0% +the growth which is often more + + + align:start position:0% +the growth which is often more +convenient the interest rate we think of + + align:start position:0% +convenient the interest rate we think of + + + align:start position:0% +convenient the interest rate we think of +is like you know so imagine I have a + + align:start position:0% +is like you know so imagine I have a + + + align:start position:0% +is like you know so imagine I have a +three percent interest rate right so I + + align:start position:0% +three percent interest rate right so I + + + align:start position:0% +three percent interest rate right so I +would have to pay three percent of an + + align:start position:0% +would have to pay three percent of an + + + align:start position:0% +would have to pay three percent of an +interest the gross interest rate is like + + align:start position:0% +interest the gross interest rate is like + + + align:start position:0% +interest the gross interest rate is like +1.03 it's the total amount you have to + + align:start position:0% +1.03 it's the total amount you have to + + + align:start position:0% +1.03 it's the total amount you have to +pay back okay and that just turns out to + + align:start position:0% +pay back okay and that just turns out to + + + align:start position:0% +pay back okay and that just turns out to +be convenient uh for the math sometimes + + align:start position:0% +be convenient uh for the math sometimes + + + align:start position:0% +be convenient uh for the math sometimes +so imagine I default + + align:start position:0% +so imagine I default + + + align:start position:0% +so imagine I default +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +uh and different people differ in their + + align:start position:0% +uh and different people differ in their + + + align:start position:0% +uh and different people differ in their +default risks + + align:start position:0% +default risks + + + align:start position:0% +default risks +okay then what is the bank gonna get + + align:start position:0% +okay then what is the bank gonna get + + + align:start position:0% +okay then what is the bank gonna get +back will the bank seem to get back well + + align:start position:0% +back will the bank seem to get back well + + + align:start position:0% +back will the bank seem to get back well +with with probability D it's going to + + align:start position:0% +with with probability D it's going to + + + align:start position:0% +with with probability D it's going to +get nothing with probability 1 minus D + + align:start position:0% +get nothing with probability 1 minus D + + + align:start position:0% +get nothing with probability 1 minus D +it's going to get the gross interest + + align:start position:0% +it's going to get the gross interest + + + align:start position:0% +it's going to get the gross interest +rate + + align:start position:0% +rate + + + align:start position:0% +rate +so if the if there's a in kind of the + + align:start position:0% +so if the if there's a in kind of the + + + align:start position:0% +so if the if there's a in kind of the +basic kind of Market if there we have + + align:start position:0% +basic kind of Market if there we have + + + align:start position:0% +basic kind of Market if there we have +different chances of default and that + + align:start position:0% +different chances of default and that + + + align:start position:0% +different chances of default and that +chance it's not chance is is exogenous + + align:start position:0% +chance it's not chance is is exogenous + + + align:start position:0% +chance it's not chance is is exogenous +or whatever and observable then I'll + + align:start position:0% +or whatever and observable then I'll + + + align:start position:0% +or whatever and observable then I'll +just be happy to offer you different all + + align:start position:0% +just be happy to offer you different all + + + align:start position:0% +just be happy to offer you different all +for you all different loans and the rate + + align:start position:0% +for you all different loans and the rate + + + align:start position:0% +for you all different loans and the rate +I'm going to charge the gross interest + + align:start position:0% +I'm going to charge the gross interest + + + align:start position:0% +I'm going to charge the gross interest +rate I'm going to charge for your loan + + align:start position:0% +rate I'm going to charge for your loan + + + align:start position:0% +rate I'm going to charge for your loan +is 1 minus D times r + + align:start position:0% +is 1 minus D times r + + + align:start position:0% +is 1 minus D times r +right so I'm going to get back kind of + + align:start position:0% +right so I'm going to get back kind of + + + align:start position:0% +right so I'm going to get back kind of +like my uh my my uh + + align:start position:0% +like my uh my my uh + + + align:start position:0% +like my uh my my uh +my uh my RN equilibrium + + align:start position:0% +my uh my RN equilibrium + + + align:start position:0% +my uh my RN equilibrium +okay + + align:start position:0% + + + + align:start position:0% + +um and basically that's kind of what you + + align:start position:0% +um and basically that's kind of what you + + + align:start position:0% +um and basically that's kind of what you +get uh + + align:start position:0% +get uh + + + align:start position:0% +get uh +um + + align:start position:0% +um + + + align:start position:0% +um +uh that's what you get and then then the + + align:start position:0% +uh that's what you get and then then the + + + align:start position:0% +uh that's what you get and then then the +expected marginal product of capital + + align:start position:0% +expected marginal product of capital + + + align:start position:0% +expected marginal product of capital +should be equal to one minus D times R + + align:start position:0% +should be equal to one minus D times R + + + align:start position:0% +should be equal to one minus D times R +right because that's the the interest + + align:start position:0% +right because that's the the interest + + + align:start position:0% +right because that's the the interest +rate you have to pay + + align:start position:0% +rate you have to pay + + + align:start position:0% +rate you have to pay +fine + + align:start position:0% +fine + + + align:start position:0% +fine +so here are some um some stylized facts + + align:start position:0% +so here are some um some stylized facts + + + align:start position:0% +so here are some um some stylized facts +I'm not going to go into sort of the + + align:start position:0% +I'm not going to go into sort of the + + + align:start position:0% +I'm not going to go into sort of the +detail between these but there's there's + + align:start position:0% +detail between these but there's there's + + + align:start position:0% +detail between these but there's there's +there's uh some work that sort of + + align:start position:0% +there's uh some work that sort of + + + align:start position:0% +there's uh some work that sort of +um + + align:start position:0% +um + + + align:start position:0% +um +suggest these are true + + align:start position:0% + + + + align:start position:0% + +so we suggest that maybe that simple + + align:start position:0% +so we suggest that maybe that simple + + + align:start position:0% +so we suggest that maybe that simple +neoclassical model is not everything + + align:start position:0% +neoclassical model is not everything + + + align:start position:0% +neoclassical model is not everything +that's going on + + align:start position:0% +that's going on + + + align:start position:0% +that's going on +um + + align:start position:0% +um + + + align:start position:0% +um +so one thing is so so then by the way + + align:start position:0% +so one thing is so so then by the way + + + align:start position:0% +so one thing is so so then by the way +one other implication of this by the way + + align:start position:0% +one other implication of this by the way + + + align:start position:0% +one other implication of this by the way +is that sort of the you know what's + + align:start position:0% +is that sort of the you know what's + + + align:start position:0% +is that sort of the you know what's +happening to depositors and what's + + align:start position:0% +happening to depositors and what's + + + align:start position:0% +happening to depositors and what's +happening to sort of the the uh the + + align:start position:0% +happening to sort of the the uh the + + + align:start position:0% +happening to sort of the the uh the +people who are are getting the capital + + align:start position:0% +people who are are getting the capital + + + align:start position:0% +people who are are getting the capital +should be small just to sort of a you + + align:start position:0% +should be small just to sort of a you + + + align:start position:0% +should be small just to sort of a you +know if there's if there's um imagine + + align:start position:0% +know if there's if there's um imagine + + + align:start position:0% +know if there's if there's um imagine +they're sort of free entry into Banks + + align:start position:0% +they're sort of free entry into Banks + + + align:start position:0% +they're sort of free entry into Banks +then basically that that sort of you + + align:start position:0% +then basically that that sort of you + + + align:start position:0% +then basically that that sort of you +know that Gap will be kind of competed + + align:start position:0% +know that Gap will be kind of competed + + + align:start position:0% +know that Gap will be kind of competed +to zero right could be positive along at + + align:start position:0% +to zero right could be positive along at + + + align:start position:0% +to zero right could be positive along at +the highest interest rate look bars look + + align:start position:0% +the highest interest rate look bars look + + + align:start position:0% +the highest interest rate look bars look +at the lowest interest rate that Gap + + align:start position:0% +at the lowest interest rate that Gap + + + align:start position:0% +at the lowest interest rate that Gap +will be very small + + align:start position:0% +will be very small + + + align:start position:0% +will be very small +so what do we see so we see first of all + + align:start position:0% +so what do we see so we see first of all + + + align:start position:0% +so what do we see so we see first of all +there's a big gap between sometimes + + align:start position:0% +there's a big gap between sometimes + + + align:start position:0% +there's a big gap between sometimes +between deposit rates the the deposit + + align:start position:0% +between deposit rates the the deposit + + + align:start position:0% +between deposit rates the the deposit +rates and and loan rates so it seems + + align:start position:0% +rates and and loan rates so it seems + + + align:start position:0% +rates and and loan rates so it seems +like there's a lot of money going in in + + align:start position:0% +like there's a lot of money going in in + + + align:start position:0% +like there's a lot of money going in in +that sort of intermediary sector like + + align:start position:0% +that sort of intermediary sector like + + + align:start position:0% +that sort of intermediary sector like +what's what's that about let's talk + + align:start position:0% +what's what's that about let's talk + + + align:start position:0% +what's what's that about let's talk +about that + + align:start position:0% +about that + + + align:start position:0% +about that +um a lot of variability in interest rate + + align:start position:0% +um a lot of variability in interest rate + + + align:start position:0% +um a lot of variability in interest rate +uh within the same sub-economy and + + align:start position:0% +uh within the same sub-economy and + + + align:start position:0% +uh within the same sub-economy and +that's true even with very low levels of + + align:start position:0% +that's true even with very low levels of + + + align:start position:0% +that's true even with very low levels of +default + + align:start position:0% +default + + + align:start position:0% +default +so we're going to see + + align:start position:0% +so we're going to see + + + align:start position:0% +so we're going to see +um heterogeneity in interest rates that + + align:start position:0% +um heterogeneity in interest rates that + + + align:start position:0% +um heterogeneity in interest rates that +doesn't seem to that seems to be maybe + + align:start position:0% +doesn't seem to that seems to be maybe + + + align:start position:0% +doesn't seem to that seems to be maybe +some something else going on Beyond just + + align:start position:0% +some something else going on Beyond just + + + align:start position:0% +some something else going on Beyond just +kind of defaults so we'll see if there's + + align:start position:0% +kind of defaults so we'll see if there's + + + align:start position:0% +kind of defaults so we'll see if there's +something about that uh even though + + align:start position:0% +something about that uh even though + + + align:start position:0% +something about that uh even though +there is xandy competition in markets + + align:start position:0% +there is xandy competition in markets + + + align:start position:0% +there is xandy competition in markets +another thing we're going to find is + + align:start position:0% +another thing we're going to find is + + + align:start position:0% +another thing we're going to find is +that richer people seem to be able to + + align:start position:0% +that richer people seem to be able to + + + align:start position:0% +that richer people seem to be able to +borrow more and pay lower rates of + + align:start position:0% +borrow more and pay lower rates of + + + align:start position:0% +borrow more and pay lower rates of +Interest than poorer people + + align:start position:0% +Interest than poorer people + + + align:start position:0% +Interest than poorer people +and more generally it seems like people + + align:start position:0% +and more generally it seems like people + + + align:start position:0% +and more generally it seems like people +who borrow more are paying lower + + align:start position:0% +who borrow more are paying lower + + + align:start position:0% +who borrow more are paying lower +interest rates and that seems a little + + align:start position:0% +interest rates and that seems a little + + + align:start position:0% +interest rates and that seems a little +weird actually when you think about it + + align:start position:0% +weird actually when you think about it + + + align:start position:0% +weird actually when you think about it +right you might have thought that uh you + + align:start position:0% +right you might have thought that uh you + + + align:start position:0% +right you might have thought that uh you +know maybe you're sort of the the more + + align:start position:0% +know maybe you're sort of the the more + + + align:start position:0% +know maybe you're sort of the the more +you borrow kind of the riskier you are + + align:start position:0% +you borrow kind of the riskier you are + + + align:start position:0% +you borrow kind of the riskier you are +and maybe the default rates should go up + + align:start position:0% +and maybe the default rates should go up + + + align:start position:0% +and maybe the default rates should go up +but actually doesn't seem that way it + + align:start position:0% +but actually doesn't seem that way it + + + align:start position:0% +but actually doesn't seem that way it +seems like there's actually a positive + + align:start position:0% +seems like there's actually a positive + + + align:start position:0% +seems like there's actually a positive +correlation between sort of the amount + + align:start position:0% +correlation between sort of the amount + + + align:start position:0% +correlation between sort of the amount +you borrow and the oh sorry negative + + align:start position:0% +you borrow and the oh sorry negative + + + align:start position:0% +you borrow and the oh sorry negative +correlation between the event you + + align:start position:0% +correlation between the event you + + + align:start position:0% +correlation between the event you +borrowing the interest rate + + align:start position:0% +borrowing the interest rate + + + align:start position:0% +borrowing the interest rate +so that also seems kind of interesting + + align:start position:0% +so that also seems kind of interesting + + + align:start position:0% +so that also seems kind of interesting +so it seems like there's something a + + align:start position:0% +so it seems like there's something a + + + align:start position:0% +so it seems like there's something a +little more complicated going on in the + + align:start position:0% +little more complicated going on in the + + + align:start position:0% +little more complicated going on in the +credit markets and so what might what + + align:start position:0% +credit markets and so what might what + + + align:start position:0% +credit markets and so what might what +might that be + + align:start position:0% +might that be + + + align:start position:0% +might that be +so here's a Model A simple model that + + align:start position:0% +so here's a Model A simple model that + + + align:start position:0% +so here's a Model A simple model that +has of moral hazard uh in investment + + align:start position:0% +has of moral hazard uh in investment + + + align:start position:0% +has of moral hazard uh in investment +choices + + align:start position:0% + + + + align:start position:0% + +so imagine + + align:start position:0% +so imagine + + + align:start position:0% +so imagine +that there's + + align:start position:0% +that there's + + + align:start position:0% +that there's +um a menu of possible Investments that I + + align:start position:0% +um a menu of possible Investments that I + + + align:start position:0% +um a menu of possible Investments that I +as a firm can choose + + align:start position:0% +as a firm can choose + + + align:start position:0% +as a firm can choose +and they each differ in their + + align:start position:0% +and they each differ in their + + + align:start position:0% +and they each differ in their +probability of success p + + align:start position:0% +probability of success p + + + align:start position:0% +probability of success p +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and investment p is going to yield some + + align:start position:0% +and investment p is going to yield some + + + align:start position:0% +and investment p is going to yield some +return RFP with probability p and return + + align:start position:0% +return RFP with probability p and return + + + align:start position:0% +return RFP with probability p and return +uh zero with probability one minus p + + align:start position:0% +uh zero with probability one minus p + + + align:start position:0% +uh zero with probability one minus p +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +so my expected return + + align:start position:0% +so my expected return + + + align:start position:0% +so my expected return +is going to be uh e of P right and + + align:start position:0% +is going to be uh e of P right and + + + align:start position:0% +is going to be uh e of P right and +that's just going to be our that's going + + align:start position:0% +that's just going to be our that's going + + + align:start position:0% +that's just going to be our that's going +to be the probability of getting the + + align:start position:0% +to be the probability of getting the + + + align:start position:0% +to be the probability of getting the +positive the return times the return if + + align:start position:0% +positive the return times the return if + + + align:start position:0% +positive the return times the return if +you get it okay that's my expected + + align:start position:0% +you get it okay that's my expected + + + align:start position:0% +you get it okay that's my expected +return + + align:start position:0% +return + + + align:start position:0% +return +um we're going to assume that R Prime is + + align:start position:0% +um we're going to assume that R Prime is + + + align:start position:0% +um we're going to assume that R Prime is +negative + + align:start position:0% +negative + + + align:start position:0% +negative +right that sort of the uh the the the + + align:start position:0% +right that sort of the uh the the the + + + align:start position:0% +right that sort of the uh the the the +the project with lower + + align:start position:0% +the project with lower + + + align:start position:0% +the project with lower +um the the products with higher + + align:start position:0% +um the the products with higher + + + align:start position:0% +um the the products with higher +probabilities of success are going to + + align:start position:0% +probabilities of success are going to + + + align:start position:0% +probabilities of success are going to +return lower amounts if they succeed and + + align:start position:0% +return lower amounts if they succeed and + + + align:start position:0% +return lower amounts if they succeed and +I think that's a pretty General + + align:start position:0% +I think that's a pretty General + + + align:start position:0% +I think that's a pretty General +assumption because otherwise there would + + align:start position:0% +assumption because otherwise there would + + + align:start position:0% +assumption because otherwise there would +be like dominated projects right so we + + align:start position:0% +be like dominated projects right so we + + + align:start position:0% +be like dominated projects right so we +can choose the best project for every p + + align:start position:0% +can choose the best project for every p + + + align:start position:0% +can choose the best project for every p +and then it would have to okay + + align:start position:0% +and then it would have to okay + + + align:start position:0% +and then it would have to okay +um otherwise not very interesting + + align:start position:0% +um otherwise not very interesting + + + align:start position:0% +um otherwise not very interesting +and we're going to assume that this + + align:start position:0% +and we're going to assume that this + + + align:start position:0% +and we're going to assume that this +that's gonna that's gonna yield and then + + align:start position:0% +that's gonna that's gonna yield and then + + + align:start position:0% +that's gonna that's gonna yield and then +we'll assume that there's sort of uh + + align:start position:0% +we'll assume that there's sort of uh + + + align:start position:0% +we'll assume that there's sort of uh +this this e function is concave so it'll + + align:start position:0% +this this e function is concave so it'll + + + align:start position:0% +this this e function is concave so it'll +be an interior level of kind of the + + align:start position:0% +be an interior level of kind of the + + + align:start position:0% +be an interior level of kind of the +optimal project for maximizing expected + + align:start position:0% +optimal project for maximizing expected + + + align:start position:0% +optimal project for maximizing expected +returns + + align:start position:0% +returns + + + align:start position:0% +returns +okay so and we're going to note by P + + align:start position:0% +okay so and we're going to note by P + + + align:start position:0% +okay so and we're going to note by P +star the maximizing uh project for the + + align:start position:0% +star the maximizing uh project for the + + + align:start position:0% +star the maximizing uh project for the +efficient project that's the one that + + align:start position:0% +efficient project that's the one that + + + align:start position:0% +efficient project that's the one that +maximizes the efficient returns + + align:start position:0% +maximizes the efficient returns + + + align:start position:0% +maximizes the efficient returns +okay so that's just maximized P star is + + align:start position:0% +okay so that's just maximized P star is + + + align:start position:0% +okay so that's just maximized P star is +just the max of this thing + + align:start position:0% +just the max of this thing + + + align:start position:0% +just the max of this thing +okay so we would like people to choose P + + align:start position:0% +okay so we would like people to choose P + + + align:start position:0% +okay so we would like people to choose P +star and sometimes + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +in addition to the project Choice the p + + align:start position:0% +in addition to the project Choice the p + + + align:start position:0% +in addition to the project Choice the p +there's a return to scale parameter + + align:start position:0% +there's a return to scale parameter + + + align:start position:0% +there's a return to scale parameter +okay which is given by F of K + + align:start position:0% +okay which is given by F of K + + + align:start position:0% +okay which is given by F of K +right and that could be you know maybe + + align:start position:0% +right and that could be you know maybe + + + align:start position:0% +right and that could be you know maybe +that's going to be diminishing returns + + align:start position:0% +that's going to be diminishing returns + + + align:start position:0% +that's going to be diminishing returns +to scale or whatever + + align:start position:0% +to scale or whatever + + + align:start position:0% +to scale or whatever +um + + align:start position:0% +um + + + align:start position:0% +um +but then you so your choice is I'm going + + align:start position:0% +but then you so your choice is I'm going + + + align:start position:0% +but then you so your choice is I'm going +to invest capital K + + align:start position:0% +to invest capital K + + + align:start position:0% +to invest capital K +in Project P so I'm going to make two + + align:start position:0% +in Project P so I'm going to make two + + + align:start position:0% +in Project P so I'm going to make two +choices a k and a p right and my return + + align:start position:0% +choices a k and a p right and my return + + + align:start position:0% +choices a k and a p right and my return +is going to be that the p is going to + + align:start position:0% +is going to be that the p is going to + + + align:start position:0% +is going to be that the p is going to +choose the the expected p and then I'm + + align:start position:0% +choose the the expected p and then I'm + + + align:start position:0% +choose the the expected p and then I'm +going to scale It Up by this F of K + + align:start position:0% + + + + align:start position:0% + +okay is that clear so like you know I + + align:start position:0% +okay is that clear so like you know I + + + align:start position:0% +okay is that clear so like you know I +could go into making you know I don't + + align:start position:0% +could go into making you know I don't + + + align:start position:0% +could go into making you know I don't +know belts or t-shirts that's p and then + + align:start position:0% +know belts or t-shirts that's p and then + + + align:start position:0% +know belts or t-shirts that's p and then +I can choose how many of them I want to + + align:start position:0% +I can choose how many of them I want to + + + align:start position:0% +I can choose how many of them I want to +do that's the F of K + + align:start position:0% + + + + align:start position:0% + +okay clear + + align:start position:0% + + + + align:start position:0% + +finally + + align:start position:0% +finally + + + align:start position:0% +finally +suppose how do we that that the investor + + align:start position:0% +suppose how do we that that the investor + + + align:start position:0% +suppose how do we that that the investor +has some wealth w + + align:start position:0% +has some wealth w + + + align:start position:0% +has some wealth w +so if the investor wants to borrow she's + + align:start position:0% +so if the investor wants to borrow she's + + + align:start position:0% +so if the investor wants to borrow she's +got a who wants to invest K she has to + + align:start position:0% +got a who wants to invest K she has to + + + align:start position:0% +got a who wants to invest K she has to +borrow K minus w + + align:start position:0% +borrow K minus w + + + align:start position:0% +borrow K minus w +okay so that's the that's the the credit + + align:start position:0% +okay so that's the that's the the credit + + + align:start position:0% +okay so that's the that's the the credit +that's credit is how much they have to + + align:start position:0% +that's credit is how much they have to + + + align:start position:0% +that's credit is how much they have to +borrow + + align:start position:0% +borrow + + + align:start position:0% +borrow +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the gross interest rates are + + align:start position:0% +the gross interest rates are + + + align:start position:0% +the gross interest rates are +and we'll have limited liability which + + align:start position:0% +and we'll have limited liability which + + + align:start position:0% +and we'll have limited liability which +is if you can't pay + + align:start position:0% +is if you can't pay + + + align:start position:0% +is if you can't pay +what can they do they can take your what + + align:start position:0% +what can they do they can take your what + + + align:start position:0% +what can they do they can take your what +there's some collateral you put another + + align:start position:0% +there's some collateral you put another + + + align:start position:0% +there's some collateral you put another +thing about is you you put up your + + align:start position:0% +thing about is you you put up your + + + align:start position:0% +thing about is you you put up your +wealth as collateral they can take your + + align:start position:0% +wealth as collateral they can take your + + + align:start position:0% +wealth as collateral they can take your +your wealth but but nothing else + + align:start position:0% +your wealth but but nothing else + + + align:start position:0% +your wealth but but nothing else +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that's it that that I'll just tell + + align:start position:0% +so that's it that that I'll just tell + + + align:start position:0% +so that's it that that I'll just tell +you that is important right because + + align:start position:0% +you that is important right because + + + align:start position:0% +you that is important right because +um you're you see how this is gonna + + align:start position:0% +um you're you see how this is gonna + + + align:start position:0% +um you're you see how this is gonna +matter right so if I'm um + + align:start position:0% +matter right so if I'm um + + + align:start position:0% +matter right so if I'm um +if I'm investing K and my wealth W is + + align:start position:0% +if I'm investing K and my wealth W is + + + align:start position:0% +if I'm investing K and my wealth W is +approximately equal to case I'm only + + align:start position:0% +approximately equal to case I'm only + + + align:start position:0% +approximately equal to case I'm only +borrowing a little bit then if if my + + align:start position:0% +borrowing a little bit then if if my + + + align:start position:0% +borrowing a little bit then if if my +project kind of fails they're gonna I'm + + align:start position:0% +project kind of fails they're gonna I'm + + + align:start position:0% +project kind of fails they're gonna I'm +gonna lose a lot right they're gonna + + align:start position:0% +gonna lose a lot right they're gonna + + + align:start position:0% +gonna lose a lot right they're gonna +take kind of almost my entire wealth + + align:start position:0% +take kind of almost my entire wealth + + + align:start position:0% +take kind of almost my entire wealth +whereas if my my wealth is say zero then + + align:start position:0% +whereas if my my wealth is say zero then + + + align:start position:0% +whereas if my my wealth is say zero then +if I might probably fails I I get + + align:start position:0% +if I might probably fails I I get + + + align:start position:0% +if I might probably fails I I get +nothing in that state so I'm only + + align:start position:0% +nothing in that state so I'm only + + + align:start position:0% +nothing in that state so I'm only +interested in the upside so sort of the + + align:start position:0% +interested in the upside so sort of the + + + align:start position:0% +interested in the upside so sort of the +amount of wealth the amount of + + align:start position:0% +amount of wealth the amount of + + + align:start position:0% +amount of wealth the amount of +collateral I have is sort of uh + + align:start position:0% +collateral I have is sort of uh + + + align:start position:0% +collateral I have is sort of uh +determining kind of what share of the + + align:start position:0% +determining kind of what share of the + + + align:start position:0% +determining kind of what share of the +downside I have to of the downside of + + align:start position:0% +downside I have to of the downside of + + + align:start position:0% +downside I have to of the downside of +this project I have to bear versus the + + align:start position:0% +this project I have to bear versus the + + + align:start position:0% +this project I have to bear versus the +bank has to bear + + align:start position:0% +bank has to bear + + + align:start position:0% +bank has to bear +right and this idea + + align:start position:0% +right and this idea + + + align:start position:0% +right and this idea +um + + align:start position:0% +um + + + align:start position:0% +um +is you you can so you can immediately + + align:start position:0% +is you you can so you can immediately + + + align:start position:0% +is you you can so you can immediately +see why + + align:start position:0% +see why + + + align:start position:0% +see why +um it's going to be nice for for banks + + align:start position:0% +um it's going to be nice for for banks + + + align:start position:0% +um it's going to be nice for for banks +to kind of want you to have some + + align:start position:0% +to kind of want you to have some + + + align:start position:0% +to kind of want you to have some +collateral uh and and particularly why + + align:start position:0% +collateral uh and and particularly why + + + align:start position:0% +collateral uh and and particularly why +they're going to want you to put some of + + align:start position:0% +they're going to want you to put some of + + + align:start position:0% +they're going to want you to put some of +your own money into projects is because + + align:start position:0% +your own money into projects is because + + + align:start position:0% +your own money into projects is because +that they want to make sure that you're + + align:start position:0% +that they want to make sure that you're + + + align:start position:0% +that they want to make sure that you're +bearing some of the the downside risk so + + align:start position:0% +bearing some of the the downside risk so + + + align:start position:0% +bearing some of the the downside risk so +you're not taking otherwise you take + + align:start position:0% +you're not taking otherwise you take + + + align:start position:0% +you're not taking otherwise you take +super risky projects because like you + + align:start position:0% +super risky projects because like you + + + align:start position:0% +super risky projects because like you +know heads you win Tails they lose right + + align:start position:0% +know heads you win Tails they lose right + + + align:start position:0% +know heads you win Tails they lose right +you don't the bank that that's not a + + align:start position:0% +you don't the bank that that's not a + + + align:start position:0% +you don't the bank that that's not a +very good deal for the bank + + align:start position:0% +very good deal for the bank + + + align:start position:0% +very good deal for the bank +right + + align:start position:0% +right + + + align:start position:0% +right +um and so you know lots of loans have + + align:start position:0% +um and so you know lots of loans have + + + align:start position:0% +um and so you know lots of loans have +this feature right so for example if you + + align:start position:0% +this feature right so for example if you + + + align:start position:0% +this feature right so for example if you +want to buy a house you need to put you + + align:start position:0% +want to buy a house you need to put you + + + align:start position:0% +want to buy a house you need to put you +know 20 down on the house or something + + align:start position:0% +know 20 down on the house or something + + + align:start position:0% +know 20 down on the house or something +that's basically saying they want you + + align:start position:0% +that's basically saying they want you + + + align:start position:0% +that's basically saying they want you +know uh the loan to be no more than 80 + + align:start position:0% +know uh the loan to be no more than 80 + + + align:start position:0% +know uh the loan to be no more than 80 +of the total because they want you to + + align:start position:0% +of the total because they want you to + + + align:start position:0% +of the total because they want you to +have some stake and kind of like what + + align:start position:0% +have some stake and kind of like what + + + align:start position:0% +have some stake and kind of like what +happens if things go wrong + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +there are more complicated situations in + + align:start position:0% +there are more complicated situations in + + + align:start position:0% +there are more complicated situations in +in in mortgage markets actually because + + align:start position:0% +in in mortgage markets actually because + + + align:start position:0% +in in mortgage markets actually because +in addition uh you know often when the + + align:start position:0% +in addition uh you know often when the + + + align:start position:0% +in addition uh you know often when the +loan goes bad it starts from the top and + + align:start position:0% +loan goes bad it starts from the top and + + + align:start position:0% +loan goes bad it starts from the top and +so yeah you actually you lose the the + + align:start position:0% +so yeah you actually you lose the the + + + align:start position:0% +so yeah you actually you lose the the +first if you have 20 down right the the + + align:start position:0% +first if you have 20 down right the the + + + align:start position:0% +first if you have 20 down right the the +first 20 is your loss and the bank kind + + align:start position:0% +first 20 is your loss and the bank kind + + + align:start position:0% +first 20 is your loss and the bank kind +of only loses it more than that so + + align:start position:0% +of only loses it more than that so + + + align:start position:0% +of only loses it more than that so +actually the The Ordering of it is + + align:start position:0% +actually the The Ordering of it is + + + align:start position:0% +actually the The Ordering of it is +important too but we're not going to get + + align:start position:0% +important too but we're not going to get + + + align:start position:0% +important too but we're not going to get +into that in this model + + align:start position:0% +into that in this model + + + align:start position:0% +into that in this model +okay is this clear so far + + align:start position:0% +okay is this clear so far + + + align:start position:0% +okay is this clear so far +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so suppose + + align:start position:0% +so suppose + + + align:start position:0% +so suppose +um that we can contract over k + + align:start position:0% +um that we can contract over k + + + align:start position:0% +um that we can contract over k +the amount of capital + + align:start position:0% +the amount of capital + + + align:start position:0% +the amount of capital +but we cannot contract over the project + + align:start position:0% +but we cannot contract over the project + + + align:start position:0% +but we cannot contract over the project +Choice p + + align:start position:0% + + + + align:start position:0% + +so uh so K is just is going to be fixed + + align:start position:0% +so uh so K is just is going to be fixed + + + align:start position:0% +so uh so K is just is going to be fixed +but then the borrower is going to want + + align:start position:0% +but then the borrower is going to want + + + align:start position:0% +but then the borrower is going to want +for a given k + + align:start position:0% +for a given k + + + align:start position:0% +for a given k +right once we agree on K the borrower + + align:start position:0% +right once we agree on K the borrower + + + align:start position:0% +right once we agree on K the borrower +gets to say okay now I know my K is I'm + + align:start position:0% +gets to say okay now I know my K is I'm + + + align:start position:0% +gets to say okay now I know my K is I'm +going to choose my P and they can't + + align:start position:0% +going to choose my P and they can't + + + align:start position:0% +going to choose my P and they can't +contract over that + + align:start position:0% +contract over that + + + align:start position:0% +contract over that +so in particular what are they going to + + align:start position:0% +so in particular what are they going to + + + align:start position:0% +so in particular what are they going to +solve well with probability p + + align:start position:0% +solve well with probability p + + + align:start position:0% +solve well with probability p +they're going to get F of K times the + + align:start position:0% +they're going to get F of K times the + + + align:start position:0% +they're going to get F of K times the +return so the F of K times RFP that's + + align:start position:0% +return so the F of K times RFP that's + + + align:start position:0% +return so the F of K times RFP that's +sort of how good the project is times + + align:start position:0% +sort of how good the project is times + + + align:start position:0% +sort of how good the project is times +the times the scale + + align:start position:0% + + + + align:start position:0% + +um and then they have to pay the + + align:start position:0% +um and then they have to pay the + + + align:start position:0% +um and then they have to pay the +interest on the amount they borrowed + + align:start position:0% +interest on the amount they borrowed + + + align:start position:0% +interest on the amount they borrowed +right + + align:start position:0% + + + + align:start position:0% + +with probably 1 minus P the bank takes + + align:start position:0% +with probably 1 minus P the bank takes + + + align:start position:0% +with probably 1 minus P the bank takes +their wealth and nothing else okay so + + align:start position:0% +their wealth and nothing else okay so + + + align:start position:0% +their wealth and nothing else okay so +another way you can also equivalently + + align:start position:0% +another way you can also equivalently + + + align:start position:0% +another way you can also equivalently +rewrite this as sort of saying they pay + + align:start position:0% +rewrite this as sort of saying they pay + + + align:start position:0% +rewrite this as sort of saying they pay +the gross interest rate on K kind of in + + align:start position:0% +the gross interest rate on K kind of in + + + align:start position:0% +the gross interest rate on K kind of in +all periods and then + + align:start position:0% +all periods and then + + + align:start position:0% +all periods and then +um uh they they lose their wealth in uh + + align:start position:0% +um uh they they lose their wealth in uh + + + align:start position:0% +um uh they they lose their wealth in uh +in this other period + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the the first order condition is + + align:start position:0% +so the the first order condition is + + + align:start position:0% +so the the first order condition is +um that the uh + + align:start position:0% +um that the uh + + + align:start position:0% +um that the uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the F of K times e Prime e Prime is sort + + align:start position:0% +the F of K times e Prime e Prime is sort + + + align:start position:0% +the F of K times e Prime e Prime is sort +of the you know the derivative of the + + align:start position:0% +of the you know the derivative of the + + + align:start position:0% +of the you know the derivative of the +expected value with respect to P has to + + align:start position:0% +expected value with respect to P has to + + + align:start position:0% +expected value with respect to P has to +be equal to the effective kind of the r + + align:start position:0% +be equal to the effective kind of the r + + + align:start position:0% +be equal to the effective kind of the r +times K minus W right this period this + + align:start position:0% +times K minus W right this period this + + + align:start position:0% +times K minus W right this period this +this part doesn't matter right + + align:start position:0% +this part doesn't matter right + + + align:start position:0% +this part doesn't matter right +um and so we're just going to get so p p + + align:start position:0% +um and so we're just going to get so p p + + + align:start position:0% +um and so we're just going to get so p p +times R that's e right so the derivative + + align:start position:0% +times R that's e right so the derivative + + + align:start position:0% +times R that's e right so the derivative +so P times R was easy the expected + + align:start position:0% +so P times R was easy the expected + + + align:start position:0% +so P times R was easy the expected +returns so it's just F Prime sorry F of + + align:start position:0% +returns so it's just F Prime sorry F of + + + align:start position:0% +returns so it's just F Prime sorry F of +K times e Prime of p is equal to you + + align:start position:0% +K times e Prime of p is equal to you + + + align:start position:0% +K times e Prime of p is equal to you +know the there's a p in here so that's + + align:start position:0% +know the there's a p in here so that's + + + align:start position:0% +know the there's a p in here so that's +just equal to R times K minus w + + align:start position:0% +just equal to R times K minus w + + + align:start position:0% +just equal to R times K minus w +okay so that's the the first order + + align:start position:0% +okay so that's the the first order + + + align:start position:0% +okay so that's the the first order +condition + + align:start position:0% + + + + align:start position:0% + +so uh recall that the optimal p + + align:start position:0% + + + + align:start position:0% + +had uh e Prime of P equal to zero that + + align:start position:0% +had uh e Prime of P equal to zero that + + + align:start position:0% +had uh e Prime of P equal to zero that +was a socially efficient level of P + + align:start position:0% +was a socially efficient level of P + + + align:start position:0% +was a socially efficient level of P +right + + align:start position:0% +right + + + align:start position:0% +right +so + + align:start position:0% +so + + + align:start position:0% +so +um what you can see is that whenever uh + + align:start position:0% +um what you can see is that whenever uh + + + align:start position:0% +um what you can see is that whenever uh +K is whenever W is less than k + + align:start position:0% +K is whenever W is less than k + + + align:start position:0% +K is whenever W is less than k +whenever you're borrowing something + + align:start position:0% +whenever you're borrowing something + + + align:start position:0% +whenever you're borrowing something +right so if W is equal to K by the way + + align:start position:0% +right so if W is equal to K by the way + + + align:start position:0% +right so if W is equal to K by the way +if it's all your own Capital you pick + + align:start position:0% +if it's all your own Capital you pick + + + align:start position:0% +if it's all your own Capital you pick +the socially efficient level of level of + + align:start position:0% +the socially efficient level of level of + + + align:start position:0% +the socially efficient level of level of +the social efficient project why because + + align:start position:0% +the social efficient project why because + + + align:start position:0% +the social efficient project why because +you the the costs and the benefits you + + align:start position:0% +you the the costs and the benefits you + + + align:start position:0% +you the the costs and the benefits you +sort of totally internalize + + align:start position:0% +sort of totally internalize + + + align:start position:0% +sort of totally internalize +whenever we have a wedge where you're + + align:start position:0% +whenever we have a wedge where you're + + + align:start position:0% +whenever we have a wedge where you're +sort of gaining more of the upside the + + align:start position:0% +sort of gaining more of the upside the + + + align:start position:0% +sort of gaining more of the upside the +downside that's going to lead you to + + align:start position:0% +downside that's going to lead you to + + + align:start position:0% +downside that's going to lead you to +take riskier projects + + align:start position:0% +take riskier projects + + + align:start position:0% +take riskier projects +okay and how do we see that + + align:start position:0% +okay and how do we see that + + + align:start position:0% +okay and how do we see that +um uh we see that basically that's + + align:start position:0% +um uh we see that basically that's + + + align:start position:0% +um uh we see that basically that's +because uh e Prime is uh + + align:start position:0% +because uh e Prime is uh + + + align:start position:0% +because uh e Prime is uh +is uh is greater than zero and um + + align:start position:0% +is uh is greater than zero and um + + + align:start position:0% +is uh is greater than zero and um +and so uh + + align:start position:0% +and so uh + + + align:start position:0% +and so uh +because + + align:start position:0% +because + + + align:start position:0% +because +in order to make this thing positive the + + align:start position:0% +in order to make this thing positive the + + + align:start position:0% +in order to make this thing positive the +the the + + align:start position:0% +the the + + + align:start position:0% +the the +um + + align:start position:0% +um + + + align:start position:0% +um +oh no sorry you're gonna take more risks + + align:start position:0% +oh no sorry you're gonna take more risks + + + align:start position:0% +oh no sorry you're gonna take more risks +sorry because e double Prime is less + + align:start position:0% +sorry because e double Prime is less + + + align:start position:0% +sorry because e double Prime is less +than zero we're gonna uh we're gonna + + align:start position:0% +than zero we're gonna uh we're gonna + + + align:start position:0% +than zero we're gonna uh we're gonna +take a little bit more risk in order to + + align:start position:0% +take a little bit more risk in order to + + + align:start position:0% +take a little bit more risk in order to +make this thing positive + + align:start position:0% + + + + align:start position:0% + +okay so the the optimal project is going + + align:start position:0% +okay so the the optimal project is going + + + align:start position:0% +okay so the the optimal project is going +to be a little bit riskier + + align:start position:0% +to be a little bit riskier + + + align:start position:0% +to be a little bit riskier +uh in order to make e Prime positive + + align:start position:0% +uh in order to make e Prime positive + + + align:start position:0% +uh in order to make e Prime positive +okay and that's the sort of what I was + + align:start position:0% +okay and that's the sort of what I was + + + align:start position:0% +okay and that's the sort of what I was +intuitively saying before whenever + + align:start position:0% +intuitively saying before whenever + + + align:start position:0% +intuitively saying before whenever +you're not perfect whenever you're sort + + align:start position:0% +you're not perfect whenever you're sort + + + align:start position:0% +you're not perfect whenever you're sort +of getting more of the upside and the + + align:start position:0% +of getting more of the upside and the + + + align:start position:0% +of getting more of the upside and the +downside that's going to lead you to + + align:start position:0% +downside that's going to lead you to + + + align:start position:0% +downside that's going to lead you to +take uh too much risk than a socially + + align:start position:0% +take uh too much risk than a socially + + + align:start position:0% +take uh too much risk than a socially +socially efficient + + align:start position:0% +socially efficient + + + align:start position:0% +socially efficient +okay is that clear + + align:start position:0% +okay is that clear + + + align:start position:0% +okay is that clear +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um that's basically what I said + + align:start position:0% + + + + align:start position:0% + +okay clear so far yeah + + align:start position:0% +okay clear so far yeah + + + align:start position:0% +okay clear so far yeah +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so + + align:start position:0% +so + + + align:start position:0% +so +um this already gives us some + + align:start position:0% +um this already gives us some + + + align:start position:0% +um this already gives us some +comparative Statics + + align:start position:0% +comparative Statics + + + align:start position:0% +comparative Statics +so this is the condition that I just + + align:start position:0% +so this is the condition that I just + + + align:start position:0% +so this is the condition that I just +arrived in the last slide that F of K + + align:start position:0% +arrived in the last slide that F of K + + + align:start position:0% +arrived in the last slide that F of K +times e Prime of uh P was equal to r k + + align:start position:0% +times e Prime of uh P was equal to r k + + + align:start position:0% +times e Prime of uh P was equal to r k +minus w + + align:start position:0% +minus w + + + align:start position:0% +minus w +so we can just + + align:start position:0% +so we can just + + + align:start position:0% +so we can just +um uh divide uh through by uh + + align:start position:0% +um uh divide uh through by uh + + + align:start position:0% +um uh divide uh through by uh +so we can pull out a k to make this 1 + + align:start position:0% +so we can pull out a k to make this 1 + + + align:start position:0% +so we can pull out a k to make this 1 +minus W over K divide through by F of K + + align:start position:0% +minus W over K divide through by F of K + + + align:start position:0% +minus W over K divide through by F of K +we get the second expression here e + + align:start position:0% +we get the second expression here e + + + align:start position:0% +we get the second expression here e +Prime of p is equal to K Over F of K + + align:start position:0% +Prime of p is equal to K Over F of K + + + align:start position:0% +Prime of p is equal to K Over F of K +times R times one minus W over K so Y is + + align:start position:0% +times R times one minus W over K so Y is + + + align:start position:0% +times R times one minus W over K so Y is +sort of writing things in that way + + align:start position:0% +sort of writing things in that way + + + align:start position:0% +sort of writing things in that way +helpful it's because we can immediately + + align:start position:0% +helpful it's because we can immediately + + + align:start position:0% +helpful it's because we can immediately +start to see a few comparative Statics + + align:start position:0% +start to see a few comparative Statics + + + align:start position:0% +start to see a few comparative Statics +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the first one is we can see how does + + align:start position:0% +so the first one is we can see how does + + + align:start position:0% +so the first one is we can see how does +p Prime depend on interest rate okay so + + align:start position:0% +p Prime depend on interest rate okay so + + + align:start position:0% +p Prime depend on interest rate okay so +P hat how does the equilibrium choice of + + align:start position:0% +P hat how does the equilibrium choice of + + + align:start position:0% +P hat how does the equilibrium choice of +project depend on the interest rate okay + + align:start position:0% +project depend on the interest rate okay + + + align:start position:0% +project depend on the interest rate okay +so when interest rate goes up e Prime + + align:start position:0% +so when interest rate goes up e Prime + + + align:start position:0% +so when interest rate goes up e Prime +goes up therefore p goes down + + align:start position:0% +goes up therefore p goes down + + + align:start position:0% +goes up therefore p goes down +right so when the interest rate is + + align:start position:0% +right so when the interest rate is + + + align:start position:0% +right so when the interest rate is +higher we're going to be choosing + + align:start position:0% +higher we're going to be choosing + + + align:start position:0% +higher we're going to be choosing +riskier projects + + align:start position:0% +riskier projects + + + align:start position:0% +riskier projects +okay again assuming that we're in a + + align:start position:0% +okay again assuming that we're in a + + + align:start position:0% +okay again assuming that we're in a +world where you're borrowing something + + align:start position:0% +world where you're borrowing something + + + align:start position:0% +world where you're borrowing something +obviously if W over K if W is equal to k + + align:start position:0% +obviously if W over K if W is equal to k + + + align:start position:0% +obviously if W over K if W is equal to k +then then we're just at the socially + + align:start position:0% +then then we're just at the socially + + + align:start position:0% +then then we're just at the socially +efficient level but assuming W is less + + align:start position:0% +efficient level but assuming W is less + + + align:start position:0% +efficient level but assuming W is less +than K we have that sort of higher + + align:start position:0% +than K we have that sort of higher + + + align:start position:0% +than K we have that sort of higher +interest rates are going to lead to sort + + align:start position:0% +interest rates are going to lead to sort + + + align:start position:0% +interest rates are going to lead to sort +of riskier projects + + align:start position:0% + + + + align:start position:0% + +clear by the way stop me if I'm going + + align:start position:0% +clear by the way stop me if I'm going + + + align:start position:0% +clear by the way stop me if I'm going +too fast so you know sometimes when you + + align:start position:0% +too fast so you know sometimes when you + + + align:start position:0% +too fast so you know sometimes when you +go through a model on the slides it's + + align:start position:0% +go through a model on the slides it's + + + align:start position:0% +go through a model on the slides it's +it's too fast but if anything's + + align:start position:0% +it's too fast but if anything's + + + align:start position:0% +it's too fast but if anything's +so + + align:start position:0% +so + + + align:start position:0% +so +higher Intruders + + align:start position:0% + + + + align:start position:0% + +look no lower p is higher risk so higher + + align:start position:0% +look no lower p is higher risk so higher + + + align:start position:0% +look no lower p is higher risk so higher +R means higher e Prime but we have e is + + align:start position:0% +R means higher e Prime but we have e is + + + align:start position:0% +R means higher e Prime but we have e is +concave + + align:start position:0% +concave + + + align:start position:0% +concave +so so to go we're going to go we're + + align:start position:0% +so so to go we're going to go we're + + + align:start position:0% +so so to go we're going to go we're +gonna go down on the on the + + align:start position:0% +gonna go down on the on the + + + align:start position:0% +gonna go down on the on the +um + + align:start position:0% +um + + + align:start position:0% +um +to get sort of a positive uh + + align:start position:0% +to get sort of a positive uh + + + align:start position:0% +to get sort of a positive uh +yeah it's the same it's the same thing + + align:start position:0% +yeah it's the same it's the same thing + + + align:start position:0% +yeah it's the same it's the same thing +if you see like you know F Prime is + + align:start position:0% +if you see like you know F Prime is + + + align:start position:0% +if you see like you know F Prime is +concave and right the higher sort of + + align:start position:0% +concave and right the higher sort of + + + align:start position:0% +concave and right the higher sort of +marginal products meaning we have less + + align:start position:0% +marginal products meaning we have less + + + align:start position:0% +marginal products meaning we have less +Capital same idea basically because we + + align:start position:0% +Capital same idea basically because we + + + align:start position:0% +Capital same idea basically because we +have higher we have higher levels of uh + + align:start position:0% +have higher we have higher levels of uh + + + align:start position:0% +have higher we have higher levels of uh +of e prime or we're going to get higher + + align:start position:0% +of e prime or we're going to get higher + + + align:start position:0% +of e prime or we're going to get higher +levels with Prime with lower levels of P + + align:start position:0% +levels with Prime with lower levels of P + + + align:start position:0% +levels with Prime with lower levels of P +because e Prime was concave because he + + align:start position:0% +because e Prime was concave because he + + + align:start position:0% +because e Prime was concave because he +sorry he was concave uh similarly we can + + align:start position:0% +sorry he was concave uh similarly we can + + + align:start position:0% +sorry he was concave uh similarly we can +say like how does p depend on the + + align:start position:0% +say like how does p depend on the + + + align:start position:0% +say like how does p depend on the +returns right returns is sort of uh F of + + align:start position:0% +returns right returns is sort of uh F of + + + align:start position:0% +returns right returns is sort of uh F of +K that's kind of like f of K divided F + + align:start position:0% +K that's kind of like f of K divided F + + + align:start position:0% +K that's kind of like f of K divided F +of K divided by K sort of what is the it + + align:start position:0% +of K divided by K sort of what is the it + + + align:start position:0% +of K divided by K sort of what is the it +was like the return on Capital right + + align:start position:0% +was like the return on Capital right + + + align:start position:0% +was like the return on Capital right +like you you invest K and you get back F + + align:start position:0% +like you you invest K and you get back F + + + align:start position:0% +like you you invest K and you get back F +you go back F of K + + align:start position:0% +you go back F of K + + + align:start position:0% +you go back F of K +so this is like the the average return + + align:start position:0% +so this is like the the average return + + + align:start position:0% +so this is like the the average return +on Capital + + align:start position:0% +on Capital + + + align:start position:0% +on Capital +um this is going to be increasing for + + align:start position:0% +um this is going to be increasing for + + + align:start position:0% +um this is going to be increasing for +the same reason this is you know because + + align:start position:0% +the same reason this is you know because + + + align:start position:0% +the same reason this is you know because +this is one over that so it's it all + + align:start position:0% +this is one over that so it's it all + + + align:start position:0% +this is one over that so it's it all +goes backwards so uh higher returns + + align:start position:0% +goes backwards so uh higher returns + + + align:start position:0% +goes backwards so uh higher returns +leads you to choose + + align:start position:0% +leads you to choose + + + align:start position:0% +leads you to choose +um a higher probability success + + align:start position:0% +um a higher probability success + + + align:start position:0% +um a higher probability success +projects + + align:start position:0% +projects + + + align:start position:0% +projects +and this is this one I think is kind of + + align:start position:0% +and this is this one I think is kind of + + + align:start position:0% +and this is this one I think is kind of +these two are sort of going to be the + + align:start position:0% +these two are sort of going to be the + + + align:start position:0% +these two are sort of going to be the +most relevant for us the third one is + + align:start position:0% +most relevant for us the third one is + + + align:start position:0% +most relevant for us the third one is +sort of how does uh P hat depend on K + + align:start position:0% +sort of how does uh P hat depend on K + + + align:start position:0% +sort of how does uh P hat depend on K +Over W or k over W is leverage K Over W + + align:start position:0% +Over W or k over W is leverage K Over W + + + align:start position:0% +Over W or k over W is leverage K Over W +is sort of uh obviously one over WK + + align:start position:0% +is sort of uh obviously one over WK + + + align:start position:0% +is sort of uh obviously one over WK +um but you can sort of how does it + + align:start position:0% +um but you can sort of how does it + + + align:start position:0% +um but you can sort of how does it +depend on sort of what fraction you're + + align:start position:0% +depend on sort of what fraction you're + + + align:start position:0% +depend on sort of what fraction you're +borrowing well we know that it's going + + align:start position:0% +borrowing well we know that it's going + + + align:start position:0% +borrowing well we know that it's going +to be decreasing again we know that sort + + align:start position:0% +to be decreasing again we know that sort + + + align:start position:0% +to be decreasing again we know that sort +of when K is equal to to W right we're + + align:start position:0% +of when K is equal to to W right we're + + + align:start position:0% +of when K is equal to to W right we're +at the optimal level and as we start to + + align:start position:0% +at the optimal level and as we start to + + + align:start position:0% +at the optimal level and as we start to +increase K we're going to be sort of + + align:start position:0% +increase K we're going to be sort of + + + align:start position:0% +increase K we're going to be sort of +choosing riskier holding wfx we're going + + align:start position:0% +choosing riskier holding wfx we're going + + + align:start position:0% +choosing riskier holding wfx we're going +to be sort of choosing riskier and risky + + align:start position:0% +to be sort of choosing riskier and risky + + + align:start position:0% +to be sort of choosing riskier and risky +projects + + align:start position:0% + + + + align:start position:0% + +okay clear what's the intuition for the + + align:start position:0% +okay clear what's the intuition for the + + + align:start position:0% +okay clear what's the intuition for the +second Point + + align:start position:0% +second Point + + + align:start position:0% +second Point +um + + align:start position:0% +um + + + align:start position:0% +um +so I think it's a similar one that + + align:start position:0% +so I think it's a similar one that + + + align:start position:0% +so I think it's a similar one that +basically + + align:start position:0% +basically + + + align:start position:0% +basically +uh the + + align:start position:0% +uh the + + + align:start position:0% +uh the +actually I don't have a good intuition + + align:start position:0% +actually I don't have a good intuition + + + align:start position:0% +actually I don't have a good intuition +for the second wife does anyone else + + align:start position:0% +for the second wife does anyone else + + + align:start position:0% +for the second wife does anyone else +want to give it a shot sorry I don't + + align:start position:0% +want to give it a shot sorry I don't + + + align:start position:0% +want to give it a shot sorry I don't +actually I take back I don't have a good + + align:start position:0% +actually I take back I don't have a good + + + align:start position:0% +actually I take back I don't have a good +one it's a little hard to think about + + align:start position:0% +one it's a little hard to think about + + + align:start position:0% +one it's a little hard to think about +because you're holding W over K fix + + align:start position:0% +because you're holding W over K fix + + + align:start position:0% +because you're holding W over K fix +um + + align:start position:0% + + + + align:start position:0% + +hold on one second let me see if I can + + align:start position:0% +hold on one second let me see if I can + + + align:start position:0% +hold on one second let me see if I can +give you a good intuition + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +I'm sorry no I don't have a good + + align:start position:0% +I'm sorry no I don't have a good + + + align:start position:0% +I'm sorry no I don't have a good +intuition let me think about it + + align:start position:0% +intuition let me think about it + + + align:start position:0% +intuition let me think about it +anyone else want to try + + align:start position:0% + + + + align:start position:0% + +Ed do you have a good intuition for you + + align:start position:0% +Ed do you have a good intuition for you + + + align:start position:0% +Ed do you have a good intuition for you +no sorry I should think about sorry I + + align:start position:0% +no sorry I should think about sorry I + + + align:start position:0% +no sorry I should think about sorry I +don't have a good answer for it + + align:start position:0% +don't have a good answer for it + + + align:start position:0% +don't have a good answer for it +okay but luckily I'm going to mostly + + align:start position:0% +okay but luckily I'm going to mostly + + + align:start position:0% +okay but luckily I'm going to mostly +talk about R and the other one which I + + align:start position:0% +talk about R and the other one which I + + + align:start position:0% +talk about R and the other one which I +do have a good question for + + align:start position:0% +do have a good question for + + + align:start position:0% +do have a good question for +me yeah Hazel so we're assuming that + + align:start position:0% +me yeah Hazel so we're assuming that + + + align:start position:0% +me yeah Hazel so we're assuming that +zabara is risky first division would be + + align:start position:0% +zabara is risky first division would be + + + align:start position:0% +zabara is risky first division would be +like is that taking too much risks so if + + align:start position:0% +like is that taking too much risks so if + + + align:start position:0% +like is that taking too much risks so if +we assume that they will listen to this + + align:start position:0% +we assume that they will listen to this + + + align:start position:0% +we assume that they will listen to this +if we get rid of that + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +if we assume their risk-averse it's + + align:start position:0% +if we assume their risk-averse it's + + + align:start position:0% +if we assume their risk-averse it's +going to lead them to take less risk + + align:start position:0% +going to lead them to take less risk + + + align:start position:0% +going to lead them to take less risk +um hold on let me let me think what + + align:start position:0% +um hold on let me let me think what + + + align:start position:0% +um hold on let me let me think what +sorry + + align:start position:0% + + + + align:start position:0% + +no go ahead Hazel oh I said because I've + + align:start position:0% +no go ahead Hazel oh I said because I've + + + align:start position:0% +no go ahead Hazel oh I said because I've +been taking too much risks before right + + align:start position:0% +been taking too much risks before right + + + align:start position:0% +been taking too much risks before right +and then a few introduce your exhibition + + align:start position:0% +and then a few introduce your exhibition + + + align:start position:0% +and then a few introduce your exhibition +they might take us yes that that clearly + + align:start position:0% +they might take us yes that that clearly + + + align:start position:0% +they might take us yes that that clearly +sounds right if they're if they're risk + + align:start position:0% +sounds right if they're if they're risk + + + align:start position:0% +sounds right if they're if they're risk +but you know the optimal + + align:start position:0% +but you know the optimal + + + align:start position:0% +but you know the optimal +I think it's still going to be the case + + align:start position:0% +I think it's still going to be the case + + + align:start position:0% +I think it's still going to be the case +they're going to take + + align:start position:0% + + + + align:start position:0% + +so yes for sure if their risk-averse are + + align:start position:0% +so yes for sure if their risk-averse are + + + align:start position:0% +so yes for sure if their risk-averse are +going to take less risk that's going to + + align:start position:0% +going to take less risk that's going to + + + align:start position:0% +going to take less risk that's going to +shift the whole thing in the direction + + align:start position:0% +shift the whole thing in the direction + + + align:start position:0% +shift the whole thing in the direction +of less riskiness and you could get that + + align:start position:0% +of less riskiness and you could get that + + + align:start position:0% +of less riskiness and you could get that +maybe the optimal thing is supposed to + + align:start position:0% +maybe the optimal thing is supposed to + + + align:start position:0% +maybe the optimal thing is supposed to +get to get e star but e-star may no + + align:start position:0% +get to get e star but e-star may no + + + align:start position:0% +get to get e star but e-star may no +longer be the same P Star May no longer + + align:start position:0% +longer be the same P Star May no longer + + + align:start position:0% +longer be the same P Star May no longer +be optimal because it's no longer + + align:start position:0% +be optimal because it's no longer + + + align:start position:0% +be optimal because it's no longer +optimal for them so I think it's still + + align:start position:0% +optimal for them so I think it's still + + + align:start position:0% +optimal for them so I think it's still +going to be the case that if you think + + align:start position:0% +going to be the case that if you think + + + align:start position:0% +going to be the case that if you think +about sort of social socially optimal + + align:start position:0% +about sort of social socially optimal + + + align:start position:0% +about sort of social socially optimal +including kind of the risk of like the + + align:start position:0% +including kind of the risk of like the + + + align:start position:0% +including kind of the risk of like the +riskiness to them it's still going to be + + align:start position:0% +riskiness to them it's still going to be + + + align:start position:0% +riskiness to them it's still going to be +the case they're going to take too much + + align:start position:0% +the case they're going to take too much + + + align:start position:0% +the case they're going to take too much +risk well over for that + + align:start position:0% + + + + align:start position:0% + +but yes you're right certainly if we add + + align:start position:0% +but yes you're right certainly if we add + + + align:start position:0% +but yes you're right certainly if we add +risk aversion they're going to take less + + align:start position:0% +risk aversion they're going to take less + + + align:start position:0% +risk aversion they're going to take less +risk and that's going to shift the whole + + align:start position:0% +risk and that's going to shift the whole + + + align:start position:0% +risk and that's going to shift the whole +thing up + + align:start position:0% + + + + align:start position:0% + +okay I think the intuition is just you + + align:start position:0% +okay I think the intuition is just you + + + align:start position:0% +okay I think the intuition is just you +care about F times e and if F goes up do + + align:start position:0% +care about F times e and if F goes up do + + + align:start position:0% +care about F times e and if F goes up do +you care about what you care about F + + align:start position:0% +you care about what you care about F + + + align:start position:0% +you care about what you care about F +times T ultimately + + align:start position:0% + + + + align:start position:0% + +then you get more invested in the return + + align:start position:0% + + + + align:start position:0% + +whereas your repayments linear + + align:start position:0% +whereas your repayments linear + + + align:start position:0% +whereas your repayments linear +oh I see it you're this relative to that + + align:start position:0% +oh I see it you're this relative to that + + + align:start position:0% +oh I see it you're this relative to that +okay there you go + + align:start position:0% +okay there you go + + + align:start position:0% +okay there you go +thank you right + + align:start position:0% + + + + align:start position:0% + +okay thanks Ed + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +the other thing I want to note here that + + align:start position:0% +the other thing I want to note here that + + + align:start position:0% +the other thing I want to note here that +comes out of this model which comes out + + align:start position:0% +comes out of this model which comes out + + + align:start position:0% +comes out of this model which comes out +of many of these models is there's a + + align:start position:0% +of many of these models is there's a + + + align:start position:0% +of many of these models is there's a +positive probability is that positive + + align:start position:0% +positive probability is that positive + + + align:start position:0% +positive probability is that positive +correlation between the default + + align:start position:0% +correlation between the default + + + align:start position:0% +correlation between the default +probability which is 1 minus p and the + + align:start position:0% +probability which is 1 minus p and the + + + align:start position:0% +probability which is 1 minus p and the +interest rate right so in general we had + + align:start position:0% +interest rate right so in general we had + + + align:start position:0% +interest rate right so in general we had +like higher interest rates lead to sort + + align:start position:0% +like higher interest rates lead to sort + + + align:start position:0% +like higher interest rates lead to sort +of riskier projects and we get that in + + align:start position:0% +of riskier projects and we get that in + + + align:start position:0% +of riskier projects and we get that in +this model that was this prediction over + + align:start position:0% +this model that was this prediction over + + + align:start position:0% +this model that was this prediction over +here and that positive correlation + + align:start position:0% +here and that positive correlation + + + align:start position:0% +here and that positive correlation +between sort of the the interest rate + + align:start position:0% +between sort of the the interest rate + + + align:start position:0% +between sort of the the interest rate +and the + + align:start position:0% +and the + + + align:start position:0% +and the +um and the riskiness is a classic sort + + align:start position:0% +um and the riskiness is a classic sort + + + align:start position:0% +um and the riskiness is a classic sort +of uh prediction of many of these kinds + + align:start position:0% +of uh prediction of many of these kinds + + + align:start position:0% +of uh prediction of many of these kinds +of asymmetric information models + + align:start position:0% +of asymmetric information models + + + align:start position:0% +of asymmetric information models +including wall Hazard models like this + + align:start position:0% +including wall Hazard models like this + + + align:start position:0% +including wall Hazard models like this +one + + align:start position:0% +one + + + align:start position:0% +one +okay clear so far + + align:start position:0% + + + + align:start position:0% + +okay so the final thing that we need to + + align:start position:0% +okay so the final thing that we need to + + + align:start position:0% +okay so the final thing that we need to +do is we need to add a um a uh + + align:start position:0% +do is we need to add a um a uh + + + align:start position:0% +do is we need to add a um a uh +sort of a exogenous supply of funds for + + align:start position:0% +sort of a exogenous supply of funds for + + + align:start position:0% +sort of a exogenous supply of funds for +the lender + + align:start position:0% +the lender + + + align:start position:0% +the lender +okay so the lender can go out to the + + align:start position:0% +okay so the lender can go out to the + + + align:start position:0% +okay so the lender can go out to the +capital markets like call it Wall Street + + align:start position:0% +capital markets like call it Wall Street + + + align:start position:0% +capital markets like call it Wall Street +or whatever and they can borrow at rate + + align:start position:0% +or whatever and they can borrow at rate + + + align:start position:0% +or whatever and they can borrow at rate +row okay + + align:start position:0% +row okay + + + align:start position:0% +row okay +so they're only getting repaid of course + + align:start position:0% +so they're only getting repaid of course + + + align:start position:0% +so they're only getting repaid of course +with probability p + + align:start position:0% +with probability p + + + align:start position:0% +with probability p +right so their equilibrium condition is + + align:start position:0% +right so their equilibrium condition is + + + align:start position:0% +right so their equilibrium condition is +that their sort of cost of funds row has + + align:start position:0% +that their sort of cost of funds row has + + + align:start position:0% +that their sort of cost of funds row has +to be equal to their kind of expected + + align:start position:0% +to be equal to their kind of expected + + + align:start position:0% +to be equal to their kind of expected +return which is prop with probability P + + align:start position:0% +return which is prop with probability P + + + align:start position:0% +return which is prop with probability P +they get r with probably one minus P + + align:start position:0% +they get r with probably one minus P + + + align:start position:0% +they get r with probably one minus P +they they don't and so um and so that's + + align:start position:0% +they they don't and so um and so that's + + + align:start position:0% +they they don't and so um and so that's +gonna gonna determine their um their + + align:start position:0% +gonna gonna determine their um their + + + align:start position:0% +gonna gonna determine their um their +return + + align:start position:0% + + + + align:start position:0% + +so what is this going to look like for + + align:start position:0% +so what is this going to look like for + + + align:start position:0% +so what is this going to look like for +equilibrium so there's two different + + align:start position:0% +equilibrium so there's two different + + + align:start position:0% +equilibrium so there's two different +things going on + + align:start position:0% +things going on + + + align:start position:0% +things going on +the first is with this market clearing + + align:start position:0% +the first is with this market clearing + + + align:start position:0% +the first is with this market clearing +thing which is that rho is equal to to P + + align:start position:0% +thing which is that rho is equal to to P + + + align:start position:0% +thing which is that rho is equal to to P +times R okay so this is RSP + + align:start position:0% +times R okay so this is RSP + + + align:start position:0% +times R okay so this is RSP +and then we also derive from the from + + align:start position:0% +and then we also derive from the from + + + align:start position:0% +and then we also derive from the from +the previous model this moral hazard + + align:start position:0% +the previous model this moral hazard + + + align:start position:0% +the previous model this moral hazard +kind of equilibrium which also give you + + align:start position:0% +kind of equilibrium which also give you + + + align:start position:0% +kind of equilibrium which also give you +p as a function of r + + align:start position:0% +p as a function of r + + + align:start position:0% +p as a function of r +okay so as I've drawn here there's like + + align:start position:0% +okay so as I've drawn here there's like + + + align:start position:0% +okay so as I've drawn here there's like +a single equilibrium this is going to be + + align:start position:0% +a single equilibrium this is going to be + + + align:start position:0% +a single equilibrium this is going to be +the equilibrium of this Market where + + align:start position:0% +the equilibrium of this Market where + + + align:start position:0% +the equilibrium of this Market where +we're going to have kind of uh interest + + align:start position:0% +we're going to have kind of uh interest + + + align:start position:0% +we're going to have kind of uh interest +projects P down here and and this is and + + align:start position:0% +projects P down here and and this is and + + + align:start position:0% +projects P down here and and this is and +this interest rate + + align:start position:0% +this interest rate + + + align:start position:0% +this interest rate +okay but the this thing + + align:start position:0% +okay but the this thing + + + align:start position:0% +okay but the this thing +is I mean obviously this is not drawn + + align:start position:0% +is I mean obviously this is not drawn + + + align:start position:0% +is I mean obviously this is not drawn +exactly right but but this this function + + align:start position:0% +exactly right but but this this function + + + align:start position:0% +exactly right but but this this function +here I guess this hyperbola given by + + align:start position:0% +here I guess this hyperbola given by + + + align:start position:0% +here I guess this hyperbola given by +this rho equals PR that's fixed + + align:start position:0% +this rho equals PR that's fixed + + + align:start position:0% +this rho equals PR that's fixed +but the shape of this particular P hat + + align:start position:0% +but the shape of this particular P hat + + + align:start position:0% +but the shape of this particular P hat +of R is not obvious what it's going to + + align:start position:0% +of R is not obvious what it's going to + + + align:start position:0% +of R is not obvious what it's going to +be it's going to depend on sort of the + + align:start position:0% +be it's going to depend on sort of the + + + align:start position:0% +be it's going to depend on sort of the +underlying kind of things that went into + + align:start position:0% +underlying kind of things that went into + + + align:start position:0% +underlying kind of things that went into +that previous model + + align:start position:0% +that previous model + + + align:start position:0% +that previous model +like in particular it's going to depend + + align:start position:0% +like in particular it's going to depend + + + align:start position:0% +like in particular it's going to depend +on this e function right which could be + + align:start position:0% +on this e function right which could be + + + align:start position:0% +on this e function right which could be +you know we haven't sort of specified + + align:start position:0% +you know we haven't sort of specified + + + align:start position:0% +you know we haven't sort of specified +but that's going to be + + align:start position:0% +but that's going to be + + + align:start position:0% +but that's going to be +so we could draw it like this with the + + align:start position:0% +so we could draw it like this with the + + + align:start position:0% +so we could draw it like this with the +single equilibrium + + align:start position:0% +single equilibrium + + + align:start position:0% +single equilibrium +we can draw it could look like this + + align:start position:0% +we can draw it could look like this + + + align:start position:0% +we can draw it could look like this +um which has a I mean we know that it + + align:start position:0% +um which has a I mean we know that it + + + align:start position:0% +um which has a I mean we know that it +has to be decreasing but sort of the + + align:start position:0% +has to be decreasing but sort of the + + + align:start position:0% +has to be decreasing but sort of the +shape of this thing is not clear + + align:start position:0% +shape of this thing is not clear + + + align:start position:0% +shape of this thing is not clear +um so it could have if I've drawn it + + align:start position:0% +um so it could have if I've drawn it + + + align:start position:0% +um so it could have if I've drawn it +like this there are sort of three + + align:start position:0% +like this there are sort of three + + + align:start position:0% +like this there are sort of three +equilibria + + align:start position:0% +equilibria + + + align:start position:0% +equilibria +right + + align:start position:0% +right + + + align:start position:0% +right +um where uh where these are both I think + + align:start position:0% +um where uh where these are both I think + + + align:start position:0% +um where uh where these are both I think +the stable equilibria + + align:start position:0% + + + + align:start position:0% + +um and here there could be two equals so + + align:start position:0% +um and here there could be two equals so + + + align:start position:0% +um and here there could be two equals so +here there could be two equilibrium this + + align:start position:0% +here there could be two equilibrium this + + + align:start position:0% +here there could be two equilibrium this +credit Market we could have one where we + + align:start position:0% +credit Market we could have one where we + + + align:start position:0% +credit Market we could have one where we +sort of have really high interest rates + + align:start position:0% +sort of have really high interest rates + + + align:start position:0% +sort of have really high interest rates +um and very risky projects or we can + + align:start position:0% +um and very risky projects or we can + + + align:start position:0% +um and very risky projects or we can +have very low interest rates and not + + align:start position:0% +have very low interest rates and not + + + align:start position:0% +have very low interest rates and not +very risky projects both of those could + + align:start position:0% +very risky projects both of those could + + + align:start position:0% +very risky projects both of those could +be could be equilibria + + align:start position:0% +be could be equilibria + + + align:start position:0% +be could be equilibria +um + + align:start position:0% +um + + + align:start position:0% +um +but you know it's multiple equivalent + + align:start position:0% +but you know it's multiple equivalent + + + align:start position:0% +but you know it's multiple equivalent +model + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +you know or you could maybe have a Nolan + + align:start position:0% +you know or you could maybe have a Nolan + + + align:start position:0% +you know or you could maybe have a Nolan +equilibrium where sort of the again you + + align:start position:0% +equilibrium where sort of the again you + + + align:start position:0% +equilibrium where sort of the again you +have to sort of draw both of these + + align:start position:0% +have to sort of draw both of these + + + align:start position:0% +have to sort of draw both of these +things kind of going out + + align:start position:0% +things kind of going out + + + align:start position:0% +things kind of going out +like this but it's not obvious these + + align:start position:0% +like this but it's not obvious these + + + align:start position:0% +like this but it's not obvious these +things are necessarily going to + + align:start position:0% +things are necessarily going to + + + align:start position:0% +things are necessarily going to +intersect + + align:start position:0% +intersect + + + align:start position:0% +intersect +right and so in this model there's + + align:start position:0% +right and so in this model there's + + + align:start position:0% +right and so in this model there's +actually the the credit memory could + + align:start position:0% +actually the the credit memory could + + + align:start position:0% +actually the the credit memory could +collapse entirely if there's no kind of + + align:start position:0% +collapse entirely if there's no kind of + + + align:start position:0% +collapse entirely if there's no kind of +intersection between these two points + + align:start position:0% +intersection between these two points + + + align:start position:0% +intersection between these two points +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um + + align:start position:0% + + + + align:start position:0% + +so this this already sort of gives us + + align:start position:0% +so this this already sort of gives us + + + align:start position:0% +so this this already sort of gives us +some important uh things going on it can + + align:start position:0% +some important uh things going on it can + + + align:start position:0% +some important uh things going on it can +be it can already be an explanation for + + align:start position:0% +be it can already be an explanation for + + + align:start position:0% +be it can already be an explanation for +example why you might have you know + + align:start position:0% +example why you might have you know + + + align:start position:0% +example why you might have you know +multiple different things going on you + + align:start position:0% +multiple different things going on you + + + align:start position:0% +multiple different things going on you +could have kind of really high interest + + align:start position:0% +could have kind of really high interest + + + align:start position:0% +could have kind of really high interest +rates and and really terrible projects + + align:start position:0% +rates and and really terrible projects + + + align:start position:0% +rates and and really terrible projects +for example + + align:start position:0% +for example + + + align:start position:0% +for example +um or sometimes you can have credit + + align:start position:0% +um or sometimes you can have credit + + + align:start position:0% +um or sometimes you can have credit +markers that collapse entirely + + align:start position:0% +markers that collapse entirely + + + align:start position:0% +markers that collapse entirely +okay that just depends on the sort of + + align:start position:0% +okay that just depends on the sort of + + + align:start position:0% +okay that just depends on the sort of +the shape of these of that P hat of our + + align:start position:0% +the shape of these of that P hat of our + + + align:start position:0% +the shape of these of that P hat of our +function + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um what's what's happening with capital + + align:start position:0% +um what's what's happening with capital + + + align:start position:0% +um what's what's happening with capital +well you can think of us as having + + align:start position:0% +well you can think of us as having + + + align:start position:0% +well you can think of us as having +derived kind of that optimal P hat of a + + align:start position:0% +derived kind of that optimal P hat of a + + + align:start position:0% +derived kind of that optimal P hat of a +p hat function which was a function of + + align:start position:0% +p hat function which was a function of + + + align:start position:0% +p hat function which was a function of +sort of the the the returns the sort of + + align:start position:0% +sort of the the the returns the sort of + + + align:start position:0% +sort of the the the returns the sort of +the leverage ratio and the interest rate + + align:start position:0% +the leverage ratio and the interest rate + + + align:start position:0% +the leverage ratio and the interest rate +which is in itself kind of an endogenous + + align:start position:0% +which is in itself kind of an endogenous + + + align:start position:0% +which is in itself kind of an endogenous +function of K + + align:start position:0% +function of K + + + align:start position:0% +function of K +um + + align:start position:0% +um + + + align:start position:0% +um +so now + + align:start position:0% +so now + + + align:start position:0% +so now +um we can we all know the bank and the + + align:start position:0% +um we can we all know the bank and the + + + align:start position:0% +um we can we all know the bank and the +and the lender know that if conditional + + align:start position:0% +and the lender know that if conditional + + + align:start position:0% +and the lender know that if conditional +on a level K an interest rate + + align:start position:0% +on a level K an interest rate + + + align:start position:0% +on a level K an interest rate +um they're going to pick project p + + align:start position:0% +um they're going to pick project p + + + align:start position:0% +um they're going to pick project p +they can't contract or repeat but they + + align:start position:0% +they can't contract or repeat but they + + + align:start position:0% +they can't contract or repeat but they +know kind of what that P function is + + align:start position:0% +know kind of what that P function is + + + align:start position:0% +know kind of what that P function is +and so uh they can make a choice kind of + + align:start position:0% +and so uh they can make a choice kind of + + + align:start position:0% +and so uh they can make a choice kind of +collectively like what's the you know + + align:start position:0% +collectively like what's the you know + + + align:start position:0% +collectively like what's the you know +what how much Capital would you like to + + align:start position:0% +what how much Capital would you like to + + + align:start position:0% +what how much Capital would you like to +borrow + + align:start position:0% +borrow + + + align:start position:0% +borrow +right so then I can sort of solve I can + + align:start position:0% +right so then I can sort of solve I can + + + align:start position:0% +right so then I can sort of solve I can +maximize the uh over Capital uh the + + align:start position:0% +maximize the uh over Capital uh the + + + align:start position:0% +maximize the uh over Capital uh the +return here + + align:start position:0% +return here + + + align:start position:0% +return here +um + + align:start position:0% +um + + + align:start position:0% +um +where uh I'm going to maximize you know + + align:start position:0% +where uh I'm going to maximize you know + + + align:start position:0% +where uh I'm going to maximize you know +the the + + align:start position:0% +the the + + + align:start position:0% +the the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the amount I I get times the expected + + align:start position:0% +the amount I I get times the expected + + + align:start position:0% +the amount I I get times the expected +return minus the the amount I have to + + align:start position:0% +return minus the the amount I have to + + + align:start position:0% +return minus the the amount I have to +pay back + + align:start position:0% +pay back + + + align:start position:0% +pay back +uh and and here I've just substituted + + align:start position:0% +uh and and here I've just substituted + + + align:start position:0% +uh and and here I've just substituted +Lin for the fact that like in + + align:start position:0% +Lin for the fact that like in + + + align:start position:0% +Lin for the fact that like in +equilibrium I have to pay back row + + align:start position:0% +equilibrium I have to pay back row + + + align:start position:0% +equilibrium I have to pay back row +right so with probability P + + align:start position:0% +right so with probability P + + + align:start position:0% +right so with probability P +um I have to pay back uh + + align:start position:0% +um I have to pay back uh + + + align:start position:0% +um I have to pay back uh +our time if playback R so I know this is + + align:start position:0% +our time if playback R so I know this is + + + align:start position:0% +our time if playback R so I know this is +PR so I just substitute for row + + align:start position:0% + + + + align:start position:0% + +the the market + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um what's right still the same Hardware + + align:start position:0% +um what's right still the same Hardware + + + align:start position:0% +um what's right still the same Hardware +uh this this is contractable so they can + + align:start position:0% +uh this this is contractable so they can + + + align:start position:0% +uh this this is contractable so they can +decide together the borrower the + + align:start position:0% +decide together the borrower the + + + align:start position:0% +decide together the borrower the +borrower can the borrower can decide it + + align:start position:0% +borrower can the borrower can decide it + + + align:start position:0% +borrower can the borrower can decide it +but the bank will be happy to do this + + align:start position:0% +but the bank will be happy to do this + + + align:start position:0% +but the bank will be happy to do this +incorporate + + align:start position:0% +incorporate + + + align:start position:0% +incorporate +right the key the the key thing we had + + align:start position:0% +right the key the the key thing we had + + + align:start position:0% +right the key the the key thing we had +to keep track of is once they choose K + + align:start position:0% +to keep track of is once they choose K + + + align:start position:0% +to keep track of is once they choose K +together or whatever like this is a + + align:start position:0% +together or whatever like this is a + + + align:start position:0% +together or whatever like this is a +contract then the borrower goes off and + + align:start position:0% +contract then the borrower goes off and + + + align:start position:0% +contract then the borrower goes off and +chooses p so you the key point is we're + + align:start position:0% +chooses p so you the key point is we're + + + align:start position:0% +chooses p so you the key point is we're +choosing the level of K taking the + + align:start position:0% +choosing the level of K taking the + + + align:start position:0% +choosing the level of K taking the +borrowers like second period choice of + + align:start position:0% +borrowers like second period choice of + + + align:start position:0% +borrowers like second period choice of +of p as like that that function is kind + + align:start position:0% +of p as like that that function is kind + + + align:start position:0% +of p as like that that function is kind +of given + + align:start position:0% + + + + align:start position:0% + +okay and that's what I said right we're + + align:start position:0% +okay and that's what I said right we're + + + align:start position:0% +okay and that's what I said right we're +only maximizing so for K we can't choose + + align:start position:0% +only maximizing so for K we can't choose + + + align:start position:0% +only maximizing so for K we can't choose +K and P jointly uh because we know that + + align:start position:0% +K and P jointly uh because we know that + + + align:start position:0% +K and P jointly uh because we know that +like you know once we choose K I'm gonna + + align:start position:0% +like you know once we choose K I'm gonna + + + align:start position:0% +like you know once we choose K I'm gonna +go do whatever P I want + + align:start position:0% +go do whatever P I want + + + align:start position:0% +go do whatever P I want +right we might do better if we commit to + + align:start position:0% +right we might do better if we commit to + + + align:start position:0% +right we might do better if we commit to +sort of a level of KMP together but we + + align:start position:0% +sort of a level of KMP together but we + + + align:start position:0% +sort of a level of KMP together but we +can't + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the that gives us a first order + + align:start position:0% +so the that gives us a first order + + + align:start position:0% +so the that gives us a first order +condition so what's the first order + + align:start position:0% +condition so what's the first order + + + align:start position:0% +condition so what's the first order +condition well uh it's just F Prime of K + + align:start position:0% +condition well uh it's just F Prime of K + + + align:start position:0% +condition well uh it's just F Prime of K +times e of P right plus uh the other + + align:start position:0% +times e of P right plus uh the other + + + align:start position:0% +times e of P right plus uh the other +sort of term F of K times e Prime of of + + align:start position:0% +sort of term F of K times e Prime of of + + + align:start position:0% +sort of term F of K times e Prime of of +P times uh P Prime uh time P Prime to + + align:start position:0% +P times uh P Prime uh time P Prime to + + + align:start position:0% +P times uh P Prime uh time P Prime to +dpdk + + align:start position:0% +dpdk + + + align:start position:0% +dpdk +okay and all that has to be equal to rho + + align:start position:0% + + + + align:start position:0% + +clear + + align:start position:0% +clear + + + align:start position:0% +clear +by the way and thank thanks to Ed for + + align:start position:0% +by the way and thank thanks to Ed for + + + align:start position:0% +by the way and thank thanks to Ed for +helping me clean up some of my algebra + + align:start position:0% +helping me clean up some of my algebra + + + align:start position:0% +helping me clean up some of my algebra +on this slide which I + + align:start position:0% +on this slide which I + + + align:start position:0% +on this slide which I +I had some issues before + + align:start position:0% +I had some issues before + + + align:start position:0% +I had some issues before +but pretty sure this is correct + + align:start position:0% +but pretty sure this is correct + + + align:start position:0% +but pretty sure this is correct +so that's what we just had + + align:start position:0% +so that's what we just had + + + align:start position:0% +so that's what we just had +what would be the first best + + align:start position:0% +what would be the first best + + + align:start position:0% +what would be the first best +kind of uh the the first best would be + + align:start position:0% +kind of uh the the first best would be + + + align:start position:0% +kind of uh the the first best would be +that sort of the overall return + + align:start position:0% +that sort of the overall return + + + align:start position:0% +that sort of the overall return +right F Prime of K times the expected + + align:start position:0% +right F Prime of K times the expected + + + align:start position:0% +right F Prime of K times the expected +return should just be equal to kind of + + align:start position:0% +return should just be equal to kind of + + + align:start position:0% +return should just be equal to kind of +the market interest rate + + align:start position:0% +the market interest rate + + + align:start position:0% +the market interest rate +so that would be sort of the the optimal + + align:start position:0% +so that would be sort of the the optimal + + + align:start position:0% +so that would be sort of the the optimal +level of capital to invest + + align:start position:0% +level of capital to invest + + + align:start position:0% +level of capital to invest +um + + align:start position:0% +um + + + align:start position:0% +um +but + + align:start position:0% +but + + + align:start position:0% +but +and we can see what's going to happen to + + align:start position:0% +and we can see what's going to happen to + + + align:start position:0% +and we can see what's going to happen to +the level of capital so in particular we + + align:start position:0% +the level of capital so in particular we + + + align:start position:0% +the level of capital so in particular we +can rewrite this equation as F Prime e + + align:start position:0% +can rewrite this equation as F Prime e + + + align:start position:0% +can rewrite this equation as F Prime e +of p is equal to rho minus this term + + align:start position:0% +of p is equal to rho minus this term + + + align:start position:0% +of p is equal to rho minus this term +over here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +F of K is positive e Prime is positive + + align:start position:0% +F of K is positive e Prime is positive + + + align:start position:0% +F of K is positive e Prime is positive +that we've had that from one of our + + align:start position:0% +that we've had that from one of our + + + align:start position:0% +that we've had that from one of our +assumptions before + + align:start position:0% +assumptions before + + + align:start position:0% +assumptions before +and uh we also just showed earlier that + + align:start position:0% +and uh we also just showed earlier that + + + align:start position:0% +and uh we also just showed earlier that +um that dpdk is less than zero + + align:start position:0% + + + + align:start position:0% + +okay you know for because of say for the + + align:start position:0% +okay you know for because of say for the + + + align:start position:0% +okay you know for because of say for the +for example the like the uh The Leverage + + align:start position:0% +for example the like the uh The Leverage + + + align:start position:0% +for example the like the uh The Leverage +channel for example + + align:start position:0% + + + + align:start position:0% + +okay so uh what this means is that uh if + + align:start position:0% +okay so uh what this means is that uh if + + + align:start position:0% +okay so uh what this means is that uh if +we have a concave function a concave + + align:start position:0% +we have a concave function a concave + + + align:start position:0% +we have a concave function a concave +production function then the level of + + align:start position:0% +production function then the level of + + + align:start position:0% +production function then the level of +investment we're going to have is less + + align:start position:0% +investment we're going to have is less + + + align:start position:0% +investment we're going to have is less +than sort of k-star + + align:start position:0% +than sort of k-star + + + align:start position:0% +than sort of k-star +the optimal level of investment + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +and sort of intuitively what's going on + + align:start position:0% +and sort of intuitively what's going on + + + align:start position:0% +and sort of intuitively what's going on +what's going on is sort of uh you know + + align:start position:0% +what's going on is sort of uh you know + + + align:start position:0% +what's going on is sort of uh you know +the interest rate is kind of high kind + + align:start position:0% +the interest rate is kind of high kind + + + align:start position:0% +the interest rate is kind of high kind +of given the moral hazard and you know + + align:start position:0% +of given the moral hazard and you know + + + align:start position:0% +of given the moral hazard and you know +there's going to be more of this with + + align:start position:0% +there's going to be more of this with + + + align:start position:0% +there's going to be more of this with +kind of more Capital + + align:start position:0% +kind of more Capital + + + align:start position:0% +kind of more Capital +um holding a trade fixed right so so the + + align:start position:0% +um holding a trade fixed right so so the + + + align:start position:0% +um holding a trade fixed right so so the +interest rate is already high that's + + align:start position:0% +interest rate is already high that's + + + align:start position:0% +interest rate is already high that's +going to drive down kind of the optimal + + align:start position:0% +going to drive down kind of the optimal + + + align:start position:0% +going to drive down kind of the optimal +level of K and then the sort of + + align:start position:0% +level of K and then the sort of + + + align:start position:0% +level of K and then the sort of +additional channel is kind of only going + + align:start position:0% +additional channel is kind of only going + + + align:start position:0% +additional channel is kind of only going +to reinforce that right so the interest + + align:start position:0% +to reinforce that right so the interest + + + align:start position:0% +to reinforce that right so the interest +rate is like high because we have a + + align:start position:0% +rate is like high because we have a + + + align:start position:0% +rate is like high because we have a +moral hazard problem + + align:start position:0% +moral hazard problem + + + align:start position:0% +moral hazard problem +and then + + align:start position:0% +and then + + + align:start position:0% +and then +if you hire interest rate I choose kind + + align:start position:0% +if you hire interest rate I choose kind + + + align:start position:0% +if you hire interest rate I choose kind +of a lower level of project that kind of + + align:start position:0% +of a lower level of project that kind of + + + align:start position:0% +of a lower level of project that kind of +makes the industry even higher and sort + + align:start position:0% +makes the industry even higher and sort + + + align:start position:0% +makes the industry even higher and sort +of we end up kind of in a in a the + + align:start position:0% +of we end up kind of in a in a the + + + align:start position:0% +of we end up kind of in a in a the +equilibrium of that has a kind of a you + + align:start position:0% +equilibrium of that has a kind of a you + + + align:start position:0% +equilibrium of that has a kind of a you +know drives Capital kind of even lower + + align:start position:0% + + + + align:start position:0% + +okay and so again that sort of says look + + align:start position:0% +okay and so again that sort of says look + + + align:start position:0% +okay and so again that sort of says look +we prefer to sort of be able to commit + + align:start position:0% +we prefer to sort of be able to commit + + + align:start position:0% +we prefer to sort of be able to commit +to this level of P that wouldn't have + + align:start position:0% +to this level of P that wouldn't have + + + align:start position:0% +to this level of P that wouldn't have +this problem would give us a lower level + + align:start position:0% +this problem would give us a lower level + + + align:start position:0% +this problem would give us a lower level +of interest rate and sort of a higher + + align:start position:0% +of interest rate and sort of a higher + + + align:start position:0% +of interest rate and sort of a higher +level of capital a higher level return + + align:start position:0% +level of capital a higher level return + + + align:start position:0% +level of capital a higher level return +we can't commit to that + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +we can also show sort of similarly that + + align:start position:0% +we can also show sort of similarly that + + + align:start position:0% +we can also show sort of similarly that +DK DW is greater than zero for through + + align:start position:0% +DK DW is greater than zero for through + + + align:start position:0% +DK DW is greater than zero for through +sort of a similar argument + + align:start position:0% +sort of a similar argument + + + align:start position:0% +sort of a similar argument +just stepping back what have we shown + + align:start position:0% +just stepping back what have we shown + + + align:start position:0% +just stepping back what have we shown +this is a moral hazard moral hazard + + align:start position:0% +this is a moral hazard moral hazard + + + align:start position:0% +this is a moral hazard moral hazard +model where sort of the choice of + + align:start position:0% +model where sort of the choice of + + + align:start position:0% +model where sort of the choice of +projects was uncertain or sorry what was + + align:start position:0% +projects was uncertain or sorry what was + + + align:start position:0% +projects was uncertain or sorry what was +uncontractable + + align:start position:0% +uncontractable + + + align:start position:0% +uncontractable +and kind of the that and that plus + + align:start position:0% +and kind of the that and that plus + + + align:start position:0% +and kind of the that and that plus +limited liability LED people to choose + + align:start position:0% +limited liability LED people to choose + + + align:start position:0% +limited liability LED people to choose +these risky projects the sort of choice + + align:start position:0% +these risky projects the sort of choice + + + align:start position:0% +these risky projects the sort of choice +of risky projects leads to kind of these + + align:start position:0% +of risky projects leads to kind of these + + + align:start position:0% +of risky projects leads to kind of these +higher interest rates which sort of + + align:start position:0% +higher interest rates which sort of + + + align:start position:0% +higher interest rates which sort of +leads to kind of lower levels of capital + + align:start position:0% +leads to kind of lower levels of capital + + + align:start position:0% +leads to kind of lower levels of capital +in equilibrium + + align:start position:0% +in equilibrium + + + align:start position:0% +in equilibrium +in the real world don't people often + + align:start position:0% +in the real world don't people often + + + align:start position:0% +in the real world don't people often +contract or repeat when they're like oh + + align:start position:0% +contract or repeat when they're like oh + + + align:start position:0% +contract or repeat when they're like oh +what do you want the money for for this + + align:start position:0% +what do you want the money for for this + + + align:start position:0% +what do you want the money for for this +business idea okay no I don't like your + + align:start position:0% +business idea okay no I don't like your + + + align:start position:0% +business idea okay no I don't like your +idea I won't if you don't yes so I think + + align:start position:0% +idea I won't if you don't yes so I think + + + align:start position:0% +idea I won't if you don't yes so I think +you're exactly right so I think there's + + align:start position:0% +you're exactly right so I think there's + + + align:start position:0% +you're exactly right so I think there's +a whole a whole lot of kind of like what + + align:start position:0% +a whole a whole lot of kind of like what + + + align:start position:0% +a whole a whole lot of kind of like what +banks are doing is trying to you can + + align:start position:0% +banks are doing is trying to you can + + + align:start position:0% +banks are doing is trying to you can +think of a lot of what banks are doing + + align:start position:0% +think of a lot of what banks are doing + + + align:start position:0% +think of a lot of what banks are doing +well let me also talk about the average + + align:start position:0% +well let me also talk about the average + + + align:start position:0% +well let me also talk about the average +selection uh model two + + align:start position:0% +selection uh model two + + + align:start position:0% +selection uh model two +um + + align:start position:0% +um + + + align:start position:0% +um +it's not obviously how much they're + + align:start position:0% +it's not obviously how much they're + + + align:start position:0% +it's not obviously how much they're +doing they're screening about the + + align:start position:0% +doing they're screening about the + + + align:start position:0% +doing they're screening about the +adverse lesson kind of they're + + align:start position:0% +adverse lesson kind of they're + + + align:start position:0% +adverse lesson kind of they're +definitely trying to figure out p and + + align:start position:0% +definitely trying to figure out p and + + + align:start position:0% +definitely trying to figure out p and +whether it's the X anti whether it's the + + align:start position:0% +whether it's the X anti whether it's the + + + align:start position:0% +whether it's the X anti whether it's the +more Hazard part or it's the + + align:start position:0% +more Hazard part or it's the + + + align:start position:0% +more Hazard part or it's the +um average selection part is less clear + + align:start position:0% +um average selection part is less clear + + + align:start position:0% +um average selection part is less clear +to me so we can we can come back to kind + + align:start position:0% +to me so we can we can come back to kind + + + align:start position:0% +to me so we can we can come back to kind +of what they're doing in the real world + + align:start position:0% +of what they're doing in the real world + + + align:start position:0% +of what they're doing in the real world +I think a lot of what they're doing + + align:start position:0% +I think a lot of what they're doing + + + align:start position:0% +I think a lot of what they're doing +looks more like the average selection + + align:start position:0% +looks more like the average selection + + + align:start position:0% +looks more like the average selection +part so the the selection part is the is + + align:start position:0% +part so the the selection part is the is + + + align:start position:0% +part so the the selection part is the is +kind of the X which we'll talk about in + + align:start position:0% +kind of the X which we'll talk about in + + + align:start position:0% +kind of the X which we'll talk about in +the next model is kind of accidentally + + align:start position:0% +the next model is kind of accidentally + + + align:start position:0% +the next model is kind of accidentally +saying like hey like ishana like what + + align:start position:0% +saying like hey like ishana like what + + + align:start position:0% +saying like hey like ishana like what +are you planning on doing with the money + + align:start position:0% +are you planning on doing with the money + + + align:start position:0% +are you planning on doing with the money +what's your P you could think of that as + + align:start position:0% +what's your P you could think of that as + + + align:start position:0% +what's your P you could think of that as +like like that's X and you're trying to + + align:start position:0% +like like that's X and you're trying to + + + align:start position:0% +like like that's X and you're trying to +figure out like we have different P's + + align:start position:0% +figure out like we have different P's + + + align:start position:0% +figure out like we have different P's +like your p is this you know Aaron's p + + align:start position:0% +like your p is this you know Aaron's p + + + align:start position:0% +like your p is this you know Aaron's p +is this and so on and so forth like + + align:start position:0% +is this and so on and so forth like + + + align:start position:0% +is this and so on and so forth like +we're trying to figure out who's got the + + align:start position:0% +we're trying to figure out who's got the + + + align:start position:0% +we're trying to figure out who's got the +good P's and lend to them that's ever + + align:start position:0% +good P's and lend to them that's ever + + + align:start position:0% +good P's and lend to them that's ever +selection this model would basically say + + align:start position:0% +selection this model would basically say + + + align:start position:0% +selection this model would basically say +like I want you to come in here every + + align:start position:0% +like I want you to come in here every + + + align:start position:0% +like I want you to come in here every +month and I want you to tell me what + + align:start position:0% +month and I want you to tell me what + + + align:start position:0% +month and I want you to tell me what +you're doing and like you know kind of + + align:start position:0% +you're doing and like you know kind of + + + align:start position:0% +you're doing and like you know kind of +that very very regular monitoring you + + align:start position:0% +that very very regular monitoring you + + + align:start position:0% +that very very regular monitoring you +guys also do that but that's kind of the + + align:start position:0% +guys also do that but that's kind of the + + + align:start position:0% +guys also do that but that's kind of the +closer to this one so I think you're + + align:start position:0% +closer to this one so I think you're + + + align:start position:0% +closer to this one so I think you're +right I think that you can think about + + align:start position:0% +right I think that you can think about + + + align:start position:0% +right I think that you can think about +kind of the whole you know a lot of the + + align:start position:0% +kind of the whole you know a lot of the + + + align:start position:0% +kind of the whole you know a lot of the +relationship between Banks and their + + align:start position:0% +relationship between Banks and their + + + align:start position:0% +relationship between Banks and their +clients as being about trying to sort of + + align:start position:0% +clients as being about trying to sort of + + + align:start position:0% +clients as being about trying to sort of +combat these two basic issues + + align:start position:0% +combat these two basic issues + + + align:start position:0% +combat these two basic issues +and if they're perfect at combating then + + align:start position:0% +and if they're perfect at combating then + + + align:start position:0% +and if they're perfect at combating then +this kind of goes away in reality I + + align:start position:0% +this kind of goes away in reality I + + + align:start position:0% +this kind of goes away in reality I +think we probably think they can combat + + align:start position:0% +think we probably think they can combat + + + align:start position:0% +think we probably think they can combat +them to some extent and this is kind of + + align:start position:0% +them to some extent and this is kind of + + + align:start position:0% +them to some extent and this is kind of +capturing a residual + + align:start position:0% + + + + align:start position:0% + +other questions or comments + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so question + + align:start position:0% +so question + + + align:start position:0% +so question +like would you say there are credit + + align:start position:0% +like would you say there are credit + + + align:start position:0% +like would you say there are credit +constraints in this model + + align:start position:0% +constraints in this model + + + align:start position:0% +constraints in this model +what do we mean by credit we're going to + + align:start position:0% +what do we mean by credit we're going to + + + align:start position:0% +what do we mean by credit we're going to +talk a lot about credit constraints do + + align:start position:0% +talk a lot about credit constraints do + + + align:start position:0% +talk a lot about credit constraints do +we think people are credit constrained + + align:start position:0% +we think people are credit constrained + + + align:start position:0% +we think people are credit constrained +in this model + + align:start position:0% + + + + align:start position:0% + +it's kind of a little definitional but + + align:start position:0% +it's kind of a little definitional but + + + align:start position:0% +it's kind of a little definitional but +I'm curious like what do you what do you + + align:start position:0% + + + + align:start position:0% + +yes no + + align:start position:0% +yes no + + + align:start position:0% +yes no +I think + + align:start position:0% +I think + + + align:start position:0% +I think +okay so no because they can borrow as + + align:start position:0% +okay so no because they can borrow as + + + align:start position:0% +okay so no because they can borrow as +much around right there's choosing K + + align:start position:0% +much around right there's choosing K + + + align:start position:0% +much around right there's choosing K +kind of as much as they want right what + + align:start position:0% +kind of as much as they want right what + + + align:start position:0% +kind of as much as they want right what +would be the argument to say that they + + align:start position:0% +would be the argument to say that they + + + align:start position:0% +would be the argument to say that they +are credit constrained + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +exactly so that's exactly right so I + + align:start position:0% +exactly so that's exactly right so I + + + align:start position:0% +exactly so that's exactly right so I +just want to be clear on this this is a + + align:start position:0% +just want to be clear on this this is a + + + align:start position:0% +just want to be clear on this this is a +model where I think you're exactly right + + align:start position:0% +model where I think you're exactly right + + + align:start position:0% +model where I think you're exactly right +uh Kash that basically like this is a + + align:start position:0% +uh Kash that basically like this is a + + + align:start position:0% +uh Kash that basically like this is a +model where they're not constrained in + + align:start position:0% +model where they're not constrained in + + + align:start position:0% +model where they're not constrained in +the sense that like they could get more + + align:start position:0% +the sense that like they could get more + + + align:start position:0% +the sense that like they could get more +K if they wanted to but they just shoot + + align:start position:0% +K if they wanted to but they just shoot + + + align:start position:0% +K if they wanted to but they just shoot +the optimal level of K for them to + + align:start position:0% +the optimal level of K for them to + + + align:start position:0% +the optimal level of K for them to +borrow is kind of but whether it's gonna + + align:start position:0% +borrow is kind of but whether it's gonna + + + align:start position:0% +borrow is kind of but whether it's gonna +the industry will adjust is because they + + align:start position:0% +the industry will adjust is because they + + + align:start position:0% +the industry will adjust is because they +kind of like borrow more k + + align:start position:0% +kind of like borrow more k + + + align:start position:0% +kind of like borrow more k +right + + align:start position:0% +right + + + align:start position:0% +right +um and uh and that's gonna that's gonna + + align:start position:0% +um and uh and that's gonna that's gonna + + + align:start position:0% +um and uh and that's gonna that's gonna +um lead there to be + + align:start position:0% +um lead there to be + + + align:start position:0% +um lead there to be +um uh it look like kind of they're + + align:start position:0% +um uh it look like kind of they're + + + align:start position:0% +um uh it look like kind of they're +they're they're not borrowing as much K + + align:start position:0% +they're they're not borrowing as much K + + + align:start position:0% +they're they're not borrowing as much K +as they might have wanted to if these + + align:start position:0% +as they might have wanted to if these + + + align:start position:0% +as they might have wanted to if these +information uh asymmetries hadn't hadn't + + align:start position:0% +information uh asymmetries hadn't hadn't + + + align:start position:0% +information uh asymmetries hadn't hadn't +been there + + align:start position:0% + + + + align:start position:0% + +okay so that's model one that's the the + + align:start position:0% +okay so that's model one that's the the + + + align:start position:0% +okay so that's model one that's the the +moral hazard model + + align:start position:0% +moral hazard model + + + align:start position:0% +moral hazard model +here's another model + + align:start position:0% +here's another model + + + align:start position:0% +here's another model +which is the an adverse election model + + align:start position:0% +which is the an adverse election model + + + align:start position:0% +which is the an adverse election model +there's an alternative story and sort of + + align:start position:0% +there's an alternative story and sort of + + + align:start position:0% +there's an alternative story and sort of +going back to what I was talking about + + align:start position:0% +going back to what I was talking about + + + align:start position:0% +going back to what I was talking about +with Shauna this is kind of like + + align:start position:0% +with Shauna this is kind of like + + + align:start position:0% +with Shauna this is kind of like +screaming like heterogeneity among + + align:start position:0% +screaming like heterogeneity among + + + align:start position:0% +screaming like heterogeneity among +projects + + align:start position:0% +projects + + + align:start position:0% +projects +so now in this model we're going to + + align:start position:0% +so now in this model we're going to + + + align:start position:0% +so now in this model we're going to +suppose that P is a fixed characteristic + + align:start position:0% +suppose that P is a fixed characteristic + + + align:start position:0% +suppose that P is a fixed characteristic +of an individual + + align:start position:0% +of an individual + + + align:start position:0% +of an individual +some people have high P some people have + + align:start position:0% +some people have high P some people have + + + align:start position:0% +some people have high P some people have +low p + + align:start position:0% +low p + + + align:start position:0% +low p +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so in this model we say look suppose the + + align:start position:0% +so in this model we say look suppose the + + + align:start position:0% +so in this model we say look suppose the +bank offers an interest rate r + + align:start position:0% +bank offers an interest rate r + + + align:start position:0% +bank offers an interest rate r +who's going to take that loan who wants + + align:start position:0% +who's going to take that loan who wants + + + align:start position:0% +who's going to take that loan who wants +that loan + + align:start position:0% +that loan + + + align:start position:0% +that loan +well I'm gonna take that loan + + align:start position:0% +well I'm gonna take that loan + + + align:start position:0% +well I'm gonna take that loan +if with again same little liability prob + + align:start position:0% +if with again same little liability prob + + + align:start position:0% +if with again same little liability prob +the project fails probably one minus P I + + align:start position:0% +the project fails probably one minus P I + + + align:start position:0% +the project fails probably one minus P I +pay nothing + + align:start position:0% +pay nothing + + + align:start position:0% +pay nothing +probability p i get F of k r of P that's + + align:start position:0% +probability p i get F of k r of P that's + + + align:start position:0% +probability p i get F of k r of P that's +my return and I have to pay this gross + + align:start position:0% +my return and I have to pay this gross + + + align:start position:0% +my return and I have to pay this gross +interest rate R of the value bar which + + align:start position:0% +interest rate R of the value bar which + + + align:start position:0% +interest rate R of the value bar which +is K minus w + + align:start position:0% +is K minus w + + + align:start position:0% +is K minus w +so if R is greater than + + align:start position:0% +so if R is greater than + + + align:start position:0% +so if R is greater than +um + + align:start position:0% +um + + + align:start position:0% +um +so so p is going to drop out if R but if + + align:start position:0% +so so p is going to drop out if R but if + + + align:start position:0% +so so p is going to drop out if R but if +R is greater than uh so Big R the return + + align:start position:0% +R is greater than uh so Big R the return + + + align:start position:0% +R is greater than uh so Big R the return +is greater than R the the sort of amount + + align:start position:0% +is greater than R the the sort of amount + + + align:start position:0% +is greater than R the the sort of amount +I have to pay back + + align:start position:0% +I have to pay back + + + align:start position:0% +I have to pay back +R times the amount I borrow divided by F + + align:start position:0% +R times the amount I borrow divided by F + + + align:start position:0% +R times the amount I borrow divided by F +of K then I'm gonna I'm gonna want that + + align:start position:0% +of K then I'm gonna I'm gonna want that + + + align:start position:0% +of K then I'm gonna I'm gonna want that +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so um + + align:start position:0% +so um + + + align:start position:0% +so um +if you recall from the beginning we had + + align:start position:0% +if you recall from the beginning we had + + + align:start position:0% +if you recall from the beginning we had +that sort of the + + align:start position:0% +that sort of the + + + align:start position:0% +that sort of the +um that R Prime was + + align:start position:0% +um that R Prime was + + + align:start position:0% +um that R Prime was +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +less than zero that we had sort of the + + align:start position:0% +less than zero that we had sort of the + + + align:start position:0% +less than zero that we had sort of the +the the lower the riskier projects were + + align:start position:0% +the the lower the riskier projects were + + + align:start position:0% +the the lower the riskier projects were +the ones that paying the most the the + + align:start position:0% +the ones that paying the most the the + + + align:start position:0% +the ones that paying the most the the +higher return projects were paying less + + align:start position:0% +higher return projects were paying less + + + align:start position:0% +higher return projects were paying less +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +what that means is there's going to be a + + align:start position:0% +what that means is there's going to be a + + + align:start position:0% +what that means is there's going to be a +a a cutoff value + + align:start position:0% +a a cutoff value + + + align:start position:0% +a a cutoff value +okay where people with p with with P + + align:start position:0% +okay where people with p with with P + + + align:start position:0% +okay where people with p with with P +less than some cutoff value are going to + + align:start position:0% +less than some cutoff value are going to + + + align:start position:0% +less than some cutoff value are going to +be the ones who are going to sort of + + align:start position:0% +be the ones who are going to sort of + + + align:start position:0% +be the ones who are going to sort of +pick are going to take up the the loan + + align:start position:0% + + + + align:start position:0% + +right R of P less than some cutoff is uh + + align:start position:0% +right R of P less than some cutoff is uh + + + align:start position:0% +right R of P less than some cutoff is uh +the same as saying you know that P is + + align:start position:0% +the same as saying you know that P is + + + align:start position:0% +the same as saying you know that P is +going to be uh less than some cutoff + + align:start position:0% +going to be uh less than some cutoff + + + align:start position:0% +going to be uh less than some cutoff +right so only so the super Ricky project + + align:start position:0% +right so only so the super Ricky project + + + align:start position:0% +right so only so the super Ricky project +up to some cutoff for the ones are going + + align:start position:0% +up to some cutoff for the ones are going + + + align:start position:0% +up to some cutoff for the ones are going +to take the loan + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we can Define p tilde of of r as + + align:start position:0% +so we can Define p tilde of of r as + + + align:start position:0% +so we can Define p tilde of of r as +exactly that cut off so we can just + + align:start position:0% +exactly that cut off so we can just + + + align:start position:0% +exactly that cut off so we can just +Define p tilde such that R of P tilde is + + align:start position:0% +Define p tilde such that R of P tilde is + + + align:start position:0% +Define p tilde such that R of P tilde is +exactly equal to this and everybody with + + align:start position:0% +exactly equal to this and everybody with + + + align:start position:0% +exactly equal to this and everybody with +a p less than P tilde will borrow + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +um and so what happens well as I + + align:start position:0% +um and so what happens well as I + + + align:start position:0% +um and so what happens well as I +increase + + align:start position:0% +increase + + + align:start position:0% +increase +r + + align:start position:0% +r + + + align:start position:0% +r +so increase the interest rate + + align:start position:0% +so increase the interest rate + + + align:start position:0% +so increase the interest rate +right the P tilde is going to shift to + + align:start position:0% +right the P tilde is going to shift to + + + align:start position:0% +right the P tilde is going to shift to +the left + + align:start position:0% +the left + + + align:start position:0% +the left +right because if I increase the interest + + align:start position:0% +right because if I increase the interest + + + align:start position:0% +right because if I increase the interest +rate the returns got to be higher higher + + align:start position:0% +rate the returns got to be higher higher + + + align:start position:0% +rate the returns got to be higher higher +return projects were the ones with the + + align:start position:0% +return projects were the ones with the + + + align:start position:0% +return projects were the ones with the +lower P so again higher interest rates + + align:start position:0% +lower P so again higher interest rates + + + align:start position:0% +lower P so again higher interest rates +are going to shift that kind of + + align:start position:0% +are going to shift that kind of + + + align:start position:0% +are going to shift that kind of +threshold to the left and we're going to + + align:start position:0% +threshold to the left and we're going to + + + align:start position:0% +threshold to the left and we're going to +get riskier projects + + align:start position:0% +get riskier projects + + + align:start position:0% +get riskier projects +so we're also going to get that same + + align:start position:0% +so we're also going to get that same + + + align:start position:0% +so we're also going to get that same +correlation that we had from the moral + + align:start position:0% +correlation that we had from the moral + + + align:start position:0% +correlation that we had from the moral +hazard model which is a correlation + + align:start position:0% +hazard model which is a correlation + + + align:start position:0% +hazard model which is a correlation +between the interest rate and the + + align:start position:0% +between the interest rate and the + + + align:start position:0% +between the interest rate and the +riskiness of the projects although it's + + align:start position:0% +riskiness of the projects although it's + + + align:start position:0% +riskiness of the projects although it's +happening through this different Channel + + align:start position:0% +happening through this different Channel + + + align:start position:0% +happening through this different Channel +right one was this xnd who wants the + + align:start position:0% +right one was this xnd who wants the + + + align:start position:0% +right one was this xnd who wants the +projects the other is sort of the + + align:start position:0% +projects the other is sort of the + + + align:start position:0% +projects the other is sort of the +um uh X post + + align:start position:0% +um uh X post + + + align:start position:0% +um uh X post +um + + align:start position:0% + + + + align:start position:0% + +uh who's um + + align:start position:0% +uh who's um + + + align:start position:0% +uh who's um +the interest rates and kind of + + align:start position:0% +the interest rates and kind of + + + align:start position:0% +the interest rates and kind of +intuitively what's going on in this + + align:start position:0% +intuitively what's going on in this + + + align:start position:0% +intuitively what's going on in this +model what's going on here is like look + + align:start position:0% +model what's going on here is like look + + + align:start position:0% +model what's going on here is like look +you know imagine the return is is is re + + align:start position:0% +you know imagine the return is is is re + + + align:start position:0% +you know imagine the return is is is re +the the the value of the in the good + + align:start position:0% +the the the value of the in the good + + + align:start position:0% +the the the value of the in the good +State I have to pay back a lot right + + align:start position:0% +State I have to pay back a lot right + + + align:start position:0% +State I have to pay back a lot right +who's gonna want that only people who + + align:start position:0% +who's gonna want that only people who + + + align:start position:0% +who's gonna want that only people who +were whom the good state is like really + + align:start position:0% +were whom the good state is like really + + + align:start position:0% +were whom the good state is like really +really good and those are the people who + + align:start position:0% +really good and those are the people who + + + align:start position:0% +really good and those are the people who +were risky + + align:start position:0% +were risky + + + align:start position:0% +were risky +right + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so we also so again we have this + + align:start position:0% +so we also so again we have this + + + align:start position:0% +so we also so again we have this +negative correlation here + + align:start position:0% +negative correlation here + + + align:start position:0% +negative correlation here +now what's the market equilibrium here + + align:start position:0% +now what's the market equilibrium here + + + align:start position:0% +now what's the market equilibrium here +well again we have that row that R times + + align:start position:0% +well again we have that row that R times + + + align:start position:0% +well again we have that row that R times +the amount you get so so here we have a + + align:start position:0% +the amount you get so so here we have a + + + align:start position:0% +the amount you get so so here we have a +slightly different condition we have the + + align:start position:0% +slightly different condition we have the + + + align:start position:0% +slightly different condition we have the +expect what is the the the P for a given + + align:start position:0% +expect what is the the the P for a given + + + align:start position:0% +expect what is the the the P for a given +R Who borrows well it's everybody with + + align:start position:0% +R Who borrows well it's everybody with + + + align:start position:0% +R Who borrows well it's everybody with +um interest rate with P less than that + + align:start position:0% +um interest rate with P less than that + + + align:start position:0% +um interest rate with P less than that +cutoff value + + align:start position:0% +cutoff value + + + align:start position:0% +cutoff value +so what's the kind of average + + align:start position:0% +so what's the kind of average + + + align:start position:0% +so what's the kind of average +probability of success + + align:start position:0% +probability of success + + + align:start position:0% +probability of success +right + + align:start position:0% +right + + + align:start position:0% +right +um it is the uh + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +it's just the expectation this is this + + align:start position:0% +it's just the expectation this is this + + + align:start position:0% +it's just the expectation this is this +is a + + align:start position:0% +is a + + + align:start position:0% +is a +e meaning expectation not e meaning like + + align:start position:0% +e meaning expectation not e meaning like + + + align:start position:0% +e meaning expectation not e meaning like +the expected return + + align:start position:0% +the expected return + + + align:start position:0% +the expected return +um it's just the expectation uh so sorry + + align:start position:0% +um it's just the expectation uh so sorry + + + align:start position:0% +um it's just the expectation uh so sorry +for limitation is the expectation of P + + align:start position:0% +for limitation is the expectation of P + + + align:start position:0% +for limitation is the expectation of P +conditional on P less than than P tilde + + align:start position:0% +conditional on P less than than P tilde + + + align:start position:0% +conditional on P less than than P tilde +and that's also kind of like + + align:start position:0% +and that's also kind of like + + + align:start position:0% +and that's also kind of like +um + + align:start position:0% +um + + + align:start position:0% +um +we know that sort of as P tilde goes + + align:start position:0% +we know that sort of as P tilde goes + + + align:start position:0% +we know that sort of as P tilde goes +down uh the expectation of P tilde goes + + align:start position:0% +down uh the expectation of P tilde goes + + + align:start position:0% +down uh the expectation of P tilde goes +down but kind of beyond that it's kind + + align:start position:0% +down but kind of beyond that it's kind + + + align:start position:0% +down but kind of beyond that it's kind +of the shape of that thing kind of + + align:start position:0% +of the shape of that thing kind of + + + align:start position:0% +of the shape of that thing kind of +depends on just what the distribution of + + align:start position:0% +depends on just what the distribution of + + + align:start position:0% +depends on just what the distribution of +peas is in the population + + align:start position:0% + + + + align:start position:0% + +okay that also is going to mean that r + + align:start position:0% +okay that also is going to mean that r + + + align:start position:0% +okay that also is going to mean that r +right R the interest rate charge is + + align:start position:0% +right R the interest rate charge is + + + align:start position:0% +right R the interest rate charge is +going to be equal to rho divided by the + + align:start position:0% +going to be equal to rho divided by the + + + align:start position:0% +going to be equal to rho divided by the +deputation things this thing is less + + align:start position:0% +deputation things this thing is less + + + align:start position:0% +deputation things this thing is less +than one that means the the r's are + + align:start position:0% +than one that means the the r's are + + + align:start position:0% +than one that means the the r's are +going to be that are recharged to people + + align:start position:0% +going to be that are recharged to people + + + align:start position:0% +going to be that are recharged to people +are going to be higher than rho so we're + + align:start position:0% +are going to be higher than rho so we're + + + align:start position:0% +are going to be higher than rho so we're +also going to have kind of higher + + align:start position:0% +also going to have kind of higher + + + align:start position:0% +also going to have kind of higher +interest rates than it's not equilibrium + + align:start position:0% +interest rates than it's not equilibrium + + + align:start position:0% +interest rates than it's not equilibrium +and kind of in the the sorry the then + + align:start position:0% +and kind of in the the sorry the then + + + align:start position:0% +and kind of in the the sorry the then +then the first best or whatever then + + align:start position:0% +then the first best or whatever then + + + align:start position:0% +then the first best or whatever then +that row thing but sort of the reasoning + + align:start position:0% +that row thing but sort of the reasoning + + + align:start position:0% +that row thing but sort of the reasoning +is a bit different + + align:start position:0% +is a bit different + + + align:start position:0% +is a bit different +okay it's all about this xng screening + + align:start position:0% +okay it's all about this xng screening + + + align:start position:0% +okay it's all about this xng screening +and this going back to your point this + + align:start position:0% +and this going back to your point this + + + align:start position:0% +and this going back to your point this +is yes the banks are going to want to + + align:start position:0% +is yes the banks are going to want to + + + align:start position:0% +is yes the banks are going to want to +invest in doing everything that we can + + align:start position:0% +invest in doing everything that we can + + + align:start position:0% +invest in doing everything that we can +sort of say to like to screen people + + align:start position:0% +sort of say to like to screen people + + + align:start position:0% +sort of say to like to screen people +kind of exante and and get rid of the + + align:start position:0% +kind of exante and and get rid of the + + + align:start position:0% +kind of exante and and get rid of the +people who are going to be kind of lower + + align:start position:0% +people who are going to be kind of lower + + + align:start position:0% +people who are going to be kind of lower +row because for a given interest rate + + align:start position:0% +row because for a given interest rate + + + align:start position:0% +row because for a given interest rate +that the bank's charging + + align:start position:0% +that the bank's charging + + + align:start position:0% +that the bank's charging +conditional on charging are if it can + + align:start position:0% +conditional on charging are if it can + + + align:start position:0% +conditional on charging are if it can +like weed out some people who are kind + + align:start position:0% +like weed out some people who are kind + + + align:start position:0% +like weed out some people who are kind +of the worst it's going to do better + + align:start position:0% +of the worst it's going to do better + + + align:start position:0% +of the worst it's going to do better +that's not necessarily an equilibrium + + align:start position:0% +that's not necessarily an equilibrium + + + align:start position:0% +that's not necessarily an equilibrium +but sort of that's going to be the + + align:start position:0% +but sort of that's going to be the + + + align:start position:0% +but sort of that's going to be the +bank's incentive function right so I + + align:start position:0% +bank's incentive function right so I + + + align:start position:0% +bank's incentive function right so I +announce R I know that everyone with P + + align:start position:0% +announce R I know that everyone with P + + + align:start position:0% +announce R I know that everyone with P +less and P Kilda would like it what how + + align:start position:0% +less and P Kilda would like it what how + + + align:start position:0% +less and P Kilda would like it what how +can I make more even more money so I'm + + align:start position:0% +can I make more even more money so I'm + + + align:start position:0% +can I make more even more money so I'm +going to be I'll break even but I can + + align:start position:0% +going to be I'll break even but I can + + + align:start position:0% +going to be I'll break even but I can +make even more money if I can find the + + align:start position:0% +make even more money if I can find the + + + align:start position:0% +make even more money if I can find the +really low people and sort of knock them + + align:start position:0% +really low people and sort of knock them + + + align:start position:0% +really low people and sort of knock them +out + + align:start position:0% +out + + + align:start position:0% +out +right I want to get people who are just + + align:start position:0% +right I want to get people who are just + + + align:start position:0% +right I want to get people who are just +kind of as close as possible + + align:start position:0% +kind of as close as possible + + + align:start position:0% +kind of as close as possible +and you can think of a lot of kind of + + align:start position:0% +and you can think of a lot of kind of + + + align:start position:0% +and you can think of a lot of kind of +what banks are doing in sort of that + + align:start position:0% +what banks are doing in sort of that + + + align:start position:0% +what banks are doing in sort of that +screening process is trying to figure + + align:start position:0% +screening process is trying to figure + + + align:start position:0% +screening process is trying to figure +out like who are the good borrowers who + + align:start position:0% +out like who are the good borrowers who + + + align:start position:0% +out like who are the good borrowers who +are the bad borrowers can I remove kind + + align:start position:0% +are the bad borrowers can I remove kind + + + align:start position:0% +are the bad borrowers can I remove kind +of really bad ones + + align:start position:0% + + + + align:start position:0% + +um so this is what the so again we can + + align:start position:0% +um so this is what the so again we can + + + align:start position:0% +um so this is what the so again we can +draw that same kind of equilibrium here + + align:start position:0% +draw that same kind of equilibrium here + + + align:start position:0% +draw that same kind of equilibrium here +it's you know this thing is sort of the + + align:start position:0% +it's you know this thing is sort of the + + + align:start position:0% +it's you know this thing is sort of the +same market clearing condition but now + + align:start position:0% +same market clearing condition but now + + + align:start position:0% +same market clearing condition but now +we have kind of a different + + align:start position:0% +we have kind of a different + + + align:start position:0% +we have kind of a different +um instead of a moral hazard condition + + align:start position:0% +um instead of a moral hazard condition + + + align:start position:0% +um instead of a moral hazard condition +we have an X an average sorry an average + + align:start position:0% +we have an X an average sorry an average + + + align:start position:0% +we have an X an average sorry an average +selection condition which says that you + + align:start position:0% +selection condition which says that you + + + align:start position:0% +selection condition which says that you +know here is the expectation of of P + + align:start position:0% +know here is the expectation of of P + + + align:start position:0% +know here is the expectation of of P +given that p is less than P tilde where + + align:start position:0% +given that p is less than P tilde where + + + align:start position:0% +given that p is less than P tilde where +P tilde is a function of r + + align:start position:0% +P tilde is a function of r + + + align:start position:0% +P tilde is a function of r +okay and that's so this + + align:start position:0% +okay and that's so this + + + align:start position:0% +okay and that's so this +curve here + + align:start position:0% +curve here + + + align:start position:0% +curve here +doesn't come from Project choice this is + + align:start position:0% +doesn't come from Project choice this is + + + align:start position:0% +doesn't come from Project choice this is +just a question of kind of what is the + + align:start position:0% +just a question of kind of what is the + + + align:start position:0% +just a question of kind of what is the +distribution of P's in the population + + align:start position:0% +distribution of P's in the population + + + align:start position:0% +distribution of P's in the population +this is just like a property of like the + + align:start position:0% +this is just like a property of like the + + + align:start position:0% +this is just like a property of like the +um the the the P function of the + + align:start position:0% +um the the the P function of the + + + align:start position:0% +um the the the P function of the +population + + align:start position:0% +population + + + align:start position:0% +population +the the like the what is the + + align:start position:0% +the the like the what is the + + + align:start position:0% +the the like the what is the +distribution of peace + + align:start position:0% +distribution of peace + + + align:start position:0% +distribution of peace +okay and again you can draw that in + + align:start position:0% +okay and again you can draw that in + + + align:start position:0% +okay and again you can draw that in +funky different ways it can like this it + + align:start position:0% +funky different ways it can like this it + + + align:start position:0% +funky different ways it can like this it +can intersect it can almost Liberia and + + align:start position:0% +can intersect it can almost Liberia and + + + align:start position:0% +can intersect it can almost Liberia and +so on and so forth + + align:start position:0% + + + + align:start position:0% + +it's got to be downward sloping beyond + + align:start position:0% +it's got to be downward sloping beyond + + + align:start position:0% +it's got to be downward sloping beyond +that like unclear + + align:start position:0% +that like unclear + + + align:start position:0% +that like unclear +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh clear so far + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +both of those models the moral hazard + + align:start position:0% +both of those models the moral hazard + + + align:start position:0% +both of those models the moral hazard +model and the average selection model + + align:start position:0% +model and the average selection model + + + align:start position:0% +model and the average selection model +um are going to feature kind of high + + align:start position:0% +um are going to feature kind of high + + + align:start position:0% +um are going to feature kind of high +interest rates + + align:start position:0% +interest rates + + + align:start position:0% +interest rates +right or at least like they're gonna + + align:start position:0% +right or at least like they're gonna + + + align:start position:0% +right or at least like they're gonna +both of those are reasons why the + + align:start position:0% +both of those are reasons why the + + + align:start position:0% +both of those are reasons why the +industry will be higher than kind of the + + align:start position:0% +industry will be higher than kind of the + + + align:start position:0% +industry will be higher than kind of the +Market clearance this is like why the + + align:start position:0% +Market clearance this is like why the + + + align:start position:0% +Market clearance this is like why the +market for say microfinance you know the + + align:start position:0% +market for say microfinance you know the + + + align:start position:0% +market for say microfinance you know the +interest rate would be higher than say + + align:start position:0% +interest rate would be higher than say + + + align:start position:0% +interest rate would be higher than say +the you know what you know you have a + + align:start position:0% +the you know what you know you have a + + + align:start position:0% +the you know what you know you have a +model where sort of micro imagine you + + align:start position:0% +model where sort of micro imagine you + + + align:start position:0% +model where sort of micro imagine you +have a simple model where like microfi + + align:start position:0% +have a simple model where like microfi + + + align:start position:0% +have a simple model where like microfi +institutions are you know raising + + align:start position:0% +institutions are you know raising + + + align:start position:0% +institutions are you know raising +capital on Wall Street and lending it to + + align:start position:0% +capital on Wall Street and lending it to + + + align:start position:0% +capital on Wall Street and lending it to +you know small lenders this already + + align:start position:0% +you know small lenders this already + + + align:start position:0% +you know small lenders this already +tells you there should be reasons why + + align:start position:0% +tells you there should be reasons why + + + align:start position:0% +tells you there should be reasons why +the interest rate paid somehow borrowers + + align:start position:0% +the interest rate paid somehow borrowers + + + align:start position:0% +the interest rate paid somehow borrowers +it already tells you why the interest + + align:start position:0% +it already tells you why the interest + + + align:start position:0% +it already tells you why the interest +rate paid by the borrower should be a + + align:start position:0% +rate paid by the borrower should be a + + + align:start position:0% +rate paid by the borrower should be a +lot higher than the level that that the + + align:start position:0% +lot higher than the level that that the + + + align:start position:0% +lot higher than the level that that the +bank is charging on interest rates but + + align:start position:0% +bank is charging on interest rates but + + + align:start position:0% +bank is charging on interest rates but +it comes from the default Channel + + align:start position:0% +it comes from the default Channel + + + align:start position:0% +it comes from the default Channel +right + + align:start position:0% +right + + + align:start position:0% +right +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +so those models predict High interest + + align:start position:0% +so those models predict High interest + + + align:start position:0% +so those models predict High interest +rates and they do it and but the reason + + align:start position:0% +rates and they do it and but the reason + + + align:start position:0% +rates and they do it and but the reason +for the high interest rates is to cover + + align:start position:0% +for the high interest rates is to cover + + + align:start position:0% +for the high interest rates is to cover +the expected defaults + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so one + + align:start position:0% +so one + + + align:start position:0% +so one +unfortunate fact for this model + + align:start position:0% +unfortunate fact for this model + + + align:start position:0% +unfortunate fact for this model +is that at least in microfinance uh at + + align:start position:0% +is that at least in microfinance uh at + + + align:start position:0% +is that at least in microfinance uh at +least in some cases + + align:start position:0% +least in some cases + + + align:start position:0% +least in some cases +um interest rates are high + + align:start position:0% +um interest rates are high + + + align:start position:0% +um interest rates are high +but often repayment rates are actually + + align:start position:0% +but often repayment rates are actually + + + align:start position:0% +but often repayment rates are actually +kind of high too + + align:start position:0% +kind of high too + + + align:start position:0% +kind of high too +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so then + + align:start position:0% +so then + + + align:start position:0% +so then +that doesn't work in this model right + + align:start position:0% +that doesn't work in this model right + + + align:start position:0% +that doesn't work in this model right +because the only reason that in both + + align:start position:0% +because the only reason that in both + + + align:start position:0% +because the only reason that in both +those models the rates were high was to + + align:start position:0% +those models the rates were high was to + + + align:start position:0% +those models the rates were high was to +cover kind of the defaults + + align:start position:0% +cover kind of the defaults + + + align:start position:0% +cover kind of the defaults +so if you want to ex if you to the + + align:start position:0% +so if you want to ex if you to the + + + align:start position:0% +so if you want to ex if you to the +extent this is also kind of a force + + align:start position:0% +extent this is also kind of a force + + + align:start position:0% +extent this is also kind of a force +right if there are reasons for kind of + + align:start position:0% +right if there are reasons for kind of + + + align:start position:0% +right if there are reasons for kind of +that wedge beyond the default rates we + + align:start position:0% +that wedge beyond the default rates we + + + align:start position:0% +that wedge beyond the default rates we +need to add something else to the model + + align:start position:0% +need to add something else to the model + + + align:start position:0% +need to add something else to the model +one simple way to do it by the way is if + + align:start position:0% +one simple way to do it by the way is if + + + align:start position:0% +one simple way to do it by the way is if +you thought that the the lenders were + + align:start position:0% +you thought that the the lenders were + + + align:start position:0% +you thought that the the lenders were +not competitive + + align:start position:0% +not competitive + + + align:start position:0% +not competitive +right then they're discharging markups + + align:start position:0% +right then they're discharging markups + + + align:start position:0% +right then they're discharging markups +okay that then if the lenders are not + + align:start position:0% +okay that then if the lenders are not + + + align:start position:0% +okay that then if the lenders are not +it's not on the slide but the lenders + + align:start position:0% +it's not on the slide but the lenders + + + align:start position:0% +it's not on the slide but the lenders +are not competitive then of course they + + align:start position:0% +are not competitive then of course they + + + align:start position:0% +are not competitive then of course they +can they're gonna jack up the interest + + align:start position:0% +can they're gonna jack up the interest + + + align:start position:0% +can they're gonna jack up the interest +rate and and uh and uh and make more + + align:start position:0% +rate and and uh and uh and make more + + + align:start position:0% +rate and and uh and uh and make more +profits so fine that could be part of it + + align:start position:0% +profits so fine that could be part of it + + + align:start position:0% +profits so fine that could be part of it +um and then by the way and there are + + align:start position:0% +um and then by the way and there are + + + align:start position:0% +um and then by the way and there are +reasons to think that there may be + + align:start position:0% +reasons to think that there may be + + + align:start position:0% +reasons to think that there may be +non-competition in um in lending markets + + align:start position:0% +non-competition in um in lending markets + + + align:start position:0% +non-competition in um in lending markets +in particular this whole question that + + align:start position:0% +in particular this whole question that + + + align:start position:0% +in particular this whole question that +we're talking about about getting to + + align:start position:0% +we're talking about about getting to + + + align:start position:0% +we're talking about about getting to +know people's peas and sort of + + align:start position:0% +know people's peas and sort of + + + align:start position:0% +know people's peas and sort of +monitoring them there's an important + + align:start position:0% +monitoring them there's an important + + + align:start position:0% +monitoring them there's an important +rule for uh information right so in + + align:start position:0% +rule for uh information right so in + + + align:start position:0% +rule for uh information right so in +particular imagine that you know I'm a + + align:start position:0% +particular imagine that you know I'm a + + + align:start position:0% +particular imagine that you know I'm a +Shauna's lender and you know she and I + + align:start position:0% +Shauna's lender and you know she and I + + + align:start position:0% +Shauna's lender and you know she and I +have been working together for years I + + align:start position:0% +have been working together for years I + + + align:start position:0% +have been working together for years I +may have + + align:start position:0% +may have + + + align:start position:0% +may have +um information about her P from my sort + + align:start position:0% +um information about her P from my sort + + + align:start position:0% +um information about her P from my sort +of you know years of interaction with + + align:start position:0% +of you know years of interaction with + + + align:start position:0% +of you know years of interaction with +her that like you know if obviously it's + + align:start position:0% +her that like you know if obviously it's + + + align:start position:0% +her that like you know if obviously it's +another lender that opposite doesn't + + align:start position:0% +another lender that opposite doesn't + + + align:start position:0% +another lender that opposite doesn't +have right so that may mean I have some + + align:start position:0% +have right so that may mean I have some + + + align:start position:0% +have right so that may mean I have some +advantage of lending to Ashana or robish + + align:start position:0% +advantage of lending to Ashana or robish + + + align:start position:0% +advantage of lending to Ashana or robish +it and I'd be able to use that and + + align:start position:0% +it and I'd be able to use that and + + + align:start position:0% +it and I'd be able to use that and +extract some rents from that + + align:start position:0% +extract some rents from that + + + align:start position:0% +extract some rents from that +okay so in particular uh that may be a + + align:start position:0% +okay so in particular uh that may be a + + + align:start position:0% +okay so in particular uh that may be a +there may be good reasons to think that + + align:start position:0% +there may be good reasons to think that + + + align:start position:0% +there may be good reasons to think that +sort of the model of perfect competition + + align:start position:0% +sort of the model of perfect competition + + + align:start position:0% +sort of the model of perfect competition +is not necessarily the only model it's + + align:start position:0% +is not necessarily the only model it's + + + align:start position:0% +is not necessarily the only model it's +not necessarily a perfect model for this + + align:start position:0% +not necessarily a perfect model for this + + + align:start position:0% +not necessarily a perfect model for this +for this + + align:start position:0% +for this + + + align:start position:0% +for this +that's one but here's another here's + + align:start position:0% +that's one but here's another here's + + + align:start position:0% +that's one but here's another here's +another sort of model that also could be + + align:start position:0% +another sort of model that also could be + + + align:start position:0% +another sort of model that also could be +sort of relevant which is monitoring + + align:start position:0% +sort of relevant which is monitoring + + + align:start position:0% +sort of relevant which is monitoring +costs + + align:start position:0% +costs + + + align:start position:0% +costs +and in particular this monitoring cost + + align:start position:0% +and in particular this monitoring cost + + + align:start position:0% +and in particular this monitoring cost +idea captures + + align:start position:0% +idea captures + + + align:start position:0% +idea captures +um the uh + + align:start position:0% +um the uh + + + align:start position:0% +um the uh +uh + + align:start position:0% +uh + + + align:start position:0% +uh +uh this idea this is actually it's not + + align:start position:0% +uh this idea this is actually it's not + + + align:start position:0% +uh this idea this is actually it's not +going to quite capture it uh the way + + align:start position:0% +going to quite capture it uh the way + + + align:start position:0% +going to quite capture it uh the way +it's going to be written down here but + + align:start position:0% +it's going to be written down here but + + + align:start position:0% +it's going to be written down here but +it captures the idea that banks are sort + + align:start position:0% +it captures the idea that banks are sort + + + align:start position:0% +it captures the idea that banks are sort +of spending a lot of money doing stuff + + align:start position:0% +of spending a lot of money doing stuff + + + align:start position:0% +of spending a lot of money doing stuff +to kind of make sure people repay + + align:start position:0% +to kind of make sure people repay + + + align:start position:0% +to kind of make sure people repay +okay and um so it's actually it's not + + align:start position:0% +okay and um so it's actually it's not + + + align:start position:0% +okay and um so it's actually it's not +quite this model so one version of + + align:start position:0% +quite this model so one version of + + + align:start position:0% +quite this model so one version of +monitoring is we have to spend a lot of + + align:start position:0% +monitoring is we have to spend a lot of + + + align:start position:0% +monitoring is we have to spend a lot of +money up front figuring out who the good + + align:start position:0% +money up front figuring out who the good + + + align:start position:0% +money up front figuring out who the good +keys and who are the bad PS that's one + + align:start position:0% +keys and who are the bad PS that's one + + + align:start position:0% +keys and who are the bad PS that's one +version of it a second version is the is + + align:start position:0% +version of it a second version is the is + + + align:start position:0% +version of it a second version is the is +the the the moral hazard version I think + + align:start position:0% +the the the moral hazard version I think + + + align:start position:0% +the the the moral hazard version I think +that we were talking about earlier which + + align:start position:0% +that we were talking about earlier which + + + align:start position:0% +that we were talking about earlier which +is to say like look I'm going to meet + + align:start position:0% +is to say like look I'm going to meet + + + align:start position:0% +is to say like look I'm going to meet +with you every single month and make + + align:start position:0% +with you every single month and make + + + align:start position:0% +with you every single month and make +sure you're doing what you said you were + + align:start position:0% +sure you're doing what you said you were + + + align:start position:0% +sure you're doing what you said you were +going to do and and not kind of + + align:start position:0% +going to do and and not kind of + + + align:start position:0% +going to do and and not kind of +deviating and kind of like doing kind of + + align:start position:0% +deviating and kind of like doing kind of + + + align:start position:0% +deviating and kind of like doing kind of +a worse project + + align:start position:0% + + + + align:start position:0% + +um but a third one is maybe I can + + align:start position:0% +um but a third one is maybe I can + + + align:start position:0% +um but a third one is maybe I can +actually just sort of like uh + + align:start position:0% +actually just sort of like uh + + + align:start position:0% +actually just sort of like uh +um uh spend some effort to sort of um + + align:start position:0% +um uh spend some effort to sort of um + + + align:start position:0% +um uh spend some effort to sort of um +get you to repay okay so so here that's + + align:start position:0% +get you to repay okay so so here that's + + + align:start position:0% +get you to repay okay so so here that's +sort of what this model is about + + align:start position:0% +sort of what this model is about + + + align:start position:0% +sort of what this model is about +so so let's so let's let's uh let's + + align:start position:0% +so so let's so let's let's uh let's + + + align:start position:0% +so so let's so let's let's uh let's +think about about monitoring here so + + align:start position:0% +think about about monitoring here so + + + align:start position:0% +think about about monitoring here so +let's let's abstract from the project + + align:start position:0% +let's let's abstract from the project + + + align:start position:0% +let's let's abstract from the project +choices for the moment just to make like + + align:start position:0% +choices for the moment just to make like + + + align:start position:0% +choices for the moment just to make like +and the Project's failing + + align:start position:0% +and the Project's failing + + + align:start position:0% +and the Project's failing +um but instead we're going to think + + align:start position:0% +um but instead we're going to think + + + align:start position:0% +um but instead we're going to think +about repayment + + align:start position:0% + + + + align:start position:0% + +so as before in the previous model + + align:start position:0% +so as before in the previous model + + + align:start position:0% +so as before in the previous model +suppose that if I invest + + align:start position:0% +suppose that if I invest + + + align:start position:0% +suppose that if I invest +um K dollars + + align:start position:0% +um K dollars + + + align:start position:0% +um K dollars +I get a gross return F of K + + align:start position:0% +I get a gross return F of K + + + align:start position:0% +I get a gross return F of K +uh the gross interest rate are + + align:start position:0% +uh the gross interest rate are + + + align:start position:0% +uh the gross interest rate are +and so if I have wealth W and I want to + + align:start position:0% +and so if I have wealth W and I want to + + + align:start position:0% +and so if I have wealth W and I want to +invest K I need to borrow K minus W and + + align:start position:0% +invest K I need to borrow K minus W and + + + align:start position:0% +invest K I need to borrow K minus W and +the amount I'm supposed to pay is K + + align:start position:0% +the amount I'm supposed to pay is K + + + align:start position:0% +the amount I'm supposed to pay is K +minus W Times R that's saying this + + align:start position:0% +minus W Times R that's saying this + + + align:start position:0% +minus W Times R that's saying this +before + + align:start position:0% + + + + align:start position:0% + +but now + + align:start position:0% +but now + + + align:start position:0% +but now +um suppose that it's not sort of like + + align:start position:0% +um suppose that it's not sort of like + + + align:start position:0% +um suppose that it's not sort of like +the good State or the bad State anymore + + align:start position:0% +the good State or the bad State anymore + + + align:start position:0% +the good State or the bad State anymore +suppose that basically I can just choose + + align:start position:0% +suppose that basically I can just choose + + + align:start position:0% +suppose that basically I can just choose +to stiff you and uh and not repay + + align:start position:0% +to stiff you and uh and not repay + + + align:start position:0% +to stiff you and uh and not repay +um by paying a course a a cost + + align:start position:0% +um by paying a course a a cost + + + align:start position:0% +um by paying a course a a cost +Ada right Ada yes okay we don't have an + + align:start position:0% +Ada right Ada yes okay we don't have an + + + align:start position:0% +Ada right Ada yes okay we don't have an +eight of variant yet do we + + align:start position:0% + + + + align:start position:0% + +huh it's earlier + + align:start position:0% +huh it's earlier + + + align:start position:0% +huh it's earlier +it just wasn't it wasn't a big one + + align:start position:0% +it just wasn't it wasn't a big one + + + align:start position:0% +it just wasn't it wasn't a big one +yeah they skipped a couple recently they + + align:start position:0% +yeah they skipped a couple recently they + + + align:start position:0% +yeah they skipped a couple recently they +skipped the new very they skipped new + + align:start position:0% +skipped the new very they skipped new + + + align:start position:0% +skipped the new very they skipped new +apparently because everyone thought it + + align:start position:0% +apparently because everyone thought it + + + align:start position:0% +apparently because everyone thought it +was going to copy called the new variant + + align:start position:0% +was going to copy called the new variant + + + align:start position:0% +was going to copy called the new variant +and they thought that would be confusing + + align:start position:0% +and they thought that would be confusing + + + align:start position:0% +and they thought that would be confusing +so anyway Ada okay uh uh by cost Ada + + align:start position:0% +so anyway Ada okay uh uh by cost Ada + + + align:start position:0% +so anyway Ada okay uh uh by cost Ada +there's portional to the amount invested + + align:start position:0% +there's portional to the amount invested + + + align:start position:0% +there's portional to the amount invested +so um so what's gonna happen so lenders + + align:start position:0% +so um so what's gonna happen so lenders + + + align:start position:0% +so um so what's gonna happen so lenders +are going to provide uh financing + + align:start position:0% +are going to provide uh financing + + + align:start position:0% +are going to provide uh financing +up to the point where the borrower is + + align:start position:0% +up to the point where the borrower is + + + align:start position:0% +up to the point where the borrower is +going to repay okay so it's a solution + + align:start position:0% +going to repay okay so it's a solution + + + align:start position:0% +going to repay okay so it's a solution +model but but in this case in particular + + align:start position:0% +model but but in this case in particular + + + align:start position:0% +model but but in this case in particular +they'd like to get paid back + + align:start position:0% +they'd like to get paid back + + + align:start position:0% +they'd like to get paid back +right + + align:start position:0% +right + + + align:start position:0% +right +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% + + + + align:start position:0% + +what's the borrower's choice well the + + align:start position:0% +what's the borrower's choice well the + + + align:start position:0% +what's the borrower's choice well the +borrower could pay back and get F of K + + align:start position:0% +borrower could pay back and get F of K + + + align:start position:0% +borrower could pay back and get F of K +and the borrower's net return if they + + align:start position:0% +and the borrower's net return if they + + + align:start position:0% +and the borrower's net return if they +pay back if K minus the amount they have + + align:start position:0% +pay back if K minus the amount they have + + + align:start position:0% +pay back if K minus the amount they have +to pay + + align:start position:0% +to pay + + + align:start position:0% +to pay +or the borrower could pay this kind of + + align:start position:0% +or the borrower could pay this kind of + + + align:start position:0% +or the borrower could pay this kind of +default cost + + align:start position:0% +default cost + + + align:start position:0% +default cost +right and get F of K minus uh Nu of K uh + + align:start position:0% +right and get F of K minus uh Nu of K uh + + + align:start position:0% +right and get F of K minus uh Nu of K uh +Ada of K okay and you could think of + + align:start position:0% +Ada of K okay and you could think of + + + align:start position:0% +Ada of K okay and you could think of +this as kind of like they come and seize + + align:start position:0% +this as kind of like they come and seize + + + align:start position:0% +this as kind of like they come and seize +my factory or like you know and take you + + align:start position:0% +my factory or like you know and take you + + + align:start position:0% +my factory or like you know and take you +know some share of it + + align:start position:0% + + + + align:start position:0% + +okay so it's slightly different slightly + + align:start position:0% +okay so it's slightly different slightly + + + align:start position:0% +okay so it's slightly different slightly +different model + + align:start position:0% +different model + + + align:start position:0% +different model +so if we rearrange um + + align:start position:0% + + + + align:start position:0% + +terms here + + align:start position:0% +terms here + + + align:start position:0% +terms here +the + + align:start position:0% +the + + + align:start position:0% +the +uh the kind of key equality condition is + + align:start position:0% +uh the kind of key equality condition is + + + align:start position:0% +uh the kind of key equality condition is +that r k minus W has to equal + + align:start position:0% +that r k minus W has to equal + + + align:start position:0% +that r k minus W has to equal +um uh + + align:start position:0% +um uh + + + align:start position:0% +um uh +ETA K or that K Over W is equal to R + + align:start position:0% +ETA K or that K Over W is equal to R + + + align:start position:0% +ETA K or that K Over W is equal to R +over R minus ETA + + align:start position:0% +over R minus ETA + + + align:start position:0% +over R minus ETA +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so um + + align:start position:0% + + + + align:start position:0% + +so in this model + + align:start position:0% +so in this model + + + align:start position:0% +so in this model +this is actually going to give sort of a + + align:start position:0% +this is actually going to give sort of a + + + align:start position:0% +this is actually going to give sort of a +maximum amount the bank is going to want + + align:start position:0% +maximum amount the bank is going to want + + + align:start position:0% +maximum amount the bank is going to want +to lend you + + align:start position:0% + + + + align:start position:0% + +um with amount of borrowing that's going + + align:start position:0% +um with amount of borrowing that's going + + + align:start position:0% +um with amount of borrowing that's going +to be increasing in W right the the more + + align:start position:0% +to be increasing in W right the the more + + + align:start position:0% +to be increasing in W right the the more +um W you have the more uh the more you + + align:start position:0% +um W you have the more uh the more you + + + align:start position:0% +um W you have the more uh the more you +can um + + align:start position:0% +can um + + + align:start position:0% +can um +uh you can more you can borrow and + + align:start position:0% +uh you can more you can borrow and + + + align:start position:0% +uh you can more you can borrow and +decreasing in r + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so now let's suppose there's a + + align:start position:0% +so now let's suppose there's a + + + align:start position:0% +so now let's suppose there's a +monitoring technology + + align:start position:0% + + + + align:start position:0% + +so um the lender needs to spend some + + align:start position:0% +so um the lender needs to spend some + + + align:start position:0% +so um the lender needs to spend some +resources in order to make the borrower + + align:start position:0% +resources in order to make the borrower + + + align:start position:0% +resources in order to make the borrower +want to repay like basically in other + + align:start position:0% +want to repay like basically in other + + + align:start position:0% +want to repay like basically in other +words 8 is equal to zero if the borrower + + align:start position:0% +words 8 is equal to zero if the borrower + + + align:start position:0% +words 8 is equal to zero if the borrower +doesn't spending money but if a borrower + + align:start position:0% +doesn't spending money but if a borrower + + + align:start position:0% +doesn't spending money but if a borrower +sort of like does some stuff they can + + align:start position:0% +sort of like does some stuff they can + + + align:start position:0% +sort of like does some stuff they can +get you to repay + + align:start position:0% +get you to repay + + + align:start position:0% +get you to repay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +you know maybe that's like finding out + + align:start position:0% +you know maybe that's like finding out + + + align:start position:0% +you know maybe that's like finding out +where you live like maybe it's + + align:start position:0% +where you live like maybe it's + + + align:start position:0% +where you live like maybe it's +um you know getting to you know if you + + align:start position:0% +um you know getting to you know if you + + + align:start position:0% +um you know getting to you know if you +think about a lot of the sort of + + align:start position:0% +think about a lot of the sort of + + + align:start position:0% +think about a lot of the sort of +microfinance Institutions we'll talk + + align:start position:0% +microfinance Institutions we'll talk + + + align:start position:0% +microfinance Institutions we'll talk +about next time they maybe got you + + align:start position:0% +about next time they maybe got you + + + align:start position:0% +about next time they maybe got you +together in groups of people and the + + align:start position:0% +together in groups of people and the + + + align:start position:0% +together in groups of people and the +basic idea is if you if you're defaulted + + align:start position:0% +basic idea is if you if you're defaulted + + + align:start position:0% +basic idea is if you if you're defaulted +kind of other people in your group kind + + align:start position:0% +kind of other people in your group kind + + + align:start position:0% +kind of other people in your group kind +of like impose social sanctions on you + + align:start position:0% +of like impose social sanctions on you + + + align:start position:0% +of like impose social sanctions on you +you default like there's some cost we + + align:start position:0% +you default like there's some cost we + + + align:start position:0% +you default like there's some cost we +have to sort of create to sort of get + + align:start position:0% +have to sort of create to sort of get + + + align:start position:0% +have to sort of create to sort of get +you to repay and in this model they're + + align:start position:0% +you to repay and in this model they're + + + align:start position:0% +you to repay and in this model they're +going to say suppose those are a fixed + + align:start position:0% +going to say suppose those are a fixed + + + align:start position:0% +going to say suppose those are a fixed +cost + + align:start position:0% +cost + + + align:start position:0% +cost +okay it's basically a cost per borrower + + align:start position:0% +okay it's basically a cost per borrower + + + align:start position:0% +okay it's basically a cost per borrower +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um and there are some estimates from + + align:start position:0% +um and there are some estimates from + + + align:start position:0% +um and there are some estimates from +this like Old Paper violin which says + + align:start position:0% +this like Old Paper violin which says + + + align:start position:0% +this like Old Paper violin which says +that maybe they're pretty high + + align:start position:0% +that maybe they're pretty high + + + align:start position:0% +that maybe they're pretty high +okay and to me particularly for very + + align:start position:0% +okay and to me particularly for very + + + align:start position:0% +okay and to me particularly for very +small loans and this could also be a + + align:start position:0% +small loans and this could also be a + + + align:start position:0% +small loans and this could also be a +reason why basically like microfinance + + align:start position:0% +reason why basically like microfinance + + + align:start position:0% +reason why basically like microfinance +has really high interest rates because + + align:start position:0% +has really high interest rates because + + + align:start position:0% +has really high interest rates because +you know if I have to like find out yes + + align:start position:0% +you know if I have to like find out yes + + + align:start position:0% +you know if I have to like find out yes +it's probably maybe face costs maybe a + + align:start position:0% +it's probably maybe face costs maybe a + + + align:start position:0% +it's probably maybe face costs maybe a +little bit much like it's probably def + + align:start position:0% +little bit much like it's probably def + + + align:start position:0% +little bit much like it's probably def +probably cheaper to find out if like you + + align:start position:0% +probably cheaper to find out if like you + + + align:start position:0% +probably cheaper to find out if like you +know + + align:start position:0% +know + + + align:start position:0% +know +um + + align:start position:0% +um + + + align:start position:0% +um +Joe's dry cleaner is a better sort of + + align:start position:0% +Joe's dry cleaner is a better sort of + + + align:start position:0% +Joe's dry cleaner is a better sort of +like you know investment or you know + + align:start position:0% +like you know investment or you know + + + align:start position:0% +like you know investment or you know +Joe's Taylor is a better Joe's Taylor is + + align:start position:0% +Joe's Taylor is a better Joe's Taylor is + + + align:start position:0% +Joe's Taylor is a better Joe's Taylor is +probably easier to figure out if they're + + align:start position:0% +probably easier to figure out if they're + + + align:start position:0% +probably easier to figure out if they're +worth lending to than you know the gap + + align:start position:0% +worth lending to than you know the gap + + + align:start position:0% +worth lending to than you know the gap +or something it's probably not totally + + align:start position:0% +or something it's probably not totally + + + align:start position:0% +or something it's probably not totally +fixed + + align:start position:0% +fixed + + + align:start position:0% +fixed +um but uh the idea that sort of it has + + align:start position:0% +um but uh the idea that sort of it has + + + align:start position:0% +um but uh the idea that sort of it has +this kind of large you know fixed + + align:start position:0% +this kind of large you know fixed + + + align:start position:0% +this kind of large you know fixed +component or sort of like you know + + align:start position:0% +component or sort of like you know + + + align:start position:0% +component or sort of like you know +definitely sort of not increasing very + + align:start position:0% +definitely sort of not increasing very + + + align:start position:0% +definitely sort of not increasing very +much seems kind of reasonable and if + + align:start position:0% +much seems kind of reasonable and if + + + align:start position:0% +much seems kind of reasonable and if +that's true that that's going to give us + + align:start position:0% +that's true that that's going to give us + + + align:start position:0% +that's true that that's going to give us +a reasoning why kind of microfinance is + + align:start position:0% +a reasoning why kind of microfinance is + + + align:start position:0% +a reasoning why kind of microfinance is +making lots of small loans is going to + + align:start position:0% +making lots of small loans is going to + + + align:start position:0% +making lots of small loans is going to +have to have really high interest rates + + align:start position:0% +have to have really high interest rates + + + align:start position:0% +have to have really high interest rates +because they have to cover kind of this + + align:start position:0% +because they have to cover kind of this + + + align:start position:0% +because they have to cover kind of this +fixed monitoring cost + + align:start position:0% +fixed monitoring cost + + + align:start position:0% +fixed monitoring cost +so basically if you're making a small + + align:start position:0% +so basically if you're making a small + + + align:start position:0% +so basically if you're making a small +loan you have this fixed cost you have + + align:start position:0% +loan you have this fixed cost you have + + + align:start position:0% +loan you have this fixed cost you have +to sort of like recoup it kind of on a + + align:start position:0% +to sort of like recoup it kind of on a + + + align:start position:0% +to sort of like recoup it kind of on a +you know in terms of an interest rate + + align:start position:0% +you know in terms of an interest rate + + + align:start position:0% +you know in terms of an interest rate +it's going to be sort of a small a large + + align:start position:0% +it's going to be sort of a small a large + + + align:start position:0% +it's going to be sort of a small a large +percent of a small base whereas if it's + + align:start position:0% +percent of a small base whereas if it's + + + align:start position:0% +percent of a small base whereas if it's +sort of a really big loan that sort of + + align:start position:0% +sort of a really big loan that sort of + + + align:start position:0% +sort of a really big loan that sort of +fixed cost is going to be sort of much + + align:start position:0% +fixed cost is going to be sort of much + + + align:start position:0% +fixed cost is going to be sort of much +smaller that's basically what's going on + + align:start position:0% +smaller that's basically what's going on + + + align:start position:0% +smaller that's basically what's going on +in this model + + align:start position:0% +in this model + + + align:start position:0% +in this model +okay so so how's that going to work so + + align:start position:0% +okay so so how's that going to work so + + + align:start position:0% +okay so so how's that going to work so +if it's a fixed cost right uh then with + + align:start position:0% +if it's a fixed cost right uh then with + + + align:start position:0% +if it's a fixed cost right uh then with +then the lender is going to just break + + align:start position:0% +then the lender is going to just break + + + align:start position:0% +then the lender is going to just break +even so the sort of the + + align:start position:0% +even so the sort of the + + + align:start position:0% +even so the sort of the +um their return has to equal kind of the + + align:start position:0% +um their return has to equal kind of the + + + align:start position:0% +um their return has to equal kind of the +market return plus the fixed cost + + align:start position:0% +market return plus the fixed cost + + + align:start position:0% +market return plus the fixed cost +and so you know that's kind of that + + align:start position:0% +and so you know that's kind of that + + + align:start position:0% +and so you know that's kind of that +that's kind of it basically if if the + + align:start position:0% +that's kind of it basically if if the + + + align:start position:0% +that's kind of it basically if if the +amount they're borrowing is really small + + align:start position:0% +amount they're borrowing is really small + + + align:start position:0% +amount they're borrowing is really small +then we only have to raise the interest + + align:start position:0% +then we only have to raise the interest + + + align:start position:0% +then we only have to raise the interest +rate a little bit to cover this fixed + + align:start position:0% +rate a little bit to cover this fixed + + + align:start position:0% +rate a little bit to cover this fixed +cost of the amount that borrowing it's + + align:start position:0% +cost of the amount that borrowing it's + + + align:start position:0% +cost of the amount that borrowing it's +really it's really big sorry for the + + align:start position:0% +really it's really big sorry for the + + + align:start position:0% +really it's really big sorry for the +monthly program is really small if + + align:start position:0% +monthly program is really small if + + + align:start position:0% +monthly program is really small if +you're really interest rate a lot to + + align:start position:0% +you're really interest rate a lot to + + + align:start position:0% +you're really interest rate a lot to +cover it the fixed cost if you + + align:start position:0% +cover it the fixed cost if you + + + align:start position:0% +cover it the fixed cost if you +manageably small we don't + + align:start position:0% +manageably small we don't + + + align:start position:0% +manageably small we don't +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +so if we had this condition from before + + align:start position:0% +so if we had this condition from before + + + align:start position:0% +so if we had this condition from before +sort of what the optimal level of uh uh + + align:start position:0% +sort of what the optimal level of uh uh + + + align:start position:0% +sort of what the optimal level of uh uh +the credit constraint is we can sort of + + align:start position:0% +the credit constraint is we can sort of + + + align:start position:0% +the credit constraint is we can sort of +get the we can just substitute that in + + align:start position:0% +get the we can just substitute that in + + + align:start position:0% +get the we can just substitute that in +and sort of get the sort of the the + + align:start position:0% +and sort of get the sort of the the + + + align:start position:0% +and sort of get the sort of the the +return is going to be equal to the + + align:start position:0% +return is going to be equal to the + + + align:start position:0% +return is going to be equal to the +market return plus it's kind of this + + align:start position:0% +market return plus it's kind of this + + + align:start position:0% +market return plus it's kind of this +this markup term which is going to be a + + align:start position:0% +this markup term which is going to be a + + + align:start position:0% +this markup term which is going to be a +function of their wealth right that's + + align:start position:0% +function of their wealth right that's + + + align:start position:0% +function of their wealth right that's +just sort of combining these these two + + align:start position:0% +just sort of combining these these two + + + align:start position:0% +just sort of combining these these two +points + + align:start position:0% +points + + + align:start position:0% +points +um and that basically sort of for + + align:start position:0% +um and that basically sort of for + + + align:start position:0% +um and that basically sort of for +um you know really and so what's kind of + + align:start position:0% +um you know really and so what's kind of + + + align:start position:0% +um you know really and so what's kind of +the point for really rich Borrowers + + align:start position:0% +the point for really rich Borrowers + + + align:start position:0% +the point for really rich Borrowers +right + + align:start position:0% +right + + + align:start position:0% +right +um uh for really rich borrowers they can + + align:start position:0% +um uh for really rich borrowers they can + + + align:start position:0% +um uh for really rich borrowers they can +borrow a lot + + align:start position:0% +borrow a lot + + + align:start position:0% +borrow a lot +um and therefore sort of the we can sort + + align:start position:0% +um and therefore sort of the we can sort + + + align:start position:0% +um and therefore sort of the we can sort +of spread that fixed cost over a small + + align:start position:0% +of spread that fixed cost over a small + + + align:start position:0% +of spread that fixed cost over a small +amount for kind of really poor borrowers + + align:start position:0% +amount for kind of really poor borrowers + + + align:start position:0% +amount for kind of really poor borrowers +that credit is actually really binding + + align:start position:0% +that credit is actually really binding + + + align:start position:0% +that credit is actually really binding +We're not gonna we're going to London + + align:start position:0% +We're not gonna we're going to London + + + align:start position:0% +We're not gonna we're going to London +very much and therefore that interest + + align:start position:0% +very much and therefore that interest + + + align:start position:0% +very much and therefore that interest +rate we're going to charge them is going + + align:start position:0% +rate we're going to charge them is going + + + align:start position:0% +rate we're going to charge them is going +to be kind of a lot and then you just + + align:start position:0% +to be kind of a lot and then you just + + + align:start position:0% +to be kind of a lot and then you just +sort of solve and then of course that + + align:start position:0% +sort of solve and then of course that + + + align:start position:0% +sort of solve and then of course that +has this additional thing which the + + align:start position:0% +has this additional thing which the + + + align:start position:0% +has this additional thing which the +interest rates kind of you know in + + align:start position:0% +interest rates kind of you know in + + + align:start position:0% +interest rates kind of you know in +equilibrium condition so you have to do + + align:start position:0% +equilibrium condition so you have to do + + + align:start position:0% +equilibrium condition so you have to do +a little algebra to sort of solve that + + align:start position:0% +a little algebra to sort of solve that + + + align:start position:0% +a little algebra to sort of solve that +out but that's kind of the basic logic + + align:start position:0% +out but that's kind of the basic logic + + + align:start position:0% +out but that's kind of the basic logic +of + + align:start position:0% +of + + + align:start position:0% +of +so in this model some people will never + + align:start position:0% +so in this model some people will never + + + align:start position:0% +so in this model some people will never +be able to borrow + + align:start position:0% +be able to borrow + + + align:start position:0% +be able to borrow +uh and and sort of this this this + + align:start position:0% +uh and and sort of this this this + + + align:start position:0% +uh and and sort of this this this +condition over here if V is greater than + + align:start position:0% +condition over here if V is greater than + + + align:start position:0% +condition over here if V is greater than +uh a to W then there's sort of no + + align:start position:0% +uh a to W then there's sort of no + + + align:start position:0% +uh a to W then there's sort of no +equilibrium then sort of the rate would + + align:start position:0% +equilibrium then sort of the rate would + + + align:start position:0% +equilibrium then sort of the rate would +there's no sort of solution to where you + + align:start position:0% +there's no sort of solution to where you + + + align:start position:0% +there's no sort of solution to where you +can sort of cover the kind of the the + + align:start position:0% +can sort of cover the kind of the the + + + align:start position:0% +can sort of cover the kind of the the +the the the monitoring cost with the + + align:start position:0% +the the the monitoring cost with the + + + align:start position:0% +the the the monitoring cost with the +industry because the industry gets too + + align:start position:0% +industry because the industry gets too + + + align:start position:0% +industry because the industry gets too +high and then they won't repay and so on + + align:start position:0% +high and then they won't repay and so on + + + align:start position:0% +high and then they won't repay and so on +and so forth there's no solution to that + + align:start position:0% +and so forth there's no solution to that + + + align:start position:0% +and so forth there's no solution to that +and and if if it's less than that then + + align:start position:0% +and and if if it's less than that then + + + align:start position:0% +and and if if it's less than that then +there is a solution and then you have + + align:start position:0% +there is a solution and then you have + + + align:start position:0% +there is a solution and then you have +this condition I said before that sort + + align:start position:0% +this condition I said before that sort + + + align:start position:0% +this condition I said before that sort +of R is going down with wealth is going + + align:start position:0% +of R is going down with wealth is going + + + align:start position:0% +of R is going down with wealth is going +up + + align:start position:0% +up + + + align:start position:0% +up +so this is a model where we have people + + align:start position:0% +so this is a model where we have people + + + align:start position:0% +so this is a model where we have people +who are going to be actually credit + + align:start position:0% +who are going to be actually credit + + + align:start position:0% +who are going to be actually credit +constrained some people just they cannot + + align:start position:0% +constrained some people just they cannot + + + align:start position:0% +constrained some people just they cannot +borrow at all right it's not sort of + + align:start position:0% +borrow at all right it's not sort of + + + align:start position:0% +borrow at all right it's not sort of +this you know but here's some people + + align:start position:0% +this you know but here's some people + + + align:start position:0% +this you know but here's some people +just totally cut out of the market and + + align:start position:0% +just totally cut out of the market and + + + align:start position:0% +just totally cut out of the market and +we also have this can have this thing + + align:start position:0% +we also have this can have this thing + + + align:start position:0% +we also have this can have this thing +now we're sort of the people who are uh + + align:start position:0% +now we're sort of the people who are uh + + + align:start position:0% +now we're sort of the people who are uh +borrowing a little are the ones who are + + align:start position:0% +borrowing a little are the ones who are + + + align:start position:0% +borrowing a little are the ones who are +paying the high interest rates which is + + align:start position:0% +paying the high interest rates which is + + + align:start position:0% +paying the high interest rates which is +sort of one if you think back to sort of + + align:start position:0% +sort of one if you think back to sort of + + + align:start position:0% +sort of one if you think back to sort of +one of the motivating facts I kind of + + align:start position:0% +one of the motivating facts I kind of + + + align:start position:0% +one of the motivating facts I kind of +gave you at the beginning of the talk + + align:start position:0% +gave you at the beginning of the talk + + + align:start position:0% +gave you at the beginning of the talk +this is now something that sort of + + align:start position:0% +this is now something that sort of + + + align:start position:0% +this is now something that sort of +explains that and that also is sort of + + align:start position:0% +explains that and that also is sort of + + + align:start position:0% +explains that and that also is sort of +consistent why we all consistent with + + align:start position:0% +consistent why we all consistent with + + + align:start position:0% +consistent why we all consistent with +sort of finding the fact that we have + + align:start position:0% +sort of finding the fact that we have + + + align:start position:0% +sort of finding the fact that we have +all these kind of like very small loans + + align:start position:0% +all these kind of like very small loans + + + align:start position:0% +all these kind of like very small loans +having kind of very high rates uh we + + align:start position:0% +having kind of very high rates uh we + + + align:start position:0% +having kind of very high rates uh we +also get + + align:start position:0% +also get + + + align:start position:0% +also get +um maybe I won't make sure this way this + + align:start position:0% +um maybe I won't make sure this way this + + + align:start position:0% +um maybe I won't make sure this way this +multiplier property which basically sort + + align:start position:0% +multiplier property which basically sort + + + align:start position:0% +multiplier property which basically sort +of that you know Dr D D row sort of how + + align:start position:0% +of that you know Dr D D row sort of how + + + align:start position:0% +of that you know Dr D D row sort of how +the rate charge depends on sort of the + + align:start position:0% +the rate charge depends on sort of the + + + align:start position:0% +the rate charge depends on sort of the +underlying market rate is is very this + + align:start position:0% +underlying market rate is is very this + + + align:start position:0% +underlying market rate is is very this +thing is going to be less than less than + + align:start position:0% +thing is going to be less than less than + + + align:start position:0% +thing is going to be less than less than +this this is this thing is going to be + + align:start position:0% +this this is this thing is going to be + + + align:start position:0% +this this is this thing is going to be +sort of a multiplier that's going to + + align:start position:0% +sort of a multiplier that's going to + + + align:start position:0% +sort of a multiplier that's going to +sort of like make this sort of the rape + + align:start position:0% +sort of like make this sort of the rape + + + align:start position:0% +sort of like make this sort of the rape +be very sensitive to the underlying rate + + align:start position:0% +be very sensitive to the underlying rate + + + align:start position:0% +be very sensitive to the underlying rate +so it also kind of moves around a lot so + + align:start position:0% +so it also kind of moves around a lot so + + + align:start position:0% +so it also kind of moves around a lot so +but I'm not going to focus not as much + + align:start position:0% + + + + align:start position:0% + +so you know what is it what did this + + align:start position:0% +so you know what is it what did this + + + align:start position:0% +so you know what is it what did this +model add to these other things a few + + align:start position:0% +model add to these other things a few + + + align:start position:0% +model add to these other things a few +things so without it it says there's a + + align:start position:0% +things so without it it says there's a + + + align:start position:0% +things so without it it says there's a +wedge between the cost of capital and + + align:start position:0% +wedge between the cost of capital and + + + align:start position:0% +wedge between the cost of capital and +the interest rate + + align:start position:0% +the interest rate + + + align:start position:0% +the interest rate +um that was given by high monitoring + + align:start position:0% +um that was given by high monitoring + + + align:start position:0% +um that was given by high monitoring +cost + + align:start position:0% +cost + + + align:start position:0% +cost +um + + align:start position:0% +um + + + align:start position:0% +um +it gave this sort of sensitivity when I + + align:start position:0% +it gave this sort of sensitivity when I + + + align:start position:0% +it gave this sort of sensitivity when I +sort of talked about the last slide + + align:start position:0% +sort of talked about the last slide + + + align:start position:0% +sort of talked about the last slide +um it also implies that sort of + + align:start position:0% +um it also implies that sort of + + + align:start position:0% +um it also implies that sort of +subsidizing the cost of capital can we + + align:start position:0% +subsidizing the cost of capital can we + + + align:start position:0% +subsidizing the cost of capital can we +do well for gains because R will go down + + align:start position:0% +do well for gains because R will go down + + + align:start position:0% +do well for gains because R will go down +right and this kind of allows firms to + + align:start position:0% +right and this kind of allows firms to + + + align:start position:0% +right and this kind of allows firms to +borrow more + + align:start position:0% +borrow more + + + align:start position:0% +borrow more +um it also suggests that these + + align:start position:0% +um it also suggests that these + + + align:start position:0% +um it also suggests that these +monitoring costs are really important + + align:start position:0% +monitoring costs are really important + + + align:start position:0% +monitoring costs are really important +because these monitoring costs are sort + + align:start position:0% +because these monitoring costs are sort + + + align:start position:0% +because these monitoring costs are sort +of what's like uh sort of excluding + + align:start position:0% +of what's like uh sort of excluding + + + align:start position:0% +of what's like uh sort of excluding +people from credits and this question of + + align:start position:0% +people from credits and this question of + + + align:start position:0% +people from credits and this question of +sort of how do we think about kind of + + align:start position:0% +sort of how do we think about kind of + + + align:start position:0% +sort of how do we think about kind of +what what kinds of monitoring costs are + + align:start position:0% +what what kinds of monitoring costs are + + + align:start position:0% +what what kinds of monitoring costs are +going to be really effective is going to + + align:start position:0% +going to be really effective is going to + + + align:start position:0% +going to be really effective is going to +be something we're going to talk about a + + align:start position:0% +be something we're going to talk about a + + + align:start position:0% +be something we're going to talk about a +lot more next time in kind of the mega + + align:start position:0% +lot more next time in kind of the mega + + + align:start position:0% +lot more next time in kind of the mega +credit lectures + + align:start position:0% + + + + align:start position:0% + +okay yes + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +oh + + align:start position:0% +oh + + + align:start position:0% +oh +these lenders are not wildly profitable + + align:start position:0% +these lenders are not wildly profitable + + + align:start position:0% +these lenders are not wildly profitable +that's all it means + + align:start position:0% +that's all it means + + + align:start position:0% +that's all it means +so we're seeing these big spreads but + + align:start position:0% +so we're seeing these big spreads but + + + align:start position:0% +so we're seeing these big spreads but +it's not like the microfinance + + align:start position:0% +it's not like the microfinance + + + align:start position:0% +it's not like the microfinance +organizations are like making tons and + + align:start position:0% +organizations are like making tons and + + + align:start position:0% +organizations are like making tons and +tons of money + + align:start position:0% +tons of money + + + align:start position:0% +tons of money +right so that was sort of rejected like + + align:start position:0% +right so that was sort of rejected like + + + align:start position:0% +right so that was sort of rejected like +I said this other thing is maybe they're + + align:start position:0% +I said this other thing is maybe they're + + + align:start position:0% +I said this other thing is maybe they're +not competitive that's running rents + + align:start position:0% +not competitive that's running rents + + + align:start position:0% +not competitive that's running rents +this bullet points say well maybe it's + + align:start position:0% +this bullet points say well maybe it's + + + align:start position:0% +this bullet points say well maybe it's +not that they're totally making lots of + + align:start position:0% +not that they're totally making lots of + + + align:start position:0% +not that they're totally making lots of +rounds I mean I think it could be part + + align:start position:0% +rounds I mean I think it could be part + + + align:start position:0% +rounds I mean I think it could be part +of it but I think like in general these + + align:start position:0% +of it but I think like in general these + + + align:start position:0% +of it but I think like in general these +organizations are not wildly profitable + + align:start position:0% +organizations are not wildly profitable + + + align:start position:0% +organizations are not wildly profitable +a lot of them actually losing money or + + align:start position:0% +a lot of them actually losing money or + + + align:start position:0% +a lot of them actually losing money or +certainly kind of breaking even we + + align:start position:0% +certainly kind of breaking even we + + + align:start position:0% +certainly kind of breaking even we +suggest that it's not + + align:start position:0% +suggest that it's not + + + align:start position:0% +suggest that it's not +although I think the rent I do think the + + align:start position:0% +although I think the rent I do think the + + + align:start position:0% +although I think the rent I do think the +rent thing could be part of it + + align:start position:0% +rent thing could be part of it + + + align:start position:0% +rent thing could be part of it +it's not mostly about rents and that's + + align:start position:0% +it's not mostly about rents and that's + + + align:start position:0% +it's not mostly about rents and that's +why we kind of need these real costs + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the the final + + align:start position:0% +so the the final + + + align:start position:0% +so the the final +um + + align:start position:0% +um + + + align:start position:0% +um +finals or penultimate thing I want to + + align:start position:0% +finals or penultimate thing I want to + + + align:start position:0% +finals or penultimate thing I want to +talk about today is this paper bike + + align:start position:0% +talk about today is this paper bike + + + align:start position:0% +talk about today is this paper bike +because that's all I want to talk about + + align:start position:0% +because that's all I want to talk about + + + align:start position:0% +because that's all I want to talk about +with the theory okay so basically we had + + align:start position:0% +with the theory okay so basically we had + + + align:start position:0% +with the theory okay so basically we had +three models that you should keep in + + align:start position:0% +three models that you should keep in + + + align:start position:0% +three models that you should keep in +mind more Hazard model of a reflection + + align:start position:0% +mind more Hazard model of a reflection + + + align:start position:0% +mind more Hazard model of a reflection +model and kind of monitoring cost model + + align:start position:0% +model and kind of monitoring cost model + + + align:start position:0% +model and kind of monitoring cost model +so those are sort of three + + align:start position:0% +so those are sort of three + + + align:start position:0% +so those are sort of three +I would say like + + align:start position:0% +I would say like + + + align:start position:0% +I would say like +Frameworks or tools that you should keep + + align:start position:0% +Frameworks or tools that you should keep + + + align:start position:0% +Frameworks or tools that you should keep +in mind as you sort of think through + + align:start position:0% +in mind as you sort of think through + + + align:start position:0% +in mind as you sort of think through +some of these kind of credit issues + + align:start position:0% +some of these kind of credit issues + + + align:start position:0% +some of these kind of credit issues +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this Carl and Zimmerman paper was + + align:start position:0% +so this Carl and Zimmerman paper was + + + align:start position:0% +so this Carl and Zimmerman paper was +basically trying to understand how do we + + align:start position:0% +basically trying to understand how do we + + + align:start position:0% +basically trying to understand how do we +think about + + align:start position:0% +think about + + + align:start position:0% +think about +can we differentiate between the first + + align:start position:0% +can we differentiate between the first + + + align:start position:0% +can we differentiate between the first +two models our selection models and + + align:start position:0% +two models our selection models and + + + align:start position:0% +two models our selection models and +moral hazardous models + + align:start position:0% +moral hazardous models + + + align:start position:0% +moral hazardous models +and prior to this paper there was sort + + align:start position:0% +and prior to this paper there was sort + + + align:start position:0% +and prior to this paper there was sort +of a bunch of a bunch of previous papers + + align:start position:0% +of a bunch of a bunch of previous papers + + + align:start position:0% +of a bunch of a bunch of previous papers +who sort of said look can we test for + + align:start position:0% +who sort of said look can we test for + + + align:start position:0% +who sort of said look can we test for +asymmetric information + + align:start position:0% +asymmetric information + + + align:start position:0% +asymmetric information +um by looking for like a you know a + + align:start position:0% +um by looking for like a you know a + + + align:start position:0% +um by looking for like a you know a +say a positive correlation between sort + + align:start position:0% +say a positive correlation between sort + + + align:start position:0% +say a positive correlation between sort +of like the the the uh + + align:start position:0% +of like the the the uh + + + align:start position:0% +of like the the the uh +uh the industry and the default risk + + align:start position:0% +uh the industry and the default risk + + + align:start position:0% +uh the industry and the default risk +right that was kind of that was coming + + align:start position:0% +right that was kind of that was coming + + + align:start position:0% +right that was kind of that was coming +out for both they didn't really say like + + align:start position:0% +out for both they didn't really say like + + + align:start position:0% +out for both they didn't really say like +was the average section well however + + align:start position:0% +was the average section well however + + + align:start position:0% +was the average section well however +because both of those models kind of + + align:start position:0% +because both of those models kind of + + + align:start position:0% +because both of those models kind of +produce the same thing + + align:start position:0% +produce the same thing + + + align:start position:0% +produce the same thing +so they will say well can we actually do + + align:start position:0% +so they will say well can we actually do + + + align:start position:0% +so they will say well can we actually do +something to sort of like + + align:start position:0% +something to sort of like + + + align:start position:0% +something to sort of like +differentiate between those two + + align:start position:0% +differentiate between those two + + + align:start position:0% +differentiate between those two +and in particular uh they wanna sort of + + align:start position:0% +and in particular uh they wanna sort of + + + align:start position:0% +and in particular uh they wanna sort of +uh so again average selection is that + + align:start position:0% +uh so again average selection is that + + + align:start position:0% +uh so again average selection is that +some people the idea some people are + + align:start position:0% +some people the idea some people are + + + align:start position:0% +some people the idea some people are +riskier than others and it's a + + align:start position:0% +riskier than others and it's a + + + align:start position:0% +riskier than others and it's a +characteristic about you and while + + align:start position:0% +characteristic about you and while + + + align:start position:0% +characteristic about you and while +hazardous people can choose how much + + align:start position:0% +hazardous people can choose how much + + + align:start position:0% +hazardous people can choose how much +risk they want to sort of take and + + align:start position:0% +risk they want to sort of take and + + + align:start position:0% +risk they want to sort of take and +that's kind of a character an ex-post + + align:start position:0% +that's kind of a character an ex-post + + + align:start position:0% +that's kind of a character an ex-post +kind of choice + + align:start position:0% +kind of choice + + + align:start position:0% +kind of choice +and so + + align:start position:0% +and so + + + align:start position:0% +and so +um these are going to look similar in + + align:start position:0% +um these are going to look similar in + + + align:start position:0% +um these are going to look similar in +the cross section + + align:start position:0% +the cross section + + + align:start position:0% +the cross section +uh we basically sort of talked about + + align:start position:0% +uh we basically sort of talked about + + + align:start position:0% +uh we basically sort of talked about +that okay but the idea of of their paper + + align:start position:0% +that okay but the idea of of their paper + + + align:start position:0% +that okay but the idea of of their paper +to say well can experimentally we do + + align:start position:0% +to say well can experimentally we do + + + align:start position:0% +to say well can experimentally we do +something to sort of tease us apart + + align:start position:0% +something to sort of tease us apart + + + align:start position:0% +something to sort of tease us apart +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +um this paper kind of pioneered this + + align:start position:0% +um this paper kind of pioneered this + + + align:start position:0% +um this paper kind of pioneered this +experimental design uh but it's now been + + align:start position:0% +experimental design uh but it's now been + + + align:start position:0% +experimental design uh but it's now been +used for many many many different kinds + + align:start position:0% +used for many many many different kinds + + + align:start position:0% +used for many many many different kinds +of things uh and I think we may have + + align:start position:0% +of things uh and I think we may have + + + align:start position:0% +of things uh and I think we may have +already seen it already but this is kind + + align:start position:0% +already seen it already but this is kind + + + align:start position:0% +already seen it already but this is kind +of the original paper so I wanted to + + align:start position:0% +of the original paper so I wanted to + + + align:start position:0% +of the original paper so I wanted to +kind of go through it + + align:start position:0% +kind of go through it + + + align:start position:0% +kind of go through it +a little bit + + align:start position:0% +a little bit + + + align:start position:0% +a little bit +so their idea was + + align:start position:0% +so their idea was + + + align:start position:0% +so their idea was +adverse selection is driven by the + + align:start position:0% +adverse selection is driven by the + + + align:start position:0% +adverse selection is driven by the +x-anti interest rate + + align:start position:0% +x-anti interest rate + + + align:start position:0% +x-anti interest rate +more Hazard driven by the exposed + + align:start position:0% +more Hazard driven by the exposed + + + align:start position:0% +more Hazard driven by the exposed +interest rate + + align:start position:0% +interest rate + + + align:start position:0% +interest rate +and in the world these are the same + + align:start position:0% +and in the world these are the same + + + align:start position:0% +and in the world these are the same +right the interest rate that you get + + align:start position:0% +right the interest rate that you get + + + align:start position:0% +right the interest rate that you get +when you like I advertise and say hey + + align:start position:0% +when you like I advertise and say hey + + + align:start position:0% +when you like I advertise and say hey +I'm offering a loan at you know whatever + + align:start position:0% +I'm offering a loan at you know whatever + + + align:start position:0% +I'm offering a loan at you know whatever +10 percent + + align:start position:0% +10 percent + + + align:start position:0% +10 percent +if you sign up for that loan you pay + + align:start position:0% +if you sign up for that loan you pay + + + align:start position:0% +if you sign up for that loan you pay +like the rate is 10 so those things are + + align:start position:0% +like the rate is 10 so those things are + + + align:start position:0% +like the rate is 10 so those things are +in general in the world are the same + + align:start position:0% +in general in the world are the same + + + align:start position:0% +in general in the world are the same +but maybe in an experiment we can + + align:start position:0% +but maybe in an experiment we can + + + align:start position:0% +but maybe in an experiment we can +differentiate between them + + align:start position:0% +differentiate between them + + + align:start position:0% +differentiate between them +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +we can do that by surprising people with + + align:start position:0% +we can do that by surprising people with + + + align:start position:0% +we can do that by surprising people with +an interest rate with a change in the + + align:start position:0% +an interest rate with a change in the + + + align:start position:0% +an interest rate with a change in the +interest rate after they've accepted the + + align:start position:0% +interest rate after they've accepted the + + + align:start position:0% +interest rate after they've accepted the +loan okay so you advertise One Rate you + + align:start position:0% +loan okay so you advertise One Rate you + + + align:start position:0% +loan okay so you advertise One Rate you +get take up on one thing you change the + + align:start position:0% +get take up on one thing you change the + + + align:start position:0% +get take up on one thing you change the +next post and you get something else + + align:start position:0% +next post and you get something else + + + align:start position:0% +next post and you get something else +right and + + align:start position:0% +right and + + + align:start position:0% +right and +um + + align:start position:0% +um + + + align:start position:0% +um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +in particular you can't I think make + + align:start position:0% +in particular you can't I think make + + + align:start position:0% +in particular you can't I think make +people worse off + + align:start position:0% +people worse off + + + align:start position:0% +people worse off +I can't advertise 10 and then surprise + + align:start position:0% +I can't advertise 10 and then surprise + + + align:start position:0% +I can't advertise 10 and then surprise +you to 20 because number one people be + + align:start position:0% +you to 20 because number one people be + + + align:start position:0% +you to 20 because number one people be +really annoyed at you and number two + + align:start position:0% +really annoyed at you and number two + + + align:start position:0% +really annoyed at you and number two +you're still getting the selection + + align:start position:0% +you're still getting the selection + + + align:start position:0% +you're still getting the selection +effect because people will drop out + + align:start position:0% +effect because people will drop out + + + align:start position:0% +effect because people will drop out +again right + + align:start position:0% +again right + + + align:start position:0% +again right +but on the other hand almost everyone is + + align:start position:0% +but on the other hand almost everyone is + + + align:start position:0% +but on the other hand almost everyone is +going to be happy with sort of an + + align:start position:0% +going to be happy with sort of an + + + align:start position:0% +going to be happy with sort of an +improvement in their terms + + align:start position:0% +improvement in their terms + + + align:start position:0% +improvement in their terms +so if I advertise a rate of 20 percent + + align:start position:0% +so if I advertise a rate of 20 percent + + + align:start position:0% +so if I advertise a rate of 20 percent +right and then surprising people with a + + align:start position:0% +right and then surprising people with a + + + align:start position:0% +right and then surprising people with a +rate of 10 + + align:start position:0% +rate of 10 + + + align:start position:0% +rate of 10 +there's going to be essentially no + + align:start position:0% +there's going to be essentially no + + + align:start position:0% +there's going to be essentially no +selection difference because everyone + + align:start position:0% +selection difference because everyone + + + align:start position:0% +selection difference because everyone +who wanted the thing at 20 will be happy + + align:start position:0% +who wanted the thing at 20 will be happy + + + align:start position:0% +who wanted the thing at 20 will be happy +to take you to 10 so you can hold your + + align:start position:0% +to take you to 10 so you can hold your + + + align:start position:0% +to take you to 10 so you can hold your +selection constant but get a different + + align:start position:0% +selection constant but get a different + + + align:start position:0% +selection constant but get a different +kind of uh interest rate X post + + align:start position:0% +kind of uh interest rate X post + + + align:start position:0% +kind of uh interest rate X post +so that's basically their their their + + align:start position:0% +so that's basically their their their + + + align:start position:0% +so that's basically their their their +idea is to they have this other sort of + + align:start position:0% +idea is to they have this other sort of + + + align:start position:0% +idea is to they have this other sort of +um other Dynamic incentive thing but + + align:start position:0% +um other Dynamic incentive thing but + + + align:start position:0% +um other Dynamic incentive thing but +that's sort of I think maybe here nor + + align:start position:0% +that's sort of I think maybe here nor + + + align:start position:0% +that's sort of I think maybe here nor +there the basic idea is this which is + + align:start position:0% +there the basic idea is this which is + + + align:start position:0% +there the basic idea is this which is +say look we offer + + align:start position:0% +say look we offer + + + align:start position:0% +say look we offer +um uh we offer people either a high rate + + align:start position:0% +um uh we offer people either a high rate + + + align:start position:0% +um uh we offer people either a high rate +or a low rate + + align:start position:0% +or a low rate + + + align:start position:0% +or a low rate +ex-ante if you sign up with a loan with + + align:start position:0% +ex-ante if you sign up with a loan with + + + align:start position:0% +ex-ante if you sign up with a loan with +a low rate + + align:start position:0% +a low rate + + + align:start position:0% +a low rate +you get the low rate + + align:start position:0% +you get the low rate + + + align:start position:0% +you get the low rate +if you sign up for the loan with a high + + align:start position:0% +if you sign up for the loan with a high + + + align:start position:0% +if you sign up for the loan with a high +rate with some probability we surprise + + align:start position:0% +rate with some probability we surprise + + + align:start position:0% +rate with some probability we surprise +you and give you the low rate + + align:start position:0% +you and give you the low rate + + + align:start position:0% +you and give you the low rate +so now we have three boxes right and if + + align:start position:0% +so now we have three boxes right and if + + + align:start position:0% +so now we have three boxes right and if +we compare the high offers to the high + + align:start position:0% +we compare the high offers to the high + + + align:start position:0% +we compare the high offers to the high +offer so so if we compare and this kind + + align:start position:0% +offer so so if we compare and this kind + + + align:start position:0% +offer so so if we compare and this kind +of middle box is kind of the key box + + align:start position:0% +of middle box is kind of the key box + + + align:start position:0% +of middle box is kind of the key box +because if we compare the high offer if + + align:start position:0% +because if we compare the high offer if + + + align:start position:0% +because if we compare the high offer if +we hold fix the high offer rate and look + + align:start position:0% +we hold fix the high offer rate and look + + + align:start position:0% +we hold fix the high offer rate and look +at the actual contract rate this box or + + align:start position:0% +at the actual contract rate this box or + + + align:start position:0% +at the actual contract rate this box or +this box tells the moral hazard effect + + align:start position:0% +this box tells the moral hazard effect + + + align:start position:0% +this box tells the moral hazard effect +because you both selected in at say 20 + + align:start position:0% +because you both selected in at say 20 + + + align:start position:0% +because you both selected in at say 20 +but only some of you experience 20 and + + align:start position:0% +but only some of you experience 20 and + + + align:start position:0% +but only some of you experience 20 and +some have experience 10. and if we + + align:start position:0% +some have experience 10. and if we + + + align:start position:0% +some have experience 10. and if we +compare this box to this box we get + + align:start position:0% +compare this box to this box we get + + + align:start position:0% +compare this box to this box we get +um we get the pure selection effect + + align:start position:0% +um we get the pure selection effect + + + align:start position:0% +um we get the pure selection effect +because both of you guys experience 10 x + + align:start position:0% +because both of you guys experience 10 x + + + align:start position:0% +because both of you guys experience 10 x +post but here you were selected in as + + align:start position:0% +post but here you were selected in as + + + align:start position:0% +post but here you were selected in as +kind of having a 20 rate in here + + align:start position:0% +kind of having a 20 rate in here + + + align:start position:0% +kind of having a 20 rate in here +reflecting this having a 10 rate + + align:start position:0% +reflecting this having a 10 rate + + + align:start position:0% +reflecting this having a 10 rate +and um + + align:start position:0% +and um + + + align:start position:0% +and um +this design is useful for distinguishing + + align:start position:0% +this design is useful for distinguishing + + + align:start position:0% +this design is useful for distinguishing +between selection and moral hazard not + + align:start position:0% +between selection and moral hazard not + + + align:start position:0% +between selection and moral hazard not +just in credit but kind of uh everywhere + + align:start position:0% +just in credit but kind of uh everywhere + + + align:start position:0% +just in credit but kind of uh everywhere +basically and so people have done this + + align:start position:0% +basically and so people have done this + + + align:start position:0% +basically and so people have done this +sort of thing in all the other settings + + align:start position:0% +sort of thing in all the other settings + + + align:start position:0% +sort of thing in all the other settings +to kind of like use this kind of + + align:start position:0% +to kind of like use this kind of + + + align:start position:0% +to kind of like use this kind of +surprise Improvement to sort of + + align:start position:0% +surprise Improvement to sort of + + + align:start position:0% +surprise Improvement to sort of +differentiate between selection and + + align:start position:0% +differentiate between selection and + + + align:start position:0% +differentiate between selection and +moral hazard that's a very general + + align:start position:0% +moral hazard that's a very general + + + align:start position:0% +moral hazard that's a very general +purpose experimental design it's also I + + align:start position:0% +purpose experimental design it's also I + + + align:start position:0% +purpose experimental design it's also I +think a nice example of how an + + align:start position:0% +think a nice example of how an + + + align:start position:0% +think a nice example of how an +experiment can let you do something that + + align:start position:0% +experiment can let you do something that + + + align:start position:0% +experiment can let you do something that +you could not do in the real world + + align:start position:0% +you could not do in the real world + + + align:start position:0% +you could not do in the real world +right it's only because you have this + + align:start position:0% +right it's only because you have this + + + align:start position:0% +right it's only because you have this +ability to sort of manipulate and sort + + align:start position:0% +ability to sort of manipulate and sort + + + align:start position:0% +ability to sort of manipulate and sort +of expose change people's um yeah maybe + + align:start position:0% +of expose change people's um yeah maybe + + + align:start position:0% +of expose change people's um yeah maybe +you could find a natural experiment sort + + align:start position:0% +you could find a natural experiment sort + + + align:start position:0% +you could find a natural experiment sort +of mimic this but like uh in general + + align:start position:0% +of mimic this but like uh in general + + + align:start position:0% +of mimic this but like uh in general +would be sort of hard to do + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +okay is this clear + + align:start position:0% +okay is this clear + + + align:start position:0% +okay is this clear +yeah one cool question is in the in the + + align:start position:0% +yeah one cool question is in the in the + + + align:start position:0% +yeah one cool question is in the in the +design of their View + + align:start position:0% +design of their View + + + align:start position:0% +design of their View +the information yeah the the type of + + align:start position:0% +the information yeah the the type of + + + align:start position:0% +the information yeah the the type of +selection is some like + + align:start position:0% +selection is some like + + + align:start position:0% +selection is some like +bundle of the + + align:start position:0% +bundle of the + + + align:start position:0% +bundle of the +selection on like my type but also + + align:start position:0% +selection on like my type but also + + + align:start position:0% +selection on like my type but also +potentially + + align:start position:0% +potentially + + + align:start position:0% +potentially +selection on + + align:start position:0% +selection on + + + align:start position:0% +selection on +like selection on moral hazard basically + + align:start position:0% +like selection on moral hazard basically + + + align:start position:0% +like selection on moral hazard basically +right like you wouldn't be able to + + align:start position:0% +right like you wouldn't be able to + + + align:start position:0% +right like you wouldn't be able to +distinguish that just from from this + + align:start position:0% +distinguish that just from from this + + + align:start position:0% +distinguish that just from from this +like 202 uh sorry say again what you + + align:start position:0% +like 202 uh sorry say again what you + + + align:start position:0% +like 202 uh sorry say again what you +mean so like if with adverse selection + + align:start position:0% +mean so like if with adverse selection + + + align:start position:0% +mean so like if with adverse selection +there's both you know I'm selecting I'm + + align:start position:0% +there's both you know I'm selecting I'm + + + align:start position:0% +there's both you know I'm selecting I'm +like P but also I know how I would + + align:start position:0% +like P but also I know how I would + + + align:start position:0% +like P but also I know how I would +respond + + align:start position:0% +respond + + + align:start position:0% +respond +um + + align:start position:0% +um + + + align:start position:0% +um +like there's also I guess this this + + align:start position:0% +like there's also I guess this this + + + align:start position:0% +like there's also I guess this this +notion that + + align:start position:0% +notion that + + + align:start position:0% +notion that +you can select on how you would respond + + align:start position:0% +you can select on how you would respond + + + align:start position:0% +you can select on how you would respond +to different incentives + + align:start position:0% +to different incentives + + + align:start position:0% +to different incentives +oh I think I understand so you're saying + + align:start position:0% +oh I think I understand so you're saying + + + align:start position:0% +oh I think I understand so you're saying +there's right it's a general in a more + + align:start position:0% +there's right it's a general in a more + + + align:start position:0% +there's right it's a general in a more +General model in addition to sort of + + align:start position:0% +General model in addition to sort of + + + align:start position:0% +General model in addition to sort of +like selecting on just having like fixed + + align:start position:0% +like selecting on just having like fixed + + + align:start position:0% +like selecting on just having like fixed +P's or sort of totally endogenous Peas I + + align:start position:0% +P's or sort of totally endogenous Peas I + + + align:start position:0% +P's or sort of totally endogenous Peas I +have another thing which I some people + + align:start position:0% +have another thing which I some people + + + align:start position:0% +have another thing which I some people +have different P bars right yeah exactly + + align:start position:0% +have different P bars right yeah exactly + + + align:start position:0% +have different P bars right yeah exactly +yeah so it's like not not anything that + + align:start position:0% +yeah so it's like not not anything that + + + align:start position:0% +yeah so it's like not not anything that +we've discussed previously but there's + + align:start position:0% +we've discussed previously but there's + + + align:start position:0% +we've discussed previously but there's +this other dimension that you could + + align:start position:0% +this other dimension that you could + + + align:start position:0% +this other dimension that you could +model that isn't captured by the + + align:start position:0% +model that isn't captured by the + + + align:start position:0% +model that isn't captured by the +comparisons so so what's gonna so okay + + align:start position:0% +comparisons so so what's gonna so okay + + + align:start position:0% +comparisons so so what's gonna so okay +let's think that through together so how + + align:start position:0% +let's think that through together so how + + + align:start position:0% +let's think that through together so how +what's gonna be picked up here so if we + + align:start position:0% +what's gonna be picked up here so if we + + + align:start position:0% +what's gonna be picked up here so if we +have so so you're saying we have three + + align:start position:0% +have so so you're saying we have three + + + align:start position:0% +have so so you're saying we have three +dimensions we have sort of heterogeneity + + align:start position:0% +dimensions we have sort of heterogeneity + + + align:start position:0% +dimensions we have sort of heterogeneity +and p x anti kind of your your choice of + + align:start position:0% +and p x anti kind of your your choice of + + + align:start position:0% +and p x anti kind of your your choice of +p and then you have this other thing + + align:start position:0% +p and then you have this other thing + + + align:start position:0% +p and then you have this other thing +with people may differ in their sort of + + align:start position:0% +with people may differ in their sort of + + + align:start position:0% +with people may differ in their sort of +P of our function so uh + + align:start position:0% +P of our function so uh + + + align:start position:0% +P of our function so uh +so how does that affect your + + align:start position:0% +so how does that affect your + + + align:start position:0% +so how does that affect your +interpretation here + + align:start position:0% +interpretation here + + + align:start position:0% +interpretation here +I I guess what my interpretation is that + + align:start position:0% +I I guess what my interpretation is that + + + align:start position:0% +I I guess what my interpretation is that +the hidden information effect that + + align:start position:0% +the hidden information effect that + + + align:start position:0% +the hidden information effect that +they're picking up is something like + + align:start position:0% +they're picking up is something like + + + align:start position:0% +they're picking up is something like +composite of the two different types of + + align:start position:0% +composite of the two different types of + + + align:start position:0% +composite of the two different types of +selection + + align:start position:0% +selection + + + align:start position:0% +selection +that is both selection types and + + align:start position:0% +that is both selection types and + + + align:start position:0% +that is both selection types and +selection on slopes basically + + align:start position:0% + + + + align:start position:0% + +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +it's clearly the case yes I think that's + + align:start position:0% +it's clearly the case yes I think that's + + + align:start position:0% +it's clearly the case yes I think that's +right so it's clearly the case if we + + align:start position:0% +right so it's clearly the case if we + + + align:start position:0% +right so it's clearly the case if we +compare the hot these people with the + + align:start position:0% +compare the hot these people with the + + + align:start position:0% +compare the hot these people with the +same selection something like the lower + + align:start position:0% +same selection something like the lower + + + align:start position:0% +same selection something like the lower +interest rates that's a pure moral + + align:start position:0% +interest rates that's a pure moral + + + align:start position:0% +interest rates that's a pure moral +hazard effect right and I and if they + + align:start position:0% +hazard effect right and I and if they + + + align:start position:0% +hazard effect right and I and if they +compare this versus this then uh + + align:start position:0% + + + + align:start position:0% + +yeah you're right I mean yes we don't + + align:start position:0% +yeah you're right I mean yes we don't + + + align:start position:0% +yeah you're right I mean yes we don't +know we don't know what women they're + + align:start position:0% +know we don't know what women they're + + + align:start position:0% +know we don't know what women they're +experiencing the same PX post also so + + align:start position:0% +experiencing the same PX post also so + + + align:start position:0% +experiencing the same PX post also so +what what we're getting is like in my + + align:start position:0% +what what we're getting is like in my + + + align:start position:0% +what what we're getting is like in my +example of we're both lowered to 10 + + align:start position:0% +example of we're both lowered to 10 + + + align:start position:0% +example of we're both lowered to 10 +we're getting kind of group number one + + align:start position:0% +we're getting kind of group number one + + + align:start position:0% +we're getting kind of group number one +experience at 10 and group number two + + align:start position:0% +experience at 10 and group number two + + + align:start position:0% +experience at 10 and group number two +experience ten percent so you're right + + align:start position:0% +experience ten percent so you're right + + + align:start position:0% +experience ten percent so you're right +we don't know is that because that like + + align:start position:0% +we don't know is that because that like + + + align:start position:0% +we don't know is that because that like +what was the slope of their moral of + + align:start position:0% +what was the slope of their moral of + + + align:start position:0% +what was the slope of their moral of +their selection thing we're just + + align:start position:0% +their selection thing we're just + + + align:start position:0% +their selection thing we're just +evaluate but we are at least evaluating + + align:start position:0% +evaluate but we are at least evaluating + + + align:start position:0% +evaluate but we are at least evaluating +it at the same point yeah so it's still + + align:start position:0% +it at the same point yeah so it's still + + + align:start position:0% +it at the same point yeah so it's still +clearly sort of picking up kind of I + + align:start position:0% +clearly sort of picking up kind of I + + + align:start position:0% +clearly sort of picking up kind of I +think an after selection point but here + + align:start position:0% +think an after selection point but here + + + align:start position:0% +think an after selection point but here +but yes exactly whether the average + + align:start position:0% +but yes exactly whether the average + + + align:start position:0% +but yes exactly whether the average +section is like a level or a slope and a + + align:start position:0% +section is like a level or a slope and a + + + align:start position:0% +section is like a level or a slope and a +level like we are at least evaluating at + + align:start position:0% +level like we are at least evaluating at + + + align:start position:0% +level like we are at least evaluating at +the same point + + align:start position:0% + + + + align:start position:0% + +um one thing I'll say is that actually + + align:start position:0% +um one thing I'll say is that actually + + + align:start position:0% +um one thing I'll say is that actually +if you read the details of this paper + + align:start position:0% +if you read the details of this paper + + + align:start position:0% +if you read the details of this paper +it's not the like + + align:start position:0% +it's not the like + + + align:start position:0% +it's not the like +perfect perfect setting to sort of map + + align:start position:0% +perfect perfect setting to sort of map + + + align:start position:0% +perfect perfect setting to sort of map +into the model it's like consumer credit + + align:start position:0% +into the model it's like consumer credit + + + align:start position:0% +into the model it's like consumer credit +and so like it's it's a little harder to + + align:start position:0% +and so like it's it's a little harder to + + + align:start position:0% +and so like it's it's a little harder to +think about it I mean of course we can + + align:start position:0% +think about it I mean of course we can + + + align:start position:0% +think about it I mean of course we can +think about the same issues in consumer + + align:start position:0% +think about the same issues in consumer + + + align:start position:0% +think about the same issues in consumer +credit as as in firm credit but I don't + + align:start position:0% +credit as as in firm credit but I don't + + + align:start position:0% +credit as as in firm credit but I don't +think it necessarily Maps as one of that + + align:start position:0% +think it necessarily Maps as one of that + + + align:start position:0% +think it necessarily Maps as one of that +model that we had in mind kind of as + + align:start position:0% +model that we had in mind kind of as + + + align:start position:0% +model that we had in mind kind of as +nicely as maybe it could but I think + + align:start position:0% +nicely as maybe it could but I think + + + align:start position:0% +nicely as maybe it could but I think +this paper was really Innovative for + + align:start position:0% +this paper was really Innovative for + + + align:start position:0% +this paper was really Innovative for +um creating this kind of general purpose + + align:start position:0% +um creating this kind of general purpose + + + align:start position:0% +um creating this kind of general purpose +I mean the better there may be another + + align:start position:0% +I mean the better there may be another + + + align:start position:0% +I mean the better there may be another +paper that like it this is the one that + + align:start position:0% +paper that like it this is the one that + + + align:start position:0% +paper that like it this is the one that +I certainly know of it at first there + + align:start position:0% +I certainly know of it at first there + + + align:start position:0% +I certainly know of it at first there +would be the other beforehand but + + align:start position:0% +would be the other beforehand but + + + align:start position:0% +would be the other beforehand but +certainly it certainly um you know uh + + align:start position:0% + + + + align:start position:0% + +this design that they use here I think + + align:start position:0% +this design that they use here I think + + + align:start position:0% +this design that they use here I think +became kind of very popular and I think + + align:start position:0% +became kind of very popular and I think + + + align:start position:0% +became kind of very popular and I think +people have used it in a wide variety of + + align:start position:0% +people have used it in a wide variety of + + + align:start position:0% +people have used it in a wide variety of +settings okay + + align:start position:0% +settings okay + + + align:start position:0% +settings okay +um so you know in the end you know I + + align:start position:0% +um so you know in the end you know I + + + align:start position:0% +um so you know in the end you know I +actually think the the results are not + + align:start position:0% +actually think the the results are not + + + align:start position:0% +actually think the the results are not +super duper strong + + align:start position:0% +super duper strong + + + align:start position:0% +super duper strong +um they find a little bit of evidence of + + align:start position:0% +um they find a little bit of evidence of + + + align:start position:0% +um they find a little bit of evidence of +sort of the contract rate + + align:start position:0% +sort of the contract rate + + + align:start position:0% +sort of the contract rate +um you know uh not a huge amount on the + + align:start position:0% +um you know uh not a huge amount on the + + + align:start position:0% +um you know uh not a huge amount on the +offer rate but you know as I said I want + + align:start position:0% +offer rate but you know as I said I want + + + align:start position:0% +offer rate but you know as I said I want +to focus on this paper less kind of for + + align:start position:0% +to focus on this paper less kind of for + + + align:start position:0% +to focus on this paper less kind of for +the particular results they have but + + align:start position:0% +the particular results they have but + + + align:start position:0% +the particular results they have but +more for that design of how you might + + align:start position:0% +more for that design of how you might + + + align:start position:0% +more for that design of how you might +think about sort of distinguishing + + align:start position:0% +think about sort of distinguishing + + + align:start position:0% +think about sort of distinguishing +booking average selection of all hazard + + align:start position:0% +booking average selection of all hazard + + + align:start position:0% +booking average selection of all hazard +okay so I'll stop here and then I will + + align:start position:0% +okay so I'll stop here and then I will + + + align:start position:0% +okay so I'll stop here and then I will +talk about microfinance including kind + + align:start position:0% +talk about microfinance including kind + + + align:start position:0% +talk about microfinance including kind +of the reading you guys did on Wednesday \ No newline at end of file diff --git a/7T30ihcHFmk.txt b/7T30ihcHFmk.txt new file mode 100644 index 0000000000000000000000000000000000000000..a357fc6ad343d8f44039ab5231ae12c3220e502d --- /dev/null +++ b/7T30ihcHFmk.txt @@ -0,0 +1,105 @@ +Hi. This is Curt from the Publication Team +at MIT OpenCourseWare. + +I'd like to show you a class called SP.722 +D-Lab: Design. It's one of several classes + +we've published from MIT's D-Lab program, +where students get to develop solutions for + +some very fundamental human needs like clean +water, healthy food, health care, and earning + +a living. Using "low-tech" materials – +like bicycle parts and 2-liter soda bottles + +– the students experience the challenges +and benefits of making technology radically + +affordable, easy to manufacture, and sustainable. + +I worked with instructor Amy Smith on this +class. She’s the founder of the D-Lab + +program. + +The class is a mix of classroom instruction +and hands-on project work. Here we see the + +final prototype for one project, a pedal-powered +washing machine. + +Overall, five project teams worked with community +partners in Brazil, Guatemala Lesotho, and + +Zambia, and mentors around MIT. The Assignments +page shows how they got it all done in just + +13 weeks: from a problem statement, throug +stakeholder analysis, design specifications, + +a spring break visit to the partner country, +design reviews with panels of experts, and + +finally building the prototype. + +Here we've posted milestone materials from +each team, especially videos of the review + +panels, to illustrate the D-Lab design process. +Let's look at the washing machine project. + +In developing countries, millions of people +have to wash clothes by hand. It's a chore + +that can take an entire day, and definitely +takes a lot of energy. It's an example of + +how uncompensated labor limits opportunities +for educational and economic development, + +especially for women. + +Bicycle technology, being relatively low cost, +and good for local manufacture and maintenance, + +might help. So, working with two bicycle-based +NGOs - Maya Pedal in Guatemala and Bikes Not + +Bombs in Boston – these three students +designed and built a prototype pedal-powered + +washing machine. + +And after the term ended, they returned to +Guatemala for more testing and refinements. + +In addition to the pleasure of building truly +useful stuff, students attended twice-weekly + +lectures on development, design, and case +studies. I took notes in many classes, plus + +photos of in-class activites. They're all +posted here. + +For instance, here are some notes for a hands-on +lab on water testing, complete with photos. + +The water testing kit is built with a baby +bottle and is another example of the D-Lab + +approach. + +By the way, OCW’s site for D-Lab: Design +can be downloaded for use offline. The link + +and instructions are right here. + +You can explore more courses like this one +at ocw.mit.edu, or get email updates from + +OCW by subscribing to our monthly newsletter. +We hope you’ll help us keep going and + +growing by making a donation at ocw.mit.edu/donate. \ No newline at end of file diff --git a/8TPJUR378f0.txt b/8TPJUR378f0.txt new file mode 100644 index 0000000000000000000000000000000000000000..0f407c9f5506a01d4a022c530eb3b591a251b2a5 --- /dev/null +++ b/8TPJUR378f0.txt @@ -0,0 +1,803 @@ +align:start position:0% + +my name is Andrew Grant I'm the + + align:start position:0% +my name is Andrew Grant I'm the + + + align:start position:0% +my name is Andrew Grant I'm the +technical director for the MIT game lab + + align:start position:0% +technical director for the MIT game lab + + + align:start position:0% +technical director for the MIT game lab +and sometime lecture I've been playing + + align:start position:0% +and sometime lecture I've been playing + + + align:start position:0% +and sometime lecture I've been playing +games pretty much all my life that's + + align:start position:0% +games pretty much all my life that's + + + align:start position:0% +games pretty much all my life that's +what my family does when they get + + align:start position:0% +what my family does when they get + + + align:start position:0% +what my family does when they get +together uh and then when computer + + align:start position:0% +together uh and then when computer + + + align:start position:0% +together uh and then when computer +started doing it too that's what I did + + align:start position:0% +started doing it too that's what I did + + + align:start position:0% +started doing it too that's what I did +with computers um I went to the games + + align:start position:0% +with computers um I went to the games + + + align:start position:0% +with computers um I went to the games +industry in 1994 worked for Looking + + align:start position:0% +industry in 1994 worked for Looking + + + align:start position:0% +industry in 1994 worked for Looking +Glass Technologies and then moved out to + + align:start position:0% +Glass Technologies and then moved out to + + + align:start position:0% +Glass Technologies and then moved out to +California to work for dreamix + + align:start position:0% +California to work for dreamix + + + align:start position:0% +California to work for dreamix +interactive and actually all told that + + align:start position:0% +interactive and actually all told that + + + align:start position:0% +interactive and actually all told that +didn't last terribly long I burned out + + align:start position:0% +didn't last terribly long I burned out + + + align:start position:0% +didn't last terribly long I burned out +after about five or six years in the G + + align:start position:0% +after about five or six years in the G + + + align:start position:0% +after about five or six years in the G +industry and went to be a solo + + align:start position:0% +industry and went to be a solo + + + align:start position:0% +industry and went to be a solo +programmer doing random contracts and + + align:start position:0% +programmer doing random contracts and + + + align:start position:0% +programmer doing random contracts and +work for hire kind of like a a + + align:start position:0% +work for hire kind of like a a + + + align:start position:0% +work for hire kind of like a a +gunslinger from the wild west for a + + align:start position:0% +gunslinger from the wild west for a + + + align:start position:0% +gunslinger from the wild west for a +while but no matter what I do I keep + + align:start position:0% +while but no matter what I do I keep + + + align:start position:0% +while but no matter what I do I keep +getting dragged back into games industry + + align:start position:0% +getting dragged back into games industry + + + align:start position:0% +getting dragged back into games industry +I like making games it's what I want to + + align:start position:0% + + + + align:start position:0% + +do right now I'm playing a lot of things + + align:start position:0% +do right now I'm playing a lot of things + + + align:start position:0% +do right now I'm playing a lot of things +um I'm playing a lot of uh the The + + align:start position:0% +um I'm playing a lot of uh the The + + + align:start position:0% +um I'm playing a lot of uh the The +Cooperative Lego games with my son he's + + align:start position:0% +Cooperative Lego games with my son he's + + + align:start position:0% +Cooperative Lego games with my son he's +four and we're playing through Lego + + align:start position:0% +four and we're playing through Lego + + + align:start position:0% +four and we're playing through Lego +Batman and that sort of thing and + + align:start position:0% +Batman and that sort of thing and + + + align:start position:0% +Batman and that sort of thing and +recently started Lego Lord of the Rings + + align:start position:0% +recently started Lego Lord of the Rings + + + align:start position:0% +recently started Lego Lord of the Rings +which has been a bit of a challenge for + + align:start position:0% +which has been a bit of a challenge for + + + align:start position:0% +which has been a bit of a challenge for +it's a much darker Lego game oddly + + align:start position:0% +it's a much darker Lego game oddly + + + align:start position:0% +it's a much darker Lego game oddly +enough and so he'll say things like is + + align:start position:0% +enough and so he'll say things like is + + + align:start position:0% +enough and so he'll say things like is +Bor Amir a bad guy and I'm like well + + align:start position:0% +Bor Amir a bad guy and I'm like well + + + align:start position:0% +Bor Amir a bad guy and I'm like well +that's hard let me explain to you your + + align:start position:0% +that's hard let me explain to you your + + + align:start position:0% +that's hard let me explain to you your +four um he's he's confused is Gollum a + + align:start position:0% +four um he's he's confused is Gollum a + + + align:start position:0% +four um he's he's confused is Gollum a +bad guy no he's he's definitely a bad + + align:start position:0% +bad guy no he's he's definitely a bad + + + align:start position:0% +bad guy no he's he's definitely a bad +guy yeah but why is he going with the + + align:start position:0% +guy yeah but why is he going with the + + + align:start position:0% +guy yeah but why is he going with the +hobbits oh right he's kind of a good guy + + align:start position:0% +hobbits oh right he's kind of a good guy + + + align:start position:0% +hobbits oh right he's kind of a good guy +too I don't know anyway it's a + + align:start position:0% +too I don't know anyway it's a + + + align:start position:0% +too I don't know anyway it's a +complicated story for him for a + + align:start position:0% +complicated story for him for a + + + align:start position:0% +complicated story for him for a +four-year-old and it's kind of + + align:start position:0% + + + + align:start position:0% + +fun I'm working on a number of things + + align:start position:0% +fun I'm working on a number of things + + + align:start position:0% +fun I'm working on a number of things +right now I'm working on a a side + + align:start position:0% +right now I'm working on a a side + + + align:start position:0% +right now I'm working on a a side +project with the astronomy department on + + align:start position:0% +project with the astronomy department on + + + align:start position:0% +project with the astronomy department on +some software for them I'm working on an + + align:start position:0% +some software for them I'm working on an + + + align:start position:0% +some software for them I'm working on an +iOS Port of a game called yomi and I'm + + align:start position:0% +iOS Port of a game called yomi and I'm + + + align:start position:0% +iOS Port of a game called yomi and I'm +also working on a fractal tagram + + align:start position:0% +also working on a fractal tagram + + + align:start position:0% +also working on a fractal tagram +independent game and with Rick also at + + align:start position:0% +independent game and with Rick also at + + + align:start position:0% +independent game and with Rick also at +the lab I'm working on a massively + + align:start position:0% +the lab I'm working on a massively + + + align:start position:0% +the lab I'm working on a massively +cooperative strategy + + align:start position:0% + + + + align:start position:0% + +game this semester we're trying a couple + + align:start position:0% +game this semester we're trying a couple + + + align:start position:0% +game this semester we're trying a couple +new game engines we always try a couple + + align:start position:0% +new game engines we always try a couple + + + align:start position:0% +new game engines we always try a couple +new game engines but I always like to + + align:start position:0% +new game engines but I always like to + + + align:start position:0% +new game engines but I always like to +get let the students sink their teeth + + align:start position:0% +get let the students sink their teeth + + + align:start position:0% +get let the students sink their teeth +into a couple of them and then come back + + align:start position:0% +into a couple of them and then come back + + + align:start position:0% +into a couple of them and then come back +and tell us what they found out there's + + align:start position:0% +and tell us what they found out there's + + + align:start position:0% +and tell us what they found out there's +a to which I can do that myself but it + + align:start position:0% +a to which I can do that myself but it + + + align:start position:0% +a to which I can do that myself but it +really is more useful I think to get + + align:start position:0% +really is more useful I think to get + + + align:start position:0% +really is more useful I think to get +some people with fresh eyes to come in + + align:start position:0% +some people with fresh eyes to come in + + + align:start position:0% +some people with fresh eyes to come in +and try them out usually they come back + + align:start position:0% +and try them out usually they come back + + + align:start position:0% +and try them out usually they come back +and tell us the old standby the ones + + align:start position:0% +and tell us the old standby the ones + + + align:start position:0% +and tell us the old standby the ones +they want to go with we usually end up + + align:start position:0% +they want to go with we usually end up + + + align:start position:0% +they want to go with we usually end up +going with unity and flixel as our + + align:start position:0% +going with unity and flixel as our + + + align:start position:0% +going with unity and flixel as our +reliable ones but this year we're trying + + align:start position:0% +reliable ones but this year we're trying + + + align:start position:0% +reliable ones but this year we're trying +out a new language hacks which also has + + align:start position:0% +out a new language hacks which also has + + + align:start position:0% +out a new language hacks which also has +a flexible implementation and we're also + + align:start position:0% +a flexible implementation and we're also + + + align:start position:0% +a flexible implementation and we're also +trying a thing called phaser which is + + align:start position:0% +trying a thing called phaser which is + + + align:start position:0% +trying a thing called phaser which is +used by the education arcade and so we + + align:start position:0% +used by the education arcade and so we + + + align:start position:0% +used by the education arcade and so we +really want to get our teeth into that + + align:start position:0% +really want to get our teeth into that + + + align:start position:0% +really want to get our teeth into that +and see how we like + + align:start position:0% + + + + align:start position:0% + +it I've always been interested in + + align:start position:0% +it I've always been interested in + + + align:start position:0% +it I've always been interested in +artificial intelligence when I have a + + align:start position:0% +artificial intelligence when I have a + + + align:start position:0% +artificial intelligence when I have a +chance to sort of sit down and play with + + align:start position:0% +chance to sort of sit down and play with + + + align:start position:0% +chance to sort of sit down and play with +stuff I want to make my computer figure + + align:start position:0% +stuff I want to make my computer figure + + + align:start position:0% +stuff I want to make my computer figure +out how to do things that it couldn't do + + align:start position:0% +out how to do things that it couldn't do + + + align:start position:0% +out how to do things that it couldn't do +before it's a lot of + + align:start position:0% + + + + align:start position:0% + +fun we're in a really interesting place + + align:start position:0% +fun we're in a really interesting place + + + align:start position:0% +fun we're in a really interesting place +I think in games right now uh it used to + + align:start position:0% +I think in games right now uh it used to + + + align:start position:0% +I think in games right now uh it used to +be the case that when I first started + + align:start position:0% +be the case that when I first started + + + align:start position:0% +be the case that when I first started +playing that there would be two or three + + align:start position:0% +playing that there would be two or three + + + align:start position:0% +playing that there would be two or three +interesting games a year and you could + + align:start position:0% +interesting games a year and you could + + + align:start position:0% +interesting games a year and you could +play them and then you waited very + + align:start position:0% +play them and then you waited very + + + align:start position:0% +play them and then you waited very +impatiently for the next ones to come + + align:start position:0% +impatiently for the next ones to come + + + align:start position:0% +impatiently for the next ones to come +out and now we're in a place where you + + align:start position:0% +out and now we're in a place where you + + + align:start position:0% +out and now we're in a place where you +cannot play all the interesting games in + + align:start position:0% +cannot play all the interesting games in + + + align:start position:0% +cannot play all the interesting games in +fact I can't even play all the really + + align:start position:0% +fact I can't even play all the really + + + align:start position:0% +fact I can't even play all the really +interesting games there's just too many + + align:start position:0% +interesting games there's just too many + + + align:start position:0% +interesting games there's just too many +of them but in spite of that I still + + align:start position:0% +of them but in spite of that I still + + + align:start position:0% +of them but in spite of that I still +kind of want more um one of the neat + + align:start position:0% +kind of want more um one of the neat + + + align:start position:0% +kind of want more um one of the neat +things about games is there's a whole + + align:start position:0% +things about games is there's a whole + + + align:start position:0% +things about games is there's a whole +bunch of different games you can make + + align:start position:0% +bunch of different games you can make + + + align:start position:0% +bunch of different games you can make +and I feel like a lot of times we get + + align:start position:0% +and I feel like a lot of times we get + + + align:start position:0% +and I feel like a lot of times we get +stuck on a couple types we don't + + align:start position:0% +stuck on a couple types we don't + + + align:start position:0% +stuck on a couple types we don't +necessarily need another first person + + align:start position:0% +necessarily need another first person + + + align:start position:0% +necessarily need another first person +shooter that's super realistic Modern + + align:start position:0% +shooter that's super realistic Modern + + + align:start position:0% +shooter that's super realistic Modern +Combat there's some good games there + + align:start position:0% +Combat there's some good games there + + + align:start position:0% +Combat there's some good games there +don't get me wrong but we don't need + + align:start position:0% +don't get me wrong but we don't need + + + align:start position:0% +don't get me wrong but we don't need +five of them a year but what I really + + align:start position:0% +five of them a year but what I really + + + align:start position:0% +five of them a year but what I really +looking forward to is seeing all the + + align:start position:0% +looking forward to is seeing all the + + + align:start position:0% +looking forward to is seeing all the +weird stuff the stuff that no one + + align:start position:0% +weird stuff the stuff that no one + + + align:start position:0% +weird stuff the stuff that no one +expects the the new crazy things and the + + align:start position:0% +expects the the new crazy things and the + + + align:start position:0% +expects the the new crazy things and the +more games get made the more crazy stuff + + align:start position:0% +more games get made the more crazy stuff + + + align:start position:0% +more games get made the more crazy stuff +gets made and I love that stuff \ No newline at end of file diff --git a/8autJMHEzBU.txt b/8autJMHEzBU.txt new file mode 100644 index 0000000000000000000000000000000000000000..d782b4357bb42aa05c4980a875112a4a7d3805d5 --- /dev/null +++ b/8autJMHEzBU.txt @@ -0,0 +1,14171 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a creative commons license your support + + align:start position:0% +a creative commons license your support + + + align:start position:0% +a creative commons license your support +will help mit opencourseware continue to + + align:start position:0% +will help mit opencourseware continue to + + + align:start position:0% +will help mit opencourseware continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of mit courses + + align:start position:0% +materials from hundreds of mit courses + + + align:start position:0% +materials from hundreds of mit courses +visit mit opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so let's start with the uh thermal air + + align:start position:0% +so let's start with the uh thermal air + + + align:start position:0% +so let's start with the uh thermal air +camera + + align:start position:0% +camera + + + align:start position:0% +camera +and you can see it has a very strange + + align:start position:0% +and you can see it has a very strange + + + align:start position:0% +and you can see it has a very strange +properties + + align:start position:0% + + + + align:start position:0% + +who's who are we looking at here that's + + align:start position:0% +who's who are we looking at here that's + + + align:start position:0% +who's who are we looking at here that's +you + + align:start position:0% + + + + align:start position:0% + +and then as it turns on it's uh lighter + + align:start position:0% +and then as it turns on it's uh lighter + + + align:start position:0% +and then as it turns on it's uh lighter +it goes in an automatic + + align:start position:0% +it goes in an automatic + + + align:start position:0% +it goes in an automatic +automatic game mode i guess + + align:start position:0% +automatic game mode i guess + + + align:start position:0% +automatic game mode i guess +and this image gets very dark + + align:start position:0% + + + + align:start position:0% + +and uh + + align:start position:0% +and uh + + + align:start position:0% +and uh +who's in the picture can you wave + + align:start position:0% +who's in the picture can you wave + + + align:start position:0% +who's in the picture can you wave +oh that's sad + + align:start position:0% +oh that's sad + + + align:start position:0% +oh that's sad +excellent and i could recognize you in + + align:start position:0% +excellent and i could recognize you in + + + align:start position:0% +excellent and i could recognize you in +thermal layer + + align:start position:0% +thermal layer + + + align:start position:0% +thermal layer +uh and if you just put a cold finger on + + align:start position:0% +uh and if you just put a cold finger on + + + align:start position:0% +uh and if you just put a cold finger on +here on your cheek + + align:start position:0% + + + + align:start position:0% + +and pick it up yeah you can see the mark + + align:start position:0% +and pick it up yeah you can see the mark + + + align:start position:0% +and pick it up yeah you can see the mark +things that are completely transparent + + align:start position:0% +things that are completely transparent + + + align:start position:0% +things that are completely transparent +in + + align:start position:0% +in + + + align:start position:0% +in +in visible are actually completely + + align:start position:0% +in visible are actually completely + + + align:start position:0% +in visible are actually completely +opaque + + align:start position:0% +opaque + + + align:start position:0% +opaque +in + + align:start position:0% +in + + + align:start position:0% +in +these focuses + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +that's completely opaque actually if you + + align:start position:0% +that's completely opaque actually if you + + + align:start position:0% +that's completely opaque actually if you +just put your glasses down + + align:start position:0% +just put your glasses down + + + align:start position:0% +just put your glasses down +as well + + align:start position:0% +as well + + + align:start position:0% +as well +you won't see yeah what others will say + + align:start position:0% +you won't see yeah what others will say + + + align:start position:0% +you won't see yeah what others will say +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so they're completely opaque in uh these + + align:start position:0% +so they're completely opaque in uh these + + + align:start position:0% +so they're completely opaque in uh these +are actually glass lenses not plastic + + align:start position:0% +are actually glass lenses not plastic + + + align:start position:0% +are actually glass lenses not plastic +ones there might be some difference okay + + align:start position:0% +ones there might be some difference okay + + + align:start position:0% +ones there might be some difference okay +i don't know + + align:start position:0% +i don't know + + + align:start position:0% +i don't know +um so it's really looking at + + align:start position:0% +um so it's really looking at + + + align:start position:0% +um so it's really looking at +looking at uh + + align:start position:0% +looking at uh + + + align:start position:0% +looking at uh +about 8 000 + + align:start position:0% +about 8 000 + + + align:start position:0% +about 8 000 +nanometer which fortunately is also the + + align:start position:0% +nanometer which fortunately is also the + + + align:start position:0% +nanometer which fortunately is also the +wavelength in which you know the human + + align:start position:0% +wavelength in which you know the human + + + align:start position:0% +wavelength in which you know the human +body's + + align:start position:0% +body's + + + align:start position:0% +body's +the black body radiation of a human body + + align:start position:0% +the black body radiation of a human body + + + align:start position:0% +the black body radiation of a human body +is + + align:start position:0% +is + + + align:start position:0% +is +peaks + + align:start position:0% + + + + align:start position:0% + +so you can do some amazing things with + + align:start position:0% +so you can do some amazing things with + + + align:start position:0% +so you can do some amazing things with +this + + align:start position:0% +this + + + align:start position:0% +this +chrysler and bmw + + align:start position:0% +chrysler and bmw + + + align:start position:0% +chrysler and bmw +are thinking about or maybe already put + + align:start position:0% +are thinking about or maybe already put + + + align:start position:0% +are thinking about or maybe already put +them in + + align:start position:0% +them in + + + align:start position:0% +them in +in + + align:start position:0% + + + + align:start position:0% + +in automobiles so that you can see + + align:start position:0% +in automobiles so that you can see + + + align:start position:0% +in automobiles so that you can see +things very far away so one benefit of + + align:start position:0% +things very far away so one benefit of + + + align:start position:0% +things very far away so one benefit of +this as you can see is even if you turn + + align:start position:0% +this as you can see is even if you turn + + + align:start position:0% +this as you can see is even if you turn +off the room light + + align:start position:0% +off the room light + + + align:start position:0% +off the room light +the intensity will not change + + align:start position:0% +the intensity will not change + + + align:start position:0% +the intensity will not change +so somebody wants to take the + + align:start position:0% + + + + align:start position:0% + +it's completely independent of the room + + align:start position:0% +it's completely independent of the room + + + align:start position:0% +it's completely independent of the room +lighting + + align:start position:0% +lighting + + + align:start position:0% +lighting +right + + align:start position:0% +right + + + align:start position:0% +right +so because it's it's not looking at the + + align:start position:0% +so because it's it's not looking at the + + + align:start position:0% +so because it's it's not looking at the +visible spectrum that's being emitted by + + align:start position:0% +visible spectrum that's being emitted by + + + align:start position:0% +visible spectrum that's being emitted by +uh these tube lights + + align:start position:0% +uh these tube lights + + + align:start position:0% +uh these tube lights +uh but it's a function of uh + + align:start position:0% +uh but it's a function of uh + + + align:start position:0% +uh but it's a function of uh +just + + align:start position:0% +just + + + align:start position:0% +just +uh thermal radiation so + + align:start position:0% +uh thermal radiation so + + + align:start position:0% +uh thermal radiation so +at night when you're driving if there + + align:start position:0% +at night when you're driving if there + + + align:start position:0% +at night when you're driving if there +are any uh animals or even intruders + + align:start position:0% +are any uh animals or even intruders + + + align:start position:0% +are any uh animals or even intruders +in your backyard you can detect them + + align:start position:0% +in your backyard you can detect them + + + align:start position:0% +in your backyard you can detect them +with uh with thermal iron there's a lot + + align:start position:0% +with uh with thermal iron there's a lot + + + align:start position:0% +with uh with thermal iron there's a lot +of reflection in the table yes yes + + align:start position:0% +of reflection in the table yes yes + + + align:start position:0% +of reflection in the table yes yes +because remember this is a very large + + align:start position:0% +because remember this is a very large + + + align:start position:0% +because remember this is a very large +wavelength so at that wavelength the + + align:start position:0% +wavelength so at that wavelength the + + + align:start position:0% +wavelength so at that wavelength the +table's roughness disappears and it + + align:start position:0% +table's roughness disappears and it + + + align:start position:0% +table's roughness disappears and it +becomes highly reflective + + align:start position:0% +becomes highly reflective + + + align:start position:0% +becomes highly reflective +um + + align:start position:0% +um + + + align:start position:0% +um +is this + + align:start position:0% +is this + + + align:start position:0% +is this +last time i tried to focus something + + align:start position:0% +last time i tried to focus something + + + align:start position:0% +last time i tried to focus something +went wrong + + align:start position:0% + + + + align:start position:0% + +all the people with glasses look cool + + align:start position:0% + + + + align:start position:0% + +what is the lens made out of + + align:start position:0% +what is the lens made out of + + + align:start position:0% +what is the lens made out of +so that's a good question because uh a + + align:start position:0% +so that's a good question because uh a + + + align:start position:0% +so that's a good question because uh a +typical glass will not + + align:start position:0% +typical glass will not + + + align:start position:0% +typical glass will not +transmit + + align:start position:0% +transmit + + + align:start position:0% +transmit +yeah that's a good demonstration so + + align:start position:0% +yeah that's a good demonstration so + + + align:start position:0% +yeah that's a good demonstration so +a lot of these lenses are made up of + + align:start position:0% +a lot of these lenses are made up of + + + align:start position:0% +a lot of these lenses are made up of +germanium + + align:start position:0% +germanium + + + align:start position:0% +germanium +um and also certain types of plastic + + align:start position:0% +um and also certain types of plastic + + + align:start position:0% +um and also certain types of plastic +can be used for for this but the image + + align:start position:0% +can be used for for this but the image + + + align:start position:0% +can be used for for this but the image +quality is not that great + + align:start position:0% +quality is not that great + + + align:start position:0% +quality is not that great +but germanium is very common + + align:start position:0% +but germanium is very common + + + align:start position:0% +but germanium is very common +does this have different + + align:start position:0% +does this have different + + + align:start position:0% +does this have different +focal characteristics because it's such + + align:start position:0% +focal characteristics because it's such + + + align:start position:0% +focal characteristics because it's such +a long wave such long wavelengths it has + + align:start position:0% +a long wave such long wavelengths it has + + + align:start position:0% +a long wave such long wavelengths it has +uh you mean eight to twelve it's just in + + align:start position:0% +uh you mean eight to twelve it's just in + + + align:start position:0% +uh you mean eight to twelve it's just in +terms of the ratios it's like + + align:start position:0% +terms of the ratios it's like + + + align:start position:0% +terms of the ratios it's like +300 to 400 is the same as 8 microns to + + align:start position:0% +300 to 400 is the same as 8 microns to + + + align:start position:0% +300 to 400 is the same as 8 microns to +12 microns + + align:start position:0% +12 microns + + + align:start position:0% +12 microns +so + + align:start position:0% +so + + + align:start position:0% +so +um so it should be able to focus in + + align:start position:0% +um so it should be able to focus in + + + align:start position:0% +um so it should be able to focus in +majority of that + + align:start position:0% +majority of that + + + align:start position:0% +majority of that +of that band + + align:start position:0% +of that band + + + align:start position:0% +of that band +but um + + align:start position:0% +but um + + + align:start position:0% +but um +because you need a larger lens + + align:start position:0% +because you need a larger lens + + + align:start position:0% +because you need a larger lens +the depth of field is pretty narrow + + align:start position:0% + + + + align:start position:0% + +so you know with this you can build a + + align:start position:0% +so you know with this you can build a + + + align:start position:0% +so you know with this you can build a +glass detector you know if i look + + align:start position:0% +glass detector you know if i look + + + align:start position:0% +glass detector you know if i look +outside the window for + + align:start position:0% +outside the window for + + + align:start position:0% +outside the window for +example it's completely + + align:start position:0% +example it's completely + + + align:start position:0% +example it's completely +opaque + + align:start position:0% +opaque + + + align:start position:0% +opaque +can you wait last person + + align:start position:0% +can you wait last person + + + align:start position:0% +can you wait last person +yeah so it's completely opaque the glass + + align:start position:0% +yeah so it's completely opaque the glass + + + align:start position:0% +yeah so it's completely opaque the glass +so you can you can build a glass + + align:start position:0% +so you can you can build a glass + + + align:start position:0% +so you can you can build a glass +detector you can take a photo with a + + align:start position:0% +detector you can take a photo with a + + + align:start position:0% +detector you can take a photo with a +visible regular camera and take a photo + + align:start position:0% +visible regular camera and take a photo + + + align:start position:0% +visible regular camera and take a photo +of this and if it's opaque in one but + + align:start position:0% +of this and if it's opaque in one but + + + align:start position:0% +of this and if it's opaque in one but +transparent in the other then + + align:start position:0% +transparent in the other then + + + align:start position:0% +transparent in the other then +you know that's class so you can do all + + align:start position:0% +you know that's class so you can do all + + + align:start position:0% +you know that's class so you can do all +kinds of interesting things and again if + + align:start position:0% +kinds of interesting things and again if + + + align:start position:0% +kinds of interesting things and again if +matthias is successful and other + + align:start position:0% +matthias is successful and other + + + align:start position:0% +matthias is successful and other +companies are successful + + align:start position:0% +companies are successful + + + align:start position:0% +companies are successful +not in five years but in six years it + + align:start position:0% +not in five years but in six years it + + + align:start position:0% +not in five years but in six years it +might be here in your cell phone + + align:start position:0% +might be here in your cell phone + + + align:start position:0% +might be here in your cell phone +thanks a lot + + align:start position:0% + + + + align:start position:0% + +all right so let's continue here + + align:start position:0% +all right so let's continue here + + + align:start position:0% +all right so let's continue here +has anybody seen this snake illusion + + align:start position:0% +has anybody seen this snake illusion + + + align:start position:0% +has anybody seen this snake illusion +before yeah + + align:start position:0% +before yeah + + + align:start position:0% +before yeah +do you does everybody see uh + + align:start position:0% +do you does everybody see uh + + + align:start position:0% +do you does everybody see uh +rotating snakes + + align:start position:0% +rotating snakes + + + align:start position:0% +rotating snakes +no no + + align:start position:0% +no no + + + align:start position:0% +no no +i think it'd be like head-on + + align:start position:0% +i think it'd be like head-on + + + align:start position:0% +i think it'd be like head-on +yeah it doesn't work + + align:start position:0% +yeah it doesn't work + + + align:start position:0% +yeah it doesn't work +at an angle + + align:start position:0% +at an angle + + + align:start position:0% +at an angle +all right maybe i can + + align:start position:0% + + + + align:start position:0% + +how many of you can see it how can you + + align:start position:0% +how many of you can see it how can you + + + align:start position:0% +how many of you can see it how can you +how many of you can see + + align:start position:0% +how many of you can see + + + align:start position:0% +how many of you can see +and how many cannot see + + align:start position:0% +and how many cannot see + + + align:start position:0% +and how many cannot see +a rotating pattern + + align:start position:0% + + + + align:start position:0% + +so okay i i've heard this before because + + align:start position:0% +so okay i i've heard this before because + + + align:start position:0% +so okay i i've heard this before because +this is different than those really + + align:start position:0% +this is different than those really + + + align:start position:0% +this is different than those really +annoying you know random dot stereograms + + align:start position:0% +annoying you know random dot stereograms + + + align:start position:0% +annoying you know random dot stereograms +the magic eye that a lot of people have + + align:start position:0% +the magic eye that a lot of people have + + + align:start position:0% +the magic eye that a lot of people have +trouble seeing but this is not based on + + align:start position:0% +trouble seeing but this is not based on + + + align:start position:0% +trouble seeing but this is not based on +the symptoms it's based on a different + + align:start position:0% +the symptoms it's based on a different + + + align:start position:0% +the symptoms it's based on a different +principle it's just looking at + + align:start position:0% +principle it's just looking at + + + align:start position:0% +principle it's just looking at +the + + align:start position:0% +the + + + align:start position:0% +the +the + + align:start position:0% +the + + + align:start position:0% +the +the decay in your in your retina how + + align:start position:0% +the decay in your in your retina how + + + align:start position:0% +the decay in your in your retina how +long it takes for your retina when it's + + align:start position:0% +long it takes for your retina when it's + + + align:start position:0% +long it takes for your retina when it's +doing circuits + + align:start position:0% +doing circuits + + + align:start position:0% +doing circuits +to + + align:start position:0% +to + + + align:start position:0% +to +basically do center surround + + align:start position:0% +basically do center surround + + + align:start position:0% +basically do center surround +subtractions + + align:start position:0% +subtractions + + + align:start position:0% +subtractions +so it's a very different principle so + + align:start position:0% +so it's a very different principle so + + + align:start position:0% +so it's a very different principle so +uh those of you who cannot + + align:start position:0% +uh those of you who cannot + + + align:start position:0% +uh those of you who cannot +perceive motion + + align:start position:0% +perceive motion + + + align:start position:0% +perceive motion +and this one do you also have problems + + align:start position:0% +and this one do you also have problems + + + align:start position:0% +and this one do you also have problems +with magic eye + + align:start position:0% + + + + align:start position:0% + +yeah i think magic is probably a lot how + + align:start position:0% +yeah i think magic is probably a lot how + + + align:start position:0% +yeah i think magic is probably a lot how +many people have problems with magic eye + + align:start position:0% +many people have problems with magic eye + + + align:start position:0% +many people have problems with magic eye +yeah i think that's that's a lot but + + align:start position:0% +yeah i think that's that's a lot but + + + align:start position:0% +yeah i think that's that's a lot but +so it looks like the the the two sets + + align:start position:0% +so it looks like the the the two sets + + + align:start position:0% +so it looks like the the the two sets +don't have any relationships + + align:start position:0% + + + + align:start position:0% + +so how can i take a photo of a seam that + + align:start position:0% +so how can i take a photo of a seam that + + + align:start position:0% +so how can i take a photo of a seam that +has motion print it on a piece of paper + + align:start position:0% +has motion print it on a piece of paper + + + align:start position:0% +has motion print it on a piece of paper +and create an illusion of motion + + align:start position:0% + + + + align:start position:0% + +that's a research problem for your + + align:start position:0% +that's a research problem for your + + + align:start position:0% +that's a research problem for your +project + + align:start position:0% +project + + + align:start position:0% +project +you can print that out + + align:start position:0% +you can print that out + + + align:start position:0% +you can print that out +yeah but that's only for this particular + + align:start position:0% +yeah but that's only for this particular + + + align:start position:0% +yeah but that's only for this particular +scene i want to take a photo of a car + + align:start position:0% +scene i want to take a photo of a car + + + align:start position:0% +scene i want to take a photo of a car +moving or somebody running and i just + + align:start position:0% +moving or somebody running and i just + + + align:start position:0% +moving or somebody running and i just +want to take a couple of maybe five + + align:start position:0% +want to take a couple of maybe five + + + align:start position:0% +want to take a couple of maybe five +frames of that video and create one + + align:start position:0% +frames of that video and create one + + + align:start position:0% +frames of that video and create one +photo out of that + + align:start position:0% +photo out of that + + + align:start position:0% +photo out of that +so that it looks like the person is + + align:start position:0% +so that it looks like the person is + + + align:start position:0% +so that it looks like the person is +constantly moving + + align:start position:0% + + + + align:start position:0% + +i think we can put on the lights again + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% + + + + align:start position:0% + +let me skip this so + + align:start position:0% +let me skip this so + + + align:start position:0% +let me skip this so +all right here was that question and how + + align:start position:0% +all right here was that question and how + + + align:start position:0% +all right here was that question and how +can i look around the corner so this is + + align:start position:0% +can i look around the corner so this is + + + align:start position:0% +can i look around the corner so this is +actually a a huge project in our group + + align:start position:0% +actually a a huge project in our group + + + align:start position:0% +actually a a huge project in our group +uh of how can you look around the corner + + align:start position:0% +uh of how can you look around the corner + + + align:start position:0% +uh of how can you look around the corner +and uh the way we do it is we actually + + align:start position:0% +and uh the way we do it is we actually + + + align:start position:0% +and uh the way we do it is we actually +use + + align:start position:0% +use + + + align:start position:0% +use +some really cheap devices + + align:start position:0% +some really cheap devices + + + align:start position:0% +some really cheap devices +about a so-called transient imaging + + align:start position:0% +about a so-called transient imaging + + + align:start position:0% +about a so-called transient imaging +camera where we use a + + align:start position:0% +camera where we use a + + + align:start position:0% +camera where we use a +impulse response of a scene we transmit + + align:start position:0% +impulse response of a scene we transmit + + + align:start position:0% +impulse response of a scene we transmit +a signal + + align:start position:0% + + + + align:start position:0% + +we transmit a + + align:start position:0% +we transmit a + + + align:start position:0% +we transmit a +very tiny pulse which reflects off of + + align:start position:0% +very tiny pulse which reflects off of + + + align:start position:0% +very tiny pulse which reflects off of +the door + + align:start position:0% +the door + + + align:start position:0% +the door +uh you know bounces around inside the + + align:start position:0% +uh you know bounces around inside the + + + align:start position:0% +uh you know bounces around inside the +scene reflects back from the door and it + + align:start position:0% +scene reflects back from the door and it + + + align:start position:0% +scene reflects back from the door and it +is captured back again at the camera and + + align:start position:0% +is captured back again at the camera and + + + align:start position:0% +is captured back again at the camera and +by analyzing this multi-boss reflections + + align:start position:0% +by analyzing this multi-boss reflections + + + align:start position:0% +by analyzing this multi-boss reflections +we can figure out what's inside the room + + align:start position:0% +we can figure out what's inside the room + + + align:start position:0% +we can figure out what's inside the room +by just looking at the door + + align:start position:0% +by just looking at the door + + + align:start position:0% +by just looking at the door +so the devices are extremely cheap we + + align:start position:0% +so the devices are extremely cheap we + + + align:start position:0% +so the devices are extremely cheap we +need a femtosecond laser that costs + + align:start position:0% +need a femtosecond laser that costs + + + align:start position:0% +need a femtosecond laser that costs +about two hundred thousand dollars + + align:start position:0% +about two hundred thousand dollars + + + align:start position:0% +about two hundred thousand dollars +and we need a photo detector that cost + + align:start position:0% +and we need a photo detector that cost + + + align:start position:0% +and we need a photo detector that cost +about three thousand dollars but we + + align:start position:0% +about three thousand dollars but we + + + align:start position:0% +about three thousand dollars but we +found some cheaper versions and then we + + align:start position:0% +found some cheaper versions and then we + + + align:start position:0% +found some cheaper versions and then we +also need a + + align:start position:0% +also need a + + + align:start position:0% +also need a +a ten gigahertz scope that's about fifty + + align:start position:0% +a ten gigahertz scope that's about fifty + + + align:start position:0% +a ten gigahertz scope that's about fifty +thousand dollars so you know after about + + align:start position:0% +thousand dollars so you know after about + + + align:start position:0% +thousand dollars so you know after about +quarter million dollars + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +maybe not in five years but maybe in 10 + + align:start position:0% +maybe not in five years but maybe in 10 + + + align:start position:0% +maybe not in five years but maybe in 10 +years or 20 years + + align:start position:0% +years or 20 years + + + align:start position:0% +years or 20 years +you will have devices which will allow + + align:start position:0% +you will have devices which will allow + + + align:start position:0% +you will have devices which will allow +you to look around the corner and right + + align:start position:0% +you to look around the corner and right + + + align:start position:0% +you to look around the corner and right +now in our lab + + align:start position:0% +now in our lab + + + align:start position:0% +now in our lab +you can do it + + align:start position:0% +you can do it + + + align:start position:0% +you can do it +and this is going to completely change + + align:start position:0% +and this is going to completely change + + + align:start position:0% +and this is going to completely change +the way you think about photography + + align:start position:0% +the way you think about photography + + + align:start position:0% +the way you think about photography +because line of sight is you know almost + + align:start position:0% +because line of sight is you know almost + + + align:start position:0% +because line of sight is you know almost +a fundamental assumption we think + + align:start position:0% +a fundamental assumption we think + + + align:start position:0% +a fundamental assumption we think +it's + + align:start position:0% +it's + + + align:start position:0% +it's +a lot of us think that's one of the laws + + align:start position:0% +a lot of us think that's one of the laws + + + align:start position:0% +a lot of us think that's one of the laws +of physics we can only see things that + + align:start position:0% +of physics we can only see things that + + + align:start position:0% +of physics we can only see things that +are within the line of sight + + align:start position:0% +are within the line of sight + + + align:start position:0% +are within the line of sight +but you know we are not violating any + + align:start position:0% +but you know we are not violating any + + + align:start position:0% +but you know we are not violating any +laws of physics if you are violating the + + align:start position:0% +laws of physics if you are violating the + + + align:start position:0% +laws of physics if you are violating the +laws you are welcome to report us + + align:start position:0% +laws you are welcome to report us + + + align:start position:0% +laws you are welcome to report us +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +this is possible so throughout this + + align:start position:0% +this is possible so throughout this + + + align:start position:0% +this is possible so throughout this +class what you'll see is that the laws + + align:start position:0% +class what you'll see is that the laws + + + align:start position:0% +class what you'll see is that the laws +that you take for granted and the laws + + align:start position:0% +that you take for granted and the laws + + + align:start position:0% +that you take for granted and the laws +that uh are shackling the way you think + + align:start position:0% +that uh are shackling the way you think + + + align:start position:0% +that uh are shackling the way you think +about visual capture and visual displays + + align:start position:0% +about visual capture and visual displays + + + align:start position:0% +about visual capture and visual displays +are just + + align:start position:0% +are just + + + align:start position:0% +are just +you know just there because + + align:start position:0% +you know just there because + + + align:start position:0% +you know just there because +you know somebody taught you that + + align:start position:0% +you know somebody taught you that + + + align:start position:0% +you know somebody taught you that +but you can challenge all those + + align:start position:0% +but you can challenge all those + + + align:start position:0% +but you can challenge all those +assumptions with modern tools whether + + align:start position:0% +assumptions with modern tools whether + + + align:start position:0% +assumptions with modern tools whether +they're sensors and optics and modern + + align:start position:0% +they're sensors and optics and modern + + + align:start position:0% +they're sensors and optics and modern +computational methods what's the point + + align:start position:0% +computational methods what's the point + + + align:start position:0% +computational methods what's the point +of the femtosecond laser if it + + align:start position:0% +of the femtosecond laser if it + + + align:start position:0% +of the femtosecond laser if it +has such a short coherence length + + align:start position:0% +has such a short coherence length + + + align:start position:0% +has such a short coherence length +you can't really be using the the laser + + align:start position:0% +you can't really be using the the laser + + + align:start position:0% +you can't really be using the the laser +so the reason why you need extremely + + align:start position:0% +so the reason why you need extremely + + + align:start position:0% +so the reason why you need extremely +short duration uh + + align:start position:0% +short duration uh + + + align:start position:0% +short duration uh +laser is that + + align:start position:0% +laser is that + + + align:start position:0% +laser is that +if you just imagine you build a camera + + align:start position:0% +if you just imagine you build a camera + + + align:start position:0% +if you just imagine you build a camera +so those cameras this + + align:start position:0% +so those cameras this + + + align:start position:0% +so those cameras this +time of flight camera that jay was + + align:start position:0% +time of flight camera that jay was + + + align:start position:0% +time of flight camera that jay was +showing + + align:start position:0% +showing + + + align:start position:0% +showing +uh emits a pulse uh at about 50 + + align:start position:0% +uh emits a pulse uh at about 50 + + + align:start position:0% +uh emits a pulse uh at about 50 +megahertz so it's um it's 20 nanosecond + + align:start position:0% +megahertz so it's um it's 20 nanosecond + + + align:start position:0% +megahertz so it's um it's 20 nanosecond +repetition + + align:start position:0% +repetition + + + align:start position:0% +repetition +and light travels + + align:start position:0% +and light travels + + + align:start position:0% +and light travels +how much in one nanosecond + + align:start position:0% +how much in one nanosecond + + + align:start position:0% +how much in one nanosecond +one millimeter per micro second yeah but + + align:start position:0% +one millimeter per micro second yeah but + + + align:start position:0% +one millimeter per micro second yeah but +that's too complicated + + align:start position:0% +that's too complicated + + + align:start position:0% +that's too complicated +how many how many uh how many um how + + align:start position:0% +how many how many uh how many um how + + + align:start position:0% +how many how many uh how many um how +much in one nanosecond + + align:start position:0% +much in one nanosecond + + + align:start position:0% +much in one nanosecond +about a micron no much more + + align:start position:0% +about a micron no much more + + + align:start position:0% +about a micron no much more +more than that + + align:start position:0% + + + + align:start position:0% + +a foot yes right there okay so sorry + + align:start position:0% +a foot yes right there okay so sorry + + + align:start position:0% +a foot yes right there okay so sorry +very simple thing to remember right + + align:start position:0% +very simple thing to remember right + + + align:start position:0% +very simple thing to remember right +right travels one foot in one nanosecond + + align:start position:0% +right travels one foot in one nanosecond + + + align:start position:0% +right travels one foot in one nanosecond +and what about sound in in in + + align:start position:0% +and what about sound in in in + + + align:start position:0% +and what about sound in in in +at room temperature + + align:start position:0% +at room temperature + + + align:start position:0% +at room temperature +how much + + align:start position:0% +how much + + + align:start position:0% +how much +how much does it take + + align:start position:0% +how much does it take + + + align:start position:0% +how much does it take +for sound to travel one foot + + align:start position:0% + + + + align:start position:0% + +you know all the numbers it's 330 meters + + align:start position:0% +you know all the numbers it's 330 meters + + + align:start position:0% +you know all the numbers it's 330 meters +per second + + align:start position:0% +per second + + + align:start position:0% +per second +for + + align:start position:0% +for + + + align:start position:0% +for +for + + align:start position:0% +for + + + align:start position:0% +for +for sound and three times ten to the + + align:start position:0% +for sound and three times ten to the + + + align:start position:0% +for sound and three times ten to the +eight meters per second for light but + + align:start position:0% +eight meters per second for light but + + + align:start position:0% +eight meters per second for light but +that's too complicated to think about we + + align:start position:0% +that's too complicated to think about we + + + align:start position:0% +that's too complicated to think about we +want some simple rules of thumb so + + align:start position:0% +want some simple rules of thumb so + + + align:start position:0% +want some simple rules of thumb so +10 minutes + + align:start position:0% +10 minutes + + + align:start position:0% +10 minutes +10 milliseconds for one foot + + align:start position:0% +10 milliseconds for one foot + + + align:start position:0% +10 milliseconds for one foot +it's one millisecond + + align:start position:0% +it's one millisecond + + + align:start position:0% +it's one millisecond +right so very easy to remember light + + align:start position:0% +right so very easy to remember light + + + align:start position:0% +right so very easy to remember light +travels one foot in one nanosecond + + align:start position:0% +travels one foot in one nanosecond + + + align:start position:0% +travels one foot in one nanosecond +light sound travels + + align:start position:0% +light sound travels + + + align:start position:0% +light sound travels +one foot in one millisecond + + align:start position:0% +one foot in one millisecond + + + align:start position:0% +one foot in one millisecond +so + + align:start position:0% +so + + + align:start position:0% +so +light travels one nanosecond + + align:start position:0% +light travels one nanosecond + + + align:start position:0% +light travels one nanosecond +sound travels one millisecond + + align:start position:0% +sound travels one millisecond + + + align:start position:0% +sound travels one millisecond +unfortunately unfortunately there's + + align:start position:0% +unfortunately unfortunately there's + + + align:start position:0% +unfortunately unfortunately there's +nothing that travels + + align:start position:0% +nothing that travels + + + align:start position:0% +nothing that travels +in one microsecond if somebody comes + + align:start position:0% +in one microsecond if somebody comes + + + align:start position:0% +in one microsecond if somebody comes +with a new physical + + align:start position:0% +with a new physical + + + align:start position:0% +with a new physical +propagation uh physical propagation + + align:start position:0% +propagation uh physical propagation + + + align:start position:0% +propagation uh physical propagation +channel + + align:start position:0% +channel + + + align:start position:0% +channel +that travels + + align:start position:0% +that travels + + + align:start position:0% +that travels +one foot in one micro second rather than + + align:start position:0% +one foot in one micro second rather than + + + align:start position:0% +one foot in one micro second rather than +melee and nano + + align:start position:0% +melee and nano + + + align:start position:0% +melee and nano +then you'll see a completely new range + + align:start position:0% +then you'll see a completely new range + + + align:start position:0% +then you'll see a completely new range +of applications so you have + + align:start position:0% +of applications so you have + + + align:start position:0% +of applications so you have +electromagnetics + + align:start position:0% +electromagnetics + + + align:start position:0% +electromagnetics +em spectrum that's one nanosecond for + + align:start position:0% +em spectrum that's one nanosecond for + + + align:start position:0% +em spectrum that's one nanosecond for +one foot + + align:start position:0% +one foot + + + align:start position:0% +one foot +and sound + + align:start position:0% +and sound + + + align:start position:0% +and sound +one millisecond for one foot so sound is + + align:start position:0% +one millisecond for one foot so sound is + + + align:start position:0% +one millisecond for one foot so sound is +too slow and light is too fast + + align:start position:0% +too slow and light is too fast + + + align:start position:0% +too slow and light is too fast +in almost everything we want to do + + align:start position:0% + + + + align:start position:0% + +and so here uh we want something that's + + align:start position:0% +and so here uh we want something that's + + + align:start position:0% +and so here uh we want something that's +even faster + + align:start position:0% +even faster + + + align:start position:0% +even faster +than traditional light propagation so + + align:start position:0% +than traditional light propagation so + + + align:start position:0% +than traditional light propagation so +if i in this room if i just + + align:start position:0% +if i in this room if i just + + + align:start position:0% +if i in this room if i just +send a beam of light very narrow pulse + + align:start position:0% +send a beam of light very narrow pulse + + + align:start position:0% +send a beam of light very narrow pulse +by the time it goes to that wall and + + align:start position:0% +by the time it goes to that wall and + + + align:start position:0% +by the time it goes to that wall and +comes all the way back to me let's say + + align:start position:0% +comes all the way back to me let's say + + + align:start position:0% +comes all the way back to me let's say +this is about 20 foot uh it's going to + + align:start position:0% +this is about 20 foot uh it's going to + + + align:start position:0% +this is about 20 foot uh it's going to +take me about 40 + + align:start position:0% +take me about 40 + + + align:start position:0% +take me about 40 +nanoseconds to come back + + align:start position:0% +nanoseconds to come back + + + align:start position:0% +nanoseconds to come back +uh on the other hand if i just want to + + align:start position:0% +uh on the other hand if i just want to + + + align:start position:0% +uh on the other hand if i just want to +see you know + + align:start position:0% +see you know + + + align:start position:0% +see you know +where you know + + align:start position:0% +where you know + + + align:start position:0% +where you know +where where somebody's + + align:start position:0% +where where somebody's + + + align:start position:0% +where where somebody's +within a couple of feet of that wall + + align:start position:0% +within a couple of feet of that wall + + + align:start position:0% +within a couple of feet of that wall +then i need to start measuring in + + align:start position:0% +then i need to start measuring in + + + align:start position:0% +then i need to start measuring in +picoseconds not 10 to the minus nine + + align:start position:0% +picoseconds not 10 to the minus nine + + + align:start position:0% +picoseconds not 10 to the minus nine +seconds but minus twelve seconds + + align:start position:0% +seconds but minus twelve seconds + + + align:start position:0% +seconds but minus twelve seconds +uh and that's why you know that's + + align:start position:0% +uh and that's why you know that's + + + align:start position:0% +uh and that's why you know that's +extremely fast so you'll be able to do + + align:start position:0% +extremely fast so you'll be able to do + + + align:start position:0% +extremely fast so you'll be able to do +any um + + align:start position:0% +any um + + + align:start position:0% +any um +so a traditional time of flight camera + + align:start position:0% +so a traditional time of flight camera + + + align:start position:0% +so a traditional time of flight camera +will just look at this door + + align:start position:0% +will just look at this door + + + align:start position:0% +will just look at this door +and that's it there's nothing more you + + align:start position:0% +and that's it there's nothing more you + + + align:start position:0% +and that's it there's nothing more you +can do but if you want to look at + + align:start position:0% +can do but if you want to look at + + + align:start position:0% +can do but if you want to look at +different reflections then you need to + + align:start position:0% +different reflections then you need to + + + align:start position:0% +different reflections then you need to +be able to resolve time at a much higher + + align:start position:0% +be able to resolve time at a much higher + + + align:start position:0% +be able to resolve time at a much higher +uh temporal resolution + + align:start position:0% +uh temporal resolution + + + align:start position:0% +uh temporal resolution +uh so from the second lasers are + + align:start position:0% +uh so from the second lasers are + + + align:start position:0% +uh so from the second lasers are +not something i'm they're not exotic + + align:start position:0% +not something i'm they're not exotic + + + align:start position:0% +not something i'm they're not exotic +they're used in oct they're using two + + align:start position:0% +they're used in oct they're using two + + + align:start position:0% +they're used in oct they're using two +photon microscopy and they use a lot of + + align:start position:0% +photon microscopy and they use a lot of + + + align:start position:0% +photon microscopy and they use a lot of +their applications but still not + + align:start position:0% +their applications but still not + + + align:start position:0% +their applications but still not +consumer applications they're used in + + align:start position:0% +consumer applications they're used in + + + align:start position:0% +consumer applications they're used in +medical imaging + + align:start position:0% +medical imaging + + + align:start position:0% +medical imaging +and once they become solid state and + + align:start position:0% +and once they become solid state and + + + align:start position:0% +and once they become solid state and +easy to carry + + align:start position:0% +easy to carry + + + align:start position:0% +easy to carry +we can do that i mean a lot of lidar + + align:start position:0% +we can do that i mean a lot of lidar + + + align:start position:0% +we can do that i mean a lot of lidar +also happens in not frame per second but + + align:start position:0% +also happens in not frame per second but + + + align:start position:0% +also happens in not frame per second but +nanosecond ranges with very high power + + align:start position:0% + + + + align:start position:0% + +so uh if you can look around the corner + + align:start position:0% +so uh if you can look around the corner + + + align:start position:0% +so uh if you can look around the corner +like this what about looking around a + + align:start position:0% +like this what about looking around a + + + align:start position:0% +like this what about looking around a +a beautiful uh artifact like this one + + align:start position:0% +a beautiful uh artifact like this one + + + align:start position:0% +a beautiful uh artifact like this one +you know if i have a bottle there's no + + align:start position:0% +you know if i have a bottle there's no + + + align:start position:0% +you know if i have a bottle there's no +water + + align:start position:0% +water + + + align:start position:0% +water +you know if i if i as a as a as a human + + align:start position:0% +you know if i if i as a as a as a human + + + align:start position:0% +you know if i if i as a as a as a human +when i look at this bottle i look around + + align:start position:0% +when i look at this bottle i look around + + + align:start position:0% +when i look at this bottle i look around +it and i create a mental representation + + align:start position:0% +it and i create a mental representation + + + align:start position:0% +it and i create a mental representation +of what this looks like + + align:start position:0% +of what this looks like + + + align:start position:0% +of what this looks like +but if i capture a photo it's going to + + align:start position:0% +but if i capture a photo it's going to + + + align:start position:0% +but if i capture a photo it's going to +be only from a single view it's trying + + align:start position:0% +be only from a single view it's trying + + + align:start position:0% +be only from a single view it's trying +to mimic my you know perspective and so + + align:start position:0% +to mimic my you know perspective and so + + + align:start position:0% +to mimic my you know perspective and so +on but my mental representation is + + align:start position:0% +on but my mental representation is + + + align:start position:0% +on but my mental representation is +actually something like that + + align:start position:0% +actually something like that + + + align:start position:0% +actually something like that +right so how can we build a camera that + + align:start position:0% +right so how can we build a camera that + + + align:start position:0% +right so how can we build a camera that +takes an object + + align:start position:0% +takes an object + + + align:start position:0% +takes an object +and creates + + align:start position:0% +and creates + + + align:start position:0% +and creates +a rollout imagery like that now this + + align:start position:0% +a rollout imagery like that now this + + + align:start position:0% +a rollout imagery like that now this +particular object is straightforward i + + align:start position:0% +particular object is straightforward i + + + align:start position:0% +particular object is straightforward i +can just put it on a flatbed scanner and + + align:start position:0% +can just put it on a flatbed scanner and + + + align:start position:0% +can just put it on a flatbed scanner and +i can just hold it + + align:start position:0% +i can just hold it + + + align:start position:0% +i can just hold it +but some other objects are not so easy + + align:start position:0% +but some other objects are not so easy + + + align:start position:0% +but some other objects are not so easy +this object for example which is not + + align:start position:0% +this object for example which is not + + + align:start position:0% +this object for example which is not +completely cylindrical has + + align:start position:0% +completely cylindrical has + + + align:start position:0% +completely cylindrical has +uh you know uh doesn't have a constant + + align:start position:0% +uh you know uh doesn't have a constant + + + align:start position:0% +uh you know uh doesn't have a constant +radius around its axis of rotation so if + + align:start position:0% +radius around its axis of rotation so if + + + align:start position:0% +radius around its axis of rotation so if +i just roll it on a flatbed scanner i + + align:start position:0% +i just roll it on a flatbed scanner i + + + align:start position:0% +i just roll it on a flatbed scanner i +will not get that + + align:start position:0% +will not get that + + + align:start position:0% +will not get that +so maybe i need a special camera or i + + align:start position:0% +so maybe i need a special camera or i + + + align:start position:0% +so maybe i need a special camera or i +can use my existing camera and use some + + align:start position:0% +can use my existing camera and use some + + + align:start position:0% +can use my existing camera and use some +interesting tricks computational tricks + + align:start position:0% +interesting tricks computational tricks + + + align:start position:0% +interesting tricks computational tricks +to create rollout imagery another + + align:start position:0% +to create rollout imagery another + + + align:start position:0% +to create rollout imagery another +research problem + + align:start position:0% +research problem + + + align:start position:0% +research problem +and i would i'm sure a camera company + + align:start position:0% +and i would i'm sure a camera company + + + align:start position:0% +and i would i'm sure a camera company +would love to have this feature as you + + align:start position:0% +would love to have this feature as you + + + align:start position:0% +would love to have this feature as you +know you have all the boring features av + + align:start position:0% +know you have all the boring features av + + + align:start position:0% +know you have all the boring features av +tv panorama movie and then you have + + align:start position:0% +tv panorama movie and then you have + + + align:start position:0% +tv panorama movie and then you have +roll up + + align:start position:0% +roll up + + + align:start position:0% +roll up +mode + + align:start position:0% +mode + + + align:start position:0% +mode +so that will be fun + + align:start position:0% +so that will be fun + + + align:start position:0% +so that will be fun +and maybe you can do it with an ordinary + + align:start position:0% +and maybe you can do it with an ordinary + + + align:start position:0% +and maybe you can do it with an ordinary +camera or maybe you can do it with a do + + align:start position:0% +camera or maybe you can do it with a do + + + align:start position:0% +camera or maybe you can do it with a do +it with a femtosecond laser + + align:start position:0% +it with a femtosecond laser + + + align:start position:0% +it with a femtosecond laser +if you have quarter million dollars + + align:start position:0% +if you have quarter million dollars + + + align:start position:0% +if you have quarter million dollars +all right so let's do a very fast + + align:start position:0% +all right so let's do a very fast + + + align:start position:0% +all right so let's do a very fast +forward preview of the rest of the class + + align:start position:0% +forward preview of the rest of the class + + + align:start position:0% +forward preview of the rest of the class +and + + align:start position:0% +and + + + align:start position:0% +and +uh here i'm mostly going to talk about + + align:start position:0% +uh here i'm mostly going to talk about + + + align:start position:0% +uh here i'm mostly going to talk about +what's the input what's the output + + align:start position:0% +what's the input what's the output + + + align:start position:0% +what's the input what's the output +i may not go into the detail of exactly + + align:start position:0% +i may not go into the detail of exactly + + + align:start position:0% +i may not go into the detail of exactly +how this works because again these are + + align:start position:0% +how this works because again these are + + + align:start position:0% +how this works because again these are +teasers of what's coming in the class + + align:start position:0% +teasers of what's coming in the class + + + align:start position:0% +teasers of what's coming in the class +and what i would like you to + + align:start position:0% +and what i would like you to + + + align:start position:0% +and what i would like you to +think about + + align:start position:0% +think about + + + align:start position:0% +think about +during this preview is how this applies + + align:start position:0% +during this preview is how this applies + + + align:start position:0% +during this preview is how this applies +to some problem you may be already + + align:start position:0% +to some problem you may be already + + + align:start position:0% +to some problem you may be already +working on or what are some parallels + + align:start position:0% +working on or what are some parallels + + + align:start position:0% +working on or what are some parallels +with things you already know + + align:start position:0% +with things you already know + + + align:start position:0% +with things you already know +and again + + align:start position:0% +and again + + + align:start position:0% +and again +most of these techniques will be about + + align:start position:0% +most of these techniques will be about + + + align:start position:0% +most of these techniques will be about +changing the rules of the game if you're + + align:start position:0% +changing the rules of the game if you're + + + align:start position:0% +changing the rules of the game if you're +doing if you have a project where you're + + align:start position:0% +doing if you have a project where you're + + + align:start position:0% +doing if you have a project where you're +tracking your fingers with a cheap + + align:start position:0% +tracking your fingers with a cheap + + + align:start position:0% +tracking your fingers with a cheap +webcam and it's not working because when + + align:start position:0% +webcam and it's not working because when + + + align:start position:0% +webcam and it's not working because when +the light changes or person with a + + align:start position:0% +the light changes or person with a + + + align:start position:0% +the light changes or person with a +different skin color + + align:start position:0% +different skin color + + + align:start position:0% +different skin color +walks into the scene + + align:start position:0% +walks into the scene + + + align:start position:0% +walks into the scene +there are solutions here uh if you are + + align:start position:0% +there are solutions here uh if you are + + + align:start position:0% +there are solutions here uh if you are +worried about how to track crowds there + + align:start position:0% +worried about how to track crowds there + + + align:start position:0% +worried about how to track crowds there +are solutions here you want to see you + + align:start position:0% +are solutions here you want to see you + + + align:start position:0% +are solutions here you want to see you +know what's + + align:start position:0% +know what's + + + align:start position:0% +know what's +behind a glass that's murky and diffuse + + align:start position:0% +behind a glass that's murky and diffuse + + + align:start position:0% +behind a glass that's murky and diffuse +the solutions here and so on and then of + + align:start position:0% +the solutions here and so on and then of + + + align:start position:0% +the solutions here and so on and then of +course there are + + align:start position:0% +course there are + + + align:start position:0% +course there are +really interesting devices that you + + align:start position:0% +really interesting devices that you + + + align:start position:0% +really interesting devices that you +could use in new forms of photography + + align:start position:0% +could use in new forms of photography + + + align:start position:0% +could use in new forms of photography +so um here's a really simple example + + align:start position:0% +so um here's a really simple example + + + align:start position:0% +so um here's a really simple example +of how we can get started so + + align:start position:0% +of how we can get started so + + + align:start position:0% +of how we can get started so +paul heavily + + align:start position:0% +paul heavily + + + align:start position:0% +paul heavily +in 92 simple idea take an object turn on + + align:start position:0% +in 92 simple idea take an object turn on + + + align:start position:0% +in 92 simple idea take an object turn on +the flashlight + + align:start position:0% +the flashlight + + + align:start position:0% +the flashlight +on the left + + align:start position:0% +on the left + + + align:start position:0% +on the left +turn on a flashlight on the right + + align:start position:0% +turn on a flashlight on the right + + + align:start position:0% +turn on a flashlight on the right +uh and then you can form this image by + + align:start position:0% +uh and then you can form this image by + + + align:start position:0% +uh and then you can form this image by +combining these two how would you do it + + align:start position:0% +combining these two how would you do it + + + align:start position:0% +combining these two how would you do it +this this looks like a blue light and + + align:start position:0% +this this looks like a blue light and + + + align:start position:0% +this this looks like a blue light and +this looks like a red light just from + + align:start position:0% +this looks like a red light just from + + + align:start position:0% +this looks like a red light just from +these two equal photos you want to + + align:start position:0% +these two equal photos you want to + + + align:start position:0% +these two equal photos you want to +create this one + + align:start position:0% + + + + align:start position:0% + +yeah just make sure + + align:start position:0% +yeah just make sure + + + align:start position:0% +yeah just make sure +exactly just like the blue channel from + + align:start position:0% +exactly just like the blue channel from + + + align:start position:0% +exactly just like the blue channel from +here and red channel from here that's it + + align:start position:0% +here and red channel from here that's it + + + align:start position:0% +here and red channel from here that's it +and creates this beautiful relating + + align:start position:0% +and creates this beautiful relating + + + align:start position:0% +and creates this beautiful relating +artifact so that's going to be actually + + align:start position:0% +artifact so that's going to be actually + + + align:start position:0% +artifact so that's going to be actually +assignment number one + + align:start position:0% +assignment number one + + + align:start position:0% +assignment number one +just a warm-up assignment + + align:start position:0% + + + + align:start position:0% + +all you have to do is take an object + + align:start position:0% +all you have to do is take an object + + + align:start position:0% +all you have to do is take an object +and + + align:start position:0% +and + + + align:start position:0% +and +take two or three photos by moving your + + align:start position:0% +take two or three photos by moving your + + + align:start position:0% +take two or three photos by moving your +light source + + align:start position:0% +light source + + + align:start position:0% +light source +and then mix and match the color + + align:start position:0% +and then mix and match the color + + + align:start position:0% +and then mix and match the color +channels to create very beautiful color + + align:start position:0% +channels to create very beautiful color + + + align:start position:0% +channels to create very beautiful color +artifacts + + align:start position:0% +artifacts + + + align:start position:0% +artifacts +and this will help you to + + align:start position:0% +and this will help you to + + + align:start position:0% +and this will help you to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know get your whole pipeline for a + + align:start position:0% +you know get your whole pipeline for a + + + align:start position:0% +you know get your whole pipeline for a +semester going you will have your own + + align:start position:0% +semester going you will have your own + + + align:start position:0% +semester going you will have your own +camera you're welcome to use your you + + align:start position:0% +camera you're welcome to use your you + + + align:start position:0% +camera you're welcome to use your you +know regular camera like even even a + + align:start position:0% +know regular camera like even even a + + + align:start position:0% +know regular camera like even even a +cell phone camera but ideally you should + + align:start position:0% +cell phone camera but ideally you should + + + align:start position:0% +cell phone camera but ideally you should +start using a camera that has more + + align:start position:0% +start using a camera that has more + + + align:start position:0% +start using a camera that has more +manual controls + + align:start position:0% +manual controls + + + align:start position:0% +manual controls +um and it will get you set up with your + + align:start position:0% +um and it will get you set up with your + + + align:start position:0% +um and it will get you set up with your +matlab or java or flash whatever you + + align:start position:0% +matlab or java or flash whatever you + + + align:start position:0% +matlab or java or flash whatever you +want to use + + align:start position:0% +want to use + + + align:start position:0% +want to use +c plus plus opencv + + align:start position:0% +c plus plus opencv + + + align:start position:0% +c plus plus opencv +there's a lot of easy ways to do this + + align:start position:0% +there's a lot of easy ways to do this + + + align:start position:0% +there's a lot of easy ways to do this +but i would like you to use + + align:start position:0% +but i would like you to use + + + align:start position:0% +but i would like you to use +i would like you to + + align:start position:0% +i would like you to + + + align:start position:0% +i would like you to +set up your your your environment so + + align:start position:0% +set up your your your environment so + + + align:start position:0% +set up your your your environment so +that this type of operations are very + + align:start position:0% +that this type of operations are very + + + align:start position:0% +that this type of operations are very +easy to do and that will be your + + align:start position:0% +easy to do and that will be your + + + align:start position:0% +easy to do and that will be your +uh assignment number one regardless + + align:start position:0% + + + + align:start position:0% + +um of course this is what you would do + + align:start position:0% +um of course this is what you would do + + + align:start position:0% +um of course this is what you would do +at home + + align:start position:0% +at home + + + align:start position:0% +at home +but if you have a couple of million + + align:start position:0% +but if you have a couple of million + + + align:start position:0% +but if you have a couple of million +dollars + + align:start position:0% +dollars + + + align:start position:0% +dollars +then this is how you would do it in the + + align:start position:0% +then this is how you would do it in the + + + align:start position:0% +then this is how you would do it in the +hollywood so this is a project from uh + + align:start position:0% +hollywood so this is a project from uh + + + align:start position:0% +hollywood so this is a project from uh +paul the berwick and his group a really + + align:start position:0% +paul the berwick and his group a really + + + align:start position:0% +paul the berwick and his group a really +excellent set of work where they're + + align:start position:0% +excellent set of work where they're + + + align:start position:0% +excellent set of work where they're +building different light stages + + align:start position:0% +building different light stages + + + align:start position:0% +building different light stages +um and uh instead of turning on one + + align:start position:0% +um and uh instead of turning on one + + + align:start position:0% +um and uh instead of turning on one +light at a time or moving uh it it + + align:start position:0% +light at a time or moving uh it it + + + align:start position:0% +light at a time or moving uh it it +manually they have a dome with about 150 + + align:start position:0% +manually they have a dome with about 150 + + + align:start position:0% +manually they have a dome with about 150 +lights + + align:start position:0% +lights + + + align:start position:0% +lights +and then they use a high speed camera + + align:start position:0% +and then they use a high speed camera + + + align:start position:0% +and then they use a high speed camera +here + + align:start position:0% +here + + + align:start position:0% +here +and turn on one light at a time so + + align:start position:0% +and turn on one light at a time so + + + align:start position:0% +and turn on one light at a time so +they can photograph this actress under + + align:start position:0% +they can photograph this actress under + + + align:start position:0% +they can photograph this actress under +150 lightning conditions + + align:start position:0% +150 lightning conditions + + + align:start position:0% +150 lightning conditions +in 150 frames + + align:start position:0% +in 150 frames + + + align:start position:0% +in 150 frames +very quickly and then i can start from + + align:start position:0% +very quickly and then i can start from + + + align:start position:0% +very quickly and then i can start from +the beginning and so on + + align:start position:0% +the beginning and so on + + + align:start position:0% +the beginning and so on +that's one way to do it + + align:start position:0% +that's one way to do it + + + align:start position:0% +that's one way to do it +the other way to do that is let's say + + align:start position:0% +the other way to do that is let's say + + + align:start position:0% +the other way to do that is let's say +all you want to do is insert + + align:start position:0% +all you want to do is insert + + + align:start position:0% +all you want to do is insert +a + + align:start position:0% +a + + + align:start position:0% +a +this actress + + align:start position:0% +this actress + + + align:start position:0% +this actress +in a scene that may have been shot + + align:start position:0% +in a scene that may have been shot + + + align:start position:0% +in a scene that may have been shot +somewhere else so + + align:start position:0% +somewhere else so + + + align:start position:0% +somewhere else so +she's in a lane and you want to insert + + align:start position:0% +she's in a lane and you want to insert + + + align:start position:0% +she's in a lane and you want to insert +her + + align:start position:0% +her + + + align:start position:0% +her +in a + + align:start position:0% +in a + + + align:start position:0% +in a +on top of a photo that was actually + + align:start position:0% +on top of a photo that was actually + + + align:start position:0% +on top of a photo that was actually +taken in milan + + align:start position:0% +taken in milan + + + align:start position:0% +taken in milan +now if you just take the photo and + + align:start position:0% +now if you just take the photo and + + + align:start position:0% +now if you just take the photo and +superimpose it it looks very fake + + align:start position:0% +superimpose it it looks very fake + + + align:start position:0% +superimpose it it looks very fake +because the lighting doesn't match up + + align:start position:0% +because the lighting doesn't match up + + + align:start position:0% +because the lighting doesn't match up +so the trick they use is + + align:start position:0% +so the trick they use is + + + align:start position:0% +so the trick they use is +uh you know some guy + + align:start position:0% +uh you know some guy + + + align:start position:0% +uh you know some guy +puts a shiny sphere in milan and takes a + + align:start position:0% +puts a shiny sphere in milan and takes a + + + align:start position:0% +puts a shiny sphere in milan and takes a +environment map of that courtyard + + align:start position:0% +environment map of that courtyard + + + align:start position:0% +environment map of that courtyard +then you feed this image onto these + + align:start position:0% +then you feed this image onto these + + + align:start position:0% +then you feed this image onto these +lights so if the left corner is reddish + + align:start position:0% +lights so if the left corner is reddish + + + align:start position:0% +lights so if the left corner is reddish +the the light at + + align:start position:0% +the the light at + + + align:start position:0% +the the light at +on the left left side of this dome is is + + align:start position:0% +on the left left side of this dome is is + + + align:start position:0% +on the left left side of this dome is is +reddish + + align:start position:0% +reddish + + + align:start position:0% +reddish +uh if it's yellowish here and so on so + + align:start position:0% +uh if it's yellowish here and so on so + + + align:start position:0% +uh if it's yellowish here and so on so +for all this four pi + + align:start position:0% +for all this four pi + + + align:start position:0% +for all this four pi +uh you turn on the lights + + align:start position:0% +uh you turn on the lights + + + align:start position:0% +uh you turn on the lights +correspondingly and now she's bathed in + + align:start position:0% +correspondingly and now she's bathed in + + + align:start position:0% +correspondingly and now she's bathed in +light + + align:start position:0% +light + + + align:start position:0% +light +as if she was in that courtyard in milan + + align:start position:0% +as if she was in that courtyard in milan + + + align:start position:0% +as if she was in that courtyard in milan +and now if you take her photo + + align:start position:0% +and now if you take her photo + + + align:start position:0% +and now if you take her photo +uh and cut out and superimpose on that + + align:start position:0% +uh and cut out and superimpose on that + + + align:start position:0% +uh and cut out and superimpose on that +uh background it will look more + + align:start position:0% +uh background it will look more + + + align:start position:0% +uh background it will look more +realistic + + align:start position:0% +realistic + + + align:start position:0% +realistic +and they have done videos where they + + align:start position:0% +and they have done videos where they + + + align:start position:0% +and they have done videos where they +took this shiny spheres + + align:start position:0% + + + + align:start position:0% + +and christmas is coming up so you can + + align:start position:0% +and christmas is coming up so you can + + + align:start position:0% +and christmas is coming up so you can +pick up your your shiny spheres + + align:start position:0% +pick up your your shiny spheres + + + align:start position:0% +pick up your your shiny spheres +um and you just put the shiny sphere and + + align:start position:0% +um and you just put the shiny sphere and + + + align:start position:0% +um and you just put the shiny sphere and +move in the + + align:start position:0% +move in the + + + align:start position:0% +move in the +in the courtyard with it + + align:start position:0% +in the courtyard with it + + + align:start position:0% +in the courtyard with it +so you're constantly capturing the + + align:start position:0% +so you're constantly capturing the + + + align:start position:0% +so you're constantly capturing the +environment map as you move along and in + + align:start position:0% +environment map as you move along and in + + + align:start position:0% +environment map as you move along and in +the scene she just stands in one place + + align:start position:0% +the scene she just stands in one place + + + align:start position:0% +the scene she just stands in one place +but the dome + + align:start position:0% +but the dome + + + align:start position:0% +but the dome +is lit up by the environment map that + + align:start position:0% +is lit up by the environment map that + + + align:start position:0% +is lit up by the environment map that +was captured + + align:start position:0% +was captured + + + align:start position:0% +was captured +from these + + align:start position:0% +from these + + + align:start position:0% +from these +shiny spheres so + + align:start position:0% +shiny spheres so + + + align:start position:0% +shiny spheres so +in a video sequence it appears as if + + align:start position:0% +in a video sequence it appears as if + + + align:start position:0% +in a video sequence it appears as if +she's walking through this environment + + align:start position:0% +she's walking through this environment + + + align:start position:0% +she's walking through this environment +at least she's lit up as if she's + + align:start position:0% +at least she's lit up as if she's + + + align:start position:0% +at least she's lit up as if she's +walking through this environment + + align:start position:0% +walking through this environment + + + align:start position:0% +walking through this environment +so you know these are some of the tricks + + align:start position:0% +so you know these are some of the tricks + + + align:start position:0% +so you know these are some of the tricks +that are being used currently in uh in + + align:start position:0% +that are being used currently in uh in + + + align:start position:0% +that are being used currently in uh in +major productions so matrix uh all the + + align:start position:0% +major productions so matrix uh all the + + + align:start position:0% +major productions so matrix uh all the +movies that came uh in in the last 10 + + align:start position:0% +movies that came uh in in the last 10 + + + align:start position:0% +movies that came uh in in the last 10 +years or so + + align:start position:0% +years or so + + + align:start position:0% +years or so +are using this particular mechanism to + + align:start position:0% +are using this particular mechanism to + + + align:start position:0% +are using this particular mechanism to +create maps that + + align:start position:0% +create maps that + + + align:start position:0% +create maps that +have + + align:start position:0% +have + + + align:start position:0% +have +correct + + align:start position:0% +correct + + + align:start position:0% +correct +lighting + + align:start position:0% +lighting + + + align:start position:0% +lighting +match like itself + + align:start position:0% + + + + align:start position:0% + +and if you don't want to spend + + align:start position:0% +and if you don't want to spend + + + align:start position:0% +and if you don't want to spend +two million dollars back to something + + align:start position:0% +two million dollars back to something + + + align:start position:0% +two million dollars back to something +something really cheap + + align:start position:0% +something really cheap + + + align:start position:0% +something really cheap +you can to create the silhouettes and so + + align:start position:0% +you can to create the silhouettes and so + + + align:start position:0% +you can to create the silhouettes and so +on you can use a multi-flash camera so + + align:start position:0% +on you can use a multi-flash camera so + + + align:start position:0% +on you can use a multi-flash camera so +here are some cameras that you can buy + + align:start position:0% +here are some cameras that you can buy + + + align:start position:0% +here are some cameras that you can buy +uh this is a believer lumo + + align:start position:0% +uh this is a believer lumo + + + align:start position:0% +uh this is a believer lumo +yeah this is a lomo so i think it's + + align:start position:0% +yeah this is a lomo so i think it's + + + align:start position:0% +yeah this is a lomo so i think it's +about 30 dollars and + + align:start position:0% +about 30 dollars and + + + align:start position:0% +about 30 dollars and +what it does is let's see if it's + + align:start position:0% + + + + align:start position:0% + +did the lights go off + + align:start position:0% + + + + align:start position:0% + +so when you release the shutter + + align:start position:0% +so when you release the shutter + + + align:start position:0% +so when you release the shutter +it uh + + align:start position:0% + + + + align:start position:0% + +we're too cheap to put the frame inside + + align:start position:0% +we're too cheap to put the frame inside + + + align:start position:0% +we're too cheap to put the frame inside +so manually + + align:start position:0% + + + + align:start position:0% + +here unfortunately + + align:start position:0% +here unfortunately + + + align:start position:0% +here unfortunately +uh but anyway when you release the + + align:start position:0% +uh but anyway when you release the + + + align:start position:0% +uh but anyway when you release the +shutter + + align:start position:0% +shutter + + + align:start position:0% +shutter +it takes + + align:start position:0% +it takes + + + align:start position:0% +it takes +four photos by exposing + + align:start position:0% +four photos by exposing + + + align:start position:0% +four photos by exposing +one pinhole at a time + + align:start position:0% +one pinhole at a time + + + align:start position:0% +one pinhole at a time +and at the same time + + align:start position:0% +and at the same time + + + align:start position:0% +and at the same time +because it cannot recharge the flash + + align:start position:0% +because it cannot recharge the flash + + + align:start position:0% +because it cannot recharge the flash +that quickly + + align:start position:0% +that quickly + + + align:start position:0% +that quickly +the simple solution was to actually put + + align:start position:0% +the simple solution was to actually put + + + align:start position:0% +the simple solution was to actually put +four different flashes + + align:start position:0% +four different flashes + + + align:start position:0% +four different flashes +so + + align:start position:0% +so + + + align:start position:0% +so +this shutter goes off then this light + + align:start position:0% +this shutter goes off then this light + + + align:start position:0% +this shutter goes off then this light +goes off then this shutter goes up this + + align:start position:0% +goes off then this shutter goes up this + + + align:start position:0% +goes off then this shutter goes up this +light goes off and so on so it takes + + align:start position:0% +light goes off and so on so it takes + + + align:start position:0% +light goes off and so on so it takes +four pictures + + align:start position:0% +four pictures + + + align:start position:0% +four pictures +now instead of putting the lights all in + + align:start position:0% +now instead of putting the lights all in + + + align:start position:0% +now instead of putting the lights all in +one place if you place them around the + + align:start position:0% +one place if you place them around the + + + align:start position:0% +one place if you place them around the +camera + + align:start position:0% +camera + + + align:start position:0% +camera +uh you can do something interesting + + align:start position:0% +uh you can do something interesting + + + align:start position:0% +uh you can do something interesting +when the flash is to the left you know + + align:start position:0% +when the flash is to the left you know + + + align:start position:0% +when the flash is to the left you know +that we get a we get a very annoying + + align:start position:0% +that we get a we get a very annoying + + + align:start position:0% +that we get a we get a very annoying +slivers of shadow + + align:start position:0% +slivers of shadow + + + align:start position:0% +slivers of shadow +in a in an ordinary photo now if you + + align:start position:0% +in a in an ordinary photo now if you + + + align:start position:0% +in a in an ordinary photo now if you +intentionally place the flash so you can + + align:start position:0% +intentionally place the flash so you can + + + align:start position:0% +intentionally place the flash so you can +see it here + + align:start position:0% +see it here + + + align:start position:0% +see it here +so there are all these + + align:start position:0% +so there are all these + + + align:start position:0% +so there are all these +slivers of shadow at depth discontinuous + + align:start position:0% +slivers of shadow at depth discontinuous + + + align:start position:0% +slivers of shadow at depth discontinuous +and you probably see it in your own + + align:start position:0% +and you probably see it in your own + + + align:start position:0% +and you probably see it in your own +photographs + + align:start position:0% +photographs + + + align:start position:0% +photographs +if you place the flash intentionally to + + align:start position:0% +if you place the flash intentionally to + + + align:start position:0% +if you place the flash intentionally to +the right + + align:start position:0% +the right + + + align:start position:0% +the right +then the slivers move to the left + + align:start position:0% +then the slivers move to the left + + + align:start position:0% +then the slivers move to the left +if you put the flash at the top the + + align:start position:0% +if you put the flash at the top the + + + align:start position:0% +if you put the flash at the top the +slippers are shadow slivers are at the + + align:start position:0% +slippers are shadow slivers are at the + + + align:start position:0% +slippers are shadow slivers are at the +bottom and so on so by taking these four + + align:start position:0% +bottom and so on so by taking these four + + + align:start position:0% +bottom and so on so by taking these four +pictures + + align:start position:0% +pictures + + + align:start position:0% +pictures +and analyzing those tiny slivers of + + align:start position:0% +and analyzing those tiny slivers of + + + align:start position:0% +and analyzing those tiny slivers of +shadows you can figure out where the + + align:start position:0% +shadows you can figure out where the + + + align:start position:0% +shadows you can figure out where the +depth discontinuity is where the + + align:start position:0% +depth discontinuity is where the + + + align:start position:0% +depth discontinuity is where the +foreground is separated from the + + align:start position:0% +foreground is separated from the + + + align:start position:0% +foreground is separated from the +background not just the whole person and + + align:start position:0% +background not just the whole person and + + + align:start position:0% +background not just the whole person and +the wall behind them but also any + + align:start position:0% +the wall behind them but also any + + + align:start position:0% +the wall behind them but also any +internal changes so if my hand here it + + align:start position:0% +internal changes so if my hand here it + + + align:start position:0% +internal changes so if my hand here it +will create a boundary between my hand + + align:start position:0% +will create a boundary between my hand + + + align:start position:0% +will create a boundary between my hand +and uh and my body no matter how close + + align:start position:0% +and uh and my body no matter how close + + + align:start position:0% +and uh and my body no matter how close +or how far + + align:start position:0% +or how far + + + align:start position:0% +or how far +i am from from that + + align:start position:0% +i am from from that + + + align:start position:0% +i am from from that +so uh by by doing that + + align:start position:0% +so uh by by doing that + + + align:start position:0% +so uh by by doing that +you can estimate all the shape contours + + align:start position:0% +you can estimate all the shape contours + + + align:start position:0% +you can estimate all the shape contours +and this is the edge map you would get + + align:start position:0% +and this is the edge map you would get + + + align:start position:0% +and this is the edge map you would get +if you had an ordinary camera + + align:start position:0% +if you had an ordinary camera + + + align:start position:0% +if you had an ordinary camera +and this is the edge map you get with a + + align:start position:0% +and this is the edge map you get with a + + + align:start position:0% +and this is the edge map you get with a +multi-flash camera so now if you have an + + align:start position:0% +multi-flash camera so now if you have an + + + align:start position:0% +multi-flash camera so now if you have an +application you want to track a hand or + + align:start position:0% +application you want to track a hand or + + + align:start position:0% +application you want to track a hand or +track a gesture instead of taking a + + align:start position:0% +track a gesture instead of taking a + + + align:start position:0% +track a gesture instead of taking a +standard 2d image if you take a + + align:start position:0% +standard 2d image if you take a + + + align:start position:0% +standard 2d image if you take a +multi-flash image you'll get very clean + + align:start position:0% +multi-flash image you'll get very clean + + + align:start position:0% +multi-flash image you'll get very clean +contours + + align:start position:0% +contours + + + align:start position:0% +contours +and from those contours you can build an + + align:start position:0% +and from those contours you can build an + + + align:start position:0% +and from those contours you can build an +hc application that will perform + + align:start position:0% +hc application that will perform + + + align:start position:0% +hc application that will perform +very well even in strange ambient light + + align:start position:0% +very well even in strange ambient light + + + align:start position:0% +very well even in strange ambient light +and i guess it's independent of + + align:start position:0% +and i guess it's independent of + + + align:start position:0% +and i guess it's independent of +this the color of the + + align:start position:0% +this the color of the + + + align:start position:0% +this the color of the +the foreground object it only relies on + + align:start position:0% +the foreground object it only relies on + + + align:start position:0% +the foreground object it only relies on +the shadow + + align:start position:0% +the shadow + + + align:start position:0% +the shadow +so again if you want to hand track your + + align:start position:0% +so again if you want to hand track your + + + align:start position:0% +so again if you want to hand track your +hand you're not dependent on the skin + + align:start position:0% +hand you're not dependent on the skin + + + align:start position:0% +hand you're not dependent on the skin +color anymore + + align:start position:0% +color anymore + + + align:start position:0% +color anymore +so you can play these tricks + + align:start position:0% +so you can play these tricks + + + align:start position:0% +so you can play these tricks +to + + align:start position:0% +to + + + align:start position:0% +to +overcome the limitations of a + + align:start position:0% +overcome the limitations of a + + + align:start position:0% +overcome the limitations of a +traditional 2d camera + + align:start position:0% + + + + align:start position:0% + +let me skip ahead a little bit here + + align:start position:0% + + + + align:start position:0% + +another assignment we'll be looking at + + align:start position:0% +another assignment we'll be looking at + + + align:start position:0% +another assignment we'll be looking at +is this virtual optical bench + + align:start position:0% +is this virtual optical bench + + + align:start position:0% +is this virtual optical bench +and it's a very nice toy that andrew + + align:start position:0% +and it's a very nice toy that andrew + + + align:start position:0% +and it's a very nice toy that andrew +adams at stanford are put together which + + align:start position:0% +adams at stanford are put together which + + + align:start position:0% +adams at stanford are put together which +is a flash based application where you + + align:start position:0% +is a flash based application where you + + + align:start position:0% +is a flash based application where you +can insert lenses and + + align:start position:0% +can insert lenses and + + + align:start position:0% +can insert lenses and +and occluders and mirrors and + + align:start position:0% +and occluders and mirrors and + + + align:start position:0% +and occluders and mirrors and +uh ray emitters and um and so on and you + + align:start position:0% +uh ray emitters and um and so on and you + + + align:start position:0% +uh ray emitters and um and so on and you +can basically do a very quick setup + + align:start position:0% +can basically do a very quick setup + + + align:start position:0% +can basically do a very quick setup +uh very quick optical design of of a + + align:start position:0% +uh very quick optical design of of a + + + align:start position:0% +uh very quick optical design of of a +setup + + align:start position:0% +setup + + + align:start position:0% +setup +and what we'll do is we'll start with + + align:start position:0% +and what we'll do is we'll start with + + + align:start position:0% +and what we'll do is we'll start with +this one option is to start with this + + align:start position:0% +this one option is to start with this + + + align:start position:0% +this one option is to start with this +uh his score his source code and modify + + align:start position:0% +uh his score his source code and modify + + + align:start position:0% +uh his score his source code and modify +and insert a few more optical elements + + align:start position:0% +and insert a few more optical elements + + + align:start position:0% +and insert a few more optical elements +maybe a prism + + align:start position:0% +maybe a prism + + + align:start position:0% +maybe a prism +uh maybe a grating uh and so on okay + + align:start position:0% +uh maybe a grating uh and so on okay + + + align:start position:0% +uh maybe a grating uh and so on okay +this will be one option and as i said + + align:start position:0% +this will be one option and as i said + + + align:start position:0% +this will be one option and as i said +you'll have multiple options for each + + align:start position:0% +you'll have multiple options for each + + + align:start position:0% +you'll have multiple options for each +assignment + + align:start position:0% +assignment + + + align:start position:0% +assignment +so uh + + align:start position:0% +so uh + + + align:start position:0% +so uh +thinking a little bit more about lenses + + align:start position:0% +thinking a little bit more about lenses + + + align:start position:0% +thinking a little bit more about lenses +uh one constant will will come across + + align:start position:0% +uh one constant will will come across + + + align:start position:0% +uh one constant will will come across +quite a bit in this uh in this class is + + align:start position:0% +quite a bit in this uh in this class is + + + align:start position:0% +quite a bit in this uh in this class is +light field + + align:start position:0% +light field + + + align:start position:0% +light field +and now this particular camera that we + + align:start position:0% +and now this particular camera that we + + + align:start position:0% +and now this particular camera that we +saw by the five + + align:start position:0% +saw by the five + + + align:start position:0% +saw by the five +uh that work was showing us + + align:start position:0% +uh that work was showing us + + + align:start position:0% +uh that work was showing us +uh + + align:start position:0% +uh + + + align:start position:0% +uh +is actually a light field camera + + align:start position:0% +is actually a light field camera + + + align:start position:0% +is actually a light field camera +but that's made up of + + align:start position:0% +but that's made up of + + + align:start position:0% +but that's made up of +an array of cameras physical cameras + + align:start position:0% +an array of cameras physical cameras + + + align:start position:0% +an array of cameras physical cameras +and what we're going to do instead is + + align:start position:0% +and what we're going to do instead is + + + align:start position:0% +and what we're going to do instead is +we're going to take an ordinary camera + + align:start position:0% +we're going to take an ordinary camera + + + align:start position:0% +we're going to take an ordinary camera +and convert that + + align:start position:0% +and convert that + + + align:start position:0% +and convert that +into an array of virtual cameras + + align:start position:0% +into an array of virtual cameras + + + align:start position:0% +into an array of virtual cameras +so this is an array of physical cameras + + align:start position:0% +so this is an array of physical cameras + + + align:start position:0% +so this is an array of physical cameras +but it's expensive instead of that we'll + + align:start position:0% +but it's expensive instead of that we'll + + + align:start position:0% +but it's expensive instead of that we'll +take an ordinary camera and convert that + + align:start position:0% +take an ordinary camera and convert that + + + align:start position:0% +take an ordinary camera and convert that +into an array of virtual cameras + + align:start position:0% +into an array of virtual cameras + + + align:start position:0% +into an array of virtual cameras +so + + align:start position:0% +so + + + align:start position:0% +so +this is how it works you have + + align:start position:0% +this is how it works you have + + + align:start position:0% +this is how it works you have +in a traditional uh camera you + + align:start position:0% +in a traditional uh camera you + + + align:start position:0% +in a traditional uh camera you +if the object is in sharp focus + + align:start position:0% +if the object is in sharp focus + + + align:start position:0% +if the object is in sharp focus +the the radiance along each of this + + align:start position:0% +the the radiance along each of this + + + align:start position:0% +the the radiance along each of this +direction + + align:start position:0% +direction + + + align:start position:0% +direction +is convergent on a single pixel so you + + align:start position:0% +is convergent on a single pixel so you + + + align:start position:0% +is convergent on a single pixel so you +get a very sharp image of that point + + align:start position:0% +get a very sharp image of that point + + + align:start position:0% +get a very sharp image of that point +but any information about + + align:start position:0% +but any information about + + + align:start position:0% +but any information about +the radiance along each of these + + align:start position:0% +the radiance along each of these + + + align:start position:0% +the radiance along each of these +directions is completely lost + + align:start position:0% +directions is completely lost + + + align:start position:0% +directions is completely lost +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you get two image you have a 3d scene + + align:start position:0% +so you get two image you have a 3d scene + + + align:start position:0% +so you get two image you have a 3d scene +you get a 2d image + + align:start position:0% +you get a 2d image + + + align:start position:0% +you get a 2d image +so it's flattened the world is slack + + align:start position:0% + + + + align:start position:0% + +a trick you can do which was actually + + align:start position:0% +a trick you can do which was actually + + + align:start position:0% +a trick you can do which was actually +invented by + + align:start position:0% +invented by + + + align:start position:0% +invented by +ted ellison and + + align:start position:0% +ted ellison and + + + align:start position:0% +ted ellison and +and his student wong that just left + + align:start position:0% +and his student wong that just left + + + align:start position:0% +and his student wong that just left +is + + align:start position:0% + + + + align:start position:0% + +trying to capture the radiance along + + align:start position:0% +trying to capture the radiance along + + + align:start position:0% +trying to capture the radiance along +each of these directions + + align:start position:0% +each of these directions + + + align:start position:0% +each of these directions +um + + align:start position:0% +um + + + align:start position:0% +um +so how do you do that you just displace + + align:start position:0% +so how do you do that you just displace + + + align:start position:0% +so how do you do that you just displace +the sensor a little bit back + + align:start position:0% +the sensor a little bit back + + + align:start position:0% +the sensor a little bit back +and in front of that you put a micro + + align:start position:0% +and in front of that you put a micro + + + align:start position:0% +and in front of that you put a micro +lens array this is the same microlens + + align:start position:0% +lens array this is the same microlens + + + align:start position:0% +lens array this is the same microlens +array you use in lenticular displays you + + align:start position:0% +array you use in lenticular displays you + + + align:start position:0% +array you use in lenticular displays you +know those displays that change with + + align:start position:0% +know those displays that change with + + + align:start position:0% +know those displays that change with +viewpoint so + + align:start position:0% +viewpoint so + + + align:start position:0% +viewpoint so +so uh if you put that microlens array + + align:start position:0% +so uh if you put that microlens array + + + align:start position:0% +so uh if you put that microlens array +then as you can see each of this ray is + + align:start position:0% +then as you can see each of this ray is + + + align:start position:0% +then as you can see each of this ray is +actually incident on a different pixel + + align:start position:0% +actually incident on a different pixel + + + align:start position:0% +actually incident on a different pixel +and then you can capture the variation + + align:start position:0% +and then you can capture the variation + + + align:start position:0% +and then you can capture the variation +along each of the incoming grades now + + align:start position:0% +along each of the incoming grades now + + + align:start position:0% +along each of the incoming grades now +why would you care + + align:start position:0% +why would you care + + + align:start position:0% +why would you care +about + + align:start position:0% +about + + + align:start position:0% +about +capturing + + align:start position:0% +capturing + + + align:start position:0% +capturing +each of this rays it turns out + + align:start position:0% +each of this rays it turns out + + + align:start position:0% +each of this rays it turns out +that an appearance the appearance of the + + align:start position:0% +that an appearance the appearance of the + + + align:start position:0% +that an appearance the appearance of the +world + + align:start position:0% +world + + + align:start position:0% +world +coming through a lens + + align:start position:0% +coming through a lens + + + align:start position:0% +coming through a lens +can be completely described + + align:start position:0% +can be completely described + + + align:start position:0% +can be completely described +geometrically completely described by a + + align:start position:0% +geometrically completely described by a + + + align:start position:0% +geometrically completely described by a +four-dimensional function + + align:start position:0% +four-dimensional function + + + align:start position:0% +four-dimensional function +which is this light + + align:start position:0% +which is this light + + + align:start position:0% +which is this light +uh and that's a very powerful concept + + align:start position:0% +uh and that's a very powerful concept + + + align:start position:0% +uh and that's a very powerful concept +because if you do capture this + + align:start position:0% +because if you do capture this + + + align:start position:0% +because if you do capture this +full representation then you can do + + align:start position:0% +full representation then you can do + + + align:start position:0% +full representation then you can do +and that's all you could ever capture + + align:start position:0% +and that's all you could ever capture + + + align:start position:0% +and that's all you could ever capture +once you have this four different + + align:start position:0% +once you have this four different + + + align:start position:0% +once you have this four different +presentation you can manipulate that in + + align:start position:0% +presentation you can manipulate that in + + + align:start position:0% +presentation you can manipulate that in +many interesting ways + + align:start position:0% +many interesting ways + + + align:start position:0% +many interesting ways +so ted ellison and renning + + align:start position:0% +so ted ellison and renning + + + align:start position:0% +so ted ellison and renning +at stanford who also has a company now + + align:start position:0% +at stanford who also has a company now + + + align:start position:0% +at stanford who also has a company now +called refocus imaging + + align:start position:0% +called refocus imaging + + + align:start position:0% +called refocus imaging +are building these type of cameras with + + align:start position:0% +are building these type of cameras with + + + align:start position:0% +are building these type of cameras with +uh with lens letters + + align:start position:0% +uh with lens letters + + + align:start position:0% +uh with lens letters +now how did the stanford team do it + + align:start position:0% +now how did the stanford team do it + + + align:start position:0% +now how did the stanford team do it +they started with a medium format camera + + align:start position:0% +they started with a medium format camera + + + align:start position:0% +they started with a medium format camera +with a + + align:start position:0% +with a + + + align:start position:0% +with a +digital back and on the digital back + + align:start position:0% +digital back and on the digital back + + + align:start position:0% +digital back and on the digital back +they put this macro lens array where the + + align:start position:0% +they put this macro lens array where the + + + align:start position:0% +they put this macro lens array where the +pitch of the micro lens is 125 microns + + align:start position:0% +pitch of the micro lens is 125 microns + + + align:start position:0% +pitch of the micro lens is 125 microns +so pixels are about 9 microns so under + + align:start position:0% +so pixels are about 9 microns so under + + + align:start position:0% +so pixels are about 9 microns so under +each square tile they have about 14 by + + align:start position:0% +each square tile they have about 14 by + + + align:start position:0% +each square tile they have about 14 by +14 pixels + + align:start position:0% +14 pixels + + + align:start position:0% +14 pixels +uh and by so again going back here + + align:start position:0% +uh and by so again going back here + + + align:start position:0% +uh and by so again going back here +under each micro lens they have a 14 by + + align:start position:0% +under each micro lens they have a 14 by + + + align:start position:0% +under each micro lens they have a 14 by +14 array of fixes + + align:start position:0% +14 array of fixes + + + align:start position:0% +14 array of fixes +so what they're going to do now is + + align:start position:0% +so what they're going to do now is + + + align:start position:0% +so what they're going to do now is +they're going to take the 16 megapixel + + align:start position:0% +they're going to take the 16 megapixel + + + align:start position:0% +they're going to take the 16 megapixel +detector 4000 by 4000 pixels + + align:start position:0% +detector 4000 by 4000 pixels + + + align:start position:0% +detector 4000 by 4000 pixels +and have 292 by 292 pixel array sorry + + align:start position:0% +and have 292 by 292 pixel array sorry + + + align:start position:0% +and have 292 by 292 pixel array sorry +micro lens array under each micro lens + + align:start position:0% +micro lens array under each micro lens + + + align:start position:0% +micro lens array under each micro lens +14 by 14 pixels + + align:start position:0% +14 by 14 pixels + + + align:start position:0% +14 by 14 pixels +so at the end + + align:start position:0% +so at the end + + + align:start position:0% +so at the end +they have this one + + align:start position:0% +they have this one + + + align:start position:0% +they have this one +have this 116 megapixel image + + align:start position:0% +have this 116 megapixel image + + + align:start position:0% +have this 116 megapixel image +which after uh re + + align:start position:0% +which after uh re + + + align:start position:0% +which after uh re +shaping + + align:start position:0% +shaping + + + align:start position:0% +shaping +gives you this 292 by 292 pixel image + + align:start position:0% +gives you this 292 by 292 pixel image + + + align:start position:0% +gives you this 292 by 292 pixel image +one under each micro lens okay so we + + align:start position:0% +one under each micro lens okay so we + + + align:start position:0% +one under each micro lens okay so we +have given up a lot of resolution from + + align:start position:0% +have given up a lot of resolution from + + + align:start position:0% +have given up a lot of resolution from +16 megapixel we're down to + + align:start position:0% +16 megapixel we're down to + + + align:start position:0% +16 megapixel we're down to +292 by 292 okay + + align:start position:0% +292 by 292 okay + + + align:start position:0% +292 by 292 okay +but with that we can do some amazing we + + align:start position:0% +but with that we can do some amazing we + + + align:start position:0% +but with that we can do some amazing we +can do some amazing things we can do + + align:start position:0% +can do some amazing things we can do + + + align:start position:0% +can do some amazing things we can do +digital refocus + + align:start position:0% +digital refocus + + + align:start position:0% +digital refocus +completely in software + + align:start position:0% + + + + align:start position:0% + +so you have given up a lot of resolution + + align:start position:0% +so you have given up a lot of resolution + + + align:start position:0% +so you have given up a lot of resolution +but now you have complete control over + + align:start position:0% +but now you have complete control over + + + align:start position:0% +but now you have complete control over +where you can focus + + align:start position:0% +where you can focus + + + align:start position:0% +where you can focus +as you can imagine uh this is the same + + align:start position:0% +as you can imagine uh this is the same + + + align:start position:0% +as you can imagine uh this is the same +question you asked earlier from this i + + align:start position:0% +question you asked earlier from this i + + + align:start position:0% +question you asked earlier from this i +can also estimate depth + + align:start position:0% +can also estimate depth + + + align:start position:0% +can also estimate depth +because depending on when things come in + + align:start position:0% +because depending on when things come in + + + align:start position:0% +because depending on when things come in +focus i can assign a depth to each pixel + + align:start position:0% +focus i can assign a depth to each pixel + + + align:start position:0% +focus i can assign a depth to each pixel +so + + align:start position:0% +so + + + align:start position:0% +so +suddenly from a ordinary 2d sensor + + align:start position:0% +suddenly from a ordinary 2d sensor + + + align:start position:0% +suddenly from a ordinary 2d sensor +i have a camera which has + + align:start position:0% +i have a camera which has + + + align:start position:0% +i have a camera which has +how many virtual cameras + + align:start position:0% +how many virtual cameras + + + align:start position:0% +how many virtual cameras +here we have 5x5 how many virtual + + align:start position:0% +here we have 5x5 how many virtual + + + align:start position:0% +here we have 5x5 how many virtual +cameras here + + align:start position:0% + + + + align:start position:0% + +14x14 + + align:start position:0% +14x14 + + + align:start position:0% +14x14 +cameras what is that 2.8 no 196. + + align:start position:0% +cameras what is that 2.8 no 196. + + + align:start position:0% +cameras what is that 2.8 no 196. +but then each camera is 292.2 + + align:start position:0% +but then each camera is 292.2 + + + align:start position:0% +but then each camera is 292.2 +exactly it's very low resolution + + align:start position:0% +exactly it's very low resolution + + + align:start position:0% +exactly it's very low resolution +and + + align:start position:0% +and + + + align:start position:0% +and +so first kind of complaint is + + align:start position:0% +so first kind of complaint is + + + align:start position:0% +so first kind of complaint is +yes it gives you all this power but very + + align:start position:0% +yes it gives you all this power but very + + + align:start position:0% +yes it gives you all this power but very +low resolution and argument nowadays + + align:start position:0% +low resolution and argument nowadays + + + align:start position:0% +low resolution and argument nowadays +against that is + + align:start position:0% +against that is + + + align:start position:0% +against that is +whether you have a six mix of six + + align:start position:0% +whether you have a six mix of six + + + align:start position:0% +whether you have a six mix of six +megapixel camera or 16 megapixel camera + + align:start position:0% +megapixel camera or 16 megapixel camera + + + align:start position:0% +megapixel camera or 16 megapixel camera +it doesn't really matter you know we + + align:start position:0% +it doesn't really matter you know we + + + align:start position:0% +it doesn't really matter you know we +have reached uh + + align:start position:0% +have reached uh + + + align:start position:0% +have reached uh +you know + + align:start position:0% +you know + + + align:start position:0% +you know +we have you know diminishing returns + + align:start position:0% +we have you know diminishing returns + + + align:start position:0% +we have you know diminishing returns +after six megapixel + + align:start position:0% +after six megapixel + + + align:start position:0% +after six megapixel +so + + align:start position:0% +so + + + align:start position:0% +so +why not use those pixels for capturing + + align:start position:0% +why not use those pixels for capturing + + + align:start position:0% +why not use those pixels for capturing +some other information + + align:start position:0% +some other information + + + align:start position:0% +some other information +so that's what makes it extremely + + align:start position:0% +so that's what makes it extremely + + + align:start position:0% +so that's what makes it extremely +powerful + + align:start position:0% +powerful + + + align:start position:0% +powerful +and refocusing is only one + + align:start position:0% +and refocusing is only one + + + align:start position:0% +and refocusing is only one +depth sensing is another interaction + + align:start position:0% +depth sensing is another interaction + + + align:start position:0% +depth sensing is another interaction +uh dealing with operations in the scene + + align:start position:0% +uh dealing with operations in the scene + + + align:start position:0% +uh dealing with operations in the scene +a lot of interesting things you can do + + align:start position:0% +a lot of interesting things you can do + + + align:start position:0% +a lot of interesting things you can do +and again this is + + align:start position:0% +and again this is + + + align:start position:0% +and again this is +starting with a static 16 megapixel + + align:start position:0% +starting with a static 16 megapixel + + + align:start position:0% +starting with a static 16 megapixel +camera so it's not video rate + + align:start position:0% +camera so it's not video rate + + + align:start position:0% +camera so it's not video rate +but this one is video rate although it's + + align:start position:0% +but this one is video rate although it's + + + align:start position:0% +but this one is video rate although it's +only for 25 virtual cameras + + align:start position:0% + + + + align:start position:0% + +you could you could do that + + align:start position:0% +you could you could do that + + + align:start position:0% +you could you could do that +unfortunately the precision that you + + align:start position:0% +unfortunately the precision that you + + + align:start position:0% +unfortunately the precision that you +require is you know is a micrometer + + align:start position:0% +require is you know is a micrometer + + + align:start position:0% +require is you know is a micrometer +precision so + + align:start position:0% +precision so + + + align:start position:0% +precision so +it's a little bit challenging but you're + + align:start position:0% +it's a little bit challenging but you're + + + align:start position:0% +it's a little bit challenging but you're +right i mean + + align:start position:0% +right i mean + + + align:start position:0% +right i mean +i'm sure when cameras were designed in + + align:start position:0% +i'm sure when cameras were designed in + + + align:start position:0% +i'm sure when cameras were designed in +the beginning they had physical + + align:start position:0% +the beginning they had physical + + + align:start position:0% +the beginning they had physical +apertures that couldn't be changed and + + align:start position:0% +apertures that couldn't be changed and + + + align:start position:0% +apertures that couldn't be changed and +over time people figured out how to + + align:start position:0% +over time people figured out how to + + + align:start position:0% +over time people figured out how to +create variable apertures and so on so + + align:start position:0% +create variable apertures and so on so + + + align:start position:0% +create variable apertures and so on so +creating these dynamic elements is going + + align:start position:0% +creating these dynamic elements is going + + + align:start position:0% +creating these dynamic elements is going +to be the key for future cameras + + align:start position:0% +to be the key for future cameras + + + align:start position:0% +to be the key for future cameras +and people often ask me what are you + + align:start position:0% +and people often ask me what are you + + + align:start position:0% +and people often ask me what are you +know what are the things that are + + align:start position:0% +know what are the things that are + + + align:start position:0% +know what are the things that are +that you're going to see in the camera + + align:start position:0% +that you're going to see in the camera + + + align:start position:0% +that you're going to see in the camera +next and + + align:start position:0% +next and + + + align:start position:0% +next and +you know we already have high dynamic + + align:start position:0% +you know we already have high dynamic + + + align:start position:0% +you know we already have high dynamic +range next is color + + align:start position:0% +range next is color + + + align:start position:0% +range next is color +and we get a lot of you know journalists + + align:start position:0% +and we get a lot of you know journalists + + + align:start position:0% +and we get a lot of you know journalists +asking questions like this you know + + align:start position:0% +asking questions like this you know + + + align:start position:0% +asking questions like this you know +uh the future of photography you know a + + align:start position:0% +uh the future of photography you know a + + + align:start position:0% +uh the future of photography you know a +lot of popular magazine with a lot of + + align:start position:0% +lot of popular magazine with a lot of + + + align:start position:0% +lot of popular magazine with a lot of +junk in it + + align:start position:0% + + + + align:start position:0% + +including uh people who are not credible + + align:start position:0% +including uh people who are not credible + + + align:start position:0% +including uh people who are not credible +with pictures in there + + align:start position:0% +with pictures in there + + + align:start position:0% +with pictures in there +so + + align:start position:0% +so + + + align:start position:0% +so +to me the answer to that question is + + align:start position:0% +to me the answer to that question is + + + align:start position:0% +to me the answer to that question is +light fits that's going to the next big + + align:start position:0% +light fits that's going to the next big + + + align:start position:0% +light fits that's going to the next big +thing + + align:start position:0% +thing + + + align:start position:0% +thing +uh if you think about the top five + + align:start position:0% +uh if you think about the top five + + + align:start position:0% +uh if you think about the top five +feature that will appear in the camera + + align:start position:0% +feature that will appear in the camera + + + align:start position:0% +feature that will appear in the camera +it's exposure color number three is + + align:start position:0% +it's exposure color number three is + + + align:start position:0% +it's exposure color number three is +light filled + + align:start position:0% +light filled + + + align:start position:0% +light filled +so we'll see how long it's going to take + + align:start position:0% +so we'll see how long it's going to take + + + align:start position:0% +so we'll see how long it's going to take +before we have a full-fledged light fit + + align:start position:0% +before we have a full-fledged light fit + + + align:start position:0% +before we have a full-fledged light fit +camera as a consumer device + + align:start position:0% +camera as a consumer device + + + align:start position:0% +camera as a consumer device +um and again usually they're going to + + align:start position:0% +um and again usually they're going to + + + align:start position:0% +um and again usually they're going to +say hey but it's only 292 by 290 pixels + + align:start position:0% +say hey but it's only 292 by 290 pixels + + + align:start position:0% +say hey but it's only 292 by 290 pixels +but my guess is that + + align:start position:0% +but my guess is that + + + align:start position:0% +but my guess is that +by then we won't care about the the + + align:start position:0% +by then we won't care about the the + + + align:start position:0% +by then we won't care about the the +pixels + + align:start position:0% +pixels + + + align:start position:0% +pixels +number of cases + + align:start position:0% +number of cases + + + align:start position:0% +number of cases +so + + align:start position:0% +so + + + align:start position:0% +so +my group was extremely inspired by this + + align:start position:0% +my group was extremely inspired by this + + + align:start position:0% +my group was extremely inspired by this +work in 2004 2005 but we thought this is + + align:start position:0% +work in 2004 2005 but we thought this is + + + align:start position:0% +work in 2004 2005 but we thought this is +very challenging to create because you + + align:start position:0% +very challenging to create because you + + + align:start position:0% +very challenging to create because you +need a micro lens array + + align:start position:0% +need a micro lens array + + + align:start position:0% +need a micro lens array +so we said instead of using a macro lens + + align:start position:0% +so we said instead of using a macro lens + + + align:start position:0% +so we said instead of using a macro lens +array can i just print a transparency + + align:start position:0% +array can i just print a transparency + + + align:start position:0% +array can i just print a transparency +at home + + align:start position:0% +at home + + + align:start position:0% +at home +and + + align:start position:0% +and + + + align:start position:0% +and +create your site for camp + + align:start position:0% +create your site for camp + + + align:start position:0% +create your site for camp +so that's what we did + + align:start position:0% +so that's what we did + + + align:start position:0% +so that's what we did +which is called a mask-based light field + + align:start position:0% +which is called a mask-based light field + + + align:start position:0% +which is called a mask-based light field +camera + + align:start position:0% +camera + + + align:start position:0% +camera +and this is how you do it you + + align:start position:0% +and this is how you do it you + + + align:start position:0% +and this is how you do it you +start with a medium format + + align:start position:0% +start with a medium format + + + align:start position:0% +start with a medium format +camera in this case + + align:start position:0% +camera in this case + + + align:start position:0% +camera in this case +uh ammamiya + + align:start position:0% +uh ammamiya + + + align:start position:0% +uh ammamiya +on the digital back + + align:start position:0% +on the digital back + + + align:start position:0% +on the digital back +you just remove the ir filter + + align:start position:0% + + + + align:start position:0% + +and it turns out there's already some + + align:start position:0% +and it turns out there's already some + + + align:start position:0% +and it turns out there's already some +glass + + align:start position:0% +glass + + + align:start position:0% +glass +on top of the sensor which is about 1.2 + + align:start position:0% +on top of the sensor which is about 1.2 + + + align:start position:0% +on top of the sensor which is about 1.2 +millimeter sticks you just drop a + + align:start position:0% +millimeter sticks you just drop a + + + align:start position:0% +millimeter sticks you just drop a +transparency + + align:start position:0% +transparency + + + align:start position:0% +transparency +on top of it + + align:start position:0% +on top of it + + + align:start position:0% +on top of it +snap back the ir filter + + align:start position:0% +snap back the ir filter + + + align:start position:0% +snap back the ir filter +and that's it for about two dollars you + + align:start position:0% +and that's it for about two dollars you + + + align:start position:0% +and that's it for about two dollars you +can convert a medium format camera into + + align:start position:0% +can convert a medium format camera into + + + align:start position:0% +can convert a medium format camera into +a light field camera + + align:start position:0% + + + + align:start position:0% + +and the design looks something like this + + align:start position:0% +and the design looks something like this + + + align:start position:0% +and the design looks something like this +traditional camera + + align:start position:0% +traditional camera + + + align:start position:0% +traditional camera +traditional sensor but about one + + align:start position:0% +traditional sensor but about one + + + align:start position:0% +traditional sensor but about one +millimeter in front of it you have a + + align:start position:0% +millimeter in front of it you have a + + + align:start position:0% +millimeter in front of it you have a +printed mask + + align:start position:0% +printed mask + + + align:start position:0% +printed mask +very cheap + + align:start position:0% +very cheap + + + align:start position:0% +very cheap +using that we're able to convert + + align:start position:0% +using that we're able to convert + + + align:start position:0% +using that we're able to convert +this 2d camera into something that + + align:start position:0% +this 2d camera into something that + + + align:start position:0% +this 2d camera into something that +captures a 4d function + + align:start position:0% +captures a 4d function + + + align:start position:0% +captures a 4d function +and the concept is actually very similar + + align:start position:0% +and the concept is actually very similar + + + align:start position:0% +and the concept is actually very similar +to + + align:start position:0% +to + + + align:start position:0% +to +radio frequency heterodyne the reason + + align:start position:0% +radio frequency heterodyne the reason + + + align:start position:0% +radio frequency heterodyne the reason +why you can listen to multiple radio + + align:start position:0% +why you can listen to multiple radio + + + align:start position:0% +why you can listen to multiple radio +stations + + align:start position:0% +stations + + + align:start position:0% +stations +uh on a single antenna is because all + + align:start position:0% +uh on a single antenna is because all + + + align:start position:0% +uh on a single antenna is because all +those stations are transmitting using + + align:start position:0% +those stations are transmitting using + + + align:start position:0% +those stations are transmitting using +either amplitude or frequency modulation + + align:start position:0% +either amplitude or frequency modulation + + + align:start position:0% +either amplitude or frequency modulation +and then in software in your car you can + + align:start position:0% +and then in software in your car you can + + + align:start position:0% +and then in software in your car you can +tune into any one of those channels + + align:start position:0% +tune into any one of those channels + + + align:start position:0% +tune into any one of those channels +and decompose + + align:start position:0% +and decompose + + + align:start position:0% +and decompose +and decode any one of those + + align:start position:0% +and decode any one of those + + + align:start position:0% +and decode any one of those +radio stations and what we're doing here + + align:start position:0% +radio stations and what we're doing here + + + align:start position:0% +radio stations and what we're doing here +is very similar we are doing that in + + align:start position:0% +is very similar we are doing that in + + + align:start position:0% +is very similar we are doing that in +optical domain and that's why we call it + + align:start position:0% +optical domain and that's why we call it + + + align:start position:0% +optical domain and that's why we call it +optical heterodyning in space not in + + align:start position:0% +optical heterodyning in space not in + + + align:start position:0% +optical heterodyning in space not in +time where you have the object it's + + align:start position:0% +time where you have the object it's + + + align:start position:0% +time where you have the object it's +forming an image on the sensor but we're + + align:start position:0% +forming an image on the sensor but we're + + + align:start position:0% +forming an image on the sensor but we're +going to take this photographic signal + + align:start position:0% +going to take this photographic signal + + + align:start position:0% +going to take this photographic signal +which is four dimensional not + + align:start position:0% +which is four dimensional not + + + align:start position:0% +which is four dimensional not +two-dimensional + + align:start position:0% +two-dimensional + + + align:start position:0% +two-dimensional +and use this carrier + + align:start position:0% +and use this carrier + + + align:start position:0% +and use this carrier +and then create a modulated signal so + + align:start position:0% +and then create a modulated signal so + + + align:start position:0% +and then create a modulated signal so +again for those of you with a + + align:start position:0% +again for those of you with a + + + align:start position:0% +again for those of you with a +communication background + + align:start position:0% +communication background + + + align:start position:0% +communication background +this analogy will work and then a + + align:start position:0% +this analogy will work and then a + + + align:start position:0% +this analogy will work and then a +software + + align:start position:0% +software + + + align:start position:0% +software +knowing this carrier we can demodulate + + align:start position:0% +knowing this carrier we can demodulate + + + align:start position:0% +knowing this carrier we can demodulate +that and recover this four-dimensional + + align:start position:0% +that and recover this four-dimensional + + + align:start position:0% +that and recover this four-dimensional +electrode + + align:start position:0% +electrode + + + align:start position:0% +electrode +so it's possible to do it with a very + + align:start position:0% +so it's possible to do it with a very + + + align:start position:0% +so it's possible to do it with a very +low cost + + align:start position:0% +low cost + + + align:start position:0% +low cost +uh so i can keep the lights in + + align:start position:0% + + + + align:start position:0% + +yeah yeah + + align:start position:0% +yeah yeah + + + align:start position:0% +yeah yeah +maybe the other one + + align:start position:0% +maybe the other one + + + align:start position:0% +maybe the other one +thanks + + align:start position:0% +thanks + + + align:start position:0% +thanks +uh and this is a photo that we capture + + align:start position:0% +uh and this is a photo that we capture + + + align:start position:0% +uh and this is a photo that we capture +with our mask-based light camera if you + + align:start position:0% +with our mask-based light camera if you + + + align:start position:0% +with our mask-based light camera if you +zoom in it has the in-focus parts are + + align:start position:0% +zoom in it has the in-focus parts are + + + align:start position:0% +zoom in it has the in-focus parts are +actually okay the outer focus part has + + align:start position:0% +actually okay the outer focus part has + + + align:start position:0% +actually okay the outer focus part has +this really strange encoding + + align:start position:0% +this really strange encoding + + + align:start position:0% +this really strange encoding +because of the high frequency mask but + + align:start position:0% +because of the high frequency mask but + + + align:start position:0% +because of the high frequency mask but +then in software it turns and this is + + align:start position:0% +then in software it turns and this is + + + align:start position:0% +then in software it turns and this is +this is how the mask looks like + + align:start position:0% +this is how the mask looks like + + + align:start position:0% +this is how the mask looks like +the printed mask and in software it + + align:start position:0% +the printed mask and in software it + + + align:start position:0% +the printed mask and in software it +turns out that + + align:start position:0% +turns out that + + + align:start position:0% +turns out that +by applying uh appropriate signal + + align:start position:0% +by applying uh appropriate signal + + + align:start position:0% +by applying uh appropriate signal +processing framework we can decode that + + align:start position:0% +processing framework we can decode that + + + align:start position:0% +processing framework we can decode that +and recover it so this is a 2d frequency + + align:start position:0% +and recover it so this is a 2d frequency + + + align:start position:0% +and recover it so this is a 2d frequency +transform of a traditional photo where + + align:start position:0% +transform of a traditional photo where + + + align:start position:0% +transform of a traditional photo where +most of the energy is in the baseband + + align:start position:0% +most of the energy is in the baseband + + + align:start position:0% +most of the energy is in the baseband +and after applying this very high + + align:start position:0% +and after applying this very high + + + align:start position:0% +and after applying this very high +frequency mask in the optical path + + align:start position:0% +frequency mask in the optical path + + + align:start position:0% +frequency mask in the optical path +it actually encodes this information + + align:start position:0% +it actually encodes this information + + + align:start position:0% +it actually encodes this information +in + + align:start position:0% +in + + + align:start position:0% +in +in this particular case a nine by nine + + align:start position:0% +in this particular case a nine by nine + + + align:start position:0% +in this particular case a nine by nine +uh + + align:start position:0% +uh + + + align:start position:0% +uh +windows of the of the fourier transform + + align:start position:0% +windows of the of the fourier transform + + + align:start position:0% +windows of the of the fourier transform +um and this intentional aliasing or + + align:start position:0% +um and this intentional aliasing or + + + align:start position:0% +um and this intentional aliasing or +heterodyning allows you to capture the + + align:start position:0% +heterodyning allows you to capture the + + + align:start position:0% +heterodyning allows you to capture the +additional two degrees of freedom + + align:start position:0% +additional two degrees of freedom + + + align:start position:0% +additional two degrees of freedom +uh and so + + align:start position:0% +uh and so + + + align:start position:0% +uh and so +the process is very simple you take this + + align:start position:0% +the process is very simple you take this + + + align:start position:0% +the process is very simple you take this +photo which is about four megapixel uh + + align:start position:0% +photo which is about four megapixel uh + + + align:start position:0% +photo which is about four megapixel uh +you take this 2d fourier transform you + + align:start position:0% +you take this 2d fourier transform you + + + align:start position:0% +you take this 2d fourier transform you +reshape that to a 4d for 4d function and + + align:start position:0% +reshape that to a 4d for 4d function and + + + align:start position:0% +reshape that to a 4d for 4d function and +then you take the inverse fourier + + align:start position:0% +then you take the inverse fourier + + + align:start position:0% +then you take the inverse fourier +transform to create this 81 virtual + + align:start position:0% +transform to create this 81 virtual + + + align:start position:0% +transform to create this 81 virtual +canvas in this case 9x9 this was 5x5 + + align:start position:0% +canvas in this case 9x9 this was 5x5 + + + align:start position:0% +canvas in this case 9x9 this was 5x5 +this is 919. and the best way to show + + align:start position:0% +this is 919. and the best way to show + + + align:start position:0% +this is 919. and the best way to show +that is to + + align:start position:0% +that is to + + + align:start position:0% +that is to +see how that photo will look like + + align:start position:0% +see how that photo will look like + + + align:start position:0% +see how that photo will look like +when there's a small parallax between + + align:start position:0% +when there's a small parallax between + + + align:start position:0% +when there's a small parallax between +each of the virtual cameras + + align:start position:0% +each of the virtual cameras + + + align:start position:0% +each of the virtual cameras +and again from these 81 images you can + + align:start position:0% +and again from these 81 images you can + + + align:start position:0% +and again from these 81 images you can +estimate depth you can create refocused + + align:start position:0% +estimate depth you can create refocused + + + align:start position:0% +estimate depth you can create refocused +images and all that the same thing that + + align:start position:0% +images and all that the same thing that + + + align:start position:0% +images and all that the same thing that +uh wrote was showing for refocusing + + align:start position:0% +uh wrote was showing for refocusing + + + align:start position:0% +uh wrote was showing for refocusing +from here to + + align:start position:0% +from here to + + + align:start position:0% +from here to +yeah i guess infinity + + align:start position:0% +yeah i guess infinity + + + align:start position:0% +yeah i guess infinity +back and forth + + align:start position:0% +back and forth + + + align:start position:0% +back and forth +so you can do that with an ordinary + + align:start position:0% +so you can do that with an ordinary + + + align:start position:0% +so you can do that with an ordinary +camera + + align:start position:0% +camera + + + align:start position:0% +camera +with this uh + + align:start position:0% +with this uh + + + align:start position:0% +with this uh +a small change with mask and all the + + align:start position:0% +a small change with mask and all the + + + align:start position:0% +a small change with mask and all the +software is online and this will not be + + align:start position:0% +software is online and this will not be + + + align:start position:0% +software is online and this will not be +part of any assignment but you're + + align:start position:0% +part of any assignment but you're + + + align:start position:0% +part of any assignment but you're +welcome to take that up as an assignment + + align:start position:0% +welcome to take that up as an assignment + + + align:start position:0% +welcome to take that up as an assignment +or as a project + + align:start position:0% +or as a project + + + align:start position:0% +or as a project +maybe we can get likes back inside + + align:start position:0% + + + + align:start position:0% + +um what are some other things you can do + + align:start position:0% +um what are some other things you can do + + + align:start position:0% +um what are some other things you can do +um as i said + + align:start position:0% +um as i said + + + align:start position:0% +um as i said +uh in terms of the desired camera + + align:start position:0% +uh in terms of the desired camera + + + align:start position:0% +uh in terms of the desired camera +features it's + + align:start position:0% +features it's + + + align:start position:0% +features it's +dynamic range color and then lights in + + align:start position:0% +dynamic range color and then lights in + + + align:start position:0% +dynamic range color and then lights in +terms of color + + align:start position:0% +terms of color + + + align:start position:0% +terms of color +uh ankit mohan was a scientist in a + + align:start position:0% +uh ankit mohan was a scientist in a + + + align:start position:0% +uh ankit mohan was a scientist in a +group + + align:start position:0% + + + + align:start position:0% + +that was part of his thesis + + align:start position:0% +that was part of his thesis + + + align:start position:0% +that was part of his thesis +he said let's think about color as not + + align:start position:0% +he said let's think about color as not + + + align:start position:0% +he said let's think about color as not +multispectral imagery + + align:start position:0% +multispectral imagery + + + align:start position:0% +multispectral imagery +but more like an audio synthesizer you + + align:start position:0% +but more like an audio synthesizer you + + + align:start position:0% +but more like an audio synthesizer you +know if you have an audio system and + + align:start position:0% +know if you have an audio system and + + + align:start position:0% +know if you have an audio system and +you're within listening to rock or jazz + + align:start position:0% +you're within listening to rock or jazz + + + align:start position:0% +you're within listening to rock or jazz +or pop or + + align:start position:0% +or pop or + + + align:start position:0% +or pop or +you know country music uh you tune your + + align:start position:0% +you know country music uh you tune your + + + align:start position:0% +you know country music uh you tune your +boss and treble accordingly or maybe you + + align:start position:0% +boss and treble accordingly or maybe you + + + align:start position:0% +boss and treble accordingly or maybe you +have a profile so that + + align:start position:0% +have a profile so that + + + align:start position:0% +have a profile so that +the the the frequency profiler of your + + align:start position:0% +the the the frequency profiler of your + + + align:start position:0% +the the the frequency profiler of your +of your synthesizer is appropriate for + + align:start position:0% +of your synthesizer is appropriate for + + + align:start position:0% +of your synthesizer is appropriate for +that particular type of music + + align:start position:0% +that particular type of music + + + align:start position:0% +that particular type of music +the same thing should be possible for + + align:start position:0% +the same thing should be possible for + + + align:start position:0% +the same thing should be possible for +photography as well + + align:start position:0% +photography as well + + + align:start position:0% +photography as well +if you are in a you know you're in the + + align:start position:0% +if you are in a you know you're in the + + + align:start position:0% +if you are in a you know you're in the +woods you would like to + + align:start position:0% +woods you would like to + + + align:start position:0% +woods you would like to +look at most of the green channel to see + + align:start position:0% +look at most of the green channel to see + + + align:start position:0% +look at most of the green channel to see +how the variation of different leaves + + align:start position:0% +how the variation of different leaves + + + align:start position:0% +how the variation of different leaves +and and and and + + align:start position:0% +and and and and + + + align:start position:0% +and and and and +you know all the nature + + align:start position:0% +you know all the nature + + + align:start position:0% +you know all the nature +is is captured with sufficient variation + + align:start position:0% +is is captured with sufficient variation + + + align:start position:0% +is is captured with sufficient variation +maybe you don't care so much about reds + + align:start position:0% +maybe you don't care so much about reds + + + align:start position:0% +maybe you don't care so much about reds +and and blues there + + align:start position:0% +and and blues there + + + align:start position:0% +and and blues there +uh on the other hand if you are uh near + + align:start position:0% +uh on the other hand if you are uh near + + + align:start position:0% +uh on the other hand if you are uh near +an ocean maybe you mostly care about the + + align:start position:0% +an ocean maybe you mostly care about the + + + align:start position:0% +an ocean maybe you mostly care about the +blue shades + + align:start position:0% +blue shades + + + align:start position:0% +blue shades +uh and so on so what i would like to do + + align:start position:0% +uh and so on so what i would like to do + + + align:start position:0% +uh and so on so what i would like to do +my photographers do this all the time + + align:start position:0% +my photographers do this all the time + + + align:start position:0% +my photographers do this all the time +you know they carry a set of filters + + align:start position:0% +you know they carry a set of filters + + + align:start position:0% +you know they carry a set of filters +with them and if they are + + align:start position:0% +with them and if they are + + + align:start position:0% +with them and if they are +if they are looking at + + align:start position:0% +if they are looking at + + + align:start position:0% +if they are looking at +broad sunlight they put one type of + + align:start position:0% +broad sunlight they put one type of + + + align:start position:0% +broad sunlight they put one type of +filter if they are on the beach they put + + align:start position:0% +filter if they are on the beach they put + + + align:start position:0% +filter if they are on the beach they put +another filter and so on what i would + + align:start position:0% +another filter and so on what i would + + + align:start position:0% +another filter and so on what i would +like to do is create a + + align:start position:0% +like to do is create a + + + align:start position:0% +like to do is create a +knob right on the camera just like an + + align:start position:0% +knob right on the camera just like an + + + align:start position:0% +knob right on the camera just like an +audio synthesizer that says boost red + + align:start position:0% +audio synthesizer that says boost red + + + align:start position:0% +audio synthesizer that says boost red +suppress green + + align:start position:0% +suppress green + + + align:start position:0% +suppress green +and you know create any profile you want + + align:start position:0% +and you know create any profile you want + + + align:start position:0% +and you know create any profile you want +so creating this programmable wavelength + + align:start position:0% +so creating this programmable wavelength + + + align:start position:0% +so creating this programmable wavelength +uh would be extremely powerful so unkits + + align:start position:0% +uh would be extremely powerful so unkits + + + align:start position:0% +uh would be extremely powerful so unkits +project basically achieved that which he + + align:start position:0% +project basically achieved that which he + + + align:start position:0% +project basically achieved that which he +calls agile spectrum imaging or + + align:start position:0% +calls agile spectrum imaging or + + + align:start position:0% +calls agile spectrum imaging or +programmable wavelength imaging so it's + + align:start position:0% +programmable wavelength imaging so it's + + + align:start position:0% +programmable wavelength imaging so it's +very powerful concept and hopefully it + + align:start position:0% +very powerful concept and hopefully it + + + align:start position:0% +very powerful concept and hopefully it +will appear + + align:start position:0% +will appear + + + align:start position:0% +will appear +in in cameras as well you can imagine + + align:start position:0% +in in cameras as well you can imagine + + + align:start position:0% +in in cameras as well you can imagine +this is very useful for medical imaging + + align:start position:0% +this is very useful for medical imaging + + + align:start position:0% +this is very useful for medical imaging +uh you know when you go to the dentist + + align:start position:0% +uh you know when you go to the dentist + + + align:start position:0% +uh you know when you go to the dentist +and they're putting + + align:start position:0% +and they're putting + + + align:start position:0% +and they're putting +what's it called enamel + + align:start position:0% +what's it called enamel + + + align:start position:0% +what's it called enamel +to change the color of your tooth + + align:start position:0% + + + + align:start position:0% + +the whitening yeah the whitening what is + + align:start position:0% +the whitening yeah the whitening what is + + + align:start position:0% +the whitening yeah the whitening what is +it called + + align:start position:0% +it called + + + align:start position:0% +it called +bleach yeah yeah and you know the + + align:start position:0% +bleach yeah yeah and you know the + + + align:start position:0% +bleach yeah yeah and you know the +problem with that is + + align:start position:0% +problem with that is + + + align:start position:0% +problem with that is +in the the + + align:start position:0% +in the the + + + align:start position:0% +in the the +dentist's office everything looks fine + + align:start position:0% +dentist's office everything looks fine + + + align:start position:0% +dentist's office everything looks fine +but you know you go elsewhere and + + align:start position:0% +but you know you go elsewhere and + + + align:start position:0% +but you know you go elsewhere and +somebody takes a flash photo and the guy + + align:start position:0% +somebody takes a flash photo and the guy + + + align:start position:0% +somebody takes a flash photo and the guy +with the teeth fake teeth or or bleach + + align:start position:0% +with the teeth fake teeth or or bleach + + + align:start position:0% +with the teeth fake teeth or or bleach +teeth you know + + align:start position:0% +teeth you know + + + align:start position:0% +teeth you know +looks looks extremely different and + + align:start position:0% +looks looks extremely different and + + + align:start position:0% +looks looks extremely different and +that's mental because the wavelength + + align:start position:0% +that's mental because the wavelength + + + align:start position:0% +that's mental because the wavelength +profile of a flash is very different + + align:start position:0% +profile of a flash is very different + + + align:start position:0% +profile of a flash is very different +from weapon profile of + + align:start position:0% +from weapon profile of + + + align:start position:0% +from weapon profile of +tube lights + + align:start position:0% +tube lights + + + align:start position:0% +tube lights +so what doctors would like to do is see + + align:start position:0% +so what doctors would like to do is see + + + align:start position:0% +so what doctors would like to do is see +the neighboring teeth under all + + align:start position:0% +the neighboring teeth under all + + + align:start position:0% +the neighboring teeth under all +different lighting conditions + + align:start position:0% +different lighting conditions + + + align:start position:0% +different lighting conditions +so that they're still matched + + align:start position:0% +so that they're still matched + + + align:start position:0% +so that they're still matched +for example and this is true of + + align:start position:0% +for example and this is true of + + + align:start position:0% +for example and this is true of +i didn't show you the when we were where + + align:start position:0% +i didn't show you the when we were where + + + align:start position:0% +i didn't show you the when we were where +you want to see the wings + + align:start position:0% +you want to see the wings + + + align:start position:0% +you want to see the wings +and depending on + + align:start position:0% +and depending on + + + align:start position:0% +and depending on +oxygenated or deoxygenated blood you + + align:start position:0% +oxygenated or deoxygenated blood you + + + align:start position:0% +oxygenated or deoxygenated blood you +know the hemoglobin you can figure out + + align:start position:0% +know the hemoglobin you can figure out + + + align:start position:0% +know the hemoglobin you can figure out +which veins should be used to poke the + + align:start position:0% +which veins should be used to poke the + + + align:start position:0% +which veins should be used to poke the +needles + + align:start position:0% +needles + + + align:start position:0% +needles +uh and again that can be looked into + + align:start position:0% +uh and again that can be looked into + + + align:start position:0% +uh and again that can be looked into +very narrow wavelengths so they don't + + align:start position:0% +very narrow wavelengths so they don't + + + align:start position:0% +very narrow wavelengths so they don't +know + + align:start position:0% +know + + + align:start position:0% +know +in that case they might know but in + + align:start position:0% +in that case they might know but in + + + align:start position:0% +in that case they might know but in +different applications they may not know + + align:start position:0% +different applications they may not know + + + align:start position:0% +different applications they may not know +a priori which wavelength you should be + + align:start position:0% +a priori which wavelength you should be + + + align:start position:0% +a priori which wavelength you should be +looking at and so by creating this + + align:start position:0% +looking at and so by creating this + + + align:start position:0% +looking at and so by creating this +programmable spectrum camera you can do + + align:start position:0% +programmable spectrum camera you can do + + + align:start position:0% +programmable spectrum camera you can do +uh again very interesting things + + align:start position:0% +uh again very interesting things + + + align:start position:0% +uh again very interesting things +so we'll be looking at that + + align:start position:0% +so we'll be looking at that + + + align:start position:0% +so we'll be looking at that +glare is another challenging problem + + align:start position:0% +glare is another challenging problem + + + align:start position:0% +glare is another challenging problem +right if you have a bright sunlight uh + + align:start position:0% +right if you have a bright sunlight uh + + + align:start position:0% +right if you have a bright sunlight uh +it's very clear sometimes it's for + + align:start position:0% +it's very clear sometimes it's for + + + align:start position:0% +it's very clear sometimes it's for +artistic effects sometimes it's just + + align:start position:0% +artistic effects sometimes it's just + + + align:start position:0% +artistic effects sometimes it's just +annoying + + align:start position:0% +annoying + + + align:start position:0% +annoying +so can you take a photo + + align:start position:0% +so can you take a photo + + + align:start position:0% +so can you take a photo +that has + + align:start position:0% +that has + + + align:start position:0% +that has +uh this concentric rings because of + + align:start position:0% +uh this concentric rings because of + + + align:start position:0% +uh this concentric rings because of +glare + + align:start position:0% +glare + + + align:start position:0% +glare +and either boost the glare + + align:start position:0% +and either boost the glare + + + align:start position:0% +and either boost the glare +you know create some cheesy effects like + + align:start position:0% +you know create some cheesy effects like + + + align:start position:0% +you know create some cheesy effects like +it's a rainbow + + align:start position:0% +it's a rainbow + + + align:start position:0% +it's a rainbow +transition here from blue to red + + align:start position:0% +transition here from blue to red + + + align:start position:0% +transition here from blue to red +or actually suppress that layer + + align:start position:0% +or actually suppress that layer + + + align:start position:0% +or actually suppress that layer +again all from a single photo + + align:start position:0% +again all from a single photo + + + align:start position:0% +again all from a single photo +so it turns out layer can also be + + align:start position:0% +so it turns out layer can also be + + + align:start position:0% +so it turns out layer can also be +captured using a light free camera + + align:start position:0% +captured using a light free camera + + + align:start position:0% +captured using a light free camera +if you have a bright light such as this + + align:start position:0% + + + + align:start position:0% + +let's see this is a bright light and + + align:start position:0% +let's see this is a bright light and + + + align:start position:0% +let's see this is a bright light and +this is some other scene the bright + + align:start position:0% +this is some other scene the bright + + + align:start position:0% +this is some other scene the bright +light will create a sharp photo but + + align:start position:0% +light will create a sharp photo but + + + align:start position:0% +light will create a sharp photo but +because of inter-reflection the frontal + + align:start position:0% +because of inter-reflection the frontal + + + align:start position:0% +because of inter-reflection the frontal +reflection in the lenses also create a + + align:start position:0% +reflection in the lenses also create a + + + align:start position:0% +reflection in the lenses also create a +glare effect and contributes to + + align:start position:0% +glare effect and contributes to + + + align:start position:0% +glare effect and contributes to +the wrong part of the image but again + + align:start position:0% +the wrong part of the image but again + + + align:start position:0% +the wrong part of the image but again +what we will learn in this class is that + + align:start position:0% +what we will learn in this class is that + + + align:start position:0% +what we will learn in this class is that +by doing this 4d sampling you have + + align:start position:0% +by doing this 4d sampling you have + + + align:start position:0% +by doing this 4d sampling you have +complete control over the lens flare and + + align:start position:0% +complete control over the lens flare and + + + align:start position:0% +complete control over the lens flare and +certain types of clear + + align:start position:0% + + + + align:start position:0% + +uh this again light fit concept for + + align:start position:0% +uh this again light fit concept for + + + align:start position:0% +uh this again light fit concept for +uh camera array stanford and professor + + align:start position:0% +uh camera array stanford and professor + + + align:start position:0% +uh camera array stanford and professor +mark lewis are the world leaders in + + align:start position:0% +mark lewis are the world leaders in + + + align:start position:0% +mark lewis are the world leaders in +thinking about light fluids and light + + align:start position:0% +thinking about light fluids and light + + + align:start position:0% +thinking about light fluids and light +filled cameras so they've built this + + align:start position:0% +filled cameras so they've built this + + + align:start position:0% +filled cameras so they've built this +amazing + + align:start position:0% + + + + align:start position:0% + +camera array the electronic storage + + align:start position:0% +camera array the electronic storage + + + align:start position:0% +camera array the electronic storage +optics and so on in this case i believe + + align:start position:0% +optics and so on in this case i believe + + + align:start position:0% +optics and so on in this case i believe +about 51 cameras uh and then they can do + + align:start position:0% +about 51 cameras uh and then they can do + + + align:start position:0% +about 51 cameras uh and then they can do +very interesting things so here's a + + align:start position:0% +very interesting things so here's a + + + align:start position:0% +very interesting things so here's a +scene we have about 51 cameras looking + + align:start position:0% +scene we have about 51 cameras looking + + + align:start position:0% +scene we have about 51 cameras looking +at the + + align:start position:0% +at the + + + align:start position:0% +at the +at the + + align:start position:0% + + + + align:start position:0% + +scene with behind the behind the + + align:start position:0% +scene with behind the behind the + + + align:start position:0% +scene with behind the behind the +bushes and trees + + align:start position:0% +bushes and trees + + + align:start position:0% +bushes and trees +and + + align:start position:0% +and + + + align:start position:0% +and +this is how it looks uh focus on that + + align:start position:0% +this is how it looks uh focus on that + + + align:start position:0% +this is how it looks uh focus on that +part + + align:start position:0% +part + + + align:start position:0% +part +and by doing refocusing + + align:start position:0% +and by doing refocusing + + + align:start position:0% +and by doing refocusing +you can see what's behind the screens + + align:start position:0% +you can see what's behind the screens + + + align:start position:0% +you can see what's behind the screens +so this is + + align:start position:0% +so this is + + + align:start position:0% +so this is +just + + align:start position:0% +just + + + align:start position:0% +just +you're just doing virtual refocusing + + align:start position:0% +you're just doing virtual refocusing + + + align:start position:0% +you're just doing virtual refocusing +in the scene + + align:start position:0% +in the scene + + + align:start position:0% +in the scene +and by doing that by using extremely + + align:start position:0% +and by doing that by using extremely + + + align:start position:0% +and by doing that by using extremely +large aperture you can see what's behind + + align:start position:0% +large aperture you can see what's behind + + + align:start position:0% +large aperture you can see what's behind +this + + align:start position:0% +this + + + align:start position:0% +this +this bushes + + align:start position:0% +this bushes + + + align:start position:0% +this bushes +and this is purely focusing you can do + + align:start position:0% +and this is purely focusing you can do + + + align:start position:0% +and this is purely focusing you can do +additional computational techniques to + + align:start position:0% +additional computational techniques to + + + align:start position:0% +additional computational techniques to +recover + + align:start position:0% +recover + + + align:start position:0% +recover +what's behind the trees + + align:start position:0% +what's behind the trees + + + align:start position:0% +what's behind the trees +uh so a lot of things in computational + + align:start position:0% +uh so a lot of things in computational + + + align:start position:0% +uh so a lot of things in computational +camera and photography are really about + + align:start position:0% +camera and photography are really about + + + align:start position:0% +camera and photography are really about +magic + + align:start position:0% +magic + + + align:start position:0% +magic +um you know how can you look around the + + align:start position:0% +um you know how can you look around the + + + align:start position:0% +um you know how can you look around the +corner how can you can look behind the + + align:start position:0% +corner how can you can look behind the + + + align:start position:0% +corner how can you can look behind the +trees how can inside the body + + align:start position:0% +trees how can inside the body + + + align:start position:0% +trees how can inside the body +uh and and so on so that's why i like + + align:start position:0% +uh and and so on so that's why i like + + + align:start position:0% +uh and and so on so that's why i like +this field it's like magic tricks and + + align:start position:0% +this field it's like magic tricks and + + + align:start position:0% +this field it's like magic tricks and +somebody shows once in a while you come + + align:start position:0% +somebody shows once in a while you come + + + align:start position:0% +somebody shows once in a while you come +up with your own magic trick + + align:start position:0% +up with your own magic trick + + + align:start position:0% +up with your own magic trick +uh and every some other times people + + align:start position:0% +uh and every some other times people + + + align:start position:0% +uh and every some other times people +show you a magic trick and different + + align:start position:0% +show you a magic trick and different + + + align:start position:0% +show you a magic trick and different +people figure out you know different + + align:start position:0% +people figure out you know different + + + align:start position:0% +people figure out you know different +ways of achieving the same magic + + align:start position:0% +ways of achieving the same magic + + + align:start position:0% +ways of achieving the same magic +uh and + + align:start position:0% +uh and + + + align:start position:0% +uh and +that's why it's such a vibrant new field + + align:start position:0% +that's why it's such a vibrant new field + + + align:start position:0% +that's why it's such a vibrant new field +uh the way synthetic aperture works is + + align:start position:0% +uh the way synthetic aperture works is + + + align:start position:0% +uh the way synthetic aperture works is +you know the same way if i if i hold a + + align:start position:0% +you know the same way if i if i hold a + + + align:start position:0% +you know the same way if i if i hold a +needle next to my eye not poking my eye + + align:start position:0% +needle next to my eye not poking my eye + + + align:start position:0% +needle next to my eye not poking my eye +but just right next to my eye then if i + + align:start position:0% +but just right next to my eye then if i + + + align:start position:0% +but just right next to my eye then if i +focus on the needle i'll see it + + align:start position:0% +focus on the needle i'll see it + + + align:start position:0% +focus on the needle i'll see it +but if i focus far away + + align:start position:0% +but if i focus far away + + + align:start position:0% +but if i focus far away +then this needle just becomes blurred + + align:start position:0% +then this needle just becomes blurred + + + align:start position:0% +then this needle just becomes blurred +and this does not occlude occlude what's + + align:start position:0% +and this does not occlude occlude what's + + + align:start position:0% +and this does not occlude occlude what's +behind and the same concept + + align:start position:0% +behind and the same concept + + + align:start position:0% +behind and the same concept +is for synthetic aperture it's used in + + align:start position:0% +is for synthetic aperture it's used in + + + align:start position:0% +is for synthetic aperture it's used in +radar it's used in astronomy + + align:start position:0% +radar it's used in astronomy + + + align:start position:0% +radar it's used in astronomy +and all you have is an array of + + align:start position:0% +and all you have is an array of + + + align:start position:0% +and all you have is an array of +array of + + align:start position:0% +array of + + + align:start position:0% +array of +receivers whether it's antennas or + + align:start position:0% +receivers whether it's antennas or + + + align:start position:0% +receivers whether it's antennas or +whether it's + + align:start position:0% +whether it's + + + align:start position:0% +whether it's +microphones whatever it is + + align:start position:0% +microphones whatever it is + + + align:start position:0% +microphones whatever it is +in this case canvas array of canvas + + align:start position:0% +in this case canvas array of canvas + + + align:start position:0% +in this case canvas array of canvas +and if you have a very very large + + align:start position:0% +and if you have a very very large + + + align:start position:0% +and if you have a very very large +aperture then a point that was occluding + + align:start position:0% +aperture then a point that was occluding + + + align:start position:0% +aperture then a point that was occluding +some point behind + + align:start position:0% +some point behind + + + align:start position:0% +some point behind +ends up being extremely blurred so it + + align:start position:0% +ends up being extremely blurred so it + + + align:start position:0% +ends up being extremely blurred so it +does not impact + + align:start position:0% +does not impact + + + align:start position:0% +does not impact +what's behind that uh if you have a very + + align:start position:0% +what's behind that uh if you have a very + + + align:start position:0% +what's behind that uh if you have a very +narrow aperture camera you cannot do + + align:start position:0% +narrow aperture camera you cannot do + + + align:start position:0% +narrow aperture camera you cannot do +that + + align:start position:0% +that + + + align:start position:0% +that +but you can do that if you have a like + + align:start position:0% +but you can do that if you have a like + + + align:start position:0% +but you can do that if you have a like +while very wide aperture cam + + align:start position:0% + + + + align:start position:0% + +so we saw that + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +what about + + align:start position:0% +what about + + + align:start position:0% +what about +medical imaging such as computer + + align:start position:0% +medical imaging such as computer + + + align:start position:0% +medical imaging such as computer +tomography + + align:start position:0% +tomography + + + align:start position:0% +tomography +and + + align:start position:0% +and + + + align:start position:0% +and +now we're jumping from photography to + + align:start position:0% +now we're jumping from photography to + + + align:start position:0% +now we're jumping from photography to +tomography + + align:start position:0% +tomography + + + align:start position:0% +tomography +now both are recording one is recording + + align:start position:0% +now both are recording one is recording + + + align:start position:0% +now both are recording one is recording +light the other one is recording slices + + align:start position:0% +light the other one is recording slices + + + align:start position:0% +light the other one is recording slices +it turns out you can use very similar + + align:start position:0% +it turns out you can use very similar + + + align:start position:0% +it turns out you can use very similar +principles + + align:start position:0% +principles + + + align:start position:0% +principles +so what's happening in tomography you + + align:start position:0% +so what's happening in tomography you + + + align:start position:0% +so what's happening in tomography you +have an x-ray source + + align:start position:0% +have an x-ray source + + + align:start position:0% +have an x-ray source +that's emitting in an omnidirectional + + align:start position:0% +that's emitting in an omnidirectional + + + align:start position:0% +that's emitting in an omnidirectional +fashion uh and you have uh detectors + + align:start position:0% +fashion uh and you have uh detectors + + + align:start position:0% +fashion uh and you have uh detectors +here + + align:start position:0% +here + + + align:start position:0% +here +uh that are um + + align:start position:0% +uh that are um + + + align:start position:0% +uh that are um +should i use this screen because most + + align:start position:0% +should i use this screen because most + + + align:start position:0% +should i use this screen because most +people are + + align:start position:0% +people are + + + align:start position:0% +people are +which big screen is better for majority + + align:start position:0% +which big screen is better for majority + + + align:start position:0% +which big screen is better for majority +of people that one sorry + + align:start position:0% +of people that one sorry + + + align:start position:0% +of people that one sorry +all right i'll use this one + + align:start position:0% +all right i'll use this one + + + align:start position:0% +all right i'll use this one +sorry + + align:start position:0% + + + + align:start position:0% + +this one was convenient for me + + align:start position:0% + + + + align:start position:0% + +you have an extra source and you have an + + align:start position:0% +you have an extra source and you have an + + + align:start position:0% +you have an extra source and you have an +area of detectors uh and basically when + + align:start position:0% +area of detectors uh and basically when + + + align:start position:0% +area of detectors uh and basically when +you put your head inside this + + align:start position:0% +you put your head inside this + + + align:start position:0% +you put your head inside this +uh extra source x-ray and the tomography + + align:start position:0% +uh extra source x-ray and the tomography + + + align:start position:0% +uh extra source x-ray and the tomography +cat scan machine the x-ray source spins + + align:start position:0% +cat scan machine the x-ray source spins + + + align:start position:0% +cat scan machine the x-ray source spins +and the detector moves in the same + + align:start position:0% +and the detector moves in the same + + + align:start position:0% +and the detector moves in the same +direction right + + align:start position:0% +direction right + + + align:start position:0% +direction right +um + + align:start position:0% +um + + + align:start position:0% +um +and let me show you a video of how this + + align:start position:0% +and let me show you a video of how this + + + align:start position:0% +and let me show you a video of how this +actually + + align:start position:0% + + + + align:start position:0% + +this actually works + + align:start position:0% + + + + align:start position:0% + +let me start from the beginning + + align:start position:0% + + + + align:start position:0% + +all right it's been opened up so you + + align:start position:0% +all right it's been opened up so you + + + align:start position:0% +all right it's been opened up so you +know what's going on + + align:start position:0% + + + + align:start position:0% + +that's what's happening imagine your + + align:start position:0% +that's what's happening imagine your + + + align:start position:0% +that's what's happening imagine your +head is inside that + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +all right that's what scat scan machine + + align:start position:0% +all right that's what scat scan machine + + + align:start position:0% +all right that's what scat scan machine +is doing and while you know they put an + + align:start position:0% +is doing and while you know they put an + + + align:start position:0% +is doing and while you know they put an +eye patch and you're just resting inside + + align:start position:0% +eye patch and you're just resting inside + + + align:start position:0% +eye patch and you're just resting inside +it's basically a jet engine + + align:start position:0% +it's basically a jet engine + + + align:start position:0% +it's basically a jet engine +it's totally crazy + + align:start position:0% +it's totally crazy + + + align:start position:0% +it's totally crazy +okay it's totally unnecessary you know + + align:start position:0% +okay it's totally unnecessary you know + + + align:start position:0% +okay it's totally unnecessary you know +we're in the 21st century + + align:start position:0% +we're in the 21st century + + + align:start position:0% +we're in the 21st century +we are in the 21st century and we are + + align:start position:0% +we are in the 21st century and we are + + + align:start position:0% +we are in the 21st century and we are +building this + + align:start position:0% +building this + + + align:start position:0% +building this +you know + + align:start position:0% +you know + + + align:start position:0% +you know +devices that are based on you know 40 + + align:start position:0% +devices that are based on you know 40 + + + align:start position:0% +devices that are based on you know 40 +year old principles it's unbelievable + + align:start position:0% +year old principles it's unbelievable + + + align:start position:0% +year old principles it's unbelievable +it's totally ridiculous what we need to + + align:start position:0% +it's totally ridiculous what we need to + + + align:start position:0% +it's totally ridiculous what we need to +do is completely rethink + + align:start position:0% +do is completely rethink + + + align:start position:0% +do is completely rethink +how this imaging is done + + align:start position:0% +how this imaging is done + + + align:start position:0% +how this imaging is done +and use new computational methods to + + align:start position:0% +and use new computational methods to + + + align:start position:0% +and use new computational methods to +overcome this totally bizarre + + align:start position:0% +overcome this totally bizarre + + + align:start position:0% +overcome this totally bizarre +you know multi-million dollar devices + + align:start position:0% +you know multi-million dollar devices + + + align:start position:0% +you know multi-million dollar devices +so + + align:start position:0% +so + + + align:start position:0% +so +that will be one of the things we'll be + + align:start position:0% +that will be one of the things we'll be + + + align:start position:0% +that will be one of the things we'll be +learning in in this class how we can + + align:start position:0% +learning in in this class how we can + + + align:start position:0% +learning in in this class how we can +take principles from signal processing + + align:start position:0% +take principles from signal processing + + + align:start position:0% +take principles from signal processing +photography scientific imaging and kind + + align:start position:0% +photography scientific imaging and kind + + + align:start position:0% +photography scientific imaging and kind +of mix and match them to build + + align:start position:0% +of mix and match them to build + + + align:start position:0% +of mix and match them to build +new things + + align:start position:0% +new things + + + align:start position:0% +new things +both whole tomography another very + + align:start position:0% +both whole tomography another very + + + align:start position:0% +both whole tomography another very +interesting problem + + align:start position:0% +interesting problem + + + align:start position:0% +interesting problem +all you do is you + + align:start position:0% +all you do is you + + + align:start position:0% +all you do is you +create + + align:start position:0% +create + + + align:start position:0% +create +you know you drill a hole + + align:start position:0% +you know you drill a hole + + + align:start position:0% +you know you drill a hole +you put explosives here + + align:start position:0% +you put explosives here + + + align:start position:0% +you put explosives here +and you put sensors here or in this case + + align:start position:0% +and you put sensors here or in this case + + + align:start position:0% +and you put sensors here or in this case +it's audio and then you fire off these + + align:start position:0% +it's audio and then you fire off these + + + align:start position:0% +it's audio and then you fire off these +bombs effectively and based on how long + + align:start position:0% +bombs effectively and based on how long + + + align:start position:0% +bombs effectively and based on how long +it takes for + + align:start position:0% +it takes for + + + align:start position:0% +it takes for +sound to travel to these detectors + + align:start position:0% +sound to travel to these detectors + + + align:start position:0% +sound to travel to these detectors +tells you what the density of material + + align:start position:0% +tells you what the density of material + + + align:start position:0% +tells you what the density of material +whether it's rock or oil or you know + + align:start position:0% +whether it's rock or oil or you know + + + align:start position:0% +whether it's rock or oil or you know +other types of formations + + align:start position:0% +other types of formations + + + align:start position:0% +other types of formations +and from that the oil companies can + + align:start position:0% +and from that the oil companies can + + + align:start position:0% +and from that the oil companies can +figure out if you know what type of oil + + align:start position:0% +figure out if you know what type of oil + + + align:start position:0% +figure out if you know what type of oil +there is and where it is so you can + + align:start position:0% +there is and where it is so you can + + + align:start position:0% +there is and where it is so you can +create a 3d map of what's inside + + align:start position:0% +create a 3d map of what's inside + + + align:start position:0% +create a 3d map of what's inside +again + + align:start position:0% +again + + + align:start position:0% +again +multi-billion dollar + + align:start position:0% +multi-billion dollar + + + align:start position:0% +multi-billion dollar +situations + + align:start position:0% +situations + + + align:start position:0% +situations +uh microscopy deconvolution also used in + + align:start position:0% +uh microscopy deconvolution also used in + + + align:start position:0% +uh microscopy deconvolution also used in +photography also used in a machine + + align:start position:0% +photography also used in a machine + + + align:start position:0% +photography also used in a machine +vision computer which we'll talk about + + align:start position:0% +vision computer which we'll talk about + + + align:start position:0% +vision computer which we'll talk about +that + + align:start position:0% +that + + + align:start position:0% +that +uh coded aperture imaging an idea that + + align:start position:0% +uh coded aperture imaging an idea that + + + align:start position:0% +uh coded aperture imaging an idea that +was used in astronomy + + align:start position:0% +was used in astronomy + + + align:start position:0% +was used in astronomy +because astronomy you're looking at + + align:start position:0% +because astronomy you're looking at + + + align:start position:0% +because astronomy you're looking at +gamma rays and x-rays and you cannot + + align:start position:0% +gamma rays and x-rays and you cannot + + + align:start position:0% +gamma rays and x-rays and you cannot +build lenses for them to form an image + + align:start position:0% +build lenses for them to form an image + + + align:start position:0% +build lenses for them to form an image +so you can either create a image with a + + align:start position:0% +so you can either create a image with a + + + align:start position:0% +so you can either create a image with a +pinhole of the sky or you can use a + + align:start position:0% +pinhole of the sky or you can use a + + + align:start position:0% +pinhole of the sky or you can use a +colored aperture so you can collect more + + align:start position:0% +colored aperture so you can collect more + + + align:start position:0% +colored aperture so you can collect more +light + + align:start position:0% +light + + + align:start position:0% +light +uh now that idea will we'll learn about + + align:start position:0% +uh now that idea will we'll learn about + + + align:start position:0% +uh now that idea will we'll learn about +that uh can also be used for photography + + align:start position:0% +that uh can also be used for photography + + + align:start position:0% +that uh can also be used for photography +so what our group did was we used a + + align:start position:0% +so what our group did was we used a + + + align:start position:0% +so what our group did was we used a +coated aperture in the lens instead of + + align:start position:0% +coated aperture in the lens instead of + + + align:start position:0% +coated aperture in the lens instead of +having a clear disc like aperture we put + + align:start position:0% +having a clear disc like aperture we put + + + align:start position:0% +having a clear disc like aperture we put +a + + align:start position:0% +a + + + align:start position:0% +a +you can barely see it + + align:start position:0% +you can barely see it + + + align:start position:0% +you can barely see it +uh + + align:start position:0% +uh + + + align:start position:0% +uh +i'm sorry supposed to go this way + + align:start position:0% +i'm sorry supposed to go this way + + + align:start position:0% +i'm sorry supposed to go this way +uh you have a coded aperture which looks + + align:start position:0% +uh you have a coded aperture which looks + + + align:start position:0% +uh you have a coded aperture which looks +like a + + align:start position:0% +like a + + + align:start position:0% +like a +crossword puzzle shaped + + align:start position:0% +crossword puzzle shaped + + + align:start position:0% +crossword puzzle shaped +mask + + align:start position:0% +mask + + + align:start position:0% +mask +and from that you can take a photo again + + align:start position:0% +and from that you can take a photo again + + + align:start position:0% +and from that you can take a photo again +which could be out of focus and then + + align:start position:0% +which could be out of focus and then + + + align:start position:0% +which could be out of focus and then +digitally refocus that + + align:start position:0% +digitally refocus that + + + align:start position:0% +digitally refocus that +so this is you know auto focus photo + + align:start position:0% +so this is you know auto focus photo + + + align:start position:0% +so this is you know auto focus photo +this is in focus photo + + align:start position:0% +this is in focus photo + + + align:start position:0% +this is in focus photo +and you can capture you know the glint + + align:start position:0% +and you can capture you know the glint + + + align:start position:0% +and you can capture you know the glint +in the eye or even uh strand of the hair + + align:start position:0% +in the eye or even uh strand of the hair + + + align:start position:0% +in the eye or even uh strand of the hair +again very minor change uh to the camera + + align:start position:0% +again very minor change uh to the camera + + + align:start position:0% +again very minor change uh to the camera +and if you originally were talking about + + align:start position:0% +and if you originally were talking about + + + align:start position:0% +and if you originally were talking about +uh you know successful biological vision + + align:start position:0% +uh you know successful biological vision + + + align:start position:0% +uh you know successful biological vision +uh if you think about the simplest + + align:start position:0% +uh if you think about the simplest + + + align:start position:0% +uh if you think about the simplest +possible + + align:start position:0% + + + + align:start position:0% + +biological + + align:start position:0% +biological + + + align:start position:0% +biological +vision which is a single pixel detector + + align:start position:0% +vision which is a single pixel detector + + + align:start position:0% +vision which is a single pixel detector +in a worm right just a single pixel + + align:start position:0% +in a worm right just a single pixel + + + align:start position:0% +in a worm right just a single pixel +it's you know in in muddy + + align:start position:0% +it's you know in in muddy + + + align:start position:0% +it's you know in in muddy +mashy waters looking for food or + + align:start position:0% +mashy waters looking for food or + + + align:start position:0% +mashy waters looking for food or +maintaining its orientation + + align:start position:0% +maintaining its orientation + + + align:start position:0% +maintaining its orientation +it doesn't need a full-fledged camera it + + align:start position:0% +it doesn't need a full-fledged camera it + + + align:start position:0% +it doesn't need a full-fledged camera it +just has a single pixel detector + + align:start position:0% +just has a single pixel detector + + + align:start position:0% +just has a single pixel detector +it just knows if there's light there's + + align:start position:0% +it just knows if there's light there's + + + align:start position:0% +it just knows if there's light there's +no light if there's light how much like + + align:start position:0% +no light if there's light how much like + + + align:start position:0% +no light if there's light how much like +this + + align:start position:0% +this + + + align:start position:0% +this +so you know when it's done when it's day + + align:start position:0% +so you know when it's done when it's day + + + align:start position:0% +so you know when it's done when it's day +when it's night + + align:start position:0% +when it's night + + + align:start position:0% +when it's night +which way is more light which has less + + align:start position:0% +which way is more light which has less + + + align:start position:0% +which way is more light which has less +light + + align:start position:0% +light + + + align:start position:0% +light +but even that + + align:start position:0% +but even that + + + align:start position:0% +but even that +single pixel detector + + align:start position:0% +single pixel detector + + + align:start position:0% +single pixel detector +has some very interesting optics in + + align:start position:0% +has some very interesting optics in + + + align:start position:0% +has some very interesting optics in +front + + align:start position:0% +front + + + align:start position:0% +front +it has this very intriguing shielding + + align:start position:0% +it has this very intriguing shielding + + + align:start position:0% +it has this very intriguing shielding +pigment in front of it + + align:start position:0% +pigment in front of it + + + align:start position:0% +pigment in front of it +can anybody guess what's the reason for + + align:start position:0% +can anybody guess what's the reason for + + + align:start position:0% +can anybody guess what's the reason for +that + + align:start position:0% +that + + + align:start position:0% +that +how does it benefit to have some random + + align:start position:0% +how does it benefit to have some random + + + align:start position:0% +how does it benefit to have some random +pigment that's blocking the light from + + align:start position:0% +pigment that's blocking the light from + + + align:start position:0% +pigment that's blocking the light from +different directions + + align:start position:0% +different directions + + + align:start position:0% +different directions +for orientation so if this worm wants to + + align:start position:0% +for orientation so if this worm wants to + + + align:start position:0% +for orientation so if this worm wants to +maintain an audio if there's a light + + align:start position:0% +maintain an audio if there's a light + + + align:start position:0% +maintain an audio if there's a light +source + + align:start position:0% +source + + + align:start position:0% +source +uh and if the sensor was hemispherical + + align:start position:0% +uh and if the sensor was hemispherical + + + align:start position:0% +uh and if the sensor was hemispherical +then if this one moves a little bit + + align:start position:0% +then if this one moves a little bit + + + align:start position:0% +then if this one moves a little bit +there will not be much change but if you + + align:start position:0% +there will not be much change but if you + + + align:start position:0% +there will not be much change but if you +have a very high frequency pigment if + + align:start position:0% +have a very high frequency pigment if + + + align:start position:0% +have a very high frequency pigment if +this one moves even a little bit + + align:start position:0% +this one moves even a little bit + + + align:start position:0% +this one moves even a little bit +there'll be a big change + + align:start position:0% +there'll be a big change + + + align:start position:0% +there'll be a big change +in the lighting right + + align:start position:0% +in the lighting right + + + align:start position:0% +in the lighting right +look as if you have a very high + + align:start position:0% +look as if you have a very high + + + align:start position:0% +look as if you have a very high +frequency mask and you're looking at the + + align:start position:0% +frequency mask and you're looking at the + + + align:start position:0% +frequency mask and you're looking at the +sun as you move + + align:start position:0% +sun as you move + + + align:start position:0% +sun as you move +you know the light goes up and down so + + align:start position:0% +you know the light goes up and down so + + + align:start position:0% +you know the light goes up and down so +the worm knows that as long as it's + + align:start position:0% +the worm knows that as long as it's + + + align:start position:0% +the worm knows that as long as it's +maintaining the same level of light it's + + align:start position:0% +maintaining the same level of light it's + + + align:start position:0% +maintaining the same level of light it's +maintaining its orientation right that's + + align:start position:0% +maintaining its orientation right that's + + + align:start position:0% +maintaining its orientation right that's +all it needs to do does it also increase + + align:start position:0% +all it needs to do does it also increase + + + align:start position:0% +all it needs to do does it also increase +the effective dynamic range of its + + align:start position:0% +the effective dynamic range of its + + + align:start position:0% +the effective dynamic range of its +sensor + + align:start position:0% +sensor + + + align:start position:0% +sensor +kind of like neutral density filters + + align:start position:0% +kind of like neutral density filters + + + align:start position:0% +kind of like neutral density filters +along certain directions it's possible + + align:start position:0% +along certain directions it's possible + + + align:start position:0% +along certain directions it's possible +it's possible maybe maybe when it's + + align:start position:0% +it's possible maybe maybe when it's + + + align:start position:0% +it's possible maybe maybe when it's +looking in one direction it's too bright + + align:start position:0% +looking in one direction it's too bright + + + align:start position:0% +looking in one direction it's too bright +so it tries to block that we don't know + + align:start position:0% +so it tries to block that we don't know + + + align:start position:0% +so it tries to block that we don't know +and if you read this book there's a + + align:start position:0% +and if you read this book there's a + + + align:start position:0% +and if you read this book there's a +beautiful book called animal eyes + + align:start position:0% +beautiful book called animal eyes + + + align:start position:0% +beautiful book called animal eyes +by land and mission + + align:start position:0% +by land and mission + + + align:start position:0% +by land and mission +which will be we'll we'll have a whole + + align:start position:0% +which will be we'll we'll have a whole + + + align:start position:0% +which will be we'll we'll have a whole +class on animal eyes i think it's the + + align:start position:0% +class on animal eyes i think it's the + + + align:start position:0% +class on animal eyes i think it's the +seventh class i remember correctly + + align:start position:0% +seventh class i remember correctly + + + align:start position:0% +seventh class i remember correctly +uh and we'll discuss all different types + + align:start position:0% +uh and we'll discuss all different types + + + align:start position:0% +uh and we'll discuss all different types +of animal eyes and and why they do it + + align:start position:0% +of animal eyes and and why they do it + + + align:start position:0% +of animal eyes and and why they do it +whether it's eagles or land creatures + + align:start position:0% +whether it's eagles or land creatures + + + align:start position:0% +whether it's eagles or land creatures +underwater creatures worms and all that + + align:start position:0% +underwater creatures worms and all that + + + align:start position:0% +underwater creatures worms and all that +and + + align:start position:0% +and + + + align:start position:0% +and +frankly most of this + + align:start position:0% +frankly most of this + + + align:start position:0% +frankly most of this +most of these + + align:start position:0% +most of these + + + align:start position:0% +most of these +biological visions visual systems + + align:start position:0% +biological visions visual systems + + + align:start position:0% +biological visions visual systems +are based on hypothesis and they are + + align:start position:0% +are based on hypothesis and they are + + + align:start position:0% +are based on hypothesis and they are +verified you know in a very + + align:start position:0% +verified you know in a very + + + align:start position:0% +verified you know in a very +very + + align:start position:0% +very + + + align:start position:0% +very +scientific but the same time very + + align:start position:0% +scientific but the same time very + + + align:start position:0% +scientific but the same time very +primitive equipment and one of the great + + align:start position:0% +primitive equipment and one of the great + + + align:start position:0% +primitive equipment and one of the great +projects would be to take some of these + + align:start position:0% +projects would be to take some of these + + + align:start position:0% +projects would be to take some of these +worms + + align:start position:0% +worms + + + align:start position:0% +worms +and put it in a controlled lighting + + align:start position:0% +and put it in a controlled lighting + + + align:start position:0% +and put it in a controlled lighting +setup to really verify this is how they + + align:start position:0% +setup to really verify this is how they + + + align:start position:0% +setup to really verify this is how they +work + + align:start position:0% +work + + + align:start position:0% +work +that'll be a lot of fun + + align:start position:0% + + + + align:start position:0% + +i'll provide the ones don't worry + + align:start position:0% + + + + align:start position:0% + +so you know this core aperture is you + + align:start position:0% +so you know this core aperture is you + + + align:start position:0% +so you know this core aperture is you +know + + align:start position:0% +know + + + align:start position:0% +know +somewhat similar + + align:start position:0% +somewhat similar + + + align:start position:0% +somewhat similar +um + + align:start position:0% +um + + + align:start position:0% +um +let me skip over this part because we + + align:start position:0% +let me skip over this part because we + + + align:start position:0% +let me skip over this part because we +talked a little bit about how to use + + align:start position:0% +talked a little bit about how to use + + + align:start position:0% +talked a little bit about how to use +mask + + align:start position:0% + + + + align:start position:0% + +all right wavefront coding + + align:start position:0% +all right wavefront coding + + + align:start position:0% +all right wavefront coding +this is a concept that was + + align:start position:0% +this is a concept that was + + + align:start position:0% +this is a concept that was +uh invented by kathy and dowsky in 1995 + + align:start position:0% +uh invented by kathy and dowsky in 1995 + + + align:start position:0% +uh invented by kathy and dowsky in 1995 +for shaping light or shaping the + + align:start position:0% +for shaping light or shaping the + + + align:start position:0% +for shaping light or shaping the +wavefront + + align:start position:0% +wavefront + + + align:start position:0% +wavefront +of incoming + + align:start position:0% +of incoming + + + align:start position:0% +of incoming +light so you have a traditional imaging + + align:start position:0% +light so you have a traditional imaging + + + align:start position:0% +light so you have a traditional imaging +setup you have an object you have a + + align:start position:0% +setup you have an object you have a + + + align:start position:0% +setup you have an object you have a +sensor you have some lenses + + align:start position:0% +sensor you have some lenses + + + align:start position:0% +sensor you have some lenses +what they proposed is placing an + + align:start position:0% +what they proposed is placing an + + + align:start position:0% +what they proposed is placing an +additional optical layer in between + + align:start position:0% +additional optical layer in between + + + align:start position:0% +additional optical layer in between +which is not a lens or a prism + + align:start position:0% +which is not a lens or a prism + + + align:start position:0% +which is not a lens or a prism +but has + + align:start position:0% +but has + + + align:start position:0% +but has +variable thickness or variable + + align:start position:0% +variable thickness or variable + + + align:start position:0% +variable thickness or variable +refractive index + + align:start position:0% +refractive index + + + align:start position:0% +refractive index +okay + + align:start position:0% +okay + + + align:start position:0% +okay +the simplest way to thinking of to think + + align:start position:0% +the simplest way to thinking of to think + + + align:start position:0% +the simplest way to thinking of to think +about that is the light in the top part + + align:start position:0% +about that is the light in the top part + + + align:start position:0% +about that is the light in the top part +might travel at one speed remember if + + align:start position:0% +might travel at one speed remember if + + + align:start position:0% +might travel at one speed remember if +you have a + + align:start position:0% +you have a + + + align:start position:0% +you have a +glass with + + align:start position:0% +glass with + + + align:start position:0% +glass with +a glass with different thickness or + + align:start position:0% +a glass with different thickness or + + + align:start position:0% +a glass with different thickness or +different impact refractive index + + align:start position:0% +different impact refractive index + + + align:start position:0% +different impact refractive index +the light is going to slow down + + align:start position:0% +the light is going to slow down + + + align:start position:0% +the light is going to slow down +right and when it comes out on the other + + align:start position:0% +right and when it comes out on the other + + + align:start position:0% +right and when it comes out on the other +side + + align:start position:0% +side + + + align:start position:0% +side +in air i can go back to + + align:start position:0% +in air i can go back to + + + align:start position:0% +in air i can go back to +one foot per + + align:start position:0% +one foot per + + + align:start position:0% +one foot per +minute nanosecond very good + + align:start position:0% +minute nanosecond very good + + + align:start position:0% +minute nanosecond very good +uh but before that it's going to travel + + align:start position:0% +uh but before that it's going to travel + + + align:start position:0% +uh but before that it's going to travel +slightly less than one foot per + + align:start position:0% +slightly less than one foot per + + + align:start position:0% +slightly less than one foot per +nanosecond right if it's 1.5 it's going + + align:start position:0% +nanosecond right if it's 1.5 it's going + + + align:start position:0% +nanosecond right if it's 1.5 it's going +to travel you know one + + align:start position:0% +to travel you know one + + + align:start position:0% +to travel you know one +one by 1.5 a foot per nanosecond so + + align:start position:0% +one by 1.5 a foot per nanosecond so + + + align:start position:0% +one by 1.5 a foot per nanosecond so +anyway + + align:start position:0% +anyway + + + align:start position:0% +anyway +so by adding class of different + + align:start position:0% +so by adding class of different + + + align:start position:0% +so by adding class of different +thickness or different refractive index + + align:start position:0% +thickness or different refractive index + + + align:start position:0% +thickness or different refractive index +each of these rays are going to be + + align:start position:0% +each of these rays are going to be + + + align:start position:0% +each of these rays are going to be +slightly out of phase with respect to + + align:start position:0% +slightly out of phase with respect to + + + align:start position:0% +slightly out of phase with respect to +each other + + align:start position:0% +each other + + + align:start position:0% +each other +so when they combine on the detector + + align:start position:0% +so when they combine on the detector + + + align:start position:0% +so when they combine on the detector +they will either add inter add + + align:start position:0% +they will either add inter add + + + align:start position:0% +they will either add inter add +they will interfere and add + + align:start position:0% +they will interfere and add + + + align:start position:0% +they will interfere and add +constructively or destructively + + align:start position:0% +constructively or destructively + + + align:start position:0% +constructively or destructively +and from that you'll form new images + + align:start position:0% +and from that you'll form new images + + + align:start position:0% +and from that you'll form new images +right so this is how they explained it + + align:start position:0% +right so this is how they explained it + + + align:start position:0% +right so this is how they explained it +and should read the papers unfortunately + + align:start position:0% +and should read the papers unfortunately + + + align:start position:0% +and should read the papers unfortunately +are very difficult to understand + + align:start position:0% +are very difficult to understand + + + align:start position:0% +are very difficult to understand +and what you'll realize is that instead + + align:start position:0% +and what you'll realize is that instead + + + align:start position:0% +and what you'll realize is that instead +of going into the math of for your + + align:start position:0% +of going into the math of for your + + + align:start position:0% +of going into the math of for your +optics and so on in this class we will + + align:start position:0% +optics and so on in this class we will + + + align:start position:0% +optics and so on in this class we will +use very simple ray diagrams + + align:start position:0% +use very simple ray diagrams + + + align:start position:0% +use very simple ray diagrams +and understand how this works in a very + + align:start position:0% +and understand how this works in a very + + + align:start position:0% +and understand how this works in a very +visual manner + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +basically what wavefront camera + + align:start position:0% +basically what wavefront camera + + + align:start position:0% +basically what wavefront camera +wavefront coding camera does is in a + + align:start position:0% +wavefront coding camera does is in a + + + align:start position:0% +wavefront coding camera does is in a +traditional camera + + align:start position:0% +traditional camera + + + align:start position:0% +traditional camera +uh race converts to a single point and + + align:start position:0% +uh race converts to a single point and + + + align:start position:0% +uh race converts to a single point and +you get a sharply focused image so if + + align:start position:0% +you get a sharply focused image so if + + + align:start position:0% +you get a sharply focused image so if +the camera goes if the sensor goes in + + align:start position:0% +the camera goes if the sensor goes in + + + align:start position:0% +the camera goes if the sensor goes in +and out of focus you get a large blur in + + align:start position:0% +and out of focus you get a large blur in + + + align:start position:0% +and out of focus you get a large blur in +case of wavefront coded camera actually + + align:start position:0% +case of wavefront coded camera actually + + + align:start position:0% +case of wavefront coded camera actually +you don't you never get a sharp spot + + align:start position:0% +you don't you never get a sharp spot + + + align:start position:0% +you don't you never get a sharp spot +what you get is basically think of + + align:start position:0% +what you get is basically think of + + + align:start position:0% +what you get is basically think of +taking a lot of straws + + align:start position:0% +taking a lot of straws + + + align:start position:0% +taking a lot of straws +instead of all of them converging to a + + align:start position:0% +instead of all of them converging to a + + + align:start position:0% +instead of all of them converging to a +single point taking them and then + + align:start position:0% +single point taking them and then + + + align:start position:0% +single point taking them and then +twisting them + + align:start position:0% +twisting them + + + align:start position:0% +twisting them +so that + + align:start position:0% +so that + + + align:start position:0% +so that +they go out again as the straws but in + + align:start position:0% +they go out again as the straws but in + + + align:start position:0% +they go out again as the straws but in +between + + align:start position:0% +between + + + align:start position:0% +between +there's a there's a there's a part where + + align:start position:0% +there's a there's a there's a part where + + + align:start position:0% +there's a there's a there's a part where +all of them are + + align:start position:0% +all of them are + + + align:start position:0% +all of them are +the cross section of them is roughly + + align:start position:0% +the cross section of them is roughly + + + align:start position:0% +the cross section of them is roughly +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +by doing that it turns out for for + + align:start position:0% +by doing that it turns out for for + + + align:start position:0% +by doing that it turns out for for +sufficiently long + + align:start position:0% +sufficiently long + + + align:start position:0% +sufficiently long +uh sufficiently large depth range + + align:start position:0% +uh sufficiently large depth range + + + align:start position:0% +uh sufficiently large depth range +and that the focus is equivalent + + align:start position:0% +and that the focus is equivalent + + + align:start position:0% +and that the focus is equivalent +and we'll study this in detail on how + + align:start position:0% +and we'll study this in detail on how + + + align:start position:0% +and we'll study this in detail on how +this works and how you can use the same + + align:start position:0% +this works and how you can use the same + + + align:start position:0% +this works and how you can use the same +techniques for new types of photography + + align:start position:0% +techniques for new types of photography + + + align:start position:0% +techniques for new types of photography +and scientific imaging now this is also + + align:start position:0% +and scientific imaging now this is also + + + align:start position:0% +and scientific imaging now this is also +very hot topic in night vision goggles + + align:start position:0% +very hot topic in night vision goggles + + + align:start position:0% +very hot topic in night vision goggles +by the way where they want to + + align:start position:0% +by the way where they want to + + + align:start position:0% +by the way where they want to +wear night vision goggles that + + align:start position:0% +wear night vision goggles that + + + align:start position:0% +wear night vision goggles that +look when you look far away they're + + align:start position:0% +look when you look far away they're + + + align:start position:0% +look when you look far away they're +it's very clear + + align:start position:0% +it's very clear + + + align:start position:0% +it's very clear +and again nitrogen bubbles have very + + align:start position:0% +and again nitrogen bubbles have very + + + align:start position:0% +and again nitrogen bubbles have very +large apertures and when you look closer + + align:start position:0% +large apertures and when you look closer + + + align:start position:0% +large apertures and when you look closer +if you want to read a map for example + + align:start position:0% +if you want to read a map for example + + + align:start position:0% +if you want to read a map for example +you should still be in focus so how do + + align:start position:0% +you should still be in focus so how do + + + align:start position:0% +you should still be in focus so how do +you how do you create a + + align:start position:0% +you how do you create a + + + align:start position:0% +you how do you create a +passive device that can focus at + + align:start position:0% +passive device that can focus at + + + align:start position:0% +passive device that can focus at +infinity and very close up at the same + + align:start position:0% +infinity and very close up at the same + + + align:start position:0% +infinity and very close up at the same +time and they have been using waveform + + align:start position:0% +time and they have been using waveform + + + align:start position:0% +time and they have been using waveform +coding as well + + align:start position:0% +coding as well + + + align:start position:0% +coding as well +i can barely see this + + align:start position:0% +i can barely see this + + + align:start position:0% +i can barely see this +all right + + align:start position:0% +all right + + + align:start position:0% +all right +this is this is the project called + + align:start position:0% +this is this is the project called + + + align:start position:0% +this is this is the project called +decoding depth via d focus blur this is + + align:start position:0% +decoding depth via d focus blur this is + + + align:start position:0% +decoding depth via d focus blur this is +from colorado from raphael pashtun and + + align:start position:0% +from colorado from raphael pashtun and + + + align:start position:0% +from colorado from raphael pashtun and +and you have shatner + + align:start position:0% +and you have shatner + + + align:start position:0% +and you have shatner +and this is very counterintuitive + + align:start position:0% +and this is very counterintuitive + + + align:start position:0% +and this is very counterintuitive +uh if you take a point light and i wish + + align:start position:0% +uh if you take a point light and i wish + + + align:start position:0% +uh if you take a point light and i wish +i could do this experiment i can i can + + align:start position:0% +i could do this experiment i can i can + + + align:start position:0% +i could do this experiment i can i can +do it here but it'll take some time if + + align:start position:0% +do it here but it'll take some time if + + + align:start position:0% +do it here but it'll take some time if +you take a point light and form an image + + align:start position:0% +you take a point light and form an image + + + align:start position:0% +you take a point light and form an image +on on this particular guy + + align:start position:0% + + + + align:start position:0% + +do you want a little flashlight yeah + + align:start position:0% + + + + align:start position:0% + +thanks + + align:start position:0% +thanks + + + align:start position:0% +thanks +so uh as you can see here + + align:start position:0% +so uh as you can see here + + + align:start position:0% +so uh as you can see here +that's the image plane right so as i + + align:start position:0% +that's the image plane right so as i + + + align:start position:0% +that's the image plane right so as i +move it in and out + + align:start position:0% +move it in and out + + + align:start position:0% +move it in and out +its shape is going to + + align:start position:0% +its shape is going to + + + align:start position:0% +its shape is going to +change the spotlight now imagine and + + align:start position:0% +change the spotlight now imagine and + + + align:start position:0% +change the spotlight now imagine and +that's what happens in the in the bottom + + align:start position:0% +that's what happens in the in the bottom + + + align:start position:0% +that's what happens in the in the bottom +part of the image + + align:start position:0% + + + + align:start position:0% + +as you are in sharp focus you get a + + align:start position:0% +as you are in sharp focus you get a + + + align:start position:0% +as you are in sharp focus you get a +small spot as you go out of focus you + + align:start position:0% +small spot as you go out of focus you + + + align:start position:0% +small spot as you go out of focus you +got a bigger disc + + align:start position:0% +got a bigger disc + + + align:start position:0% +got a bigger disc +but the kind of optics this group design + + align:start position:0% +but the kind of optics this group design + + + align:start position:0% +but the kind of optics this group design +when you're in focus you see two spots + + align:start position:0% +when you're in focus you see two spots + + + align:start position:0% +when you're in focus you see two spots +that are left and right of each other + + align:start position:0% +that are left and right of each other + + + align:start position:0% +that are left and right of each other +and when you go out of focus these two + + align:start position:0% +and when you go out of focus these two + + + align:start position:0% +and when you go out of focus these two +spots rotate + + align:start position:0% +spots rotate + + + align:start position:0% +spots rotate +one way or the other way if you are + + align:start position:0% +one way or the other way if you are + + + align:start position:0% +one way or the other way if you are +closer than plane of focus it rotates in + + align:start position:0% +closer than plane of focus it rotates in + + + align:start position:0% +closer than plane of focus it rotates in +one way away from out of focus it + + align:start position:0% +one way away from out of focus it + + + align:start position:0% +one way away from out of focus it +rotates otherwise + + align:start position:0% +rotates otherwise + + + align:start position:0% +rotates otherwise +so this rotational point spread function + + align:start position:0% +so this rotational point spread function + + + align:start position:0% +so this rotational point spread function +is a very powerful concept and right now + + align:start position:0% +is a very powerful concept and right now + + + align:start position:0% +is a very powerful concept and right now +they're using in microscopy for + + align:start position:0% +they're using in microscopy for + + + align:start position:0% +they're using in microscopy for +resolving fluorescent beads at uh + + align:start position:0% +resolving fluorescent beads at uh + + + align:start position:0% +resolving fluorescent beads at uh +nanometer precision uh but it could also + + align:start position:0% +nanometer precision uh but it could also + + + align:start position:0% +nanometer precision uh but it could also +be used in photography nobody knows how + + align:start position:0% +be used in photography nobody knows how + + + align:start position:0% +be used in photography nobody knows how +to do it this could be one of the + + align:start position:0% +to do it this could be one of the + + + align:start position:0% +to do it this could be one of the +research projects + + align:start position:0% +research projects + + + align:start position:0% +research projects +uh and we have we can we can get some of + + align:start position:0% +uh and we have we can we can get some of + + + align:start position:0% +uh and we have we can we can get some of +these prototypes from from our + + align:start position:0% +these prototypes from from our + + + align:start position:0% +these prototypes from from our +colleagues so it's a lot of fun to play + + align:start position:0% +colleagues so it's a lot of fun to play + + + align:start position:0% +colleagues so it's a lot of fun to play +with + + align:start position:0% +with + + + align:start position:0% +with +um another interesting thing we'll be + + align:start position:0% +um another interesting thing we'll be + + + align:start position:0% +um another interesting thing we'll be +looking at is relationship between + + align:start position:0% + + + + align:start position:0% + +fourier optics and ray optics now you + + align:start position:0% +fourier optics and ray optics now you + + + align:start position:0% +fourier optics and ray optics now you +know in high school we were taught you + + align:start position:0% +know in high school we were taught you + + + align:start position:0% +know in high school we were taught you +know there is particle and wave duality + + align:start position:0% +know there is particle and wave duality + + + align:start position:0% +know there is particle and wave duality +and a lot of confusion and you know we + + align:start position:0% +and a lot of confusion and you know we + + + align:start position:0% +and a lot of confusion and you know we +have to write you know in high school we + + align:start position:0% +have to write you know in high school we + + + align:start position:0% +have to write you know in high school we +have to answer questions of what + + align:start position:0% +have to answer questions of what + + + align:start position:0% +have to answer questions of what +phenomena can be shown by + + align:start position:0% +phenomena can be shown by + + + align:start position:0% +phenomena can be shown by +in particle way and what can be shown + + align:start position:0% +in particle way and what can be shown + + + align:start position:0% +in particle way and what can be shown +when in in + + align:start position:0% +when in in + + + align:start position:0% +when in in +using the wave propagation model and one + + align:start position:0% +using the wave propagation model and one + + + align:start position:0% +using the wave propagation model and one +of the standard answers was oh if + + align:start position:0% +of the standard answers was oh if + + + align:start position:0% +of the standard answers was oh if +there's interference or diffraction then + + align:start position:0% +there's interference or diffraction then + + + align:start position:0% +there's interference or diffraction then +it can only be explained with fourier + + align:start position:0% +it can only be explained with fourier + + + align:start position:0% +it can only be explained with fourier +optics not with + + align:start position:0% +optics not with + + + align:start position:0% +optics not with +a + + align:start position:0% +a + + + align:start position:0% +a +particle nature of light + + align:start position:0% +particle nature of light + + + align:start position:0% +particle nature of light +that's you know too simplistic uh it + + align:start position:0% +that's you know too simplistic uh it + + + align:start position:0% +that's you know too simplistic uh it +turns out that you can really show that + + align:start position:0% +turns out that you can really show that + + + align:start position:0% +turns out that you can really show that +they're the tools of each other + + align:start position:0% +they're the tools of each other + + + align:start position:0% +they're the tools of each other +um and explain diffraction and + + align:start position:0% +um and explain diffraction and + + + align:start position:0% +um and explain diffraction and +interference and all these mechanisms + + align:start position:0% +interference and all these mechanisms + + + align:start position:0% +interference and all these mechanisms +using purely ray propagation + + align:start position:0% +using purely ray propagation + + + align:start position:0% +using purely ray propagation +and so with sebik his name is not here + + align:start position:0% +and so with sebik his name is not here + + + align:start position:0% +and so with sebik his name is not here +sabaico and george barbastasis for + + align:start position:0% +sabaico and george barbastasis for + + + align:start position:0% +sabaico and george barbastasis for +mechanical engineering we have a project + + align:start position:0% +mechanical engineering we have a project + + + align:start position:0% +mechanical engineering we have a project +where we have created a so-called + + align:start position:0% +where we have created a so-called + + + align:start position:0% +where we have created a so-called +augmented light field + + align:start position:0% +augmented light field + + + align:start position:0% +augmented light field +which can actually + + align:start position:0% +which can actually + + + align:start position:0% +which can actually +support all the wave optics effects as + + align:start position:0% +support all the wave optics effects as + + + align:start position:0% +support all the wave optics effects as +well so traditional light field that we + + align:start position:0% +well so traditional light field that we + + + align:start position:0% +well so traditional light field that we +just described earlier + + align:start position:0% +just described earlier + + + align:start position:0% +just described earlier +where you can capture with an area of + + align:start position:0% +where you can capture with an area of + + + align:start position:0% +where you can capture with an area of +cameras + + align:start position:0% +cameras + + + align:start position:0% +cameras +and so on can do this + + align:start position:0% +and so on can do this + + + align:start position:0% +and so on can do this +position angle representation and the + + align:start position:0% +position angle representation and the + + + align:start position:0% +position angle representation and the +four dimensional representation + + align:start position:0% +four dimensional representation + + + align:start position:0% +four dimensional representation +and at that time i made a claim that if + + align:start position:0% +and at that time i made a claim that if + + + align:start position:0% +and at that time i made a claim that if +you can capture this 4d incoming + + align:start position:0% +you can capture this 4d incoming + + + align:start position:0% +you can capture this 4d incoming +function you have captured everything + + align:start position:0% +function you have captured everything + + + align:start position:0% +function you have captured everything +everything geometrically that has come + + align:start position:0% +everything geometrically that has come + + + align:start position:0% +everything geometrically that has come +through the lens + + align:start position:0% +through the lens + + + align:start position:0% +through the lens +so it's a complete representation of the + + align:start position:0% +so it's a complete representation of the + + + align:start position:0% +so it's a complete representation of the +light + + align:start position:0% +light + + + align:start position:0% +light +and + + align:start position:0% +and + + + align:start position:0% +and +some people would say wow but then + + align:start position:0% +some people would say wow but then + + + align:start position:0% +some people would say wow but then +you're not capturing the face and you're + + align:start position:0% +you're not capturing the face and you're + + + align:start position:0% +you're not capturing the face and you're +not capturing + + align:start position:0% +not capturing + + + align:start position:0% +not capturing +all these other things but turns out + + align:start position:0% +all these other things but turns out + + + align:start position:0% +all these other things but turns out +that using the same exact setup + + align:start position:0% +that using the same exact setup + + + align:start position:0% +that using the same exact setup +you are also able to capture face + + align:start position:0% +you are also able to capture face + + + align:start position:0% +you are also able to capture face +the 4d representation actually includes + + align:start position:0% +the 4d representation actually includes + + + align:start position:0% +the 4d representation actually includes +the amplitude and phase of the incoming + + align:start position:0% +the amplitude and phase of the incoming + + + align:start position:0% +the amplitude and phase of the incoming +wavefront + + align:start position:0% +wavefront + + + align:start position:0% +wavefront +and so we + + align:start position:0% +and so we + + + align:start position:0% +and so we +simply by using different mathematical + + align:start position:0% +simply by using different mathematical + + + align:start position:0% +simply by using different mathematical +terminology we have + + align:start position:0% +terminology we have + + + align:start position:0% +terminology we have +augmented this lightweight + + align:start position:0% +augmented this lightweight + + + align:start position:0% +augmented this lightweight +representation to also represent to also + + align:start position:0% +representation to also represent to also + + + align:start position:0% +representation to also represent to also +model uh wavefront effects + + align:start position:0% +model uh wavefront effects + + + align:start position:0% +model uh wavefront effects +so we'll study that uh a little bit + + align:start position:0% + + + + align:start position:0% + +uh what about photographs like this + + align:start position:0% +uh what about photographs like this + + + align:start position:0% +uh what about photographs like this +uh if you look at this heater + + align:start position:0% +uh if you look at this heater + + + align:start position:0% +uh if you look at this heater +it's creating this beautiful + + align:start position:0% +it's creating this beautiful + + + align:start position:0% +it's creating this beautiful +streams of hot air + + align:start position:0% + + + + align:start position:0% + +also this + + align:start position:0% +also this + + + align:start position:0% +also this +this + + align:start position:0% +this + + + align:start position:0% +this +lamp from the lampshade + + align:start position:0% +lamp from the lampshade + + + align:start position:0% +lamp from the lampshade +again we are trying to visualize that + + align:start position:0% +again we are trying to visualize that + + + align:start position:0% +again we are trying to visualize that +cannot be seen in the naked eye so this + + align:start position:0% +cannot be seen in the naked eye so this + + + align:start position:0% +cannot be seen in the naked eye so this +is known as the schlieren photography + + align:start position:0% +is known as the schlieren photography + + + align:start position:0% +is known as the schlieren photography +which is again looking at very minor + + align:start position:0% +which is again looking at very minor + + + align:start position:0% +which is again looking at very minor +changes + + align:start position:0% +changes + + + align:start position:0% +changes +in the optical path in this case because + + align:start position:0% +in the optical path in this case because + + + align:start position:0% +in the optical path in this case because +of heat + + align:start position:0% +of heat + + + align:start position:0% +of heat +uh if you're if you're on you know on a + + align:start position:0% +uh if you're if you're on you know on a + + + align:start position:0% +uh if you're if you're on you know on a +hot day on a on a highway you see the + + align:start position:0% +hot day on a on a highway you see the + + + align:start position:0% +hot day on a on a highway you see the +mirage + + align:start position:0% +mirage + + + align:start position:0% +mirage +but that happens extremely high + + align:start position:0% +but that happens extremely high + + + align:start position:0% +but that happens extremely high +temperatures now even at not so high + + align:start position:0% +temperatures now even at not so high + + + align:start position:0% +temperatures now even at not so high +temperatures + + align:start position:0% +temperatures + + + align:start position:0% +temperatures +you can actually capture this mirage and + + align:start position:0% +you can actually capture this mirage and + + + align:start position:0% +you can actually capture this mirage and +create a very beautiful focus + + align:start position:0% +create a very beautiful focus + + + align:start position:0% +create a very beautiful focus +so this is children photography and + + align:start position:0% +so this is children photography and + + + align:start position:0% +so this is children photography and +we'll be studying that + + align:start position:0% +we'll be studying that + + + align:start position:0% +we'll be studying that +polarization is beautiful + + align:start position:0% +polarization is beautiful + + + align:start position:0% +polarization is beautiful +you may have used polarization for + + align:start position:0% +you may have used polarization for + + + align:start position:0% +you may have used polarization for +taking + + align:start position:0% +taking + + + align:start position:0% +taking +photos of the sky or on water but + + align:start position:0% +photos of the sky or on water but + + + align:start position:0% +photos of the sky or on water but +underwater photography can be + + align:start position:0% +underwater photography can be + + + align:start position:0% +underwater photography can be +dramatically improved with polarization + + align:start position:0% +dramatically improved with polarization + + + align:start position:0% +dramatically improved with polarization +so we'll study that + + align:start position:0% + + + + align:start position:0% + +uh we'll also study some new type of + + align:start position:0% +uh we'll also study some new type of + + + align:start position:0% +uh we'll also study some new type of +sensors not just two-dimensional sensors + + align:start position:0% +sensors not just two-dimensional sensors + + + align:start position:0% +sensors not just two-dimensional sensors +but this other sensors as i said + + align:start position:0% +but this other sensors as i said + + + align:start position:0% +but this other sensors as i said +single pixel camera + + align:start position:0% +single pixel camera + + + align:start position:0% +single pixel camera +uh compressive sensing uh how many of + + align:start position:0% +uh compressive sensing uh how many of + + + align:start position:0% +uh compressive sensing uh how many of +you have heard about compressive sensing + + align:start position:0% +you have heard about compressive sensing + + + align:start position:0% +you have heard about compressive sensing +right there's a lot of hype about it and + + align:start position:0% +right there's a lot of hype about it and + + + align:start position:0% +right there's a lot of hype about it and +again if you read the papers + + align:start position:0% + + + + align:start position:0% + +sometimes it's very difficult to follow + + align:start position:0% +sometimes it's very difficult to follow + + + align:start position:0% +sometimes it's very difficult to follow +uh what exactly they're trying to say + + align:start position:0% +uh what exactly they're trying to say + + + align:start position:0% +uh what exactly they're trying to say +and and how it's done uh but as you will + + align:start position:0% +and and how it's done uh but as you will + + + align:start position:0% +and and how it's done uh but as you will +see in this class + + align:start position:0% +see in this class + + + align:start position:0% +see in this class +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you'll get the whole idea of compressor + + align:start position:0% +you'll get the whole idea of compressor + + + align:start position:0% +you'll get the whole idea of compressor +sensing in less than five minutes + + align:start position:0% +sensing in less than five minutes + + + align:start position:0% +sensing in less than five minutes +uh and we'll go through what works what + + align:start position:0% +uh and we'll go through what works what + + + align:start position:0% +uh and we'll go through what works what +doesn't work uh and actually rohit is + + align:start position:0% +doesn't work uh and actually rohit is + + + align:start position:0% +doesn't work uh and actually rohit is +working on a project which shows that + + align:start position:0% +working on a project which shows that + + + align:start position:0% +working on a project which shows that +hopefully we'll show that uh comp + + align:start position:0% +hopefully we'll show that uh comp + + + align:start position:0% +hopefully we'll show that uh comp +resistance is actually not such a great + + align:start position:0% +resistance is actually not such a great + + + align:start position:0% +resistance is actually not such a great +idea for imaging + + align:start position:0% +idea for imaging + + + align:start position:0% +idea for imaging +but it is good for something else and + + align:start position:0% +but it is good for something else and + + + align:start position:0% +but it is good for something else and +we'll study what that something else is + + align:start position:0% +we'll study what that something else is + + + align:start position:0% +we'll study what that something else is +when he and ashok's project is + + align:start position:0% +when he and ashok's project is + + + align:start position:0% +when he and ashok's project is +reaching some mature stage + + align:start position:0% +reaching some mature stage + + + align:start position:0% +reaching some mature stage +so + + align:start position:0% +so + + + align:start position:0% +so +very exciting ideas there + + align:start position:0% +very exciting ideas there + + + align:start position:0% +very exciting ideas there +so the original idea was to create a + + align:start position:0% +so the original idea was to create a + + + align:start position:0% +so the original idea was to create a +single pixel camera instead of creating + + align:start position:0% +single pixel camera instead of creating + + + align:start position:0% +single pixel camera instead of creating +a megapixel camera you have a single + + align:start position:0% +a megapixel camera you have a single + + + align:start position:0% +a megapixel camera you have a single +pixel that's uh going to take a coded + + align:start position:0% +pixel that's uh going to take a coded + + + align:start position:0% +pixel that's uh going to take a coded +combination of incoming light so this + + align:start position:0% +combination of incoming light so this + + + align:start position:0% +combination of incoming light so this +may be a scene it's been focused on the + + align:start position:0% +may be a scene it's been focused on the + + + align:start position:0% +may be a scene it's been focused on the +whole uh reflected + + align:start position:0% +whole uh reflected + + + align:start position:0% +whole uh reflected +uh mirror array and you're going to flip + + align:start position:0% +uh mirror array and you're going to flip + + + align:start position:0% +uh mirror array and you're going to flip +this mirror on and off + + align:start position:0% +this mirror on and off + + + align:start position:0% +this mirror on and off +so the light you collect will be a + + align:start position:0% +so the light you collect will be a + + + align:start position:0% +so the light you collect will be a +product of the scene with this uh vector + + align:start position:0% +product of the scene with this uh vector + + + align:start position:0% +product of the scene with this uh vector +uh and if you change this flips + + align:start position:0% +uh and if you change this flips + + + align:start position:0% +uh and if you change this flips +you get some other + + align:start position:0% +you get some other + + + align:start position:0% +you get some other +sum you're going to take a linear sum of + + align:start position:0% +sum you're going to take a linear sum of + + + align:start position:0% +sum you're going to take a linear sum of +incoming light + + align:start position:0% +incoming light + + + align:start position:0% +incoming light +and if you take millions such + + align:start position:0% +and if you take millions such + + + align:start position:0% +and if you take millions such +measurements you can reconstruct a + + align:start position:0% +measurements you can reconstruct a + + + align:start position:0% +measurements you can reconstruct a +megapixel photo + + align:start position:0% +megapixel photo + + + align:start position:0% +megapixel photo +but the claim of this group from rice is + + align:start position:0% +but the claim of this group from rice is + + + align:start position:0% +but the claim of this group from rice is +that you don't have to you don't have to + + align:start position:0% +that you don't have to you don't have to + + + align:start position:0% +that you don't have to you don't have to +actually take a million readings you + + align:start position:0% +actually take a million readings you + + + align:start position:0% +actually take a million readings you +might be able to get away with only 10 + + align:start position:0% +might be able to get away with only 10 + + + align:start position:0% +might be able to get away with only 10 +000 or 100 000 readings so you can + + align:start position:0% +000 or 100 000 readings so you can + + + align:start position:0% +000 or 100 000 readings so you can +capture a megapixel photo + + align:start position:0% +capture a megapixel photo + + + align:start position:0% +capture a megapixel photo +with possibly only 10 000 pixels of a + + align:start position:0% +with possibly only 10 000 pixels of a + + + align:start position:0% +with possibly only 10 000 pixels of a +cam + + align:start position:0% + + + + align:start position:0% + +and we'll we'll look into that and what + + align:start position:0% +and we'll we'll look into that and what + + + align:start position:0% +and we'll we'll look into that and what +part of that + + align:start position:0% +part of that + + + align:start position:0% +part of that +statement is true and what the statement + + align:start position:0% +statement is true and what the statement + + + align:start position:0% +statement is true and what the statement +requires more analysis and you'll also + + align:start position:0% +requires more analysis and you'll also + + + align:start position:0% +requires more analysis and you'll also +see that this can be used in a lot of uh + + align:start position:0% +see that this can be used in a lot of uh + + + align:start position:0% +see that this can be used in a lot of uh +other situations so for example my group + + align:start position:0% +other situations so for example my group + + + align:start position:0% +other situations so for example my group +has built a + + align:start position:0% +has built a + + + align:start position:0% +has built a +a strobing camera that can be used for + + align:start position:0% +a strobing camera that can be used for + + + align:start position:0% +a strobing camera that can be used for +lagrangioscopy + + align:start position:0% +lagrangioscopy + + + align:start position:0% +lagrangioscopy +uh where in a traditional lagrange scope + + align:start position:0% +uh where in a traditional lagrange scope + + + align:start position:0% +uh where in a traditional lagrange scope +you use very high speed strobing + + align:start position:0% +you use very high speed strobing + + + align:start position:0% +you use very high speed strobing +to slow down + + align:start position:0% +to slow down + + + align:start position:0% +to slow down +and to slow down to visualize the motion + + align:start position:0% +and to slow down to visualize the motion + + + align:start position:0% +and to slow down to visualize the motion +of of vocal force but we just came up + + align:start position:0% +of of vocal force but we just came up + + + align:start position:0% +of of vocal force but we just came up +with a new method that is dramatically + + align:start position:0% +with a new method that is dramatically + + + align:start position:0% +with a new method that is dramatically +simple and + + align:start position:0% +simple and + + + align:start position:0% +simple and +uses dramatically less light so you + + align:start position:0% +uses dramatically less light so you + + + align:start position:0% +uses dramatically less light so you +don't burn your throat when the doctor + + align:start position:0% +don't burn your throat when the doctor + + + align:start position:0% +don't burn your throat when the doctor +is looking at + + align:start position:0% +is looking at + + + align:start position:0% +is looking at +your vocal folds + + align:start position:0% +your vocal folds + + + align:start position:0% +your vocal folds +and that's based on comprehension + + align:start position:0% + + + + align:start position:0% + +so let me stop here because we're almost + + align:start position:0% +so let me stop here because we're almost + + + align:start position:0% +so let me stop here because we're almost +at 4 30 and we'll we'll come back and + + align:start position:0% +at 4 30 and we'll we'll come back and + + + align:start position:0% +at 4 30 and we'll we'll come back and +we'll come back and look at some of this + + align:start position:0% +we'll come back and look at some of this + + + align:start position:0% +we'll come back and look at some of this +some of this + + align:start position:0% +some of this + + + align:start position:0% +some of this +other projects + + align:start position:0% + + + + align:start position:0% + +so these are the kind of project + + align:start position:0% +so these are the kind of project + + + align:start position:0% +so these are the kind of project +assignments you will see + + align:start position:0% +assignments you will see + + + align:start position:0% +assignments you will see +relighting the first one that already + + align:start position:0% +relighting the first one that already + + + align:start position:0% +relighting the first one that already +described dual photography where you can + + align:start position:0% +described dual photography where you can + + + align:start position:0% +described dual photography where you can +read your opponent's card + + align:start position:0% +read your opponent's card + + + align:start position:0% +read your opponent's card +virtual optical bench light field + + align:start position:0% +virtual optical bench light field + + + align:start position:0% +virtual optical bench light field +capture + + align:start position:0% +capture + + + align:start position:0% +capture +high speed imaging thermal imaging + + align:start position:0% +high speed imaging thermal imaging + + + align:start position:0% +high speed imaging thermal imaging +multi-spectral imaging range imaging and + + align:start position:0% +multi-spectral imaging range imaging and + + + align:start position:0% +multi-spectral imaging range imaging and +so on and then a completely open-ended + + align:start position:0% +so on and then a completely open-ended + + + align:start position:0% +so on and then a completely open-ended +final project which you can choose in + + align:start position:0% +final project which you can choose in + + + align:start position:0% +final project which you can choose in +any area + + align:start position:0% +any area + + + align:start position:0% +any area +this is the first assignment the + + align:start position:0% +this is the first assignment the + + + align:start position:0% +this is the first assignment the +instructions will go out + + align:start position:0% +instructions will go out + + + align:start position:0% +instructions will go out +on the stellar web page please make sure + + align:start position:0% +on the stellar web page please make sure + + + align:start position:0% +on the stellar web page please make sure +you have uh + + align:start position:0% + + + + align:start position:0% + +the sign up sheet has it gone around + + align:start position:0% +the sign up sheet has it gone around + + + align:start position:0% +the sign up sheet has it gone around +okay please make sure your name and + + align:start position:0% +okay please make sure your name and + + + align:start position:0% +okay please make sure your name and +email is on the signup sheet uh if you + + align:start position:0% +email is on the signup sheet uh if you + + + align:start position:0% +email is on the signup sheet uh if you +don't get an email from me by monday + + align:start position:0% +don't get an email from me by monday + + + align:start position:0% +don't get an email from me by monday +morning please send me an email which + + align:start position:0% +morning please send me an email which + + + align:start position:0% +morning please send me an email which +means that i could not read your email + + align:start position:0% +means that i could not read your email + + + align:start position:0% +means that i could not read your email +address correctly + + align:start position:0% +address correctly + + + align:start position:0% +address correctly +um + + align:start position:0% +um + + + align:start position:0% +um +so yeah this will be some of the some of + + align:start position:0% +so yeah this will be some of the some of + + + align:start position:0% +so yeah this will be some of the some of +the assignments you'll be doing + + align:start position:0% +the assignments you'll be doing + + + align:start position:0% +the assignments you'll be doing +and this one is due on september 25th + + align:start position:0% +and this one is due on september 25th + + + align:start position:0% +and this one is due on september 25th +and every class we're going to starting + + align:start position:0% +and every class we're going to starting + + + align:start position:0% +and every class we're going to starting +from next class we'll have a volunteer + + align:start position:0% +from next class we'll have a volunteer + + + align:start position:0% +from next class we'll have a volunteer +who takes notes for the class and posts + + align:start position:0% +who takes notes for the class and posts + + + align:start position:0% +who takes notes for the class and posts +it + + align:start position:0% +it + + + align:start position:0% +it +because a lot of our discussion is going + + align:start position:0% +because a lot of our discussion is going + + + align:start position:0% +because a lot of our discussion is going +to be on the board and so on i'll send + + align:start position:0% +to be on the board and so on i'll send + + + align:start position:0% +to be on the board and so on i'll send +out specific instructions so we need to + + align:start position:0% +out specific instructions so we need to + + + align:start position:0% +out specific instructions so we need to +volunteer for next week + + align:start position:0% +volunteer for next week + + + align:start position:0% +volunteer for next week +you wanna do that yeah what's your name + + align:start position:0% +you wanna do that yeah what's your name + + + align:start position:0% +you wanna do that yeah what's your name +sam sam all right sam is going to + + align:start position:0% +sam sam all right sam is going to + + + align:start position:0% +sam sam all right sam is going to +volunteer for next week and we'll decide + + align:start position:0% +volunteer for next week and we'll decide + + + align:start position:0% +volunteer for next week and we'll decide +who's gonna do that + + align:start position:0% + + + + align:start position:0% + +be many people not most but many people + + align:start position:0% +be many people not most but many people + + + align:start position:0% +be many people not most but many people +are going to be listening so as far as i + + align:start position:0% +are going to be listening so as far as i + + + align:start position:0% +are going to be listening so as far as i +know + + align:start position:0% +know + + + align:start position:0% +know +it's not going to cross the the limit + + align:start position:0% +it's not going to cross the the limit + + + align:start position:0% +it's not going to cross the the limit +but but if there is there's a cap + + align:start position:0% +but but if there is there's a cap + + + align:start position:0% +but but if there is there's a cap +but i don't think it's going to reach + + align:start position:0% +but i don't think it's going to reach + + + align:start position:0% +but i don't think it's going to reach +the campus + + align:start position:0% +the campus + + + align:start position:0% +the campus +there's a cap at 30 so i don't think + + align:start position:0% +there's a cap at 30 so i don't think + + + align:start position:0% +there's a cap at 30 so i don't think +it's going to be fun + + align:start position:0% + + + + align:start position:0% + +and we'll see some of these demos next + + align:start position:0% +and we'll see some of these demos next + + + align:start position:0% +and we'll see some of these demos next +time \ No newline at end of file diff --git a/9KbpbBMThTE.txt b/9KbpbBMThTE.txt new file mode 100644 index 0000000000000000000000000000000000000000..a3dba899ae3569b9d97ef1a4534d0bed08c41fd8 --- /dev/null +++ b/9KbpbBMThTE.txt @@ -0,0 +1,2067 @@ +The task for today is to find +particular solutions. + +So, let me remind you where +we've gotten to. + +We're talking about the +second-order equation with + +constant coefficients, +which you can think of as + +modeling springs, +or simple electrical circuits. + +But, what's different now is +that the right-hand side is an + +input which is not zero. +So, we are considering, + +I'm going to use x as your book +does, keeping to a neutral + +letter. +But, again, in the + +applications, +and in many of the applications + +at any rate, it wants to be t. +But, I make it x. + +So, the independent variable is +x, and the problem is, + +remember, that to find a +particular solution, + +and the reason why we want to +do that is then the general + +solution will be of the form y +equals that particular solution + +plus the complementary solution, +the general solution to the + +reduced equation, +which we can write this way. + +So, all the work depends upon +finding out what that yp is, + +and that's what we're going to +talk about today, + +or rather, talk about for two +weeks. + +But, the point is, +not all functions that you + +could write on the right-hand +side are equally interesting. + +There's one kind, +which is far more interesting, + +but more important in the +applications than all the + +others. +And, that's the one out of + +which, in fact, +as you will see later on this + +week and into next week, +an arbitrary function can be + +built out of these simple +functions. + +So, the important function is +on the right-hand side to be + +able to solve it when it's a +simple exponential. + +But, if you allow me to make it +a complex exponential, + +so, here are the important +right-hand sides where we want, + +we want to be able to do it +when it's of the form, + +e to the ax. +In general, that will be, + +in most applications, +a is not a growing exponential, + +but a decaying exponential. +So, typically, + +a is negative. +But, it doesn't have to be. + +I'll put it in parentheses, +though, often. + +That's not any assumption that +I'm going to make today. + +It's just culture. +But, we want to be able to do + +it for sine omega x and cosine +omega x. + +In other words, + +when the right-hand side is a +pure oscillation, + +that's another important type +of input both for electrical + +circuits, think alternating +current, or the spring systems. + +That's a pure vibration is +you're imposing pure vibration + +on the spring-mass-dashpot +system, and you want to see how + +it responds to that. +Or, you could put them + +together, and make these +decaying oscillations. + +So, we could also have +something like e to the ax times + +sine omega x, +or times cosine omega x. + +Now, the point is, + +all of these together are +really just special cases of one + +general thing, +exponential, + +if you allow the exponent not +to be a real number, + +but to be a complex number. +So, they're all special cases + +of e to the, I'll write it alpha +x, + +well, why don't we write it (a +plus i omega) x, right? + +If omega is zero, + +then I've got this case. +If a is zero, + +I got this case separating into +its real and imaginary parts. + +And, if neither is zero, +I have this case. + +But, I don't want to keep +writing (a plus i omega) all the + +time. +So, I'm going to write that + +simply as e to the alpha x. + +And, you understand that alpha +is a complex number now. + +It doesn't look like a real +number. + +Okay, so the complex number. +So, the equation we are solving + +is which one? +This pretty purple equation. + +And, we are trying to find a +particular solution of it. + +And, the special functions we +are going to use are these, + +well, this one in particular, +e to the alpha x. + +That's going to be our input. + +Now, it turns out this is +amazingly easy to do because + +it's an exponential because I +write it in exponential form. + +The idea is simply to use a +rule which, in fact, + +you know already, +the rule of substitution. + +So, I'm going to write the +equation in the form, + +so, there it is. +It's y double prime plus A y + +prime plus B y equals f of x. + +But, I'm going to think of the +left-hand side as the polynomial + +operator, AD plus B. +A and B are constants, + +applied to y equals f of x. + +That's the way I write the +thing. + +And, this part, +I'm going to think of in the + +form. +This is p of D, + +a polynomial in D. +In fact, it's a simple + +quadratic polynomial. +But, most of what I'm going to + +say today would apply equally +well if we were a higher order + +polynomial, a polynomial of +higher degree. + +And, just to reinforce the +idea, I've given you one problem + +in your problem set when p is a +polynomial of higher degree. + +I should say, +the notes are written for + +general polynomials, +not just for quadratic ones. + +I'm simplifying it by leaving +it, today, I'll do what's in the + +notes, but I'll do it in the +quadratic case to save a little + +time, and because that's the one +you will be most concerned with + +in the problems. +All right, so p of D y equals f + +of x. +And now, there are just a + +couple of basic formulas that +we're going to use all the time. + +The first is that if you apply +p of D to a complex + +exponential, or a real one, +it doesn't matter, + +the answer is you get just what +you started with, + +with D substituted by alpha. +So, it's p of alpha. + +In other words, +put an alpha wherever you saw a + +D in the polynomial. +And, what is this? + +Well, this is now just an +ordinary complex number, + +and multiply that by what you +started with, + +e to the alpha x. + +So, that's a basic formula. +It's called in the notes the + +substitution rule because the +heart of it is, + +you substitute for the D, +you substitute alpha. + +Now, this hardly requires +proof. + +But, let's prove it just so you +see, to reinforce things and + +make things go a little more +slowly to make sure you are on + +board all the time. +How would I prove that? + +Well, just calculate it out, +what in fact is (D squared plus + +AD plus B) times e to the alpha +x. + +Well, it's D squared e to the +alpha x by linearity plus AD + +times e to the alpha x plus B +times e to the alpha x. + +Well, what are these? +What's the derivative of e to + +the alpha x? +It's just alpha times e to the + +alpha x. +What's a second derivative? + +Well, if you remember from the +exam, you can do tenth + +derivatives now. +So, the second derivative is + +easy. +It's alpha squared times e to + +the alpha x. + +In other words, +this law, what I'm saying + +really is that this law is +obviously, quote unquote, + +"true." +Okay, I'm not even going to put + +it in quotes. +It's obviously true for the + +operator, D, and the operator D +squared. + +In other words, +D of e to the alpha x equals + +alpha times e to the alpha x. + +D squared times e to the alpha + +x equals alpha squared times e +to the alpha x. + +And, therefore, + +it's true for linear +combinations of these as well by + +linearity. +So, therefore, + +also true for p of D. +And, in fact, + +so if you calculate it out, +what is it? + +This is alpha squared e to the +alpha x plus alpha e to the + +alpha x times the + +coefficient plus b times e to +the alpha x. + +So, it's in fact exactly this. +It's e to the alpha x times + +(alpha squared plus A alpha plus +B). + +Now, how are we going to use + +this? +Well, the idea is very simple. + +Remember, we're trying to solve +this, I should have some + +consistent notation for these +equations. + +Purple, I think, +will be the right thing here. + +You are solving purple +equations. + +The formulas which will solve +them will be orange formulas, + +and we will see what we need as +we go along. + +So, I would like to just +formulate it, + +this solution, +the particular solution now. + +I'm going to call it a theorem. +It's really too simple to be a + +theorem. +On the other hand, + +it's too important not to be a +theorem. + +So, let's call it, +as I called it in the notes, + +the exponential input theorem, +which says it all. + +Theorem says it's important. +Exponential input means it's + +taking f of x to be an +exponential. + +It's an exponential input, +and the theorem tells you what + +the response is. +So, for that equation, + +I'm not going to recopy the +equation for the purple + +equation, adequately indicated +this way. + +There. +Now try to take notes. + +For the purple equation, +a solution is e to the alpha x. + +Somewhere I neglected to say + +that f of x, all right, +so for the purple equals e to + +the alpha x, how about that? + +That equation, +y double prime plus a y prime + +plus b y equals e to +the alpha x. + +So, here's the exponential + +input. +The solution is e to the alpha + +x divided by p of alpha. + +Now, that's a very useful +formula. + +In fact, Haynes Miller, +who also teaches this course, + +in his notes calls of the most +important theorem in the course. + +Well, I don't have to totally +agree with him, + +but it's certainly important. +It's probably the most + +important theorem for these two +weeks, anyway. + +But, you will have others as +well. + +Okay, so that's a theorem. +The theorem is going green. + +You can tell what they are by +their color code. + +Well, in other words, +what I've done is simply write + +down the solution for you, +write down the particular + +solution. +But let's verify it in general. + +So, the proof would be what? +Well, I have to substitute it + +into the equation. +So, the equation is p of D + +applied to y is equal to alpha +x. + +And, I want to know, +when I substitute that + +expression in, +is it the case that when I plug + +it in, that the right-hand side, +I calculate it out, + +apply p of D to it. +Is it the case that I get e to + +the alpha x on the right? + +Well, all you have to do is do +it. + +What is p of D applied to e to +the alpha x divided by p of + +alpha? + +Well, p of D applied to e to +the alpha x is p of alpha times + +e to the alpha x. + +That's the substitution rule. +What about this guy? + +This guy is a constant, +so it just gets dragged along + +because this operator is linear. +If this applied to that is + +this, then if I apply it to one +half that, I get one half the + +answer, and so on. +So, the p of alpha + +is a constant and just gets +dragged along. + +And now, they cancel each +other, and the answer is, + +indeed, e to the alpha x. + +That's not much of a proof. +I hope that to at least half + +this class, you're wondering, +yes, but what if Peter had not + +caught the wolf? +I mean, what if? + +What if? + +I'm looking stern. +Okay, we will take care of it + +in the simplest possible way. +We will assume that p of alpha + +is not zero. +The case p of alpha is zero + +is, in fact, +an extremely important + +case, one that makes the world +go 'round, one that contributes + +to all sorts of catastrophes, +and they occur first here in + +the solution of differential +equations, and that's what + +controls all the catastrophes. +But, there's a good side to it, + +too. +It also makes a lot of good + +things happen. +So, there are no moral + +judgments in mathematics. +For the time being, + +let's assume p of alpha is not +zero. + +And, that proof is okay because +the p of alpha, + +being in the denominator, +it's okay to be in the + +denominator if you're not zero. +Okay, let's work in a simple + +example. +Well, I'm picking the most + +complicated example I can think +of. + +Simple examples, +I'll leave for your practice + +and for the recitations, +can start off with simple + +examples if you are confused by +this. + +But, let's solve an equation, +find a particular solution. + +So, y double prime plus minus y +prime plus 2y is equal to 10 e + +to the minus x sine x. + +Gulp. +Okay, so, the input is this + +function, 10 e to the minus x, + +it's a decaying oscillation. +You're seeing those already on + +the computer screen if you +started your homework, + +if you've done problem one on +your homework. + +It's a decaying exponential, +and I want to find a particular + +solution. +Well, let's find a particular + +and the general solution. +Find the general solution. + +Well, the main part of the work +is finding the particular + +solution, but let's quickly, +the general solution, + +let's find first the +complementary part of it, + +in other words, +the solution to the homogeneous + +equation. +That's D squared minus D plus + +two. No, let's not. + +I don't want to solve messy +quadratics. + +Okay, we're going to find a +particular solution. + +I thought it was going to come +out easy, and then I realized it + +wasn't because I picked the +wrong signs. + +Okay, so if you don't like, +just change the problem. + +I can do that, +but you cannot. + +Don't forget that. +So, we want a particular + +solution in our equation. +It is this equals that. + +Now, let's complexify it to +make this part of a complex + +exponential. +So, the complex exponential + +that's relevant is ten times e +to the (minus one plus i), + +you see that? x. + +What is this? +This is the imaginary part of + +this complex exponential. +So, this is imaginary part of + +that guy, e to the negative x +times e to the i x, + +and the imaginary part of e to + +the i x. + +The ten, of course, +just comes along for the ride. + +Okay, well, now, +since this is a complex + +equation, I shouldn't call this +y anymore by my notation. + +I like to call it y tilde to +indicate that the solution we + +get to this is not going to be +the original solution to the + +original problem, +but you will have to take the + +imaginary part of it to get it. +So, we are looking, + +now, for the complex solution +to this complexified equation. + +Okay, what is it? +Well, the complex particular + +solution I can write down +immediately. + +It is ten, that, +of course, just gets dragged + +along by linearity, +times e to the (minus one plus + +i) times x. +And, it's over this polynomial + +evaluated at this alpha. +So, just write it down with, + +have faith. +So, what do I get? + +The alpha is minus one plus i. + +I. +square that, + +because I'm substituting this +alpha into that polynomial. + +The reason I'm doing that is +because the formula tells me to + +do it. +That's going to be that + +solution. +Okay, so it's minus one plus i, + +the quantity squared, minus +minus one plus i plus two. + +All I've done is substitute + +minus one plus i for +D in that polynomial, + +the quadratic polynomial. +And now, all I want is the + +imaginary part of this. +The imaginary part of this will + +be the solution to the original +problem because this was the + +right hand side with the +imaginary part of the + +complexified right hand side. +Okay, now, let's make it look a + +little better, +yp tilde. + +Clearly, what we have to do +something nice to the + +denominator. +So, I'll copy the numerator. + +That's e to the minus (one plus +i) x + +and how about the denominator? +Well, again, + +don't expand things out because +it's already this long. + +And, what's the point of making +it this long? + +You want to make it as long, +right? + +Okay, then there is room here +for one real number, + +and another real number times +i, there's no more room. + +Okay, what's the real number? +Okay, we're looking for the + +real part of this expression. +So, just put it in and keep it + +mentally. +So, minus one squared: + +that's one, plus i squared, +that's minus one. + +One minus one is zero. +I can forget about that term. + +The term gives me plus one for +the real part, + +plus two. +The answer is that the real + +part is three. +How about the imaginary part? + +Well, from here, +there's negative 2i, + +negative 2i. +I'm expanding that out by the + +binomial theorem, +or whatever you like to call + +that, minus 2i minus i makes +minus 3i. + +Is that right? +Minus 2i, minus i, + +minus 3i. +So, it is ten thirds, + +and now in the denominator I +have one minus i. + +I'll put that in the numerator, +make it one plus i, + +but I have to divide by the +product of one minus i and its + +complex conjugate. +In other words, + +I'm multiplying both top and +bottom by one plus i. + +And so, that makes here one +squared plus one squared is two. + +And now, what's left is e to +the negative x times cosine x + +plus i sine x. + +Now, of that, +what we want is just the + +imaginary part. +Well, let's see. + +Two goes into ten makes five, +so that's five thirds. + +So, we're practically at our +solution. + +The solution, +then, finally, + +is going to be yp is the +imaginary part of yp tilde. + +And, what's that? +Well, what's the coefficient + +out front, first of all? +It's five thirds, + +so let's pull out to five +thirds before we forget it. + +And, we'll pull out the e to +the negative x before we forget + +that. +And then, the rest is simply a + +question of seeing what's left. +Well, it's one. + +I want the imaginary part. +So, the imaginary part is going + +to be one times cosine x, +and then the other + +imaginary part comes from these +two pieces, which is one times + +sine x. +And, that should be the + +particular solution. +Notice that most of the work is + +not getting this thing. +It's turning it into something + +human that you can take the real +and imaginary parts of. + +If we don't like this form, +you can put it in the other + +form, which many engineers would +do almost automatically, + +make it five thirds, +e to the negative x, + +and what will that be? +Well, you can use the general + +formula if you want. +Remember, cosine, + +the two coefficients are one +and one, so it's one and one. + +So, this is the square root of +two. + +So, it is times, +this part makes the square root + +of two times cosine of x minus +pi over the angle. + +This is a phi. +So, that's pi over four, + +minus pi over four. + +Okay, all right, +now let's address the case + +which is going to occupy a lot +of the rest of today, + +and in a certain sense, +all of next time. + +What happens when p of alpha is +zero? + +Well, in order to be able to +handle this decently, + +it's necessary to have one more +formula, which is very slightly + +more complicated than the +substitution rule. + +But, it's the same kind of +rule. + +I'm going to call this, +or it is called the + +exponential. +So, I'm going to first prove a + +formula, which is the analog of +that, and then I will prove a + +green formula, +which is what to do here if p + +of alpha turns out to be zero. + +But, in order to be able to +prove that, we're going to be + +the analog of the orange +formula. + +And, the analogue of the orange +formula, that tells you how to + +apply p of D to a +simple exponential. + +I need a formula which applies +p of D to that simple + +exponential times another +function. + +Now, I found I got into trouble +by continuing to call that + +alpha. +So, I'm now going to change the + +name of alpha to change alpha's +name to a. + +But, it's still complex. +I don't mean it's guaranteed to + +be complex. +I mean it's allowed to be + +complex. +So, a is now allowed to be a + +complex number. +I'm thinking of it, + +in general, as a complex +number, okay? + +I hope this doesn't upset you +too much, but you know, + +you change x to t's, +and y's to x's. + +This is no worse. +All right, what we going to do? + +Well, I'm going to use this +exponential shift rule, + +I'll call it, +exponential shift rule or + +formula or law. +That's the substitution rule + +for me. +So, this is going to be + +exponential shift law. +And, to apply, + +it tells you how to apply the +polynomial to not D, + +not just the exponential, +but the exponential times some + +function of x. +What's that? + +And now, the rule is very +simple. + +See, you can understand the +difficulty. + +If you try to start +differentiating, + +you're going to have to +calculate second derivatives of + +the stuff, and God forbid, +higher order equations. + +You would have to calculate +fourth derivatives, + +fifth derivatives. +You barely even want to + +calculate the first derivative. +That's okay. + +But, second derivative, +do I have to? + +No, not if you know the +exponential shift rule, + +which says you can get rid of +the e to the ax, + +make it pass to the left of the +operator where it's not in any + +position to do any harm any +longer, or upset the + +differentiation. +And, all you have to do is, + +when it passes over that +operator, it changes D to D plus + +a. So, the answer is, + +e to the ax. +There, it's passed over. + +But, when it did so, +it changed D to D plus a. + +And, what about the u? +Well, the u just stayed there. + +Nothing happened to it. +Okay, there's our orange + +formula. +I guess we better put the thing + +around the whole business. +Should I prove that, + +or the proof is quite easy. +So, let's do it just again to + +give you a chance to try to see, +now, if somebody gives you a + +formula like that, +you first stare at it. + +You might try a couple of +special cases, + +try it on a function and see if +it works, but already, + +you probably don't want to do +that. + +I mean, even if you took a +function like x here, + +you'd have to do a certain +amount of differentiating, + +and some quadratic thing here. +You'd calculate and calculate + +away for a little while, +and then if you did it + +correctly, the two would in fact +turn out to be equal. + +But, you would not necessarily +feel any the wiser. + +A better procedure in trying to +understand something like this + +is say, well, +let's keep the u general. + +Suppose we make D simple. +For example, + +well, if D is a constant, +of course there's nothing to + +happen because if this is just a +constant, both sides of these + +are the same. +This doesn't make any sense if + +p doesn't really have a D in it. +Well, what's the simplest + +polynomial which would have a D +in it? + +Well, D itself. +So, let's take a special case. + +p of D equals D, +and check the formula in that + +case; see if it works. +So, the formula is asking us, + +what is D, that's the p of D, +of e to the ax times u? + +I'm not going to put in the + +variable here because it's just +a waste of chalk. + +Well, what is that? +I know how to calculate that. + +I'll use the product rule. +So, it's the derivative. + +I'll tell you what; +let's do the other order first. + +So, it's e to the ax times the +derivative of u plus the + +derivative of e to the ax, +which is a times e to the ax + +times u. + +Do you follow that? +This is the product rule. + +It's e to the ax times the +derivative of u plus the + +derivative of e to the ax, +which is this thing times u, + +the other factor. + +Now, is that right? +I want to make it look like + +that. +Well, to make it look like that + +I should first factor e to the +ax out. + +And now, what's left? +Well, if I factor e to the ax + +out, what's left is Du plus au, +which is exactly (D plus a) + +operating on u, +D u plus a u. + +Well, hey, that's just what the +formula said it should be. + +If you make e to the x pass +over D, it changes D to + +D plus a. +Okay, now here's the main thing + +I want to show you. +All right, now, + +well let's try, +if this is true, + +also works out for D squared, +then the formula is + +clearly true by linearity +because an arbitrary p of D + +is just a linear +combination with constant + +coefficients of D, +D squared, and that constant + +thing, which we agreed there was +nothing to prove about. + +Now, hack, you're a hack if you +take D squared and start + +calculating the second +derivative of this. + +Okay, it's question about +hacks. + +I mean, it's just, +you haven't learned the right + +thing to do. +Okay, that will work, + +but it's not what you want to +do. + +Instead, you bootstrap your way +up. + +I have already a formula +telling me how to handle this. + +And, you can be anything. +Look at this not as D squared + +all by itself. +Calculate, instead, + +D squared e to the ax times u. + +Think of that as D, +the derivative of the + +derivative of e to the a x u. + +In other words, +we will do it one step at a + +time. +But you see now immediately the + +advantage of this. +What's D of e to the a x u? + +Well, I just calculated that. + +Now, don't go back to the +beginning. + +Don't go back to here. +Use the formula. + +After all, you worked to +calculate it, + +or I did. +So, it's D of, + +and what's this inside? +It's e to the ax times (D plus + +a) times u. +Well, that looks like a mess, + +but it isn't because I'm taking +D of e to the ax times + +something. +And I already know how to take + +D of e to the ax times +something. + +It doesn't matter what that +something is. + +Here, the something was u. +Here, the something is D plus + +(a times u) operating on u. +But, the principle is the same, + +and the answer is what? +Well, to take D of e to the ax + +times something, +you pass the e to the ax over + +the D. +That changes D to D plus a. + +And, you apply that to the + +other guy, which is (D plus a) +applied to u. + +What's the answer? +e to the a x times (D plus a) + +squared u. + +It's just what you would have +gotten if you had taken e to the + +e to the x, pass it over, +and then changed D to D plus a. + +Now, another advantage to doing + +it this way is you can see that +this argument is going to + +generalize to D cubed. +In other words, + +you would continue on in the +same way by the process of + +mathematical, +one word, mathematical, + +begins with an I, +induction. + +By induction, +you would prove the same + +formula for the nth derivative. +If you don't know what + +mathematical induction is, +shame on you. + +But it's okay. +A lot of you will be able to go + +through life without ever having +to learn what it is. + +And, the rest of you will be +computer scientists. + +Okay, so that's the idea of +this rule. + +Now, we can use it to calculate +something. + +Let's see, I'm going to need +green for this, + +I guess, for our better +formula. + +The formula, +now, that tells you what to do + +if p of alpha is zero. + +So, we're trying to solve the +equation, D squared plus A D, + +we are trying to find a + +particular solution, +e to the ax, + +let's say. +Remember, a is complex. + +a could be complex. +It doesn't have to be real. + +But, the problem is that p of +alpha is zero. + +How do I get a particular +solution? + +Well, I will write it down for +you. + +So, this is part of that +exponential input theorem. + +I think that's the way it is in +the notes. + +I gave all the cases together, +but I thought pedagogically + +it's probably a little better to +do the simplest case first, + +and then build up on the +complexity. + +So, what's yp? +The answer is yp is e to the a, + +except now you have to multiply + +it by x out front. +Where have you done something + +like that before? +Yes, don't tell me. + +I know you know. +But, what should go in the + +denominator? +Clearly not p of alpha. + +What goes in the denominator is + +the derivative. +Okay, but what if p prime of + +alpha is zero? +Couldn't that happen? + +Yes, it could happen. +So, we better make cases. + +This case is, +the case where this is okay + +corresponds to the case where +we're going to assume that alpha + +is a simple root, +is a simple root of the + +polynomial, p. +I don't know what to call the + +variable, p of D is okay. +A simple zero, + +in other words, +it's not double. + +Well, suppose is double. +One of the consequences you + +will see just in a second, +if it's a simple zero, + +that means this derivative is +not going to be zero. + +That's automatic. +Yeah, well, suppose it's not as + +simple. +Well, suppose is a double root. + +How did a-- How did that get +changed to, argh! + +[LAUGHTER] That's not an alpha. +Oh, well, yes it is, + +obviously. +Change! + +All of you, I want you to +change. + +They should have something like +in a search key where 147 + +occurrences of alpha have been +changed to a with a stroke of a, + +just your thumb. +They don't have that for the + +blackboard, unfortunately. +Well, too bad, + +for the future. +Correctable blackboards. + +Well, what if a is double root? +It can't be more than a double + +root because you've only got a +quadratic polynomial. + +Quadratic polynomials only have +two roots. + +So, the worst that can happen +is that both of them are a. + +All right, in that case the +formula should be yp is equal + +to, you are now going to need x +squared up there times e + +to the ax, +and in the denominator what you + +are going to need is the second +derivative of, + +evaluated at a. +Now, you can guess the way this + +going to go on. +For higher degree things, + +if you've got a triple root, +you will need here x cubed, + +except you're going to need a +factorial there, + +too. +So, don't worry about it. + +It's in the notes, +but I'm not going to give you + +that for higher roots. +I don't even know if I will + +give it to you for double root. +Yes, I already did, + +so it's too late. +It's too late. + +Okay, so we will make this two +formulas according to whether a + +is a single or a double root. +Okay, let's prove one of these, + +and all of that will be good +enough for my conscience. + +Let's prove the first one. +Mostly, it's an exercise in + +using the first exponential +shift rule. + +Okay, this will be a first +example actually seeing a work + +in practice as opposed to +proving it. + +Okay, so what does that thing +look like? + +So, what does the polynomial +look like, which has a as a + +simple root? +So, we're going to try to prove + +the simple root case. +So, I'm just going to calculate + +what those guys actually look +like. + +What does p of D look +like if a is a simple root? + +Well, if it's a simple root, +that means it has a factor. + +When it factors, +it factors into the product of + +(D minus a) times something +which isn't, D minus some other + +root. +And, the point is that b is not + +equal to A. +The roots are really distinct. + +Okay, what's, +then, p prime, + +I'm going to have to calculate +p prime of a. + +What is that? +Well, let's calculate p prime + +of D first. +It is, well, + +by the ordinary product rule, +it's the derivative of this + +times, which is one times (D +minus a) plus, + +that's one thing plus the same +thing on the other side, + +the derivative of this, +which is one times (D minus b). + +So, that's p prime. +And therefore, + +what's p prime of a? +It's nothing but, + +this part is zero, +and that's a minus b. + +Of course, this is not zero +because it's a simple root. + +And, that's the proof for you +if you want, that if the root is + +simple, that p prime of a +is guaranteed not to + +be zero. +And, you can see, + +it's going to be zero exactly +when b equals a, + +and that root occurs twice. +But, I'm assuming that didn't + +happen. +Okay, then all the rest we have + +to do is calculate, +do the calculation. + +So, what I want to prove now is +that with this p of D, + +what I'm trying to calculate +that p of D times that guy, + +x e to the a x, +except I'm going to + +write it as e to the a x times +x, guess why, + +divided by p prime of a. + +This is my proposed particular +solution. + +So, what I have to do is +calculate it, + +and see that it turns out to +be, what do I hope it turns out + +to be? +What the right hand side of the + +equation, the input? +The input is e to the ax. + +If this is true, + +then yp, a particular solution, +indeed, nothing will be a + +particular solution. +Of course, there could be + +others, but in this game, +I only have to find one + +particular solution, +and that certainly by far is + +the simple as one you could +possibly find. + +So, I have to calculate this. +And now, you see why I did the + +exponential shift rule because +this is begging to be + +differentiated by something +simpler than hack. + +Okay, you can also see why I +violated the natural order of + +things and put the e to the ax +on the left in order + +that it pass over more easily. +So, the answer on the left-hand + +side is e to the ax times p of +(D plus a). + +Now, what is (p of D) plus a? +Write it in this form. + +It's going to be a minus b. + +So, p of (D plus a) +is, change D to D plus a. + +So, the first factor is going + +to be D plus a minus b. + +And, what's the second factor? +Change D to D plus a. + +It turns into D. + +All this is the result of +taking that p of D, + +and changing D to D plus a. +And now, this is to be applied + +to what? +Well, e to the a x + +is already passed over. +So, what's left is x. + +And, that's to be divided by +the constant, + +p prime of a. +Now, what does this all come + +out to be? +e to the ax, + +what's D applied to x? +One, right? + +And now, what's this thing +applied to the constant one? + +Well, the D kills it, +so it has no effect. + +It makes it zero. +The rest just multiplies it by + +a minus b. +So, the answer to the top is (a + +minus b) times one. +And, the answer to the bottom + +is p prime of a, +which I showed you by just + +explicit calculation is a minus +b. + +And so the answer is, +e to the a x comes + +out right. +Now, the other one, + +the other formula comes out the +same way. + +I'll leave that as an exercise. +Also, I don't dare do it + +because it's much too close to +the problem I asked you to do + +for homework. +So, let's by way of conclusion, + +I'll do one more simple +example, okay? + +And then, you can feel you +understand something. + +I'm sort of bothered that I +haven't done any examples of + +this more complicated case. +So, I'll pick an easy version + +instead of the one that you have +in your notes, + +which is the one you have for +homework, which is even easier. + +So, this one's epsilon less +easy. + +Y double prime minus 3 y prime +plus 2 y equals e to the x. + +Okay, notice that one is a + +simple root. +The one I'm talking about is + +the a here, which is one. +One is a simple root of the + +polynomial D squared minus 3D +plus two, + +isn't it? +It's a zero. + +Put D equal one and you get +one minus three plus + +two equals zero. +It's a simple root because + +anybody can see that one is not +a double root because you know + +from critical damping, +if one were a double root, + +you know just what the +polynomial would look like, + +and it wouldn't look like that +at all. + +It would not look like D +squared minus 3D plus two. + +It would look differently. + +Therefore, that proves that one +is a simple root. + +Okay, what's the particular +solution, therefore? + +The particular solution is x +times e to the x divided by the + +derivative, the derivative +evaluated at the point, + +so, what's p prime of D? +It is 2D minus three. + +If I evaluate it at the point, +one, it is negative one. + +So, if this is to be divided by +negative one, + +in other words, +it's minus x e to the X. + +And, if you don't believe it, +you could plug it in and check + +it out. +Okay, I'm letting you out one + +minute early. +Remember that. + +I'm trying to pay off the +accumulated debt. \ No newline at end of file diff --git a/9QPqYAr-Zsc.txt b/9QPqYAr-Zsc.txt new file mode 100644 index 0000000000000000000000000000000000000000..7814e05c976033e6950d5ab00f95d362bf66bd9b --- /dev/null +++ b/9QPqYAr-Zsc.txt @@ -0,0 +1,1187 @@ +align:start position:0% + +welcome back to 8701 + + align:start position:0% +welcome back to 8701 + + + align:start position:0% +welcome back to 8701 +so in this lecture and also the next we + + align:start position:0% +so in this lecture and also the next we + + + align:start position:0% +so in this lecture and also the next we +want to look at some of the experimental + + align:start position:0% +want to look at some of the experimental + + + align:start position:0% +want to look at some of the experimental +findings of neutrinos + + align:start position:0% + + + + align:start position:0% + +given the sheer number of experiments + + align:start position:0% +given the sheer number of experiments + + + align:start position:0% +given the sheer number of experiments +and the long history in which we are + + align:start position:0% +and the long history in which we are + + + align:start position:0% +and the long history in which we are +trying to + + align:start position:0% +trying to + + + align:start position:0% +trying to +understand neutrinos and neutrinos + + align:start position:0% +understand neutrinos and neutrinos + + + align:start position:0% +understand neutrinos and neutrinos +behavior + + align:start position:0% +behavior + + + align:start position:0% +behavior +um this can be rather confusing so i'm + + align:start position:0% +um this can be rather confusing so i'm + + + align:start position:0% +um this can be rather confusing so i'm +trying to condense this + + align:start position:0% +trying to condense this + + + align:start position:0% +trying to condense this +um a little bit and just give you the + + align:start position:0% +um a little bit and just give you the + + + align:start position:0% +um a little bit and just give you the +highlights of the basic pieces of + + align:start position:0% +highlights of the basic pieces of + + + align:start position:0% +highlights of the basic pieces of +information + + align:start position:0% +information + + + align:start position:0% +information +so this one here shows a summary of what + + align:start position:0% +so this one here shows a summary of what + + + align:start position:0% +so this one here shows a summary of what +we know from neutrino oscillation so if + + align:start position:0% +we know from neutrino oscillation so if + + + align:start position:0% +we know from neutrino oscillation so if +we look at a + + align:start position:0% +we look at a + + + align:start position:0% +we look at a +atmospheric neutrinos we find that + + align:start position:0% +atmospheric neutrinos we find that + + + align:start position:0% +atmospheric neutrinos we find that +neural neutrinos and antimural neutrinos + + align:start position:0% +neural neutrinos and antimural neutrinos + + + align:start position:0% +neural neutrinos and antimural neutrinos +disappear + + align:start position:0% +disappear + + + align:start position:0% +disappear +and they're most likely converting into + + align:start position:0% +and they're most likely converting into + + + align:start position:0% +and they're most likely converting into +town adrenals and antitonatroners + + align:start position:0% +town adrenals and antitonatroners + + + align:start position:0% +town adrenals and antitonatroners +we look at accelerated neurons here we + + align:start position:0% +we look at accelerated neurons here we + + + align:start position:0% +we look at accelerated neurons here we +are using + + align:start position:0% +are using + + + align:start position:0% +are using +neural neurinas and antimurans we can + + align:start position:0% +neural neurinas and antimurans we can + + + align:start position:0% +neural neurinas and antimurans we can +show that they disappear over distances + + align:start position:0% +show that they disappear over distances + + + align:start position:0% +show that they disappear over distances +of 200 to 800 kilometers + + align:start position:0% + + + + align:start position:0% + +from accelerators we also know that + + align:start position:0% + + + + align:start position:0% + +they appear or reappear as electron or + + align:start position:0% +they appear or reappear as electron or + + + align:start position:0% +they appear or reappear as electron or +anti-electron neutrinos over those + + align:start position:0% +anti-electron neutrinos over those + + + align:start position:0% +anti-electron neutrinos over those +same distinctives from the solar + + align:start position:0% +same distinctives from the solar + + + align:start position:0% +same distinctives from the solar +neutrinos + + align:start position:0% +neutrinos + + + align:start position:0% +neutrinos +we know that electron neutrinos convert + + align:start position:0% +we know that electron neutrinos convert + + + align:start position:0% +we know that electron neutrinos convert +into more neutrinos + + align:start position:0% +into more neutrinos + + + align:start position:0% +into more neutrinos +and or tower neutrinos + + align:start position:0% +and or tower neutrinos + + + align:start position:0% +and or tower neutrinos +there is more detail to the story that + + align:start position:0% +there is more detail to the story that + + + align:start position:0% +there is more detail to the story that +i'm giving you here where we + + align:start position:0% +i'm giving you here where we + + + align:start position:0% +i'm giving you here where we +uh would have to discuss the interaction + + align:start position:0% +uh would have to discuss the interaction + + + align:start position:0% +uh would have to discuss the interaction +of the meta effects + + align:start position:0% +of the meta effects + + + align:start position:0% +of the meta effects +of neutrinos that is for a different + + align:start position:0% +of neutrinos that is for a different + + + align:start position:0% +of neutrinos that is for a different +lecture that goes beyond the scope of + + align:start position:0% +lecture that goes beyond the scope of + + + align:start position:0% +lecture that goes beyond the scope of +what i want to discuss here + + align:start position:0% +what i want to discuss here + + + align:start position:0% +what i want to discuss here +from reactor neutrinos we also know that + + align:start position:0% +from reactor neutrinos we also know that + + + align:start position:0% +from reactor neutrinos we also know that +anti-electron neutrinos disappear + + align:start position:0% +anti-electron neutrinos disappear + + + align:start position:0% +anti-electron neutrinos disappear +as well so the name of the game now is + + align:start position:0% +as well so the name of the game now is + + + align:start position:0% +as well so the name of the game now is +to + + align:start position:0% +to + + + align:start position:0% +to +you know take all of those pieces of + + align:start position:0% +you know take all of those pieces of + + + align:start position:0% +you know take all of those pieces of +information + + align:start position:0% +information + + + align:start position:0% +information +and extract information about the + + align:start position:0% +and extract information about the + + + align:start position:0% +and extract information about the +neutrinos property + + align:start position:0% +neutrinos property + + + align:start position:0% +neutrinos property +and that in order to do that + + align:start position:0% +and that in order to do that + + + align:start position:0% +and that in order to do that +one has to make assumption about the + + align:start position:0% +one has to make assumption about the + + + align:start position:0% +one has to make assumption about the +number of available neutrino generations + + align:start position:0% +number of available neutrino generations + + + align:start position:0% +number of available neutrino generations +and in some parts of the interpretation + + align:start position:0% +and in some parts of the interpretation + + + align:start position:0% +and in some parts of the interpretation +also about the nature of the nurturing + + align:start position:0% +also about the nature of the nurturing + + + align:start position:0% +also about the nature of the nurturing +um + + align:start position:0% +um + + + align:start position:0% +um +as you know you can simply figure out of + + align:start position:0% +as you know you can simply figure out of + + + align:start position:0% +as you know you can simply figure out of +the exercise we had before + + align:start position:0% +the exercise we had before + + + align:start position:0% +the exercise we had before +it matters to the neutrino oscillation + + align:start position:0% +it matters to the neutrino oscillation + + + align:start position:0% +it matters to the neutrino oscillation +probabilities whether or not one assumes + + align:start position:0% +probabilities whether or not one assumes + + + align:start position:0% +probabilities whether or not one assumes +two or three or four neutrinos + + align:start position:0% +two or three or four neutrinos + + + align:start position:0% +two or three or four neutrinos +in the mix but if you just focus here on + + align:start position:0% +in the mix but if you just focus here on + + + align:start position:0% +in the mix but if you just focus here on +three neutrinos + + align:start position:0% +three neutrinos + + + align:start position:0% +three neutrinos +um we still have the problem that we + + align:start position:0% +um we still have the problem that we + + + align:start position:0% +um we still have the problem that we +we have the generous degeneracies in + + align:start position:0% +we have the generous degeneracies in + + + align:start position:0% +we have the generous degeneracies in +in the discussion um and they can be uh + + align:start position:0% +in the discussion um and they can be uh + + + align:start position:0% +in the discussion um and they can be uh +boiled down to two major kind of trends + + align:start position:0% +boiled down to two major kind of trends + + + align:start position:0% +boiled down to two major kind of trends +one is where the spectrum of the + + align:start position:0% +one is where the spectrum of the + + + align:start position:0% +one is where the spectrum of the +neutrino masses + + align:start position:0% +neutrino masses + + + align:start position:0% +neutrino masses +follows a normal ordering meaning that + + align:start position:0% +follows a normal ordering meaning that + + + align:start position:0% +follows a normal ordering meaning that +the mass of the first + + align:start position:0% +the mass of the first + + + align:start position:0% +the mass of the first +smaller than the mass of the second is + + align:start position:0% +smaller than the mass of the second is + + + align:start position:0% +smaller than the mass of the second is +smaller than the mass of the third + + align:start position:0% +smaller than the mass of the third + + + align:start position:0% +smaller than the mass of the third +or that the spectrum is inverted + + align:start position:0% +or that the spectrum is inverted + + + align:start position:0% +or that the spectrum is inverted +meaning that the mass of the third might + + align:start position:0% +meaning that the mass of the third might + + + align:start position:0% +meaning that the mass of the third might +be smaller than the mass of the second + + align:start position:0% +be smaller than the mass of the second + + + align:start position:0% +be smaller than the mass of the second +in the mass of this first and the second + + align:start position:0% +in the mass of this first and the second + + + align:start position:0% +in the mass of this first and the second +data suggests that the difference in + + align:start position:0% +data suggests that the difference in + + + align:start position:0% +data suggests that the difference in +mass + + align:start position:0% +mass + + + align:start position:0% +mass +the difference squared in mass mass + + align:start position:0% +the difference squared in mass mass + + + align:start position:0% +the difference squared in mass mass +splittings between those states + + align:start position:0% +splittings between those states + + + align:start position:0% +splittings between those states +is such that delta m one two squared is + + align:start position:0% +is such that delta m one two squared is + + + align:start position:0% +is such that delta m one two squared is +much much smaller + + align:start position:0% +much much smaller + + + align:start position:0% +much much smaller +than delta m one three one three one + + align:start position:0% +than delta m one three one three one + + + align:start position:0% +than delta m one three one three one +squared which is approximately the same + + align:start position:0% +squared which is approximately the same + + + align:start position:0% +squared which is approximately the same +size of delta m + + align:start position:0% +size of delta m + + + align:start position:0% +size of delta m +three two squared so if we look now at + + align:start position:0% +three two squared so if we look now at + + + align:start position:0% +three two squared so if we look now at +the numbers + + align:start position:0% +the numbers + + + align:start position:0% +the numbers +for the normal hierarchy spectrum um we + + align:start position:0% +for the normal hierarchy spectrum um we + + + align:start position:0% +for the normal hierarchy spectrum um we +find that the mass of the first is much + + align:start position:0% +find that the mass of the first is much + + + align:start position:0% +find that the mass of the first is much +much smaller than the mass of the second + + align:start position:0% +much smaller than the mass of the second + + + align:start position:0% +much smaller than the mass of the second +which is a little bit smaller than the + + align:start position:0% +which is a little bit smaller than the + + + align:start position:0% +which is a little bit smaller than the +mass of this third numerically we find + + align:start position:0% +mass of this third numerically we find + + + align:start position:0% +mass of this third numerically we find +the mass of the second is in the order + + align:start position:0% +the mass of the second is in the order + + + align:start position:0% +the mass of the second is in the order +of + + align:start position:0% +of + + + align:start position:0% +of +eight times ten to the minus three + + align:start position:0% +eight times ten to the minus three + + + align:start position:0% +eight times ten to the minus three +electron volt in the mass of the third + + align:start position:0% +electron volt in the mass of the third + + + align:start position:0% +electron volt in the mass of the third +in the order of 0.05 electron volts + + align:start position:0% +in the order of 0.05 electron volts + + + align:start position:0% +in the order of 0.05 electron volts +so really really small masses + + align:start position:0% +so really really small masses + + + align:start position:0% +so really really small masses +um the inverted spectrum here the story + + align:start position:0% +um the inverted spectrum here the story + + + align:start position:0% +um the inverted spectrum here the story +is slightly different here we find that + + align:start position:0% +is slightly different here we find that + + + align:start position:0% +is slightly different here we find that +m1 is about 0.05 electron volts + + align:start position:0% +m1 is about 0.05 electron volts + + + align:start position:0% +m1 is about 0.05 electron volts +which is similar to the square root of + + align:start position:0% +which is similar to the square root of + + + align:start position:0% +which is similar to the square root of +the mass splitting between + + align:start position:0% +the mass splitting between + + + align:start position:0% +the mass splitting between +three and two which is also 0.05 + + align:start position:0% +three and two which is also 0.05 + + + align:start position:0% +three and two which is also 0.05 +electron volts + + align:start position:0% + + + + align:start position:0% + +the information of the neutrino + + align:start position:0% +the information of the neutrino + + + align:start position:0% +the information of the neutrino +oscillation experiment and then + + align:start position:0% +oscillation experiment and then + + + align:start position:0% +oscillation experiment and then +how to the map into the individual + + align:start position:0% +how to the map into the individual + + + align:start position:0% +how to the map into the individual +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +of our neutrino ckm matrix is summarized + + align:start position:0% +of our neutrino ckm matrix is summarized + + + align:start position:0% +of our neutrino ckm matrix is summarized +here and also in the mass information + + align:start position:0% +here and also in the mass information + + + align:start position:0% +here and also in the mass information +um and i don't want to read the entire + + align:start position:0% +um and i don't want to read the entire + + + align:start position:0% +um and i don't want to read the entire +lab table i just leave this + + align:start position:0% +lab table i just leave this + + + align:start position:0% +lab table i just leave this +here for you so in order to understand + + align:start position:0% +here for you so in order to understand + + + align:start position:0% +here for you so in order to understand +this one has to + + align:start position:0% +this one has to + + + align:start position:0% +this one has to +go back to the first slide and + + align:start position:0% +go back to the first slide and + + + align:start position:0% +go back to the first slide and +understand what kind of information we + + align:start position:0% +understand what kind of information we + + + align:start position:0% +understand what kind of information we +extract from the third from from various + + align:start position:0% +extract from the third from from various + + + align:start position:0% +extract from the third from from various +neutrino experiments for example the + + align:start position:0% +neutrino experiments for example the + + + align:start position:0% +neutrino experiments for example the +solar and natural experiments + + align:start position:0% +solar and natural experiments + + + align:start position:0% +solar and natural experiments +and then think about is this sensitive + + align:start position:0% +and then think about is this sensitive + + + align:start position:0% +and then think about is this sensitive +to + + align:start position:0% +to + + + align:start position:0% +to +uh oscillations between the first and + + align:start position:0% +uh oscillations between the first and + + + align:start position:0% +uh oscillations between the first and +the second generation + + align:start position:0% +the second generation + + + align:start position:0% +the second generation +or the first in the third generation + + align:start position:0% +or the first in the third generation + + + align:start position:0% +or the first in the third generation +generation + + align:start position:0% +generation + + + align:start position:0% +generation +so that's kind of the the mapping you + + align:start position:0% +so that's kind of the the mapping you + + + align:start position:0% +so that's kind of the the mapping you +have to do in order to understand this + + align:start position:0% +have to do in order to understand this + + + align:start position:0% +have to do in order to understand this +table fully + + align:start position:0% +table fully + + + align:start position:0% +table fully +some experiment where the information + + align:start position:0% +some experiment where the information + + + align:start position:0% +some experiment where the information +just dominates the position of certain + + align:start position:0% +just dominates the position of certain + + + align:start position:0% +just dominates the position of certain +measurements and others as combinations + + align:start position:0% +measurements and others as combinations + + + align:start position:0% +measurements and others as combinations +of results coming out + + align:start position:0% + + + + align:start position:0% + +the the other reason why i put this + + align:start position:0% +the the other reason why i put this + + + align:start position:0% +the the other reason why i put this +table here + + align:start position:0% +table here + + + align:start position:0% +table here +in this in this in this lecture is to + + align:start position:0% +in this in this in this lecture is to + + + align:start position:0% +in this in this in this lecture is to +just illustrate + + align:start position:0% +just illustrate + + + align:start position:0% +just illustrate +how diverse the landscape of experiments + + align:start position:0% +how diverse the landscape of experiments + + + align:start position:0% +how diverse the landscape of experiments +is + + align:start position:0% +is + + + align:start position:0% +is +and why that's needed in order to get a + + align:start position:0% +and why that's needed in order to get a + + + align:start position:0% +and why that's needed in order to get a +full picture of neutrinos and their + + align:start position:0% +full picture of neutrinos and their + + + align:start position:0% +full picture of neutrinos and their +properties + + align:start position:0% +properties + + + align:start position:0% +properties +one has to identify the individual + + align:start position:0% +one has to identify the individual + + + align:start position:0% +one has to identify the individual +properties + + align:start position:0% +properties + + + align:start position:0% +properties +in the experiments and then put the + + align:start position:0% +in the experiments and then put the + + + align:start position:0% +in the experiments and then put the +picture back together + + align:start position:0% +picture back together + + + align:start position:0% +picture back together +in global fits or in a general analysis + + align:start position:0% +in global fits or in a general analysis + + + align:start position:0% +in global fits or in a general analysis +of the data \ No newline at end of file diff --git a/9lIgAPvppk0.txt b/9lIgAPvppk0.txt new file mode 100644 index 0000000000000000000000000000000000000000..bdd7d45db11b6b0128aac6d643bc8a41e0f7ff14 --- /dev/null +++ b/9lIgAPvppk0.txt @@ -0,0 +1,7819 @@ +align:start position:0% + +all right so in today's recorded lecture + + align:start position:0% +all right so in today's recorded lecture + + + align:start position:0% +all right so in today's recorded lecture +I would like to pick up where we started + + align:start position:0% +I would like to pick up where we started + + + align:start position:0% +I would like to pick up where we started +assuming I'd like to pick up where we + + align:start position:0% +assuming I'd like to pick up where we + + + align:start position:0% +assuming I'd like to pick up where we +stopped last time so I discussed the + + align:start position:0% +stopped last time so I discussed the + + + align:start position:0% +stopped last time so I discussed the +Einstein field equations in the previous + + align:start position:0% +Einstein field equations in the previous + + + align:start position:0% +Einstein field equations in the previous +two lectures I derived them first from + + align:start position:0% +two lectures I derived them first from + + + align:start position:0% +two lectures I derived them first from +the method that was used by Einstein and + + align:start position:0% +the method that was used by Einstein and + + + align:start position:0% +the method that was used by Einstein and +his original work on this subject and + + align:start position:0% +his original work on this subject and + + + align:start position:0% +his original work on this subject and +then I laid out the way of coming to the + + align:start position:0% +then I laid out the way of coming to the + + + align:start position:0% +then I laid out the way of coming to the +Einstein field equations using an action + + align:start position:0% +Einstein field equations using an action + + + align:start position:0% +Einstein field equations using an action +principle using what we call the + + align:start position:0% +principle using what we call the + + + align:start position:0% +principle using what we call the +Einstein Hilbert action both of them + + align:start position:0% +Einstein Hilbert action both of them + + + align:start position:0% +Einstein Hilbert action both of them +lead us to this remarkably simple + + align:start position:0% +lead us to this remarkably simple + + + align:start position:0% +lead us to this remarkably simple +equation if you think about it in terms + + align:start position:0% +equation if you think about it in terms + + + align:start position:0% +equation if you think about it in terms +simply of the curvature tensor so this + + align:start position:0% +simply of the curvature tensor so this + + + align:start position:0% +simply of the curvature tensor so this +is saying that a particular version of + + align:start position:0% +is saying that a particular version of + + + align:start position:0% +is saying that a particular version of +the curvature the version of that you + + align:start position:0% +the curvature the version of that you + + + align:start position:0% +the curvature the version of that you +start with the Riemann tensor you trace + + align:start position:0% +start with the Riemann tensor you trace + + + align:start position:0% +start with the Riemann tensor you trace +over two indices you reverse the trace + + align:start position:0% +over two indices you reverse the trace + + + align:start position:0% +over two indices you reverse the trace +such that this whole thing has zero + + align:start position:0% +such that this whole thing has zero + + + align:start position:0% +such that this whole thing has zero +divergence and you simply equate that to + + align:start position:0% +divergence and you simply equate that to + + + align:start position:0% +divergence and you simply equate that to +the stress-energy tensor with a coupling + + align:start position:0% +the stress-energy tensor with a coupling + + + align:start position:0% +the stress-energy tensor with a coupling +factor with a comp a constant + + align:start position:0% +factor with a comp a constant + + + align:start position:0% +factor with a comp a constant +proportionality that ensures that this + + align:start position:0% +proportionality that ensures that this + + + align:start position:0% +proportionality that ensures that this +recovers the Newtonian limit the + + align:start position:0% +recovers the Newtonian limit the + + + align:start position:0% +recovers the Newtonian limit the +Einstein Hilbert's exercise demonstrated + + align:start position:0% +Einstein Hilbert's exercise demonstrated + + + align:start position:0% +Einstein Hilbert's exercise demonstrated +that this is in a very quantifiable way + + align:start position:0% +that this is in a very quantifiable way + + + align:start position:0% +that this is in a very quantifiable way +the simplest possible way of developing + + align:start position:0% +the simplest possible way of developing + + + align:start position:0% +the simplest possible way of developing +a theory of gravity in this framework + + align:start position:0% +a theory of gravity in this framework + + + align:start position:0% +a theory of gravity in this framework +the remainder of this course is going to + + align:start position:0% +the remainder of this course is going to + + + align:start position:0% +the remainder of this course is going to +be dedicated to solving this equation + + align:start position:0% +be dedicated to solving this equation + + + align:start position:0% +be dedicated to solving this equation +and exploring the properties of the + + align:start position:0% +and exploring the properties of the + + + align:start position:0% +and exploring the properties of the +solutions that arise from this and so + + align:start position:0% +solutions that arise from this and so + + + align:start position:0% +solutions that arise from this and so +let me continue the discussion I began + + align:start position:0% +let me continue the discussion I began + + + align:start position:0% +let me continue the discussion I began +at the end of the previous lecture we + + align:start position:0% +at the end of the previous lecture we + + + align:start position:0% +at the end of the previous lecture we +are going to find it very useful to + + align:start position:0% +are going to find it very useful to + + + align:start position:0% +are going to find it very useful to +regard this as a set of differential + + align:start position:0% +regard this as a set of differential + + + align:start position:0% +regard this as a set of differential +equations + + align:start position:0% + + + + align:start position:0% + +for the space-time metric given a source + + align:start position:0% +for the space-time metric given a source + + + align:start position:0% +for the space-time metric given a source +okay that after all is how we typically + + align:start position:0% +okay that after all is how we typically + + + align:start position:0% +okay that after all is how we typically +think of solving for fields given a + + align:start position:0% +think of solving for fields given a + + + align:start position:0% +think of solving for fields given a +particular source just pardon me I'll + + align:start position:0% +particular source just pardon me I'll + + + align:start position:0% +particular source just pardon me I'll +make sure it's as long datas I give you + + align:start position:0% +make sure it's as long datas I give you + + + align:start position:0% +make sure it's as long datas I give you +a distribution of mass you compute the + + align:start position:0% +a distribution of mass you compute the + + + align:start position:0% +a distribution of mass you compute the +Newtonian gravitational potential for + + align:start position:0% +Newtonian gravitational potential for + + + align:start position:0% +Newtonian gravitational potential for +that I give you a distribution of + + align:start position:0% +that I give you a distribution of + + + align:start position:0% +that I give you a distribution of +currents and fields you calculate the + + align:start position:0% +currents and fields you calculate the + + + align:start position:0% +currents and fields you calculate the +electric and magnetic fields that arise + + align:start position:0% +electric and magnetic fields that arise + + + align:start position:0% +electric and magnetic fields that arise +from that so I give you some + + align:start position:0% +from that so I give you some + + + align:start position:0% +from that so I give you some +distribution of mass and energy you + + align:start position:0% +distribution of mass and energy you + + + align:start position:0% +distribution of mass and energy you +compute the space-time that arises from + + align:start position:0% +compute the space-time that arises from + + + align:start position:0% +compute the space-time that arises from +that but let's stop before we dig into + + align:start position:0% +that but let's stop before we dig into + + + align:start position:0% +that but let's stop before we dig into +this and look at what this actually + + align:start position:0% +this and look at what this actually + + + align:start position:0% +this and look at what this actually +means given the mathematical equations + + align:start position:0% +means given the mathematical equations + + + align:start position:0% +means given the mathematical equations +that we have so G alpha beta is the + + align:start position:0% +that we have so G alpha beta is the + + + align:start position:0% +that we have so G alpha beta is the +Einstein tensor I construct it by taking + + align:start position:0% +Einstein tensor I construct it by taking + + + align:start position:0% +Einstein tensor I construct it by taking +several derivatives of the metric Micra + + align:start position:0% +several derivatives of the metric Micra + + + align:start position:0% +several derivatives of the metric Micra +STOVL symbols I combined those + + align:start position:0% +STOVL symbols I combined those + + + align:start position:0% +STOVL symbols I combined those +Christoffel symbols and derivatives of + + align:start position:0% +Christoffel symbols and derivatives of + + + align:start position:0% +Christoffel symbols and derivatives of +the Christoffel symbols to make the + + align:start position:0% +the Christoffel symbols to make the + + + align:start position:0% +the Christoffel symbols to make the +Riemann tensor I hit it with another + + align:start position:0% +Riemann tensor I hit it with another + + + align:start position:0% +Riemann tensor I hit it with another +power of the metric in order to trace + + align:start position:0% +power of the metric in order to trace + + + align:start position:0% +power of the metric in order to trace +and get the Ricci tensor I combined it + + align:start position:0% +and get the Ricci tensor I combined it + + + align:start position:0% +and get the Ricci tensor I combined it +with the trace of the Ricci tensor in + + align:start position:0% +with the trace of the Ricci tensor in + + + align:start position:0% +with the trace of the Ricci tensor in +the metric to get the Einstein + + align:start position:0% +the metric to get the Einstein + + + align:start position:0% +the metric to get the Einstein +schematically I can think of G alpha + + align:start position:0% +schematically I can think of G alpha + + + align:start position:0% +schematically I can think of G alpha +beta as some very complicated linear + + align:start position:0% +beta as some very complicated linear + + + align:start position:0% +beta as some very complicated linear +zooming some very complicated nonlinear + + align:start position:0% +zooming some very complicated nonlinear + + + align:start position:0% +zooming some very complicated nonlinear +differential operator acting on the + + align:start position:0% +differential operator acting on the + + + align:start position:0% +differential operator acting on the +metric + + align:start position:0% + + + + align:start position:0% + +so thinking about this is just a + + align:start position:0% +so thinking about this is just a + + + align:start position:0% +so thinking about this is just a +differential equation for the metric the + + align:start position:0% +differential equation for the metric the + + + align:start position:0% +differential equation for the metric the +left-hand side of this equation is a bit + + align:start position:0% +left-hand side of this equation is a bit + + + align:start position:0% +left-hand side of this equation is a bit +of a mess + + align:start position:0% +of a mess + + + align:start position:0% +of a mess +unfortunately the right-hand side can be + + align:start position:0% +unfortunately the right-hand side can be + + + align:start position:0% +unfortunately the right-hand side can be +a mess too let's think about this for a + + align:start position:0% +a mess too let's think about this for a + + + align:start position:0% +a mess too let's think about this for a +particular example suppose I choose as + + align:start position:0% +particular example suppose I choose as + + + align:start position:0% +particular example suppose I choose as +my force my source a perfect fluid well + + align:start position:0% +my force my source a perfect fluid well + + + align:start position:0% +my force my source a perfect fluid well +then my right-hand side it's gonna be + + align:start position:0% +then my right-hand side it's gonna be + + + align:start position:0% +then my right-hand side it's gonna be +something that involves the density and + + align:start position:0% +something that involves the density and + + + align:start position:0% +something that involves the density and +the pressure of that fluid the fluid + + align:start position:0% +the pressure of that fluid the fluid + + + align:start position:0% +the pressure of that fluid the fluid +velocity and then the metric okay so if + + align:start position:0% +velocity and then the metric okay so if + + + align:start position:0% +velocity and then the metric okay so if +I'm thinking about this as a + + align:start position:0% +I'm thinking about this as a + + + align:start position:0% +I'm thinking about this as a +differential equation for the metric the + + align:start position:0% +differential equation for the metric the + + + align:start position:0% +differential equation for the metric the +metric is appearing under this + + align:start position:0% +metric is appearing under this + + + align:start position:0% +metric is appearing under this +differential operator on the left hand + + align:start position:0% +differential operator on the left hand + + + align:start position:0% +differential operator on the left hand +side and explicitly in the source on the + + align:start position:0% +side and explicitly in the source on the + + + align:start position:0% +side and explicitly in the source on the +right hand side oh and by the way don't + + align:start position:0% +right hand side oh and by the way don't + + + align:start position:0% +right hand side oh and by the way don't +forget my fluid needs to be normalized + + align:start position:0% +forget my fluid needs to be normalized + + + align:start position:0% +forget my fluid needs to be normalized +my fluid floor velocity needs to be + + align:start position:0% +my fluid floor velocity needs to be + + + align:start position:0% +my fluid floor velocity needs to be +normalized so I have a further + + align:start position:0% +normalized so I have a further + + + align:start position:0% +normalized so I have a further +constraint that the compliment of the + + align:start position:0% +constraint that the compliment of the + + + align:start position:0% +constraint that the compliment of the +floor velocity are related to each other + + align:start position:0% +floor velocity are related to each other + + + align:start position:0% +floor velocity are related to each other +by the space-time metric so if I am + + align:start position:0% +by the space-time metric so if I am + + + align:start position:0% +by the space-time metric so if I am +going to regard this as just a + + align:start position:0% +going to regard this as just a + + + align:start position:0% +going to regard this as just a +differential equation for for the the + + align:start position:0% +differential equation for for the the + + + align:start position:0% +differential equation for for the the +space-time metric in general we're in + + align:start position:0% +space-time metric in general we're in + + + align:start position:0% +space-time metric in general we're in +for a world of pain so as I described at + + align:start position:0% +for a world of pain so as I described at + + + align:start position:0% +for a world of pain so as I described at +the end of the previous lecture we are + + align:start position:0% +the end of the previous lecture we are + + + align:start position:0% +the end of the previous lecture we are +going to examine how to solve this + + align:start position:0% +going to examine how to solve this + + + align:start position:0% +going to examine how to solve this +equation in which left of 8 962 we're + + align:start position:0% +equation in which left of 8 962 we're + + + align:start position:0% +equation in which left of 8 962 we're +going to look at three routes to solving + + align:start position:0% +going to look at three routes to solving + + + align:start position:0% +going to look at three routes to solving +this thing the one that we will begin to + + align:start position:0% +this thing the one that we will begin to + + + align:start position:0% +this thing the one that we will begin to +talk about today is we solve this for + + align:start position:0% + + + + align:start position:0% + +what I will define a little bit more + + align:start position:0% +what I will define a little bit more + + + align:start position:0% +what I will define a little bit more +precisely in a moment as weak gravity + + align:start position:0% + + + + align:start position:0% + +and what this is going to mean is that I + + align:start position:0% +and what this is going to mean is that I + + + align:start position:0% +and what this is going to mean is that I +only consider space times that are in a + + align:start position:0% +only consider space times that are in a + + + align:start position:0% +only consider space times that are in a +way that can be quantified close to flat + + align:start position:0% +way that can be quantified close to flat + + + align:start position:0% +way that can be quantified close to flat +space-time method to will be to consider + + align:start position:0% +space-time method to will be to consider + + + align:start position:0% +space-time method to will be to consider +symmetric solutions part of the reason + + align:start position:0% +symmetric solutions part of the reason + + + align:start position:0% +symmetric solutions part of the reason +the general framework is so complicated + + align:start position:0% +the general framework is so complicated + + + align:start position:0% +the general framework is so complicated +is that there are in general ten of + + align:start position:0% +is that there are in general ten of + + + align:start position:0% +is that there are in general ten of +these coupled nonlinear differential + + align:start position:0% +these coupled nonlinear differential + + + align:start position:0% +these coupled nonlinear differential +equations when we introduce symmetries + + align:start position:0% +equations when we introduce symmetries + + + align:start position:0% +equations when we introduce symmetries +or we consider things like static + + align:start position:0% +or we consider things like static + + + align:start position:0% +or we consider things like static +solutions or stationary solutions that + + align:start position:0% +solutions or stationary solutions that + + + align:start position:0% +solutions or stationary solutions that +don't have any time dynamics that at + + align:start position:0% +don't have any time dynamics that at + + + align:start position:0% +don't have any time dynamics that at +least reduces the number of equations + + align:start position:0% +least reduces the number of equations + + + align:start position:0% +least reduces the number of equations +that need to worry about they may still + + align:start position:0% +that need to worry about they may still + + + align:start position:0% +that need to worry about they may still +be coupled nonlinear and complicated but + + align:start position:0% +be coupled nonlinear and complicated but + + + align:start position:0% +be coupled nonlinear and complicated but +hopefully maybe we can reduce us from + + align:start position:0% +hopefully maybe we can reduce us from + + + align:start position:0% +hopefully maybe we can reduce us from +ten of these things need to worry about + + align:start position:0% +ten of these things need to worry about + + + align:start position:0% +ten of these things need to worry about +to just a small small number than one or + + align:start position:0% +to just a small small number than one or + + + align:start position:0% +to just a small small number than one or +two or three makes it at least a little + + align:start position:0% +two or three makes it at least a little + + + align:start position:0% +two or three makes it at least a little +easier in truth symmetric solutions if + + align:start position:0% +easier in truth symmetric solutions if + + + align:start position:0% +easier in truth symmetric solutions if +you can then add techniques for + + align:start position:0% +you can then add techniques for + + + align:start position:0% +you can then add techniques for +perturbing around them these turn out to + + align:start position:0% +perturbing around them these turn out to + + + align:start position:0% +perturbing around them these turn out to +be tremendously powerful my own research + + align:start position:0% +be tremendously powerful my own research + + + align:start position:0% +be tremendously powerful my own research +career is uses this technique a + + align:start position:0% +career is uses this technique a + + + align:start position:0% +career is uses this technique a +tremendous amount finally just basically + + align:start position:0% +tremendous amount finally just basically + + + align:start position:0% +tremendous amount finally just basically +say you know what let's just dive in and + + align:start position:0% +say you know what let's just dive in and + + + align:start position:0% +say you know what let's just dive in and +solve this puppy + + align:start position:0% + + + + align:start position:0% + +just do a numerical solution of the + + align:start position:0% +just do a numerical solution of the + + + align:start position:0% +just do a numerical solution of the +whole monster no simplifications eminent + + align:start position:0% +whole monster no simplifications eminent + + + align:start position:0% +whole monster no simplifications eminent +members of our field have dedicated + + align:start position:0% +members of our field have dedicated + + + align:start position:0% +members of our field have dedicated +entire careers to item three I will give + + align:start position:0% +entire careers to item three I will give + + + align:start position:0% +entire careers to item three I will give +you an introduction to the main concepts + + align:start position:0% +you an introduction to the main concepts + + + align:start position:0% +you an introduction to the main concepts +in the last lecture but it's not + + align:start position:0% +in the last lecture but it's not + + + align:start position:0% +in the last lecture but it's not +something we're going to be able to + + align:start position:0% +something we're going to be able to + + + align:start position:0% +something we're going to be able to +explore much detail in this class so we + + align:start position:0% +explore much detail in this class so we + + + align:start position:0% +explore much detail in this class so we +will focus on we're gonna do one in a + + align:start position:0% +will focus on we're gonna do one in a + + + align:start position:0% +will focus on we're gonna do one in a +fair amount of detail we'll look at a + + align:start position:0% +fair amount of detail we'll look at a + + + align:start position:0% +fair amount of detail we'll look at a +couple of the most important symmetric + + align:start position:0% +couple of the most important symmetric + + + align:start position:0% +couple of the most important symmetric +solutions so that you can see how these + + align:start position:0% +solutions so that you can see how these + + + align:start position:0% +solutions so that you can see how these +techniques work and then in my last two + + align:start position:0% +techniques work and then in my last two + + + align:start position:0% +techniques work and then in my last two +lectures I'm gonna describe a little bit + + align:start position:0% +lectures I'm gonna describe a little bit + + + align:start position:0% +lectures I'm gonna describe a little bit +about what happens when you perturb some + + align:start position:0% +about what happens when you perturb some + + + align:start position:0% +about what happens when you perturb some +of the most interesting symmetric + + align:start position:0% +of the most interesting symmetric + + + align:start position:0% +of the most interesting symmetric +solutions we'll talk about numerical + + align:start position:0% +solutions we'll talk about numerical + + + align:start position:0% +solutions we'll talk about numerical +solutions for the general case all right + + align:start position:0% +solutions for the general case all right + + + align:start position:0% +solutions for the general case all right +so let's begin we will begin with choice + + align:start position:0% +so let's begin we will begin with choice + + + align:start position:0% +so let's begin we will begin with choice +1 let's look at weak gravity also known + + align:start position:0% +1 let's look at weak gravity also known + + + align:start position:0% +1 let's look at weak gravity also known +as linearized general relativity so + + align:start position:0% +as linearized general relativity so + + + align:start position:0% +as linearized general relativity so +linearized general relativity is a + + align:start position:0% +linearized general relativity is a + + + align:start position:0% +linearized general relativity is a +situation in which we are only going to + + align:start position:0% +situation in which we are only going to + + + align:start position:0% +situation in which we are only going to +consider space times that are nearly + + align:start position:0% +consider space times that are nearly + + + align:start position:0% +consider space times that are nearly +flat if I am in this situation then I + + align:start position:0% +flat if I am in this situation then I + + + align:start position:0% +flat if I am in this situation then I +can choose coordinates + + align:start position:0% + + + + align:start position:0% + +such that my space-time metric is the + + align:start position:0% +such that my space-time metric is the + + + align:start position:0% +such that my space-time metric is the +metric of flat space-time plus a tensor + + align:start position:0% +metric of flat space-time plus a tensor + + + align:start position:0% +metric of flat space-time plus a tensor +H alpha beta all of whose components so + + align:start position:0% +H alpha beta all of whose components so + + + align:start position:0% +H alpha beta all of whose components so +this notation that I'm sort of inventing + + align:start position:0% +this notation that I'm sort of inventing + + + align:start position:0% +this notation that I'm sort of inventing +here double bars around H alpha beta + + align:start position:0% +here double bars around H alpha beta + + + align:start position:0% +here double bars around H alpha beta +this means the magnitude of H alpha beta + + align:start position:0% +this means the magnitude of H alpha beta + + + align:start position:0% +this means the magnitude of H alpha beta +is components these all must be much + + align:start position:0% +is components these all must be much + + + align:start position:0% +is components these all must be much +much less than one okay when you are in + + align:start position:0% +much less than one okay when you are in + + + align:start position:0% +much less than one okay when you are in +such a coordinate system you are in what + + align:start position:0% +such a coordinate system you are in what + + + align:start position:0% +such a coordinate system you are in what +we call nearly Lorentz coordinates such + + align:start position:0% +we call nearly Lorentz coordinates such + + + align:start position:0% +we call nearly Lorentz coordinates such +a coordinate system is as close to a + + align:start position:0% +a coordinate system is as close to a + + + align:start position:0% +a coordinate system is as close to a +globally a nurse'll coordinate system as + + align:start position:0% +globally a nurse'll coordinate system as + + + align:start position:0% +globally a nurse'll coordinate system as +is possible to make there are other + + align:start position:0% +is possible to make there are other + + + align:start position:0% +is possible to make there are other +coordinate choices we could make so for + + align:start position:0% +coordinate choices we could make so for + + + align:start position:0% +coordinate choices we could make so for +instance you're working in a system like + + align:start position:0% +instance you're working in a system like + + + align:start position:0% +instance you're working in a system like +that you know this basically boils down + + align:start position:0% +that you know this basically boils down + + + align:start position:0% +that you know this basically boils down +to coordinates that are Cartesian like + + align:start position:0% +to coordinates that are Cartesian like + + + align:start position:0% +to coordinates that are Cartesian like +on the spit on their spatial slices you + + align:start position:0% +on the spit on their spatial slices you + + + align:start position:0% +on the spit on their spatial slices you +could work in other ones these are + + align:start position:0% +could work in other ones these are + + + align:start position:0% +could work in other ones these are +particularly convenient because for + + align:start position:0% +particularly convenient because for + + + align:start position:0% +particularly convenient because for +instance if I work in a coordinate + + align:start position:0% +instance if I work in a coordinate + + + align:start position:0% +instance if I work in a coordinate +system whose spatial sector is spherical + + align:start position:0% +system whose spatial sector is spherical + + + align:start position:0% +system whose spatial sector is spherical +like well then there's gonna be some + + align:start position:0% +like well then there's gonna be some + + + align:start position:0% +like well then there's gonna be some +components that grow very large as I go + + align:start position:0% +components that grow very large as I go + + + align:start position:0% +components that grow very large as I go +to large radius away from some that the + + align:start position:0% +to large radius away from some that the + + + align:start position:0% +to large radius away from some that the +source of my gravitation and this just + + align:start position:0% +source of my gravitation and this just + + + align:start position:0% +source of my gravitation and this just +makes my analysis quite quite convenient + + align:start position:0% +makes my analysis quite quite convenient + + + align:start position:0% +makes my analysis quite quite convenient +in particular where I'm going to take + + align:start position:0% +in particular where I'm going to take + + + align:start position:0% +in particular where I'm going to take +advantage of this whenever I come across + + align:start position:0% +advantage of this whenever I come across + + + align:start position:0% +advantage of this whenever I come across +a term that involves the perturbation + + align:start position:0% +a term that involves the perturbation + + + align:start position:0% +a term that involves the perturbation +squared or to a higher power + + align:start position:0% + + + + align:start position:0% + +I'm just gonna approximate it a zero I + + align:start position:0% +I'm just gonna approximate it a zero I + + + align:start position:0% +I'm just gonna approximate it a zero I +will always neglect terms beyond linear + + align:start position:0% +will always neglect terms beyond linear + + + align:start position:0% +will always neglect terms beyond linear +hence the term linearized gr in my + + align:start position:0% +hence the term linearized gr in my + + + align:start position:0% +hence the term linearized gr in my +analysis now there are a couple of + + align:start position:0% +analysis now there are a couple of + + + align:start position:0% +analysis now there are a couple of +properties before I get into how to + + align:start position:0% +properties before I get into how to + + + align:start position:0% +properties before I get into how to +develop weak gravity linearized gr I + + align:start position:0% +develop weak gravity linearized gr I + + + align:start position:0% +develop weak gravity linearized gr I +want to describe I discuss a little bit + + align:start position:0% +want to describe I discuss a little bit + + + align:start position:0% +want to describe I discuss a little bit +some of the properties of space times + + align:start position:0% +some of the properties of space times + + + align:start position:0% +some of the properties of space times +that have space lines of this form what + + align:start position:0% +that have space lines of this form what + + + align:start position:0% +that have space lines of this form what +are the particularly important + + align:start position:0% +are the particularly important + + + align:start position:0% +are the particularly important +properties of these so let's consider + + align:start position:0% +properties of these so let's consider + + + align:start position:0% +properties of these so let's consider +coordinate transformations my space-time + + align:start position:0% +coordinate transformations my space-time + + + align:start position:0% +coordinate transformations my space-time +space-time metric is a tensor like any + + align:start position:0% +space-time metric is a tensor like any + + + align:start position:0% +space-time metric is a tensor like any +other and so the usual rules pertain + + align:start position:0% +other and so the usual rules pertain + + + align:start position:0% +other and so the usual rules pertain +here that I can change my coordinates + + align:start position:0% + + + + align:start position:0% + +using some matrix that relates my + + align:start position:0% +using some matrix that relates my + + + align:start position:0% +using some matrix that relates my +original coordinate system which I've + + align:start position:0% +original coordinate system which I've + + + align:start position:0% +original coordinate system which I've +denoted without bars just some new + + align:start position:0% +denoted without bars just some new + + + align:start position:0% +denoted without bars just some new +coordinate system that is barred now + + align:start position:0% +coordinate system that is barred now + + + align:start position:0% +coordinate system that is barred now +recall that when we worked in flat + + align:start position:0% +recall that when we worked in flat + + + align:start position:0% +recall that when we worked in flat +space-time there was a there was one + + align:start position:0% +space-time there was a there was one + + + align:start position:0% +space-time there was a there was one +category of coordinate transformations + + align:start position:0% +category of coordinate transformations + + + align:start position:0% +category of coordinate transformations +that was special those were the lengths + + align:start position:0% +that was special those were the lengths + + + align:start position:0% +that was special those were the lengths +Lorentz transformations + + align:start position:0% + + + + align:start position:0% + +so we are not working in flat space-time + + align:start position:0% +so we are not working in flat space-time + + + align:start position:0% +so we are not working in flat space-time +so on the face of it we don't expect + + align:start position:0% +so on the face of it we don't expect + + + align:start position:0% +so on the face of it we don't expect +Lorentz transformations to play a + + align:start position:0% +Lorentz transformations to play a + + + align:start position:0% +Lorentz transformations to play a +particularly special role except perhaps + + align:start position:0% +particularly special role except perhaps + + + align:start position:0% +particularly special role except perhaps +in the domain of a freely falling frame + + align:start position:0% + + + + align:start position:0% + +but you know what this is a nearly flat + + align:start position:0% +but you know what this is a nearly flat + + + align:start position:0% +but you know what this is a nearly flat +space-time so you know just for giggles + + align:start position:0% +space-time so you know just for giggles + + + align:start position:0% +space-time so you know just for giggles +let's see what happens if you apply the + + align:start position:0% +let's see what happens if you apply the + + + align:start position:0% +let's see what happens if you apply the +Lorentz transformation to your nearly + + align:start position:0% +Lorentz transformation to your nearly + + + align:start position:0% +Lorentz transformation to your nearly +flat space-time so if I look at G mu bar + + align:start position:0% +flat space-time so if I look at G mu bar + + + align:start position:0% +flat space-time so if I look at G mu bar +nu bar as being a Lorentz transformation + + align:start position:0% +nu bar as being a Lorentz transformation + + + align:start position:0% +nu bar as being a Lorentz transformation +applied to my nearly flat metric well + + align:start position:0% +applied to my nearly flat metric well + + + align:start position:0% +applied to my nearly flat metric well +what I get + + align:start position:0% + + + + align:start position:0% + +staying this out is this now one of the + + align:start position:0% +staying this out is this now one of the + + + align:start position:0% +staying this out is this now one of the +reasons why the Lorentz transformation + + align:start position:0% +reasons why the Lorentz transformation + + + align:start position:0% +reasons why the Lorentz transformation +was special in flat space-time is that + + align:start position:0% +was special in flat space-time is that + + + align:start position:0% +was special in flat space-time is that +it leaves the metric of flat space-time + + align:start position:0% +it leaves the metric of flat space-time + + + align:start position:0% +it leaves the metric of flat space-time +unchanged and so this just maps to eight + + align:start position:0% +unchanged and so this just maps to eight + + + align:start position:0% +unchanged and so this just maps to eight +mu nu I'm gonna define what comes out + + align:start position:0% +mu nu I'm gonna define what comes out + + + align:start position:0% +mu nu I'm gonna define what comes out +here as H mu nu okay I'm doing this in a + + align:start position:0% +here as H mu nu okay I'm doing this in a + + + align:start position:0% +here as H mu nu okay I'm doing this in a +fairly I hope obvious way this is + + align:start position:0% +fairly I hope obvious way this is + + + align:start position:0% +fairly I hope obvious way this is +interesting what this has told me is + + align:start position:0% +interesting what this has told me is + + + align:start position:0% +interesting what this has told me is +that when I apply the Lorentz + + align:start position:0% +that when I apply the Lorentz + + + align:start position:0% +that when I apply the Lorentz +transformation to my nearly flat + + align:start position:0% +transformation to my nearly flat + + + align:start position:0% +transformation to my nearly flat +space-time the background is unchanged + + align:start position:0% +space-time the background is unchanged + + + align:start position:0% +space-time the background is unchanged +and the perturbation to the background + + align:start position:0% +and the perturbation to the background + + + align:start position:0% +and the perturbation to the background +transforms just like any tensor field + + align:start position:0% +transforms just like any tensor field + + + align:start position:0% +transforms just like any tensor field +would transform in flat space now it + + align:start position:0% +would transform in flat space now it + + + align:start position:0% +would transform in flat space now it +should be emphasized we are not working + + align:start position:0% +should be emphasized we are not working + + + align:start position:0% +should be emphasized we are not working +in flat space okay we can compute + + align:start position:0% +in flat space okay we can compute + + + align:start position:0% +in flat space okay we can compute +curvature tensors if we parallel + + align:start position:0% +curvature tensors if we parallel + + + align:start position:0% +curvature tensors if we parallel +transport if we consider 2 g DS X moving + + align:start position:0% +transport if we consider 2 g DS X moving + + + align:start position:0% +transport if we consider 2 g DS X moving +through this space-time we will see that + + align:start position:0% +through this space-time we will see that + + + align:start position:0% +through this space-time we will see that +trial L transport along those two dod's + + align:start position:0% +trial L transport along those two dod's + + + align:start position:0% +trial L transport along those two dod's +X if they start out at initially + + align:start position:0% +X if they start out at initially + + + align:start position:0% +X if they start out at initially +parallel they do not remain parallel so + + align:start position:0% +parallel they do not remain parallel so + + + align:start position:0% +parallel they do not remain parallel so +this is not flat space-time but in many + + align:start position:0% +this is not flat space-time but in many + + + align:start position:0% +this is not flat space-time but in many +ways it's close enough that we can + + align:start position:0% +ways it's close enough that we can + + + align:start position:0% +ways it's close enough that we can +borrow many of the mathematical tools + + align:start position:0% +borrow many of the mathematical tools + + + align:start position:0% +borrow many of the mathematical tools +that were used in flat space-time in + + align:start position:0% +that were used in flat space-time in + + + align:start position:0% +that were used in flat space-time in +particular we can introduce the + + align:start position:0% +particular we can introduce the + + + align:start position:0% +particular we can introduce the +following think of it as a useful + + align:start position:0% +following think of it as a useful + + + align:start position:0% +following think of it as a useful +fiction + + align:start position:0% + + + + align:start position:0% + +which is that in this framework we can + + align:start position:0% +which is that in this framework we can + + + align:start position:0% +which is that in this framework we can +regard the perturbation that pushes us + + align:start position:0% +regard the perturbation that pushes us + + + align:start position:0% +regard the perturbation that pushes us +away from flat space-time as just an + + align:start position:0% +away from flat space-time as just an + + + align:start position:0% +away from flat space-time as just an +ordinary tensor field living in the + + align:start position:0% +ordinary tensor field living in the + + + align:start position:0% +ordinary tensor field living in the +manifold of special relativity living in + + align:start position:0% +manifold of special relativity living in + + + align:start position:0% +manifold of special relativity living in +the ADA alpha-beta metric it's worth + + align:start position:0% +the ADA alpha-beta metric it's worth + + + align:start position:0% +the ADA alpha-beta metric it's worth +bear in mind in in a fundamental sense + + align:start position:0% +bear in mind in in a fundamental sense + + + align:start position:0% +bear in mind in in a fundamental sense +it's not okay space-time is curved h + + align:start position:0% +it's not okay space-time is curved h + + + align:start position:0% +it's not okay space-time is curved h +alpha beta is telling me about that + + align:start position:0% +alpha beta is telling me about that + + + align:start position:0% +alpha beta is telling me about that +curvature but the mathematics works in + + align:start position:0% +curvature but the mathematics works in + + + align:start position:0% +curvature but the mathematics works in +such a way that you can borrow a lot of + + align:start position:0% +such a way that you can borrow a lot of + + + align:start position:0% +such a way that you can borrow a lot of +tools that we used in special relativity + + align:start position:0% +tools that we used in special relativity + + + align:start position:0% +tools that we used in special relativity +and just imagine H as a tensor field + + align:start position:0% +and just imagine H as a tensor field + + + align:start position:0% +and just imagine H as a tensor field +living in that special relativity + + align:start position:0% +living in that special relativity + + + align:start position:0% +living in that special relativity +manifold okay so that's useful fact one + + align:start position:0% +manifold okay so that's useful fact one + + + align:start position:0% +manifold okay so that's useful fact one +that we want to bear in mind as we work + + align:start position:0% +that we want to bear in mind as we work + + + align:start position:0% +that we want to bear in mind as we work +with as we work in this nearly flat + + align:start position:0% +with as we work in this nearly flat + + + align:start position:0% +with as we work in this nearly flat +space-time useful fact too is we want to + + align:start position:0% +space-time useful fact too is we want to + + + align:start position:0% +space-time useful fact too is we want to +think about what happens when we raise + + align:start position:0% +think about what happens when we raise + + + align:start position:0% +think about what happens when we raise +and lower indices + + align:start position:0% + + + + align:start position:0% + +so suppose now that I'm gonna regard H + + align:start position:0% +so suppose now that I'm gonna regard H + + + align:start position:0% +so suppose now that I'm gonna regard H +alpha beta as an ordinary tensor field + + align:start position:0% +alpha beta as an ordinary tensor field + + + align:start position:0% +alpha beta as an ordinary tensor field +living in this thing I might want to + + align:start position:0% +living in this thing I might want to + + + align:start position:0% +living in this thing I might want to +know what it looks like with its indices + + align:start position:0% +know what it looks like with its indices + + + align:start position:0% +know what it looks like with its indices +raised so I'm gonna do what I usually do + + align:start position:0% +raised so I'm gonna do what I usually do + + + align:start position:0% +raised so I'm gonna do what I usually do +when I want to raise the indices on a + + align:start position:0% +when I want to raise the indices on a + + + align:start position:0% +when I want to raise the indices on a +want a tensor I hit it with the metric + + align:start position:0% + + + + align:start position:0% + +we're going to talk about what my + + align:start position:0% +we're going to talk about what my + + + align:start position:0% +we're going to talk about what my +upstairs metric looks like in just a + + align:start position:0% +upstairs metric looks like in just a + + + align:start position:0% +upstairs metric looks like in just a +moment but clearly it's going to be + + align:start position:0% +moment but clearly it's going to be + + + align:start position:0% +moment but clearly it's going to be +something that looks like the metric of + + align:start position:0% +something that looks like the metric of + + + align:start position:0% +something that looks like the metric of +flat space-time plus terms that are on + + align:start position:0% +flat space-time plus terms that are on + + + align:start position:0% +flat space-time plus terms that are on +the order of H because I always drop + + align:start position:0% +the order of H because I always drop + + + align:start position:0% +the order of H because I always drop +terms of order H squared and higher I + + align:start position:0% +terms of order H squared and higher I + + + align:start position:0% +terms of order H squared and higher I +can immediately say that this must + + align:start position:0% +can immediately say that this must + + + align:start position:0% +can immediately say that this must +simply be symmetric a flat space-time + + align:start position:0% +simply be symmetric a flat space-time + + + align:start position:0% +simply be symmetric a flat space-time +with the indices in the upstairs + + align:start position:0% +with the indices in the upstairs + + + align:start position:0% +with the indices in the upstairs +position acting on H in other words at + + align:start position:0% +position acting on H in other words at + + + align:start position:0% +position acting on H in other words at +least when I am acting on tensors that + + align:start position:0% +least when I am acting on tensors that + + + align:start position:0% +least when I am acting on tensors that +are built from the space-time metric + + align:start position:0% +are built from the space-time metric + + + align:start position:0% +are built from the space-time metric +itself I'm going to always want to raise + + align:start position:0% +itself I'm going to always want to raise + + + align:start position:0% +itself I'm going to always want to raise +and lower them + + align:start position:0% + + + + align:start position:0% + +using my flat space-time ADA alpha-beta + + align:start position:0% +using my flat space-time ADA alpha-beta + + + align:start position:0% +using my flat space-time ADA alpha-beta +bearing this in mind let's carefully + + align:start position:0% +bearing this in mind let's carefully + + + align:start position:0% +bearing this in mind let's carefully +think about what the metric inverse + + align:start position:0% +think about what the metric inverse + + + align:start position:0% +think about what the metric inverse +actually looks like I actually use this + + align:start position:0% +actually looks like I actually use this + + + align:start position:0% +actually looks like I actually use this +in one of my calculations in the + + align:start position:0% +in one of my calculations in the + + + align:start position:0% +in one of my calculations in the +previous lecture and I said I'm going to + + align:start position:0% +previous lecture and I said I'm going to + + + align:start position:0% +previous lecture and I said I'm going to +justify this in the next lecture so here + + align:start position:0% +justify this in the next lecture so here + + + align:start position:0% +justify this in the next lecture so here +we are now we're going to justify it so + + align:start position:0% +we are now we're going to justify it so + + + align:start position:0% +we are now we're going to justify it so +let's use this definition okay so the + + align:start position:0% +let's use this definition okay so the + + + align:start position:0% +let's use this definition okay so the +upstairs metric is defined such that + + align:start position:0% +upstairs metric is defined such that + + + align:start position:0% +upstairs metric is defined such that +when it contracts with the downstairs + + align:start position:0% +when it contracts with the downstairs + + + align:start position:0% +when it contracts with the downstairs +metric I get the identity back this is + + align:start position:0% +metric I get the identity back this is + + + align:start position:0% +metric I get the identity back this is +the definition of the metric inverse + + align:start position:0% +the definition of the metric inverse + + + align:start position:0% +the definition of the metric inverse +working in linear theory I know that + + align:start position:0% +working in linear theory I know that + + + align:start position:0% +working in linear theory I know that +this thing is going to be something like + + align:start position:0% +this thing is going to be something like + + + align:start position:0% +this thing is going to be something like +ADA alpha beta plus a term of order H I + + align:start position:0% +ADA alpha beta plus a term of order H I + + + align:start position:0% +ADA alpha beta plus a term of order H I +don't know what that term is yet so let + + align:start position:0% +don't know what that term is yet so let + + + align:start position:0% +don't know what that term is yet so let +me just give it a new name + + align:start position:0% +me just give it a new name + + + align:start position:0% +me just give it a new name +I'm gonna call it m alpha beta whoops + + align:start position:0% + + + + align:start position:0% + +okay hopefully the math will soon show + + align:start position:0% +okay hopefully the math will soon show + + + align:start position:0% +okay hopefully the math will soon show +me what this M actually is okay it will + + align:start position:0% +me what this M actually is okay it will + + + align:start position:0% +me what this M actually is okay it will +be of order H but as of yet unknown + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +okay so you know what let's rewrite that + + align:start position:0% +okay so you know what let's rewrite that + + + align:start position:0% +okay so you know what let's rewrite that +over here so let's now multiply this guy + + align:start position:0% +over here so let's now multiply this guy + + + align:start position:0% +over here so let's now multiply this guy +out a to alpha beta hitting a to beta + + align:start position:0% +out a to alpha beta hitting a to beta + + + align:start position:0% +out a to alpha beta hitting a to beta +gamma that gives me Delta alpha gamma M + + align:start position:0% +gamma that gives me Delta alpha gamma M + + + align:start position:0% +gamma that gives me Delta alpha gamma M +hitting ADA + + align:start position:0% +hitting ADA + + + align:start position:0% +hitting ADA +now remember what I just said over here + + align:start position:0% +now remember what I just said over here + + + align:start position:0% +now remember what I just said over here +when I'm working with space-time tensors + + align:start position:0% +when I'm working with space-time tensors + + + align:start position:0% +when I'm working with space-time tensors +I always raise and lower indices using + + align:start position:0% +I always raise and lower indices using + + + align:start position:0% +I always raise and lower indices using +ADA alpha beta so when m alpha beta its + + align:start position:0% +ADA alpha beta so when m alpha beta its + + + align:start position:0% +ADA alpha beta so when m alpha beta its +ADA beta gamma this is going to give me + + align:start position:0% +ADA beta gamma this is going to give me + + + align:start position:0% +ADA beta gamma this is going to give me +m alpha gamma this ADA hits that H I get + + align:start position:0% +m alpha gamma this ADA hits that H I get + + + align:start position:0% +m alpha gamma this ADA hits that H I get +H alpha upstairs gamma Dempster's and + + align:start position:0% +H alpha upstairs gamma Dempster's and + + + align:start position:0% +H alpha upstairs gamma Dempster's and +then this guy's of order H that guy's of + + align:start position:0% +then this guy's of order H that guy's of + + + align:start position:0% +then this guy's of order H that guy's of +order H so additional terms of order H + + align:start position:0% +order H so additional terms of order H + + + align:start position:0% +order H so additional terms of order H +squared so these guys cancel and what I + + align:start position:0% +squared so these guys cancel and what I + + + align:start position:0% +squared so these guys cancel and what I +am left with is m alpha gamma equals + + align:start position:0% +am left with is m alpha gamma equals + + + align:start position:0% +am left with is m alpha gamma equals +negative H alpha gamma I can raise my + + align:start position:0% +negative H alpha gamma I can raise my + + + align:start position:0% +negative H alpha gamma I can raise my +two indices raise the gammas on both + + align:start position:0% +two indices raise the gammas on both + + + align:start position:0% +two indices raise the gammas on both +sides here and we deduce from this that + + align:start position:0% +sides here and we deduce from this that + + + align:start position:0% +sides here and we deduce from this that +my inverse metric is ADA alpha beta in + + align:start position:0% +my inverse metric is ADA alpha beta in + + + align:start position:0% +my inverse metric is ADA alpha beta in +the upstairs position minus H alpha + + align:start position:0% +the upstairs position minus H alpha + + + align:start position:0% +the upstairs position minus H alpha +better at least to linear order in H + + align:start position:0% + + + + align:start position:0% + +I'll just comment that what this is + + align:start position:0% +I'll just comment that what this is + + + align:start position:0% +I'll just comment that what this is +essentially the the matrix or tensor + + align:start position:0% +essentially the the matrix or tensor + + + align:start position:0% +essentially the the matrix or tensor +equivalent of a binomial expansion 1 + + align:start position:0% +equivalent of a binomial expansion 1 + + + align:start position:0% +equivalent of a binomial expansion 1 +over 1 plus epsilon is approximately 1 + + align:start position:0% +over 1 plus epsilon is approximately 1 + + + align:start position:0% +over 1 plus epsilon is approximately 1 +minus Epsilon + + align:start position:0% +minus Epsilon + + + align:start position:0% +minus Epsilon +that's all this says ok but this is + + align:start position:0% +that's all this says ok but this is + + + align:start position:0% +that's all this says ok but this is +important to do in fact I will I just + + align:start position:0% +important to do in fact I will I just + + + align:start position:0% +important to do in fact I will I just +sort of remark somewhat anecdotally that + + align:start position:0% +sort of remark somewhat anecdotally that + + + align:start position:0% +sort of remark somewhat anecdotally that +when I work with graduate students on + + align:start position:0% +when I work with graduate students on + + + align:start position:0% +when I work with graduate students on +projects where we have to do things in + + align:start position:0% +projects where we have to do things in + + + align:start position:0% +projects where we have to do things in +linearized theory gain the sign wrong + + align:start position:0% +linearized theory gain the sign wrong + + + align:start position:0% +linearized theory gain the sign wrong +here is one of the most common mistakes + + align:start position:0% +here is one of the most common mistakes + + + align:start position:0% +here is one of the most common mistakes +that people make all right one final + + align:start position:0% +that people make all right one final + + + align:start position:0% +that people make all right one final +detail + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so this detail is I just labeled it it's + + align:start position:0% +so this detail is I just labeled it it's + + + align:start position:0% +so this detail is I just labeled it it's +a particularly important one we talked + + align:start position:0% +a particularly important one we talked + + + align:start position:0% +a particularly important one we talked +about general coordinate transformations + + align:start position:0% +about general coordinate transformations + + + align:start position:0% +about general coordinate transformations +that I immediately went into discuss the + + align:start position:0% +that I immediately went into discuss the + + + align:start position:0% +that I immediately went into discuss the +Lorentz transformation there's a + + align:start position:0% +Lorentz transformation there's a + + + align:start position:0% +Lorentz transformation there's a +different category of coordinate + + align:start position:0% +different category of coordinate + + + align:start position:0% +different category of coordinate +transformation that plays a very + + align:start position:0% +transformation that plays a very + + + align:start position:0% +transformation that plays a very +important role in understanding the + + align:start position:0% +important role in understanding the + + + align:start position:0% +important role in understanding the +physics that the physics of systems that + + align:start position:0% +physics that the physics of systems that + + + align:start position:0% +physics that the physics of systems that +we analyzed in linearize theory so let's + + align:start position:0% +we analyzed in linearize theory so let's + + + align:start position:0% +we analyzed in linearize theory so let's +consider a different kind of coordinate + + align:start position:0% +consider a different kind of coordinate + + + align:start position:0% +consider a different kind of coordinate +transformation let's consider a + + align:start position:0% +transformation let's consider a + + + align:start position:0% +transformation let's consider a +coordinate shift which I'm going to + + align:start position:0% +coordinate shift which I'm going to + + + align:start position:0% +coordinate shift which I'm going to +define by X alpha Prime + + align:start position:0% +define by X alpha Prime + + + align:start position:0% +define by X alpha Prime +really this should be X prime alpha but + + align:start position:0% +really this should be X prime alpha but + + + align:start position:0% +really this should be X prime alpha but +you'll see why I need to name it this + + align:start position:0% +you'll see why I need to name it this + + + align:start position:0% +you'll see why I need to name it this +way right now so this is my original + + align:start position:0% +way right now so this is my original + + + align:start position:0% +way right now so this is my original +coordinate X alpha plus some little + + align:start position:0% +coordinate X alpha plus some little + + + align:start position:0% +coordinate X alpha plus some little +offset that's a function of the + + align:start position:0% +offset that's a function of the + + + align:start position:0% +offset that's a function of the +coordinates X beta so think of this as + + align:start position:0% +coordinates X beta so think of this as + + + align:start position:0% +coordinates X beta so think of this as +suppose I have a coordinate grid that + + align:start position:0% +suppose I have a coordinate grid that + + + align:start position:0% +suppose I have a coordinate grid that +looks like this and I have some function + + align:start position:0% +looks like this and I have some function + + + align:start position:0% +looks like this and I have some function +that says I want to consider a different + + align:start position:0% +that says I want to consider a different + + + align:start position:0% +that says I want to consider a different +set of coordinates that maybe pushes me + + align:start position:0% +set of coordinates that maybe pushes me + + + align:start position:0% +set of coordinates that maybe pushes me +a little bit of long away from each of + + align:start position:0% +a little bit of long away from each of + + + align:start position:0% +a little bit of long away from each of +these coordinate lines in a way that + + align:start position:0% +these coordinate lines in a way that + + + align:start position:0% +these coordinate lines in a way that +varies as a function of position here + + align:start position:0% +varies as a function of position here + + + align:start position:0% +varies as a function of position here +okay + + align:start position:0% + + + + align:start position:0% + +this notation is kind of an abuse of the + + align:start position:0% +this notation is kind of an abuse of the + + + align:start position:0% +this notation is kind of an abuse of the +indices I am really not trying to define + + align:start position:0% +indices I am really not trying to define + + + align:start position:0% +indices I am really not trying to define +a coordinate invariant relationship here + + align:start position:0% +a coordinate invariant relationship here + + + align:start position:0% +a coordinate invariant relationship here +I am just trying to connect two + + align:start position:0% +I am just trying to connect two + + + align:start position:0% +I am just trying to connect two +quantities in I'm trying to connect + + align:start position:0% +quantities in I'm trying to connect + + + align:start position:0% +quantities in I'm trying to connect +quantities and to switch to the + + align:start position:0% +quantities and to switch to the + + + align:start position:0% +quantities and to switch to the +coordinate systems and as we'll see even + + align:start position:0% +coordinate systems and as we'll see even + + + align:start position:0% +coordinate systems and as we'll see even +though this is a bit ugly + + align:start position:0% +though this is a bit ugly + + + align:start position:0% +though this is a bit ugly +it works well for what we want to do so + + align:start position:0% +it works well for what we want to do so + + + align:start position:0% +it works well for what we want to do so +my coordinate transformation matrix + + align:start position:0% + + + + align:start position:0% + +okay so I just take the matrix of I + + align:start position:0% +okay so I just take the matrix of I + + + align:start position:0% +okay so I just take the matrix of I +developed a Jacobian my matrix of + + align:start position:0% +developed a Jacobian my matrix of + + + align:start position:0% +developed a Jacobian my matrix of +partial derivatives of the new + + align:start position:0% +partial derivatives of the new + + + align:start position:0% +partial derivatives of the new +coordinate with respect to the old + + align:start position:0% +coordinate with respect to the old + + + align:start position:0% +coordinate with respect to the old +coordinate in the usual way this is + + align:start position:0% +coordinate in the usual way this is + + + align:start position:0% +coordinate in the usual way this is +going to be my first term is just a + + align:start position:0% +going to be my first term is just a + + + align:start position:0% +going to be my first term is just a +Kronecker Delta and then I'm gonna get a + + align:start position:0% +Kronecker Delta and then I'm gonna get a + + + align:start position:0% +Kronecker Delta and then I'm gonna get a +term that looks like matrix of + + align:start position:0% +term that looks like matrix of + + + align:start position:0% +term that looks like matrix of +derivatives of the function that defines + + align:start position:0% +derivatives of the function that defines + + + align:start position:0% +derivatives of the function that defines +my infinitesimal this defines my shift I + + align:start position:0% +my infinitesimal this defines my shift I + + + align:start position:0% +my infinitesimal this defines my shift I +just gave away what I was about to say + + align:start position:0% +just gave away what I was about to say + + + align:start position:0% +just gave away what I was about to say +I'm going to require when I work in + + align:start position:0% +I'm going to require when I work in + + + align:start position:0% +I'm going to require when I work in +these nearly Lorentz coordinates all + + align:start position:0% +these nearly Lorentz coordinates all + + + align:start position:0% +these nearly Lorentz coordinates all +these entries need to be small these + + align:start position:0% +these entries need to be small these + + + align:start position:0% +these entries need to be small these +will all be much much less than one and + + align:start position:0% +will all be much much less than one and + + + align:start position:0% +will all be much much less than one and +so we call this an infinitesimal + + align:start position:0% +so we call this an infinitesimal + + + align:start position:0% +so we call this an infinitesimal +coordinate transformation we are going + + align:start position:0% +coordinate transformation we are going + + + align:start position:0% +coordinate transformation we are going +to need to use the inverse of this guy + + align:start position:0% + + + + align:start position:0% + +and using the definition of the inverse + + align:start position:0% +and using the definition of the inverse + + + align:start position:0% +and using the definition of the inverse +of this thing essentially that when I + + align:start position:0% +of this thing essentially that when I + + + align:start position:0% +of this thing essentially that when I +take this and I can tract let me put it + + align:start position:0% +take this and I can tract let me put it + + + align:start position:0% +take this and I can tract let me put it +this way I'll just write it out so if I + + align:start position:0% +this way I'll just write it out so if I + + + align:start position:0% +this way I'll just write it out so if I +compute this I get my chronic or Delta + + align:start position:0% +compute this I get my chronic or Delta + + + align:start position:0% +compute this I get my chronic or Delta +back taking advantage of the smallness + + align:start position:0% +back taking advantage of the smallness + + + align:start position:0% +back taking advantage of the smallness +of the transformation it's not terribly + + align:start position:0% +of the transformation it's not terribly + + + align:start position:0% +of the transformation it's not terribly +hard to demonstrate that what comes out + + align:start position:0% +hard to demonstrate that what comes out + + + align:start position:0% +hard to demonstrate that what comes out +of that is this the minus sign is the + + align:start position:0% +of that is this the minus sign is the + + + align:start position:0% +of that is this the minus sign is the +key thing which I want to emphasize here + + align:start position:0% +key thing which I want to emphasize here + + + align:start position:0% +key thing which I want to emphasize here +okay that minus sign is very similar to + + align:start position:0% +okay that minus sign is very similar to + + + align:start position:0% +okay that minus sign is very similar to +the minus sign that I have here what + + align:start position:0% +the minus sign that I have here what + + + align:start position:0% +the minus sign that I have here what +we're doing is again just kind of the + + align:start position:0% +we're doing is again just kind of the + + + align:start position:0% +we're doing is again just kind of the +the matrix equivalent of expanding one + + align:start position:0% +the matrix equivalent of expanding one + + + align:start position:0% +the matrix equivalent of expanding one +over one plus epsilon for small epsilon + + align:start position:0% + + + + align:start position:0% + +the reason that I am doing this is that + + align:start position:0% +the reason that I am doing this is that + + + align:start position:0% +the reason that I am doing this is that +I would now like to look at how the + + align:start position:0% +I would now like to look at how the + + + align:start position:0% +I would now like to look at how the +metric changes under this coordinate + + align:start position:0% +metric changes under this coordinate + + + align:start position:0% +metric changes under this coordinate +transformation + + align:start position:0% + + + + align:start position:0% + +so what I'm going to do is define G mu + + align:start position:0% +so what I'm going to do is define G mu + + + align:start position:0% +so what I'm going to do is define G mu +nu in the new coordinate system okay + + align:start position:0% +nu in the new coordinate system okay + + + align:start position:0% +nu in the new coordinate system okay +usual operation + + align:start position:0% +usual operation + + + align:start position:0% +usual operation +let's now insert the many different + + align:start position:0% +let's now insert the many different + + + align:start position:0% +let's now insert the many different +definitions that we have introduced here + + align:start position:0% +definitions that we have introduced here + + + align:start position:0% +definitions that we have introduced here +so I'm going to notice that what I am + + align:start position:0% +so I'm going to notice that what I am + + + align:start position:0% +so I'm going to notice that what I am +using for my transformation matrix there + + align:start position:0% +using for my transformation matrix there + + + align:start position:0% +using for my transformation matrix there +is the inverse that I just wrote down so + + align:start position:0% +is the inverse that I just wrote down so + + + align:start position:0% +is the inverse that I just wrote down so +let's fill that in so I'm going to get a + + align:start position:0% +let's fill that in so I'm going to get a + + + align:start position:0% +let's fill that in so I'm going to get a +term that involves chroniker - a matrix + + align:start position:0% +term that involves chroniker - a matrix + + + align:start position:0% +term that involves chroniker - a matrix +of partial derivatives my other one + + align:start position:0% +of partial derivatives my other one + + + align:start position:0% +of partial derivatives my other one +gives me a nether chroniker matrix of + + align:start position:0% +gives me a nether chroniker matrix of + + + align:start position:0% +gives me a nether chroniker matrix of +partial derivatives and then finally + + align:start position:0% +partial derivatives and then finally + + + align:start position:0% +partial derivatives and then finally +don't forget we are working in this + + align:start position:0% +don't forget we are working in this + + + align:start position:0% +don't forget we are working in this +nearly flat space-time metric and so I + + align:start position:0% +nearly flat space-time metric and so I + + + align:start position:0% +nearly flat space-time metric and so I +insert in my last term 8 alpha beta plus + + align:start position:0% +insert in my last term 8 alpha beta plus + + + align:start position:0% +insert in my last term 8 alpha beta plus +h alpha bitter so now let's go and + + align:start position:0% +h alpha bitter so now let's go and + + + align:start position:0% +h alpha bitter so now let's go and +expand all of these terms out my + + align:start position:0% +expand all of these terms out my + + + align:start position:0% +expand all of these terms out my +chroniker first I get a term where both + + align:start position:0% +chroniker first I get a term where both + + + align:start position:0% +chroniker first I get a term where both +of the chronic errs hit the metric of + + align:start position:0% +of the chronic errs hit the metric of + + + align:start position:0% +of the chronic errs hit the metric of +flat space-time and so what I get is 8 + + align:start position:0% +flat space-time and so what I get is 8 + + + align:start position:0% +flat space-time and so what I get is 8 +mu nu then I get a term which both the + + align:start position:0% +mu nu then I get a term which both the + + + align:start position:0% +mu nu then I get a term which both the +chronic errs hit the perturbation H + + align:start position:0% +chronic errs hit the perturbation H + + + align:start position:0% +chronic errs hit the perturbation H +alpha beta excuse me hm you know then + + align:start position:0% +alpha beta excuse me hm you know then + + + align:start position:0% +alpha beta excuse me hm you know then +I'm going to get terms that involve + + align:start position:0% +I'm going to get terms that involve + + + align:start position:0% +I'm going to get terms that involve +these matrices of partial derivatives + + align:start position:0% +these matrices of partial derivatives + + + align:start position:0% +these matrices of partial derivatives +hitting the metric of flat space-time + + align:start position:0% +hitting the metric of flat space-time + + + align:start position:0% +hitting the metric of flat space-time +and what that's going to do is in + + align:start position:0% +and what that's going to do is in + + + align:start position:0% +and what that's going to do is in +keeping with our principle that we + + align:start position:0% +keeping with our principle that we + + + align:start position:0% +keeping with our principle that we +when we're dealing with space-time + + align:start position:0% +when we're dealing with space-time + + + align:start position:0% +when we're dealing with space-time +quantities we raise and lower indices + + align:start position:0% +quantities we raise and lower indices + + + align:start position:0% +quantities we raise and lower indices +with Ada this is going to now give me + + align:start position:0% +with Ada this is going to now give me + + + align:start position:0% +with Ada this is going to now give me +pardon me just one moment term that + + align:start position:0% +pardon me just one moment term that + + + align:start position:0% +pardon me just one moment term that +looks like partial everything in the + + align:start position:0% +looks like partial everything in the + + + align:start position:0% +looks like partial everything in the +downstairs position D mu C nu minus D nu + + align:start position:0% +downstairs position D mu C nu minus D nu + + + align:start position:0% +downstairs position D mu C nu minus D nu +C mu and then all the other terms are on + + align:start position:0% +C mu and then all the other terms are on + + + align:start position:0% +C mu and then all the other terms are on +the order of H times derivatives of the + + align:start position:0% +the order of H times derivatives of the + + + align:start position:0% +the order of H times derivatives of the +generators of my quarter transformation + + align:start position:0% +generators of my quarter transformation + + + align:start position:0% +generators of my quarter transformation +small times small these are + + align:start position:0% +small times small these are + + + align:start position:0% +small times small these are +infinitesimal squared we are going to + + align:start position:0% +infinitesimal squared we are going to + + + align:start position:0% +infinitesimal squared we are going to +neglect them suppose that I insist that + + align:start position:0% +neglect them suppose that I insist that + + + align:start position:0% +neglect them suppose that I insist that +I have gone from one nearly flat + + align:start position:0% +I have gone from one nearly flat + + + align:start position:0% +I have gone from one nearly flat +space-time to another okay all I'm doing + + align:start position:0% +space-time to another okay all I'm doing + + + align:start position:0% +space-time to another okay all I'm doing +bear in mind this picture I'm just + + align:start position:0% +bear in mind this picture I'm just + + + align:start position:0% +bear in mind this picture I'm just +changing my representational that I've + + align:start position:0% +changing my representational that I've + + + align:start position:0% +changing my representational that I've +not changed the physics so if I write + + align:start position:0% +not changed the physics so if I write + + + align:start position:0% +not changed the physics so if I write +this as ADA mu prime nu prime plus H nu + + align:start position:0% +this as ADA mu prime nu prime plus H nu + + + align:start position:0% +this as ADA mu prime nu prime plus H nu +prime nu prime well I've got a toes on + + align:start position:0% +prime nu prime well I've got a toes on + + + align:start position:0% +prime nu prime well I've got a toes on +both sides this thing which is + + align:start position:0% +both sides this thing which is + + + align:start position:0% +both sides this thing which is +interesting is that I have generated a + + align:start position:0% +interesting is that I have generated a + + + align:start position:0% +interesting is that I have generated a +shift to my perturbation to the metric + + align:start position:0% + + + + align:start position:0% + +let's drop the primes for a second and + + align:start position:0% +let's drop the primes for a second and + + + align:start position:0% +let's drop the primes for a second and +I'll just say that my nu H mu nu is the + + align:start position:0% +I'll just say that my nu H mu nu is the + + + align:start position:0% +I'll just say that my nu H mu nu is the +old H mu nu minus this symmetrized + + align:start position:0% +old H mu nu minus this symmetrized + + + align:start position:0% +old H mu nu minus this symmetrized +combination of derivatives of the + + align:start position:0% +combination of derivatives of the + + + align:start position:0% +combination of derivatives of the +symmetrized combination of derivatives + + align:start position:0% +symmetrized combination of derivatives + + + align:start position:0% +symmetrized combination of derivatives +of the infinitesimal core transformation + + align:start position:0% + + + + align:start position:0% + +does this remind us of anything + + align:start position:0% +does this remind us of anything + + + align:start position:0% +does this remind us of anything +this is starkly reminiscent of the way + + align:start position:0% +this is starkly reminiscent of the way + + + align:start position:0% +this is starkly reminiscent of the way +in which when we work with + + align:start position:0% +in which when we work with + + + align:start position:0% +in which when we work with +electromagnetic fields I can take a + + align:start position:0% +electromagnetic fields I can take a + + + align:start position:0% +electromagnetic fields I can take a +potential and shift it by the gradient + + align:start position:0% +potential and shift it by the gradient + + + align:start position:0% +potential and shift it by the gradient +of some scalar to generate a new + + align:start position:0% +of some scalar to generate a new + + + align:start position:0% +of some scalar to generate a new +potential in so doing what we find is + + align:start position:0% +potential in so doing what we find is + + + align:start position:0% +potential in so doing what we find is +that this leaves the fields unchanged if + + align:start position:0% +that this leaves the fields unchanged if + + + align:start position:0% +that this leaves the fields unchanged if +you compute your Faraday tensor + + align:start position:0% +you compute your Faraday tensor + + + align:start position:0% +you compute your Faraday tensor +associated with this it is unchanged + + align:start position:0% + + + + align:start position:0% + +similarly we're gonna write out the + + align:start position:0% +similarly we're gonna write out the + + + align:start position:0% +similarly we're gonna write out the +details of this in just a moment when I + + align:start position:0% +details of this in just a moment when I + + + align:start position:0% +details of this in just a moment when I +generate the Riemann curvature from this + + align:start position:0% + + + + align:start position:0% + +we find that although the metric has + + align:start position:0% +we find that although the metric has + + + align:start position:0% +we find that although the metric has +been tweaked a little bit by this court + + align:start position:0% +been tweaked a little bit by this court + + + align:start position:0% +been tweaked a little bit by this court +in transformation riemann is left + + align:start position:0% +in transformation riemann is left + + + align:start position:0% +in transformation riemann is left +unchanged in acknowledgment of this we + + align:start position:0% +unchanged in acknowledgment of this we + + + align:start position:0% +unchanged in acknowledgment of this we +call an infinitesimal current + + align:start position:0% +call an infinitesimal current + + + align:start position:0% +call an infinitesimal current +transformation of this kind a gauge + + align:start position:0% +transformation of this kind a gauge + + + align:start position:0% +transformation of this kind a gauge +transformation okay what the gauge + + align:start position:0% +transformation okay what the gauge + + + align:start position:0% +transformation okay what the gauge +transformation does is it allows us to + + align:start position:0% +transformation does is it allows us to + + + align:start position:0% +transformation does is it allows us to +change the metric or the changed way + + align:start position:0% +change the metric or the changed way + + + align:start position:0% +change the metric or the changed way +that we are representing our metric and + + align:start position:0% +that we are representing our metric and + + + align:start position:0% +that we are representing our metric and +it's going to turn out to leave + + align:start position:0% +it's going to turn out to leave + + + align:start position:0% +it's going to turn out to leave +curvature tensors unchanged in the same + + align:start position:0% +curvature tensors unchanged in the same + + + align:start position:0% +curvature tensors unchanged in the same +way that changing the potential and let + + align:start position:0% +way that changing the potential and let + + + align:start position:0% +way that changing the potential and let +your dynamics with a gauge + + align:start position:0% +your dynamics with a gauge + + + align:start position:0% +your dynamics with a gauge +transformation leaves our fields + + align:start position:0% +transformation leaves our fields + + + align:start position:0% +transformation leaves our fields +unchanged and we're gonna exploit this + + align:start position:0% +unchanged and we're gonna exploit this + + + align:start position:0% +unchanged and we're gonna exploit this +in exactly the same way that we + + align:start position:0% +in exactly the same way that we + + + align:start position:0% +in exactly the same way that we +exploited this in electrodynamics we use + + align:start position:0% +exploited this in electrodynamics we use + + + align:start position:0% +exploited this in electrodynamics we use +this in electrodynamics in order to + + align:start position:0% +this in electrodynamics in order to + + + align:start position:0% +this in electrodynamics in order to +recast the equations governing our + + align:start position:0% +recast the equations governing our + + + align:start position:0% +recast the equations governing our +potentials into a form that is maximally + + align:start position:0% +potentials into a form that is maximally + + + align:start position:0% +potentials into a form that is maximally +convenient for whatever calculation + + align:start position:0% +convenient for whatever calculation + + + align:start position:0% +convenient for whatever calculation +we're doing right now we're gonna find + + align:start position:0% +we're doing right now we're gonna find + + + align:start position:0% +we're doing right now we're gonna find +and then we're gonna drive this probably + + align:start position:0% +and then we're gonna drive this probably + + + align:start position:0% +and then we're gonna drive this probably +in about 20 minutes that the equations + + align:start position:0% +in about 20 minutes that the equations + + + align:start position:0% +in about 20 minutes that the equations +that govern H mu nu if we'd certainly + + align:start position:0% +that govern H mu nu if we'd certainly + + + align:start position:0% +that govern H mu nu if we'd certainly +things as general as possible they're a + + align:start position:0% +things as general as possible they're a + + + align:start position:0% +things as general as possible they're a +bit of a mess but by choosing the right + + align:start position:0% +bit of a mess but by choosing the right + + + align:start position:0% +bit of a mess but by choosing the right +gauge we can simplify them and wind up + + align:start position:0% +gauge we can simplify them and wind up + + + align:start position:0% +gauge we can simplify them and wind up +with a set of equations that are that + + align:start position:0% +with a set of equations that are that + + + align:start position:0% +with a set of equations that are that +they cover all physical situations that + + align:start position:0% +they cover all physical situations that + + + align:start position:0% +they cover all physical situations that +matter and that allow us to just pass + + align:start position:0% +matter and that allow us to just pass + + + align:start position:0% +matter and that allow us to just pass +things into a form that as much + + align:start position:0% +things into a form that as much + + + align:start position:0% +things into a form that as much +better for us to work with alright so we + + align:start position:0% +better for us to work with alright so we + + + align:start position:0% +better for us to work with alright so we +have now developed all of the sort of + + align:start position:0% +have now developed all of the sort of + + + align:start position:0% +have now developed all of the sort of +linguistics of linearized linearize + + align:start position:0% +linguistics of linearized linearize + + + align:start position:0% +linguistics of linearized linearize +geometry that i want to use let's now go + + align:start position:0% +geometry that i want to use let's now go + + + align:start position:0% +geometry that i want to use let's now go +from linearize geometry to linearize + + align:start position:0% +from linearize geometry to linearize + + + align:start position:0% +from linearize geometry to linearize +gravity by running this through and + + align:start position:0% +gravity by running this through and + + + align:start position:0% +gravity by running this through and +making some physics what I want to do is + + align:start position:0% +making some physics what I want to do is + + + align:start position:0% +making some physics what I want to do is +look at the field equations in this + + align:start position:0% +look at the field equations in this + + + align:start position:0% +look at the field equations in this +framework so I am NOT going to run + + align:start position:0% +framework so I am NOT going to run + + + align:start position:0% +framework so I am NOT going to run +through every step of the next couple + + align:start position:0% +through every step of the next couple + + + align:start position:0% +through every step of the next couple +calculations this is a doing so is a + + align:start position:0% +calculations this is a doing so is a + + + align:start position:0% +calculations this is a doing so is a +good illustration of the kind of + + align:start position:0% +good illustration of the kind of + + + align:start position:0% +good illustration of the kind of +calculation that a physicist likes to + + align:start position:0% +calculation that a physicist likes to + + + align:start position:0% +calculation that a physicist likes to +call straightforward but tedious so I'm + + align:start position:0% +call straightforward but tedious so I'm + + + align:start position:0% +call straightforward but tedious so I'm +gonna just write down with the results + + align:start position:0% +gonna just write down with the results + + + align:start position:0% +gonna just write down with the results +turn out today so let's run the metric + + align:start position:0% +turn out today so let's run the metric + + + align:start position:0% +turn out today so let's run the metric +through the machinery that we need to + + align:start position:0% +through the machinery that we need to + + + align:start position:0% +through the machinery that we need to +make all of our curvature tensors ok + + align:start position:0% +make all of our curvature tensors ok + + + align:start position:0% +make all of our curvature tensors ok +I'll remind you when we do this we are + + align:start position:0% +I'll remind you when we do this we are + + + align:start position:0% +I'll remind you when we do this we are +linearizing so anytime we see a term + + align:start position:0% +linearizing so anytime we see a term + + + align:start position:0% +linearizing so anytime we see a term +that looks like h squared it dies so + + align:start position:0% +that looks like h squared it dies so + + + align:start position:0% +that looks like h squared it dies so +we're only keeping things to linear + + align:start position:0% +we're only keeping things to linear + + + align:start position:0% +we're only keeping things to linear +order in h so the first thing we find is + + align:start position:0% + + + + align:start position:0% + +the Riemann tensor turns into the + + align:start position:0% +the Riemann tensor turns into the + + + align:start position:0% +the Riemann tensor turns into the +following combination of partial + + align:start position:0% +following combination of partial + + + align:start position:0% +following combination of partial +derivatives of the metric perturbation H + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +in my notes I have written out what + + align:start position:0% +in my notes I have written out what + + + align:start position:0% +in my notes I have written out what +happens when you switch from some + + align:start position:0% +happens when you switch from some + + + align:start position:0% +happens when you switch from some +original tensor H to a modified one + + align:start position:0% +original tensor H to a modified one + + + align:start position:0% +original tensor H to a modified one +using this gauge transformation and what + + align:start position:0% +using this gauge transformation and what + + + align:start position:0% +using this gauge transformation and what +I show is that just a quick aside the + + align:start position:0% +I show is that just a quick aside the + + + align:start position:0% +I show is that just a quick aside the +gauge transformation generates a delta + + align:start position:0% +gauge transformation generates a delta + + + align:start position:0% +gauge transformation generates a delta +riemann that looks like it's a whole + + align:start position:0% +riemann that looks like it's a whole + + + align:start position:0% +riemann that looks like it's a whole +bunch of with you let's count them up + + align:start position:0% +bunch of with you let's count them up + + + align:start position:0% +bunch of with you let's count them up +one two three four five six seven eight + + align:start position:0% +one two three four five six seven eight + + + align:start position:0% +one two three four five six seven eight +you have eight terms of course there's + + align:start position:0% +you have eight terms of course there's + + + align:start position:0% +you have eight terms of course there's +eight because there's four terms here + + align:start position:0% +eight because there's four terms here + + + align:start position:0% +eight because there's four terms here +and you get two more for each one so + + align:start position:0% +and you get two more for each one so + + + align:start position:0% +and you get two more for each one so +you're gonna wind up with eight + + align:start position:0% +you're gonna wind up with eight + + + align:start position:0% +you're gonna wind up with eight +additional terms that involve three + + align:start position:0% +additional terms that involve three + + + align:start position:0% +additional terms that involve three +partial derivatives of the gauge + + align:start position:0% +partial derivatives of the gauge + + + align:start position:0% +partial derivatives of the gauge +generator so there are the form D cubed + + align:start position:0% +generator so there are the form D cubed + + + align:start position:0% +generator so there are the form D cubed +on C and it's not hard to show you just + + align:start position:0% +on C and it's not hard to show you just + + + align:start position:0% +on C and it's not hard to show you just +sort of look at them they cancel in + + align:start position:0% +sort of look at them they cancel in + + + align:start position:0% +sort of look at them they cancel in +pairs and so delta riemann is 0 the + + align:start position:0% +pairs and so delta riemann is 0 the + + + align:start position:0% +pairs and so delta riemann is 0 the +Riemann tensor is invariant to the gauge + + align:start position:0% +Riemann tensor is invariant to the gauge + + + align:start position:0% +Riemann tensor is invariant to the gauge +transformation + + align:start position:0% + + + + align:start position:0% + +all right we want to take this ream on + + align:start position:0% +all right we want to take this ream on + + + align:start position:0% +all right we want to take this ream on +and use it to build the Einstein tensor + + align:start position:0% +and use it to build the Einstein tensor + + + align:start position:0% +and use it to build the Einstein tensor +our goal here is to make the field + + align:start position:0% +our goal here is to make the field + + + align:start position:0% +our goal here is to make the field +equation in linearized coordinates + + align:start position:0% + + + + align:start position:0% + +so let's start by making the Ricci + + align:start position:0% +so let's start by making the Ricci + + + align:start position:0% +so let's start by making the Ricci +tensor so we're gonna raise and lower + + align:start position:0% +tensor so we're gonna raise and lower + + + align:start position:0% +tensor so we're gonna raise and lower +indices in linear ice theory with the + + align:start position:0% +indices in linear ice theory with the + + + align:start position:0% +indices in linear ice theory with the +flat space-time so when we make this guy + + align:start position:0% +flat space-time so when we make this guy + + + align:start position:0% +flat space-time so when we make this guy +what we get is this okay + + align:start position:0% + + + + align:start position:0% + +I've introduced a couple of definitions + + align:start position:0% +I've introduced a couple of definitions + + + align:start position:0% +I've introduced a couple of definitions +here one of them you've seen before the + + align:start position:0% +here one of them you've seen before the + + + align:start position:0% +here one of them you've seen before the +box operator is just a flat space-time + + align:start position:0% +box operator is just a flat space-time + + + align:start position:0% +box operator is just a flat space-time +wave operator and H with no indices is + + align:start position:0% +wave operator and H with no indices is + + + align:start position:0% +wave operator and H with no indices is +what I get when I trace over H using + + align:start position:0% + + + + align:start position:0% + +using the flat background space-time + + align:start position:0% + + + + align:start position:0% + +okay let's do one more + + align:start position:0% + + + + align:start position:0% + +evaluating our I get one further + + align:start position:0% +evaluating our I get one further + + + align:start position:0% +evaluating our I get one further +contraction and this turns out to be D + + align:start position:0% +contraction and this turns out to be D + + + align:start position:0% +contraction and this turns out to be D +alpha D mu H alpha Mew - box of H so we + + align:start position:0% +alpha D mu H alpha Mew - box of H so we + + + align:start position:0% +alpha D mu H alpha Mew - box of H so we +now have all the pieces we need to make + + align:start position:0% +now have all the pieces we need to make + + + align:start position:0% +now have all the pieces we need to make +the Einstein tensor so I'm gonna write + + align:start position:0% +the Einstein tensor so I'm gonna write + + + align:start position:0% +the Einstein tensor so I'm gonna write +out the result and we're gonna stop and + + align:start position:0% +out the result and we're gonna stop and + + + align:start position:0% +out the result and we're gonna stop and +just look at it for a second + + align:start position:0% + + + + align:start position:0% + +Einstein is reaching minus 1/2 metric + + align:start position:0% +Einstein is reaching minus 1/2 metric + + + align:start position:0% +Einstein is reaching minus 1/2 metric +Ricci scalar keeping things to leading + + align:start position:0% +Ricci scalar keeping things to leading + + + align:start position:0% +Ricci scalar keeping things to leading +order in H this becomes flat space-time + + align:start position:0% +order in H this becomes flat space-time + + + align:start position:0% +order in H this becomes flat space-time +metric going into there so when you put + + align:start position:0% +metric going into there so when you put + + + align:start position:0% +metric going into there so when you put +all these ingredients together there's + + align:start position:0% +all these ingredients together there's + + + align:start position:0% +all these ingredients together there's +an overall prefactor of 1/2 and then + + align:start position:0% +an overall prefactor of 1/2 and then + + + align:start position:0% +an overall prefactor of 1/2 and then +there are two three four five six terms + + align:start position:0% +there are two three four five six terms + + + align:start position:0% +there are two three four five six terms +let me write them out okay so recall at + + align:start position:0% +let me write them out okay so recall at + + + align:start position:0% +let me write them out okay so recall at +the beginning of the lecture I pointed + + align:start position:0% +the beginning of the lecture I pointed + + + align:start position:0% +the beginning of the lecture I pointed +out that when one regards G alpha beta + + align:start position:0% +out that when one regards G alpha beta + + + align:start position:0% +out that when one regards G alpha beta +as just a differential operator on the + + align:start position:0% +as just a differential operator on the + + + align:start position:0% +as just a differential operator on the +space-time metric it's kind of a mess + + align:start position:0% +space-time metric it's kind of a mess + + + align:start position:0% +space-time metric it's kind of a mess +bearing in mind that what I have here is + + align:start position:0% +bearing in mind that what I have here is + + + align:start position:0% +bearing in mind that what I have here is +a simplified version of that I have + + align:start position:0% +a simplified version of that I have + + + align:start position:0% +a simplified version of that I have +discarded all of the terms that are + + align:start position:0% +discarded all of the terms that are + + + align:start position:0% +discarded all of the terms that are +higher-order in H then linear this is + + align:start position:0% +higher-order in H then linear this is + + + align:start position:0% +higher-order in H then linear this is +already pretty much a bloody mess as it + + align:start position:0% +already pretty much a bloody mess as it + + + align:start position:0% +already pretty much a bloody mess as it +is so you can sort of see my point there + + align:start position:0% +is so you can sort of see my point there + + + align:start position:0% +is so you can sort of see my point there +okay if this we're done its full + + align:start position:0% +okay if this we're done its full + + + align:start position:0% +okay if this we're done its full +generality it would be kind of a + + align:start position:0% +generality it would be kind of a + + + align:start position:0% +generality it would be kind of a +disaster now in linearized theory there + + align:start position:0% +disaster now in linearized theory there + + + align:start position:0% +disaster now in linearized theory there +is a bit of sleight of hand that lets us + + align:start position:0% +is a bit of sleight of hand that lets us + + + align:start position:0% +is a bit of sleight of hand that lets us +clean this up a little bit let me + + align:start position:0% +clean this up a little bit let me + + + align:start position:0% +clean this up a little bit let me +emphasize it the next few lines of + + align:start position:0% +emphasize it the next few lines of + + + align:start position:0% +emphasize it the next few lines of +calculation I'm going to write down + + align:start position:0% +calculation I'm going to write down + + + align:start position:0% +calculation I'm going to write down +there's nothing profound all I'm going + + align:start position:0% +there's nothing profound all I'm going + + + align:start position:0% +there's nothing profound all I'm going +to do is show a way of reorganizing the + + align:start position:0% +to do is show a way of reorganizing the + + + align:start position:0% +to do is show a way of reorganizing the +terms which simplifies this in an + + align:start position:0% +terms which simplifies this in an + + + align:start position:0% +terms which simplifies this in an +important way + + align:start position:0% + + + + align:start position:0% + +so what we're going to do is define the + + align:start position:0% +so what we're going to do is define the + + + align:start position:0% +so what we're going to do is define the +following tensor H bar is H minus 1/2 a + + align:start position:0% +following tensor H bar is H minus 1/2 a + + + align:start position:0% +following tensor H bar is H minus 1/2 a +2 alpha beta H so it's a good point to + + align:start position:0% +2 alpha beta H so it's a good point to + + + align:start position:0% +2 alpha beta H so it's a good point to +kind of go well who ordered that let's + + align:start position:0% +kind of go well who ordered that let's + + + align:start position:0% +kind of go well who ordered that let's +take the trace of this let's define H + + align:start position:0% +take the trace of this let's define H + + + align:start position:0% +take the trace of this let's define H +bar with no indices as what I get when I + + align:start position:0% +bar with no indices as what I get when I + + + align:start position:0% +bar with no indices as what I get when I +trace on this that's going to be the + + align:start position:0% +trace on this that's going to be the + + + align:start position:0% +trace on this that's going to be the +trace of H it's gonna be the trace of H + + align:start position:0% +trace of H it's gonna be the trace of H + + + align:start position:0% +trace of H it's gonna be the trace of H +alpha beta so I just get H back minus + + align:start position:0% +alpha beta so I just get H back minus + + + align:start position:0% +alpha beta so I just get H back minus +1/2 H times the trace of a 2 alpha beta + + align:start position:0% +1/2 H times the trace of a 2 alpha beta + + + align:start position:0% +1/2 H times the trace of a 2 alpha beta +and the trace of 8 alpha beta this is + + align:start position:0% +and the trace of 8 alpha beta this is + + + align:start position:0% +and the trace of 8 alpha beta this is +what I get when I raise when that one + + align:start position:0% +what I get when I raise when that one + + + align:start position:0% +what I get when I raise when that one +index and sum over the diagonal that is + + align:start position:0% +index and sum over the diagonal that is + + + align:start position:0% +index and sum over the diagonal that is +4 so the trace of H bar is negative the + + align:start position:0% +4 so the trace of H bar is negative the + + + align:start position:0% +4 so the trace of H bar is negative the +trace of H we call H bar alpha beta the + + align:start position:0% +trace of H we call H bar alpha beta the + + + align:start position:0% +trace of H we call H bar alpha beta the +trace reversed metric perturbation it's + + align:start position:0% +trace reversed metric perturbation it's + + + align:start position:0% +trace reversed metric perturbation it's +a gut exactly the same information as my + + align:start position:0% +a gut exactly the same information as my + + + align:start position:0% +a gut exactly the same information as my +original metric perturbation but I just + + align:start position:0% +original metric perturbation but I just + + + align:start position:0% +original metric perturbation but I just +redefined a couple terms in order to + + align:start position:0% +redefined a couple terms in order to + + + align:start position:0% +redefined a couple terms in order to +give it a trace that has the opposite + + align:start position:0% +give it a trace that has the opposite + + + align:start position:0% +give it a trace that has the opposite +sign of the original trace of the + + align:start position:0% +sign of the original trace of the + + + align:start position:0% +sign of the original trace of the +original perturbation H the reason why + + align:start position:0% +original perturbation H the reason why + + + align:start position:0% +original perturbation H the reason why +this is useful is recall the Einstein + + align:start position:0% +this is useful is recall the Einstein + + + align:start position:0% +this is useful is recall the Einstein +tensor is itself the trace reversed + + align:start position:0% +tensor is itself the trace reversed + + + align:start position:0% +tensor is itself the trace reversed +Ricci tensor what we're going to see is + + align:start position:0% +Ricci tensor what we're going to see is + + + align:start position:0% +Ricci tensor what we're going to see is +that if we know in acknowledgment that + + align:start position:0% +that if we know in acknowledgment that + + + align:start position:0% +that if we know in acknowledgment that +it's sort of a trace reverse thing if I + + align:start position:0% +it's sort of a trace reverse thing if I + + + align:start position:0% +it's sort of a trace reverse thing if I +plug in a trace reverse metric + + align:start position:0% +plug in a trace reverse metric + + + align:start position:0% +plug in a trace reverse metric +perturbation a couple of terms are gonna + + align:start position:0% +perturbation a couple of terms are gonna + + + align:start position:0% +perturbation a couple of terms are gonna +get cleaned up so here's how we do this + + align:start position:0% +get cleaned up so here's how we do this + + + align:start position:0% +get cleaned up so here's how we do this +so let's now insert H bar this guy is + + align:start position:0% +so let's now insert H bar this guy is + + + align:start position:0% +so let's now insert H bar this guy is +going to be equal to + + align:start position:0% +going to be equal to + + + align:start position:0% +going to be equal to +oops pardon me insert H this guy is H + + align:start position:0% +oops pardon me insert H this guy is H + + + align:start position:0% +oops pardon me insert H this guy is H +bar plus + + align:start position:0% +bar plus + + + align:start position:0% +bar plus +one half eight alpha beta H okay so just + + align:start position:0% +one half eight alpha beta H okay so just + + + align:start position:0% +one half eight alpha beta H okay so just +move that to the other side all I'm + + align:start position:0% +move that to the other side all I'm + + + align:start position:0% +move that to the other side all I'm +doing is taking the definition and I am + + align:start position:0% +doing is taking the definition and I am + + + align:start position:0% +doing is taking the definition and I am +moving part of it to the other side so + + align:start position:0% +moving part of it to the other side so + + + align:start position:0% +moving part of it to the other side so +that can substitute in for H when you + + align:start position:0% +that can substitute in for H when you + + + align:start position:0% +that can substitute in for H when you +plug this into here + + align:start position:0% +plug this into here + + + align:start position:0% +plug this into here +you'll see that there are certain + + align:start position:0% +you'll see that there are certain + + + align:start position:0% +you'll see that there are certain +cancellations in particular every term + + align:start position:0% +cancellations in particular every term + + + align:start position:0% +cancellations in particular every term +that involves the trace of H H without + + align:start position:0% +that involves the trace of H H without + + + align:start position:0% +that involves the trace of H H without +any indices is cancelled out and so what + + align:start position:0% +any indices is cancelled out and so what + + + align:start position:0% +any indices is cancelled out and so what +you find doing this algebra is that + + align:start position:0% +you find doing this algebra is that + + + align:start position:0% +you find doing this algebra is that +you're Einstein tensor turns into + + align:start position:0% + + + + align:start position:0% + +that can't be right okay so now my + + align:start position:0% +that can't be right okay so now my + + + align:start position:0% +that can't be right okay so now my +Einstein tensor has no traces of H in it + + align:start position:0% +Einstein tensor has no traces of H in it + + + align:start position:0% +Einstein tensor has no traces of H in it +every H that appears on its right hand + + align:start position:0% +every H that appears on its right hand + + + align:start position:0% +every H that appears on its right hand +side is the tensor with both of the + + align:start position:0% +side is the tensor with both of the + + + align:start position:0% +side is the tensor with both of the +indices but now it's the trace reversed + + align:start position:0% +indices but now it's the trace reversed + + + align:start position:0% +indices but now it's the trace reversed +version of that this is still a bit of a + + align:start position:0% +version of that this is still a bit of a + + + align:start position:0% +version of that this is still a bit of a +mess now we're gonna do something that's + + align:start position:0% +mess now we're gonna do something that's + + + align:start position:0% +mess now we're gonna do something that's +got a little bit more it's not just + + align:start position:0% +got a little bit more it's not just + + + align:start position:0% +got a little bit more it's not just +sleight of hand this is something it's + + align:start position:0% +sleight of hand this is something it's + + + align:start position:0% +sleight of hand this is something it's +got a little bit more of sort of the + + align:start position:0% +got a little bit more of sort of the + + + align:start position:0% +got a little bit more of sort of the +meaning of some of these manipulations + + align:start position:0% +meaning of some of these manipulations + + + align:start position:0% +meaning of some of these manipulations +that we've worked out is gonna play a + + align:start position:0% +that we've worked out is gonna play a + + + align:start position:0% +that we've worked out is gonna play a +role in helping us to understand this + + align:start position:0% +role in helping us to understand this + + + align:start position:0% +role in helping us to understand this +notice this term involves Delta mu on + + align:start position:0% +notice this term involves Delta mu on + + + align:start position:0% +notice this term involves Delta mu on +hmm excuse me partial mu on hmm partial + + align:start position:0% +hmm excuse me partial mu on hmm partial + + + align:start position:0% +hmm excuse me partial mu on hmm partial +mu on H mu partial mu and partial new on + + align:start position:0% +mu on H mu partial mu and partial new on + + + align:start position:0% +mu on H mu partial mu and partial new on +HBO this is the only term that does not + + align:start position:0% +HBO this is the only term that does not + + + align:start position:0% +HBO this is the only term that does not +look like a divergence three of the + + align:start position:0% +look like a divergence three of the + + + align:start position:0% +look like a divergence three of the +terms of my Einstein tensor look like + + align:start position:0% +terms of my Einstein tensor look like + + + align:start position:0% +terms of my Einstein tensor look like +divergences of the Tracy vers metric + + align:start position:0% +divergences of the Tracy vers metric + + + align:start position:0% +divergences of the Tracy vers metric +[Applause] + + align:start position:0% + + + + align:start position:0% + +wouldn't it be nice if we could + + align:start position:0% +wouldn't it be nice if we could + + + align:start position:0% +wouldn't it be nice if we could +eliminate them somehow well if you + + align:start position:0% +eliminate them somehow well if you + + + align:start position:0% +eliminate them somehow well if you +studied gauge transformations in + + align:start position:0% +studied gauge transformations in + + + align:start position:0% +studied gauge transformations in +electrodynamics you'll note that there's + + align:start position:0% +electrodynamics you'll note that there's + + + align:start position:0% +electrodynamics you'll note that there's +something similar that is done you can + + align:start position:0% +something similar that is done you can + + + align:start position:0% +something similar that is done you can +choose a gauge such the divergence of + + align:start position:0% +choose a gauge such the divergence of + + + align:start position:0% +choose a gauge such the divergence of +the vector for potential vanishes can we + + align:start position:0% +the vector for potential vanishes can we + + + align:start position:0% +the vector for potential vanishes can we +set the inversions of this guy equal to + + align:start position:0% +set the inversions of this guy equal to + + + align:start position:0% +set the inversions of this guy equal to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +so if you look at this Musa Dagh me + + align:start position:0% +so if you look at this Musa Dagh me + + + align:start position:0% +so if you look at this Musa Dagh me +Index this is for conditions that we are + + align:start position:0% +Index this is for conditions that we are + + + align:start position:0% +Index this is for conditions that we are +trying to set okay this has to happen + + align:start position:0% +trying to set okay this has to happen + + + align:start position:0% +trying to set okay this has to happen +for MU well we're going to sum over mu + + align:start position:0% +for MU well we're going to sum over mu + + + align:start position:0% +for MU well we're going to sum over mu +pardon me it's gonna happen for nu equal + + align:start position:0% +pardon me it's gonna happen for nu equal + + + align:start position:0% +pardon me it's gonna happen for nu equal +time and for my three spaces my these + + align:start position:0% +time and for my three spaces my these + + + align:start position:0% +time and for my three spaces my these +are four conditions my gauge generators + + align:start position:0% + + + + align:start position:0% + +Mike C nu are for free functions that + + align:start position:0% +Mike C nu are for free functions that + + + align:start position:0% +Mike C nu are for free functions that +suggests that the gauge generators give + + align:start position:0% +suggests that the gauge generators give + + + align:start position:0% +suggests that the gauge generators give +me enough freedom that I can adjust my + + align:start position:0% +me enough freedom that I can adjust my + + + align:start position:0% +me enough freedom that I can adjust my +gauge such that if I start out with some + + align:start position:0% +gauge such that if I start out with some + + + align:start position:0% +gauge such that if I start out with some +original I have an H old that is not + + align:start position:0% +original I have an H old that is not + + + align:start position:0% +original I have an H old that is not +divergence free perhaps I can make an H + + align:start position:0% +divergence free perhaps I can make an H + + + align:start position:0% +divergence free perhaps I can make an H +nu that is let's try it + + align:start position:0% +nu that is let's try it + + + align:start position:0% +nu that is let's try it +[Applause] + + align:start position:0% + + + + align:start position:0% + +so remember I just erased it but in fact + + align:start position:0% +so remember I just erased it but in fact + + + align:start position:0% +so remember I just erased it but in fact +I'll just write it down right now + + align:start position:0% +I'll just write it down right now + + + align:start position:0% +I'll just write it down right now +the shift to the metric perturbation + + align:start position:0% +the shift to the metric perturbation + + + align:start position:0% +the shift to the metric perturbation +arising from the gauge transformation + + align:start position:0% +arising from the gauge transformation + + + align:start position:0% +arising from the gauge transformation +it's on H we need to look at how it + + align:start position:0% +it's on H we need to look at how it + + + align:start position:0% +it's on H we need to look at how it +affects the trace reverse stage so if I + + align:start position:0% +affects the trace reverse stage so if I + + + align:start position:0% +affects the trace reverse stage so if I +start with my new perturbation is + + align:start position:0% +start with my new perturbation is + + + align:start position:0% +start with my new perturbation is +related to my old perturbation as + + align:start position:0% +related to my old perturbation as + + + align:start position:0% +related to my old perturbation as +follows it's not too hard to show that + + align:start position:0% +follows it's not too hard to show that + + + align:start position:0% +follows it's not too hard to show that +your trace reversed metric perturbation + + align:start position:0% + + + + align:start position:0% + +pardon pardon pardon my trace reverse + + align:start position:0% +pardon pardon pardon my trace reverse + + + align:start position:0% +pardon pardon pardon my trace reverse +perturbation transforms in almost the + + align:start position:0% +perturbation transforms in almost the + + + align:start position:0% +perturbation transforms in almost the +exact same way I get one extra term okay + + align:start position:0% +exact same way I get one extra term okay + + + align:start position:0% +exact same way I get one extra term okay +so now what I want to do is look at how + + align:start position:0% +so now what I want to do is look at how + + + align:start position:0% +so now what I want to do is look at how +the divergence of this transforms + + align:start position:0% + + + + align:start position:0% + +so I'm gonna get one term here D mu of + + align:start position:0% +so I'm gonna get one term here D mu of + + + align:start position:0% +so I'm gonna get one term here D mu of +this it gives me a wave operator acting + + align:start position:0% +this it gives me a wave operator acting + + + align:start position:0% +this it gives me a wave operator acting +on my gage generator and then I get + + align:start position:0% +on my gage generator and then I get + + + align:start position:0% +on my gage generator and then I get +another term here that looks like + + align:start position:0% +another term here that looks like + + + align:start position:0% +another term here that looks like +remember partial derivatives commute so + + align:start position:0% +remember partial derivatives commute so + + + align:start position:0% +remember partial derivatives commute so +you can think of this as D nu of the + + align:start position:0% +you can think of this as D nu of the + + + align:start position:0% +you can think of this as D nu of the +divergence of c8 mu nu acting on this + + align:start position:0% + + + + align:start position:0% + +changes this into D nu on the virgin's + + align:start position:0% +changes this into D nu on the virgin's + + + align:start position:0% +changes this into D nu on the virgin's +of C and I've messed up the sign my + + align:start position:0% +of C and I've messed up the sign my + + + align:start position:0% +of C and I've messed up the sign my +apologies that plus line should have + + align:start position:0% +apologies that plus line should have + + + align:start position:0% +apologies that plus line should have +come down here these are equal but + + align:start position:0% +come down here these are equal but + + + align:start position:0% +come down here these are equal but +opposite they cancel so let me just + + align:start position:0% +opposite they cancel so let me just + + + align:start position:0% +opposite they cancel so let me just +highlight the result + + align:start position:0% + + + + align:start position:0% + +so what this tells me is if I choose my + + align:start position:0% +so what this tells me is if I choose my + + + align:start position:0% +so what this tells me is if I choose my +gauge generators just right I can adjust + + align:start position:0% +gauge generators just right I can adjust + + + align:start position:0% +gauge generators just right I can adjust +my trace reversed metric so that it is + + align:start position:0% +my trace reversed metric so that it is + + + align:start position:0% +my trace reversed metric so that it is +divergence free if I do that then the + + align:start position:0% +divergence free if I do that then the + + + align:start position:0% +divergence free if I do that then the +first three terms in my Einstein tensor + + align:start position:0% +first three terms in my Einstein tensor + + + align:start position:0% +first three terms in my Einstein tensor +here vanish if I do that then here is my + + align:start position:0% +here vanish if I do that then here is my + + + align:start position:0% +here vanish if I do that then here is my +Einstein tensor so just as in E&M all + + align:start position:0% +Einstein tensor so just as in E&M all + + + align:start position:0% +Einstein tensor so just as in E&M all +that you need to do is say I'm gonna + + align:start position:0% +that you need to do is say I'm gonna + + + align:start position:0% +that you need to do is say I'm gonna +change my gauge such that the following + + align:start position:0% +change my gauge such that the following + + + align:start position:0% +change my gauge such that the following +condition holds okay this the condition + + align:start position:0% +condition holds okay this the condition + + + align:start position:0% +condition holds okay this the condition +that describes going into this grade + + align:start position:0% +that describes going into this grade + + + align:start position:0% +that describes going into this grade +this gauge that's at the divergence of + + align:start position:0% +this gauge that's at the divergence of + + + align:start position:0% +this gauge that's at the divergence of +your Tracy verse perturbation vanishes + + align:start position:0% +your Tracy verse perturbation vanishes + + + align:start position:0% +your Tracy verse perturbation vanishes +this is a simple wave equation okay so + + align:start position:0% +this is a simple wave equation okay so + + + align:start position:0% +this is a simple wave equation okay so +solutions to this are guaranteed to + + align:start position:0% +solutions to this are guaranteed to + + + align:start position:0% +solutions to this are guaranteed to +exist + + align:start position:0% + + + + align:start position:0% + +okay if you sit down you ask can I count + + align:start position:0% +okay if you sit down you ask can I count + + + align:start position:0% +okay if you sit down you ask can I count +with some kind of a pathological + + align:start position:0% +with some kind of a pathological + + + align:start position:0% +with some kind of a pathological +space-time or a pathological no let's + + align:start position:0% +space-time or a pathological no let's + + + align:start position:0% +space-time or a pathological no let's +start mention I'm in some original + + align:start position:0% +start mention I'm in some original + + + align:start position:0% +start mention I'm in some original +space-time it's sufficiently + + align:start position:0% +space-time it's sufficiently + + + align:start position:0% +space-time it's sufficiently +pathological that doesn't allow me to do + + align:start position:0% +pathological that doesn't allow me to do + + + align:start position:0% +pathological that doesn't allow me to do +this if you do that you're gonna end up + + align:start position:0% +this if you do that you're gonna end up + + + align:start position:0% +this if you do that you're gonna end up +violating the conditions that define + + align:start position:0% +violating the conditions that define + + + align:start position:0% +violating the conditions that define +weak space-time you can't do that in + + align:start position:0% +weak space-time you can't do that in + + + align:start position:0% +weak space-time you can't do that in +linearized gravity anyway so in practice + + align:start position:0% +linearized gravity anyway so in practice + + + align:start position:0% +linearized gravity anyway so in practice +we can always choose the gauge that puts + + align:start position:0% +we can always choose the gauge that puts + + + align:start position:0% +we can always choose the gauge that puts +in linearized gravity my Einstein tensor + + align:start position:0% +in linearized gravity my Einstein tensor + + + align:start position:0% +in linearized gravity my Einstein tensor +in this form this form is exactly + + align:start position:0% +in this form this form is exactly + + + align:start position:0% +in this form this form is exactly +analogous to the Lorentz gauge condition + + align:start position:0% +analogous to the Lorentz gauge condition + + + align:start position:0% +analogous to the Lorentz gauge condition +that is used in electrodynamics and so + + align:start position:0% +that is used in electrodynamics and so + + + align:start position:0% +that is used in electrodynamics and so +we call this Lorentz gauge in linearized + + align:start position:0% +we call this Lorentz gauge in linearized + + + align:start position:0% +we call this Lorentz gauge in linearized +gravity once we've done that here's what + + align:start position:0% +gravity once we've done that here's what + + + align:start position:0% +gravity once we've done that here's what +my Einstein field equations turn into + + align:start position:0% + + + + align:start position:0% + +in the next lecture we will solve this + + align:start position:0% +in the next lecture we will solve this + + + align:start position:0% +in the next lecture we will solve this +exactly see which I want to emphasize is + + align:start position:0% +exactly see which I want to emphasize is + + + align:start position:0% +exactly see which I want to emphasize is +this is one of those situations where + + align:start position:0% +this is one of those situations where + + + align:start position:0% +this is one of those situations where +the answer is so easy and simple for us + + align:start position:0% +the answer is so easy and simple for us + + + align:start position:0% +the answer is so easy and simple for us +to to work out + + align:start position:0% +to to work out + + + align:start position:0% +to to work out +we don't actually really need even do + + align:start position:0% +we don't actually really need even do + + + align:start position:0% +we don't actually really need even do +that much calculation I'll remind you + + align:start position:0% +that much calculation I'll remind you + + + align:start position:0% +that much calculation I'll remind you +that in electrodynamics if you work in + + align:start position:0% +that in electrodynamics if you work in + + + align:start position:0% +that in electrodynamics if you work in +Lorentz gauge of electrodynamics the + + align:start position:0% +Lorentz gauge of electrodynamics the + + + align:start position:0% +Lorentz gauge of electrodynamics the +wave equation that governs the + + align:start position:0% +wave equation that governs the + + + align:start position:0% +wave equation that governs the +electromagnetic potential turns out to + + align:start position:0% +electromagnetic potential turns out to + + + align:start position:0% +electromagnetic potential turns out to +be you know there's could be factors of + + align:start position:0% +be you know there's could be factors of + + + align:start position:0% +be you know there's could be factors of +C and things like that depending on + + align:start position:0% +C and things like that depending on + + + align:start position:0% +C and things like that depending on +which units you're working in but we + + align:start position:0% +which units you're working in but we + + + align:start position:0% +which units you're working in but we +find an equation that has exactly the + + align:start position:0% +find an equation that has exactly the + + + align:start position:0% +find an equation that has exactly the +same mathematical structure possibly + + align:start position:0% +same mathematical structure possibly + + + align:start position:0% +same mathematical structure possibly +there's a plus sign I should look that + + align:start position:0% +there's a plus sign I should look that + + + align:start position:0% +there's a plus sign I should look that +up wave operator on my vector potential + + align:start position:0% +up wave operator on my vector potential + + + align:start position:0% +up wave operator on my vector potential +is a source and this is very easily + + align:start position:0% +is a source and this is very easily + + + align:start position:0% +is a source and this is very easily +solved using what's called a radiative + + align:start position:0% +solved using what's called a radiative + + + align:start position:0% +solved using what's called a radiative +green's function + + align:start position:0% + + + + align:start position:0% + +I will discuss this in the next lecture + + align:start position:0% +I will discuss this in the next lecture + + + align:start position:0% +I will discuss this in the next lecture +you can look up the details and any + + align:start position:0% +you can look up the details and any + + + align:start position:0% +you can look up the details and any +advance let your dynamics textbook + + align:start position:0% +advance let your dynamics textbook + + + align:start position:0% +advance let your dynamics textbook +Jackson has very nice discussion of this + + align:start position:0% +Jackson has very nice discussion of this + + + align:start position:0% +Jackson has very nice discussion of this +you know I have an extra index I have a + + align:start position:0% +you know I have an extra index I have a + + + align:start position:0% +you know I have an extra index I have a +different coefficient but the + + align:start position:0% +different coefficient but the + + + align:start position:0% +different coefficient but the +mathematical structure is identical so + + align:start position:0% +mathematical structure is identical so + + + align:start position:0% +mathematical structure is identical so +as far as linearized theory is concerned + + align:start position:0% +as far as linearized theory is concerned + + + align:start position:0% +as far as linearized theory is concerned +we're basically done so I'm gonna talk + + align:start position:0% +we're basically done so I'm gonna talk + + + align:start position:0% +we're basically done so I'm gonna talk +about the exact solution of this in the + + align:start position:0% +about the exact solution of this in the + + + align:start position:0% +about the exact solution of this in the +next lecture to wrap up today's lecture + + align:start position:0% +next lecture to wrap up today's lecture + + + align:start position:0% +next lecture to wrap up today's lecture +wrap up this current lecture let me look + + align:start position:0% +wrap up this current lecture let me look + + + align:start position:0% +wrap up this current lecture let me look +at the solution of this in a particular + + align:start position:0% +at the solution of this in a particular + + + align:start position:0% +at the solution of this in a particular +limits + + align:start position:0% + + + + align:start position:0% + +so I'm gonna take my source to be a + + align:start position:0% +so I'm gonna take my source to be a + + + align:start position:0% +so I'm gonna take my source to be a +static nonrelativistic perfect fluid the + + align:start position:0% +static nonrelativistic perfect fluid the + + + align:start position:0% +static nonrelativistic perfect fluid the +fact that it is static means that all of + + align:start position:0% +fact that it is static means that all of + + + align:start position:0% +fact that it is static means that all of +my time derivatives will be zero okay + + align:start position:0% +my time derivatives will be zero okay + + + align:start position:0% +my time derivatives will be zero okay +that's true for my source it has to be + + align:start position:0% +that's true for my source it has to be + + + align:start position:0% +that's true for my source it has to be +true for the field that arises from it + + align:start position:0% +true for the field that arises from it + + + align:start position:0% +true for the field that arises from it +nonrelativistic tells me that the fluid + + align:start position:0% +nonrelativistic tells me that the fluid + + + align:start position:0% +nonrelativistic tells me that the fluid +density greatly exceeds its pressure and + + align:start position:0% + + + + align:start position:0% + +as a consequence I can write my stress + + align:start position:0% +as a consequence I can write my stress + + + align:start position:0% +as a consequence I can write my stress +energy tensor as approximately density + + align:start position:0% +energy tensor as approximately density + + + align:start position:0% +energy tensor as approximately density +for velocity for velocity and when you + + align:start position:0% +for velocity for velocity and when you + + + align:start position:0% +for velocity for velocity and when you +go and you look at the magnitudes these + + align:start position:0% +go and you look at the magnitudes these + + + align:start position:0% +go and you look at the magnitudes these +things I sort of looked at this a little + + align:start position:0% +things I sort of looked at this a little + + + align:start position:0% +things I sort of looked at this a little +bit in the previous lecture T zero zero + + align:start position:0% +bit in the previous lecture T zero zero + + + align:start position:0% +bit in the previous lecture T zero zero +is approximately Rho oh well there's + + align:start position:0% +is approximately Rho oh well there's + + + align:start position:0% +is approximately Rho oh well there's +will be negligible and there's probably + + align:start position:0% +will be negligible and there's probably + + + align:start position:0% +will be negligible and there's probably +there's a small correction to this but + + align:start position:0% +there's a small correction to this but + + + align:start position:0% +there's a small correction to this but +we can neglect that on our first pass + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so my field equation is dominated by the + + align:start position:0% +so my field equation is dominated by the + + + align:start position:0% +so my field equation is dominated by the +zero zero component okay that's gonna be + + align:start position:0% +zero zero component okay that's gonna be + + + align:start position:0% +zero zero component okay that's gonna be +the most important piece of this since + + align:start position:0% +the most important piece of this since + + + align:start position:0% +the most important piece of this since +this is static I can immediately say you + + align:start position:0% +this is static I can immediately say you + + + align:start position:0% +this is static I can immediately say you +can change that wave operator into the + + align:start position:0% +can change that wave operator into the + + + align:start position:0% +can change that wave operator into the +Laplace operator and we now notice this + + align:start position:0% +Laplace operator and we now notice this + + + align:start position:0% +Laplace operator and we now notice this +is exactly the equation governing the + + align:start position:0% +is exactly the equation governing the + + + align:start position:0% +is exactly the equation governing the +Newtonian gravitational potential modulo + + align:start position:0% +Newtonian gravitational potential modulo + + + align:start position:0% +Newtonian gravitational potential modulo +a factor of four pardon me a factor of + + align:start position:0% +a factor of four pardon me a factor of + + + align:start position:0% +a factor of four pardon me a factor of +minus four and so we see from this that + + align:start position:0% +minus four and so we see from this that + + + align:start position:0% +minus four and so we see from this that +H bar zero zero is just negative 4 times + + align:start position:0% +H bar zero zero is just negative 4 times + + + align:start position:0% +H bar zero zero is just negative 4 times +Newtonian gravitational potential at + + align:start position:0% +Newtonian gravitational potential at + + + align:start position:0% +Newtonian gravitational potential at +[Applause] + + align:start position:0% + + + + align:start position:0% + +this order in the calculation all other + + align:start position:0% +this order in the calculation all other + + + align:start position:0% +this order in the calculation all other +contributions to the trace reverse + + align:start position:0% +contributions to the trace reverse + + + align:start position:0% +contributions to the trace reverse +metric are zero + + align:start position:0% + + + + align:start position:0% + +okay so let's go from the Tracy verse + + align:start position:0% +okay so let's go from the Tracy verse + + + align:start position:0% +okay so let's go from the Tracy verse +metric back to the metric we use the + + align:start position:0% +metric back to the metric we use the + + + align:start position:0% +metric back to the metric we use the +fact that H mu nu is the trace reverse + + align:start position:0% +fact that H mu nu is the trace reverse + + + align:start position:0% +fact that H mu nu is the trace reverse +to H mu nu if we trace reverse it will + + align:start position:0% +to H mu nu if we trace reverse it will + + + align:start position:0% +to H mu nu if we trace reverse it will +get the original metric back basically + + align:start position:0% +get the original metric back basically + + + align:start position:0% +get the original metric back basically +we trace u-verse twice so the trace of + + align:start position:0% +we trace u-verse twice so the trace of + + + align:start position:0% +we trace u-verse twice so the trace of +this guy okay + + align:start position:0% + + + + align:start position:0% + +and so putting all these ingredients + + align:start position:0% +and so putting all these ingredients + + + align:start position:0% +and so putting all these ingredients +together what we see are that the only + + align:start position:0% +together what we see are that the only + + + align:start position:0% +together what we see are that the only +nonzero contributions here are H 0 0 + + align:start position:0% +nonzero contributions here are H 0 0 + + + align:start position:0% +nonzero contributions here are H 0 0 +let's do this one carefully this is + + align:start position:0% +let's do this one carefully this is + + + align:start position:0% +let's do this one carefully this is +minus 4 times Newtonian potential minus + + align:start position:0% +minus 4 times Newtonian potential minus + + + align:start position:0% +minus 4 times Newtonian potential minus +1/2 times 8 is zero zero as four times + + align:start position:0% +1/2 times 8 is zero zero as four times + + + align:start position:0% +1/2 times 8 is zero zero as four times +Newtonian potential I have a see if + + align:start position:0% +Newtonian potential I have a see if + + + align:start position:0% +Newtonian potential I have a see if +minus sign is here this turns into minus + + align:start position:0% +minus sign is here this turns into minus + + + align:start position:0% +minus sign is here this turns into minus +2 Phi N and H 1 1 equals H 2 to H equals + + align:start position:0% +2 Phi N and H 1 1 equals H 2 to H equals + + + align:start position:0% +2 Phi N and H 1 1 equals H 2 to H equals +H 3 3 this is going to be 0 minus 1/2 + + align:start position:0% +H 3 3 this is going to be 0 minus 1/2 + + + align:start position:0% +H 3 3 this is going to be 0 minus 1/2 +times 1 times 4 Phi n + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +we put all these together + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +and what we get is and I'll remind you + + align:start position:0% +and what we get is and I'll remind you + + + align:start position:0% +and what we get is and I'll remind you +this is a metric that I quoted in a + + align:start position:0% +this is a metric that I quoted in a + + + align:start position:0% +this is a metric that I quoted in a +previous lecture then I said we would + + align:start position:0% +previous lecture then I said we would + + + align:start position:0% +previous lecture then I said we would +prove in an upcoming one well here it is + + align:start position:0% +prove in an upcoming one well here it is + + + align:start position:0% +prove in an upcoming one well here it is +this is the Newtonian limit of general + + align:start position:0% +this is the Newtonian limit of general + + + align:start position:0% +this is the Newtonian limit of general +relativity and it's worth remarking that + + align:start position:0% +relativity and it's worth remarking that + + + align:start position:0% +relativity and it's worth remarking that +this thing okay we are now in the very + + align:start position:0% +this thing okay we are now in the very + + + align:start position:0% +this thing okay we are now in the very +first lecture after having derived the + + align:start position:0% +first lecture after having derived the + + + align:start position:0% +first lecture after having derived the +United stanfield equations twenty years + + align:start position:0% +United stanfield equations twenty years + + + align:start position:0% +United stanfield equations twenty years +ago almost all laboratory tests + + align:start position:0% +ago almost all laboratory tests + + + align:start position:0% +ago almost all laboratory tests +laboratory and astronomical + + align:start position:0% +laboratory and astronomical + + + align:start position:0% +laboratory and astronomical +observational tests of general + + align:start position:0% +observational tests of general + + + align:start position:0% +observational tests of general +relativity essentially came from this + + align:start position:0% +relativity essentially came from this + + + align:start position:0% +relativity essentially came from this +space-time okay this ends up being the + + align:start position:0% +space-time okay this ends up being the + + + align:start position:0% +space-time okay this ends up being the +foundation of gravitational lensing this + + align:start position:0% +foundation of gravitational lensing this + + + align:start position:0% +foundation of gravitational lensing this +is used to look at post-newtonian + + align:start position:0% +is used to look at post-newtonian + + + align:start position:0% +is used to look at post-newtonian +corrections in our solar system to a + + align:start position:0% +corrections in our solar system to a + + + align:start position:0% +corrections in our solar system to a +good approximation it describes a + + align:start position:0% +good approximation it describes a + + + align:start position:0% +good approximation it describes a +tremendous number of binary systems that + + align:start position:0% +tremendous number of binary systems that + + + align:start position:0% +tremendous number of binary systems that +we see in our galaxy and in a few other + + align:start position:0% +we see in our galaxy and in a few other + + + align:start position:0% +we see in our galaxy and in a few other +galaxies you really need to look for + + align:start position:0% +galaxies you really need to look for + + + align:start position:0% +galaxies you really need to look for +much more extreme systems before the the + + align:start position:0% +much more extreme systems before the the + + + align:start position:0% +much more extreme systems before the the +way in which the analysis changes due to + + align:start position:0% +way in which the analysis changes due to + + + align:start position:0% +way in which the analysis changes due to +going beyond linear order starts to + + align:start position:0% +going beyond linear order starts to + + + align:start position:0% +going beyond linear order starts to +become important there is an upcoming + + align:start position:0% +become important there is an upcoming + + + align:start position:0% +become important there is an upcoming +homework exercise and for students + + align:start position:0% +homework exercise and for students + + + align:start position:0% +homework exercise and for students +taking this course in spring of 2020 we + + align:start position:0% +taking this course in spring of 2020 we + + + align:start position:0% +taking this course in spring of 2020 we +it remains to determine how we're going + + align:start position:0% +it remains to determine how we're going + + + align:start position:0% +it remains to determine how we're going +to do problem sets at this point I will + + align:start position:0% +to do problem sets at this point I will + + + align:start position:0% +to do problem sets at this point I will +be making a decision on that in coming + + align:start position:0% +be making a decision on that in coming + + + align:start position:0% +be making a decision on that in coming +days but I want to tell you about + + align:start position:0% +days but I want to tell you about + + + align:start position:0% +days but I want to tell you about +on exercise on pset number 7 in which + + align:start position:0% +on exercise on pset number 7 in which + + + align:start position:0% +on exercise on pset number 7 in which +you do a variation of this calculation + + align:start position:0% +you do a variation of this calculation + + + align:start position:0% +you do a variation of this calculation +so instead of just having a static body + + align:start position:0% +so instead of just having a static body + + + align:start position:0% +so instead of just having a static body +with a body who has massive density Rho + + align:start position:0% +with a body who has massive density Rho + + + align:start position:0% +with a body who has massive density Rho +consider a rotating body and the thing + + align:start position:0% +consider a rotating body and the thing + + + align:start position:0% +consider a rotating body and the thing +which is interesting here is that in + + align:start position:0% +which is interesting here is that in + + + align:start position:0% +which is interesting here is that in +general relativity all forms all fluxes + + align:start position:0% +general relativity all forms all fluxes + + + align:start position:0% +general relativity all forms all fluxes +of energy and momentum contribute to + + align:start position:0% +of energy and momentum contribute to + + + align:start position:0% +of energy and momentum contribute to +gravity through the stress energy tensor + + align:start position:0% +gravity through the stress energy tensor + + + align:start position:0% +gravity through the stress energy tensor +so if I have a body that is rotating + + align:start position:0% +so if I have a body that is rotating + + + align:start position:0% +so if I have a body that is rotating +about an axis there's a mass flow there + + align:start position:0% +about an axis there's a mass flow there + + + align:start position:0% +about an axis there's a mass flow there +are mass currents that arise and what + + align:start position:0% +are mass currents that arise and what + + + align:start position:0% +are mass currents that arise and what +you find if you do this calculation + + align:start position:0% +you find if you do this calculation + + + align:start position:0% +you find if you do this calculation +correctly is that there is a correction + + align:start position:0% +correctly is that there is a correction + + + align:start position:0% +correctly is that there is a correction +to the space-time that enters into here + + align:start position:0% +to the space-time that enters into here + + + align:start position:0% +to the space-time that enters into here +which reflects the fact that a rotating + + align:start position:0% +which reflects the fact that a rotating + + + align:start position:0% +which reflects the fact that a rotating +body generates a unique contribution to + + align:start position:0% +body generates a unique contribution to + + + align:start position:0% +body generates a unique contribution to +the gravity that is manifested in this + + align:start position:0% +the gravity that is manifested in this + + + align:start position:0% +the gravity that is manifested in this +space-time now when one looks at the + + align:start position:0% +space-time now when one looks at the + + + align:start position:0% +space-time now when one looks at the +behavior of a body in a space-time like + + align:start position:0% +behavior of a body in a space-time like + + + align:start position:0% +behavior of a body in a space-time like +the one I've written down right here + + align:start position:0% +the one I've written down right here + + + align:start position:0% +the one I've written down right here +it's very reminiscent of well it's just + + align:start position:0% +it's very reminiscent of well it's just + + + align:start position:0% +it's very reminiscent of well it's just +like Newtonian gravity all right it's + + align:start position:0% +like Newtonian gravity all right it's + + + align:start position:0% +like Newtonian gravity all right it's +Newtonian limit and Newtonian gravity + + align:start position:0% +Newtonian limit and Newtonian gravity + + + align:start position:0% +Newtonian limit and Newtonian gravity +looks a lot like the Coulomb electric + + align:start position:0% +looks a lot like the Coulomb electric + + + align:start position:0% +looks a lot like the Coulomb electric +attraction so this is often called a + + align:start position:0% +attraction so this is often called a + + + align:start position:0% +attraction so this is often called a +gravy tow electric field people use that + + align:start position:0% +gravy tow electric field people use that + + + align:start position:0% +gravy tow electric field people use that +term but even though they're talking + + align:start position:0% +term but even though they're talking + + + align:start position:0% +term but even though they're talking +about linearized + + align:start position:0% +about linearized + + + align:start position:0% +about linearized +general relativity if I have a rotating + + align:start position:0% +general relativity if I have a rotating + + + align:start position:0% +general relativity if I have a rotating +body I now have mass currents flowing in + + align:start position:0% +body I now have mass currents flowing in + + + align:start position:0% +body I now have mass currents flowing in +this thing and the correction to the + + align:start position:0% +this thing and the correction to the + + + align:start position:0% +this thing and the correction to the +space-time that arises from this it's + + align:start position:0% +space-time that arises from this it's + + + align:start position:0% +space-time that arises from this it's +qualitatively quite different from this + + align:start position:0% +qualitatively quite different from this + + + align:start position:0% +qualitatively quite different from this +it doesn't have that simple graffito + + align:start position:0% +it doesn't have that simple graffito + + + align:start position:0% +it doesn't have that simple graffito +electric Coulomb back type of form it in + + align:start position:0% +electric Coulomb back type of form it in + + + align:start position:0% +electric Coulomb back type of form it in +fact looks a lot more like a magnetic + + align:start position:0% +fact looks a lot more like a magnetic + + + align:start position:0% +fact looks a lot more like a magnetic +field and in fact when you ask how does + + align:start position:0% +field and in fact when you ask how does + + + align:start position:0% +field and in fact when you ask how does +this new term that is generated affect + + align:start position:0% +this new term that is generated affect + + + align:start position:0% +this new term that is generated affect +the motion of bodies you find something + + align:start position:0% +the motion of bodies you find something + + + align:start position:0% +the motion of bodies you find something +that looks a lot like the magnetic + + align:start position:0% +that looks a lot like the magnetic + + + align:start position:0% +that looks a lot like the magnetic +Lorentz force law describing its motion + + align:start position:0% +Lorentz force law describing its motion + + + align:start position:0% +Lorentz force law describing its motion +so this is a very very powerful tool but + + align:start position:0% +so this is a very very powerful tool but + + + align:start position:0% +so this is a very very powerful tool but +it's already not enough ok so we can go + + align:start position:0% +it's already not enough ok so we can go + + + align:start position:0% +it's already not enough ok so we can go +a lot further than this we have done + + align:start position:0% +a lot further than this we have done + + + align:start position:0% +a lot further than this we have done +so far the simplest possible thing that + + align:start position:0% +so far the simplest possible thing that + + + align:start position:0% +so far the simplest possible thing that +we can do with this toolkit that we have + + align:start position:0% +we can do with this toolkit that we have + + + align:start position:0% +we can do with this toolkit that we have +derived so far in the next lecture that + + align:start position:0% +derived so far in the next lecture that + + + align:start position:0% +derived so far in the next lecture that +I will record we're going to return to + + align:start position:0% +I will record we're going to return to + + + align:start position:0% +I will record we're going to return to +my linearize Einstein field equations + + align:start position:0% +my linearize Einstein field equations + + + align:start position:0% +my linearize Einstein field equations +and I am going to explore general + + align:start position:0% +and I am going to explore general + + + align:start position:0% +and I am going to explore general +solutions of us this is going to lead us + + align:start position:0% +solutions of us this is going to lead us + + + align:start position:0% +solutions of us this is going to lead us +into a discussion of how things behave + + align:start position:0% +into a discussion of how things behave + + + align:start position:0% +into a discussion of how things behave +when my gravitational source is dynamic + + align:start position:0% +when my gravitational source is dynamic + + + align:start position:0% +when my gravitational source is dynamic +okay I do not want to lose the time + + align:start position:0% +okay I do not want to lose the time + + + align:start position:0% +okay I do not want to lose the time +derivatives that are present in that + + align:start position:0% +derivatives that are present in that + + + align:start position:0% +derivatives that are present in that +wave operator and so this is going to + + align:start position:0% +wave operator and so this is going to + + + align:start position:0% +wave operator and so this is going to +lead us quite naturally then to a + + align:start position:0% +lead us quite naturally then to a + + + align:start position:0% +lead us quite naturally then to a +discussion of gravitational radiation + + align:start position:0% +discussion of gravitational radiation + + + align:start position:0% +discussion of gravitational radiation +and so after the next lecture we'll + + align:start position:0% +and so after the next lecture we'll + + + align:start position:0% +and so after the next lecture we'll +spend a lecture or two discussing the + + align:start position:0% +spend a lecture or two discussing the + + + align:start position:0% +spend a lecture or two discussing the +nature of gravitational radiation and + + align:start position:0% +nature of gravitational radiation and + + + align:start position:0% +nature of gravitational radiation and +there will be an upcoming homework + + align:start position:0% +there will be an upcoming homework + + + align:start position:0% +there will be an upcoming homework +assignment or two in which you explore + + align:start position:0% +assignment or two in which you explore + + + align:start position:0% +assignment or two in which you explore +the properties of gravitational + + align:start position:0% +the properties of gravitational + + + align:start position:0% +the properties of gravitational +radiation \ No newline at end of file diff --git a/AWYzdtetQbE.txt b/AWYzdtetQbE.txt new file mode 100644 index 0000000000000000000000000000000000000000..677731ddeb940485a4f4224ee7e703212e915622 --- /dev/null +++ b/AWYzdtetQbE.txt @@ -0,0 +1,12499 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +I'm going to shift more towards this + + align:start position:0% +I'm going to shift more towards this + + + align:start position:0% +I'm going to shift more towards this +decoding space that we talked about the + + align:start position:0% +decoding space that we talked about the + + + align:start position:0% +decoding space that we talked about the +linkage between neural activity and + + align:start position:0% +linkage between neural activity and + + + align:start position:0% +linkage between neural activity and +behavioral rapport and I introduced that + + align:start position:0% +behavioral rapport and I introduced that + + + align:start position:0% +behavioral rapport and I introduced that +a bit you just saw that there's some + + align:start position:0% +a bit you just saw that there's some + + + align:start position:0% +a bit you just saw that there's some +population powerful activity in IT and + + align:start position:0% +population powerful activity in IT and + + + align:start position:0% +population powerful activity in IT and +I'm gonna expand on that a bit here but + + align:start position:0% +I'm gonna expand on that a bit here but + + + align:start position:0% +I'm gonna expand on that a bit here but +you know sort of stepping back when you + + align:start position:0% +you know sort of stepping back when you + + + align:start position:0% +you know sort of stepping back when you +think about it again what I call an end + + align:start position:0% +think about it again what I call an end + + + align:start position:0% +think about it again what I call an end +and understanding going from the image + + align:start position:0% +and understanding going from the image + + + align:start position:0% +and understanding going from the image +all the way the neural activity to the + + align:start position:0% +all the way the neural activity to the + + + align:start position:0% +all the way the neural activity to the +perceptual report one of the things we + + align:start position:0% +perceptual report one of the things we + + + align:start position:0% +perceptual report one of the things we +want to do again is just define a + + align:start position:0% +want to do again is just define a + + + align:start position:0% +want to do again is just define a +decoding mechanism that the brain uses + + align:start position:0% +decoding mechanism that the brain uses + + + align:start position:0% +decoding mechanism that the brain uses +to support these perceptual reports + + align:start position:0% +to support these perceptual reports + + + align:start position:0% +to support these perceptual reports +basically how what neural activity are + + align:start position:0% +basically how what neural activity are + + + align:start position:0% +basically how what neural activity are +directly responsible for these tasks and + + align:start position:0% +directly responsible for these tasks and + + + align:start position:0% +directly responsible for these tasks and +I'll come back to later this encoding + + align:start position:0% +I'll come back to later this encoding + + + align:start position:0% +I'll come back to later this encoding +side is like you know and I notice I'm + + align:start position:0% +side is like you know and I notice I'm + + + align:start position:0% +side is like you know and I notice I'm +putting these in this order right so + + align:start position:0% +putting these in this order right so + + + align:start position:0% +putting these in this order right so +once you know what the relevant aspects + + align:start position:0% +once you know what the relevant aspects + + + align:start position:0% +once you know what the relevant aspects +of neural activity are in IT or wherever + + align:start position:0% +of neural activity are in IT or wherever + + + align:start position:0% +of neural activity are in IT or wherever +you think they are then that sets a + + align:start position:0% +you think they are then that sets a + + + align:start position:0% +you think they are then that sets a +target for what is the image to neural + + align:start position:0% +target for what is the image to neural + + + align:start position:0% +target for what is the image to neural +transformation that you're trying to + + align:start position:0% +transformation that you're trying to + + + align:start position:0% +transformation that you're trying to +explain not predict any neural response + + align:start position:0% +explain not predict any neural response + + + align:start position:0% +explain not predict any neural response +but those particulars aspects of the + + align:start position:0% +but those particulars aspects of the + + + align:start position:0% +but those particulars aspects of the +neural response so that's what I mean by + + align:start position:0% +neural response so that's what I mean by + + + align:start position:0% +neural response so that's what I mean by +the relevant ventral stream patterns of + + align:start position:0% +the relevant ventral stream patterns of + + + align:start position:0% +the relevant ventral stream patterns of +activities so we start here we work to + + align:start position:0% +activities so we start here we work to + + + align:start position:0% +activities so we start here we work to +here and then we work to here rather + + align:start position:0% +here and then we work to here rather + + + align:start position:0% +here and then we work to here rather +than this other way around okay so I'm + + align:start position:0% +than this other way around okay so I'm + + + align:start position:0% +than this other way around okay so I'm +gonna try it again keep with the domain + + align:start position:0% +gonna try it again keep with the domain + + + align:start position:0% +gonna try it again keep with the domain +I set up I talked about core recognition + + align:start position:0% +I set up I talked about core recognition + + + align:start position:0% +I set up I talked about core recognition +I now need to start to define tasks I'm + + align:start position:0% +I now need to start to define tasks I'm + + + align:start position:0% +I now need to start to define tasks I'm +gonna talk about specific tasks that are + + align:start position:0% +gonna talk about specific tasks that are + + + align:start position:0% +gonna talk about specific tasks that are +for now let's call them basic level + + align:start position:0% +for now let's call them basic level + + + align:start position:0% +for now let's call them basic level +nouns I'm actually going to relax that + + align:start position:0% +nouns I'm actually going to relax that + + + align:start position:0% +nouns I'm actually going to relax that +to subordinate tasks in a minute but + + align:start position:0% +to subordinate tasks in a minute but + + + align:start position:0% +to subordinate tasks in a minute but +here they are car clock at these are not + + align:start position:0% +here they are car clock at these are not + + + align:start position:0% +here they are car clock at these are not +the actual nouns I'll show you the ones + + align:start position:0% +the actual nouns I'll show you the ones + + + align:start position:0% +the actual nouns I'll show you the ones +we use but just to fix ideas we're + + align:start position:0% +we use but just to fix ideas we're + + + align:start position:0% +we use but just to fix ideas we're +imagining a space of all possible nouns + + align:start position:0% +imagining a space of all possible nouns + + + align:start position:0% +imagining a space of all possible nouns +that you might use to describe what you + + align:start position:0% +that you might use to describe what you + + + align:start position:0% +that you might use to describe what you +just saw and I'm gonna have a generative + + align:start position:0% +just saw and I'm gonna have a generative + + + align:start position:0% +just saw and I'm gonna have a generative +image domain so I know that have a space + + align:start position:0% +image domain so I know that have a space + + + align:start position:0% +image domain so I know that have a space +of images here I'm not just going to + + align:start position:0% +of images here I'm not just going to + + + align:start position:0% +of images here I'm not just going to +draw these off the web we're gonna + + align:start position:0% +draw these off the web we're gonna + + + align:start position:0% +draw these off the web we're gonna +generate our own image domain that we + + align:start position:0% +generate our own image domain that we + + + align:start position:0% +generate our own image domain that we +think engages on the problem but gives + + align:start position:0% +think engages on the problem but gives + + + align:start position:0% +think engages on the problem but gives +us control of the light variables so + + align:start position:0% +us control of the light variables so + + + align:start position:0% +us control of the light variables so +I'll show you that now so the way we're + + align:start position:0% +I'll show you that now so the way we're + + + align:start position:0% +I'll show you that now so the way we're +gonna do this is by generating one + + align:start position:0% +gonna do this is by generating one + + + align:start position:0% +gonna do this is by generating one +foreground object and each image that + + align:start position:0% +foreground object and each image that + + + align:start position:0% +foreground object and each image that +we're going to show and we just do this + + align:start position:0% +we're going to show and we just do this + + + align:start position:0% +we're going to show and we just do this +by taking 3d models like these this is + + align:start position:0% +by taking 3d models like these this is + + + align:start position:0% +by taking 3d models like these this is +of a car we can control its other latent + + align:start position:0% +of a car we can control its other latent + + + align:start position:0% +of a car we can control its other latent +variables beyond its identity so this is + + align:start position:0% +variables beyond its identity so this is + + + align:start position:0% +variables beyond its identity so this is +a car it has a particular car type so + + align:start position:0% +a car it has a particular car type so + + + align:start position:0% +a car it has a particular car type so +there's a couple latent variables about + + align:start position:0% +there's a couple latent variables about + + + align:start position:0% +there's a couple latent variables about +identity here that relate to the + + align:start position:0% +identity here that relate to the + + + align:start position:0% +identity here that relate to the +geometry then there's these positional + + align:start position:0% +geometry then there's these positional + + + align:start position:0% +geometry then there's these positional +other latent variables like position + + align:start position:0% +other latent variables like position + + + align:start position:0% +other latent variables like position +size and pose that I mentioned that our + + align:start position:0% +size and pose that I mentioned that our + + + align:start position:0% +size and pose that I mentioned that our +unknowns that make the problem + + align:start position:0% +unknowns that make the problem + + + align:start position:0% +unknowns that make the problem +challenging and we can then just like + + align:start position:0% +challenging and we can then just like + + + align:start position:0% +challenging and we can then just like +render this thing and we could place it + + align:start position:0% +render this thing and we could place it + + + align:start position:0% +render this thing and we could place it +on any old background we wanted to and + + align:start position:0% +on any old background we wanted to and + + + align:start position:0% +on any old background we wanted to and +what we did was we tended to place them + + align:start position:0% +what we did was we tended to place them + + + align:start position:0% +what we did was we tended to place them +on uncorrelated naturalistic backgrounds + + align:start position:0% +on uncorrelated naturalistic backgrounds + + + align:start position:0% +on uncorrelated naturalistic backgrounds +and that creates these sort of weirdest + + align:start position:0% +and that creates these sort of weirdest + + + align:start position:0% +and that creates these sort of weirdest +looking images some of them may look + + align:start position:0% +looking images some of them may look + + + align:start position:0% +looking images some of them may look +sort of natural heads fluke this looks + + align:start position:0% +sort of natural heads fluke this looks + + + align:start position:0% +sort of natural heads fluke this looks +pretty unnatural but the reason we did + + align:start position:0% +pretty unnatural but the reason we did + + + align:start position:0% +pretty unnatural but the reason we did +this why would you do this so so we did + + align:start position:0% +this why would you do this so so we did + + + align:start position:0% +this why would you do this so so we did +this because we we could add a + + align:start position:0% +this because we we could add a + + + align:start position:0% +this because we we could add a +generative space and because it was so + + align:start position:0% +generative space and because it was so + + + align:start position:0% +generative space and because it was so +this we know what's going on with the + + align:start position:0% +this we know what's going on with the + + + align:start position:0% +this we know what's going on with the +latent variables we care about and we + + align:start position:0% +latent variables we care about and we + + + align:start position:0% +latent variables we care about and we +also when we built this it was + + align:start position:0% +also when we built this it was + + + align:start position:0% +also when we built this it was +challenging for computer vision systems + + align:start position:0% +challenging for computer vision systems + + + align:start position:0% +challenging for computer vision systems +to deal with this even though humans + + align:start position:0% +to deal with this even though humans + + + align:start position:0% +to deal with this even though humans +could naturally you know they didn't + + align:start position:0% +could naturally you know they didn't + + + align:start position:0% +could naturally you know they didn't +have advantage of any contextual cues + + align:start position:0% +have advantage of any contextual cues + + + align:start position:0% +have advantage of any contextual cues +here because by definite by construction + + align:start position:0% +here because by definite by construction + + + align:start position:0% +here because by definite by construction +these are uncorrelated we just took + + align:start position:0% +these are uncorrelated we just took + + + align:start position:0% +these are uncorrelated we just took +natural images and would randomly put + + align:start position:0% +natural images and would randomly put + + + align:start position:0% +natural images and would randomly put +objects on them but this was enough to + + align:start position:0% +objects on them but this was enough to + + + align:start position:0% +objects on them but this was enough to +fool a lot of the computer vision + + align:start position:0% +fool a lot of the computer vision + + + align:start position:0% +fool a lot of the computer vision +systems at the time it tended to rely on + + align:start position:0% +systems at the time it tended to rely on + + + align:start position:0% +systems at the time it tended to rely on +the contextual cubes like blue in the + + align:start position:0% +the contextual cubes like blue in the + + + align:start position:0% +the contextual cubes like blue in the +background signals are being an airplane + + align:start position:0% +background signals are being an airplane + + + align:start position:0% +background signals are being an airplane +we didn't want those kind of things + + align:start position:0% +we didn't want those kind of things + + + align:start position:0% +we didn't want those kind of things +being done we wanted the actual + + align:start position:0% +being done we wanted the actual + + + align:start position:0% +being done we wanted the actual +extraction of object identity and again + + align:start position:0% +extraction of object identity and again + + + align:start position:0% +extraction of object identity and again +humans could do it quite well so that's + + align:start position:0% +humans could do it quite well so that's + + + align:start position:0% +humans could do it quite well so that's +why we ended up in this sort of maybe + + align:start position:0% +why we ended up in this sort of maybe + + + align:start position:0% +why we ended up in this sort of maybe +this no-man's land of image space which + + align:start position:0% +this no-man's land of image space which + + + align:start position:0% +this no-man's land of image space which +is not simply simple but not image net + + align:start position:0% +is not simply simple but not image net + + + align:start position:0% +is not simply simple but not image net +just pulled off off the web and so + + align:start position:0% +just pulled off off the web and so + + + align:start position:0% +just pulled off off the web and so +that's how we got there and just to give + + align:start position:0% +that's how we got there and just to give + + + align:start position:0% +that's how we got there and just to give +you a sense that this is actually quite + + align:start position:0% +you a sense that this is actually quite + + + align:start position:0% +you a sense that this is actually quite +doable for humans I'll show you a few + + align:start position:0% +doable for humans I'll show you a few + + + align:start position:0% +doable for humans I'll show you a few +images I won't even cue you what they + + align:start position:0% +images I won't even cue you what they + + + align:start position:0% +images I won't even cue you what they +are I'm going to show you them for a + + align:start position:0% +are I'm going to show you them for a + + + align:start position:0% +are I'm going to show you them for a +hundred milliseconds you can kind of + + align:start position:0% +hundred milliseconds you can kind of + + + align:start position:0% +hundred milliseconds you can kind of +shout out what object you see + + align:start position:0% + + + + align:start position:0% + +right so see it's pretty straightforward + + align:start position:0% +right so see it's pretty straightforward + + + align:start position:0% +right so see it's pretty straightforward +writing those it look weird you can do + + align:start position:0% +writing those it look weird you can do + + + align:start position:0% +writing those it look weird you can do +that quite well and you know here's the + + align:start position:0% +that quite well and you know here's the + + + align:start position:0% +that quite well and you know here's the +kind of images that we would generate + + align:start position:0% +kind of images that we would generate + + + align:start position:0% +kind of images that we would generate +this is this would be so when we think + + align:start position:0% +this is this would be so when we think + + + align:start position:0% +this is this would be so when we think +of image bags we think of partitions of + + align:start position:0% +of image bags we think of partitions of + + + align:start position:0% +of image bags we think of partitions of +image space this is some images that + + align:start position:0% +image space this is some images that + + + align:start position:0% +image space this is some images that +would correspond to faces these are all + + align:start position:0% +would correspond to faces these are all + + + align:start position:0% +would correspond to faces these are all +images of faces under some + + align:start position:0% +images of faces under some + + + align:start position:0% +images of faces under some +transformations again different + + align:start position:0% +transformations again different + + + align:start position:0% +transformations again different +backgrounds these are not faces these + + align:start position:0% +backgrounds these are not faces these + + + align:start position:0% +backgrounds these are not faces these +there are other objects again under + + align:start position:0% +there are other objects again under + + + align:start position:0% +there are other objects again under +transformations and we can have as many + + align:start position:0% +transformations and we can have as many + + + align:start position:0% +transformations and we can have as many +of these as we want we call this one + + align:start position:0% +of these as we want we call this one + + + align:start position:0% +of these as we want we call this one +this distinction being shown for 100 + + align:start position:0% +this distinction being shown for 100 + + + align:start position:0% +this distinction being shown for 100 +milliseconds as one core recognition + + align:start position:0% +milliseconds as one core recognition + + + align:start position:0% +milliseconds as one core recognition +test discriminating face for nod face + + align:start position:0% +test discriminating face for nod face + + + align:start position:0% +test discriminating face for nod face +here's a subordinate task this is beetle + + align:start position:0% +here's a subordinate task this is beetle + + + align:start position:0% +here's a subordinate task this is beetle +from nappy oh so it's a particular type + + align:start position:0% +from nappy oh so it's a particular type + + + align:start position:0% +from nappy oh so it's a particular type +of car you can see it's more challenging + + align:start position:0% +of car you can see it's more challenging + + + align:start position:0% +of car you can see it's more challenging +these again we don't show these images + + align:start position:0% +these again we don't show these images + + + align:start position:0% +these again we don't show these images +like this this is just to show you the + + align:start position:0% +like this this is just to show you the + + + align:start position:0% +like this this is just to show you the +set we show them one at a time and so + + align:start position:0% +set we show them one at a time and so + + + align:start position:0% +set we show them one at a time and so +let me now go ahead and say we're gonna + + align:start position:0% +let me now go ahead and say we're gonna + + + align:start position:0% +let me now go ahead and say we're gonna +try to make predictive model using that + + align:start position:0% +try to make predictive model using that + + + align:start position:0% +try to make predictive model using that +kind of image space to see if we can + + align:start position:0% +kind of image space to see if we can + + + align:start position:0% +kind of image space to see if we can +understand what are the relevant aspects + + align:start position:0% +understand what are the relevant aspects + + + align:start position:0% +understand what are the relevant aspects +of neural activity that can predict + + align:start position:0% +of neural activity that can predict + + + align:start position:0% +of neural activity that can predict +human report on an image space and when + + align:start position:0% +human report on an image space and when + + + align:start position:0% +human report on an image space and when +I say we I mean a nojima John Hong who + + align:start position:0% +I say we I mean a nojima John Hong who + + + align:start position:0% +I say we I mean a nojima John Hong who +postdoc a graduate student that were in + + align:start position:0% +postdoc a graduate student that were in + + + align:start position:0% +postdoc a graduate student that were in +the lab that led this experimental work + + align:start position:0% +the lab that led this experimental work + + + align:start position:0% +the lab that led this experimental work +and Ethan Solomon and Dan yemen's also + + align:start position:0% +and Ethan Solomon and Dan yemen's also + + + align:start position:0% +and Ethan Solomon and Dan yemen's also +contributed to the work so what we did + + align:start position:0% +contributed to the work so what we did + + + align:start position:0% +contributed to the work so what we did +was to try to record a bunch of IT + + align:start position:0% +was to try to record a bunch of IT + + + align:start position:0% +was to try to record a bunch of IT +activity to measure what's going on in + + align:start position:0% +activity to measure what's going on in + + + align:start position:0% +activity to measure what's going on in +the population as I showed you earlier + + align:start position:0% +the population as I showed you earlier + + + align:start position:0% +the population as I showed you earlier +but now in this more defined space where + + align:start position:0% +but now in this more defined space where + + + align:start position:0% +but now in this more defined space where +we're going to collect a bunch of human + + align:start position:0% +we're going to collect a bunch of human + + + align:start position:0% +we're going to collect a bunch of human +behavior to compare possible ways of + + align:start position:0% +behavior to compare possible ways of + + + align:start position:0% +behavior to compare possible ways of +reading i.t with the behavior of the + + align:start position:0% +reading i.t with the behavior of the + + + align:start position:0% +reading i.t with the behavior of the +human this is how we started we're now + + align:start position:0% +human this is how we started we're now + + + align:start position:0% +human this is how we started we're now +doing monkeys where we're recording and + + align:start position:0% +doing monkeys where we're recording and + + + align:start position:0% +doing monkeys where we're recording and +the monkeys doing a task but what we did + + align:start position:0% +the monkeys doing a task but what we did + + + align:start position:0% +the monkeys doing a task but what we did +here was we're just passively fixating + + align:start position:0% +here was we're just passively fixating + + + align:start position:0% +here was we're just passively fixating +monkeys compared with behaving humans + + align:start position:0% +monkeys compared with behaving humans + + + align:start position:0% +monkeys compared with behaving humans +and it's assured your earlier monkeys + + align:start position:0% +and it's assured your earlier monkeys + + + align:start position:0% +and it's assured your earlier monkeys +and humans have very similar patterns of + + align:start position:0% +and humans have very similar patterns of + + + align:start position:0% +and humans have very similar patterns of +behavior so what we record from IT in + + align:start position:0% +behavior so what we record from IT in + + + align:start position:0% +behavior so what we record from IT in +this case we were using array recording + + align:start position:0% +this case we were using array recording + + + align:start position:0% +this case we were using array recording +electrodes these are chronically + + align:start position:0% +electrodes these are chronically + + + align:start position:0% +electrodes these are chronically +implanted that shows them here you + + align:start position:0% +implanted that shows them here you + + + align:start position:0% +implanted that shows them here you +implant them during a surgery kind of as + + align:start position:0% +implant them during a surgery kind of as + + + align:start position:0% +implant them during a surgery kind of as +shown here they're down into i.t cortex + + align:start position:0% +shown here they're down into i.t cortex + + + align:start position:0% +shown here they're down into i.t cortex +you can get their size here they're + + align:start position:0% +you can get their size here they're + + + align:start position:0% +you can get their size here they're +about a hundred elect there's actually + + align:start position:0% +about a hundred elect there's actually + + + align:start position:0% +about a hundred elect there's actually +96 electrons on each of them they + + align:start position:0% +96 electrons on each of them they + + + align:start position:0% +96 electrons on each of them they +typically yield about half of the + + align:start position:0% +typically yield about half of the + + + align:start position:0% +typically yield about half of the +electrodes having active neurons on them + + align:start position:0% +electrodes having active neurons on them + + + align:start position:0% +electrodes having active neurons on them +so you get you know on the order of 150 + + align:start position:0% +so you get you know on the order of 150 + + + align:start position:0% +so you get you know on the order of 150 +recording sites and you can lay them out + + align:start position:0% +recording sites and you can lay them out + + + align:start position:0% +recording sites and you can lay them out +you can lay we would typically lay out + + align:start position:0% +you can lay we would typically lay out + + + align:start position:0% +you can lay we would typically lay out +three of them across ITU and be four to + + align:start position:0% +three of them across ITU and be four to + + + align:start position:0% +three of them across ITU and be four to +record a population sample out of i.t + + align:start position:0% +record a population sample out of i.t + + + align:start position:0% +record a population sample out of i.t +and we would do this across multiple + + align:start position:0% +and we would do this across multiple + + + align:start position:0% +and we would do this across multiple +jeez and here's an example of the kind + + align:start position:0% +jeez and here's an example of the kind + + + align:start position:0% +jeez and here's an example of the kind +of data we would get this is a 168th IT + + align:start position:0% +of data we would get this is a 168th IT + + + align:start position:0% +of data we would get this is a 168th IT +recording sites this is similar to why I + + align:start position:0% +recording sites this is similar to why I + + + align:start position:0% +recording sites this is similar to why I +showed you earlier this is the mean + + align:start position:0% +showed you earlier this is the mean + + + align:start position:0% +showed you earlier this is the mean +response and a particular time window + + align:start position:0% +response and a particular time window + + + align:start position:0% +response and a particular time window +out of IT similar what I showed you + + align:start position:0% +out of IT similar what I showed you + + + align:start position:0% +out of IT similar what I showed you +earlier in that study with Gabrielle and + + align:start position:0% +earlier in that study with Gabrielle and + + + align:start position:0% +earlier in that study with Gabrielle and +what we do here is I'm just showing you + + align:start position:0% +what we do here is I'm just showing you + + + align:start position:0% +what we do here is I'm just showing you +to give you a feel that's one image + + align:start position:0% +to give you a feel that's one image + + + align:start position:0% +to give you a feel that's one image +here's eight more here's seven more + + align:start position:0% +here's eight more here's seven more + + + align:start position:0% +here's eight more here's seven more +images and these are just the population + + align:start position:0% +images and these are just the population + + + align:start position:0% +images and these are just the population +vectors in a graphic form and but we + + align:start position:0% +vectors in a graphic form and but we + + + align:start position:0% +vectors in a graphic form and but we +actually collected nearly 25 this is + + align:start position:0% +actually collected nearly 25 this is + + + align:start position:0% +actually collected nearly 25 this is +2,560 images is a sort of the mean + + align:start position:0% +2,560 images is a sort of the mean + + + align:start position:0% +2,560 images is a sort of the mean +response data of this 168 neurons and + + align:start position:0% +response data of this 168 neurons and + + + align:start position:0% +response data of this 168 neurons and +now you have this again this rich + + align:start position:0% +now you have this again this rich + + + align:start position:0% +now you have this again this rich +population data and you can ask what's + + align:start position:0% +population data and you can ask what's + + + align:start position:0% +population data and you can ask what's +available in there to support these + + align:start position:0% +available in there to support these + + + align:start position:0% +available in there to support these +tasks and how well does it predict human + + align:start position:0% +tasks and how well does it predict human + + + align:start position:0% +tasks and how well does it predict human +patterns of performance on those tasks + + align:start position:0% +patterns of performance on those tasks + + + align:start position:0% +patterns of performance on those tasks +so in this study that's all we were + + align:start position:0% +so in this study that's all we were + + + align:start position:0% +so in this study that's all we were +asking to do we're trying to do more + + align:start position:0% +asking to do we're trying to do more + + + align:start position:0% +asking to do we're trying to do more +more recently but let me show you what + + align:start position:0% +more recently but let me show you what + + + align:start position:0% +more recently but let me show you what +all we were trying to do is to say look + + align:start position:0% +all we were trying to do is to say look + + + align:start position:0% +all we were trying to do is to say look +one thing we observed even though you + + align:start position:0% +one thing we observed even though you + + + align:start position:0% +one thing we observed even though you +saw that car you could do car you can do + + align:start position:0% +saw that car you could do car you can do + + + align:start position:0% +saw that car you could do car you can do +faces it seemed like you were doing a + + align:start position:0% +faces it seemed like you were doing a + + + align:start position:0% +faces it seemed like you were doing a +hundred percent turns out you're at + + align:start position:0% +hundred percent turns out you're at + + + align:start position:0% +hundred percent turns out you're at +better at some things than others so + + align:start position:0% +better at some things than others so + + + align:start position:0% +better at some things than others so +discriminative humans so red means good + + align:start position:0% +discriminative humans so red means good + + + align:start position:0% +discriminative humans so red means good +performance Heidi prime you know D prime + + align:start position:0% +performance Heidi prime you know D prime + + + align:start position:0% +performance Heidi prime you know D prime +of three is something like on a sec + + align:start position:0% +of three is something like on a sec + + + align:start position:0% +of three is something like on a sec +physicists in the room may correct me a + + align:start position:0% +physicists in the room may correct me a + + + align:start position:0% +physicists in the room may correct me a +D prime of three is sort of on the order + + align:start position:0% +D prime of three is sort of on the order + + + align:start position:0% +D prime of three is sort of on the order +of 90 some 95 percent correct in that + + align:start position:0% +of 90 some 95 percent correct in that + + + align:start position:0% +of 90 some 95 percent correct in that +range so these are very high performance + + align:start position:0% +range so these are very high performance + + + align:start position:0% +range so these are very high performance +levels when you get up to five zero is + + align:start position:0% +levels when you get up to five zero is + + + align:start position:0% +levels when you get up to five zero is +chance so fifty percent well this is an + + align:start position:0% +chance so fifty percent well this is an + + + align:start position:0% +chance so fifty percent well this is an +eight-way task so one over eight percent + + align:start position:0% +eight-way task so one over eight percent + + + align:start position:0% +eight-way task so one over eight percent +correct so the subjects we're doing + + align:start position:0% +correct so the subjects we're doing + + + align:start position:0% +correct so the subjects we're doing +either eight way can basic level tasks + + align:start position:0% +either eight way can basic level tasks + + + align:start position:0% +either eight way can basic level tasks +or eight ways subordinate cars or eight + + align:start position:0% +or eight ways subordinate cars or eight + + + align:start position:0% +or eight ways subordinate cars or eight +way faces and these are the D prime + + align:start position:0% +way faces and these are the D prime + + + align:start position:0% +way faces and these are the D prime +levels under different amounts of + + align:start position:0% +levels under different amounts of + + + align:start position:0% +levels under different amounts of +variation of those other late variables + + align:start position:0% +variation of those other late variables + + + align:start position:0% +variation of those other late variables +position size and pose don't worry about + + align:start position:0% +position size and pose don't worry about + + + align:start position:0% +position size and pose don't worry about +those details what I want you to see is + + align:start position:0% +those details what I want you to see is + + + align:start position:0% +those details what I want you to see is +the color here so look at some tables + + align:start position:0% +the color here so look at some tables + + + align:start position:0% +the color here so look at some tables +versus you know discriminating tables + + align:start position:0% +versus you know discriminating tables + + + align:start position:0% +versus you know discriminating tables +from all these other objects you do that + + align:start position:0% +from all these other objects you do that + + + align:start position:0% +from all these other objects you do that +at a very high D prime discriminating + + align:start position:0% +at a very high D prime discriminating + + + align:start position:0% +at a very high D prime discriminating +beetles from other cars you do it a + + align:start position:0% +beetles from other cars you do it a + + + align:start position:0% +beetles from other cars you do it a +slightly lower D prime you can see this + + align:start position:0% +slightly lower D prime you can see this + + + align:start position:0% +slightly lower D prime you can see this +especially at the high variation you're + + align:start position:0% +especially at the high variation you're + + + align:start position:0% +especially at the high variation you're +actually starting to get down to lower + + align:start position:0% +actually starting to get down to lower + + + align:start position:0% +actually starting to get down to lower +performance and faces one face versus + + align:start position:0% +performance and faces one face versus + + + align:start position:0% +performance and faces one face versus +another face you're actually quite poor + + align:start position:0% +another face you're actually quite poor + + + align:start position:0% +another face you're actually quite poor +at that you're you know a little bit + + align:start position:0% +at that you're you know a little bit + + + align:start position:0% +at that you're you know a little bit +better than chance but it's actually + + align:start position:0% +better than chance but it's actually + + + align:start position:0% +better than chance but it's actually +quite challenging in 100 milliseconds + + align:start position:0% +quite challenging in 100 milliseconds + + + align:start position:0% +quite challenging in 100 milliseconds +without hair and glasses to discriminate + + align:start position:0% +without hair and glasses to discriminate + + + align:start position:0% +without hair and glasses to discriminate +those 3d kind of face models I showed + + align:start position:0% +those 3d kind of face models I showed + + + align:start position:0% +those 3d kind of face models I showed +you Sam and Joe earlier as examples + + align:start position:0% +you Sam and Joe earlier as examples + + + align:start position:0% +you Sam and Joe earlier as examples +you're actually quite quite + + align:start position:0% +you're actually quite quite + + + align:start position:0% +you're actually quite quite +challenging to do that for humans in + + align:start position:0% +challenging to do that for humans in + + + align:start position:0% +challenging to do that for humans in +that domain of faces so what I want to + + align:start position:0% +that domain of faces so what I want to + + + align:start position:0% +that domain of faces so what I want to +show you here is you have this pattern + + align:start position:0% +show you here is you have this pattern + + + align:start position:0% +show you here is you have this pattern +of behavioral performance you have all + + align:start position:0% +of behavioral performance you have all + + + align:start position:0% +of behavioral performance you have all +this IT activity this is humans this is + + align:start position:0% +this IT activity this is humans this is + + + align:start position:0% +this IT activity this is humans this is +monkeys and what we wanted to do is to + + align:start position:0% +monkeys and what we wanted to do is to + + + align:start position:0% +monkeys and what we wanted to do is to +say look we can use this pattern this is + + align:start position:0% +say look we can use this pattern this is + + + align:start position:0% +say look we can use this pattern this is +very repeatable across humans can we use + + align:start position:0% +very repeatable across humans can we use + + + align:start position:0% +very repeatable across humans can we use +this repeatable behavioral pattern to + + align:start position:0% +this repeatable behavioral pattern to + + + align:start position:0% +this repeatable behavioral pattern to +enter and understand what aspects of + + align:start position:0% +enter and understand what aspects of + + + align:start position:0% +enter and understand what aspects of +this activity could map to that and + + align:start position:0% +this activity could map to that and + + + align:start position:0% +this activity could map to that and +again this pattern is reliable I just + + align:start position:0% +again this pattern is reliable I just + + + align:start position:0% +again this pattern is reliable I just +said that and it's not as if you can + + align:start position:0% +said that and it's not as if you can + + + align:start position:0% +said that and it's not as if you can +predict this pattern by just running + + align:start position:0% +predict this pattern by just running + + + align:start position:0% +predict this pattern by just running +classifiers on pixels or v1 and in fact + + align:start position:0% +classifiers on pixels or v1 and in fact + + + align:start position:0% +classifiers on pixels or v1 and in fact +I'll show you that in a minute + + align:start position:0% +I'll show you that in a minute + + + align:start position:0% +I'll show you that in a minute +but we thought there's some aspects of + + align:start position:0% +but we thought there's some aspects of + + + align:start position:0% +but we thought there's some aspects of +IT activity that would predict this and + + align:start position:0% +IT activity that would predict this and + + + align:start position:0% +IT activity that would predict this and +we wanted to try to find those aspects + + align:start position:0% +we wanted to try to find those aspects + + + align:start position:0% +we wanted to try to find those aspects +so so and again this was motivated by + + align:start position:0% +so so and again this was motivated by + + + align:start position:0% +so so and again this was motivated by +that study I showed you earlier so which + + align:start position:0% +that study I showed you earlier so which + + + align:start position:0% +that study I showed you earlier so which +part of the IT population activity could + + align:start position:0% +part of the IT population activity could + + + align:start position:0% +part of the IT population activity could +predict this behavior overall + + align:start position:0% +predict this behavior overall + + + align:start position:0% +predict this behavior overall +recognition tasks we're seeking a + + align:start position:0% +recognition tasks we're seeking a + + + align:start position:0% +recognition tasks we're seeking a +general decoding model that would work + + align:start position:0% +general decoding model that would work + + + align:start position:0% +general decoding model that would work +here's some specific tasks but we'd like + + align:start position:0% +here's some specific tasks but we'd like + + + align:start position:0% +here's some specific tasks but we'd like +it to be work over any tasks that we + + align:start position:0% +it to be work over any tasks that we + + + align:start position:0% +it to be work over any tasks that we +could imagine testing humans within this + + align:start position:0% +could imagine testing humans within this + + + align:start position:0% +could imagine testing humans within this +domain of taking 3d models putting them + + align:start position:0% +domain of taking 3d models putting them + + + align:start position:0% +domain of taking 3d models putting them +under variation work over that entire + + align:start position:0% +under variation work over that entire + + + align:start position:0% +under variation work over that entire +domain that was what we're hoping to do + + align:start position:0% +domain that was what we're hoping to do + + + align:start position:0% +domain that was what we're hoping to do +so again I'll briefly take you through + + align:start position:0% +so again I'll briefly take you through + + + align:start position:0% +so again I'll briefly take you through +this because I already showed you this + + align:start position:0% +this because I already showed you this + + + align:start position:0% +this because I already showed you this +earlier again we previously shown that + + align:start position:0% +earlier again we previously shown that + + + align:start position:0% +earlier again we previously shown that +you can kind of take this kind of state + + align:start position:0% +you can kind of take this kind of state + + + align:start position:0% +you can kind of take this kind of state +space and say hey can you separate + + align:start position:0% +space and say hey can you separate + + + align:start position:0% +space and say hey can you separate +images of faces from non faces using + + align:start position:0% +images of faces from non faces using + + + align:start position:0% +images of faces from non faces using +this simple linear classifiers which are + + align:start position:0% +this simple linear classifiers which are + + + align:start position:0% +this simple linear classifiers which are +essentially weighted stumps on the IT + + align:start position:0% +essentially weighted stumps on the IT + + + align:start position:0% +essentially weighted stumps on the IT +activity and now we wanted to ask could + + align:start position:0% +activity and now we wanted to ask could + + + align:start position:0% +activity and now we wanted to ask could +this predict human behavioral face + + align:start position:0% +this predict human behavioral face + + + align:start position:0% +this predict human behavioral face +performance and monkey because again + + align:start position:0% +performance and monkey because again + + + align:start position:0% +performance and monkey because again +they're very similar and not only would + + align:start position:0% +they're very similar and not only would + + + align:start position:0% +they're very similar and not only would +this class of mob decoding models that + + align:start position:0% +this class of mob decoding models that + + + align:start position:0% +this class of mob decoding models that +was motivated by that earlier work + + align:start position:0% +was motivated by that earlier work + + + align:start position:0% +was motivated by that earlier work +predict this task but way to predict car + + align:start position:0% +predict this task but way to predict car + + + align:start position:0% +predict this task but way to predict car +detection with the same model predict + + align:start position:0% +detection with the same model predict + + + align:start position:0% +detection with the same model predict +car one versus car - that's a + + align:start position:0% +car one versus car - that's a + + + align:start position:0% +car one versus car - that's a +subordinate task and all such tasks + + align:start position:0% +subordinate task and all such tasks + + + align:start position:0% +subordinate task and all such tasks +again over the whole domain can you take + + align:start position:0% +again over the whole domain can you take + + + align:start position:0% +again over the whole domain can you take +a same decoding strategy and take the + + align:start position:0% +a same decoding strategy and take the + + + align:start position:0% +a same decoding strategy and take the +data and say I'm gonna just learn on a + + align:start position:0% +data and say I'm gonna just learn on a + + + align:start position:0% +data and say I'm gonna just learn on a +certain number of training examples + + align:start position:0% +certain number of training examples + + + align:start position:0% +certain number of training examples +build a classifier and then I'll say + + align:start position:0% +build a classifier and then I'll say + + + align:start position:0% +build a classifier and then I'll say +that's my model of how the human does + + align:start position:0% +that's my model of how the human does + + + align:start position:0% +that's my model of how the human does +every one of these tasks and if that's + + align:start position:0% +every one of these tasks and if that's + + + align:start position:0% +every one of these tasks and if that's +true then it should perfectly predict + + align:start position:0% +true then it should perfectly predict + + + align:start position:0% +true then it should perfectly predict +that pattern of performance that I just + + align:start position:0% +that pattern of performance that I just + + + align:start position:0% +that pattern of performance that I just +showed you earlier and so here was again + + align:start position:0% +showed you earlier and so here was again + + + align:start position:0% +showed you earlier and so here was again +this was the working hypothesis + + align:start position:0% +this was the working hypothesis + + + align:start position:0% +this was the working hypothesis +passively evoke spike rates using single + + align:start position:0% +passively evoke spike rates using single + + + align:start position:0% +passively evoke spike rates using single +fixed time scale that are spatially + + align:start position:0% +fixed time scale that are spatially + + + align:start position:0% +fixed time scale that are spatially +distributed because they're sampled over + + align:start position:0% +distributed because they're sampled over + + + align:start position:0% +distributed because they're sampled over +i.t are seeing over a single fixed + + align:start position:0% +i.t are seeing over a single fixed + + + align:start position:0% +i.t are seeing over a single fixed +number of non-human of non-human primate + + align:start position:0% +number of non-human of non-human primate + + + align:start position:0% +number of non-human of non-human primate +cortex so a single number of neurons and + + align:start position:0% +cortex so a single number of neurons and + + + align:start position:0% +cortex so a single number of neurons and +learn from a reasonable number of + + align:start position:0% +learn from a reasonable number of + + + align:start position:0% +learn from a reasonable number of +trained + + align:start position:0% +trained + + + align:start position:0% +trained +so all of that is a decoding class of + + align:start position:0% +so all of that is a decoding class of + + + align:start position:0% +so all of that is a decoding class of +models that we thought might work and if + + align:start position:0% +models that we thought might work and if + + + align:start position:0% +models that we thought might work and if +this is correct this is what I just said + + align:start position:0% +this is correct this is what I just said + + + align:start position:0% +this is correct this is what I just said +it should predict the behavioral data + + align:start position:0% +it should predict the behavioral data + + + align:start position:0% +it should predict the behavioral data +that we collect for example that T Prime + + align:start position:0% +that we collect for example that T Prime + + + align:start position:0% +that we collect for example that T Prime +data I just showed you but also more + + align:start position:0% +data I just showed you but also more + + + align:start position:0% +data I just showed you but also more +fine-grained behavioral data in + + align:start position:0% +fine-grained behavioral data in + + + align:start position:0% +fine-grained behavioral data in +principle so I wanted to step back to + + align:start position:0% +principle so I wanted to step back to + + + align:start position:0% +principle so I wanted to step back to +make it clear that it's not obvious that + + align:start position:0% +make it clear that it's not obvious that + + + align:start position:0% +make it clear that it's not obvious that +this should work right I mean it depends + + align:start position:0% +this should work right I mean it depends + + + align:start position:0% +this should work right I mean it depends +we in the audience I get people on + + align:start position:0% +we in the audience I get people on + + + align:start position:0% +we in the audience I get people on +completely different sides of this + + align:start position:0% +completely different sides of this + + + align:start position:0% +completely different sides of this +whether this should work or not so you + + align:start position:0% +whether this should work or not so you + + + align:start position:0% +whether this should work or not so you +know one thing is like well look it's + + align:start position:0% +know one thing is like well look it's + + + align:start position:0% +know one thing is like well look it's +passively evoke you heard Gabrielle say + + align:start position:0% +passively evoke you heard Gabrielle say + + + align:start position:0% +passively evoke you heard Gabrielle say +well you didn't like passive tasks so + + align:start position:0% +well you didn't like passive tasks so + + + align:start position:0% +well you didn't like passive tasks so +and I agree with that in the ideal world + + align:start position:0% +and I agree with that in the ideal world + + + align:start position:0% +and I agree with that in the ideal world +the EMA will be actively doing the tasks + + align:start position:0% +the EMA will be actively doing the tasks + + + align:start position:0% +the EMA will be actively doing the tasks +and then you'd say oh I measure while + + align:start position:0% +and then you'd say oh I measure while + + + align:start position:0% +and then you'd say oh I measure while +the animals doing the test that's gonna + + align:start position:0% +the animals doing the test that's gonna + + + align:start position:0% +the animals doing the test that's gonna +be your best chance of prediction but we + + align:start position:0% +be your best chance of prediction but we + + + align:start position:0% +be your best chance of prediction but we +also saw earlier that that passively + + align:start position:0% +also saw earlier that that passively + + + align:start position:0% +also saw earlier that that passively +evoke monkey still you know nobody would + + align:start position:0% +evoke monkey still you know nobody would + + + align:start position:0% +evoke monkey still you know nobody would +argue that a passively evoked retinal + + align:start position:0% +argue that a passively evoked retinal + + + align:start position:0% +argue that a passively evoked retinal +data is is not going to be somewhat + + align:start position:0% +data is is not going to be somewhat + + + align:start position:0% +data is is not going to be somewhat +applicable division and you know the + + align:start position:0% +applicable division and you know the + + + align:start position:0% +applicable division and you know the +question is how much of those arousal + + align:start position:0% +question is how much of those arousal + + + align:start position:0% +question is how much of those arousal +effects show up in a place like IIT + + align:start position:0% +effects show up in a place like IIT + + + align:start position:0% +effects show up in a place like IIT +cortex which is typically high typically + + align:start position:0% +cortex which is typically high typically + + + align:start position:0% +cortex which is typically high typically +which is high up in the ventral stream + + align:start position:0% +which is high up in the ventral stream + + + align:start position:0% +which is high up in the ventral stream +so you you know you could argue both + + align:start position:0% +so you you know you could argue both + + + align:start position:0% +so you you know you could argue both +sides of this but it's possible that + + align:start position:0% +sides of this but it's possible that + + + align:start position:0% +sides of this but it's possible that +attentional arousal meckel's are needed + + align:start position:0% +attentional arousal meckel's are needed + + + align:start position:0% +attentional arousal meckel's are needed +to make this a good predictive linkage + + align:start position:0% +to make this a good predictive linkage + + + align:start position:0% +to make this a good predictive linkage +between act to sort of activate IT in + + align:start position:0% +between act to sort of activate IT in + + + align:start position:0% +between act to sort of activate IT in +the sub crude way if you like some + + align:start position:0% +the sub crude way if you like some + + + align:start position:0% +the sub crude way if you like some +people have pointed out that you need + + align:start position:0% +people have pointed out that you need + + + align:start position:0% +people have pointed out that you need +the trial by trial coordinated spike + + align:start position:0% +the trial by trial coordinated spike + + + align:start position:0% +the trial by trial coordinated spike +timing structure to actually make good + + align:start position:0% +timing structure to actually make good + + + align:start position:0% +timing structure to actually make good +predictions that those are critical some + + align:start position:0% +predictions that those are critical some + + + align:start position:0% +predictions that those are critical some +people have pointed out that you have to + + align:start position:0% +people have pointed out that you have to + + + align:start position:0% +people have pointed out that you have to +kind of assign different parts of IT to + + align:start position:0% +kind of assign different parts of IT to + + + align:start position:0% +kind of assign different parts of IT to +particular roles which is a prior on the + + align:start position:0% +particular roles which is a prior on the + + + align:start position:0% +particular roles which is a prior on the +decoding space for instance that you + + align:start position:0% +decoding space for instance that you + + + align:start position:0% +decoding space for instance that you +could believe that biologically and + + align:start position:0% +could believe that biologically and + + + align:start position:0% +could believe that biologically and +animals born is some tissue that's going + + align:start position:0% +animals born is some tissue that's going + + + align:start position:0% +animals born is some tissue that's going +to be dedicated to faces you have to + + align:start position:0% +to be dedicated to faces you have to + + + align:start position:0% +to be dedicated to faces you have to +wire the neurons downstream to that + + align:start position:0% +wire the neurons downstream to that + + + align:start position:0% +wire the neurons downstream to that +tissue and that means you're gonna + + align:start position:0% +tissue and that means you're gonna + + + align:start position:0% +tissue and that means you're gonna +restrict the decoding space rather than + + align:start position:0% +restrict the decoding space rather than + + + align:start position:0% +restrict the decoding space rather than +just letting them learn from the space + + align:start position:0% +just letting them learn from the space + + + align:start position:0% +just letting them learn from the space +of ideas if they collected samples off + + align:start position:0% +of ideas if they collected samples off + + + align:start position:0% +of ideas if they collected samples off +of ayala by T so I think some people + + align:start position:0% +of ayala by T so I think some people + + + align:start position:0% +of ayala by T so I think some people +implicitly believe that even if it's not + + align:start position:0% +implicitly believe that even if it's not + + + align:start position:0% +implicitly believe that even if it's not +stated quite that way + + align:start position:0% +stated quite that way + + + align:start position:0% +stated quite that way +I T does not directly under lab degrees + + align:start position:0% +I T does not directly under lab degrees + + + align:start position:0% +I T does not directly under lab degrees +you could imagine that I mean it's not + + align:start position:0% +you could imagine that I mean it's not + + + align:start position:0% +you could imagine that I mean it's not +for sure known in some lesions of I T + + align:start position:0% +for sure known in some lesions of I T + + + align:start position:0% +for sure known in some lesions of I T +don't produce deficits in recognition + + align:start position:0% +don't produce deficits in recognition + + + align:start position:0% +don't produce deficits in recognition +that's a possibility maybe need too many + + align:start position:0% +that's a possibility maybe need too many + + + align:start position:0% +that's a possibility maybe need too many +training examples monkey neural codes + + align:start position:0% +training examples monkey neural codes + + + align:start position:0% +training examples monkey neural codes +cannot explain human behavior you know + + align:start position:0% +cannot explain human behavior you know + + + align:start position:0% +cannot explain human behavior you know +may it again but I've already showed you + + align:start position:0% +may it again but I've already showed you + + + align:start position:0% +may it again but I've already showed you +monkeys and humans are very similar so + + align:start position:0% +monkeys and humans are very similar so + + + align:start position:0% +monkeys and humans are very similar so +these are reason reasons that you might + + align:start position:0% +these are reason reasons that you might + + + align:start position:0% +these are reason reasons that you might +say this is negative might not work and + + align:start position:0% +say this is negative might not work and + + + align:start position:0% +say this is negative might not work and +probably already have guests and I'm + + align:start position:0% +probably already have guests and I'm + + + align:start position:0% +probably already have guests and I'm +telling all these negatives because it + + align:start position:0% +telling all these negatives because it + + + align:start position:0% +telling all these negatives because it +turns out this simple thing works quite + + align:start position:0% +turns out this simple thing works quite + + + align:start position:0% +turns out this simple thing works quite +well for the gray + + align:start position:0% +well for the gray + + + align:start position:0% +well for the gray +behavior that I've shown you so far and + + align:start position:0% +behavior that I've shown you so far and + + + align:start position:0% +behavior that I've shown you so far and +here's my evidence of that so this is + + align:start position:0% +here's my evidence of that so this is + + + align:start position:0% +here's my evidence of that so this is +actual behavioral performance out of + + align:start position:0% +actual behavioral performance out of + + + align:start position:0% +actual behavioral performance out of +humans that I showed you earlier this is + + align:start position:0% +humans that I showed you earlier this is + + + align:start position:0% +humans that I showed you earlier this is +mean D prime this is the predicted + + align:start position:0% +mean D prime this is the predicted + + + align:start position:0% +mean D prime this is the predicted +behavioral performance of taking a + + align:start position:0% +behavioral performance of taking a + + + align:start position:0% +behavioral performance of taking a +classifier reading from that IT + + align:start position:0% +classifier reading from that IT + + + align:start position:0% +classifier reading from that IT +population data they shown you which + + align:start position:0% +population data they shown you which + + + align:start position:0% +population data they shown you which +gives a predicted D Prime + + align:start position:0% +gives a predicted D Prime + + + align:start position:0% +gives a predicted D Prime +here's we first chose a decoder we had + + align:start position:0% +here's we first chose a decoder we had + + + align:start position:0% +here's we first chose a decoder we had +to match things like the number of + + align:start position:0% +to match things like the number of + + + align:start position:0% +to match things like the number of +neurons we had to get it in the ballpark + + align:start position:0% +neurons we had to get it in the ballpark + + + align:start position:0% +neurons we had to get it in the ballpark +so because again there's a free variable + + align:start position:0% +so because again there's a free variable + + + align:start position:0% +so because again there's a free variable +as I'll show you earlier is at least 1 + + align:start position:0% +as I'll show you earlier is at least 1 + + + align:start position:0% +as I'll show you earlier is at least 1 +but for now let's think of matching the + + align:start position:0% +but for now let's think of matching the + + + align:start position:0% +but for now let's think of matching the +number of neurons to get you near the + + align:start position:0% +number of neurons to get you near the + + + align:start position:0% +number of neurons to get you near the +diagonal so that you have a sufficient + + align:start position:0% +diagonal so that you have a sufficient + + + align:start position:0% +diagonal so that you have a sufficient +number of neural recordings to say how + + align:start position:0% +number of neural recordings to say how + + + align:start position:0% +number of neural recordings to say how +well do you do on a face detection task + + align:start position:0% +well do you do on a face detection task + + + align:start position:0% +well do you do on a face detection task +and then here's all the other tasks this + + align:start position:0% +and then here's all the other tasks this + + + align:start position:0% +and then here's all the other tasks this +is those 64 points that I showed you + + align:start position:0% +is those 64 points that I showed you + + + align:start position:0% +is those 64 points that I showed you +earlier here's some examples is like + + align:start position:0% +earlier here's some examples is like + + + align:start position:0% +earlier here's some examples is like +fruit versus other things car versus + + align:start position:0% +fruit versus other things car versus + + + align:start position:0% +fruit versus other things car versus +other things and you should see that all + + align:start position:0% +other things and you should see that all + + + align:start position:0% +other things and you should see that all +these points kind of line up along this + + align:start position:0% +these points kind of line up along this + + + align:start position:0% +these points kind of line up along this +diagonal which says wow this is actually + + align:start position:0% +diagonal which says wow this is actually + + + align:start position:0% +diagonal which says wow this is actually +quite predictive that I can take this + + align:start position:0% +quite predictive that I can take this + + + align:start position:0% +quite predictive that I can take this +simple thing and predict all the stuff + + align:start position:0% +simple thing and predict all the stuff + + + align:start position:0% +simple thing and predict all the stuff +that we've collected so far and so let + + align:start position:0% +that we've collected so far and so let + + + align:start position:0% +that we've collected so far and so let +me now kind of be more concrete about + + align:start position:0% +me now kind of be more concrete about + + + align:start position:0% +me now kind of be more concrete about +what is the inferred neural mechanism + + align:start position:0% +what is the inferred neural mechanism + + + align:start position:0% +what is the inferred neural mechanism +that we're testing here well I'll show + + align:start position:0% +that we're testing here well I'll show + + + align:start position:0% +that we're testing here well I'll show +you in a minute this is for each new + + align:start position:0% +you in a minute this is for each new + + + align:start position:0% +you in a minute this is for each new +object we think what happens is some + + align:start position:0% +object we think what happens is some + + + align:start position:0% +object we think what happens is some +downstream observer a downstream neuron + + align:start position:0% +downstream observer a downstream neuron + + + align:start position:0% +downstream observer a downstream neuron +randomly samples roughly 50,000 single + + align:start position:0% +randomly samples roughly 50,000 single + + + align:start position:0% +randomly samples roughly 50,000 single +neurons especially distributed over all + + align:start position:0% +neurons especially distributed over all + + + align:start position:0% +neurons especially distributed over all +of IT not biased to any compartments + + align:start position:0% +of IT not biased to any compartments + + + align:start position:0% +of IT not biased to any compartments +listens to each IT sites lab that when I + + align:start position:0% +listens to each IT sites lab that when I + + + align:start position:0% +listens to each IT sites lab that when I +say listen in this case we think could + + align:start position:0% +say listen in this case we think could + + + align:start position:0% +say listen in this case we think could +average over 100 milliseconds we're not + + align:start position:0% +average over 100 milliseconds we're not + + + align:start position:0% +average over 100 milliseconds we're not +sure about this this is just the version + + align:start position:0% +sure about this this is just the version + + + align:start position:0% +sure about this this is just the version +that's shown here learn an appropriate + + align:start position:0% +that's shown here learn an appropriate + + + align:start position:0% +that's shown here learn an appropriate +weighted sum of those IT spiking and + + align:start position:0% +weighted sum of those IT spiking and + + + align:start position:0% +weighted sum of those IT spiking and +then listen to 10% that's basically once + + align:start position:0% +then listen to 10% that's basically once + + + align:start position:0% +then listen to 10% that's basically once +you learn there's heavily weighted about + + align:start position:0% +you learn there's heavily weighted about + + + align:start position:0% +you learn there's heavily weighted about +10% of the I team of the IT neurons are + + align:start position:0% +10% of the I team of the IT neurons are + + + align:start position:0% +10% of the I team of the IT neurons are +heavily weighted for each of the tasks + + align:start position:0% +heavily weighted for each of the tasks + + + align:start position:0% +heavily weighted for each of the tasks +that's just an observation that we have + + align:start position:0% +that's just an observation that we have + + + align:start position:0% +that's just an observation that we have +in our data but this is trying to map it + + align:start position:0% +in our data but this is trying to map it + + + align:start position:0% +in our data but this is trying to map it +to neuroscientist language from these + + align:start position:0% +to neuroscientist language from these + + + align:start position:0% +to neuroscientist language from these +decoder versions out of IT so what that + + align:start position:0% +decoder versions out of IT so what that + + + align:start position:0% +decoder versions out of IT so what that +is is a model that says learn weighted + + align:start position:0% +is is a model that says learn weighted + + + align:start position:0% +is is a model that says learn weighted +sums of 50 thousand random average 100 + + align:start position:0% +sums of 50 thousand random average 100 + + + align:start position:0% +sums of 50 thousand random average 100 +milliseconds single unit responses + + align:start position:0% +milliseconds single unit responses + + + align:start position:0% +milliseconds single unit responses +distribute over all I T so a bunch of + + align:start position:0% +distribute over all I T so a bunch of + + + align:start position:0% +distribute over all I T so a bunch of +stuff in here that's what your your hype + + align:start position:0% +stuff in here that's what your your hype + + + align:start position:0% +stuff in here that's what your your hype +your models is sort of encapsulating + + align:start position:0% +your models is sort of encapsulating + + + align:start position:0% +your models is sort of encapsulating +that's still too long so I made a little + + align:start position:0% +that's still too long so I made a little + + + align:start position:0% +that's still too long so I made a little +acronym out of that and that caught laws + + align:start position:0% +acronym out of that and that caught laws + + + align:start position:0% +acronym out of that and that caught laws +of RAD IT decoding mechanism right so + + align:start position:0% +of RAD IT decoding mechanism right so + + + align:start position:0% +of RAD IT decoding mechanism right so +this is just to say there's a hypothesis + + align:start position:0% +this is just to say there's a hypothesis + + + align:start position:0% +this is just to say there's a hypothesis +of how everything might work that now + + align:start position:0% +of how everything might work that now + + + align:start position:0% +of how everything might work that now +can be make predictions for other + + align:start position:0% +can be make predictions for other + + + align:start position:0% +can be make predictions for other +objects and could potentially be + + align:start position:0% +objects and could potentially be + + + align:start position:0% +objects and could potentially be +falsified so so far this model works + + align:start position:0% +falsified so so far this model works + + + align:start position:0% +falsified so so far this model works +quite well over these tasks + + align:start position:0% +quite well over these tasks + + + align:start position:0% +quite well over these tasks +and in fact the correlation is 0.92 you + + align:start position:0% +and in fact the correlation is 0.92 you + + + align:start position:0% +and in fact the correlation is 0.92 you +might look at this and say oh it's not + + align:start position:0% +might look at this and say oh it's not + + + align:start position:0% +might look at this and say oh it's not +perfect but it turns out that that's + + align:start position:0% +perfect but it turns out that that's + + + align:start position:0% +perfect but it turns out that that's +about the level that which humans differ + + align:start position:0% +about the level that which humans differ + + + align:start position:0% +about the level that which humans differ +from each other so it's passing a Turing + + align:start position:0% +from each other so it's passing a Turing + + + align:start position:0% +from each other so it's passing a Turing +test that it + + align:start position:0% +test that it + + + align:start position:0% +test that it +this mechanism read off of the monkey I + + align:start position:0% +this mechanism read off of the monkey I + + + align:start position:0% +this mechanism read off of the monkey I +T is hides in the distribution of the + + align:start position:0% +T is hides in the distribution of the + + + align:start position:0% +T is hides in the distribution of the +human population that we're asking also + + align:start position:0% +human population that we're asking also + + + align:start position:0% +human population that we're asking also +perform these same tasks so it can't be + + align:start position:0% +perform these same tasks so it can't be + + + align:start position:0% +perform these same tasks so it can't be +distinguished from being a human on + + align:start position:0% +distinguished from being a human on + + + align:start position:0% +distinguished from being a human on +these in these tasks you guys I tell you + + align:start position:0% +these in these tasks you guys I tell you + + + align:start position:0% +these in these tasks you guys I tell you +watch ex machina wasn't that a movie I + + align:start position:0% +watch ex machina wasn't that a movie I + + + align:start position:0% +watch ex machina wasn't that a movie I +saw doesn't pass that test it passes + + align:start position:0% +saw doesn't pass that test it passes + + + align:start position:0% +saw doesn't pass that test it passes +just this simple core recognition test + + align:start position:0% +just this simple core recognition test + + + align:start position:0% +just this simple core recognition test +but so that was a Turing test of this so + + align:start position:0% +but so that was a Turing test of this so + + + align:start position:0% +but so that was a Turing test of this so +it's okay so this is here that + + align:start position:0% +it's okay so this is here that + + + align:start position:0% +it's okay so this is here that +quantified so this is a human human + + align:start position:0% +quantified so this is a human human + + + align:start position:0% +quantified so this is a human human +consistency that's the range I just + + align:start position:0% +consistency that's the range I just + + + align:start position:0% +consistency that's the range I just +mentioned that you know you got to get + + align:start position:0% +mentioned that you know you got to get + + + align:start position:0% +mentioned that you know you got to get +into here to pass our our Turing test on + + align:start position:0% +into here to pass our our Turing test on + + + align:start position:0% +into here to pass our our Turing test on +this and that's the decoding mechanism I + + align:start position:0% +this and that's the decoding mechanism I + + + align:start position:0% +this and that's the decoding mechanism I +just showed you there's other ways of + + align:start position:0% +just showed you there's other ways of + + + align:start position:0% +just showed you there's other ways of +reading out of IT that don't pass those + + align:start position:0% +reading out of IT that don't pass those + + + align:start position:0% +reading out of IT that don't pass those +ways of reading out of v4 which we + + align:start position:0% +ways of reading out of v4 which we + + + align:start position:0% +ways of reading out of v4 which we +recorded from none of them we've tried + + align:start position:0% +recorded from none of them we've tried + + + align:start position:0% +recorded from none of them we've tried +are able to get you to this here and it + + align:start position:0% +are able to get you to this here and it + + + align:start position:0% +are able to get you to this here and it +doesn't mean v4 isn't involved before is + + align:start position:0% +doesn't mean v4 isn't involved before is + + + align:start position:0% +doesn't mean v4 isn't involved before is +the feeder to IT it just means you can't + + align:start position:0% +the feeder to IT it just means you can't + + + align:start position:0% +the feeder to IT it just means you can't +take simple decodes off of v4 and + + align:start position:0% +take simple decodes off of v4 and + + + align:start position:0% +take simple decodes off of v4 and +naturally produces pattern and that's + + align:start position:0% +naturally produces pattern and that's + + + align:start position:0% +naturally produces pattern and that's +similar for like pixels or v1 + + align:start position:0% +similar for like pixels or v1 + + + align:start position:0% +similar for like pixels or v1 +representations so lower-level + + align:start position:0% +representations so lower-level + + + align:start position:0% +representations so lower-level +representations don't naturally predict + + align:start position:0% +representations don't naturally predict + + + align:start position:0% +representations don't naturally predict +this pattern of behavior and even some + + align:start position:0% +this pattern of behavior and even some + + + align:start position:0% +this pattern of behavior and even some +computer vision codes that we tested at + + align:start position:0% +computer vision codes that we tested at + + + align:start position:0% +computer vision codes that we tested at +the time as you can see if those even + + align:start position:0% +the time as you can see if those even + + + align:start position:0% +the time as you can see if those even +though these older computer vision + + align:start position:0% +though these older computer vision + + + align:start position:0% +though these older computer vision +models didn't didn't do this but more + + align:start position:0% +models didn't didn't do this but more + + + align:start position:0% +models didn't didn't do this but more +more recent computer vision models + + align:start position:0% +more recent computer vision models + + + align:start position:0% +more recent computer vision models +actually do and I'll show you that yeah + + align:start position:0% +actually do and I'll show you that yeah + + + align:start position:0% +actually do and I'll show you that yeah +okay so this is a little bit for the + + align:start position:0% +okay so this is a little bit for the + + + align:start position:0% +okay so this is a little bit for the +aficionados to tell you how we got there + + align:start position:0% +aficionados to tell you how we got there + + + align:start position:0% +aficionados to tell you how we got there +as we increase the number of units and + + align:start position:0% +as we increase the number of units and + + + align:start position:0% +as we increase the number of units and +i.t that drives performance up so as you + + align:start position:0% +i.t that drives performance up so as you + + + align:start position:0% +i.t that drives performance up so as you +read more and more units out of IT you + + align:start position:0% +read more and more units out of IT you + + + align:start position:0% +read more and more units out of IT you +get better and better performance that's + + align:start position:0% +get better and better performance that's + + + align:start position:0% +get better and better performance that's +also true out of v4 what I'm trying to + + align:start position:0% +also true out of v4 what I'm trying to + + + align:start position:0% +also true out of v4 what I'm trying to +show you this here is it's like not the + + align:start position:0% +show you this here is it's like not the + + + align:start position:0% +show you this here is it's like not the +absolute performance that is the good + + align:start position:0% +absolute performance that is the good + + + align:start position:0% +absolute performance that is the good +thing to compare a model with actual + + align:start position:0% +thing to compare a model with actual + + + align:start position:0% +thing to compare a model with actual +behavioral data it's the pattern of + + align:start position:0% +behavioral data it's the pattern of + + + align:start position:0% +behavioral data it's the pattern of +performance which we call the + + align:start position:0% +performance which we call the + + + align:start position:0% +performance which we call the +consistency with the humans that's that + + align:start position:0% +consistency with the humans that's that + + + align:start position:0% +consistency with the humans that's that +correlation along that diagonal they + + align:start position:0% +correlation along that diagonal they + + + align:start position:0% +correlation along that diagonal they +showed you earlier that tasks that are + + align:start position:0% +showed you earlier that tasks that are + + + align:start position:0% +showed you earlier that tasks that are +hard for the models are also hard for + + align:start position:0% +hard for the models are also hard for + + + align:start position:0% +hard for the models are also hard for +the humans tests are easy for the + + align:start position:0% +the humans tests are easy for the + + + align:start position:0% +the humans tests are easy for the +u-men's are also easy for the models and + + align:start position:0% +u-men's are also easy for the models and + + + align:start position:0% +u-men's are also easy for the models and +you could imagine doing that not just at + + align:start position:0% +you could imagine doing that not just at + + + align:start position:0% +you could imagine doing that not just at +the task level but at the image level as + + align:start position:0% +the task level but at the image level as + + + align:start position:0% +the task level but at the image level as +well and anyway that's what's quantified + + align:start position:0% +well and anyway that's what's quantified + + + align:start position:0% +well and anyway that's what's quantified +here and you see that when you get up to + + align:start position:0% +here and you see that when you get up to + + + align:start position:0% +here and you see that when you get up to +around you know about a hundred I said + + align:start position:0% +around you know about a hundred I said + + + align:start position:0% +around you know about a hundred I said +you 168 recordings out of I T that this + + align:start position:0% +you 168 recordings out of I T that this + + + align:start position:0% +you 168 recordings out of I T that this +point + + align:start position:0% +point + + + align:start position:0% +point +right there's about 500 IT features and + + align:start position:0% +right there's about 500 IT features and + + + align:start position:0% +right there's about 500 IT features and +and taking you through some things that + + align:start position:0% +and taking you through some things that + + + align:start position:0% +and taking you through some things that +maybe I won't have time for that's + + align:start position:0% +maybe I won't have time for that's + + + align:start position:0% +maybe I won't have time for that's +actually how we approximate that fifty + + align:start position:0% +actually how we approximate that fifty + + + align:start position:0% +actually how we approximate that fifty +thousand single IT neuron number that's + + align:start position:0% +thousand single IT neuron number that's + + + align:start position:0% +thousand single IT neuron number that's +an inference from our data based on if + + align:start position:0% +an inference from our data based on if + + + align:start position:0% +an inference from our data based on if +we didn't actually record fifty thousand + + align:start position:0% +we didn't actually record fifty thousand + + + align:start position:0% +we didn't actually record fifty thousand +single neurons but from these kind of + + align:start position:0% +single neurons but from these kind of + + + align:start position:0% +single neurons but from these kind of +plots were able to make it a pretty good + + align:start position:0% +plots were able to make it a pretty good + + + align:start position:0% +plots were able to make it a pretty good +guess that this this is this this kind + + align:start position:0% +guess that this this is this this kind + + + align:start position:0% +guess that this this is this this kind +of model right here would Purdue would + + align:start position:0% +of model right here would Purdue would + + + align:start position:0% +of model right here would Purdue would +land right there to be consistent with + + align:start position:0% +land right there to be consistent with + + + align:start position:0% +land right there to be consistent with +humans and would Matt would get the + + align:start position:0% +humans and would Matt would get the + + + align:start position:0% +humans and would Matt would get the +absolute level of performance with + + align:start position:0% +absolute level of performance with + + + align:start position:0% +absolute level of performance with +humans matched and you know the models + + align:start position:0% +humans matched and you know the models + + + align:start position:0% +humans matched and you know the models +we tried out of v4 this is one example + + align:start position:0% +we tried out of v4 this is one example + + + align:start position:0% +we tried out of v4 this is one example +of them they can get performance but + + align:start position:0% +of them they can get performance but + + + align:start position:0% +of them they can get performance but +they can never they don't match this + + align:start position:0% +they can never they don't match this + + + align:start position:0% +they can never they don't match this +pattern of performance naturally they + + align:start position:0% +pattern of performance naturally they + + + align:start position:0% +pattern of performance naturally they +over perform on some tests and + + align:start position:0% +over perform on some tests and + + + align:start position:0% +over perform on some tests and +underperform on others they sort of + + align:start position:0% +underperform on others they sort of + + + align:start position:0% +underperform on others they sort of +reveal themselves as not being + + align:start position:0% +reveal themselves as not being + + + align:start position:0% +reveal themselves as not being +human-like by being too good at some + + align:start position:0% +human-like by being too good at some + + + align:start position:0% +human-like by being too good at some +things right so that's a way to fail the + + align:start position:0% +things right so that's a way to fail the + + + align:start position:0% +things right so that's a way to fail the +Turing test okay maybe I'll skip through + + align:start position:0% +Turing test okay maybe I'll skip through + + + align:start position:0% +Turing test okay maybe I'll skip through +this is sort of the same thing this is + + align:start position:0% +this is sort of the same thing this is + + + align:start position:0% +this is sort of the same thing this is +about training examples if those are you + + align:start position:0% +about training examples if those are you + + + align:start position:0% +about training examples if those are you +guys care about this I can kind of take + + align:start position:0% +guys care about this I can kind of take + + + align:start position:0% +guys care about this I can kind of take +you through how we there's actually a + + align:start position:0% +you through how we there's actually a + + + align:start position:0% +you through how we there's actually a +family of solutions in there and I'm + + align:start position:0% +family of solutions in there and I'm + + + align:start position:0% +family of solutions in there and I'm +just telling you about one of them for + + align:start position:0% +just telling you about one of them for + + + align:start position:0% +just telling you about one of them for +simplicity so let me then just take it + + align:start position:0% +simplicity so let me then just take it + + + align:start position:0% +simplicity so let me then just take it +down to another grain so that was the + + align:start position:0% +down to another grain so that was the + + + align:start position:0% +down to another grain so that was the +pattern of performance is actually + + align:start position:0% +pattern of performance is actually + + + align:start position:0% +pattern of performance is actually +naturally predicted by this first + + align:start position:0% +naturally predicted by this first + + + align:start position:0% +naturally predicted by this first +decoding mechanism that we tried but + + align:start position:0% +decoding mechanism that we tried but + + + align:start position:0% +decoding mechanism that we tried but +what about the confusion pattern so not + + align:start position:0% +what about the confusion pattern so not + + + align:start position:0% +what about the confusion pattern so not +just the absolute D Prime's for each of + + align:start position:0% +just the absolute D Prime's for each of + + + align:start position:0% +just the absolute D Prime's for each of +these tasks but there's finer grained + + align:start position:0% +these tasks but there's finer grained + + + align:start position:0% +these tasks but there's finer grained +data like how often an animal is + + align:start position:0% +data like how often an animal is + + + align:start position:0% +data like how often an animal is +confused with a fruit or an animal is + + align:start position:0% +confused with a fruit or an animal is + + + align:start position:0% +confused with a fruit or an animal is +confused with a face these are the + + align:start position:0% +confused with a face these are the + + + align:start position:0% +confused with a face these are the +confusion pattern data here I'm sorry I + + align:start position:0% +confusion pattern data here I'm sorry I + + + align:start position:0% +confusion pattern data here I'm sorry I +don't have the color bars up all I'm + + align:start position:0% +don't have the color bars up all I'm + + + align:start position:0% +don't have the color bars up all I'm +going to need you to do is say well + + align:start position:0% +going to need you to do is say well + + + align:start position:0% +going to need you to do is say well +these are the confusion patterns that we + + align:start position:0% +these are the confusion patterns that we + + + align:start position:0% +these are the confusion patterns that we +are predicted and this is what this is + + align:start position:0% +are predicted and this is what this is + + + align:start position:0% +are predicted and this is what this is +the predicted confusion matter and if I + + align:start position:0% +the predicted confusion matter and if I + + + align:start position:0% +the predicted confusion matter and if I +gave the the Machine the I T these these + + align:start position:0% +gave the the Machine the I T these these + + + align:start position:0% +gave the the Machine the I T these these +ground truth labels and it predicts this + + align:start position:0% +ground truth labels and it predicts this + + + align:start position:0% +ground truth labels and it predicts this +this is what actually happened in human + + align:start position:0% +this is what actually happened in human + + + align:start position:0% +this is what actually happened in human +data and what I want you to sort of look + + align:start position:0% +data and what I want you to sort of look + + + align:start position:0% +data and what I want you to sort of look +at this and this and say they're + + align:start position:0% +at this and this and say they're + + + align:start position:0% +at this and this and say they're +actually look quite similar they're + + align:start position:0% +actually look quite similar they're + + + align:start position:0% +actually look quite similar they're +noise corrected correlation is 0.91 so + + align:start position:0% +noise corrected correlation is 0.91 so + + + align:start position:0% +noise corrected correlation is 0.91 so +we were still quite good at predicting + + align:start position:0% +we were still quite good at predicting + + + align:start position:0% +we were still quite good at predicting +confusion patterns although this did not + + align:start position:0% +confusion patterns although this did not + + + align:start position:0% +confusion patterns although this did not +hold up fully we're only at point six + + align:start position:0% +hold up fully we're only at point six + + + align:start position:0% +hold up fully we're only at point six +eight I say only some people would say + + align:start position:0% +eight I say only some people would say + + + align:start position:0% +eight I say only some people would say +this is success we're only a point six + + align:start position:0% +this is success we're only a point six + + + align:start position:0% +this is success we're only a point six +eight on high variation so there's a + + align:start position:0% +eight on high variation so there's a + + + align:start position:0% +eight on high variation so there's a +failure here of the model that isn't + + align:start position:0% +failure here of the model that isn't + + + align:start position:0% +failure here of the model that isn't +should be at one because it's noise + + align:start position:0% +should be at one because it's noise + + + align:start position:0% +should be at one because it's noise +corrected so there's something about + + align:start position:0% +corrected so there's something about + + + align:start position:0% +corrected so there's something about +this that's not quite right at + + align:start position:0% +this that's not quite right at + + + align:start position:0% +this that's not quite right at +predicting the confusion patterns of + + align:start position:0% +predicting the confusion patterns of + + + align:start position:0% +predicting the confusion patterns of +humans at high variation images and that + + align:start position:0% +humans at high variation images and that + + + align:start position:0% +humans at high variation images and that +to us that's an opening to push forward + + align:start position:0% +to us that's an opening to push forward + + + align:start position:0% +to us that's an opening to push forward +right so this is a strategy going + + align:start position:0% +right so this is a strategy going + + + align:start position:0% +right so this is a strategy going +forward as we have an initial guess + + align:start position:0% +forward as we have an initial guess + + + align:start position:0% +forward as we have an initial guess +how you read out of IT it looks pretty + + align:start position:0% +how you read out of IT it looks pretty + + + align:start position:0% +how you read out of IT it looks pretty +good for a first grain test but now we + + align:start position:0% +good for a first grain test but now we + + + align:start position:0% +good for a first grain test but now we +can turn the crank harder we need more + + align:start position:0% +can turn the crank harder we need more + + + align:start position:0% +can turn the crank harder we need more +neural data we need more of + + align:start position:0% +neural data we need more of + + + align:start position:0% +neural data we need more of +psychophysics finer grain measurements + + align:start position:0% +psychophysics finer grain measurements + + + align:start position:0% +psychophysics finer grain measurements +distinguished among not just say I t's + + align:start position:0% +distinguished among not just say I t's + + + align:start position:0% +distinguished among not just say I t's +better than v4 or those other + + align:start position:0% +better than v4 or those other + + + align:start position:0% +better than v4 or those other +representations but what exactly about + + align:start position:0% +representations but what exactly about + + + align:start position:0% +representations but what exactly about +the IT representation is it a hundred + + align:start position:0% +the IT representation is it a hundred + + + align:start position:0% +the IT representation is it a hundred +milliseconds what timescale maybe those + + align:start position:0% +milliseconds what timescale maybe those + + + align:start position:0% +milliseconds what timescale maybe those +synchronous codes do matter some of + + align:start position:0% +synchronous codes do matter some of + + + align:start position:0% +synchronous codes do matter some of +those things that I put on there earlier + + align:start position:0% +those things that I put on there earlier + + + align:start position:0% +those things that I put on there earlier +might start to matter when we push the + + align:start position:0% +might start to matter when we push the + + + align:start position:0% +might start to matter when we push the +code push this even further so what I + + align:start position:0% +code push this even further so what I + + + align:start position:0% +code push this even further so what I +take home here is that you do quite well + + align:start position:0% +take home here is that you do quite well + + + align:start position:0% +take home here is that you do quite well +with this first-order rate code reads + + align:start position:0% +with this first-order rate code reads + + + align:start position:0% +with this first-order rate code reads +out of IT but now there's an opportunity + + align:start position:0% +out of IT but now there's an opportunity + + + align:start position:0% +out of IT but now there's an opportunity +to try to dig in and say well what plot + + align:start position:0% +to try to dig in and say well what plot + + + align:start position:0% +to try to dig in and say well what plot +point did they break down and what kind + + align:start position:0% +point did they break down and what kind + + + align:start position:0% +point did they break down and what kind +of decoding models are you going to + + align:start position:0% +of decoding models are you going to + + + align:start position:0% +of decoding models are you going to +replace them with and that's what we're + + align:start position:0% +replace them with and that's what we're + + + align:start position:0% +replace them with and that's what we're +trying to do I've told you that IT does + + align:start position:0% +trying to do I've told you that IT does + + + align:start position:0% +trying to do I've told you that IT does +good at identity but remember I said + + align:start position:0% +good at identity but remember I said + + + align:start position:0% +good at identity but remember I said +earlier on remember I show you as + + align:start position:0% +earlier on remember I show you as + + + align:start position:0% +earlier on remember I show you as +manifolds and so this is other latent + + align:start position:0% +manifolds and so this is other latent + + + align:start position:0% +manifolds and so this is other latent +variables like position and scale and I + + align:start position:0% +variables like position and scale and I + + + align:start position:0% +variables like position and scale and I +said those don't get thrown away they + + align:start position:0% +said those don't get thrown away they + + + align:start position:0% +said those don't get thrown away they +just get unwrapped right remember that + + align:start position:0% +just get unwrapped right remember that + + + align:start position:0% +just get unwrapped right remember that +manifold picture I showed earlier and so + + align:start position:0% +manifold picture I showed earlier and so + + + align:start position:0% +manifold picture I showed earlier and so +one of the things we've been doing + + align:start position:0% +one of the things we've been doing + + + align:start position:0% +one of the things we've been doing +recently is asking because we built + + align:start position:0% +recently is asking because we built + + + align:start position:0% +recently is asking because we built +these images we know these other latent + + align:start position:0% +these images we know these other latent + + + align:start position:0% +these images we know these other latent +variables like position imposed that was + + align:start position:0% +variables like position imposed that was + + + align:start position:0% +variables like position imposed that was +one of the advantages of building the + + align:start position:0% +one of the advantages of building the + + + align:start position:0% +one of the advantages of building the +images this way and we've been asking + + align:start position:0% +images this way and we've been asking + + + align:start position:0% +images this way and we've been asking +how well IT encodes those other latent + + align:start position:0% +how well IT encodes those other latent + + + align:start position:0% +how well IT encodes those other latent +variables about the pose of the object + + align:start position:0% +variables about the pose of the object + + + align:start position:0% +variables about the pose of the object +the position of the object and to make + + align:start position:0% +the position of the object and to make + + + align:start position:0% +the position of the object and to make +let me just sort of skip through the to + + align:start position:0% +let me just sort of skip through the to + + + align:start position:0% +let me just sort of skip through the to +make a long story short IT actually + + align:start position:0% +make a long story short IT actually + + + align:start position:0% +make a long story short IT actually +encodes not only has information about + + align:start position:0% +encodes not only has information about + + + align:start position:0% +encodes not only has information about +these kind of variables which is really + + align:start position:0% +these kind of variables which is really + + + align:start position:0% +these kind of variables which is really +not surprising because others have shown + + align:start position:0% +not surprising because others have shown + + + align:start position:0% +not surprising because others have shown +that there's information about those + + align:start position:0% +that there's information about those + + + align:start position:0% +that there's information about those +kind of things before but that's sort of + + align:start position:0% +kind of things before but that's sort of + + + align:start position:0% +kind of things before but that's sort of +what's on here in everything what I'm + + align:start position:0% +what's on here in everything what I'm + + + align:start position:0% +what's on here in everything what I'm +showing here is here's ITV for simulated + + align:start position:0% +showing here is here's ITV for simulated + + + align:start position:0% +showing here is here's ITV for simulated +v1 in pixels and it always everything + + align:start position:0% +v1 in pixels and it always everything + + + align:start position:0% +v1 in pixels and it always everything +goes up along the ventral stream for the + + align:start position:0% +goes up along the ventral stream for the + + + align:start position:0% +goes up along the ventral stream for the +other variables which may be + + align:start position:0% +other variables which may be + + + align:start position:0% +other variables which may be +non-intuitive to some of you I mean + + align:start position:0% +non-intuitive to some of you I mean + + + align:start position:0% +non-intuitive to some of you I mean +because position is supposed to be v1 + + align:start position:0% +because position is supposed to be v1 + + + align:start position:0% +because position is supposed to be v1 +the position of an object and a complex + + align:start position:0% +the position of an object and a complex + + + align:start position:0% +the position of an object and a complex +background it's better at IT that's one + + align:start position:0% +background it's better at IT that's one + + + align:start position:0% +background it's better at IT that's one +example but met all these latent + + align:start position:0% +example but met all these latent + + + align:start position:0% +example but met all these latent +variables go up along the ventral stream + + align:start position:0% +variables go up along the ventral stream + + + align:start position:0% +variables go up along the ventral stream +in terms of their ease of decoding but + + align:start position:0% +in terms of their ease of decoding but + + + align:start position:0% +in terms of their ease of decoding but +what I'm most excited about is that if + + align:start position:0% +what I'm most excited about is that if + + + align:start position:0% +what I'm most excited about is that if +you do this comparison with humans again + + align:start position:0% +you do this comparison with humans again + + + align:start position:0% +you do this comparison with humans again +you actually get this again pretty + + align:start position:0% +you actually get this again pretty + + + align:start position:0% +you actually get this again pretty +decent not quite as tight correlation + + align:start position:0% +decent not quite as tight correlation + + + align:start position:0% +decent not quite as tight correlation +between the human behavioral performance + + align:start position:0% +between the human behavioral performance + + + align:start position:0% +between the human behavioral performance +on making estimates of those other + + align:start position:0% +on making estimates of those other + + + align:start position:0% +on making estimates of those other +latent variables and the predicted + + align:start position:0% +latent variables and the predicted + + + align:start position:0% +latent variables and the predicted +behavioral performance out of IT and + + align:start position:0% +behavioral performance out of IT and + + + align:start position:0% +behavioral performance out of IT and +they get much better correlate + + align:start position:0% +they get much better correlate + + + align:start position:0% +they get much better correlate +it's not perfect so again there's some + + align:start position:0% +it's not perfect so again there's some + + + align:start position:0% +it's not perfect so again there's some +gap you're some failure of understanding + + align:start position:0% +gap you're some failure of understanding + + + align:start position:0% +gap you're some failure of understanding +but much better than if you read out a + + align:start position:0% +but much better than if you read out a + + + align:start position:0% +but much better than if you read out a +v4 v1 or pixels so this says that the + + align:start position:0% +v4 v1 or pixels so this says that the + + + align:start position:0% +v4 v1 or pixels so this says that the +representation again isn't just an + + align:start position:0% +representation again isn't just an + + + align:start position:0% +representation again isn't just an +identity thing it seems like this could + + align:start position:0% +identity thing it seems like this could + + + align:start position:0% +identity thing it seems like this could +be representation to underlie some of + + align:start position:0% +be representation to underlie some of + + + align:start position:0% +be representation to underlie some of +these other judgments at least at the + + align:start position:0% +these other judgments at least at the + + + align:start position:0% +these other judgments at least at the +central 10° for sort of foreground + + align:start position:0% +central 10° for sort of foreground + + + align:start position:0% +central 10° for sort of foreground +objects as we've been measuring here + + align:start position:0% +objects as we've been measuring here + + + align:start position:0% +objects as we've been measuring here +that's the don't worry about the details + + align:start position:0% +that's the don't worry about the details + + + align:start position:0% +that's the don't worry about the details +on here that's the upshot of what I'm + + align:start position:0% +on here that's the upshot of what I'm + + + align:start position:0% +on here that's the upshot of what I'm +trying to say with this slide but I just + + align:start position:0% +trying to say with this slide but I just + + + align:start position:0% +trying to say with this slide but I just +wanted to put that out there so you + + align:start position:0% +wanted to put that out there so you + + + align:start position:0% +wanted to put that out there so you +didn't forget that you haven't thrown + + align:start position:0% +didn't forget that you haven't thrown + + + align:start position:0% +didn't forget that you haven't thrown +away all this other interesting stuff + + align:start position:0% +away all this other interesting stuff + + + align:start position:0% +away all this other interesting stuff +about what's out there in the scene okay + + align:start position:0% +about what's out there in the scene okay + + + align:start position:0% +about what's out there in the scene okay +let me kind of I've sort of alluded to + + align:start position:0% +let me kind of I've sort of alluded to + + + align:start position:0% +let me kind of I've sort of alluded to +this a bit I want to come back to kind + + align:start position:0% +this a bit I want to come back to kind + + + align:start position:0% +this a bit I want to come back to kind +of now this is like Mar level 3 stuff + + align:start position:0% +of now this is like Mar level 3 stuff + + + align:start position:0% +of now this is like Mar level 3 stuff +right so you have this idea of what + + align:start position:0% +right so you have this idea of what + + + align:start position:0% +right so you have this idea of what +you're trying to solve you have a Ducote + + align:start position:0% +you're trying to solve you have a Ducote + + + align:start position:0% +you're trying to solve you have a Ducote +you have an algorithm that's a decoder + + align:start position:0% +you have an algorithm that's a decoder + + + align:start position:0% +you have an algorithm that's a decoder +on a basis that's tried that looks like + + align:start position:0% +on a basis that's tried that looks like + + + align:start position:0% +on a basis that's tried that looks like +it predicts pretty well it's not perfect + + align:start position:0% +it predicts pretty well it's not perfect + + + align:start position:0% +it predicts pretty well it's not perfect +there's work to be done there but it + + align:start position:0% +there's work to be done there but it + + + align:start position:0% +there's work to be done there but it +actually does quite well now what does + + align:start position:0% +actually does quite well now what does + + + align:start position:0% +actually does quite well now what does +that mean on the physical hardware level + + align:start position:0% +that mean on the physical hardware level + + + align:start position:0% +that mean on the physical hardware level +so that's Mar level 3 so you think + + align:start position:0% +so that's Mar level 3 so you think + + + align:start position:0% +so that's Mar level 3 so you think +here's how I visualize it you have eye T + + align:start position:0% +here's how I visualize it you have eye T + + + align:start position:0% +here's how I visualize it you have eye T +cortex which I mean AIT and CI t so it's + + align:start position:0% +cortex which I mean AIT and CI t so it's + + + align:start position:0% +cortex which I mean AIT and CI t so it's +about 150 square millimeters in a monkey + + align:start position:0% +about 150 square millimeters in a monkey + + + align:start position:0% +about 150 square millimeters in a monkey +and remember I told you there was about + + align:start position:0% +and remember I told you there was about + + + align:start position:0% +and remember I told you there was about +1 millimeter scale of organization I + + align:start position:0% +1 millimeter scale of organization I + + + align:start position:0% +1 millimeter scale of organization I +showed you that earlier and others have + + align:start position:0% +showed you that earlier and others have + + + align:start position:0% +showed you that earlier and others have +shown I show this earlier too that + + align:start position:0% +shown I show this earlier too that + + + align:start position:0% +shown I show this earlier too that +there's there's sort of face regions are + + align:start position:0% +there's there's sort of face regions are + + + align:start position:0% +there's there's sort of face regions are +drawn up just search for scale here just + + align:start position:0% +drawn up just search for scale here just + + + align:start position:0% +drawn up just search for scale here just +this is a schematic that there's + + align:start position:0% +this is a schematic that there's + + + align:start position:0% +this is a schematic that there's +slightly bigger organizations or 2 to 5 + + align:start position:0% +slightly bigger organizations or 2 to 5 + + + align:start position:0% +slightly bigger organizations or 2 to 5 +millimeter so I think of IT as being + + align:start position:0% +millimeter so I think of IT as being + + + align:start position:0% +millimeter so I think of IT as being +this sort of like 100 to 200 little + + align:start position:0% +this sort of like 100 to 200 little + + + align:start position:0% +this sort of like 100 to 200 little +similar to Tanaka this is not a new + + align:start position:0% +similar to Tanaka this is not a new + + + align:start position:0% +similar to Tanaka this is not a new +conceptual idea but there's sort of just + + align:start position:0% +conceptual idea but there's sort of just + + + align:start position:0% +conceptual idea but there's sort of just +the simple version of each millimeter + + align:start position:0% +the simple version of each millimeter + + + align:start position:0% +the simple version of each millimeter +does exactly the same thing is a feature + + align:start position:0% +does exactly the same thing is a feature + + + align:start position:0% +does exactly the same thing is a feature +and if you sample off of that you take + + align:start position:0% +and if you sample off of that you take + + + align:start position:0% +and if you sample off of that you take +5,000 neurons but they're really + + align:start position:0% +5,000 neurons but they're really + + + align:start position:0% +5,000 neurons but they're really +sampling from only about a hundred and + + align:start position:0% +sampling from only about a hundred and + + + align:start position:0% +sampling from only about a hundred and +fifty IT features at one millimeter + + align:start position:0% +fifty IT features at one millimeter + + + align:start position:0% +fifty IT features at one millimeter +scale remember I don't know if you + + align:start position:0% +scale remember I don't know if you + + + align:start position:0% +scale remember I don't know if you +caught that but I showed 150 100 150 I + + align:start position:0% +caught that but I showed 150 100 150 I + + + align:start position:0% +caught that but I showed 150 100 150 I +showed you 168 IT neurons predicted the + + align:start position:0% +showed you 168 IT neurons predicted the + + + align:start position:0% +showed you 168 IT neurons predicted the +pattern of human performance I showed + + align:start position:0% +pattern of human performance I showed + + + align:start position:0% +pattern of human performance I showed +that a few slides ago but I told you the + + align:start position:0% +that a few slides ago but I told you the + + + align:start position:0% +that a few slides ago but I told you the +real number of neurons is probably + + align:start position:0% +real number of neurons is probably + + + align:start position:0% +real number of neurons is probably +50,000 most of those are redundant + + align:start position:0% +50,000 most of those are redundant + + + align:start position:0% +50,000 most of those are redundant +copies of that 168 dimensional feature + + align:start position:0% +copies of that 168 dimensional feature + + + align:start position:0% +copies of that 168 dimensional feature +set that's how we think about it so you + + align:start position:0% +set that's how we think about it so you + + + align:start position:0% +set that's how we think about it so you +could imagine there's just a redundant + + align:start position:0% +could imagine there's just a redundant + + + align:start position:0% +could imagine there's just a redundant +set of about I like to think of about a + + align:start position:0% +set of about I like to think of about a + + + align:start position:0% +set of about I like to think of about a +hundred features in IT which are sampled + + align:start position:0% +hundred features in IT which are sampled + + + align:start position:0% +hundred features in IT which are sampled +maybe randomly downstream neurons that + + align:start position:0% +maybe randomly downstream neurons that + + + align:start position:0% +maybe randomly downstream neurons that +are then learned so when you learn face + + align:start position:0% +are then learned so when you learn face + + + align:start position:0% +are then learned so when you learn face +versus other things hey there's lots of + + align:start position:0% +versus other things hey there's lots of + + + align:start position:0% +versus other things hey there's lots of +good information about faces versus + + align:start position:0% +good information about faces versus + + + align:start position:0% +good information about faces versus +other things in these face patches + + align:start position:0% +other things in these face patches + + + align:start position:0% +other things in these face patches +that's how they're defined that those + + align:start position:0% +that's how they're defined that those + + + align:start position:0% +that's how they're defined that those +neurons are gonna lean heavily on this + + align:start position:0% +neurons are gonna lean heavily on this + + + align:start position:0% +neurons are gonna lean heavily on this +downstream neurons gonna lean heavily on + + align:start position:0% +downstream neurons gonna lean heavily on + + + align:start position:0% +downstream neurons gonna lean heavily on +those neurons and then these so that + + align:start position:0% +those neurons and then these so that + + + align:start position:0% +those neurons and then these so that +would make these regions causally + + align:start position:0% +would make these regions causally + + + align:start position:0% +would make these regions causally +involved so that doesn't mean you had to + + align:start position:0% +involved so that doesn't mean you had to + + + align:start position:0% +involved so that doesn't mean you had to +pre build in anything here you just + + align:start position:0% +pre build in anything here you just + + + align:start position:0% +pre build in anything here you just +learn this on a downstream version and + + align:start position:0% +learn this on a downstream version and + + + align:start position:0% +learn this on a downstream version and +you would get something that looks like + + align:start position:0% +you would get something that looks like + + + align:start position:0% +you would get something that looks like +it would explain our data so we like + + align:start position:0% +it would explain our data so we like + + + align:start position:0% +it would explain our data so we like +that because it captures that case but + + align:start position:0% +that because it captures that case but + + + align:start position:0% +that because it captures that case but +it also captures the more general case + + align:start position:0% +it also captures the more general case + + + align:start position:0% +it also captures the more general case +if you learn cars you're gonna sample + + align:start position:0% +if you learn cars you're gonna sample + + + align:start position:0% +if you learn cars you're gonna sample +from a different subset of neurons but + + align:start position:0% +from a different subset of neurons but + + + align:start position:0% +from a different subset of neurons but +you're following the same learning rule + + align:start position:0% +you're following the same learning rule + + + align:start position:0% +you're following the same learning rule +that's what I said earlier on so you end + + align:start position:0% +that's what I said earlier on so you end + + + align:start position:0% +that's what I said earlier on so you end +up we think this is the initial state + + align:start position:0% +up we think this is the initial state + + + align:start position:0% +up we think this is the initial state +this is when you learn objects and so + + align:start position:0% +this is when you learn objects and so + + + align:start position:0% +this is when you learn objects and so +what we think is a post learning what + + align:start position:0% +what we think is a post learning what + + + align:start position:0% +what we think is a post learning what +you have is again about a hundred to 150 + + align:start position:0% +you have is again about a hundred to 150 + + + align:start position:0% +you have is again about a hundred to 150 +IT sub regions each at one millimeter + + align:start position:0% +IT sub regions each at one millimeter + + + align:start position:0% +IT sub regions each at one millimeter +scale that are supporting a number of + + align:start position:0% +scale that are supporting a number of + + + align:start position:0% +scale that are supporting a number of +noun tasks read off this common basis + + align:start position:0% +noun tasks read off this common basis + + + align:start position:0% +noun tasks read off this common basis +here that's that's the model that we + + align:start position:0% +here that's that's the model that we + + + align:start position:0% +here that's that's the model that we +like given the kind of data that I've + + align:start position:0% +like given the kind of data that I've + + + align:start position:0% +like given the kind of data that I've +been showing you the post learning model + + align:start position:0% +been showing you the post learning model + + + align:start position:0% +been showing you the post learning model +as we call so the reason I'm bringing + + align:start position:0% +as we call so the reason I'm bringing + + + align:start position:0% +as we call so the reason I'm bringing +this up is partly for the neuroscientist + + align:start position:0% +this up is partly for the neuroscientist + + + align:start position:0% +this up is partly for the neuroscientist +to fix ideas about how we think about IT + + align:start position:0% +to fix ideas about how we think about IT + + + align:start position:0% +to fix ideas about how we think about IT +as a basis set and this is this I think + + align:start position:0% +as a basis set and this is this I think + + + align:start position:0% +as a basis set and this is this I think +I'm sort of set this up nicely Eastern + + align:start position:0% +I'm sort of set this up nicely Eastern + + + align:start position:0% +I'm sort of set this up nicely Eastern +applied similar things that's somebody + + align:start position:0% +applied similar things that's somebody + + + align:start position:0% +applied similar things that's somebody +downstream reads from it okay but now we + + align:start position:0% +downstream reads from it okay but now we + + + align:start position:0% +downstream reads from it okay but now we +have a more you know we're starting to + + align:start position:0% +have a more you know we're starting to + + + align:start position:0% +have a more you know we're starting to +have a more concrete model but we now + + align:start position:0% +have a more concrete model but we now + + + align:start position:0% +have a more concrete model but we now +I'm trying to start to be physical about + + align:start position:0% +I'm trying to start to be physical about + + + align:start position:0% +I'm trying to start to be physical about +it about the size of these regions + + align:start position:0% +it about the size of these regions + + + align:start position:0% +it about the size of these regions +connecting to earlier data how many + + align:start position:0% +connecting to earlier data how many + + + align:start position:0% +connecting to earlier data how many +there are + + align:start position:0% +there are + + + align:start position:0% +there are +so we're gaining inference on that from + + align:start position:0% +so we're gaining inference on that from + + + align:start position:0% +so we're gaining inference on that from +these different experiments and now if + + align:start position:0% +these different experiments and now if + + + align:start position:0% +these different experiments and now if +you believe this it starts to make a + + align:start position:0% +you believe this it starts to make a + + + align:start position:0% +you believe this it starts to make a +prediction of what's now we can do + + align:start position:0% +prediction of what's now we can do + + + align:start position:0% +prediction of what's now we can do +causality right somebody mentioned that + + align:start position:0% +causality right somebody mentioned that + + + align:start position:0% +causality right somebody mentioned that +earlier and so one of the things we've + + align:start position:0% +earlier and so one of the things we've + + + align:start position:0% +earlier and so one of the things we've +been doing recently is if we could start + + align:start position:0% +been doing recently is if we could start + + + align:start position:0% +been doing recently is if we could start +to silence look at the way I've drawn us + + align:start position:0% +to silence look at the way I've drawn us + + + align:start position:0% +to silence look at the way I've drawn us +this bit of tissue for this is a + + align:start position:0% +this bit of tissue for this is a + + + align:start position:0% +this bit of tissue for this is a +schematic is somehow involved in this + + align:start position:0% +schematic is somehow involved in this + + + align:start position:0% +schematic is somehow involved in this +task and that task face task and car + + align:start position:0% +task and that task face task and car + + + align:start position:0% +task and that task face task and car +task but this bit of tissue only face + + align:start position:0% +task but this bit of tissue only face + + + align:start position:0% +task but this bit of tissue only face +tasks and that bit of tissue only car + + align:start position:0% +tasks and that bit of tissue only car + + + align:start position:0% +tasks and that bit of tissue only car +tasks in this patient issue neither + + align:start position:0% +tasks in this patient issue neither + + + align:start position:0% +tasks in this patient issue neither +right so if you believe that you have + + align:start position:0% +right so if you believe that you have + + + align:start position:0% +right so if you believe that you have +the tools you should be able to go in + + align:start position:0% +the tools you should be able to go in + + + align:start position:0% +the tools you should be able to go in +and start to silence little bits of IT + + align:start position:0% +and start to silence little bits of IT + + + align:start position:0% +and start to silence little bits of IT +and you should get predictable patterns + + align:start position:0% +and you should get predictable patterns + + + align:start position:0% +and you should get predictable patterns +out of the behavioral deficits of the + + align:start position:0% +out of the behavioral deficits of the + + + align:start position:0% +out of the behavioral deficits of the +animal when you make those manipulations + + align:start position:0% +animal when you make those manipulations + + + align:start position:0% +animal when you make those manipulations +right everybody follow that right okay + + align:start position:0% +right everybody follow that right okay + + + align:start position:0% +right everybody follow that right okay +and now the models give you a framework + + align:start position:0% +and now the models give you a framework + + + align:start position:0% +and now the models give you a framework +to build those predictions and to also + + align:start position:0% +to build those predictions and to also + + + align:start position:0% +to build those predictions and to also +estimate the magnitude of those effects + + align:start position:0% +estimate the magnitude of those effects + + + align:start position:0% +estimate the magnitude of those effects +that you should see and so that's what + + align:start position:0% +that you should see and so that's what + + + align:start position:0% +that you should see and so that's what +we've been doing more recently and I'll + + align:start position:0% +we've been doing more recently and I'll + + + align:start position:0% +we've been doing more recently and I'll +just give you a taste of this because + + align:start position:0% +just give you a taste of this because + + + align:start position:0% +just give you a taste of this because +this is really ongoing but I think it + + align:start position:0% +this is really ongoing but I think it + + + align:start position:0% +this is really ongoing but I think it +connects to what Gabrielle said earlier + + align:start position:0% +connects to what Gabrielle said earlier + + + align:start position:0% +connects to what Gabrielle said earlier +about now there are these tools + + align:start position:0% +about now there are these tools + + + align:start position:0% +about now there are these tools +available to do that oh I put that in + + align:start position:0% +available to do that oh I put that in + + + align:start position:0% +available to do that oh I put that in +from an earlier + + align:start position:0% +from an earlier + + + align:start position:0% +from an earlier +awkward I think Google has a thing + + align:start position:0% +awkward I think Google has a thing + + + align:start position:0% +awkward I think Google has a thing +called inception and I don't know how it + + align:start position:0% +called inception and I don't know how it + + + align:start position:0% +called inception and I don't know how it +was it Google if somebody has it you + + align:start position:0% +was it Google if somebody has it you + + + align:start position:0% +was it Google if somebody has it you +can't do inception unless you're + + align:start position:0% +can't do inception unless you're + + + align:start position:0% +can't do inception unless you're +actually in a brain so so are you gonna + + align:start position:0% +actually in a brain so so are you gonna + + + align:start position:0% +actually in a brain so so are you gonna +try to insert the reason we do this is + + align:start position:0% +try to insert the reason we do this is + + + align:start position:0% +try to insert the reason we do this is +my student is working on it really wants + + align:start position:0% +my student is working on it really wants + + + align:start position:0% +my student is working on it really wants +to inject signals in the rent this is a + + align:start position:0% +to inject signals in the rent this is a + + + align:start position:0% +to inject signals in the rent this is a +dream about BMI right could you kind of + + align:start position:0% +dream about BMI right could you kind of + + + align:start position:0% +dream about BMI right could you kind of +inject a percept and to do that you're + + align:start position:0% +inject a percept and to do that you're + + + align:start position:0% +inject a percept and to do that you're +gonna need to do experiments like this + + align:start position:0% +gonna need to do experiments like this + + + align:start position:0% +gonna need to do experiments like this +and you understand this hardware to + + align:start position:0% +and you understand this hardware to + + + align:start position:0% +and you understand this hardware to +interact with it something we talked + + align:start position:0% +interact with it something we talked + + + align:start position:0% +interact with it something we talked +about earlier so actually on and Susumu + + align:start position:0% +about earlier so actually on and Susumu + + + align:start position:0% +about earlier so actually on and Susumu +tonegawa slab has some cool inception + + align:start position:0% +tonegawa slab has some cool inception + + + align:start position:0% +tonegawa slab has some cool inception +stuff on memory but this is like + + align:start position:0% +stuff on memory but this is like + + + align:start position:0% +stuff on memory but this is like +inserting an object person so to do that + + align:start position:0% +inserting an object person so to do that + + + align:start position:0% +inserting an object person so to do that +and this has been a dream for many of us + + align:start position:0% +and this has been a dream for many of us + + + align:start position:0% +and this has been a dream for many of us +for a long time can we rely ibly disrupt + + align:start position:0% +for a long time can we rely ibly disrupt + + + align:start position:0% +for a long time can we rely ibly disrupt +performance by suppressing one + + align:start position:0% +performance by suppressing one + + + align:start position:0% +performance by suppressing one +millimeter bits of i.t so to do that + + align:start position:0% +millimeter bits of i.t so to do that + + + align:start position:0% +millimeter bits of i.t so to do that +what we're doing is testing a large + + align:start position:0% +what we're doing is testing a large + + + align:start position:0% +what we're doing is testing a large +battery of tasks and a battery + + align:start position:0% +battery of tasks and a battery + + + align:start position:0% +battery of tasks and a battery +suppression pattern so not just sort of + + align:start position:0% +suppression pattern so not just sort of + + + align:start position:0% +suppression pattern so not just sort of +saying can we affect face tasks or one + + align:start position:0% +saying can we affect face tasks or one + + + align:start position:0% +saying can we affect face tasks or one +test but let's imagine we test a battery + + align:start position:0% +test but let's imagine we test a battery + + + align:start position:0% +test but let's imagine we test a battery +of tasks and then we in the idea where + + align:start position:0% +of tasks and then we in the idea where + + + align:start position:0% +of tasks and then we in the idea where +we'd have a whole bunch of tasks and we + + align:start position:0% +we'd have a whole bunch of tasks and we + + + align:start position:0% +we'd have a whole bunch of tasks and we +do every bit of IT one by one and then + + align:start position:0% +do every bit of IT one by one and then + + + align:start position:0% +do every bit of IT one by one and then +in combination and we'd get all that + + align:start position:0% +in combination and we'd get all that + + + align:start position:0% +in combination and we'd get all that +data and figure out what's going on + + align:start position:0% +data and figure out what's going on + + + align:start position:0% +data and figure out what's going on +right that's sort of the dream right so + + align:start position:0% +right that's sort of the dream right so + + + align:start position:0% +right that's sort of the dream right so +we're trying to build towards that dream + + align:start position:0% +we're trying to build towards that dream + + + align:start position:0% +we're trying to build towards that dream +you guys get it all right I mean I don't + + align:start position:0% +you guys get it all right I mean I don't + + + align:start position:0% +you guys get it all right I mean I don't +know and then we're motivated by this + + align:start position:0% +know and then we're motivated by this + + + align:start position:0% +know and then we're motivated by this +kind of idea here right so to build so + + align:start position:0% +kind of idea here right so to build so + + + align:start position:0% +kind of idea here right so to build so +we started I'll just sort of give you a + + align:start position:0% +we started I'll just sort of give you a + + + align:start position:0% +we started I'll just sort of give you a +quick tour of we have tools to start to + + align:start position:0% +quick tour of we have tools to start to + + + align:start position:0% +quick tour of we have tools to start to +do this I you know this is our recording + + align:start position:0% +do this I you know this is our recording + + + align:start position:0% +do this I you know this is our recording +we can localize where we're recording to + + align:start position:0% +we can localize where we're recording to + + + align:start position:0% +we can localize where we're recording to +very fine-grain using x-rays so we know + + align:start position:0% +very fine-grain using x-rays so we know + + + align:start position:0% +very fine-grain using x-rays so we know +exactly we were recording an IT to like + + align:start position:0% +exactly we were recording an IT to like + + + align:start position:0% +exactly we were recording an IT to like +about 300 micron resolution so that's + + align:start position:0% +about 300 micron resolution so that's + + + align:start position:0% +about 300 micron resolution so that's +why I'm putting this slide up and what + + align:start position:0% +why I'm putting this slide up and what + + + align:start position:0% +why I'm putting this slide up and what +we're interested in is been going if I + + align:start position:0% +we're interested in is been going if I + + + align:start position:0% +we're interested in is been going if I +silence this bit of IT or that bit of IT + + align:start position:0% +silence this bit of IT or that bit of IT + + + align:start position:0% +silence this bit of IT or that bit of IT +or that of IQ so actually do this + + align:start position:0% +or that of IQ so actually do this + + + align:start position:0% +or that of IQ so actually do this +experiment what happens behaviorally and + + align:start position:0% +experiment what happens behaviorally and + + + align:start position:0% +experiment what happens behaviorally and +Arashi Frost is a postdoc in the lab + + align:start position:0% +Arashi Frost is a postdoc in the lab + + + align:start position:0% +Arashi Frost is a postdoc in the lab +started these actual experiments and one + + align:start position:0% +started these actual experiments and one + + + align:start position:0% +started these actual experiments and one +of the things that Raj did was to first + + align:start position:0% +of the things that Raj did was to first + + + align:start position:0% +of the things that Raj did was to first +say let's see if we can get this + + align:start position:0% +say let's see if we can get this + + + align:start position:0% +say let's see if we can get this +silencing of optogenetics tool to work + + align:start position:0% +silencing of optogenetics tool to work + + + align:start position:0% +silencing of optogenetics tool to work +in our hands and the reason we were so + + align:start position:0% +in our hands and the reason we were so + + + align:start position:0% +in our hands and the reason we were so +excited about that is because we think + + align:start position:0% +excited about that is because we think + + + align:start position:0% +excited about that is because we think +lesions if we can make temporary brief + + align:start position:0% +lesions if we can make temporary brief + + + align:start position:0% +lesions if we can make temporary brief +silencing that that might that will be a + + align:start position:0% +silencing that that might that will be a + + + align:start position:0% +silencing that that might that will be a +much more reliable disruption of + + align:start position:0% +much more reliable disruption of + + + align:start position:0% +much more reliable disruption of +behavior that that then if we started to + + align:start position:0% +behavior that that then if we started to + + + align:start position:0% +behavior that that then if we started to +try to inject signals which would be our + + align:start position:0% +try to inject signals which would be our + + + align:start position:0% +try to inject signals which would be our +dream but that seems too risky to us we + + align:start position:0% +dream but that seems too risky to us we + + + align:start position:0% +dream but that seems too risky to us we +just want to say what is a temporary + + align:start position:0% +just want to say what is a temporary + + + align:start position:0% +just want to say what is a temporary +lesion of each bit of IT do and + + align:start position:0% +lesion of each bit of IT do and + + + align:start position:0% +lesion of each bit of IT do and +optogenetics is cool because there's no + + align:start position:0% +optogenetics is cool because there's no + + + align:start position:0% +optogenetics is cool because there's no +other technique that can briefly silence + + align:start position:0% +other technique that can briefly silence + + + align:start position:0% +other technique that can briefly silence +temporarily silence activity you can do + + align:start position:0% +temporarily silence activity you can do + + + align:start position:0% +temporarily silence activity you can do +pharmacal + + align:start position:0% +pharmacal + + + align:start position:0% +pharmacal +manipulations those last four hours so + + align:start position:0% +manipulations those last four hours so + + + align:start position:0% +manipulations those last four hours so +this could briefly silence bits of + + align:start position:0% +this could briefly silence bits of + + + align:start position:0% +this could briefly silence bits of +i-team that's why we were excited about + + align:start position:0% +i-team that's why we were excited about + + + align:start position:0% +i-team that's why we were excited about +it we also did pharmacological + + align:start position:0% +it we also did pharmacological + + + align:start position:0% +it we also did pharmacological +manipulation as a reference to get + + align:start position:0% +manipulation as a reference to get + + + align:start position:0% +manipulation as a reference to get +started but what we're doing is trying + + align:start position:0% +started but what we're doing is trying + + + align:start position:0% +started but what we're doing is trying +to silence one millimetre regions of IT + + align:start position:0% +to silence one millimetre regions of IT + + + align:start position:0% +to silence one millimetre regions of IT +using light delivered through optical + + align:start position:0% +using light delivered through optical + + + align:start position:0% +using light delivered through optical +fibers is a recording electrode and just + + align:start position:0% +fibers is a recording electrode and just + + + align:start position:0% +fibers is a recording electrode and just +to silence some bits of neurons here and + + align:start position:0% +to silence some bits of neurons here and + + + align:start position:0% +to silence some bits of neurons here and +so what arash did was first show that + + align:start position:0% +so what arash did was first show that + + + align:start position:0% +so what arash did was first show that +you can actually silence neurons in this + + align:start position:0% +you can actually silence neurons in this + + + align:start position:0% +you can actually silence neurons in this +way so the user guys haven't seen up to + + align:start position:0% +way so the user guys haven't seen up to + + + align:start position:0% +way so the user guys haven't seen up to +genetics plots this is data from our lab + + align:start position:0% +genetics plots this is data from our lab + + + align:start position:0% +genetics plots this is data from our lab +what's quite cool about this again is + + align:start position:0% +what's quite cool about this again is + + + align:start position:0% +what's quite cool about this again is +you have the same images are being + + align:start position:0% +you have the same images are being + + + align:start position:0% +you have the same images are being +presented so this green line should be + + align:start position:0% +presented so this green line should be + + + align:start position:0% +presented so this green line should be +up here but arash turns the laser on + + align:start position:0% +up here but arash turns the laser on + + + align:start position:0% +up here but arash turns the laser on +right here shines light on there and + + align:start position:0% +right here shines light on there and + + + align:start position:0% +right here shines light on there and +there's some options as expressed in the + + align:start position:0% +there's some options as expressed in the + + + align:start position:0% +there's some options as expressed in the +neurons in that local area and you can + + align:start position:0% +neurons in that local area and you can + + + align:start position:0% +neurons in that local area and you can +see it just sort of shuts the thing down + + align:start position:0% +see it just sort of shuts the thing down + + + align:start position:0% +see it just sort of shuts the thing down +and sort of deletes or blocks this you + + align:start position:0% +and sort of deletes or blocks this you + + + align:start position:0% +and sort of deletes or blocks this you +have the same input coming in but you + + align:start position:0% +have the same input coming in but you + + + align:start position:0% +have the same input coming in but you +can sort of delete it here there's + + align:start position:0% +can sort of delete it here there's + + + align:start position:0% +can sort of delete it here there's +another example these are some pretty + + align:start position:0% +another example these are some pretty + + + align:start position:0% +another example these are some pretty +strong example it's not always this + + align:start position:0% +strong example it's not always this + + + align:start position:0% +strong example it's not always this +strong but that this is again you can + + align:start position:0% +strong but that this is again you can + + + align:start position:0% +strong but that this is again you can +see we can return back to normal right + + align:start position:0% +see we can return back to normal right + + + align:start position:0% +see we can return back to normal right +away right so this is a 200 millisecond + + align:start position:0% +away right so this is a 200 millisecond + + + align:start position:0% +away right so this is a 200 millisecond +silencing you could go even narrower + + align:start position:0% +silencing you could go even narrower + + + align:start position:0% +silencing you could go even narrower +than that but so this is what we had + + align:start position:0% +than that but so this is what we had + + + align:start position:0% +than that but so this is what we had +done so far and again what we did was + + align:start position:0% +done so far and again what we did was + + + align:start position:0% +done so far and again what we did was +say look this as a risky tool isn't that + + align:start position:0% +say look this as a risky tool isn't that + + + align:start position:0% +say look this as a risky tool isn't that +going to work at all so a rash just + + align:start position:0% +going to work at all so a rash just + + + align:start position:0% +going to work at all so a rash just +wanted to test something that was likely + + align:start position:0% +wanted to test something that was likely + + + align:start position:0% +wanted to test something that was likely +to work and so we picked a face task + + align:start position:0% +to work and so we picked a face task + + + align:start position:0% +to work and so we picked a face task +because there was a lot of evidence of + + align:start position:0% +because there was a lot of evidence of + + + align:start position:0% +because there was a lot of evidence of +that spatial clustering of faces that + + align:start position:0% +that spatial clustering of faces that + + + align:start position:0% +that spatial clustering of faces that +you you'll hear from vin rick and you + + align:start position:0% +you you'll hear from vin rick and you + + + align:start position:0% +you you'll hear from vin rick and you +also known in the literature so what we + + align:start position:0% +also known in the literature so what we + + + align:start position:0% +also known in the literature so what we +did was to say we depict the task of + + align:start position:0% +did was to say we depict the task of + + + align:start position:0% +did was to say we depict the task of +discriminating males from females we put + + align:start position:0% +discriminating males from females we put + + + align:start position:0% +discriminating males from females we put +in our notion of invariance it's not + + align:start position:0% +in our notion of invariance it's not + + + align:start position:0% +in our notion of invariance it's not +just do this image access but you have + + align:start position:0% +just do this image access but you have + + + align:start position:0% +just do this image access but you have +to do it across a bunch of + + align:start position:0% +to do it across a bunch of + + + align:start position:0% +to do it across a bunch of +transformations in this case it's + + align:start position:0% +transformations in this case it's + + + align:start position:0% +transformations in this case it's +identity as a transformation so you + + align:start position:0% +identity as a transformation so you + + + align:start position:0% +identity as a transformation so you +saying all of these are supposed to be + + align:start position:0% +saying all of these are supposed to be + + + align:start position:0% +saying all of these are supposed to be +called male and all these are called + + align:start position:0% +called male and all these are called + + + align:start position:0% +called male and all these are called +female and we wanted you to distinguish + + align:start position:0% +female and we wanted you to distinguish + + + align:start position:0% +female and we wanted you to distinguish +this from this that's what he trained a + + align:start position:0% +this from this that's what he trained a + + + align:start position:0% +this from this that's what he trained a +monkey to do and just to give you the + + align:start position:0% +monkey to do and just to give you the + + + align:start position:0% +monkey to do and just to give you the +upshot is that you know we do all this + + align:start position:0% +upshot is that you know we do all this + + + align:start position:0% +upshot is that you know we do all this +work we silence the bits of cortex and + + align:start position:0% +work we silence the bits of cortex and + + + align:start position:0% +work we silence the bits of cortex and +here's the the big take-home you get a + + align:start position:0% +here's the the big take-home you get a + + + align:start position:0% +here's the the big take-home you get a +2% deficit of single one millimeter + + align:start position:0% +2% deficit of single one millimeter + + + align:start position:0% +2% deficit of single one millimeter +silencing a bits of IT cortex the parts + + align:start position:0% +silencing a bits of IT cortex the parts + + + align:start position:0% +silencing a bits of IT cortex the parts +of IT cortex not all of IT cortex + + align:start position:0% +of IT cortex not all of IT cortex + + + align:start position:0% +of IT cortex not all of IT cortex +protruded two percent deficit here's the + + align:start position:0% +protruded two percent deficit here's the + + + align:start position:0% +protruded two percent deficit here's the +animal running at 80 percent six percent + + align:start position:0% +animal running at 80 percent six percent + + + align:start position:0% +animal running at 80 percent six percent +correct these are interleaved trials + + align:start position:0% +correct these are interleaved trials + + + align:start position:0% +correct these are interleaved trials +where we silence some local bit of IP + + align:start position:0% +where we silence some local bit of IP + + + align:start position:0% +where we silence some local bit of IP +you get a two percent deficit that's + + align:start position:0% +you get a two percent deficit that's + + + align:start position:0% +you get a two percent deficit that's +true only in the contralateral field not + + align:start position:0% +true only in the contralateral field not + + + align:start position:0% +true only in the contralateral field not +the ipsilateral field for the + + align:start position:0% +the ipsilateral field for the + + + align:start position:0% +the ipsilateral field for the +aficionados you might look at this two + + align:start position:0% +aficionados you might look at this two + + + align:start position:0% +aficionados you might look at this two +percent and go oh that's time but we + + align:start position:0% +percent and go oh that's time but we + + + align:start position:0% +percent and go oh that's time but we +look this but this is exactly what's + + align:start position:0% +look this but this is exactly what's + + + align:start position:0% +look this but this is exactly what's +predicted by the skew Tamale + + align:start position:0% +predicted by the skew Tamale + + + align:start position:0% +predicted by the skew Tamale +talking about it's right in the range of + + align:start position:0% +talking about it's right in the range of + + + align:start position:0% +talking about it's right in the range of +what should happen and so this to us is + + align:start position:0% +what should happen and so this to us is + + + align:start position:0% +what should happen and so this to us is +really quite cool this is highly + + align:start position:0% +really quite cool this is highly + + + align:start position:0% +really quite cool this is highly +significant and now we sort of are in + + align:start position:0% +significant and now we sort of are in + + + align:start position:0% +significant and now we sort of are in +position to start to say okay these + + align:start position:0% +position to start to say okay these + + + align:start position:0% +position to start to say okay these +tools work they do what they're supposed + + align:start position:0% +tools work they do what they're supposed + + + align:start position:0% +tools work they do what they're supposed +to and now we can start to expand that + + align:start position:0% +to and now we can start to expand that + + + align:start position:0% +to and now we can start to expand that +past space so this this result has been + + align:start position:0% +past space so this this result has been + + + align:start position:0% +past space so this this result has been +published recently if you if you're + + align:start position:0% +published recently if you if you're + + + align:start position:0% +published recently if you if you're +interested in this and here's one of the + + align:start position:0% +interested in this and here's one of the + + + align:start position:0% +interested in this and here's one of the +ways we're going forward is that rishi + + align:start position:0% +ways we're going forward is that rishi + + + align:start position:0% +ways we're going forward is that rishi +Roger Lingam the one doing those pass in + + align:start position:0% +Roger Lingam the one doing those pass in + + + align:start position:0% +Roger Lingam the one doing those pass in +the monkey showed you earlier silencing + + align:start position:0% +the monkey showed you earlier silencing + + + align:start position:0% +the monkey showed you earlier silencing +different parts of IT this is now with + + align:start position:0% +different parts of IT this is now with + + + align:start position:0% +different parts of IT this is now with +Newsome all different bits of IT these + + align:start position:0% +Newsome all different bits of IT these + + + align:start position:0% +Newsome all different bits of IT these +are different tasks lead to different + + align:start position:0% +are different tasks lead to different + + + align:start position:0% +are different tasks lead to different +patterns that's what these dots are here + + align:start position:0% +patterns that's what these dots are here + + + align:start position:0% +patterns that's what these dots are here +different patterns of deficits and if + + align:start position:0% +different patterns of deficits and if + + + align:start position:0% +different patterns of deficits and if +you go back to the same location you get + + align:start position:0% +you go back to the same location you get + + + align:start position:0% +you go back to the same location you get +the same pattern of deficits so this is + + align:start position:0% +the same pattern of deficits so this is + + + align:start position:0% +the same pattern of deficits so this is +only ten tasks but I think it hopefully + + align:start position:0% +only ten tasks but I think it hopefully + + + align:start position:0% +only ten tasks but I think it hopefully +gives you the spirit of what we're + + align:start position:0% +gives you the spirit of what we're + + + align:start position:0% +gives you the spirit of what we're +trying to do and and again this is only + + align:start position:0% +trying to do and and again this is only + + + align:start position:0% +trying to do and and again this is only +new samal which is doesn't have all the + + align:start position:0% +new samal which is doesn't have all the + + + align:start position:0% +new samal which is doesn't have all the +advantages of optogenetics but this is + + align:start position:0% +advantages of optogenetics but this is + + + align:start position:0% +advantages of optogenetics but this is +what we're we're building towards here + + align:start position:0% +what we're we're building towards here + + + align:start position:0% +what we're we're building towards here +so I'm just giving you the sort of the + + align:start position:0% +so I'm just giving you the sort of the + + + align:start position:0% +so I'm just giving you the sort of the +sort of state of the art so our aim is + + align:start position:0% +sort of state of the art so our aim is + + + align:start position:0% +sort of state of the art so our aim is +to measure the specific pattern + + align:start position:0% +to measure the specific pattern + + + align:start position:0% +to measure the specific pattern +behavioral change and deuce by the + + align:start position:0% +behavioral change and deuce by the + + + align:start position:0% +behavioral change and deuce by the +suppression of each IT sub region + + align:start position:0% +suppression of each IT sub region + + + align:start position:0% +suppression of each IT sub region +ideally tested many of them and to + + align:start position:0% +ideally tested many of them and to + + + align:start position:0% +ideally tested many of them and to +compare with the model predictions I'm + + align:start position:0% +compare with the model predictions I'm + + + align:start position:0% +compare with the model predictions I'm +saying there's this domain and I want to + + align:start position:0% +saying there's this domain and I want to + + + align:start position:0% +saying there's this domain and I want to +set a sample the whole domain so far + + align:start position:0% +set a sample the whole domain so far + + + align:start position:0% +set a sample the whole domain so far +I've given you only just samples of + + align:start position:0% +I've given you only just samples of + + + align:start position:0% +I've given you only just samples of +tasks in the domain but we're really + + align:start position:0% +tasks in the domain but we're really + + + align:start position:0% +tasks in the domain but we're really +trying to define the domain and and I'm + + align:start position:0% +trying to define the domain and and I'm + + + align:start position:0% +trying to define the domain and and I'm +just gonna I'm gonna skip through this + + align:start position:0% +just gonna I'm gonna skip through this + + + align:start position:0% +just gonna I'm gonna skip through this +just to give you the punchline is that + + align:start position:0% +just to give you the punchline is that + + + align:start position:0% +just to give you the punchline is that +we do a whole bunch of behavioral + + align:start position:0% +we do a whole bunch of behavioral + + + align:start position:0% +we do a whole bunch of behavioral +measurements we presented this work + + align:start position:0% +measurements we presented this work + + + align:start position:0% +measurements we presented this work +before it's like this is now up to 3 + + align:start position:0% +before it's like this is now up to 3 + + + align:start position:0% +before it's like this is now up to 3 +million Mechanical Turk trials it seems + + align:start position:0% +million Mechanical Turk trials it seems + + + align:start position:0% +million Mechanical Turk trials it seems +to us that we can embed all objects even + + align:start position:0% +to us that we can embed all objects even + + + align:start position:0% +to us that we can embed all objects even +subordinate objects of the type of task + + align:start position:0% +subordinate objects of the type of task + + + align:start position:0% +subordinate objects of the type of task +I've been telling you in roughly in + + align:start position:0% +I've been telling you in roughly in + + + align:start position:0% +I've been telling you in roughly in +essentially a 20 dimensional space so + + align:start position:0% +essentially a 20 dimensional space so + + + align:start position:0% +essentially a 20 dimensional space so +there's 20 dimensions we think we infer + + align:start position:0% +there's 20 dimensions we think we infer + + + align:start position:0% +there's 20 dimensions we think we infer +that humans are projecting to about 20 + + align:start position:0% +that humans are projecting to about 20 + + + align:start position:0% +that humans are projecting to about 20 +dimensions to do these kind of the tasks + + align:start position:0% +dimensions to do these kind of the tasks + + + align:start position:0% +dimensions to do these kind of the tasks +that we've shown here which is serve + + align:start position:0% +that we've shown here which is serve + + + align:start position:0% +that we've shown here which is serve +smaller but here really close to that in + + align:start position:0% +smaller but here really close to that in + + + align:start position:0% +smaller but here really close to that in +the turbine or a magnitude to that + + align:start position:0% +the turbine or a magnitude to that + + + align:start position:0% +the turbine or a magnitude to that +hundred or so features that I've been + + align:start position:0% +hundred or so features that I've been + + + align:start position:0% +hundred or so features that I've been +talking about so that's we're regardless + + align:start position:0% +talking about so that's we're regardless + + + align:start position:0% +talking about so that's we're regardless +of you know whether this is these are + + align:start position:0% +of you know whether this is these are + + + align:start position:0% +of you know whether this is these are +some of the dimensions and how we're + + align:start position:0% +some of the dimensions and how we're + + + align:start position:0% +some of the dimensions and how we're +projecting them again I won't take you + + align:start position:0% +projecting them again I won't take you + + + align:start position:0% +projecting them again I won't take you +through this because I think we've + + align:start position:0% +through this because I think we've + + + align:start position:0% +through this because I think we've +already used up enough time and I want + + align:start position:0% +already used up enough time and I want + + + align:start position:0% +already used up enough time and I want +to get out of this part but we're trying + + align:start position:0% +to get out of this part but we're trying + + + align:start position:0% +to get out of this part but we're trying +to define a domain of all tasks where we + + align:start position:0% +to define a domain of all tasks where we + + + align:start position:0% +to define a domain of all tasks where we +consider predict what would happen + + align:start position:0% +consider predict what would happen + + + align:start position:0% +consider predict what would happen +across anything within that domain and + + align:start position:0% +across anything within that domain and + + + align:start position:0% +across anything within that domain and +that raises questions of like the + + align:start position:0% +that raises questions of like the + + + align:start position:0% +that raises questions of like the +dimensionality of that domain and there + + align:start position:0% +dimensionality of that domain and there + + + align:start position:0% +dimensionality of that domain and there +would behave ural methods to do that and + + align:start position:0% +would behave ural methods to do that and + + + align:start position:0% +would behave ural methods to do that and +we've been doing some work on that so + + align:start position:0% +we've been doing some work on that so + + + align:start position:0% +we've been doing some work on that so +I'll just leave it at that and if you + + align:start position:0% +I'll just leave it at that and if you + + + align:start position:0% +I'll just leave it at that and if you +guys have questions we can talk about + + align:start position:0% +guys have questions we can talk about + + + align:start position:0% +guys have questions we can talk about +that some more I want to sort of in the + + align:start position:0% +that some more I want to sort of in the + + + align:start position:0% +that some more I want to sort of in the +time I really have left is to talk about + + align:start position:0% +time I really have left is to talk about + + + align:start position:0% +time I really have left is to talk about +the encoding side + + align:start position:0% +the encoding side + + + align:start position:0% +the encoding side +things because I promised you guys I + + align:start position:0% +things because I promised you guys I + + + align:start position:0% +things because I promised you guys I +would get to this unless if you have any + + align:start position:0% +would get to this unless if you have any + + + align:start position:0% +would get to this unless if you have any +more burning questions on this decoding + + align:start position:0% +more burning questions on this decoding + + + align:start position:0% +more burning questions on this decoding +side so if I've been talk about the link + + align:start position:0% +side so if I've been talk about the link + + + align:start position:0% +side so if I've been talk about the link +between IT and perception now I'm gonna + + align:start position:0% +between IT and perception now I'm gonna + + + align:start position:0% +between IT and perception now I'm gonna +switch gears and talk about this other + + align:start position:0% +switch gears and talk about this other + + + align:start position:0% +switch gears and talk about this other +side which is so I talked about this and + + align:start position:0% +side which is so I talked about this and + + + align:start position:0% +side which is so I talked about this and +that tells us that the mean rates and + + align:start position:0% +that tells us that the mean rates and + + + align:start position:0% +that tells us that the mean rates and +i.t are something that seem to be highly + + align:start position:0% +i.t are something that seem to be highly + + + align:start position:0% +i.t are something that seem to be highly +predictive I showed you at least one + + align:start position:0% +predictive I showed you at least one + + + align:start position:0% +predictive I showed you at least one +modeled as the laws of RAD IT model but + + align:start position:0% +modeled as the laws of RAD IT model but + + + align:start position:0% +modeled as the laws of RAD IT model but +now it's like now we can turn to the + + align:start position:0% +now it's like now we can turn to the + + + align:start position:0% +now it's like now we can turn to the +encoding encoding side and saying we + + align:start position:0% +encoding encoding side and saying we + + + align:start position:0% +encoding encoding side and saying we +need to protect the mean rates of I T + + align:start position:0% +need to protect the mean rates of I T + + + align:start position:0% +need to protect the mean rates of I T +and that that should be our goal if we + + align:start position:0% +and that that should be our goal if we + + + align:start position:0% +and that that should be our goal if we +want to explain images to IT activity so + + align:start position:0% +want to explain images to IT activity so + + + align:start position:0% +want to explain images to IT activity so +there's these would be predictive + + align:start position:0% +there's these would be predictive + + + align:start position:0% +there's these would be predictive +encoding mechanisms so well now you guys + + align:start position:0% +encoding mechanisms so well now you guys + + + align:start position:0% +encoding mechanisms so well now you guys +have heard about deep convolutional + + align:start position:0% +have heard about deep convolutional + + + align:start position:0% +have heard about deep convolutional +networks you not you'll you heard about + + align:start position:0% +networks you not you'll you heard about + + + align:start position:0% +networks you not you'll you heard about +them already you'll probably hear about + + align:start position:0% +them already you'll probably hear about + + + align:start position:0% +them already you'll probably hear about +them some more so we started messing + + align:start position:0% +them some more so we started messing + + + align:start position:0% +them some more so we started messing +around in 2008 this is a model inspired + + align:start position:0% +around in 2008 this is a model inspired + + + align:start position:0% +around in 2008 this is a model inspired +I mentioned this family of models before + + align:start position:0% +I mentioned this family of models before + + + align:start position:0% +I mentioned this family of models before +a human weasel Fukushima and there's a + + align:start position:0% +a human weasel Fukushima and there's a + + + align:start position:0% +a human weasel Fukushima and there's a +whole H max family of models that really + + align:start position:0% +whole H max family of models that really + + + align:start position:0% +whole H max family of models that really +was the the inspiration of this larger + + align:start position:0% +was the the inspiration of this larger + + + align:start position:0% +was the the inspiration of this larger +this large family of models that have + + align:start position:0% +this large family of models that have + + + align:start position:0% +this large family of models that have +this repeating structure that it is that + + align:start position:0% +this repeating structure that it is that + + + align:start position:0% +this repeating structure that it is that +are now really the sort of modern-day + + align:start position:0% +are now really the sort of modern-day + + + align:start position:0% +are now really the sort of modern-day +deconvolution networks really grew out + + align:start position:0% +deconvolution networks really grew out + + + align:start position:0% +deconvolution networks really grew out +of all of this earlier work and so we + + align:start position:0% +of all of this earlier work and so we + + + align:start position:0% +of all of this earlier work and so we +started exploring the family in 2008 and + + align:start position:0% +started exploring the family in 2008 and + + + align:start position:0% +started exploring the family in 2008 and +just this is a slide that you've you've + + align:start position:0% +just this is a slide that you've you've + + + align:start position:0% +just this is a slide that you've you've +already sort of seen a version of this + + align:start position:0% +already sort of seen a version of this + + + align:start position:0% +already sort of seen a version of this +from Gabriel where you you know for you + + align:start position:0% +from Gabriel where you you know for you + + + align:start position:0% +from Gabriel where you you know for you +take an image you pass it through a set + + align:start position:0% +take an image you pass it through a set + + + align:start position:0% +take an image you pass it through a set +of operators so you have filters so + + align:start position:0% +of operators so you have filters so + + + align:start position:0% +of operators so you have filters so +these are dot products over some + + align:start position:0% +these are dot products over some + + + align:start position:0% +these are dot products over some +restricted spatial restricted region + + align:start position:0% +restricted spatial restricted region + + + align:start position:0% +restricted spatial restricted region +like receptive fields you have a + + align:start position:0% +like receptive fields you have a + + + align:start position:0% +like receptive fields you have a +non-linearity like a threshold and a + + align:start position:0% +non-linearity like a threshold and a + + + align:start position:0% +non-linearity like a threshold and a +saturation you have pooling operation + + align:start position:0% +saturation you have pooling operation + + + align:start position:0% +saturation you have pooling operation +then you have a normalization so you + + align:start position:0% +then you have a normalization so you + + + align:start position:0% +then you have a normalization so you +have all these operations happen here + + align:start position:0% +have all these operations happen here + + + align:start position:0% +have all these operations happen here +and that produces a stack so think of + + align:start position:0% +and that produces a stack so think of + + + align:start position:0% +and that produces a stack so think of +like if there are four filters here like + + align:start position:0% +like if there are four filters here like + + + align:start position:0% +like if there are four filters here like +four orientations you get four images + + align:start position:0% +four orientations you get four images + + + align:start position:0% +four orientations you get four images +you have one image in and get four + + align:start position:0% +you have one image in and get four + + + align:start position:0% +you have one image in and get four +images out but you had ten of these and + + align:start position:0% +images out but you had ten of these and + + + align:start position:0% +images out but you had ten of these and +get ten of these out then you repeat + + align:start position:0% +get ten of these out then you repeat + + + align:start position:0% +get ten of these out then you repeat +this here right and so as you keep + + align:start position:0% +this here right and so as you keep + + + align:start position:0% +this here right and so as you keep +adding more filters the stack just keeps + + align:start position:0% +adding more filters the stack just keeps + + + align:start position:0% +adding more filters the stack just keeps +getting bigger and bigger and it keeps + + align:start position:0% +getting bigger and bigger and it keeps + + + align:start position:0% +getting bigger and bigger and it keeps +because you're spatially pooling it + + align:start position:0% +because you're spatially pooling it + + + align:start position:0% +because you're spatially pooling it +keeps getting narrower and narrower + + align:start position:0% +keeps getting narrower and narrower + + + align:start position:0% +keeps getting narrower and narrower +right so you go from this image to this + + align:start position:0% +right so you go from this image to this + + + align:start position:0% +right so you go from this image to this +deep stack of features it has less + + align:start position:0% +deep stack of features it has less + + + align:start position:0% +deep stack of features it has less +retina top he still has a little bit of + + align:start position:0% +retina top he still has a little bit of + + + align:start position:0% +retina top he still has a little bit of +retina top.you and that you can see has + + align:start position:0% +retina top.you and that you can see has + + + align:start position:0% +retina top.you and that you can see has +been exactly a very good model why + + align:start position:0% +been exactly a very good model why + + + align:start position:0% +been exactly a very good model why +people liked it of what how people think + + align:start position:0% +people liked it of what how people think + + + align:start position:0% +people liked it of what how people think +about the ventral stream so these models + + align:start position:0% +about the ventral stream so these models + + + align:start position:0% +about the ventral stream so these models +typically have thousands of feature ons + + align:start position:0% +typically have thousands of feature ons + + + align:start position:0% +typically have thousands of feature ons +or features at the top level just to + + align:start position:0% +or features at the top level just to + + + align:start position:0% +or features at the top level just to +give you a sense of scale of wonder how + + align:start position:0% +give you a sense of scale of wonder how + + + align:start position:0% +give you a sense of scale of wonder how +they're run and just to take you through + + align:start position:0% +they're run and just to take you through + + + align:start position:0% +they're run and just to take you through +the you know the you know I guess maybe + + align:start position:0% +the you know the you know I guess maybe + + + align:start position:0% +the you know the you know I guess maybe +you hear about this we've not already + + align:start position:0% +you hear about this we've not already + + + align:start position:0% +you hear about this we've not already +each element has like + + align:start position:0% +each element has like + + + align:start position:0% +each element has like +filter has a large fan in like these are + + align:start position:0% +filter has a large fan in like these are + + + align:start position:0% +filter has a large fan in like these are +like neuroscience related things they + + align:start position:0% +like neuroscience related things they + + + align:start position:0% +like neuroscience related things they +have nonlinearities like thresholds of + + align:start position:0% +have nonlinearities like thresholds of + + + align:start position:0% +have nonlinearities like thresholds of +neurons each layers convolutional which + + align:start position:0% +neurons each layers convolutional which + + + align:start position:0% +neurons each layers convolutional which +means you apply the same filters across + + align:start position:0% +means you apply the same filters across + + + align:start position:0% +means you apply the same filters across +visual space which is like retina toppy + + align:start position:0% +visual space which is like retina toppy + + + align:start position:0% +visual space which is like retina toppy +that is a v1 cell that's oriented here + + align:start position:0% +that is a v1 cell that's oriented here + + + align:start position:0% +that is a v1 cell that's oriented here +it'll be another v1 cell that's that's + + align:start position:0% +it'll be another v1 cell that's that's + + + align:start position:0% +it'll be another v1 cell that's that's +it in another spatial position same + + align:start position:0% +it in another spatial position same + + + align:start position:0% +it in another spatial position same +orientation different spatial position + + align:start position:0% +orientation different spatial position + + + align:start position:0% +orientation different spatial position +that's what the convolute convolutional + + align:start position:0% +that's what the convolute convolutional + + + align:start position:0% +that's what the convolute convolutional +models are just an implementation of + + align:start position:0% +models are just an implementation of + + + align:start position:0% +models are just an implementation of +that idea of copying the same filter + + align:start position:0% +that idea of copying the same filter + + + align:start position:0% +that idea of copying the same filter +type across the retina and there's a + + align:start position:0% +type across the retina and there's a + + + align:start position:0% +type across the retina and there's a +deep stack of layers these are all + + align:start position:0% +deep stack of layers these are all + + + align:start position:0% +deep stack of layers these are all +things that I think are commensurate + + align:start position:0% +things that I think are commensurate + + + align:start position:0% +things that I think are commensurate +with the with the ventral stream anatomy + + align:start position:0% +with the with the ventral stream anatomy + + + align:start position:0% +with the with the ventral stream anatomy +and physiology so um but one of the key + + align:start position:0% +and physiology so um but one of the key + + + align:start position:0% +and physiology so um but one of the key +things that those even work with these + + align:start position:0% +things that those even work with these + + + align:start position:0% +things that those even work with these +models know is that they have lots of + + align:start position:0% +models know is that they have lots of + + + align:start position:0% +models know is that they have lots of +unknown parameters that are not + + align:start position:0% +unknown parameters that are not + + + align:start position:0% +unknown parameters that are not +determined from the neural biology even + + align:start position:0% +determined from the neural biology even + + + align:start position:0% +determined from the neural biology even +though the family of models is well + + align:start position:0% +though the family of models is well + + + align:start position:0% +though the family of models is well +described what are the exact filter + + align:start position:0% +described what are the exact filter + + + align:start position:0% +described what are the exact filter +weights this what are the threshold + + align:start position:0% +weights this what are the threshold + + + align:start position:0% +weights this what are the threshold +parameter is how exactly do you pool how + + align:start position:0% +parameter is how exactly do you pool how + + + align:start position:0% +parameter is how exactly do you pool how +do you normalize there's lots of + + align:start position:0% +do you normalize there's lots of + + + align:start position:0% +do you normalize there's lots of +parameters when you build these things + + align:start position:0% +parameters when you build these things + + + align:start position:0% +parameters when you build these things +essentially thousands of parameters + + align:start position:0% +essentially thousands of parameters + + + align:start position:0% +essentially thousands of parameters +most of them hidden in the weight + + align:start position:0% +most of them hidden in the weight + + + align:start position:0% +most of them hidden in the weight +structure here which if you think about + + align:start position:0% +structure here which if you think about + + + align:start position:0% +structure here which if you think about +the first layer that would be like + + align:start position:0% +the first layer that would be like + + + align:start position:0% +the first layer that would be like +should I choose Gabor filters or should + + align:start position:0% +should I choose Gabor filters or should + + + align:start position:0% +should I choose Gabor filters or should +I do some other you know Heim was + + align:start position:0% +I do some other you know Heim was + + + align:start position:0% +I do some other you know Heim was +talking about random weights right so + + align:start position:0% +talking about random weights right so + + + align:start position:0% +talking about random weights right so +there's choices there there's lots of + + align:start position:0% +there's choices there there's lots of + + + align:start position:0% +there's choices there there's lots of +parameters so the upshot is there's a + + align:start position:0% +parameters so the upshot is there's a + + + align:start position:0% +parameters so the upshot is there's a +big that's why I call it a family of + + align:start position:0% +big that's why I call it a family of + + + align:start position:0% +big that's why I call it a family of +models and how do you choose which one + + align:start position:0% +models and how do you choose which one + + + align:start position:0% +models and how do you choose which one +is the right one so to speak or is there + + align:start position:0% +is the right one so to speak or is there + + + align:start position:0% +is the right one so to speak or is there +a right one or maybe the whole family is + + align:start position:0% +a right one or maybe the whole family is + + + align:start position:0% +a right one or maybe the whole family is +wrong right these are the interesting + + align:start position:0% +wrong right these are the interesting + + + align:start position:0% +wrong right these are the interesting +discussions so so what we what I like + + align:start position:0% +discussions so so what we what I like + + + align:start position:0% +discussions so so what we what I like +about it is at least when you said it + + align:start position:0% +about it is at least when you said it + + + align:start position:0% +about it is at least when you said it +it's a model it makes predictions and + + align:start position:0% +it's a model it makes predictions and + + + align:start position:0% +it's a model it makes predictions and +then you can test it so it's at least + + align:start position:0% +then you can test it so it's at least + + + align:start position:0% +then you can test it so it's at least +the model and it predicts the entire you + + align:start position:0% +the model and it predicts the entire you + + + align:start position:0% +the model and it predicts the entire you +know if you start to map these who say + + align:start position:0% +know if you start to map these who say + + + align:start position:0% +know if you start to map these who say +this is V 1 this is V 2 this is before + + align:start position:0% +this is V 1 this is V 2 this is before + + + align:start position:0% +this is V 1 this is V 2 this is before +it predicts the full neural population + + align:start position:0% +it predicts the full neural population + + + align:start position:0% +it predicts the full neural population +to response to any image across these + + align:start position:0% +to response to any image across these + + + align:start position:0% +to response to any image across these +the area so it's a strongly predictive + + align:start position:0% +the area so it's a strongly predictive + + + align:start position:0% +the area so it's a strongly predictive +model once built so that's nice but now + + align:start position:0% +model once built so that's nice but now + + + align:start position:0% +model once built so that's nice but now +you have to determine how am I going to + + align:start position:0% +you have to determine how am I going to + + + align:start position:0% +you have to determine how am I going to +build it how do I set the parameters so + + align:start position:0% +build it how do I set the parameters so + + + align:start position:0% +build it how do I set the parameters so +how do we do that well there's lots of + + align:start position:0% +how do we do that well there's lots of + + + align:start position:0% +how do we do that well there's lots of +ways you could do it and I'll tell you + + align:start position:0% +ways you could do it and I'll tell you + + + align:start position:0% +ways you could do it and I'll tell you +the way we chose to do it which was to + + align:start position:0% +the way we chose to do it which was to + + + align:start position:0% +the way we chose to do it which was to +just not use any neural data it was just + + align:start position:0% +just not use any neural data it was just + + + align:start position:0% +just not use any neural data it was just +to use optimization methods to find + + align:start position:0% +to use optimization methods to find + + + align:start position:0% +to use optimization methods to find +specific models to set up parameters + + align:start position:0% +specific models to set up parameters + + + align:start position:0% +specific models to set up parameters +inside this model class and we chose an + + align:start position:0% +inside this model class and we chose an + + + align:start position:0% +inside this model class and we chose an +optimization target this is a little bit + + align:start position:0% +optimization target this is a little bit + + + align:start position:0% +optimization target this is a little bit +again inspired from the top-down view of + + align:start position:0% +again inspired from the top-down view of + + + align:start position:0% +again inspired from the top-down view of +what the systems doing what a visual + + align:start position:0% +what the systems doing what a visual + + + align:start position:0% +what the systems doing what a visual +tasks that we suppose the ventral stream + + align:start position:0% +tasks that we suppose the ventral stream + + + align:start position:0% +tasks that we suppose the ventral stream +was supposed to solve which I already + + align:start position:0% +was supposed to solve which I already + + + align:start position:0% +was supposed to solve which I already +told you we think it's in very + + align:start position:0% +told you we think it's in very + + + align:start position:0% +told you we think it's in very +recognition that's what makes the + + align:start position:0% +recognition that's what makes the + + + align:start position:0% +recognition that's what makes the +problem hard so we tried to optimize + + align:start position:0% +problem hard so we tried to optimize + + + align:start position:0% +problem hard so we tried to optimize +models to solve that and essentially + + align:start position:0% +models to solve that and essentially + + + align:start position:0% +models to solve that and essentially +when we're doing that we're kind of + + align:start position:0% +when we're doing that we're kind of + + + align:start position:0% +when we're doing that we're kind of +doing the same thing that computer + + align:start position:0% +doing the same thing that computer + + + align:start position:0% +doing the same thing that computer +vision is trying to do except we're + + align:start position:0% +vision is trying to do except we're + + + align:start position:0% +vision is trying to do except we're +doing it in our own domain of images and + + align:start position:0% +doing it in our own domain of images and + + + align:start position:0% +doing it in our own domain of images and +tasks that we set up but we essentially + + align:start position:0% +tasks that we set up but we essentially + + + align:start position:0% +tasks that we set up but we essentially +there's a meeting between computer + + align:start position:0% +there's a meeting between computer + + + align:start position:0% +there's a meeting between computer +vision and what we were trying to do + + align:start position:0% +vision and what we were trying to do + + + align:start position:0% +vision and what we were trying to do +here and when I say we this is work by + + align:start position:0% +here and when I say we this is work by + + + align:start position:0% +here and when I say we this is work by +Dan yemen's a postdoc in the lab and + + align:start position:0% +Dan yemen's a postdoc in the lab and + + + align:start position:0% +Dan yemen's a postdoc in the lab and +haha a graduate student and what we did + + align:start position:0% +haha a graduate student and what we did + + + align:start position:0% +haha a graduate student and what we did +was to just try to simulate again as I + + align:start position:0% +was to just try to simulate again as I + + + align:start position:0% +was to just try to simulate again as I +did earlier we took these simple 3d + + align:start position:0% +did earlier we took these simple 3d + + + align:start position:0% +did earlier we took these simple 3d +objects we could render them just as + + align:start position:0% +objects we could render them just as + + + align:start position:0% +objects we could render them just as +before a place on my naturalistic + + align:start position:0% +before a place on my naturalistic + + + align:start position:0% +before a place on my naturalistic +background and then we just built models + + align:start position:0% +background and then we just built models + + + align:start position:0% +background and then we just built models +that would try to discriminate bodies + + align:start position:0% +that would try to discriminate bodies + + + align:start position:0% +that would try to discriminate bodies +from buildings from flowers from guns so + + align:start position:0% +from buildings from flowers from guns so + + + align:start position:0% +from buildings from flowers from guns so +we that would have good feature sets + + align:start position:0% +we that would have good feature sets + + + align:start position:0% +we that would have good feature sets +that would discriminate between these + + align:start position:0% +that would discriminate between these + + + align:start position:0% +that would discriminate between these +things and again these were essentially + + align:start position:0% +things and again these were essentially + + + align:start position:0% +things and again these were essentially +trained by various forms of supervision + + align:start position:0% +trained by various forms of supervision + + + align:start position:0% +trained by various forms of supervision +now there's lots of ways you can train + + align:start position:0% +now there's lots of ways you can train + + + align:start position:0% +now there's lots of ways you can train +these models + + align:start position:0% +these models + + + align:start position:0% +these models +I could tell you about how we did it and + + align:start position:0% +I could tell you about how we did it and + + + align:start position:0% +I could tell you about how we did it and +how others have done it I think those + + align:start position:0% +how others have done it I think those + + + align:start position:0% +how others have done it I think those +details are beyond what I want to talk + + align:start position:0% +details are beyond what I want to talk + + + align:start position:0% +details are beyond what I want to talk +about today but just it's a supervised + + align:start position:0% +about today but just it's a supervised + + + align:start position:0% +about today but just it's a supervised +class that's probably not learned in the + + align:start position:0% +class that's probably not learned in the + + + align:start position:0% +class that's probably not learned in the +same way but the brain has learned most + + align:start position:0% +same way but the brain has learned most + + + align:start position:0% +same way but the brain has learned most +people don't think so but the + + align:start position:0% +people don't think so but the + + + align:start position:0% +people don't think so but the +interesting thing is the end state of + + align:start position:0% +interesting thing is the end state of + + + align:start position:0% +interesting thing is the end state of +these models might look very much like + + align:start position:0% +these models might look very much like + + + align:start position:0% +these models might look very much like +the current adult state of the brain and + + align:start position:0% +the current adult state of the brain and + + + align:start position:0% +the current adult state of the brain and +that's what I want to try to tell you + + align:start position:0% +that's what I want to try to tell you + + + align:start position:0% +that's what I want to try to tell you +next so first let me show you that when + + align:start position:0% +next so first let me show you that when + + + align:start position:0% +next so first let me show you that when +we built these models in 2012 we had a + + align:start position:0% +we built these models in 2012 we had a + + + align:start position:0% +we built these models in 2012 we had a +particular optimization approach that we + + align:start position:0% +particular optimization approach that we + + + align:start position:0% +particular optimization approach that we +called HMO that was trying to solve + + align:start position:0% +called HMO that was trying to solve + + + align:start position:0% +called HMO that was trying to solve +these kind of problems that I showed you + + align:start position:0% +these kind of problems that I showed you + + + align:start position:0% +these kind of problems that I showed you +earlier on these kind of images and I + + align:start position:0% +earlier on these kind of images and I + + + align:start position:0% +earlier on these kind of images and I +showed you AI T was pretty good with + + align:start position:0% +showed you AI T was pretty good with + + + align:start position:0% +showed you AI T was pretty good with +humans I show you it's performance was + + align:start position:0% +humans I show you it's performance was + + + align:start position:0% +humans I show you it's performance was +almost up to humans even with just 168 + + align:start position:0% +almost up to humans even with just 168 + + + align:start position:0% +almost up to humans even with just 168 +samples and when we first built a model + + align:start position:0% +samples and when we first built a model + + + align:start position:0% +samples and when we first built a model +here we were able able to do much better + + align:start position:0% +here we were able able to do much better + + + align:start position:0% +here we were able able to do much better +than some of our previous models that on + + align:start position:0% +than some of our previous models that on + + + align:start position:0% +than some of our previous models that on +these same kind of cast I told you we + + align:start position:0% +these same kind of cast I told you we + + + align:start position:0% +these same kind of cast I told you we +constructed because we knew it made + + align:start position:0% +constructed because we knew it made + + + align:start position:0% +constructed because we knew it made +these things we made these models not do + + align:start position:0% +these things we made these models not do + + + align:start position:0% +these things we made these models not do +so well so we built these hide + + align:start position:0% +so well so we built these hide + + + align:start position:0% +so well so we built these hide +invariance tasks to push these models + + align:start position:0% +invariance tasks to push these models + + + align:start position:0% +invariance tasks to push these models +down and then we had space to build a + + align:start position:0% +down and then we had space to build a + + + align:start position:0% +down and then we had space to build a +model that would that we could do better + + align:start position:0% +model that would that we could do better + + + align:start position:0% +model that would that we could do better +on then we built called at HMO 1.0 and + + align:start position:0% +on then we built called at HMO 1.0 and + + + align:start position:0% +on then we built called at HMO 1.0 and +then we word started to say now we have + + align:start position:0% +then we word started to say now we have + + + align:start position:0% +then we word started to say now we have +this model that was been optimized for + + align:start position:0% +this model that was been optimized for + + + align:start position:0% +this model that was been optimized for +performance let's see how well it does + + align:start position:0% +performance let's see how well it does + + + align:start position:0% +performance let's see how well it does +on comparing with neurons let's see if + + align:start position:0% +on comparing with neurons let's see if + + + align:start position:0% +on comparing with neurons let's see if +its internals look like the neural data + + align:start position:0% +its internals look like the neural data + + + align:start position:0% +its internals look like the neural data +so here's the model we build HMO 1.0 + + align:start position:0% +so here's the model we build HMO 1.0 + + + align:start position:0% +so here's the model we build HMO 1.0 +it's a deep convolutional network it has + + align:start position:0% +it's a deep convolutional network it has + + + align:start position:0% +it's a deep convolutional network it has +these different layers it had four + + align:start position:0% +these different layers it had four + + + align:start position:0% +these different layers it had four +levels had a bunch of parameters that we + + align:start position:0% +levels had a bunch of parameters that we + + + align:start position:0% +levels had a bunch of parameters that we +set by optimization that I'm just + + align:start position:0% +set by optimization that I'm just + + + align:start position:0% +set by optimization that I'm just +telling you kind of what we optimize + + align:start position:0% +telling you kind of what we optimize + + + align:start position:0% +telling you kind of what we optimize +that I didn't tell you not telling you + + align:start position:0% +that I didn't tell you not telling you + + + align:start position:0% +that I didn't tell you not telling you +any of the parameters and now we come + + align:start position:0% +any of the parameters and now we come + + + align:start position:0% +any of the parameters and now we come +back to say well look we can show the + + align:start position:0% +back to say well look we can show the + + + align:start position:0% +back to say well look we can show the +same images to the model that we show to + + align:start position:0% +same images to the model that we show to + + + align:start position:0% +same images to the model that we show to +the + + align:start position:0% +the + + + align:start position:0% +the +neurons and then we can compare how well + + align:start position:0% +neurons and then we can compare how well + + + align:start position:0% +neurons and then we can compare how well +these populations look like that + + align:start position:0% +these populations look like that + + + align:start position:0% +these populations look like that +population or this population looks like + + align:start position:0% +population or this population looks like + + + align:start position:0% +population or this population looks like +that and and so what we did was we asked + + align:start position:0% +that and and so what we did was we asked + + + align:start position:0% +that and and so what we did was we asked +how well can layer four predict i.t + + align:start position:0% +how well can layer four predict i.t + + + align:start position:0% +how well can layer four predict i.t +first that was the first thing we wanted + + align:start position:0% +first that was the first thing we wanted + + + align:start position:0% +first that was the first thing we wanted +to do take the top layer of this model + + align:start position:0% +to do take the top layer of this model + + + align:start position:0% +to do take the top layer of this model +the last layer before the linear readout + + align:start position:0% +the last layer before the linear readout + + + align:start position:0% +the last layer before the linear readout +of this model and what to do that you + + align:start position:0% +of this model and what to do that you + + + align:start position:0% +of this model and what to do that you +might sort of say well wait a minute the + + align:start position:0% +might sort of say well wait a minute the + + + align:start position:0% +might sort of say well wait a minute the +model doesn't have mappings it has sort + + align:start position:0% +model doesn't have mappings it has sort + + + align:start position:0% +model doesn't have mappings it has sort +of neuron simulated here they're on 12 + + align:start position:0% +of neuron simulated here they're on 12 + + + align:start position:0% +of neuron simulated here they're on 12 +or something and there's something + + align:start position:0% +or something and there's something + + + align:start position:0% +or something and there's something +around we recorded but there's no + + align:start position:0% +around we recorded but there's no + + + align:start position:0% +around we recorded but there's no +linkage between that neuron and that + + align:start position:0% +linkage between that neuron and that + + + align:start position:0% +linkage between that neuron and that +neuron right you have to kind of make + + align:start position:0% +neuron right you have to kind of make + + + align:start position:0% +neuron right you have to kind of make +that map so what we do is we take each + + align:start position:0% +that map so what we do is we take each + + + align:start position:0% +that map so what we do is we take each +IT neuron and treat this as sort of a + + align:start position:0% +IT neuron and treat this as sort of a + + + align:start position:0% +IT neuron and treat this as sort of a +generative space you can generate as + + align:start position:0% +generative space you can generate as + + + align:start position:0% +generative space you can generate as +many simulated i.t neurons as you want + + align:start position:0% +many simulated i.t neurons as you want + + + align:start position:0% +many simulated i.t neurons as you want +you just ask let's take this neuron take + + align:start position:0% +you just ask let's take this neuron take + + + align:start position:0% +you just ask let's take this neuron take +some of its data and try to build a + + align:start position:0% +some of its data and try to build a + + + align:start position:0% +some of its data and try to build a +linear regression to this neuron tree + + align:start position:0% +linear regression to this neuron tree + + + align:start position:0% +linear regression to this neuron tree +this has a basis to explain that neuron + + align:start position:0% +this has a basis to explain that neuron + + + align:start position:0% +this has a basis to explain that neuron +and that's then test the predictive + + align:start position:0% +and that's then test the predictive + + + align:start position:0% +and that's then test the predictive +power on the held-out IT data that's + + align:start position:0% +power on the held-out IT data that's + + + align:start position:0% +power on the held-out IT data that's +what I'm writing here cross validated + + align:start position:0% +what I'm writing here cross validated + + + align:start position:0% +what I'm writing here cross validated +linear regression so I'm going to show + + align:start position:0% +linear regression so I'm going to show + + + align:start position:0% +linear regression so I'm going to show +you predictions on held-out data where + + align:start position:0% +you predictions on held-out data where + + + align:start position:0% +you predictions on held-out data where +some of the data were used to make the + + align:start position:0% +some of the data were used to make the + + + align:start position:0% +some of the data were used to make the +mapping and there's lots of ways we + + align:start position:0% +mapping and there's lots of ways we + + + align:start position:0% +mapping and there's lots of ways we +chose that we could make the mapping and + + align:start position:0% +chose that we could make the mapping and + + + align:start position:0% +chose that we could make the mapping and +we did essentially all of them then I + + align:start position:0% +we did essentially all of them then I + + + align:start position:0% +we did essentially all of them then I +could talk about that if you want but + + align:start position:0% +could talk about that if you want but + + + align:start position:0% +could talk about that if you want but +that's this central idea take some of + + align:start position:0% +that's this central idea take some of + + + align:start position:0% +that's this central idea take some of +your data say is this in the linear + + align:start position:0% +your data say is this in the linear + + + align:start position:0% +your data say is this in the linear +space spanned by this basis set so can I + + align:start position:0% +space spanned by this basis set so can I + + + align:start position:0% +space spanned by this basis set so can I +can I fit that well with this with this + + align:start position:0% +can I fit that well with this with this + + + align:start position:0% +can I fit that well with this with this +linear basis here because that's a + + align:start position:0% +linear basis here because that's a + + + align:start position:0% +linear basis here because that's a +linear map from this basis and here's + + align:start position:0% +linear map from this basis and here's + + + align:start position:0% +linear map from this basis and here's +what we actually here's what it looks + + align:start position:0% +what we actually here's what it looks + + + align:start position:0% +what we actually here's what it looks +like here's the IT neural response of + + align:start position:0% +like here's the IT neural response of + + + align:start position:0% +like here's the IT neural response of +one simulated I once actual IT neuron in + + align:start position:0% +one simulated I once actual IT neuron in + + + align:start position:0% +one simulated I once actual IT neuron in +black this is not time these are images + + align:start position:0% +black this is not time these are images + + + align:start position:0% +black this is not time these are images +there's I think there's like 1600 images + + align:start position:0% +there's I think there's like 1600 images + + + align:start position:0% +there's I think there's like 1600 images +here so each black line going up and + + align:start position:0% +here so each black line going up and + + + align:start position:0% +here so each black line going up and +down you can barely see is the response + + align:start position:0% +down you can barely see is the response + + + align:start position:0% +down you can barely see is the response +the mean response to different images + + align:start position:0% +the mean response to different images + + + align:start position:0% +the mean response to different images +and you see we group them by categories + + align:start position:0% +and you see we group them by categories + + + align:start position:0% +and you see we group them by categories +just so just to help you kind of + + align:start position:0% +just so just to help you kind of + + + align:start position:0% +just so just to help you kind of +understand the data otherwise would just + + align:start position:0% +understand the data otherwise would just + + + align:start position:0% +understand the data otherwise would just +be a big mess because I tune or else do + + align:start position:0% +be a big mess because I tune or else do + + + align:start position:0% +be a big mess because I tune or else do +you can kind of see they have a bit of + + align:start position:0% +you can kind of see they have a bit of + + + align:start position:0% +you can kind of see they have a bit of +category selectivity again this was + + align:start position:0% +category selectivity again this was + + + align:start position:0% +category selectivity again this was +known this neuron seems to like chair + + align:start position:0% +known this neuron seems to like chair + + + align:start position:0% +known this neuron seems to like chair +images but not all chair images is + + align:start position:0% +images but not all chair images is + + + align:start position:0% +images but not all chair images is +sometimes it likes boats and some planes + + align:start position:0% +sometimes it likes boats and some planes + + + align:start position:0% +sometimes it likes boats and some planes +a little bit and yet the red line is the + + align:start position:0% +a little bit and yet the red line is the + + + align:start position:0% +a little bit and yet the red line is the +prediction of the model once once fit to + + align:start position:0% +prediction of the model once once fit to + + + align:start position:0% +prediction of the model once once fit to +part of it to this neuron this is the + + align:start position:0% +part of it to this neuron this is the + + + align:start position:0% +part of it to this neuron this is the +prediction on the held out data for the + + align:start position:0% +prediction on the held out data for the + + + align:start position:0% +prediction on the held out data for the +neuron you can see the r-squared is 0.48 + + align:start position:0% +neuron you can see the r-squared is 0.48 + + + align:start position:0% +neuron you can see the r-squared is 0.48 +so half the explainable response + + align:start position:0% +so half the explainable response + + + align:start position:0% +so half the explainable response +variance is explained by this model + + align:start position:0% +variance is explained by this model + + + align:start position:0% +variance is explained by this model +and again these these are predictions + + align:start position:0% +and again these these are predictions + + + align:start position:0% +and again these these are predictions +the images were never seen + + align:start position:0% +the images were never seen + + + align:start position:0% +the images were never seen +the objects even were never seen by this + + align:start position:0% +the objects even were never seen by this + + + align:start position:0% +the objects even were never seen by this +model before when before it makes these + + align:start position:0% +model before when before it makes these + + + align:start position:0% +model before when before it makes these +predictions here so this is just saying + + align:start position:0% +predictions here so this is just saying + + + align:start position:0% +predictions here so this is just saying +that the IT neurons live in this space + + align:start position:0% +that the IT neurons live in this space + + + align:start position:0% +that the IT neurons live in this space +it's actually quite well captured by the + + align:start position:0% +it's actually quite well captured by the + + + align:start position:0% +it's actually quite well captured by the +top level in this case of this first HMO + + align:start position:0% +top level in this case of this first HMO + + + align:start position:0% +top level in this case of this first HMO +model we built I'll show you some other + + align:start position:0% +model we built I'll show you some other + + + align:start position:0% +model we built I'll show you some other +models in a minute + + align:start position:0% +models in a minute + + + align:start position:0% +models in a minute +here's another neuron that you might + + align:start position:0% +here's another neuron that you might + + + align:start position:0% +here's another neuron that you might +call a face neuron because it tends to + + align:start position:0% +call a face neuron because it tends to + + + align:start position:0% +call a face neuron because it tends to +like faces over not other categories so + + align:start position:0% +like faces over not other categories so + + + align:start position:0% +like faces over not other categories so +it might it would pass the test the + + align:start position:0% +it might it would pass the test the + + + align:start position:0% +it might it would pass the test the +operational definition of a face neuron + + align:start position:0% +operational definition of a face neuron + + + align:start position:0% +operational definition of a face neuron +this model this neuron was well + + align:start position:0% +this model this neuron was well + + + align:start position:0% +this model this neuron was well +predicted again but both it's preferred + + align:start position:0% +predicted again but both it's preferred + + + align:start position:0% +predicted again but both it's preferred +and non-preferred face images by this + + align:start position:0% +and non-preferred face images by this + + + align:start position:0% +and non-preferred face images by this +HMO model again a slightly an r-squared + + align:start position:0% +HMO model again a slightly an r-squared + + + align:start position:0% +HMO model again a slightly an r-squared +near 0.5 here's a neuron that you look + + align:start position:0% +near 0.5 here's a neuron that you look + + + align:start position:0% +near 0.5 here's a neuron that you look +at the category structure and you don't + + align:start position:0% +at the category structure and you don't + + + align:start position:0% +at the category structure and you don't +even you can't really see the egg + + align:start position:0% +even you can't really see the egg + + + align:start position:0% +even you can't really see the egg +categories here they're still here but + + align:start position:0% +categories here they're still here but + + + align:start position:0% +categories here they're still here but +you don't see these six blocks you just + + align:start position:0% +you don't see these six blocks you just + + + align:start position:0% +you don't see these six blocks you just +see this there were some images at likes + + align:start position:0% +see this there were some images at likes + + + align:start position:0% +see this there were some images at likes +and some it doesn't it's hard to even + + align:start position:0% +and some it doesn't it's hard to even + + + align:start position:0% +and some it doesn't it's hard to even +know what's driving this neuron but it's + + align:start position:0% +know what's driving this neuron but it's + + + align:start position:0% +know what's driving this neuron but it's +still actually quite well predicted I + + align:start position:0% +still actually quite well predicted I + + + align:start position:0% +still actually quite well predicted I +think I don't have the r-squared but + + align:start position:0% +think I don't have the r-squared but + + + align:start position:0% +think I don't have the r-squared but +it's it's similar it's about half the + + align:start position:0% +it's it's similar it's about half the + + + align:start position:0% +it's it's similar it's about half the +explainable variance just another + + align:start position:0% +explainable variance just another + + + align:start position:0% +explainable variance just another +example and here's a sort of summary + + align:start position:0% +example and here's a sort of summary + + + align:start position:0% +example and here's a sort of summary +here if you take this is a distribution + + align:start position:0% +here if you take this is a distribution + + + align:start position:0% +here if you take this is a distribution +of the explainable variance for the top + + align:start position:0% +of the explainable variance for the top + + + align:start position:0% +of the explainable variance for the top +level of the model fitting about I think + + align:start position:0% +level of the model fitting about I think + + + align:start position:0% +level of the model fitting about I think +this is 168 IT sites some sites are fit + + align:start position:0% +this is 168 IT sites some sites are fit + + + align:start position:0% +this is 168 IT sites some sites are fit +really well near a hundred percent some + + align:start position:0% +really well near a hundred percent some + + + align:start position:0% +really well near a hundred percent some +are it fit not as well the average is + + align:start position:0% +are it fit not as well the average is + + + align:start position:0% +are it fit not as well the average is +about 50 percent which is shown here so + + align:start position:0% +about 50 percent which is shown here so + + + align:start position:0% +about 50 percent which is shown here so +this is the median of that distribution + + align:start position:0% +this is the median of that distribution + + + align:start position:0% +this is the median of that distribution +here so the summary take-home is about + + align:start position:0% +here so the summary take-home is about + + + align:start position:0% +here so the summary take-home is about +50 percent of single gate response + + align:start position:0% +50 percent of single gate response + + + align:start position:0% +50 percent of single gate response +variance is predicted and this is a big + + align:start position:0% +variance is predicted and this is a big + + + align:start position:0% +variance is predicted and this is a big +improvement over previous models I'll + + align:start position:0% +improvement over previous models I'll + + + align:start position:0% +improvement over previous models I'll +show you in a minute + + align:start position:0% +show you in a minute + + + align:start position:0% +show you in a minute +the other levels of the model don't + + align:start position:0% +the other levels of the model don't + + + align:start position:0% +the other levels of the model don't +predict nearly well so the first level + + align:start position:0% +predict nearly well so the first level + + + align:start position:0% +predict nearly well so the first level +doesn't predict well second low a better + + align:start position:0% +doesn't predict well second low a better + + + align:start position:0% +doesn't predict well second low a better +third level better the fourth level the + + align:start position:0% +third level better the fourth level the + + + align:start position:0% +third level better the fourth level the +best if you take other models see some + + align:start position:0% +best if you take other models see some + + + align:start position:0% +best if you take other models see some +of the models I showed you earlier + + align:start position:0% +of the models I showed you earlier + + + align:start position:0% +of the models I showed you earlier +they don't fit nearly as well here's + + align:start position:0% +they don't fit nearly as well here's + + + align:start position:0% +they don't fit nearly as well here's +their distributions and here's their + + align:start position:0% +their distributions and here's their + + + align:start position:0% +their distributions and here's their +average they're meet their median + + align:start position:0% +average they're meet their median + + + align:start position:0% +average they're meet their median +explained variants and just to fix to + + align:start position:0% +explained variants and just to fix to + + + align:start position:0% +explained variants and just to fix to +just fix ideas you might think well look + + align:start position:0% +just fix ideas you might think well look + + + align:start position:0% +just fix ideas you might think well look +we built a model that's a good + + align:start position:0% +we built a model that's a good + + + align:start position:0% +we built a model that's a good +categorize er + + align:start position:0% +categorize er + + + align:start position:0% +categorize er +so of course it fits I Tina runs well + + align:start position:0% +so of course it fits I Tina runs well + + + align:start position:0% +so of course it fits I Tina runs well +because I T neurons are categorizes well + + align:start position:0% +because I T neurons are categorizes well + + + align:start position:0% +because I T neurons are categorizes well +here's a model that actually has + + align:start position:0% +here's a model that actually has + + + align:start position:0% +here's a model that actually has +explicit knowledge of the category it's + + align:start position:0% +explicit knowledge of the category it's + + + align:start position:0% +explicit knowledge of the category it's +not an image computable model and that's + + align:start position:0% +not an image computable model and that's + + + align:start position:0% +not an image computable model and that's +not an easy one but it's just given that + + align:start position:0% +not an easy one but it's just given that + + + align:start position:0% +not an easy one but it's just given that +sort of an Oracle that's given the + + align:start position:0% +sort of an Oracle that's given the + + + align:start position:0% +sort of an Oracle that's given the +category and how well it explains IT and + + align:start position:0% +category and how well it explains IT and + + + align:start position:0% +category and how well it explains IT and +you can see explains IT much worse than + + align:start position:0% +you can see explains IT much worse than + + + align:start position:0% +you can see explains IT much worse than +the actual model so this implies a model + + align:start position:0% +the actual model so this implies a model + + + align:start position:0% +the actual model so this implies a model +is limited by the real there art the + + align:start position:0% +is limited by the real there art the + + + align:start position:0% +is limited by the real there art the +architecture puts constraints on the + + align:start position:0% +architecture puts constraints on the + + + align:start position:0% +architecture puts constraints on the +model on how it adds variants that are + + align:start position:0% +model on how it adds variants that are + + + align:start position:0% +model on how it adds variants that are +that this is just a nineteen rounds or + + align:start position:0% +that this is just a nineteen rounds or + + + align:start position:0% +that this is just a nineteen rounds or +categories does not easily capture so so + + align:start position:0% +categories does not easily capture so so + + + align:start position:0% +categories does not easily capture so so +um that kind of that sort of inspired us + + align:start position:0% +um that kind of that sort of inspired us + + + align:start position:0% +um that kind of that sort of inspired us +to say okay what about if we go down and + + align:start position:0% +to say okay what about if we go down and + + + align:start position:0% +to say okay what about if we go down and +say not just IT but let's go to v4 + + align:start position:0% +say not just IT but let's go to v4 + + + align:start position:0% +say not just IT but let's go to v4 +because we had a bunch of v4 data and so + + align:start position:0% +because we had a bunch of v4 data and so + + + align:start position:0% +because we had a bunch of v4 data and so +we play the same game in v4 let's take + + align:start position:0% +we play the same game in v4 let's take + + + align:start position:0% +we play the same game in v4 let's take +level three and see if we can predict v4 + + align:start position:0% +level three and see if we can predict v4 + + + align:start position:0% +level three and see if we can predict v4 +and here's the IT data I just showed you + + align:start position:0% +and here's the IT data I just showed you + + + align:start position:0% +and here's the IT data I just showed you +a minute ago and here's the v4 data so + + align:start position:0% +a minute ago and here's the v4 data so + + + align:start position:0% +a minute ago and here's the v4 data so +the v4 neurons are highly predicted in + + align:start position:0% +the v4 neurons are highly predicted in + + + align:start position:0% +the v4 neurons are highly predicted in +the middle layer layer three is the best + + align:start position:0% +the middle layer layer three is the best + + + align:start position:0% +the middle layer layer three is the best +predictor of v4 a little top layer is + + align:start position:0% +predictor of v4 a little top layer is + + + align:start position:0% +predictor of v4 a little top layer is +actually not so predictive less + + align:start position:0% +actually not so predictive less + + + align:start position:0% +actually not so predictive less +predictive of v4 neurons than the middle + + align:start position:0% +predictive of v4 neurons than the middle + + + align:start position:0% +predictive of v4 neurons than the middle +layers and the first layer is not so + + align:start position:0% +layers and the first layer is not so + + + align:start position:0% +layers and the first layer is not so +well predictive and again the other + + align:start position:0% +well predictive and again the other + + + align:start position:0% +well predictive and again the other +models are actually now you can see + + align:start position:0% +models are actually now you can see + + + align:start position:0% +models are actually now you can see +they're getting on it and relatively + + align:start position:0% +they're getting on it and relatively + + + align:start position:0% +they're getting on it and relatively +better you can think of them as sort of + + align:start position:0% +better you can think of them as sort of + + + align:start position:0% +better you can think of them as sort of +lower lower level models and they're + + align:start position:0% +lower lower level models and they're + + + align:start position:0% +lower lower level models and they're +they're getting better which is what + + align:start position:0% +they're getting better which is what + + + align:start position:0% +they're getting better which is what +you'd expect but interestingly this is + + align:start position:0% +you'd expect but interestingly this is + + + align:start position:0% +you'd expect but interestingly this is +really exciting to us because look this + + align:start position:0% +really exciting to us because look this + + + align:start position:0% +really exciting to us because look this +model was not optimized to fit any + + align:start position:0% +model was not optimized to fit any + + + align:start position:0% +model was not optimized to fit any +neural data other than that last mapping + + align:start position:0% +neural data other than that last mapping + + + align:start position:0% +neural data other than that last mapping +step all it is is a bio-inspired + + align:start position:0% +step all it is is a bio-inspired + + + align:start position:0% +step all it is is a bio-inspired +algorithm class which is the + + align:start position:0% +algorithm class which is the + + + align:start position:0% +algorithm class which is the +neuroscience sort of view of the + + align:start position:0% +neuroscience sort of view of the + + + align:start position:0% +neuroscience sort of view of the +feed-forward class of the field and + + align:start position:0% +feed-forward class of the field and + + + align:start position:0% +feed-forward class of the field and +tasks that we and others hypothesize are + + align:start position:0% +tasks that we and others hypothesize are + + + align:start position:0% +tasks that we and others hypothesize are +important that the ventral shoe might be + + align:start position:0% +important that the ventral shoe might be + + + align:start position:0% +important that the ventral shoe might be +optimized to solve an an actual + + align:start position:0% +optimized to solve an an actual + + + align:start position:0% +optimized to solve an an actual +optimization procedure that we applied + + align:start position:0% +optimization procedure that we applied + + + align:start position:0% +optimization procedure that we applied +and that leads to neuro like encoding + + align:start position:0% +and that leads to neuro like encoding + + + align:start position:0% +and that leads to neuro like encoding +functions at the top and in the middle + + align:start position:0% +functions at the top and in the middle + + + align:start position:0% +functions at the top and in the middle +layer so you don't you know you this so + + align:start position:0% +layer so you don't you know you this so + + + align:start position:0% +layer so you don't you know you this so +this sort of leads to funny things like + + align:start position:0% +this sort of leads to funny things like + + + align:start position:0% +this sort of leads to funny things like +saying what does v4 do the answer here + + align:start position:0% +saying what does v4 do the answer here + + + align:start position:0% +saying what does v4 do the answer here +would be well it's an intermediate layer + + align:start position:0% +would be well it's an intermediate layer + + + align:start position:0% +would be well it's an intermediate layer +in a network milk then to optimize these + + align:start position:0% +in a network milk then to optimize these + + + align:start position:0% +in a network milk then to optimize these +things that's the way to describe what + + align:start position:0% +things that's the way to describe what + + + align:start position:0% +things that's the way to describe what +b4 does according to this kind of + + align:start position:0% +b4 does according to this kind of + + + align:start position:0% +b4 does according to this kind of +modeling approach now I want to point + + align:start position:0% +modeling approach now I want to point + + + align:start position:0% +modeling approach now I want to point +out this is only half of the explainable + + align:start position:0% +out this is only half of the explainable + + + align:start position:0% +out this is only half of the explainable +variance so it's far from perfect + + align:start position:0% +variance so it's far from perfect + + + align:start position:0% +variance so it's far from perfect +there's room to improve here but it's + + align:start position:0% +there's room to improve here but it's + + + align:start position:0% +there's room to improve here but it's +really dramatic how much improvement we + + align:start position:0% +really dramatic how much improvement we + + + align:start position:0% +really dramatic how much improvement we +got out of these kind of models and so + + align:start position:0% +got out of these kind of models and so + + + align:start position:0% +got out of these kind of models and so +if you take you take this sort of you + + align:start position:0% +if you take you take this sort of you + + + align:start position:0% +if you take you take this sort of you +know I'll skip this as other if you take + + align:start position:0% +know I'll skip this as other if you take + + + align:start position:0% +know I'll skip this as other if you take +this back to you know big picture what + + align:start position:0% +this back to you know big picture what + + + align:start position:0% +this back to you know big picture what +did we do here what we're doing is we + + align:start position:0% +did we do here what we're doing is we + + + align:start position:0% +did we do here what we're doing is we +have performance of a model on high + + align:start position:0% +have performance of a model on high + + + align:start position:0% +have performance of a model on high +invariance recognition test for saying + + align:start position:0% +invariance recognition test for saying + + + align:start position:0% +invariance recognition test for saying +this is what we were seeing what we've + + align:start position:0% +this is what we were seeing what we've + + + align:start position:0% +this is what we were seeing what we've +been trying to optimize and when we + + align:start position:0% +been trying to optimize and when we + + + align:start position:0% +been trying to optimize and when we +noticed is that if you plot these dots + + align:start position:0% +noticed is that if you plot these dots + + + align:start position:0% +noticed is that if you plot these dots +are samples out of that model family + + align:start position:0% +are samples out of that model family + + + align:start position:0% +are samples out of that model family +these black dots are other models I + + align:start position:0% +these black dots are other models I + + + align:start position:0% +these black dots are other models I +showed you through control models that + + align:start position:0% +showed you through control models that + + + align:start position:0% +showed you through control models that +were in the field at the time and this + + align:start position:0% +were in the field at the time and this + + + align:start position:0% +were in the field at the time and this +is the ability of the top of that model + + align:start position:0% +is the ability of the top of that model + + + align:start position:0% +is the ability of the top of that model +the top level of the any of the models + + align:start position:0% +the top level of the any of the models + + + align:start position:0% +the top level of the any of the models +to predict IT responses so you know how + + align:start position:0% +to predict IT responses so you know how + + + align:start position:0% +to predict IT responses so you know how +good they are predicting the this is + + align:start position:0% +good they are predicting the this is + + + align:start position:0% +good they are predicting the this is +sort of the median variance explained of + + align:start position:0% +sort of the median variance explained of + + + align:start position:0% +sort of the median variance explained of +responses and you see there's a + + align:start position:0% +responses and you see there's a + + + align:start position:0% +responses and you see there's a +correlation here if you're better at + + align:start position:0% +correlation here if you're better at + + + align:start position:0% +correlation here if you're better at +this + + align:start position:0% +this + + + align:start position:0% +this +you're better predicting that and all we + + align:start position:0% +you're better predicting that and all we + + + align:start position:0% +you're better predicting that and all we +did was optimize this way which we think + + align:start position:0% +did was optimize this way which we think + + + align:start position:0% +did was optimize this way which we think +of as like evolution or development so + + align:start position:0% +of as like evolution or development so + + + align:start position:0% +of as like evolution or development so +we're not fitting your old data we're + + align:start position:0% +we're not fitting your old data we're + + + align:start position:0% +we're not fitting your old data we're +just optimizing for task performance and + + align:start position:0% +just optimizing for task performance and + + + align:start position:0% +just optimizing for task performance and +that led in 2012 to a model that I just + + align:start position:0% +that led in 2012 to a model that I just + + + align:start position:0% +that led in 2012 to a model that I just +showed you explained about half of the + + align:start position:0% +showed you explained about half of the + + + align:start position:0% +showed you explained about half of the +IT response variance okay so if like + + align:start position:0% +IT response variance okay so if like + + + align:start position:0% +IT response variance okay so if like +well this looks like it's continuing up + + align:start position:0% +well this looks like it's continuing up + + + align:start position:0% +well this looks like it's continuing up +this way okay so if you believe that + + align:start position:0% +this way okay so if you believe that + + + align:start position:0% +this way okay so if you believe that +story then that says if we can optimize + + align:start position:0% +story then that says if we can optimize + + + align:start position:0% +story then that says if we can optimize +further on these kind of tasks maybe we + + align:start position:0% +further on these kind of tasks maybe we + + + align:start position:0% +further on these kind of tasks maybe we +can explain more variance and it turned + + align:start position:0% +can explain more variance and it turned + + + align:start position:0% +can explain more variance and it turned +out we didn't actually need to do that + + align:start position:0% +out we didn't actually need to do that + + + align:start position:0% +out we didn't actually need to do that +because again I said computer vision was + + align:start position:0% +because again I said computer vision was + + + align:start position:0% +because again I said computer vision was +already working on this and they got a + + align:start position:0% +already working on this and they got a + + + align:start position:0% +already working on this and they got a +lot more resources they're already doing + + align:start position:0% +lot more resources they're already doing + + + align:start position:0% +lot more resources they're already doing +it they're already better than us on + + align:start position:0% +it they're already better than us on + + + align:start position:0% +it they're already better than us on +this so here was our HMO model this is + + align:start position:0% +this so here was our HMO model this is + + + align:start position:0% +this so here was our HMO model this is +now Charles could do a postdoc in the + + align:start position:0% +now Charles could do a postdoc in the + + + align:start position:0% +now Charles could do a postdoc in the +lab these were models that came out the + + align:start position:0% +lab these were models that came out the + + + align:start position:0% +lab these were models that came out the +time this is Chris chefs key at all + + align:start position:0% +time this is Chris chefs key at all + + + align:start position:0% +time this is Chris chefs key at all +supervision is either at Fergus 2013 + + align:start position:0% +supervision is either at Fergus 2013 + + + align:start position:0% +supervision is either at Fergus 2013 +they were better than the model that we + + align:start position:0% +they were better than the model that we + + + align:start position:0% +they were better than the model that we +had built you know we were in this + + align:start position:0% +had built you know we were in this + + + align:start position:0% +had built you know we were in this +restricted image domain you know we + + align:start position:0% +restricted image domain you know we + + + align:start position:0% +restricted image domain you know we +there's lots of reasons why we could say + + align:start position:0% +there's lots of reasons why we could say + + + align:start position:0% +there's lots of reasons why we could say +they're better regardless they were + + align:start position:0% +they're better regardless they were + + + align:start position:0% +they're better regardless they were +better at our own tasks than the models + + align:start position:0% +better at our own tasks than the models + + + align:start position:0% +better at our own tasks than the models +that we had built right so they were + + align:start position:0% +that we had built right so they were + + + align:start position:0% +that we had built right so they were +already ahead of us upon the tasks that + + align:start position:0% +already ahead of us upon the tasks that + + + align:start position:0% +already ahead of us upon the tasks that +we had designed and so they were up here + + align:start position:0% +we had designed and so they were up here + + + align:start position:0% +we had designed and so they were up here +and then they're up here and so if you + + align:start position:0% +and then they're up here and so if you + + + align:start position:0% +and then they're up here and so if you +follow that prediction that means these + + align:start position:0% +follow that prediction that means these + + + align:start position:0% +follow that prediction that means these +models might be better predictors of our + + align:start position:0% +models might be better predictors of our + + + align:start position:0% +models might be better predictors of our +neural data right these guys don't have + + align:start position:0% +neural data right these guys don't have + + + align:start position:0% +neural data right these guys don't have +our neural date all they're doing is + + align:start position:0% +our neural date all they're doing is + + + align:start position:0% +our neural date all they're doing is +building models to optimize performance + + align:start position:0% +building models to optimize performance + + + align:start position:0% +building models to optimize performance +on tasks and but we could take their + + align:start position:0% +on tasks and but we could take their + + + align:start position:0% +on tasks and but we could take their +features from the neural data play the + + align:start position:0% +features from the neural data play the + + + align:start position:0% +features from the neural data play the +same game and we actually explained our + + align:start position:0% +same game and we actually explained our + + + align:start position:0% +same game and we actually explained our +respond our model explained our own data + + align:start position:0% +respond our model explained our own data + + + align:start position:0% +respond our model explained our own data +so this is a nice statement that is it's + + align:start position:0% +so this is a nice statement that is it's + + + align:start position:0% +so this is a nice statement that is it's +not even in our own lab just to continue + + align:start position:0% +not even in our own lab just to continue + + + align:start position:0% +not even in our own lab just to continue +to optimization for those kind of tasks + + align:start position:0% +to optimization for those kind of tasks + + + align:start position:0% +to optimization for those kind of tasks +leads to features that are good + + align:start position:0% +leads to features that are good + + + align:start position:0% +leads to features that are good +predictors of the IT responses and + + align:start position:0% +predictors of the IT responses and + + + align:start position:0% +predictors of the IT responses and +that's what's shown here so I think + + align:start position:0% +that's what's shown here so I think + + + align:start position:0% +that's what's shown here so I think +that's what I I just said there so that + + align:start position:0% +that's what I I just said there so that + + + align:start position:0% +that's what I I just said there so that +Charles took this further and analyzed + + align:start position:0% +Charles took this further and analyzed + + + align:start position:0% +Charles took this further and analyzed +this in more detail this is a summary + + align:start position:0% +this in more detail this is a summary + + + align:start position:0% +this in more detail this is a summary +what I presented in the second half now + + align:start position:0% +what I presented in the second half now + + + align:start position:0% +what I presented in the second half now +showing that IT firing rates are feature + + align:start position:0% +showing that IT firing rates are feature + + + align:start position:0% +showing that IT firing rates are feature +based learned object judgments naturally + + align:start position:0% +based learned object judgments naturally + + + align:start position:0% +based learned object judgments naturally +predict human monkey performance this is + + align:start position:0% +predict human monkey performance this is + + + align:start position:0% +predict human monkey performance this is +why we've the laws of RAD IT I've picked + + align:start position:0% +why we've the laws of RAD IT I've picked + + + align:start position:0% +why we've the laws of RAD IT I've picked +a particular model which is a 100 + + align:start position:0% +a particular model which is a 100 + + + align:start position:0% +a particular model which is a 100 +millisecond read on this time window + + align:start position:0% +millisecond read on this time window + + + align:start position:0% +millisecond read on this time window +50,000 neurons 100 training examples + + align:start position:0% +50,000 neurons 100 training examples + + + align:start position:0% +50,000 neurons 100 training examples +that's one particular choice of a decode + + align:start position:0% +that's one particular choice of a decode + + + align:start position:0% +that's one particular choice of a decode +model that's just a is a current current + + align:start position:0% +model that's just a is a current current + + + align:start position:0% +model that's just a is a current current +set of decode miles it fits a lot of our + + align:start position:0% +set of decode miles it fits a lot of our + + + align:start position:0% +set of decode miles it fits a lot of our +data but not all of our data and we also + + align:start position:0% +data but not all of our data and we also + + + align:start position:0% +data but not all of our data and we also +want to get finer + + align:start position:0% +want to get finer + + + align:start position:0% +want to get finer +brain data the inference is this might + + align:start position:0% +brain data the inference is this might + + + align:start position:0% +brain data the inference is this might +be the specific neural code and decoding + + align:start position:0% +be the specific neural code and decoding + + + align:start position:0% +be the specific neural code and decoding +mechanism that the brain uses to support + + align:start position:0% +mechanism that the brain uses to support + + + align:start position:0% +mechanism that the brain uses to support +these tasks that's we'd like to think + + align:start position:0% +these tasks that's we'd like to think + + + align:start position:0% +these tasks that's we'd like to think +but now we're trying to do systemic + + align:start position:0% +but now we're trying to do systemic + + + align:start position:0% +but now we're trying to do systemic +causal tests and we talked a lot about + + align:start position:0% +causal tests and we talked a lot about + + + align:start position:0% +causal tests and we talked a lot about +trying to silence bits of ideas one + + align:start position:0% +trying to silence bits of ideas one + + + align:start position:0% +trying to silence bits of ideas one +example of that and the tools are still + + align:start position:0% +example of that and the tools are still + + + align:start position:0% +example of that and the tools are still +not clear we'd like them to be but you + + align:start position:0% +not clear we'd like them to be but you + + + align:start position:0% +not clear we'd like them to be but you +see we're making progress there + + align:start position:0% +see we're making progress there + + + align:start position:0% +see we're making progress there +so the second was I showed that + + align:start position:0% +so the second was I showed that + + + align:start position:0% +so the second was I showed that +optimization of deep CN n models for + + align:start position:0% +optimization of deep CN n models for + + + align:start position:0% +optimization of deep CN n models for +invariant object recognition tabs led to + + align:start position:0% +invariant object recognition tabs led to + + + align:start position:0% +invariant object recognition tabs led to +dramatic improvements and our ability to + + align:start position:0% +dramatic improvements and our ability to + + + align:start position:0% +dramatic improvements and our ability to +predict IT in v4 responses I showed you + + align:start position:0% +predict IT in v4 responses I showed you + + + align:start position:0% +predict IT in v4 responses I showed you +our male chamo but then the + + align:start position:0% +our male chamo but then the + + + align:start position:0% +our male chamo but then the +convolutional neural networks in the + + align:start position:0% +convolutional neural networks in the + + + align:start position:0% +convolutional neural networks in the +field have already surpassed our + + align:start position:0% +field have already surpassed our + + + align:start position:0% +field have already surpassed our +predictive ability on earth I don't own + + align:start position:0% +predictive ability on earth I don't own + + + align:start position:0% +predictive ability on earth I don't own +data and so the inference is that these + + align:start position:0% +data and so the inference is that these + + + align:start position:0% +data and so the inference is that these +encoding mechanisms in these models + + align:start position:0% +encoding mechanisms in these models + + + align:start position:0% +encoding mechanisms in these models +might be similar to does it work in the + + align:start position:0% +might be similar to does it work in the + + + align:start position:0% +might be similar to does it work in the +ventral stream and and now you know + + align:start position:0% +ventral stream and and now you know + + + align:start position:0% +ventral stream and and now you know +there's a whole sort of area where you + + align:start position:0% +there's a whole sort of area where you + + + align:start position:0% +there's a whole sort of area where you +can start to think about doing + + align:start position:0% +can start to think about doing + + + align:start position:0% +can start to think about doing +physiology on the models so to speak and + + align:start position:0% +physiology on the models so to speak and + + + align:start position:0% +physiology on the models so to speak and +that problems almost as hard as doing + + align:start position:0% +that problems almost as hard as doing + + + align:start position:0% +that problems almost as hard as doing +physiology except on the animal except + + align:start position:0% +physiology except on the animal except + + + align:start position:0% +physiology except on the animal except +that you gain a lot more data and so and + + align:start position:0% +that you gain a lot more data and so and + + + align:start position:0% +that you gain a lot more data and so and +this is allowing a field of design + + align:start position:0% +this is allowing a field of design + + + align:start position:0% +this is allowing a field of design +Explorer meaning what's unique and + + align:start position:0% +Explorer meaning what's unique and + + + align:start position:0% +Explorer meaning what's unique and +powerful about primary object + + align:start position:0% +powerful about primary object + + + align:start position:0% +powerful about primary object +perceptions so within core object + + align:start position:0% +perceptions so within core object + + + align:start position:0% +perceptions so within core object +recognition or perhaps having to extend + + align:start position:0% +recognition or perhaps having to extend + + + align:start position:0% +recognition or perhaps having to extend +out of that I think is now what people + + align:start position:0% +out of that I think is now what people + + + align:start position:0% +out of that I think is now what people +are trying to do so a big picture in + + align:start position:0% +are trying to do so a big picture in + + + align:start position:0% +are trying to do so a big picture in +terms of us for the future I've talked + + align:start position:0% +terms of us for the future I've talked + + + align:start position:0% +terms of us for the future I've talked +about this laws of RAD IT can we perturb + + align:start position:0% +about this laws of RAD IT can we perturb + + + align:start position:0% +about this laws of RAD IT can we perturb +here and get effects here that are + + align:start position:0% +here and get effects here that are + + + align:start position:0% +here and get effects here that are +predictable can we predict for each + + align:start position:0% +predictable can we predict for each + + + align:start position:0% +predictable can we predict for each +image coding model at hand for the + + align:start position:0% +image coding model at hand for the + + + align:start position:0% +image coding model at hand for the +optical manipulations we talked about + + align:start position:0% +optical manipulations we talked about + + + align:start position:0% +optical manipulations we talked about +that dynamics and feedback are something + + align:start position:0% +that dynamics and feedback are something + + + align:start position:0% +that dynamics and feedback are something +that we're interested in but I haven't + + align:start position:0% +that we're interested in but I haven't + + + align:start position:0% +that we're interested in but I haven't +talked much at all about I think that's + + align:start position:0% +talked much at all about I think that's + + + align:start position:0% +talked much at all about I think that's +a good point a discussion topic I can + + align:start position:0% +a good point a discussion topic I can + + + align:start position:0% +a good point a discussion topic I can +tell you how we're thinking about it we + + align:start position:0% +tell you how we're thinking about it we + + + align:start position:0% +tell you how we're thinking about it we +have some some some efforts in that + + align:start position:0% +have some some some efforts in that + + + align:start position:0% +have some some some efforts in that +regard I talked on the encoding side + + align:start position:0% +regard I talked on the encoding side + + + align:start position:0% +regard I talked on the encoding side +about these kind of deep convolutional + + align:start position:0% +about these kind of deep convolutional + + + align:start position:0% +about these kind of deep convolutional +networks that map from images but the + + align:start position:0% +networks that map from images but the + + + align:start position:0% +networks that map from images but the +dashed lines mean they're only 50% + + align:start position:0% +dashed lines mean they're only 50% + + + align:start position:0% +dashed lines mean they're only 50% +predicted both of these cases they're + + align:start position:0% +predicted both of these cases they're + + + align:start position:0% +predicted both of these cases they're +not perfect right so there's work to be + + align:start position:0% +not perfect right so there's work to be + + + align:start position:0% +not perfect right so there's work to be +done there and one of the really + + align:start position:0% +done there and one of the really + + + align:start position:0% +done there and one of the really +exciting things is here is how these + + align:start position:0% +exciting things is here is how these + + + align:start position:0% +exciting things is here is how these +models learn this supervised way of + + align:start position:0% +models learn this supervised way of + + + align:start position:0% +models learn this supervised way of +learning these models is almost surely + + align:start position:0% +learning these models is almost surely + + + align:start position:0% +learning these models is almost surely +not what's going on in the brain so + + align:start position:0% +not what's going on in the brain so + + + align:start position:0% +not what's going on in the brain so +finding more less supervised motivated + + align:start position:0% +finding more less supervised motivated + + + align:start position:0% +finding more less supervised motivated +learning of these models is a good is + + align:start position:0% +learning of these models is a good is + + + align:start position:0% +learning of these models is a good is +the next step I think for much of the + + align:start position:0% +the next step I think for much of the + + + align:start position:0% +the next step I think for much of the +field but what's nice is it needs to + + align:start position:0% +field but what's nice is it needs to + + + align:start position:0% +field but what's nice is it needs to +have an end state that's much better + + align:start position:0% +have an end state that's much better + + + align:start position:0% +have an end state that's much better +than any previous end state we'd had + + align:start position:0% +than any previous end state we'd had + + + align:start position:0% +than any previous end state we'd had +before so that that sets a target of + + align:start position:0% +before so that that sets a target of + + + align:start position:0% +before so that that sets a target of +what success might look like and you + + align:start position:0% +what success might look like and you + + + align:start position:0% +what success might look like and you +know + + align:start position:0% +know + + + align:start position:0% +know +maybe we can think about expanding + + align:start position:0% +maybe we can think about expanding + + + align:start position:0% +maybe we can think about expanding +beyond core recognition in the question + + align:start position:0% +beyond core recognition in the question + + + align:start position:0% +beyond core recognition in the question +period about that what when is the right + + align:start position:0% +period about that what when is the right + + + align:start position:0% +period about that what when is the right +time to kind of keep working within the + + align:start position:0% +time to kind of keep working within the + + + align:start position:0% +time to kind of keep working within the +domain of core recognition of that said + + align:start position:0% +domain of core recognition of that said + + + align:start position:0% +domain of core recognition of that said +that I set up versus expanding beyond + + align:start position:0% +that I set up versus expanding beyond + + + align:start position:0% +that I set up versus expanding beyond +that because there's lots of aspects of + + align:start position:0% +that because there's lots of aspects of + + + align:start position:0% +that because there's lots of aspects of +object recognition that I didn't touch + + align:start position:0% +object recognition that I didn't touch + + + align:start position:0% +object recognition that I didn't touch +on here and that comes up in the + + align:start position:0% +on here and that comes up in the + + + align:start position:0% +on here and that comes up in the +questions I I think this this both of + + align:start position:0% +questions I I think this this both of + + + align:start position:0% +questions I I think this this both of +there's there's lots of work to be done + + align:start position:0% +there's there's lots of work to be done + + + align:start position:0% +there's there's lots of work to be done +within the domain but there's also + + align:start position:0% +within the domain but there's also + + + align:start position:0% +within the domain but there's also +interesting sections that extend outside + + align:start position:0% +interesting sections that extend outside + + + align:start position:0% +interesting sections that extend outside +of that domain + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/AobB_-N_rGM.txt b/AobB_-N_rGM.txt new file mode 100644 index 0000000000000000000000000000000000000000..c12ea972e296b8d797ebb581af7c64a37c556c72 --- /dev/null +++ b/AobB_-N_rGM.txt @@ -0,0 +1,1643 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +an artificial dialectric made from an + + align:start position:0% +an artificial dialectric made from an + + + align:start position:0% +an artificial dialectric made from an +array of conducting spheres demonstrates + + align:start position:0% +array of conducting spheres demonstrates + + + align:start position:0% +array of conducting spheres demonstrates +how polarization of media gives rise to + + align:start position:0% +how polarization of media gives rise to + + + align:start position:0% +how polarization of media gives rise to +the properties of a linear + + align:start position:0% + + + + align:start position:0% + +dialectric when the region between + + align:start position:0% +dialectric when the region between + + + align:start position:0% +dialectric when the region between +electrodes is filled with a dialectric + + align:start position:0% +electrodes is filled with a dialectric + + + align:start position:0% +electrodes is filled with a dialectric +material the capacitance is + + align:start position:0% +material the capacitance is + + + align:start position:0% +material the capacitance is +increased this increase is due to + + align:start position:0% +increased this increase is due to + + + align:start position:0% +increased this increase is due to +polarization of molecules of the + + align:start position:0% +polarization of molecules of the + + + align:start position:0% +polarization of molecules of the +material + + align:start position:0% +material + + + align:start position:0% +material +we form an appreciation for how this + + align:start position:0% +we form an appreciation for how this + + + align:start position:0% +we form an appreciation for how this +happens by replacing the molecules with + + align:start position:0% +happens by replacing the molecules with + + + align:start position:0% +happens by replacing the molecules with +macroscopic spheres suspended in + + align:start position:0% +macroscopic spheres suspended in + + + align:start position:0% +macroscopic spheres suspended in +air this artificial dialectric is + + align:start position:0% +air this artificial dialectric is + + + align:start position:0% +air this artificial dialectric is +composed of what we can think of as + + align:start position:0% +composed of what we can think of as + + + align:start position:0% +composed of what we can think of as +molecules that are actually essentially + + align:start position:0% +molecules that are actually essentially + + + align:start position:0% +molecules that are actually essentially +perfectly conducting + + align:start position:0% +perfectly conducting + + + align:start position:0% +perfectly conducting +spheres each has radius + + align:start position:0% +spheres each has radius + + + align:start position:0% +spheres each has radius +R and they're in a cubic array with + + align:start position:0% +R and they're in a cubic array with + + + align:start position:0% +R and they're in a cubic array with +spacing + + align:start position:0% + + + + align:start position:0% + +s application of voltage to the + + align:start position:0% +s application of voltage to the + + + align:start position:0% +s application of voltage to the +electrodes results in the Spheres + + align:start position:0% +electrodes results in the Spheres + + + align:start position:0% +electrodes results in the Spheres +acquiring positive and negative surface + + align:start position:0% +acquiring positive and negative surface + + + align:start position:0% +acquiring positive and negative surface +charges on their + + align:start position:0% +charges on their + + + align:start position:0% +charges on their +poles in addition to the uniform field + + align:start position:0% +poles in addition to the uniform field + + + align:start position:0% +poles in addition to the uniform field +due to the applied voltage the field + + align:start position:0% +due to the applied voltage the field + + + align:start position:0% +due to the applied voltage the field +outside the Spheres also includes the + + align:start position:0% +outside the Spheres also includes the + + + align:start position:0% +outside the Spheres also includes the +dipole fields from the array of + + align:start position:0% +dipole fields from the array of + + + align:start position:0% +dipole fields from the array of +spheres the Spheres like the molecules + + align:start position:0% +spheres the Spheres like the molecules + + + align:start position:0% +spheres the Spheres like the molecules +of a material are polarized by an + + align:start position:0% +of a material are polarized by an + + + align:start position:0% +of a material are polarized by an +applied + + align:start position:0% +applied + + + align:start position:0% +applied +field the artificial dialectric is + + align:start position:0% +field the artificial dialectric is + + + align:start position:0% +field the artificial dialectric is +composed of an array of pingpong balls + + align:start position:0% +composed of an array of pingpong balls + + + align:start position:0% +composed of an array of pingpong balls +with conducting + + align:start position:0% + + + + align:start position:0% + +Coatings we're going to measure the + + align:start position:0% +Coatings we're going to measure the + + + align:start position:0% +Coatings we're going to measure the +effective primitivity by measuring the + + align:start position:0% +effective primitivity by measuring the + + + align:start position:0% +effective primitivity by measuring the +change in capacitance as the array is + + align:start position:0% +change in capacitance as the array is + + + align:start position:0% +change in capacitance as the array is +placed between the plates of this plain + + align:start position:0% +placed between the plates of this plain + + + align:start position:0% +placed between the plates of this plain +parallel plate + + align:start position:0% + + + + align:start position:0% + +capacitor the cage is grounded for + + align:start position:0% +capacitor the cage is grounded for + + + align:start position:0% +capacitor the cage is grounded for +shielding and to keep us from touching + + align:start position:0% +shielding and to keep us from touching + + + align:start position:0% +shielding and to keep us from touching +the bottom electrode + + align:start position:0% +the bottom electrode + + + align:start position:0% +the bottom electrode +it's driven to 400 volts RMS at 250 + + align:start position:0% +it's driven to 400 volts RMS at 250 + + + align:start position:0% +it's driven to 400 volts RMS at 250 +Hertz by this + + align:start position:0% +Hertz by this + + + align:start position:0% +Hertz by this +Transformer which is itself driven by an + + align:start position:0% +Transformer which is itself driven by an + + + align:start position:0% +Transformer which is itself driven by an +oscillator and + + align:start position:0% + + + + align:start position:0% + +amplifier here's the top + + align:start position:0% + + + + align:start position:0% + +electrode to avoid fringing effects only + + align:start position:0% +electrode to avoid fringing effects only + + + align:start position:0% +electrode to avoid fringing effects only +the charge induced on this Central + + align:start position:0% +the charge induced on this Central + + + align:start position:0% +the charge induced on this Central +section will be measured when we measure + + align:start position:0% +section will be measured when we measure + + + align:start position:0% +section will be measured when we measure +the capacitance + + align:start position:0% + + + + align:start position:0% + +here's how the dialectric is inserted + + align:start position:0% +here's how the dialectric is inserted + + + align:start position:0% +here's how the dialectric is inserted +between the + + align:start position:0% + + + + align:start position:0% + +plates this is a picture of the + + align:start position:0% +plates this is a picture of the + + + align:start position:0% +plates this is a picture of the +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +here's the Transformer driving the lower + + align:start position:0% +here's the Transformer driving the lower + + + align:start position:0% +here's the Transformer driving the lower +electrode here's the top plate connected + + align:start position:0% +electrode here's the top plate connected + + + align:start position:0% +electrode here's the top plate connected +to one side of a differential + + align:start position:0% +to one side of a differential + + + align:start position:0% +to one side of a differential +amplifier because the spacing between + + align:start position:0% +amplifier because the spacing between + + + align:start position:0% +amplifier because the spacing between +spheres is more than two diameters the + + align:start position:0% +spheres is more than two diameters the + + + align:start position:0% +spheres is more than two diameters the +increase in capacitance caused by the + + align:start position:0% +increase in capacitance caused by the + + + align:start position:0% +increase in capacitance caused by the +Spheres is + + align:start position:0% +Spheres is + + + align:start position:0% +Spheres is +small to measure the small change in + + align:start position:0% +small to measure the small change in + + + align:start position:0% +small to measure the small change in +capacitance that results from inserting + + align:start position:0% +capacitance that results from inserting + + + align:start position:0% +capacitance that results from inserting +the array the parallel plate capacitor + + align:start position:0% +the array the parallel plate capacitor + + + align:start position:0% +the array the parallel plate capacitor +is in one leg of a + + align:start position:0% +is in one leg of a + + + align:start position:0% +is in one leg of a +bridge these capacitors are in the other + + align:start position:0% +bridge these capacitors are in the other + + + align:start position:0% +bridge these capacitors are in the other +legs of the + + align:start position:0% + + + + align:start position:0% + +bridge it helps to draw the circuit like + + align:start position:0% +bridge it helps to draw the circuit like + + + align:start position:0% +bridge it helps to draw the circuit like +this here are the pingpong + + align:start position:0% +this here are the pingpong + + + align:start position:0% +this here are the pingpong +balls these capacitors are those of the + + align:start position:0% +balls these capacitors are those of the + + + align:start position:0% +balls these capacitors are those of the +balanced amplifiers on the + + align:start position:0% +balanced amplifiers on the + + + align:start position:0% +balanced amplifiers on the +scope so the oscilloscope displays the + + align:start position:0% +scope so the oscilloscope displays the + + + align:start position:0% +scope so the oscilloscope displays the +output voltage V + + align:start position:0% + + + + align:start position:0% + +subz with the array removed this + + align:start position:0% +subz with the array removed this + + + align:start position:0% +subz with the array removed this +capacitor C sub 2 is adjusted to null + + align:start position:0% +capacitor C sub 2 is adjusted to null + + + align:start position:0% +capacitor C sub 2 is adjusted to null +the output voltage V Sub + + align:start position:0% +the output voltage V Sub + + + align:start position:0% +the output voltage V Sub +0 the output voltage resulting from the + + align:start position:0% +0 the output voltage resulting from the + + + align:start position:0% +0 the output voltage resulting from the +insertion of the array is a measure of + + align:start position:0% +insertion of the array is a measure of + + + align:start position:0% +insertion of the array is a measure of +the change in + + align:start position:0% + + + + align:start position:0% + +capacitance to simplify the + + align:start position:0% +capacitance to simplify the + + + align:start position:0% +capacitance to simplify the +interpretation of this voltage the + + align:start position:0% +interpretation of this voltage the + + + align:start position:0% +interpretation of this voltage the +resistances r Subs are made small + + align:start position:0% +resistances r Subs are made small + + + align:start position:0% +resistances r Subs are made small +compared to the impedance of the + + align:start position:0% +compared to the impedance of the + + + align:start position:0% +compared to the impedance of the +parallel plate capacitor they're 100 + + align:start position:0% +parallel plate capacitor they're 100 + + + align:start position:0% +parallel plate capacitor they're 100 +KMS as a result almost all of the + + align:start position:0% +KMS as a result almost all of the + + + align:start position:0% +KMS as a result almost all of the +applied voltage V from the + + align:start position:0% +applied voltage V from the + + + align:start position:0% +applied voltage V from the +Transformer appears across the lower + + align:start position:0% +Transformer appears across the lower + + + align:start position:0% +Transformer appears across the lower +legs of the + + align:start position:0% +legs of the + + + align:start position:0% +legs of the +bridge with the introduction of the + + align:start position:0% +bridge with the introduction of the + + + align:start position:0% +bridge with the introduction of the +array there's a change in current + + align:start position:0% +array there's a change in current + + + align:start position:0% +array there's a change in current +through the parallel plate + + align:start position:0% +through the parallel plate + + + align:start position:0% +through the parallel plate +capacitor this results in a change in + + align:start position:0% +capacitor this results in a change in + + + align:start position:0% +capacitor this results in a change in +current in the resistance in the right + + align:start position:0% +current in the resistance in the right + + + align:start position:0% +current in the resistance in the right +leg and hence a change of voltage across + + align:start position:0% +leg and hence a change of voltage across + + + align:start position:0% +leg and hence a change of voltage across +the + + align:start position:0% +the + + + align:start position:0% +the +resistance because the current through + + align:start position:0% +resistance because the current through + + + align:start position:0% +resistance because the current through +the left leg has remained essentially + + align:start position:0% +the left leg has remained essentially + + + align:start position:0% +the left leg has remained essentially +the same this change in voltage is the + + align:start position:0% +the same this change in voltage is the + + + align:start position:0% +the same this change in voltage is the +measured output voltage + + align:start position:0% + + + + align:start position:0% + +with many widely spaced and therefore + + align:start position:0% +with many widely spaced and therefore + + + align:start position:0% +with many widely spaced and therefore +non-interacting + + align:start position:0% +non-interacting + + + align:start position:0% +non-interacting +spheres the effective susceptibility and + + align:start position:0% +spheres the effective susceptibility and + + + align:start position:0% +spheres the effective susceptibility and +the changing capacitance caused by + + align:start position:0% +the changing capacitance caused by + + + align:start position:0% +the changing capacitance caused by +inserting the array between the plates + + align:start position:0% +inserting the array between the plates + + + align:start position:0% +inserting the array between the plates +are given by these + + align:start position:0% +are given by these + + + align:start position:0% +are given by these +Expressions remember R is the radius of + + align:start position:0% +Expressions remember R is the radius of + + + align:start position:0% +Expressions remember R is the radius of +a pingpong ball and S is the spacing + + align:start position:0% +a pingpong ball and S is the spacing + + + align:start position:0% +a pingpong ball and S is the spacing +between + + align:start position:0% +between + + + align:start position:0% +between +balls a is the active area of an + + align:start position:0% +balls a is the active area of an + + + align:start position:0% +balls a is the active area of an +electrode and D is the + + align:start position:0% +electrode and D is the + + + align:start position:0% +electrode and D is the +spacing so this is the capacitance + + align:start position:0% +spacing so this is the capacitance + + + align:start position:0% +spacing so this is the capacitance +without the + + align:start position:0% + + + + align:start position:0% + +array the radius of the pingpong balls + + align:start position:0% +array the radius of the pingpong balls + + + align:start position:0% +array the radius of the pingpong balls +is 1.87 + + align:start position:0% +is 1.87 + + + align:start position:0% +is 1.87 +CM the spacing s is 8 + + align:start position:0% +CM the spacing s is 8 + + + align:start position:0% +CM the spacing s is 8 +cm the electric susceptibility is then + + align:start position:0% +cm the electric susceptibility is then + + + align:start position:0% +cm the electric susceptibility is then +0.16 this means that the relative + + align:start position:0% +0.16 this means that the relative + + + align:start position:0% +0.16 this means that the relative +permitivity is 1.16 + + align:start position:0% + + + + align:start position:0% + +to compute the resulting change in + + align:start position:0% +to compute the resulting change in + + + align:start position:0% +to compute the resulting change in +capacitance we multiply the + + align:start position:0% +capacitance we multiply the + + + align:start position:0% +capacitance we multiply the +susceptibility we've + + align:start position:0% +susceptibility we've + + + align:start position:0% +susceptibility we've +computed by the electrode + + align:start position:0% +computed by the electrode + + + align:start position:0% +computed by the electrode +area4 M + + align:start position:0% +area4 M + + + align:start position:0% +area4 M +squared the permitivity of free + + align:start position:0% +squared the permitivity of free + + + align:start position:0% +squared the permitivity of free +space and divide by the electrode + + align:start position:0% +space and divide by the electrode + + + align:start position:0% +space and divide by the electrode +spacing + + align:start position:0% +spacing + + + align:start position:0% +spacing +D 15 + + align:start position:0% + + + + align:start position:0% + +cm so the predicted change in + + align:start position:0% +cm so the predicted change in + + + align:start position:0% +cm so the predicted change in +capacitance is 1.5 picofarads + + align:start position:0% + + + + align:start position:0% + +what change in voltage should we measure + + align:start position:0% +what change in voltage should we measure + + + align:start position:0% +what change in voltage should we measure +when the array is + + align:start position:0% +when the array is + + + align:start position:0% +when the array is +inserted here's what we + + align:start position:0% +inserted here's what we + + + align:start position:0% +inserted here's what we +predict for our experiment R Subs is 100 + + align:start position:0% +predict for our experiment R Subs is 100 + + + align:start position:0% +predict for our experiment R Subs is 100 +kilms the frequency f is 250 + + align:start position:0% +kilms the frequency f is 250 + + + align:start position:0% +kilms the frequency f is 250 +Hertz Delta C is 1.5 + + align:start position:0% +Hertz Delta C is 1.5 + + + align:start position:0% +Hertz Delta C is 1.5 +picofarads and V is 400 volts RMS or 566 + + align:start position:0% +picofarads and V is 400 volts RMS or 566 + + + align:start position:0% +picofarads and V is 400 volts RMS or 566 +volts + + align:start position:0% +volts + + + align:start position:0% +volts +Peak for this applied voltage this + + align:start position:0% +Peak for this applied voltage this + + + align:start position:0% +Peak for this applied voltage this +change engine capacitance should result + + align:start position:0% +change engine capacitance should result + + + align:start position:0% +change engine capacitance should result +in a change in voltage of 133 M volts + + align:start position:0% + + + + align:start position:0% + +Peak before balancing the bridge we + + align:start position:0% +Peak before balancing the bridge we + + + align:start position:0% +Peak before balancing the bridge we +remove the array of ping pong + + align:start position:0% + + + + align:start position:0% + +balls we've already set the driving + + align:start position:0% +balls we've already set the driving + + + align:start position:0% +balls we've already set the driving +voltage to about 400 volts + + align:start position:0% + + + + align:start position:0% + +RMS here are the resistors in the two + + align:start position:0% +RMS here are the resistors in the two + + + align:start position:0% +RMS here are the resistors in the two +upper legs of the + + align:start position:0% + + + + align:start position:0% + +bridge they shunt the scope differential + + align:start position:0% + + + + align:start position:0% + +amplifier so the scope signal is the + + align:start position:0% +amplifier so the scope signal is the + + + align:start position:0% +amplifier so the scope signal is the +voltage V subz + + align:start position:0% + + + + align:start position:0% + +the balancing capacitance C2 is + + align:start position:0% + + + + align:start position:0% + +here this is the capacitor + + align:start position:0% +here this is the capacitor + + + align:start position:0% +here this is the capacitor +C1 which is there for + + align:start position:0% + + + + align:start position:0% + +fine-tuning we can balance the signal + + align:start position:0% +fine-tuning we can balance the signal + + + align:start position:0% +fine-tuning we can balance the signal +with this + + align:start position:0% + + + + align:start position:0% + +capacitor so we tune C2 to null the + + align:start position:0% +capacitor so we tune C2 to null the + + + align:start position:0% +capacitor so we tune C2 to null the +bridge voltage + + align:start position:0% + + + + align:start position:0% + +and C1 to fine-tune the + + align:start position:0% + + + + align:start position:0% + +null we're ready to insert the + + align:start position:0% +null we're ready to insert the + + + align:start position:0% +null we're ready to insert the +artificial + + align:start position:0% + + + + align:start position:0% + +dialectric as the array is + + align:start position:0% + + + + align:start position:0% + +inserted the bridge becomes + + align:start position:0% +inserted the bridge becomes + + + align:start position:0% +inserted the bridge becomes +unbalanced indicating that the Capac + + align:start position:0% +unbalanced indicating that the Capac + + + align:start position:0% +unbalanced indicating that the Capac +fance is + + align:start position:0% +fance is + + + align:start position:0% +fance is +changed we measure a voltage of 135 + + align:start position:0% +changed we measure a voltage of 135 + + + align:start position:0% +changed we measure a voltage of 135 +molts + + align:start position:0% +molts + + + align:start position:0% +molts +Peak remember what we predicted was a + + align:start position:0% +Peak remember what we predicted was a + + + align:start position:0% +Peak remember what we predicted was a +change of 133 molts + + align:start position:0% +change of 133 molts + + + align:start position:0% +change of 133 molts +Peak the agreement is perhaps better + + align:start position:0% +Peak the agreement is perhaps better + + + align:start position:0% +Peak the agreement is perhaps better +than we should + + align:start position:0% + + + + align:start position:0% + +expect has the capacitance actually been + + align:start position:0% +expect has the capacitance actually been + + + align:start position:0% +expect has the capacitance actually been +increased by the insertion of the + + align:start position:0% +increased by the insertion of the + + + align:start position:0% +increased by the insertion of the +Spheres let's try the experiment + + align:start position:0% +Spheres let's try the experiment + + + align:start position:0% +Spheres let's try the experiment +again we can see that it has by looking + + align:start position:0% +again we can see that it has by looking + + + align:start position:0% +again we can see that it has by looking +at the balancing capacitor + + align:start position:0% + + + + align:start position:0% + +here the array is out and we balance the + + align:start position:0% + + + + align:start position:0% + +capacitor now we insert the + + align:start position:0% + + + + align:start position:0% + +array note the position of the tuning + + align:start position:0% +array note the position of the tuning + + + align:start position:0% +array note the position of the tuning +capacitor + + align:start position:0% +capacitor + + + align:start position:0% +capacitor +plates if the capacitance has been + + align:start position:0% +plates if the capacitance has been + + + align:start position:0% +plates if the capacitance has been +increased to balance the bridge the knob + + align:start position:0% +increased to balance the bridge the knob + + + align:start position:0% +increased to balance the bridge the knob +must be turned so that they have greater + + align:start position:0% +must be turned so that they have greater + + + align:start position:0% +must be turned so that they have greater +area of + + align:start position:0% + + + + align:start position:0% + +overlap the balancing capacitance is + + align:start position:0% +overlap the balancing capacitance is + + + align:start position:0% +overlap the balancing capacitance is +increased so the artificial dialectric + + align:start position:0% +increased so the artificial dialectric + + + align:start position:0% +increased so the artificial dialectric +does increase the capacitance of the + + align:start position:0% +does increase the capacitance of the + + + align:start position:0% +does increase the capacitance of the +plain parallel capacitor + + align:start position:0% + + + + align:start position:0% + +our model for how the polarization of + + align:start position:0% +our model for how the polarization of + + + align:start position:0% +our model for how the polarization of +the Spheres increases the capacitance + + align:start position:0% +the Spheres increases the capacitance + + + align:start position:0% +the Spheres increases the capacitance +appears to be a good + + align:start position:0% + + + + align:start position:0% + +one it is because the individual spheres + + align:start position:0% +one it is because the individual spheres + + + align:start position:0% +one it is because the individual spheres +have a polarizability that we can + + align:start position:0% +have a polarizability that we can + + + align:start position:0% +have a polarizability that we can +calculate and because they're well + + align:start position:0% +calculate and because they're well + + + align:start position:0% +calculate and because they're well +remove from each + + align:start position:0% +remove from each + + + align:start position:0% +remove from each +other that we can predict the equivalent + + align:start position:0% +other that we can predict the equivalent + + + align:start position:0% +other that we can predict the equivalent +permitivity of the artificial + + align:start position:0% +permitivity of the artificial + + + align:start position:0% +permitivity of the artificial +dialectric insertion of the artificial + + align:start position:0% +dialectric insertion of the artificial + + + align:start position:0% +dialectric insertion of the artificial +dialectric increases the capacitance \ No newline at end of file diff --git a/CBToKajn2u4.txt b/CBToKajn2u4.txt new file mode 100644 index 0000000000000000000000000000000000000000..63e49cab3c02b6f6dee9cd6105c01c3ab90bbdfe --- /dev/null +++ b/CBToKajn2u4.txt @@ -0,0 +1,1155 @@ +align:start position:0% + +welcome to the third week of our course + + align:start position:0% +welcome to the third week of our course + + + align:start position:0% +welcome to the third week of our course +on shaping the future of work now that + + align:start position:0% +on shaping the future of work now that + + + align:start position:0% +on shaping the future of work now that +we've laid the historical foundation by + + align:start position:0% +we've laid the historical foundation by + + + align:start position:0% +we've laid the historical foundation by +looking at what made the social contract + + align:start position:0% +looking at what made the social contract + + + align:start position:0% +looking at what made the social contract +work in our countries in the past it's + + align:start position:0% +work in our countries in the past it's + + + align:start position:0% +work in our countries in the past it's +time to start to lay out a framework for + + align:start position:0% +time to start to lay out a framework for + + + align:start position:0% +time to start to lay out a framework for +the future so this week we're going to + + align:start position:0% +the future so this week we're going to + + + align:start position:0% +the future so this week we're going to +pay special attention to the time when + + align:start position:0% +pay special attention to the time when + + + align:start position:0% +pay special attention to the time when +we first began to identify what made for + + align:start position:0% +we first began to identify what made for + + + align:start position:0% +we first began to identify what made for +high road firms versus low road firms + + align:start position:0% +high road firms versus low road firms + + + align:start position:0% +high road firms versus low road firms +remember the diagram that we had in the + + align:start position:0% +remember the diagram that we had in the + + + align:start position:0% +remember the diagram that we had in the +first chapter of the book that we are + + align:start position:0% +first chapter of the book that we are + + + align:start position:0% +first chapter of the book that we are +reading for this course where we + + align:start position:0% +reading for this course where we + + + align:start position:0% +reading for this course where we +identified what differentiates firms + + align:start position:0% +identified what differentiates firms + + + align:start position:0% +identified what differentiates firms +that are perhaps good for shareholders + + align:start position:0% +that are perhaps good for shareholders + + + align:start position:0% +that are perhaps good for shareholders +and produce good financial results but + + align:start position:0% +and produce good financial results but + + + align:start position:0% +and produce good financial results but +not such good results for workers + + align:start position:0% +not such good results for workers + + + align:start position:0% +not such good results for workers +compared to those that produce good + + align:start position:0% +compared to those that produce good + + + align:start position:0% +compared to those that produce good +results for both we're going to try to + + align:start position:0% +results for both we're going to try to + + + align:start position:0% +results for both we're going to try to +understand what makes these different + + align:start position:0% +understand what makes these different + + + align:start position:0% +understand what makes these different +firms work and we're going to see if we + + align:start position:0% +firms work and we're going to see if we + + + align:start position:0% +firms work and we're going to see if we +can identify how we can use these ideas + + align:start position:0% +can identify how we can use these ideas + + + align:start position:0% +can identify how we can use these ideas +in the future now when we look at these + + align:start position:0% +in the future now when we look at these + + + align:start position:0% +in the future now when we look at these +organizations and we'll bring in + + align:start position:0% +organizations and we'll bring in + + + align:start position:0% +organizations and we'll bring in +examples like market basket patagonia i + + align:start position:0% +examples like market basket patagonia i + + + align:start position:0% +examples like market basket patagonia i +do saturn costco southwest airlines and + + align:start position:0% +do saturn costco southwest airlines and + + + align:start position:0% +do saturn costco southwest airlines and +others we're not doing that to put these + + align:start position:0% +others we're not doing that to put these + + + align:start position:0% +others we're not doing that to put these +organizations on a pedestal but really + + align:start position:0% +organizations on a pedestal but really + + + align:start position:0% +organizations on a pedestal but really +to dig deeply to understand what makes + + align:start position:0% +to dig deeply to understand what makes + + + align:start position:0% +to dig deeply to understand what makes +them work and how can we apply these in + + align:start position:0% +them work and how can we apply these in + + + align:start position:0% +them work and how can we apply these in +the industries and organizations of + + align:start position:0% +the industries and organizations of + + + align:start position:0% +the industries and organizations of +interest to us and to do that we're + + align:start position:0% +interest to us and to do that we're + + + align:start position:0% +interest to us and to do that we're +going to really focus on two objectives + + align:start position:0% +going to really focus on two objectives + + + align:start position:0% +going to really focus on two objectives +this week one is just what I said what + + align:start position:0% +this week one is just what I said what + + + align:start position:0% +this week one is just what I said what +are the ingredients of these high road + + align:start position:0% +are the ingredients of these high road + + + align:start position:0% +are the ingredients of these high road +firms and then how might we use this + + align:start position:0% +firms and then how might we use this + + + align:start position:0% +firms and then how might we use this +understanding to decide whether or not + + align:start position:0% +understanding to decide whether or not + + + align:start position:0% +understanding to decide whether or not +we want to work for an employer that has + + align:start position:0% +we want to work for an employer that has + + + align:start position:0% +we want to work for an employer that has +some of these characteristics will do + + align:start position:0% +some of these characteristics will do + + + align:start position:0% +some of these characteristics will do +that by applying a tool that you'll find + + align:start position:0% +that by applying a tool that you'll find + + + align:start position:0% +that by applying a tool that you'll find +in the assignment tab of the course it's + + align:start position:0% +in the assignment tab of the course it's + + + align:start position:0% +in the assignment tab of the course it's +called a good job survey and it asks you + + align:start position:0% +called a good job survey and it asks you + + + align:start position:0% +called a good job survey and it asks you +to go out find a firm of interest to you + + align:start position:0% +to go out find a firm of interest to you + + + align:start position:0% +to go out find a firm of interest to you +or in an industry that you may have a + + align:start position:0% +or in an industry that you may have a + + + align:start position:0% +or in an industry that you may have a +particular interest in working in talk + + align:start position:0% +particular interest in working in talk + + + align:start position:0% +particular interest in working in talk +to someone talk to an employee in that + + align:start position:0% +to someone talk to an employee in that + + + align:start position:0% +to someone talk to an employee in that +firm ask them about the conditions of + + align:start position:0% +firm ask them about the conditions of + + + align:start position:0% +firm ask them about the conditions of +work that are present in that + + align:start position:0% +work that are present in that + + + align:start position:0% +work that are present in that +organization you'll find a rating form + + align:start position:0% +organization you'll find a rating form + + + align:start position:0% +organization you'll find a rating form +you can fill out the form then you + + align:start position:0% +you can fill out the form then you + + + align:start position:0% +you can fill out the form then you +provide your answers on the platform for + + align:start position:0% +provide your answers on the platform for + + + align:start position:0% +provide your answers on the platform for +the course and down the road we will + + align:start position:0% +the course and down the road we will + + + align:start position:0% +the course and down the road we will +report what everyone learned from that + + align:start position:0% +report what everyone learned from that + + + align:start position:0% +report what everyone learned from that +experience we want you to remember these + + align:start position:0% +experience we want you to remember these + + + align:start position:0% +experience we want you to remember these +ideas though because we'll use them + + align:start position:0% +ideas though because we'll use them + + + align:start position:0% +ideas though because we'll use them +throughout the rest of the course + + align:start position:0% +throughout the rest of the course + + + align:start position:0% +throughout the rest of the course +particularly we're going to put them to + + align:start position:0% +particularly we're going to put them to + + + align:start position:0% +particularly we're going to put them to +work when we come to the grand finale of + + align:start position:0% +work when we come to the grand finale of + + + align:start position:0% +work when we come to the grand finale of +this course where we negotiate a new + + align:start position:0% +this course where we negotiate a new + + + align:start position:0% +this course where we negotiate a new +social contract the next generation + + align:start position:0% +social contract the next generation + + + align:start position:0% +social contract the next generation +social contract governing conditions of + + align:start position:0% +social contract governing conditions of + + + align:start position:0% +social contract governing conditions of +employment in our workplaces of the + + align:start position:0% +employment in our workplaces of the + + + align:start position:0% +employment in our workplaces of the +future so we want you to use some of the + + align:start position:0% +future so we want you to use some of the + + + align:start position:0% +future so we want you to use some of the +ideas that you learn from both the good + + align:start position:0% +ideas that you learn from both the good + + + align:start position:0% +ideas that you learn from both the good +job survey but also from observing and + + align:start position:0% +job survey but also from observing and + + + align:start position:0% +job survey but also from observing and +learning about some of the organizations + + align:start position:0% +learning about some of the organizations + + + align:start position:0% +learning about some of the organizations +that have good practices that we can + + align:start position:0% +that have good practices that we can + + + align:start position:0% +that have good practices that we can +then apply in our own organizations so + + align:start position:0% +then apply in our own organizations so + + + align:start position:0% +then apply in our own organizations so +that's a good deal of what we will do + + align:start position:0% +that's a good deal of what we will do + + + align:start position:0% +that's a good deal of what we will do +this week and I hope that you will have + + align:start position:0% +this week and I hope that you will have + + + align:start position:0% +this week and I hope that you will have +a good time with the materials and that + + align:start position:0% +a good time with the materials and that + + + align:start position:0% +a good time with the materials and that +you'll have a good time applying them as + + align:start position:0% +you'll have a good time applying them as + + + align:start position:0% +you'll have a good time applying them as +we go forward but I'd like to make two + + align:start position:0% +we go forward but I'd like to make two + + + align:start position:0% +we go forward but I'd like to make two +quick comments on what we learned from + + align:start position:0% +quick comments on what we learned from + + + align:start position:0% +quick comments on what we learned from +last week's discussion I was + + align:start position:0% +last week's discussion I was + + + align:start position:0% +last week's discussion I was +particularly impressed with the sample + + align:start position:0% +particularly impressed with the sample + + + align:start position:0% +particularly impressed with the sample +of organizations that you identified as + + align:start position:0% +of organizations that you identified as + + + align:start position:0% +of organizations that you identified as +you went through your career planning + + align:start position:0% +you went through your career planning + + + align:start position:0% +you went through your career planning +exercise a wide array of very + + align:start position:0% +exercise a wide array of very + + + align:start position:0% +exercise a wide array of very +interesting jobs from engineering clergy + + align:start position:0% +interesting jobs from engineering clergy + + + align:start position:0% +interesting jobs from engineering clergy +members disability teachers HR managers + + align:start position:0% +members disability teachers HR managers + + + align:start position:0% +members disability teachers HR managers +labor leaders artists sports agents for + + align:start position:0% +labor leaders artists sports agents for + + + align:start position:0% +labor leaders artists sports agents for +the National Football League nor less + + align:start position:0% +the National Football League nor less + + + align:start position:0% +the National Football League nor less +psychometricians people who use + + align:start position:0% +psychometricians people who use + + + align:start position:0% +psychometricians people who use +mathematics to try to understand how to + + align:start position:0% +mathematics to try to understand how to + + + align:start position:0% +mathematics to try to understand how to +measure individual behavior and + + align:start position:0% +measure individual behavior and + + + align:start position:0% +measure individual behavior and +attitudes futurists graphic artists + + align:start position:0% +attitudes futurists graphic artists + + + align:start position:0% +attitudes futurists graphic artists +technical editor's note that all of + + align:start position:0% +technical editor's note that all of + + + align:start position:0% +technical editor's note that all of +these are jobs that really are going to + + align:start position:0% +these are jobs that really are going to + + + align:start position:0% +these are jobs that really are going to +require considerable human touch + + align:start position:0% +require considerable human touch + + + align:start position:0% +require considerable human touch +creativity and effort none of these are + + align:start position:0% +creativity and effort none of these are + + + align:start position:0% +creativity and effort none of these are +going to be totally replaced by robots + + align:start position:0% +going to be totally replaced by robots + + + align:start position:0% +going to be totally replaced by robots +or artificial intelligence or machine + + align:start position:0% +or artificial intelligence or machine + + + align:start position:0% +or artificial intelligence or machine +learning and so I don't want you to be + + align:start position:0% +learning and so I don't want you to be + + + align:start position:0% +learning and so I don't want you to be +too scared about the future of work I + + align:start position:0% +too scared about the future of work I + + + align:start position:0% +too scared about the future of work I +want you to prepare for it that's what + + align:start position:0% +want you to prepare for it that's what + + + align:start position:0% +want you to prepare for it that's what +we're learning from this course that's + + align:start position:0% +we're learning from this course that's + + + align:start position:0% +we're learning from this course that's +what we're learning from this particular + + align:start position:0% +what we're learning from this particular + + + align:start position:0% +what we're learning from this particular +exercise so put the pathways of + + align:start position:0% +exercise so put the pathways of + + + align:start position:0% +exercise so put the pathways of +education that you identified in the + + align:start position:0% +education that you identified in the + + + align:start position:0% +education that you identified in the +career planning exercise to work do your + + align:start position:0% +career planning exercise to work do your + + + align:start position:0% +career planning exercise to work do your +part to be prepared for the future and + + align:start position:0% +part to be prepared for the future and + + + align:start position:0% +part to be prepared for the future and +then + + align:start position:0% +then + + + align:start position:0% +then +work with us and with other stakeholders + + align:start position:0% +work with us and with other stakeholders + + + align:start position:0% +work with us and with other stakeholders +to make sure that the conditions are + + align:start position:0% +to make sure that the conditions are + + + align:start position:0% +to make sure that the conditions are +present to make it successful I was also + + align:start position:0% +present to make it successful I was also + + + align:start position:0% +present to make it successful I was also +very interested to learn what you had to + + align:start position:0% +very interested to learn what you had to + + + align:start position:0% +very interested to learn what you had to +say about the great debate over + + align:start position:0% +say about the great debate over + + + align:start position:0% +say about the great debate over +productivity in wages you completed a + + align:start position:0% +productivity in wages you completed a + + + align:start position:0% +productivity in wages you completed a +poll and here's the results of that pole + + align:start position:0% +poll and here's the results of that pole + + + align:start position:0% +poll and here's the results of that pole +eighty-five percent of you agreed that + + align:start position:0% +eighty-five percent of you agreed that + + + align:start position:0% +eighty-five percent of you agreed that +wages and productivity ought to move + + align:start position:0% +wages and productivity ought to move + + + align:start position:0% +wages and productivity ought to move +together about seven percent seven a + + align:start position:0% +together about seven percent seven a + + + align:start position:0% +together about seven percent seven a +half percent said you're not sure and + + align:start position:0% +half percent said you're not sure and + + + align:start position:0% +half percent said you're not sure and +another seven percent said well maybe + + align:start position:0% +another seven percent said well maybe + + + align:start position:0% +another seven percent said well maybe +not anymore in fact many of you + + align:start position:0% +not anymore in fact many of you + + + align:start position:0% +not anymore in fact many of you +indicated while you believe in this + + align:start position:0% +indicated while you believe in this + + + align:start position:0% +indicated while you believe in this +principle you believe it's also going to + + align:start position:0% +principle you believe it's also going to + + + align:start position:0% +principle you believe it's also going to +be difficult to apply it in the current + + align:start position:0% +be difficult to apply it in the current + + + align:start position:0% +be difficult to apply it in the current +economy given changes in technology + + align:start position:0% +economy given changes in technology + + + align:start position:0% +economy given changes in technology +changes in international competition and + + align:start position:0% +changes in international competition and + + + align:start position:0% +changes in international competition and +the the way in which organizations are + + align:start position:0% +the the way in which organizations are + + + align:start position:0% +the the way in which organizations are +structured today but I believe there are + + align:start position:0% +structured today but I believe there are + + + align:start position:0% +structured today but I believe there are +ways we can apply these concepts but we + + align:start position:0% +ways we can apply these concepts but we + + + align:start position:0% +ways we can apply these concepts but we +have to do it in ways that are + + align:start position:0% +have to do it in ways that are + + + align:start position:0% +have to do it in ways that are +consistent with the economy in the + + align:start position:0% +consistent with the economy in the + + + align:start position:0% +consistent with the economy in the +workforce today so I've been added some + + align:start position:0% +workforce today so I've been added some + + + align:start position:0% +workforce today so I've been added some +more comments on the discussion board + + align:start position:0% +more comments on the discussion board + + + align:start position:0% +more comments on the discussion board +about how we can apply productivity and + + align:start position:0% +about how we can apply productivity and + + + align:start position:0% +about how we can apply productivity and +wage movements at the national level at + + align:start position:0% +wage movements at the national level at + + + align:start position:0% +wage movements at the national level at +the organizational level even at the + + align:start position:0% +the organizational level even at the + + + align:start position:0% +the organizational level even at the +individual level so take a look keep + + align:start position:0% +individual level so take a look keep + + + align:start position:0% +individual level so take a look keep +that great discussion going and let's + + align:start position:0% +that great discussion going and let's + + + align:start position:0% +that great discussion going and let's +see what we can do to apply this concept + + align:start position:0% +see what we can do to apply this concept + + + align:start position:0% +see what we can do to apply this concept +appropriately in the economy today and + + align:start position:0% +appropriately in the economy today and + + + align:start position:0% +appropriately in the economy today and +in the jobs of the future and finally + + align:start position:0% +in the jobs of the future and finally + + + align:start position:0% +in the jobs of the future and finally +there are going to be some new ideas + + align:start position:0% +there are going to be some new ideas + + + align:start position:0% +there are going to be some new ideas +raised by our MBA TAS as they contribute + + align:start position:0% +raised by our MBA TAS as they contribute + + + align:start position:0% +raised by our MBA TAS as they contribute +from their own knowledge and experience + + align:start position:0% +from their own knowledge and experience + + + align:start position:0% +from their own knowledge and experience +base from around the world and from some + + align:start position:0% +base from around the world and from some + + + align:start position:0% +base from around the world and from some +of special experts that we will + + align:start position:0% +of special experts that we will + + + align:start position:0% +of special experts that we will +introduce into the course on topics as + + align:start position:0% +introduce into the course on topics as + + + align:start position:0% +introduce into the course on topics as +we go forward this week so have a good + + align:start position:0% +we go forward this week so have a good + + + align:start position:0% +we go forward this week so have a good +time engage the materials and let's keep + + align:start position:0% +time engage the materials and let's keep + + + align:start position:0% +time engage the materials and let's keep +the good conversation going \ No newline at end of file diff --git a/Cks6Wn29TLg.txt b/Cks6Wn29TLg.txt new file mode 100644 index 0000000000000000000000000000000000000000..18b34c9c8831772493b8972dde5d6e1b52bffcc2 --- /dev/null +++ b/Cks6Wn29TLg.txt @@ -0,0 +1,499 @@ +align:start position:0% + +at long last we're ready to split our + + align:start position:0% +at long last we're ready to split our + + + align:start position:0% +at long last we're ready to split our +data into a training and testing set and + + align:start position:0% +data into a training and testing set and + + + align:start position:0% +data into a training and testing set and +to actually build a model so we'll start + + align:start position:0% +to actually build a model so we'll start + + + align:start position:0% +to actually build a model so we'll start +by loading the CA tools package so that + + align:start position:0% +by loading the CA tools package so that + + + align:start position:0% +by loading the CA tools package so that +we can split our data so we'll do a + + align:start position:0% +we can split our data so we'll do a + + + align:start position:0% +we can split our data so we'll do a +library of C tools and then as usual + + align:start position:0% +library of C tools and then as usual + + + align:start position:0% +library of C tools and then as usual +we're gonna set our random seed so that + + align:start position:0% +we're gonna set our random seed so that + + + align:start position:0% +we're gonna set our random seed so that +everybody has the same results so you + + align:start position:0% +everybody has the same results so you + + + align:start position:0% +everybody has the same results so you +set dot seed and we'll pick the number + + align:start position:0% +set dot seed and we'll pick the number + + + align:start position:0% +set dot seed and we'll pick the number +144 again the number isn't particularly + + align:start position:0% +144 again the number isn't particularly + + + align:start position:0% +144 again the number isn't particularly +important the important thing is that we + + align:start position:0% +important the important thing is that we + + + align:start position:0% +important the important thing is that we +all use the same one so as usual we're + + align:start position:0% +all use the same one so as usual we're + + + align:start position:0% +all use the same one so as usual we're +going to obtain the split variable we'll + + align:start position:0% +going to obtain the split variable we'll + + + align:start position:0% +going to obtain the split variable we'll +call it SPL using the sample dot split + + align:start position:0% +call it SPL using the sample dot split + + + align:start position:0% +call it SPL using the sample dot split +function the outcome variable that we + + align:start position:0% +function the outcome variable that we + + + align:start position:0% +function the outcome variable that we +pass is labeled terms dollar sign + + align:start position:0% +pass is labeled terms dollar sign + + + align:start position:0% +pass is labeled terms dollar sign +responsive we'll do a 70/30 split so + + align:start position:0% +responsive we'll do a 70/30 split so + + + align:start position:0% +responsive we'll do a 70/30 split so +we'll pass 0.7 here so then train the + + align:start position:0% +we'll pass 0.7 here so then train the + + + align:start position:0% +we'll pass 0.7 here so then train the +training data frame can be obtained + + align:start position:0% +training data frame can be obtained + + + align:start position:0% +training data frame can be obtained +using subset on the labeled terms where + + align:start position:0% +using subset on the labeled terms where + + + align:start position:0% +using subset on the labeled terms where +SPL is true and test is the subset when + + align:start position:0% +SPL is true and test is the subset when + + + align:start position:0% +SPL is true and test is the subset when +SPL is false all right so now we're + + align:start position:0% +SPL is false all right so now we're + + + align:start position:0% +SPL is false all right so now we're +ready to build the model and we'll build + + align:start position:0% +ready to build the model and we'll build + + + align:start position:0% +ready to build the model and we'll build +a simple cart model using the default + + align:start position:0% +a simple cart model using the default + + + align:start position:0% +a simple cart model using the default +parameters but a random force would be + + align:start position:0% +parameters but a random force would be + + + align:start position:0% +parameters but a random force would be +another good choice from our tool set so + + align:start position:0% +another good choice from our tool set so + + + align:start position:0% +another good choice from our tool set so +we'll start by loading up the packages + + align:start position:0% +we'll start by loading up the packages + + + align:start position:0% +we'll start by loading up the packages +for the cart model will do library our + + align:start position:0% +for the cart model will do library our + + + align:start position:0% +for the cart model will do library our +part and we'll also load up the our part + + align:start position:0% +part and we'll also load up the our part + + + align:start position:0% +part and we'll also load up the our part +dot plot package so that we can plot the + + align:start position:0% +dot plot package so that we can plot the + + + align:start position:0% +dot plot package so that we can plot the +outcome so we'll create a model called + + align:start position:0% +outcome so we'll create a model called + + + align:start position:0% +outcome so we'll create a model called +email cart using the our part function + + align:start position:0% +email cart using the our part function + + + align:start position:0% +email cart using the our part function +we're predicting responsive and we're + + align:start position:0% +we're predicting responsive and we're + + + align:start position:0% +we're predicting responsive and we're +predicting it using all of the + + align:start position:0% +predicting it using all of the + + + align:start position:0% +predicting it using all of the +additional variables all the frequencies + + align:start position:0% +additional variables all the frequencies + + + align:start position:0% +additional variables all the frequencies +of the terms that are included obviously + + align:start position:0% +of the terms that are included obviously + + + align:start position:0% +of the terms that are included obviously +tilde period is important here because + + align:start position:0% +tilde period is important here because + + + align:start position:0% +tilde period is important here because +there's 788 terms way too many to + + align:start position:0% +there's 788 terms way too many to + + + align:start position:0% +there's 788 terms way too many to +actually type out the data that we're + + align:start position:0% +actually type out the data that we're + + + align:start position:0% +actually type out the data that we're +using to train the model it's just our + + align:start position:0% +using to train the model it's just our + + + align:start position:0% +using to train the model it's just our +training data frame train and then the + + align:start position:0% +training data frame train and then the + + + align:start position:0% +training data frame train and then the +method is class since we have a + + align:start position:0% +method is class since we have a + + + align:start position:0% +method is class since we have a +classification problem here + + align:start position:0% +classification problem here + + + align:start position:0% +classification problem here +and once we've trained the card model we + + align:start position:0% +and once we've trained the card model we + + + align:start position:0% +and once we've trained the card model we +can plot it out using PRP there we go so + + align:start position:0% +can plot it out using PRP there we go so + + + align:start position:0% +can plot it out using PRP there we go so +we can see at the very top is the word + + align:start position:0% +we can see at the very top is the word + + + align:start position:0% +we can see at the very top is the word +California if California appears at + + align:start position:0% +California if California appears at + + + align:start position:0% +California if California appears at +least twice in email we're gonna take + + align:start position:0% +least twice in email we're gonna take + + + align:start position:0% +least twice in email we're gonna take +the right part over here and predict + + align:start position:0% +the right part over here and predict + + + align:start position:0% +the right part over here and predict +that a document is responsive it's + + align:start position:0% +that a document is responsive it's + + + align:start position:0% +that a document is responsive it's +somewhat unsurprising the California + + align:start position:0% +somewhat unsurprising the California + + + align:start position:0% +somewhat unsurprising the California +shows up because we know that and run + + align:start position:0% +shows up because we know that and run + + + align:start position:0% +shows up because we know that and run +had a heavy involvement in the + + align:start position:0% +had a heavy involvement in the + + + align:start position:0% +had a heavy involvement in the +California energy markets so further + + align:start position:0% +California energy markets so further + + + align:start position:0% +California energy markets so further +down the tree we see a number of other + + align:start position:0% +down the tree we see a number of other + + + align:start position:0% +down the tree we see a number of other +terms that we could you know plausibly + + align:start position:0% +terms that we could you know plausibly + + + align:start position:0% +terms that we could you know plausibly +expect to be related to energy bids and + + align:start position:0% +expect to be related to energy bids and + + + align:start position:0% +expect to be related to energy bids and +energy scheduling like system demand bid + + align:start position:0% +energy scheduling like system demand bid + + + align:start position:0% +energy scheduling like system demand bid +and gas and down here at the bottom is + + align:start position:0% +and gas and down here at the bottom is + + + align:start position:0% +and gas and down here at the bottom is +Jeff which is perhaps a reference to + + align:start position:0% +Jeff which is perhaps a reference to + + + align:start position:0% +Jeff which is perhaps a reference to +Enron CEO Jeff Skilling's who ended up + + align:start position:0% +Enron CEO Jeff Skilling's who ended up + + + align:start position:0% +Enron CEO Jeff Skilling's who ended up +actually being jailed for his + + align:start position:0% +actually being jailed for his + + + align:start position:0% +actually being jailed for his +involvement in the fraud at the company \ No newline at end of file diff --git a/ECmy2HP1gwA.txt b/ECmy2HP1gwA.txt new file mode 100644 index 0000000000000000000000000000000000000000..0d8c0f0caa70c9fbab6cd4d2f697a10eba57d955 --- /dev/null +++ b/ECmy2HP1gwA.txt @@ -0,0 +1,115 @@ +align:start position:0% + +experimental physics is cool um it's + + align:start position:0% +experimental physics is cool um it's + + + align:start position:0% +experimental physics is cool um it's +jlab has a very wide range of + + align:start position:0% +jlab has a very wide range of + + + align:start position:0% +jlab has a very wide range of +experiments that you can do actually um + + align:start position:0% +experiments that you can do actually um + + + align:start position:0% +experiments that you can do actually um +so my partner and I we did a biophysics + + align:start position:0% +so my partner and I we did a biophysics + + + align:start position:0% +so my partner and I we did a biophysics +experiment we did uh a spectroscopy + + align:start position:0% +experiment we did uh a spectroscopy + + + align:start position:0% +experiment we did uh a spectroscopy +experiment which is like physical + + align:start position:0% +experiment which is like physical + + + align:start position:0% +experiment which is like physical +chemistry and then we did an experiment + + align:start position:0% +chemistry and then we did an experiment + + + align:start position:0% +chemistry and then we did an experiment +with cosmic ray muons so particle + + align:start position:0% +with cosmic ray muons so particle + + + align:start position:0% +with cosmic ray muons so particle +physics so we covered a wide range of + + align:start position:0% +physics so we covered a wide range of + + + align:start position:0% +physics so we covered a wide range of +ways to apply physics to the the real + + align:start position:0% +ways to apply physics to the the real + + + align:start position:0% +ways to apply physics to the the real +world which was uh and it was really + + align:start position:0% +world which was uh and it was really + + + align:start position:0% +world which was uh and it was really +neat to see that range and interact with + + align:start position:0% +neat to see that range and interact with + + + align:start position:0% +neat to see that range and interact with +it and analyze data um for lots of + + align:start position:0% +it and analyze data um for lots of + + + align:start position:0% +it and analyze data um for lots of +different fields of physics so that was + + align:start position:0% +different fields of physics so that was + + + align:start position:0% +different fields of physics so that was +nice \ No newline at end of file diff --git a/EGDQfE7MREw.txt b/EGDQfE7MREw.txt new file mode 100644 index 0000000000000000000000000000000000000000..b9d1044716fa34029432ff8dfa7447a1fa034796 --- /dev/null +++ b/EGDQfE7MREw.txt @@ -0,0 +1,1027 @@ +align:start position:0% + +the problem that we have studied so far + + align:start position:0% +the problem that we have studied so far + + + align:start position:0% +the problem that we have studied so far +captures the essential features of the + + align:start position:0% +captures the essential features of the + + + align:start position:0% +captures the essential features of the +AdWords problem but it can be extended + + align:start position:0% +AdWords problem but it can be extended + + + align:start position:0% +AdWords problem but it can be extended +in several ways we will shortly talk in + + align:start position:0% +in several ways we will shortly talk in + + + align:start position:0% +in several ways we will shortly talk in +some more detail about two of these + + align:start position:0% +some more detail about two of these + + + align:start position:0% +some more detail about two of these +which relate to the idea of slates or + + align:start position:0% +which relate to the idea of slates or + + + align:start position:0% +which relate to the idea of slates or +positions which relate to the idea of + + align:start position:0% +positions which relate to the idea of + + + align:start position:0% +positions which relate to the idea of +personalization aside from these two + + align:start position:0% +personalization aside from these two + + + align:start position:0% +personalization aside from these two +extensions there are also many other + + align:start position:0% +extensions there are also many other + + + align:start position:0% +extensions there are also many other +issues that Google deals with on a daily + + align:start position:0% +issues that Google deals with on a daily + + + align:start position:0% +issues that Google deals with on a daily +basis one of these is related to + + align:start position:0% +basis one of these is related to + + + align:start position:0% +basis one of these is related to +click-through rates in particular how + + align:start position:0% +click-through rates in particular how + + + align:start position:0% +click-through rates in particular how +does Google know the chance that the + + align:start position:0% +does Google know the chance that the + + + align:start position:0% +does Google know the chance that the +user clicks on a given at Google does + + align:start position:0% +user clicks on a given at Google does + + + align:start position:0% +user clicks on a given at Google does +this by analyzing large amounts of user + + align:start position:0% +this by analyzing large amounts of user + + + align:start position:0% +this by analyzing large amounts of user +data and building predictive models + + align:start position:0% +data and building predictive models + + + align:start position:0% +data and building predictive models +similar to those we studied in this + + align:start position:0% +similar to those we studied in this + + + align:start position:0% +similar to those we studied in this +class to predict how often users click + + align:start position:0% +class to predict how often users click + + + align:start position:0% +class to predict how often users click +on different ads when they are shown + + align:start position:0% +on different ads when they are shown + + + align:start position:0% +on different ads when they are shown +with different queries another issue is + + align:start position:0% +with different queries another issue is + + + align:start position:0% +with different queries another issue is +related to the advertisers we saw + + align:start position:0% +related to the advertisers we saw + + + align:start position:0% +related to the advertisers we saw +earlier that the price per click depends + + align:start position:0% +earlier that the price per click depends + + + align:start position:0% +earlier that the price per click depends +on how the advertisers placed their bids + + align:start position:0% +on how the advertisers placed their bids + + + align:start position:0% +on how the advertisers placed their bids +so understanding the behavior of + + align:start position:0% +so understanding the behavior of + + + align:start position:0% +so understanding the behavior of +advertisers and incorporating this + + align:start position:0% +advertisers and incorporating this + + + align:start position:0% +advertisers and incorporating this +behavior in the optimization model is + + align:start position:0% +behavior in the optimization model is + + + align:start position:0% +behavior in the optimization model is +also another important consideration + + align:start position:0% +also another important consideration + + + align:start position:0% +also another important consideration +let's not let's move on to discuss the + + align:start position:0% +let's not let's move on to discuss the + + + align:start position:0% +let's not let's move on to discuss the +idea of slates in our example with AT&T + + align:start position:0% +idea of slates in our example with AT&T + + + align:start position:0% +idea of slates in our example with AT&T +t-mobile and Verizon we assumed that the + + align:start position:0% +t-mobile and Verizon we assumed that the + + + align:start position:0% +t-mobile and Verizon we assumed that the +search page for each query has space for + + align:start position:0% +search page for each query has space for + + + align:start position:0% +search page for each query has space for +only one ad now typically as we saw in + + align:start position:0% +only one ad now typically as we saw in + + + align:start position:0% +only one ad now typically as we saw in +video 1 when we searched for Nine Inch + + align:start position:0% +video 1 when we searched for Nine Inch + + + align:start position:0% +video 1 when we searched for Nine Inch +Nails tickets there's usually space for + + align:start position:0% +Nails tickets there's usually space for + + + align:start position:0% +Nails tickets there's usually space for +many ads in this case Google has to + + align:start position:0% +many ads in this case Google has to + + + align:start position:0% +many ads in this case Google has to +decide which combination of ads or slate + + align:start position:0% +decide which combination of ads or slate + + + align:start position:0% +decide which combination of ads or slate +to display with each query although this + + align:start position:0% +to display with each query although this + + + align:start position:0% +to display with each query although this +would seem to be a more complicated + + align:start position:0% +would seem to be a more complicated + + + align:start position:0% +would seem to be a more complicated +problem it can still be solved using + + align:start position:0% +problem it can still be solved using + + + align:start position:0% +problem it can still be solved using +linear optimization before our variables + + align:start position:0% +linear optimization before our variables + + + align:start position:0% +linear optimization before our variables +were defined as X of a given advertiser + + align:start position:0% +were defined as X of a given advertiser + + + align:start position:0% +were defined as X of a given advertiser +and a given query but now we would + + align:start position:0% +and a given query but now we would + + + align:start position:0% +and a given query but now we would +instead define them as X for a given + + align:start position:0% +instead define them as X for a given + + + align:start position:0% +instead define them as X for a given +slate and a given query so for example + + align:start position:0% +slate and a given query so for example + + + align:start position:0% +slate and a given query so for example +for a wireless service provider example + + align:start position:0% +for a wireless service provider example + + + align:start position:0% +for a wireless service provider example +if we had two spaces on a results page + + align:start position:0% +if we had two spaces on a results page + + + align:start position:0% +if we had two spaces on a results page +then forget query 1 we'd still have X a + + align:start position:0% +then forget query 1 we'd still have X a + + + align:start position:0% +then forget query 1 we'd still have X a +1 XT 1 and X V 1 we're here for example + + align:start position:0% +1 XT 1 and X V 1 we're here for example + + + align:start position:0% +1 XT 1 and X V 1 we're here for example +xB 1 is is a number of times that we + + align:start position:0% +xB 1 is is a number of times that we + + + align:start position:0% +xB 1 is is a number of times that we +display Verizon with query 1 + + align:start position:0% +display Verizon with query 1 + + + align:start position:0% +display Verizon with query 1 +but we would also have X 81 X a v1 an X + + align:start position:0% +but we would also have X 81 X a v1 an X + + + align:start position:0% +but we would also have X 81 X a v1 an X +TV one here for example X AV 1 + + align:start position:0% +TV one here for example X AV 1 + + + align:start position:0% +TV one here for example X AV 1 +represents the number of times that we + + align:start position:0% +represents the number of times that we + + + align:start position:0% +represents the number of times that we +display the slate containing AT&T and + + align:start position:0% +display the slate containing AT&T and + + + align:start position:0% +display the slate containing AT&T and +Verizon with query 1 now this can become + + align:start position:0% +Verizon with query 1 now this can become + + + align:start position:0% +Verizon with query 1 now this can become +even more complicated as the position of + + align:start position:0% +even more complicated as the position of + + + align:start position:0% +even more complicated as the position of +the ad within the slate is important for + + align:start position:0% +the ad within the slate is important for + + + align:start position:0% +the ad within the slate is important for +example ad to the right of the search + + align:start position:0% +example ad to the right of the search + + + align:start position:0% +example ad to the right of the search +results might not attract as many clicks + + align:start position:0% +results might not attract as many clicks + + + align:start position:0% +results might not attract as many clicks +as those above the search results in + + align:start position:0% +as those above the search results in + + + align:start position:0% +as those above the search results in +this case we would also consider XT a 1 + + align:start position:0% +this case we would also consider XT a 1 + + + align:start position:0% +this case we would also consider XT a 1 +X V a 1 and X V T 1 and here the first + + align:start position:0% +X V a 1 and X V T 1 and here the first + + + align:start position:0% +X V a 1 and X V T 1 and here the first +ad in the combination is the ad that is + + align:start position:0% +ad in the combination is the ad that is + + + align:start position:0% +ad in the combination is the ad that is +placed in the first position so for + + align:start position:0% +placed in the first position so for + + + align:start position:0% +placed in the first position so for +example here T Mobile is placed in the + + align:start position:0% +example here T Mobile is placed in the + + + align:start position:0% +example here T Mobile is placed in the +first position for X T a 1 and AT&T is + + align:start position:0% +first position for X T a 1 and AT&T is + + + align:start position:0% +first position for X T a 1 and AT&T is +placed in the second position + + align:start position:0% +placed in the second position + + + align:start position:0% +placed in the second position +we would formulate our objective and our + + align:start position:0% +we would formulate our objective and our + + + align:start position:0% +we would formulate our objective and our +budget and query constraints in the same + + align:start position:0% +budget and query constraints in the same + + + align:start position:0% +budget and query constraints in the same +way as before but making sure that + + align:start position:0% +way as before but making sure that + + + align:start position:0% +way as before but making sure that +slates that contain a certain advertiser + + align:start position:0% +slates that contain a certain advertiser + + + align:start position:0% +slates that contain a certain advertiser +use up that advertisers budget and + + align:start position:0% +use up that advertisers budget and + + + align:start position:0% +use up that advertisers budget and +slates on a given query account towards + + align:start position:0% +slates on a given query account towards + + + align:start position:0% +slates on a given query account towards +that queries estimated number of + + align:start position:0% +that queries estimated number of + + + align:start position:0% +that queries estimated number of +requests let's now discuss the idea of + + align:start position:0% +requests let's now discuss the idea of + + + align:start position:0% +requests let's now discuss the idea of +personalization in addition to the query + + align:start position:0% +personalization in addition to the query + + + align:start position:0% +personalization in addition to the query +Google can use other information to the + + align:start position:0% +Google can use other information to the + + + align:start position:0% +Google can use other information to the +side which add to display for example + + align:start position:0% +side which add to display for example + + + align:start position:0% +side which add to display for example +Google might know the geographic + + align:start position:0% +Google might know the geographic + + + align:start position:0% +Google might know the geographic +location of the user as determined from + + align:start position:0% +location of the user as determined from + + + align:start position:0% +location of the user as determined from +their IP address Google might also know + + align:start position:0% +their IP address Google might also know + + + align:start position:0% +their IP address Google might also know +other information such as different + + align:start position:0% +other information such as different + + + align:start position:0% +other information such as different +Google searches that the user has + + align:start position:0% +Google searches that the user has + + + align:start position:0% +Google searches that the user has +conducted and browser activity on + + align:start position:0% +conducted and browser activity on + + + align:start position:0% +conducted and browser activity on +Google's web site the question then is + + align:start position:0% +Google's web site the question then is + + + align:start position:0% +Google's web site the question then is +how can Google take this into account + + align:start position:0% +how can Google take this into account + + + align:start position:0% +how can Google take this into account +when deciding which ads display for + + align:start position:0% +when deciding which ads display for + + + align:start position:0% +when deciding which ads display for +which queries well just like slates we + + align:start position:0% +which queries well just like slates we + + + align:start position:0% +which queries well just like slates we +can also incorporate this into our + + align:start position:0% +can also incorporate this into our + + + align:start position:0% +can also incorporate this into our +linear optimization model rather than + + align:start position:0% +linear optimization model rather than + + + align:start position:0% +linear optimization model rather than +working with queries we would work with + + align:start position:0% +working with queries we would work with + + + align:start position:0% +working with queries we would work with +combinations of queries and user + + align:start position:0% +combinations of queries and user + + + align:start position:0% +combinations of queries and user +profiles so rather than having X defined + + align:start position:0% +profiles so rather than having X defined + + + align:start position:0% +profiles so rather than having X defined +for a given advertiser and a given query + + align:start position:0% +for a given advertiser and a given query + + + align:start position:0% +for a given advertiser and a given query +we would define X for a given advertiser + + align:start position:0% +we would define X for a given advertiser + + + align:start position:0% +we would define X for a given advertiser +a given query and a given user profile + + align:start position:0% +a given query and a given user profile + + + align:start position:0% +a given query and a given user profile +so here a user profile just describes + + align:start position:0% +so here a user profile just describes + + + align:start position:0% +so here a user profile just describes +the type of user for instance a profile + + align:start position:0% +the type of user for instance a profile + + + align:start position:0% +the type of user for instance a profile +might be men aged 20 to 25 who live in + + align:start position:0% +might be men aged 20 to 25 who live in + + + align:start position:0% +might be men aged 20 to 25 who live in +Boston Massachusetts in the United + + align:start position:0% +Boston Massachusetts in the United + + + align:start position:0% +Boston Massachusetts in the United +States if we had three user profiles we + + align:start position:0% +States if we had three user profiles we + + + align:start position:0% +States if we had three user profiles we +could name them P 1 P 2 P 3 and then for + + align:start position:0% +could name them P 1 P 2 P 3 and then for + + + align:start position:0% +could name them P 1 P 2 P 3 and then for +AT&T for query 1 we would use X a 1 P 1 + + align:start position:0% +AT&T for query 1 we would use X a 1 P 1 + + + align:start position:0% +AT&T for query 1 we would use X a 1 P 1 +to denote the number of times that we + + align:start position:0% +to denote the number of times that we + + + align:start position:0% +to denote the number of times that we +display a TN t--'s ad with query 1 for a + + align:start position:0% +display a TN t--'s ad with query 1 for a + + + align:start position:0% +display a TN t--'s ad with query 1 for a +user of profile P 1 the rest of the + + align:start position:0% +user of profile P 1 the rest of the + + + align:start position:0% +user of profile P 1 the rest of the +model could then be easily accommodated + + align:start position:0% +model could then be easily accommodated + + + align:start position:0% +model could then be easily accommodated +for this new type of modeling + + align:start position:0% +for this new type of modeling + + + align:start position:0% +for this new type of modeling +consideration let us now summarize the + + align:start position:0% +consideration let us now summarize the + + + align:start position:0% +consideration let us now summarize the +salient points of this recitation so so + + align:start position:0% +salient points of this recitation so so + + + align:start position:0% +salient points of this recitation so so +far we have studied a small instance of + + align:start position:0% +far we have studied a small instance of + + + align:start position:0% +far we have studied a small instance of +Google's ad allocation problem where we + + align:start position:0% +Google's ad allocation problem where we + + + align:start position:0% +Google's ad allocation problem where we +had just three advertisers or bidders + + align:start position:0% +had just three advertisers or bidders + + + align:start position:0% +had just three advertisers or bidders +and three queries we saw how an + + align:start position:0% +and three queries we saw how an + + + align:start position:0% +and three queries we saw how an +optimization solution increases revenue + + align:start position:0% +optimization solution increases revenue + + + align:start position:0% +optimization solution increases revenue +by 16% over a simple common sense + + align:start position:0% +by 16% over a simple common sense + + + align:start position:0% +by 16% over a simple common sense +solution what I'd like you to remember + + align:start position:0% +solution what I'd like you to remember + + + align:start position:0% +solution what I'd like you to remember +is that in reality this problem is much + + align:start position:0% +is that in reality this problem is much + + + align:start position:0% +is that in reality this problem is much +larger for each query that Google + + align:start position:0% +larger for each query that Google + + + align:start position:0% +larger for each query that Google +receives on its search engine there may + + align:start position:0% +receives on its search engine there may + + + align:start position:0% +receives on its search engine there may +be hundreds to thousands of advertisers + + align:start position:0% +be hundreds to thousands of advertisers + + + align:start position:0% +be hundreds to thousands of advertisers +bidding on it in terms of dollar amounts + + align:start position:0% +bidding on it in terms of dollar amounts + + + align:start position:0% +bidding on it in terms of dollar amounts +in 2012 Google's total revenue from + + align:start position:0% +in 2012 Google's total revenue from + + + align:start position:0% +in 2012 Google's total revenue from +advertising was over 40 billion dollars + + align:start position:0% +advertising was over 40 billion dollars + + + align:start position:0% +advertising was over 40 billion dollars +at this scale the gains that are + + align:start position:0% +at this scale the gains that are + + + align:start position:0% +at this scale the gains that are +possible from optimization become + + align:start position:0% +possible from optimization become + + + align:start position:0% +possible from optimization become +enormous and I hope this convinces you + + align:start position:0% +enormous and I hope this convinces you + + + align:start position:0% +enormous and I hope this convinces you +of the value of linear optimization in + + align:start position:0% +of the value of linear optimization in + + + align:start position:0% +of the value of linear optimization in +online advertising \ No newline at end of file diff --git a/EO9SMD6fIsI.txt b/EO9SMD6fIsI.txt new file mode 100644 index 0000000000000000000000000000000000000000..05402b433d854656403a2f16f4fb5a5e9c5e1c35 --- /dev/null +++ b/EO9SMD6fIsI.txt @@ -0,0 +1,5243 @@ +align:start position:0% + +what I've what we've talked about in + + align:start position:0% +what I've what we've talked about in + + + align:start position:0% +what I've what we've talked about in +recom and DNA so + + align:start position:0% +recom and DNA so + + + align:start position:0% +recom and DNA so +far is how to get a piece of DNA from + + align:start position:0% +far is how to get a piece of DNA from + + + align:start position:0% +far is how to get a piece of DNA from +somewhere and make a whole lot of copies + + align:start position:0% +somewhere and make a whole lot of copies + + + align:start position:0% +somewhere and make a whole lot of copies +of it so instead of working with ex DNA + + align:start position:0% +of it so instead of working with ex DNA + + + align:start position:0% +of it so instead of working with ex DNA +extracted from my cells which there's + + align:start position:0% +extracted from my cells which there's + + + align:start position:0% +extracted from my cells which there's +three billion different base pairs of + + align:start position:0% +three billion different base pairs of + + + align:start position:0% +three billion different base pairs of +sequin we can find a little stretch of + + align:start position:0% +sequin we can find a little stretch of + + + align:start position:0% +sequin we can find a little stretch of +DNA but simply being able to clone it + + align:start position:0% +DNA but simply being able to clone it + + + align:start position:0% +DNA but simply being able to clone it +there was it was a long way from being + + align:start position:0% +there was it was a long way from being + + + align:start position:0% +there was it was a long way from being +able to get a lot of a fragment of DNA + + align:start position:0% +able to get a lot of a fragment of DNA + + + align:start position:0% +able to get a lot of a fragment of DNA +to being able to figure out what that + + align:start position:0% +to being able to figure out what that + + + align:start position:0% +to being able to figure out what that +sequence is that sequence of that Gene + + align:start position:0% +sequence is that sequence of that Gene + + + align:start position:0% +sequence is that sequence of that Gene +is actually from this xeroderma the gene + + align:start position:0% +is actually from this xeroderma the gene + + + align:start position:0% +is actually from this xeroderma the gene +in that's broken in the xeroderma + + align:start position:0% +in that's broken in the xeroderma + + + align:start position:0% +in that's broken in the xeroderma +pigmentosum variant uh patient who + + align:start position:0% +pigmentosum variant uh patient who + + + align:start position:0% +pigmentosum variant uh patient who +um missing one of these translesion DNA + + align:start position:0% +um missing one of these translesion DNA + + + align:start position:0% +um missing one of these translesion DNA +polymerases that can copy over a thyine + + align:start position:0% +polymerases that can copy over a thyine + + + align:start position:0% +polymerases that can copy over a thyine +thyine thyine pine dimer that's induced + + align:start position:0% +thyine thyine pine dimer that's induced + + + align:start position:0% +thyine thyine pine dimer that's induced +by UV light so the reason they have that + + align:start position:0% +by UV light so the reason they have that + + + align:start position:0% +by UV light so the reason they have that +problem with their skin after sunlight + + align:start position:0% +problem with their skin after sunlight + + + align:start position:0% +problem with their skin after sunlight +is because they're missing a plase that + + align:start position:0% +is because they're missing a plase that + + + align:start position:0% +is because they're missing a plase that +can't copy over accurately over this + + align:start position:0% +can't copy over accurately over this + + + align:start position:0% +can't copy over accurately over this +this very common lesion caused by DNA + + align:start position:0% +this very common lesion caused by DNA + + + align:start position:0% +this very common lesion caused by DNA +damage but how do you get from having a + + align:start position:0% +damage but how do you get from having a + + + align:start position:0% +damage but how do you get from having a +piece of DNA and having having the the + + align:start position:0% +piece of DNA and having having the the + + + align:start position:0% +piece of DNA and having having the the +sequence so the first thing that people + + align:start position:0% +sequence so the first thing that people + + + align:start position:0% +sequence so the first thing that people +learn to do and you still do this all + + align:start position:0% +learn to do and you still do this all + + + align:start position:0% +learn to do and you still do this all +the time in any molecular biology lab + + align:start position:0% +the time in any molecular biology lab + + + align:start position:0% +the time in any molecular biology lab +we're sort of switching now to + + align:start position:0% +we're sort of switching now to + + + align:start position:0% +we're sort of switching now to +engineering if you'll as you'll see + + align:start position:0% +engineering if you'll as you'll see + + + align:start position:0% +engineering if you'll as you'll see +we're taking you're going to see in the + + align:start position:0% +we're taking you're going to see in the + + + align:start position:0% +we're taking you're going to see in the +next things I'm going to say uh proteins + + align:start position:0% +next things I'm going to say uh proteins + + + align:start position:0% +next things I'm going to say uh proteins +that were I I talked to you about + + align:start position:0% +that were I I talked to you about + + + align:start position:0% +that were I I talked to you about +because their biological roles DNA + + align:start position:0% +because their biological roles DNA + + + align:start position:0% +because their biological roles DNA +polymerases ligases we learned what they + + align:start position:0% +polymerases ligases we learned what they + + + align:start position:0% +polymerases ligases we learned what they +do and now you're going to see them used + + align:start position:0% +do and now you're going to see them used + + + align:start position:0% +do and now you're going to see them used +in in manipulative ways and restriction + + align:start position:0% +in in manipulative ways and restriction + + + align:start position:0% +in in manipulative ways and restriction +enzymes they have a biological purpose + + align:start position:0% +enzymes they have a biological purpose + + + align:start position:0% +enzymes they have a biological purpose +too they weren't put on Earth for me to + + align:start position:0% +too they weren't put on Earth for me to + + + align:start position:0% +too they weren't put on Earth for me to +cut up things into fragments and clone + + align:start position:0% +cut up things into fragments and clone + + + align:start position:0% +cut up things into fragments and clone +they were there to give the the bacteria + + align:start position:0% +they were there to give the the bacteria + + + align:start position:0% +they were there to give the the bacteria +some kind of sort of primitive primitive + + align:start position:0% +some kind of sort of primitive primitive + + + align:start position:0% +some kind of sort of primitive primitive +immune system but the first uh thing + + align:start position:0% +immune system but the first uh thing + + + align:start position:0% +immune system but the first uh thing +that you often have to do when you have + + align:start position:0% +that you often have to do when you have + + + align:start position:0% +that you often have to do when you have +let's say a plasmid that in into which + + align:start position:0% +let's say a plasmid that in into which + + + align:start position:0% +let's say a plasmid that in into which +we've inserted a fragment and let's say + + align:start position:0% +we've inserted a fragment and let's say + + + align:start position:0% +we've inserted a fragment and let's say +it was the kind of cloning that we + + align:start position:0% +it was the kind of cloning that we + + + align:start position:0% +it was the kind of cloning that we +described the other day where I had cut + + align:start position:0% +described the other day where I had cut + + + align:start position:0% +described the other day where I had cut +the vector with an Eco R1 site and uh + + align:start position:0% +the vector with an Eco R1 site and uh + + + align:start position:0% +the vector with an Eco R1 site and uh +the other DNA with an Eco R1 site so + + align:start position:0% +the other DNA with an Eco R1 site so + + + align:start position:0% +the other DNA with an Eco R1 site so +these The + + align:start position:0% +these The + + + align:start position:0% +these The +Junction uh between the inserted + + align:start position:0% +Junction uh between the inserted + + + align:start position:0% +Junction uh between the inserted +fragment and the and the cut Vector has + + align:start position:0% +fragment and the and the cut Vector has + + + align:start position:0% +fragment and the and the cut Vector has +recreated to Eco R1 sites now and if I + + align:start position:0% +recreated to Eco R1 sites now and if I + + + align:start position:0% +recreated to Eco R1 sites now and if I +cut with Eco R1 I'll just undo what I + + align:start position:0% +cut with Eco R1 I'll just undo what I + + + align:start position:0% +cut with Eco R1 I'll just undo what I +did in the cloning and we should get the + + align:start position:0% +did in the cloning and we should get the + + + align:start position:0% +did in the cloning and we should get the +vector DNA and the insert DNA back again + + align:start position:0% +vector DNA and the insert DNA back again + + + align:start position:0% +vector DNA and the insert DNA back again +so this is I think for this Vector to + + align:start position:0% +so this is I think for this Vector to + + + align:start position:0% +so this is I think for this Vector to +give us a an orientation I'm going to + + align:start position:0% +give us a an orientation I'm going to + + + align:start position:0% +give us a an orientation I'm going to +imagine that it has one + + align:start position:0% +imagine that it has one + + + align:start position:0% +imagine that it has one +more uh restriction site this one's + + align:start position:0% +more uh restriction site this one's + + + align:start position:0% +more uh restriction site this one's +called S one uh it just recognizes a + + align:start position:0% +called S one uh it just recognizes a + + + align:start position:0% +called S one uh it just recognizes a +different sequence so let's take this if + + align:start position:0% +different sequence so let's take this if + + + align:start position:0% +different sequence so let's take this if +I take the plasma + + align:start position:0% + + + + align:start position:0% + +DNA and cut + + align:start position:0% + + + + align:start position:0% + +with Eco R1 I'm just reversing the + + align:start position:0% +with Eco R1 I'm just reversing the + + + align:start position:0% +with Eco R1 I'm just reversing the +cloning so what I should + + align:start position:0% +cloning so what I should + + + align:start position:0% +cloning so what I should +get is the vector + + align:start position:0% + + + + align:start position:0% + +DNA and the insert that I generated in + + align:start position:0% +DNA and the insert that I generated in + + + align:start position:0% +DNA and the insert that I generated in +the first place but I have to detect + + align:start position:0% +the first place but I have to detect + + + align:start position:0% +the first place but I have to detect +them somehow I can't Unfortunately they + + align:start position:0% +them somehow I can't Unfortunately they + + + align:start position:0% +them somehow I can't Unfortunately they +don't just look in the test tube like + + align:start position:0% +don't just look in the test tube like + + + align:start position:0% +don't just look in the test tube like +that so the what people do is they use a + + align:start position:0% +that so the what people do is they use a + + + align:start position:0% +that so the what people do is they use a +very simple uh principle it's called gel + + align:start position:0% +very simple uh principle it's called gel + + + align:start position:0% +very simple uh principle it's called gel +electropheresis + + align:start position:0% + + + + align:start position:0% + +and the idea is you just make a gel of + + align:start position:0% +and the idea is you just make a gel of + + + align:start position:0% +and the idea is you just make a gel of +something in this in this particular + + align:start position:0% +something in this in this particular + + + align:start position:0% +something in this in this particular +case it's just made of of augur which is + + align:start position:0% +case it's just made of of augur which is + + + align:start position:0% +case it's just made of of augur which is +is + + align:start position:0% + + + + align:start position:0% + +auros these are polysaccharide products + + align:start position:0% +auros these are polysaccharide products + + + align:start position:0% +auros these are polysaccharide products +often derived from seaweed or something + + align:start position:0% +often derived from seaweed or something + + + align:start position:0% +often derived from seaweed or something +like that they have the property that if + + align:start position:0% +like that they have the property that if + + + align:start position:0% +like that they have the property that if +you if you warm them up they they're a + + align:start position:0% +you if you warm them up they they're a + + + align:start position:0% +you if you warm them up they they're a +liquid and then if you let them cool + + align:start position:0% +liquid and then if you let them cool + + + align:start position:0% +liquid and then if you let them cool +down they're a gel you've run into a + + align:start position:0% +down they're a gel you've run into a + + + align:start position:0% +down they're a gel you've run into a +Jello it has that property that's + + align:start position:0% +Jello it has that property that's + + + align:start position:0% +Jello it has that property that's +actually with made of a protein rather + + align:start position:0% +actually with made of a protein rather + + + align:start position:0% +actually with made of a protein rather +than a carbohydrate but it's that kind + + align:start position:0% +than a carbohydrate but it's that kind + + + align:start position:0% +than a carbohydrate but it's that kind +of principle so it's very easy to to + + align:start position:0% +of principle so it's very easy to to + + + align:start position:0% +of principle so it's very easy to to +pour a something and then let it + + align:start position:0% +pour a something and then let it + + + align:start position:0% +pour a something and then let it +solidify now you've got a slab and it's + + align:start position:0% +solidify now you've got a slab and it's + + + align:start position:0% +solidify now you've got a slab and it's +just a network of of things that + + align:start position:0% +just a network of of things that + + + align:start position:0% +just a network of of things that +interact and the principle of the thing + + align:start position:0% +interact and the principle of the thing + + + align:start position:0% +interact and the principle of the thing +is if you you're a very big so you have + + align:start position:0% +is if you you're a very big so you have + + + align:start position:0% +is if you you're a very big so you have +to get the molecules to move well that's + + align:start position:0% +to get the molecules to move well that's + + + align:start position:0% +to get the molecules to move well that's +pretty easy with nucleic acids because + + align:start position:0% +pretty easy with nucleic acids because + + + align:start position:0% +pretty easy with nucleic acids because +they're charged they have all those + + align:start position:0% +they're charged they have all those + + + align:start position:0% +they're charged they have all those +phosphates they got a lot of negative + + align:start position:0% +phosphates they got a lot of negative + + + align:start position:0% +phosphates they got a lot of negative +charge so if you apply an electric + + align:start position:0% + + + + align:start position:0% + +field they'll move and the principle of + + align:start position:0% +field they'll move and the principle of + + + align:start position:0% +field they'll move and the principle of +the thing is if you're big takes it's + + align:start position:0% +the thing is if you're big takes it's + + + align:start position:0% +the thing is if you're big takes it's +harder to wiggle through this network + + align:start position:0% +harder to wiggle through this network + + + align:start position:0% +harder to wiggle through this network +than if you're small or you can think of + + align:start position:0% +than if you're small or you can think of + + + align:start position:0% +than if you're small or you can think of +a big fat person trying to go through a + + align:start position:0% +a big fat person trying to go through a + + + align:start position:0% +a big fat person trying to go through a +forest with a lot of trees and a little + + align:start position:0% +forest with a lot of trees and a little + + + align:start position:0% +forest with a lot of trees and a little +skinny one and if we let them have a + + align:start position:0% +skinny one and if we let them have a + + + align:start position:0% +skinny one and if we let them have a +race eventually the skinny one will + + align:start position:0% +race eventually the skinny one will + + + align:start position:0% +race eventually the skinny one will +emerge quick you know from the forest + + align:start position:0% +emerge quick you know from the forest + + + align:start position:0% +emerge quick you know from the forest +first and so if we + + align:start position:0% +first and so if we + + + align:start position:0% +first and so if we +had a set of markers down the side where + + align:start position:0% +had a set of markers down the side where + + + align:start position:0% +had a set of markers down the side where +this is + + align:start position:0% +this is + + + align:start position:0% +this is +big this is small and we take this piece + + align:start position:0% +big this is small and we take this piece + + + align:start position:0% +big this is small and we take this piece +of DNA we're going to + + align:start position:0% +of DNA we're going to + + + align:start position:0% +of DNA we're going to +get two + + align:start position:0% +get two + + + align:start position:0% +get two +fragments this the bigger one be the + + align:start position:0% + + + + align:start position:0% + +vector and the smaller one would be an + + align:start position:0% +vector and the smaller one would be an + + + align:start position:0% +vector and the smaller one would be an +insert so from that we could say oh well + + align:start position:0% +insert so from that we could say oh well + + + align:start position:0% +insert so from that we could say oh well +what we must if I didn't know what I + + align:start position:0% +what we must if I didn't know what I + + + align:start position:0% +what we must if I didn't know what I +started with I could say what what must + + align:start position:0% +started with I could say what what must + + + align:start position:0% +started with I could say what what must +be in that plasma is the vector and I + + align:start position:0% +be in that plasma is the vector and I + + + align:start position:0% +be in that plasma is the vector and I +can run it all by itself and see it's + + align:start position:0% +can run it all by itself and see it's + + + align:start position:0% +can run it all by itself and see it's +exactly the same size and I got an + + align:start position:0% +exactly the same size and I got an + + + align:start position:0% +exactly the same size and I got an +insert of this particular size but now + + align:start position:0% +insert of this particular size but now + + + align:start position:0% +insert of this particular size but now +can I learn anything more about that + + align:start position:0% +can I learn anything more about that + + + align:start position:0% +can I learn anything more about that +just using restriction enzymes well + + align:start position:0% +just using restriction enzymes well + + + align:start position:0% +just using restriction enzymes well +let's say I now + + align:start position:0% + + + + align:start position:0% + +take the same + + align:start position:0% + + + + align:start position:0% + +actually maybe maybe I'll do it over + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +here so let's cut this time + + align:start position:0% +here so let's cut this time + + + align:start position:0% +here so let's cut this time +with Eco + + align:start position:0% +with Eco + + + align:start position:0% +with Eco +R1 plus another restriction enzyme they + + align:start position:0% +R1 plus another restriction enzyme they + + + align:start position:0% +R1 plus another restriction enzyme they +all have these weird names bam H1 and + + align:start position:0% +all have these weird names bam H1 and + + + align:start position:0% +all have these weird names bam H1 and +let's see what happens well suppose I do + + align:start position:0% +let's see what happens well suppose I do + + + align:start position:0% +let's see what happens well suppose I do +that and I get something like this + + align:start position:0% + + + + align:start position:0% + +well it looks like the vector wasn't cut + + align:start position:0% +well it looks like the vector wasn't cut + + + align:start position:0% +well it looks like the vector wasn't cut +at all that still seems to be the same + + align:start position:0% +at all that still seems to be the same + + + align:start position:0% +at all that still seems to be the same +but it looks as + + align:start position:0% +but it looks as + + + align:start position:0% +but it looks as +though the insert got cut into two + + align:start position:0% +though the insert got cut into two + + + align:start position:0% +though the insert got cut into two +pieces since it was linear it must have + + align:start position:0% +pieces since it was linear it must have + + + align:start position:0% +pieces since it was linear it must have +one bamh one site in it and so this + + align:start position:0% +one bamh one site in it and so this + + + align:start position:0% +one bamh one site in it and so this +molecule that I've cloned could + + align:start position:0% +molecule that I've cloned could + + + align:start position:0% +molecule that I've cloned could +look be one of two two kinds of ways it + + align:start position:0% +look be one of two two kinds of ways it + + + align:start position:0% +look be one of two two kinds of ways it +could be + + align:start position:0% +could be + + + align:start position:0% +could be +like like this well let's say this is + + align:start position:0% +like like this well let's say this is + + + align:start position:0% +like like this well let's say this is +the insert here's + + align:start position:0% +the insert here's + + + align:start position:0% +the insert here's +the E1 I'll use this S one to orient + + align:start position:0% + + + + align:start position:0% + +us so the BAM + + align:start position:0% +us so the BAM + + + align:start position:0% +us so the BAM +site could either be close over here + + align:start position:0% + + + + align:start position:0% + +or it could be over on + + align:start position:0% +or it could be over on + + + align:start position:0% +or it could be over on +the on the other side that makes sense + + align:start position:0% +the on the other side that makes sense + + + align:start position:0% +the on the other side that makes sense +logic is pretty + + align:start position:0% +logic is pretty + + + align:start position:0% +logic is pretty +simple how could I tell which of those + + align:start position:0% +simple how could I tell which of those + + + align:start position:0% +simple how could I tell which of those +is + + align:start position:0% + + + + align:start position:0% + +correct just doing the kind of stuff I'm + + align:start position:0% +correct just doing the kind of stuff I'm + + + align:start position:0% +correct just doing the kind of stuff I'm +doing yeah + + align:start position:0% +doing yeah + + + align:start position:0% +doing yeah +[Music] + + align:start position:0% + + + + align:start position:0% + +beautiful beautiful so if we cut + + align:start position:0% + + + + align:start position:0% + +with with the Sal + + align:start position:0% +with with the Sal + + + align:start position:0% +with with the Sal +H1 excuse me Sal one + + align:start position:0% +H1 excuse me Sal one + + + align:start position:0% +H1 excuse me Sal one +plus the mamh one in one case we'll get + + align:start position:0% +plus the mamh one in one case we'll get + + + align:start position:0% +plus the mamh one in one case we'll get +a one we' get a fragment like + + align:start position:0% +a one we' get a fragment like + + + align:start position:0% +a one we' get a fragment like +that in the other case get a fragment + + align:start position:0% +that in the other case get a fragment + + + align:start position:0% +that in the other case get a fragment +like that that should feel uneasily + + align:start position:0% +like that that should feel uneasily + + + align:start position:0% +like that that should feel uneasily +familiar to + + align:start position:0% +familiar to + + + align:start position:0% +familiar to +you it should feel just like what we + + align:start position:0% +you it should feel just like what we + + + align:start position:0% +you it should feel just like what we +were doing when we did that Fage cross + + align:start position:0% +were doing when we did that Fage cross + + + align:start position:0% +were doing when we did that Fage cross +and we had some some genes that were + + align:start position:0% +and we had some some genes that were + + + align:start position:0% +and we had some some genes that were +lined up and we were trying to figure + + align:start position:0% +lined up and we were trying to figure + + + align:start position:0% +lined up and we were trying to figure +was it the orientation this way or was + + align:start position:0% +was it the orientation this way or was + + + align:start position:0% +was it the orientation this way or was +the orientation that was exactly the + + align:start position:0% +the orientation that was exactly the + + + align:start position:0% +the orientation that was exactly the +same principle and so this is usually uh + + align:start position:0% +same principle and so this is usually uh + + + align:start position:0% +same principle and so this is usually uh +in the lab you'd call this restriction + + align:start position:0% +in the lab you'd call this restriction + + + align:start position:0% +in the lab you'd call this restriction +mapping or making a restriction map and + + align:start position:0% +mapping or making a restriction map and + + + align:start position:0% +mapping or making a restriction map and +it enabled people to manipulate + + align:start position:0% +it enabled people to manipulate + + + align:start position:0% +it enabled people to manipulate +fragments of DNA and make inferences + + align:start position:0% +fragments of DNA and make inferences + + + align:start position:0% +fragments of DNA and make inferences +about their orientation and and other + + align:start position:0% +about their orientation and and other + + + align:start position:0% +about their orientation and and other +features before we could actually even + + align:start position:0% +features before we could actually even + + + align:start position:0% +features before we could actually even +sequence uh sequence DNA and it's just + + align:start position:0% +sequence uh sequence DNA and it's just + + + align:start position:0% +sequence uh sequence DNA and it's just +part of a routine sort of stuff you do + + align:start position:0% +part of a routine sort of stuff you do + + + align:start position:0% +part of a routine sort of stuff you do +in a lab the equipment is discerningly + + align:start position:0% +in a lab the equipment is discerningly + + + align:start position:0% +in a lab the equipment is discerningly +simple they look something it looks + + align:start position:0% +simple they look something it looks + + + align:start position:0% +simple they look something it looks +something like that usually you put in + + align:start position:0% +something like that usually you put in + + + align:start position:0% +something like that usually you put in +some colored Dy you can see that the the + + align:start position:0% +some colored Dy you can see that the the + + + align:start position:0% +some colored Dy you can see that the the +things are um moving down the down the + + align:start position:0% +things are um moving down the down the + + + align:start position:0% +things are um moving down the down the +gel and the way you visualize the DNA is + + align:start position:0% +gel and the way you visualize the DNA is + + + align:start position:0% +gel and the way you visualize the DNA is +you add a a + + align:start position:0% +you add a a + + + align:start position:0% +you add a a +molecule the name of it doesn't + + align:start position:0% +molecule the name of it doesn't + + + align:start position:0% +molecule the name of it doesn't +particularly matter it's called ethidium + + align:start position:0% +particularly matter it's called ethidium + + + align:start position:0% +particularly matter it's called ethidium +bromide but its property is it doesn't + + align:start position:0% +bromide but its property is it doesn't + + + align:start position:0% +bromide but its property is it doesn't +fluorescent when it's just in solution + + align:start position:0% +fluorescent when it's just in solution + + + align:start position:0% +fluorescent when it's just in solution +but if it it's a flat molecule and it + + align:start position:0% +but if it it's a flat molecule and it + + + align:start position:0% +but if it it's a flat molecule and it +can intercalate in between the base + + align:start position:0% +can intercalate in between the base + + + align:start position:0% +can intercalate in between the base +pairs in DNA you have all those stacked + + align:start position:0% +pairs in DNA you have all those stacked + + + align:start position:0% +pairs in DNA you have all those stacked +base pairs going down a helix and this + + align:start position:0% +base pairs going down a helix and this + + + align:start position:0% +base pairs going down a helix and this +molecule is flat and it likes to slip + + align:start position:0% +molecule is flat and it likes to slip + + + align:start position:0% +molecule is flat and it likes to slip +inside and now it's in a much more + + align:start position:0% +inside and now it's in a much more + + + align:start position:0% +inside and now it's in a much more +hydrophobic environment it's hidden from + + align:start position:0% +hydrophobic environment it's hidden from + + + align:start position:0% +hydrophobic environment it's hidden from +the water becomes fluorescent and so DNA + + align:start position:0% +the water becomes fluorescent and so DNA + + + align:start position:0% +the water becomes fluorescent and so DNA +that soaked up this D then will fluores + + align:start position:0% +that soaked up this D then will fluores + + + align:start position:0% +that soaked up this D then will fluores +if you put a UV light on it so if I take + + align:start position:0% +if you put a UV light on it so if I take + + + align:start position:0% +if you put a UV light on it so if I take +the gel out of there after I've run it + + align:start position:0% +the gel out of there after I've run it + + + align:start position:0% +the gel out of there after I've run it +and soak it in this D and then hold + + align:start position:0% +and soak it in this D and then hold + + + align:start position:0% +and soak it in this D and then hold +shine a little handheld UV light on it + + align:start position:0% +shine a little handheld UV light on it + + + align:start position:0% +shine a little handheld UV light on it +it would look something like that if I + + align:start position:0% +it would look something like that if I + + + align:start position:0% +it would look something like that if I +photographed it and so the you'd end up + + align:start position:0% +photographed it and so the you'd end up + + + align:start position:0% +photographed it and so the you'd end up +with those patterns that look exactly + + align:start position:0% +with those patterns that look exactly + + + align:start position:0% +with those patterns that look exactly +like that here's another oops I guess I + + align:start position:0% +like that here's another oops I guess I + + + align:start position:0% +like that here's another oops I guess I +took the other one out but you can of + + align:start position:0% +took the other one out but you can of + + + align:start position:0% +took the other one out but you can of +course you depending on how complicated + + align:start position:0% +course you depending on how complicated + + + align:start position:0% +course you depending on how complicated +it is you could have a lot of different + + align:start position:0% +it is you could have a lot of different + + + align:start position:0% +it is you could have a lot of different +fragments okay so the next big thing + + align:start position:0% +fragments okay so the next big thing + + + align:start position:0% +fragments okay so the next big thing +that had to happen in us for us to + + align:start position:0% +that had to happen in us for us to + + + align:start position:0% +that had to happen in us for us to +really move to where we are in today's + + align:start position:0% +really move to where we are in today's + + + align:start position:0% +really move to where we are in today's +molecular biology was somehow DNA had to + + align:start position:0% +molecular biology was somehow DNA had to + + + align:start position:0% +molecular biology was somehow DNA had to +be + + align:start position:0% +be + + + align:start position:0% +be +sequenced and as I say when I was a an + + align:start position:0% +sequenced and as I say when I was a an + + + align:start position:0% +sequenced and as I say when I was a an +undergrad or even when I was starting + + align:start position:0% +undergrad or even when I was starting + + + align:start position:0% +undergrad or even when I was starting +just about to start when I was a postto + + align:start position:0% +just about to start when I was a postto + + + align:start position:0% +just about to start when I was a postto +anyway it just again seemed like how + + align:start position:0% +anyway it just again seemed like how + + + align:start position:0% +anyway it just again seemed like how +would you ever do it because every + + align:start position:0% +would you ever do it because every + + + align:start position:0% +would you ever do it because every +nucleotide was was joined by a + + align:start position:0% +nucleotide was was joined by a + + + align:start position:0% +nucleotide was was joined by a +phosphodiester bond the only difference + + align:start position:0% +phosphodiester bond the only difference + + + align:start position:0% +phosphodiester bond the only difference +was the was the base that was there it + + align:start position:0% +was the was the base that was there it + + + align:start position:0% +was the was the base that was there it +seemed very very difficult they hard to + + align:start position:0% +seemed very very difficult they hard to + + + align:start position:0% +seemed very very difficult they hard to +imagine you would ever be able to sort + + align:start position:0% +imagine you would ever be able to sort + + + align:start position:0% +imagine you would ever be able to sort +out the sequence of a billion base pairs + + align:start position:0% +out the sequence of a billion base pairs + + + align:start position:0% +out the sequence of a billion base pairs +of course once you get a you can clone + + align:start position:0% +of course once you get a you can clone + + + align:start position:0% +of course once you get a you can clone +now you've got maybe a fragment of DNA + + align:start position:0% +now you've got maybe a fragment of DNA + + + align:start position:0% +now you've got maybe a fragment of DNA +that's a couple of hundred n base pairs + + align:start position:0% +that's a couple of hundred n base pairs + + + align:start position:0% +that's a couple of hundred n base pairs +long and at least the problem becomes + + align:start position:0% +long and at least the problem becomes + + + align:start position:0% +long and at least the problem becomes +smaller maybe you could work it out now + + align:start position:0% +smaller maybe you could work it out now + + + align:start position:0% +smaller maybe you could work it out now +there were there were a couple of + + align:start position:0% +there were there were a couple of + + + align:start position:0% +there were there were a couple of +different ways of doing it one was by + + align:start position:0% +different ways of doing it one was by + + + align:start position:0% +different ways of doing it one was by +Wally Gilbert who's up at Harvard who + + align:start position:0% +Wally Gilbert who's up at Harvard who + + + align:start position:0% +Wally Gilbert who's up at Harvard who +got part of a half the Nobel Prize for + + align:start position:0% +got part of a half the Nobel Prize for + + + align:start position:0% +got part of a half the Nobel Prize for +doing this the other princip the other + + align:start position:0% +doing this the other princip the other + + + align:start position:0% +doing this the other princip the other +one the one that's really proved to be + + align:start position:0% +one the one that's really proved to be + + + align:start position:0% +one the one that's really proved to be +generally most generally useful was Fred + + align:start position:0% +generally most generally useful was Fred + + + align:start position:0% +generally most generally useful was Fred +Sanger from England uh and he he and + + align:start position:0% +Sanger from England uh and he he and + + + align:start position:0% +Sanger from England uh and he he and +Wally shared the Nobel Prize for + + align:start position:0% +Wally shared the Nobel Prize for + + + align:start position:0% +Wally shared the Nobel Prize for +discovering sequencing and the the + + align:start position:0% +discovering sequencing and the the + + + align:start position:0% +discovering sequencing and the the +principle was disarmingly simple I I I + + align:start position:0% +principle was disarmingly simple I I I + + + align:start position:0% +principle was disarmingly simple I I I +think it's one of these great ideas that + + align:start position:0% +think it's one of these great ideas that + + + align:start position:0% +think it's one of these great ideas that +you look back at afterwards and you + + align:start position:0% +you look back at afterwards and you + + + align:start position:0% +you look back at afterwards and you +think I could have thought of that you + + align:start position:0% +think I could have thought of that you + + + align:start position:0% +think I could have thought of that you +guys already know everything you need to + + align:start position:0% +guys already know everything you need to + + + align:start position:0% +guys already know everything you need to +invent how to sequence DNA he I've told + + align:start position:0% +invent how to sequence DNA he I've told + + + align:start position:0% +invent how to sequence DNA he I've told +you all the stuff already but I don't + + align:start position:0% +you all the stuff already but I don't + + + align:start position:0% +you all the stuff already but I don't +nobody's come down to tell me yet that + + align:start position:0% +nobody's come down to tell me yet that + + + align:start position:0% +nobody's come down to tell me yet that +you've got it and I didn't think of it + + align:start position:0% +you've got it and I didn't think of it + + + align:start position:0% +you've got it and I didn't think of it +so here was the principle what we've T + + align:start position:0% +so here was the principle what we've T + + + align:start position:0% +so here was the principle what we've T +we've talked about if we take a DNA + + align:start position:0% + + + + align:start position:0% + +polymerase plus the + + align:start position:0% +polymerase plus the + + + align:start position:0% +polymerase plus the +four deoxy nucleotide triphosphates + + align:start position:0% +four deoxy nucleotide triphosphates + + + align:start position:0% +four deoxy nucleotide triphosphates +remember + + align:start position:0% +remember + + + align:start position:0% +remember +deoxy uh adenosine deoxy + + align:start position:0% +deoxy uh adenosine deoxy + + + align:start position:0% +deoxy uh adenosine deoxy +ribonucleotide U the Denine triphosphate + + align:start position:0% +ribonucleotide U the Denine triphosphate + + + align:start position:0% +ribonucleotide U the Denine triphosphate +and so on the four different ones and we + + align:start position:0% +and so on the four different ones and we + + + align:start position:0% +and so on the four different ones and we +take a + + align:start position:0% + + + + align:start position:0% + +primer and there's a thre Prime hydroxy + + align:start position:0% +primer and there's a thre Prime hydroxy + + + align:start position:0% +primer and there's a thre Prime hydroxy +right there and the so this is the other + + align:start position:0% +right there and the so this is the other + + + align:start position:0% +right there and the so this is the other +strand is going in the + + align:start position:0% +strand is going in the + + + align:start position:0% +strand is going in the +opposite uh direction that if we add + + align:start position:0% +opposite uh direction that if we add + + + align:start position:0% +opposite uh direction that if we add +that I think you all know what's what's + + align:start position:0% +that I think you all know what's what's + + + align:start position:0% +that I think you all know what's what's +going to happen we're going to get + + align:start position:0% +going to happen we're going to get + + + align:start position:0% +going to happen we're going to get +an extension to the other end and what + + align:start position:0% +an extension to the other end and what + + + align:start position:0% +an extension to the other end and what +happens every time we add a nucleotide + + align:start position:0% +happens every time we add a nucleotide + + + align:start position:0% +happens every time we add a nucleotide +is that three prime uh hydroxy attacks + + align:start position:0% +is that three prime uh hydroxy attacks + + + align:start position:0% +is that three prime uh hydroxy attacks +the phosphate of the triphosphate we + + align:start position:0% +the phosphate of the triphosphate we + + + align:start position:0% +the phosphate of the triphosphate we +lose P two of the phosphates that's + + align:start position:0% +lose P two of the phosphates that's + + + align:start position:0% +lose P two of the phosphates that's +called pyrophosphate and we've created a + + align:start position:0% +called pyrophosphate and we've created a + + + align:start position:0% +called pyrophosphate and we've created a +new 5 to three prime linkage that gives + + align:start position:0% +new 5 to three prime linkage that gives + + + align:start position:0% +new 5 to three prime linkage that gives +us a new three prime hydroxy and we + + align:start position:0% +us a new three prime hydroxy and we + + + align:start position:0% +us a new three prime hydroxy and we +repeat the process right that's what we + + align:start position:0% +repeat the process right that's what we + + + align:start position:0% +repeat the process right that's what we +talked about so what would happen + + align:start position:0% +talked about so what would happen + + + align:start position:0% +talked about so what would happen +happen + + align:start position:0% + + + + align:start position:0% + +let's spike + + align:start position:0% + + + + align:start position:0% + +in a + + align:start position:0% + + + + align:start position:0% + +little let me do this little deoxy + + align:start position:0% +little let me do this little deoxy + + + align:start position:0% +little let me do this little deoxy +TTP um so this + + align:start position:0% +TTP um so this + + + align:start position:0% +TTP um so this +is + + align:start position:0% +is + + + align:start position:0% +is +D deoxy well what would we mean by that + + align:start position:0% + + + + align:start position:0% + +well if + + align:start position:0% +well if + + + align:start position:0% +well if +this remember where the deoxy came from + + align:start position:0% +this remember where the deoxy came from + + + align:start position:0% +this remember where the deoxy came from +the ribos has at the two prime position + + align:start position:0% +the ribos has at the two prime position + + + align:start position:0% +the ribos has at the two prime position +has a hydrogen instead of a hydroxy + + align:start position:0% + + + + align:start position:0% + +and and at the three prime position it + + align:start position:0% +and and at the three prime position it + + + align:start position:0% +and and at the three prime position it +has a hydroxy if we made a + + align:start position:0% +has a hydroxy if we made a + + + align:start position:0% +has a hydroxy if we made a +dioxy what we' + + align:start position:0% +dioxy what we' + + + align:start position:0% +dioxy what we' +do is we'd make that and what could that + + align:start position:0% +do is we'd make that and what could that + + + align:start position:0% +do is we'd make that and what could that +nucleotide do well as long as the piz + + align:start position:0% +nucleotide do well as long as the piz + + + align:start position:0% +nucleotide do well as long as the piz +thought it was useful it would it could + + align:start position:0% +thought it was useful it would it could + + + align:start position:0% +thought it was useful it would it could +use this end would have its triphosphate + + align:start position:0% +use this end would have its triphosphate + + + align:start position:0% +use this end would have its triphosphate +up + + align:start position:0% + + + + align:start position:0% + +here so somebody + + align:start position:0% +here so somebody + + + align:start position:0% +here so somebody +else's 3 Prime o could come down and + + align:start position:0% +else's 3 Prime o could come down and + + + align:start position:0% +else's 3 Prime o could come down and +form a bond to here and we'd lose this + + align:start position:0% +form a bond to here and we'd lose this + + + align:start position:0% +form a bond to here and we'd lose this +so it could get + + align:start position:0% +so it could get + + + align:start position:0% +so it could get +Incorporated but once it was + + align:start position:0% +Incorporated but once it was + + + align:start position:0% +Incorporated but once it was +incorporated that chain is finished + + align:start position:0% +incorporated that chain is finished + + + align:start position:0% +incorporated that chain is finished +can't be elongated anymore so let's + + align:start position:0% +can't be elongated anymore so let's + + + align:start position:0% +can't be elongated anymore so let's +think what would happen if if we + + align:start position:0% +think what would happen if if we + + + align:start position:0% +think what would happen if if we +had stretch this out a little bit + + align:start position:0% +had stretch this out a little bit + + + align:start position:0% +had stretch this out a little bit +here and let's imagine we had a + + align:start position:0% + + + + align:start position:0% + +few A's in this in this sequence so + + align:start position:0% +few A's in this in this sequence so + + + align:start position:0% +few A's in this in this sequence so +we're just going to spike in a bit so + + align:start position:0% +we're just going to spike in a bit so + + + align:start position:0% +we're just going to spike in a bit so +most of the things will not see a dioxy + + align:start position:0% +most of the things will not see a dioxy + + + align:start position:0% +most of the things will not see a dioxy +so this primer will put a we'll put a um + + align:start position:0% +so this primer will put a we'll put a um + + + align:start position:0% +so this primer will put a we'll put a um +okay so we we'll try elongating this so + + align:start position:0% +okay so we we'll try elongating this so + + + align:start position:0% +okay so we we'll try elongating this so +when we get to this + + align:start position:0% +when we get to this + + + align:start position:0% +when we get to this +point this point many of them will put + + align:start position:0% +point this point many of them will put + + + align:start position:0% +point this point many of them will put +in an ordinary a but a few will put in a + + align:start position:0% +in an ordinary a but a few will put in a + + + align:start position:0% +in an ordinary a but a few will put in a +dioxy and those will finish at that + + align:start position:0% +dioxy and those will finish at that + + + align:start position:0% +dioxy and those will finish at that +point they can't go any + + align:start position:0% +point they can't go any + + + align:start position:0% +point they can't go any +further the rest of them keep going they + + align:start position:0% +further the rest of them keep going they + + + align:start position:0% +further the rest of them keep going they +add various nucleotides when we get to + + align:start position:0% +add various nucleotides when we get to + + + align:start position:0% +add various nucleotides when we get to +the next + + align:start position:0% +the next + + + align:start position:0% +the next +a most of them will put in a good uh t + + align:start position:0% +a most of them will put in a good uh t + + + align:start position:0% +a most of them will put in a good uh t +but the ones that put in the dioxy will + + align:start position:0% +but the ones that put in the dioxy will + + + align:start position:0% +but the ones that put in the dioxy will +stop and they will generate a fragment + + align:start position:0% +stop and they will generate a fragment + + + align:start position:0% +stop and they will generate a fragment +that looks like that okay you get the + + align:start position:0% +that looks like that okay you get the + + + align:start position:0% +that looks like that okay you get the +idea we do this again out of this + + align:start position:0% +idea we do this again out of this + + + align:start position:0% +idea we do this again out of this +reaction we're going to get a set + + align:start position:0% + + + + align:start position:0% + +of fragments and each one terminates + + align:start position:0% +of fragments and each one terminates + + + align:start position:0% +of fragments and each one terminates +where there was an a up there now in the + + align:start position:0% +where there was an a up there now in the + + + align:start position:0% +where there was an a up there now in the +the newer emulation of this thing we + + align:start position:0% +the newer emulation of this thing we + + + align:start position:0% +the newer emulation of this thing we +have a t and the trick is to put a die + + align:start position:0% +have a t and the trick is to put a die + + + align:start position:0% +have a t and the trick is to put a die +that you can attach to this nucleotide + + align:start position:0% +that you can attach to this nucleotide + + + align:start position:0% +that you can attach to this nucleotide +so it has a particular color so suppose + + align:start position:0% +so it has a particular color so suppose + + + align:start position:0% +so it has a particular color so suppose +we had something that was yellow then + + align:start position:0% +we had something that was yellow then + + + align:start position:0% +we had something that was yellow then +this particular set of + + align:start position:0% + + + + align:start position:0% + +fragments would be + + align:start position:0% + + + + align:start position:0% + +yellow and maybe you can begin to see + + align:start position:0% +yellow and maybe you can begin to see + + + align:start position:0% +yellow and maybe you can begin to see +what would happen now if we did the same + + align:start position:0% +what would happen now if we did the same + + + align:start position:0% +what would happen now if we did the same +game three more times each time using a + + align:start position:0% +game three more times each time using a + + + align:start position:0% +game three more times each time using a +different deoxy next time maybe we'll + + align:start position:0% +different deoxy next time maybe we'll + + + align:start position:0% +different deoxy next time maybe we'll +use di deoxy a and we'll put a different + + align:start position:0% +use di deoxy a and we'll put a different + + + align:start position:0% +use di deoxy a and we'll put a different +color Dy on it then every time in this + + align:start position:0% +color Dy on it then every time in this + + + align:start position:0% +color Dy on it then every time in this +case we'd come to a t in the template it + + align:start position:0% +case we'd come to a t in the template it + + + align:start position:0% +case we'd come to a t in the template it +would stop and we'd get a little + + align:start position:0% +would stop and we'd get a little + + + align:start position:0% +would stop and we'd get a little +fragment that's stopped because it + + align:start position:0% +fragment that's stopped because it + + + align:start position:0% +fragment that's stopped because it +incorp Incorporated a dioxy a and those + + align:start position:0% +incorp Incorporated a dioxy a and those + + + align:start position:0% +incorp Incorporated a dioxy a and those +would be let's say green so by the end + + align:start position:0% +would be let's say green so by the end + + + align:start position:0% +would be let's say green so by the end +of this we would have all possible + + align:start position:0% +of this we would have all possible + + + align:start position:0% +of this we would have all possible +fragments if we mix them all together + + align:start position:0% +fragments if we mix them all together + + + align:start position:0% +fragments if we mix them all together +and the + + align:start position:0% +and the + + + align:start position:0% +and the +uh the last nucleotide on the on each + + align:start position:0% +uh the last nucleotide on the on each + + + align:start position:0% +uh the last nucleotide on the on each +fragment would say who it was by its + + align:start position:0% +fragment would say who it was by its + + + align:start position:0% +fragment would say who it was by its +color so if you were to then take this + + align:start position:0% +color so if you were to then take this + + + align:start position:0% +color so if you were to then take this +whole mixture of DNA fragments and you + + align:start position:0% +whole mixture of DNA fragments and you + + + align:start position:0% +whole mixture of DNA fragments and you +run them down a gel in this case it's a + + align:start position:0% +run them down a gel in this case it's a + + + align:start position:0% +run them down a gel in this case it's a +different it's a polyacrylamid gel + + align:start position:0% +different it's a polyacrylamid gel + + + align:start position:0% +different it's a polyacrylamid gel +because you have smaller trying to get + + align:start position:0% +because you have smaller trying to get + + + align:start position:0% +because you have smaller trying to get +things to go by smaller fragments you + + align:start position:0% +things to go by smaller fragments you + + + align:start position:0% +things to go by smaller fragments you +could sort of see what would happen this + + align:start position:0% +could sort of see what would happen this + + + align:start position:0% +could sort of see what would happen this +the big ones would be at the top the + + align:start position:0% +the big ones would be at the top the + + + align:start position:0% +the big ones would be at the top the +small ones would be at the bottom bottom + + align:start position:0% +small ones would be at the bottom bottom + + + align:start position:0% +small ones would be at the bottom bottom +and you'd see each band would have a + + align:start position:0% +and you'd see each band would have a + + + align:start position:0% +and you'd see each band would have a +different color depending on the dioxy + + align:start position:0% +different color depending on the dioxy + + + align:start position:0% +different color depending on the dioxy +that terminated its chain so if you had + + align:start position:0% +that terminated its chain so if you had + + + align:start position:0% +that terminated its chain so if you had +a little scanner that just goes along it + + align:start position:0% +a little scanner that just goes along it + + + align:start position:0% +a little scanner that just goes along it +can read this and it'll print out uh + + align:start position:0% +can read this and it'll print out uh + + + align:start position:0% +can read this and it'll print out uh +something and these are always slightly + + align:start position:0% +something and these are always slightly + + + align:start position:0% +something and these are always slightly +idealized this is a real one but this is + + align:start position:0% +idealized this is a real one but this is + + + align:start position:0% +idealized this is a real one but this is +the sort of stuff you'd get back if you + + align:start position:0% +the sort of stuff you'd get back if you + + + align:start position:0% +the sort of stuff you'd get back if you +send a piece of DNA over to a Sequencing + + align:start position:0% +send a piece of DNA over to a Sequencing + + + align:start position:0% +send a piece of DNA over to a Sequencing +Center they'd send this back as a as a + + align:start position:0% +Center they'd send this back as a as a + + + align:start position:0% +Center they'd send this back as a as a +file or something and you'd sit there + + align:start position:0% +file or something and you'd sit there + + + align:start position:0% +file or something and you'd sit there +and it + + align:start position:0% +and it + + + align:start position:0% +and it +it's very good these days used the + + align:start position:0% +it's very good these days used the + + + align:start position:0% +it's very good these days used the +technology wasn't as good but they can + + align:start position:0% +technology wasn't as good but they can + + + align:start position:0% +technology wasn't as good but they can +almost always now uh get the sequence + + align:start position:0% +almost always now uh get the sequence + + + align:start position:0% +almost always now uh get the sequence +occasionally if you get something like a + + align:start position:0% +occasionally if you get something like a + + + align:start position:0% +occasionally if you get something like a +run of G's it gets a little hard but + + align:start position:0% +run of G's it gets a little hard but + + + align:start position:0% +run of G's it gets a little hard but +what they do is they'll they'll sort of + + align:start position:0% +what they do is they'll they'll sort of + + + align:start position:0% +what they do is they'll they'll sort of +what they call sequencing both strands + + align:start position:0% +what they call sequencing both strands + + + align:start position:0% +what they call sequencing both strands +you can see this way we're really only + + align:start position:0% +you can see this way we're really only + + + align:start position:0% +you can see this way we're really only +looking at the information for one + + align:start position:0% +looking at the information for one + + + align:start position:0% +looking at the information for one +strand so if we took the other strand + + align:start position:0% +strand so if we took the other strand + + + align:start position:0% +strand so if we took the other strand +and we did the same thing then we should + + align:start position:0% +and we did the same thing then we should + + + align:start position:0% +and we did the same thing then we should +get the + + align:start position:0% +get the + + + align:start position:0% +get the +complimentary um piece of information so + + align:start position:0% +complimentary um piece of information so + + + align:start position:0% +complimentary um piece of information so +what this DNA um sequencing allows you + + align:start position:0% +what this DNA um sequencing allows you + + + align:start position:0% +what this DNA um sequencing allows you +to do then is to + + align:start position:0% +to do then is to + + + align:start position:0% +to do then is to +determine the exact sequence of + + align:start position:0% +determine the exact sequence of + + + align:start position:0% +determine the exact sequence of +nucleotides in some kind of piece and + + align:start position:0% +nucleotides in some kind of piece and + + + align:start position:0% +nucleotides in some kind of piece and +much of the art from the rest of it then + + align:start position:0% +much of the art from the rest of it then + + + align:start position:0% +much of the art from the rest of it then +comes how do you assemble all of those + + align:start position:0% +comes how do you assemble all of those + + + align:start position:0% +comes how do you assemble all of those +things together in a case of a bacterium + + align:start position:0% +things together in a case of a bacterium + + + align:start position:0% +things together in a case of a bacterium +or something it wasn't so bad because + + align:start position:0% +or something it wasn't so bad because + + + align:start position:0% +or something it wasn't so bad because +its DNA was small enough you could cut + + align:start position:0% +its DNA was small enough you could cut + + + align:start position:0% +its DNA was small enough you could cut +it into a bunch of sort of big fragments + + align:start position:0% +it into a bunch of sort of big fragments + + + align:start position:0% +it into a bunch of sort of big fragments +and then take each one of those and you + + align:start position:0% +and then take each one of those and you + + + align:start position:0% +and then take each one of those and you +were the Sorting problem was relatively + + align:start position:0% +were the Sorting problem was relatively + + + align:start position:0% +were the Sorting problem was relatively +simple in the case of some something + + align:start position:0% +simple in the case of some something + + + align:start position:0% +simple in the case of some something +like humans it was really complicated + + align:start position:0% +like humans it was really complicated + + + align:start position:0% +like humans it was really complicated +because it was so much more DNA and the + + align:start position:0% +because it was so much more DNA and the + + + align:start position:0% +because it was so much more DNA and the +other thing is higher organisms such as + + align:start position:0% +other thing is higher organisms such as + + + align:start position:0% +other thing is higher organisms such as +ourselves have a lot of repeated DNA + + align:start position:0% +ourselves have a lot of repeated DNA + + + align:start position:0% +ourselves have a lot of repeated DNA +it's it's just the same sequence and + + align:start position:0% +it's it's just the same sequence and + + + align:start position:0% +it's it's just the same sequence and +sometimes there's quite a bit of it a + + align:start position:0% +sometimes there's quite a bit of it a + + + align:start position:0% +sometimes there's quite a bit of it a +bunch of repeats and so if you see that + + align:start position:0% +bunch of repeats and so if you see that + + + align:start position:0% +bunch of repeats and so if you see that +at the end of your thing you don't + + align:start position:0% +at the end of your thing you don't + + + align:start position:0% +at the end of your thing you don't +really quite know where you are in the + + align:start position:0% +really quite know where you are in the + + + align:start position:0% +really quite know where you are in the +genome so a lot of other tricks had to + + align:start position:0% +genome so a lot of other tricks had to + + + align:start position:0% +genome so a lot of other tricks had to +be brought into play including knowledge + + align:start position:0% +be brought into play including knowledge + + + align:start position:0% +be brought into play including knowledge +of the human genetic map and so you + + align:start position:0% +of the human genetic map and so you + + + align:start position:0% +of the human genetic map and so you +could get yourself anchored at various + + align:start position:0% +could get yourself anchored at various + + + align:start position:0% +could get yourself anchored at various +places because you knew on this partic + + align:start position:0% +places because you knew on this partic + + + align:start position:0% +places because you knew on this partic +particular piece of DNA because it was + + align:start position:0% +particular piece of DNA because it was + + + align:start position:0% +particular piece of DNA because it was +associated with some Gene had to be here + + align:start position:0% +associated with some Gene had to be here + + + align:start position:0% +associated with some Gene had to be here +on the chromosome and therefore things + + align:start position:0% +on the chromosome and therefore things + + + align:start position:0% +on the chromosome and therefore things +at least beside it were there on the + + align:start position:0% +at least beside it were there on the + + + align:start position:0% +at least beside it were there on the +chromosome there were a whole lot of + + align:start position:0% +chromosome there were a whole lot of + + + align:start position:0% +chromosome there were a whole lot of +tricks to putting it together but the + + align:start position:0% +tricks to putting it together but the + + + align:start position:0% +tricks to putting it together but the +the very basic principle of how we + + align:start position:0% +the very basic principle of how we + + + align:start position:0% +the very basic principle of how we +sequence DNA has as its heart the same + + align:start position:0% +sequence DNA has as its heart the same + + + align:start position:0% +sequence DNA has as its heart the same +process that I was talking to you about + + align:start position:0% +process that I was talking to you about + + + align:start position:0% +process that I was talking to you about +as when we were doing uh DNA replication + + align:start position:0% +as when we were doing uh DNA replication + + + align:start position:0% +as when we were doing uh DNA replication +except in this case it's it's just um + + align:start position:0% +except in this case it's it's just um + + + align:start position:0% +except in this case it's it's just um +used in a in a very clever way and that + + align:start position:0% +used in a in a very clever way and that + + + align:start position:0% +used in a in a very clever way and that +was an amazing + + align:start position:0% +was an amazing + + + align:start position:0% +was an amazing +idea you know got a Nobel Prize and + + align:start position:0% +idea you know got a Nobel Prize and + + + align:start position:0% +idea you know got a Nobel Prize and +you've been sitting here for the last + + align:start position:0% +you've been sitting here for the last + + + align:start position:0% +you've been sitting here for the last +month with all the knowledge to do it I + + align:start position:0% +month with all the knowledge to do it I + + + align:start position:0% +month with all the knowledge to do it I +keep emphasizing that got to have that + + align:start position:0% +keep emphasizing that got to have that + + + align:start position:0% +keep emphasizing that got to have that +three prime hydroxy but some of the + + align:start position:0% +three prime hydroxy but some of the + + + align:start position:0% +three prime hydroxy but some of the +great ideas oftener when you look back + + align:start position:0% +great ideas oftener when you look back + + + align:start position:0% +great ideas oftener when you look back +you could see it was the hurdle was kind + + align:start position:0% +you could see it was the hurdle was kind + + + align:start position:0% +you could see it was the hurdle was kind +of small and they didn't have even have + + align:start position:0% +of small and they didn't have even have + + + align:start position:0% +of small and they didn't have even have +to do this with with dyes at the + + align:start position:0% +to do this with with dyes at the + + + align:start position:0% +to do this with with dyes at the +beginning in fact that was a later inov + + align:start position:0% +beginning in fact that was a later inov + + + align:start position:0% +beginning in fact that was a later inov +the key thing was just the dioxy + + align:start position:0% +the key thing was just the dioxy + + + align:start position:0% +the key thing was just the dioxy +stopping it in each + + align:start position:0% +stopping it in each + + + align:start position:0% +stopping it in each +place I was lucky enough to live through + + align:start position:0% +place I was lucky enough to live through + + + align:start position:0% +place I was lucky enough to live through +some of this the development of this + + align:start position:0% +some of this the development of this + + + align:start position:0% +some of this the development of this +technology okay so um I've got one more + + align:start position:0% +technology okay so um I've got one more + + + align:start position:0% +technology okay so um I've got one more +really big thing to tell you which again + + align:start position:0% +really big thing to tell you which again + + + align:start position:0% +really big thing to tell you which again +was + + align:start position:0% +was + + + align:start position:0% +was +extraordinarily uh clever but + + align:start position:0% +extraordinarily uh clever but + + + align:start position:0% +extraordinarily uh clever but +extraordinarily simple once you heard + + align:start position:0% +extraordinarily simple once you heard + + + align:start position:0% +extraordinarily simple once you heard +about it and it gave was one more + + align:start position:0% +about it and it gave was one more + + + align:start position:0% +about it and it gave was one more +Technologic + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +Advance it wasn't um wasn't a big + + align:start position:0% +Advance it wasn't um wasn't a big + + + align:start position:0% +Advance it wasn't um wasn't a big +insight into biology in and of itself + + align:start position:0% +insight into biology in and of itself + + + align:start position:0% +insight into biology in and of itself +but it was a technology that opened up + + align:start position:0% +but it was a technology that opened up + + + align:start position:0% +but it was a technology that opened up +uh just incredible experimental + + align:start position:0% +uh just incredible experimental + + + align:start position:0% +uh just incredible experimental +possibilities and it's something known + + align:start position:0% +possibilities and it's something known + + + align:start position:0% +possibilities and it's something known +as The pimas Chain Reaction + + align:start position:0% + + + + align:start position:0% + +and this allows in principle someone + + align:start position:0% +and this allows in principle someone + + + align:start position:0% +and this allows in principle someone +like me to go in to + + align:start position:0% +like me to go in to + + + align:start position:0% +like me to go in to +grab a single cell from you take its + + align:start position:0% +grab a single cell from you take its + + + align:start position:0% +grab a single cell from you take its +DNA and get a copy of any Gene I want + + align:start position:0% +DNA and get a copy of any Gene I want + + + align:start position:0% +DNA and get a copy of any Gene I want +from your genome and I can look and see + + align:start position:0% +from your genome and I can look and see + + + align:start position:0% +from your genome and I can look and see +whether you have any mutations in that + + align:start position:0% +whether you have any mutations in that + + + align:start position:0% +whether you have any mutations in that +genome or if there are different + + align:start position:0% +genome or if there are different + + + align:start position:0% +genome or if there are different +polymorphic alals in the population + + align:start position:0% +polymorphic alals in the population + + + align:start position:0% +polymorphic alals in the population +which one you got from your mom or which + + align:start position:0% +which one you got from your mom or which + + + align:start position:0% +which one you got from your mom or which +one you got from your dad so you take + + align:start position:0% +one you got from your dad so you take + + + align:start position:0% +one you got from your dad so you take +from a single DNA molecule I can make as + + align:start position:0% +from a single DNA molecule I can make as + + + align:start position:0% +from a single DNA molecule I can make as +much as I want and this is just like DNA + + align:start position:0% +much as I want and this is just like DNA + + + align:start position:0% +much as I want and this is just like DNA +sequencing you guys already know + + align:start position:0% +sequencing you guys already know + + + align:start position:0% +sequencing you guys already know +everything you need to know to invent + + align:start position:0% +everything you need to know to invent + + + align:start position:0% +everything you need to know to invent +this technique as well it has very much + + align:start position:0% +this technique as well it has very much + + + align:start position:0% +this technique as well it has very much +that same property it's another one of + + align:start position:0% +that same property it's another one of + + + align:start position:0% +that same property it's another one of +these very brilliant sort of insights + + align:start position:0% +these very brilliant sort of insights + + + align:start position:0% +these very brilliant sort of insights +that was actually + + align:start position:0% +that was actually + + + align:start position:0% +that was actually +you just had to put things in the right + + align:start position:0% +you just had to put things in the right + + + align:start position:0% +you just had to put things in the right +place so let me explain the principle so + + align:start position:0% +place so let me explain the principle so + + + align:start position:0% +place so let me explain the principle so +suppose that I would like to know + + align:start position:0% +suppose that I would like to know + + + align:start position:0% +suppose that I would like to know +there's a gene that + + align:start position:0% +there's a gene that + + + align:start position:0% +there's a gene that +I'm uh I know there's a family history + + align:start position:0% +I'm uh I know there's a family history + + + align:start position:0% +I'm uh I know there's a family history +something and I would like to know did I + + align:start position:0% +something and I would like to know did I + + + align:start position:0% +something and I would like to know did I +happen to get the AL that carries that + + align:start position:0% +happen to get the AL that carries that + + + align:start position:0% +happen to get the AL that carries that +or did I get the one that didn't so in + + align:start position:0% +or did I get the one that didn't so in + + + align:start position:0% +or did I get the one that didn't so in +principle what I'd like to do would be + + align:start position:0% +principle what I'd like to do would be + + + align:start position:0% +principle what I'd like to do would be +to to take that get hold of um that + + align:start position:0% +to to take that get hold of um that + + + align:start position:0% +to to take that get hold of um that +particular a piece of DNA for that Gene + + align:start position:0% +particular a piece of DNA for that Gene + + + align:start position:0% +particular a piece of DNA for that Gene +from my own cells but all I'm starting + + align:start position:0% +from my own cells but all I'm starting + + + align:start position:0% +from my own cells but all I'm starting +with is my entire DNA well I could clone + + align:start position:0% +with is my entire DNA well I could clone + + + align:start position:0% +with is my entire DNA well I could clone +it I could make a recombinant library I + + align:start position:0% +it I could make a recombinant library I + + + align:start position:0% +it I could make a recombinant library I +could do everything else but there's + + align:start position:0% +could do everything else but there's + + + align:start position:0% +could do everything else but there's +this other simple way and one way this + + align:start position:0% +this other simple way and one way this + + + align:start position:0% +this other simple way and one way this +involves what it involves taking is + + align:start position:0% +involves what it involves taking is + + + align:start position:0% +involves what it involves taking is +since I know the sequence of the genome + + align:start position:0% +since I know the sequence of the genome + + + align:start position:0% +since I know the sequence of the genome +now I know that you know almost + + align:start position:0% +now I know that you know almost + + + align:start position:0% +now I know that you know almost +everything's going to be the same + + align:start position:0% +everything's going to be the same + + + align:start position:0% +everything's going to be the same +there'll be little differences in + + align:start position:0% +there'll be little differences in + + + align:start position:0% +there'll be little differences in +between individuals I'll make a little + + align:start position:0% +between individuals I'll make a little + + + align:start position:0% +between individuals I'll make a little +primer that corresponds to the sequence + + align:start position:0% +primer that corresponds to the sequence + + + align:start position:0% +primer that corresponds to the sequence +that one end of the DNA and one end of + + align:start position:0% +that one end of the DNA and one end of + + + align:start position:0% +that one end of the DNA and one end of +the Gene and another primer that + + align:start position:0% +the Gene and another primer that + + + align:start position:0% +the Gene and another primer that +corresponds to the DNA at the other end + + align:start position:0% +corresponds to the DNA at the other end + + + align:start position:0% +corresponds to the DNA at the other end +of the gene or whatever fragment I want + + align:start position:0% +of the gene or whatever fragment I want + + + align:start position:0% +of the gene or whatever fragment I want +to uh use + + align:start position:0% +to uh use + + + align:start position:0% +to uh use +and that's all I have to do in terms of + + align:start position:0% +and that's all I have to do in terms of + + + align:start position:0% +and that's all I have to do in terms of +getting anything made now the rest we're + + align:start position:0% +getting anything made now the rest we're + + + align:start position:0% +getting anything made now the rest we're +just going to play games with DNA DNA + + align:start position:0% +just going to play games with DNA DNA + + + align:start position:0% +just going to play games with DNA DNA +polymerase and nucleoside triphosphates + + align:start position:0% +polymerase and nucleoside triphosphates + + + align:start position:0% +polymerase and nucleoside triphosphates +just all the stuff I dragged you through + + align:start position:0% +just all the stuff I dragged you through + + + align:start position:0% +just all the stuff I dragged you through +talking about DNA replication so here's + + align:start position:0% +talking about DNA replication so here's + + + align:start position:0% +talking about DNA replication so here's +here's the idea so let's let's take a + + align:start position:0% +here's the idea so let's let's take a + + + align:start position:0% +here's the idea so let's let's take a +here's here's my DNA let's say or a part + + align:start position:0% +here's here's my DNA let's say or a part + + + align:start position:0% +here's here's my DNA let's say or a part +of + + align:start position:0% +of + + + align:start position:0% +of +it and right if I could actually see the + + align:start position:0% +it and right if I could actually see the + + + align:start position:0% +it and right if I could actually see the +sequence I would know let's say the gene + + align:start position:0% +sequence I would know let's say the gene + + + align:start position:0% +sequence I would know let's say the gene +I'm interested in is in here so what I + + align:start position:0% +I'm interested in is in here so what I + + + align:start position:0% +I'm interested in is in here so what I +would do is make a little primer it just + + align:start position:0% +would do is make a little primer it just + + + align:start position:0% +would do is make a little primer it just +has to be enough to confer specificity + + align:start position:0% +has to be enough to confer specificity + + + align:start position:0% +has to be enough to confer specificity +for something with humans if I make + + align:start position:0% +for something with humans if I make + + + align:start position:0% +for something with humans if I make +something probably 30 nucleotides long + + align:start position:0% +something probably 30 nucleotides long + + + align:start position:0% +something probably 30 nucleotides long +that's enough it'll only bind one place + + align:start position:0% +that's enough it'll only bind one place + + + align:start position:0% +that's enough it'll only bind one place +in the DNA + + align:start position:0% +in the DNA + + + align:start position:0% +in the DNA +and I make one let's say for the op for + + align:start position:0% +and I make one let's say for the op for + + + align:start position:0% +and I make one let's say for the op for +the opposite strand over here so + + align:start position:0% +the opposite strand over here so + + + align:start position:0% +the opposite strand over here so +remember this is five Prime three + + align:start position:0% +remember this is five Prime three + + + align:start position:0% +remember this is five Prime three +prime I prime to to three + + align:start position:0% +prime I prime to to three + + + align:start position:0% +prime I prime to to three +prime so + + align:start position:0% + + + + align:start position:0% + +the principle is we'll heat to 95° + + align:start position:0% +the principle is we'll heat to 95° + + + align:start position:0% +the principle is we'll heat to 95° +centigrade and we'll denature the + + align:start position:0% + + + + align:start position:0% + +DNA We'll add + + align:start position:0% + + + + align:start position:0% + +an excess of the two + + align:start position:0% + + + + align:start position:0% + +primers let's say We'll cool + + align:start position:0% +primers let's say We'll cool + + + align:start position:0% +primers let's say We'll cool +to 55° Centigrade or something we'll + + align:start position:0% +to 55° Centigrade or something we'll + + + align:start position:0% +to 55° Centigrade or something we'll +cool it down enough so that we can get + + align:start position:0% +cool it down enough so that we can get + + + align:start position:0% +cool it down enough so that we can get +the primers on but we're not going to go + + align:start position:0% +the primers on but we're not going to go + + + align:start position:0% +the primers on but we're not going to go +all the way and let all the strands find + + align:start position:0% +all the way and let all the strands find + + + align:start position:0% +all the way and let all the strands find +their way + + align:start position:0% + + + + align:start position:0% + +back we'll add a DNA polymerase + + align:start position:0% + + + + align:start position:0% + +plus + + align:start position:0% +plus + + + align:start position:0% +plus +four deoxy + + align:start position:0% +four deoxy + + + align:start position:0% +four deoxy +nucleotide dry + + align:start position:0% + + + + align:start position:0% + +phosphates well what'll happen well + + align:start position:0% +phosphates well what'll happen well + + + align:start position:0% +phosphates well what'll happen well +here's one of the + + align:start position:0% +here's one of the + + + align:start position:0% +here's one of the +strands and we'll prime it here let's + + align:start position:0% +strands and we'll prime it here let's + + + align:start position:0% +strands and we'll prime it here let's +say so it'll + + align:start position:0% +say so it'll + + + align:start position:0% +say so it'll +it'll copy down here and go as far as it + + align:start position:0% +it'll copy down here and go as far as it + + + align:start position:0% +it'll copy down here and go as far as it +can go + + align:start position:0% + + + + align:start position:0% + +the other one whatever it was starts + + align:start position:0% +the other one whatever it was starts + + + align:start position:0% +the other one whatever it was starts +here and it's going to go down all that + + align:start position:0% + + + + align:start position:0% + +way let's just repeat the whole process + + align:start position:0% +way let's just repeat the whole process + + + align:start position:0% +way let's just repeat the whole process +now okay what'll happen now when we pull + + align:start position:0% +now okay what'll happen now when we pull + + + align:start position:0% +now okay what'll happen now when we pull +them apart we ought to + + align:start position:0% +them apart we ought to + + + align:start position:0% +them apart we ought to +have four strands we'll + + align:start position:0% +have four strands we'll + + + align:start position:0% +have four strands we'll +have the original ones here and when I + + align:start position:0% +have the original ones here and when I + + + align:start position:0% +have the original ones here and when I +repeat the process the same thing's + + align:start position:0% +repeat the process the same thing's + + + align:start position:0% +repeat the process the same thing's +going to happen again this one will go + + align:start position:0% +going to happen again this one will go + + + align:start position:0% +going to happen again this one will go +here and it'll and it'll copy out this + + align:start position:0% +here and it'll and it'll copy out this + + + align:start position:0% +here and it'll and it'll copy out this +one will go + + align:start position:0% +one will go + + + align:start position:0% +one will go +here it will copy + + align:start position:0% +here it will copy + + + align:start position:0% +here it will copy +out but what about this guy so this + + align:start position:0% +out but what about this guy so this + + + align:start position:0% +out but what about this guy so this +one this one becomes this one + + align:start position:0% +one this one becomes this one + + + align:start position:0% +one this one becomes this one +here so the primer that it + + align:start position:0% +here so the primer that it + + + align:start position:0% +here so the primer that it +does well cop it and I can't go any + + align:start position:0% +does well cop it and I can't go any + + + align:start position:0% +does well cop it and I can't go any +further I've just generated a piece + + align:start position:0% +further I've just generated a piece + + + align:start position:0% +further I've just generated a piece +that's exactly what I wanted and the + + align:start position:0% +that's exactly what I wanted and the + + + align:start position:0% +that's exactly what I wanted and the +same deal down here as long as I don't + + align:start position:0% +same deal down here as long as I don't + + + align:start position:0% +same deal down here as long as I don't +get lost uh which one did I do + + align:start position:0% +get lost uh which one did I do + + + align:start position:0% +get lost uh which one did I do +so + + align:start position:0% +so + + + align:start position:0% +so +um so we've got this guy here so it + + align:start position:0% +um so we've got this guy here so it + + + align:start position:0% +um so we've got this guy here so it +starts there and and when so this + + align:start position:0% +starts there and and when so this + + + align:start position:0% +starts there and and when so this +one comes this one and we'll prime it + + align:start position:0% +one comes this one and we'll prime it + + + align:start position:0% +one comes this one and we'll prime it +here and it'll go along and it'll stop + + align:start position:0% +here and it'll go along and it'll stop + + + align:start position:0% +here and it'll go along and it'll stop +so there's the complimentary strand to + + align:start position:0% +so there's the complimentary strand to + + + align:start position:0% +so there's the complimentary strand to +the one + + align:start position:0% +the one + + + align:start position:0% +the one +here + + align:start position:0% + + + + align:start position:0% + +and if you I think this is sort of like + + align:start position:0% +and if you I think this is sort of like + + + align:start position:0% +and if you I think this is sort of like +doing a math problem you can't just look + + align:start position:0% +doing a math problem you can't just look + + + align:start position:0% +doing a math problem you can't just look +at it and say well maybe a few you can + + align:start position:0% +at it and say well maybe a few you can + + + align:start position:0% +at it and say well maybe a few you can +we'll get it but there's nothing like + + align:start position:0% +we'll get it but there's nothing like + + + align:start position:0% +we'll get it but there's nothing like +sitting down with a pencil and paper and + + align:start position:0% +sitting down with a pencil and paper and + + + align:start position:0% +sitting down with a pencil and paper and +take yourself through several Cycles + + align:start position:0% +take yourself through several Cycles + + + align:start position:0% +take yourself through several Cycles +what you won't believe is how quickly + + align:start position:0% +what you won't believe is how quickly + + + align:start position:0% +what you won't believe is how quickly +you get to get being nothing but almost + + align:start position:0% +you get to get being nothing but almost + + + align:start position:0% +you get to get being nothing but almost +nothing but the sequence that you're + + align:start position:0% +nothing but the sequence that you're + + + align:start position:0% +nothing but the sequence that you're +that you're trying to trying to + + align:start position:0% +that you're trying to trying to + + + align:start position:0% +that you're trying to trying to +amplify and so this this again is what's + + align:start position:0% +amplify and so this this again is what's + + + align:start position:0% +amplify and so this this again is what's +had an an astonishing effect this is why + + align:start position:0% +had an an astonishing effect this is why + + + align:start position:0% +had an an astonishing effect this is why +you hear about uh DNA testing all the + + align:start position:0% +you hear about uh DNA testing all the + + + align:start position:0% +you hear about uh DNA testing all the +time in forensics because you can take a + + align:start position:0% +time in forensics because you can take a + + + align:start position:0% +time in forensics because you can take a +tiny bit of DNA from saliva or semen or + + align:start position:0% +tiny bit of DNA from saliva or semen or + + + align:start position:0% +tiny bit of DNA from saliva or semen or +blood or whatever they might find on a + + align:start position:0% +blood or whatever they might find on a + + + align:start position:0% +blood or whatever they might find on a +on a crime scene and then they can + + align:start position:0% +on a crime scene and then they can + + + align:start position:0% +on a crime scene and then they can +amplify little pieces and they compare + + align:start position:0% +amplify little pieces and they compare + + + align:start position:0% +amplify little pieces and they compare +and there's a trick they use use in in + + align:start position:0% + + + + align:start position:0% + +um in forensics and that is that there + + align:start position:0% +um in forensics and that is that there + + + align:start position:0% +um in forensics and that is that there +are sequences within the uh Human Genome + + align:start position:0% +are sequences within the uh Human Genome + + + align:start position:0% +are sequences within the uh Human Genome +where there are little variable repeats + + align:start position:0% +where there are little variable repeats + + + align:start position:0% +where there are little variable repeats +like GT GT GT GT GT GT and I might have + + align:start position:0% +like GT GT GT GT GT GT and I might have + + + align:start position:0% +like GT GT GT GT GT GT and I might have +14 of them in one of my chromosomes the + + align:start position:0% +14 of them in one of my chromosomes the + + + align:start position:0% +14 of them in one of my chromosomes the +one I got from my mom might have 40 you + + align:start position:0% +one I got from my mom might have 40 you + + + align:start position:0% +one I got from my mom might have 40 you +might have 24 and and something else and + + align:start position:0% +might have 24 and and something else and + + + align:start position:0% +might have 24 and and something else and +so on so if you were to do PC R around + + align:start position:0% +so on so if you were to do PC R around + + + align:start position:0% +so on so if you were to do PC R around +that little that little region that was + + align:start position:0% +that little that little region that was + + + align:start position:0% +that little that little region that was +known to be variable if you had 14 + + align:start position:0% +known to be variable if you had 14 + + + align:start position:0% +known to be variable if you had 14 +repeats you'd get a shorter fragment and + + align:start position:0% +repeats you'd get a shorter fragment and + + + align:start position:0% +repeats you'd get a shorter fragment and +if you had 40 repeats you get a longer + + align:start position:0% +if you had 40 repeats you get a longer + + + align:start position:0% +if you had 40 repeats you get a longer +fragment + + align:start position:0% +fragment + + + align:start position:0% +fragment +so I'll come back to that in a sec so if + + align:start position:0% +so I'll come back to that in a sec so if + + + align:start position:0% +so I'll come back to that in a sec so if +you were for example take something with + + align:start position:0% +you were for example take something with + + + align:start position:0% +you were for example take something with +a a short repeat a long repeat and a + + align:start position:0% +a a short repeat a long repeat and a + + + align:start position:0% +a a short repeat a long repeat and a +short Peak and do this kind of thing we + + align:start position:0% +short Peak and do this kind of thing we + + + align:start position:0% +short Peak and do this kind of thing we +get two fragments say one from the + + align:start position:0% +get two fragments say one from the + + + align:start position:0% +get two fragments say one from the +maternal one from the paternal and if + + align:start position:0% +maternal one from the paternal and if + + + align:start position:0% +maternal one from the paternal and if +you do this with several such sites + + align:start position:0% +you do this with several such sites + + + align:start position:0% +you do this with several such sites +around the genome pretty soon you run in + + align:start position:0% +around the genome pretty soon you run in + + + align:start position:0% +around the genome pretty soon you run in +these situations where the odds of a + + align:start position:0% +these situations where the odds of a + + + align:start position:0% +these situations where the odds of a +particular combination of a long one at + + align:start position:0% +particular combination of a long one at + + + align:start position:0% +particular combination of a long one at +this site a short one at this site and + + align:start position:0% +this site a short one at this site and + + + align:start position:0% +this site a short one at this site and +so on BEC statistically improbable that + + align:start position:0% +so on BEC statistically improbable that + + + align:start position:0% +so on BEC statistically improbable that +it's anyone other than yourself so in a + + align:start position:0% +it's anyone other than yourself so in a + + + align:start position:0% +it's anyone other than yourself so in a +crime scene if they did this they for + + align:start position:0% +crime scene if they did this they for + + + align:start position:0% +crime scene if they did this they for +example might have three individuals + + align:start position:0% +example might have three individuals + + + align:start position:0% +example might have three individuals +that they were thinking was possible and + + align:start position:0% +that they were thinking was possible and + + + align:start position:0% +that they were thinking was possible and +they generate patterns like this say + + align:start position:0% +they generate patterns like this say + + + align:start position:0% +they generate patterns like this say +using three different Loi like this and + + align:start position:0% +using three different Loi like this and + + + align:start position:0% +using three different Loi like this and +then have the forensic sample and it was + + align:start position:0% +then have the forensic sample and it was + + + align:start position:0% +then have the forensic sample and it was +pretty evident who didn't do it and who + + align:start position:0% +pretty evident who didn't do it and who + + + align:start position:0% +pretty evident who didn't do it and who +at least remains a suspect this probably + + align:start position:0% +at least remains a suspect this probably + + + align:start position:0% +at least remains a suspect this probably +wouldn't prove it the very last thing + + align:start position:0% +wouldn't prove it the very last thing + + + align:start position:0% +wouldn't prove it the very last thing +just to close this off is when people + + align:start position:0% +just to close this off is when people + + + align:start position:0% +just to close this off is when people +develop this PCR technique you had to + + align:start position:0% +develop this PCR technique you had to + + + align:start position:0% +develop this PCR technique you had to +sit there with your pipet because every + + align:start position:0% +sit there with your pipet because every + + + align:start position:0% +sit there with your pipet because every +time you raised it to 90° to the nature + + align:start position:0% +time you raised it to 90° to the nature + + + align:start position:0% +time you raised it to 90° to the nature +of the DNA you killed your + + align:start position:0% +of the DNA you killed your + + + align:start position:0% +of the DNA you killed your +enzyme so you cooled it down 55 you + + align:start position:0% +enzyme so you cooled it down 55 you + + + align:start position:0% +enzyme so you cooled it down 55 you +squirted in new DNA plas and then + + align:start position:0% +squirted in new DNA plas and then + + + align:start position:0% +squirted in new DNA plas and then +someone finally said another brilliant + + align:start position:0% +someone finally said another brilliant + + + align:start position:0% +someone finally said another brilliant +idea what if the I had a thermo + + align:start position:0% +idea what if the I had a thermo + + + align:start position:0% +idea what if the I had a thermo +resistant ply + + align:start position:0% +resistant ply + + + align:start position:0% +resistant ply +where would I find those + + align:start position:0% +where would I find those + + + align:start position:0% +where would I find those +well oops SEC sorry go back here um + + align:start position:0% +well oops SEC sorry go back here um + + + align:start position:0% +well oops SEC sorry go back here um +Penny was talking to you about those + + align:start position:0% +Penny was talking to you about those + + + align:start position:0% +Penny was talking to you about those +vents where it's really really hot and + + align:start position:0% +vents where it's really really hot and + + + align:start position:0% +vents where it's really really hot and +those black smokers and everything so + + align:start position:0% +those black smokers and everything so + + + align:start position:0% +those black smokers and everything so +maybe you got a bacterium from there it + + align:start position:0% +maybe you got a bacterium from there it + + + align:start position:0% +maybe you got a bacterium from there it +would have a temperature resistant + + align:start position:0% +would have a temperature resistant + + + align:start position:0% +would have a temperature resistant +polymerase so here you are from the New + + align:start position:0% +polymerase so here you are from the New + + + align:start position:0% +polymerase so here you are from the New +England bio catalog vent XOM minus DNA + + align:start position:0% +England bio catalog vent XOM minus DNA + + + align:start position:0% +England bio catalog vent XOM minus DNA +pyase deep vent DNA polymerase people + + align:start position:0% +pyase deep vent DNA polymerase people + + + align:start position:0% +pyase deep vent DNA polymerase people +went grabbed those bacteria from there + + align:start position:0% +went grabbed those bacteria from there + + + align:start position:0% +went grabbed those bacteria from there +grabbed the DNA polymerase Gene and now + + align:start position:0% +grabbed the DNA polymerase Gene and now + + + align:start position:0% +grabbed the DNA polymerase Gene and now +the DNA polymerase just sits there it + + align:start position:0% +the DNA polymerase just sits there it + + + align:start position:0% +the DNA polymerase just sits there it +just laughs when you bring it up to 90° + + align:start position:0% +just laughs when you bring it up to 90° + + + align:start position:0% +just laughs when you bring it up to 90° +and when you cool it back down and give + + align:start position:0% +and when you cool it back down and give + + + align:start position:0% +and when you cool it back down and give +it a substrate again it let do its thing + + align:start position:0% +it a substrate again it let do its thing + + + align:start position:0% +it a substrate again it let do its thing +and so this whole thing can be done + + align:start position:0% +and so this whole thing can be done + + + align:start position:0% +and so this whole thing can be done +automatic and you don't have to sit + + align:start position:0% +automatic and you don't have to sit + + + align:start position:0% +automatic and you don't have to sit +there and pip pet something in at the + + align:start position:0% +there and pip pet something in at the + + + align:start position:0% +there and pip pet something in at the +end of every run another little cute + + align:start position:0% +end of every run another little cute + + + align:start position:0% +end of every run another little cute +sort of engineering trick that combined + + align:start position:0% +sort of engineering trick that combined + + + align:start position:0% +sort of engineering trick that combined +ecology together with Biology okay see + + align:start position:0% +ecology together with Biology okay see + + + align:start position:0% +ecology together with Biology okay see +you on Friday \ No newline at end of file diff --git a/FSW9EQNZvxI.txt b/FSW9EQNZvxI.txt new file mode 100644 index 0000000000000000000000000000000000000000..19bf6c0217c9d8b8900621139e829dfc84be77cd --- /dev/null +++ b/FSW9EQNZvxI.txt @@ -0,0 +1,155 @@ +align:start position:0% + +let's consider the motion of an object + + align:start position:0% +let's consider the motion of an object + + + align:start position:0% +let's consider the motion of an object +that is under the action of a force so + + align:start position:0% +that is under the action of a force so + + + align:start position:0% +that is under the action of a force so +we have some force that's acting on this + + align:start position:0% +we have some force that's acting on this + + + align:start position:0% +we have some force that's acting on this +object and we have a little displacement + + align:start position:0% +object and we have a little displacement + + + align:start position:0% +object and we have a little displacement +D s so this is a small displacement of + + align:start position:0% +D s so this is a small displacement of + + + align:start position:0% +D s so this is a small displacement of +the object then we know that the small + + align:start position:0% +the object then we know that the small + + + align:start position:0% +the object then we know that the small +amount of work done by the action of + + align:start position:0% +amount of work done by the action of + + + align:start position:0% +amount of work done by the action of +this force is f dot d s and the rate of + + align:start position:0% +this force is f dot d s and the rate of + + + align:start position:0% +this force is f dot d s and the rate of +doing work + + align:start position:0% +doing work + + + align:start position:0% +doing work +so let's now introduce the concept of + + align:start position:0% +so let's now introduce the concept of + + + align:start position:0% +so let's now introduce the concept of +power which is the rate of doing work + + align:start position:0% +power which is the rate of doing work + + + align:start position:0% +power which is the rate of doing work +that is f dot DS over DT and D s DT is + + align:start position:0% +that is f dot DS over DT and D s DT is + + + align:start position:0% +that is f dot DS over DT and D s DT is +just the velocity of the object so we + + align:start position:0% +just the velocity of the object so we + + + align:start position:0% +just the velocity of the object so we +see very simply that when we talk about + + align:start position:0% +see very simply that when we talk about + + + align:start position:0% +see very simply that when we talk about +power and sometimes people use the + + align:start position:0% +power and sometimes people use the + + + align:start position:0% +power and sometimes people use the +symbol P although we can also talk about + + align:start position:0% +symbol P although we can also talk about + + + align:start position:0% +symbol P although we can also talk about +pressure and momentum so it's a little + + align:start position:0% +pressure and momentum so it's a little + + + align:start position:0% +pressure and momentum so it's a little +bit tricky but here the power is f dot V + + align:start position:0% +bit tricky but here the power is f dot V + + + align:start position:0% +bit tricky but here the power is f dot V +and power is a concept that will appear + + align:start position:0% +and power is a concept that will appear + + + align:start position:0% +and power is a concept that will appear +in many different settings \ No newline at end of file diff --git a/FndNHiuFeFU.txt b/FndNHiuFeFU.txt new file mode 100644 index 0000000000000000000000000000000000000000..2a04ceb5267178b559473b72d2268a5a59cea520 --- /dev/null +++ b/FndNHiuFeFU.txt @@ -0,0 +1,5939 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +I've been getting to play with this + + align:start position:0% +I've been getting to play with this + + + align:start position:0% +I've been getting to play with this +robot for a few years now three years of + + align:start position:0% +robot for a few years now three years of + + + align:start position:0% +robot for a few years now three years of +my life basically devoted to that robot + + align:start position:0% +my life basically devoted to that robot + + + align:start position:0% +my life basically devoted to that robot +it was one of the most exciting + + align:start position:0% +it was one of the most exciting + + + align:start position:0% +it was one of the most exciting +technically challenging exhausting + + align:start position:0% +technically challenging exhausting + + + align:start position:0% +technically challenging exhausting +stressful but ultimately fulfilling + + align:start position:0% +stressful but ultimately fulfilling + + + align:start position:0% +stressful but ultimately fulfilling +things I've ever done we got to + + align:start position:0% +things I've ever done we got to + + + align:start position:0% +things I've ever done we got to +basically take this robot make it drive + + align:start position:0% +basically take this robot make it drive + + + align:start position:0% +basically take this robot make it drive +a car get out of the car that was tough + + align:start position:0% +a car get out of the car that was tough + + + align:start position:0% +a car get out of the car that was tough +open the door turned valves pickup drill + + align:start position:0% +open the door turned valves pickup drill + + + align:start position:0% +open the door turned valves pickup drill +cut a hole out of the wall notice + + align:start position:0% +cut a hole out of the wall notice + + + align:start position:0% +cut a hole out of the wall notice +there's no safety harness its battery + + align:start position:0% +there's no safety harness its battery + + + align:start position:0% +there's no safety harness its battery +autonomous it has a walk over some rough + + align:start position:0% +autonomous it has a walk over some rough + + + align:start position:0% +autonomous it has a walk over some rough +terrain climb some stairs at the end it + + align:start position:0% +terrain climb some stairs at the end it + + + align:start position:0% +terrain climb some stairs at the end it +had to do this in front of an audience + + align:start position:0% +had to do this in front of an audience + + + align:start position:0% +had to do this in front of an audience +with basically we got two tries and if + + align:start position:0% +with basically we got two tries and if + + + align:start position:0% +with basically we got two tries and if +your robot breaks the breaks right and + + align:start position:0% +your robot breaks the breaks right and + + + align:start position:0% +your robot breaks the breaks right and +there was a there was a two million + + align:start position:0% +there was a there was a two million + + + align:start position:0% +there was a there was a two million +dollar prize at the end right we we + + align:start position:0% +dollar prize at the end right we we + + + align:start position:0% +dollar prize at the end right we we +wanted to do it out for the two million + + align:start position:0% +wanted to do it out for the two million + + + align:start position:0% +wanted to do it out for the two million +dollar prize but for the technical + + align:start position:0% +dollar prize but for the technical + + + align:start position:0% +dollar prize but for the technical +challenge and myself and a group of + + align:start position:0% +challenge and myself and a group of + + + align:start position:0% +challenge and myself and a group of +students just like I said absolutely + + align:start position:0% +students just like I said absolutely + + + align:start position:0% +students just like I said absolutely +devoted our lives to this we spent all + + align:start position:0% +devoted our lives to this we spent all + + + align:start position:0% +devoted our lives to this we spent all +of our waking hours on this we worked + + align:start position:0% +of our waking hours on this we worked + + + align:start position:0% +of our waking hours on this we worked +incredibly incredibly hard so just to + + align:start position:0% +incredibly incredibly hard so just to + + + align:start position:0% +incredibly incredibly hard so just to +give you a little bit of context DARPA + + align:start position:0% +give you a little bit of context DARPA + + + align:start position:0% +give you a little bit of context DARPA +are our National Defense funding agency + + align:start position:0% +are our National Defense funding agency + + + align:start position:0% +are our National Defense funding agency +has gotten excited about the idea of + + align:start position:0% +has gotten excited about the idea of + + + align:start position:0% +has gotten excited about the idea of +these grand challenges which get people + + align:start position:0% +these grand challenges which get people + + + align:start position:0% +these grand challenges which get people +to work really really hard the + + align:start position:0% +to work really really hard the + + + align:start position:0% +to work really really hard the +self-driving cars were were the first + + align:start position:0% +self-driving cars were were the first + + + align:start position:0% +self-driving cars were were the first +one and MIT had a very successful team + + align:start position:0% +one and MIT had a very successful team + + + align:start position:0% +one and MIT had a very successful team +in the urban challenge led by John and + + align:start position:0% +in the urban challenge led by John and + + + align:start position:0% +in the urban challenge led by John and +then it's unquestionably had transition + + align:start position:0% +then it's unquestionably had transition + + + align:start position:0% +then it's unquestionably had transition +impact into the world via Google uber + + align:start position:0% +impact into the world via Google uber + + + align:start position:0% +impact into the world via Google uber +apple and John John will tell you all + + align:start position:0% +apple and John John will tell you all + + + align:start position:0% +apple and John John will tell you all +about it I think in 2012 DARPA was + + align:start position:0% +about it I think in 2012 DARPA was + + + align:start position:0% +about it I think in 2012 DARPA was +scratching their head saying people + + align:start position:0% +scratching their head saying people + + + align:start position:0% +scratching their head saying people +haven't worked hard enough and you know + + align:start position:0% +haven't worked hard enough and you know + + + align:start position:0% +haven't worked hard enough and you know +what's the new challenge going to be and + + align:start position:0% +what's the new challenge going to be and + + + align:start position:0% +what's the new challenge going to be and +and right around that time there was a + + align:start position:0% +and right around that time there was a + + + align:start position:0% +and right around that time there was a +disaster that that maybe helped focus + + align:start position:0% +disaster that that maybe helped focus + + + align:start position:0% +disaster that that maybe helped focus +their attention towards disaster + + align:start position:0% +their attention towards disaster + + + align:start position:0% +their attention towards disaster +response + + align:start position:0% +response + + + align:start position:0% +response +so in ultimately it was October 2012 + + align:start position:0% +so in ultimately it was October 2012 + + + align:start position:0% +so in ultimately it was October 2012 +that everything started with this + + align:start position:0% +that everything started with this + + + align:start position:0% +that everything started with this +kickoff for the DARPA Robotics Challenge + + align:start position:0% +kickoff for the DARPA Robotics Challenge + + + align:start position:0% +kickoff for the DARPA Robotics Challenge +the official challenge was was cast in + + align:start position:0% +the official challenge was was cast in + + + align:start position:0% +the official challenge was was cast in +the in the light of disaster response in + + align:start position:0% +the in the light of disaster response in + + + align:start position:0% +the in the light of disaster response in +the the scenario of the nuclear disaster + + align:start position:0% +the the scenario of the nuclear disaster + + + align:start position:0% +the the scenario of the nuclear disaster +as a backdrop but I think really their + + align:start position:0% +as a backdrop but I think really their + + + align:start position:0% +as a backdrop but I think really their +goal was to evaluate in advance + + align:start position:0% +goal was to evaluate in advance + + + align:start position:0% +goal was to evaluate in advance +state-of-the-art in mobile manipulation + + align:start position:0% +state-of-the-art in mobile manipulation + + + align:start position:0% +state-of-the-art in mobile manipulation +okay so if I'm the funding agency what I + + align:start position:0% +okay so if I'm the funding agency what I + + + align:start position:0% +okay so if I'm the funding agency what I +think is that you see Hardware coming + + align:start position:0% +think is that you see Hardware coming + + + align:start position:0% +think is that you see Hardware coming +out of industry that's fantastic + + align:start position:0% +out of industry that's fantastic + + + align:start position:0% +out of industry that's fantastic +so Boston Dynamics was building these + + align:start position:0% +so Boston Dynamics was building these + + + align:start position:0% +so Boston Dynamics was building these +these walking robots and the like this + + align:start position:0% +these walking robots and the like this + + + align:start position:0% +these walking robots and the like this +one is the one we've been playing with + + align:start position:0% +one is the one we've been playing with + + + align:start position:0% +one is the one we've been playing with +Atlas built by Boston Dynamics which is + + align:start position:0% +Atlas built by Boston Dynamics which is + + + align:start position:0% +Atlas built by Boston Dynamics which is +now Google oh yeah + + align:start position:0% +now Google oh yeah + + + align:start position:0% +now Google oh yeah +and and then I think from the research + + align:start position:0% +and and then I think from the research + + + align:start position:0% +and and then I think from the research +labs we've been seeing really + + align:start position:0% +labs we've been seeing really + + + align:start position:0% +labs we've been seeing really +sophisticated algorithms coming out but + + align:start position:0% +sophisticated algorithms coming out but + + + align:start position:0% +sophisticated algorithms coming out but +on relatively modest hardware and I + + align:start position:0% +on relatively modest hardware and I + + + align:start position:0% +on relatively modest hardware and I +think it was time for a mashup right so + + align:start position:0% +think it was time for a mashup right so + + + align:start position:0% +think it was time for a mashup right so +they were they were very interesting in + + align:start position:0% +they were they were very interesting in + + + align:start position:0% +they were they were very interesting in +the way they set up the competition + + align:start position:0% +the way they set up the competition + + + align:start position:0% +the way they set up the competition +it wasn't about making it a completely + + align:start position:0% +it wasn't about making it a completely + + + align:start position:0% +it wasn't about making it a completely +autonomous robot it was there was there + + align:start position:0% +autonomous robot it was there was there + + + align:start position:0% +autonomous robot it was there was there +was a twist you could have a human + + align:start position:0% +was a twist you could have a human + + + align:start position:0% +was a twist you could have a human +operator but they wanted to encourage + + align:start position:0% +operator but they wanted to encourage + + + align:start position:0% +operator but they wanted to encourage +autonomy so what they did is they had a + + align:start position:0% +autonomy so what they did is they had a + + + align:start position:0% +autonomy so what they did is they had a +degraded network link between the human + + align:start position:0% +degraded network link between the human + + + align:start position:0% +degraded network link between the human +and the robot and some reward for going + + align:start position:0% +and the robot and some reward for going + + + align:start position:0% +and the robot and some reward for going +a little bit faster than the other guy + + align:start position:0% +a little bit faster than the other guy + + + align:start position:0% +a little bit faster than the other guy +so the idea would be that if you had to + + align:start position:0% +so the idea would be that if you had to + + + align:start position:0% +so the idea would be that if you had to +stop and and work over the degraded + + align:start position:0% +stop and and work over the degraded + + + align:start position:0% +stop and and work over the degraded +network link and control every joint of + + align:start position:0% +network link and control every joint of + + + align:start position:0% +network link and control every joint of +your robot then you're gonna be slower + + align:start position:0% +your robot then you're gonna be slower + + + align:start position:0% +your robot then you're gonna be slower +than the guy whose robot is making the + + align:start position:0% +than the guy whose robot is making the + + + align:start position:0% +than the guy whose robot is making the +decisions by itself that didn't play out + + align:start position:0% +decisions by itself that didn't play out + + + align:start position:0% +decisions by itself that didn't play out +as much as we expected but that was that + + align:start position:0% +as much as we expected but that was that + + + align:start position:0% +as much as we expected but that was that +was the set up that set up a spectrum + + align:start position:0% +was the set up that set up a spectrum + + + align:start position:0% +was the set up that set up a spectrum +where people could do to fully full + + align:start position:0% +where people could do to fully full + + + align:start position:0% +where people could do to fully full +teleoperation meaning joystick control + + align:start position:0% +teleoperation meaning joystick control + + + align:start position:0% +teleoperation meaning joystick control +of each of the joints if they wanted to + + align:start position:0% +of each of the joints if they wanted to + + + align:start position:0% +of each of the joints if they wanted to +you know and maybe the goal is to have + + align:start position:0% +you know and maybe the goal is to have + + + align:start position:0% +you know and maybe the goal is to have +complete autonomy and you could pick + + align:start position:0% +complete autonomy and you could pick + + + align:start position:0% +complete autonomy and you could pick +your place on the spectrum right so MIT + + align:start position:0% +your place on the spectrum right so MIT + + + align:start position:0% +your place on the spectrum right so MIT +possibly to a fault aimed for the full + + align:start position:0% +possibly to a fault aimed for the full + + + align:start position:0% +possibly to a fault aimed for the full +autonomy side the idea was was let's + + align:start position:0% +autonomy side the idea was was let's + + + align:start position:0% +autonomy side the idea was was let's +just get a few clicks of information + + align:start position:0% +just get a few clicks of information + + + align:start position:0% +just get a few clicks of information +from the human eye let the humans solve + + align:start position:0% +from the human eye let the humans solve + + + align:start position:0% +from the human eye let the humans solve +the really really hard problems that he + + align:start position:0% +the really really hard problems that he + + + align:start position:0% +the really really hard problems that he +could solve efficiently object + + align:start position:0% +could solve efficiently object + + + align:start position:0% +could solve efficiently object +recognition scene understanding we don't + + align:start position:0% +recognition scene understanding we don't + + + align:start position:0% +recognition scene understanding we don't +have to to do that a few clicks from the + + align:start position:0% +have to to do that a few clicks from the + + + align:start position:0% +have to to do that a few clicks from the +human can communicate that but the robot + + align:start position:0% +human can communicate that but the robot + + + align:start position:0% +human can communicate that but the robot +do all the dynamics and control and + + align:start position:0% +do all the dynamics and control and + + + align:start position:0% +do all the dynamics and control and +planning side of things okay so those + + align:start position:0% +planning side of things okay so those + + + align:start position:0% +planning side of things okay so those +few clicks should cede nearly autonomous + + align:start position:0% +few clicks should cede nearly autonomous + + + align:start position:0% +few clicks should cede nearly autonomous +algorithms for perception planning and + + align:start position:0% +algorithms for perception planning and + + + align:start position:0% +algorithms for perception planning and +control okay so technically I I don't I + + align:start position:0% +control okay so technically I I don't I + + + align:start position:0% +control okay so technically I I don't I +don't intend to go into too many details + + align:start position:0% +don't intend to go into too many details + + + align:start position:0% +don't intend to go into too many details +but I would love to answer questions if + + align:start position:0% +but I would love to answer questions if + + + align:start position:0% +but I would love to answer questions if +you guys ask and we can talk as much as + + align:start position:0% +you guys ask and we can talk as much as + + + align:start position:0% +you guys ask and we can talk as much as +we want about it but but the theme the + + align:start position:0% +we want about it but but the theme the + + + align:start position:0% +we want about it but but the theme the +overarching theme to our approach is + + align:start position:0% +overarching theme to our approach is + + + align:start position:0% +overarching theme to our approach is +when we're controlling perceiving + + align:start position:0% +when we're controlling perceiving + + + align:start position:0% +when we're controlling perceiving +everything is to formulate everything is + + align:start position:0% +everything is to formulate everything is + + + align:start position:0% +everything is to formulate everything is +an optimization problem so even sort of + + align:start position:0% +an optimization problem so even sort of + + + align:start position:0% +an optimization problem so even sort of +the simplest example in robotics is is + + align:start position:0% +the simplest example in robotics is is + + + align:start position:0% +the simplest example in robotics is is +the inverse can + + align:start position:0% +the inverse can + + + align:start position:0% +the inverse can +Maddox problem where you're just trying + + align:start position:0% +Maddox problem where you're just trying + + + align:start position:0% +Maddox problem where you're just trying +to decide if I want to put my hand in + + align:start position:0% +to decide if I want to put my hand in + + + align:start position:0% +to decide if I want to put my hand in +some particular place I have to figure + + align:start position:0% +some particular place I have to figure + + + align:start position:0% +some particular place I have to figure +out if I have a goal in the world + + align:start position:0% +out if I have a goal in the world + + + align:start position:0% +out if I have a goal in the world +coordinates I to figure out what the + + align:start position:0% +coordinates I to figure out what the + + + align:start position:0% +coordinates I to figure out what the +joint coordinates should be to make that + + align:start position:0% +joint coordinates should be to make that + + + align:start position:0% +joint coordinates should be to make that +happen okay so we have joint positions + + align:start position:0% +happen okay so we have joint positions + + + align:start position:0% +happen okay so we have joint positions +in some vector q and we just say I'd + + align:start position:0% +in some vector q and we just say I'd + + + align:start position:0% +in some vector q and we just say I'd +like to be as close as possible I have + + align:start position:0% +like to be as close as possible I have + + + align:start position:0% +like to be as close as possible I have +some comfortable position for my robot + + align:start position:0% +some comfortable position for my robot + + + align:start position:0% +some comfortable position for my robot +then we formulate the problem as an + + align:start position:0% +then we formulate the problem as an + + + align:start position:0% +then we formulate the problem as an +optimization say I'd like to be as close + + align:start position:0% +optimization say I'd like to be as close + + + align:start position:0% +optimization say I'd like to be as close +to comfortable as possible and some in + + align:start position:0% +to comfortable as possible and some in + + + align:start position:0% +to comfortable as possible and some in +some simple cost function and then I'm + + align:start position:0% +some simple cost function and then I'm + + + align:start position:0% +some simple cost function and then I'm +gonna start putting in constraints like + + align:start position:0% +gonna start putting in constraints like + + + align:start position:0% +gonna start putting in constraints like +my hand is in the desired configuration + + align:start position:0% +my hand is in the desired configuration + + + align:start position:0% +my hand is in the desired configuration +but we have very advanced constraints so + + align:start position:0% +but we have very advanced constraints so + + + align:start position:0% +but we have very advanced constraints so +so especially for the balancing humanoid + + align:start position:0% +so especially for the balancing humanoid + + + align:start position:0% +so especially for the balancing humanoid +we can say for instance that the center + + align:start position:0% +we can say for instance that the center + + + align:start position:0% +we can say for instance that the center +mass has to be inside the support + + align:start position:0% +mass has to be inside the support + + + align:start position:0% +mass has to be inside the support +polygon we can say we're about to + + align:start position:0% +polygon we can say we're about to + + + align:start position:0% +polygon we can say we're about to +manipulate something so I'd like the + + align:start position:0% +manipulate something so I'd like the + + + align:start position:0% +manipulate something so I'd like the +thing I'm going to manipulate to be in + + align:start position:0% +thing I'm going to manipulate to be in + + + align:start position:0% +thing I'm going to manipulate to be in +the cone of visibility of my sensors of + + align:start position:0% +the cone of visibility of my sensors of + + + align:start position:0% +the cone of visibility of my sensors of +my vision sensors I'd like my hand to + + align:start position:0% +my vision sensors I'd like my hand to + + + align:start position:0% +my vision sensors I'd like my hand to +approach it doesn't matter where it + + align:start position:0% +approach it doesn't matter where it + + + align:start position:0% +approach it doesn't matter where it +approaches along the table maybe but it + + align:start position:0% +approaches along the table maybe but it + + + align:start position:0% +approaches along the table maybe but it +should be might the palm should be + + align:start position:0% +should be might the palm should be + + + align:start position:0% +should be might the palm should be +orthogonal to the table and should + + align:start position:0% +orthogonal to the table and should + + + align:start position:0% +orthogonal to the table and should +approach you know like this and we can + + align:start position:0% +approach you know like this and we can + + + align:start position:0% +approach you know like this and we can +we put in a you know sort of more and + + align:start position:0% +we put in a you know sort of more and + + + align:start position:0% +we put in a you know sort of more and +more sophisticated collision avoidance + + align:start position:0% +more sophisticated collision avoidance + + + align:start position:0% +more sophisticated collision avoidance +type constraints and everything like + + align:start position:0% +type constraints and everything like + + + align:start position:0% +type constraints and everything like +this and the optimization framework is + + align:start position:0% +this and the optimization framework is + + + align:start position:0% +this and the optimization framework is +general and it can and it can accept + + align:start position:0% +general and it can and it can accept + + + align:start position:0% +general and it can and it can accept +those type of constraints and then we + + align:start position:0% +those type of constraints and then we + + + align:start position:0% +those type of constraints and then we +can solve them extremely efficiently + + align:start position:0% +can solve them extremely efficiently + + + align:start position:0% +can solve them extremely efficiently +with with highly optimized algorithms so + + align:start position:0% +with with highly optimized algorithms so + + + align:start position:0% +with with highly optimized algorithms so +for instance that helped us with what I + + align:start position:0% +for instance that helped us with what I + + + align:start position:0% +for instance that helped us with what I +like to call the big robot little car + + align:start position:0% +like to call the big robot little car + + + align:start position:0% +like to call the big robot little car +problem so we have a very big robot it's + + align:start position:0% +problem so we have a very big robot it's + + + align:start position:0% +problem so we have a very big robot it's +a 400-pound six-foot-something + + align:start position:0% +a 400-pound six-foot-something + + + align:start position:0% +a 400-pound six-foot-something +machine and they asked us to drive a + + align:start position:0% +machine and they asked us to drive a + + + align:start position:0% +machine and they asked us to drive a +very little car okay so to the point + + align:start position:0% +very little car okay so to the point + + + align:start position:0% +very little car okay so to the point +where the robot physically does not fit + + align:start position:0% +where the robot physically does not fit + + + align:start position:0% +where the robot physically does not fit +behind the steering wheel impossible it + + align:start position:0% +behind the steering wheel impossible it + + + align:start position:0% +behind the steering wheel impossible it +just doesn't fit kinematically torsos + + align:start position:0% +just doesn't fit kinematically torsos + + + align:start position:0% +just doesn't fit kinematically torsos +too big steering wheels right there no + + align:start position:0% +too big steering wheels right there no + + + align:start position:0% +too big steering wheels right there no +chance so you have to drive from the + + align:start position:0% +chance so you have to drive from the + + + align:start position:0% +chance so you have to drive from the +passenger seat you have to put your foot + + align:start position:0% +passenger seat you have to put your foot + + + align:start position:0% +passenger seat you have to put your foot +over the console you have to drive like + + align:start position:0% +over the console you have to drive like + + + align:start position:0% +over the console you have to drive like +this and then our only option was to get + + align:start position:0% +this and then our only option was to get + + + align:start position:0% +this and then our only option was to get +out of the passenger side okay so that + + align:start position:0% +out of the passenger side okay so that + + + align:start position:0% +out of the passenger side okay so that +was you know a hard problem + + align:start position:0% +was you know a hard problem + + + align:start position:0% +was you know a hard problem +kinematically but we have this rich + + align:start position:0% +kinematically but we have this rich + + + align:start position:0% +kinematically but we have this rich +library of optimizations we can drag it + + align:start position:0% +library of optimizations we can drag it + + + align:start position:0% +library of optimizations we can drag it +around we can explore different + + align:start position:0% +around we can explore different + + + align:start position:0% +around we can explore different +kinematic configurations of the robot + + align:start position:0% +kinematic configurations of the robot + + + align:start position:0% +kinematic configurations of the robot +but we also use the same language of + + align:start position:0% +but we also use the same language of + + + align:start position:0% +but we also use the same language of +optimization and constraints and then we + + align:start position:0% +optimization and constraints and then we + + + align:start position:0% +optimization and constraints and then we +put in the dynamics of the robot is + + align:start position:0% +put in the dynamics of the robot is + + + align:start position:0% +put in the dynamics of the robot is +another constraint and we can start + + align:start position:0% +another constraint and we can start + + + align:start position:0% +another constraint and we can start +doing efficient dynamic motion planning + + align:start position:0% +doing efficient dynamic motion planning + + + align:start position:0% +doing efficient dynamic motion planning +with the same tools so for instance if + + align:start position:0% +with the same tools so for instance if + + + align:start position:0% +with the same tools so for instance if +we wanted Atlas to suddenly start + + align:start position:0% +we wanted Atlas to suddenly start + + + align:start position:0% +we wanted Atlas to suddenly start +jumping off cinder blocks or or or + + align:start position:0% +jumping off cinder blocks or or or + + + align:start position:0% +jumping off cinder blocks or or or +running we did a lot of work in the + + align:start position:0% +running we did a lot of work in the + + + align:start position:0% +running we did a lot of work in the +regarde to make our optimization + + align:start position:0% +regarde to make our optimization + + + align:start position:0% +regarde to make our optimization +algorithms efficient enough to scale to + + align:start position:0% +algorithms efficient enough to scale to + + + align:start position:0% +algorithms efficient enough to scale to +very complex motions that could be + + align:start position:0% +very complex motions that could be + + + align:start position:0% +very complex motions that could be +planned on the fly at interactive rates + + align:start position:0% +planned on the fly at interactive rates + + + align:start position:0% +planned on the fly at interactive rates +so one of the things you might might be + + align:start position:0% +so one of the things you might might be + + + align:start position:0% +so one of the things you might might be +familiar with is sort of a Honda azzam + + align:start position:0% +familiar with is sort of a Honda azzam + + + align:start position:0% +familiar with is sort of a Honda azzam +oh no the famous robots that walks + + align:start position:0% +oh no the famous robots that walks + + + align:start position:0% +oh no the famous robots that walks +around like this and it does it's it's a + + align:start position:0% +around like this and it does it's it's a + + + align:start position:0% +around like this and it does it's it's a +beautiful machine they are extremely + + align:start position:0% +beautiful machine they are extremely + + + align:start position:0% +beautiful machine they are extremely +good at real-time planning using + + align:start position:0% +good at real-time planning using + + + align:start position:0% +good at real-time planning using +limiting assumptions of keeping your + + align:start position:0% +limiting assumptions of keeping your + + + align:start position:0% +limiting assumptions of keeping your +center of mass at a constant height and + + align:start position:0% +center of mass at a constant height and + + + align:start position:0% +center of mass at a constant height and +things like this and one of the + + align:start position:0% +things like this and one of the + + + align:start position:0% +things like this and one of the +questions we asked is could we take some + + align:start position:0% +questions we asked is could we take some + + + align:start position:0% +questions we asked is could we take some +of the insights that have worked so well + + align:start position:0% +of the insights that have worked so well + + + align:start position:0% +of the insights that have worked so well +on those robots and generalize them to + + align:start position:0% +on those robots and generalize them to + + + align:start position:0% +on those robots and generalize them to +more general dynamic tasks and one of + + align:start position:0% +more general dynamic tasks and one of + + + align:start position:0% +more general dynamic tasks and one of +the big ideas I want to try to + + align:start position:0% +the big ideas I want to try to + + + align:start position:0% +the big ideas I want to try to +communicate quickly is that even though + + align:start position:0% +communicate quickly is that even though + + + align:start position:0% +communicate quickly is that even though +our robot is extremely complicated + + align:start position:0% +our robot is extremely complicated + + + align:start position:0% +our robot is extremely complicated +there's sort of a low dimensional + + align:start position:0% +there's sort of a low dimensional + + + align:start position:0% +there's sort of a low dimensional +problem sitting inside the big high + + align:start position:0% +problem sitting inside the big high + + + align:start position:0% +problem sitting inside the big high +dimensional problem right so I start + + align:start position:0% +dimensional problem right so I start + + + align:start position:0% +dimensional problem right so I start +worrying about every joint angle in my + + align:start position:0% +worrying about every joint angle in my + + + align:start position:0% +worrying about every joint angle in my +hand while I'm thinking about walking + + align:start position:0% +hand while I'm thinking about walking + + + align:start position:0% +hand while I'm thinking about walking +I'm dead right so but actually when + + align:start position:0% +I'm dead right so but actually when + + + align:start position:0% +I'm dead right so but actually when +you're thinking about walking even doing + + align:start position:0% +you're thinking about walking even doing + + + align:start position:0% +you're thinking about walking even doing +gymnastics or something like this I + + align:start position:0% +gymnastics or something like this I + + + align:start position:0% +gymnastics or something like this I +think the fundamental representation is + + align:start position:0% +think the fundamental representation is + + + align:start position:0% +think the fundamental representation is +the dynamics of your center of mass your + + align:start position:0% +the dynamics of your center of mass your + + + align:start position:0% +the dynamics of your center of mass your +angular momentum sort of some bulk + + align:start position:0% +angular momentum sort of some bulk + + + align:start position:0% +angular momentum sort of some bulk +dynamics of your robot and the contact + + align:start position:0% +dynamics of your robot and the contact + + + align:start position:0% +dynamics of your robot and the contact +forces you're exerting on the world + + align:start position:0% +forces you're exerting on the world + + + align:start position:0% +forces you're exerting on the world +which are also constrained and in this + + align:start position:0% +which are also constrained and in this + + + align:start position:0% +which are also constrained and in this +sort of six dimensional twelve + + align:start position:0% +sort of six dimensional twelve + + + align:start position:0% +sort of six dimensional twelve +dimensional uh if you'd have velocities + + align:start position:0% +dimensional uh if you'd have velocities + + + align:start position:0% +dimensional uh if you'd have velocities +space with with these relatively limited + + align:start position:0% +space with with these relatively limited + + + align:start position:0% +space with with these relatively limited +constraints you can actually do very + + align:start position:0% +constraints you can actually do very + + + align:start position:0% +constraints you can actually do very +efficient planning and then map that in + + align:start position:0% +efficient planning and then map that in + + + align:start position:0% +efficient planning and then map that in +a second pass back to the full you know + + align:start position:0% +a second pass back to the full you know + + + align:start position:0% +a second pass back to the full you know +figure out what my pinky's gonna do okay + + align:start position:0% +figure out what my pinky's gonna do okay + + + align:start position:0% +figure out what my pinky's gonna do okay +so we do that we spend a lot of time + + align:start position:0% +so we do that we spend a lot of time + + + align:start position:0% +so we do that we spend a lot of time +doing that and we can now plan + + align:start position:0% +doing that and we can now plan + + + align:start position:0% +doing that and we can now plan +motions for complicated humanoids that + + align:start position:0% +motions for complicated humanoids that + + + align:start position:0% +motions for complicated humanoids that +were far beyond our ability to do it a + + align:start position:0% +were far beyond our ability to do it a + + + align:start position:0% +were far beyond our ability to do it a +few years ago this was a major effort + + align:start position:0% +few years ago this was a major effort + + + align:start position:0% +few years ago this was a major effort +for us my kids and I were watching + + align:start position:0% +for us my kids and I were watching + + + align:start position:0% +for us my kids and I were watching +American Ninja Warrior at the time so we + + align:start position:0% +American Ninja Warrior at the time so we + + + align:start position:0% +American Ninja Warrior at the time so we +we did all these other Ninja Warrior + + align:start position:0% +we did all these other Ninja Warrior + + + align:start position:0% +we did all these other Ninja Warrior +tasks so you know that was that was + + align:start position:0% +tasks so you know that was that was + + + align:start position:0% +tasks so you know that was that was +there was some algorithmic ideas that + + align:start position:0% +there was some algorithmic ideas that + + + align:start position:0% +there was some algorithmic ideas that +were required for that it was also just + + align:start position:0% +were required for that it was also just + + + align:start position:0% +were required for that it was also just +a software engineering exercise to build + + align:start position:0% +a software engineering exercise to build + + + align:start position:0% +a software engineering exercise to build +a dynamics engine that was that provided + + align:start position:0% +a dynamics engine that was that provided + + + align:start position:0% +a dynamics engine that was that provided +analytical gradients exposed all the + + align:start position:0% +analytical gradients exposed all the + + + align:start position:0% +analytical gradients exposed all the +sparsity and the problem and and wrote + + align:start position:0% +sparsity and the problem and and wrote + + + align:start position:0% +sparsity and the problem and and wrote +custom solvers and things like that to + + align:start position:0% +custom solvers and things like that to + + + align:start position:0% +custom solvers and things like that to +make that work it's not just about + + align:start position:0% +make that work it's not just about + + + align:start position:0% +make that work it's not just about +humanoids we spent you know a day after + + align:start position:0% +humanoids we spent you know a day after + + + align:start position:0% +humanoids we spent you know a day after +we got as I'm was doing those those + + align:start position:0% +we got as I'm was doing those those + + + align:start position:0% +we got as I'm was doing those those +things to show that we could make a + + align:start position:0% +things to show that we could make a + + + align:start position:0% +things to show that we could make a +quadruped ed + + align:start position:0% +quadruped ed + + + align:start position:0% +quadruped ed +run around using the same exact + + align:start position:0% +run around using the same exact + + + align:start position:0% +run around using the same exact +algorithms it took literally less than a + + align:start position:0% +algorithms it took literally less than a + + + align:start position:0% +algorithms it took literally less than a +data to make all these examples work um + + align:start position:0% +data to make all these examples work um + + + align:start position:0% +data to make all these examples work um +there's another level of optimization + + align:start position:0% +there's another level of optimization + + + align:start position:0% +there's another level of optimization +that's plot that's goin kicking around + + align:start position:0% +that's plot that's goin kicking around + + + align:start position:0% +that's plot that's goin kicking around +in here so the humanoid in some sense + + align:start position:0% +in here so the humanoid in some sense + + + align:start position:0% +in here so the humanoid in some sense +when it's moving around is a fairly + + align:start position:0% +when it's moving around is a fairly + + + align:start position:0% +when it's moving around is a fairly +continuous dynamical system + + align:start position:0% +continuous dynamical system + + + align:start position:0% +continuous dynamical system +there's punctuation that when your foot + + align:start position:0% +there's punctuation that when your foot + + + align:start position:0% +there's punctuation that when your foot +hits the ground or something like this + + align:start position:0% +hits the ground or something like this + + + align:start position:0% +hits the ground or something like this +so you think of that as sort of a smooth + + align:start position:0% +so you think of that as sort of a smooth + + + align:start position:0% +so you think of that as sort of a smooth +optimization problem there's also a + + align:start position:0% +optimization problem there's also a + + + align:start position:0% +optimization problem there's also a +discrete optimization problem sitting in + + align:start position:0% +discrete optimization problem sitting in + + + align:start position:0% +discrete optimization problem sitting in +there too even for walking so if you + + align:start position:0% +there too even for walking so if you + + + align:start position:0% +there too even for walking so if you +think about it you know the methods I + + align:start position:0% +think about it you know the methods I + + + align:start position:0% +think about it you know the methods I +just talked about we're really talking + + align:start position:0% +just talked about we're really talking + + + align:start position:0% +just talked about we're really talking +about you know okay I moved like this I + + align:start position:0% +about you know okay I moved like this I + + + align:start position:0% +about you know okay I moved like this I +want to prefer I would prefer to move + + align:start position:0% +want to prefer I would prefer to move + + + align:start position:0% +want to prefer I would prefer to move +something like this but there's a + + align:start position:0% +something like this but there's a + + + align:start position:0% +something like this but there's a +continuum of solutions I could possibly + + align:start position:0% +continuum of solutions I could possibly + + + align:start position:0% +continuum of solutions I could possibly +take for walking there's also this + + align:start position:0% +take for walking there's also this + + + align:start position:0% +take for walking there's also this +problem of just saying you know am I + + align:start position:0% +problem of just saying you know am I + + + align:start position:0% +problem of just saying you know am I +going to move my right foot first or my + + align:start position:0% +going to move my right foot first or my + + + align:start position:0% +going to move my right foot first or my +left foot first + + align:start position:0% +left foot first + + + align:start position:0% +left foot first +am I gonna step on cinder block one or + + align:start position:0% +am I gonna step on cinder block one or + + + align:start position:0% +am I gonna step on cinder block one or +cinder block two right there's that + + align:start position:0% +cinder block two right there's that + + + align:start position:0% +cinder block two right there's that +there really is a discrete problem which + + align:start position:0% +there really is a discrete problem which + + + align:start position:0% +there really is a discrete problem which +gives a combinatorial problem if you + + align:start position:0% +gives a combinatorial problem if you + + + align:start position:0% +gives a combinatorial problem if you +have to make long-term decisions on that + + align:start position:0% +have to make long-term decisions on that + + + align:start position:0% +have to make long-term decisions on that +and one of the things we've tried to do + + align:start position:0% +and one of the things we've tried to do + + + align:start position:0% +and one of the things we've tried to do +well is is be very explicit about + + align:start position:0% +well is is be very explicit about + + + align:start position:0% +well is is be very explicit about +modeling the discrete aspects and the + + align:start position:0% +modeling the discrete aspects and the + + + align:start position:0% +modeling the discrete aspects and the +continuous aspects of that problem + + align:start position:0% +continuous aspects of that problem + + + align:start position:0% +continuous aspects of that problem +individually and and using the solvers + + align:start position:0% +individually and and using the solvers + + + align:start position:0% +individually and and using the solvers +the right solvers that could think about + + align:start position:0% +the right solvers that could think about + + + align:start position:0% +the right solvers that could think about +both of those together so here's an + + align:start position:0% +both of those together so here's an + + + align:start position:0% +both of those together so here's an +example of how we do interactive + + align:start position:0% +example of how we do interactive + + + align:start position:0% +example of how we do interactive +footstep planning with the robot if it's + + align:start position:0% +footstep planning with the robot if it's + + + align:start position:0% +footstep planning with the robot if it's +standing in front of so some perceived + + align:start position:0% +standing in front of so some perceived + + + align:start position:0% +standing in front of so some perceived +cinder blocks for instance the human can + + align:start position:0% +cinder blocks for instance the human can + + + align:start position:0% +cinder blocks for instance the human can +quickly label discrete regions just by + + align:start position:0% +quickly label discrete regions just by + + + align:start position:0% +quickly label discrete regions just by +moving a mouse around the regions that + + align:start position:0% +moving a mouse around the regions that + + + align:start position:0% +moving a mouse around the regions that +come out are actually fit by an + + align:start position:0% +come out are actually fit by an + + + align:start position:0% +come out are actually fit by an +algorithm they're deciding there's they + + align:start position:0% +algorithm they're deciding there's they + + + align:start position:0% +algorithm they're deciding there's they +look small because they're trying to + + align:start position:0% +look small because they're trying to + + + align:start position:0% +look small because they're trying to +figure out where if the center of the + + align:start position:0% +figure out where if the center of the + + + align:start position:0% +figure out where if the center of the +foot was inside that region the whole + + align:start position:0% +foot was inside that region the whole + + + align:start position:0% +foot was inside that region the whole +foot would fit on the right on that okay + + align:start position:0% +foot would fit on the right on that okay + + + align:start position:0% +foot would fit on the right on that okay +and they're also think about balance + + align:start position:0% +and they're also think about balance + + + align:start position:0% +and they're also think about balance +constraints and other things like that + + align:start position:0% +constraints and other things like that + + + align:start position:0% +constraints and other things like that +but that we have discrete regions to + + align:start position:0% +but that we have discrete regions to + + + align:start position:0% +but that we have discrete regions to +possibly step in we have a combinatorial + + align:start position:0% +possibly step in we have a combinatorial + + + align:start position:0% +possibly step in we have a combinatorial +problem and the smooth problem of moving + + align:start position:0% +problem and the smooth problem of moving + + + align:start position:0% +problem and the smooth problem of moving +my center of mass and the like and we + + align:start position:0% +my center of mass and the like and we + + + align:start position:0% +my center of mass and the like and we +have very good news solvers to do that + + align:start position:0% +have very good news solvers to do that + + + align:start position:0% +have very good news solvers to do that +and you know seated inside that hour I + + align:start position:0% +and you know seated inside that hour I + + + align:start position:0% +and you know seated inside that hour I +just want to sort of communicate that + + align:start position:0% +just want to sort of communicate that + + + align:start position:0% +just want to sort of communicate that +there's all these little technical + + align:start position:0% +there's all these little technical + + + align:start position:0% +there's all these little technical +nuggets of we had to find a new way to + + align:start position:0% +nuggets of we had to find a new way to + + + align:start position:0% +nuggets of we had to find a new way to +make really fast approximations of big + + align:start position:0% +make really fast approximations of big + + + align:start position:0% +make really fast approximations of big +convex regions of free space so you know + + align:start position:0% +convex regions of free space so you know + + + align:start position:0% +convex regions of free space so you know +we have optimizations that just figured + + align:start position:0% +we have optimizations that just figured + + + align:start position:0% +we have optimizations that just figured +out the the problem of finding the + + align:start position:0% +out the the problem of finding the + + + align:start position:0% +out the the problem of finding the +biggest polygon that fits inside all + + align:start position:0% +biggest polygon that fits inside all + + + align:start position:0% +biggest polygon that fits inside all +those obstacles is np-hard we're not + + align:start position:0% +those obstacles is np-hard we're not + + + align:start position:0% +those obstacles is np-hard we're not +going to solve that but it turns out + + align:start position:0% +going to solve that but it turns out + + + align:start position:0% +going to solve that but it turns out +finding a pretty good polygon can be + + align:start position:0% +finding a pretty good polygon can be + + + align:start position:0% +finding a pretty good polygon can be +done extremely fast now and + + align:start position:0% +done extremely fast now and + + + align:start position:0% +done extremely fast now and +particular way we did it scales to very + + align:start position:0% +particular way we did it scales to very + + + align:start position:0% +particular way we did it scales to very +high dimensions and complicated + + align:start position:0% +high dimensions and complicated + + + align:start position:0% +high dimensions and complicated +obstacles to the point where we could do + + align:start position:0% +obstacles to the point where we could do + + + align:start position:0% +obstacles to the point where we could do +it on raw sensor data and that was that + + align:start position:0% +it on raw sensor data and that was that + + + align:start position:0% +it on raw sensor data and that was that +was an enabling technology for us so our + + align:start position:0% +was an enabling technology for us so our + + + align:start position:0% +was an enabling technology for us so our +robot now when it's making plans so the + + align:start position:0% +robot now when it's making plans so the + + + align:start position:0% +robot now when it's making plans so the +one on the left is just walking towards + + align:start position:0% +one on the left is just walking towards + + + align:start position:0% +one on the left is just walking towards +the gold okay the one on the right we + + align:start position:0% +the gold okay the one on the right we + + + align:start position:0% +the gold okay the one on the right we +removed a cinder block and normally a + + align:start position:0% +removed a cinder block and normally a + + + align:start position:0% +removed a cinder block and normally a +robot would kind of get confused and + + align:start position:0% +robot would kind of get confused and + + + align:start position:0% +robot would kind of get confused and +stuff because it's just thinking about + + align:start position:0% +stuff because it's just thinking about + + + align:start position:0% +stuff because it's just thinking about +this local plan local plan local plan + + align:start position:0% +this local plan local plan local plan + + + align:start position:0% +this local plan local plan local plan +that's it you know it wouldn't be able + + align:start position:0% +that's it you know it wouldn't be able + + + align:start position:0% +that's it you know it wouldn't be able +to stop and go completely the other + + align:start position:0% +to stop and go completely the other + + + align:start position:0% +to stop and go completely the other +direction but now since we have this + + align:start position:0% +direction but now since we have this + + + align:start position:0% +direction but now since we have this +higher-level combinatorial planning on + + align:start position:0% +higher-level combinatorial planning on + + + align:start position:0% +higher-level combinatorial planning on +top we can we can make these big + + align:start position:0% +top we can we can make these big + + + align:start position:0% +top we can we can make these big +long-term decision-making tasks and at + + align:start position:0% +long-term decision-making tasks and at + + + align:start position:0% +long-term decision-making tasks and at +interactive rates so we we also the + + align:start position:0% +interactive rates so we we also the + + + align:start position:0% +interactive rates so we we also the +robot was too big to walk through a door + + align:start position:0% +robot was too big to walk through a door + + + align:start position:0% +robot was too big to walk through a door +so we had to walk sideways through a + + align:start position:0% +so we had to walk sideways through a + + + align:start position:0% +so we had to walk sideways through a +door and that was sort of a standing + + align:start position:0% +door and that was sort of a standing + + + align:start position:0% +door and that was sort of a standing +challenge for the guy who started the + + align:start position:0% +challenge for the guy who started the + + + align:start position:0% +challenge for the guy who started the +the program putting footsteps down by + + align:start position:0% +the program putting footsteps down by + + + align:start position:0% +the program putting footsteps down by +hand said whatever I do in footstep + + align:start position:0% +hand said whatever I do in footstep + + + align:start position:0% +hand said whatever I do in footstep +planning it will I will never lay down + + align:start position:0% +planning it will I will never lay down + + + align:start position:0% +planning it will I will never lay down +foot steps to walk through a door again + + align:start position:0% +foot steps to walk through a door again + + + align:start position:0% +foot steps to walk through a door again +that was this challenge we did a lot of + + align:start position:0% +that was this challenge we did a lot of + + + align:start position:0% +that was this challenge we did a lot of +work on the balancing control for the + + align:start position:0% +work on the balancing control for the + + + align:start position:0% +work on the balancing control for the +robot so it's a force controlled robot + + align:start position:0% +robot so it's a force controlled robot + + + align:start position:0% +robot so it's a force controlled robot +using hydraulic actuators everywhere I + + align:start position:0% +using hydraulic actuators everywhere I + + + align:start position:0% +using hydraulic actuators everywhere I +will again I will go to the details but + + align:start position:0% +will again I will go to the details but + + + align:start position:0% +will again I will go to the details but +we thought a lot about the dynamics of + + align:start position:0% +we thought a lot about the dynamics of + + + align:start position:0% +we thought a lot about the dynamics of +the robot how do you cast that as an + + align:start position:0% +the robot how do you cast that as an + + + align:start position:0% +the robot how do you cast that as an +efficient optimization that we can solve + + align:start position:0% +efficient optimization that we can solve + + + align:start position:0% +efficient optimization that we can solve +on the fly okay and we were solving an + + align:start position:0% +on the fly okay and we were solving an + + + align:start position:0% +on the fly okay and we were solving an +optimization at a kilohertz + + align:start position:0% +optimization at a kilohertz + + + align:start position:0% +optimization at a kilohertz +to balance the robot okay so you put it + + align:start position:0% +to balance the robot okay so you put it + + + align:start position:0% +to balance the robot okay so you put it +all together and as a as a basic + + align:start position:0% +all together and as a as a basic + + + align:start position:0% +all together and as a as a basic +competency you know how well does our + + align:start position:0% +competency you know how well does our + + + align:start position:0% +competency you know how well does our +robot walk around and balance here's + + align:start position:0% +robot walk around and balance here's + + + align:start position:0% +robot walk around and balance here's +sort of a one of the examples at a + + align:start position:0% +sort of a one of the examples at a + + + align:start position:0% +sort of a one of the examples at a +normal speed from the from the challenge + + align:start position:0% +normal speed from the from the challenge + + + align:start position:0% +normal speed from the from the challenge +so the robot just puts its foot steps + + align:start position:0% +so the robot just puts its foot steps + + + align:start position:0% +so the robot just puts its foot steps +down ahead the operator is mostly just + + align:start position:0% +down ahead the operator is mostly just + + + align:start position:0% +down ahead the operator is mostly just +watching giving high-level directions I + + align:start position:0% +watching giving high-level directions I + + + align:start position:0% +watching giving high-level directions I +want to go over here the robots doing + + align:start position:0% +want to go over here the robots doing + + + align:start position:0% +want to go over here the robots doing +its own thing + + align:start position:0% + + + + align:start position:0% + +now all the other teams I know about + + align:start position:0% +now all the other teams I know about + + + align:start position:0% +now all the other teams I know about +we're putting down the foot steps by + + align:start position:0% +we're putting down the foot steps by + + + align:start position:0% +we're putting down the foot steps by +hand on the on the obstacles I don't + + align:start position:0% +hand on the on the obstacles I don't + + + align:start position:0% +hand on the on the obstacles I don't +know if someone else was doing it + + align:start position:0% +know if someone else was doing it + + + align:start position:0% +know if someone else was doing it +autonomously we you know we chose to do + + align:start position:0% +autonomously we you know we chose to do + + + align:start position:0% +autonomously we you know we chose to do +it autonomously we were a little bit + + align:start position:0% +it autonomously we were a little bit + + + align:start position:0% +it autonomously we were a little bit +faster because of it but I don't know if + + align:start position:0% +faster because of it but I don't know if + + + align:start position:0% +faster because of it but I don't know if +it was enabling but very proud of our of + + align:start position:0% +it was enabling but very proud of our of + + + align:start position:0% +it was enabling but very proud of our of +our walking even though it's still + + align:start position:0% +our walking even though it's still + + + align:start position:0% +our walking even though it's still +conservative mean this is lousy compared + + align:start position:0% +conservative mean this is lousy compared + + + align:start position:0% +conservative mean this is lousy compared +to a human yeah so so we knew they were + + align:start position:0% +to a human yeah so so we knew they were + + + align:start position:0% +to a human yeah so so we knew they were +going to be cinder blocks we didn't know + + align:start position:0% +going to be cinder blocks we didn't know + + + align:start position:0% +going to be cinder blocks we didn't know +the orientation or positions are them so + + align:start position:0% +the orientation or positions are them so + + + align:start position:0% +the orientation or positions are them so +we had a cinder block fitting algorithm + + align:start position:0% +we had a cinder block fitting algorithm + + + align:start position:0% +we had a cinder block fitting algorithm +that would run on the fly snap things + + align:start position:0% +that would run on the fly snap things + + + align:start position:0% +that would run on the fly snap things +into place with the cameras yeah yeah + + align:start position:0% +into place with the cameras yeah yeah + + + align:start position:0% +into place with the cameras yeah yeah +actually laser scanner and then we walk + + align:start position:0% +actually laser scanner and then we walk + + + align:start position:0% +actually laser scanner and then we walk +up stairs you know little things if you + + align:start position:0% +up stairs you know little things if you + + + align:start position:0% +up stairs you know little things if you +care about walking you know the heels + + align:start position:0% +care about walking you know the heels + + + align:start position:0% +care about walking you know the heels +are hanging off the back you know + + align:start position:0% +are hanging off the back you know + + + align:start position:0% +are hanging off the back you know +they're you know there's special + + align:start position:0% +they're you know there's special + + + align:start position:0% +they're you know there's special +algorithms and they're sort of to the + + align:start position:0% +algorithms and they're sort of to the + + + align:start position:0% +algorithms and they're sort of to the +balance on partial foot contact and + + align:start position:0% +balance on partial foot contact and + + + align:start position:0% +balance on partial foot contact and +things like that and that made the + + align:start position:0% +things like that and that made the + + + align:start position:0% +things like that and that made the +difference we could go up there and + + align:start position:0% +difference we could go up there and + + + align:start position:0% +difference we could go up there and +efficiently robustly so I would say + + align:start position:0% +efficiently robustly so I would say + + + align:start position:0% +efficiently robustly so I would say +though you know for for conservative + + align:start position:0% +though you know for for conservative + + + align:start position:0% +though you know for for conservative +walking we it really works well they + + align:start position:0% +walking we it really works well they + + + align:start position:0% +walking we it really works well they +don't we could we could plan these + + align:start position:0% +don't we could we could plan these + + + align:start position:0% +don't we could we could plan these +things on the fly and we also had this + + align:start position:0% +things on the fly and we also had this + + + align:start position:0% +things on the fly and we also had this +user interface that if the footstep + + align:start position:0% +user interface that if the footstep + + + align:start position:0% +user interface that if the footstep +planner ever did something stupid the + + align:start position:0% +planner ever did something stupid the + + + align:start position:0% +planner ever did something stupid the +human could chris drag a foot around add + + align:start position:0% +human could chris drag a foot around add + + + align:start position:0% +human could chris drag a foot around add +a new constraint to the solver ii would + + align:start position:0% +a new constraint to the solver ii would + + + align:start position:0% +a new constraint to the solver ii would +continue to solve with a new constraint + + align:start position:0% +continue to solve with a new constraint + + + align:start position:0% +continue to solve with a new constraint +and adjust its solutions we could do + + align:start position:0% +and adjust its solutions we could do + + + align:start position:0% +and adjust its solutions we could do +more dynamic plans we could have it run + + align:start position:0% +more dynamic plans we could have it run + + + align:start position:0% +more dynamic plans we could have it run +and everything like that we actually + + align:start position:0% +and everything like that we actually + + + align:start position:0% +and everything like that we actually +never tried this on the robot before the + + align:start position:0% +never tried this on the robot before the + + + align:start position:0% +never tried this on the robot before the +competition because we were terrified of + + align:start position:0% +competition because we were terrified of + + + align:start position:0% +competition because we were terrified of +breaking the robot and we didn't have + + align:start position:0% +breaking the robot and we didn't have + + + align:start position:0% +breaking the robot and we didn't have +couldn't accept the down time but now + + align:start position:0% +couldn't accept the down time but now + + + align:start position:0% +couldn't accept the down time but now +that the competition is over this is + + align:start position:0% +that the competition is over this is + + + align:start position:0% +that the competition is over this is +exactly what we're trying but the you + + align:start position:0% +exactly what we're trying but the you + + + align:start position:0% +exactly what we're trying but the you +know the optimizations are slower and + + align:start position:0% +know the optimizations are slower and + + + align:start position:0% +know the optimizations are slower and +didn't always succeed so so in the real + + align:start position:0% +didn't always succeed so so in the real + + + align:start position:0% +didn't always succeed so so in the real +scenario we were using our we were + + align:start position:0% +scenario we were using our we were + + + align:start position:0% +scenario we were using our we were +putting some more constraints on and + + align:start position:0% +putting some more constraints on and + + + align:start position:0% +putting some more constraints on and +doing much more conservative gates the + + align:start position:0% +doing much more conservative gates the + + + align:start position:0% +doing much more conservative gates the +balance control I'd say worked extremely + + align:start position:0% +balance control I'd say worked extremely + + + align:start position:0% +balance control I'd say worked extremely +well you know so the hardest task was + + align:start position:0% +well you know so the hardest task was + + + align:start position:0% +well you know so the hardest task was +this getting out of the car tasks we + + align:start position:0% +this getting out of the car tasks we + + + align:start position:0% +this getting out of the car tasks we +worked like crazy we didn't work on it + + align:start position:0% +worked like crazy we didn't work on it + + + align:start position:0% +worked like crazy we didn't work on it +until the end I thought I thought DARPA + + align:start position:0% +until the end I thought I thought DARPA + + + align:start position:0% +until the end I thought I thought DARPA +was gonna scratch it honestly and then + + align:start position:0% +was gonna scratch it honestly and then + + + align:start position:0% +was gonna scratch it honestly and then +but in the last month it was B was + + align:start position:0% +but in the last month it was B was + + + align:start position:0% +but in the last month it was B was +became clear that we had to do it and + + align:start position:0% +became clear that we had to do it and + + + align:start position:0% +became clear that we had to do it and +then we spent a lot of effort on it and + + align:start position:0% +then we spent a lot of effort on it and + + + align:start position:0% +then we spent a lot of effort on it and +you know we put the car in every + + align:start position:0% +you know we put the car in every + + + align:start position:0% +you know we put the car in every +possible situation this was on cinder + + align:start position:0% +possible situation this was on cinder + + + align:start position:0% +possible situation this was on cinder +blocks it's way high you know it has to + + align:start position:0% +blocks it's way high you know it has to + + + align:start position:0% +blocks it's way high you know it has to +step down + + align:start position:0% +step down + + + align:start position:0% +step down +beyond its reach ability in the leg you + + align:start position:0% +beyond its reach ability in the leg you + + + align:start position:0% +beyond its reach ability in the leg you +know this thing was just super solid you + + align:start position:0% +know this thing was just super solid you + + + align:start position:0% +know this thing was just super solid you +know so Andres and Lucas were the main + + align:start position:0% +know so Andres and Lucas were the main + + + align:start position:0% +know so Andres and Lucas were the main +designers of this algorithm + + align:start position:0% +designers of this algorithm + + + align:start position:0% +designers of this algorithm +you see it's doing i'd say it's super + + align:start position:0% +you see it's doing i'd say it's super + + + align:start position:0% +you see it's doing i'd say it's super +human in this regard right now you know + + align:start position:0% +human in this regard right now you know + + + align:start position:0% +human in this regard right now you know +one on a human would not would not do + + align:start position:0% +one on a human would not would not do + + + align:start position:0% +one on a human would not would not do +that okay you know but standing on one + + align:start position:0% +that okay you know but standing on one + + + align:start position:0% +that okay you know but standing on one +foot while someone's jumping on the car + + align:start position:0% +foot while someone's jumping on the car + + + align:start position:0% +foot while someone's jumping on the car +like this you know it's it's it's really + + align:start position:0% +like this you know it's it's it's really + + + align:start position:0% +like this you know it's it's it's really +works well in fact the hardest part of + + align:start position:0% +works well in fact the hardest part of + + + align:start position:0% +works well in fact the hardest part of +that for the algorithm was the fact that + + align:start position:0% +that for the algorithm was the fact that + + + align:start position:0% +that for the algorithm was the fact that +the it's trying to find out where the + + align:start position:0% +the it's trying to find out where the + + + align:start position:0% +the it's trying to find out where the +ground is and the camera is going like + + align:start position:0% +ground is and the camera is going like + + + align:start position:0% +ground is and the camera is going like +this right so that was the reason that + + align:start position:0% +this right so that was the reason that + + + align:start position:0% +this right so that was the reason that +it has this long pause before it went + + align:start position:0% +it has this long pause before it went + + + align:start position:0% +it has this long pause before it went +down okay but there was one time that it + + align:start position:0% +down okay but there was one time that it + + + align:start position:0% +down okay but there was one time that it +didn't work well okay so and it's hard + + align:start position:0% +didn't work well okay so and it's hard + + + align:start position:0% +didn't work well okay so and it's hard +for me to watch this but you know it + + align:start position:0% +for me to watch this but you know it + + + align:start position:0% +for me to watch this but you know it +turns out on the front you saw that + + align:start position:0% +turns out on the front you saw that + + + align:start position:0% +turns out on the front you saw that +little dead kick okay + + align:start position:0% +little dead kick okay + + + align:start position:0% +little dead kick okay +this was horrible okay + + align:start position:0% +this was horrible okay + + + align:start position:0% +this was horrible okay +so exactly what happened but I think it + + align:start position:0% +so exactly what happened but I think it + + + align:start position:0% +so exactly what happened but I think it +really exposed the limitation of our of + + align:start position:0% +really exposed the limitation of our of + + + align:start position:0% +really exposed the limitation of our of +the tools the state of the art you know + + align:start position:0% +the tools the state of the art you know + + + align:start position:0% +the tools the state of the art you know +so what what happened in that particular + + align:start position:0% +so what what happened in that particular + + + align:start position:0% +so what what happened in that particular +situation was the robot was almost + + align:start position:0% +situation was the robot was almost + + + align:start position:0% +situation was the robot was almost +autonomous in some ways and we basically + + align:start position:0% +autonomous in some ways and we basically + + + align:start position:0% +autonomous in some ways and we basically +tried to have the human have to do + + align:start position:0% +tried to have the human have to do + + + align:start position:0% +tried to have the human have to do +almost nothing and in the end the we got + + align:start position:0% +almost nothing and in the end the we got + + + align:start position:0% +almost nothing and in the end the we got +that humans checklist down to about five + + align:start position:0% +that humans checklist down to about five + + + align:start position:0% +that humans checklist down to about five +items which was probably a mistake + + align:start position:0% +items which was probably a mistake + + + align:start position:0% +items which was probably a mistake +because we screwed up on the checklist + + align:start position:0% +because we screwed up on the checklist + + + align:start position:0% +because we screwed up on the checklist +so so one of the things I Tomas - we + + align:start position:0% +so so one of the things I Tomas - we + + + align:start position:0% +so so one of the things I Tomas - we +have one set of programs that are + + align:start position:0% +have one set of programs that are + + + align:start position:0% +have one set of programs that are +running when the robots driving the car + + align:start position:0% +running when the robots driving the car + + + align:start position:0% +running when the robots driving the car +and then all the human had to do was + + align:start position:0% +and then all the human had to do was + + + align:start position:0% +and then all the human had to do was +turn off the driving controller and turn + + align:start position:0% +turn off the driving controller and turn + + + align:start position:0% +turn off the driving controller and turn +on the balancing controller but who was + + align:start position:0% +on the balancing controller but who was + + + align:start position:0% +on the balancing controller but who was +exciting in the first day of the + + align:start position:0% +exciting in the first day of the + + + align:start position:0% +exciting in the first day of the +competition and then and we've turned on + + align:start position:0% +competition and then and we've turned on + + + align:start position:0% +competition and then and we've turned on +the balancing controller forgot to turn + + align:start position:0% +the balancing controller forgot to turn + + + align:start position:0% +the balancing controller forgot to turn +off the driving controller so the ankle + + align:start position:0% +off the driving controller so the ankle + + + align:start position:0% +off the driving controller so the ankle +was still trying to drive the car even + + align:start position:0% +was still trying to drive the car even + + + align:start position:0% +was still trying to drive the car even +that the controller was robust enough so + + align:start position:0% +that the controller was robust enough so + + + align:start position:0% +that the controller was robust enough so +you know I really think there's this + + align:start position:0% +you know I really think there's this + + + align:start position:0% +you know I really think there's this +fundamental thing that if we were if + + align:start position:0% +fundamental thing that if we were if + + + align:start position:0% +fundamental thing that if we were if +you're close to your nominal plan things + + align:start position:0% +you're close to your nominal plan things + + + align:start position:0% +you're close to your nominal plan things +are very robust but what happened is the + + align:start position:0% +are very robust but what happened is the + + + align:start position:0% +are very robust but what happened is the +ankle is still driving the car I think + + align:start position:0% +ankle is still driving the car I think + + + align:start position:0% +ankle is still driving the car I think +we could balance with the ankle doing + + align:start position:0% +we could balance with the ankle doing + + + align:start position:0% +we could balance with the ankle doing +the wrong thing except the ankle did the + + align:start position:0% +the wrong thing except the ankle did the + + + align:start position:0% +the wrong thing except the ankle did the +wrong thing just enough that the + + align:start position:0% +wrong thing just enough that the + + + align:start position:0% +wrong thing just enough that the +tailbone hit the seat of the car that + + align:start position:0% +tailbone hit the seat of the car that + + + align:start position:0% +tailbone hit the seat of the car that +was no longer something we could handle + + align:start position:0% +was no longer something we could handle + + + align:start position:0% +was no longer something we could handle +right so there was no contact sensor in + + align:start position:0% +right so there was no contact sensor in + + + align:start position:0% +right so there was no contact sensor in +the but that meant the dynamics model + + align:start position:0% +the but that meant the dynamics model + + + align:start position:0% +the but that meant the dynamics model +was very wrong the state estimator got + + align:start position:0% +was very wrong the state estimator got + + + align:start position:0% +was very wrong the state estimator got +very confused the foot came off the + + align:start position:0% +very confused the foot came off the + + + align:start position:0% +very confused the foot came off the +ground of the state estimator had an + + align:start position:0% +ground of the state estimator had an + + + align:start position:0% +ground of the state estimator had an +assumption that the feet should be on + + align:start position:0% +assumption that the feet should be on + + + align:start position:0% +assumption that the feet should be on +the + + align:start position:0% +the + + + align:start position:0% +the +that's how it knew where it was in the + + align:start position:0% +that's how it knew where it was in the + + + align:start position:0% +that's how it knew where it was in the +world and that basically the controller + + align:start position:0% +world and that basically the controller + + + align:start position:0% +world and that basically the controller +was hosed right and that was sort of the + + align:start position:0% +was hosed right and that was sort of the + + + align:start position:0% +was hosed right and that was sort of the +only time we could have done that badly + + align:start position:0% +only time we could have done that badly + + + align:start position:0% +only time we could have done that badly +and I think that the vibrations and + + align:start position:0% +and I think that the vibrations and + + + align:start position:0% +and I think that the vibrations and +everything I had emails from people of + + align:start position:0% +everything I had emails from people of + + + align:start position:0% +everything I had emails from people of +all walks of life telling me what they + + align:start position:0% +all walks of life telling me what they + + + align:start position:0% +all walks of life telling me what they +thought was wrong with the brain of the + + align:start position:0% +thought was wrong with the brain of the + + + align:start position:0% +thought was wrong with the brain of the +robot from shaking like that but that + + align:start position:0% +robot from shaking like that but that + + + align:start position:0% +robot from shaking like that but that +was that was a bad thing okay so you + + align:start position:0% +was that was a bad thing okay so you + + + align:start position:0% +was that was a bad thing okay so you +know I think fundamentally if we're + + align:start position:0% +know I think fundamentally if we're + + + align:start position:0% +know I think fundamentally if we're +thinking about plans and that's what we + + align:start position:0% +thinking about plans and that's what we + + + align:start position:0% +thinking about plans and that's what we +know how to do at scale for high + + align:start position:0% +know how to do at scale for high + + + align:start position:0% +know how to do at scale for high +dimensional systems as single solutions + + align:start position:0% +dimensional systems as single solutions + + + align:start position:0% +dimensional systems as single solutions +then we're close to the plan things are + + align:start position:0% +then we're close to the plan things are + + + align:start position:0% +then we're close to the plan things are +good when we're far from the plan we're + + align:start position:0% +good when we're far from the plan we're + + + align:start position:0% +good when we're far from the plan we're +not very good and a change in the + + align:start position:0% +not very good and a change in the + + + align:start position:0% +not very good and a change in the +contact situation even if it's sort of + + align:start position:0% +contact situation even if it's sort of + + + align:start position:0% +contact situation even if it's sort of +hurt in a Cartesian space very close + + align:start position:0% +hurt in a Cartesian space very close + + + align:start position:0% +hurt in a Cartesian space very close +change in the contact situation is as a + + align:start position:0% +change in the contact situation is as a + + + align:start position:0% +change in the contact situation is as a +big change to the plan there's lots of + + align:start position:0% +big change to the plan there's lots of + + + align:start position:0% +big change to the plan there's lots of +ways to address it we're doing all of + + align:start position:0% +ways to address it we're doing all of + + + align:start position:0% +ways to address it we're doing all of +them now you know it's all fundamentally + + align:start position:0% +them now you know it's all fundamentally + + + align:start position:0% +them now you know it's all fundamentally +about robustness but ironically the car + + align:start position:0% +about robustness but ironically the car + + + align:start position:0% +about robustness but ironically the car +was the only time we could have done + + align:start position:0% +was the only time we could have done + + + align:start position:0% +was the only time we could have done +that badly right so we every other place + + align:start position:0% +that badly right so we every other place + + + align:start position:0% +that badly right so we every other place +we worked out all these situations where + + align:start position:0% +we worked out all these situations where + + + align:start position:0% +we worked out all these situations where +okay the robots walking and then + + align:start position:0% +okay the robots walking and then + + + align:start position:0% +okay the robots walking and then +something bad happens and and you know + + align:start position:0% +something bad happens and and you know + + + align:start position:0% +something bad happens and and you know +someone lamp + + align:start position:0% +someone lamp + + + align:start position:0% +someone lamp +you know Lance's you or something you + + align:start position:0% +you know Lance's you or something you + + + align:start position:0% +you know Lance's you or something you +know we had recovery and then even if + + align:start position:0% +know we had recovery and then even if + + + align:start position:0% +know we had recovery and then even if +this even it tried to take a step even + + align:start position:0% +this even it tried to take a step even + + + align:start position:0% +this even it tried to take a step even +if that failed it would go into her a + + align:start position:0% +if that failed it would go into her a + + + align:start position:0% +if that failed it would go into her a +gentle mode where protect its hands + + align:start position:0% +gentle mode where protect its hands + + + align:start position:0% +gentle mode where protect its hands +because we were afraid to break my hands + + align:start position:0% +because we were afraid to break my hands + + + align:start position:0% +because we were afraid to break my hands +it would fall very gently to the ground + + align:start position:0% +it would fall very gently to the ground + + + align:start position:0% +it would fall very gently to the ground +all that was good we turned it off + + align:start position:0% +all that was good we turned it off + + + align:start position:0% +all that was good we turned it off +exactly once in the competition we + + align:start position:0% +exactly once in the competition we + + + align:start position:0% +exactly once in the competition we +turned it off when we were in the car + + align:start position:0% +turned it off when we were in the car + + + align:start position:0% +turned it off when we were in the car +because we can't take a step to recover + + align:start position:0% +because we can't take a step to recover + + + align:start position:0% +because we can't take a step to recover +when you're in the car and you're the + + align:start position:0% +when you're in the car and you're the + + + align:start position:0% +when you're in the car and you're the +same size of the car and we didn't even + + align:start position:0% +same size of the car and we didn't even + + + align:start position:0% +same size of the car and we didn't even +want to protect our hands because we + + align:start position:0% +want to protect our hands because we + + + align:start position:0% +want to protect our hands because we +didn't wanna get hit we once we got our + + align:start position:0% +didn't wanna get hit we once we got our + + + align:start position:0% +didn't wanna get hit we once we got our +hands stuck in the steering wheel and + + align:start position:0% +hands stuck in the steering wheel and + + + align:start position:0% +hands stuck in the steering wheel and +Reaper so yeah so anyways that was the + + align:start position:0% +Reaper so yeah so anyways that was the + + + align:start position:0% +Reaper so yeah so anyways that was the +only time we could have sort of shaken + + align:start position:0% +only time we could have sort of shaken + + + align:start position:0% +only time we could have sort of shaken +ourselves silly and fallen you know and + + align:start position:0% +ourselves silly and fallen you know and + + + align:start position:0% +ourselves silly and fallen you know and +what happened it we fell down with our + + align:start position:0% +what happened it we fell down with our + + + align:start position:0% +what happened it we fell down with our +400 pound robot we broke the arm the + + align:start position:0% +400 pound robot we broke the arm the + + + align:start position:0% +400 pound robot we broke the arm the +left arm or the right arm sadly all of + + align:start position:0% +left arm or the right arm sadly all of + + + align:start position:0% +left arm or the right arm sadly all of +our practices ever we're doing all the + + align:start position:0% +our practices ever we're doing all the + + + align:start position:0% +our practices ever we're doing all the +tasks right handed but we got to show + + align:start position:0% +tasks right handed but we got to show + + + align:start position:0% +tasks right handed but we got to show +off a different form of robustness so we + + align:start position:0% +off a different form of robustness so we + + + align:start position:0% +off a different form of robustness so we +actually because we had so much autonomy + + align:start position:0% +actually because we had so much autonomy + + + align:start position:0% +actually because we had so much autonomy +in the system we flipped a bit and said + + align:start position:0% +in the system we flipped a bit and said + + + align:start position:0% +in the system we flipped a bit and said +let's use the left arm for everything + + align:start position:0% +let's use the left arm for everything + + + align:start position:0% +let's use the left arm for everything +which is more than just you know map the + + align:start position:0% +which is more than just you know map the + + + align:start position:0% +which is more than just you know map the +joint chord it's over here I meant and + + align:start position:0% +joint chord it's over here I meant and + + + align:start position:0% +joint chord it's over here I meant and +then you had to walk up to the door on + + align:start position:0% +then you had to walk up to the door on + + + align:start position:0% +then you had to walk up to the door on +the other side of the door you know and + + align:start position:0% +the other side of the door you know and + + + align:start position:0% +the other side of the door you know and +you had it really backs the implications + + align:start position:0% +you had it really backs the implications + + + align:start position:0% +you had it really backs the implications +back up quite a bit and we were able to + + align:start position:0% +back up quite a bit and we were able to + + + align:start position:0% +back up quite a bit and we were able to +after having our arm just completely + + align:start position:0% +after having our arm just completely + + + align:start position:0% +after having our arm just completely +hosed we're able to go through and do + + align:start position:0% +hosed we're able to go through and do + + + align:start position:0% +hosed we're able to go through and do +all the rest of the tasks except for the + + align:start position:0% +all the rest of the tasks except for the + + + align:start position:0% +all the rest of the tasks except for the +drill which required to hear + + align:start position:0% +drill which required to hear + + + align:start position:0% +drill which required to hear +we couldn't do that one we had to pick + + align:start position:0% +we couldn't do that one we had to pick + + + align:start position:0% +we couldn't do that one we had to pick +up the drill and turn it on so we ended + + align:start position:0% +up the drill and turn it on so we ended + + + align:start position:0% +up the drill and turn it on so we ended +the day in second place with the you + + align:start position:0% +the day in second place with the you + + + align:start position:0% +the day in second place with the you +know with a different display of + + align:start position:0% +know with a different display of + + + align:start position:0% +know with a different display of +robustness we were happy but not as + + align:start position:0% +robustness we were happy but not as + + + align:start position:0% +robustness we were happy but not as +happy as if we had not fallen so okay so + + align:start position:0% +happy as if we had not fallen so okay so + + + align:start position:0% +happy as if we had not fallen so okay so +I think walking around balancing you + + align:start position:0% +I think walking around balancing you + + + align:start position:0% +I think walking around balancing you +know we're pretty good but there's a + + align:start position:0% +know we're pretty good but there's a + + + align:start position:0% +know we're pretty good but there's a +limitation I really do think that's + + align:start position:0% +limitation I really do think that's + + + align:start position:0% +limitation I really do think that's +that's a fundamental everybody has that + + align:start position:0% +that's a fundamental everybody has that + + + align:start position:0% +that's a fundamental everybody has that +limitation to some extent the + + align:start position:0% +limitation to some extent the + + + align:start position:0% +limitation to some extent the +manipulation capabilities of the robot + + align:start position:0% +manipulation capabilities of the robot + + + align:start position:0% +manipulation capabilities of the robot +were we're pretty limited just because + + align:start position:0% +were we're pretty limited just because + + + align:start position:0% +were we're pretty limited just because +we didn't need to do it for the + + align:start position:0% +we didn't need to do it for the + + + align:start position:0% +we didn't need to do it for the +challenge we know we had the + + align:start position:0% +challenge we know we had the + + + align:start position:0% +challenge we know we had the +manipulation requirements were minimal + + align:start position:0% +manipulation requirements were minimal + + + align:start position:0% +manipulation requirements were minimal +you know you had to open doors picking + + align:start position:0% +you know you had to open doors picking + + + align:start position:0% +you know you had to open doors picking +up a drill was the most complicated + + align:start position:0% +up a drill was the most complicated + + + align:start position:0% +up a drill was the most complicated +thing we actually had a lot of really + + align:start position:0% +thing we actually had a lot of really + + + align:start position:0% +thing we actually had a lot of really +nice robotic hands to play with but they + + align:start position:0% +nice robotic hands to play with but they + + + align:start position:0% +nice robotic hands to play with but they +all broke when you started really + + align:start position:0% +all broke when you started really + + + align:start position:0% +all broke when you started really +running them through these hard tests so + + align:start position:0% +running them through these hard tests so + + + align:start position:0% +running them through these hard tests so +we ended up with these sort of + + align:start position:0% +we ended up with these sort of + + + align:start position:0% +we ended up with these sort of +lobster-claw kind of grippers because + + align:start position:0% +lobster-claw kind of grippers because + + + align:start position:0% +lobster-claw kind of grippers because +they didn't break and they were robust + + align:start position:0% +they didn't break and they were robust + + + align:start position:0% +they didn't break and they were robust +and they worked well but it limited what + + align:start position:0% +and they worked well but it limited what + + + align:start position:0% +and they worked well but it limited what +we could do in manipulation again the + + align:start position:0% +we could do in manipulation again the + + + align:start position:0% +we could do in manipulation again the +planning worked very well we could even + + align:start position:0% +planning worked very well we could even + + + align:start position:0% +planning worked very well we could even +we could pick up a board and even plan + + align:start position:0% +we could pick up a board and even plan + + + align:start position:0% +we could pick up a board and even plan +to make sure that the board now you know + + align:start position:0% +to make sure that the board now you know + + + align:start position:0% +to make sure that the board now you know +didn't intersect with other place boards + + align:start position:0% +didn't intersect with other place boards + + + align:start position:0% +didn't intersect with other place boards +in the world and we have really good + + align:start position:0% +in the world and we have really good + + + align:start position:0% +in the world and we have really good +planning capabilities and those worked + + align:start position:0% +planning capabilities and those worked + + + align:start position:0% +planning capabilities and those worked +at interactive rates the kinematic plans + + align:start position:0% +at interactive rates the kinematic plans + + + align:start position:0% +at interactive rates the kinematic plans +but the grasping was was open-loop so + + align:start position:0% +but the grasping was was open-loop so + + + align:start position:0% +but the grasping was was open-loop so +there's really no feedback so there's + + align:start position:0% +there's really no feedback so there's + + + align:start position:0% +there's really no feedback so there's +current sensing just to not over to + + align:start position:0% +current sensing just to not over to + + + align:start position:0% +current sensing just to not over to +overheat the hands but basically you do + + align:start position:0% +overheat the hands but basically you do + + + align:start position:0% +overheat the hands but basically you do +a lot of thinking to figure out how to + + align:start position:0% +a lot of thinking to figure out how to + + + align:start position:0% +a lot of thinking to figure out how to +get your hand near the board and then + + align:start position:0% +get your hand near the board and then + + + align:start position:0% +get your hand near the board and then +you kind of close your eyes and go like + + align:start position:0% +you kind of close your eyes and go like + + + align:start position:0% +you kind of close your eyes and go like +this and hope it lands in the in the + + align:start position:0% +this and hope it lands in the in the + + + align:start position:0% +this and hope it lands in the in the +board and my in the hand and most of the + + align:start position:0% +board and my in the hand and most of the + + + align:start position:0% +board and my in the hand and most of the +time it does every once in a while it + + align:start position:0% +time it does every once in a while it + + + align:start position:0% +time it does every once in a while it +doesn't you know we we experimented with + + align:start position:0% +doesn't you know we we experimented with + + + align:start position:0% +doesn't you know we we experimented with +every touch sensor we could get our + + align:start position:0% +every touch sensor we could get our + + + align:start position:0% +every touch sensor we could get our +hands on that wasn't meant to be a pun + + align:start position:0% +hands on that wasn't meant to be a pun + + + align:start position:0% +hands on that wasn't meant to be a pun +and we tried cameras and everything but + + align:start position:0% +and we tried cameras and everything but + + + align:start position:0% +and we tried cameras and everything but +they were all just too fragile and + + align:start position:0% +they were all just too fragile and + + + align:start position:0% +they were all just too fragile and +difficult to use further for the + + align:start position:0% +difficult to use further for the + + + align:start position:0% +difficult to use further for the +competition we're doing a lot of work + + align:start position:0% +competition we're doing a lot of work + + + align:start position:0% +competition we're doing a lot of work +now doing optimization for grasping but + + align:start position:0% +now doing optimization for grasping but + + + align:start position:0% +now doing optimization for grasping but +I'll skip over that for time and so the + + align:start position:0% +I'll skip over that for time and so the + + + align:start position:0% +I'll skip over that for time and so the +other piece was hard so how does the + + align:start position:0% +other piece was hard so how does the + + + align:start position:0% +other piece was hard so how does the +human come into the to the perception + + align:start position:0% +human come into the to the perception + + + align:start position:0% +human come into the to the perception +side of the story right so one of these + + align:start position:0% +side of the story right so one of these + + + align:start position:0% +side of the story right so one of these +tasks was moving debris out from in + + align:start position:0% +tasks was moving debris out from in + + + align:start position:0% +tasks was moving debris out from in +front of the door and this is sort of + + align:start position:0% +front of the door and this is sort of + + + align:start position:0% +front of the door and this is sort of +what it looked like actually in the trot + + align:start position:0% +what it looked like actually in the trot + + + align:start position:0% +what it looked like actually in the trot +in the in the original version of the + + align:start position:0% +in the in the original version of the + + + align:start position:0% +in the in the original version of the +competition the trials would come up and + + align:start position:0% +competition the trials would come up and + + + align:start position:0% +competition the trials would come up and +throw these boards out of the way and + + align:start position:0% +throw these boards out of the way and + + + align:start position:0% +throw these boards out of the way and +you see the human operators over there + + align:start position:0% +you see the human operators over there + + + align:start position:0% +you see the human operators over there +with their you know big console of this + + align:start position:0% +with their you know big console of this + + + align:start position:0% +with their you know big console of this +displays this is + + align:start position:0% +displays this is + + + align:start position:0% +displays this is +what the laser in the robots head sees + + align:start position:0% +what the laser in the robots head sees + + + align:start position:0% +what the laser in the robots head sees +we have a spinning laser we also have + + align:start position:0% +we have a spinning laser we also have + + + align:start position:0% +we have a spinning laser we also have +stereo vision but the laser + + align:start position:0% +stereo vision but the laser + + + align:start position:0% +stereo vision but the laser +reconstruction of this gives you a mess + + align:start position:0% +reconstruction of this gives you a mess + + + align:start position:0% +reconstruction of this gives you a mess +of points if you asked a vision + + align:start position:0% +of points if you asked a vision + + + align:start position:0% +of points if you asked a vision +algorithm you have some of you are + + align:start position:0% +algorithm you have some of you are + + + align:start position:0% +algorithm you have some of you are +vision experts I'm sure in the room if + + align:start position:0% +vision experts I'm sure in the room if + + + align:start position:0% +vision experts I'm sure in the room if +you asked a vision algorithm to figure + + align:start position:0% +you asked a vision algorithm to figure + + + align:start position:0% +you asked a vision algorithm to figure +out what's going on and that's massive + + align:start position:0% +out what's going on and that's massive + + + align:start position:0% +out what's going on and that's massive +points it's extremely hard problem but + + align:start position:0% +points it's extremely hard problem but + + + align:start position:0% +points it's extremely hard problem but +we have a human in the loop so the idea + + align:start position:0% +we have a human in the loop so the idea + + + align:start position:0% +we have a human in the loop so the idea +is that one or two clicks from a human + + align:start position:0% +is that one or two clicks from a human + + + align:start position:0% +is that one or two clicks from a human +can turn that from an intractable + + align:start position:0% +can turn that from an intractable + + + align:start position:0% +can turn that from an intractable +problem to a pretty simple problem right + + align:start position:0% +problem to a pretty simple problem right + + + align:start position:0% +problem to a pretty simple problem right +just say there's a 2x4 here and then now + + align:start position:0% +just say there's a 2x4 here and then now + + + align:start position:0% +just say there's a 2x4 here and then now +a local search can do sort of ransacked + + align:start position:0% +a local search can do sort of ransacked + + + align:start position:0% +a local search can do sort of ransacked +type local optimizations to find that + + align:start position:0% +type local optimizations to find that + + + align:start position:0% +type local optimizations to find that +the the best fit to a 2x4 to that local + + align:start position:0% +the the best fit to a 2x4 to that local + + + align:start position:0% +the the best fit to a 2x4 to that local +group of points and that networks well + + align:start position:0% +group of points and that networks well + + + align:start position:0% +group of points and that networks well +and so the robot didn't have to think + + align:start position:0% +and so the robot didn't have to think + + + align:start position:0% +and so the robot didn't have to think +about the messy point clouds when it's + + align:start position:0% +about the messy point clouds when it's + + + align:start position:0% +about the messy point clouds when it's +doing its planning it could think about + + align:start position:0% +doing its planning it could think about + + + align:start position:0% +doing its planning it could think about +the simplified geometry from the CAD + + align:start position:0% +the simplified geometry from the CAD + + + align:start position:0% +the simplified geometry from the CAD +models and all the most of the planning + + align:start position:0% +models and all the most of the planning + + + align:start position:0% +models and all the most of the planning +was just on the the CAD models so this + + align:start position:0% +was just on the the CAD models so this + + + align:start position:0% +was just on the the CAD models so this +is what it looks like to drive the robot + + align:start position:0% +is what it looks like to drive the robot + + + align:start position:0% +is what it looks like to drive the robot +so the robot you click somewhere saying + + align:start position:0% +so the robot you click somewhere saying + + + align:start position:0% +so the robot you click somewhere saying +there's a valve then the perception + + align:start position:0% +there's a valve then the perception + + + align:start position:0% +there's a valve then the perception +algorithm finds a valve then the robot + + align:start position:0% +algorithm finds a valve then the robot + + + align:start position:0% +algorithm finds a valve then the robot +starts going it actually shows you a + + align:start position:0% +starts going it actually shows you a + + + align:start position:0% +starts going it actually shows you a +ghost of what it's about to do and then + + align:start position:0% +ghost of what it's about to do and then + + + align:start position:0% +ghost of what it's about to do and then +if you're happy with it and if all + + align:start position:0% +if you're happy with it and if all + + + align:start position:0% +if you're happy with it and if all +things are going well you just watch but + + align:start position:0% +things are going well you just watch but + + + align:start position:0% +things are going well you just watch but +if it looks like it's about to do + + align:start position:0% +if it looks like it's about to do + + + align:start position:0% +if it looks like it's about to do +something stupid you can come in stop + + align:start position:0% +something stupid you can come in stop + + + align:start position:0% +something stupid you can come in stop +interact change the plans and and let it + + align:start position:0% +interact change the plans and and let it + + + align:start position:0% +interact change the plans and and let it +do its thing it's kind of fun to watch + + align:start position:0% +do its thing it's kind of fun to watch + + + align:start position:0% +do its thing it's kind of fun to watch +the view robot view of the world right + + align:start position:0% +the view robot view of the world right + + + align:start position:0% +the view robot view of the world right +so this is sort of you know what the + + align:start position:0% +so this is sort of you know what the + + + align:start position:0% +so this is sort of you know what the +robot sees it throws down its foot steps + + align:start position:0% +robot sees it throws down its foot steps + + + align:start position:0% +robot sees it throws down its foot steps +it's deciding how to walk up to that + + align:start position:0% +it's deciding how to walk up to that + + + align:start position:0% +it's deciding how to walk up to that +valve you know again so when when the + + align:start position:0% +valve you know again so when when the + + + align:start position:0% +valve you know again so when when the +right arm was broken this was one of our + + align:start position:0% +right arm was broken this was one of our + + + align:start position:0% +right arm was broken this was one of our +practice runs but with right arm was + + align:start position:0% +practice runs but with right arm was + + + align:start position:0% +practice runs but with right arm was +broken it had a valve we had a bit + + align:start position:0% +broken it had a valve we had a bit + + + align:start position:0% +broken it had a valve we had a bit +flipped now it had to walk over to the + + align:start position:0% +flipped now it had to walk over to the + + + align:start position:0% +flipped now it had to walk over to the +other side of the valve and you know + + align:start position:0% +other side of the valve and you know + + + align:start position:0% +other side of the valve and you know +there's a lot of things going on a lot + + align:start position:0% +there's a lot of things going on a lot + + + align:start position:0% +there's a lot of things going on a lot +of pieces had to work well together to + + align:start position:0% +of pieces had to work well together to + + + align:start position:0% +of pieces had to work well together to +make all this work one of the questions + + align:start position:0% +make all this work one of the questions + + + align:start position:0% +make all this work one of the questions +that I'll I'll get before you ask it + + align:start position:0% +that I'll I'll get before you ask it + + + align:start position:0% +that I'll I'll get before you ask it +you've written it down okay yeah that's + + align:start position:0% +you've written it down okay yeah that's + + + align:start position:0% +you've written it down okay yeah that's +fine why were the robots so slow why + + align:start position:0% +fine why were the robots so slow why + + + align:start position:0% +fine why were the robots so slow why +were they standing still a lot of people + + align:start position:0% +were they standing still a lot of people + + + align:start position:0% +were they standing still a lot of people +out there waiting for the human maybe a + + align:start position:0% +out there waiting for the human maybe a + + + align:start position:0% +out there waiting for the human maybe a +lot but for us it wasn't it wasn't the + + align:start position:0% +lot but for us it wasn't it wasn't the + + + align:start position:0% +lot but for us it wasn't it wasn't the +planning time the planning algorithms + + align:start position:0% +planning time the planning algorithms + + + align:start position:0% +planning time the planning algorithms +were super fast most of the time we were + + align:start position:0% +were super fast most of the time we were + + + align:start position:0% +were super fast most of the time we were +waiting for sensor data and that meant + + align:start position:0% +waiting for sensor data and that meant + + + align:start position:0% +waiting for sensor data and that meant +there was two things there was waiting + + align:start position:0% +there was two things there was waiting + + + align:start position:0% +there was two things there was waiting +for the laser to go spin out completely + + align:start position:0% +for the laser to go spin out completely + + + align:start position:0% +for the laser to go spin out completely +around and also just being conservative + + align:start position:0% +around and also just being conservative + + + align:start position:0% +around and also just being conservative +or wanting to get that laser data while + + align:start position:0% +or wanting to get that laser data while + + + align:start position:0% +or wanting to get that laser data while +the robot was stopped and then there was + + align:start position:0% +the robot was stopped and then there was + + + align:start position:0% +the robot was stopped and then there was +getting the laser data back to the + + align:start position:0% +getting the laser data back to the + + + align:start position:0% +getting the laser data back to the +computer + + align:start position:0% +computer + + + align:start position:0% +computer +had the fast planning algorithms and + + align:start position:0% +had the fast planning algorithms and + + + align:start position:0% +had the fast planning algorithms and +back so if there was a network blackout + + align:start position:0% +back so if there was a network blackout + + + align:start position:0% +back so if there was a network blackout +we had to wait a little bit and that + + align:start position:0% +we had to wait a little bit and that + + + align:start position:0% +we had to wait a little bit and that +meant we were standing still but we've + + align:start position:0% +meant we were standing still but we've + + + align:start position:0% +meant we were standing still but we've +actually done a lot of work in lab to + + align:start position:0% +actually done a lot of work in lab to + + + align:start position:0% +actually done a lot of work in lab to +show that we don't have to stand still + + align:start position:0% +show that we don't have to stand still + + + align:start position:0% +show that we don't have to stand still +this is now the robot walking with its + + align:start position:0% +this is now the robot walking with its + + + align:start position:0% +this is now the robot walking with its +laser blindfolded and using only stereo + + align:start position:0% +laser blindfolded and using only stereo + + + align:start position:0% +laser blindfolded and using only stereo +vision using one of the capabilities + + align:start position:0% +vision using one of the capabilities + + + align:start position:0% +vision using one of the capabilities +that came out of John's lab and others + + align:start position:0% +that came out of John's lab and others + + + align:start position:0% +that came out of John's lab and others +to do connect stereo fusion so that + + align:start position:0% +to do connect stereo fusion so that + + + align:start position:0% +to do connect stereo fusion so that +compared the laser gives gives very + + align:start position:0% +compared the laser gives gives very + + + align:start position:0% +compared the laser gives gives very +accurate points but it gives them slowly + + align:start position:0% +accurate points but it gives them slowly + + + align:start position:0% +accurate points but it gives them slowly +you know low radon you have to wait for + + align:start position:0% +you know low radon you have to wait for + + + align:start position:0% +you know low radon you have to wait for +it to spin around the the camera is very + + align:start position:0% +it to spin around the the camera is very + + + align:start position:0% +it to spin around the the camera is very +dense very high rate but very noisy and + + align:start position:0% +dense very high rate but very noisy and + + + align:start position:0% +dense very high rate but very noisy and +John and others have developed these new + + align:start position:0% +John and others have developed these new + + + align:start position:0% +John and others have developed these new +algorithms that can do real-time + + align:start position:0% +algorithms that can do real-time + + + align:start position:0% +algorithms that can do real-time +filtering of that noisy data and we + + align:start position:0% +filtering of that noisy data and we + + + align:start position:0% +filtering of that noisy data and we +demonstrated that that was they were + + align:start position:0% +demonstrated that that was they were + + + align:start position:0% +demonstrated that that was they were +good enough to do walking on and so we'd + + align:start position:0% +good enough to do walking on and so we'd + + + align:start position:0% +good enough to do walking on and so we'd +put all the pieces together real time + + align:start position:0% +put all the pieces together real time + + + align:start position:0% +put all the pieces together real time +implant foot step planning real sight + + align:start position:0% +implant foot step planning real sight + + + align:start position:0% +implant foot step planning real sight +balancing real-time perception and we + + align:start position:0% +balancing real-time perception and we + + + align:start position:0% +balancing real-time perception and we +were able to show we can walk + + align:start position:0% +were able to show we can walk + + + align:start position:0% +were able to show we can walk +continuously this will be the future so + + align:start position:0% +continuously this will be the future so + + + align:start position:0% +continuously this will be the future so +you know we had to do networking we've + + align:start position:0% +you know we had to do networking we've + + + align:start position:0% +you know we had to do networking we've +optimized network systems we had to you + + align:start position:0% +optimized network systems we had to you + + + align:start position:0% +optimized network systems we had to you +know build servers unit test logistics + + align:start position:0% +know build servers unit test logistics + + + align:start position:0% +know build servers unit test logistics +politics you know it was exhausting but + + align:start position:0% +politics you know it was exhausting but + + + align:start position:0% +politics you know it was exhausting but +I think it was overall incredibly good + + align:start position:0% +I think it was overall incredibly good + + + align:start position:0% +I think it was overall incredibly good +experience a huge success + + align:start position:0% +experience a huge success + + + align:start position:0% +experience a huge success +I think the robots can move faster with + + align:start position:0% +I think the robots can move faster with + + + align:start position:0% +I think the robots can move faster with +only small changes mostly in the + + align:start position:0% +only small changes mostly in the + + + align:start position:0% +only small changes mostly in the +perception side you know the walking was + + align:start position:0% +perception side you know the walking was + + + align:start position:0% +perception side you know the walking was +sufficient we can definitely do better + + align:start position:0% +sufficient we can definitely do better + + + align:start position:0% +sufficient we can definitely do better +the the manipulation was very basic I + + align:start position:0% +the the manipulation was very basic I + + + align:start position:0% +the the manipulation was very basic I +think we need to do better there we + + align:start position:0% +think we need to do better there we + + + align:start position:0% +think we need to do better there we +didn't have to for those tasks the + + align:start position:0% +didn't have to for those tasks the + + + align:start position:0% +didn't have to for those tasks the +robustness dominated everything so I'll + + align:start position:0% +robustness dominated everything so I'll + + + align:start position:0% +robustness dominated everything so I'll +just end and take questions but I'll + + align:start position:0% +just end and take questions but I'll + + + align:start position:0% +just end and take questions but I'll +show this sort of fun again robot view + + align:start position:0% +show this sort of fun again robot view + + + align:start position:0% +show this sort of fun again robot view +of this is the robots you know God's eye + + align:start position:0% +of this is the robots you know God's eye + + + align:start position:0% +of this is the robots you know God's eye +view of the world as well it's doing all + + align:start position:0% +view of the world as well it's doing all + + + align:start position:0% +view of the world as well it's doing all +these tasks you can sort of see what the + + align:start position:0% +these tasks you can sort of see what the + + + align:start position:0% +these tasks you can sort of see what the +robot labels with geometry and what it + + align:start position:0% +robot labels with geometry and what it + + + align:start position:0% +robot labels with geometry and what it +what it's leaving is points and it's + + align:start position:0% +what it's leaving is points and it's + + + align:start position:0% +what it's leaving is points and it's +just kind of fun to have on the + + align:start position:0% +just kind of fun to have on the + + + align:start position:0% +just kind of fun to have on the +background and and I'll I'll take any + + align:start position:0% +background and and I'll I'll take any + + + align:start position:0% +background and and I'll I'll take any +questions yeah + + align:start position:0% + + + + align:start position:0% + +you + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/G534bz09B4A.txt b/G534bz09B4A.txt new file mode 100644 index 0000000000000000000000000000000000000000..59b1eb3c84e7eb5935fde7e2f884125abf95ec65 --- /dev/null +++ b/G534bz09B4A.txt @@ -0,0 +1,3464 @@ +align:start position:0% + +welcome back to recitation in this video + + align:start position:0% +welcome back to recitation in this video + + + align:start position:0% +welcome back to recitation in this video +we want to work on using change the + + align:start position:0% +we want to work on using change the + + + align:start position:0% +we want to work on using change the +change of variables technique in + + align:start position:0% +change of variables technique in + + + align:start position:0% +change of variables technique in +particular we're going to look at the + + align:start position:0% +particular we're going to look at the + + + align:start position:0% +particular we're going to look at the +following problem it says using the + + align:start position:0% +following problem it says using the + + + align:start position:0% +following problem it says using the +change of variables U is equal to x^2 - + + align:start position:0% +change of variables U is equal to x^2 - + + + align:start position:0% +change of variables U is equal to x^2 - +y^2 and V is equal to Y / X Supply the + + align:start position:0% +y^2 and V is equal to Y / X Supply the + + + align:start position:0% +y^2 and V is equal to Y / X Supply the +limits and integrand for the following + + align:start position:0% +limits and integrand for the following + + + align:start position:0% +limits and integrand for the following +integral which is the double integral + + align:start position:0% +integral which is the double integral + + + align:start position:0% +integral which is the double integral +over a region R of 1x^2 DX D Y and R is + + align:start position:0% +over a region R of 1x^2 DX D Y and R is + + + align:start position:0% +over a region R of 1x^2 DX D Y and R is +the infinite region in the first + + align:start position:0% +the infinite region in the first + + + align:start position:0% +the infinite region in the first +quadrant that is both under the curve y + + align:start position:0% +quadrant that is both under the curve y + + + align:start position:0% +quadrant that is both under the curve y += 1X and to the right of the curve x^2 - + + align:start position:0% += 1X and to the right of the curve x^2 - + + + align:start position:0% += 1X and to the right of the curve x^2 - +y^2 = 1 so this is a challenging problem + + align:start position:0% +y^2 = 1 so this is a challenging problem + + + align:start position:0% +y^2 = 1 so this is a challenging problem +again I want to point out we just want + + align:start position:0% +again I want to point out we just want + + + align:start position:0% +again I want to point out we just want +to find the limits in the integrand you + + align:start position:0% +to find the limits in the integrand you + + + align:start position:0% +to find the limits in the integrand you +don't actually have to compute uh the + + align:start position:0% +don't actually have to compute uh the + + + align:start position:0% +don't actually have to compute uh the +integral but it is it is going to be + + align:start position:0% +integral but it is it is going to be + + + align:start position:0% +integral but it is it is going to be +tough but stick with it uh pause the + + align:start position:0% +tough but stick with it uh pause the + + + align:start position:0% +tough but stick with it uh pause the +video give it your best shot hopefully + + align:start position:0% +video give it your best shot hopefully + + + align:start position:0% +video give it your best shot hopefully +you find you find this the appropriate + + align:start position:0% +you find you find this the appropriate + + + align:start position:0% +you find you find this the appropriate +limits into Grand and then when you feel + + align:start position:0% +limits into Grand and then when you feel + + + align:start position:0% +limits into Grand and then when you feel +comfortable bring the video back up and + + align:start position:0% +comfortable bring the video back up and + + + align:start position:0% +comfortable bring the video back up and +I'll show you how I do + + align:start position:0% + + + + align:start position:0% + +it okay welcome back so what again what + + align:start position:0% +it okay welcome back so what again what + + + align:start position:0% +it okay welcome back so what again what +we want to do is this change of + + align:start position:0% +we want to do is this change of + + + align:start position:0% +we want to do is this change of +variables problem where we've defined U + + align:start position:0% +variables problem where we've defined U + + + align:start position:0% +variables problem where we've defined U +to be x^2 - y^2 V to be y / X and we + + align:start position:0% +to be x^2 - y^2 V to be y / X and we + + + align:start position:0% +to be x^2 - y^2 V to be y / X and we +have this region that is in the first + + align:start position:0% +have this region that is in the first + + + align:start position:0% +have this region that is in the first +quadrant it's under the curve yal 1 / X + + align:start position:0% +quadrant it's under the curve yal 1 / X + + + align:start position:0% +quadrant it's under the curve yal 1 / X +and it's to the right of the curve x^2 - + + align:start position:0% +and it's to the right of the curve x^2 - + + + align:start position:0% +and it's to the right of the curve x^2 - +y^2 = 1 and we want to compute the + + align:start position:0% +y^2 = 1 and we want to compute the + + + align:start position:0% +y^2 = 1 and we want to compute the +limits and integrant for that particular + + align:start position:0% +limits and integrant for that particular + + + align:start position:0% +limits and integrant for that particular +integral so what I'm going to do to try + + align:start position:0% +integral so what I'm going to do to try + + + align:start position:0% +integral so what I'm going to do to try +and make this as organized as possible + + align:start position:0% +and make this as organized as possible + + + align:start position:0% +and make this as organized as possible +is I'm going to try first to graph the + + align:start position:0% +is I'm going to try first to graph the + + + align:start position:0% +is I'm going to try first to graph the +region r or to show to figure out what + + align:start position:0% +region r or to show to figure out what + + + align:start position:0% +region r or to show to figure out what +the region R is in the XY plane then I'm + + align:start position:0% +the region R is in the XY plane then I'm + + + align:start position:0% +the region R is in the XY plane then I'm +going to try and figure out what the + + align:start position:0% +going to try and figure out what the + + + align:start position:0% +going to try and figure out what the +region R is mapped to in the UV plane so + + align:start position:0% +region R is mapped to in the UV plane so + + + align:start position:0% +region R is mapped to in the UV plane so +what it looks like in the UV plane that + + align:start position:0% +what it looks like in the UV plane that + + + align:start position:0% +what it looks like in the UV plane that +will give me my limit and then I'm going + + align:start position:0% +will give me my limit and then I'm going + + + align:start position:0% +will give me my limit and then I'm going +to try and determine the Jacobian and + + align:start position:0% +to try and determine the Jacobian and + + + align:start position:0% +to try and determine the Jacobian and +then I will determine from that and the + + align:start position:0% +then I will determine from that and the + + + align:start position:0% +then I will determine from that and the +fact that I'm started with 1 divid x^2 + + align:start position:0% +fact that I'm started with 1 divid x^2 + + + align:start position:0% +fact that I'm started with 1 divid x^2 +as my function I was integrating I will + + align:start position:0% +as my function I was integrating I will + + + align:start position:0% +as my function I was integrating I will +put those two together to figure out the + + align:start position:0% +put those two together to figure out the + + + align:start position:0% +put those two together to figure out the +integrant so there are a bunch of steps + + align:start position:0% +integrant so there are a bunch of steps + + + align:start position:0% +integrant so there are a bunch of steps +to this problems but the first one again + + align:start position:0% +to this problems but the first one again + + + align:start position:0% +to this problems but the first one again +is I'm going to to graph the region R so + + align:start position:0% +is I'm going to to graph the region R so + + + align:start position:0% +is I'm going to to graph the region R so +I'm going to give you a very rough + + align:start position:0% +I'm going to give you a very rough + + + align:start position:0% +I'm going to give you a very rough +sketch over + + align:start position:0% +sketch over + + + align:start position:0% +sketch over +here of the region R and I know it's in + + align:start position:0% +here of the region R and I know it's in + + + align:start position:0% +here of the region R and I know it's in +the first quadrant and I know it's + + align:start position:0% +the first quadrant and I know it's + + + align:start position:0% +the first quadrant and I know it's +infinite I was already told + + align:start position:0% +infinite I was already told + + + align:start position:0% +infinite I was already told +that okay so in the XY plane the region + + align:start position:0% +that okay so in the XY plane the region + + + align:start position:0% +that okay so in the XY plane the region +R is below the curve y 1X so let me draw + + align:start position:0% +R is below the curve y 1X so let me draw + + + align:start position:0% +R is below the curve y 1X so let me draw +that + + align:start position:0% + + + + align:start position:0% + +curve again this is very rough this is a + + align:start position:0% +curve again this is very rough this is a + + + align:start position:0% +curve again this is very rough this is a +rough sketch I'm putting up no scale on + + align:start position:0% +rough sketch I'm putting up no scale on + + + align:start position:0% +rough sketch I'm putting up no scale on +purpose I'll put in one one value maybe + + align:start position:0% +purpose I'll put in one one value maybe + + + align:start position:0% +purpose I'll put in one one value maybe +in this whole thing okay and that's this + + align:start position:0% +in this whole thing okay and that's this + + + align:start position:0% +in this whole thing okay and that's this +so this is the curve yal + + align:start position:0% +so this is the curve yal + + + align:start position:0% +so this is the curve yal +1X and then I need the curve which is + + align:start position:0% +1X and then I need the curve which is + + + align:start position:0% +1X and then I need the curve which is +part of the hyperbola that is x^2 - y^2 + + align:start position:0% +part of the hyperbola that is x^2 - y^2 + + + align:start position:0% +part of the hyperbola that is x^2 - y^2 += 1 so I'll draw in the part we need + + align:start position:0% += 1 so I'll draw in the part we need + + + align:start position:0% += 1 so I'll draw in the part we need +which looks roughly like this + + align:start position:0% +which looks roughly like this + + + align:start position:0% +which looks roughly like this +this something like that again this + + align:start position:0% +this something like that again this + + + align:start position:0% +this something like that again this +is not meant to be an exact graph but to + + align:start position:0% +is not meant to be an exact graph but to + + + align:start position:0% +is not meant to be an exact graph but to +give you an idea of of what the region + + align:start position:0% +give you an idea of of what the region + + + align:start position:0% +give you an idea of of what the region +looks like and the only the only thing + + align:start position:0% +looks like and the only the only thing + + + align:start position:0% +looks like and the only the only thing +I'm going to mention is that this point + + align:start position:0% +I'm going to mention is that this point + + + align:start position:0% +I'm going to mention is that this point +we know is xal 1 and y equals 0 so the + + align:start position:0% +we know is xal 1 and y equals 0 so the + + + align:start position:0% +we know is xal 1 and y equals 0 so the +region we're interested in that is both + + align:start position:0% +region we're interested in that is both + + + align:start position:0% +region we're interested in that is both +to the right of x^2 - y^2 = 1 and Below + + align:start position:0% +to the right of x^2 - y^2 = 1 and Below + + + align:start position:0% +to the right of x^2 - y^2 = 1 and Below +y = 1X and in the first quadrant is + + align:start position:0% +y = 1X and in the first quadrant is + + + align:start position:0% +y = 1X and in the first quadrant is +exactly this region + + align:start position:0% +exactly this region + + + align:start position:0% +exactly this region +I'm shading + + align:start position:0% +I'm shading + + + align:start position:0% +I'm shading +here so we want to understand what the + + align:start position:0% +here so we want to understand what the + + + align:start position:0% +here so we want to understand what the +values of u and v + + align:start position:0% +values of u and v + + + align:start position:0% +values of u and v +are along these bounds we need to + + align:start position:0% +are along these bounds we need to + + + align:start position:0% +are along these bounds we need to +understand where where this region maps + + align:start position:0% +understand where where this region maps + + + align:start position:0% +understand where where this region maps +to when I do the change of variables in + + align:start position:0% +to when I do the change of variables in + + + align:start position:0% +to when I do the change of variables in +in order to understand what the limits + + align:start position:0% +in order to understand what the limits + + + align:start position:0% +in order to understand what the limits +are so let me put a put the graph of + + align:start position:0% +are so let me put a put the graph of + + + align:start position:0% +are so let me put a put the graph of +this region in the UV plane so that we + + align:start position:0% +this region in the UV plane so that we + + + align:start position:0% +this region in the UV plane so that we +can really understand what our bounds + + align:start position:0% +can really understand what our bounds + + + align:start position:0% +can really understand what our bounds +are and I know already where it's going + + align:start position:0% +are and I know already where it's going + + + align:start position:0% +are and I know already where it's going +so I'm going to just make the first + + align:start position:0% +so I'm going to just make the first + + + align:start position:0% +so I'm going to just make the first +quadrant because I know this is going + + align:start position:0% +quadrant because I know this is going + + + align:start position:0% +quadrant because I know this is going +into the first quadrant so doesn't + + align:start position:0% +into the first quadrant so doesn't + + + align:start position:0% +into the first quadrant so doesn't +always work that something in the first + + align:start position:0% +always work that something in the first + + + align:start position:0% +always work that something in the first +quadrant Maps into the first quadrant + + align:start position:0% +quadrant Maps into the first quadrant + + + align:start position:0% +quadrant Maps into the first quadrant +but in this case I already did the work + + align:start position:0% +but in this case I already did the work + + + align:start position:0% +but in this case I already did the work +so I know it does so let me point out a + + align:start position:0% +so I know it does so let me point out a + + + align:start position:0% +so I know it does so let me point out a +few things about where this region R + + align:start position:0% +few things about where this region R + + + align:start position:0% +few things about where this region R +Maps the first thing I want to point out + + align:start position:0% +Maps the first thing I want to point out + + + align:start position:0% +Maps the first thing I want to point out +is that we actually know that this + + align:start position:0% +is that we actually know that this + + + align:start position:0% +is that we actually know that this +curve under the change of variables maps + + align:start position:0% +curve under the change of variables maps + + + align:start position:0% +curve under the change of variables maps +to U equals 1 because if you remember U + + align:start position:0% +to U equals 1 because if you remember U + + + align:start position:0% +to U equals 1 because if you remember U +is equal to x^2 - y^2 so this whole + + align:start position:0% +is equal to x^2 - y^2 so this whole + + + align:start position:0% +is equal to x^2 - y^2 so this whole +curve is going to map to u = 1 now I + + align:start position:0% +curve is going to map to u = 1 now I + + + align:start position:0% +curve is going to map to u = 1 now I +don't want the whole curve for my region + + align:start position:0% +don't want the whole curve for my region + + + align:start position:0% +don't want the whole curve for my region +I only want this little piece of it so I + + align:start position:0% +I only want this little piece of it so I + + + align:start position:0% +I only want this little piece of it so I +am going to have in my UV plane I'm + + align:start position:0% +am going to have in my UV plane I'm + + + align:start position:0% +am going to have in my UV plane I'm +going to have some segment at at one and + + align:start position:0% +going to have some segment at at one and + + + align:start position:0% +going to have some segment at at one and +I I actually I'll just know that it's + + align:start position:0% +I I actually I'll just know that it's + + + align:start position:0% +I I actually I'll just know that it's +it's some part of the line U equals 1 is + + align:start position:0% +it's some part of the line U equals 1 is + + + align:start position:0% +it's some part of the line U equals 1 is +going to show up in there but if you + + align:start position:0% +going to show up in there but if you + + + align:start position:0% +going to show up in there but if you +notice I know where it starts right away + + align:start position:0% +notice I know where it starts right away + + + align:start position:0% +notice I know where it starts right away +because at xal 1 yal 0 + + align:start position:0% +because at xal 1 yal 0 + + + align:start position:0% +because at xal 1 yal 0 +if I look at what V is if we come back + + align:start position:0% +if I look at what V is if we come back + + + align:start position:0% +if I look at what V is if we come back +here and remember what V is at xal 1 y + + align:start position:0% +here and remember what V is at xal 1 y + + + align:start position:0% +here and remember what V is at xal 1 y +equal 0 V is zero and so my starting + + align:start position:0% +equal 0 V is zero and so my starting + + + align:start position:0% +equal 0 V is zero and so my starting +point on this segment if we come back + + align:start position:0% +point on this segment if we come back + + + align:start position:0% +point on this segment if we come back +here my starting point on this segment + + align:start position:0% +here my starting point on this segment + + + align:start position:0% +here my starting point on this segment +is actually also at one + + align:start position:0% +is actually also at one + + + align:start position:0% +is actually also at one +Z okay so I know there's some point + + align:start position:0% +Z okay so I know there's some point + + + align:start position:0% +Z okay so I know there's some point +right here that Maps down to here where + + align:start position:0% +right here that Maps down to here where + + + align:start position:0% +right here that Maps down to here where +where the segment will stop I'll find + + align:start position:0% +where the segment will stop I'll find + + + align:start position:0% +where the segment will stop I'll find +that point later + + align:start position:0% +that point later + + + align:start position:0% +that point later +algebraically right and then now we need + + align:start position:0% +algebraically right and then now we need + + + align:start position:0% +algebraically right and then now we need +to figure out where these two curves go + + align:start position:0% +to figure out where these two curves go + + + align:start position:0% +to figure out where these two curves go +and then we can we can get a picture and + + align:start position:0% +and then we can we can get a picture and + + + align:start position:0% +and then we can we can get a picture and +then we'll figure out what that point is + + align:start position:0% +then we'll figure out what that point is + + + align:start position:0% +then we'll figure out what that point is +and we'll understand all the limits so + + align:start position:0% +and we'll understand all the limits so + + + align:start position:0% +and we'll understand all the limits so +the first thing I want to point out is + + align:start position:0% +the first thing I want to point out is + + + align:start position:0% +the first thing I want to point out is +along this + + align:start position:0% +along this + + + align:start position:0% +along this +curve we have y equals 0 and x non zero + + align:start position:0% +curve we have y equals 0 and x non zero + + + align:start position:0% +curve we have y equals 0 and x non zero +and just to help ourselves I'm going to + + align:start position:0% +and just to help ourselves I'm going to + + + align:start position:0% +and just to help ourselves I'm going to +rewrite what the change of variables is + + align:start position:0% +rewrite what the change of variables is + + + align:start position:0% +rewrite what the change of variables is +here so I don't have to keep walking + + align:start position:0% +here so I don't have to keep walking + + + align:start position:0% +here so I don't have to keep walking +over to the other + + align:start position:0% +over to the other + + + align:start position:0% +over to the other +side our change of variables was U is + + align:start position:0% +side our change of variables was U is + + + align:start position:0% +side our change of variables was U is +equal to x^2 - y^2 and V was equal to Y + + align:start position:0% +equal to x^2 - y^2 and V was equal to Y + + + align:start position:0% +equal to x^2 - y^2 and V was equal to Y +/ X so this this whole curve has yal 0 + + align:start position:0% +/ X so this this whole curve has yal 0 + + + align:start position:0% +/ X so this this whole curve has yal 0 +so what happens to U and what happens to + + align:start position:0% +so what happens to U and what happens to + + + align:start position:0% +so what happens to U and what happens to +V along that curve well U is going to be + + align:start position:0% +V along that curve well U is going to be + + + align:start position:0% +V along that curve well U is going to be +x + + align:start position:0% +x + + + align:start position:0% +x +s and V is going to equal zero and so + + align:start position:0% +s and V is going to equal zero and so + + + align:start position:0% +s and V is going to equal zero and so +the point of this really is that even + + align:start position:0% +the point of this really is that even + + + align:start position:0% +the point of this really is that even +though even though in you this curve + + align:start position:0% +though even though in you this curve + + + align:start position:0% +though even though in you this curve +maybe is mapping at a different speed in + + align:start position:0% +maybe is mapping at a different speed in + + + align:start position:0% +maybe is mapping at a different speed in +some form to this curve here it still is + + align:start position:0% +some form to this curve here it still is + + + align:start position:0% +some form to this curve here it still is +just taking that segment goes or that + + align:start position:0% +just taking that segment goes or that + + + align:start position:0% +just taking that segment goes or that +infinitely long Ray goes to an + + align:start position:0% +infinitely long Ray goes to an + + + align:start position:0% +infinitely long Ray goes to an +infinitely long Ray here along the U + + align:start position:0% +infinitely long Ray here along the U + + + align:start position:0% +infinitely long Ray here along the U +axis and again that's because along this + + align:start position:0% +axis and again that's because along this + + + align:start position:0% +axis and again that's because along this +Ray y equals Zer and so V is equal to + + align:start position:0% +Ray y equals Zer and so V is equal to + + + align:start position:0% +Ray y equals Zer and so V is equal to +zero everywhere on that Ray and U is is + + align:start position:0% +zero everywhere on that Ray and U is is + + + align:start position:0% +zero everywhere on that Ray and U is is +positive it's equal to X2 okay so I'm + + align:start position:0% +positive it's equal to X2 okay so I'm + + + align:start position:0% +positive it's equal to X2 okay so I'm +going to move the U out of the way + + align:start position:0% +going to move the U out of the way + + + align:start position:0% +going to move the U out of the way +because we're going to say this is part + + align:start position:0% +because we're going to say this is part + + + align:start position:0% +because we're going to say this is part +of the region or that's one bound of the + + align:start position:0% +of the region or that's one bound of the + + + align:start position:0% +of the region or that's one bound of the +region and now I have to figure out + + align:start position:0% +region and now I have to figure out + + + align:start position:0% +region and now I have to figure out +where this curve goes this curve is + + align:start position:0% +where this curve goes this curve is + + + align:start position:0% +where this curve goes this curve is +slightly more complicated but I can + + align:start position:0% +slightly more complicated but I can + + + align:start position:0% +slightly more complicated but I can +still figure it out so I'm going to I'm + + align:start position:0% +still figure it out so I'm going to I'm + + + align:start position:0% +still figure it out so I'm going to I'm +going to show you how I do that sort of + + align:start position:0% +going to show you how I do that sort of + + + align:start position:0% +going to show you how I do that sort of +algebraically that curve if you notice + + align:start position:0% +algebraically that curve if you notice + + + align:start position:0% +algebraically that curve if you notice +if you remember is yal 1 / + + align:start position:0% +if you remember is yal 1 / + + + align:start position:0% +if you remember is yal 1 / +X so that means that on that curve let + + align:start position:0% +X so that means that on that curve let + + + align:start position:0% +X so that means that on that curve let +me even write it down on yal 1 / x v is + + align:start position:0% +me even write it down on yal 1 / x v is + + + align:start position:0% +me even write it down on yal 1 / x v is +equal to 1 / x divid x so V is equal to + + align:start position:0% +equal to 1 / x divid x so V is equal to + + + align:start position:0% +equal to 1 / x divid x so V is equal to +1 / + + align:start position:0% +1 / + + + align:start position:0% +1 / +x^2 right and then what does that mean + + align:start position:0% +x^2 right and then what does that mean + + + align:start position:0% +x^2 right and then what does that mean +about u u then is equal to well x^2 is 1 + + align:start position:0% +about u u then is equal to well x^2 is 1 + + + align:start position:0% +about u u then is equal to well x^2 is 1 +/ + + align:start position:0% +/ + + + align:start position:0% +/ +V and then y^ 2 because y^2 on that + + align:start position:0% +V and then y^ 2 because y^2 on that + + + align:start position:0% +V and then y^ 2 because y^2 on that +curve is just 1 / x^2 + + align:start position:0% +curve is just 1 / x^2 + + + align:start position:0% +curve is just 1 / x^2 +is V so let me let me just make sure we + + align:start position:0% +is V so let me let me just make sure we + + + align:start position:0% +is V so let me let me just make sure we +all follow that one more time we're + + align:start position:0% +all follow that one more time we're + + + align:start position:0% +all follow that one more time we're +looking at where the curve yals 1/x goes + + align:start position:0% +looking at where the curve yals 1/x goes + + + align:start position:0% +looking at where the curve yals 1/x goes +in the change of variables right so + + align:start position:0% +in the change of variables right so + + + align:start position:0% +in the change of variables right so +that's the top curve up here y 1X is the + + align:start position:0% +that's the top curve up here y 1X is the + + + align:start position:0% +that's the top curve up here y 1X is the +top curve of our region + + align:start position:0% +top curve of our region + + + align:start position:0% +top curve of our region +R so we want to know where that goes + + align:start position:0% +R so we want to know where that goes + + + align:start position:0% +R so we want to know where that goes +well on y = 1X V is exactly equal to + + align:start position:0% +well on y = 1X V is exactly equal to + + + align:start position:0% +well on y = 1X V is exactly equal to +1x^2 because V we know is YX so if I + + align:start position:0% +1x^2 because V we know is YX so if I + + + align:start position:0% +1x^2 because V we know is YX so if I +just substitute in for y I get 1x^2 + + align:start position:0% +just substitute in for y I get 1x^2 + + + align:start position:0% +just substitute in for y I get 1x^2 +now if I look at this relationship this + + align:start position:0% +now if I look at this relationship this + + + align:start position:0% +now if I look at this relationship this +means x^2 is equal to 1 over V so in + + align:start position:0% +means x^2 is equal to 1 over V so in + + + align:start position:0% +means x^2 is equal to 1 over V so in +terms of U X2 becomes 1 over V and then + + align:start position:0% +terms of U X2 becomes 1 over V and then + + + align:start position:0% +terms of U X2 becomes 1 over V and then +y^2 which is 1/x^2 + + align:start position:0% +y^2 which is 1/x^2 + + + align:start position:0% +y^2 which is 1/x^2 +becomes V so that curve is U equal 1 + + align:start position:0% +becomes V so that curve is U equal 1 + + + align:start position:0% +becomes V so that curve is U equal 1 +over V minus V now that curve roughly is + + align:start position:0% +over V minus V now that curve roughly is + + + align:start position:0% +over V minus V now that curve roughly is +going to look something like this + + align:start position:0% + + + + align:start position:0% + +and it might seem strange the thing is + + align:start position:0% +and it might seem strange the thing is + + + align:start position:0% +and it might seem strange the thing is +I'm graphing this in the UV plane and + + align:start position:0% +I'm graphing this in the UV plane and + + + align:start position:0% +I'm graphing this in the UV plane and +I'm writing it what looks like U as a + + align:start position:0% +I'm writing it what looks like U as a + + + align:start position:0% +I'm writing it what looks like U as a +function of v and so it's sort of turned + + align:start position:0% +function of v and so it's sort of turned + + + align:start position:0% +function of v and so it's sort of turned +around how you usually see these things + + align:start position:0% +around how you usually see these things + + + align:start position:0% +around how you usually see these things +written but this is the curve that + + align:start position:0% +written but this is the curve that + + + align:start position:0% +written but this is the curve that +describes or this is the equation that + + align:start position:0% +describes or this is the equation that + + + align:start position:0% +describes or this is the equation that +describes this curve and that is + + align:start position:0% +describes this curve and that is + + + align:start position:0% +describes this curve and that is +sufficient to understand because when we + + align:start position:0% +sufficient to understand because when we + + + align:start position:0% +sufficient to understand because when we +use our when we determine our bounds we + + align:start position:0% +use our when we determine our bounds we + + + align:start position:0% +use our when we determine our bounds we +can determine our bounds from U equals 0 + + align:start position:0% +can determine our bounds from U equals 0 + + + align:start position:0% +can determine our bounds from U equals 0 +now to U equal 1 vus V so we now have + + align:start position:0% +now to U equal 1 vus V so we now have + + + align:start position:0% +now to U equal 1 vus V so we now have +the bounds in U we're actually doing + + align:start position:0% +the bounds in U we're actually doing + + + align:start position:0% +the bounds in U we're actually doing +quite well so we have this + + align:start position:0% +quite well so we have this + + + align:start position:0% +quite well so we have this +region we now have the bounds completely + + align:start position:0% +region we now have the bounds completely + + + align:start position:0% +region we now have the bounds completely +in U it's U is going from U equal 0 to u + + align:start position:0% +in U it's U is going from U equal 0 to u + + + align:start position:0% +in U it's U is going from U equal 0 to u += 1 over V minus V but the problem is + + align:start position:0% += 1 over V minus V but the problem is + + + align:start position:0% += 1 over V minus V but the problem is +now we don't know the bounds in V right + + align:start position:0% +now we don't know the bounds in V right + + + align:start position:0% +now we don't know the bounds in V right +we don't know what the bounds are in v + + align:start position:0% +we don't know what the bounds are in v + + + align:start position:0% +we don't know what the bounds are in v +and so we have to be a little bit + + align:start position:0% +and so we have to be a little bit + + + align:start position:0% +and so we have to be a little bit +careful so actually no I think I was + + align:start position:0% +careful so actually no I think I was + + + align:start position:0% +careful so actually no I think I was +wrong it's not zero is it I said that + + align:start position:0% +wrong it's not zero is it I said that + + + align:start position:0% +wrong it's not zero is it I said that +twice now and that was incorrect U is + + align:start position:0% +twice now and that was incorrect U is + + + align:start position:0% +twice now and that was incorrect U is +going from one to 1 over V minus V so I + + align:start position:0% +going from one to 1 over V minus V so I + + + align:start position:0% +going from one to 1 over V minus V so I +apologize because the slices of U are + + align:start position:0% +apologize because the slices of U are + + + align:start position:0% +apologize because the slices of U are +going from whatever the U value starts + + align:start position:0% +going from whatever the U value starts + + + align:start position:0% +going from whatever the U value starts +which is at the value one and it's + + align:start position:0% +which is at the value one and it's + + + align:start position:0% +which is at the value one and it's +coming this way so I apologize I was + + align:start position:0% +coming this way so I apologize I was + + + align:start position:0% +coming this way so I apologize I was +actually looking I was moving my arm + + align:start position:0% +actually looking I was moving my arm + + + align:start position:0% +actually looking I was moving my arm +like I was doing the Val values but I + + align:start position:0% +like I was doing the Val values but I + + + align:start position:0% +like I was doing the Val values but I +actually wanted to do the u values so I + + align:start position:0% +actually wanted to do the u values so I + + + align:start position:0% +actually wanted to do the u values so I +want to go from where U starts which is + + align:start position:0% +want to go from where U starts which is + + + align:start position:0% +want to go from where U starts which is +at U equal 1 to where U stops which is + + align:start position:0% +at U equal 1 to where U stops which is + + + align:start position:0% +at U equal 1 to where U stops which is +when it hits the curve 1 over vus V + + align:start position:0% +when it hits the curve 1 over vus V + + + align:start position:0% +when it hits the curve 1 over vus V +equals U so hopefully I didn't confuse + + align:start position:0% +equals U so hopefully I didn't confuse + + + align:start position:0% +equals U so hopefully I didn't confuse +anyone by that I'm glad I caught it then + + align:start position:0% +anyone by that I'm glad I caught it then + + + align:start position:0% +anyone by that I'm glad I caught it then +okay so now we understand the bounds in + + align:start position:0% +okay so now we understand the bounds in + + + align:start position:0% +okay so now we understand the bounds in +U and then to understand the bounds and + + align:start position:0% +U and then to understand the bounds and + + + align:start position:0% +U and then to understand the bounds and +V all we need to understand is what is + + align:start position:0% +V all we need to understand is what is + + + align:start position:0% +V all we need to understand is what is +the Val value at this + + align:start position:0% +the Val value at this + + + align:start position:0% +the Val value at this +point so once I know the valv value at + + align:start position:0% +point so once I know the valv value at + + + align:start position:0% +point so once I know the valv value at +this point then I'm then I'm done with + + align:start position:0% +this point then I'm then I'm done with + + + align:start position:0% +this point then I'm then I'm done with +the bounds so let's see if we can find + + align:start position:0% +the bounds so let's see if we can find + + + align:start position:0% +the bounds so let's see if we can find +that well the Val value at that point is + + align:start position:0% +that well the Val value at that point is + + + align:start position:0% +that well the Val value at that point is +going to be at the point where these two + + align:start position:0% +going to be at the point where these two + + + align:start position:0% +going to be at the point where these two +curves intersect so let's see if we can + + align:start position:0% +curves intersect so let's see if we can + + + align:start position:0% +curves intersect so let's see if we can +do a little algebra to understand + + align:start position:0% +do a little algebra to understand + + + align:start position:0% +do a little algebra to understand +uh what what that curve what that will + + align:start position:0% +uh what what that curve what that will + + + align:start position:0% +uh what what that curve what that will +look like so let me point out that where + + align:start position:0% +look like so let me point out that where + + + align:start position:0% +look like so let me point out that where +those curves intersect I have the + + align:start position:0% +those curves intersect I have the + + + align:start position:0% +those curves intersect I have the +equation x^2 - 1 /x^2 is equal to 1 and + + align:start position:0% +equation x^2 - 1 /x^2 is equal to 1 and + + + align:start position:0% +equation x^2 - 1 /x^2 is equal to 1 and +if I want to find X values that satisfy + + align:start position:0% +if I want to find X values that satisfy + + + align:start position:0% +if I want to find X values that satisfy +this I'm also looking for X values that + + align:start position:0% +this I'm also looking for X values that + + + align:start position:0% +this I'm also looking for X values that +satisfy x 4 - 1 is equal to x^2 which I + + align:start position:0% +satisfy x 4 - 1 is equal to x^2 which I + + + align:start position:0% +satisfy x 4 - 1 is equal to x^2 which I +can rewrite as x 4 - x^2 - 1 is equal to + + align:start position:0% +can rewrite as x 4 - x^2 - 1 is equal to + + + align:start position:0% +can rewrite as x 4 - x^2 - 1 is equal to + + align:start position:0% + + + align:start position:0% +so I can actually use the quadratic uh + + align:start position:0% +so I can actually use the quadratic uh + + + align:start position:0% +so I can actually use the quadratic uh +quadratic formula on this in terms of + + align:start position:0% +quadratic formula on this in terms of + + + align:start position:0% +quadratic formula on this in terms of +X2 so what I get is I get + + align:start position:0% +X2 so what I get is I get + + + align:start position:0% +X2 so what I get is I get +x^2 is equal to 1 I get plus or minus < + + align:start position:0% +x^2 is equal to 1 I get plus or minus < + + + align:start position:0% +x^2 is equal to 1 I get plus or minus < +TK 5 over two and if you look at it the + + align:start position:0% +TK 5 over two and if you look at it the + + + align:start position:0% +TK 5 over two and if you look at it the +one you're actually interested in you + + align:start position:0% +one you're actually interested in you + + + align:start position:0% +one you're actually interested in you +can figure this out pretty quickly is + + align:start position:0% +can figure this out pretty quickly is + + + align:start position:0% +can figure this out pretty quickly is +the one that is plus okay I want the one + + align:start position:0% +the one that is plus okay I want the one + + + align:start position:0% +the one that is plus okay I want the one +that is plusun 5/2 so then that means X + + align:start position:0% +that is plusun 5/2 so then that means X + + + align:start position:0% +that is plusun 5/2 so then that means X +is is the square root of this + + align:start position:0% +is is the square root of this + + + align:start position:0% +is is the square root of this +quantity on that at that point right or + + align:start position:0% +quantity on that at that point right or + + + align:start position:0% +quantity on that at that point right or +I could actually think about it this way + + align:start position:0% +I could actually think about it this way + + + align:start position:0% +I could actually think about it this way +let me know let me point out this V is + + align:start position:0% +let me know let me point out this V is + + + align:start position:0% +let me know let me point out this V is +equal to 1x^2 at that point because it's + + align:start position:0% +equal to 1x^2 at that point because it's + + + align:start position:0% +equal to 1x^2 at that point because it's +on that curve where we were talking + + align:start position:0% +on that curve where we were talking + + + align:start position:0% +on that curve where we were talking +about yal 1X so V is 1/x^2 so 1 /x^2 + + align:start position:0% +about yal 1X so V is 1/x^2 so 1 /x^2 + + + align:start position:0% +about yal 1X so V is 1/x^2 so 1 /x^2 +is just one over this quantity so it's + + align:start position:0% +is just one over this quantity so it's + + + align:start position:0% +is just one over this quantity so it's +the reciprocal of this it's also -1 time + + align:start position:0% +the reciprocal of this it's also -1 time + + + align:start position:0% +the reciprocal of this it's also -1 time +negative 1 +un 5 over2 you can check + + align:start position:0% +negative 1 +un 5 over2 you can check + + + align:start position:0% +negative 1 +un 5 over2 you can check +that if you need to but I will write it + + align:start position:0% +that if you need to but I will write it + + + align:start position:0% +that if you need to but I will write it +down this way as the following this is + + align:start position:0% +down this way as the following this is + + + align:start position:0% +down this way as the following this is +the point 1 comma + + align:start position:0% +the point 1 comma + + + align:start position:0% +the point 1 comma +a and if I come over here I will I will + + align:start position:0% +a and if I come over here I will I will + + + align:start position:0% +a and if I come over here I will I will +denote a will equal -1 + < TK 5/ 2 and + + align:start position:0% +denote a will equal -1 + < TK 5/ 2 and + + + align:start position:0% +denote a will equal -1 + < TK 5/ 2 and +that's really just 1 / x^2 so let me + + align:start position:0% +that's really just 1 / x^2 so let me + + + align:start position:0% +that's really just 1 / x^2 so let me +point that out again that a is equal to + + align:start position:0% +point that out again that a is equal to + + + align:start position:0% +point that out again that a is equal to +1 / + + align:start position:0% +1 / + + + align:start position:0% +1 / +x^2 at at the point of intersection + + align:start position:0% + + + + align:start position:0% + +so hopefully you can see all that so + + align:start position:0% +so hopefully you can see all that so + + + align:start position:0% +so hopefully you can see all that so +that tells us our bounds completely we + + align:start position:0% +that tells us our bounds completely we + + + align:start position:0% +that tells us our bounds completely we +still have some work to do so I'm going + + align:start position:0% +still have some work to do so I'm going + + + align:start position:0% +still have some work to do so I'm going +to put in the bounds and I'm going to + + align:start position:0% +to put in the bounds and I'm going to + + + align:start position:0% +to put in the bounds and I'm going to +leave an empty space and then we'll come + + align:start position:0% +leave an empty space and then we'll come + + + align:start position:0% +leave an empty space and then we'll come +actually no I won't do that because + + align:start position:0% +actually no I won't do that because + + + align:start position:0% +actually no I won't do that because +that's is this can get a little messy + + align:start position:0% +that's is this can get a little messy + + + align:start position:0% +that's is this can get a little messy +and confusing so I'm just going to do + + align:start position:0% +and confusing so I'm just going to do + + + align:start position:0% +and confusing so I'm just going to do +the Jacobian and then we'll figure it + + align:start position:0% +the Jacobian and then we'll figure it + + + align:start position:0% +the Jacobian and then we'll figure it +all out and write the answer right at + + align:start position:0% +all out and write the answer right at + + + align:start position:0% +all out and write the answer right at +the end so there's no confusion but + + align:start position:0% +the end so there's no confusion but + + + align:start position:0% +the end so there's no confusion but +hopefully you see at this point that we + + align:start position:0% +hopefully you see at this point that we + + + align:start position:0% +hopefully you see at this point that we +have the bounds we know that U goes from + + align:start position:0% +have the bounds we know that U goes from + + + align:start position:0% +have the bounds we know that U goes from +1 to 1 over V us V and V goes from Z up + + align:start position:0% +1 to 1 over V us V and V goes from Z up + + + align:start position:0% +1 to 1 over V us V and V goes from Z up +to a where a is the value I've written + + align:start position:0% +to a where a is the value I've written + + + align:start position:0% +to a where a is the value I've written +here so we know the bounds so now we + + align:start position:0% +here so we know the bounds so now we + + + align:start position:0% +here so we know the bounds so now we +have to figure out the + + align:start position:0% +have to figure out the + + + align:start position:0% +have to figure out the +integrant so let's first compute the + + align:start position:0% +integrant so let's first compute the + + + align:start position:0% +integrant so let's first compute the +Jacobian + + align:start position:0% +Jacobian + + + align:start position:0% +Jacobian +okay so now we're looking at D + + align:start position:0% +okay so now we're looking at D + + + align:start position:0% +okay so now we're looking at D +UV D XY using the notation we we've seen + + align:start position:0% +UV D XY using the notation we we've seen + + + align:start position:0% +UV D XY using the notation we we've seen +in class and so D UV dxy is going to be + + align:start position:0% +in class and so D UV dxy is going to be + + + align:start position:0% +in class and so D UV dxy is going to be +the determinant of the following Matrix + + align:start position:0% +the determinant of the following Matrix + + + align:start position:0% +the determinant of the following Matrix +2X -2 Y and then the derivative respect + + align:start position:0% +2X -2 Y and then the derivative respect + + + align:start position:0% +2X -2 Y and then the derivative respect +to V of X is- y over x^2 and the + + align:start position:0% +to V of X is- y over x^2 and the + + + align:start position:0% +to V of X is- y over x^2 and the +derivative V with respect to Y is just 1 + + align:start position:0% +derivative V with respect to Y is just 1 + + + align:start position:0% +derivative V with respect to Y is just 1 +overx so if I take that the if I take + + align:start position:0% +overx so if I take that the if I take + + + align:start position:0% +overx so if I take that the if I take +the determinant of that I get + + align:start position:0% +the determinant of that I get + + + align:start position:0% +the determinant of that I get +two + + align:start position:0% +two + + + align:start position:0% +two +minus 2 y^2 over + + align:start position:0% +minus 2 y^2 over + + + align:start position:0% +minus 2 y^2 over +x^2 which if you notice in terms of our + + align:start position:0% +x^2 which if you notice in terms of our + + + align:start position:0% +x^2 which if you notice in terms of our +change of variables is exactly equal to + + align:start position:0% +change of variables is exactly equal to + + + align:start position:0% +change of variables is exactly equal to +2 - 2 V + + align:start position:0% +2 - 2 V + + + align:start position:0% +2 - 2 V +uh s because V is + + align:start position:0% +uh s because V is + + + align:start position:0% +uh s because V is +YX and so I can rewrite this as 2 * + + align:start position:0% +YX and so I can rewrite this as 2 * + + + align:start position:0% +YX and so I can rewrite this as 2 * +thean 1 minus + + align:start position:0% +thean 1 minus + + + align:start position:0% +thean 1 minus +v^2 okay so so far so good + + align:start position:0% +v^2 okay so so far so good + + + align:start position:0% +v^2 okay so so far so good +hopefully now let's figure + + align:start position:0% +hopefully now let's figure + + + align:start position:0% +hopefully now let's figure +out let's figure out how to do the final + + align:start position:0% +out let's figure out how to do the final + + + align:start position:0% +out let's figure out how to do the final +step so the final step I want to I'm + + align:start position:0% +step so the final step I want to I'm + + + align:start position:0% +step so the final step I want to I'm +going to come back over and just remind + + align:start position:0% +going to come back over and just remind + + + align:start position:0% +going to come back over and just remind +us what the integram was okay if we come + + align:start position:0% +us what the integram was okay if we come + + + align:start position:0% +us what the integram was okay if we come +over here we're reminded that we were + + align:start position:0% +over here we're reminded that we were + + + align:start position:0% +over here we're reminded that we were +integrating over the region R of 1x^2 DX + + align:start position:0% +integrating over the region R of 1x^2 DX + + + align:start position:0% +integrating over the region R of 1x^2 DX +Dy right that's what we were interested + + align:start position:0% +Dy right that's what we were interested + + + align:start position:0% +Dy right that's what we were interested +in initially so now if we come back I'm + + align:start position:0% +in initially so now if we come back I'm + + + align:start position:0% +in initially so now if we come back I'm +going to write that down just to have it + + align:start position:0% +going to write that down just to have it + + + align:start position:0% +going to write that down just to have it +as a + + align:start position:0% + + + + align:start position:0% + +reference okay that's what we had + + align:start position:0% +reference okay that's what we had + + + align:start position:0% +reference okay that's what we had +initially me make sure yes that's what + + align:start position:0% +initially me make sure yes that's what + + + align:start position:0% +initially me make sure yes that's what +we had initially and so now we know DX + + align:start position:0% +we had initially and so now we know DX + + + align:start position:0% +we had initially and so now we know DX +Dy is equal to Du 2 + + align:start position:0% +Dy is equal to Du 2 + + + align:start position:0% +Dy is equal to Du 2 +DV over 2 * 1 - V ^ 2 so that is going + + align:start position:0% +DV over 2 * 1 - V ^ 2 so that is going + + + align:start position:0% +DV over 2 * 1 - V ^ 2 so that is going +to replace the dxdy and now we have to + + align:start position:0% +to replace the dxdy and now we have to + + + align:start position:0% +to replace the dxdy and now we have to +figure out what to do with the 1/x^2 + + align:start position:0% +figure out what to do with the 1/x^2 + + + align:start position:0% +figure out what to do with the 1/x^2 +but what do we have here we have now I + + align:start position:0% +but what do we have here we have now I + + + align:start position:0% +but what do we have here we have now I +have to remind myself I can't remember + + align:start position:0% +have to remind myself I can't remember + + + align:start position:0% +have to remind myself I can't remember +all the steps anymore we have oh U is + + align:start position:0% +all the steps anymore we have oh U is + + + align:start position:0% +all the steps anymore we have oh U is +equal to x^2 minus + + align:start position:0% +equal to x^2 minus + + + align:start position:0% +equal to x^2 minus +y^2 let me come back now I've forgotten + + align:start position:0% +y^2 let me come back now I've forgotten + + + align:start position:0% +y^2 let me come back now I've forgotten +what I was doing + + align:start position:0% + + + + align:start position:0% + +ah yes now I remember + + align:start position:0% +ah yes now I remember + + + align:start position:0% +ah yes now I remember +sorry okay so the point I should have + + align:start position:0% +sorry okay so the point I should have + + + align:start position:0% +sorry okay so the point I should have +should have remembered that I forgot is + + align:start position:0% +should have remembered that I forgot is + + + align:start position:0% +should have remembered that I forgot is +that 1 - v^2 is equal to U / x^2 that's + + align:start position:0% +that 1 - v^2 is equal to U / x^2 that's + + + align:start position:0% +that 1 - v^2 is equal to U / x^2 that's +what I had figured out earlier that I + + align:start position:0% +what I had figured out earlier that I + + + align:start position:0% +what I had figured out earlier that I +just forgot when I was staring at the + + align:start position:0% +just forgot when I was staring at the + + + align:start position:0% +just forgot when I was staring at the +board and to to notice that what do we + + align:start position:0% +board and to to notice that what do we + + + align:start position:0% +board and to to notice that what do we +have to remember U is x^2 minus y^2 so + + align:start position:0% +have to remember U is x^2 minus y^2 so + + + align:start position:0% +have to remember U is x^2 minus y^2 so +if I divide everything by x s the first + + align:start position:0% +if I divide everything by x s the first + + + align:start position:0% +if I divide everything by x s the first +term is one and the second term is v^2 + + align:start position:0% +term is one and the second term is v^2 + + + align:start position:0% +term is one and the second term is v^2 +so that's good so I was a little nervous + + align:start position:0% +so that's good so I was a little nervous + + + align:start position:0% +so that's good so I was a little nervous +there for a second but I did in fact do + + align:start position:0% +there for a second but I did in fact do + + + align:start position:0% +there for a second but I did in fact do +this earlier and I'd forgotten what I + + align:start position:0% +this earlier and I'd forgotten what I + + + align:start position:0% +this earlier and I'd forgotten what I +what I did so now the 1us v^2 is + + align:start position:0% +what I did so now the 1us v^2 is + + + align:start position:0% +what I did so now the 1us v^2 is +actually the same as U / + + align:start position:0% +actually the same as U / + + + align:start position:0% +actually the same as U / +x^2 and notice what that does to this + + align:start position:0% +x^2 and notice what that does to this + + + align:start position:0% +x^2 and notice what that does to this +term here that tells us that + + align:start position:0% +term here that tells us that + + + align:start position:0% +term here that tells us that +dxdy dxdy over + + align:start position:0% +dxdy dxdy over + + + align:start position:0% +dxdy dxdy over +x^2 is actually equal to Du + + align:start position:0% +x^2 is actually equal to Du + + + align:start position:0% +x^2 is actually equal to Du +DV over well if I instead of the instead + + align:start position:0% +DV over well if I instead of the instead + + + align:start position:0% +DV over well if I instead of the instead +of the one over V or 1 - V ^2 I put U + + align:start position:0% +of the one over V or 1 - V ^2 I put U + + + align:start position:0% +of the one over V or 1 - V ^2 I put U +over x^2 I get notice I get an x^2 * 2 U + + align:start position:0% +over x^2 I get notice I get an x^2 * 2 U + + + align:start position:0% +over x^2 I get notice I get an x^2 * 2 U +/ X + + align:start position:0% +/ X + + + align:start position:0% +/ X +squ right I just replace the 1us v^2 + + align:start position:0% +squ right I just replace the 1us v^2 + + + align:start position:0% +squ right I just replace the 1us v^2 +with what I know it is the X squs divide + + align:start position:0% +with what I know it is the X squs divide + + + align:start position:0% +with what I know it is the X squs divide +out and so I get + + align:start position:0% +out and so I get + + + align:start position:0% +out and so I get +duv over 2 + + align:start position:0% +duv over 2 + + + align:start position:0% +duv over 2 +U so now the good news is I have all the + + align:start position:0% +U so now the good news is I have all the + + + align:start position:0% +U so now the good news is I have all the +pieces because I'm about to run out of + + align:start position:0% +pieces because I'm about to run out of + + + align:start position:0% +pieces because I'm about to run out of +board space so I have all the pieces so + + align:start position:0% +board space so I have all the pieces so + + + align:start position:0% +board space so I have all the pieces so +I'm just going to put them together and + + align:start position:0% +I'm just going to put them together and + + + align:start position:0% +I'm just going to put them together and +then we're done so let me come here in + + align:start position:0% +then we're done so let me come here in + + + align:start position:0% +then we're done so let me come here in +the final spot and this is our this is + + align:start position:0% +the final spot and this is our this is + + + align:start position:0% +the final spot and this is our this is +our final + + align:start position:0% +our final + + + align:start position:0% +our final +answer our final answer is that we're + + align:start position:0% +answer our final answer is that we're + + + align:start position:0% +answer our final answer is that we're +integrating U from + + align:start position:0% +integrating U from + + + align:start position:0% +integrating U from +one to 1 over V minus V and then we're + + align:start position:0% +one to 1 over V minus V and then we're + + + align:start position:0% +one to 1 over V minus V and then we're +integrating V from zero to a where a is + + align:start position:0% +integrating V from zero to a where a is + + + align:start position:0% +integrating V from zero to a where a is +the value I determined earlier + + align:start position:0% +the value I determined earlier + + + align:start position:0% +the value I determined earlier +of 1 over 2 U + + align:start position:0% +of 1 over 2 U + + + align:start position:0% +of 1 over 2 U +duv so this is the final final answer + + align:start position:0% +duv so this is the final final answer + + + align:start position:0% +duv so this is the final final answer +this was a long one and I'm sorry I had + + align:start position:0% +this was a long one and I'm sorry I had + + + align:start position:0% +this was a long one and I'm sorry I had +a little brain freeze in the middle I + + align:start position:0% +a little brain freeze in the middle I + + + align:start position:0% +a little brain freeze in the middle I +couldn't remember how I'd fixed that + + align:start position:0% +couldn't remember how I'd fixed that + + + align:start position:0% +couldn't remember how I'd fixed that +problem so what I what I did at that + + align:start position:0% +problem so what I what I did at that + + + align:start position:0% +problem so what I what I did at that +point I just want to point out that when + + align:start position:0% +point I just want to point out that when + + + align:start position:0% +point I just want to point out that when +I was working on this problem and I had + + align:start position:0% +I was working on this problem and I had + + + align:start position:0% +I was working on this problem and I had +a 1 minus v^2 I knew somehow I had to + + align:start position:0% +a 1 minus v^2 I knew somehow I had to + + + align:start position:0% +a 1 minus v^2 I knew somehow I had to +figure out how to relate that and the X + + align:start position:0% +figure out how to relate that and the X + + + align:start position:0% +figure out how to relate that and the X +squ in terms of u and v and so I + + align:start position:0% +squ in terms of u and v and so I + + + align:start position:0% +squ in terms of u and v and so I +actually saw this expression I could + + align:start position:0% +actually saw this expression I could + + + align:start position:0% +actually saw this expression I could +have written it better maybe as x^2 time + + align:start position:0% +have written it better maybe as x^2 time + + + align:start position:0% +have written it better maybe as x^2 time +this equals U okay maybe that would have + + align:start position:0% +this equals U okay maybe that would have + + + align:start position:0% +this equals U okay maybe that would have +been more obvious that that's the case + + align:start position:0% +been more obvious that that's the case + + + align:start position:0% +been more obvious that that's the case +but that was really the step that + + align:start position:0% +but that was really the step that + + + align:start position:0% +but that was really the step that +allowed me to replace all of this by + + align:start position:0% +allowed me to replace all of this by + + + align:start position:0% +allowed me to replace all of this by +things in terms of u and v which I know + + align:start position:0% +things in terms of u and v which I know + + + align:start position:0% +things in terms of u and v which I know +I should have been able to do it's just + + align:start position:0% +I should have been able to do it's just + + + align:start position:0% +I should have been able to do it's just +a matter of figuring it out so let me + + align:start position:0% +a matter of figuring it out so let me + + + align:start position:0% +a matter of figuring it out so let me +just go back to the beginning remind you + + align:start position:0% +just go back to the beginning remind you + + + align:start position:0% +just go back to the beginning remind you +of each of the steps very briefly and + + align:start position:0% +of each of the steps very briefly and + + + align:start position:0% +of each of the steps very briefly and +then we'll be + + align:start position:0% +then we'll be + + + align:start position:0% +then we'll be +done so if we come back over to the + + align:start position:0% +done so if we come back over to the + + + align:start position:0% +done so if we come back over to the +beginning we were starting with change + + align:start position:0% +beginning we were starting with change + + + align:start position:0% +beginning we were starting with change +of variables supplied for us we already + + align:start position:0% +of variables supplied for us we already + + + align:start position:0% +of variables supplied for us we already +had an integral in terms of X and Y and + + align:start position:0% +had an integral in terms of X and Y and + + + align:start position:0% +had an integral in terms of X and Y and +we had an infinite region and what we + + align:start position:0% +we had an infinite region and what we + + + align:start position:0% +we had an infinite region and what we +were asked to do is find the limits in + + align:start position:0% +were asked to do is find the limits in + + + align:start position:0% +were asked to do is find the limits in +integrand so the first step for me what + + align:start position:0% +integrand so the first step for me what + + + align:start position:0% +integrand so the first step for me what +I always find helpful is I always find + + align:start position:0% +I always find helpful is I always find + + + align:start position:0% +I always find helpful is I always find +it very helpful to draw the region in + + align:start position:0% +it very helpful to draw the region in + + + align:start position:0% +it very helpful to draw the region in +the XY plane and then draw the new + + align:start position:0% +the XY plane and then draw the new + + + align:start position:0% +the XY plane and then draw the new +region in the UV plane neither one of + + align:start position:0% +region in the UV plane neither one of + + + align:start position:0% +region in the UV plane neither one of +them has to be perfect but the + + align:start position:0% +them has to be perfect but the + + + align:start position:0% +them has to be perfect but the +understanding of the of the values uh of + + align:start position:0% +understanding of the of the values uh of + + + align:start position:0% +understanding of the of the values uh of +the the Curves in terms of equations of + + align:start position:0% +the the Curves in terms of equations of + + + align:start position:0% +the the Curves in terms of equations of +u and v are very important to understand + + align:start position:0% +u and v are very important to understand + + + align:start position:0% +u and v are very important to understand +that that gives you the bounds the + + align:start position:0% +that that gives you the bounds the + + + align:start position:0% +that that gives you the bounds the +limits and then so we did all this work + + align:start position:0% +limits and then so we did all this work + + + align:start position:0% +limits and then so we did all this work +we found the limits there was a little + + align:start position:0% +we found the limits there was a little + + + align:start position:0% +we found the limits there was a little +algebra in the middle we found the + + align:start position:0% +algebra in the middle we found the + + + align:start position:0% +algebra in the middle we found the +limits and then we found the Jacobian + + align:start position:0% +limits and then we found the Jacobian + + + align:start position:0% +limits and then we found the Jacobian +which was going to tell us how the + + align:start position:0% +which was going to tell us how the + + + align:start position:0% +which was going to tell us how the +variables were + + align:start position:0% +variables were + + + align:start position:0% +variables were +changing we found it in terms of X and Y + + align:start position:0% +changing we found it in terms of X and Y + + + align:start position:0% +changing we found it in terms of X and Y +we rewrote it in terms of u and v and so + + align:start position:0% +we rewrote it in terms of u and v and so + + + align:start position:0% +we rewrote it in terms of u and v and so +when we came back and we compared what + + align:start position:0% +when we came back and we compared what + + + align:start position:0% +when we came back and we compared what +our integrant was what our integrand was + + align:start position:0% +our integrant was what our integrand was + + + align:start position:0% +our integrant was what our integrand was +initially we could compare DX Dy to + + align:start position:0% +initially we could compare DX Dy to + + + align:start position:0% +initially we could compare DX Dy to +DV but then we also had to figure out + + align:start position:0% +DV but then we also had to figure out + + + align:start position:0% +DV but then we also had to figure out +how to replace the x s the one overx squ + + align:start position:0% +how to replace the x s the one overx squ + + + align:start position:0% +how to replace the x s the one overx squ +so once we did all that we had + + align:start position:0% +so once we did all that we had + + + align:start position:0% +so once we did all that we had +everything in terms of u and v and then + + align:start position:0% +everything in terms of u and v and then + + + align:start position:0% +everything in terms of u and v and then +we finally had what the integrand was + + align:start position:0% +we finally had what the integrand was + + + align:start position:0% +we finally had what the integrand was +going to be so there were lot of steps + + align:start position:0% +going to be so there were lot of steps + + + align:start position:0% +going to be so there were lot of steps +but this was ultimately what the problem + + align:start position:0% +but this was ultimately what the problem + + + align:start position:0% +but this was ultimately what the problem +was and again I just point out this is + + align:start position:0% +was and again I just point out this is + + + align:start position:0% +was and again I just point out this is +the final solution right here we + + align:start position:0% +the final solution right here we + + + align:start position:0% +the final solution right here we +integrated from one to 1 over V minus V + + align:start position:0% +integrated from one to 1 over V minus V + + + align:start position:0% +integrated from one to 1 over V minus V +for d for U and we integrated from 0 to + + align:start position:0% +for d for U and we integrated from 0 to + + + align:start position:0% +for d for U and we integrated from 0 to +a in V the function 1 over 2 + + align:start position:0% +a in V the function 1 over 2 + + + align:start position:0% +a in V the function 1 over 2 +U okay that is where I will stop \ No newline at end of file diff --git a/GqVQTRb-QoA.txt b/GqVQTRb-QoA.txt new file mode 100644 index 0000000000000000000000000000000000000000..6b7583fcfcee836f803f504e377c034671d51d26 --- /dev/null +++ b/GqVQTRb-QoA.txt @@ -0,0 +1,1687 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation, or to view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: Hi. + +Our lecture today is called +'Rolle's Theorem and Its + +Consequences'. + +And I suppose we could've made +a take off on what goes up + +must come down, and say that +what Rolle's theorem says + +intuitively is that what goes +up smoothly and comes down + +smoothly must level +off somewhere. + +OK? + +Now because that may sound too +easy to understand, let's + +cloak that in the language of +more formal mathematics. + +Rolle's theorem says this. + +Let 'f' be defined and +continuous on the closed + +interval from 'a' to 'b'. + +In other words, what? + +The domain of 'f' is the closed + +interval from 'a' to 'b'. + +The graph of 'f' is unbroken +on this interval. + +And differentiable in the open +interval from 'a' to 'b'. + +In other words, you want the +function to be continuous on + +the entire interval, but for +differentiability, you only + +require that it be smooth, +differentiable, in the + +interior of the interval, +in the open interval. + +Suppose also that 'f of +a' and 'f of b' are 0. + +Then, what Rolle's theorem says +is that 'f prime of c', + +the derivative of 'f of x', must +be 0 for some number 'c', + +at least one number +'c', in the open + +interval from 'a' to 'b'. + +Now what this thing says +intuitively is simply this, + +suppose you have a curve that is +unbroken for all values of + +'x' between 'a' and +'b' inclusively. + +Suppose the curve is smooth. + +Suppose the curve starts here +and ends here, then what we're + +saying is there must be some +point in here where the curve + +levels off. + +In other words, someplace where +you have a horizontal + +tangent, which is what 'f prime +of c' equals 0 means. + +In this particular diagram, this +would be the value of 'c' + +that we're talking about. + +By the way, I think the proof +is intuitively clear. + +Namely, if the curve never +leaves the x-axis, then it's + +leveled off for the +entire domain. + +And if the curve does leave the +x-axis, for example, if + +the curve starts to rise, OK, +since it must eventually get + +back to the x-axis when 'b' is +0, it must ultimately begin to + +fall again. + +Well, if the curve goes from +rising to falling, + +it must have what? + +Since it's coming up and then +going down, it must attain a + +maximum value. + +Because the curve is unbroken +and smooth, as we saw in our + +previous lecture, the maximum +value is characterized by the + +derivative at that +point being 0. + +In fact, the analytic proof is +precisely what we've just + +said, only translated into more +mathematical language. + +By the way, I would like to +make a slight aside here, + +because I think it sometimes +gets confusing to students to + +see, why do you say that the +function has to be continuous + +on the closed interval, but +differentiable only in the + +open interval? + +I thought you might like to see +a contrived example as to + +what goes wrong if you allow the +curve to be broken at the + +end points. + +See, all I'm thinking of +is something like this. + +Suppose I say, look, let's +define a curve as follows. + +At 'x' equals 'a' and +'x' equals 'b', the + +curve will be 0. + +So in other words, it'll +cross the x-axis. + +Then immediately, for 'x' +greater than 'a', the curve + +jumps up to here, comes down +along this line, and then, you + +see, when 'x' equals 'b', it +jumps down here again. + +In other words, why +not let the curve + +be defined as follows? + +It will be 0 at these +two endpoints. + +It'll be this curve on +the open interval. + +Notice in this contrived example +that 'f of a' and 'f + +of b' are both equal to 0, but +there is no place in the open + +interval where the curve has +a horizontal tangent line. + +In other words, the significance +is you've got to + +be sure that the curve doesn't +get broken at the ends, + +because with these gaps, +all sorts of + +crazy things can happen. + +Now, just as in our previous +lecture, there are some rather + +important cautions that have to +be taken in understanding + +Rolle's theorem. + +As simple as it is, we have to +be sure that we understand + +exactly what's really +happening here. + +The first caution is that +Rolle's theorem is what we + +mathematicians call an +'existence theorem'. + +It says, under certain +conditions, there exists at + +least one number 'c' that +has a certain property. + +It doesn't tell us how +many "c's" there are. + +It doesn't tell us where +to find them. + +It just says, what? + +There exists at least +one such 'c'. + +And the point is, you must +be careful to remember-- + +so let's take an example. + +Here's 'a', here's 'b'. + +If the function is continuous +and smooth, in other words, if + +the graph is continuous and +smooth, all we're saying is + +that at least one number between +'a' and 'b', the + +curve, must possess a +horizontal tangent. + +There may be more than one. + +You see, the curve, for +example, could do + +something like this. + +See, in other words, here is one +value of 'c', which we'll + +call 'c1', horizontal +tangent here. + +Here's another value, which +we'll call 'c2', horizontal + +tangent here. + +See, again, the meaning +of at least one. + +Secondly, we must make sure +that we remember that the + +curve is smooth. + +Meaning what? + +That the function is +differentiable. + +Now I'm taking the liberty +of drawing + +these things in freehand. + +There's some mixed emotions +here, if I draw the diagrams + +too smoothly all the time, you +lose the significance of + +what's going on because +of the picture. + +And if I draw them freehand +all the time, you won't + +understand what I'm +doing, because I + +don't draw very well. + +But I think here we can +get away with this. + +What I'm driving at is this. + +Let's suppose you have +'a' and 'b' here. + +Let's suppose that the function, +the curve that we're + +drawing, passes through +these two points. + +But suppose there happens to +be a sharp corner in here. + +Maybe the curve goes like this, +it goes up like this, + +then very abruptly comes +down like this. + +Notice, what? + +That the curve is continuous. + +It does reach a local maximum. + +But the point is, for this +particular value of 'c', 'f + +prime of c' is not +0 by default. + +Namely, 'f prime of c' +doesn't even exist. + +So in other words, Rolle's +theorem doesn't apply if you + +don't have differentiabilities. + +I want to make sure you see +where each of the parts of the + +hypotheses for the +theorem are used. + +By the way, here's another +interesting result, which has + +nothing to do with the statement +of the theorem, but + +again, another piece of evidence +as to why we like to + +shy away from functions which +are not single value. + +See, for example, suppose you +allowed the function to be + +multivalued, and you say, OK, +I want the curve to pass + +through here and here. + +And I want it to be smooth. + +But the curve does not have +to be single value. + +Notice what you can do. + +You could have a curve that +does something like this. + +I don't know. + +Now you see, there will be +a point 'c' where the + +derivative will be 0. + +Even as badly as I've drawn +this, I think roughly + +speaking, we can see that 'c' +would be something like this. + +Notice, however, that in +Rolle's theorem, the + +statement is what? + +That 'c' must be on the open +interval from 'a' to 'b'. + +If the function is not single +value, as long as the curve is + +smooth, there will be places +where the curve levels off. + +But the x-coordinate of the +point at which the curve + +levels off may not be +in the interval-- + +may not be, it could be, but +it might not be, I should + +say-- in the open interval +from 'a' to 'b'. + +This is a very, very +important result. + +In fact, I'll have reason to +make reference to this in a + +little while later +in the lecture. + +I couldn't make reference to +it later earlier in the + +lecture, I guess. + +The fourth assumption here is +also an aside, and it's one + +that's rather crucial. + +In most textbooks in which +Rolle's theorem is stated, the + +condition is what? + +That 'f of a' equals +'f of b' equals 0. + +It turns out that this is too +restrictive, that essentially, + +all you need is 'f of +a' equals 'f of b'. + +What I mean by that is, let's +suppose 'f of a' is not 0. + +Let's suppose this height +represents 'f of a'. + +What I'm saying is suppose +that 'f of a' and + +'f of b' are equal. + +What that means is, if I want to +think of a new axis, which + +I call the 'x sub 1' axis-- + +see, with respect to the 'x sub +1' axis, the curve crosses + +the axis at these two points. + +In other words, notice that as +long as these two points are + +at the same level, the same +argument that we used to prove + +Rolle's theorem goes through +unimpeded over here. + +Namely, we say what? + +What goes up smoothly and +comes down smoothly-- + +because it has to come down, +because it comes back to the + +same level here-- must reach a +point someplace in here where + +it levels off. + +So these are the four cautions +that I'd like you to look at + +when we view Rolle's theorem. + +Now, if somebody were to say +to us, what's so important + +about Rolle's theorem? + +And this happens so often in +mathematics that frequently, + +the most important thing about +one particular theorem, is + +that it may be the building +block by which a more + +important, or more +useful, or more + +practical theorem is derived. + +And in this respect, I would say +for my own opinion, that + +the most important application +of Rolle's theorem is that it + +facilitates a very famous result +known as the 'Mean + +Value theorem'. + +As our course proceeds, from +time to time we will have + +ample reason to back track and +make references to the mean + +value theorem. + +I intend not to make too deep +references to the mean value + +theorem now, because what +I would like to do is to + +establish the result, give you +enough of an intuitive feeling + +so that you can tuck it under +your belt without feeling too + +overwhelmed by it, and just +enough applications of it so + +that we can get into the next +phase of our calculus course. + +But the mean value theorem is +another one of these things + +where if you state the thing +analytically, and have no + +feeling for what's going on +pictorially, the thing can + +become overwhelming. + +Let's, in fact, do it in an +overwhelming way, and then + +show what the thing +means pictorially. + +Notice again how this thing now +starts off the same way as + +Rolle's theorem. + +Let 'f' be continuous on the +closed interval from 'a' to + +'b', and differentiable in the +open interval from 'a' to 'b'. + +By the way, this is just an +idiosyncrasy of mine, I don't + +know if it's standard. + +When I talk about the closed +interval, I have the habit of + +saying 'on' the interval. + +When I talk about the open +interval, I like to say 'in' + +the interval, to sort of +emphasize the interior. + +It's just a vocabulary +trait, and don't read + +too much into this. + +Don't be upset by it. + +But it's continuous on +the closed interval, + +differentiable in the +open interval. + +Now it's again an existence +theorem. + +It says then there exists +a number 'c'. + +When I say there exists, +it means what? + +There is at least one number 'c' +in the open interval from + +'a' to 'b'-- + +and this is the part that +looks kind of tough-- + +such that ''f of b' minus 'f of +a'' divided by 'b - a' is + +'f prime of c'. + +And this somehow or other may +seem at first glance to be + +more ominous than the intuitive +feeling about + +Rolle's theorem. + +By the way, as the name implies, +where by 'mean' we + +don't mean nasty, we mean +average, if you'd like to see + +what this thing means, and I'll +draw you a picture in a + +second, all it says is that if +a particle is moving from + +point 'a' to point 'b', say, at +at least one point during + +its trip, the instantaneous +speed must + +equal the average speed. + +You see? + +Because after all, if you're +always going less than your + +average speed, how could you +have had an average speed as + +high as your average speed? + +And if you're always going less +than your average speed, + +how could you have had, you see, +an average speed equaling + +this, what it did? + +So that somehow or other, all +you're saying is that somehow + +or other, the instantaneous +speed at a particular instance + +must equal your average speed +someplace along the path. + +Now what that means pictorially +is this-- + +again, I'll chance a +freehand diagram-- + +suppose our curve is 'y' +equals 'f of x'. + +See, I've drawn it +to be smooth. + +Suppose it's continuous and +smooth on this open interval + +from 'a' to 'b'. + +Now what is, if I think of a +particle moving from point 'p' + +to point 'q', how do I identify +the average speed? + +The average speed is the slope +of the straight line that + +joins 'p' to 'q'. + +On the other hand, what is +the instantaneous speed? + +If we think of it in terms of +the picture, it's the slope of + +the line tangent to the curve +at a particular point. + +So in other words, what +we're saying is this. + +You see, if we were to take the +line 'PQ', and we shift it + +parallel to itself, I think you +can sense that the points + +'P' and 'Q', if we labeled 'P' +and 'Q' the points at which + +this chord intersects the curve, +the points 'P' and 'Q' + +will roll in closer and +closer together. + +Ultimately, the line will fail +to intersect the curve, and at + +the transition point, if the +curve is smooth, all we're + +saying is that the last point at +which that line touches the + +curve as we move it out, OK, +that the line would be tangent + +to the curve at that +particular point. + +You see, all we're +saying is what? + +That someplace between here and +here there must be a point + +where the tangent line to +the curve is parallel + +to the chord 'PQ'. + +And now, we have all the +ingredients that we need to + +see what the mean value theorem +says geometrically. + +Let's call the tangent +line 'l'. + +First of all, what is the +slope of the line 'PQ'? + +Well, it's a straight line. + +The slope of a straight +line is 'delta y' + +divided by 'delta x'. + +Well, notice that this +height here is by + +definition 'f of b'. + +This height here is 'f of a'. + +So this height here is just +'f of b' minus 'f of a'. + +This length here is +just 'b - a'. + +So the slope, 'delta y' divided +by 'delta x', is just + +''f of b' minus 'f of +a'', over 'b - a'. + +On the other hand, what is the +slope of the line 'l'? + +By definition, it's 'f prime of +x' evaluated at 'x' equals + +'c', that's 'f prime of c'. + +Now what does it mean in +terms of slopes for + +two lines to be parallel? + +It means that their +slopes are equal. + +And where is 'c'? + +'c' is someplace in the open +interval from 'a' to 'b'. + +Now the reason I call this +intuitively an extension of + +Rolle's theorem-- + +and by the way, you'll notice +that what I have to say is a + +much simpler demonstration than +what's given in the book. + +But before you think I'm being +egotistic about this, let me + +point out, as is so often the +case that wherever my + +demonstrations are easier than +the one in the book, I'm + +losing something in +my presentation. + +Either I haven't shown the most +analytic representation, + +or I'm overlooking a particular +complicated side + +effect that might occur. + +But disregarding that for the +moment, you see what I'm + +saying is this, let's suppose, +for the sake of argument, we + +visualize the line 'PQ' as +being our new x-axis. + +I'll call that the x1-axis. + +And now let's take a line +perpendicular to 'PQ' and call + +that our new y-axis, +the y1-axis. + +Now look at the curve +that we've drawn. + +With respect to the y1- x1-axis, +notice that the curve + +is smooth, right? + +It's unbroken. + +And it cuts the x1-axis +at two points. + +Now if we apply Rolle's theorem +with respect to the + +x1- y1-axis, we say, look, +here's a curve + +which cuts the x-axis-- + +the x1-axis-- + +at two points. + +It's smooth. + +Therefore, it must level +off someplace. + +In other words, there must be +some point on this curve where + +the tangent line to the curve +is parallel to the x1-axis. + +That's exactly, you see, what +this thing here says. + +That's another geometric +interpretation that indicates + +how Rolle's theorem +might be used. + +However, there is a very, very +subtle flaw in what I've said. + +One that is so subtle that you +may not even notice it until I + +point it out to you, and even +after I point it out, there's + +a chance you may not realize +what I've said. + +Because it's a point that I know +took me a long, long time + +to discover for myself. + +And it all hinges on +the concept of + +single valuedness again. + +The trouble with this +interpretation is the + +following-- + +and by the way, let me point +out, I'm not knocking my + +interpretation, I think it's +still a tremendous way of + +visualizing the result, but from +an analytical point of + +view, why we have +to be careful. + +Let's suppose that my curve 'y' +equals 'f of x' happens to + +look something like this, OK? + +Happens to look something +like this. + +Notice, barring any bad drawing +that I've done here, + +that this curve is single value, +that no line parallel + +to the y-axis cuts this curve +in more than one place. + +Now here's my 'a' and +here's my 'b'. + +And so I say, OK, by Rolle's +theorem, if I look at this as + +being the x-axis and this +as being the y-axis-- + +in other words, the x1- +y1-axis again-- + +I say to myself, look, here's +a smooth curve, it cuts the + +x-axis in two points, therefore, +someplace between + +these two points, there must +be a place where the curve + +levels off, et cetera, +et cetera, et cetera. + +And the interesting point is to +notice that a given curve, + +as to whether it's single valued +or not, is dependent + +upon the orientation +of the axes. + +In other words, notice that +I've drawn this particular + +curve so it is single valued +with respect to the xy-plane. + +On the other hand, with +respect to the x1- + +y1-coordinate system, this curve +is not single valued. + +Namely, observe how a line +parallel to the y1-axis can + +intersect this curve at +more than one point. + +In other words, whether a curve +is single valued or not + +is not an absolute property +independent of + +the coordinate system. + +So again, if I could be sure +that when I rotated my + +coordinate axes the original +single valued curve was still + +single valued, then +my above proof + +would have been rigorous. + +But of course, I can't +be sure of that. + +By the way, the technique used +in the book is quite standard, + +and what it does is the +following, it still utilizes + +Rolle's theorem, but the +technique behind the proof in + +the book is this. + +The function that we set up is +the vertical distance between + +the chord and the curve, as +we move along this way. + +And notice that that distance +is 0 at these two endpoints. + +OK? + +And therefore, Rolle's theorem +applies to that function. + +And the whole idea is +something like this. + +All we say is-- + +and the analytic part +proves this-- + +all we say is look, the point at +which this chord would have + +been tangent to the curve is the +place where the vertical + +distance between the chord +and the curve is what? + +Maximum. + +And we won't go into that +right now, that + +is done in the text. + +All I wanted to do, as I always +will do when possible, + +is that whenever the rigorous +proof seems far more + +complicated than proofs which +are more intuitive, I will not + +take the time in general, in our +lectures, to give the more + +rigorous proof. + +What I will take the time to +do is to show why the less + +rigorous proof has pitfalls. + +Well, enough said about +the statement of + +the mean value theorem. + +Time is getting very short, and +we don't need much more + +time to make the home run +ball pitch that we + +want to make now. + +And the idea is this, that the +most important analytical + +reason for having the mean value +theorem is, for those of + +us who like to use our geometric +intuition, it turns + +out that almost every +geometrically obvious fact + +that has a proper analytic +counterpart has the property + +that the analytic counterpart +is proven by + +the mean value theorem. + +See, let me give you a +simple for instance. + +In fact, in the text book this +is called the first corollary + +to the mean value theorem. + +Suppose we have a function +capital 'F of x', and we know + +that the derivative is +always equal to 0. + +The claim is that 'F of x' +itself must be a constant. + +By the way, two cautions here. + +Don't say that we've had +this result before. + +The result that we had +before was actually + +the converse of this. + +The result that we had before +was the one that said what? + +If 'F of x' is a constant, +then its derivative is 0. + +Now we're saying the +opposite--not the opposite, + +but the converse. + +Now we're saying, look, if the +derivative is always 0-- + +notice the use of my identity +symbol here-- + +if the derivative is 0 for all +values of 'x', then the + +function must've been +a constant. + +Now, you know, geometrically +this is a very + +simple thing to visualize. + +You say, look, the derivative +is the slope. + +And if you're saying that the +slope of the curve is always + +horizontal, the curve itself +must be a straight line. + +And if the curve is a straight +line, that's exactly what you + +mean by saying that the function +is a constant. + +How do we prove this using +the mean value theorem? + +See, and I just wanted to go +through a proof here once, + +just so to get the idea +of what a proof means. + +You see, to show that +something is a + +constant should mean what? + +That if 'a' is unequal to 'b' +for any two values 'a' and + +'b', 'F of a'-- + +well, I'm using capital 'F' +here--capital 'F of a' has to + +equal capital 'F of b'. + +That's what you mean for a +function to be a constant. + +No matter what the input is, the +outputs are always equal. + +By the way, if 'a' equals 'b', +it's trivial that 'F of a' + +equals 'F of b'. + +But essentially, to prove that +capital F is a constant, this + +is what I have to prove. + +That if 'a' is different from +'b', no matter what 'a' and + +'b' I use, that 'F of +a' equals 'F of b'. + +And the idea is by the mean +value theorem, we say, look, + +what does the mean value +theorem say? + +We're assuming now that 'F' +is a continuous and + +differentiable function on an +interval, OK, from 'a' to 'b'. + +The mean value theorem says +under these conditions, there + +exists a number 'c' +between 'a' and + +'b' with what property? + +That ''F of b' minus 'F of a'' +over 'b - a' is equal to 'F + +prime of c'. + +That's just a statement of +the mean value theorem. + +This is always true if the +conditions of the mean value + +theorem apply. + +Now all we're saying is, in this +particular problem, what + +property that capital +'F' have? + +It had the property that +its derivative for all + +values of 'x' was 0. + +In particular then, when 'c' +is the value that we're + +talking about, if 'F prime of x' +is 0 for all values of 'x', + +in particular, then, it's 0 +when 'x' is equal to 'c'. + +In other words, by our given +hypothesis, this is 0. + +But if a fraction is 0, its +numerator must be 0. + +That says what? + +'F of b' minus 'F of a' is 0. + +See, the only way a quotient +can be 0 is for the + +numerator-- + +or the dividend, the divisor, +I don't know these formal + +names, they slipped my mind, but +the top one has to be 0. + +And if 'F of b' minus 'F of a' +is 0, that says 'F of b' + +equals 'F of a', and that's +precisely what we had to show + +to show that 'F' +was a constant. + +OK? + +So again, notice, it's not that +we're saying that the + +mean value theorem is a harder +way of proving what we already + +know to be intuitively true, +what we're saying is what? + +That we know that many +intuitively obvious results + +frequently turn out +to be false. + +We would like some analytical +way of knowing which of the + +intuitive results are +actually correct. + +All I'm saying is the mean value +theorem gives us a big + +hint that way. + +By the way, let me close by +giving you one more important + +illustration of what +we can prove by + +the mean value theorem. + +And this is called a corollary +of a corollary, as I'll show + +you what I mean in a minute. + +The next example that I want to +use is what it means to say + +suppose I'm given two functions +'f' and 'g', and all + +I know about these two +functions is that the + +derivatives are identical. + +In other ways, that 'f' and 'g' +have the property that for + +every value of 'x', 'f +prime of x' is equal + +to 'g prime of x'. + +By the way, when I say every +value of 'x', again, it's + +local versus global. + +It's not necessary that this +happens for all 'x', what is + +important is what? + +That 'x' be defined +on some interval. + +In other words, even if I know +that this property is true for + +some interval, I don't really +care what happens outside of + +that interval. + +In terms of local properties, +all I'm saying is, all I know + +is that for some interval, maybe +the whole axis, doesn't + +make any difference, 'f prime' +is identical to 'g prime'. + +Now, you would like to be able +to say, maybe, that if 'f + +prime' is equal to 'g prime', +'f' equals 'g'. + +But that's not the case. + +What is the case is that the +difference between the two + +functions must be a constant. + +Again, geometrically, what +you're saying is what? + +That if you have two curves, +which point by point always + +have the same slope-- + +in other words, for each +'x' value, the + +slopes are the same-- + +is just essentially +saying that the + +two curves are parallel. + +And if they're parallel curves, +what's a way of + +stating that two curves +are parallel? + +That one is a constant +displacement of the other. + +In other words, the geometric +impact of two curves having + +the same derivative is not that +the curves are the same, + +but that they're parallel. + +And by the way, the proof of +this result is again a + +corollary to the mean +value theorem. + +Namely, let's look at +the function 'f of + +x' minus 'g of x'. + +Call that capital 'F of x'. + +Let capital 'F of x' be ''f +of x' minus 'g of x''. + +Since the derivative of a +difference is the difference + +of the derivatives, that would +say the derivative of capital + +'F' is the derivative +little 'f' minus the + +derivative of 'g'. + +OK? + +Now what do we know about 'f +prime' and 'g prime of x'? + +We know that 'f prime of +x' equals 'g prime + +of x' for all 'x'. + +Consequently, the difference +between these two must be 0. + +Remember, if two functions +are identical, their + +difference is 0. + +That says, therefore, that +capital 'F prime of x' is + +identically 0. + +And by our previous theorem-- + +notice the beautiful +logic of this-- + +from the mean value theorem, +we proved that if the + +derivative of a function is +identically 0, the function + +must be a constant. + +So we apply that here. + +But what was capital 'F'? + +It was 'little 'f - g'. + +And that proves our +desired result. + +Again, what I want you to see +here is that we have not done + +anything different with the +mean value theorem. + +We're not trying to say we're +going to prove results we + +couldn't prove before. + +Rather, what? + +The mean value theorem is our +way of showing that certain + +intuitive results hold true +analytically, that we can talk + +about parallel curves, +and things like this. + +Most important, in terms of +summarizing this lecture from + +a point of view of what's coming +next, it's crucial to + +observe that this last example +is what is going to allow us + +to enter the study of +something called the + +'indefinite integral'. + +Or in another manner of +speaking, something called the + +inverse of taking +a derivative. + +You see, the idea is, notice +that in these two examples we + +start with information about +the derivative and deduce + +what's true about the +original function. + +That's inverting the emphasis +of what we've been doing up + +until now, where we've started +with the function and + +investigated its derivative. + +To see this in more detail, +join me again next time. + +And until next time, goodbye. + +Funding for the publication of +this video was provided by the + +Gabriella and Paul Rosenbaum +Foundation. + +Help OCW continue to provide +free and open access to MIT + +courses by making a donation +at ocw.mit.edu/donate. \ No newline at end of file diff --git a/HanUSsBG-FU.txt b/HanUSsBG-FU.txt new file mode 100644 index 0000000000000000000000000000000000000000..c4f2b01913f36851fec60965d39b9ca6ab7b9591 --- /dev/null +++ b/HanUSsBG-FU.txt @@ -0,0 +1,9027 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT opencourseware continue to + + align:start position:0% +will help MIT opencourseware continue to + + + align:start position:0% +will help MIT opencourseware continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +okay this class class A + + align:start position:0% +okay this class class A + + + align:start position:0% +okay this class class A +uh we're going to talk about this + + align:start position:0% + + + + align:start position:0% + +what happens to that cord whose the + + align:start position:0% +what happens to that cord whose the + + + align:start position:0% +what happens to that cord whose the +development of which we were talking + + align:start position:0% +development of which we were talking + + + align:start position:0% +development of which we were talking +about last time so we're going to look + + align:start position:0% +about last time so we're going to look + + + align:start position:0% +about last time so we're going to look +at the adults spinal cord + + align:start position:0% +at the adults spinal cord + + + align:start position:0% +at the adults spinal cord +and that will + + align:start position:0% +and that will + + + align:start position:0% +and that will +lead to a discussion of the autonomic + + align:start position:0% +lead to a discussion of the autonomic + + + align:start position:0% +lead to a discussion of the autonomic +nervous system for the last part of + + align:start position:0% +nervous system for the last part of + + + align:start position:0% +nervous system for the last part of +class + + align:start position:0% +class + + + align:start position:0% +class +so look at the different levels + + align:start position:0% +so look at the different levels + + + align:start position:0% +so look at the different levels +uh talk about the sensory channels that + + align:start position:0% +uh talk about the sensory channels that + + + align:start position:0% +uh talk about the sensory channels that +we've already introduced + + align:start position:0% +we've already introduced + + + align:start position:0% +we've already introduced +reflex spinal cerebellar spinal columnic + + align:start position:0% +reflex spinal cerebellar spinal columnic + + + align:start position:0% +reflex spinal cerebellar spinal columnic +cracks and other + + align:start position:0% +cracks and other + + + align:start position:0% +cracks and other +major limistical tracks + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% +and then + + + align:start position:0% +and then +you'll see the major descending Pathways + + align:start position:0% +you'll see the major descending Pathways + + + align:start position:0% +you'll see the major descending Pathways +in the court + + align:start position:0% +in the court + + + align:start position:0% +in the court +at this point because they originate + + align:start position:0% +at this point because they originate + + + align:start position:0% +at this point because they originate +from above the chord Aries we've not + + align:start position:0% +from above the chord Aries we've not + + + align:start position:0% +from above the chord Aries we've not +talked about in detail + + align:start position:0% +talked about in detail + + + align:start position:0% +talked about in detail +this is really just an introduction to + + align:start position:0% +this is really just an introduction to + + + align:start position:0% +this is really just an introduction to +those pathways + + align:start position:0% + + + + align:start position:0% + +but the more you're exposed to it the + + align:start position:0% +but the more you're exposed to it the + + + align:start position:0% +but the more you're exposed to it the +more likely you are to remember it and + + align:start position:0% +more likely you are to remember it and + + + align:start position:0% +more likely you are to remember it and +then we'll talk about proprio spinal + + align:start position:0% +then we'll talk about proprio spinal + + + align:start position:0% +then we'll talk about proprio spinal +fibers okay so first of all + + align:start position:0% +fibers okay so first of all + + + align:start position:0% +fibers okay so first of all +how does how do The Columns of axons of + + align:start position:0% +how does how do The Columns of axons of + + + align:start position:0% +how does how do The Columns of axons of +the chord change as you go from one + + align:start position:0% +the chord change as you go from one + + + align:start position:0% +the chord change as you go from one +level to the other + + align:start position:0% +level to the other + + + align:start position:0% +level to the other +it's really a very simple question + + align:start position:0% + + + + align:start position:0% + +and I'm asking why they change and the + + align:start position:0% +and I'm asking why they change and the + + + align:start position:0% +and I'm asking why they change and the +answer there is also pretty simple and + + align:start position:0% +answer there is also pretty simple and + + + align:start position:0% +answer there is also pretty simple and +then I asked one other thing about those + + align:start position:0% +then I asked one other thing about those + + + align:start position:0% +then I asked one other thing about those +outlines what's the lateral horn + + align:start position:0% +outlines what's the lateral horn + + + align:start position:0% +outlines what's the lateral horn +so did you try to figure that out + + align:start position:0% + + + + align:start position:0% + +The Columns of fibers + + align:start position:0% +The Columns of fibers + + + align:start position:0% +The Columns of fibers +if you compare say the cervical level + + align:start position:0% +if you compare say the cervical level + + + align:start position:0% +if you compare say the cervical level +and the lower lumbar level + + align:start position:0% +and the lower lumbar level + + + align:start position:0% +and the lower lumbar level +yes + + align:start position:0% +yes + + + align:start position:0% +yes +sorry + + align:start position:0% +sorry + + + align:start position:0% +sorry +no the myelin + + align:start position:0% +no the myelin + + + align:start position:0% +no the myelin +will be there at all those + + align:start position:0% + + + + align:start position:0% + +yeah the relative size will change why + + align:start position:0% + + + + align:start position:0% + +speak up + + align:start position:0% + + + + align:start position:0% + +one of them are terminated as you come + + align:start position:0% +one of them are terminated as you come + + + align:start position:0% +one of them are terminated as you come +down so there's few and fewer axons that + + align:start position:0% +down so there's few and fewer axons that + + + align:start position:0% +down so there's few and fewer axons that +haven't permeated yet and what about the + + align:start position:0% +haven't permeated yet and what about the + + + align:start position:0% +haven't permeated yet and what about the +ones going up + + align:start position:0% + + + + align:start position:0% + +more and more are being added okay very + + align:start position:0% +more and more are being added okay very + + + align:start position:0% +more and more are being added okay very +straightforward + + align:start position:0% +straightforward + + + align:start position:0% +straightforward +and you remember what the lateral horn + + align:start position:0% +and you remember what the lateral horn + + + align:start position:0% +and you remember what the lateral horn +is we talk about dorsal horn and ventral + + align:start position:0% +is we talk about dorsal horn and ventral + + + align:start position:0% +is we talk about dorsal horn and ventral +horn all the time when we talk about + + align:start position:0% +horn all the time when we talk about + + + align:start position:0% +horn all the time when we talk about +spinal cord + + align:start position:0% + + + + align:start position:0% + +look at it here + + align:start position:0% +look at it here + + + align:start position:0% +look at it here +white matter is in brown here + + align:start position:0% +white matter is in brown here + + + align:start position:0% +white matter is in brown here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +we call it remember why we call it white + + align:start position:0% +we call it remember why we call it white + + + align:start position:0% +we call it remember why we call it white +matter + + align:start position:0% + + + + align:start position:0% + +and it's unstained in the in the whole + + align:start position:0% +and it's unstained in the in the whole + + + align:start position:0% +and it's unstained in the in the whole +brain if you do a dissection or if you + + align:start position:0% +brain if you do a dissection or if you + + + align:start position:0% +brain if you do a dissection or if you +do a section but don't stain it + + align:start position:0% +do a section but don't stain it + + + align:start position:0% +do a section but don't stain it +the the myelin reflects the light more + + align:start position:0% +the the myelin reflects the light more + + + align:start position:0% +the the myelin reflects the light more +so it looks White + + align:start position:0% +so it looks White + + + align:start position:0% +so it looks White +it reflects all the different colors + + align:start position:0% +it reflects all the different colors + + + align:start position:0% +it reflects all the different colors +and the gray matter here I've shown in a + + align:start position:0% +and the gray matter here I've shown in a + + + align:start position:0% +and the gray matter here I've shown in a +lighter color + + align:start position:0% + + + + align:start position:0% + +this is something you see I do quite + + align:start position:0% +this is something you see I do quite + + + align:start position:0% +this is something you see I do quite +freely and you have to get used to it + + align:start position:0% +freely and you have to get used to it + + + align:start position:0% +freely and you have to get used to it +you have to get familiar enough with it + + align:start position:0% +you have to get familiar enough with it + + + align:start position:0% +you have to get familiar enough with it +so that's never a problem and you will + + align:start position:0% +so that's never a problem and you will + + + align:start position:0% +so that's never a problem and you will +you know when we use different stains + + align:start position:0% +you know when we use different stains + + + align:start position:0% +you know when we use different stains +it's going to look different + + align:start position:0% +it's going to look different + + + align:start position:0% +it's going to look different +you see and almost all stains for axons + + align:start position:0% +you see and almost all stains for axons + + + align:start position:0% +you see and almost all stains for axons +make them dark + + align:start position:0% +make them dark + + + align:start position:0% +make them dark +so in any axon stain it's going to look + + align:start position:0% +so in any axon stain it's going to look + + + align:start position:0% +so in any axon stain it's going to look +more like this + + align:start position:0% +more like this + + + align:start position:0% +more like this +okay + + align:start position:0% + + + + align:start position:0% + +so you see that the dorsal columns the + + align:start position:0% +so you see that the dorsal columns the + + + align:start position:0% +so you see that the dorsal columns the +lateral columns and the ventral columns + + align:start position:0% +lateral columns and the ventral columns + + + align:start position:0% +lateral columns and the ventral columns +here are all much bigger at the top at + + align:start position:0% +here are all much bigger at the top at + + + align:start position:0% +here are all much bigger at the top at +the bottom just for the reasons we were + + align:start position:0% +the bottom just for the reasons we were + + + align:start position:0% +the bottom just for the reasons we were +just talking about + + align:start position:0% +just talking about + + + align:start position:0% +just talking about +now what about that lateral heart just + + align:start position:0% +now what about that lateral heart just + + + align:start position:0% +now what about that lateral heart just +to identify it here you'll see + + align:start position:0% +to identify it here you'll see + + + align:start position:0% +to identify it here you'll see +that there's a dorsal horn in a ventral + + align:start position:0% +that there's a dorsal horn in a ventral + + + align:start position:0% +that there's a dorsal horn in a ventral +horn the ventral horn is is pretty wide + + align:start position:0% +horn the ventral horn is is pretty wide + + + align:start position:0% +horn the ventral horn is is pretty wide +here because the cervical enlargement + + align:start position:0% +here because the cervical enlargement + + + align:start position:0% +here because the cervical enlargement +but right here + + align:start position:0% +but right here + + + align:start position:0% +but right here +see on the left side there's a little + + align:start position:0% +see on the left side there's a little + + + align:start position:0% +see on the left side there's a little +lateral horn and here it's on both sides + + align:start position:0% +lateral horn and here it's on both sides + + + align:start position:0% +lateral horn and here it's on both sides +a little bump on the side + + align:start position:0% +a little bump on the side + + + align:start position:0% +a little bump on the side +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and it's still there + + align:start position:0% +and it's still there + + + align:start position:0% +and it's still there +in the upper upper part of the lumbar + + align:start position:0% +in the upper upper part of the lumbar + + + align:start position:0% +in the upper upper part of the lumbar +chord and then it just appears + + align:start position:0% +chord and then it just appears + + + align:start position:0% +chord and then it just appears +so you remember what that is + + align:start position:0% + + + + align:start position:0% + +preganglionic motor neurons + + align:start position:0% +preganglionic motor neurons + + + align:start position:0% +preganglionic motor neurons +of what + + align:start position:0% + + + + align:start position:0% + +the sympathetic part the sympathetic + + align:start position:0% +the sympathetic part the sympathetic + + + align:start position:0% +the sympathetic part the sympathetic +nervous system so we'll talk about that + + align:start position:0% +nervous system so we'll talk about that + + + align:start position:0% +nervous system so we'll talk about that +we'll see it in in large figures and so + + align:start position:0% +we'll see it in in large figures and so + + + align:start position:0% +we'll see it in in large figures and so +forth and we'll see exactly what's there + + align:start position:0% +forth and we'll see exactly what's there + + + align:start position:0% +forth and we'll see exactly what's there +all right + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +the other the thing we didn't talk about + + align:start position:0% +the other the thing we didn't talk about + + + align:start position:0% +the other the thing we didn't talk about +here + + align:start position:0% +here + + + align:start position:0% +here +we talked about gray and white matter + + align:start position:0% +we talked about gray and white matter + + + align:start position:0% +we talked about gray and white matter +of course gray matter also in unstained + + align:start position:0% +of course gray matter also in unstained + + + align:start position:0% +of course gray matter also in unstained +sections or in the section it looks + + align:start position:0% +sections or in the section it looks + + + align:start position:0% +sections or in the section it looks +grayer because of the cells and fewer + + align:start position:0% +grayer because of the cells and fewer + + + align:start position:0% +grayer because of the cells and fewer +myelinated axons + + align:start position:0% +myelinated axons + + + align:start position:0% +myelinated axons +okay but look at those + + align:start position:0% +okay but look at those + + + align:start position:0% +okay but look at those +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the ventral horn in particular and also + + align:start position:0% +the ventral horn in particular and also + + + align:start position:0% +the ventral horn in particular and also +just the size of the cord + + align:start position:0% +just the size of the cord + + + align:start position:0% +just the size of the cord +look the biggest section is here not + + align:start position:0% +look the biggest section is here not + + + align:start position:0% +look the biggest section is here not +just above it + + align:start position:0% +just above it + + + align:start position:0% +just above it +that's the cervical enlargement so + + align:start position:0% +that's the cervical enlargement so + + + align:start position:0% +that's the cervical enlargement so +what's the reason for the cervical + + align:start position:0% +what's the reason for the cervical + + + align:start position:0% +what's the reason for the cervical +enlargement and then a smaller one down + + align:start position:0% +enlargement and then a smaller one down + + + align:start position:0% +enlargement and then a smaller one down +here the lumbar enlargement + + align:start position:0% + + + + align:start position:0% + +gotta speak up + + align:start position:0% +gotta speak up + + + align:start position:0% +gotta speak up +arms and legs okay so that means it + + align:start position:0% +arms and legs okay so that means it + + + align:start position:0% +arms and legs okay so that means it +should be different + + align:start position:0% +should be different + + + align:start position:0% +should be different +in animals without arms and legs right + + align:start position:0% +in animals without arms and legs right + + + align:start position:0% +in animals without arms and legs right +and that's true Okay so + + align:start position:0% +and that's true Okay so + + + align:start position:0% +and that's true Okay so +uh + + align:start position:0% + + + + align:start position:0% + +so if we take the animal that has the + + align:start position:0% +so if we take the animal that has the + + + align:start position:0% +so if we take the animal that has the +largest legs of any animal that's ever + + align:start position:0% +largest legs of any animal that's ever + + + align:start position:0% +largest legs of any animal that's ever +lived + + align:start position:0% +lived + + + align:start position:0% +lived +brontosaurus where we have complete + + align:start position:0% +brontosaurus where we have complete + + + align:start position:0% +brontosaurus where we have complete +skeleton + + align:start position:0% +skeleton + + + align:start position:0% +skeleton +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it's on display still at Yale University + + align:start position:0% +it's on display still at Yale University + + + align:start position:0% +it's on display still at Yale University +where the curator discovered + + align:start position:0% +where the curator discovered + + + align:start position:0% +where the curator discovered +the character at Yale discovered it look + + align:start position:0% +the character at Yale discovered it look + + + align:start position:0% +the character at Yale discovered it look +at the lumbar enlargement and where + + align:start position:0% +at the lumbar enlargement and where + + + align:start position:0% +at the lumbar enlargement and where +they're showing this whole central + + align:start position:0% +they're showing this whole central + + + align:start position:0% +they're showing this whole central +nervous system here and compared to the + + align:start position:0% +nervous system here and compared to the + + + align:start position:0% +nervous system here and compared to the +size of the brain you'll see that the + + align:start position:0% +size of the brain you'll see that the + + + align:start position:0% +size of the brain you'll see that the +lumbar enlargement is bigger than the + + align:start position:0% +lumbar enlargement is bigger than the + + + align:start position:0% +lumbar enlargement is bigger than the +brain in Brontosaurus + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +because + + align:start position:0% +because + + + align:start position:0% +because +the huge number of neurons + + align:start position:0% + + + + align:start position:0% + +motor neurons and inner neurons + + align:start position:0% +motor neurons and inner neurons + + + align:start position:0% +motor neurons and inner neurons +innervating those motor neurons to + + align:start position:0% +innervating those motor neurons to + + + align:start position:0% +innervating those motor neurons to +control these huge legs and of course + + align:start position:0% +control these huge legs and of course + + + align:start position:0% +control these huge legs and of course +there's also a lot of skin area there + + align:start position:0% +there's also a lot of skin area there + + + align:start position:0% +there's also a lot of skin area there +it's a lot of surface area getting + + align:start position:0% +it's a lot of surface area getting + + + align:start position:0% +it's a lot of surface area getting +sensory input up above it's illustrating + + align:start position:0% +sensory input up above it's illustrating + + + align:start position:0% +sensory input up above it's illustrating +a turtle spinal cord now what's + + align:start position:0% +a turtle spinal cord now what's + + + align:start position:0% +a turtle spinal cord now what's +different about the turtle + + align:start position:0% +different about the turtle + + + align:start position:0% +different about the turtle +well he's got a shell so the body + + align:start position:0% +well he's got a shell so the body + + + align:start position:0% +well he's got a shell so the body +surface except for his legs and uh + + align:start position:0% + + + + align:start position:0% + +there can't be much innervation there's + + align:start position:0% +there can't be much innervation there's + + + align:start position:0% +there can't be much innervation there's +not much to respond he doesn't respond + + align:start position:0% +not much to respond he doesn't respond + + + align:start position:0% +not much to respond he doesn't respond +from his shell so here in between the + + align:start position:0% +from his shell so here in between the + + + align:start position:0% +from his shell so here in between the +cervical cervical and landmark + + align:start position:0% +cervical cervical and landmark + + + align:start position:0% +cervical cervical and landmark +enlargements you do see a lot of motor + + align:start position:0% +enlargements you do see a lot of motor + + + align:start position:0% +enlargements you do see a lot of motor +neurons controlling these lens + + align:start position:0% +neurons controlling these lens + + + align:start position:0% +neurons controlling these lens +cervical enlargement would include this + + align:start position:0% +cervical enlargement would include this + + + align:start position:0% +cervical enlargement would include this +one far to the left + + align:start position:0% +one far to the left + + + align:start position:0% +one far to the left +okay but in between + + align:start position:0% +okay but in between + + + align:start position:0% +okay but in between +and below the lumbar enlargement this + + align:start position:0% +and below the lumbar enlargement this + + + align:start position:0% +and below the lumbar enlargement this +gorgeous very small it's still needed + + align:start position:0% +gorgeous very small it's still needed + + + align:start position:0% +gorgeous very small it's still needed +because it is innervating various bodily + + align:start position:0% +because it is innervating various bodily + + + align:start position:0% +because it is innervating various bodily +organs in those levels too + + align:start position:0% +organs in those levels too + + + align:start position:0% +organs in those levels too +all right + + align:start position:0% + + + + align:start position:0% + +so who is this guy bror rexin + + align:start position:0% +so who is this guy bror rexin + + + align:start position:0% +so who is this guy bror rexin +notice the pronunciation + + align:start position:0% +notice the pronunciation + + + align:start position:0% +notice the pronunciation +Rex said + + align:start position:0% + + + + align:start position:0% + +he added something to the way we talk + + align:start position:0% +he added something to the way we talk + + + align:start position:0% +he added something to the way we talk +about the spinal cord + + align:start position:0% +about the spinal cord + + + align:start position:0% +about the spinal cord +especially when we're doing + + align:start position:0% +especially when we're doing + + + align:start position:0% +especially when we're doing +cyto and fiber architecture of the Court + + align:start position:0% +cyto and fiber architecture of the Court + + + align:start position:0% +cyto and fiber architecture of the Court +what was it he had + + align:start position:0% +what was it he had + + + align:start position:0% +what was it he had +layers + + align:start position:0% +layers + + + align:start position:0% +layers +he showed how you can and he studied the + + align:start position:0% +he showed how you can and he studied the + + + align:start position:0% +he showed how you can and he studied the +spinal cord of various animals as well + + align:start position:0% +spinal cord of various animals as well + + + align:start position:0% +spinal cord of various animals as well +as human and published a series of + + align:start position:0% +as human and published a series of + + + align:start position:0% +as human and published a series of +papers and was consistently able to find + + align:start position:0% +papers and was consistently able to find + + + align:start position:0% +papers and was consistently able to find +it Define the same layers + + align:start position:0% +it Define the same layers + + + align:start position:0% +it Define the same layers +okay and this is just an example uh + + align:start position:0% + + + + align:start position:0% + +where you see the missile stain section + + align:start position:0% +where you see the missile stain section + + + align:start position:0% +where you see the missile stain section +uh + + align:start position:0% +uh + + + align:start position:0% +uh +this is the seventh cervical segment + + align:start position:0% +this is the seventh cervical segment + + + align:start position:0% +this is the seventh cervical segment +so these are motor neurons innervating + + align:start position:0% +so these are motor neurons innervating + + + align:start position:0% +so these are motor neurons innervating +the farlands + + align:start position:0% +the farlands + + + align:start position:0% +the farlands +or the arms and hands + + align:start position:0% +or the arms and hands + + + align:start position:0% +or the arms and hands +and you can see a lot of motor neurons + + align:start position:0% +and you can see a lot of motor neurons + + + align:start position:0% +and you can see a lot of motor neurons +but they're in two groups a lateral + + align:start position:0% +but they're in two groups a lateral + + + align:start position:0% +but they're in two groups a lateral +group that's actually got several + + align:start position:0% +group that's actually got several + + + align:start position:0% +group that's actually got several +different clumps there and he's outlined + + align:start position:0% +different clumps there and he's outlined + + + align:start position:0% +different clumps there and he's outlined +it here + + align:start position:0% +it here + + + align:start position:0% +it here +so + + align:start position:0% +so + + + align:start position:0% +so +layer nine + + align:start position:0% +layer nine + + + align:start position:0% +layer nine +and this one he called layer eight in + + align:start position:0% +and this one he called layer eight in + + + align:start position:0% +and this one he called layer eight in +here these aren't so much layers as + + align:start position:0% +here these aren't so much layers as + + + align:start position:0% +here these aren't so much layers as +groupings these are the motor neurons + + align:start position:0% +groupings these are the motor neurons + + + align:start position:0% +groupings these are the motor neurons +innervating the body axis + + align:start position:0% +innervating the body axis + + + align:start position:0% +innervating the body axis +and then all the endocrines + + align:start position:0% +and then all the endocrines + + + align:start position:0% +and then all the endocrines +that tend to be pre-motor they they + + align:start position:0% +that tend to be pre-motor they they + + + align:start position:0% +that tend to be pre-motor they they +contact the motor neurons most of them + + align:start position:0% + + + + align:start position:0% + +that's layer seven + + align:start position:0% +that's layer seven + + + align:start position:0% +that's layer seven +oh he does have a layer 12 this area + + align:start position:0% +oh he does have a layer 12 this area + + + align:start position:0% +oh he does have a layer 12 this area +right around the + + align:start position:0% +right around the + + + align:start position:0% +right around the +ventricle there notice how small + + align:start position:0% +ventricle there notice how small + + + align:start position:0% +ventricle there notice how small +relatively small The ventricle looks now + + align:start position:0% +relatively small The ventricle looks now + + + align:start position:0% +relatively small The ventricle looks now +it's not because it got smaller since + + align:start position:0% +it's not because it got smaller since + + + align:start position:0% +it's not because it got smaller since +the embryo it's that everything else got + + align:start position:0% +the embryo it's that everything else got + + + align:start position:0% +the embryo it's that everything else got +so much bigger all right and then you + + align:start position:0% +so much bigger all right and then you + + + align:start position:0% +so much bigger all right and then you +see his other layers and the dorsal horn + + align:start position:0% +see his other layers and the dorsal horn + + + align:start position:0% +see his other layers and the dorsal horn +in particular it's very easy to identify + + align:start position:0% +in particular it's very easy to identify + + + align:start position:0% +in particular it's very easy to identify +the layers + + align:start position:0% +the layers + + + align:start position:0% +the layers +so if I ask you to describe some + + align:start position:0% +so if I ask you to describe some + + + align:start position:0% +so if I ask you to describe some +differences in cyto architecture of the + + align:start position:0% +differences in cyto architecture of the + + + align:start position:0% +differences in cyto architecture of the +dorsal and ventral horns you see + + align:start position:0% +dorsal and ventral horns you see + + + align:start position:0% +dorsal and ventral horns you see +you would mention the motor neurons + + align:start position:0% +you would mention the motor neurons + + + align:start position:0% +you would mention the motor neurons +they're the largest and usually deep + + align:start position:0% +they're the largest and usually deep + + + align:start position:0% +they're the largest and usually deep +staining neurons + + align:start position:0% +staining neurons + + + align:start position:0% +staining neurons +the motor neurons in the ventral horn + + align:start position:0% +the motor neurons in the ventral horn + + + align:start position:0% +the motor neurons in the ventral horn +and the dorsal horn has the most clearly + + align:start position:0% +and the dorsal horn has the most clearly + + + align:start position:0% +and the dorsal horn has the most clearly +defined layers you can see it best in a + + align:start position:0% +defined layers you can see it best in a + + + align:start position:0% +defined layers you can see it best in a +fibrous oops the wrong way and a fiber + + align:start position:0% +fibrous oops the wrong way and a fiber + + + align:start position:0% +fibrous oops the wrong way and a fiber +stain + + align:start position:0% +stain + + + align:start position:0% +stain +like here here's a human lumbar level + + align:start position:0% +like here here's a human lumbar level + + + align:start position:0% +like here here's a human lumbar level +and you can see very light myelin there + + align:start position:0% +and you can see very light myelin there + + + align:start position:0% +and you can see very light myelin there +in layer three and you can so you see + + align:start position:0% +in layer three and you can so you see + + + align:start position:0% +in layer three and you can so you see +layers one two and three always stand + + align:start position:0% +layers one two and three always stand + + + align:start position:0% +layers one two and three always stand +out the layers are easy to identify + + align:start position:0% + + + + align:start position:0% + +there's one of a rat + + align:start position:0% +there's one of a rat + + + align:start position:0% +there's one of a rat +where because of myelinated axons you + + align:start position:0% +where because of myelinated axons you + + + align:start position:0% +where because of myelinated axons you +can hardly see + + align:start position:0% +can hardly see + + + align:start position:0% +can hardly see +layer Layer Two doesn't look very light + + align:start position:0% +layer Layer Two doesn't look very light + + + align:start position:0% +layer Layer Two doesn't look very light +and also I've done it with a very high + + align:start position:0% +and also I've done it with a very high + + + align:start position:0% +and also I've done it with a very high +contrast here + + align:start position:0% +contrast here + + + align:start position:0% +contrast here +but layer the upper layers are very very + + align:start position:0% +but layer the upper layers are very very + + + align:start position:0% +but layer the upper layers are very very +white + + align:start position:0% +white + + + align:start position:0% +white +all right + + align:start position:0% + + + + align:start position:0% + +so myelin + + align:start position:0% +so myelin + + + align:start position:0% +so myelin +has been called a crucial vertebrate + + align:start position:0% +has been called a crucial vertebrate + + + align:start position:0% +has been called a crucial vertebrate +Innovation innovation + + align:start position:0% +Innovation innovation + + + align:start position:0% +Innovation innovation +that was a quote from Almond's book + + align:start position:0% +that was a quote from Almond's book + + + align:start position:0% +that was a quote from Almond's book +so what is it that made myelin such a + + align:start position:0% +so what is it that made myelin such a + + + align:start position:0% +so what is it that made myelin such a +crucial innovation of the vertebrates + + align:start position:0% +crucial innovation of the vertebrates + + + align:start position:0% +crucial innovation of the vertebrates +it's not found in invertebrates + + align:start position:0% +it's not found in invertebrates + + + align:start position:0% +it's not found in invertebrates +and it's actually not found in the most + + align:start position:0% +and it's actually not found in the most + + + align:start position:0% +and it's actually not found in the most +primitive vertebrates the jawless for + + align:start position:0% +primitive vertebrates the jawless for + + + align:start position:0% +primitive vertebrates the jawless for +the brace the hagfish and Lamprey but it + + align:start position:0% +the brace the hagfish and Lamprey but it + + + align:start position:0% +the brace the hagfish and Lamprey but it +is found in all the rest of them + + align:start position:0% +is found in all the rest of them + + + align:start position:0% +is found in all the rest of them +okay so why was it so important + + align:start position:0% +okay so why was it so important + + + align:start position:0% +okay so why was it so important +yes + + align:start position:0% + + + + align:start position:0% + +it helps to increase it allows the + + align:start position:0% +it helps to increase it allows the + + + align:start position:0% +it helps to increase it allows the +increase in speed of the action + + align:start position:0% +increase in speed of the action + + + align:start position:0% +increase in speed of the action +potential without increasing the + + align:start position:0% +potential without increasing the + + + align:start position:0% +potential without increasing the +diameter so much invertebrates do have + + align:start position:0% +diameter so much invertebrates do have + + + align:start position:0% +diameter so much invertebrates do have +pretty fast conduction like in the squid + + align:start position:0% +pretty fast conduction like in the squid + + + align:start position:0% +pretty fast conduction like in the squid +okay they're a pretty big animal and to + + align:start position:0% +okay they're a pretty big animal and to + + + align:start position:0% +okay they're a pretty big animal and to +get past enough conduction + + align:start position:0% +get past enough conduction + + + align:start position:0% +get past enough conduction +for their escape response they've + + align:start position:0% +for their escape response they've + + + align:start position:0% +for their escape response they've +developed these giant accents they're + + align:start position:0% +developed these giant accents they're + + + align:start position:0% +developed these giant accents they're +like a millimeter in diameter but that + + align:start position:0% +like a millimeter in diameter but that + + + align:start position:0% +like a millimeter in diameter but that +is a lot of cell to maintain + + align:start position:0% +is a lot of cell to maintain + + + align:start position:0% +is a lot of cell to maintain +and if you want very many accents to get + + align:start position:0% +and if you want very many accents to get + + + align:start position:0% +and if you want very many accents to get +finer control you know + + align:start position:0% +finer control you know + + + align:start position:0% +finer control you know +that wouldn't be very good for the + + align:start position:0% +that wouldn't be very good for the + + + align:start position:0% +that wouldn't be very good for the +vertebrates + + align:start position:0% +vertebrates + + + align:start position:0% +vertebrates +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the larger animals okay + + align:start position:0% +the larger animals okay + + + align:start position:0% +the larger animals okay +you imagine a whale trying to control + + align:start position:0% +you imagine a whale trying to control + + + align:start position:0% +you imagine a whale trying to control +his muscles with any speed at all if he + + align:start position:0% +his muscles with any speed at all if he + + + align:start position:0% +his muscles with any speed at all if he +didn't have my own + + align:start position:0% +didn't have my own + + + align:start position:0% +didn't have my own +his movements would be incredibly slow + + align:start position:0% +his movements would be incredibly slow + + + align:start position:0% +his movements would be incredibly slow +his reaction time would be very slow + + align:start position:0% + + + + align:start position:0% + +okay you look if you want to search in + + align:start position:0% +okay you look if you want to search in + + + align:start position:0% +okay you look if you want to search in +my book just search + + align:start position:0% +my book just search + + + align:start position:0% +my book just search +you've got the PDF files so you can + + align:start position:0% +you've got the PDF files so you can + + + align:start position:0% +you've got the PDF files so you can +search + + align:start position:0% +search + + + align:start position:0% +search +under uh myelin and you can look for + + align:start position:0% +under uh myelin and you can look for + + + align:start position:0% +under uh myelin and you can look for +saltatory conduction + + align:start position:0% +saltatory conduction + + + align:start position:0% +saltatory conduction +solitary means jumping + + align:start position:0% +solitary means jumping + + + align:start position:0% +solitary means jumping +the the the + + align:start position:0% +the the the + + + align:start position:0% +the the the +I did talk about this briefly in class + + align:start position:0% +I did talk about this briefly in class + + + align:start position:0% +I did talk about this briefly in class +before the action potential jumps from + + align:start position:0% +before the action potential jumps from + + + align:start position:0% +before the action potential jumps from +node to node a node is where there's no + + align:start position:0% +node to node a node is where there's no + + + align:start position:0% +node to node a node is where there's no +mileage the myelin is never continuous + + align:start position:0% +mileage the myelin is never continuous + + + align:start position:0% +mileage the myelin is never continuous +and where it is present it insulates it + + align:start position:0% +and where it is present it insulates it + + + align:start position:0% +and where it is present it insulates it +you can't get the iron flow through the + + align:start position:0% +you can't get the iron flow through the + + + align:start position:0% +you can't get the iron flow through the +memory so that means all the ions have + + align:start position:0% +memory so that means all the ions have + + + align:start position:0% +memory so that means all the ions have +to flow at those nodes they're close + + align:start position:0% +to flow at those nodes they're close + + + align:start position:0% +to flow at those nodes they're close +enough together + + align:start position:0% +enough together + + + align:start position:0% +enough together +so the decremental conduction down the + + align:start position:0% +so the decremental conduction down the + + + align:start position:0% +so the decremental conduction down the +membrane + + align:start position:0% +membrane + + + align:start position:0% +membrane +okay + + align:start position:0% +okay + + + align:start position:0% +okay +which is very very fast + + align:start position:0% +which is very very fast + + + align:start position:0% +which is very very fast +he's strong enough it won't Decay enough + + align:start position:0% +he's strong enough it won't Decay enough + + + align:start position:0% +he's strong enough it won't Decay enough +that it will reach the next node and + + align:start position:0% +that it will reach the next node and + + + align:start position:0% +that it will reach the next node and +Trigger the next action potential there + + align:start position:0% +Trigger the next action potential there + + + align:start position:0% +Trigger the next action potential there +so it literally goes + + align:start position:0% +so it literally goes + + + align:start position:0% +so it literally goes +oh you only get the extra potential at + + align:start position:0% +oh you only get the extra potential at + + + align:start position:0% +oh you only get the extra potential at +the notes + + align:start position:0% + + + + align:start position:0% + +yeah exactly it's like a series of + + align:start position:0% +yeah exactly it's like a series of + + + align:start position:0% +yeah exactly it's like a series of +dominoes falling + + align:start position:0% + + + + align:start position:0% + +and of course if something happens if + + align:start position:0% +and of course if something happens if + + + align:start position:0% +and of course if something happens if +you get an area where + + align:start position:0% +you get an area where + + + align:start position:0% +you get an area where +the node is too far you will the action + + align:start position:0% +the node is too far you will the action + + + align:start position:0% +the node is too far you will the action +Position will just stop + + align:start position:0% +Position will just stop + + + align:start position:0% +Position will just stop +okay and this does happen sometimes + + align:start position:0% +okay and this does happen sometimes + + + align:start position:0% +okay and this does happen sometimes +especially in certain pathologies Okay + + align:start position:0% +especially in certain pathologies Okay + + + align:start position:0% +especially in certain pathologies Okay +so + + align:start position:0% +so + + + align:start position:0% +so +one more question here how does this + + align:start position:0% +one more question here how does this + + + align:start position:0% +one more question here how does this +final chord of humans differ from the + + align:start position:0% +final chord of humans differ from the + + + align:start position:0% +final chord of humans differ from the +spinal cords of other mammals + + align:start position:0% +spinal cords of other mammals + + + align:start position:0% +spinal cords of other mammals +how + + align:start position:0% +how + + + align:start position:0% +how +are humans different + + align:start position:0% + + + + align:start position:0% + +what do we do better than other animals + + align:start position:0% + + + + align:start position:0% + +well for one thing this kind of thing + + align:start position:0% +well for one thing this kind of thing + + + align:start position:0% +well for one thing this kind of thing +that requires a lot of dexterity + + align:start position:0% +that requires a lot of dexterity + + + align:start position:0% +that requires a lot of dexterity +tremendous control of these fingers + + align:start position:0% +tremendous control of these fingers + + + align:start position:0% +tremendous control of these fingers +that requires a lot of actions coming + + align:start position:0% +that requires a lot of actions coming + + + align:start position:0% +that requires a lot of actions coming +from the brain + + align:start position:0% +from the brain + + + align:start position:0% +from the brain +that controls motor neurons + + align:start position:0% +that controls motor neurons + + + align:start position:0% +that controls motor neurons +so that's going to mean a lot of + + align:start position:0% +so that's going to mean a lot of + + + align:start position:0% +so that's going to mean a lot of +descending actions so the white matter + + align:start position:0% +descending actions so the white matter + + + align:start position:0% +descending actions so the white matter +with those + + align:start position:0% +with those + + + align:start position:0% +with those +descending myelinated axons is going to + + align:start position:0% +descending myelinated axons is going to + + + align:start position:0% +descending myelinated axons is going to +be big another question + + align:start position:0% + + + + align:start position:0% + +yeah all the animals have these same + + align:start position:0% +yeah all the animals have these same + + + align:start position:0% +yeah all the animals have these same +Parts you know what the caudi equina is + + align:start position:0% + + + + align:start position:0% + +their roots + + align:start position:0% +their roots + + + align:start position:0% +their roots +their dorsal and ventral roots + + align:start position:0% +their dorsal and ventral roots + + + align:start position:0% +their dorsal and ventral roots +below the level of the spinal cord you + + align:start position:0% +below the level of the spinal cord you + + + align:start position:0% +below the level of the spinal cord you +see because the our spinal cord doesn't + + align:start position:0% +see because the our spinal cord doesn't + + + align:start position:0% +see because the our spinal cord doesn't +grow as fast as the rest of our body so + + align:start position:0% +grow as fast as the rest of our body so + + + align:start position:0% +grow as fast as the rest of our body so +the spinal cord ends and the smaller + + align:start position:0% +the spinal cord ends and the smaller + + + align:start position:0% +the spinal cord ends and the smaller +your bathroom you know fairly high up + + align:start position:0% +your bathroom you know fairly high up + + + align:start position:0% +your bathroom you know fairly high up +but your spinal column the Bony spinal + + align:start position:0% +but your spinal column the Bony spinal + + + align:start position:0% +but your spinal column the Bony spinal +column continues further down + + align:start position:0% +column continues further down + + + align:start position:0% +column continues further down +and in that spinal column + + align:start position:0% +and in that spinal column + + + align:start position:0% +and in that spinal column +okay you have the dorsal and dental + + align:start position:0% +okay you have the dorsal and dental + + + align:start position:0% +okay you have the dorsal and dental +roots for the Cod almost part of the + + align:start position:0% +roots for the Cod almost part of the + + + align:start position:0% +roots for the Cod almost part of the +cord + + align:start position:0% +cord + + + align:start position:0% +cord +okay that will be somewhere in animals + + align:start position:0% +okay that will be somewhere in animals + + + align:start position:0% +okay that will be somewhere in animals +it's very similar in priming other + + align:start position:0% +it's very similar in priming other + + + align:start position:0% +it's very similar in priming other +primates and humans + + align:start position:0% +primates and humans + + + align:start position:0% +primates and humans +but it's present in other animals too + + align:start position:0% +but it's present in other animals too + + + align:start position:0% +but it's present in other animals too +the biggest difference is in sensation + + align:start position:0% +the biggest difference is in sensation + + + align:start position:0% +the biggest difference is in sensation +and dexterity + + align:start position:0% +and dexterity + + + align:start position:0% +and dexterity +to get that very + + align:start position:0% +to get that very + + + align:start position:0% +to get that very +we have a lot of dense innervation of + + align:start position:0% +we have a lot of dense innervation of + + + align:start position:0% +we have a lot of dense innervation of +these fingertips + + align:start position:0% +these fingertips + + + align:start position:0% +these fingertips +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now for the spider monkey he's got some + + align:start position:0% +now for the spider monkey he's got some + + + align:start position:0% +now for the spider monkey he's got some +dense innervation of his tail too and + + align:start position:0% +dense innervation of his tail too and + + + align:start position:0% +dense innervation of his tail too and +he's very dexterous it is stale he uses + + align:start position:0% +he's very dexterous it is stale he uses + + + align:start position:0% +he's very dexterous it is stale he uses +it a lot + + align:start position:0% +it a lot + + + align:start position:0% +it a lot +so he also has a lot of fibers for that + + align:start position:0% +so he also has a lot of fibers for that + + + align:start position:0% +so he also has a lot of fibers for that +so that means the dorsal roots and that + + align:start position:0% +so that means the dorsal roots and that + + + align:start position:0% +so that means the dorsal roots and that +leads then to the dorsal columns + + align:start position:0% +leads then to the dorsal columns + + + align:start position:0% +leads then to the dorsal columns +for the fast conducting pathway it's + + align:start position:0% +for the fast conducting pathway it's + + + align:start position:0% +for the fast conducting pathway it's +also bigger in humans + + align:start position:0% + + + + align:start position:0% + +the ability to stand upright + + align:start position:0% +the ability to stand upright + + + align:start position:0% +the ability to stand upright +that required evolution of special feed + + align:start position:0% +that required evolution of special feed + + + align:start position:0% +that required evolution of special feed +special vestibular control vestibular + + align:start position:0% +special vestibular control vestibular + + + align:start position:0% +special vestibular control vestibular +reflexes and some sensory reflexes from + + align:start position:0% +reflexes and some sensory reflexes from + + + align:start position:0% +reflexes and some sensory reflexes from +the soles of our feet + + align:start position:0% +the soles of our feet + + + align:start position:0% +the soles of our feet +so people that wear thick Prosthetics + + align:start position:0% +so people that wear thick Prosthetics + + + align:start position:0% +so people that wear thick Prosthetics +and their feet don't lose some of that + + align:start position:0% + + + + align:start position:0% + +but uh we compensate very well for it in + + align:start position:0% +but uh we compensate very well for it in + + + align:start position:0% +but uh we compensate very well for it in +various places so don't worry about it + + align:start position:0% +various places so don't worry about it + + + align:start position:0% +various places so don't worry about it +okay + + align:start position:0% + + + + align:start position:0% + +all right so + + align:start position:0% +all right so + + + align:start position:0% +all right so +just note here I'm going to compare + + align:start position:0% +just note here I'm going to compare + + + align:start position:0% +just note here I'm going to compare +human + + align:start position:0% +human + + + align:start position:0% +human +and rat + + align:start position:0% +and rat + + + align:start position:0% +and rat +okay look at the lateral column here + + align:start position:0% +okay look at the lateral column here + + + align:start position:0% +okay look at the lateral column here +you can see it in the drawing more + + align:start position:0% +you can see it in the drawing more + + + align:start position:0% +you can see it in the drawing more +easily + + align:start position:0% +easily + + + align:start position:0% +easily +and I'll look at it in the red + + align:start position:0% + + + + align:start position:0% + +there it is in human + + align:start position:0% +there it is in human + + + align:start position:0% +there it is in human +why is this so much bigger especially + + align:start position:0% +why is this so much bigger especially + + + align:start position:0% +why is this so much bigger especially +because of the descending accents + + align:start position:0% +because of the descending accents + + + align:start position:0% +because of the descending accents +you see coming from + + align:start position:0% +you see coming from + + + align:start position:0% +you see coming from +the neocortex + + align:start position:0% + + + + align:start position:0% + +the dorsal columns are also bigger but + + align:start position:0% +the dorsal columns are also bigger but + + + align:start position:0% +the dorsal columns are also bigger but +this is a lumbar level where the + + align:start position:0% +this is a lumbar level where the + + + align:start position:0% +this is a lumbar level where the +differences is great but + + align:start position:0% + + + + align:start position:0% + +you can see + + align:start position:0% +you can see + + + align:start position:0% +you can see +this + + align:start position:0% +this + + + align:start position:0% +this +is not as big as this + + align:start position:0% +is not as big as this + + + align:start position:0% +is not as big as this +but you notice that difference + + align:start position:0% +but you notice that difference + + + align:start position:0% +but you notice that difference +very much more at the cervical level all + + align:start position:0% +very much more at the cervical level all + + + align:start position:0% +very much more at the cervical level all +right + + align:start position:0% +right + + + align:start position:0% +right +so let's look at the sensory channels + + align:start position:0% +so let's look at the sensory channels + + + align:start position:0% +so let's look at the sensory channels +now talk about reflexes the spinal + + align:start position:0% +now talk about reflexes the spinal + + + align:start position:0% +now talk about reflexes the spinal +reticulators spinal thalamic cracks + + align:start position:0% +reticulators spinal thalamic cracks + + + align:start position:0% +reticulators spinal thalamic cracks +spinal cerebellar + + align:start position:0% +spinal cerebellar + + + align:start position:0% +spinal cerebellar +and how the dorsal column axons get + + align:start position:0% +and how the dorsal column axons get + + + align:start position:0% +and how the dorsal column axons get +started + + align:start position:0% + + + + align:start position:0% + +we'll start with this question + + align:start position:0% +we'll start with this question + + + align:start position:0% +we'll start with this question +where do the largest axons in the dorsal + + align:start position:0% +where do the largest axons in the dorsal + + + align:start position:0% +where do the largest axons in the dorsal +Roots originate + + align:start position:0% +Roots originate + + + align:start position:0% +Roots originate +so now we're going to start looking at + + align:start position:0% +so now we're going to start looking at + + + align:start position:0% +so now we're going to start looking at +Cross sections of the chord we're going + + align:start position:0% +Cross sections of the chord we're going + + + align:start position:0% +Cross sections of the chord we're going +to look at these axons coming in and the + + align:start position:0% +to look at these axons coming in and the + + + align:start position:0% +to look at these axons coming in and the +circuits they form + + align:start position:0% +circuits they form + + + align:start position:0% +circuits they form +but what where do the largest axons rise + + align:start position:0% +but what where do the largest axons rise + + + align:start position:0% +but what where do the largest axons rise +I've talked about it twice in the class + + align:start position:0% +I've talked about it twice in the class + + + align:start position:0% +I've talked about it twice in the class +already but you may not remember + + align:start position:0% +already but you may not remember + + + align:start position:0% +already but you may not remember +that's why I repeat myself a lot okay + + align:start position:0% +that's why I repeat myself a lot okay + + + align:start position:0% +that's why I repeat myself a lot okay +because I know + + align:start position:0% +because I know + + + align:start position:0% +because I know +that when you're learning neural Anatomy + + align:start position:0% +that when you're learning neural Anatomy + + + align:start position:0% +that when you're learning neural Anatomy +you're hit with a lot of these things + + align:start position:0% +you're hit with a lot of these things + + + align:start position:0% +you're hit with a lot of these things +you have to hear it again and again so I + + align:start position:0% +you have to hear it again and again so I + + + align:start position:0% +you have to hear it again and again so I +often tell you just understand me don't + + align:start position:0% +often tell you just understand me don't + + + align:start position:0% +often tell you just understand me don't +worry about writing it all down just + + align:start position:0% +worry about writing it all down just + + + align:start position:0% +worry about writing it all down just +understand me if you understand and you + + align:start position:0% +understand me if you understand and you + + + align:start position:0% +understand me if you understand and you +keep encountering it you'll start to + + align:start position:0% +keep encountering it you'll start to + + + align:start position:0% +keep encountering it you'll start to +remember it + + align:start position:0% +remember it + + + align:start position:0% +remember it +all right and that's also why it's + + align:start position:0% +all right and that's also why it's + + + align:start position:0% +all right and that's also why it's +useful to come to class those of you who + + align:start position:0% +useful to come to class those of you who + + + align:start position:0% +useful to come to class those of you who +are not here because going over + + align:start position:0% +are not here because going over + + + align:start position:0% +are not here because going over +going over it + + align:start position:0% +going over it + + + align:start position:0% +going over it +is actually very helpful for learning + + align:start position:0% +is actually very helpful for learning + + + align:start position:0% +is actually very helpful for learning +it's not some of you and some of your + + align:start position:0% +it's not some of you and some of your + + + align:start position:0% +it's not some of you and some of your +classes can read it once and you'll be + + align:start position:0% +classes can read it once and you'll be + + + align:start position:0% +classes can read it once and you'll be +fine if you do that neuronatomy you + + align:start position:0% +fine if you do that neuronatomy you + + + align:start position:0% +fine if you do that neuronatomy you +won't be fine + + align:start position:0% +won't be fine + + + align:start position:0% +won't be fine +unless you are maybe Sheldon + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +in case you don't know what I'm talking + + align:start position:0% +in case you don't know what I'm talking + + + align:start position:0% +in case you don't know what I'm talking +about you don't watch TV in the evenings + + align:start position:0% +about you don't watch TV in the evenings + + + align:start position:0% +about you don't watch TV in the evenings +The Big Bang Theory okay + + align:start position:0% +The Big Bang Theory okay + + + align:start position:0% +The Big Bang Theory okay +here's is a section of the court and + + align:start position:0% +here's is a section of the court and + + + align:start position:0% +here's is a section of the court and +it's ill this is from a medical book and + + align:start position:0% +it's ill this is from a medical book and + + + align:start position:0% +it's ill this is from a medical book and +it's illustrating different sizes of + + align:start position:0% +it's illustrating different sizes of + + + align:start position:0% +it's illustrating different sizes of +axons in the dorsal roof it just gives + + align:start position:0% +axons in the dorsal roof it just gives + + + align:start position:0% +axons in the dorsal roof it just gives +one example of the largest axons here + + align:start position:0% + + + + align:start position:0% + +they're called a alpha accents do you + + align:start position:0% +they're called a alpha accents do you + + + align:start position:0% +they're called a alpha accents do you +remember where they're coming from + + align:start position:0% +remember where they're coming from + + + align:start position:0% +remember where they're coming from +coming from the stretch receptors in + + align:start position:0% +coming from the stretch receptors in + + + align:start position:0% +coming from the stretch receptors in +muscles + + align:start position:0% +muscles + + + align:start position:0% +muscles +where are the stretch receptors the + + align:start position:0% +where are the stretch receptors the + + + align:start position:0% +where are the stretch receptors the +densest + + align:start position:0% + + + + align:start position:0% + +these muscles doing this + + align:start position:0% +these muscles doing this + + + align:start position:0% +these muscles doing this +you know any place we have really good + + align:start position:0% +you know any place we have really good + + + align:start position:0% +you know any place we have really good +control where would another good example + + align:start position:0% +control where would another good example + + + align:start position:0% +control where would another good example +be + + align:start position:0% +be + + + align:start position:0% +be +the tongue exactly we have to have + + align:start position:0% +the tongue exactly we have to have + + + align:start position:0% +the tongue exactly we have to have +extremely precise control of the tongue + + align:start position:0% +extremely precise control of the tongue + + + align:start position:0% +extremely precise control of the tongue +in order to talk + + align:start position:0% +in order to talk + + + align:start position:0% +in order to talk +and we're also pretty good at eating all + + align:start position:0% +and we're also pretty good at eating all + + + align:start position:0% +and we're also pretty good at eating all +right so here they are big axes and + + align:start position:0% +right so here they are big axes and + + + align:start position:0% +right so here they are big axes and +there's the branch going into the + + align:start position:0% +there's the branch going into the + + + align:start position:0% +there's the branch going into the +Duracell column and here it comes into + + align:start position:0% +Duracell column and here it comes into + + + align:start position:0% +Duracell column and here it comes into +the card and it's terminating + + align:start position:0% +the card and it's terminating + + + align:start position:0% +the card and it's terminating +here in layer six + + align:start position:0% +here in layer six + + + align:start position:0% +here in layer six +including some very immediately + + align:start position:0% +including some very immediately + + + align:start position:0% +including some very immediately +those are ones destined for the + + align:start position:0% +those are ones destined for the + + + align:start position:0% +those are ones destined for the +cerebellum and we'll see that in a + + align:start position:0% +cerebellum and we'll see that in a + + + align:start position:0% +cerebellum and we'll see that in a +minute but then they but the most + + align:start position:0% +minute but then they but the most + + + align:start position:0% +minute but then they but the most +important thing here is they go directly + + align:start position:0% +important thing here is they go directly + + + align:start position:0% +important thing here is they go directly +to motor neurons some of them contact + + align:start position:0% +to motor neurons some of them contact + + + align:start position:0% +to motor neurons some of them contact +the motor neurons so it's a monosynaptic + + align:start position:0% +the motor neurons so it's a monosynaptic + + + align:start position:0% +the motor neurons so it's a monosynaptic +reflex the stretch reflex whenever a + + align:start position:0% +reflex the stretch reflex whenever a + + + align:start position:0% +reflex the stretch reflex whenever a +muscle stretches okay + + align:start position:0% +muscle stretches okay + + + align:start position:0% +muscle stretches okay +it triggers those receptors and it tends + + align:start position:0% +it triggers those receptors and it tends + + + align:start position:0% +it triggers those receptors and it tends +to cause the same muscle to contract you + + align:start position:0% +to cause the same muscle to contract you + + + align:start position:0% +to cause the same muscle to contract you +say well that's counterproductive no it + + align:start position:0% +say well that's counterproductive no it + + + align:start position:0% +say well that's counterproductive no it +is it's a perfect way to maintain + + align:start position:0% +is it's a perfect way to maintain + + + align:start position:0% +is it's a perfect way to maintain +a good muscle tone so you're ready to + + align:start position:0% +a good muscle tone so you're ready to + + + align:start position:0% +a good muscle tone so you're ready to +move + + align:start position:0% +move + + + align:start position:0% +move +if you're if you don't have good stretch + + align:start position:0% +if you're if you don't have good stretch + + + align:start position:0% +if you're if you don't have good stretch +reflexes so you don't have some tension + + align:start position:0% +reflexes so you don't have some tension + + + align:start position:0% +reflexes so you don't have some tension +in those muscles you can't respond + + align:start position:0% +in those muscles you can't respond + + + align:start position:0% +in those muscles you can't respond +quickly + + align:start position:0% + + + + align:start position:0% + +and if you wonder when you're moving + + align:start position:0% +and if you wonder when you're moving + + + align:start position:0% +and if you wonder when you're moving +your arm or apathy + + align:start position:0% +your arm or apathy + + + align:start position:0% +your arm or apathy +if I'm moving my arm like this you might + + align:start position:0% +if I'm moving my arm like this you might + + + align:start position:0% +if I'm moving my arm like this you might +be surprised if you you do this + + align:start position:0% +be surprised if you you do this + + + align:start position:0% +be surprised if you you do this +feel the counteract the muscle on the + + align:start position:0% +feel the counteract the muscle on the + + + align:start position:0% +feel the counteract the muscle on the +other side + + align:start position:0% +other side + + + align:start position:0% +other side +it should just be the biceps here right + + align:start position:0% +it should just be the biceps here right + + + align:start position:0% +it should just be the biceps here right +but you'll see that the triceps contract + + align:start position:0% +but you'll see that the triceps contract + + + align:start position:0% +but you'll see that the triceps contract +also when I do + + align:start position:0% +also when I do + + + align:start position:0% +also when I do +any rapid movement that's true all right + + align:start position:0% +any rapid movement that's true all right + + + align:start position:0% +any rapid movement that's true all right +so + + align:start position:0% + + + + align:start position:0% + +we already talked about that + + align:start position:0% +we already talked about that + + + align:start position:0% +we already talked about that +describe the actions and connections and + + align:start position:0% +describe the actions and connections and + + + align:start position:0% +describe the actions and connections and +we'll withdrawals reflection reflex this + + align:start position:0% +we'll withdrawals reflection reflex this + + + align:start position:0% +we'll withdrawals reflection reflex this +came up before + + align:start position:0% +came up before + + + align:start position:0% +came up before +and then describe the origins of the + + align:start position:0% +and then describe the origins of the + + + align:start position:0% +and then describe the origins of the +spinal thalamic tract within the spinal + + align:start position:0% +spinal thalamic tract within the spinal + + + align:start position:0% +spinal thalamic tract within the spinal +cordial contrasts that with the spinal + + align:start position:0% +cordial contrasts that with the spinal + + + align:start position:0% +cordial contrasts that with the spinal +reticular tract so first of all what was + + align:start position:0% +reticular tract so first of all what was + + + align:start position:0% +reticular tract so first of all what was +the characteristic of the withdrawal + + align:start position:0% +the characteristic of the withdrawal + + + align:start position:0% +the characteristic of the withdrawal +reflex + + align:start position:0% +reflex + + + align:start position:0% +reflex +how is it different + + align:start position:0% +how is it different + + + align:start position:0% +how is it different +from the stretch reflex + + align:start position:0% + + + + align:start position:0% + +what would be the difference + + align:start position:0% + + + + align:start position:0% + +the first synapse would not be on the + + align:start position:0% +the first synapse would not be on the + + + align:start position:0% +the first synapse would not be on the +motor neuron + + align:start position:0% +motor neuron + + + align:start position:0% +motor neuron +it always involves at least two synapses + + align:start position:0% +it always involves at least two synapses + + + align:start position:0% +it always involves at least two synapses +in the chord + + align:start position:0% +in the chord + + + align:start position:0% +in the chord +so here + + align:start position:0% +so here + + + align:start position:0% +so here +in this little sketch I show first of + + align:start position:0% +in this little sketch I show first of + + + align:start position:0% +in this little sketch I show first of +all they're not the largest actions + + align:start position:0% +all they're not the largest actions + + + align:start position:0% +all they're not the largest actions +but they're at axons that terminate in + + align:start position:0% +but they're at axons that terminate in + + + align:start position:0% +but they're at axons that terminate in +the dorsal horn + + align:start position:0% +the dorsal horn + + + align:start position:0% +the dorsal horn +or in the intermediate layer there + + align:start position:0% +or in the intermediate layer there + + + align:start position:0% +or in the intermediate layer there +and then those cells like this one + + align:start position:0% +and then those cells like this one + + + align:start position:0% +and then those cells like this one +you can contact a motor neuron that + + align:start position:0% +you can contact a motor neuron that + + + align:start position:0% +you can contact a motor neuron that +would be the shortest Pathway to a + + align:start position:0% +would be the shortest Pathway to a + + + align:start position:0% +would be the shortest Pathway to a +flexor muscle + + align:start position:0% +flexor muscle + + + align:start position:0% +flexor muscle +to get the withdrawal reflex + + align:start position:0% +to get the withdrawal reflex + + + align:start position:0% +to get the withdrawal reflex +the fibers carrying that input tend to + + align:start position:0% +the fibers carrying that input tend to + + + align:start position:0% +the fibers carrying that input tend to +be small carrying input from pain + + align:start position:0% +be small carrying input from pain + + + align:start position:0% +be small carrying input from pain +Sensations + + align:start position:0% +Sensations + + + align:start position:0% +Sensations +okay + + align:start position:0% +okay + + + align:start position:0% +okay +it also happens with extreme pressure + + align:start position:0% +it also happens with extreme pressure + + + align:start position:0% +it also happens with extreme pressure +and so forth + + align:start position:0% +and so forth + + + align:start position:0% +and so forth +okay + + align:start position:0% +okay + + + align:start position:0% +okay +note that our similar connections here I + + align:start position:0% +note that our similar connections here I + + + align:start position:0% +note that our similar connections here I +show the same Axon + + align:start position:0% +show the same Axon + + + align:start position:0% +show the same Axon +with a branch that gives rise to a + + align:start position:0% +with a branch that gives rise to a + + + align:start position:0% +with a branch that gives rise to a +flexor reflex and there's a branch here + + align:start position:0% +flexor reflex and there's a branch here + + + align:start position:0% +flexor reflex and there's a branch here +contacting a neuron + + align:start position:0% +contacting a neuron + + + align:start position:0% +contacting a neuron +that sends its axon across to the other + + align:start position:0% +that sends its axon across to the other + + + align:start position:0% +that sends its axon across to the other +side becomes a spinal thalamic tract + + align:start position:0% +side becomes a spinal thalamic tract + + + align:start position:0% +side becomes a spinal thalamic tract +axon that's the typical origin of spinal + + align:start position:0% +axon that's the typical origin of spinal + + + align:start position:0% +axon that's the typical origin of spinal +thalamic tract okay remember this final + + align:start position:0% +thalamic tract okay remember this final + + + align:start position:0% +thalamic tract okay remember this final +fly on the track + + align:start position:0% +fly on the track + + + align:start position:0% +fly on the track +only if + + align:start position:0% +only if + + + align:start position:0% +only if +no more than 20 percent of the axons + + align:start position:0% +no more than 20 percent of the axons + + + align:start position:0% +no more than 20 percent of the axons +even in the higher primates actually + + align:start position:0% +even in the higher primates actually + + + align:start position:0% +even in the higher primates actually +reach the thousands + + align:start position:0% +reach the thousands + + + align:start position:0% +reach the thousands +they go to the reticular formation of + + align:start position:0% +they go to the reticular formation of + + + align:start position:0% +they go to the reticular formation of +the hindbrain the midbrain they go to + + align:start position:0% +the hindbrain the midbrain they go to + + + align:start position:0% +the hindbrain the midbrain they go to +the older Parts the thalamus and then + + align:start position:0% +the older Parts the thalamus and then + + + align:start position:0% +the older Parts the thalamus and then +some of them go to the + + align:start position:0% +some of them go to the + + + align:start position:0% +some of them go to the +the new parts of the founders that + + align:start position:0% +the new parts of the founders that + + + align:start position:0% +the new parts of the founders that +project in new cortex + + align:start position:0% +project in new cortex + + + align:start position:0% +project in new cortex +okay so how is the spinal reticular + + align:start position:0% +okay so how is the spinal reticular + + + align:start position:0% +okay so how is the spinal reticular +pathway different + + align:start position:0% +pathway different + + + align:start position:0% +pathway different +we call this spinal thalamic even though + + align:start position:0% +we call this spinal thalamic even though + + + align:start position:0% +we call this spinal thalamic even though +it does go to reticular formation too + + align:start position:0% +it does go to reticular formation too + + + align:start position:0% +it does go to reticular formation too +but we call it when we call it spinal + + align:start position:0% +but we call it when we call it spinal + + + align:start position:0% +but we call it when we call it spinal +reticular we're talking about an even + + align:start position:0% +reticular we're talking about an even + + + align:start position:0% +reticular we're talking about an even +older pathway before there was any + + align:start position:0% +older pathway before there was any + + + align:start position:0% +older pathway before there was any +Crossing so a pathway you found you find + + align:start position:0% +Crossing so a pathway you found you find + + + align:start position:0% +Crossing so a pathway you found you find +in the most ancient of the vertebrates + + align:start position:0% +in the most ancient of the vertebrates + + + align:start position:0% +in the most ancient of the vertebrates +like hagfish and lionfish + + align:start position:0% +like hagfish and lionfish + + + align:start position:0% +like hagfish and lionfish +and even amphioaxis has Pathways like + + align:start position:0% +and even amphioaxis has Pathways like + + + align:start position:0% +and even amphioaxis has Pathways like +the spinal reticular okay there they are + + align:start position:0% +the spinal reticular okay there they are + + + align:start position:0% +the spinal reticular okay there they are +they come from neurons here they get + + align:start position:0% +they come from neurons here they get + + + align:start position:0% +they come from neurons here they get +input from Reversal roots + + align:start position:0% +input from Reversal roots + + + align:start position:0% +input from Reversal roots +the Axon + + align:start position:0% +the Axon + + + align:start position:0% +the Axon +enters the lateral column collateral + + align:start position:0% +enters the lateral column collateral + + + align:start position:0% +enters the lateral column collateral +columns on the same site and the + + align:start position:0% +columns on the same site and the + + + align:start position:0% +columns on the same site and the +Excellence ascent + + align:start position:0% +Excellence ascent + + + align:start position:0% +Excellence ascent +okay some of them actually terminated in + + align:start position:0% +okay some of them actually terminated in + + + align:start position:0% +okay some of them actually terminated in +the spinal cord but many of them are + + align:start position:0% +the spinal cord but many of them are + + + align:start position:0% +the spinal cord but many of them are +reaching the brain they're called spinal + + align:start position:0% +reaching the brain they're called spinal + + + align:start position:0% +reaching the brain they're called spinal +reticulator + + align:start position:0% +reticulator + + + align:start position:0% +reticulator +because they terminate mainly in + + align:start position:0% +because they terminate mainly in + + + align:start position:0% +because they terminate mainly in +reticular formation + + align:start position:0% +reticular formation + + + align:start position:0% +reticular formation +at all levels of the brain stem + + align:start position:0% +at all levels of the brain stem + + + align:start position:0% +at all levels of the brain stem +the longest ones do get into Thalamus + + align:start position:0% +the longest ones do get into Thalamus + + + align:start position:0% +the longest ones do get into Thalamus +but most most of them terminate in the + + align:start position:0% +but most most of them terminate in the + + + align:start position:0% +but most most of them terminate in the +older parts of the fifth Thalamus and + + align:start position:0% +older parts of the fifth Thalamus and + + + align:start position:0% +older parts of the fifth Thalamus and +symptoms + + align:start position:0% +symptoms + + + align:start position:0% +symptoms +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that is the parts that don't project + + align:start position:0% +that is the parts that don't project + + + align:start position:0% +that is the parts that don't project +the neocortex or at least that's not + + align:start position:0% +the neocortex or at least that's not + + + align:start position:0% +the neocortex or at least that's not +their only projection + + align:start position:0% +their only projection + + + align:start position:0% +their only projection +this is just for those of you who are + + align:start position:0% +this is just for those of you who are + + + align:start position:0% +this is just for those of you who are +curious what you might encounter in + + align:start position:0% +curious what you might encounter in + + + align:start position:0% +curious what you might encounter in +medical school you will get pictures + + align:start position:0% +medical school you will get pictures + + + align:start position:0% +medical school you will get pictures +like this where they show in blue here's + + align:start position:0% +like this where they show in blue here's + + + align:start position:0% +like this where they show in blue here's +spinal reticular Pathways in a bunch of + + align:start position:0% +spinal reticular Pathways in a bunch of + + + align:start position:0% +spinal reticular Pathways in a bunch of +sections of the human brain this is + + align:start position:0% +sections of the human brain this is + + + align:start position:0% +sections of the human brain this is +midbrain up here caudal midbrain here + + align:start position:0% +midbrain up here caudal midbrain here + + + align:start position:0% +midbrain up here caudal midbrain here +and there's the ponds and human + + align:start position:0% +and there's the ponds and human + + + align:start position:0% +and there's the ponds and human +you can see how much I've simplified + + align:start position:0% +you can see how much I've simplified + + + align:start position:0% +you can see how much I've simplified +when I + + align:start position:0% +when I + + + align:start position:0% +when I +present this introduction to neuron atom + + align:start position:0% +present this introduction to neuron atom + + + align:start position:0% +present this introduction to neuron atom +you can say understanding the concepts + + align:start position:0% +you can say understanding the concepts + + + align:start position:0% +you can say understanding the concepts +is the most important thing once you + + align:start position:0% +is the most important thing once you + + + align:start position:0% +is the most important thing once you +understand them well and get that + + align:start position:0% +understand them well and get that + + + align:start position:0% +understand them well and get that +organization in your mind then + + align:start position:0% +organization in your mind then + + + align:start position:0% +organization in your mind then +figures like this won't confuse you so + + align:start position:0% +figures like this won't confuse you so + + + align:start position:0% +figures like this won't confuse you so +much and they do show + + align:start position:0% +much and they do show + + + align:start position:0% +much and they do show +some of the actions right here + + align:start position:0% +some of the actions right here + + + align:start position:0% +some of the actions right here +going above the midbrain + + align:start position:0% +going above the midbrain + + + align:start position:0% +going above the midbrain +to + + align:start position:0% +to + + + align:start position:0% +to +interlamine or thalamic nuclei and + + align:start position:0% +interlamine or thalamic nuclei and + + + align:start position:0% +interlamine or thalamic nuclei and +hypothalamus + + align:start position:0% +hypothalamus + + + align:start position:0% +hypothalamus +we haven't talked about what what are + + align:start position:0% +we haven't talked about what what are + + + align:start position:0% +we haven't talked about what what are +the intra laminariland nuclei but that's + + align:start position:0% +the intra laminariland nuclei but that's + + + align:start position:0% +the intra laminariland nuclei but that's +the name for the older parts of the + + align:start position:0% +the name for the older parts of the + + + align:start position:0% +the name for the older parts of the +balance parts that survive complete + + align:start position:0% +balance parts that survive complete + + + align:start position:0% +balance parts that survive complete +removal of the neocortex all right + + align:start position:0% +removal of the neocortex all right + + + align:start position:0% +removal of the neocortex all right +so where do the longest actions of the + + align:start position:0% +so where do the longest actions of the + + + align:start position:0% +so where do the longest actions of the +dorsal columns originate + + align:start position:0% +dorsal columns originate + + + align:start position:0% +dorsal columns originate +and where do they terminate + + align:start position:0% +and where do they terminate + + + align:start position:0% +and where do they terminate +we introduce the dorsal column medial + + align:start position:0% +we introduce the dorsal column medial + + + align:start position:0% +we introduce the dorsal column medial +meniscus pathway less time + + align:start position:0% +meniscus pathway less time + + + align:start position:0% +meniscus pathway less time +okay it's different from the spinal + + align:start position:0% +okay it's different from the spinal + + + align:start position:0% +okay it's different from the spinal +thalamic tract but like the spinal + + align:start position:0% +thalamic tract but like the spinal + + + align:start position:0% +thalamic tract but like the spinal +thalamic tract + + align:start position:0% +thalamic tract + + + align:start position:0% +thalamic tract +it's a pathway that carries input to the + + align:start position:0% +it's a pathway that carries input to the + + + align:start position:0% +it's a pathway that carries input to the +opposite side of the Forum + + align:start position:0% +opposite side of the Forum + + + align:start position:0% +opposite side of the Forum +okay + + align:start position:0% + + + + align:start position:0% + +so we're the longest accidents of that + + align:start position:0% +so we're the longest accidents of that + + + align:start position:0% +so we're the longest accidents of that +pathway originate + + align:start position:0% + + + + align:start position:0% + +well we know where they terminate the + + align:start position:0% +well we know where they terminate the + + + align:start position:0% +well we know where they terminate the +dorsal columns are primary sensory axons + + align:start position:0% +dorsal columns are primary sensory axons + + + align:start position:0% +dorsal columns are primary sensory axons +they're these axons we're talking about + + align:start position:0% +they're these axons we're talking about + + + align:start position:0% +they're these axons we're talking about +up here the dorsal columns + + align:start position:0% +up here the dorsal columns + + + align:start position:0% +up here the dorsal columns +and as I show here + + align:start position:0% +and as I show here + + + align:start position:0% +and as I show here +the primary sensory Axon + + align:start position:0% +the primary sensory Axon + + + align:start position:0% +the primary sensory Axon +doesn't terminate on anything there it + + align:start position:0% +doesn't terminate on anything there it + + + align:start position:0% +doesn't terminate on anything there it +just turns rostrally + + align:start position:0% +just turns rostrally + + + align:start position:0% +just turns rostrally +that often has a caudal Branch to + + align:start position:0% +that often has a caudal Branch to + + + align:start position:0% +that often has a caudal Branch to +but we're concerned about the rostral + + align:start position:0% +but we're concerned about the rostral + + + align:start position:0% +but we're concerned about the rostral +branch + + align:start position:0% +branch + + + align:start position:0% +branch +primary sensory action + + align:start position:0% +primary sensory action + + + align:start position:0% +primary sensory action +goes all the way up to the top of the + + align:start position:0% +goes all the way up to the top of the + + + align:start position:0% +goes all the way up to the top of the +spinal cord + + align:start position:0% +spinal cord + + + align:start position:0% +spinal cord +to the dorsal column nuclei + + align:start position:0% +to the dorsal column nuclei + + + align:start position:0% +to the dorsal column nuclei +they have names the dorsal column nuclei + + align:start position:0% +they have names the dorsal column nuclei + + + align:start position:0% +they have names the dorsal column nuclei +I don't care if you remember that right + + align:start position:0% +I don't care if you remember that right + + + align:start position:0% +I don't care if you remember that right +now + + align:start position:0% +now + + + align:start position:0% +now +they're called the slender nucleus and + + align:start position:0% +they're called the slender nucleus and + + + align:start position:0% +they're called the slender nucleus and +the wedge-shaped nucleus the grossile + + align:start position:0% +the wedge-shaped nucleus the grossile + + + align:start position:0% +the wedge-shaped nucleus the grossile +and cuneat nuclei nucleus paracillus + + align:start position:0% +and cuneat nuclei nucleus paracillus + + + align:start position:0% +and cuneat nuclei nucleus paracillus +nucleus cumulus + + align:start position:0% +nucleus cumulus + + + align:start position:0% +nucleus cumulus +whenever you learn medical school + + align:start position:0% +whenever you learn medical school + + + align:start position:0% +whenever you learn medical school +Anatomy you learn these names but + + align:start position:0% +Anatomy you learn these names but + + + align:start position:0% +Anatomy you learn these names but +remember them as just as the dorsal + + align:start position:0% +remember them as just as the dorsal + + + align:start position:0% +remember them as just as the dorsal +column nuclei for now and they + + align:start position:0% +column nuclei for now and they + + + align:start position:0% +column nuclei for now and they +that's they are the secondary Sensory + + align:start position:0% +that's they are the secondary Sensory + + + align:start position:0% +that's they are the secondary Sensory +neurons + + align:start position:0% + + + + align:start position:0% + +so we know where they where were the + + align:start position:0% +so we know where they where were the + + + align:start position:0% +so we know where they where were the +longest axons originate we know the + + align:start position:0% +longest axons originate we know the + + + align:start position:0% +longest axons originate we know the +nuclei are way up at the top of the + + align:start position:0% +nuclei are way up at the top of the + + + align:start position:0% +nuclei are way up at the top of the +spinal cord + + align:start position:0% +spinal cord + + + align:start position:0% +spinal cord +so the longest axons originate from the + + align:start position:0% +so the longest axons originate from the + + + align:start position:0% +so the longest axons originate from the +most caudal part + + align:start position:0% +most caudal part + + + align:start position:0% +most caudal part +of the body + + align:start position:0% +of the body + + + align:start position:0% +of the body +that's not the feet + + align:start position:0% +that's not the feet + + + align:start position:0% +that's not the feet +remember the dermatome map + + align:start position:0% + + + + align:start position:0% + +the call they originate in the caudal + + align:start position:0% +the call they originate in the caudal + + + align:start position:0% +the call they originate in the caudal +most dermatodes right around your + + align:start position:0% +most dermatodes right around your + + + align:start position:0% +most dermatodes right around your +tailbone + + align:start position:0% +tailbone + + + align:start position:0% +tailbone +in the region of your tail + + align:start position:0% +in the region of your tail + + + align:start position:0% +in the region of your tail +okay that's where they originate and + + align:start position:0% +okay that's where they originate and + + + align:start position:0% +okay that's where they originate and +they go all the way up to the top of the + + align:start position:0% +they go all the way up to the top of the + + + align:start position:0% +they go all the way up to the top of the +spinal cord and their primary sensory + + align:start position:0% +spinal cord and their primary sensory + + + align:start position:0% +spinal cord and their primary sensory +excellence + + align:start position:0% +excellence + + + align:start position:0% +excellence +rapidly conducting May tend to be larger + + align:start position:0% +rapidly conducting May tend to be larger + + + align:start position:0% +rapidly conducting May tend to be larger +than spinal thalamic correct accents + + align:start position:0% +than spinal thalamic correct accents + + + align:start position:0% +than spinal thalamic correct accents +so they conduct more rapidly + + align:start position:0% + + + + align:start position:0% + +they those longest axons terminate in + + align:start position:0% +they those longest axons terminate in + + + align:start position:0% +they those longest axons terminate in +the most medial + + align:start position:0% +the most medial + + + align:start position:0% +the most medial +nuclei + + align:start position:0% +nuclei + + + align:start position:0% +nuclei +it's characteristic of dorsal columns + + align:start position:0% +it's characteristic of dorsal columns + + + align:start position:0% +it's characteristic of dorsal columns +that the axons of the dorsal Roots enter + + align:start position:0% +that the axons of the dorsal Roots enter + + + align:start position:0% +that the axons of the dorsal Roots enter +join the dorsal columns from lateral + + align:start position:0% +join the dorsal columns from lateral + + + align:start position:0% +join the dorsal columns from lateral +side so the further up you go + + align:start position:0% +side so the further up you go + + + align:start position:0% +side so the further up you go +the more lateral the axons are + + align:start position:0% +the more lateral the axons are + + + align:start position:0% +the more lateral the axons are +the ones that originated more caudally + + align:start position:0% +the ones that originated more caudally + + + align:start position:0% +the ones that originated more caudally +are more medial Okay so + + align:start position:0% +are more medial Okay so + + + align:start position:0% +are more medial Okay so +and when you get then to the dorsal + + align:start position:0% +and when you get then to the dorsal + + + align:start position:0% +and when you get then to the dorsal +column nuclei + + align:start position:0% +column nuclei + + + align:start position:0% +column nuclei +they have an organization there it's + + align:start position:0% +they have an organization there it's + + + align:start position:0% +they have an organization there it's +quite topographic + + align:start position:0% +quite topographic + + + align:start position:0% +quite topographic +and then if you once you understand that + + align:start position:0% +and then if you once you understand that + + + align:start position:0% +and then if you once you understand that +you can answer this question explain how + + align:start position:0% +you can answer this question explain how + + + align:start position:0% +you can answer this question explain how +there's an organized representation of + + align:start position:0% +there's an organized representation of + + + align:start position:0% +there's an organized representation of +the surface of the entire body in cell + + align:start position:0% +the surface of the entire body in cell + + + align:start position:0% +the surface of the entire body in cell +group + + align:start position:0% +group + + + align:start position:0% +group +that the dorsal most in the spinal cord + + align:start position:0% +that the dorsal most in the spinal cord + + + align:start position:0% +that the dorsal most in the spinal cord +those those are calling okay + + align:start position:0% +those those are calling okay + + + align:start position:0% +those those are calling okay +but wait a minute + + align:start position:0% + + + + align:start position:0% + +if it's the entire body it has to + + align:start position:0% +if it's the entire body it has to + + + align:start position:0% +if it's the entire body it has to +include the face and head right + + align:start position:0% + + + + align:start position:0% + +so why is that represented up there I + + align:start position:0% +so why is that represented up there I + + + align:start position:0% +so why is that represented up there I +say the whole body + + align:start position:0% + + + + align:start position:0% + +so here's my picture of it here's the + + align:start position:0% +so here's my picture of it here's the + + + align:start position:0% +so here's my picture of it here's the +dorsal columns and as you get up to the + + align:start position:0% +dorsal columns and as you get up to the + + + align:start position:0% +dorsal columns and as you get up to the +top of the cord cells appear right there + + align:start position:0% +top of the cord cells appear right there + + + align:start position:0% +top of the cord cells appear right there +right within those among those axons and + + align:start position:0% +right within those among those axons and + + + align:start position:0% +right within those among those axons and +there are some columns + + align:start position:0% +there are some columns + + + align:start position:0% +there are some columns +one group here medially that's the more + + align:start position:0% +one group here medially that's the more + + + align:start position:0% +one group here medially that's the more +slender nucleus represents the lower + + align:start position:0% +slender nucleus represents the lower + + + align:start position:0% +slender nucleus represents the lower +part of the body + + align:start position:0% +part of the body + + + align:start position:0% +part of the body +the tail region the lower legs + + align:start position:0% +the tail region the lower legs + + + align:start position:0% +the tail region the lower legs +and then the nucleus cumulus tends to be + + align:start position:0% +and then the nucleus cumulus tends to be + + + align:start position:0% +and then the nucleus cumulus tends to be +larger because the four limbs + + align:start position:0% +larger because the four limbs + + + align:start position:0% +larger because the four limbs +certainly in humans especially the arms + + align:start position:0% +certainly in humans especially the arms + + + align:start position:0% +certainly in humans especially the arms +and hands are highly innervated + + align:start position:0% +and hands are highly innervated + + + align:start position:0% +and hands are highly innervated +so you have many more axons terminating + + align:start position:0% +so you have many more axons terminating + + + align:start position:0% +so you have many more axons terminating +that's where the upper bodies represent + + align:start position:0% +that's where the upper bodies represent + + + align:start position:0% +that's where the upper bodies represent +but out here in the dorsal Columns of + + align:start position:0% +but out here in the dorsal Columns of + + + align:start position:0% +but out here in the dorsal Columns of +the spinal cord + + align:start position:0% +the spinal cord + + + align:start position:0% +the spinal cord +the face is represented + + align:start position:0% +the face is represented + + + align:start position:0% +the face is represented +that seems really odd when you first + + align:start position:0% +that seems really odd when you first + + + align:start position:0% +that seems really odd when you first +encounter it but it's because axons that + + align:start position:0% +encounter it but it's because axons that + + + align:start position:0% +encounter it but it's because axons that +come in through the trigeminal nerve + + align:start position:0% +come in through the trigeminal nerve + + + align:start position:0% +come in through the trigeminal nerve +some of them + + align:start position:0% +some of them + + + align:start position:0% +some of them +extend and run along + + align:start position:0% +extend and run along + + + align:start position:0% +extend and run along +through the hindbrain and into the top + + align:start position:0% +through the hindbrain and into the top + + + align:start position:0% +through the hindbrain and into the top +of the spinal cord they're found right + + align:start position:0% +of the spinal cord they're found right + + + align:start position:0% +of the spinal cord they're found right +here at this level + + align:start position:0% +here at this level + + + align:start position:0% +here at this level +it's an upper cervical cord they are + + align:start position:0% +it's an upper cervical cord they are + + + align:start position:0% +it's an upper cervical cord they are +terminating in those cells there of the + + align:start position:0% +terminating in those cells there of the + + + align:start position:0% +terminating in those cells there of the +dorsal columns representing the face + + align:start position:0% +dorsal columns representing the face + + + align:start position:0% +dorsal columns representing the face +the sensation + + align:start position:0% +the sensation + + + align:start position:0% +the sensation +that they + + align:start position:0% +that they + + + align:start position:0% +that they +are responsible for + + align:start position:0% +are responsible for + + + align:start position:0% +are responsible for +those ones that descend that car are + + align:start position:0% +those ones that descend that car are + + + align:start position:0% +those ones that descend that car are +pain and temperature + + align:start position:0% +pain and temperature + + + align:start position:0% +pain and temperature +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and that's why a surgical operation for + + align:start position:0% +and that's why a surgical operation for + + + align:start position:0% +and that's why a surgical operation for +very difficult to control pain sometimes + + align:start position:0% +very difficult to control pain sometimes + + + align:start position:0% +very difficult to control pain sometimes +consists in going to the very top of the + + align:start position:0% +consists in going to the very top of the + + + align:start position:0% +consists in going to the very top of the +spinal cord it's dangerous surgery + + align:start position:0% +spinal cord it's dangerous surgery + + + align:start position:0% +spinal cord it's dangerous surgery +because you can't + + align:start position:0% +because you can't + + + align:start position:0% +because you can't +do much extra damage but they will + + align:start position:0% +do much extra damage but they will + + + align:start position:0% +do much extra damage but they will +actually cut these accents + + align:start position:0% +actually cut these accents + + + align:start position:0% +actually cut these accents +to reduce the pain the only trouble is + + align:start position:0% +to reduce the pain the only trouble is + + + align:start position:0% +to reduce the pain the only trouble is +surgery to control pain + + align:start position:0% +surgery to control pain + + + align:start position:0% +surgery to control pain +is almost never permanently successful + + align:start position:0% +is almost never permanently successful + + + align:start position:0% +is almost never permanently successful +pain always tends to come back and + + align:start position:0% +pain always tends to come back and + + + align:start position:0% +pain always tends to come back and +there's various reasons for that but + + align:start position:0% +there's various reasons for that but + + + align:start position:0% +there's various reasons for that but +there is still an area of active + + align:start position:0% +there is still an area of active + + + align:start position:0% +there is still an area of active +research + + align:start position:0% + + + + align:start position:0% + +the representation of pain in the body + + align:start position:0% +the representation of pain in the body + + + align:start position:0% +the representation of pain in the body +okay so the entire body here represented + + align:start position:0% +okay so the entire body here represented + + + align:start position:0% +okay so the entire body here represented +in a topographic way from the caudal in + + align:start position:0% +in a topographic way from the caudal in + + + align:start position:0% +in a topographic way from the caudal in +medially + + align:start position:0% +medially + + + align:start position:0% +medially +to the face area laterally + + align:start position:0% +to the face area laterally + + + align:start position:0% +to the face area laterally +at the level of the dorsal colony + + align:start position:0% +at the level of the dorsal colony + + + align:start position:0% +at the level of the dorsal colony +so now let's talk about spinal + + align:start position:0% +so now let's talk about spinal + + + align:start position:0% +so now let's talk about spinal +cerebellar + + align:start position:0% + + + + align:start position:0% + +the source of axons terminating in this + + align:start position:0% +the source of axons terminating in this + + + align:start position:0% +the source of axons terminating in this +column of cells we call Clark's columns + + align:start position:0% +column of cells we call Clark's columns + + + align:start position:0% +column of cells we call Clark's columns +sometimes just called nucleus or cells + + align:start position:0% +sometimes just called nucleus or cells + + + align:start position:0% +sometimes just called nucleus or cells +of the spinal cord + + align:start position:0% +of the spinal cord + + + align:start position:0% +of the spinal cord +from the lower limbs + + align:start position:0% +from the lower limbs + + + align:start position:0% +from the lower limbs +and the ascending fiber tract that + + align:start position:0% +and the ascending fiber tract that + + + align:start position:0% +and the ascending fiber tract that +originates in Clark's column is one of + + align:start position:0% +originates in Clark's column is one of + + + align:start position:0% +originates in Clark's column is one of +the spinal cerebellar drugs + + align:start position:0% +the spinal cerebellar drugs + + + align:start position:0% +the spinal cerebellar drugs +this one's called the dorsal spinal + + align:start position:0% +this one's called the dorsal spinal + + + align:start position:0% +this one's called the dorsal spinal +cerebellar tract it travels like this + + align:start position:0% +cerebellar tract it travels like this + + + align:start position:0% +cerebellar tract it travels like this +so here we are + + align:start position:0% + + + + align:start position:0% + +axons coming in + + align:start position:0% +axons coming in + + + align:start position:0% +axons coming in +terminating in nucleus darcellus or + + align:start position:0% +terminating in nucleus darcellus or + + + align:start position:0% +terminating in nucleus darcellus or +Clark's column + + align:start position:0% +Clark's column + + + align:start position:0% +Clark's column +right there + + align:start position:0% +right there + + + align:start position:0% +right there +there's a lateral horns you know you're + + align:start position:0% +there's a lateral horns you know you're + + + align:start position:0% +there's a lateral horns you know you're +in the most likely the thoracic spinal + + align:start position:0% +in the most likely the thoracic spinal + + + align:start position:0% +in the most likely the thoracic spinal +cord + + align:start position:0% +cord + + + align:start position:0% +cord +could be even after Lombard + + align:start position:0% +could be even after Lombard + + + align:start position:0% +could be even after Lombard +and the cells there send their axon into + + align:start position:0% +and the cells there send their axon into + + + align:start position:0% +and the cells there send their axon into +the + + align:start position:0% +the + + + align:start position:0% +the +more dorsal parts of the lateral column + + align:start position:0% +more dorsal parts of the lateral column + + + align:start position:0% +more dorsal parts of the lateral column +and then turn prostrate and they ascend + + align:start position:0% +and then turn prostrate and they ascend + + + align:start position:0% +and then turn prostrate and they ascend +all the way to the cerebellum + + align:start position:0% +all the way to the cerebellum + + + align:start position:0% +all the way to the cerebellum +that's one of + + align:start position:0% +that's one of + + + align:start position:0% +that's one of +two or three Pathways depending on the + + align:start position:0% +two or three Pathways depending on the + + + align:start position:0% +two or three Pathways depending on the +animal + + align:start position:0% +animal + + + align:start position:0% +animal +but most most of them have at least this + + align:start position:0% +but most most of them have at least this + + + align:start position:0% +but most most of them have at least this +level two different Pathways an + + align:start position:0% +level two different Pathways an + + + align:start position:0% +level two different Pathways an +uncrossed pathway like this and a cross + + align:start position:0% +uncrossed pathway like this and a cross + + + align:start position:0% +uncrossed pathway like this and a cross +pathway where the axons cross over and + + align:start position:0% +pathway where the axons cross over and + + + align:start position:0% +pathway where the axons cross over and +are much more like the spinal Calamity + + align:start position:0% +are much more like the spinal Calamity + + + align:start position:0% +are much more like the spinal Calamity +but also go to the cerebellum so where + + align:start position:0% +but also go to the cerebellum so where + + + align:start position:0% +but also go to the cerebellum so where +they originating + + align:start position:0% +they originating + + + align:start position:0% +they originating +what kind of information is important + + align:start position:0% +what kind of information is important + + + align:start position:0% +what kind of information is important +for the cerebellum + + align:start position:0% +for the cerebellum + + + align:start position:0% +for the cerebellum +they carry information on joint + + align:start position:0% +they carry information on joint + + + align:start position:0% +they carry information on joint +movements + + align:start position:0% +movements + + + align:start position:0% +movements +primarily from the laurelins and the + + align:start position:0% +primarily from the laurelins and the + + + align:start position:0% +primarily from the laurelins and the +trunk + + align:start position:0% +trunk + + + align:start position:0% +trunk +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so whenever you're moving you are + + align:start position:0% +so whenever you're moving you are + + + align:start position:0% +so whenever you're moving you are +generating Sensations that you can't we + + align:start position:0% +generating Sensations that you can't we + + + align:start position:0% +generating Sensations that you can't we +don't have as much conscious sensation + + align:start position:0% +don't have as much conscious sensation + + + align:start position:0% +don't have as much conscious sensation +although we do have some sense of where + + align:start position:0% +although we do have some sense of where + + + align:start position:0% +although we do have some sense of where +our arms position + + align:start position:0% +our arms position + + + align:start position:0% +our arms position +because we do some of that input doesn't + + align:start position:0% +because we do some of that input doesn't + + + align:start position:0% +because we do some of that input doesn't +go directly to the cerebellum + + align:start position:0% +go directly to the cerebellum + + + align:start position:0% +go directly to the cerebellum +it goes also to + + align:start position:0% +it goes also to + + + align:start position:0% +it goes also to +the cortex + + align:start position:0% + + + + align:start position:0% + +but that's the dorsal spinal + + align:start position:0% +but that's the dorsal spinal + + + align:start position:0% +but that's the dorsal spinal +cerebellatry + + align:start position:0% +cerebellatry + + + align:start position:0% +cerebellatry +okay another group of accents proprio + + align:start position:0% +okay another group of accents proprio + + + align:start position:0% +okay another group of accents proprio +spinal + + align:start position:0% + + + + align:start position:0% + +it literally means proper to the spinal + + align:start position:0% +it literally means proper to the spinal + + + align:start position:0% +it literally means proper to the spinal +cord + + align:start position:0% +cord + + + align:start position:0% +cord +in other words they never leave the + + align:start position:0% +in other words they never leave the + + + align:start position:0% +in other words they never leave the +spinal cord + + align:start position:0% +spinal cord + + + align:start position:0% +spinal cord +there's a lot of accidents like that + + align:start position:0% +there's a lot of accidents like that + + + align:start position:0% +there's a lot of accidents like that +so for example + + align:start position:0% +so for example + + + align:start position:0% +so for example +if we transect the spinal cord in an + + align:start position:0% +if we transect the spinal cord in an + + + align:start position:0% +if we transect the spinal cord in an +animal + + align:start position:0% +animal + + + align:start position:0% +animal +uh + + align:start position:0% +uh + + + align:start position:0% +uh +keep him alive we can do if we make the + + align:start position:0% +keep him alive we can do if we make the + + + align:start position:0% +keep him alive we can do if we make the +cut low enough he will live even + + align:start position:0% +cut low enough he will live even + + + align:start position:0% +cut low enough he will live even +without artificial respiration we're + + align:start position:0% +without artificial respiration we're + + + align:start position:0% +without artificial respiration we're +below the level of C4 you'll still be + + align:start position:0% +below the level of C4 you'll still be + + + align:start position:0% +below the level of C4 you'll still be +able to breathe + + align:start position:0% +able to breathe + + + align:start position:0% +able to breathe +um + + align:start position:0% +um + + + align:start position:0% +um +but + + align:start position:0% +but + + + align:start position:0% +but +if we really completely transacted the + + align:start position:0% +if we really completely transacted the + + + align:start position:0% +if we really completely transacted the +spinal cord the movements of the entire + + align:start position:0% +spinal cord the movements of the entire + + + align:start position:0% +spinal cord the movements of the entire +body coddle to that level will have to + + align:start position:0% +body coddle to that level will have to + + + align:start position:0% +body coddle to that level will have to +be controlled only by the spinal cord + + align:start position:0% +be controlled only by the spinal cord + + + align:start position:0% +be controlled only by the spinal cord +and after a period of recovery you can + + align:start position:0% +and after a period of recovery you can + + + align:start position:0% +and after a period of recovery you can +get + + align:start position:0% +get + + + align:start position:0% +get +different Gates you can get locomotor + + align:start position:0% +different Gates you can get locomotor + + + align:start position:0% +different Gates you can get locomotor +patterns + + align:start position:0% +patterns + + + align:start position:0% +patterns +because of proprio's final connections + + align:start position:0% +because of proprio's final connections + + + align:start position:0% +because of proprio's final connections +which are responsible for fixed action + + align:start position:0% +which are responsible for fixed action + + + align:start position:0% +which are responsible for fixed action +patterns that is they're under genetic + + align:start position:0% +patterns that is they're under genetic + + + align:start position:0% +patterns that is they're under genetic +control + + align:start position:0% +control + + + align:start position:0% +control +and uh + + align:start position:0% + + + + align:start position:0% + +let's look at this picture on the left + + align:start position:0% +let's look at this picture on the left + + + align:start position:0% +let's look at this picture on the left +side the orange ones + + align:start position:0% +side the orange ones + + + align:start position:0% +side the orange ones +just sketched + + align:start position:0% +just sketched + + + align:start position:0% +just sketched +copiospinal axons they tend to a run in + + align:start position:0% +copiospinal axons they tend to a run in + + + align:start position:0% +copiospinal axons they tend to a run in +The Columns of axons nearest the gray + + align:start position:0% +The Columns of axons nearest the gray + + + align:start position:0% +The Columns of axons nearest the gray +matter + + align:start position:0% +matter + + + align:start position:0% +matter +and I'm showing cells in the gray matter + + align:start position:0% +and I'm showing cells in the gray matter + + + align:start position:0% +and I'm showing cells in the gray matter +sending accents into that group + + align:start position:0% +sending accents into that group + + + align:start position:0% +sending accents into that group +they go to another level and then they + + align:start position:0% +they go to another level and then they + + + align:start position:0% +they go to another level and then they +terminate so it goes from one part they + + align:start position:0% +terminate so it goes from one part they + + + align:start position:0% +terminate so it goes from one part they +mostly in + + align:start position:0% +mostly in + + + align:start position:0% +mostly in +tersegnative essence + + align:start position:0% +tersegnative essence + + + align:start position:0% +tersegnative essence +passing from one segment to the other + + align:start position:0% +passing from one segment to the other + + + align:start position:0% +passing from one segment to the other +okay and then I'm asking about + + align:start position:0% +okay and then I'm asking about + + + align:start position:0% +okay and then I'm asking about +the descending axons + + align:start position:0% +the descending axons + + + align:start position:0% +the descending axons +that influence uh + + align:start position:0% + + + + align:start position:0% + +movements of the lens and other + + align:start position:0% +movements of the lens and other + + + align:start position:0% +movements of the lens and other +movements + + align:start position:0% + + + + align:start position:0% + +a lot a lot those movements are heavily + + align:start position:0% +a lot a lot those movements are heavily + + + align:start position:0% +a lot a lot those movements are heavily +influenced + + align:start position:0% +influenced + + + align:start position:0% +influenced +by uh Pathways from the brain and at + + align:start position:0% +by uh Pathways from the brain and at + + + align:start position:0% +by uh Pathways from the brain and at +this point + + align:start position:0% +this point + + + align:start position:0% +this point +just + + align:start position:0% +just + + + align:start position:0% +just +read the names get an idea where they're + + align:start position:0% +read the names get an idea where they're + + + align:start position:0% +read the names get an idea where they're +coming from the big ones here in human + + align:start position:0% +coming from the big ones here in human + + + align:start position:0% +coming from the big ones here in human +and other + + align:start position:0% +and other + + + align:start position:0% +and other +primates especially the large primates + + align:start position:0% +primates especially the large primates + + + align:start position:0% +primates especially the large primates +coming from neocortex + + align:start position:0% +coming from neocortex + + + align:start position:0% +coming from neocortex +this is the position of the cortical + + align:start position:0% +this is the position of the cortical + + + align:start position:0% +this is the position of the cortical +spinal tract the blue dots here + + align:start position:0% +spinal tract the blue dots here + + + align:start position:0% +spinal tract the blue dots here +in humans and monkeys and Eights and I'm + + align:start position:0% +in humans and monkeys and Eights and I'm + + + align:start position:0% +in humans and monkeys and Eights and I'm +showing how the actions tend to + + align:start position:0% +showing how the actions tend to + + + align:start position:0% +showing how the actions tend to +distribute you know throughout the + + align:start position:0% +distribute you know throughout the + + + align:start position:0% +distribute you know throughout the +spinal gray matter + + align:start position:0% + + + + align:start position:0% + +I show another pathway there that has a + + align:start position:0% +I show another pathway there that has a + + + align:start position:0% +I show another pathway there that has a +fairly similar trajectory coming from + + align:start position:0% +fairly similar trajectory coming from + + + align:start position:0% +fairly similar trajectory coming from +the midbrain we call it the rubro's + + align:start position:0% +the midbrain we call it the rubro's + + + align:start position:0% +the midbrain we call it the rubro's +final track ruber means red they come + + align:start position:0% +final track ruber means red they come + + + align:start position:0% +final track ruber means red they come +from the red nucleus the midbrain will + + align:start position:0% +from the red nucleus the midbrain will + + + align:start position:0% +from the red nucleus the midbrain will +be talking about that when we talk about + + align:start position:0% +be talking about that when we talk about + + + align:start position:0% +be talking about that when we talk about +Midway they have a little bit more + + align:start position:0% +Midway they have a little bit more + + + align:start position:0% +Midway they have a little bit more +limited distribution + + align:start position:0% +limited distribution + + + align:start position:0% +limited distribution +and they terminate mainly in the + + align:start position:0% +and they terminate mainly in the + + + align:start position:0% +and they terminate mainly in the +enlargements not in between the + + align:start position:0% +enlargements not in between the + + + align:start position:0% +enlargements not in between the +enlargements + + align:start position:0% +enlargements + + + align:start position:0% +enlargements +whereas cortical spinal tends to + + align:start position:0% +whereas cortical spinal tends to + + + align:start position:0% +whereas cortical spinal tends to +germinate on everything + + align:start position:0% +germinate on everything + + + align:start position:0% +germinate on everything +okay + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% +and then + + + align:start position:0% +and then +oh I should mention one more thing about + + align:start position:0% +oh I should mention one more thing about + + + align:start position:0% +oh I should mention one more thing about +the corticospinal + + align:start position:0% +the corticospinal + + + align:start position:0% +the corticospinal +it's not always in the lateral comes + + align:start position:0% +it's not always in the lateral comes + + + align:start position:0% +it's not always in the lateral comes +when your comparative anatomist like I + + align:start position:0% +when your comparative anatomist like I + + + align:start position:0% +when your comparative anatomist like I +am you really have to pay attention to + + align:start position:0% +am you really have to pay attention to + + + align:start position:0% +am you really have to pay attention to +this especially if you're using the + + align:start position:0% +this especially if you're using the + + + align:start position:0% +this especially if you're using the +animals for + + align:start position:0% +animals for + + + align:start position:0% +animals for +um to study the pathways like I did a + + align:start position:0% +um to study the pathways like I did a + + + align:start position:0% +um to study the pathways like I did a +study with a student of the cortical + + align:start position:0% +study with a student of the cortical + + + align:start position:0% +study with a student of the cortical +spinal Pathways in the hamster + + align:start position:0% +spinal Pathways in the hamster + + + align:start position:0% +spinal Pathways in the hamster +and their role in the behavior of the + + align:start position:0% +and their role in the behavior of the + + + align:start position:0% +and their role in the behavior of the +animal and it turns out we wanted to cut + + align:start position:0% +animal and it turns out we wanted to cut + + + align:start position:0% +animal and it turns out we wanted to cut +the pathway + + align:start position:0% +the pathway + + + align:start position:0% +the pathway +they don't travel here + + align:start position:0% +they don't travel here + + + align:start position:0% +they don't travel here +they travel + + align:start position:0% +they travel + + + align:start position:0% +they travel +in the ventral part of the dorsal cause + + align:start position:0% +in the ventral part of the dorsal cause + + + align:start position:0% +in the ventral part of the dorsal cause +that's true of the Rat too it's true the + + align:start position:0% +that's true of the Rat too it's true the + + + align:start position:0% +that's true of the Rat too it's true the +tree shoe it's true of many animals for + + align:start position:0% +tree shoe it's true of many animals for + + + align:start position:0% +tree shoe it's true of many animals for +a while we thought the tree shoe was A + + align:start position:0% +a while we thought the tree shoe was A + + + align:start position:0% +a while we thought the tree shoe was A +Primitive priming until somebody looked + + align:start position:0% +Primitive priming until somebody looked + + + align:start position:0% +Primitive priming until somebody looked +at the cortical spinal Pathways and + + align:start position:0% +at the cortical spinal Pathways and + + + align:start position:0% +at the cortical spinal Pathways and +found they were in the position primates + + align:start position:0% +found they were in the position primates + + + align:start position:0% +found they were in the position primates +they were in the position of + + align:start position:0% +they were in the position of + + + align:start position:0% +they were in the position of +insectivores and Roads + + align:start position:0% +insectivores and Roads + + + align:start position:0% +insectivores and Roads +okay here + + align:start position:0% +okay here + + + align:start position:0% +okay here +okay the other the ventral columns here + + align:start position:0% +okay the other the ventral columns here + + + align:start position:0% +okay the other the ventral columns here +which are written relative terms are + + align:start position:0% +which are written relative terms are + + + align:start position:0% +which are written relative terms are +similar throughout most mammals they + + align:start position:0% +similar throughout most mammals they + + + align:start position:0% +similar throughout most mammals they +contain the axons + + align:start position:0% +contain the axons + + + align:start position:0% +contain the axons +that control the body axis or posture + + align:start position:0% +that control the body axis or posture + + + align:start position:0% +that control the body axis or posture +vestibular reflexes writing reflexes + + align:start position:0% +vestibular reflexes writing reflexes + + + align:start position:0% +vestibular reflexes writing reflexes +uh + + align:start position:0% +uh + + + align:start position:0% +uh +also orienting movements if they're very + + align:start position:0% +also orienting movements if they're very + + + align:start position:0% +also orienting movements if they're very +car astral so I've listed the main ones + + align:start position:0% +car astral so I've listed the main ones + + + align:start position:0% +car astral so I've listed the main ones +here reticulous fine a lot of axons in + + align:start position:0% +here reticulous fine a lot of axons in + + + align:start position:0% +here reticulous fine a lot of axons in +the reticular formation the control + + align:start position:0% +the reticular formation the control + + + align:start position:0% +the reticular formation the control +fixed action paths they send their + + align:start position:0% +fixed action paths they send their + + + align:start position:0% +fixed action paths they send their +accents most of those involved + + align:start position:0% +accents most of those involved + + + align:start position:0% +accents most of those involved +seal muscle control or at least whole + + align:start position:0% +seal muscle control or at least whole + + + align:start position:0% +seal muscle control or at least whole +body movements + + align:start position:0% +body movements + + + align:start position:0% +body movements +so some of them might go + + align:start position:0% +so some of them might go + + + align:start position:0% +so some of them might go +to the motor neurons controlling the + + align:start position:0% +to the motor neurons controlling the + + + align:start position:0% +to the motor neurons controlling the +limbs as well okay but always whole body + + align:start position:0% +limbs as well okay but always whole body + + + align:start position:0% +limbs as well okay but always whole body +movements or axial muscles then + + align:start position:0% +movements or axial muscles then + + + align:start position:0% +movements or axial muscles then +vestibular spinal + + align:start position:0% + + + + align:start position:0% + +sorry but that's the nucleus fastidious + + align:start position:0% +sorry but that's the nucleus fastidious + + + align:start position:0% +sorry but that's the nucleus fastidious +is a deep nucleus to cerebellum so you + + align:start position:0% +is a deep nucleus to cerebellum so you + + + align:start position:0% +is a deep nucleus to cerebellum so you +can think of it at this point it's just + + align:start position:0% +can think of it at this point it's just + + + align:start position:0% +can think of it at this point it's just +cerebellum spinal + + align:start position:0% +cerebellum spinal + + + align:start position:0% +cerebellum spinal +and then technospinal from the tectum of + + align:start position:0% +and then technospinal from the tectum of + + + align:start position:0% +and then technospinal from the tectum of +the midbrain for turning movements and + + align:start position:0% +the midbrain for turning movements and + + + align:start position:0% +the midbrain for turning movements and +they only go to the cervical part of the + + align:start position:0% +they only go to the cervical part of the + + + align:start position:0% +they only go to the cervical part of the +cord + + align:start position:0% +cord + + + align:start position:0% +cord +there are + + align:start position:0% +there are + + + align:start position:0% +there are +postural adjustments whenever the animal + + align:start position:0% +postural adjustments whenever the animal + + + align:start position:0% +postural adjustments whenever the animal +makes a head movement like that + + align:start position:0% +makes a head movement like that + + + align:start position:0% +makes a head movement like that +but that involves + + align:start position:0% +but that involves + + + align:start position:0% +but that involves +that involves other neurons usually from + + align:start position:0% +that involves other neurons usually from + + + align:start position:0% +that involves other neurons usually from +the reticular formation reticular spine + + align:start position:0% +the reticular formation reticular spine + + + align:start position:0% +the reticular formation reticular spine +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so and here I just have the same picture + + align:start position:0% +so and here I just have the same picture + + + align:start position:0% +so and here I just have the same picture +and I'm just showing that these are + + align:start position:0% +and I'm just showing that these are + + + align:start position:0% +and I'm just showing that these are +almost all ascending axons in humans and + + align:start position:0% +almost all ascending axons in humans and + + + align:start position:0% +almost all ascending axons in humans and +Prime other primates in the dorsal + + align:start position:0% +Prime other primates in the dorsal + + + align:start position:0% +Prime other primates in the dorsal +columns + + align:start position:0% +columns + + + align:start position:0% +columns +okay + + align:start position:0% +okay + + + align:start position:0% +okay +if you're a rat or a tree shoe + + align:start position:0% +if you're a rat or a tree shoe + + + align:start position:0% +if you're a rat or a tree shoe +Heaven you'll find some cortical spinals + + align:start position:0% +Heaven you'll find some cortical spinals + + + align:start position:0% +Heaven you'll find some cortical spinals +here but these are otherwise in us all + + align:start position:0% +here but these are otherwise in us all + + + align:start position:0% +here but these are otherwise in us all +ascending actions the lateral columns + + align:start position:0% +ascending actions the lateral columns + + + align:start position:0% +ascending actions the lateral columns +are ascending and descending + + align:start position:0% +are ascending and descending + + + align:start position:0% +are ascending and descending +and by the way I'm not including here + + align:start position:0% +and by the way I'm not including here + + + align:start position:0% +and by the way I'm not including here +proprio spine they're always both + + align:start position:0% +proprio spine they're always both + + + align:start position:0% +proprio spine they're always both +ascending and descending they just don't + + align:start position:0% +ascending and descending they just don't + + + align:start position:0% +ascending and descending they just don't +leave the spinal cord and in the ventral + + align:start position:0% +leave the spinal cord and in the ventral + + + align:start position:0% +leave the spinal cord and in the ventral +columns here they're all descending + + align:start position:0% +columns here they're all descending + + + align:start position:0% +columns here they're all descending +actions + + align:start position:0% +actions + + + align:start position:0% +actions +almost all + + align:start position:0% +almost all + + + align:start position:0% +almost all +right + + align:start position:0% + + + + align:start position:0% + +we have only a little bit of time + + align:start position:0% +we have only a little bit of time + + + align:start position:0% +we have only a little bit of time +introduce the autonomic nervous system + + align:start position:0% +introduce the autonomic nervous system + + + align:start position:0% +introduce the autonomic nervous system +the peripheral nervous system compounds + + align:start position:0% +the peripheral nervous system compounds + + + align:start position:0% +the peripheral nervous system compounds +to innervate the glands and smooth + + align:start position:0% +to innervate the glands and smooth + + + align:start position:0% +to innervate the glands and smooth +muscle and also the cardiac muscle which + + align:start position:0% +muscle and also the cardiac muscle which + + + align:start position:0% +muscle and also the cardiac muscle which +is another type of stride muscle + + align:start position:0% +is another type of stride muscle + + + align:start position:0% +is another type of stride muscle +but it's innervated by the autonomic + + align:start position:0% +but it's innervated by the autonomic + + + align:start position:0% +but it's innervated by the autonomic +nervousness + + align:start position:0% + + + + align:start position:0% + +and so I'm giving you the answer talking + + align:start position:0% +and so I'm giving you the answer talking + + + align:start position:0% +and so I'm giving you the answer talking +about sometimes it's called visceral + + align:start position:0% +about sometimes it's called visceral + + + align:start position:0% +about sometimes it's called visceral +nervous system and it innovates the + + align:start position:0% +nervous system and it innovates the + + + align:start position:0% +nervous system and it innovates the +viscera but we call it autonomic + + align:start position:0% +viscera but we call it autonomic + + + align:start position:0% +viscera but we call it autonomic +uh + + align:start position:0% + + + + align:start position:0% + +and it contains these two components as + + align:start position:0% +and it contains these two components as + + + align:start position:0% +and it contains these two components as +most of you already know sympathetic and + + align:start position:0% +most of you already know sympathetic and + + + align:start position:0% +most of you already know sympathetic and +parasympathetic there's a third + + align:start position:0% +parasympathetic there's a third + + + align:start position:0% +parasympathetic there's a third +component that we can think of though as + + align:start position:0% +component that we can think of though as + + + align:start position:0% +component that we can think of though as +more like parasympathetic but + + align:start position:0% +more like parasympathetic but + + + align:start position:0% +more like parasympathetic but +we'll mention that as well + + align:start position:0% +we'll mention that as well + + + align:start position:0% +we'll mention that as well +we want to contrast the functions + + align:start position:0% +we want to contrast the functions + + + align:start position:0% +we want to contrast the functions +how do people usually summarize the + + align:start position:0% +how do people usually summarize the + + + align:start position:0% +how do people usually summarize the +functions + + align:start position:0% +functions + + + align:start position:0% +functions +functional difference between + + align:start position:0% +functional difference between + + + align:start position:0% +functional difference between +sympathetic and parasympathetic nervous + + align:start position:0% +sympathetic and parasympathetic nervous + + + align:start position:0% +sympathetic and parasympathetic nervous +system take the heart for example + + align:start position:0% +system take the heart for example + + + align:start position:0% +system take the heart for example +sympathetic nervous system what does it + + align:start position:0% +sympathetic nervous system what does it + + + align:start position:0% +sympathetic nervous system what does it +do to the heart + + align:start position:0% +do to the heart + + + align:start position:0% +do to the heart +speeds it up + + align:start position:0% +speeds it up + + + align:start position:0% +speeds it up +so parasympathetic so it's a doubt okay + + align:start position:0% +so parasympathetic so it's a doubt okay + + + align:start position:0% +so parasympathetic so it's a doubt okay +what about the gut + + align:start position:0% +what about the gut + + + align:start position:0% +what about the gut +peristalsis and all that + + align:start position:0% +peristalsis and all that + + + align:start position:0% +peristalsis and all that +most of that has control locally + + align:start position:0% +most of that has control locally + + + align:start position:0% +most of that has control locally +but it's also affected by autonomic + + align:start position:0% +but it's also affected by autonomic + + + align:start position:0% +but it's also affected by autonomic +nervous system + + align:start position:0% +nervous system + + + align:start position:0% +nervous system +the sympathetic nervous system tends to + + align:start position:0% +the sympathetic nervous system tends to + + + align:start position:0% +the sympathetic nervous system tends to +stop that + + align:start position:0% + + + + align:start position:0% + +intense suits + + align:start position:0% +intense suits + + + align:start position:0% +intense suits +increased blood flow to the muscles we + + align:start position:0% +increased blood flow to the muscles we + + + align:start position:0% +increased blood flow to the muscles we +call the sympathetic nervous system the + + align:start position:0% +call the sympathetic nervous system the + + + align:start position:0% +call the sympathetic nervous system the +fight or flight system because those are + + align:start position:0% +fight or flight system because those are + + + align:start position:0% +fight or flight system because those are +two situations where the sympathetic + + align:start position:0% +two situations where the sympathetic + + + align:start position:0% +two situations where the sympathetic +nervous system becomes totally dominant + + align:start position:0% +nervous system becomes totally dominant + + + align:start position:0% +nervous system becomes totally dominant +the autonomic system is always active at + + align:start position:0% +the autonomic system is always active at + + + align:start position:0% +the autonomic system is always active at +rest it can hits the the normal + + align:start position:0% +rest it can hits the the normal + + + align:start position:0% +rest it can hits the the normal +functions of organs controlled by the + + align:start position:0% +functions of organs controlled by the + + + align:start position:0% +functions of organs controlled by the +parasympathetic nervous system + + align:start position:0% +parasympathetic nervous system + + + align:start position:0% +parasympathetic nervous system +not involved in emergencies and + + align:start position:0% +not involved in emergencies and + + + align:start position:0% +not involved in emergencies and +fighting and fleeing okay + + align:start position:0% +fighting and fleeing okay + + + align:start position:0% +fighting and fleeing okay +this table you should read get familiar + + align:start position:0% +this table you should read get familiar + + + align:start position:0% +this table you should read get familiar +with so I'm just listing some of the + + align:start position:0% +with so I'm just listing some of the + + + align:start position:0% +with so I'm just listing some of the +major organs + + align:start position:0% + + + + align:start position:0% + +describe some of the things we just + + align:start position:0% +describe some of the things we just + + + align:start position:0% +describe some of the things we just +talked about there are some areas which + + align:start position:0% +talked about there are some areas which + + + align:start position:0% +talked about there are some areas which +are a little harder to to figure out + + align:start position:0% +are a little harder to to figure out + + + align:start position:0% +are a little harder to to figure out +just from that fight or flight analogy + + align:start position:0% +just from that fight or flight analogy + + + align:start position:0% +just from that fight or flight analogy +like the sex organs you can read that + + align:start position:0% +like the sex organs you can read that + + + align:start position:0% +like the sex organs you can read that +that involves also but it's just almost + + align:start position:0% +that involves also but it's just almost + + + align:start position:0% +that involves also but it's just almost +all the bodily organs are innervated by + + align:start position:0% +all the bodily organs are innervated by + + + align:start position:0% +all the bodily organs are innervated by +both sympathetic and parasympathetic + + align:start position:0% +both sympathetic and parasympathetic + + + align:start position:0% +both sympathetic and parasympathetic +okay and I just wanna and the + + align:start position:0% +okay and I just wanna and the + + + align:start position:0% +okay and I just wanna and the +innervation is a little bit different + + align:start position:0% +innervation is a little bit different + + + align:start position:0% +innervation is a little bit different +from the innervation of striated muscles + + align:start position:0% +from the innervation of striated muscles + + + align:start position:0% +from the innervation of striated muscles +if you look at the motor system most + + align:start position:0% +if you look at the motor system most + + + align:start position:0% +if you look at the motor system most +broadly this was from Swanson + + align:start position:0% +broadly this was from Swanson + + + align:start position:0% +broadly this was from Swanson +uh + + align:start position:0% +uh + + + align:start position:0% +uh +we know + + align:start position:0% +we know + + + align:start position:0% +we know +striated muscles are innervated + + align:start position:0% +striated muscles are innervated + + + align:start position:0% +striated muscles are innervated +this is the somatic muscles Innovative + + align:start position:0% +this is the somatic muscles Innovative + + + align:start position:0% +this is the somatic muscles Innovative +synaptically local synapses that act + + align:start position:0% +synaptically local synapses that act + + + align:start position:0% +synaptically local synapses that act +locally but the autonomic is innervated + + align:start position:0% +locally but the autonomic is innervated + + + align:start position:0% +locally but the autonomic is innervated +differently we call it paracrying + + align:start position:0% +differently we call it paracrying + + + align:start position:0% +differently we call it paracrying +innovation the neurotransmitter is + + align:start position:0% +innovation the neurotransmitter is + + + align:start position:0% +innovation the neurotransmitter is +released and it's it sort of spritzed + + align:start position:0% +released and it's it sort of spritzed + + + align:start position:0% +released and it's it sort of spritzed +out and affects a bunch of nearby cells + + align:start position:0% +out and affects a bunch of nearby cells + + + align:start position:0% +out and affects a bunch of nearby cells +so you don't have the type + + align:start position:0% +so you don't have the type + + + align:start position:0% +so you don't have the type +synapse synaptic context the striated + + align:start position:0% +synapse synaptic context the striated + + + align:start position:0% +synapse synaptic context the striated +muscles have the muscle inputs + + align:start position:0% +muscles have the muscle inputs + + + align:start position:0% +muscles have the muscle inputs +and then of course you have the + + align:start position:0% +and then of course you have the + + + align:start position:0% +and then of course you have the +neuroendocrine system which is really a + + align:start position:0% +neuroendocrine system which is really a + + + align:start position:0% +neuroendocrine system which is really a +third motor system where the sea + + align:start position:0% +third motor system where the sea + + + align:start position:0% +third motor system where the sea +secretion is in the bloodstream + + align:start position:0% +secretion is in the bloodstream + + + align:start position:0% +secretion is in the bloodstream +so then you + + align:start position:0% +so then you + + + align:start position:0% +so then you +it's like apocrying to an extreme the + + align:start position:0% +it's like apocrying to an extreme the + + + align:start position:0% +it's like apocrying to an extreme the +whole body + + align:start position:0% +whole body + + + align:start position:0% +whole body +affected + + align:start position:0% +affected + + + align:start position:0% +affected +now the two diversion sympathetic and + + align:start position:0% +now the two diversion sympathetic and + + + align:start position:0% +now the two diversion sympathetic and +parasympathetic they both have apocrine + + align:start position:0% +parasympathetic they both have apocrine + + + align:start position:0% +parasympathetic they both have apocrine +innovation + + align:start position:0% +innovation + + + align:start position:0% +innovation +of the end organs but the the + + align:start position:0% +of the end organs but the the + + + align:start position:0% +of the end organs but the the +innervation is through ganglion cells in + + align:start position:0% +innervation is through ganglion cells in + + + align:start position:0% +innervation is through ganglion cells in +the periphery + + align:start position:0% +the periphery + + + align:start position:0% +the periphery +so here the dashed line represents + + align:start position:0% +so here the dashed line represents + + + align:start position:0% +so here the dashed line represents +the + + align:start position:0% +the + + + align:start position:0% +the +the division between CNS here + + align:start position:0% +the division between CNS here + + + align:start position:0% +the division between CNS here +and purple nervous system here + + align:start position:0% +and purple nervous system here + + + align:start position:0% +and purple nervous system here +but in each case sympathetic and + + align:start position:0% +but in each case sympathetic and + + + align:start position:0% +but in each case sympathetic and +parasympathetic there's a ganglion cell + + align:start position:0% +parasympathetic there's a ganglion cell + + + align:start position:0% +parasympathetic there's a ganglion cell +they're located near the CNS if their + + align:start position:0% +they're located near the CNS if their + + + align:start position:0% +they're located near the CNS if their +sympathetic nervous system and they're + + align:start position:0% +sympathetic nervous system and they're + + + align:start position:0% +sympathetic nervous system and they're +located near the end organ in the Paris + + align:start position:0% +located near the end organ in the Paris + + + align:start position:0% +located near the end organ in the Paris +case of the parasympic nervous system so + + align:start position:0% +case of the parasympic nervous system so + + + align:start position:0% +case of the parasympic nervous system so +just one example here + + align:start position:0% +just one example here + + + align:start position:0% +just one example here +uh + + align:start position:0% +uh + + + align:start position:0% +uh +my schematic view I've only showed the + + align:start position:0% +my schematic view I've only showed the + + + align:start position:0% +my schematic view I've only showed the +innovation of the iris of the eye + + align:start position:0% +innovation of the iris of the eye + + + align:start position:0% +innovation of the iris of the eye +and the dot here + + align:start position:0% +and the dot here + + + align:start position:0% +and the dot here +and here I've just called the pelvic + + align:start position:0% +and here I've just called the pelvic + + + align:start position:0% +and here I've just called the pelvic +organs I've not drawn any pictures + + align:start position:0% +organs I've not drawn any pictures + + + align:start position:0% +organs I've not drawn any pictures +so we just take these three the + + align:start position:0% +so we just take these three the + + + align:start position:0% +so we just take these three the +look at the iris + + align:start position:0% +look at the iris + + + align:start position:0% +look at the iris +sympathetic nervous system the ganglion + + align:start position:0% +sympathetic nervous system the ganglion + + + align:start position:0% +sympathetic nervous system the ganglion +cells are always near + + align:start position:0% +cells are always near + + + align:start position:0% +cells are always near +the spinal cord they extend from this + + align:start position:0% +the spinal cord they extend from this + + + align:start position:0% +the spinal cord they extend from this +Superior cervical ganglion in the neck + + align:start position:0% +Superior cervical ganglion in the neck + + + align:start position:0% +Superior cervical ganglion in the neck +all the way down to below the court + + align:start position:0% +all the way down to below the court + + + align:start position:0% +all the way down to below the court +they're always innervated by axons + + align:start position:0% +they're always innervated by axons + + + align:start position:0% +they're always innervated by axons +coming from + + align:start position:0% +coming from + + + align:start position:0% +coming from +somewhere between T1 and L2 in tree + + align:start position:0% +somewhere between T1 and L2 in tree + + + align:start position:0% +somewhere between T1 and L2 in tree +that's where the preganglionic motor + + align:start position:0% +that's where the preganglionic motor + + + align:start position:0% +that's where the preganglionic motor +neurons are + + align:start position:0% +neurons are + + + align:start position:0% +neurons are +but this rostral most ganglion here + + align:start position:0% +but this rostral most ganglion here + + + align:start position:0% +but this rostral most ganglion here +Superior cyclical gang sends the + + align:start position:0% +Superior cyclical gang sends the + + + align:start position:0% +Superior cyclical gang sends the +Excellence into the head region + + align:start position:0% +Excellence into the head region + + + align:start position:0% +Excellence into the head region +and some of them go directly to the iris + + align:start position:0% +and some of them go directly to the iris + + + align:start position:0% +and some of them go directly to the iris +so when we get pupillary dilation + + align:start position:0% +so when we get pupillary dilation + + + align:start position:0% +so when we get pupillary dilation +when our sympathetic nervous system is + + align:start position:0% +when our sympathetic nervous system is + + + align:start position:0% +when our sympathetic nervous system is +activated like if we're angry or we're + + align:start position:0% +activated like if we're angry or we're + + + align:start position:0% +activated like if we're angry or we're +fighting + + align:start position:0% +fighting + + + align:start position:0% +fighting +pupils dilate bring in my life + + align:start position:0% +pupils dilate bring in my life + + + align:start position:0% +pupils dilate bring in my life +reduce our resolution a bit + + align:start position:0% +reduce our resolution a bit + + + align:start position:0% +reduce our resolution a bit +okay + + align:start position:0% +okay + + + align:start position:0% +okay +that comes from here the other the the + + align:start position:0% +that comes from here the other the the + + + align:start position:0% +that comes from here the other the the +parasympathetic system is that's the + + align:start position:0% +parasympathetic system is that's the + + + align:start position:0% +parasympathetic system is that's the +craniosacral system it comes from a + + align:start position:0% +craniosacral system it comes from a + + + align:start position:0% +craniosacral system it comes from a +cranial + + align:start position:0% +cranial + + + align:start position:0% +cranial +the the third nerve nucleus here + + align:start position:0% +the the third nerve nucleus here + + + align:start position:0% +the the third nerve nucleus here +there's a little subcomponent of the + + align:start position:0% +there's a little subcomponent of the + + + align:start position:0% +there's a little subcomponent of the +third nerve nucleus that's parasympa + + align:start position:0% +third nerve nucleus that's parasympa + + + align:start position:0% +third nerve nucleus that's parasympa +Petty it's called the aiding or Westfall + + align:start position:0% +Petty it's called the aiding or Westfall + + + align:start position:0% +Petty it's called the aiding or Westfall +nucleus so I've written there the ew + + align:start position:0% +nucleus so I've written there the ew + + + align:start position:0% +nucleus so I've written there the ew +nucleus it's in the midbrain the axons + + align:start position:0% +nucleus it's in the midbrain the axons + + + align:start position:0% +nucleus it's in the midbrain the axons +go out they don't go directly to the + + align:start position:0% +go out they don't go directly to the + + + align:start position:0% +go out they don't go directly to the +iris they go to a ganglion behind the + + align:start position:0% +iris they go to a ganglion behind the + + + align:start position:0% +iris they go to a ganglion behind the +eye + + align:start position:0% +eye + + + align:start position:0% +eye +okay the ciliary ganglion + + align:start position:0% +okay the ciliary ganglion + + + align:start position:0% +okay the ciliary ganglion +the axons of those ciliary against + + align:start position:0% +the axons of those ciliary against + + + align:start position:0% +the axons of those ciliary against +ciliary ganglion cells they're the ones + + align:start position:0% +ciliary ganglion cells they're the ones + + + align:start position:0% +ciliary ganglion cells they're the ones +that intervape the artists + + align:start position:0% +that intervape the artists + + + align:start position:0% +that intervape the artists +okay and they use different + + align:start position:0% +okay and they use different + + + align:start position:0% +okay and they use different +neurotransmitters the neurotransmitter + + align:start position:0% +neurotransmitters the neurotransmitter + + + align:start position:0% +neurotransmitters the neurotransmitter +in the ganglion is the same it's always + + align:start position:0% +in the ganglion is the same it's always + + + align:start position:0% +in the ganglion is the same it's always +acetylcholine and then the most the + + align:start position:0% +acetylcholine and then the most the + + + align:start position:0% +acetylcholine and then the most the +purple cell + + align:start position:0% +purple cell + + + align:start position:0% +purple cell +the final cell there it's acetylcholine + + align:start position:0% +the final cell there it's acetylcholine + + + align:start position:0% +the final cell there it's acetylcholine +again for the parasympathetic but it's + + align:start position:0% +again for the parasympathetic but it's + + + align:start position:0% +again for the parasympathetic but it's +Nar epinephrine for the sympathetic and + + align:start position:0% +Nar epinephrine for the sympathetic and + + + align:start position:0% +Nar epinephrine for the sympathetic and +we're going to stop here + + align:start position:0% +we're going to stop here + + + align:start position:0% +we're going to stop here +I will put all these slides online + + align:start position:0% +I will put all these slides online + + + align:start position:0% +I will put all these slides online +I might review a few of them at the + + align:start position:0% +I might review a few of them at the + + + align:start position:0% +I might review a few of them at the +beginning of the next class okay \ No newline at end of file diff --git a/I0vEDYqXLeg.txt b/I0vEDYqXLeg.txt new file mode 100644 index 0000000000000000000000000000000000000000..3253155f1945d2220c6fbfaf02b179be3f0ba87e --- /dev/null +++ b/I0vEDYqXLeg.txt @@ -0,0 +1,1977 @@ +PROFESSOR: All right, an +announcement that I must make, + +after developing all these +friendships and working + +together, we will, next Tuesday, +once again, enter a + +brief adversarial +relationship. + +And we will have quiz +number two. + +What we will cover on that +quiz will be about 50%, + +perhaps a little bit +more, on symmetry. + +And I'll remind you in just a +minute what we've covered + +since the last quiz. + +And the second half or 40% of +the quiz will be on the + +formalism of tensors and +tensor manipulation. + +And obviously, you've +had a chance only to + +do a very few problems. + +So these will be pretty basic +questions and nothing tricky + +or very difficult. + +So let me remind you very, very +quickly just by topics + +what we've covered. + +We began the period following +the first quiz discussing how + +we can take the plane groups, +two-dimensional symmetries + +that are translationally +periodic, and defining a third + +translation to stack up the +plane groups to give us a + +three-dimensional periodic + +arrangement of symmetry elements. + +In doing so, we found that +we had to pick that third + +translation such that the +symmetry elements that were in + +the plane group, and those were +the things that made the + +lattices of the plane groups +special, made them square or + +hexagonal or rectangular, that +was true because there was + +symmetry there. + +Once again, symmetry and the +specialness of a lattice are + +two inseparable parts +of the story. + +But if we did this, +the symmetry + +elements had to coincide. + +Otherwise, we would reproduce +new symmetry elements in the + +base of the cell and +wreck everything. + +So when we did that, there were +a very limited number of + +ways of doing it. + +In the course of doing that, +we fell headlong over screw + +axis in the same way that we +fell over glide planes as soon + +as we put mirror lines in a +two-dimensional lattice. + +The interesting thing was that +that exercise of stacking the + +two-dimensional plane groups +gave us almost all of the + +lattice types that exist +in three dimensions. + +And the reason for that is we +showed very directly that + +inversion requires nothing. + +So therefore, any of the point +groups that were used in + +deriving the plane groups, when +augmented by inversion to + +give a three-dimensional point +group, are going to require + +nothing more than the lattices +that we derived by stacking + +the plane groups. + +And that took care of just about +everything except for + +the cubic symmetries. + +And we disposed of those +in very short order. + +So that led us to the +14 space lattices, + +so-called bravais lattices. + +And then we proceeded to work +with those lattices and put in + +the point groups that could +accommodate them. + +Having discovered glide planes, +we then, if we had + +done the process systematically, +would have + +replaced mirror planes +by glide planes. + +And having discovered screw +axes, we replace pure rotation + +by screw axis rotations. + +And then doing what we did but +didn't have to do very often, + +mercifully, for the plane +groups, we said one could also + +interweave symmetry elements. + +And that gave a few additional +space groups. + +We did not derive very +many of them. + +What is important at this stage +is simply to realize + +that their properties and +applications are very similar + +to what we discovered for the +two-dimensional plane groups. + +The notation is a little +bit different. + +Because there can be symmetry +elements parallel to the plane + +of the paper so that in +depicting the arrangement of + +symmetry elements you need a +little [? chevron-type ?] + +device to indicate whether +you've got a mirror plane or a + +glide plane in the +base of the cell. + +And similarly with two-fold +axes, and that's about the + +only thing that would be in the +plane of the paper if the + +principal symmetry is normal to +the paper, we need a device + +for indicating the elevation +and whether the axis is a + +two-fold rotation +axis or a screw. + +So there's a geometrical +language for describing the + +arrangement of the +space groups. + +We had a few problems in +determining space group + +symbols and interpreting +what these mean. + +But again, I don't think I would +be sadistic enough to + +ask you to derive a complicated +three-dimensional + +space group. + +I don't know. + +Maybe over the weekend, if I get +to feeling mean, I might + +ask you something in +those directions. + +But it will not be anything +terribly formidable. + +Then finally, we looked at the +way in which space groups can + +be used to describe +three-dimensional periodic + +arrays of atoms. + +And that again was strictly +analogous to what we did in + +two dimensions. + +The description of the +three-dimensional arrangement + +of atoms, particularly if it +is too complicated to be + +readily appreciated in a +projection, would have to be + +given in terms of the space +group, the type of position + +that is occupied, either +special or the general + +position, and then depending on +how many degrees of freedom + +are available in those positions +to give you the + +coordinates of the element or +just the x-coordinate or the x + +and y-coordinate. + +And then you run to the +international tables. + +You don't have to work +this out yourself. + +And you find the list of +coordinates that are related + +by symmetry for that particular +special position + +and then plug in x and y to get +all the coordinates of the + +atoms in the unit cell. + +To go to the practical aspects +of this, usually only simple + +structures can be projected +with any clarity that lets + +them be interpreted. + +And even with a computer these +days one can show an + +orthographic projection of the +structure and then in real + +time manipulate it so you +can see this beautiful + +construction with colored +shiny spheres + +in it rotating around. + +But if it's a complicated +structure, even that doesn't + +do you very much. + +It works for NaCO and +zinc sulfide. + +But you know what +those look like. + +And so you don't really need +this very attractive, real + +time interaction. + +What I found works well is to +take the structure and slice + +it apart in layers like a +layer cake and look at a + +limited range of the one +translation, generally, one of + +the shorter translations, and +examine the coordination of + +atoms within that layer. + +And so by slicing the structure +away and looking at + +it in several layers that are +stacked on top of one another, + +the way I work between the ears, +usually lets me gain an + +appreciation of what's going +on in that structure. + +Something different might +work for you. + +Matter of fact, you might be a +gifted person who can see the + +things spinning around on a +computer screen and understand + +exactly what it is. + +But everybody's mind works in +a slightly different way. + +OK, that is roughly what we'll +be covering on symmetry. + +Then we got into the connection +between symmetry + +and physical properties. + +And we defined what we +meant by a tensor. + +A tensor of the second +rank is something + +that relates to vectors. + +We got into a notation involving +the assumption that + +any repeated subscript, and +there's subscripts all over + +the place in tensor +properties. + +Any repeated subscript is +automatically implied to be + +summed over from 1 to 3. + +We then derived the laws for +transformation of a tensor. + +Namely that, if you specify +the change of coordinate + +system by a direction cosine +scheme, cij, where cij is the + +cosine of the angle between x of +i prime and x sub j, that, + +since these direction cosines +constitute unit vectors, there + +had to be relations +between them. + +Namely the sum of the squares +of the terms in any row or + +column had to be unity. + +The sum of corresponding terms +in any row or column + +had to add to 0. + +Because these represented dot +products of unit vectors in a + +Cartesian coordinate system. + +And then using this array of +direction cosines, we found + +that the way in which a second +ranked tensor transformed was + +that each tensor element was +given by a linear combination + +of all of the elements of +the original tensor. + +And out in front of the tensor +was a product of two direction + +cosines, the subscripts of which +were determined by the + +indices of that element. + +A vector could be regarded +as a first ranked tensor. + +And everybody understands +the law for + +transformation of a vector. + +Namely that each component +of the vector is a linear + +combination of every component +of the original vector with + +one direction cosine +out in front. + +Tensor of second rank has a +product of two direction + +cosines summed over all +the elements of + +the original tensor. + +Third ranked tensors, which, +believe it or not, we'll get + +into after the quiz in +considerable detail, and even + +shudder fourth ranked tensors +are going to involve + +summations that involve scads of +terms and products of three + +and four direction cosines +respectively. + +So we won't get very +far into tensors. + +We will perhaps have a couple of +questions on the nature of + +anisotropy that's implied +by these relations. + +And I think, if you looked at +the problem sets to this + +point, that's as far as +we'll go on the quiz. + +And we will not throw something +at you that you've + +not seen before. + +So it'll be merciful. + +We'll pull out all the stops +in the last quiz. + +Because then you'll +be leaving. + +And you can hate me. + +But I never have to deal +with you again. + +So that will not make +any difference. + +All right, I have handed back +all of the problem sets except + +two, which are partly done. + +I never again will ask anybody +to draw out patterns of + +rotoinversion and rotoreflection +axes. + +Because they go on +and on and on. + +And I am so tired of staring at +little circles and trying + +to tell which ones are right +and which one are wrong. + +But that's something else +we have in common. + +You probably hated looking at +them when you were drawing + +them out for yourself. + +So let me tell you what's going +to go on for the next + +several days. + +Tomorrow is a holiday, not for +instructors who are making up + +a quiz, however. + +So I will be in my office from +early morning on for the rest + +of the day. + +So if you want to come by to ask +questions, what I will be + +doing primarily is finishing up +grading the problem sets. + +And if you want to pick up your +problem sets and ask a + +question about those, I am +there at your disposal + +hopefully with no ringing phone +calls and no committee + +meetings and nothing +of that sort. + +If I have finished the problem +sets and you haven't gotten + +yours yet, what I will do is +tape an envelope to my door + +and have them tucked in there. + +So you can come by any time over +the weekend and pick them + +up if you want to get hold of +them and look them over at + +your leisure. + +I have to tell you, looking +ahead in the schedule, I, + +unfortunately, bad timing, I +have to be away on Monday. + +So if you have a last minute +question or you need to be + +calmed down from a last minute +panic, you can catch me + +Tuesday morning. + +I'll be in all of the earlier +part of the day. + +But if you do have questions, +please come in on Friday. + +Because I'll have lots of +time to spend with you. + +So your problem sets, anything +turned in to this point and + +turned in today, should be on my +door, if you haven't called + +for it no, later than the +beginning of the week. + +OK, any questions? + +Any puzzles that you want to go +over before we launch into + +new material? + +OK, what we have done with +second ranked tensor + +properties is to derive a +whole set of symmetry + +constraints on something aij +that represents a physical + +property of a crystal. + +And one of the things that +we've seen, let's look at + +conductivity once more since +that's something we're all + +familiar with and can readily +appreciate, that the + +components of the current +density vector depend on all + +of the components of the +applied electric field, + +voltage per unit length. + +And in as much as for anything +other than a crystal of cubic + +symmetry, the numbers in this +array, at least some of them, + +are different. + +And that gives two surprising +results. + +One is that the direction of +J relative to the applied + +electric field will change +as you apply the field in + +different directions +in the crystal. + +And moreover, the magnitude of +the current is going to change + +as you change the orientation +of field. + +That's true of every crystal +in a crystal + +system other than cubic. + +So the thing that I would like +to address today is the + +interesting matter of what is +the nature of this anisotropy + +and if a consequence of a second +ranked tensor relation + +is that, if we apply an electric +field, the current + +doesn't go in the +same direction + +as the applied field. + +It runs off in some other +direction as non-intuitive as + +that might seem. + +First of all, there are +two directions. + +If we talk about a property +varying with direction, which + +direction are we talking about, +the direction of the + +applied field, the direction of +the resulting current flux, + +or something halfway in between, +split the difference? + +Well, we can answer that +question by doing a couple of + +thought experiments. + +Suppose we had decided that we +want to measure the electrical + +conductivity along the 1, +0, 0 direction of an + +orthorhombic crystal. + +What would we do? + +Well, we get a hold +of that crystal. + +And we would cut surfaces on +it such that this was the + +direction of 1, 0, 0, if that's +what we wanted to do. + +We would glom on electrodes and +put a voltage across this + +crystal, this chunk of crystal +that we had cut out. + +So when we say we're going to +measure the property along 1, + +0, 0 or 1, 1, 1, what we really +mean is that we're + +going to cut the crystal normal +to that direction and + +then apply some sort of +electrodes or attach + +some sort of probe. + +So when we talk about the +direction of the property, the + +direction of the property will +be the direction of the + +applied vector. + +And we had a very fancy name +for the applied vector. + +We said we could think of that +as a generalized force. + +And what happens is a +generalized displacement. + +Notice that, when we apply the +field, there are all sorts of + +components to J. And so the +direction of the property, + +although we would get a number +out of this experiment, the + +property really is a tensor. + +And there are nine different +quantities involved in it. + +OK, so the direction of the +property is going to be the + +direction in which we apply +the generalized + +force of the stimulus. + +When we do that, however, that +is going to unequivocally, at + +least in this experiment, place +the electric field in a + +direction along the +crystallographic orientation + +of interest. + +Because the electric field in a +pair of electrodes like this + +extends normal to those +electrodes. + +The current flow, the charge per +unit area per unit time, + +goes off in some direction +like this. + +Well, conductivity relates +current flow to applied + +electric field. + +So would we say that the +conductivity, when we apply + +field in that direction, is +simply J/E, magnitude of J + +over magnitude of E since +these are both vectors + +question mark? + +The answer to that, if we do +this in terms of a thought + +experiment, is no. + +That is not what we're +measuring. + +What we can imagine is that +between our electrodes is some + +window of unit area between +those electrodes. + +And what we're going to measure +as the current flow is + +the amount of charge per unit +area per unit time that passes + +between the electrodes, namely +the charge per unit area per + +unit time that gets through this +window and reaches the + +other electrode. + +That's what we're going +to measure. + +And what we're going to want +to call the conductivity is + +the ratio of this part of the +current flux, let me call that + +J parallel, over the magnitude +of E. And that's what we'll + +mean by the conductivity in the +direction in which we've + +applied the field. + +The actual flow of +current goes off + +in some other direction. + +But what we measure, at least +in this experiment, is the + +component of that charge flux +that goes through a window, + +that pair of unit area, that's +parallel to the electrode. + +And we don't really care if the +current is going off in a + +different direction. + +We don't even care if it jumps +around in majestic + +loop-de-loops. + +What we're going to measure is +the amount of that charge + +motion that moves normal to our +window and gets through + +one unit area from one +electrode to another. + +So the conductivity and the +direction of E then is going + +to be measured by the parallel +part of the resulting + +generalized displacement divided +by the magnitude of + +the applied generalized force. + +If you're not convinced and +completely overwhelmed by + +that, let me give you +another experiment. + +Another tensor relation, another +tensor property, is + +the diffusivity of a material. + +And if you put a material in a +concentration gradient dc dx, + +you produce a flux of matter. + +And the proportionality constant +is the diffusion + +coefficient. + +And this has units of length +per unit time if you put in + +the units of the concentration +gradient and the flux. + +Well, dc dx is a gradient. + +That's a vector really. + +So a proper tensor relation, +instead of a scalar relation + +like this, would be the change +of concentration with the i-th + +coordinate. + +And out in front would be a +diffusion coefficient Dij. + +And this tensor relation would +give us the components of the + +mass flux J1 J2 J3. + +Actually, thermodynamically we +shouldn't be talking about a + +concentration gradient. + +We should be talking about a +gradient in free energy. + +The concentration works +well enough. + +And the concentration is +what one would measure. + +So what might a typical +experiment be? + +If you wanted to know what the +diffusion was in the 1, 1, 1 + +direction of some crystal, you +would, again, cut a plate that + +is normal to the direction +of interest. + +And then your boundary +conditions can be different. + +But what you would typically do +for a simple experiment is + +to put some sort of solute on +the surface of the crystal. + +And what you would see after +heating the sample up for a + +period of time is that the +material would have migrated + +into the sample. + +And if you plotted concentration +as a function of + +distance along the normal to +the plate that you've cut, + +this would do something +like that. + +What can you say about this +process after you've done the + +experiment? + +All that you can say is that +some front of concentration + +has advanced parallel +to the surface. + +And you have no idea what the +individual atoms have done. + +Then they could be doing +loop-de-loops + +or little hip hops. + +And all that you measure is +the rate at which material + +advances in the direction +of the current gradient. + +So again, I think I've convinced +you, hopefully, that + +what you're measuring is the +flux of matter unit area per + +unit time that is in the +direction of the applied + +concentration gradient. + +And you do not measure, and in +fact, in this instance, I + +don't think I could come up +with even a very clever + +experiment that would let you +measure in a single experiment + +the magnitude and direction +of the net flux. + +All right, so if we're measuring +a property then like + +conductivity, the value of the +conductivity in the direction + +of the applied field is going +to be the part of the + +conductivity that is parallel +to the field divided by the + +magnitude of the field. + +We all agree on that. + +Let's have a show of hands. + +Fine. + +I saw just a few tired hands +saying, OK, I believe, I + +believe, let's get on with it. + +All right, let me now put this +using our tensor relationship + +into a nice analytic form that +we can not only do something + +with but can gain +some insight. + +The components of the charge +density vector are given by + +the conductivity tensor sigma +1, 1 times the component of + +the electric field E1 plus sigma +1, 2 times the component + +of field E2 plus sigma +1, 3 times E3. + +Or in general, I don't have to +write out every equation. + +We can say that the i-th +component of J, our old friend + +the second ranked tensor +property, again, is given by + +sigma ij times each component +of applied field. + +If we specify the direction +relative to the same + +coordinate system in which the +electric field is being + +applied, we can specify that +direction by a set of three + +direction cosines, +l1, l2, and l3. + +So we can write as the three +components of the electric + +field E sub i as the magnitude +of E times the direction + +cosines l1, l2, and l3. + +So here we now have +the components of + +the electric field. + +If these are the components of +the electric field, we can say + +that J sub i is going +to be equal to sigma + +ij times E sub j. + +And I can write for E sub j the +magnitude of E times the + +direction cosines l sub j +where these are the same + +direction cosines of +the applied field. + +OK, now we have two relations in +reduced subscript form that + +we can do something with. + +The magnitude of the +conductivity in the direction + +of E, that is in the direction +that has direction cosines li, + +is going to be J parallel over +the magnitude of E. We can + +write that as J.E, except that +involves the magnitude of J, + +the magnitude of E times +the cosine of the + +angle between them. + +And so if I just want J +parallel, I'd want to divide + +this by the magnitude of E. And +that will give me just the + +part of J that falls parallel +to E. And then down here in + +the denominator, I'll +have magnitude of E. + +So if I tidy this up a little +bit to bring everything on the + +same level, we can write the dot +product of J and E as Ji + +Ei, like J1 E1 plus +J2 E2 plus J3 E3. + +And then I will have +in the denominator + +magnitude of E squared. + +But we know what Ei is. + +It's going to be magnitude +of E times li. + +I know how to find the i-th +component of J. That's going + +to be sigma ij times E sub j +over magnitude of E squared. + +And I can write E sub j as +magnitude of E times l sub j + +times l sub i times magnitude +of E divided by + +magnitude of E squared. + +Magnitude of E drops out. + +Again, the conductivity +is linear the way + +we've defined it. + +It shouldn't depend on the +magnitude of E. And what I'm + +left with then is a +very simple and a + +rather profound relation. + +It says that in a direction +specified by the set of + +direction cosines l sub i that +the magnitude of conductivity + +in that direction is going to +be li lj times sigma ij. + +So that is an expression that +involves the three direction + +cosines in which you're +applying the field and + +measuring the property. + +But this is a linear combination +of every one of + +the elements in the +original tensor. + +So if I write this out, because +this is an important + +relation, it's going to be l1 +squared sigma 1, 1 plus l2 + +squared sigma 2, 2 plus +l3 squared sigma 3, 3. + +And then there will be +cross-terms of the form 2 l1 + +l2 sigma 1, 2 plus 2 l2 l3 times +sigma 2, 3 plus 2 l3 l1 + +times sigma 1, 3. + +That has made an assumption. + +And probably I should not have +done it at this point. + +That's assuming that the term l1 +l2 sigma 1, 2 and the term + +l2 l1 sigma 2, 1 can +be lumped together. + +And maybe I shouldn't +write it that way. + +Because that assumes that +the tensor is symmetric. + +And it doesn't have to be +for some properties. + +So let me back off and write +it without any assumptions. + +So this would be sigma 1, 2 l1 +l2 plus sigma 1, 3 l1 l3 plus + +sigma 2, 1 times l2 l1 and then +corresponding terms-- + +let me put this one +down here-- + +sigma 2, 1 times l2 l1 plus +sigma 3, 1 l3 l1. + +And then the one that I'm +missing is sigma 2, 3 times l2 + +l3 plus sigma 3, +2 times l2 l3. + +So there is an explicit +statement of this more compact + +expression written in reduced +subscript notation. + +OK, so this is something that is +going to tell us in a very + +neat sort of way what the +anisotropy of the property is. + +You pick the direction in +which you're interested. + +And this will tell you the value +of the property in that + +direction and, therefore, by +inference how things will + +change with direction. + +Let me quickly, and then I'll +pause to see if you have any + +questions, give you an +interpretation of the meaning + +of some of these elements +of the tensor. + +We've really not been +able to do that. + +We've been able to use them to +give the value of the property + +in a given direction but not +their individual meaning. + +Suppose I ask what the value of +the property would be along + +the x1 direction. + +So suppose we ask what value of +the conductivity would we + +measure along x1 for a given +tensor sigma ij. + +If that is the case, +l1 is equal to 1. + +The angle between the +x1 axis and x2 is 0. + +So l2 is 0. + +90 degrees cosine of +90 degrees is zero. + +l3 would be equal to 0. + +So if I put this set of +direction cosines into this + +complicated polynomial, +the term l1 squared + +sigma 1, 1 stays in. + +But l2 is 0. + +l3 is 0. + +And I've got either an l2 or an +l3 or both in all of these + +other terms. + +So along the x1 direction, the +only term that stays in is + +sigma 1, 1 squared +times l1 squared. + +But l1 is unity. + +So along the x1 direction the +value of sigma is sigma 1, 1. + +And by inference the value of +the property that we would + +measure along x2 would +be sigma 2, 2. + +And the value of the property +along x3, guess + +what, sigma 3, 3. + +So in this three by three array +of numbers for sigma ij, + +there's a very direct meaning +to the diagonal + +values of the tensor. + +These are the values that you +would measure along x1, along + +x2, and along x3 directly. + +So the off diagonal terms are +going to be saying something + +about how the extreme values +of the property are aligned + +relative to our reference +axes. + +OK, any comment or questions +at this point? + +Yeah, [INAUDIBLE]? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yeah, we've defined +those as the cosines of the + +angles between the +reference axes. + +And this is the direction in +which we're applying our + +electric field or our +generalized forced temperature + +gradient, concentration +gradient, magnetic field, or + +what have you. + +OK, I've got some time left. + +So let me push this further into +a different form by using + +the elements of the tensor to +define a locus in space. + +Again, what I'll do is something +that may seem silly. + +But we'll see that there are +some very useful and profound + +conclusions to be +drawn from it. + +Let me take the elements of +the tensor and use them as + +coefficients to define +a surface. + +I'm going to take sigma 1, 1 and +multiply it by the product + +of the coordinate x1 times x1. + +What I'm viewing this +now is a variable. + +I'm going to take sigma 2, +2 and multiply it by the + +coordinate x2 and x2 again. + +Sigma 3, 3 and I multiply +that by x3 times x3. + +And then I'll have these +cross-terms, sigma 1, 2, x1, + +x2, and so on. + +Or in short, I'm going +to define a + +function sigma ij xi xj. + +And xi and xj are running +variables. + +x1, x2, x3, they can extend +from 0 to infinity. + +But now I'm going to take this +sum of nine terms and I'm + +going to set it equal +to a constant. + +And what constant could be +neater and cleaner and more + +abstract than unity? + +But I could say that some +function of x1, x2, x3 equal + +to a constant is going to define +a locus of points in + +space, which satisfy +that equation. + +And we do that all the time. + +We specify some functional +relationship that defines in + +the space some surface f of +xi xj equals a constant. + +And that's done all time +in mathematics. + +I've yet to encounter yet a +department of mathematics that + +did not have in its corridors +some glass case that was + +filled with yellowing plaster +figures, that some of them + +cracking or already cracked, +that represented exotic + +surfaces, like elliptic +paraboloids and + +things of that sort. + +I think the last time I walked +down the corridor of building + +two there really was one of +those in our mathematics + +department in the little door +that opened out onto the great + +court about halfway down +that corridor. + +But you've seen these things I'm +sure, elliptic cylinders, + +elliptic cones, and all sorts +of glorious things. + +This function, though, is +a very special one. + +This is a quadratic equation +in the second order of + +coordinates. + +And this is referred to +as a quadratic form. + +And sometimes for short, since +that's something of a + +mouthful, one refers to +this as a quadric. + +And we are going to very shortly +demonstrate that this + +particular function tells you +everything you could possibly + +want to know about the variation +of a tensor property + +with direction, how the +magnitude of the property + +changes, how the direction of +the resulting current flow or + +flux is oriented. + +And this is, consequently, +called, when applied to a + +tensor, the representation +quadric. + +Because it really does represent +anything you would + +like to know about the +physical property. + +This will be demonstrated +in short order. + +Let's first notice, though, that +there's only a limited + +number of surfaces that can be +represented by this equation. + +One of them is one +that we're all + +familiar with, an ellipsoid. + +And that's most easily +represented when we've + +referred it to the principal +axes of the ellipsoid. + +So an ellipsoid is +a quasi-sausage + +like thing like this. + +These sections perpendicular +to x3, x1, and x2 are all + +ellipsoids. + +And if this semi-axis is a and +this semi-axis is b and this + +semi-axis is c, the equation of +the surface in that special + +orientation is x1 squared over a +squared plus x2 squared over + +b squared plus x3 squared +over c squared equals 1. + +OK, the surface that +we have defined + +involves tensor elements. + +And if the equation is ever +going to get into this form, + +we've had to get rid of +these cross-terms. + +And we are going to have +principal axes that are some + +function of the tensor elements +that would be out + +here in the form of some +aggregate sigma ij prime. + +So we'll have to see how one +could go from a tensor that + +describes an ellipsoid in +a general orientation to + +something that has been +diagonalized and has the + +coordinate system taken along +the principal axes. + +But that's only one +possible surface + +that we could encounter. + +The second one is one that we +might encounter that, when we + +put it in diagonal form, has +this form, x1 squared over a + +squared plus x2 squared over b +squared minus z squared over c + +squared equals 1. + +This is something that +has a peculiar shape. + +It's sort of an hourglass +like figure. + +It has an ellipsoidal +cross-section. + +This is x3. + +This is x1. + +This is x2. + +It has an ellipsoidal section +perpendicular to x3. + +But it has, as a cross-section +in planes that are parallel to + +x3, paraboloids. + +And the shape of the paraboloids +depends on which + +particular section that +you take through x3. + +This is a surface that's +called a hyperboloid. + +And it's all one continuous +surface. + +So this is called a hyperboloid +of one sheet, + +sheet in the sense of surface. + +And then down in here when x3 +is 0, it would again be an + +ellipsoidal cross-section but a +little bit smaller than when + +we increase x3 above 0. + +OK, and the other surface, +another surface, a third kind + +of surface is something that +occurs when the terms in front + +of two coordinates are negative, +x2 squared over b + +squared x3 squared over +c squared equals 1. + +This is something that +looks like two + +surfaces nose to nose. + +The cross-section of these two +different sheets are ellipsis. + +The cross-sections +passing through-- + +let's see. + +This would be the +shape for x1. + +That would be the special +direction. + +And then this could +be x2 and this x3. + +OK, this is called an +hyperboloid of two sheets. + +And it has the property that the +distance to the surface in + +orientations in between the +asymptotes of these hyperbolic + +sections, these radii, +are imaginary. + +And between the asymptotes, if +we take a section, we would + +have two hyperboloids +in a cross-section. + +And again, a range of directions +between the + +asymptotes in which the radius +would be imaginary in + +directions along the coordinate +which has the + +positive sign we'd have +a minimum radius. + +And this would get progressively +larger and go to + +infinity along the asymptote. + +Finally, there's a third +surface in which, by + +extension, all three terms +in x1, x2, and x3 + +have negative signs. + +And what does this look like? + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: No, it does. + +It's something that's called +an imaginary ellipsoid. + +So called because the radius in +all direction is imaginary. + +And what does it look like? + +You just have to use +your imagination. + +That's all. + +Because it's an imaginary +ellipsoid. + +Is that something that we could +ever get if we were + +using the elements of +a property tensor? + +The answer, he says with +a big wink, yes. + +It's unusual but yes. + +You can get physical properties +whose magnitude as + +a function of direction +do this. + +All right, I think that is +a sufficiently formal and + +deadening component to our +presentation that it would be + +appropriate to take a break +and stretch a little bit. + +When we return, I will show +you an amazing connection + +between the anisotropy of a +physical property and this + +representation surface. + +So called because it +tells you how the + +property is going to change. \ No newline at end of file diff --git a/ISaYWm8T8n4.txt b/ISaYWm8T8n4.txt new file mode 100644 index 0000000000000000000000000000000000000000..ceb7b1d6fc9a109263133dc6c680037e8b3ceb67 --- /dev/null +++ b/ISaYWm8T8n4.txt @@ -0,0 +1,361 @@ +The problem with our simple multicore system +is that there is no communication when the + +value of a shared variable is changed. + +The fix is to provide the necessary communications +over a shared bus that's watched by all the + +caches. + +A cache can then "snoop" on what's happening +in other caches and then update its local + +state to be consistent. + +The required communications protocol is called +a "cache coherence protocol". + +In designing the protocol, we'd like to incur +the communications overhead only when there's + +actual sharing in progress, i.e., when multiple +caches have local copies of a shared variable. + +To implement a cache coherence protocol, we'll +change the state maintained for each cache + +line. + +The initial state for all cache lines is INVALID +indicating that the tag and data fields do + +not contain up-to-date information. + +This corresponds to setting the valid bit +to 0 in our original cache implementation. + +When the cache line state is EXCLUSIVE, this +cache has the only copy of those memory locations + +and indicates that the local data is the same +as that in main memory. + +This corresponds to setting the valid bit +to 1 in our original cache implementation. + +If the cache line state is MODIFIED, that +means the cache line data is the sole valid + +copy of the data. + +This corresponds to setting both the dirty +and valid bits to 1 in our original cache + +implementation. + +To deal with sharing issues, there's a fourth +state called SHARED that indicates when other + +caches may also have a copy of the same unmodified +memory data. + +When filling a cache from main memory, other +caches can snoop on the read request and participate + +if fulfilling the read request. + +If no other cache has the requested data, +the data is fetched from main memory and the + +requesting cache sets the state of that cache +line to EXCLUSIVE. + +If some other cache has the requested in line +in the EXCLUSIVE or SHARED state, it supplies + +the data and asserts the SHARED signal on +the snoopy bus to indicate that more than + +one cache now has a copy of the data. + +All caches will mark the state of the cache +line as SHARED. + +If another cache has a MODIFIED copy of the +cache line, it supplies the changed data, + +providing the correct values for the requesting +cache as well as updating the values in main + +memory. + +Again the SHARED signal is asserted and both +the reading and responding cache will set + +the state for that cache line to SHARED. + +So, at the end of the read request, if there +are multiple copies of the cache line, they + +will all be in the SHARED state. + +If there's only one copy of the cache line +it will be in the EXCLUSIVE state. + +Writing to a cache line is when the sharing +magic happens. + +If there's a cache miss, the first cache performs +a cache line read as described above. + +If the cache line is now in the SHARED state, +a write will cause the cache to send an INVALIDATE + +message on the snoopy bus, +telling all other caches to invalidate their + +copy of the cache line, guaranteeing the local +cache now has EXCLUSIVE access to the cache + +line. + +If the cache line is in the EXCLUSIVE state +when the write happens, no communication is + +necessary. + +Now the cache data can be changed and the +cache line state set to MODIFIED, completing + +the write. + +This protocol is called "MESI" after the first +initials of the possible states. + +Note that the the valid and dirty state bits +in our original cache implementation have + +been repurposed to encode one of the four +MESI states. + +The key to success is that each cache now +knows when a cache line may be shared by another + +cache, prompting the necessary communication +when the value of a shared location is changed. + +No attempt is made to update shared values, +they're simply invalidated and the other caches + +will issue read requests if they need the +value of the shared variable at some future + +time. + +To support cache coherence, the cache hardware +has to be modified to support two request + +streams: one from the CPU and one from the +snoopy bus. + +The CPU side includes a queue of store requests +that were delayed by cache misses. + +This allows the CPU to proceed without having +to wait for the cache refill operation to + +complete. + +Note that CPU read requests will need to check +the store queue before they check the cache + +to ensure the most-recent value is supplied +to the CPU. + +Usually there's a STORE_BARRIER instruction +that stalls the CPU until the store queue + +is empty, guaranteeing that all processors +have seen the effect of the writes before + +execution resumes. + +On the snoopy side, the cache has to snoop +on the transactions from other caches, invalidating + +or supplying cache line data as appropriate, +and then updating the local cache line state. + +If the cache is busy with, say, a refill operation, +INVALIDATE requests may be queued until they + +can be processed. + +Usually there's a READ_BARRIER instruction +that stalls the CPU until the invalidate queue + +is empty, guaranteeing that updates from other +processors have been applied to the local + +cache state before execution resumes. + +Note that the "read with intent to modify" +transaction shown here is just protocol shorthand + +for a READ immediately followed by an INVALIDATE, +indicating that the requester will be changing + +the contents of the cache line. + +How do the CPU and snoopy cache requests affect +the cache state? + +Here in micro type is a flow chart showing +what happens when. + +If you're interested, try following the actions +required to complete various transactions. + +Intel, in its wisdom, adds a fifth "F" state, +used to determine which cache will respond + +to read requests when the requested cache +line is shared by multiple caches + +basically it selects which of the SHARED cache +lines gets to be the responder. + +But this is a bit abstract. + +Let's try the MESI cache coherence protocol +on our earlier example! + +Here are our two threads and their local cache +states indicating that values of locations + +X and Y are shared by both caches. + +Let's see what happens when the operations +happen in the order (1 through 4) shown here. + +You can check what happens when the transactions +are in a different order or happen concurrently. + +First, Thread A changes X to 3. + +Since this location is marked as SHARED [S] +in the local cache, the cache for core 0 ($_0) + +issues an INVALIDATE transaction for location +X to the other caches, + +giving it exclusive access to location X, +which it changes to have the value 3. + +At the end of this step, the cache for core +1 ($_1) no longer has a copy of the value + +for location X. + +In step 2, Thread B changes Y to 4. + +Since this location is marked as SHARED in +the local cache, cache 1 issues an INVALIDATE + +transaction for location Y to the other caches, +giving it exclusive access to location Y, + +which it changes to have the value 4. + +In step 3, execution continues in Thread B, +which needs the value of location X. + +That's a cache miss, so it issues a read request +on the snoopy bus, and cache 0 responds with + +its updated value, and both caches mark the +location X as SHARED. + +Main memory, which is also watching the snoopy +bus, also updates its copy of the X value. + +Finally, in step 4, Thread A needs the value +for Y, which results in a similar transaction + +on the snoopy bus. + +Note the outcome corresponds exactly to that +produced by the same execution sequence on + +a timeshared core +since the coherence protocol guarantees that + +no cache has an out-of-date copy of a shared +memory location. + +And both caches agree on the ending values +for the shared variables X and Y. + +If you try other execution orders, you'll +see that sequential consistency and shared + +memory semantics are maintained in each case. + +The cache coherency protocol has done it's +job! + +Let's summarize our discussion of parallel +processing. + +At the moment, it seems that the architecture +of a single core has reached a stable point. + +At least with the current ISAs, pipeline depths +are unlikely to increase and out-of-order, + +superscalar instruction execution has reached +the point of diminishing performance returns. + +So it seems unlikely there will be dramatic +performance improvements due to architectural + +changes inside the CPU core. + +GPU architectures continue to evolve as they +adapt to new uses in specific application + +areas, but they are unlikely to impact general-purpose +computing. + +At the system level, the trend is toward increasing +the number of cores and figuring out how to + +best exploit parallelism with new algorithms. + +Looking further ahead, notice that the brain +is able to accomplish remarkable results using + +fairly slow mechanisms +It takes ~.01 seconds to get a message to + +the brain and synapses fire somewhere between +0.3 to 1.8 times per second. + +Is it massive parallelism that gives the brain +its "computational" power? + +Or is it that the brain uses a different computation +model, e.g., neural nets, to decide upon new + +actions given new inputs? + +At least for applications involving cognition +there are new architectural and technology + +frontiers to explore. + +You have some interesting challenges ahead +if you get interested in the future of parallel + +processing! \ No newline at end of file diff --git a/IlkbvrpAbPU.txt b/IlkbvrpAbPU.txt new file mode 100644 index 0000000000000000000000000000000000000000..b1af3a8a518d8daa80ca0699263fe6c07e26b688 --- /dev/null +++ b/IlkbvrpAbPU.txt @@ -0,0 +1,1795 @@ +align:start position:0% + +the climate is changing low carbon + + align:start position:0% +the climate is changing low carbon + + + align:start position:0% +the climate is changing low carbon +development is an approach to reducing + + align:start position:0% +development is an approach to reducing + + + align:start position:0% +development is an approach to reducing +carbon dioxide emission and mitigating + + align:start position:0% +carbon dioxide emission and mitigating + + + align:start position:0% +carbon dioxide emission and mitigating +global warming human activities in + + align:start position:0% +global warming human activities in + + + align:start position:0% +global warming human activities in +cities produce + + align:start position:0% +cities produce + + + align:start position:0% +cities produce +78% of global carbon emission this is + + align:start position:0% +78% of global carbon emission this is + + + align:start position:0% +78% of global carbon emission this is +because most cities rely heavily on fil + + align:start position:0% +because most cities rely heavily on fil + + + align:start position:0% +because most cities rely heavily on fil +fo based + + align:start position:0% +fo based + + + align:start position:0% +fo based +energy low carbon development refers to + + align:start position:0% +energy low carbon development refers to + + + align:start position:0% +energy low carbon development refers to +ways of shaping economic growth so that + + align:start position:0% +ways of shaping economic growth so that + + + align:start position:0% +ways of shaping economic growth so that +greenhouse gas emissions can be kept to + + align:start position:0% +greenhouse gas emissions can be kept to + + + align:start position:0% +greenhouse gas emissions can be kept to +levels that can be absorbed by Nature + + align:start position:0% +levels that can be absorbed by Nature + + + align:start position:0% +levels that can be absorbed by Nature +low carbon development involves a push + + align:start position:0% +low carbon development involves a push + + + align:start position:0% +low carbon development involves a push +towards simpler Lifestyles that rely on + + align:start position:0% +towards simpler Lifestyles that rely on + + + align:start position:0% +towards simpler Lifestyles that rely on +environmentally friendly + + align:start position:0% +environmentally friendly + + + align:start position:0% +environmentally friendly +Technologies hello my name is is kadam + + align:start position:0% +Technologies hello my name is is kadam + + + align:start position:0% +Technologies hello my name is is kadam +abdulaziz and I'm a research scholar + + align:start position:0% +abdulaziz and I'm a research scholar + + + align:start position:0% +abdulaziz and I'm a research scholar +with the MIT UTM Malaysia sustainable + + align:start position:0% +with the MIT UTM Malaysia sustainable + + + align:start position:0% +with the MIT UTM Malaysia sustainable +cities program in this video I will + + align:start position:0% +cities program in this video I will + + + align:start position:0% +cities program in this video I will +discuss why and how low carbon + + align:start position:0% +discuss why and how low carbon + + + align:start position:0% +discuss why and how low carbon +development is proceeding in the second + + align:start position:0% +development is proceeding in the second + + + align:start position:0% +development is proceeding in the second +largest city in Malaysia + + align:start position:0% +largest city in Malaysia + + + align:start position:0% +largest city in Malaysia +joobu the city is in the iscandar + + align:start position:0% +joobu the city is in the iscandar + + + align:start position:0% +joobu the city is in the iscandar +Malaysia region which has announced a + + align:start position:0% +Malaysia region which has announced a + + + align:start position:0% +Malaysia region which has announced a +goal of reducing carbon emission by 58% + + align:start position:0% +goal of reducing carbon emission by 58% + + + align:start position:0% +goal of reducing carbon emission by 58% +by year + + align:start position:0% +by year + + + align:start position:0% +by year +2025 I will reflect on some of the + + align:start position:0% +2025 I will reflect on some of the + + + align:start position:0% +2025 I will reflect on some of the +city's achievements and the challenges + + align:start position:0% +city's achievements and the challenges + + + align:start position:0% +city's achievements and the challenges +it faces in meeting that Target joob + + align:start position:0% +it faces in meeting that Target joob + + + align:start position:0% +it faces in meeting that Target joob +baru is one of the five local + + align:start position:0% +baru is one of the five local + + + align:start position:0% +baru is one of the five local +authorities in isanda Malaysia region it + + align:start position:0% +authorities in isanda Malaysia region it + + + align:start position:0% +authorities in isanda Malaysia region it +is an important Flagship for low carbon + + align:start position:0% +is an important Flagship for low carbon + + + align:start position:0% +is an important Flagship for low carbon +development in the region the city is a + + align:start position:0% +development in the region the city is a + + + align:start position:0% +development in the region the city is a +regional transport manufacturing Hub and + + align:start position:0% +regional transport manufacturing Hub and + + + align:start position:0% +regional transport manufacturing Hub and +a main shopping destination for tourists + + align:start position:0% +a main shopping destination for tourists + + + align:start position:0% +a main shopping destination for tourists +from Indonesia and + + align:start position:0% +from Indonesia and + + + align:start position:0% +from Indonesia and +Singapore at present it is less + + align:start position:0% +Singapore at present it is less + + + align:start position:0% +Singapore at present it is less +organized and much merer than its ly + + align:start position:0% +organized and much merer than its ly + + + align:start position:0% +organized and much merer than its ly +neighbor sing + + align:start position:0% +neighbor sing + + + align:start position:0% +neighbor sing +in an effort to compete with Singapore + + align:start position:0% +in an effort to compete with Singapore + + + align:start position:0% +in an effort to compete with Singapore +the Malaysian government announced a + + align:start position:0% +the Malaysian government announced a + + + align:start position:0% +the Malaysian government announced a +commitment to sustainable Urban + + align:start position:0% +commitment to sustainable Urban + + + align:start position:0% +commitment to sustainable Urban +Development its goal was to attract + + align:start position:0% +Development its goal was to attract + + + align:start position:0% +Development its goal was to attract +foreign investment in joob baru's + + align:start position:0% +foreign investment in joob baru's + + + align:start position:0% +foreign investment in joob baru's +industrial commercial and real estate + + align:start position:0% +industrial commercial and real estate + + + align:start position:0% +industrial commercial and real estate +activities economic investment usually + + align:start position:0% +activities economic investment usually + + + align:start position:0% +activities economic investment usually +means more construction of buildings + + align:start position:0% +means more construction of buildings + + + align:start position:0% +means more construction of buildings +more manufacturing and Industrial + + align:start position:0% +more manufacturing and Industrial + + + align:start position:0% +more manufacturing and Industrial +Development more retail and shopping + + align:start position:0% +Development more retail and shopping + + + align:start position:0% +Development more retail and shopping +activities more concentration of human + + align:start position:0% +activities more concentration of human + + + align:start position:0% +activities more concentration of human +activities and more energy consumption + + align:start position:0% +activities and more energy consumption + + + align:start position:0% +activities and more energy consumption +for transport and electricity under + + align:start position:0% +for transport and electricity under + + + align:start position:0% +for transport and electricity under +normal + + align:start position:0% +normal + + + align:start position:0% +normal +circumstances all these will increase + + align:start position:0% +circumstances all these will increase + + + align:start position:0% +circumstances all these will increase +carbon emission however the government + + align:start position:0% +carbon emission however the government + + + align:start position:0% +carbon emission however the government +is trying to promote economic growth + + align:start position:0% +is trying to promote economic growth + + + align:start position:0% +is trying to promote economic growth +while reducing carbon + + align:start position:0% +while reducing carbon + + + align:start position:0% +while reducing carbon +intensity how can this be done and how + + align:start position:0% +intensity how can this be done and how + + + align:start position:0% +intensity how can this be done and how +is low carbon development being + + align:start position:0% +is low carbon development being + + + align:start position:0% +is low carbon development being +practiced in + + align:start position:0% +practiced in + + + align:start position:0% +practiced in +joobu two key organizations are leading + + align:start position:0% +joobu two key organizations are leading + + + align:start position:0% +joobu two key organizations are leading +the low carbon ini initiative in joobu + + align:start position:0% +the low carbon ini initiative in joobu + + + align:start position:0% +the low carbon ini initiative in joobu +the first is the office of low carbon + + align:start position:0% +the first is the office of low carbon + + + align:start position:0% +the first is the office of low carbon +Society at the University technology + + align:start position:0% +Society at the University technology + + + align:start position:0% +Society at the University technology +Malaysia also called UTM professor H + + align:start position:0% +Malaysia also called UTM professor H + + + align:start position:0% +Malaysia also called UTM professor H +jinong the head of the low carbon + + align:start position:0% +jinong the head of the low carbon + + + align:start position:0% +jinong the head of the low carbon +Society office at UTM explains some of + + align:start position:0% +Society office at UTM explains some of + + + align:start position:0% +Society office at UTM explains some of +the practices he has been trying to + + align:start position:0% +the practices he has been trying to + + + align:start position:0% +the practices he has been trying to +encourage in joobu we use the concept of + + align:start position:0% +encourage in joobu we use the concept of + + + align:start position:0% +encourage in joobu we use the concept of +uh town + + align:start position:0% +uh town + + + align:start position:0% +uh town +planning where they have already some + + align:start position:0% +planning where they have already some + + + align:start position:0% +planning where they have already some +form of a structure plan local plan or + + align:start position:0% +form of a structure plan local plan or + + + align:start position:0% +form of a structure plan local plan or +any s plan and then the other thing is + + align:start position:0% +any s plan and then the other thing is + + + align:start position:0% +any s plan and then the other thing is +the the climate change policy how can we + + align:start position:0% +the the climate change policy how can we + + + align:start position:0% +the the climate change policy how can we +integrate them together in such way that + + align:start position:0% +integrate them together in such way that + + + align:start position:0% +integrate them together in such way that +urban planning can decarbonize that that + + align:start position:0% +urban planning can decarbonize that that + + + align:start position:0% +urban planning can decarbonize that that +plan basically guide us how to be low + + align:start position:0% +plan basically guide us how to be low + + + align:start position:0% +plan basically guide us how to be low +carbon and then from there we prepare + + align:start position:0% +carbon and then from there we prepare + + + align:start position:0% +carbon and then from there we prepare +another plan called the road map that is + + align:start position:0% +another plan called the road map that is + + + align:start position:0% +another plan called the road map that is +the detail implementation of the plan + + align:start position:0% +the detail implementation of the plan + + + align:start position:0% +the detail implementation of the plan +and then I at the moment we are now + + align:start position:0% +and then I at the moment we are now + + + align:start position:0% +and then I at the moment we are now +going into more detail working with the + + align:start position:0% +going into more detail working with the + + + align:start position:0% +going into more detail working with the +local authorities with the Mayors um + + align:start position:0% +local authorities with the Mayors um + + + align:start position:0% +local authorities with the Mayors um +with the uh the engineers the second + + align:start position:0% +with the uh the engineers the second + + + align:start position:0% +with the uh the engineers the second +organization concerned with promoting + + align:start position:0% +organization concerned with promoting + + + align:start position:0% +organization concerned with promoting +low carbon development initiatives in + + align:start position:0% +low carbon development initiatives in + + + align:start position:0% +low carbon development initiatives in +jovaru is the iscandar regional + + align:start position:0% +jovaru is the iscandar regional + + + align:start position:0% +jovaru is the iscandar regional +Development Authority also known as + + align:start position:0% +Development Authority also known as + + + align:start position:0% +Development Authority also known as +Eda together with UTM Ida is helping + + align:start position:0% +Eda together with UTM Ida is helping + + + align:start position:0% +Eda together with UTM Ida is helping +local authorities prepare action plans + + align:start position:0% +local authorities prepare action plans + + + align:start position:0% +local authorities prepare action plans +for reducing carbon + + align:start position:0% +for reducing carbon + + + align:start position:0% +for reducing carbon +intensity Mr Boyd Joan explains what Ida + + align:start position:0% +intensity Mr Boyd Joan explains what Ida + + + align:start position:0% +intensity Mr Boyd Joan explains what Ida +is doing along these lines the process + + align:start position:0% +is doing along these lines the process + + + align:start position:0% +is doing along these lines the process +of getting to that point is very + + align:start position:0% +of getting to that point is very + + + align:start position:0% +of getting to that point is very +important so Municipal planning critical + + align:start position:0% +important so Municipal planning critical + + + align:start position:0% +important so Municipal planning critical +and that's why um we are working with + + align:start position:0% +and that's why um we are working with + + + align:start position:0% +and that's why um we are working with +the five local authorities to prepare + + align:start position:0% +the five local authorities to prepare + + + align:start position:0% +the five local authorities to prepare +their own low carbon action plan at at + + align:start position:0% +their own low carbon action plan at at + + + align:start position:0% +their own low carbon action plan at at +the municipal level through that process + + align:start position:0% +the municipal level through that process + + + align:start position:0% +the municipal level through that process +we can then say we have done one step + + align:start position:0% +we can then say we have done one step + + + align:start position:0% +we can then say we have done one step +further from Regional to Municipal they + + align:start position:0% +further from Regional to Municipal they + + + align:start position:0% +further from Regional to Municipal they +can then look at it front Point View of + + align:start position:0% +can then look at it front Point View of + + + align:start position:0% +can then look at it front Point View of +how they develop their respective areas + + align:start position:0% +how they develop their respective areas + + + align:start position:0% +how they develop their respective areas +so we bring them to Japan and let them + + align:start position:0% +so we bring them to Japan and let them + + + align:start position:0% +so we bring them to Japan and let them +see a bigger picture how it's being done + + align:start position:0% +see a bigger picture how it's being done + + + align:start position:0% +see a bigger picture how it's being done +in a developed country then they they + + align:start position:0% +in a developed country then they they + + + align:start position:0% +in a developed country then they they +bring back and then they disseminate and + + align:start position:0% +bring back and then they disseminate and + + + align:start position:0% +bring back and then they disseminate and +share the information so through that + + align:start position:0% +share the information so through that + + + align:start position:0% +share the information so through that +process Ira can play a big role in terms + + align:start position:0% +process Ira can play a big role in terms + + + align:start position:0% +process Ira can play a big role in terms +of making sure that everyone is + + align:start position:0% +of making sure that everyone is + + + align:start position:0% +of making sure that everyone is +connected as it will regarding what has + + align:start position:0% +connected as it will regarding what has + + + align:start position:0% +connected as it will regarding what has +been achieved thus far in joobu + + align:start position:0% +been achieved thus far in joobu + + + align:start position:0% +been achieved thus far in joobu +Professor who has this to say the first + + align:start position:0% +Professor who has this to say the first + + + align:start position:0% +Professor who has this to say the first +thing I think awareness awareness + + align:start position:0% +thing I think awareness awareness + + + align:start position:0% +thing I think awareness awareness +certainly we have achieved lower Caron + + align:start position:0% +certainly we have achieved lower Caron + + + align:start position:0% +certainly we have achieved lower Caron +Society is not a new term anymore in + + align:start position:0% +Society is not a new term anymore in + + + align:start position:0% +Society is not a new term anymore in +isanda area or in putraa area people are + + align:start position:0% +isanda area or in putraa area people are + + + align:start position:0% +isanda area or in putraa area people are +talking about low carbon society and + + align:start position:0% +talking about low carbon society and + + + align:start position:0% +talking about low carbon society and +people believe that actually low carbon + + align:start position:0% +people believe that actually low carbon + + + align:start position:0% +people believe that actually low carbon +Society will improve the quality of life + + align:start position:0% +Society will improve the quality of life + + + align:start position:0% +Society will improve the quality of life +another achievement is the creation of + + align:start position:0% +another achievement is the creation of + + + align:start position:0% +another achievement is the creation of +environmentally friendly rural + + align:start position:0% +environmentally friendly rural + + + align:start position:0% +environmentally friendly rural +communities one of these Villages Felder + + align:start position:0% +communities one of these Villages Felder + + + align:start position:0% +communities one of these Villages Felder +type andak has been supported by the + + align:start position:0% +type andak has been supported by the + + + align:start position:0% +type andak has been supported by the +government as a model for low carbon + + align:start position:0% +government as a model for low carbon + + + align:start position:0% +government as a model for low carbon +lifestyle The Village has implemented a + + align:start position:0% +lifestyle The Village has implemented a + + + align:start position:0% +lifestyle The Village has implemented a +series of action plans in various + + align:start position:0% +series of action plans in various + + + align:start position:0% +series of action plans in various +sectors such as AG Agriculture and waste + + align:start position:0% +sectors such as AG Agriculture and waste + + + align:start position:0% +sectors such as AG Agriculture and waste +disposal that demonstrat how a community + + align:start position:0% +disposal that demonstrat how a community + + + align:start position:0% +disposal that demonstrat how a community +can live more + + align:start position:0% +can live more + + + align:start position:0% +can live more +sustainably type andak project was + + align:start position:0% +sustainably type andak project was + + + align:start position:0% +sustainably type andak project was +adapted by the residents of felda and + + align:start position:0% +adapted by the residents of felda and + + + align:start position:0% +adapted by the residents of felda and +shows how the population can benefit + + align:start position:0% +shows how the population can benefit + + + align:start position:0% +shows how the population can benefit +socially environmentally and + + align:start position:0% +socially environmentally and + + + align:start position:0% +socially environmentally and +economically through various low carbon + + align:start position:0% +economically through various low carbon + + + align:start position:0% +economically through various low carbon +development efforts among the key + + align:start position:0% +development efforts among the key + + + align:start position:0% +development efforts among the key +obstacles to promoting low carbon + + align:start position:0% +obstacles to promoting low carbon + + + align:start position:0% +obstacles to promoting low carbon +development is changing the mindset of + + align:start position:0% +development is changing the mindset of + + + align:start position:0% +development is changing the mindset of +those who have not embraced + + align:start position:0% +those who have not embraced + + + align:start position:0% +those who have not embraced +the need to reduce carbon intensity + + align:start position:0% +the need to reduce carbon intensity + + + align:start position:0% +the need to reduce carbon intensity +Professor ho offers some suggestions + + align:start position:0% +Professor ho offers some suggestions + + + align:start position:0% +Professor ho offers some suggestions +regarding ways of changing local + + align:start position:0% +regarding ways of changing local + + + align:start position:0% +regarding ways of changing local +thinking the ptic approach is actually + + align:start position:0% +thinking the ptic approach is actually + + + align:start position:0% +thinking the ptic approach is actually +focusing on the co benefit I I think + + align:start position:0% +focusing on the co benefit I I think + + + align:start position:0% +focusing on the co benefit I I think +it's too early stage for developing + + align:start position:0% +it's too early stage for developing + + + align:start position:0% +it's too early stage for developing +country when you tell them okay let us + + align:start position:0% +country when you tell them okay let us + + + align:start position:0% +country when you tell them okay let us +go for low Carbon Let's Save the Planet + + align:start position:0% +go for low Carbon Let's Save the Planet + + + align:start position:0% +go for low Carbon Let's Save the Planet +let us cut down CO2 it it may not make + + align:start position:0% +let us cut down CO2 it it may not make + + + align:start position:0% +let us cut down CO2 it it may not make +sense to many of them but if you tell + + align:start position:0% +sense to many of them but if you tell + + + align:start position:0% +sense to many of them but if you tell +them that there is a co- benefit for + + align:start position:0% +them that there is a co- benefit for + + + align:start position:0% +them that there is a co- benefit for +instance by having by going low carbon + + align:start position:0% +instance by having by going low carbon + + + align:start position:0% +instance by having by going low carbon +you can save money by having low carbon + + align:start position:0% +you can save money by having low carbon + + + align:start position:0% +you can save money by having low carbon +you have a co- benefit of better air + + align:start position:0% +you have a co- benefit of better air + + + align:start position:0% +you have a co- benefit of better air +quality Better Health better quality of + + align:start position:0% +quality Better Health better quality of + + + align:start position:0% +quality Better Health better quality of +life or by having even going green or + + align:start position:0% +life or by having even going green or + + + align:start position:0% +life or by having even going green or +low carbon you can do composting or you + + align:start position:0% +low carbon you can do composting or you + + + align:start position:0% +low carbon you can do composting or you +can do Recycling and then by doing that + + align:start position:0% +can do Recycling and then by doing that + + + align:start position:0% +can do Recycling and then by doing that +activities you can generate certain + + align:start position:0% +activities you can generate certain + + + align:start position:0% +activities you can generate certain +extra income for the family okay those + + align:start position:0% +extra income for the family okay those + + + align:start position:0% +extra income for the family okay those +those are co- benefit I believe strongly + + align:start position:0% +those are co- benefit I believe strongly + + + align:start position:0% +those are co- benefit I believe strongly +that that help us + + align:start position:0% +that that help us + + + align:start position:0% +that that help us +to uh promote + + align:start position:0% +to uh promote + + + align:start position:0% +to uh promote +it measuring and monitoring carbon + + align:start position:0% +it measuring and monitoring carbon + + + align:start position:0% +it measuring and monitoring carbon +emissions from electricity and the + + align:start position:0% +emissions from electricity and the + + + align:start position:0% +emissions from electricity and the +transport sector is carried out for ITA + + align:start position:0% +transport sector is carried out for ITA + + + align:start position:0% +transport sector is carried out for ITA +by UTM and Japanese researchers as Mr + + align:start position:0% +by UTM and Japanese researchers as Mr + + + align:start position:0% +by UTM and Japanese researchers as Mr +Boyd jman explains through the low C + + align:start position:0% +Boyd jman explains through the low C + + + align:start position:0% +Boyd jman explains through the low C +blueprint which was prepared by UTM and + + align:start position:0% +blueprint which was prepared by UTM and + + + align:start position:0% +blueprint which was prepared by UTM and +Japan Kyo University and Oka University + + align:start position:0% +Japan Kyo University and Oka University + + + align:start position:0% +Japan Kyo University and Oka University +and the N through that they did the + + align:start position:0% +and the N through that they did the + + + align:start position:0% +and the N through that they did the +homework I.E what are the existing + + align:start position:0% +homework I.E what are the existing + + + align:start position:0% +homework I.E what are the existing +emissions or the um output of um + + align:start position:0% +emissions or the um output of um + + + align:start position:0% +emissions or the um output of um +electricity for example or transport so + + align:start position:0% +electricity for example or transport so + + + align:start position:0% +electricity for example or transport so +from then on we have a base figure 2005 + + align:start position:0% +from then on we have a base figure 2005 + + + align:start position:0% +from then on we have a base figure 2005 +at this point it's being monitored + + align:start position:0% +at this point it's being monitored + + + align:start position:0% +at this point it's being monitored +through the project I.E uh by UTM and + + align:start position:0% +through the project I.E uh by UTM and + + + align:start position:0% +through the project I.E uh by UTM and +Japan but + + align:start position:0% +Japan but + + + align:start position:0% +Japan but +eventually IR needs to sit down and + + align:start position:0% +eventually IR needs to sit down and + + + align:start position:0% +eventually IR needs to sit down and +monitor ourselves one cannot manage what + + align:start position:0% +monitor ourselves one cannot manage what + + + align:start position:0% +monitor ourselves one cannot manage what +one cannot measure and monitoring is + + align:start position:0% +one cannot measure and monitoring is + + + align:start position:0% +one cannot measure and monitoring is +only possible once there is agreement on + + align:start position:0% +only possible once there is agreement on + + + align:start position:0% +only possible once there is agreement on +what to + + align:start position:0% +what to + + + align:start position:0% +what to +measure emissions from transp ort and + + align:start position:0% +measure emissions from transp ort and + + + align:start position:0% +measure emissions from transp ort and +electricity production must be measured + + align:start position:0% +electricity production must be measured + + + align:start position:0% +electricity production must be measured +and + + align:start position:0% +and + + + align:start position:0% +and +monitored mhet is an emissions measuring + + align:start position:0% +monitored mhet is an emissions measuring + + + align:start position:0% +monitored mhet is an emissions measuring +tool that is being used to assess carbon + + align:start position:0% +tool that is being used to assess carbon + + + align:start position:0% +tool that is being used to assess carbon +dioxide emission from transport and + + align:start position:0% +dioxide emission from transport and + + + align:start position:0% +dioxide emission from transport and +electricity the tool measures fossil fo + + align:start position:0% +electricity the tool measures fossil fo + + + align:start position:0% +electricity the tool measures fossil fo +based energy use by category type and + + align:start position:0% +based energy use by category type and + + + align:start position:0% +based energy use by category type and +sector it inent electricity use in + + align:start position:0% +sector it inent electricity use in + + + align:start position:0% +sector it inent electricity use in +kilowatt hours and liters of oil these + + align:start position:0% +kilowatt hours and liters of oil these + + + align:start position:0% +kilowatt hours and liters of oil these +are automatically converted into carbon + + align:start position:0% +are automatically converted into carbon + + + align:start position:0% +are automatically converted into carbon +dioxide equivalent the emission + + align:start position:0% +dioxide equivalent the emission + + + align:start position:0% +dioxide equivalent the emission +reduction goal can be achieved using + + align:start position:0% +reduction goal can be achieved using + + + align:start position:0% +reduction goal can be achieved using +mushet to monitor the carbon reduction + + align:start position:0% +mushet to monitor the carbon reduction + + + align:start position:0% +mushet to monitor the carbon reduction +from transport and electricity in joob + + align:start position:0% +from transport and electricity in joob + + + align:start position:0% +from transport and electricity in joob +baru the Malaysian economy is growing at + + align:start position:0% +baru the Malaysian economy is growing at + + + align:start position:0% +baru the Malaysian economy is growing at +almost 2% per year so reducing carbon + + align:start position:0% +almost 2% per year so reducing carbon + + + align:start position:0% +almost 2% per year so reducing carbon +intensity will not be easy The Way + + align:start position:0% +intensity will not be easy The Way + + + align:start position:0% +intensity will not be easy The Way +Forward is to create support for the + + align:start position:0% +Forward is to create support for the + + + align:start position:0% +Forward is to create support for the +world we want to live in + + align:start position:0% +world we want to live in + + + align:start position:0% +world we want to live in +reducing carbon intensity and promoting + + align:start position:0% +reducing carbon intensity and promoting + + + align:start position:0% +reducing carbon intensity and promoting +low carbon development in joob baru and + + align:start position:0% +low carbon development in joob baru and + + + align:start position:0% +low carbon development in joob baru and +elsewhere will require changing the + + align:start position:0% +elsewhere will require changing the + + + align:start position:0% +elsewhere will require changing the +mindset of many people it will also be + + align:start position:0% +mindset of many people it will also be + + + align:start position:0% +mindset of many people it will also be +necessary to agree on what to measure + + align:start position:0% +necessary to agree on what to measure + + + align:start position:0% +necessary to agree on what to measure +and how to monitor changes in carbon + + align:start position:0% +and how to monitor changes in carbon + + + align:start position:0% +and how to monitor changes in carbon +intensity in each sector more low carbon + + align:start position:0% +intensity in each sector more low carbon + + + align:start position:0% +intensity in each sector more low carbon +model Villages should be created to show + + align:start position:0% +model Villages should be created to show + + + align:start position:0% +model Villages should be created to show +how low carbon development can meet the + + align:start position:0% +how low carbon development can meet the + + + align:start position:0% +how low carbon development can meet the +needs of the + + align:start position:0% +needs of the + + + align:start position:0% +needs of the +population other experiments and + + align:start position:0% +population other experiments and + + + align:start position:0% +population other experiments and +prototype living arrangements will be + + align:start position:0% +prototype living arrangements will be + + + align:start position:0% +prototype living arrangements will be +necessary to convince people that change + + align:start position:0% +necessary to convince people that change + + + align:start position:0% +necessary to convince people that change +is + + align:start position:0% +is + + + align:start position:0% +is +possible shifting to clean energy will + + align:start position:0% +possible shifting to clean energy will + + + align:start position:0% +possible shifting to clean energy will +undoubtedly be important along these + + align:start position:0% +undoubtedly be important along these + + + align:start position:0% +undoubtedly be important along these +lines joobu will probably need to + + align:start position:0% +lines joobu will probably need to + + + align:start position:0% +lines joobu will probably need to +implement Financial incentives to + + align:start position:0% +implement Financial incentives to + + + align:start position:0% +implement Financial incentives to +encourage investment in renewable energy + + align:start position:0% +encourage investment in renewable energy + + + align:start position:0% +encourage investment in renewable energy +along with multiple changes in consumer + + align:start position:0% +along with multiple changes in consumer + + + align:start position:0% +along with multiple changes in consumer +Behavior city planners will need to to + + align:start position:0% +Behavior city planners will need to to + + + align:start position:0% +Behavior city planners will need to to +explain what less energy intensive + + align:start position:0% +explain what less energy intensive + + + align:start position:0% +explain what less energy intensive +patterns of development might look like \ No newline at end of file diff --git a/IrKUM3nNXJE.txt b/IrKUM3nNXJE.txt new file mode 100644 index 0000000000000000000000000000000000000000..26b9acf41e2fafbb64441cfadcd54fac35ec9e8a --- /dev/null +++ b/IrKUM3nNXJE.txt @@ -0,0 +1,1099 @@ +align:start position:0% + +in this segment we will first discuss + + align:start position:0% +in this segment we will first discuss + + + align:start position:0% +in this segment we will first discuss +and compare different views of the sum + + align:start position:0% +and compare different views of the sum + + + align:start position:0% +and compare different views of the sum +of independent identically distributed + + align:start position:0% +of independent identically distributed + + + align:start position:0% +of independent identically distributed +random variables and then we will + + align:start position:0% +random variables and then we will + + + align:start position:0% +random variables and then we will +conclude with the statement of the + + align:start position:0% +conclude with the statement of the + + + align:start position:0% +conclude with the statement of the +central limit theorem so let x1 up to xn + + align:start position:0% +central limit theorem so let x1 up to xn + + + align:start position:0% +central limit theorem so let x1 up to xn +be independent identically distributed + + align:start position:0% +be independent identically distributed + + + align:start position:0% +be independent identically distributed +random variables that have a certain + + align:start position:0% +random variables that have a certain + + + align:start position:0% +random variables that have a certain +finite mean and finite variance that we + + align:start position:0% +finite mean and finite variance that we + + + align:start position:0% +finite mean and finite variance that we +denote by mu and Sigma squared in order + + align:start position:0% +denote by mu and Sigma squared in order + + + align:start position:0% +denote by mu and Sigma squared in order +to have a concrete example in our hands + + align:start position:0% +to have a concrete example in our hands + + + align:start position:0% +to have a concrete example in our hands +let us assume that this random variable + + align:start position:0% +let us assume that this random variable + + + align:start position:0% +let us assume that this random variable +has a distribution let's say a PDF that + + align:start position:0% +has a distribution let's say a PDF that + + + align:start position:0% +has a distribution let's say a PDF that +ranges from minus 1 to plus 1 and has a + + align:start position:0% +ranges from minus 1 to plus 1 and has a + + + align:start position:0% +ranges from minus 1 to plus 1 and has a +mean of 0 let us look at the sum of + + align:start position:0% +mean of 0 let us look at the sum of + + + align:start position:0% +mean of 0 let us look at the sum of +these random variables the sum has a + + align:start position:0% +these random variables the sum has a + + + align:start position:0% +these random variables the sum has a +variance of n times Sigma squared which + + align:start position:0% +variance of n times Sigma squared which + + + align:start position:0% +variance of n times Sigma squared which +goes to infinity and correspondingly + + align:start position:0% +goes to infinity and correspondingly + + + align:start position:0% +goes to infinity and correspondingly +the standard deviation of this random + + align:start position:0% +the standard deviation of this random + + + align:start position:0% +the standard deviation of this random +variable also grows to infinity this + + align:start position:0% +variable also grows to infinity this + + + align:start position:0% +variable also grows to infinity this +random variable takes values between + + align:start position:0% +random variable takes values between + + + align:start position:0% +random variable takes values between +minus N and plus N and because the + + align:start position:0% +minus N and plus N and because the + + + align:start position:0% +minus N and plus N and because the +variance and the standard deviation + + align:start position:0% +variance and the standard deviation + + + align:start position:0% +variance and the standard deviation +increase this means that for larger and + + align:start position:0% +increase this means that for larger and + + + align:start position:0% +increase this means that for larger and +larger n the width of this distribution + + align:start position:0% +larger n the width of this distribution + + + align:start position:0% +larger n the width of this distribution +is going to be larger and larger we can + + align:start position:0% +is going to be larger and larger we can + + + align:start position:0% +is going to be larger and larger we can +obtain a different view of this sum if + + align:start position:0% +obtain a different view of this sum if + + + align:start position:0% +obtain a different view of this sum if +we divided by n in which case we obtain + + align:start position:0% +we divided by n in which case we obtain + + + align:start position:0% +we divided by n in which case we obtain +the sample mean in this case the + + align:start position:0% +the sample mean in this case the + + + align:start position:0% +the sample mean in this case the +variance goes to 0 as n goes to infinity + + align:start position:0% +variance goes to 0 as n goes to infinity + + + align:start position:0% +variance goes to 0 as n goes to infinity +and as a consequence the distribution is + + align:start position:0% +and as a consequence the distribution is + + + align:start position:0% +and as a consequence the distribution is +highly concentrated around 0 this is + + align:start position:0% +highly concentrated around 0 this is + + + align:start position:0% +highly concentrated around 0 this is +also what the weak law of large numbers + + align:start position:0% +also what the weak law of large numbers + + + align:start position:0% +also what the weak law of large numbers +tells us the bulk of the distribution is + + align:start position:0% +tells us the bulk of the distribution is + + + align:start position:0% +tells us the bulk of the distribution is +concentrated in an arbitrarily small + + align:start position:0% +concentrated in an arbitrarily small + + + align:start position:0% +concentrated in an arbitrarily small +interval around 0 so this width becomes + + align:start position:0% +interval around 0 so this width becomes + + + align:start position:0% +interval around 0 so this width becomes +smaller and smaller as n goes to + + align:start position:0% +smaller and smaller as n goes to + + + align:start position:0% +smaller and smaller as n goes to +infinity so in this case we obtain a + + align:start position:0% +infinity so in this case we obtain a + + + align:start position:0% +infinity so in this case we obtain a +limiting distribution but this limiting + + align:start position:0% +limiting distribution but this limiting + + + align:start position:0% +limiting distribution but this limiting +distribution is trivial it's degenerate + + align:start position:0% +distribution is trivial it's degenerate + + + align:start position:0% +distribution is trivial it's degenerate +it's all concentrated on a single point + + align:start position:0% +it's all concentrated on a single point + + + align:start position:0% +it's all concentrated on a single point +how can we make it so that we obtain a + + align:start position:0% +how can we make it so that we obtain a + + + align:start position:0% +how can we make it so that we obtain a +limiting distribution that is more + + align:start position:0% +limiting distribution that is more + + + align:start position:0% +limiting distribution that is more +interesting the key is to divide not by + + align:start position:0% +interesting the key is to divide not by + + + align:start position:0% +interesting the key is to divide not by +n + + align:start position:0% +n + + + align:start position:0% +n +but to divide by the square root of n + + align:start position:0% +but to divide by the square root of n + + + align:start position:0% +but to divide by the square root of n +this has the following effect the + + align:start position:0% +this has the following effect the + + + align:start position:0% +this has the following effect the +variance of this ratio is calculated as + + align:start position:0% +variance of this ratio is calculated as + + + align:start position:0% +variance of this ratio is calculated as +follows we take the variance of the + + align:start position:0% +follows we take the variance of the + + + align:start position:0% +follows we take the variance of the +numerator which is n times Sigma squared + + align:start position:0% +numerator which is n times Sigma squared + + + align:start position:0% +numerator which is n times Sigma squared +and then we divide by the square of this + + align:start position:0% +and then we divide by the square of this + + + align:start position:0% +and then we divide by the square of this +number which is N and therefore the + + align:start position:0% +number which is N and therefore the + + + align:start position:0% +number which is N and therefore the +variance is equal to Sigma squared + + align:start position:0% +variance is equal to Sigma squared + + + align:start position:0% +variance is equal to Sigma squared +what's important here is that the + + align:start position:0% +what's important here is that the + + + align:start position:0% +what's important here is that the +variance stays constant no matter what n + + align:start position:0% +variance stays constant no matter what n + + + align:start position:0% +variance stays constant no matter what n +is the width of this distribution is + + align:start position:0% +is the width of this distribution is + + + align:start position:0% +is the width of this distribution is +going to be more or less the same the + + align:start position:0% +going to be more or less the same the + + + align:start position:0% +going to be more or less the same the +distribution itself might change as n + + align:start position:0% +distribution itself might change as n + + + align:start position:0% +distribution itself might change as n +changes but the distribution in list in + + align:start position:0% +changes but the distribution in list in + + + align:start position:0% +changes but the distribution in list in +this case where we assumed zero mean the + + align:start position:0% +this case where we assumed zero mean the + + + align:start position:0% +this case where we assumed zero mean the +distribution stays in place it doesn't + + align:start position:0% +distribution stays in place it doesn't + + + align:start position:0% +distribution stays in place it doesn't +move to the right or to the left and its + + align:start position:0% +move to the right or to the left and its + + + align:start position:0% +move to the right or to the left and its +width stays the same so one can wonder + + align:start position:0% +width stays the same so one can wonder + + + align:start position:0% +width stays the same so one can wonder +in the limit as n goes to infinity does + + align:start position:0% +in the limit as n goes to infinity does + + + align:start position:0% +in the limit as n goes to infinity does +this shape start to approach a certain + + align:start position:0% +this shape start to approach a certain + + + align:start position:0% +this shape start to approach a certain +limiting shape and if it does what is + + align:start position:0% +limiting shape and if it does what is + + + align:start position:0% +limiting shape and if it does what is +the limiting shape that it approaches + + align:start position:0% +the limiting shape that it approaches + + + align:start position:0% +the limiting shape that it approaches +the central limit theorem will give us + + align:start position:0% +the central limit theorem will give us + + + align:start position:0% +the central limit theorem will give us +the answers to these questions the + + align:start position:0% +the answers to these questions the + + + align:start position:0% +the answers to these questions the +setting for the central limit theorem + + align:start position:0% +setting for the central limit theorem + + + align:start position:0% +setting for the central limit theorem +will be pretty much the setting that we + + align:start position:0% +will be pretty much the setting that we + + + align:start position:0% +will be pretty much the setting that we +were just discussing so we will be + + align:start position:0% +were just discussing so we will be + + + align:start position:0% +were just discussing so we will be +looking into the case where we divide + + align:start position:0% +looking into the case where we divide + + + align:start position:0% +looking into the case where we divide +the sum of the random variables by + + align:start position:0% +the sum of the random variables by + + + align:start position:0% +the sum of the random variables by +square root of n except for a few + + align:start position:0% +square root of n except for a few + + + align:start position:0% +square root of n except for a few +additional twists since this ratio has a + + align:start position:0% +additional twists since this ratio has a + + + align:start position:0% +additional twists since this ratio has a +variance of Sigma squared it would help + + align:start position:0% +variance of Sigma squared it would help + + + align:start position:0% +variance of Sigma squared it would help +to divide by a further factor of Sigma + + align:start position:0% +to divide by a further factor of Sigma + + + align:start position:0% +to divide by a further factor of Sigma +here so that the variance is going to + + align:start position:0% +here so that the variance is going to + + + align:start position:0% +here so that the variance is going to +become 1 and there's another issue if + + align:start position:0% +become 1 and there's another issue if + + + align:start position:0% +become 1 and there's another issue if +the mean of the XS is nonzero then the + + align:start position:0% +the mean of the XS is nonzero then the + + + align:start position:0% +the mean of the XS is nonzero then the +distribution is centered at the quantity + + align:start position:0% +distribution is centered at the quantity + + + align:start position:0% +distribution is centered at the quantity +that keeps changing with n so the + + align:start position:0% +that keeps changing with n so the + + + align:start position:0% +that keeps changing with n so the +distribution will be drifting away from + + align:start position:0% +distribution will be drifting away from + + + align:start position:0% +distribution will be drifting away from +0 it's not staying in place and so it + + align:start position:0% +0 it's not staying in place and so it + + + align:start position:0% +0 it's not staying in place and so it +wouldn't have any hope of converging to + + align:start position:0% +wouldn't have any hope of converging to + + + align:start position:0% +wouldn't have any hope of converging to +something for this reason instead of + + align:start position:0% +something for this reason instead of + + + align:start position:0% +something for this reason instead of +looking at this ratio in particular what + + align:start position:0% +looking at this ratio in particular what + + + align:start position:0% +looking at this ratio in particular what +we do is + + align:start position:0% +we do is + + + align:start position:0% +we do is +we first subtract the mean of the sum + + align:start position:0% +we first subtract the mean of the sum + + + align:start position:0% +we first subtract the mean of the sum +which is n times the mean and then we + + align:start position:0% +which is n times the mean and then we + + + align:start position:0% +which is n times the mean and then we +divide by a further factor of Sigma this + + align:start position:0% +divide by a further factor of Sigma this + + + align:start position:0% +divide by a further factor of Sigma this +random variable that we obtained here + + align:start position:0% +random variable that we obtained here + + + align:start position:0% +random variable that we obtained here +has nice properties the mean of this + + align:start position:0% +has nice properties the mean of this + + + align:start position:0% +has nice properties the mean of this +random variable is equal to 0 because we + + align:start position:0% +random variable is equal to 0 because we + + + align:start position:0% +random variable is equal to 0 because we +did subtract the mean of the axes and + + align:start position:0% +did subtract the mean of the axes and + + + align:start position:0% +did subtract the mean of the axes and +the variance of this random variable is + + align:start position:0% +the variance of this random variable is + + + align:start position:0% +the variance of this random variable is +going to be equal to 1 the reason is + + align:start position:0% +going to be equal to 1 the reason is + + + align:start position:0% +going to be equal to 1 the reason is +that the variance is the variance of the + + align:start position:0% +that the variance is the variance of the + + + align:start position:0% +that the variance is the variance of the +numerator which is n times Sigma squared + + align:start position:0% +numerator which is n times Sigma squared + + + align:start position:0% +numerator which is n times Sigma squared +divided by the square of the denominator + + align:start position:0% +divided by the square of the denominator + + + align:start position:0% +divided by the square of the denominator +which is also n times Sigma squared so + + align:start position:0% +which is also n times Sigma squared so + + + align:start position:0% +which is also n times Sigma squared so +as n changes the distribution of the + + align:start position:0% +as n changes the distribution of the + + + align:start position:0% +as n changes the distribution of the +random variable Z n stays in place it + + align:start position:0% +random variable Z n stays in place it + + + align:start position:0% +random variable Z n stays in place it +has a mean of 0 and its width more or + + align:start position:0% +has a mean of 0 and its width more or + + + align:start position:0% +has a mean of 0 and its width more or +less stays the same because we have a + + align:start position:0% +less stays the same because we have a + + + align:start position:0% +less stays the same because we have a +constant variance we will compare this + + align:start position:0% +constant variance we will compare this + + + align:start position:0% +constant variance we will compare this +random variable with a standard normal + + align:start position:0% +random variable with a standard normal + + + align:start position:0% +random variable with a standard normal +random variable that has 0 mean and unit + + align:start position:0% +random variable that has 0 mean and unit + + + align:start position:0% +random variable that has 0 mean and unit +variance the central limit theorem + + align:start position:0% +variance the central limit theorem + + + align:start position:0% +variance the central limit theorem +states the amazing fact that as n goes + + align:start position:0% +states the amazing fact that as n goes + + + align:start position:0% +states the amazing fact that as n goes +to infinity the distribution of this + + align:start position:0% +to infinity the distribution of this + + + align:start position:0% +to infinity the distribution of this +random variable converges to the + + align:start position:0% +random variable converges to the + + + align:start position:0% +random variable converges to the +standard normal distribution in the + + align:start position:0% +standard normal distribution in the + + + align:start position:0% +standard normal distribution in the +following sense that this probability + + align:start position:0% +following sense that this probability + + + align:start position:0% +following sense that this probability +here converges to that probability for + + align:start position:0% +here converges to that probability for + + + align:start position:0% +here converges to that probability for +any choice of little Z now what we have + + align:start position:0% +any choice of little Z now what we have + + + align:start position:0% +any choice of little Z now what we have +here is just the CDF of this random + + align:start position:0% +here is just the CDF of this random + + + align:start position:0% +here is just the CDF of this random +variable Z n so it tells us that the CDF + + align:start position:0% +variable Z n so it tells us that the CDF + + + align:start position:0% +variable Z n so it tells us that the CDF +of the random variable Z n converges to + + align:start position:0% +of the random variable Z n converges to + + + align:start position:0% +of the random variable Z n converges to +the CDF of a standard normal and + + align:start position:0% +the CDF of a standard normal and + + + align:start position:0% +the CDF of a standard normal and +fortunately for the standard normal the + + align:start position:0% +fortunately for the standard normal the + + + align:start position:0% +fortunately for the standard normal the +CDF is available in tables so if we need + + align:start position:0% +CDF is available in tables so if we need + + + align:start position:0% +CDF is available in tables so if we need +to calculate the numerical value here we + + align:start position:0% +to calculate the numerical value here we + + + align:start position:0% +to calculate the numerical value here we +can just look up the normal tables and + + align:start position:0% +can just look up the normal tables and + + + align:start position:0% +can just look up the normal tables and +this suggests an approximation to this + + align:start position:0% +this suggests an approximation to this + + + align:start position:0% +this suggests an approximation to this +probability for the case where n is + + align:start position:0% +probability for the case where n is + + + align:start position:0% +probability for the case where n is +finite but large when n is large we can + + align:start position:0% +finite but large when n is large we can + + + align:start position:0% +finite but large when n is large we can +approximate this probability by this + + align:start position:0% +approximate this probability by this + + + align:start position:0% +approximate this probability by this +probable + + align:start position:0% +probable + + + align:start position:0% +probable +on the right which we can find from the + + align:start position:0% +on the right which we can find from the + + + align:start position:0% +on the right which we can find from the +normal tables the central limit theorem + + align:start position:0% +normal tables the central limit theorem + + + align:start position:0% +normal tables the central limit theorem +is a very important result for this + + align:start position:0% +is a very important result for this + + + align:start position:0% +is a very important result for this +reason we will spend some time + + align:start position:0% +reason we will spend some time + + + align:start position:0% +reason we will spend some time +discussing how to interpret it what it + + align:start position:0% +discussing how to interpret it what it + + + align:start position:0% +discussing how to interpret it what it +means how we use it and we will go + + align:start position:0% +means how we use it and we will go + + + align:start position:0% +means how we use it and we will go +through a few examples to see how we + + align:start position:0% +through a few examples to see how we + + + align:start position:0% +through a few examples to see how we +actually apply it \ No newline at end of file diff --git a/LHBc2mE71yc.txt b/LHBc2mE71yc.txt new file mode 100644 index 0000000000000000000000000000000000000000..7075e928dd469b97af95e3904b11340cf85f1b5d --- /dev/null +++ b/LHBc2mE71yc.txt @@ -0,0 +1,14643 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu all right so today we finish + + align:start position:0% +ocw.mit.edu all right so today we finish + + + align:start position:0% +ocw.mit.edu all right so today we finish +our game characterization + + align:start position:0% +our game characterization + + + align:start position:0% +our game characterization +uh we had this giant table we've done uh + + align:start position:0% +uh we had this giant table we've done uh + + + align:start position:0% +uh we had this giant table we've done uh +two players zero players one player of + + align:start position:0% +two players zero players one player of + + + align:start position:0% +two players zero players one player of +course that's the oldest uh today we're + + align:start position:0% +course that's the oldest uh today we're + + + align:start position:0% +course that's the oldest uh today we're +going to do team imperfect information + + align:start position:0% +going to do team imperfect information + + + align:start position:0% +going to do team imperfect information +games which when you have a polinomial + + align:start position:0% +games which when you have a polinomial + + + align:start position:0% +games which when you have a polinomial +bound on the number of moves you get NX + + align:start position:0% +bound on the number of moves you get NX + + + align:start position:0% +bound on the number of moves you get NX +time non-deterministic exponential time + + align:start position:0% +time non-deterministic exponential time + + + align:start position:0% +time non-deterministic exponential time +this is the exponential version of NP + + align:start position:0% +this is the exponential version of NP + + + align:start position:0% +this is the exponential version of NP +and for games with unbounded number of + + align:start position:0% +and for games with unbounded number of + + + align:start position:0% +and for games with unbounded number of +moves normally I would say exponentially + + align:start position:0% +moves normally I would say exponentially + + + align:start position:0% +moves normally I would say exponentially +many moves but in fact this will be + + align:start position:0% +many moves but in fact this will be + + + align:start position:0% +many moves but in fact this will be +really unbounded could be close to infin + + align:start position:0% +really unbounded could be close to infin + + + align:start position:0% +really unbounded could be close to infin +itely many moves um we get + + align:start position:0% +itely many moves um we get + + + align:start position:0% +itely many moves um we get +undecidability so no algorithm + + align:start position:0% +undecidability so no algorithm + + + align:start position:0% +undecidability so no algorithm +whatsoever to solve it we don't know any + + align:start position:0% +whatsoever to solve it we don't know any + + + align:start position:0% +whatsoever to solve it we don't know any +natural games in these classes but I + + align:start position:0% +natural games in these classes but I + + + align:start position:0% +natural games in these classes but I +have a couple question marks here bridge + + align:start position:0% +have a couple question marks here bridge + + + align:start position:0% +have a couple question marks here bridge +is an example of a game with imperfect + + align:start position:0% +is an example of a game with imperfect + + + align:start position:0% +is an example of a game with imperfect +information and teams in one hand uh and + + align:start position:0% +information and teams in one hand uh and + + + align:start position:0% +information and teams in one hand uh and +it has bounded play once you play your + + align:start position:0% +it has bounded play once you play your + + + align:start position:0% +it has bounded play once you play your +cards all the cards are down you're + + align:start position:0% +cards all the cards are down you're + + + align:start position:0% +cards all the cards are down you're +you're done so potentially it falls in + + align:start position:0% +you're done so potentially it falls in + + + align:start position:0% +you're done so potentially it falls in +this class although I don't know if + + align:start position:0% +this class although I don't know if + + + align:start position:0% +this class although I don't know if +bridge is sophisticated enough or it + + align:start position:0% +bridge is sophisticated enough or it + + + align:start position:0% +bridge is sophisticated enough or it +depends on your notion of the bidding + + align:start position:0% +depends on your notion of the bidding + + + align:start position:0% +depends on your notion of the bidding +rules um and what can be communicated + + align:start position:0% +rules um and what can be communicated + + + align:start position:0% +rules um and what can be communicated +there on the other hand uh for the + + align:start position:0% +there on the other hand uh for the + + + align:start position:0% +there on the other hand uh for the +unbounded game one candidate problem is + + align:start position:0% +unbounded game one candidate problem is + + + align:start position:0% +unbounded game one candidate problem is +called Rango Creeks Spiel Creeks Spiel + + align:start position:0% +called Rango Creeks Spiel Creeks Spiel + + + align:start position:0% +called Rango Creeks Spiel Creeks Spiel +is blind chess Rango Creeks Spiel is + + align:start position:0% +is blind chess Rango Creeks Spiel is + + + align:start position:0% +is blind chess Rango Creeks Spiel is +blind go with teams so they're two black + + align:start position:0% +blind go with teams so they're two black + + + align:start position:0% +blind go with teams so they're two black +players two white players and you make + + align:start position:0% +players two white players and you make + + + align:start position:0% +players two white players and you make +moves without knowing what the other + + align:start position:0% +moves without knowing what the other + + + align:start position:0% +moves without knowing what the other +moves of any of the other players are + + align:start position:0% +moves of any of the other players are + + + align:start position:0% +moves of any of the other players are +usually by writing on a piece of paper + + align:start position:0% +usually by writing on a piece of paper + + + align:start position:0% +usually by writing on a piece of paper +and giving it to some referee who tells + + align:start position:0% +and giving it to some referee who tells + + + align:start position:0% +and giving it to some referee who tells +you whether that was + + align:start position:0% +you whether that was + + + align:start position:0% +you whether that was +valid so this is a game people actually + + align:start position:0% +valid so this is a game people actually + + + align:start position:0% +valid so this is a game people actually +play um and I'm told I know Bob Hearn + + align:start position:0% +play um and I'm told I know Bob Hearn + + + align:start position:0% +play um and I'm told I know Bob Hearn +has played it he's he likes playing go + + align:start position:0% +has played it he's he likes playing go + + + align:start position:0% +has played it he's he likes playing go +uh and uh but it's open whether this + + align:start position:0% +uh and uh but it's open whether this + + + align:start position:0% +uh and uh but it's open whether this +that problem is undecidable potentially + + align:start position:0% +that problem is undecidable potentially + + + align:start position:0% +that problem is undecidable potentially +yes that seems more likely um and then + + align:start position:0% +yes that seems more likely um and then + + + align:start position:0% +yes that seems more likely um and then +finally one other sell that we didn't do + + align:start position:0% +finally one other sell that we didn't do + + + align:start position:0% +finally one other sell that we didn't do +which I'll get to after those two is uh + + align:start position:0% +which I'll get to after those two is uh + + + align:start position:0% +which I'll get to after those two is uh +this box um which sounds pretty boring + + align:start position:0% +this box um which sounds pretty boring + + + align:start position:0% +this box um which sounds pretty boring +because it's just polinomial time things + + align:start position:0% +because it's just polinomial time things + + + align:start position:0% +because it's just polinomial time things +polinom bounded zero player games is + + align:start position:0% +polinom bounded zero player games is + + + align:start position:0% +polinom bounded zero player games is +just uh like Game of Life running for a + + align:start position:0% +just uh like Game of Life running for a + + + align:start position:0% +just uh like Game of Life running for a +PO amount of time you can generate I + + align:start position:0% +PO amount of time you can generate I + + + align:start position:0% +PO amount of time you can generate I +mean you can solve uh those problems in + + align:start position:0% +mean you can solve uh those problems in + + + align:start position:0% +mean you can solve uh those problems in +polinomial time but there's a stronger + + align:start position:0% +polinomial time but there's a stronger + + + align:start position:0% +polinomial time but there's a stronger +sense in which all polinomial time + + align:start position:0% +sense in which all polinomial time + + + align:start position:0% +sense in which all polinomial time +problems can be represented Say by Game + + align:start position:0% +problems can be represented Say by Game + + + align:start position:0% +problems can be represented Say by Game +of Life and uh this actually is relevant + + align:start position:0% +of Life and uh this actually is relevant + + + align:start position:0% +of Life and uh this actually is relevant +to parallel Computing and it essentially + + align:start position:0% +to parallel Computing and it essentially + + + align:start position:0% +to parallel Computing and it essentially +says there's no good way to parallelize + + align:start position:0% +says there's no good way to parallelize + + + align:start position:0% +says there's no good way to parallelize +game of life among other problems so uh + + align:start position:0% +game of life among other problems so uh + + + align:start position:0% +game of life among other problems so uh +I mentioned that way back in lecture one + + align:start position:0% +I mentioned that way back in lecture one + + + align:start position:0% +I mentioned that way back in lecture one +and lots of people said oh what's this P + + align:start position:0% +and lots of people said oh what's this P + + + align:start position:0% +and lots of people said oh what's this P +completeness business and so today we + + align:start position:0% +completeness business and so today we + + + align:start position:0% +completeness business and so today we +will cover that as well uh but let's + + align:start position:0% +will cover that as well uh but let's + + + align:start position:0% +will cover that as well uh but let's +start with NX time and and + + align:start position:0% +start with NX time and and + + + align:start position:0% +start with NX time and and +undecidability um let's start with the + + align:start position:0% +undecidability um let's start with the + + + align:start position:0% +undecidability um let's start with the +bounded + + align:start position:0% + + + + align:start position:0% + +case so in the bounded case um this cool + + align:start position:0% +case so in the bounded case um this cool + + + align:start position:0% +case so in the bounded case um this cool +paper by Peterson and R uh introducing a + + align:start position:0% +paper by Peterson and R uh introducing a + + + align:start position:0% +paper by Peterson and R uh introducing a +problem A variation of + + align:start position:0% + + + + align:start position:0% + +qet uh remember Q set also known as qbf + + align:start position:0% +qet uh remember Q set also known as qbf + + + align:start position:0% +qet uh remember Q set also known as qbf +so so this is + + align:start position:0% + + + + align:start position:0% + +dqbf and it's it's a funny problem first + + align:start position:0% +dqbf and it's it's a funny problem first + + + align:start position:0% +dqbf and it's it's a funny problem first +off phrase it as a formula problem and + + align:start position:0% +off phrase it as a formula problem and + + + align:start position:0% +off phrase it as a formula problem and +then I'll talk about it as a + + align:start position:0% + + + + align:start position:0% + +game so normally in Q set qbf we have n + + align:start position:0% +game so normally in Q set qbf we have n + + + align:start position:0% +game so normally in Q set qbf we have n +alternating quantifiers and that's P + + align:start position:0% +alternating quantifiers and that's P + + + align:start position:0% +alternating quantifiers and that's P +space complete and every quantifier can + + align:start position:0% +space complete and every quantifier can + + + align:start position:0% +space complete and every quantifier can +depend on all the previous values but + + align:start position:0% +depend on all the previous values but + + + align:start position:0% +depend on all the previous values but +now we're going to have two sort of in + + align:start position:0% +now we're going to have two sort of in + + + align:start position:0% +now we're going to have two sort of in +parallel existential quantifiers so we + + align:start position:0% +parallel existential quantifiers so we + + + align:start position:0% +parallel existential quantifiers so we +have two uh Universal I should mentioned + + align:start position:0% +have two uh Universal I should mentioned + + + align:start position:0% +have two uh Universal I should mentioned +the capital letters that's a bunch of + + align:start position:0% +the capital letters that's a bunch of + + + align:start position:0% +the capital letters that's a bunch of +variables so there's like n Bits here n + + align:start position:0% +variables so there's like n Bits here n + + + align:start position:0% +variables so there's like n Bits here n +Bits here that has to work for all + + align:start position:0% +Bits here that has to work for all + + + align:start position:0% +Bits here that has to work for all +choices of those why do I separate them + + align:start position:0% +choices of those why do I separate them + + + align:start position:0% +choices of those why do I separate them +out because over here I'm going to + + align:start position:0% +out because over here I'm going to + + + align:start position:0% +out because over here I'm going to +separate them out and y1 the choice of + + align:start position:0% +separate them out and y1 the choice of + + + align:start position:0% +separate them out and y1 the choice of +y1 is only allowed to depend on on X1 + + align:start position:0% +y1 is only allowed to depend on on X1 + + + align:start position:0% +y1 is only allowed to depend on on X1 +and the choice of Y2 is only allowed to + + align:start position:0% +and the choice of Y2 is only allowed to + + + align:start position:0% +and the choice of Y2 is only allowed to +depend on + + align:start position:0% +depend on + + + align:start position:0% +depend on +x2 um and then we're going to have some + + align:start position:0% +x2 um and then we're going to have some + + + align:start position:0% +x2 um and then we're going to have some +CNF formula on X1 X2 y1 + + align:start position:0% + + + + align:start position:0% + +Y2 so uh we can think of that as this is + + align:start position:0% +Y2 so uh we can think of that as this is + + + align:start position:0% +Y2 so uh we can think of that as this is +one player we'll call it could be two + + align:start position:0% +one player we'll call it could be two + + + align:start position:0% +one player we'll call it could be two +players but uh doesn't really matter so + + align:start position:0% +players but uh doesn't really matter so + + + align:start position:0% +players but uh doesn't really matter so +make it one simpler it's going to be a + + align:start position:0% +make it one simpler it's going to be a + + + align:start position:0% +make it one simpler it's going to be a +three-player game black + + align:start position:0% +three-player game black + + + align:start position:0% +three-player game black +makes these choices and then uh White + + align:start position:0% +makes these choices and then uh White + + + align:start position:0% +makes these choices and then uh White +player + + align:start position:0% +player + + + align:start position:0% +player +one uh chooses the y1s and the the + + align:start position:0% +one uh chooses the y1s and the the + + + align:start position:0% +one uh chooses the y1s and the the +private information aspect of this game + + align:start position:0% +private information aspect of this game + + + align:start position:0% +private information aspect of this game +is that the white player one can only + + align:start position:0% +is that the white player one can only + + + align:start position:0% +is that the white player one can only +see the X1 variables made choices made + + align:start position:0% +see the X1 variables made choices made + + + align:start position:0% +see the X1 variables made choices made +by black uh you could maybe it's more + + align:start position:0% +by black uh you could maybe it's more + + + align:start position:0% +by black uh you could maybe it's more +intuitive to think of this is a four + + align:start position:0% +intuitive to think of this is a four + + + align:start position:0% +intuitive to think of this is a four +player game there are two black players + + align:start position:0% +player game there are two black players + + + align:start position:0% +player game there are two black players +and the white one player can see the + + align:start position:0% +and the white one player can see the + + + align:start position:0% +and the white one player can see the +values chosen by the black one player + + align:start position:0% +values chosen by the black one player + + + align:start position:0% +values chosen by the black one player +but not the values chosen by the black + + align:start position:0% +but not the values chosen by the black + + + align:start position:0% +but not the values chosen by the black +two player and then over here we have uh + + align:start position:0% +two player and then over here we have uh + + + align:start position:0% +two player and then over here we have uh +White player two who can only see the + + align:start position:0% +White player two who can only see the + + + align:start position:0% +White player two who can only see the +variables chosen X2 question does the + + align:start position:0% +variables chosen X2 question does the + + + align:start position:0% +variables chosen X2 question does the +black team have full information black + + align:start position:0% +black team have full information black + + + align:start position:0% +black team have full information black +team has full information I mean the + + align:start position:0% +team has full information I mean the + + + align:start position:0% +team has full information I mean the +black team goes first so it doesn't + + align:start position:0% +black team goes first so it doesn't + + + align:start position:0% +black team goes first so it doesn't +obviously see y1 and Y2 but they can see + + align:start position:0% +obviously see y1 and Y2 but they can see + + + align:start position:0% +obviously see y1 and Y2 but they can see +each other yeah so X2 can see + + align:start position:0% +each other yeah so X2 can see + + + align:start position:0% +each other yeah so X2 can see +X1 yeah so if if I don't write a a + + align:start position:0% +X1 yeah so if if I don't write a a + + + align:start position:0% +X1 yeah so if if I don't write a a +parenthetical dependency then you can + + align:start position:0% +parenthetical dependency then you can + + + align:start position:0% +parenthetical dependency then you can +depend on + + align:start position:0% +depend on + + + align:start position:0% +depend on +everything yeah uh really this is one + + align:start position:0% +everything yeah uh really this is one + + + align:start position:0% +everything yeah uh really this is one +player so they get to choose everything + + align:start position:0% +player so they get to choose everything + + + align:start position:0% +player so they get to choose everything +uh in the X xise okay so then the + + align:start position:0% +uh in the X xise okay so then the + + + align:start position:0% +uh in the X xise okay so then the +question is given this I mean this uh + + align:start position:0% +question is given this I mean this uh + + + align:start position:0% +question is given this I mean this uh +Quantified formula is equivalent to + + align:start position:0% +Quantified formula is equivalent to + + + align:start position:0% +Quantified formula is equivalent to +saying uh can white force a + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +win where white wins if that formula is + + align:start position:0% +win where white wins if that formula is + + + align:start position:0% +win where white wins if that formula is +satisfied uh and white collectively + + align:start position:0% +satisfied uh and white collectively + + + align:start position:0% +satisfied uh and white collectively +needs to make these choices but it it's + + align:start position:0% +needs to make these choices but it it's + + + align:start position:0% +needs to make these choices but it it's +acting as a team with impartial + + align:start position:0% +acting as a team with impartial + + + align:start position:0% +acting as a team with impartial +information so it's not acting as a + + align:start position:0% +information so it's not acting as a + + + align:start position:0% +information so it's not acting as a +single player anymore unlike when we had + + align:start position:0% +single player anymore unlike when we had + + + align:start position:0% +single player anymore unlike when we had +full information then three play was the + + align:start position:0% +full information then three play was the + + + align:start position:0% +full information then three play was the +same as + + align:start position:0% +same as + + + align:start position:0% +same as +two okay uh so let's first observe that + + align:start position:0% +two okay uh so let's first observe that + + + align:start position:0% +two okay uh so let's first observe that +this is in anx time and then furthermore + + align:start position:0% +this is in anx time and then furthermore + + + align:start position:0% +this is in anx time and then furthermore +the claim which I won't prove is that + + align:start position:0% +the claim which I won't prove is that + + + align:start position:0% +the claim which I won't prove is that +this is NX time + + align:start position:0% +this is NX time + + + align:start position:0% +this is NX time +complete uh so the idea is there are + + align:start position:0% +complete uh so the idea is there are + + + align:start position:0% +complete uh so the idea is there are +only exponentially many choices for + + align:start position:0% +only exponentially many choices for + + + align:start position:0% +only exponentially many choices for +these variables uh so then I can guess + + align:start position:0% +these variables uh so then I can guess + + + align:start position:0% +these variables uh so then I can guess +uh both player one and player two can + + align:start position:0% +uh both player one and player two can + + + align:start position:0% +uh both player one and player two can +guess what uh white one and white two + + align:start position:0% +guess what uh white one and white two + + + align:start position:0% +guess what uh white one and white two +can guess what the possibilities are for + + align:start position:0% +can guess what the possibilities are for + + + align:start position:0% +can guess what the possibilities are for +all Poss I choices of X1 and X2 so + + align:start position:0% +all Poss I choices of X1 and X2 so + + + align:start position:0% +all Poss I choices of X1 and X2 so +they're making exponentially many + + align:start position:0% +they're making exponentially many + + + align:start position:0% +they're making exponentially many +guesses for every state of + + align:start position:0% +guesses for every state of + + + align:start position:0% +guesses for every state of +x1x2 uh guess what the right strategy is + + align:start position:0% +x1x2 uh guess what the right strategy is + + + align:start position:0% +x1x2 uh guess what the right strategy is +and then just combine then check whether + + align:start position:0% +and then just combine then check whether + + + align:start position:0% +and then just combine then check whether +all the everything is everyone plays + + align:start position:0% +all the everything is everyone plays + + + align:start position:0% +all the everything is everyone plays +properly uh so then white can decide + + align:start position:0% +properly uh so then white can decide + + + align:start position:0% +properly uh so then white can decide +whether they can + + align:start position:0% +whether they can + + + align:start position:0% +whether they can +win + + align:start position:0% +win + + + align:start position:0% +win +uh that's cool uh the this can be + + align:start position:0% +uh that's cool uh the this can be + + + align:start position:0% +uh that's cool uh the this can be +reduced to a bounded team private + + align:start position:0% +reduced to a bounded team private + + + align:start position:0% +reduced to a bounded team private +information version of constraint logic + + align:start position:0% +information version of constraint logic + + + align:start position:0% +information version of constraint logic +tpcl uh let me Define + + align:start position:0% + + + + align:start position:0% + +that uh we're going to do this + + align:start position:0% +that uh we're going to do this + + + align:start position:0% +that uh we're going to do this +with uh three + + align:start position:0% + + + + align:start position:0% + +players and a planer + + align:start position:0% + + + + align:start position:0% + +graph I think just Andor graph is enough + + align:start position:0% +graph I think just Andor graph is enough + + + align:start position:0% +graph I think just Andor graph is enough +um but it's uh Team they're going to be + + align:start position:0% +um but it's uh Team they're going to be + + + align:start position:0% +um but it's uh Team they're going to be +again two white players one black player + + align:start position:0% +again two white players one black player + + + align:start position:0% +again two white players one black player +um and it's private information meaning + + align:start position:0% +um and it's private information meaning + + + align:start position:0% +um and it's private information meaning +that uh each Edge is marked as visible + + align:start position:0% +that uh each Edge is marked as visible + + + align:start position:0% +that uh each Edge is marked as visible +to white or visible to Black now in the + + align:start position:0% +to white or visible to Black now in the + + + align:start position:0% +to white or visible to Black now in the +figures it's a little hard to draw so + + align:start position:0% +figures it's a little hard to draw so + + + align:start position:0% +figures it's a little hard to draw so +the figures the color is just indicating + + align:start position:0% +the figures the color is just indicating + + + align:start position:0% +the figures the color is just indicating +whether that player is allowed to flip + + align:start position:0% +whether that player is allowed to flip + + + align:start position:0% +whether that player is allowed to flip +that edge each player can only flip each + + align:start position:0% +that edge each player can only flip each + + + align:start position:0% +that edge each player can only flip each +white player can only flip white edges + + align:start position:0% +white player can only flip white edges + + + align:start position:0% +white player can only flip white edges +black player can only flip black edges + + align:start position:0% +black player can only flip black edges + + + align:start position:0% +black player can only flip black edges +just like before uh well now it's white + + align:start position:0% +just like before uh well now it's white + + + align:start position:0% +just like before uh well now it's white +team can only flip either of the white + + align:start position:0% +team can only flip either of the white + + + align:start position:0% +team can only flip either of the white +players can only flip a white Edge uh so + + align:start position:0% +players can only flip a white Edge uh so + + + align:start position:0% +players can only flip a white Edge uh so +some edges are flippable by two + + align:start position:0% +some edges are flippable by two + + + align:start position:0% +some edges are flippable by two +players um but then in addition some + + align:start position:0% +players um but then in addition some + + + align:start position:0% +players um but then in addition some +edges some white edges are going to be + + align:start position:0% +edges some white edges are going to be + + + align:start position:0% +edges some white edges are going to be +marked as invisible to Black and some + + align:start position:0% +marked as invisible to Black and some + + + align:start position:0% +marked as invisible to Black and some +black edges are going to be marked + + align:start position:0% +black edges are going to be marked + + + align:start position:0% +black edges are going to be marked +invisible to White and furthermore you + + align:start position:0% +invisible to White and furthermore you + + + align:start position:0% +invisible to White and furthermore you +can say invisible to this white player + + align:start position:0% +can say invisible to this white player + + + align:start position:0% +can say invisible to this white player +or this white player okay so it's a + + align:start position:0% +or this white player okay so it's a + + + align:start position:0% +or this white player okay so it's a +little bit more General and the rules of + + align:start position:0% +little bit more General and the rules of + + + align:start position:0% +little bit more General and the rules of +the game are pretty simple you can make + + align:start position:0% +the game are pretty simple you can make + + + align:start position:0% +the game are pretty simple you can make +moves just like before but you must be + + align:start position:0% +moves just like before but you must be + + + align:start position:0% +moves just like before but you must be +able to know uh that that move is + + align:start position:0% + + + + align:start position:0% + +legal so unlike Rango Creek Spiel you're + + align:start position:0% +legal so unlike Rango Creek Spiel you're + + + align:start position:0% +legal so unlike Rango Creek Spiel you're +not allowed to make uh impossible + + align:start position:0% + + + + align:start position:0% + +moves you you must know based on the + + align:start position:0% +moves you you must know based on the + + + align:start position:0% +moves you you must know based on the +information that you can see that the + + align:start position:0% +information that you can see that the + + + align:start position:0% +information that you can see that the +move is + + align:start position:0% +move is + + + align:start position:0% +move is +valid um I don't think they're probably + + align:start position:0% +valid um I don't think they're probably + + + align:start position:0% +valid um I don't think they're probably +other variations that work but this is a + + align:start position:0% +other variations that work but this is a + + + align:start position:0% +other variations that work but this is a +a clean one to work with so if you can + + align:start position:0% +a clean one to work with so if you can + + + align:start position:0% +a clean one to work with so if you can +see all the edges or you see that + + align:start position:0% +see all the edges or you see that + + + align:start position:0% +see all the edges or you see that +there's enough incoming weight to an + + align:start position:0% +there's enough incoming weight to an + + + align:start position:0% +there's enough incoming weight to an +edge then you can reverse one of the + + align:start position:0% +edge then you can reverse one of the + + + align:start position:0% +edge then you can reverse one of the +ones you have control + + align:start position:0% +ones you have control + + + align:start position:0% +ones you have control +over um so this problem uh I mean so a + + align:start position:0% +over um so this problem uh I mean so a + + + align:start position:0% +over um so this problem uh I mean so a +funny thing about dqbf is that there's + + align:start position:0% +funny thing about dqbf is that there's + + + align:start position:0% +funny thing about dqbf is that there's +sort of only one round to the game I + + align:start position:0% +sort of only one round to the game I + + + align:start position:0% +sort of only one round to the game I +mean black plays white plays white plays + + align:start position:0% +mean black plays white plays white plays + + + align:start position:0% +mean black plays white plays white plays +and then you see who won um whereas most + + align:start position:0% +and then you see who won um whereas most + + + align:start position:0% +and then you see who won um whereas most +games we think of is having many rounds + + align:start position:0% +games we think of is having many rounds + + + align:start position:0% +games we think of is having many rounds +and particular bounded tpcl has many + + align:start position:0% +and particular bounded tpcl has many + + + align:start position:0% +and particular bounded tpcl has many +rounds uh they play in round robin + + align:start position:0% +rounds uh they play in round robin + + + align:start position:0% +rounds uh they play in round robin +you've got black white one white two + + align:start position:0% +you've got black white one white two + + + align:start position:0% +you've got black white one white two +black white one white two you play in + + align:start position:0% +black white one white two you play in + + + align:start position:0% +black white one white two you play in +that sequence over and over each turn + + align:start position:0% +that sequence over and over each turn + + + align:start position:0% +that sequence over and over each turn +someone is just reversing a single edge + + align:start position:0% +someone is just reversing a single edge + + + align:start position:0% +someone is just reversing a single edge +whereas over here you're choosing a ton + + align:start position:0% +whereas over here you're choosing a ton + + + align:start position:0% +whereas over here you're choosing a ton +of + + align:start position:0% +of + + + align:start position:0% +of +variables um turns out this problem is + + align:start position:0% +variables um turns out this problem is + + + align:start position:0% +variables um turns out this problem is +also in NX + + align:start position:0% +also in NX + + + align:start position:0% +also in NX +time uh essentially + + align:start position:0% +time uh essentially + + + align:start position:0% +time uh essentially +because uh if if there is a winning + + align:start position:0% +because uh if if there is a winning + + + align:start position:0% +because uh if if there is a winning +strategy for white over here that + + align:start position:0% +strategy for white over here that + + + align:start position:0% +strategy for white over here that +winning strategy is deterministic and + + align:start position:0% +winning strategy is deterministic and + + + align:start position:0% +winning strategy is deterministic and +it's just a function of the visible + + align:start position:0% +it's just a function of the visible + + + align:start position:0% +it's just a function of the visible +State and there are n at most n + + align:start position:0% +State and there are n at most n + + + align:start position:0% +State and there are n at most n +different edges that you can see so + + align:start position:0% +different edges that you can see so + + + align:start position:0% +different edges that you can see so +number of possible States is exponential + + align:start position:0% +number of possible States is exponential + + + align:start position:0% +number of possible States is exponential +so at the beginning you just guess your + + align:start position:0% +so at the beginning you just guess your + + + align:start position:0% +so at the beginning you just guess your +strategy uh that's exponentially many + + align:start position:0% +strategy uh that's exponentially many + + + align:start position:0% +strategy uh that's exponentially many +bits to guess so in NX time you can do + + align:start position:0% +bits to guess so in NX time you can do + + + align:start position:0% +bits to guess so in NX time you can do +that and then you just play + + align:start position:0% +that and then you just play + + + align:start position:0% +that and then you just play +deterministically with that strategy so + + align:start position:0% +deterministically with that strategy so + + + align:start position:0% +deterministically with that strategy so +even though the game may run for a very + + align:start position:0% +even though the game may run for a very + + + align:start position:0% +even though the game may run for a very +long time and you do many many rounds uh + + align:start position:0% +long time and you do many many rounds uh + + + align:start position:0% +long time and you do many many rounds uh +still the information you need to guess + + align:start position:0% +still the information you need to guess + + + align:start position:0% +still the information you need to guess +was only exponential so you can do this + + align:start position:0% +was only exponential so you can do this + + + align:start position:0% +was only exponential so you can do this +in NX time so it's funny thing here + + align:start position:0% +in NX time so it's funny thing here + + + align:start position:0% +in NX time so it's funny thing here +there in this particular World unlike + + align:start position:0% +there in this particular World unlike + + + align:start position:0% +there in this particular World unlike +all the other cells of that Matrix um + + align:start position:0% +all the other cells of that Matrix um + + + align:start position:0% +all the other cells of that Matrix um +one round versus many rounds is the same + + align:start position:0% +one round versus many rounds is the same + + + align:start position:0% +one round versus many rounds is the same +you get NX time completeness in both + + align:start position:0% +you get NX time completeness in both + + + align:start position:0% +you get NX time completeness in both +cases okay so let me tell you how we + + align:start position:0% +cases okay so let me tell you how we + + + align:start position:0% +cases okay so let me tell you how we +reduce from + + align:start position:0% +reduce from + + + align:start position:0% +reduce from +dqbf to bounded + + align:start position:0% +dqbf to bounded + + + align:start position:0% +dqbf to bounded +tpcl so many + + align:start position:0% +tpcl so many + + + align:start position:0% +tpcl so many +acronyms + + align:start position:0% +acronyms + + + align:start position:0% +acronyms +um so uh the idea is pretty simple um + + align:start position:0% +um so uh the idea is pretty simple um + + + align:start position:0% +um so uh the idea is pretty simple um +again we want black to play first so + + align:start position:0% +again we want black to play first so + + + align:start position:0% +again we want black to play first so +there's a bunch of black variables here + + align:start position:0% +there's a bunch of black variables here + + + align:start position:0% +there's a bunch of black variables here +which are represented by by this these + + align:start position:0% +which are represented by by this these + + + align:start position:0% +which are represented by by this these +two figures are almost the same just + + align:start position:0% +two figures are almost the same just + + + align:start position:0% +two figures are almost the same just +these edges are black down here and + + align:start position:0% +these edges are black down here and + + + align:start position:0% +these edges are black down here and +white down here that's going to + + align:start position:0% +white down here that's going to + + + align:start position:0% +white down here that's going to +correspond to the variable setting um in + + align:start position:0% +correspond to the variable setting um in + + + align:start position:0% +correspond to the variable setting um in +this in this context we only want + + align:start position:0% +this in this context we only want + + + align:start position:0% +this in this context we only want +variables to be set once you don't get + + align:start position:0% +variables to be set once you don't get + + + align:start position:0% +variables to be set once you don't get +to reset them because it's a bounded + + align:start position:0% +to reset them because it's a bounded + + + align:start position:0% +to reset them because it's a bounded +game uh every and as as in all the + + align:start position:0% +game uh every and as as in all the + + + align:start position:0% +game uh every and as as in all the +bounded constraint logic games you can + + align:start position:0% +bounded constraint logic games you can + + + align:start position:0% +bounded constraint logic games you can +only flip each Edge once question um + + align:start position:0% +only flip each Edge once question um + + + align:start position:0% +only flip each Edge once question um +this is kind of a question about your + + align:start position:0% +this is kind of a question about your + + + align:start position:0% +this is kind of a question about your +earlier point but could you clarify the + + align:start position:0% +earlier point but could you clarify the + + + align:start position:0% +earlier point but could you clarify the +difference between um why like having + + align:start position:0% +difference between um why like having + + + align:start position:0% +difference between um why like having +one round of one of the games is AB to + + align:start position:0% +one round of one of the games is AB to + + + align:start position:0% +one round of one of the games is AB to +having like all rounds of the other game + + align:start position:0% +having like all rounds of the other game + + + align:start position:0% +having like all rounds of the other game +uh + + align:start position:0% +uh + + + align:start position:0% +uh +I don't have an intuitive reason why + + align:start position:0% +I don't have an intuitive reason why + + + align:start position:0% +I don't have an intuitive reason why +only that this game is in NX time and + + align:start position:0% +only that this game is in NX time and + + + align:start position:0% +only that this game is in NX time and +this game is NX time complete I mean + + align:start position:0% +this game is NX time complete I mean + + + align:start position:0% +this game is NX time complete I mean +they both are Annex time complete so in + + align:start position:0% +they both are Annex time complete so in + + + align:start position:0% +they both are Annex time complete so in +that sense they're equivalent uh yeah so + + align:start position:0% +that sense they're equivalent uh yeah so + + + align:start position:0% +that sense they're equivalent uh yeah so +we're going to simulate this one round + + align:start position:0% +we're going to simulate this one round + + + align:start position:0% +we're going to simulate this one round +game with multiple rounds over here uh + + align:start position:0% +game with multiple rounds over here uh + + + align:start position:0% +game with multiple rounds over here uh +but yeah it's a little bit odd that + + align:start position:0% +but yeah it's a little bit odd that + + + align:start position:0% +but yeah it's a little bit odd that +alternation doesn't help it doesn't give + + align:start position:0% +alternation doesn't help it doesn't give + + + align:start position:0% +alternation doesn't help it doesn't give +you more power all the other game + + align:start position:0% +you more power all the other game + + + align:start position:0% +you more power all the other game +settings that it does but it's just a + + align:start position:0% +settings that it does but it's just a + + + align:start position:0% +settings that it does but it's just a +weird thing about team yeah uh so your + + align:start position:0% +weird thing about team yeah uh so your + + + align:start position:0% +weird thing about team yeah uh so your +argument that b tpcl is in NX kind of + + align:start position:0% +argument that b tpcl is in NX kind of + + + align:start position:0% +argument that b tpcl is in NX kind of +relied on the fact that white doesn't + + align:start position:0% +relied on the fact that white doesn't + + + align:start position:0% +relied on the fact that white doesn't +learn anything from Black's moves when + + align:start position:0% +learn anything from Black's moves when + + + align:start position:0% +learn anything from Black's moves when +black moves on an invisible Edge so it + + align:start position:0% +black moves on an invisible Edge so it + + + align:start position:0% +black moves on an invisible Edge so it +seems like in some board configurations + + align:start position:0% +seems like in some board configurations + + + align:start position:0% +seems like in some board configurations +if black moves invisible Edge you can + + align:start position:0% +if black moves invisible Edge you can + + + align:start position:0% +if black moves invisible Edge you can +actually learn something based on what + + align:start position:0% +actually learn something based on what + + + align:start position:0% +actually learn something based on what +moves were allowed and not allowed from + + align:start position:0% +moves were allowed and not allowed from + + + align:start position:0% +moves were allowed and not allowed from +black uh maybe I should say that passing + + align:start position:0% +black uh maybe I should say that passing + + + align:start position:0% +black uh maybe I should say that passing +is allowed in this game uh otherwise the + + align:start position:0% +is allowed in this game uh otherwise the + + + align:start position:0% +is allowed in this game uh otherwise the +fact that you moved does tell you + + align:start position:0% +fact that you moved does tell you + + + align:start position:0% +fact that you moved does tell you +something but if you're always allowed + + align:start position:0% +something but if you're always allowed + + + align:start position:0% +something but if you're always allowed +to pass you really have no idea whether + + align:start position:0% +to pass you really have no idea whether + + + align:start position:0% +to pass you really have no idea whether +something happened except by what was + + align:start position:0% +something happened except by what was + + + align:start position:0% +something happened except by what was +visible yeah so let's uh make explicit + + align:start position:0% +visible yeah so let's uh make explicit + + + align:start position:0% +visible yeah so let's uh make explicit +passing is + + align:start position:0% + + + + align:start position:0% + +allowed yeah these are a bit + + align:start position:0% +allowed yeah these are a bit + + + align:start position:0% +allowed yeah these are a bit +subtle okay so um the intent is first we + + align:start position:0% +subtle okay so um the intent is first we + + + align:start position:0% +subtle okay so um the intent is first we +let black choose variables either by + + align:start position:0% +let black choose variables either by + + + align:start position:0% +let black choose variables either by +flipping true Edge flipping the false + + align:start position:0% +flipping true Edge flipping the false + + + align:start position:0% +flipping true Edge flipping the false +Edge we want to set it up so you can't + + align:start position:0% +Edge we want to set it up so you can't + + + align:start position:0% +Edge we want to set it up so you can't +do uh well you can't do both because of + + align:start position:0% +do uh well you can't do both because of + + + align:start position:0% +do uh well you can't do both because of +this vertex constraint so that's cool as + + align:start position:0% +this vertex constraint so that's cool as + + + align:start position:0% +this vertex constraint so that's cool as +soon as that as that happens probably uh + + align:start position:0% +soon as that as that happens probably uh + + + align:start position:0% +soon as that as that happens probably uh +White will flip this Edge and black will + + align:start position:0% +White will flip this Edge and black will + + + align:start position:0% +White will flip this Edge and black will +flip this Edge uh that's a split + + align:start position:0% +flip this Edge uh that's a split + + + align:start position:0% +flip this Edge uh that's a split +activating um well not yet activating + + align:start position:0% +activating um well not yet activating + + + align:start position:0% +activating um well not yet activating +the formula part uh but enabling black + + align:start position:0% +the formula part uh but enabling black + + + align:start position:0% +the formula part uh but enabling black +to activate the chosen Edge saying that + + align:start position:0% +to activate the chosen Edge saying that + + + align:start position:0% +to activate the chosen Edge saying that +this variable has been chosen and uh so + + align:start position:0% +this variable has been chosen and uh so + + + align:start position:0% +this variable has been chosen and uh so +black will sort of output that then in + + align:start position:0% +black will sort of output that then in + + + align:start position:0% +black will sort of output that then in +here so there's n such variables and B1 + + align:start position:0% +here so there's n such variables and B1 + + + align:start position:0% +here so there's n such variables and B1 +and B2 are both in here uh and we take + + align:start position:0% +and B2 are both in here uh and we take + + + align:start position:0% +and B2 are both in here uh and we take +the end of all of those chosen edges and + + align:start position:0% +the end of all of those chosen edges and + + + align:start position:0% +the end of all of those chosen edges and +that's this chosen wire + + align:start position:0% +that's this chosen wire + + + align:start position:0% +that's this chosen wire +uh so this black is motivated to do this + + align:start position:0% +uh so this black is motivated to do this + + + align:start position:0% +uh so this black is motivated to do this +black wants to set their variables some + + align:start position:0% +black wants to set their variables some + + + align:start position:0% +black wants to set their variables some +way um and they could I guess set them + + align:start position:0% +way um and they could I guess set them + + + align:start position:0% +way um and they could I guess set them +back and change the variables but there + + align:start position:0% +back and change the variables but there + + + align:start position:0% +back and change the variables but there +won't be any motivation to do that the + + align:start position:0% +won't be any motivation to do that the + + + align:start position:0% +won't be any motivation to do that the +goal for black is to flip this Edge + + align:start position:0% +goal for black is to flip this Edge + + + align:start position:0% +goal for black is to flip this Edge +which is connected by a long path from + + align:start position:0% +which is connected by a long path from + + + align:start position:0% +which is connected by a long path from +the and of all the chosen wires so + + align:start position:0% +the and of all the chosen wires so + + + align:start position:0% +the and of all the chosen wires so +basically B has to choose all the + + align:start position:0% +basically B has to choose all the + + + align:start position:0% +basically B has to choose all the +variables get this n to be true and then + + align:start position:0% +variables get this n to be true and then + + + align:start position:0% +variables get this n to be true and then +just sit there flipping these edges + + align:start position:0% +just sit there flipping these edges + + + align:start position:0% +just sit there flipping these edges +until this Edge is flipped so that's a a + + align:start position:0% +until this Edge is flipped so that's a a + + + align:start position:0% +until this Edge is flipped so that's a a +threat line uh once B has set their + + align:start position:0% +threat line uh once B has set their + + + align:start position:0% +threat line uh once B has set their +variables so B is going to erase to do + + align:start position:0% +variables so B is going to erase to do + + + align:start position:0% +variables so B is going to erase to do +that white is going to have just enough + + align:start position:0% +that white is going to have just enough + + + align:start position:0% +that white is going to have just enough +time to satisfy the formula and flip + + align:start position:0% +time to satisfy the formula and flip + + + align:start position:0% +time to satisfy the formula and flip +this Edge uh if the formula was true + + align:start position:0% +this Edge uh if the formula was true + + + align:start position:0% +this Edge uh if the formula was true +obviously uh so what happens NE white + + align:start position:0% +obviously uh so what happens NE white + + + align:start position:0% +obviously uh so what happens NE white +will basically sit there and and twiddle + + align:start position:0% +will basically sit there and and twiddle + + + align:start position:0% +will basically sit there and and twiddle +twiddle their thumbs um flipping some + + align:start position:0% +twiddle their thumbs um flipping some + + + align:start position:0% +twiddle their thumbs um flipping some +non some useless Edge until all the + + align:start position:0% +non some useless Edge until all the + + + align:start position:0% +non some useless Edge until all the +black variables are set they could + + align:start position:0% +black variables are set they could + + + align:start position:0% +black variables are set they could +actually do something else but uh + + align:start position:0% +actually do something else but uh + + + align:start position:0% +actually do something else but uh +there's going to be enough time to wait + + align:start position:0% +there's going to be enough time to wait + + + align:start position:0% +there's going to be enough time to wait +so it's better to wait because then uh + + align:start position:0% +so it's better to wait because then uh + + + align:start position:0% +so it's better to wait because then uh +the white variable can depend on the + + align:start position:0% +the white variable can depend on the + + + align:start position:0% +the white variable can depend on the +black variables they can see um + + align:start position:0% +black variables they can see um + + + align:start position:0% +black variables they can see um +obviously uh pretty much all the edges + + align:start position:0% +obviously uh pretty much all the edges + + + align:start position:0% +obviously uh pretty much all the edges +in here are visible to only one of the + + align:start position:0% +in here are visible to only one of the + + + align:start position:0% +in here are visible to only one of the +white players if this is a B1 variable + + align:start position:0% +white players if this is a B1 variable + + + align:start position:0% +white players if this is a B1 variable +uh then this is only visible to white + + align:start position:0% +uh then this is only visible to white + + + align:start position:0% +uh then this is only visible to white +one white one can see that it was chosen + + align:start position:0% +one white one can see that it was chosen + + + align:start position:0% +one white one can see that it was chosen +but can't see which of these edges got + + align:start position:0% +but can't see which of these edges got + + + align:start position:0% +but can't see which of these edges got +flipped and can't see which of these + + align:start position:0% +flipped and can't see which of these + + + align:start position:0% +flipped and can't see which of these +edges got flipped or these + + align:start position:0% +edges got flipped or these + + + align:start position:0% +edges got flipped or these +ones okay so that's representing the + + align:start position:0% +ones okay so that's representing the + + + align:start position:0% +ones okay so that's representing the +visibility um and so then white will set + + align:start position:0% +visibility um and so then white will set + + + align:start position:0% +visibility um and so then white will set +their variables the same kind of + + align:start position:0% +their variables the same kind of + + + align:start position:0% +their variables the same kind of +construction uh and once uh + + align:start position:0% +construction uh and once uh + + + align:start position:0% +construction uh and once uh +chosen is activated for both of them uh + + align:start position:0% +chosen is activated for both of them uh + + + align:start position:0% +chosen is activated for both of them uh +we take the and here and we trigger uh + + align:start position:0% +we take the and here and we trigger uh + + + align:start position:0% +we take the and here and we trigger uh +the unlock paths it's going to unlock + + align:start position:0% +the unlock paths it's going to unlock + + + align:start position:0% +the unlock paths it's going to unlock +the white one unlock the white two + + align:start position:0% +the white one unlock the white two + + + align:start position:0% +the white one unlock the white two +unlock all the black + + align:start position:0% +unlock all the black + + + align:start position:0% +unlock all the black +variables um and the unlock part is what + + align:start position:0% +variables um and the unlock part is what + + + align:start position:0% +variables um and the unlock part is what +lets you trigger the formula uh + + align:start position:0% +lets you trigger the formula uh + + + align:start position:0% +lets you trigger the formula uh +Activation so if if true was selected + + align:start position:0% +Activation so if if true was selected + + + align:start position:0% +Activation so if if true was selected +here and this was flipped once the + + align:start position:0% +here and this was flipped once the + + + align:start position:0% +here and this was flipped once the +unlock is flipped then this guy can + + align:start position:0% +unlock is flipped then this guy can + + + align:start position:0% +unlock is flipped then this guy can +activate and start inputting all the + + align:start position:0% +activate and start inputting all the + + + align:start position:0% +activate and start inputting all the +true variables into the formula and then + + align:start position:0% +true variables into the formula and then + + + align:start position:0% +true variables into the formula and then +you sit white will sit there and + + align:start position:0% +you sit white will sit there and + + + align:start position:0% +you sit white will sit there and +evaluate the formula has just enough + + align:start position:0% +evaluate the formula has just enough + + + align:start position:0% +evaluate the formula has just enough +time if it's satisfied to flip and be + + align:start position:0% +time if it's satisfied to flip and be + + + align:start position:0% +time if it's satisfied to flip and be +done so that's how we represent + + align:start position:0% +done so that's how we represent + + + align:start position:0% +done so that's how we represent +dependency qbf I mean it's pretty + + align:start position:0% +dependency qbf I mean it's pretty + + + align:start position:0% +dependency qbf I mean it's pretty +natural um it's just some fun stuff to + + align:start position:0% +natural um it's just some fun stuff to + + + align:start position:0% +natural um it's just some fun stuff to +get these to happen in essentially two + + align:start position:0% +get these to happen in essentially two + + + align:start position:0% +get these to happen in essentially two +rounds the visibility constraints of the + + align:start position:0% +rounds the visibility constraints of the + + + align:start position:0% +rounds the visibility constraints of the +partial the privateness of visible + + align:start position:0% +partial the privateness of visible + + + align:start position:0% +partial the privateness of visible +information + + align:start position:0% +information + + + align:start position:0% +information +uh makes this part really easy to + + align:start position:0% +uh makes this part really easy to + + + align:start position:0% +uh makes this part really easy to +implement so no big + + align:start position:0% +implement so no big + + + align:start position:0% +implement so no big +surprise + + align:start position:0% +surprise + + + align:start position:0% +surprise +questions okay uh let's go to the + + align:start position:0% +questions okay uh let's go to the + + + align:start position:0% +questions okay uh let's go to the +unbounded case which is the much more + + align:start position:0% +unbounded case which is the much more + + + align:start position:0% +unbounded case which is the much more +exciting + + align:start position:0% +exciting + + + align:start position:0% +exciting +one uh and first I + + align:start position:0% +one uh and first I + + + align:start position:0% +one uh and first I +will uh this so I mean undecidability is + + align:start position:0% +will uh this so I mean undecidability is + + + align:start position:0% +will uh this so I mean undecidability is +weird uh and unusual it's weird in this + + align:start position:0% +weird uh and unusual it's weird in this + + + align:start position:0% +weird uh and unusual it's weird in this +context because uh this game has finite + + align:start position:0% +context because uh this game has finite + + + align:start position:0% +context because uh this game has finite +resources all of our games in particular + + align:start position:0% +resources all of our games in particular + + + align:start position:0% +resources all of our games in particular +in constraint logic you have some graph + + align:start position:0% +in constraint logic you have some graph + + + align:start position:0% +in constraint logic you have some graph +of sizen um and undecidability is about + + align:start position:0% +of sizen um and undecidability is about + + + align:start position:0% +of sizen um and undecidability is about +essentially simulating a turning machine + + align:start position:0% +essentially simulating a turning machine + + + align:start position:0% +essentially simulating a turning machine +for arbitrary amounts of time and + + align:start position:0% +for arbitrary amounts of time and + + + align:start position:0% +for arbitrary amounts of time and +arbitrary amounts of space so uh you + + align:start position:0% +arbitrary amounts of space so uh you + + + align:start position:0% +arbitrary amounts of space so uh you +know it's not it's bigger than 2 to the + + align:start position:0% +know it's not it's bigger than 2 to the + + + align:start position:0% +know it's not it's bigger than 2 to the +N it's bigger than 2 2 the N it's bigger + + align:start position:0% +N it's bigger than 2 2 the N it's bigger + + + align:start position:0% +N it's bigger than 2 2 the N it's bigger +than 2 Tower n it's bigger than any I + + align:start position:0% +than 2 Tower n it's bigger than any I + + + align:start position:0% +than 2 Tower n it's bigger than any I +guess it's any computable function of n + + align:start position:0% +guess it's any computable function of n + + + align:start position:0% +guess it's any computable function of n +is how far you have to go so a little + + align:start position:0% +is how far you have to go so a little + + + align:start position:0% +is how far you have to go so a little +bit less than Busy Beaver um that's a + + align:start position:0% +bit less than Busy Beaver um that's a + + + align:start position:0% +bit less than Busy Beaver um that's a +lot of space so we in the game graph we + + align:start position:0% +lot of space so we in the game graph we + + + align:start position:0% +lot of space so we in the game graph we +can't + + align:start position:0% +can't + + + align:start position:0% +can't +represent uh the state of the machine + + align:start position:0% +represent uh the state of the machine + + + align:start position:0% +represent uh the state of the machine +that we're trying to simulate so I + + align:start position:0% +that we're trying to simulate so I + + + align:start position:0% +that we're trying to simulate so I +should say + + align:start position:0% +should say + + + align:start position:0% +should say +uh we haven't done undecidability at all + + align:start position:0% +uh we haven't done undecidability at all + + + align:start position:0% +uh we haven't done undecidability at all +but the canonical problem to start + + align:start position:0% +but the canonical problem to start + + + align:start position:0% +but the canonical problem to start +from is a halting problem uh you're + + align:start position:0% +from is a halting problem uh you're + + + align:start position:0% +from is a halting problem uh you're +given a turing + + align:start position:0% +given a turing + + + align:start position:0% +given a turing +machine and here I'd like to say + + align:start position:0% +machine and here I'd like to say + + + align:start position:0% +machine and here I'd like to say +algorithm but we need some model of the + + align:start position:0% +algorithm but we need some model of the + + + align:start position:0% +algorithm but we need some model of the +machine growing to arbitrarily large + + align:start position:0% +machine growing to arbitrarily large + + + align:start position:0% +machine growing to arbitrarily large +sizes and this turning machine is really + + align:start position:0% +sizes and this turning machine is really + + + align:start position:0% +sizes and this turning machine is really +ideal for this uh given a turning + + align:start position:0% +ideal for this uh given a turning + + + align:start position:0% +ideal for this uh given a turning +machine does it ever + + align:start position:0% + + + + align:start position:0% + +halt so remember turning machine you + + align:start position:0% +halt so remember turning machine you + + + align:start position:0% +halt so remember turning machine you +have some + + align:start position:0% +have some + + + align:start position:0% +have some +tape uh let's say initially all of the + + align:start position:0% +tape uh let's say initially all of the + + + align:start position:0% +tape uh let's say initially all of the +tape squares are empty you have some + + align:start position:0% +tape squares are empty you have some + + + align:start position:0% +tape squares are empty you have some +pointer into the tape starts at some + + align:start position:0% +pointer into the tape starts at some + + + align:start position:0% +pointer into the tape starts at some +canonical position um and you can read + + align:start position:0% +canonical position um and you can read + + + align:start position:0% +canonical position um and you can read +in white read and white right squares in + + align:start position:0% +in white read and white right squares in + + + align:start position:0% +in white read and white right squares in +the tape and you can move left and right + + align:start position:0% +the tape and you can move left and right + + + align:start position:0% +the tape and you can move left and right +and that's it uh this is the feeling is + + align:start position:0% +and that's it uh this is the feeling is + + + align:start position:0% +and that's it uh this is the feeling is +this corresponds this includes all + + align:start position:0% +this corresponds this includes all + + + align:start position:0% +this corresponds this includes all +possible computation and so deciding + + align:start position:0% +possible computation and so deciding + + + align:start position:0% +possible computation and so deciding +whether this machine will ever finish so + + align:start position:0% +whether this machine will ever finish so + + + align:start position:0% +whether this machine will ever finish so +there's an instruction that just says + + align:start position:0% +there's an instruction that just says + + + align:start position:0% +there's an instruction that just says +halt um or whether it just keep going on + + align:start position:0% +halt um or whether it just keep going on + + + align:start position:0% +halt um or whether it just keep going on +forever uh seems or is provably + + align:start position:0% +forever uh seems or is provably + + + align:start position:0% +forever uh seems or is provably +impossible there is no algorithm to + + align:start position:0% +impossible there is no algorithm to + + + align:start position:0% +impossible there is no algorithm to +decide that essentially because it's an + + align:start position:0% +decide that essentially because it's an + + + align:start position:0% +decide that essentially because it's an +algorithm to study algorithms but I + + align:start position:0% +algorithm to study algorithms but I + + + align:start position:0% +algorithm to study algorithms but I +won't prove that here I'm going to + + align:start position:0% +won't prove that here I'm going to + + + align:start position:0% +won't prove that here I'm going to +reduce from this problem and so I need + + align:start position:0% +reduce from this problem and so I need + + + align:start position:0% +reduce from this problem and so I need +to be able to simulated turing machine + + align:start position:0% +to be able to simulated turing machine + + + align:start position:0% +to be able to simulated turing machine +of arbitrary size and + + align:start position:0% + + + + align:start position:0% + +time cool uh + + align:start position:0% +time cool uh + + + align:start position:0% +time cool uh +so while most of the time I don't show + + align:start position:0% +so while most of the time I don't show + + + align:start position:0% +so while most of the time I don't show +you the The Source problem I think here + + align:start position:0% +you the The Source problem I think here + + + align:start position:0% +you the The Source problem I think here +it's it's instructive to see well I + + align:start position:0% +it's it's instructive to see well I + + + align:start position:0% +it's it's instructive to see well I +guess I'm not proving this is + + align:start position:0% +guess I'm not proving this is + + + align:start position:0% +guess I'm not proving this is +undecidable but it's instructive to see + + align:start position:0% +undecidable but it's instructive to see + + + align:start position:0% +undecidable but it's instructive to see +how we turn this into a game with + + align:start position:0% +how we turn this into a game with + + + align:start position:0% +how we turn this into a game with +bounded resources so before I get to the + + align:start position:0% +bounded resources so before I get to the + + + align:start position:0% +bounded resources so before I get to the +constraint logic version uh I'm going to + + align:start position:0% +constraint logic version uh I'm going to + + + align:start position:0% +constraint logic version uh I'm going to +talk about something called a team + + align:start position:0% +talk about something called a team + + + align:start position:0% +talk about something called a team +computation game + + align:start position:0% + + + + align:start position:0% + +this is + + align:start position:0% +this is + + + align:start position:0% +this is +from our book games puzzles + + align:start position:0% +from our book games puzzles + + + align:start position:0% +from our book games puzzles +computation + + align:start position:0% +computation + + + align:start position:0% +computation +um that will allow us to simulate the + + align:start position:0% +um that will allow us to simulate the + + + align:start position:0% +um that will allow us to simulate the +halting problem but using finite + + align:start position:0% +halting problem but using finite + + + align:start position:0% +halting problem but using finite +resources this is where the action is + + align:start position:0% +resources this is where the action is + + + align:start position:0% +resources this is where the action is +going from here to constraint logic is + + align:start position:0% +going from here to constraint logic is + + + align:start position:0% +going from here to constraint logic is +not that hard and not super interesting + + align:start position:0% +not that hard and not super interesting + + + align:start position:0% +not that hard and not super interesting +but this part is quite + + align:start position:0% + + + + align:start position:0% + +interesting okay so in team comput game + + align:start position:0% +interesting okay so in team comput game + + + align:start position:0% +interesting okay so in team comput game +is going to be three players one one + + align:start position:0% +is going to be three players one one + + + align:start position:0% +is going to be three players one one +black player two white players um and + + align:start position:0% +black player two white players um and + + + align:start position:0% +black player two white players um and +the instance to the game the sort of the + + align:start position:0% +the instance to the game the sort of the + + + align:start position:0% +the instance to the game the sort of the +board setup whatever um is going to + + align:start position:0% +board setup whatever um is going to + + + align:start position:0% +board setup whatever um is going to +be + + align:start position:0% + + + + align:start position:0% + +uh here I could use any algorithm or + + align:start position:0% +uh here I could use any algorithm or + + + align:start position:0% +uh here I could use any algorithm or +turning machine it's uh going to be a + + align:start position:0% +turning machine it's uh going to be a + + + align:start position:0% +turning machine it's uh going to be a +machine and it has some + + align:start position:0% +machine and it has some + + + align:start position:0% +machine and it has some +spacebound uh which I'll called k k is + + align:start position:0% +spacebound uh which I'll called k k is + + + align:start position:0% +spacebound uh which I'll called k k is +going to be essentially a constant what + + align:start position:0% +going to be essentially a constant what + + + align:start position:0% +going to be essentially a constant what +but it's part of the + + align:start position:0% +but it's part of the + + + align:start position:0% +but it's part of the +input + + align:start position:0% +input + + + align:start position:0% +input +um and the if this is an algorithm it + + align:start position:0% +um and the if this is an algorithm it + + + align:start position:0% +um and the if this is an algorithm it +starts with blank memory if it's + + align:start position:0% +starts with blank memory if it's + + + align:start position:0% +starts with blank memory if it's +training machine it starts with a blank + + align:start position:0% +training machine it starts with a blank + + + align:start position:0% +training machine it starts with a blank +tape uh and then we're going to Define + + align:start position:0% +tape uh and then we're going to Define + + + align:start position:0% +tape uh and then we're going to Define +black moves and white + + align:start position:0% + + + + align:start position:0% + +moves so remember there's one black + + align:start position:0% +moves so remember there's one black + + + align:start position:0% +moves so remember there's one black +player um + + align:start position:0% +player um + + + align:start position:0% +player um +and black player does it or what the + + align:start position:0% +and black player does it or what the + + + align:start position:0% +and black player does it or what the +black player is forced to do is run the + + align:start position:0% +black player is forced to do is run the + + + align:start position:0% +black player is forced to do is run the +algorithm or the machine for uh K time + + align:start position:0% + + + + align:start position:0% + +steps so K obviously is an input so + + align:start position:0% +steps so K obviously is an input so + + + align:start position:0% +steps so K obviously is an input so +black is forced to do + + align:start position:0% +black is forced to do + + + align:start position:0% +black is forced to do +that um now that algorithm May return an + + align:start position:0% +that um now that algorithm May return an + + + align:start position:0% +that um now that algorithm May return an +answer and the answer is always black + + align:start position:0% +answer and the answer is always black + + + align:start position:0% +answer and the answer is always black +wins or white wins or it may not do + + align:start position:0% +wins or white wins or it may not do + + + align:start position:0% +wins or white wins or it may not do +anything in in which case it wants to + + align:start position:0% +anything in in which case it wants to + + + align:start position:0% +anything in in which case it wants to +keep running in the next Black move uh + + align:start position:0% +keep running in the next Black move uh + + + align:start position:0% +keep running in the next Black move uh +it's going to run for another K steps + + align:start position:0% +it's going to run for another K steps + + + align:start position:0% +it's going to run for another K steps +and then the next Black move runs for + + align:start position:0% +and then the next Black move runs for + + + align:start position:0% +and then the next Black move runs for +another K steps and so on think if K is + + align:start position:0% +another K steps and so on think if K is + + + align:start position:0% +another K steps and so on think if K is +constant um + + align:start position:0% + + + + align:start position:0% + +so if there's output from this algorithm + + align:start position:0% +so if there's output from this algorithm + + + align:start position:0% +so if there's output from this algorithm +or machine + + align:start position:0% +or machine + + + align:start position:0% +or machine +uh that will determine the + + align:start position:0% + + + + align:start position:0% + +winner okay and + + align:start position:0% +winner okay and + + + align:start position:0% +winner okay and +otherwise black actually gets to make a + + align:start position:0% +otherwise black actually gets to make a + + + align:start position:0% +otherwise black actually gets to make a +choice this was completely forced what + + align:start position:0% +choice this was completely forced what + + + align:start position:0% +choice this was completely forced what +black had to do here you can think of it + + align:start position:0% +black had to do here you can think of it + + + align:start position:0% +black had to do here you can think of it +as part of Black's move but it's really + + align:start position:0% +as part of Black's move but it's really + + + align:start position:0% +as part of Black's move but it's really +the the game mechanics make this happen + + align:start position:0% +the the game mechanics make this happen + + + align:start position:0% +the the game mechanics make this happen +um + + align:start position:0% +um + + + align:start position:0% +um +and in this case uh black can set two + + align:start position:0% +and in this case uh black can set two + + + align:start position:0% +and in this case uh black can set two +variables X1 and X2 to be anything in + + align:start position:0% +variables X1 and X2 to be anything in + + + align:start position:0% +variables X1 and X2 to be anything in +the set a comma B okay so they get black + + align:start position:0% +the set a comma B okay so they get black + + + align:start position:0% +the set a comma B okay so they get black +gets to choose two bits if the machine + + align:start position:0% +gets to choose two bits if the machine + + + align:start position:0% +gets to choose two bits if the machine +doesn't say that the game is over okay + + align:start position:0% +doesn't say that the game is over okay + + + align:start position:0% +doesn't say that the game is over okay +we'll see what those bits do in a + + align:start position:0% + + + + align:start position:0% + +moment okay so that was Black's + + align:start position:0% +moment okay so that was Black's + + + align:start position:0% +moment okay so that was Black's +move uh now what about white again there + + align:start position:0% +move uh now what about white again there + + + align:start position:0% +move uh now what about white again there +are two players white one and white two + + align:start position:0% +are two players white one and white two + + + align:start position:0% +are two players white one and white two +and white + + align:start position:0% +and white + + + align:start position:0% +and white +eye is basically + + align:start position:0% +eye is basically + + + align:start position:0% +eye is basically +blind uh white eye can only see XI so + + align:start position:0% +blind uh white eye can only see XI so + + + align:start position:0% +blind uh white eye can only see XI so +this x these XI are messages to the + + align:start position:0% +this x these XI are messages to the + + + align:start position:0% +this x these XI are messages to the +white players and that's all that white + + align:start position:0% +white players and that's all that white + + + align:start position:0% +white players and that's all that white +can see white can't see anything else + + align:start position:0% +can see white can't see anything else + + + align:start position:0% +can see white can't see anything else +about the + + align:start position:0% +about the + + + align:start position:0% +about the +machine okay that knows what the machine + + align:start position:0% +machine okay that knows what the machine + + + align:start position:0% +machine okay that knows what the machine +is and knows what it's doing probably + + align:start position:0% +is and knows what it's doing probably + + + align:start position:0% +is and knows what it's doing probably +knows K but that's because that's all + + align:start position:0% +knows K but that's because that's all + + + align:start position:0% +knows K but that's because that's all +part of the instance but you don't know + + align:start position:0% +part of the instance but you don't know + + + align:start position:0% +part of the instance but you don't know +anything else about the state of the + + align:start position:0% +anything else about the state of the + + + align:start position:0% +anything else about the state of the +machine um + + align:start position:0% +machine um + + + align:start position:0% +machine um +and white can also do one other + + align:start position:0% + + + + align:start position:0% + +thing there's one uh memory cell in the + + align:start position:0% +thing there's one uh memory cell in the + + + align:start position:0% +thing there's one uh memory cell in the +machine called M1 and there's another + + align:start position:0% +machine called M1 and there's another + + + align:start position:0% +machine called M1 and there's another +one called M2 and player white ey can uh + + align:start position:0% +one called M2 and player white ey can uh + + + align:start position:0% +one called M2 and player white ey can uh +set + + align:start position:0% +set + + + align:start position:0% +set +Mi and so that will communicate back + + align:start position:0% +Mi and so that will communicate back + + + align:start position:0% +Mi and so that will communicate back +into the machine what uh White ey did + + align:start position:0% +into the machine what uh White ey did + + + align:start position:0% +into the machine what uh White ey did +and that is exactly the move of white + + align:start position:0% +and that is exactly the move of white + + + align:start position:0% +and that is exactly the move of white +eye white eye move + + align:start position:0% +eye white eye move + + + align:start position:0% +eye white eye move +is just set + + align:start position:0% +is just set + + + align:start position:0% +is just set +Mi and I'm not specifying how big that + + align:start position:0% +Mi and I'm not specifying how big that + + + align:start position:0% +Mi and I'm not specifying how big that +is it's not just a single bit um it + + align:start position:0% +is it's not just a single bit um it + + + align:start position:0% +is it's not just a single bit um it +could + + align:start position:0% +could + + + align:start position:0% +could +be uh some stuff uh in particular it's + + align:start position:0% +be uh some stuff uh in particular it's + + + align:start position:0% +be uh some stuff uh in particular it's +going to be one cell in the in the Sim + + align:start position:0% +going to be one cell in the in the Sim + + + align:start position:0% +going to be one cell in the in the Sim +turning machine we want to simulate + + align:start position:0% +turning machine we want to simulate + + + align:start position:0% +turning machine we want to simulate +essentially but + + align:start position:0% +essentially but + + + align:start position:0% +essentially but +uh okay so now the question is does + + align:start position:0% +uh okay so now the question is does + + + align:start position:0% +uh okay so now the question is does +white have a forc TN + + align:start position:0% + + + + align:start position:0% + +so this is the problem I want to prove + + align:start position:0% +so this is the problem I want to prove + + + align:start position:0% +so this is the problem I want to prove +undecidable by a reduction + + align:start position:0% +undecidable by a reduction + + + align:start position:0% +undecidable by a reduction +from halting + + align:start position:0% + + + + align:start position:0% + +problem + + align:start position:0% + + + + align:start position:0% + +okay so is the problem clear we we have + + align:start position:0% +okay so is the problem clear we we have + + + align:start position:0% +okay so is the problem clear we we have +a finite setup which is this space k + + align:start position:0% +a finite setup which is this space k + + + align:start position:0% +a finite setup which is this space k +situation that the entire state of the + + align:start position:0% +situation that the entire state of the + + + align:start position:0% +situation that the entire state of the +game is in some sense encoded by that uh + + align:start position:0% +game is in some sense encoded by that uh + + + align:start position:0% +game is in some sense encoded by that uh +the state of that algorithm it would + + align:start position:0% +the state of that algorithm it would + + + align:start position:0% +the state of that algorithm it would +seem um and white I mean and black is + + align:start position:0% +seem um and white I mean and black is + + + align:start position:0% +seem um and white I mean and black is +just telling U each in each turn uh + + align:start position:0% +just telling U each in each turn uh + + + align:start position:0% +just telling U each in each turn uh +white one it says A or B white two it + + align:start position:0% +white one it says A or B white two it + + + align:start position:0% +white one it says A or B white two it +says A or B white one and two then + + align:start position:0% +says A or B white one and two then + + + align:start position:0% +says A or B white one and two then +respond with some symbol and then the + + align:start position:0% +respond with some symbol and then the + + + align:start position:0% +respond with some symbol and then the +game continues so pretty simple setup + + align:start position:0% +game continues so pretty simple setup + + + align:start position:0% +game continues so pretty simple setup +but amazingly uh this can simulate any + + align:start position:0% +but amazingly uh this can simulate any + + + align:start position:0% +but amazingly uh this can simulate any +touring machine + + align:start position:0% + + + + align:start position:0% + +so let's do + + align:start position:0% + + + + align:start position:0% + +it so what we want to do basically uh so + + align:start position:0% +it so what we want to do basically uh so + + + align:start position:0% +it so what we want to do basically uh so +this algorithm is going to be a function + + align:start position:0% +this algorithm is going to be a function + + + align:start position:0% +this algorithm is going to be a function +given the turning machine we're going to + + align:start position:0% +given the turning machine we're going to + + + align:start position:0% +given the turning machine we're going to +construct the algorithm naturally so we + + align:start position:0% +construct the algorithm naturally so we + + + align:start position:0% +construct the algorithm naturally so we +basically need a constant space + + align:start position:0% + + + + align:start position:0% + +algorithm uh to check + + align:start position:0% + + + + align:start position:0% + +check that the white + + align:start position:0% +check that the white + + + align:start position:0% +check that the white +players uh produce uh so the white + + align:start position:0% +players uh produce uh so the white + + + align:start position:0% +players uh produce uh so the white +players are outputting a string of + + align:start position:0% +players are outputting a string of + + + align:start position:0% +players are outputting a string of +symbols white one is outputting M1 and + + align:start position:0% +symbols white one is outputting M1 and + + + align:start position:0% +symbols white one is outputting M1 and +then outputting something else to M1 and + + align:start position:0% +then outputting something else to M1 and + + + align:start position:0% +then outputting something else to M1 and +so on that string of symbols for both + + align:start position:0% +so on that string of symbols for both + + + align:start position:0% +so on that string of symbols for both +white + + align:start position:0% +white + + + align:start position:0% +white +players uh should essentially form a + + align:start position:0% +players uh should essentially form a + + + align:start position:0% +players uh should essentially form a +valid computation history an execution + + align:start position:0% +valid computation history an execution + + + align:start position:0% +valid computation history an execution +trace of the turing machine we want to + + align:start position:0% +trace of the turing machine we want to + + + align:start position:0% +trace of the turing machine we want to +simulate the given turing machine + + align:start position:0% + + + + align:start position:0% + +it's a little bit more complicated than + + align:start position:0% +it's a little bit more complicated than + + + align:start position:0% +it's a little bit more complicated than +that but that's the idea + + align:start position:0% + + + + align:start position:0% + +and we'd like it to end in a halt State + + align:start position:0% +and we'd like it to end in a halt State + + + align:start position:0% +and we'd like it to end in a halt State +uh so uh there are lots of canonical + + align:start position:0% +uh so uh there are lots of canonical + + + align:start position:0% +uh so uh there are lots of canonical +ways to write down uh the state of a + + align:start position:0% +ways to write down uh the state of a + + + align:start position:0% +ways to write down uh the state of a +turning machine basically write down the + + align:start position:0% +turning machine basically write down the + + + align:start position:0% +turning machine basically write down the +tape and uh where what instruction it's + + align:start position:0% +tape and uh where what instruction it's + + + align:start position:0% +tape and uh where what instruction it's +on um and that should be about it and + + align:start position:0% +on um and that should be about it and + + + align:start position:0% +on um and that should be about it and +we're going to put a special symbol hash + + align:start position:0% +we're going to put a special symbol hash + + + align:start position:0% +we're going to put a special symbol hash +mark in between each of these states so + + align:start position:0% +mark in between each of these states so + + + align:start position:0% +mark in between each of these states so +this is the state of the machine at Time + + align:start position:0% +this is the state of the machine at Time + + + align:start position:0% +this is the state of the machine at Time +Zero it's going to be a blank tape uh + + align:start position:0% +Zero it's going to be a blank tape uh + + + align:start position:0% +Zero it's going to be a blank tape uh +and you only have to write as many + + align:start position:0% +and you only have to write as many + + + align:start position:0% +and you only have to write as many +symbols as you need so in the beginning + + align:start position:0% +symbols as you need so in the beginning + + + align:start position:0% +symbols as you need so in the beginning +don't write any symbols uh as you start + + align:start position:0% +don't write any symbols uh as you start + + + align:start position:0% +don't write any symbols uh as you start +writing stuff to tape this will get + + align:start position:0% +writing stuff to tape this will get + + + align:start position:0% +writing stuff to tape this will get +longer um and yeah and then goal is to + + align:start position:0% +longer um and yeah and then goal is to + + + align:start position:0% +longer um and yeah and then goal is to +get it to a Hal State each of these + + align:start position:0% +get it to a Hal State each of these + + + align:start position:0% +get it to a Hal State each of these +states should be the uniquely determined + + align:start position:0% +states should be the uniquely determined + + + align:start position:0% +states should be the uniquely determined +state from the previous one which is if + + align:start position:0% +state from the previous one which is if + + + align:start position:0% +state from the previous one which is if +I do one instruction what + + align:start position:0% +I do one instruction what + + + align:start position:0% +I do one instruction what +happens okay now uh this is problematic + + align:start position:0% +happens okay now uh this is problematic + + + align:start position:0% +happens okay now uh this is problematic +so our goal we're we're trying to design + + align:start position:0% +so our goal we're we're trying to design + + + align:start position:0% +so our goal we're we're trying to design +this algorithm to to confirm that these + + align:start position:0% +this algorithm to to confirm that these + + + align:start position:0% +this algorithm to to confirm that these +states are being generated correctly um + + align:start position:0% +states are being generated correctly um + + + align:start position:0% +states are being generated correctly um +that's really hard to do because we + + align:start position:0% +that's really hard to do because we + + + align:start position:0% +that's really hard to do because we +can't compute the next state from the + + align:start position:0% +can't compute the next state from the + + + align:start position:0% +can't compute the next state from the +previous one because we can't even store + + align:start position:0% +previous one because we can't even store + + + align:start position:0% +previous one because we can't even store +the previous state in space k we have + + align:start position:0% +the previous state in space k we have + + + align:start position:0% +the previous state in space k we have +constant space very soon the state is + + align:start position:0% +constant space very soon the state is + + + align:start position:0% +constant space very soon the state is +going to get huge so you think of this + + align:start position:0% +going to get huge so you think of this + + + align:start position:0% +going to get huge so you think of this +as kind of a streaming algorithm we're + + align:start position:0% +as kind of a streaming algorithm we're + + + align:start position:0% +as kind of a streaming algorithm we're +just seeing these characters go by and + + align:start position:0% +just seeing these characters go by and + + + align:start position:0% +just seeing these characters go by and +uh we can't remember the entire previous + + align:start position:0% +uh we can't remember the entire previous + + + align:start position:0% +uh we can't remember the entire previous +state so the fact to check the next + + align:start position:0% +state so the fact to check the next + + + align:start position:0% +state so the fact to check the next +state is almost the same as the previous + + align:start position:0% +state is almost the same as the previous + + + align:start position:0% +state is almost the same as the previous +one is very + + align:start position:0% +one is very + + + align:start position:0% +one is very +hard and that's where we're going to use + + align:start position:0% +hard and that's where we're going to use + + + align:start position:0% +hard and that's where we're going to use +this AB thing uh this is not uh + + align:start position:0% +this AB thing uh this is not uh + + + align:start position:0% +this AB thing uh this is not uh +literally true um the sequence of + + align:start position:0% +literally true um the sequence of + + + align:start position:0% +literally true um the sequence of +characters uh M1 say will not produce a + + align:start position:0% +characters uh M1 say will not produce a + + + align:start position:0% +characters uh M1 say will not produce a +valid uh State essentially uh what we + + align:start position:0% +valid uh State essentially uh what we + + + align:start position:0% +valid uh State essentially uh what we +want player uh white one to do is to + + align:start position:0% +want player uh white one to do is to + + + align:start position:0% +want player uh white one to do is to +maintain two pointers into this state A + + align:start position:0% +maintain two pointers into this state A + + + align:start position:0% +maintain two pointers into this state A +and + + align:start position:0% +and + + + align:start position:0% +and +B and when we so I'm I'm identifying + + align:start position:0% +B and when we so I'm I'm identifying + + + align:start position:0% +B and when we so I'm I'm identifying +with black here uh when we specify X1 + + align:start position:0% +with black here uh when we specify X1 + + + align:start position:0% +with black here uh when we specify X1 +equal a we would like to know what + + align:start position:0% +equal a we would like to know what + + + align:start position:0% +equal a we would like to know what +character is being pointed to uh by + + align:start position:0% +character is being pointed to uh by + + + align:start position:0% +character is being pointed to uh by +pointer a and then we'd like to advance + + align:start position:0% +pointer a and then we'd like to advance + + + align:start position:0% +pointer a and then we'd like to advance +a to the next + + align:start position:0% +a to the next + + + align:start position:0% +a to the next +character okay when we request B with X1 + + align:start position:0% +character okay when we request B with X1 + + + align:start position:0% +character okay when we request B with X1 +equal B we want to know what character + + align:start position:0% +equal B we want to know what character + + + align:start position:0% +equal B we want to know what character +is at position B and then advance to the + + align:start position:0% +is at position B and then advance to the + + + align:start position:0% +is at position B and then advance to the +next character so there's one string + + align:start position:0% +next character so there's one string + + + align:start position:0% +next character so there's one string +that we're trying to look at and each + + align:start position:0% +that we're trying to look at and each + + + align:start position:0% +that we're trying to look at and each +white player has to maintain an a + + align:start position:0% +white player has to maintain an a + + + align:start position:0% +white player has to maintain an a +pointer and a b pointer and as black we + + align:start position:0% +pointer and a b pointer and as black we + + + align:start position:0% +pointer and a b pointer and as black we +can make independent requests to each of + + align:start position:0% +can make independent requests to each of + + + align:start position:0% +can make independent requests to each of +the two it's like you have two discs + + align:start position:0% +the two it's like you have two discs + + + align:start position:0% +the two it's like you have two discs +with uh two heads on the disc um and + + align:start position:0% +with uh two heads on the disc um and + + + align:start position:0% +with uh two heads on the disc um and +they both have the exact same data that + + align:start position:0% +they both have the exact same data that + + + align:start position:0% +they both have the exact same data that +they're supposed to and I can say give + + align:start position:0% +they're supposed to and I can say give + + + align:start position:0% +they're supposed to and I can say give +me the next character at this pointer + + align:start position:0% +me the next character at this pointer + + + align:start position:0% +me the next character at this pointer +from this disc and I can give you ask + + align:start position:0% +from this disc and I can give you ask + + + align:start position:0% +from this disc and I can give you ask +for what is simultaneously I get uh one + + align:start position:0% +for what is simultaneously I get uh one + + + align:start position:0% +for what is simultaneously I get uh one +character from one of the two pointers + + align:start position:0% +character from one of the two pointers + + + align:start position:0% +character from one of the two pointers +on the other disk and then it advances + + align:start position:0% +on the other disk and then it advances + + + align:start position:0% +on the other disk and then it advances +by one okay seems almost the same but + + align:start position:0% +by one okay seems almost the same but + + + align:start position:0% +by one okay seems almost the same but +that's what will make this undecidable + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +uh so here's the trick how we're going + + align:start position:0% +uh so here's the trick how we're going + + + align:start position:0% +uh so here's the trick how we're going +to build this algorithm uh I mean the + + align:start position:0% +to build this algorithm uh I mean the + + + align:start position:0% +to build this algorithm uh I mean the +real trick is that we have + + align:start position:0% +real trick is that we have + + + align:start position:0% +real trick is that we have +non-determinism we're asking whether uh + + align:start position:0% +non-determinism we're asking whether uh + + + align:start position:0% +non-determinism we're asking whether uh +White wins that means or or whether + + align:start position:0% +White wins that means or or whether + + + align:start position:0% +White wins that means or or whether +white has a winning strategy for white + + align:start position:0% +white has a winning strategy for white + + + align:start position:0% +white has a winning strategy for white +to have a winning strategy that must + + align:start position:0% +to have a winning strategy that must + + + align:start position:0% +to have a winning strategy that must +mean uh it can win or the white team can + + align:start position:0% +mean uh it can win or the white team can + + + align:start position:0% +mean uh it can win or the white team can +win no matter how black + + align:start position:0% +win no matter how black + + + align:start position:0% +win no matter how black +plays and black is just non so basically + + align:start position:0% +plays and black is just non so basically + + + align:start position:0% +plays and black is just non so basically +black is non-deterministically choosing + + align:start position:0% +black is non-deterministically choosing + + + align:start position:0% +black is non-deterministically choosing +uh between the A and the B uh pointer + + align:start position:0% +uh between the A and the B uh pointer + + + align:start position:0% +uh between the A and the B uh pointer +requests and so what this is saying is + + align:start position:0% +requests and so what this is saying is + + + align:start position:0% +requests and so what this is saying is +no matter what sequence of A's and B's + + align:start position:0% +no matter what sequence of A's and B's + + + align:start position:0% +no matter what sequence of A's and B's +you get white must + + align:start position:0% +you get white must + + + align:start position:0% +you get white must +win okay and winning is going to happen + + align:start position:0% +win okay and winning is going to happen + + + align:start position:0% +win okay and winning is going to happen +because we we'll build this algorithm to + + align:start position:0% +because we we'll build this algorithm to + + + align:start position:0% +because we we'll build this algorithm to +only output yes when uh it gets to a + + align:start position:0% +only output yes when uh it gets to a + + + align:start position:0% +only output yes when uh it gets to a +halt State + + align:start position:0% +halt State + + + align:start position:0% +halt State +basically and so it must get get to we + + align:start position:0% +basically and so it must get get to we + + + align:start position:0% +basically and so it must get get to we +must uh the algorithm must not complain + + align:start position:0% +must uh the algorithm must not complain + + + align:start position:0% +must uh the algorithm must not complain +no matter how we choose the A and B + + align:start position:0% +no matter how we choose the A and B + + + align:start position:0% +no matter how we choose the A and B +sequence so let me get to what we're + + align:start position:0% +sequence so let me get to what we're + + + align:start position:0% +sequence so let me get to what we're +going to + + align:start position:0% + + + + align:start position:0% + +do so the algorithm + + align:start position:0% + + + + align:start position:0% + +contains let's call this white + + align:start position:0% + + + + align:start position:0% + +one I would like to know when um Let Me + + align:start position:0% +one I would like to know when um Let Me + + + align:start position:0% +one I would like to know when um Let Me +Be specific when white one's a state + + align:start position:0% +Be specific when white one's a state + + + align:start position:0% +Be specific when white one's a state +equals white 2's B state but in fact + + align:start position:0% +equals white 2's B state but in fact + + + align:start position:0% +equals white 2's B state but in fact +we'll do this for all pairs there'll be + + align:start position:0% +we'll do this for all pairs there'll be + + + align:start position:0% +we'll do this for all pairs there'll be +four different things a here a here um + + align:start position:0% +four different things a here a here um + + + align:start position:0% +four different things a here a here um +but let's say I want to know when white + + align:start position:0% +but let's say I want to know when white + + + align:start position:0% +but let's say I want to know when white +one's a state is in exactly the same + + align:start position:0% +one's a state is in exactly the same + + + align:start position:0% +one's a state is in exactly the same +place as white 2's B state so um we have + + align:start position:0% +place as white 2's B state so um we have + + + align:start position:0% +place as white 2's B state so um we have +in in some sense there there are two of + + align:start position:0% +in in some sense there there are two of + + + align:start position:0% +in in some sense there there are two of +these strings one for white one one for + + align:start position:0% +these strings one for white one one for + + + align:start position:0% +these strings one for white one one for +white two uh and I want to know when uh + + align:start position:0% +white two uh and I want to know when uh + + + align:start position:0% +white two uh and I want to know when uh +I have just read through a state uh by + + align:start position:0% +I have just read through a state uh by + + + align:start position:0% +I have just read through a state uh by +white one and I've also read through the + + align:start position:0% +white one and I've also read through the + + + align:start position:0% +white one and I've also read through the +exact same state from White + + align:start position:0% +exact same state from White + + + align:start position:0% +exact same state from White +2 so that will happen when uh first of + + align:start position:0% +2 so that will happen when uh first of + + + align:start position:0% +2 so that will happen when uh first of +all both uh White players should have + + align:start position:0% +all both uh White players should have + + + align:start position:0% +all both uh White players should have +just returned a + + align:start position:0% +just returned a + + + align:start position:0% +just returned a +hashmark and then hashtag if you prefer + + align:start position:0% +hashmark and then hashtag if you prefer + + + align:start position:0% +hashmark and then hashtag if you prefer +um and then uh also while we were + + align:start position:0% +um and then uh also while we were + + + align:start position:0% +um and then uh also while we were +running through this tape I I see + + align:start position:0% +running through this tape I I see + + + align:start position:0% +running through this tape I I see +whether they happen to always return the + + align:start position:0% +whether they happen to always return the + + + align:start position:0% +whether they happen to always return the +same result so this will basically + + align:start position:0% +same result so this will basically + + + align:start position:0% +same result so this will basically +happen when uh + + align:start position:0% + + + + align:start position:0% + +so whenever uh both a and so if we just + + align:start position:0% +so whenever uh both a and so if we just + + + align:start position:0% +so whenever uh both a and so if we just +asked for a comma a and white one + + align:start position:0% +asked for a comma a and white one + + + align:start position:0% +asked for a comma a and white one +returns a hash mark and White 2 returns + + align:start position:0% +returns a hash mark and White 2 returns + + + align:start position:0% +returns a hash mark and White 2 returns +a hash mark then we're going to start + + align:start position:0% +a hash mark then we're going to start + + + align:start position:0% +a hash mark then we're going to start +paying attention to every single + + align:start position:0% +paying attention to every single + + + align:start position:0% +paying attention to every single +character we see uh if assuming we keep + + align:start position:0% +character we see uh if assuming we keep + + + align:start position:0% +character we see uh if assuming we keep +playing a comma a is black and this has + + align:start position:0% +playing a comma a is black and this has + + + align:start position:0% +playing a comma a is black and this has +to work for all possible assign choices + + align:start position:0% +to work for all possible assign choices + + + align:start position:0% +to work for all possible assign choices +of a so in particular there will be an + + align:start position:0% +of a so in particular there will be an + + + align:start position:0% +of a so in particular there will be an +execution where we play a comma a + + align:start position:0% +execution where we play a comma a + + + align:start position:0% +execution where we play a comma a +throughout this entire State and as + + align:start position:0% +throughout this entire State and as + + + align:start position:0% +throughout this entire State and as +we're doing that we just check character + + align:start position:0% +we're doing that we just check character + + + align:start position:0% +we're doing that we just check character +by character are they returning exactly + + align:start position:0% +by character are they returning exactly + + + align:start position:0% +by character are they returning exactly +the same result and have they so far + + align:start position:0% +the same result and have they so far + + + align:start position:0% +the same result and have they so far +have they always uh since the last hash + + align:start position:0% + + + + align:start position:0% + +mark okay and if they did that's a + + align:start position:0% +mark okay and if they did that's a + + + align:start position:0% +mark okay and if they did that's a +constant space algorithm I just compare + + align:start position:0% +constant space algorithm I just compare + + + align:start position:0% +constant space algorithm I just compare +character by character remember uh the + + align:start position:0% +character by character remember uh the + + + align:start position:0% +character by character remember uh the +and of all of those comparisons if they + + align:start position:0% +and of all of those comparisons if they + + + align:start position:0% +and of all of those comparisons if they +were all the same and I reach a hash + + align:start position:0% +were all the same and I reach a hash + + + align:start position:0% +were all the same and I reach a hash +mark that means I know that both + + align:start position:0% +mark that means I know that both + + + align:start position:0% +mark that means I know that both +uh the W1 string and the W2 string just + + align:start position:0% +uh the W1 string and the W2 string just + + + align:start position:0% +uh the W1 string and the W2 string just +output the same state so that means the + + align:start position:0% +output the same state so that means the + + + align:start position:0% +output the same state so that means the +A and the a pointers are in the same + + align:start position:0% +A and the a pointers are in the same + + + align:start position:0% +A and the a pointers are in the same +place at this + + align:start position:0% + + + + align:start position:0% + +moment cool that's not quite where I + + align:start position:0% +moment cool that's not quite where I + + + align:start position:0% +moment cool that's not quite where I +want them but at least I can detect that + + align:start position:0% +want them but at least I can detect that + + + align:start position:0% +want them but at least I can detect that +okay I can detect identical States + + align:start position:0% +okay I can detect identical States + + + align:start position:0% +okay I can detect identical States +remember I can't even store I can't even + + align:start position:0% +remember I can't even store I can't even + + + align:start position:0% +remember I can't even store I can't even +count A and B because these could get to + + align:start position:0% +count A and B because these could get to + + + align:start position:0% +count A and B because these could get to +really huge numbers that only buys me an + + align:start position:0% +really huge numbers that only buys me an + + + align:start position:0% +really huge numbers that only buys me an +exponential when I write things in + + align:start position:0% +exponential when I write things in + + + align:start position:0% +exponential when I write things in +binary so I can't afford to write down + + align:start position:0% +binary so I can't afford to write down + + + align:start position:0% +binary so I can't afford to write down +the am theb pointers it's what I'd like + + align:start position:0% +the am theb pointers it's what I'd like + + + align:start position:0% +the am theb pointers it's what I'd like +to do but I can check oh did they just + + align:start position:0% +to do but I can check oh did they just + + + align:start position:0% +to do but I can check oh did they just +output the same state so far so good now + + align:start position:0% +output the same state so far so good now + + + align:start position:0% +output the same state so far so good now +what I'd really like them to be is one + + align:start position:0% +what I'd really like them to be is one + + + align:start position:0% +what I'd really like them to be is one +step out of sync because what what I do + + align:start position:0% +step out of sync because what what I do + + + align:start position:0% +step out of sync because what what I do +have a streaming algorithm for is if I + + align:start position:0% +have a streaming algorithm for is if I + + + align:start position:0% +have a streaming algorithm for is if I +have the previous state of a turning + + align:start position:0% +have the previous state of a turning + + + align:start position:0% +have the previous state of a turning +machine and the proposed next state of + + align:start position:0% +machine and the proposed next state of + + + align:start position:0% +machine and the proposed next state of +this turning machine and I compare them + + align:start position:0% +this turning machine and I compare them + + + align:start position:0% +this turning machine and I compare them +letter by letter I can just check are + + align:start position:0% +letter by letter I can just check are + + + align:start position:0% +letter by letter I can just check are +all of the tape squares identical except + + align:start position:0% +all of the tape squares identical except + + + align:start position:0% +all of the tape squares identical except +for the one that the pointer is on uh + + align:start position:0% +for the one that the pointer is on uh + + + align:start position:0% +for the one that the pointer is on uh +and that got changed by simple rule and + + align:start position:0% +and that got changed by simple rule and + + + align:start position:0% +and that got changed by simple rule and +then all the others should be identical + + align:start position:0% +then all the others should be identical + + + align:start position:0% +then all the others should be identical +so it's very easy in a streaming sense + + align:start position:0% +so it's very easy in a streaming sense + + + align:start position:0% +so it's very easy in a streaming sense +if I'm giving the previous state and the + + align:start position:0% +if I'm giving the previous state and the + + + align:start position:0% +if I'm giving the previous state and the +next state I'd be happy uh so my goal is + + align:start position:0% +next state I'd be happy uh so my goal is + + + align:start position:0% +next state I'd be happy uh so my goal is +to get uh W1 state to be one step out of + + align:start position:0% +to get uh W1 state to be one step out of + + + align:start position:0% +to get uh W1 state to be one step out of +sync one step behind W2 + + align:start position:0% + + + + align:start position:0% + +State okay so + + align:start position:0% +State okay so + + + align:start position:0% +State okay so +uh how can I make that happen + + align:start position:0% + + + + align:start position:0% + +again uh so I mean black isn't really + + align:start position:0% +again uh so I mean black isn't really + + + align:start position:0% +again uh so I mean black isn't really +making well black is making all possible + + align:start position:0% +making well black is making all possible + + + align:start position:0% +making well black is making all possible +choices among A and B at all times so in + + align:start position:0% +choices among A and B at all times so in + + + align:start position:0% +choices among A and B at all times so in +particular we can consider the situation + + align:start position:0% +particular we can consider the situation + + + align:start position:0% +particular we can consider the situation +in which black plays + + align:start position:0% +in which black plays + + + align:start position:0% +in which black plays +um let's say a for on the W1 player and + + align:start position:0% +um let's say a for on the W1 player and + + + align:start position:0% +um let's say a for on the W1 player and +plays B on the other player W2's a state + + align:start position:0% +plays B on the other player W2's a state + + + align:start position:0% +plays B on the other player W2's a state +does not change because we're advancing + + align:start position:0% +does not change because we're advancing + + + align:start position:0% +does not change because we're advancing +B and then uh W 1's a state is + + align:start position:0% +B and then uh W 1's a state is + + + align:start position:0% +B and then uh W 1's a state is +advancing and if I keep doing that and + + align:start position:0% +advancing and if I keep doing that and + + + align:start position:0% +advancing and if I keep doing that and +then at some point I get a hash mark + + align:start position:0% +then at some point I get a hash mark + + + align:start position:0% +then at some point I get a hash mark +which I can obviously detect in constant + + align:start position:0% +which I can obviously detect in constant + + + align:start position:0% +which I can obviously detect in constant +space then I I Advance my my finance + + align:start position:0% +space then I I Advance my my finance + + + align:start position:0% +space then I I Advance my my finance +State machine say okay cool uh that + + align:start position:0% +State machine say okay cool uh that + + + align:start position:0% +State machine say okay cool uh that +means W1 is one step ahead one state + + align:start position:0% +means W1 is one step ahead one state + + + align:start position:0% +means W1 is one step ahead one state +ahead of W2 + + align:start position:0% +ahead of W2 + + + align:start position:0% +ahead of W2 +two and now I'm going to + + align:start position:0% +two and now I'm going to + + + align:start position:0% +two and now I'm going to +compare so when that + + align:start position:0% +compare so when that + + + align:start position:0% +compare so when that +happens + + align:start position:0% +happens + + + align:start position:0% +happens +uh so then uh out of sync by + + align:start position:0% + + + + align:start position:0% + +one uh and now what I'd like to happen + + align:start position:0% +one uh and now what I'd like to happen + + + align:start position:0% +one uh and now what I'd like to happen +next is X1 and X2 + + align:start position:0% + + + + align:start position:0% + +moves then uh + + align:start position:0% +moves then uh + + + align:start position:0% +moves then uh +now I'm going to run my streaming + + align:start position:0% +now I'm going to run my streaming + + + align:start position:0% +now I'm going to run my streaming +algorithm to check uh that this was a + + align:start position:0% +algorithm to check uh that this was a + + + align:start position:0% +algorithm to check uh that this was a +valid + + align:start position:0% + + + + align:start position:0% + +transition so from whatever W2 is + + align:start position:0% +transition so from whatever W2 is + + + align:start position:0% +transition so from whatever W2 is +outputting uh to whatever W1 is without + + align:start position:0% +outputting uh to whatever W1 is without + + + align:start position:0% +outputting uh to whatever W1 is without +putting CU W1 is ahead that should be a + + align:start position:0% +putting CU W1 is ahead that should be a + + + align:start position:0% +putting CU W1 is ahead that should be a +valid state so basically I had uh I ran + + align:start position:0% +valid state so basically I had uh I ran + + + align:start position:0% +valid state so basically I had uh I ran +for some time who knows what happened + + align:start position:0% +for some time who knows what happened + + + align:start position:0% +for some time who knows what happened +then I got uh this thing which is + + align:start position:0% +then I got uh this thing which is + + + align:start position:0% +then I got uh this thing which is +identical to this thing I detect that + + align:start position:0% +identical to this thing I detect that + + + align:start position:0% +identical to this thing I detect that +and I see a hash mark So I say okay they + + align:start position:0% +and I see a hash mark So I say okay they + + + align:start position:0% +and I see a hash mark So I say okay they +must be in the same state uh now I'm + + align:start position:0% +must be in the same state uh now I'm + + + align:start position:0% +must be in the same state uh now I'm +going to skip over whatever state was + + align:start position:0% +going to skip over whatever state was + + + align:start position:0% +going to skip over whatever state was +written here and then I'm going to check + + align:start position:0% +written here and then I'm going to check + + + align:start position:0% +written here and then I'm going to check +that every thing I get here + + align:start position:0% +that every thing I get here + + + align:start position:0% +that every thing I get here +is a valid transition from whatever I + + align:start position:0% +is a valid transition from whatever I + + + align:start position:0% +is a valid transition from whatever I +get + + align:start position:0% + + + + align:start position:0% + +here so this should go to that this + + align:start position:0% +here so this should go to that this + + + align:start position:0% +here so this should go to that this +should go to that and I uh I don't need + + align:start position:0% +should go to that and I uh I don't need + + + align:start position:0% +should go to that and I uh I don't need +any memory to do this I'm just looking + + align:start position:0% +any memory to do this I'm just looking + + + align:start position:0% +any memory to do this I'm just looking +at this Square knowing the state of this + + align:start position:0% +at this Square knowing the state of this + + + align:start position:0% +at this Square knowing the state of this +uh machine looking at this Square making + + align:start position:0% +uh machine looking at this Square making + + + align:start position:0% +uh machine looking at this Square making +sure that that was a valid transition + + align:start position:0% +sure that that was a valid transition + + + align:start position:0% +sure that that was a valid transition +usually it's just that this is equal to + + align:start position:0% +usually it's just that this is equal to + + + align:start position:0% +usually it's just that this is equal to +that except that the one place where the + + align:start position:0% +that except that the one place where the + + + align:start position:0% +that except that the one place where the +tape head is which is written on that in + + align:start position:0% +tape head is which is written on that in + + + align:start position:0% +tape head is which is written on that in +that little symbol um and in that spot I + + align:start position:0% +that little symbol um and in that spot I + + + align:start position:0% +that little symbol um and in that spot I +do whatever the turing machine does to + + align:start position:0% +do whatever the turing machine does to + + + align:start position:0% +do whatever the turing machine does to +that symbol if it WR to it it might + + align:start position:0% +that symbol if it WR to it it might + + + align:start position:0% +that symbol if it WR to it it might +change uh maybe it moves the pointer + + align:start position:0% +change uh maybe it moves the pointer + + + align:start position:0% +change uh maybe it moves the pointer +left or right but in constant space I + + align:start position:0% +left or right but in constant space I + + + align:start position:0% +left or right but in constant space I +just need to know what's happening here + + align:start position:0% +just need to know what's happening here + + + align:start position:0% +just need to know what's happening here +and maybe it's it's neighboring squares + + align:start position:0% +and maybe it's it's neighboring squares + + + align:start position:0% +and maybe it's it's neighboring squares +I can figure out what should be written + + align:start position:0% +I can figure out what should be written + + + align:start position:0% +I can figure out what should be written +here and if white one ever does the + + align:start position:0% +here and if white one ever does the + + + align:start position:0% +here and if white one ever does the +wrong thing if it's not a valid + + align:start position:0% +wrong thing if it's not a valid + + + align:start position:0% +wrong thing if it's not a valid +transition then uh I will say black + + align:start position:0% +transition then uh I will say black + + + align:start position:0% +transition then uh I will say black +wins as this + + align:start position:0% +wins as this + + + align:start position:0% +wins as this +algorithm so for white to + + align:start position:0% +algorithm so for white to + + + align:start position:0% +algorithm so for white to +win it can't make any + + align:start position:0% +win it can't make any + + + align:start position:0% +win it can't make any +mistakes white has to conform to this + + align:start position:0% +mistakes white has to conform to this + + + align:start position:0% +mistakes white has to conform to this +idea that uh basically first it well + + align:start position:0% +idea that uh basically first it well + + + align:start position:0% +idea that uh basically first it well +basically as it's playing uh it must be + + align:start position:0% +basically as it's playing uh it must be + + + align:start position:0% +basically as it's playing uh it must be +Computing whatever the turing machine + + align:start position:0% +Computing whatever the turing machine + + + align:start position:0% +Computing whatever the turing machine +that was that's part of the game + + align:start position:0% +that was that's part of the game + + + align:start position:0% +that was that's part of the game +essentially it's embedded in this + + align:start position:0% +essentially it's embedded in this + + + align:start position:0% +essentially it's embedded in this +algorithm that that turning machine um + + align:start position:0% +algorithm that that turning machine um + + + align:start position:0% +algorithm that that turning machine um +and + + align:start position:0% +and + + + align:start position:0% +and +so we have to it has to be simulating + + align:start position:0% +so we have to it has to be simulating + + + align:start position:0% +so we have to it has to be simulating +the turning machine maintaining these + + align:start position:0% +the turning machine maintaining these + + + align:start position:0% +the turning machine maintaining these +pointers A and B and running through it + + align:start position:0% +pointers A and B and running through it + + + align:start position:0% +pointers A and B and running through it +has to do that because it has to win no + + align:start position:0% +has to do that because it has to win no + + + align:start position:0% +has to do that because it has to win no +matter what black does and it could be + + align:start position:0% +matter what black does and it could be + + + align:start position:0% +matter what black does and it could be +that black does this really weird + + align:start position:0% +that black does this really weird + + + align:start position:0% +that black does this really weird +sequence of A's and B's + + align:start position:0% +sequence of A's and B's + + + align:start position:0% +sequence of A's and B's +in order to verify uh the one place + + align:start position:0% +in order to verify uh the one place + + + align:start position:0% +in order to verify uh the one place +where you lied about one of these being + + align:start position:0% +where you lied about one of these being + + + align:start position:0% +where you lied about one of these being +an invalid transition it will eventually + + align:start position:0% +an invalid transition it will eventually + + + align:start position:0% +an invalid transition it will eventually +check for some choices of the A and B + + align:start position:0% +check for some choices of the A and B + + + align:start position:0% +check for some choices of the A and B +moves it will check that it was a valid + + align:start position:0% +moves it will check that it was a valid + + + align:start position:0% +moves it will check that it was a valid +transition from here to + + align:start position:0% +transition from here to + + + align:start position:0% +transition from here to +here um and therefore uh all transitions + + align:start position:0% +here um and therefore uh all transitions + + + align:start position:0% +here um and therefore uh all transitions +must be + + align:start position:0% +must be + + + align:start position:0% +must be +valid so it's a pretty crazy use of + + align:start position:0% +valid so it's a pretty crazy use of + + + align:start position:0% +valid so it's a pretty crazy use of +essentially the universal quantifier + + align:start position:0% +essentially the universal quantifier + + + align:start position:0% +essentially the universal quantifier +that's given to black black has to uh + + align:start position:0% +that's given to black black has to uh + + + align:start position:0% +that's given to black black has to uh +White has to win no matter what Black's + + align:start position:0% +White has to win no matter what Black's + + + align:start position:0% +White has to win no matter what Black's +moves + + align:start position:0% + + + + align:start position:0% + +are so uh you might ask where + + align:start position:0% +are so uh you might ask where + + + align:start position:0% +are so uh you might ask where +uh where is the turing machine State and + + align:start position:0% +uh where is the turing machine State and + + + align:start position:0% +uh where is the turing machine State and +it's essentially in the heads of the + + align:start position:0% +it's essentially in the heads of the + + + align:start position:0% +it's essentially in the heads of the +white players which are not represented + + align:start position:0% +white players which are not represented + + + align:start position:0% +white players which are not represented +directly by the game the game is just + + align:start position:0% +directly by the game the game is just + + + align:start position:0% +directly by the game the game is just +you know what is the state of this + + align:start position:0% +you know what is the state of this + + + align:start position:0% +you know what is the state of this +algorithm and it's in some sense + + align:start position:0% +algorithm and it's in some sense + + + align:start position:0% +algorithm and it's in some sense +informed by the the history of the plays + + align:start position:0% +informed by the the history of the plays + + + align:start position:0% +informed by the the history of the plays +the sequence of moves that have been + + align:start position:0% +the sequence of moves that have been + + + align:start position:0% +the sequence of moves that have been +made um that will + + align:start position:0% +made um that will + + + align:start position:0% +made um that will +that that's in some sense where you + + align:start position:0% +that that's in some sense where you + + + align:start position:0% +that that's in some sense where you +where you can also see the this long + + align:start position:0% +where you can also see the this long + + + align:start position:0% +where you can also see the this long +sequence of moves uh I mean each of + + align:start position:0% +sequence of moves uh I mean each of + + + align:start position:0% +sequence of moves uh I mean each of +these got output at some + + align:start position:0% +these got output at some + + + align:start position:0% +these got output at some +point uh but initially you can sort of + + align:start position:0% +point uh but initially you can sort of + + + align:start position:0% +point uh but initially you can sort of +think of all the execution was in the + + align:start position:0% +think of all the execution was in the + + + align:start position:0% +think of all the execution was in the +player heads then they're just + + align:start position:0% +player heads then they're just + + + align:start position:0% +player heads then they're just +maintaining these A and B pointers and + + align:start position:0% +maintaining these A and B pointers and + + + align:start position:0% +maintaining these A and B pointers and +playing and there must be such an + + align:start position:0% +playing and there must be such an + + + align:start position:0% +playing and there must be such an +execution in order for white to win so + + align:start position:0% +execution in order for white to win so + + + align:start position:0% +execution in order for white to win so +white will win if and only if there is a + + align:start position:0% +white will win if and only if there is a + + + align:start position:0% +white will win if and only if there is a +uh the machine halts basically because + + align:start position:0% +uh the machine halts basically because + + + align:start position:0% +uh the machine halts basically because +this algorithm will only output yes uh + + align:start position:0% +this algorithm will only output yes uh + + + align:start position:0% +this algorithm will only output yes uh +output the that white wins when the + + align:start position:0% +output the that white wins when the + + + align:start position:0% +output the that white wins when the +machine halts and it will report that + + align:start position:0% +machine halts and it will report that + + + align:start position:0% +machine halts and it will report that +black wins if you ever cheat so you have + + align:start position:0% +black wins if you ever cheat so you have + + + align:start position:0% +black wins if you ever cheat so you have +to not cheat and you have to get to a + + align:start position:0% +to not cheat and you have to get to a + + + align:start position:0% +to not cheat and you have to get to a +halting state so it's pretty crazy and + + align:start position:0% +halting state so it's pretty crazy and + + + align:start position:0% +halting state so it's pretty crazy and +this probably won't make sense the first + + align:start position:0% +this probably won't make sense the first + + + align:start position:0% +this probably won't make sense the first +or second time but uh it's clear to me + + align:start position:0% +or second time but uh it's clear to me + + + align:start position:0% +or second time but uh it's clear to me +again every time I learn it's like oh + + align:start position:0% +again every time I learn it's like oh + + + align:start position:0% +again every time I learn it's like oh +yeah that's really cool um hopefully it + + align:start position:0% +yeah that's really cool um hopefully it + + + align:start position:0% +yeah that's really cool um hopefully it +will become clear to you but if there + + align:start position:0% +will become clear to you but if there + + + align:start position:0% +will become clear to you but if there +any questions yeah why is it important + + align:start position:0% +any questions yeah why is it important + + + align:start position:0% +any questions yeah why is it important +that the algorithm is one space in the + + align:start position:0% +that the algorithm is one space in the + + + align:start position:0% +that the algorithm is one space in the +first place though uh I mean + + align:start position:0% +first place though uh I mean + + + align:start position:0% +first place though uh I mean +it's it's not technically uh the overall + + align:start position:0% +it's it's not technically uh the overall + + + align:start position:0% +it's it's not technically uh the overall +algorithm is not technically constant + + align:start position:0% +algorithm is not technically constant + + + align:start position:0% +algorithm is not technically constant +space because it needs to uh include the + + align:start position:0% +space because it needs to uh include the + + + align:start position:0% +space because it needs to uh include the +entire turing machine as part of it to + + align:start position:0% +entire turing machine as part of it to + + + align:start position:0% +entire turing machine as part of it to +know how to run um but the I I mentioned + + align:start position:0% +know how to run um but the I I mentioned + + + align:start position:0% +know how to run um but the I I mentioned +the checking algorithm is constant space + + align:start position:0% +the checking algorithm is constant space + + + align:start position:0% +the checking algorithm is constant space +and the the point is really that uh the + + align:start position:0% +and the the point is really that uh the + + + align:start position:0% +and the the point is really that uh the +size of of thisa space k algorithm has + + align:start position:0% +size of of thisa space k algorithm has + + + align:start position:0% +size of of thisa space k algorithm has +to be only a function of the given + + align:start position:0% +to be only a function of the given + + + align:start position:0% +to be only a function of the given +turing machine uh it can't depend on the + + align:start position:0% +turing machine uh it can't depend on the + + + align:start position:0% +turing machine uh it can't depend on the +execution time or the execution space of + + align:start position:0% +execution time or the execution space of + + + align:start position:0% +execution time or the execution space of +of the turning machine that that's all I + + align:start position:0% +of the turning machine that that's all I + + + align:start position:0% +of the turning machine that that's all I +want to emphasize so um effectively I + + align:start position:0% +want to emphasize so um effectively I + + + align:start position:0% +want to emphasize so um effectively I +mean if you think of the turing machine + + align:start position:0% +mean if you think of the turing machine + + + align:start position:0% +mean if you think of the turing machine +as being pretty small but it's running + + align:start position:0% +as being pretty small but it's running + + + align:start position:0% +as being pretty small but it's running +for some huge amount of time like Busy + + align:start position:0% +for some huge amount of time like Busy + + + align:start position:0% +for some huge amount of time like Busy +Beaver time uh relative to that we're + + align:start position:0% +Beaver time uh relative to that we're + + + align:start position:0% +Beaver time uh relative to that we're +thinking basically constant space and + + align:start position:0% +thinking basically constant space and + + + align:start position:0% +thinking basically constant space and +and and so and in fact we can get away + + align:start position:0% +and and so and in fact we can get away + + + align:start position:0% +and and so and in fact we can get away +with constant space that's for the + + align:start position:0% +with constant space that's for the + + + align:start position:0% +with constant space that's for the +checking part that's my point uh if you + + align:start position:0% +checking part that's my point uh if you + + + align:start position:0% +checking part that's my point uh if you +if you view the turning machine + + align:start position:0% +if you view the turning machine + + + align:start position:0% +if you view the turning machine +execution is an oracle so when I check + + align:start position:0% +execution is an oracle so when I check + + + align:start position:0% +execution is an oracle so when I check +that this goes to this in fact I have to + + align:start position:0% +that this goes to this in fact I have to + + + align:start position:0% +that this goes to this in fact I have to +run the machine or on on this tapeh head + + align:start position:0% +run the machine or on on this tapeh head + + + align:start position:0% +run the machine or on on this tapeh head +input to see what it would output uh but + + align:start position:0% +input to see what it would output uh but + + + align:start position:0% +input to see what it would output uh but +the turning machine is inside the + + align:start position:0% +the turning machine is inside the + + + align:start position:0% +the turning machine is inside the +algorithm so I can do that in constant + + align:start position:0% +algorithm so I can do that in constant + + + align:start position:0% +algorithm so I can do that in constant +time with the lookup + + align:start position:0% +time with the lookup + + + align:start position:0% +time with the lookup +table uh so the point is really you you + + align:start position:0% +table uh so the point is really you you + + + align:start position:0% +table uh so the point is really you you +need effectively a streaming algorithm + + align:start position:0% +need effectively a streaming algorithm + + + align:start position:0% +need effectively a streaming algorithm +to do this uh because these states get + + align:start position:0% +to do this uh because these states get + + + align:start position:0% +to do this uh because these states get +to be really really + + align:start position:0% + + + + align:start position:0% + +huge uh because we want this reduction + + align:start position:0% +huge uh because we want this reduction + + + align:start position:0% +huge uh because we want this reduction +to be polinomial time uh and + + align:start position:0% +to be polinomial time uh and + + + align:start position:0% +to be polinomial time uh and +it + + align:start position:0% +it + + + align:start position:0% +it +is basically copy the turing machine + + align:start position:0% +is basically copy the turing machine + + + align:start position:0% +is basically copy the turing machine +over write some constant amount of code + + align:start position:0% +over write some constant amount of code + + + align:start position:0% +over write some constant amount of code +to do this checking and that's all you + + align:start position:0% +to do this checking and that's all you + + + align:start position:0% +to do this checking and that's all you +need uh I guess we don't need it to be + + align:start position:0% +need uh I guess we don't need it to be + + + align:start position:0% +need uh I guess we don't need it to be +polinomial time uh but it is so it's + + align:start position:0% +polinomial time uh but it is so it's + + + align:start position:0% +polinomial time uh but it is so it's +kind of nice uh but it we need that it's + + align:start position:0% +kind of nice uh but it we need that it's + + + align:start position:0% +kind of nice uh but it we need that it's +finite + + align:start position:0% +finite + + + align:start position:0% +finite +time and there's no finite way to give + + align:start position:0% +time and there's no finite way to give + + + align:start position:0% +time and there's no finite way to give +an upper bound on the running time of a + + align:start position:0% +an upper bound on the running time of a + + + align:start position:0% +an upper bound on the running time of a +turning machine other than running it + + align:start position:0% +turning machine other than running it + + + align:start position:0% +turning machine other than running it +so uh polinomial time is good + + align:start position:0% + + + + align:start position:0% + +okay uh let me briefly mention a more + + align:start position:0% +okay uh let me briefly mention a more + + + align:start position:0% +okay uh let me briefly mention a more +formula oriented + + align:start position:0% + + + + align:start position:0% + +game although this is not terribly + + align:start position:0% +game although this is not terribly + + + align:start position:0% +game although this is not terribly +exciting + + align:start position:0% + + + + align:start position:0% + +uh just write it down quickly + + align:start position:0% + + + + align:start position:0% + +basically you can convert uh this + + align:start position:0% +basically you can convert uh this + + + align:start position:0% +basically you can convert uh this +problem team computation game which is + + align:start position:0% +problem team computation game which is + + + align:start position:0% +problem team computation game which is +which where black is forced to run a + + align:start position:0% +which where black is forced to run a + + + align:start position:0% +which where black is forced to run a +particular machine you can convert + + align:start position:0% +particular machine you can convert + + + align:start position:0% +particular machine you can convert +machines into formulas so uh it ends up + + align:start position:0% +machines into formulas so uh it ends up + + + align:start position:0% +machines into formulas so uh it ends up +looking something like this might be + + align:start position:0% +looking something like this might be + + + align:start position:0% +looking something like this might be +possible to + + align:start position:0% +possible to + + + align:start position:0% +possible to +simplify but + + align:start position:0% + + + + align:start position:0% + +this is one thing that definitely works + + align:start position:0% + + + + align:start position:0% + +okay so uh again white one can only see + + align:start position:0% +okay so uh again white one can only see + + + align:start position:0% +okay so uh again white one can only see +one variable X1 uh that is set by black + + align:start position:0% +one variable X1 uh that is set by black + + + align:start position:0% +one variable X1 uh that is set by black +and white two can only see one variable + + align:start position:0% +and white two can only see one variable + + + align:start position:0% +and white two can only see one variable +X2 that's set by black um black can set + + align:start position:0% +X2 that's set by black um black can set + + + align:start position:0% +X2 that's set by black um black can set +a bunch of variables in one round um and + + align:start position:0% +a bunch of variables in one round um and + + + align:start position:0% +a bunch of variables in one round um and +there's some condition that it has to + + align:start position:0% +there's some condition that it has to + + + align:start position:0% +there's some condition that it has to +satisfy this will basically force you to + + align:start position:0% +satisfy this will basically force you to + + + align:start position:0% +satisfy this will basically force you to +simulate the turning machine and not + + align:start position:0% +simulate the turning machine and not + + + align:start position:0% +simulate the turning machine and not +break any rules um and if black ever + + align:start position:0% +break any rules um and if black ever + + + align:start position:0% +break any rules um and if black ever +satisfies something which is when the + + align:start position:0% +satisfies something which is when the + + + align:start position:0% +satisfies something which is when the +Turning machine's hey uh black wins uh + + align:start position:0% +Turning machine's hey uh black wins uh + + + align:start position:0% +Turning machine's hey uh black wins uh +then black wins I you just turn that + + align:start position:0% +then black wins I you just turn that + + + align:start position:0% +then black wins I you just turn that +into a formula um and then black sets + + align:start position:0% +into a formula um and then black sets + + + align:start position:0% +into a formula um and then black sets +some uh other stuff and so this is more + + align:start position:0% +some uh other stuff and so this is more + + + align:start position:0% +some uh other stuff and so this is more +in the style of dependency qbf again you + + align:start position:0% +in the style of dependency qbf again you + + + align:start position:0% +in the style of dependency qbf again you +have this kind of dependency but now + + align:start position:0% +have this kind of dependency but now + + + align:start position:0% +have this kind of dependency but now +there are multiple rounds and now + + align:start position:0% +there are multiple rounds and now + + + align:start position:0% +there are multiple rounds and now +there's no bound on the number of moves + + align:start position:0% +there's no bound on the number of moves + + + align:start position:0% +there's no bound on the number of moves +you make uh you uh we can reset + + align:start position:0% +you make uh you uh we can reset + + + align:start position:0% +you make uh you uh we can reset +variables many times and this is also + + align:start position:0% +variables many times and this is also + + + align:start position:0% +variables many times and this is also +undecidable by essentially simulating + + align:start position:0% +undecidable by essentially simulating + + + align:start position:0% +undecidable by essentially simulating +this machine tur that machine into a + + align:start position:0% + + + + align:start position:0% + +formula so uh once we have that we can + + align:start position:0% +formula so uh once we have that we can + + + align:start position:0% +formula so uh once we have that we can +turn it into uh constraint logic version + + align:start position:0% +turn it into uh constraint logic version + + + align:start position:0% +turn it into uh constraint logic version +this is team private but not bounded + + align:start position:0% +this is team private but not bounded + + + align:start position:0% +this is team private but not bounded +constraint logic pretty much the same + + align:start position:0% +constraint logic pretty much the same + + + align:start position:0% +constraint logic pretty much the same +setup uh black has these variables x and + + align:start position:0% +setup uh black has these variables x and + + + align:start position:0% +setup uh black has these variables x and +x Prime y one has these variables y1 Y 2 + + align:start position:0% +x Prime y one has these variables y1 Y 2 + + + align:start position:0% +x Prime y one has these variables y1 Y 2 +has these variables Y2 uh they're fed + + align:start position:0% +has these variables Y2 uh they're fed + + + align:start position:0% +has these variables Y2 uh they're fed +into this formula and there are various + + align:start position:0% +into this formula and there are various + + + align:start position:0% +into this formula and there are various +things to that when those conditions I + + align:start position:0% +things to that when those conditions I + + + align:start position:0% +things to that when those conditions I +wrote down happen you trigger the + + align:start position:0% +wrote down happen you trigger the + + + align:start position:0% +wrote down happen you trigger the +apprpriate Target Edge uh and then black + + align:start position:0% +apprpriate Target Edge uh and then black + + + align:start position:0% +apprpriate Target Edge uh and then black +winds up there or white winds down there + + align:start position:0% +winds up there or white winds down there + + + align:start position:0% +winds up there or white winds down there +so not too exciting to go through the + + align:start position:0% +so not too exciting to go through the + + + align:start position:0% +so not too exciting to go through the +details of that but the result is uh + + align:start position:0% +details of that but the result is uh + + + align:start position:0% +details of that but the result is uh +Team private information constraint + + align:start position:0% +Team private information constraint + + + align:start position:0% +Team private information constraint +logic is undecidable for three players + + align:start position:0% +logic is undecidable for three players + + + align:start position:0% +logic is undecidable for three players +and you can use a crossover and even + + align:start position:0% +and you can use a crossover and even + + + align:start position:0% +and you can use a crossover and even +make this planer graphs if you + + align:start position:0% + + + + align:start position:0% + +want any question more questions about + + align:start position:0% +want any question more questions about + + + align:start position:0% +want any question more questions about +uh + + align:start position:0% +uh + + + align:start position:0% +uh +undecidability are you ever going to + + align:start position:0% +undecidability are you ever going to + + + align:start position:0% +undecidability are you ever going to +give some examples of + + align:start position:0% +give some examples of + + + align:start position:0% +give some examples of +undable uh like real games no there are + + align:start position:0% +undable uh like real games no there are + + + align:start position:0% +undable uh like real games no there are +no known examp good examples of games + + align:start position:0% +no known examp good examples of games + + + align:start position:0% +no known examp good examples of games +these are the games I'm + + align:start position:0% +these are the games I'm + + + align:start position:0% +these are the games I'm +afraid yeah + + align:start position:0% +afraid yeah + + + align:start position:0% +afraid yeah +sorry so I would like to switch gears + + align:start position:0% +sorry so I would like to switch gears + + + align:start position:0% +sorry so I would like to switch gears +and go to the extreme opposite instead + + align:start position:0% +and go to the extreme opposite instead + + + align:start position:0% +and go to the extreme opposite instead +of undecidability when there's no + + align:start position:0% +of undecidability when there's no + + + align:start position:0% +of undecidability when there's no +algorithm let's go back to Good + + align:start position:0% +algorithm let's go back to Good + + + align:start position:0% +algorithm let's go back to Good +oldfashioned polinomial Time + + align:start position:0% +oldfashioned polinomial Time + + + align:start position:0% +oldfashioned polinomial Time +algorithms I think you remember what p + + align:start position:0% +algorithms I think you remember what p + + + align:start position:0% +algorithms I think you remember what p +is + + align:start position:0% + + + + align:start position:0% + +but let me tell + + align:start position:0% +but let me tell + + + align:start position:0% +but let me tell +you a stronger notion of P which comes + + align:start position:0% +you a stronger notion of P which comes + + + align:start position:0% +you a stronger notion of P which comes +up in parallel algorithms there are many + + align:start position:0% +up in parallel algorithms there are many + + + align:start position:0% +up in parallel algorithms there are many +different models of parallel + + align:start position:0% +different models of parallel + + + align:start position:0% +different models of parallel +Computing uh so it's a little + + align:start position:0% +Computing uh so it's a little + + + align:start position:0% +Computing uh so it's a little +bit you know it's hard to write down + + align:start position:0% +bit you know it's hard to write down + + + align:start position:0% +bit you know it's hard to write down +one good model of computation for + + align:start position:0% +one good model of computation for + + + align:start position:0% +one good model of computation for +parallel Computing but fortunately if + + align:start position:0% +parallel Computing but fortunately if + + + align:start position:0% +parallel Computing but fortunately if +we're proving lower bounds it doesn't + + align:start position:0% +we're proving lower bounds it doesn't + + + align:start position:0% +we're proving lower bounds it doesn't +matter whether a model is good it really + + align:start position:0% +matter whether a model is good it really + + + align:start position:0% +matter whether a model is good it really +matters that our model is super powerful + + align:start position:0% +matters that our model is super powerful + + + align:start position:0% +matters that our model is super powerful +if we can prove something as impossible + + align:start position:0% +if we can prove something as impossible + + + align:start position:0% +if we can prove something as impossible +in a super powerful model that means + + align:start position:0% +in a super powerful model that means + + + align:start position:0% +in a super powerful model that means +it's impossible in weaker models too so + + align:start position:0% +it's impossible in weaker models too so + + + align:start position:0% +it's impossible in weaker models too so +I'm going to give you a super powerful + + align:start position:0% +I'm going to give you a super powerful + + + align:start position:0% +I'm going to give you a super powerful +model called + + align:start position:0% +model called + + + align:start position:0% +model called +NC so NC is Nick's class named after + + align:start position:0% +NC so NC is Nick's class named after + + + align:start position:0% +NC so NC is Nick's class named after +Nick pippinger who did a lot of parallel + + align:start position:0% +Nick pippinger who did a lot of parallel + + + align:start position:0% +Nick pippinger who did a lot of parallel +algorithms uh + + align:start position:0% +algorithms uh + + + align:start position:0% +algorithms uh +and there are a few equivalent + + align:start position:0% +and there are a few equivalent + + + align:start position:0% +and there are a few equivalent +definitions uh let me give you two of + + align:start position:0% + + + + align:start position:0% + +them I would like my problem to be + + align:start position:0% +them I would like my problem to be + + + align:start position:0% +them I would like my problem to be +solvable with P we wanted things to be + + align:start position:0% +solvable with P we wanted things to be + + + align:start position:0% +solvable with P we wanted things to be +solvable in poly time so a natural + + align:start position:0% +solvable in poly time so a natural + + + align:start position:0% +solvable in poly time so a natural +Improvement is that I want to run in + + align:start position:0% +Improvement is that I want to run in + + + align:start position:0% +Improvement is that I want to run in +poly log time uh for par algorithms + + align:start position:0% +poly log time uh for par algorithms + + + align:start position:0% +poly log time uh for par algorithms +given a huge number of processors but + + align:start position:0% +given a huge number of processors but + + + align:start position:0% +given a huge number of processors but +not incredibly huge just polinomial + + align:start position:0% +not incredibly huge just polinomial + + + align:start position:0% +not incredibly huge just polinomial +number of + + align:start position:0% +number of + + + align:start position:0% +number of +processors okay we can + + align:start position:0% +processors okay we can + + + align:start position:0% +processors okay we can +solve if I was given an exponential + + align:start position:0% +solve if I was given an exponential + + + align:start position:0% +solve if I was given an exponential +number of processors I could solve sat + + align:start position:0% +number of processors I could solve sat + + + align:start position:0% +number of processors I could solve sat +and all sorts of crazy things so + + align:start position:0% +and all sorts of crazy things so + + + align:start position:0% +and all sorts of crazy things so +shouldn't go too extreme uh but let's + + align:start position:0% +shouldn't go too extreme uh but let's + + + align:start position:0% +shouldn't go too extreme uh but let's +say polinomial + + align:start position:0% +say polinomial + + + align:start position:0% +say polinomial +not problems but + + align:start position:0% + + + + align:start position:0% + +processors polinomial number processors + + align:start position:0% +processors polinomial number processors + + + align:start position:0% +processors polinomial number processors +is reasonable maybe a little Overkill + + align:start position:0% +is reasonable maybe a little Overkill + + + align:start position:0% +is reasonable maybe a little Overkill +but okay with polinomial number + + align:start position:0% +but okay with polinomial number + + + align:start position:0% +but okay with polinomial number +processors I like to get poly log time + + align:start position:0% +processors I like to get poly log time + + + align:start position:0% +processors I like to get poly log time +that's a pretty natural good situation + + align:start position:0% +that's a pretty natural good situation + + + align:start position:0% +that's a pretty natural good situation +um I let these processors communicate + + align:start position:0% +um I let these processors communicate + + + align:start position:0% +um I let these processors communicate +however they want super fast um you can + + align:start position:0% +however they want super fast um you can + + + align:start position:0% +however they want super fast um you can +think of + + align:start position:0% +think of + + + align:start position:0% +think of +it as a + + align:start position:0% + + + + align:start position:0% + +circuit if you're thinking about the + + align:start position:0% +circuit if you're thinking about the + + + align:start position:0% +circuit if you're thinking about the +piece set you'll be thinking about small + + align:start position:0% +piece set you'll be thinking about small + + + align:start position:0% +piece set you'll be thinking about small +weft circuits but uh here it's just good + + align:start position:0% +weft circuits but uh here it's just good + + + align:start position:0% +weft circuits but uh here it's just good +oldfashioned depth we want polylog depth + + align:start position:0% +oldfashioned depth we want polylog depth + + + align:start position:0% +oldfashioned depth we want polylog depth +that will be the running time if every + + align:start position:0% +that will be the running time if every + + + align:start position:0% +that will be the running time if every +gate of the circuit can run in + + align:start position:0% +gate of the circuit can run in + + + align:start position:0% +gate of the circuit can run in +parallel uh you still have to run in in + + align:start position:0% +parallel uh you still have to run in in + + + align:start position:0% +parallel uh you still have to run in in +sequence along the depth lines but if + + align:start position:0% +sequence along the depth lines but if + + + align:start position:0% +sequence along the depth lines but if +there are polinomial number of gates so + + align:start position:0% +there are polinomial number of gates so + + + align:start position:0% +there are polinomial number of gates so +that should be of + + align:start position:0% +that should be of + + + align:start position:0% +that should be of +size Pol number of gates and poly log + + align:start position:0% +size Pol number of gates and poly log + + + align:start position:0% +size Pol number of gates and poly log +depth then in particular uh you this + + align:start position:0% +depth then in particular uh you this + + + align:start position:0% +depth then in particular uh you this +gives you an algorithm each processor + + align:start position:0% +gives you an algorithm each processor + + + align:start position:0% +gives you an algorithm each processor +just waits for the inputs to be ready + + align:start position:0% +just waits for the inputs to be ready + + + align:start position:0% +just waits for the inputs to be ready +and then writes out the output to the + + align:start position:0% +and then writes out the output to the + + + align:start position:0% +and then writes out the output to the +next gate that or to whatever Gates it + + align:start position:0% +next gate that or to whatever Gates it + + + align:start position:0% +next gate that or to whatever Gates it +has uh that it's connected to via wire + + align:start position:0% +has uh that it's connected to via wire + + + align:start position:0% +has uh that it's connected to via wire +and you'll get an algorithm that runs in + + align:start position:0% +and you'll get an algorithm that runs in + + + align:start position:0% +and you'll get an algorithm that runs in +polylog time polinomial number + + align:start position:0% +polylog time polinomial number + + + align:start position:0% +polylog time polinomial number +processors so whichever you think of is + + align:start position:0% +processors so whichever you think of is + + + align:start position:0% +processors so whichever you think of is +more intuitive + + align:start position:0% +more intuitive + + + align:start position:0% +more intuitive +um + + align:start position:0% +um + + + align:start position:0% +um +okay so I have a small example here + + align:start position:0% +okay so I have a small example here + + + align:start position:0% +okay so I have a small example here +suppose you want to sort n numbers in + + align:start position:0% +suppose you want to sort n numbers in + + + align:start position:0% +suppose you want to sort n numbers in +the comparison + + align:start position:0% +the comparison + + + align:start position:0% +the comparison +model you can do that and there are good + + align:start position:0% +model you can do that and there are good + + + align:start position:0% +model you can do that and there are good +algorithms to do it I will give you a + + align:start position:0% +algorithms to do it I will give you a + + + align:start position:0% +algorithms to do it I will give you a +not so great algorithm but at least it + + align:start position:0% +not so great algorithm but at least it + + + align:start position:0% +not so great algorithm but at least it +works in NC namely uh with n squ + + align:start position:0% +works in NC namely uh with n squ + + + align:start position:0% +works in NC namely uh with n squ +processors I'm going to compare in + + align:start position:0% +processors I'm going to compare in + + + align:start position:0% +processors I'm going to compare in +parallel all pairs of items I'm going to + + align:start position:0% +parallel all pairs of items I'm going to + + + align:start position:0% +parallel all pairs of items I'm going to +compare AI to AJ for all I and J now I + + align:start position:0% +compare AI to AJ for all I and J now I + + + align:start position:0% +compare AI to AJ for all I and J now I +know which items are less than which and + + align:start position:0% +know which items are less than which and + + + align:start position:0% +know which items are less than which and +now for each item I I basically just + + align:start position:0% +now for each item I I basically just + + + align:start position:0% +now for each item I I basically just +want to compute how many items are + + align:start position:0% +want to compute how many items are + + + align:start position:0% +want to compute how many items are +smaller than it if their I item smaller + + align:start position:0% +smaller than it if their I item smaller + + + align:start position:0% +smaller than it if their I item smaller +than it let's say all the items are + + align:start position:0% +than it let's say all the items are + + + align:start position:0% +than it let's say all the items are +distinct then that item should go to the + + align:start position:0% +distinct then that item should go to the + + + align:start position:0% +distinct then that item should go to the +I position in the array so uh basically + + align:start position:0% +I position in the array so uh basically + + + align:start position:0% +I position in the array so uh basically +I compute this Matrix I versus J each + + align:start position:0% +I compute this Matrix I versus J each + + + align:start position:0% +I compute this Matrix I versus J each +one says uh AI is smaller or greater + + align:start position:0% +one says uh AI is smaller or greater + + + align:start position:0% +one says uh AI is smaller or greater +than uh AJ and now uh for a given what + + align:start position:0% +than uh AJ and now uh for a given what + + + align:start position:0% +than uh AJ and now uh for a given what +did I say a given row I want to compute + + align:start position:0% +did I say a given row I want to compute + + + align:start position:0% +did I say a given row I want to compute +how many less than signs are in that row + + align:start position:0% +how many less than signs are in that row + + + align:start position:0% +how many less than signs are in that row +this is basically Computing a sum where + + align:start position:0% +this is basically Computing a sum where + + + align:start position:0% +this is basically Computing a sum where +you less than is one and greater than is + + align:start position:0% +you less than is one and greater than is + + + align:start position:0% +you less than is one and greater than is +zero and you can compute a sum of N + + align:start position:0% +zero and you can compute a sum of N + + + align:start position:0% +zero and you can compute a sum of N +items in log n time just by building a + + align:start position:0% +items in log n time just by building a + + + align:start position:0% +items in log n time just by building a +binary tree right I add these two guys + + align:start position:0% +binary tree right I add these two guys + + + align:start position:0% +binary tree right I add these two guys +and parallel with these two guys and so + + align:start position:0% +and parallel with these two guys and so + + + align:start position:0% +and parallel with these two guys and so +on um and then I compute my sum so in in + + align:start position:0% +on um and then I compute my sum so in in + + + align:start position:0% +on um and then I compute my sum so in in +Lo and I can do each of these rows in + + align:start position:0% +Lo and I can do each of these rows in + + + align:start position:0% +Lo and I can do each of these rows in +parallel so in log and time I can + + align:start position:0% +parallel so in log and time I can + + + align:start position:0% +parallel so in log and time I can +compute all of these sums then I know + + align:start position:0% +compute all of these sums then I know + + + align:start position:0% +compute all of these sums then I know +where every item needs to go I put it + + align:start position:0% +where every item needs to go I put it + + + align:start position:0% +where every item needs to go I put it +there so this is a little Overkill and + + align:start position:0% +there so this is a little Overkill and + + + align:start position:0% +there so this is a little Overkill and +that I use a ton of processors but still + + align:start position:0% +that I use a ton of processors but still + + + align:start position:0% +that I use a ton of processors but still +polinomial so in N Square processors I + + align:start position:0% +polinomial so in N Square processors I + + + align:start position:0% +polinomial so in N Square processors I +can easily in log and time sort end + + align:start position:0% +can easily in log and time sort end + + + align:start position:0% +can easily in log and time sort end +numbers there are more efficient + + align:start position:0% +numbers there are more efficient + + + align:start position:0% +numbers there are more efficient +algorithms but that it the point is when + + align:start position:0% +algorithms but that it the point is when + + + align:start position:0% +algorithms but that it the point is when +you have a par when there is a parallel + + align:start position:0% +you have a par when there is a parallel + + + align:start position:0% +you have a par when there is a parallel +algorithm in this powerful model you can + + align:start position:0% +algorithm in this powerful model you can + + + align:start position:0% +algorithm in this powerful model you can +do it without too much effort but what + + align:start position:0% +do it without too much effort but what + + + align:start position:0% +do it without too much effort but what +we're going to show here is something + + align:start position:0% +we're going to show here is something + + + align:start position:0% +we're going to show here is something +called P + + align:start position:0% + + + + align:start position:0% + +hardness uh which assuming not all + + align:start position:0% +hardness uh which assuming not all + + + align:start position:0% +hardness uh which assuming not all +problems can be solved in this not all + + align:start position:0% +problems can be solved in this not all + + + align:start position:0% +problems can be solved in this not all +polinomial time algorithms can be solved + + align:start position:0% +polinomial time algorithms can be solved + + + align:start position:0% +polinomial time algorithms can be solved +in this model uh these problems can't + + align:start position:0% +in this model uh these problems can't + + + align:start position:0% +in this model uh these problems can't +just like NP hardness uh note in + + align:start position:0% +just like NP hardness uh note in + + + align:start position:0% +just like NP hardness uh note in +particular NC is contained in P if I had + + align:start position:0% +particular NC is contained in P if I had + + + align:start position:0% +particular NC is contained in P if I had +such an algorithm I could simulate this + + align:start position:0% +such an algorithm I could simulate this + + + align:start position:0% +such an algorithm I could simulate this +algorithm because I have parallelism + + align:start position:0% +algorithm because I have parallelism + + + align:start position:0% +algorithm because I have parallelism +only polinomial I could simulate the + + align:start position:0% +only polinomial I could simulate the + + + align:start position:0% +only polinomial I could simulate the +whole algorithm in polinomial time still + + align:start position:0% +whole algorithm in polinomial time still + + + align:start position:0% +whole algorithm in polinomial time still +so this is stronger than being in p and + + align:start position:0% +so this is stronger than being in p and + + + align:start position:0% +so this is stronger than being in p and +p hardness means that all problems in + + align:start position:0% +p hardness means that all problems in + + + align:start position:0% +p hardness means that all problems in +NC can be + + align:start position:0% + + + + align:start position:0% + +reduced in the usual carp style + + align:start position:0% +reduced in the usual carp style + + + align:start position:0% +reduced in the usual carp style +reduction and P reduction but now uh the + + align:start position:0% +reduction and P reduction but now uh the + + + align:start position:0% +reduction and P reduction but now uh the +reduction must be a parallel time + + align:start position:0% +reduction must be a parallel time + + + align:start position:0% +reduction must be a parallel time +reduction so it must be an NC algorithm + + align:start position:0% + + + + align:start position:0% + +uh to your + + align:start position:0% + + + + align:start position:0% + +problem so P hard means you're as hard + + align:start position:0% +problem so P hard means you're as hard + + + align:start position:0% +problem so P hard means you're as hard +as all problems in p and reductions must + + align:start position:0% +as all problems in p and reductions must + + + align:start position:0% +as all problems in p and reductions must +be parall algorithms it must be in NC um + + align:start position:0% +be parall algorithms it must be in NC um + + + align:start position:0% +be parall algorithms it must be in NC um +and so this implies that uh you are not + + align:start position:0% +and so this implies that uh you are not + + + align:start position:0% +and so this implies that uh you are not +in + + align:start position:0% +in + + + align:start position:0% +in +NC uh + + align:start position:0% + + + + align:start position:0% + +assuming uh NC does not equal + + align:start position:0% +assuming uh NC does not equal + + + align:start position:0% +assuming uh NC does not equal +P which is another standard complexity + + align:start position:0% +P which is another standard complexity + + + align:start position:0% +P which is another standard complexity +theoretic assumption makes sense not all + + align:start position:0% +theoretic assumption makes sense not all + + + align:start position:0% +theoretic assumption makes sense not all +problems should be parallelizable so uh + + align:start position:0% +problems should be parallelizable so uh + + + align:start position:0% +problems should be parallelizable so uh +in particular P hard problems would be + + align:start position:0% +in particular P hard problems would be + + + align:start position:0% +in particular P hard problems would be +such problems and P complete of course + + align:start position:0% +such problems and P complete of course + + + align:start position:0% +such problems and P complete of course +means you're in P and P + + align:start position:0% +means you're in P and P + + + align:start position:0% +means you're in P and P +hard + + align:start position:0% +hard + + + align:start position:0% +hard +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so should it be that all problems in P + + align:start position:0% +so should it be that all problems in P + + + align:start position:0% +so should it be that all problems in P +can be reduced + + align:start position:0% + + + + align:start position:0% + +by yes + + align:start position:0% +by yes + + + align:start position:0% +by yes +thank + + align:start position:0% + + + + align:start position:0% + +you all problems in P yeah cool so all + + align:start position:0% +you all problems in P yeah cool so all + + + align:start position:0% +you all problems in P yeah cool so all +problems presumably including the ones + + align:start position:0% +problems presumably including the ones + + + align:start position:0% +problems presumably including the ones +that are hard to parallelize not just + + align:start position:0% +that are hard to parallelize not just + + + align:start position:0% +that are hard to parallelize not just +the NC ones uh can be reduced to your + + align:start position:0% +the NC ones uh can be reduced to your + + + align:start position:0% +the NC ones uh can be reduced to your +problem and so that means your problem + + align:start position:0% +problem and so that means your problem + + + align:start position:0% +problem and so that means your problem +is probably in P minus + + align:start position:0% +is probably in P minus + + + align:start position:0% +is probably in P minus +NC good + + align:start position:0% + + + + align:start position:0% + +so uh let me give you some base P + + align:start position:0% +so uh let me give you some base P + + + align:start position:0% +so uh let me give you some base P +complete + + align:start position:0% + + + + align:start position:0% + +problems starting with uh a very natural + + align:start position:0% +problems starting with uh a very natural + + + align:start position:0% +problems starting with uh a very natural +one uh General machine + + align:start position:0% +one uh General machine + + + align:start position:0% +one uh General machine +simulation sequential machine + + align:start position:0% + + + + align:start position:0% + +okay so uh given a sequential algorithm + + align:start position:0% +okay so uh given a sequential algorithm + + + align:start position:0% +okay so uh given a sequential algorithm +such as a turning + + align:start position:0% + + + + align:start position:0% + +machine run it for + + align:start position:0% +machine run it for + + + align:start position:0% +machine run it for +teps now uh this is a little bit + + align:start position:0% + + + + align:start position:0% + +subtle let me write this down and then + + align:start position:0% +subtle let me write this down and then + + + align:start position:0% +subtle let me write this down and then +I'm going to modify it uh + + align:start position:0% + + + + align:start position:0% + +does the algorithm say + + align:start position:0% +does the algorithm say + + + align:start position:0% +does the algorithm say +halt within + + align:start position:0% + + + + align:start position:0% + +teps or does it keep running for longer + + align:start position:0% +teps or does it keep running for longer + + + align:start position:0% +teps or does it keep running for longer +than T so this is a version of the + + align:start position:0% +than T so this is a version of the + + + align:start position:0% +than T so this is a version of the +halting problem I mean we've uh we same + + align:start position:0% +halting problem I mean we've uh we same + + + align:start position:0% +halting problem I mean we've uh we same +thing with a non-deterministic turning + + align:start position:0% +thing with a non-deterministic turning + + + align:start position:0% +thing with a non-deterministic turning +machine and running for polinomial time + + align:start position:0% +machine and running for polinomial time + + + align:start position:0% +machine and running for polinomial time +was a prototype for NP problems uh you + + align:start position:0% +was a prototype for NP problems uh you + + + align:start position:0% +was a prototype for NP problems uh you +we've done this kind of problem a lot we + + align:start position:0% +we've done this kind of problem a lot we + + + align:start position:0% +we've done this kind of problem a lot we +did a similar thing with W1 there a run + + align:start position:0% +did a similar thing with W1 there a run + + + align:start position:0% +did a similar thing with W1 there a run +for K steps and K was a parameter uh I + + align:start position:0% +for K steps and K was a parameter uh I + + + align:start position:0% +for K steps and K was a parameter uh I +want this problem to be in P but if I + + align:start position:0% +want this problem to be in P but if I + + + align:start position:0% +want this problem to be in P but if I +phrase it this way it would be X time + + align:start position:0% +phrase it this way it would be X time + + + align:start position:0% +phrase it this way it would be X time +Complete because T could represent an + + align:start position:0% +Complete because T could represent an + + + align:start position:0% +Complete because T could represent an +exponentially large value so what I want + + align:start position:0% +exponentially large value so what I want + + + align:start position:0% +exponentially large value so what I want +is for this to be encoded in + + align:start position:0% +is for this to be encoded in + + + align:start position:0% +is for this to be encoded in +un which usually we're not supposed to + + align:start position:0% +un which usually we're not supposed to + + + align:start position:0% +un which usually we're not supposed to +do but here I'm going to explicitly say + + align:start position:0% +do but here I'm going to explicitly say + + + align:start position:0% +do but here I'm going to explicitly say +look T is bounded by a polinomial in the + + align:start position:0% +look T is bounded by a polinomial in the + + + align:start position:0% +look T is bounded by a polinomial in the +size of the machine or equivalently uh + + align:start position:0% +size of the machine or equivalently uh + + + align:start position:0% +size of the machine or equivalently uh +it's It Was Written in uny and now I can + + align:start position:0% +it's It Was Written in uny and now I can + + + align:start position:0% +it's It Was Written in uny and now I can +do this in polinomial time I just + + align:start position:0% +do this in polinomial time I just + + + align:start position:0% +do this in polinomial time I just +because I have teps to do it I'll just + + align:start position:0% +because I have teps to do it I'll just + + + align:start position:0% +because I have teps to do it I'll just +run the machine + + align:start position:0% +run the machine + + + align:start position:0% +run the machine +teps okay so this is in p and if you + + align:start position:0% +teps okay so this is in p and if you + + + align:start position:0% +teps okay so this is in p and if you +believe anything is not parallelizable + + align:start position:0% +believe anything is not parallelizable + + + align:start position:0% +believe anything is not parallelizable +then this shouldn't be because this lets + + align:start position:0% +then this shouldn't be because this lets + + + align:start position:0% +then this shouldn't be because this lets +you simulate all things so pretty easy + + align:start position:0% +you simulate all things so pretty easy + + + align:start position:0% +you simulate all things so pretty easy +to reduce all problems in P you just if + + align:start position:0% +to reduce all problems in P you just if + + + align:start position:0% +to reduce all problems in P you just if +they're in P that means there's an + + align:start position:0% +they're in P that means there's an + + + align:start position:0% +they're in P that means there's an +algorithm to solve them sequential + + align:start position:0% +algorithm to solve them sequential + + + align:start position:0% +algorithm to solve them sequential +algorithm so you plug it in here it's + + align:start position:0% +algorithm so you plug it in here it's + + + align:start position:0% +algorithm so you plug it in here it's +going to run for only polinomial time so + + align:start position:0% +going to run for only polinomial time so + + + align:start position:0% +going to run for only polinomial time so +you can set T to that polinomial and + + align:start position:0% +you can set T to that polinomial and + + + align:start position:0% +you can set T to that polinomial and +boom uh you know what the algorithm + + align:start position:0% +boom uh you know what the algorithm + + + align:start position:0% +boom uh you know what the algorithm +halting is it answering yes or you could + + align:start position:0% +halting is it answering yes or you could + + + align:start position:0% +halting is it answering yes or you could +change this to returning yes or + + align:start position:0% + + + + align:start position:0% + +whatever okay so that's actually how you + + align:start position:0% +whatever okay so that's actually how you + + + align:start position:0% +whatever okay so that's actually how you +prove this problem is p hard actually P + + align:start position:0% +prove this problem is p hard actually P + + + align:start position:0% +prove this problem is p hard actually P +complete is there any problem with + + align:start position:0% +complete is there any problem with + + + align:start position:0% +complete is there any problem with +symmetry between yes and no answers here + + align:start position:0% +symmetry between yes and no answers here + + + align:start position:0% +symmetry between yes and no answers here +uh uh here yes and no are the same yeah + + align:start position:0% +uh uh here yes and no are the same yeah + + + align:start position:0% +uh uh here yes and no are the same yeah +we don't unlike NP NP had an asymmetry + + align:start position:0% +we don't unlike NP NP had an asymmetry + + + align:start position:0% +we don't unlike NP NP had an asymmetry +between yes and no so I could also + + align:start position:0% +between yes and no so I could also + + + align:start position:0% +between yes and no so I could also +change this to return no that would also + + align:start position:0% +change this to return no that would also + + + align:start position:0% +change this to return no that would also +be as hard yeah + + align:start position:0% + + + + align:start position:0% + +so uh but of course this is not a very + + align:start position:0% +so uh but of course this is not a very + + + align:start position:0% +so uh but of course this is not a very +useful problem it's just a starting + + align:start position:0% +useful problem it's just a starting + + + align:start position:0% +useful problem it's just a starting +point and it's very natural and uh P + + align:start position:0% +point and it's very natural and uh P + + + align:start position:0% +point and it's very natural and uh P +complete + + align:start position:0% +complete + + + align:start position:0% +complete +problem more useful for reductions are + + align:start position:0% +problem more useful for reductions are + + + align:start position:0% +problem more useful for reductions are +these uh circuit value + + align:start position:0% + + + + align:start position:0% + +problems CVP + + align:start position:0% + + + + align:start position:0% + +this is going to be like circuit set so + + align:start position:0% +this is going to be like circuit set so + + + align:start position:0% +this is going to be like circuit set so +with circuit set we were given an + + align:start position:0% +with circuit set we were given an + + + align:start position:0% +with circuit set we were given an +acyclic Boolean + + align:start position:0% +acyclic Boolean + + + align:start position:0% +acyclic Boolean +circuit which had one + + align:start position:0% +circuit which had one + + + align:start position:0% +circuit which had one +output or maybe we're given a particular + + align:start position:0% +output or maybe we're given a particular + + + align:start position:0% +output or maybe we're given a particular +output we care about uh and we wanted to + + align:start position:0% +output we care about uh and we wanted to + + + align:start position:0% +output we care about uh and we wanted to +know whether there's some input setting + + align:start position:0% +know whether there's some input setting + + + align:start position:0% +know whether there's some input setting +that made the output true here we are + + align:start position:0% +that made the output true here we are + + + align:start position:0% +that made the output true here we are +given the input + + align:start position:0% + + + + align:start position:0% + +setting so uh I mean the circuit + + align:start position:0% +setting so uh I mean the circuit + + + align:start position:0% +setting so uh I mean the circuit +actually has the the inputs written down + + align:start position:0% +actually has the the inputs written down + + + align:start position:0% +actually has the the inputs written down +like 0 1 1 um and then let's say we take + + align:start position:0% +like 0 1 1 um and then let's say we take + + + align:start position:0% +like 0 1 1 um and then let's say we take +an and and then we take an or something + + align:start position:0% +an and and then we take an or something + + + align:start position:0% +an and and then we take an or something +like that and we want to know what is + + align:start position:0% +like that and we want to know what is + + + align:start position:0% +like that and we want to know what is +this thing at the output of course this + + align:start position:0% +this thing at the output of course this + + + align:start position:0% +this thing at the output of course this +can be solved in polinomial time you + + align:start position:0% +can be solved in polinomial time you + + + align:start position:0% +can be solved in polinomial time you +compute this and you get a zero this was + + align:start position:0% +compute this and you get a zero this was + + + align:start position:0% +compute this and you get a zero this was +a one so you compute this or and you get + + align:start position:0% +a one so you compute this or and you get + + + align:start position:0% +a one so you compute this or and you get +one so the answer is one okay and you + + align:start position:0% +one so the answer is one okay and you + + + align:start position:0% +one so the answer is one okay and you +can do that in linear time but to do it + + align:start position:0% +can do that in linear time but to do it + + + align:start position:0% +can do that in linear time but to do it +in parallel is really hard because it's + + align:start position:0% +in parallel is really hard because it's + + + align:start position:0% +in parallel is really hard because it's +really hard to know to predict what + + align:start position:0% +really hard to know to predict what + + + align:start position:0% +really hard to know to predict what +these inputs are going to be so you + + align:start position:0% +these inputs are going to be so you + + + align:start position:0% +these inputs are going to be so you +can't do anything on this gate until the + + align:start position:0% +can't do anything on this gate until the + + + align:start position:0% +can't do anything on this gate until the +inputs are ready basically so uh + + align:start position:0% +inputs are ready basically so uh + + + align:start position:0% +inputs are ready basically so uh +presumably this circuit will not have + + align:start position:0% +presumably this circuit will not have + + + align:start position:0% +presumably this circuit will not have +polylog depth otherwise it is in NC uh + + align:start position:0% +polylog depth otherwise it is in NC uh + + + align:start position:0% +polylog depth otherwise it is in NC uh +but if you have a really large depth + + align:start position:0% +but if you have a really large depth + + + align:start position:0% +but if you have a really large depth +circuit simulating uh running it in + + align:start position:0% +circuit simulating uh running it in + + + align:start position:0% +circuit simulating uh running it in +parallel uh is just as hard as this + + align:start position:0% +parallel uh is just as hard as this + + + align:start position:0% +parallel uh is just as hard as this +problem so you can reduce uh General + + align:start position:0% +problem so you can reduce uh General + + + align:start position:0% +problem so you can reduce uh General +machine simulation to Circuit value and + + align:start position:0% +machine simulation to Circuit value and + + + align:start position:0% +machine simulation to Circuit value and +standard way of represent converting + + align:start position:0% +standard way of represent converting + + + align:start position:0% +standard way of represent converting +machines into circuits that's the + + align:start position:0% +machines into circuits that's the + + + align:start position:0% +machines into circuits that's the +electrical engineering problem + + align:start position:0% +electrical engineering problem + + + align:start position:0% +electrical engineering problem +okay uh what was the question is the + + align:start position:0% +okay uh what was the question is the + + + align:start position:0% +okay uh what was the question is the +output + + align:start position:0% + + + + align:start position:0% + +true okay uh now there are many special + + align:start position:0% +true okay uh now there are many special + + + align:start position:0% +true okay uh now there are many special +cases of this that are also hard for + + align:start position:0% +cases of this that are also hard for + + + align:start position:0% +cases of this that are also hard for +example Nan CVP okay we know how to + + align:start position:0% +example Nan CVP okay we know how to + + + align:start position:0% +example Nan CVP okay we know how to +build computers out of nand we know how + + align:start position:0% +build computers out of nand we know how + + + align:start position:0% +build computers out of nand we know how +to build computers out of nor cool so + + align:start position:0% +to build computers out of nor cool so + + + align:start position:0% +to build computers out of nor cool so +that's + + align:start position:0% +that's + + + align:start position:0% +that's +easy uh more + + align:start position:0% +easy uh more + + + align:start position:0% +easy uh more +interesting is mon Monon + + align:start position:0% + + + + align:start position:0% + +CVP so in monotone CVP you just have and + + align:start position:0% +CVP so in monotone CVP you just have and + + + align:start position:0% +CVP so in monotone CVP you just have and +in orates you don't have + + align:start position:0% +in orates you don't have + + + align:start position:0% +in orates you don't have +negation or nand or nor or xor those + + align:start position:0% +negation or nand or nor or xor those + + + align:start position:0% +negation or nand or nor or xor those +sorts of things this is also hard + + align:start position:0% +sorts of things this is also hard + + + align:start position:0% +sorts of things this is also hard +essentially by dual rail logic + + align:start position:0% +essentially by dual rail logic + + + align:start position:0% +essentially by dual rail logic +representing the true and the false is + + align:start position:0% +representing the true and the false is + + + align:start position:0% +representing the true and the false is +separate wires and manipulating them you + + align:start position:0% +separate wires and manipulating them you + + + align:start position:0% +separate wires and manipulating them you +can get this to be hard also kind of + + align:start position:0% +can get this to be hard also kind of + + + align:start position:0% +can get this to be hard also kind of +similar to constraint logic + + align:start position:0% +similar to constraint logic + + + align:start position:0% +similar to constraint logic +working uh but I won't prove it + + align:start position:0% +working uh but I won't prove it + + + align:start position:0% +working uh but I won't prove it +here uh a little strong stronger is + + align:start position:0% +here uh a little strong stronger is + + + align:start position:0% +here uh a little strong stronger is +alternating monotone + + align:start position:0% +alternating monotone + + + align:start position:0% +alternating monotone +CVP this + + align:start position:0% +CVP this + + + align:start position:0% +CVP this +alternates uh and + + align:start position:0% + + + + align:start position:0% + +or down any path so if you take a path + + align:start position:0% +or down any path so if you take a path + + + align:start position:0% +or down any path so if you take a path +from an input bit to the output it + + align:start position:0% +from an input bit to the output it + + + align:start position:0% +from an input bit to the output it +alternates Andor Andor Andor and + + align:start position:0% +alternates Andor Andor Andor and + + + align:start position:0% +alternates Andor Andor Andor and +furthermore we can assume uh that it + + align:start position:0% +furthermore we can assume uh that it + + + align:start position:0% +furthermore we can assume uh that it +starts and ends with + + align:start position:0% + + + + align:start position:0% + +or it's nice to na this down it's not + + align:start position:0% +or it's nice to na this down it's not + + + align:start position:0% +or it's nice to na this down it's not +hard to + + align:start position:0% +hard to + + + align:start position:0% +hard to +prove although I will prove it in a + + align:start position:0% +prove although I will prove it in a + + + align:start position:0% +prove although I will prove it in a +moment once I tell you + + align:start position:0% +moment once I tell you + + + align:start position:0% +moment once I tell you +a general enough version that I want to + + align:start position:0% +a general enough version that I want to + + + align:start position:0% +a general enough version that I want to +analyze uh this will just let us worry + + align:start position:0% +analyze uh this will just let us worry + + + align:start position:0% +analyze uh this will just let us worry +about fewer gadgets so up here we had to + + align:start position:0% +about fewer gadgets so up here we had to + + + align:start position:0% +about fewer gadgets so up here we had to +think about all Boolean Gates now we + + align:start position:0% +think about all Boolean Gates now we + + + align:start position:0% +think about all Boolean Gates now we +just have to think about and and or and + + align:start position:0% +just have to think about and and or and + + + align:start position:0% +just have to think about and and or and +we can always assume the output of an + + align:start position:0% +we can always assume the output of an + + + align:start position:0% +we can always assume the output of an +and is the input of an or and vice versa + + align:start position:0% +and is the input of an or and vice versa + + + align:start position:0% +and is the input of an or and vice versa +um and that we only need to connect + + align:start position:0% +um and that we only need to connect + + + align:start position:0% +um and that we only need to connect +inputs to or Gates so not like this + + align:start position:0% +inputs to or Gates so not like this + + + align:start position:0% +inputs to or Gates so not like this +picture and we only have to connect the + + align:start position:0% +picture and we only have to connect the + + + align:start position:0% +picture and we only have to connect the +output get the output from an orgate so + + align:start position:0% +output get the output from an orgate so + + + align:start position:0% +output get the output from an orgate so +it reduces the number of cases we need + + align:start position:0% +it reduces the number of cases we need + + + align:start position:0% +it reduces the number of cases we need +to worry + + align:start position:0% + + + + align:start position:0% + +about yeah so is this with founded + + align:start position:0% +about yeah so is this with founded + + + align:start position:0% +about yeah so is this with founded +panon ah good + + align:start position:0% + + + + align:start position:0% + +question + + align:start position:0% +question + + + align:start position:0% +question +uh basically bounded fanin doesn't + + align:start position:0% +uh basically bounded fanin doesn't + + + align:start position:0% +uh basically bounded fanin doesn't +matter with this model uh so usually + + align:start position:0% +matter with this model uh so usually + + + align:start position:0% +matter with this model uh so usually +when NC is defined it's bounded fan + + align:start position:0% +when NC is defined it's bounded fan + + + align:start position:0% +when NC is defined it's bounded fan +in uh and fan out + + align:start position:0% +in uh and fan out + + + align:start position:0% +in uh and fan out +uh but and there's another class called + + align:start position:0% +uh but and there's another class called + + + align:start position:0% +uh but and there's another class called +AC which is when you have unbounded fan + + align:start position:0% +AC which is when you have unbounded fan + + + align:start position:0% +AC which is when you have unbounded fan +out and fan in let's say uh but that + + align:start position:0% +out and fan in let's say uh but that + + + align:start position:0% +out and fan in let's say uh but that +only hurts us by a log Factor so it + + align:start position:0% +only hurts us by a log Factor so it + + + align:start position:0% +only hurts us by a log Factor so it +matters if you're worried about + + align:start position:0% +matters if you're worried about + + + align:start position:0% +matters if you're worried about +something called ac0 and nc0 when this + + align:start position:0% +something called ac0 and nc0 when this + + + align:start position:0% +something called ac0 and nc0 when this +this is zero and you want constant + + align:start position:0% +this is zero and you want constant + + + align:start position:0% +this is zero and you want constant +height it matters for alternation as + + align:start position:0% +height it matters for alternation as + + + align:start position:0% +height it matters for alternation as +well please wait I + + align:start position:0% +well please wait I + + + align:start position:0% +well please wait I +guess it won't matter is is the answer + + align:start position:0% +guess it won't matter is is the answer + + + align:start position:0% +guess it won't matter is is the answer +is this the only setting of starting and + + align:start position:0% +is this the only setting of starting and + + + align:start position:0% +is this the only setting of starting and +ending + + align:start position:0% +ending + + + align:start position:0% +ending +that that works like starting and ending + + align:start position:0% +that that works like starting and ending + + + align:start position:0% +that that works like starting and ending +with both and or starting with and oh + + align:start position:0% +with both and or starting with and oh + + + align:start position:0% +with both and or starting with and oh +yeah I think you could also make this an + + align:start position:0% +yeah I think you could also make this an + + + align:start position:0% +yeah I think you could also make this an +and although I haven't checked that I + + align:start position:0% +and although I haven't checked that I + + + align:start position:0% +and although I haven't checked that I +don't think it's critical that this is + + align:start position:0% +don't think it's critical that this is + + + align:start position:0% +don't think it's critical that this is +or but you could probably do one of them + + align:start position:0% +or but you could probably do one of them + + + align:start position:0% +or but you could probably do one of them +in or and one of them in and and all + + align:start position:0% +in or and one of them in and and all + + + align:start position:0% +in or and one of them in and and all +those combinations but uh this is the + + align:start position:0% +those combinations but uh this is the + + + align:start position:0% +those combinations but uh this is the +one I've seen proved we' need to check + + align:start position:0% +one I've seen proved we' need to check + + + align:start position:0% +one I've seen proved we' need to check +the other cases but I think it's not + + align:start position:0% + + + + align:start position:0% + +hard this is called uh + + align:start position:0% +hard this is called uh + + + align:start position:0% +hard this is called uh +am2 C + + align:start position:0% +am2 C + + + align:start position:0% +am2 C +VP great + + align:start position:0% +VP great + + + align:start position:0% +VP great +acronyms um every gate has fan in two + + align:start position:0% +acronyms um every gate has fan in two + + + align:start position:0% +acronyms um every gate has fan in two +and fan out two so in particular bounded + + align:start position:0% +and fan out two so in particular bounded + + + align:start position:0% +and fan out two so in particular bounded +but also nice and uniform every single + + align:start position:0% +but also nice and uniform every single + + + align:start position:0% +but also nice and uniform every single +not less than or equal to two this is + + align:start position:0% +not less than or equal to two this is + + + align:start position:0% +not less than or equal to two this is +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +two okay we'll prove that and even + + align:start position:0% + + + + align:start position:0% + +stronger synchronous uh am2 + + align:start position:0% + + + + align:start position:0% + +CVP I prefer AVP personally but uh so + + align:start position:0% +CVP I prefer AVP personally but uh so + + + align:start position:0% +CVP I prefer AVP personally but uh so +this is Sam to + + align:start position:0% + + + + align:start position:0% + +CVP uh synchronous means that all the + + align:start position:0% +CVP uh synchronous means that all the + + + align:start position:0% +CVP uh synchronous means that all the +inputs of a gate are available at + + align:start position:0% +inputs of a gate are available at + + + align:start position:0% +inputs of a gate are available at +exactly the same time if you imagine + + align:start position:0% +exactly the same time if you imagine + + + align:start position:0% +exactly the same time if you imagine +running all of the gates of depth I at + + align:start position:0% +running all of the gates of depth I at + + + align:start position:0% +running all of the gates of depth I at +time I then you can do that at time I + + align:start position:0% +time I then you can do that at time I + + + align:start position:0% +time I then you can do that at time I +all Gates of depth I will be ready + + align:start position:0% +all Gates of depth I will be ready + + + align:start position:0% +all Gates of depth I will be ready +they'll have all their inputs in other + + align:start position:0% +they'll have all their inputs in other + + + align:start position:0% +they'll have all their inputs in other +words a gate of depth I gate of depth I + + align:start position:0% +words a gate of depth I gate of depth I + + + align:start position:0% +words a gate of depth I gate of depth I +has one of its inputs at depth I minus + + align:start position:0% +has one of its inputs at depth I minus + + + align:start position:0% +has one of its inputs at depth I minus +one but in a synchronous circuit both of + + align:start position:0% +one but in a synchronous circuit both of + + + align:start position:0% +one but in a synchronous circuit both of +the inputs will have depth I minus one + + align:start position:0% +the inputs will have depth I minus one + + + align:start position:0% +the inputs will have depth I minus one +and so at time I you'll actually be + + align:start position:0% +and so at time I you'll actually be + + + align:start position:0% +and so at time I you'll actually be +ready to do it this is useful in + + align:start position:0% +ready to do it this is useful in + + + align:start position:0% +ready to do it this is useful in +particular for things like constraint + + align:start position:0% +particular for things like constraint + + + align:start position:0% +particular for things like constraint +logic but other constructions as + + align:start position:0% +logic but other constructions as + + + align:start position:0% +logic but other constructions as +well uh one more planer + + align:start position:0% +well uh one more planer + + + align:start position:0% +well uh one more planer +CVP I don't know how many of these + + align:start position:0% +CVP I don't know how many of these + + + align:start position:0% +CVP I don't know how many of these +things you can import into the planer + + align:start position:0% +things you can import into the planer + + + align:start position:0% +things you can import into the planer +case probably many of them um but just + + align:start position:0% +case probably many of them um but just + + + align:start position:0% +case probably many of them um but just +like planer circuit Set uh out of nand + + align:start position:0% +like planer circuit Set uh out of nand + + + align:start position:0% +like planer circuit Set uh out of nand +and no for example you can build + + align:start position:0% +and no for example you can build + + + align:start position:0% +and no for example you can build +Crossovers and so planer graphs planer + + align:start position:0% +Crossovers and so planer graphs planer + + + align:start position:0% +Crossovers and so planer graphs planer +circuits are also + + align:start position:0% +circuits are also + + + align:start position:0% +circuits are also +hard uh uh but actually not all of them + + align:start position:0% +hard uh uh but actually not all of them + + + align:start position:0% +hard uh uh but actually not all of them +because + + align:start position:0% +because + + + align:start position:0% +because +planer + + align:start position:0% +planer + + + align:start position:0% +planer +monotone + + align:start position:0% + + + + align:start position:0% + +CVP uh is in + + align:start position:0% +CVP uh is in + + + align:start position:0% +CVP uh is in +NC so you can't take the monotone and + + align:start position:0% +NC so you can't take the monotone and + + + align:start position:0% +NC so you can't take the monotone and +orness with planarity which is kind of + + align:start position:0% +orness with planarity which is kind of + + + align:start position:0% +orness with planarity which is kind of +annoying uh because that problem can be + + align:start position:0% +annoying uh because that problem can be + + + align:start position:0% +annoying uh because that problem can be +done in parallel but planer with a nand + + align:start position:0% +done in parallel but planer with a nand + + + align:start position:0% +done in parallel but planer with a nand +then you've got negation and you can you + + align:start position:0% +then you've got negation and you can you + + + align:start position:0% +then you've got negation and you can you +can build a + + align:start position:0% +can build a + + + align:start position:0% +can build a +crossover okay let me prove some of + + align:start position:0% +crossover okay let me prove some of + + + align:start position:0% +crossover okay let me prove some of +these things this was to give you a + + align:start position:0% +these things this was to give you a + + + align:start position:0% +these things this was to give you a +flavor for what's hard still all of + + align:start position:0% +flavor for what's hard still all of + + + align:start position:0% +flavor for what's hard still all of +these problems up our uh P + + align:start position:0% + + + + align:start position:0% + +complete and we're going to do it in a + + align:start position:0% +complete and we're going to do it in a + + + align:start position:0% +complete and we're going to do it in a +series of reductions so + + align:start position:0% +series of reductions so + + + align:start position:0% +series of reductions so +first + + align:start position:0% + + + + align:start position:0% + +um first let's deal with uh starting and + + align:start position:0% +um first let's deal with uh starting and + + + align:start position:0% +um first let's deal with uh starting and +ending with ores so this is the part + + align:start position:0% +ending with ores so this is the part + + + align:start position:0% +ending with ores so this is the part +you'd switch if you want to start or end + + align:start position:0% +you'd switch if you want to start or end + + + align:start position:0% +you'd switch if you want to start or end +with an and should be no problem um so + + align:start position:0% +with an and should be no problem um so + + + align:start position:0% +with an and should be no problem um so +this is an input bit either zero or one + + align:start position:0% +this is an input bit either zero or one + + + align:start position:0% +this is an input bit either zero or one +they're going to be drawn with squares + + align:start position:0% +they're going to be drawn with squares + + + align:start position:0% +they're going to be drawn with squares +um oh I should mention by the way + + align:start position:0% +um oh I should mention by the way + + + align:start position:0% +um oh I should mention by the way +there's a a textbook devoted to P + + align:start position:0% +there's a a textbook devoted to P + + + align:start position:0% +there's a a textbook devoted to P +completeness it's a short textbook but + + align:start position:0% +completeness it's a short textbook but + + + align:start position:0% +completeness it's a short textbook but +it's a nice read and it's online so we I + + align:start position:0% +it's a nice read and it's online so we I + + + align:start position:0% +it's a nice read and it's online so we I +link to it from the website now uh so if + + align:start position:0% +link to it from the website now uh so if + + + align:start position:0% +link to it from the website now uh so if +you want to learn a little more check + + align:start position:0% +you want to learn a little more check + + + align:start position:0% +you want to learn a little more check +out that book these are figures from + + align:start position:0% +out that book these are figures from + + + align:start position:0% +out that book these are figures from +that book uh so um if I have uh you know + + align:start position:0% +that book uh so um if I have uh you know + + + align:start position:0% +that book uh so um if I have uh you know +some input being sent to some gates I'm + + align:start position:0% +some input being sent to some gates I'm + + + align:start position:0% +some input being sent to some gates I'm +just going to put an or there and let's + + align:start position:0% +just going to put an or there and let's + + + align:start position:0% +just going to put an or there and let's +say I or that bit with itself so now + + align:start position:0% +say I or that bit with itself so now + + + align:start position:0% +say I or that bit with itself so now +everything starts with an or done if I + + align:start position:0% +everything starts with an or done if I + + + align:start position:0% +everything starts with an or done if I +want to make things end with an or and + + align:start position:0% +want to make things end with an or and + + + align:start position:0% +want to make things end with an or and +they end with an and I'll just put an + + align:start position:0% +they end with an and I'll just put an + + + align:start position:0% +they end with an and I'll just put an +orgate i uh I don't know why here we use + + align:start position:0% +orgate i uh I don't know why here we use + + + align:start position:0% +orgate i uh I don't know why here we use +only one input here we put two inputs + + align:start position:0% +only one input here we put two inputs + + + align:start position:0% +only one input here we put two inputs +but uh could have just put one input up + + align:start position:0% +but uh could have just put one input up + + + align:start position:0% +but uh could have just put one input up +there I'm allowing for now one input + + align:start position:0% +there I'm allowing for now one input + + + align:start position:0% +there I'm allowing for now one input +orgate so I'm going to fix that later + + align:start position:0% +orgate so I'm going to fix that later + + + align:start position:0% +orgate so I'm going to fix that later +question coming soon so this is just to + + align:start position:0% +question coming soon so this is just to + + + align:start position:0% +question coming soon so this is just to +start and end with + + align:start position:0% +start and end with + + + align:start position:0% +start and end with +orse uh next thing I'd like to to do is + + align:start position:0% +orse uh next thing I'd like to to do is + + + align:start position:0% +orse uh next thing I'd like to to do is +make things alternating so if I have two + + align:start position:0% +make things alternating so if I have two + + + align:start position:0% +make things alternating so if I have two +gates uh actually before I do this uh I + + align:start position:0% +gates uh actually before I do this uh I + + + align:start position:0% +gates uh actually before I do this uh I +need to do this later it's important to + + align:start position:0% +need to do this later it's important to + + + align:start position:0% +need to do this later it's important to +get the sequence right first I want to + + align:start position:0% +get the sequence right first I want to + + + align:start position:0% +get the sequence right first I want to +make sure the fan out is less than or + + align:start position:0% +make sure the fan out is less than or + + + align:start position:0% +make sure the fan out is less than or +equal to two in this way this is a + + align:start position:0% +equal to two in this way this is a + + + align:start position:0% +equal to two in this way this is a +standard trick uh if I have large fan + + align:start position:0% +standard trick uh if I have large fan + + + align:start position:0% +standard trick uh if I have large fan +out I just build a binary tree and you + + align:start position:0% +out I just build a binary tree and you + + + align:start position:0% +out I just build a binary tree and you +could put ores or ands here there's only + + align:start position:0% +could put ores or ands here there's only + + + align:start position:0% +could put ores or ands here there's only +one input so it doesn't do anything to + + align:start position:0% +one input so it doesn't do anything to + + + align:start position:0% +one input so it doesn't do anything to +it but now I have fan out at most two + + align:start position:0% +it but now I have fan out at most two + + + align:start position:0% +it but now I have fan out at most two +fan in uh is whatever did we deal with + + align:start position:0% +fan in uh is whatever did we deal with + + + align:start position:0% +fan in uh is whatever did we deal with +uh large fan in not yet so + + align:start position:0% +uh large fan in not yet so + + + align:start position:0% +uh large fan in not yet so +um so I'm going to do that first this + + align:start position:0% +um so I'm going to do that first this + + + align:start position:0% +um so I'm going to do that first this +will make lots of ores next to each + + align:start position:0% +will make lots of ores next to each + + + align:start position:0% +will make lots of ores next to each +other uh but then whenever I have two + + align:start position:0% +other uh but then whenever I have two + + + align:start position:0% +other uh but then whenever I have two +ores or two ANS next to each other I + + align:start position:0% +ores or two ANS next to each other I + + + align:start position:0% +ores or two ANS next to each other I +just add the opposite gate in between + + align:start position:0% +just add the opposite gate in between + + + align:start position:0% +just add the opposite gate in between +okay so now it's alternating fan out at + + align:start position:0% +okay so now it's alternating fan out at + + + align:start position:0% +okay so now it's alternating fan out at +most two so we've gotten this property + + align:start position:0% +most two so we've gotten this property + + + align:start position:0% +most two so we've gotten this property +in a weak sense with it less than or + + align:start position:0% +in a weak sense with it less than or + + + align:start position:0% +in a weak sense with it less than or +equal to two we're going to fix the ones + + align:start position:0% +equal to two we're going to fix the ones + + + align:start position:0% +equal to two we're going to fix the ones +later uh we haven't dealt with this yet + + align:start position:0% +later uh we haven't dealt with this yet + + + align:start position:0% +later uh we haven't dealt with this yet +uh but we have uh I assumed sorry that + + align:start position:0% +uh but we have uh I assumed sorry that + + + align:start position:0% +uh but we have uh I assumed sorry that +I'm starting with monoton so I just have + + align:start position:0% +I'm starting with monoton so I just have + + + align:start position:0% +I'm starting with monoton so I just have +an and + + align:start position:0% +an and + + + align:start position:0% +an and +no negation I'm reducing from monotone + + align:start position:0% +no negation I'm reducing from monotone + + + align:start position:0% +no negation I'm reducing from monotone +CVP to these other problems I've got + + align:start position:0% +CVP to these other problems I've got + + + align:start position:0% +CVP to these other problems I've got +alternation starting and ending with or + + align:start position:0% +alternation starting and ending with or + + + align:start position:0% +alternation starting and ending with or +and fan out at most two at this point + + align:start position:0% +and fan out at most two at this point + + + align:start position:0% +and fan out at most two at this point +next reduction is to make fan in exactly + + align:start position:0% +next reduction is to make fan in exactly + + + align:start position:0% +next reduction is to make fan in exactly +two um so yeah I guess I didn't write it + + align:start position:0% +two um so yeah I guess I didn't write it + + + align:start position:0% +two um so yeah I guess I didn't write it +but we can use the same trick on the + + align:start position:0% +but we can use the same trick on the + + + align:start position:0% +but we can use the same trick on the +other side if you have fan in larger + + align:start position:0% +other side if you have fan in larger + + + align:start position:0% +other side if you have fan in larger +than two then you can just take you know + + align:start position:0% +than two then you can just take you know + + + align:start position:0% +than two then you can just take you know +ANS of ANS of ANS uh so you can also get + + align:start position:0% +ANS of ANS of ANS uh so you can also get + + + align:start position:0% +ANS of ANS of ANS uh so you can also get +fan in at most to now if I have fan in + + align:start position:0% +fan in at most to now if I have fan in + + + align:start position:0% +fan in at most to now if I have fan in +one one which I've used all over the + + align:start position:0% +one one which I've used all over the + + + align:start position:0% +one one which I've used all over the +place now I'm going to get rid of it uh + + align:start position:0% +place now I'm going to get rid of it uh + + + align:start position:0% +place now I'm going to get rid of it uh +in two different ways if I have an + + align:start position:0% +in two different ways if I have an + + + align:start position:0% +in two different ways if I have an +orgate with one input um happens to be + + align:start position:0% +orgate with one input um happens to be + + + align:start position:0% +orgate with one input um happens to be +an and or original bit I'll just add in + + align:start position:0% +an and or original bit I'll just add in + + + align:start position:0% +an and or original bit I'll just add in +another input of zero that won't affect + + align:start position:0% +another input of zero that won't affect + + + align:start position:0% +another input of zero that won't affect +things and if I have an N bit uh I would + + align:start position:0% +things and if I have an N bit uh I would + + + align:start position:0% +things and if I have an N bit uh I would +like to put a one here but I'm not + + align:start position:0% +like to put a one here but I'm not + + + align:start position:0% +like to put a one here but I'm not +allowed to feed a number an input + + align:start position:0% +allowed to feed a number an input + + + align:start position:0% +allowed to feed a number an input +directly to an and gate because I want + + align:start position:0% +directly to an and gate because I want + + + align:start position:0% +directly to an and gate because I want +to preserve the property that I start an + + align:start position:0% +to preserve the property that I start an + + + align:start position:0% +to preserve the property that I start an +end with ORS so this is one thing that + + align:start position:0% +end with ORS so this is one thing that + + + align:start position:0% +end with ORS so this is one thing that +would be you'd have to tweak a little + + align:start position:0% +would be you'd have to tweak a little + + + align:start position:0% +would be you'd have to tweak a little +bit if you want to start an end with ANS + + align:start position:0% +bit if you want to start an end with ANS + + + align:start position:0% +bit if you want to start an end with ANS +but you can do I think a similar trick I + + align:start position:0% +but you can do I think a similar trick I + + + align:start position:0% +but you can do I think a similar trick I +want to build a one bit using an orgate + + align:start position:0% +want to build a one bit using an orgate + + + align:start position:0% +want to build a one bit using an orgate +so I take two one bits or them together + + align:start position:0% +so I take two one bits or them together + + + align:start position:0% +so I take two one bits or them together +now I have a one bit fit into here and + + align:start position:0% +now I have a one bit fit into here and + + + align:start position:0% +now I have a one bit fit into here and +then that will just pass through okay so + + align:start position:0% +then that will just pass through okay so + + + align:start position:0% +then that will just pass through okay so +now I have fan and exactly two no once + + align:start position:0% +now I have fan and exactly two no once + + + align:start position:0% +now I have fan and exactly two no once +to worry about you can imagine this is + + align:start position:0% +to worry about you can imagine this is + + + align:start position:0% +to worry about you can imagine this is +useful when you're actually building + + align:start position:0% +useful when you're actually building + + + align:start position:0% +useful when you're actually building +gadgets because then you don't have to + + align:start position:0% +gadgets because then you don't have to + + + align:start position:0% +gadgets because then you don't have to +do any + + align:start position:0% + + + + align:start position:0% + +work uh not I haven't dealt with fan out + + align:start position:0% +work uh not I haven't dealt with fan out + + + align:start position:0% +work uh not I haven't dealt with fan out +two yet this point just fan in two so + + align:start position:0% +two yet this point just fan in two so + + + align:start position:0% +two yet this point just fan in two so +variables some of them still only have + + align:start position:0% +variables some of them still only have + + + align:start position:0% +variables some of them still only have +fan out one but they will have at most + + align:start position:0% +fan out one but they will have at most + + + align:start position:0% +fan out one but they will have at most +two so now we're going to do fan out + + align:start position:0% +two so now we're going to do fan out + + + align:start position:0% +two so now we're going to do fan out +exactly two so uh what I'm going to do + + align:start position:0% +exactly two so uh what I'm going to do + + + align:start position:0% +exactly two so uh what I'm going to do +is take my circuit make two copies of it + + align:start position:0% +is take my circuit make two copies of it + + + align:start position:0% +is take my circuit make two copies of it +uh there's the primed copy and the + + align:start position:0% +uh there's the primed copy and the + + + align:start position:0% +uh there's the primed copy and the +original copy okay so now I just need to + + align:start position:0% +original copy okay so now I just need to + + + align:start position:0% +original copy okay so now I just need to +hook things up how I want them um the + + align:start position:0% +hook things up how I want them um the + + + align:start position:0% +hook things up how I want them um the +inputs which are not drawn here if I + + align:start position:0% +inputs which are not drawn here if I + + + align:start position:0% +inputs which are not drawn here if I +have an input with uh outdegree one I'll + + align:start position:0% +have an input with uh outdegree one I'll + + + align:start position:0% +have an input with uh outdegree one I'll +merge them into one copy then I'll have + + align:start position:0% +merge them into one copy then I'll have + + + align:start position:0% +merge them into one copy then I'll have +out degree 2 two if they already have + + align:start position:0% +out degree 2 two if they already have + + + align:start position:0% +out degree 2 two if they already have +out degree 2 just leave them as two + + align:start position:0% +out degree 2 just leave them as two + + + align:start position:0% +out degree 2 just leave them as two +copies okay so now all the inputs have + + align:start position:0% +copies okay so now all the inputs have + + + align:start position:0% +copies okay so now all the inputs have +out degree 2 or fan out two uh if I have + + align:start position:0% +out degree 2 or fan out two uh if I have + + + align:start position:0% +out degree 2 or fan out two uh if I have +an andate with uh without degree two + + align:start position:0% +an andate with uh without degree two + + + align:start position:0% +an andate with uh without degree two +again I don't touch it I'll leave them + + align:start position:0% +again I don't touch it I'll leave them + + + align:start position:0% +again I don't touch it I'll leave them +as two copies if I have an and gate with + + align:start position:0% +as two copies if I have an and gate with + + + align:start position:0% +as two copies if I have an and gate with +one uh fan out of one then here are the + + align:start position:0% +one uh fan out of one then here are the + + + align:start position:0% +one uh fan out of one then here are the +two copies of it uh I basically want to + + align:start position:0% +two copies of it uh I basically want to + + + align:start position:0% +two copies of it uh I basically want to +add an extra output that gets thrown + + align:start position:0% +add an extra output that gets thrown + + + align:start position:0% +add an extra output that gets thrown +away so because I have to end with an or + + align:start position:0% +away so because I have to end with an or + + + align:start position:0% +away so because I have to end with an or +I'm going to put an or here and then + + align:start position:0% +I'm going to put an or here and then + + + align:start position:0% +I'm going to put an or here and then +that's an output it's not the the output + + align:start position:0% +that's an output it's not the the output + + + align:start position:0% +that's an output it's not the the output +that we're asking the question about + + align:start position:0% +that we're asking the question about + + + align:start position:0% +that we're asking the question about +where want to know uh does the output + + align:start position:0% +where want to know uh does the output + + + align:start position:0% +where want to know uh does the output +become true that's a specific output so + + align:start position:0% +become true that's a specific output so + + + align:start position:0% +become true that's a specific output so +for this reduction I need to allow there + + align:start position:0% +for this reduction I need to allow there + + + align:start position:0% +for this reduction I need to allow there +to be multiple outputs in my circuit but + + align:start position:0% +to be multiple outputs in my circuit but + + + align:start position:0% +to be multiple outputs in my circuit but +only one of them of + + align:start position:0% +only one of them of + + + align:start position:0% +only one of them of +Interest okay so now uh and the rest is + + align:start position:0% +Interest okay so now uh and the rest is + + + align:start position:0% +Interest okay so now uh and the rest is +connected as before so um now these guys + + align:start position:0% +connected as before so um now these guys + + + align:start position:0% +connected as before so um now these guys +have fan out two if I have an orgate + + align:start position:0% +have fan out two if I have an orgate + + + align:start position:0% +have fan out two if I have an orgate +with one output this is a little + + align:start position:0% +with one output this is a little + + + align:start position:0% +with one output this is a little +trickier because I want to end with ores + + align:start position:0% +trickier because I want to end with ores + + + align:start position:0% +trickier because I want to end with ores +I guess um we're going to combine these + + align:start position:0% +I guess um we're going to combine these + + + align:start position:0% +I guess um we're going to combine these +two bits and I have to alternate so next + + align:start position:0% +two bits and I have to alternate so next + + + align:start position:0% +two bits and I have to alternate so next +thing is I have to go to an and um this + + align:start position:0% +thing is I have to go to an and um this + + + align:start position:0% +thing is I have to go to an and um this +also has to have two outputs so I'm + + align:start position:0% +also has to have two outputs so I'm + + + align:start position:0% +also has to have two outputs so I'm +going to put one of them here and one of + + align:start position:0% +going to put one of them here and one of + + + align:start position:0% +going to put one of them here and one of +them here uh I can I these these guys + + align:start position:0% +them here uh I can I these these guys + + + align:start position:0% +them here uh I can I these these guys +need two inputs because I don't want to + + align:start position:0% +need two inputs because I don't want to + + + align:start position:0% +need two inputs because I don't want to +violate the two input conditions so I + + align:start position:0% +violate the two input conditions so I + + + align:start position:0% +violate the two input conditions so I +add another bit uh could be Zer one + + align:start position:0% +add another bit uh could be Zer one + + + align:start position:0% +add another bit uh could be Zer one +doesn't matter feed it to both of them + + align:start position:0% +doesn't matter feed it to both of them + + + align:start position:0% +doesn't matter feed it to both of them +now this has outdegree to these have in + + align:start position:0% +now this has outdegree to these have in + + + align:start position:0% +now this has outdegree to these have in +degree to uh and this is an output so + + align:start position:0% +degree to uh and this is an output so + + + align:start position:0% +degree to uh and this is an output so +output is uh you could think of there as + + align:start position:0% +output is uh you could think of there as + + + align:start position:0% +output is uh you could think of there as +being two of + + align:start position:0% +being two of + + + align:start position:0% +being two of +them yeah you change the outputs + + align:start position:0% +them yeah you change the outputs + + + align:start position:0% +them yeah you change the outputs +together so that there's only one output + + align:start position:0% +together so that there's only one output + + + align:start position:0% +together so that there's only one output +oh combine the different outputs + + align:start position:0% +oh combine the different outputs + + + align:start position:0% +oh combine the different outputs +together if you have fan out exactly two + + align:start position:0% +together if you have fan out exactly two + + + align:start position:0% +together if you have fan out exactly two +and fan in exactly two doesn't that mean + + align:start position:0% +and fan in exactly two doesn't that mean + + + align:start position:0% +and fan in exactly two doesn't that mean +that you're preserving the number of + + align:start position:0% +that you're preserving the number of + + + align:start position:0% +that you're preserving the number of +inputs uh so that you can't reduce those + + align:start position:0% +inputs uh so that you can't reduce those + + + align:start position:0% +inputs uh so that you can't reduce those +extra outputs to + + align:start position:0% +extra outputs to + + + align:start position:0% +extra outputs to +one yes good so I think if we tried to + + align:start position:0% +one yes good so I think if we tried to + + + align:start position:0% +one yes good so I think if we tried to +combine all the outputs together we'd + + align:start position:0% +combine all the outputs together we'd + + + align:start position:0% +combine all the outputs together we'd +end up with a similar problem and we + + align:start position:0% +end up with a similar problem and we + + + align:start position:0% +end up with a similar problem and we +would basically have to do this + + align:start position:0% +would basically have to do this + + + align:start position:0% +would basically have to do this +construction again and then produce more + + align:start position:0% +construction again and then produce more + + + align:start position:0% +construction again and then produce more +outputs + + align:start position:0% +outputs + + + align:start position:0% +outputs +good yeah so we we violate fan in to + + align:start position:0% +good yeah so we we violate fan in to + + + align:start position:0% +good yeah so we we violate fan in to +obviously at the inputs but you're right + + align:start position:0% +obviously at the inputs but you're right + + + align:start position:0% +obviously at the inputs but you're right +after the input level the number of + + align:start position:0% +after the input level the number of + + + align:start position:0% +after the input level the number of +lines should be + + align:start position:0% +lines should be + + + align:start position:0% +lines should be +preserved okay so never mind we do need + + align:start position:0% +preserved okay so never mind we do need + + + align:start position:0% +preserved okay so never mind we do need +multiple outputs and exactly one of them + + align:start position:0% +multiple outputs and exactly one of them + + + align:start position:0% +multiple outputs and exactly one of them +is uh marked as the one we care about + + align:start position:0% +is uh marked as the one we care about + + + align:start position:0% +is uh marked as the one we care about +whether it outputs + + align:start position:0% +whether it outputs + + + align:start position:0% +whether it outputs +true uh is that the end yes that is at + + align:start position:0% +true uh is that the end yes that is at + + + align:start position:0% +true uh is that the end yes that is at +this point we've proved am2 + + align:start position:0% +this point we've proved am2 + + + align:start position:0% +this point we've proved am2 +CVP is p + + align:start position:0% +CVP is p + + + align:start position:0% +CVP is p +complete okay um so one more reduction + + align:start position:0% +complete okay um so one more reduction + + + align:start position:0% +complete okay um so one more reduction +is for the synchronous case + + align:start position:0% +is for the synchronous case + + + align:start position:0% +is for the synchronous case +uh this is + + align:start position:0% +uh this is + + + align:start position:0% +uh this is +cool um Let Me Maybe first say what + + align:start position:0% +cool um Let Me Maybe first say what + + + align:start position:0% +cool um Let Me Maybe first say what +we're + + align:start position:0% +we're + + + align:start position:0% +we're +doing + + align:start position:0% +doing + + + align:start position:0% +doing +uh so for the synchronous reduction + + align:start position:0% +uh so for the synchronous reduction + + + align:start position:0% +uh so for the synchronous reduction +we're going to make n/2 copies of the + + align:start position:0% +we're going to make n/2 copies of the + + + align:start position:0% +we're going to make n/2 copies of the +circuit where n is the number of + + align:start position:0% + + + + align:start position:0% + +gates um at a high level that's that's + + align:start position:0% +gates um at a high level that's that's + + + align:start position:0% +gates um at a high level that's that's +what we're doing and basically the I + + align:start position:0% +what we're doing and basically the I + + + align:start position:0% +what we're doing and basically the I +copy will feed into the plus first copy + + align:start position:0% +copy will feed into the plus first copy + + + align:start position:0% +copy will feed into the plus first copy +well not quite uh because we want to + + align:start position:0% +well not quite uh because we want to + + + align:start position:0% +well not quite uh because we want to +alternate ands and ores so um in the I + + align:start position:0% +alternate ands and ores so um in the I + + + align:start position:0% +alternate ands and ores so um in the I +copy the I copy of this circuit will be + + align:start position:0% +copy the I copy of this circuit will be + + + align:start position:0% +copy the I copy of this circuit will be +uh the depth levels uh 2 I and 2 I + 1 + + align:start position:0% +uh the depth levels uh 2 I and 2 I + 1 + + + align:start position:0% +uh the depth levels uh 2 I and 2 I + 1 +in the final circuit that I'm producing + + align:start position:0% +in the final circuit that I'm producing + + + align:start position:0% +in the final circuit that I'm producing +where these are + + align:start position:0% +where these are + + + align:start position:0% +where these are +ands and inputs + + align:start position:0% + + + + align:start position:0% + +and this level is going to be + + align:start position:0% +and this level is going to be + + + align:start position:0% +and this level is going to be +ORS okay so basically I want to take a u + + align:start position:0% +ORS okay so basically I want to take a u + + + align:start position:0% +ORS okay so basically I want to take a u +an and level and an or level from one + + align:start position:0% +an and level and an or level from one + + + align:start position:0% +an and level and an or level from one +copy then an and level and or level from + + align:start position:0% +copy then an and level and or level from + + + align:start position:0% +copy then an and level and or level from +the next copy and so on um the uh inputs + + align:start position:0% +the next copy and so on um the uh inputs + + + align:start position:0% +the next copy and so on um the uh inputs +are a little more subtle but in + + align:start position:0% +are a little more subtle but in + + + align:start position:0% +are a little more subtle but in +particular I'm at least going to make + + align:start position:0% +particular I'm at least going to make + + + align:start position:0% +particular I'm at least going to make +the copies of the inputs and I'm going + + align:start position:0% +the copies of the inputs and I'm going + + + align:start position:0% +the copies of the inputs and I'm going +to change them later um and so the + + align:start position:0% +to change them later um and so the + + + align:start position:0% +to change them later um and so the +outputs of the ores from one copy will + + align:start position:0% +outputs of the ores from one copy will + + + align:start position:0% +outputs of the ores from one copy will +go to the inputs of the ands at the in + + align:start position:0% +go to the inputs of the ands at the in + + + align:start position:0% +go to the inputs of the ands at the in +the next copy + + align:start position:0% +the next copy + + + align:start position:0% +the next copy +and and vice versa so from the outputs + + align:start position:0% +and and vice versa so from the outputs + + + align:start position:0% +and and vice versa so from the outputs +from the ANS stay within the same copy + + align:start position:0% +from the ANS stay within the same copy + + + align:start position:0% +from the ANS stay within the same copy +and then the outputs from here go to the + + align:start position:0% +and then the outputs from here go to the + + + align:start position:0% +and then the outputs from here go to the +next copy basically I want to this will + + align:start position:0% +next copy basically I want to this will + + + align:start position:0% +next copy basically I want to this will +force synchronization in a sense now the + + align:start position:0% +force synchronization in a sense now the + + + align:start position:0% +force synchronization in a sense now the +one tricky part is the inputs I want + + align:start position:0% +one tricky part is the inputs I want + + + align:start position:0% +one tricky part is the inputs I want +everything I want the I copy to be + + align:start position:0% +everything I want the I copy to be + + + align:start position:0% +everything I want the I copy to be +triggered at time to I exactly and so + + align:start position:0% +triggered at time to I exactly and so + + + align:start position:0% +triggered at time to I exactly and so +for that I can't just have the inputs + + align:start position:0% +for that I can't just have the inputs + + + align:start position:0% +for that I can't just have the inputs +you maybe some of the the gates in there + + align:start position:0% +you maybe some of the the gates in there + + + align:start position:0% +you maybe some of the the gates in there +take an input from sort of straight I + + align:start position:0% +take an input from sort of straight I + + + align:start position:0% +take an input from sort of straight I +need to delay that that input from + + align:start position:0% +need to delay that that input from + + + align:start position:0% +need to delay that that input from +coming and still Preserve in fan in and + + align:start position:0% +coming and still Preserve in fan in and + + + align:start position:0% +coming and still Preserve in fan in and +fan out to and alternation so to do that + + align:start position:0% +fan out to and alternation so to do that + + + align:start position:0% +fan out to and alternation so to do that +uh going to use this gadget so Norm so I + + align:start position:0% +uh going to use this gadget so Norm so I + + + align:start position:0% +uh going to use this gadget so Norm so I +just I have the same the same bit + + align:start position:0% +just I have the same the same bit + + + align:start position:0% +just I have the same the same bit +written twice and then I or them with + + align:start position:0% +written twice and then I or them with + + + align:start position:0% +written twice and then I or them with +themselves and then and them with + + align:start position:0% +themselves and then and them with + + + align:start position:0% +themselves and then and them with +themselves and or them okay it seems + + align:start position:0% +themselves and or them okay it seems + + + align:start position:0% +themselves and or them okay it seems +innocent enough that ladder obviously + + align:start position:0% +innocent enough that ladder obviously + + + align:start position:0% +innocent enough that ladder obviously +will not change any of the bits so just + + align:start position:0% +will not change any of the bits so just + + + align:start position:0% +will not change any of the bits so just +duplicating those + + align:start position:0% +duplicating those + + + align:start position:0% +duplicating those +bits uh at every time step it's all + + align:start position:0% +bits uh at every time step it's all + + + align:start position:0% +bits uh at every time step it's all +about timing here uh now here's the fun + + align:start position:0% +about timing here uh now here's the fun + + + align:start position:0% +about timing here uh now here's the fun +thing if this gate needs this bit uh + + align:start position:0% +thing if this gate needs this bit uh + + + align:start position:0% +thing if this gate needs this bit uh +obviously I can just take it out here + + align:start position:0% +obviously I can just take it out here + + + align:start position:0% +obviously I can just take it out here +that will still preserve fan out to here + + align:start position:0% +that will still preserve fan out to here + + + align:start position:0% +that will still preserve fan out to here +um and if I'm taking one bit from here + + align:start position:0% +um and if I'm taking one bit from here + + + align:start position:0% +um and if I'm taking one bit from here +I'm going to have to throw away another + + align:start position:0% +I'm going to have to throw away another + + + align:start position:0% +I'm going to have to throw away another +bit and magically this is very cool uh + + align:start position:0% +bit and magically this is very cool uh + + + align:start position:0% +bit and magically this is very cool uh +if I throw away a bit here doesn't + + align:start position:0% +if I throw away a bit here doesn't + + + align:start position:0% +if I throw away a bit here doesn't +matter what that bit value is this will + + align:start position:0% +matter what that bit value is this will + + + align:start position:0% +matter what that bit value is this will +still be uh + + align:start position:0% + + + + align:start position:0% + +X2 um you can think of the two cases + + align:start position:0% +X2 um you can think of the two cases + + + align:start position:0% +X2 um you can think of the two cases +either X2 is zero in which case uh this + + align:start position:0% +either X2 is zero in which case uh this + + + align:start position:0% +either X2 is zero in which case uh this +is zero and then doesn't matter what + + align:start position:0% +is zero and then doesn't matter what + + + align:start position:0% +is zero and then doesn't matter what +this bit is it will output zero okay or + + align:start position:0% +this bit is it will output zero okay or + + + align:start position:0% +this bit is it will output zero okay or +this bit could be a one then I go here + + align:start position:0% +this bit could be a one then I go here + + + align:start position:0% +this bit could be a one then I go here +uh and I mean it actually doesn't matter + + align:start position:0% +uh and I mean it actually doesn't matter + + + align:start position:0% +uh and I mean it actually doesn't matter +that is preserved but it is I think it's + + align:start position:0% +that is preserved but it is I think it's + + + align:start position:0% +that is preserved but it is I think it's +kind of cool um if this is a one then + + align:start position:0% +kind of cool um if this is a one then + + + align:start position:0% +kind of cool um if this is a one then +this will output whatever that bit is um + + align:start position:0% +this will output whatever that bit is um + + + align:start position:0% +this will output whatever that bit is um +but because again this is this will be a + + align:start position:0% +but because again this is this will be a + + + align:start position:0% +but because again this is this will be a +one because it gets it from here uh then + + align:start position:0% +one because it gets it from here uh then + + + align:start position:0% +one because it gets it from here uh then +the or will turn it back into a one + + align:start position:0% +the or will turn it back into a one + + + align:start position:0% +the or will turn it back into a one +so either way the bit is restored so you + + align:start position:0% +so either way the bit is restored so you + + + align:start position:0% +so either way the bit is restored so you +could actually reuse this gadget a few + + align:start position:0% +could actually reuse this gadget a few + + + align:start position:0% +could actually reuse this gadget a few +times if you wanted but we can also be + + align:start position:0% +times if you wanted but we can also be + + + align:start position:0% +times if you wanted but we can also be +lazy and just make many copies of this + + align:start position:0% +lazy and just make many copies of this + + + align:start position:0% +lazy and just make many copies of this +gadget uh because we have polinomial + + align:start position:0% +gadget uh because we have polinomial + + + align:start position:0% +gadget uh because we have polinomial +size uh so basically we can get a one + + align:start position:0% +size uh so basically we can get a one + + + align:start position:0% +size uh so basically we can get a one +bit and also destroy an output basically + + align:start position:0% +bit and also destroy an output basically + + + align:start position:0% +bit and also destroy an output basically +um with with this kind of Gadget uh and + + align:start position:0% +um with with this kind of Gadget uh and + + + align:start position:0% +um with with this kind of Gadget uh and +get the inputs to be triggered at + + align:start position:0% +get the inputs to be triggered at + + + align:start position:0% +get the inputs to be triggered at +exactly the right time so the I copy all + + align:start position:0% +exactly the right time so the I copy all + + + align:start position:0% +exactly the right time so the I copy all +of the gates will trigger at time uh 2i + + align:start position:0% +of the gates will trigger at time uh 2i + + + align:start position:0% +of the gates will trigger at time uh 2i +and then all the and Gates will trigger + + align:start position:0% +and then all the and Gates will trigger + + + align:start position:0% +and then all the and Gates will trigger +at 2 I and then all the orates will + + align:start position:0% +at 2 I and then all the orates will + + + align:start position:0% +at 2 I and then all the orates will +Trigger Time 2 I + 1 they'll feed into + + align:start position:0% +Trigger Time 2 I + 1 they'll feed into + + + align:start position:0% +Trigger Time 2 I + 1 they'll feed into +the next uh the next copy all those will + + align:start position:0% +the next uh the next copy all those will + + + align:start position:0% +the next uh the next copy all those will +trigger and so on so it's a little bit + + align:start position:0% +trigger and so on so it's a little bit + + + align:start position:0% +trigger and so on so it's a little bit +redundant but uh it + + align:start position:0% + + + + align:start position:0% + +works and then the output is going to be + + align:start position:0% +works and then the output is going to be + + + align:start position:0% +works and then the output is going to be +the output of the last copy the N over + + align:start position:0% +the output of the last copy the N over + + + align:start position:0% +the output of the last copy the N over +second n over second copy I guess you + + align:start position:0% +second n over second copy I guess you + + + align:start position:0% +second n over second copy I guess you +call it okay uh + + align:start position:0% +call it okay uh + + + align:start position:0% +call it okay uh +so you can of course uh convert this + + align:start position:0% +so you can of course uh convert this + + + align:start position:0% +so you can of course uh convert this +into bounded deterministic constraint + + align:start position:0% +into bounded deterministic constraint + + + align:start position:0% +into bounded deterministic constraint +logic where each Edge only flips once uh + + align:start position:0% +logic where each Edge only flips once uh + + + align:start position:0% +logic where each Edge only flips once uh +once you have the synchronous version of + + align:start position:0% +once you have the synchronous version of + + + align:start position:0% +once you have the synchronous version of +CVP it's very easy I didn't draw a + + align:start position:0% +CVP it's very easy I didn't draw a + + + align:start position:0% +CVP it's very easy I didn't draw a +synchronous picture here because it's + + align:start position:0% +synchronous picture here because it's + + + align:start position:0% +synchronous picture here because it's +tedious to draw these pictures but um if + + align:start position:0% +tedious to draw these pictures but um if + + + align:start position:0% +tedious to draw these pictures but um if +you just set these uh whichever the one + + align:start position:0% +you just set these uh whichever the one + + + align:start position:0% +you just set these uh whichever the one +bits are as your initially active edges + + align:start position:0% +bits are as your initially active edges + + + align:start position:0% +bits are as your initially active edges +those are the ones that just flipped + + align:start position:0% +those are the ones that just flipped + + + align:start position:0% +those are the ones that just flipped +just reversed uh then things will just + + align:start position:0% +just reversed uh then things will just + + + align:start position:0% +just reversed uh then things will just +propagate and everything will be timed + + align:start position:0% +propagate and everything will be timed + + + align:start position:0% +propagate and everything will be timed +exactly right whenever you arrive at a + + align:start position:0% +exactly right whenever you arrive at a + + + align:start position:0% +exactly right whenever you arrive at a +gate uh both of the inputs have just + + align:start position:0% +gate uh both of the inputs have just + + + align:start position:0% +gate uh both of the inputs have just +activated and then the output will + + align:start position:0% +activated and then the output will + + + align:start position:0% +activated and then the output will +activate so just like before but now + + align:start position:0% +activate so just like before but now + + + align:start position:0% +activate so just like before but now +each Edge only has to reverse once and + + align:start position:0% +each Edge only has to reverse once and + + + align:start position:0% +each Edge only has to reverse once and +you'll get the the result at the end so + + align:start position:0% +you'll get the the result at the end so + + + align:start position:0% +you'll get the the result at the end so +deciding whether the last Edge flips is + + align:start position:0% +deciding whether the last Edge flips is + + + align:start position:0% +deciding whether the last Edge flips is +the same as whether the output was a one + + align:start position:0% +the same as whether the output was a one + + + align:start position:0% +the same as whether the output was a one +in the + + align:start position:0% +in the + + + align:start position:0% +in the +circuit uh open problem I guess would be + + align:start position:0% +circuit uh open problem I guess would be + + + align:start position:0% +circuit uh open problem I guess would be +to use bounded deterministic constraint + + align:start position:0% +to use bounded deterministic constraint + + + align:start position:0% +to use bounded deterministic constraint +logic to prove interesting games P + + align:start position:0% +logic to prove interesting games P + + + align:start position:0% +logic to prove interesting games P +complete or interesting Problems P + + align:start position:0% +complete or interesting Problems P + + + align:start position:0% +complete or interesting Problems P +complete that hasn't been + + align:start position:0% +complete that hasn't been + + + align:start position:0% +complete that hasn't been +done but + + align:start position:0% +done but + + + align:start position:0% +done but +uh I have for + + align:start position:0% +uh I have for + + + align:start position:0% +uh I have for +fun a an example of a p completeness p p + + align:start position:0% +fun a an example of a p completeness p p + + + align:start position:0% +fun a an example of a p completeness p p +hardness + + align:start position:0% +hardness + + + align:start position:0% +hardness +reduction uh so suppose you want to find + + align:start position:0% +reduction uh so suppose you want to find + + + align:start position:0% +reduction uh so suppose you want to find +an independent set independent set is + + align:start position:0% +an independent set independent set is + + + align:start position:0% +an independent set independent set is +hard suppose I want to find a maximal + + align:start position:0% +hard suppose I want to find a maximal + + + align:start position:0% +hard suppose I want to find a maximal +independent set an independent set where + + align:start position:0% +independent set an independent set where + + + align:start position:0% +independent set an independent set where +I can't add any more vertices so here's + + align:start position:0% +I can't add any more vertices so here's + + + align:start position:0% +I can't add any more vertices so here's +a way to do that I start with nothing uh + + align:start position:0% +a way to do that I start with nothing uh + + + align:start position:0% +a way to do that I start with nothing uh +I do a for Loop let's say the vertices + + align:start position:0% +I do a for Loop let's say the vertices + + + align:start position:0% +I do a for Loop let's say the vertices +are numbered it's going to be important + + align:start position:0% +are numbered it's going to be important + + + align:start position:0% +are numbered it's going to be important +um + + align:start position:0% + + + + align:start position:0% + +and if I can add that vertex add it if + + align:start position:0% +and if I can add that vertex add it if + + + align:start position:0% +and if I can add that vertex add it if +he is not adjacent to S add it okay I + + align:start position:0% +he is not adjacent to S add it okay I + + + align:start position:0% +he is not adjacent to S add it okay I +mean this is this whole world is weird + + align:start position:0% +mean this is this whole world is weird + + + align:start position:0% +mean this is this whole world is weird +because it's all about polinomial time + + align:start position:0% +because it's all about polinomial time + + + align:start position:0% +because it's all about polinomial time +problems here's a polinomial Time + + align:start position:0% +problems here's a polinomial Time + + + align:start position:0% +problems here's a polinomial Time +algorithm it produces what I would call + + align:start position:0% +algorithm it produces what I would call + + + align:start position:0% +algorithm it produces what I would call +the lexically first uh maximal + + align:start position:0% +the lexically first uh maximal + + + align:start position:0% +the lexically first uh maximal +independent set because it adds one if + + align:start position:0% +independent set because it adds one if + + + align:start position:0% +independent set because it adds one if +it can and then subject to that it adds + + align:start position:0% +it can and then subject to that it adds + + + align:start position:0% +it can and then subject to that it adds +two if it can and so on we always add + + align:start position:0% +two if it can and so on we always add + + + align:start position:0% +two if it can and so on we always add +one I guess uh so in in with this + + align:start position:0% +one I guess uh so in in with this + + + align:start position:0% +one I guess uh so in in with this +labeling of vertices it finds the + + align:start position:0% +labeling of vertices it finds the + + + align:start position:0% +labeling of vertices it finds the +lexically smallest one suppose you want + + align:start position:0% +lexically smallest one suppose you want + + + align:start position:0% +lexically smallest one suppose you want +to find the lexically smallest maximal + + align:start position:0% +to find the lexically smallest maximal + + + align:start position:0% +to find the lexically smallest maximal +independent set finding a maximal + + align:start position:0% +independent set finding a maximal + + + align:start position:0% +independent set finding a maximal +independent set is uh can be done in + + align:start position:0% +independent set is uh can be done in + + + align:start position:0% +independent set is uh can be done in +parallel but finding lexically smallest + + align:start position:0% +parallel but finding lexically smallest + + + align:start position:0% +parallel but finding lexically smallest +one cannot + + align:start position:0% +one cannot + + + align:start position:0% +one cannot +uh this is p + + align:start position:0% + + + + align:start position:0% + +complete and the reduction is super cute + + align:start position:0% +complete and the reduction is super cute + + + align:start position:0% +complete and the reduction is super cute +um + + align:start position:0% +um + + + align:start position:0% +um +reduction + + align:start position:0% +reduction + + + align:start position:0% +reduction +from + + align:start position:0% +from + + + align:start position:0% +from +nor + + align:start position:0% +nor + + + align:start position:0% +nor +CVP suppose I give you a nor circuit and + + align:start position:0% +CVP suppose I give you a nor circuit and + + + align:start position:0% +CVP suppose I give you a nor circuit and +I want to know whether the output + + align:start position:0% +I want to know whether the output + + + align:start position:0% +I want to know whether the output +becomes true uh what I'm going to do is + + align:start position:0% +becomes true uh what I'm going to do is + + + align:start position:0% +becomes true uh what I'm going to do is +build a special vertex called zero + + align:start position:0% +build a special vertex called zero + + + align:start position:0% +build a special vertex called zero +uh which is connected to all of the zero + + align:start position:0% +uh which is connected to all of the zero + + + align:start position:0% +uh which is connected to all of the zero +inputs so the circuit has zero inputs + + align:start position:0% +inputs so the circuit has zero inputs + + + align:start position:0% +inputs so the circuit has zero inputs +and one inputs I'm going to make the + + align:start position:0% +and one inputs I'm going to make the + + + align:start position:0% +and one inputs I'm going to make the +inputs into + + align:start position:0% +inputs into + + + align:start position:0% +inputs into +nodes okay and so there are some one + + align:start position:0% +nodes okay and so there are some one + + + align:start position:0% +nodes okay and so there are some one +nodes those are just going to be nodes + + align:start position:0% +nodes those are just going to be nodes + + + align:start position:0% +nodes those are just going to be nodes +they connect to whatever the gates are + + align:start position:0% +they connect to whatever the gates are + + + align:start position:0% +they connect to whatever the gates are +uh then these things are combined with + + align:start position:0% +uh then these things are combined with + + + align:start position:0% +uh then these things are combined with +various Gates and so on I'm just going + + align:start position:0% +various Gates and so on I'm just going + + + align:start position:0% +various Gates and so on I'm just going +to replace a gate with a node I'm going + + align:start position:0% +to replace a gate with a node I'm going + + + align:start position:0% +to replace a gate with a node I'm going +to replace a an input with a node and + + align:start position:0% +to replace a an input with a node and + + + align:start position:0% +to replace a an input with a node and +I'm going to add a special node zero + + align:start position:0% +I'm going to add a special node zero + + + align:start position:0% +I'm going to add a special node zero +which is numbered first that next to all + + align:start position:0% +which is numbered first that next to all + + + align:start position:0% +which is numbered first that next to all +of the zero inputs and then I'm also + + align:start position:0% +of the zero inputs and then I'm also + + + align:start position:0% +of the zero inputs and then I'm also +going to order the vertices in a + + align:start position:0% +going to order the vertices in a + + + align:start position:0% +going to order the vertices in a +topological sort so this will have the + + align:start position:0% +topological sort so this will have the + + + align:start position:0% +topological sort so this will have the +earliest number then these guys and so + + align:start position:0% +earliest number then these guys and so + + + align:start position:0% +earliest number then these guys and so +on so any topological sort uh Lemma + + align:start position:0% +on so any topological sort uh Lemma + + + align:start position:0% +on so any topological sort uh Lemma +topological sorting can be done in + + align:start position:0% +topological sorting can be done in + + + align:start position:0% +topological sorting can be done in +parallel there's an NC algorithm for + + align:start position:0% +parallel there's an NC algorithm for + + + align:start position:0% +parallel there's an NC algorithm for +topological sorting we need that here + + align:start position:0% +topological sorting we need that here + + + align:start position:0% +topological sorting we need that here +because this reduction has to be in + + align:start position:0% +because this reduction has to be in + + + align:start position:0% +because this reduction has to be in +NC but once you do that I claim uh that + + align:start position:0% +NC but once you do that I claim uh that + + + align:start position:0% +NC but once you do that I claim uh that +V will be in s + + align:start position:0% +V will be in s + + + align:start position:0% +V will be in s +if and only if uh that gate outputs a + + align:start position:0% +if and only if uh that gate outputs a + + + align:start position:0% +if and only if uh that gate outputs a +one proof by + + align:start position:0% +one proof by + + + align:start position:0% +one proof by +induction so initially this is going to + + align:start position:0% +induction so initially this is going to + + + align:start position:0% +induction so initially this is going to +be put in the independent set which + + align:start position:0% +be put in the independent set which + + + align:start position:0% +be put in the independent set which +means these guys won't but these guys + + align:start position:0% +means these guys won't but these guys + + + align:start position:0% +means these guys won't but these guys +will because they're lexically first or + + align:start position:0% +will because they're lexically first or + + + align:start position:0% +will because they're lexically first or +they're first in the topological order + + align:start position:0% +they're first in the topological order + + + align:start position:0% +they're first in the topological order +and then + + align:start position:0% +and then + + + align:start position:0% +and then +induction there's only one type of gate + + align:start position:0% +induction there's only one type of gate + + + align:start position:0% +induction there's only one type of gate +here it's a nor so basically this guy + + align:start position:0% +here it's a nor so basically this guy + + + align:start position:0% +here it's a nor so basically this guy +will be circled if and only if uh + + align:start position:0% +will be circled if and only if uh + + + align:start position:0% +will be circled if and only if uh +neither of the inputs are circled so + + align:start position:0% +neither of the inputs are circled so + + + align:start position:0% +neither of the inputs are circled so +that's a nor and so then the decision + + align:start position:0% +that's a nor and so then the decision + + + align:start position:0% +that's a nor and so then the decision +question is there's some last thing + + align:start position:0% +question is there's some last thing + + + align:start position:0% +question is there's some last thing +corresponding to the output it's going + + align:start position:0% +corresponding to the output it's going + + + align:start position:0% +corresponding to the output it's going +to be circled if and only if the circuit + + align:start position:0% +to be circled if and only if the circuit + + + align:start position:0% +to be circled if and only if the circuit +outputs one and that's it it's kind of + + align:start position:0% +outputs one and that's it it's kind of + + + align:start position:0% +outputs one and that's it it's kind of +beautiful reduction and I just for fun I + + align:start position:0% +beautiful reduction and I just for fun I + + + align:start position:0% +beautiful reduction and I just for fun I +have a list of some more Peak complete + + align:start position:0% +have a list of some more Peak complete + + + align:start position:0% +have a list of some more Peak complete +problems without proofs uh Game of Life + + align:start position:0% +problems without proofs uh Game of Life + + + align:start position:0% +problems without proofs uh Game of Life +obviously uh when you're given a Time + + align:start position:0% +obviously uh when you're given a Time + + + align:start position:0% +obviously uh when you're given a Time +bound that is written in uny and I want + + align:start position:0% +bound that is written in uny and I want + + + align:start position:0% +bound that is written in uny and I want +to know does this cell is this cell + + align:start position:0% +to know does this cell is this cell + + + align:start position:0% +to know does this cell is this cell +alive at time T where T is written in + + align:start position:0% +alive at time T where T is written in + + + align:start position:0% +alive at time T where T is written in +uny by the proof we did already that's P + + align:start position:0% +uny by the proof we did already that's P + + + align:start position:0% +uny by the proof we did already that's P +complete um + + align:start position:0% +complete um + + + align:start position:0% +complete um +and just it's with the UN un version + + align:start position:0% +and just it's with the UN un version + + + align:start position:0% +and just it's with the UN un version +also onedimensional cellular automa same + + align:start position:0% +also onedimensional cellular automa same + + + align:start position:0% +also onedimensional cellular automa same +kind of thing generalized geography + + align:start position:0% +kind of thing generalized geography + + + align:start position:0% +kind of thing generalized geography +remember that uh pbas complete problem + + align:start position:0% +remember that uh pbas complete problem + + + align:start position:0% +remember that uh pbas complete problem +but if you have an ayylic directed graph + + align:start position:0% +but if you have an ayylic directed graph + + + align:start position:0% +but if you have an ayylic directed graph +and you want to solve geography on an + + align:start position:0% +and you want to solve geography on an + + + align:start position:0% +and you want to solve geography on an +ayylic directed graph so two-player game + + align:start position:0% +ayylic directed graph so two-player game + + + align:start position:0% +ayylic directed graph so two-player game +that can be done in polinomial time but + + align:start position:0% +that can be done in polinomial time but + + + align:start position:0% +that can be done in polinomial time but +it's p complete uh if I have a point set + + align:start position:0% +it's p complete uh if I have a point set + + + align:start position:0% +it's p complete uh if I have a point set +in the plane and I compute the convex + + align:start position:0% +in the plane and I compute the convex + + + align:start position:0% +in the plane and I compute the convex +Hall remove remove those points compute + + align:start position:0% +Hall remove remove those points compute + + + align:start position:0% +Hall remove remove those points compute +the convex Hall remove those points it's + + align:start position:0% +the convex Hall remove those points it's + + + align:start position:0% +the convex Hall remove those points it's +called an onion peeling and I given a a + + align:start position:0% +called an onion peeling and I given a a + + + align:start position:0% +called an onion peeling and I given a a +point I want to know uh is it on the K + + align:start position:0% +point I want to know uh is it on the K + + + align:start position:0% +point I want to know uh is it on the K +layer for some value K that's P complete + + align:start position:0% +layer for some value K that's P complete + + + align:start position:0% +layer for some value K that's P complete +basically you have to sequentially + + align:start position:0% +basically you have to sequentially + + + align:start position:0% +basically you have to sequentially +compute the convex + + align:start position:0% +compute the convex + + + align:start position:0% +compute the convex +holse uh another good canonical one is + + align:start position:0% +holse uh another good canonical one is + + + align:start position:0% +holse uh another good canonical one is +multi- Lisk ranking suppose I give you K + + align:start position:0% +multi- Lisk ranking suppose I give you K + + + align:start position:0% +multi- Lisk ranking suppose I give you K +say sorted lists of numbers and I want + + align:start position:0% +say sorted lists of numbers and I want + + + align:start position:0% +say sorted lists of numbers and I want +to know given an + + align:start position:0% +to know given an + + + align:start position:0% +to know given an +item uh what is its rank in the union of + + align:start position:0% +item uh what is its rank in the union of + + + align:start position:0% +item uh what is its rank in the union of +the lists so items can appear in + + align:start position:0% +the lists so items can appear in + + + align:start position:0% +the lists so items can appear in +multiple lists and I want to know is it + + align:start position:0% +multiple lists and I want to know is it + + + align:start position:0% +multiple lists and I want to know is it +the Ki item in sorted order in the union + + align:start position:0% +the Ki item in sorted order in the union + + + align:start position:0% +the Ki item in sorted order in the union +so basically want to sort the Union uh + + align:start position:0% +so basically want to sort the Union uh + + + align:start position:0% +so basically want to sort the Union uh +that's P + + align:start position:0% +that's P + + + align:start position:0% +that's P +complete um if I want to compute a mod + + align:start position:0% +complete um if I want to compute a mod + + + align:start position:0% +complete um if I want to compute a mod +B1 mod B2 mod B3 mod B4 n times so the + + align:start position:0% +B1 mod B2 mod B3 mod B4 n times so the + + + align:start position:0% +B1 mod B2 mod B3 mod B4 n times so the +repeated mod I want to know whether that + + align:start position:0% +repeated mod I want to know whether that + + + align:start position:0% +repeated mod I want to know whether that +equals zero that's P complete uh if I + + align:start position:0% +equals zero that's P complete uh if I + + + align:start position:0% +equals zero that's P complete uh if I +wanted to linear programming that's + + align:start position:0% +wanted to linear programming that's + + + align:start position:0% +wanted to linear programming that's +polinomial time uh this is p complete + + align:start position:0% +polinomial time uh this is p complete + + + align:start position:0% +polinomial time uh this is p complete +even when the coefficients are zero and + + align:start position:0% +even when the coefficients are zero and + + + align:start position:0% +even when the coefficients are zero and +one so this is called strongly P + + align:start position:0% +one so this is called strongly P + + + align:start position:0% +one so this is called strongly P +complete you don't need large numbers + + align:start position:0% +complete you don't need large numbers + + + align:start position:0% +complete you don't need large numbers +whereas something like Max + + align:start position:0% +whereas something like Max + + + align:start position:0% +whereas something like Max +flow uh is weekly PE complete and can be + + align:start position:0% +flow uh is weekly PE complete and can be + + + align:start position:0% +flow uh is weekly PE complete and can be +in the analogy to fully full pasas fully + + align:start position:0% +in the analogy to fully full pasas fully + + + align:start position:0% +in the analogy to fully full pasas fully +polinomial time approximation scheme + + align:start position:0% +polinomial time approximation scheme + + + align:start position:0% +polinomial time approximation scheme +there is a fully RNC approximation + + align:start position:0% +there is a fully RNC approximation + + + align:start position:0% +there is a fully RNC approximation +scheme R means there's randomization I + + align:start position:0% +scheme R means there's randomization I + + + align:start position:0% +scheme R means there's randomization I +think it's open whether you can get rid + + align:start position:0% +think it's open whether you can get rid + + + align:start position:0% +think it's open whether you can get rid +of that uh there's some fun open + + align:start position:0% +of that uh there's some fun open + + + align:start position:0% +of that uh there's some fun open +problems like deciding whether two + + align:start position:0% +problems like deciding whether two + + + align:start position:0% +problems like deciding whether two +numbers are relatively prime is + + align:start position:0% +numbers are relatively prime is + + + align:start position:0% +numbers are relatively prime is +conjectured to be P complete but we + + align:start position:0% +conjectured to be P complete but we + + + align:start position:0% +conjectured to be P complete but we +don't know Computing a to the B mod C is + + align:start position:0% +don't know Computing a to the B mod C is + + + align:start position:0% +don't know Computing a to the B mod C is +conjectured to be P complete uh maximum + + align:start position:0% +conjectured to be P complete uh maximum + + + align:start position:0% +conjectured to be P complete uh maximum +matching is conjectured to be uh with + + align:start position:0% +matching is conjectured to be uh with + + + align:start position:0% +matching is conjectured to be uh with +large Edge weights is conjectured to be + + align:start position:0% +large Edge weights is conjectured to be + + + align:start position:0% +large Edge weights is conjectured to be +P complete but there is a pseudo RNC + + align:start position:0% +P complete but there is a pseudo RNC + + + align:start position:0% +P complete but there is a pseudo RNC +algorithm so the weights are small and + + align:start position:0% +algorithm so the weights are small and + + + align:start position:0% +algorithm so the weights are small and +you allow randomization then it's then + + align:start position:0% +you allow randomization then it's then + + + align:start position:0% +you allow randomization then it's then +it's parallelizable uh another open + + align:start position:0% +it's parallelizable uh another open + + + align:start position:0% +it's parallelizable uh another open +problem is graph isomorphism with + + align:start position:0% +problem is graph isomorphism with + + + align:start position:0% +problem is graph isomorphism with +bounded degree which is polinomial time + + align:start position:0% +bounded degree which is polinomial time + + + align:start position:0% +bounded degree which is polinomial time +I didn't know that but bounded degree + + align:start position:0% +I didn't know that but bounded degree + + + align:start position:0% +I didn't know that but bounded degree +graph morphism is easy in a Serial + + align:start position:0% +graph morphism is easy in a Serial + + + align:start position:0% +graph morphism is easy in a Serial +setting but conjectures as hard in a + + align:start position:0% +setting but conjectures as hard in a + + + align:start position:0% +setting but conjectures as hard in a +parallel setting so lots of things out + + align:start position:0% +parallel setting so lots of things out + + + align:start position:0% +parallel setting so lots of things out +there um I would I don't see too many + + align:start position:0% +there um I would I don't see too many + + + align:start position:0% +there um I would I don't see too many +papers about PE completeness these days + + align:start position:0% +papers about PE completeness these days + + + align:start position:0% +papers about PE completeness these days +but it's a fun thing when once you + + align:start position:0% +but it's a fun thing when once you + + + align:start position:0% +but it's a fun thing when once you +decide your problem is in P next thing + + align:start position:0% +decide your problem is in P next thing + + + align:start position:0% +decide your problem is in P next thing +next level you can find hardness + + align:start position:0% +next level you can find hardness + + + align:start position:0% +next level you can find hardness +anywhere it turns out next thing is to + + align:start position:0% +anywhere it turns out next thing is to + + + align:start position:0% +anywhere it turns out next thing is to +prove uh P completeness for your problem + + align:start position:0% +prove uh P completeness for your problem + + + align:start position:0% +prove uh P completeness for your problem +make sure there's no parallel algorithm + + align:start position:0% +make sure there's no parallel algorithm + + + align:start position:0% +make sure there's no parallel algorithm +or find an NC algorithm if you do the + + align:start position:0% +or find an NC algorithm if you do the + + + align:start position:0% +or find an NC algorithm if you do the +upper bound side once you have NC you + + align:start position:0% +upper bound side once you have NC you + + + align:start position:0% +upper bound side once you have NC you +want to get the smallest depth possible + + align:start position:0% +want to get the smallest depth possible + + + align:start position:0% +want to get the smallest depth possible +that's another + + align:start position:0% +that's another + + + align:start position:0% +that's another +story cool that's it for today \ No newline at end of file diff --git a/LM5f-g40Gxg.txt b/LM5f-g40Gxg.txt new file mode 100644 index 0000000000000000000000000000000000000000..a4c6234dc9fbbed0a819f8238c65787efcc27567 --- /dev/null +++ b/LM5f-g40Gxg.txt @@ -0,0 +1,7899 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu I want to go over the + + align:start position:0% +ocw.mit.edu I want to go over the + + + align:start position:0% +ocw.mit.edu I want to go over the +uh homework I will post right after the + + align:start position:0% +uh homework I will post right after the + + + align:start position:0% +uh homework I will post right after the +class I wanted to talk talk to you about + + align:start position:0% +class I wanted to talk talk to you about + + + align:start position:0% +class I wanted to talk talk to you about +it first these are really worksheets + + align:start position:0% +it first these are really worksheets + + + align:start position:0% +it first these are really worksheets +It's + + align:start position:0% +It's + + + align:start position:0% +It's +homework that you should all get + + align:start position:0% +homework that you should all get + + + align:start position:0% +homework that you should all get +everything + + align:start position:0% +everything + + + align:start position:0% +everything +right uh I will do a separate homework + + align:start position:0% +right uh I will do a separate homework + + + align:start position:0% +right uh I will do a separate homework +that will make up for some of the bad + + align:start position:0% +that will make up for some of the bad + + + align:start position:0% +that will make up for some of the bad +quiz + + align:start position:0% +quiz + + + align:start position:0% +quiz +performances I know you requested that + + align:start position:0% +performances I know you requested that + + + align:start position:0% +performances I know you requested that +that's not what this is this is to help + + align:start position:0% +that's not what this is this is to help + + + align:start position:0% +that's not what this is this is to help +you review and uh I selected a bunch of + + align:start position:0% +you review and uh I selected a bunch of + + + align:start position:0% +you review and uh I selected a bunch of +pictures I'm just giving you it this + + align:start position:0% +pictures I'm just giving you it this + + + align:start position:0% +pictures I'm just giving you it this +will all be posted + + align:start position:0% + + + + align:start position:0% + +uh I guess + + align:start position:0% +uh I guess + + + align:start position:0% +uh I guess +uh do you all do you all have access to + + align:start position:0% + + + + align:start position:0% + +printers if you have problems printing + + align:start position:0% +printers if you have problems printing + + + align:start position:0% +printers if you have problems printing +it just uh come with us after class + + align:start position:0% +it just uh come with us after class + + + align:start position:0% +it just uh come with us after class +we'll print it for you but I'm going to + + align:start position:0% +we'll print it for you but I'm going to + + + align:start position:0% +we'll print it for you but I'm going to +show you what it is this these are the + + align:start position:0% +show you what it is this these are the + + + align:start position:0% +show you what it is this these are the +worksheets and you can see if we look at + + align:start position:0% +worksheets and you can see if we look at + + + align:start position:0% +worksheets and you can see if we look at +one of them here this is a pretty + + align:start position:0% +one of them here this is a pretty + + + align:start position:0% +one of them here this is a pretty +straightforward one that you should + + align:start position:0% +straightforward one that you should + + + align:start position:0% +straightforward one that you should +remember remember + + align:start position:0% +remember remember + + + align:start position:0% +remember remember +now uh here you + + align:start position:0% +now uh here you + + + align:start position:0% +now uh here you +have places to uh to write the names and + + align:start position:0% +have places to uh to write the names and + + + align:start position:0% +have places to uh to write the names and +so to just to remind you what I want + + align:start position:0% +so to just to remind you what I want + + + align:start position:0% +so to just to remind you what I want +here in question one I say in slide + + align:start position:0% +here in question one I say in slide + + + align:start position:0% +here in question one I say in slide +number one that refers to the number of + + align:start position:0% +number one that refers to the number of + + + align:start position:0% +number one that refers to the number of +the slide is + + align:start position:0% +the slide is + + + align:start position:0% +the slide is +that + + align:start position:0% +that + + + align:start position:0% +that +okay the number is actually written in + + align:start position:0% +okay the number is actually written in + + + align:start position:0% +okay the number is actually written in +the corner okay and then I list ABCDE E + + align:start position:0% +the corner okay and then I list ABCDE E + + + align:start position:0% +the corner okay and then I list ABCDE E +I just want you to write the the English + + align:start position:0% +I just want you to write the the English + + + align:start position:0% +I just want you to write the the English +and the Greek or Latin okay for each of + + align:start position:0% +and the Greek or Latin okay for each of + + + align:start position:0% +and the Greek or Latin okay for each of +those subdivisions that's what you do + + align:start position:0% +those subdivisions that's what you do + + + align:start position:0% +those subdivisions that's what you do +for that + + align:start position:0% +for that + + + align:start position:0% +for that +one okay and uh for something like this + + align:start position:0% +one okay and uh for something like this + + + align:start position:0% +one okay and uh for something like this +all all of these are like that here I + + align:start position:0% +all all of these are like that here I + + + align:start position:0% +all all of these are like that here I +ask you to to name the + + align:start position:0% +ask you to to name the + + + align:start position:0% +ask you to to name the +parts that the that are being pointed to + + align:start position:0% +parts that the that are being pointed to + + + align:start position:0% +parts that the that are being pointed to +here I ask you to color in the pathway + + align:start position:0% +here I ask you to color in the pathway + + + align:start position:0% +here I ask you to color in the pathway +like I did in class and I want a local + + align:start position:0% +like I did in class and I want a local + + + align:start position:0% +like I did in class and I want a local +reflex Channel + + align:start position:0% +reflex Channel + + + align:start position:0% +reflex Channel +okay now whereas this they're blank + + align:start position:0% +okay now whereas this they're blank + + + align:start position:0% +okay now whereas this they're blank +brain + + align:start position:0% +brain + + + align:start position:0% +brain +diagrams they're pretty similar to the + + align:start position:0% +diagrams they're pretty similar to the + + + align:start position:0% +diagrams they're pretty similar to the +ones I used in class but they match the + + align:start position:0% +ones I used in class but they match the + + + align:start position:0% +ones I used in class but they match the +text of the + + align:start position:0% +text of the + + + align:start position:0% +text of the +book uh very well so and then I ask you + + align:start position:0% +book uh very well so and then I ask you + + + align:start position:0% +book uh very well so and then I ask you +questions about them + + align:start position:0% +questions about them + + + align:start position:0% +questions about them +so but for those because you have to if + + align:start position:0% +so but for those because you have to if + + + align:start position:0% +so but for those because you have to if +you have to draw on it notice I put it + + align:start position:0% +you have to draw on it notice I put it + + + align:start position:0% +you have to draw on it notice I put it +put it right in those are the ones you + + align:start position:0% +put it right in those are the ones you + + + align:start position:0% +put it right in those are the ones you +would need + + align:start position:0% +would need + + + align:start position:0% +would need +printed + + align:start position:0% +printed + + + align:start position:0% +printed +and for this one too because I'm asking + + align:start position:0% +and for this one too because I'm asking + + + align:start position:0% +and for this one too because I'm asking +for + + align:start position:0% +for + + + align:start position:0% +for +drawing + + align:start position:0% +drawing + + + align:start position:0% +drawing +uh and then I ask the question up here + + align:start position:0% +uh and then I ask the question up here + + + align:start position:0% +uh and then I ask the question up here +here I want you to draw a primary sensor + + align:start position:0% +here I want you to draw a primary sensor + + + align:start position:0% +here I want you to draw a primary sensor +neuron I've already drawn it for you on + + align:start position:0% +neuron I've already drawn it for you on + + + align:start position:0% +neuron I've already drawn it for you on +the + + align:start position:0% +the + + + align:start position:0% +the +horizontal + + align:start position:0% +horizontal + + + align:start position:0% +horizontal +uh diagram there but I want you to do + + align:start position:0% +uh diagram there but I want you to do + + + align:start position:0% +uh diagram there but I want you to do +that here too and I want you to show the + + align:start position:0% +that here too and I want you to show the + + + align:start position:0% +that here too and I want you to show the +spinothalamic track and then later I do + + align:start position:0% +spinothalamic track and then later I do + + + align:start position:0% +spinothalamic track and then later I do +the same thing for the I column and + + align:start position:0% +the same thing for the I column and + + + align:start position:0% +the same thing for the I column and +medial liscus and then I do the same + + align:start position:0% +medial liscus and then I do the same + + + align:start position:0% +medial liscus and then I do the same +thing for the cortical spinal so you can + + align:start position:0% +thing for the cortical spinal so you can + + + align:start position:0% +thing for the cortical spinal so you can +find those figures they're all in the + + align:start position:0% +find those figures they're all in the + + + align:start position:0% +find those figures they're all in the +book they were all in the slides too and + + align:start position:0% + + + + align:start position:0% + +uh and I want you to draw them in but if + + align:start position:0% +uh and I want you to draw them in but if + + + align:start position:0% +uh and I want you to draw them in but if +all you're going to do is find it and + + align:start position:0% +all you're going to do is find it and + + + align:start position:0% +all you're going to do is find it and +then go back and forth to get every + + align:start position:0% +then go back and forth to get every + + + align:start position:0% +then go back and forth to get every +detail right you're not learning much + + align:start position:0% +detail right you're not learning much + + + align:start position:0% +detail right you're not learning much +you have to study it then put it aside + + align:start position:0% +you have to study it then put it aside + + + align:start position:0% +you have to study it then put it aside +and then try it try to draw it and if + + align:start position:0% +and then try it try to draw it and if + + + align:start position:0% +and then try it try to draw it and if +you hand something in that's with all + + align:start position:0% +you hand something in that's with all + + + align:start position:0% +you hand something in that's with all +kinds of things crossed out because you + + align:start position:0% +kinds of things crossed out because you + + + align:start position:0% +kinds of things crossed out because you +didn't write it that's all right I want + + align:start position:0% +didn't write it that's all right I want + + + align:start position:0% +didn't write it that's all right I want +you to use it to learn about these + + align:start position:0% + + + + align:start position:0% + +things some of these might be on the + + align:start position:0% +things some of these might be on the + + + align:start position:0% +things some of these might be on the +midterm okay or I might just ask + + align:start position:0% +midterm okay or I might just ask + + + align:start position:0% +midterm okay or I might just ask +questions about them but yeah there + + align:start position:0% +questions about them but yeah there + + + align:start position:0% +questions about them but yeah there +might be things like this on the midterm + + align:start position:0% +might be things like this on the midterm + + + align:start position:0% +might be things like this on the midterm +definitely okay so that'll all be posted + + align:start position:0% +definitely okay so that'll all be posted + + + align:start position:0% +definitely okay so that'll all be posted +and that is just to help you review + + align:start position:0% + + + + align:start position:0% + +we can have it due Monday I + + align:start position:0% +we can have it due Monday I + + + align:start position:0% +we can have it due Monday I +think and I will get another one posted + + align:start position:0% +think and I will get another one posted + + + align:start position:0% +think and I will get another one posted +where you just have because these are + + align:start position:0% +where you just have because these are + + + align:start position:0% +where you just have because these are +all very straight PR you just have to + + align:start position:0% +all very straight PR you just have to + + + align:start position:0% +all very straight PR you just have to +find them learn + + align:start position:0% +find them learn + + + align:start position:0% +find them learn +them try to do it you + + align:start position:0% +them try to do it you + + + align:start position:0% +them try to do it you +know some of many of them are they I + + align:start position:0% +know some of many of them are they I + + + align:start position:0% +know some of many of them are they I +give you the diagram and I want you to + + align:start position:0% +give you the diagram and I want you to + + + align:start position:0% +give you the diagram and I want you to +I've eliminated a lot of the labels + + align:start position:0% +I've eliminated a lot of the labels + + + align:start position:0% +I've eliminated a lot of the labels +you know so like in the one with the + + align:start position:0% +you know so like in the one with the + + + align:start position:0% +you know so like in the one with the +meninges and the Gia you know you should + + align:start position:0% +meninges and the Gia you know you should + + + align:start position:0% +meninges and the Gia you know you should +know which ones here are the as sites + + align:start position:0% +know which ones here are the as sites + + + align:start position:0% +know which ones here are the as sites +which is the Duro is what is the pan + + align:start position:0% +which is the Duro is what is the pan + + + align:start position:0% +which is the Duro is what is the pan +what is + + align:start position:0% +what is + + + align:start position:0% +what is +the the uh Ira noid + + align:start position:0% +the the uh Ira noid + + + align:start position:0% +the the uh Ira noid +so you need to know those things and + + align:start position:0% +so you need to know those things and + + + align:start position:0% +so you need to know those things and +it's good to have have it not just the + + align:start position:0% +it's good to have have it not just the + + + align:start position:0% +it's good to have have it not just the +words but have it in your spatial memory + + align:start position:0% +words but have it in your spatial memory + + + align:start position:0% +words but have it in your spatial memory +too so that's why we're doing it + + align:start position:0% +too so that's why we're doing it + + + align:start position:0% +too so that's why we're doing it +use it to to practice and + + align:start position:0% +use it to to practice and + + + align:start position:0% +use it to to practice and +review and then I will give you some + + align:start position:0% +review and then I will give you some + + + align:start position:0% +review and then I will give you some +questions I think mostly on the motor + + align:start position:0% +questions I think mostly on the motor + + + align:start position:0% +questions I think mostly on the motor +system because you haven't had any + + align:start position:0% +system because you haven't had any + + + align:start position:0% +system because you haven't had any +homework on that and I could give a + + align:start position:0% +homework on that and I could give a + + + align:start position:0% +homework on that and I could give a +little bit on + + align:start position:0% +little bit on + + + align:start position:0% +little bit on +development things that I know you can + + align:start position:0% +development things that I know you can + + + align:start position:0% +development things that I know you can +find and + + align:start position:0% +find and + + + align:start position:0% +find and +uh we'll use that as I promised to make + + align:start position:0% +uh we'll use that as I promised to make + + + align:start position:0% +uh we'll use that as I promised to make +up for bad quiz + + align:start position:0% +up for bad quiz + + + align:start position:0% +up for bad quiz +grades we'll decide exactly how we're + + align:start position:0% +grades we'll decide exactly how we're + + + align:start position:0% +grades we'll decide exactly how we're +going to do that but I think that's fine + + align:start position:0% +going to do that but I think that's fine + + + align:start position:0% +going to do that but I think that's fine +all right so + + align:start position:0% + + + + align:start position:0% + +let's 17 17 through the brain States + + align:start position:0% + + + + align:start position:0% + +chapter then we do the start sensory + + align:start position:0% +chapter then we do the start sensory + + + align:start position:0% +chapter then we do the start sensory +systems afterward + + align:start position:0% + + + + align:start position:0% + +afterwards after the break or wait a + + align:start position:0% +afterwards after the break or wait a + + + align:start position:0% +afterwards after the break or wait a +minute do we have a Friday I guess + + align:start position:0% +minute do we have a Friday I guess + + + align:start position:0% +minute do we have a Friday I guess +there's a we started + + align:start position:0% +there's a we started + + + align:start position:0% +there's a we started +start it just before the break all right + + align:start position:0% +start it just before the break all right + + + align:start position:0% +start it just before the break all right +so this is where we were uh it's a + + align:start position:0% +so this is where we were uh it's a + + + align:start position:0% +so this is where we were uh it's a +little bit more on + + align:start position:0% + + + + align:start position:0% + +the a little bit more in the + + align:start position:0% +the a little bit more in the + + + align:start position:0% +the a little bit more in the +introductory chapter to the motor system + + align:start position:0% +introductory chapter to the motor system + + + align:start position:0% +introductory chapter to the motor system +where we're talking about uh these uh + + align:start position:0% +where we're talking about uh these uh + + + align:start position:0% +where we're talking about uh these uh +multi-purpose movements there was a lot + + align:start position:0% +multi-purpose movements there was a lot + + + align:start position:0% +multi-purpose movements there was a lot +about Locomotion last time um we've also + + align:start position:0% +about Locomotion last time um we've also + + + align:start position:0% +about Locomotion last time um we've also +talked about the other + + align:start position:0% +talked about the other + + + align:start position:0% +talked about the other +movements + + align:start position:0% +movements + + + align:start position:0% +movements +uh all that I have what remains is I + + align:start position:0% +uh all that I have what remains is I + + + align:start position:0% +uh all that I have what remains is I +discuss a little bit about uh evolution + + align:start position:0% +discuss a little bit about uh evolution + + + align:start position:0% +discuss a little bit about uh evolution +of that ability and just because we know + + align:start position:0% +of that ability and just because we know + + + align:start position:0% +of that ability and just because we know +that the tectum is the dominant + + align:start position:0% +that the tectum is the dominant + + + align:start position:0% +that the tectum is the dominant +structure now in most + + align:start position:0% + + + + align:start position:0% + +animals except perhaps in animals like + + align:start position:0% +animals except perhaps in animals like + + + align:start position:0% +animals except perhaps in animals like +humans and even monkeys where the + + align:start position:0% +humans and even monkeys where the + + + align:start position:0% +humans and even monkeys where the +cortexes become so dominant over most of + + align:start position:0% +cortexes become so dominant over most of + + + align:start position:0% +cortexes become so dominant over most of +these functions but in most animals it + + align:start position:0% +these functions but in most animals it + + + align:start position:0% +these functions but in most animals it +is still very important and has an + + align:start position:0% +is still very important and has an + + + align:start position:0% +is still very important and has an +importance even in humans More Than + + align:start position:0% +importance even in humans More Than + + + align:start position:0% +importance even in humans More Than +People + + align:start position:0% + + + + align:start position:0% + +realize so I do mention a little bit + + align:start position:0% +realize so I do mention a little bit + + + align:start position:0% +realize so I do mention a little bit +about + + align:start position:0% + + + + align:start position:0% + +uh some of the early controls and + + align:start position:0% +uh some of the early controls and + + + align:start position:0% +uh some of the early controls and +I then I but I'm mostly emphasizing two + + align:start position:0% +I then I but I'm mostly emphasizing two + + + align:start position:0% +I then I but I'm mostly emphasizing two +very different functions of the tectum + + align:start position:0% +very different functions of the tectum + + + align:start position:0% +very different functions of the tectum +one involving Locomotion we talked about + + align:start position:0% +one involving Locomotion we talked about + + + align:start position:0% +one involving Locomotion we talked about +Escape movements you know + + align:start position:0% +Escape movements you know + + + align:start position:0% +Escape movements you know +uh but normally when animals are + + align:start position:0% +uh but normally when animals are + + + align:start position:0% +uh but normally when animals are +escaping they also Orient they don't + + align:start position:0% +escaping they also Orient they don't + + + align:start position:0% +escaping they also Orient they don't +generally Orient with respect to the + + align:start position:0% +generally Orient with respect to the + + + align:start position:0% +generally Orient with respect to the +animal they're escaping from they Orient + + align:start position:0% +animal they're escaping from they Orient + + + align:start position:0% +animal they're escaping from they Orient +towards safe places if they're near + + align:start position:0% +towards safe places if they're near + + + align:start position:0% +towards safe places if they're near +their tunnel they head for the tunnel if + + align:start position:0% +their tunnel they head for the tunnel if + + + align:start position:0% +their tunnel they head for the tunnel if +they're near any Hiding Place uh any + + align:start position:0% +they're near any Hiding Place uh any + + + align:start position:0% +they're near any Hiding Place uh any +place they can crawl into to get away + + align:start position:0% +place they can crawl into to get away + + + align:start position:0% +place they can crawl into to get away +they head for that and they're extremely + + align:start position:0% +they head for that and they're extremely + + + align:start position:0% +they head for that and they're extremely +good at finding that very very + + align:start position:0% +good at finding that very very + + + align:start position:0% +good at finding that very very +rapidly + + align:start position:0% +rapidly + + + align:start position:0% +rapidly +and I say a little bit about the tectum + + align:start position:0% +and I say a little bit about the tectum + + + align:start position:0% +and I say a little bit about the tectum +and pretectum here because I go over + + align:start position:0% +and pretectum here because I go over + + + align:start position:0% +and pretectum here because I go over +this in the visual system later on if I + + align:start position:0% +this in the visual system later on if I + + + align:start position:0% +this in the visual system later on if I +were you I would just read this uh and + + align:start position:0% +were you I would just read this uh and + + + align:start position:0% +were you I would just read this uh and +use it it it does help prepare you for + + align:start position:0% +use it it it does help prepare you for + + + align:start position:0% +use it it it does help prepare you for +what's coming but we right now you need + + align:start position:0% +what's coming but we right now you need + + + align:start position:0% +what's coming but we right now you need +to know this the different major outputs + + align:start position:0% +to know this the different major outputs + + + align:start position:0% +to know this the different major outputs +the + + align:start position:0% +the + + + align:start position:0% +the +tectum + + align:start position:0% +tectum + + + align:start position:0% +tectum +okay so a little bit more about grasping + + align:start position:0% +okay so a little bit more about grasping + + + align:start position:0% +okay so a little bit more about grasping +we know why it's so + + align:start position:0% +we know why it's so + + + align:start position:0% +we know why it's so +important + + align:start position:0% +important + + + align:start position:0% +important +uh we know what muscles are involved we + + align:start position:0% +uh we know what muscles are involved we + + + align:start position:0% +uh we know what muscles are involved we +know that there's different kinds of + + align:start position:0% +know that there's different kinds of + + + align:start position:0% +know that there's different kinds of +grasping grasping with the hands we know + + align:start position:0% +grasping grasping with the hands we know + + + align:start position:0% +grasping grasping with the hands we know +in primate large primates it's largely a + + align:start position:0% +in primate large primates it's largely a + + + align:start position:0% +in primate large primates it's largely a +neocortical function + + align:start position:0% +neocortical function + + + align:start position:0% +neocortical function +but animals without neocortex can still + + align:start position:0% +but animals without neocortex can still + + + align:start position:0% +but animals without neocortex can still +feed themselves they still have to grasp + + align:start position:0% +feed themselves they still have to grasp + + + align:start position:0% +feed themselves they still have to grasp +things either with the mouth or with the + + align:start position:0% +things either with the mouth or with the + + + align:start position:0% +things either with the mouth or with the +hands uh so structures evolved to do + + align:start position:0% +hands uh so structures evolved to do + + + align:start position:0% +hands uh so structures evolved to do +that and they're in the + + align:start position:0% + + + + align:start position:0% + +midra so that's what those questions are + + align:start position:0% +midra so that's what those questions are + + + align:start position:0% +midra so that's what those questions are +about + + align:start position:0% + + + + align:start position:0% + +uh and we talked about this a little bit + + align:start position:0% +uh and we talked about this a little bit + + + align:start position:0% +uh and we talked about this a little bit +last time so I'm not going to go over it + + align:start position:0% +last time so I'm not going to go over it + + + align:start position:0% +last time so I'm not going to go over it +again uh but I didn't talk about the red + + align:start position:0% +again uh but I didn't talk about the red + + + align:start position:0% +again uh but I didn't talk about the red +nucleus in a little more detail there's + + align:start position:0% +nucleus in a little more detail there's + + + align:start position:0% +nucleus in a little more detail there's +two major parts of the red nucleus and + + align:start position:0% +two major parts of the red nucleus and + + + align:start position:0% +two major parts of the red nucleus and +it's quite interesting when you compare + + align:start position:0% +it's quite interesting when you compare + + + align:start position:0% +it's quite interesting when you compare +different animals there's a large cell + + align:start position:0% +different animals there's a large cell + + + align:start position:0% +different animals there's a large cell +part in the that's the coddle part of + + align:start position:0% +part in the that's the coddle part of + + + align:start position:0% +part in the that's the coddle part of +the nucleus and then there's a small + + align:start position:0% +the nucleus and then there's a small + + + align:start position:0% +the nucleus and then there's a small +cell part so we refer to the magnos + + align:start position:0% +cell part so we refer to the magnos + + + align:start position:0% +cell part so we refer to the magnos +cellular red part of the red + + align:start position:0% +cellular red part of the red + + + align:start position:0% +cellular red part of the red +nucleus it's abbreviated NR for nucleus + + align:start position:0% +nucleus it's abbreviated NR for nucleus + + + align:start position:0% +nucleus it's abbreviated NR for nucleus +rhar and then MC for magnos cellular or + + align:start position:0% +rhar and then MC for magnos cellular or + + + align:start position:0% +rhar and then MC for magnos cellular or +NR nucleus rubar PC for parvo cellular + + align:start position:0% +NR nucleus rubar PC for parvo cellular + + + align:start position:0% +NR nucleus rubar PC for parvo cellular +parvo means small okay so those are the + + align:start position:0% +parvo means small okay so those are the + + + align:start position:0% +parvo means small okay so those are the +two parts and it's really interesting if + + align:start position:0% +two parts and it's really interesting if + + + align:start position:0% +two parts and it's really interesting if +you look across uh the primates + + align:start position:0% +you look across uh the primates + + + align:start position:0% +you look across uh the primates +and even if you went here to primitive + + align:start position:0% +and even if you went here to primitive + + + align:start position:0% +and even if you went here to primitive +primates it would be like the carnivore + + align:start position:0% +primates it would be like the carnivore + + + align:start position:0% +primates it would be like the carnivore +here in + + align:start position:0% +here in + + + align:start position:0% +here in +humans the parvocellular part the rostal + + align:start position:0% +humans the parvocellular part the rostal + + + align:start position:0% +humans the parvocellular part the rostal +part is by far the largest + + align:start position:0% +part is by far the largest + + + align:start position:0% +part is by far the largest +part the magnos cellular part is + + align:start position:0% +part the magnos cellular part is + + + align:start position:0% +part the magnos cellular part is +smaller so what do these two parts do + + align:start position:0% +smaller so what do these two parts do + + + align:start position:0% +smaller so what do these two parts do +well the out outputs are very different + + align:start position:0% +well the out outputs are very different + + + align:start position:0% +well the out outputs are very different +and of course their inputs are different + + align:start position:0% +and of course their inputs are different + + + align:start position:0% +and of course their inputs are different +too let's just deal with the outputs the + + align:start position:0% +too let's just deal with the outputs the + + + align:start position:0% +too let's just deal with the outputs the +the rubos spinal tract okay the output + + align:start position:0% +the rubos spinal tract okay the output + + + align:start position:0% +the rubos spinal tract okay the output +to the spinal cord that comes from the + + align:start position:0% +to the spinal cord that comes from the + + + align:start position:0% +to the spinal cord that comes from the +large cells the magnos or part of the + + align:start position:0% +large cells the magnos or part of the + + + align:start position:0% +large cells the magnos or part of the +red nucleus so in animals where that + + align:start position:0% +red nucleus so in animals where that + + + align:start position:0% +red nucleus so in animals where that +pathway is more + + align:start position:0% +pathway is more + + + align:start position:0% +pathway is more +important more important than + + align:start position:0% +important more important than + + + align:start position:0% +important more important than +neocortex it'll be like + + align:start position:0% +neocortex it'll be like + + + align:start position:0% +neocortex it'll be like +this the codal part is relatively larger + + align:start position:0% +this the codal part is relatively larger + + + align:start position:0% +this the codal part is relatively larger +that's true in carnivores it's true in + + align:start position:0% +that's true in carnivores it's true in + + + align:start position:0% +that's true in carnivores it's true in +rodents true in most animals but animals + + align:start position:0% +rodents true in most animals but animals + + + align:start position:0% +rodents true in most animals but animals +that have really + + align:start position:0% +that have really + + + align:start position:0% +that have really +developed um more endbrain control of + + align:start position:0% +developed um more endbrain control of + + + align:start position:0% +developed um more endbrain control of +their + + align:start position:0% +their + + + align:start position:0% +their +hands then the powerful cellular part is + + align:start position:0% +hands then the powerful cellular part is + + + align:start position:0% +hands then the powerful cellular part is +more so why is + + align:start position:0% +more so why is + + + align:start position:0% +more so why is +that well what does IT project to first + + align:start position:0% +that well what does IT project to first + + + align:start position:0% +that well what does IT project to first +of all it IT projects forward not like + + align:start position:0% +of all it IT projects forward not like + + + align:start position:0% +of all it IT projects forward not like +the rubos spinal tract this this + + align:start position:0% +the rubos spinal tract this this + + + align:start position:0% +the rubos spinal tract this this +projects Rost paracellular + + align:start position:0% +projects Rost paracellular + + + align:start position:0% +projects Rost paracellular +nucleus uh projects to the thamus mostly + + align:start position:0% +nucleus uh projects to the thamus mostly + + + align:start position:0% +nucleus uh projects to the thamus mostly +to the ventral lateral thamus the part + + align:start position:0% +to the ventral lateral thamus the part + + + align:start position:0% +to the ventral lateral thamus the part +of the thalamus that projects to the + + align:start position:0% +of the thalamus that projects to the + + + align:start position:0% +of the thalamus that projects to the +primary motor + + align:start position:0% +primary motor + + + align:start position:0% +primary motor +cortex + + align:start position:0% +cortex + + + align:start position:0% +cortex +okay + + align:start position:0% + + + + align:start position:0% + +and it also projects to the + + align:start position:0% +and it also projects to the + + + align:start position:0% +and it also projects to the +precerebellar nucleo so the inputs to + + align:start position:0% +precerebellar nucleo so the inputs to + + + align:start position:0% +precerebellar nucleo so the inputs to +the cerebellum and to the + + align:start position:0% +the cerebellum and to the + + + align:start position:0% +the cerebellum and to the +neocortex depend on that for control + + align:start position:0% +neocortex depend on that for control + + + align:start position:0% +neocortex depend on that for control +hand + + align:start position:0% +hand + + + align:start position:0% +hand +movements go through that carb cellular + + align:start position:0% +movements go through that carb cellular + + + align:start position:0% +movements go through that carb cellular +part and this also shows a correlation + + align:start position:0% +part and this also shows a correlation + + + align:start position:0% +part and this also shows a correlation +with a structure in the + + align:start position:0% +with a structure in the + + + align:start position:0% +with a structure in the +cerebellum it's this structure they just + + align:start position:0% +cerebellum it's this structure they just + + + align:start position:0% +cerebellum it's this structure they just +pick that out of the cerebellum it's the + + align:start position:0% +pick that out of the cerebellum it's the + + + align:start position:0% +pick that out of the cerebellum it's the +lateral most deep nucleus it's the part + + align:start position:0% +lateral most deep nucleus it's the part + + + align:start position:0% +lateral most deep nucleus it's the part +of the + + align:start position:0% +of the + + + align:start position:0% +of the +cerebellum that gets input from the very + + align:start position:0% +cerebellum that gets input from the very + + + align:start position:0% +cerebellum that gets input from the very +large hemispheres in human + + align:start position:0% +large hemispheres in human + + + align:start position:0% +large hemispheres in human +cerebellum but any animal what they're + + align:start position:0% +cerebellum but any animal what they're + + + align:start position:0% +cerebellum but any animal what they're +not showing here is the whole cerebell + + align:start position:0% +not showing here is the whole cerebell + + + align:start position:0% +not showing here is the whole cerebell +or hemispheres growing + + align:start position:0% +or hemispheres growing + + + align:start position:0% +or hemispheres growing +bigger uh in these animals at the right + + align:start position:0% +bigger uh in these animals at the right + + + align:start position:0% +bigger uh in these animals at the right +in apes and humans and also + + align:start position:0% +in apes and humans and also + + + align:start position:0% +in apes and humans and also +monkeys whereas in other animals with + + align:start position:0% +monkeys whereas in other animals with + + + align:start position:0% +monkeys whereas in other animals with +less of this kind of + + align:start position:0% +less of this kind of + + + align:start position:0% +less of this kind of +control that lateral cerebellar output + + align:start position:0% +control that lateral cerebellar output + + + align:start position:0% +control that lateral cerebellar output +nucleus is also smaller so as the + + align:start position:0% +nucleus is also smaller so as the + + + align:start position:0% +nucleus is also smaller so as the +cerebellum evolves so does the cortex + + align:start position:0% +cerebellum evolves so does the cortex + + + align:start position:0% +cerebellum evolves so does the cortex +and the red nucleus + + align:start position:0% +and the red nucleus + + + align:start position:0% +and the red nucleus +changes also um I'm + + align:start position:0% + + + + align:start position:0% + +know + + align:start position:0% + + + + align:start position:0% + +having I animals no because animals can + + align:start position:0% +having I animals no because animals can + + + align:start position:0% +having I animals no because animals can +still be pretty dextrous without so much + + align:start position:0% +still be pretty dextrous without so much + + + align:start position:0% +still be pretty dextrous without so much +visual input but it there is a there is + + align:start position:0% +visual input but it there is a there is + + + align:start position:0% +visual input but it there is a there is +a general + + align:start position:0% +a general + + + align:start position:0% +a general +correspondence uh if you look there are + + align:start position:0% +correspondence uh if you look there are + + + align:start position:0% +correspondence uh if you look there are +prosimians for example that where the + + align:start position:0% +prosimians for example that where the + + + align:start position:0% +prosimians for example that where the +red nucleus is more prominent than it is + + align:start position:0% +red nucleus is more prominent than it is + + + align:start position:0% +red nucleus is more prominent than it is +even in humans uh that have incredible + + align:start position:0% +even in humans uh that have incredible + + + align:start position:0% +even in humans uh that have incredible +dexterity but it's mostly fixed action + + align:start position:0% +dexterity but it's mostly fixed action + + + align:start position:0% +dexterity but it's mostly fixed action +patterns they use it for grabbing bugs + + align:start position:0% +patterns they use it for grabbing bugs + + + align:start position:0% +patterns they use it for grabbing bugs +out of the + + align:start position:0% +out of the + + + align:start position:0% +out of the +air you know + + align:start position:0% + + + + align:start position:0% + +so all the animals I mentioned that have + + align:start position:0% +so all the animals I mentioned that have + + + align:start position:0% +so all the animals I mentioned that have +a small one are less + + align:start position:0% + + + + align:start position:0% + +visual + + align:start position:0% +visual + + + align:start position:0% +visual +you have these different types of cells + + align:start position:0% +you have these different types of cells + + + align:start position:0% +you have these different types of cells +in other systems too but no there's no + + align:start position:0% +in other systems too but no there's no + + + align:start position:0% +in other systems too but no there's no +real strict correlation animals can be + + align:start position:0% +real strict correlation animals can be + + + align:start position:0% +real strict correlation animals can be +very dextrous even without using vision + + align:start position:0% +very dextrous even without using vision + + + align:start position:0% +very dextrous even without using vision +and humans without Vision can very very + + align:start position:0% +and humans without Vision can very very + + + align:start position:0% +and humans without Vision can very very +dexterous sand + + align:start position:0% +dexterous sand + + + align:start position:0% +dexterous sand +movements all right + + align:start position:0% + + + + align:start position:0% + +so there's interesting there's an + + align:start position:0% +so there's interesting there's an + + + align:start position:0% +so there's interesting there's an +interesting study of of the projections + + align:start position:0% +interesting study of of the projections + + + align:start position:0% +interesting study of of the projections +of the red + + align:start position:0% +of the red + + + align:start position:0% +of the red +nucleus because they're they're in + + align:start position:0% +nucleus because they're they're in + + + align:start position:0% +nucleus because they're they're in +concerned with control of distal muscles + + align:start position:0% +concerned with control of distal muscles + + + align:start position:0% +concerned with control of distal muscles +well there's distal muscles in the for + + align:start position:0% +well there's distal muscles in the for + + + align:start position:0% +well there's distal muscles in the for +limbs but also in the hind limbs so the + + align:start position:0% +limbs but also in the hind limbs so the + + + align:start position:0% +limbs but also in the hind limbs so the +question is are those kept separate in + + align:start position:0% +question is are those kept separate in + + + align:start position:0% +question is are those kept separate in +the red nucleus so you look at the + + align:start position:0% +the red nucleus so you look at the + + + align:start position:0% +the red nucleus so you look at the +projections to the cervical + + align:start position:0% +projections to the cervical + + + align:start position:0% +projections to the cervical +enlargement and the lumbar enlargement + + align:start position:0% +enlargement and the lumbar enlargement + + + align:start position:0% +enlargement and the lumbar enlargement +this is just a cartoon to + + align:start position:0% +this is just a cartoon to + + + align:start position:0% +this is just a cartoon to +illustrate uh those two parts of the + + align:start position:0% +illustrate uh those two parts of the + + + align:start position:0% +illustrate uh those two parts of the +spinal cord + + align:start position:0% +spinal cord + + + align:start position:0% +spinal cord +and then the red nucleus projections and + + align:start position:0% +and then the red nucleus projections and + + + align:start position:0% +and then the red nucleus projections and +what this shows is neurons that project + + align:start position:0% +what this shows is neurons that project + + + align:start position:0% +what this shows is neurons that project +to the cervical enlargement neurons that + + align:start position:0% +to the cervical enlargement neurons that + + + align:start position:0% +to the cervical enlargement neurons that +project to the lumbar enlargement and + + align:start position:0% +project to the lumbar enlargement and + + + align:start position:0% +project to the lumbar enlargement and +neurons that project to both they have a + + align:start position:0% +neurons that project to both they have a + + + align:start position:0% +neurons that project to both they have a +an a branch to both + + align:start position:0% +an a branch to both + + + align:start position:0% +an a branch to both +nuclei so if you look at look at the + + align:start position:0% +nuclei so if you look at look at the + + + align:start position:0% +nuclei so if you look at look at the +osum you'll see that there is some inter + + align:start position:0% +osum you'll see that there is some inter + + + align:start position:0% +osum you'll see that there is some inter +mixture here the topographic separation + + align:start position:0% +mixture here the topographic separation + + + align:start position:0% +mixture here the topographic separation +of the represent + + align:start position:0% +of the represent + + + align:start position:0% +of the represent +presentation for hand control and foot + + align:start position:0% +presentation for hand control and foot + + + align:start position:0% +presentation for hand control and foot +control is is not all that good in the + + align:start position:0% +control is is not all that good in the + + + align:start position:0% +control is is not all that good in the +rat it's a little better and in the + + align:start position:0% +rat it's a little better and in the + + + align:start position:0% +rat it's a little better and in the +cadets the separation is really good and + + align:start position:0% +cadets the separation is really good and + + + align:start position:0% +cadets the separation is really good and +of course in primates it is + + align:start position:0% +of course in primates it is + + + align:start position:0% +of course in primates it is +too just an interesting thing about how + + align:start position:0% +too just an interesting thing about how + + + align:start position:0% +too just an interesting thing about how +you find these correspondences with + + align:start position:0% +you find these correspondences with + + + align:start position:0% +you find these correspondences with +function and + + align:start position:0% +function and + + + align:start position:0% +function and +Anatomy uh in these descending + + align:start position:0% +Anatomy uh in these descending + + + align:start position:0% +Anatomy uh in these descending +projections + + align:start position:0% +projections + + + align:start position:0% +projections +okay so now I want to talk about the + + align:start position:0% +okay so now I want to talk about the + + + align:start position:0% +okay so now I want to talk about the +outputs and I'm I want to start with the + + align:start position:0% +outputs and I'm I want to start with the + + + align:start position:0% +outputs and I'm I want to start with the +motor + + align:start position:0% +motor + + + align:start position:0% +motor +neurons uh so then we can talk about the + + align:start position:0% +neurons uh so then we can talk about the + + + align:start position:0% +neurons uh so then we can talk about the +pathways that connect to those motor + + align:start position:0% +pathways that connect to those motor + + + align:start position:0% +pathways that connect to those motor +neurons and how the pathways save from + + align:start position:0% +neurons and how the pathways save from + + + align:start position:0% +neurons and how the pathways save from +the cortex and brain stem connect to the + + align:start position:0% +the cortex and brain stem connect to the + + + align:start position:0% +the cortex and brain stem connect to the +motor neurons the spinal + + align:start position:0% +motor neurons the spinal + + + align:start position:0% +motor neurons the spinal +cord and the we're talking here about + + align:start position:0% +cord and the we're talking here about + + + align:start position:0% +cord and the we're talking here about +sematic motor neurons okay we talked + + align:start position:0% +sematic motor neurons okay we talked + + + align:start position:0% +sematic motor neurons okay we talked +earlier about autonomic + + align:start position:0% +earlier about autonomic + + + align:start position:0% +earlier about autonomic +and we've said a little bit about Nur + + align:start position:0% +and we've said a little bit about Nur + + + align:start position:0% +and we've said a little bit about Nur +endocrine control through the + + align:start position:0% +endocrine control through the + + + align:start position:0% +endocrine control through the +hypothalamus we talk a lot more about + + align:start position:0% +hypothalamus we talk a lot more about + + + align:start position:0% +hypothalamus we talk a lot more about +that when we talk specifically about + + align:start position:0% +that when we talk specifically about + + + align:start position:0% +that when we talk specifically about +hypothalamus we're just talking about + + align:start position:0% +hypothalamus we're just talking about + + + align:start position:0% +hypothalamus we're just talking about +the sematic + + align:start position:0% +the sematic + + + align:start position:0% +the sematic +system with synaptic connections to + + align:start position:0% +system with synaptic connections to + + + align:start position:0% +system with synaptic connections to +muscles not paracrine as in the + + align:start position:0% +muscles not paracrine as in the + + + align:start position:0% +muscles not paracrine as in the +autonomic system and not endocrine as in + + align:start position:0% +autonomic system and not endocrine as in + + + align:start position:0% +autonomic system and not endocrine as in +the endocrine system + + align:start position:0% +the endocrine system + + + align:start position:0% +the endocrine system +so this is Lor Swanson's ha ation of the + + align:start position:0% +so this is Lor Swanson's ha ation of the + + + align:start position:0% +so this is Lor Swanson's ha ation of the +entire motor system he says the three + + align:start position:0% +entire motor system he says the three + + + align:start position:0% +entire motor system he says the three +motor systems this is the sematic number + + align:start position:0% +motor systems this is the sematic number + + + align:start position:0% +motor systems this is the sematic number +three here number one is the endocrine + + align:start position:0% +three here number one is the endocrine + + + align:start position:0% +three here number one is the endocrine +and he shows this the dash line + + align:start position:0% +and he shows this the dash line + + + align:start position:0% +and he shows this the dash line +indicates + + align:start position:0% +indicates + + + align:start position:0% +indicates +connections there's no synapse at all + + align:start position:0% +connections there's no synapse at all + + + align:start position:0% +connections there's no synapse at all +they're just through the + + align:start position:0% +they're just through the + + + align:start position:0% +they're just through the +bloodstream and then the paracrine + + align:start position:0% +bloodstream and then the paracrine + + + align:start position:0% +bloodstream and then the paracrine +intervation of the autonomic system + + align:start position:0% +intervation of the autonomic system + + + align:start position:0% +intervation of the autonomic system +parap sympathetic and sympathetic that's + + align:start position:0% +parap sympathetic and sympathetic that's + + + align:start position:0% +parap sympathetic and sympathetic that's +motor system 2 and motor system 3 and + + align:start position:0% +motor system 2 and motor system 3 and + + + align:start position:0% +motor system 2 and motor system 3 and +when he discussed is that it's + + align:start position:0% +when he discussed is that it's + + + align:start position:0% +when he discussed is that it's +interesting he + + align:start position:0% +interesting he + + + align:start position:0% +interesting he +says we don't + + align:start position:0% +says we don't + + + align:start position:0% +says we don't +know what are the uh what are the + + align:start position:0% +know what are the uh what are the + + + align:start position:0% +know what are the uh what are the +pattern generators that are coordinating + + align:start position:0% +pattern generators that are coordinating + + + align:start position:0% +pattern generators that are coordinating +these three systems and + + align:start position:0% +these three systems and + + + align:start position:0% +these three systems and +my comment about that is just that we + + align:start position:0% +my comment about that is just that we + + + align:start position:0% +my comment about that is just that we +don't know if there is very much direct + + align:start position:0% +don't know if there is very much direct + + + align:start position:0% +don't know if there is very much direct +coordination centrally of these systems + + align:start position:0% +coordination centrally of these systems + + + align:start position:0% +coordination centrally of these systems +but there probably is some but it's not + + align:start position:0% +but there probably is some but it's not + + + align:start position:0% +but there probably is some but it's not +then specifically we know a lot less + + align:start position:0% +then specifically we know a lot less + + + align:start position:0% +then specifically we know a lot less +about that than we know about control of + + align:start position:0% +about that than we know about control of + + + align:start position:0% +about that than we know about control of +pattern movements + + align:start position:0% +pattern movements + + + align:start position:0% +pattern movements +okay and this just distribution of + + align:start position:0% +okay and this just distribution of + + + align:start position:0% +okay and this just distribution of +sematic motor + + align:start position:0% +sematic motor + + + align:start position:0% +sematic motor +neurons uh I've had that in other + + align:start position:0% +neurons uh I've had that in other + + + align:start position:0% +neurons uh I've had that in other +pictures that I showed you early on that + + align:start position:0% +pictures that I showed you early on that + + + align:start position:0% +pictures that I showed you early on that +you probably didn't pay much attention + + align:start position:0% +you probably didn't pay much attention + + + align:start position:0% +you probably didn't pay much attention +except I always showed the motor neurons + + align:start position:0% +except I always showed the motor neurons + + + align:start position:0% +except I always showed the motor neurons +ventrally so I asked this question here + + align:start position:0% +ventrally so I asked this question here + + + align:start position:0% +ventrally so I asked this question here +this is a horizontal view it doesn't + + align:start position:0% +this is a horizontal view it doesn't + + + align:start position:0% +this is a horizontal view it doesn't +indicate anything about dorsal and + + align:start position:0% +indicate anything about dorsal and + + + align:start position:0% +indicate anything about dorsal and +ventral so I say where are these neurons + + align:start position:0% +ventral so I say where are these neurons + + + align:start position:0% +ventral so I say where are these neurons +located in frontal sections so well here + + align:start position:0% +located in frontal sections so well here + + + align:start position:0% +located in frontal sections so well here +this is all spinal cord where most of + + align:start position:0% +this is all spinal cord where most of + + + align:start position:0% +this is all spinal cord where most of +those neurons are and you can see most + + align:start position:0% +those neurons are and you can see most + + + align:start position:0% +those neurons are and you can see most +of them are in the + + align:start position:0% +of them are in the + + + align:start position:0% +of them are in the +enlargements because there's many more + + align:start position:0% +enlargements because there's many more + + + align:start position:0% +enlargements because there's many more +muscles to control in the limbs and we + + align:start position:0% +muscles to control in the limbs and we + + + align:start position:0% +muscles to control in the limbs and we +need finer control so we've got more + + align:start position:0% +need finer control so we've got more + + + align:start position:0% +need finer control so we've got more +motor neurons controlling them they're + + align:start position:0% +motor neurons controlling them they're + + + align:start position:0% +motor neurons controlling them they're +always in the ventral horn and that's + + align:start position:0% +always in the ventral horn and that's + + + align:start position:0% +always in the ventral horn and that's +what we're going to talk about uh next + + align:start position:0% +what we're going to talk about uh next + + + align:start position:0% +what we're going to talk about uh next +but these are the groups of + + align:start position:0% + + + + align:start position:0% + +neurons in these columns that aren't + + align:start position:0% +neurons in these columns that aren't + + + align:start position:0% +neurons in these columns that aren't +directly connected with each other that + + align:start position:0% +directly connected with each other that + + + align:start position:0% +directly connected with each other that +we talked about when we talked about + + align:start position:0% +we talked about when we talked about + + + align:start position:0% +we talked about when we talked about +hindbrain and + + align:start position:0% +hindbrain and + + + align:start position:0% +hindbrain and +midbrain and notice the most rostal ones + + align:start position:0% +midbrain and notice the most rostal ones + + + align:start position:0% +midbrain and notice the most rostal ones +are in the midbrain that came up did it + + align:start position:0% +are in the midbrain that came up did it + + + align:start position:0% +are in the midbrain that came up did it +did come up a couple times in the class + + align:start position:0% +did come up a couple times in the class + + + align:start position:0% +did come up a couple times in the class +if you didn't remember fine but with the + + align:start position:0% +if you didn't remember fine but with the + + + align:start position:0% +if you didn't remember fine but with the +help of the quiz you'll probably + + align:start position:0% +help of the quiz you'll probably + + + align:start position:0% +help of the quiz you'll probably +remember it now the most rostal sematic + + align:start position:0% +remember it now the most rostal sematic + + + align:start position:0% +remember it now the most rostal sematic +motor + + align:start position:0% +motor + + + align:start position:0% +motor +neurons if you include the endocrine + + align:start position:0% +neurons if you include the endocrine + + + align:start position:0% +neurons if you include the endocrine +system as + + align:start position:0% +system as + + + align:start position:0% +system as +motor and like Swanson does then you + + align:start position:0% +motor and like Swanson does then you + + + align:start position:0% +motor and like Swanson does then you +could say well there's another kind of + + align:start position:0% +could say well there's another kind of + + + align:start position:0% +could say well there's another kind of +motor n in the hypothalamus and even + + align:start position:0% +motor n in the hypothalamus and even + + + align:start position:0% +motor n in the hypothalamus and even +even further + + align:start position:0% +even further + + + align:start position:0% +even further +forward okay secretory cells we're not + + align:start position:0% +forward okay secretory cells we're not + + + align:start position:0% +forward okay secretory cells we're not +talking about secretory cells now at all + + align:start position:0% +talking about secretory cells now at all + + + align:start position:0% +talking about secretory cells now at all +just control of sematic motor + + align:start position:0% +just control of sematic motor + + + align:start position:0% +just control of sematic motor +neurons all + + align:start position:0% + + + + align:start position:0% + +right so I want to talk about it's a + + align:start position:0% +right so I want to talk about it's a + + + align:start position:0% +right so I want to talk about it's a +chapter centered on the studies of + + align:start position:0% +chapter centered on the studies of + + + align:start position:0% +chapter centered on the studies of +descending Pathways they the anatomy and + + align:start position:0% +descending Pathways they the anatomy and + + + align:start position:0% +descending Pathways they the anatomy and +their function and these are the ones we + + align:start position:0% +their function and these are the ones we + + + align:start position:0% +their function and these are the ones we +just saw I want to answer this question + + align:start position:0% +just saw I want to answer this question + + + align:start position:0% +just saw I want to answer this question +now what's the basic spatial layout of + + align:start position:0% +now what's the basic spatial layout of + + + align:start position:0% +now what's the basic spatial layout of +motor neurons at one of the spinal cord + + align:start position:0% +motor neurons at one of the spinal cord + + + align:start position:0% +motor neurons at one of the spinal cord +enlargements how is it organized + + align:start position:0% +enlargements how is it organized + + + align:start position:0% +enlargements how is it organized +and then we'll talk about what connects + + align:start position:0% +and then we'll talk about what connects + + + align:start position:0% +and then we'll talk about what connects +to those motor neurons and the main type + + align:start position:0% +to those motor neurons and the main type + + + align:start position:0% +to those motor neurons and the main type +of neuron that connects to them is + + align:start position:0% +of neuron that connects to them is + + + align:start position:0% +of neuron that connects to them is +interneurons in their intermediate + + align:start position:0% +interneurons in their intermediate + + + align:start position:0% +interneurons in their intermediate +layers of the spinal + + align:start position:0% +layers of the spinal + + + align:start position:0% +layers of the spinal +Court yes there are some coming directly + + align:start position:0% +Court yes there are some coming directly + + + align:start position:0% +Court yes there are some coming directly +from cortex 2o and we'll talk about + + align:start position:0% +from cortex 2o and we'll talk about + + + align:start position:0% +from cortex 2o and we'll talk about +those uh those connections connect + + align:start position:0% +those uh those connections connect + + + align:start position:0% +those uh those connections connect +mainly to those + + align:start position:0% +mainly to those + + + align:start position:0% +mainly to those +interneurons okay and this this is a + + align:start position:0% +interneurons okay and this this is a + + + align:start position:0% +interneurons okay and this this is a +kind of figure you often will see in a + + align:start position:0% +kind of figure you often will see in a + + + align:start position:0% +kind of figure you often will see in a +medical school book what does that + + align:start position:0% +medical school book what does that + + + align:start position:0% +medical school book what does that +mean is that Atlas holding the world up + + align:start position:0% +mean is that Atlas holding the world up + + + align:start position:0% +mean is that Atlas holding the world up +no it's he's holding a spinal cord up + + align:start position:0% +no it's he's holding a spinal cord up + + + align:start position:0% +no it's he's holding a spinal cord up +but why do they have him pictured like + + align:start position:0% +but why do they have him pictured like + + + align:start position:0% +but why do they have him pictured like +that with his arms like + + align:start position:0% +that with his arms like + + + align:start position:0% +that with his arms like +this because it's showing that the motor + + align:start position:0% +this because it's showing that the motor + + + align:start position:0% +this because it's showing that the motor +neurons in the ventral horns + + align:start position:0% +neurons in the ventral horns + + + align:start position:0% +neurons in the ventral horns +here the motor neurons controlling the + + align:start position:0% +here the motor neurons controlling the + + + align:start position:0% +here the motor neurons controlling the +axial muscles so the muscles of the neck + + align:start position:0% +axial muscles so the muscles of the neck + + + align:start position:0% +axial muscles so the muscles of the neck +or the along the back those are the + + align:start position:0% +or the along the back those are the + + + align:start position:0% +or the along the back those are the +axial muscles control very important in + + align:start position:0% +axial muscles control very important in + + + align:start position:0% +axial muscles control very important in +postural + + align:start position:0% +postural + + + align:start position:0% +postural +control and + + align:start position:0% + + + + align:start position:0% + +uh they're most medial and then we talk + + align:start position:0% +uh they're most medial and then we talk + + + align:start position:0% +uh they're most medial and then we talk +about the girdle muscles the muscles + + align:start position:0% +about the girdle muscles the muscles + + + align:start position:0% +about the girdle muscles the muscles +that control shoulders or hips okay + + align:start position:0% +that control shoulders or hips okay + + + align:start position:0% +that control shoulders or hips okay +separate from the muscles controlling + + align:start position:0% +separate from the muscles controlling + + + align:start position:0% +separate from the muscles controlling +the + + align:start position:0% +the + + + align:start position:0% +the +limbs uh you find those next moving + + align:start position:0% +limbs uh you find those next moving + + + align:start position:0% +limbs uh you find those next moving +laterally and then the arms and finally + + align:start position:0% +laterally and then the arms and finally + + + align:start position:0% +laterally and then the arms and finally +the hands and feet depending on whether + + align:start position:0% +the hands and feet depending on whether + + + align:start position:0% +the hands and feet depending on whether +you're in the cervical or lumbar + + align:start position:0% +you're in the cervical or lumbar + + + align:start position:0% +you're in the cervical or lumbar +enlargement okay so this is the picture + + align:start position:0% +enlargement okay so this is the picture + + + align:start position:0% +enlargement okay so this is the picture +from the Lawrence and pyer study that I + + align:start position:0% +from the Lawrence and pyer study that I + + + align:start position:0% +from the Lawrence and pyer study that I +use in the + + align:start position:0% +use in the + + + align:start position:0% +use in the +book it shows a a section of the spinal + + align:start position:0% +book it shows a a section of the spinal + + + align:start position:0% +book it shows a a section of the spinal +cord and it it just by just putting in a + + align:start position:0% +cord and it it just by just putting in a + + + align:start position:0% +cord and it it just by just putting in a +few neurons they're showing you groups + + align:start position:0% +few neurons they're showing you groups + + + align:start position:0% +few neurons they're showing you groups +of neurons that are located medially and + + align:start position:0% +of neurons that are located medially and + + + align:start position:0% +of neurons that are located medially and +then more and more + + align:start position:0% + + + + align:start position:0% + +laterally and uh so axial muscles + + align:start position:0% +laterally and uh so axial muscles + + + align:start position:0% +laterally and uh so axial muscles +medially then the girdle muscles and + + align:start position:0% +medially then the girdle muscles and + + + align:start position:0% +medially then the girdle muscles and +then the distal muscles and there is + + align:start position:0% +then the distal muscles and there is + + + align:start position:0% +then the distal muscles and there is +some separation that you see in that + + align:start position:0% +some separation that you see in that + + + align:start position:0% +some separation that you see in that +other picture of the flexors and + + align:start position:0% +other picture of the flexors and + + + align:start position:0% +other picture of the flexors and +extensors as well + + align:start position:0% +extensors as well + + + align:start position:0% +extensors as well +okay you don't need to worry about + + align:start position:0% +okay you don't need to worry about + + + align:start position:0% +okay you don't need to worry about +flexor and extensor extensor separation + + align:start position:0% +flexor and extensor extensor separation + + + align:start position:0% +flexor and extensor extensor separation +because it is fairly complex there's no + + align:start position:0% +because it is fairly complex there's no + + + align:start position:0% +because it is fairly complex there's no +need to memorize + + align:start position:0% +need to memorize + + + align:start position:0% +need to memorize +it okay but you need to know about the + + align:start position:0% +it okay but you need to know about the + + + align:start position:0% +it okay but you need to know about the +relation of the topography in the chord + + align:start position:0% +relation of the topography in the chord + + + align:start position:0% +relation of the topography in the chord +and the control of different muscles in + + align:start position:0% +and the control of different muscles in + + + align:start position:0% +and the control of different muscles in +the + + align:start position:0% +the + + + align:start position:0% +the +body okay so now we know about prox IND + + align:start position:0% +body okay so now we know about prox IND + + + align:start position:0% +body okay so now we know about prox IND +distal represent in the cord the next + + align:start position:0% +distal represent in the cord the next + + + align:start position:0% +distal represent in the cord the next +question we'll go back to this one is + + align:start position:0% +question we'll go back to this one is + + + align:start position:0% +question we'll go back to this one is +the interneurons and yes they are + + align:start position:0% +the interneurons and yes they are + + + align:start position:0% +the interneurons and yes they are +radially arranged so the inter neurons + + align:start position:0% +radially arranged so the inter neurons + + + align:start position:0% +radially arranged so the inter neurons +way out laterally here do connect to the + + align:start position:0% +way out laterally here do connect to the + + + align:start position:0% +way out laterally here do connect to the +lateral most motor neurons where's the + + align:start position:0% +lateral most motor neurons where's the + + + align:start position:0% +lateral most motor neurons where's the +ones located imediately connect to the + + align:start position:0% +ones located imediately connect to the + + + align:start position:0% +ones located imediately connect to the +medial ones controlling axial muscles + + align:start position:0% +medial ones controlling axial muscles + + + align:start position:0% +medial ones controlling axial muscles +and there's another + + align:start position:0% +and there's another + + + align:start position:0% +and there's another +difference that's quite important some + + align:start position:0% +difference that's quite important some + + + align:start position:0% +difference that's quite important some +of those inter neurons that connect to + + align:start position:0% +of those inter neurons that connect to + + + align:start position:0% +of those inter neurons that connect to +the medial motor neurons project both + + align:start position:0% +the medial motor neurons project both + + + align:start position:0% +the medial motor neurons project both +sides of the cord + + align:start position:0% +sides of the cord + + + align:start position:0% +sides of the cord +because when you control axial muscles + + align:start position:0% +because when you control axial muscles + + + align:start position:0% +because when you control axial muscles +you're always dealing with movements + + align:start position:0% +you're always dealing with movements + + + align:start position:0% +you're always dealing with movements +that are never they always involve both + + align:start position:0% +that are never they always involve both + + + align:start position:0% +that are never they always involve both +sides of the + + align:start position:0% +sides of the + + + align:start position:0% +sides of the +body so both sides of the cord tend to + + align:start position:0% +body so both sides of the cord tend to + + + align:start position:0% +body so both sides of the cord tend to +be involved okay and the same thing is + + align:start position:0% +be involved okay and the same thing is + + + align:start position:0% +be involved okay and the same thing is +true for descending connections + + align:start position:0% +true for descending connections + + + align:start position:0% +true for descending connections +connections that go to those that are + + align:start position:0% +connections that go to those that are + + + align:start position:0% +connections that go to those that are +for the control of axial muscles tend to + + align:start position:0% +for the control of axial muscles tend to + + + align:start position:0% +for the control of axial muscles tend to +be + + align:start position:0% +be + + + align:start position:0% +be +bilateral that's a very important point + + align:start position:0% +bilateral that's a very important point + + + align:start position:0% +bilateral that's a very important point +if you're studying studying doing lesion + + align:start position:0% +if you're studying studying doing lesion + + + align:start position:0% +if you're studying studying doing lesion +studies the + + align:start position:0% +studies the + + + align:start position:0% +studies the +function okay so then + + align:start position:0% +function okay so then + + + align:start position:0% +function okay so then +in this study by it's a classic study by + + align:start position:0% +in this study by it's a classic study by + + + align:start position:0% +in this study by it's a classic study by +uh henriquez tyers a very well-known + + align:start position:0% +uh henriquez tyers a very well-known + + + align:start position:0% +uh henriquez tyers a very well-known +neuroanatomist a Dutch neuroanatomist a + + align:start position:0% +neuroanatomist a Dutch neuroanatomist a + + + align:start position:0% +neuroanatomist a Dutch neuroanatomist a +colleague of + + align:start position:0% +colleague of + + + align:start position:0% +colleague of +Na um and his student Lawrence that did + + align:start position:0% +Na um and his student Lawrence that did + + + align:start position:0% +Na um and his student Lawrence that did +this study back in the 60s published it + + align:start position:0% +this study back in the 60s published it + + + align:start position:0% +this study back in the 60s published it +in + + align:start position:0% +in + + + align:start position:0% +in +brain and everything they found applies + + align:start position:0% +brain and everything they found applies + + + align:start position:0% +brain and everything they found applies +pretty much to humans as well and + + align:start position:0% +pretty much to humans as well and + + + align:start position:0% +pretty much to humans as well and +corresponds to many findings in the + + align:start position:0% +corresponds to many findings in the + + + align:start position:0% +corresponds to many findings in the +clinic okay but what this the upper + + align:start position:0% +clinic okay but what this the upper + + + align:start position:0% +clinic okay but what this the upper +section show here are the patterns of + + align:start position:0% +section show here are the patterns of + + + align:start position:0% +section show here are the patterns of +termination of first of all at the left + + align:start position:0% +termination of first of all at the left + + + align:start position:0% +termination of first of all at the left +the cortical spinal tract or the part of + + align:start position:0% +the cortical spinal tract or the part of + + + align:start position:0% +the cortical spinal tract or the part of +the cortical spinal tract coming from + + align:start position:0% +the cortical spinal tract coming from + + + align:start position:0% +the cortical spinal tract coming from +precentral gyrus the motor cortex okay + + align:start position:0% +precentral gyrus the motor cortex okay + + + align:start position:0% +precentral gyrus the motor cortex okay +and it shows that it goes + + align:start position:0% +and it shows that it goes + + + align:start position:0% +and it shows that it goes +everywhere if we include the post + + align:start position:0% +everywhere if we include the post + + + align:start position:0% +everywhere if we include the post +Central gyrus then you'll see it goes to + + align:start position:0% +Central gyrus then you'll see it goes to + + + align:start position:0% +Central gyrus then you'll see it goes to +the dorsal horn too so pretty much + + align:start position:0% +the dorsal horn too so pretty much + + + align:start position:0% +the dorsal horn too so pretty much +everything and it also crosses the + + align:start position:0% +everything and it also crosses the + + + align:start position:0% +everything and it also crosses the +midline this is just the left cortical + + align:start position:0% +midline this is just the left cortical + + + align:start position:0% +midline this is just the left cortical +spinal track it goes to both sides but + + align:start position:0% +spinal track it goes to both sides but + + + align:start position:0% +spinal track it goes to both sides but +only in that ventromedial + + align:start position:0% +only in that ventromedial + + + align:start position:0% +only in that ventromedial +area the part that controls the axial + + align:start position:0% +area the part that controls the axial + + + align:start position:0% +area the part that controls the axial +muscle + + align:start position:0% +muscle + + + align:start position:0% +muscle +muscles okay so then he's got Pathways + + align:start position:0% +muscles okay so then he's got Pathways + + + align:start position:0% +muscles okay so then he's got Pathways +that travel through the come from the + + align:start position:0% +that travel through the come from the + + + align:start position:0% +that travel through the come from the +lateral brain stem including the red + + align:start position:0% +lateral brain stem including the red + + + align:start position:0% +lateral brain stem including the red +nocus the midbrain and they travel + + align:start position:0% +nocus the midbrain and they travel + + + align:start position:0% +nocus the midbrain and they travel +laterally through the hindbrain they're + + align:start position:0% +laterally through the hindbrain they're + + + align:start position:0% +laterally through the hindbrain they're +joined by axons from lateral reticular + + align:start position:0% +joined by axons from lateral reticular + + + align:start position:0% +joined by axons from lateral reticular +formation cells okay and they terminate + + align:start position:0% +formation cells okay and they terminate + + + align:start position:0% +formation cells okay and they terminate +in this dorsal lateral part of the + + align:start position:0% +in this dorsal lateral part of the + + + align:start position:0% +in this dorsal lateral part of the +interneuronal + + align:start position:0% +interneuronal + + + align:start position:0% +interneuronal +group they tend to spare the ventral + + align:start position:0% +group they tend to spare the ventral + + + align:start position:0% +group they tend to spare the ventral +medial area for the most part and they + + align:start position:0% +medial area for the most part and they + + + align:start position:0% +medial area for the most part and they +generally don't cross the + + align:start position:0% +generally don't cross the + + + align:start position:0% +generally don't cross the +midline then if you look at the medial + + align:start position:0% +midline then if you look at the medial + + + align:start position:0% +midline then if you look at the medial +Pathways medial Rin + + align:start position:0% + + + + align:start position:0% + +stem I'm calling ventromedial here + + align:start position:0% +stem I'm calling ventromedial here + + + align:start position:0% +stem I'm calling ventromedial here +because they're terminating + + align:start position:0% +because they're terminating + + + align:start position:0% +because they're terminating +ventromedially in the + + align:start position:0% +ventromedially in the + + + align:start position:0% +ventromedially in the +cord they that's where You' the + + align:start position:0% +cord they that's where You' the + + + align:start position:0% +cord they that's where You' the +tectospinal pathway terminating the + + align:start position:0% +tectospinal pathway terminating the + + + align:start position:0% +tectospinal pathway terminating the +vestibulospinal the ones from the + + align:start position:0% +vestibulospinal the ones from the + + + align:start position:0% +vestibulospinal the ones from the +cerebellum the pigos spinal and medial + + align:start position:0% +cerebellum the pigos spinal and medial + + + align:start position:0% +cerebellum the pigos spinal and medial +reticular spinals a lot of lot of + + align:start position:0% +reticular spinals a lot of lot of + + + align:start position:0% +reticular spinals a lot of lot of +different groups of axons send their + + align:start position:0% +different groups of axons send their + + + align:start position:0% +different groups of axons send their +axons always down in these medial + + align:start position:0% +axons always down in these medial + + + align:start position:0% +axons always down in these medial +regions of the vental column and they + + align:start position:0% +regions of the vental column and they + + + align:start position:0% +regions of the vental column and they +terminate in that pattern + + align:start position:0% + + + + align:start position:0% + +again if you just look at projections + + align:start position:0% +again if you just look at projections + + + align:start position:0% +again if you just look at projections +from the left side here + + align:start position:0% +from the left side here + + + align:start position:0% +from the left side here +they terminate more on the left than the + + align:start position:0% +they terminate more on the left than the + + + align:start position:0% +they terminate more on the left than the +right but they terminate + + align:start position:0% + + + + align:start position:0% + +bilaterally + + align:start position:0% +bilaterally + + + align:start position:0% +bilaterally +okay so now we can we can draw pictures + + align:start position:0% +okay so now we can we can draw pictures + + + align:start position:0% +okay so now we can we can draw pictures +like this to represent these three + + align:start position:0% +like this to represent these three + + + align:start position:0% +like this to represent these three +descending Pathways from cortex from the + + align:start position:0% +descending Pathways from cortex from the + + + align:start position:0% +descending Pathways from cortex from the +lateral brain stem and from the medial + + align:start position:0% +lateral brain stem and from the medial + + + align:start position:0% +lateral brain stem and from the medial +brain + + align:start position:0% +brain + + + align:start position:0% +brain +stem okay + + align:start position:0% +stem okay + + + align:start position:0% +stem okay +and I have this in color in the book so + + align:start position:0% +and I have this in color in the book so + + + align:start position:0% +and I have this in color in the book so +a little easier but all I do is show an + + align:start position:0% +a little easier but all I do is show an + + + align:start position:0% +a little easier but all I do is show an +a monkey brain with the enlarged spinal + + align:start position:0% +a monkey brain with the enlarged spinal + + + align:start position:0% +a monkey brain with the enlarged spinal +cord so we can see it a little better + + align:start position:0% +cord so we can see it a little better + + + align:start position:0% +cord so we can see it a little better +just separate the + + align:start position:0% +just separate the + + + align:start position:0% +just separate the +ones coming from the representation in + + align:start position:0% +ones coming from the representation in + + + align:start position:0% +ones coming from the representation in +the motor cortex of the body axis that + + align:start position:0% +the motor cortex of the body axis that + + + align:start position:0% +the motor cortex of the body axis that +is the back and neck and then + + align:start position:0% +is the back and neck and then + + + align:start position:0% +is the back and neck and then +representation of the + + align:start position:0% + + + + align:start position:0% + +limbs these are not this is a common + + align:start position:0% +limbs these are not this is a common + + + align:start position:0% +limbs these are not this is a common +mistake that most of your compatriots + + align:start position:0% +mistake that most of your compatriots + + + align:start position:0% +mistake that most of your compatriots +that don't take this class will make + + align:start position:0% +that don't take this class will make + + + align:start position:0% +that don't take this class will make +these are not motor neurons remember the + + align:start position:0% +these are not motor neurons remember the + + + align:start position:0% +these are not motor neurons remember the +defin how do we Define a motor + + align:start position:0% +defin how do we Define a motor + + + align:start position:0% +defin how do we Define a motor +neuron an axon that leaves the central + + align:start position:0% +neuron an axon that leaves the central + + + align:start position:0% +neuron an axon that leaves the central +nervous system and terminates on an + + align:start position:0% +nervous system and terminates on an + + + align:start position:0% +nervous system and terminates on an +eector organ usually a muscle okay those + + align:start position:0% +eector organ usually a muscle okay those + + + align:start position:0% +eector organ usually a muscle okay those +are the true motor neurons these are + + align:start position:0% +are the true motor neurons these are + + + align:start position:0% +are the true motor neurons these are +Pathways that among other things connect + + align:start position:0% +Pathways that among other things connect + + + align:start position:0% +Pathways that among other things connect +with motor neurons but most of them go + + align:start position:0% +with motor neurons but most of them go + + + align:start position:0% +with motor neurons but most of them go +to inter + + align:start position:0% +to inter + + + align:start position:0% +to inter +okay and if it's motor cortex they're + + align:start position:0% +okay and if it's motor cortex they're + + + align:start position:0% +okay and if it's motor cortex they're +usually concerned with movement but they + + align:start position:0% +usually concerned with movement but they + + + align:start position:0% +usually concerned with movement but they +go other places too they go to the + + align:start position:0% +go other places too they go to the + + + align:start position:0% +go other places too they go to the +cerebellum they go to the part of the + + align:start position:0% +cerebellum they go to the part of the + + + align:start position:0% +cerebellum they go to the part of the +inter neuronal um the great network but + + align:start position:0% +inter neuronal um the great network but + + + align:start position:0% +inter neuronal um the great network but +but now to describe okay so I separate + + align:start position:0% +but now to describe okay so I separate + + + align:start position:0% +but now to describe okay so I separate +them on these two diagrams and you just + + align:start position:0% +them on these two diagrams and you just + + + align:start position:0% +them on these two diagrams and you just +notice the ones controlling distal + + align:start position:0% +notice the ones controlling distal + + + align:start position:0% +notice the ones controlling distal +muscles which I've drawn in solid line + + align:start position:0% +muscles which I've drawn in solid line + + + align:start position:0% +muscles which I've drawn in solid line +here + + align:start position:0% +here + + + align:start position:0% +here +uh I show show them I show them in blue + + align:start position:0% +uh I show show them I show them in blue + + + align:start position:0% +uh I show show them I show them in blue +and book they they're terminating mainly + + align:start position:0% +and book they they're terminating mainly + + + align:start position:0% +and book they they're terminating mainly +in the enlargements so in the two + + align:start position:0% +in the enlargements so in the two + + + align:start position:0% +in the enlargements so in the two +enlargements you see them here too and + + align:start position:0% +enlargements you see them here too and + + + align:start position:0% +enlargements you see them here too and +see the color helps a lot you don't it's + + align:start position:0% +see the color helps a lot you don't it's + + + align:start position:0% +see the color helps a lot you don't it's +a little harder to separate here but + + align:start position:0% +a little harder to separate here but + + + align:start position:0% +a little harder to separate here but +it's the concept is very simple okay and + + align:start position:0% +it's the concept is very simple okay and + + + align:start position:0% +it's the concept is very simple okay and +then + + align:start position:0% +then + + + align:start position:0% +then +we I show here the position of those + + align:start position:0% +we I show here the position of those + + + align:start position:0% +we I show here the position of those +corticospinal axons here they are + + align:start position:0% +corticospinal axons here they are + + + align:start position:0% +corticospinal axons here they are +throughout the paramal tract in the + + align:start position:0% +throughout the paramal tract in the + + + align:start position:0% +throughout the paramal tract in the +hindbrain here in the midbrain they're + + align:start position:0% +hindbrain here in the midbrain they're + + + align:start position:0% +hindbrain here in the midbrain they're +in the middle portion of the Cal pet + + align:start position:0% +in the middle portion of the Cal pet + + + align:start position:0% +in the middle portion of the Cal pet +unle the other ones are going to + + align:start position:0% +unle the other ones are going to + + + align:start position:0% +unle the other ones are going to +terminate before they get to spinal cord + + align:start position:0% +terminate before they get to spinal cord + + + align:start position:0% +terminate before they get to spinal cord +a lot of them in the the pontine + + align:start position:0% +a lot of them in the the pontine + + + align:start position:0% +a lot of them in the the pontine +gray all right so here I showed the rub + + align:start position:0% +gray all right so here I showed the rub + + + align:start position:0% +gray all right so here I showed the rub +the tech the rubrospinal + + align:start position:0% +the tech the rubrospinal + + + align:start position:0% +the tech the rubrospinal +axons which cross and + + align:start position:0% +axons which cross and + + + align:start position:0% +axons which cross and +travel then they move laterally as they + + align:start position:0% +travel then they move laterally as they + + + align:start position:0% +travel then they move laterally as they +descend and here they are in the hind R + + align:start position:0% +descend and here they are in the hind R + + + align:start position:0% +descend and here they are in the hind R +right out here at the lateral lateral + + align:start position:0% +right out here at the lateral lateral + + + align:start position:0% +right out here at the lateral lateral +Edge so now the axon's controlling the + + align:start position:0% +Edge so now the axon's controlling the + + + align:start position:0% +Edge so now the axon's controlling the +more distal muscles if the anatomy is + + align:start position:0% +more distal muscles if the anatomy is + + + align:start position:0% +more distal muscles if the anatomy is +giving us the right idea can be found in + + align:start position:0% +giving us the right idea can be found in + + + align:start position:0% +giving us the right idea can be found in +those two places here and here coming + + align:start position:0% +those two places here and here coming + + + align:start position:0% +those two places here and here coming +from + + align:start position:0% + + + + align:start position:0% + +the except if I want these to + + align:start position:0% + + + + align:start position:0% + +correspond I have to say here and + + align:start position:0% +correspond I have to say here and + + + align:start position:0% +correspond I have to say here and +here because these haven't crossed yet + + align:start position:0% +here because these haven't crossed yet + + + align:start position:0% +here because these haven't crossed yet +these have crossed okay that's just + + align:start position:0% +these have crossed okay that's just + + + align:start position:0% +these have crossed okay that's just +that's a detail to keep in mind okay so + + align:start position:0% +that's a detail to keep in mind okay so + + + align:start position:0% +that's a detail to keep in mind okay so +and then here for the medial Pathways I + + align:start position:0% +and then here for the medial Pathways I + + + align:start position:0% +and then here for the medial Pathways I +show The + + align:start position:0% +show The + + + align:start position:0% +show The +tectospinal + + align:start position:0% +tectospinal + + + align:start position:0% +tectospinal +Crossing and then the + + align:start position:0% +Crossing and then the + + + align:start position:0% +Crossing and then the +vestibulospinal are + + align:start position:0% +vestibulospinal are + + + align:start position:0% +vestibulospinal are +uncrossed + + align:start position:0% +uncrossed + + + align:start position:0% +uncrossed +okay because they're + + align:start position:0% +okay because they're + + + align:start position:0% +okay because they're +hindra okay and I could have added the + + align:start position:0% +hindra okay and I could have added the + + + align:start position:0% +hindra okay and I could have added the +the ones from + + align:start position:0% +the ones from + + + align:start position:0% +the ones from +cerebellum I do show a few from + + align:start position:0% +cerebellum I do show a few from + + + align:start position:0% +cerebellum I do show a few from +reticular formation here that are + + align:start position:0% +reticular formation here that are + + + align:start position:0% +reticular formation here that are +joining that pathway and those are the + + align:start position:0% +joining that pathway and those are the + + + align:start position:0% +joining that pathway and those are the +ones that go down + + align:start position:0% +ones that go down + + + align:start position:0% +ones that go down +through the cord and terminate the ne + + align:start position:0% +through the cord and terminate the ne + + + align:start position:0% +through the cord and terminate the ne +intermedial region and here I show + + align:start position:0% +intermedial region and here I show + + + align:start position:0% +intermedial region and here I show +them in the + + align:start position:0% +them in the + + + align:start position:0% +them in the +cross-sections + + align:start position:0% +cross-sections + + + align:start position:0% +cross-sections +tectospinal I just showed the + + align:start position:0% +tectospinal I just showed the + + + align:start position:0% +tectospinal I just showed the +tectospinal and and the reticul spinal + + align:start position:0% +tectospinal and and the reticul spinal + + + align:start position:0% +tectospinal and and the reticul spinal +Origins here the disbo spinal is only on + + align:start position:0% +Origins here the disbo spinal is only on + + + align:start position:0% +Origins here the disbo spinal is only on +this one all right + + align:start position:0% + + + + align:start position:0% + +so so + + align:start position:0% +so so + + + align:start position:0% +so so +then what are the three lesions that + + align:start position:0% +then what are the three lesions that + + + align:start position:0% +then what are the three lesions that +lawren and kypers + + align:start position:0% +lawren and kypers + + + align:start position:0% +lawren and kypers +made let's just go through the logic of + + align:start position:0% +made let's just go through the logic of + + + align:start position:0% +made let's just go through the logic of +lawren and Kyper study very + + align:start position:0% +lawren and Kyper study very + + + align:start position:0% +lawren and Kyper study very +straightforward they did try just + + align:start position:0% +straightforward they did try just + + + align:start position:0% +straightforward they did try just +eliminating the medial hindbrain + + align:start position:0% +eliminating the medial hindbrain + + + align:start position:0% +eliminating the medial hindbrain +Pathways or the lateral Pathways and + + align:start position:0% +Pathways or the lateral Pathways and + + + align:start position:0% +Pathways or the lateral Pathways and +otherwise intact monkeys they didn't get + + align:start position:0% +otherwise intact monkeys they didn't get + + + align:start position:0% +otherwise intact monkeys they didn't get +long lasting effects at + + align:start position:0% +long lasting effects at + + + align:start position:0% +long lasting effects at +all so they reason that the re that + + align:start position:0% +all so they reason that the re that + + + align:start position:0% +all so they reason that the re that +probably that's because the cortex is so + + align:start position:0% +probably that's because the cortex is so + + + align:start position:0% +probably that's because the cortex is so +dominant and they had spared the whole + + align:start position:0% +dominant and they had spared the whole + + + align:start position:0% +dominant and they had spared the whole +cortical spinal pathway so they always + + align:start position:0% +cortical spinal pathway so they always + + + align:start position:0% +cortical spinal pathway so they always +started by + + align:start position:0% +started by + + + align:start position:0% +started by +eliminating Pathways from cortex they + + align:start position:0% +eliminating Pathways from cortex they + + + align:start position:0% +eliminating Pathways from cortex they +cut the paramal tract + + align:start position:0% +cut the paramal tract + + + align:start position:0% +cut the paramal tract +yes you have to talk Lou this this + + align:start position:0% +yes you have to talk Lou this this + + + align:start position:0% +yes you have to talk Lou this this +ventilation is pretty + + align:start position:0% + + + + align:start position:0% + +lck the type yeah you do get some + + align:start position:0% +lck the type yeah you do get some + + + align:start position:0% +lck the type yeah you do get some +recovery but remember there's a lot of + + align:start position:0% +recovery but remember there's a lot of + + + align:start position:0% +recovery but remember there's a lot of +different Pathways involved here and + + align:start position:0% +different Pathways involved here and + + + align:start position:0% +different Pathways involved here and +it's very difficult to get all of them + + align:start position:0% +it's very difficult to get all of them + + + align:start position:0% +it's very difficult to get all of them +you know and also there so there's + + align:start position:0% +you know and also there so there's + + + align:start position:0% +you know and also there so there's +various ways the brain can compensate + + align:start position:0% +various ways the brain can compensate + + + align:start position:0% +various ways the brain can compensate +but it's remarkable how little the + + align:start position:0% +but it's remarkable how little the + + + align:start position:0% +but it's remarkable how little the +compensation is when they do a really + + align:start position:0% +compensation is when they do a really + + + align:start position:0% +compensation is when they do a really +good + + align:start position:0% +good + + + align:start position:0% +good +leion and then I ask uh the functions of + + align:start position:0% +leion and then I ask uh the functions of + + + align:start position:0% +leion and then I ask uh the functions of +these three major Pathways well when I I + + align:start position:0% +these three major Pathways well when I I + + + align:start position:0% +these three major Pathways well when I I +introduced it with the outputs you can + + align:start position:0% +introduced it with the outputs you can + + + align:start position:0% +introduced it with the outputs you can +pretty much predict the function so + + align:start position:0% +pretty much predict the function so + + + align:start position:0% +pretty much predict the function so +we're going to go through through that + + align:start position:0% +we're going to go through through that + + + align:start position:0% +we're going to go through through that +uh and I want to know why would diis + + align:start position:0% +uh and I want to know why would diis + + + align:start position:0% +uh and I want to know why would diis +effects of lesions of one of the + + align:start position:0% +effects of lesions of one of the + + + align:start position:0% +effects of lesions of one of the +descending Pathways in the study be + + align:start position:0% +descending Pathways in the study be + + + align:start position:0% +descending Pathways in the study be +greater in humans than in + + align:start position:0% +greater in humans than in + + + align:start position:0% +greater in humans than in +monkeys so we'll come back to that when + + align:start position:0% +monkeys so we'll come back to that when + + + align:start position:0% +monkeys so we'll come back to that when +we talk about + + align:start position:0% +we talk about + + + align:start position:0% +we talk about +these these functional effects of the + + align:start position:0% +these these functional effects of the + + + align:start position:0% +these these functional effects of the +lesions this is their + + align:start position:0% +lesions this is their + + + align:start position:0% +lesions this is their +logic you eliminate the cortical clinal + + align:start position:0% +logic you eliminate the cortical clinal + + + align:start position:0% +logic you eliminate the cortical clinal +projections they did that at the + + align:start position:0% +projections they did that at the + + + align:start position:0% +projections they did that at the +hindbrain L + + align:start position:0% +hindbrain L + + + align:start position:0% +hindbrain L +by coming in through the roof of the + + align:start position:0% +by coming in through the roof of the + + + align:start position:0% +by coming in through the roof of the +mouth I've done this also in + + align:start position:0% +mouth I've done this also in + + + align:start position:0% +mouth I've done this also in +hamsters with a student cine C who's + + align:start position:0% +hamsters with a student cine C who's + + + align:start position:0% +hamsters with a student cine C who's +been at the University of Wisconsin now + + align:start position:0% +been at the University of Wisconsin now + + + align:start position:0% +been at the University of Wisconsin now +for many + + align:start position:0% +for many + + + align:start position:0% +for many +years I don't know if anybody else has + + align:start position:0% +years I don't know if anybody else has + + + align:start position:0% +years I don't know if anybody else has +attempted that in these little animals + + align:start position:0% +attempted that in these little animals + + + align:start position:0% +attempted that in these little animals +but we did and we succeeded to do it at + + align:start position:0% +but we did and we succeeded to do it at + + + align:start position:0% +but we did and we succeeded to do it at +least + + align:start position:0% +least + + + align:start position:0% +least +unilaterally but we you can see you see + + align:start position:0% +unilaterally but we you can see you see + + + align:start position:0% +unilaterally but we you can see you see +this in the Sheep Ranger section you can + + align:start position:0% +this in the Sheep Ranger section you can + + + align:start position:0% +this in the Sheep Ranger section you can +see the paranal track if the problem is + + align:start position:0% +see the paranal track if the problem is + + + align:start position:0% +see the paranal track if the problem is +you also see this huge artery called the + + align:start position:0% +you also see this huge artery called the + + + align:start position:0% +you also see this huge artery called the +Basler artery so what we do and also + + align:start position:0% +Basler artery so what we do and also + + + align:start position:0% +Basler artery so what we do and also +there's other problems when you're doing + + align:start position:0% +there's other problems when you're doing + + + align:start position:0% +there's other problems when you're doing +that kind of surgery you tend to stretch + + align:start position:0% +that kind of surgery you tend to stretch + + + align:start position:0% +that kind of surgery you tend to stretch +nerves in the neck and that can cause + + align:start position:0% +nerves in the neck and that can cause + + + align:start position:0% +nerves in the neck and that can cause +them to pull their breath in and hold it + + align:start position:0% +them to pull their breath in and hold it + + + align:start position:0% +them to pull their breath in and hold it +because you're eliminating normal + + align:start position:0% +because you're eliminating normal + + + align:start position:0% +because you're eliminating normal +Pathways involved in breathing so what + + align:start position:0% +Pathways involved in breathing so what + + + align:start position:0% +Pathways involved in breathing so what +we found is if we just flood the whole + + align:start position:0% +we found is if we just flood the whole + + + align:start position:0% +we found is if we just flood the whole +area with ice cold + + align:start position:0% +area with ice cold + + + align:start position:0% +area with ice cold +sailing we reduce the conduction so much + + align:start position:0% +sailing we reduce the conduction so much + + + align:start position:0% +sailing we reduce the conduction so much +in those nerves that they they keep + + align:start position:0% +in those nerves that they they keep + + + align:start position:0% +in those nerves that they they keep +breathing just fine and + + align:start position:0% +breathing just fine and + + + align:start position:0% +breathing just fine and +then then we take a little spatula nudge + + align:start position:0% +then then we take a little spatula nudge + + + align:start position:0% +then then we take a little spatula nudge +the Basler artery + + align:start position:0% +the Basler artery + + + align:start position:0% +the Basler artery +over and we have a little spatula like + + align:start position:0% +over and we have a little spatula like + + + align:start position:0% +over and we have a little spatula like +knife very sharp we know exactly how + + align:start position:0% +knife very sharp we know exactly how + + + align:start position:0% +knife very sharp we know exactly how +deep to go and we can do what Lawrence + + align:start position:0% +deep to go and we can do what Lawrence + + + align:start position:0% +deep to go and we can do what Lawrence +and kypers did here here's their lesions + + align:start position:0% +and kypers did here here's their lesions + + + align:start position:0% +and kypers did here here's their lesions +cut the paramal track this is the level + + align:start position:0% +cut the paramal track this is the level + + + align:start position:0% +cut the paramal track this is the level +they cut + + align:start position:0% +they cut + + + align:start position:0% +they cut +it they're making a cut from the ventral + + align:start position:0% +it they're making a cut from the ventral + + + align:start position:0% +it they're making a cut from the ventral +side just cutting the parameter tracks + + align:start position:0% +side just cutting the parameter tracks + + + align:start position:0% +side just cutting the parameter tracks +and + + align:start position:0% +and + + + align:start position:0% +and +usually just above the paramet tract is + + align:start position:0% +usually just above the paramet tract is + + + align:start position:0% +usually just above the paramet tract is +the medial medial liscus so they often + + align:start position:0% +the medial medial liscus so they often + + + align:start position:0% +the medial medial liscus so they often +did cut damage medial liscus fibers so + + align:start position:0% +did cut damage medial liscus fibers so + + + align:start position:0% +did cut damage medial liscus fibers so +because of that they had to have + + align:start position:0% +because of that they had to have + + + align:start position:0% +because of that they had to have +controls where they had lesions for + + align:start position:0% +controls where they had lesions for + + + align:start position:0% +controls where they had lesions for +example the dorsal column nuclei so they + + align:start position:0% +example the dorsal column nuclei so they + + + align:start position:0% +example the dorsal column nuclei so they +didn't they got rid of the medial + + align:start position:0% +didn't they got rid of the medial + + + align:start position:0% +didn't they got rid of the medial +miniscus fiber so they could see that + + align:start position:0% +miniscus fiber so they could see that + + + align:start position:0% +miniscus fiber so they could see that +the functional effects they were seeing + + align:start position:0% +the functional effects they were seeing + + + align:start position:0% +the functional effects they were seeing +in their monkeys weren't caused by the + + align:start position:0% +in their monkeys weren't caused by the + + + align:start position:0% +in their monkeys weren't caused by the +medial liscus damage okay and then they + + align:start position:0% +medial liscus damage okay and then they + + + align:start position:0% +medial liscus damage okay and then they +allowed them to recover from that lesion + + align:start position:0% +allowed them to recover from that lesion + + + align:start position:0% +allowed them to recover from that lesion +as much as they could and then they did + + align:start position:0% +as much as they could and then they did + + + align:start position:0% +as much as they could and then they did +one of these two lesions either they cut + + align:start position:0% +one of these two lesions either they cut + + + align:start position:0% +one of these two lesions either they cut +the lateral pathways on one + + align:start position:0% + + + + align:start position:0% + +side and remember that doesn't it stays + + align:start position:0% +side and remember that doesn't it stays + + + align:start position:0% +side and remember that doesn't it stays +on one side so you can compare the two + + align:start position:0% +on one side so you can compare the two + + + align:start position:0% +on one side so you can compare the two +sides of the + + align:start position:0% +sides of the + + + align:start position:0% +sides of the +animal or they they did the medial + + align:start position:0% +animal or they they did the medial + + + align:start position:0% +animal or they they did the medial +Pathways they tried it unilaterally + + align:start position:0% +Pathways they tried it unilaterally + + + align:start position:0% +Pathways they tried it unilaterally +didn't get much effect + + align:start position:0% +didn't get much effect + + + align:start position:0% +didn't get much effect +but if they did it bilaterally then they + + align:start position:0% +but if they did it bilaterally then they + + + align:start position:0% +but if they did it bilaterally then they +got drastic effects + + align:start position:0% +got drastic effects + + + align:start position:0% +got drastic effects +so this is what they're doing they'll + + align:start position:0% +so this is what they're doing they'll + + + align:start position:0% +so this is what they're doing they'll +going right through the damaged paramal + + align:start position:0% +going right through the damaged paramal + + + align:start position:0% +going right through the damaged paramal +track and it's already degenerating + + align:start position:0% +track and it's already degenerating + + + align:start position:0% +track and it's already degenerating +remember from the earlier lesion and + + align:start position:0% +remember from the earlier lesion and + + + align:start position:0% +remember from the earlier lesion and +they cut all those medial Pathways they + + align:start position:0% +they cut all those medial Pathways they + + + align:start position:0% +they cut all those medial Pathways they +all descend right near the midline + + align:start position:0% + + + + align:start position:0% + +yes yeah that's a good question there's + + align:start position:0% +yes yeah that's a good question there's + + + align:start position:0% +yes yeah that's a good question there's +there's a little a little bit and it's + + align:start position:0% +there's a little a little bit and it's + + + align:start position:0% +there's a little a little bit and it's +somewhat variable it's not as much as in + + align:start position:0% +somewhat variable it's not as much as in + + + align:start position:0% +somewhat variable it's not as much as in +humans but there is some lateral dominas + + align:start position:0% +humans but there is some lateral dominas + + + align:start position:0% +humans but there is some lateral dominas +there is some asymmetry in the brains + + align:start position:0% +there is some asymmetry in the brains + + + align:start position:0% +there is some asymmetry in the brains +too the most drastic asymmetry they + + align:start position:0% +too the most drastic asymmetry they + + + align:start position:0% +too the most drastic asymmetry they +found though in animals is in fish in + + align:start position:0% +found though in animals is in fish in + + + align:start position:0% +found though in animals is in fish in +the haban OR nuclei and they don't still + + align:start position:0% +the haban OR nuclei and they don't still + + + align:start position:0% +the haban OR nuclei and they don't still +don't know a whole lot about why that is + + align:start position:0% +don't know a whole lot about why that is + + + align:start position:0% +don't know a whole lot about why that is +okay so here's what happens you start + + align:start position:0% +okay so here's what happens you start + + + align:start position:0% +okay so here's what happens you start +with the Pam paramid aomy you get rid of + + align:start position:0% +with the Pam paramid aomy you get rid of + + + align:start position:0% +with the Pam paramid aomy you get rid of +those cortical spinal fibers you do it + + align:start position:0% +those cortical spinal fibers you do it + + + align:start position:0% +those cortical spinal fibers you do it +bilaterally initially they seem almost + + align:start position:0% +bilaterally initially they seem almost + + + align:start position:0% +bilaterally initially they seem almost +paralyzed and if you do this I here the + + align:start position:0% +paralyzed and if you do this I here the + + + align:start position:0% +paralyzed and if you do this I here the +question refers + + align:start position:0% +question refers + + + align:start position:0% +question refers +to this is the diasis effect because + + align:start position:0% +to this is the diasis effect because + + + align:start position:0% +to this is the diasis effect because +they recover a lot from it but why is + + align:start position:0% +they recover a lot from it but why is + + + align:start position:0% +they recover a lot from it but why is +that effect so much greater in humans + + align:start position:0% +that effect so much greater in humans + + + align:start position:0% +that effect so much greater in humans +remember it's just + + align:start position:0% +remember it's just + + + align:start position:0% +remember it's just +quantitative the pathway is bigger in + + align:start position:0% +quantitative the pathway is bigger in + + + align:start position:0% +quantitative the pathway is bigger in +humans the motor cortex is even more + + align:start position:0% +humans the motor cortex is even more + + + align:start position:0% +humans the motor cortex is even more +important in humans so humans after a + + align:start position:0% +important in humans so humans after a + + + align:start position:0% +important in humans so humans after a +paramal track + + align:start position:0% +paramal track + + + align:start position:0% +paramal track +section you know lose even their spinal + + align:start position:0% +section you know lose even their spinal + + + align:start position:0% +section you know lose even their spinal +reflexes for a well clear that's just + + align:start position:0% +reflexes for a well clear that's just + + + align:start position:0% +reflexes for a well clear that's just +like spinal shock transction to spinal + + align:start position:0% +like spinal shock transction to spinal + + + align:start position:0% +like spinal shock transction to spinal +cord but the monkeys lose speed and + + align:start position:0% +cord but the monkeys lose speed and + + + align:start position:0% +cord but the monkeys lose speed and +strength and they never completely + + align:start position:0% +strength and they never completely + + + align:start position:0% +strength and they never completely +recover normal speed and normal + + align:start position:0% +recover normal speed and normal + + + align:start position:0% +recover normal speed and normal +strength uh but they do recover a lot + + align:start position:0% +strength uh but they do recover a lot + + + align:start position:0% +strength uh but they do recover a lot +okay humans recover their strength they + + align:start position:0% +okay humans recover their strength they + + + align:start position:0% +okay humans recover their strength they +never recover full + + align:start position:0% +never recover full + + + align:start position:0% +never recover full +coordination + + align:start position:0% +coordination + + + align:start position:0% +coordination +uh but strength they do pretty well in + + align:start position:0% +uh but strength they do pretty well in + + + align:start position:0% +uh but strength they do pretty well in +fact sometimes the reflexes become + + align:start position:0% +fact sometimes the reflexes become + + + align:start position:0% +fact sometimes the reflexes become +overactive stronger than + + align:start position:0% +overactive stronger than + + + align:start position:0% +overactive stronger than +normal because of sprouting that happens + + align:start position:0% +normal because of sprouting that happens + + + align:start position:0% +normal because of sprouting that happens +in the spinal + + align:start position:0% +in the spinal + + + align:start position:0% +in the spinal +cord but the one thing they do lose + + align:start position:0% +cord but the one thing they do lose + + + align:start position:0% +cord but the one thing they do lose +that's that's a qualitative difference + + align:start position:0% +that's that's a qualitative difference + + + align:start position:0% +that's that's a qualitative difference +from normals is they can't do that + + align:start position:0% +from normals is they can't do that + + + align:start position:0% +from normals is they can't do that +anymore they can't pick something up + + align:start position:0% +anymore they can't pick something up + + + align:start position:0% +anymore they can't pick something up +with single digits they have to use + + align:start position:0% +with single digits they have to use + + + align:start position:0% +with single digits they have to use +their whole hand + + align:start position:0% +their whole hand + + + align:start position:0% +their whole hand +together so apparently those latal + + align:start position:0% +together so apparently those latal + + + align:start position:0% +together so apparently those latal +brainstem pathways are quite capable of + + align:start position:0% +brainstem pathways are quite capable of + + + align:start position:0% +brainstem pathways are quite capable of +controlling fairly organized hand + + align:start position:0% +controlling fairly organized hand + + + align:start position:0% +controlling fairly organized hand +movements but when it involves + + align:start position:0% +movements but when it involves + + + align:start position:0% +movements but when it involves +separation separate control of the + + align:start position:0% +separation separate control of the + + + align:start position:0% +separation separate control of the +digits they never really recover all + + align:start position:0% + + + + align:start position:0% + +right I mention + + align:start position:0% +right I mention + + + align:start position:0% +right I mention +here a question that I think I should + + align:start position:0% +here a question that I think I should + + + align:start position:0% +here a question that I think I should +give as a + + align:start position:0% +give as a + + + align:start position:0% +give as a +homework but you will just see a + + align:start position:0% +homework but you will just see a + + + align:start position:0% +homework but you will just see a +discussion in the the + + align:start position:0% +discussion in the the + + + align:start position:0% +discussion in the the +book I'll try to remember this since I'm + + align:start position:0% +book I'll try to remember this since I'm + + + align:start position:0% +book I'll try to remember this since I'm +telling it to you now there is a + + align:start position:0% +telling it to you now there is a + + + align:start position:0% +telling it to you now there is a +discussion of fixed action patterns of + + align:start position:0% +discussion of fixed action patterns of + + + align:start position:0% +discussion of fixed action patterns of +it's comes the only study I know of is I + + align:start position:0% +it's comes the only study I know of is I + + + align:start position:0% +it's comes the only study I know of is I +did with a student Katherine Cayla the + + align:start position:0% +did with a student Katherine Cayla the + + + align:start position:0% +did with a student Katherine Cayla the +woman I mentioned uh we found that they + + align:start position:0% +woman I mentioned uh we found that they + + + align:start position:0% +woman I mentioned uh we found that they +need the paramal track coming from + + align:start position:0% +need the paramal track coming from + + + align:start position:0% +need the paramal track coming from +cortex to do their fixed action patterns + + align:start position:0% +cortex to do their fixed action patterns + + + align:start position:0% +cortex to do their fixed action patterns +of seed shell so read about that and you + + align:start position:0% +of seed shell so read about that and you + + + align:start position:0% +of seed shell so read about that and you +can answer this question + + align:start position:0% + + + + align:start position:0% + +this the corrium for any kind of learned + + align:start position:0% +this the corrium for any kind of learned + + + align:start position:0% +this the corrium for any kind of learned +movements yes but in this hamster study + + align:start position:0% +movements yes but in this hamster study + + + align:start position:0% +movements yes but in this hamster study +we were looking at unlearned movements + + align:start position:0% +we were looking at unlearned movements + + + align:start position:0% +we were looking at unlearned movements +the first time they ever see I we raised + + align:start position:0% +the first time they ever see I we raised + + + align:start position:0% +the first time they ever see I we raised +them in the lab so you can they never + + align:start position:0% +them in the lab so you can they never + + + align:start position:0% +them in the lab so you can they never +they only see food pallets + + align:start position:0% +they only see food pallets + + + align:start position:0% +they only see food pallets +they never see seeds and yet the first + + align:start position:0% +they never see seeds and yet the first + + + align:start position:0% +they never see seeds and yet the first +time I give a hamster a seed I can let + + align:start position:0% +time I give a hamster a seed I can let + + + align:start position:0% +time I give a hamster a seed I can let +him become an adult and I can give them + + align:start position:0% +him become an adult and I can give them + + + align:start position:0% +him become an adult and I can give them +a seed and they can pick it up and shell + + align:start position:0% +a seed and they can pick it up and shell + + + align:start position:0% +a seed and they can pick it up and shell +it faster than you can because it's a + + align:start position:0% +it faster than you can because it's a + + + align:start position:0% +it faster than you can because it's a +fix it's + + align:start position:0% + + + + align:start position:0% + +inborn there are aspects of the sequence + + align:start position:0% +inborn there are aspects of the sequence + + + align:start position:0% +inborn there are aspects of the sequence +that are learned but most grooming is + + align:start position:0% +that are learned but most grooming is + + + align:start position:0% +that are learned but most grooming is +unlearned and uh so you don't get a + + align:start position:0% +unlearned and uh so you don't get a + + + align:start position:0% +unlearned and uh so you don't get a +permanent + + align:start position:0% +permanent + + + align:start position:0% +permanent +disruption uh there's some very good + + align:start position:0% +disruption uh there's some very good + + + align:start position:0% +disruption uh there's some very good +Studies by John Fentress if you look his + + align:start position:0% +Studies by John Fentress if you look his + + + align:start position:0% +Studies by John Fentress if you look his +name up he said El Housey University + + align:start position:0% +name up he said El Housey University + + + align:start position:0% +name up he said El Housey University +he's done many studies of grooming in + + align:start position:0% +he's done many studies of grooming in + + + align:start position:0% +he's done many studies of grooming in +mice + + align:start position:0% +mice + + + align:start position:0% +mice +uh genetic effects as well as lesion + + align:start position:0% +uh genetic effects as well as lesion + + + align:start position:0% +uh genetic effects as well as lesion +effects and showing that they are fixed + + align:start position:0% +effects and showing that they are fixed + + + align:start position:0% +effects and showing that they are fixed +action + + align:start position:0% + + + + align:start position:0% + +patterns + + align:start position:0% +patterns + + + align:start position:0% +patterns +this second question number seven here + + align:start position:0% +this second question number seven here + + + align:start position:0% +this second question number seven here +it refers + + align:start position:0% +it refers + + + align:start position:0% +it refers +to a study of motor system by The Beat + + align:start position:0% +to a study of motor system by The Beat + + + align:start position:0% +to a study of motor system by The Beat +Lab here at + + align:start position:0% +Lab here at + + + align:start position:0% +Lab here at +MIT so U read that and uh see if you can + + align:start position:0% +MIT so U read that and uh see if you can + + + align:start position:0% +MIT so U read that and uh see if you can +figure out I think I make it clear there + + align:start position:0% +figure out I think I make it clear there + + + align:start position:0% +figure out I think I make it clear there +in the book and this + + align:start position:0% +in the book and this + + + align:start position:0% +in the book and this +one we can deal with right now you + + align:start position:0% +one we can deal with right now you + + + align:start position:0% +one we can deal with right now you +should know what best cells are does + + align:start position:0% +should know what best cells are does + + + align:start position:0% +should know what best cells are does +anybody + + align:start position:0% +anybody + + + align:start position:0% +anybody +remember and I want to know how it's + + align:start position:0% +remember and I want to know how it's + + + align:start position:0% +remember and I want to know how it's +related to discovery of frit and H who + + align:start position:0% +related to discovery of frit and H who + + + align:start position:0% +related to discovery of frit and H who +are they + + align:start position:0% +are they + + + align:start position:0% +are they +1870 the first guys + + align:start position:0% +1870 the first guys + + + align:start position:0% +1870 the first guys +to study motor cortex by electrical + + align:start position:0% +to study motor cortex by electrical + + + align:start position:0% +to study motor cortex by electrical +stimulation they defined it as the area + + align:start position:0% +stimulation they defined it as the area + + + align:start position:0% +stimulation they defined it as the area +which when + + align:start position:0% +which when + + + align:start position:0% +which when +stimulated it was a horrible time in + + align:start position:0% +stimulated it was a horrible time in + + + align:start position:0% +stimulated it was a horrible time in +Neuroscience because they didn't have + + align:start position:0% +Neuroscience because they didn't have + + + align:start position:0% +Neuroscience because they didn't have +good anesthesia at all okay so it's very + + align:start position:0% +good anesthesia at all okay so it's very + + + align:start position:0% +good anesthesia at all okay so it's very +difficult to do these experiments they + + align:start position:0% +difficult to do these experiments they + + + align:start position:0% +difficult to do these experiments they +actually did some of it on humans men in + + align:start position:0% +actually did some of it on humans men in + + + align:start position:0% +actually did some of it on humans men in +the Frank oppression War who had had + + align:start position:0% +the Frank oppression War who had had + + + align:start position:0% +the Frank oppression War who had had +their skulls blown off + + align:start position:0% +their skulls blown off + + + align:start position:0% +their skulls blown off +and so they were dying + + align:start position:0% +and so they were dying + + + align:start position:0% +and so they were dying +soldiers they still did some of this + + align:start position:0% +soldiers they still did some of this + + + align:start position:0% +soldiers they still did some of this +work that you know they were their first + + align:start position:0% +work that you know they were their first + + + align:start position:0% +work that you know they were their first +purpose was + + align:start position:0% +purpose was + + + align:start position:0% +purpose was +Medical but then they were able to do a + + align:start position:0% +Medical but then they were able to do a + + + align:start position:0% +Medical but then they were able to do a +little bit of this at the same time but + + align:start position:0% +little bit of this at the same time but + + + align:start position:0% +little bit of this at the same time but +most of the work was done on dogs and + + align:start position:0% +most of the work was done on dogs and + + + align:start position:0% +most of the work was done on dogs and +they were able to uh map out the motor + + align:start position:0% +they were able to uh map out the motor + + + align:start position:0% +they were able to uh map out the motor +cortex it's where with the smallest + + align:start position:0% +cortex it's where with the smallest + + + align:start position:0% +cortex it's where with the smallest +electrical currents you can get movement + + align:start position:0% +electrical currents you can get movement + + + align:start position:0% +electrical currents you can get movement +it doesn't mean you can't get movement + + align:start position:0% +it doesn't mean you can't get movement + + + align:start position:0% +it doesn't mean you can't get movement +from other places in the cortex you can + + align:start position:0% +from other places in the cortex you can + + + align:start position:0% +from other places in the cortex you can +they're descending connections from + + align:start position:0% +they're descending connections from + + + align:start position:0% +they're descending connections from +visual cortex too they don't all go to + + align:start position:0% +visual cortex too they don't all go to + + + align:start position:0% +visual cortex too they don't all go to +motor + + align:start position:0% +motor + + + align:start position:0% +motor +cortex most of them they don't go at all + + align:start position:0% +cortex most of them they don't go at all + + + align:start position:0% +cortex most of them they don't go at all +the motor cortex but they do go to the + + align:start position:0% +the motor cortex but they do go to the + + + align:start position:0% +the motor cortex but they do go to the +brain stem they go to the tectum for + + align:start position:0% +brain stem they go to the tectum for + + + align:start position:0% +brain stem they go to the tectum for +example so they control our anti + + align:start position:0% +example so they control our anti + + + align:start position:0% +example so they control our anti +movements directly from visual cortex by + + align:start position:0% +movements directly from visual cortex by + + + align:start position:0% +movements directly from visual cortex by +projecting to detect them so that's a + + align:start position:0% +projecting to detect them so that's a + + + align:start position:0% +projecting to detect them so that's a +type of motor cortex too but what we + + align:start position:0% +type of motor cortex too but what we + + + align:start position:0% +type of motor cortex too but what we +call the motor cortex is the specialized + + align:start position:0% +call the motor cortex is the specialized + + + align:start position:0% +call the motor cortex is the specialized +somat sensory + + align:start position:0% +somat sensory + + + align:start position:0% +somat sensory +area rostal to the primary sensory + + align:start position:0% +area rostal to the primary sensory + + + align:start position:0% +area rostal to the primary sensory +cortex in + + align:start position:0% +cortex in + + + align:start position:0% +cortex in +mammals okay B cells are the giant + + align:start position:0% +mammals okay B cells are the giant + + + align:start position:0% +mammals okay B cells are the giant +paramal cells that you find in that area + + align:start position:0% +paramal cells that you find in that area + + + align:start position:0% +paramal cells that you find in that area +that sh hitc mapped out as the motor + + align:start position:0% +that sh hitc mapped out as the motor + + + align:start position:0% +that sh hitc mapped out as the motor +cortex it was just four years + + align:start position:0% +cortex it was just four years + + + align:start position:0% +cortex it was just four years +later 187 + + align:start position:0% +later 187 + + + align:start position:0% +later 187 +1874 that bets described these giant + + align:start position:0% +1874 that bets described these giant + + + align:start position:0% +1874 that bets described these giant +cells they are the cells that give rise + + align:start position:0% +cells they are the cells that give rise + + + align:start position:0% +cells they are the cells that give rise +to the very long aons that go all the + + align:start position:0% +to the very long aons that go all the + + + align:start position:0% +to the very long aons that go all the +way down the spinal cord and they no + + align:start position:0% +way down the spinal cord and they no + + + align:start position:0% +way down the spinal cord and they no +doubt include neurons that project + + align:start position:0% +doubt include neurons that project + + + align:start position:0% +doubt include neurons that project +directly to motor + + align:start position:0% + + + + align:start position:0% + +neurons no no they're just the really + + align:start position:0% +neurons no no they're just the really + + + align:start position:0% +neurons no no they're just the really +big ones some of them are much bigger + + align:start position:0% +big ones some of them are much bigger + + + align:start position:0% +big ones some of them are much bigger +than + + align:start position:0% + + + + align:start position:0% + +others you see bed cells even in the + + align:start position:0% +others you see bed cells even in the + + + align:start position:0% +others you see bed cells even in the +hamster when we did those sections of + + align:start position:0% +hamster when we did those sections of + + + align:start position:0% +hamster when we did those sections of +the parameter tract and we looked at the + + align:start position:0% +the parameter tract and we looked at the + + + align:start position:0% +the parameter tract and we looked at the +motor + + align:start position:0% +motor + + + align:start position:0% +motor +cortex + + align:start position:0% +cortex + + + align:start position:0% +cortex +we wanted to know if the bet the the big + + align:start position:0% +we wanted to know if the bet the the big + + + align:start position:0% +we wanted to know if the bet the the big +cells or any cells + + align:start position:0% +cells or any cells + + + align:start position:0% +cells or any cells +degenerated and they didn't degenerate + + align:start position:0% +degenerated and they didn't degenerate + + + align:start position:0% +degenerated and they didn't degenerate +they just lose weight they get smaller + + align:start position:0% +they just lose weight they get smaller + + + align:start position:0% +they just lose weight they get smaller +they don't look as much like bet cells + + align:start position:0% +they don't look as much like bet cells + + + align:start position:0% +they don't look as much like bet cells +but we did cell count so we know that + + align:start position:0% +but we did cell count so we know that + + + align:start position:0% +but we did cell count so we know that +all the cells are still there they just + + align:start position:0% +all the cells are still there they just + + + align:start position:0% +all the cells are still there they just +get smaller when they don't support a + + align:start position:0% +get smaller when they don't support a + + + align:start position:0% +get smaller when they don't support a +long accent + + align:start position:0% +long accent + + + align:start position:0% +long accent +anymore okay just very quickly the + + align:start position:0% +anymore okay just very quickly the + + + align:start position:0% +anymore okay just very quickly the +medial lesions and this is described in + + align:start position:0% +medial lesions and this is described in + + + align:start position:0% +medial lesions and this is described in +the book you've got to do the lesion + + align:start position:0% +the book you've got to do the lesion + + + align:start position:0% +the book you've got to do the lesion +bilaterally remember the reason is + + align:start position:0% +bilaterally remember the reason is + + + align:start position:0% +bilaterally remember the reason is +because they cross over many accents do + + align:start position:0% +because they cross over many accents do + + + align:start position:0% +because they cross over many accents do +cross over but you get drastic effects + + align:start position:0% +cross over but you get drastic effects + + + align:start position:0% +cross over but you get drastic effects +on + + align:start position:0% +on + + + align:start position:0% +on +writing they did get some recovery why + + align:start position:0% +writing they did get some recovery why + + + align:start position:0% +writing they did get some recovery why +do you think they recovered you asked me + + align:start position:0% +do you think they recovered you asked me + + + align:start position:0% +do you think they recovered you asked me +this earlier even after as much as 40 + + align:start position:0% +this earlier even after as much as 40 + + + align:start position:0% +this earlier even after as much as 40 +days + + align:start position:0% + + + + align:start position:0% + +because there's other ways to write just + + align:start position:0% +because there's other ways to write just + + + align:start position:0% +because there's other ways to write just +with spinal + + align:start position:0% +with spinal + + + align:start position:0% +with spinal +reflexes the the input from the somat + + align:start position:0% +reflexes the the input from the somat + + + align:start position:0% +reflexes the the input from the somat +sensory system and from the joints can + + align:start position:0% +sensory system and from the joints can + + + align:start position:0% +sensory system and from the joints can +support some + + align:start position:0% +support some + + + align:start position:0% +support some +writing okay but the vestibular spinal + + align:start position:0% +writing okay but the vestibular spinal + + + align:start position:0% +writing okay but the vestibular spinal +tract is gone so they can't use do the + + align:start position:0% +tract is gone so they can't use do the + + + align:start position:0% +tract is gone so they can't use do the +normal means or tectus spinal also so + + align:start position:0% +normal means or tectus spinal also so + + + align:start position:0% +normal means or tectus spinal also so +they can't use Visual and they can't + + align:start position:0% +they can't use Visual and they can't + + + align:start position:0% +they can't use Visual and they can't +use C sens the distributor input to + + align:start position:0% +use C sens the distributor input to + + + align:start position:0% +use C sens the distributor input to +write + + align:start position:0% +write + + + align:start position:0% +write +anymore so when they walk they stumble + + align:start position:0% +anymore so when they walk they stumble + + + align:start position:0% +anymore so when they walk they stumble +around they don't know which way to go + + align:start position:0% +around they don't know which way to go + + + align:start position:0% +around they don't know which way to go +it's not I shouldn't say that they know + + align:start position:0% +it's not I shouldn't say that they know + + + align:start position:0% +it's not I shouldn't say that they know +which way to go because they still + + align:start position:0% +which way to go because they still + + + align:start position:0% +which way to go because they still +control our eye movements and you can + + align:start position:0% +control our eye movements and you can + + + align:start position:0% +control our eye movements and you can +see where they're looking you can see + + align:start position:0% +see where they're looking you can see + + + align:start position:0% +see where they're looking you can see +where they're trying to get to but yet + + align:start position:0% +where they're trying to get to but yet + + + align:start position:0% +where they're trying to get to but yet +they can't make their body do + + align:start position:0% +they can't make their body do + + + align:start position:0% +they can't make their body do +it it's a very interesting kind of you + + align:start position:0% +it it's a very interesting kind of you + + + align:start position:0% +it it's a very interesting kind of you +don't really call it a paralysis but + + align:start position:0% +don't really call it a paralysis but + + + align:start position:0% +don't really call it a paralysis but +they clearly can't control those + + align:start position:0% +they clearly can't control those + + + align:start position:0% +they clearly can't control those +movements well at all okay and then the + + align:start position:0% +movements well at all okay and then the + + + align:start position:0% +movements well at all okay and then the +lateral Pathways they lose we'll talk + + align:start position:0% +lateral Pathways they lose we'll talk + + + align:start position:0% +lateral Pathways they lose we'll talk +we'll come back to this and talk a + + align:start position:0% +we'll come back to this and talk a + + + align:start position:0% +we'll come back to this and talk a +little bit next time the way the way + + align:start position:0% +little bit next time the way the way + + + align:start position:0% +little bit next time the way the way +they did it I actually have films of + + align:start position:0% +they did it I actually have films of + + + align:start position:0% +they did it I actually have films of +this but it's I I need to see if we can + + align:start position:0% +this but it's I I need to see if we can + + + align:start position:0% +this but it's I I need to see if we can +find something online and so I could + + align:start position:0% +find something online and so I could + + + align:start position:0% +find something online and so I could +show it in + + align:start position:0% +show it in + + + align:start position:0% +show it in +class the video the the films take + + align:start position:0% +class the video the the films take + + + align:start position:0% +class the video the the films take +forever to set up and show in the + + align:start position:0% +forever to set up and show in the + + + align:start position:0% +forever to set up and show in the +classroom that was a very nice + + align:start position:0% + + + + align:start position:0% + +study + + align:start position:0% + + + + align:start position:0% + +sorry + + align:start position:0% + + + + align:start position:0% + +ocular M they're both true because the + + align:start position:0% +ocular M they're both true because the + + + align:start position:0% +ocular M they're both true because the +ocular motor the most rostal ocular + + align:start position:0% +ocular motor the most rostal ocular + + + align:start position:0% +ocular motor the most rostal ocular +motor nuclei are in the mid brain so + + align:start position:0% +motor nuclei are in the mid brain so + + + align:start position:0% +motor nuclei are in the mid brain so +either one is + + align:start position:0% + + + + align:start position:0% + +correct \ No newline at end of file diff --git a/MpJe7SMzi0E.txt b/MpJe7SMzi0E.txt new file mode 100644 index 0000000000000000000000000000000000000000..ee05d7e260ae4005b60e6097f53ffb83eb219cb5 --- /dev/null +++ b/MpJe7SMzi0E.txt @@ -0,0 +1,267 @@ +6.004 students work around the dryer bottleneck +by finding a laundromat that has two dryers + +for every washer. + +Looking at the timeline you can see the plan, +which is divided into 30-minute steps. + +The washer is in use every step, producing +a newly-washed load every 30 minutes. + +Dryer usage is interleaved, where Dryer #1 +is used to dry the odd-numbered loads and + +Dryer #2 is used to dry the even-numbered +loads. + +Once started, a dryer runs for a duration +of two steps, a total of 60 minutes. + +Since the dryers run on a staggered schedule, +the system as a whole produces a load of clean, + +dry laundry every 30 minutes. + +The steady-state throughput is 1 load of laundry +every 30 minutes and the latency for a particular + +load of laundry is 90 minutes. + +And now here's the take-home message from +this example. + +Consider the operation of the two-dryer system. + +Even though the component dryers themselves +aren't pipelined, the two-dryer interleaving + +system is acting like a 2-stage pipeline with +a clock period of 30 minutes and a latency + +of 60 minutes. + +In other words, by interleaving the operation +of 2 unpipelined components we can achieve + +the effect of a 2-stage pipeline. + +Returning to the example of the previous section, +we couldn't improve the throughput of our + +pipelined system past 1/8 ns because the minimum +clock period was set by the 8 ns latency of + +the C module. + +To improve the throughput further we either +need to find a pipelined version of the C + +component or use an interleaving strategy +to achieve the effect of a 2-stage pipeline + +using two instances of the unpipelined C component. + +Let's try that… + +Here's a circuit for a general-purpose two-way +interleaver, using, in this case, two copies + +of the unpipelined C component, C_0 and C_1. + +The input for each C component comes from +a D-latch, which has the job of capturing + +and holding the input value. + +There's also a multiplexer to select which +C-component output will be captured by the + +output register. + +In the lower left-hand corner of the circuit +is a very simple 2-state FSM with one state + +bit. + +The next-state logic is a single inverter, +which causes the state to alternate between + +0 and 1 on successive clock cycles. + +This timing diagram shows how the state bit +changes right after each rising clock edge. + +To help us understand the circuit, we'll look +at some signal waveforms to illustrate its + +operation. + +To start, here are the waveforms for the CLK +signal and our FSM state bit from the previous + +slide. + +A new X input arrives from the previous stage +just after the rising edge of the clock. + +Next, let's follow the operation of the C_0 +component. + +Its input latch is open when FSM Q is low, +so the newly arriving X_1 input passes through + +the latch and C_0 can begin its computation, +producing its result at the end of clock cycle + +#2. + +Note that the C_0 input latch closes at the +beginning of the second clock cycle, holding + +the X_1 input value stable even though the +X input is starting to change. + +The effect is that C_0 has a valid and stable +input for the better part of 2 clock cycles + +giving it enough time to compute its result. + +The C_1 waveforms are similar, just shifted +by one clock cycle. + +C_1's input latch is open when FSM Q is high, +so the newly arriving X_2 input passes through + +the latch and C_1 can begin its computation, +producing its result at the end of clock cycle + +#3. + +Now let's check the output of the multiplexer. + +When FSM Q is high, it selects the value from +C_0 and when FSM Q is low, it selects the + +value from C_1. + +We can see that happening in the waveform +shown. + +Finally, at the rising edge of the clock, +the output register captures the value on + +its input and holds it stable for the remainder +of the clock cycle. + +The behavior of the interleaving circuit is +like a 2-stage pipeline: the input value arriving + +in cycle i is processed over two clock cycles +and the result output becomes available on + +cycle i+2. + +What about the clock period for the interleaving +system? + +Well, there is some time lost to the propagation +delays of the upstream pipeline register that + +supplies the X input, the internal latches +and multiplexer, and the setup time of the + +output register. + +So the clock cycle has to be just a little +bit longer than half the propagation delay + +of the C module. + +We can treat the interleaving circuit as a +2-stage pipeline, consuming an input value + +every clock cycle and producing a result two +cycles later. + +When incorporating an N-way interleaved component +in our pipeline diagrams, we treat it just + +like a N-stage pipeline. + +So N of our pipelining contours have to pass +through the component. + +Here we've replaced the slow unpipelined C +component with a 2-way interleaved C-prime + +component. + +We can follow our process for drawing pipeline +contours. + +First we draw a contour across all the outputs. + +Then we add contours, ensuring that two of +them pass through the C-prime component. + +Then we add pipeline registers at the intersections +of the contours with the signal connections. + +We see that the contours passing through C-prime +have caused extra pipeline registers to be + +added on the other inputs to the F module, +accommodating the 2-cycle delay through C-prime. + +Somewhat optimistically we've specified the +C-prime minimum t_CLK to be 4 ns, so that + +means that the slow component which determines +the system's clock period is now the F module, + +with a propagation delay of 5 ns. + +So the throughput of our new pipelined circuit +is 1 output every 5 ns, and with 5 contours, + +it's a 5-pipeline so the latency is 5 times +the clock period or 25 ns. + +By running pipelined systems in parallel we +can continue to increase the throughput. + +Here we show a laundry with 2 washers and +4 dryers, essentially just two copies of the + +1-washer, 2-dryer system shown earlier. + +The operation is as described before, except +that at each step the system produces and + +consumes two loads of laundry. + +So the throughput is 2 loads every 30 minutes +for an effective rate of 1 load every 15 minutes. + +The latency for a load hasn't changed; it's +still 90 minutes per load. + +We've seen that even with slow components +we can use interleaving and parallelism to + +continue to increase throughput. + +Is there an upper bound on the throughput +we can achieve? + +Yes! + +The timing overhead of the pipeline registers +and interleaving components will set a lower + +bound on the achievable clock period, thus +setting an upper bound on the achievable throughput. + +Sorry, no infinite speed-up is possible in +the real world. \ No newline at end of file diff --git a/NYOcZx6Kxsw.txt b/NYOcZx6Kxsw.txt new file mode 100644 index 0000000000000000000000000000000000000000..1c1a3fecf10f418ef1703f9cab91ada175bbe027 --- /dev/null +++ b/NYOcZx6Kxsw.txt @@ -0,0 +1,870 @@ +Hey, everyone. + +Welcome back. + +Today, we're going to do another +fun problem that has + +to do with a random number +of coin flips. + +So the experiment we're going +to run is as follows. + +We're given a fair six-sided +die, and we roll it. + +And then we take a fair coin, +and we flip it the number of + +times indicated by the die. + +That is to say, if I roll a four +on my die, then I flip + +the coin four times. + +And then we're interested in +some statistics regarding the + +number of heads that show +up in our sequence. + +In particular, we want to +compute the expectation and + +the variance of the number +of heads that we see. + +So the first step of this +problem is to translate the + +English to the math. + +So we have to define +some notation. + +I went ahead and did +that for us. + +I defined n to be the outcome +of the die role. + +Now, since we flip the coin the +number of times shown by + +the die roll, n is equivalently +the number of + +flips that we perform. + +And n, of course, is a random +variable, and I've written its + +PMF up here. + +So Pn of n is just a discrete +uniform random variable + +between 1 and 6, because we're +told that the die has six + +sides and that it's fair. + +Now, I also defined h +to be the number of + +heads that we see. + +So that's the quantity +of interest. + +And it turns out that Bernoulli +random variables + +will be very helpful to +us in this problem. + +So I defined x sub i as +1 if the ith flip is + +heads, and 0 otherwise. + +And what we're going to do now +is, we're going to use these x + +sub i's to come up with +an expression for h. + +So if you want to count the +number of heads, one possible + +thing you could do is start with +0 and then look at the + +first coin flip. + +If it's heads, you add 1 to 0, +which I'm going to call your + +running sum. + +If the first flip is +tails, you add 0. + +And similarly, after that, after +every trial, if you see + +heads, you add 1 to +your running sum. + +If you see a tails, you add 0. + +And in that way, we can +precisely compute h. + +So the mathematical statement of +what I just said is that h + +is equal to x1 plus x2 +plus x3, all the way + +through x sub n. + +So now, we are interested +in computing e of h, the + +expectation of h. + +So your knee jerk reaction might +be to say, oh, well, by + +linearity of expectation, +we know that this is an + +expectation of x1, et cetera +through the expectation of xn. + +But in this case, you would +actually be wrong. + +Don't do that. + +And the reason that this is not +going to work for us is + +because we're dealing +with a random + +number of random variables. + +So each xi is a random +variable. + +And we have capital n of them. + +But capital n is a +random variable. + +It denotes the outcome +of our die roll. + +So we actually cannot just +take the sum of these + +expectations. + +Instead, we're going to have +to condition on n and use + +iterated expectation. + +So this is the mathematical +statement of what I just said. + +And the reason why this works +is because conditioning on n + +will take us to the case that +we already know how to deal + +with, where we have a known +number of random variables. + +And of course, iterated +expectations holds, as you saw + +in lecture. + +I will briefly mention here that +the formula we're going + +to derive is derived +in the book. + +And it was probably derived +in lecture. + +So if you want, you can just +go to that formula + +immediately. + +But I think the derivation of +the formula that we need is + +quick and is helpful. + +So I'm going to go through +it quickly. + + + +Let's do it over here. + +Plugging in our running +sum for h, we get this + +expression-- + +x1 plus x2 et cetera plus +xn, conditioned on n. + +And this, of course, +is n times the + +expectation of x sub i. + +So again, I'm going through +this quickly, + +because it's in the book. + +But this step holds, because +each of these xi's have the + +same statistics. + +They're all Bernoulli with +parameter of 1/2, because our + +coin is fair. + +And so I used x sub i to say it +doesn't really matter which + +integer you pick for i, because +the expectation of xi + +is the same for all i. + +So this now, the expectation +of x sub i, this is just a + +number, it's just some constant, +so you can pull it + +out of the expectation. + +So you get the expectation +of x sub i times the + +expectation of n. + +So I gave away the answer +to this a second ago. + +But x sub i is just a Bernoulli +random variable with + +parameter of success of 1/2. + +And we know already that the +expectation of such a random + +variable is just p, or 1/2. + +So this is 1/2 times +expectation of n. + +And now n we know is a discrete + +uniform random variable. + +And there's a formula that I'm +going to use, which hopefully + +some of you may remember. + +If you have a discrete uniform +random variable that takes on + +values between a and b-- + + + +let's use w-- + +if you call this random variable +w, then we have that + +the variance of w is equal to b +minus a times b minus a plus + +2 divided by 12. + +So that's the variance. + +We don't actually need the +variance, but we will need + +this later. + +And the expectation of w-- + +actually, let's just +do it up here right + +ahead for this problem. + +Because we have a discrete +uniform random variable, the + +expectation is just +the middle. + +So you agree hopefully that the +middle is right at 3.5, + +which is also 7/2. + +So this is times 7/2, which +is equal to 7/4. + + + +So we are done with +part of part a. + +I'm going to write this answer +over here, so I can erase. + + + +And we're going to do something +very similar to + +compute the variance. + +To compute the variance, +we are going to also + +condition on n. + +So we get rid of this source +of randomness. + +And then we're going to use law +of total variance, which + +you've also seen in lecture. + +And again, the formula +for this variance is + +derived in the book. + +So I'm going to go through +it quickly. + +But make sure you understand +this derivation, because it + +exercises a lot of stuff +we taught you. + +So this, just using law of +total variance, is the + +variance of expectation of h +given n, plus the expectation + +of the variance of h given n. + +And now, plugging in +this running sum + +for h, you get this. + +It's a mouthful to write. + +Bear with me. + +x1 through xn given n-- + +so I didn't do anything fancy. + +I just plugged this into here. + +So this term is similar +to what we saw + +in a previous problem. + +By linearity of expectation and +due to the fact that all + +of the x i's are distributed in +the same way, they have the + +same expectation, this +becomes n times the + +expectation of x sub i. + +And let's do this +term over here. + +This term-- + +well, conditioned on +n, this n is known. + +So we essentially have +a finite known sum of + +independent random variables. + +We know that the variance of +a sum of independent random + +variables is the sum +of the variances. + +So this is the variance of x1 +plus the variance of x2 et + +cetera, plus the +variance of xn. + +And furthermore, again, because +all of these xi's have + +the same distribution, the +variance is the same. + +So we can actually write this +as n times the variance of x + +sub i, where x sub i +just corresponds + +to one of the trials. + +It doesn't matter which one, +because they all have the same + +variance and expectation. + +So now, we're almost +home free. + +This is just some scaler. + +So we can take it out of +the variance, but we + +have to square it. + +So this becomes expectation +of xi squared times + +the variance of n. + +And then this variance is also +just a scalar, so we can take + +it outside. + +So then we get variance of x sub +i times expectation of n. + +Now, we know that the +expectation of x sub i is just + +the probability of success, +which is 1/2. + +So we have 1/2 squared, or 1/4, +times the variance of n. + +So that's where this formula +comes in handy. + +b is equal to 6, a +is equal to 1. + +So we get that the variance +of n is equal to 5 times-- + +and then 5 plus 2 is 7-- + +divided by 12. + +So this is just a formula from +the book that you guys + +hopefully remember. + +So we get 35/12. + + + +And then the variance of xi, +we know the variance of a + +Bernoulli random variable is +just p times 1 minus p. + +So in our case, that's 1/2 +times 1/2, which is 1/4. + +So we get 1/4. + +And then the expectation of n, +we remember from our previous + +computation, is just 7/2. + +So I will let you guys do this +arithmetic on your own time. + +But the answer comes +out to be 77/48. + + + +So I will go ahead and put +our answer over here-- + +77/48-- + +so that I can erase. + + + +So I want you guys to +start thinking about + +part b while I erase. + +Essentially, you do the same +experiment that we did in part + +a, except now we use two +dice instead of one. + +So in part b, just to repeat, +you now have two dice. + +You roll them. + +You look at the outcome. + +If you have an outcome of four +on one die and six on another + +die, then you flip the +coin 10 times. + +So it's the same exact +experiment. + +We're interested in the number +of heads we want the + +expectation and the variance. + +But this step is now a +little bit different. + + + +Again, let's approach this by +defining some notation first. + +Now, I want to let n1 be the +outcome of the first die. + + + +And then you can let n2 be the +outcome of the second die. + + + +And we'll start with +just that. + +So one way you could approach +this problem is say, OK, if n1 + +is the outcome of my first die +and n2 is the outcome of my + +second die, then the number of +coin flips that I'm going to + +make is n1 plus n2. + + + +This is the total coin flips. + + + +So you could just repeat the +same exact math that we did in + +part a, except everywhere that +you see an n, you replace that + +n with n1 plus n2. + +So that will get you to your +answer, but it will require + +slightly more work. + +We're going to think about +this problem slightly + +differently. + +So the way we are thinking about +it just now, we roll two + +dice at the same time. + +We add the results +of the die rolls. + +And then we flip the coin +that number of times. + +But another way you can think +about this is, you roll one + +die, and then you flip the coin +the number of times shown + +by that die and count +the number of heads. + +And then you take the second +die and you roll it. + +And then you flip the coin that +many more times and count + +the number of heads +after that. + +So you could define h1 to be +number of heads in the first + +n1 coin flips. + + + +And you could just let h2 be +the number of heads in the + +last n2 coin flips. + +So hopefully that terminology +is not confusing you. + +Essentially, what I'm saying +is, n1 plus n2 means you'll + +have n1 flips, followed by +n2 flips, for a total + +of n1 plus n2 flips. + +And then within the first n1 +flips, you can get some number + +of heads, which we're +calling h1. + +And in the last n2 flips, you +can get some number of heads, + +which is h2. + +So the total number of heads +that we get at the end-- + +I'm going to call it h star-- + +is equal to h1 plus h2. + +And what part b is really +asking us for is the + +expectation of h star and +the variance of h star. + +But here's where something +really beautiful happens. + +h1 and h2 are independent, +and they are + +statistically the same. + +So the reason why they're +independent is because-- + +well, first of all, all of our +coin flips are independent. + +And they're statistically the +same, because the experiment + +is exactly the same. + +And everything's independent. + +So instead of imagining one +person rolling two die and + +then summing the outcomes and +flipping a coin that many + +times and counting heads, you +can imagine one person takes + +one die and goes +into one room. + +A second person takes a +second die and goes + +into another room. + +They run their experiments. + +Then they report back +to a third person + +the number of heads. + +And that person adds them +together to get h star. + +And in that scenario, everything +is very clearly + +independent. + +So the expectation of h star-- + +you actually don't need +independence for this part, + +because linearly of expectation +always holds. + +But you get the expectation of +h1 plus the expectation of h2. + +And because these guys are +statistically equivalent, this + +is just two times the +expectation of h. + +And the expectation of h we +calculated in part a. + +So this is 2 times 7 over 4. + +Now, for the variance, +here's where the + +independence comes in. + +I'm actually going to write this +somewhere where I don't + +have to bend over. + +So the variance of h star is +equal to the variance of h1 + +plus the variance of +h2 by independence. + +And that's equal to 2 times +the variance of h, because + +they are statistically +the same. + +And the variance of h +we computed already. + +So this is just 2 times +77 over 48. + +So the succient answer to part +b is that both the mean and + +the variance double from part +A. So hopefully you guys + +enjoyed this problem. + +We covered a bunch of things. + +So we saw how to deal with +having a random number of + +random variables. + +Usually we have a fixed number +of random variables. + +In this problem, the number of +random variables we were + +adding together was +itself random. + +So to handle that, we +conditioned on n. + +And to compute expectation, we +use iterated expectation. + +To compute variance, we used +law of total variance. + +And then in part b, we were +just a little bit clever. + +We thought about how can we +reinterpret this experiment to + +reduce computation. + +And we realized that part b is +essentially two independent + +trials of part a. + +So both the mean and the +variance should double. \ No newline at end of file diff --git a/OHiu2F18dFA.txt b/OHiu2F18dFA.txt new file mode 100644 index 0000000000000000000000000000000000000000..16e7fcb26b8915b709d2d65591960f8010c2e4df --- /dev/null +++ b/OHiu2F18dFA.txt @@ -0,0 +1,14259 @@ +align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so let's get started last time + + align:start position:0% +so let's get started last time + + + align:start position:0% +so let's get started last time +at the end of the last lecture we + + align:start position:0% +at the end of the last lecture we + + + align:start position:0% +at the end of the last lecture we +introduced outer measure + + align:start position:0% +introduced outer measure + + + align:start position:0% +introduced outer measure +so we first discussed what we wanted a + + align:start position:0% +so we first discussed what we wanted a + + + align:start position:0% +so we first discussed what we wanted a +measure the properties of a of kind of a + + align:start position:0% +measure the properties of a of kind of a + + + align:start position:0% +measure the properties of a of kind of a +notion of + + align:start position:0% +notion of + + + align:start position:0% +notion of +measure of subsets of r to satisfy + + align:start position:0% +measure of subsets of r to satisfy + + + align:start position:0% +measure of subsets of r to satisfy +we wanted it to first off be defined for + + align:start position:0% +we wanted it to first off be defined for + + + align:start position:0% +we wanted it to first off be defined for +all subsets we then wanted the measure + + align:start position:0% +all subsets we then wanted the measure + + + align:start position:0% +all subsets we then wanted the measure +of an interval to be the length of the + + align:start position:0% +of an interval to be the length of the + + + align:start position:0% +of an interval to be the length of the +interval + + align:start position:0% +interval + + + align:start position:0% +interval +we also wanted the + + align:start position:0% +we also wanted the + + + align:start position:0% +we also wanted the +measure of a union of disjoint + + align:start position:0% +measure of a union of disjoint + + + align:start position:0% +measure of a union of disjoint +subsets to be the sum + + align:start position:0% +subsets to be the sum + + + align:start position:0% +subsets to be the sum +of the measures + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +that we wanted it to be translation + + align:start position:0% +that we wanted it to be translation + + + align:start position:0% +that we wanted it to be translation +invariant meaning if i take a set and i + + align:start position:0% +invariant meaning if i take a set and i + + + align:start position:0% +invariant meaning if i take a set and i +shift it by a fixed amount then the + + align:start position:0% +shift it by a fixed amount then the + + + align:start position:0% +shift it by a fixed amount then the +measure of the shifted set is the same + + align:start position:0% +measure of the shifted set is the same + + + align:start position:0% +measure of the shifted set is the same +as the measure of the original set + + align:start position:0% +as the measure of the original set + + + align:start position:0% +as the measure of the original set +um + + align:start position:0% +um + + + align:start position:0% +um +but as i said last time that's + + align:start position:0% +but as i said last time that's + + + align:start position:0% +but as i said last time that's +impossible you can't there does not + + align:start position:0% +impossible you can't there does not + + + align:start position:0% +impossible you can't there does not +exist such a thing defined on every + + align:start position:0% +exist such a thing defined on every + + + align:start position:0% +exist such a thing defined on every +subset of real numbers so + + align:start position:0% + + + + align:start position:0% + +what we're going to do is + + align:start position:0% +what we're going to do is + + + align:start position:0% +what we're going to do is +define + + align:start position:0% +define + + + align:start position:0% +define +or what we're doing right now is + + align:start position:0% +or what we're doing right now is + + + align:start position:0% +or what we're doing right now is +defining outer measure which is + + align:start position:0% +defining outer measure which is + + + align:start position:0% +defining outer measure which is +you know will satisfy almost uh + + align:start position:0% +you know will satisfy almost uh + + + align:start position:0% +you know will satisfy almost uh +all of the properties we wanted and is + + align:start position:0% +all of the properties we wanted and is + + + align:start position:0% +all of the properties we wanted and is +defined for every subset of r + + align:start position:0% +defined for every subset of r + + + align:start position:0% +defined for every subset of r +but + + align:start position:0% +but + + + align:start position:0% +but +and then we'll + + align:start position:0% +and then we'll + + + align:start position:0% +and then we'll +restrict this outer measure to a certain + + align:start position:0% +restrict this outer measure to a certain + + + align:start position:0% +restrict this outer measure to a certain +class of subsets of r that are well + + align:start position:0% +class of subsets of r that are well + + + align:start position:0% +class of subsets of r that are well +behaved + + align:start position:0% +behaved + + + align:start position:0% +behaved +with respect to measure and then we'll + + align:start position:0% +with respect to measure and then we'll + + + align:start position:0% +with respect to measure and then we'll +get a + + align:start position:0% + + + + align:start position:0% + +function now defined on a + + align:start position:0% +function now defined on a + + + align:start position:0% +function now defined on a +collection of subsets of r what we'll + + align:start position:0% +collection of subsets of r what we'll + + + align:start position:0% +collection of subsets of r what we'll +call measurable sets + + align:start position:0% +call measurable sets + + + align:start position:0% +call measurable sets +and this set function which we call + + align:start position:0% +and this set function which we call + + + align:start position:0% +and this set function which we call +measure libate measure will satisfy the + + align:start position:0% +measure libate measure will satisfy the + + + align:start position:0% +measure libate measure will satisfy the +three properties uh the main three + + align:start position:0% +three properties uh the main three + + + align:start position:0% +three properties uh the main three +properties we wanted that + + align:start position:0% +properties we wanted that + + + align:start position:0% +properties we wanted that +the measure of an interval is the length + + align:start position:0% +the measure of an interval is the length + + + align:start position:0% +the measure of an interval is the length +of the interval the measure of a + + align:start position:0% +of the interval the measure of a + + + align:start position:0% +of the interval the measure of a +countable + + align:start position:0% +countable + + + align:start position:0% +countable +disjoint union of of sets is is the sum + + align:start position:0% +disjoint union of of sets is is the sum + + + align:start position:0% +disjoint union of of sets is is the sum +of the measures and its translation + + align:start position:0% +of the measures and its translation + + + align:start position:0% +of the measures and its translation +invariant okay + + align:start position:0% +invariant okay + + + align:start position:0% +invariant okay +now + + align:start position:0% +now + + + align:start position:0% +now +at the + + align:start position:0% +at the + + + align:start position:0% +at the +end of last time so we defined outer + + align:start position:0% +end of last time so we defined outer + + + align:start position:0% +end of last time so we defined outer +measure and we also proved this theorem + + align:start position:0% +measure and we also proved this theorem + + + align:start position:0% +measure and we also proved this theorem +that if we have a countable collection + + align:start position:0% +that if we have a countable collection + + + align:start position:0% +that if we have a countable collection +of subsets of r + + align:start position:0% +of subsets of r + + + align:start position:0% +of subsets of r +then + + align:start position:0% +then + + + align:start position:0% +then +the measure of the union is less than or + + align:start position:0% +the measure of the union is less than or + + + align:start position:0% +the measure of the union is less than or +equal to the sum of the measures now you + + align:start position:0% +equal to the sum of the measures now you + + + align:start position:0% +equal to the sum of the measures now you +know what we would like in the end like + + align:start position:0% +know what we would like in the end like + + + align:start position:0% +know what we would like in the end like +i said is to be able to have equality + + align:start position:0% +i said is to be able to have equality + + + align:start position:0% +i said is to be able to have equality +whenever + + align:start position:0% +whenever + + + align:start position:0% +whenever +the subsets are disjoint now this + + align:start position:0% +the subsets are disjoint now this + + + align:start position:0% +the subsets are disjoint now this +doesn't hold for outer measure but as + + align:start position:0% +doesn't hold for outer measure but as + + + align:start position:0% +doesn't hold for outer measure but as +we'll see once we restrict outer measure + + align:start position:0% +we'll see once we restrict outer measure + + + align:start position:0% +we'll see once we restrict outer measure +to a certain + + align:start position:0% +to a certain + + + align:start position:0% +to a certain +class of subsets we will get the + + align:start position:0% +class of subsets we will get the + + + align:start position:0% +class of subsets we will get the +property that we want + + align:start position:0% +property that we want + + + align:start position:0% +property that we want +now + + align:start position:0% +now + + + align:start position:0% +now +um + + align:start position:0% +um + + + align:start position:0% +um +so outer measure almost satisfies + + align:start position:0% +so outer measure almost satisfies + + + align:start position:0% +so outer measure almost satisfies +uh one of those properties we wanted of + + align:start position:0% +uh one of those properties we wanted of + + + align:start position:0% +uh one of those properties we wanted of +a measure + + align:start position:0% +a measure + + + align:start position:0% +a measure +what we're going to verify now is that + + align:start position:0% +what we're going to verify now is that + + + align:start position:0% +what we're going to verify now is that +outer measure does satisfy one of the + + align:start position:0% +outer measure does satisfy one of the + + + align:start position:0% +outer measure does satisfy one of the +properties we wanted of a + + align:start position:0% +properties we wanted of a + + + align:start position:0% +properties we wanted of a +of a measure namely that the measure of + + align:start position:0% +of a measure namely that the measure of + + + align:start position:0% +of a measure namely that the measure of +a interval ought to be its length so + + align:start position:0% +a interval ought to be its length so + + + align:start position:0% +a interval ought to be its length so +that's the following + + align:start position:0% + + + + align:start position:0% + +if i is + + align:start position:0% +if i is + + + align:start position:0% +if i is +an interval + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +measure the outer measure of i is equal + + align:start position:0% +measure the outer measure of i is equal + + + align:start position:0% +measure the outer measure of i is equal +to the length of i + + align:start position:0% +to the length of i + + + align:start position:0% +to the length of i +so here the length of i remember if + + align:start position:0% +so here the length of i remember if + + + align:start position:0% +so here the length of i remember if +if it's an interval of the form a b + + align:start position:0% +if it's an interval of the form a b + + + align:start position:0% +if it's an interval of the form a b +with the + + align:start position:0% +with the + + + align:start position:0% +with the +endpoints included or not the length of + + align:start position:0% +endpoints included or not the length of + + + align:start position:0% +endpoints included or not the length of +the interval is b minus a if it's a + + align:start position:0% +the interval is b minus a if it's a + + + align:start position:0% +the interval is b minus a if it's a +you know infinite interval uh then the + + align:start position:0% +you know infinite interval uh then the + + + align:start position:0% +you know infinite interval uh then the +length is infinite + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +uh + + align:start position:0% +uh + + + align:start position:0% +uh +kind of the + + align:start position:0% +kind of the + + + align:start position:0% +kind of the +most involved part is or at least the + + align:start position:0% +most involved part is or at least the + + + align:start position:0% +most involved part is or at least the +crux of proving this is is doing + + align:start position:0% +crux of proving this is is doing + + + align:start position:0% +crux of proving this is is doing +you know the simplest + + align:start position:0% +you know the simplest + + + align:start position:0% +you know the simplest +uh kind of interval which is a closed + + align:start position:0% +uh kind of interval which is a closed + + + align:start position:0% +uh kind of interval which is a closed +and bounded interval uh a b + + align:start position:0% +and bounded interval uh a b + + + align:start position:0% +and bounded interval uh a b +so + + align:start position:0% +so + + + align:start position:0% +so +let's do that case first suppose + + align:start position:0% +let's do that case first suppose + + + align:start position:0% +let's do that case first suppose +i is equal to + + align:start position:0% +i is equal to + + + align:start position:0% +i is equal to +a b + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +and also you know something that i + + align:start position:0% +and also you know something that i + + + align:start position:0% +and also you know something that i +didn't write down here + + align:start position:0% +didn't write down here + + + align:start position:0% +didn't write down here +is we have + + align:start position:0% +is we have + + + align:start position:0% +is we have +you know immediately from the definition + + align:start position:0% +you know immediately from the definition + + + align:start position:0% +you know immediately from the definition +of outer measure so let me just pause + + align:start position:0% +of outer measure so let me just pause + + + align:start position:0% +of outer measure so let me just pause +that real quick that + + align:start position:0% +that real quick that + + + align:start position:0% +that real quick that +if a is a subset of b then the outer + + align:start position:0% +if a is a subset of b then the outer + + + align:start position:0% +if a is a subset of b then the outer +measure of a + + align:start position:0% +measure of a + + + align:start position:0% +measure of a +is less than or equal to the outer + + align:start position:0% +is less than or equal to the outer + + + align:start position:0% +is less than or equal to the outer +measure of b + + align:start position:0% +measure of b + + + align:start position:0% +measure of b +simply because you know if i + + align:start position:0% +simply because you know if i + + + align:start position:0% +simply because you know if i +take any open collection of open + + align:start position:0% +take any open collection of open + + + align:start position:0% +take any open collection of open +intervals covering b then that will be a + + align:start position:0% +intervals covering b then that will be a + + + align:start position:0% +intervals covering b then that will be a +collection of open intervals covering + + align:start position:0% +collection of open intervals covering + + + align:start position:0% +collection of open intervals covering +covering a so and since in femums of + + align:start position:0% +covering a so and since in femums of + + + align:start position:0% +covering a so and since in femums of +bigger sets you know + + align:start position:0% + + + + align:start position:0% + +let's see which direction is that + + align:start position:0% + + + + align:start position:0% + +since in femums of bigger sets have to + + align:start position:0% +since in femums of bigger sets have to + + + align:start position:0% +since in femums of bigger sets have to +decrease + + align:start position:0% +decrease + + + align:start position:0% +decrease +that gives me the inequality that i want + + align:start position:0% +that gives me the inequality that i want + + + align:start position:0% +that gives me the inequality that i want +okay + + align:start position:0% + + + + align:start position:0% + +okay so going back to + + align:start position:0% +okay so going back to + + + align:start position:0% +okay so going back to +the proof of this theorem let's suppose + + align:start position:0% +the proof of this theorem let's suppose + + + align:start position:0% +the proof of this theorem let's suppose +i equals a b what we're going to show is + + align:start position:0% +i equals a b what we're going to show is + + + align:start position:0% +i equals a b what we're going to show is +that + + align:start position:0% +that + + + align:start position:0% +that +the outer measure is less than or equal + + align:start position:0% +the outer measure is less than or equal + + + align:start position:0% +the outer measure is less than or equal +to the length of i and then + + align:start position:0% +to the length of i and then + + + align:start position:0% +to the length of i and then +the converse that the length of i is + + align:start position:0% +the converse that the length of i is + + + align:start position:0% +the converse that the length of i is +less than or equal to the outer measure + + align:start position:0% +less than or equal to the outer measure + + + align:start position:0% +less than or equal to the outer measure +of i + + align:start position:0% +of i + + + align:start position:0% +of i +so the simpler one is showing the outer + + align:start position:0% +so the simpler one is showing the outer + + + align:start position:0% +so the simpler one is showing the outer +measure of i is less than or equal to + + align:start position:0% +measure of i is less than or equal to + + + align:start position:0% +measure of i is less than or equal to +the length of i + + align:start position:0% +the length of i + + + align:start position:0% +the length of i +so + + align:start position:0% +so + + + align:start position:0% +so +an i + + align:start position:0% +an i + + + align:start position:0% +an i +is contained in the open interval the + + align:start position:0% +is contained in the open interval the + + + align:start position:0% +is contained in the open interval the +single open interval + + align:start position:0% +single open interval + + + align:start position:0% +single open interval +i minus so + + align:start position:0% + + + + align:start position:0% + +i minus epsilon b plus epsilon + + align:start position:0% +i minus epsilon b plus epsilon + + + align:start position:0% +i minus epsilon b plus epsilon +for all epsilon positive + + align:start position:0% +for all epsilon positive + + + align:start position:0% +for all epsilon positive +and therefore since the outer measure of + + align:start position:0% +and therefore since the outer measure of + + + align:start position:0% +and therefore since the outer measure of +i is the infimum of the lengths of the + + align:start position:0% +i is the infimum of the lengths of the + + + align:start position:0% +i is the infimum of the lengths of the +sum of lengths of intervals covering i + + align:start position:0% +sum of lengths of intervals covering i + + + align:start position:0% +sum of lengths of intervals covering i +this implies that the outer measure of i + + align:start position:0% +this implies that the outer measure of i + + + align:start position:0% +this implies that the outer measure of i +is + + align:start position:0% +is + + + align:start position:0% +is +less than or equal to + + align:start position:0% +less than or equal to + + + align:start position:0% +less than or equal to +the length of this interval + + align:start position:0% + + + + align:start position:0% + +which is equal to b minus a plus 2 + + align:start position:0% +which is equal to b minus a plus 2 + + + align:start position:0% +which is equal to b minus a plus 2 +epsilon for all + + align:start position:0% +epsilon for all + + + align:start position:0% +epsilon for all +epsilon positive and therefore + + align:start position:0% +epsilon positive and therefore + + + align:start position:0% +epsilon positive and therefore +if i have this is less than or equal to + + align:start position:0% +if i have this is less than or equal to + + + align:start position:0% +if i have this is less than or equal to +b minus a plus 2 epsilon for all epsilon + + align:start position:0% +b minus a plus 2 epsilon for all epsilon + + + align:start position:0% +b minus a plus 2 epsilon for all epsilon +positive i can then send epsilon to zero + + align:start position:0% + + + + align:start position:0% + +to conclude that the outer measure of + + align:start position:0% +to conclude that the outer measure of + + + align:start position:0% +to conclude that the outer measure of +the interval is less than or equal to + + align:start position:0% +the interval is less than or equal to + + + align:start position:0% +the interval is less than or equal to +b minus a the length of the interval + + align:start position:0% +b minus a the length of the interval + + + align:start position:0% +b minus a the length of the interval +okay so that's the that's the simple + + align:start position:0% +okay so that's the that's the simple + + + align:start position:0% +okay so that's the that's the simple +part + + align:start position:0% + + + + align:start position:0% + +so now we're going to show + + align:start position:0% + + + + align:start position:0% + +now we show that + + align:start position:0% +now we show that + + + align:start position:0% +now we show that +b minus a is less than or equal to + + align:start position:0% + + + + align:start position:0% + +the outer measure of + + align:start position:0% +the outer measure of + + + align:start position:0% +the outer measure of +of uh the interval okay + + align:start position:0% +of uh the interval okay + + + align:start position:0% +of uh the interval okay +all right so also what this shows is + + align:start position:0% +all right so also what this shows is + + + align:start position:0% +all right so also what this shows is +that the outer measure of this interval + + align:start position:0% +that the outer measure of this interval + + + align:start position:0% +that the outer measure of this interval +is finite okay it's a finite number + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +to show this what we have to show is + + align:start position:0% +to show this what we have to show is + + + align:start position:0% +to show this what we have to show is +that if i take any + + align:start position:0% +that if i take any + + + align:start position:0% +that if i take any +collection of open intervals covering i + + align:start position:0% +collection of open intervals covering i + + + align:start position:0% +collection of open intervals covering i +then the sum of the lengths of those + + align:start position:0% +then the sum of the lengths of those + + + align:start position:0% +then the sum of the lengths of those +intervals is bounded below by b minus a + + align:start position:0% +intervals is bounded below by b minus a + + + align:start position:0% +intervals is bounded below by b minus a +right + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +and if i don't write n equals 1 to + + align:start position:0% +and if i don't write n equals 1 to + + + align:start position:0% +and if i don't write n equals 1 to +infinity it should be understood that n + + align:start position:0% +infinity it should be understood that n + + + align:start position:0% +infinity it should be understood that n +is always going from 1 to infinity + + align:start position:0% +is always going from 1 to infinity + + + align:start position:0% +is always going from 1 to infinity +let i n b + + align:start position:0% + + + + align:start position:0% + +collection of + + align:start position:0% + + + + align:start position:0% + +open intervals + + align:start position:0% + + + + align:start position:0% + +such that + + align:start position:0% + + + + align:start position:0% + +this interval i + + align:start position:0% +this interval i + + + align:start position:0% +this interval i +a b + + align:start position:0% +a b + + + align:start position:0% +a b +is contained in + + align:start position:0% +is contained in + + + align:start position:0% +is contained in +the union + + align:start position:0% +the union + + + align:start position:0% +the union +we now want to show that b minus a is + + align:start position:0% +we now want to show that b minus a is + + + align:start position:0% +we now want to show that b minus a is +less than or equal to the sum of the + + align:start position:0% +less than or equal to the sum of the + + + align:start position:0% +less than or equal to the sum of the +measures of the ins now + + align:start position:0% +measures of the ins now + + + align:start position:0% +measures of the ins now +the closed and bounded interval a b this + + align:start position:0% +the closed and bounded interval a b this + + + align:start position:0% +the closed and bounded interval a b this +is a compact set okay so you + + align:start position:0% +is a compact set okay so you + + + align:start position:0% +is a compact set okay so you +look back to 100 b + + align:start position:0% +look back to 100 b + + + align:start position:0% +look back to 100 b +which is covered by a collection of open + + align:start position:0% +which is covered by a collection of open + + + align:start position:0% +which is covered by a collection of open +intervals in other words open sets now + + align:start position:0% +intervals in other words open sets now + + + align:start position:0% +intervals in other words open sets now +fundamental + + align:start position:0% +fundamental + + + align:start position:0% +fundamental +i mean the definition of compactness + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +since + + align:start position:0% +since + + + align:start position:0% +since +this close and bounded interval is + + align:start position:0% +this close and bounded interval is + + + align:start position:0% +this close and bounded interval is +compact + + align:start position:0% +compact + + + align:start position:0% +compact +this has a special this is due to a + + align:start position:0% +this has a special this is due to a + + + align:start position:0% +this has a special this is due to a +special theorem by + + align:start position:0% + + + + align:start position:0% + +haina and barrel + + align:start position:0% +haina and barrel + + + align:start position:0% +haina and barrel +we can find + + align:start position:0% +we can find + + + align:start position:0% +we can find +a finite covering of this interval by + + align:start position:0% +a finite covering of this interval by + + + align:start position:0% +a finite covering of this interval by +finitely many of these intervals okay + + align:start position:0% +finitely many of these intervals okay + + + align:start position:0% +finitely many of these intervals okay +so i can choose finitely many of these + + align:start position:0% +so i can choose finitely many of these + + + align:start position:0% +so i can choose finitely many of these +intervals to cover a b + + align:start position:0% + + + + align:start position:0% + +there exists a finite collection which i + + align:start position:0% +there exists a finite collection which i + + + align:start position:0% +there exists a finite collection which i +will now denote uh + + align:start position:0% +will now denote uh + + + align:start position:0% +will now denote uh +let's say j k + + align:start position:0% +let's say j k + + + align:start position:0% +let's say j k +k equals one to n + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +contained inside this collection of open + + align:start position:0% +contained inside this collection of open + + + align:start position:0% +contained inside this collection of open +intervals so these are just finitely + + align:start position:0% +intervals so these are just finitely + + + align:start position:0% +intervals so these are just finitely +many open intervals from this collection + + align:start position:0% + + + + align:start position:0% + +such that uh + + align:start position:0% +such that uh + + + align:start position:0% +such that uh +a b is contained in + + align:start position:0% +a b is contained in + + + align:start position:0% +a b is contained in +k equals 1 to n + + align:start position:0% +k equals 1 to n + + + align:start position:0% +k equals 1 to n +j k + + align:start position:0% +j k + + + align:start position:0% +j k +all right + + align:start position:0% +all right + + + align:start position:0% +all right +[Applause] + + align:start position:0% + + + + align:start position:0% + +okay so now i have these um + + align:start position:0% +okay so now i have these um + + + align:start position:0% +okay so now i have these um +uh + + align:start position:0% +uh + + + align:start position:0% +uh +open intervals and now what i'm gonna + + align:start position:0% +open intervals and now what i'm gonna + + + align:start position:0% +open intervals and now what i'm gonna +argue is that i can do this is that uh + + align:start position:0% +argue is that i can do this is that uh + + + align:start position:0% +argue is that i can do this is that uh +here's here's the plan + + align:start position:0% +here's here's the plan + + + align:start position:0% +here's here's the plan +a + + align:start position:0% +a + + + align:start position:0% +a +there's b + + align:start position:0% +there's b + + + align:start position:0% +there's b +um what i'm going to argue now to you is + + align:start position:0% +um what i'm going to argue now to you is + + + align:start position:0% +um what i'm going to argue now to you is +that you know + + align:start position:0% +that you know + + + align:start position:0% +that you know +rearranging how i'm indexing these these + + align:start position:0% +rearranging how i'm indexing these these + + + align:start position:0% +rearranging how i'm indexing these these +open intervals + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +i can + + align:start position:0% + + + + align:start position:0% + +cover a b in the following way so that + + align:start position:0% +cover a b in the following way so that + + + align:start position:0% +cover a b in the following way so that +i have + + align:start position:0% + + + + align:start position:0% + +so this is the first + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +i'm going to argue that we can cover + + align:start position:0% +i'm going to argue that we can cover + + + align:start position:0% +i'm going to argue that we can cover +this uh interval like this so that i can + + align:start position:0% +this uh interval like this so that i can + + + align:start position:0% +this uh interval like this so that i can +choose + + align:start position:0% +choose + + + align:start position:0% +choose +um the first interval to cover sum of a + + align:start position:0% +um the first interval to cover sum of a + + + align:start position:0% +um the first interval to cover sum of a +b + + align:start position:0% +b + + + align:start position:0% +b +and then maybe it covers all in which + + align:start position:0% +and then maybe it covers all in which + + + align:start position:0% +and then maybe it covers all in which +case i'm would stop my construction + + align:start position:0% +case i'm would stop my construction + + + align:start position:0% +case i'm would stop my construction +if it doesn't cover all of a b then i + + align:start position:0% +if it doesn't cover all of a b then i + + + align:start position:0% +if it doesn't cover all of a b then i +can cover it + + align:start position:0% +can cover it + + + align:start position:0% +can cover it +with + + align:start position:0% +with + + + align:start position:0% +with +j2 + + align:start position:0% +j2 + + + align:start position:0% +j2 +so now i have a2 + + align:start position:0% +so now i have a2 + + + align:start position:0% +so now i have a2 +b2 + + align:start position:0% +b2 + + + align:start position:0% +b2 +and if that doesn't cover all of a b i + + align:start position:0% +and if that doesn't cover all of a b i + + + align:start position:0% +and if that doesn't cover all of a b i +will + + align:start position:0% +will + + + align:start position:0% +will +still have to + + align:start position:0% +still have to + + + align:start position:0% +still have to +choose some more intervals + + align:start position:0% +choose some more intervals + + + align:start position:0% +choose some more intervals +to cover it and eventually + + align:start position:0% +to cover it and eventually + + + align:start position:0% +to cover it and eventually +i'll get to + + align:start position:0% +i'll get to + + + align:start position:0% +i'll get to +at least in this picture since i can't + + align:start position:0% +at least in this picture since i can't + + + align:start position:0% +at least in this picture since i can't +draw in intervals i will be able to + + align:start position:0% +draw in intervals i will be able to + + + align:start position:0% +draw in intervals i will be able to +cover a b in such a way + + align:start position:0% +cover a b in such a way + + + align:start position:0% +cover a b in such a way +that + + align:start position:0% + + + + align:start position:0% + +you know these are kind of linked + + align:start position:0% +you know these are kind of linked + + + align:start position:0% +you know these are kind of linked +together so that these intervals are + + align:start position:0% +together so that these intervals are + + + align:start position:0% +together so that these intervals are +linked + + align:start position:0% + + + + align:start position:0% + +and then i cover all of a b + + align:start position:0% +and then i cover all of a b + + + align:start position:0% +and then i cover all of a b +now why is that great well then because + + align:start position:0% +now why is that great well then because + + + align:start position:0% +now why is that great well then because +the sum of the lengths of these + + align:start position:0% +the sum of the lengths of these + + + align:start position:0% +the sum of the lengths of these +intervals is going to be bigger than or + + align:start position:0% +intervals is going to be bigger than or + + + align:start position:0% +intervals is going to be bigger than or +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the sum of the lengths of these + + align:start position:0% +the sum of the lengths of these + + + align:start position:0% +the sum of the lengths of these +intervals is going to be what b3 minus + + align:start position:0% +intervals is going to be what b3 minus + + + align:start position:0% +intervals is going to be what b3 minus +a1 which is bigger than or equal to b + + align:start position:0% +a1 which is bigger than or equal to b + + + align:start position:0% +a1 which is bigger than or equal to b +minus a all right and that would give me + + align:start position:0% +minus a all right and that would give me + + + align:start position:0% +minus a all right and that would give me +the lower bound that i desire + + align:start position:0% +the lower bound that i desire + + + align:start position:0% +the lower bound that i desire +so now let me argue that we can do this + + align:start position:0% +so now let me argue that we can do this + + + align:start position:0% +so now let me argue that we can do this +that this is kind of + + align:start position:0% +that this is kind of + + + align:start position:0% +that this is kind of +that this picture is correct + + align:start position:0% + + + + align:start position:0% + +since a + + align:start position:0% +since a + + + align:start position:0% +since a +is in this + + align:start position:0% + + + + align:start position:0% + +you know it's in a b so it has to be in + + align:start position:0% +you know it's in a b so it has to be in + + + align:start position:0% +you know it's in a b so it has to be in +this finite union of open intervals + + align:start position:0% +this finite union of open intervals + + + align:start position:0% +this finite union of open intervals +there exists + + align:start position:0% +there exists + + + align:start position:0% +there exists +k1 + + align:start position:0% +k1 + + + align:start position:0% +k1 +such that a is in + + align:start position:0% + + + + align:start position:0% + +j of k1 + + align:start position:0% +j of k1 + + + align:start position:0% +j of k1 +all right so there's some one of these + + align:start position:0% +all right so there's some one of these + + + align:start position:0% +all right so there's some one of these +intervals a has to be in it + + align:start position:0% +intervals a has to be in it + + + align:start position:0% +intervals a has to be in it +and + + align:start position:0% +and + + + align:start position:0% +and +by + + align:start position:0% + + + + align:start position:0% + +rearranging + + align:start position:0% + + + + align:start position:0% + +the intervals + + align:start position:0% + + + + align:start position:0% + +i can assume that + + align:start position:0% +i can assume that + + + align:start position:0% +i can assume that +k1 equals one + + align:start position:0% +k1 equals one + + + align:start position:0% +k1 equals one +ie + + align:start position:0% + + + + align:start position:0% + +a is in + + align:start position:0% +a is in + + + align:start position:0% +a is in +j1 which is + + align:start position:0% +j1 which is + + + align:start position:0% +j1 which is +a1 + + align:start position:0% +a1 + + + align:start position:0% +a1 +b1 + + align:start position:0% +b1 + + + align:start position:0% +b1 +okay + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +um + + align:start position:0% +um + + + align:start position:0% +um +you know it's possible that this whole + + align:start position:0% +you know it's possible that this whole + + + align:start position:0% +you know it's possible that this whole +interval covers a b in which case i + + align:start position:0% +interval covers a b in which case i + + + align:start position:0% +interval covers a b in which case i +would stop the construction + + align:start position:0% + + + + align:start position:0% + +otherwise i continue + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% +if + + + align:start position:0% +if +b1 is + + align:start position:0% +b1 is + + + align:start position:0% +b1 is +less than or equal to b + + align:start position:0% +less than or equal to b + + + align:start position:0% +less than or equal to b +then + + align:start position:0% +then + + + align:start position:0% +then +b1 is certainly in + + align:start position:0% +b1 is certainly in + + + align:start position:0% +b1 is certainly in +this interval which implies + + align:start position:0% +this interval which implies + + + align:start position:0% +this interval which implies +there exists a j + + align:start position:0% +there exists a j + + + align:start position:0% +there exists a j +k sub 2. + + align:start position:0% + + + + align:start position:0% + +or let me write it this way there exists + + align:start position:0% + + + + align:start position:0% + +k sub 2 + + align:start position:0% +k sub 2 + + + align:start position:0% +k sub 2 +such that + + align:start position:0% +such that + + + align:start position:0% +such that +b 1 is in j sub k sub 2. + + align:start position:0% +b 1 is in j sub k sub 2. + + + align:start position:0% +b 1 is in j sub k sub 2. +and again + + align:start position:0% + + + + align:start position:0% + +by rearranging + + align:start position:0% + + + + align:start position:0% + +we can assume that + + align:start position:0% +we can assume that + + + align:start position:0% +we can assume that +k sub 2 + + align:start position:0% +k sub 2 + + + align:start position:0% +k sub 2 +we can assume + + align:start position:0% + + + + align:start position:0% + +equals 2. + + align:start position:0% +equals 2. + + + align:start position:0% +equals 2. +all right so by rearranging the + + align:start position:0% +all right so by rearranging the + + + align:start position:0% +all right so by rearranging the +remaining intervals i can assume k2 is + + align:start position:0% +remaining intervals i can assume k2 is + + + align:start position:0% +remaining intervals i can assume k2 is +2. all right so + + align:start position:0% +2. all right so + + + align:start position:0% +2. all right so +if in the case like i've drawn in the + + align:start position:0% +if in the case like i've drawn in the + + + align:start position:0% +if in the case like i've drawn in the +picture b1 is not bigger than b then i + + align:start position:0% +picture b1 is not bigger than b then i + + + align:start position:0% +picture b1 is not bigger than b then i +can find another interval j2 + + align:start position:0% +can find another interval j2 + + + align:start position:0% +can find another interval j2 +that + + align:start position:0% +that + + + align:start position:0% +that +contains + + align:start position:0% +contains + + + align:start position:0% +contains +b1 + + align:start position:0% +b1 + + + align:start position:0% +b1 +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +b1 is in + + align:start position:0% +b1 is in + + + align:start position:0% +b1 is in +j2 which is + + align:start position:0% + + + + align:start position:0% + +a2 b2 + + align:start position:0% +a2 b2 + + + align:start position:0% +a2 b2 +okay and at some point uh + + align:start position:0% +okay and at some point uh + + + align:start position:0% +okay and at some point uh +and i will just continue this until + + align:start position:0% +and i will just continue this until + + + align:start position:0% +and i will just continue this until +uh the end point + + align:start position:0% +uh the end point + + + align:start position:0% +uh the end point +of one of these intervals passes b + + align:start position:0% +of one of these intervals passes b + + + align:start position:0% +of one of these intervals passes b +okay the first instance when one of + + align:start position:0% +okay the first instance when one of + + + align:start position:0% +okay the first instance when one of +these intervals passes b i stop this + + align:start position:0% +these intervals passes b i stop this + + + align:start position:0% +these intervals passes b i stop this +process + + align:start position:0% +process + + + align:start position:0% +process +and it has to stop because all of these + + align:start position:0% +and it has to stop because all of these + + + align:start position:0% +and it has to stop because all of these +intervals do cover b so it has to occur + + align:start position:0% +intervals do cover b so it has to occur + + + align:start position:0% +intervals do cover b so it has to occur +at some point and there's only finitely + + align:start position:0% +at some point and there's only finitely + + + align:start position:0% +at some point and there's only finitely +many intervals all right + + align:start position:0% +many intervals all right + + + align:start position:0% +many intervals all right +so + + align:start position:0% + + + + align:start position:0% + +and i'm going to write + + align:start position:0% +and i'm going to write + + + align:start position:0% +and i'm going to write +if b 2 is less than or equal to b + + align:start position:0% +if b 2 is less than or equal to b + + + align:start position:0% +if b 2 is less than or equal to b +i'm going to put dot dot there + + align:start position:0% +i'm going to put dot dot there + + + align:start position:0% +i'm going to put dot dot there +so what have we done + + align:start position:0% +so what have we done + + + align:start position:0% +so what have we done +by this argument + + align:start position:0% + + + + align:start position:0% + +thus + + align:start position:0% + + + + align:start position:0% + +we conclude + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +maybe that's a little bit bad notation + + align:start position:0% +maybe that's a little bit bad notation + + + align:start position:0% +maybe that's a little bit bad notation +because i have n there and + + align:start position:0% +because i have n there and + + + align:start position:0% +because i have n there and +let's let's make this a capital n sorry + + align:start position:0% +let's let's make this a capital n sorry + + + align:start position:0% +let's let's make this a capital n sorry +about that + + align:start position:0% +about that + + + align:start position:0% +about that +[Applause] + + align:start position:0% + + + + align:start position:0% + +let's make that a capital n + + align:start position:0% +let's make that a capital n + + + align:start position:0% +let's make that a capital n +since that little n appears also to + + align:start position:0% +since that little n appears also to + + + align:start position:0% +since that little n appears also to +index the isobins okay + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +thus we conclude that + + align:start position:0% +thus we conclude that + + + align:start position:0% +thus we conclude that +there exists a k + + align:start position:0% +there exists a k + + + align:start position:0% +there exists a k +with one less than or equal to k + + align:start position:0% +with one less than or equal to k + + + align:start position:0% +with one less than or equal to k +less than or equal to n + + align:start position:0% +less than or equal to n + + + align:start position:0% +less than or equal to n +such that um two things + + align:start position:0% +such that um two things + + + align:start position:0% +such that um two things +i should say three things hold + + align:start position:0% +i should say three things hold + + + align:start position:0% +i should say three things hold +for all k equals one + + align:start position:0% +for all k equals one + + + align:start position:0% +for all k equals one +to + + align:start position:0% +to + + + align:start position:0% +to +k minus 1 + + align:start position:0% +k minus 1 + + + align:start position:0% +k minus 1 +we have that + + align:start position:0% + + + + align:start position:0% + +b k is less than or equal to b + + align:start position:0% +b k is less than or equal to b + + + align:start position:0% +b k is less than or equal to b +and + + align:start position:0% + + + + align:start position:0% + +a k plus one is less than b k is less + + align:start position:0% +a k plus one is less than b k is less + + + align:start position:0% +a k plus one is less than b k is less +than b k plus one + + align:start position:0% +than b k plus one + + + align:start position:0% +than b k plus one +okay so think of this as a condition + + align:start position:0% +okay so think of this as a condition + + + align:start position:0% +okay so think of this as a condition +where we have not yet covered uh + + align:start position:0% +where we have not yet covered uh + + + align:start position:0% +where we have not yet covered uh +the entire interval a b + + align:start position:0% + + + + align:start position:0% + +so right for k equals uh one + + align:start position:0% +so right for k equals uh one + + + align:start position:0% +so right for k equals uh one +um + + align:start position:0% +um + + + align:start position:0% +um +this was basically the argument i just + + align:start position:0% +this was basically the argument i just + + + align:start position:0% +this was basically the argument i just +gave here + + align:start position:0% + + + + align:start position:0% + +and two that this has to stop at some + + align:start position:0% +and two that this has to stop at some + + + align:start position:0% +and two that this has to stop at some +point so that + + align:start position:0% +point so that + + + align:start position:0% +point so that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +b + + align:start position:0% +b + + + align:start position:0% +b +is less than + + align:start position:0% +is less than + + + align:start position:0% +is less than +b capital k + + align:start position:0% +b capital k + + + align:start position:0% +b capital k +okay + + align:start position:0% + + + + align:start position:0% + +so what i drew here so the picture is + + align:start position:0% +so what i drew here so the picture is + + + align:start position:0% +so what i drew here so the picture is +for + + align:start position:0% + + + + align:start position:0% + +is for the case k equals three + + align:start position:0% +is for the case k equals three + + + align:start position:0% +is for the case k equals three +okay + + align:start position:0% + + + + align:start position:0% + +okay so we have this k + + align:start position:0% +okay so we have this k + + + align:start position:0% +okay so we have this k +and i drew the picture over there for b3 + + align:start position:0% +and i drew the picture over there for b3 + + + align:start position:0% +and i drew the picture over there for b3 +now i'm going to show that the sum of + + align:start position:0% +now i'm going to show that the sum of + + + align:start position:0% +now i'm going to show that the sum of +the lengths + + align:start position:0% +the lengths + + + align:start position:0% +the lengths +of + + align:start position:0% +of + + + align:start position:0% +of +the intervals you know and this is just + + align:start position:0% +the intervals you know and this is just + + + align:start position:0% +the intervals you know and this is just +a finite collection + + align:start position:0% +a finite collection + + + align:start position:0% +a finite collection +uh + + align:start position:0% +uh + + + align:start position:0% +uh +from the bigger collection of intervals + + align:start position:0% +from the bigger collection of intervals + + + align:start position:0% +from the bigger collection of intervals +is now bounded by b minus a which is + + align:start position:0% +is now bounded by b minus a which is + + + align:start position:0% +is now bounded by b minus a which is +kind of clear from the picture that i + + align:start position:0% +kind of clear from the picture that i + + + align:start position:0% +kind of clear from the picture that i +drew but we still have to write stuff + + align:start position:0% +drew but we still have to write stuff + + + align:start position:0% +drew but we still have to write stuff +down this is not topology + + align:start position:0% +down this is not topology + + + align:start position:0% +down this is not topology +then + + align:start position:0% + + + + align:start position:0% + +sum of length of + + align:start position:0% +sum of length of + + + align:start position:0% +sum of length of +i sub n's this is certainly less than or + + align:start position:0% +i sub n's this is certainly less than or + + + align:start position:0% +i sub n's this is certainly less than or +equal to the sum over this finite + + align:start position:0% +equal to the sum over this finite + + + align:start position:0% +equal to the sum over this finite +subcollection of + + align:start position:0% +subcollection of + + + align:start position:0% +subcollection of +intervals + + align:start position:0% +intervals + + + align:start position:0% +intervals +lengths of + + align:start position:0% +lengths of + + + align:start position:0% +lengths of +j + + align:start position:0% +j + + + align:start position:0% +j +k + + align:start position:0% + + + + align:start position:0% + +and this is less than or equal to + + align:start position:0% +and this is less than or equal to + + + align:start position:0% +and this is less than or equal to +sum k + + align:start position:0% +sum k + + + align:start position:0% +sum k +k now here this capital k is coming from + + align:start position:0% +k now here this capital k is coming from + + + align:start position:0% +k now here this capital k is coming from +over there length of + + align:start position:0% +over there length of + + + align:start position:0% +over there length of +j k + + align:start position:0% +j k + + + align:start position:0% +j k +and now what is this this is equal to + + align:start position:0% +and now what is this this is equal to + + + align:start position:0% +and now what is this this is equal to +b k minus + + align:start position:0% +b k minus + + + align:start position:0% +b k minus +a k + + align:start position:0% +a k + + + align:start position:0% +a k +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +plus + + align:start position:0% +plus + + + align:start position:0% +plus +b k minus 1 minus ak + + align:start position:0% +b k minus 1 minus ak + + + align:start position:0% +b k minus 1 minus ak +minus 1 plus + + align:start position:0% +minus 1 plus + + + align:start position:0% +minus 1 plus +and then all the way down to + + align:start position:0% +and then all the way down to + + + align:start position:0% +and then all the way down to +b1 minus + + align:start position:0% + + + + align:start position:0% + +now what am i doing b1 minus a1 + + align:start position:0% +now what am i doing b1 minus a1 + + + align:start position:0% +now what am i doing b1 minus a1 +okay + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +but here's the here's the trick remember + + align:start position:0% +but here's the here's the trick remember + + + align:start position:0% +but here's the here's the trick remember +each of the + + align:start position:0% +each of the + + + align:start position:0% +each of the +bk minus ones + + align:start position:0% +bk minus ones + + + align:start position:0% +bk minus ones +you know + + align:start position:0% +you know + + + align:start position:0% +you know +they lie ahead of a k so the the index + + align:start position:0% +they lie ahead of a k so the the index + + + align:start position:0% +they lie ahead of a k so the the index +here is shifted uh just by a little bit + + align:start position:0% +here is shifted uh just by a little bit + + + align:start position:0% +here is shifted uh just by a little bit +but this says that the next b + + align:start position:0% +but this says that the next b + + + align:start position:0% +but this says that the next b +or the + + align:start position:0% +or the + + + align:start position:0% +or the +the previous b + + align:start position:0% +the previous b + + + align:start position:0% +the previous b +is in front of the next a + + align:start position:0% +is in front of the next a + + + align:start position:0% +is in front of the next a +so i can collect terms and write this as + + align:start position:0% +so i can collect terms and write this as + + + align:start position:0% +so i can collect terms and write this as +b k + + align:start position:0% +b k + + + align:start position:0% +b k +plus + + align:start position:0% +plus + + + align:start position:0% +plus +b k minus 1 minus a k + + align:start position:0% +b k minus 1 minus a k + + + align:start position:0% +b k minus 1 minus a k +plus + + align:start position:0% +plus + + + align:start position:0% +plus +b k + + align:start position:0% +b k + + + align:start position:0% +b k +minus 2 + + align:start position:0% +minus 2 + + + align:start position:0% +minus 2 +minus ak minus 1. + + align:start position:0% +minus ak minus 1. + + + align:start position:0% +minus ak minus 1. +okay so i just borrowed a b coming after + + align:start position:0% +okay so i just borrowed a b coming after + + + align:start position:0% +okay so i just borrowed a b coming after +this term + + align:start position:0% +this term + + + align:start position:0% +this term +so on and so on + + align:start position:0% +so on and so on + + + align:start position:0% +so on and so on +uh until i get b1 minus a2 + + align:start position:0% +uh until i get b1 minus a2 + + + align:start position:0% +uh until i get b1 minus a2 +and then i'm stuck with a a1 + + align:start position:0% +and then i'm stuck with a a1 + + + align:start position:0% +and then i'm stuck with a a1 +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and by the second condition over here + + align:start position:0% +and by the second condition over here + + + align:start position:0% +and by the second condition over here +everything in parentheses is + + align:start position:0% +everything in parentheses is + + + align:start position:0% +everything in parentheses is +non-negative so + + align:start position:0% +non-negative so + + + align:start position:0% +non-negative so +this is bigger than or equal to b k + + align:start position:0% +this is bigger than or equal to b k + + + align:start position:0% +this is bigger than or equal to b k +minus a1 + + align:start position:0% +minus a1 + + + align:start position:0% +minus a1 +okay and what do we know we know bk is + + align:start position:0% +okay and what do we know we know bk is + + + align:start position:0% +okay and what do we know we know bk is +bigger than b and we know a1 is less + + align:start position:0% +bigger than b and we know a1 is less + + + align:start position:0% +bigger than b and we know a1 is less +than a right because a is in a1 uh b1 so + + align:start position:0% +than a right because a is in a1 uh b1 so + + + align:start position:0% +than a right because a is in a1 uh b1 so +this length is bigger than + + align:start position:0% +this length is bigger than + + + align:start position:0% +this length is bigger than +b minus a + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +and since we've shown that the sum of + + align:start position:0% +and since we've shown that the sum of + + + align:start position:0% +and since we've shown that the sum of +lengths of intervals + + align:start position:0% +lengths of intervals + + + align:start position:0% +lengths of intervals +covering i is bigger than or equal to + + align:start position:0% +covering i is bigger than or equal to + + + align:start position:0% +covering i is bigger than or equal to +b minus a no matter what the collection + + align:start position:0% +b minus a no matter what the collection + + + align:start position:0% +b minus a no matter what the collection +of intervals is then the infimum has to + + align:start position:0% +of intervals is then the infimum has to + + + align:start position:0% +of intervals is then the infimum has to +be bigger than or equal to b minus a + + align:start position:0% +be bigger than or equal to b minus a + + + align:start position:0% +be bigger than or equal to b minus a +and we conclude that + + align:start position:0% +and we conclude that + + + align:start position:0% +and we conclude that +the outer measure of this interval b + + align:start position:0% +the outer measure of this interval b + + + align:start position:0% +the outer measure of this interval b +minus a b a a b + + align:start position:0% +minus a b a a b + + + align:start position:0% +minus a b a a b +is bigger than or equal to + + align:start position:0% +is bigger than or equal to + + + align:start position:0% +is bigger than or equal to +b minus a and therefore + + align:start position:0% +b minus a and therefore + + + align:start position:0% +b minus a and therefore +uh i have both sides of the inequality i + + align:start position:0% +uh i have both sides of the inequality i + + + align:start position:0% +uh i have both sides of the inequality i +want and therefore i have equality + + align:start position:0% +want and therefore i have equality + + + align:start position:0% +want and therefore i have equality +so + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now this was for a closed and bounded + + align:start position:0% +now this was for a closed and bounded + + + align:start position:0% +now this was for a closed and bounded +interval but + + align:start position:0% +interval but + + + align:start position:0% +interval but +this essentially gives us the result for + + align:start position:0% +this essentially gives us the result for + + + align:start position:0% +this essentially gives us the result for +any interval + + align:start position:0% +any interval + + + align:start position:0% +any interval +so + + align:start position:0% + + + + align:start position:0% + +if i is + + align:start position:0% +if i is + + + align:start position:0% +if i is +any finite interval + + align:start position:0% +any finite interval + + + align:start position:0% +any finite interval +of the form + + align:start position:0% + + + + align:start position:0% + +you know + + align:start position:0% + + + + align:start position:0% + +a b + + align:start position:0% +a b + + + align:start position:0% +a b +a b + + align:start position:0% +a b + + + align:start position:0% +a b +not including a + + align:start position:0% + + + + align:start position:0% + +open and then + + align:start position:0% + + + + align:start position:0% + +then we're all epsilon positive at least + + align:start position:0% +then we're all epsilon positive at least + + + align:start position:0% +then we're all epsilon positive at least +sufficiently small what do i have i have + + align:start position:0% +sufficiently small what do i have i have + + + align:start position:0% +sufficiently small what do i have i have +that + + align:start position:0% +that + + + align:start position:0% +that +a plus epsilon + + align:start position:0% +a plus epsilon + + + align:start position:0% +a plus epsilon +b minus epsilon + + align:start position:0% +b minus epsilon + + + align:start position:0% +b minus epsilon +is contained in + + align:start position:0% +is contained in + + + align:start position:0% +is contained in +i which is contained in + + align:start position:0% + + + + align:start position:0% + +a minus epsilon + + align:start position:0% +a minus epsilon + + + align:start position:0% +a minus epsilon +b plus epsilon okay you know i is one of + + align:start position:0% +b plus epsilon okay you know i is one of + + + align:start position:0% +b plus epsilon okay you know i is one of +these intervals so if i just make it a + + align:start position:0% +these intervals so if i just make it a + + + align:start position:0% +these intervals so if i just make it a +little fatter and take that closed + + align:start position:0% +little fatter and take that closed + + + align:start position:0% +little fatter and take that closed +interval + + align:start position:0% +interval + + + align:start position:0% +interval +containing it + + align:start position:0% +containing it + + + align:start position:0% +containing it +i get this side and then if i just kind + + align:start position:0% +i get this side and then if i just kind + + + align:start position:0% +i get this side and then if i just kind +of shrink the interval a little bit and + + align:start position:0% +of shrink the interval a little bit and + + + align:start position:0% +of shrink the interval a little bit and +take the closed interval + + align:start position:0% +take the closed interval + + + align:start position:0% +take the closed interval +this guy this will be contained inside + + align:start position:0% +this guy this will be contained inside + + + align:start position:0% +this guy this will be contained inside +of it + + align:start position:0% + + + + align:start position:0% + +and therefore the measure of this + + align:start position:0% +and therefore the measure of this + + + align:start position:0% +and therefore the measure of this +interval has to be less than or equal to + + align:start position:0% +interval has to be less than or equal to + + + align:start position:0% +interval has to be less than or equal to +the measure outer measure of this + + align:start position:0% +the measure outer measure of this + + + align:start position:0% +the measure outer measure of this +interval which is less than or equal to + + align:start position:0% +interval which is less than or equal to + + + align:start position:0% +interval which is less than or equal to +the outer measure of this interval + + align:start position:0% +the outer measure of this interval + + + align:start position:0% +the outer measure of this interval +and i get that now the measure of this + + align:start position:0% +and i get that now the measure of this + + + align:start position:0% +and i get that now the measure of this +interval + + align:start position:0% +interval + + + align:start position:0% +interval +so i'll just write this + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +this over here + + align:start position:0% +this over here + + + align:start position:0% +this over here +is + + align:start position:0% +is + + + align:start position:0% +is +b minus a minus 2 epsilon is less than + + align:start position:0% +b minus a minus 2 epsilon is less than + + + align:start position:0% +b minus a minus 2 epsilon is less than +or equal to + + align:start position:0% +or equal to + + + align:start position:0% +or equal to +the outer measure of the interval which + + align:start position:0% +the outer measure of the interval which + + + align:start position:0% +the outer measure of the interval which +is less than or equal to + + align:start position:0% +is less than or equal to + + + align:start position:0% +is less than or equal to +the outer measure of b minus a + + align:start position:0% +the outer measure of b minus a + + + align:start position:0% +the outer measure of b minus a +plus 2 epsilon + + align:start position:0% +plus 2 epsilon + + + align:start position:0% +plus 2 epsilon +okay + + align:start position:0% + + + + align:start position:0% + +and this holds for all epsilon positive + + align:start position:0% + + + + align:start position:0% + +you recall that i was starting off for + + align:start position:0% +you recall that i was starting off for + + + align:start position:0% +you recall that i was starting off for +all epsilon positive at least + + align:start position:0% +all epsilon positive at least + + + align:start position:0% +all epsilon positive at least +sufficiently small depending on b and a + + align:start position:0% +sufficiently small depending on b and a + + + align:start position:0% +sufficiently small depending on b and a +you know smaller than the difference of + + align:start position:0% +you know smaller than the difference of + + + align:start position:0% +you know smaller than the difference of +b and a + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and therefore if i send epsilon to zero + + align:start position:0% +and therefore if i send epsilon to zero + + + align:start position:0% +and therefore if i send epsilon to zero +i get b minus a is less than or equal to + + align:start position:0% +i get b minus a is less than or equal to + + + align:start position:0% +i get b minus a is less than or equal to +the outer measure of this interval this + + align:start position:0% +the outer measure of this interval this + + + align:start position:0% +the outer measure of this interval this +finite interval uh is less than or equal + + align:start position:0% +finite interval uh is less than or equal + + + align:start position:0% +finite interval uh is less than or equal +to + + align:start position:0% +to + + + align:start position:0% +to +um + + align:start position:0% +um + + + align:start position:0% +um +why do i have this here + + align:start position:0% + + + + align:start position:0% + +is + + align:start position:0% +is + + + align:start position:0% +is +less than or equal to b minus a and + + align:start position:0% +less than or equal to b minus a and + + + align:start position:0% +less than or equal to b minus a and +therefore + + align:start position:0% + + + + align:start position:0% + +the outer measure of any one of these + + align:start position:0% +the outer measure of any one of these + + + align:start position:0% +the outer measure of any one of these +finite intervals is is the length of the + + align:start position:0% +finite intervals is is the length of the + + + align:start position:0% +finite intervals is is the length of the +interval and then i'm going to leave it + + align:start position:0% +interval and then i'm going to leave it + + + align:start position:0% +interval and then i'm going to leave it +to you as an exercise + + align:start position:0% +to you as an exercise + + + align:start position:0% +to you as an exercise +so + + align:start position:0% + + + + align:start position:0% + +which is not difficult + + align:start position:0% +which is not difficult + + + align:start position:0% +which is not difficult +you know if i is equal to + + align:start position:0% +you know if i is equal to + + + align:start position:0% +you know if i is equal to +r + + align:start position:0% +r + + + align:start position:0% +r +negative infinity to a + + align:start position:0% + + + + align:start position:0% + +a infinity + + align:start position:0% +a infinity + + + align:start position:0% +a infinity +or + + align:start position:0% +or + + + align:start position:0% +or +you + + align:start position:0% +you + + + align:start position:0% +you +know including + + align:start position:0% +know including + + + align:start position:0% +know including +i can include + + align:start position:0% + + + + align:start position:0% + +then the outer measure of + + align:start position:0% + + + + align:start position:0% + +this interval is infinity + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +in other words i cannot ever cover these + + align:start position:0% +in other words i cannot ever cover these + + + align:start position:0% +in other words i cannot ever cover these +intervals by a countable collection of + + align:start position:0% +intervals by a countable collection of + + + align:start position:0% +intervals by a countable collection of +intervals + + align:start position:0% +intervals + + + align:start position:0% +intervals +whose sum of lengths is a finite number + + align:start position:0% +whose sum of lengths is a finite number + + + align:start position:0% +whose sum of lengths is a finite number +again this is not this is not hard + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um + + align:start position:0% +um + + + align:start position:0% +um +so we get + + align:start position:0% +so we get + + + align:start position:0% +so we get +kind of a + + align:start position:0% +kind of a + + + align:start position:0% +kind of a +nice little fact from + + align:start position:0% +nice little fact from + + + align:start position:0% +nice little fact from +the theorem we proved last time which + + align:start position:0% +the theorem we proved last time which + + + align:start position:0% +the theorem we proved last time which +was that if i have a collection of + + align:start position:0% +was that if i have a collection of + + + align:start position:0% +was that if i have a collection of +subsets of r + + align:start position:0% +subsets of r + + + align:start position:0% +subsets of r +then the measure of the union is less + + align:start position:0% +then the measure of the union is less + + + align:start position:0% +then the measure of the union is less +than or equal to the sum of the measures + + align:start position:0% +than or equal to the sum of the measures + + + align:start position:0% +than or equal to the sum of the measures +and this theorem which says that the + + align:start position:0% +and this theorem which says that the + + + align:start position:0% +and this theorem which says that the +measure of an interval is the length of + + align:start position:0% +measure of an interval is the length of + + + align:start position:0% +measure of an interval is the length of +the interval + + align:start position:0% +the interval + + + align:start position:0% +the interval +which is the following + + align:start position:0% + + + + align:start position:0% + +for every + + align:start position:0% +for every + + + align:start position:0% +for every +subset of r + + align:start position:0% + + + + align:start position:0% + +and epsilon positive + + align:start position:0% + + + + align:start position:0% + +there exists an open set + + align:start position:0% +there exists an open set + + + align:start position:0% +there exists an open set +o + + align:start position:0% + + + + align:start position:0% + +such that a is contained in o + + align:start position:0% +such that a is contained in o + + + align:start position:0% +such that a is contained in o +and + + align:start position:0% +and + + + align:start position:0% +and +the measure of a which is less than or + + align:start position:0% +the measure of a which is less than or + + + align:start position:0% +the measure of a which is less than or +equal to the measure of o simply because + + align:start position:0% +equal to the measure of o simply because + + + align:start position:0% +equal to the measure of o simply because +a is contained in o + + align:start position:0% +a is contained in o + + + align:start position:0% +a is contained in o +is less than or equal to + + align:start position:0% +is less than or equal to + + + align:start position:0% +is less than or equal to +the outer measure of + + align:start position:0% +the outer measure of + + + align:start position:0% +the outer measure of +a + + align:start position:0% +a + + + align:start position:0% +a +plus epsilon okay so somehow you know + + align:start position:0% + + + + align:start position:0% + +the outer measure of subsets can be + + align:start position:0% +the outer measure of subsets can be + + + align:start position:0% +the outer measure of subsets can be +approximately + + align:start position:0% +approximately + + + align:start position:0% +approximately +measured by the outer measure of open + + align:start position:0% +measured by the outer measure of open + + + align:start position:0% +measured by the outer measure of open +sets + + align:start position:0% +sets + + + align:start position:0% +sets +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so another way to say this is at least + + align:start position:0% +so another way to say this is at least + + + align:start position:0% +so another way to say this is at least +with respect to outer measure every open + + align:start position:0% +with respect to outer measure every open + + + align:start position:0% +with respect to outer measure every open +set can be or every set can be + + align:start position:0% +set can be or every set can be + + + align:start position:0% +set can be or every set can be +approximated by an open set in outer + + align:start position:0% +approximated by an open set in outer + + + align:start position:0% +approximated by an open set in outer +measure okay what's the proof of this + + align:start position:0% +measure okay what's the proof of this + + + align:start position:0% +measure okay what's the proof of this +so this is uh + + align:start position:0% + + + + align:start position:0% + +clear if + + align:start position:0% + + + + align:start position:0% + +the outer measure is infinite then i + + align:start position:0% +the outer measure is infinite then i + + + align:start position:0% +the outer measure is infinite then i +just take o to be the entire real number + + align:start position:0% +just take o to be the entire real number + + + align:start position:0% +just take o to be the entire real number +line + + align:start position:0% + + + + align:start position:0% + +so suppose + + align:start position:0% + + + + align:start position:0% + +is finite + + align:start position:0% + + + + align:start position:0% + +let + + align:start position:0% +let + + + align:start position:0% +let +i n + + align:start position:0% +i n + + + align:start position:0% +i n +be + + align:start position:0% + + + + align:start position:0% + +a collection of open intervals + + align:start position:0% + + + + align:start position:0% + +such that they cover a + + align:start position:0% + + + + align:start position:0% + +and remember the outer measure is the + + align:start position:0% +and remember the outer measure is the + + + align:start position:0% +and remember the outer measure is the +enthemum so i can get arbitrarily close + + align:start position:0% +enthemum so i can get arbitrarily close + + + align:start position:0% +enthemum so i can get arbitrarily close +to that in femum by summing lengths of + + align:start position:0% +to that in femum by summing lengths of + + + align:start position:0% +to that in femum by summing lengths of +certain collections of open intervals + + align:start position:0% +certain collections of open intervals + + + align:start position:0% +certain collections of open intervals +and + + align:start position:0% + + + + align:start position:0% + +some of the links + + align:start position:0% + + + + align:start position:0% + +is less than + + align:start position:0% +is less than + + + align:start position:0% +is less than +or equal to if you like + + align:start position:0% +or equal to if you like + + + align:start position:0% +or equal to if you like +the outer measure of a plus epsilon + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so i should have said at the beginning + + align:start position:0% +so i should have said at the beginning + + + align:start position:0% +so i should have said at the beginning +let a be a subset of r and epsilon b + + align:start position:0% +let a be a subset of r and epsilon b + + + align:start position:0% +let a be a subset of r and epsilon b +positive but + + align:start position:0% + + + + align:start position:0% + +okay you understand + + align:start position:0% + + + + align:start position:0% + +okay and so what i do is i just take o + + align:start position:0% +okay and so what i do is i just take o + + + align:start position:0% +okay and so what i do is i just take o +to be this uh union of of open intervals + + align:start position:0% +to be this uh union of of open intervals + + + align:start position:0% +to be this uh union of of open intervals +then + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +o is a union of open intervals each of + + align:start position:0% +o is a union of open intervals each of + + + align:start position:0% +o is a union of open intervals each of +these open intervals is an open set and + + align:start position:0% +these open intervals is an open set and + + + align:start position:0% +these open intervals is an open set and +you should know that the union of open + + align:start position:0% +you should know that the union of open + + + align:start position:0% +you should know that the union of open +sets any collection of open sets is + + align:start position:0% +sets any collection of open sets is + + + align:start position:0% +sets any collection of open sets is +again an open set so this is open + + align:start position:0% + + + + align:start position:0% + +is open + + align:start position:0% +is open + + + align:start position:0% +is open +a is contained in o because + + align:start position:0% +a is contained in o because + + + align:start position:0% +a is contained in o because +a is contained in the union + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% + + + + align:start position:0% + +the outer measure of o which is + + align:start position:0% +the outer measure of o which is + + + align:start position:0% +the outer measure of o which is +equal to the outer measure of + + align:start position:0% +equal to the outer measure of + + + align:start position:0% +equal to the outer measure of +this union of open intervals + + align:start position:0% +this union of open intervals + + + align:start position:0% +this union of open intervals +is by the theorem we proved last time + + align:start position:0% +is by the theorem we proved last time + + + align:start position:0% +is by the theorem we proved last time +which i stated with the definition + + align:start position:0% +which i stated with the definition + + + align:start position:0% +which i stated with the definition +of or when i recall the definition is + + align:start position:0% +of or when i recall the definition is + + + align:start position:0% +of or when i recall the definition is +less than or equal to the sum + + align:start position:0% +less than or equal to the sum + + + align:start position:0% +less than or equal to the sum +of the outer measures of + + align:start position:0% +of the outer measures of + + + align:start position:0% +of the outer measures of +uh the intervals which we just proved is + + align:start position:0% +uh the intervals which we just proved is + + + align:start position:0% +uh the intervals which we just proved is +the length + + align:start position:0% +the length + + + align:start position:0% +the length +of these intervals + + align:start position:0% +of these intervals + + + align:start position:0% +of these intervals +and + + align:start position:0% +and + + + align:start position:0% +and +how we chose these intervals remember + + align:start position:0% +how we chose these intervals remember + + + align:start position:0% +how we chose these intervals remember +remember is so that we have this + + align:start position:0% +remember is so that we have this + + + align:start position:0% +remember is so that we have this +condition + + align:start position:0% +condition + + + align:start position:0% +condition +and this is less than or equal to + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so with respect to outer measure + + align:start position:0% + + + + align:start position:0% + +every set um + + align:start position:0% +every set um + + + align:start position:0% +every set um +can be + + align:start position:0% +can be + + + align:start position:0% +can be +approximated by the + + align:start position:0% +approximated by the + + + align:start position:0% +approximated by the +approximation with respect to outer + + align:start position:0% +approximation with respect to outer + + + align:start position:0% +approximation with respect to outer +measure + + align:start position:0% +measure + + + align:start position:0% +measure +by an open set by a suitable open set + + align:start position:0% +by an open set by a suitable open set + + + align:start position:0% +by an open set by a suitable open set +[Applause] + + align:start position:0% + + + + align:start position:0% + +all right so + + align:start position:0% +all right so + + + align:start position:0% +all right so +we've defined outer measure we've proven + + align:start position:0% +we've defined outer measure we've proven + + + align:start position:0% +we've defined outer measure we've proven +some properties of it now we're in a + + align:start position:0% +some properties of it now we're in a + + + align:start position:0% +some properties of it now we're in a +position to at least define measurable + + align:start position:0% +position to at least define measurable + + + align:start position:0% +position to at least define measurable +sets + + align:start position:0% + + + + align:start position:0% + +and i should say these are labay + + align:start position:0% +and i should say these are labay + + + align:start position:0% +and i should say these are labay +measurable sets + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +a subset of real numbers is + + align:start position:0% + + + + align:start position:0% + +the bag + + align:start position:0% + + + + align:start position:0% + +measurable + + align:start position:0% + + + + align:start position:0% + +so this is the new + + align:start position:0% +so this is the new + + + align:start position:0% +so this is the new +piece of terminology + + align:start position:0% +piece of terminology + + + align:start position:0% +piece of terminology +if + + align:start position:0% + + + + align:start position:0% + +for all + + align:start position:0% +for all + + + align:start position:0% +for all +subsets of r if i look at + + align:start position:0% +subsets of r if i look at + + + align:start position:0% +subsets of r if i look at +the outer measure of a this is equal to + + align:start position:0% +the outer measure of a this is equal to + + + align:start position:0% +the outer measure of a this is equal to +the + + align:start position:0% +the + + + align:start position:0% +the +outer measure of a intersect e plus + + align:start position:0% +outer measure of a intersect e plus + + + align:start position:0% +outer measure of a intersect e plus +the outer measure of e + + align:start position:0% +the outer measure of e + + + align:start position:0% +the outer measure of e +a intersect + + align:start position:0% +a intersect + + + align:start position:0% +a intersect +e complement okay this is the the + + align:start position:0% +e complement okay this is the the + + + align:start position:0% +e complement okay this is the the +definition of being a big measurable set + + align:start position:0% +definition of being a big measurable set + + + align:start position:0% +definition of being a big measurable set +so in some sense it's a well e is a + + align:start position:0% +so in some sense it's a well e is a + + + align:start position:0% +so in some sense it's a well e is a +well-behaved set if it you know kind of + + align:start position:0% +well-behaved set if it you know kind of + + + align:start position:0% +well-behaved set if it you know kind of +cuts a into into reasonable sets uh + + align:start position:0% +cuts a into into reasonable sets uh + + + align:start position:0% +cuts a into into reasonable sets uh +what's the best way to say that well i i + + align:start position:0% +what's the best way to say that well i i + + + align:start position:0% +what's the best way to say that well i i +guess that's that's okay + + align:start position:0% +guess that's that's okay + + + align:start position:0% +guess that's that's okay +um + + align:start position:0% +um + + + align:start position:0% +um +okay so a set is measurable if and only + + align:start position:0% +okay so a set is measurable if and only + + + align:start position:0% +okay so a set is measurable if and only +if and only if for all a we have this + + align:start position:0% +if and only if for all a we have this + + + align:start position:0% +if and only if for all a we have this +equality here + + align:start position:0% +equality here + + + align:start position:0% +equality here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +let me make a few remarks + + align:start position:0% + + + + align:start position:0% + +um first off + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% +this + + + align:start position:0% +this +is all the left-hand side no matter what + + align:start position:0% +is all the left-hand side no matter what + + + align:start position:0% +is all the left-hand side no matter what +a and e are + + align:start position:0% +a and e are + + + align:start position:0% +a and e are +the left-hand side is always less than + + align:start position:0% +the left-hand side is always less than + + + align:start position:0% +the left-hand side is always less than +or equal to the right-hand side + + align:start position:0% +or equal to the right-hand side + + + align:start position:0% +or equal to the right-hand side +okay by + + align:start position:0% +okay by + + + align:start position:0% +okay by +you know the theorem we have up there + + align:start position:0% +you know the theorem we have up there + + + align:start position:0% +you know the theorem we have up there +that the outer measure of the union is + + align:start position:0% +that the outer measure of the union is + + + align:start position:0% +that the outer measure of the union is +less than or equal to the sum of the + + align:start position:0% +less than or equal to the sum of the + + + align:start position:0% +less than or equal to the sum of the +measures so + + align:start position:0% + + + + align:start position:0% + +since for all + + align:start position:0% +since for all + + + align:start position:0% +since for all +ae + + align:start position:0% + + + + align:start position:0% + +a is contained in + + align:start position:0% +a is contained in + + + align:start position:0% +a is contained in +or in fact + + align:start position:0% +or in fact + + + align:start position:0% +or in fact +you know equal to a intersect + + align:start position:0% +you know equal to a intersect + + + align:start position:0% +you know equal to a intersect +e union + + align:start position:0% +e union + + + align:start position:0% +e union +a intersect + + align:start position:0% + + + + align:start position:0% + +e complement + + align:start position:0% +e complement + + + align:start position:0% +e complement +okay okay + + align:start position:0% + + + + align:start position:0% + +we get that the + + align:start position:0% +we get that the + + + align:start position:0% +we get that the +outer measure of a + + align:start position:0% +outer measure of a + + + align:start position:0% +outer measure of a +is always less than or equal to + + align:start position:0% +is always less than or equal to + + + align:start position:0% +is always less than or equal to +the outer measure of a intersect e plus + + align:start position:0% +the outer measure of a intersect e plus + + + align:start position:0% +the outer measure of a intersect e plus +the outer measure of a intersect the + + align:start position:0% +the outer measure of a intersect the + + + align:start position:0% +the outer measure of a intersect the +complement of e this is regardless of a + + align:start position:0% +complement of e this is regardless of a + + + align:start position:0% +complement of e this is regardless of a +and e + + align:start position:0% +and e + + + align:start position:0% +and e +i mean if e is measurable or not this + + align:start position:0% +i mean if e is measurable or not this + + + align:start position:0% +i mean if e is measurable or not this +always holds okay + + align:start position:0% +always holds okay + + + align:start position:0% +always holds okay +so + + align:start position:0% +so + + + align:start position:0% +so +since this always holds + + align:start position:0% + + + + align:start position:0% + +we could state being measurable just by + + align:start position:0% +we could state being measurable just by + + + align:start position:0% +we could state being measurable just by +instead of equality satisfying one of + + align:start position:0% +instead of equality satisfying one of + + + align:start position:0% +instead of equality satisfying one of +the inequalities thus + + align:start position:0% +the inequalities thus + + + align:start position:0% +the inequalities thus +e is measurable + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% +if + + + align:start position:0% +if +for all subsets of r + + align:start position:0% +for all subsets of r + + + align:start position:0% +for all subsets of r +we have that + + align:start position:0% + + + + align:start position:0% + +is less than or equal to + + align:start position:0% +is less than or equal to + + + align:start position:0% +is less than or equal to +the outer measure of a + + align:start position:0% +the outer measure of a + + + align:start position:0% +the outer measure of a +all right because like i said + + align:start position:0% +all right because like i said + + + align:start position:0% +all right because like i said +we know no matter what a and e are this + + align:start position:0% +we know no matter what a and e are this + + + align:start position:0% +we know no matter what a and e are this +holds all right so + + align:start position:0% +holds all right so + + + align:start position:0% +holds all right so +if i want equality then i have to have + + align:start position:0% +if i want equality then i have to have + + + align:start position:0% +if i want equality then i have to have +this is less than or equal to that so e + + align:start position:0% +this is less than or equal to that so e + + + align:start position:0% +this is less than or equal to that so e +is measurable if and only if this + + align:start position:0% +is measurable if and only if this + + + align:start position:0% +is measurable if and only if this +is less than or equal to the outer + + align:start position:0% +is less than or equal to the outer + + + align:start position:0% +is less than or equal to the outer +measure of a + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +now we have the silliest + + align:start position:0% + + + + align:start position:0% + +uh well let's not + + align:start position:0% +uh well let's not + + + align:start position:0% +uh well let's not +state it as an example but let's + + align:start position:0% +state it as an example but let's + + + align:start position:0% +state it as an example but let's +we can state it as a theorem + + align:start position:0% + + + + align:start position:0% + +it will be a silly theorem one which i + + align:start position:0% +it will be a silly theorem one which i + + + align:start position:0% +it will be a silly theorem one which i +will not write the actual proof of but + + align:start position:0% +will not write the actual proof of but + + + align:start position:0% +will not write the actual proof of but +the empty set + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +again i've told you before that + + align:start position:0% +again i've told you before that + + + align:start position:0% +again i've told you before that +when i'm + + align:start position:0% +when i'm + + + align:start position:0% +when i'm +writing on the board writing in my notes + + align:start position:0% +writing on the board writing in my notes + + + align:start position:0% +writing on the board writing in my notes +i typically + + align:start position:0% +i typically + + + align:start position:0% +i typically +uh + + align:start position:0% +uh + + + align:start position:0% +uh +shorten words so + + align:start position:0% +shorten words so + + + align:start position:0% +shorten words so +measurable + + align:start position:0% +measurable + + + align:start position:0% +measurable +you will see written as mble + + align:start position:0% +you will see written as mble + + + align:start position:0% +you will see written as mble +throughout the notes and also when i + + align:start position:0% +throughout the notes and also when i + + + align:start position:0% +throughout the notes and also when i +write on the board + + align:start position:0% +write on the board + + + align:start position:0% +write on the board +okay + + align:start position:0% +okay + + + align:start position:0% +okay +i forget the word for what it means to + + align:start position:0% +i forget the word for what it means to + + + align:start position:0% +i forget the word for what it means to +shorten words but + + align:start position:0% +shorten words but + + + align:start position:0% +shorten words but +uh + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +the empty set is measurable + + align:start position:0% +the empty set is measurable + + + align:start position:0% +the empty set is measurable +all r + + align:start position:0% +all r + + + align:start position:0% +all r +is measurable + + align:start position:0% +is measurable + + + align:start position:0% +is measurable +and + + align:start position:0% +and + + + align:start position:0% +and +we have the + + align:start position:0% +we have the + + + align:start position:0% +we have the +fact that + + align:start position:0% +fact that + + + align:start position:0% +fact that +a subset of r + + align:start position:0% +a subset of r + + + align:start position:0% +a subset of r +is measurable if and only if + + align:start position:0% +is measurable if and only if + + + align:start position:0% +is measurable if and only if +its complement + + align:start position:0% +its complement + + + align:start position:0% +its complement +is + + align:start position:0% + + + + align:start position:0% + +measurable right because this um + + align:start position:0% +measurable right because this um + + + align:start position:0% +measurable right because this um +you know + + align:start position:0% +you know + + + align:start position:0% +you know +either one of these definitions remember + + align:start position:0% +either one of these definitions remember + + + align:start position:0% +either one of these definitions remember +these are + + align:start position:0% +these are + + + align:start position:0% +these are +by what we've proven about outer measure + + align:start position:0% +by what we've proven about outer measure + + + align:start position:0% +by what we've proven about outer measure +this + + align:start position:0% +this + + + align:start position:0% +this +equality is equivalent to requiring this + + align:start position:0% +equality is equivalent to requiring this + + + align:start position:0% +equality is equivalent to requiring this +inequality + + align:start position:0% + + + + align:start position:0% + +these are symmetric in e and e + + align:start position:0% +these are symmetric in e and e + + + align:start position:0% +these are symmetric in e and e +complement right + + align:start position:0% +complement right + + + align:start position:0% +complement right +so e is measurable if and only if its + + align:start position:0% +so e is measurable if and only if its + + + align:start position:0% +so e is measurable if and only if its +complement is measurable + + align:start position:0% +complement is measurable + + + align:start position:0% +complement is measurable +all right + + align:start position:0% + + + + align:start position:0% + +all right so those are kind of these are + + align:start position:0% +all right so those are kind of these are + + + align:start position:0% +all right so those are kind of these are +kind of the the stupidest + + align:start position:0% +kind of the the stupidest + + + align:start position:0% +kind of the the stupidest +uh measurable sets + + align:start position:0% +uh measurable sets + + + align:start position:0% +uh measurable sets +you could have + + align:start position:0% +you could have + + + align:start position:0% +you could have +um again + + align:start position:0% +um again + + + align:start position:0% +um again +the empty set y because this is then + + align:start position:0% +the empty set y because this is then + + + align:start position:0% +the empty set y because this is then +empty and the outer measure of the empty + + align:start position:0% +empty and the outer measure of the empty + + + align:start position:0% +empty and the outer measure of the empty +set is zero uh and then over here i + + align:start position:0% +set is zero uh and then over here i + + + align:start position:0% +set is zero uh and then over here i +would just get the measure of a + + align:start position:0% +would just get the measure of a + + + align:start position:0% +would just get the measure of a +intersect the empty set complement which + + align:start position:0% +intersect the empty set complement which + + + align:start position:0% +intersect the empty set complement which +is just r so i get uh + + align:start position:0% +is just r so i get uh + + + align:start position:0% +is just r so i get uh +the outer measure of a is equal to the + + align:start position:0% +the outer measure of a is equal to the + + + align:start position:0% +the outer measure of a is equal to the +outer measure of a and since the empty + + align:start position:0% +outer measure of a and since the empty + + + align:start position:0% +outer measure of a and since the empty +set is measurable its complement r is + + align:start position:0% +set is measurable its complement r is + + + align:start position:0% +set is measurable its complement r is +also measurable + + align:start position:0% + + + + align:start position:0% + +so let's do some non-stupid uh + + align:start position:0% + + + + align:start position:0% + +examples of + + align:start position:0% +examples of + + + align:start position:0% +examples of +measurable sets + + align:start position:0% + + + + align:start position:0% + +still kind of trivial because they don't + + align:start position:0% +still kind of trivial because they don't + + + align:start position:0% +still kind of trivial because they don't +make up very much but + + align:start position:0% + + + + align:start position:0% + +if a set has outer measure zero + + align:start position:0% + + + + align:start position:0% + +then it's measurable + + align:start position:0% +then it's measurable + + + align:start position:0% +then it's measurable +okay + + align:start position:0% + + + + align:start position:0% + +all right so how do we prove this again + + align:start position:0% +all right so how do we prove this again + + + align:start position:0% +all right so how do we prove this again +we just need to prove this inequality + + align:start position:0% +we just need to prove this inequality + + + align:start position:0% +we just need to prove this inequality +here + + align:start position:0% +here + + + align:start position:0% +here +for every subset of r so let a + + align:start position:0% +for every subset of r so let a + + + align:start position:0% +for every subset of r so let a +be a subset of r + + align:start position:0% +be a subset of r + + + align:start position:0% +be a subset of r +then + + align:start position:0% +then + + + align:start position:0% +then +a intersect e this is contained in e + + align:start position:0% +a intersect e this is contained in e + + + align:start position:0% +a intersect e this is contained in e +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +since we know outer measure is + + align:start position:0% +since we know outer measure is + + + align:start position:0% +since we know outer measure is +so the fancy word for for when a is a + + align:start position:0% +so the fancy word for for when a is a + + + align:start position:0% +so the fancy word for for when a is a +subset of b the outer measure of a is + + align:start position:0% +subset of b the outer measure of a is + + + align:start position:0% +subset of b the outer measure of a is +less than or equal to outer measure b + + align:start position:0% +less than or equal to outer measure b + + + align:start position:0% +less than or equal to outer measure b +this is a + + align:start position:0% +this is a + + + align:start position:0% +this is a +the fancy word for that is monotonicity + + align:start position:0% +the fancy word for that is monotonicity + + + align:start position:0% +the fancy word for that is monotonicity +but since the outer measure is monotonic + + align:start position:0% +but since the outer measure is monotonic + + + align:start position:0% +but since the outer measure is monotonic +that tells me that the outer + + align:start position:0% +that tells me that the outer + + + align:start position:0% +that tells me that the outer +measure of e is less than or equal to + + align:start position:0% +measure of e is less than or equal to + + + align:start position:0% +measure of e is less than or equal to +the + + align:start position:0% +the + + + align:start position:0% +the +a intersect e is less than or equal to + + align:start position:0% +a intersect e is less than or equal to + + + align:start position:0% +a intersect e is less than or equal to +the outer measure of e and since that + + align:start position:0% +the outer measure of e and since that + + + align:start position:0% +the outer measure of e and since that +is zero + + align:start position:0% +is zero + + + align:start position:0% +is zero +that implies that + + align:start position:0% + + + + align:start position:0% + +the outer measure of a intersect e is + + align:start position:0% +the outer measure of a intersect e is + + + align:start position:0% +the outer measure of a intersect e is +zero because the outer measure is always + + align:start position:0% +zero because the outer measure is always + + + align:start position:0% +zero because the outer measure is always +a non-negative number + + align:start position:0% +a non-negative number + + + align:start position:0% +a non-negative number +okay + + align:start position:0% + + + + align:start position:0% + +thus + + align:start position:0% + + + + align:start position:0% + +the outer measure of a + + align:start position:0% +the outer measure of a + + + align:start position:0% +the outer measure of a +intersect e + + align:start position:0% +intersect e + + + align:start position:0% +intersect e +plus the outer measure + + align:start position:0% +plus the outer measure + + + align:start position:0% +plus the outer measure +of a intersect + + align:start position:0% +of a intersect + + + align:start position:0% +of a intersect +e complement this is zero + + align:start position:0% +e complement this is zero + + + align:start position:0% +e complement this is zero +so this is equal to the outer measure of + + align:start position:0% +so this is equal to the outer measure of + + + align:start position:0% +so this is equal to the outer measure of +a intersect e complement + + align:start position:0% +a intersect e complement + + + align:start position:0% +a intersect e complement +a intersect e complement is contained in + + align:start position:0% +a intersect e complement is contained in + + + align:start position:0% +a intersect e complement is contained in +a + + align:start position:0% +a + + + align:start position:0% +a +right so the outer measure of a + + align:start position:0% +right so the outer measure of a + + + align:start position:0% +right so the outer measure of a +intersect e complement is going to be + + align:start position:0% +intersect e complement is going to be + + + align:start position:0% +intersect e complement is going to be +less than or equal to + + align:start position:0% +less than or equal to + + + align:start position:0% +less than or equal to +the outer measure of a again because + + align:start position:0% +the outer measure of a again because + + + align:start position:0% +the outer measure of a again because +this set is contained within a + + align:start position:0% +this set is contained within a + + + align:start position:0% +this set is contained within a +and thus + + align:start position:0% + + + + align:start position:0% + +e is measurable + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +you know right now + + align:start position:0% +you know right now + + + align:start position:0% +you know right now +after two theorems + + align:start position:0% +after two theorems + + + align:start position:0% +after two theorems +we've shown that + + align:start position:0% +we've shown that + + + align:start position:0% +we've shown that +the uninteresting sets are measurable if + + align:start position:0% +the uninteresting sets are measurable if + + + align:start position:0% +the uninteresting sets are measurable if +by uninteresting we mean having + + align:start position:0% +by uninteresting we mean having + + + align:start position:0% +by uninteresting we mean having +you know kind of very little measure + + align:start position:0% +you know kind of very little measure + + + align:start position:0% +you know kind of very little measure +even though i haven't defined measure + + align:start position:0% +even though i haven't defined measure + + + align:start position:0% +even though i haven't defined measure +yet i've just defined outer measure i'm + + align:start position:0% +yet i've just defined outer measure i'm + + + align:start position:0% +yet i've just defined outer measure i'm +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +um + + align:start position:0% +um + + + align:start position:0% +um +using these + + align:start position:0% + + + + align:start position:0% + +terms interchangeably + + align:start position:0% +terms interchangeably + + + align:start position:0% +terms interchangeably +unfortunately but you'll see why in a + + align:start position:0% +unfortunately but you'll see why in a + + + align:start position:0% +unfortunately but you'll see why in a +either by the end of this class or the + + align:start position:0% +either by the end of this class or the + + + align:start position:0% +either by the end of this class or the +end of next class + + align:start position:0% + + + + align:start position:0% + +um but + + align:start position:0% + + + + align:start position:0% + +so so far we don't have very many + + align:start position:0% +so so far we don't have very many + + + align:start position:0% +so so far we don't have very many +interesting examples of measurable sets + + align:start position:0% +interesting examples of measurable sets + + + align:start position:0% +interesting examples of measurable sets +um + + align:start position:0% +um + + + align:start position:0% +um +what we will show is that there's a lot + + align:start position:0% +what we will show is that there's a lot + + + align:start position:0% +what we will show is that there's a lot +of interesting measurable sets + + align:start position:0% +of interesting measurable sets + + + align:start position:0% +of interesting measurable sets +in fact every + + align:start position:0% +in fact every + + + align:start position:0% +in fact every +open set is measurable + + align:start position:0% +open set is measurable + + + align:start position:0% +open set is measurable +and + + align:start position:0% +and + + + align:start position:0% +and +since + + align:start position:0% +since + + + align:start position:0% +since +if an open set is measurable its + + align:start position:0% +if an open set is measurable its + + + align:start position:0% +if an open set is measurable its +complement is measurable and the + + align:start position:0% +complement is measurable and the + + + align:start position:0% +complement is measurable and the +complements are clos of open sets or + + align:start position:0% +complements are clos of open sets or + + + align:start position:0% +complements are clos of open sets or +closed sets then we have that every + + align:start position:0% +closed sets then we have that every + + + align:start position:0% +closed sets then we have that every +close that is uh measurable as well + + align:start position:0% +close that is uh measurable as well + + + align:start position:0% +close that is uh measurable as well +um + + align:start position:0% +um + + + align:start position:0% +um +but in fact it's much + + align:start position:0% +but in fact it's much + + + align:start position:0% +but in fact it's much +richer than that as we'll see + + align:start position:0% + + + + align:start position:0% + +you can take a countable collection of + + align:start position:0% +you can take a countable collection of + + + align:start position:0% +you can take a countable collection of +open sets and take their intersection + + align:start position:0% +open sets and take their intersection + + + align:start position:0% +open sets and take their intersection +that's not necessarily an open set okay + + align:start position:0% +that's not necessarily an open set okay + + + align:start position:0% +that's not necessarily an open set okay +so it's not clear if it's measurable by + + align:start position:0% +so it's not clear if it's measurable by + + + align:start position:0% +so it's not clear if it's measurable by +what i just said + + align:start position:0% +what i just said + + + align:start position:0% +what i just said +but it turns out + + align:start position:0% +but it turns out + + + align:start position:0% +but it turns out +uh + + align:start position:0% +uh + + + align:start position:0% +uh +that uh this intersection of open sets + + align:start position:0% +that uh this intersection of open sets + + + align:start position:0% +that uh this intersection of open sets +will be measurable + + align:start position:0% +will be measurable + + + align:start position:0% +will be measurable +and again by taking complements you get + + align:start position:0% +and again by taking complements you get + + + align:start position:0% +and again by taking complements you get +unions of closed sets which are not + + align:start position:0% +unions of closed sets which are not + + + align:start position:0% +unions of closed sets which are not +necessarily closed or are also + + align:start position:0% +necessarily closed or are also + + + align:start position:0% +necessarily closed or are also +measurable + + align:start position:0% +measurable + + + align:start position:0% +measurable +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% +so + + + align:start position:0% +so +um + + align:start position:0% +um + + + align:start position:0% +um +when i learned measure theory my + + align:start position:0% +when i learned measure theory my + + + align:start position:0% +when i learned measure theory my +instructor told me that + + align:start position:0% + + + + align:start position:0% + +if you can write down the set chances + + align:start position:0% +if you can write down the set chances + + + align:start position:0% +if you can write down the set chances +are it's measurable okay + + align:start position:0% +are it's measurable okay + + + align:start position:0% +are it's measurable okay +you know if + + align:start position:0% +you know if + + + align:start position:0% +you know if +you can sit down and write down you know + + align:start position:0% +you can sit down and write down you know + + + align:start position:0% +you can sit down and write down you know +a union of intersections of complements + + align:start position:0% +a union of intersections of complements + + + align:start position:0% +a union of intersections of complements +of so on and so on of you know some + + align:start position:0% +of so on and so on of you know some + + + align:start position:0% +of so on and so on of you know some +basic sets then that's measurable and + + align:start position:0% +basic sets then that's measurable and + + + align:start position:0% +basic sets then that's measurable and +we'll kind of see why that's true + + align:start position:0% +we'll kind of see why that's true + + + align:start position:0% +we'll kind of see why that's true +shortly + + align:start position:0% +shortly + + + align:start position:0% +shortly +now let's prove uh + + align:start position:0% +now let's prove uh + + + align:start position:0% +now let's prove uh +um now before we get to showing you know + + align:start position:0% +um now before we get to showing you know + + + align:start position:0% +um now before we get to showing you know +everything i just told you we need some + + align:start position:0% +everything i just told you we need some + + + align:start position:0% +everything i just told you we need some +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +general facts about measurable sets you + + align:start position:0% +general facts about measurable sets you + + + align:start position:0% +general facts about measurable sets you +know about the structure of + + align:start position:0% +know about the structure of + + + align:start position:0% +know about the structure of +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the collection of measurable sets + + align:start position:0% + + + + align:start position:0% + +right now we just know that + + align:start position:0% +right now we just know that + + + align:start position:0% +right now we just know that +the collection of measurable sets + + align:start position:0% +the collection of measurable sets + + + align:start position:0% +the collection of measurable sets +uh includes the empty set r + + align:start position:0% +uh includes the empty set r + + + align:start position:0% +uh includes the empty set r +and + + align:start position:0% +and + + + align:start position:0% +and +the set of + + align:start position:0% +the set of + + + align:start position:0% +the set of +and and the sets that have outer measure + + align:start position:0% +and and the sets that have outer measure + + + align:start position:0% +and and the sets that have outer measure +equal to zero + + align:start position:0% +equal to zero + + + align:start position:0% +equal to zero +which i didn't + + align:start position:0% +which i didn't + + + align:start position:0% +which i didn't +i see + + align:start position:0% +i see + + + align:start position:0% +i see +i didn't write okay + + align:start position:0% + + + + align:start position:0% + +this is also the danger of + + align:start position:0% +this is also the danger of + + + align:start position:0% +this is also the danger of +lecturing in an empty classroom is that + + align:start position:0% +lecturing in an empty classroom is that + + + align:start position:0% +lecturing in an empty classroom is that +if i make a mistake on the board there's + + align:start position:0% +if i make a mistake on the board there's + + + align:start position:0% +if i make a mistake on the board there's +no one to correct me + + align:start position:0% +no one to correct me + + + align:start position:0% +no one to correct me +so next + + align:start position:0% + + + + align:start position:0% + +proves the following theorem about + + align:start position:0% +proves the following theorem about + + + align:start position:0% +proves the following theorem about +measurable sets that if i have two + + align:start position:0% +measurable sets that if i have two + + + align:start position:0% +measurable sets that if i have two +measurable sets their union is + + align:start position:0% +measurable sets their union is + + + align:start position:0% +measurable sets their union is +measurable + + align:start position:0% +measurable + + + align:start position:0% +measurable +if e1 + + align:start position:0% +if e1 + + + align:start position:0% +if e1 +e2 + + align:start position:0% + + + + align:start position:0% + +are measurable + + align:start position:0% +are measurable + + + align:start position:0% +are measurable +then their union + + align:start position:0% +then their union + + + align:start position:0% +then their union +u1 union need to + + align:start position:0% +u1 union need to + + + align:start position:0% +u1 union need to +is measurable + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +again we have to verify that inequality + + align:start position:0% +again we have to verify that inequality + + + align:start position:0% +again we have to verify that inequality +to show that it's measurable so let a be + + align:start position:0% +to show that it's measurable so let a be + + + align:start position:0% +to show that it's measurable so let a be +a subset of r + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +since e2 + + align:start position:0% + + + + align:start position:0% + +is measurable + + align:start position:0% + + + + align:start position:0% + +we get that + + align:start position:0% +we get that + + + align:start position:0% +we get that +the measure of a + + align:start position:0% +the measure of a + + + align:start position:0% +the measure of a +intersect + + align:start position:0% +intersect + + + align:start position:0% +intersect +the complement of e1 + + align:start position:0% +the complement of e1 + + + align:start position:0% +the complement of e1 +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +the outer measure of a + + align:start position:0% +the outer measure of a + + + align:start position:0% +the outer measure of a +intersect b1 complement + + align:start position:0% +intersect b1 complement + + + align:start position:0% +intersect b1 complement +intersect + + align:start position:0% +intersect + + + align:start position:0% +intersect +e2 + + align:start position:0% +e2 + + + align:start position:0% +e2 +plus + + align:start position:0% +plus + + + align:start position:0% +plus +the outer measure of e + + align:start position:0% +the outer measure of e + + + align:start position:0% +the outer measure of e +of a intersect + + align:start position:0% +of a intersect + + + align:start position:0% +of a intersect +e1 + + align:start position:0% +e1 + + + align:start position:0% +e1 +complement intersect + + align:start position:0% +complement intersect + + + align:start position:0% +complement intersect +e2 complement okay + + align:start position:0% +e2 complement okay + + + align:start position:0% +e2 complement okay +you know you may be asking where the + + align:start position:0% +you know you may be asking where the + + + align:start position:0% +you know you may be asking where the +hell did this come from why do i care + + align:start position:0% +hell did this come from why do i care + + + align:start position:0% +hell did this come from why do i care +well it's because i'm getting something + + align:start position:0% +well it's because i'm getting something + + + align:start position:0% +well it's because i'm getting something +remember this looks like + + align:start position:0% +remember this looks like + + + align:start position:0% +remember this looks like +this is equal to + + align:start position:0% +this is equal to + + + align:start position:0% +this is equal to +by de morgan's law + + align:start position:0% + + + + align:start position:0% + +the complement of the union of e1 and e2 + + align:start position:0% +the complement of the union of e1 and e2 + + + align:start position:0% +the complement of the union of e1 and e2 +right so i want to somehow have some + + align:start position:0% +right so i want to somehow have some + + + align:start position:0% +right so i want to somehow have some +relation involving + + align:start position:0% +relation involving + + + align:start position:0% +relation involving +uh the complement of e1 union e2 + + align:start position:0% +uh the complement of e1 union e2 + + + align:start position:0% +uh the complement of e1 union e2 +intersect a because + + align:start position:0% +intersect a because + + + align:start position:0% +intersect a because +again i'm trying to show that the + + align:start position:0% +again i'm trying to show that the + + + align:start position:0% +again i'm trying to show that the +measure of a intersect e1 union e2 plus + + align:start position:0% +measure of a intersect e1 union e2 plus + + + align:start position:0% +measure of a intersect e1 union e2 plus +the outer measure of a intersect + + align:start position:0% +the outer measure of a intersect + + + align:start position:0% +the outer measure of a intersect +the complement of e1 union e2 which is + + align:start position:0% +the complement of e1 union e2 which is + + + align:start position:0% +the complement of e1 union e2 which is +exactly this term equals the measure of + + align:start position:0% +exactly this term equals the measure of + + + align:start position:0% +exactly this term equals the measure of +a + + align:start position:0% +a + + + align:start position:0% +a +right so + + align:start position:0% +right so + + + align:start position:0% +right so +you know + + align:start position:0% +you know + + + align:start position:0% +you know +it looks like this relation was just + + align:start position:0% +it looks like this relation was just + + + align:start position:0% +it looks like this relation was just +grabbed out of left field but that's the + + align:start position:0% +grabbed out of left field but that's the + + + align:start position:0% +grabbed out of left field but that's the +thinking behind why you would care + + align:start position:0% +thinking behind why you would care + + + align:start position:0% +thinking behind why you would care +okay + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +now a + + align:start position:0% +now a + + + align:start position:0% +now a +if i take a and intersect it with e1 + + align:start position:0% +if i take a and intersect it with e1 + + + align:start position:0% +if i take a and intersect it with e1 +union e2 + + align:start position:0% +union e2 + + + align:start position:0% +union e2 +this is equal to + + align:start position:0% +this is equal to + + + align:start position:0% +this is equal to +uh + + align:start position:0% +uh + + + align:start position:0% +uh +a + + align:start position:0% +a + + + align:start position:0% +a +intersect + + align:start position:0% +intersect + + + align:start position:0% +intersect +e1 + + align:start position:0% + + + + align:start position:0% + +union a + + align:start position:0% +union a + + + align:start position:0% +union a +intersect e2 + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +everything from here that also has + + align:start position:0% +everything from here that also has + + + align:start position:0% +everything from here that also has +something in common with e1 is contained + + align:start position:0% +something in common with e1 is contained + + + align:start position:0% +something in common with e1 is contained +in this set so this union is at actually + + align:start position:0% +in this set so this union is at actually + + + align:start position:0% +in this set so this union is at actually +equal to a intersect e1 + + align:start position:0% +equal to a intersect e1 + + + align:start position:0% +equal to a intersect e1 +union a intersect + + align:start position:0% +union a intersect + + + align:start position:0% +union a intersect +e2 intersect + + align:start position:0% + + + + align:start position:0% + +e1 complement + + align:start position:0% +e1 complement + + + align:start position:0% +e1 complement +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% +now + + + align:start position:0% +now +this appeared here so you can kind of + + align:start position:0% +this appeared here so you can kind of + + + align:start position:0% +this appeared here so you can kind of +see maybe some magic is going to start + + align:start position:0% +see maybe some magic is going to start + + + align:start position:0% +see maybe some magic is going to start +to to happen in a minute when we start + + align:start position:0% +to to happen in a minute when we start + + + align:start position:0% +to to happen in a minute when we start +taking the measure so + + align:start position:0% + + + + align:start position:0% + +what do we get + + align:start position:0% +what do we get + + + align:start position:0% +what do we get +we get that the measure of + + align:start position:0% + + + + align:start position:0% + +a intersect e1 + + align:start position:0% +a intersect e1 + + + align:start position:0% +a intersect e1 +union + + align:start position:0% +union + + + align:start position:0% +union +e2 + + align:start position:0% +e2 + + + align:start position:0% +e2 +which is + + align:start position:0% +which is + + + align:start position:0% +which is +uh this side this is less than or equal + + align:start position:0% +uh this side this is less than or equal + + + align:start position:0% +uh this side this is less than or equal +to + + align:start position:0% + + + + align:start position:0% + +the measure of the outer measure of + + align:start position:0% +the measure of the outer measure of + + + align:start position:0% +the measure of the outer measure of +a so this is a + + align:start position:0% +a so this is a + + + align:start position:0% +a so this is a +equal to this union so the outer measure + + align:start position:0% +equal to this union so the outer measure + + + align:start position:0% +equal to this union so the outer measure +of this is less than or equal to the sum + + align:start position:0% +of this is less than or equal to the sum + + + align:start position:0% +of this is less than or equal to the sum +of the outer measure of this + + align:start position:0% +of the outer measure of this + + + align:start position:0% +of the outer measure of this +and the outer measure of this + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now + + align:start position:0% + + + + align:start position:0% + +we use the fact that e1 is measurable + + align:start position:0% +we use the fact that e1 is measurable + + + align:start position:0% +we use the fact that e1 is measurable +right so since e1 is measurable + + align:start position:0% +right so since e1 is measurable + + + align:start position:0% +right so since e1 is measurable +the outer measure of a intersect e1 is + + align:start position:0% +the outer measure of a intersect e1 is + + + align:start position:0% +the outer measure of a intersect e1 is +equal to the outer measure of a minus + + align:start position:0% +equal to the outer measure of a minus + + + align:start position:0% +equal to the outer measure of a minus +the outer + + align:start position:0% +the outer + + + align:start position:0% +the outer +measure of a intersect e1 complement + + align:start position:0% + + + + align:start position:0% + +uh or i should say that backwards + + align:start position:0% + + + + align:start position:0% + +right and then plus still this outer + + align:start position:0% +right and then plus still this outer + + + align:start position:0% +right and then plus still this outer +measure here + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% +but + + + align:start position:0% +but +now we're now we're in good shape + + align:start position:0% +now we're now we're in good shape + + + align:start position:0% +now we're now we're in good shape +because what do we have + + align:start position:0% +because what do we have + + + align:start position:0% +because what do we have +uh we have this term here appearing here + + align:start position:0% +uh we have this term here appearing here + + + align:start position:0% +uh we have this term here appearing here +right + + align:start position:0% +right + + + align:start position:0% +right +and + + align:start position:0% +and + + + align:start position:0% +and +uh + + align:start position:0% +uh + + + align:start position:0% +uh +so + + align:start position:0% +so + + + align:start position:0% +so +i also have this term here is appearing + + align:start position:0% +i also have this term here is appearing + + + align:start position:0% +i also have this term here is appearing +here + + align:start position:0% +here + + + align:start position:0% +here +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so subtracting this over here + + align:start position:0% +so subtracting this over here + + + align:start position:0% +so subtracting this over here +and subtracting that over there + + align:start position:0% +and subtracting that over there + + + align:start position:0% +and subtracting that over there +i get that + + align:start position:0% +i get that + + + align:start position:0% +i get that +the right hand side is equal to + + align:start position:0% +the right hand side is equal to + + + align:start position:0% +the right hand side is equal to +the outer measure of a + + align:start position:0% +the outer measure of a + + + align:start position:0% +the outer measure of a +minus the outer measure of a + + align:start position:0% +minus the outer measure of a + + + align:start position:0% +minus the outer measure of a +intersect + + align:start position:0% +intersect + + + align:start position:0% +intersect +and i'll just + + align:start position:0% + + + + align:start position:0% + +you know rewrite this + + align:start position:0% +you know rewrite this + + + align:start position:0% +you know rewrite this +intersection of complements as + + align:start position:0% +intersection of complements as + + + align:start position:0% +intersection of complements as +you know the complement of the union by + + align:start position:0% +you know the complement of the union by + + + align:start position:0% +you know the complement of the union by +de morgan's law + + align:start position:0% +de morgan's law + + + align:start position:0% +de morgan's law +and remember i started off with + + align:start position:0% +and remember i started off with + + + align:start position:0% +and remember i started off with +the outer measure of a intersect e1 + + align:start position:0% +the outer measure of a intersect e1 + + + align:start position:0% +the outer measure of a intersect e1 +union e2 and i showed it's it's less + + align:start position:0% +union e2 and i showed it's it's less + + + align:start position:0% +union e2 and i showed it's it's less +than or equal to the outer measure of a + + align:start position:0% +than or equal to the outer measure of a + + + align:start position:0% +than or equal to the outer measure of a +minus + + align:start position:0% +minus + + + align:start position:0% +minus +the outer measure of a intersect the + + align:start position:0% +the outer measure of a intersect the + + + align:start position:0% +the outer measure of a intersect the +complement and therefore + + align:start position:0% +complement and therefore + + + align:start position:0% +complement and therefore +the outer measure of a intersect + + align:start position:0% +the outer measure of a intersect + + + align:start position:0% +the outer measure of a intersect +e1 + + align:start position:0% +e1 + + + align:start position:0% +e1 +e2 + + align:start position:0% +e2 + + + align:start position:0% +e2 +plus the outer measure of + + align:start position:0% +plus the outer measure of + + + align:start position:0% +plus the outer measure of +a intersect + + align:start position:0% +a intersect + + + align:start position:0% +a intersect +e1 union + + align:start position:0% +e1 union + + + align:start position:0% +e1 union +e2 complement + + align:start position:0% +e2 complement + + + align:start position:0% +e2 complement +is less than or equal to + + align:start position:0% +is less than or equal to + + + align:start position:0% +is less than or equal to +the outer measure of a + + align:start position:0% +the outer measure of a + + + align:start position:0% +the outer measure of a +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +that's what we wanted to prove and + + align:start position:0% +that's what we wanted to prove and + + + align:start position:0% +that's what we wanted to prove and +therefore a our e1 union e2 + + align:start position:0% +therefore a our e1 union e2 + + + align:start position:0% +therefore a our e1 union e2 +is measurable + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +now + + align:start position:0% +now + + + align:start position:0% +now +uh + + align:start position:0% + + + + align:start position:0% + +if you can + + align:start position:0% +if you can + + + align:start position:0% +if you can +do something for two things you can do + + align:start position:0% +do something for two things you can do + + + align:start position:0% +do something for two things you can do +something for n things typically by an + + align:start position:0% +something for n things typically by an + + + align:start position:0% +something for n things typically by an +induction argument so + + align:start position:0% +induction argument so + + + align:start position:0% +induction argument so +the previous theorem implies the + + align:start position:0% +the previous theorem implies the + + + align:start position:0% +the previous theorem implies the +following + + align:start position:0% +following + + + align:start position:0% +following +that if e1 + + align:start position:0% +that if e1 + + + align:start position:0% +that if e1 +up to en + + align:start position:0% + + + + align:start position:0% + +are measurable + + align:start position:0% + + + + align:start position:0% + +then this finite union + + align:start position:0% +then this finite union + + + align:start position:0% +then this finite union +k equals 1 to n + + align:start position:0% +k equals 1 to n + + + align:start position:0% +k equals 1 to n +ek + + align:start position:0% + + + + align:start position:0% + +is measurable and how do you prove this + + align:start position:0% +is measurable and how do you prove this + + + align:start position:0% +is measurable and how do you prove this +you prove it by induction so proof + + align:start position:0% + + + + align:start position:0% + +by induction + + align:start position:0% + + + + align:start position:0% + +when n equals one + + align:start position:0% + + + + align:start position:0% + +the base case this is clear + + align:start position:0% + + + + align:start position:0% + +suppose + + align:start position:0% + + + + align:start position:0% + +so called this claim star + + align:start position:0% +so called this claim star + + + align:start position:0% +so called this claim star +suppose this claim star holds + + align:start position:0% + + + + align:start position:0% + +for n equals m + + align:start position:0% +for n equals m + + + align:start position:0% +for n equals m +now we want to show it holds that this + + align:start position:0% +now we want to show it holds that this + + + align:start position:0% +now we want to show it holds that this +implies that + + align:start position:0% +implies that + + + align:start position:0% +implies that +the claim of the theorem holds with n + + align:start position:0% +the claim of the theorem holds with n + + + align:start position:0% +the claim of the theorem holds with n +equals n plus one + + align:start position:0% + + + + align:start position:0% + +n equals n plus one so + + align:start position:0% +n equals n plus one so + + + align:start position:0% +n equals n plus one so +let e1 + + align:start position:0% + + + + align:start position:0% + +em plus one + + align:start position:0% + + + + align:start position:0% + +be measurable + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% +then + + + align:start position:0% +then +the union + + align:start position:0% +the union + + + align:start position:0% +the union +k equals 1 to n plus 1 + + align:start position:0% +k equals 1 to n plus 1 + + + align:start position:0% +k equals 1 to n plus 1 +of e k + + align:start position:0% +of e k + + + align:start position:0% +of e k +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +union k equals 1 to m + + align:start position:0% +union k equals 1 to m + + + align:start position:0% +union k equals 1 to m +of e k + + align:start position:0% +of e k + + + align:start position:0% +of e k +union + + align:start position:0% +union + + + align:start position:0% +union +equals + + align:start position:0% +equals + + + align:start position:0% +equals +or e sub n plus one + + align:start position:0% +or e sub n plus one + + + align:start position:0% +or e sub n plus one +now + + align:start position:0% +now + + + align:start position:0% +now +by the induction hypothesis + + align:start position:0% +by the induction hypothesis + + + align:start position:0% +by the induction hypothesis +a + + align:start position:0% +a + + + align:start position:0% +a +collection of m measurable sets uh their + + align:start position:0% +collection of m measurable sets uh their + + + align:start position:0% +collection of m measurable sets uh their +union is measurable so this is + + align:start position:0% +union is measurable so this is + + + align:start position:0% +union is measurable so this is +measurable + + align:start position:0% + + + + align:start position:0% + +by the induction hypothesis + + align:start position:0% +by the induction hypothesis + + + align:start position:0% +by the induction hypothesis +and we're assuming this is measurable + + align:start position:0% +and we're assuming this is measurable + + + align:start position:0% +and we're assuming this is measurable +and then by the previous theorem the + + align:start position:0% +and then by the previous theorem the + + + align:start position:0% +and then by the previous theorem the +union of two measurable sets is + + align:start position:0% +union of two measurable sets is + + + align:start position:0% +union of two measurable sets is +measurable so + + align:start position:0% + + + + align:start position:0% + +and that proves + + align:start position:0% +and that proves + + + align:start position:0% +and that proves +the theorem + + align:start position:0% +the theorem + + + align:start position:0% +the theorem +okay + + align:start position:0% + + + + align:start position:0% + +all right so up to this point we've + + align:start position:0% +all right so up to this point we've + + + align:start position:0% +all right so up to this point we've +shown + + align:start position:0% +shown + + + align:start position:0% +shown +um + + align:start position:0% + + + + align:start position:0% + +two basic things + + align:start position:0% +two basic things + + + align:start position:0% +two basic things +about measurable sets + + align:start position:0% +about measurable sets + + + align:start position:0% +about measurable sets +really three okay first off + + align:start position:0% +really three okay first off + + + align:start position:0% +really three okay first off +it's non-empty + + align:start position:0% +it's non-empty + + + align:start position:0% +it's non-empty +you know it's a non-empty collection of + + align:start position:0% +you know it's a non-empty collection of + + + align:start position:0% +you know it's a non-empty collection of +measurable sets + + align:start position:0% +measurable sets + + + align:start position:0% +measurable sets +we've shown + + align:start position:0% +we've shown + + + align:start position:0% +we've shown +that + + align:start position:0% +that + + + align:start position:0% +that +a set is measurable if and only if its + + align:start position:0% +a set is measurable if and only if its + + + align:start position:0% +a set is measurable if and only if its +complement is measurable + + align:start position:0% +complement is measurable + + + align:start position:0% +complement is measurable +and we've also shown that + + align:start position:0% +and we've also shown that + + + align:start position:0% +and we've also shown that +uh + + align:start position:0% +uh + + + align:start position:0% +uh +finite unions of measurable sets + + align:start position:0% +finite unions of measurable sets + + + align:start position:0% +finite unions of measurable sets +are again measurable + + align:start position:0% +are again measurable + + + align:start position:0% +are again measurable +and + + align:start position:0% +and + + + align:start position:0% +and +therefore if i + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +define + + align:start position:0% +define + + + align:start position:0% +define +the set of measurable or if i look at + + align:start position:0% +the set of measurable or if i look at + + + align:start position:0% +the set of measurable or if i look at +the collection of all measurable sets + + align:start position:0% +the collection of all measurable sets + + + align:start position:0% +the collection of all measurable sets +this has a very special structure okay + + align:start position:0% +this has a very special structure okay + + + align:start position:0% +this has a very special structure okay +or a very uh + + align:start position:0% +or a very uh + + + align:start position:0% +or a very uh +general type of structure which i'm now + + align:start position:0% +general type of structure which i'm now + + + align:start position:0% +general type of structure which i'm now +going to + + align:start position:0% +going to + + + align:start position:0% +going to +elaborate on + + align:start position:0% +elaborate on + + + align:start position:0% +elaborate on +so + + align:start position:0% + + + + align:start position:0% + +let's take a pause here + + align:start position:0% +let's take a pause here + + + align:start position:0% +let's take a pause here +about measurable sets because now we're + + align:start position:0% +about measurable sets because now we're + + + align:start position:0% +about measurable sets because now we're +going to say + + align:start position:0% +going to say + + + align:start position:0% +going to say +a few general things about certain + + align:start position:0% +a few general things about certain + + + align:start position:0% +a few general things about certain +classes of sets + + align:start position:0% + + + + align:start position:0% + +or certain classes of collections of + + align:start position:0% +or certain classes of collections of + + + align:start position:0% +or certain classes of collections of +sets so + + align:start position:0% + + + + align:start position:0% + +let me make a definition here + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% + + + + align:start position:0% + +non-empty + + align:start position:0% + + + + align:start position:0% + +collection of + + align:start position:0% +collection of + + + align:start position:0% +collection of +uh + + align:start position:0% +uh + + + align:start position:0% +uh +sets + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +this is a collection of subsets of r so + + align:start position:0% +this is a collection of subsets of r so + + + align:start position:0% +this is a collection of subsets of r so +it's a subset of the power set of r + + align:start position:0% +it's a subset of the power set of r + + + align:start position:0% +it's a subset of the power set of r +is an algebra + + align:start position:0% + + + + align:start position:0% + +so some of you have taken algebra are + + align:start position:0% +so some of you have taken algebra are + + + align:start position:0% +so some of you have taken algebra are +taking algebra so you + + align:start position:0% +taking algebra so you + + + align:start position:0% +taking algebra so you +there's a notion of what an algebra is + + align:start position:0% +there's a notion of what an algebra is + + + align:start position:0% +there's a notion of what an algebra is +in algebra here we say a collection of + + align:start position:0% +in algebra here we say a collection of + + + align:start position:0% +in algebra here we say a collection of +sets is an algebra if in some sense it's + + align:start position:0% +sets is an algebra if in some sense it's + + + align:start position:0% +sets is an algebra if in some sense it's +closed undertaking + + align:start position:0% +closed undertaking + + + align:start position:0% +closed undertaking +or if it's closed undertaking + + align:start position:0% +or if it's closed undertaking + + + align:start position:0% +or if it's closed undertaking +complements and finite unions + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% +if + + + align:start position:0% +if +two conditions are satisfied + + align:start position:0% + + + + align:start position:0% + +if e is in the algebra then its + + align:start position:0% +if e is in the algebra then its + + + align:start position:0% +if e is in the algebra then its +complement is in the algebra + + align:start position:0% +complement is in the algebra + + + align:start position:0% +complement is in the algebra +and two + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +if i take + + align:start position:0% +if i take + + + align:start position:0% +if i take +finitely many elements in the algebra + + align:start position:0% +finitely many elements in the algebra + + + align:start position:0% +finitely many elements in the algebra +infinitely many + + align:start position:0% +infinitely many + + + align:start position:0% +infinitely many +subsets from this algebra of subsets + + align:start position:0% +subsets from this algebra of subsets + + + align:start position:0% +subsets from this algebra of subsets +then + + align:start position:0% +then + + + align:start position:0% +then +this union + + align:start position:0% + + + + align:start position:0% + +is also in this algebra + + align:start position:0% +is also in this algebra + + + align:start position:0% +is also in this algebra +okay + + align:start position:0% + + + + align:start position:0% + +now this is for finite + + align:start position:0% +now this is for finite + + + align:start position:0% +now this is for finite +unions you can ask + + align:start position:0% +unions you can ask + + + align:start position:0% +unions you can ask +what about + + align:start position:0% +what about + + + align:start position:0% +what about +infinite unions + + align:start position:0% +infinite unions + + + align:start position:0% +infinite unions +that's not equivalent to + + align:start position:0% +that's not equivalent to + + + align:start position:0% +that's not equivalent to +finite unions meaning that's a stronger + + align:start position:0% +finite unions meaning that's a stronger + + + align:start position:0% +finite unions meaning that's a stronger +condition to impose so + + align:start position:0% +condition to impose so + + + align:start position:0% +condition to impose so +we have a special name for collections + + align:start position:0% +we have a special name for collections + + + align:start position:0% +we have a special name for collections +of + + align:start position:0% +of + + + align:start position:0% +of +subsets of that type + + align:start position:0% +subsets of that type + + + align:start position:0% +subsets of that type +we say + + align:start position:0% + + + + align:start position:0% + +an algebra + + align:start position:0% +an algebra + + + align:start position:0% +an algebra +a + + align:start position:0% +a + + + align:start position:0% +a +is a + + align:start position:0% +is a + + + align:start position:0% +is a +sigma algebra + + align:start position:0% +sigma algebra + + + align:start position:0% +sigma algebra +sigma for if you like sum + + align:start position:0% +sigma for if you like sum + + + align:start position:0% +sigma for if you like sum +because we really have + + align:start position:0% +because we really have + + + align:start position:0% +because we really have +uh + + align:start position:0% +uh + + + align:start position:0% +uh +you know summation in + + align:start position:0% +you know summation in + + + align:start position:0% +you know summation in +in mind + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% +if + + + align:start position:0% +if +also + + align:start position:0% +also + + + align:start position:0% +also +the following condition is satisfied the + + align:start position:0% +the following condition is satisfied the + + + align:start position:0% +the following condition is satisfied the +the stronger following stronger + + align:start position:0% +the stronger following stronger + + + align:start position:0% +the stronger following stronger +condition is satisfied + + align:start position:0% +condition is satisfied + + + align:start position:0% +condition is satisfied +if + + align:start position:0% +if + + + align:start position:0% +if +i have a countable collection + + align:start position:0% + + + + align:start position:0% + +of subsets in a + + align:start position:0% + + + + align:start position:0% + +so accountable collection of elements of + + align:start position:0% +so accountable collection of elements of + + + align:start position:0% +so accountable collection of elements of +the algebra + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +their union + + align:start position:0% + + + + align:start position:0% + +is in + + align:start position:0% +is in + + + align:start position:0% +is in +the algebra so + + align:start position:0% +the algebra so + + + align:start position:0% +the algebra so +an algebra is closed undertaking + + align:start position:0% +an algebra is closed undertaking + + + align:start position:0% +an algebra is closed undertaking +complements in finite unions + + align:start position:0% +complements in finite unions + + + align:start position:0% +complements in finite unions +a sigma algebra is closed under + + align:start position:0% +a sigma algebra is closed under + + + align:start position:0% +a sigma algebra is closed under +complements and also the stronger + + align:start position:0% +complements and also the stronger + + + align:start position:0% +complements and also the stronger +condition of taking countable unions so + + align:start position:0% +condition of taking countable unions so + + + align:start position:0% +condition of taking countable unions so +of course this condition implies this + + align:start position:0% +of course this condition implies this + + + align:start position:0% +of course this condition implies this +condition + + align:start position:0% +condition + + + align:start position:0% +condition +well actually that's not yet clear + + align:start position:0% + + + + align:start position:0% + +we'll see + + align:start position:0% +we'll see + + + align:start position:0% +we'll see +well + + align:start position:0% +well + + + align:start position:0% +well +although it's not in the in the + + align:start position:0% +although it's not in the in the + + + align:start position:0% +although it's not in the in the +definition + + align:start position:0% +definition + + + align:start position:0% +definition +we'll see in just a second that + + align:start position:0% +we'll see in just a second that + + + align:start position:0% +we'll see in just a second that +in fact this implies that the empty set + + align:start position:0% +in fact this implies that the empty set + + + align:start position:0% +in fact this implies that the empty set +has to be a member of an of the algebra + + align:start position:0% +has to be a member of an of the algebra + + + align:start position:0% +has to be a member of an of the algebra +and therefore this condition implies + + align:start position:0% +and therefore this condition implies + + + align:start position:0% +and therefore this condition implies +this condition if you just take finitely + + align:start position:0% +this condition if you just take finitely + + + align:start position:0% +this condition if you just take finitely +many of these and then uh take them to + + align:start position:0% +many of these and then uh take them to + + + align:start position:0% +many of these and then uh take them to +be empty for you know + + align:start position:0% +be empty for you know + + + align:start position:0% +be empty for you know +after some finite n + + align:start position:0% + + + + align:start position:0% + +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +that's the definition of an algebra + + align:start position:0% +that's the definition of an algebra + + + align:start position:0% +that's the definition of an algebra +that's the definition of a sigma algebra + + align:start position:0% + + + + align:start position:0% + +um let me + + align:start position:0% + + + + align:start position:0% + +let me give a few examples real quick + + align:start position:0% +let me give a few examples real quick + + + align:start position:0% +let me give a few examples real quick +or a few + + align:start position:0% +or a few + + + align:start position:0% +or a few +remarks about + + align:start position:0% + + + + align:start position:0% + +about this + + align:start position:0% +about this + + + align:start position:0% +about this +first off + + align:start position:0% +first off + + + align:start position:0% +first off +you know + + align:start position:0% + + + + align:start position:0% + +by de morgan's laws + + align:start position:0% +by de morgan's laws + + + align:start position:0% +by de morgan's laws +you know which tells you the complement + + align:start position:0% +you know which tells you the complement + + + align:start position:0% +you know which tells you the complement +of a union is an intersect of the + + align:start position:0% +of a union is an intersect of the + + + align:start position:0% +of a union is an intersect of the +intersection of the complements + + align:start position:0% +intersection of the complements + + + align:start position:0% +intersection of the complements +we get that + + align:start position:0% + + + + align:start position:0% + +e1 + + align:start position:0% +e1 + + + align:start position:0% +e1 +en + + align:start position:0% + + + + align:start position:0% + +in the algebra implies that + + align:start position:0% + + + + align:start position:0% + +e1 intersect so their intersection + + align:start position:0% + + + + align:start position:0% + +so this is just for for an algebra now + + align:start position:0% +so this is just for for an algebra now + + + align:start position:0% +so this is just for for an algebra now +their intersection which is equal to + + align:start position:0% +their intersection which is equal to + + + align:start position:0% +their intersection which is equal to +uh + + align:start position:0% + + + + align:start position:0% + +the complement of the union of their + + align:start position:0% +the complement of the union of their + + + align:start position:0% +the complement of the union of their +complements + + align:start position:0% +complements + + + align:start position:0% +complements +so since each of these is in the algebra + + align:start position:0% +so since each of these is in the algebra + + + align:start position:0% +so since each of these is in the algebra +the complements is in the out the + + align:start position:0% +the complements is in the out the + + + align:start position:0% +the complements is in the out the +complement is in the algebra and + + align:start position:0% +complement is in the algebra and + + + align:start position:0% +complement is in the algebra and +therefore the finite union is in the + + align:start position:0% +therefore the finite union is in the + + + align:start position:0% +therefore the finite union is in the +algebra and therefore the complement of + + align:start position:0% +algebra and therefore the complement of + + + align:start position:0% +algebra and therefore the complement of +that is in the algebra so + + align:start position:0% +that is in the algebra so + + + align:start position:0% +that is in the algebra so +okay so not only uh + + align:start position:0% +okay so not only uh + + + align:start position:0% +okay so not only uh +is an algebra closed undertaking + + align:start position:0% +is an algebra closed undertaking + + + align:start position:0% +is an algebra closed undertaking +complements and finite unions it's also + + align:start position:0% +complements and finite unions it's also + + + align:start position:0% +complements and finite unions it's also +closed undertaking + + align:start position:0% +closed undertaking + + + align:start position:0% +closed undertaking +uh intersections finite intersections + + align:start position:0% +uh intersections finite intersections + + + align:start position:0% +uh intersections finite intersections +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +thus + + align:start position:0% +thus + + + align:start position:0% +thus +if i take some element from my non-empty + + align:start position:0% +if i take some element from my non-empty + + + align:start position:0% +if i take some element from my non-empty +collection of + + align:start position:0% +collection of + + + align:start position:0% +collection of +my non-empty algebra + + align:start position:0% + + + + align:start position:0% + +the empty set which is equal to + + align:start position:0% +the empty set which is equal to + + + align:start position:0% +the empty set which is equal to +e intersect e complement + + align:start position:0% +e intersect e complement + + + align:start position:0% +e intersect e complement +that's in the algebra + + align:start position:0% + + + + align:start position:0% + +so let me pause for a minute and write + + align:start position:0% +so let me pause for a minute and write + + + align:start position:0% +so let me pause for a minute and write +this a little carefully + + align:start position:0% + + + + align:start position:0% + +if i take an element of the algebra + + align:start position:0% +if i take an element of the algebra + + + align:start position:0% +if i take an element of the algebra +which is + + align:start position:0% +which is + + + align:start position:0% +which is +supposed to be non-empty + + align:start position:0% +supposed to be non-empty + + + align:start position:0% +supposed to be non-empty +then the empty set + + align:start position:0% +then the empty set + + + align:start position:0% +then the empty set +which is equal to e intersect its + + align:start position:0% +which is equal to e intersect its + + + align:start position:0% +which is equal to e intersect its +complement that's in the algebra that's + + align:start position:0% +complement that's in the algebra that's + + + align:start position:0% +complement that's in the algebra that's +in the algebra the intersection of two + + align:start position:0% +in the algebra the intersection of two + + + align:start position:0% +in the algebra the intersection of two +things and then in the algebra is in the + + align:start position:0% +things and then in the algebra is in the + + + align:start position:0% +things and then in the algebra is in the +algebra uh + + align:start position:0% +algebra uh + + + align:start position:0% +algebra uh +so that's also in the algebra and also + + align:start position:0% +so that's also in the algebra and also + + + align:start position:0% +so that's also in the algebra and also +this implies that r which is equal to + + align:start position:0% +this implies that r which is equal to + + + align:start position:0% +this implies that r which is equal to +the complement of the empty set + + align:start position:0% +the complement of the empty set + + + align:start position:0% +the complement of the empty set +is also in the algebra so + + align:start position:0% +is also in the algebra so + + + align:start position:0% +is also in the algebra so +for algebras of sets + + align:start position:0% +for algebras of sets + + + align:start position:0% +for algebras of sets +they always contain the empty set for + + align:start position:0% +they always contain the empty set for + + + align:start position:0% +they always contain the empty set for +non-empty ones the which is the only + + align:start position:0% +non-empty ones the which is the only + + + align:start position:0% +non-empty ones the which is the only +kind we're ever going to care about uh + + align:start position:0% +kind we're ever going to care about uh + + + align:start position:0% +kind we're ever going to care about uh +they always contain the empty set in r + + align:start position:0% +they always contain the empty set in r + + + align:start position:0% +they always contain the empty set in r +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and not only are they closed under + + align:start position:0% +and not only are they closed under + + + align:start position:0% +and not only are they closed under +taking + + align:start position:0% +taking + + + align:start position:0% +taking +uh + + align:start position:0% +uh + + + align:start position:0% +uh +compliments but also finite unions + + align:start position:0% +compliments but also finite unions + + + align:start position:0% +compliments but also finite unions +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and just like we proved uh + + align:start position:0% +and just like we proved uh + + + align:start position:0% +and just like we proved uh +you know that for algebras finite + + align:start position:0% +you know that for algebras finite + + + align:start position:0% +you know that for algebras finite +intersections are also in the algebra + + align:start position:0% +intersections are also in the algebra + + + align:start position:0% +intersections are also in the algebra +you can also prove that for sigma + + align:start position:0% +you can also prove that for sigma + + + align:start position:0% +you can also prove that for sigma +algebra + + align:start position:0% +algebra + + + align:start position:0% +algebra +countable intersections are also in the + + align:start position:0% +countable intersections are also in the + + + align:start position:0% +countable intersections are also in the +sigma algebra so let me make a point of + + align:start position:0% +sigma algebra so let me make a point of + + + align:start position:0% +sigma algebra so let me make a point of +that + + align:start position:0% + + + + align:start position:0% + +if a is a + + align:start position:0% +if a is a + + + align:start position:0% +if a is a +sigma algebra + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +ian accountable collection of + + align:start position:0% +ian accountable collection of + + + align:start position:0% +ian accountable collection of +elements of the sigma algebra implies + + align:start position:0% +elements of the sigma algebra implies + + + align:start position:0% +elements of the sigma algebra implies +that + + align:start position:0% + + + + align:start position:0% + +the its countable intersection is also + + align:start position:0% + + + + align:start position:0% + +in the algebra + + align:start position:0% +in the algebra + + + align:start position:0% +in the algebra +okay again by de morgan's law + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +so why am i making all these uh general + + align:start position:0% +so why am i making all these uh general + + + align:start position:0% +so why am i making all these uh general +definitions now so + + align:start position:0% + + + + align:start position:0% + +what we're going to show soon is + + align:start position:0% + + + + align:start position:0% + +at least in the next uh lex next lecture + + align:start position:0% +at least in the next uh lex next lecture + + + align:start position:0% +at least in the next uh lex next lecture +will soon show that + + align:start position:0% +will soon show that + + + align:start position:0% +will soon show that +if i define + + align:start position:0% +if i define + + + align:start position:0% +if i define +script m as a set of all + + align:start position:0% +script m as a set of all + + + align:start position:0% +script m as a set of all +measurable + + align:start position:0% + + + + align:start position:0% + +subsets + + align:start position:0% +subsets + + + align:start position:0% +subsets +of r + + align:start position:0% +of r + + + align:start position:0% +of r +okay + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +this is a collection of subsets of r + + align:start position:0% +this is a collection of subsets of r + + + align:start position:0% +this is a collection of subsets of r +that this is a sigma algebra + + align:start position:0% + + + + align:start position:0% + +one of the things we'll show + + align:start position:0% +one of the things we'll show + + + align:start position:0% +one of the things we'll show +okay + + align:start position:0% + + + + align:start position:0% + +now how we're doing this now is um + + align:start position:0% +now how we're doing this now is um + + + align:start position:0% +now how we're doing this now is um +you know we had these + + align:start position:0% +you know we had these + + + align:start position:0% +you know we had these +ideals of what a measure should be + + align:start position:0% +ideals of what a measure should be + + + align:start position:0% +ideals of what a measure should be +and + + align:start position:0% +and + + + align:start position:0% +and +we're building it up from this way and + + align:start position:0% +we're building it up from this way and + + + align:start position:0% +we're building it up from this way and +we're kind of you know + + align:start position:0% +we're kind of you know + + + align:start position:0% +we're kind of you know +in the end we're going to come up with + + align:start position:0% +in the end we're going to come up with + + + align:start position:0% +in the end we're going to come up with +the + + align:start position:0% +the + + + align:start position:0% +the +you know this collection of measurable + + align:start position:0% +you know this collection of measurable + + + align:start position:0% +you know this collection of measurable +sets which will have this uh + + align:start position:0% +sets which will have this uh + + + align:start position:0% +sets which will have this uh +special structure of being a sigma + + align:start position:0% +special structure of being a sigma + + + align:start position:0% +special structure of being a sigma +algebra okay and then our measure will + + align:start position:0% +algebra okay and then our measure will + + + align:start position:0% +algebra okay and then our measure will +be defined on this sigma algebra of sets + + align:start position:0% +be defined on this sigma algebra of sets + + + align:start position:0% +be defined on this sigma algebra of sets +um when you go on to general measure + + align:start position:0% +um when you go on to general measure + + + align:start position:0% +um when you go on to general measure +theory that is the input for you okay + + align:start position:0% +theory that is the input for you okay + + + align:start position:0% +theory that is the input for you okay +a measure space will then be a + + align:start position:0% +a measure space will then be a + + + align:start position:0% +a measure space will then be a +collection a sigma algebra of subsets of + + align:start position:0% +collection a sigma algebra of subsets of + + + align:start position:0% +collection a sigma algebra of subsets of +a set + + align:start position:0% +a set + + + align:start position:0% +a set +and with a measure on it that's your + + align:start position:0% +and with a measure on it that's your + + + align:start position:0% +and with a measure on it that's your +input here it's you know you're building + + align:start position:0% +input here it's you know you're building + + + align:start position:0% +input here it's you know you're building +if you like one of the + + align:start position:0% +if you like one of the + + + align:start position:0% +if you like one of the +first non-trivial measures + + align:start position:0% +first non-trivial measures + + + align:start position:0% +first non-trivial measures +okay that's what that's what we're doing + + align:start position:0% +okay that's what that's what we're doing + + + align:start position:0% +okay that's what that's what we're doing +you know one of the + + align:start position:0% + + + + align:start position:0% + +most important uh + + align:start position:0% +most important uh + + + align:start position:0% +most important uh +measures + + align:start position:0% +measures + + + align:start position:0% +measures +really + + align:start position:0% +really + + + align:start position:0% +really +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um so we have that definition + + align:start position:0% +um so we have that definition + + + align:start position:0% +um so we have that definition +if you've taken my class before + + align:start position:0% + + + + align:start position:0% + +you know that if + + align:start position:0% +you know that if + + + align:start position:0% +you know that if +there's a definition then we should see + + align:start position:0% +there's a definition then we should see + + + align:start position:0% +there's a definition then we should see +an example or two i said that + + align:start position:0% +an example or two i said that + + + align:start position:0% +an example or two i said that +measurable sets will be + + align:start position:0% +measurable sets will be + + + align:start position:0% +measurable sets will be +the set of measurable sets will be a + + align:start position:0% +the set of measurable sets will be a + + + align:start position:0% +the set of measurable sets will be a +sigma algebra that's going to take a + + align:start position:0% +sigma algebra that's going to take a + + + align:start position:0% +sigma algebra that's going to take a +little work to get to + + align:start position:0% +little work to get to + + + align:start position:0% +little work to get to +but + + align:start position:0% +but + + + align:start position:0% +but +we can come up with a few examples + + align:start position:0% +we can come up with a few examples + + + align:start position:0% +we can come up with a few examples +already + + align:start position:0% + + + + align:start position:0% + +so some simple examples um + + align:start position:0% +so some simple examples um + + + align:start position:0% +so some simple examples um +we have the stupidest example + + align:start position:0% +we have the stupidest example + + + align:start position:0% +we have the stupidest example +always start off with the stupidest + + align:start position:0% +always start off with the stupidest + + + align:start position:0% +always start off with the stupidest +examples that's that's + + align:start position:0% +examples that's that's + + + align:start position:0% +examples that's that's +the way to go + + align:start position:0% +the way to go + + + align:start position:0% +the way to go +um + + align:start position:0% +um + + + align:start position:0% +um +so + + align:start position:0% + + + + align:start position:0% + +the simplest sigma algebra is given by + + align:start position:0% +the simplest sigma algebra is given by + + + align:start position:0% +the simplest sigma algebra is given by +this + + align:start position:0% +this + + + align:start position:0% +this +collection of subsets consisting only of + + align:start position:0% +collection of subsets consisting only of + + + align:start position:0% +collection of subsets consisting only of +the empty set and r + + align:start position:0% + + + + align:start position:0% + +the next stupidest one is on the other + + align:start position:0% +the next stupidest one is on the other + + + align:start position:0% +the next stupidest one is on the other +end of the spectrum where every subset + + align:start position:0% +end of the spectrum where every subset + + + align:start position:0% +end of the spectrum where every subset +is + + align:start position:0% +is + + + align:start position:0% +is +uh in this + + align:start position:0% +uh in this + + + align:start position:0% +uh in this +sigma algebra so these are all these are + + align:start position:0% + + + + align:start position:0% + +sigma algebras + + align:start position:0% + + + + align:start position:0% + +what's a + + align:start position:0% +what's a + + + align:start position:0% +what's a +non-stupid one so let's say we take + + align:start position:0% +non-stupid one so let's say we take + + + align:start position:0% +non-stupid one so let's say we take +a to be the set the collection of all + + align:start position:0% +a to be the set the collection of all + + + align:start position:0% +a to be the set the collection of all +subsets e + + align:start position:0% +subsets e + + + align:start position:0% +subsets e +such that + + align:start position:0% +such that + + + align:start position:0% +such that +either e + + align:start position:0% + + + + align:start position:0% + +is countable or + + align:start position:0% +is countable or + + + align:start position:0% +is countable or +a complement + + align:start position:0% + + + + align:start position:0% + +is countable + + align:start position:0% +is countable + + + align:start position:0% +is countable +okay + + align:start position:0% + + + + align:start position:0% + +all right um + + align:start position:0% +all right um + + + align:start position:0% +all right um +so + + align:start position:0% + + + + align:start position:0% + +why + + align:start position:0% +why + + + align:start position:0% +why +why is this so i claim this is also a + + align:start position:0% +why is this so i claim this is also a + + + align:start position:0% +why is this so i claim this is also a +sigma algebra + + align:start position:0% + + + + align:start position:0% + +okay why is this a sigma algebra + + align:start position:0% + + + + align:start position:0% + +first off it's clear that e if e is in a + + align:start position:0% +first off it's clear that e if e is in a + + + align:start position:0% +first off it's clear that e if e is in a +then its complement is a is an a right + + align:start position:0% +then its complement is a is an a right + + + align:start position:0% +then its complement is a is an a right +because if e is countable then its + + align:start position:0% +because if e is countable then its + + + align:start position:0% +because if e is countable then its +complement + + align:start position:0% +complement + + + align:start position:0% +complement +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the complement of its complement is e is + + align:start position:0% +the complement of its complement is e is + + + align:start position:0% +the complement of its complement is e is +countable so + + align:start position:0% +countable so + + + align:start position:0% +countable so +you know + + align:start position:0% +you know + + + align:start position:0% +you know +e in a implies that e complement is a in + + align:start position:0% +e in a implies that e complement is a in + + + align:start position:0% +e in a implies that e complement is a in +other words uh this condition is + + align:start position:0% +other words uh this condition is + + + align:start position:0% +other words uh this condition is +symmetric in e and e complement okay + + align:start position:0% +symmetric in e and e complement okay + + + align:start position:0% +symmetric in e and e complement okay +why is it uh closed undertaking + + align:start position:0% +why is it uh closed undertaking + + + align:start position:0% +why is it uh closed undertaking +countable + + align:start position:0% +countable + + + align:start position:0% +countable +unions + + align:start position:0% +unions + + + align:start position:0% +unions +so + + align:start position:0% + + + + align:start position:0% + +suppose i take a collection of + + align:start position:0% +suppose i take a collection of + + + align:start position:0% +suppose i take a collection of +elements from my + + align:start position:0% + + + + align:start position:0% + +uh collection here a i want to show the + + align:start position:0% +uh collection here a i want to show the + + + align:start position:0% +uh collection here a i want to show the +union is in + + align:start position:0% +union is in + + + align:start position:0% +union is in +uh a + + align:start position:0% +uh a + + + align:start position:0% +uh a +then + + align:start position:0% + + + + align:start position:0% + +if + + align:start position:0% + + + + align:start position:0% + +all + + align:start position:0% + + + + align:start position:0% + +if for all n e n + + align:start position:0% +if for all n e n + + + align:start position:0% +if for all n e n +is countable + + align:start position:0% +is countable + + + align:start position:0% +is countable +then + + align:start position:0% + + + + align:start position:0% + +the union + + align:start position:0% +the union + + + align:start position:0% +the union +over n of e sub + + align:start position:0% +over n of e sub + + + align:start position:0% +over n of e sub +n + + align:start position:0% +n + + + align:start position:0% +n +is a countable union of countable sets + + align:start position:0% +is a countable union of countable sets + + + align:start position:0% +is a countable union of countable sets +and therefore + + align:start position:0% +and therefore + + + align:start position:0% +and therefore +this is countable + + align:start position:0% +this is countable + + + align:start position:0% +this is countable +which implies + + align:start position:0% + + + + align:start position:0% + +this guy is in uh + + align:start position:0% +this guy is in uh + + + align:start position:0% +this guy is in uh +in the + + align:start position:0% +in the + + + align:start position:0% +in the +set collection a + + align:start position:0% +set collection a + + + align:start position:0% +set collection a +so this is the case that all of these + + align:start position:0% +so this is the case that all of these + + + align:start position:0% +so this is the case that all of these +are countable + + align:start position:0% +are countable + + + align:start position:0% +are countable +if there exists an integer in 0 such + + align:start position:0% +if there exists an integer in 0 such + + + align:start position:0% +if there exists an integer in 0 such +that + + align:start position:0% +that + + + align:start position:0% +that +e in + + align:start position:0% +e in + + + align:start position:0% +e in +complement + + align:start position:0% + + + + align:start position:0% + +is countable + + align:start position:0% +is countable + + + align:start position:0% +is countable +e n sub 0. + + align:start position:0% +e n sub 0. + + + align:start position:0% +e n sub 0. +then if i take + + align:start position:0% + + + + align:start position:0% + +so remember what i have to verify + + align:start position:0% +so remember what i have to verify + + + align:start position:0% +so remember what i have to verify +is that + + align:start position:0% +is that + + + align:start position:0% +is that +the union of ens is in the + + align:start position:0% +the union of ens is in the + + + align:start position:0% +the union of ens is in the +set a which means either it's countable + + align:start position:0% +set a which means either it's countable + + + align:start position:0% +set a which means either it's countable +or its + + align:start position:0% +or its + + + align:start position:0% +or its +complement is countable so if i look at + + align:start position:0% +complement is countable so if i look at + + + align:start position:0% +complement is countable so if i look at +uh the complement of the union + + align:start position:0% +uh the complement of the union + + + align:start position:0% +uh the complement of the union +this is then equal to + + align:start position:0% +this is then equal to + + + align:start position:0% +this is then equal to +by de morgan's law the intersection of + + align:start position:0% +by de morgan's law the intersection of + + + align:start position:0% +by de morgan's law the intersection of +the complements and this is contained in + + align:start position:0% + + + + align:start position:0% + +one of these guys + + align:start position:0% +one of these guys + + + align:start position:0% +one of these guys +and therefore this is a subset of a + + align:start position:0% +and therefore this is a subset of a + + + align:start position:0% +and therefore this is a subset of a +countable set + + align:start position:0% +countable set + + + align:start position:0% +countable set +which implies that + + align:start position:0% + + + + align:start position:0% + +this is + + align:start position:0% +this is + + + align:start position:0% +this is +countable and + + align:start position:0% +countable and + + + align:start position:0% +countable and +which is a + + align:start position:0% +which is a + + + align:start position:0% +which is a +condition that which is one of the + + align:start position:0% +condition that which is one of the + + + align:start position:0% +condition that which is one of the +conditions of a and therefore + + align:start position:0% + + + + align:start position:0% + +this is in uh + + align:start position:0% +this is in uh + + + align:start position:0% +this is in uh +a so therefore + + align:start position:0% +a so therefore + + + align:start position:0% +a so therefore +this collection of subsets of r such + + align:start position:0% +this collection of subsets of r such + + + align:start position:0% +this collection of subsets of r such +that e is countable or the complement of + + align:start position:0% +that e is countable or the complement of + + + align:start position:0% +that e is countable or the complement of +e is countable uh is a sigma algebra of + + align:start position:0% +e is countable uh is a sigma algebra of + + + align:start position:0% +e is countable uh is a sigma algebra of +sub of uh sets it's usually referred to + + align:start position:0% +sub of uh sets it's usually referred to + + + align:start position:0% +sub of uh sets it's usually referred to +as a set of uh + + align:start position:0% +as a set of uh + + + align:start position:0% +as a set of uh +as the co-countable + + align:start position:0% +as the co-countable + + + align:start position:0% +as the co-countable +sigma algebra + + align:start position:0% +sigma algebra + + + align:start position:0% +sigma algebra +okay + + align:start position:0% + + + + align:start position:0% + +and one can define a measure on you know + + align:start position:0% +and one can define a measure on you know + + + align:start position:0% +and one can define a measure on you know +this collection this sigma algebra um + + align:start position:0% +this collection this sigma algebra um + + + align:start position:0% +this collection this sigma algebra um +but we're only interested in the big + + align:start position:0% +but we're only interested in the big + + + align:start position:0% +but we're only interested in the big +measure + + align:start position:0% + + + + align:start position:0% + +which + + align:start position:0% +which + + + align:start position:0% +which +is going to be defined on as we'll see + + align:start position:0% +is going to be defined on as we'll see + + + align:start position:0% +is going to be defined on as we'll see +the + + align:start position:0% +the + + + align:start position:0% +the +sigma algebra of + + align:start position:0% +sigma algebra of + + + align:start position:0% +sigma algebra of +measurable subsets of r look at + + align:start position:0% +measurable subsets of r look at + + + align:start position:0% +measurable subsets of r look at +measurable subsets of r + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% +uh + + + align:start position:0% +uh +let's do one more + + align:start position:0% +let's do one more + + + align:start position:0% +let's do one more +example + + align:start position:0% + + + + align:start position:0% + +uh this will just take a minute and it's + + align:start position:0% +uh this will just take a minute and it's + + + align:start position:0% +uh this will just take a minute and it's +not too technical i know it's the end of + + align:start position:0% +not too technical i know it's the end of + + + align:start position:0% +not too technical i know it's the end of +the lecture so maybe uh well i mean + + align:start position:0% +the lecture so maybe uh well i mean + + + align:start position:0% +the lecture so maybe uh well i mean +you're at home watching this you can + + align:start position:0% +you're at home watching this you can + + + align:start position:0% +you're at home watching this you can +pause it at some point get a snack + + align:start position:0% +pause it at some point get a snack + + + align:start position:0% +pause it at some point get a snack +uh change pajamas whatever + + align:start position:0% +uh change pajamas whatever + + + align:start position:0% +uh change pajamas whatever +but anyways uh here's one last example + + align:start position:0% +but anyways uh here's one last example + + + align:start position:0% +but anyways uh here's one last example +of a sigma algebra which is in fact a + + align:start position:0% +of a sigma algebra which is in fact a + + + align:start position:0% +of a sigma algebra which is in fact a +very important + + align:start position:0% +very important + + + align:start position:0% +very important +sigma algebra + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +which is the following + + align:start position:0% + + + + align:start position:0% + +let + + align:start position:0% +let + + + align:start position:0% +let +capital sigma be + + align:start position:0% +capital sigma be + + + align:start position:0% +capital sigma be +the collection + + align:start position:0% +the collection + + + align:start position:0% +the collection +of + + align:start position:0% +of + + + align:start position:0% +of +all sigma algebras + + align:start position:0% + + + + align:start position:0% + +containing all open sets + + align:start position:0% + + + + align:start position:0% + +okay so let's unwind this definition for + + align:start position:0% +okay so let's unwind this definition for + + + align:start position:0% +okay so let's unwind this definition for +a minute + + align:start position:0% +a minute + + + align:start position:0% +a minute +so you are in this collection of sigma + + align:start position:0% +so you are in this collection of sigma + + + align:start position:0% +so you are in this collection of sigma +algebras if you are a sigma algebra and + + align:start position:0% +algebras if you are a sigma algebra and + + + align:start position:0% +algebras if you are a sigma algebra and +you contain all open subsets of r so for + + align:start position:0% +you contain all open subsets of r so for + + + align:start position:0% +you contain all open subsets of r so for +example + + align:start position:0% + + + + align:start position:0% + +the power set of r + + align:start position:0% +the power set of r + + + align:start position:0% +the power set of r +which is a sigma algebra a trivial one + + align:start position:0% +which is a sigma algebra a trivial one + + + align:start position:0% +which is a sigma algebra a trivial one +contains every subset of r so it + + align:start position:0% +contains every subset of r so it + + + align:start position:0% +contains every subset of r so it +certainly contains every sub every open + + align:start position:0% +certainly contains every sub every open + + + align:start position:0% +certainly contains every sub every open +subset of r this is in this collection + + align:start position:0% +subset of r this is in this collection + + + align:start position:0% +subset of r this is in this collection +of uh sigma algebras + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +and let me define + + align:start position:0% +and let me define + + + align:start position:0% +and let me define +script b to be the intersection + + align:start position:0% +script b to be the intersection + + + align:start position:0% +script b to be the intersection +over all + + align:start position:0% + + + + align:start position:0% + +sigma algebras in this collection of + + align:start position:0% +sigma algebras in this collection of + + + align:start position:0% +sigma algebras in this collection of +sigma algebras okay so this is the + + align:start position:0% +sigma algebras okay so this is the + + + align:start position:0% +sigma algebras okay so this is the +intersection + + align:start position:0% +intersection + + + align:start position:0% +intersection +of every sigma algebra containing + + align:start position:0% +of every sigma algebra containing + + + align:start position:0% +of every sigma algebra containing +all open sets + + align:start position:0% +all open sets + + + align:start position:0% +all open sets +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so first off + + align:start position:0% +so first off + + + align:start position:0% +so first off +this is non-empty right + + align:start position:0% +this is non-empty right + + + align:start position:0% +this is non-empty right +this is a non-empty + + align:start position:0% +this is a non-empty + + + align:start position:0% +this is a non-empty +interception intersection so note this + + align:start position:0% +interception intersection so note this + + + align:start position:0% +interception intersection so note this +is a intersection of + + align:start position:0% +is a intersection of + + + align:start position:0% +is a intersection of +subsets of collections of subsets of r + + align:start position:0% +subsets of collections of subsets of r + + + align:start position:0% +subsets of collections of subsets of r +so this is + + align:start position:0% +so this is + + + align:start position:0% +so this is +uh + + align:start position:0% + + + + align:start position:0% + +are and it does it's non-empty + + align:start position:0% + + + + align:start position:0% + +then b + + align:start position:0% +then b + + + align:start position:0% +then b +is + + align:start position:0% +is + + + align:start position:0% +is +i'm going to say a lot in these next few + + align:start position:0% +i'm going to say a lot in these next few + + + align:start position:0% +i'm going to say a lot in these next few +words is the smallest + + align:start position:0% + + + + align:start position:0% + +sigma algebra + + align:start position:0% + + + + align:start position:0% + +containing + + align:start position:0% +containing + + + align:start position:0% +containing +all + + align:start position:0% +all + + + align:start position:0% +all +open + + align:start position:0% + + + + align:start position:0% + +subsets of r + + align:start position:0% +subsets of r + + + align:start position:0% +subsets of r +and we call it the burel sigma algebra + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so + + align:start position:0% +so + + + align:start position:0% +so +you know how do you think of this you + + align:start position:0% +you know how do you think of this you + + + align:start position:0% +you know how do you think of this you +take every sigma algebra uh in the + + align:start position:0% +take every sigma algebra uh in the + + + align:start position:0% +take every sigma algebra uh in the +universe you + + align:start position:0% +universe you + + + align:start position:0% +universe you +that + + align:start position:0% +that + + + align:start position:0% +that +contain every open set you take the + + align:start position:0% +contain every open set you take the + + + align:start position:0% +contain every open set you take the +intersection of all these sigma algebras + + align:start position:0% +intersection of all these sigma algebras + + + align:start position:0% +intersection of all these sigma algebras +my claim is that you get a sigma algebra + + align:start position:0% +my claim is that you get a sigma algebra + + + align:start position:0% +my claim is that you get a sigma algebra +and this is the smallest sigma algebra + + align:start position:0% +and this is the smallest sigma algebra + + + align:start position:0% +and this is the smallest sigma algebra +containing all open subsets of r okay + + align:start position:0% +containing all open subsets of r okay + + + align:start position:0% +containing all open subsets of r okay +so another way to say this last sentence + + align:start position:0% +so another way to say this last sentence + + + align:start position:0% +so another way to say this last sentence +is + + align:start position:0% +is + + + align:start position:0% +is +b is in sigma + + align:start position:0% +b is in sigma + + + align:start position:0% +b is in sigma +and for all + + align:start position:0% +and for all + + + align:start position:0% +and for all +in + + align:start position:0% +in + + + align:start position:0% +in +sigma + + align:start position:0% + + + + align:start position:0% + +b is contained in + + align:start position:0% +b is contained in + + + align:start position:0% +b is contained in +a + + align:start position:0% +a + + + align:start position:0% +a +okay so it's the smallest + + align:start position:0% +okay so it's the smallest + + + align:start position:0% +okay so it's the smallest +sigma algebra containing all open + + align:start position:0% +sigma algebra containing all open + + + align:start position:0% +sigma algebra containing all open +subsets of r + + align:start position:0% +subsets of r + + + align:start position:0% +subsets of r +all right um the proof so + + align:start position:0% +all right um the proof so + + + align:start position:0% +all right um the proof so +the proof is not hard + + align:start position:0% +the proof is not hard + + + align:start position:0% +the proof is not hard +you just need to + + align:start position:0% +you just need to + + + align:start position:0% +you just need to +make sure you understand exactly what + + align:start position:0% +make sure you understand exactly what + + + align:start position:0% +make sure you understand exactly what +i'm saying here and if you understand + + align:start position:0% +i'm saying here and if you understand + + + align:start position:0% +i'm saying here and if you understand +what i'm saying here uh + + align:start position:0% + + + + align:start position:0% + +the proof is is quite simple and i'm + + align:start position:0% +the proof is is quite simple and i'm + + + align:start position:0% +the proof is is quite simple and i'm +only going to do + + align:start position:0% +only going to do + + + align:start position:0% +only going to do +um you know one part so + + align:start position:0% +um you know one part so + + + align:start position:0% +um you know one part so +first off once i show that b is a sigma + + align:start position:0% +first off once i show that b is a sigma + + + align:start position:0% +first off once i show that b is a sigma +algebra then + + align:start position:0% +algebra then + + + align:start position:0% +algebra then +uh + + align:start position:0% +uh + + + align:start position:0% +uh +the rest + + align:start position:0% +the rest + + + align:start position:0% +the rest +follows right because + + align:start position:0% +follows right because + + + align:start position:0% +follows right because +if i take any open subset of r it's + + align:start position:0% +if i take any open subset of r it's + + + align:start position:0% +if i take any open subset of r it's +contained in every one of these and + + align:start position:0% +contained in every one of these and + + + align:start position:0% +contained in every one of these and +therefore it's contained in the + + align:start position:0% +therefore it's contained in the + + + align:start position:0% +therefore it's contained in the +intersection so every open subset is + + align:start position:0% +intersection so every open subset is + + + align:start position:0% +intersection so every open subset is +contained in b or every open subset is + + align:start position:0% +contained in b or every open subset is + + + align:start position:0% +contained in b or every open subset is +an element of b i shouldn't say contain + + align:start position:0% +an element of b i shouldn't say contain + + + align:start position:0% +an element of b i shouldn't say contain +but every open uh + + align:start position:0% +but every open uh + + + align:start position:0% +but every open uh +subset + + align:start position:0% +subset + + + align:start position:0% +subset +is an element of b + + align:start position:0% +is an element of b + + + align:start position:0% +is an element of b +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so i just need to show that b is a sigma + + align:start position:0% +so i just need to show that b is a sigma + + + align:start position:0% +so i just need to show that b is a sigma +algebra and since it's equal to the + + align:start position:0% +algebra and since it's equal to the + + + align:start position:0% +algebra and since it's equal to the +intersection of all sigma algebras + + align:start position:0% +intersection of all sigma algebras + + + align:start position:0% +intersection of all sigma algebras +containing every open subset + + align:start position:0% +containing every open subset + + + align:start position:0% +containing every open subset +it has to be the smallest one any other + + align:start position:0% +it has to be the smallest one any other + + + align:start position:0% +it has to be the smallest one any other +one + + align:start position:0% +one + + + align:start position:0% +one +right this intersect for any fixed one + + align:start position:0% +right this intersect for any fixed one + + + align:start position:0% +right this intersect for any fixed one +this intersection is contained in any + + align:start position:0% +this intersection is contained in any + + + align:start position:0% +this intersection is contained in any +fixed one and therefore b is contained + + align:start position:0% +fixed one and therefore b is contained + + + align:start position:0% +fixed one and therefore b is contained +in any fixed + + align:start position:0% +in any fixed + + + align:start position:0% +in any fixed +sigma algebra which contains all the + + align:start position:0% +sigma algebra which contains all the + + + align:start position:0% +sigma algebra which contains all the +open subsets so i just need to verify + + align:start position:0% +open subsets so i just need to verify + + + align:start position:0% +open subsets so i just need to verify +that b is a sigma algebra + + align:start position:0% + + + + align:start position:0% + +since i'm running out of time i'm going + + align:start position:0% +since i'm running out of time i'm going + + + align:start position:0% +since i'm running out of time i'm going +to do + + align:start position:0% +to do + + + align:start position:0% +to do +one part + + align:start position:0% +one part + + + align:start position:0% +one part +or + + align:start position:0% +or + + + align:start position:0% +or +verify just one part of the definition + + align:start position:0% +verify just one part of the definition + + + align:start position:0% +verify just one part of the definition +because the other parts + + align:start position:0% +because the other parts + + + align:start position:0% +because the other parts +essentially the same except you have to + + align:start position:0% +essentially the same except you have to + + + align:start position:0% +essentially the same except you have to +use more chalk + + align:start position:0% +use more chalk + + + align:start position:0% +use more chalk +so i just need to verify that b is a + + align:start position:0% +so i just need to verify that b is a + + + align:start position:0% +so i just need to verify that b is a +sigma algebra + + align:start position:0% +sigma algebra + + + align:start position:0% +sigma algebra +okay + + align:start position:0% + + + + align:start position:0% + +now suppose + + align:start position:0% +now suppose + + + align:start position:0% +now suppose +e is an element of b so this means it's + + align:start position:0% +e is an element of b so this means it's + + + align:start position:0% +e is an element of b so this means it's +a subset of r + + align:start position:0% +a subset of r + + + align:start position:0% +a subset of r +uh + + align:start position:0% +uh + + + align:start position:0% +uh +it's + + align:start position:0% +it's + + + align:start position:0% +it's +one of these subsets of r that's uh an + + align:start position:0% +one of these subsets of r that's uh an + + + align:start position:0% +one of these subsets of r that's uh an +element of b + + align:start position:0% + + + + align:start position:0% + +then + + align:start position:0% + + + + align:start position:0% + +for all + + align:start position:0% +for all + + + align:start position:0% +for all +sigma algebras in this collection + + align:start position:0% +sigma algebras in this collection + + + align:start position:0% +sigma algebras in this collection +since b is the intersection over all of + + align:start position:0% +since b is the intersection over all of + + + align:start position:0% +since b is the intersection over all of +these + + align:start position:0% +these + + + align:start position:0% +these +sigma algebras + + align:start position:0% +sigma algebras + + + align:start position:0% +sigma algebras +e is in + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% +a + + + align:start position:0% +a +and since each of these is a sigma + + align:start position:0% +and since each of these is a sigma + + + align:start position:0% +and since each of these is a sigma +algebra + + align:start position:0% + + + + align:start position:0% + +i get that the complement is in a + + align:start position:0% +i get that the complement is in a + + + align:start position:0% +i get that the complement is in a +and this statement says for every + + align:start position:0% +and this statement says for every + + + align:start position:0% +and this statement says for every +sigma algebra in this collection the + + align:start position:0% +sigma algebra in this collection the + + + align:start position:0% +sigma algebra in this collection the +complement is in that sigma algebra and + + align:start position:0% +complement is in that sigma algebra and + + + align:start position:0% +complement is in that sigma algebra and +therefore + + align:start position:0% +therefore + + + align:start position:0% +therefore +e complement is in + + align:start position:0% +e complement is in + + + align:start position:0% +e complement is in +intersection + + align:start position:0% + + + + align:start position:0% + +which is remember how i've defined the + + align:start position:0% +which is remember how i've defined the + + + align:start position:0% +which is remember how i've defined the +burel sigma algebra okay + + align:start position:0% + + + + align:start position:0% + +okay and again + + align:start position:0% +okay and again + + + align:start position:0% +okay and again +the proof of + + align:start position:0% +the proof of + + + align:start position:0% +the proof of +being closed under accountable unions is + + align:start position:0% +being closed under accountable unions is + + + align:start position:0% +being closed under accountable unions is +sort of the same take a countable + + align:start position:0% +sort of the same take a countable + + + align:start position:0% +sort of the same take a countable +collection + + align:start position:0% +collection + + + align:start position:0% +collection +of elements of b + + align:start position:0% +of elements of b + + + align:start position:0% +of elements of b +then this countable collection + + align:start position:0% +then this countable collection + + + align:start position:0% +then this countable collection +they all have to be elements of a for + + align:start position:0% +they all have to be elements of a for + + + align:start position:0% +they all have to be elements of a for +every a and sigma therefore their union + + align:start position:0% +every a and sigma therefore their union + + + align:start position:0% +every a and sigma therefore their union +has to be an element of a for every a + + align:start position:0% +has to be an element of a for every a + + + align:start position:0% +has to be an element of a for every a +and sigma because a is a sigma algebra + + align:start position:0% +and sigma because a is a sigma algebra + + + align:start position:0% +and sigma because a is a sigma algebra +and therefore the union is in the + + align:start position:0% +and therefore the union is in the + + + align:start position:0% +and therefore the union is in the +intersection over all a's + + align:start position:0% +intersection over all a's + + + align:start position:0% +intersection over all a's +which is equal to b the burel sigma + + align:start position:0% +which is equal to b the burel sigma + + + align:start position:0% +which is equal to b the burel sigma +algebra + + align:start position:0% +algebra + + + align:start position:0% +algebra +okay all right so + + align:start position:0% +okay all right so + + + align:start position:0% +okay all right so +what we're working towards and what + + align:start position:0% +what we're working towards and what + + + align:start position:0% +what we're working towards and what +we're gonna do next lecture is + + align:start position:0% +we're gonna do next lecture is + + + align:start position:0% +we're gonna do next lecture is +we're going to show + + align:start position:0% +we're going to show + + + align:start position:0% +we're going to show +that um + + align:start position:0% +that um + + + align:start position:0% +that um +m the collection of + + align:start position:0% +m the collection of + + + align:start position:0% +m the collection of +uh measurable labaid measurable subsets + + align:start position:0% +uh measurable labaid measurable subsets + + + align:start position:0% +uh measurable labaid measurable subsets +of r + + align:start position:0% +of r + + + align:start position:0% +of r +is a sigma algebra and it contains the + + align:start position:0% +is a sigma algebra and it contains the + + + align:start position:0% +is a sigma algebra and it contains the +borrel sigma algebra okay so it contains + + align:start position:0% +borrel sigma algebra okay so it contains + + + align:start position:0% +borrel sigma algebra okay so it contains +this very big collection of subsets of r + + align:start position:0% +this very big collection of subsets of r + + + align:start position:0% +this very big collection of subsets of r +all right i mean this is truly a very + + align:start position:0% +all right i mean this is truly a very + + + align:start position:0% +all right i mean this is truly a very +big subset of r like i was saying it + + align:start position:0% +big subset of r like i was saying it + + + align:start position:0% +big subset of r like i was saying it +contains all open subsets and since it's + + align:start position:0% +contains all open subsets and since it's + + + align:start position:0% +contains all open subsets and since it's +a sigma algebra it contains the + + align:start position:0% +a sigma algebra it contains the + + + align:start position:0% +a sigma algebra it contains the +complements of all open subsets i.e + + align:start position:0% +complements of all open subsets i.e + + + align:start position:0% +complements of all open subsets i.e +closed subsets + + align:start position:0% +closed subsets + + + align:start position:0% +closed subsets +but then it also contains all + + align:start position:0% +but then it also contains all + + + align:start position:0% +but then it also contains all +intersections of open subsets because uh + + align:start position:0% +intersections of open subsets because uh + + + align:start position:0% +intersections of open subsets because uh +sigma algebras are + + align:start position:0% +sigma algebras are + + + align:start position:0% +sigma algebras are +um + + align:start position:0% +um + + + align:start position:0% +um +closed undertaking countable + + align:start position:0% +closed undertaking countable + + + align:start position:0% +closed undertaking countable +intersections as well + + align:start position:0% +intersections as well + + + align:start position:0% +intersections as well +and then it's + + align:start position:0% +and then it's + + + align:start position:0% +and then it's +you know you could take countable unions + + align:start position:0% +you know you could take countable unions + + + align:start position:0% +you know you could take countable unions +of those countable intersections of open + + align:start position:0% +of those countable intersections of open + + + align:start position:0% +of those countable intersections of open +subsets and then you know and so on and + + align:start position:0% +subsets and then you know and so on and + + + align:start position:0% +subsets and then you know and so on and +so on um so you get you know a very rich + + align:start position:0% +so on um so you get you know a very rich + + + align:start position:0% +so on um so you get you know a very rich +class of subsets of r that's contained + + align:start position:0% +class of subsets of r that's contained + + + align:start position:0% +class of subsets of r that's contained +in the sigma algebra and what we're + + align:start position:0% +in the sigma algebra and what we're + + + align:start position:0% +in the sigma algebra and what we're +going to show is that + + align:start position:0% + + + + align:start position:0% + +like i said the + + align:start position:0% +like i said the + + + align:start position:0% +like i said the +collection of le big measurable subsets + + align:start position:0% +collection of le big measurable subsets + + + align:start position:0% +collection of le big measurable subsets +of r that's a sigma algebra and it + + align:start position:0% +of r that's a sigma algebra and it + + + align:start position:0% +of r that's a sigma algebra and it +contains the burrell sigma algebra so + + align:start position:0% +contains the burrell sigma algebra so + + + align:start position:0% +contains the burrell sigma algebra so +you know it's a very rich class of + + align:start position:0% +you know it's a very rich class of + + + align:start position:0% +you know it's a very rich class of +subsets even though up to this point all + + align:start position:0% +subsets even though up to this point all + + + align:start position:0% +subsets even though up to this point all +we've shown is that uh the empty set r + + align:start position:0% +we've shown is that uh the empty set r + + + align:start position:0% +we've shown is that uh the empty set r +and the sets with outer measure equal to + + align:start position:0% +and the sets with outer measure equal to + + + align:start position:0% +and the sets with outer measure equal to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +are lebeg measurable so we'll do that + + align:start position:0% +are lebeg measurable so we'll do that + + + align:start position:0% +are lebeg measurable so we'll do that +next time and i'll stop there \ No newline at end of file diff --git a/Offa8tyTRQE.txt b/Offa8tyTRQE.txt new file mode 100644 index 0000000000000000000000000000000000000000..d72b25f05d0514e249714f227a68b56338aaee8d --- /dev/null +++ b/Offa8tyTRQE.txt @@ -0,0 +1,675 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high-quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +GREG HUTKO: Hi, welcome +back to the 14.01 + +problem-solving videos. + +Today I'm going to be working +on Fall 2010 Problem Set 5, + +Problem Number 4. + +And I'm only going to be working +the last few sections, + +E, F, G, and H in this video. + +But if you need help with the +earlier sections, you should + +go ahead and should look +at PSET Number 4, + +Problem Number 3. + +And in that problem, we work +through the production + +function, and we go through and +we find conditional supply + +and the conditional +demand curves. + +But this problem is going to +have us looking at aggregated + +supply in a market. + +We have to consider what +production should be occurring + +in the market given a set number +of firms in the market. + +And then we're going to think +about the case of perfect + +competition where firms have +to be operating at the + +absolute best efficiency +possible. + +And we're going to look +at how that affects + +the production level. + +Part E is introduced by saying, +consider now that r + +equals 4 and w equals 1. + +And that the market demand for +coffee is given by quantity + +demanded equals 20 minus p. + +There are eight other companies +operating in this + +market and all companies have +the cost structures identical + +to Sebastian's company, the +company that we've been + +dealing with earlier +in the problem. + +Part E asks us, what +is the aggregate + +supply in this market? + +And if you look back earlier +in this problem, the other + +piece of information that we're +going to need is we're + +going to need this cost function +that gives all of the + +cost in terms of the rental rate +of capital or how much it + +cost to use each machine per +hour, the wage rate or how + +much labor cost per hour, and q, +the quantity, that's output + +by a specific firm. + +Now, to find the aggregated +supply, what we're first going + +to find is we're going to first +find the supply curve + +for one firm within +this market. + +And then we're going to set the +demand or the supply curve + +in terms of quantity +in terms of price. + +We're going to multiply by +eight to aggregate it. + +And then we'll have our +aggregated supply curve. + +But before we do that, we also +have to think of a limiting + +case as well. + +When we're representing the +costs for a firm, we're going + +to represent both the marginal +cost and the average cost. The + +marginal cost is the cost of +one single additional unit, + +while the average cost tells us +all the costs including the + +fixed costs divided by the total +that we're producing, + +what does that look like? + +If the price in a market is +below the minimum of the + +average cost of a firm in the +market, they're not going to + +produce in the market. + +So if the price is below this +critical p star, since the + +firm, even if they're producing +right at the minimum + +of average cost, they can never +recover their cost. So a + +firm is only going to produce +if this p where the price + +that's being charged is above +the p star, the minimum of + +average cost. So we're going +to find the supply curve in + +two cases, one where the price +is above this minimum of + +average cost. And two, we're +going to find it when the + +price is below that minimum. + +Let's start off by finding the +marginal cost to get our + +supply curve. + +Taking the marginal cost, the +derivative with respect to q. + +Or before we can take the +marginal cost, sorry, let's + +plug-in for the variables +w and r. + +We're going to find that our +cost curve is given by 4 plus + +4q squared. + +Now we can find the marginal +cost, which will be our supply + +curve for a single firm. + +So in most cases, we know that +this supply curve is going to + +represent the supply for a +single firm where marginal + +cost, the price, is +going to equal 8q. + +So in most cases, this will be +our supply curve for one firm. + +Putting it in terms of q, +we'll have q equals p/8. + +Now since we have eight firms, +we multiply by 8. + +And in this case, we're going +to have the aggregated + +quantity, which we represent by +a capital Q. So that's the + +quantity produced by all eight +firms in the market. + +And that's going +to equal price. + +So this is one part of +the supply curve. + +And what we need to know is, +what's the critical price at + +which this will represent +the supply curve? + +So when the average cost curve +crosses the marginal cost + +curve, that's the minimum of the +average cost. It's always + +like that for all cost curves +for a producer. + +So if we set marginal cost equal +to average cost, we find + +this critical p star at which +the firm is going to produce + +at any price above +that p star. + +So we're going to go back to our +marginal cost. And what we + +have to do is we have to find +the average cost as well to + +set it equal. + +To get the average cost, we're +just going to go back up to + +our cost curve and we're going +to divide through the whole + +thing by q. + +So the average cost is going to +be 4 divided by q plus 4q. + +Now we're going to set average +cost and marginal cost equal. + +And when we set marginal cost +and average cost equal to find + +the intersection point on our +graph, what we're going to + +find is we're going to find that +critical p star is going + +to be equal to 8. + +So Qs is going to equal p for +any price that's greater than + +or equal to 8. + +But what happens in the +case where the price + +is less than 8? + +In that case, no single firm can +make a profit by being in + +the market. + +So for any price less than 8, +the production level is going + +to be equal to 0. + +Now we're going to move +on to the next case. + +Now we're going to take the +demand curve that we're given + +and we're going to calculate +the equilibrium price, the + +aggregate quantity sold, and +the quantity sold by each + +firm, and the economic +profit of each firm. + +So let's start off in solving +this problem, we're going to + +just assume that the price, +the equilibrium price, is + +going to be greater than +or equal to 8. + +And as we're solving through the +problem, if we end up with + +a price that's less than 8, then +we're just going to go + +back and we're going to say, +OK, there's going to be no + +production, and we're done. + +But let's work with the +assumption that we're working + +with this supply curve +to begin with. + +All we have to do in this case +is we're just going to set the + +supply curve we just found +equal to the demand curve + +that's given in the problem. + +Solving through for p, we're +going to find that the price + +in this market is going +to be equal to 10. + +And plugging in the price back +into the demand curve, you can + +find that the aggregate +quantity is going + +to be equal to 10. + +So the price for each unit is 10 +and the aggregate quantity + +is 10 as well. + +Now to find the quantity +produced by each of the eight + +firms, all the firms, since +they have identical cost + +structures, are going to be +producing the same amount. + +So we're just going to divide +this quantity by 8 to find the + +quantity produced by the +individual firms. So each firm + +in this case produces +5/4 of a unit. + +The last thing that we have to +do is we have to calculate the + +economic profits for each of +the single firms. So the + +profit is going to be equal to +the revenue, which is just + +price, times the quantity +for a single firm. + +A big mistake here would be to +use the aggregated quantity. + +And then you're going +to subtract out the + +cost for each firm. + +And we're just going to use +the cost function that was + +given after plugging +in w and r. + +And this is going to represent +the economic profit for each + +of the firms. And this leads +right into the next part of + +the problem. + +It asks us, can this be a long +run equilibrium where we have + +these prices, quantities, +and profits? + +And why or why not? + +And how will the supply +side of the market + +adjust in the long run? + +Now when other firms are +considering entering the + +market, the only thing that +they're going to consider is + +they're going to consider, is a +firm that's existing in the + +market currently +making profit? + +If they're not currently making +profit, then the firm + +that's considering entering +would have to have a better + +technology, a better way of +producing at lower cost, to + +enter the market and +be able to actually + +produce with a profit. + +But if there is profit being +made, in this case 2.25 for + +each firm, then more and more +firms are going to enter until + +profits are driven down to 0. + +So is this a long +run equilibrium? + +The answer is no. + +And why not? + +More firms are going to enter on +the supply side until we're + +driven to equilibrium. + +The last part that we're going +to do is we're going to do + +part H. Part H asks us, what +is going to be the price in + +the long run? + +How many firms will +be present in this + +market in the long run? + +And how much will each +firm produce? + +Now in the long run, we know +that profits are going to be + +driven down to 0, and that each +firm is going to have to + +be leaner and meaner. + +They're going to have to produce +at maximum efficiency + +to be competitive within +the market. + +So if we go back to the graph +that we started with, we can + +look at, at which point are +firms operating optimally? + +It's when marginal cost is equal +to average cost. It's at + +this critical p star that +we calculated to + +be equal to 8 earlier. + +So in the long run, all the +firms are going to have to be + +lean and mean. + +They're going to have to operate +at a very low average + +cost. And we're going to +calculate how many firms are + +going to be in the market +producing at this point where + +marginal cost intersects +average cost. + +So to start off H, we know that +p is going to be equal to + +the minimum of average cost, +which we calculated in one of + +the earlier parts of the problem +to be equal to 8. + +When we have this equal to 8, +we can plug-in to our demand + +curve that price. + +And we can find that the +quantity demanded is going to + +be equal to 12. + +Now what we can do now is we can +go back and we can look at + +the individual supply +curve for each firm. + +And each firm, when we had our +individual supply curves that + +we calculated in the first part +of the problem, had a + +supply function that was equal +to q equals p divided by 8. + +And in this case, if we know +that the price when the firms + +are operating optimally is equal +to 8, then we know that + +each firm is going +to be producing + +one unit of the good. + +So to find the total number of +firms, we just have to take + +this aggregated amount, the +total amount that's being + +produced, and divide through +by the amount each firm is + +producing to find out the number +of firms that have to + +be producing. + +So in the long run, we're going +to have 12 firms each + +producing one unit at a price +of 8, which is the optimal + +price where marginal cost is +equal to the minimum of the + +average cost. So just to +summarize what this problem + +had us look at, we looked at the +case where we had instead + +of just one firm, we +had multiple firms + +operating in a market. + +We saw that when we have +multiple firms operating that + +if there's any economic profit +that more firms are going to + +enter until the firms that exist +in the market are forced + +to operate optimally with +no economic profit. + +I hope that you found this +problem helpful. + +And go ahead and again, you can +do the earlier parts, and + +you can look to PSET 4 +Problem Number 3 for + +help on those problems. \ No newline at end of file diff --git a/PJ_5VNvJGtA.txt b/PJ_5VNvJGtA.txt new file mode 100644 index 0000000000000000000000000000000000000000..ca1fa3fa3a75695c854352bfc7889d89d6d7695f --- /dev/null +++ b/PJ_5VNvJGtA.txt @@ -0,0 +1,13253 @@ +align:start position:0% + +okay so let's get started on today's + + align:start position:0% +okay so let's get started on today's + + + align:start position:0% +okay so let's get started on today's +lecture um last lecture I left you off + + align:start position:0% +lecture um last lecture I left you off + + + align:start position:0% +lecture um last lecture I left you off +with the promise of bigger and better + + align:start position:0% +with the promise of bigger and better + + + align:start position:0% +with the promise of bigger and better +algorithms to do what we've been trying + + align:start position:0% +algorithms to do what we've been trying + + + align:start position:0% +algorithms to do what we've been trying +to do which is to approximate square + + align:start position:0% +to do which is to approximate square + + + align:start position:0% +to do which is to approximate square +roots and things like that so today will + + align:start position:0% +roots and things like that so today will + + + align:start position:0% +roots and things like that so today will +be uh the introduction of our last + + align:start position:0% +be uh the introduction of our last + + + align:start position:0% +be uh the introduction of our last +algorithm for a bit before we'll start + + align:start position:0% +algorithm for a bit before we'll start + + + align:start position:0% +algorithm for a bit before we'll start +talking about more python syntax but + + align:start position:0% +talking about more python syntax but + + + align:start position:0% +talking about more python syntax but +today we're going to introduce the + + align:start position:0% +today we're going to introduce the + + + align:start position:0% +today we're going to introduce the +bisection search algorithm okay but + + align:start position:0% +bisection search algorithm okay but + + + align:start position:0% +bisection search algorithm okay but +before we get into that let's try to + + align:start position:0% +before we get into that let's try to + + + align:start position:0% +before we get into that let's try to +remember where we left off last time so + + align:start position:0% +remember where we left off last time so + + + align:start position:0% +remember where we left off last time so +last time we talked about floating Point + + align:start position:0% +last time we talked about floating Point + + + align:start position:0% +last time we talked about floating Point +numbers and then we talked about + + align:start position:0% +numbers and then we talked about + + + align:start position:0% +numbers and then we talked about +approximation algorithms right so the + + align:start position:0% +approximation algorithms right so the + + + align:start position:0% +approximation algorithms right so the +reason why we talked about floating + + align:start position:0% +reason why we talked about floating + + + align:start position:0% +reason why we talked about floating +Point numbers is because we wanted to + + align:start position:0% +Point numbers is because we wanted to + + + align:start position:0% +Point numbers is because we wanted to +come up with an algorithm that was + + align:start position:0% +come up with an algorithm that was + + + align:start position:0% +come up with an algorithm that was +better than guess and check right guess + + align:start position:0% +better than guess and check right guess + + + align:start position:0% +better than guess and check right guess +and check was really limiting we were + + align:start position:0% +and check was really limiting we were + + + align:start position:0% +and check was really limiting we were +basically limited to some exhaustive + + align:start position:0% +basically limited to some exhaustive + + + align:start position:0% +basically limited to some exhaustive +number of uh potential Solutions but we + + align:start position:0% +number of uh potential Solutions but we + + + align:start position:0% +number of uh potential Solutions but we +didn't just want to have an exhaustive + + align:start position:0% +didn't just want to have an exhaustive + + + align:start position:0% +didn't just want to have an exhaustive +set to look through for a solution we + + align:start position:0% +set to look through for a solution we + + + align:start position:0% +set to look through for a solution we +wanted to be able to actually come up + + align:start position:0% +wanted to be able to actually come up + + + align:start position:0% +wanted to be able to actually come up +with an approximation to solve our + + align:start position:0% +with an approximation to solve our + + + align:start position:0% +with an approximation to solve our +problems right and so we talked about + + align:start position:0% +problems right and so we talked about + + + align:start position:0% +problems right and so we talked about +floating Point numbers because we said + + align:start position:0% +floating Point numbers because we said + + + align:start position:0% +floating Point numbers because we said +well instead of having for example + + align:start position:0% +well instead of having for example + + + align:start position:0% +well instead of having for example +integer increments when we searched for + + align:start position:0% +integer increments when we searched for + + + align:start position:0% +integer increments when we searched for +uh uh square roots of values let's try + + align:start position:0% +uh uh square roots of values let's try + + + align:start position:0% +uh uh square roots of values let's try +to have smaller increments okay and so + + align:start position:0% +to have smaller increments okay and so + + + align:start position:0% +to have smaller increments okay and so +if we have smaller increments than an + + align:start position:0% +if we have smaller increments than an + + + align:start position:0% +if we have smaller increments than an +integ integ ger well we were starting to + + align:start position:0% +integ integ ger well we were starting to + + + align:start position:0% +integ integ ger well we were starting to +look at incrementing by 0.1 or 0. 25 or + + align:start position:0% +look at incrementing by 0.1 or 0. 25 or + + + align:start position:0% +look at incrementing by 0.1 or 0. 25 or +0.001 whatever we + + align:start position:0% +0.001 whatever we + + + align:start position:0% +0.001 whatever we +want and so then since we started + + align:start position:0% +want and so then since we started + + + align:start position:0% +want and so then since we started +talking about these floating Point + + align:start position:0% +talking about these floating Point + + + align:start position:0% +talking about these floating Point +numbers it was important to kind of + + align:start position:0% +numbers it was important to kind of + + + align:start position:0% +numbers it was important to kind of +understand what happens behind the + + align:start position:0% +understand what happens behind the + + + align:start position:0% +understand what happens behind the +scenes and we saw that these floating + + align:start position:0% +scenes and we saw that these floating + + + align:start position:0% +scenes and we saw that these floating +Point numbers can't actually be + + align:start position:0% +Point numbers can't actually be + + + align:start position:0% +Point numbers can't actually be +represented in memory directly exactly + + align:start position:0% +represented in memory directly exactly + + + align:start position:0% +represented in memory directly exactly +right there's always for the majority of + + align:start position:0% +right there's always for the majority of + + + align:start position:0% +right there's always for the majority of +the numbers there's going to be some + + align:start position:0% +the numbers there's going to be some + + + align:start position:0% +the numbers there's going to be some +sort of rounding that happens when that + + align:start position:0% +sort of rounding that happens when that + + + align:start position:0% +sort of rounding that happens when that +number is stored in memory and the + + align:start position:0% +number is stored in memory and the + + + align:start position:0% +number is stored in memory and the +rounding is very small it's something + + align:start position:0% +rounding is very small it's something + + + align:start position:0% +rounding is very small it's something +like 10 to the -10 or or sorry 10 to two + + align:start position:0% +like 10 to the -10 or or sorry 10 to two + + + align:start position:0% +like 10 to the -10 or or sorry 10 to two +2 to the -32 which is approximately 10 + + align:start position:0% +2 to the -32 which is approximately 10 + + + align:start position:0% +2 to the -32 which is approximately 10 +to the -10 which seems small but we saw + + align:start position:0% +to the -10 which seems small but we saw + + + align:start position:0% +to the -10 which seems small but we saw +even with just a loop that added 0.1 to + + align:start position:0% +even with just a loop that added 0.1 to + + + align:start position:0% +even with just a loop that added 0.1 to +itself 10 times we were already getting + + align:start position:0% +itself 10 times we were already getting + + + align:start position:0% +itself 10 times we were already getting +very surprising results right so the + + align:start position:0% +very surprising results right so the + + + align:start position:0% +very surprising results right so the +approximation + + align:start position:0% +approximation + + + align:start position:0% +approximation +method introduced the idea of yes we can + + align:start position:0% +method introduced the idea of yes we can + + + align:start position:0% +method introduced the idea of yes we can +get an approximation for the square root + + align:start position:0% +get an approximation for the square root + + + align:start position:0% +get an approximation for the square root +of a number but we can't check for + + align:start position:0% +of a number but we can't check for + + + align:start position:0% +of a number but we can't check for +equality we can't say I'm going to come + + align:start position:0% +equality we can't say I'm going to come + + + align:start position:0% +equality we can't say I'm going to come +up with this uh this approximation such + + align:start position:0% +up with this uh this approximation such + + + align:start position:0% +up with this uh this approximation such +that you know this approximation squared + + align:start position:0% +that you know this approximation squared + + + align:start position:0% +that you know this approximation squared +or whatever problem we're trying to + + align:start position:0% +or whatever problem we're trying to + + + align:start position:0% +or whatever problem we're trying to +solve is exactly equal to the number + + align:start position:0% +solve is exactly equal to the number + + + align:start position:0% +solve is exactly equal to the number +we're looking for so we had to have a + + align:start position:0% +we're looking for so we had to have a + + + align:start position:0% +we're looking for so we had to have a +little wiggle room and that wiggle room + + align:start position:0% +little wiggle room and that wiggle room + + + align:start position:0% +little wiggle room and that wiggle room +came in the form of an Epsilon right so + + align:start position:0% +came in the form of an Epsilon right so + + + align:start position:0% +came in the form of an Epsilon right so +we were approximating a solution uh by + + align:start position:0% +we were approximating a solution uh by + + + align:start position:0% +we were approximating a solution uh by +basically saying does this solution come + + align:start position:0% +basically saying does this solution come + + + align:start position:0% +basically saying does this solution come +within plus or minus Epsilon of my + + align:start position:0% +within plus or minus Epsilon of my + + + align:start position:0% +within plus or minus Epsilon of my +desired + + align:start position:0% +desired + + + align:start position:0% +desired +value so we came up with a nice + + align:start position:0% +value so we came up with a nice + + + align:start position:0% +value so we came up with a nice +algorithm the approximation algorithm + + align:start position:0% +algorithm the approximation algorithm + + + align:start position:0% +algorithm the approximation algorithm +and we we tested on a bunch of different + + align:start position:0% +and we we tested on a bunch of different + + + align:start position:0% +and we we tested on a bunch of different +values right we were incrementing a + + align:start position:0% +values right we were incrementing a + + + align:start position:0% +values right we were incrementing a +small increment a little bit at a time + + align:start position:0% +small increment a little bit at a time + + + align:start position:0% +small increment a little bit at a time +and for the problem where we're trying + + align:start position:0% +and for the problem where we're trying + + + align:start position:0% +and for the problem where we're trying +to find approximate the square root of + + align:start position:0% +to find approximate the square root of + + + align:start position:0% +to find approximate the square root of +some value X we were saying well I'm + + align:start position:0% +some value X we were saying well I'm + + + align:start position:0% +some value X we were saying well I'm +going to keep making these small + + align:start position:0% +going to keep making these small + + + align:start position:0% +going to keep making these small +incremental changes to my guess until I + + align:start position:0% +incremental changes to my guess until I + + + align:start position:0% +incremental changes to my guess until I +come within plus or minus Epsilon of my + + align:start position:0% +come within plus or minus Epsilon of my + + + align:start position:0% +come within plus or minus Epsilon of my +actual value right the guest squared was + + align:start position:0% +actual value right the guest squared was + + + align:start position:0% +actual value right the guest squared was +within plus or minus Epsilon of my X and + + align:start position:0% +within plus or minus Epsilon of my X and + + + align:start position:0% +within plus or minus Epsilon of my X and +this was the nice slide that we let that + + align:start position:0% +this was the nice slide that we let that + + + align:start position:0% +this was the nice slide that we let that +we that was kind of the the you know the + + align:start position:0% +we that was kind of the the you know the + + + align:start position:0% +we that was kind of the the you know the +like the Big Bang of last lecture where + + align:start position:0% +like the Big Bang of last lecture where + + + align:start position:0% +like the Big Bang of last lecture where +we said we have to be careful about the + + align:start position:0% +we said we have to be careful about the + + + align:start position:0% +we said we have to be careful about the +way we write these approximation + + align:start position:0% +way we write these approximation + + + align:start position:0% +way we write these approximation +algorithms because we might over uh + + align:start position:0% +algorithms because we might over uh + + + align:start position:0% +algorithms because we might over uh +overshoot our Epsilon so if this is um + + align:start position:0% +overshoot our Epsilon so if this is um + + + align:start position:0% +overshoot our Epsilon so if this is um +our guess and this is a guess squared + + align:start position:0% +our guess and this is a guess squared + + + align:start position:0% +our guess and this is a guess squared +the blue arrow increments normally right + + align:start position:0% +the blue arrow increments normally right + + + align:start position:0% +the blue arrow increments normally right +whatever increment we choose but then + + align:start position:0% +whatever increment we choose but then + + + align:start position:0% +whatever increment we choose but then +it's possible that at some point the + + align:start position:0% +it's possible that at some point the + + + align:start position:0% +it's possible that at some point the +guest squar comes just short of the + + align:start position:0% +guest squar comes just short of the + + + align:start position:0% +guest squar comes just short of the +Epsilon right the lower the the uh x + + align:start position:0% +Epsilon right the lower the the uh x + + + align:start position:0% +Epsilon right the lower the the uh x +minus + + align:start position:0% +minus + + + align:start position:0% +minus +Epsilon and with the following increment + + align:start position:0% +Epsilon and with the following increment + + + align:start position:0% +Epsilon and with the following increment +the guess squared becomes just past X + + align:start position:0% +the guess squared becomes just past X + + + align:start position:0% +the guess squared becomes just past X +Plus Epsilon and so the code that we + + align:start position:0% +Plus Epsilon and so the code that we + + + align:start position:0% +Plus Epsilon and so the code that we +ended up writing right which was it made + + align:start position:0% +ended up writing right which was it made + + + align:start position:0% +ended up writing right which was it made +sense right when we wrote it actually + + align:start position:0% +sense right when we wrote it actually + + + align:start position:0% +sense right when we wrote it actually +ended up giving us an infinite Loop + + align:start position:0% +ended up giving us an infinite Loop + + + align:start position:0% +ended up giving us an infinite Loop +because it never stopped we never were + + align:start position:0% +because it never stopped we never were + + + align:start position:0% +because it never stopped we never were +within that plus minus Epsilon and so we + + align:start position:0% +within that plus minus Epsilon and so we + + + align:start position:0% +within that plus minus Epsilon and so we +would just keep making guesses from + + align:start position:0% +would just keep making guesses from + + + align:start position:0% +would just keep making guesses from +there on out okay so we ended up uh + + align:start position:0% +there on out okay so we ended up uh + + + align:start position:0% +there on out okay so we ended up uh +getting an infinite Loop for our + + align:start position:0% +getting an infinite Loop for our + + + align:start position:0% +getting an infinite Loop for our +program the solution was to take a + + align:start position:0% +program the solution was to take a + + + align:start position:0% +program the solution was to take a +little bit of uh of code from guess and + + align:start position:0% +little bit of uh of code from guess and + + + align:start position:0% +little bit of uh of code from guess and +check and said let's add an additional + + align:start position:0% +check and said let's add an additional + + + align:start position:0% +check and said let's add an additional +little sanity check stopping condition + + align:start position:0% +little sanity check stopping condition + + + align:start position:0% +little sanity check stopping condition +right and so everything except for this + + align:start position:0% +right and so everything except for this + + + align:start position:0% +right and so everything except for this +box was the approximation algorithm and + + align:start position:0% +box was the approximation algorithm and + + + align:start position:0% +box was the approximation algorithm and +we added the thing that I've boxed here + + align:start position:0% +we added the thing that I've boxed here + + + align:start position:0% +we added the thing that I've boxed here +as our sanity check that we grabbed from + + align:start position:0% +as our sanity check that we grabbed from + + + align:start position:0% +as our sanity check that we grabbed from +the guest and check algorithm that + + align:start position:0% +the guest and check algorithm that + + + align:start position:0% +the guest and check algorithm that +basically said if we've made a guess + + align:start position:0% +basically said if we've made a guess + + + align:start position:0% +basically said if we've made a guess +that's that is just past the reasonable + + align:start position:0% +that's that is just past the reasonable + + + align:start position:0% +that's that is just past the reasonable +uh number a reasonable guess we know + + align:start position:0% +uh number a reasonable guess we know + + + align:start position:0% +uh number a reasonable guess we know +that all the guesses from here on out + + align:start position:0% +that all the guesses from here on out + + + align:start position:0% +that all the guesses from here on out +will also be unreasonable and so there's + + align:start position:0% +will also be unreasonable and so there's + + + align:start position:0% +will also be unreasonable and so there's +no need to keep searching and that + + align:start position:0% +no need to keep searching and that + + + align:start position:0% +no need to keep searching and that +condition will cause us to stop um stop + + align:start position:0% +condition will cause us to stop um stop + + + align:start position:0% +condition will cause us to stop um stop +our infinite Loop or our potential + + align:start position:0% +our infinite Loop or our potential + + + align:start position:0% +our infinite Loop or our potential +infinite Loop okay so this guess squared + + align:start position:0% +infinite Loop okay so this guess squared + + + align:start position:0% +infinite Loop okay so this guess squared +is less than or equal to X basically + + align:start position:0% +is less than or equal to X basically + + + align:start position:0% +is less than or equal to X basically +says stop when we go past the last re + + align:start position:0% +says stop when we go past the last re + + + align:start position:0% +says stop when we go past the last re +reasonable guess and that condition plus + + align:start position:0% +reasonable guess and that condition plus + + + align:start position:0% +reasonable guess and that condition plus +the regular condition from an + + align:start position:0% +the regular condition from an + + + align:start position:0% +the regular condition from an +approximation algorithm which says I + + align:start position:0% +approximation algorithm which says I + + + align:start position:0% +approximation algorithm which says I +want my guess squar to be plus or minus + + align:start position:0% +want my guess squar to be plus or minus + + + align:start position:0% +want my guess squar to be plus or minus +Epsilon of the actual x uh + + align:start position:0% +Epsilon of the actual x uh + + + align:start position:0% +Epsilon of the actual x uh +those two conditions Together made up my + + align:start position:0% +those two conditions Together made up my + + + align:start position:0% +those two conditions Together made up my +algorithm and it's that that's the + + align:start position:0% +algorithm and it's that that's the + + + align:start position:0% +algorithm and it's that that's the +algorithm it's just this Loop right here + + align:start position:0% +algorithm it's just this Loop right here + + + align:start position:0% +algorithm it's just this Loop right here +this y loop with this increment okay so + + align:start position:0% +this y loop with this increment okay so + + + align:start position:0% +this y loop with this increment okay so +it looks really really simple and so + + align:start position:0% +it looks really really simple and so + + + align:start position:0% +it looks really really simple and so +what we ended up having is these two + + align:start position:0% +what we ended up having is these two + + + align:start position:0% +what we ended up having is these two +conditions right so I want to be within + + align:start position:0% +conditions right so I want to be within + + + align:start position:0% +conditions right so I want to be within +Epsilon and I want to still be making + + align:start position:0% +Epsilon and I want to still be making + + + align:start position:0% +Epsilon and I want to still be making +reasonable guesses to be uh sorry I want + + align:start position:0% +reasonable guesses to be uh sorry I want + + + align:start position:0% +reasonable guesses to be uh sorry I want +to be sorry outside of the bounds of + + align:start position:0% +to be sorry outside of the bounds of + + + align:start position:0% +to be sorry outside of the bounds of +Epsilon and still be making reasonable + + align:start position:0% +Epsilon and still be making reasonable + + + align:start position:0% +Epsilon and still be making reasonable +guesses that's the condition that causes + + align:start position:0% +guesses that's the condition that causes + + + align:start position:0% +guesses that's the condition that causes +me to keep making more guesses and when + + align:start position:0% +me to keep making more guesses and when + + + align:start position:0% +me to keep making more guesses and when +either either one of these becomes false + + align:start position:0% +either either one of these becomes false + + + align:start position:0% +either either one of these becomes false +I'm going to stop making + + align:start position:0% +I'm going to stop making + + + align:start position:0% +I'm going to stop making +guesses and that's what the if else down + + align:start position:0% +guesses and that's what the if else down + + + align:start position:0% +guesses and that's what the if else down +here says it says one of these + + align:start position:0% +here says it says one of these + + + align:start position:0% +here says it says one of these +conditions became false either this one + + align:start position:0% +conditions became false either this one + + + align:start position:0% +conditions became false either this one +I'm making unreasonable guesses now or + + align:start position:0% +I'm making unreasonable guesses now or + + + align:start position:0% +I'm making unreasonable guesses now or +I've come within plus or minus Epsilon + + align:start position:0% +I've come within plus or minus Epsilon + + + align:start position:0% +I've come within plus or minus Epsilon +so which one is it so here I'm making + + align:start position:0% +so which one is it so here I'm making + + + align:start position:0% +so which one is it so here I'm making +unreasonable guesses so I've exited the + + align:start position:0% +unreasonable guesses so I've exited the + + + align:start position:0% +unreasonable guesses so I've exited the +loop because I've gone too far in which + + align:start position:0% +loop because I've gone too far in which + + + align:start position:0% +loop because I've gone too far in which +case I print I failed to find the square + + align:start position:0% +case I print I failed to find the square + + + align:start position:0% +case I print I failed to find the square +root um and otherwise I've exited + + align:start position:0% +root um and otherwise I've exited + + + align:start position:0% +root um and otherwise I've exited +because I am now within plus or minus + + align:start position:0% +because I am now within plus or minus + + + align:start position:0% +because I am now within plus or minus +Epsilon so let me just run the code to + + align:start position:0% +Epsilon so let me just run the code to + + + align:start position:0% +Epsilon so let me just run the code to +remind ourselves what it looked + + align:start position:0% +remind ourselves what it looked + + + align:start position:0% +remind ourselves what it looked +like so here we're trying to find uh + + align:start position:0% +like so here we're trying to find uh + + + align:start position:0% +like so here we're trying to find uh +54321 was this Troublesome value being + + align:start position:0% +54321 was this Troublesome value being + + + align:start position:0% +54321 was this Troublesome value being +within plus or minus 01 right our guest + + align:start position:0% +within plus or minus 01 right our guest + + + align:start position:0% +within plus or minus 01 right our guest +squared to be plusus 01 of + + align:start position:0% +squared to be plusus 01 of + + + align:start position:0% +squared to be plusus 01 of +54321 our increment was seemed really + + align:start position:0% +54321 our increment was seemed really + + + align:start position:0% +54321 our increment was seemed really +small + + align:start position:0% +small + + + align:start position:0% +small +00001 but when we ran + + align:start position:0% +00001 but when we ran + + + align:start position:0% +00001 but when we ran +it took a couple seconds and we made + + align:start position:0% +it took a couple seconds and we made + + + align:start position:0% +it took a couple seconds and we made +about 2.3 million guesses and the code + + align:start position:0% +about 2.3 million guesses and the code + + + align:start position:0% +about 2.3 million guesses and the code +says we failed to find the square root + + align:start position:0% +says we failed to find the square root + + + align:start position:0% +says we failed to find the square root +right and we're also reporting what the + + align:start position:0% +right and we're also reporting what the + + + align:start position:0% +right and we're also reporting what the +last guess was and what the last guess + + align:start position:0% +last guess was and what the last guess + + + align:start position:0% +last guess was and what the last guess +squared was as + + align:start position:0% +squared was as + + + align:start position:0% +squared was as +well so what's the solution to this + + align:start position:0% +well so what's the solution to this + + + align:start position:0% +well so what's the solution to this +right the solution was well we can make + + align:start position:0% +right the solution was well we can make + + + align:start position:0% +right the solution was well we can make +our Epsilon bigger right so if we made + + align:start position:0% +our Epsilon bigger right so if we made + + + align:start position:0% +our Epsilon bigger right so if we made +our Epsilon be one so if we wanted to be + + align:start position:0% +our Epsilon be one so if we wanted to be + + + align:start position:0% +our Epsilon be one so if we wanted to be +within plus or minus one of 54 + + align:start position:0% +within plus or minus one of 54 + + + align:start position:0% +within plus or minus one of 54 +4,321 yeah that code works right it + + align:start position:0% +4,321 yeah that code works right it + + + align:start position:0% +4,321 yeah that code works right it +didn't fail it made still about 2.3 + + align:start position:0% +didn't fail it made still about 2.3 + + + align:start position:0% +didn't fail it made still about 2.3 +million guesses and it came up with this + + align:start position:0% +million guesses and it came up with this + + + align:start position:0% +million guesses and it came up with this +estimate so as soon as we came with an + + align:start position:0% +estimate so as soon as we came with an + + + align:start position:0% +estimate so as soon as we came with an +Epsilon that boundary we stopped the + + align:start position:0% +Epsilon that boundary we stopped the + + + align:start position:0% +Epsilon that boundary we stopped the +program right it didn't try to do better + + align:start position:0% +program right it didn't try to do better + + + align:start position:0% +program right it didn't try to do better +it didn't try to get closer to + + align:start position:0% +it didn't try to get closer to + + + align:start position:0% +it didn't try to get closer to +X the other solution if we were unhappy + + align:start position:0% +X the other solution if we were unhappy + + + align:start position:0% +X the other solution if we were unhappy +with the fact that we failed was to make + + align:start position:0% +with the fact that we failed was to make + + + align:start position:0% +with the fact that we failed was to make +our steps + + align:start position:0% +our steps + + + align:start position:0% +our steps +smaller but what's the problem if we + + align:start position:0% +smaller but what's the problem if we + + + align:start position:0% +smaller but what's the problem if we +make our steps smaller you guys remember + + align:start position:0% +make our steps smaller you guys remember + + + align:start position:0% +make our steps smaller you guys remember +when I run the + + align:start position:0% + + + + align:start position:0% + +program yeah it takes longer and do you + + align:start position:0% +program yeah it takes longer and do you + + + align:start position:0% +program yeah it takes longer and do you +can you approximate how much longer + + align:start position:0% +can you approximate how much longer + + + align:start position:0% +can you approximate how much longer +it'll + + align:start position:0% + + + + align:start position:0% + +take I decreased my step size by 10 so + + align:start position:0% +take I decreased my step size by 10 so + + + align:start position:0% +take I decreased my step size by 10 so +every one step I made last run I'm now + + align:start position:0% +every one step I made last run I'm now + + + align:start position:0% +every one step I made last run I'm now +going to take 10 steps right so I'm + + align:start position:0% +going to take 10 steps right so I'm + + + align:start position:0% +going to take 10 steps right so I'm +waiting basically what 15 20 seconds + + align:start position:0% +waiting basically what 15 20 seconds + + + align:start position:0% +waiting basically what 15 20 seconds +here if uh the last run took two seconds + + align:start position:0% +here if uh the last run took two seconds + + + align:start position:0% +here if uh the last run took two seconds +to run and now I've also doubled the + + align:start position:0% +to run and now I've also doubled the + + + align:start position:0% +to run and now I've also doubled the +number of guesses right or sorry not + + align:start position:0% +number of guesses right or sorry not + + + align:start position:0% +number of guesses right or sorry not +double A 10 time I'm making 10 times the + + align:start position:0% +double A 10 time I'm making 10 times the + + + align:start position:0% +double A 10 time I'm making 10 times the +number of guesses 23 million as opposed + + align:start position:0% +number of guesses 23 million as opposed + + + align:start position:0% +number of guesses 23 million as opposed +to 2.3 million but the code didn't fail + + align:start position:0% +to 2.3 million but the code didn't fail + + + align:start position:0% +to 2.3 million but the code didn't fail +right it found something that's pretty + + align:start position:0% +right it found something that's pretty + + + align:start position:0% +right it found something that's pretty +close to the square root of 54,2 31 + + align:start position:0% +close to the square root of 54,2 31 + + + align:start position:0% +close to the square root of 54,2 31 + + align:start position:0% + + + align:start position:0% +okay so that's where we left off and I + + align:start position:0% +okay so that's where we left off and I + + + align:start position:0% +okay so that's where we left off and I +don't know about you but I don't want to + + align:start position:0% +don't know about you but I don't want to + + + align:start position:0% +don't know about you but I don't want to +wait 20 seconds to figure out what the + + align:start position:0% +wait 20 seconds to figure out what the + + + align:start position:0% +wait 20 seconds to figure out what the +square root of 54,000 is that seems like + + align:start position:0% +square root of 54,000 is that seems like + + + align:start position:0% +square root of 54,000 is that seems like +an unreasonably long amount of time to + + align:start position:0% +an unreasonably long amount of time to + + + align:start position:0% +an unreasonably long amount of time to +come come up with uh with an + + align:start position:0% +come come up with uh with an + + + align:start position:0% +come come up with uh with an +approximation right and we don't wait + + align:start position:0% +approximation right and we don't wait + + + align:start position:0% +approximation right and we don't wait +that long when we do it on the computer + + align:start position:0% +that long when we do it on the computer + + + align:start position:0% +that long when we do it on the computer +or when we do it on the calculator and + + align:start position:0% +or when we do it on the calculator and + + + align:start position:0% +or when we do it on the calculator and +so that leads me to the bisection search + + align:start position:0% +so that leads me to the bisection search + + + align:start position:0% +so that leads me to the bisection search +algorithm it's going to be a better way + + align:start position:0% +algorithm it's going to be a better way + + + align:start position:0% +algorithm it's going to be a better way +for us to solve certain types of + + align:start position:0% +for us to solve certain types of + + + align:start position:0% +for us to solve certain types of +problems much faster but only certain + + align:start position:0% +problems much faster but only certain + + + align:start position:0% +problems much faster but only certain +types of problems so to motivate the + + align:start position:0% +types of problems so to motivate the + + + align:start position:0% +types of problems so to motivate the +bisection search before we even look at + + align:start position:0% +bisection search before we even look at + + + align:start position:0% +bisection search before we even look at +code I just want to give you a bit of + + align:start position:0% +code I just want to give you a bit of + + + align:start position:0% +code I just want to give you a bit of +motivation with a few different examples + + align:start position:0% +motivation with a few different examples + + + align:start position:0% +motivation with a few different examples +okay the first one is I'm going to give + + align:start position:0% +okay the first one is I'm going to give + + + align:start position:0% +okay the first one is I'm going to give +you guys a chance to win some money okay + + align:start position:0% +you guys a chance to win some money okay + + + align:start position:0% +you guys a chance to win some money okay +so suppose I put a $100 bill at one page + + align:start position:0% +so suppose I put a $100 bill at one page + + + align:start position:0% +so suppose I put a $100 bill at one page +in this book okay this is uh actually + + align:start position:0% +in this book okay this is uh actually + + + align:start position:0% +in this book okay this is uh actually +the last Edition not the Edition we're + + align:start position:0% +the last Edition not the Edition we're + + + align:start position:0% +the last Edition not the Edition we're +using this year but um I don't have this + + align:start position:0% +using this year but um I don't have this + + + align:start position:0% +using this year but um I don't have this +year's Edition unfortunately in my + + align:start position:0% +year's Edition unfortunately in my + + + align:start position:0% +year's Edition unfortunately in my +office so this P this book is 448 pages + + align:start position:0% +office so this P this book is 448 pages + + + align:start position:0% +office so this P this book is 448 pages +long okay and I've put some money in + + align:start position:0% +long okay and I've put some money in + + + align:start position:0% +long okay and I've put some money in +this book and if you can guess where the + + align:start position:0% +this book and if you can guess where the + + + align:start position:0% +this book and if you can guess where the +money is in eight or fewer guesses I + + align:start position:0% +money is in eight or fewer guesses I + + + align:start position:0% +money is in eight or fewer guesses I +will give you the money and if you + + align:start position:0% +will give you the money and if you + + + align:start position:0% +will give you the money and if you +you get an F not really is this a game + + align:start position:0% +you get an F not really is this a game + + + align:start position:0% +you get an F not really is this a game +anyone would want to + + align:start position:0% +anyone would want to + + + align:start position:0% +anyone would want to +play no that's what I thought and in + + align:start position:0% +play no that's what I thought and in + + + align:start position:0% +play no that's what I thought and in +fact your chances of winning are about + + align:start position:0% +fact your chances of winning are about + + + align:start position:0% +fact your chances of winning are about +one and 56 okay and it I I I yeah I I + + align:start position:0% +one and 56 okay and it I I I yeah I I + + + align:start position:0% +one and 56 okay and it I I I yeah I I +don't want to play that game either but + + align:start position:0% +don't want to play that game either but + + + align:start position:0% +don't want to play that game either but +now let's say I give you some additional + + align:start position:0% +now let's say I give you some additional + + + align:start position:0% +now let's say I give you some additional +information okay with each guess you + + align:start position:0% +information okay with each guess you + + + align:start position:0% +information okay with each guess you +make I will tell you whether you are + + align:start position:0% +make I will tell you whether you are + + + align:start position:0% +make I will tell you whether you are +correct too low or too high + + align:start position:0% +correct too low or too high + + + align:start position:0% +correct too low or too high +okay so I give you some additional + + align:start position:0% +okay so I give you some additional + + + align:start position:0% +okay so I give you some additional +information is this a game that now you + + align:start position:0% +information is this a game that now you + + + align:start position:0% +information is this a game that now you +would want to + + align:start position:0% +would want to + + + align:start position:0% +would want to +play would anyone like to play the game + + align:start position:0% +play would anyone like to play the game + + + align:start position:0% +play would anyone like to play the game +with + + align:start position:0% +with + + + align:start position:0% +with +me you want to play the game okay all + + align:start position:0% +me you want to play the game okay all + + + align:start position:0% +me you want to play the game okay all +right so you're up + + align:start position:0% +right so you're up + + + align:start position:0% +right so you're up +okay all right so I'm going to write + + align:start position:0% +okay all right so I'm going to write + + + align:start position:0% +okay all right so I'm going to write +down your guesses because you only have + + align:start position:0% +down your guesses because you only have + + + align:start position:0% +down your guesses because you only have +eight all right you remember that + + align:start position:0% +eight all right you remember that + + + align:start position:0% +eight all right you remember that +there's only eight guesses all right so + + align:start position:0% +there's only eight guesses all right so + + + align:start position:0% +there's only eight guesses all right so +what's your first gu there's 448 pages + + align:start position:0% +what's your first gu there's 448 pages + + + align:start position:0% +what's your first gu there's 448 pages +so between yeah you pick one to 448 + + align:start position:0% +so between yeah you pick one to 448 + + + align:start position:0% +so between yeah you pick one to 448 +what's your first guess 224 + + align:start position:0% +what's your first guess 224 + + + align:start position:0% +what's your first guess 224 +224 all right smack in the middle right + + align:start position:0% +224 all right smack in the middle right + + + align:start position:0% +224 all right smack in the middle right +there all right 224 don't + + align:start position:0% +there all right 224 don't + + + align:start position:0% +there all right 224 don't +look all + + align:start position:0% + + + + align:start position:0% + +right no money all right so but now I + + align:start position:0% +right no money all right so but now I + + + align:start position:0% +right no money all right so but now I +give you extra information the guess is + + align:start position:0% +give you extra information the guess is + + + align:start position:0% +give you extra information the guess is +too high my guess was too high yes your + + align:start position:0% +too high my guess was too high yes your + + + align:start position:0% +too high my guess was too high yes your +guess was too high so not 224 112 112 So + + align:start position:0% +guess was too high so not 224 112 112 So + + + align:start position:0% +guess was too high so not 224 112 112 So +you want to go here 112 all right that's + + align:start position:0% +you want to go here 112 all right that's + + + align:start position:0% +you want to go here 112 all right that's +two guesses + + align:start position:0% + + + + align:start position:0% + +now nope the guess is too high as well + + align:start position:0% +now nope the guess is too high as well + + + align:start position:0% +now nope the guess is too high as well +still too high still too + + align:start position:0% + + + + align:start position:0% + +high + + align:start position:0% +high + + + align:start position:0% +high +56 okay so here somewhere + + align:start position:0% +56 okay so here somewhere + + + align:start position:0% +56 okay so here somewhere +okay all right + + align:start position:0% + + + + align:start position:0% + +56 the guest is too + + align:start position:0% + + + + align:start position:0% + +high still too + + align:start position:0% + + + + align:start position:0% + +high 28 all right 28 I'm going to start + + align:start position:0% +high 28 all right 28 I'm going to start + + + align:start position:0% +high 28 all right 28 I'm going to start +writing up here + + align:start position:0% +writing up here + + + align:start position:0% +writing up here +28 you have one two three you're at four + + align:start position:0% +28 you have one two three you're at four + + + align:start position:0% +28 you have one two three you're at four +guesses now 28 okay + + align:start position:0% +guesses now 28 okay + + + align:start position:0% +guesses now 28 okay +it + + align:start position:0% +it + + + align:start position:0% +it +[Music] + + align:start position:0% + + + + align:start position:0% + +is no wait I now I have to remember + + align:start position:0% +is no wait I now I have to remember + + + align:start position:0% +is no wait I now I have to remember +where I put it + + align:start position:0% +where I put it + + + align:start position:0% +where I put it +uh it's too high it's too high + + align:start position:0% +uh it's too high it's too high + + + align:start position:0% +uh it's too high it's too high +sorry still too high 14 14 okay 14 oh + + align:start position:0% +sorry still too high 14 14 okay 14 oh + + + align:start position:0% +sorry still too high 14 14 okay 14 oh +right + + align:start position:0% +right + + + align:start position:0% +right +there okay now + + align:start position:0% + + + + align:start position:0% + +14 now it's too low now that I + + align:start position:0% +14 now it's too low now that I + + + align:start position:0% +14 now it's too low now that I +remembered now that I remember where I + + align:start position:0% +remembered now that I remember where I + + + align:start position:0% +remembered now that I remember where I +actually put + + align:start position:0% +actually put + + + align:start position:0% +actually put +it it's too low turns out it's on page + + align:start position:0% +it it's too low turns out it's on page + + + align:start position:0% +it it's too low turns out it's on page +like + + align:start position:0% +like + + + align:start position:0% +like +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +400 between yeah 14 and 28 so now you + + align:start position:0% +400 between yeah 14 and 28 so now you + + + align:start position:0% +400 between yeah 14 and 28 so now you +know it's yeah 21 okay so right there 21 + + align:start position:0% +know it's yeah 21 okay so right there 21 + + + align:start position:0% +know it's yeah 21 okay so right there 21 +okay let's + + align:start position:0% + + + + align:start position:0% + +see guys I'm + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +shaking it's not a 100 but there is a + + align:start position:0% +shaking it's not a 100 but there is a + + + align:start position:0% +shaking it's not a 100 but there is a +one and a zero in it so there you go all + + align:start position:0% +one and a zero in it so there you go all + + + align:start position:0% +one and a zero in it so there you go all +right that was + + align:start position:0% +right that was + + + align:start position:0% +right that was +awesome so yes you I'm really glad you + + align:start position:0% +awesome so yes you I'm really glad you + + + align:start position:0% +awesome so yes you I'm really glad you +played and actually you only took seven + + align:start position:0% +played and actually you only took seven + + + align:start position:0% +played and actually you only took seven +guesses to get it so I could have + + align:start position:0% +guesses to get it so I could have + + + align:start position:0% +guesses to get it so I could have +probably um rigged it a little bit + + align:start position:0% +probably um rigged it a little bit + + + align:start position:0% +probably um rigged it a little bit +better because your chances of winning + + align:start position:0% +better because your chances of winning + + + align:start position:0% +better because your chances of winning +this game are about one and three okay + + align:start position:0% +this game are about one and three okay + + + align:start position:0% +this game are about one and three okay +and you and you did a really good job so + + align:start position:0% +and you and you did a really good job so + + + align:start position:0% +and you and you did a really good job so +what was your thought process basically + + align:start position:0% +what was your thought process basically + + + align:start position:0% +what was your thought process basically +and I think once you did a couple of the + + align:start position:0% +and I think once you did a couple of the + + + align:start position:0% +and I think once you did a couple of the +um anyone who maybe didn't think about + + align:start position:0% +um anyone who maybe didn't think about + + + align:start position:0% +um anyone who maybe didn't think about +this way and have figured it out you + + align:start position:0% +this way and have figured it out you + + + align:start position:0% +this way and have figured it out you +were basically guessing the halfway + + align:start position:0% +were basically guessing the halfway + + + align:start position:0% +were basically guessing the halfway +point right each time I told you too + + align:start position:0% +point right each time I told you too + + + align:start position:0% +point right each time I told you too +high or too low and so bisection search + + align:start position:0% +high or too low and so bisection search + + + align:start position:0% +high or too low and so bisection search +is a method that you can use to solve + + align:start position:0% +is a method that you can use to solve + + + align:start position:0% +is a method that you can use to solve +problems where there's some sort of + + align:start position:0% +problems where there's some sort of + + + align:start position:0% +problems where there's some sort of +order to the thing you're trying to + + align:start position:0% +order to the thing you're trying to + + + align:start position:0% +order to the thing you're trying to +search right so let's say we know uh our + + align:start position:0% +search right so let's say we know uh our + + + align:start position:0% +search right so let's say we know uh our +interval in this case in the book we + + align:start position:0% +interval in this case in the book we + + + align:start position:0% +interval in this case in the book we +knew that we had page one to to + + align:start position:0% +knew that we had page one to to + + + align:start position:0% +knew that we had page one to to +448 right so we had this low Point page + + align:start position:0% +448 right so we had this low Point page + + + align:start position:0% +448 right so we had this low Point page +one and this High Point + + align:start position:0% +one and this High Point + + + align:start position:0% +one and this High Point +448 and we know that our answer lies + + align:start position:0% +448 and we know that our answer lies + + + align:start position:0% +448 and we know that our answer lies +within this interval and it can be + + align:start position:0% +within this interval and it can be + + + align:start position:0% +within this interval and it can be +integers like in this book or it can be + + align:start position:0% +integers like in this book or it can be + + + align:start position:0% +integers like in this book or it can be +you know fractional pieces as well and + + align:start position:0% +you know fractional pieces as well and + + + align:start position:0% +you know fractional pieces as well and +the idea is you're just guessing the + + align:start position:0% +the idea is you're just guessing the + + + align:start position:0% +the idea is you're just guessing the +midpoint between this interval it's as + + align:start position:0% +midpoint between this interval it's as + + + align:start position:0% +midpoint between this interval it's as +good as a guess as anything right but + + align:start position:0% +good as a guess as anything right but + + + align:start position:0% +good as a guess as anything right but +based on the answer that I give you + + align:start position:0% +based on the answer that I give you + + + align:start position:0% +based on the answer that I give you +because now I give you extra information + + align:start position:0% +because now I give you extra information + + + align:start position:0% +because now I give you extra information +if it's too high too low you can + + align:start position:0% +if it's too high too low you can + + + align:start position:0% +if it's too high too low you can +basically eliminate half of the search + + align:start position:0% +basically eliminate half of the search + + + align:start position:0% +basically eliminate half of the search +space right so with the guess + + align:start position:0% +space right so with the guess + + + align:start position:0% +space right so with the guess +224 what ended up happening is you + + align:start position:0% +224 what ended up happening is you + + + align:start position:0% +224 what ended up happening is you +eliminated this entire half of the book + + align:start position:0% +eliminated this entire half of the book + + + align:start position:0% +eliminated this entire half of the book +right so it's like I take this original + + align:start position:0% +right so it's like I take this original + + + align:start position:0% +right so it's like I take this original +book 448 Pages get the midpoint rip it + + align:start position:0% +book 448 Pages get the midpoint rip it + + + align:start position:0% +book 448 Pages get the midpoint rip it +in half throw away these upper pages and + + align:start position:0% +in half throw away these upper pages and + + + align:start position:0% +in half throw away these upper pages and +now you kind of think of it like having + + align:start position:0% +now you kind of think of it like having + + + align:start position:0% +now you kind of think of it like having +this skinnier book and this is now the + + align:start position:0% +this skinnier book and this is now the + + + align:start position:0% +this skinnier book and this is now the +book you're searching through right and + + align:start position:0% +book you're searching through right and + + + align:start position:0% +book you're searching through right and +then you're repeating the process all + + align:start position:0% +then you're repeating the process all + + + align:start position:0% +then you're repeating the process all +over again the low end is still page one + + align:start position:0% +over again the low end is still page one + + + align:start position:0% +over again the low end is still page one +right because I have no information + + align:start position:0% +right because I have no information + + + align:start position:0% +right because I have no information +about how low I need to go but my + + align:start position:0% +about how low I need to go but my + + + align:start position:0% +about how low I need to go but my +highend point becomes the guess that I + + align:start position:0% +highend point becomes the guess that I + + + align:start position:0% +highend point becomes the guess that I +had just made right + + align:start position:0% +had just made right + + + align:start position:0% +had just made right +224 right and now I make another guess + + align:start position:0% +224 right and now I make another guess + + + align:start position:0% +224 right and now I make another guess +midpoint in this skinnier book and so + + align:start position:0% +midpoint in this skinnier book and so + + + align:start position:0% +midpoint in this skinnier book and so +this should kind of trigger something in + + align:start position:0% +this should kind of trigger something in + + + align:start position:0% +this should kind of trigger something in +your brain about computation and things + + align:start position:0% +your brain about computation and things + + + align:start position:0% +your brain about computation and things +that we've learned as soon as we're + + align:start position:0% +that we've learned as soon as we're + + + align:start position:0% +that we've learned as soon as we're +saying I'm repeating this process right + + align:start position:0% +saying I'm repeating this process right + + + align:start position:0% +saying I'm repeating this process right +of now just doing the guess again with + + align:start position:0% +of now just doing the guess again with + + + align:start position:0% +of now just doing the guess again with +this smaller version of a book we're + + align:start position:0% +this smaller version of a book we're + + + align:start position:0% +this smaller version of a book we're +basically we have a loop right that's + + align:start position:0% +basically we have a loop right that's + + + align:start position:0% +basically we have a loop right that's +something that you should be thinking + + align:start position:0% +something that you should be thinking + + + align:start position:0% +something that you should be thinking +about and this Loop is going to + + align:start position:0% +about and this Loop is going to + + + align:start position:0% +about and this Loop is going to +something that is going to be something + + align:start position:0% +something that is going to be something + + + align:start position:0% +something that is going to be something +that just repeats the same process over + + align:start position:0% +that just repeats the same process over + + + align:start position:0% +that just repeats the same process over +and over again once I've eliminated this + + align:start position:0% +and over again once I've eliminated this + + + align:start position:0% +and over again once I've eliminated this +upper half of the book now I'm looking + + align:start position:0% +upper half of the book now I'm looking + + + align:start position:0% +upper half of the book now I'm looking +through this lower half midpoint based + + align:start position:0% +through this lower half midpoint based + + + align:start position:0% +through this lower half midpoint based +on the answer I give you you can rip the + + align:start position:0% +on the answer I give you you can rip the + + + align:start position:0% +on the answer I give you you can rip the +book again in half where you are now and + + align:start position:0% +book again in half where you are now and + + + align:start position:0% +book again in half where you are now and +now you're searching the skinnier + + align:start position:0% +now you're searching the skinnier + + + align:start position:0% +now you're searching the skinnier +version of the book right so we're + + align:start position:0% +version of the book right so we're + + + align:start position:0% +version of the book right so we're +basically cut cutting the number of + + align:start position:0% +basically cut cutting the number of + + + align:start position:0% +basically cut cutting the number of +things we need to search for in half + + align:start position:0% +things we need to search for in half + + + align:start position:0% +things we need to search for in half +every time we make a guess which is + + align:start position:0% +every time we make a guess which is + + + align:start position:0% +every time we make a guess which is +really powerful right with guess and + + align:start position:0% +really powerful right with guess and + + + align:start position:0% +really powerful right with guess and +check or with bin or with approximation + + align:start position:0% +check or with bin or with approximation + + + align:start position:0% +check or with bin or with approximation +method if we're going to do guess and + + align:start position:0% +method if we're going to do guess and + + + align:start position:0% +method if we're going to do guess and +check on this book we'd be asking is it + + align:start position:0% +check on this book we'd be asking is it + + + align:start position:0% +check on this book we'd be asking is it +page one is it page two is it page three + + align:start position:0% +page one is it page two is it page three + + + align:start position:0% +page one is it page two is it page three +is it page four and that's tedious right + + align:start position:0% +is it page four and that's tedious right + + + align:start position:0% +is it page four and that's tedious right +we're not doing we're not eliminating + + align:start position:0% +we're not doing we're not eliminating + + + align:start position:0% +we're not doing we're not eliminating +half the book with each guest we're just + + align:start position:0% +half the book with each guest we're just + + + align:start position:0% +half the book with each guest we're just +eliminating one page with each guess + + align:start position:0% +eliminating one page with each guess + + + align:start position:0% +eliminating one page with each guess +okay so this idea of logarithmic growth + + align:start position:0% +okay so this idea of logarithmic growth + + + align:start position:0% +okay so this idea of logarithmic growth +which is what happens when you eliminate + + align:start position:0% +which is what happens when you eliminate + + + align:start position:0% +which is what happens when you eliminate +this uh the search space in half each + + align:start position:0% +this uh the search space in half each + + + align:start position:0% +this uh the search space in half each +with each stage is logarithmic growth + + align:start position:0% +with each stage is logarithmic growth + + + align:start position:0% +with each stage is logarithmic growth +and we'll come back to this idea again + + align:start position:0% +and we'll come back to this idea again + + + align:start position:0% +and we'll come back to this idea again +towards the last few weeks of lecture + + align:start position:0% +towards the last few weeks of lecture + + + align:start position:0% +towards the last few weeks of lecture +when we talk about comparing uh + + align:start position:0% +when we talk about comparing uh + + + align:start position:0% +when we talk about comparing uh +algorithms in this class and what does + + align:start position:0% +algorithms in this class and what does + + + align:start position:0% +algorithms in this class and what does +it mean for one algorithm to be more + + align:start position:0% +it mean for one algorithm to be more + + + align:start position:0% +it mean for one algorithm to be more +efficient than another algorithm what + + align:start position:0% +efficient than another algorithm what + + + align:start position:0% +efficient than another algorithm what +does it mean to run faster okay um so + + align:start position:0% +does it mean to run faster okay um so + + + align:start position:0% +does it mean to run faster okay um so +that's just something I mentioned when + + align:start position:0% +that's just something I mentioned when + + + align:start position:0% +that's just something I mentioned when +we do guess and check where we ask one + + align:start position:0% +we do guess and check where we ask one + + + align:start position:0% +we do guess and check where we ask one +page at a time that's linear growth + + align:start position:0% +page at a time that's linear growth + + + align:start position:0% +page at a time that's linear growth +because if the book If I give you now a + + align:start position:0% +because if the book If I give you now a + + + align:start position:0% +because if the book If I give you now a +book that's double the size and just by + + align:start position:0% +book that's double the size and just by + + + align:start position:0% +book that's double the size and just by +bad luck I put the money away at the end + + align:start position:0% +bad luck I put the money away at the end + + + align:start position:0% +bad luck I put the money away at the end +if I put the money at the end in this + + align:start position:0% +if I put the money at the end in this + + + align:start position:0% +if I put the money at the end in this +book that's twice as big then you're + + align:start position:0% +book that's twice as big then you're + + + align:start position:0% +book that's twice as big then you're +going to have to ask me twice as many + + align:start position:0% +going to have to ask me twice as many + + + align:start position:0% +going to have to ask me twice as many +questions until you get to the answer + + align:start position:0% +questions until you get to the answer + + + align:start position:0% +questions until you get to the answer +but with logarithmic growth if I still + + align:start position:0% +but with logarithmic growth if I still + + + align:start position:0% +but with logarithmic growth if I still +put the the money in this book that's + + align:start position:0% +put the the money in this book that's + + + align:start position:0% +put the the money in this book that's +double the size somewhere all you need + + align:start position:0% +double the size somewhere all you need + + + align:start position:0% +double the size somewhere all you need +to do is make one extra guess not 400 + + align:start position:0% +to do is make one extra guess not 400 + + + align:start position:0% +to do is make one extra guess not 400 +extra guesses to figure out which + + align:start position:0% +extra guesses to figure out which + + + align:start position:0% +extra guesses to figure out which +interval it's in right you take from + + align:start position:0% +interval it's in right you take from + + + align:start position:0% +interval it's in right you take from +this double book make your first guess + + align:start position:0% +this double book make your first guess + + + align:start position:0% +this double book make your first guess +and all of a sudden said and we are at + + align:start position:0% +and all of a sudden said and we are at + + + align:start position:0% +and all of a sudden said and we are at +this book again okay all + + align:start position:0% +this book again okay all + + + align:start position:0% +this book again okay all +right so let's do another analogy just + + align:start position:0% +right so let's do another analogy just + + + align:start position:0% +right so let's do another analogy just +so uh we get kind of the sense of where + + align:start position:0% +so uh we get kind of the sense of where + + + align:start position:0% +so uh we get kind of the sense of where +this is going so suppose that you know + + align:start position:0% +this is going so suppose that you know + + + align:start position:0% +this is going so suppose that you know +we don't just need to work with numbers + + align:start position:0% +we don't just need to work with numbers + + + align:start position:0% +we don't just need to work with numbers +we can also work with anything that has + + align:start position:0% +we can also work with anything that has + + + align:start position:0% +we can also work with anything that has +an ordering property to it so suppose + + align:start position:0% +an ordering property to it so suppose + + + align:start position:0% +an ordering property to it so suppose +when you came in I asked you to sit + + align:start position:0% +when you came in I asked you to sit + + + align:start position:0% +when you came in I asked you to sit +alphabetically right front left is last + + align:start position:0% +alphabetically right front left is last + + + align:start position:0% +alphabetically right front left is last +name a back right is last name Z and + + align:start position:0% +name a back right is last name Z and + + + align:start position:0% +name a back right is last name Z and +then I'm looking for a particular person + + align:start position:0% +then I'm looking for a particular person + + + align:start position:0% +then I'm looking for a particular person +right for me the C the bisection search + + align:start position:0% +right for me the C the bisection search + + + align:start position:0% +right for me the C the bisection search +algorithm could be basically ask the + + align:start position:0% +algorithm could be basically ask the + + + align:start position:0% +algorithm could be basically ask the +person in the middle of the class what + + align:start position:0% +person in the middle of the class what + + + align:start position:0% +person in the middle of the class what +is their last name right if they if you + + align:start position:0% +is their last name right if they if you + + + align:start position:0% +is their last name right if they if you +know they say what it is and and + + align:start position:0% +know they say what it is and and + + + align:start position:0% +know they say what it is and and +depending on what they say right I can + + align:start position:0% +depending on what they say right I can + + + align:start position:0% +depending on what they say right I can +basically dismiss half of the people if + + align:start position:0% +basically dismiss half of the people if + + + align:start position:0% +basically dismiss half of the people if +their last name starts with a letter + + align:start position:0% +their last name starts with a letter + + + align:start position:0% +their last name starts with a letter +later than the one I'm looking for in + + align:start position:0% +later than the one I'm looking for in + + + align:start position:0% +later than the one I'm looking for in +the alphabet I dismiss the upper half + + align:start position:0% +the alphabet I dismiss the upper half + + + align:start position:0% +the alphabet I dismiss the upper half +and vice versa right and then I have + + align:start position:0% +and vice versa right and then I have + + + align:start position:0% +and vice versa right and then I have +this only half of the people to search + + align:start position:0% +this only half of the people to search + + + align:start position:0% +this only half of the people to search +through and I keep repeating this + + align:start position:0% +through and I keep repeating this + + + align:start position:0% +through and I keep repeating this +process until I have only one person + + align:start position:0% +process until I have only one person + + + align:start position:0% +process until I have only one person +left + + align:start position:0% +left + + + align:start position:0% +left +and either that person is the one I'm + + align:start position:0% +and either that person is the one I'm + + + align:start position:0% +and either that person is the one I'm +looking for in which case I've decreased + + align:start position:0% +looking for in which case I've decreased + + + align:start position:0% +looking for in which case I've decreased +by half the size of the class with each + + align:start position:0% +by half the size of the class with each + + + align:start position:0% +by half the size of the class with each +guess and I have one person left to ask + + align:start position:0% +guess and I have one person left to ask + + + align:start position:0% +guess and I have one person left to ask +the one I'm looking for or that person + + align:start position:0% +the one I'm looking for or that person + + + align:start position:0% +the one I'm looking for or that person +just isn't here + + align:start position:0% +just isn't here + + + align:start position:0% +just isn't here +okay so let's try to apply the same idea + + align:start position:0% +okay so let's try to apply the same idea + + + align:start position:0% +okay so let's try to apply the same idea +of bisection search to programming and + + align:start position:0% +of bisection search to programming and + + + align:start position:0% +of bisection search to programming and +specifically let's do the problem we've + + align:start position:0% +specifically let's do the problem we've + + + align:start position:0% +specifically let's do the problem we've +been trying to solve kind of as a Common + + align:start position:0% +been trying to solve kind of as a Common + + + align:start position:0% +been trying to solve kind of as a Common +Thread throughout these algorithms + + align:start position:0% +Thread throughout these algorithms + + + align:start position:0% +Thread throughout these algorithms +figuring out the square root of of a + + align:start position:0% +figuring out the square root of of a + + + align:start position:0% +figuring out the square root of of a +number not exact actually we're still + + align:start position:0% +number not exact actually we're still + + + align:start position:0% +number not exact actually we're still +going to be looking only for an + + align:start position:0% +going to be looking only for an + + + align:start position:0% +going to be looking only for an +approximation to the square root of a + + align:start position:0% +approximation to the square root of a + + + align:start position:0% +approximation to the square root of a +number so the idea here is that our + + align:start position:0% +number so the idea here is that our + + + align:start position:0% +number so the idea here is that our +interval is if we're trying to find the + + align:start position:0% +interval is if we're trying to find the + + + align:start position:0% +interval is if we're trying to find the +square root of x is going to be between + + align:start position:0% +square root of x is going to be between + + + align:start position:0% +square root of x is going to be between +zero and X right so basically I can just + + align:start position:0% +zero and X right so basically I can just + + + align:start position:0% +zero and X right so basically I can just +reuse this number line + + align:start position:0% +reuse this number line + + + align:start position:0% +reuse this number line +here right and I have my interval for + + align:start position:0% +here right and I have my interval for + + + align:start position:0% +here right and I have my interval for +the square root is zero and X okay so + + align:start position:0% +the square root is zero and X okay so + + + align:start position:0% +the square root is zero and X okay so +like that + + align:start position:0% +like that + + + align:start position:0% +like that +so with approximation method we would + + align:start position:0% +so with approximation method we would + + + align:start position:0% +so with approximation method we would +start at zero and painstakingly make our + + align:start position:0% +start at zero and painstakingly make our + + + align:start position:0% +start at zero and painstakingly make our +way little by + + align:start position:0% +way little by + + + align:start position:0% +way little by +little but with bisection search we're + + align:start position:0% +little but with bisection search we're + + + align:start position:0% +little but with bisection search we're +make we're making our initial guess to + + align:start position:0% +make we're making our initial guess to + + + align:start position:0% +make we're making our initial guess to +be the halfway point okay again we're + + align:start position:0% +be the halfway point okay again we're + + + align:start position:0% +be the halfway point okay again we're +working with numbers so the ordering + + align:start position:0% +working with numbers so the ordering + + + align:start position:0% +working with numbers so the ordering +properties is is very intuitive we ask + + align:start position:0% +properties is is very intuitive we ask + + + align:start position:0% +properties is is very intuitive we ask +at this halfway point what is uh with + + align:start position:0% +at this halfway point what is uh with + + + align:start position:0% +at this halfway point what is uh with +this guess at the halfway point what is + + align:start position:0% +this guess at the halfway point what is + + + align:start position:0% +this guess at the halfway point what is +the guess + + align:start position:0% +the guess + + + align:start position:0% +the guess +squared okay so if the guest + + align:start position:0% +squared okay so if the guest + + + align:start position:0% +squared okay so if the guest +squared is up here right so G2 is up + + align:start position:0% +squared is up here right so G2 is up + + + align:start position:0% +squared is up here right so G2 is up +here then I know this guess is too big + + align:start position:0% +here then I know this guess is too big + + + align:start position:0% +here then I know this guess is too big +so I know I do not need to make any + + align:start position:0% +so I know I do not need to make any + + + align:start position:0% +so I know I do not need to make any +further guesses up here right so that's + + align:start position:0% +further guesses up here right so that's + + + align:start position:0% +further guesses up here right so that's +this case + + align:start position:0% +this case + + + align:start position:0% +this case +here if I know this guess is too big + + align:start position:0% +here if I know this guess is too big + + + align:start position:0% +here if I know this guess is too big +then my interval now becomes this is + + align:start position:0% +then my interval now becomes this is + + + align:start position:0% +then my interval now becomes this is +going to be the low still but now this + + align:start position:0% +going to be the low still but now this + + + align:start position:0% +going to be the low still but now this +is going to be my high point right and + + align:start position:0% +is going to be my high point right and + + + align:start position:0% +is going to be my high point right and +this is kind of this new interval I'm + + align:start position:0% +this is kind of this new interval I'm + + + align:start position:0% +this is kind of this new interval I'm +looking through but if you think about + + align:start position:0% +looking through but if you think about + + + align:start position:0% +looking through but if you think about +it it's the the exact same problem I + + align:start position:0% +it it's the the exact same problem I + + + align:start position:0% +it it's the the exact same problem I +started with when my interval was was + + align:start position:0% +started with when my interval was was + + + align:start position:0% +started with when my interval was was +larger right I still have an interval + + align:start position:0% +larger right I still have an interval + + + align:start position:0% +larger right I still have an interval +with a low and a high I'm still going to + + align:start position:0% +with a low and a high I'm still going to + + + align:start position:0% +with a low and a high I'm still going to +make a guess halfway this new G here and + + align:start position:0% +make a guess halfway this new G here and + + + align:start position:0% +make a guess halfway this new G here and +I'm going to ask again is this new + + align:start position:0% +I'm going to ask again is this new + + + align:start position:0% +I'm going to ask again is this new +guess uh squared less than or greater + + align:start position:0% +guess uh squared less than or greater + + + align:start position:0% +guess uh squared less than or greater +than x let's say this case it's less + + align:start position:0% +than x let's say this case it's less + + + align:start position:0% +than x let's say this case it's less +than so if the new guess new G is less + + align:start position:0% +than so if the new guess new G is less + + + align:start position:0% +than so if the new guess new G is less +than x the new G squared is less than x + + align:start position:0% +than x the new G squared is less than x + + + align:start position:0% +than x the new G squared is less than x +then I know this is new G then I know + + align:start position:0% +then I know this is new G then I know + + + align:start position:0% +then I know this is new G then I know +that anything lower than this is + + align:start position:0% +that anything lower than this is + + + align:start position:0% +that anything lower than this is +definitely not going to be closer to the + + align:start position:0% +definitely not going to be closer to the + + + align:start position:0% +definitely not going to be closer to the +to the answer I'm looking for so now I'm + + align:start position:0% +to the answer I'm looking for so now I'm + + + align:start position:0% +to the answer I'm looking for so now I'm +eliminating this half of this search + + align:start position:0% +eliminating this half of this search + + + align:start position:0% +eliminating this half of this search +space and then I keep making the same uh + + align:start position:0% +space and then I keep making the same uh + + + align:start position:0% +space and then I keep making the same uh +guesses next g g latest G this is like + + align:start position:0% +guesses next g g latest G this is like + + + align:start position:0% +guesses next g g latest G this is like +when you guys name your files remember + + align:start position:0% +when you guys name your files remember + + + align:start position:0% +when you guys name your files remember +and you know you got new new file final + + align:start position:0% +and you know you got new new file final + + + align:start position:0% +and you know you got new new file final +file latest file version two all that + + align:start position:0% +file latest file version two all that + + + align:start position:0% +file latest file version two all that +stuff that's basically what I did there + + align:start position:0% +stuff that's basically what I did there + + + align:start position:0% +stuff that's basically what I did there +so anyway I have this latest G here + + align:start position:0% +so anyway I have this latest G here + + + align:start position:0% +so anyway I have this latest G here +right which is my new midpoint and I + + align:start position:0% +right which is my new midpoint and I + + + align:start position:0% +right which is my new midpoint and I +keep making these guesses and asking the + + align:start position:0% +keep making these guesses and asking the + + + align:start position:0% +keep making these guesses and asking the +question whether this guess squared is + + align:start position:0% +question whether this guess squared is + + + align:start position:0% +question whether this guess squared is +greater than or equal or less than x and + + align:start position:0% +greater than or equal or less than x and + + + align:start position:0% +greater than or equal or less than x and +I adjust my boundaries + + align:start position:0% +I adjust my boundaries + + + align:start position:0% +I adjust my boundaries +accordingly okay so at each stage the + + align:start position:0% +accordingly okay so at each stage the + + + align:start position:0% +accordingly okay so at each stage the +number of uh values I have to search + + align:start position:0% +number of uh values I have to search + + + align:start position:0% +number of uh values I have to search +through are just half of what I had to + + align:start position:0% +through are just half of what I had to + + + align:start position:0% +through are just half of what I had to +search through last guess okay so the + + align:start position:0% +search through last guess okay so the + + + align:start position:0% +search through last guess okay so the +bisection search takes advantage of two + + align:start position:0% +bisection search takes advantage of two + + + align:start position:0% +bisection search takes advantage of two +properties and you can only use it when + + align:start position:0% +properties and you can only use it when + + + align:start position:0% +properties and you can only use it when +you have these prop properties in hand + + align:start position:0% +you have these prop properties in hand + + + align:start position:0% +you have these prop properties in hand +right there's some sort of ordering to + + align:start position:0% +right there's some sort of ordering to + + + align:start position:0% +right there's some sort of ordering to +the thing you're searching so you know + + align:start position:0% +the thing you're searching so you know + + + align:start position:0% +the thing you're searching so you know +last names are alphabetical you know you + + align:start position:0% +last names are alphabetical you know you + + + align:start position:0% +last names are alphabetical you know you +have this range of + + align:start position:0% +have this range of + + + align:start position:0% +have this range of +values um and you have some sort of + + align:start position:0% +values um and you have some sort of + + + align:start position:0% +values um and you have some sort of +feedback the feedback tell uh it tells + + align:start position:0% +feedback the feedback tell uh it tells + + + align:start position:0% +feedback the feedback tell uh it tells +you whether the guest that you made was + + align:start position:0% +you whether the guest that you made was + + + align:start position:0% +you whether the guest that you made was +too low or too high or exact or + + align:start position:0% +too low or too high or exact or + + + align:start position:0% +too low or too high or exact or +approximate whatever you + + align:start position:0% +approximate whatever you + + + align:start position:0% +approximate whatever you +want okay so an think about this for a + + align:start position:0% +want okay so an think about this for a + + + align:start position:0% +want okay so an think about this for a +second and answer uh the question so + + align:start position:0% +second and answer uh the question so + + + align:start position:0% +second and answer uh the question so +you're guessing a four-digit PIN code + + align:start position:0% +you're guessing a four-digit PIN code + + + align:start position:0% +you're guessing a four-digit PIN code +right on a phone or whatever and the + + align:start position:0% +right on a phone or whatever and the + + + align:start position:0% +right on a phone or whatever and the +feedback the phone tells you is whether + + align:start position:0% +feedback the phone tells you is whether + + + align:start position:0% +feedback the phone tells you is whether +the guess is correct or + + align:start position:0% +the guess is correct or + + + align:start position:0% +the guess is correct or +not can you use bsection search in this + + align:start position:0% +not can you use bsection search in this + + + align:start position:0% +not can you use bsection search in this +situation to quickly and correctly guess + + align:start position:0% +situation to quickly and correctly guess + + + align:start position:0% +situation to quickly and correctly guess +the + + align:start position:0% +the + + + align:start position:0% +the +code no why is that what are we + + align:start position:0% +code no why is that what are we + + + align:start position:0% +code no why is that what are we +missing it doesn't tell you if it's too + + align:start position:0% +missing it doesn't tell you if it's too + + + align:start position:0% +missing it doesn't tell you if it's too +big or too small yeah so guessing random + + align:start position:0% +big or too small yeah so guessing random + + + align:start position:0% +big or too small yeah so guessing random +I mean you could use bsection search and + + align:start position:0% +I mean you could use bsection search and + + + align:start position:0% +I mean you could use bsection search and +you could choose which half to look + + align:start position:0% +you could choose which half to look + + + align:start position:0% +you could choose which half to look +through but then basically you just have + + align:start position:0% +through but then basically you just have + + + align:start position:0% +through but then basically you just have +to search through all the values anyway + + align:start position:0% +to search through all the values anyway + + + align:start position:0% +to search through all the values anyway +in worst case right and then you might + + align:start position:0% +in worst case right and then you might + + + align:start position:0% +in worst case right and then you might +as well have just gone from you know + + align:start position:0% +as well have just gone from you know + + + align:start position:0% +as well have just gone from you know +00000000 0000 1 002 just have gone um + + align:start position:0% +00000000 0000 1 002 just have gone um + + + align:start position:0% +00000000 0000 1 002 just have gone um +incrementally + + align:start position:0% + + + + align:start position:0% + +upward okay so how about this extreme + + align:start position:0% +upward okay so how about this extreme + + + align:start position:0% +upward okay so how about this extreme +guessing game all right so you have a + + align:start position:0% +guessing game all right so you have a + + + align:start position:0% +guessing game all right so you have a +friend uh and You' like to play this + + align:start position:0% +friend uh and You' like to play this + + + align:start position:0% +friend uh and You' like to play this +extreme guessing game where you want to + + align:start position:0% +extreme guessing game where you want to + + + align:start position:0% +extreme guessing game where you want to +guess a number exactly okay so your + + align:start position:0% +guess a number exactly okay so your + + + align:start position:0% +guess a number exactly okay so your +friend has a decimal number in mind so + + align:start position:0% +friend has a decimal number in mind so + + + align:start position:0% +friend has a decimal number in mind so +it can be uh + + align:start position:0% +it can be uh + + + align:start position:0% +it can be uh +with a decimal point like any real + + align:start position:0% +with a decimal point like any real + + + align:start position:0% +with a decimal point like any real +number from 0 to 10 let's say including + + align:start position:0% +number from 0 to 10 let's say including + + + align:start position:0% +number from 0 to 10 let's say including +zero including 10 to any Precision in + + align:start position:0% +zero including 10 to any Precision in + + + align:start position:0% +zero including 10 to any Precision in +mind so the feedback your friend gives + + align:start position:0% +mind so the feedback your friend gives + + + align:start position:0% +mind so the feedback your friend gives +you when you play this extreme guessing + + align:start position:0% +you when you play this extreme guessing + + + align:start position:0% +you when you play this extreme guessing +game is whether your guess was correct + + align:start position:0% +game is whether your guess was correct + + + align:start position:0% +game is whether your guess was correct +too low or too high in this case can you + + align:start position:0% +too low or too high in this case can you + + + align:start position:0% +too low or too high in this case can you +use bisection search to quickly and + + align:start position:0% +use bisection search to quickly and + + + align:start position:0% +use bisection search to quickly and +correctly guess the + + align:start position:0% + + + + align:start position:0% + +number could but the number might be + + align:start position:0% +number could but the number might be + + + align:start position:0% +number could but the number might be +really long it would take a long time + + align:start position:0% +really long it would take a long time + + + align:start position:0% +really long it would take a long time +yeah yeah so I I I included this word + + align:start position:0% +yeah yeah so I I I included this word + + + align:start position:0% +yeah yeah so I I I included this word +exactly here right if I didn't include + + align:start position:0% +exactly here right if I didn't include + + + align:start position:0% +exactly here right if I didn't include +that I think the answer could be um + + align:start position:0% +that I think the answer could be um + + + align:start position:0% +that I think the answer could be um +could be yes because you could play the + + align:start position:0% +could be yes because you could play the + + + align:start position:0% +could be yes because you could play the +game to a round or approximation to two + + align:start position:0% +game to a round or approximation to two + + + align:start position:0% +game to a round or approximation to two +decimal places or something like that + + align:start position:0% +decimal places or something like that + + + align:start position:0% +decimal places or something like that +but I guess if your friend wants to flex + + align:start position:0% +but I guess if your friend wants to flex + + + align:start position:0% +but I guess if your friend wants to flex +with pi right in your extreme guessing + + align:start position:0% +with pi right in your extreme guessing + + + align:start position:0% +with pi right in your extreme guessing +game then bisection search wouldn't work + + align:start position:0% +game then bisection search wouldn't work + + + align:start position:0% +game then bisection search wouldn't work +because if you're trying to find that + + align:start position:0% +because if you're trying to find that + + + align:start position:0% +because if you're trying to find that +number + + align:start position:0% +number + + + align:start position:0% +number +exactly then you'll never get to it + + align:start position:0% +exactly then you'll never get to it + + + align:start position:0% +exactly then you'll never get to it +right so yeah you're using bisection + + align:start position:0% +right so yeah you're using bisection + + + align:start position:0% +right so yeah you're using bisection +search but it's going to basically be an + + align:start position:0% +search but it's going to basically be an + + + align:start position:0% +search but it's going to basically be an +infinite algorithm right it won't + + align:start position:0% + + + + align:start position:0% + +terminate okay so this is the same slide + + align:start position:0% +terminate okay so this is the same slide + + + align:start position:0% +terminate okay so this is the same slide +I had at the beginning of lecture just + + align:start position:0% +I had at the beginning of lecture just + + + align:start position:0% +I had at the beginning of lecture just +to remind ourselves what the code looks + + align:start position:0% +to remind ourselves what the code looks + + + align:start position:0% +to remind ourselves what the code looks +like when we use the approximation + + align:start position:0% +like when we use the approximation + + + align:start position:0% +like when we use the approximation +algorithm and nothing new here so we had + + align:start position:0% +algorithm and nothing new here so we had + + + align:start position:0% +algorithm and nothing new here so we had +our the thing that basically did the + + align:start position:0% +our the thing that basically did the + + + align:start position:0% +our the thing that basically did the +work was this y Loop right while we were + + align:start position:0% +work was this y Loop right while we were + + + align:start position:0% +work was this y Loop right while we were +still farther away from Epsilon and we + + align:start position:0% +still farther away from Epsilon and we + + + align:start position:0% +still farther away from Epsilon and we +were still still making reasonable + + align:start position:0% +were still still making reasonable + + + align:start position:0% +were still still making reasonable +guesses increment our guess by + + align:start position:0% + + + + align:start position:0% + +01 now let's write the code for the + + align:start position:0% +01 now let's write the code for the + + + align:start position:0% +01 now let's write the code for the +finding approximating the square root of + + align:start position:0% +finding approximating the square root of + + + align:start position:0% +finding approximating the square root of +a number but with bisection search so + + align:start position:0% +a number but with bisection search so + + + align:start position:0% +a number but with bisection search so +we're going to follow the same kind of + + align:start position:0% +we're going to follow the same kind of + + + align:start position:0% +we're going to follow the same kind of +procedure we did here and we're actually + + align:start position:0% +procedure we did here and we're actually + + + align:start position:0% +procedure we did here and we're actually +going to sort of write it together on + + align:start position:0% +going to sort of write it together on + + + align:start position:0% +going to sort of write it together on +the slides and I'm going to explain sort + + align:start position:0% +the slides and I'm going to explain sort + + + align:start position:0% +the slides and I'm going to explain sort +of the thought process that goes behind + + align:start position:0% +of the thought process that goes behind + + + align:start position:0% +of the thought process that goes behind +uh the each + + align:start position:0% +uh the each + + + align:start position:0% +uh the each +step okay so the first thing we're doing + + align:start position:0% +step okay so the first thing we're doing + + + align:start position:0% +step okay so the first thing we're doing +is we're initializing some stuff up here + + align:start position:0% +is we're initializing some stuff up here + + + align:start position:0% +is we're initializing some stuff up here +so the thing we want to find the square + + align:start position:0% +so the thing we want to find the square + + + align:start position:0% +so the thing we want to find the square +root of right let's why not do the same + + align:start position:0% +root of right let's why not do the same + + + align:start position:0% +root of right let's why not do the same +number that gave us trouble last time + + align:start position:0% +number that gave us trouble last time + + + align:start position:0% +number that gave us trouble last time +and we still want to be within some plus + + align:start position:0% +and we still want to be within some plus + + + align:start position:0% +and we still want to be within some plus +or minus Epsilon again because we do not + + align:start position:0% +or minus Epsilon again because we do not + + + align:start position:0% +or minus Epsilon again because we do not +want to be comparing floats + + align:start position:0% +want to be comparing floats + + + align:start position:0% +want to be comparing floats +right and this numb guesses is going to + + align:start position:0% +right and this numb guesses is going to + + + align:start position:0% +right and this numb guesses is going to +keep track of how many guesses we've + + align:start position:0% +keep track of how many guesses we've + + + align:start position:0% +keep track of how many guesses we've +made basically when we played the + + align:start position:0% +made basically when we played the + + + align:start position:0% +made basically when we played the +guessing game how many guesses did you + + align:start position:0% +guessing game how many guesses did you + + + align:start position:0% +guessing game how many guesses did you +do to get to the to the um to the + + align:start position:0% +do to get to the to the um to the + + + align:start position:0% +do to get to the to the um to the +money all + + align:start position:0% +money all + + + align:start position:0% +money all +right uh good and then at the bottom + + align:start position:0% +right uh good and then at the bottom + + + align:start position:0% +right uh good and then at the bottom +here here we're going to print out the + + align:start position:0% +here here we're going to print out the + + + align:start position:0% +here here we're going to print out the +uh the number of guesses and what the + + align:start position:0% +uh the number of guesses and what the + + + align:start position:0% +uh the number of guesses and what the +guess was that brought us close to the + + align:start position:0% +guess was that brought us close to the + + + align:start position:0% +guess was that brought us close to the +plus or minus + + align:start position:0% +plus or minus + + + align:start position:0% +plus or minus +Epsilon okay so the first thing we do is + + align:start position:0% +Epsilon okay so the first thing we do is + + + align:start position:0% +Epsilon okay so the first thing we do is +we noticed there was a + + align:start position:0% +we noticed there was a + + + align:start position:0% +we noticed there was a +repetition and the while loop here is + + align:start position:0% +repetition and the while loop here is + + + align:start position:0% +repetition and the while loop here is +exactly the same as the while loop for + + align:start position:0% +exactly the same as the while loop for + + + align:start position:0% +exactly the same as the while loop for +the approximation method okay while + + align:start position:0% +the approximation method okay while + + + align:start position:0% +the approximation method okay while +we're still farther than Epsilon away + + align:start position:0% +we're still farther than Epsilon away + + + align:start position:0% +we're still farther than Epsilon away +right while I while our guest Square + + align:start position:0% +right while I while our guest Square + + + align:start position:0% +right while I while our guest Square +squ um is plus or minus Epsilon away + + align:start position:0% +squ um is plus or minus Epsilon away + + + align:start position:0% +squ um is plus or minus Epsilon away +from X right so absolute value of gu^ s + + align:start position:0% +from X right so absolute value of gu^ s + + + align:start position:0% +from X right so absolute value of gu^ s +minus X is greater or equal to Epsilon I + + align:start position:0% +minus X is greater or equal to Epsilon I + + + align:start position:0% +minus X is greater or equal to Epsilon I +guess the this could just be greater + + align:start position:0% +guess the this could just be greater + + + align:start position:0% +guess the this could just be greater +than details um let's keep making + + align:start position:0% +than details um let's keep making + + + align:start position:0% +than details um let's keep making +guesses now the guesses are we're not + + align:start position:0% +guesses now the guesses are we're not + + + align:start position:0% +guesses now the guesses are we're not +incrementing anything right this isn't + + align:start position:0% +incrementing anything right this isn't + + + align:start position:0% +incrementing anything right this isn't +the approximation method we need to make + + align:start position:0% +the approximation method we need to make + + + align:start position:0% +the approximation method we need to make +the guesses in a smart way okay so we're + + align:start position:0% +the guesses in a smart way okay so we're + + + align:start position:0% +the guesses in a smart way okay so we're +going to initialize some stuff for our + + align:start position:0% +going to initialize some stuff for our + + + align:start position:0% +going to initialize some stuff for our +algorithm to work like our original end + + align:start position:0% +algorithm to work like our original end + + + align:start position:0% +algorithm to work like our original end +points and then we're going to do some + + align:start position:0% +points and then we're going to do some + + + align:start position:0% +points and then we're going to do some +stuff inside the loop whatever is + + align:start position:0% +stuff inside the loop whatever is + + + align:start position:0% +stuff inside the loop whatever is +repeated whatever we noted right when we + + align:start position:0% +repeated whatever we noted right when we + + + align:start position:0% +repeated whatever we noted right when we +were talking about the algorithm what + + align:start position:0% +were talking about the algorithm what + + + align:start position:0% +were talking about the algorithm what +did we note that gets repeated every + + align:start position:0% +did we note that gets repeated every + + + align:start position:0% +did we note that gets repeated every +time okay let's talk about the + + align:start position:0% + + + + align:start position:0% + +initializations we need to initialize + + align:start position:0% +initializations we need to initialize + + + align:start position:0% +initializations we need to initialize +our two end points right we need the for + + align:start position:0% +our two end points right we need the for + + + align:start position:0% +our two end points right we need the for +the bisection search to work we need to + + align:start position:0% +the bisection search to work we need to + + + align:start position:0% +the bisection search to work we need to +know what our end points are so the low + + align:start position:0% +know what our end points are so the low + + + align:start position:0% +know what our end points are so the low +is going to be Z so if we're trying to + + align:start position:0% +is going to be Z so if we're trying to + + + align:start position:0% +is going to be Z so if we're trying to +find the square root of x we might as + + align:start position:0% +find the square root of x we might as + + + align:start position:0% +find the square root of x we might as +well make our low + + align:start position:0% +well make our low + + + align:start position:0% +well make our low +zero and let's make our high point + + align:start position:0% +zero and let's make our high point + + + align:start position:0% +zero and let's make our high point +x our high point can be 2x it could be + + align:start position:0% +x our high point can be 2x it could be + + + align:start position:0% +x our high point can be 2x it could be +3x whatever we want but that's too big + + align:start position:0% +3x whatever we want but that's too big + + + align:start position:0% +3x whatever we want but that's too big +we know using algebra that definitely it + + align:start position:0% +we know using algebra that definitely it + + + align:start position:0% +we know using algebra that definitely it +won't be that big so we can just make + + align:start position:0% +won't be that big so we can just make + + + align:start position:0% +won't be that big so we can just make +our high point + + align:start position:0% +our high point + + + align:start position:0% +our high point +x and then we just kick off this + + align:start position:0% +x and then we just kick off this + + + align:start position:0% +x and then we just kick off this +algorithm with our initial guess is + + align:start position:0% +algorithm with our initial guess is + + + align:start position:0% +algorithm with our initial guess is +going to be the midpoint of low and high + + align:start position:0% +going to be the midpoint of low and high + + + align:start position:0% +going to be the midpoint of low and high +so high plus low divided by two + + align:start position:0% +so high plus low divided by two + + + align:start position:0% +so high plus low divided by two +okay so that brings us to just before + + align:start position:0% +okay so that brings us to just before + + + align:start position:0% +okay so that brings us to just before +the while loop here right + + align:start position:0% +the while loop here right + + + align:start position:0% +the while loop here right +here okay and now there we're going to + + align:start position:0% +here okay and now there we're going to + + + align:start position:0% +here okay and now there we're going to +repeat some stuff while we're still far + + align:start position:0% +repeat some stuff while we're still far + + + align:start position:0% +repeat some stuff while we're still far +away farther than Epsilon away uh from + + align:start position:0% +away farther than Epsilon away uh from + + + align:start position:0% +away farther than Epsilon away uh from +our + + align:start position:0% +our + + + align:start position:0% +our +answer so the thing that we're repeating + + align:start position:0% +answer so the thing that we're repeating + + + align:start position:0% +answer so the thing that we're repeating +is going to be checking if we are too + + align:start position:0% +is going to be checking if we are too + + + align:start position:0% +is going to be checking if we are too +low or too high right like we have a + + align:start position:0% +low or too high right like we have a + + + align:start position:0% +low or too high right like we have a +guess in hand now this bid point here + + align:start position:0% +guess in hand now this bid point here + + + align:start position:0% +guess in hand now this bid point here +and now with this guess in hand that + + align:start position:0% +and now with this guess in hand that + + + align:start position:0% +and now with this guess in hand that +kind of kicked off our algorithm we're + + align:start position:0% +kind of kicked off our algorithm we're + + + align:start position:0% +kind of kicked off our algorithm we're +going to say is this guess too low or + + align:start position:0% +going to say is this guess too low or + + + align:start position:0% +going to say is this guess too low or +too high right that's what the algorithm + + align:start position:0% +too high right that's what the algorithm + + + align:start position:0% +too high right that's what the algorithm +needs so that's an if else a little + + align:start position:0% +needs so that's an if else a little + + + align:start position:0% +needs so that's an if else a little +conditional here if the guest squared is + + align:start position:0% +conditional here if the guest squared is + + + align:start position:0% +conditional here if the guest squared is +less than x then the guess is too + + align:start position:0% +less than x then the guess is too + + + align:start position:0% +less than x then the guess is too +low okay so if this is this guess + + align:start position:0% +low okay so if this is this guess + + + align:start position:0% +low okay so if this is this guess +squared brings us to somewhere here + + align:start position:0% +squared brings us to somewhere here + + + align:start position:0% +squared brings us to somewhere here +right then we know this guess is too + + align:start position:0% +right then we know this guess is too + + + align:start position:0% +right then we know this guess is too +low what do I do in this case what does + + align:start position:0% +low what do I do in this case what does + + + align:start position:0% +low what do I do in this case what does +the algorithm say to + + align:start position:0% + + + + align:start position:0% + +do + + align:start position:0% + + + + align:start position:0% + +yes other way around yes so this is too + + align:start position:0% +yes other way around yes so this is too + + + align:start position:0% +yes other way around yes so this is too +low so I definitely don't want anything + + align:start position:0% +low so I definitely don't want anything + + + align:start position:0% +low so I definitely don't want anything +lower than here exactly so we're going + + align:start position:0% +lower than here exactly so we're going + + + align:start position:0% +lower than here exactly so we're going +to set our low end point if the guess is + + align:start position:0% +to set our low end point if the guess is + + + align:start position:0% +to set our low end point if the guess is +too low let's set our low end point to + + align:start position:0% +too low let's set our low end point to + + + align:start position:0% +too low let's set our low end point to +be whatever guess we just made because + + align:start position:0% +be whatever guess we just made because + + + align:start position:0% +be whatever guess we just made because +we know this is too low anything lower + + align:start position:0% +we know this is too low anything lower + + + align:start position:0% +we know this is too low anything lower +than this is definitely too low so I + + align:start position:0% +than this is definitely too low so I + + + align:start position:0% +than this is definitely too low so I +don't care about + + align:start position:0% +don't care about + + + align:start position:0% +don't care about +these else we don't need an L if because + + align:start position:0% +these else we don't need an L if because + + + align:start position:0% +these else we don't need an L if because +we know the else is the other way around + + align:start position:0% +we know the else is the other way around + + + align:start position:0% +we know the else is the other way around +else our guess was too high right so if + + align:start position:0% +else our guess was too high right so if + + + align:start position:0% +else our guess was too high right so if +the next time around we make a guess + + align:start position:0% +the next time around we make a guess + + + align:start position:0% +the next time around we make a guess +here or something like that then we know + + align:start position:0% +here or something like that then we know + + + align:start position:0% +here or something like that then we know +we're too + + align:start position:0% +we're too + + + align:start position:0% +we're too +high and then we need to set our high + + align:start position:0% +high and then we need to set our high + + + align:start position:0% +high and then we need to set our high +end point to be the + + align:start position:0% +end point to be the + + + align:start position:0% +end point to be the +guess is everyone okay with that so + + align:start position:0% +guess is everyone okay with that so + + + align:start position:0% +guess is everyone okay with that so +far + + align:start position:0% +far + + + align:start position:0% +far +okay what remains so I changed one of my + + align:start position:0% +okay what remains so I changed one of my + + + align:start position:0% +okay what remains so I changed one of my +boundaries either my low or my high + + align:start position:0% +boundaries either my low or my high + + + align:start position:0% +boundaries either my low or my high +boundary to be whatever guess I just + + align:start position:0% +boundary to be whatever guess I just + + + align:start position:0% +boundary to be whatever guess I just +made what is the next step what is the + + align:start position:0% +made what is the next step what is the + + + align:start position:0% +made what is the next step what is the +what does this algorithm do or this Loop + + align:start position:0% +what does this algorithm do or this Loop + + + align:start position:0% +what does this algorithm do or this Loop +do as + + align:start position:0% + + + + align:start position:0% + +is it finished doing whatever is inside + + align:start position:0% +is it finished doing whatever is inside + + + align:start position:0% +is it finished doing whatever is inside +and it goes back and uses the guess and + + align:start position:0% +and it goes back and uses the guess and + + + align:start position:0% +and it goes back and uses the guess and +check whether the guess squ minus X is + + align:start position:0% +check whether the guess squ minus X is + + + align:start position:0% +check whether the guess squ minus X is +greater or equal to + + align:start position:0% +greater or equal to + + + align:start position:0% +greater or equal to +Epsilon have I changed my guess inside + + align:start position:0% +Epsilon have I changed my guess inside + + + align:start position:0% +Epsilon have I changed my guess inside +this Loop yet no so that's the last step + + align:start position:0% +this Loop yet no so that's the last step + + + align:start position:0% +this Loop yet no so that's the last step +that remains make the + + align:start position:0% +that remains make the + + + align:start position:0% +that remains make the +guess be the new + + align:start position:0% +guess be the new + + + align:start position:0% +guess be the new +midpoint using either the changed high + + align:start position:0% +midpoint using either the changed high + + + align:start position:0% +midpoint using either the changed high +or the changed low right so each time + + align:start position:0% +or the changed low right so each time + + + align:start position:0% +or the changed low right so each time +through my Loop I'm either changing my + + align:start position:0% +through my Loop I'm either changing my + + + align:start position:0% +through my Loop I'm either changing my +low to be the guess or changing my high + + align:start position:0% +low to be the guess or changing my high + + + align:start position:0% +low to be the guess or changing my high +to be the guess so I'm making one of + + align:start position:0% +to be the guess so I'm making one of + + + align:start position:0% +to be the guess so I'm making one of +those two + + align:start position:0% +those two + + + align:start position:0% +those two +changes after I've made that change I + + align:start position:0% +changes after I've made that change I + + + align:start position:0% +changes after I've made that change I +need to find the new midpoint right so + + align:start position:0% +need to find the new midpoint right so + + + align:start position:0% +need to find the new midpoint right so +if I change my low now I need to make my + + align:start position:0% +if I change my low now I need to make my + + + align:start position:0% +if I change my low now I need to make my +new + + align:start position:0% + + + + align:start position:0% + +guess and with this new guess then I'm + + align:start position:0% +guess and with this new guess then I'm + + + align:start position:0% +guess and with this new guess then I'm +happy for the while loop to check it + + align:start position:0% +happy for the while loop to check it + + + align:start position:0% +happy for the while loop to check it +again right take that guess squared see + + align:start position:0% +again right take that guess squared see + + + align:start position:0% +again right take that guess squared see +how far away it is from X and then it + + align:start position:0% +how far away it is from X and then it + + + align:start position:0% +how far away it is from X and then it +does the the changing of the boundary + + align:start position:0% +does the the changing of the boundary + + + align:start position:0% +does the the changing of the boundary +all over again and that's it there's no + + align:start position:0% +all over again and that's it there's no + + + align:start position:0% +all over again and that's it there's no +other lines of code in here right so in + + align:start position:0% +other lines of code in here right so in + + + align:start position:0% +other lines of code in here right so in +some sense there's a little bit of trust + + align:start position:0% +some sense there's a little bit of trust + + + align:start position:0% +some sense there's a little bit of trust +right with this Loop that it does the + + align:start position:0% +right with this Loop that it does the + + + align:start position:0% +right with this Loop that it does the +right thing but if you kind of do a + + align:start position:0% +right thing but if you kind of do a + + + align:start position:0% +right thing but if you kind of do a +little bit of iteration in your brain or + + align:start position:0% +little bit of iteration in your brain or + + + align:start position:0% +little bit of iteration in your brain or +through the python tutor you'll see that + + align:start position:0% +through the python tutor you'll see that + + + align:start position:0% +through the python tutor you'll see that +it actually does it correctly right + + align:start position:0% +it actually does it correctly right + + + align:start position:0% +it actually does it correctly right +so we can just use that same number line + + align:start position:0% +so we can just use that same number line + + + align:start position:0% +so we can just use that same number line +and let's look at the square root uh + + align:start position:0% +and let's look at the square root uh + + + align:start position:0% +and let's look at the square root uh +let's find approximation to the square + + align:start position:0% +let's find approximation to the square + + + align:start position:0% +let's find approximation to the square +root of + + align:start position:0% +root of + + + align:start position:0% +root of +36 the Epsilon I made it one just + + align:start position:0% +36 the Epsilon I made it one just + + + align:start position:0% +36 the Epsilon I made it one just +because I don't want to do so many steps + + align:start position:0% +because I don't want to do so many steps + + + align:start position:0% +because I don't want to do so many steps +in the python tutor + + align:start position:0% +in the python tutor + + + align:start position:0% +in the python tutor +but you can imagine if it's smaller + + align:start position:0% +but you can imagine if it's smaller + + + align:start position:0% +but you can imagine if it's smaller +it'll just give us a better + + align:start position:0% +it'll just give us a better + + + align:start position:0% +it'll just give us a better +approximation so we're initializing the + + align:start position:0% +approximation so we're initializing the + + + align:start position:0% +approximation so we're initializing the +X the thing we want to find the square + + align:start position:0% +X the thing we want to find the square + + + align:start position:0% +X the thing we want to find the square +root of and Epsilon the low and the high + + align:start position:0% +root of and Epsilon the low and the high + + + align:start position:0% +root of and Epsilon the low and the high +zero and 36 in this particular case + + align:start position:0% +zero and 36 in this particular case + + + align:start position:0% +zero and 36 in this particular case +right okay stepping through the first + + align:start position:0% +right okay stepping through the first + + + align:start position:0% +right okay stepping through the first +guess is half of 36 and zero so + + align:start position:0% +guess is half of 36 and zero so + + + align:start position:0% +guess is half of 36 and zero so +18 so here's my guess is 18 and now we + + align:start position:0% +18 so here's my guess is 18 and now we + + + align:start position:0% +18 so here's my guess is 18 and now we +kick off our while loop by saying what + + align:start position:0% +kick off our while loop by saying what + + + align:start position:0% +kick off our while loop by saying what +is 18 squared oh it's pretty big + + align:start position:0% +is 18 squared oh it's pretty big + + + align:start position:0% +is 18 squared oh it's pretty big +definitely bigger than + + align:start position:0% +definitely bigger than + + + align:start position:0% +definitely bigger than +36 so I'm going to go inside this else + + align:start position:0% +36 so I'm going to go inside this else + + + align:start position:0% +36 so I'm going to go inside this else +because my guess is too high so my high + + align:start position:0% +because my guess is too high so my high + + + align:start position:0% +because my guess is too high so my high +becomes this and this is still the low + + align:start position:0% +becomes this and this is still the low + + + align:start position:0% +becomes this and this is still the low +right I know nothing about the low end + + align:start position:0% +right I know nothing about the low end + + + align:start position:0% +right I know nothing about the low end +at this + + align:start position:0% +at this + + + align:start position:0% +at this +point so then my guess becomes the high + + align:start position:0% +point so then my guess becomes the high + + + align:start position:0% +point so then my guess becomes the high +plus low 0 + 18 divided 2 right so + + align:start position:0% +plus low 0 + 18 divided 2 right so + + + align:start position:0% +plus low 0 + 18 divided 2 right so +that's going to be n so you can see my + + align:start position:0% +that's going to be n so you can see my + + + align:start position:0% +that's going to be n so you can see my +guess has updated to + + align:start position:0% +guess has updated to + + + align:start position:0% +guess has updated to +9 and now I find the guess squared what + + align:start position:0% +9 and now I find the guess squared what + + + align:start position:0% +9 and now I find the guess squared what +is 9 squared is it still farther than + + align:start position:0% +is 9 squared is it still farther than + + + align:start position:0% +is 9 squared is it still farther than +plus or minus uh 36 plusus one yes in + + align:start position:0% +plus or minus uh 36 plusus one yes in + + + align:start position:0% +plus or minus uh 36 plusus one yes in +fact it's still way too big so now my + + align:start position:0% +fact it's still way too big so now my + + + align:start position:0% +fact it's still way too big so now my +high since I know nine is still way too + + align:start position:0% +high since I know nine is still way too + + + align:start position:0% +high since I know nine is still way too +big for my guess my high + + align:start position:0% +big for my guess my high + + + align:start position:0% +big for my guess my high +becomes + + align:start position:0% + + + + align:start position:0% + +nine like + + align:start position:0% +nine like + + + align:start position:0% +nine like +that and then I make a new gu s based on + + align:start position:0% +that and then I make a new gu s based on + + + align:start position:0% +that and then I make a new gu s based on +0er and n and the halfway point between + + align:start position:0% +0er and n and the halfway point between + + + align:start position:0% +0er and n and the halfway point between +there so 4 and + + align:start position:0% + + + + align:start position:0% + +A2 right so there it is updated and + + align:start position:0% +A2 right so there it is updated and + + + align:start position:0% +A2 right so there it is updated and +using this guess Square it and see + + align:start position:0% +using this guess Square it and see + + + align:start position:0% +using this guess Square it and see +whether it's less than 36 or greater + + align:start position:0% +whether it's less than 36 or greater + + + align:start position:0% +whether it's less than 36 or greater +than 36 it's less than 36 so + + align:start position:0% +than 36 it's less than 36 so + + + align:start position:0% +than 36 it's less than 36 so +now this 4.5 becomes my low end point + + align:start position:0% +now this 4.5 becomes my low end point + + + align:start position:0% +now this 4.5 becomes my low end point +right now I have some information about + + align:start position:0% +right now I have some information about + + + align:start position:0% +right now I have some information about +the low end point like + + align:start position:0% +the low end point like + + + align:start position:0% +the low end point like +that right so I know my final answer is + + align:start position:0% +that right so I know my final answer is + + + align:start position:0% +that right so I know my final answer is +within this little interval right + + align:start position:0% +within this little interval right + + + align:start position:0% +within this little interval right +here okay and then I'm just going to go + + align:start position:0% +here okay and then I'm just going to go + + + align:start position:0% +here okay and then I'm just going to go +quicker because now we're dealing with + + align:start position:0% +quicker because now we're dealing with + + + align:start position:0% +quicker because now we're dealing with +some + + align:start position:0% +some + + + align:start position:0% +some +fractions um my lowend point becomes 4.5 + + align:start position:0% +fractions um my lowend point becomes 4.5 + + + align:start position:0% +fractions um my lowend point becomes 4.5 +and now I get the midpoint between 4 and + + align:start position:0% +and now I get the midpoint between 4 and + + + align:start position:0% +and now I get the midpoint between 4 and +a half and nine and that's + + align:start position:0% +a half and nine and that's + + + align:start position:0% +a half and nine and that's +675 and then we keep doing the same + + align:start position:0% +675 and then we keep doing the same + + + align:start position:0% +675 and then we keep doing the same +process over and over again hopefully + + align:start position:0% +process over and over again hopefully + + + align:start position:0% +process over and over again hopefully +you get the idea now where we keep + + align:start position:0% +you get the idea now where we keep + + + align:start position:0% +you get the idea now where we keep +changing this while the guest squared is + + align:start position:0% +changing this while the guest squared is + + + align:start position:0% +changing this while the guest squared is +still + + align:start position:0% +still + + + align:start position:0% +still +36 great outside of the boundary of 36 + + align:start position:0% +36 great outside of the boundary of 36 + + + align:start position:0% +36 great outside of the boundary of 36 +plus or minus one right so if it's less + + align:start position:0% +plus or minus one right so if it's less + + + align:start position:0% +plus or minus one right so if it's less +than 35 or greater than 37 keep making + + align:start position:0% +than 35 or greater than 37 keep making + + + align:start position:0% +than 35 or greater than 37 keep making +guesses so we're going to go till + + align:start position:0% +guesses so we're going to go till + + + align:start position:0% +guesses so we're going to go till +probably 60 + + align:start position:0% +probably 60 + + + align:start position:0% +probably 60 +something there I think that's the end + + align:start position:0% +something there I think that's the end + + + align:start position:0% +something there I think that's the end +yep so the guest being + + align:start position:0% + + + + align:start position:0% + +60469 brings us to a guest squared + + align:start position:0% +60469 brings us to a guest squared + + + align:start position:0% +60469 brings us to a guest squared +within plus or minus + + align:start position:0% +within plus or minus + + + align:start position:0% +within plus or minus +one yes question + + align:start position:0% + + + + align:start position:0% + +if the guess was if my guess was correct + + align:start position:0% +if the guess was if my guess was correct + + + align:start position:0% +if the guess was if my guess was correct +[Music] + + align:start position:0% + + + + align:start position:0% + +then uh we would break + + align:start position:0% +then uh we would break + + + align:start position:0% +then uh we would break +immediately + + align:start position:0% +immediately + + + align:start position:0% +immediately +right because this becomes this is + + align:start position:0% +right because this becomes this is + + + align:start position:0% +right because this becomes this is +false as yeah we don't even enter the Y + + align:start position:0% +false as yeah we don't even enter the Y + + + align:start position:0% +false as yeah we don't even enter the Y +Loop + + align:start position:0% +Loop + + + align:start position:0% +Loop +yeah okay okay so let's run the code so + + align:start position:0% +yeah okay okay so let's run the code so + + + align:start position:0% +yeah okay okay so let's run the code so +this is the + + align:start position:0% +this is the + + + align:start position:0% +this is the +the uh this is the uh bisection search + + align:start position:0% +the uh this is the uh bisection search + + + align:start position:0% +the uh this is the uh bisection search +code that I just ran through the python + + align:start position:0% +code that I just ran through the python + + + align:start position:0% +code that I just ran through the python +tutor we looked on the slides but um + + align:start position:0% +tutor we looked on the slides but um + + + align:start position:0% +tutor we looked on the slides but um +running with + + align:start position:0% +running with + + + align:start position:0% +running with +54321 so just to recap the number of + + align:start position:0% +54321 so just to recap the number of + + + align:start position:0% +54321 so just to recap the number of +guesses we did with the approximation + + align:start position:0% +guesses we did with the approximation + + + align:start position:0% +guesses we did with the approximation +method was 23 + + align:start position:0% +method was 23 + + + align:start position:0% +method was 23 +million okay to give us an answer that + + align:start position:0% +million okay to give us an answer that + + + align:start position:0% +million okay to give us an answer that +said the square root of 23 the square + + align:start position:0% +said the square root of 23 the square + + + align:start position:0% +said the square root of 23 the square +root of 5 54,000 is about 233 and now we + + align:start position:0% +root of 5 54,000 is about 233 and now we + + + align:start position:0% +root of 5 54,000 is about 233 and now we +run it with our bisection search and I + + align:start position:0% +run it with our bisection search and I + + + align:start position:0% +run it with our bisection search and I +didn't even have to to wait that took + + align:start position:0% +didn't even have to to wait that took + + + align:start position:0% +didn't even have to to wait that took +less than a second right compared to 20 + + align:start position:0% +less than a second right compared to 20 + + + align:start position:0% +less than a second right compared to 20 +seconds that we had to wait for and it + + align:start position:0% +seconds that we had to wait for and it + + + align:start position:0% +seconds that we had to wait for and it +didn't + + align:start position:0% +didn't + + + align:start position:0% +didn't +fail it gave us very similar answer it's + + align:start position:0% +fail it gave us very similar answer it's + + + align:start position:0% +fail it gave us very similar answer it's +this 23306 eight is close to the square + + align:start position:0% +this 23306 eight is close to the square + + + align:start position:0% +this 23306 eight is close to the square +OT of + + align:start position:0% +OT of + + + align:start position:0% +OT of +54,000 and we did 30 + + align:start position:0% + + + + align:start position:0% + +guesses dramatic + + align:start position:0% +guesses dramatic + + + align:start position:0% +guesses dramatic +pause 23 million for the approximation + + align:start position:0% +pause 23 million for the approximation + + + align:start position:0% +pause 23 million for the approximation +method 20 seconds later + + align:start position:0% +method 20 seconds later + + + align:start position:0% +method 20 seconds later +versus 30 guesses less than a second + + align:start position:0% +versus 30 guesses less than a second + + + align:start position:0% +versus 30 guesses less than a second +later so it's not like we went from 23 + + align:start position:0% +later so it's not like we went from 23 + + + align:start position:0% +later so it's not like we went from 23 +million to five million guesses right we + + align:start position:0% +million to five million guesses right we + + + align:start position:0% +million to five million guesses right we +went from the order of millions to just + + align:start position:0% +went from the order of millions to just + + + align:start position:0% +went from the order of millions to just +tens which is really really cool right + + align:start position:0% +tens which is really really cool right + + + align:start position:0% +tens which is really really cool right +that's very + + align:start position:0% +that's very + + + align:start position:0% +that's very +impressive and that's what logarithmic + + align:start position:0% +impressive and that's what logarithmic + + + align:start position:0% +impressive and that's what logarithmic +growth means right that's the power of + + align:start position:0% +growth means right that's the power of + + + align:start position:0% +growth means right that's the power of +logarithmic growth and kind of + + align:start position:0% +logarithmic growth and kind of + + + align:start position:0% +logarithmic growth and kind of +recognizing that we can apply bisection + + align:start position:0% +recognizing that we can apply bisection + + + align:start position:0% +recognizing that we can apply bisection +search to these problems + + align:start position:0% +search to these problems + + + align:start position:0% +search to these problems +right um so with approximation method + + align:start position:0% +right um so with approximation method + + + align:start position:0% +right um so with approximation method +again we're decreasing our search Space + + align:start position:0% +again we're decreasing our search Space + + + align:start position:0% +again we're decreasing our search Space +by + + align:start position:0% +by + + + align:start position:0% +by +0.00001 with each guess but with the + + align:start position:0% +0.00001 with each guess but with the + + + align:start position:0% +0.00001 with each guess but with the +bisection search we're decreasing our + + align:start position:0% +bisection search we're decreasing our + + + align:start position:0% +bisection search we're decreasing our +search Space by half with each guess + + align:start position:0% +search Space by half with each guess + + + align:start position:0% +search Space by half with each guess +right so if we had you know however many + + align:start position:0% +right so if we had you know however many + + + align:start position:0% +right so if we had you know however many +things to search for in the book we had + + align:start position:0% +things to search for in the book we had + + + align:start position:0% +things to search for in the book we had +400 pages to search through right with + + align:start position:0% +400 pages to search through right with + + + align:start position:0% +400 pages to search through right with +our first guess we now only have 200 + + align:start position:0% +our first guess we now only have 200 + + + align:start position:0% +our first guess we now only have 200 +pages to search through through with the + + align:start position:0% +pages to search through through with the + + + align:start position:0% +pages to search through through with the +second guess we only have 100 pages to + + align:start position:0% +second guess we only have 100 pages to + + + align:start position:0% +second guess we only have 100 pages to +search through with the next guess we + + align:start position:0% +search through with the next guess we + + + align:start position:0% +search through with the next guess we +only have 50 pages to search through and + + align:start position:0% +only have 50 pages to search through and + + + align:start position:0% +only have 50 pages to search through and +the idea of bisection search just that + + align:start position:0% +the idea of bisection search just that + + + align:start position:0% +the idea of bisection search just that +it's logarithmic comes from the fact + + align:start position:0% +it's logarithmic comes from the fact + + + align:start position:0% +it's logarithmic comes from the fact +that we have to ask ourselves how many + + align:start position:0% +that we have to ask ourselves how many + + + align:start position:0% +that we have to ask ourselves how many +guesses do we make until we have only + + align:start position:0% +guesses do we make until we have only + + + align:start position:0% +guesses do we make until we have only +you know for example one page left to + + align:start position:0% +you know for example one page left to + + + align:start position:0% +you know for example one page left to +search through for the money or how many + + align:start position:0% +search through for the money or how many + + + align:start position:0% +search through for the money or how many +guesses do we have to make till we are + + align:start position:0% +guesses do we have to make till we are + + + align:start position:0% +guesses do we have to make till we are +within Epsilon there's only that + + align:start position:0% +within Epsilon there's only that + + + align:start position:0% +within Epsilon there's only that +one we reach the one value that gives us + + align:start position:0% +one we reach the one value that gives us + + + align:start position:0% +one we reach the one value that gives us +with an Epsilon okay and so this K many + + align:start position:0% +with an Epsilon okay and so this K many + + + align:start position:0% +with an Epsilon okay and so this K many +guesses means that we've divided our + + align:start position:0% +guesses means that we've divided our + + + align:start position:0% +guesses means that we've divided our +search Space by two to the power of K + + align:start position:0% +search Space by two to the power of K + + + align:start position:0% +search Space by two to the power of K +many + + align:start position:0% +many + + + align:start position:0% +many +times okay and that's when we've + + align:start position:0% +times okay and that's when we've + + + align:start position:0% +times okay and that's when we've +converged on the answer and so to + + align:start position:0% +converged on the answer and so to + + + align:start position:0% +converged on the answer and so to +converge on the answer means you've + + align:start position:0% +converge on the answer means you've + + + align:start position:0% +converge on the answer means you've +divided your search space By by two k + + align:start position:0% +divided your search space By by two k + + + align:start position:0% +divided your search space By by two k +times so n divided 2 to the^ k equals 1 + + align:start position:0% +times so n divided 2 to the^ k equals 1 + + + align:start position:0% +times so n divided 2 to the^ k equals 1 +you have reached your one answer the + + align:start position:0% +you have reached your one answer the + + + align:start position:0% +you have reached your one answer the +money's at this page the student is + + align:start position:0% +money's at this page the student is + + + align:start position:0% +money's at this page the student is +sitting there or we have come within 01 + + align:start position:0% +sitting there or we have come within 01 + + + align:start position:0% +sitting there or we have come within 01 +of you know of of the actual answer and + + align:start position:0% +of you know of of the actual answer and + + + align:start position:0% +of you know of of the actual answer and +so when this is true n is equal to 2 to + + align:start position:0% +so when this is true n is equal to 2 to + + + align:start position:0% +so when this is true n is equal to 2 to +the K and what we want is to kind of + + align:start position:0% +the K and what we want is to kind of + + + align:start position:0% +the K and what we want is to kind of +solve this problem in terms of n so K is + + align:start position:0% +solve this problem in terms of n so K is + + + align:start position:0% +solve this problem in terms of n so K is +equal to log of N and that's where the + + align:start position:0% +equal to log of N and that's where the + + + align:start position:0% +equal to log of N and that's where the +logarithmic growth comes from for this + + align:start position:0% +logarithmic growth comes from for this + + + align:start position:0% +logarithmic growth comes from for this +particular problem okay so in terms of + + align:start position:0% +particular problem okay so in terms of + + + align:start position:0% +particular problem okay so in terms of +Loops yes it took us K times through the + + align:start position:0% +Loops yes it took us K times through the + + + align:start position:0% +Loops yes it took us K times through the +Y Loop to figure out the answer but in + + align:start position:0% +Y Loop to figure out the answer but in + + + align:start position:0% +Y Loop to figure out the answer but in +terms of the size of our search space it + + align:start position:0% +terms of the size of our search space it + + + align:start position:0% +terms of the size of our search space it +took us log of n times to get to our + + align:start position:0% +took us log of n times to get to our + + + align:start position:0% +took us log of n times to get to our +answer okay so let's look at a couple of + + align:start position:0% +answer okay so let's look at a couple of + + + align:start position:0% +answer okay so let's look at a couple of +nuances of the code we just wrote so if + + align:start position:0% +nuances of the code we just wrote so if + + + align:start position:0% +nuances of the code we just wrote so if +we try to run the code for values + + align:start position:0% +we try to run the code for values + + + align:start position:0% +we try to run the code for values +between zero + + align:start position:0% +between zero + + + align:start position:0% +between zero +and uh one what actually happen so if we + + align:start position:0% +and uh one what actually happen so if we + + + align:start position:0% +and uh one what actually happen so if we +run it with for example what's the + + align:start position:0% +run it with for example what's the + + + align:start position:0% +run it with for example what's the +square root of + + align:start position:0% + + + + align:start position:0% + +0.5 it's + + align:start position:0% +0.5 it's + + + align:start position:0% +0.5 it's +running it's still running I'm pretty + + align:start position:0% +running it's still running I'm pretty + + + align:start position:0% +running it's still running I'm pretty +sure it should have given us an answer + + align:start position:0% +sure it should have given us an answer + + + align:start position:0% +sure it should have given us an answer +by now so let's just stop it we've + + align:start position:0% +by now so let's just stop it we've + + + align:start position:0% +by now so let's just stop it we've +entered an infinite + + align:start position:0% +entered an infinite + + + align:start position:0% +entered an infinite +Loop so in that case let's see what + + align:start position:0% +Loop so in that case let's see what + + + align:start position:0% +Loop so in that case let's see what +actually it's printing out so when + + align:start position:0% +actually it's printing out so when + + + align:start position:0% +actually it's printing out so when +you've entered an infinite loop it's + + align:start position:0% +you've entered an infinite loop it's + + + align:start position:0% +you've entered an infinite loop it's +time to put some print + + align:start position:0% +time to put some print + + + align:start position:0% +time to put some print +statements best place to put print + + align:start position:0% +statements best place to put print + + + align:start position:0% +statements best place to put print +statements is within the loop itself and + + align:start position:0% +statements is within the loop itself and + + + align:start position:0% +statements is within the loop itself and +just print out some values for things so + + align:start position:0% +just print out some values for things so + + + align:start position:0% +just print out some values for things so +here I have this print statement where + + align:start position:0% +here I have this print statement where + + + align:start position:0% +here I have this print statement where +we print out what oops let me get that + + align:start position:0% +we print out what oops let me get that + + + align:start position:0% +we print out what oops let me get that +out of the way what the low value + + align:start position:0% +out of the way what the low value + + + align:start position:0% +out of the way what the low value +is so we've got low equals and actually + + align:start position:0% +is so we've got low equals and actually + + + align:start position:0% +is so we've got low equals and actually +I don't need to convert this to string + + align:start position:0% +I don't need to convert this to string + + + align:start position:0% +I don't need to convert this to string +it should just be low and oops and then + + align:start position:0% +it should just be low and oops and then + + + align:start position:0% +it should just be low and oops and then +the high + + align:start position:0% +the high + + + align:start position:0% +the high +value and then the guess + + align:start position:0% + + + + align:start position:0% + +itself oops like + + align:start position:0% +itself oops like + + + align:start position:0% +itself oops like +that so if we run + + align:start position:0% + + + + align:start position:0% + +it that's what we get and it looks like + + align:start position:0% +it that's what we get and it looks like + + + align:start position:0% +it that's what we get and it looks like +it's just repeating repeating over and + + align:start position:0% +it's just repeating repeating over and + + + align:start position:0% +it's just repeating repeating over and +over + + align:start position:0% +over + + + align:start position:0% +over +again so what happens when I'm looking + + align:start position:0% +again so what happens when I'm looking + + + align:start position:0% +again so what happens when I'm looking +for a square root of uh a value between + + align:start position:0% +for a square root of uh a value between + + + align:start position:0% +for a square root of uh a value between +zero and + + align:start position:0% + + + + align:start position:0% + +one + + align:start position:0% +one + + + align:start position:0% +one +so this is my you know Zer to + + align:start position:0% +so this is my you know Zer to + + + align:start position:0% +so this is my you know Zer to +X but if x is between zero and one the + + align:start position:0% +X but if x is between zero and one the + + + align:start position:0% +X but if x is between zero and one the +square root of + + align:start position:0% +square root of + + + align:start position:0% +square root of +x it's bigger than x itself right so the + + align:start position:0% +x it's bigger than x itself right so the + + + align:start position:0% +x it's bigger than x itself right so the +square root of5 five is bigger than 0.5 + + align:start position:0% +square root of5 five is bigger than 0.5 + + + align:start position:0% +square root of5 five is bigger than 0.5 +it's not smaller than 0. five + + align:start position:0% + + + + align:start position:0% + +right so what this program is doing is + + align:start position:0% +right so what this program is doing is + + + align:start position:0% +right so what this program is doing is +it's making its initial guess + + align:start position:0% +it's making its initial guess + + + align:start position:0% +it's making its initial guess +right um High plus low divided by two so + + align:start position:0% +right um High plus low divided by two so + + + align:start position:0% +right um High plus low divided by two so +zero uh if my initial guess is 0 to X + + align:start position:0% +zero uh if my initial guess is 0 to X + + + align:start position:0% +zero uh if my initial guess is 0 to X +it's making an initial guess there and + + align:start position:0% +it's making an initial guess there and + + + align:start position:0% +it's making an initial guess there and +then at some point it just gets stuck in + + align:start position:0% +then at some point it just gets stuck in + + + align:start position:0% +then at some point it just gets stuck in +this Loop because the low becomes 0.5 + + align:start position:0% +this Loop because the low becomes 0.5 + + + align:start position:0% +this Loop because the low becomes 0.5 +after our first guess the high becomes + + align:start position:0% +after our first guess the high becomes + + + align:start position:0% +after our first guess the high becomes +0.5 as well and the halfway point + + align:start position:0% +0.5 as well and the halfway point + + + align:start position:0% +0.5 as well and the halfway point +between 0.5 and 0.5 is just + + align:start position:0% +between 0.5 and 0.5 is just + + + align:start position:0% +between 0.5 and 0.5 is just +0.5 so now it's just reassigning it the + + align:start position:0% +0.5 so now it's just reassigning it the + + + align:start position:0% +0.5 so now it's just reassigning it the +the new guess to itself over and over + + align:start position:0% + + + + align:start position:0% + +again okay so we need to make a fix to + + align:start position:0% +again okay so we need to make a fix to + + + align:start position:0% +again okay so we need to make a fix to +that and I'm going to have you guys make + + align:start position:0% +that and I'm going to have you guys make + + + align:start position:0% +that and I'm going to have you guys make +the fix to that okay so just you don't + + align:start position:0% +the fix to that okay so just you don't + + + align:start position:0% +the fix to that okay so just you don't +need to account for both cases but write + + align:start position:0% +need to account for both cases but write + + + align:start position:0% +need to account for both cases but write +change the + + align:start position:0% +change the + + + align:start position:0% +change the +change the end points for this + + align:start position:0% +change the end points for this + + + align:start position:0% +change the end points for this +particular problem uh such that it works + + align:start position:0% +particular problem uh such that it works + + + align:start position:0% +particular problem uh such that it works +with values of X between zero and one so + + align:start position:0% +with values of X between zero and one so + + + align:start position:0% +with values of X between zero and one so +if we're trying to find the square root + + align:start position:0% +if we're trying to find the square root + + + align:start position:0% +if we're trying to find the square root +of a decimal number between zero and one + + align:start position:0% +of a decimal number between zero and one + + + align:start position:0% +of a decimal number between zero and one +what are the end points that you want to + + align:start position:0% +what are the end points that you want to + + + align:start position:0% +what are the end points that you want to +choose for the code to now work and the + + align:start position:0% +choose for the code to now work and the + + + align:start position:0% +choose for the code to now work and the +code is exactly the same as before okay + + align:start position:0% +code is exactly the same as before okay + + + align:start position:0% +code is exactly the same as before okay +so all you need to do is choose + + align:start position:0% +so all you need to do is choose + + + align:start position:0% +so all you need to do is choose +different end points yes I don't + + align:start position:0% +different end points yes I don't + + + align:start position:0% +different end points yes I don't +understand why why it got stuck like the + + align:start position:0% +understand why why it got stuck like the + + + align:start position:0% +understand why why it got stuck like the +high oh okay we can um we can run it + + align:start position:0% +high oh okay we can um we can run it + + + align:start position:0% +high oh okay we can um we can run it +with the python + + align:start position:0% +with the python + + + align:start position:0% +with the python +tutor and so for this is + + align:start position:0% +tutor and so for this is + + + align:start position:0% +tutor and so for this is +0.5 all right so basically we've made + + align:start position:0% +0.5 all right so basically we've made + + + align:start position:0% +0.5 all right so basically we've made +our guess like that right and then we're + + align:start position:0% +our guess like that right and then we're + + + align:start position:0% +our guess like that right and then we're +changing our + + align:start position:0% +changing our + + + align:start position:0% +changing our +guesses and so you can see that it's + + align:start position:0% +guesses and so you can see that it's + + + align:start position:0% +guesses and so you can see that it's +actually changing the + + align:start position:0% + + + + align:start position:0% + +low and the high and it originally did + + align:start position:0% +low and the high and it originally did + + + align:start position:0% +low and the high and it originally did +the right + + align:start position:0% +the right + + + align:start position:0% +the right +thing right like the first few guesses + + align:start position:0% +thing right like the first few guesses + + + align:start position:0% +thing right like the first few guesses +it's it's making the changes appropriate + + align:start position:0% +it's it's making the changes appropriate + + + align:start position:0% +it's it's making the changes appropriate +but then the floating Point errors come + + align:start position:0% +but then the floating Point errors come + + + align:start position:0% +but then the floating Point errors come +into play where at some point this 4999 + + align:start position:0% +into play where at some point this 4999 + + + align:start position:0% +into play where at some point this 4999 +and this low that it's keep it keeps + + align:start position:0% +and this low that it's keep it keeps + + + align:start position:0% +and this low that it's keep it keeps +dividing is just going to become 0. five + + align:start position:0% +dividing is just going to become 0. five + + + align:start position:0% +dividing is just going to become 0. five +and 0 five is a is a power of two + + align:start position:0% +and 0 five is a is a power of two + + + align:start position:0% +and 0 five is a is a power of two +remember as as floating points are uh + + align:start position:0% +remember as as floating points are uh + + + align:start position:0% +remember as as floating points are uh +and in this particular case once it + + align:start position:0% +and in this particular case once it + + + align:start position:0% +and in this particular case once it +reaches the0 five then floating Point + + align:start position:0% +reaches the0 five then floating Point + + + align:start position:0% +reaches the0 five then floating Point +errors don't come into play anymore + + align:start position:0% +errors don't come into play anymore + + + align:start position:0% +errors don't come into play anymore +because that 0 five can just be + + align:start position:0% +because that 0 five can just be + + + align:start position:0% +because that 0 five can just be +represented exactly so I'm going to have + + align:start position:0% +represented exactly so I'm going to have + + + align:start position:0% +represented exactly so I'm going to have +to probably hit next for quite a a few + + align:start position:0% +to probably hit next for quite a a few + + + align:start position:0% +to probably hit next for quite a a few +more times but you can kind of see right + + align:start position:0% +more times but you can kind of see right + + + align:start position:0% +more times but you can kind of see right +where that's getting that 0 five from + + align:start position:0% +where that's getting that 0 five from + + + align:start position:0% +where that's getting that 0 five from +does that + + align:start position:0% +does that + + + align:start position:0% +does that +help yeah theing point erus + + align:start position:0% + + + + align:start position:0% + +toip that and also the fact that we we + + align:start position:0% +toip that and also the fact that we we + + + align:start position:0% +toip that and also the fact that we we +didn't really account this code doesn't + + align:start position:0% +didn't really account this code doesn't + + + align:start position:0% +didn't really account this code doesn't +actually work correctly with these + + align:start position:0% +actually work correctly with these + + + align:start position:0% +actually work correctly with these +values so it enters in an infinite Loop + + align:start position:0% +values so it enters in an infinite Loop + + + align:start position:0% +values so it enters in an infinite Loop +because of the floating Point error + + align:start position:0% +because of the floating Point error + + + align:start position:0% +because of the floating Point error +towards the end um and that causes us to + + align:start position:0% +towards the end um and that causes us to + + + align:start position:0% +towards the end um and that causes us to +see just 0. + + align:start position:0% +see just 0. + + + align:start position:0% +see just 0. +5.5.5 but if we were doing it to like + + align:start position:0% +5.5.5 but if we were doing it to like + + + align:start position:0% +5.5.5 but if we were doing it to like +infinite Precision you would start to + + align:start position:0% +infinite Precision you would start to + + + align:start position:0% +infinite Precision you would start to +see numbers that approach 0. five but + + align:start position:0% +see numbers that approach 0. five but + + + align:start position:0% +see numbers that approach 0. five but +never quite get there yeah but I think + + align:start position:0% +never quite get there yeah but I think + + + align:start position:0% +never quite get there yeah but I think +our code the reason we saw 0.5 here is + + align:start position:0% +our code the reason we saw 0.5 here is + + + align:start position:0% +our code the reason we saw 0.5 here is +because it already ran like you know a + + align:start position:0% +because it already ran like you know a + + + align:start position:0% +because it already ran like you know a +100 times 200 times and so now we're + + align:start position:0% +100 times 200 times and so now we're + + + align:start position:0% +100 times 200 times and so now we're +just seeing this uh this the tail end of + + align:start position:0% +just seeing this uh this the tail end of + + + align:start position:0% +just seeing this uh this the tail end of +it yeah + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so here is the code for fixing + + align:start position:0% +so here is the code for fixing + + + align:start position:0% +so here is the code for fixing +that so what do you guys think the low + + align:start position:0% +that so what do you guys think the low + + + align:start position:0% +that so what do you guys think the low +end point should be and the high end + + align:start position:0% +end point should be and the high end + + + align:start position:0% +end point should be and the high end +point should be if we wanted this to + + align:start position:0% +point should be if we wanted this to + + + align:start position:0% +point should be if we wanted this to +work with negative uh with the values + + align:start position:0% +work with negative uh with the values + + + align:start position:0% +work with negative uh with the values +between zero and + + align:start position:0% +between zero and + + + align:start position:0% +between zero and +one so if this is our + + align:start position:0% +one so if this is our + + + align:start position:0% +one so if this is our +um right this is our X and we know X is + + align:start position:0% +um right this is our X and we know X is + + + align:start position:0% +um right this is our X and we know X is +you know less than one greater than zero + + align:start position:0% +you know less than one greater than zero + + + align:start position:0% +you know less than one greater than zero +the square root of x is going to be + + align:start position:0% +the square root of x is going to be + + + align:start position:0% +the square root of x is going to be +somewhere up here right and we know the + + align:start position:0% +somewhere up here right and we know the + + + align:start position:0% +somewhere up here right and we know the +maximum place it will be is + + align:start position:0% +maximum place it will be is + + + align:start position:0% +maximum place it will be is +one and what's the minimum place that + + align:start position:0% +one and what's the minimum place that + + + align:start position:0% +one and what's the minimum place that +the square root of x could be for values + + align:start position:0% +the square root of x could be for values + + + align:start position:0% +the square root of x could be for values +within this range I heard yeah X so this + + align:start position:0% +within this range I heard yeah X so this + + + align:start position:0% +within this range I heard yeah X so this +is the minimum value for the square root + + align:start position:0% +is the minimum value for the square root + + + align:start position:0% +is the minimum value for the square root +of x and this is the maximum value for + + align:start position:0% +of x and this is the maximum value for + + + align:start position:0% +of x and this is the maximum value for +the square root of x + + align:start position:0% + + + + align:start position:0% + +so all we need to do is say the low is + + align:start position:0% +so all we need to do is say the low is + + + align:start position:0% +so all we need to do is say the low is +equal to + + align:start position:0% +equal to + + + align:start position:0% +equal to +X and the high is equal to one and then + + align:start position:0% +X and the high is equal to one and then + + + align:start position:0% +X and the high is equal to one and then +I think this code should + + align:start position:0% +I think this code should + + + align:start position:0% +I think this code should +work + + align:start position:0% + + + + align:start position:0% + +y okay and so I did just that down here + + align:start position:0% +y okay and so I did just that down here + + + align:start position:0% +y okay and so I did just that down here +so here is the code with um actually + + align:start position:0% +so here is the code with um actually + + + align:start position:0% +so here is the code with um actually +allowing for the user to give us any + + align:start position:0% +allowing for the user to give us any + + + align:start position:0% +allowing for the user to give us any +value not just between zero and one or + + align:start position:0% +value not just between zero and one or + + + align:start position:0% +value not just between zero and one or +greater than + + align:start position:0% +greater than + + + align:start position:0% +greater than +one so all I did here to make the code + + align:start position:0% +one so all I did here to make the code + + + align:start position:0% +one so all I did here to make the code +work and be uh robust is add an if else + + align:start position:0% +work and be uh robust is add an if else + + + align:start position:0% +work and be uh robust is add an if else +right at the + + align:start position:0% +right at the + + + align:start position:0% +right at the +beginning so I allow the user to give me + + align:start position:0% +beginning so I allow the user to give me + + + align:start position:0% +beginning so I allow the user to give me +whatever X they'd like but then I do a + + align:start position:0% +whatever X they'd like but then I do a + + + align:start position:0% +whatever X they'd like but then I do a +little check here that says if the x is + + align:start position:0% +little check here that says if the x is + + + align:start position:0% +little check here that says if the x is +greater or equal to + + align:start position:0% +greater or equal to + + + align:start position:0% +greater or equal to +one then my low and high end points + + align:start position:0% +one then my low and high end points + + + align:start position:0% +one then my low and high end points +become 0 to X right because I know the + + align:start position:0% +become 0 to X right because I know the + + + align:start position:0% +become 0 to X right because I know the +square root is going to be within that + + align:start position:0% +square root is going to be within that + + + align:start position:0% +square root is going to be within that +boundary but then otherwise if the user + + align:start position:0% +boundary but then otherwise if the user + + + align:start position:0% +boundary but then otherwise if the user +gave me a value that's less than + + align:start position:0% +gave me a value that's less than + + + align:start position:0% +gave me a value that's less than +one and I guess I should uh do greater + + align:start position:0% +one and I guess I should uh do greater + + + align:start position:0% +one and I guess I should uh do greater +than zero just in case the user gives me + + align:start position:0% +than zero just in case the user gives me + + + align:start position:0% +than zero just in case the user gives me +negative numbers then I would choose the + + align:start position:0% +negative numbers then I would choose the + + + align:start position:0% +negative numbers then I would choose the +boundary for the low to be X and the + + align:start position:0% +boundary for the low to be X and the + + + align:start position:0% +boundary for the low to be X and the +high to be one so just a very simple if + + align:start position:0% +high to be one so just a very simple if + + + align:start position:0% +high to be one so just a very simple if +else here and otherwise the rest of the + + align:start position:0% +else here and otherwise the rest of the + + + align:start position:0% +else here and otherwise the rest of the +code works just the same + + align:start position:0% + + + + align:start position:0% + +okay yeah so this is exactly what we + + align:start position:0% +okay yeah so this is exactly what we + + + align:start position:0% +okay yeah so this is exactly what we +just saw in the slides right an if and + + align:start position:0% +just saw in the slides right an if and + + + align:start position:0% +just saw in the slides right an if and +an else where I choose the end points + + align:start position:0% +an else where I choose the end points + + + align:start position:0% +an else where I choose the end points +accordingly any questions about this + + align:start position:0% +accordingly any questions about this + + + align:start position:0% +accordingly any questions about this +code does it make + + align:start position:0% +code does it make + + + align:start position:0% +code does it make +sense yeah I made the low equal to zero + + align:start position:0% +sense yeah I made the low equal to zero + + + align:start position:0% +sense yeah I made the low equal to zero +and still G me the same answer + + align:start position:0% +and still G me the same answer + + + align:start position:0% +and still G me the same answer +for oh if you make the low equal to zero + + align:start position:0% +for oh if you make the low equal to zero + + + align:start position:0% +for oh if you make the low equal to zero +here oops + + align:start position:0% + + + + align:start position:0% + +I think that's fine right because then + + align:start position:0% +I think that's fine right because then + + + align:start position:0% +I think that's fine right because then +that means you're looking you're making + + align:start position:0% +that means you're looking you're making + + + align:start position:0% +that means you're looking you're making +your low lower than it needs to be and + + align:start position:0% +your low lower than it needs to be and + + + align:start position:0% +your low lower than it needs to be and +so your first guess is basically the + + align:start position:0% +so your first guess is basically the + + + align:start position:0% +so your first guess is basically the +halfway point x itself and then it it + + align:start position:0% +halfway point x itself and then it it + + + align:start position:0% +halfway point x itself and then it it +fixes I think it it just fixes it h so + + align:start position:0% +fixes I think it it just fixes it h so + + + align:start position:0% +fixes I think it it just fixes it h so +it just goes through one extra guess it + + align:start position:0% +it just goes through one extra guess it + + + align:start position:0% +it just goes through one extra guess it +goes through one extra guess exactly and + + align:start position:0% +goes through one extra guess exactly and + + + align:start position:0% +goes through one extra guess exactly and +that's again the power of bisection + + align:start position:0% +that's again the power of bisection + + + align:start position:0% +that's again the power of bisection +search right if for values um for values + + align:start position:0% +search right if for values um for values + + + align:start position:0% +search right if for values um for values +greater than one if we made our high + + align:start position:0% +greater than one if we made our high + + + align:start position:0% +greater than one if we made our high +boundary be + + align:start position:0% +boundary be + + + align:start position:0% +boundary be +2x it would just make one extra guess to + + align:start position:0% +2x it would just make one extra guess to + + + align:start position:0% +2x it would just make one extra guess to +bring us to X and then you know below + + align:start position:0% +bring us to X and then you know below + + + align:start position:0% +bring us to X and then you know below +and so on and so on so like one extra + + align:start position:0% +and so on and so on so like one extra + + + align:start position:0% +and so on and so on so like one extra +guess is nothing to the computer + + align:start position:0% + + + + align:start position:0% + +right okay so a couple observations with + + align:start position:0% +right okay so a couple observations with + + + align:start position:0% +right okay so a couple observations with +bisection uh for bisection search + + align:start position:0% + + + + align:start position:0% + +so it takes a significantly less amount + + align:start position:0% +so it takes a significantly less amount + + + align:start position:0% +so it takes a significantly less amount +of time to solve problems using B search + + align:start position:0% +of time to solve problems using B search + + + align:start position:0% +of time to solve problems using B search +than it does using the approximation + + align:start position:0% +than it does using the approximation + + + align:start position:0% +than it does using the approximation +method and it gives us an approximation + + align:start position:0% +method and it gives us an approximation + + + align:start position:0% +method and it gives us an approximation +to in this case the square root of a + + align:start position:0% +to in this case the square root of a + + + align:start position:0% +to in this case the square root of a +number that was pretty just as you know + + align:start position:0% +number that was pretty just as you know + + + align:start position:0% +number that was pretty just as you know +just as good as the approximation method + + align:start position:0% +just as good as the approximation method + + + align:start position:0% +just as good as the approximation method +itself um when we did the book example + + align:start position:0% +itself um when we did the book example + + + align:start position:0% +itself um when we did the book example +and that's kind of the second Point here + + align:start position:0% +and that's kind of the second Point here + + + align:start position:0% +and that's kind of the second Point here +might be easier to illustrate when we + + align:start position:0% +might be easier to illustrate when we + + + align:start position:0% +might be easier to illustrate when we +did the book example um the very first + + align:start position:0% +did the book example um the very first + + + align:start position:0% +did the book example um the very first +guess + + align:start position:0% +guess + + + align:start position:0% +guess +eliminated more number of pages than + + align:start position:0% +eliminated more number of pages than + + + align:start position:0% +eliminated more number of pages than +later guesses right our first guess + + align:start position:0% +later guesses right our first guess + + + align:start position:0% +later guesses right our first guess +eliminated 200 pages right off the bat + + align:start position:0% +eliminated 200 pages right off the bat + + + align:start position:0% +eliminated 200 pages right off the bat +right our second guest only eliminated + + align:start position:0% +right our second guest only eliminated + + + align:start position:0% +right our second guest only eliminated +100 Pages our third only 50 and at some + + align:start position:0% +100 Pages our third only 50 and at some + + + align:start position:0% +100 Pages our third only 50 and at some +point you can imagine that we're only + + align:start position:0% +point you can imagine that we're only + + + align:start position:0% +point you can imagine that we're only +eliminating something like four pages + + align:start position:0% +eliminating something like four pages + + + align:start position:0% +eliminating something like four pages +and then we're El eliminating only two + + align:start position:0% +and then we're El eliminating only two + + + align:start position:0% +and then we're El eliminating only two +pages at a time right as the more and + + align:start position:0% +pages at a time right as the more and + + + align:start position:0% +pages at a time right as the more and +more guesses you make so it feels more + + align:start position:0% +more guesses you make so it feels more + + + align:start position:0% +more guesses you make so it feels more +dramatic at first but then you know it + + align:start position:0% +dramatic at first but then you know it + + + align:start position:0% +dramatic at first but then you know it +it it kind of dies down but that's just + + align:start position:0% +it it kind of dies down but that's just + + + align:start position:0% +it it kind of dies down but that's just +logarithmic growth right it feels + + align:start position:0% +logarithmic growth right it feels + + + align:start position:0% +logarithmic growth right it feels +dramatic at first but then you get as + + align:start position:0% +dramatic at first but then you get as + + + align:start position:0% +dramatic at first but then you get as +you get closer closer to the actual + + align:start position:0% +you get closer closer to the actual + + + align:start position:0% +you get closer closer to the actual +approximation the actual answer you're + + align:start position:0% +approximation the actual answer you're + + + align:start position:0% +approximation the actual answer you're +not making taking that as big of steps + + align:start position:0% +not making taking that as big of steps + + + align:start position:0% +not making taking that as big of steps +or you're not making such dramatic cuts + + align:start position:0% +or you're not making such dramatic cuts + + + align:start position:0% +or you're not making such dramatic cuts +to the book okay and so the bisection + + align:start position:0% +to the book okay and so the bisection + + + align:start position:0% +to the book okay and so the bisection +search algorithm is really awesome but + + align:start position:0% +search algorithm is really awesome but + + + align:start position:0% +search algorithm is really awesome but +again there are some limitations to when + + align:start position:0% +again there are some limitations to when + + + align:start position:0% +again there are some limitations to when +you can use it right you have to have + + align:start position:0% +you can use it right you have to have + + + align:start position:0% +you can use it right you have to have +your search space have end points that + + align:start position:0% +your search space have end points that + + + align:start position:0% +your search space have end points that +search space needs to be ordered right + + align:start position:0% +search space needs to be ordered right + + + align:start position:0% +search space needs to be ordered right +alphabetically in order by you know + + align:start position:0% +alphabetically in order by you know + + + align:start position:0% +alphabetically in order by you know +numerical whatever and you have to be + + align:start position:0% +numerical whatever and you have to be + + + align:start position:0% +numerical whatever and you have to be +able to get the feedback is this guess + + align:start position:0% +able to get the feedback is this guess + + + align:start position:0% +able to get the feedback is this guess +too low or too high right if you don't + + align:start position:0% +too low or too high right if you don't + + + align:start position:0% +too low or too high right if you don't +have those then you can't use bisection + + align:start position:0% +have those then you can't use bisection + + + align:start position:0% +have those then you can't use bisection +search for this okay I'm going to give + + align:start position:0% +search for this okay I'm going to give + + + align:start position:0% +search for this okay I'm going to give +you a couple moments to work on this + + align:start position:0% +you a couple moments to work on this + + + align:start position:0% +you a couple moments to work on this +code by yourself so this is you writing + + align:start position:0% +code by yourself so this is you writing + + + align:start position:0% +code by yourself so this is you writing +the bisection search algorithm to find + + align:start position:0% +the bisection search algorithm to find + + + align:start position:0% +the bisection search algorithm to find +the cube root of positive cubes so don't + + align:start position:0% +the cube root of positive cubes so don't + + + align:start position:0% +the cube root of positive cubes so don't +worry about you know negatives or + + align:start position:0% +worry about you know negatives or + + + align:start position:0% +worry about you know negatives or +whatever just assume the user gives you + + align:start position:0% +whatever just assume the user gives you + + + align:start position:0% +whatever just assume the user gives you +a positive Cube I'm initializing the + + align:start position:0% +a positive Cube I'm initializing the + + + align:start position:0% +a positive Cube I'm initializing the +values for you here so the cube is + + align:start position:0% +values for you here so the cube is + + + align:start position:0% +values for you here so the cube is +27 I want you to be within plus or minus + + align:start position:0% +27 I want you to be within plus or minus + + + align:start position:0% +27 I want you to be within plus or minus +01 right so your guest squared should be + + align:start position:0% +01 right so your guest squared should be + + + align:start position:0% +01 right so your guest squared should be +within plus orus 01 of 27 start with a + + align:start position:0% +within plus orus 01 of 27 start with a + + + align:start position:0% +within plus orus 01 of 27 start with a +low of zero and a high of + + align:start position:0% +low of zero and a high of + + + align:start position:0% +low of zero and a high of +Cube and write the rest of the algorithm + + align:start position:0% +Cube and write the rest of the algorithm + + + align:start position:0% +Cube and write the rest of the algorithm +don't copy and paste what we did for + + align:start position:0% +don't copy and paste what we did for + + + align:start position:0% +don't copy and paste what we did for +square um try to write it all by + + align:start position:0% +square um try to write it all by + + + align:start position:0% +square um try to write it all by +yourself all over again it'll a give you + + align:start position:0% +yourself all over again it'll a give you + + + align:start position:0% +yourself all over again it'll a give you +practice coding B make sure that you + + align:start position:0% +practice coding B make sure that you + + + align:start position:0% +practice coding B make sure that you +understand the actual steps of the + + align:start position:0% +understand the actual steps of the + + + align:start position:0% +understand the actual steps of the +algorithm you don't need to write it top + + align:start position:0% +algorithm you don't need to write it top + + + align:start position:0% +algorithm you don't need to write it top +to bottom you can write the inside of + + align:start position:0% +to bottom you can write the inside of + + + align:start position:0% +to bottom you can write the inside of +the Y Loop first or what whatever you + + align:start position:0% +the Y Loop first or what whatever you + + + align:start position:0% +the Y Loop first or what whatever you +whatever feels Comfort comfortable for + + align:start position:0% +whatever feels Comfort comfortable for + + + align:start position:0% +whatever feels Comfort comfortable for +you but as long as you try to write it + + align:start position:0% +you but as long as you try to write it + + + align:start position:0% +you but as long as you try to write it +all by yourself to try to make you know + + align:start position:0% +all by yourself to try to make you know + + + align:start position:0% +all by yourself to try to make you know +this coding um second nature I'm all for + + align:start position:0% +this coding um second nature I'm all for + + + align:start position:0% +this coding um second nature I'm all for +that so I'll give you a couple moments + + align:start position:0% +that so I'll give you a couple moments + + + align:start position:0% +that so I'll give you a couple moments +to do that and then we can write it + + align:start position:0% +to do that and then we can write it + + + align:start position:0% +to do that and then we can write it +together but basically it's going to be + + align:start position:0% +together but basically it's going to be + + + align:start position:0% +together but basically it's going to be +almost the same as what we've been + + align:start position:0% +almost the same as what we've been + + + align:start position:0% +almost the same as what we've been +seeing on this on the + + align:start position:0% + + + + align:start position:0% + +slides all right does anyone have a + + align:start position:0% +slides all right does anyone have a + + + align:start position:0% +slides all right does anyone have a +start for me what do you want to start + + align:start position:0% +start for me what do you want to start + + + align:start position:0% +start for me what do you want to start +with do you want to do a while loop or a + + align:start position:0% +with do you want to do a while loop or a + + + align:start position:0% +with do you want to do a while loop or a +for Loop let's ask that + + align:start position:0% +for Loop let's ask that + + + align:start position:0% +for Loop let's ask that +a while loop okay let's do while and + + align:start position:0% +a while loop okay let's do while and + + + align:start position:0% +a while loop okay let's do while and +what's the condition going to be right + + align:start position:0% +what's the condition going to be right + + + align:start position:0% +what's the condition going to be right +for the + + align:start position:0% +for the + + + align:start position:0% +for the +approximation yep oh I needed to find a + + align:start position:0% +approximation yep oh I needed to find a + + + align:start position:0% +approximation yep oh I needed to find a +guess perfect okay what should my guess + + align:start position:0% + + + + align:start position:0% + +be yes High plus low over + + align:start position:0% +be yes High plus low over + + + align:start position:0% +be yes High plus low over +two okay so I have my initial guess and + + align:start position:0% +two okay so I have my initial guess and + + + align:start position:0% +two okay so I have my initial guess and +then what what is happening with my + + align:start position:0% +then what what is happening with my + + + align:start position:0% +then what what is happening with my +loop I want to keep doing things as long + + align:start position:0% + + + + align:start position:0% + +as guess to the + + align:start position:0% +as guess to the + + + align:start position:0% +as guess to the +thir + + align:start position:0% +thir + + + align:start position:0% +thir +minus Cube + + align:start position:0% + + + + align:start position:0% + +AB yep absolute value of guest + + align:start position:0% +AB yep absolute value of guest + + + align:start position:0% +AB yep absolute value of guest +yep + + align:start position:0% + + + + align:start position:0% + +okay exactly we want it to be larger + + align:start position:0% +okay exactly we want it to be larger + + + align:start position:0% +okay exactly we want it to be larger +larger equal whatever you'd like Epsilon + + align:start position:0% +larger equal whatever you'd like Epsilon + + + align:start position:0% +larger equal whatever you'd like Epsilon +yeah so while I'm still too far + + align:start position:0% + + + + align:start position:0% + +away no because then we're comparing + + align:start position:0% +away no because then we're comparing + + + align:start position:0% +away no because then we're comparing +floats we want to be + + align:start position:0% + + + + align:start position:0% + +farther right because if it's not equal + + align:start position:0% +farther right because if it's not equal + + + align:start position:0% +farther right because if it's not equal +to you only stop when it becomes exactly + + align:start position:0% +to you only stop when it becomes exactly + + + align:start position:0% +to you only stop when it becomes exactly + + align:start position:0% + + + align:start position:0% +away right and wait so yeah so we can + + align:start position:0% +away right and wait so yeah so we can + + + align:start position:0% +away right and wait so yeah so we can +draw it's easier if we + + align:start position:0% +draw it's easier if we + + + align:start position:0% +draw it's easier if we +draw this is our + + align:start position:0% +draw this is our + + + align:start position:0% +draw this is our +X and this is Epsilon + + align:start position:0% +X and this is Epsilon + + + align:start position:0% +X and this is Epsilon +right and our guest cubed + + align:start position:0% +right and our guest cubed + + + align:start position:0% +right and our guest cubed +um if it's equal to that means G + + align:start position:0% +um if it's equal to that means G + + + align:start position:0% +um if it's equal to that means G +cubed is exactly here I guess or exactly + + align:start position:0% +cubed is exactly here I guess or exactly + + + align:start position:0% +cubed is exactly here I guess or exactly +here oh so we have to bound yes you want + + align:start position:0% +here oh so we have to bound yes you want + + + align:start position:0% +here oh so we have to bound yes you want +to be out of bounds to still be making + + align:start position:0% +to be out of bounds to still be making + + + align:start position:0% +to be out of bounds to still be making +guesses + + align:start position:0% +guesses + + + align:start position:0% +guesses +yep what's our process for making a new + + align:start position:0% +yep what's our process for making a new + + + align:start position:0% +yep what's our process for making a new +guess using bisection + + align:start position:0% +guess using bisection + + + align:start position:0% +guess using bisection +search so we have a guess and now what + + align:start position:0% +search so we have a guess and now what + + + align:start position:0% +search so we have a guess and now what +do we need to do we need to decide + + align:start position:0% +do we need to do we need to decide + + + align:start position:0% +do we need to do we need to decide +whether it's too low or too high right + + align:start position:0% +whether it's too low or too high right + + + align:start position:0% +whether it's too low or too high right +that's what that's what the um the + + align:start position:0% +that's what that's what the um the + + + align:start position:0% +that's what that's what the um the +bisection sech says so + + align:start position:0% +bisection sech says so + + + align:start position:0% +bisection sech says so +guess or guess cubed is too low or too + + align:start position:0% + + + + align:start position:0% + +high + + align:start position:0% +high + + + align:start position:0% +high +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +if the guess + + align:start position:0% + + + + align:start position:0% + +cubed yep larger than + + align:start position:0% +cubed yep larger than + + + align:start position:0% +cubed yep larger than +Cube then our guess is too high so I can + + align:start position:0% +Cube then our guess is too high so I can + + + align:start position:0% +Cube then our guess is too high so I can +even make a note for myself here guess + + align:start position:0% +even make a note for myself here guess + + + align:start position:0% +even make a note for myself here guess +too high + + align:start position:0% +too high + + + align:start position:0% +too high +right so if it's too high I know + + align:start position:0% +right so if it's too high I know + + + align:start position:0% +right so if it's too high I know +anything bigger than it I don't want so + + align:start position:0% +anything bigger than it I don't want so + + + align:start position:0% +anything bigger than it I don't want so +I need to set my high boundary or my low + + align:start position:0% +I need to set my high boundary or my low + + + align:start position:0% +I need to set my high boundary or my low +or my high end point or my low end + + align:start position:0% + + + + align:start position:0% + +point yeah my high end point becomes my + + align:start position:0% +point yeah my high end point becomes my + + + align:start position:0% +point yeah my high end point becomes my +guess right I'm resetting my high to be + + align:start position:0% +guess right I'm resetting my high to be + + + align:start position:0% +guess right I'm resetting my high to be +the guess because I know that guess is + + align:start position:0% +the guess because I know that guess is + + + align:start position:0% +the guess because I know that guess is +too big + + align:start position:0% +too big + + + align:start position:0% +too big +anyway else opposite my lowend point is + + align:start position:0% +anyway else opposite my lowend point is + + + align:start position:0% +anyway else opposite my lowend point is +my guess + + align:start position:0% + + + + align:start position:0% + +am I + + align:start position:0% +am I + + + align:start position:0% +am I +done nope okay what do I need to + + align:start position:0% + + + + align:start position:0% + +do I need to redefine my guess yep if I + + align:start position:0% +do I need to redefine my guess yep if I + + + align:start position:0% +do I need to redefine my guess yep if I +don't redefine my guess my code has an + + align:start position:0% +don't redefine my guess my code has an + + + align:start position:0% +don't redefine my guess my code has an +infinite Loop so my guess is exactly as + + align:start position:0% +infinite Loop so my guess is exactly as + + + align:start position:0% +infinite Loop so my guess is exactly as +before high plus low divided by + + align:start position:0% + + + + align:start position:0% + +two and then at the end same indentation + + align:start position:0% +two and then at the end same indentation + + + align:start position:0% +two and then at the end same indentation +level as the while loop we can just + + align:start position:0% +level as the while loop we can just + + + align:start position:0% +level as the while loop we can just +print our guess because I know I'm going + + align:start position:0% +print our guess because I know I'm going + + + align:start position:0% +print our guess because I know I'm going +to break as soon as I become + + align:start position:0% +to break as soon as I become + + + align:start position:0% +to break as soon as I become +within or equal to + + align:start position:0% + + + + align:start position:0% + +Epsilon y that's what we were expecting + + align:start position:0% +Epsilon y that's what we were expecting + + + align:start position:0% +Epsilon y that's what we were expecting +right and it's fine that it's + + align:start position:0% +right and it's fine that it's + + + align:start position:0% +right and it's fine that it's +3.00 something right I wouldn't expect + + align:start position:0% +3.00 something right I wouldn't expect + + + align:start position:0% +3.00 something right I wouldn't expect +it to be exactly three even though we as + + align:start position:0% +it to be exactly three even though we as + + + align:start position:0% +it to be exactly three even though we as +humans know it is three because the + + align:start position:0% +humans know it is three because the + + + align:start position:0% +humans know it is three because the +algorithm says to stop as soon as we + + align:start position:0% +algorithm says to stop as soon as we + + + align:start position:0% +algorithm says to stop as soon as we +came with an Epsilon right yes we can + + align:start position:0% +came with an Epsilon right yes we can + + + align:start position:0% +came with an Epsilon right yes we can +find a better answer if we keep going + + align:start position:0% +find a better answer if we keep going + + + align:start position:0% +find a better answer if we keep going +but that's not what we asked the code to + + align:start position:0% +but that's not what we asked the code to + + + align:start position:0% +but that's not what we asked the code to +do we asked the code to stop as soon as + + align:start position:0% +do we asked the code to stop as soon as + + + align:start position:0% +do we asked the code to stop as soon as +we came within plus or minus Epsilon of + + align:start position:0% +we came within plus or minus Epsilon of + + + align:start position:0% +we came within plus or minus Epsilon of +this + + align:start position:0% + + + + align:start position:0% + +right goes in the if or low it does not + + align:start position:0% +right goes in the if or low it does not + + + align:start position:0% +right goes in the if or low it does not +matter if you put the high in the or the + + align:start position:0% +matter if you put the high in the or the + + + align:start position:0% +matter if you put the high in the or the +yeah or the low I mean as long as you're + + align:start position:0% +yeah or the low I mean as long as you're + + + align:start position:0% +yeah or the low I mean as long as you're +consistent right if it's greater than + + align:start position:0% +consistent right if it's greater than + + + align:start position:0% +consistent right if it's greater than +you have to reassign the high if this is + + align:start position:0% +you have to reassign the high if this is + + + align:start position:0% +you have to reassign the high if this is +less than you reassign them low yeah + + align:start position:0% + + + + align:start position:0% + +okay okay so we're going to look at one + + align:start position:0% +okay okay so we're going to look at one + + + align:start position:0% +okay okay so we're going to look at one +more um algorithm to figure out the an + + align:start position:0% +more um algorithm to figure out the an + + + align:start position:0% +more um algorithm to figure out the an +approximation to the square root of a + + align:start position:0% +approximation to the square root of a + + + align:start position:0% +approximation to the square root of a +number just to show you that there is + + align:start position:0% +number just to show you that there is + + + align:start position:0% +number just to show you that there is +something else uh yet another thing and + + align:start position:0% +something else uh yet another thing and + + + align:start position:0% +something else uh yet another thing and +this particular algorithm only works to + + align:start position:0% +this particular algorithm only works to + + + align:start position:0% +this particular algorithm only works to +find roots of a + + align:start position:0% +find roots of a + + + align:start position:0% +find roots of a +polom okay so this is a Newton rapson + + align:start position:0% +polom okay so this is a Newton rapson + + + align:start position:0% +polom okay so this is a Newton rapson +algorithm and basically we don't need to + + align:start position:0% +algorithm and basically we don't need to + + + align:start position:0% +algorithm and basically we don't need to +prove this but basically they uh he + + align:start position:0% +prove this but basically they uh he + + + align:start position:0% +prove this but basically they uh he +showed that um they showed that if you + + align:start position:0% +showed that um they showed that if you + + + align:start position:0% +showed that um they showed that if you +have a polinomial of this form so you + + align:start position:0% +have a polinomial of this form so you + + + align:start position:0% +have a polinomial of this form so you +know ax S Plus BX plus C or ax to the^ + + align:start position:0% +know ax S Plus BX plus C or ax to the^ + + + align:start position:0% +know ax S Plus BX plus C or ax to the^ +of 4 plus BX Cub plus CX plus d + + align:start position:0% +of 4 plus BX Cub plus CX plus d + + + align:start position:0% +of 4 plus BX Cub plus CX plus d +something like that if you have a + + align:start position:0% +something like that if you have a + + + align:start position:0% +something like that if you have a +polinomial like that then you + + align:start position:0% +polinomial like that then you + + + align:start position:0% +polinomial like that then you +can start with a guess any guess you'd + + align:start position:0% +can start with a guess any guess you'd + + + align:start position:0% +can start with a guess any guess you'd +like and you can come up with a better + + align:start position:0% + + + + align:start position:0% + +approximation to the square root by + + align:start position:0% +approximation to the square root by + + + align:start position:0% +approximation to the square root by +saying a new guess so the new better + + align:start position:0% +saying a new guess so the new better + + + align:start position:0% +saying a new guess so the new better +approximation for the guess is whatever + + align:start position:0% +approximation for the guess is whatever + + + align:start position:0% +approximation for the guess is whatever +your current guess is minus that polom + + align:start position:0% +your current guess is minus that polom + + + align:start position:0% +your current guess is minus that polom +evaluated at the guess so replace x with + + align:start position:0% +evaluated at the guess so replace x with + + + align:start position:0% +evaluated at the guess so replace x with +your guess divided by the derivative of + + align:start position:0% +your guess divided by the derivative of + + + align:start position:0% +your guess divided by the derivative of +that polinomial evaluated at the guess + + align:start position:0% +that polinomial evaluated at the guess + + + align:start position:0% +that polinomial evaluated at the guess +so get the derivative and replace x with + + align:start position:0% +so get the derivative and replace x with + + + align:start position:0% +so get the derivative and replace x with +your guess this should sound familiar + + align:start position:0% +your guess this should sound familiar + + + align:start position:0% +your guess this should sound familiar +because lecture two we actually + + align:start position:0% +because lecture two we actually + + + align:start position:0% +because lecture two we actually +implemented just this part remember when + + align:start position:0% +implemented just this part remember when + + + align:start position:0% +implemented just this part remember when +we were learning about expressions and + + align:start position:0% +we were learning about expressions and + + + align:start position:0% +we were learning about expressions and +combining them together I mentioned this + + align:start position:0% +combining them together I mentioned this + + + align:start position:0% +combining them together I mentioned this +algorithm and I said we're not going to + + align:start position:0% +algorithm and I said we're not going to + + + align:start position:0% +algorithm and I said we're not going to +be writing the whole algorithm today but + + align:start position:0% +be writing the whole algorithm today but + + + align:start position:0% +be writing the whole algorithm today but +we are going to be implementing the part + + align:start position:0% +we are going to be implementing the part + + + align:start position:0% +we are going to be implementing the part +that makes a new better guess for the + + align:start position:0% +that makes a new better guess for the + + + align:start position:0% +that makes a new better guess for the +square root of a number well today we're + + align:start position:0% +square root of a number well today we're + + + align:start position:0% +square root of a number well today we're +actually going to take that line put a + + align:start position:0% +actually going to take that line put a + + + align:start position:0% +actually going to take that line put a +wrapper around it the wrapper being a + + align:start position:0% +wrapper around it the wrapper being a + + + align:start position:0% +wrapper around it the wrapper being a +little Loop that makes successive + + align:start position:0% +little Loop that makes successive + + + align:start position:0% +little Loop that makes successive +guesses better and better guesses using + + align:start position:0% +guesses better and better guesses using + + + align:start position:0% +guesses better and better guesses using +guesses uh that we have just made to get + + align:start position:0% +guesses uh that we have just made to get + + + align:start position:0% +guesses uh that we have just made to get +Us close to the approx approximation for + + align:start position:0% +Us close to the approx approximation for + + + align:start position:0% +Us close to the approx approximation for +a square root + + align:start position:0% +a square root + + + align:start position:0% +a square root +okay so let's start with this so the + + align:start position:0% +okay so let's start with this so the + + + align:start position:0% +okay so let's start with this so the +idea here for finding the square root of + + align:start position:0% +idea here for finding the square root of + + + align:start position:0% +idea here for finding the square root of +a number is to kind of realize that if + + align:start position:0% +a number is to kind of realize that if + + + align:start position:0% +a number is to kind of realize that if +we want to find the square root of let's + + align:start position:0% +we want to find the square root of let's + + + align:start position:0% +we want to find the square root of let's +say + + align:start position:0% +say + + + align:start position:0% +say +24 that's essentially us applying this + + align:start position:0% +24 that's essentially us applying this + + + align:start position:0% +24 that's essentially us applying this +algorithm to the polinomial that says + + align:start position:0% +algorithm to the polinomial that says + + + align:start position:0% +algorithm to the polinomial that says +that's x^2 minus + + align:start position:0% +that's x^2 minus + + + align:start position:0% +that's x^2 minus +24 okay because if x^2 - 24 equal 0 then + + align:start position:0% +24 okay because if x^2 - 24 equal 0 then + + + align:start position:0% +24 okay because if x^2 - 24 equal 0 then +basically x^2 is equal to 24 and to + + align:start position:0% +basically x^2 is equal to 24 and to + + + align:start position:0% +basically x^2 is equal to 24 and to +solve for x means that we are looking + + align:start position:0% +solve for x means that we are looking + + + align:start position:0% +solve for x means that we are looking +for the square root of 24 so we can try + + align:start position:0% +for the square root of 24 so we can try + + + align:start position:0% +for the square root of 24 so we can try +to apply this Newton rapson method to + + align:start position:0% +to apply this Newton rapson method to + + + align:start position:0% +to apply this Newton rapson method to +find the an approximation to the square + + align:start position:0% +find the an approximation to the square + + + align:start position:0% +find the an approximation to the square +root of a number by simply solving using + + align:start position:0% +root of a number by simply solving using + + + align:start position:0% +root of a number by simply solving using +their method to solve uh applied to this + + align:start position:0% +their method to solve uh applied to this + + + align:start position:0% +their method to solve uh applied to this +polinomial x^2 minus whatever value you + + align:start position:0% +polinomial x^2 minus whatever value you + + + align:start position:0% +polinomial x^2 minus whatever value you +want to find the square root of okay so + + align:start position:0% +want to find the square root of okay so + + + align:start position:0% +want to find the square root of okay so +just to give you a little intuition for + + align:start position:0% +just to give you a little intuition for + + + align:start position:0% +just to give you a little intuition for +how this works is so we have a an + + align:start position:0% +how this works is so we have a an + + + align:start position:0% +how this works is so we have a an +initial guess let's say it's this X1 + + align:start position:0% +initial guess let's say it's this X1 + + + align:start position:0% +initial guess let's say it's this X1 +right here + + align:start position:0% +right here + + + align:start position:0% +right here +and you take F of X1 that brings you + + align:start position:0% +and you take F of X1 that brings you + + + align:start position:0% +and you take F of X1 that brings you +oops that brings you up + + align:start position:0% +oops that brings you up + + + align:start position:0% +oops that brings you up +here you find the derivative over here + + align:start position:0% +here you find the derivative over here + + + align:start position:0% +here you find the derivative over here +and you follow the tangent line to the + + align:start position:0% +and you follow the tangent line to the + + + align:start position:0% +and you follow the tangent line to the +x- axis for the next guess and you + + align:start position:0% +x- axis for the next guess and you + + + align:start position:0% +x- axis for the next guess and you +repeat the process evaluate this guess + + align:start position:0% +repeat the process evaluate this guess + + + align:start position:0% +repeat the process evaluate this guess +to get F of that guess this is the + + align:start position:0% +to get F of that guess this is the + + + align:start position:0% +to get F of that guess this is the +tangent line follow it down to the xaxis + + align:start position:0% +tangent line follow it down to the xaxis + + + align:start position:0% +tangent line follow it down to the xaxis +for in better guess and you keep doing + + align:start position:0% +for in better guess and you keep doing + + + align:start position:0% +for in better guess and you keep doing +this until you get as close as you'd + + align:start position:0% +this until you get as close as you'd + + + align:start position:0% +this until you get as close as you'd +like to the square root here okay so + + align:start position:0% +like to the square root here okay so + + + align:start position:0% +like to the square root here okay so +just um for completeness sake since I + + align:start position:0% +just um for completeness sake since I + + + align:start position:0% +just um for completeness sake since I +did link it this is what it looks like + + align:start position:0% +did link it this is what it looks like + + + align:start position:0% +did link it this is what it looks like +that's your initial guess that's your F + + align:start position:0% +that's your initial guess that's your F + + + align:start position:0% +that's your initial guess that's your F +there's your tangent line that gives you + + align:start position:0% +there's your tangent line that gives you + + + align:start position:0% +there's your tangent line that gives you +the next guess evaluate that get your + + align:start position:0% +the next guess evaluate that get your + + + align:start position:0% +the next guess evaluate that get your +tangent line get your next guess + + align:start position:0% +tangent line get your next guess + + + align:start position:0% +tangent line get your next guess +evaluate that get the tangent line + + align:start position:0% +evaluate that get the tangent line + + + align:start position:0% +evaluate that get the tangent line +there's your next guess and it basically + + align:start position:0% +there's your next guess and it basically + + + align:start position:0% +there's your next guess and it basically +works for any polinomial okay but we are + + align:start position:0% +works for any polinomial okay but we are + + + align:start position:0% +works for any polinomial okay but we are +applying it to just finding the square + + align:start position:0% +applying it to just finding the square + + + align:start position:0% +applying it to just finding the square +root of a number so our polinomial is + + align:start position:0% +root of a number so our polinomial is + + + align:start position:0% +root of a number so our polinomial is +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +simple um so if we want to find the + + align:start position:0% +simple um so if we want to find the + + + align:start position:0% +simple um so if we want to find the +square root of K the polinomial we're + + align:start position:0% +square root of K the polinomial we're + + + align:start position:0% +square root of K the polinomial we're +interested in here is x^2 minus K the + + align:start position:0% +interested in here is x^2 minus K the + + + align:start position:0% +interested in here is x^2 minus K the +derivative I think have you guys done + + align:start position:0% +derivative I think have you guys done + + + align:start position:0% +derivative I think have you guys done +derivatives yet right in math okay good + + align:start position:0% +derivatives yet right in math okay good + + + align:start position:0% +derivatives yet right in math okay good +the derivative of x^2 minus K is just 2x + + align:start position:0% +the derivative of x^2 minus K is just 2x + + + align:start position:0% +the derivative of x^2 minus K is just 2x +right and then um we can initialize our + + align:start position:0% +right and then um we can initialize our + + + align:start position:0% +right and then um we can initialize our +guess to be whatever we'd like and then + + align:start position:0% +guess to be whatever we'd like and then + + + align:start position:0% +guess to be whatever we'd like and then +all we need to do for a better guess + + align:start position:0% +all we need to do for a better guess + + + align:start position:0% +all we need to do for a better guess +than the one we currently have is to + + align:start position:0% +than the one we currently have is to + + + align:start position:0% +than the one we currently have is to +take our current guess minus that + + align:start position:0% +take our current guess minus that + + + align:start position:0% +take our current guess minus that +guess uh plugged into the polinomial of + + align:start position:0% +guess uh plugged into the polinomial of + + + align:start position:0% +guess uh plugged into the polinomial of +interest so g^ 2 minus K divided by the + + align:start position:0% +interest so g^ 2 minus K divided by the + + + align:start position:0% +interest so g^ 2 minus K divided by the +derivative with the guest plugged in 2 * + + align:start position:0% +derivative with the guest plugged in 2 * + + + align:start position:0% +derivative with the guest plugged in 2 * +G okay and if we repeat this many many + + align:start position:0% +G okay and if we repeat this many many + + + align:start position:0% +G okay and if we repeat this many many +many times this will eventually get us + + align:start position:0% +many times this will eventually get us + + + align:start position:0% +many times this will eventually get us +to a nice approximation for the square + + align:start position:0% +to a nice approximation for the square + + + align:start position:0% +to a nice approximation for the square +root of the number and this is the + + align:start position:0% +root of the number and this is the + + + align:start position:0% +root of the number and this is the +code it's even simpler than the + + align:start position:0% +code it's even simpler than the + + + align:start position:0% +code it's even simpler than the +bisection search + + align:start position:0% +bisection search + + + align:start position:0% +bisection search +code so let's say we want to be within + + align:start position:0% +code so let's say we want to be within + + + align:start position:0% +code so let's say we want to be within +plus or minus 01 of 24 with our guess + + align:start position:0% +plus or minus 01 of 24 with our guess + + + align:start position:0% +plus or minus 01 of 24 with our guess +right um we can start with any guess + + align:start position:0% +right um we can start with any guess + + + align:start position:0% +right um we can start with any guess +we'd like but I guess a reasonable guess + + align:start position:0% +we'd like but I guess a reasonable guess + + + align:start position:0% +we'd like but I guess a reasonable guess +is to just take that K the thing you + + align:start position:0% +is to just take that K the thing you + + + align:start position:0% +is to just take that K the thing you +want to find the square root of divide + + align:start position:0% +want to find the square root of divide + + + align:start position:0% +want to find the square root of divide +by two once again we can keep track of + + align:start position:0% +by two once again we can keep track of + + + align:start position:0% +by two once again we can keep track of +how many guesses we do and surprise the + + align:start position:0% +how many guesses we do and surprise the + + + align:start position:0% +how many guesses we do and surprise the +while loop condition for while we keep + + align:start position:0% +while loop condition for while we keep + + + align:start position:0% +while loop condition for while we keep +making guesses is exactly the same as + + align:start position:0% +making guesses is exactly the same as + + + align:start position:0% +making guesses is exactly the same as +what we've seen before in approximation + + align:start position:0% +what we've seen before in approximation + + + align:start position:0% +what we've seen before in approximation +method and in bisection search method + + align:start position:0% +method and in bisection search method + + + align:start position:0% +method and in bisection search method +right as long as we're outside this plus + + align:start position:0% +right as long as we're outside this plus + + + align:start position:0% +right as long as we're outside this plus +or minus Epsilon boundary keep making + + align:start position:0% +or minus Epsilon boundary keep making + + + align:start position:0% +or minus Epsilon boundary keep making +guesses because I'm not happy with my + + align:start position:0% +guesses because I'm not happy with my + + + align:start position:0% +guesses because I'm not happy with my +guess right so here while the absolute + + align:start position:0% +guess right so here while the absolute + + + align:start position:0% +guess right so here while the absolute +value of guess squar minus k k being the + + align:start position:0% +value of guess squar minus k k being the + + + align:start position:0% +value of guess squar minus k k being the +thing we want to find the square root of + + align:start position:0% +thing we want to find the square root of + + + align:start position:0% +thing we want to find the square root of +is bigger than Epsilon right so if we're + + align:start position:0% +is bigger than Epsilon right so if we're + + + align:start position:0% +is bigger than Epsilon right so if we're +farther away in both + + align:start position:0% +farther away in both + + + align:start position:0% +farther away in both +ends we keep track of how many guesses + + align:start position:0% +ends we keep track of how many guesses + + + align:start position:0% +ends we keep track of how many guesses +we've done and make our new guess so + + align:start position:0% +we've done and make our new guess so + + + align:start position:0% +we've done and make our new guess so +this is what's different than bisection + + align:start position:0% +this is what's different than bisection + + + align:start position:0% +this is what's different than bisection +or approximation the guess is done by + + align:start position:0% +or approximation the guess is done by + + + align:start position:0% +or approximation the guess is done by +the Newton rapson method and this line + + align:start position:0% +the Newton rapson method and this line + + + align:start position:0% +the Newton rapson method and this line +right here is what we wrote in lecture + + align:start position:0% +right here is what we wrote in lecture + + + align:start position:0% +right here is what we wrote in lecture +two or three right our new guess is our + + align:start position:0% +two or three right our new guess is our + + + align:start position:0% +two or three right our new guess is our +old guess + + align:start position:0% +old guess + + + align:start position:0% +old guess +minus the guess evaluated at X so gu^ + + align:start position:0% +minus the guess evaluated at X so gu^ + + + align:start position:0% +minus the guess evaluated at X so gu^ +squ minus K divided by the derivative + + align:start position:0% +squ minus K divided by the derivative + + + align:start position:0% +squ minus K divided by the derivative +evaluated at guess 2 * + + align:start position:0% +evaluated at guess 2 * + + + align:start position:0% +evaluated at guess 2 * +guess and that's it the loop takes care + + align:start position:0% +guess and that's it the loop takes care + + + align:start position:0% +guess and that's it the loop takes care +of the rest and it'll keep making new + + align:start position:0% +of the rest and it'll keep making new + + + align:start position:0% +of the rest and it'll keep making new +guesses until it comes within plus or + + align:start position:0% +guesses until it comes within plus or + + + align:start position:0% +guesses until it comes within plus or +minus Epsilon right so this that's our K + + align:start position:0% +minus Epsilon right so this that's our K + + + align:start position:0% +minus Epsilon right so this that's our K +that's our function right that's F of + + align:start position:0% +that's our function right that's F of + + + align:start position:0% +that's our function right that's F of +guess and that's fime of guess + + align:start position:0% +guess and that's fime of guess + + + align:start position:0% +guess and that's fime of guess +so let's run + + align:start position:0% + + + + align:start position:0% + +it here it + + align:start position:0% + + + + align:start position:0% + +is okay so we made four guesses to find + + align:start position:0% +is okay so we made four guesses to find + + + align:start position:0% +is okay so we made four guesses to find +the square root of uh 24 is about 4.9 + + align:start position:0% +the square root of uh 24 is about 4.9 + + + align:start position:0% +the square root of uh 24 is about 4.9 +which is pretty good we came within 01 + + align:start position:0% +which is pretty good we came within 01 + + + align:start position:0% +which is pretty good we came within 01 +and if we try 54321 our favorite number + + align:start position:0% +and if we try 54321 our favorite number + + + align:start position:0% +and if we try 54321 our favorite number +so far in this class + + align:start position:0% +so far in this class + + + align:start position:0% +so far in this class +we only did 10 guesses and it gave us + + align:start position:0% +we only did 10 guesses and it gave us + + + align:start position:0% +we only did 10 guesses and it gave us +just as good an approximation as + + align:start position:0% +just as good an approximation as + + + align:start position:0% +just as good an approximation as +bisection search and that ridiculously + + align:start position:0% +bisection search and that ridiculously + + + align:start position:0% +bisection search and that ridiculously +long approximation method + + align:start position:0% + + + + align:start position:0% + +right yes + + align:start position:0% + + + + align:start position:0% + +why uh why is the GU K over two it can + + align:start position:0% +why uh why is the GU K over two it can + + + align:start position:0% +why uh why is the GU K over two it can +be anything you want we just started + + align:start position:0% +be anything you want we just started + + + align:start position:0% +be anything you want we just started +with something reasonable that's a + + align:start position:0% +with something reasonable that's a + + + align:start position:0% +with something reasonable that's a +function of + + align:start position:0% +function of + + + align:start position:0% +function of +K it it yeah it can be you know 100 it + + align:start position:0% +K it it yeah it can be you know 100 it + + + align:start position:0% +K it it yeah it can be you know 100 it +could be whatever you you'd want to + + align:start position:0% +could be whatever you you'd want to + + + align:start position:0% +could be whatever you you'd want to +do yeah because the algorithm will work + + align:start position:0% +do yeah because the algorithm will work + + + align:start position:0% +do yeah because the algorithm will work +no matter + + align:start position:0% + + + + align:start position:0% + +what so that's awesome there's less + + align:start position:0% +what so that's awesome there's less + + + align:start position:0% +what so that's awesome there's less +guesses but this is a pretty limiting + + align:start position:0% +guesses but this is a pretty limiting + + + align:start position:0% +guesses but this is a pretty limiting +algorithm right you can only use it to + + align:start position:0% +algorithm right you can only use it to + + + align:start position:0% +algorithm right you can only use it to +find square roots of a particular value + + align:start position:0% +find square roots of a particular value + + + align:start position:0% +find square roots of a particular value +we can't use it you know apply it this + + align:start position:0% +we can't use it you know apply it this + + + align:start position:0% +we can't use it you know apply it this +algorithm to finding you know the person + + align:start position:0% +algorithm to finding you know the person + + + align:start position:0% +algorithm to finding you know the person +in the middle of the room or you know or + + align:start position:0% +in the middle of the room or you know or + + + align:start position:0% +in the middle of the room or you know or +something like that right it's really + + align:start position:0% +something like that right it's really + + + align:start position:0% +something like that right it's really +spe specific to this particular + + align:start position:0% + + + + align:start position:0% + +problem so a little wrap up before we go + + align:start position:0% +problem so a little wrap up before we go + + + align:start position:0% +problem so a little wrap up before we go +on to just in introducing the next uh + + align:start position:0% +on to just in introducing the next uh + + + align:start position:0% +on to just in introducing the next uh +the next lecture is uh we talked about + + align:start position:0% +the next lecture is uh we talked about + + + align:start position:0% +the next lecture is uh we talked about +um iteration right that was kind of the + + align:start position:0% +um iteration right that was kind of the + + + align:start position:0% +um iteration right that was kind of the +big thing that we added uh after + + align:start position:0% +big thing that we added uh after + + + align:start position:0% +big thing that we added uh after +conditional so finding a way to repeat + + align:start position:0% +conditional so finding a way to repeat + + + align:start position:0% +conditional so finding a way to repeat +certain lines of code to uh to do + + align:start position:0% +certain lines of code to uh to do + + + align:start position:0% +certain lines of code to uh to do +something useful for us and we looked at + + align:start position:0% +something useful for us and we looked at + + + align:start position:0% +something useful for us and we looked at +guess and check methods now I I guess + + align:start position:0% +guess and check methods now I I guess + + + align:start position:0% +guess and check methods now I I guess +I'm putting all the methods we saw under + + align:start position:0% +I'm putting all the methods we saw under + + + align:start position:0% +I'm putting all the methods we saw under +guess and check because they're kind of + + align:start position:0% +guess and check because they're kind of + + + align:start position:0% +guess and check because they're kind of +all guess and check right we're guessing + + align:start position:0% +all guess and check right we're guessing + + + align:start position:0% +all guess and check right we're guessing +a value and we're checking whether that + + align:start position:0% +a value and we're checking whether that + + + align:start position:0% +a value and we're checking whether that +value is exact or within some Epsilon of + + align:start position:0% +value is exact or within some Epsilon of + + + align:start position:0% +value is exact or within some Epsilon of +what we want to be right and all these + + align:start position:0% +what we want to be right and all these + + + align:start position:0% +what we want to be right and all these +guess and check methods have the same + + align:start position:0% +guess and check methods have the same + + + align:start position:0% +guess and check methods have the same +kind of three things associated with + + align:start position:0% +kind of three things associated with + + + align:start position:0% +kind of three things associated with +them there's some sort of loop right + + align:start position:0% +them there's some sort of loop right + + + align:start position:0% +them there's some sort of loop right +there's something that you need to do + + align:start position:0% +there's something that you need to do + + + align:start position:0% +there's something that you need to do +over and over again we need some way to + + align:start position:0% +over and over again we need some way to + + + align:start position:0% +over and over again we need some way to +generate the guesses and that's where + + align:start position:0% +generate the guesses and that's where + + + align:start position:0% +generate the guesses and that's where +things are different between the + + align:start position:0% +things are different between the + + + align:start position:0% +things are different between the +different algorithms + + align:start position:0% +different algorithms + + + align:start position:0% +different algorithms +and then we need some way to check that + + align:start position:0% +and then we need some way to check that + + + align:start position:0% +and then we need some way to check that +the guess is right or within some + + align:start position:0% +the guess is right or within some + + + align:start position:0% +the guess is right or within some +Epsilon or something like that and then + + align:start position:0% +Epsilon or something like that and then + + + align:start position:0% +Epsilon or something like that and then +a way for us to continue making guesses + + align:start position:0% +a way for us to continue making guesses + + + align:start position:0% +a way for us to continue making guesses +so we saw exhaustive enumeration okay + + align:start position:0% +so we saw exhaustive enumeration okay + + + align:start position:0% +so we saw exhaustive enumeration okay +the original guess and check method + + align:start position:0% +the original guess and check method + + + align:start position:0% +the original guess and check method +where we basically had integers or some + + align:start position:0% +where we basically had integers or some + + + align:start position:0% +where we basically had integers or some +set values that we wanted to check it + + align:start position:0% +set values that we wanted to check it + + + align:start position:0% +set values that we wanted to check it +was exhaustive so we knew exactly how + + align:start position:0% +was exhaustive so we knew exactly how + + + align:start position:0% +was exhaustive so we knew exactly how +many values we would have to iterate + + align:start position:0% +many values we would have to iterate + + + align:start position:0% +many values we would have to iterate +over um approximation algorithms allowed + + align:start position:0% +over um approximation algorithms allowed + + + align:start position:0% +over um approximation algorithms allowed +us to have smaller increments and we + + align:start position:0% +us to have smaller increments and we + + + align:start position:0% +us to have smaller increments and we +were able to search for uh + + align:start position:0% +were able to search for uh + + + align:start position:0% +were able to search for uh +approximations to uh square roots or + + align:start position:0% +approximations to uh square roots or + + + align:start position:0% +approximations to uh square roots or +cube roots or whatever problem we were + + align:start position:0% +cube roots or whatever problem we were + + + align:start position:0% +cube roots or whatever problem we were +trying to solve by section search we saw + + align:start position:0% +trying to solve by section search we saw + + + align:start position:0% +trying to solve by section search we saw +was an improvement over approximation + + align:start position:0% +was an improvement over approximation + + + align:start position:0% +was an improvement over approximation +methods but only for problems that had + + align:start position:0% +methods but only for problems that had + + + align:start position:0% +methods but only for problems that had +an ordering property and for problems + + align:start position:0% +an ordering property and for problems + + + align:start position:0% +an ordering property and for problems +that you could figure out whether your + + align:start position:0% +that you could figure out whether your + + + align:start position:0% +that you could figure out whether your +guesses were too high or too low if you + + align:start position:0% +guesses were too high or too low if you + + + align:start position:0% +guesses were too high or too low if you +can't have those then you can't apply + + align:start position:0% +can't have those then you can't apply + + + align:start position:0% +can't have those then you can't apply +bisection search so you're stuck with an + + align:start position:0% +bisection search so you're stuck with an + + + align:start position:0% +bisection search so you're stuck with an +approximation algorithm or something + + align:start position:0% +approximation algorithm or something + + + align:start position:0% +approximation algorithm or something +else and then this Newton rapson was + + align:start position:0% +else and then this Newton rapson was + + + align:start position:0% +else and then this Newton rapson was +kind of the last thing we saw it's very + + align:start position:0% +kind of the last thing we saw it's very + + + align:start position:0% +kind of the last thing we saw it's very +specific algorithm for finding square + + align:start position:0% +specific algorithm for finding square + + + align:start position:0% +specific algorithm for finding square +roots of values but still valuable um in + + align:start position:0% +roots of values but still valuable um in + + + align:start position:0% +roots of values but still valuable um in +kind of showcasing this looping + + align:start position:0% +kind of showcasing this looping + + + align:start position:0% +kind of showcasing this looping +construct checking for something and + + align:start position:0% +construct checking for something and + + + align:start position:0% +construct checking for something and +then making a new guess okay um this is + + align:start position:0% +then making a new guess okay um this is + + + align:start position:0% +then making a new guess okay um this is +basically a summary of what I just said + + align:start position:0% +basically a summary of what I just said + + + align:start position:0% +basically a summary of what I just said +also + + align:start position:0% +also + + + align:start position:0% +also +so um we don't need to go over it but + + align:start position:0% +so um we don't need to go over it but + + + align:start position:0% +so um we don't need to go over it but +are there any questions about these + + align:start position:0% +are there any questions about these + + + align:start position:0% +are there any questions about these +three algorithms do they make sense + + align:start position:0% +three algorithms do they make sense + + + align:start position:0% +three algorithms do they make sense +hopefully the coding practice kind of + + align:start position:0% +hopefully the coding practice kind of + + + align:start position:0% +hopefully the coding practice kind of +helped a little bit during the lectures + + align:start position:0% +helped a little bit during the lectures + + + align:start position:0% +helped a little bit during the lectures +any questions + + align:start position:0% +any questions + + + align:start position:0% +any questions +no okay so in the last five or so + + align:start position:0% +no okay so in the last five or so + + + align:start position:0% +no okay so in the last five or so +minutes I want to + + align:start position:0% +minutes I want to + + + align:start position:0% +minutes I want to +introduce um the next uh the next the + + align:start position:0% +introduce um the next uh the next the + + + align:start position:0% +introduce um the next uh the next the +motivation for the next topic we're + + align:start position:0% +motivation for the next topic we're + + + align:start position:0% +motivation for the next topic we're +going to talk about okay so so far we've + + align:start position:0% +going to talk about okay so so far we've + + + align:start position:0% +going to talk about okay so so far we've +basically uh learned how to write a + + align:start position:0% +basically uh learned how to write a + + + align:start position:0% +basically uh learned how to write a +bunch of code right we learned + + align:start position:0% +bunch of code right we learned + + + align:start position:0% +bunch of code right we learned +Expressions we learned variables we + + align:start position:0% +Expressions we learned variables we + + + align:start position:0% +Expressions we learned variables we +learned conditionals we learned uh uh + + align:start position:0% +learned conditionals we learned uh uh + + + align:start position:0% +learned conditionals we learned uh uh +Loops right conditionals and Loops as a + + align:start position:0% +Loops right conditionals and Loops as a + + + align:start position:0% +Loops right conditionals and Loops as a +way to add control flow to our program + + align:start position:0% +way to add control flow to our program + + + align:start position:0% +way to add control flow to our program +and we had this nice little toolbox of + + align:start position:0% +and we had this nice little toolbox of + + + align:start position:0% +and we had this nice little toolbox of +things + + align:start position:0% +things + + + align:start position:0% +things +to use to write algorithms okay so we + + align:start position:0% +to use to write algorithms okay so we + + + align:start position:0% +to use to write algorithms okay so we +actually it is true we have all that you + + align:start position:0% +actually it is true we have all that you + + + align:start position:0% +actually it is true we have all that you +need to know to write interesting + + align:start position:0% +need to know to write interesting + + + align:start position:0% +need to know to write interesting +algorithms right we wrote These + + align:start position:0% +algorithms right we wrote These + + + align:start position:0% +algorithms right we wrote These +interesting algorithms but we actually + + align:start position:0% +interesting algorithms but we actually + + + align:start position:0% +interesting algorithms but we actually +haven't taught you about some important + + align:start position:0% +haven't taught you about some important + + + align:start position:0% +haven't taught you about some important +Concepts in programming and these + + align:start position:0% +Concepts in programming and these + + + align:start position:0% +Concepts in programming and these +Concepts actually exist in all of the + + align:start position:0% +Concepts actually exist in all of the + + + align:start position:0% +Concepts actually exist in all of the +modern programming languages okay and + + align:start position:0% +modern programming languages okay and + + + align:start position:0% +modern programming languages okay and +these ideas are decomposition and + + align:start position:0% +these ideas are decomposition and + + + align:start position:0% +these ideas are decomposition and +abstraction okay so I'll just motivate + + align:start position:0% +abstraction okay so I'll just motivate + + + align:start position:0% +abstraction okay so I'll just motivate +these ideas today we're not going to + + align:start position:0% +these ideas today we're not going to + + + align:start position:0% +these ideas today we're not going to +look at any code but I'll kind of show + + align:start position:0% +look at any code but I'll kind of show + + + align:start position:0% +look at any code but I'll kind of show +you some some sort of simpler version of + + align:start position:0% +you some some sort of simpler version of + + + align:start position:0% +you some some sort of simpler version of +decomposition abstraction that you've + + align:start position:0% +decomposition abstraction that you've + + + align:start position:0% +decomposition abstraction that you've +already been kind of doing and then next + + align:start position:0% +already been kind of doing and then next + + + align:start position:0% +already been kind of doing and then next +lecture we'll see how we can actually + + align:start position:0% +lecture we'll see how we can actually + + + align:start position:0% +lecture we'll see how we can actually +Implement these ideas in + + align:start position:0% +Implement these ideas in + + + align:start position:0% +Implement these ideas in +code so the idea of decomposition is + + align:start position:0% +code so the idea of decomposition is + + + align:start position:0% +code so the idea of decomposition is +that you take a large + + align:start position:0% +that you take a large + + + align:start position:0% +that you take a large +program and you try to divide it into + + align:start position:0% +program and you try to divide it into + + + align:start position:0% +program and you try to divide it into +smaller parts each one of these parts + + align:start position:0% +smaller parts each one of these parts + + + align:start position:0% +smaller parts each one of these parts +will be self-contained right so they + + align:start position:0% +will be self-contained right so they + + + align:start position:0% +will be self-contained right so they +won't really interfere with each other + + align:start position:0% +won't really interfere with each other + + + align:start position:0% +won't really interfere with each other +as in the code from one part is not + + align:start position:0% +as in the code from one part is not + + + align:start position:0% +as in the code from one part is not +going to influence the code in another + + align:start position:0% +going to influence the code in another + + + align:start position:0% +going to influence the code in another +part but they can sort of talk to each + + align:start position:0% +part but they can sort of talk to each + + + align:start position:0% +part but they can sort of talk to each +other they can send values to each other + + align:start position:0% +other they can send values to each other + + + align:start position:0% +other they can send values to each other +back and forth okay so if you take one + + align:start position:0% +back and forth okay so if you take one + + + align:start position:0% +back and forth okay so if you take one +large spaghetti code program and you try + + align:start position:0% +large spaghetti code program and you try + + + align:start position:0% +large spaghetti code program and you try +to divide in into these nice + + align:start position:0% +to divide in into these nice + + + align:start position:0% +to divide in into these nice +self-contained Parts you can have each + + align:start position:0% +self-contained Parts you can have each + + + align:start position:0% +self-contained Parts you can have each +one of these parts solve a different + + align:start position:0% +one of these parts solve a different + + + align:start position:0% +one of these parts solve a different +part a different portion of your large + + align:start position:0% +part a different portion of your large + + + align:start position:0% +part a different portion of your large +program and in the end they can kind of + + align:start position:0% +program and in the end they can kind of + + + align:start position:0% +program and in the end they can kind of +come together to solve the larger + + align:start position:0% +come together to solve the larger + + + align:start position:0% +come together to solve the larger +program that's the idea of composition + + align:start position:0% +program that's the idea of composition + + + align:start position:0% +program that's the idea of composition +and the idea of abstraction is once you + + align:start position:0% +and the idea of abstraction is once you + + + align:start position:0% +and the idea of abstraction is once you +write these self-contained Parts one + + align:start position:0% +write these self-contained Parts one + + + align:start position:0% +write these self-contained Parts one +time right and you've done the work + + align:start position:0% +time right and you've done the work + + + align:start position:0% +time right and you've done the work +you've done the thought process you've + + align:start position:0% +you've done the thought process you've + + + align:start position:0% +you've done the thought process you've +thought about how to write them in an + + align:start position:0% +thought about how to write them in an + + + align:start position:0% +thought about how to write them in an +efficient way nobody else needs to know + + align:start position:0% +efficient way nobody else needs to know + + + align:start position:0% +efficient way nobody else needs to know +exactly how you implemented them you + + align:start position:0% +exactly how you implemented them you + + + align:start position:0% +exactly how you implemented them you +want to abstract away all the details + + align:start position:0% +want to abstract away all the details + + + align:start position:0% +want to abstract away all the details +that went into figuring out how to solve + + align:start position:0% +that went into figuring out how to solve + + + align:start position:0% +that went into figuring out how to solve +that problem into just some some text or + + align:start position:0% +that problem into just some some text or + + + align:start position:0% +that problem into just some some text or +some interface that allows you to say + + align:start position:0% +some interface that allows you to say + + + align:start position:0% +some interface that allows you to say +hey + + align:start position:0% +hey + + + align:start position:0% +hey +I solved this problem all you need to do + + align:start position:0% +I solved this problem all you need to do + + + align:start position:0% +I solved this problem all you need to do +is give me this input and this input and + + align:start position:0% +is give me this input and this input and + + + align:start position:0% +is give me this input and this input and +this this input and my code will solve + + align:start position:0% +this this input and my code will solve + + + align:start position:0% +this this input and my code will solve +your problem and give you this output + + align:start position:0% +your problem and give you this output + + + align:start position:0% +your problem and give you this output +back right kind of like if you're + + align:start position:0% +back right kind of like if you're + + + align:start position:0% +back right kind of like if you're +working in a group project every one of + + align:start position:0% +working in a group project every one of + + + align:start position:0% +working in a group project every one of +you right goes and does your own part I + + align:start position:0% +you right goes and does your own part I + + + align:start position:0% +you right goes and does your own part I +don't care if you use you know the + + align:start position:0% +don't care if you use you know the + + + align:start position:0% +don't care if you use you know the +internet or the library to solve your + + align:start position:0% +internet or the library to solve your + + + align:start position:0% +internet or the library to solve your +part all I care is that you give you we + + align:start position:0% +part all I care is that you give you we + + + align:start position:0% +part all I care is that you give you we +all come back together and we put our + + align:start position:0% +all come back together and we put our + + + align:start position:0% +all come back together and we put our +results together right and so that's the + + align:start position:0% +results together right and so that's the + + + align:start position:0% +results together right and so that's the +idea of abstraction there's some + + align:start position:0% +idea of abstraction there's some + + + align:start position:0% +idea of abstraction there's some +unnecessary details that might be in + + align:start position:0% +unnecessary details that might be in + + + align:start position:0% +unnecessary details that might be in +some code I don't care about those + + align:start position:0% +some code I don't care about those + + + align:start position:0% +some code I don't care about those +details how you solved your problem I + + align:start position:0% +details how you solved your problem I + + + align:start position:0% +details how you solved your problem I +just care that you solved the problem so + + align:start position:0% +just care that you solved the problem so + + + align:start position:0% +just care that you solved the problem so +tell me how I can interact with + + align:start position:0% +tell me how I can interact with + + + align:start position:0% +tell me how I can interact with +you so this is sort + + align:start position:0% +you so this is sort + + + align:start position:0% +you so this is sort +of very very uh low level I guess in + + align:start position:0% +of very very uh low level I guess in + + + align:start position:0% +of very very uh low level I guess in +some ways that we've already been + + align:start position:0% +some ways that we've already been + + + align:start position:0% +some ways that we've already been +employing the ideas of of decomposition + + align:start position:0% +employing the ideas of of decomposition + + + align:start position:0% +employing the ideas of of decomposition +and abstraction okay so um decomposition + + align:start position:0% +and abstraction okay so um decomposition + + + align:start position:0% +and abstraction okay so um decomposition +is the idea that you can write smaller + + align:start position:0% +is the idea that you can write smaller + + + align:start position:0% +is the idea that you can write smaller +pieces of code that are kind of + + align:start position:0% +pieces of code that are kind of + + + align:start position:0% +pieces of code that are kind of +self-contained + + align:start position:0% +self-contained + + + align:start position:0% +self-contained +okay so if I gave you this I kind of you + + align:start position:0% +okay so if I gave you this I kind of you + + + align:start position:0% +okay so if I gave you this I kind of you +know talked about spaghetti code this is + + align:start position:0% +know talked about spaghetti code this is + + + align:start position:0% +know talked about spaghetti code this is +kind of like a simpler version of + + align:start position:0% +kind of like a simpler version of + + + align:start position:0% +kind of like a simpler version of +spaghetti code if I gave you this line + + align:start position:0% +spaghetti code if I gave you this line + + + align:start position:0% +spaghetti code if I gave you this line +of code it's a little bit messy right + + align:start position:0% +of code it's a little bit messy right + + + align:start position:0% +of code it's a little bit messy right +I've got some value here that I know is + + align:start position:0% +I've got some value here that I know is + + + align:start position:0% +I've got some value here that I know is +going to have is going to be important + + align:start position:0% +going to have is going to be important + + + align:start position:0% +going to have is going to be important +right especially if I Define it to some + + align:start position:0% +right especially if I Define it to some + + + align:start position:0% +right especially if I Define it to some +large number of decimal uh places I've + + align:start position:0% +large number of decimal uh places I've + + + align:start position:0% +large number of decimal uh places I've +got these two values here that I'm + + align:start position:0% +got these two values here that I'm + + + align:start position:0% +got these two values here that I'm +copying over basically This Is Not Great + + align:start position:0% +copying over basically This Is Not Great + + + align:start position:0% +copying over basically This Is Not Great +coding style right it's not great coding + + align:start position:0% +coding style right it's not great coding + + + align:start position:0% +coding style right it's not great coding +practice + + align:start position:0% +practice + + + align:start position:0% +practice +but I can kind of take these values and + + align:start position:0% +but I can kind of take these values and + + + align:start position:0% +but I can kind of take these values and +save them and or sort of decompose them + + align:start position:0% +save them and or sort of decompose them + + + align:start position:0% +save them and or sort of decompose them +into things that are reusable right so + + align:start position:0% +into things that are reusable right so + + + align:start position:0% +into things that are reusable right so +I've got Pi here which has some which is + + align:start position:0% +I've got Pi here which has some which is + + + align:start position:0% +I've got Pi here which has some which is +which is interesting to me I can save it + + align:start position:0% +which is interesting to me I can save it + + + align:start position:0% +which is interesting to me I can save it +in a variable I've got R here right 2.2 + + align:start position:0% +in a variable I've got R here right 2.2 + + + align:start position:0% +in a variable I've got R here right 2.2 +I'm saving it as a variable named r that + + align:start position:0% +I'm saving it as a variable named r that + + + align:start position:0% +I'm saving it as a variable named r that +I know I'm going to use in many places + + align:start position:0% +I know I'm going to use in many places + + + align:start position:0% +I know I'm going to use in many places +so instead of copying and pasting 2.2 + + align:start position:0% +so instead of copying and pasting 2.2 + + + align:start position:0% +so instead of copying and pasting 2.2 +here and here right I might make a + + align:start position:0% +here and here right I might make a + + + align:start position:0% +here and here right I might make a +mistake if I type it out I just use the + + align:start position:0% +mistake if I type it out I just use the + + + align:start position:0% +mistake if I type it out I just use the +variable and so I've decomposed this + + align:start position:0% +variable and so I've decomposed this + + + align:start position:0% +variable and so I've decomposed this +little bit of spaghetti code into these + + align:start position:0% +little bit of spaghetti code into these + + + align:start position:0% +little bit of spaghetti code into these +nice modular pieces right I've got pi as + + align:start position:0% +nice modular pieces right I've got pi as + + + align:start position:0% +nice modular pieces right I've got pi as +a module r as a module and then I'm just + + align:start position:0% +a module r as a module and then I'm just + + + align:start position:0% +a module r as a module and then I'm just +putting them together to achieve this + + align:start position:0% +putting them together to achieve this + + + align:start position:0% +putting them together to achieve this +common goal which is Define the + + align:start position:0% +common goal which is Define the + + + align:start position:0% +common goal which is Define the +area and we're going to see this on a + + align:start position:0% +area and we're going to see this on a + + + align:start position:0% +area and we're going to see this on a +larger scale using these uh using these + + align:start position:0% +larger scale using these uh using these + + + align:start position:0% +larger scale using these uh using these +things called functions next + + align:start position:0% +things called functions next + + + align:start position:0% +things called functions next +lecture now the idea of abstraction + + align:start position:0% +lecture now the idea of abstraction + + + align:start position:0% +lecture now the idea of abstraction +again we've already been kind of doing + + align:start position:0% +again we've already been kind of doing + + + align:start position:0% +again we've already been kind of doing +this hopefully you guys have been doing + + align:start position:0% +this hopefully you guys have been doing + + + align:start position:0% +this hopefully you guys have been doing +this through uh comments in your code so + + align:start position:0% +this through uh comments in your code so + + + align:start position:0% +this through uh comments in your code so +if you spend some time on your problem + + align:start position:0% +if you spend some time on your problem + + + align:start position:0% +if you spend some time on your problem +set you know when it's first released + + align:start position:0% +set you know when it's first released + + + align:start position:0% +set you know when it's first released +and you write a whole chunk of code and + + align:start position:0% +and you write a whole chunk of code and + + + align:start position:0% +and you write a whole chunk of code and +you do a really good job at it and you + + align:start position:0% +you do a really good job at it and you + + + align:start position:0% +you do a really good job at it and you +you did it in a really cool way come you + + align:start position:0% +you did it in a really cool way come you + + + align:start position:0% +you did it in a really cool way come you +know a week later you forgot some + + align:start position:0% +know a week later you forgot some + + + align:start position:0% +know a week later you forgot some +details that you've done right and you + + align:start position:0% +details that you've done right and you + + + align:start position:0% +details that you've done right and you +didn't comment your code that's that's a + + align:start position:0% +didn't comment your code that's that's a + + + align:start position:0% +didn't comment your code that's that's a +that's that that could Lead You In uh + + align:start position:0% +that's that that could Lead You In uh + + + align:start position:0% +that's that that could Lead You In uh +into big trouble right because now you + + align:start position:0% +into big trouble right because now you + + + align:start position:0% +into big trouble right because now you +have to figure out what the code is + + align:start position:0% +have to figure out what the code is + + + align:start position:0% +have to figure out what the code is +doing if you had just written a little + + align:start position:0% +doing if you had just written a little + + + align:start position:0% +doing if you had just written a little +bit of comment right at the beginning of + + align:start position:0% +bit of comment right at the beginning of + + + align:start position:0% +bit of comment right at the beginning of +the code for something that you know an + + align:start position:0% +the code for something that you know an + + + align:start position:0% +the code for something that you know an +interesting way or hey I use the + + align:start position:0% +interesting way or hey I use the + + + align:start position:0% +interesting way or hey I use the +bisection search algorithm here or so on + + align:start position:0% +bisection search algorithm here or so on + + + align:start position:0% +bisection search algorithm here or so on +so that would actually suppress a lot of + + align:start position:0% +so that would actually suppress a lot of + + + align:start position:0% +so that would actually suppress a lot of +the details from your code but you would + + align:start position:0% +the details from your code but you would + + + align:start position:0% +the details from your code but you would +still be able to remember what the code + + align:start position:0% +still be able to remember what the code + + + align:start position:0% +still be able to remember what the code +is doing right and so the idea of + + align:start position:0% +is doing right and so the idea of + + + align:start position:0% +is doing right and so the idea of +suppressing details is done through + + align:start position:0% +suppressing details is done through + + + align:start position:0% +suppressing details is done through +comments and we're going to see in the + + align:start position:0% +comments and we're going to see in the + + + align:start position:0% +comments and we're going to see in the +next lecture how we can suppress details + + align:start position:0% +next lecture how we can suppress details + + + align:start position:0% +next lecture how we can suppress details +for larger chunks of code as well okay + + align:start position:0% +for larger chunks of code as well okay + + + align:start position:0% +for larger chunks of code as well okay +so that's the idea of abstraction + + align:start position:0% +so that's the idea of abstraction + + + align:start position:0% +so that's the idea of abstraction +here so the big idea that we're going to + + align:start position:0% +here so the big idea that we're going to + + + align:start position:0% +here so the big idea that we're going to +look through in the next lecture is to + + align:start position:0% +look through in the next lecture is to + + + align:start position:0% +look through in the next lecture is to +stop writing large chunks of code where + + align:start position:0% +stop writing large chunks of code where + + + align:start position:0% +stop writing large chunks of code where +we copy and paste things that do the + + align:start position:0% +we copy and paste things that do the + + + align:start position:0% +we copy and paste things that do the +same thing over and over again because + + align:start position:0% +same thing over and over again because + + + align:start position:0% +same thing over and over again because +that could lead to errors being + + align:start position:0% +that could lead to errors being + + + align:start position:0% +that could lead to errors being +introduced right you change it in one + + align:start position:0% +introduced right you change it in one + + + align:start position:0% +introduced right you change it in one +place you forget to change it in another + + align:start position:0% +place you forget to change it in another + + + align:start position:0% +place you forget to change it in another +place we're going to see how we can + + align:start position:0% +place we're going to see how we can + + + align:start position:0% +place we're going to see how we can +write these little modules called + + align:start position:0% +write these little modules called + + + align:start position:0% +write these little modules called +functions that you write only once you + + align:start position:0% +functions that you write only once you + + + align:start position:0% +functions that you write only once you +debug only once and then you can use + + align:start position:0% +debug only once and then you can use + + + align:start position:0% +debug only once and then you can use +them over and over and over again in + + align:start position:0% +them over and over and over again in + + + align:start position:0% +them over and over and over again in +your code with different inputs to give + + align:start position:0% +your code with different inputs to give + + + align:start position:0% +your code with different inputs to give +you different outputs + + align:start position:0% +you different outputs + + + align:start position:0% +you different outputs +okay so the idea here is we want to + + align:start position:0% +okay so the idea here is we want to + + + align:start position:0% +okay so the idea here is we want to +create code um that's easy to modify + + align:start position:0% +create code um that's easy to modify + + + align:start position:0% +create code um that's easy to modify +right easy to maintain and easy to + + align:start position:0% +right easy to maintain and easy to + + + align:start position:0% +right easy to maintain and easy to +understand so if you come back to it a + + align:start position:0% +understand so if you come back to it a + + + align:start position:0% +understand so if you come back to it a +week from now a year from now you'll + + align:start position:0% +week from now a year from now you'll + + + align:start position:0% +week from now a year from now you'll +still be able to know what that code is + + align:start position:0% +still be able to know what that code is + + + align:start position:0% +still be able to know what that code is +doing okay so that's the motivation for + + align:start position:0% +doing okay so that's the motivation for + + + align:start position:0% +doing okay so that's the motivation for +next lecture we'll start with a little + + align:start position:0% +next lecture we'll start with a little + + + align:start position:0% +next lecture we'll start with a little +real life example and then we'll Dive + + align:start position:0% +real life example and then we'll Dive + + + align:start position:0% +real life example and then we'll Dive +Right into functions all right \ No newline at end of file diff --git a/PPDWaZPu7MU.txt b/PPDWaZPu7MU.txt new file mode 100644 index 0000000000000000000000000000000000000000..b3ee099acfba067b53046cf77616a084671e289e --- /dev/null +++ b/PPDWaZPu7MU.txt @@ -0,0 +1,4023 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +ocw.mit.edu. + +PROFESSOR: Our guest today, this +is Neil Leonard from Berkeley. + +As you can see by +your handout, he's + +the director of the +interdisciplinary Arts + +Institute there, and professor +of electronic production + +and design. + +He's been a friend of mine. + +He was a former student, +briefly, at NEC, + +and gone on to great, +wonderful things, + +including travels +around the world, + +as you can see by +the bio so we're + +very fortunate that +he's here today. + +He's got an assignment +on the handout which + +he'll talk about +as we go through. + +And that'll be due +next Monday like we've + +done before with other +of our presenters. + +Don't forget, Wednesday we +have a concert with Neil + +and an associate +Robin Eubanks, who's + +one of the great +improvisers on the scene + +today, wonderful trombonist. + +So they'll be in Killian Hall, +Wednesday night, 8 o'clock. + +So bring everybody +you know for that. + +It's free. + +And once again, there will be a +concert reflection, as we know. + +So turn it over to +Neil, welcome him. + +Thank you. + +NEIL LEONARD: Hi. + +So I'm going to give a +short presentation on a work + +I've created, a little +bit of background + +and why I made the +work, and leave you + +with an assignment, +which is to create + +your own work along the +same lines and with the idea + +that when I come +back next Monday + +I'll be able to hear what +you guys have come up with. + +And we could even play together. + +So this is all kind of going +in the direction of you taking + +some of these ideas and +running with them on your own. + +I have a background +as a jazz saxophonist + +with some activity in the area +of fine arts, which kind of + +means that I've always had not +like a singular vision of what + +I want to do, but +I've always kind of + +been looking on the +peripheral for other things + +that will be interesting. + +When I was a teenager, +really, I played in bands + +in Philadelphia. + +And one of the bands +that I was part of + +had these two brothers +Robin and Kevin Eubanks. + +And Kevin Eubanks, +you might have known, + +was the band director +of the Jay Leno Show + +for I think about +18 years or so. + +And he recently retired. + +And his older brother, Robin, +is going to, as Mark said, + +participate in the +concert on Wednesday + +evening, fantastic +trombone player. + +So he's a guy I've +known as a kind + +of young musician +in Philadelphia. + +And that was sort +of the background + +I came from, just kind +of people playing jazz, + +a little bit of pop musical, +a little bit of funk, + +occasionally a Latin gig, as +a teenager in Philadelphia + +before I moved out +of Philadelphia + +to go to a conservatory. + +In the course of +playing the saxophone, + +I came across a few things +which really interest me. + +One was a reel-to-reel +tape deck. + +So the school I went to had +a small electronic music + +studio with a EMS synthesizer +and a two reel-to-reel tape + +decks. + +And we were essentially +just shown this stuff + +and invited to come +to use it somehow. + +And at that time, I was really +interested in pop music. + +That was kind of +before jazz, I had + +listened to pop music that +had very interesting things + +happening in the production. + +So this would be Jimi +Hendrix, Pink Floyd, + +you name it bands of say +the '70s, so to speak, + +if I can really date myself. + +And I began to teach +myself a little bit + +about how to use this tape deck. + +And one of the +first performances + +I can remember doing was with +a trumpet player, my brother + +Devin who played +trumpet, a pianist. + +I played some objects +which I had just collected, + +pieces of hardware, +chains, stuff like that. + +I had some recordings +that I played back + +from this reel-to-reel +tape deck. + +And for me, this just +seemed like a normal way + +that someone would +want to play music. + +So you'd learn to +play your instrument. + +You'd take lessons. + +You'd be in ensembles. + +You'd do all the things that +an instrumentalist would do. + +But at least to +me, it just seemed + +interesting to see +what else I could bring + +to the mix of playing +improvised music. + +And now a few decades +later, I'm really + +still kind of doing that. + +So I'd like to introduce +a work that I did that in. + +But I guess first before +I show my own work, + +I want to talk a +little bit about things + +that were in the +air when I started, + +a little more about things +that were in the air. + +And two of the things that +I think had an impact on me + +as a young musician, and +musicians in general, + +was number one, John Cage. + +And mark has +mentioned that you've + +spoken a little bit about John +Cage's work in this class. + +And did you talk +about Four Minutes + +and 33 Seconds of +Silence by chance? + +Do you know that work? + +OK, so this is a work, seminal +work of 20th century music. + +It's a piece in three parts. + +And in the premier performance, +as I understand it, + +the pianist went to +the concert hall, + +opened up the lid +of the piano, sat + +for four minutes and 33 seconds, +and then closed the piano lid. + +And the piece was done. + +I heard a really +interesting lecture on Cage + +and his impact on today's +music in the last week. + +And the person who gave +the talk pointed out + +that Four Minutes and +33 Seconds of Silence + +was not about listening +to the sound in the room. + +But it was about +diverting your attention. + +So you go to the concert +hall with the expectation + +of seeing the lid +goes up on the piano, + +this virtuoso plays +this incredible piece. + +We're all in awe. + +We applaud. + +We go home. + +And this piece was +like opening up + +the door to shifting your +attention away from that. + +And that has some really +interesting implications + +because I think even for +Cage-- Cage was thinking + +about the impact of +convention, but also + +the impact of big +business on music. + +So he wrote a lecture that +was called Lecture on Nothing. + +And in this lecture, he talks +about the impact of media + +culture, Time Magazine, +Life Magazine, Pepsi-Cola, + +and how they have a bearing +on what we understand culture + +to be. + +I got a text for my son +during the last Superbowl. + +And Rihanna was on. + +And so I went to go catch +a little bit of this thing + +he was all excited about. + +And it was sponsored +by Pepsi, wasn't it? + +Wasn't Rihanna's Superbowl +performance sponsored by Pepsi? + +So, again, it was +like big business + +is investing a lot of time, +money, and energy on what they + +want us to see, +which is probably + +going to lead us to +buy Pepsi-Cola, which + +is why they're putting +money into this. + +But all this is to say +that one of the things that + +was interesting about Cage +was his music was encouraging, + +or his work was encouraging +us, to look outside + +of the prevailing +orthodox models of making + +music, and thinking of other +ways to think about music, + +to approach music, to +approach working with sound. + +So somehow that stuck. + +Another thing that was +in the air at the time + +that I was starting to +play music was, I think, + +one of the first albums-- +I remember at one point, + +for my birthday +and for Christmas, + +all I wanted was recordings. + +My mother's in the +back of the room. + +So I remember giving her my +wish list, like, I want records. + +And I remember one +of the recordings + +I got for Christmas was +The Beatles White Album. + +And The Beatles White +Album had a piece + +called Revolution Number Nine. + +Do anybody know that piece? + +Raise your hand if +you know that piece. + +And goes up, OK, good. + +Two, OK, two people +know that piece. + +John Lennon's wife, +Yoko Ono, no was + +part of a group +called Fluxus artists. + +And they were kind of +radical, experimental artists + +who did all kinds of +really fascinating things + +with performance, with music, +with film, kind of opening up + +all genres and medium as +tools for them to explore. + +And through Yoko Ono, John +Lennon knew John Cage. + +And one of the things +he did upon becoming + +in contact with John Cage +and these ideas is he + +made this piece. + +And I'd like to play just +a little bit of it that's + +called Revolution Number Nine. + +Now, I have colleagues who +say that this is a song + +because John Lennon +only made songs. + +So you could think +of this as a song. + +I always sort of thought of as a +tape piece, or a sound collage, + +because that's the kind of +terms I understand it in. + +So let me see if I +can get this to play. + +Can we turn this up? + +[MUSIC PLAYING] + +NEIL LEONARD: I'm +going to stop it here. + +The piece is eight +minutes and 22 seconds. + +So it's a sizable piece from +this recording The White Album. + +So somehow this +stuff was in the air. + +And I think it really +had an impact on me. + +As I was alluding to +earlier, did something + +to my peripheral vision. + +It made me think that there's +something interesting there + +on the side to think +about and investigate. + +With The Beatles it wasn't +just I Want To Hold Your Hand, + +and these wonderful pop tunes +that I made, all of which + +I really enjoyed. + +But there was sort of +another world, other ways, + +to think about +working with sound. + +So what I would like to do +now is kind of fast forward + +and show you fragments +of a piece I made, + +a long piece I made, +in the past few years. + +But before I do +that, I just want + +to invite you, if you have +questions or comments, please + +just blurt out your +questions or raise your hand. + +And I'm happy to stop +anywhere along the way + +and hear what's on your mind. + +OK? + +And actually, I +have a new tactic + +which I'm using with my +students at Berkeley, which + +is I don't let anybody leave the +room until they ask a question. + +So that works pretty well. + +Yes, you're leaving the room? + +AUDIENCE: How did he make that? + +Did he splice tapes together? + +NEIL LEONARD: Splicing +tape together, + +sometimes the +tapes are reversed. + +It sounds like +snippets of a band + +playing that were reversed. + +They had a brilliant +producer who's + +often referred to as the fifth +Beatle, George Martin, who + +had a background in +orchestral writing. + +So he had a very +robust skill set. + +And if they came in +with an idea that + +was kind of outside the norm +of making just pop hits, + +or the way popular +music had been made, + +he was often their collaborator +in going on a tangent + +and doing things. + +One example would be for +the piece Penny Lane. + +I don't know if you +know that piece. + +It's a fabulous song of theirs. + +I think it was Paul McCartney +had seen the London Symphony + +Orchestra. + +He heard a Piccolo trumpet +in a Baroque concerto. + +He went back and told +George Martin, like, + +that was really cool. + +And George Martin +said, oh, let's + +get the Piccolo +player from the LSO. + +And we'll use him on a piece. + +So George Martin probably wrote +the part of the Piccolo trumpet + +on Penny Lane. + +And it doesn't sound like any +other track they ever made. + +It's a wonderful, +idiosyncratic, playful track. + +So, yeah, you get +to leave the room. + +You asked a question. + +I should give you a ticket. + +So I'm going to fast forward. + +And I spent a few years actually +working at Mass College of Art. + +I thought it was going +to be a short-term job. + +And it turned out to be an +eight year residency there and. + +And I kind of went in +knowing a little bit + +about computers, and +some teaching experience, + +and a little bit of +administrative experience. + +And they said, great, +you'll do all of that. + +And I ended up staying +there because they + +had a few really +interesting people who + +came to work with us. + +One was this jazz trombonist +named George Lois, who + +is a seminal person working +with jazz and electronics, which + +only fueled all this +curiosity even more. + +John Cage was in town for a +year we did the Norton Lectures. + +And he came to Mass +Art a few times + +to meet with us, to +see what we were doing. + +I got a chance to +show him my work. + +There was a famous video +artist named Tony [? Allison ?] + +who was on the faculty. + +So all this is to say, +I ended up staying. + +I really didn't think +I'd be staying there. + +But I did. + +I stayed there for +eight years, kind of + +got involved once again in +working with visual artists. + +Not so much me +making visual art, + +but collaborating +with visual artists + +on all kinds of projects, +performances, films, videos, + +dance projects, theater +projects, happenings, + +computer graphics with sound. + +And then, eventually, I married +a woman who is a visual artist. + +And we've done a lot of +work around the world. + +We're doing a piece +in the upcoming Venice + +Biennial in May. + +We did piece in the +Havana Biennial last May. + +And so I've kind of +worked quite a bit + +with people who aren't +just playing saxophone, + +or just play with saxophonists. + +I've been very interested +in finding artists outside + +of music to collaborate with. + +So in this kind of journey of +working with artists outside + +of music, I was at an Italian +estate on top of a mountain, + +fantastic villa that +had two incredible view. + +One is the marble +quarries of Carrara. + +So across the valley, you can +see these mountains of Carrara. + +And even though it's +summer and it's warm, + +there's just white spilling +out of the mountains, which + +is the fragments of marble +that didn't get schlepped away, + +but are just kind of like +tumbling down the mountains. + +So the mountains had these +sort of white residual marble, + +chunks of marble. + +The other side is +the Ligurian Sea. + +And so my wife and +I were asked to make + +a permanent installation +at this Italian estate. + +And the owners, +every two years they + +would go to the Venice +Biennial and pick an artist + +to commission to make a +permanent, site-specific work + +for their estate. + +And we met them, +they'd say, hey, + +would you do something +for our estate? + +And we said, yep, we +got this great idea. + +And they said, no, we don't +want to see your great idea. + +We want you to come to the +estate, look at the place, + +look at the territory, +and think of an idea that + +would work for the space. + +So its site specific, which +is a very important concept + +in visual art. + +So we developed a relationship +with this commissioner + +of private sculptures for +this private sculpture park. + +And one year I was going +back to visit them, + +and they said, you know, we +have this sculpture which you've + +seen that is this huge-- +maybe you could draw it-- + +it's this huge pit that's +maybe eight feet across. + +It's like a pit that goes +straight down the Earth. + +And there's just a +spiral of church bells, + +with no clappers in them. + +Very large church bells, I +mean, they might be like, + +from top to bottom, if +the hinge was up here, + +the clapper would be down here. + +They're very, very big. + +But they're turned +upside down and they're + +arranged in a spiral kind +of like facing the sky. + +And so the owner said, +would you record these bells + +and make something with this? + +And I thought, well, I have no +idea what I'll make of this, + +but why not? + +I'll record these bells. + +So I recorded the +sounds of these bells. + +And I kind of had them around. + +I started to play with +them, didn't really know + +what I'd do with them. + +And I met a choreographer, +also Italy, in Naples, + +and then she asked me for a +composition for a dance piece. + +And I thought, OK, well +I have these sounds + +I made with these bells. + +So maybe it would be +interesting to do something + +with these belts. + +So I'm going to play just a +fragment of this recording + +that I made. + +So you know when you +take a JPEG image + +and you stretch it +horizontally, all of a sudden + +the image is unrecognizable? + +This is sort of what +I've done with sound. + +And some of this I did +with some free software + +which I could show you. + +There's commercial software. + +There's free software. + +Lots of different software +does time stretching of audio. + +So this could be +two seconds of audio + +that's stretched +out for a minute. + +The computer's going +to kind of sputter. + +And then this is sounds of just +bells straight because I wanted + +the listeners in the +dance performance + +to be able to hear an actual +bell so this wash of sound + +in the background would +make some kind of sense, + +would have some context. + +[MUSIC PLAYING] + +NEIL LEONARD: Now, +the dance performance + +was 40 minutes long. + +So it's a very +kind of slow, kind + +of glacially moving performance. + +So nothing in the music +happens too quickly. + +The music goes through a +lot of different phases. + +But each phase is +maybe five minutes. + +[MUSIC PLAYING] + +NEIL LEONARD: And this goes on. + +But essentially, these +were recordings of bells + +that I put in a program called +Spear, which we could look at. + +And I began playing with ways +to time stretch the audio, + +listening to what +sounded interesting, + +throwing away a lot of stuff. + +I kind of went into a phase +where when I make a piece, + +I want to have a +phase in the beginning + +where I call it sort of like +your work-- a research phase, + +research, slash, +play, slash, failure. + +Meaning, I take sounds, +I put them in a software. + +I play around with them. + +I research what I can do, +knowing that I probably + +have time to throw +a lot of these away. + +So I'm not doing this the +day before the performance. + +This might be a few +weeks or a few months + +before the performance. + +And I want to build +in time to experiment, + +knowing that a lot of the +experiments won't work. + +So out of many of +those experiments, + +I came out with this file. + +Sent it to the dancer. + +The dancer said, that's really +going to work for the idea + +that she was thinking of. + +And then she proposed a site +to do this performance, which + +was Mount Vesuvius. + +So Mount Vesuvius, as you +know, is the volcanic mountain + +that erupted and buried Pompeii. + +It is still an active volcano. + +There are people who occupy the +side of the volcano pretty much + +against, or in defiance of, +kind of zoning limitations + +because the authorities +don't want people + +to live in this volcano +because it's dangerous. + +The people live there all +have gas masks in their house, + +because the biggest +the problem is + +the toxic gas that +comes from the volcano. + +So in any case, there +was an art center + +on the side of +this mountain where + +we staged this performance. + +And it kind of grounded +the whole piece right then, + +because I begin to think of +what is it I'm working on? + +I'm working with these bells. + +We're doing something +on Mount Vesuvius. + +How am I going to +begin to kind of focus + +on an idea for this piece? + +And there's an author +named Murray Schafer who + +wrote a book called The +Tuning of the World, which + +has been republished under +the title Soundscape. + +You can find it on Amazon. + +It's probably in the library +here, Murray H. Schafer. + +And one of the things +he writes about + +is that for any environment +there's a keynote sound. + +There is a sound +that we human beings + +associate with +every environment. + +So with this +environment right now, + +it's probably the sound of the +fan on the video projector, + +or maybe the hiss coming +out of the speakers. + +This would be +keynote sound here. + +Perhaps in the +hallway, it's the sound + +of footsteps within this space +that you know is very long. + +It's not very wide. + +And it's a fairly +reverberant space. + +So every place you +go, there are sounds + +that let you know +you're in that place. + +When I was standing at +the subway the other day, + +the metro in Brookline, +I was recording the sound + +of the train because I've +taken that train, the D Line, + +for ages. + +And if I heard that +sound in my sleep, + +I would know, Green Line, +lightrail vehicle, Green Line. + +So I would say that +one of the things I'm + +really interested +in doing is thinking + +of pieces that have +a particular meaning, + +have a meaning that's +tied to a particular site. + +That fascinates me. + +And that's a way to kind of get +out of doing what I always do. + +So if I'm going to +work at Mount Vesuvius + +I don't want to do just +what I do in Boston. + +I want to do something +which is kind + +of specific to a +performance which + +is going to premiere +at Mount Vesuvius. + +If I do something in +a rice paddy in Japan, + +what's something about +a rice paddy in Japan + +that I wouldn't +think of in Boston? + +How can I respond to the +site where the work is? + +So one of the ways +to respond to a site + +where you're working +as a musician is + +to think of the keynote +sounds, and play with those. + +What are the sounds that are +typical to that environment + +that kind of tell you +you're in that environment + +that you can play with? + +I should say, very briefly, +that one of the things which + +is fascinating in Murray +Schafer's book and his ideas, + +is that he also kind of points +to this way of reflecting + +on your environment is an +integral part of literature + +that we know, that we've +known for centuries. + +So, for example, for Dickens +to talk about England + +in the period of Oliver +Twist, cobblestone streets + +have a particular sound, +horses on cobblestone streets + +have a particular sound. + +Those sounds are +sounds that Dickens + +is very aware of being very +important to your understanding + +of that place. + +Those are parts +of Dickens' world. + +Tolstoy, same, the example +I like most is Dante. + +In Dante's Inferno, when Virgil +and Dante head off to hell, + +they decide they're +going to go over to hell, + +see what's over there. + +They pass Cerberus. + +They make it to +the mouth of hell. + +There are no stars above hell. + +The damned don't +get to have stars. + +There's a black sky above hell. + +And because the sky is +black and there's no light, + +there are two paragraphs +of The Inferno + +that the contact with +hell is an audio contact. + +It's an audible contact. + +They hear the sounds +of the damned. + +And there is a two paragraph +description of the sighs, + +and the gasping, +and the kind of toil + +that these people are +experiencing in hell. + +So all this is fascinating +to me because it + +means that Dante, Tolstoy, +Dickens, were audio artists. + +They were interested in oral +analysis, or oral reflection, + +of their environment. + +So this is part of +something we can do. + +Our environment might be +like the vending machines + +downstairs. + +They may be the sound of +going up and down the hallway, + +or going up and down +the staircases which + +have wonderful echoes. + +It could be the sound +of radiators just + +kind of flapping. + +But these are +sounds which can be + +really interesting to work with. + +So when I began to work +on this piece, which + +I'm going to play not +the rest of, but more of, + +I just wanted to say that +it occurred to me that there + +was this wonderful opportunity +in that one of the most + +incredible sounds ever in Italy +was Mount Vesuvius blowing up. + +And period accounts +of that explosion + +say that the explosion could +be heard 100 kilometers away. + +So you could +practically be in Rome + +and hear the sound of +this colossal boom. + +The colossal mountain now +is kind of like a big mouth + +waiting to erupt again, +like these bells. + +The mouths the bells were +all facing the ceiling. + +So this became kind +of an idea that I + +began to play with and work +with in the piece, this idea + +of a kind of silent tongue. + +As the piece evolved-- +and I'll play you + +maybe five minutes of a kind of +finished version of the piece, + +of a radio edit of the +peace, a short version. + +I wanted to also process +not just bells, but voice. + +And I asked the host +if they could find me + +a singer who lived +on Mount Vesuvius. + +And they said, oh, yeah, +we've got a singer for you. + +So they found a singer. + +And it was great. + +She was in this metal band. + +And she told me her my favorite +singer was Diamanda Galas. + +I don't know if you +know Diamanda Galas, + +but she is a very kind of +eccentric, powerful force + +of a vocalist. + +So she came with some +people from her band + +to the place where +I was staying. + +I recorded her voice. + +And I began to also play around +with time stretching her voice. + +Kind of moving forward to +the final stage of the work, + +because there were several +versions of this piece. + +There was a piece for the +opening with a dancer. + +There were a couple concerts. + +I liked it enough that I +use it concerts a few times. + +I'll actually play parts +of this on Wednesday night. + +But I also had this +experience where + +I was in China for the +first time, in Beijing. + +And I gave a concert. + +Somebody came up to +me after the concert + +and was really +interested in this piece. + +Or actually was interested +in a piece I played. + +So a conversation began. + +And it turned out +the person who had + +come to talk to me after the +concert was a singer trained + +in kind of Peking +opera style, so + +very traditional Chinese music. + +Does anybody know +Chinese music here? + +I really don't. + +I've just been to China and +know some Chinese musicians. + +So in any case, I +said, OK, would you + +be interested in +singing a piece? + +And she said sure. + +I said, here's an MP3. + +Come tomorrow night +at five o'clock. + +We have a sound check. + +We'll see how this goes. + +So let me find a +version of this, + +so kind of a later generation +of this piece I played you + +earlier with the bells, +I'll just play an excerpt. + +You'll hear three things +which are new here. + +One is there's a sound of a +singer from Napoli singing not + +Italian syllables, just kind +of making up her syllables. + +And then on top of that there's +also a Chinese vocalist. + +So this kind of became this +sort of vocal time collage that + +kept on getting elaborated on +in the course of a few projects. + +And I'm playing +saxophone as well. + +And the bells are kind +of fading out here. + +Those are the bells. + +[MUSIC PLAYING] + +I'll stop that here. + +I won't play all +of it because I'll + +play the whole +thing on Wednesday. + +So we'll hear the +whole thing then. + +But that piece turned into +kind of a trio voices. + +There's a saxophone. + +There's this very time +stretched processed voice, which + +is mostly based on this +Italian woman singing. + +And there's an improvisation by +a person who does Peking opera, + +but was interested in +doing electronic music + +for the first time basically. + +And so that piece kind +of took its course + +through just interacting +with people that I found, + +a choreographer, a +singer, a collector + +who had interest in a +sculpture that he thought + +might make a sound. + +Actually nobody was a jazz +musician except for me. + +So that's just an +example of a piece + +I did in which these interests +I have kind of coalesce. + +There's an interest in +working with artists outside + +of music, choreographer. + +There's interest in fine +art, working with a collector + +to get his idea +for materials that + +might be interesting +to play with sonically. + +And I'm still +playing the saxophone + +in a way which is not +completely unlike how + +I play in a jazz setting. + +Any questions, +comments thus far? + +Yeah? + +AUDIENCE: So did you get both +the singers first and then + +decide whether [INAUDIBLE] and +how did you do your sax part? + +Is that what came last? + +NEIL LEONARD: Well in this +case it did come last. + +There was a lot of +sound design work. + +I guess for the premiere +that we did in Napoli-- I'm + +not worried about +playing the sax. + +I can play the sax for +40 minutes no problem. + +I was concerned about having +enough electronic material, + +enough of the sound collage. + +So I invested a lot of time in +getting that happening first. + +And that probably +took for the premiere, + +I had and some +fragments of it made, + +but there was a couple +weeks of work nonstop + +on the electronic score. + +And then probably two +days before the concert, + +I began to play around +the saxophone and kind + +of find where it fit in, +although I kind of intuitively + +knew here's a place I +left for me to fit in. + +Here's a place for me to fit in. + +Other questions? + +Yeah + +AUDIENCE: What sort +of [INAUDIBLE]. + +AUDIENCE: Vocal recordings? + +I did one which I'll show +you, which is really-- + +I'll do a very +quick version of it. + +I found out that a piece of +software that worked really + +well, is a piece of +software that's free. + +It's Windows and PC. + +It's called Spear. + +And I'll show you +one of the things. + +I don't want to spend +too much time on it + +because it's really fun. + +It's a lot of fun. + +But there it is. + +This is a recording +of the trombonist + +I'm playing with on Wednesday. + +It's a solo trombone track. + +And what the software's +going to do-- just + +going to say yes +to the defaults. + +It's going to do an +analysis of the sound. + +And the analysis +takes the sound. + +And it describes the sound. + +Try and shrink this, zoom +out as far as possible. + +It's freeware. + +It's kind of clunky, +but it works. + +So this file, let me see +if I can just play it. + +[TROMBONE] + +NEIL LEONARD: So +just a trombone. + +Now, just a trombone-- you +really don't see everything + +on the projector, but that's OK. + +These are frequencies from +zero Hertz up 8,500 Hertz. + +And this, of course, is +a timeline over here. + +And it deconstructs the sound +into a plot of sine waves. + +So without really +getting too far into it, + +let me just do one +thing to convince you + +that it's really doing that. + +So we'll go over here. + +And I'm going to take +some of these sine waves. + +I'm going to select them just +by control clicking on them. + +And I'll just grab some of them. + +There they are. + +And now I'll go to +New from Select. + +We'll make a new +file from selection. + +And there's only the +sine waves I selected. + +Let's play those and +see what it sounds like. + +[SOUNDS] + +NEIL LEONARD: Those are +sounds that are in there. + +Now, there happen to be hundreds +of sine waves at a given + +moment. + +What we just heard is this. + +[TROMBONE] + +NEIL LEONARD: If we grab +some more sine waves-- + +actually I'll do it like this. + +What's the first +letter of your name? + +AUDIENCE: V. + +NEIL LEONARD: OK, we'll +make a V. Not a great V, + +you could do better. + +And I can select them that way +just to have fun with this. + +And there we go. + +And we can play this. + +[SOUNDS] + +NEIL LEONARD: You can probably +see it on my laptop better. + +The greys show up +better on this. + +But do you get the idea? + +That sound, the sound +of the trombone, + +the trombone performance, +is deconstructed + +into a series of sine waves. + +If we play them all, we hear +the whole trombone performance. + +If we take out +certain ones, then it + +sounds like a filtered trombone. + +Now, here's one of the +things I did quite a bit, + +in terms of, what did +you do with voice. + +And what was the +question you asked me? + +AUDIENCE: Yeah, what sort +of things did you play? + +NEIL LEONARD: OK, here's one. + +[TROMBONE] + +NEIL LEONARD: Let's take that. + +Let's go right there where I +think he kind of changes a note + +and gets a bit more complicated. + +I want to time stretch it. + +So I'm going to say +Transform, Time Stretch. + +And I'm going to make it four +times longer, times four. + +So. + +[TROMBONE] + +NEIL LEONARD: So you can also +hear him move from one note + +to another. + +All of a sudden it +doesn't sound so clean. + +He's a very articulate player. + +But all of a sudden +you get this moment + +of transition, which +is pretty cool. + +In fact, if I thought that I +really wanted more of that, + +I'll Time Stretch the same +thing again times four. + +What do we get now? + +[TROMBONE] + +NEIL LEONARD: It's +like a tri tone. + +It's a pretty difficult +to play and you kind of + +get some of that tension +of him playing it. + +There are many different +ways to time stretch. + +They all have artifacts. + +None of them are perfect. + +But some of the +artifacts I like. + +So some ways of +stretching it are useful. + +And other ways just sound bad. + +So there was quite a +bit of time stretching. + +But I guess that piece is +not really that extravagant. + +I also sort of +collaged at this level. + +So, for example, we can make a +collage of just these partials. + +We can take these lines and +treat it like a drawing, + +and rearrange where +the lines are. + +So, in fact, I +think I can, again, + +without going too far in +this, I can offset this time. + +And I'll push all +that stuff over here. + +Now, it's probably +going to be a mess + +because you can hear +two notes at a time. + +Or we're going to see +what you can here. + +[TROMBONE] + +NEIL LEONARD: So all this is +to say that, like in Photoshop, + +you have this sort of +incredible facility + +for rearranging the +pixels in an image. + +This is like dealing with +sound at the pixel level. + +Every component +sine wave of sound + +can be stretched independently, +shrunk independently, + +transposed. + +In face, we could take some +of these sounds-- actually + +I won't go any further because +I'll just go on and on. + +And none of this will be what +we really want to listen to. + +But you get the idea. + +So I used off the shelf +software you pay for. + +I used freeware, spent +hours, and hours, + +and hours in that play, +research, failure, + +mode of just trying +more stuff out. + +Let me just see if I begin to +experiment, what will I get? + +How are we doing for time? + +We're probably OK. + +I guess where George Martin +and The Beatles were, is + +they did this by +tape manipulation, + +as you had pointed +us to earlier. + +And now, of course, +nobody's using tape. + +It's expensive. + +It's not as flexible. + +It has a particular +sound that people love. + +But nobody's using it. + +I work at Berkeley. + +There's a Department of +production engineering + +which is like the tape tribe. + +They still worship +reel-to-reel reel tape decks. + +They grew up with +reel-to-reel tape decks. + +They learned their craft +with reel-to-reel tape decks. + +They edited Bruce +Springsteen's recordings + +on reel-to-reel tape decks. + +They think it has +to be understood. + +But they can't use it +either because it's + +big, and expensive, and slow. + +And production has +to be cheap and fast. + +So we're doing it +in the computer now. + +But quite a bit of +this is being done. + +Other than the time +stretching, a lot of that work + +was not that extravagant. + +And what I wanted to do was +take the phrases of that singer + +and really kind of +distort her lines in time. + +So when she sang, some lines +were held for a very long time. + +Some syllables went at +the natural sung rate. + +So they appeared +normal, so to speak. + +But I'll also +point out something + +that Mark and I talked +about on the telephone + +when we were +discussing this class + +and your assignment, which +is the next we'll talk about, + +is that this semester I hosted +a composer named Hans Tutschku. + +Hans Tutschku is the director +of the computer music + +program at Harvard. + +And if you ever get +a chance, there's + +probably a concert coming up +probably at the end of April. + +And he does concerts with what +he calls the hydra system. + +The hydra system is a +collection of 40 speakers. + +And you sit inside +the 40 speakers. + +And it's a little bit like going +to a cathedral, where there's + +like a dome, and the dome +has a painting on it. + +If you ever go to the +Vatican, for example, there's + +this beautiful dome, +with this ring, + +with this text which +is really important. + +And it's just a +great experience. + +It's an installation. + +It's a work of art. + +The dome is a work of art. + +This is the sonic dome. + +And there are three +rings of speaker. + +One's at ear level. + +One kind of maybe six +feet above ear level, + +and like 12 feet +above ear level. + +And the rings the rings +go really wide, smaller, + +and smallest. + +So he came to Berkeley. + +And the students +were all excited. + +Here's this guy from Harvard. + +He's got to be important. + +And he uses 40 speakers. + +So he's got to be more +sophisticated than us. + +He knows things we don't know. + +And the fascinating thing was he +showed us these pieces he made, + +which were fantastic +piece of music. + +He made them like-- +I'm recording + +this lecture on this little +Sony handheld recorder. + +it's not that expensive. + +He made all his recordings +with a little Zoom + +handheld recorder, like $400. + +And he was saying one of things +he likes to do is wave it. + +So if he's playing +an antique piano, + +which is all out of tune. + +And he's recording the sound. + +He'll move, he'll sweep, +like a visual artist + +would move a camera. + +If a visual artist is going +to shoot a video of a rock, + +they're probably not going +to put the video on a tripod + +to shoot the rock. + +I mean, there's a +pretty good chance + +they'll want to move to show us +different aspects of this rock. + +Well, this is what Hans +loves to do with microphones, + +move them across the surface. + +Because his argument +is if you have a gone, + +and you hit the gong, and +you move it by your ear, + +the gong sounds one way +if it's 30 feet away, + +one way if it's 10 feet away, +and one way it it's very soft + +and you're right next to it. + +Those are three completely +different sounds. + +They're all gong. + +But the details you get +are radically different. + +So one thing I want +to point out is + +that the selection +of the materials + +is a major part of the work. + +And one of the things Hans said, +which I also had been doing, + +but I'd never really thought +about in quite the way he + +was discussing it, was he only +uses sounds he records himself. + +And he's been doing this +for a long time, decades. + +And so he has all +kinds of sounds + +he's made all over the world. + +But the important thing +about all the sounds + +is that he has a +memory of recording + +each one, of choosing +to record each one. + +So of these thousands +of sounds he might have, + +he has a visceral +experience that's + +associated with every sound. + +So those bells I recorded, +are bells I recorded. + +And I know the +weight of the bell. + +I know the color of the bell. + +I know where it +was in the Earth. + +I remember what it was like +to put the mic on there. + +I remember how hot +it was that day. + +I remember how we kind +of hit them with hammers, + +did all kinds of things to +try to get a sound out of them + +because they weren't free +standing bells really + +made to be struck. + +Same with the vocalist, I +remember hearing this vocalist, + +and we had a discussion +about getting something + +that would work in this piece. + +So all those memories are +valuable when you go back + +to your material +because otherwise it's + +just a sound file. + +Like every other sound file, +maybe I like it, maybe I don't. + +But because you have been +involved in physically + +recording and +capturing that sound, + +it's as if it was in your hands. + +You have a kind of +tactile relation + +to the sound that you +wouldn't have otherwise. + +Now here's what I'm going +to ask you guys to do. + +So I understand you've +worked not only with Mark, + +but you've work with +my colleague Tom Hall. + +And I'm actually playing a +concert with Tom Hall on Sunday + +at a place called The +Outpost with a bassist named + +Jamaaladeen Tacuma, who +is known for his work + +with Ornette Coleman, +very good bassist. + +Mark has also told +me that you work + +in pairs, or sometimes +groups of three. + +And with your pair, +I'm going to ask + +you to make a +collaborative improvisation + +with audio recordings. + +And your goal is to, with +your partner or partners, + +create small sound +library to utilize + +in a two to three +minute improvisation. + +And you're going to prepare +a performance that integrates + +the playback of +some of the sounds + +you record in this performance. + +So let me ask you one thing. + +How do you like to improvise? + +And how do you +improvise in this class? + +Is it more along the lines +of free improvisation? + +Are people improvising with +a chord, or with a tonic, + +or is it all of the above? + +PROFESSOR: We've done +modal improvisation. + +We've done graphic notation, +like Cage's notations. + +We've created our own scripts +for that, and then done that. + +We've done a lot of free. + +We've done a lot of with +small little parameters. + +Indian concepts +of Phil Scarf too. + +NEIL LEONARD: So all +of those are fine. + +Any of the approaches +to improvisation + +that you have been +working with this semester + +that you want to use for the +improvisation you do for me + +next week, or I'll do with +you next week, is welcome. + +It's going to be much more +interesting for all of us + +if you're doing something +which you like to do so. + +And I don't know +you that well so I + +don't want to tell you what +to do with the improvisation + +except I want you to use +whatever technology you have + +at your disposal, which might +be your iPhone-- probably + +everybody has a phone +that can record audio. + +It could be a phone. + +It could be an iPad. + +It could be a portable +recording device. + +And I want you to make +a collection of sounds. + +Say how many, it could be four. + +It could be 10. + +And I want you to use +this original material + +as source material for +this improvisation. + +So it can be valuable +to go to the internet, + +and find an audio archive, and +get audio, and do a piece based + +on what you found +on the Internet. + +And I can think of some +really cool examples. + +But I'm going to encourage +you not to do that. + +So I actually want you +to think about the sounds + +that-- you don't have to leave +where you live, where you work, + +where you study. + +Within this part of the +world that you travel in, + +you can get the sounds there. + +So plan a recording in a +location that you frequent + +daily, your walk to school, +your apartment, your job. + +The idea is to listen +to your environment + +and discover new details that +help divert the audience's + +attention from the +typical mode of listening + +to everyday sounds. + +So when you think of +the role of audio, + +of using audio recordings, +in improvisation, + +you get a few things. + +One is you get what +Luciano Berio said + +is we open the sound +pallet up to everything. + +Now, you could prepare +your guitar, for example. + +If you play acoustic guitar, or +cello, or piano, or whatever, + +you could prepare your guitar. + +Do you know that is to prepare +your guitar in the John Cage + +sense? + +In the John Cage, +preparing a piano + +meant like putting +bolts in the strengths. + +I'm not going to encourage you +to do that with this piano. + +But people put paper clips, +erasers, and screws and stuff + +in the piano. + +And it changed +the way it sounds. + +There's a beautiful Cage +recording of prepared piano. + +It makes it sound kind +of like a gamelan. + +You could prepare +your instrument. + +As long as you're +making the recording, + +I'm probably not going to +say, you can't do that. + +You could record +sounds of cars whizzing + +by you on Memorial Drive. + +But one of the things +which I didn't really + +put in writing here, but +I think is important, + +is if you can find either +one keynote sound, or one + +idea about sound, that you'd +like to play with, it might + +be-- you might get +more out of that then + +recording like 15 +completely different sounds. + +If you want to record 15 +completely different sounds, + +I'm not going to stop you, but +I'm actually encourage you to-- + +Think of it this way. + +If you had a play, if we were +doing theater for next week, + +and we said, let's make a play. + +And there are going +to be five actors. + +The first actor is probably +not going to come on the scene + +and then never come back again. + +They're probably not going +to just say one thing + +and then leave. + +Although, now that I say this, +I can think of some examples + +where that happens. + +In fact, I went to go see +Mahler's Third at the BSO. + +And there's a singer who +sang literally five lines. + +And she came out halfway. + +This is 100 minute symphony. + +She came out halfway through, +sang literally five lines, + +and stood on the stage +for the rest of the time. + +It was really weird. + +It was a great piece of music. + +But it was weird. + +But the point is this, if +you're thinking prepared guitar, + +or if you're thinking of the +sound of opening and closing + +windows in your +apartment, or whatever + +it is that you're +interested in, what does it + +sound like in the quad, or +between the buildings here? + +You get sort of a theme and +variation potential, or a kind + +of multiple perspective feature +in your piece, if you will, + +if you have more than one +recording of a certain thing. + +So let me ask you. + +I'm just going to pick +your brains right now. + +If you were to choose +something to record + +to include in an +improvisation-- I + +don't want your +final answer now. + +But I'm just going to +pick on all of you guys + +just to kind of get +the conversation going. + +What's your name? + +AUDIENCE: James. + +PROFESSOR: James, +so what would you + +do if you had to pick right now? + +AUDIENCE: I think +the sounds of riding + +the bus would be interesting, +the doors opening and closing, + +or stop requests. + +I feel like you could play a lot +with all the different sounds + +involved. + +PROFESSOR: For sure, +and it would also + +have the built in connotation +of the piece's emotion. + +The piece is stopping. + +The piece is starting. + +The motion of the +piece is stopping. + +The motion is starting. + +I had a teacher who when I went +back to my master's degree, + +a really wonderful composer +named Bob Brookmeyer. + +And he said music is motion. + +Anything you do to impede the +motion has to be questioned. + +It doesn't mean to you +can't impede the motion. + +But think twice if you're +going to impede the motion. + +Well, this is a +piece about a bus. + +Or a piece that's including +sounds from the bus, + +so that's kind of +like a built in idea. + +The bus has stops. + +Good. + +Perfect. + +Your name again? + +AUDIENCE: Vineet. + +The sounds of an elevator. + +NEIL LEONARD: +Elevator, sure, good. + +And there must be +different elevators + +in different places on campus. + +Hopefully old, clunky ones. + +And ones that are not +so old and clunky. + +When I got this new +recorder, that's + +the first thing I think +I recorded was elevator. + +I was in a hotel that made +a really strange sound. + +So I figured, OK, +I've got to grab this. + +And I'll see if I make +something out of it? + +What is your name? + +AUDIENCE: Sarah, I think +I'd do my roommate cooking. + +NEIL LEONARD: Roommate +cooking, great, good. + +The piece is cooking. + +There's kitchen, lots of stuff. + +There is a teacher +at Berkeley who + +has his students do a piece. + +I think the piece +is in their kitchen. + +It's found sound in the kitchen. + +There's so many things +to rattle, and shake, + +and make stuff out of, good. + +And, again, what we're +thinking of doing is + +we're not making a grand opus. + +We're making a piece that's +two or three minutes long. + +So you definitely have a few +minutes of sound from cooking. + +What is your name? + +AUDIENCE: Jacob. + +I was thinking various +machines around a dorm, + +so washing machine, +microwave, people typing. + +NEIL LEONARD: Good. + +That would be fine. + +Tons of automation, which is +a really interesting topic. + +When I first got +into computers, one + +of the things that they +seem to offer to music, + +which was a big question +mark, was automation. + +You can automate a musical +process with a computer. + +If you're writing software, +if you're creating software, + +you can describe a process +of generating notes or sounds + +and have it do that. + +So automation sounds, fine. + +So all of these four ideas +that we just touched on + +are exactly what I was +kind of hoping to get to, + +where you have an idea of +something you can play with. + +These are all fine. + +Your name is in +the orange shirt? + +AUDIENCE: Ben. + +NEIL LEONARD: Ben? + +What do you think +would you record? + +AUDIENCE: I was thinking maybe +the sounds of the locker room, + +which the loudest of +which are probably + +people slamming their lockers. + +NEIL LEONARD: Yeah, good. + +Percussion piece. + +PROFESSOR: I want to clarify +something for myself and maybe + +for others. + +So when we've had these +other assignments, + +I've called them +design assignments. + +And that's what we talked about. + +So should we be thinking about +how we design the framework? + +In other words, +you had a framework + +with your certain +phases, certain segments. + +Should we be thinking that way? + +NEIL LEONARD: +Absolutely, and we want + +to think about how +to use these sounds. + +So before we get to +framework, let just say, + +in terms of the playback +of these sounds, + +it's kind of flexible. + +I mean, a simple thing +that you could do + +is you could make a playlist in +iTunes of sounds you've created + +and play with this playlist. + +You also probably want to +make some sound of silence. + +The sound might be more +effective if you're not + +hearing your recorded +sounds all the time, + +but you're hearing the +sounds some of the time. + +So you don't have to inundate +us with recorded sound. + +It could be very, very poetic. + +It might just be that a few +moments of recorded sound + +add another dimension +to improvisation. + +So that would be the simplest +way to use the sounds. + +Is everybody OK with that? + +I mean, everybody has iTunes. + +So you could do it that way. + +Everybody can record a sound +which is basically really, + +really quiet or +silent, so to speak. + +So you can also put in blocks. + +You can space out silence. + +That kind of would +be a composition. + +The other way to think of +this would be-- and then + +let's make sure we have time +to talk a little bit more + +about context-- is when +you're working in pairs, + +one person could use the iPhone, +or the computer, or the iPad. + +And the other person could play. + +So the two of you don't have +to improvise simultaneously. + +One person could be more +working the computer. + +And one person could +do the playing. + +So, for example, if-- +what's your name? + +AUDIENCE: Forest. + +NEIL LEONARD: And what +instrument is that? + +Is that yours? + +AUDIENCE: No, I play the piano. + +NEIL LEONARD: So +Forest, for example, + +who would your partner be? + +AUDIENCE: Austin. + +NEIL LEONARD: Austin, OK, +good, so if Forest and Austin + +did a piece, and Forest is +playing piano and improvising, + +and Austin is +working the computer, + +one thing you could +do, Austin, is + +you could trigger the +sounds at your discretion + +in a spontaneous way. + +You could improvise. + +It won't be like +playing the piano + +where there's a whole +lot of finger motion. + +But you could choose in +relation to Forest's performance + +when to trigger the sounds. + +So you're not triggering +them all at once. + +You're not triggering them in a +sequence that's predetermined. + +You could trigger +them as you go. + +So does that makes sense? + +So I think in order for this +to be successful-- in order + +for the use of the +recorded playback of sound + +to be more robust and to +give you more flexibility, + +it probably make sense, +unless you think otherwise + +and have a difference scheme, +but my first suggestion + +would be to have one +person improvising + +with these sound files +and another person + +improvising on the +traditional instrument. + +Yeah? + +AUDIENCE: In your +performances, is it + +usually balanced like that? + +Where one person is operating +some part of the electronics? + +The electronics are +also improvised? + +Or it more just +straight recording. + +NEIL LEONARD: It's a +very good question. + +Because I only have two hands, +and the saxophone, really, + +you can't do it with one hand. + +Piano, you could probably +pull it off a little better. + +But I'm usually doing three +things, playing the saxophone, + +doing live audio processing of +the saxophone, which we didn't + +touch on, which I don't think +we'll have time to today, + +but we could touch +on it next time. + +And then playing +back sound files. + +So at certain times, I tried to +improvise everything, and write + +software to +improvise everything. + +And I've sort of moved +away from that approach + +in favor of building these sound +collages which I know very well + +and perform with. + +But I do live sax processing +which is improvised. + +And that's what I'll +do on Wednesday. + +But I wan to go +back to the issue + +that Mark raises about +a formal structure. + +And I'm going to ask you to +help with this as well because I + +didn't come today with a +very exact formal structure. + +Or really I didn't come +with a formal structure. + +So one of the things +that comes to mind + +is-- and actually +maybe Mark you should + +help with the +brainstorming of this. + +But one of the things +that does come to mind + +is do the sounds you record +suggest any kind of structure? + +So, for example, if you're +thinking locker room, + +if I go to the gym, I +have a combination lock. + +I don't how much +noise that makes. + +It's probably pretty quiet. + +But the bang of the lockers. + +What do you do with the +banging of the lockers? + +They can be kind of cacophonous, +as they sort of are. + +They don't really +kind of open and close + +with any kind of logic. + +If I go to the gym at 6 o'clock, +and a lot of people are there, + +there's a lot of opening +and closing of doors. + +But because you're +recording, potentially you + +could trigger things live, who +would your partner be in this? + +Who was your last partner +in an improv project? + +AUDIENCE: James + +NEIL LEONARD: And James is you? + +So if you did this +with James, James + +could do something which is +not typical of a locker room, + +where things are opening +and closing periodically. + +So you're making a rhythm +out of these lockers. + +I do want to mention +something about that. + +But I want to talk +about a slamming door + +piece, or a banging piece that +maybe I can bring next time + +and play for you. + +But maybe it's a binary form. + +One part is more free. + +And the banging feels +like less-- just + +seems a little random. + +And another other part +seems decisively not random. + +Mark, what do you think? + +What have they done with form +that would be applicable here? + +PROFESSOR: I think we've +done a lot of these things. + +So I would say leave it +up to people's ideas. + +NEIL LEONARD: OK, that's fine. + +I have the impression +anything you've + +thought about with form +already probably is still-- + +could be applicable here. + +PROFESSOR: And we +could apply things. + +I think what I would say is +if you could think of a way + +to have a beginning +and an ending, + +and maybe a middle +marker of some sort. + +If that makes sense. + +NEIL LEONARD: Good, good. + +I do want to say one thing +about noise and banging doors. + +I just want to say +a couple that does + +sound art, Janet Cardiff and +George Miller is her partner. + +And Janet Cardiff just did +a piece in a New York armory + +in the last 12 months. + +But she's famous for +making these pieces where + +they were like audio walks, +where you would headphones on. + +And it would be like she +was on the walk with you. + +And she would tell +you where to go. + +There was a Central Park one. + +And as you're walking with +this person who's not there, + +it's like a disembodied voice, +she begins to tell you a story. + +And you're getting kind of +wrapped up in the story. + +And the next thing, a +helicopter flies right by you. + +And you turn around, +and it's not there. + +So it's a kind of a +talk kind of reshapes + +your audio experience +on a specific + +walk that she's designed it for. + +So, again, a site-specific +piece of art. + +But she and George +Miller were invited + +to do a piece at the +Eastern State Penitentiary + +in Pennsylvania, which +is in Philadelphia. + +It's a penitentiary +which is infamous + +for, among other +things, it was maybe + +the first penitentiary +in the United States + +where they had +this big experiment + +in solitary confinement. + +So one of the wings, or +maybe in all of the wings, + +prisoners were isolated +in cells by themselves + +with only a Bible with the idea +that if they were by themselves + +with a Bible they +would have nothing + +to do but reform themselves. + +And I think that it did not +become the model for reform. + +But they now commission +artworks in the Eastern State + +Penitentiary. + +And so what they did is they +made these kind of robots-- + +I won't call them robots-- +but these beaters that + +were motorized. + +And they were maybe +in this one corridor + +there were like 162 +cell blocks, both sides + +of the corridor, first +and second floor. + +And they had at least +one of these beaters + +in every one of +these cell blocks. + +Now, this corridor had +not been renovated. + +It was still like totally +dilapidated, paint + +chipping all over the +place, water damage. + +But they never cleaned it out. + +So there was still +some furniture, + +which means like beds, +bed pans, whatever it as. + +So they put beaters +in every cell block. + +And they controlled them. + +They were controlled +by computer. + +And they did exactly +what I was saying, + +which is where I +got the idea, is + +they made this 16 minute score. + +And they did it with a computer. + +And they did it in a sequence. + +They did it actually +in the same one + +I'm using now, Logic, and +the piano roll notation. + +And everyone little +note in the piano roll + +was a different hammer +in a different cell. + +So in some parts +of the recording. + +It's very pointalistic. + +You would hear a sound +from one cell, then + +something from the other +side of the corridor. + +There's kind of a +race section where + +they're all pounding +out a rhythm. + +But they're kind +of different sounds + +that-- I mean, you can only +imagine what the inmates would + +have thought if +whatever it would be, + +really 150 years later. + +This is long-- this is +like totally over, pretty + +horrible place. + +But it was a banging piece. + +Lockers bang. + +So it was a piece that +was all about banging, + +banging in a corridor, kind +of almost like a prison riot + +kind of vibe from the +recording I've heard of it. + +I didn't actually see the piece. + +But they had a structure too. + +And part of the structure +was have a rave. + +So there was kind +of a beat, or I + +don't know if you could call +it a recognizable groove. + +But there was sort of +like a periodic thumping + +happening at one +part of the piece. + +Other parts were more +noisy and pointalistic. + +So given that I don't know +what you're going to record, + +and I also don't want to +make the piece for you, + +I'm kind of open to form. + +But I would say this, open +to your ideas about form. + +But be prepared to tell us why +you recorded these sounds, what + +was attractive about recording +the sounds, what it was + +like after you recorded them +because everything's different + +after you record it. + +The classic example +are gunshots. + +You think a gunshot +would be powerful. + +But when they made +the film Terminator, + +they took Howitzer's, and +cannons, and bazookas, + +and they put them all together +to make these guns that Arnold + +Schwarzenegger would shoot to +make them sound like comic book + +big, larger than life. + +But guns don't sound +larger than life. + +They sound smaller than +life, just like a little pop. + +In Hollywood, there +is a job in Hollywood, + +should you be interested, +in making guns sound big. + +Many of my students +go and do that stuff. + +So why did you want +to record these? + +What was your initial thought +about recording these sounds? + +Like, the kitchen, my +roommate makes all this, + +boiling, there's sauteing, +there's stuff coming out + +of the toaster, there's +water boiling, all that. + +And that seemed like +it's a pallet which + +could be interesting. + +Whatever your +reason is, whatever + +your experience is after. + +And then also going back to +what mark suggested, how did you + +think about +organizing the sound? + +Because I'm not so much +interested in right or wrong, + +but what were your +thoughts about putting + +this stuff together? + +Did you have a thought +before you improvised + +about how to arrange +this improvisation + +with your partner? + +Did you guys just +plunge into it? + +If you had a thought about +how to use it, with the bus, + +does it begin with +starting the bus? + +Does it end with +the bus stopping? + +It doesn't have to. + +But that would be +another valuable part + +of your experience to +bring to the discourse. + +Once you had those +sounds, how did you + +go from there to +finishing a piece? + +So as you see with me, +it's like, I come up + +with some cool sounds. + +I record some +elevators, some bells. + +And sometimes I just start +messing with the stuff. + +But at some point, it's +actually got to finish a piece. + +So once I start to set +out to make a piece, + +then typically I'm beginning +to think of what kind of shape + +should the piece have? + +I have a degree in +music composition + +so I kind of neurotically +have to deal with it that way. + +You don't have to. + +And I think any way you +deal with it can potentially + +be successful. + +But one of the things I learned +from a teacher I had was + +that the first thing you do +when you write a piece of music + +is you decide the duration. + +The second you can do is can +could think about the form. + +And when you're thinking about +the form, the order in which + +stuff's going to happen, +you're actually preparing, + +if you call this +composition, you're + +actually composing music +without hearing a sound. + +I could think start +soft, end loud. + +I could think, start +fast, end slow. + +And those are really +compositional decisions + +which I can make +without making a sound. + +I can think of only +lockers opening + +at the beginning, only +lockers closing at the end. + +That's a compositional decision. + +That came from George Russell. + +You can compose. + +Or, because this is a +class in improvisation, + +you can create sonic ideas +without making a sound. + +And my neurosis as a composer +and as a lifelong student + +of composition, is I want to +use that approach, at least + +to some level. + +Not in everything +I do, but I'm often + +trying to think about what are +some ideas about these pieces + +before I roll up my sleeves +and start making stuff? + +PROFESSOR: I'm sorry. + +We're going to have to call +time because we have to leave. + +NEIL LEONARD: I think +that's a good place to stop. + +PROFESSOR: Thank you very much. + +I just have one +practical question. + +We should think about how +we're going to present these + +because we're going +to wind up with 16. + +Does that mean +we're going to have + +six computers with individual +sound files or what? + +NEIL LEONARD: I think +so, because it's probably + +easiest for you +just to set it up + +on your phone, or your +iPad, or your computer, + +and plug them in here. + +The only thing +about that is this + +seemed to behave better when +video is plugged in as well. + +But maybe we can just +plug video into my machine + +and swap in and out of +this cable if need be. + +PROFESSOR: OK, so in +each team, one person + +should bring some device. + +Is that OK? + +Great. + +Assignment for Wednesday, +I got inspired. + +I'm improvising. + +We're going to bring +our instruments. + +I want you to think between now +and then of at least one sound + +that is not a conventional +sound on your instrument. + +If you can think +of two or three, + +that's great, but at +least one sound that + +not conventional +to your instrument. + +OK? \ No newline at end of file diff --git a/PaI-oaOBHKU.txt b/PaI-oaOBHKU.txt new file mode 100644 index 0000000000000000000000000000000000000000..8f14cc8c167697457c052a2b269d23c92845e94e --- /dev/null +++ b/PaI-oaOBHKU.txt @@ -0,0 +1,1427 @@ +align:start position:0% + +we have already worked through some + + align:start position:0% +we have already worked through some + + + align:start position:0% +we have already worked through some +examples in which X was a random + + align:start position:0% +examples in which X was a random + + + align:start position:0% +examples in which X was a random +variable with a given PDF and we + + align:start position:0% +variable with a given PDF and we + + + align:start position:0% +variable with a given PDF and we +considered the problem of finding the + + align:start position:0% +considered the problem of finding the + + + align:start position:0% +considered the problem of finding the +PDF of Y for the case where Y was the + + align:start position:0% +PDF of Y for the case where Y was the + + + align:start position:0% +PDF of Y for the case where Y was the +function X cube or the function of the + + align:start position:0% +function X cube or the function of the + + + align:start position:0% +function X cube or the function of the +form a over X what both of these + + align:start position:0% +form a over X what both of these + + + align:start position:0% +form a over X what both of these +examples have in common is that Y is a + + align:start position:0% +examples have in common is that Y is a + + + align:start position:0% +examples have in common is that Y is a +monotonic function of X in this case Y + + align:start position:0% +monotonic function of X in this case Y + + + align:start position:0% +monotonic function of X in this case Y +is increasing with X in this case Y was + + align:start position:0% +is increasing with X in this case Y was + + + align:start position:0% +is increasing with X in this case Y was +decreasing with X it turns out that + + align:start position:0% +decreasing with X it turns out that + + + align:start position:0% +decreasing with X it turns out that +there is a general formula that gives us + + align:start position:0% +there is a general formula that gives us + + + align:start position:0% +there is a general formula that gives us +the PDF of y in terms of the PDF of X in + + align:start position:0% +the PDF of y in terms of the PDF of X in + + + align:start position:0% +the PDF of y in terms of the PDF of X in +the special case where we're dealing + + align:start position:0% +the special case where we're dealing + + + align:start position:0% +the special case where we're dealing +with a monotonic function so let us + + align:start position:0% +with a monotonic function so let us + + + align:start position:0% +with a monotonic function so let us +assume that G is a strictly increasing + + align:start position:0% +assume that G is a strictly increasing + + + align:start position:0% +assume that G is a strictly increasing +function and what that means is that if + + align:start position:0% +function and what that means is that if + + + align:start position:0% +function and what that means is that if +X is a number smaller than some other + + align:start position:0% +X is a number smaller than some other + + + align:start position:0% +X is a number smaller than some other +number X Prime the value of G of X is + + align:start position:0% +number X Prime the value of G of X is + + + align:start position:0% +number X Prime the value of G of X is +going to be smaller than the value of G + + align:start position:0% +going to be smaller than the value of G + + + align:start position:0% +going to be smaller than the value of G +X Prime so when you increase the + + align:start position:0% +X Prime so when you increase the + + + align:start position:0% +X Prime so when you increase the +argument of the function the function + + align:start position:0% +argument of the function the function + + + align:start position:0% +argument of the function the function +increases to keep things simple we will + + align:start position:0% +increases to keep things simple we will + + + align:start position:0% +increases to keep things simple we will +also assume that the function G is + + align:start position:0% +also assume that the function G is + + + align:start position:0% +also assume that the function G is +smooth in particular that it is + + align:start position:0% +smooth in particular that it is + + + align:start position:0% +smooth in particular that it is +differentiable then we have a diagram + + align:start position:0% +differentiable then we have a diagram + + + align:start position:0% +differentiable then we have a diagram +such as this one here is x + y is given + + align:start position:0% +such as this one here is x + y is given + + + align:start position:0% +such as this one here is x + y is given +by a function of X it's a smooth + + align:start position:0% +by a function of X it's a smooth + + + align:start position:0% +by a function of X it's a smooth +function and that function keeps + + align:start position:0% +function and that function keeps + + + align:start position:0% +function and that function keeps +increasing now because of the + + align:start position:0% +increasing now because of the + + + align:start position:0% +increasing now because of the +assumptions we have made on G we have an + + align:start position:0% +assumptions we have made on G we have an + + + align:start position:0% +assumptions we have made on G we have an +interesting situation given a value of x + + align:start position:0% +interesting situation given a value of x + + + align:start position:0% +interesting situation given a value of x +of corresponding value of y will be + + align:start position:0% +of corresponding value of y will be + + + align:start position:0% +of corresponding value of y will be +determined according to the function G + + align:start position:0% +determined according to the function G + + + align:start position:0% +determined according to the function G +but we can also go the other way if I + + align:start position:0% +but we can also go the other way if I + + + align:start position:0% +but we can also go the other way if I +tell you a value of y then you can + + align:start position:0% +tell you a value of y then you can + + + align:start position:0% +tell you a value of y then you can +specify for me one and only one value of + + align:start position:0% +specify for me one and only one value of + + + align:start position:0% +specify for me one and only one value of +x that gives rise to this particular Y + + align:start position:0% +x that gives rise to this particular Y + + + align:start position:0% +x that gives rise to this particular Y +so the function G takes us from X's to + + align:start position:0% +so the function G takes us from X's to + + + align:start position:0% +so the function G takes us from X's to +Y's but you can also go back the + + align:start position:0% +Y's but you can also go back the + + + align:start position:0% +Y's but you can also go back the +opposite way from Y's to values of X and + + align:start position:0% +opposite way from Y's to values of X and + + + align:start position:0% +opposite way from Y's to values of X and +the mapping that takes us from Y is 2x + + align:start position:0% +the mapping that takes us from Y is 2x + + + align:start position:0% +the mapping that takes us from Y is 2x +is this is the inverse of the function G + + align:start position:0% +is this is the inverse of the function G + + + align:start position:0% +is this is the inverse of the function G +and we give a name to that inverse + + align:start position:0% +and we give a name to that inverse + + + align:start position:0% +and we give a name to that inverse +function and we call it H so H of Y is + + align:start position:0% +function and we call it H so H of Y is + + + align:start position:0% +function and we call it H so H of Y is +the value of x that produces a specific + + align:start position:0% +the value of x that produces a specific + + + align:start position:0% +the value of x that produces a specific +value Y let us now move on with the + + align:start position:0% +value Y let us now move on with the + + + align:start position:0% +value Y let us now move on with the +program of finding the PDF of Y we will + + align:start position:0% +program of finding the PDF of Y we will + + + align:start position:0% +program of finding the PDF of Y we will +follow the usual two-step procedure and + + align:start position:0% +follow the usual two-step procedure and + + + align:start position:0% +follow the usual two-step procedure and +the first step is to find the CDF of Y + + align:start position:0% + + + + align:start position:0% + +so we fix some little why and we want to + + align:start position:0% +so we fix some little why and we want to + + + align:start position:0% +so we fix some little why and we want to +find the probability that the random + + align:start position:0% +find the probability that the random + + + align:start position:0% +find the probability that the random +variable Y takes a value in this range + + align:start position:0% +variable Y takes a value in this range + + + align:start position:0% +variable Y takes a value in this range +when does this happen for Y to take a + + align:start position:0% +when does this happen for Y to take a + + + align:start position:0% +when does this happen for Y to take a +value in this range it must be the case + + align:start position:0% +value in this range it must be the case + + + align:start position:0% +value in this range it must be the case +that X takes a value in this range here + + align:start position:0% +that X takes a value in this range here + + + align:start position:0% +that X takes a value in this range here +values of X smaller than this particular + + align:start position:0% +values of X smaller than this particular + + + align:start position:0% +values of X smaller than this particular +number results in values of Y that are + + align:start position:0% +number results in values of Y that are + + + align:start position:0% +number results in values of Y that are +less than or equal to this particular + + align:start position:0% +less than or equal to this particular + + + align:start position:0% +less than or equal to this particular +number so we can rewrite the event of + + align:start position:0% +number so we can rewrite the event of + + + align:start position:0% +number so we can rewrite the event of +interest in terms of the random variable + + align:start position:0% +interest in terms of the random variable + + + align:start position:0% +interest in terms of the random variable +X and write it as follows we need to + + align:start position:0% +X and write it as follows we need to + + + align:start position:0% +X and write it as follows we need to +have X less than or equal to H of little + + align:start position:0% +have X less than or equal to H of little + + + align:start position:0% +have X less than or equal to H of little +Y but this is just the CDF of X + + align:start position:0% +Y but this is just the CDF of X + + + align:start position:0% +Y but this is just the CDF of X +evaluated at H of Y we now carry out the + + align:start position:0% +evaluated at H of Y we now carry out the + + + align:start position:0% +evaluated at H of Y we now carry out the +second step of our program we take + + align:start position:0% +second step of our program we take + + + align:start position:0% +second step of our program we take +derivatives of both sides and we find + + align:start position:0% +derivatives of both sides and we find + + + align:start position:0% +derivatives of both sides and we find +that the PDF of y is equal to the + + align:start position:0% +that the PDF of y is equal to the + + + align:start position:0% +that the PDF of y is equal to the +derivative of the right-hand side the + + align:start position:0% +derivative of the right-hand side the + + + align:start position:0% +derivative of the right-hand side the +derivative of the CDF is a PDF and then + + align:start position:0% +derivative of the CDF is a PDF and then + + + align:start position:0% +derivative of the CDF is a PDF and then +the chain rule tells us that we also + + align:start position:0% +the chain rule tells us that we also + + + align:start position:0% +the chain rule tells us that we also +need to take the derivative of the term + + align:start position:0% +need to take the derivative of the term + + + align:start position:0% +need to take the derivative of the term +inside here with respect to its argument + + align:start position:0% + + + + align:start position:0% + +and this is a general formula for the + + align:start position:0% +and this is a general formula for the + + + align:start position:0% +and this is a general formula for the +PDF of a strictly increasing function of + + align:start position:0% +PDF of a strictly increasing function of + + + align:start position:0% +PDF of a strictly increasing function of +a random variable X how about the case + + align:start position:0% +a random variable X how about the case + + + align:start position:0% +a random variable X how about the case +of a decreasing function so let us + + align:start position:0% +of a decreasing function so let us + + + align:start position:0% +of a decreasing function so let us +assume that G now is a strictly + + align:start position:0% +assume that G now is a strictly + + + align:start position:0% +assume that G now is a strictly +decreasing function of X so we might + + align:start position:0% +decreasing function of X so we might + + + align:start position:0% +decreasing function of X so we might +have a plot for G that looks something + + align:start position:0% +have a plot for G that looks something + + + align:start position:0% +have a plot for G that looks something +like this what happens in this case we + + align:start position:0% +like this what happens in this case we + + + align:start position:0% +like this what happens in this case we +can start doing a calculation of this + + align:start position:0% +can start doing a calculation of this + + + align:start position:0% +can start doing a calculation of this +kind + + align:start position:0% + + + + align:start position:0% + +but now how can we rewrite this event + + align:start position:0% +but now how can we rewrite this event + + + align:start position:0% +but now how can we rewrite this event +the random variable Y will take a value + + align:start position:0% +the random variable Y will take a value + + + align:start position:0% +the random variable Y will take a value +less than or equal to this number little + + align:start position:0% +less than or equal to this number little + + + align:start position:0% +less than or equal to this number little +Y when when does this happen when the + + align:start position:0% +Y when when does this happen when the + + + align:start position:0% +Y when when does this happen when the +value of G of X is less than Y and that + + align:start position:0% +value of G of X is less than Y and that + + + align:start position:0% +value of G of X is less than Y and that +happens for X's in this range so this is + + align:start position:0% +happens for X's in this range so this is + + + align:start position:0% +happens for X's in this range so this is +the set of X's for which the value of G + + align:start position:0% +the set of X's for which the value of G + + + align:start position:0% +the set of X's for which the value of G +of X is less than or equal to this + + align:start position:0% +of X is less than or equal to this + + + align:start position:0% +of X is less than or equal to this +particular number Y so the event of + + align:start position:0% +particular number Y so the event of + + + align:start position:0% +particular number Y so the event of +interest in that case is the event that + + align:start position:0% +interest in that case is the event that + + + align:start position:0% +interest in that case is the event that +X is larger than or equal to H of Y + + align:start position:0% +X is larger than or equal to H of Y + + + align:start position:0% +X is larger than or equal to H of Y +which is 1 minus the probability that X + + align:start position:0% +which is 1 minus the probability that X + + + align:start position:0% +which is 1 minus the probability that X +is less than H of Y because X is a + + align:start position:0% +is less than H of Y because X is a + + + align:start position:0% +is less than H of Y because X is a +continuous random variable we can change + + align:start position:0% +continuous random variable we can change + + + align:start position:0% +continuous random variable we can change +this inequality to one that allows the + + align:start position:0% +this inequality to one that allows the + + + align:start position:0% +this inequality to one that allows the +possibility of equality and so this is 1 + + align:start position:0% +possibility of equality and so this is 1 + + + align:start position:0% +possibility of equality and so this is 1 +minus the CDF of X evaluated at H of Y + + align:start position:0% +minus the CDF of X evaluated at H of Y + + + align:start position:0% +minus the CDF of X evaluated at H of Y +now we take the red buttons of both + + align:start position:0% +now we take the red buttons of both + + + align:start position:0% +now we take the red buttons of both +sides and we find the PDF of Y being + + align:start position:0% +sides and we find the PDF of Y being + + + align:start position:0% +sides and we find the PDF of Y being +equal to there's a minus sign here then + + align:start position:0% +equal to there's a minus sign here then + + + align:start position:0% +equal to there's a minus sign here then +the derivative of the CDF which is the + + align:start position:0% +the derivative of the CDF which is the + + + align:start position:0% +the derivative of the CDF which is the +PDF and finally the derivative of the + + align:start position:0% +PDF and finally the derivative of the + + + align:start position:0% +PDF and finally the derivative of the +function H now in this case G is a + + align:start position:0% +function H now in this case G is a + + + align:start position:0% +function H now in this case G is a +decreasing function of X so when X goes + + align:start position:0% +decreasing function of X so when X goes + + + align:start position:0% +decreasing function of X so when X goes +down Y goes up when X goes up Y goes + + align:start position:0% +down Y goes up when X goes up Y goes + + + align:start position:0% +down Y goes up when X goes up Y goes +down this means that when Y goes up X + + align:start position:0% +down this means that when Y goes up X + + + align:start position:0% +down this means that when Y goes up X +goes down so it means that the inverse + + align:start position:0% +goes down so it means that the inverse + + + align:start position:0% +goes down so it means that the inverse +function age is going to be also + + align:start position:0% +function age is going to be also + + + align:start position:0% +function age is going to be also +monotonically decreasing since it is + + align:start position:0% +monotonically decreasing since it is + + + align:start position:0% +monotonically decreasing since it is +decreasing it means that the slope the + + align:start position:0% +decreasing it means that the slope the + + + align:start position:0% +decreasing it means that the slope the +derivative of the function a + + align:start position:0% +derivative of the function a + + + align:start position:0% +derivative of the function a +is going to be either zero or negative + + align:start position:0% +is going to be either zero or negative + + + align:start position:0% +is going to be either zero or negative +and so minus a negative value gives us + + align:start position:0% +and so minus a negative value gives us + + + align:start position:0% +and so minus a negative value gives us +the absolute value of that number so we + + align:start position:0% +the absolute value of that number so we + + + align:start position:0% +the absolute value of that number so we +can rewrite this by removing this minus + + align:start position:0% +can rewrite this by removing this minus + + + align:start position:0% +can rewrite this by removing this minus +sign here and putting an absolute value + + align:start position:0% +sign here and putting an absolute value + + + align:start position:0% +sign here and putting an absolute value +in this place of course in the case + + align:start position:0% +in this place of course in the case + + + align:start position:0% +in this place of course in the case +where G is an increasing function when X + + align:start position:0% +where G is an increasing function when X + + + align:start position:0% +where G is an increasing function when X +goes up Y goes up this means that when Y + + align:start position:0% +goes up Y goes up this means that when Y + + + align:start position:0% +goes up Y goes up this means that when Y +goes up X goes up so H in that case + + align:start position:0% +goes up X goes up so H in that case + + + align:start position:0% +goes up X goes up so H in that case +would have been an increasing function + + align:start position:0% +would have been an increasing function + + + align:start position:0% +would have been an increasing function +so this number here would have been a + + align:start position:0% +so this number here would have been a + + + align:start position:0% +so this number here would have been a +non-negative number and so it would be + + align:start position:0% +non-negative number and so it would be + + + align:start position:0% +non-negative number and so it would be +the same as the absolute value so using + + align:start position:0% +the same as the absolute value so using + + + align:start position:0% +the same as the absolute value so using +these absolute values we obtain formulas + + align:start position:0% +these absolute values we obtain formulas + + + align:start position:0% +these absolute values we obtain formulas +that are exactly the same in both cases + + align:start position:0% +that are exactly the same in both cases + + + align:start position:0% +that are exactly the same in both cases +of increasing and decreasing functions + + align:start position:0% +of increasing and decreasing functions + + + align:start position:0% +of increasing and decreasing functions +and so our final conclusion is that in + + align:start position:0% +and so our final conclusion is that in + + + align:start position:0% +and so our final conclusion is that in +either case the PDF of Y is given in + + align:start position:0% +either case the PDF of Y is given in + + + align:start position:0% +either case the PDF of Y is given in +terms of the PDF of x times the + + align:start position:0% +terms of the PDF of x times the + + + align:start position:0% +terms of the PDF of x times the +derivative of this inverse function let + + align:start position:0% +derivative of this inverse function let + + + align:start position:0% +derivative of this inverse function let +us now apply the formula that we have in + + align:start position:0% +us now apply the formula that we have in + + + align:start position:0% +us now apply the formula that we have in +our hands for the monotonic case to a + + align:start position:0% +our hands for the monotonic case to a + + + align:start position:0% +our hands for the monotonic case to a +particular example where Y is the square + + align:start position:0% +particular example where Y is the square + + + align:start position:0% +particular example where Y is the square +of X and where X is uniform on the + + align:start position:0% +of X and where X is uniform on the + + + align:start position:0% +of X and where X is uniform on the +interval 0 to 1 so the function G in our + + align:start position:0% +interval 0 to 1 so the function G in our + + + align:start position:0% +interval 0 to 1 so the function G in our +case the function G is the square + + align:start position:0% +case the function G is the square + + + align:start position:0% +case the function G is the square +function now you could argue here that + + align:start position:0% +function now you could argue here that + + + align:start position:0% +function now you could argue here that +this function is not monotonic so how + + align:start position:0% +this function is not monotonic so how + + + align:start position:0% +this function is not monotonic so how +can we apply our results on the other + + align:start position:0% +can we apply our results on the other + + + align:start position:0% +can we apply our results on the other +hand the random variable X takes values + + align:start position:0% +hand the random variable X takes values + + + align:start position:0% +hand the random variable X takes values +on the interval from 0 to 1 and + + align:start position:0% +on the interval from 0 to 1 and + + + align:start position:0% +on the interval from 0 to 1 and +therefore the form of the function G + + align:start position:0% +therefore the form of the function G + + + align:start position:0% +therefore the form of the function G +outside that range does not concern us + + align:start position:0% +outside that range does not concern us + + + align:start position:0% +outside that range does not concern us +over the range of values of interest the + + align:start position:0% +over the range of values of interest the + + + align:start position:0% +over the range of values of interest the +function G is a monotonic function so + + align:start position:0% +function G is a monotonic function so + + + align:start position:0% +function G is a monotonic function so +what is the correspondence Y is going to + + align:start position:0% +what is the correspondence Y is going to + + + align:start position:0% +what is the correspondence Y is going to +be equal to X + + align:start position:0% +be equal to X + + + align:start position:0% +be equal to X +that's the G of X function and when that + + align:start position:0% +that's the G of X function and when that + + + align:start position:0% +that's the G of X function and when that +happens we have the relation that X is + + align:start position:0% +happens we have the relation that X is + + + align:start position:0% +happens we have the relation that X is +going to be the square root of Y this + + align:start position:0% +going to be the square root of Y this + + + align:start position:0% +going to be the square root of Y this +tells us that the inverse function H of + + align:start position:0% +tells us that the inverse function H of + + + align:start position:0% +tells us that the inverse function H of +Y which tells us what is the particular + + align:start position:0% +Y which tells us what is the particular + + + align:start position:0% +Y which tells us what is the particular +X associated with a given Y the inverse + + align:start position:0% +X associated with a given Y the inverse + + + align:start position:0% +X associated with a given Y the inverse +function takes the form square root of Y + + align:start position:0% +function takes the form square root of Y + + + align:start position:0% +function takes the form square root of Y +so now we can go ahead and use the + + align:start position:0% +so now we can go ahead and use the + + + align:start position:0% +so now we can go ahead and use the +formula the density at some particular + + align:start position:0% +formula the density at some particular + + + align:start position:0% +formula the density at some particular +little Y where that little y belongs to + + align:start position:0% +little Y where that little y belongs to + + + align:start position:0% +little Y where that little y belongs to +the range of values of interest X takes + + align:start position:0% +the range of values of interest X takes + + + align:start position:0% +the range of values of interest X takes +values between 0 & 1 so Y also takes + + align:start position:0% +values between 0 & 1 so Y also takes + + + align:start position:0% +values between 0 & 1 so Y also takes +values between 0 & 1 + + align:start position:0% +values between 0 & 1 + + + align:start position:0% +values between 0 & 1 +so over that range the density of Y is + + align:start position:0% +so over that range the density of Y is + + + align:start position:0% +so over that range the density of Y is +the density of X which is uniform + + align:start position:0% +the density of X which is uniform + + + align:start position:0% +the density of X which is uniform +therefore it is equal to 1 times the + + align:start position:0% +therefore it is equal to 1 times the + + + align:start position:0% +therefore it is equal to 1 times the +derivative of the square root function + + align:start position:0% +derivative of the square root function + + + align:start position:0% +derivative of the square root function +and the derivative of the square root + + align:start position:0% +and the derivative of the square root + + + align:start position:0% +and the derivative of the square root +function is 1 over 2 times the square + + align:start position:0% +function is 1 over 2 times the square + + + align:start position:0% +function is 1 over 2 times the square +root of Y as you can see the amount of + + align:start position:0% +root of Y as you can see the amount of + + + align:start position:0% +root of Y as you can see the amount of +calculations involved here are rather + + align:start position:0% +calculations involved here are rather + + + align:start position:0% +calculations involved here are rather +simpler compared to what we would have + + align:start position:0% +simpler compared to what we would have + + + align:start position:0% +simpler compared to what we would have +to do if we were to go through our + + align:start position:0% +to do if we were to go through our + + + align:start position:0% +to do if we were to go through our +two-step program and work with CDF all + + align:start position:0% +two-step program and work with CDF all + + + align:start position:0% +two-step program and work with CDF all +that you need to do is essentially to + + align:start position:0% +that you need to do is essentially to + + + align:start position:0% +that you need to do is essentially to +identify the inverse function that given + + align:start position:0% +identify the inverse function that given + + + align:start position:0% +identify the inverse function that given +a Y produces X's and write down the + + align:start position:0% +a Y produces X's and write down the + + + align:start position:0% +a Y produces X's and write down the +corresponding derivative \ No newline at end of file diff --git a/QOtA76ga_fY.txt b/QOtA76ga_fY.txt new file mode 100644 index 0000000000000000000000000000000000000000..33a7671ca27b9616787581f9cf5513c000ffa4bf --- /dev/null +++ b/QOtA76ga_fY.txt @@ -0,0 +1,5424 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help +MIT OpenCourseWare + +continue to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: So today, we're going +to talk about Kerberos, which + +is a cryptographically +secure, in some ways, + +protocol for +authenticating computers + +and applications to one +another over the network. + +So this is now finally +going to use cryptography + +whereas last lecture, +we looked at just + +using these TCP sequence +numbers to provide security. + +So before we dive +into the details, + +I want to mention there's +two bits of administrivia + +that you might want to know. + +There's a quiz review today +7 to 9 o'clock in some room, + +I think 32 or 23. + +It's on schedule page and +the quiz is next Wednesday. + +And also, we want +you guys to post + +some idea for your +final project on Piazza + +by tomorrow just so +that your classmates can + +know what you're thinking +and help you form groups. + +All right, so let's talk +about Kerberos, all right? + +So what is the +setting that Kerberos + +is trying to support, here? + +So the model for +Kerberos, what these guys + +had in mind when +they were designing + +Athena guess 25 or +30 years ago now, + +is that they were +imagining they were + +going to have a network +with many server machines + +and many client machines +interacting with one another. + +So you could imagine, well, you +have a file server somewhere + +out there. + +You probably have a mail server +connected to the network, maybe + +other services-- printer. + +And all these are just connected +to some sort of a network + +rather than being processes +on a single machine. + +So the prelude to +Athena and Kerberos + +is that you just have a +time sharing machine where + +everything was a single +process and everyone would just + +log into the same system +and store their files there. + +So these guys wanted a +more distributed system. + +So this meant that you'd have +these servers on one side + +and you'd also have a +bunch of workstations + +that users would +use themselves which + +would run applications +and potentially + +connect to these servers +and store the user's files, + +get their mail et cetera. + +And the problem that +they wanted to solve + +was how to authenticate +the users that + +are using these workstations +to all these different servers + +in the back end without +having to trust the network + +to be correct, which seems +like a sensible design + +requirement in many ways. + +And I should +mention that I guess + +the alternative to +Kerberos at the time + +was these R login +commands that we're + +looking at in last lecture, +which seems like a bad plan. + +They just use IP addresses +to authenticate the users. + +And Kerberos was +reasonably successful. + +It actually still +is used at MIT. + +And actually, it's the basis +of Microsoft's Active Directory + +server. + +So pretty much every Microsoft +based sort of Windows Server + +uses Kerberos in +some form or another. + +But of course, +because this protocol + +was designed 25 or 30 years +ago, requirements change. + +What people assume change. + +People now understand +much more about security. + +So their version of +Kerberos that's in use today + +is noticeably +different in many ways + +from the version in the paper. + +And we'll look at exactly what +assumptions aren't good enough + +anymore today and what +did they get wrong. + +It's sort of inevitable +for any protocol that + +was the first protocol to +really use cryptography + +to authenticate parties over +the network in this sort + +of full system scale. + +Anyway, so that's the sort +of setting for Kerberos. + +And it might be +interesting to figure out + +what's the trust model, right? + +So Kerberos is going to +introduce this extra Kerberos + +server sitting on the side. + +So our third model +at some level is + +that the network is +untrusted like we were + +thinking about in last lecture. + +But who do we have to trust +in this Kerberos setting? + +So of course, one thing is +everyone-- all parties have + +to trust the Kerberos server. + +So that's an assumption +these guys were + +willing to make at the time +that this Kerberos server would + +be in charge of all +network authentication + +in some form or another. + +Do we have anyone else +that has to trust anything + +in the setting? + +For example, yeah. + +STUDENT: Well users should +trust their own machines. + +PROFESSOR: Yes, so that's +a good point, right? + +There's the users that +I didn't draw here. + +But these guys are +using some workstation. + +And it's actually pretty +important in Kerberos + +that the user trusts +their workstation. + +So what goes wrong if you +don't trust your workstation? + +Or presumably, it can +just sniff your password + +and do whatever you type-- you +know, LS, it tries-- runs RMX. + +That seems kind of unfortunate. + +Yeah. + +STUDENT: But it's +more than that though, + +because they could even, like, +sniff your Kerberos ticket. + +PROFESSOR: Yeah, exactly. + +Or when you log in, you +type in your password, which + +is even worse than the ticket. + +Yeah, absolutely, yeah. + +So this is actually a bit +of a problem with Kerberos + +in the sense that if you don't +trust the workstation, then + +you're in a bit of trouble. + +So if you have your +own laptop, this + +seems like a sensible +assumption to make. + +If you're using a +public computer, + +this is a bit more questionable. + +And we'll see exactly +what could go wrong. + +Yeah. + +STUDENT: You have to trust the +people administrating aren't + +doing anything bad with +[INAUDIBLE] servers + +and giving them privilege +access to one another. + +STUDENT: So what do you mean? + +So of course, +like, ISNT is going + +to run these machines down here. + +But I think the machines +themselves don't necessarily + +have to trust one another. + +So the mail server doesn't trust +the print server or the file + +server necessarily. + +STUDENT: Not to +trust, but he might + +be able to access +a server you're not + +supposed to have access to by +going through another server. + +PROFESSOR: Yeah, +that's true, I guess. + +Yeah, so if you set up +any trust relationship + +between these guys-- like, +if you give the mail server + +some back end to go access your +files just for convenience, + +then this could be abused, yeah. + +So you have to be careful +about not introducing + +additional sort of levels of +trust or trust relations here. + +All right, anything +else that matters here? + +Do the servers have +to trust the users + +in any way or the workstations? + +No, I guess presumably not. + +So this was the whole +goal that the server + +doesn't have to a priori +even know necessarily + +what all these users or +how to authenticate them + +or what this workstation +is doing until it can + +cryptographically prove that +this is a legitimate user + +and they should have access +to their data or whatnot. + +All right, so let's look +at how does Kerberos work + +or what's the overall +architecture, at least. + +So the plan that +these guys had in mind + +is that there would be +this Kerberos server. + +We have drawn it up +there but let's draw it + +in a slightly bigger scale. + +So this is the Kerberos server. + +And today, it's typically called +KDC-- Key Distribution Center. + +And there's all these users +out here somewhere and also + +services that you might +want to connect to. + +And the plan is that +the Kerberos server + +is going to be responsible +for storing a shared + +key between the Kerberos server +and every entity in the world, + +or in this realm at least. + +So if the user has some +sort of a key KC for client, + +than the Kerberos +server is going + +to remember this +key somewhere here. + +And similarly for the +server, the key KS + +is going to be known +to the service itself + +and to the Kerberos server +but hopefully no one else. + +So you can think of it as like +a generalization of passwords, + +right? + +So you know a password +and the Kerberos server + +knows your password +but no one else. + +And this is how you guys are +going to prove to each other, + +yeah, I'm the right guy. + +I know this password +and no one else does. + +Makes sense? + +And the other thing the Kerberos +server is going to have to do + +is, of course, keep +track of who is + +it that owns this key, right? + +So it's going to have this table +mapping some sort of a name. + +So this is some sort of a user. + +This is maybe service maybe +AFS or something like this. + +And the KDC is responsible for +storing the gigantic table-- + +well, not very large in +terms of the number of bytes, + +necessarily, but +one entry per entity + +at MIT that the Kerberos +server knows about. + +Makes sense? + +All right, and then we're +going to have sort of provide + +two interfaces, right? + +The paper is a little +fuzzy above this + +or it pretends like there's +really two services. + +But really, what's going on +is that there's two interfaces + +to the same machine. + +One of them is called Kerberos +in the paper and one of them + +is called TGS for +Ticket Granting Service. + +And really, these +are just two ways + +of talking to the same +thing in the back end. + +And the protocol is a little +different for these things. + +So initially, when +the user logs in, + +they're going to talk +to this guy over here. + +And they're going to +send their client name, + +C. So this might be +your Athena username. + +And the server is +going to respond + +to back with a ticket, +a TGS or-- well, + +some sort of a ticket. + +We'll look at the +details in a bit. + +And then when you want to +talk to some server down here, + +KS, then you're going to +talk to this TGS first + +and say, oh, hey, +I already logged in + +through the Kerberos interface. + +Now, I want to talk +to the server S. + +So you'd tell the TGS about +the server you want to talk to. + +And then it returns you +back some sort of a ticket + +for talking to the server +S. And then you can finally + +start talking to +the server over here + +by initially passing +it this ticket for S. + +Does this all make sense? + +This is the sort +of high level plan. + +So why do these guys +have two interfaces? + +Well, I guess I +wanted to actually ask + +a bunch of questions. + +Like, in the case of a +service, this service + +is probably going to +be stored on disk. + +What's going on with +this KC on the user side? + +Where does KC come +from in Kerberos? + +Yeah. + +STUDENT: KDMS +[INAUDIBLE] the database. + +PROFESSOR: Yeah, well, +the key C sits here. + +And that's absolutely true. + +It's sits on this +giant database. + +But it also has to +be known to the user + +because the user has to +prove that they are the user. + +Yeah. + +STUDENT: Is that a one way +function and then the password? + +PROFESSOR: Yeah, +so they actually + +have this sort of cute plan +where the KC is actually + +going to be derived by +hashing the user's password + +or really some sort of +key duration function. + +And there's several different +ones of perverse uses. + +But you're basically +going to take a password, + +transform it in some +way, and get this key KC. + +All right, so that seems good. + +Why do we need two +protocols, right? + +You could imagine that you just +always ask the Kerberos server + +for tickets directly this way. + +You say, well, hey, +I want a ticket + +for this particular +principle name. + +And it'll send you back a +ticket and you can decrypt it + +with your KC afterwards. + +Yeah. + +STUDENT: Can you +[INAUDIBLE] or ask the user + +to reenter their +password each time they + +want to [INAUDIBLE] service? + +PROFESSOR: Right, so the +reason for the difference + +between these two interfaces +is that on this interface, + +all the responses come back +encrypted with your key KC. + +And the Kerberos designers +are a little worried + +about keeping this KC +around for a long time. + +Because either you have to +ask the user to enter it, + +which is just +annoying for the user, + +or it sits around in memory. + +And this is basically as +good as the user's password. + +So if this gets disclosed, +then someone with access to KC + +can keep accessing the user's +files until the user maybe + +changes their password and +potentially even longer. + +We'll see about that. + +So this KC is a really +dangerous thing to leak. + +So the whole point of using +this interface first and using + +this interface later for +all subsequent requests + +is that you can +actually forget KC + +as soon as you decrypt this +TGS response from the Kerberos + +interface. + +And from that point on, +even if you leak it, + +there is a lifetime +associated with this ticket. + +So worst case, +someone gets access + +to your account for +a couple of hours, + +not for an unbounded +amount of time. + +So that's the sort +of main difference + +why you guys have this slightly +more complicated picture + +with two ways of +accessing the same thing. + +All right, so before we dive +into the mechanics of how + +these protocols actually +look like on the wire, + +let's talk a little bit about +this naming aspect in Kerberos, + +right? + +So at some level, you +could think of Kerberos + +as being a name registry, right? + +So it's really +responsible for mapping + +these cryptographic +keys onto string names. + +And this is the fundamental +sort of operation + +that Kerberos needs to provide. + +In fact, you'll see in the +next lecture even on the web, + +we need some function like this. + +It's implemented +differently from Kerberos + +but this is a fundamentally +very important thing + +to have in almost any +distributed system + +for security. + +So let's look at how Kerberos +actually deals with names. + +So in Kerberos, +the sort of system + +calls every entity in +this database a principal + +And a principal in Kerberos is +actually just a string, right? + +So you can actually have some +principal like, I don't know, + +nickolei. + +So that's a string. + +And that could be a principal +in some Kerberos realm. + +So it would literally +be the thing + +that sits in this left +column of the KDC's table. + +And there's also +some extra instances + +that the protocl supports. + +I could say, you know, +nikolai.extra secure + +or something. + +And I might use this +as a different entity + +for machines I +really care about. + +So maybe I will have +a different password + +for really secure things +and a different password + +for my regular account. + +So this is just sort +of how Kerberos-- + +this is what the paper +talks about with instances. + +So one might actually +wonder-- where + +do you actually see instances? + +Where do influences come from? + +So the Kerberos service +maps names to keys for you, + +but how do you know +which name to ask for + +or which name to expect when +you are talking to some machine? + +So I guess what I'm asking is, +what are names appear outside + +of the Kerberos machine. + +So I guess we could ask, OK, +where do user names appear? + +Any ideas? + +Yeah. + +STUDENT: You can ask the +MIT server for usernames + +presumably. + +PROFESSOR: Right, yeah. + +So you could enumerate +these things. + +Also, the users just +type them in when + +they log into a machine. + +So that's where it +initially comes from. + +Do usernames appear +anywhere else? + +Should they appear +anywhere else? + +Yeah. + +STUDENT: Possibly +access the [INAUDIBLE] + +lists on the various services. + +PROFESSOR: Yes, that's actually +an important point, right? + +The goal of Kerberos is +just to map keys to names. + +But it doesn't tell you what +that name should have access + +to. + +In fact, the way the +applications typically + +use Kerberos is that +one of these servers + +uses Kerberos to figure out, +OK, what string name am I + +talking to? + +So when the mail server +gets a connection + +from some workstation and it +get the Kerberos ticket that + +prove that maybe this +user is called Nikolai, + +then the mail server +internally now + +has to figure out, +OK, well, what + +should that guy have access to? + +And same for a file server. + +So inside of all +these servers, there's + +probably things like access +control lists, maybe groups, + +maybe other things that actually +do the authorization step. + +So Kerberos provides +authentication + +which tells you who is +this person I'm talking to. + +And the service itself is +responsible for implementing + +the authorization part where +they decide what access + +you should have based +on your username here. + +Makes sense? + +All right, so that's where +the user names appear. + +There's also other +principal names + +the Kerberos supports +for services, right? + +So services, I guess +the paper suggests, + +look something like this. + +That's rcmd.hostname. + +And the reason that you need a +name for one of these services + +is that you want to +know, for example, when + +I connect to a file +server, I actually + +want mutual authentication. + +It's not just the final +server learns who I am, + +but I, the user or +the workstation, + +want to be convinced that +I'm talking to the right file + +server and not some +fake file server that's + +impersonating my files. + +Because maybe I'll +look at the grades + +file and submit it +to the registrar. + +It would be too bad +if some file server + +can impersonate the response and +give me the wrong grades file + +all of a sudden. + +So this is why the +service principles also + +need their own name and the +workstations need to figure out + +what name should I expect to see +when I connect to the service. + +And typically, this comes +from the user at some level. + +So for example, if I type +SSH some machine foo, + +then this means that +I should be expecting + +a Kerberos principal +called rcmd.foo + +on the other end +of this connection. + +And if it turns out +to be someone else, + +this SSH client +should abort and not + +let me connect because then +I will be misled into talking + +to some other machine. + +That make sense? + +So here's one +interesting question. + +When can we reuse +names in Kerberos? + +It's like, all of you +guys have Athena accounts. + +And when you +graduate, could MIT, + +like, wipe out +your database entry + +and allow someone else to +register that same username? + +Would that be a good idea? + +Well, aside from the fact +that you guys want accounts. + +Yeah. + +STUDENT: Updated services +as well so that they would, + +like map that username +to [INAUDIBLE] permission + +theoretically? + +PROFESSOR: Yeah, because +these guys are actually + +just string entries somewhere +in some ACL on a file + +server on a mail server. + +And just because you wipe out +this entry in the Kerberos + +database doesn't mean +that this entry is gone. + +And they're not versioning +in any way, right? + +This entry could +literally say, you know, + +Alice has access to +some Athena locker. + +And if this Alice graduates +and her entry gets removed, + +then some new Alice +comes along, registers, + +in the Kerberos database. + +But she gets a +principal that looks + +identical to the old Alice. + +It's the same string. + +So all of a sudden, +the file server + +will give access to the new +Alice to old Alice's data. + +So there's a bit of +a complicated process + +for reclaiming principal +names in Kerberos + +because there's +no real connection + +or versioning +between these guys. + +So as a result, it's +actually kind of + +hard to reuse principal names. + +Once you register a +principal, you probably + +don't want to reuse +it very often. + +And same for, in some +sense, these principal names + +for service as well. + +As long as this hostname +remain some well-known service + +that people expect to +function in a certain way, + +you probably don't want +to get rid of its key + +even if the service goes on. + +Because maybe a year later, +some guy tries to connect to it + +and expects certain things. + +And if it's been reused +for a different service, + +that guy can impersonate things. + +Probably not as dramatic +or as bad, but still, + +you have to be careful with +reusing principal names + +in this kind of protocol. + +Makes sense? + +Any questions? + +All right, so let's look at how +the protocol itself now works. + +So we'll look first and +this step of the protocol + +where you initially get your +ticket with your password. + +And then we'll look at how +this TGS interface works + +and how it differs +then a little bit. + +All right, so I guess +there's this main data + +structure that Kerberos +uses called a ticket. + +And this ticket looks like this. + +So there's a ticket to +between a client and a server. + +And this guy is +basically the names + +of the server and +the client that we're + +talking about-- the IP +address of the client, + +some kind of timestamp, and an +expiration time for how long + +the stick is valid. + +And there's also +a key, KCS, that's + +going to be shared between +the client and the server. + +So that's what's in a ticket. + +And there's also this +other weird data structure + +that Kerberos introduces +called an authenticator. + +And an authenticator goes +with a particular client C. + +And this thing is just +the client's name, + +the IP address of the +client, and the time stamp + +when the client generated +this authenticator. + +And typically, both of +these things are encrypted. + +And authenticator is +typically scripted + +with the key between the +client on the server. + +So the authenticator +sort of has to do + +with a particular connection +between a client and a server. + +And the Kerberos +ticket itself here + +is typically encrypted with +the key for the service KS. + +So the subscript +notation denotes here + +encryption with +a particular key. + +All right, so what does this-- +so using this sort of notation + +here, let's try to figure +out what is the protocol. + +By which the user initially +logs into this Kerberos + +and gets their TGS ticket. + +So as we saw here +before, right, the plan + +is the client is going to +send their username over + +to the Kerberos server +or that interface. + +And the response is +going to be a ticket. + +And what precisely +the client actually + +sends over-- both the username +C of the client that's + +issuing the request as well +as the principal name-- well, + +the client is also +a principal name. + +But the client also +sends the principal name + +of the service for which it +would like to get a ticket. + +And typically, the service name +is actually the service name + +of this TGS guy over here. + +So you get a ticket for them. + +But you could get a ticket +for almost any service + +you want in this way. + +And their response +is going to be + +this sort of interesting tuple. + +It's going to be your +ticket between the client + +and the server encrypted +just with that key KS + +as shown above. + +I guess we should +write that down with KS + +And also, you get to +this shared key-- key CS. + +And this whole thing +is encrypted with KC. + +So that's the wire protocol. + +So I guess let's try to +figure out a couple things. + +So first of all, how +does the Kerberos server + +authenticate the client here? + +How does it know that this +is the right user making + +this request? + +Yeah. + +STUDENT: It can make +sure that the ticket + +that it sent because it has KC. + +PROFESSOR: Yes, I think +that's what's going on + +is that the Kerberos server +again on some level actually + +doesn't know whether this +is the right client or not. + +But it thinks oh, well, +sure, it doesn't matter + +who is making this request. + +I'll just send this blob +out and the only person + +who should be able to +make any use of this blob + +is the person that knows +this key KC over here. + +So that's actually kind +of cool because the client + +doesn't have to +send their password + +over the network at all. + +So in some ways, this is +actually better than the client + +sending a password to +the Kerberos server + +because even if the +Kerberos server here + +was listening for +these passwords + +and trying to record them, it +would never get your password. + +Or maybe if someone was +impersonating the Kerberos + +server, they wouldn't get +a copy of your password. + +All right, yeah. + +STUDENT: [INAUDIBLE] +adversary wants to [INAUDIBLE] + +your password offline without-- + +PROFESSOR: Yeah, so this is +actually not a great aspect + +of Kerberos, in fact, right? + +So does everyone see +what the problem is? + +The problem is that the +way the client could + +tell if they got the +right password or not + +or the workstation tells +if the client supplied + +the right password is they +try to decrypt this ticket + +and they see if it works or not. + +And decryption is fairly cheap. + +This is symmetric +encryption and you + +can do probably +millions of decryptions + +a second if you try +hard on modern machines. + +And this means that +you can try millions + +of potential +passwords per second + +to guess what the +person's password is. + +And you could do this +for any person at all. + +You could just send +their principal + +to the Kerberos server. + +It'll very happily give you +back this response encrypted + +with the user's password. + +Then you can just try different +passwords and just see what + +works or what doesn't. + +Yeah. + +STUDENT: But won't the +content [INAUDIBLE] + +decrypted [INAUDIBLE] advantage? + +How can we be sure +that you directly-- + +PROFESSOR: Yes, this is actually +another interesting aspect + +where the Kerberos 4 +developers didn't quite + +realize that the time they were +building this that they really + +should have been very careful +about separating encryption + +from authentication. + +So in the paper, there's +this implicit assumption + +that-- hopefully, that's not us. + +All right, sorry. + +So in the paper, there's +this implicit assumption + +that whenever you +encrypt a piece of data + +and you send it to someone +else, if that person can decrypt + +the data and it +sort of looks OK, + +then no, they must have +gotten the right key + +and the data wasn't +tampered with in flight. + +But it seems like a +totally bad plan now + +that we think of +it 30 years later. + +But at the time, +it wasn't so clear. + +So in order to do +Kerberos right, + +and in fact, what +Kerberos 5 does now, + +is they both encrypt +all the pieces of data + +and they also +authenticate the message + +by basically computing +a hash with a key. + +And then the result +actually tells you + +that, oh, that piece of data +just wasn't tampered with. + +It was correctly signed +with this key, et cetera. + +And what actually +happens in Kerberos + +version 4 is there +are some extra bits + +in this thing that was +encrypted that should all + +be some pattern like zeros. + +And typically, if you +get the key wrong, + +that pattern will not look +like all zeros just by chance. + +It's not cryptographically +guaranteed to be that. + +But most times, it will +not look like zeros + +and you will be able to decide +whether you got the correct key + +or not. + +All right, so that's +sort of the plan + +for how the clients +tells, I guess, + +whether the ticket is valid. + +They just try to decrypt +it and see how it works. + +So another interesting +question is + +why is this key +KCS included twice + +in the ticket in +some form, right? + +So it's included once here +and another time actually sort + +of implicitly in +this ticket T. Why + +do we have two copies +of the same key KCS? + +Yeah. + +STUDENT: The client +can't decrypt that ticket + +because it's encrypted +with a service key. + +PROFESSOR: Yeah, so it's +actually kind of cute, right? + +Like, there's this key +that the client can get to. + +But then there's another +copy of it in here. + +It's encrypted with KS. + +And the reason for this is that +the Kerberos server is actually + +trying to set up the +client and this other guy + +to talk to each other securely. + +So the Kerberos generates +this hopefully random key KCS + +and wants to give one copy +to the client and one copy + +to the write other server +that you want to talk to. + +And one thing you could +imagine doing naively + +is maybe the Kerberos will +just go and say, hey service, + +this guy wants to talk to you. + +Here's the key for it. + +But that would be +kind of unfortunate. + +You'd have to have the Kerberos +server call back to the service + +and so on. + +So instead, these guys have +this nice trick where they just + +to give the client does +blob that the client + +can't actually do +anything with other + +than give to the right service. + +And if the service +has the right key KS, + +they'll decrypt it and say, aha. + +Well, here's the key I should be +using to speak to this client. + +And that's how these two guys, +the client and the service, + +are going to establish a +shared key for protecting + +their communication. + +Yeah. + +STUDENT: So what exactly is TGS? + +PROFESSOR: So TGS +is-- OK, so there's + +sort of two sides to it. + +From the client's point of +view, it's just another service + +that you can get a ticket for. + +And the kinds of +operations it supports + +is getting more tickets. + +It's a Ticket Granting Service. + +STUDENT: Sorry, I meant what +is the ticket called TGS. + +PROFESSOR: Oh, yeah, sorry. + +This TGS is just shorthand +for this whole blob + +except where S is actually +the principal name of this TGS + +service. + +So you can think of it as +like, well, there's a Kerberos + +server, there's this +TGS service out there, + +and then there's the real +thing I want to get to. + +So you first ask +this guy to give me + +a ticket for some service. + +You could ask it to give you +directly a ticket for the file + +server. + +And this would work. + +But you'd need your +KC to decrypt it + +and then you'd need your +KC around all the time. + +So instead, what +you do is you get + +a ticket for this special +service over here. + +It looks just like a service +except that it happens + +to be provided by the same box. + +And then this guy will +happily give you more tickets + +later without having to +present your initial KC again. + +Makes sense? + +All right, other questions? + +Yeah. + +STUDENT: So [INAUDIBLE] the idea +is once you get the TGS ticket, + +you can just get rid of your KC? + +PROFESSOR: Yes, +so that's actually + +the cool thing about +it is that once + +you get this ticket-- well, this +ticket with the S being TGS, + +then you're going to get +rid of the password and KC. + +So you log into Athena +workstation and a couple + +of seconds into +the boot process, + +you already get +your ticket here. + +It scrubs the +password from memory. + +So even if someone, like, +grabs you and grab the machine + +and runs off, all they +got was your ticket. + +And OK, well, maybe they can +access your stuff for 10 hours + +or whatever the +ticket lifetime was, + +but not for longer than that. + +The password is gone. + +Yeah. + +So if the password's +gone, then on that picture + +there when Kerberos +sends a reply + +encrypted with KC, +how does the client-- + +Oh yeah, so this is the one +place you need your password. + +So you send this message, +you get this reply, + +you decrypt this, and then +you forget the password. + +So you can't forget +about the password + +before you use it for +decryption of course. + +STUDENT: [INAUDIBLE] + +PROFESSOR: Ah, no, so this is +just this interface, right? + +So this is the thing +you do initially. + +And we'll talk in a second +about how you basically also + +can get any ticket you want +from the second interface + +without needing +the initial key KC. + +Right, make sense? + +All right, so I guess +we already talked + +about two particular problems +that the Kerberos protocol had + +sort of baked into it, which +is a little unfortunate. + +One is that they assumed +that encryption also + +provides authentication +or integrity of messages. + +So don't do that. + +And Kerberos +version 5 fixes this + +by explicitly +authenticating messages. + +Another thing they sort +of had a problem with + +is the ability for +arbitrary clients + +to guess people's passwords. + +So any suggestions of +how we could fix this? + +How do you prevent +guessing attacks + +in a protocol like this? + +What could we try? + +Yeah. + +STUDENT: Some sort of salting? + +I'm not sure. + +PROFESSOR: Well, so +salting would just + +means that the client +has to hash the password + +in different ways, maybe. + +But it still +doesn't prevent them + +from trying lots of things. + +So maybe it'll be more +expensive to build a dictionary. + +Yeah. + +STUDENT: You could [INAUDIBLE] +derivation function? + +PROFESSOR: Yeah, so +another good idea + +is to make this hashing +process super expensive. + +So that might be +kind of nice, right? + +So if this hash function took +a second to compute like you + +guys did in lab two, +then OK, wow, this + +would be actually +really expensive + +to try different passwords. + +So that seems like +a reasonable plan. + +So in combination +with salting, those + +would be make it pretty +expensive to do password + +guessing attacks. + +Anything else? + +So another thing is, +yeah, challenge respond. + +So you could actually hear +in the initial protocol, + +the Kerberos server +doesn't have any idea + +if this was the +right client or not. + +But in fact, what +you could do is maybe + +give a little bit of a +proof that, well, you're + +probably the right client. + +So maybe you could encrypt +the current time stamp + +with your hash +password or something + +like this-- has them together. + +And then the Kerberos +server could just + +check if that's the right-- if +that matches, and if so, return + +you back a ticket. + +You probably don't want to +necessarily add more rounds + +but this could work. + +So just to precise about +what I'm sort of suggesting. + +OK, well, maybe you take +the current time stamp + +and maybe you hash the current +time stamp and the KC together. + +And maybe you include +the timestamp as well. + +And then the server could +see, well, it has your KC. + +It could hash the current +timestamp as well. + +If it gets the same +value, then yeah, + +it's probably the right +user requesting it. + +And I can send back the ticket. + +If not, then it wasn't +the right password at all. + +Question? + +STUDENT: [INAUDIBLE] you just do +[INAUDIBLE] if the servers see + +too many requests [INAUDIBLE] + +PROFESSOR: That's right. + +So the problem is that +we could write limit. + +But there's no +reason for the hacker + +to request this more than once. + +That hacker requests a +particular user more than once + +and then it gets +this encrypted blob. + +And then it can try decrypting +it offline as many times + +as it wants with +different passwords + +without having to re request it. + +So I think the whole +point of including + +some sort of a +challenge response thing + +like this in the particle +is so that the server will-- + +you'll have to actually +ask the server again + +and again to try to log in +with different passwords. + +And then you could rate +limit of the server + +and get a much better defense. + +Yeah. + +STUDENT: [INAUDIBLE] Kerberos? + +PROFESSOR: So I think you could +certainly replay this message + +so if I sent this message +now, you could probably + +look at that message +and send it as well + +and get a response back +from the Kerberos server. + +I guess if you're +watching the network, + +you could observe this +thing on the wire as well. + +So I think this is sort of a bit +of a stopgap measure-- improves + +security a bit. + +But certainly if you're +watching someone else's network, + +then you're going to see this +packet coming back regardless + +of what happened in this step. + +So coming back, +you'll see this guy + +and you can then +try to attack it. + +There's probably some +more elaborate schemes + +you could design +but I didn't think + +Kerberos 5 even +implements anything more + +elaborate than roughly this +plan, which seems good enough + +to prevent arbitrary +people from trying + +to break anyone's or brute +force anyone's password. + +Make sense? + +Yeah. + +STUDENT: So presume +that you could + +do authenticated [INAUDIBLE] +or something here + +to establish the shared key. + +And then you could +encrypt this thing + +with KC and the shared key. + +PROFESSOR: That's right, yeah. + +So if you're really +doing this right, + +there's all these nice +particles out there + +that are basically called +password authenticated key + +exchange particles, which is +exactly what's going on here. + +So if you're actually +building a system, + +you should basically +Google for SRP or PAKE. + +And these protocols +and related particles + +will actually do this in +a much better way where + +you can prove to both +parties that you established + +a new key and both parties +are convinced that it's + +the right other party +and there's no way + +to mount these offline +password guessing attacks + +on the set of network packets +that you observe and so on. + +So these are the +sort of protocols. + +And they're much more +elaborate in terms + +of crypto they rely on. + +So it's hard to explain on a +board exactly why they work. + +Yeah. + +STUDENT: [INAUDIBLE] +part of the reason + +they did it this +way is because they + +wanted to maintain the ability +of just sending the password. + +And protocols just allow +you to send a single thing + +as your authentication +[INAUDIBLE]. + +PROFESSOR: Well, +yeah, there's lots + +of sort of weird requirements +that these guys had in mind. + +I think they-- well, +certainly in practice, + +these servers could accept +both Kerberos and non Kerberos + +connections. + +And for non Kerberos +connections, + +you get-- like someone +connects to the mail server + +but they're not using +an Athena workstation. + +They just want to +send their password. + +And then the mail +client here, let's say, + +is going to take +your password and is + +going to get a ticket on +your behalf just to check it. + +And then it's going to +allow you to use it. + +So you certainly want conversion +from Kerberos from passwords + +into checking against Kerberos. + +I don't think this precludes +it because certainly + +Kerberos 5 deploys although +this hashes of timestamps, + +et cetera. + +STUDENT: Yeah but it's +because they wouldn't + +want multiple [INAUDIBLE]. + +PROFESSOR: Yeah, well, +I think that probably + +doesn't matter quite as much. + +You could certainly have +multiple rounds in the back end + +behind your library. + +But there's some downsides +to these particles-- + +probably not significant enough +to stop you from using them. + +Other questions? + +All right, I guess +the other thing + +I want to mention that +you should watch out + +for in the paper is that these +guys, in designing Kerberos 4, + +they picked a single +encryption scheme. + +And at the time, +they basically picked + +DES, which was a popular +encryption scheme of the time. + +It's a symmetric block cypher. + +It goes pretty fast. + +It was reasonably secure, +not necessarily the best, + +but certainly good +enough at the time. + +And they just baked +it into the protocol. + +Everything in Kerberos has +to use single DES or at least + +everything in +Kerberos version 4. + +And this was a bit problematic +because 25 years later, + +30 years later +now, it's actually + +very cheap to brute +force DES encryption + +because the keys are +actually very small. + +They're 56 bits. + +So you could just search build +some custom hardware that + +iterates over all the possible +2 to the 56 combinations + +and tries them all and figures +out what someone's password is. + +So this is something +also you want to avoid + +in any protocol you design now. + +Kerberos version 5 +actually supports + +multiple different +encryption schemes including + +AES and other things as well. + +So that seems like a +much better way to do it. + +On the other hand, MIT +actually kept supporting DES up + +until two years ago, which +is a little unfortunate. + +But now they don't. + +So that's good. + +Your principal is secure at +least from this kind of attack. + +All right, so does +that make sense? + +This is the initial +way you'd get + +any ticket at all in Kerberos. + +And typically, you'd get this +ticket from this TGS service. + +So now let's look at what's +going on in this TGS service. + +So here, the interaction +with the TGS service + +is going to be a +little different. + +On one hand, you're +going to-- as a client, + +you're going to have +to speak to it as + +if you're speaking to any +other Kerberos enabled service. + +So we'll see how you +authenticate yourself + +with a ticket to some machine. + +But then the response +you're going to get back + +is just a ticket for +some other principle + +that you're going to want to +communicate with like your file + +server. + +So the protocol level messages +that show up here kind of + +look like this. + +So here's your TGS service. + +And here's a client. + +The client already +got a ticket for TGS + +using this protocol above. + +So what the client is +actually going to send over + +is some combination +of messages that + +prove that this is +the right client + +and they're issuing a request +for some particular principle + +through TGS. + +So what the client is going +to send to TGS is this tuple. + +So first, it's +going to say, well, + +here's the service that +I want to talk to next. + +So this might be your mail +server or your file server. + +Then is going to +include the ticket. + +It already got 4TGS. + +So this is going to be TC +of TGS encrypted with KTGS. + +So this is just this +thing where S is TGS. + +And then you're going to have +to include this authenticator + +blob. + +This is this AC +thing from up there. + +And this thing is +going to be encrypted + +with a shared key between the +client and the TGS service. + +So this is the message that +you're going to send to TGS. + +It's going to look +at this message, + +do something with it that +we'll talk about in a second, + +and respond back with a +ticket for this new service S. + +So the response here looks +almost exactly like here. + +In fact, it is exactly +the same thing. + +It's going to be a +ticket between the client + +and this new service +S encrypted with KS + +and the shared key between the +client and this new service + +S encrypted-- well, now, +here's a little bit different. + +Instead of encrypting with KC, +which the client has probably + +forgotten since +then, now we're going + +to encrypt it with this +shared key between the client + +and the TGS service. + +Makes sense? + +All right, so in this-- how does +the server actually figure out + +what the client wants to do? + +Or, how does server +authenticate the client? + +Well, in this case, it's +going to-- TGS server actually + +knows its own key, KTGS. + +So it's going to first +decrypt this blob + +and look inside the ticket and +figure out what's going on. + +And there's all those +nice fields in the ticket. + +So let's just double check. + +Why do we need all those +fields in the ticket? + +So is it important to have the +server name S in the ticket? + +What would go wrong if you +didn't have S in there? + +Anything? + +Yeah. + +STUDENT: They could +potentially get + +authorized to use any server. + +PROFESSOR: Yeah, so it's +in general a good idea + +to be very explicit +in network protocols + +and to say exactly +what a message means. + +So in this case, +if you omit an S, + +you might be relying +on the fact that, well, + +if it's the wrong S that you're +trying to use the ticket for, + +then maybe you'll have a +different key over here + +and then it wouldn't decrypt +or something like this. + +But it seems like a good idea +to include it to make sure + +that the server that +receives this tickets + +decrypts and checks. + +Is that a ticket for +me or for someone else? + +Yeah. + +STUDENT: What does the +client get KTGS on? + +PROFESSOR: Ah, good question. + +The client has no +idea what this is. + +Because this is like +a super secret key. + +If you knew this, +you'd probably be + +able to break all of Kerberos. + +So the client has no +idea what KTGS is. + +STUDENT: [INAUDIBLE] + +PROFESSOR: Ah, yeah, yeah. + +And then the where +you get it from + +is actually-- it's the +Kerberos server itself + +that generates this whole blob +for you where this is actually + +TGS and this is KTGS over here. + +So you don't construct +this yourself. + +You just copy it over. + +OK + +So what is the client +name there important for? + +That should be +fairly easy, right? + +If you don't put the +client name in the ticket, + +then the server +gets this nice blob + +but it has no idea who +it's trying to talk to. + +So it has no idea +whether it should + +issue a ticket for my +principal or for someone else's + +principle, et cetera. + +So what's the deal +with the other fields? + +Why do these guys stick +an address in the ticket? + +This is the client's IP address. + +Does it matter? + +Yeah. + +STUDENT: Can they +use that address + +with the ticket to verify +against the [INAUDIBLE]? + +PROFESSOR: Sort of. + +Well, so I think +the general plan + +for why there's +addresses appearing + +everywhere here, +these IP addresses, + +is that these guys at the +time were still slightly + +confused and-- +well, in some ways-- + +they were still +thinking, OK, well, + +we're going to rely +on IP addresses + +for a little bit of security. + +So they wanted to make sure +that if the client logged in + +from some IP address, then +everything else going on + +with that ticket happen +from that same IP address. + +So if you logged in +from some IP address + +on 18.26.4.9 or something, +then every connection + +you make to a file server +or to a mail server + +has to be from the +same IP address. + +Otherwise, the server should +reject your connection + +as being stolen by-- or +someone stole your ticket. + +So we're thinking, +OK, well, maybe we'll + +defend against ticket +theft this way. + +If you still a ticket, +well, but you're + +not using the same IP address. + +So it won't work. + +It's probably a little bit +misguided at this point + +but-- that sort of gets in the +way And Kerberos 5 still has it + +but it's largely optional. + +Really, you should just rely on +cryptography instead of any IP + +address security. + +So what's the point of the +time stamp and lifetime things + +in the ticket up there? + +One are those guys good for? + +Are they useful? + +Yeah. + +STUDENT: Preventing +replay attacks. + +PROFESSOR: Well, +so the syndicator + +is the thing that's +going to help us prevent + +replay attacks in a second. + +Because that thing gets +generated every time + +you do a new request. + +On the other hand, the +ticket just stays the same. + +So it's certainly not +preventing replay attacks there. + +Yeah. + +STUDENT: It prevents somebody +from stealing your ticket then + +using it [INAUDIBLE] + +PROFESSOR: Oh, sorry, yes. + +This just bounds the time +for which a ticket is valid, + +meaning that the damage +from disclosing it + +is hopefully reduced. + +So the plan is the timestamp +is roughly the time when + +you initially got the ticket. + +And a lifetime in +the ticket represents + +how many hours, +let's say, it's valid + +from that initial timestamp. + +So if you try to use it +too early or too late, + +then every server should +reject such a ticket + +in the Kerberos protocol. + +So this kind of means +that every server + +has to have a loosely +synchronized, clock which + +is a bit of a-- well, +maybe you've run into this. + +Like, your laptop clock is off +and you can't log into Kerberos + +anymore. + +Question? + +Yeah. + +STUDENT: You said before +that the client discards KC + +but they're still +keeping KCS [INAUDIBLE] + +the TGS. [INAUDIBLE] + +PROFESSOR: That's right, yeah. + +So the client discards +KC after logging in. + +But it still keeps KCS. + +You're exactly right. + +STUDENT: So if someone +steals the KCS, + +then they have access +to [INAUDIBLE]. + +PROFESSOR: Yeah, OK. + +So how bad is that? + +Like, why is it better +to disclose this KCS + +fof-- actually, well, +this is TGS, right? + +Why is it better to +disclose KCTGS than KC? + +Yeah. + +STUDENT: Someone [INAUDIBLE] +somewhere [INAUDIBLE]. + +PROFESSOR: It's +the kind of thing + +that they're both keys, though. + +So neither of them are +really hashed, yeah. + +STUDENT: You would take +KCS and you'd just steal + +that session between those two. + +But if you steal KC, you +can impersonate the client. + +PROFESSOR: That's right. + +Yeah. + +So I guess one +way to answer this + +is that KCTGS, this is actually +a new key generated every time + +you log in initially. + +And this thing is only good +because you have this ticket + +that goes along with it. + +If you lose this ticket or if +this ticket is no longer valid, + +then yeah, you have these +56 bits in this key. + +But no one is going to assume +anything from those bits. + +The only reason these +bits are interesting + +is because this ticket talks +about this KCS being valid + +right now. + +And there's a bound on it. + +STUDENT: Yeah, so if +they stole both of those + +[INAUDIBLE] be bounded. + +PROFESSOR: Yeah, if someone +steals both of these blogs, + +than they can impersonate you +or, like, log into your file + +server, mail server for the +lifetime of that ticket, which + +is a couple of +hours or 10 hours. + +Stealing this, there's no time +bound on that until you change + +your password and maybe worse. + +Make sense? + +All right, so it +seems like, yeah, + +all those fields are +kind of important, + +IP address maybe less so. + +And now in response, right, we +can get this ticket finally. + +And because we know KCTGS, +we can decrypt the response + +from this TGS server. + +And now we have a +ticket for any server + +we want-- a file server, +mail server, whatever + +it is that we finally +care about connecting to. + +Make sense? + +All right, so let's look at +how you might sort of finally + +use this in some +application level protocol. + +So suppose that maybe I'm +talking to a mail server + +to fetch my messages. + +So presumably, what my client +workstation is going to do + +is going to send a tickets +requesting for, I don't know, + +mail.po12. + +And it'll get back a ticket +for the principal mail.po12 + +or something like this. + +And then inside of this ticket +or inside of this response, + +now I have a shared +key between me + +and the mail server-- S is +the male server over here-- + +and this ticket a blob +that I can to the mail + +server to convince it +that I'm the right guy + +or anyone with this key +is the right principle. + +And then we can actually have +an encrypted conversation + +with the mail server +using this new key KCS. + +So what I might do as +a client is-- well, + +initially, I send some +message to the mail server + +that includes this +ticket TC mail encrypted + +with the key of the mail server. + +And then I can actually +send some message along + +with this request that maybe +says something like, well, + +delete some message-- delete 5. + +And I can encrypt +this with KC mail. + +Does that make sense? + +OK, so what happens in this +protocol on the mail server + +side? + +The mail server is going to +use its secret key K mail + +to decrypt this ticket first. + +And then it looks +inside there and finds + +two important things-- the +principal name C of who + +is it that's talking to it in +the first place and the key KCS + +that it should be +using to decrypt + +all the subsequent traffic +and authenticate it ideally + +in Kerberos 5, at least. + +And then you can decrypt this +message and say oh, well, yeah. + +User C is trying to +delete message five. + +So I'll run this command. + +Make sense? + +You had a question? + +STUDENT: Yeah, so +Kerberos initially + +sends the TGS ticket in KCTGS. + +Where's [INAUDIBLE]? + +PROFESSOR: So AC, those +authenticators are actually + +generated by the client. + +Note that the client +only needs KCS + +to generate an authenticator. + +So the client can make +these up any time it wants. + +So the general plan for +indicators or the reason + +to use authenticators is roughly +to prevent replay attack. + +So the client, or at least in +the way that the Kerberos 4 + +developers were +intending it, the client, + +every time it sends +a new request , + +it would generate a new +authenticator to say OK, well, + +this is a new request. + +I'm issuing it now. + +It's different from all +the previous requests. + +Go do it. + +And the general plan +was that the server + +would keep a cache of +these authenticators that + +were sent within the +last five minutes or so. + +So if it ever sees a +duplicate authenticator, + +it says oh, that's +a replay request. + +I'm going to reject it. + +And if it sees an +authenticator that's + +outside of a five +minute boundary, + +it doesn't have it in the cache. + +But it will look at the time +stamp in the authenticator + +and say, well, this is a +very old authenticator. + +I'll just reject your +request because it's too old. + +Send it again if +you really care. + +So that's the general +plan for indicators. + +As with many things +in Kerberos, they + +were slightly broken-- +in Kerberos 4, at least. + +Because this +authenticator actually + +says nothing about the +message you're sending, right? + +It's some blob. + +So the way you would +use it, for example, + +in this mail server protocol +is-- or at least in Kerberos + +4-- well, you would +generate some authenticator + +and you would be to +take the authenticator + +and you would encrypt +it with also KC mail. + +And the mail server would +keep track of, well, yeah, + +you've sent this [INAUDIBLE] +indicator before. + +No, you haven't. + +But there's nothing here that +connects the authenticator + +to the message you are sending. + +So for the first +message, this was great. + +But when you send +a second message, + +you're going to generate +a second authenticator. + +And someone on the +network can say, oh, yeah, + +I got your new authenticator. + +I can take your +new authenticator + +and splice in the +old delete message. + +So I'll force you to delete +the fifth message twice, + +even though the +second command meant + +to send some other operation. + +So Kerberos 5 gets this +right where you actually + +stick something in the +authenticator that relates + +to the command you're issuing. + +You could do this, of course, +but sort of took a while + +for people to realize +that, well, here's + +how you should design +a protocol correctly. + +Make sense? + +Yeah, other question. + +STUDENT: [INAUDIBLE] + +PROFESSOR: Ah, so the +client gets case email + +from this response. + +So the client, when it wants +to talk to the mail server, + +it's going to ask the TGS for +a ticket for the mail server. + +And here, S is basically this +mail server's principal name. + +So when it comes back, +this says S equals mail + +and this server key +S is equal to mail. + +And this KCS is +actually KC mail. + +So this is how the client +learns of the shared key + +that it has between it and the +files and the mail server here. + +And there's a copy of +it inside the ticket. + +Question back there? + +STUDENT: How does the +mail server get KC mail? + +PROFESSOR: Ah, yes. + +So how does the mail +server get this shared key? + +Like, the mail server +might have never heard + +of your connection before, +never heard of you. + +Where does KC mail come from +on the mail server side? + +Yeah. + +STUDENT: Isn't it +part of the ticket? + +PROFESSOR: Yeah, yeah, so +this is the cool thing. + +You send this ticket over to the +mail server and the mail server + +knows its own secret key K mail. + +And it uses that to decrypt the +ticket TC mail and the shared + +key is in there along +with the name of whoever + +it is that you're +sharing this key with. + +That's how it finds out, +oh, I'm talking to the guy + +and that's the shared +key we should use. + +Makes sense? + +All right, so that's +the sort of basic plan + +for how you use this protocol +in some actual application. + +There's-- well, there's a +bunch of problems with this. + +So Kerberos is-- it's +a nice paper to read + +but then there's all these +problems these guys didn't + +know about 30 years ago. + +So it's sort of inevitable +that there's problems + +you have to go through. + +So one interesting +problem in the way + +Kerberos 4 encrypted and +authenticated messages + +for applications is that +they use the same key + +for encrypting messages from +the client to the server + +as well as messages from the +server back to the client. + +So suppose that the client +issues, I don't know, + +a request to fetch a +particular message. + +So then I say, you know, +fetch the message 7. + +And I encrypt this +thing with KC mail. + +That seems all great. + +The mail server has +the shared key that's + +going to decrypt this message. + +And it's going to send me back +the body of this email message + +also encrypted with KC mail. + +Does anyone see a +problem with this? + +Why is this is potentially +a bad thing to do? + +Anyone else? + +Sure. + +STUDENT: So there's +a chapter [INAUDIBLE] + +they can make [INAUDIBLE] look +like some other things they + +want [INAUDIBLE] + +PROFESSOR: Yes, so +those are actually + +worrisome because I could send +you any email message I want. + +So suppose I really want +to delete some message that + +is sitting here in +your inbox and I + +don't want you to read it. + +I know it's maybe +message, I don't know, 23. + +So I'm going to send you an +email that says, delete 23. + +You're going to read it. + +You're going to fetch +it and a response + +is going to come from +the mail server saying, + +delete 23 encrypted +with this key. + +And so far, it's not being +sent to the mail server. + +But if I look at the +network at the right time + +and capture this packet, +I can send the packet back + +to the mail server. + +It would look like a message +saying delete 23 encrypted + +with the right key. + +And the mail server +will say, oh yeah, sure. + +You're trying to +delete this message. + +I'll do it. + +So this is a bit of +a problem because we + +are allowing an adversary +to confuse the mail + +server into whether our +message was generated by it + +or was sent to it +in the first place. + +So this is quite troublesome. + +So these are what's +typically called + +in cryptography and +protocol literature + +as reflection attacks. + +So you have any suggestions for +how we can avoid this problem? + +Yeah. + +STUDENT: Can't you just include +a header saying its origins? + +PROFESSOR: Yeah, +so typically, you + +want to have some very +unambiguous way to state what's + +going on. + +One way is to have a header +in every message that says, + +this is going from the client +to the server or from server + +to the client. + +And even better plan +in practice turns out + +to be just use +two separate keys. + +Because you might want to +have a long stream of data + +where you don't really have +space for this header bit. + +So instead, what Kerberos 5 +does is every time you establish + +a connection with some service , +you actually negotiate two keys + +instead of just one key. + +And the first key is going to +be used for encrypting stuff + +from client to server and other +from server back to the client. + +So that seems like a much +better way to do it in practice. + +Make sense? + +All right, so I guess +let's now talk a little bit + +about what happens with KDC. + +So the Kerberos server is +pretty important to the system. + +But what happens if +this KDC goes down? + +So how bad is it to our system. + +Like, in Athena, +suppose if KDC crashes, + +does this affect your life? + +Well, if you use Athena. + +STUDENT: Is that why +you can't log in? + +PROFESSOR: Yeah, so +you can't log in. + +I guess the other thing is +you also can't get tickets + +to new things as well. + +But kind of the cool thing +is that the KDC is largely + +off the critical path +for existing connection. + +So no data passes +through the KDC. + +And if you already have +a ticket for something, + +you can keep using +it and keep logging + +into some service +over the network. + +So in that way, it's actually +quite nicely cacheable. + +I guess the other +nice thing these guys + +do is they actually have +a way of replicating + +the KDC potentially. + +So they have one +master Kerberos server + +that stores the sort of primary +copy of this whole database. + +And then they can have +read only replicas that + +hold a copy of this database. + +They don't allow +any updates to this + +like registering users +or updating keys. + +But they do allow responding +to login and TJS requests. + +So this way, these backup +clones of this Kerberos database + +allow you to keep logging in +and keep talking to services + +even if the master +crashed and hopefully + +make it possible to upgrade +to master without breaking + +everything at the same time. + +Makes sense? + +Any questions? + +Yeah. + +STUDENT: How hard +is it to compromise + +the KDC server and [INAUDIBLE]? + +PROFESSOR: Well, yes, +this is a huge sort + +of target for any system +that runs Kerberos. + +Because if you +compromise this guy, + +you're in complete +control of the system. + +You can mint tickets for +any service you want, + +pretending to be +client you want. + +So this is pretty bad. + +So you really want to +keep this guy secure. + +Now, how hard is +it to compromise? + +Well, ideally, it's hard. + +And I don't know +of any instances + +where the MIT KDC has actually +been compromised in, I guess, + +20 years or so. + +So it's , I think, possible to +run this reasonably security. + +But presumably, the things +you would worry about + +are just software +implementation security + +of the things that's listening +on these two services, right? + +So if there's buffer +overflows on this guys + +or some other vulnerability +like that, that's really bad. + +Or if there's an SSH server +running on the Kerberos KDC + +and someone guesses the root +password on that SSH server, + +they'll just log in and +copy the database over. + +So I think you really want +to be careful in minimizing + +the attack surface there. + +Maybe be very careful +writing the KDC code. + +Don't allow you to +log into it directly. + +Maybe you even worry about +physical security, et cetera. + +Absolutely. + +Luckily, this is actually +one of the few places + +where you have to be +super paranoid, though. + +Right, so the servers, +unlike in some other systems + +that do trust all the +machines, the servers + +are actually not that important. + +They of course store some data. + +But if someone compromises a +mail server or a print server, + +you can probably +recover reasonably well. + +So actually, here's an +interesting question. + +Like, suppose someone +compromised the mail server. + +What should you do to +recover from this attack? + +Like, if someone +stole your mail, + +I guess that's kind +of unfortunate. + +But what do you do so that the +attacker doesn't keep accessing + +your mail in the future? + +Yeah. + +STUDENT: [INAUDIBLE] + +PROFESSOR: Yeah, so +in Kerberos, there's + +no sort of revoke operation. + +But what you could +do is you could + +change generate a new +key for the mail server + +and stick it in this +database over here. + +And then you install a new mail +server, give it the new key, + +and then some attacker that +has the mail server's old key + +has no way of-- like, no +influence at all on this mail + +server now, right? + +On the other hand, suppose you +didn't change the mail server's + +key, K mail. + +How that is that? + +STUDENT: [INAUDIBLE] fine. + +PROFESSOR: OK, so suppose +you didn't change the mail. + +You, like, install +the new mail server. + +You patch whatever bug +that hacker exploited. + +But it still has +the same key K mail. + +And maybe it's taken a day so +all the tickets are expired. + +Can that hacker do anything +interesting in the system + +anymore? + +Yeah. + +STUDENT: [INAUDIBLE] + +PROFESSOR: Yeah, OK, so you give +the new mail server the old K + +mail. + +Is that bad? + +Yeah. + +STUDENT: This is-- + +PROFESSOR: Sure. + +STUDENT: [INAUDIBLE] +mail server. + +And [INAUDIBLE] mail +server because you can + +encrypt that initial ticket. + +PROFESSOR: Right. + +So K mail is actually +super important. + +And, OK, so you're saying you +can decrypt all the things + +going on to the mail server. + +So suppose the client now +connects to the mail server + +after it's been fixed up. + +But the attacker +still knows K mail + +from the last time they +compromised the system. + +They can now decrypt +this ticket k mail + +and they can now look inside the +ticket to get the session key + +and they can use that to +decrypt all the messages you + +send, all the responses +you get back, and so on. + +So it's pretty important +to change this key K mail. + +And in many ways, it's +actually even worse + +than just looking +at the traffic. + +Because if the attacker +know this key K mail, + +they can synthesize new +tickets for the mail server + +without talking to the key DC. + +So suppose that I +know K mail and I + +want to read your mail +from the mail server. + +I'll just make up this ticket. + +I'll plop down all those five +fields in the right order. + +I'll generate a new key. + +I'll encrypt it with K mail. + +It'll look like the real +thing generated by the KDC. + +And I'll just connect +to the mail server. + +And it'll decrypt it. + +It'll decrypt correctly and +then it'll think, oh, yeah, + +this is some particular user. + +And you can read all their mail +and you know the shared key + +and so on. + +So it's critically important +too that no one knows + +the secret key of a service. + +Because otherwise, not +only is the traffic + +to the service decryptable +and observable, + +but also you could impersonate +anyone to that service. + +So this is actually all +pretty important in Kerberos. + +Makes sense? + +Any questions? + +Yeah. + +STUDENT: So if the attacker +has to [INAUDIBLE], + +what's stopping him from +changing the [INAUDIBLE] key + +[INAUDIBLE]? + +PROFESSOR: Yeah, so presumably, +how you'd recover-- like, + +ISNT would, like, call up +the guy that runs this KDC + +and say, oh man, our mail +server got compromised. + +Why don't you go and, like, +delete this key from there + +and put in this new key instead? + +So you'd probably want to +have some out of bounds + +mechanism for proving that +you're really the mail server. + +Because we'll look +at a second on how do + +you change keys-- like a +password changing protocol, + +for example. + +And you can in general +change passwords in Kerberos. + +So if you know the +old password, you + +can change the user's password +to a new password here. + +So in order to recover, you +probably-- like the attacker, + +might get your key mail, +change it to something else. + +Someone with ISNT basically has +to go to the Accounts office + +and say, hey, +we're hear at ISNT. + +Could you please change the +password of the mail server + +for us? + +And they're going to +generate some new password + +the attacker doesn't know. + +So yeah, otherwise, if the +attacker knows this key K mail, + +there's nothing differentiating +the attacker from you, + +from the real mail +server operator. + +In fact, the attacker probably +changed the key so now they + +know the new thing +and you don't. + +It's like you're not on +the mail server anymore. + +So absolutely, you need +some out of band protocol + +for initially registering +principles in the database + +and for changing keys if you +forget your password or someone + +changes for you and +you lose it as well. + +So there's someone +at MIT or there's + +a group of people at +MIT that help users + +register for accounts and +change their passwords + +by, you know, you present your +MIT ID and say, oh, well, OK. + +Well, whatever +happened, we'll be + +able to change your +key for you then. + +Make sense? + +So it's pretty +important, of course, + +to do that right so +if the person that + +is allowing password resets does +the wrong thing when checking + +your MIT ID, you'll be able to +compromise the system as well, + +right? + +So they are sort of part +of the trusted computing + +base in Kerberos, right? + +Like, anyone that can go +and muck with the database + +is pretty important +for security here. + +All right, so let's look at +another sort of interesting use + +of Kerberos, right? + +So you could use Kerberos to try +to log into some remote machine + +over SSH. + +And the way this would work +is, of course, very similar + +to a mail server. + +You'd get a ticket +for the SSH server + +and you'd send the ticket +along with your SSH connection. + +But what if you're SSHing +into Athena dot dial-up + +and you don't have a Kerberos +client on your machine? + +You just want to log +into Athena dot dial-up + +with your regular password. + +So how would Athena dial-up +authenticate you, then, + +if you're just plugging into +this machine with a password? + +But you have no password +for Athena dot dial-up. + +It's on a Kerberos server. + +So which should +the dial-up machine + +do when you log into +it with a password? + +Yeah. + +STUDENT: You can +access the [INAUDIBLE]. + +PROFESSOR: Yeah, so +the dial-up is then + +going to basically play the +same protocol logging you in. + +So it's going to send a request. + +This thing, right? + +It's going to send a request +to the Kerberos service asking, + +give me a ticket for, I +don't know, this user Alice. + +And in response, it's going to +get back this reply encrypted + +with Alice's password. + +And then it's going to try +the password you just applied + +and see if it +decrypts correctly. + +And if it decrypts +correctly, it's + +going to let you log in, right? + +Yeah. + +STUDENT: You don't +even really have + +to send your key +to the SSH server. + +Because it could +relay this back-- + +the dot encrypted thing with KC. + +It could relay that back to the +user over the SSH connection. + +PROFESSOR: Potentially, yeah. + +Right, so this requires +some fancy SSH client + +that you might not have. + +But-- so yeah, absolutely right. + +If you want to do +this right, you + +probably want to have a +Kerberos client on your machine + +and get a ticket +yourself or maybe + +proxy it somehow +through the SSH server + +but not allow the SSH +server to have your key. + +That's probably a good plan. + +STUDENT: [INAUDIBLE] +just, the server could get + +through this wall [INAUDIBLE] + +PROFESSOR: That's right. + +Then you might decrypt +it and send back. + +OK, but in either case, +right, all we're doing here + +is someone is going to try +to decrypt this blob with KC. + +And then the server is +going to get this resolved + +and see if it looks right. + +It's going to allow you in. + +Seem like a good plan? + +So, turns out this is actually +a fairly dangerous thing to do + +and allows you to potentially +log into the SSH server + +as anyone. + +And the reason is +that previously, + +when we were talking about +a client trying to log in, + +the client basically +knew that it + +was trying to supply +a legitimate password, + +it was getting a reply from +the right Kerberos server, + +and if it can decrypt it, then +probably the password works out + +correctly. + +However, there's nothing +here in this protocol that + +authenticates the fact +that this reply is coming + +from the right Kerberos server. + +So if I try to log into a +machine by typing in a password + +and the machine sends +out this request + +and some response +comes back that seems + +to be encrypted with +the password I typed in, + +this response might not be +from the Kerberos server. + +So suppose I have some +machine I want to log into. + +I type a password X into it. + +And then the machine +sends out this response. + +And before the Kerberos +server can respond back + +with the real reply, I'll +send my own reply that + +looks like this real response +encrypted with my password X. + +And the workstation to which I +try to log in or the SSH server + +is going to decrypt it +with my fake password. + +It's going to look OK +because this response was + +generated by me rather than +the real Kerberos server. + +And you'll be able to +log in This make sense? + +Why does this happen? + +Yeah. + +STUDENT: [INAUDIBLE] +there's no authentication + +from the Kerberos +server [INAUDIBLE] + +PROFESSOR: Right, +yeah, so there's + +nothing really here that's +tying this to the real Kerberos + +server. + +So the way that +Kerberos fixes this + +for remotely accessible +machines like Athena + +dot dial-up is that +the dial-ups themselves + +have some sort of a secret key +that they share with the KDC. + +So in order to log +you in into a dial-up + +or to any workstation that +really cares about checking + +whether you are +really the right user, + +it's actually going +to do two things. + +It's going to first log you +into Kerberos like this. + +But then just because this +reply decrypts correctly, + +it's not going to trust that. + +It's going to try +to get a service + +ticket for itself using TGS. + +So the dial-up machine here +has its own secret key. + +And it logs you in +with this round one. + +Then it talks to TGS +saying, oh, please give me + +a service ticket for +my own principle, + +from the dial-up +principle, for this client. + +Then it gets the response back. + +And then it checks if it can +decrypt the response correctly. + +Because it knows the +dial-up key for this KS. + +And if this decrpyts, +that it knows, oh yeah, + +I must have talked to the +right Kerberos server. + +Because only the +right Kerberos server + +would have sent me this +second round ticket encrypted + +with my secret key K dial-up. + +So this is actually +pretty important. + +And typically, +Athena workstations + +don't do this extra step because +Athena workstations don't + +have any secret +key stored on them + +that's shared with the KDC. + +Why is this OK for Athena +workstations to let you + +log in in this one round +trip and not for dial-ups? + +Yeah. + +STUDENT: If you don't have +access to any services + +because the attacker +couldn't forge the ticket. + +PROFESSOR: That's right, yeah. + +So there's nothing interesting +on the dial-up machine itself-- + +sorry, on the +workstation itself. + +So workstation, whenever-- you +have root access on it anyway. + +So if you log into it with +a fake password, who cares? + +It's not like you'll be +able to do anything else + +outside of your workstation. + +Whereas on a dial-up, things +are much more interesting. + +It might be that you have +other processes running + +on the dial-up from +other login sessions. + +And there, the fact that you log +in with a particular Unix UID + +is actually pretty important. + +And there, they really +want to authenticate + +that you are the right entity. + +So that's why they do this sort +of 2-step process for logging + +into some shared +time-sharing machine. + +Make sense? + +All right, so the last +thing I want to talk about + +is how do we change keys. + +So we sort of talked about +it briefly here with the idea + +that the mail server's +key might get compromised. + +But as a user, you +probably also want + +to change passwords as well. + +Like, maybe you're thinking, oh, +that password is not so great + +anymore. + +Maybe I accidentally wrote it +on a piece of paper and someone + +looked at it. + +So you probably +want to change it. + +So the way this +works is actually + +at some level fairly +straightforward. + +So there's an extra interface +to this Kerberos server. + +In addition to Kerberos +and TGS, there's + +this extra service +called kpassword. + +And the service lets you +change your password. + +And the way it works is you +get a ticket for this service + +very much like you'd get +a ticket for the mail + +server or any other service. + +And then you send +your new password + +to this kpassword service +encrypted with your session + +key. + +And then if everything checks +out, your key in the database + +is going to be updated +to the new key. + +Question. + +STUDENT: [INAUDIBLE] +if there was, like, + +no [INAUDIBLE] they wanted to +have them use a [INAUDIBLE] had + +to go through this. + +PROFESSOR: That's right. + +OK, yeah, OK. + +So this is a good point. + +So for changing your +password, remember + +that we have this whole +goal that if someone steals + +your ticket, it shouldn't be +good enough to completely take + +over your account. + +So for this reason, the key +password service actually + +doesn't accept just any ticket. + +It accepts a ticket that you +initially get from the Kerberos + +service with your KC. + +So the way this actually works +is that inside of every ticket, + +in addition to all the stuff +I showed you there, there's + +an extra bit that tells you +which of these two things + +gave you the ticket. + +So if you get the ticket +from this Kerberos server, + +the bit has one. + +If you get the ticket from the +TGS server, the bit is zero, + +let's say. + +And then the kpassword service, +in addition to everything + +that any mail server or +file server would do, + +it also looks at the +bit on the ticket + +and says, well, if you got it +from Kerberos, that's good. + +If you got it from +TGS, that means + +that maybe you stole +someone's ticket + +and you didn't know their +password right away. + +So I'm not going to accept this. + +So this is how a key password +ensures that you can only + +change the password if you just +knew the password immediately + +prior to this. + +So you never actually supply +the old password to kpassword. + +You supply that to-- well, +you supply that in order + +to decrypt the response +from the Kerberos + +server for the kpassword +password principal. + +Makes sense? + +All right, so let's +just actually spell out + +the interactions with +the key password service + +because there'll be something +a little bit interesting there. + +So when you're going to +change your password, what + +the client is going +to do is, of course, + +obtain this initial +ticket from Kerberos. + +So it sends a message to the +Kerberos service saying here + +is my client ID and I want to +talk to the kpassword service. + +And the Kerberos server is +going to send a response back + +including the ticket +between the client + +and the kpassword service +encrypted with a key of kpass + +and the shared key +between KC and kpass. + +Makes sense? + +This is exactly this thing +up here encrypted with KC. + +Makes sense? + +Everyone's runs on board? + +And then very much like you talk +to a mail server, you take this + +and you send it to kpassword. + +You say, well, here's my +ticket-- tckpass encrypted + +with kpass. + +And in addition, you +send your new password + +and you encrypt this +with the key kcpass + +with shared key for +your interaction. + +I just separated these +two things out here. + +Make sense? + +So this is the thing you +send to the kpassword service + +with a new password encrypted +with the session key. + +Yeah. + +STUDENT: But in the [INAUDIBLE] + +PROFESSOR: So if the +attacker knows your password, + +they can change your +password-- absolutely. + +So it seems reasonable, right? + +Like, there's no other way to +tell whether it's you or not. + +If someone walks up to an +Athena workstation, types + +in your username and +password, runs password, + +change my password to this new +thing, they know your password? + +They're going to be +able to change it. + +So that's totally the +same in almost any system + +you could imagine. + +This is true for Gmail probably. + +This is true for any system +that uses passwords in general. + +The reason that we had to talk +to the Kerberos server instead + +of the TGS server here is that +if someone steals your ticket, + +then we don't want them to be +able to change your password. + +So if someone corrupts an Athena +workstation after you log in, + +your password is gone from +memory, the ticket remains. + +You could, in principle, +use the ticket + +to obtain more tickets for +the password changing service. + +But the password +changing service + +says that's not going +to be good enough. + +It's going to look +at this ticket + +here-- ticket between the +client and the password service. + +And if that was +updated through TGS, + +it's going to +reject your request. + +It's only going to accept it +if it was obtained directly + +from the Kerberos +service using KC. + +Makes sense? + +Question. + +STUDENT: So if you [INAUDIBLE] +password with the [INAUDIBLE] + +Athena, right? + +PROFESSOR: Yeah. + +STUDENT: So if I would +steal your private key-- + +PROFESSOR: Yeah, +so actually, KC is + +basically equivalent +to your password here. + +As far as the Kerberos +protocol is concerned, + +that don't even think +that you have a password. + +It thinks you have +a private key KC. + +If someone knows KC, that's +basically your password. + +So you can change +your key from KC + +to something else so you +don't lose this thing, yeah. + +Uh, yeah, question? + +STUDENT: [INAUDIBLE] +initial message [INAUDIBLE] + +from changing the [INAUDIBLE] + +PROFESSOR: Oh, you +can certainly get + +a ticket for some other +service or an attacker + +could drop this message +altogether or corrupt + +this exchange. + +And then you're not going +to successfully change + +your password. + +STUDENT: [INAUDIBLE] + +PROFESSOR: Yeah, so +the client actually + +knows exactly what service +it wants to talk to. + +So if it-- it's going +to make sure, well, + +there are some messages, some +parts of this protocol I'm not + +showing that allow the +client to make sure + +they actually got the +ticket for the right thing. + +But yeah, so the-- sorry. + +Question? + +STUDENT: [INAUDIBLE] very easy +to denial of service attack + +when an attacker [INAUDIBLE] +modifying the encrypted version + +of the new password. + +PROFESSOR: Yeah, so there's +actually lot of things. + +Because, for example, Kerberos +doesn't do authentication + +properly of messages-- +it just does + +encryption-- you could +totally corrupt this blob. + +And-- + +STUDENT: [INAUDIBLE] + +PROFESSOR: Yeah, you +could flip it around + +and it'll decrypt +to something else. + +The service was like, oh +yeah, that's the new password, + +and set it. + +And then you're +sort of locked out. + +So it seems really unfortunate. + +And this is yet +another reason why + +you want separate encryption and +authentication in the protocol. + +There's actually an even +bigger problem here. + +But actually, yeah, question? + +STUDENT: What's the +point of having a one way + +function to [INAUDIBLE] your +password in KC if they're + +essentially [INAUDIBLE]? + +PROFESSOR: Basically because +KC is a 56-bit ds key + +and your password might +be of different lengths. + +And even if it's longer +than 56 bits, which + +is seven bites or +seven characters, + +you want to use all +those extra bytes too. + +So it's mostly just to condense +it down to a fixed width blob, + +yeah. + +But there's actually a much +more interesting problem here, + +which is that suppose +that I change my password + +and then I decide, OK, +well, I change my password. + +A day goes by and I'm +thinking, oh yeah, sure. + +I'll tell everyone what my +stupid old password was. + +Is this a good idea in Kerberos? + +Yeah. + +STUDENT: [INAUDIBLE] +immediately expire until the-- + +PROFESSOR: Yeah, OK. + +But someone's got to wait +for all my tickets to expire. + +I wait for, like, a week. + +And then no tickets +are good anymore. + +Can I give out my +old password now? + +Yeah. + +STUDENT: It might take +a while to replicate. + +PROFESSOR: Yeah, +suppose the replicas + +are all updated, +yeah, all the stuff. + +Yeah. + +STUDENT: [INAUDIBLE] if someone +saves the initial transaction + +[INAUDIBLE] to get, +like, your old password + +now that they have +your new password. + +PROFESSOR: Yeah, +so this is actually + +super worrisome +in Kerberos, which + +is that-- suppose +some attacker was + +watching all of my +previous password changes. + +They didn't know what my +password was or is or anything. + +But they're just saving these +packets very diligently. + +And then a month later, I +go and say, oh, my password + +was poodle or something +silly like this. + +And then they go say ah, ha, ha. + +I can now decrypt +this initial thing + +because it was encrypted +with your old KC. + +And I can get this KC +with pass that you shared. + +Then I can use this to +decrypt the new password + +you sent to the KDC. + +And even if you change +the password again, + +I can decrypt the +next round as well. + +And you can just keep going +and get the newest password. + +So in this particular password, +changing protocol, if you ever + +disclose an old +password, then someone + +could sort of unzip this whole +chain of encrypted messages + +and get your newest +password as well. + +This is actually very +troublesome in the design. + +Yeah. + +STUDENT: Doesn't the later +version of Kerberos [INAUDIBLE] + +PROFESSOR: Absolutely, yes. + +So there's actually +a solution to this + +that's not sort of fundamental. + +And this is +something they didn't + +realize in Kerberos version 4. + +There's actually this nice +mechanism called Diffie-Hellman + +that I'll just sketch +out in like one minute + +just so that you guys know +when to use it or et cetera. + +But it's basically a solution +for this kind of a problem + +where you want to stop this +unzipping from happening. + +So what happens in +the Kerberos version + +5 password changing protocol +is that actually you + +want to establish a new secret +that will not be apparent + +if you happen to decrypt all +the messages on the wire. + +And the way this works +is-- this is like some math + +that you don't have +to fully understand. + +But the client some random value +X. And the kpassword server is + +going to pick some +other random value Y. + +And what they send to each +other are exponentiations + +of these values. + +So the client sends +G to the power X + +to the server and the server +sends G to the power Y + +back to the client. + +And it turns out +that mathematically, + +what we can do now is the +client can take G to the Y, + +raise it to X, and get +this value G to the XY. + +The server can take G to the +X, raise it to the power Y, + +and get G to the XY as well. + +They can now use this +secret value G to the XY + +to encrypt their +subsequent messages, + +including the new password. + +So you send the new password +encrypted with this value G + +to the XY, roughly speaking. + +But for some +mathematical reasons + +that we're not going +to cover right now, + +it turns out to be super +difficult for someone that just + +gets G to the X and G to the Y +by examining your packets later + +from figuring out +what was G to the XY. + +So this is something called +the discrete log problem. + +Yeah, question? + +STUDENT: But they have to +[INAUDIBLE] G at some point. + +PROFESSOR: Yeah, yeah. + +So G is some parameter +you could sort of send + +at the beginning of a protocol +or it could be just cooked + +into Kerberos. + +It turns out to be +relatively less important. + +All right, so anyway, use +Diffie-Hellman because this + +is called-- well, what you +should Google for if you're + +building a protocol like this +is this Diffie-Hellman key + +exchange protocol. + +And Kerberos 5 actually +does this correctly. + +But this is something +to really watch out + +for if you're designing any +kind of new protocol yourself. + +All right, so that's +it for Kerberos. + +Let's talk about SSL on Monday. \ No newline at end of file diff --git a/QYP-oC1kP_s.txt b/QYP-oC1kP_s.txt new file mode 100644 index 0000000000000000000000000000000000000000..292c5a9582bf50f06da0ba8ca014b225f4f2bad5 --- /dev/null +++ b/QYP-oC1kP_s.txt @@ -0,0 +1,6493 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu in a minute I'll I want + + align:start position:0% +ocw.mit.edu in a minute I'll I want + + + align:start position:0% +ocw.mit.edu in a minute I'll I want +we're going to go through this exercise + + align:start position:0% +we're going to go through this exercise + + + align:start position:0% +we're going to go through this exercise +of key concepts for the week but while + + align:start position:0% +of key concepts for the week but while + + + align:start position:0% +of key concepts for the week but while +for you early birds I'll offer and we + + align:start position:0% +for you early birds I'll offer and we + + + align:start position:0% +for you early birds I'll offer and we +may get to some of this + + align:start position:0% +may get to some of this + + + align:start position:0% +may get to some of this +um is there just something from the week + + align:start position:0% +um is there just something from the week + + + align:start position:0% +um is there just something from the week +or the problem set just some topic + + align:start position:0% +or the problem set just some topic + + + align:start position:0% +or the problem set just some topic +that's still bugging you that you just + + align:start position:0% +that's still bugging you that you just + + + align:start position:0% +that's still bugging you that you just +don't that you just don't get and you'd + + align:start position:0% +don't that you just don't get and you'd + + + align:start position:0% +don't that you just don't get and you'd +like me to put on a little list and I + + align:start position:0% +like me to put on a little list and I + + + align:start position:0% +like me to put on a little list and I +might get to + + align:start position:0% + + + + align:start position:0% + +it so we solve for velocity is it enough + + align:start position:0% +it so we solve for velocity is it enough + + + align:start position:0% +it so we solve for velocity is it enough +to take time + + align:start position:0% +to take time + + + align:start position:0% +to take time +to yes so if you have the all of the + + align:start position:0% +to yes so if you have the all of the + + + align:start position:0% +to yes so if you have the all of the +terms the full velocity expression in + + align:start position:0% +terms the full velocity expression in + + + align:start position:0% +terms the full velocity expression in +Vector + + align:start position:0% +Vector + + + align:start position:0% +Vector +notation and you want to know the + + align:start position:0% +notation and you want to know the + + + align:start position:0% +notation and you want to know the +acceleration of that point just take the + + align:start position:0% +acceleration of that point just take the + + + align:start position:0% +acceleration of that point just take the +derivatives taking care of all the + + align:start position:0% +derivatives taking care of all the + + + align:start position:0% +derivatives taking care of all the +rotating unit vectors and all that stuff + + align:start position:0% +rotating unit vectors and all that stuff + + + align:start position:0% +rotating unit vectors and all that stuff +yeah when you take the derivative of the + + align:start position:0% +yeah when you take the derivative of the + + + align:start position:0% +yeah when you take the derivative of the +Velocity where does the coris + + align:start position:0% +Velocity where does the coris + + + align:start position:0% +Velocity where does the coris +acceleration term drop from what does it + + align:start position:0% +acceleration term drop from what does it + + + align:start position:0% +acceleration term drop from what does it +fall out of um I'm I can't I can't + + align:start position:0% +fall out of um I'm I can't I can't + + + align:start position:0% +fall out of um I'm I can't I can't +answer it in words can't remember + + align:start position:0% +answer it in words can't remember + + + align:start position:0% +answer it in words can't remember +exactly it actually but I Coral St it + + align:start position:0% +exactly it actually but I Coral St it + + + align:start position:0% +exactly it actually but I Coral St it +does come curiously it comes from two + + align:start position:0% +does come curiously it comes from two + + + align:start position:0% +does come curiously it comes from two +different + + align:start position:0% +different + + + align:start position:0% +different +places each part you know it's two Omega + + align:start position:0% +places each part you know it's two Omega + + + align:start position:0% +places each part you know it's two Omega +or two Omega V kind of term and it + + align:start position:0% +or two Omega V kind of term and it + + + align:start position:0% +or two Omega V kind of term and it +actually it comes from two different + + align:start position:0% +actually it comes from two different + + + align:start position:0% +actually it comes from two different +places when you grind out the + + align:start position:0% +places when you grind out the + + + align:start position:0% +places when you grind out the +derivatives of the Velocity so we can't + + align:start position:0% +derivatives of the Velocity so we can't + + + align:start position:0% +derivatives of the Velocity so we can't +just use the general + + align:start position:0% + + + + align:start position:0% + +and so uh the in terms of using the + + align:start position:0% +and so uh the in terms of using the + + + align:start position:0% +and so uh the in terms of using the +general + + align:start position:0% +general + + + align:start position:0% +general +that so I remember and I what I want you + + align:start position:0% +that so I remember and I what I want you + + + align:start position:0% +that so I remember and I what I want you +to do and partly what the session is + + align:start position:0% +to do and partly what the session is + + + align:start position:0% +to do and partly what the session is +going to do is make you use get you to + + align:start position:0% +going to do is make you use get you to + + + align:start position:0% +going to do is make you use get you to +use the acceleration formulas enough + + align:start position:0% +use the acceleration formulas enough + + + align:start position:0% +use the acceleration formulas enough +that you have those just committed to + + align:start position:0% +that you have those just committed to + + + align:start position:0% +that you have those just committed to +memory now we're going to let you have + + align:start position:0% +memory now we're going to let you have + + + align:start position:0% +memory now we're going to let you have +crib sheets when you go into quizzes and + + align:start position:0% +crib sheets when you go into quizzes and + + + align:start position:0% +crib sheets when you go into quizzes and +I would always have the Velocity and + + align:start position:0% +I would always have the Velocity and + + + align:start position:0% +I would always have the Velocity and +acceleration formulas in polar + + align:start position:0% +acceleration formulas in polar + + + align:start position:0% +acceleration formulas in polar +coordinates and in full Vector form + + align:start position:0% +coordinates and in full Vector form + + + align:start position:0% +coordinates and in full Vector form +right but if you identify each of the + + align:start position:0% +right but if you identify each of the + + + align:start position:0% +right but if you identify each of the +terms correctly that that formula will + + align:start position:0% +terms correctly that that formula will + + + align:start position:0% +terms correctly that that formula will +work just + + align:start position:0% +work just + + + align:start position:0% +work just +fine getting the right components of + + align:start position:0% +fine getting the right components of + + + align:start position:0% +fine getting the right components of +rotation rates can be a little tricky as + + align:start position:0% +rotation rates can be a little tricky as + + + align:start position:0% +rotation rates can be a little tricky as +you might have found in that homework + + align:start position:0% +you might have found in that homework + + + align:start position:0% +you might have found in that homework +problem from this week right you have + + align:start position:0% +problem from this week right you have + + + align:start position:0% +problem from this week right you have +what is the uh in that time derivative + + align:start position:0% +what is the uh in that time derivative + + + align:start position:0% +what is the uh in that time derivative +that of a rotating Vector the Omega + + align:start position:0% +that of a rotating Vector the Omega + + + align:start position:0% +that of a rotating Vector the Omega +cross the vector what Omega is that + + align:start position:0% +cross the vector what Omega is that + + + align:start position:0% +cross the vector what Omega is that +that's a tricky that that you have to be + + align:start position:0% +that's a tricky that that you have to be + + + align:start position:0% +that's a tricky that that you have to be +just careful with but I want but really + + align:start position:0% +just careful with but I want but really + + + align:start position:0% +just careful with but I want but really +get remember if you remember the + + align:start position:0% +get remember if you remember the + + + align:start position:0% +get remember if you remember the +velocity and acceleration equations you + + align:start position:0% +velocity and acceleration equations you + + + align:start position:0% +velocity and acceleration equations you +can trust them they will + + align:start position:0% +can trust them they will + + + align:start position:0% +can trust them they will +work as so we are okay we can start + + align:start position:0% +work as so we are okay we can start + + + align:start position:0% +work as so we are okay we can start +now and I'll go back to my + + align:start position:0% +now and I'll go back to my + + + align:start position:0% +now and I'll go back to my +to + + align:start position:0% + + + + align:start position:0% + +here + + align:start position:0% +here + + + align:start position:0% +here +so take that minute like we did last + + align:start position:0% +so take that minute like we did last + + + align:start position:0% +so take that minute like we did last +time write down a piece of paper 2 three + + align:start position:0% +time write down a piece of paper 2 three + + + align:start position:0% +time write down a piece of paper 2 three +4 what you think of the key Concepts + + align:start position:0% +4 what you think of the key Concepts + + + align:start position:0% +4 what you think of the key Concepts +that were important in the past week you + + align:start position:0% +that were important in the past week you + + + align:start position:0% +that were important in the past week you +know by important you need to know them + + align:start position:0% +know by important you need to know them + + + align:start position:0% +know by important you need to know them +to do a good job on the quiz coming up + + align:start position:0% +to do a good job on the quiz coming up + + + align:start position:0% +to do a good job on the quiz coming up +important + + align:start position:0% +important + + + align:start position:0% +important +Concepts okay let's make a list + + align:start position:0% +Concepts okay let's make a list + + + align:start position:0% +Concepts okay let's make a list +coordinates polar + + align:start position:0% +coordinates polar + + + align:start position:0% +coordinates polar +coordinates and I'm going to generalize + + align:start position:0% +coordinates and I'm going to generalize + + + align:start position:0% +coordinates and I'm going to generalize +that to to call + + align:start position:0% + + + + align:start position:0% + +it choosing + + align:start position:0% +it choosing + + + align:start position:0% +it choosing +coordinate + + align:start position:0% + + + + align:start position:0% + +systems there's an art to that so when + + align:start position:0% +systems there's an art to that so when + + + align:start position:0% +systems there's an art to that so when +to use them subset of that yeah the + + align:start position:0% +to use them subset of that yeah the + + + align:start position:0% +to use them subset of that yeah the +equation for the sum of the Tor ah yeah + + align:start position:0% +equation for the sum of the Tor ah yeah + + + align:start position:0% +equation for the sum of the Tor ah yeah +the torque + + align:start position:0% +the torque + + + align:start position:0% +the torque +equation sum of the external + + align:start position:0% +equation sum of the external + + + align:start position:0% +equation sum of the external +torqus vectors + + align:start position:0% +torqus vectors + + + align:start position:0% +torqus vectors +is + + align:start position:0% +is + + + align:start position:0% +is +d + + align:start position:0% +d + + + align:start position:0% +d +h DT and torqu are always with respect + + align:start position:0% +h DT and torqu are always with respect + + + align:start position:0% +h DT and torqu are always with respect +to some point so + + align:start position:0% +to some point so + + + align:start position:0% +to some point so +dhdt angular momentum is with respect to + + align:start position:0% +dhdt angular momentum is with respect to + + + align:start position:0% +dhdt angular momentum is with respect to +some + + align:start position:0% +some + + + align:start position:0% +some +point and the SEC there's a second term + + align:start position:0% +point and the SEC there's a second term + + + align:start position:0% +point and the SEC there's a second term +to this though and it is velocity + + align:start position:0% +to this though and it is velocity + + + align:start position:0% +to this though and it is velocity +of the point in the inertial frame cross + + align:start position:0% +of the point in the inertial frame cross + + + align:start position:0% +of the point in the inertial frame cross +the linear momentum in the inertial + + align:start position:0% +the linear momentum in the inertial + + + align:start position:0% +the linear momentum in the inertial +frame no that one you haven't had to use + + align:start position:0% +frame no that one you haven't had to use + + + align:start position:0% +frame no that one you haven't had to use +it much yet but that's the going to + + align:start position:0% +it much yet but that's the going to + + + align:start position:0% +it much yet but that's the going to +that's one of the two really important + + align:start position:0% +that's one of the two really important + + + align:start position:0% +that's one of the two really important +Newton Law kind of things that we use in + + align:start position:0% +Newton Law kind of things that we use in + + + align:start position:0% +Newton Law kind of things that we use in +the course sum of forces equals + + align:start position:0% +the course sum of forces equals + + + align:start position:0% +the course sum of forces equals +masstimes acceleration sum of torqus + + align:start position:0% +masstimes acceleration sum of torqus + + + align:start position:0% +masstimes acceleration sum of torqus +equals that okay I have another + + align:start position:0% +equals that okay I have another + + + align:start position:0% +equals that okay I have another +one of rotating vectors derivative of + + align:start position:0% +one of rotating vectors derivative of + + + align:start position:0% +one of rotating vectors derivative of +rotating + + align:start position:0% + + + + align:start position:0% + +vectors and taking derivatives rotating + + align:start position:0% +vectors and taking derivatives rotating + + + align:start position:0% +vectors and taking derivatives rotating +vectors always boils down to eventually + + align:start position:0% +vectors always boils down to eventually + + + align:start position:0% +vectors always boils down to eventually +it's down to you got to do the unit + + align:start position:0% +it's down to you got to do the unit + + + align:start position:0% +it's down to you got to do the unit +Vector so that's part of it how about + + align:start position:0% +Vector so that's part of it how about + + + align:start position:0% +Vector so that's part of it how about +another + + align:start position:0% +another + + + align:start position:0% +another +one can + + align:start position:0% +one can + + + align:start position:0% +one can +solve forces Okay so + + align:start position:0% +solve forces Okay so + + + align:start position:0% +solve forces Okay so +I will generalize that to essentially + + align:start position:0% +I will generalize that to essentially + + + align:start position:0% +I will generalize that to essentially +you being able to write um + + align:start position:0% + + + + align:start position:0% + +find equations of + + align:start position:0% +find equations of + + + align:start position:0% +find equations of +motion + + align:start position:0% +motion + + + align:start position:0% +motion +so + + align:start position:0% + + + + align:start position:0% + +from sum of forces + + align:start position:0% + + + + align:start position:0% + +and right + + align:start position:0% +and right + + + align:start position:0% +and right +okay anything + + align:start position:0% + + + + align:start position:0% + +else I say + + align:start position:0% +else I say + + + align:start position:0% +else I say +one it's not not I think there's one + + align:start position:0% +one it's not not I think there's one + + + align:start position:0% +one it's not not I think there's one +really important one that you've + + align:start position:0% + + + + align:start position:0% + +been maybe you think we did it last week + + align:start position:0% +been maybe you think we did it last week + + + align:start position:0% +been maybe you think we did it last week +i' I'd say + + align:start position:0% +i' I'd say + + + align:start position:0% +i' I'd say +uh being able to find accelerations and + + align:start position:0% +uh being able to find accelerations and + + + align:start position:0% +uh being able to find accelerations and +moving coordinate systems we we did + + align:start position:0% +moving coordinate systems we we did + + + align:start position:0% +moving coordinate systems we we did +mostly velocities last week but finding + + align:start position:0% +mostly velocities last week but finding + + + align:start position:0% +mostly velocities last week but finding +velocities and accelerations in rotating + + align:start position:0% +velocities and accelerations in rotating + + + align:start position:0% +velocities and accelerations in rotating +and moving frames + + align:start position:0% + + + + align:start position:0% + +okay so that's a pretty good list I if + + align:start position:0% +okay so that's a pretty good list I if + + + align:start position:0% +okay so that's a pretty good list I if +you had ask me what I thought the + + align:start position:0% +you had ask me what I thought the + + + align:start position:0% +you had ask me what I thought the +important things from the week + + align:start position:0% + + + + align:start position:0% + +were that that hits the important stuff + + align:start position:0% + + + + align:start position:0% + +okay what we were talking about as + + align:start position:0% +okay what we were talking about as + + + align:start position:0% +okay what we were talking about as +people were arriving is is I might not + + align:start position:0% +people were arriving is is I might not + + + align:start position:0% +people were arriving is is I might not +get this today if we run out of time but + + align:start position:0% +get this today if we run out of time but + + + align:start position:0% +get this today if we run out of time but +is anybody just got a burning question + + align:start position:0% +is anybody just got a burning question + + + align:start position:0% +is anybody just got a burning question +about some concept that just isn't + + align:start position:0% +about some concept that just isn't + + + align:start position:0% +about some concept that just isn't +didn't work out for you on a problem set + + align:start position:0% +didn't work out for you on a problem set + + + align:start position:0% +didn't work out for you on a problem set +that came up or + + align:start position:0% + + + + align:start position:0% + +yeah so that's really the derivative of + + align:start position:0% +yeah so that's really the derivative of + + + align:start position:0% +yeah so that's really the derivative of +a rotation rate Vector that was kind of + + align:start position:0% +a rotation rate Vector that was kind of + + + align:start position:0% +a rotation rate Vector that was kind of +a nasty problem the first time you hit + + align:start position:0% +a nasty problem the first time you hit + + + align:start position:0% +a nasty problem the first time you hit +that that's a that was new + + align:start position:0% +that that's a that was new + + + align:start position:0% +that that's a that was new +right let me write that one down + + align:start position:0% + + + + align:start position:0% + +yeah rotating frames and all that I get + + align:start position:0% +yeah rotating frames and all that I get + + + align:start position:0% +yeah rotating frames and all that I get +it somebody else have another + + align:start position:0% +it somebody else have another + + + align:start position:0% +it somebody else have another +one that just like which Omega is it + + align:start position:0% +one that just like which Omega is it + + + align:start position:0% +one that just like which Omega is it +when + + align:start position:0% +when + + + align:start position:0% +when +you're right oh yeah yeah right okay um + + align:start position:0% +you're right oh yeah yeah right okay um + + + align:start position:0% +you're right oh yeah yeah right okay um +let's anybody else a burn in question I + + align:start position:0% +let's anybody else a burn in question I + + + align:start position:0% +let's anybody else a burn in question I +think I'm actually going to start there + + align:start position:0% +think I'm actually going to start there + + + align:start position:0% +think I'm actually going to start there +we're going to spend just a minute on + + align:start position:0% +we're going to spend just a minute on + + + align:start position:0% +we're going to spend just a minute on +this on this + + align:start position:0% +this on this + + + align:start position:0% +this on this +one and I did + + align:start position:0% +one and I did + + + align:start position:0% +one and I did +did as an example problem yesterday in + + align:start position:0% +did as an example problem yesterday in + + + align:start position:0% +did as an example problem yesterday in +the + + align:start position:0% +the + + + align:start position:0% +the +lecture I basically did the same I had a + + align:start position:0% +lecture I basically did the same I had a + + + align:start position:0% +lecture I basically did the same I had a +rotor here could have a disc on it just + + align:start position:0% +rotor here could have a disc on it just + + + align:start position:0% +rotor here could have a disc on it just +to make it clear so this thing is + + align:start position:0% +to make it clear so this thing is + + + align:start position:0% +to make it clear so this thing is +rotating at some Omega 2 and it was on a + + align:start position:0% +rotating at some Omega 2 and it was on a + + + align:start position:0% +rotating at some Omega 2 and it was on a +merga + + align:start position:0% +merga + + + align:start position:0% +merga +round going at some omega + + align:start position:0% +round going at some omega + + + align:start position:0% +round going at some omega +1 and I'll pick a coordinate system here + + align:start position:0% +1 and I'll pick a coordinate system here + + + align:start position:0% +1 and I'll pick a coordinate system here +I think it was + + align:start position:0% + + + + align:start position:0% + +y x z that I wrote in the lecture notes + + align:start position:0% +y x z that I wrote in the lecture notes + + + align:start position:0% +y x z that I wrote in the lecture notes +and that's the rotating one and so you + + align:start position:0% +and that's the rotating one and so you + + + align:start position:0% +and that's the rotating one and so you +have an O and an a here and you have a + + align:start position:0% +have an O and an a here and you have a + + + align:start position:0% +have an O and an a here and you have a +fixed frame that + + align:start position:0% + + + + align:start position:0% + +uh but the Y one little one's attached + + align:start position:0% +uh but the Y one little one's attached + + + align:start position:0% +uh but the Y one little one's attached +to the platform it's going around okay + + align:start position:0% +to the platform it's going around okay + + + align:start position:0% +to the platform it's going around okay +so + + align:start position:0% +so + + + align:start position:0% +so +the rotation rate of the platform here + + align:start position:0% +the rotation rate of the platform here + + + align:start position:0% +the rotation rate of the platform here +is what + + align:start position:0% + + + + align:start position:0% + +in in magnitude and unit + + align:start position:0% +in in magnitude and unit + + + align:start position:0% +in in magnitude and unit +Vector + + align:start position:0% +Vector + + + align:start position:0% +Vector +pardon Omega + + align:start position:0% +pardon Omega + + + align:start position:0% +pardon Omega +one k hat and does it matter which K + + align:start position:0% +one k hat and does it matter which K + + + align:start position:0% +one k hat and does it matter which K +because they're both they're parallel + + align:start position:0% +because they're both they're parallel + + + align:start position:0% +because they're both they're parallel +the little K and the Big K okay what's + + align:start position:0% +the little K and the Big K okay what's + + + align:start position:0% +the little K and the Big K okay what's +the rotation rate of this shaft + + align:start position:0% + + + + align:start position:0% + +in terms of a magnitude and a unit + + align:start position:0% +in terms of a magnitude and a unit + + + align:start position:0% +in terms of a magnitude and a unit +Vector + + align:start position:0% +Vector + + + align:start position:0% +Vector +ler okay Omega 2 and I'll call it a J1 + + align:start position:0% +ler okay Omega 2 and I'll call it a J1 + + + align:start position:0% +ler okay Omega 2 and I'll call it a J1 +here well just because I it's hard to + + align:start position:0% +here well just because I it's hard to + + + align:start position:0% +here well just because I it's hard to +distinguish my handwriting on the board + + align:start position:0% +distinguish my handwriting on the board + + + align:start position:0% +distinguish my handwriting on the board +between the uppers and lowers so Z1S + + align:start position:0% +between the uppers and lowers so Z1S + + + align:start position:0% +between the uppers and lowers so Z1S +x1's okay so it's in the J1 direction + + align:start position:0% +x1's okay so it's in the J1 direction + + + align:start position:0% +x1's okay so it's in the J1 direction +right and I've just intentionally made + + align:start position:0% +right and I've just intentionally made + + + align:start position:0% +right and I've just intentionally made +it positive if it were in the other + + align:start position:0% +it positive if it were in the other + + + align:start position:0% +it positive if it were in the other +direction You' have a minus there okay + + align:start position:0% +direction You' have a minus there okay + + + align:start position:0% +direction You' have a minus there okay +so now now then + + align:start position:0% + + + + align:start position:0% + +um the problem asked for the time + + align:start position:0% +um the problem asked for the time + + + align:start position:0% +um the problem asked for the time +derivative of the + + align:start position:0% +derivative of the + + + align:start position:0% +derivative of the +rotation rate of + + align:start position:0% + + + + align:start position:0% + +the spinning the problem that you that + + align:start position:0% +the spinning the problem that you that + + + align:start position:0% +the spinning the problem that you that +in the homework this thing was actually + + align:start position:0% +in the homework this thing was actually + + + align:start position:0% +in the homework this thing was actually +inclined basically um + + align:start position:0% + + + + align:start position:0% + +it's it's easy to just say the the + + align:start position:0% + + + + align:start position:0% + +total rotation rate of the + + align:start position:0% +total rotation rate of the + + + align:start position:0% +total rotation rate of the +shaft let's get that settled first in a + + align:start position:0% +shaft let's get that settled first in a + + + align:start position:0% +shaft let's get that settled first in a +fixed inertial + + align:start position:0% +fixed inertial + + + align:start position:0% +fixed inertial +frame the total rotation rate of this is + + align:start position:0% +frame the total rotation rate of this is + + + align:start position:0% +frame the total rotation rate of this is +what yeah and you can sum rotation right + + align:start position:0% +what yeah and you can sum rotation right + + + align:start position:0% +what yeah and you can sum rotation right +so it's Omega 1 K hat plus Omega 2 + + align:start position:0% +so it's Omega 1 K hat plus Omega 2 + + + align:start position:0% +so it's Omega 1 K hat plus Omega 2 +J1 right + + align:start position:0% +J1 right + + + align:start position:0% +J1 right +and I want to take the time derivative + + align:start position:0% +and I want to take the time derivative + + + align:start position:0% +and I want to take the time derivative +of this Omega shaft + + align:start position:0% + + + + align:start position:0% + +total so it's D by DT of these things so + + align:start position:0% +total so it's D by DT of these things so + + + align:start position:0% +total so it's D by DT of these things so +I can start to do that so d by DT is in + + align:start position:0% +I can start to do that so d by DT is in + + + align:start position:0% +I can start to do that so d by DT is in +this case is K change in Direction no + + align:start position:0% +this case is K change in Direction no + + + align:start position:0% +this case is K change in Direction no +problem could that + + align:start position:0% +problem could that + + + align:start position:0% +problem could that +change could + + align:start position:0% +change could + + + align:start position:0% +change could +it yeah sure I it could be accelerating + + align:start position:0% +it yeah sure I it could be accelerating + + + align:start position:0% +it yeah sure I it could be accelerating +right if it is then you get a term here + + align:start position:0% +right if it is then you get a term here + + + align:start position:0% +right if it is then you get a term here +that comes from this one that would be + + align:start position:0% +that comes from this one that would be + + + align:start position:0% +that comes from this one that would be +an Omega 1. KH hat plus and now we need + + align:start position:0% +an Omega 1. KH hat plus and now we need + + + align:start position:0% +an Omega 1. KH hat plus and now we need +to take the derivative of this + + align:start position:0% +to take the derivative of this + + + align:start position:0% +to take the derivative of this +piece + + align:start position:0% +piece + + + align:start position:0% +piece +right um and that's now a rotating + + align:start position:0% +right um and that's now a rotating + + + align:start position:0% +right um and that's now a rotating +vector and we've said that the + + align:start position:0% +vector and we've said that the + + + align:start position:0% +vector and we've said that the +derivative of any rotating Vector + + align:start position:0% +derivative of any rotating Vector + + + align:start position:0% +derivative of any rotating Vector +dqdt is the derivative of t as if the + + align:start position:0% +dqdt is the derivative of t as if the + + + align:start position:0% +dqdt is the derivative of t as if the +rotation is zero you know it's is its + + align:start position:0% +rotation is zero you know it's is its + + + align:start position:0% +rotation is zero you know it's is its +magnitude increasing not its direction + + align:start position:0% +magnitude increasing not its direction + + + align:start position:0% +magnitude increasing not its direction +changing plus Omega cross q and I've + + align:start position:0% +changing plus Omega cross q and I've + + + align:start position:0% +changing plus Omega cross q and I've +intentionally left subscripts and + + align:start position:0% +intentionally left subscripts and + + + align:start position:0% +intentionally left subscripts and +superscripts off here because that's the + + align:start position:0% +superscripts off here because that's the + + + align:start position:0% +superscripts off here because that's the +issue here what what which ones go where + + align:start position:0% +issue here what what which ones go where + + + align:start position:0% +issue here what what which ones go where +right all right so this is what we are + + align:start position:0% +right all right so this is what we are + + + align:start position:0% +right all right so this is what we are +need to apply to taking that derivative + + align:start position:0% +need to apply to taking that derivative + + + align:start position:0% +need to apply to taking that derivative +we've taken like we took this derivative + + align:start position:0% +we've taken like we took this derivative + + + align:start position:0% +we've taken like we took this derivative +and found this + + align:start position:0% +and found this + + + align:start position:0% +and found this +term was what gave us the Omega 1. k and + + align:start position:0% +term was what gave us the Omega 1. k and + + + align:start position:0% +term was what gave us the Omega 1. k and +when taking derivative of this uh what + + align:start position:0% +when taking derivative of this uh what + + + align:start position:0% +when taking derivative of this uh what +was the answer + + align:start position:0% +was the answer + + + align:start position:0% +was the answer +here zero because the rotation rate is + + align:start position:0% +here zero because the rotation rate is + + + align:start position:0% +here zero because the rotation rate is +Omega 1 you're Crossing it Omega 1 K + + align:start position:0% +Omega 1 you're Crossing it Omega 1 K + + + align:start position:0% +Omega 1 you're Crossing it Omega 1 K +cross with Omega 1 K that goes to zero + + align:start position:0% +cross with Omega 1 K that goes to zero + + + align:start position:0% +cross with Omega 1 K that goes to zero +there's no change in Direction so we + + align:start position:0% +there's no change in Direction so we + + + align:start position:0% +there's no change in Direction so we +applied this formula once to this now + + align:start position:0% +applied this formula once to this now + + + align:start position:0% +applied this formula once to this now +we're going to apply this formula here + + align:start position:0% +we're going to apply this formula here + + + align:start position:0% +we're going to apply this formula here +so this I'll do it this way so this is + + align:start position:0% +so this I'll do it this way so this is + + + align:start position:0% +so this I'll do it this way so this is +term one + + align:start position:0% + + + + align:start position:0% + +so term one gave us this term two is + + align:start position:0% +so term one gave us this term two is + + + align:start position:0% +so term one gave us this term two is +going to give us this so apply what's + + align:start position:0% +going to give us this so apply what's + + + align:start position:0% +going to give us this so apply what's +the take this take the derivative of + + align:start position:0% +the take this take the derivative of + + + align:start position:0% +the take this take the derivative of +where' we go here this + + align:start position:0% +where' we go here this + + + align:start position:0% +where' we go here this +guy now when I say this is the it's a + + align:start position:0% +guy now when I say this is the it's a + + + align:start position:0% +guy now when I say this is the it's a +partial derivative of this + + align:start position:0% +partial derivative of this + + + align:start position:0% +partial derivative of this +thing ignoring the contribution from the + + align:start position:0% +thing ignoring the contribution from the + + + align:start position:0% +thing ignoring the contribution from the +change of + + align:start position:0% +change of + + + align:start position:0% +change of +Direction so it's as if some rotation + + align:start position:0% +Direction so it's as if some rotation + + + align:start position:0% +Direction so it's as if some rotation +were zero which rotation rate + + align:start position:0% +were zero which rotation rate + + + align:start position:0% +were zero which rotation rate +Omega one good so what is the answer to + + align:start position:0% +Omega one good so what is the answer to + + + align:start position:0% +Omega one good so what is the answer to +this piece of that + + align:start position:0% + + + + align:start position:0% + +derivative Omega + + align:start position:0% +derivative Omega + + + align:start position:0% +derivative Omega +2 dot what + + align:start position:0% +2 dot what + + + align:start position:0% +2 dot what +direction same direction right now we + + align:start position:0% +direction same direction right now we + + + align:start position:0% +direction same direction right now we +want to apply this piece and so now the + + align:start position:0% +want to apply this piece and so now the + + + align:start position:0% +want to apply this piece and so now the +question comes down plus some omega + + align:start position:0% +question comes down plus some omega + + + align:start position:0% +question comes down plus some omega +cross with the Q and what's the Q in + + align:start position:0% +cross with the Q and what's the Q in + + + align:start position:0% +cross with the Q and what's the Q in +this case + + align:start position:0% + + + + align:start position:0% + +two so this is Omega 2 J1 hat that + + align:start position:0% +two so this is Omega 2 J1 hat that + + + align:start position:0% +two so this is Omega 2 J1 hat that +that's the coming from here that's what + + align:start position:0% +that's the coming from here that's what + + + align:start position:0% +that's the coming from here that's what +this piece is so now we need what's + + align:start position:0% +this piece is so now we need what's + + + align:start position:0% +this piece is so now we need what's +crossed with + + align:start position:0% + + + + align:start position:0% + +it what now so this is I'm trying to + + align:start position:0% +it what now so this is I'm trying to + + + align:start position:0% +it what now so this is I'm trying to +think of a clear way to help + + align:start position:0% +think of a clear way to help + + + align:start position:0% +think of a clear way to help +you what is + + align:start position:0% +you what is + + + align:start position:0% +you what is +causing its direction to + + align:start position:0% + + + + align:start position:0% + +change right that's the one you care + + align:start position:0% +change right that's the one you care + + + align:start position:0% +change right that's the one you care +about what's causing its direction to + + align:start position:0% +about what's causing its direction to + + + align:start position:0% +about what's causing its direction to +change is causing this thing to come up + + align:start position:0% +change is causing this thing to come up + + + align:start position:0% +change is causing this thing to come up +and its direction is changing because + + align:start position:0% +and its direction is changing because + + + align:start position:0% +and its direction is changing because +the platforms are moving and so it's + + align:start position:0% +the platforms are moving and so it's + + + align:start position:0% +the platforms are moving and so it's +Omega + + align:start position:0% +Omega + + + align:start position:0% +Omega + + align:start position:0% + + + align:start position:0% +K cross J so K cross J gives + + align:start position:0% + + + + align:start position:0% + +you K cross J negative i1 in the + + align:start position:0% +you K cross J negative i1 in the + + + align:start position:0% +you K cross J negative i1 in the +rotating frame + + align:start position:0% +rotating frame + + + align:start position:0% +rotating frame +right this whole thing Omega 1 dot + + align:start position:0% +right this whole thing Omega 1 dot + + + align:start position:0% +right this whole thing Omega 1 dot +k plus Omega 2. + + align:start position:0% +k plus Omega 2. + + + align:start position:0% +k plus Omega 2. +J1 plus now this is a minus actually we + + align:start position:0% +J1 plus now this is a minus actually we + + + align:start position:0% +J1 plus now this is a minus actually we +said minus Omega + + align:start position:0% +said minus Omega + + + align:start position:0% +said minus Omega +1 Omega 2 K cross J is i1 + + align:start position:0% + + + + align:start position:0% + +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +finally how do you deal with the fact if + + align:start position:0% +finally how do you deal with the fact if + + + align:start position:0% +finally how do you deal with the fact if +I this rotor had been on an inclined + + align:start position:0% +I this rotor had been on an inclined + + + align:start position:0% +I this rotor had been on an inclined +angle some + + align:start position:0% +angle some + + + align:start position:0% +angle some +Fe which is now this is the exact + + align:start position:0% +Fe which is now this is the exact + + + align:start position:0% +Fe which is now this is the exact +problem that was on + + align:start position:0% +problem that was on + + + align:start position:0% +problem that was on +homework so propose a way of attacking + + align:start position:0% +homework so propose a way of attacking + + + align:start position:0% +homework so propose a way of attacking +that changes this problem just a little + + align:start position:0% +that changes this problem just a little + + + align:start position:0% +that changes this problem just a little +bit do you change the reference screen + + align:start position:0% +bit do you change the reference screen + + + align:start position:0% +bit do you change the reference screen +to + + align:start position:0% +to + + + align:start position:0% +to +no you don't change the reference frame + + align:start position:0% +no you don't change the reference frame + + + align:start position:0% +no you don't change the reference frame +you can you still have a coordinate + + align:start position:0% +you can you still have a coordinate + + + align:start position:0% +you can you still have a coordinate +system and this you know you work with + + align:start position:0% +system and this you know you work with + + + align:start position:0% +system and this you know you work with +the coordinates you got break components + + align:start position:0% +the coordinates you got break components + + + align:start position:0% +the coordinates you got break components +in which reference + + align:start position:0% + + + + align:start position:0% + +frame yeah the moving one that makes it + + align:start position:0% +frame yeah the moving one that makes it + + + align:start position:0% +frame yeah the moving one that makes it +easy because this thing now has it has a + + align:start position:0% +easy because this thing now has it has a + + + align:start position:0% +easy because this thing now has it has a +vector Omega 2 like that and you can + + align:start position:0% +vector Omega 2 like that and you can + + + align:start position:0% +vector Omega 2 like that and you can +break it up into a piece like that and a + + align:start position:0% +break it up into a piece like that and a + + + align:start position:0% +break it up into a piece like that and a +piece like that so now this and if this + + align:start position:0% +piece like that so now this and if this + + + align:start position:0% +piece like that so now this and if this +is Fe + + align:start position:0% +is Fe + + + align:start position:0% +is Fe +Omega 2 cine is this side right Omega 2 + + align:start position:0% +Omega 2 cine is this side right Omega 2 + + + align:start position:0% +Omega 2 cine is this side right Omega 2 +sin is that side what direction is + + align:start position:0% +sin is that side what direction is + + + align:start position:0% +sin is that side what direction is +it what's its unit Vector Direction this + + align:start position:0% +it what's its unit Vector Direction this + + + align:start position:0% +it what's its unit Vector Direction this +piece K okay and we're going to end up + + align:start position:0% +piece K okay and we're going to end up + + + align:start position:0% +piece K okay and we're going to end up +Crossing it + + align:start position:0% +Crossing it + + + align:start position:0% +Crossing it +with this term right so K cross + + align:start position:0% +with this term right so K cross + + + align:start position:0% +with this term right so K cross +K nothing so in fact this bit doesn't + + align:start position:0% +K nothing so in fact this bit doesn't + + + align:start position:0% +K nothing so in fact this bit doesn't +change in direction as it's rotating + + align:start position:0% +change in direction as it's rotating + + + align:start position:0% +change in direction as it's rotating +does it so it isn't going to contribute + + align:start position:0% +does it so it isn't going to contribute + + + align:start position:0% +does it so it isn't going to contribute +to that second term + + align:start position:0% +to that second term + + + align:start position:0% +to that second term +only piece you have to be concerned with + + align:start position:0% +only piece you have to be concerned with + + + align:start position:0% +only piece you have to be concerned with +is this one so down in here right in + + align:start position:0% +is this one so down in here right in + + + align:start position:0% +is this one so down in here right in +this part of it all you would do is say + + align:start position:0% +this part of it all you would do is say + + + align:start position:0% +this part of it all you would do is say +Omega 1 K cross and now you just put in + + align:start position:0% +Omega 1 K cross and now you just put in + + + align:start position:0% +Omega 1 K cross and now you just put in +the + + align:start position:0% +the + + + align:start position:0% +the +full Q full Omega 2 which is Omega 2 sin + + align:start position:0% +full Q full Omega 2 which is Omega 2 sin + + + align:start position:0% +full Q full Omega 2 which is Omega 2 sin +K plus Omega 2 cosine sorry about the + + align:start position:0% +K plus Omega 2 cosine sorry about the + + + align:start position:0% +K plus Omega 2 cosine sorry about the +writing here and you know do the cross + + align:start position:0% +writing here and you know do the cross + + + align:start position:0% +writing here and you know do the cross +product you find out that term + + align:start position:0% +product you find out that term + + + align:start position:0% +product you find out that term +disappears and you get an Omega 1 Omega + + align:start position:0% +disappears and you get an Omega 1 Omega + + + align:start position:0% +disappears and you get an Omega 1 Omega + + align:start position:0% + + + align:start position:0% +cosine and this term here this is still + + align:start position:0% +cosine and this term here this is still + + + align:start position:0% +cosine and this term here this is still +the answer but you end up with a cosine + + align:start position:0% +the answer but you end up with a cosine + + + align:start position:0% +the answer but you end up with a cosine +V in + + align:start position:0% +V in + + + align:start position:0% +V in +here because it's just the component of + + align:start position:0% +here because it's just the component of + + + align:start position:0% +here because it's just the component of +Omega 2 that's in the J1 Direction now + + align:start position:0% +Omega 2 that's in the J1 Direction now + + + align:start position:0% +Omega 2 that's in the J1 Direction now +that contributes okay great good that + + align:start position:0% +that contributes okay great good that + + + align:start position:0% +that contributes okay great good that +help all right uh let's I'll leave this + + align:start position:0% +help all right uh let's I'll leave this + + + align:start position:0% +help all right uh let's I'll leave this +let's get on to the problem for the day + + align:start position:0% +let's get on to the problem for the day + + + align:start position:0% +let's get on to the problem for the day +problem for the + + align:start position:0% + + + + align:start position:0% + +day is you've got + + align:start position:0% +day is you've got + + + align:start position:0% +day is you've got +a rotating arm have a mass sitting on it + + align:start position:0% +a rotating arm have a mass sitting on it + + + align:start position:0% +a rotating arm have a mass sitting on it +the arm can is rotating at some rotation + + align:start position:0% +the arm can is rotating at some rotation + + + align:start position:0% +the arm can is rotating at some rotation +rate Omega might have an + + align:start position:0% +rate Omega might have an + + + align:start position:0% +rate Omega might have an +acceleration uh Omega dot Theta double + + align:start position:0% +acceleration uh Omega dot Theta double + + + align:start position:0% +acceleration uh Omega dot Theta double +dot + + align:start position:0% +dot + + + align:start position:0% +dot +um this mask and slide + + align:start position:0% + + + + align:start position:0% + +so the problem is this thing is + + align:start position:0% + + + + align:start position:0% + +uh we I'll start here so it's rotating + + align:start position:0% +uh we I'll start here so it's rotating + + + align:start position:0% +uh we I'll start here so it's rotating +like this and eventually the thing + + align:start position:0% +like this and eventually the thing + + + align:start position:0% +like this and eventually the thing +begins to slide and in fact if I do it + + align:start position:0% +begins to slide and in fact if I do it + + + align:start position:0% +begins to slide and in fact if I do it +this actually works a little better + + align:start position:0% +this actually works a little better + + + align:start position:0% +this actually works a little better +here because I have a little tiny groove + + align:start position:0% +here because I have a little tiny groove + + + align:start position:0% +here because I have a little tiny groove +in this it helps a little bit so it's + + align:start position:0% +in this it helps a little bit so it's + + + align:start position:0% +in this it helps a little bit so it's +rotating like that eventually begins to + + align:start position:0% +rotating like that eventually begins to + + + align:start position:0% +rotating like that eventually begins to +slide and if the rotation rate is slow + + align:start position:0% +slide and if the rotation rate is slow + + + align:start position:0% +slide and if the rotation rate is slow +it slides down if I made the rotation + + align:start position:0% +it slides down if I made the rotation + + + align:start position:0% +it slides down if I made the rotation +rate fast enough slides + + align:start position:0% +rate fast enough slides + + + align:start position:0% +rate fast enough slides +up right and and the angle at which it + + align:start position:0% +up right and and the angle at which it + + + align:start position:0% +up right and and the angle at which it +happens clearly depends on rotation + + align:start position:0% +happens clearly depends on rotation + + + align:start position:0% +happens clearly depends on rotation +rates accelerations the angle friction + + align:start position:0% +rates accelerations the angle friction + + + align:start position:0% +rates accelerations the angle friction +coefficients and things of that sort so + + align:start position:0% +coefficients and things of that sort so + + + align:start position:0% +coefficients and things of that sort so +what I want you to start with is here's + + align:start position:0% +what I want you to start with is here's + + + align:start position:0% +what I want you to start with is here's +basically a drawing of + + align:start position:0% +basically a drawing of + + + align:start position:0% +basically a drawing of +it + + align:start position:0% + + + + align:start position:0% + +and don't want to give you any excess + + align:start position:0% +and don't want to give you any excess + + + align:start position:0% +and don't want to give you any excess +information what I want you to do is is + + align:start position:0% +information what I want you to do is is + + + align:start position:0% +information what I want you to do is is +each by yourselves take just a minute + + align:start position:0% +each by yourselves take just a minute + + + align:start position:0% +each by yourselves take just a minute +and draw a free body diagram of this + + align:start position:0% +and draw a free body diagram of this + + + align:start position:0% +and draw a free body diagram of this +problem and then after that I'm going to + + align:start position:0% +problem and then after that I'm going to + + + align:start position:0% +problem and then after that I'm going to +have you get in groups and improve on it + + align:start position:0% +have you get in groups and improve on it + + + align:start position:0% +have you get in groups and improve on it +but start yourself draw a free body + + align:start position:0% +but start yourself draw a free body + + + align:start position:0% +but start yourself draw a free body +diagram that uh will describe this Mass + + align:start position:0% +diagram that uh will describe this Mass + + + align:start position:0% +diagram that uh will describe this Mass +on this thing + + align:start position:0% + + + + align:start position:0% + +plank okay so now even we've got it got + + align:start position:0% +plank okay so now even we've got it got + + + align:start position:0% +plank okay so now even we've got it got +a sketch with a little free B diagram on + + align:start position:0% +a sketch with a little free B diagram on + + + align:start position:0% +a sketch with a little free B diagram on +it what I want you to do now we're going + + align:start position:0% +it what I want you to do now we're going + + + align:start position:0% +it what I want you to do now we're going +to use do this two or three times to + + align:start position:0% +to use do this two or three times to + + + align:start position:0% +to use do this two or three times to +today get in groups of four or five here + + align:start position:0% +today get in groups of four or five here + + + align:start position:0% +today get in groups of four or five here +compare notes and come up with a group + + align:start position:0% +compare notes and come up with a group + + + align:start position:0% +compare notes and come up with a group +free body + + align:start position:0% +free body + + + align:start position:0% +free body +diagram so you're pretty you're you're + + align:start position:0% +diagram so you're pretty you're you're + + + align:start position:0% +diagram so you're pretty you're you're +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +close + + align:start position:0% +close + + + align:start position:0% +close +um let me look where was your guys + + align:start position:0% +um let me look where was your guys + + + align:start position:0% +um let me look where was your guys +solution + + align:start position:0% + + + + align:start position:0% + +again there's may be about Good As It + + align:start position:0% + + + + align:start position:0% + +Gets so + + align:start position:0% + + + + align:start position:0% + +here's our Mass I think everybody had an + + align:start position:0% +here's our Mass I think everybody had an + + + align:start position:0% +here's our Mass I think everybody had an +mg almost everybody had + + align:start position:0% +mg almost everybody had + + + align:start position:0% +mg almost everybody had +a normal + + align:start position:0% +a normal + + + align:start position:0% +a normal +force everybody had a friction Force + + align:start position:0% +force everybody had a friction Force + + + align:start position:0% +force everybody had a friction Force +some discussion about what direction the + + align:start position:0% +some discussion about what direction the + + + align:start position:0% +some discussion about what direction the +friction Force ought to be in I'll draw + + align:start position:0% +friction Force ought to be in I'll draw + + + align:start position:0% +friction Force ought to be in I'll draw +it + + align:start position:0% +it + + + align:start position:0% +it +uh uphill here and I'll call it f t for + + align:start position:0% +uh uphill here and I'll call it f t for + + + align:start position:0% +uh uphill here and I'll call it f t for +tangential here and + + align:start position:0% +tangential here and + + + align:start position:0% +tangential here and +so some had about that much there's a + + align:start position:0% +so some had about that much there's a + + + align:start position:0% +so some had about that much there's a +very important missing + + align:start position:0% +very important missing + + + align:start position:0% +very important missing +piece which actually several groups + + align:start position:0% +piece which actually several groups + + + align:start position:0% +piece which actually several groups +had what is + + align:start position:0% +had what is + + + align:start position:0% +had what is +that let me guess what I'm what what's + + align:start position:0% +that let me guess what I'm what what's + + + align:start position:0% +that let me guess what I'm what what's +on your group three of your groups had + + align:start position:0% +on your group three of your groups had + + + align:start position:0% +on your group three of your groups had +something on here that I don't have up + + align:start position:0% +something on here that I don't have up + + + align:start position:0% +something on here that I don't have up +here + + align:start position:0% +here + + + align:start position:0% +here +yet I hear coordinates got to you really + + align:start position:0% +yet I hear coordinates got to you really + + + align:start position:0% +yet I hear coordinates got to you really +need to this one you can almost get away + + align:start position:0% +need to this one you can almost get away + + + align:start position:0% +need to this one you can almost get away +with not putting in the coordinate + + align:start position:0% +with not putting in the coordinate + + + align:start position:0% +with not putting in the coordinate +system first but you usually need to + + align:start position:0% +system first but you usually need to + + + align:start position:0% +system first but you usually need to +have a coordinate system in order to + + align:start position:0% +have a coordinate system in order to + + + align:start position:0% +have a coordinate system in order to +determine the direction of the + + align:start position:0% +determine the direction of the + + + align:start position:0% +determine the direction of the +forces okay we'll get to that in a + + align:start position:0% +forces okay we'll get to that in a + + + align:start position:0% +forces okay we'll get to that in a +second + + align:start position:0% +second + + + align:start position:0% +second +so uh everybody that I saw had written + + align:start position:0% +so uh everybody that I saw had written + + + align:start position:0% +so uh everybody that I saw had written +down I saw a number of little XYZ frames + + align:start position:0% +down I saw a number of little XYZ frames + + + align:start position:0% +down I saw a number of little XYZ frames +sitting out here like that uh maybe one + + align:start position:0% +sitting out here like that uh maybe one + + + align:start position:0% +sitting out here like that uh maybe one +that was lined up not sure most not most + + align:start position:0% +that was lined up not sure most not most + + + align:start position:0% +that was lined up not sure most not most +like + + align:start position:0% +like + + + align:start position:0% +like +this is polar coordinates a good choice + + align:start position:0% +this is polar coordinates a good choice + + + align:start position:0% +this is polar coordinates a good choice +for this problem why not + + align:start position:0% + + + + align:start position:0% + +so the question is whether or not R + + align:start position:0% +so the question is whether or not R + + + align:start position:0% +so the question is whether or not R +Theta and Z can completely describe the + + align:start position:0% +Theta and Z can completely describe the + + + align:start position:0% +Theta and Z can completely describe the +motion in the problem you have + + align:start position:0% +motion in the problem you have + + + align:start position:0% +motion in the problem you have +tangential forces so it's better if use + + align:start position:0% +tangential forces so it's better if use + + + align:start position:0% +tangential forces so it's better if use +rectangular the radius is the radius is + + align:start position:0% +rectangular the radius is the radius is + + + align:start position:0% +rectangular the radius is the radius is +changing but that's known as r + + align:start position:0% +changing but that's known as r + + + align:start position:0% +changing but that's known as r +dot r dot can handle the motion of this + + align:start position:0% +dot r dot can handle the motion of this + + + align:start position:0% +dot r dot can handle the motion of this +this way our double dot can handle + + align:start position:0% +this way our double dot can handle + + + align:start position:0% +this way our double dot can handle +accelerations this way Theta dot can + + align:start position:0% +accelerations this way Theta dot can + + + align:start position:0% +accelerations this way Theta dot can +handle this motion Theta double dot can + + align:start position:0% +handle this motion Theta double dot can + + + align:start position:0% +handle this motion Theta double dot can +handle that acceleration actually and is + + align:start position:0% +handle that acceleration actually and is + + + align:start position:0% +handle that acceleration actually and is +there any Z motion or Z forces no + + align:start position:0% +there any Z motion or Z forces no + + + align:start position:0% +there any Z motion or Z forces no +actually say polar coordinates will + + align:start position:0% +actually say polar coordinates will + + + align:start position:0% +actually say polar coordinates will +actually work here just fine so you + + align:start position:0% +actually work here just fine so you + + + align:start position:0% +actually work here just fine so you +definitely have to pick a coordinate + + align:start position:0% +definitely have to pick a coordinate + + + align:start position:0% +definitely have to pick a coordinate +system and so we're going to use have an + + align:start position:0% +system and so we're going to use have an + + + align:start position:0% +system and so we're going to use have an +R hat system and Theta hat in this + + align:start position:0% +R hat system and Theta hat in this + + + align:start position:0% +R hat system and Theta hat in this +direction because in this problem you + + align:start position:0% +direction because in this problem you + + + align:start position:0% +direction because in this problem you +really want to have a whether use X and + + align:start position:0% +really want to have a whether use X and + + + align:start position:0% +really want to have a whether use X and +Y as a X and Y as a rotating frame here + + align:start position:0% +Y as a X and Y as a rotating frame here + + + align:start position:0% +Y as a X and Y as a rotating frame here +or R Theta you want to pick your + + align:start position:0% +or R Theta you want to pick your + + + align:start position:0% +or R Theta you want to pick your +coordinate system so that these things + + align:start position:0% +coordinate system so that these things + + + align:start position:0% +coordinate system so that these things +break down easily in this case the + + align:start position:0% +break down easily in this case the + + + align:start position:0% +break down easily in this case the +normal equation will be in the Theta hat + + align:start position:0% +normal equation will be in the Theta hat + + + align:start position:0% +normal equation will be in the Theta hat +Direction the sliding direction will be + + align:start position:0% +Direction the sliding direction will be + + + align:start position:0% +Direction the sliding direction will be +in just one unit Vector Direction so you + + align:start position:0% +in just one unit Vector Direction so you + + + align:start position:0% +in just one unit Vector Direction so you +don't have multiple components in this + + align:start position:0% +don't have multiple components in this + + + align:start position:0% +don't have multiple components in this +direction if you use that coordinate + + align:start position:0% +direction if you use that coordinate + + + align:start position:0% +direction if you use that coordinate +system to describe this motion you have + + align:start position:0% +system to describe this motion you have + + + align:start position:0% +system to describe this motion you have +X and Y terms makes it harder so this is + + align:start position:0% +X and Y terms makes it harder so this is + + + align:start position:0% +X and Y terms makes it harder so this is +a pretty good coordinate system to use + + align:start position:0% +a pretty good coordinate system to use + + + align:start position:0% +a pretty good coordinate system to use +so that's a really important missing + + align:start position:0% +so that's a really important missing + + + align:start position:0% +so that's a really important missing +piece is the coordinate system if you + + align:start position:0% +piece is the coordinate system if you + + + align:start position:0% +piece is the coordinate system if you +don't have + + align:start position:0% +don't have + + + align:start position:0% +don't have +it and as an aside about free body + + align:start position:0% + + + + align:start position:0% + +diagrams free body diagrams right except + + align:start position:0% +diagrams free body diagrams right except + + + align:start position:0% +diagrams free body diagrams right except +my D is turned around + + align:start position:0% + + + + align:start position:0% + +um how do you know that the friction + + align:start position:0% +um how do you know that the friction + + + align:start position:0% +um how do you know that the friction +force is in that direction you had to + + align:start position:0% +force is in that direction you had to + + + align:start position:0% +force is in that direction you had to +assume + + align:start position:0% + + + + align:start position:0% + +something you actually kind this such a + + align:start position:0% +something you actually kind this such a + + + align:start position:0% +something you actually kind this such a +trivial problem you can kind of figure + + align:start position:0% +trivial problem you can kind of figure + + + align:start position:0% +trivial problem you can kind of figure +out in your head I gave the + + align:start position:0% +out in your head I gave the + + + align:start position:0% +out in your head I gave the +demonstration it slid down but also I + + align:start position:0% +demonstration it slid down but also I + + + align:start position:0% +demonstration it slid down but also I +said you do it fast enough it goes up + + align:start position:0% +said you do it fast enough it goes up + + + align:start position:0% +said you do it fast enough it goes up +right so you don't really know so you + + align:start position:0% +right so you don't really know so you + + + align:start position:0% +right so you don't really know so you +have to you have to have made assumption + + align:start position:0% +have to you have to have made assumption + + + align:start position:0% +have to you have to have made assumption +about about it and Norm so the general + + align:start position:0% +about about it and Norm so the general + + + align:start position:0% +about about it and Norm so the general +rule is to + + align:start position:0% + + + + align:start position:0% + +assign sign or + + align:start position:0% + + + + align:start position:0% + +assume + + align:start position:0% + + + + align:start position:0% + +positive values + + align:start position:0% +positive values + + + align:start position:0% +positive values +for + + align:start position:0% + + + + align:start position:0% + +all motions + + align:start position:0% +all motions + + + align:start position:0% +all motions +and then you + + align:start position:0% + + + + align:start position:0% + +deduce the direction of + + align:start position:0% + + + + align:start position:0% + +forces and I'll take a quick another + + align:start position:0% +forces and I'll take a quick another + + + align:start position:0% +forces and I'll take a quick another +quick aside here to drive to illustrate + + align:start position:0% +quick aside here to drive to illustrate + + + align:start position:0% +quick aside here to drive to illustrate +this in a problem that's works better + + align:start position:0% +this in a problem that's works better + + + align:start position:0% +this in a problem that's works better +than the current one for + + align:start position:0% +than the current one for + + + align:start position:0% +than the current one for +this an obvious coordinate system for + + align:start position:0% +this an obvious coordinate system for + + + align:start position:0% +this an obvious coordinate system for +this little Mass on rollers ntial frame + + align:start position:0% +this little Mass on rollers ntial frame + + + align:start position:0% +this little Mass on rollers ntial frame +here's a an + + align:start position:0% +here's a an + + + align:start position:0% +here's a an +X and I asked you to do a free body + + align:start position:0% +X and I asked you to do a free body + + + align:start position:0% +X and I asked you to do a free body +diagram of + + align:start position:0% +diagram of + + + align:start position:0% +diagram of +that well you would show me a normal + + align:start position:0% +that well you would show me a normal + + + align:start position:0% +that well you would show me a normal +force you'd show me an mg but now I ask + + align:start position:0% +force you'd show me an mg but now I ask + + + align:start position:0% +force you'd show me an mg but now I ask +you to tell me the direction to draw the + + align:start position:0% +you to tell me the direction to draw the + + + align:start position:0% +you to tell me the direction to draw the +spring + + align:start position:0% + + + + align:start position:0% + +Force so if you just if you if you adopt + + align:start position:0% +Force so if you just if you if you adopt + + + align:start position:0% +Force so if you just if you if you adopt +the rule that for each body you're + + align:start position:0% +the rule that for each body you're + + + align:start position:0% +the rule that for each body you're +working with you assume that it has + + align:start position:0% +working with you assume that it has + + + align:start position:0% +working with you assume that it has +positive X positive x dot positive y + + align:start position:0% +positive X positive x dot positive y + + + align:start position:0% +positive X positive x dot positive y +positive y dot then you can deduce what + + align:start position:0% +positive y dot then you can deduce what + + + align:start position:0% +positive y dot then you can deduce what +direction of the forces would result so + + align:start position:0% +direction of the forces would result so + + + align:start position:0% +direction of the forces would result so +so in this case the only motion that + + align:start position:0% +so in this case the only motion that + + + align:start position:0% +so in this case the only motion that +generates a force up here is + + align:start position:0% + + + + align:start position:0% + +what is X x dot xou dot only for only + + align:start position:0% +what is X x dot xou dot only for only + + + align:start position:0% +what is X x dot xou dot only for only +motion that'll generate a force is + + align:start position:0% +motion that'll generate a force is + + + align:start position:0% +motion that'll generate a force is +displacement because it generates a + + align:start position:0% +displacement because it generates a + + + align:start position:0% +displacement because it generates a +force + + align:start position:0% +force + + + align:start position:0% +force +where in the spring if they add a + + align:start position:0% +where in the spring if they add a + + + align:start position:0% +where in the spring if they add a +dashbot here then velocity generates a + + align:start position:0% +dashbot here then velocity generates a + + + align:start position:0% +dashbot here then velocity generates a +force too but displacement if you assume + + align:start position:0% +force too but displacement if you assume + + + align:start position:0% +force too but displacement if you assume +the displacement is + + align:start position:0% + + + + align:start position:0% + +positive then which direction is the + + align:start position:0% +positive then which direction is the + + + align:start position:0% +positive then which direction is the +spring Force okay so then you have + + align:start position:0% +spring Force okay so then you have + + + align:start position:0% +spring Force okay so then you have +spring Force this way and that's value + + align:start position:0% +spring Force this way and that's value + + + align:start position:0% +spring Force this way and that's value +KX and when you write it into equation + + align:start position:0% +KX and when you write it into equation + + + align:start position:0% +KX and when you write it into equation +of motion youd put a minus sign to + + align:start position:0% +of motion youd put a minus sign to + + + align:start position:0% +of motion youd put a minus sign to +account for the direction of that + + align:start position:0% +account for the direction of that + + + align:start position:0% +account for the direction of that +Arrow okay so in this problem we kind of + + align:start position:0% +Arrow okay so in this problem we kind of + + + align:start position:0% +Arrow okay so in this problem we kind of +and you know if you ever do it wrong if + + align:start position:0% +and you know if you ever do it wrong if + + + align:start position:0% +and you know if you ever do it wrong if +you pick this direction wrong what + + align:start position:0% +you pick this direction wrong what + + + align:start position:0% +you pick this direction wrong what +happens in the answer answer well you + + align:start position:0% +happens in the answer answer well you + + + align:start position:0% +happens in the answer answer well you +still get the right answer if you're + + align:start position:0% +still get the right answer if you're + + + align:start position:0% +still get the right answer if you're +consistent it'll just you'll get another + + align:start position:0% +consistent it'll just you'll get another + + + align:start position:0% +consistent it'll just you'll get another +negative sign popping up to fix it + + align:start position:0% +negative sign popping up to fix it + + + align:start position:0% +negative sign popping up to fix it +okay next so that's I think we're on in + + align:start position:0% +okay next so that's I think we're on in + + + align:start position:0% +okay next so that's I think we're on in +good shape now I'm going to draw the + + align:start position:0% +good shape now I'm going to draw the + + + align:start position:0% +good shape now I'm going to draw the +friction Force uphill because I'm going + + align:start position:0% +friction Force uphill because I'm going + + + align:start position:0% +friction Force uphill because I'm going +to assume this thing's going to slide + + align:start position:0% +to assume this thing's going to slide + + + align:start position:0% +to assume this thing's going to slide +down and I'm going to simplify the + + align:start position:0% +down and I'm going to simplify the + + + align:start position:0% +down and I'm going to simplify the +problem a little bit for you and I'm + + align:start position:0% +problem a little bit for you and I'm + + + align:start position:0% +problem a little bit for you and I'm +going to say that there's no angular + + align:start position:0% +going to say that there's no angular + + + align:start position:0% +going to say that there's no angular +acceleration constant angular + + align:start position:0% +acceleration constant angular + + + align:start position:0% +acceleration constant angular +rate the distance that the mass starts + + align:start position:0% +rate the distance that the mass starts + + + align:start position:0% +rate the distance that the mass starts +off up the slope is at 1 and 1/2 + + align:start position:0% +off up the slope is at 1 and 1/2 + + + align:start position:0% +off up the slope is at 1 and 1/2 +ft the N so it's going up like this and + + align:start position:0% +ft the N so it's going up like this and + + + align:start position:0% +ft the N so it's going up like this and +it eventually reaches 50° and at 50° it + + align:start position:0% +it eventually reaches 50° and at 50° it + + + align:start position:0% +it eventually reaches 50° and at 50° it +begins to slide + + align:start position:0% +begins to slide + + + align:start position:0% +begins to slide +downhill so it's going up a constant + + align:start position:0% +downhill so it's going up a constant + + + align:start position:0% +downhill so it's going up a constant +rate and starts a slide point is so + + align:start position:0% +rate and starts a slide point is so + + + align:start position:0% +rate and starts a slide point is so +there must be some friction coefficient + + align:start position:0% +there must be some friction coefficient + + + align:start position:0% +there must be some friction coefficient +that provides a system with the property + + align:start position:0% +that provides a system with the property + + + align:start position:0% +that provides a system with the property +such that it slides at 50° so the + + align:start position:0% +such that it slides at 50° so the + + + align:start position:0% +such that it slides at 50° so the +problem here is to find the coefficient + + align:start position:0% +problem here is to find the coefficient + + + align:start position:0% +problem here is to find the coefficient +of + + align:start position:0% +of + + + align:start position:0% +of +friction so now you're in your groups + + align:start position:0% +friction so now you're in your groups + + + align:start position:0% +friction so now you're in your groups +solve the problem and I what I really + + align:start position:0% +solve the problem and I what I really + + + align:start position:0% +solve the problem and I what I really +want you to do is to come up with an + + align:start position:0% +want you to do is to come up with an + + + align:start position:0% +want you to do is to come up with an +expression mu equals in variables and + + align:start position:0% +expression mu equals in variables and + + + align:start position:0% +expression mu equals in variables and +constants don't get don't get around + + align:start position:0% +constants don't get don't get around + + + align:start position:0% +constants don't get don't get around +don't bother plugging in numbers in + + align:start position:0% + + + + align:start position:0% + +that and I see well if you're + + align:start position:0% +that and I see well if you're + + + align:start position:0% +that and I see well if you're +comfortable using polar coordinates + + align:start position:0% +comfortable using polar coordinates + + + align:start position:0% +comfortable using polar coordinates +that' be the way to do it but you need + + align:start position:0% +that' be the way to do it but you need + + + align:start position:0% +that' be the way to do it but you need +to write some equations now and I + + align:start position:0% +to write some equations now and I + + + align:start position:0% +to write some equations now and I +suggest you need to think in terms of + + align:start position:0% +suggest you need to think in terms of + + + align:start position:0% +suggest you need to think in terms of +equations of motion I think it's time to + + align:start position:0% +equations of motion I think it's time to + + + align:start position:0% +equations of motion I think it's time to +uh to go to back to come back together + + align:start position:0% +uh to go to back to come back together + + + align:start position:0% +uh to go to back to come back together +here and work on this + + align:start position:0% +here and work on this + + + align:start position:0% +here and work on this +um two three four groups are sort of + + align:start position:0% +um two three four groups are sort of + + + align:start position:0% +um two three four groups are sort of +struggling with this and it's because + + align:start position:0% +struggling with this and it's because + + + align:start position:0% +struggling with this and it's because +you're + + align:start position:0% +you're + + + align:start position:0% +you're +not really going to first principles and + + align:start position:0% +not really going to first principles and + + + align:start position:0% +not really going to first principles and +doing the problem step by step you're + + align:start position:0% +doing the problem step by step you're + + + align:start position:0% +doing the problem step by step you're +sort of jumping to the answer because + + align:start position:0% +sort of jumping to the answer because + + + align:start position:0% +sort of jumping to the answer because +it's a trivial simple Mickey Mouse + + align:start position:0% +it's a trivial simple Mickey Mouse + + + align:start position:0% +it's a trivial simple Mickey Mouse +problem that you did in high school + + align:start position:0% +problem that you did in high school + + + align:start position:0% +problem that you did in high school +and so you're I'm I'm kind of pounding + + align:start position:0% +and so you're I'm I'm kind of pounding + + + align:start position:0% +and so you're I'm I'm kind of pounding +on you a little bit we give you simple + + align:start position:0% +on you a little bit we give you simple + + + align:start position:0% +on you a little bit we give you simple +problems so we can do them in a short + + align:start position:0% +problems so we can do them in a short + + + align:start position:0% +problems so we can do them in a short +period of time but you need to learn to + + align:start position:0% +period of time but you need to learn to + + + align:start position:0% +period of time but you need to learn to +do them in the rigorous way so that you + + align:start position:0% +do them in the rigorous way so that you + + + align:start position:0% +do them in the rigorous way so that you +learn the real fundamental stuff that + + align:start position:0% +learn the real fundamental stuff that + + + align:start position:0% +learn the real fundamental stuff that +you have to know this this so none of + + align:start position:0% +you have to know this this so none of + + + align:start position:0% +you have to know this this so none of +you you all have sort of thinking about + + align:start position:0% +you you all have sort of thinking about + + + align:start position:0% +you you all have sort of thinking about +well we got some of forces here we got + + align:start position:0% +well we got some of forces here we got + + + align:start position:0% +well we got some of forces here we got +an acceleration there but nobody is just + + align:start position:0% +an acceleration there but nobody is just + + + align:start position:0% +an acceleration there but nobody is just +sitting down and saying that some of the + + align:start position:0% +sitting down and saying that some of the + + + align:start position:0% +sitting down and saying that some of the +forces + + align:start position:0% +forces + + + align:start position:0% +forces +is equal to the mass times the + + align:start position:0% +is equal to the mass times the + + + align:start position:0% +is equal to the mass times the +acceleration and working the problem + + align:start position:0% + + + + align:start position:0% + +out okay bad dog you + + align:start position:0% +out okay bad dog you + + + align:start position:0% +out okay bad dog you +know just because this problem is almost + + align:start position:0% +know just because this problem is almost + + + align:start position:0% +know just because this problem is almost +a Statics problem doesn't mean you when + + align:start position:0% +a Statics problem doesn't mean you when + + + align:start position:0% +a Statics problem doesn't mean you when +you have Statics when things are Statics + + align:start position:0% +you have Statics when things are Statics + + + align:start position:0% +you have Statics when things are Statics +problems it just means the acceleration + + align:start position:0% +problems it just means the acceleration + + + align:start position:0% +problems it just means the acceleration +goes to zero and the sum of the forces + + align:start position:0% +goes to zero and the sum of the forces + + + align:start position:0% +goes to zero and the sum of the forces +is now zero and you solve the problem + + align:start position:0% +is now zero and you solve the problem + + + align:start position:0% +is now zero and you solve the problem +start with Newton's this case it's + + align:start position:0% +start with Newton's this case it's + + + align:start position:0% +start with Newton's this case it's +Newton's second law + + align:start position:0% +Newton's second law + + + align:start position:0% +Newton's second law +uh it helps to know an expression for + + align:start position:0% +uh it helps to know an expression for + + + align:start position:0% +uh it helps to know an expression for +acceleration so you don't have to grind + + align:start position:0% +acceleration so you don't have to grind + + + align:start position:0% +acceleration so you don't have to grind +it out so we're a polar coordinates + + align:start position:0% +it out so we're a polar coordinates + + + align:start position:0% +it out so we're a polar coordinates +works pretty well in this problem and I + + align:start position:0% +works pretty well in this problem and I + + + align:start position:0% +works pretty well in this problem and I +want want you to commit to memory two + + align:start position:0% +want want you to commit to memory two + + + align:start position:0% +want want you to commit to memory two +acceleration equations one in polar + + align:start position:0% +acceleration equations one in polar + + + align:start position:0% +acceleration equations one in polar +coordinates and the one the general + + align:start position:0% +coordinates and the one the general + + + align:start position:0% +coordinates and the one the general +Vector one so in polar coordinates the + + align:start position:0% +Vector one so in polar coordinates the + + + align:start position:0% +Vector one so in polar coordinates the +one that I memorize is a with respect to + + align:start position:0% +one that I memorize is a with respect to + + + align:start position:0% +one that I memorize is a with respect to +o + + align:start position:0% +o + + + align:start position:0% +o +plus r + + align:start position:0% + + + + align:start position:0% + +dot- R Theta dot SAR R + + align:start position:0% +dot- R Theta dot SAR R + + + align:start position:0% +dot- R Theta dot SAR R +hat plus r Theta dble dot + 2 + + align:start position:0% +hat plus r Theta dble dot + 2 + + + align:start position:0% +hat plus r Theta dble dot + 2 +Omega r + + align:start position:0% +Omega r + + + align:start position:0% +Omega r +dot Theta hat coris or laran centripetal + + align:start position:0% +dot Theta hat coris or laran centripetal + + + align:start position:0% +dot Theta hat coris or laran centripetal +and your linear acceleration what's this + + align:start position:0% +and your linear acceleration what's this + + + align:start position:0% +and your linear acceleration what's this +term why is it what's it doing there + + align:start position:0% +term why is it what's it doing there + + + align:start position:0% +term why is it what's it doing there +because it + + align:start position:0% + + + + align:start position:0% + +yeah but the reason I remember it is we + + align:start position:0% +yeah but the reason I remember it is we + + + align:start position:0% +yeah but the reason I remember it is we +we we in this subject in this course we + + align:start position:0% +we we in this subject in this course we + + + align:start position:0% +we we in this subject in this course we +break down every Dynamics problem we're + + align:start position:0% +break down every Dynamics problem we're + + + align:start position:0% +break down every Dynamics problem we're +confronted with into sub problems that + + align:start position:0% +confronted with into sub problems that + + + align:start position:0% +confronted with into sub problems that +can be solved as the sum of a + + align:start position:0% +can be solved as the sum of a + + + align:start position:0% +can be solved as the sum of a +translation of a body plus a + + align:start position:0% +translation of a body plus a + + + align:start position:0% +translation of a body plus a +rotation and so this expression allows + + align:start position:0% +rotation and so this expression allows + + + align:start position:0% +rotation and so this expression allows +you to write down the acceleration of a + + align:start position:0% +you to write down the acceleration of a + + + align:start position:0% +you to write down the acceleration of a +point on a body which is both translated + + align:start position:0% +point on a body which is both translated + + + align:start position:0% +point on a body which is both translated +in and + + align:start position:0% +in and + + + align:start position:0% +in and +rotating what this term accounts + + align:start position:0% + + + + align:start position:0% + +for the acceleration contributed by + + align:start position:0% + + + + align:start position:0% + +what so this so I've got this + + align:start position:0% +what so this so I've got this + + + align:start position:0% +what so this so I've got this +General let's see I got a Miro round + + align:start position:0% +General let's see I got a Miro round + + + align:start position:0% +General let's see I got a Miro round +that's on a you know on on wheel and + + align:start position:0% +that's on a you know on on wheel and + + + align:start position:0% +that's on a you know on on wheel and +it's rolling along here and I have an + + align:start position:0% +it's rolling along here and I have an + + + align:start position:0% +it's rolling along here and I have an +inertial + + align:start position:0% + + + + align:start position:0% + +frame and I got a point a here but now + + align:start position:0% +frame and I got a point a here but now + + + align:start position:0% +frame and I got a point a here but now +I've also got a system in here which I'm + + align:start position:0% +I've also got a system in here which I'm + + + align:start position:0% +I've also got a system in here which I'm +describing with an R Theta connected to + + align:start position:0% +describing with an R Theta connected to + + + align:start position:0% +describing with an R Theta connected to +this this thing can have translational + + align:start position:0% +this this thing can have translational + + + align:start position:0% +this this thing can have translational +acceleration that's that term this + + align:start position:0% +acceleration that's that term this + + + align:start position:0% +acceleration that's that term this +problem doesn't happen to have that it + + align:start position:0% +problem doesn't happen to have that it + + + align:start position:0% +problem doesn't happen to have that it +goes to zero in this problem that's zero + + align:start position:0% +goes to zero in this problem that's zero + + + align:start position:0% +goes to zero in this problem that's zero +in this problem + + align:start position:0% + + + + align:start position:0% + +um we can now apply this equation to + + align:start position:0% +um we can now apply this equation to + + + align:start position:0% +um we can now apply this equation to +that problem how + + align:start position:0% +that problem how + + + align:start position:0% +that problem how +many sub equations are we going to get + + align:start position:0% + + + + align:start position:0% + +and why not + + align:start position:0% +and why not + + + align:start position:0% +and why not +three I know you said two but I'm asking + + align:start position:0% +three I know you said two but I'm asking + + + align:start position:0% +three I know you said two but I'm asking +you why not + + align:start position:0% +you why not + + + align:start position:0% +you why not +three and and + + align:start position:0% +three and and + + + align:start position:0% +three and and +a z which you need because it describes + + align:start position:0% +a z which you need because it describes + + + align:start position:0% +a z which you need because it describes +Theta dot so you have a z Direction but + + align:start position:0% +Theta dot so you have a z Direction but + + + align:start position:0% +Theta dot so you have a z Direction but +is there any forces in this problem in + + align:start position:0% +is there any forces in this problem in + + + align:start position:0% +is there any forces in this problem in +the Z direction are there any + + align:start position:0% +the Z direction are there any + + + align:start position:0% +the Z direction are there any +accelerations in the Z Direction no so + + align:start position:0% +accelerations in the Z Direction no so + + + align:start position:0% +accelerations in the Z Direction no so +you get a trivial answer there so you + + align:start position:0% +you get a trivial answer there so you + + + align:start position:0% +you get a trivial answer there so you +can just write that one down masstimes + + align:start position:0% +can just write that one down masstimes + + + align:start position:0% +can just write that one down masstimes +acceleration equals zero and there's no + + align:start position:0% +acceleration equals zero and there's no + + + align:start position:0% +acceleration equals zero and there's no +forces so there's three possible + + align:start position:0% +forces so there's three possible + + + align:start position:0% +forces so there's three possible +equations only two of them are + + align:start position:0% +equations only two of them are + + + align:start position:0% +equations only two of them are +meaningful in this problem and we have + + align:start position:0% +meaningful in this problem and we have + + + align:start position:0% +meaningful in this problem and we have +one that we can summon the r hat + + align:start position:0% +one that we can summon the r hat + + + align:start position:0% +one that we can summon the r hat +component and one in the Theta hat so + + align:start position:0% +component and one in the Theta hat so + + + align:start position:0% +component and one in the Theta hat so +the sum of the + + align:start position:0% +the sum of the + + + align:start position:0% +the sum of the +forces in the Theta hat direction for + + align:start position:0% +forces in the Theta hat direction for + + + align:start position:0% +forces in the Theta hat direction for +this problem are + + align:start position:0% + + + + align:start position:0% + +what from your free B + + align:start position:0% + + + + align:start position:0% + +diagram noral the normal in the positive + + align:start position:0% +diagram noral the normal in the positive + + + align:start position:0% +diagram noral the normal in the positive +Theta hat Direction and + + align:start position:0% + + + + align:start position:0% + +minus mg and is it I think it's + + align:start position:0% +minus mg and is it I think it's + + + align:start position:0% +minus mg and is it I think it's +coine Thea and that's your Theta hat and + + align:start position:0% +coine Thea and that's your Theta hat and + + + align:start position:0% +coine Thea and that's your Theta hat and +is um what is the acceleration in that + + align:start position:0% +is um what is the acceleration in that + + + align:start position:0% +is um what is the acceleration in that +direction well you go to acceleration + + align:start position:0% +direction well you go to acceleration + + + align:start position:0% +direction well you go to acceleration +formula and now let's inspect the terms + + align:start position:0% +formula and now let's inspect the terms + + + align:start position:0% +formula and now let's inspect the terms +this one's zero because the platform is + + align:start position:0% +this one's zero because the platform is + + + align:start position:0% +this one's zero because the platform is +is + + align:start position:0% +is + + + align:start position:0% +is +fixed R do zero because we're just + + align:start position:0% +fixed R do zero because we're just + + + align:start position:0% +fixed R do zero because we're just +waiting just the point we're wait it's + + align:start position:0% +waiting just the point we're wait it's + + + align:start position:0% +waiting just the point we're wait it's +just trying to calculate when it be + + align:start position:0% +just trying to calculate when it be + + + align:start position:0% +just trying to calculate when it be +begins to slide R Theta dot + + align:start position:0% +begins to slide R Theta dot + + + align:start position:0% +begins to slide R Theta dot +squ not zero uh R Theta double dot not + + align:start position:0% +squ not zero uh R Theta double dot not + + + align:start position:0% +squ not zero uh R Theta double dot not +well it might be but I said Omega do0 + + align:start position:0% +well it might be but I said Omega do0 + + + align:start position:0% +well it might be but I said Omega do0 +constant so that one's zero for this + + align:start position:0% +constant so that one's zero for this + + + align:start position:0% +constant so that one's zero for this +problem and this term + + align:start position:0% +problem and this term + + + align:start position:0% +problem and this term +coris zero + + align:start position:0% +coris zero + + + align:start position:0% +coris zero +because our DOT is zero we're really + + align:start position:0% +because our DOT is zero we're really + + + align:start position:0% +because our DOT is zero we're really +treating this like a Statics problem it + + align:start position:0% +treating this like a Statics problem it + + + align:start position:0% +treating this like a Statics problem it +hasn't started to move yet so the only + + align:start position:0% +hasn't started to move yet so the only + + + align:start position:0% +hasn't started to move yet so the only +we're only left with one term here so + + align:start position:0% +we're only left with one term here so + + + align:start position:0% +we're only left with one term here so +the sum of the forces in the normal + + align:start position:0% +the sum of the forces in the normal + + + align:start position:0% +the sum of the forces in the normal +Direction which is the Theta dot + + align:start position:0% +Direction which is the Theta dot + + + align:start position:0% +Direction which is the Theta dot +Direction Theta hat direction + + align:start position:0% +Direction Theta hat direction + + + align:start position:0% +Direction Theta hat direction +are zero and that allows us to solve for + + align:start position:0% +are zero and that allows us to solve for + + + align:start position:0% +are zero and that allows us to solve for +the normal + + align:start position:0% + + + + align:start position:0% + +force so you need that you need Newton's + + align:start position:0% +force so you need that you need Newton's + + + align:start position:0% +force so you need that you need Newton's +law to find the normal force to start + + align:start position:0% +law to find the normal force to start + + + align:start position:0% +law to find the normal force to start +with and you need the normal force to + + align:start position:0% +with and you need the normal force to + + + align:start position:0% +with and you need the normal force to +find the friction Force so now let's do + + align:start position:0% +find the friction Force so now let's do + + + align:start position:0% +find the friction Force so now let's do +the sum of the + + align:start position:0% +the sum of the + + + align:start position:0% +the sum of the +forces in the r hat Direction and that's + + align:start position:0% +forces in the r hat Direction and that's + + + align:start position:0% +forces in the r hat Direction and that's +going to maybe uh let's do the + + align:start position:0% +going to maybe uh let's do the + + + align:start position:0% +going to maybe uh let's do the +acceleration first it's the mass times + + align:start position:0% +acceleration first it's the mass times + + + align:start position:0% +acceleration first it's the mass times +the + + align:start position:0% +the + + + align:start position:0% +the +acceleration in the r hat + + align:start position:0% +acceleration in the r hat + + + align:start position:0% +acceleration in the r hat +Direction and that's the mass and now + + align:start position:0% +Direction and that's the mass and now + + + align:start position:0% +Direction and that's the mass and now +what's the + + align:start position:0% +what's the + + + align:start position:0% +what's the +acceleration these are the r directed + + align:start position:0% +acceleration these are the r directed + + + align:start position:0% +acceleration these are the r directed +terms we have + + align:start position:0% +terms we have + + + align:start position:0% +terms we have +one one term right minus r Theta do^ + + align:start position:0% + + + + align:start position:0% + +2 no other terms and and those that got + + align:start position:0% +2 no other terms and and those that got + + + align:start position:0% +2 no other terms and and those that got +to be equal to the external forces in + + align:start position:0% +to be equal to the external forces in + + + align:start position:0% +to be equal to the external forces in +the radial Direction and what are + + align:start position:0% +the radial Direction and what are + + + align:start position:0% +the radial Direction and what are +they from + + align:start position:0% + + + + align:start position:0% + +3 plus or + + align:start position:0% +3 plus or + + + align:start position:0% +3 plus or +minus plus mu n but we know n is + + align:start position:0% +minus plus mu n but we know n is + + + align:start position:0% +minus plus mu n but we know n is +mg cine Theta okay what + + align:start position:0% +mg cine Theta okay what + + + align:start position:0% +mg cine Theta okay what +else minus + + align:start position:0% +else minus + + + align:start position:0% +else minus +mg sin Theta + + align:start position:0% +mg sin Theta + + + align:start position:0% +mg sin Theta +all + + align:start position:0% + + + + align:start position:0% + +right you could you can now you know + + align:start position:0% +right you could you can now you know + + + align:start position:0% +right you could you can now you know +everything in this expression you know + + align:start position:0% +everything in this expression you know + + + align:start position:0% +everything in this expression you know +given Theta dot you're given R you know + + align:start position:0% +given Theta dot you're given R you know + + + align:start position:0% +given Theta dot you're given R you know +mg you know given + + align:start position:0% +mg you know given + + + align:start position:0% +mg you know given +Theta you could solve this expression + + align:start position:0% +Theta you could solve this expression + + + align:start position:0% +Theta you could solve this expression +for + + align:start position:0% + + + + align:start position:0% + +Mu right and and the mg comes to goes to + + align:start position:0% +Mu right and and the mg comes to goes to + + + align:start position:0% +Mu right and and the mg comes to goes to +the other side and you have a + + align:start position:0% +the other side and you have a + + + align:start position:0% +the other side and you have a +minus r Theta squ notice the M's cancel + + align:start position:0% +minus r Theta squ notice the M's cancel + + + align:start position:0% +minus r Theta squ notice the M's cancel +all the way through + + align:start position:0% + + + + align:start position:0% + +right so mu would looks like it equals + + align:start position:0% +right so mu would looks like it equals + + + align:start position:0% +right so mu would looks like it equals +to + + align:start position:0% +to + + + align:start position:0% +to +me + + align:start position:0% +me + + + align:start position:0% +me +G sin + + align:start position:0% + + + + align:start position:0% + +Theta minus r Theta Dot 2ar + + align:start position:0% + + + + align:start position:0% + +all divided + + align:start position:0% +all divided + + + align:start position:0% +all divided +by + + align:start position:0% +by + + + align:start position:0% +by +what + + align:start position:0% +what + + + align:start position:0% +what +G cosine + + align:start position:0% + + + + align:start position:0% + +Theta this this bre break these two + + align:start position:0% +Theta this this bre break these two + + + align:start position:0% +Theta this this bre break these two +apart this gives me a + + align:start position:0% +apart this gives me a + + + align:start position:0% +apart this gives me a +tan Theta + + align:start position:0% +tan Theta + + + align:start position:0% +tan Theta +minus r Theta do 2ar over G cos + + align:start position:0% +minus r Theta do 2ar over G cos + + + align:start position:0% +minus r Theta do 2ar over G cos +Theta that has units of acceleration G + + align:start position:0% +Theta that has units of acceleration G + + + align:start position:0% +Theta that has units of acceleration G +has units of acceleration This Is + + align:start position:0% +has units of acceleration This Is + + + align:start position:0% +has units of acceleration This Is +dimensionless The Answer has got to be + + align:start position:0% +dimensionless The Answer has got to be + + + align:start position:0% +dimensionless The Answer has got to be +dimensionless so there's the uh there's + + align:start position:0% +dimensionless so there's the uh there's + + + align:start position:0% +dimensionless so there's the uh there's +your + + align:start position:0% +your + + + align:start position:0% +your +answer but you really had to use the + + align:start position:0% +answer but you really had to use the + + + align:start position:0% +answer but you really had to use the +equations of motion okay now there's + + align:start position:0% +equations of motion okay now there's + + + align:start position:0% +equations of motion okay now there's +another thing I want to address because + + align:start position:0% +another thing I want to address because + + + align:start position:0% +another thing I want to address because +I heard it pop up two or three times do + + align:start position:0% +I heard it pop up two or three times do + + + align:start position:0% +I heard it pop up two or three times do +not + + align:start position:0% +not + + + align:start position:0% +not +confuse + + align:start position:0% +confuse + + + align:start position:0% +confuse +accelerations with + + align:start position:0% +accelerations with + + + align:start position:0% +accelerations with +forces Newton's law second makes it + + align:start position:0% +forces Newton's law second makes it + + + align:start position:0% +forces Newton's law second makes it +really clear where each one goes the sum + + align:start position:0% +really clear where each one goes the sum + + + align:start position:0% +really clear where each one goes the sum +of the external forces go on one side of + + align:start position:0% +of the external forces go on one side of + + + align:start position:0% +of the external forces go on one side of +the equal sign the mass times the + + align:start position:0% +the equal sign the mass times the + + + align:start position:0% +the equal sign the mass times the +acceleration goes on the + + align:start position:0% +acceleration goes on the + + + align:start position:0% +acceleration goes on the +other so don't let don't get the two + + align:start position:0% +other so don't let don't get the two + + + align:start position:0% +other so don't let don't get the two +mixed up solve for the accelerations if + + align:start position:0% +mixed up solve for the accelerations if + + + align:start position:0% +mixed up solve for the accelerations if +you + + align:start position:0% +you + + + align:start position:0% +you +can plug them in and multiply them by + + align:start position:0% +can plug them in and multiply them by + + + align:start position:0% +can plug them in and multiply them by +mass and now you have that one side of + + align:start position:0% +mass and now you have that one side of + + + align:start position:0% +mass and now you have that one side of +the equation the free body diagram the + + align:start position:0% + + + + align:start position:0% + +only vectors that should show up on a + + align:start position:0% +only vectors that should show up on a + + + align:start position:0% +only vectors that should show up on a +free body diag + + align:start position:0% +free body diag + + + align:start position:0% +free body diag +are + + align:start position:0% +are + + + align:start position:0% +are +what forces forces the real forces in + + align:start position:0% +what forces forces the real forces in + + + align:start position:0% +what forces forces the real forces in +the problem so in that problem in that + + align:start position:0% +the problem so in that problem in that + + + align:start position:0% +the problem so in that problem in that +free body diagram there is no R Theta do + + align:start position:0% +free body diagram there is no R Theta do + + + align:start position:0% +free body diagram there is no R Theta do +squ + + align:start position:0% +squ + + + align:start position:0% +squ +term it doesn't belong there and that's + + align:start position:0% +term it doesn't belong there and that's + + + align:start position:0% +term it doesn't belong there and that's +it'll keep you from making these sign + + align:start position:0% +it'll keep you from making these sign + + + align:start position:0% +it'll keep you from making these sign +errors and things like that so the + + align:start position:0% +errors and things like that so the + + + align:start position:0% +errors and things like that so the +business about this thing comes up minus + + align:start position:0% +business about this thing comes up minus + + + align:start position:0% +business about this thing comes up minus +because it's minus right out of the + + align:start position:0% +because it's minus right out of the + + + align:start position:0% +because it's minus right out of the +acceleration + + align:start position:0% +acceleration + + + align:start position:0% +acceleration +equation all right what would happen if + + align:start position:0% +equation all right what would happen if + + + align:start position:0% +equation all right what would happen if +I I had not + + align:start position:0% +I I had not + + + align:start position:0% +I I had not +allowed if I had not made the + + align:start position:0% +allowed if I had not made the + + + align:start position:0% +allowed if I had not made the +um where we + + align:start position:0% + + + + align:start position:0% + +go this term zero I allow this to have + + align:start position:0% +go this term zero I allow this to have + + + align:start position:0% +go this term zero I allow this to have +some angular acceleration to it that's + + align:start position:0% +some angular acceleration to it that's + + + align:start position:0% +some angular acceleration to it that's +what's got to that's what's got to + + align:start position:0% +what's got to that's what's got to + + + align:start position:0% +what's got to that's what's got to +happen to um well you don't have to do + + align:start position:0% +happen to um well you don't have to do + + + align:start position:0% +happen to um well you don't have to do +it if it's if it's kind I can't do it + + align:start position:0% +it if it's if it's kind I can't do it + + + align:start position:0% +it if it's if it's kind I can't do it +constant rate but if you can make this + + align:start position:0% +constant rate but if you can make this + + + align:start position:0% +constant rate but if you can make this +constant rate fast enough it goes up + + align:start position:0% +constant rate fast enough it goes up + + + align:start position:0% +constant rate fast enough it goes up +right so even if it's concentr rate fast + + align:start position:0% +right so even if it's concentr rate fast + + + align:start position:0% +right so even if it's concentr rate fast +enough this thing will slide up the + + align:start position:0% +enough this thing will slide up the + + + align:start position:0% +enough this thing will slide up the +thing immediately when you start it uh + + align:start position:0% +thing immediately when you start it uh + + + align:start position:0% +thing immediately when you start it uh +almost immed you start down here G the + + align:start position:0% +almost immed you start down here G the + + + align:start position:0% +almost immed you start down here G the +friction force is pretty high and the + + align:start position:0% +friction force is pretty high and the + + + align:start position:0% +friction force is pretty high and the +friction force of course diminishes as + + align:start position:0% +friction force of course diminishes as + + + align:start position:0% +friction force of course diminishes as +you get further up and + + align:start position:0% +you get further up and + + + align:start position:0% +you get further up and +eventually it takes off right that's + + align:start position:0% +eventually it takes off right that's + + + align:start position:0% +eventually it takes off right that's +because that minus r theta. squ that's a + + align:start position:0% +because that minus r theta. squ that's a + + + align:start position:0% +because that minus r theta. squ that's a +centripetal centripetal acceleration + + align:start position:0% +centripetal centripetal acceleration + + + align:start position:0% +centripetal centripetal acceleration +inwards and if you don't provide the + + align:start position:0% +inwards and if you don't provide the + + + align:start position:0% +inwards and if you don't provide the +force that causes that centripetal + + align:start position:0% +force that causes that centripetal + + + align:start position:0% +force that causes that centripetal +acceleration to happen it says I want to + + align:start position:0% +acceleration to happen it says I want to + + + align:start position:0% +acceleration to happen it says I want to +leave you town + + align:start position:0% + + + + align:start position:0% + +now uh how about though if I had angular + + align:start position:0% +now uh how about though if I had angular + + + align:start position:0% +now uh how about though if I had angular +acceleration as well if I have allow + + align:start position:0% +acceleration as well if I have allow + + + align:start position:0% +acceleration as well if I have allow +angular acceleration this problem how + + align:start position:0% +angular acceleration this problem how + + + align:start position:0% +angular acceleration this problem how +does it change the two equations that we + + align:start position:0% +does it change the two equations that we + + + align:start position:0% +does it change the two equations that we +wrote where what does it change which + + align:start position:0% +wrote where what does it change which + + + align:start position:0% +wrote where what does it change which +side it change the forces does it change + + align:start position:0% +side it change the forces does it change + + + align:start position:0% +side it change the forces does it change +the free body diagram not a bit changes + + align:start position:0% +the free body diagram not a bit changes + + + align:start position:0% +the free body diagram not a bit changes +the acceleration side of the equation + + align:start position:0% +the acceleration side of the equation + + + align:start position:0% +the acceleration side of the equation +and what term now turns + + align:start position:0% +and what term now turns + + + align:start position:0% +and what term now turns +up that you didn't have + + align:start position:0% +up that you didn't have + + + align:start position:0% +up that you didn't have +before this one so now have a dynamic + + align:start position:0% +before this one so now have a dynamic + + + align:start position:0% +before this one so now have a dynamic +term in the Theta hat equation and it + + align:start position:0% +term in the Theta hat equation and it + + + align:start position:0% +term in the Theta hat equation and it +comes into into this expression for some + + align:start position:0% +comes into into this expression for some + + + align:start position:0% +comes into into this expression for some +of the forces in this direction and you + + align:start position:0% +of the forces in this direction and you + + + align:start position:0% +of the forces in this direction and you +would end up equals 2 m r Theta double + + align:start position:0% +would end up equals 2 m r Theta double + + + align:start position:0% +would end up equals 2 m r Theta double +dot now it's entirely different + + align:start position:0% +dot now it's entirely different + + + align:start position:0% +dot now it's entirely different +problem gets gets a little harder to + + align:start position:0% +problem gets gets a little harder to + + + align:start position:0% +problem gets gets a little harder to +solve okay but good uh you know really + + align:start position:0% +solve okay but good uh you know really + + + align:start position:0% +solve okay but good uh you know really +good fundamental + + align:start position:0% +good fundamental + + + align:start position:0% +good fundamental +practices fals Ma and write out both + + align:start position:0% +practices fals Ma and write out both + + + align:start position:0% +practices fals Ma and write out both +sides car Y and then you won't make sign + + align:start position:0% +sides car Y and then you won't make sign + + + align:start position:0% +sides car Y and then you won't make sign +mistakes and so forth thanks good to see + + align:start position:0% +mistakes and so forth thanks good to see + + + align:start position:0% +mistakes and so forth thanks good to see +you \ No newline at end of file diff --git a/Qf6OVR8MLnU.txt b/Qf6OVR8MLnU.txt new file mode 100644 index 0000000000000000000000000000000000000000..ee9938a58cbb92704f880c7102145f1a332a9efd --- /dev/null +++ b/Qf6OVR8MLnU.txt @@ -0,0 +1,8907 @@ +align:start position:0% + +okay so last lecture we started talking + + align:start position:0% +okay so last lecture we started talking + + + align:start position:0% +okay so last lecture we started talking +about the idea of decomposition and + + align:start position:0% +about the idea of decomposition and + + + align:start position:0% +about the idea of decomposition and +abstraction and we talked a little bit + + align:start position:0% +abstraction and we talked a little bit + + + align:start position:0% +abstraction and we talked a little bit +about what that means and how it ties + + align:start position:0% +about what that means and how it ties + + + align:start position:0% +about what that means and how it ties +into what we've already been doing today + + align:start position:0% +into what we've already been doing today + + + align:start position:0% +into what we've already been doing today +we're going to do a real world example + + align:start position:0% +we're going to do a real world example + + + align:start position:0% +we're going to do a real world example +of decomposition and abstraction and + + align:start position:0% +of decomposition and abstraction and + + + align:start position:0% +of decomposition and abstraction and +then we'll see exactly how we can + + align:start position:0% +then we'll see exactly how we can + + + align:start position:0% +then we'll see exactly how we can +achieve this in Pro programming so let's + + align:start position:0% +achieve this in Pro programming so let's + + + align:start position:0% +achieve this in Pro programming so let's +start by talking about an example in the + + align:start position:0% +start by talking about an example in the + + + align:start position:0% +start by talking about an example in the +real world the + + align:start position:0% +real world the + + + align:start position:0% +real world the +smartphone so a lot of us have it but + + align:start position:0% +smartphone so a lot of us have it but + + + align:start position:0% +smartphone so a lot of us have it but +for a lot of us it's really just a black + + align:start position:0% +for a lot of us it's really just a black + + + align:start position:0% +for a lot of us it's really just a black +box right for me I know it is for most + + align:start position:0% +box right for me I know it is for most + + + align:start position:0% +box right for me I know it is for most +of the people in the world the phone is + + align:start position:0% +of the people in the world the phone is + + + align:start position:0% +of the people in the world the phone is +a black box we basically view the phone + + align:start position:0% +a black box we basically view the phone + + + align:start position:0% +a black box we basically view the phone +in terms of its inputs and in terms of + + align:start position:0% +in terms of its inputs and in terms of + + + align:start position:0% +in terms of its inputs and in terms of +its outputs right so the phone has uh + + align:start position:0% +its outputs right so the phone has uh + + + align:start position:0% +its outputs right so the phone has uh +some buttons you can scroll you can + + align:start position:0% +some buttons you can scroll you can + + + align:start position:0% +some buttons you can scroll you can +touch things um but we don't really know + + align:start position:0% +touch things um but we don't really know + + + align:start position:0% +touch things um but we don't really know +exactly how all of these buttons and + + align:start position:0% +exactly how all of these buttons and + + + align:start position:0% +exactly how all of these buttons and +scrolling and all these internal + + align:start position:0% +scrolling and all these internal + + + align:start position:0% +scrolling and all these internal +workings actually do their job and in + + align:start position:0% +workings actually do their job and in + + + align:start position:0% +workings actually do their job and in +fact we don't need to know how they do + + align:start position:0% +fact we don't need to know how they do + + + align:start position:0% +fact we don't need to know how they do +their job right to us as the user all we + + align:start position:0% +their job right to us as the user all we + + + align:start position:0% +their job right to us as the user all we +really care about is the interface + + align:start position:0% +really care about is the interface + + + align:start position:0% +really care about is the interface +between us and what task we want to + + align:start position:0% +between us and what task we want to + + + align:start position:0% +between us and what task we want to +achieve okay so what we need to know + + align:start position:0% +achieve okay so what we need to know + + + align:start position:0% +achieve okay so what we need to know +that Rel that that interface is + + align:start position:0% +that Rel that that interface is + + + align:start position:0% +that Rel that that interface is +basically the relationship between the + + align:start position:0% +basically the relationship between the + + + align:start position:0% +basically the relationship between the +input we give to the um to the phone and + + align:start position:0% +input we give to the um to the phone and + + + align:start position:0% +input we give to the um to the phone and +the output we get so when we push that + + align:start position:0% +the output we get so when we push that + + + align:start position:0% +the output we get so when we push that +button Buton the phone turns off when we + + align:start position:0% +button Buton the phone turns off when we + + + align:start position:0% +button Buton the phone turns off when we +push this other button the volume + + align:start position:0% +push this other button the volume + + + align:start position:0% +push this other button the volume +increases + + align:start position:0% +increases + + + align:start position:0% +increases +okay and so that's the idea of + + align:start position:0% +okay and so that's the idea of + + + align:start position:0% +okay and so that's the idea of +abstraction right the the the the phone + + align:start position:0% +abstraction right the the the the phone + + + align:start position:0% +abstraction right the the the the phone +basically abstracted away all of those + + align:start position:0% +basically abstracted away all of those + + + align:start position:0% +basically abstracted away all of those +Hardware details all of those + + align:start position:0% +Hardware details all of those + + + align:start position:0% +Hardware details all of those +implementations that make it actually + + align:start position:0% +implementations that make it actually + + + align:start position:0% +implementations that make it actually +work for the user right so the user + + align:start position:0% +work for the user right so the user + + + align:start position:0% +work for the user right so the user +doesn't need to know how it works in + + align:start position:0% +doesn't need to know how it works in + + + align:start position:0% +doesn't need to know how it works in +order to use it now abstraction actually + + align:start position:0% +order to use it now abstraction actually + + + align:start position:0% +order to use it now abstraction actually +enables decomp decomposition what does + + align:start position:0% +enables decomp decomposition what does + + + align:start position:0% +enables decomp decomposition what does +that mean well once we abstract away + + align:start position:0% +that mean well once we abstract away + + + align:start position:0% +that mean well once we abstract away +detail + + align:start position:0% +detail + + + align:start position:0% +detail +we can have different manufacturers + + align:start position:0% +we can have different manufacturers + + + align:start position:0% +we can have different manufacturers +working on different components of the + + align:start position:0% +working on different components of the + + + align:start position:0% +working on different components of the +phone to build these different + + align:start position:0% +phone to build these different + + + align:start position:0% +phone to build these different +components and if different + + align:start position:0% +components and if different + + + align:start position:0% +components and if different +manufacturers are working to build these + + align:start position:0% +manufacturers are working to build these + + + align:start position:0% +manufacturers are working to build these +hundreds of distinct Parts within the + + align:start position:0% +hundreds of distinct Parts within the + + + align:start position:0% +hundreds of distinct Parts within the +phone separately they need to have some + + align:start position:0% +phone separately they need to have some + + + align:start position:0% +phone separately they need to have some +way to put these parts back together and + + align:start position:0% +way to put these parts back together and + + + align:start position:0% +way to put these parts back together and +when they're working on their on their + + align:start position:0% +when they're working on their on their + + + align:start position:0% +when they're working on their on their +pieces separately that's the idea of + + align:start position:0% +pieces separately that's the idea of + + + align:start position:0% +pieces separately that's the idea of +decomposition how do they know that what + + align:start position:0% +decomposition how do they know that what + + + align:start position:0% +decomposition how do they know that what +they're working on will actually fit in + + align:start position:0% +they're working on will actually fit in + + + align:start position:0% +they're working on will actually fit in +with the rest of the components well + + align:start position:0% +with the rest of the components well + + + align:start position:0% +with the rest of the components well +they use the idea of decomposition + + align:start position:0% +they use the idea of decomposition + + + align:start position:0% +they use the idea of decomposition +they're basically following a + + align:start position:0% +they're basically following a + + + align:start position:0% +they're basically following a +specification they're following a set of + + align:start position:0% +specification they're following a set of + + + align:start position:0% +specification they're following a set of +inputs that maybe come into their + + align:start position:0% +inputs that maybe come into their + + + align:start position:0% +inputs that maybe come into their +component and a set of outputs that + + align:start position:0% +component and a set of outputs that + + + align:start position:0% +component and a set of outputs that +maybe their component needs to give to + + align:start position:0% +maybe their component needs to give to + + + align:start position:0% +maybe their component needs to give to +other components and all these different + + align:start position:0% +other components and all these different + + + align:start position:0% +other components and all these different +manufacturers that build that are + + align:start position:0% +manufacturers that build that are + + + align:start position:0% +manufacturers that build that are +building these different parts need to + + align:start position:0% +building these different parts need to + + + align:start position:0% +building these different parts need to +know is that interface bit they don't + + align:start position:0% +know is that interface bit they don't + + + align:start position:0% +know is that interface bit they don't +need to know how other manufacturers + + align:start position:0% +need to know how other manufacturers + + + align:start position:0% +need to know how other manufacturers +build their components all they need to + + align:start position:0% +build their components all they need to + + + align:start position:0% +build their components all they need to +know is what functionality those other + + align:start position:0% +know is what functionality those other + + + align:start position:0% +know is what functionality those other +components have and so all of these + + align:start position:0% +components have and so all of these + + + align:start position:0% +components have and so all of these +different manufacturers can build all + + align:start position:0% +different manufacturers can build all + + + align:start position:0% +different manufacturers can build all +these different components the + + align:start position:0% +these different components the + + + align:start position:0% +these different components the +interfaces are going to be sort of + + align:start position:0% +interfaces are going to be sort of + + + align:start position:0% +interfaces are going to be sort of +standardized so to speak and that's all + + align:start position:0% +standardized so to speak and that's all + + + align:start position:0% +standardized so to speak and that's all +that they care about so once you know + + align:start position:0% +that they care about so once you know + + + align:start position:0% +that they care about so once you know +the interface you can come together and + + align:start position:0% +the interface you can come together and + + + align:start position:0% +the interface you can come together and +put all these different components + + align:start position:0% +put all these different components + + + align:start position:0% +put all these different components +together to work towards a common goal + + align:start position:0% +together to work towards a common goal + + + align:start position:0% +together to work towards a common goal +as in to make a phone + + align:start position:0% +as in to make a phone + + + align:start position:0% +as in to make a phone +work so this is true for Hardware as in + + align:start position:0% +work so this is true for Hardware as in + + + align:start position:0% +work so this is true for Hardware as in +the phone example but it's also true for + + align:start position:0% +the phone example but it's also true for + + + align:start position:0% +the phone example but it's also true for +software and that's exactly what we will + + align:start position:0% +software and that's exactly what we will + + + align:start position:0% +software and that's exactly what we will +be doing in this uh in this lecture on + + align:start position:0% +be doing in this uh in this lecture on + + + align:start position:0% +be doing in this uh in this lecture on +functions we're going to achieve + + align:start position:0% +functions we're going to achieve + + + align:start position:0% +functions we're going to achieve +decomposition and abstraction in + + align:start position:0% +decomposition and abstraction in + + + align:start position:0% +decomposition and abstraction in +programming so treating code as a black + + align:start position:0% +programming so treating code as a black + + + align:start position:0% +programming so treating code as a black +box and making uh a large program kind + + align:start position:0% +box and making uh a large program kind + + + align:start position:0% +box and making uh a large program kind +of splitting it up into these different + + align:start position:0% +of splitting it up into these different + + + align:start position:0% +of splitting it up into these different +self-contained Parts okay so in + + align:start position:0% +self-contained Parts okay so in + + + align:start position:0% +self-contained Parts okay so in +programming we want to suppress details + + align:start position:0% +programming we want to suppress details + + + align:start position:0% +programming we want to suppress details +as well right not just in in Hardware + + align:start position:0% +as well right not just in in Hardware + + + align:start position:0% +as well right not just in in Hardware +like with the phone we want to suppress + + align:start position:0% +like with the phone we want to suppress + + + align:start position:0% +like with the phone we want to suppress +details in uh in programming as well and + + align:start position:0% +details in uh in programming as well and + + + align:start position:0% +details in uh in programming as well and +we do this using this idea of + + align:start position:0% +we do this using this idea of + + + align:start position:0% +we do this using this idea of +abstraction so we will be uh writing + + align:start position:0% +abstraction so we will be uh writing + + + align:start position:0% +abstraction so we will be uh writing +code as we have already been + + align:start position:0% +code as we have already been + + + align:start position:0% +code as we have already been +doing uh with the with the thought that + + align:start position:0% +doing uh with the with the thought that + + + align:start position:0% +doing uh with the with the thought that +what the code we're writing will be done + + align:start position:0% +what the code we're writing will be done + + + align:start position:0% +what the code we're writing will be done +will be written only once we will have + + align:start position:0% +will be written only once we will have + + + align:start position:0% +will be written only once we will have +some functional piece of code that will + + align:start position:0% +some functional piece of code that will + + + align:start position:0% +some functional piece of code that will +do a very useful task and then after + + align:start position:0% +do a very useful task and then after + + + align:start position:0% +do a very useful task and then after +we've written that code and debugged it + + align:start position:0% +we've written that code and debugged it + + + align:start position:0% +we've written that code and debugged it +and made sure it works well we'll treat + + align:start position:0% +and made sure it works well we'll treat + + + align:start position:0% +and made sure it works well we'll treat +that code as a black box so from there + + align:start position:0% +that code as a black box so from there + + + align:start position:0% +that code as a black box so from there +on out as long as we know what inputs + + align:start position:0% +on out as long as we know what inputs + + + align:start position:0% +on out as long as we know what inputs +that piece of code needs and what + + align:start position:0% +that piece of code needs and what + + + align:start position:0% +that piece of code needs and what +outputs that piece of code gives back to + + align:start position:0% +outputs that piece of code gives back to + + + align:start position:0% +outputs that piece of code gives back to +somebody else or to us we don't care + + align:start position:0% +somebody else or to us we don't care + + + align:start position:0% +somebody else or to us we don't care +exactly how it does it we just care that + + align:start position:0% +exactly how it does it we just care that + + + align:start position:0% +exactly how it does it we just care that +it is there and it is available for use + + align:start position:0% +it is there and it is available for use + + + align:start position:0% +it is there and it is available for use +okay so today's lecture we're going to + + align:start position:0% +okay so today's lecture we're going to + + + align:start position:0% +okay so today's lecture we're going to +be seeing how we can actually create + + align:start position:0% +be seeing how we can actually create + + + align:start position:0% +be seeing how we can actually create +these little functional pieces of code + + align:start position:0% +these little functional pieces of code + + + align:start position:0% +these little functional pieces of code +we can then give these pieces of code to + + align:start position:0% +we can then give these pieces of code to + + + align:start position:0% +we can then give these pieces of code to +ourselves we can definitely use these + + align:start position:0% +ourselves we can definitely use these + + + align:start position:0% +ourselves we can definitely use these +functional pieces of code that we + + align:start position:0% +functional pieces of code that we + + + align:start position:0% +functional pieces of code that we +written or we can give them to other + + align:start position:0% +written or we can give them to other + + + align:start position:0% +written or we can give them to other +people so that they can use them uh as + + align:start position:0% +people so that they can use them uh as + + + align:start position:0% +people so that they can use them uh as +well okay so we're going to write these + + align:start position:0% +well okay so we're going to write these + + + align:start position:0% +well okay so we're going to write these +functional pieces of code uh and we'll + + align:start position:0% +functional pieces of code uh and we'll + + + align:start position:0% +functional pieces of code uh and we'll +call the uh we'll call them functions or + + align:start position:0% +call the uh we'll call them functions or + + + align:start position:0% +call the uh we'll call them functions or +procedures and in fact we've already + + align:start position:0% +procedures and in fact we've already + + + align:start position:0% +procedures and in fact we've already +been using functions believe it or not + + align:start position:0% +been using functions believe it or not + + + align:start position:0% +been using functions believe it or not +um these three uh are examples of + + align:start position:0% +um these three uh are examples of + + + align:start position:0% +um these three uh are examples of +functions we've already been using in + + align:start position:0% +functions we've already been using in + + + align:start position:0% +functions we've already been using in +Python so max is a function so it's some + + align:start position:0% +Python so max is a function so it's some + + + align:start position:0% +Python so max is a function so it's some +useful piece of code that when we use it + + align:start position:0% +useful piece of code that when we use it + + + align:start position:0% +useful piece of code that when we use it +in this particular way it says uh it's + + align:start position:0% +in this particular way it says uh it's + + + align:start position:0% +in this particular way it says uh it's +taking in two inputs and it gives me + + align:start position:0% +taking in two inputs and it gives me + + + align:start position:0% +taking in two inputs and it gives me +back the biggest of those two + + align:start position:0% +back the biggest of those two + + + align:start position:0% +back the biggest of those two +inputs the middle one ABS is the + + align:start position:0% +inputs the middle one ABS is the + + + align:start position:0% +inputs the middle one ABS is the +absolute value function and its input is + + align:start position:0% +absolute value function and its input is + + + align:start position:0% +absolute value function and its input is +one number an integer and it gives back + + align:start position:0% +one number an integer and it gives back + + + align:start position:0% +one number an integer and it gives back +to me the absolute value of that + + align:start position:0% +to me the absolute value of that + + + align:start position:0% +to me the absolute value of that +number and Len is also a really useful + + align:start position:0% +number and Len is also a really useful + + + align:start position:0% +number and Len is also a really useful +one that we've been uh using with + + align:start position:0% +one that we've been uh using with + + + align:start position:0% +one that we've been uh using with +strings and basically its input is a + + align:start position:0% +strings and basically its input is a + + + align:start position:0% +strings and basically its input is a +string and its output is going to be how + + align:start position:0% +string and its output is going to be how + + + align:start position:0% +string and its output is going to be how +many characters are in the string right + + align:start position:0% +many characters are in the string right + + + align:start position:0% +many characters are in the string right +so we've already been using functions + + align:start position:0% +so we've already been using functions + + + align:start position:0% +so we've already been using functions +fun the point of today's lecture is + + align:start position:0% +fun the point of today's lecture is + + + align:start position:0% +fun the point of today's lecture is +you're going to start to write your own + + align:start position:0% +you're going to start to write your own + + + align:start position:0% +you're going to start to write your own +functions uh hopefully useful + + align:start position:0% +functions uh hopefully useful + + + align:start position:0% +functions uh hopefully useful +ones okay so the idea of a function is + + align:start position:0% +ones okay so the idea of a function is + + + align:start position:0% +ones okay so the idea of a function is +that we want to abstract away exactly + + align:start position:0% +that we want to abstract away exactly + + + align:start position:0% +that we want to abstract away exactly +how that function achieves something + + align:start position:0% +how that function achieves something + + + align:start position:0% +how that function achieves something +useful right some useful task and so the + + align:start position:0% +useful right some useful task and so the + + + align:start position:0% +useful right some useful task and so the +way that uh we're going to tell other + + align:start position:0% +way that uh we're going to tell other + + + align:start position:0% +way that uh we're going to tell other +people how to use our function is using + + align:start position:0% +people how to use our function is using + + + align:start position:0% +people how to use our function is using +this idea of abstraction and we capture + + align:start position:0% +this idea of abstraction and we capture + + + align:start position:0% +this idea of abstraction and we capture +what the function does with these things + + align:start position:0% +what the function does with these things + + + align:start position:0% +what the function does with these things +called + + align:start position:0% +called + + + align:start position:0% +called +specifications um they're also called + + align:start position:0% +specifications um they're also called + + + align:start position:0% +specifications um they're also called +dock strings and the dock string is kind + + align:start position:0% +dock strings and the dock string is kind + + + align:start position:0% +dock strings and the dock string is kind +of like a contract between somebody who + + align:start position:0% +of like a contract between somebody who + + + align:start position:0% +of like a contract between somebody who +creates this useful function and + + align:start position:0% +creates this useful function and + + + align:start position:0% +creates this useful function and +somebody who wants to use the function + + align:start position:0% +somebody who wants to use the function + + + align:start position:0% +somebody who wants to use the function +the person who uses the function might + + align:start position:0% +the person who uses the function might + + + align:start position:0% +the person who uses the function might +be you the person who wrote it or it + + align:start position:0% +be you the person who wrote it or it + + + align:start position:0% +be you the person who wrote it or it +might be somebody else and in the + + align:start position:0% +might be somebody else and in the + + + align:start position:0% +might be somebody else and in the +contract the things that we're going to + + align:start position:0% +contract the things that we're going to + + + align:start position:0% +contract the things that we're going to +mention are what are the inputs to the + + align:start position:0% +mention are what are the inputs to the + + + align:start position:0% +mention are what are the inputs to the +function so in you know in the length + + align:start position:0% +function so in you know in the length + + + align:start position:0% +function so in you know in the length +function you know it needs a string um + + align:start position:0% +function you know it needs a string um + + + align:start position:0% +function you know it needs a string um +what is the function doing and what is + + align:start position:0% +what is the function doing and what is + + + align:start position:0% +what is the function doing and what is +the output of the function what does the + + align:start position:0% +the output of the function what does the + + + align:start position:0% +the output of the function what does the +function give back to somebody who uses + + align:start position:0% +function give back to somebody who uses + + + align:start position:0% +function give back to somebody who uses +this + + align:start position:0% +this + + + align:start position:0% +this +function and we haven't actually done + + align:start position:0% +function and we haven't actually done + + + align:start position:0% +function and we haven't actually done +this explicitly but you've probably seen + + align:start position:0% +this explicitly but you've probably seen + + + align:start position:0% +this explicitly but you've probably seen +this as you type uh your code in so + + align:start position:0% +this as you type uh your code in so + + + align:start position:0% +this as you type uh your code in so +here's an example of the absolute value + + align:start position:0% +here's an example of the absolute value + + + align:start position:0% +here's an example of the absolute value +function and it comes up with this + + align:start position:0% +function and it comes up with this + + + align:start position:0% +function and it comes up with this +little popup here whenever you type it + + align:start position:0% +little popup here whenever you type it + + + align:start position:0% +little popup here whenever you type it +in so for example ABS + + align:start position:0% +in so for example ABS + + + align:start position:0% +in so for example ABS +parenthesis right here or if you hover + + align:start position:0% +parenthesis right here or if you hover + + + align:start position:0% +parenthesis right here or if you hover +over a function in your file editor + + align:start position:0% +over a function in your file editor + + + align:start position:0% +over a function in your file editor +you'll see it pop up this little text + + align:start position:0% +you'll see it pop up this little text + + + align:start position:0% +you'll see it pop up this little text +box that says the specification or the + + align:start position:0% +box that says the specification or the + + + align:start position:0% +box that says the specification or the +doc string and here you see exactly sort + + align:start position:0% +doc string and here you see exactly sort + + + align:start position:0% +doc string and here you see exactly sort +of the signature of the function so it + + align:start position:0% +of the signature of the function so it + + + align:start position:0% +of the signature of the function so it +takes in one input the X the value you + + align:start position:0% +takes in one input the X the value you + + + align:start position:0% +takes in one input the X the value you +want to find the absolute value of and + + align:start position:0% +want to find the absolute value of and + + + align:start position:0% +want to find the absolute value of and +then some text here which is what the + + align:start position:0% +then some text here which is what the + + + align:start position:0% +then some text here which is what the +function does so the specification of + + align:start position:0% +function does so the specification of + + + align:start position:0% +function does so the specification of +the doc string is literally just a + + align:start position:0% +the doc string is literally just a + + + align:start position:0% +the doc string is literally just a +multi-line comment there's nothing + + align:start position:0% +multi-line comment there's nothing + + + align:start position:0% +multi-line comment there's nothing +special about it as long as you kind of + + align:start position:0% +special about it as long as you kind of + + + align:start position:0% +special about it as long as you kind of +hit those points the inputs what the + + align:start position:0% +hit those points the inputs what the + + + align:start position:0% +hit those points the inputs what the +function does and what the function + + align:start position:0% +function does and what the function + + + align:start position:0% +function does and what the function +gives back to you you've written a good + + align:start position:0% +gives back to you you've written a good + + + align:start position:0% +gives back to you you've written a good +uh specification + + align:start position:0% +uh specification + + + align:start position:0% +uh specification +a + + align:start position:0% +a + + + align:start position:0% +a +okay um also I should mention that these + + align:start position:0% +okay um also I should mention that these + + + align:start position:0% +okay um also I should mention that these +contracts even though I call them + + align:start position:0% +contracts even though I call them + + + align:start position:0% +contracts even though I call them +contract there they're not actually + + align:start position:0% +contract there they're not actually + + + align:start position:0% +contract there they're not actually +enforced by python so it's really just + + align:start position:0% +enforced by python so it's really just + + + align:start position:0% +enforced by python so it's really just +up to the person who writes the code to + + align:start position:0% +up to the person who writes the code to + + + align:start position:0% +up to the person who writes the code to +make sure that their specification is + + align:start position:0% +make sure that their specification is + + + align:start position:0% +make sure that their specification is +really um detailed and you your function + + align:start position:0% +really um detailed and you your function + + + align:start position:0% +really um detailed and you your function +does what you say you will right so if + + align:start position:0% +does what you say you will right so if + + + align:start position:0% +does what you say you will right so if +your function can take in both positive + + align:start position:0% +your function can take in both positive + + + align:start position:0% +your function can take in both positive +and negative integers for example then + + align:start position:0% +and negative integers for example then + + + align:start position:0% +and negative integers for example then +you better make sure that the function + + align:start position:0% +you better make sure that the function + + + align:start position:0% +you better make sure that the function +itself doing whatever task it needs to + + align:start position:0% +itself doing whatever task it needs to + + + align:start position:0% +itself doing whatever task it needs to +do can handle both positive and negative + + align:start position:0% +do can handle both positive and negative + + + align:start position:0% +do can handle both positive and negative +integers so once we write these + + align:start position:0% +integers so once we write these + + + align:start position:0% +integers so once we write these +functions we now have these little bits + + align:start position:0% +functions we now have these little bits + + + align:start position:0% +functions we now have these little bits +of code that perform some useful task + + align:start position:0% +of code that perform some useful task + + + align:start position:0% +of code that perform some useful task +right given some input it'll perform + + align:start position:0% +right given some input it'll perform + + + align:start position:0% +right given some input it'll perform +this task and give me back some output + + align:start position:0% +this task and give me back some output + + + align:start position:0% +this task and give me back some output +and now that we have these different + + align:start position:0% +and now that we have these different + + + align:start position:0% +and now that we have these different +little pieces of functionality we can go + + align:start position:0% +little pieces of functionality we can go + + + align:start position:0% +little pieces of functionality we can go +ahead and take this large file of code + + align:start position:0% +ahead and take this large file of code + + + align:start position:0% +ahead and take this large file of code +which you might you know write from now + + align:start position:0% +which you might you know write from now + + + align:start position:0% +which you might you know write from now +on and kind of see exactly which which + + align:start position:0% +on and kind of see exactly which which + + + align:start position:0% +on and kind of see exactly which which +pieces of code maybe are getting + + align:start position:0% +pieces of code maybe are getting + + + align:start position:0% +pieces of code maybe are getting +repeated that's a clue that that's + + align:start position:0% +repeated that's a clue that that's + + + align:start position:0% +repeated that's a clue that that's +something that you can kind of abstract + + align:start position:0% +something that you can kind of abstract + + + align:start position:0% +something that you can kind of abstract +away into a little module AKA a function + + align:start position:0% +away into a little module AKA a function + + + align:start position:0% +away into a little module AKA a function +and then you can just use these + + align:start position:0% +and then you can just use these + + + align:start position:0% +and then you can just use these +functions to break up the code a very + + align:start position:0% +functions to break up the code a very + + + align:start position:0% +functions to break up the code a very +large piece of code into smaller little + + align:start position:0% +large piece of code into smaller little + + + align:start position:0% +large piece of code into smaller little +self-contain modules and then the maybe + + align:start position:0% +self-contain modules and then the maybe + + + align:start position:0% +self-contain modules and then the maybe +the bulk of the work that the code is + + align:start position:0% +the bulk of the work that the code is + + + align:start position:0% +the bulk of the work that the code is +doing is just saying hey mod you you + + align:start position:0% +doing is just saying hey mod you you + + + align:start position:0% +doing is just saying hey mod you you +know this module please give me this + + align:start position:0% +know this module please give me this + + + align:start position:0% +know this module please give me this +answer and then this module give me this + + align:start position:0% +answer and then this module give me this + + + align:start position:0% +answer and then this module give me this +answer and then uh putting those values + + align:start position:0% +answer and then uh putting those values + + + align:start position:0% +answer and then uh putting those values +back together again + + align:start position:0% + + + + align:start position:0% + +so these reusable pieces of code are + + align:start position:0% +so these reusable pieces of code are + + + align:start position:0% +so these reusable pieces of code are +called functions or procedures we're + + align:start position:0% +called functions or procedures we're + + + align:start position:0% +called functions or procedures we're +basically going to try to capture some + + align:start position:0% +basically going to try to capture some + + + align:start position:0% +basically going to try to capture some +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +computation uh a very useful task that + + align:start position:0% +computation uh a very useful task that + + + align:start position:0% +computation uh a very useful task that +you'd want to do over and over again + + align:start position:0% +you'd want to do over and over again + + + align:start position:0% +you'd want to do over and over again +and we're going to see some details + + align:start position:0% +and we're going to see some details + + + align:start position:0% +and we're going to see some details +about how to write functions but + + align:start position:0% +about how to write functions but + + + align:start position:0% +about how to write functions but +essentially it's just going to be code + + align:start position:0% +essentially it's just going to be code + + + align:start position:0% +essentially it's just going to be code +that you've already been writing just + + align:start position:0% +that you've already been writing just + + + align:start position:0% +that you've already been writing just +written in a special way that makes it + + align:start position:0% +written in a special way that makes it + + + align:start position:0% +written in a special way that makes it +reusable Okay so we're going to have to + + align:start position:0% +reusable Okay so we're going to have to + + + align:start position:0% +reusable Okay so we're going to have to +kind of switch the way we've been + + align:start position:0% +kind of switch the way we've been + + + align:start position:0% +kind of switch the way we've been +thinking about code for a bit now that + + align:start position:0% +thinking about code for a bit now that + + + align:start position:0% +thinking about code for a bit now that +we're introducing functions because + + align:start position:0% +we're introducing functions because + + + align:start position:0% +we're introducing functions because +right now when we've been writing + + align:start position:0% +right now when we've been writing + + + align:start position:0% +right now when we've been writing +functions in a file we basically write + + align:start position:0% +functions in a file we basically write + + + align:start position:0% +functions in a file we basically write +some code top to + + align:start position:0% +some code top to + + + align:start position:0% +some code top to +bottom and then we think about that code + + align:start position:0% +bottom and then we think about that code + + + align:start position:0% +bottom and then we think about that code +as being executed line by line top to + + align:start position:0% +as being executed line by line top to + + + align:start position:0% +as being executed line by line top to +bottom but now that we're creating these + + align:start position:0% +bottom but now that we're creating these + + + align:start position:0% +bottom but now that we're creating these +things called functions little blocks of + + align:start position:0% +things called functions little blocks of + + + align:start position:0% +things called functions little blocks of +code that we can use many times in many + + align:start position:0% +code that we can use many times in many + + + align:start position:0% +code that we can use many times in many +different places in our code we're + + align:start position:0% +different places in our code we're + + + align:start position:0% +different places in our code we're +actually going to introduce the idea of + + align:start position:0% +actually going to introduce the idea of + + + align:start position:0% +actually going to introduce the idea of +defining a function so that means we're + + align:start position:0% +defining a function so that means we're + + + align:start position:0% +defining a function so that means we're +going to write a piece of codee and all + + align:start position:0% +going to write a piece of codee and all + + + align:start position:0% +going to write a piece of codee and all +that piece of code is going to do is + + align:start position:0% +that piece of code is going to do is + + + align:start position:0% +that piece of code is going to do is +tell python that this is a module or a + + align:start position:0% +tell python that this is a module or a + + + align:start position:0% +tell python that this is a module or a +function that exists in my + + align:start position:0% +function that exists in my + + + align:start position:0% +function that exists in my +program all we're doing is defining the + + align:start position:0% +program all we're doing is defining the + + + align:start position:0% +program all we're doing is defining the +function but we're not actually going to + + align:start position:0% +function but we're not actually going to + + + align:start position:0% +function but we're not actually going to +run the function when we Define it okay + + align:start position:0% +run the function when we Define it okay + + + align:start position:0% +run the function when we Define it okay +and that's kind of the difference that + + align:start position:0% +and that's kind of the difference that + + + align:start position:0% +and that's kind of the difference that +the way that we're going to have to + + align:start position:0% +the way that we're going to have to + + + align:start position:0% +the way that we're going to have to +shift our thinking here so when you + + align:start position:0% +shift our thinking here so when you + + + align:start position:0% +shift our thinking here so when you +define a function you just tell python + + align:start position:0% +define a function you just tell python + + + align:start position:0% +define a function you just tell python +that here's some useful piece of code + + align:start position:0% +that here's some useful piece of code + + + align:start position:0% +that here's some useful piece of code +that exists that does something but it + + align:start position:0% +that exists that does something but it + + + align:start position:0% +that exists that does something but it +doesn't actually run until you call the + + align:start position:0% +doesn't actually run until you call the + + + align:start position:0% +doesn't actually run until you call the +function and the cool thing about + + align:start position:0% +function and the cool thing about + + + align:start position:0% +function and the cool thing about +writing a function is you once you wrote + + align:start position:0% +writing a function is you once you wrote + + + align:start position:0% +writing a function is you once you wrote +it once you can make a hundred different + + align:start position:0% +it once you can make a hundred different + + + align:start position:0% +it once you can make a hundred different +function calls to that one piece of code + + align:start position:0% +function calls to that one piece of code + + + align:start position:0% +function calls to that one piece of code +that you wrote later on in your program + + align:start position:0% +that you wrote later on in your program + + + align:start position:0% +that you wrote later on in your program +so you can call the function many times + + align:start position:0% +so you can call the function many times + + + align:start position:0% +so you can call the function many times +with different inputs to give you + + align:start position:0% +with different inputs to give you + + + align:start position:0% +with different inputs to give you +different outputs but you only had to + + align:start position:0% +different outputs but you only had to + + + align:start position:0% +different outputs but you only had to +write it one time so I would compare + + align:start position:0% +write it one time so I would compare + + + align:start position:0% +write it one time so I would compare +this to when we write code in a file + + align:start position:0% +this to when we write code in a file + + + align:start position:0% +this to when we write code in a file +right when we write code in a file yes + + align:start position:0% +right when we write code in a file yes + + + align:start position:0% +right when we write code in a file yes +we can write a whole bunch of lines but + + align:start position:0% +we can write a whole bunch of lines but + + + align:start position:0% +we can write a whole bunch of lines but +this code isn't running as we're writing + + align:start position:0% +this code isn't running as we're writing + + + align:start position:0% +this code isn't running as we're writing +it right we have to actually push the + + align:start position:0% +it right we have to actually push the + + + align:start position:0% +it right we have to actually push the +Run button to run that file so similarly + + align:start position:0% +Run button to run that file so similarly + + + align:start position:0% +Run button to run that file so similarly +when we're telling python that I'm going + + align:start position:0% +when we're telling python that I'm going + + + align:start position:0% +when we're telling python that I'm going +to create this function that does + + align:start position:0% +to create this function that does + + + align:start position:0% +to create this function that does +something useful it's not actually + + align:start position:0% +something useful it's not actually + + + align:start position:0% +something useful it's not actually +running those lines we have to tell + + align:start position:0% +running those lines we have to tell + + + align:start position:0% +running those lines we have to tell +python that we want to run this + + align:start position:0% +python that we want to run this + + + align:start position:0% +python that we want to run this +function so the first thing we're going + + align:start position:0% +function so the first thing we're going + + + align:start position:0% +function so the first thing we're going +to do in this uh in this lecture is just + + align:start position:0% +to do in this uh in this lecture is just + + + align:start position:0% +to do in this uh in this lecture is just +actually create a function we're gonna + + align:start position:0% +actually create a function we're gonna + + + align:start position:0% +actually create a function we're gonna +I'm going to show you how to define a + + align:start position:0% +I'm going to show you how to define a + + + align:start position:0% +I'm going to show you how to define a +function so tell python that this + + align:start position:0% +function so tell python that this + + + align:start position:0% +function so tell python that this +function exists and then we'll see how + + align:start position:0% +function exists and then we'll see how + + + align:start position:0% +function exists and then we'll see how +to actually run the function to give us + + align:start position:0% +to actually run the function to give us + + + align:start position:0% +to actually run the function to give us +some useful + + align:start position:0% +some useful + + + align:start position:0% +some useful +values so the function characteristics + + align:start position:0% +values so the function characteristics + + + align:start position:0% +values so the function characteristics +are going to be uh the function has to + + align:start position:0% +are going to be uh the function has to + + + align:start position:0% +are going to be uh the function has to +have a name so just like when you create + + align:start position:0% +have a name so just like when you create + + + align:start position:0% +have a name so just like when you create +variables right that store some useful + + align:start position:0% +variables right that store some useful + + + align:start position:0% +variables right that store some useful +value like pi to 20 decimal digits that + + align:start position:0% +value like pi to 20 decimal digits that + + + align:start position:0% +value like pi to 20 decimal digits that +you want to reuse over and over again + + align:start position:0% +you want to reuse over and over again + + + align:start position:0% +you want to reuse over and over again +we're going to create a function and + + align:start position:0% +we're going to create a function and + + + align:start position:0% +we're going to create a function and +that name is kind of like a handle for + + align:start position:0% +that name is kind of like a handle for + + + align:start position:0% +that name is kind of like a handle for +us to refer to this large chunk of code + + align:start position:0% +us to refer to this large chunk of code + + + align:start position:0% +us to refer to this large chunk of code +that does something useful for us + + align:start position:0% +that does something useful for us + + + align:start position:0% +that does something useful for us +a function has some inputs called + + align:start position:0% +a function has some inputs called + + + align:start position:0% +a function has some inputs called +parameters or arguments it could have no + + align:start position:0% +parameters or arguments it could have no + + + align:start position:0% +parameters or arguments it could have no +inputs or more or one or + + align:start position:0% +inputs or more or one or + + + align:start position:0% +inputs or more or one or +more and a function should have a doc + + align:start position:0% +more and a function should have a doc + + + align:start position:0% +more and a function should have a doc +string so this is the specification + + align:start position:0% +string so this is the specification + + + align:start position:0% +string so this is the specification +again just a multi-line comment that + + align:start position:0% +again just a multi-line comment that + + + align:start position:0% +again just a multi-line comment that +tells the user the person who wants to + + align:start position:0% +tells the user the person who wants to + + + align:start position:0% +tells the user the person who wants to +use this function the inputs what the + + align:start position:0% +use this function the inputs what the + + + align:start position:0% +use this function the inputs what the +function does and what the output or the + + align:start position:0% +function does and what the output or the + + + align:start position:0% +function does and what the output or the +return or whatever this function will do + + align:start position:0% +return or whatever this function will do + + + align:start position:0% +return or whatever this function will do +for + + align:start position:0% +for + + + align:start position:0% +for +you and then the body of the function is + + align:start position:0% +you and then the body of the function is + + + align:start position:0% +you and then the body of the function is +just python code exactly the kind of + + align:start position:0% +just python code exactly the kind of + + + align:start position:0% +just python code exactly the kind of +code we've already already been writing + + align:start position:0% +code we've already already been writing + + + align:start position:0% +code we've already already been writing +except not wrapped in a function right + + align:start position:0% +except not wrapped in a function right + + + align:start position:0% +except not wrapped in a function right +so if you found yourself writing a piece + + align:start position:0% +so if you found yourself writing a piece + + + align:start position:0% +so if you found yourself writing a piece +of code that did something useful you + + align:start position:0% +of code that did something useful you + + + align:start position:0% +of code that did something useful you +can totally wrap that in a function and + + align:start position:0% +can totally wrap that in a function and + + + align:start position:0% +can totally wrap that in a function and +um we'll see how to do that today right + + align:start position:0% +um we'll see how to do that today right + + + align:start position:0% +um we'll see how to do that today right +so the body of the function is just a + + align:start position:0% +so the body of the function is just a + + + align:start position:0% +so the body of the function is just a +bunch of lines of code that do this + + align:start position:0% +bunch of lines of code that do this + + + align:start position:0% +bunch of lines of code that do this +useful task the only difference in the + + align:start position:0% +useful task the only difference in the + + + align:start position:0% +useful task the only difference in the +body is that at some point this function + + align:start position:0% +body is that at some point this function + + + align:start position:0% +body is that at some point this function +has to end right it has finished its + + align:start position:0% +has to end right it has finished its + + + align:start position:0% +has to end right it has finished its +task it figured out a final value this + + align:start position:0% +task it figured out a final value this + + + align:start position:0% +task it figured out a final value this +useful thing that's kind of the result + + align:start position:0% +useful thing that's kind of the result + + + align:start position:0% +useful thing that's kind of the result +of your task and you want to give this + + align:start position:0% +of your task and you want to give this + + + align:start position:0% +of your task and you want to give this +value back to somebody who's using this + + align:start position:0% +value back to somebody who's using this + + + align:start position:0% +value back to somebody who's using this +function and we do that using this + + align:start position:0% +function and we do that using this + + + align:start position:0% +function and we do that using this +return keyword as we're going to see in + + align:start position:0% +return keyword as we're going to see in + + + align:start position:0% +return keyword as we're going to see in +the next + + align:start position:0% +the next + + + align:start position:0% +the next +slide so here's an example of a really + + align:start position:0% +slide so here's an example of a really + + + align:start position:0% +slide so here's an example of a really +simple + + align:start position:0% +simple + + + align:start position:0% +simple +function so it's just a definition so + + align:start position:0% +function so it's just a definition so + + + align:start position:0% +function so it's just a definition so +again this these lines of code do not + + align:start position:0% +again this these lines of code do not + + + align:start position:0% +again this these lines of code do not +run here we're just telling python that + + align:start position:0% +run here we're just telling python that + + + align:start position:0% +run here we're just telling python that +we're creating a function that does + + align:start position:0% +we're creating a function that does + + + align:start position:0% +we're creating a function that does +something so we kick that off with a DF + + align:start position:0% +something so we kick that off with a DF + + + align:start position:0% +something so we kick that off with a DF +defin keyword so notice it's blue if you + + align:start position:0% +defin keyword so notice it's blue if you + + + align:start position:0% +defin keyword so notice it's blue if you +type it in your code you'll notice it + + align:start position:0% +type it in your code you'll notice it + + + align:start position:0% +type it in your code you'll notice it +changes color color um so DF tells + + align:start position:0% +changes color color um so DF tells + + + align:start position:0% +changes color color um so DF tells +python we're defining a function the + + align:start position:0% +python we're defining a function the + + + align:start position:0% +python we're defining a function the +next is the name of the function so this + + align:start position:0% +next is the name of the function so this + + + align:start position:0% +next is the name of the function so this +should be something descriptive usually + + align:start position:0% +should be something descriptive usually + + + align:start position:0% +should be something descriptive usually +an action word right because a function + + align:start position:0% +an action word right because a function + + + align:start position:0% +an action word right because a function +does something so you want kind of like + + align:start position:0% +does something so you want kind of like + + + align:start position:0% +does something so you want kind of like +an action-y type uh uh name for your + + align:start position:0% +an action-y type uh uh name for your + + + align:start position:0% +an action-y type uh uh name for your +function then we have + + align:start position:0% +function then we have + + + align:start position:0% +function then we have +parenthesis and inside the parentheses + + align:start position:0% +parenthesis and inside the parentheses + + + align:start position:0% +parenthesis and inside the parentheses +you have any of the inputs the + + align:start position:0% +you have any of the inputs the + + + align:start position:0% +you have any of the inputs the +parameters the arguments to the function + + align:start position:0% +parameters the arguments to the function + + + align:start position:0% +parameters the arguments to the function +right so what should the user give you + + align:start position:0% +right so what should the user give you + + + align:start position:0% +right so what should the user give you +as input to this function and then of + + align:start position:0% +as input to this function and then of + + + align:start position:0% +as input to this function and then of +course a Cod + + align:start position:0% +course a Cod + + + align:start position:0% +course a Cod +so in that line right there the only + + align:start position:0% +so in that line right there the only + + + align:start position:0% +so in that line right there the only +thing that is sort of customizable quote + + align:start position:0% +thing that is sort of customizable quote + + + align:start position:0% +thing that is sort of customizable quote +unquote is the name of the function and + + align:start position:0% +unquote is the name of the function and + + + align:start position:0% +unquote is the name of the function and +the parameters if there's zero + + align:start position:0% +the parameters if there's zero + + + align:start position:0% +the parameters if there's zero +parameters you put nothing in there if + + align:start position:0% +parameters you put nothing in there if + + + align:start position:0% +parameters you put nothing in there if +there's more than one you separate them + + align:start position:0% +there's more than one you separate them + + + align:start position:0% +there's more than one you separate them +by + + align:start position:0% +by + + + align:start position:0% +by +commas everything else should be uh is + + align:start position:0% +commas everything else should be uh is + + + align:start position:0% +commas everything else should be uh is +standard the DF the parenthesis and the + + align:start position:0% +standard the DF the parenthesis and the + + + align:start position:0% +standard the DF the parenthesis and the +colon at the + + align:start position:0% +colon at the + + + align:start position:0% +colon at the +end since we have a colon at the end + + align:start position:0% +end since we have a colon at the end + + + align:start position:0% +end since we have a colon at the end +then we uh that means we have to indent + + align:start position:0% +then we uh that means we have to indent + + + align:start position:0% +then we uh that means we have to indent +the next bit of code um that the indent + + align:start position:0% +the next bit of code um that the indent + + + align:start position:0% +the next bit of code um that the indent +ation will tell python that the rest of + + align:start position:0% +ation will tell python that the rest of + + + align:start position:0% +ation will tell python that the rest of +this is part of the function so + + align:start position:0% +this is part of the function so + + + align:start position:0% +this is part of the function so +everything from here on out is part of + + align:start position:0% +everything from here on out is part of + + + align:start position:0% +everything from here on out is part of +the function definition so we have our + + align:start position:0% +the function definition so we have our + + + align:start position:0% +the function definition so we have our +doc string of course um you start with + + align:start position:0% +doc string of course um you start with + + + align:start position:0% +doc string of course um you start with +triple quotes and you end it with triple + + align:start position:0% +triple quotes and you end it with triple + + + align:start position:0% +triple quotes and you end it with triple +quotes and in it you can write whatever + + align:start position:0% +quotes and in it you can write whatever + + + align:start position:0% +quotes and in it you can write whatever +you want just treat it like a comment + + align:start position:0% +you want just treat it like a comment + + + align:start position:0% +you want just treat it like a comment +that's on multiple lines okay and you + + align:start position:0% +that's on multiple lines okay and you + + + align:start position:0% +that's on multiple lines okay and you +can see here I've said that this + + align:start position:0% +can see here I've said that this + + + align:start position:0% +can see here I've said that this +function takes in an input I which I + + align:start position:0% +function takes in an input I which I + + + align:start position:0% +function takes in an input I which I +restrict to be a positive integer and + + align:start position:0% +restrict to be a positive integer and + + + align:start position:0% +restrict to be a positive integer and +then I say what the input uh gives back + + align:start position:0% +then I say what the input uh gives back + + + align:start position:0% +then I say what the input uh gives back +to the user so it will return true if I + + align:start position:0% +to the user so it will return true if I + + + align:start position:0% +to the user so it will return true if I +is an even number and uh it will return + + align:start position:0% +is an even number and uh it will return + + + align:start position:0% +is an even number and uh it will return +false otherwise okay so I've hit all the + + align:start position:0% +false otherwise okay so I've hit all the + + + align:start position:0% +false otherwise okay so I've hit all the +points the inputs what the function does + + align:start position:0% +points the inputs what the function does + + + align:start position:0% +points the inputs what the function does +and what it gives back to whoever wants + + align:start position:0% +and what it gives back to whoever wants + + + align:start position:0% +and what it gives back to whoever wants +this function to run + + align:start position:0% +this function to run + + + align:start position:0% +this function to run +okay um beyond that we have the body of + + align:start position:0% +okay um beyond that we have the body of + + + align:start position:0% +okay um beyond that we have the body of +the function so here you notice it's + + align:start position:0% +the function so here you notice it's + + + align:start position:0% +the function so here you notice it's +just lines of code that you would have + + align:start position:0% +just lines of code that you would have + + + align:start position:0% +just lines of code that you would have +written otherwise right if you g if you + + align:start position:0% +written otherwise right if you g if you + + + align:start position:0% +written otherwise right if you g if you +were given uh the problem on a quiz that + + align:start position:0% +were given uh the problem on a quiz that + + + align:start position:0% +were given uh the problem on a quiz that +said given I defined for you you write + + align:start position:0% +said given I defined for you you write + + + align:start position:0% +said given I defined for you you write +some code that that you know prints true + + align:start position:0% +some code that that you know prints true + + + align:start position:0% +some code that that you know prints true +if the number is O is um even and false + + align:start position:0% +if the number is O is um even and false + + + align:start position:0% +if the number is O is um even and false +if the number is odd this is basically + + align:start position:0% +if the number is odd this is basically + + + align:start position:0% +if the number is odd this is basically +lines of code that you would type in the + + align:start position:0% +lines of code that you would type in the + + + align:start position:0% +lines of code that you would type in the +only difference is this little return + + align:start position:0% +only difference is this little return + + + align:start position:0% +only difference is this little return +here right the function is sort of some + + align:start position:0% +here right the function is sort of some + + + align:start position:0% +here right the function is sort of some +lines of code that do a task and that + + align:start position:0% +lines of code that do a task and that + + + align:start position:0% +lines of code that do a task and that +task when it finishes has to give + + align:start position:0% +task when it finishes has to give + + + align:start position:0% +task when it finishes has to give +something back right it can't just sit + + align:start position:0% +something back right it can't just sit + + + align:start position:0% +something back right it can't just sit +there I guess um and the thing that it + + align:start position:0% +there I guess um and the thing that it + + + align:start position:0% +there I guess um and the thing that it +gives back whoever called whoever wants + + align:start position:0% +gives back whoever called whoever wants + + + align:start position:0% +gives back whoever called whoever wants +this function to + + align:start position:0% +this function to + + + align:start position:0% +this function to +run is uh is set up by this return + + align:start position:0% +run is uh is set up by this return + + + align:start position:0% +run is uh is set up by this return +statement here okay so if the number is + + align:start position:0% +statement here okay so if the number is + + + align:start position:0% +statement here okay so if the number is +divisible by zero we return true and + + align:start position:0% +divisible by zero we return true and + + + align:start position:0% +divisible by zero we return true and +else we return false so one of these + + align:start position:0% +else we return false so one of these + + + align:start position:0% +else we return false so one of these +either true or false values will be + + align:start position:0% +either true or false values will be + + + align:start position:0% +either true or false values will be +returned by the function so this is kind + + align:start position:0% +returned by the function so this is kind + + + align:start position:0% +returned by the function so this is kind +of you can think of it like the output + + align:start position:0% +of you can think of it like the output + + + align:start position:0% +of you can think of it like the output +of the function + + align:start position:0% + + + + align:start position:0% + +okay okay question so far does this make + + align:start position:0% +okay okay question so far does this make + + + align:start position:0% +okay okay question so far does this make +sense again this is just us creating + + align:start position:0% +sense again this is just us creating + + + align:start position:0% +sense again this is just us creating +this function inside the computer inside + + align:start position:0% +this function inside the computer inside + + + align:start position:0% +this function inside the computer inside +python we're not actually running these + + align:start position:0% +python we're not actually running these + + + align:start position:0% +python we're not actually running these +lines of code + + align:start position:0% +lines of code + + + align:start position:0% +lines of code +yet + + align:start position:0% +yet + + + align:start position:0% +yet +okay so if you are given sort of a + + align:start position:0% +okay so if you are given sort of a + + + align:start position:0% +okay so if you are given sort of a +larger problem I just want to take a + + align:start position:0% +larger problem I just want to take a + + + align:start position:0% +larger problem I just want to take a +couple slides to talk about how you + + align:start position:0% +couple slides to talk about how you + + + align:start position:0% +couple slides to talk about how you +think about writing the function um this + + align:start position:0% +think about writing the function um this + + + align:start position:0% +think about writing the function um this +was a really easy one so you know + + align:start position:0% +was a really easy one so you know + + + align:start position:0% +was a really easy one so you know +obviously it's not that hard to um to + + align:start position:0% +obviously it's not that hard to um to + + + align:start position:0% +obviously it's not that hard to um to +write but sort of what is the thought + + align:start position:0% +write but sort of what is the thought + + + align:start position:0% +write but sort of what is the thought +process if you were given a larger + + align:start position:0% +process if you were given a larger + + + align:start position:0% +process if you were given a larger +problem like in English or something + + align:start position:0% +problem like in English or something + + + align:start position:0% +problem like in English or something +like that and you wanted to translate + + align:start position:0% +like that and you wanted to translate + + + align:start position:0% +like that and you wanted to translate +this into uh a piece of code that does + + align:start position:0% +this into uh a piece of code that does + + + align:start position:0% +this into uh a piece of code that does +something functionally interesting okay + + align:start position:0% +something functionally interesting okay + + + align:start position:0% +something functionally interesting okay +so you think about what the problem is + + align:start position:0% +so you think about what the problem is + + + align:start position:0% +so you think about what the problem is +so our problem is given an integer + + align:start position:0% +so our problem is given an integer + + + align:start position:0% +so our problem is given an integer +figure out if it's even or odd okay so + + align:start position:0% +figure out if it's even or odd okay so + + + align:start position:0% +figure out if it's even or odd okay so +given this statement you could uh you + + align:start position:0% +given this statement you could uh you + + + align:start position:0% +given this statement you could uh you +could come up with the name of this uh + + align:start position:0% +could come up with the name of this uh + + + align:start position:0% +could come up with the name of this uh +piece of code that's functionally + + align:start position:0% +piece of code that's functionally + + + align:start position:0% +piece of code that's functionally +interesting so isore even is a good a + + align:start position:0% +interesting so isore even is a good a + + + align:start position:0% +interesting so isore even is a good a +good name + + align:start position:0% +good name + + + align:start position:0% +good name +and give and and we can also come up + + align:start position:0% +and give and and we can also come up + + + align:start position:0% +and give and and we can also come up +with the inputs for this function right + + align:start position:0% +with the inputs for this function right + + + align:start position:0% +with the inputs for this function right +so I we are only given one number so + + align:start position:0% +so I we are only given one number so + + + align:start position:0% +so I we are only given one number so +there's no need for this function to + + align:start position:0% +there's no need for this function to + + + align:start position:0% +there's no need for this function to +take in any other + + align:start position:0% +take in any other + + + align:start position:0% +take in any other +inputs and then using that description + + align:start position:0% +inputs and then using that description + + + align:start position:0% +inputs and then using that description +we can now start to fill in the doc + + align:start position:0% +we can now start to fill in the doc + + + align:start position:0% +we can now start to fill in the doc +string that says well our input is going + + align:start position:0% +string that says well our input is going + + + align:start position:0% +string that says well our input is going +to be a positive integer right we could + + align:start position:0% +to be a positive integer right we could + + + align:start position:0% +to be a positive integer right we could +use sort of math to figure out + + align:start position:0% +use sort of math to figure out + + + align:start position:0% +use sort of math to figure out +restrictions on the inputs and then we + + align:start position:0% +restrictions on the inputs and then we + + + align:start position:0% +restrictions on the inputs and then we +can write the do the rest of the dock + + align:start position:0% +can write the do the rest of the dock + + + align:start position:0% +can write the do the rest of the dock +string that tells us what to return and + + align:start position:0% +string that tells us what to return and + + + align:start position:0% +string that tells us what to return and +when right what the function is + + align:start position:0% +when right what the function is + + + align:start position:0% +when right what the function is +doing and once you have that you can + + align:start position:0% +doing and once you have that you can + + + align:start position:0% +doing and once you have that you can +just uh solve the problem so for us we + + align:start position:0% +just uh solve the problem so for us we + + + align:start position:0% +just uh solve the problem so for us we +solve the problem by basically saying if + + align:start position:0% +solve the problem by basically saying if + + + align:start position:0% +solve the problem by basically saying if +the remainder when we divide I by two is + + align:start position:0% +the remainder when we divide I by two is + + + align:start position:0% +the remainder when we divide I by two is +zero we return true and otherwise we + + align:start position:0% +zero we return true and otherwise we + + + align:start position:0% +zero we return true and otherwise we +return false okay so that's some that's + + align:start position:0% +return false okay so that's some that's + + + align:start position:0% +return false okay so that's some that's +code that you could have already written + + align:start position:0% +code that you could have already written + + + align:start position:0% +code that you could have already written +um right without actually this function + + align:start position:0% +um right without actually this function + + + align:start position:0% +um right without actually this function +lecture but now we're putting it in the + + align:start position:0% +lecture but now we're putting it in the + + + align:start position:0% +lecture but now we're putting it in the +context of a function definition so + + align:start position:0% +context of a function definition so + + + align:start position:0% +context of a function definition so +we're going to be able to run this + + align:start position:0% +we're going to be able to run this + + + align:start position:0% +we're going to be able to run this +function with many different inputs to + + align:start position:0% +function with many different inputs to + + + align:start position:0% +function with many different inputs to +give us a bunch of different different + + align:start position:0% +give us a bunch of different different + + + align:start position:0% +give us a bunch of different different +outputs whether a bunch of these + + align:start position:0% +outputs whether a bunch of these + + + align:start position:0% +outputs whether a bunch of these +different numbers are um are even or + + align:start position:0% +different numbers are um are even or + + + align:start position:0% +different numbers are um are even or +not + + align:start position:0% +not + + + align:start position:0% +not +okay so when we're writing the body of + + align:start position:0% +okay so when we're writing the body of + + + align:start position:0% +okay so when we're writing the body of +the code the only difference is from + + align:start position:0% +the code the only difference is from + + + align:start position:0% +the code the only difference is from +what you've been doing is the return + + align:start position:0% +what you've been doing is the return + + + align:start position:0% +what you've been doing is the return +statement right instead of printing + + align:start position:0% +statement right instead of printing + + + align:start position:0% +statement right instead of printing +something out to the console we're going + + align:start position:0% +something out to the console we're going + + + align:start position:0% +something out to the console we're going +to return a value to somebody who + + align:start position:0% +to return a value to somebody who + + + align:start position:0% +to return a value to somebody who +wants to know whether the number I is + + align:start position:0% +wants to know whether the number I is + + + align:start position:0% +wants to know whether the number I is +even or odd the function can also print + + align:start position:0% +even or odd the function can also print + + + align:start position:0% +even or odd the function can also print +stuff to the console but the key thing + + align:start position:0% +stuff to the console but the key thing + + + align:start position:0% +stuff to the console but the key thing +here is you want to return a value to + + align:start position:0% +here is you want to return a value to + + + align:start position:0% +here is you want to return a value to +the + + align:start position:0% +the + + + align:start position:0% +the +user and after you wrote code you know + + align:start position:0% +user and after you wrote code you know + + + align:start position:0% +user and after you wrote code you know +right off the bat and you tested and + + align:start position:0% +right off the bat and you tested and + + + align:start position:0% +right off the bat and you tested and +made sure it works you can uh improve + + align:start position:0% +made sure it works you can uh improve + + + align:start position:0% +made sure it works you can uh improve +the code a little bit so here we're + + align:start position:0% +the code a little bit so here we're + + + align:start position:0% +the code a little bit so here we're +improving it by noticing that i% 2 equal + + align:start position:0% +improving it by noticing that i% 2 equal + + + align:start position:0% +improving it by noticing that i% 2 equal +equal Z here is actually already a + + align:start position:0% +equal Z here is actually already a + + + align:start position:0% +equal Z here is actually already a +Boolean right if I is even 3% 2 equal + + align:start position:0% +Boolean right if I is even 3% 2 equal + + + align:start position:0% +Boolean right if I is even 3% 2 equal +equal Z is true and otherwise it's + + align:start position:0% +equal Z is true and otherwise it's + + + align:start position:0% +equal Z is true and otherwise it's +already false so this line uh these four + + align:start position:0% +already false so this line uh these four + + + align:start position:0% +already false so this line uh these four +lines of code basically say if true + + align:start position:0% +lines of code basically say if true + + + align:start position:0% +lines of code basically say if true +return true else return + + align:start position:0% +return true else return + + + align:start position:0% +return true else return +false so our Improvement can just be to + + align:start position:0% +false so our Improvement can just be to + + + align:start position:0% +false so our Improvement can just be to +return whether I percent two equal equal + + align:start position:0% +return whether I percent two equal equal + + + align:start position:0% +return whether I percent two equal equal +Zer right off the bat okay so here we're + + align:start position:0% +Zer right off the bat okay so here we're + + + align:start position:0% +Zer right off the bat okay so here we're +going to return either true or return + + align:start position:0% +going to return either true or return + + + align:start position:0% +going to return either true or return +false based on what i + + align:start position:0% +false based on what i + + + align:start position:0% +false based on what i +is so at this point again sorry I'm if + + align:start position:0% +is so at this point again sorry I'm if + + + align:start position:0% +is so at this point again sorry I'm if +I'm stressing this enough uh too much + + align:start position:0% +I'm stressing this enough uh too much + + + align:start position:0% +I'm stressing this enough uh too much +but it's really important to understand + + align:start position:0% +but it's really important to understand + + + align:start position:0% +but it's really important to understand +that once we write these lines of code + + align:start position:0% +that once we write these lines of code + + + align:start position:0% +that once we write these lines of code +in the context of a function definition + + align:start position:0% +in the context of a function definition + + + align:start position:0% +in the context of a function definition +these lines of code do not run they + + align:start position:0% +these lines of code do not run they + + + align:start position:0% +these lines of code do not run they +basically just sit in + + align:start position:0% +basically just sit in + + + align:start position:0% +basically just sit in +Python saying that there are these lines + + align:start position:0% +Python saying that there are these lines + + + align:start position:0% +Python saying that there are these lines +of code that correspond to some function + + align:start position:0% +of code that correspond to some function + + + align:start position:0% +of code that correspond to some function +object whose name is is even that's + + align:start position:0% +object whose name is is even that's + + + align:start position:0% +object whose name is is even that's +it so what we need to do now is to + + align:start position:0% +it so what we need to do now is to + + + align:start position:0% +it so what we need to do now is to +actually tell python to run these lines + + align:start position:0% +actually tell python to run these lines + + + align:start position:0% +actually tell python to run these lines +of + + align:start position:0% +of + + + align:start position:0% +of +code to do that we make a function call + + align:start position:0% +code to do that we make a function call + + + align:start position:0% +code to do that we make a function call +and again we've already been doing + + align:start position:0% +and again we've already been doing + + + align:start position:0% +and again we've already been doing +function calls just to functions that + + align:start position:0% +function calls just to functions that + + + align:start position:0% +function calls just to functions that +already exist in Python right just + + align:start position:0% +already exist in Python right just + + + align:start position:0% +already exist in Python right just +python itself Max absolute Len all that + + align:start position:0% +python itself Max absolute Len all that + + + align:start position:0% +python itself Max absolute Len all that +stuff but now we're making a function + + align:start position:0% +stuff but now we're making a function + + + align:start position:0% +stuff but now we're making a function +call to something that we + + align:start position:0% +call to something that we + + + align:start position:0% +call to something that we +wrote right this nice piece of code that + + align:start position:0% +wrote right this nice piece of code that + + + align:start position:0% +wrote right this nice piece of code that +tells us if a number the input is even + + align:start position:0% +tells us if a number the input is even + + + align:start position:0% +tells us if a number the input is even +or + + align:start position:0% +or + + + align:start position:0% +or +not so here I've got an uh I'm going to + + align:start position:0% +not so here I've got an uh I'm going to + + + align:start position:0% +not so here I've got an uh I'm going to +invoke the name of my function so I'm + + align:start position:0% +invoke the name of my function so I'm + + + align:start position:0% +invoke the name of my function so I'm +AKA I'm going to call the name of my + + align:start position:0% +AKA I'm going to call the name of my + + + align:start position:0% +AKA I'm going to call the name of my +function I'm basically just typing in + + align:start position:0% +function I'm basically just typing in + + + align:start position:0% +function I'm basically just typing in +the name of my function in the code + + align:start position:0% +the name of my function in the code + + + align:start position:0% +the name of my function in the code +parentheses and then the inputs the + + align:start position:0% +parentheses and then the inputs the + + + align:start position:0% +parentheses and then the inputs the +function expects there's only one right + + align:start position:0% +function expects there's only one right + + + align:start position:0% +function expects there's only one right +the number I want to figure out if it's + + align:start position:0% +the number I want to figure out if it's + + + align:start position:0% +the number I want to figure out if it's +even or odd and then that's it right so + + align:start position:0% +even or odd and then that's it right so + + + align:start position:0% +even or odd and then that's it right so +I've got the name of my function and + + align:start position:0% +I've got the name of my function and + + + align:start position:0% +I've got the name of my function and +then all the uh inputs the parameters + + align:start position:0% +then all the uh inputs the parameters + + + align:start position:0% +then all the uh inputs the parameters +that this function + + align:start position:0% +that this function + + + align:start position:0% +that this function +expects at this point python goes into + + align:start position:0% +expects at this point python goes into + + + align:start position:0% +expects at this point python goes into +the function body it runs the + + align:start position:0% +the function body it runs the + + + align:start position:0% +the function body it runs the +function and it returns back a value so + + align:start position:0% +function and it returns back a value so + + + align:start position:0% +function and it returns back a value so +whatever the value is associated with + + align:start position:0% +whatever the value is associated with + + + align:start position:0% +whatever the value is associated with +the + + align:start position:0% +the + + + align:start position:0% +the +return is that value will immediately be + + align:start position:0% +return is that value will immediately be + + + align:start position:0% +return is that value will immediately be +given back to whoever called it what + + align:start position:0% +given back to whoever called it what + + + align:start position:0% +given back to whoever called it what +does that mean well that return value + + align:start position:0% +does that mean well that return value + + + align:start position:0% +does that mean well that return value +will completely replace this function + + align:start position:0% +will completely replace this function + + + align:start position:0% +will completely replace this function +call okay + + align:start position:0% +call okay + + + align:start position:0% +call okay +so let's think back to Expressions do + + align:start position:0% +so let's think back to Expressions do + + + align:start position:0% +so let's think back to Expressions do +you remember when we were learning about + + align:start position:0% +you remember when we were learning about + + + align:start position:0% +you remember when we were learning about +python expressions and I said you have + + align:start position:0% +python expressions and I said you have + + + align:start position:0% +python expressions and I said you have +something like object operator object + + align:start position:0% +something like object operator object + + + align:start position:0% +something like object operator object +like 3 + 2 that was an expression and + + align:start position:0% +like 3 + 2 that was an expression and + + + align:start position:0% +like 3 + 2 that was an expression and +python went in evaluated that expression + + align:start position:0% +python went in evaluated that expression + + + align:start position:0% +python went in evaluated that expression +and replaced that entire expression by + + align:start position:0% +and replaced that entire expression by + + + align:start position:0% +and replaced that entire expression by +the value + + align:start position:0% +the value + + + align:start position:0% +the value +five this is exactly the same thing in + + align:start position:0% +five this is exactly the same thing in + + + align:start position:0% +five this is exactly the same thing in +fact functions are kind of like python + + align:start position:0% +fact functions are kind of like python + + + align:start position:0% +fact functions are kind of like python +Expressions they do something useful + + align:start position:0% +Expressions they do something useful + + + align:start position:0% +Expressions they do something useful +right it's just that it's not math or + + align:start position:0% +right it's just that it's not math or + + + align:start position:0% +right it's just that it's not math or +something like that that gets evaluated + + align:start position:0% +something like that that gets evaluated + + + align:start position:0% +something like that that gets evaluated +it's a bunch of lines of code that get + + align:start position:0% +it's a bunch of lines of code that get + + + align:start position:0% +it's a bunch of lines of code that get +evaluated but in the end that function + + align:start position:0% +evaluated but in the end that function + + + align:start position:0% +evaluated but in the end that function +returns back only one + + align:start position:0% +returns back only one + + + align:start position:0% +returns back only one +value okay and that value replaces the + + align:start position:0% +value okay and that value replaces the + + + align:start position:0% +value okay and that value replaces the +entire function call so this entire + + align:start position:0% +entire function call so this entire + + + align:start position:0% +entire function call so this entire +function call is going to be basically + + align:start position:0% +function call is going to be basically + + + align:start position:0% +function call is going to be basically +replaced by uh false right because it's + + align:start position:0% +replaced by uh false right because it's + + + align:start position:0% +replaced by uh false right because it's +an odd number and the next one is going + + align:start position:0% +an odd number and the next one is going + + + align:start position:0% +an odd number and the next one is going +to be replaced by + + align:start position:0% +to be replaced by + + + align:start position:0% +to be replaced by +true right the return from the + + align:start position:0% +true right the return from the + + + align:start position:0% +true right the return from the +function so the way that the code looks + + align:start position:0% +function so the way that the code looks + + + align:start position:0% +function so the way that the code looks +just this definition of is even and then + + align:start position:0% +just this definition of is even and then + + + align:start position:0% +just this definition of is even and then +running a function call is this this is + + align:start position:0% +running a function call is this this is + + + align:start position:0% +running a function call is this this is +all that we would have in our in our + + align:start position:0% +all that we would have in our in our + + + align:start position:0% +all that we would have in our in our +file right so here we have our function + + align:start position:0% +file right so here we have our function + + + align:start position:0% +file right so here we have our function +definition and then at the same + + align:start position:0% +definition and then at the same + + + align:start position:0% +definition and then at the same +indentation level we have a function + + align:start position:0% +indentation level we have a function + + + align:start position:0% +indentation level we have a function +call right because it's not the call is + + align:start position:0% +call right because it's not the call is + + + align:start position:0% +call right because it's not the call is +not part of the function the call is + + align:start position:0% +not part of the function the call is + + + align:start position:0% +not part of the function the call is +just making use of the function that we + + align:start position:0% +just making use of the function that we + + + align:start position:0% +just making use of the function that we +wrote okay so what exactly happens we'll + + align:start position:0% +wrote okay so what exactly happens we'll + + + align:start position:0% +wrote okay so what exactly happens we'll +do a little bit of step by step now + + align:start position:0% +do a little bit of step by step now + + + align:start position:0% +do a little bit of step by step now +going a little bit into more detail as + + align:start position:0% +going a little bit into more detail as + + + align:start position:0% +going a little bit into more detail as +to what exactly happens when we make the + + align:start position:0% +to what exactly happens when we make the + + + align:start position:0% +to what exactly happens when we make the +function + + align:start position:0% +function + + + align:start position:0% +function +call so when we make the function call + + align:start position:0% +call so when we make the function call + + + align:start position:0% +call so when we make the function call +so again function definition this just + + align:start position:0% +so again function definition this just + + + align:start position:0% +so again function definition this just +tells python we have this this function + + align:start position:0% +tells python we have this this function + + + align:start position:0% +tells python we have this this function +that does something in in in our in our + + align:start position:0% +that does something in in in our in our + + + align:start position:0% +that does something in in in our in our +program and then here we have the + + align:start position:0% +program and then here we have the + + + align:start position:0% +program and then here we have the +function called + + align:start position:0% +function called + + + align:start position:0% +function called +when as soon as python sees the function + + align:start position:0% +when as soon as python sees the function + + + align:start position:0% +when as soon as python sees the function +call that's when it starts doing + + align:start position:0% +call that's when it starts doing + + + align:start position:0% +call that's when it starts doing +something useful up here it just sort of + + align:start position:0% +something useful up here it just sort of + + + align:start position:0% +something useful up here it just sort of +stores this in memory so as soon as it + + align:start position:0% +stores this in memory so as soon as it + + + align:start position:0% +stores this in memory so as soon as it +sees the function call is even three it + + align:start position:0% +sees the function call is even three it + + + align:start position:0% +sees the function call is even three it +looks at the input parameter to the + + align:start position:0% +looks at the input parameter to the + + + align:start position:0% +looks at the input parameter to the +function call and here you see we have a + + align:start position:0% +function call and here you see we have a + + + align:start position:0% +function call and here you see we have a +value right it's an actual tangible + + align:start position:0% +value right it's an actual tangible + + + align:start position:0% +value right it's an actual tangible +object it's not a some random variable + + align:start position:0% +object it's not a some random variable + + + align:start position:0% +object it's not a some random variable +it's not something abstract it's a + + align:start position:0% +it's not something abstract it's a + + + align:start position:0% +it's not something abstract it's a +number + + align:start position:0% +number + + + align:start position:0% +number +three the I up here from our function + + align:start position:0% +three the I up here from our function + + + align:start position:0% +three the I up here from our function +definition is called a formal parameter + + align:start position:0% +definition is called a formal parameter + + + align:start position:0% +definition is called a formal parameter +it's abstract right we wrote the body of + + align:start position:0% +it's abstract right we wrote the body of + + + align:start position:0% +it's abstract right we wrote the body of +the function assuming the user will + + align:start position:0% +the function assuming the user will + + + align:start position:0% +the function assuming the user will +eventually give us a value for I but in + + align:start position:0% +eventually give us a value for I but in + + + align:start position:0% +eventually give us a value for I but in +the actual body of the function I is + + align:start position:0% +the actual body of the function I is + + + align:start position:0% +the actual body of the function I is +just a variable we're using kind of like + + align:start position:0% +just a variable we're using kind of like + + + align:start position:0% +just a variable we're using kind of like +in the quizzes right for now I've been + + align:start position:0% +in the quizzes right for now I've been + + + align:start position:0% +in the quizzes right for now I've been +I've been saying you know assume you're + + align:start position:0% +I've been saying you know assume you're + + + align:start position:0% +I've been saying you know assume you're +given some number n that's defined for + + align:start position:0% +given some number n that's defined for + + + align:start position:0% +given some number n that's defined for +you write the code assuming you know + + align:start position:0% +you write the code assuming you know + + + align:start position:0% +you write the code assuming you know +this number it's the exact same thing we + + align:start position:0% +this number it's the exact same thing we + + + align:start position:0% +this number it's the exact same thing we +write the code at the body of the + + align:start position:0% +write the code at the body of the + + + align:start position:0% +write the code at the body of the +function assuming we know a value for I + + align:start position:0% +function assuming we know a value for I + + + align:start position:0% +function assuming we know a value for I +so when python sees this function call + + align:start position:0% +so when python sees this function call + + + align:start position:0% +so when python sees this function call +with three it goes into the body of the + + align:start position:0% +with three it goes into the body of the + + + align:start position:0% +with three it goes into the body of the +function and says all right what are my + + align:start position:0% +function and says all right what are my + + + align:start position:0% +function and says all right what are my +parameters there's only one it's I and + + align:start position:0% +parameters there's only one it's I and + + + align:start position:0% +parameters there's only one it's I and +it's going to map them one by one to all + + align:start position:0% +it's going to map them one by one to all + + + align:start position:0% +it's going to map them one by one to all +the uh actual parameters given in the + + align:start position:0% +the uh actual parameters given in the + + + align:start position:0% +the uh actual parameters given in the +function call so basically just Maps I + + align:start position:0% +function call so basically just Maps I + + + align:start position:0% +function call so basically just Maps I +to + + align:start position:0% +to + + + align:start position:0% +to +three and then it executes the body of + + align:start position:0% +three and then it executes the body of + + + align:start position:0% +three and then it executes the body of +the function so it replaces everywhere + + align:start position:0% +the function so it replaces everywhere + + + align:start position:0% +the function so it replaces everywhere +you see I so it might have a longer bit + + align:start position:0% +you see I so it might have a longer bit + + + align:start position:0% +you see I so it might have a longer bit +of code here but here we just have one + + align:start position:0% +of code here but here we just have one + + + align:start position:0% +of code here but here we just have one +line it replaces I with + + align:start position:0% +line it replaces I with + + + align:start position:0% +line it replaces I with +three so we have 3% 2 equal equal Z now + + align:start position:0% +three so we have 3% 2 equal equal Z now + + + align:start position:0% +three so we have 3% 2 equal equal Z now +we have a tangible value right + + align:start position:0% +we have a tangible value right + + + align:start position:0% +we have a tangible value right +false so this expression is replaced + + align:start position:0% +false so this expression is replaced + + + align:start position:0% +false so this expression is replaced +with false and so this line of code here + + align:start position:0% +with false and so this line of code here + + + align:start position:0% +with false and so this line of code here +will return false and as soon as python + + align:start position:0% +will return false and as soon as python + + + align:start position:0% +will return false and as soon as python +sees that return value it immediately + + align:start position:0% +sees that return value it immediately + + + align:start position:0% +sees that return value it immediately +exits the function and gives back the + + align:start position:0% +exits the function and gives back the + + + align:start position:0% +exits the function and gives back the +value that you're returning to whoever + + align:start position:0% +value that you're returning to whoever + + + align:start position:0% +value that you're returning to whoever +called it so this entire function call + + align:start position:0% +called it so this entire function call + + + align:start position:0% +called it so this entire function call +here will be replaced by false + + align:start position:0% + + + + align:start position:0% + +okay that was very step by step but does + + align:start position:0% +okay that was very step by step but does + + + align:start position:0% +okay that was very step by step but does +it make + + align:start position:0% +it make + + + align:start position:0% +it make +sense okay so this is a program that + + align:start position:0% +sense okay so this is a program that + + + align:start position:0% +sense okay so this is a program that +doesn't do anything right if somebody + + align:start position:0% +doesn't do anything right if somebody + + + align:start position:0% +doesn't do anything right if somebody +were to write this program and run it it + + align:start position:0% +were to write this program and run it it + + + align:start position:0% +were to write this program and run it it +doesn't actually show anything to the + + align:start position:0% +doesn't actually show anything to the + + + align:start position:0% +doesn't actually show anything to the +user that's because in our program it's + + align:start position:0% +user that's because in our program it's + + + align:start position:0% +user that's because in our program it's +like we had just written a line of code + + align:start position:0% +like we had just written a line of code + + + align:start position:0% +like we had just written a line of code +that said false does that get printed to + + align:start position:0% +that said false does that get printed to + + + align:start position:0% +that said false does that get printed to +the + + align:start position:0% +the + + + align:start position:0% +the +output no right right what we need to do + + align:start position:0% +output no right right what we need to do + + + align:start position:0% +output no right right what we need to do +is do something useful now that we have + + align:start position:0% +is do something useful now that we have + + + align:start position:0% +is do something useful now that we have +the result of a function call so one + + align:start position:0% +the result of a function call so one + + + align:start position:0% +the result of a function call so one +useful thing we can do is to actually + + align:start position:0% +useful thing we can do is to actually + + + align:start position:0% +useful thing we can do is to actually +print the result of the function call + + align:start position:0% +print the result of the function call + + + align:start position:0% +print the result of the function call +right so here we have print and then I + + align:start position:0% +right so here we have print and then I + + + align:start position:0% +right so here we have print and then I +have my function call I had up here I'm + + align:start position:0% +have my function call I had up here I'm + + + align:start position:0% +have my function call I had up here I'm +just sticking it inside the print + + align:start position:0% +just sticking it inside the print + + + align:start position:0% +just sticking it inside the print +statement and python will as before + + align:start position:0% +statement and python will as before + + + align:start position:0% +statement and python will as before +evaluate is even three this is replaced + + align:start position:0% +evaluate is even three this is replaced + + + align:start position:0% +evaluate is even three this is replaced +with false and this line essentially + + align:start position:0% +with false and this line essentially + + + align:start position:0% +with false and this line essentially +becomes print + + align:start position:0% +becomes print + + + align:start position:0% +becomes print +false okay + + align:start position:0% +false okay + + + align:start position:0% +false okay +and so the way this looks in our actual + + align:start position:0% +and so the way this looks in our actual + + + align:start position:0% +and so the way this looks in our actual +code is this right so here I + + align:start position:0% +code is this right so here I + + + align:start position:0% +code is this right so here I +have + + align:start position:0% +have + + + align:start position:0% +have +um uh this is even function the uh + + align:start position:0% +um uh this is even function the uh + + + align:start position:0% +um uh this is even function the uh +inefficient way of writing it I've got + + align:start position:0% +inefficient way of writing it I've got + + + align:start position:0% +inefficient way of writing it I've got +two function calls here but if I run the + + align:start position:0% +two function calls here but if I run the + + + align:start position:0% +two function calls here but if I run the +code it doesn't print anything + + align:start position:0% +code it doesn't print anything + + + align:start position:0% +code it doesn't print anything +right I need to do something useful with + + align:start position:0% +right I need to do something useful with + + + align:start position:0% +right I need to do something useful with +them and one useful thing we can do is + + align:start position:0% +them and one useful thing we can do is + + + align:start position:0% +them and one useful thing we can do is +to print the result of these function + + align:start position:0% +to print the result of these function + + + align:start position:0% +to print the result of these function +calls so now that I've wrapped these + + align:start position:0% +calls so now that I've wrapped these + + + align:start position:0% +calls so now that I've wrapped these +calls inside a print statement I see the + + align:start position:0% +calls inside a print statement I see the + + + align:start position:0% +calls inside a print statement I see the +output in my + + align:start position:0% + + + + align:start position:0% + +console okay so we're writing so we're + + align:start position:0% +console okay so we're writing so we're + + + align:start position:0% +console okay so we're writing so we're +kind of separating ourselves right when + + align:start position:0% +kind of separating ourselves right when + + + align:start position:0% +kind of separating ourselves right when +we're writing code now one we're + + align:start position:0% +we're writing code now one we're + + + align:start position:0% +we're writing code now one we're +defining a function some code that does + + align:start position:0% +defining a function some code that does + + + align:start position:0% +defining a function some code that does +something useful and then two we're + + align:start position:0% +something useful and then two we're + + + align:start position:0% +something useful and then two we're +using this function that we wrote to + + align:start position:0% +using this function that we wrote to + + + align:start position:0% +using this function that we wrote to +make function calls and the beauty about + + align:start position:0% +make function calls and the beauty about + + + align:start position:0% +make function calls and the beauty about +writing the function is we only write it + + align:start position:0% +writing the function is we only write it + + + align:start position:0% +writing the function is we only write it +once and debug it once but now we can + + align:start position:0% +once and debug it once but now we can + + + align:start position:0% +once and debug it once but now we can +write run run it as many times as we'd + + align:start position:0% +write run run it as many times as we'd + + + align:start position:0% +write run run it as many times as we'd +like without functions we'd find + + align:start position:0% +like without functions we'd find + + + align:start position:0% +like without functions we'd find +ourselves copying and pasting right that + + align:start position:0% +ourselves copying and pasting right that + + + align:start position:0% +ourselves copying and pasting right that +piece of code that does something useful + + align:start position:0% +piece of code that does something useful + + + align:start position:0% +piece of code that does something useful +in many places in our code which could + + align:start position:0% +in many places in our code which could + + + align:start position:0% +in many places in our code which could +lead to errors the code is hard to + + align:start position:0% +lead to errors the code is hard to + + + align:start position:0% +lead to errors the code is hard to +modify it's hard to debug you might all + + align:start position:0% +modify it's hard to debug you might all + + + align:start position:0% +modify it's hard to debug you might all +that + + align:start position:0% +that + + + align:start position:0% +that +stuff + + align:start position:0% +stuff + + + align:start position:0% +stuff +okay okay I'll give you a chance to try + + align:start position:0% +okay okay I'll give you a chance to try + + + align:start position:0% +okay okay I'll give you a chance to try +this out for about a minute so let's + + align:start position:0% +this out for about a minute so let's + + + align:start position:0% +this out for about a minute so let's +have you write this code so here I'm + + align:start position:0% +have you write this code so here I'm + + + align:start position:0% +have you write this code so here I'm +giving you the function specification + + align:start position:0% +giving you the function specification + + + align:start position:0% +giving you the function specification +most of the time I'll give it to you + + align:start position:0% +most of the time I'll give it to you + + + align:start position:0% +most of the time I'll give it to you +even in quizzes I want you to write for + + align:start position:0% +even in quizzes I want you to write for + + + align:start position:0% +even in quizzes I want you to write for +me a function called divor by this one + + align:start position:0% +me a function called divor by this one + + + align:start position:0% +me a function called divor by this one +takes two + + align:start position:0% +takes two + + + align:start position:0% +takes two +parameters um both integers greater than + + align:start position:0% +parameters um both integers greater than + + + align:start position:0% +parameters um both integers greater than +zero n and d and this function will + + align:start position:0% +zero n and d and this function will + + + align:start position:0% +zero n and d and this function will +return true if D divides n evenly and + + align:start position:0% +return true if D divides n evenly and + + + align:start position:0% +return true if D divides n evenly and +false if it does not divide uh n + + align:start position:0% +false if it does not divide uh n + + + align:start position:0% +false if it does not divide uh n +evenly right so if you test it out with + + align:start position:0% +evenly right so if you test it out with + + + align:start position:0% +evenly right so if you test it out with +those two values the first one should + + align:start position:0% +those two values the first one should + + + align:start position:0% +those two values the first one should +give us false and the second one should + + align:start position:0% +give us false and the second one should + + + align:start position:0% +give us false and the second one should +give us true so as usual this is down in + + align:start position:0% +give us true so as usual this is down in + + + align:start position:0% +give us true so as usual this is down in +the python file so we have around line + + align:start position:0% +the python file so we have around line + + + align:start position:0% +the python file so we have around line +28 is is where you should start typing + + align:start position:0% +28 is is where you should start typing + + + align:start position:0% +28 is is where you should start typing +in your + + align:start position:0% + + + + align:start position:0% + +code does anyone have a start for + + align:start position:0% + + + + align:start position:0% + +me should be very similar to what we + + align:start position:0% +me should be very similar to what we + + + align:start position:0% +me should be very similar to what we +just + + align:start position:0% +just + + + align:start position:0% +just +yeah and like equal Z then print + + align:start position:0% + + + + align:start position:0% + +true + + align:start position:0% + + + + align:start position:0% + +print + + align:start position:0% +print + + + align:start position:0% +print +false okay so let's run the + + align:start position:0% +false okay so let's run the + + + align:start position:0% +false okay so let's run the +function oh let's just do it with one so + + align:start position:0% +function oh let's just do it with one so + + + align:start position:0% +function oh let's just do it with one so +the first one I'm expecting to print + + align:start position:0% + + + + align:start position:0% + +false it does print false but it also + + align:start position:0% +false it does print false but it also + + + align:start position:0% +false it does print false but it also +prints this weird none right after it + + align:start position:0% +prints this weird none right after it + + + align:start position:0% +prints this weird none right after it +actually this is something we want we're + + align:start position:0% +actually this is something we want we're + + + align:start position:0% +actually this is something we want we're +going to talk about uh next lecture but + + align:start position:0% +going to talk about uh next lecture but + + + align:start position:0% +going to talk about uh next lecture but +does anyone know an improvement we can + + align:start position:0% +does anyone know an improvement we can + + + align:start position:0% +does anyone know an improvement we can +make to the code + + align:start position:0% + + + + align:start position:0% + +Yes Yes actually you're right so instead + + align:start position:0% +Yes Yes actually you're right so instead + + + align:start position:0% +Yes Yes actually you're right so instead +of printing true right remember it's a + + align:start position:0% +of printing true right remember it's a + + + align:start position:0% +of printing true right remember it's a +function we want it to give us back the + + align:start position:0% +function we want it to give us back the + + + align:start position:0% +function we want it to give us back the +value true right so instead of printing + + align:start position:0% +value true right so instead of printing + + + align:start position:0% +value true right so instead of printing +we'll do a return true and we don't need + + align:start position:0% +we'll do a return true and we don't need + + + align:start position:0% +we'll do a return true and we don't need +the parentheses in this + + align:start position:0% +the parentheses in this + + + align:start position:0% +the parentheses in this +case and then we'll do a return + + align:start position:0% + + + + align:start position:0% + +false + + align:start position:0% +false + + + align:start position:0% +false +right so now we don't have that weird + + align:start position:0% +right so now we don't have that weird + + + align:start position:0% +right so now we don't have that weird +none right after it that's something I + + align:start position:0% +none right after it that's something I + + + align:start position:0% +none right after it that's something I +want I was going to talk about next + + align:start position:0% +want I was going to talk about next + + + align:start position:0% +want I was going to talk about next +lecture but basically when we had prints + + align:start position:0% +lecture but basically when we had prints + + + align:start position:0% +lecture but basically when we had prints +here what did the function return did it + + align:start position:0% +here what did the function return did it + + + align:start position:0% +here what did the function return did it +have a return statement inside + + align:start position:0% +have a return statement inside + + + align:start position:0% +have a return statement inside +it no right and so if there's no return + + align:start position:0% +it no right and so if there's no return + + + align:start position:0% +it no right and so if there's no return +statement inside the function python + + align:start position:0% +statement inside the function python + + + align:start position:0% +statement inside the function python +automatically returns this special none + + align:start position:0% +automatically returns this special none + + + align:start position:0% +automatically returns this special none +okay this is something we'll talk about + + align:start position:0% +okay this is something we'll talk about + + + align:start position:0% +okay this is something we'll talk about +next lecture more in detail but yeah the + + align:start position:0% +next lecture more in detail but yeah the + + + align:start position:0% +next lecture more in detail but yeah the +return true return false is is correct + + align:start position:0% +return true return false is is correct + + + align:start position:0% +return true return false is is correct +here + + align:start position:0% + + + + align:start position:0% + +yes return yeah yeah you don't need the + + align:start position:0% +yes return yeah yeah you don't need the + + + align:start position:0% +yes return yeah yeah you don't need the +return uh the if else just like before + + align:start position:0% +return uh the if else just like before + + + align:start position:0% +return uh the if else just like before +so we can just do + + align:start position:0% +so we can just do + + + align:start position:0% +so we can just do +return + + align:start position:0% +return + + + align:start position:0% +return +um this directly + + align:start position:0% +um this directly + + + align:start position:0% +um this directly +right then we can run it with the other + + align:start position:0% + + + + align:start position:0% + +one so the second one should actually + + align:start position:0% +one so the second one should actually + + + align:start position:0% +one so the second one should actually +return + + align:start position:0% +return + + + align:start position:0% +return +true but it returned false does anyone + + align:start position:0% +true but it returned false does anyone + + + align:start position:0% +true but it returned false does anyone +know the problem + + align:start position:0% + + + + align:start position:0% + +yeah yes exactly so actually we want the + + align:start position:0% +yeah yes exactly so actually we want the + + + align:start position:0% +yeah yes exactly so actually we want the +remainder when we divide uh n by D right + + align:start position:0% +remainder when we divide uh n by D right + + + align:start position:0% +remainder when we divide uh n by D right +so this is just flipped around and + + align:start position:0% +so this is just flipped around and + + + align:start position:0% +so this is just flipped around and +percent D equal equals zero + + align:start position:0% +percent D equal equals zero + + + align:start position:0% +percent D equal equals zero +yeah so it's a good thing we had two + + align:start position:0% +yeah so it's a good thing we had two + + + align:start position:0% +yeah so it's a good thing we had two +test cases to test for that and you + + align:start position:0% +test cases to test for that and you + + + align:start position:0% +test cases to test for that and you +don't have to test them with such big + + align:start position:0% +don't have to test them with such big + + + align:start position:0% +don't have to test them with such big +numbers you could obviously test them + + align:start position:0% +numbers you could obviously test them + + + align:start position:0% +numbers you could obviously test them +with some smaller numbers um as well so + + align:start position:0% +with some smaller numbers um as well so + + + align:start position:0% +with some smaller numbers um as well so +let's zoom out a little bit and talk + + align:start position:0% +let's zoom out a little bit and talk + + + align:start position:0% +let's zoom out a little bit and talk +about how how exactly functions are + + align:start position:0% +about how how exactly functions are + + + align:start position:0% +about how how exactly functions are +stored in memory right because I + + align:start position:0% +stored in memory right because I + + + align:start position:0% +stored in memory right because I +mentioned this thing about defining a + + align:start position:0% +mentioned this thing about defining a + + + align:start position:0% +mentioned this thing about defining a +function and that just doesn't do + + align:start position:0% +function and that just doesn't do + + + align:start position:0% +function and that just doesn't do +anything really that we can see but what + + align:start position:0% +anything really that we can see but what + + + align:start position:0% +anything really that we can see but what +exactly happens in memory well let's + + align:start position:0% +exactly happens in memory well let's + + + align:start position:0% +exactly happens in memory well let's +think about what happens when we create + + align:start position:0% +think about what happens when we create + + + align:start position:0% +think about what happens when we create +variables so when we create a is equal + + align:start position:0% +variables so when we create a is equal + + + align:start position:0% +variables so when we create a is equal +to three inside memory or the program + + align:start position:0% +to three inside memory or the program + + + align:start position:0% +to three inside memory or the program +scope again we'll talk about this next + + align:start position:0% +scope again we'll talk about this next + + + align:start position:0% +scope again we'll talk about this next +lecture but you can think of this as the + + align:start position:0% +lecture but you can think of this as the + + + align:start position:0% +lecture but you can think of this as the +memory what happens is a becomes a + + align:start position:0% +memory what happens is a becomes a + + + align:start position:0% +memory what happens is a becomes a +variable that's bound to Value three b + + align:start position:0% +variable that's bound to Value three b + + + align:start position:0% +variable that's bound to Value three b +equals 4 is a variable B bound to value + + align:start position:0% +equals 4 is a variable B bound to value + + + align:start position:0% +equals 4 is a variable B bound to value +four and C is going to be bound to Value + + align:start position:0% +four and C is going to be bound to Value + + + align:start position:0% +four and C is going to be bound to Value +seven clear right we already know + + align:start position:0% +seven clear right we already know + + + align:start position:0% +seven clear right we already know +this what happens when we create a + + align:start position:0% +this what happens when we create a + + + align:start position:0% +this what happens when we create a +function so again this is something I + + align:start position:0% +function so again this is something I + + + align:start position:0% +function so again this is something I +might write in a code file the top bit + + align:start position:0% +might write in a code file the top bit + + + align:start position:0% +might write in a code file the top bit +is my function definition so as soon as + + align:start position:0% +is my function definition so as soon as + + + align:start position:0% +is my function definition so as soon as +python sees this DF + + align:start position:0% +python sees this DF + + + align:start position:0% +python sees this DF +keyword everything that's indented + + align:start position:0% +keyword everything that's indented + + + align:start position:0% +keyword everything that's indented +that's part of the function definition + + align:start position:0% +that's part of the function definition + + + align:start position:0% +that's part of the function definition +in the body is essentially just some + + align:start position:0% +in the body is essentially just some + + + align:start position:0% +in the body is essentially just some +code right + + align:start position:0% +code right + + + align:start position:0% +code right +to the to python it does not care at + + align:start position:0% +to the to python it does not care at + + + align:start position:0% +to the to python it does not care at +this point what that code is or what + + align:start position:0% +this point what that code is or what + + + align:start position:0% +this point what that code is or what +that code does all it knows is that + + align:start position:0% +that code does all it knows is that + + + align:start position:0% +that code does all it knows is that +there is a function object and functions + + align:start position:0% +there is a function object and functions + + + align:start position:0% +there is a function object and functions +are actually objects in Python there is + + align:start position:0% +are actually objects in Python there is + + + align:start position:0% +are actually objects in Python there is +a function object whose name is is even + + align:start position:0% +a function object whose name is is even + + + align:start position:0% +a function object whose name is is even +that is all it knows when we get to this + + align:start position:0% +that is all it knows when we get to this + + + align:start position:0% +that is all it knows when we get to this +point here in the code right after we + + align:start position:0% +point here in the code right after we + + + align:start position:0% +point here in the code right after we +Define the function right right before a + + align:start position:0% +Define the function right right before a + + + align:start position:0% +Define the function right right before a +equals okay so we think about the + + align:start position:0% +equals okay so we think about the + + + align:start position:0% +equals okay so we think about the +function as kind of like a variable + + align:start position:0% +function as kind of like a variable + + + align:start position:0% +function as kind of like a variable +quote unquote it's not actually a + + align:start position:0% +quote unquote it's not actually a + + + align:start position:0% +quote unquote it's not actually a +variable but it's like a variable whose + + align:start position:0% +variable but it's like a variable whose + + + align:start position:0% +variable but it's like a variable whose +name is is even and it points to it's + + align:start position:0% +name is is even and it points to it's + + + align:start position:0% +name is is even and it points to it's +bound to some code in memory and we + + align:start position:0% +bound to some code in memory and we + + + align:start position:0% +bound to some code in memory and we +don't care what that code is right now + + align:start position:0% +don't care what that code is right now + + + align:start position:0% +don't care what that code is right now +because we might never use it we only + + align:start position:0% +because we might never use it we only + + + align:start position:0% +because we might never use it we only +care what the code is when we make + + align:start position:0% +care what the code is when we make + + + align:start position:0% +care what the code is when we make +function + + align:start position:0% +function + + + align:start position:0% +function +calls so down here is where the action + + align:start position:0% +calls so down here is where the action + + + align:start position:0% +calls so down here is where the action +actually happens when we make our + + align:start position:0% +actually happens when we make our + + + align:start position:0% +actually happens when we make our +function calls I have a is going to be + + align:start position:0% +function calls I have a is going to be + + + align:start position:0% +function calls I have a is going to be +as usual a variable right that's going + + align:start position:0% +as usual a variable right that's going + + + align:start position:0% +as usual a variable right that's going +to be bound to some value + + align:start position:0% +to be bound to some value + + + align:start position:0% +to be bound to some value +so the function definition is kind of + + align:start position:0% +so the function definition is kind of + + + align:start position:0% +so the function definition is kind of +just like a black box right once you + + align:start position:0% +just like a black box right once you + + + align:start position:0% +just like a black box right once you +wrote it once and you know it works you + + align:start position:0% +wrote it once and you know it works you + + + align:start position:0% +wrote it once and you know it works you +don't care + + align:start position:0% +don't care + + + align:start position:0% +don't care +anymore how it actually achieves its + + align:start position:0% +anymore how it actually achieves its + + + align:start position:0% +anymore how it actually achieves its +task all you care is that it takes in a + + align:start position:0% +task all you care is that it takes in a + + + align:start position:0% +task all you care is that it takes in a +number and tells you whether that number + + align:start position:0% +number and tells you whether that number + + + align:start position:0% +number and tells you whether that number +is even or odd via true false okay so + + align:start position:0% +is even or odd via true false okay so + + + align:start position:0% +is even or odd via true false okay so +down here where we make our function + + align:start position:0% +down here where we make our function + + + align:start position:0% +down here where we make our function +calls we're just using our Black + + align:start position:0% +calls we're just using our Black + + + align:start position:0% +calls we're just using our Black +Box okay and we're using the Black Box + + align:start position:0% +Box okay and we're using the Black Box + + + align:start position:0% +Box okay and we're using the Black Box +by making function calls so a is going + + align:start position:0% +by making function calls so a is going + + + align:start position:0% +by making function calls so a is going +to be a + + align:start position:0% +to be a + + + align:start position:0% +to be a +variable that's bound to the value + + align:start position:0% +variable that's bound to the value + + + align:start position:0% +variable that's bound to the value +returned by is even so it's going to be + + align:start position:0% +returned by is even so it's going to be + + + align:start position:0% +returned by is even so it's going to be +uh based on the function call + + align:start position:0% +uh based on the function call + + + align:start position:0% +uh based on the function call +false and then here I have another + + align:start position:0% +false and then here I have another + + + align:start position:0% +false and then here I have another +function call I'm using this useful + + align:start position:0% +function call I'm using this useful + + + align:start position:0% +function call I'm using this useful +piece of uh code that I wrote up here + + align:start position:0% +piece of uh code that I wrote up here + + + align:start position:0% +piece of uh code that I wrote up here +and B is going to be a variable that's + + align:start position:0% +and B is going to be a variable that's + + + align:start position:0% +and B is going to be a variable that's +bound to true and C is going to be a + + align:start position:0% +bound to true and C is going to be a + + + align:start position:0% +bound to true and C is going to be a +variable that's bound to True + + align:start position:0% +variable that's bound to True + + + align:start position:0% +variable that's bound to True +right does that make sense it's kind of + + align:start position:0% +right does that make sense it's kind of + + + align:start position:0% +right does that make sense it's kind of +separating the code we write which + + align:start position:0% +separating the code we write which + + + align:start position:0% +separating the code we write which +doesn't run until we actually make + + align:start position:0% +doesn't run until we actually make + + + align:start position:0% +doesn't run until we actually make +function calls that's that's the thing + + align:start position:0% +function calls that's that's the thing + + + align:start position:0% +function calls that's that's the thing +about functions and that's how it helps + + align:start position:0% +about functions and that's how it helps + + + align:start position:0% +about functions and that's how it helps +us write more um more robust + + align:start position:0% +us write more um more robust + + + align:start position:0% +us write more um more robust +code so now here we can have a more + + align:start position:0% +code so now here we can have a more + + + align:start position:0% +code so now here we can have a more +complex piece of code where we're using + + align:start position:0% +complex piece of code where we're using + + + align:start position:0% +complex piece of code where we're using +the function that we wrote okay not just + + align:start position:0% +the function that we wrote okay not just + + + align:start position:0% +the function that we wrote okay not just +making a function call and printing the + + align:start position:0% +making a function call and printing the + + + align:start position:0% +making a function call and printing the +result but we're actually using it + + align:start position:0% +result but we're actually using it + + + align:start position:0% +result but we're actually using it +inside a more interesting program so + + align:start position:0% +inside a more interesting program so + + + align:start position:0% +inside a more interesting program so +here I've got a program that will print + + align:start position:0% +here I've got a program that will print + + + align:start position:0% +here I've got a program that will print +for me the numbers between and 10 and + + align:start position:0% +for me the numbers between and 10 and + + + align:start position:0% +for me the numbers between and 10 and +it'll print whether that number is odd + + align:start position:0% +it'll print whether that number is odd + + + align:start position:0% +it'll print whether that number is odd +or even so if you were just to read this + + align:start position:0% +or even so if you were just to read this + + + align:start position:0% +or even so if you were just to read this +code it's pretty easy to read right we + + align:start position:0% +code it's pretty easy to read right we + + + align:start position:0% +code it's pretty easy to read right we +have a loop that goes through the + + align:start position:0% +have a loop that goes through the + + + align:start position:0% +have a loop that goes through the +numbers one to 10 not including 10 and + + align:start position:0% +numbers one to 10 not including 10 and + + + align:start position:0% +numbers one to 10 not including 10 and +then I have this if is + + align:start position:0% +then I have this if is + + + align:start position:0% +then I have this if is +even well that's cool here I'm using the + + align:start position:0% +even well that's cool here I'm using the + + + align:start position:0% +even well that's cool here I'm using the +function that I wrote kind of just in + + align:start position:0% +function that I wrote kind of just in + + + align:start position:0% +function that I wrote kind of just in +the middle of another piece of + + align:start position:0% +the middle of another piece of + + + align:start position:0% +the middle of another piece of +code right which is fine because as I + + align:start position:0% +code right which is fine because as I + + + align:start position:0% +code right which is fine because as I +said you know a few slides ago go p uh + + align:start position:0% +said you know a few slides ago go p uh + + + align:start position:0% +said you know a few slides ago go p uh +function calls are basically just + + align:start position:0% +function calls are basically just + + + align:start position:0% +function calls are basically just +Expressions right they get run they get + + align:start position:0% +Expressions right they get run they get + + + align:start position:0% +Expressions right they get run they get +evaluated you get one value back out of + + align:start position:0% +evaluated you get one value back out of + + + align:start position:0% +evaluated you get one value back out of +them and then that value replaces the + + align:start position:0% +them and then that value replaces the + + + align:start position:0% +them and then that value replaces the +function call so that's fine let's use + + align:start position:0% +function call so that's fine let's use + + + align:start position:0% +function call so that's fine let's use +the is even uh result the return from + + align:start position:0% +the is even uh result the return from + + + align:start position:0% +the is even uh result the return from +the is even method inside a conditional + + align:start position:0% +the is even method inside a conditional + + + align:start position:0% +the is even method inside a conditional +if I uh if if calling is even with I + + align:start position:0% +if I uh if if calling is even with I + + + align:start position:0% +if I uh if if calling is even with I +returns true that means if the number is + + align:start position:0% +returns true that means if the number is + + + align:start position:0% +returns true that means if the number is +even we print that value comma even + + align:start position:0% +even we print that value comma even + + + align:start position:0% +even we print that value comma even +else we print that value comma odd so + + align:start position:0% +else we print that value comma odd so + + + align:start position:0% +else we print that value comma odd so +here I'm not defining a function notice + + align:start position:0% +here I'm not defining a function notice + + + align:start position:0% +here I'm not defining a function notice +it's not wrapped in the DF or anything + + align:start position:0% +it's not wrapped in the DF or anything + + + align:start position:0% +it's not wrapped in the DF or anything +like that I'm just using a function that + + align:start position:0% +like that I'm just using a function that + + + align:start position:0% +like that I'm just using a function that +I already + + align:start position:0% +I already + + + align:start position:0% +I already +wrote so inside + + align:start position:0% +wrote so inside + + + align:start position:0% +wrote so inside +here just comment that + + align:start position:0% +here just comment that + + + align:start position:0% +here just comment that +out this is the code we just had on the + + align:start position:0% +out this is the code we just had on the + + + align:start position:0% +out this is the code we just had on the +slide so again notice it's not within + + align:start position:0% +slide so again notice it's not within + + + align:start position:0% +slide so again notice it's not within +it's not wrapped within a function it's + + align:start position:0% +it's not wrapped within a function it's + + + align:start position:0% +it's not wrapped within a function it's +just a loop that tells me uh the numbers + + align:start position:0% +just a loop that tells me uh the numbers + + + align:start position:0% +just a loop that tells me uh the numbers +one at a time whether they're odd or + + align:start position:0% +one at a time whether they're odd or + + + align:start position:0% +one at a time whether they're odd or +even right so prints one comma yeah what + + align:start position:0% +even right so prints one comma yeah what + + + align:start position:0% +even right so prints one comma yeah what +are you doing when you select like + + align:start position:0% +are you doing when you select like + + + align:start position:0% +are you doing when you select like +everything in a common make it oh when I + + align:start position:0% +everything in a common make it oh when I + + + align:start position:0% +everything in a common make it oh when I +select everything I just use um spiders + + align:start position:0% +select everything I just use um spiders + + + align:start position:0% +select everything I just use um spiders +like ability to com so I do control one + + align:start position:0% +like ability to com so I do control one + + + align:start position:0% +like ability to com so I do control one +or command one probably on a Mac and it + + align:start position:0% +or command one probably on a Mac and it + + + align:start position:0% +or command one probably on a Mac and it +just comments and uncomment things in + + align:start position:0% +just comments and uncomment things in + + + align:start position:0% +just comments and uncomment things in +batch yeah very useful + + align:start position:0% +batch yeah very useful + + + align:start position:0% +batch yeah very useful +yeah and so this code is now very easy + + align:start position:0% +yeah and so this code is now very easy + + + align:start position:0% +yeah and so this code is now very easy +to modify right I can just choose a 100 + + align:start position:0% +to modify right I can just choose a 100 + + + align:start position:0% +to modify right I can just choose a 100 +and then I can run it again and it gives + + align:start position:0% +and then I can run it again and it gives + + + align:start position:0% +and then I can run it again and it gives +me the numbers uh one through 100 odd or + + align:start position:0% +me the numbers uh one through 100 odd or + + + align:start position:0% +me the numbers uh one through 100 odd or +even and you can imagine using your is + + align:start position:0% +even and you can imagine using your is + + + align:start position:0% +even and you can imagine using your is +even function in a more complex setting + + align:start position:0% +even function in a more complex setting + + + align:start position:0% +even function in a more complex setting +right and is even is a really simple + + align:start position:0% +right and is even is a really simple + + + align:start position:0% +right and is even is a really simple +function to write but again you can + + align:start position:0% +function to write but again you can + + + align:start position:0% +function to write but again you can +imagine writing a more complex function + + align:start position:0% +imagine writing a more complex function + + + align:start position:0% +imagine writing a more complex function +and then that complex function isn't a + + align:start position:0% +and then that complex function isn't a + + + align:start position:0% +and then that complex function isn't a +whole chunk of code that just gets stuck + + align:start position:0% +whole chunk of code that just gets stuck + + + align:start position:0% +whole chunk of code that just gets stuck +into this program this loop it's going + + align:start position:0% +into this program this loop it's going + + + align:start position:0% +into this program this loop it's going +to be a function that you call that you + + align:start position:0% +to be a function that you call that you + + + align:start position:0% +to be a function that you call that you +can just easily uh read the + + align:start position:0% +can just easily uh read the + + + align:start position:0% +can just easily uh read the +specification for and you don't need to + + align:start position:0% +specification for and you don't need to + + + align:start position:0% +specification for and you don't need to +completely uh um understand how it works + + align:start position:0% +completely uh um understand how it works + + + align:start position:0% +completely uh um understand how it works +in order to use + + align:start position:0% + + + + align:start position:0% + +it + + align:start position:0% +it + + + align:start position:0% +it +okay so we're going to go through one + + align:start position:0% +okay so we're going to go through one + + + align:start position:0% +okay so we're going to go through one +other example um to write a little + + align:start position:0% +other example um to write a little + + + align:start position:0% +other example um to write a little +function and this will also showcase + + align:start position:0% +function and this will also showcase + + + align:start position:0% +function and this will also showcase +kind of the uh best practices for + + align:start position:0% +kind of the uh best practices for + + + align:start position:0% +kind of the uh best practices for +writing a function and writing code + + align:start position:0% +writing a function and writing code + + + align:start position:0% +writing a function and writing code +especially maybe in a quiz situation or + + align:start position:0% +especially maybe in a quiz situation or + + + align:start position:0% +especially maybe in a quiz situation or +something like that how to write + + align:start position:0% +something like that how to write + + + align:start position:0% +something like that how to write +incremental code how to test it a little + + align:start position:0% +incremental code how to test it a little + + + align:start position:0% +incremental code how to test it a little +bit at a time and so on so the last + + align:start position:0% +bit at a time and so on so the last + + + align:start position:0% +bit at a time and so on so the last +example I want to go through is I want + + align:start position:0% +example I want to go through is I want + + + align:start position:0% +example I want to go through is I want +to uh write some code that c that adds + + align:start position:0% +to uh write some code that c that adds + + + align:start position:0% +to uh write some code that c that adds +all the odd integers between and + + align:start position:0% +all the odd integers between and + + + align:start position:0% +all the odd integers between and +including A and + + align:start position:0% +including A and + + + align:start position:0% +including A and +B might be something you're on a quiz + + align:start position:0% +B might be something you're on a quiz + + + align:start position:0% +B might be something you're on a quiz +um what uh the first thing you do when + + align:start position:0% +um what uh the first thing you do when + + + align:start position:0% +um what uh the first thing you do when +you're faced with such a task is to + + align:start position:0% +you're faced with such a task is to + + + align:start position:0% +you're faced with such a task is to +think about a nice name for the function + + align:start position:0% +think about a nice name for the function + + + align:start position:0% +think about a nice name for the function +so some odd or some odds is a reasonable + + align:start position:0% +so some odd or some odds is a reasonable + + + align:start position:0% +so some odd or some odds is a reasonable +name the inputs to the function well + + align:start position:0% +name the inputs to the function well + + + align:start position:0% +name the inputs to the function well +I've got two end points I want to Su OD + + align:start position:0% +I've got two end points I want to Su OD + + + align:start position:0% +I've got two end points I want to Su OD +numbers in between so the inputs might + + align:start position:0% +numbers in between so the inputs might + + + align:start position:0% +numbers in between so the inputs might +well be my two end points and then what + + align:start position:0% +well be my two end points and then what + + + align:start position:0% +well be my two end points and then what +is the thing your function achieves + + align:start position:0% +is the thing your function achieves + + + align:start position:0% +is the thing your function achieves +right well in the end it's going to give + + align:start position:0% +right well in the end it's going to give + + + align:start position:0% +right well in the end it's going to give +me some sum so let's call that sum a + + align:start position:0% +me some sum so let's call that sum a + + + align:start position:0% +me some sum so let's call that sum a +variable sum of underscore odds and + + align:start position:0% +variable sum of underscore odds and + + + align:start position:0% +variable sum of underscore odds and +we'll return it at the end of our + + align:start position:0% + + + + align:start position:0% + +function and in between we're going to + + align:start position:0% +function and in between we're going to + + + align:start position:0% +function and in between we're going to +have some code + + align:start position:0% +have some code + + + align:start position:0% +have some code +okay so first thing to do is to not + + align:start position:0% +okay so first thing to do is to not + + + align:start position:0% +okay so first thing to do is to not +write code right away when you're faced + + align:start position:0% +write code right away when you're faced + + + align:start position:0% +write code right away when you're faced +with a task again on a quiz or something + + align:start position:0% +with a task again on a quiz or something + + + align:start position:0% +with a task again on a quiz or something +like that it's best to take a piece of + + align:start position:0% +like that it's best to take a piece of + + + align:start position:0% +like that it's best to take a piece of +paper write a little bit one example and + + align:start position:0% +paper write a little bit one example and + + + align:start position:0% +paper write a little bit one example and +try to think about how you'd solve it + + align:start position:0% +try to think about how you'd solve it + + + align:start position:0% +try to think about how you'd solve it +not like a human would because for us we + + align:start position:0% +not like a human would because for us we + + + align:start position:0% +not like a human would because for us we +would immediately F know the sum right + + align:start position:0% +would immediately F know the sum right + + + align:start position:0% +would immediately F know the sum right +it's very easy for hum identify the + + align:start position:0% +it's very easy for hum identify the + + + align:start position:0% +it's very easy for hum identify the +solutions to these problems but try to + + align:start position:0% +solutions to these problems but try to + + + align:start position:0% +solutions to these problems but try to +think about how you would write how what + + align:start position:0% +think about how you would write how what + + + align:start position:0% +think about how you would write how what +kind of a recipe would work for this + + align:start position:0% +kind of a recipe would work for this + + + align:start position:0% +kind of a recipe would work for this +would you Loop would you have a + + align:start position:0% +would you Loop would you have a + + + align:start position:0% +would you Loop would you have a +conditional would you use a for Loop or + + align:start position:0% +conditional would you use a for Loop or + + + align:start position:0% +conditional would you use a for Loop or +a while loop and a bunch of other uh + + align:start position:0% +a while loop and a bunch of other uh + + + align:start position:0% +a while loop and a bunch of other uh +Concepts that we'll learn about in in uh + + align:start position:0% +Concepts that we'll learn about in in uh + + + align:start position:0% +Concepts that we'll learn about in in uh +in the following lectures but the key + + align:start position:0% +in the following lectures but the key + + + align:start position:0% +in the following lectures but the key +thing is to just not write code right + + align:start position:0% +thing is to just not write code right + + + align:start position:0% +thing is to just not write code right +away so if we TR start with a really + + align:start position:0% +away so if we TR start with a really + + + align:start position:0% +away so if we TR start with a really +simple example on paper we can say let's + + align:start position:0% +simple example on paper we can say let's + + + align:start position:0% +simple example on paper we can say let's +choose end points uh a is two and B is + + align:start position:0% +choose end points uh a is two and B is + + + align:start position:0% +choose end points uh a is two and B is +four on paper I would probably write out + + align:start position:0% +four on paper I would probably write out + + + align:start position:0% +four on paper I would probably write out +two three four in a row right so I know + + align:start position:0% +two three four in a row right so I know + + + align:start position:0% +two three four in a row right so I know +the numbers I need to look at I would + + align:start position:0% +the numbers I need to look at I would + + + align:start position:0% +the numbers I need to look at I would +say two is my a four is my B I need to + + align:start position:0% +say two is my a four is my B I need to + + + align:start position:0% +say two is my a four is my B I need to +look at every one of these numbers one + + align:start position:0% +look at every one of these numbers one + + + align:start position:0% +look at every one of these numbers one +at a + + align:start position:0% +at a + + + align:start position:0% +at a +time reasonable I can do another example + + align:start position:0% +time reasonable I can do another example + + + align:start position:0% +time reasonable I can do another example +sorry and I know what the answer should + + align:start position:0% +sorry and I know what the answer should + + + align:start position:0% +sorry and I know what the answer should +be so I figure out what the answer + + align:start position:0% +be so I figure out what the answer + + + align:start position:0% +be so I figure out what the answer +should be so that when I write my code I + + align:start position:0% +should be so that when I write my code I + + + align:start position:0% +should be so that when I write my code I +actually know what uh I'm looking for I + + align:start position:0% +actually know what uh I'm looking for I + + + align:start position:0% +actually know what uh I'm looking for I +look at another example let's say a + + align:start position:0% +look at another example let's say a + + + align:start position:0% +look at another example let's say a +little bit more complicated a bigger + + align:start position:0% +little bit more complicated a bigger + + + align:start position:0% +little bit more complicated a bigger +range a is 2 b is 7 I try to use the + + align:start position:0% +range a is 2 b is 7 I try to use the + + + align:start position:0% +range a is 2 b is 7 I try to use the +same strategy I use used same recipe I + + align:start position:0% +same strategy I use used same recipe I + + + align:start position:0% +same strategy I use used same recipe I +used to solve that simpler example in + + align:start position:0% +used to solve that simpler example in + + + align:start position:0% +used to solve that simpler example in +this harder one so again I'm going to + + align:start position:0% +this harder one so again I'm going to + + + align:start position:0% +this harder one so again I'm going to +write out all the numbers between two + + align:start position:0% +write out all the numbers between two + + + align:start position:0% +write out all the numbers between two +and seven inclusive this is my first + + align:start position:0% +and seven inclusive this is my first + + + align:start position:0% +and seven inclusive this is my first +this is my last and my strategy was to + + align:start position:0% +this is my last and my strategy was to + + + align:start position:0% +this is my last and my strategy was to +go through one at a time and if it's odd + + align:start position:0% +go through one at a time and if it's odd + + + align:start position:0% +go through one at a time and if it's odd +I take it to my running sum and add it + + align:start position:0% +I take it to my running sum and add it + + + align:start position:0% +I take it to my running sum and add it +to my running sum and if it's even I + + align:start position:0% +to my running sum and if it's even I + + + align:start position:0% +to my running sum and if it's even I +don't I ignore it okay and again I know + + align:start position:0% +don't I ignore it okay and again I know + + + align:start position:0% +don't I ignore it okay and again I know +the answer for this should be 15 so with + + align:start position:0% +the answer for this should be 15 so with + + + align:start position:0% +the answer for this should be 15 so with +these two examples in mind I can start + + align:start position:0% +these two examples in mind I can start + + + align:start position:0% +these two examples in mind I can start +writing code but instead of writing code + + align:start position:0% +writing code but instead of writing code + + + align:start position:0% +writing code but instead of writing code +for for the big problem that might + + align:start position:0% +for for the big problem that might + + + align:start position:0% +for for the big problem that might +include some nuances or some edge cases + + align:start position:0% +include some nuances or some edge cases + + + align:start position:0% +include some nuances or some edge cases +I can actually try to solve a similar + + align:start position:0% +I can actually try to solve a similar + + + align:start position:0% +I can actually try to solve a similar +problem right so instead of summing all + + align:start position:0% +problem right so instead of summing all + + + align:start position:0% +problem right so instead of summing all +the odd numbers between A and B let's + + align:start position:0% +the odd numbers between A and B let's + + + align:start position:0% +the odd numbers between A and B let's +just sum all the numbers between a and b + + align:start position:0% +just sum all the numbers between a and b + + + align:start position:0% +just sum all the numbers between a and b +and see if we can get code right working + + align:start position:0% +and see if we can get code right working + + + align:start position:0% +and see if we can get code right working +for that once we do figuring out the odd + + align:start position:0% +for that once we do figuring out the odd + + + align:start position:0% +for that once we do figuring out the odd +ones should be a small tweak to our code + + align:start position:0% +ones should be a small tweak to our code + + + align:start position:0% +ones should be a small tweak to our code +okay so if we start with figuring out + + align:start position:0% +okay so if we start with figuring out + + + align:start position:0% +okay so if we start with figuring out +the sum of all the odd numbers between + + align:start position:0% +the sum of all the odd numbers between + + + align:start position:0% +the sum of all the odd numbers between +an including A and B that sounds like a + + align:start position:0% +an including A and B that sounds like a + + + align:start position:0% +an including A and B that sounds like a +loop because I knew when I wrote my exam + + align:start position:0% +loop because I knew when I wrote my exam + + + align:start position:0% +loop because I knew when I wrote my exam +example on paper I'd have to touch each + + align:start position:0% +example on paper I'd have to touch each + + + align:start position:0% +example on paper I'd have to touch each +number between an including A and B + + align:start position:0% +number between an including A and B + + + align:start position:0% +number between an including A and B +right so I know I need to Loop through + + align:start position:0% +right so I know I need to Loop through + + + align:start position:0% +right so I know I need to Loop through +uh every one of these + + align:start position:0% +uh every one of these + + + align:start position:0% +uh every one of these +values while or a for Loop your choice + + align:start position:0% +values while or a for Loop your choice + + + align:start position:0% +values while or a for Loop your choice +in the slides I'll do both just to see + + align:start position:0% +in the slides I'll do both just to see + + + align:start position:0% +in the slides I'll do both just to see +what it looks like so with a for loop + + align:start position:0% +what it looks like so with a for loop + + + align:start position:0% +what it looks like so with a for loop +it's easy it's just for I in range a but + + align:start position:0% +it's easy it's just for I in range a but + + + align:start position:0% +it's easy it's just for I in range a but +with a Y Loop remember we have to + + align:start position:0% +with a Y Loop remember we have to + + + align:start position:0% +with a Y Loop remember we have to +initialize our Loop variable if we have + + align:start position:0% +initialize our Loop variable if we have + + + align:start position:0% +initialize our Loop variable if we have +one I equals a our Loop condition is + + align:start position:0% +one I equals a our Loop condition is + + + align:start position:0% +one I equals a our Loop condition is +while I is less than or equal to B right + + align:start position:0% +while I is less than or equal to B right + + + align:start position:0% +while I is less than or equal to B right +so we're going to Loop through while I + + align:start position:0% +so we're going to Loop through while I + + + align:start position:0% +so we're going to Loop through while I +I'm looking at all these values up to an + + align:start position:0% +I'm looking at all these values up to an + + + align:start position:0% +I'm looking at all these values up to an +including B and I need to remember to + + align:start position:0% +including B and I need to remember to + + + align:start position:0% +including B and I need to remember to +increment my Loop variable within the + + align:start position:0% +increment my Loop variable within the + + + align:start position:0% +increment my Loop variable within the +loop by one each time in this case + + align:start position:0% +loop by one each time in this case + + + align:start position:0% +loop by one each time in this case +okay okay and then what do I do within + + align:start position:0% +okay okay and then what do I do within + + + align:start position:0% +okay okay and then what do I do within +my Loop well I'm going to remember we're + + align:start position:0% +my Loop well I'm going to remember we're + + + align:start position:0% +my Loop well I'm going to remember we're +solving the similar problem I'm going to + + align:start position:0% +solving the similar problem I'm going to + + + align:start position:0% +solving the similar problem I'm going to +keep a running sum so as soon as I see a + + align:start position:0% +keep a running sum so as soon as I see a + + + align:start position:0% +keep a running sum so as soon as I see a +new I I'm going to add it to my + + align:start position:0% +new I I'm going to add it to my + + + align:start position:0% +new I I'm going to add it to my +sum I realized here probably my IDE + + align:start position:0% +sum I realized here probably my IDE + + + align:start position:0% +sum I realized here probably my IDE +would show me that there's an error I + + align:start position:0% +would show me that there's an error I + + + align:start position:0% +would show me that there's an error I +didn't initialize sum of odds so I + + align:start position:0% +didn't initialize sum of odds so I + + + align:start position:0% +didn't initialize sum of odds so I +remembered in initialize some of odds + + align:start position:0% +remembered in initialize some of odds + + + align:start position:0% +remembered in initialize some of odds +right before the loop and then this is a + + align:start position:0% +right before the loop and then this is a + + + align:start position:0% +right before the loop and then this is a +good place to test the code for a little + + align:start position:0% +good place to test the code for a little + + + align:start position:0% +good place to test the code for a little +bit so we'll test it with a really + + align:start position:0% +bit so we'll test it with a really + + + align:start position:0% +bit so we'll test it with a really +simple example 2 comma + + align:start position:0% +simple example 2 comma + + + align:start position:0% +simple example 2 comma +4 okay if we test it with 2 comma four + + align:start position:0% +4 okay if we test it with 2 comma four + + + align:start position:0% +4 okay if we test it with 2 comma four +the four Loop gives me a five but the uh + + align:start position:0% +the four Loop gives me a five but the uh + + + align:start position:0% +the four Loop gives me a five but the uh +the Y Loop gives me a nine so you guys + + align:start position:0% +the Y Loop gives me a nine so you guys + + + align:start position:0% +the Y Loop gives me a nine so you guys +might have noticed what the problem is + + align:start position:0% +might have noticed what the problem is + + + align:start position:0% +might have noticed what the problem is +my for Loop goes through up to but not + + align:start position:0% +my for Loop goes through up to but not + + + align:start position:0% +my for Loop goes through up to but not +including the end variable right the B + + align:start position:0% +including the end variable right the B + + + align:start position:0% +including the end variable right the B +so we can add a print statement in case + + align:start position:0% +so we can add a print statement in case + + + align:start position:0% +so we can add a print statement in case +you didn't figure that out and the print + + align:start position:0% +you didn't figure that out and the print + + + align:start position:0% +you didn't figure that out and the print +statement would actually tell us right + + align:start position:0% +statement would actually tell us right + + + align:start position:0% +statement would actually tell us right +it tells us what we're incrementing + + align:start position:0% +it tells us what we're incrementing + + + align:start position:0% +it tells us what we're incrementing +first it's two then it's three but I + + align:start position:0% +first it's two then it's three but I + + + align:start position:0% +first it's two then it's three but I +never hit the + + align:start position:0% +never hit the + + + align:start position:0% +never hit the +four so the fix is to just change my end + + align:start position:0% +four so the fix is to just change my end + + + align:start position:0% +four so the fix is to just change my end +range to be B+ one and then we run it + + align:start position:0% +range to be B+ one and then we run it + + + align:start position:0% +range to be B+ one and then we run it +again and we see the answers + + align:start position:0% +again and we see the answers + + + align:start position:0% +again and we see the answers +match okay and this solves the SI the + + align:start position:0% +match okay and this solves the SI the + + + align:start position:0% +match okay and this solves the SI the +the the bigger problem so now all we + + align:start position:0% +the the bigger problem so now all we + + + align:start position:0% +the the bigger problem so now all we +need to do is adding the the the Nuance + + align:start position:0% +need to do is adding the the the Nuance + + + align:start position:0% +need to do is adding the the the Nuance +the piece where we just grab the odd + + align:start position:0% +the piece where we just grab the odd + + + align:start position:0% +the piece where we just grab the odd +numbers and here we say well if I'm just + + align:start position:0% +numbers and here we say well if I'm just + + + align:start position:0% +numbers and here we say well if I'm just +grabbing the odd numbers I only want to + + align:start position:0% +grabbing the odd numbers I only want to + + + align:start position:0% +grabbing the odd numbers I only want to +add I to my sum of odds when I see an + + align:start position:0% +add I to my sum of odds when I see an + + + align:start position:0% +add I to my sum of odds when I see an +odd number so here I could use my is + + align:start position:0% +odd number so here I could use my is + + + align:start position:0% +odd number so here I could use my is +even function that I already wrote I + + align:start position:0% +even function that I already wrote I + + + align:start position:0% +even function that I already wrote I +would say if not is even or I can just + + align:start position:0% +would say if not is even or I can just + + + align:start position:0% +would say if not is even or I can just +do it all over again if i%c 2 equal one + + align:start position:0% +do it all over again if i%c 2 equal one + + + align:start position:0% +do it all over again if i%c 2 equal one +then we do this right and now we can run + + align:start position:0% +then we do this right and now we can run + + + align:start position:0% +then we do this right and now we can run +it again and hopefully this now matches + + align:start position:0% +it again and hopefully this now matches + + + align:start position:0% +it again and hopefully this now matches +with the example I had on paper and it + + align:start position:0% +with the example I had on paper and it + + + align:start position:0% +with the example I had on paper and it +does okay so the idea here is to try to + + align:start position:0% +does okay so the idea here is to try to + + + align:start position:0% +does okay so the idea here is to try to +solve a simpler problem first and then + + align:start position:0% +solve a simpler problem first and then + + + align:start position:0% +solve a simpler problem first and then +as you see more nuances to the problem + + align:start position:0% +as you see more nuances to the problem + + + align:start position:0% +as you see more nuances to the problem +add in the functionality just a little + + align:start position:0% +add in the functionality just a little + + + align:start position:0% +add in the functionality just a little +bit at a time so you don't actually get + + align:start position:0% +bit at a time so you don't actually get + + + align:start position:0% +bit at a time so you don't actually get +bogged down by a whole bunch of pro uh + + align:start position:0% +bogged down by a whole bunch of pro uh + + + align:start position:0% +bogged down by a whole bunch of pro uh +uh issues that might come up when you + + align:start position:0% +uh issues that might come up when you + + + align:start position:0% +uh issues that might come up when you +wrote a whole bunch of + + align:start position:0% +wrote a whole bunch of + + + align:start position:0% +wrote a whole bunch of +code the last step is just to test it on + + align:start position:0% +code the last step is just to test it on + + + align:start position:0% +code the last step is just to test it on +the other example just to make sure that + + align:start position:0% +the other example just to make sure that + + + align:start position:0% +the other example just to make sure that +it still works right and so if we R + + align:start position:0% +it still works right and so if we R + + + align:start position:0% +it still works right and so if we R +print some of odds between two and seven + + align:start position:0% +print some of odds between two and seven + + + align:start position:0% +print some of odds between two and seven +again this matches what I had written + + align:start position:0% +again this matches what I had written + + + align:start position:0% +again this matches what I had written +down on paper okay if you don't want to + + align:start position:0% +down on paper okay if you don't want to + + + align:start position:0% +down on paper okay if you don't want to +use print statements the python tutor is + + align:start position:0% +use print statements the python tutor is + + + align:start position:0% +use print statements the python tutor is +also a great debugging tool okay + + align:start position:0% +also a great debugging tool okay + + + align:start position:0% +also a great debugging tool okay +so testing code often very useful I + + align:start position:0% +so testing code often very useful I + + + align:start position:0% +so testing code often very useful I +think I've stressed this in previous + + align:start position:0% +think I've stressed this in previous + + + align:start position:0% +think I've stressed this in previous +lectures as well using prints or the + + align:start position:0% +lectures as well using prints or the + + + align:start position:0% +lectures as well using prints or the +python tutor did debug it's also very + + align:start position:0% +python tutor did debug it's also very + + + align:start position:0% +python tutor did debug it's also very +useful I don't actually intend to go + + align:start position:0% +useful I don't actually intend to go + + + align:start position:0% +useful I don't actually intend to go +through this you try it but this along + + align:start position:0% +through this you try it but this along + + + align:start position:0% +through this you try it but this along +with a bunch of other examples or uh uh + + align:start position:0% +with a bunch of other examples or uh uh + + + align:start position:0% +with a bunch of other examples or uh uh +things to try at home are in the python + + align:start position:0% +things to try at home are in the python + + + align:start position:0% +things to try at home are in the python +file so just functions you can you can + + align:start position:0% +file so just functions you can you can + + + align:start position:0% +file so just functions you can you can +write is palindrome this keep consonants + + align:start position:0% +write is palindrome this keep consonants + + + align:start position:0% +write is palindrome this keep consonants +this first to last if read the function + + align:start position:0% +this first to last if read the function + + + align:start position:0% +this first to last if read the function +specification and try to write code that + + align:start position:0% +specification and try to write code that + + + align:start position:0% +specification and try to write code that +that um that matches the specification + + align:start position:0% +that um that matches the specification + + + align:start position:0% +that um that matches the specification +and as usual the answers are in the + + align:start position:0% +and as usual the answers are in the + + + align:start position:0% +and as usual the answers are in the +python file but please please try to do + + align:start position:0% +python file but please please try to do + + + align:start position:0% +python file but please please try to do +them on your own first before looking at + + align:start position:0% +them on your own first before looking at + + + align:start position:0% +them on your own first before looking at +the answers um okay uh a quick + + align:start position:0% +the answers um okay uh a quick + + + align:start position:0% +the answers um okay uh a quick +summary functions are very useful allows + + align:start position:0% +summary functions are very useful allows + + + align:start position:0% +summary functions are very useful allows +us to abstract certain useful tasks + + align:start position:0% +us to abstract certain useful tasks + + + align:start position:0% +us to abstract certain useful tasks +right basically abstract away + + align:start position:0% +right basically abstract away + + + align:start position:0% +right basically abstract away +functionality that we might reuse many + + align:start position:0% +functionality that we might reuse many + + + align:start position:0% +functionality that we might reuse many +times in our program functions taken + + align:start position:0% +times in our program functions taken + + + align:start position:0% +times in our program functions taken +inputs they have something to return + + align:start position:0% +inputs they have something to return + + + align:start position:0% +inputs they have something to return +we're going to see next time what + + align:start position:0% +we're going to see next time what + + + align:start position:0% +we're going to see next time what +happens when we don't return + + align:start position:0% +happens when we don't return + + + align:start position:0% +happens when we don't return +anything um creating the function is + + align:start position:0% +anything um creating the function is + + + align:start position:0% +anything um creating the function is +different than running the function + + align:start position:0% +different than running the function + + + align:start position:0% +different than running the function +right so you create the function once + + align:start position:0% +right so you create the function once + + + align:start position:0% +right so you create the function once +but you can run it many many times and + + align:start position:0% +but you can run it many many times and + + + align:start position:0% +but you can run it many many times and +that's what makes functions useful it + + align:start position:0% +that's what makes functions useful it + + + align:start position:0% +that's what makes functions useful it +makes code easy to write read debug + + align:start position:0% +makes code easy to write read debug + + + align:start position:0% +makes code easy to write read debug +modify uh leads to very nice robust code + + align:start position:0% + + + + align:start position:0% + +okay \ No newline at end of file diff --git a/QyishgPCBfg.txt b/QyishgPCBfg.txt new file mode 100644 index 0000000000000000000000000000000000000000..ead1e2b632e5530b8e2fe1b2909e6038f59bc3de --- /dev/null +++ b/QyishgPCBfg.txt @@ -0,0 +1,1821 @@ +The following content is +provided by MIT OpenCourseWare + +under a Creative Commons +license. + +Additional information about +our license and MIT + +OpenCourseWare in general is +available at ocw.mit.edu. + +I just wanted to briefly remind +you of some of the periodic + +trends that we talked about. +As you go across the periodic + +table, both the electron +affinity and the ionization + +energy increase. +They increase because the + +nuclear charge increases. +Remember, the potential energy + +of interaction is Z times e, +where that is the nuclear + +charges, times e over 4 pi +epsilon nought r. + +Z increases as you go across +the periodic table here. + +As you go across, +r is remaining the same because + +you are essentially still in the +same shell. + +And so what increases is that +attractive interaction, + +meaning the electrons are more +strongly bound, + +meaning ionization energy and +electron affinity increases as + +you go across. +And this also means, + +as you go across, +r, the radius decreases. + +The radius decreases again +because Z increases. + +The nucleus is pulling the +electrons in closer. + +Since they are all in the same +shell, r is remaining the same. + +And so, the overall effect is +that the radius of the atoms + +decreases. +As you go down the Periodic + +Table, the ionization energy and +the electron affinity decrease. + +They decrease because it is the +r dependence, + +here, that takes over. +Z is, of course, + +increasing, but not as fast as +r. + +As you go down the Periodic +Table, you are going to shells + +that, on the average, +are further out from the + +nucleus. +And that dependence takes over, + +causing EA and IE to decrease. +And then the radius, + +of course, increases, +because, as you go down, + +you are putting the electrons +into shells which are on the + +average farther away from the +nucleus. + +That is just a review of those +trends. + +Then, finally, +I want to just define another + +term, and that is the +electronegativity. + +Sometimes we give that the +symbol chi. + +The electronegativity is an +empirical quantity. + +We are going to use Mulliken's +definition for the + +electronegativity. +There is a Pauling definition. + +Mulliken is a little bit more +straightforward. + +And that electronegativity is +defined as one-half times the + +quantity ionization energy plus +the electron affinity. + +The electronegativity is + +proportional to the average of +the ionization energy and the + +electron affinity. +The electronegativity is a + +measure of the tendency of an +atom to accept or to donate an + +electron. +If you look at the Periodic + +Table, here, you have atoms in +the upper right-hand corner of + +the Periodic Table. +Well, they have high + +electronegativities. +They are good electron + +acceptors. +They have high + +electronegativities because they +have high electron affinities. + +Adding an electron to them +means that there is a larger + +amount of energy release. +The anion is much more stable + +than the neutral. +And the electron affinity is + +minus that energy change, +remember from last time. + +These atoms here, +with their high electron + +affinities, are good electron +acceptors. + +They are also good electron +acceptors because their + +ionization energies are also +high, which means you have to + +put in a lot of energy to pull +an electron off. + +They don't like to donate +electrons, rather they are good + +electron acceptors. +And then, the elements that are + +in the bottom left-hand corner +of the Periodic Table have low + +electronegativities. +They are good electron donors + +because their ionization energy +is low in this part of the + +periodic table. +You don't have to put in so + +much energy to pull an electron +off. + +They are also good electron +donors because their electron + +affinity is low. +You don't get as much energy + +back when you put an electron on +them. + +These are good electron donors. +High chi, here. + +These are good electron +acceptors. + +And one thing you already know +probably is that some of the + +strongest ionic bonds are made +between elements in these two + +corners of the periodic table. +An ionic bond, + +as we are going to talk about, +is one in which the electrons + +are not shared equally. +And so these strong ionic bonds + +occur between elements with high +electronegativity and low + +electronegativity. +So that's that concept. + +And then, finally, +one other kind of odd and end + +here. +That is this term + +isoelectronic. +I have listed here a bunch of + +atoms and ions that are +isoelectronic. + +Isoelectronic means having the +same electron structure. + +All of these atoms and ions +have the electron configuration + +1s 2 2s 2 2p 6. + +For example, +this nitrogen, + +N minus 3, +it has added three electrons to + +be nitrogen minus three. +It has added three electrons to + +get this electron configuration, +this rare gas configuration, + +this octet configuration which +is a very stable configuration. + +Aluminum has three electrons +removed to obtain this + +particular electron +configuration. + +The common ions, +ions that you see commonly in + +nature, are ions that, +in fact, do have this octet + +configuration, +this electron configuration of + +an inert gas. +For example, + +you will often see compounds +with nitrogen minus three. + +You won't very often see a + +compound with nitrogen minus two +or nitrogen minus one + +because those are not +as stable as nitrogen minus + +three, +given this rare gas or the + +octet configuration. +All right. + +That is just a little odd and +end. + +I just wanted to make sure that +everybody was on the same level + +with the understanding of the +word isoelectronic there. + +Well, now what I thought I +would do is talk a little bit + +about wave functions and the +usefulness of wave functions. + +This is going to be on the side +boards here. + +I wanted to just show you in +kind of simple terms how a wave + +function actually determines the +intensity of some transition. + +Many of you have asked me about +the intensities of transitions, + +and so I thought I would show +you just a little bit about how + +these wave functions determine +the intensities of transitions. + +First of all, +I have to explain this diagram + +to you. +This is going to be a diagram + +for a hydrogen atom. +That is what we are going to + +talk about here. +What we are going to start with + +is an energy level diagram for +the hydrogen atoms. + +That is what this axis is. +And so, I am plotting in that + +diagram, energy, +going up. + +And I plot the energy level for +n equals 1. + +I plot the energy level for n +equals 2, n equals 3, + +all the way up to n equals 235, +which is really very close to + +zero. +That is part of what is on this + +plot right here, +n equals 1, n equals 2, + +n equals 3. +But then, what is also + +typically done on the same plot +is that the potential energy of + +interaction is plotted as a +function of r. + +And so, on this axis here, +kind of superimposed, + +is this distance r. +And we plot often the potential + +energy of interaction. +The potential energy of + +interaction kind of looks like +that. + +This potential energy of +interaction is the Coulomb + +interaction, minus e squared 4 +pi epsilon nought times r. + +That is what that line is on + +this plot. +Then what we do is we actually + +plot the form of the wave +function, kind of on top of the + +energy levels. +What we do is to say, + +for example, +take the n equals 1 wave + +function, which starts at r +equals 0 at some finite value + +and it is just an exponential +decay. + +And we plot it on this diagram, +but we use the n equals 1 + +energy here as the value of Psi +equals 0. + +In other words, +the n equals 1 wave function + +looks kind of like that. +This level here is Psi equals + +0. +This is the value of Psi, + +whatever it is, +at r equals 0, + +and there is just an +exponential decay. + +We plot the wave function on +top of that energy level. + +In other words, +this is a complex diagram here. + +You are going to see, +if you take any course beyond + +this, this diagram a lot, +with energy levels and wave + +functions plotted on top of +them. + +And then, the n equals 2 wave +function is plotted on top of + +the n equals 2 energy level. +Again, at r equals 0, + +it is some finite value and +then it drops. + +At some value of r, +we have a node for n equals 2 + +here. +The n equals 2 is the Psi + +equals 0. +Right here, you have a radial + +node. +Then it goes up and then it + +comes back. +It goes down to a negative + +value and then comes back up. +That is n equals 2. + +And so forth and so on. +n equals 3 looks like this. + +It has two radial nodes. +That is what that diagram is + +showing here. +And then we get to n equals + +235. +Here is the wave function. + +Is this is a hydrogen atom and +you have n equals 235, + +how many radial nodes do you +have? + +234. +This wave function is passing + +through this origin 234 times. +That is the wave function. + +And then it tails off. +There is always an exponential + +dependence there. +That is what that wave function + +looks like. +Now, how do these relate to the + +intensity of some transition? +Well, the intensity of a + +transition is related to the +overlap between the wave + +function of the initial state +and the wave function of the + +final state. +What do I mean by overlap? + +Well, by overlap, +I mean you take the wave + +function, here, +of the initial state, + +so I am going to pretend we +have a hydrogen atom in the 235 + +state, this is its wave +function. + +And that hydrogen atom is going +to be relaxing to the n equals 1 + +state. +What I am going to do, + +to get the overlap, +is I'm going to take the + +product of the wave function of +the initial state times that of + +the final state, +and essentially I am going to + +integrate that resulting +function. + +I am going to multiply these +two wave functions together, + +and I am going to integrate +over all r the resulting + +function. +That is what I mean by overlap. + +But there is another term here. +There is an r, + +too. +That r is important. + +It has to do with the +transition moment dipole. + +And we won't go into that, +but it is there. + +But it won't affect the +argument I am going to make for + +you right now. +We take the wave function of + +the initial state, +multiply it by the final state + +times r, and then we integrate +this whole thing from r equals 0 + +to infinity and then square it. +That quantity is proportional + +to the intensity of some +transition. + +Let's do that. +Here is Psi n equals 235, + +we are multiplying it by Psi of + +n equals 0 and +actually multiplying it by r. + +And what we are going to see, +if we just look at this product + +here, if we just looked at Psi n +equals 235 and + +Psi n equals 1, +if we just looked at that + +product, we are going to +multiply this times that. + +In a graphical form, +it is going to look like this. + +It is going to go up, +down, up, down, + +up, down. +It is going to oscillate and + +then tail off in an exponential +way because we are multiply this + +up, down, up, +down, up down times this + +exponential decay. +It is going to look something + +like that. +But now, we are going to + +integrate this resulting curve. +What you can see is that the + +area above this curve is equal +to the area below this curve, + +approximately. +And, when we integrate + +something, we are calculating +the area underneath the curve. + +These positive areas are going +to cancel these negative areas. + +The result is that this +integral is going to be very + +small. +And the result is that the + +intensity of that line is very +low. + +The intensities are +proportional to this overlap, + +the overlap of the initial +state wave function and the + +final state wave function. +And you can see, + +here, graphically, +how if you integrate that + +product in this case, +the positive areas cancel the + +negative areas, +and you don't have a very + +intense transition. +However, suppose we look at the + +transition from n equals 3 to n +equals 2. + +Well, here is the n equals 3 +wave function, + +here is the n equals 2 wave +function. + +And our intensity expression +says that we have to multiply + +these two. +Let's do that. + +Let's multiply n equals 3 times +n equals 2, here. + +Well, the result, +if you excuse my not so great + +drawing, is we start out with a +very positive function here. + +But then we have two negatives +here, which make it a little bit + +less negative. +But then, we have a positive, + +here, times a negative, +and what that makes is a large + +area that is negative. +And, if we go and integrate + +that, now we don't have the same +cancellation of positive and + +negative areas. +We integrate that, + +and that transition energy is +large. + +Or, that area is large, +therefore the intensity of that + +transition is large. +Bottom line, + +that is one of the elements +that dictates the intensity of a + +transition. +It is also one of the elements + +that dictates the intensity of +your photoelectron spectra. + +Somebody asked me about it the +other day. + +I had drawn lines in the +photoelectronic spectra that + +were of the same intensity, +1s, 2s, 2p 6. + +Somebody said, +well, you have more electrons + +in the 2p state. +Why don't you have a larger + +number of electrons coming off? +The answer is, + +that is part of what goes into +determining the intensity of the + +transition, but there is more to +it. + +It is not just the number of +electrons. + +Here is one of the elements +that goes into determining the + +intensity of some transition. +It is the wave functions and + +the overlap between the final +and the initial state. + +And then, I just wanted to also +show you, here, + +for this atom in the n equals +235 state, I plotted just for + +fun, kind of schematically, +what the radial probability + +distribution would look like. +That is just r squared times + +the radial part squared. +And, of course, + +since the wave function goes +like this, oscillates, + +that is what the radial +probability distribution is + +going to do. +And you are going to see 234 + +nodes here, 234 values of r, +that is going to make the wave + +function be equal to zero. +And then way out here, + +you are going to have a +feature. + +That last feature, +here, is going to have the + +maximum probability, +and that is your value of r + +that is most probable. +It turns out for n equals 235 + +that the most probable value of +r is 43,800 angstroms. + +That is about 4.38x10^-6 +meters. + +This is a really large hydrogen +atom, n equals 235. + +Do they exist? +The answer is yes, + +they do exist. +They exist, particularly in + +outer space, where there is lots +of UV radiation to get these + +hydrogen atoms up into these +very excited states. + +And they exist in deep outer +space, where the temperatures + +are pretty cold. +And you need those cold + +temperatures because this +hydrogen atom is not very stable + +in n equals 235. +And, if you went and calculated + +here, I am going to draw a line, +here. + +This is going to be n equals +235, and this is the zero of + +energy. +This energy difference here is + +about 4x10^-23 joules. +Whereas, at room temperature, + +we will just talk about the +thermal energy, + +thermal energy is about +4x10^-21 joules. + +You can see that any little +fluctuation at room temperature, + +since this is two orders of +magnitude larger than what this + +bound by, any little fluctuation +would kick this very weakly + +bound electron up and ionize it. +And it would. + +You really only see these in +environments that are very cold, + +where you don't perturb what +are called Rydberg atoms + +sometimes. +I think in the laboratory the + +largest Rydberg atom that has +been made is n equals 180 or n + +equals 200 or so. +Anyway, that was really just + +for fun that I wanted to tell +you about that. + +Now, there is another little +tidbit that I want to talk to + +you about that has to do with +how knowing something about the + +energy levels in an atom leads +to a nice practical device, + +like a helium neon laser. +We have to take a look at the + +neon energy levels. +And so we have another + +discharge lamp here, +and we have some more of these + +glasses, here, +so that you can resolve the + +neon lines here. +The TAs will get them out. + +Here is our neon discharge +lamp. + +You can resolve, +here, the neon spectrum. + +The spectrum that you should +see should be what is shown on + +the side walls here. +Let me turn off the lights so + +that you can see it a little bit +better, hopefully. + +You can see lots of lines in +the case of neon because we have + +lots of different occupied +states. + +The glasses that I have +actually are doing a phenomenal + +job in resolving those very +closely spaced lines. + +I must have a better quality +glass today. + +And, if you look at the side +walls, you can see that I drew + +one of those lines. +One of those emission lines is + +at 632 nanometers, +which is the emission line of a + +helium neon laser. +But it is really a neon + +transition that we will talk +about in a moment. + +I drew it as very thick on the +board. + +Because when I looked at the +discharge lamp and drew that + +picture, my glasses did not +resolve those lines so very + +well. +And so that one looked really + +thick to me. +At least my glasses, + +I can really see lots and lots +of discrete lines. + +But it is this transition, +632 nanometers, + +that is the output of the +helium neon laser, + +which is the red laser that I +use sometimes in the lecture, + +here, to point. +It is the basis of the laser + +that is used in the grocery +stores to scan the prices on + +your items. +And it turns out that what is + +going on, here, +is the following. + +If you look on the side walls, +we have neon in the ground + +state before we turn the +discharge on. + +And then, when we turn the +discharge on, + +that pumps energy into the neon +atoms such that one of those + +electrons, the 2p electron, +gets promoted into the 5s + +state. +And then, of course, + +that atom wants to relax. +And so here it comes again. + +That 5s state relaxes. +That electron relaxes to the 3p + +state. +And it is actually that + +transition that occurs at 632.8 +nanometers, the basis of the + +helium neon laser. +It is that transition, + +from the 5s to the 3p. +It is not all the way down, + +but ultimately, +of course, that state relaxes. + +But what is going on in the +helium neon laser? + +Well, in the helium neon laser, +we have a discharge ignited + +where we have a lot of neon +atoms here in this excited + +state, with the one electron in +the 5s state right as I show + +you. +And that is emitting, + +a photon comes out. +But what is happening here is + +that the photon that is emitted +is able to, because of the + +construction of this laser, +contact or to interact with + +another neon atom in this same +excited state, + +that 2p 5 5s state. +That photon interacts with this + +excited atom. +When it interacts with that + +excited atom, +what happens is that the photon + +stimulates that excited atom to +actually emit a photon of the + +same energy. +This photon stimulates this + +excited atom to release its +energy right at that time. + +The result is that you have two +photons coming out. + +They are going to come out in +the same direction and they are + +going to be what is called +coherent. + +That is, their phases are going +to match. + +If you think now of the photon +as a wave, they are going to be + +coherent. +And the result is that you are + +going to have some radiation +that is going to be twice as + +intense because they are +coherent. + +They are in phase. +And then, what happens is that + +these two photons, +they each then interact with + +another neon atom in this same +excited state. + +And each of those photons +stimulates another atom to emit + +photons. +And the result is now that you + +have four photons being emitted, +the same frequency, + +same direction, +and same phase. + +And it is in this way that we +amplify the light in any kind of + +laser. +This is what is going on, + +this process of simulated +emission. + +Where you have a photon that +now is exactly the frequency of + +the energy difference of the +transition that you are going to + +make in this excited atom. +This stimulates that atom to + +emit a photon. +The two photons then come off + +coherently. +And then, these two interact + +with two other atoms. +Now you have four photons that + +are coming off. +That is the process of + +amplification in any type of +laser. + +Of course, in order to make +this work, you have to have a + +lot of these excited neon atoms +around because you have to be + +able to have a photon interact +with them before they just emit + +spontaneously. +This is stimulated emission. + +The other kind of emission that +we were talking about is + +spontaneous emission. +In other words, + +you have to have a high +concentration of these excited + +neon atoms so that the photons +that are originally emitted + +here, by just spontaneous +emission, can interact with + +those excited state neon atoms +and stimulate the emission and + +get this whole process rolling. +In order to produce a whole lot + +of those excited neon atoms, +what happens is we add in a + +little bit of helium. +It turns out that in helium + +there are some excited states +that are just, + +by accident, +at the same energy as this + +excited state of neon. +And the helium actually + +transfers its energy to the +neon, into this state, + +and maintains, +then, that very high population + +of neon atoms here in this +excited state. + +That is the function of the +helium. + +It is just the energy transfer +from the helium excited state to + +the neon excited state. +It keeps the population of the + +neon atoms really high. +The helium, you don't see that + +emission. +That is just a helper in this + +device. +It is the neon transition that + +you are looking at here. +That was just a short story + +about the usefulness of knowing +about the energy levels in atoms + +and how ultimately you can make +a practical device because you + +know something about the energy +levels of your atoms. + +Well, that is going to finish +up, right now, + +our discussion of atoms. +And now, it is time to move + +onto one of the very important +parts of chemistry, + +and that is chemical bonds and +the combination of atoms to form + +a chemical bond. +That is what we are going to + +start talking about, +now. + +Today, what we are going to do +is just talk about the + +fundamental interactions that +are present in every chemical + +bond. +Let's start with that. + +Let me come over here while the +lights are warming up so you can + +see that board. +Suppose we have a hydrogen atom + +here, nucleus a, +plus charge. + +And it, of course, +has electron a attached to it. + +And way out here, +we have nucleus b and electron + +b that is attached to it. +And they are very far apart. + +And so, in this case, +where they are very far apart, + +the energy of interaction is +just the energy of interaction + +between the electron and the +nucleus, the electron-nuclear + +attraction. +Here it is, the + +electron-nuclear attraction. +However, as we bring these two + +hydrogen atoms together, +at some point this electron + +that was only attracted to +nucleus a is now begins to + +experience an attraction with +nucleus b. + +And this electron that was +attracted only to nucleus b + +experiences an interaction +whereby it is now attracted to + +nucleus a. +And that kind of mutual + +attractive interaction then +brings those two nuclei closer + +together. +However, at the same time, + +when you bring those two nuclei +closer together, + +you are bringing the electrons +closer together. + +And so there is an +electron-electron repulsion that + +is present. +In addition, + +as you bring these two nuclei +together, what is happening here + +is you are having a +nuclear-nuclear repulsion. + +A chemical bond is really the +sum of these three interactions + +and the interplay between these +three interactions. + +That is what we want to try to +look at and try to understand. + +How are we going to do that? +Well, the first thing I am + +going to do is I am going to +draw an energy of interaction as + +a function of the distance +between the two hydrogen atoms. + +I am going to take two hydrogen +atoms and I am going to call the + +distance between them r. +Now, I have changed my + +definition of r. +r is the distance between the + +two nuclei. +It is no longer the distance + +between the nucleus and the +electron. + +I have just changed my +definition of r. + +And I am going to plot the +energy of interaction as a + +function of that distance +between the two nuclei. + +Here is my energy of +interaction. + +There is going to be a zero of +energy, here. + +I am going to plot this as a +function of r, + +and the plot is going to look +like this. + +Way out here, +where r is large, + +I have two separated hydrogen +atoms. + +The energy, here, +is minus 2,624 kilojoules per + +mole. +That is what this energy of + +interaction is, +here. + +Now, as I bring these two +hydrogen atoms together, + +what happens is that this +energy is going to decrease. + +And it is going to keep +decreasing until we get to some + +point. +And then, as r gets even + +smaller, that energy of +interaction is going to + +skyrocket and go to infinity. +Starting about here somewhere, + +where the energy of interaction +is less, is more negative than + +the separated hydrogen atoms. +Well, what that means is that + +we are forming a chemical bond. +The two hydrogen atoms are more + +stable then when they are +separated. + +The two hydrogen atoms are +bound as soon as this energy of + +interaction gets more negative +than the separated atom limit. + +And it keeps getting more +negative. + +And, of course, +the value of r at which that + +energy of interaction is a +maximum negative number, + +well, that is the equilibrium +bond length. + +This is the most stable value +of r at which the energy is the + +lowest. +It is the most stable + +configuration. +In the case of hydrogen, + +that value of r is 0.74 +angstroms. + +In this potential energy curve, +as it is often called, + +everywhere where this energy of +interaction is lower than the + +separated hydrogen atom limit, +everywhere here, + +this is called the attractive +region of the interaction + +potential. +It is attractive because the + +hydrogen atoms bound are more +stable than they are separated. + +Or, the hydrogen atoms are +bound. + +They are more stable than the +two hydrogen atoms separated. + +We call this the attractive +region of the potential energy + +curve. +We also call this region, + +this attractive region, +we call that the well. + +And the well depth, +here, from the bottom to the + +separated hydrogen atom limit, +if you measure the energy from + +the bottom up, +that energy is the bond + +association energy. +We are going to call it delta E + +sub d, +from the bottom here to the + +separated hydrogen atom limit. +That is the bond energy. + +432 kilojoules per mole is the +energy that you have to put into + +the H two molecule to +separate it. + +You have to get it from the +bottom of this well to the + +separated hydrogen atom limit +here. + +Now, you can also see, +here, as you push those two + +hydrogen atoms even closer +together than the equilibrium + +bond length, you can see that +the energy is going back up. + +And at some point, +if you push the two hydrogen + +atoms close enough together such +that the energy is equal to that + +of the separated hydrogen atom, +it then becomes greater than + +that of the separated hydrogen +atom. + +From this value of r on, +the hydrogen atoms are no + +longer bound because their +energy is greater than the + +separated hydrogen atom limit. +We call this part of the + +potential energy of interaction +the repulsive part. + +In other words, +as you push the two hydrogen + +atoms closer together, +they form a bond. + +But if you push them too close, +they are going to fly apart. + +They are no longer bound. +This is the general potential + +energy of interaction for every +chemical bond. + +Every single bond has this +general shape. + +That is important. +But that shape is really a + +consequence of these three +interactions that I talked about + +when we started this problem, +here. + +And so, what I want to try to +do is now try to dissect that + +curve into the three components +that give rise to that potential + +energy of interaction, +that dependence as a function + +of r. +I want to pull that apart. + +This energy of interaction is +the sum of the nuclear + +repulsion. +Pushing the nuclei too close + +together, there is a repulsive +interaction. + +That is one of the +interactions. + +Plus, the electron-nuclear +attraction is the attraction + +between the electron and the +nucleus on which it came in. + +And also between the electron +and the other nucleus. + +That is the electron-nuclear +attraction. + +Plus the electron-electron +repulsive. + +Well, when you bring two +hydrogen atoms together those + +electrons are going to repel. +That is the energy of + +interaction. +It is the sum of those three + +fundamental interactions. +But what I want to do is figure + +out an r dependence for each one +of these interactions. + +And the sum of that r +dependence should give me a + +shape that looks like this. +I want to see which + +interactions are important at +what values of r. + +Let me start. +Let's start with the + +nuclear-nuclear repulsion here. +If I wanted an r dependence for + +what that nuclear-nuclear +repulsion looked like, + +what would that be? + +Coulomb force. +It is the repulsive Coulomb + +interaction. +It is e squared over 4 pi + +epsilon nought r. + +This is just two like charges +that are repelling. + +And so now let me draw that +repulsive interaction as a + +function of r on an energy level +diagram. + +Here is my energy of +interaction. + +It is a function of r. +There is going to be a zero + +here. +And this repulsive interaction + +is going to be positive +everywhere. + +It is going to be infinite here +and a one over r + +dependence coming down. +This is the Coulomb + +interaction. +This is the nuclear-nuclear + +repulsion. +That is what it looks like as a + +function of r. +That is one component. + +Now, what about the other +components here? + +Well, it turns out I have no +simple way of estimating what + +the r dependence is for the +electron-nuclear attraction. + +I have no simple way of +estimating what the r dependence + +is for the electron-electron +repulsion. + +And I have no simple way of +doing that for the sum of those + +two terms. +Actually, the sum of these two + +terms, I am going to call the +electron interactions. + +Each one of these terms +involves the electrons. + +The is the electron-electron +repulsion, electron-nuclear + +attraction. +This term does not have any + +electrons in it. +I have no simple way of telling + +you or estimating what the r +dependence is of the sum of + +these two terms. +However, what I can do is + +figure out what the energy is +for the sum of those two + +interactions at two extremes. +I can tell you what the energy + +is at r equal infinity, +and then I can tell you what it + +is at r equal zero. +And, therefore, + +on this plot, +I am going to come in with a + +value for r equal infinity and a +value for r equal zero. + +I am going to draw a straight +line as an estimate for the r + +dependence. +Then I am going to add them up + +and see if the result looks, +in fact, like this energy of + +interaction that I drew for you. +And so that is what I am going + +to have to do on Friday. +I will see you on Wednesday, + +if not sooner. \ No newline at end of file diff --git a/R6_jm8BOrjw.txt b/R6_jm8BOrjw.txt new file mode 100644 index 0000000000000000000000000000000000000000..df669182a51e6aede54ecf0485c17f0b6fd601aa --- /dev/null +++ b/R6_jm8BOrjw.txt @@ -0,0 +1,14891 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following 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how we see + + + align:start position:0% +is to talk about how we see +um + + align:start position:0% +um + + + align:start position:0% +um +what I'm going to do today is talk about + + align:start position:0% +what I'm going to do today is talk about + + + align:start position:0% +what I'm going to do today is talk about +how we take information in next Tuesday + + align:start position:0% +how we take information in next Tuesday + + + align:start position:0% +how we take information in next Tuesday +I'll talk about the fact that we take in + + align:start position:0% +I'll talk about the fact that we take in + + + align:start position:0% +I'll talk about the fact that we take in +too much information more information + + align:start position:0% +too much information more information + + + align:start position:0% +too much information more information +than we can use and we have to select + + align:start position:0% +than we can use and we have to select + + + align:start position:0% +than we can use and we have to select +amongst that information + + align:start position:0% +amongst that information + + + align:start position:0% +amongst that information +um and + + align:start position:0% +um and + + + align:start position:0% +um and +um on uh Thursday of next week what I'll + + align:start position:0% +um on uh Thursday of next week what I'll + + + align:start position:0% +um on uh Thursday of next week what I'll +talk about is the fact that perception + + align:start position:0% +talk about is the fact that perception + + + align:start position:0% +talk about is the fact that perception +is never just a direct somehow + + align:start position:0% +is never just a direct somehow + + + align:start position:0% +is never just a direct somehow +registration of the outside world it's + + align:start position:0% +registration of the outside world it's + + + align:start position:0% +registration of the outside world it's +always an active interpretation of the + + align:start position:0% +always an active interpretation of the + + + align:start position:0% +always an active interpretation of the +world and I'll talk about how we go + + align:start position:0% +world and I'll talk about how we go + + + align:start position:0% +world and I'll talk about how we go +about interpreting the information that + + align:start position:0% +about interpreting the information that + + + align:start position:0% +about interpreting the information that +we've gotten from the outside I will be + + align:start position:0% +we've gotten from the outside I will be + + + align:start position:0% +we've gotten from the outside I will be +barely able to scratch the surface of + + align:start position:0% +barely able to scratch the surface of + + + align:start position:0% +barely able to scratch the surface of +the topic I will abandon all discussion + + align:start position:0% +the topic I will abandon all discussion + + + align:start position:0% +the topic I will abandon all discussion +of the other senses for instance which + + align:start position:0% +of the other senses for instance which + + + align:start position:0% +of the other senses for instance which +is a great pity now it's true that I can + + align:start position:0% +is a great pity now it's true that I can + + + align:start position:0% +is a great pity now it's true that I can +barely scratch the surface of almost any + + align:start position:0% +barely scratch the surface of almost any + + + align:start position:0% +barely scratch the surface of almost any +Topic in this course but here here the + + align:start position:0% +Topic in this course but here here the + + + align:start position:0% +Topic in this course but here here the +danger is greater because this is + + align:start position:0% +danger is greater because this is + + + align:start position:0% +danger is greater because this is +actually what I do for a living and so + + align:start position:0% +actually what I do for a living and so + + + align:start position:0% +actually what I do for a living and so +on any little bit of the of of this I + + align:start position:0% +on any little bit of the of of this I + + + align:start position:0% +on any little bit of the of of this I +can I can talk forever + + align:start position:0% +can I can talk forever + + + align:start position:0% +can I can talk forever +um and so exactly how much of the + + align:start position:0% +um and so exactly how much of the + + + align:start position:0% +um and so exactly how much of the +surface I I uh I scratch will be + + align:start position:0% +surface I I uh I scratch will be + + + align:start position:0% +surface I I uh I scratch will be +determined by how how far afield I end + + align:start position:0% +determined by how how far afield I end + + + align:start position:0% +determined by how how far afield I end +up going + + align:start position:0% +up going + + + align:start position:0% +up going +um this slide is up there + + align:start position:0% +um this slide is up there + + + align:start position:0% +um this slide is up there +to uh + + align:start position:0% +to uh + + + align:start position:0% +to uh +to illustrate in some sense those three + + align:start position:0% +to illustrate in some sense those three + + + align:start position:0% +to illustrate in some sense those three +bits let's see if I take the stage + + align:start position:0% +bits let's see if I take the stage + + + align:start position:0% +bits let's see if I take the stage +chalkboard light off there we go you + + align:start position:0% +chalkboard light off there we go you + + + align:start position:0% +chalkboard light off there we go you +want to go off then they can oh then you + + align:start position:0% +want to go off then they can oh then you + + + align:start position:0% +want to go off then they can oh then you +can see a little bit better + + align:start position:0% +can see a little bit better + + + align:start position:0% +can see a little bit better +um + + align:start position:0% +um + + + align:start position:0% +um +well you know but I can sort of see + + align:start position:0% +well you know but I can sort of see + + + align:start position:0% +well you know but I can sort of see +stuff this is this is + + align:start position:0% +stuff this is this is + + + align:start position:0% +stuff this is this is +that hurt + + align:start position:0% +that hurt + + + align:start position:0% +that hurt +that's his bruegel's painting of + + align:start position:0% +that's his bruegel's painting of + + + align:start position:0% +that's his bruegel's painting of +um the the uh the battle between the + + align:start position:0% +um the the uh the battle between the + + + align:start position:0% +um the the uh the battle between the +good angels and and and the bad Angels + + align:start position:0% +good angels and and and the bad Angels + + + align:start position:0% +good angels and and and the bad Angels +um but for me the purpose is to say look + + align:start position:0% +um but for me the purpose is to say look + + + align:start position:0% +um but for me the purpose is to say look +it's clear that you see something + + align:start position:0% +it's clear that you see something + + + align:start position:0% +it's clear that you see something +it's clear that what you are seeing is + + align:start position:0% +it's clear that what you are seeing is + + + align:start position:0% +it's clear that what you are seeing is +an active interpretation in fact you had + + align:start position:0% +an active interpretation in fact you had + + + align:start position:0% +an active interpretation in fact you had +no you may not have particularly known + + align:start position:0% +no you may not have particularly known + + + align:start position:0% +no you may not have particularly known +that it was a battle between good angels + + align:start position:0% +that it was a battle between good angels + + + align:start position:0% +that it was a battle between good angels +and bad Angels + + align:start position:0% +and bad Angels + + + align:start position:0% +and bad Angels +um before you look at it and it's also + + align:start position:0% +um before you look at it and it's also + + + align:start position:0% +um before you look at it and it's also +clear that even though you in some sense + + align:start position:0% +clear that even though you in some sense + + + align:start position:0% +clear that even though you in some sense +see the whole thing you're not + + align:start position:0% +see the whole thing you're not + + + align:start position:0% +see the whole thing you're not +processing it fully so uh at least not + + align:start position:0% +processing it fully so uh at least not + + + align:start position:0% +processing it fully so uh at least not +all at once so for instance you may not + + align:start position:0% +all at once so for instance you may not + + + align:start position:0% +all at once so for instance you may not +have particularly noticed I don't know + + align:start position:0% +have particularly noticed I don't know + + + align:start position:0% +have particularly noticed I don't know +what he is he's a really cool Beast I'm + + align:start position:0% +what he is he's a really cool Beast I'm + + + align:start position:0% +what he is he's a really cool Beast I'm +not sure if that's a bad Angel falling + + align:start position:0% +not sure if that's a bad Angel falling + + + align:start position:0% +not sure if that's a bad Angel falling +or something but you probably hadn't + + align:start position:0% +or something but you probably hadn't + + + align:start position:0% +or something but you probably hadn't +particularly noticed you know this fish + + align:start position:0% +particularly noticed you know this fish + + + align:start position:0% +particularly noticed you know this fish +guy + + align:start position:0% +guy + + + align:start position:0% +guy +um actually you know in this picture + + align:start position:0% +um actually you know in this picture + + + align:start position:0% +um actually you know in this picture +you're probably still not noticing the + + align:start position:0% +you're probably still not noticing the + + + align:start position:0% +you're probably still not noticing the +fish guy he just looks like a blob + + align:start position:0% +fish guy he just looks like a blob + + + align:start position:0% +fish guy he just looks like a blob +it's a great picture look at it sometime + + align:start position:0% +it's a great picture look at it sometime + + + align:start position:0% +it's a great picture look at it sometime +oh and this guy's got very bad stomach + + align:start position:0% +oh and this guy's got very bad stomach + + + align:start position:0% +oh and this guy's got very bad stomach +problems + + align:start position:0% +problems + + + align:start position:0% +problems +um + + align:start position:0% +um + + + align:start position:0% +um +whatever he's doing okay + + align:start position:0% +whatever he's doing okay + + + align:start position:0% +whatever he's doing okay +rather than continuing to try to look at + + align:start position:0% +rather than continuing to try to look at + + + align:start position:0% +rather than continuing to try to look at +a murky picture let's go to a less murky + + align:start position:0% +a murky picture let's go to a less murky + + + align:start position:0% +a murky picture let's go to a less murky +picture and let's start by talking about + + align:start position:0% +picture and let's start by talking about + + + align:start position:0% +picture and let's start by talking about +how you actually get information in from + + align:start position:0% +how you actually get information in from + + + align:start position:0% +how you actually get information in from +the visual system which obviously + + align:start position:0% +the visual system which obviously + + + align:start position:0% +the visual system which obviously +involves come on get off of there going + + align:start position:0% +involves come on get off of there going + + + align:start position:0% +involves come on get off of there going +through + + align:start position:0% +through + + + align:start position:0% +through +the uh + + align:start position:0% +the uh + + + align:start position:0% +the uh +um the eye + + align:start position:0% +um the eye + + + align:start position:0% +um the eye +um on the handout which do I have a copy + + align:start position:0% +um on the handout which do I have a copy + + + align:start position:0% +um on the handout which do I have a copy +of it here yes okay + + align:start position:0% +of it here yes okay + + + align:start position:0% +of it here yes okay +um a lot of terminology + + align:start position:0% +um a lot of terminology + + + align:start position:0% +um a lot of terminology +uh are you responsible for it yes of + + align:start position:0% +uh are you responsible for it yes of + + + align:start position:0% +uh are you responsible for it yes of +course + + align:start position:0% +course + + + align:start position:0% +course +um if you miss some little bit of + + align:start position:0% +um if you miss some little bit of + + + align:start position:0% +um if you miss some little bit of +terminology that's not going to sink you + + align:start position:0% +terminology that's not going to sink you + + + align:start position:0% +terminology that's not going to sink you +in in the course either on this topic or + + align:start position:0% +in in the course either on this topic or + + + align:start position:0% +in in the course either on this topic or +on any other topic + + align:start position:0% +on any other topic + + + align:start position:0% +on any other topic +um you you want to put your your effort + + align:start position:0% +um you you want to put your your effort + + + align:start position:0% +um you you want to put your your effort +into thinking about the broader uh topic + + align:start position:0% +into thinking about the broader uh topic + + + align:start position:0% +into thinking about the broader uh topic +but um it's useful in being able to talk + + align:start position:0% +but um it's useful in being able to talk + + + align:start position:0% +but um it's useful in being able to talk +intelligently about it to to to get a + + align:start position:0% +intelligently about it to to to get a + + + align:start position:0% +intelligently about it to to to get a +grip on some of this terminology and + + align:start position:0% +grip on some of this terminology and + + + align:start position:0% +grip on some of this terminology and +hence the tour of the visual system that + + align:start position:0% +hence the tour of the visual system that + + + align:start position:0% +hence the tour of the visual system that +I will now embark on + + align:start position:0% +I will now embark on + + + align:start position:0% +I will now embark on +um from the outside in + + align:start position:0% +um from the outside in + + + align:start position:0% +um from the outside in +light your the the purpose of the eyed + + align:start position:0% +light your the the purpose of the eyed + + + align:start position:0% +light your the the purpose of the eyed +or at least the front half of the eye is + + align:start position:0% +or at least the front half of the eye is + + + align:start position:0% +or at least the front half of the eye is +to form an image on the back half of the + + align:start position:0% +to form an image on the back half of the + + + align:start position:0% +to form an image on the back half of the +eye do I have a little cursor here so + + align:start position:0% +eye do I have a little cursor here so + + + align:start position:0% +eye do I have a little cursor here so +all of this sometimes called the + + align:start position:0% +all of this sometimes called the + + + align:start position:0% +all of this sometimes called the +anterior segment of the eye is there to + + align:start position:0% +anterior segment of the eye is there to + + + align:start position:0% +anterior segment of the eye is there to +form an image like a camera would on the + + align:start position:0% +form an image like a camera would on the + + + align:start position:0% +form an image like a camera would on the +back surface of the eye most of the + + align:start position:0% +back surface of the eye most of the + + + align:start position:0% +back surface of the eye most of the +optical power of the eye is at the very + + align:start position:0% +optical power of the eye is at the very + + + align:start position:0% +optical power of the eye is at the very +front surface of it that front surface + + align:start position:0% +front surface of it that front surface + + + align:start position:0% +front surface of it that front surface +is called the cornea + + align:start position:0% +is called the cornea + + + align:start position:0% +is called the cornea +um it has apart from its virtues as a a + + align:start position:0% +um it has apart from its virtues as a a + + + align:start position:0% +um it has apart from its virtues as a a +a lens focusing light it is also one of + + align:start position:0% +a lens focusing light it is also one of + + + align:start position:0% +a lens focusing light it is also one of +the two uh surfaces in the body most + + align:start position:0% +the two uh surfaces in the body most + + + align:start position:0% +the two uh surfaces in the body most +sensitive to pain you may try this out + + align:start position:0% +sensitive to pain you may try this out + + + align:start position:0% +sensitive to pain you may try this out +if you want at home I don't recommend it + + align:start position:0% +if you want at home I don't recommend it + + + align:start position:0% +if you want at home I don't recommend it +but you if you scratch your cornea you + + align:start position:0% +but you if you scratch your cornea you + + + align:start position:0% +but you if you scratch your cornea you +will know it + + align:start position:0% +will know it + + + align:start position:0% +will know it +um and and you will not be happy what's + + align:start position:0% +um and and you will not be happy what's + + + align:start position:0% +um and and you will not be happy what's +the other one + + align:start position:0% +the other one + + + align:start position:0% +the other one +what's the other surface do you think + + align:start position:0% +what's the other surface do you think + + + align:start position:0% +what's the other surface do you think +anybody uh care to venture I guess + + align:start position:0% +anybody uh care to venture I guess + + + align:start position:0% +anybody uh care to venture I guess +thumbs + + align:start position:0% + + + + align:start position:0% + +nowhere that's a a novel thought + + align:start position:0% +nowhere that's a a novel thought + + + align:start position:0% +nowhere that's a a novel thought +um no look you're he's thinking like the + + align:start position:0% +um no look you're he's thinking like the + + + align:start position:0% +um no look you're he's thinking like the +cartoons right you hit the thumb with + + align:start position:0% +cartoons right you hit the thumb with + + + align:start position:0% +cartoons right you hit the thumb with +the hammer and oh it hurts let me tell + + align:start position:0% +the hammer and oh it hurts let me tell + + + align:start position:0% +the hammer and oh it hurts let me tell +you if you hit your cornea with the + + align:start position:0% +you if you hit your cornea with the + + + align:start position:0% +you if you hit your cornea with the +hammer it hurts a lot more yes + + align:start position:0% +hammer it hurts a lot more yes + + + align:start position:0% +hammer it hurts a lot more yes +someplace inside the mouth no again you + + align:start position:0% +someplace inside the mouth no again you + + + align:start position:0% +someplace inside the mouth no again you +think about that as a the the inside the + + align:start position:0% +think about that as a the the inside the + + + align:start position:0% +think about that as a the the inside the +mouth is a place where pairing happens + + align:start position:0% +mouth is a place where pairing happens + + + align:start position:0% +mouth is a place where pairing happens +but that's because you do stupid things + + align:start position:0% +but that's because you do stupid things + + + align:start position:0% +but that's because you do stupid things +with your mouth like hey that pizza + + align:start position:0% +with your mouth like hey that pizza + + + align:start position:0% +with your mouth like hey that pizza +looks good oh now you would never stick + + align:start position:0% +looks good oh now you would never stick + + + align:start position:0% +looks good oh now you would never stick +the pizza on your eyeball + + align:start position:0% +the pizza on your eyeball + + + align:start position:0% +the pizza on your eyeball +um it just so again yes good nicely + + align:start position:0% +um it just so again yes good nicely + + + align:start position:0% +um it just so again yes good nicely +innovated for pain but but not + + align:start position:0% +innovated for pain but but not + + + align:start position:0% +innovated for pain but but not +particularly + + align:start position:0% +particularly + + + align:start position:0% +particularly +um not not not the other great location + + align:start position:0% +um not not not the other great location + + + align:start position:0% +um not not not the other great location +I'll take one more here + + align:start position:0% + + + + align:start position:0% + +yeah yeah same sort of thing right right + + align:start position:0% +yeah yeah same sort of thing right right + + + align:start position:0% +yeah yeah same sort of thing right right +you know I used to step on nails or + + align:start position:0% +you know I used to step on nails or + + + align:start position:0% +you know I used to step on nails or +something yeah bottom of your foot's a + + align:start position:0% +something yeah bottom of your foot's a + + + align:start position:0% +something yeah bottom of your foot's a +good place but no that you oh oh oh + + align:start position:0% +good place but no that you oh oh oh + + + align:start position:0% +good place but no that you oh oh oh + there's two people here I've just + + align:start position:0% + there's two people here I've just + + + align:start position:0% + there's two people here I've just +got to take their answers because + + align:start position:0% +got to take their answers because + + + align:start position:0% +got to take their answers because +they're so eager but yeah + + align:start position:0% +they're so eager but yeah + + + align:start position:0% +they're so eager but yeah +somewhere inside your ear is the point + + align:start position:0% +somewhere inside your ear is the point + + + align:start position:0% +somewhere inside your ear is the point +not not your not the chunk that that so + + align:start position:0% +not not your not the chunk that that so + + + align:start position:0% +not not your not the chunk that that so +many people are thrilled with you know + + align:start position:0% +many people are thrilled with you know + + + align:start position:0% +many people are thrilled with you know +oh let's put a hole in this oh that was + + align:start position:0% +oh let's put a hole in this oh that was + + + align:start position:0% +oh let's put a hole in this oh that was +fun let's do it again you know that + + align:start position:0% +fun let's do it again you know that + + + align:start position:0% +fun let's do it again you know that +obviously hurts but I I guess I've never + + align:start position:0% +obviously hurts but I I guess I've never + + + align:start position:0% +obviously hurts but I I guess I've never +gone in for this myself + + align:start position:0% +gone in for this myself + + + align:start position:0% +gone in for this myself +um but not no it it's the reason one of + + align:start position:0% +um but not no it it's the reason one of + + + align:start position:0% +um but not no it it's the reason one of +the reasons your mother said don't put + + align:start position:0% +the reasons your mother said don't put + + + align:start position:0% +the reasons your mother said don't put +anything inside your your uh your ear + + align:start position:0% +anything inside your your uh your ear + + + align:start position:0% +anything inside your your uh your ear +that's bigger than your elbow is because + + align:start position:0% +that's bigger than your elbow is because + + + align:start position:0% +that's bigger than your elbow is because +if you put something small and pointy in + + align:start position:0% +if you put something small and pointy in + + + align:start position:0% +if you put something small and pointy in +there it eventually reaches your eardrum + + align:start position:0% +there it eventually reaches your eardrum + + + align:start position:0% +there it eventually reaches your eardrum +and that's the other surface when you + + align:start position:0% +and that's the other surface when you + + + align:start position:0% +and that's the other surface when you +had an ear infection as a kid + + align:start position:0% +had an ear infection as a kid + + + align:start position:0% +had an ear infection as a kid +and um that uh and and and the pressure + + align:start position:0% +and um that uh and and and the pressure + + + align:start position:0% +and um that uh and and and the pressure +from your middle ear the fluid in your + + align:start position:0% +from your middle ear the fluid in your + + + align:start position:0% +from your middle ear the fluid in your +ear + + align:start position:0% +ear + + + align:start position:0% +ear +stretch that it hurt and and it that + + align:start position:0% +stretch that it hurt and and it that + + + align:start position:0% +stretch that it hurt and and it that +hurts a lot so you know don't put the + + align:start position:0% +hurts a lot so you know don't put the + + + align:start position:0% +hurts a lot so you know don't put the +hot pizza in your ear either + + align:start position:0% +hot pizza in your ear either + + + align:start position:0% +hot pizza in your ear either +um okay the cornea is just a relatively + + align:start position:0% +um okay the cornea is just a relatively + + + align:start position:0% +um okay the cornea is just a relatively +thin layer it it's held in shape by + + align:start position:0% +thin layer it it's held in shape by + + + align:start position:0% +thin layer it it's held in shape by +fluid + + align:start position:0% +fluid + + + align:start position:0% +fluid +um a watery like fluid which is known + + align:start position:0% +um a watery like fluid which is known + + + align:start position:0% +um a watery like fluid which is known +technically as the aqueous humor humor + + align:start position:0% +technically as the aqueous humor humor + + + align:start position:0% +technically as the aqueous humor humor +in this case has nothing to do with + + align:start position:0% +in this case has nothing to do with + + + align:start position:0% +in this case has nothing to do with +being funny it's the and you know an old + + align:start position:0% +being funny it's the and you know an old + + + align:start position:0% +being funny it's the and you know an old +word from a for a fluid + + align:start position:0% +word from a for a fluid + + + align:start position:0% +word from a for a fluid +um that's what's that it forms a space + + align:start position:0% +um that's what's that it forms a space + + + align:start position:0% +um that's what's that it forms a space +that separates the cornea from the uh + + align:start position:0% +that separates the cornea from the uh + + + align:start position:0% +that separates the cornea from the uh +from the iris the iris is uh that the + + align:start position:0% +from the iris the iris is uh that the + + + align:start position:0% +from the iris the iris is uh that the +the bit that gives your eye its color + + align:start position:0% +the bit that gives your eye its color + + + align:start position:0% +the bit that gives your eye its color +but it's basically a sphincter of muscle + + align:start position:0% +but it's basically a sphincter of muscle + + + align:start position:0% +but it's basically a sphincter of muscle +um with a hole in it and that hole is + + align:start position:0% +um with a hole in it and that hole is + + + align:start position:0% +um with a hole in it and that hole is +the pupil of the eye + + align:start position:0% +the pupil of the eye + + + align:start position:0% +the pupil of the eye +um and which is the aperture of the + + align:start position:0% +um and which is the aperture of the + + + align:start position:0% +um and which is the aperture of the +camera that's where that's you know + + align:start position:0% +camera that's where that's you know + + + align:start position:0% +camera that's where that's you know +that's where lights getting in from the + + align:start position:0% +that's where lights getting in from the + + + align:start position:0% +that's where lights getting in from the +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um + + align:start position:0% +um + + + align:start position:0% +um +from the outside into the in into the + + align:start position:0% +from the outside into the in into the + + + align:start position:0% +from the outside into the in into the +inner portions + + align:start position:0% +inner portions + + + align:start position:0% +inner portions +um of the eye okay + + align:start position:0% +um of the eye okay + + + align:start position:0% +um of the eye okay +the pupil changes size because you got + + align:start position:0% +the pupil changes size because you got + + + align:start position:0% +the pupil changes size because you got +this sphincter of muscle that either + + align:start position:0% +this sphincter of muscle that either + + + align:start position:0% +this sphincter of muscle that either +relaxes or contracts what makes it + + align:start position:0% +relaxes or contracts what makes it + + + align:start position:0% +relaxes or contracts what makes it +change size + + align:start position:0% +change size + + + align:start position:0% +change size +light we know that more light makes it + + align:start position:0% +light we know that more light makes it + + + align:start position:0% +light we know that more light makes it +do what + + align:start position:0% +do what + + + align:start position:0% +do what +get smaller why + + align:start position:0% + + + + align:start position:0% + +yeah so there's less like we know we + + align:start position:0% +yeah so there's less like we know we + + + align:start position:0% +yeah so there's less like we know we +know yeah sure it's going to be less + + align:start position:0% +know yeah sure it's going to be less + + + align:start position:0% +know yeah sure it's going to be less +light but why why why do you have this + + align:start position:0% +light but why why why do you have this + + + align:start position:0% +light but why why why do you have this +what did they teach you in third grade + + align:start position:0% +what did they teach you in third grade + + + align:start position:0% +what did they teach you in third grade +never stick your elbow in your eye yes I + + align:start position:0% +never stick your elbow in your eye yes I + + + align:start position:0% +never stick your elbow in your eye yes I +know that + + align:start position:0% +know that + + + align:start position:0% +know that +um no I need a hand here there's too + + align:start position:0% +um no I need a hand here there's too + + + align:start position:0% +um no I need a hand here there's too +much too many too many mutterings + + align:start position:0% +much too many too many mutterings + + + align:start position:0% +much too many too many mutterings +there's a hand + + align:start position:0% + + + + align:start position:0% + +because you don't want to go blind why + + align:start position:0% +because you don't want to go blind why + + + align:start position:0% +because you don't want to go blind why +would you go blind + + align:start position:0% +would you go blind + + + align:start position:0% +would you go blind +there's too much light see that's what + + align:start position:0% +there's too much light see that's what + + + align:start position:0% +there's too much light see that's what +they teach you in third grade it's bogus + + align:start position:0% +they teach you in third grade it's bogus + + + align:start position:0% +they teach you in third grade it's bogus +it sounds good and it seems to make + + align:start position:0% +it sounds good and it seems to make + + + align:start position:0% +it sounds good and it seems to make +sense but um but here + + align:start position:0% +sense but um but here + + + align:start position:0% +sense but um but here +ask yourself what level of um protection + + align:start position:0% +ask yourself what level of um protection + + + align:start position:0% +ask yourself what level of um protection +that pupil can give you right so how + + align:start position:0% +that pupil can give you right so how + + + align:start position:0% +that pupil can give you right so how +much light is it going to cut out the + + align:start position:0% +much light is it going to cut out the + + + align:start position:0% +much light is it going to cut out the +answer is it can uh it it cuts out a bit + + align:start position:0% +answer is it can uh it it cuts out a bit + + + align:start position:0% +answer is it can uh it it cuts out a bit +more than a factor of ten from the + + align:start position:0% +more than a factor of ten from the + + + align:start position:0% +more than a factor of ten from the +largest it can be to the smallest it'll + + align:start position:0% +largest it can be to the smallest it'll + + + align:start position:0% +largest it can be to the smallest it'll +be if you stare at you know if you're + + align:start position:0% +be if you stare at you know if you're + + + align:start position:0% +be if you stare at you know if you're +out in really bright light so it can it + + align:start position:0% +out in really bright light so it can it + + + align:start position:0% +out in really bright light so it can it +can change light levels by about a + + align:start position:0% +can change light levels by about a + + + align:start position:0% +can change light levels by about a +factor of ten if you go from in here + + align:start position:0% +factor of ten if you go from in here + + + align:start position:0% +factor of ten if you go from in here +right now actually it's fairly dim in + + align:start position:0% +right now actually it's fairly dim in + + + align:start position:0% +right now actually it's fairly dim in +here but if you go from here to just you + + align:start position:0% +here but if you go from here to just you + + + align:start position:0% +here but if you go from here to just you +know go outside into the the courtyard + + align:start position:0% +know go outside into the the courtyard + + + align:start position:0% +know go outside into the the courtyard +the change in light level is going to be + + align:start position:0% +the change in light level is going to be + + + align:start position:0% +the change in light level is going to be +on the order of a factor of a thousand + + align:start position:0% +on the order of a factor of a thousand + + + align:start position:0% +on the order of a factor of a thousand +right there the change in light level + + align:start position:0% +right there the change in light level + + + align:start position:0% +right there the change in light level +that your visual system can deal with + + align:start position:0% +that your visual system can deal with + + + align:start position:0% +that your visual system can deal with +from say a moonlit Knight to um bright + + align:start position:0% +from say a moonlit Knight to um bright + + + align:start position:0% +from say a moonlit Knight to um bright +sun on a snow field is on the order of + + align:start position:0% +sun on a snow field is on the order of + + + align:start position:0% +sun on a snow field is on the order of +10 to the 12th or 10 to the 13th so + + align:start position:0% +10 to the 12th or 10 to the 13th so + + + align:start position:0% +10 to the 12th or 10 to the 13th so +there's no way that the need to protect + + align:start position:0% +there's no way that the need to protect + + + align:start position:0% +there's no way that the need to protect +yourself + + align:start position:0% +yourself + + + align:start position:0% +yourself +um is going to be taken care of by the + + align:start position:0% +um is going to be taken care of by the + + + align:start position:0% +um is going to be taken care of by the +um by the pupil of the eye there's just + + align:start position:0% +um by the pupil of the eye there's just + + + align:start position:0% +um by the pupil of the eye there's just +not enough range there what the the + + align:start position:0% +not enough range there what the the + + + align:start position:0% +not enough range there what the the +pupil the pupillary constriction what + + align:start position:0% +pupil the pupillary constriction what + + + align:start position:0% +pupil the pupillary constriction what +it's probably doing for you those of you + + align:start position:0% +it's probably doing for you those of you + + + align:start position:0% +it's probably doing for you those of you +who are photographers + + align:start position:0% +who are photographers + + + align:start position:0% +who are photographers +um is it's increasing the depth of field + + align:start position:0% +um is it's increasing the depth of field + + + align:start position:0% +um is it's increasing the depth of field +on your camera + + align:start position:0% +on your camera + + + align:start position:0% +on your camera +um a pinhole camera will focus many + + align:start position:0% +um a pinhole camera will focus many + + + align:start position:0% +um a pinhole camera will focus many +different distances at once a larger + + align:start position:0% +different distances at once a larger + + + align:start position:0% +different distances at once a larger +aperture will only focus one plane at at + + align:start position:0% +aperture will only focus one plane at at + + + align:start position:0% +aperture will only focus one plane at at +one time and so if you've got lots of + + align:start position:0% +one time and so if you've got lots of + + + align:start position:0% +one time and so if you've got lots of +light you crank down the pupil in order + + align:start position:0% +light you crank down the pupil in order + + + align:start position:0% +light you crank down the pupil in order +to be able to focus in order to get + + align:start position:0% +to be able to focus in order to get + + + align:start position:0% +to be able to focus in order to get +better focus basically but the + + align:start position:0% +better focus basically but the + + + align:start position:0% +better focus basically but the +protection thing just doesn't it's not + + align:start position:0% +protection thing just doesn't it's not + + + align:start position:0% +protection thing just doesn't it's not +it's not a stupid answer because it's + + align:start position:0% +it's not a stupid answer because it's + + + align:start position:0% +it's not a stupid answer because it's +what everybody believes + + align:start position:0% +what everybody believes + + + align:start position:0% +what everybody believes +um but it's it's it's just not a it + + align:start position:0% +um but it's it's it's just not a it + + + align:start position:0% +um but it's it's it's just not a it +doesn't turn out to be a correct + + align:start position:0% +doesn't turn out to be a correct + + + align:start position:0% +doesn't turn out to be a correct +um answer oh now there's one other + + align:start position:0% +um answer oh now there's one other + + + align:start position:0% +um answer oh now there's one other +there's several other things that will + + align:start position:0% +there's several other things that will + + + align:start position:0% +there's several other things that will +change the size of your pupil but one + + align:start position:0% +change the size of your pupil but one + + + align:start position:0% +change the size of your pupil but one +other of Interest what else changes the + + align:start position:0% +other of Interest what else changes the + + + align:start position:0% +other of Interest what else changes the +size of your pupil anybody know anything + + align:start position:0% +size of your pupil anybody know anything + + + align:start position:0% +size of your pupil anybody know anything +else that they can change the size yep + + align:start position:0% +else that they can change the size yep + + + align:start position:0% +else that they can change the size yep +looking all the way down there at me + + align:start position:0% +looking all the way down there at me + + + align:start position:0% +looking all the way down there at me +well yes but for reasons that are + + align:start position:0% +well yes but for reasons that are + + + align:start position:0% +well yes but for reasons that are +um why didn't why + + align:start position:0% + + + + align:start position:0% + +well no no what you're changing sorry + + align:start position:0% +well no no what you're changing sorry + + + align:start position:0% +well no no what you're changing sorry +that that's that's the next bullet here + + align:start position:0% +that that's that's the next bullet here + + + align:start position:0% +that that's that's the next bullet here +um what you're changing when you change + + align:start position:0% +um what you're changing when you change + + + align:start position:0% +um what you're changing when you change +focus of the eye is you're changing the + + align:start position:0% +focus of the eye is you're changing the + + + align:start position:0% +focus of the eye is you're changing the +shape of the lens at least you are I'm + + align:start position:0% +shape of the lens at least you are I'm + + + align:start position:0% +shape of the lens at least you are I'm +not because at my age the lens has + + align:start position:0% +not because at my age the lens has + + + align:start position:0% +not because at my age the lens has +basically become a rigid lump and so + + align:start position:0% +basically become a rigid lump and so + + + align:start position:0% +basically become a rigid lump and so +when I want to look from there to here I + + align:start position:0% +when I want to look from there to here I + + + align:start position:0% +when I want to look from there to here I +use an external lens + + align:start position:0% +use an external lens + + + align:start position:0% +use an external lens +um yes back to the pupil + + align:start position:0% +um yes back to the pupil + + + align:start position:0% +um yes back to the pupil +when you lie yes that will work + + align:start position:0% +when you lie yes that will work + + + align:start position:0% +when you lie yes that will work +um a little bit maybe not reliably + + align:start position:0% +um a little bit maybe not reliably + + + align:start position:0% +um a little bit maybe not reliably +enough to uh you know the you know the + + align:start position:0% +enough to uh you know the you know the + + + align:start position:0% +enough to uh you know the you know the +CIA or something every now and then gets + + align:start position:0% +CIA or something every now and then gets + + + align:start position:0% +CIA or something every now and then gets +its idea the idea that that really works + + align:start position:0% +its idea the idea that that really works + + + align:start position:0% +its idea the idea that that really works +but it it's it's on the right General + + align:start position:0% +but it it's it's on the right General + + + align:start position:0% +but it it's it's on the right General +track yeah + + align:start position:0% + + + + align:start position:0% + +yep some drug some drugs will uh will + + align:start position:0% +yep some drug some drugs will uh will + + + align:start position:0% +yep some drug some drugs will uh will +will certainly module modulate it and uh + + align:start position:0% +will certainly module modulate it and uh + + + align:start position:0% +will certainly module modulate it and uh +all right + + align:start position:0% + + + + align:start position:0% + +there you go that's that's the one I + + align:start position:0% +there you go that's that's the one I + + + align:start position:0% +there you go that's that's the one I +particularly when I was fishing for + + align:start position:0% +particularly when I was fishing for + + + align:start position:0% +particularly when I was fishing for +um + + align:start position:0% +um + + + align:start position:0% +um +your level of arousal + + align:start position:0% +your level of arousal + + + align:start position:0% +your level of arousal +will change the size of your pupil and + + align:start position:0% +will change the size of your pupil and + + + align:start position:0% +will change the size of your pupil and +notably if you look at something that + + align:start position:0% +notably if you look at something that + + + align:start position:0% +notably if you look at something that +you like or someone that you like your + + align:start position:0% +you like or someone that you like your + + + align:start position:0% +you like or someone that you like your +pupils get bigger + + align:start position:0% +pupils get bigger + + + align:start position:0% +pupils get bigger +um you didn't know yeah I mean obviously + + align:start position:0% +um you didn't know yeah I mean obviously + + + align:start position:0% +um you didn't know yeah I mean obviously +not everybody here knew that explicitly + + align:start position:0% +not everybody here knew that explicitly + + + align:start position:0% +not everybody here knew that explicitly +but you sort of knew that implicitly + + align:start position:0% +but you sort of knew that implicitly + + + align:start position:0% +but you sort of knew that implicitly +because the result of that is that you + + align:start position:0% +because the result of that is that you + + + align:start position:0% +because the result of that is that you +think that things with big pupils are + + align:start position:0% +think that things with big pupils are + + + align:start position:0% +think that things with big pupils are +cuter than things with little pinhole + + align:start position:0% +cuter than things with little pinhole + + + align:start position:0% +cuter than things with little pinhole +pupils right so that's why sappy + + align:start position:0% +pupils right so that's why sappy + + + align:start position:0% +pupils right so that's why sappy +cartoons or or cards have big pupils it + + align:start position:0% +cartoons or or cards have big pupils it + + + align:start position:0% +cartoons or or cards have big pupils it +is also why in Years Gone by women would + + align:start position:0% +is also why in Years Gone by women would + + + align:start position:0% +is also why in Years Gone by women would +put a drug known as atropine or known as + + align:start position:0% +put a drug known as atropine or known as + + + align:start position:0% +put a drug known as atropine or known as +a cosmetic as Belladonna for Pretty + + align:start position:0% +a cosmetic as Belladonna for Pretty + + + align:start position:0% +a cosmetic as Belladonna for Pretty +Woman Pretty Girl In Their Eyes what it + + align:start position:0% +Woman Pretty Girl In Their Eyes what it + + + align:start position:0% +Woman Pretty Girl In Their Eyes what it +did was it paralyzed and relaxed the + + align:start position:0% +did was it paralyzed and relaxed the + + + align:start position:0% +did was it paralyzed and relaxed the +muscles of the iris and made a great big + + align:start position:0% +muscles of the iris and made a great big + + + align:start position:0% +muscles of the iris and made a great big +pure didn't do anything good for their + + align:start position:0% +pure didn't do anything good for their + + + align:start position:0% +pure didn't do anything good for their +Vision because it made things kind of + + align:start position:0% +Vision because it made things kind of + + + align:start position:0% +Vision because it made things kind of +blurry it also paralyzes the lens but it + + align:start position:0% +blurry it also paralyzes the lens but it + + + align:start position:0% +blurry it also paralyzes the lens but it +gave them great big pupils and so + + align:start position:0% +gave them great big pupils and so + + + align:start position:0% +gave them great big pupils and so +they're looking at the guy who may or + + align:start position:0% +they're looking at the guy who may or + + + align:start position:0% +they're looking at the guy who may or +may not be the object of their desire + + align:start position:0% +may not be the object of their desire + + + align:start position:0% +may not be the object of their desire +looking at some guy they can't see him + + align:start position:0% +looking at some guy they can't see him + + + align:start position:0% +looking at some guy they can't see him +so well because + + align:start position:0% +so well because + + + align:start position:0% +so well because +which who knows that may have helped but + + align:start position:0% +which who knows that may have helped but + + + align:start position:0% +which who knows that may have helped but +he's looking at her thinking + + align:start position:0% +he's looking at her thinking + + + align:start position:0% +he's looking at her thinking +implicitly her pupils are really big I + + align:start position:0% +implicitly her pupils are really big I + + + align:start position:0% +implicitly her pupils are really big I +know what that means + + align:start position:0% +know what that means + + + align:start position:0% +know what that means +turns out following up on whoever it was + + align:start position:0% +turns out following up on whoever it was + + + align:start position:0% +turns out following up on whoever it was +over there it actually means she's on + + align:start position:0% +over there it actually means she's on + + + align:start position:0% +over there it actually means she's on +drugs but + + align:start position:0% + + + + align:start position:0% + +in any case + + align:start position:0% +in any case + + + align:start position:0% +in any case +um pupil size is uh modulated by + + align:start position:0% +um pupil size is uh modulated by + + + align:start position:0% +um pupil size is uh modulated by +emotional state and and + + align:start position:0% +emotional state and and + + + align:start position:0% +emotional state and and +um it's one of these things that we sort + + align:start position:0% +um it's one of these things that we sort + + + align:start position:0% +um it's one of these things that we sort +of knew implicitly people know + + align:start position:0% +of knew implicitly people know + + + align:start position:0% +of knew implicitly people know +implicitly and think big pupils are + + align:start position:0% +implicitly and think big pupils are + + + align:start position:0% +implicitly and think big pupils are +attractive for that reason but uh um + + align:start position:0% +attractive for that reason but uh um + + + align:start position:0% +attractive for that reason but uh um +it's only when you show up here you find + + align:start position:0% +it's only when you show up here you find + + + align:start position:0% +it's only when you show up here you find +out these things explicitly + + align:start position:0% +out these things explicitly + + + align:start position:0% +out these things explicitly +um all right I've already said something + + align:start position:0% +um all right I've already said something + + + align:start position:0% +um all right I've already said something +about the lens the most notable thing + + align:start position:0% +about the lens the most notable thing + + + align:start position:0% +about the lens the most notable thing +about the lens is it gets + + align:start position:0% +about the lens is it gets + + + align:start position:0% +about the lens is it gets +with age and less you can try this out + + align:start position:0% +with age and less you can try this out + + + align:start position:0% +with age and less you can try this out +um in fact here is a good time in your + + align:start position:0% +um in fact here is a good time in your + + + align:start position:0% +um in fact here is a good time in your +life to uh uh to um to start this + + align:start position:0% +life to uh uh to um to start this + + + align:start position:0% +life to uh uh to um to start this +experiment + + align:start position:0% +experiment + + + align:start position:0% +experiment +um to take something like the the + + align:start position:0% +um to take something like the the + + + align:start position:0% +um to take something like the the +handout and ask yourself how close you + + align:start position:0% +handout and ask yourself how close you + + + align:start position:0% +handout and ask yourself how close you +can get and have the letters still be in + + align:start position:0% +can get and have the letters still be in + + + align:start position:0% +can get and have the letters still be in +sharp Focus + + align:start position:0% + + + + align:start position:0% + +this is so sad it like makes me weep but + + align:start position:0% +this is so sad it like makes me weep but + + + align:start position:0% +this is so sad it like makes me weep but +um but I know you're getting there too + + align:start position:0% +um but I know you're getting there too + + + align:start position:0% +um but I know you're getting there too +now what you can do keep it you could + + align:start position:0% +now what you can do keep it you could + + + align:start position:0% +now what you can do keep it you could +actually if you're compulsive about + + align:start position:0% +actually if you're compulsive about + + + align:start position:0% +actually if you're compulsive about +these sort of things write it down + + align:start position:0% +these sort of things write it down + + + align:start position:0% +these sort of things write it down +somewhere and just check every year this + + align:start position:0% +somewhere and just check every year this + + + align:start position:0% +somewhere and just check every year this +is one of those things where the signs + + align:start position:0% +is one of those things where the signs + + + align:start position:0% +is one of those things where the signs +of aging start showing up now + + align:start position:0% +of aging start showing up now + + + align:start position:0% +of aging start showing up now +um you will be able to see even during + + align:start position:0% +um you will be able to see even during + + + align:start position:0% +um you will be able to see even during +the course of your 20s that that + + align:start position:0% +the course of your 20s that that + + + align:start position:0% +the course of your 20s that that +so-called near point is moving further + + align:start position:0% +so-called near point is moving further + + + align:start position:0% +so-called near point is moving further +out for me for me without my glasses + + align:start position:0% +out for me for me without my glasses + + + align:start position:0% +out for me for me without my glasses +we're out here somewhere + + align:start position:0% +we're out here somewhere + + + align:start position:0% +we're out here somewhere +um it's uh and and eventually you're + + align:start position:0% +um it's uh and and eventually you're + + + align:start position:0% +um it's uh and and eventually you're +locked at one plane of focus and + + align:start position:0% +locked at one plane of focus and + + + align:start position:0% +locked at one plane of focus and +depending on where that is it determines + + align:start position:0% +depending on where that is it determines + + + align:start position:0% +depending on where that is it determines +which particular set of glasses you need + + align:start position:0% +which particular set of glasses you need + + + align:start position:0% +which particular set of glasses you need +you need glasses to read you need + + align:start position:0% +you need glasses to read you need + + + align:start position:0% +you need glasses to read you need +bifocals whatever it's because you've + + align:start position:0% +bifocals whatever it's because you've + + + align:start position:0% +bifocals whatever it's because you've +lost the ability to fine tune that that + + align:start position:0% +lost the ability to fine tune that that + + + align:start position:0% +lost the ability to fine tune that that +Focus now you need something to hold the + + align:start position:0% +Focus now you need something to hold the + + + align:start position:0% +Focus now you need something to hold the +rest of the eye + + align:start position:0% +rest of the eye + + + align:start position:0% +rest of the eye +um in shape what you've got in there is + + align:start position:0% +um in shape what you've got in there is + + + align:start position:0% +um in shape what you've got in there is +um it's really a jelly + + align:start position:0% +um it's really a jelly + + + align:start position:0% +um it's really a jelly +um called the vitreous humor for the + + align:start position:0% +um called the vitreous humor for the + + + align:start position:0% +um called the vitreous humor for the +glass-like substance + + align:start position:0% +glass-like substance + + + align:start position:0% +glass-like substance +um and it's it's you know for our + + align:start position:0% +um and it's it's you know for our + + + align:start position:0% +um and it's it's you know for our +purposes not desperately interesting + + align:start position:0% +purposes not desperately interesting + + + align:start position:0% +purposes not desperately interesting +it's there to hold your eye out + + align:start position:0% +it's there to hold your eye out + + + align:start position:0% +it's there to hold your eye out +um so that the front end of the eye can + + align:start position:0% +um so that the front end of the eye can + + + align:start position:0% +um so that the front end of the eye can +make an image on this back surface the + + align:start position:0% +make an image on this back surface the + + + align:start position:0% +make an image on this back surface the +back surface of the eye where the + + align:start position:0% +back surface of the eye where the + + + align:start position:0% +back surface of the eye where the +where the transduction from photons from + + align:start position:0% +where the transduction from photons from + + + align:start position:0% +where the transduction from photons from +light energy into signals in the nervous + + align:start position:0% +light energy into signals in the nervous + + + align:start position:0% +light energy into signals in the nervous +system where that takes place that + + align:start position:0% +system where that takes place that + + + align:start position:0% +system where that takes place that +tissue is known as the retina the word + + align:start position:0% +tissue is known as the retina the word + + + align:start position:0% +tissue is known as the retina the word +comes from the word for a net + + align:start position:0% +comes from the word for a net + + + align:start position:0% +comes from the word for a net +um + + align:start position:0% +um + + + align:start position:0% +um +and um + + align:start position:0% + + + + align:start position:0% + +the fovea is the point uh is it phobia + + align:start position:0% +the fovea is the point uh is it phobia + + + align:start position:0% +the fovea is the point uh is it phobia +comes from the word for pit it's the + + align:start position:0% +comes from the word for pit it's the + + + align:start position:0% +comes from the word for pit it's the +point on the retino + + align:start position:0% +point on the retino + + + align:start position:0% +point on the retino +um where you have the uh the the highest + + align:start position:0% +um where you have the uh the the highest + + + align:start position:0% +um where you have the uh the the highest +visual Acuity the strongest the the + + align:start position:0% +visual Acuity the strongest the the + + + align:start position:0% +visual Acuity the strongest the the +greatest ability to resolve small + + align:start position:0% +greatest ability to resolve small + + + align:start position:0% +greatest ability to resolve small +details + + align:start position:0% +details + + + align:start position:0% +details +um you don't particularly realize in the + + align:start position:0% +um you don't particularly realize in the + + + align:start position:0% +um you don't particularly realize in the +course of your normal uh day-to-day + + align:start position:0% +course of your normal uh day-to-day + + + align:start position:0% +course of your normal uh day-to-day +existence just how bad vision gets away + + align:start position:0% +existence just how bad vision gets away + + + align:start position:0% +existence just how bad vision gets away +from the fovea + + align:start position:0% +from the fovea + + + align:start position:0% +from the fovea +um you have this notion of a of a highly + + align:start position:0% +um you have this notion of a of a highly + + + align:start position:0% +um you have this notion of a of a highly +detailed world that's in Focus all over + + align:start position:0% +detailed world that's in Focus all over + + + align:start position:0% +detailed world that's in Focus all over +the place + + align:start position:0% +the place + + + align:start position:0% +the place +um but that to jump ahead to the third + + align:start position:0% +um but that to jump ahead to the third + + + align:start position:0% +um but that to jump ahead to the third +lecture in this series is is a + + align:start position:0% +lecture in this series is is a + + + align:start position:0% +lecture in this series is is a +construction it's not reality and that + + align:start position:0% +construction it's not reality and that + + + align:start position:0% +construction it's not reality and that +you can prove to yourself take the + + align:start position:0% +you can prove to yourself take the + + + align:start position:0% +you can prove to yourself take the +handout again hold it at some + + align:start position:0% +handout again hold it at some + + + align:start position:0% +handout again hold it at some +comfortable read at reading distance + + align:start position:0% +comfortable read at reading distance + + + align:start position:0% +comfortable read at reading distance +fixate on the L that uh on that second + + align:start position:0% +fixate on the L that uh on that second + + + align:start position:0% +fixate on the L that uh on that second +line there where it says lecture four + + align:start position:0% +line there where it says lecture four + + + align:start position:0% +line there where it says lecture four +um if you're fixating on the L the L is + + align:start position:0% +um if you're fixating on the L the L is + + + align:start position:0% +um if you're fixating on the L the L is +falling in your eye it make you forming + + align:start position:0% +falling in your eye it make you forming + + + align:start position:0% +falling in your eye it make you forming +an image on your fovea ask yourself + + align:start position:0% +an image on your fovea ask yourself + + + align:start position:0% +an image on your fovea ask yourself +while you're fixated on the L how many + + align:start position:0% +while you're fixated on the L how many + + + align:start position:0% +while you're fixated on the L how many +letters off to the right you can + + align:start position:0% +letters off to the right you can + + + align:start position:0% +letters off to the right you can +actually read + + align:start position:0% +actually read + + + align:start position:0% +actually read +and the answer is going to be not many + + align:start position:0% +and the answer is going to be not many + + + align:start position:0% +and the answer is going to be not many +if you're I mean if you think you can + + align:start position:0% +if you're I mean if you think you can + + + align:start position:0% +if you're I mean if you think you can +read to the end of the line it's because + + align:start position:0% +read to the end of the line it's because + + + align:start position:0% +read to the end of the line it's because +you're not fixating you're you're moving + + align:start position:0% +you're not fixating you're you're moving + + + align:start position:0% +you're not fixating you're you're moving +your eyes around I mean again like the + + align:start position:0% +your eyes around I mean again like the + + + align:start position:0% +your eyes around I mean again like the +pupil thing this is something you knew + + align:start position:0% +pupil thing this is something you knew + + + align:start position:0% +pupil thing this is something you knew +implicitly nobody sits there and says + + align:start position:0% +implicitly nobody sits there and says + + + align:start position:0% +implicitly nobody sits there and says +you know I'm gonna read this handout all + + align:start position:0% +you know I'm gonna read this handout all + + + align:start position:0% +you know I'm gonna read this handout all +right you yeah I can see it it's there + + align:start position:0% +right you yeah I can see it it's there + + + align:start position:0% +right you yeah I can see it it's there +but I can't read it because the the + + align:start position:0% +but I can't read it because the the + + + align:start position:0% +but I can't read it because the the +outside of the fovea + + align:start position:0% +outside of the fovea + + + align:start position:0% +outside of the fovea +um I simply don't have the uh resolving + + align:start position:0% +um I simply don't have the uh resolving + + + align:start position:0% +um I simply don't have the uh resolving +ability to um uh to to do it why not + + align:start position:0% +ability to um uh to to do it why not + + + align:start position:0% +ability to um uh to to do it why not +well I can give you at least one reason + + align:start position:0% +well I can give you at least one reason + + + align:start position:0% +well I can give you at least one reason +you have about a hundred million + + align:start position:0% +you have about a hundred million + + + align:start position:0% +you have about a hundred million +photoreceptors in your retina + + align:start position:0% +photoreceptors in your retina + + + align:start position:0% +photoreceptors in your retina +um photoreceptors are the cells that + + align:start position:0% +um photoreceptors are the cells that + + + align:start position:0% +um photoreceptors are the cells that +convert uh light energy into a signal in + + align:start position:0% +convert uh light energy into a signal in + + + align:start position:0% +convert uh light energy into a signal in +the nervous system they're the + + align:start position:0% +the nervous system they're the + + + align:start position:0% +the nervous system they're the +transduction elements + + align:start position:0% +transduction elements + + + align:start position:0% +transduction elements +um you have only about + + align:start position:0% +um you have only about + + + align:start position:0% +um you have only about +um uh a quarter of a million to a + + align:start position:0% +um uh a quarter of a million to a + + + align:start position:0% +um uh a quarter of a million to a +million uh axons + + align:start position:0% +million uh axons + + + align:start position:0% +million uh axons +nerve fibers running from the eye to the + + align:start position:0% +nerve fibers running from the eye to the + + + align:start position:0% +nerve fibers running from the eye to the +brain so that hundred million has got to + + align:start position:0% +brain so that hundred million has got to + + + align:start position:0% +brain so that hundred million has got to +get uh boiled down to the the much + + align:start position:0% +get uh boiled down to the the much + + + align:start position:0% +get uh boiled down to the the much +smaller number that that you've got + + align:start position:0% +smaller number that that you've got + + + align:start position:0% +smaller number that that you've got +available to you and so that means you + + align:start position:0% +available to you and so that means you + + + align:start position:0% +available to you and so that means you +can't treat each photoreceptor as a um + + align:start position:0% +can't treat each photoreceptor as a um + + + align:start position:0% +can't treat each photoreceptor as a um +oops that's not what I wanted to turn + + align:start position:0% +oops that's not what I wanted to turn + + + align:start position:0% +oops that's not what I wanted to turn +full on that was stupid I wanted to turn + + align:start position:0% +full on that was stupid I wanted to turn + + + align:start position:0% +full on that was stupid I wanted to turn +where'd it go + + align:start position:0% +where'd it go + + + align:start position:0% +where'd it go +Union chalkboard that one + + align:start position:0% +Union chalkboard that one + + + align:start position:0% +Union chalkboard that one +um + + align:start position:0% +um + + + align:start position:0% +um +that means you can't treat each + + align:start position:0% +that means you can't treat each + + + align:start position:0% +that means you can't treat each +photoreceptor as a a pixel with a + + align:start position:0% +photoreceptor as a a pixel with a + + + align:start position:0% +photoreceptor as a a pixel with a +private line to the brain you do have + + align:start position:0% +private line to the brain you do have + + + align:start position:0% +private line to the brain you do have +something approximating this in the + + align:start position:0% +something approximating this in the + + + align:start position:0% +something approximating this in the +fovea where you have fine detailed + + align:start position:0% +fovea where you have fine detailed + + + align:start position:0% +fovea where you have fine detailed +resolution but in the um in the + + align:start position:0% +resolution but in the um in the + + + align:start position:0% +resolution but in the um in the +periphery away from the fovea what you + + align:start position:0% +periphery away from the fovea what you + + + align:start position:0% +periphery away from the fovea what you +have is many many many many many + + align:start position:0% +have is many many many many many + + + align:start position:0% +have is many many many many many +photoreceptors that are all ganged + + align:start position:0% +photoreceptors that are all ganged + + + align:start position:0% +photoreceptors that are all ganged +together to send their signal off to the + + align:start position:0% +together to send their signal off to the + + + align:start position:0% +together to send their signal off to the +central nervous system and so you lose + + align:start position:0% +central nervous system and so you lose + + + align:start position:0% +central nervous system and so you lose +resolution + + align:start position:0% +resolution + + + align:start position:0% +resolution +out there in the um uh + + align:start position:0% +out there in the um uh + + + align:start position:0% +out there in the um uh +in the periphery well let's say a little + + align:start position:0% +in the periphery well let's say a little + + + align:start position:0% +in the periphery well let's say a little +more about the details of that retina oh + + align:start position:0% +more about the details of that retina oh + + + align:start position:0% +more about the details of that retina oh +the optic nerve is is the bundle of + + align:start position:0% +the optic nerve is is the bundle of + + + align:start position:0% +the optic nerve is is the bundle of +fibers going off from the um uh from the + + align:start position:0% +fibers going off from the um uh from the + + + align:start position:0% +fibers going off from the um uh from the +eye to the brain I'll say a bit more + + align:start position:0% +eye to the brain I'll say a bit more + + + align:start position:0% +eye to the brain I'll say a bit more +about that in a minute or so a quick + + align:start position:0% +about that in a minute or so a quick + + + align:start position:0% +about that in a minute or so a quick +tour of of the retina itself up at the + + align:start position:0% +tour of of the retina itself up at the + + + align:start position:0% +tour of of the retina itself up at the +top there you've got the the + + align:start position:0% +top there you've got the the + + + align:start position:0% +top there you've got the the +photoreceptors these transduction + + align:start position:0% +photoreceptors these transduction + + + align:start position:0% +photoreceptors these transduction +elements there are two flavors of them + + align:start position:0% +elements there are two flavors of them + + + align:start position:0% +elements there are two flavors of them +called rods and cones named rods and + + align:start position:0% +called rods and cones named rods and + + + align:start position:0% +called rods and cones named rods and +cones because under the microscope rods + + align:start position:0% +cones because under the microscope rods + + + align:start position:0% +cones because under the microscope rods +are Rod shaped and Cones are cone-shaped + + align:start position:0% +are Rod shaped and Cones are cone-shaped + + + align:start position:0% +are Rod shaped and Cones are cone-shaped +um + + align:start position:0% +um + + + align:start position:0% +um +they are different in their uh their + + align:start position:0% +they are different in their uh their + + + align:start position:0% +they are different in their uh their +their functions and capabilities cones + + align:start position:0% +their functions and capabilities cones + + + align:start position:0% +their functions and capabilities cones +operate in bright light in at daylight + + align:start position:0% +operate in bright light in at daylight + + + align:start position:0% +operate in bright light in at daylight +levels they do mediate color vision + + align:start position:0% +levels they do mediate color vision + + + align:start position:0% +levels they do mediate color vision +um and they are concentrated at the + + align:start position:0% +um and they are concentrated at the + + + align:start position:0% +um and they are concentrated at the +phobia they are most densely represented + + align:start position:0% +phobia they are most densely represented + + + align:start position:0% +phobia they are most densely represented +at the + + align:start position:0% +at the + + + align:start position:0% +at the +at the phobia rods work in dim light + + align:start position:0% +at the phobia rods work in dim light + + + align:start position:0% +at the phobia rods work in dim light +levels they are not able to mediate + + align:start position:0% +levels they are not able to mediate + + + align:start position:0% +levels they are not able to mediate +color vision + + align:start position:0% +color vision + + + align:start position:0% +color vision +um which is why under moonlit you know + + align:start position:0% +um which is why under moonlit you know + + + align:start position:0% +um which is why under moonlit you know +on a moonlit night you don't see colors + + align:start position:0% +on a moonlit night you don't see colors + + + align:start position:0% +on a moonlit night you don't see colors +it's not because colors somehow drained + + align:start position:0% +it's not because colors somehow drained + + + align:start position:0% +it's not because colors somehow drained +out of the world it's because the visual + + align:start position:0% +out of the world it's because the visual + + + align:start position:0% +out of the world it's because the visual +system that's looking at that world can + + align:start position:0% +system that's looking at that world can + + + align:start position:0% +system that's looking at that world can +no longer + + align:start position:0% +no longer + + + align:start position:0% +no longer +um analyze the input for color + + align:start position:0% +um analyze the input for color + + + align:start position:0% +um analyze the input for color +information but only for grayscale + + align:start position:0% +information but only for grayscale + + + align:start position:0% +information but only for grayscale +information and + + align:start position:0% +information and + + + align:start position:0% +information and +um Rod photoreceptors are traded away + + align:start position:0% +um Rod photoreceptors are traded away + + + align:start position:0% +um Rod photoreceptors are traded away +from the retina I'm sorry away from the + + align:start position:0% +from the retina I'm sorry away from the + + + align:start position:0% +from the retina I'm sorry away from the +phobia + + align:start position:0% +phobia + + + align:start position:0% +phobia +they are in fact absent from the central + + align:start position:0% +they are in fact absent from the central + + + align:start position:0% +they are in fact absent from the central +phobia so that if you go if you they're + + align:start position:0% +phobia so that if you go if you they're + + + align:start position:0% +phobia so that if you go if you they're +the best place to see this actually is + + align:start position:0% +the best place to see this actually is + + + align:start position:0% +the best place to see this actually is +if your room gets dim enough + + align:start position:0% +if your room gets dim enough + + + align:start position:0% +if your room gets dim enough +um at night if your room is dimming up + + align:start position:0% +um at night if your room is dimming up + + + align:start position:0% +um at night if your room is dimming up +at night that you can't see color you're + + align:start position:0% +at night that you can't see color you're + + + align:start position:0% +at night that you can't see color you're +working in in the rod realm and then you + + align:start position:0% +working in in the rod realm and then you + + + align:start position:0% +working in in the rod realm and then you +will discover that if you fixate on a + + align:start position:0% +will discover that if you fixate on a + + + align:start position:0% +will discover that if you fixate on a +dim spot of light you can't see it that + + align:start position:0% +dim spot of light you can't see it that + + + align:start position:0% +dim spot of light you can't see it that +you might there might be something out + + align:start position:0% +you might there might be something out + + + align:start position:0% +you might there might be something out +here you notice it and then you move + + align:start position:0% +here you notice it and then you move + + + align:start position:0% +here you notice it and then you move +your eye to look at it and it'll + + align:start position:0% +your eye to look at it and it'll + + + align:start position:0% +your eye to look at it and it'll +disappear because it'll the image if + + align:start position:0% +disappear because it'll the image if + + + align:start position:0% +disappear because it'll the image if +it's small enough will now fall into the + + align:start position:0% +it's small enough will now fall into the + + + align:start position:0% +it's small enough will now fall into the +fovea and + + align:start position:0% +fovea and + + + align:start position:0% +fovea and +um there are no rods there and you can't + + align:start position:0% +um there are no rods there and you can't + + + align:start position:0% +um there are no rods there and you can't +see it the this is why um if you're a + + align:start position:0% +see it the this is why um if you're a + + + align:start position:0% +see it the this is why um if you're a +stargazer and you're looking at a dim + + align:start position:0% +stargazer and you're looking at a dim + + + align:start position:0% +stargazer and you're looking at a dim +star you want to look at that star out + + align:start position:0% +star you want to look at that star out + + + align:start position:0% +star you want to look at that star out +of the so-called corner of your eye the + + align:start position:0% +of the so-called corner of your eye the + + + align:start position:0% +of the so-called corner of your eye the +corner of your eye is about 20 degrees + + align:start position:0% +corner of your eye is about 20 degrees + + + align:start position:0% +corner of your eye is about 20 degrees +away from straight ahead because that's + + align:start position:0% +away from straight ahead because that's + + + align:start position:0% +away from straight ahead because that's +where the density of Rod photoreceptors + + align:start position:0% +where the density of Rod photoreceptors + + + align:start position:0% +where the density of Rod photoreceptors +turns out to be greatest the um + + align:start position:0% +turns out to be greatest the um + + + align:start position:0% +turns out to be greatest the um +odd + + align:start position:0% +odd + + + align:start position:0% +odd +it's going to say something else about + + align:start position:0% +it's going to say something else about + + + align:start position:0% +it's going to say something else about +Rod photoreceptors but that has + + align:start position:0% +Rod photoreceptors but that has + + + align:start position:0% +Rod photoreceptors but that has +disappeared from my mind so I will say + + align:start position:0% +disappeared from my mind so I will say + + + align:start position:0% +disappeared from my mind so I will say +that the rest of this is another as a + + align:start position:0% +that the rest of this is another as a + + + align:start position:0% +that the rest of this is another as a +collection of um nerve cells of neurons + + align:start position:0% +collection of um nerve cells of neurons + + + align:start position:0% +collection of um nerve cells of neurons +it's really a little chunk of brain + + align:start position:0% +it's really a little chunk of brain + + + align:start position:0% +it's really a little chunk of brain +developmentally the retina is a chunk of + + align:start position:0% +developmentally the retina is a chunk of + + + align:start position:0% +developmentally the retina is a chunk of +brain that's pushed out into the eye and + + align:start position:0% +brain that's pushed out into the eye and + + + align:start position:0% +brain that's pushed out into the eye and +this is the start of nervous the you + + align:start position:0% +this is the start of nervous the you + + + align:start position:0% +this is the start of nervous the you +know the visual nervous system + + align:start position:0% +know the visual nervous system + + + align:start position:0% +know the visual nervous system +um for present purposes it's worth + + align:start position:0% +um for present purposes it's worth + + + align:start position:0% +um for present purposes it's worth +thinking about two aspects of + + align:start position:0% +thinking about two aspects of + + + align:start position:0% +thinking about two aspects of +this organization one is a through path + + align:start position:0% +this organization one is a through path + + + align:start position:0% +this organization one is a through path +that runs from do I have a little you + + align:start position:0% +that runs from do I have a little you + + + align:start position:0% +that runs from do I have a little you +know it's coming back where'd my little + + align:start position:0% +know it's coming back where'd my little + + + align:start position:0% +know it's coming back where'd my little +cursor go there we go from the + + align:start position:0% +cursor go there we go from the + + + align:start position:0% +cursor go there we go from the +photoreceptors through so-called bipolar + + align:start position:0% +photoreceptors through so-called bipolar + + + align:start position:0% +photoreceptors through so-called bipolar +cells to ganglion cells sort of a + + align:start position:0% +cells to ganglion cells sort of a + + + align:start position:0% +cells to ganglion cells sort of a +vertical path in this picture + + align:start position:0% +vertical path in this picture + + + align:start position:0% +vertical path in this picture +um heading from the photoreceptors out + + align:start position:0% +um heading from the photoreceptors out + + + align:start position:0% +um heading from the photoreceptors out +to the brain and then there are cells + + align:start position:0% +to the brain and then there are cells + + + align:start position:0% +to the brain and then there are cells +um whose whose processes are sitting + + align:start position:0% +um whose whose processes are sitting + + + align:start position:0% +um whose whose processes are sitting +here and here making horizontal + + align:start position:0% +here and here making horizontal + + + align:start position:0% +here and here making horizontal +connections so that uh so that + + align:start position:0% +connections so that uh so that + + + align:start position:0% +connections so that uh so that +photoreceptors don't behave like + + align:start position:0% +photoreceptors don't behave like + + + align:start position:0% +photoreceptors don't behave like +isolated pixels so that they can talk to + + align:start position:0% +isolated pixels so that they can talk to + + + align:start position:0% +isolated pixels so that they can talk to +each other and so you can start doing + + align:start position:0% +each other and so you can start doing + + + align:start position:0% +each other and so you can start doing +some sort of uh calculations if you like + + align:start position:0% +some sort of uh calculations if you like + + + align:start position:0% +some sort of uh calculations if you like +um and those are cells like horizontal + + align:start position:0% +um and those are cells like horizontal + + + align:start position:0% +um and those are cells like horizontal +cells that have their processes up here + + align:start position:0% +cells that have their processes up here + + + align:start position:0% +cells that have their processes up here +and amocrine cells that have their + + align:start position:0% +and amocrine cells that have their + + + align:start position:0% +and amocrine cells that have their +processes down here so those are things + + align:start position:0% +processes down here so those are things + + + align:start position:0% +processes down here so those are things +making horizontal connections across the + + align:start position:0% +making horizontal connections across the + + + align:start position:0% +making horizontal connections across the +retina + + align:start position:0% +retina + + + align:start position:0% +retina +photoreceptors bipolar cells ganglion + + align:start position:0% +photoreceptors bipolar cells ganglion + + + align:start position:0% +photoreceptors bipolar cells ganglion +cells are forming this through pathway + + align:start position:0% +cells are forming this through pathway + + + align:start position:0% +cells are forming this through pathway +going from I + + align:start position:0% +going from I + + + align:start position:0% +going from I +to um to brain now if you were to look + + align:start position:0% +to um to brain now if you were to look + + + align:start position:0% +to um to brain now if you were to look +at this and I was to say where is light + + align:start position:0% +at this and I was to say where is light + + + align:start position:0% +at this and I was to say where is light +coming from in this picture + + align:start position:0% +coming from in this picture + + + align:start position:0% +coming from in this picture +the reasonable answer would be + + align:start position:0% + + + + align:start position:0% + +or reasonable actually + + align:start position:0% + + + + align:start position:0% + +it would seem like a reasonable answer + + align:start position:0% +it would seem like a reasonable answer + + + align:start position:0% +it would seem like a reasonable answer +would be like it's coming from the top + + align:start position:0% +would be like it's coming from the top + + + align:start position:0% +would be like it's coming from the top +hit in the photoreceptors and heading + + align:start position:0% +hit in the photoreceptors and heading + + + align:start position:0% +hit in the photoreceptors and heading +off to the brain out the bottom but in + + align:start position:0% +off to the brain out the bottom but in + + + align:start position:0% +off to the brain out the bottom but in +fact light's coming from there + + align:start position:0% +fact light's coming from there + + + align:start position:0% +fact light's coming from there +um the retina is put on backwards in an + + align:start position:0% +um the retina is put on backwards in an + + + align:start position:0% +um the retina is put on backwards in an +interesting kind of a way or intuitively + + align:start position:0% +interesting kind of a way or intuitively + + + align:start position:0% +interesting kind of a way or intuitively +backwards at least so that light shines + + align:start position:0% +backwards at least so that light shines + + + align:start position:0% +backwards at least so that light shines +through all of this stuff + + align:start position:0% +through all of this stuff + + + align:start position:0% +through all of this stuff +before actually getting to the + + align:start position:0% +before actually getting to the + + + align:start position:0% +before actually getting to the +photoreceptors why is that that well + + align:start position:0% +photoreceptors why is that that well + + + align:start position:0% +photoreceptors why is that that well +there are a variety of possible answers + + align:start position:0% +there are a variety of possible answers + + + align:start position:0% +there are a variety of possible answers +but one of the answers is let's see the + + align:start position:0% +but one of the answers is let's see the + + + align:start position:0% +but one of the answers is let's see the +remaining term on the list that I + + align:start position:0% +remaining term on the list that I + + + align:start position:0% +remaining term on the list that I +haven't mentioned in that retinal list + + align:start position:0% +haven't mentioned in that retinal list + + + align:start position:0% +haven't mentioned in that retinal list +which is a + + align:start position:0% +which is a + + + align:start position:0% +which is a +which is actually the top of the list it + + align:start position:0% +which is actually the top of the list it + + + align:start position:0% +which is actually the top of the list it +says pigment epithelium Come Back Little + + align:start position:0% +says pigment epithelium Come Back Little + + + align:start position:0% +says pigment epithelium Come Back Little +cursor + + align:start position:0% +cursor + + + align:start position:0% +cursor +it doesn't oh there it is here we go up + + align:start position:0% +it doesn't oh there it is here we go up + + + align:start position:0% +it doesn't oh there it is here we go up +here + + align:start position:0% +here + + + align:start position:0% +here +there would be a layer of what boils + + align:start position:0% +there would be a layer of what boils + + + align:start position:0% +there would be a layer of what boils +down to Black Gunk coating the back + + align:start position:0% +down to Black Gunk coating the back + + + align:start position:0% +down to Black Gunk coating the back +surface of the eye and the + + align:start position:0% +surface of the eye and the + + + align:start position:0% +surface of the eye and the +photoreceptors are stuck into that + + align:start position:0% +photoreceptors are stuck into that + + + align:start position:0% +photoreceptors are stuck into that +that's the pigment epithelium what it's + + align:start position:0% +that's the pigment epithelium what it's + + + align:start position:0% +that's the pigment epithelium what it's +there for + + align:start position:0% +there for + + + align:start position:0% +there for +is + + align:start position:0% +is + + + align:start position:0% +is +um well let's let's suppose that all of + + align:start position:0% +um well let's let's suppose that all of + + + align:start position:0% +um well let's let's suppose that all of +you guys are photoreceptors and and you + + align:start position:0% +you guys are photoreceptors and and you + + + align:start position:0% +you guys are photoreceptors and and you +know here I am I'm a photon + + align:start position:0% +know here I am I'm a photon + + + align:start position:0% +know here I am I'm a photon +and um you know I'm part of this image + + align:start position:0% +and um you know I'm part of this image + + + align:start position:0% +and um you know I'm part of this image +of the world on the outside and I'm + + align:start position:0% +of the world on the outside and I'm + + + align:start position:0% +of the world on the outside and I'm +coming flying in you know and and with + + align:start position:0% +coming flying in you know and and with + + + align:start position:0% +coming flying in you know and and with +luck I'll be absorbed by Mr + + align:start position:0% +luck I'll be absorbed by Mr + + + align:start position:0% +luck I'll be absorbed by Mr +photoreceptor here + + align:start position:0% +photoreceptor here + + + align:start position:0% +photoreceptor here +um but suppose I I don't suppose I hit + + align:start position:0% +um but suppose I I don't suppose I hit + + + align:start position:0% +um but suppose I I don't suppose I hit +over here + + align:start position:0% +over here + + + align:start position:0% +over here +well I don't want to God well I photons + + align:start position:0% +well I don't want to God well I photons + + + align:start position:0% +well I don't want to God well I photons +don't have much conscious life as far as + + align:start position:0% +don't have much conscious life as far as + + + align:start position:0% +don't have much conscious life as far as +we know you the owner of this visual + + align:start position:0% +we know you the owner of this visual + + + align:start position:0% +we know you the owner of this visual +system don't want that Photon bouncing + + align:start position:0% +system don't want that Photon bouncing + + + align:start position:0% +system don't want that Photon bouncing +around anywhere else you want it either + + align:start position:0% +around anywhere else you want it either + + + align:start position:0% +around anywhere else you want it either +to be absorbed by a photo uh + + align:start position:0% +to be absorbed by a photo uh + + + align:start position:0% +to be absorbed by a photo uh +photoreceptor or to be gone because if + + align:start position:0% +photoreceptor or to be gone because if + + + align:start position:0% +photoreceptor or to be gone because if +it bounces and hits up there somewhere + + align:start position:0% +it bounces and hits up there somewhere + + + align:start position:0% +it bounces and hits up there somewhere +it's going to degrade the image right + + align:start position:0% +it's going to degrade the image right + + + align:start position:0% +it's going to degrade the image right +it's going to be like Haze across the + + align:start position:0% +it's going to be like Haze across the + + + align:start position:0% +it's going to be like Haze across the +image if it's not Landing where it + + align:start position:0% +image if it's not Landing where it + + + align:start position:0% +image if it's not Landing where it +should in in uh to make a a nice Sharp + + align:start position:0% +should in in uh to make a a nice Sharp + + + align:start position:0% +should in in uh to make a a nice Sharp +nice sharp image and so this black Gunk + + align:start position:0% +nice sharp image and so this black Gunk + + + align:start position:0% +nice sharp image and so this black Gunk +is there to + + align:start position:0% +is there to + + + align:start position:0% +is there to +um to soak up extra photoreceptors a + + align:start position:0% +um to soak up extra photoreceptors a + + + align:start position:0% +um to soak up extra photoreceptors a +very good idea if you are a diurnal + + align:start position:0% +very good idea if you are a diurnal + + + align:start position:0% +very good idea if you are a diurnal +animal + + align:start position:0% +animal + + + align:start position:0% +animal +an animal who works out in bright light + + align:start position:0% +an animal who works out in bright light + + + align:start position:0% +an animal who works out in bright light +they're not such a good idea if you're + + align:start position:0% +they're not such a good idea if you're + + + align:start position:0% +they're not such a good idea if you're +an animal who um is nocturnal or running + + align:start position:0% +an animal who um is nocturnal or running + + + align:start position:0% +an animal who um is nocturnal or running +around in in dim light there what you + + align:start position:0% +around in in dim light there what you + + + align:start position:0% +around in in dim light there what you +want to do is catch every Photon that + + align:start position:0% +want to do is catch every Photon that + + + align:start position:0% +want to do is catch every Photon that +you can possibly catch and so if you're + + align:start position:0% +you can possibly catch and so if you're + + + align:start position:0% +you can possibly catch and so if you're +a cat for example you do this + + align:start position:0% +a cat for example you do this + + + align:start position:0% +a cat for example you do this +differently instead of a pigment + + align:start position:0% +differently instead of a pigment + + + align:start position:0% +differently instead of a pigment +epithelium at the back of your eye you + + align:start position:0% +epithelium at the back of your eye you + + + align:start position:0% +epithelium at the back of your eye you +have a structure + + align:start position:0% +have a structure + + + align:start position:0% +have a structure +known as the tapedum it's actually very + + align:start position:0% +known as the tapedum it's actually very + + + align:start position:0% +known as the tapedum it's actually very +beautiful it looks like mother of pearl + + align:start position:0% +beautiful it looks like mother of pearl + + + align:start position:0% +beautiful it looks like mother of pearl +but you only get to see that if you take + + align:start position:0% +but you only get to see that if you take + + + align:start position:0% +but you only get to see that if you take +it out of the cat + + align:start position:0% +it out of the cat + + + align:start position:0% +it out of the cat +which makes the cat less beautiful + + align:start position:0% +which makes the cat less beautiful + + + align:start position:0% +which makes the cat less beautiful +um but it's it's a reflective surface + + align:start position:0% +um but it's it's a reflective surface + + + align:start position:0% +um but it's it's a reflective surface +this is why if you get a cat in in your + + align:start position:0% +this is why if you get a cat in in your + + + align:start position:0% +this is why if you get a cat in in your +or uh in your + + align:start position:0% +or uh in your + + + align:start position:0% +or uh in your +flashlight beam its eyes seem to Glow at + + align:start position:0% +flashlight beam its eyes seem to Glow at + + + align:start position:0% +flashlight beam its eyes seem to Glow at +you because the light comes in if it + + align:start position:0% +you because the light comes in if it + + + align:start position:0% +you because the light comes in if it +doesn't get absorbed by say the + + align:start position:0% +doesn't get absorbed by say the + + + align:start position:0% +doesn't get absorbed by say the +photoreceptors it can bounce and it'll + + align:start position:0% +photoreceptors it can bounce and it'll + + + align:start position:0% +photoreceptors it can bounce and it'll +and an amount of it will bounce back out + + align:start position:0% +and an amount of it will bounce back out + + + align:start position:0% +and an amount of it will bounce back out +some amount of light will bounce back + + align:start position:0% +some amount of light will bounce back + + + align:start position:0% +some amount of light will bounce back +out of your eyes that's what you see + + align:start position:0% +out of your eyes that's what you see + + + align:start position:0% +out of your eyes that's what you see +um as red eye in a um in a unlucky + + align:start position:0% +um as red eye in a um in a unlucky + + + align:start position:0% +um as red eye in a um in a unlucky +photograph for example is that a hand + + align:start position:0% +photograph for example is that a hand + + + align:start position:0% +photograph for example is that a hand +again + + align:start position:0% +again + + + align:start position:0% +again +wouldn't + + align:start position:0% +wouldn't + + + align:start position:0% +wouldn't +for the cat yeah yeah absolutely that's + + align:start position:0% +for the cat yeah yeah absolutely that's + + + align:start position:0% +for the cat yeah yeah absolutely that's +why you you almost never see cats + + align:start position:0% +why you you almost never see cats + + + align:start position:0% +why you you almost never see cats +reading the New York Times + + align:start position:0% +reading the New York Times + + + align:start position:0% +reading the New York Times +um no cat cat visual Acuity is pretty + + align:start position:0% +um no cat cat visual Acuity is pretty + + + align:start position:0% +um no cat cat visual Acuity is pretty +lousy but + + align:start position:0% +lousy but + + + align:start position:0% +lousy but +um a cat has has a different visual + + align:start position:0% +um a cat has has a different visual + + + align:start position:0% +um a cat has has a different visual +desires than you and I do the cat's not + + align:start position:0% +desires than you and I do the cat's not + + + align:start position:0% +desires than you and I do the cat's not +big on sweating the uh the visual Acuity + + align:start position:0% +big on sweating the uh the visual Acuity + + + align:start position:0% +big on sweating the uh the visual Acuity +thing the cat wants to know did it move + + align:start position:0% +thing the cat wants to know did it move + + + align:start position:0% +thing the cat wants to know did it move +can I jump on it can I bite it yeah I + + align:start position:0% +can I jump on it can I bite it yeah I + + + align:start position:0% +can I jump on it can I bite it yeah I +know is it another cat can we do stuff + + align:start position:0% +know is it another cat can we do stuff + + + align:start position:0% +know is it another cat can we do stuff +you know all this sort of stuff + + align:start position:0% +you know all this sort of stuff + + + align:start position:0% +you know all this sort of stuff +this sort of thing doesn't require a lot + + align:start position:0% +this sort of thing doesn't require a lot + + + align:start position:0% +this sort of thing doesn't require a lot +of visual Acuity and the cat wants to be + + align:start position:0% +of visual Acuity and the cat wants to be + + + align:start position:0% +of visual Acuity and the cat wants to be +able to do it in dim light + + align:start position:0% +able to do it in dim light + + + align:start position:0% +able to do it in dim light +um so you know we have this notion that + + align:start position:0% +um so you know we have this notion that + + + align:start position:0% +um so you know we have this notion that +cats can see in the dark which of course + + align:start position:0% +cats can see in the dark which of course + + + align:start position:0% +cats can see in the dark which of course +is not really true No Light No Vision + + align:start position:0% +is not really true No Light No Vision + + + align:start position:0% +is not really true No Light No Vision +um but cats people think cats can see in + + align:start position:0% +um but cats people think cats can see in + + + align:start position:0% +um but cats people think cats can see in +the dark because cats can see stuff in + + align:start position:0% +the dark because cats can see stuff in + + + align:start position:0% +the dark because cats can see stuff in +dim light that you and I can't and part + + align:start position:0% +dim light that you and I can't and part + + + align:start position:0% +dim light that you and I can't and part +of the reason for that is that they are + + align:start position:0% +of the reason for that is that they are + + + align:start position:0% +of the reason for that is that they are +willing to let + + align:start position:0% +willing to let + + + align:start position:0% +willing to let +um stray photo photons go where they + + align:start position:0% +um stray photo photons go where they + + + align:start position:0% +um stray photo photons go where they +will because in fact you know I gave a + + align:start position:0% +will because in fact you know I gave a + + + align:start position:0% +will because in fact you know I gave a +sort of a a radical example if my + + align:start position:0% +sort of a a radical example if my + + + align:start position:0% +sort of a a radical example if my +hypothetical Photon missed my + + align:start position:0% +hypothetical Photon missed my + + + align:start position:0% +hypothetical Photon missed my +hypothetical photoreceptor here odds are + + align:start position:0% +hypothetical photoreceptor here odds are + + + align:start position:0% +hypothetical photoreceptor here odds are +it's not going to go out to outer + + align:start position:0% +it's not going to go out to outer + + + align:start position:0% +it's not going to go out to outer +Mongolia it's going to get absorbed + + align:start position:0% +Mongolia it's going to get absorbed + + + align:start position:0% +Mongolia it's going to get absorbed +someplace nearby and so the effect will + + align:start position:0% +someplace nearby and so the effect will + + + align:start position:0% +someplace nearby and so the effect will +be a blurring + + align:start position:0% +be a blurring + + + align:start position:0% +be a blurring +um not a complete degradation of the + + align:start position:0% +um not a complete degradation of the + + + align:start position:0% +um not a complete degradation of the +image I think the cat can cope the cat + + align:start position:0% +image I think the cat can cope the cat + + + align:start position:0% +image I think the cat can cope the cat +doesn't cat doesn't mind too much + + align:start position:0% +doesn't cat doesn't mind too much + + + align:start position:0% +doesn't cat doesn't mind too much +um by the way + + align:start position:0% +um by the way + + + align:start position:0% +um by the way +a if if you're interested in uh in + + align:start position:0% +a if if you're interested in uh in + + + align:start position:0% +a if if you're interested in uh in +design + + align:start position:0% +design + + + align:start position:0% +design +um taking a look at the um + + align:start position:0% +um taking a look at the um + + + align:start position:0% +um taking a look at the um +the design of eyes across the animal + + align:start position:0% +the design of eyes across the animal + + + align:start position:0% +the design of eyes across the animal +kingdom is a beautiful business and the + + align:start position:0% +kingdom is a beautiful business and the + + + align:start position:0% +kingdom is a beautiful business and the +the number of different ways that + + align:start position:0% +the number of different ways that + + + align:start position:0% +the number of different ways that +um Evolution or the hand of God you can + + align:start position:0% +um Evolution or the hand of God you can + + + align:start position:0% +um Evolution or the hand of God you can +take your pick has chosen to solve the + + align:start position:0% +take your pick has chosen to solve the + + + align:start position:0% +take your pick has chosen to solve the +problem of collecting light an amazing + + align:start position:0% +problem of collecting light an amazing + + + align:start position:0% +problem of collecting light an amazing +array of possibilities + + align:start position:0% +array of possibilities + + + align:start position:0% +array of possibilities +um once you start um cats are one thing + + align:start position:0% +um once you start um cats are one thing + + + align:start position:0% +um once you start um cats are one thing +but you go off into your into insects + + align:start position:0% +but you go off into your into insects + + + align:start position:0% +but you go off into your into insects +and and and and uh + + align:start position:0% +and and and and uh + + + align:start position:0% +and and and and uh +and other beasties and it's great + + align:start position:0% +and other beasties and it's great + + + align:start position:0% +and other beasties and it's great +wonderful stuff uh you know if you want + + align:start position:0% +wonderful stuff uh you know if you want + + + align:start position:0% +wonderful stuff uh you know if you want +to be an engineer + + align:start position:0% +to be an engineer + + + align:start position:0% +to be an engineer +probably lots of good plan lots of lots + + align:start position:0% +probably lots of good plan lots of lots + + + align:start position:0% +probably lots of good plan lots of lots +of lots of good uh industrial design + + align:start position:0% +of lots of good uh industrial design + + + align:start position:0% +of lots of good uh industrial design +there + + align:start position:0% +there + + + align:start position:0% +there +um all right let me take a quick trip up + + align:start position:0% +um all right let me take a quick trip up + + + align:start position:0% +um all right let me take a quick trip up +into the rest of the visual system here + + align:start position:0% +into the rest of the visual system here + + + align:start position:0% +into the rest of the visual system here +this picture that's up on the screen now + + align:start position:0% +this picture that's up on the screen now + + + align:start position:0% +this picture that's up on the screen now +is is mimicking + + align:start position:0% +is is mimicking + + + align:start position:0% +is is mimicking +um the picture on the upper left of the + + align:start position:0% +um the picture on the upper left of the + + + align:start position:0% +um the picture on the upper left of the +second page of the handout + + align:start position:0% +second page of the handout + + + align:start position:0% +second page of the handout +um it's showing the connections oh I + + align:start position:0% +um it's showing the connections oh I + + + align:start position:0% +um it's showing the connections oh I +just remembered I want to do a quick + + align:start position:0% +just remembered I want to do a quick + + + align:start position:0% +just remembered I want to do a quick +demo here before I do that + + align:start position:0% +demo here before I do that + + + align:start position:0% +demo here before I do that +um let's go back and do that oops not + + align:start position:0% +um let's go back and do that oops not + + + align:start position:0% +um let's go back and do that oops not +that way this way + + align:start position:0% +that way this way + + + align:start position:0% +that way this way +um if the eye if the retina is on + + align:start position:0% +um if the eye if the retina is on + + + align:start position:0% +um if the eye if the retina is on +backwards + + align:start position:0% +backwards + + + align:start position:0% +backwards +you've got this interesting problem + + align:start position:0% +you've got this interesting problem + + + align:start position:0% +you've got this interesting problem +let's go forward + + align:start position:0% +let's go forward + + + align:start position:0% +let's go forward +um so you know there are those optic + + align:start position:0% +um so you know there are those optic + + + align:start position:0% +um so you know there are those optic +nerve nerve fibers to the optic nerve + + align:start position:0% +nerve nerve fibers to the optic nerve + + + align:start position:0% +nerve nerve fibers to the optic nerve +how are they going to get out of the eye + + align:start position:0% +how are they going to get out of the eye + + + align:start position:0% +how are they going to get out of the eye +if if light is coming from there + + align:start position:0% +if if light is coming from there + + + align:start position:0% +if if light is coming from there +um what they do food come back there we + + align:start position:0% +um what they do food come back there we + + + align:start position:0% +um what they do food come back there we +go is they run across the surface of the + + align:start position:0% +go is they run across the surface of the + + + align:start position:0% +go is they run across the surface of the +retina + + align:start position:0% +retina + + + align:start position:0% +retina +until they reach the optic nerve and + + align:start position:0% +until they reach the optic nerve and + + + align:start position:0% +until they reach the optic nerve and +then they go out up to the brain where + + align:start position:0% +then they go out up to the brain where + + + align:start position:0% +then they go out up to the brain where +the photoreceptors at the optic nerve + + align:start position:0% +the photoreceptors at the optic nerve + + + align:start position:0% +the photoreceptors at the optic nerve +the answer is there aren't any + + align:start position:0% +the answer is there aren't any + + + align:start position:0% +the answer is there aren't any +photoreceptors at the optic nerve if + + align:start position:0% +photoreceptors at the optic nerve if + + + align:start position:0% +photoreceptors at the optic nerve if +there aren't any photoreceptors at the + + align:start position:0% +there aren't any photoreceptors at the + + + align:start position:0% +there aren't any photoreceptors at the +optic nerve + + align:start position:0% +optic nerve + + + align:start position:0% +optic nerve +what do you see there the answer well + + align:start position:0% +what do you see there the answer well + + + align:start position:0% +what do you see there the answer well +the answer isn't nothing because you + + align:start position:0% +the answer isn't nothing because you + + + align:start position:0% +the answer isn't nothing because you +don't see you you're not aware of the + + align:start position:0% +don't see you you're not aware of the + + + align:start position:0% +don't see you you're not aware of the +fact that there's some big hole in your + + align:start position:0% +fact that there's some big hole in your + + + align:start position:0% +fact that there's some big hole in your +visuals in your visual field but there + + align:start position:0% +visuals in your visual field but there + + + align:start position:0% +visuals in your visual field but there +is + + align:start position:0% +is + + + align:start position:0% +is +um + + align:start position:0% +um + + + align:start position:0% +um +you automatically fill it in because if + + align:start position:0% +you automatically fill it in because if + + + align:start position:0% +you automatically fill it in because if +it's green here and green here and + + align:start position:0% +it's green here and green here and + + + align:start position:0% +it's green here and green here and +there's no information there it's a good + + align:start position:0% +there's no information there it's a good + + + align:start position:0% +there's no information there it's a good +bet that it's probably green all the way + + align:start position:0% +bet that it's probably green all the way + + + align:start position:0% +bet that it's probably green all the way +across and your visual system can figure + + align:start position:0% +across and your visual system can figure + + + align:start position:0% +across and your visual system can figure +this out but it's worth it to prove it + + align:start position:0% +this out but it's worth it to prove it + + + align:start position:0% +this out but it's worth it to prove it +to yourself that there is a blind spot + + align:start position:0% +to yourself that there is a blind spot + + + align:start position:0% +to yourself that there is a blind spot +there let's see on the handout well flip + + align:start position:0% +there let's see on the handout well flip + + + align:start position:0% +there let's see on the handout well flip +to the back of the handout where you got + + align:start position:0% +to the back of the handout where you got + + + align:start position:0% +to the back of the handout where you got +a little extra white space + + align:start position:0% +a little extra white space + + + align:start position:0% +a little extra white space +and um + + align:start position:0% +and um + + + align:start position:0% +and um +put an X put an x on the on the and the + + align:start position:0% +put an X put an x on the on the and the + + + align:start position:0% +put an X put an x on the on the and the +handout here like this + + align:start position:0% +handout here like this + + + align:start position:0% +handout here like this +and a little ways away like about like + + align:start position:0% +and a little ways away like about like + + + align:start position:0% +and a little ways away like about like +that put a little black dot or a little + + align:start position:0% +that put a little black dot or a little + + + align:start position:0% +that put a little black dot or a little +dot I don't care if it's black + + align:start position:0% +dot I don't care if it's black + + + align:start position:0% +dot I don't care if it's black +um and then what you want to do so the + + align:start position:0% +um and then what you want to do so the + + + align:start position:0% +um and then what you want to do so the +dot is to the right of the um of the X + + align:start position:0% +dot is to the right of the um of the X + + + align:start position:0% +dot is to the right of the um of the X +close the left eye cover your left eye + + align:start position:0% +close the left eye cover your left eye + + + align:start position:0% +close the left eye cover your left eye +look at the X hold it so that the dot is + + align:start position:0% +look at the X hold it so that the dot is + + + align:start position:0% +look at the X hold it so that the dot is +straight out to the right and then move + + align:start position:0% +straight out to the right and then move + + + align:start position:0% +straight out to the right and then move +the the paper back and forth and you + + align:start position:0% +the the paper back and forth and you + + + align:start position:0% +the the paper back and forth and you +will find that there's a spot where the + + align:start position:0% +will find that there's a spot where the + + + align:start position:0% +will find that there's a spot where the +dot completely disappears + + align:start position:0% +dot completely disappears + + + align:start position:0% +dot completely disappears +what you've done at that point is move + + align:start position:0% +what you've done at that point is move + + + align:start position:0% +what you've done at that point is move +the dot into + + align:start position:0% +the dot into + + + align:start position:0% +the dot into +the optic nerve head the place where the + + align:start position:0% +the optic nerve head the place where the + + + align:start position:0% +the optic nerve head the place where the +optic nerve is leaving the eye + + align:start position:0% + + + + align:start position:0% + +if you're saying I can't do this I don't + + align:start position:0% +if you're saying I can't do this I don't + + + align:start position:0% +if you're saying I can't do this I don't +see a blind spot it's not because you're + + align:start position:0% +see a blind spot it's not because you're + + + align:start position:0% +see a blind spot it's not because you're +special and don't have one it's because + + align:start position:0% +special and don't have one it's because + + + align:start position:0% +special and don't have one it's because +you're doing it wrong + + align:start position:0% +you're doing it wrong + + + align:start position:0% +you're doing it wrong +um well there is an alternative + + align:start position:0% +um well there is an alternative + + + align:start position:0% +um well there is an alternative +I'm given to understand that the octopus + + align:start position:0% +I'm given to understand that the octopus + + + align:start position:0% +I'm given to understand that the octopus +retina is not put on backwards in this + + align:start position:0% +retina is not put on backwards in this + + + align:start position:0% +retina is not put on backwards in this +way and so perhaps you're an octopus + + align:start position:0% + + + + align:start position:0% + +okay let's go back to this uh this + + align:start position:0% +okay let's go back to this uh this + + + align:start position:0% +okay let's go back to this uh this +wiring diagram here + + align:start position:0% +wiring diagram here + + + align:start position:0% +wiring diagram here +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +what I want to + + align:start position:0% + + + + align:start position:0% + +you can play with this later it's cool + + align:start position:0% +you can play with this later it's cool + + + align:start position:0% +you can play with this later it's cool +do things like well if you flip it + + align:start position:0% +do things like well if you flip it + + + align:start position:0% +do things like well if you flip it +around you can find that you got one in + + align:start position:0% +around you can find that you got one in + + + align:start position:0% +around you can find that you got one in +the other eye too you can also do things + + align:start position:0% +the other eye too you can also do things + + + align:start position:0% +the other eye too you can also do things +like draw a line with a hole in it you + + align:start position:0% +like draw a line with a hole in it you + + + align:start position:0% +like draw a line with a hole in it you +draw a line with the Gap in it put the + + align:start position:0% +draw a line with the Gap in it put the + + + align:start position:0% +draw a line with the Gap in it put the +Gap in the hole the line will appear to + + align:start position:0% +Gap in the hole the line will appear to + + + align:start position:0% +Gap in the hole the line will appear to +complete + + align:start position:0% +complete + + + align:start position:0% +complete +if you get really Adept at this you can + + align:start position:0% +if you get really Adept at this you can + + + align:start position:0% +if you get really Adept at this you can +do what King Charles II of England was + + align:start position:0% +do what King Charles II of England was + + + align:start position:0% +do what King Charles II of England was +reputed to have liked to do which is you + + align:start position:0% +reputed to have liked to do which is you + + + align:start position:0% +reputed to have liked to do which is you +can look at your friends and put their + + align:start position:0% +can look at your friends and put their + + + align:start position:0% +can look at your friends and put their +heads in blind spots and watch their + + align:start position:0% +heads in blind spots and watch their + + + align:start position:0% +heads in blind spots and watch their +heads disappear + + align:start position:0% +heads disappear + + + align:start position:0% +heads disappear +Charles II didn't get the chop off as + + align:start position:0% +Charles II didn't get the chop off as + + + align:start position:0% +Charles II didn't get the chop off as +many heads as as you know his + + align:start position:0% +many heads as as you know his + + + align:start position:0% +many heads as as you know his +predecessors had so this was the best he + + align:start position:0% +predecessors had so this was the best he + + + align:start position:0% +predecessors had so this was the best he +could do I guess + + align:start position:0% +could do I guess + + + align:start position:0% +could do I guess +um all right + + align:start position:0% +um all right + + + align:start position:0% +um all right +how do the + + align:start position:0% +how do the + + + align:start position:0% +how do the +sons from the optic nerve + + align:start position:0% +sons from the optic nerve + + + align:start position:0% +sons from the optic nerve +feed the visual centers of the brain + + align:start position:0% +feed the visual centers of the brain + + + align:start position:0% +feed the visual centers of the brain +you will recall from the first lecture + + align:start position:0% +you will recall from the first lecture + + + align:start position:0% +you will recall from the first lecture +perhaps that everything from the uh you + + align:start position:0% +perhaps that everything from the uh you + + + align:start position:0% +perhaps that everything from the uh you +know my right the right side of my body + + align:start position:0% +know my right the right side of my body + + + align:start position:0% +know my right the right side of my body +on the skin senses gets represented in + + align:start position:0% +on the skin senses gets represented in + + + align:start position:0% +on the skin senses gets represented in +the sensory homunculus on the left and + + align:start position:0% +the sensory homunculus on the left and + + + align:start position:0% +the sensory homunculus on the left and +everything from the left in the sensory + + align:start position:0% +everything from the left in the sensory + + + align:start position:0% +everything from the left in the sensory +homunculus on the right + + align:start position:0% +homunculus on the right + + + align:start position:0% +homunculus on the right +um + + align:start position:0% +um + + + align:start position:0% +um +the way to not do this in the visual + + align:start position:0% +the way to not do this in the visual + + + align:start position:0% +the way to not do this in the visual +system + + align:start position:0% +system + + + align:start position:0% +system +would be to have let's have everything + + align:start position:0% +would be to have let's have everything + + + align:start position:0% +would be to have let's have everything +from the right that's my right eye my + + align:start position:0% +from the right that's my right eye my + + + align:start position:0% +from the right that's my right eye my +right eye go to my left hemisphere and + + align:start position:0% +right eye go to my left hemisphere and + + + align:start position:0% +right eye go to my left hemisphere and +everything from the left eye go to the + + align:start position:0% +everything from the left eye go to the + + + align:start position:0% +everything from the left eye go to the +right hemisphere that wouldn't be any + + align:start position:0% +right hemisphere that wouldn't be any + + + align:start position:0% +right hemisphere that wouldn't be any +good + + align:start position:0% +good + + + align:start position:0% +good +Isaac Newton figured out without + + align:start position:0% +Isaac Newton figured out without + + + align:start position:0% +Isaac Newton figured out without +bothering to do any Anatomy Isaac Newton + + align:start position:0% +bothering to do any Anatomy Isaac Newton + + + align:start position:0% +bothering to do any Anatomy Isaac Newton +figured out that that wouldn't be any + + align:start position:0% +figured out that that wouldn't be any + + + align:start position:0% +figured out that that wouldn't be any +good because I want to look out at the + + align:start position:0% +good because I want to look out at the + + + align:start position:0% +good because I want to look out at the +world with two eyes and I want to see + + align:start position:0% +world with two eyes and I want to see + + + align:start position:0% +world with two eyes and I want to see +one world + + align:start position:0% +one world + + + align:start position:0% +one world +so I'm going to have to do something + + align:start position:0% +so I'm going to have to do something + + + align:start position:0% +so I'm going to have to do something +that brings the information from the two + + align:start position:0% +that brings the information from the two + + + align:start position:0% +that brings the information from the two +eyes together what you actually do + + align:start position:0% +eyes together what you actually do + + + align:start position:0% +eyes together what you actually do +is the following everything from the + + align:start position:0% +is the following everything from the + + + align:start position:0% +is the following everything from the +left side of each retina + + align:start position:0% +left side of each retina + + + align:start position:0% +left side of each retina +ends up in the left hemisphere and + + align:start position:0% +ends up in the left hemisphere and + + + align:start position:0% +ends up in the left hemisphere and +everything from the right side of each + + align:start position:0% +everything from the right side of each + + + align:start position:0% +everything from the right side of each +retina ends up in the right hemisphere + + align:start position:0% +retina ends up in the right hemisphere + + + align:start position:0% +retina ends up in the right hemisphere +the image on the eye is flipped + + align:start position:0% +the image on the eye is flipped + + + align:start position:0% +the image on the eye is flipped +DJ that's that's just simple uh simple + + align:start position:0% +DJ that's that's just simple uh simple + + + align:start position:0% +DJ that's that's just simple uh simple +lenses do that right so I've got a + + align:start position:0% +lenses do that right so I've got a + + + align:start position:0% +lenses do that right so I've got a +simple lens in the front of my uh in + + align:start position:0% +simple lens in the front of my uh in + + + align:start position:0% +simple lens in the front of my uh in +that anterior portion of my eye that + + align:start position:0% +that anterior portion of my eye that + + + align:start position:0% +that anterior portion of my eye that +means that the image of you guys landing + + align:start position:0% +means that the image of you guys landing + + + align:start position:0% +means that the image of you guys landing +on my retina has your feet up your head + + align:start position:0% +on my retina has your feet up your head + + + align:start position:0% +on my retina has your feet up your head +down and left and right reversed so what + + align:start position:0% +down and left and right reversed so what + + + align:start position:0% +down and left and right reversed so what +that means here is what have I done um + + align:start position:0% +that means here is what have I done um + + + align:start position:0% +that means here is what have I done um +what that means here is okay if I stare + + align:start position:0% +what that means here is okay if I stare + + + align:start position:0% +what that means here is okay if I stare +at the the the the the the the person + + align:start position:0% +at the the the the the the the person + + + align:start position:0% +at the the the the the the the person +wearing yellow here + + align:start position:0% +wearing yellow here + + + align:start position:0% +wearing yellow here +um that if I stare at the person wearing + + align:start position:0% +um that if I stare at the person wearing + + + align:start position:0% +um that if I stare at the person wearing +yellow she'll look embarrassed it always + + align:start position:0% +yellow she'll look embarrassed it always + + + align:start position:0% +yellow she'll look embarrassed it always +works but that's a different phenomenon + + align:start position:0% +works but that's a different phenomenon + + + align:start position:0% +works but that's a different phenomenon +all right but I'm staring at you but I'm + + align:start position:0% +all right but I'm staring at you but I'm + + + align:start position:0% +all right but I'm staring at you but I'm +not actually paying any attention to you + + align:start position:0% +not actually paying any attention to you + + + align:start position:0% +not actually paying any attention to you +what I'm actually doing is looking at I + + align:start position:0% +what I'm actually doing is looking at I + + + align:start position:0% +what I'm actually doing is looking at I +don't see my Acuity is so bad it's a + + align:start position:0% +don't see my Acuity is so bad it's a + + + align:start position:0% +don't see my Acuity is so bad it's a +black blob right about there + + align:start position:0% +black blob right about there + + + align:start position:0% +black blob right about there +um I assume she's a person or he's a are + + align:start position:0% +um I assume she's a person or he's a are + + + align:start position:0% +um I assume she's a person or he's a are +you yeah she's a person okay + + align:start position:0% +you yeah she's a person okay + + + align:start position:0% +you yeah she's a person okay +um anyway Acuity is very bad but the + + align:start position:0% +um anyway Acuity is very bad but the + + + align:start position:0% +um anyway Acuity is very bad but the +image of if if you're on my phobia the + + align:start position:0% +image of if if you're on my phobia the + + + align:start position:0% +image of if if you're on my phobia the +woman to the right is in the right half + + align:start position:0% +woman to the right is in the right half + + + align:start position:0% +woman to the right is in the right half +of my visual field landing on the left + + align:start position:0% +of my visual field landing on the left + + + align:start position:0% +of my visual field landing on the left +side of my retina she lands on the left + + align:start position:0% +side of my retina she lands on the left + + + align:start position:0% +side of my retina she lands on the left +side in both eyes and as a result she's + + align:start position:0% +side in both eyes and as a result she's + + + align:start position:0% +side in both eyes and as a result she's +Landing in the my left hemisphere if I'm + + align:start position:0% +Landing in the my left hemisphere if I'm + + + align:start position:0% +Landing in the my left hemisphere if I'm +looking at you some arbitrary blob + + align:start position:0% +looking at you some arbitrary blob + + + align:start position:0% +looking at you some arbitrary blob +there's a blob that just moved over + + align:start position:0% +there's a blob that just moved over + + + align:start position:0% +there's a blob that just moved over +there oh she's a person too okay + + align:start position:0% +there oh she's a person too okay + + + align:start position:0% +there oh she's a person too okay +um this person in the left visual field + + align:start position:0% +um this person in the left visual field + + + align:start position:0% +um this person in the left visual field +ends up on the right retina in each eye + + align:start position:0% +ends up on the right retina in each eye + + + align:start position:0% +ends up on the right retina in each eye +and in the right Hemisphere and in that + + align:start position:0% +and in the right Hemisphere and in that + + + align:start position:0% +and in the right Hemisphere and in that +way so there's only one of her in a + + align:start position:0% +way so there's only one of her in a + + + align:start position:0% +way so there's only one of her in a +sense up in my brain and only one of her + + align:start position:0% +sense up in my brain and only one of her + + + align:start position:0% +sense up in my brain and only one of her +up in my my brain and and their um + + align:start position:0% +up in my my brain and and their um + + + align:start position:0% +up in my my brain and and their um +they're getting together in that fat and + + align:start position:0% +they're getting together in that fat and + + + align:start position:0% +they're getting together in that fat and +the result is that half the fibers from + + align:start position:0% +the result is that half the fibers from + + + align:start position:0% +the result is that half the fibers from +the from each retina have to cross to + + align:start position:0% +the from each retina have to cross to + + + align:start position:0% +the from each retina have to cross to +the other side that's what this uh cute + + align:start position:0% +the other side that's what this uh cute + + + align:start position:0% +the other side that's what this uh cute +little map on on the um + + align:start position:0% +little map on on the um + + + align:start position:0% +little map on on the um +on page two is is is telling you but um + + align:start position:0% +on page two is is is telling you but um + + + align:start position:0% +on page two is is is telling you but um +but the important thing not to get + + align:start position:0% +but the important thing not to get + + + align:start position:0% +but the important thing not to get +confused about is is don't don't tell us + + align:start position:0% +confused about is is don't don't tell us + + + align:start position:0% +confused about is is don't don't tell us +on some exam that your left eye goes to + + align:start position:0% +on some exam that your left eye goes to + + + align:start position:0% +on some exam that your left eye goes to +your right Hemisphere or something it's + + align:start position:0% +your right Hemisphere or something it's + + + align:start position:0% +your right Hemisphere or something it's +left half of each retina goes to left + + align:start position:0% +left half of each retina goes to left + + + align:start position:0% +left half of each retina goes to left +hemisphere left half of each uh right + + align:start position:0% +hemisphere left half of each uh right + + + align:start position:0% +hemisphere left half of each uh right +half of each retina goes to the right + + align:start position:0% +half of each retina goes to the right + + + align:start position:0% +half of each retina goes to the right +hemisphere + + align:start position:0% +hemisphere + + + align:start position:0% +hemisphere +um what it does once it gets there + + align:start position:0% + + + + align:start position:0% + +is um this is a monkey brain + + align:start position:0% +is um this is a monkey brain + + + align:start position:0% +is um this is a monkey brain +and uh what you're looking at is the + + align:start position:0% +and uh what you're looking at is the + + + align:start position:0% +and uh what you're looking at is the +cortical surface here that's the um + + align:start position:0% +cortical surface here that's the um + + + align:start position:0% +cortical surface here that's the um +let's see that must be the outside + + align:start position:0% +let's see that must be the outside + + + align:start position:0% +let's see that must be the outside +surface and this is the inner surface of + + align:start position:0% +surface and this is the inner surface of + + + align:start position:0% +surface and this is the inner surface of +the hemisphere if there are two + + align:start position:0% +the hemisphere if there are two + + + align:start position:0% +the hemisphere if there are two +hemispheres the the one on the bottom is + + align:start position:0% +hemispheres the the one on the bottom is + + + align:start position:0% +hemispheres the the one on the bottom is +looking at the inside surface the + + align:start position:0% +looking at the inside surface the + + + align:start position:0% +looking at the inside surface the +colored areas are ones that are + + align:start position:0% +colored areas are ones that are + + + align:start position:0% +colored areas are ones that are +important in Vision I talked at the + + align:start position:0% +important in Vision I talked at the + + + align:start position:0% +important in Vision I talked at the +beginning about the fact that primary + + align:start position:0% +beginning about the fact that primary + + + align:start position:0% +beginning about the fact that primary +visible cortex is right here at the back + + align:start position:0% +visible cortex is right here at the back + + + align:start position:0% +visible cortex is right here at the back +of the brain but it's amazing how much + + align:start position:0% +of the brain but it's amazing how much + + + align:start position:0% +of the brain but it's amazing how much +of the brain is devoted to Vision + + align:start position:0% +of the brain is devoted to Vision + + + align:start position:0% +of the brain is devoted to Vision +um it's very hard to look at in a + + align:start position:0% +um it's very hard to look at in a + + + align:start position:0% +um it's very hard to look at in a +picture it's very hard to look at period + + align:start position:0% +picture it's very hard to look at period + + + align:start position:0% +picture it's very hard to look at period +but um what what what Vision researchers + + align:start position:0% +but um what what what Vision researchers + + + align:start position:0% +but um what what what Vision researchers +like to do is to make maps like this + + align:start position:0% +like to do is to make maps like this + + + align:start position:0% +like to do is to make maps like this +where you take the cortical surface and + + align:start position:0% +where you take the cortical surface and + + + align:start position:0% +where you take the cortical surface and +flatten it + + align:start position:0% +flatten it + + + align:start position:0% +flatten it +um I mean as as you know it's all this + + align:start position:0% +um I mean as as you know it's all this + + + align:start position:0% +um I mean as as you know it's all this +wrinkly curve + + align:start position:0% +wrinkly curve + + + align:start position:0% +wrinkly curve +involuted structure + + align:start position:0% +involuted structure + + + align:start position:0% +involuted structure +um use a variety of techniques to + + align:start position:0% +um use a variety of techniques to + + + align:start position:0% +um use a variety of techniques to +flatten it out like a map and then you + + align:start position:0% +flatten it out like a map and then you + + + align:start position:0% +flatten it out like a map and then you +see that this is the piece that's at the + + align:start position:0% +see that this is the piece that's at the + + + align:start position:0% +see that this is the piece that's at the +back of the head V1 primary visual + + align:start position:0% +back of the head V1 primary visual + + + align:start position:0% +back of the head V1 primary visual +cortex then you've got all these + + align:start position:0% +cortex then you've got all these + + + align:start position:0% +cortex then you've got all these +gazillion other regions that are + + align:start position:0% +gazillion other regions that are + + + align:start position:0% +gazillion other regions that are +important in um in visual processing + + align:start position:0% +important in um in visual processing + + + align:start position:0% +important in um in visual processing +some of them for rather precise sort of + + align:start position:0% +some of them for rather precise sort of + + + align:start position:0% +some of them for rather precise sort of +things where did Mt go oh I lost my + + align:start position:0% +things where did Mt go oh I lost my + + + align:start position:0% +things where did Mt go oh I lost my +cursor again come back + + align:start position:0% +cursor again come back + + + align:start position:0% +cursor again come back +I don't there it is I think right there + + align:start position:0% +I don't there it is I think right there + + + align:start position:0% +I don't there it is I think right there +is Mt for example which is important in + + align:start position:0% +is Mt for example which is important in + + + align:start position:0% +is Mt for example which is important in +motion processing + + align:start position:0% +motion processing + + + align:start position:0% +motion processing +um lots of work being done trying to + + align:start position:0% +um lots of work being done trying to + + + align:start position:0% +um lots of work being done trying to +figure out what different bits of it do + + align:start position:0% +figure out what different bits of it do + + + align:start position:0% +figure out what different bits of it do +look let me give you a broad organizing + + align:start position:0% +look let me give you a broad organizing + + + align:start position:0% +look let me give you a broad organizing +scheme for how to think about this + + align:start position:0% +scheme for how to think about this + + + align:start position:0% +scheme for how to think about this +um it's not perfect but it ain't bad + + align:start position:0% +um it's not perfect but it ain't bad + + + align:start position:0% +um it's not perfect but it ain't bad +from primary visual cortex we're very + + align:start position:0% +from primary visual cortex we're very + + + align:start position:0% +from primary visual cortex we're very +basic information about uh spots and + + align:start position:0% +basic information about uh spots and + + + align:start position:0% +basic information about uh spots and +lines and primitive bits of motion gets + + align:start position:0% +lines and primitive bits of motion gets + + + align:start position:0% +lines and primitive bits of motion gets +pulled out + + align:start position:0% +pulled out + + + align:start position:0% +pulled out +um more advanced processing goes um Can + + align:start position:0% +um more advanced processing goes um Can + + + align:start position:0% +um more advanced processing goes um Can +can be thought of as in two large + + align:start position:0% +can be thought of as in two large + + + align:start position:0% +can be thought of as in two large +streams one large stream going up + + align:start position:0% +streams one large stream going up + + + align:start position:0% +streams one large stream going up +towards the parietal lobe is telling you + + align:start position:0% +towards the parietal lobe is telling you + + + align:start position:0% +towards the parietal lobe is telling you +things about where stuff is in the in in + + align:start position:0% +things about where stuff is in the in in + + + align:start position:0% +things about where stuff is in the in in +the world how is the world laid out + + align:start position:0% +the world how is the world laid out + + + align:start position:0% +the world how is the world laid out +so the my notion that this that this + + align:start position:0% +so the my notion that this that this + + + align:start position:0% +so the my notion that this that this +space is laid out as a big slanted plane + + align:start position:0% +space is laid out as a big slanted plane + + + align:start position:0% +space is laid out as a big slanted plane +in front of me + + align:start position:0% +in front of me + + + align:start position:0% +in front of me +um probably has has counterparts in in + + align:start position:0% +um probably has has counterparts in in + + + align:start position:0% +um probably has has counterparts in in +um it is probably a product of this sort + + align:start position:0% +um it is probably a product of this sort + + + align:start position:0% +um it is probably a product of this sort +of a pathway + + align:start position:0% +of a pathway + + + align:start position:0% +of a pathway +um a second pathway going down into the + + align:start position:0% +um a second pathway going down into the + + + align:start position:0% +um a second pathway going down into the +temporal lobe + + align:start position:0% +temporal lobe + + + align:start position:0% +temporal lobe +um + + align:start position:0% +um + + + align:start position:0% +um +is very concerned with what stimuli + + align:start position:0% +is very concerned with what stimuli + + + align:start position:0% +is very concerned with what stimuli +might be + + align:start position:0% +might be + + + align:start position:0% +might be +so + + align:start position:0% +so + + + align:start position:0% +so +um there if I if I if you're a monkey + + align:start position:0% +um there if I if I if you're a monkey + + + align:start position:0% +um there if I if I if you're a monkey +and I spear individual cells it might be + + align:start position:0% +and I spear individual cells it might be + + + align:start position:0% +and I spear individual cells it might be +where I would find a cell that was + + align:start position:0% +where I would find a cell that was + + + align:start position:0% +where I would find a cell that was +particularly interested in in um uh a + + align:start position:0% +particularly interested in in um uh a + + + align:start position:0% +particularly interested in in um uh a +hand a monkey hand or a hairy leg or + + align:start position:0% +hand a monkey hand or a hairy leg or + + + align:start position:0% +hand a monkey hand or a hairy leg or +something like that it does it turns out + + align:start position:0% +something like that it does it turns out + + + align:start position:0% +something like that it does it turns out +that the hairy part can be important + + align:start position:0% +that the hairy part can be important + + + align:start position:0% +that the hairy part can be important +when this work was first being some of + + align:start position:0% +when this work was first being some of + + + align:start position:0% +when this work was first being some of +the work on on things like monkey hand + + align:start position:0% +the work on on things like monkey hand + + + align:start position:0% +the work on on things like monkey hand +detectors was being done by one of uh + + align:start position:0% +detectors was being done by one of uh + + + align:start position:0% +detectors was being done by one of uh +one of my professors at Princeton and + + align:start position:0% +one of my professors at Princeton and + + + align:start position:0% +one of my professors at Princeton and +actually my TA in intro psych when I was + + align:start position:0% +actually my TA in intro psych when I was + + + align:start position:0% +actually my TA in intro psych when I was +an undergrad was a grad student who was + + align:start position:0% +an undergrad was a grad student who was + + + align:start position:0% +an undergrad was a grad student who was +working on this and he reported to us + + align:start position:0% +working on this and he reported to us + + + align:start position:0% +working on this and he reported to us +that he was recording the way which the + + align:start position:0% +that he was recording the way which the + + + align:start position:0% +that he was recording the way which the +Ghost spirit cell it's one thing if + + align:start position:0% +Ghost spirit cell it's one thing if + + + align:start position:0% +Ghost spirit cell it's one thing if +you're just trying to figure out if it + + align:start position:0% +you're just trying to figure out if it + + + align:start position:0% +you're just trying to figure out if it +likes spots of light but how do you + + align:start position:0% +likes spots of light but how do you + + + align:start position:0% +likes spots of light but how do you +figure out if the cell likes something + + align:start position:0% +figure out if the cell likes something + + + align:start position:0% +figure out if the cell likes something +like a hand + + align:start position:0% +like a hand + + + align:start position:0% +like a hand +well they had in those days + + align:start position:0% +well they had in those days + + + align:start position:0% +well they had in those days +um drawers full of stuff + + align:start position:0% +um drawers full of stuff + + + align:start position:0% +um drawers full of stuff +and you waved all this stuff in front of + + align:start position:0% +and you waved all this stuff in front of + + + align:start position:0% +and you waved all this stuff in front of +the monkey and see what makes the cell + + align:start position:0% +the monkey and see what makes the cell + + + align:start position:0% +the monkey and see what makes the cell +go + + align:start position:0% +go + + + align:start position:0% +go +and um and these experiments in the good + + align:start position:0% +and um and these experiments in the good + + + align:start position:0% +and um and these experiments in the good +old days tended to run for a very long + + align:start position:0% +old days tended to run for a very long + + + align:start position:0% +old days tended to run for a very long +time because this was an esthetized + + align:start position:0% +time because this was an esthetized + + + align:start position:0% +time because this was an esthetized +monkey and uh the monkey wasn't going to + + align:start position:0% +monkey and uh the monkey wasn't going to + + + align:start position:0% +monkey and uh the monkey wasn't going to +wake up from this particular operation + + align:start position:0% +wake up from this particular operation + + + align:start position:0% +wake up from this particular operation +and you ran the experiment for days and + + align:start position:0% +and you ran the experiment for days and + + + align:start position:0% +and you ran the experiment for days and +days and days + + align:start position:0% +days and days + + + align:start position:0% +days and days +um and you stayed up the whole time so + + align:start position:0% +um and you stayed up the whole time so + + + align:start position:0% +um and you stayed up the whole time so +Bob Desmond now a famous visual + + align:start position:0% +Bob Desmond now a famous visual + + + align:start position:0% +Bob Desmond now a famous visual +neuroscientist is up late at night with + + align:start position:0% +neuroscientist is up late at night with + + + align:start position:0% +neuroscientist is up late at night with +this stupid monkey with his stupid cell + + align:start position:0% +this stupid monkey with his stupid cell + + + align:start position:0% +this stupid monkey with his stupid cell +and the cell isn't doing anything he's + + align:start position:0% +and the cell isn't doing anything he's + + + align:start position:0% +and the cell isn't doing anything he's +waving everything at it so finally + + align:start position:0% +waving everything at it so finally + + + align:start position:0% +waving everything at it so finally +he took off his pants wrapped the towel + + align:start position:0% +he took off his pants wrapped the towel + + + align:start position:0% +he took off his pants wrapped the towel +around his waist and did a little dance + + align:start position:0% +around his waist and did a little dance + + + align:start position:0% +around his waist and did a little dance +in front of the monkey the cell went + + align:start position:0% +in front of the monkey the cell went + + + align:start position:0% +in front of the monkey the cell went +nuts + + align:start position:0% + + + + align:start position:0% + +being a good scientist he then narrowed + + align:start position:0% +being a good scientist he then narrowed + + + align:start position:0% +being a good scientist he then narrowed +this that this down to the notion that + + align:start position:0% +this that this down to the notion that + + + align:start position:0% +this that this down to the notion that +the this this was a cell that actually + + align:start position:0% +the this this was a cell that actually + + + align:start position:0% +the this this was a cell that actually +seemed to be interested in hairy legs + + align:start position:0% +seemed to be interested in hairy legs + + + align:start position:0% +seemed to be interested in hairy legs +um the uh and and the hairy part turned + + align:start position:0% +um the uh and and the hairy part turned + + + align:start position:0% +um the uh and and the hairy part turned +out to be um to be important I feel free + + align:start position:0% +out to be um to be important I feel free + + + align:start position:0% +out to be um to be important I feel free +to tell this story about Bob DeSimone + + align:start position:0% +to tell this story about Bob DeSimone + + + align:start position:0% +to tell this story about Bob DeSimone +because Bob DeSimone is running around + + align:start position:0% +because Bob DeSimone is running around + + + align:start position:0% +because Bob DeSimone is running around +the country telling that with a with a + + align:start position:0% +the country telling that with a with a + + + align:start position:0% +the country telling that with a with a +talk at the moment that has a picture of + + align:start position:0% +talk at the moment that has a picture of + + + align:start position:0% +talk at the moment that has a picture of +me in it kissing a wombat so + + align:start position:0% +me in it kissing a wombat so + + + align:start position:0% +me in it kissing a wombat so +foreign + + align:start position:0% + + + + align:start position:0% + +it all seems fair to me + + align:start position:0% +it all seems fair to me + + + align:start position:0% +it all seems fair to me +um all right well so if you go up into + + align:start position:0% +um all right well so if you go up into + + + align:start position:0% +um all right well so if you go up into +you know way down here in the temporal + + align:start position:0% +you know way down here in the temporal + + + align:start position:0% +you know way down here in the temporal +lobe you might find cells that are that + + align:start position:0% +lobe you might find cells that are that + + + align:start position:0% +lobe you might find cells that are that +respond only to something like a hairy + + align:start position:0% +respond only to something like a hairy + + + align:start position:0% +respond only to something like a hairy +leg or a monkey hand or something like + + align:start position:0% +leg or a monkey hand or something like + + + align:start position:0% +leg or a monkey hand or something like +that if you're hanging out + + align:start position:0% +that if you're hanging out + + + align:start position:0% +that if you're hanging out +back + + align:start position:0% +back + + + align:start position:0% +back +here in primary visual cortex + + align:start position:0% +here in primary visual cortex + + + align:start position:0% +here in primary visual cortex +um uh well actually let's go let's go + + align:start position:0% +um uh well actually let's go let's go + + + align:start position:0% +um uh well actually let's go let's go +back and and hang out in the retina even + + align:start position:0% +back and and hang out in the retina even + + + align:start position:0% +back and and hang out in the retina even +though look at that we'll hang out right + + align:start position:0% +though look at that we'll hang out right + + + align:start position:0% +though look at that we'll hang out right +there + + align:start position:0% +there + + + align:start position:0% +there +um if you're hanging out in the retina + + align:start position:0% +um if you're hanging out in the retina + + + align:start position:0% +um if you're hanging out in the retina +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +the cells have + + align:start position:0% +the cells have + + + align:start position:0% +the cells have +um if you like much simpler needs than + + align:start position:0% +um if you like much simpler needs than + + + align:start position:0% +um if you like much simpler needs than +this uh hairy leg detector somewhere up + + align:start position:0% +this uh hairy leg detector somewhere up + + + align:start position:0% +this uh hairy leg detector somewhere up +in in in the temporal lobe + + align:start position:0% +in in in the temporal lobe + + + align:start position:0% +in in in the temporal lobe +um + + align:start position:0% + + + + align:start position:0% + +I mentioned before that you might be + + align:start position:0% +I mentioned before that you might be + + + align:start position:0% +I mentioned before that you might be +bringing together + + align:start position:0% + + + + align:start position:0% + +a whole bunch of photoreceptors + + align:start position:0% +a whole bunch of photoreceptors + + + align:start position:0% +a whole bunch of photoreceptors +through say a bipolar cell to a ganglion + + align:start position:0% +through say a bipolar cell to a ganglion + + + align:start position:0% +through say a bipolar cell to a ganglion +cell + + align:start position:0% +cell + + + align:start position:0% +cell +um to uh to bring together a whole bunch + + align:start position:0% +um to uh to bring together a whole bunch + + + align:start position:0% +um to uh to bring together a whole bunch +of them to send a signal off to the + + align:start position:0% +of them to send a signal off to the + + + align:start position:0% +of them to send a signal off to the +brain but what I didn't mention is that + + align:start position:0% +brain but what I didn't mention is that + + + align:start position:0% +brain but what I didn't mention is that +not all the photoreceptors that are + + align:start position:0% +not all the photoreceptors that are + + + align:start position:0% +not all the photoreceptors that are +hooked up to stimulate a ganglion cell + + align:start position:0% +hooked up to stimulate a ganglion cell + + + align:start position:0% +hooked up to stimulate a ganglion cell +are going to excite that cell let's draw + + align:start position:0% +are going to excite that cell let's draw + + + align:start position:0% +are going to excite that cell let's draw +some pictures over here what actually + + align:start position:0% +some pictures over here what actually + + + align:start position:0% +some pictures over here what actually +happens + + align:start position:0% + + + + align:start position:0% + +and I'm just going to mimic this over + + align:start position:0% +and I'm just going to mimic this over + + + align:start position:0% +and I'm just going to mimic this over +here is that you you'd have some + + align:start position:0% +here is that you you'd have some + + + align:start position:0% +here is that you you'd have some +photoreceptors + + align:start position:0% + + + + align:start position:0% + +who are set up + + align:start position:0% +who are set up + + + align:start position:0% +who are set up +to excite + + align:start position:0% + + + + align:start position:0% + +a ganglion cell and then some other guys + + align:start position:0% +a ganglion cell and then some other guys + + + align:start position:0% +a ganglion cell and then some other guys +around them + + align:start position:0% +around them + + + align:start position:0% +around them +who would be set up to + + align:start position:0% +who would be set up to + + + align:start position:0% +who would be set up to +in uh inhibited + + align:start position:0% +in uh inhibited + + + align:start position:0% +in uh inhibited +and + + align:start position:0% +and + + + align:start position:0% +and +um + + align:start position:0% +um + + + align:start position:0% +um +so here's this + + align:start position:0% +so here's this + + + align:start position:0% +so here's this +oh + + align:start position:0% +oh + + + align:start position:0% +oh +the result is that what this cell and + + align:start position:0% +the result is that what this cell and + + + align:start position:0% +the result is that what this cell and +and now and what that that's that's a + + align:start position:0% +and now and what that that's that's a + + + align:start position:0% +and now and what that that's that's a +one-dimensional slice and this would be + + align:start position:0% +one-dimensional slice and this would be + + + align:start position:0% +one-dimensional slice and this would be +a two-dimensional picture that threaten + + align:start position:0% +a two-dimensional picture that threaten + + + align:start position:0% +a two-dimensional picture that threaten +is after all a two-dimensional surface + + align:start position:0% +is after all a two-dimensional surface + + + align:start position:0% +is after all a two-dimensional surface +so what you'd really get is some region + + align:start position:0% + + + + align:start position:0% + +some region of photoreceptors that + + align:start position:0% +some region of photoreceptors that + + + align:start position:0% +some region of photoreceptors that +excite the cell and some surrounding + + align:start position:0% +excite the cell and some surrounding + + + align:start position:0% +excite the cell and some surrounding +region where light inhibits the + + align:start position:0% +region where light inhibits the + + + align:start position:0% +region where light inhibits the +subsequent ganglion cell and then excuse + + align:start position:0% +subsequent ganglion cell and then excuse + + + align:start position:0% +subsequent ganglion cell and then excuse +me + + align:start position:0% +me + + + align:start position:0% +me +um you know light out here does nothing + + align:start position:0% +um you know light out here does nothing + + + align:start position:0% +um you know light out here does nothing +so this is the receptive field of this + + align:start position:0% +so this is the receptive field of this + + + align:start position:0% +so this is the receptive field of this +cell this is the only part of the retina + + align:start position:0% +cell this is the only part of the retina + + + align:start position:0% +cell this is the only part of the retina +that that this cell over here + + align:start position:0% +that that this cell over here + + + align:start position:0% +that that this cell over here +cares about + + align:start position:0% +cares about + + + align:start position:0% +cares about +and it's going to send its signal off to + + align:start position:0% +and it's going to send its signal off to + + + align:start position:0% +and it's going to send its signal off to +the brain and so now you see what does + + align:start position:0% +the brain and so now you see what does + + + align:start position:0% +the brain and so now you see what does +this cell do well among the things that + + align:start position:0% +this cell do well among the things that + + + align:start position:0% +this cell do well among the things that +this cell can do is it can tell you I am + + align:start position:0% +this cell can do is it can tell you I am + + + align:start position:0% +this cell can do is it can tell you I am +most excited by a spot that's exactly + + align:start position:0% +most excited by a spot that's exactly + + + align:start position:0% +most excited by a spot that's exactly +this size + + align:start position:0% + + + + align:start position:0% + +if the spot gets any bigger it's going + + align:start position:0% +if the spot gets any bigger it's going + + + align:start position:0% +if the spot gets any bigger it's going +to encroach on this inhibitory stuff and + + align:start position:0% +to encroach on this inhibitory stuff and + + + align:start position:0% +to encroach on this inhibitory stuff and +and reduce my excitation if the spot's + + align:start position:0% +and reduce my excitation if the spot's + + + align:start position:0% +and reduce my excitation if the spot's +any smaller I'm not going to get the all + + align:start position:0% +any smaller I'm not going to get the all + + + align:start position:0% +any smaller I'm not going to get the all +of my excitatory uh guys excited and the + + align:start position:0% +of my excitatory uh guys excited and the + + + align:start position:0% +of my excitatory uh guys excited and the +response that gets more so I'm most + + align:start position:0% +response that gets more so I'm most + + + align:start position:0% +response that gets more so I'm most +excited by a spot of exactly this side + + align:start position:0% +excited by a spot of exactly this side + + + align:start position:0% +excited by a spot of exactly this side +if I build + + align:start position:0% +if I build + + + align:start position:0% +if I build +receptors with different size centers + + align:start position:0% +receptors with different size centers + + + align:start position:0% +receptors with different size centers +now this guy is only going to be excited + + align:start position:0% +now this guy is only going to be excited + + + align:start position:0% +now this guy is only going to be excited +by a little spot and I can make one that + + align:start position:0% +by a little spot and I can make one that + + + align:start position:0% +by a little spot and I can make one that +would be excited by a bigger spot and so + + align:start position:0% +would be excited by a bigger spot and so + + + align:start position:0% +would be excited by a bigger spot and so +even at the level of the retina you can + + align:start position:0% +even at the level of the retina you can + + + align:start position:0% +even at the level of the retina you can +start to get cells that are telling you + + align:start position:0% +start to get cells that are telling you + + + align:start position:0% +start to get cells that are telling you +more than just light on light off + + align:start position:0% +more than just light on light off + + + align:start position:0% +more than just light on light off +they're starting to tell you something + + align:start position:0% +they're starting to tell you something + + + align:start position:0% +they're starting to tell you something +about the size of things in the visual + + align:start position:0% +about the size of things in the visual + + + align:start position:0% +about the size of things in the visual +in the visual field when you get up to + + align:start position:0% +in the visual field when you get up to + + + align:start position:0% +in the visual field when you get up to +the cortex + + align:start position:0% +the cortex + + + align:start position:0% +the cortex +you find that now cells come to be + + align:start position:0% +you find that now cells come to be + + + align:start position:0% +you find that now cells come to be +interested in things like lines not just + + align:start position:0% +interested in things like lines not just + + + align:start position:0% +interested in things like lines not just +a spot but a line and it'll say you know + + align:start position:0% +a spot but a line and it'll say you know + + + align:start position:0% +a spot but a line and it'll say you know +this cell will say I like lines in this + + align:start position:0% +this cell will say I like lines in this + + + align:start position:0% +this cell will say I like lines in this +orientation I don't like lines and + + align:start position:0% +orientation I don't like lines and + + + align:start position:0% +orientation I don't like lines and +disorientation in fact I like lines in + + align:start position:0% +disorientation in fact I like lines in + + + align:start position:0% +disorientation in fact I like lines in +this orientation only if they move this + + align:start position:0% +this orientation only if they move this + + + align:start position:0% +this orientation only if they move this +direction + + align:start position:0% +direction + + + align:start position:0% +direction +and so you can imagine that what you + + align:start position:0% +and so you can imagine that what you + + + align:start position:0% +and so you can imagine that what you +start to do early in the visual system + + align:start position:0% +start to do early in the visual system + + + align:start position:0% +start to do early in the visual system +is to pull out a whole bunch of + + align:start position:0% +is to pull out a whole bunch of + + + align:start position:0% +is to pull out a whole bunch of +um + + align:start position:0% +um + + + align:start position:0% +um +little features if you like + + align:start position:0% +little features if you like + + + align:start position:0% +little features if you like +that you can then use subsequently to to + + align:start position:0% +that you can then use subsequently to to + + + align:start position:0% +that you can then use subsequently to to +try to figure out you know is there a + + align:start position:0% +try to figure out you know is there a + + + align:start position:0% +try to figure out you know is there a +monkey hand here + + align:start position:0% +monkey hand here + + + align:start position:0% +monkey hand here +um you know is is there a laptop + + align:start position:0% +um you know is is there a laptop + + + align:start position:0% +um you know is is there a laptop +computer or something like that so + + align:start position:0% +computer or something like that so + + + align:start position:0% +computer or something like that so +you've got this base early in the system + + align:start position:0% +you've got this base early in the system + + + align:start position:0% +you've got this base early in the system +you've got + + align:start position:0% +you've got + + + align:start position:0% +you've got +um uh you you you've got basic features + + align:start position:0% +um uh you you you've got basic features + + + align:start position:0% +um uh you you you've got basic features +being pulled out of the image now + + align:start position:0% +being pulled out of the image now + + + align:start position:0% +being pulled out of the image now +this presents a problem + + align:start position:0% +this presents a problem + + + align:start position:0% +this presents a problem +suppose that what you want to do well + + align:start position:0% +suppose that what you want to do well + + + align:start position:0% +suppose that what you want to do well +let's let's start with orientation + + align:start position:0% +let's let's start with orientation + + + align:start position:0% +let's let's start with orientation +suppose you want to decide that a line + + align:start position:0% +suppose you want to decide that a line + + + align:start position:0% +suppose you want to decide that a line +is is a particular orientation how good + + align:start position:0% +is is a particular orientation how good + + + align:start position:0% +is is a particular orientation how good +are you at that the answer turns out to + + align:start position:0% +are you at that the answer turns out to + + + align:start position:0% +are you at that the answer turns out to +be that you are + + align:start position:0% +be that you are + + + align:start position:0% +be that you are +um good enough to be able to tell sort + + align:start position:0% +um good enough to be able to tell sort + + + align:start position:0% +um good enough to be able to tell sort +of one roughly one degree increments + + align:start position:0% +of one roughly one degree increments + + + align:start position:0% +of one roughly one degree increments +how are you going to do that well you + + align:start position:0% +how are you going to do that well you + + + align:start position:0% +how are you going to do that well you +could have a cell specifically designed + + align:start position:0% +could have a cell specifically designed + + + align:start position:0% +could have a cell specifically designed +to look for zero degrees vertical one + + align:start position:0% +to look for zero degrees vertical one + + + align:start position:0% +to look for zero degrees vertical one +degree two degree Three Degree four + + align:start position:0% +degree two degree Three Degree four + + + align:start position:0% +degree two degree Three Degree four +degree and you need one of those + + align:start position:0% +degree and you need one of those + + + align:start position:0% +degree and you need one of those +everywhere in the visual field and at a + + align:start position:0% +everywhere in the visual field and at a + + + align:start position:0% +everywhere in the visual field and at a +whole different size it's a little line + + align:start position:0% +whole different size it's a little line + + + align:start position:0% +whole different size it's a little line +it's vertical a big line that's vertical + + align:start position:0% +it's vertical a big line that's vertical + + + align:start position:0% +it's vertical a big line that's vertical +you're going to need an awful lot of + + align:start position:0% +you're going to need an awful lot of + + + align:start position:0% +you're going to need an awful lot of +cells then + + align:start position:0% +cells then + + + align:start position:0% +cells then +that's not what we do what we seem to do + + align:start position:0% +that's not what we do what we seem to do + + + align:start position:0% +that's not what we do what we seem to do +all over the place in the visual system + + align:start position:0% +all over the place in the visual system + + + align:start position:0% +all over the place in the visual system +and in sensory systems in general is to + + align:start position:0% +and in sensory systems in general is to + + + align:start position:0% +and in sensory systems in general is to +make comparisons + + align:start position:0% +make comparisons + + + align:start position:0% +make comparisons +um + + align:start position:0% +um + + + align:start position:0% +um +that comparisons are very are are very + + align:start position:0% +that comparisons are very are are very + + + align:start position:0% +that comparisons are very are are very +powerful in this game so how do you + + align:start position:0% +powerful in this game so how do you + + + align:start position:0% +powerful in this game so how do you +decide that something's vertical to a + + align:start position:0% +decide that something's vertical to a + + + align:start position:0% +decide that something's vertical to a +first approximation what you do is you + + align:start position:0% +first approximation what you do is you + + + align:start position:0% +first approximation what you do is you +look at whether or not the left tilted + + align:start position:0% +look at whether or not the left tilted + + + align:start position:0% +look at whether or not the left tilted +guys and the right tilted guys the cells + + align:start position:0% +guys and the right tilted guys the cells + + + align:start position:0% +guys and the right tilted guys the cells +that like stuff well that's going to be + + align:start position:0% +that like stuff well that's going to be + + + align:start position:0% +that like stuff well that's going to be +right till good for you the stuff that + + align:start position:0% +right till good for you the stuff that + + + align:start position:0% +right till good for you the stuff that +the cells that look for something that's + + align:start position:0% +the cells that look for something that's + + + align:start position:0% +the cells that look for something that's +still a little to the right cells that + + align:start position:0% +still a little to the right cells that + + + align:start position:0% +still a little to the right cells that +are interested in stuff that's tilted to + + align:start position:0% +are interested in stuff that's tilted to + + + align:start position:0% +are interested in stuff that's tilted to +the left are they roughly equally + + align:start position:0% +the left are they roughly equally + + + align:start position:0% +the left are they roughly equally +excited + + align:start position:0% +excited + + + align:start position:0% +excited +if they're roughly equally excited in + + align:start position:0% +if they're roughly equally excited in + + + align:start position:0% +if they're roughly equally excited in +Balance one with the other + + align:start position:0% +Balance one with the other + + + align:start position:0% +Balance one with the other +then odds are that + + align:start position:0% +then odds are that + + + align:start position:0% +then odds are that +um that you're gonna see uh that that + + align:start position:0% +um that you're gonna see uh that that + + + align:start position:0% +um that you're gonna see uh that that +you're looking at a vertical stimulus + + align:start position:0% +you're looking at a vertical stimulus + + + align:start position:0% +you're looking at a vertical stimulus +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um if the if the right tilted stuff is + + align:start position:0% +um if the if the right tilted stuff is + + + align:start position:0% +um if the if the right tilted stuff is +stronger than the left tilted stuff so + + align:start position:0% +stronger than the left tilted stuff so + + + align:start position:0% +stronger than the left tilted stuff so +that balance gets tilted you're going to + + align:start position:0% +that balance gets tilted you're going to + + + align:start position:0% +that balance gets tilted you're going to +say that the stimulus is tilted + + align:start position:0% +say that the stimulus is tilted + + + align:start position:0% +say that the stimulus is tilted +um it turns out + + align:start position:0% +um it turns out + + + align:start position:0% +um it turns out +that if you + + align:start position:0% +that if you + + + align:start position:0% +that if you +um suppose if you do something to make + + align:start position:0% +um suppose if you do something to make + + + align:start position:0% +um suppose if you do something to make +um well let's say you go off and you + + align:start position:0% +um well let's say you go off and you + + + align:start position:0% +um well let's say you go off and you +make the uh the left tilted stuff + + align:start position:0% +make the uh the left tilted stuff + + + align:start position:0% +make the uh the left tilted stuff +um week by tiring it out how do you Tire + + align:start position:0% +um week by tiring it out how do you Tire + + + align:start position:0% +um week by tiring it out how do you Tire +it out you show it a bunch of left + + align:start position:0% +it out you show it a bunch of left + + + align:start position:0% +it out you show it a bunch of left +show a bunch of left lines that makes + + align:start position:0% +show a bunch of left lines that makes + + + align:start position:0% +show a bunch of left lines that makes +this weaker then something that's + + align:start position:0% +this weaker then something that's + + + align:start position:0% +this weaker then something that's +vertical is going to turn out to look + + align:start position:0% +vertical is going to turn out to look + + + align:start position:0% +vertical is going to turn out to look +tilted to the uh you're not going to + + align:start position:0% +tilted to the uh you're not going to + + + align:start position:0% +tilted to the uh you're not going to +believe that let me show this to you + + align:start position:0% +believe that let me show this to you + + + align:start position:0% +believe that let me show this to you +I'll show it to you in I'm going to jump + + align:start position:0% +I'll show it to you in I'm going to jump + + + align:start position:0% +I'll show it to you in I'm going to jump +to um okay we'll jump here well we'll + + align:start position:0% +to um okay we'll jump here well we'll + + + align:start position:0% +to um okay we'll jump here well we'll +jump here first + + align:start position:0% +jump here first + + + align:start position:0% +jump here first +look at that okay here are very boring + + align:start position:0% +look at that okay here are very boring + + + align:start position:0% +look at that okay here are very boring +a very boring picture + + align:start position:0% +a very boring picture + + + align:start position:0% +a very boring picture +um it will be even more boring if I turn + + align:start position:0% +um it will be even more boring if I turn + + + align:start position:0% +um it will be even more boring if I turn +out a little more of the lights here I'm + + align:start position:0% +out a little more of the lights here I'm + + + align:start position:0% +out a little more of the lights here I'm +gonna chalkboard right there we go + + align:start position:0% +gonna chalkboard right there we go + + + align:start position:0% +gonna chalkboard right there we go +um Okay so + + align:start position:0% +um Okay so + + + align:start position:0% +um Okay so +how do you know that something's white + + align:start position:0% +how do you know that something's white + + + align:start position:0% +how do you know that something's white +or or gray or a chromatic again in this + + align:start position:0% +or or gray or a chromatic again in this + + + align:start position:0% +or or gray or a chromatic again in this +case you've got color mechanisms that + + align:start position:0% +case you've got color mechanisms that + + + align:start position:0% +case you've got color mechanisms that +say how red or green it turns out that + + align:start position:0% +say how red or green it turns out that + + + align:start position:0% +say how red or green it turns out that +what you've got is how red or green is + + align:start position:0% +what you've got is how red or green is + + + align:start position:0% +what you've got is how red or green is +this + + align:start position:0% +this + + + align:start position:0% +this +if the answer is well it's balanced + + align:start position:0% +if the answer is well it's balanced + + + align:start position:0% +if the answer is well it's balanced +between red and green + + align:start position:0% +between red and green + + + align:start position:0% +between red and green +um then uh it might be and you also ask + + align:start position:0% +um then uh it might be and you also ask + + + align:start position:0% +um then uh it might be and you also ask +how blue or yellow is this if it's not + + align:start position:0% +how blue or yellow is this if it's not + + + align:start position:0% +how blue or yellow is this if it's not +blue and it's not yellow and it's not + + align:start position:0% +blue and it's not yellow and it's not + + + align:start position:0% +blue and it's not yellow and it's not +red and it's not green well you know + + align:start position:0% +red and it's not green well you know + + + align:start position:0% +red and it's not green well you know +what it's probably White + + align:start position:0% +what it's probably White + + + align:start position:0% +what it's probably White +okay well so here let's take this red + + align:start position:0% +okay well so here let's take this red + + + align:start position:0% +okay well so here let's take this red +green thing and let's make the green + + align:start position:0% +green thing and let's make the green + + + align:start position:0% +green thing and let's make the green +side + + align:start position:0% +side + + + align:start position:0% +side +Weak by wearing it out we'll show you + + align:start position:0% +Weak by wearing it out we'll show you + + + align:start position:0% +Weak by wearing it out we'll show you +some green + + align:start position:0% +some green + + + align:start position:0% +some green +now I'm going to show you something + + align:start position:0% +now I'm going to show you something + + + align:start position:0% +now I'm going to show you something +white the green is weak the red is + + align:start position:0% +white the green is weak the red is + + + align:start position:0% +white the green is weak the red is +strong the balance goes this way and you + + align:start position:0% +strong the balance goes this way and you + + + align:start position:0% +strong the balance goes this way and you +think that something that was once white + + align:start position:0% +think that something that was once white + + + align:start position:0% +think that something that was once white +now looks kind of green + + align:start position:0% +now looks kind of green + + + align:start position:0% +now looks kind of green +um + + align:start position:0% +um + + + align:start position:0% +um +there see isn't that amazing + + align:start position:0% +there see isn't that amazing + + + align:start position:0% +there see isn't that amazing +they're not convinced + + align:start position:0% +they're not convinced + + + align:start position:0% +they're not convinced +um the ones who are convinced are + + align:start position:0% +um the ones who are convinced are + + + align:start position:0% +um the ones who are convinced are +confused + + align:start position:0% +confused + + + align:start position:0% +confused +um star stare at the black dot at the at + + align:start position:0% +um star stare at the black dot at the at + + + align:start position:0% +um star stare at the black dot at the at +the uh at the center here you just want + + align:start position:0% +the uh at the center here you just want + + + align:start position:0% +the uh at the center here you just want +to stare at the black dot + + align:start position:0% +to stare at the black dot + + + align:start position:0% +to stare at the black dot +um and and think about say that red dot + + align:start position:0% +um and and think about say that red dot + + + align:start position:0% +um and and think about say that red dot +up at 12 o'clock what you're doing is + + align:start position:0% +up at 12 o'clock what you're doing is + + + align:start position:0% +up at 12 o'clock what you're doing is +you're tiring out the red side of this + + align:start position:0% +you're tiring out the red side of this + + + align:start position:0% +you're tiring out the red side of this +red green equation in this particular + + align:start position:0% +red green equation in this particular + + + align:start position:0% +red green equation in this particular +case and just keep staring there and + + align:start position:0% +case and just keep staring there and + + + align:start position:0% +case and just keep staring there and +then I'm gonna go boink + + align:start position:0% + + + + align:start position:0% + +so the people who went ooh presumably + + align:start position:0% +so the people who went ooh presumably + + + align:start position:0% +so the people who went ooh presumably +saw colors all right let's do that again + + align:start position:0% +saw colors all right let's do that again + + + align:start position:0% +saw colors all right let's do that again +here + + align:start position:0% +here + + + align:start position:0% +here +what you ought to notice is that you're + + align:start position:0% +what you ought to notice is that you're + + + align:start position:0% +what you ought to notice is that you're +seeing you you what you want to want it + + align:start position:0% +seeing you you what you want to want it + + + align:start position:0% +seeing you you what you want to want it +what you ought to think of wanna + + align:start position:0% +what you ought to think of wanna + + + align:start position:0% +what you ought to think of wanna +what you want to notice is that the + + align:start position:0% +what you want to notice is that the + + + align:start position:0% +what you want to notice is that the +color is the is this opposite color it's + + align:start position:0% +color is the is this opposite color it's + + + align:start position:0% +color is the is this opposite color it's +going the other direction so the red one + + align:start position:0% +going the other direction so the red one + + + align:start position:0% +going the other direction so the red one +will turn green the yellow one will turn + + align:start position:0% +will turn green the yellow one will turn + + + align:start position:0% +will turn green the yellow one will turn +uh bluish the green one will turn + + align:start position:0% +uh bluish the green one will turn + + + align:start position:0% +uh bluish the green one will turn +reddish right so stare at the center + + align:start position:0% +reddish right so stare at the center + + + align:start position:0% +reddish right so stare at the center +boink + + align:start position:0% +boink + + + align:start position:0% +boink +yeah well it works + + align:start position:0% + + + + align:start position:0% + +there we go that's what's known as a + + align:start position:0% +there we go that's what's known as a + + + align:start position:0% +there we go that's what's known as a +negative after image + + align:start position:0% +negative after image + + + align:start position:0% +negative after image +um you can do you don't you don't need + + align:start position:0% +um you can do you don't you don't need + + + align:start position:0% +um you can do you don't you don't need +you you can just toggle back and forth + + align:start position:0% +you you can just toggle back and forth + + + align:start position:0% +you you can just toggle back and forth +if you look at the black dot on the on + + align:start position:0% +if you look at the black dot on the on + + + align:start position:0% +if you look at the black dot on the on +the why am I pointing at my computer + + align:start position:0% +the why am I pointing at my computer + + + align:start position:0% +the why am I pointing at my computer +that's useless + + align:start position:0% +that's useless + + + align:start position:0% +that's useless +um if you if you look at the black dot + + align:start position:0% +um if you if you look at the black dot + + + align:start position:0% +um if you if you look at the black dot +on the right and then flip it move your + + align:start position:0% +on the right and then flip it move your + + + align:start position:0% +on the right and then flip it move your +eyes to the left you'll see the colors + + align:start position:0% +eyes to the left you'll see the colors + + + align:start position:0% +eyes to the left you'll see the colors +show up in the left hand circles because + + align:start position:0% +show up in the left hand circles because + + + align:start position:0% +show up in the left hand circles because +that after image is essentially cooked + + align:start position:0% +that after image is essentially cooked + + + align:start position:0% +that after image is essentially cooked +onto your retina it's there in retinal + + align:start position:0% +onto your retina it's there in retinal + + + align:start position:0% +onto your retina it's there in retinal +coordinates and moves with your eyes + + align:start position:0% +coordinates and moves with your eyes + + + align:start position:0% +coordinates and moves with your eyes +right all sorts of good all right now + + align:start position:0% +right all sorts of good all right now + + + align:start position:0% +right all sorts of good all right now +let me illustrate to you that this is a + + align:start position:0% +let me illustrate to you that this is a + + + align:start position:0% +let me illustrate to you that this is a +ubiquitous phenomenon that shows up for + + align:start position:0% +ubiquitous phenomenon that shows up for + + + align:start position:0% +ubiquitous phenomenon that shows up for +basic phenomena all over the place + + align:start position:0% +basic phenomena all over the place + + + align:start position:0% +basic phenomena all over the place +by + + align:start position:0% +by + + + align:start position:0% +by +turning this back on is that going to be + + align:start position:0% +turning this back on is that going to be + + + align:start position:0% +turning this back on is that going to be +enough light for this yeah I'm sure all + + align:start position:0% +enough light for this yeah I'm sure all + + + align:start position:0% +enough light for this yeah I'm sure all +right + + align:start position:0% +right + + + align:start position:0% +right +so I won't show you the orientation one + + align:start position:0% +so I won't show you the orientation one + + + align:start position:0% +so I won't show you the orientation one +even though I managed to get a PhD + + align:start position:0% +even though I managed to get a PhD + + + align:start position:0% +even though I managed to get a PhD +studying it + + align:start position:0% +studying it + + + align:start position:0% +studying it +um but I'll show you the motion + + align:start position:0% +um but I'll show you the motion + + + align:start position:0% +um but I'll show you the motion +equivalent of it here's what you want to + + align:start position:0% +equivalent of it here's what you want to + + + align:start position:0% +equivalent of it here's what you want to +do let's go here's some good bright + + align:start position:0% +do let's go here's some good bright + + + align:start position:0% +do let's go here's some good bright +light + + align:start position:0% +light + + + align:start position:0% +light +um you'll still see it over there except + + align:start position:0% +um you'll still see it over there except + + + align:start position:0% +um you'll still see it over there except +for the guy who's asleep behind the + + align:start position:0% +for the guy who's asleep behind the + + + align:start position:0% +for the guy who's asleep behind the +pillar that's his tough luck + + align:start position:0% +pillar that's his tough luck + + + align:start position:0% +pillar that's his tough luck +um anyway uh don't all stare at him + + align:start position:0% +um anyway uh don't all stare at him + + + align:start position:0% +um anyway uh don't all stare at him +it'll just embarrass him + + align:start position:0% +it'll just embarrass him + + + align:start position:0% +it'll just embarrass him +um stare at this because it's much more + + align:start position:0% +um stare at this because it's much more + + + align:start position:0% +um stare at this because it's much more +interesting uh so look at this and we're + + align:start position:0% +interesting uh so look at this and we're + + + align:start position:0% +interesting uh so look at this and we're +doing the same game we're just taking + + align:start position:0% +doing the same game we're just taking + + + align:start position:0% +doing the same game we're just taking +the game and transferring from the color + + align:start position:0% +the game and transferring from the color + + + align:start position:0% +the game and transferring from the color +realm or the orientation realm down to + + align:start position:0% +realm or the orientation realm down to + + + align:start position:0% +realm or the orientation realm down to +the motion realm so this is Contracting + + align:start position:0% +the motion realm so this is Contracting + + + align:start position:0% +the motion realm so this is Contracting +right + + align:start position:0% +right + + + align:start position:0% +right +yeah yeah stare at the center that's + + align:start position:0% +yeah yeah stare at the center that's + + + align:start position:0% +yeah yeah stare at the center that's +important so stare at the center again + + align:start position:0% +important so stare at the center again + + + align:start position:0% +important so stare at the center again +think about 12 o'clock all the Contours + + align:start position:0% +think about 12 o'clock all the Contours + + + align:start position:0% +think about 12 o'clock all the Contours +are moving down you know that + + align:start position:0% +are moving down you know that + + + align:start position:0% +are moving down you know that +something's stationary because it's not + + align:start position:0% +something's stationary because it's not + + + align:start position:0% +something's stationary because it's not +moving up down left or right but at 12 + + align:start position:0% +moving up down left or right but at 12 + + + align:start position:0% +moving up down left or right but at 12 +o'clock I'm wearing out your down + + align:start position:0% +o'clock I'm wearing out your down + + + align:start position:0% +o'clock I'm wearing out your down +detectors and at six o'clock I'm wearing + + align:start position:0% +detectors and at six o'clock I'm wearing + + + align:start position:0% +detectors and at six o'clock I'm wearing +out your up detectors and so on the + + align:start position:0% +out your up detectors and so on the + + + align:start position:0% +out your up detectors and so on the +consequences of this evil Act of mine + + align:start position:0% +consequences of this evil Act of mine + + + align:start position:0% +consequences of this evil Act of mine +will be seen vividly if when I take it + + align:start position:0% +will be seen vividly if when I take it + + + align:start position:0% +will be seen vividly if when I take it +away what you do is to is look at my + + align:start position:0% +away what you do is to is look at my + + + align:start position:0% +away what you do is to is look at my +nose + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +of course + + align:start position:0% + + + + align:start position:0% + +of course what really worries me here is + + align:start position:0% +of course what really worries me here is + + + align:start position:0% +of course what really worries me here is +that I thought several people's uh + + align:start position:0% +that I thought several people's uh + + + align:start position:0% +that I thought several people's uh +several people's pupils got much larger + + align:start position:0% +several people's pupils got much larger + + + align:start position:0% +several people's pupils got much larger +which means they think I look better + + align:start position:0% +which means they think I look better + + + align:start position:0% +which means they think I look better +that way + + align:start position:0% +that way + + + align:start position:0% +that way +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +um + + align:start position:0% +um + + + align:start position:0% +um +okay now a word of warning + + align:start position:0% +okay now a word of warning + + + align:start position:0% +okay now a word of warning +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +two words of warning this is the best + + align:start position:0% +two words of warning this is the best + + + align:start position:0% +two words of warning this is the best +demo in the whole class it's all + + align:start position:0% +demo in the whole class it's all + + + align:start position:0% +demo in the whole class it's all +downhill from here + + align:start position:0% +downhill from here + + + align:start position:0% +downhill from here +the other word of warning is it's a very + + align:start position:0% +the other word of warning is it's a very + + + align:start position:0% +the other word of warning is it's a very +Salient demo but it's there for a + + align:start position:0% +Salient demo but it's there for a + + + align:start position:0% +Salient demo but it's there for a +purpose and + + align:start position:0% +purpose and + + + align:start position:0% +purpose and +um it's it's really lame on the midterm + + align:start position:0% +um it's it's really lame on the midterm + + + align:start position:0% +um it's it's really lame on the midterm +or the final when some motion at this is + + align:start position:0% +or the final when some motion at this is + + + align:start position:0% +or the final when some motion at this is +called a motion after effect when + + align:start position:0% +called a motion after effect when + + + align:start position:0% +called a motion after effect when +emotion after effect question shows up + + align:start position:0% +emotion after effect question shows up + + + align:start position:0% +emotion after effect question shows up +to say oh man it was cool man his head + + align:start position:0% +to say oh man it was cool man his head + + + align:start position:0% +to say oh man it was cool man his head +was shrinking and and stuff + + align:start position:0% +was shrinking and and stuff + + + align:start position:0% +was shrinking and and stuff +um because you don't get much points for + + align:start position:0% +um because you don't get much points for + + + align:start position:0% +um because you don't get much points for +that what you want to know is why this + + align:start position:0% +that what you want to know is why this + + + align:start position:0% +that what you want to know is why this +is actually uh interesting which I will + + align:start position:0% +is actually uh interesting which I will + + + align:start position:0% +is actually uh interesting which I will +reiterate by going the other direction + + align:start position:0% +reiterate by going the other direction + + + align:start position:0% +reiterate by going the other direction +since it seems a Pity not to right + + align:start position:0% +since it seems a Pity not to right + + + align:start position:0% +since it seems a Pity not to right +um okay so again the way you figure out + + align:start position:0% +um okay so again the way you figure out + + + align:start position:0% +um okay so again the way you figure out +that something is in this case + + align:start position:0% +that something is in this case + + + align:start position:0% +that something is in this case +stationary is by making a set of + + align:start position:0% +stationary is by making a set of + + + align:start position:0% +stationary is by making a set of +comparisons and I am using this clever + + align:start position:0% +comparisons and I am using this clever + + + align:start position:0% +comparisons and I am using this clever +little tool to systematically distort + + align:start position:0% +little tool to systematically distort + + + align:start position:0% +little tool to systematically distort +the comparisons that you're making by + + align:start position:0% +the comparisons that you're making by + + + align:start position:0% +the comparisons that you're making by +the way I'm also causing you to make one + + align:start position:0% +the way I'm also causing you to make one + + + align:start position:0% +the way I'm also causing you to make one +of these inferences that we'll talk + + align:start position:0% +of these inferences that we'll talk + + + align:start position:0% +of these inferences that we'll talk +about uh next week + + align:start position:0% +about uh next week + + + align:start position:0% +about uh next week +um by seeing all these various bits of + + align:start position:0% +um by seeing all these various bits of + + + align:start position:0% +um by seeing all these various bits of +odd motion you are making the conclusion + + align:start position:0% +odd motion you are making the conclusion + + + align:start position:0% +odd motion you are making the conclusion +that my head is drinking or growing or + + align:start position:0% +that my head is drinking or growing or + + + align:start position:0% +that my head is drinking or growing or +something like that so this is expanding + + align:start position:0% +something like that so this is expanding + + + align:start position:0% +something like that so this is expanding +right okay so this is the amazing + + align:start position:0% +right okay so this is the amazing + + + align:start position:0% +right okay so this is the amazing +Pinhead version ready + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +the original version of this by the way + + align:start position:0% +the original version of this by the way + + + align:start position:0% +the original version of this by the way +is known in the um + + align:start position:0% +is known in the um + + + align:start position:0% +is known in the um +this is known in the literature as + + align:start position:0% +this is known in the literature as + + + align:start position:0% +this is known in the literature as +sometimes it's the waterfall illusion + + align:start position:0% +sometimes it's the waterfall illusion + + + align:start position:0% +sometimes it's the waterfall illusion +um because it gets described multiple + + align:start position:0% +um because it gets described multiple + + + align:start position:0% +um because it gets described multiple +times in in the literature but one of + + align:start position:0% +times in in the literature but one of + + + align:start position:0% +times in in the literature but one of +them is uh by a Scotsman named Adams + + align:start position:0% +them is uh by a Scotsman named Adams + + + align:start position:0% +them is uh by a Scotsman named Adams +um who uh was staring at a waterfall and + + align:start position:0% +um who uh was staring at a waterfall and + + + align:start position:0% +um who uh was staring at a waterfall and +then noticed that the rocks on the side + + align:start position:0% +then noticed that the rocks on the side + + + align:start position:0% +then noticed that the rocks on the side +of the waterfall seem to be drifting up + + align:start position:0% +of the waterfall seem to be drifting up + + + align:start position:0% +of the waterfall seem to be drifting up +and this is a a known waterfall in a + + align:start position:0% +and this is a a known waterfall in a + + + align:start position:0% +and this is a a known waterfall in a +known spot in Scotland and there's a + + align:start position:0% +known spot in Scotland and there's a + + + align:start position:0% +known spot in Scotland and there's a +group of vision researchers who meet + + align:start position:0% +group of vision researchers who meet + + + align:start position:0% +group of vision researchers who meet +there every year and the entry + + align:start position:0% +there every year and the entry + + + align:start position:0% +there every year and the entry +requirement for joining this particular + + align:start position:0% +requirement for joining this particular + + + align:start position:0% +requirement for joining this particular +Elite group is a bottle of Scotch of a + + align:start position:0% +Elite group is a bottle of Scotch of a + + + align:start position:0% +Elite group is a bottle of Scotch of a +variety that they have not tried before + + align:start position:0% +variety that they have not tried before + + + align:start position:0% +variety that they have not tried before +which I think helps make the rocks move + + align:start position:0% +which I think helps make the rocks move + + + align:start position:0% +which I think helps make the rocks move +in all sorts of interesting ways + + align:start position:0% +in all sorts of interesting ways + + + align:start position:0% +in all sorts of interesting ways +um though they've never invited me so + + align:start position:0% +um though they've never invited me so + + + align:start position:0% +um though they've never invited me so +how would I know + + align:start position:0% +how would I know + + + align:start position:0% +how would I know +um all right let's see okay this is what + + align:start position:0% +um all right let's see okay this is what + + + align:start position:0% +um all right let's see okay this is what +I'm gonna do let me + + align:start position:0% +I'm gonna do let me + + + align:start position:0% +I'm gonna do let me +follow-up so that you've seen a a + + align:start position:0% +follow-up so that you've seen a a + + + align:start position:0% +follow-up so that you've seen a a +negative color after image you've seen a + + align:start position:0% +negative color after image you've seen a + + + align:start position:0% +negative color after image you've seen a +negative + + align:start position:0% +negative + + + align:start position:0% +negative +um uh motion after effect I've asserted + + align:start position:0% +um uh motion after effect I've asserted + + + align:start position:0% +um uh motion after effect I've asserted +that these exist in in orientation you + + align:start position:0% +that these exist in in orientation you + + + align:start position:0% +that these exist in in orientation you +can show this off and you know you + + align:start position:0% +can show this off and you know you + + + align:start position:0% +can show this off and you know you +showed somebody big stuff and then + + align:start position:0% +showed somebody big stuff and then + + + align:start position:0% +showed somebody big stuff and then +medium stuff looks small it's ubiquitous + + align:start position:0% +medium stuff looks small it's ubiquitous + + + align:start position:0% +medium stuff looks small it's ubiquitous +it shows up all over the place I want to + + align:start position:0% +it shows up all over the place I want to + + + align:start position:0% +it shows up all over the place I want to +show you one more version of this kind + + align:start position:0% +show you one more version of this kind + + + align:start position:0% +show you one more version of this kind +of effect + + align:start position:0% +of effect + + + align:start position:0% +of effect +um and that's going to take a certain + + align:start position:0% +um and that's going to take a certain + + + align:start position:0% +um and that's going to take a certain +amount of build up here + + align:start position:0% +amount of build up here + + + align:start position:0% +amount of build up here +so the first thing to do is say uh the + + align:start position:0% +so the first thing to do is say uh the + + + align:start position:0% +so the first thing to do is say uh the +vertical and horizontal stripes do they + + align:start position:0% +vertical and horizontal stripes do they + + + align:start position:0% +vertical and horizontal stripes do they +look different to you + + align:start position:0% +look different to you + + + align:start position:0% +look different to you +if they look different somebody raised + + align:start position:0% +if they look different somebody raised + + + align:start position:0% +if they look different somebody raised +their hand tell me what the difference + + align:start position:0% +their hand tell me what the difference + + + align:start position:0% +their hand tell me what the difference +is what's the difference + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +in their color or shading in some + + align:start position:0% +in their color or shading in some + + + align:start position:0% +in their color or shading in some +fashion yeah + + align:start position:0% +fashion yeah + + + align:start position:0% +fashion yeah +the word vertical ones look a little + + align:start position:0% +the word vertical ones look a little + + + align:start position:0% +the word vertical ones look a little +blur they do look a little blurry that + + align:start position:0% +blur they do look a little blurry that + + + align:start position:0% +blur they do look a little blurry that +may be the uh yeah + + align:start position:0% + + + + align:start position:0% + +now it's thicker we're not getting a lot + + align:start position:0% +now it's thicker we're not getting a lot + + + align:start position:0% +now it's thicker we're not getting a lot +of vivid color reports here + + align:start position:0% +of vivid color reports here + + + align:start position:0% +of vivid color reports here +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +brighter nobody knows what the word + + align:start position:0% +brighter nobody knows what the word + + + align:start position:0% +brighter nobody knows what the word +color means yeah okay last try + + align:start position:0% + + + + align:start position:0% + +okay look this makes the point just fine + + align:start position:0% +okay look this makes the point just fine + + + align:start position:0% +okay look this makes the point just fine +now never mind guys + + align:start position:0% +now never mind guys + + + align:start position:0% +now never mind guys +um there's no General consensus here I + + align:start position:0% +um there's no General consensus here I + + + align:start position:0% +um there's no General consensus here I +am about to produce a general consensus + + align:start position:0% +am about to produce a general consensus + + + align:start position:0% +am about to produce a general consensus +um that's that's not that that's sort of + + align:start position:0% +um that's that's not that that's sort of + + + align:start position:0% +um that's that's not that that's sort of +a that's that's the motivational part of + + align:start position:0% +a that's that's the motivational part of + + + align:start position:0% +a that's that's the motivational part of +today's lecture + + align:start position:0% +today's lecture + + + align:start position:0% +today's lecture +um no actually what it is is what I have + + align:start position:0% +um no actually what it is is what I have + + + align:start position:0% +um no actually what it is is what I have +to do now is + + align:start position:0% +to do now is + + + align:start position:0% +to do now is +um for the next few minutes what you + + align:start position:0% +um for the next few minutes what you + + + align:start position:0% +um for the next few minutes what you +want to do is keep your head upright you + + align:start position:0% +want to do is keep your head upright you + + + align:start position:0% +want to do is keep your head upright you +don't have to stare at any one spot well + + align:start position:0% +don't have to stare at any one spot well + + + align:start position:0% +don't have to stare at any one spot well +I don't catch you don't even have to + + align:start position:0% +I don't catch you don't even have to + + + align:start position:0% +I don't catch you don't even have to +keep your header upright just keep it in + + align:start position:0% +keep your header upright just keep it in + + + align:start position:0% +keep your header upright just keep it in +the same orientation if you flop all + + align:start position:0% +the same orientation if you flop all + + + align:start position:0% +the same orientation if you flop all +over the place and and fall asleep + + align:start position:0% +over the place and and fall asleep + + + align:start position:0% +over the place and and fall asleep +nothing good happens + + align:start position:0% +nothing good happens + + + align:start position:0% +nothing good happens +um so you're going to look at these + + align:start position:0% +um so you're going to look at these + + + align:start position:0% +um so you're going to look at these +green vertical lines and these red + + align:start position:0% +green vertical lines and these red + + + align:start position:0% +green vertical lines and these red +horizontal lines and see I also have a + + align:start position:0% +horizontal lines and see I also have a + + + align:start position:0% +horizontal lines and see I also have a +go back one just so that I remember + + align:start position:0% +go back one just so that I remember + + + align:start position:0% +go back one just so that I remember +which way I have to go + + align:start position:0% +which way I have to go + + + align:start position:0% +which way I have to go +all I need to do here is toggle back and + + align:start position:0% +all I need to do here is toggle back and + + + align:start position:0% +all I need to do here is toggle back and +forth between them now you can see the + + align:start position:0% +forth between them now you can see the + + + align:start position:0% +forth between them now you can see the +negative after image here if you stare + + align:start position:0% +negative after image here if you stare + + + align:start position:0% +negative after image here if you stare +at this green oh I should have done it + + align:start position:0% +at this green oh I should have done it + + + align:start position:0% +at this green oh I should have done it +quickly before so stare at this green + + align:start position:0% +quickly before so stare at this green + + + align:start position:0% +quickly before so stare at this green +thing for a while do you see they get a + + align:start position:0% +thing for a while do you see they get a + + + align:start position:0% +thing for a while do you see they get a +nice purpley red thing + + align:start position:0% +nice purpley red thing + + + align:start position:0% +nice purpley red thing +okay well and so that's just the + + align:start position:0% +okay well and so that's just the + + + align:start position:0% +okay well and so that's just the +negative after image but we're not that + + align:start position:0% +negative after image but we're not that + + + align:start position:0% +negative after image but we're not that +interest whoops we're not that + + align:start position:0% +interest whoops we're not that + + + align:start position:0% +interest whoops we're not that +interested in the negative after image + + align:start position:0% +interested in the negative after image + + + align:start position:0% +interested in the negative after image +anymore + + align:start position:0% +anymore + + + align:start position:0% +anymore +um actually we are there's an ex aspect + + align:start position:0% +um actually we are there's an ex aspect + + + align:start position:0% +um actually we are there's an ex aspect +of the negative after image that's + + align:start position:0% +of the negative after image that's + + + align:start position:0% +of the negative after image that's +really cool here + + align:start position:0% +really cool here + + + align:start position:0% +really cool here +which you may start to notice + + align:start position:0% +which you may start to notice + + + align:start position:0% +which you may start to notice +shortly + + align:start position:0% +shortly + + + align:start position:0% +shortly +during the blank period + + align:start position:0% +during the blank period + + + align:start position:0% +during the blank period +shout out the orientation that you see + + align:start position:0% + + + + align:start position:0% + +that's a little weird + + align:start position:0% +that's a little weird + + + align:start position:0% +that's a little weird +wouldn't you think + + align:start position:0% +wouldn't you think + + + align:start position:0% +wouldn't you think +now that's a little weird because if you + + align:start position:0% +now that's a little weird because if you + + + align:start position:0% +now that's a little weird because if you +stare at + + align:start position:0% +stare at + + + align:start position:0% +stare at +um you know these horizontal stripes in + + align:start position:0% +um you know these horizontal stripes in + + + align:start position:0% +um you know these horizontal stripes in +fact I should be able to get you back to + + align:start position:0% +fact I should be able to get you back to + + + align:start position:0% +fact I should be able to get you back to +seeing a horizontal so stare at these + + align:start position:0% +seeing a horizontal so stare at these + + + align:start position:0% +seeing a horizontal so stare at these +don't fixate don't move your eyes around + + align:start position:0% +don't fixate don't move your eyes around + + + align:start position:0% +don't fixate don't move your eyes around +and we'll just stare at that for a + + align:start position:0% +and we'll just stare at that for a + + + align:start position:0% +and we'll just stare at that for a +minute or so + + align:start position:0% + + + + align:start position:0% + +and then + + align:start position:0% + + + + align:start position:0% + +long enough yeah + + align:start position:0% +long enough yeah + + + align:start position:0% +long enough yeah +does it look horizontal still looks + + align:start position:0% +does it look horizontal still looks + + + align:start position:0% +does it look horizontal still looks +vertical oh boy well + + align:start position:0% + + + + align:start position:0% + +here is the uh + + align:start position:0% +here is the uh + + + align:start position:0% +here is the uh +here here's the get rich quick part of + + align:start position:0% +here here's the get rich quick part of + + + align:start position:0% +here here's the get rich quick part of +this lecture uh assuming that you're + + align:start position:0% +this lecture uh assuming that you're + + + align:start position:0% +this lecture uh assuming that you're +unscrupulous + + align:start position:0% +unscrupulous + + + align:start position:0% +unscrupulous +you can use this to make your fortune + + align:start position:0% +you can use this to make your fortune + + + align:start position:0% +you can use this to make your fortune +claiming that you can teach people to be + + align:start position:0% +claiming that you can teach people to be + + + align:start position:0% +claiming that you can teach people to be +psychic + + align:start position:0% +psychic + + + align:start position:0% +psychic +right what's the next orientation I'm + + align:start position:0% +right what's the next orientation I'm + + + align:start position:0% +right what's the next orientation I'm +going to show + + align:start position:0% +going to show + + + align:start position:0% +going to show +what's the next orientation I'm going to + + align:start position:0% +what's the next orientation I'm going to + + + align:start position:0% +what's the next orientation I'm going to +show + + align:start position:0% +show + + + align:start position:0% +show +um + + align:start position:0% +um + + + align:start position:0% +um +if you can make your fortune out of that + + align:start position:0% +if you can make your fortune out of that + + + align:start position:0% +if you can make your fortune out of that +uh well just send me 10 + + align:start position:0% +uh well just send me 10 + + + align:start position:0% +uh well just send me 10 +um but + + align:start position:0% +um but + + + align:start position:0% +um but +what's really going on here + + align:start position:0% +what's really going on here + + + align:start position:0% +what's really going on here +um that what what this is actually + + align:start position:0% +um that what what this is actually + + + align:start position:0% +um that what what this is actually +illustrating this aspect of it is + + align:start position:0% +illustrating this aspect of it is + + + align:start position:0% +illustrating this aspect of it is +illustrating is that you're seeing with + + align:start position:0% +illustrating is that you're seeing with + + + align:start position:0% +illustrating is that you're seeing with +your whole visual system not with you + + align:start position:0% +your whole visual system not with you + + + align:start position:0% +your whole visual system not with you +know your retina all by itself or + + align:start position:0% +know your retina all by itself or + + + align:start position:0% +know your retina all by itself or +something like that so + + align:start position:0% +something like that so + + + align:start position:0% +something like that so +um each time you look at say the red + + align:start position:0% +um each time you look at say the red + + + align:start position:0% +um each time you look at say the red +horizontal you're building up a green + + align:start position:0% +horizontal you're building up a green + + + align:start position:0% +horizontal you're building up a green +horizontal negative after image on your + + align:start position:0% +horizontal negative after image on your + + + align:start position:0% +horizontal negative after image on your +retina right + + align:start position:0% +retina right + + + align:start position:0% +retina right +and this is building up a red vertical + + align:start position:0% +and this is building up a red vertical + + + align:start position:0% +and this is building up a red vertical +kind of after image on your retina and + + align:start position:0% +kind of after image on your retina and + + + align:start position:0% +kind of after image on your retina and +if you go back and forth + + align:start position:0% +if you go back and forth + + + align:start position:0% +if you go back and forth +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +you know this is fun + + align:start position:0% +you know this is fun + + + align:start position:0% +you know this is fun +um you build up a sort of a plaid so + + align:start position:0% +um you build up a sort of a plaid so + + + align:start position:0% +um you build up a sort of a plaid so +think about your retina as having a a + + align:start position:0% +think about your retina as having a a + + + align:start position:0% +think about your retina as having a a +plaid on it now you don't see it here + + align:start position:0% +plaid on it now you don't see it here + + + align:start position:0% +plaid on it now you don't see it here +but the Plaid is is is is + + align:start position:0% +but the Plaid is is is is + + + align:start position:0% +but the Plaid is is is is +when you're looking at a blank screen + + align:start position:0% +when you're looking at a blank screen + + + align:start position:0% +when you're looking at a blank screen +it's just that plaid that's getting + + align:start position:0% +it's just that plaid that's getting + + + align:start position:0% +it's just that plaid that's getting +shipped up to your brain basically okay + + align:start position:0% +shipped up to your brain basically okay + + + align:start position:0% +shipped up to your brain basically okay +well what else is happening well when + + align:start position:0% +well what else is happening well when + + + align:start position:0% +well what else is happening well when +you're staring at this green vertical + + align:start position:0% +you're staring at this green vertical + + + align:start position:0% +you're staring at this green vertical +thing up in your brain the cells that + + align:start position:0% +thing up in your brain the cells that + + + align:start position:0% +thing up in your brain the cells that +are interested in vertical are saying + + align:start position:0% +are interested in vertical are saying + + + align:start position:0% +are interested in vertical are saying +we're getting tired go to the blank part + + align:start position:0% +we're getting tired go to the blank part + + + align:start position:0% +we're getting tired go to the blank part +tired vertical guys and more awake the + + align:start position:0% +tired vertical guys and more awake the + + + align:start position:0% +tired vertical guys and more awake the +horizontal guys are looking at this weak + + align:start position:0% +horizontal guys are looking at this weak + + + align:start position:0% +horizontal guys are looking at this weak +plan and they're only seeing the + + align:start position:0% +plan and they're only seeing the + + + align:start position:0% +plan and they're only seeing the +horizontal part now you look at the + + align:start position:0% +horizontal part now you look at the + + + align:start position:0% +horizontal part now you look at the +horizontal the horizontal guys get tired + + align:start position:0% +horizontal the horizontal guys get tired + + + align:start position:0% +horizontal the horizontal guys get tired +out oh we can only see the vertical and + + align:start position:0% +out oh we can only see the vertical and + + + align:start position:0% +out oh we can only see the vertical and +so on + + align:start position:0% +so on + + + align:start position:0% +so on +let's see oh haven't been that you may + + align:start position:0% +let's see oh haven't been that you may + + + align:start position:0% +let's see oh haven't been that you may +ask + + align:start position:0% +ask + + + align:start position:0% +ask +isn't it about time we saw something + + align:start position:0% +isn't it about time we saw something + + + align:start position:0% +isn't it about time we saw something +interesting here + + align:start position:0% +interesting here + + + align:start position:0% +interesting here +the answer is undoubtedly so but this + + align:start position:0% +the answer is undoubtedly so but this + + + align:start position:0% +the answer is undoubtedly so but this +particular effect takes a few minutes to + + align:start position:0% +particular effect takes a few minutes to + + + align:start position:0% +particular effect takes a few minutes to +build up + + align:start position:0% +build up + + + align:start position:0% +build up +um and so you got to keep looking at + + align:start position:0% +um and so you got to keep looking at + + + align:start position:0% +um and so you got to keep looking at +this and oh you've got to ask yourself + + align:start position:0% +this and oh you've got to ask yourself + + + align:start position:0% +this and oh you've got to ask yourself +what the effect + + align:start position:0% + + + + align:start position:0% + +ought to be what what this this is what + + align:start position:0% +ought to be what what this this is what + + + align:start position:0% +ought to be what what this this is what +I'm building up here is an effect called + + align:start position:0% +I'm building up here is an effect called + + + align:start position:0% +I'm building up here is an effect called +the McCullough effect named after + + align:start position:0% +the McCullough effect named after + + + align:start position:0% +the McCullough effect named after +Celeste McCullough who unlike most + + align:start position:0% +Celeste McCullough who unlike most + + + align:start position:0% +Celeste McCullough who unlike most +people + + align:start position:0% +people + + + align:start position:0% +people +um who discover visual effects was + + align:start position:0% +um who discover visual effects was + + + align:start position:0% +um who discover visual effects was +actually looking for this + + align:start position:0% +actually looking for this + + + align:start position:0% +actually looking for this +she knew what she was looking for and + + align:start position:0% +she knew what she was looking for and + + + align:start position:0% +she knew what she was looking for and +she knew what she could find now I + + align:start position:0% +she knew what she could find now I + + + align:start position:0% +she knew what she could find now I +already showed you that the the pattern + + align:start position:0% +already showed you that the the pattern + + + align:start position:0% +already showed you that the the pattern +you're going to look at again right it + + align:start position:0% +you're going to look at again right it + + + align:start position:0% +you're going to look at again right it +was that black and white pattern of + + align:start position:0% +was that black and white pattern of + + + align:start position:0% +was that black and white pattern of +vertical and horizontal lines + + align:start position:0% +vertical and horizontal lines + + + align:start position:0% +vertical and horizontal lines +um what do you think the vertical lines + + align:start position:0% +um what do you think the vertical lines + + + align:start position:0% +um what do you think the vertical lines +should look like when we're done + + align:start position:0% +should look like when we're done + + + align:start position:0% +should look like when we're done +they should look kind of reddish maybe + + align:start position:0% +they should look kind of reddish maybe + + + align:start position:0% +they should look kind of reddish maybe +and the horizontal should look green + + align:start position:0% +and the horizontal should look green + + + align:start position:0% +and the horizontal should look green +let's see well we might have done this + + align:start position:0% +let's see well we might have done this + + + align:start position:0% +let's see well we might have done this +long enough this is one of these things + + align:start position:0% +long enough this is one of these things + + + align:start position:0% +long enough this is one of these things +where if I do it long enough I can hit + + align:start position:0% +where if I do it long enough I can hit + + + align:start position:0% +where if I do it long enough I can hit +absolutely everybody and if I quit + + align:start position:0% +absolutely everybody and if I quit + + + align:start position:0% +absolutely everybody and if I quit +too soon not everybody will see the + + align:start position:0% +too soon not everybody will see the + + + align:start position:0% +too soon not everybody will see the +effect go for it all right + + align:start position:0% + + + + align:start position:0% + +so oh now it's 308. all right here we go + + align:start position:0% +so oh now it's 308. all right here we go + + + align:start position:0% +so oh now it's 308. all right here we go +so close your eyes + + align:start position:0% +so close your eyes + + + align:start position:0% +so close your eyes +because that will let me get to the + + align:start position:0% +because that will let me get to the + + + align:start position:0% +because that will let me get to the +right slide but it will also let you + + align:start position:0% +right slide but it will also let you + + + align:start position:0% +right slide but it will also let you +perhaps see that checkerboard floating + + align:start position:0% +perhaps see that checkerboard floating + + + align:start position:0% +perhaps see that checkerboard floating +there in the dark + + align:start position:0% +there in the dark + + + align:start position:0% +there in the dark +murmur if you can see a checkerboard + + align:start position:0% +murmur if you can see a checkerboard + + + align:start position:0% +murmur if you can see a checkerboard +floating in the dark okay good that's + + align:start position:0% +floating in the dark okay good that's + + + align:start position:0% +floating in the dark okay good that's +that's the negative after image thing + + align:start position:0% +that's the negative after image thing + + + align:start position:0% +that's the negative after image thing +okay now take a look at at this test + + align:start position:0% +okay now take a look at at this test + + + align:start position:0% +okay now take a look at at this test +pattern again + + align:start position:0% + + + + align:start position:0% + +how many people think that the vertical + + align:start position:0% +how many people think that the vertical + + + align:start position:0% +how many people think that the vertical +and horizontal look different now in + + align:start position:0% +and horizontal look different now in + + + align:start position:0% +and horizontal look different now in +terms of their color + + align:start position:0% +terms of their color + + + align:start position:0% +terms of their color +how many people think it might look a + + align:start position:0% +how many people think it might look a + + + align:start position:0% +how many people think it might look a +little sort of maybe kind of different + + align:start position:0% +little sort of maybe kind of different + + + align:start position:0% +little sort of maybe kind of different +but it's not exactly biting me on the + + align:start position:0% +but it's not exactly biting me on the + + + align:start position:0% +but it's not exactly biting me on the +posterior + + align:start position:0% +posterior + + + align:start position:0% +posterior +all right that's a better test + + align:start position:0% +all right that's a better test + + + align:start position:0% +all right that's a better test +um now the way to find out whether + + align:start position:0% +um now the way to find out whether + + + align:start position:0% +um now the way to find out whether +you've actually got the right effect is + + align:start position:0% +you've actually got the right effect is + + + align:start position:0% +you've actually got the right effect is +without knocking out your neighbor tilt + + align:start position:0% +without knocking out your neighbor tilt + + + align:start position:0% +without knocking out your neighbor tilt +your head 90 degrees + + align:start position:0% + + + + align:start position:0% + +see that's cooler + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +um I'll say a word more about this but I + + align:start position:0% +um I'll say a word more about this but I + + + align:start position:0% +um I'll say a word more about this but I +won't say a word more about this until + + align:start position:0% +won't say a word more about this until + + + align:start position:0% +won't say a word more about this until +until you've had a chance to get up and + + align:start position:0% +until you've had a chance to get up and + + + align:start position:0% +until you've had a chance to get up and +stretch for a second look at that isn't + + align:start position:0% +stretch for a second look at that isn't + + + align:start position:0% +stretch for a second look at that isn't +that nice we'll leave him up there too + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% +all right + + + align:start position:0% +all right +foreign + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +foreign + + align:start position:0% +foreign + + + align:start position:0% +foreign +[Applause] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +how many people + + align:start position:0% + + + + align:start position:0% + +how many people when they look at these + + align:start position:0% +how many people when they look at these + + + align:start position:0% +how many people when they look at these +dots + + align:start position:0% +dots + + + align:start position:0% +dots +still see reasonably compelling colors + + align:start position:0% +still see reasonably compelling colors + + + align:start position:0% +still see reasonably compelling colors +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +not many how many people when they look + + align:start position:0% +not many how many people when they look + + + align:start position:0% +not many how many people when they look +at my head still see it shrinking + + align:start position:0% +at my head still see it shrinking + + + align:start position:0% +at my head still see it shrinking +yeah except for the weird people yeah + + align:start position:0% +yeah except for the weird people yeah + + + align:start position:0% +yeah except for the weird people yeah +yeah yeah yeah right + + align:start position:0% +yeah yeah yeah right + + + align:start position:0% +yeah yeah yeah right +that that's because these are well + + align:start position:0% +that that's because these are well + + + align:start position:0% +that that's because these are well +um + + align:start position:0% +um + + + align:start position:0% +um +your visual system is continuously + + align:start position:0% +your visual system is continuously + + + align:start position:0% +your visual system is continuously +regenerating itself right you know you + + align:start position:0% +regenerating itself right you know you + + + align:start position:0% +regenerating itself right you know you +stare at you know go stare at the red + + align:start position:0% +stare at you know go stare at the red + + + align:start position:0% +stare at you know go stare at the red +thing you'll wear out in a sense the red + + align:start position:0% +thing you'll wear out in a sense the red + + + align:start position:0% +thing you'll wear out in a sense the red +detecting chunk of your visual system + + align:start position:0% +detecting chunk of your visual system + + + align:start position:0% +detecting chunk of your visual system +and then if you flip your eyes over you + + align:start position:0% +and then if you flip your eyes over you + + + align:start position:0% +and then if you flip your eyes over you +find out that you see the white thing is + + align:start position:0% +find out that you see the white thing is + + + align:start position:0% +find out that you see the white thing is +green + + align:start position:0% +green + + + align:start position:0% +green +um but then you recover from it right + + align:start position:0% +um but then you recover from it right + + + align:start position:0% +um but then you recover from it right +good + + align:start position:0% +good + + + align:start position:0% +good +how many people still see this effect + + align:start position:0% + + + + align:start position:0% + +yeah I've tilt your head just to make + + align:start position:0% +yeah I've tilt your head just to make + + + align:start position:0% +yeah I've tilt your head just to make +sure if you think it's there a little + + align:start position:0% +sure if you think it's there a little + + + align:start position:0% +sure if you think it's there a little +weak today we probably should have gone + + align:start position:0% +weak today we probably should have gone + + + align:start position:0% +weak today we probably should have gone +a little bit longer + + align:start position:0% +a little bit longer + + + align:start position:0% +a little bit longer +um those of you who are seeing it and + + align:start position:0% +um those of you who are seeing it and + + + align:start position:0% +um those of you who are seeing it and +perhaps even those of you who are not uh + + align:start position:0% +perhaps even those of you who are not uh + + + align:start position:0% +perhaps even those of you who are not uh +did I did I put a test pattern on the + + align:start position:0% +did I did I put a test pattern on the + + + align:start position:0% +did I did I put a test pattern on the +handout I forget + + align:start position:0% +handout I forget + + + align:start position:0% +handout I forget +no okay I'll just bring the PowerPoint + + align:start position:0% +no okay I'll just bring the PowerPoint + + + align:start position:0% +no okay I'll just bring the PowerPoint +back next week + + align:start position:0% +back next week + + + align:start position:0% +back next week +um not only are you still seeing this + + align:start position:0% +um not only are you still seeing this + + + align:start position:0% +um not only are you still seeing this +some minutes afterwards + + align:start position:0% +some minutes afterwards + + + align:start position:0% +some minutes afterwards +um but particularly if I don't show you + + align:start position:0% +um but particularly if I don't show you + + + align:start position:0% +um but particularly if I don't show you +the test pattern a lot + + align:start position:0% +the test pattern a lot + + + align:start position:0% +the test pattern a lot +um you may see it for days + + align:start position:0% +um you may see it for days + + + align:start position:0% +um you may see it for days +and weeks + + align:start position:0% +and weeks + + + align:start position:0% +and weeks +the longest report in the literature for + + align:start position:0% +the longest report in the literature for + + + align:start position:0% +the longest report in the literature for +the McCullough effect is three months + + align:start position:0% +the McCullough effect is three months + + + align:start position:0% +the McCullough effect is three months +the only reason it's only three months + + align:start position:0% +the only reason it's only three months + + + align:start position:0% +the only reason it's only three months +uh is because at that point the + + align:start position:0% +uh is because at that point the + + + align:start position:0% +uh is because at that point the +undergraduates who of course were the + + align:start position:0% +undergraduates who of course were the + + + align:start position:0% +undergraduates who of course were the +subjects went away on vacation + + align:start position:0% +subjects went away on vacation + + + align:start position:0% +subjects went away on vacation +and the experiment ended the evidence + + align:start position:0% +and the experiment ended the evidence + + + align:start position:0% +and the experiment ended the evidence +suggests that if we locked you in the + + align:start position:0% +suggests that if we locked you in the + + + align:start position:0% +suggests that if we locked you in the +dark + + align:start position:0% +dark + + + align:start position:0% +dark +that the McCullough effect would last + + align:start position:0% +that the McCullough effect would last + + + align:start position:0% +that the McCullough effect would last +forever + + align:start position:0% +forever + + + align:start position:0% +forever +um we won't lock you in the dark and uh + + align:start position:0% +um we won't lock you in the dark and uh + + + align:start position:0% +um we won't lock you in the dark and uh +and and and and you know those of you I + + align:start position:0% +and and and and you know those of you I + + + align:start position:0% +and and and and you know those of you I +teach this up at Harvard where there are + + align:start position:0% +teach this up at Harvard where there are + + + align:start position:0% +teach this up at Harvard where there are +many more pre-law students and and the + + align:start position:0% +many more pre-law students and and the + + + align:start position:0% +many more pre-law students and and the +immediate reaction to this news is half + + align:start position:0% +immediate reaction to this news is half + + + align:start position:0% +immediate reaction to this news is half +of them consider filing suit + + align:start position:0% +of them consider filing suit + + + align:start position:0% +of them consider filing suit +um + + align:start position:0% +um + + + align:start position:0% +um +but either this will not in fact ruin + + align:start position:0% +but either this will not in fact ruin + + + align:start position:0% +but either this will not in fact ruin +your life in any fashion in fact it'll + + align:start position:0% +your life in any fashion in fact it'll + + + align:start position:0% +your life in any fashion in fact it'll +only be noticeable you know if you + + align:start position:0% +only be noticeable you know if you + + + align:start position:0% +only be noticeable you know if you +happen to end up looking at a test + + align:start position:0% +happen to end up looking at a test + + + align:start position:0% +happen to end up looking at a test +pattern like this or perhaps serving + + align:start position:0% +pattern like this or perhaps serving + + + align:start position:0% +pattern like this or perhaps serving +time + + align:start position:0% +time + + + align:start position:0% +time +um in the near future but + + align:start position:0% +um in the near future but + + + align:start position:0% +um in the near future but +this was something that McCullough was + + align:start position:0% +this was something that McCullough was + + + align:start position:0% +this was something that McCullough was +not expecting McCullough thought that + + align:start position:0% +not expecting McCullough thought that + + + align:start position:0% +not expecting McCullough thought that +what she had done here was okay you've + + align:start position:0% +what she had done here was okay you've + + + align:start position:0% +what she had done here was okay you've +got + + align:start position:0% +got + + + align:start position:0% +got +um you know you can fatigue color you + + align:start position:0% +um you know you can fatigue color you + + + align:start position:0% +um you know you can fatigue color you +can fatigue orientation well I'll + + align:start position:0% +can fatigue orientation well I'll + + + align:start position:0% +can fatigue orientation well I'll +fatigue the cells in the brain and there + + align:start position:0% +fatigue the cells in the brain and there + + + align:start position:0% +fatigue the cells in the brain and there +are cells in the brain that are + + align:start position:0% +are cells in the brain that are + + + align:start position:0% +are cells in the brain that are +interested in red vertical lines they'll + + align:start position:0% +interested in red vertical lines they'll + + + align:start position:0% +interested in red vertical lines they'll +get tired I'll see white vertical as + + align:start position:0% +get tired I'll see white vertical as + + + align:start position:0% +get tired I'll see white vertical as +green they'll recover I'll see white + + align:start position:0% +green they'll recover I'll see white + + + align:start position:0% +green they'll recover I'll see white +vertical is white but what happened was + + align:start position:0% +vertical is white but what happened was + + + align:start position:0% +vertical is white but what happened was +you looked at red vertical lines for a + + align:start position:0% +you looked at red vertical lines for a + + + align:start position:0% +you looked at red vertical lines for a +while white vertical looked green and + + align:start position:0% +while white vertical looked green and + + + align:start position:0% +while white vertical looked green and +white vertical looked green fur like a + + align:start position:0% +white vertical looked green fur like a + + + align:start position:0% +white vertical looked green fur like a +really really long time thereafter + + align:start position:0% +really really long time thereafter + + + align:start position:0% +really really long time thereafter +what seems to be going on here is + + align:start position:0% +what seems to be going on here is + + + align:start position:0% +what seems to be going on here is +something like this + + align:start position:0% +something like this + + + align:start position:0% +something like this +um + + align:start position:0% + + + + align:start position:0% + +let's suppose + + align:start position:0% +let's suppose + + + align:start position:0% +let's suppose +you know I've been lecturing from this + + align:start position:0% +you know I've been lecturing from this + + + align:start position:0% +you know I've been lecturing from this +side of the class almost all day today + + align:start position:0% +side of the class almost all day today + + + align:start position:0% +side of the class almost all day today +I'm worried that somebody's busy + + align:start position:0% +I'm worried that somebody's busy + + + align:start position:0% +I'm worried that somebody's busy +reinforcing me to stand over here + + align:start position:0% +reinforcing me to stand over here + + + align:start position:0% +reinforcing me to stand over here +let's see actually it's them + + align:start position:0% +let's see actually it's them + + + align:start position:0% +let's see actually it's them +they won't no never mind + + align:start position:0% +they won't no never mind + + + align:start position:0% +they won't no never mind +um so the uh um suppose that the way you + + align:start position:0% +um so the uh um suppose that the way you + + + align:start position:0% +um so the uh um suppose that the way you +decide that something is white vertical + + align:start position:0% +decide that something is white vertical + + + align:start position:0% +decide that something is white vertical +is by looking at the balance + + align:start position:0% +is by looking at the balance + + + align:start position:0% +is by looking at the balance +of well here let's draw it this way + + align:start position:0% +of well here let's draw it this way + + + align:start position:0% +of well here let's draw it this way +um + + align:start position:0% +um + + + align:start position:0% +um +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +you know you've got red vertical input + + align:start position:0% +you know you've got red vertical input + + + align:start position:0% +you know you've got red vertical input +and you've got green vertical input + + align:start position:0% +and you've got green vertical input + + + align:start position:0% +and you've got green vertical input +and there beings like you know some well + + align:start position:0% +and there beings like you know some well + + + align:start position:0% +and there beings like you know some well +let's put a little dial here + + align:start position:0% + + + + align:start position:0% + +equal you decide that looks white so I + + align:start position:0% +equal you decide that looks white so I + + + align:start position:0% +equal you decide that looks white so I +show you red vertical for a while and + + align:start position:0% +show you red vertical for a while and + + + align:start position:0% +show you red vertical for a while and +this thing gets weak and cruddy and now + + align:start position:0% +this thing gets weak and cruddy and now + + + align:start position:0% +this thing gets weak and cruddy and now +something that should be producing equal + + align:start position:0% +something that should be producing equal + + + align:start position:0% +something that should be producing equal +input gets more from there and and and + + align:start position:0% +input gets more from there and and and + + + align:start position:0% +input gets more from there and and and +it ends up looking a little green all + + align:start position:0% +it ends up looking a little green all + + + align:start position:0% +it ends up looking a little green all +right that's fine + + align:start position:0% +right that's fine + + + align:start position:0% +right that's fine +what happens + + align:start position:0% + + + + align:start position:0% + +if this cell gets sick it's not going to + + align:start position:0% +if this cell gets sick it's not going to + + + align:start position:0% +if this cell gets sick it's not going to +be one cell but you know suppose that + + align:start position:0% +be one cell but you know suppose that + + + align:start position:0% +be one cell but you know suppose that +this process gets weak in some fashion + + align:start position:0% +this process gets weak in some fashion + + + align:start position:0% +this process gets weak in some fashion +not because you were looking at uh at at + + align:start position:0% +not because you were looking at uh at at + + + align:start position:0% +not because you were looking at uh at at +some stimulus but because + + align:start position:0% +some stimulus but because + + + align:start position:0% +some stimulus but because +um yeah yeah you went out and and + + align:start position:0% +um yeah yeah you went out and and + + + align:start position:0% +um yeah yeah you went out and and +um + + align:start position:0% +um + + + align:start position:0% +um +uh ate the mushroom that you shouldn't + + align:start position:0% +uh ate the mushroom that you shouldn't + + + align:start position:0% +uh ate the mushroom that you shouldn't +have eaten or whatever and and this cell + + align:start position:0% +have eaten or whatever and and this cell + + + align:start position:0% +have eaten or whatever and and this cell +just you know took a hit and so now this + + align:start position:0% +just you know took a hit and so now this + + + align:start position:0% +just you know took a hit and so now this +is kind of a cruddy cell + + align:start position:0% + + + + align:start position:0% + +um well there are a couple of + + align:start position:0% +um well there are a couple of + + + align:start position:0% +um well there are a couple of +possibilities one of them is that for + + align:start position:0% +possibilities one of them is that for + + + align:start position:0% +possibilities one of them is that for +the rest of time you're going to end up + + align:start position:0% +the rest of time you're going to end up + + + align:start position:0% +the rest of time you're going to end up +seeing white things as looking green + + align:start position:0% +seeing white things as looking green + + + align:start position:0% +seeing white things as looking green +uh that's not gonna be good + + align:start position:0% +uh that's not gonna be good + + + align:start position:0% +uh that's not gonna be good +right you don't you don't want that to + + align:start position:0% +right you don't you don't want that to + + + align:start position:0% +right you don't you don't want that to +uh you don't want that to happen so if + + align:start position:0% +uh you don't want that to happen so if + + + align:start position:0% +uh you don't want that to happen so if +you decided that you had that that this + + align:start position:0% +you decided that you had that that this + + + align:start position:0% +you decided that you had that that this +was the situation + + align:start position:0% +was the situation + + + align:start position:0% +was the situation +what you would want to do is + + align:start position:0% +what you would want to do is + + + align:start position:0% +what you would want to do is +change the game + + align:start position:0% +change the game + + + align:start position:0% +change the game +on here so if this was previously just + + align:start position:0% +on here so if this was previously just + + + align:start position:0% +on here so if this was previously just +you know equal gain let's crank this up + + align:start position:0% +you know equal gain let's crank this up + + + align:start position:0% +you know equal gain let's crank this up +a little bit so that we can drag that + + align:start position:0% +a little bit so that we can drag that + + + align:start position:0% +a little bit so that we can drag that +back up to being + + align:start position:0% +back up to being + + + align:start position:0% +back up to being +equal + + align:start position:0% +equal + + + align:start position:0% +equal +that sounds okay that seems like a + + align:start position:0% +that sounds okay that seems like a + + + align:start position:0% +that sounds okay that seems like a +clever enough thing to do but how are + + align:start position:0% +clever enough thing to do but how are + + + align:start position:0% +clever enough thing to do but how are +you going to do that + + align:start position:0% +you going to do that + + + align:start position:0% +you going to do that +how are you going to figure out + + align:start position:0% +how are you going to figure out + + + align:start position:0% +how are you going to figure out +that um that you're broken + + align:start position:0% +that um that you're broken + + + align:start position:0% +that um that you're broken +how would you know that your visual + + align:start position:0% +how would you know that your visual + + + align:start position:0% +how would you know that your visual +system was not reporting the truth to + + align:start position:0% +system was not reporting the truth to + + + align:start position:0% +system was not reporting the truth to +you well I mean one way would be you're + + align:start position:0% +you well I mean one way would be you're + + + align:start position:0% +you well I mean one way would be you're +saying hey that looks white to me and + + align:start position:0% +saying hey that looks white to me and + + + align:start position:0% +saying hey that looks white to me and +somebody else says that looks green and + + align:start position:0% +somebody else says that looks green and + + + align:start position:0% +somebody else says that looks green and +they laugh at you or something and ah it + + align:start position:0% +they laugh at you or something and ah it + + + align:start position:0% +they laugh at you or something and ah it +doesn't work + + align:start position:0% +doesn't work + + + align:start position:0% +doesn't work +no evidence that that works + + align:start position:0% +no evidence that that works + + + align:start position:0% +no evidence that that works +um what you do is that you seem to have + + align:start position:0% +um what you do is that you seem to have + + + align:start position:0% +um what you do is that you seem to have +some sort of + + align:start position:0% +some sort of + + + align:start position:0% +some sort of +um notion of the statistics of the world + + align:start position:0% +um notion of the statistics of the world + + + align:start position:0% +um notion of the statistics of the world +the way the world ought to be if the + + align:start position:0% +the way the world ought to be if the + + + align:start position:0% +the way the world ought to be if the +world is systematically different from + + align:start position:0% +world is systematically different from + + + align:start position:0% +world is systematically different from +that + + align:start position:0% +that + + + align:start position:0% +that +you draw the conclusion that + + align:start position:0% +you draw the conclusion that + + + align:start position:0% +you draw the conclusion that +um uh that that you've got trouble here + + align:start position:0% +um uh that that you've got trouble here + + + align:start position:0% +um uh that that you've got trouble here +of some variety or other well not + + align:start position:0% +of some variety or other well not + + + align:start position:0% +of some variety or other well not +necessarily you don't necessarily draw + + align:start position:0% +necessarily you don't necessarily draw + + + align:start position:0% +necessarily you don't necessarily draw +the let me give you a non-troubled + + align:start position:0% +the let me give you a non-troubled + + + align:start position:0% +the let me give you a non-troubled +version of this how many people have + + align:start position:0% +version of this how many people have + + + align:start position:0% +version of this how many people have +been to one of these Omni theater kind + + align:start position:0% +been to one of these Omni theater kind + + + align:start position:0% +been to one of these Omni theater kind +of movies + + align:start position:0% +of movies + + + align:start position:0% +of movies +right the main reason for going to an + + align:start position:0% +right the main reason for going to an + + + align:start position:0% +right the main reason for going to an +Omni Theater movie is what + + align:start position:0% +Omni Theater movie is what + + + align:start position:0% +Omni Theater movie is what +you want to feel like you're moving + + align:start position:0% +you want to feel like you're moving + + + align:start position:0% +you want to feel like you're moving +right when you're not moving because all + + align:start position:0% +right when you're not moving because all + + + align:start position:0% +right when you're not moving because all +the movies that they ever show you at + + align:start position:0% +the movies that they ever show you at + + + align:start position:0% +the movies that they ever show you at +the science museum right are you know + + align:start position:0% +the science museum right are you know + + + align:start position:0% +the science museum right are you know +things where you go driving around in + + align:start position:0% +things where you go driving around in + + + align:start position:0% +things where you go driving around in +race cars + + align:start position:0% +race cars + + + align:start position:0% +race cars +stuff like that + + align:start position:0% +stuff like that + + + align:start position:0% +stuff like that +um or something like Anyway why is this + + align:start position:0% +um or something like Anyway why is this + + + align:start position:0% +um or something like Anyway why is this +why does this work you're sitting in + + align:start position:0% +why does this work you're sitting in + + + align:start position:0% +why does this work you're sitting in +this huge + + align:start position:0% +this huge + + + align:start position:0% +this huge +um + + align:start position:0% +um + + + align:start position:0% +um +screen looking at this huge screen and + + align:start position:0% +screen looking at this huge screen and + + + align:start position:0% +screen looking at this huge screen and +everything in your visual field is + + align:start position:0% +everything in your visual field is + + + align:start position:0% +everything in your visual field is +moving in the same way + + align:start position:0% +moving in the same way + + + align:start position:0% +moving in the same way +you know something about the world the + + align:start position:0% +you know something about the world the + + + align:start position:0% +you know something about the world the +world on average is stationary + + align:start position:0% +world on average is stationary + + + align:start position:0% +world on average is stationary +if the whole world is moving + + align:start position:0% +if the whole world is moving + + + align:start position:0% +if the whole world is moving +there's a good explanation for that + + align:start position:0% +there's a good explanation for that + + + align:start position:0% +there's a good explanation for that +typically the answer is it's not the + + align:start position:0% +typically the answer is it's not the + + + align:start position:0% +typically the answer is it's not the +world it's you + + align:start position:0% +world it's you + + + align:start position:0% +world it's you +right what is it that causes the whole + + align:start position:0% +right what is it that causes the whole + + + align:start position:0% +right what is it that causes the whole +world to slide across your retina this + + align:start position:0% +world to slide across your retina this + + + align:start position:0% +world to slide across your retina this +is what causes the whole world to slide + + align:start position:0% +is what causes the whole world to slide + + + align:start position:0% +is what causes the whole world to slide +across the retina sit in the Omni and + + align:start position:0% +across the retina sit in the Omni and + + + align:start position:0% +across the retina sit in the Omni and +the world is sliding across your retina + + align:start position:0% +the world is sliding across your retina + + + align:start position:0% +the world is sliding across your retina +your brain says uh-uh the world isn't + + align:start position:0% +your brain says uh-uh the world isn't + + + align:start position:0% +your brain says uh-uh the world isn't +moving I'm moving and I think I'll throw + + align:start position:0% +moving I'm moving and I think I'll throw + + + align:start position:0% +moving I'm moving and I think I'll throw +up now for a while or something like + + align:start position:0% +up now for a while or something like + + + align:start position:0% +up now for a while or something like +that that's a separate interesting + + align:start position:0% +that that's a separate interesting + + + align:start position:0% +that that's a separate interesting +question + + align:start position:0% +question + + + align:start position:0% +question +um + + align:start position:0% +um + + + align:start position:0% +um +what is it here that could tell you that + + align:start position:0% +what is it here that could tell you that + + + align:start position:0% +what is it here that could tell you that +you're out of whack well what is the + + align:start position:0% +you're out of whack well what is the + + + align:start position:0% +you're out of whack well what is the +normal relationship between color and + + align:start position:0% +normal relationship between color and + + + align:start position:0% +normal relationship between color and +orientation in the world + + align:start position:0% +orientation in the world + + + align:start position:0% +orientation in the world +what's the core what what + + align:start position:0% +what's the core what what + + + align:start position:0% +what's the core what what +typically in the world if you see some + + align:start position:0% +typically in the world if you see some + + + align:start position:0% +typically in the world if you see some +that's vertical what do you know about + + align:start position:0% +that's vertical what do you know about + + + align:start position:0% +that's vertical what do you know about +its color + + align:start position:0% +its color + + + align:start position:0% +its color +that's right nothing + + align:start position:0% +that's right nothing + + + align:start position:0% +that's right nothing +so what's going on here oops + + align:start position:0% +so what's going on here oops + + + align:start position:0% +so what's going on here oops +if it's vertical it's green if it's + + align:start position:0% +if it's vertical it's green if it's + + + align:start position:0% +if it's vertical it's green if it's +horizontal it's red if it's vertical + + align:start position:0% +horizontal it's red if it's vertical + + + align:start position:0% +horizontal it's red if it's vertical +it's green if it's horizontal it's red + + align:start position:0% +it's green if it's horizontal it's red + + + align:start position:0% +it's green if it's horizontal it's red +you do this for long enough and a little + + align:start position:0% +you do this for long enough and a little + + + align:start position:0% +you do this for long enough and a little +chunk of your brain rather like the + + align:start position:0% +chunk of your brain rather like the + + + align:start position:0% +chunk of your brain rather like the +little chunk of your brain that's saying + + align:start position:0% +little chunk of your brain that's saying + + + align:start position:0% +little chunk of your brain that's saying +you know I ate the cupcakes I threw up + + align:start position:0% +you know I ate the cupcakes I threw up + + + align:start position:0% +you know I ate the cupcakes I threw up +I'd better do something about this this + + align:start position:0% +I'd better do something about this this + + + align:start position:0% +I'd better do something about this this +little chunk of your brain is saying oh + + align:start position:0% +little chunk of your brain is saying oh + + + align:start position:0% +little chunk of your brain is saying oh +there's a correlation between color and + + align:start position:0% +there's a correlation between color and + + + align:start position:0% +there's a correlation between color and +orientation the only way that happens + + align:start position:0% +orientation the only way that happens + + + align:start position:0% +orientation the only way that happens +is if I'm broken + + align:start position:0% +is if I'm broken + + + align:start position:0% +is if I'm broken +and the only thing to do about that is + + align:start position:0% +and the only thing to do about that is + + + align:start position:0% +and the only thing to do about that is +to adjust the gain on chunks of my + + align:start position:0% +to adjust the gain on chunks of my + + + align:start position:0% +to adjust the gain on chunks of my +visual system so uh everything + + align:start position:0% +visual system so uh everything + + + align:start position:0% +visual system so uh everything +everything looks everything looks green + + align:start position:0% +everything looks everything looks green + + + align:start position:0% +everything looks everything looks green +you know all the vertical things look + + align:start position:0% +you know all the vertical things look + + + align:start position:0% +you know all the vertical things look +green oh my goodness what am I going to + + align:start position:0% +green oh my goodness what am I going to + + + align:start position:0% +green oh my goodness what am I going to +do well I better crank down the gain on + + align:start position:0% +do well I better crank down the gain on + + + align:start position:0% +do well I better crank down the gain on +the green side it's obviously too high + + align:start position:0% +the green side it's obviously too high + + + align:start position:0% +the green side it's obviously too high +and Crown I'll crank up the gain on the + + align:start position:0% +and Crown I'll crank up the gain on the + + + align:start position:0% +and Crown I'll crank up the gain on the +red side unfortunately that was a goof + + align:start position:0% +red side unfortunately that was a goof + + + align:start position:0% +red side unfortunately that was a goof +and it was wrong so then when you look + + align:start position:0% +and it was wrong so then when you look + + + align:start position:0% +and it was wrong so then when you look +at a white thing it now looks red + + align:start position:0% +at a white thing it now looks red + + + align:start position:0% +at a white thing it now looks red +because you crank the gain up too much + + align:start position:0% +because you crank the gain up too much + + + align:start position:0% +because you crank the gain up too much +over here + + align:start position:0% +over here + + + align:start position:0% +over here +um how do you recover from this well if + + align:start position:0% +um how do you recover from this well if + + + align:start position:0% +um how do you recover from this well if +I now show you + + align:start position:0% +I now show you + + + align:start position:0% +I now show you +um + + align:start position:0% +um + + + align:start position:0% +um +if I show you the opposite one what were + + align:start position:0% +if I show you the opposite one what were + + + align:start position:0% +if I show you the opposite one what were +we doing before what was it green + + align:start position:0% +we doing before what was it green + + + align:start position:0% +we doing before what was it green +vertical if I show you red verticals and + + align:start position:0% +vertical if I show you red verticals and + + + align:start position:0% +vertical if I show you red verticals and +green horizontals for a while that'll + + align:start position:0% +green horizontals for a while that'll + + + align:start position:0% +green horizontals for a while that'll +push it back the other way but that + + align:start position:0% +push it back the other way but that + + + align:start position:0% +push it back the other way but that +doesn't typically happen in the world + + align:start position:0% +doesn't typically happen in the world + + + align:start position:0% +doesn't typically happen in the world +simply being exposed to a world where + + align:start position:0% +simply being exposed to a world where + + + align:start position:0% +simply being exposed to a world where +there's no correlation will slowly push + + align:start position:0% +there's no correlation will slowly push + + + align:start position:0% +there's no correlation will slowly push +you back + + align:start position:0% +you back + + + align:start position:0% +you back +but it's a little but the reason the + + align:start position:0% +but it's a little but the reason the + + + align:start position:0% +but it's a little but the reason the +effect lasts so long is that the + + align:start position:0% +effect lasts so long is that the + + + align:start position:0% +effect lasts so long is that the +evidence from The Real World is kind of + + align:start position:0% +evidence from The Real World is kind of + + + align:start position:0% +evidence from The Real World is kind of +weak compared to this artificial + + align:start position:0% +weak compared to this artificial + + + align:start position:0% +weak compared to this artificial +situation that I I + + align:start position:0% +situation that I I + + + align:start position:0% +situation that I I +um that I cooked up here the way of + + align:start position:0% +um that I cooked up here the way of + + + align:start position:0% +um that I cooked up here the way of +thinking about this is like here's + + align:start position:0% +thinking about this is like here's + + + align:start position:0% +thinking about this is like here's +another way of thinking about this + + align:start position:0% +another way of thinking about this + + + align:start position:0% +another way of thinking about this +suppose all right I'll go over here just + + align:start position:0% +suppose all right I'll go over here just + + + align:start position:0% +suppose all right I'll go over here just +so they don't feel bad + + align:start position:0% +so they don't feel bad + + + align:start position:0% +so they don't feel bad +um or maybe so they don't feel bad + + align:start position:0% +um or maybe so they don't feel bad + + + align:start position:0% +um or maybe so they don't feel bad +suppose you're measuring average weight + + align:start position:0% +suppose you're measuring average weight + + + align:start position:0% +suppose you're measuring average weight +of people I'm just going to keep + + align:start position:0% +of people I'm just going to keep + + + align:start position:0% +of people I'm just going to keep +weighing people and I'm going to keep + + align:start position:0% +weighing people and I'm going to keep + + + align:start position:0% +weighing people and I'm going to keep +all the Box + + align:start position:0% +all the Box + + + align:start position:0% +all the Box +what's the average weight of people + + align:start position:0% +what's the average weight of people + + + align:start position:0% +what's the average weight of people +it'll bounce around a little bit all + + align:start position:0% +it'll bounce around a little bit all + + + align:start position:0% +it'll bounce around a little bit all +right this is how much people on average + + align:start position:0% +right this is how much people on average + + + align:start position:0% +right this is how much people on average +weigh now what I do is what happens is + + align:start position:0% +weigh now what I do is what happens is + + + align:start position:0% +weigh now what I do is what happens is +the amazing 1 000 pound guy comes into + + align:start position:0% +the amazing 1 000 pound guy comes into + + + align:start position:0% +the amazing 1 000 pound guy comes into +my experiment what happens to the + + align:start position:0% +my experiment what happens to the + + + align:start position:0% +my experiment what happens to the +average + + align:start position:0% +average + + + align:start position:0% +average +oh yeah + + align:start position:0% +oh yeah + + + align:start position:0% +oh yeah +now now I start weighing normal people + + align:start position:0% +now now I start weighing normal people + + + align:start position:0% +now now I start weighing normal people +again does it just go no it'll take + + align:start position:0% +again does it just go no it'll take + + + align:start position:0% +again does it just go no it'll take +weighing regular people it'll take a + + align:start position:0% +weighing regular people it'll take a + + + align:start position:0% +weighing regular people it'll take a +long comparatively long time for me to + + align:start position:0% +long comparatively long time for me to + + + align:start position:0% +long comparatively long time for me to +get back to normal so that's what's + + align:start position:0% +get back to normal so that's what's + + + align:start position:0% +get back to normal so that's what's +going on here the McCullough effect + + align:start position:0% +going on here the McCullough effect + + + align:start position:0% +going on here the McCullough effect +adapting stimulus is the thousand pound + + align:start position:0% +adapting stimulus is the thousand pound + + + align:start position:0% +adapting stimulus is the thousand pound +guy that's causing you to think that + + align:start position:0% +guy that's causing you to think that + + + align:start position:0% +guy that's causing you to think that +your brain is broken you go and readjust + + align:start position:0% +your brain is broken you go and readjust + + + align:start position:0% +your brain is broken you go and readjust +your brain and um and now slowly it will + + align:start position:0% +your brain and um and now slowly it will + + + align:start position:0% +your brain and um and now slowly it will +get better so + + align:start position:0% +get better so + + + align:start position:0% +get better so +how's it look there + + align:start position:0% +how's it look there + + + align:start position:0% +how's it look there +not better yet how many people how many + + align:start position:0% +not better yet how many people how many + + + align:start position:0% +not better yet how many people how many +people have a nice after effect still + + align:start position:0% +people have a nice after effect still + + + align:start position:0% +people have a nice after effect still +nice McCullough effect + + align:start position:0% +nice McCullough effect + + + align:start position:0% +nice McCullough effect +Celeste McCullough would be so proud + + align:start position:0% +Celeste McCullough would be so proud + + + align:start position:0% +Celeste McCullough would be so proud +um okay you will notice + + align:start position:0% +um okay you will notice + + + align:start position:0% +um okay you will notice +that I have not said a word about signal + + align:start position:0% +that I have not said a word about signal + + + align:start position:0% +that I have not said a word about signal +detection Theory I I noticed that too + + align:start position:0% +detection Theory I I noticed that too + + + align:start position:0% +detection Theory I I noticed that too +um there is a chunk Enlightenment about + + align:start position:0% +um there is a chunk Enlightenment about + + + align:start position:0% +um there is a chunk Enlightenment about +it I might decide to talk about it on + + align:start position:0% +it I might decide to talk about it on + + + align:start position:0% +it I might decide to talk about it on +Thursday oh you may also notice that you + + align:start position:0% +Thursday oh you may also notice that you + + + align:start position:0% +Thursday oh you may also notice that you +have lost your cell phone if that is + + align:start position:0% +have lost your cell phone if that is + + + align:start position:0% +have lost your cell phone if that is +true come and talk to me about it + + align:start position:0% +true come and talk to me about it + + + align:start position:0% +true come and talk to me about it +because we found it one last thing + + align:start position:0% +because we found it one last thing + + + align:start position:0% +because we found it one last thing +how many people know what that is + + align:start position:0% + + + + align:start position:0% + +shush I didn't ask you what it was I + + align:start position:0% +shush I didn't ask you what it was I + + + align:start position:0% +shush I didn't ask you what it was I +just wanted to know if you knew what it + + align:start position:0% +just wanted to know if you knew what it + + + align:start position:0% +just wanted to know if you knew what it +was how many people recognize this + + align:start position:0% +was how many people recognize this + + + align:start position:0% +was how many people recognize this +only a few okay now you can shout out + + align:start position:0% +only a few okay now you can shout out + + + align:start position:0% +only a few okay now you can shout out +it's a dog how many people does that + + align:start position:0% +it's a dog how many people does that + + + align:start position:0% +it's a dog how many people does that +help + + align:start position:0% + + + + align:start position:0% + +maybe okay wait wait wait + + align:start position:0% +maybe okay wait wait wait + + + align:start position:0% +maybe okay wait wait wait +its head is well wait a second maybe I + + align:start position:0% +its head is well wait a second maybe I + + + align:start position:0% +its head is well wait a second maybe I +can get my little there we go there's + + align:start position:0% +can get my little there we go there's + + + align:start position:0% +can get my little there we go there's +its head + + align:start position:0% +its head + + + align:start position:0% +its head +foot back paw + + align:start position:0% +foot back paw + + + align:start position:0% +foot back paw +it's back it's sort of sniffing at a + + align:start position:0% +it's back it's sort of sniffing at a + + + align:start position:0% +it's back it's sort of sniffing at a +ground plane that's like here + + align:start position:0% +ground plane that's like here + + + align:start position:0% +ground plane that's like here +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so just you can store that one away till + + align:start position:0% +so just you can store that one away till + + + align:start position:0% +so just you can store that one away till +next week and we'll talk about it + + align:start position:0% +next week and we'll talk about it + + + align:start position:0% +next week and we'll talk about it +foreign \ No newline at end of file diff --git a/RN4gSBTANUY.txt b/RN4gSBTANUY.txt new file mode 100644 index 0000000000000000000000000000000000000000..94e92d1a1a7875b9811a6ec90d2c704448cd14c9 --- /dev/null +++ b/RN4gSBTANUY.txt @@ -0,0 +1,11072 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu so my goal for today is + + align:start position:0% +ocw.mit.edu so my goal for today is + + + align:start position:0% +ocw.mit.edu so my goal for today is +twofold the first is uh We've looked at + + align:start position:0% +twofold the first is uh We've looked at + + + align:start position:0% +twofold the first is uh We've looked at +the history of the internet in the 60s + + align:start position:0% +the history of the internet in the 60s + + + align:start position:0% +the history of the internet in the 60s +and the' 70s and today my goal is to + + align:start position:0% +and the' 70s and today my goal is to + + + align:start position:0% +and the' 70s and today my goal is to +tell you about what happened in the 80s + + align:start position:0% +tell you about what happened in the 80s + + + align:start position:0% +tell you about what happened in the 80s +and the 90s and as well as the the last + + align:start position:0% +and the 90s and as well as the the last + + + align:start position:0% +and the 90s and as well as the the last +decade and we'll do that maybe you know + + align:start position:0% +decade and we'll do that maybe you know + + + align:start position:0% +decade and we'll do that maybe you know +30 35 minutes but I you know I want to + + align:start position:0% +30 35 minutes but I you know I want to + + + align:start position:0% +30 35 minutes but I you know I want to +tell you about two interesting problems + + align:start position:0% +tell you about two interesting problems + + + align:start position:0% +tell you about two interesting problems +that got solved both related to topics + + align:start position:0% +that got solved both related to topics + + + align:start position:0% +that got solved both related to topics +we've studied the first is on how the + + align:start position:0% +we've studied the first is on how the + + + align:start position:0% +we've studied the first is on how the +internet dealt with a serious problem + + align:start position:0% +internet dealt with a serious problem + + + align:start position:0% +internet dealt with a serious problem +called congestion collapse which + + align:start position:0% +called congestion collapse which + + + align:start position:0% +called congestion collapse which +happened in the mid + + align:start position:0% +happened in the mid + + + align:start position:0% +happened in the mid +1980s where + + align:start position:0% +1980s where + + + align:start position:0% +1980s where +TCP the transmission protocol at the + + align:start position:0% +TCP the transmission protocol at the + + + align:start position:0% +TCP the transmission protocol at the +time and still the dominant protocol in + + align:start position:0% +time and still the dominant protocol in + + + align:start position:0% +time and still the dominant protocol in +the world didn't have many of the new + + align:start position:0% +the world didn't have many of the new + + + align:start position:0% +the world didn't have many of the new +ideas that it now has in fact the + + align:start position:0% +ideas that it now has in fact the + + + align:start position:0% +ideas that it now has in fact the +implementation of TCP in the + + align:start position:0% +implementation of TCP in the + + + align:start position:0% +implementation of TCP in the +1980s was almost exactly the + + align:start position:0% +1980s was almost exactly the + + + align:start position:0% +1980s was almost exactly the +implementation of your sliding window + + align:start position:0% +implementation of your sliding window + + + align:start position:0% +implementation of your sliding window +protocol from the second lab uh from the + + align:start position:0% +protocol from the second lab uh from the + + + align:start position:0% +protocol from the second lab uh from the +second task of the last + + align:start position:0% +second task of the last + + + align:start position:0% +second task of the last +lab and in fact as some of you um I + + align:start position:0% +lab and in fact as some of you um I + + + align:start position:0% +lab and in fact as some of you um I +think there was I think Tyler posted on + + align:start position:0% +think there was I think Tyler posted on + + + align:start position:0% +think there was I think Tyler posted on +pza you know there was this particular + + align:start position:0% +pza you know there was this particular + + + align:start position:0% +pza you know there was this particular +way in which he had dealt with the + + align:start position:0% +way in which he had dealt with the + + + align:start position:0% +way in which he had dealt with the +window scheme that happened to do better + + align:start position:0% +window scheme that happened to do better + + + align:start position:0% +window scheme that happened to do better +than the lab Solutions and I remarked + + align:start position:0% +than the lab Solutions and I remarked + + + align:start position:0% +than the lab Solutions and I remarked +there that the reason the lab Solutions + + align:start position:0% +there that the reason the lab Solutions + + + align:start position:0% +there that the reason the lab Solutions +the way they are are a little bit more + + align:start position:0% +the way they are are a little bit more + + + align:start position:0% +the way they are are a little bit more +General than the particular topology but + + align:start position:0% +General than the particular topology but + + + align:start position:0% +General than the particular topology but +the topology that I picked was + + align:start position:0% +the topology that I picked was + + + align:start position:0% +the topology that I picked was +specifically picked in the lab so you + + align:start position:0% +specifically picked in the lab so you + + + align:start position:0% +specifically picked in the lab so you +didn't have to worry about congestion + + align:start position:0% +didn't have to worry about congestion + + + align:start position:0% +didn't have to worry about congestion +happening but today I'll tell you what + + align:start position:0% +happening but today I'll tell you what + + + align:start position:0% +happening but today I'll tell you what +happens when congestion happens and and + + align:start position:0% +happens when congestion happens and and + + + align:start position:0% +happens when congestion happens and and +the solutions that were adopted and + + align:start position:0% +the solutions that were adopted and + + + align:start position:0% +the solutions that were adopted and +it'll be a little bit of a preview to + + align:start position:0% +it'll be a little bit of a preview to + + + align:start position:0% +it'll be a little bit of a preview to +6033 you'll study this topic at some + + align:start position:0% +6033 you'll study this topic at some + + + align:start position:0% +6033 you'll study this topic at some +length in 6033 the other problem I want + + align:start position:0% +length in 6033 the other problem I want + + + align:start position:0% +length in 6033 the other problem I want +to tell you about today when uh through + + align:start position:0% +to tell you about today when uh through + + + align:start position:0% +to tell you about today when uh through +these remarks is about how easy it is to + + align:start position:0% +these remarks is about how easy it is to + + + align:start position:0% +these remarks is about how easy it is to +hijack routes on the internet and I'll + + align:start position:0% +hijack routes on the internet and I'll + + + align:start position:0% +hijack routes on the internet and I'll +go through some examples of this + + align:start position:0% +go through some examples of this + + + align:start position:0% +go through some examples of this +happening in reality I mean it is + + align:start position:0% +happening in reality I mean it is + + + align:start position:0% +happening in reality I mean it is +literally something a bunch of you know + + align:start position:0% +literally something a bunch of you know + + + align:start position:0% +literally something a bunch of you know +you could do in your dorm you just have + + align:start position:0% +you could do in your dorm you just have + + + align:start position:0% +you could do in your dorm you just have +to convince some sort of an you know + + align:start position:0% +to convince some sort of an you know + + + align:start position:0% +to convince some sort of an you know +pretend you're an ISP or set yourself up + + align:start position:0% +pretend you're an ISP or set yourself up + + + align:start position:0% +pretend you're an ISP or set yourself up +as a small internet service provider and + + align:start position:0% +as a small internet service provider and + + + align:start position:0% +as a small internet service provider and +you can actually take a fair bit of + + align:start position:0% +you can actually take a fair bit of + + + align:start position:0% +you can actually take a fair bit of +damage onto the rest of the world uh if + + align:start position:0% +damage onto the rest of the world uh if + + + align:start position:0% +damage onto the rest of the world uh if +you're so inclined uh and then pretend + + align:start position:0% +you're so inclined uh and then pretend + + + align:start position:0% +you're so inclined uh and then pretend +that it was just a you know + + align:start position:0% +that it was just a you know + + + align:start position:0% +that it was just a you know +error so those are the two technical + + align:start position:0% +error so those are the two technical + + + align:start position:0% +error so those are the two technical +ideas I mean none of the stuff is really + + align:start position:0% +ideas I mean none of the stuff is really + + + align:start position:0% +ideas I mean none of the stuff is really +on the you know on the quiz though it's + + align:start position:0% +on the you know on the quiz though it's + + + align:start position:0% +on the you know on the quiz though it's +probably helpful to think about these + + align:start position:0% +probably helpful to think about these + + + align:start position:0% +probably helpful to think about these +things about route hijacking because you + + align:start position:0% +things about route hijacking because you + + + align:start position:0% +things about route hijacking because you +know those apply to some of the concepts + + align:start position:0% +know those apply to some of the concepts + + + align:start position:0% +know those apply to some of the concepts +we've studied but you know a lot of this + + align:start position:0% +we've studied but you know a lot of this + + + align:start position:0% +we've studied but you know a lot of this +is just for out of your own interest and + + align:start position:0% +is just for out of your own interest and + + + align:start position:0% +is just for out of your own interest and +I'm hoping to Peak your curiosity so + + align:start position:0% +I'm hoping to Peak your curiosity so + + + align:start position:0% +I'm hoping to Peak your curiosity so +later courses um in the department would + + align:start position:0% +later courses um in the department would + + + align:start position:0% +later courses um in the department would +be interesting okay so in the 1980s the + + align:start position:0% +be interesting okay so in the 1980s the + + + align:start position:0% +be interesting okay so in the 1980s the +internet the people designing the + + align:start position:0% +internet the people designing the + + + align:start position:0% +internet the people designing the +protocols of the internet started to get + + align:start position:0% +protocols of the internet started to get + + + align:start position:0% +protocols of the internet started to get +organized and as you recall V Surf and + + align:start position:0% +organized and as you recall V Surf and + + + align:start position:0% +organized and as you recall V Surf and +Bob Khan were the leaders of the effort + + align:start position:0% +Bob Khan were the leaders of the effort + + + align:start position:0% +Bob Khan were the leaders of the effort +was a big community commun of people + + align:start position:0% +was a big community commun of people + + + align:start position:0% +was a big community commun of people +contributing to what became the internet + + align:start position:0% +contributing to what became the internet + + + align:start position:0% +contributing to what became the internet +and back in those days it was still the + + align:start position:0% +and back in those days it was still the + + + align:start position:0% +and back in those days it was still the +arpanet arpa had funded this entire + + align:start position:0% +arpanet arpa had funded this entire + + + align:start position:0% +arpanet arpa had funded this entire +project and it was starting to be + + align:start position:0% +project and it was starting to be + + + align:start position:0% +project and it was starting to be +successful in the 1980s rapid growth + + align:start position:0% +successful in the 1980s rapid growth + + + align:start position:0% +successful in the 1980s rapid growth +started people say how the internet is + + align:start position:0% +started people say how the internet is + + + align:start position:0% +started people say how the internet is +booming and how it's exploding at 80 or + + align:start position:0% +booming and how it's exploding at 80 or + + + align:start position:0% +booming and how it's exploding at 80 or +90% a year it's been growing at about 80 + + align:start position:0% +90% a year it's been growing at about 80 + + + align:start position:0% +90% a year it's been growing at about 80 +to 90% a year since about 1983 or 1984 + + align:start position:0% +to 90% a year since about 1983 or 1984 + + + align:start position:0% +to 90% a year since about 1983 or 1984 +this explosive growth has been happening + + align:start position:0% +this explosive growth has been happening + + + align:start position:0% +this explosive growth has been happening +for many many uh for for several decades + + align:start position:0% +for many many uh for for several decades + + + align:start position:0% +for many many uh for for several decades +Now Dave Clark who's a senior research + + align:start position:0% +Now Dave Clark who's a senior research + + + align:start position:0% +Now Dave Clark who's a senior research +scientist at MIT and the faculty in our + + align:start position:0% +scientist at MIT and the faculty in our + + + align:start position:0% +scientist at MIT and the faculty in our +department was um designated as the + + align:start position:0% +department was um designated as the + + + align:start position:0% +department was um designated as the +internet's Chief Architect and one of + + align:start position:0% +internet's Chief Architect and one of + + + align:start position:0% +internet's Chief Architect and one of +the things he did was to get the + + align:start position:0% +the things he did was to get the + + + align:start position:0% +the things he did was to get the +community organized and formalize the + + align:start position:0% +community organized and formalize the + + + align:start position:0% +community organized and formalize the +creation of Internet standards you know + + align:start position:0% +creation of Internet standards you know + + + align:start position:0% +creation of Internet standards you know +you have all these different companies + + align:start position:0% +you have all these different companies + + + align:start position:0% +you have all these different companies +and organizations and universities + + align:start position:0% +and organizations and universities + + + align:start position:0% +and organizations and universities +coming together how do you standardize + + align:start position:0% +coming together how do you standardize + + + align:start position:0% +coming together how do you standardize +protocols and the argument that the way + + align:start position:0% +protocols and the argument that the way + + + align:start position:0% +protocols and the argument that the way +they came up with the uh the approach + + align:start position:0% +they came up with the uh the approach + + + align:start position:0% +they came up with the uh the approach +they came up with was called the + + align:start position:0% +they came up with was called the + + + align:start position:0% +they came up with was called the +internet engineering task force or ietf + + align:start position:0% +internet engineering task force or ietf + + + align:start position:0% +internet engineering task force or ietf +and they would write these proposals um + + align:start position:0% +and they would write these proposals um + + + align:start position:0% +and they would write these proposals um +they had been there had been this trend + + align:start position:0% +they had been there had been this trend + + + align:start position:0% +they had been there had been this trend +of writing these proposals for people to + + align:start position:0% +of writing these proposals for people to + + + align:start position:0% +of writing these proposals for people to +comment on called rfc's or requests for + + align:start position:0% +comment on called rfc's or requests for + + + align:start position:0% +comment on called rfc's or requests for +comment uh and now there are several + + align:start position:0% +comment uh and now there are several + + + align:start position:0% +comment uh and now there are several +thousand requests for comment nowadays + + align:start position:0% +thousand requests for comment nowadays + + + align:start position:0% +thousand requests for comment nowadays +requests for comment are after the + + align:start position:0% +requests for comment are after the + + + align:start position:0% +requests for comment are after the +comments have been made usually you go + + align:start position:0% +comments have been made usually you go + + + align:start position:0% +comments have been made usually you go +through an internet draft stage and by + + align:start position:0% +through an internet draft stage and by + + + align:start position:0% +through an internet draft stage and by +the time there's a it's a request for + + align:start position:0% +the time there's a it's a request for + + + align:start position:0% +the time there's a it's a request for +comment it's pretty much means the + + align:start position:0% +comment it's pretty much means the + + + align:start position:0% +comment it's pretty much means the +comments have already been done but + + align:start position:0% +comments have already been done but + + + align:start position:0% +comments have already been done but +historically they were requests for + + align:start position:0% +historically they were requests for + + + align:start position:0% +historically they were requests for +comments so they call requests for + + align:start position:0% +comments so they call requests for + + + align:start position:0% +comments so they call requests for +comments so if you if you ever go to a + + align:start position:0% +comments so if you if you ever go to a + + + align:start position:0% +comments so if you if you ever go to a +company where you're asked to you know + + align:start position:0% +company where you're asked to you know + + + align:start position:0% +company where you're asked to you know +uh uh uh lots of things are on internet + + align:start position:0% +uh uh uh lots of things are on internet + + + align:start position:0% +uh uh uh lots of things are on internet +requests for comments and often people + + align:start position:0% +requests for comments and often people + + + align:start position:0% +requests for comments and often people +are asked to implement pieces of various + + align:start position:0% +are asked to implement pieces of various + + + align:start position:0% +are asked to implement pieces of various +standards and you typically look at this + + align:start position:0% +standards and you typically look at this + + + align:start position:0% +standards and you typically look at this +document and you try to see if there's + + align:start position:0% +document and you try to see if there's + + + align:start position:0% +document and you try to see if there's +someone written code around it and then + + align:start position:0% +someone written code around it and then + + + align:start position:0% +someone written code around it and then +you adapt it or write it from scratch to + + align:start position:0% +you adapt it or write it from scratch to + + + align:start position:0% +you adapt it or write it from scratch to +the specification so it specifies the + + align:start position:0% +the specification so it specifies the + + + align:start position:0% +the specification so it specifies the +protocols and the interesting part of + + align:start position:0% +protocols and the interesting part of + + + align:start position:0% +protocols and the interesting part of +the standard was very much in keeping + + align:start position:0% +the standard was very much in keeping + + + align:start position:0% +the standard was very much in keeping +with the general approach of the the + + align:start position:0% +with the general approach of the the + + + align:start position:0% +with the general approach of the the +internet ethos which was to try to make + + align:start position:0% +internet ethos which was to try to make + + + align:start position:0% +internet ethos which was to try to make +everything be open there are many + + align:start position:0% +everything be open there are many + + + align:start position:0% +everything be open there are many +standards bodies in the world I the i e + + align:start position:0% +standards bodies in the world I the i e + + + align:start position:0% +standards bodies in the world I the i e +has uh things various committees uh the + + align:start position:0% +has uh things various committees uh the + + + align:start position:0% +has uh things various committees uh the +international telecommunications Union + + align:start position:0% +international telecommunications Union + + + align:start position:0% +international telecommunications Union +does the various telephone standards + + align:start position:0% +does the various telephone standards + + + align:start position:0% +does the various telephone standards +there's many many standards and often + + align:start position:0% +there's many many standards and often + + + align:start position:0% +there's many many standards and often +they're based on voting and voting means + + align:start position:0% +they're based on voting and voting means + + + align:start position:0% +they're based on voting and voting means +that people horse trade you know you + + align:start position:0% +that people horse trade you know you + + + align:start position:0% +that people horse trade you know you +have a favorite feature I have a + + align:start position:0% +have a favorite feature I have a + + + align:start position:0% +have a favorite feature I have a +favorite feature um they're both pretty + + align:start position:0% +favorite feature um they're both pretty + + + align:start position:0% +favorite feature um they're both pretty +crappy features but you know I'll vote + + align:start position:0% +crappy features but you know I'll vote + + + align:start position:0% +crappy features but you know I'll vote +for your feature if you vote for mine + + align:start position:0% +for your feature if you vote for mine + + + align:start position:0% +for your feature if you vote for mine +and people end up horse trading and on + + align:start position:0% +and people end up horse trading and on + + + align:start position:0% +and people end up horse trading and on +in the ITF at least in the good old days + + align:start position:0% +in the ITF at least in the good old days + + + align:start position:0% +in the ITF at least in the good old days +this kind of stuff didn't happen now + + align:start position:0% +this kind of stuff didn't happen now + + + align:start position:0% +this kind of stuff didn't happen now +it's changed but in the good old days it + + align:start position:0% +it's changed but in the good old days it + + + align:start position:0% +it's changed but in the good old days it +you know there was this quote which says + + align:start position:0% +you know there was this quote which says + + + align:start position:0% +you know there was this quote which says +we reject Kings presidents and voting we + + align:start position:0% +we reject Kings presidents and voting we + + + align:start position:0% +we reject Kings presidents and voting we +believe in rough consensus and running + + align:start position:0% +believe in rough consensus and running + + + align:start position:0% +believe in rough consensus and running +code the idea was that you you show me + + align:start position:0% +code the idea was that you you show me + + + align:start position:0% +code the idea was that you you show me +what it does allow people to experiment + + align:start position:0% +what it does allow people to experiment + + + align:start position:0% +what it does allow people to experiment +with it and only after we see some + + align:start position:0% +with it and only after we see some + + + align:start position:0% +with it and only after we see some +prototypes and some actual experiments + + align:start position:0% +prototypes and some actual experiments + + + align:start position:0% +prototypes and some actual experiments +in the lab will we even consider making + + align:start position:0% +in the lab will we even consider making + + + align:start position:0% +in the lab will we even consider making +it into a standard and this was the good + + align:start position:0% +it into a standard and this was the good + + + align:start position:0% +it into a standard and this was the good +old days of the internet in which things + + align:start position:0% +old days of the internet in which things + + + align:start position:0% +old days of the internet in which things +were on rough consensus and running code + + align:start position:0% +were on rough consensus and running code + + + align:start position:0% +were on rough consensus and running code +so it wasn't around you know what let's + + align:start position:0% +so it wasn't around you know what let's + + + align:start position:0% +so it wasn't around you know what let's +just vote and we'll get all our lousy + + align:start position:0% +just vote and we'll get all our lousy + + + align:start position:0% +just vote and we'll get all our lousy +features in just because we care enough + + align:start position:0% +features in just because we care enough + + + align:start position:0% +features in just because we care enough +about it + + align:start position:0% +about it + + + align:start position:0% +about it +personally a big break happened in 1982 + + align:start position:0% +personally a big break happened in 1982 + + + align:start position:0% +personally a big break happened in 1982 +when the US Department of Defense + + align:start position:0% +when the US Department of Defense + + + align:start position:0% +when the US Department of Defense +decided that proprietary technology was + + align:start position:0% +decided that proprietary technology was + + + align:start position:0% +decided that proprietary technology was +not the way to go with networking and + + align:start position:0% +not the way to go with networking and + + + align:start position:0% +not the way to go with networking and +and standardized on tcpip as the + + align:start position:0% +and standardized on tcpip as the + + + align:start position:0% +and standardized on tcpip as the +standard and back in those days the + + align:start position:0% +standard and back in those days the + + + align:start position:0% +standard and back in those days the +defense department was a huge consumer + + align:start position:0% +defense department was a huge consumer + + + align:start position:0% +defense department was a huge consumer +of it it still is but back then it was + + align:start position:0% +of it it still is but back then it was + + + align:start position:0% +of it it still is but back then it was +just hugely dominant and they could + + align:start position:0% +just hugely dominant and they could + + + align:start position:0% +just hugely dominant and they could +really influence how the world + + align:start position:0% +really influence how the world + + + align:start position:0% +really influence how the world +went 1983 MIT created Athena the large + + align:start position:0% +went 1983 MIT created Athena the large + + + align:start position:0% +went 1983 MIT created Athena the large +first and really big large scale + + align:start position:0% +first and really big large scale + + + align:start position:0% +first and really big large scale +Computing project we still have Athena + + align:start position:0% +Computing project we still have Athena + + + align:start position:0% +Computing project we still have Athena +machines and it showed how to build + + align:start position:0% +machines and it showed how to build + + + align:start position:0% +machines and it showed how to build +campus area networks and campus area + + align:start position:0% +campus area networks and campus area + + + align:start position:0% +campus area networks and campus area +Technologies they built distributed file + + align:start position:0% +Technologies they built distributed file + + + align:start position:0% +Technologies they built distributed file +systems they built systems like + + align:start position:0% +systems they built systems like + + + align:start position:0% +systems they built systems like +and in fact they were one of the first + + align:start position:0% +and in fact they were one of the first + + + align:start position:0% +and in fact they were one of the first +groups the first networks to experience + + align:start position:0% +groups the first networks to experience + + + align:start position:0% +groups the first networks to experience +Network congestion problems because + + align:start position:0% +Network congestion problems because + + + align:start position:0% +Network congestion problems because +everybody started using the network to + + align:start position:0% +everybody started using the network to + + + align:start position:0% +everybody started using the network to +do their work rather than have their own + + align:start position:0% +do their work rather than have their own + + + align:start position:0% +do their work rather than have their own +uh computers at their desk or use the + + align:start position:0% +uh computers at their desk or use the + + + align:start position:0% +uh computers at their desk or use the +terminal to log in to some remote + + align:start position:0% +terminal to log in to some remote + + + align:start position:0% +terminal to log in to some remote +Mainframe which was the way in which + + align:start position:0% +Mainframe which was the way in which + + + align:start position:0% +Mainframe which was the way in which +things used to be + + align:start position:0% +things used to be + + + align:start position:0% +things used to be +done uh I mentioned last time that in + + align:start position:0% +done uh I mentioned last time that in + + + align:start position:0% +done uh I mentioned last time that in +1984 we created the domain name system + + align:start position:0% +1984 we created the domain name system + + + align:start position:0% +1984 we created the domain name system +this is the system that goes between + + align:start position:0% +this is the system that goes between + + + align:start position:0% +this is the system that goes between +domain names like mit.edu to a an IP + + align:start position:0% +domain names like mit.edu to a an IP + + + align:start position:0% +domain names like mit.edu to a an IP +address and before that it was an FTP + + align:start position:0% +address and before that it was an FTP + + + align:start position:0% +address and before that it was an FTP +how many people have heard of FTP a few + + align:start position:0% +how many people have heard of FTP a few + + + align:start position:0% +how many people have heard of FTP a few +of few okay file transfer protocol + + align:start position:0% +of few okay file transfer protocol + + + align:start position:0% +of few okay file transfer protocol +nobody really uses that these days but + + align:start position:0% +nobody really uses that these days but + + + align:start position:0% +nobody really uses that these days but +you used to download this every night + + align:start position:0% +you used to download this every night + + + align:start position:0% +you used to download this every night +computers would computers would download + + align:start position:0% +computers would computers would download + + + align:start position:0% +computers would computers would download +it from one machine located I believe in + + align:start position:0% +it from one machine located I believe in + + + align:start position:0% +it from one machine located I believe in +California and it didn't really scale + + align:start position:0% +California and it didn't really scale + + + align:start position:0% +California and it didn't really scale +you know and um and people would uh + + align:start position:0% +you know and um and people would uh + + + align:start position:0% +you know and um and people would uh +decided that you needed to get organized + + align:start position:0% +decided that you needed to get organized + + + align:start position:0% +decided that you needed to get organized +and build a domain name system in 1985 + + align:start position:0% +and build a domain name system in 1985 + + + align:start position:0% +and build a domain name system in 1985 +arpa was the defense department was + + align:start position:0% +arpa was the defense department was + + + align:start position:0% +arpa was the defense department was +starting to get out a little bit of + + align:start position:0% +starting to get out a little bit of + + + align:start position:0% +starting to get out a little bit of +maintaining the the entire communication + + align:start position:0% +maintaining the the entire communication + + + align:start position:0% +maintaining the the entire communication +Network and the National Science + + align:start position:0% +Network and the National Science + + + align:start position:0% +Network and the National Science +Foundation started taking over the + + align:start position:0% +Foundation started taking over the + + + align:start position:0% +Foundation started taking over the +running of the backbone connecting all + + align:start position:0% +running of the backbone connecting all + + + align:start position:0% +running of the backbone connecting all +the non-military networks in in the + + align:start position:0% +the non-military networks in in the + + + align:start position:0% +the non-military networks in in the +United States and this led to the NSF + + align:start position:0% +United States and this led to the NSF + + + align:start position:0% +United States and this led to the NSF +net I'll have more to say about NSF net + + align:start position:0% +net I'll have more to say about NSF net + + + align:start position:0% +net I'll have more to say about NSF net +uh in in a little + + align:start position:0% +uh in in a little + + + align:start position:0% +uh in in a little +bit now one of the there are two big + + align:start position:0% +bit now one of the there are two big + + + align:start position:0% +bit now one of the there are two big +growth problems that were experienced + + align:start position:0% +growth problems that were experienced + + + align:start position:0% +growth problems that were experienced +the first was congestion and the second + + align:start position:0% +the first was congestion and the second + + + align:start position:0% +the first was congestion and the second +had to do with how addresses started + + align:start position:0% +had to do with how addresses started + + + align:start position:0% +had to do with how addresses started +running out and we had to deal with uh + + align:start position:0% +running out and we had to deal with uh + + + align:start position:0% +running out and we had to deal with uh +problems in the routing system so I want + + align:start position:0% +problems in the routing system so I want + + + align:start position:0% +problems in the routing system so I want +to talk about conest + + align:start position:0% +to talk about conest + + + align:start position:0% +to talk about conest +in 1986 the internet experienced uh the + + align:start position:0% +in 1986 the internet experienced uh the + + + align:start position:0% +in 1986 the internet experienced uh the +first of a series of congestion + + align:start position:0% +first of a series of congestion + + + align:start position:0% +first of a series of congestion +collapses a congestion collapse is a + + align:start position:0% +collapses a congestion collapse is a + + + align:start position:0% +collapses a congestion collapse is a +situation where you end up with a + + align:start position:0% +situation where you end up with a + + + align:start position:0% +situation where you end up with a +picture that looks like this where if + + align:start position:0% +picture that looks like this where if + + + align:start position:0% +picture that looks like this where if +you were to + + align:start position:0% +you were to + + + align:start position:0% +you were to +draw the offered load on a network or + + align:start position:0% +draw the offered load on a network or + + + align:start position:0% +draw the offered load on a network or +any system for that + + align:start position:0% +any system for that + + + align:start position:0% +any system for that +matter which is just you know how many + + align:start position:0% +matter which is just you know how many + + + align:start position:0% +matter which is just you know how many +people are clamoring to get access to + + align:start position:0% +people are clamoring to get access to + + + align:start position:0% +people are clamoring to get access to +the network and send the data on the + + align:start position:0% +the network and send the data on the + + + align:start position:0% +the network and send the data on the +network if you were to plot the + + align:start position:0% +network if you were to plot the + + + align:start position:0% +network if you were to plot the +throughput + + align:start position:0% + + + + align:start position:0% + +that you get you know or the utilization + + align:start position:0% +that you get you know or the utilization + + + align:start position:0% +that you get you know or the utilization +that you get from the network you + + align:start position:0% +that you get from the network you + + + align:start position:0% +that you get from the network you +typically would see a curve that looks + + align:start position:0% +typically would see a curve that looks + + + align:start position:0% +typically would see a curve that looks +like this as the offer load grows you + + align:start position:0% +like this as the offer load grows you + + + align:start position:0% +like this as the offer load grows you +might see a somewhat linear increase in + + align:start position:0% +might see a somewhat linear increase in + + + align:start position:0% +might see a somewhat linear increase in +the throughput with slope one because + + align:start position:0% +the throughput with slope one because + + + align:start position:0% +the throughput with slope one because +the network isn't congested no packets + + align:start position:0% +the network isn't congested no packets + + + align:start position:0% +the network isn't congested no packets +are being dropped you push some data in + + align:start position:0% +are being dropped you push some data in + + + align:start position:0% +are being dropped you push some data in +you get the data out the offered load + + align:start position:0% +you get the data out the offered load + + + align:start position:0% +you get the data out the offered load +the throughput tracks the offered load + + align:start position:0% +the throughput tracks the offered load + + + align:start position:0% +the throughput tracks the offered load +and at some point you reach the capacity + + align:start position:0% +and at some point you reach the capacity + + + align:start position:0% +and at some point you reach the capacity +of the of the link or of the network in + + align:start position:0% +of the of the link or of the network in + + + align:start position:0% +of the of the link or of the network in +general and you might end up with a flat + + align:start position:0% +general and you might end up with a flat + + + align:start position:0% +general and you might end up with a flat +curve like that and that's fine what you + + align:start position:0% +curve like that and that's fine what you + + + align:start position:0% +curve like that and that's fine what you +would really like to do is as the + + align:start position:0% +would really like to do is as the + + + align:start position:0% +would really like to do is as the +offered load keeps increasing and the + + align:start position:0% +offered load keeps increasing and the + + + align:start position:0% +offered load keeps increasing and the +throughput saturates at the capacity of + + align:start position:0% +throughput saturates at the capacity of + + + align:start position:0% +throughput saturates at the capacity of +course it means that what does it mean + + align:start position:0% +course it means that what does it mean + + + align:start position:0% +course it means that what does it mean +either the delays are growing to + + align:start position:0% +either the delays are growing to + + + align:start position:0% +either the delays are growing to +infinity or packets are being dropped + + align:start position:0% +infinity or packets are being dropped + + + align:start position:0% +infinity or packets are being dropped +right and what you would really like + + align:start position:0% +right and what you would really like + + + align:start position:0% +right and what you would really like +intuitively is for the sources to + + align:start position:0% +intuitively is for the sources to + + + align:start position:0% +intuitively is for the sources to +realize that packets are being dropped + + align:start position:0% +realize that packets are being dropped + + + align:start position:0% +realize that packets are being dropped +or they're not being delivered in time + + align:start position:0% +or they're not being delivered in time + + + align:start position:0% +or they're not being delivered in time +so it maybe slow down something has to + + align:start position:0% +so it maybe slow down something has to + + + align:start position:0% +so it maybe slow down something has to +happen but congestion collapse is a + + align:start position:0% +happen but congestion collapse is a + + + align:start position:0% +happen but congestion collapse is a +worse phenomenon what happens is beyond + + align:start position:0% +worse phenomenon what happens is beyond + + + align:start position:0% +worse phenomenon what happens is beyond +a point the threr Satur drops sometimes + + align:start position:0% +a point the threr Satur drops sometimes + + + align:start position:0% +a point the threr Satur drops sometimes +precipitously and it might go down to + + align:start position:0% +precipitously and it might go down to + + + align:start position:0% +precipitously and it might go down to +zero so people were running Network + + align:start position:0% +zero so people were running Network + + + align:start position:0% +zero so people were running Network +applications you know FTP and remote + + align:start position:0% +applications you know FTP and remote + + + align:start position:0% +applications you know FTP and remote +logins and so email and so forth and + + align:start position:0% +logins and so email and so forth and + + + align:start position:0% +logins and so email and so forth and +what they were finding was that you + + align:start position:0% +what they were finding was that you + + + align:start position:0% +what they were finding was that you +could be running the the ratio between + + align:start position:0% +could be running the the ratio between + + + align:start position:0% +could be running the the ratio between +what the capacity of the network was and + + align:start position:0% +what the capacity of the network was and + + + align:start position:0% +what the capacity of the network was and +what you were getting when you were + + align:start position:0% +what you were getting when you were + + + align:start position:0% +what you were getting when you were +running was a factor of 100 to th000 + + align:start position:0% +running was a factor of 100 to th000 + + + align:start position:0% +running was a factor of 100 to th000 +wor so this is a real collapse even mean + + align:start position:0% +wor so this is a real collapse even mean + + + align:start position:0% +wor so this is a real collapse even mean +you wouldn't be able to get anything + + align:start position:0% +you wouldn't be able to get anything + + + align:start position:0% +you wouldn't be able to get anything +through so people were talking about + + align:start position:0% +through so people were talking about + + + align:start position:0% +through so people were talking about +going from many Kil in those days tens + + align:start position:0% +going from many Kil in those days tens + + + align:start position:0% +going from many Kil in those days tens +of kilobits per second to bits per + + align:start position:0% +of kilobits per second to bits per + + + align:start position:0% +of kilobits per second to bits per +second in fact there was a joke that + + align:start position:0% +second in fact there was a joke that + + + align:start position:0% +second in fact there was a joke that +there was a path between um in Berkeley + + align:start position:0% +there was a path between um in Berkeley + + + align:start position:0% +there was a path between um in Berkeley +between the University of California and + + align:start position:0% +between the University of California and + + + align:start position:0% +between the University of California and +Lawrence Berkeley labs which is probably + + align:start position:0% +Lawrence Berkeley labs which is probably + + + align:start position:0% +Lawrence Berkeley labs which is probably +400 meters from each other and the + + align:start position:0% +400 meters from each other and the + + + align:start position:0% +400 meters from each other and the +network rate was such that you could + + align:start position:0% +network rate was such that you could + + + align:start position:0% +network rate was such that you could +actually run up the hill with a tape + + align:start position:0% +actually run up the hill with a tape + + + align:start position:0% +actually run up the hill with a tape +drive and you'd get 100 times higher + + align:start position:0% +drive and you'd get 100 times higher + + + align:start position:0% +drive and you'd get 100 times higher +throughput than uh what you were getting + + align:start position:0% +throughput than uh what you were getting + + + align:start position:0% +throughput than uh what you were getting +through the network and you know this + + align:start position:0% +through the network and you know this + + + align:start position:0% +through the network and you know this +was not even running up very fast so + + align:start position:0% +was not even running up very fast so + + + align:start position:0% +was not even running up very fast so +this was a serious problem this problem + + align:start position:0% +this was a serious problem this problem + + + align:start position:0% +this was a serious problem this problem +was dealt with by multiple people who + + align:start position:0% +was dealt with by multiple people who + + + align:start position:0% +was dealt with by multiple people who +were working on it and it led to a set + + align:start position:0% +were working on it and it led to a set + + + align:start position:0% +were working on it and it led to a set +of algorithms where the the idea was + + align:start position:0% +of algorithms where the the idea was + + + align:start position:0% +of algorithms where the the idea was +that you would like you know because all + + align:start position:0% +that you would like you know because all + + + align:start position:0% +that you would like you know because all +these switches and routers were already + + align:start position:0% +these switches and routers were already + + + align:start position:0% +these switches and routers were already +deployed people were interested in end + + align:start position:0% +deployed people were interested in end + + + align:start position:0% +deployed people were interested in end +to-end solutions to the problem by end + + align:start position:0% +to-end solutions to the problem by end + + + align:start position:0% +to-end solutions to the problem by end +to end I mean Solutions you could deploy + + align:start position:0% +to end I mean Solutions you could deploy + + + align:start position:0% +to end I mean Solutions you could deploy +at the senders and the receivers in the + + align:start position:0% +at the senders and the receivers in the + + + align:start position:0% +at the senders and the receivers in the +network without worrying about what the + + align:start position:0% +network without worrying about what the + + + align:start position:0% +network without worrying about what the +network was doing in + + align:start position:0% +network was doing in + + + align:start position:0% +network was doing in +between the actual algorithm that we all + + align:start position:0% +between the actual algorithm that we all + + + align:start position:0% +between the actual algorithm that we all +run today had its roots in an algorithm + + align:start position:0% +run today had its roots in an algorithm + + + align:start position:0% +run today had its roots in an algorithm +developed by Van Jacob + + align:start position:0% +developed by Van Jacob + + + align:start position:0% +developed by Van Jacob +at uh at Lawrence Berkeley + + align:start position:0% +at uh at Lawrence Berkeley + + + align:start position:0% +at uh at Lawrence Berkeley +Lads but and there's a lot of work that + + align:start position:0% +Lads but and there's a lot of work that + + + align:start position:0% +Lads but and there's a lot of work that +has been done since then by many other + + align:start position:0% +has been done since then by many other + + + align:start position:0% +has been done since then by many other +people in the community as well and in + + align:start position:0% +people in the community as well and in + + + align:start position:0% +people in the community as well and in +parallel there were people inside of + + align:start position:0% +parallel there were people inside of + + + align:start position:0% +parallel there were people inside of +digital Equipment Corporation over here + + align:start position:0% +digital Equipment Corporation over here + + + align:start position:0% +digital Equipment Corporation over here +in Massachusetts working on similar + + align:start position:0% +in Massachusetts working on similar + + + align:start position:0% +in Massachusetts working on similar +problems and they came up with ideas and + + align:start position:0% +problems and they came up with ideas and + + + align:start position:0% +problems and they came up with ideas and +both these ideas were basically the same + + align:start position:0% +both these ideas were basically the same + + + align:start position:0% +both these ideas were basically the same +idea uh more or less except in the + + align:start position:0% +idea uh more or less except in the + + + align:start position:0% +idea uh more or less except in the +detail and they also resembled what + + align:start position:0% +detail and they also resembled what + + + align:start position:0% +detail and they also resembled what +we've seen with Mac protocols the idea + + align:start position:0% +we've seen with Mac protocols the idea + + + align:start position:0% +we've seen with Mac protocols the idea +is that if the network is working + + align:start position:0% +is that if the network is working + + + align:start position:0% +is that if the network is working +reasonably well we're going to try to be + + align:start position:0% +reasonably well we're going to try to be + + + align:start position:0% +reasonably well we're going to try to be +greedy and start to send faster and + + align:start position:0% +greedy and start to send faster and + + + align:start position:0% +greedy and start to send faster and +faster at some point we're going to find + + align:start position:0% +faster at some point we're going to find + + + align:start position:0% +faster at some point we're going to find +that the network doesn't work so well + + align:start position:0% +that the network doesn't work so well + + + align:start position:0% +that the network doesn't work so well +and we can determine that in one of a + + align:start position:0% +and we can determine that in one of a + + + align:start position:0% +and we can determine that in one of a +few different ways one way to determine + + align:start position:0% +few different ways one way to determine + + + align:start position:0% +few different ways one way to determine +that is that packets start getting + + align:start position:0% +that is that packets start getting + + + align:start position:0% +that is that packets start getting +lost and we will assume that packets are + + align:start position:0% +lost and we will assume that packets are + + + align:start position:0% +lost and we will assume that packets are +lost because cu's overflow and + + align:start position:0% +lost because cu's overflow and + + + align:start position:0% +lost because cu's overflow and +congestion + + align:start position:0% +congestion + + + align:start position:0% +congestion +happens we might also alternatively + + align:start position:0% +happens we might also alternatively + + + align:start position:0% +happens we might also alternatively +assume that as cues in the network grow + + align:start position:0% +assume that as cues in the network grow + + + align:start position:0% +assume that as cues in the network grow +packets get delayed more and more when + + align:start position:0% +packets get delayed more and more when + + + align:start position:0% +packets get delayed more and more when +the network starts to get congested and + + align:start position:0% +the network starts to get congested and + + + align:start position:0% +the network starts to get congested and +if we find that the roundt trip times + + align:start position:0% +if we find that the roundt trip times + + + align:start position:0% +if we find that the roundt trip times +are starting to increase maybe we + + align:start position:0% +are starting to increase maybe we + + + align:start position:0% +are starting to increase maybe we +determine that congestion has + + align:start position:0% +determine that congestion has + + + align:start position:0% +determine that congestion has +happened now there's been 30 years of + + align:start position:0% +happened now there's been 30 years of + + + align:start position:0% +happened now there's been 30 years of +literature the problem has not yet been + + align:start position:0% +literature the problem has not yet been + + + align:start position:0% +literature the problem has not yet been +completely solved and in fact uh we have + + align:start position:0% +completely solved and in fact uh we have + + + align:start position:0% +completely solved and in fact uh we have +now an active research project going on + + align:start position:0% +now an active research project going on + + + align:start position:0% +now an active research project going on +in my group about how to deal with these + + align:start position:0% +in my group about how to deal with these + + + align:start position:0% +in my group about how to deal with these +problems in the context of video and + + align:start position:0% +problems in the context of video and + + + align:start position:0% +problems in the context of video and +video conferencing in Cellular in + + align:start position:0% +video conferencing in Cellular in + + + align:start position:0% +video conferencing in Cellular in +wireless networks that you might that + + align:start position:0% +wireless networks that you might that + + + align:start position:0% +wireless networks that you might that +you run with your phone on your phone so + + align:start position:0% +you run with your phone on your phone so + + + align:start position:0% +you run with your phone on your phone so +it's still an open problem lots of + + align:start position:0% +it's still an open problem lots of + + + align:start position:0% +it's still an open problem lots of +interesting research but the basic idea + + align:start position:0% +interesting research but the basic idea + + + align:start position:0% +interesting research but the basic idea +is + + align:start position:0% + + + + align:start position:0% + +that you have to adapt to what the + + align:start position:0% +that you have to adapt to what the + + + align:start position:0% +that you have to adapt to what the +network is doing and the way you adapt + + align:start position:0% +network is doing and the way you adapt + + + align:start position:0% +network is doing and the way you adapt +is by watching things in the network you + + align:start position:0% +is by watching things in the network you + + + align:start position:0% +is by watching things in the network you +watch whether packets are being lost you + + align:start position:0% +watch whether packets are being lost you + + + align:start position:0% +watch whether packets are being lost you +watch whether delays are growing you + + align:start position:0% +watch whether delays are growing you + + + align:start position:0% +watch whether delays are growing you +might watch um what the receiver is + + align:start position:0% +might watch um what the receiver is + + + align:start position:0% +might watch um what the receiver is +getting you know how fast is the + + align:start position:0% +getting you know how fast is the + + + align:start position:0% +getting you know how fast is the +receiver getting data from the sender + + align:start position:0% +receiver getting data from the sender + + + align:start position:0% +receiver getting data from the sender +and the network and the intuition is the + + align:start position:0% +and the network and the intuition is the + + + align:start position:0% +and the network and the intuition is the +following let's suppose that we were to + + align:start position:0% +following let's suppose that we were to + + + align:start position:0% +following let's suppose that we were to +pick the correct window size you know + + align:start position:0% +pick the correct window size you know + + + align:start position:0% +pick the correct window size you know +this goes to the sliding window and the + + align:start position:0% +this goes to the sliding window and the + + + align:start position:0% +this goes to the sliding window and the +window size that you use we've said that + + align:start position:0% +window size that you use we've said that + + + align:start position:0% +window size that you use we've said that +the right value of the window size is + + align:start position:0% +the right value of the window size is + + + align:start position:0% +the right value of the window size is +roughly the bandwidth delay product + + align:start position:0% +roughly the bandwidth delay product + + + align:start position:0% +roughly the bandwidth delay product +where the bandwidth delay product is the + + align:start position:0% +where the bandwidth delay product is the + + + align:start position:0% +where the bandwidth delay product is the +product of the bottleneck link rate + + align:start position:0% +product of the bottleneck link rate + + + align:start position:0% +product of the bottleneck link rate +multiplied by the minimum round trip TI + + align:start position:0% +multiplied by the minimum round trip TI + + + align:start position:0% +multiplied by the minimum round trip TI +but the problem is the bottl neck link + + align:start position:0% +but the problem is the bottl neck link + + + align:start position:0% +but the problem is the bottl neck link +rate is not fixed it is in the lab we + + align:start position:0% +rate is not fixed it is in the lab we + + + align:start position:0% +rate is not fixed it is in the lab we +studied but in reality you have many + + align:start position:0% +studied but in reality you have many + + + align:start position:0% +studied but in reality you have many +connections sharing the network many + + align:start position:0% +connections sharing the network many + + + align:start position:0% +connections sharing the network many +applications sharing the network and + + align:start position:0% +applications sharing the network and + + + align:start position:0% +applications sharing the network and +people come and go so the rate keeps + + align:start position:0% +people come and go so the rate keeps + + + align:start position:0% +people come and go so the rate keeps +changing at one moment you might be + + align:start position:0% +changing at one moment you might be + + + align:start position:0% +changing at one moment you might be +getting 100 kilobits a second the next + + align:start position:0% +getting 100 kilobits a second the next + + + align:start position:0% +getting 100 kilobits a second the next +moment you might be getting a megabit + + align:start position:0% +moment you might be getting a megabit + + + align:start position:0% +moment you might be getting a megabit +per second and on wireless networks it's + + align:start position:0% +per second and on wireless networks it's + + + align:start position:0% +per second and on wireless networks it's +even worse uh quite literally if I were + + align:start position:0% +even worse uh quite literally if I were + + + align:start position:0% +even worse uh quite literally if I were +to um start an application on my phone + + align:start position:0% +to um start an application on my phone + + + align:start position:0% +to um start an application on my phone +now connecting to you know Verizon or + + align:start position:0% +now connecting to you know Verizon or + + + align:start position:0% +now connecting to you know Verizon or +AT&T and if I step out of this room it's + + align:start position:0% +AT&T and if I step out of this room it's + + + align:start position:0% +AT&T and if I step out of this room it's +quite likely that the actual rate + + align:start position:0% +quite likely that the actual rate + + + align:start position:0% +quite likely that the actual rate +experienced by my phone might change by + + align:start position:0% +experienced by my phone might change by + + + align:start position:0% +experienced by my phone might change by +a factor of four or factor of eight + + align:start position:0% +a factor of four or factor of eight + + + align:start position:0% +a factor of four or factor of eight +within two + + align:start position:0% +within two + + + align:start position:0% +within two +seconds and that has to do of course + + align:start position:0% +seconds and that has to do of course + + + align:start position:0% +seconds and that has to do of course +with the fact that the signal to noise + + align:start position:0% +with the fact that the signal to noise + + + align:start position:0% +with the fact that the signal to noise +ratio I mean we're we're surrounded by + + align:start position:0% +ratio I mean we're we're surrounded by + + + align:start position:0% +ratio I mean we're we're surrounded by +thick walls and Metal and the moment I + + align:start position:0% +thick walls and Metal and the moment I + + + align:start position:0% +thick walls and Metal and the moment I +go out it's going to be different so how + + align:start position:0% +go out it's going to be different so how + + + align:start position:0% +go out it's going to be different so how +do you deal with this problem there's + + align:start position:0% +do you deal with this problem there's + + + align:start position:0% +do you deal with this problem there's +this one basic idea that's used uh + + align:start position:0% +this one basic idea that's used uh + + + align:start position:0% +this one basic idea that's used uh +that's a fundamental idea very important + + align:start position:0% +that's a fundamental idea very important + + + align:start position:0% +that's a fundamental idea very important +idea and it's called conservation of + + align:start position:0% +idea and it's called conservation of + + + align:start position:0% +idea and it's called conservation of +packets it's the same idea that you saw + + align:start position:0% +packets it's the same idea that you saw + + + align:start position:0% +packets it's the same idea that you saw +when you built your slotting window + + align:start position:0% +when you built your slotting window + + + align:start position:0% +when you built your slotting window +protocol it says that when you put in a + + align:start position:0% +protocol it says that when you put in a + + + align:start position:0% +protocol it says that when you put in a +packet into the network and the packet + + align:start position:0% +packet into the network and the packet + + + align:start position:0% +packet into the network and the packet +reaches the other end and you get an + + align:start position:0% +reaches the other end and you get an + + + align:start position:0% +reaches the other end and you get an +acknowledgement for the other + + align:start position:0% +acknowledgement for the other + + + align:start position:0% +acknowledgement for the other +end it means that one packet has left + + align:start position:0% +end it means that one packet has left + + + align:start position:0% +end it means that one packet has left +this pipe if you view this as that + + align:start position:0% +this pipe if you view this as that + + + align:start position:0% +this pipe if you view this as that +picture as you see in that picture up + + align:start position:0% +picture as you see in that picture up + + + align:start position:0% +picture as you see in that picture up +there packets are like water entering a + + align:start position:0% +there packets are like water entering a + + + align:start position:0% +there packets are like water entering a +pipe and then they leave the pipe and + + align:start position:0% +pipe and then they leave the pipe and + + + align:start position:0% +pipe and then they leave the pipe and +then an acknowledgement comes + + align:start position:0% +then an acknowledgement comes + + + align:start position:0% +then an acknowledgement comes +back if you have managed to somehow by + + align:start position:0% +back if you have managed to somehow by + + + align:start position:0% +back if you have managed to somehow by +some magic pick the appropriate window + + align:start position:0% +some magic pick the appropriate window + + + align:start position:0% +some magic pick the appropriate window +size then conservation of packets is a + + align:start position:0% +size then conservation of packets is a + + + align:start position:0% +size then conservation of packets is a +good principle for you to apply because + + align:start position:0% +good principle for you to apply because + + + align:start position:0% +good principle for you to apply because +what it says is that the only time + + align:start position:0% +what it says is that the only time + + + align:start position:0% +what it says is that the only time +you're allowed to put one more packet + + align:start position:0% +you're allowed to put one more packet + + + align:start position:0% +you're allowed to put one more packet +into the network is when you're sure + + align:start position:0% +into the network is when you're sure + + + align:start position:0% +into the network is when you're sure +that a packet has left the network and + + align:start position:0% +that a packet has left the network and + + + align:start position:0% +that a packet has left the network and +the way you know that a packet has left + + align:start position:0% +the way you know that a packet has left + + + align:start position:0% +the way you know that a packet has left +the network is because you receive an + + align:start position:0% +the network is because you receive an + + + align:start position:0% +the network is because you receive an +acknowledgement for that packet + + align:start position:0% + + + + align:start position:0% + +now of course this assumes that you know + + align:start position:0% +now of course this assumes that you know + + + align:start position:0% +now of course this assumes that you know +the right window size conservation + + align:start position:0% +the right window size conservation + + + align:start position:0% +the right window size conservation +packets has another really nice + + align:start position:0% +packets has another really nice + + + align:start position:0% +packets has another really nice +Advantage which is that let's say that + + align:start position:0% +Advantage which is that let's say that + + + align:start position:0% +Advantage which is that let's say that +you think you have the right window + + align:start position:0% +you think you have the right window + + + align:start position:0% +you think you have the right window +size but in fact more traffic comes + + align:start position:0% +size but in fact more traffic comes + + + align:start position:0% +size but in fact more traffic comes +in and the bandwidth the rate at which + + align:start position:0% +in and the bandwidth the rate at which + + + align:start position:0% +in and the bandwidth the rate at which +you can send data + + align:start position:0% +you can send data + + + align:start position:0% +you can send data +reduces what's going to happen is that + + align:start position:0% +reduces what's going to happen is that + + + align:start position:0% +reduces what's going to happen is that +because other traffic came in the + + align:start position:0% +because other traffic came in the + + + align:start position:0% +because other traffic came in the +roundtrip times are going to grow + + align:start position:0% +roundtrip times are going to grow + + + align:start position:0% +roundtrip times are going to grow +which means that acknowledgements to + + align:start position:0% +which means that acknowledgements to + + + align:start position:0% +which means that acknowledgements to +your packets are going to come back a + + align:start position:0% +your packets are going to come back a + + + align:start position:0% +your packets are going to come back a +little + + align:start position:0% +little + + + align:start position:0% +little +slower which means that you have a + + align:start position:0% +slower which means that you have a + + + align:start position:0% +slower which means that you have a +natural slowdown because + + align:start position:0% +natural slowdown because + + + align:start position:0% +natural slowdown because +acknowledgements come slower you + + align:start position:0% +acknowledgements come slower you + + + align:start position:0% +acknowledgements come slower you +naturally slow down and send packets a + + align:start position:0% +naturally slow down and send packets a + + + align:start position:0% +naturally slow down and send packets a +little + + align:start position:0% +little + + + align:start position:0% +little +slower and then of course then if the + + align:start position:0% +slower and then of course then if the + + + align:start position:0% +slower and then of course then if the +congestion persists packets are going to + + align:start position:0% +congestion persists packets are going to + + + align:start position:0% +congestion persists packets are going to +get + + align:start position:0% +get + + + align:start position:0% +get +lost and when packets get lost the trick + + align:start position:0% +lost and when packets get lost the trick + + + align:start position:0% +lost and when packets get lost the trick +is you have to reduce your window + + align:start position:0% +is you have to reduce your window + + + align:start position:0% +is you have to reduce your window +size so let's say you're running at a + + align:start position:0% +size so let's say you're running at a + + + align:start position:0% +size so let's say you're running at a +window size uh in your lab of + + align:start position:0% +window size uh in your lab of + + + align:start position:0% +window size uh in your lab of +packets when you implement this if you + + align:start position:0% +packets when you implement this if you + + + align:start position:0% +packets when you implement this if you +find that packets are getting lost you + + align:start position:0% +find that packets are getting lost you + + + align:start position:0% +find that packets are getting lost you +should drop your window size and one way + + align:start position:0% +should drop your window size and one way + + + align:start position:0% +should drop your window size and one way +to drop the window size that TCP uses is + + align:start position:0% +to drop the window size that TCP uses is + + + align:start position:0% +to drop the window size that TCP uses is +to reduce it by 1 + + align:start position:0% +to reduce it by 1 + + + align:start position:0% +to reduce it by 1 +half and then every time you find that + + align:start position:0% +half and then every time you find that + + + align:start position:0% +half and then every time you find that +acknowledgements are coming back you get + + align:start position:0% +acknowledgements are coming back you get + + + align:start position:0% +acknowledgements are coming back you get +a little greedy and you try to increase + + align:start position:0% +a little greedy and you try to increase + + + align:start position:0% +a little greedy and you try to increase +the window size and there are many ways + + align:start position:0% +the window size and there are many ways + + + align:start position:0% +the window size and there are many ways +to increase the window + + align:start position:0% +to increase the window + + + align:start position:0% +to increase the window +size now all of this stuff leads you + + align:start position:0% +size now all of this stuff leads you + + + align:start position:0% +size now all of this stuff leads you +know requires a way when you start the + + align:start position:0% +know requires a way when you start the + + + align:start position:0% +know requires a way when you start the +connection when you start an application + + align:start position:0% +connection when you start an application + + + align:start position:0% +connection when you start an application +what do you do and I think you pointed + + align:start position:0% +what do you do and I think you pointed + + + align:start position:0% +what do you do and I think you pointed +out an idea the last time when I first + + align:start position:0% +out an idea the last time when I first + + + align:start position:0% +out an idea the last time when I first +talked about this problem which is in + + align:start position:0% +talked about this problem which is in + + + align:start position:0% +talked about this problem which is in +the beginning you let your window size + + align:start position:0% +the beginning you let your window size + + + align:start position:0% +the beginning you let your window size +be one packet okay so you start your + + align:start position:0% +be one packet okay so you start your + + + align:start position:0% +be one packet okay so you start your +window size at one packet so it's like + + align:start position:0% +window size at one packet so it's like + + + align:start position:0% +window size at one packet so it's like +stop and wait so at the beginning of a + + align:start position:0% +stop and wait so at the beginning of a + + + align:start position:0% +stop and wait so at the beginning of a +connection if I were to draw time here + + align:start position:0% +connection if I were to draw time here + + + align:start position:0% +connection if I were to draw time here +against the window size you start at one + + align:start position:0% +against the window size you start at one + + + align:start position:0% +against the window size you start at one +packet and you just Shi that packet out + + align:start position:0% +packet and you just Shi that packet out + + + align:start position:0% +packet and you just Shi that packet out +it takes an entire round trip to get to + + align:start position:0% +it takes an entire round trip to get to + + + align:start position:0% +it takes an entire round trip to get to +the other side you get an + + align:start position:0% +the other side you get an + + + align:start position:0% +the other side you get an +acknowledgement back at that point + + align:start position:0% +acknowledgement back at that point + + + align:start position:0% +acknowledgement back at that point +with regular stop and wait you keep the + + align:start position:0% +with regular stop and wait you keep the + + + align:start position:0% +with regular stop and wait you keep the +same pack window size of one and you + + align:start position:0% +same pack window size of one and you + + + align:start position:0% +same pack window size of one and you +send one more packet you're not being + + align:start position:0% +send one more packet you're not being + + + align:start position:0% +send one more packet you're not being +greedy + + align:start position:0% +greedy + + + align:start position:0% +greedy +enough so one thing you can do is when + + align:start position:0% +enough so one thing you can do is when + + + align:start position:0% +enough so one thing you can do is when +you get one acknowledgement you double + + align:start position:0% +you get one acknowledgement you double + + + align:start position:0% +you get one acknowledgement you double +the window size or rather increase the + + align:start position:0% +the window size or rather increase the + + + align:start position:0% +the window size or rather increase the +window size by one every time you get an + + align:start position:0% +window size by one every time you get an + + + align:start position:0% +window size by one every time you get an +acknowledgement you increase the window + + align:start position:0% +acknowledgement you increase the window + + + align:start position:0% +acknowledgement you increase the window +size by one so the rule is um on and + + align:start position:0% +size by one so the rule is um on and + + + align:start position:0% +size by one so the rule is um on and +act you take W and you go to w+ + + align:start position:0% +act you take W and you go to w+ + + + align:start position:0% +act you take W and you go to w+ +one what does that do well after one + + align:start position:0% +one what does that do well after one + + + align:start position:0% +one what does that do well after one +round Tri if I draw this in in multiples + + align:start position:0% +round Tri if I draw this in in multiples + + + align:start position:0% +round Tri if I draw this in in multiples +of the round trip time this is one rtt + + align:start position:0% +of the round trip time this is one rtt + + + align:start position:0% +of the round trip time this is one rtt +this is two + + align:start position:0% +this is two + + + align:start position:0% +this is two +RTS this is three + + align:start position:0% +RTS this is three + + + align:start position:0% +RTS this is three +rtts and so forth so at the first at the + + align:start position:0% +rtts and so forth so at the first at the + + + align:start position:0% +rtts and so forth so at the first at the +beginning at the zero rtt your window + + align:start position:0% +beginning at the zero rtt your window + + + align:start position:0% +beginning at the zero rtt your window +size is one you get an + + align:start position:0% +size is one you get an + + + align:start position:0% +size is one you get an +acknowledgement you make your window + + align:start position:0% +acknowledgement you make your window + + + align:start position:0% +acknowledgement you make your window +size be two right 1+ one so at this + + align:start position:0% +size be two right 1+ one so at this + + + align:start position:0% +size be two right 1+ one so at this +point your window size is + + align:start position:0% +point your window size is + + + align:start position:0% +point your window size is +two what is the window size after two + + align:start position:0% +two what is the window size after two + + + align:start position:0% +two what is the window size after two +RTS it's four because cuz why is it four + + align:start position:0% +RTS it's four because cuz why is it four + + + align:start position:0% +RTS it's four because cuz why is it four +you set out two + + align:start position:0% +you set out two + + + align:start position:0% +you set out two +packets you get two AXS back your wi so + + align:start position:0% +packets you get two AXS back your wi so + + + align:start position:0% +packets you get two AXS back your wi so +for the first one you went from two to + + align:start position:0% +for the first one you went from two to + + + align:start position:0% +for the first one you went from two to +three then you went from three to four + + align:start position:0% +three then you went from three to four + + + align:start position:0% +three then you went from three to four +so your window size grow to + + align:start position:0% + + + + align:start position:0% + +four and then out here if there's no + + align:start position:0% +four and then out here if there's no + + + align:start position:0% +four and then out here if there's no +losses and you haven't yet reached if + + align:start position:0% +losses and you haven't yet reached if + + + align:start position:0% +losses and you haven't yet reached if +the window size hasn't yet reached the + + align:start position:0% +the window size hasn't yet reached the + + + align:start position:0% +the window size hasn't yet reached the +bandwidth delay product of the + + align:start position:0% +bandwidth delay product of the + + + align:start position:0% +bandwidth delay product of the +connection you're uh increasing + + align:start position:0% +connection you're uh increasing + + + align:start position:0% +connection you're uh increasing +exponentially so this is at eight and so + + align:start position:0% +exponentially so this is at eight and so + + + align:start position:0% +exponentially so this is at eight and so +forth you're growing fairly rapidly and + + align:start position:0% +forth you're growing fairly rapidly and + + + align:start position:0% +forth you're growing fairly rapidly and +at some point you're going to grow too + + align:start position:0% +at some point you're going to grow too + + + align:start position:0% +at some point you're going to grow too +fast your window size is going to + + align:start position:0% +fast your window size is going to + + + align:start position:0% +fast your window size is going to +exceed the bandwidth delay product plus + + align:start position:0% +exceed the bandwidth delay product plus + + + align:start position:0% +exceed the bandwidth delay product plus +the Q size of the bottleneck causing a + + align:start position:0% +the Q size of the bottleneck causing a + + + align:start position:0% +the Q size of the bottleneck causing a +packet to be lost and at that point you + + align:start position:0% +packet to be lost and at that point you + + + align:start position:0% +packet to be lost and at that point you +can do a bunch of things but one thing + + align:start position:0% +can do a bunch of things but one thing + + + align:start position:0% +can do a bunch of things but one thing +you can do is to drop the window size by + + align:start position:0% +you can do is to drop the window size by + + + align:start position:0% +you can do is to drop the window size by +a factor of two so whenever that happens + + align:start position:0% +a factor of two so whenever that happens + + + align:start position:0% +a factor of two so whenever that happens +um if there's a packet loss you drop by + + align:start position:0% +um if there's a packet loss you drop by + + + align:start position:0% +um if there's a packet loss you drop by +a factor of two and you could continue + + align:start position:0% +a factor of two and you could continue + + + align:start position:0% +a factor of two and you could continue +to try to grow exponentially but that + + align:start position:0% +to try to grow exponentially but that + + + align:start position:0% +to try to grow exponentially but that +would be stupid because you would grow + + align:start position:0% +would be stupid because you would grow + + + align:start position:0% +would be stupid because you would grow +exponentially and if the network + + align:start position:0% +exponentially and if the network + + + align:start position:0% +exponentially and if the network +conditions haven't changed you're going + + align:start position:0% +conditions haven't changed you're going + + + align:start position:0% +conditions haven't changed you're going +to again drop so at this point you could + + align:start position:0% +to again drop so at this point you could + + + align:start position:0% +to again drop so at this point you could +do something else and what TC P does is + + align:start position:0% +do something else and what TC P does is + + + align:start position:0% +do something else and what TC P does is +to start to grow linearly rather than + + align:start position:0% +to start to grow linearly rather than + + + align:start position:0% +to start to grow linearly rather than +exponential growth once you experience + + align:start position:0% +exponential growth once you experience + + + align:start position:0% +exponential growth once you experience +congestion you start to grow linearly + + align:start position:0% +congestion you start to grow linearly + + + align:start position:0% +congestion you start to grow linearly +and then maybe you experience congestion + + align:start position:0% +and then maybe you experience congestion + + + align:start position:0% +and then maybe you experience congestion +here you drop by one2 and grow linearly + + align:start position:0% +here you drop by one2 and grow linearly + + + align:start position:0% +here you drop by one2 and grow linearly +and you have this sort of Sawtooth + + align:start position:0% +and you have this sort of Sawtooth + + + align:start position:0% +and you have this sort of Sawtooth +behavior and for most web connections + + align:start position:0% +behavior and for most web connections + + + align:start position:0% +behavior and for most web connections +that involve downloading a small amount + + align:start position:0% +that involve downloading a small amount + + + align:start position:0% +that involve downloading a small amount +of data you end over here for video and + + align:start position:0% +of data you end over here for video and + + + align:start position:0% +of data you end over here for video and +everything else you go all the way and + + align:start position:0% +everything else you go all the way and + + + align:start position:0% +everything else you go all the way and +this is one strategy and there are many + + align:start position:0% +this is one strategy and there are many + + + align:start position:0% +this is one strategy and there are many +many others and like I said in in in in + + align:start position:0% +many others and like I said in in in in + + + align:start position:0% +many others and like I said in in in in +various kinds of networks like wireless + + align:start position:0% +various kinds of networks like wireless + + + align:start position:0% +various kinds of networks like wireless +networks it turns out this approach is + + align:start position:0% +networks it turns out this approach is + + + align:start position:0% +networks it turns out this approach is +not really that good and there there are + + align:start position:0% +not really that good and there there are + + + align:start position:0% +not really that good and there there are +open questions around how you should + + align:start position:0% +open questions around how you should + + + align:start position:0% +open questions around how you should +actually design uh the system so + + align:start position:0% +actually design uh the system so + + + align:start position:0% +actually design uh the system so +everyone understand the basic idea this + + align:start position:0% +everyone understand the basic idea this + + + align:start position:0% +everyone understand the basic idea this +is an example of adaptive congestion + + align:start position:0% +is an example of adaptive congestion + + + align:start position:0% +is an example of adaptive congestion +control you'll look at this in 6033 and + + align:start position:0% +control you'll look at this in 6033 and + + + align:start position:0% +control you'll look at this in 6033 and +in 6829 in more detail if you took those + + align:start position:0% +in 6829 in more detail if you took those + + + align:start position:0% +in 6829 in more detail if you took those +classes any + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +okay all right I'm now moving over to + + align:start position:0% +okay all right I'm now moving over to + + + align:start position:0% +okay all right I'm now moving over to +the 1990s nothing else interesting + + align:start position:0% +the 1990s nothing else interesting + + + align:start position:0% +the 1990s nothing else interesting +happened in the ' 80s but in the 1990s + + align:start position:0% +happened in the ' 80s but in the 1990s + + + align:start position:0% +happened in the ' 80s but in the 1990s +more things happened uh aranet + + align:start position:0% +more things happened uh aranet + + + align:start position:0% +more things happened uh aranet +essentially ended as far as universities + + align:start position:0% +essentially ended as far as universities + + + align:start position:0% +essentially ended as far as universities +and everybody else was concerned and in + + align:start position:0% +and everybody else was concerned and in + + + align:start position:0% +and everybody else was concerned and in +fact it transitioned into you know there + + align:start position:0% +fact it transitioned into you know there + + + align:start position:0% +fact it transitioned into you know there +were separate military networks and in + + align:start position:0% +were separate military networks and in + + + align:start position:0% +were separate military networks and in +1991 Tim berners Le who's also now here + + align:start position:0% +1991 Tim berners Le who's also now here + + + align:start position:0% +1991 Tim berners Le who's also now here +at MIT uh an a professor uh invented + + align:start position:0% +at MIT uh an a professor uh invented + + + align:start position:0% +at MIT uh an a professor uh invented +some a little thing called the worldwide + + align:start position:0% +some a little thing called the worldwide + + + align:start position:0% +some a little thing called the worldwide +web he called with one word worldwide + + align:start position:0% +web he called with one word worldwide + + + align:start position:0% +web he called with one word worldwide +web was the name of the program and I + + align:start position:0% +web was the name of the program and I + + + align:start position:0% +web was the name of the program and I +found this thing uh which is very + + align:start position:0% +found this thing uh which is very + + + align:start position:0% +found this thing uh which is very +interesting so he wrote a proposal in 19 + + align:start position:0% +interesting so he wrote a proposal in 19 + + + align:start position:0% +interesting so he wrote a proposal in 19 +I think + + align:start position:0% +I think + + + align:start position:0% +I think + + align:start position:0% + + + align:start position:0% +19889 I think um to CERN where he was + + align:start position:0% +19889 I think um to CERN where he was + + + align:start position:0% +19889 I think um to CERN where he was +working to his B at C and it's called + + align:start position:0% +working to his B at C and it's called + + + align:start position:0% +working to his B at C and it's called +Information Management a proposal and + + align:start position:0% +Information Management a proposal and + + + align:start position:0% +Information Management a proposal and +there was all these things you know + + align:start position:0% +there was all these things you know + + + align:start position:0% +there was all these things you know +about how the how what you know what + + align:start position:0% +about how the how what you know what + + + align:start position:0% +about how the how what you know what +became the web should work with links + + align:start position:0% +became the web should work with links + + + align:start position:0% +became the web should work with links +and so forth and his boss at the time on + + align:start position:0% +and so forth and his boss at the time on + + + align:start position:0% +and so forth and his boss at the time on +top wrote vague but interesting as his + + align:start position:0% +top wrote vague but interesting as his + + + align:start position:0% +top wrote vague but interesting as his +feedback in The Proposal presumably + + align:start position:0% +feedback in The Proposal presumably + + + align:start position:0% +feedback in The Proposal presumably +interesting part Trump the vague part + + align:start position:0% +interesting part Trump the vague part + + + align:start position:0% +interesting part Trump the vague part +and you know allowed him to actually + + align:start position:0% +and you know allowed him to actually + + + align:start position:0% +and you know allowed him to actually +proceed on this project uh which became + + align:start position:0% +proceed on this project uh which became + + + align:start position:0% +proceed on this project uh which became +the worldwide web obviously it's been + + align:start position:0% +the worldwide web obviously it's been + + + align:start position:0% +the worldwide web obviously it's been +tremendously + + align:start position:0% + + + + align:start position:0% + +successful now by the mid 1990s the NSF + + align:start position:0% +successful now by the mid 1990s the NSF + + + align:start position:0% +successful now by the mid 1990s the NSF +net which was the backbone connecting + + align:start position:0% +net which was the backbone connecting + + + align:start position:0% +net which was the backbone connecting +the US um various us organizations the + + align:start position:0% +the US um various us organizations the + + + align:start position:0% +the US um various us organizations the +government decided to essentially get + + align:start position:0% +government decided to essentially get + + + align:start position:0% +government decided to essentially get +out of the internet service provider + + align:start position:0% +out of the internet service provider + + + align:start position:0% +out of the internet service provider +business or rather the government + + align:start position:0% +business or rather the government + + + align:start position:0% +business or rather the government +decided not to fund that activity + + align:start position:0% +decided not to fund that activity + + + align:start position:0% +decided not to fund that activity +anymore and you know many of you have + + align:start position:0% +anymore and you know many of you have + + + align:start position:0% +anymore and you know many of you have +probably heard about this joke about + + align:start position:0% +probably heard about this joke about + + + align:start position:0% +probably heard about this joke about +alore inventing the internet and not + + align:start position:0% +alore inventing the internet and not + + + align:start position:0% +alore inventing the internet and not +inventing the internet and people saying + + align:start position:0% +inventing the internet and people saying + + + align:start position:0% +inventing the internet and people saying +he didn't invent the internet well the + + align:start position:0% +he didn't invent the internet well the + + + align:start position:0% +he didn't invent the internet well the +you know sort of a little bit of Truth + + align:start position:0% +you know sort of a little bit of Truth + + + align:start position:0% +you know sort of a little bit of Truth +in this alore was very instrumental in + + align:start position:0% +in this alore was very instrumental in + + + align:start position:0% +in this alore was very instrumental in +the government kind of getting out of + + align:start position:0% +the government kind of getting out of + + + align:start position:0% +the government kind of getting out of +the internet uh business and set up was + + align:start position:0% +the internet uh business and set up was + + + align:start position:0% +the internet uh business and set up was +involved in committing is that set of + + align:start position:0% +involved in committing is that set of + + + align:start position:0% +involved in committing is that set of +regulations that led to internet service + + align:start position:0% +regulations that led to internet service + + + align:start position:0% +regulations that led to internet service +providers commercial internet service + + align:start position:0% +providers commercial internet service + + + align:start position:0% +providers commercial internet service +providers actually forming and + + align:start position:0% +providers actually forming and + + + align:start position:0% +providers actually forming and +Commercial isps started to take off + + align:start position:0% +Commercial isps started to take off + + + align:start position:0% +Commercial isps started to take off +which was a really really big change for + + align:start position:0% +which was a really really big change for + + + align:start position:0% +which was a really really big change for +the internet because no longer was it + + align:start position:0% +the internet because no longer was it + + + align:start position:0% +the internet because no longer was it +the case that there's this one + + align:start position:0% +the case that there's this one + + + align:start position:0% +the case that there's this one +organization and one backbone Network + + align:start position:0% +organization and one backbone Network + + + align:start position:0% +organization and one backbone Network +that connects you know MIT and Harvard + + align:start position:0% +that connects you know MIT and Harvard + + + align:start position:0% +that connects you know MIT and Harvard +and everybody else together and all the + + align:start position:0% +and everybody else together and all the + + + align:start position:0% +and everybody else together and all the +companies together you had many many + + align:start position:0% +companies together you had many many + + + align:start position:0% +companies together you had many many +people who could offer internet service + + align:start position:0% +people who could offer internet service + + + align:start position:0% +people who could offer internet service +and in fact compete with each other the + + align:start position:0% +and in fact compete with each other the + + + align:start position:0% +and in fact compete with each other the +idea was this uh you know the internet + + align:start position:0% +idea was this uh you know the internet + + + align:start position:0% +idea was this uh you know the internet +Serv providers or different network + + align:start position:0% +Serv providers or different network + + + align:start position:0% +Serv providers or different network +operators have to cooperate with each + + align:start position:0% +operators have to cooperate with each + + + align:start position:0% +operators have to cooperate with each +other because we are interested in + + align:start position:0% +other because we are interested in + + + align:start position:0% +other because we are interested in +connecting everybody on the internet + + align:start position:0% +connecting everybody on the internet + + + align:start position:0% +connecting everybody on the internet +together but they also compete with each + + align:start position:0% +together but they also compete with each + + + align:start position:0% +together but they also compete with each +other and the reason they compete is + + align:start position:0% +other and the reason they compete is + + + align:start position:0% +other and the reason they compete is +they compete for customers if I'm a + + align:start position:0% +they compete for customers if I'm a + + + align:start position:0% +they compete for customers if I'm a +customer of Verizon I'm not a customer + + align:start position:0% +customer of Verizon I'm not a customer + + + align:start position:0% +customer of Verizon I'm not a customer +of Comcast for example and yet Verizon + + align:start position:0% +of Comcast for example and yet Verizon + + + align:start position:0% +of Comcast for example and yet Verizon +and Comcast and other isps have to + + align:start position:0% +and Comcast and other isps have to + + + align:start position:0% +and Comcast and other isps have to +actually cooperate to get packets + + align:start position:0% +actually cooperate to get packets + + + align:start position:0% +actually cooperate to get packets +through so how do you do this and it + + align:start position:0% +through so how do you do this and it + + + align:start position:0% +through so how do you do this and it +turns out that this is a tougher problem + + align:start position:0% +turns out that this is a tougher problem + + + align:start position:0% +turns out that this is a tougher problem +than you might + + align:start position:0% +than you might + + + align:start position:0% +than you might +think and the world the people invented + + align:start position:0% +think and the world the people invented + + + align:start position:0% +think and the world the people invented +this protocol called bgp or the Border + + align:start position:0% +this protocol called bgp or the Border + + + align:start position:0% +this protocol called bgp or the Border +Gateway protocol which uses an idea + + align:start position:0% +Gateway protocol which uses an idea + + + align:start position:0% +Gateway protocol which uses an idea +we've seen it uses path Vector to solve + + align:start position:0% +we've seen it uses path Vector to solve + + + align:start position:0% +we've seen it uses path Vector to solve +this problem and I'll talk a little bit + + align:start position:0% +this problem and I'll talk a little bit + + + align:start position:0% +this problem and I'll talk a little bit +about that as + + align:start position:0% +about that as + + + align:start position:0% +about that as +well the other thing that happened in + + align:start position:0% +well the other thing that happened in + + + align:start position:0% +well the other thing that happened in +the internet was that IP addresses + + align:start position:0% +the internet was that IP addresses + + + align:start position:0% +the internet was that IP addresses +started to get depleted and we saw why + + align:start position:0% +started to get depleted and we saw why + + + align:start position:0% +started to get depleted and we saw why +the last time everybody wanted those + + align:start position:0% +the last time everybody wanted those + + + align:start position:0% +the last time everybody wanted those +Class B addresses and um now in fact + + align:start position:0% +Class B addresses and um now in fact + + + align:start position:0% +Class B addresses and um now in fact +quite literally there are no more IP + + align:start position:0% +quite literally there are no more IP + + + align:start position:0% +quite literally there are no more IP +version 4 IP addresses and so there were + + align:start position:0% +version 4 IP addresses and so there were + + + align:start position:0% +version 4 IP addresses and so there were +there was a lot of work done on moving + + align:start position:0% +there was a lot of work done on moving + + + align:start position:0% +there was a lot of work done on moving +to other versions of Ip but the part + + align:start position:0% +to other versions of Ip but the part + + + align:start position:0% +to other versions of Ip but the part +that is interesting is this idea of + + align:start position:0% +that is interesting is this idea of + + + align:start position:0% +that is interesting is this idea of +class classless addressing so the idea + + align:start position:0% +class classless addressing so the idea + + + align:start position:0% +class classless addressing so the idea +was rather than have organizations that + + align:start position:0% +was rather than have organizations that + + + align:start position:0% +was rather than have organizations that +either had to have two to the 24 + + align:start position:0% +either had to have two to the 24 + + + align:start position:0% +either had to have two to the 24 +addresses or two to the 16 addresses or + + align:start position:0% +addresses or two to the 16 addresses or + + + align:start position:0% +addresses or two to the 16 addresses or +two to the eight addresses let's allow + + align:start position:0% +two to the eight addresses let's allow + + + align:start position:0% +two to the eight addresses let's allow +organizations to have any number of + + align:start position:0% +organizations to have any number of + + + align:start position:0% +organizations to have any number of +addresses so I want to tell you a little + + align:start position:0% +addresses so I want to tell you a little + + + align:start position:0% +addresses so I want to tell you a little +bit about what an IP address means + + align:start position:0% +bit about what an IP address means + + + align:start position:0% +bit about what an IP address means +because everyone has seen an IP address + + align:start position:0% +because everyone has seen an IP address + + + align:start position:0% +because everyone has seen an IP address +I want to explain how what it means and + + align:start position:0% +I want to explain how what it means and + + + align:start position:0% +I want to explain how what it means and +how it really actually works + + align:start position:0% +how it really actually works + + + align:start position:0% +how it really actually works +so if you look at an IP address 18.310 + + align:start position:0% +so if you look at an IP address 18.310 + + + align:start position:0% +so if you look at an IP address 18.310 +82 which is U which is one of my + + align:start position:0% +82 which is U which is one of my + + + align:start position:0% +82 which is U which is one of my +machines that dotted decimal notation + + align:start position:0% +machines that dotted decimal notation + + + align:start position:0% +machines that dotted decimal notation +with you know human readable numbers + + align:start position:0% +with you know human readable numbers + + + align:start position:0% +with you know human readable numbers +used to make sense in the old days it + + align:start position:0% +used to make sense in the old days it + + + align:start position:0% +used to make sense in the old days it +used to be that this is a class A + + align:start position:0% +used to be that this is a class A + + + align:start position:0% +used to be that this is a class A +address from MIT it's 18 dot whatever + + align:start position:0% +address from MIT it's 18 dot whatever + + + align:start position:0% +address from MIT it's 18 dot whatever +and MIT owned all of that stuff now that + + align:start position:0% +and MIT owned all of that stuff now that + + + align:start position:0% +and MIT owned all of that stuff now that +also happens to be true but as far as + + align:start position:0% +also happens to be true but as far as + + + align:start position:0% +also happens to be true but as far as +the network infrastructure and the + + align:start position:0% +the network infrastructure and the + + + align:start position:0% +the network infrastructure and the +switches are concerned this thing is + + align:start position:0% +switches are concerned this thing is + + + align:start position:0% +switches are concerned this thing is +nothing more than a 32-bit number that + + align:start position:0% +nothing more than a 32-bit number that + + + align:start position:0% +nothing more than a 32-bit number that +looks like that okay + + align:start position:0% + + + + align:start position:0% + +now when this when a packet with that + + align:start position:0% +now when this when a packet with that + + + align:start position:0% +now when this when a packet with that +number shows up at the switch with a + + align:start position:0% +number shows up at the switch with a + + + align:start position:0% +number shows up at the switch with a +destination address with that + + align:start position:0% +destination address with that + + + align:start position:0% +destination address with that +number really what happens is that the + + align:start position:0% +number really what happens is that the + + + align:start position:0% +number really what happens is that the +switch the router does not have an entry + + align:start position:0% +switch the router does not have an entry + + + align:start position:0% +switch the router does not have an entry +for every one of those destinations in + + align:start position:0% +for every one of those destinations in + + + align:start position:0% +for every one of those destinations in +the world if it did it just would be too + + align:start position:0% +the world if it did it just would be too + + + align:start position:0% +the world if it did it just would be too +much information so what it has is + + align:start position:0% +much information so what it has is + + + align:start position:0% +much information so what it has is +information corresponding to a certain + + align:start position:0% +information corresponding to a certain + + + align:start position:0% +information corresponding to a certain +prefix now that prefix could be of + + align:start position:0% +prefix now that prefix could be of + + + align:start position:0% +prefix now that prefix could be of +arbitrary length it could have an entry + + align:start position:0% +arbitrary length it could have an entry + + + align:start position:0% +arbitrary length it could have an entry +in it with just the first eight bits + + align:start position:0% +in it with just the first eight bits + + + align:start position:0% +in it with just the first eight bits +which would signify that all packets + + align:start position:0% +which would signify that all packets + + + align:start position:0% +which would signify that all packets +that show up with that first prefix of 8 + + align:start position:0% +that show up with that first prefix of 8 + + + align:start position:0% +that show up with that first prefix of 8 +Bits would have to be forwarded + + align:start position:0% +Bits would have to be forwarded + + + align:start position:0% +Bits would have to be forwarded +according to a rule according to the + + align:start position:0% +according to a rule according to the + + + align:start position:0% +according to a rule according to the +link that was set for those first eight + + align:start position:0% +link that was set for those first eight + + + align:start position:0% +link that was set for those first eight +bits or it could have an entry in the + + align:start position:0% +bits or it could have an entry in the + + + align:start position:0% +bits or it could have an entry in the +routing table for 16 bits or it could + + align:start position:0% +routing table for 16 bits or it could + + + align:start position:0% +routing table for 16 bits or it could +have an entry in the routing table for + + align:start position:0% +have an entry in the routing table for + + + align:start position:0% +have an entry in the routing table for +19 bits or whatever and that depends on + + align:start position:0% +19 bits or whatever and that depends on + + + align:start position:0% +19 bits or whatever and that depends on +how the routing system you know how we + + align:start position:0% +how the routing system you know how we + + + align:start position:0% +how the routing system you know how we +advertise the routes and what it + + align:start position:0% +advertise the routes and what it + + + align:start position:0% +advertise the routes and what it +contains so there's an important lesson + + align:start position:0% +contains so there's an important lesson + + + align:start position:0% +contains so there's an important lesson +here when a switch advertises a route + + align:start position:0% +here when a switch advertises a route + + + align:start position:0% +here when a switch advertises a route +for a destination on the internet the + + align:start position:0% +for a destination on the internet the + + + align:start position:0% +for a destination on the internet the +destination is not the destination of an + + align:start position:0% +destination is not the destination of an + + + align:start position:0% +destination is not the destination of an +is not the IP address of an endpoint but + + align:start position:0% +is not the IP address of an endpoint but + + + align:start position:0% +is not the IP address of an endpoint but +what that destination is + + align:start position:0% +what that destination is + + + align:start position:0% +what that destination is +is a prefix that represents a range of + + align:start position:0% +is a prefix that represents a range of + + + align:start position:0% +is a prefix that represents a range of +IP addresses all of which are forwarded + + align:start position:0% +IP addresses all of which are forwarded + + + align:start position:0% +IP addresses all of which are forwarded +the same way by the + + align:start position:0% +the same way by the + + + align:start position:0% +the same way by the +switch so one way of writing this in + + align:start position:0% +switch so one way of writing this in + + + align:start position:0% +switch so one way of writing this in +notation that we can understand as human + + align:start position:0% +notation that we can understand as human + + + align:start position:0% +notation that we can understand as human +beings more conveniently is this idea of + + align:start position:0% +beings more conveniently is this idea of + + + align:start position:0% +beings more conveniently is this idea of +writing it as + + align:start position:0% +writing it as + + + align:start position:0% +writing it as +18/8 what that means is this notation + + align:start position:0% +18/8 what that means is this notation + + + align:start position:0% +18/8 what that means is this notation +stands for all IP + + align:start position:0% +stands for all IP + + + align:start position:0% +stands for all IP +addresses which have the first eight + + align:start position:0% +addresses which have the first eight + + + align:start position:0% +addresses which have the first eight +bits in common which would be 00001 0 + + align:start position:0% +bits in common which would be 00001 0 + + + align:start position:0% +bits in common which would be 00001 0 +010 which stands for the human readable + + align:start position:0% +010 which stands for the human readable + + + align:start position:0% +010 which stands for the human readable +number 18 and it contains all two to the + + align:start position:0% +number 18 and it contains all two to the + + + align:start position:0% +number 18 and it contains all two to the +24 addresses corresponding to that + + align:start position:0% +24 addresses corresponding to that + + + align:start position:0% +24 addresses corresponding to that +quence so as another example if I have + + align:start position:0% +quence so as another example if I have + + + align:start position:0% +quence so as another example if I have +that in my routing table with a + + align:start position:0% +that in my routing table with a + + + align:start position:0% +that in my routing table with a +sl17 it stands for two to the + + align:start position:0% +sl17 it stands for two to the + + + align:start position:0% +sl17 it stands for two to the +15 consecutive IP addresses all of which + + align:start position:0% +15 consecutive IP addresses all of which + + + align:start position:0% +15 consecutive IP addresses all of which +the first 17 bits um in common okay does + + align:start position:0% +the first 17 bits um in common okay does + + + align:start position:0% +the first 17 bits um in common okay does +this make + + align:start position:0% +this make + + + align:start position:0% +this make +sense so this is what an IP address + + align:start position:0% +sense so this is what an IP address + + + align:start position:0% +sense so this is what an IP address +means and as far as a switch is + + align:start position:0% +means and as far as a switch is + + + align:start position:0% +means and as far as a switch is +concerned an rting table entry is + + align:start position:0% +concerned an rting table entry is + + + align:start position:0% +concerned an rting table entry is +not the IP is not a destination IP + + align:start position:0% +not the IP is not a destination IP + + + align:start position:0% +not the IP is not a destination IP +address but it's something in this form + + align:start position:0% +address but it's something in this form + + + align:start position:0% +address but it's something in this form +it contains a prefix and it contains a a + + align:start position:0% +it contains a prefix and it contains a a + + + align:start position:0% +it contains a prefix and it contains a a +a length + + align:start position:0% +a length + + + align:start position:0% +a length +so in human notation + + align:start position:0% +so in human notation + + + align:start position:0% +so in human notation +18317 would be 17 um 2 to the 15 bits + + align:start position:0% +18317 would be 17 um 2 to the 15 bits + + + align:start position:0% +18317 would be 17 um 2 to the 15 bits +which share the first 17 bits in + + align:start position:0% +which share the first 17 bits in + + + align:start position:0% +which share the first 17 bits in +common so what this means is that with + + align:start position:0% +common so what this means is that with + + + align:start position:0% +common so what this means is that with +this notation inside the forwarding + + align:start position:0% +this notation inside the forwarding + + + align:start position:0% +this notation inside the forwarding +table you can have an entry for one IP + + align:start position:0% +table you can have an entry for one IP + + + align:start position:0% +table you can have an entry for one IP +address or two or four or eight or 16 + + align:start position:0% +address or two or four or eight or 16 + + + align:start position:0% +address or two or four or eight or 16 +all the way up to you know whatever the + + align:start position:0% +all the way up to you know whatever the + + + align:start position:0% +all the way up to you know whatever the +maximum is right so it allows us to + + align:start position:0% +maximum is right so it allows us to + + + align:start position:0% +maximum is right so it allows us to +build networks of different sizes and + + align:start position:0% +build networks of different sizes and + + + align:start position:0% +build networks of different sizes and +let that networks identifier be known to + + align:start position:0% +let that networks identifier be known to + + + align:start position:0% +let that networks identifier be known to +the rest of the internet now in + + align:start position:0% +the rest of the internet now in + + + align:start position:0% +the rest of the internet now in +principle you could put every host in + + align:start position:0% +principle you could put every host in + + + align:start position:0% +principle you could put every host in +the network and that would mean that you + + align:start position:0% +the network and that would mean that you + + + align:start position:0% +the network and that would mean that you +have an entry that Each of which looks + + align:start position:0% +have an entry that Each of which looks + + + align:start position:0% +have an entry that Each of which looks +like a sl32 if I did a sl32 it meant + + align:start position:0% +like a sl32 if I did a sl32 it meant + + + align:start position:0% +like a sl32 if I did a sl32 it meant +that it's an individual IP address but + + align:start position:0% +that it's an individual IP address but + + + align:start position:0% +that it's an individual IP address but +that wouldn't scale and so we want to + + align:start position:0% +that wouldn't scale and so we want to + + + align:start position:0% +that wouldn't scale and so we want to +allow people the flexibility of having + + align:start position:0% +allow people the flexibility of having + + + align:start position:0% +allow people the flexibility of having +very different ranges sitting inside the + + align:start position:0% +very different ranges sitting inside the + + + align:start position:0% +very different ranges sitting inside the +routing + + align:start position:0% +routing + + + align:start position:0% +routing +system and there's one more Rule and + + align:start position:0% +system and there's one more Rule and + + + align:start position:0% +system and there's one more Rule and +this rule is important because I want to + + align:start position:0% +this rule is important because I want to + + + align:start position:0% +this rule is important because I want to +tell you this rule because I'm going to + + align:start position:0% +tell you this rule because I'm going to + + + align:start position:0% +tell you this rule because I'm going to +tell you how YouTube was hijacked by an + + align:start position:0% +tell you how YouTube was hijacked by an + + + align:start position:0% +tell you how YouTube was hijacked by an +ISP in Pakistan and it relies on your + + align:start position:0% +ISP in Pakistan and it relies on your + + + align:start position:0% +ISP in Pakistan and it relies on your +understanding this particular forwarding + + align:start position:0% +understanding this particular forwarding + + + align:start position:0% +understanding this particular forwarding +Rule and then I'll tell you about how uh + + align:start position:0% +Rule and then I'll tell you about how uh + + + align:start position:0% +Rule and then I'll tell you about how uh +an ISP in China hijacked 15% of the + + align:start position:0% +an ISP in China hijacked 15% of the + + + align:start position:0% +an ISP in China hijacked 15% of the +internet for a couple of for a few hours + + align:start position:0% +internet for a couple of for a few hours + + + align:start position:0% +internet for a couple of for a few hours +and that didn't require this rule but it + + align:start position:0% +and that didn't require this rule but it + + + align:start position:0% +and that didn't require this rule but it +it's twoo examples I want to tell you + + align:start position:0% +it's twoo examples I want to tell you + + + align:start position:0% +it's twoo examples I want to tell you +about but let me explain the rule the + + align:start position:0% +about but let me explain the rule the + + + align:start position:0% +about but let me explain the rule the +forwarding at a switch uses an idea + + align:start position:0% +forwarding at a switch uses an idea + + + align:start position:0% +forwarding at a switch uses an idea +called the longest prefix match so what + + align:start position:0% +called the longest prefix match so what + + + align:start position:0% +called the longest prefix match so what +that means is that if you have entries + + align:start position:0% +that means is that if you have entries + + + align:start position:0% +that means is that if you have entries +in your forwarding table let's take + + align:start position:0% +in your forwarding table let's take + + + align:start position:0% +in your forwarding table let's take +those two examples let's say I have an + + align:start position:0% +those two examples let's say I have an + + + align:start position:0% +those two examples let's say I have an +entry in the forwarding table this is a + + align:start position:0% +entry in the forwarding table this is a + + + align:start position:0% +entry in the forwarding table this is a +at a particular switch I have a + + align:start position:0% +at a particular switch I have a + + + align:start position:0% +at a particular switch I have a +forwarding table or a routing table and + + align:start position:0% +forwarding table or a routing table and + + + align:start position:0% +forwarding table or a routing table and +the first entry says 18 SL + + align:start position:0% +the first entry says 18 SL + + + align:start position:0% +the first entry says 18 SL +eight so what this means is it's 2 to + + align:start position:0% +eight so what this means is it's 2 to + + + align:start position:0% +eight so what this means is it's 2 to +the 24 + + align:start position:0% +the 24 + + + align:start position:0% +the 24 +addresses that share the first 8 Bits uh + + align:start position:0% +addresses that share the first 8 Bits uh + + + align:start position:0% +addresses that share the first 8 Bits uh +which is whatever corresponds to 18 0 0 + + align:start position:0% +which is whatever corresponds to 18 0 0 + + + align:start position:0% +which is whatever corresponds to 18 0 0 +whatever it is right and + + align:start position:0% + + + + align:start position:0% + +then and then let's say I have another + + align:start position:0% +then and then let's say I have another + + + align:start position:0% +then and then let's say I have another +entry which is some + + align:start position:0% + + + + align:start position:0% + +18317 and what that would be of course + + align:start position:0% +18317 and what that would be of course + + + align:start position:0% +18317 and what that would be of course +is 2 to the 15 + + align:start position:0% +is 2 to the 15 + + + align:start position:0% +is 2 to the 15 +addresses and the prefix would be as + + align:start position:0% +addresses and the prefix would be as + + + align:start position:0% +addresses and the prefix would be as +shown in that picture there whatever the + + align:start position:0% +shown in that picture there whatever the + + + align:start position:0% +shown in that picture there whatever the +first 17 bits are so some 17 + + align:start position:0% + + + + align:start position:0% + +bits now if the switch received a packet + + align:start position:0% +bits now if the switch received a packet + + + align:start position:0% +bits now if the switch received a packet +with an IP address and that IP address + + align:start position:0% +with an IP address and that IP address + + + align:start position:0% +with an IP address and that IP address +matched multiple entries you know you + + align:start position:0% +matched multiple entries you know you + + + align:start position:0% +matched multiple entries you know you +might have other entries sitting here + + align:start position:0% +might have other entries sitting here + + + align:start position:0% +might have other entries sitting here +you know um + + align:start position:0% +you know um + + + align:start position:0% +you know um +let's say that I have + + align:start position:0% +let's say that I have + + + align:start position:0% +let's say that I have +128. 32 something and I might have + + align:start position:0% +128. 32 something and I might have + + + align:start position:0% +128. 32 something and I might have +various other entries sitting in my + + align:start position:0% +various other entries sitting in my + + + align:start position:0% +various other entries sitting in my +forwarding table when a packet arrives + + align:start position:0% +forwarding table when a packet arrives + + + align:start position:0% +forwarding table when a packet arrives +it may in general Match multiple entries + + align:start position:0% +it may in general Match multiple entries + + + align:start position:0% +it may in general Match multiple entries +here right because the packet has a + + align:start position:0% +here right because the packet has a + + + align:start position:0% +here right because the packet has a +certain bit string in its destination + + align:start position:0% +certain bit string in its destination + + + align:start position:0% +certain bit string in its destination +address and that destination address now + + align:start position:0% +address and that destination address now + + + align:start position:0% +address and that destination address now +matches multiple of these it could match + + align:start position:0% +matches multiple of these it could match + + + align:start position:0% +matches multiple of these it could match +one or more of these entries here what + + align:start position:0% +one or more of these entries here what + + + align:start position:0% +one or more of these entries here what +an IP router does when it gets such a + + align:start position:0% +an IP router does when it gets such a + + + align:start position:0% +an IP router does when it gets such a +packet is to find the entry which + + align:start position:0% +packet is to find the entry which + + + align:start position:0% +packet is to find the entry which +matches in the longest prefix + + align:start position:0% +matches in the longest prefix + + + align:start position:0% +matches in the longest prefix +in other words the routing table entry + + align:start position:0% +in other words the routing table entry + + + align:start position:0% +in other words the routing table entry +that corresponds to the longest prefix + + align:start position:0% +that corresponds to the longest prefix + + + align:start position:0% +that corresponds to the longest prefix +match between the destination address of + + align:start position:0% +match between the destination address of + + + align:start position:0% +match between the destination address of +the packet and between the entry in the + + align:start position:0% +the packet and between the entry in the + + + align:start position:0% +the packet and between the entry in the +forwarding table is what you use to send + + align:start position:0% +forwarding table is what you use to send + + + align:start position:0% +forwarding table is what you use to send +the packet on so if you got a packet + + align:start position:0% +the packet on so if you got a packet + + + align:start position:0% +the packet on so if you got a packet +that was you know + + align:start position:0% +that was you know + + + align:start position:0% +that was you know +18316 do5 and it happened to match this + + align:start position:0% +18316 do5 and it happened to match this + + + align:start position:0% +18316 do5 and it happened to match this +entry it would go on one link let's say + + align:start position:0% +entry it would go on one link let's say + + + align:start position:0% +entry it would go on one link let's say +this is link one and if you got this + + align:start position:0% +this is link one and if you got this + + + align:start position:0% +this is link one and if you got this +other thing that didn't match this but + + align:start position:0% +other thing that didn't match this but + + + align:start position:0% +other thing that didn't match this but +match that you might have a different + + align:start position:0% +match that you might have a different + + + align:start position:0% +match that you might have a different +link let's call link zero so the output + + align:start position:0% +link let's call link zero so the output + + + align:start position:0% +link let's call link zero so the output +link that you use depends on the longest + + align:start position:0% +link that you use depends on the longest + + + align:start position:0% +link that you use depends on the longest +prefix match and MIT many organizations + + align:start position:0% +prefix match and MIT many organizations + + + align:start position:0% +prefix match and MIT many organizations +use this extremely well so I was + + align:start position:0% +use this extremely well so I was + + + align:start position:0% +use this extremely well so I was +remarking to some of you the uh at the + + align:start position:0% +remarking to some of you the uh at the + + + align:start position:0% +remarking to some of you the uh at the +end of class last time that you know + + align:start position:0% +end of class last time that you know + + + align:start position:0% +end of class last time that you know +it's funny MIT has multiple internet + + align:start position:0% +it's funny MIT has multiple internet + + + align:start position:0% +it's funny MIT has multiple internet +service providers and it turns out that + + align:start position:0% +service providers and it turns out that + + + align:start position:0% +service providers and it turns out that +if I use this network here and I + + align:start position:0% +if I use this network here and I + + + align:start position:0% +if I use this network here and I +download you know I go to linux.org + + align:start position:0% +download you know I go to linux.org + + + align:start position:0% +download you know I go to linux.org +which is the place you could download + + align:start position:0% +which is the place you could download + + + align:start position:0% +which is the place you could download +Linux code if I go from here it so + + align:start position:0% +Linux code if I go from here it so + + + align:start position:0% +Linux code if I go from here it so +happens that MIT uses level three which + + align:start position:0% +happens that MIT uses level three which + + + align:start position:0% +happens that MIT uses level three which +is I think the world's biggest or US's + + align:start position:0% +is I think the world's biggest or US's + + + align:start position:0% +is I think the world's biggest or US's +biggest internet service provider to get + + align:start position:0% +biggest internet service provider to get + + + align:start position:0% +biggest internet service provider to get +those packets the same thing if I just + + align:start position:0% +those packets the same thing if I just + + + align:start position:0% +those packets the same thing if I just +go up to stata and I connect to the + + align:start position:0% +go up to stata and I connect to the + + + align:start position:0% +go up to stata and I connect to the +stata wireless and go to linux.org + + align:start position:0% +stata wireless and go to linux.org + + + align:start position:0% +stata wireless and go to linux.org +packets from linux.org come back to me + + align:start position:0% +packets from linux.org come back to me + + + align:start position:0% +packets from linux.org come back to me +through a different ISP coent so MIT has + + align:start position:0% +through a different ISP coent so MIT has + + + align:start position:0% +through a different ISP coent so MIT has +decided that it wants to load balance + + align:start position:0% +decided that it wants to load balance + + + align:start position:0% +decided that it wants to load balance +its traffic so it advertises the prefix + + align:start position:0% +its traffic so it advertises the prefix + + + align:start position:0% +its traffic so it advertises the prefix +corresponding to the network in this + + align:start position:0% +corresponding to the network in this + + + align:start position:0% +corresponding to the network in this +room whatever the Wi-Fi network in this + + align:start position:0% +room whatever the Wi-Fi network in this + + + align:start position:0% +room whatever the Wi-Fi network in this +room U through one of the isps and it + + align:start position:0% +room U through one of the isps and it + + + align:start position:0% +room U through one of the isps and it +advertises the other prefix in stata to + + align:start position:0% +advertises the other prefix in stata to + + + align:start position:0% +advertises the other prefix in stata to +through the other ISP and it does it + + align:start position:0% +through the other ISP and it does it + + + align:start position:0% +through the other ISP and it does it +presumably load balance traffic and it + + align:start position:0% +presumably load balance traffic and it + + + align:start position:0% +presumably load balance traffic and it +also has this idea that if one of those + + align:start position:0% +also has this idea that if one of those + + + align:start position:0% +also has this idea that if one of those +links were to fail it would switch the + + align:start position:0% +links were to fail it would switch the + + + align:start position:0% +links were to fail it would switch the +traffic to the other link organizations + + align:start position:0% +traffic to the other link organizations + + + align:start position:0% +traffic to the other link organizations +do this because they would like to + + align:start position:0% +do this because they would like to + + + align:start position:0% +do this because they would like to +provide good service to the people + + align:start position:0% +provide good service to the people + + + align:start position:0% +provide good service to the people +inside their inside their organization + + align:start position:0% +inside their inside their organization + + + align:start position:0% +inside their inside their organization +so the longest prefix match is very + + align:start position:0% +so the longest prefix match is very + + + align:start position:0% +so the longest prefix match is very +crucial to how this all how this stuff + + align:start position:0% +crucial to how this all how this stuff + + + align:start position:0% +crucial to how this all how this stuff +really um kind of works so keep that in + + align:start position:0% +really um kind of works so keep that in + + + align:start position:0% +really um kind of works so keep that in +mind I'm going to come back to this uh + + align:start position:0% +mind I'm going to come back to this uh + + + align:start position:0% +mind I'm going to come back to this uh +onto the next + + align:start position:0% + + + + align:start position:0% + +slide in the rest of the 1990s + + align:start position:0% +slide in the rest of the 1990s + + + align:start position:0% +slide in the rest of the 1990s +a few interesting things happened one of + + align:start position:0% +a few interesting things happened one of + + + align:start position:0% +a few interesting things happened one of +them was that work started on this new + + align:start position:0% +them was that work started on this new + + + align:start position:0% +them was that work started on this new +proposal for IP called IPv6 which said + + align:start position:0% +proposal for IP called IPv6 which said + + + align:start position:0% +proposal for IP called IPv6 which said +let's not use 32-bit addresses let's go + + align:start position:0% +let's not use 32-bit addresses let's go + + + align:start position:0% +let's not use 32-bit addresses let's go +to 128bit bigger addresses and try to + + align:start position:0% +to 128bit bigger addresses and try to + + + align:start position:0% +to 128bit bigger addresses and try to +solve the address deplo problem IPv6 has + + align:start position:0% +solve the address deplo problem IPv6 has + + + align:start position:0% +solve the address deplo problem IPv6 has +taken a really really long time to get + + align:start position:0% +taken a really really long time to get + + + align:start position:0% +taken a really really long time to get +deployed for reasons I won't go into + + align:start position:0% +deployed for reasons I won't go into + + + align:start position:0% +deployed for reasons I won't go into +here but it seems to be happening now + + align:start position:0% +here but it seems to be happening now + + + align:start position:0% +here but it seems to be happening now +but people keep saying that it seems to + + align:start position:0% +but people keep saying that it seems to + + + align:start position:0% +but people keep saying that it seems to +be happening now I said that three years + + align:start position:0% +be happening now I said that three years + + + align:start position:0% +be happening now I said that three years +ago when I did the app up in this class + + align:start position:0% +ago when I did the app up in this class + + + align:start position:0% +ago when I did the app up in this class +so sometime at some point in the future + + align:start position:0% +so sometime at some point in the future + + + align:start position:0% +so sometime at some point in the future +that that statement will actually be + + align:start position:0% +that that statement will actually be + + + align:start position:0% +that that statement will actually be +true + + align:start position:0% + + + + align:start position:0% + +now you know everybody knows about + + align:start position:0% +now you know everybody knows about + + + align:start position:0% +now you know everybody knows about +Google Reinventing how search is done + + align:start position:0% +Google Reinventing how search is done + + + align:start position:0% +Google Reinventing how search is done +and starts to dominate another thing + + align:start position:0% +and starts to dominate another thing + + + align:start position:0% +and starts to dominate another thing +that happened in 1998 was content + + align:start position:0% +that happened in 1998 was content + + + align:start position:0% +that happened in 1998 was content +distribution networks started getting + + align:start position:0% +distribution networks started getting + + + align:start position:0% +distribution networks started getting +created and these are networks that you + + align:start position:0% +created and these are networks that you + + + align:start position:0% +created and these are networks that you +deploy as overly networks on top the + + align:start position:0% +deploy as overly networks on top the + + + align:start position:0% +deploy as overly networks on top the +internet to serve content better in a + + align:start position:0% +internet to serve content better in a + + + align:start position:0% +internet to serve content better in a +more reliable + + align:start position:0% +more reliable + + + align:start position:0% +more reliable +way now in in the 2000s the internet + + align:start position:0% +way now in in the 2000s the internet + + + align:start position:0% +way now in in the 2000s the internet +mature and I have the top five things + + align:start position:0% +mature and I have the top five things + + + align:start position:0% +mature and I have the top five things +that I think happened in networking uh + + align:start position:0% +that I think happened in networking uh + + + align:start position:0% +that I think happened in networking uh +in the networking industry and + + align:start position:0% +in the networking industry and + + + align:start position:0% +in the networking industry and +networking World in 2000s so this you + + align:start position:0% +networking World in 2000s so this you + + + align:start position:0% +networking World in 2000s so this you +know + + align:start position:0% +know + + + align:start position:0% +know +bust happened and then 911 + + align:start position:0% +bust happened and then 911 + + + align:start position:0% +bust happened and then 911 +happened the first thing that happened + + align:start position:0% +happened the first thing that happened + + + align:start position:0% +happened the first thing that happened +was the rise of peer-to-peer networks + + align:start position:0% +was the rise of peer-to-peer networks + + + align:start position:0% +was the rise of peer-to-peer networks +I'm sure many of you have used this + + align:start position:0% +I'm sure many of you have used this + + + align:start position:0% +I'm sure many of you have used this +Nutella freet you know bit torrent is + + align:start position:0% +Nutella freet you know bit torrent is + + + align:start position:0% +Nutella freet you know bit torrent is +the latest one uh there was a lot of + + align:start position:0% +the latest one uh there was a lot of + + + align:start position:0% +the latest one uh there was a lot of +research done including here at MIT on + + align:start position:0% +research done including here at MIT on + + + align:start position:0% +research done including here at MIT on +how you build these peer-to-peer + + align:start position:0% +how you build these peer-to-peer + + + align:start position:0% +how you build these peer-to-peer +networks the idea being you don't have a + + align:start position:0% +networks the idea being you don't have a + + + align:start position:0% +networks the idea being you don't have a +central point of failure and you can use + + align:start position:0% +central point of failure and you can use + + + align:start position:0% +central point of failure and you can use +this to distribute files extremely + + align:start position:0% +this to distribute files extremely + + + align:start position:0% +this to distribute files extremely +efficiently I mean bit tet is still + + align:start position:0% +efficiently I mean bit tet is still + + + align:start position:0% +efficiently I mean bit tet is still +highly dominant and distributed hash + + align:start position:0% +highly dominant and distributed hash + + + align:start position:0% +highly dominant and distributed hash +tables like card which was developed + + align:start position:0% +tables like card which was developed + + + align:start position:0% +tables like card which was developed +here and other schemes are used now by + + align:start position:0% +here and other schemes are used now by + + + align:start position:0% +here and other schemes are used now by +systems like Skype um they're used + + align:start position:0% +systems like Skype um they're used + + + align:start position:0% +systems like Skype um they're used +inside data centers like Amazon if you + + align:start position:0% +inside data centers like Amazon if you + + + align:start position:0% +inside data centers like Amazon if you +go to Amazon and buy stuff it uses a + + align:start position:0% +go to Amazon and buy stuff it uses a + + + align:start position:0% +go to Amazon and buy stuff it uses a +system called Dynamo which is a key + + align:start position:0% +system called Dynamo which is a key + + + align:start position:0% +system called Dynamo which is a key +value store that basically builds a + + align:start position:0% +value store that basically builds a + + + align:start position:0% +value store that basically builds a +distributed hash table so it's had a lot + + align:start position:0% +distributed hash table so it's had a lot + + + align:start position:0% +distributed hash table so it's had a lot +of impact both in data centers and in + + align:start position:0% +of impact both in data centers and in + + + align:start position:0% +of impact both in data centers and in +systems like uh + + align:start position:0% +systems like uh + + + align:start position:0% +systems like uh +Skype the second thing that happened was + + align:start position:0% +Skype the second thing that happened was + + + align:start position:0% +Skype the second thing that happened was +that in the in the early to mid 2000s + + align:start position:0% +that in the in the early to mid 2000s + + + align:start position:0% +that in the in the early to mid 2000s +security was became a huge deal people + + align:start position:0% +security was became a huge deal people + + + align:start position:0% +security was became a huge deal people +started attacking the internet which was + + align:start position:0% +started attacking the internet which was + + + align:start position:0% +started attacking the internet which was +which came somewhat of a surprise to + + align:start position:0% +which came somewhat of a surprise to + + + align:start position:0% +which came somewhat of a surprise to +people who grew up in the good old days + + align:start position:0% +people who grew up in the good old days + + + align:start position:0% +people who grew up in the good old days +of the internet where you know as I + + align:start position:0% +of the internet where you know as I + + + align:start position:0% +of the internet where you know as I +mentioned last time there were computers + + align:start position:0% +mentioned last time there were computers + + + align:start position:0% +mentioned last time there were computers +with root passwords that were empty + + align:start position:0% +with root passwords that were empty + + + align:start position:0% +with root passwords that were empty +because you know everybody could be + + align:start position:0% +because you know everybody could be + + + align:start position:0% +because you know everybody could be +trusted and then they found that as + + align:start position:0% +trusted and then they found that as + + + align:start position:0% +trusted and then they found that as +people started making money on the + + align:start position:0% +people started making money on the + + + align:start position:0% +people started making money on the +internet people started trying to attack + + align:start position:0% +internet people started trying to attack + + + align:start position:0% +internet people started trying to attack +uh the internet as well denial of + + align:start position:0% +uh the internet as well denial of + + + align:start position:0% +uh the internet as well denial of +service attacks started where people + + align:start position:0% +service attacks started where people + + + align:start position:0% +service attacks started where people +would launch attacks on websites and + + align:start position:0% +would launch attacks on websites and + + + align:start position:0% +would launch attacks on websites and +they they would often use it to extort + + align:start position:0% +they they would often use it to extort + + + align:start position:0% +they they would often use it to extort +money this would be like if you don't + + align:start position:0% +money this would be like if you don't + + + align:start position:0% +money this would be like if you don't +pay me I'm going to continue to Pummel + + align:start position:0% +pay me I'm going to continue to Pummel + + + align:start position:0% +pay me I'm going to continue to Pummel +your website so that you can't sell + + align:start position:0% +your website so that you can't sell + + + align:start position:0% +your website so that you can't sell +flowers or whatever it is you were doing + + align:start position:0% +flowers or whatever it is you were doing + + + align:start position:0% +flowers or whatever it is you were doing +on the + + align:start position:0% +on the + + + align:start position:0% +on the +web people found abilities in software + + align:start position:0% +web people found abilities in software + + + align:start position:0% +web people found abilities in software +and there were many worms that spread + + align:start position:0% +and there were many worms that spread + + + align:start position:0% +and there were many worms that spread +often pretty quickly SQL Slammer is a + + align:start position:0% +often pretty quickly SQL Slammer is a + + + align:start position:0% +often pretty quickly SQL Slammer is a +particularly interesting one of these we + + align:start position:0% +particularly interesting one of these we + + + align:start position:0% +particularly interesting one of these we +studied this stuff in 829 and in 6033 in + + align:start position:0% +studied this stuff in 829 and in 6033 in + + + align:start position:0% +studied this stuff in 829 and in 6033 in +some detail but this was remarkable + + align:start position:0% +some detail but this was remarkable + + + align:start position:0% +some detail but this was remarkable +because in 30 minutes it clogged the + + align:start position:0% +because in 30 minutes it clogged the + + + align:start position:0% +because in 30 minutes it clogged the +world's networks here's a picture of a + + align:start position:0% +world's networks here's a picture of a + + + align:start position:0% +world's networks here's a picture of a +screenshot this was at uh 5:30 or 5:30 + + align:start position:0% +screenshot this was at uh 5:30 or 5:30 + + + align:start position:0% +screenshot this was at uh 5:30 or 5:30 +in the morning uh I guess UTC grench + + align:start position:0% +in the morning uh I guess UTC grench + + + align:start position:0% +in the morning uh I guess UTC grench +time and you know nothing's going on and + + align:start position:0% +time and you know nothing's going on and + + + align:start position:0% +time and you know nothing's going on and +then half an hour later + + align:start position:0% +then half an hour later + + + align:start position:0% +then half an hour later +the blue splotches show the networks + + align:start position:0% +the blue splotches show the networks + + + align:start position:0% +the blue splotches show the networks +that were clogged and almost every + + align:start position:0% +that were clogged and almost every + + + align:start position:0% +that were clogged and almost every +computer that was vulnerable to this + + align:start position:0% +computer that was vulnerable to this + + + align:start position:0% +computer that was vulnerable to this +there weren't that many computers + + align:start position:0% +there weren't that many computers + + + align:start position:0% +there weren't that many computers +relative to the world's computers that + + align:start position:0% +relative to the world's computers that + + + align:start position:0% +relative to the world's computers that +were vulnerable to this but all these + + align:start position:0% +were vulnerable to this but all these + + + align:start position:0% +were vulnerable to this but all these +networks got hammered and in fact + + align:start position:0% +networks got hammered and in fact + + + align:start position:0% +networks got hammered and in fact +traffic came to a halt and this worm + + align:start position:0% +traffic came to a halt and this worm + + + align:start position:0% +traffic came to a halt and this worm +showed that the power of spreading you + + align:start position:0% +showed that the power of spreading you + + + align:start position:0% +showed that the power of spreading you +know if if machines trust each other or + + align:start position:0% +know if if machines trust each other or + + + align:start position:0% +know if if machines trust each other or +or you know either implicitly or + + align:start position:0% +or you know either implicitly or + + + align:start position:0% +or you know either implicitly or +explicitly it's very easy to actually + + align:start position:0% +explicitly it's very easy to actually + + + align:start position:0% +explicitly it's very easy to actually +find a vulnerability in one and then + + align:start position:0% +find a vulnerability in one and then + + + align:start position:0% +find a vulnerability in one and then +spread very very quickly so a lot of + + align:start position:0% +spread very very quickly so a lot of + + + align:start position:0% +spread very very quickly so a lot of +work was done on how to handle worm + + align:start position:0% +work was done on how to handle worm + + + align:start position:0% +work was done on how to handle worm +attacks + + align:start position:0% +attacks + + + align:start position:0% +attacks +uh a lot of this has to do with putting + + align:start position:0% +uh a lot of this has to do with putting + + + align:start position:0% +uh a lot of this has to do with putting +things inside of network switches + + align:start position:0% +things inside of network switches + + + align:start position:0% +things inside of network switches +running at high speeds to identify + + align:start position:0% +running at high speeds to identify + + + align:start position:0% +running at high speeds to identify +patterns that of in the payload of the + + align:start position:0% +patterns that of in the payload of the + + + align:start position:0% +patterns that of in the payload of the +in the data that's being sent in packets + + align:start position:0% +in the data that's being sent in packets + + + align:start position:0% +in the data that's being sent in packets +to quickly identify that this + + align:start position:0% +to quickly identify that this + + + align:start position:0% +to quickly identify that this +corresponds to a worm and then throw + + align:start position:0% +corresponds to a worm and then throw + + + align:start position:0% +corresponds to a worm and then throw +those packets away before they hit the + + align:start position:0% +those packets away before they hit the + + + align:start position:0% +those packets away before they hit the +actual end points uh right now we don't + + align:start position:0% +actual end points uh right now we don't + + + align:start position:0% +actual end points uh right now we don't +see too many worms spreading the ones + + align:start position:0% +see too many worms spreading the ones + + + align:start position:0% +see too many worms spreading the ones +that spread now are slow spreading worms + + align:start position:0% +that spread now are slow spreading worms + + + align:start position:0% +that spread now are slow spreading worms +um that often spread by human you know + + align:start position:0% +um that often spread by human you know + + + align:start position:0% +um that often spread by human you know +human contact it's like people clicking + + align:start position:0% +human contact it's like people clicking + + + align:start position:0% +human contact it's like people clicking +on links they shouldn't click on it runs + + align:start position:0% +on links they shouldn't click on it runs + + + align:start position:0% +on links they shouldn't click on it runs +program finds a vulnerability on their + + align:start position:0% +program finds a vulnerability on their + + + align:start position:0% +program finds a vulnerability on their +machine and then it resides on their + + align:start position:0% +machine and then it resides on their + + + align:start position:0% +machine and then it resides on their +machine uh and often these are then used + + align:start position:0% +machine uh and often these are then used + + + align:start position:0% +machine uh and often these are then used +to create these big bot Nets that are + + align:start position:0% +to create these big bot Nets that are + + + align:start position:0% +to create these big bot Nets that are +used to launch denial of service attacks + + align:start position:0% +used to launch denial of service attacks + + + align:start position:0% +used to launch denial of service attacks +or often used to send spam and do other + + align:start position:0% +or often used to send spam and do other + + + align:start position:0% +or often used to send spam and do other +things like that so they're still going + + align:start position:0% +things like that so they're still going + + + align:start position:0% +things like that so they're still going +on but you don't hear about them in the + + align:start position:0% +on but you don't hear about them in the + + + align:start position:0% +on but you don't hear about them in the +newspaper a Spam became a huge problem + + align:start position:0% +newspaper a Spam became a huge problem + + + align:start position:0% +newspaper a Spam became a huge problem +and it continues to be somewhat of a + + align:start position:0% +and it continues to be somewhat of a + + + align:start position:0% +and it continues to be somewhat of a +problem though these days you know the + + align:start position:0% +problem though these days you know the + + + align:start position:0% +problem though these days you know the +distinction between spam and internet + + align:start position:0% +distinction between spam and internet + + + align:start position:0% +distinction between spam and internet +marketing internet marketing is kind of + + align:start position:0% +marketing internet marketing is kind of + + + align:start position:0% +marketing internet marketing is kind of +you know coming down the gap's closing + + align:start position:0% +you know coming down the gap's closing + + + align:start position:0% +you know coming down the gap's closing +but by and large spam now + + align:start position:0% +but by and large spam now + + + align:start position:0% +but by and large spam now +is why I wouldn't say it's a solt + + align:start position:0% +is why I wouldn't say it's a solt + + + align:start position:0% +is why I wouldn't say it's a solt +problem is generally combed by you know + + align:start position:0% +problem is generally combed by you know + + + align:start position:0% +problem is generally combed by you know +uh big organizations that have enough + + align:start position:0% +uh big organizations that have enough + + + align:start position:0% +uh big organizations that have enough +data enough email coming in that they + + align:start position:0% +data enough email coming in that they + + + align:start position:0% +data enough email coming in that they +can identify spam and then filter those + + align:start position:0% +can identify spam and then filter those + + + align:start position:0% +can identify spam and then filter those +away route hijacking is the other + + align:start position:0% +away route hijacking is the other + + + align:start position:0% +away route hijacking is the other +problem that remains a huge + + align:start position:0% +problem that remains a huge + + + align:start position:0% +problem that remains a huge +vulnerability so I want to tell you + + align:start position:0% +vulnerability so I want to tell you + + + align:start position:0% +vulnerability so I want to tell you +about two examples of Route hijacking + + align:start position:0% +about two examples of Route hijacking + + + align:start position:0% +about two examples of Route hijacking +and I I don't think there's easy the + + align:start position:0% +and I I don't think there's easy the + + + align:start position:0% +and I I don't think there's easy the +technical side of this problem we + + align:start position:0% +technical side of this problem we + + + align:start position:0% +technical side of this problem we +understand how to solve but how to + + align:start position:0% +understand how to solve but how to + + + align:start position:0% +understand how to solve but how to +deploy good Solutions is still unfair so + + align:start position:0% +deploy good Solutions is still unfair so + + + align:start position:0% +deploy good Solutions is still unfair so +the first example um is from this + + align:start position:0% +the first example um is from this + + + align:start position:0% +the first example um is from this +problem has been going on every 3 years + + align:start position:0% +problem has been going on every 3 years + + + align:start position:0% +problem has been going on every 3 years +you see a big route hijacking problem + + align:start position:0% +you see a big route hijacking problem + + + align:start position:0% +you see a big route hijacking problem +the first one was uh from 2008 I think + + align:start position:0% +the first one was uh from 2008 I think + + + align:start position:0% +the first one was uh from 2008 I think +it was 2008 where YouTube was + + align:start position:0% +it was 2008 where YouTube was + + + align:start position:0% +it was 2008 where YouTube was +unavailable to people for a few hours + + align:start position:0% +unavailable to people for a few hours + + + align:start position:0% +unavailable to people for a few hours +everywhere in the + + align:start position:0% +everywhere in the + + + align:start position:0% +everywhere in the +world now you could argue whether + + align:start position:0% +world now you could argue whether + + + align:start position:0% +world now you could argue whether +watching cats dance or whatever is that + + align:start position:0% +watching cats dance or whatever is that + + + align:start position:0% +watching cats dance or whatever is that +important but the fact is that YouTube + + align:start position:0% +important but the fact is that YouTube + + + align:start position:0% +important but the fact is that YouTube +has a lot of money Google has a lot of + + align:start position:0% +has a lot of money Google has a lot of + + + align:start position:0% +has a lot of money Google has a lot of +money and even they were vulnerable to + + align:start position:0% +money and even they were vulnerable to + + + align:start position:0% +money and even they were vulnerable to +this problem the second example was a + + align:start position:0% +this problem the second example was a + + + align:start position:0% +this problem the second example was a +little different uh China + + align:start position:0% +little different uh China + + + align:start position:0% +little different uh China +Telecom managed to get about 15% roughly + + align:start position:0% +Telecom managed to get about 15% roughly + + + align:start position:0% +Telecom managed to get about 15% roughly +speaking of the internet traffic to go + + align:start position:0% +speaking of the internet traffic to go + + + align:start position:0% +speaking of the internet traffic to go +through them now the interesting thing + + align:start position:0% +through them now the interesting thing + + + align:start position:0% +through them now the interesting thing +about that attack is that it wasn't + + align:start position:0% +about that attack is that it wasn't + + + align:start position:0% +about that attack is that it wasn't +clear it was an attack uh I should just + + align:start position:0% +clear it was an attack uh I should just + + + align:start position:0% +clear it was an attack uh I should just +say of + + align:start position:0% +say of + + + align:start position:0% +say of +that error or failure was that people + + align:start position:0% +that error or failure was that people + + + align:start position:0% +that error or failure was that people +didn't even notice because unlike + + align:start position:0% +didn't even notice because unlike + + + align:start position:0% +didn't even notice because unlike +YouTube where you know you go you + + align:start position:0% +YouTube where you know you go you + + + align:start position:0% +YouTube where you know you go you +couldn't get your data and then you + + align:start position:0% +couldn't get your data and then you + + + align:start position:0% +couldn't get your data and then you +people noticed it and then they were + + align:start position:0% +people noticed it and then they were + + + align:start position:0% +people noticed it and then they were +trying to scambling to solve the problem + + align:start position:0% +trying to scambling to solve the problem + + + align:start position:0% +trying to scambling to solve the problem +with the chin Chinese attack what ended + + align:start position:0% +with the chin Chinese attack what ended + + + align:start position:0% +with the chin Chinese attack what ended +or Chinese vulnerability what happened + + align:start position:0% +or Chinese vulnerability what happened + + + align:start position:0% +or Chinese vulnerability what happened +was the China Telecom managed to divert + + align:start position:0% +was the China Telecom managed to divert + + + align:start position:0% +was the China Telecom managed to divert +the traffic that wasn't supposed to go + + align:start position:0% +the traffic that wasn't supposed to go + + + align:start position:0% +the traffic that wasn't supposed to go +through them to them and then they + + align:start position:0% +through them to them and then they + + + align:start position:0% +through them to them and then they +forwarded the traffic on to the rest of + + align:start position:0% +forwarded the traffic on to the rest of + + + align:start position:0% +forwarded the traffic on to the rest of +their destinations the acual destination + + align:start position:0% +their destinations the acual destination + + + align:start position:0% +their destinations the acual destination +so you would find things like instead of + + align:start position:0% +so you would find things like instead of + + + align:start position:0% +so you would find things like instead of +my latency being 100 millisecs it might + + align:start position:0% +my latency being 100 millisecs it might + + + align:start position:0% +my latency being 100 millisecs it might +be 500 + + align:start position:0% +be 500 + + + align:start position:0% +be 500 +milliseconds which is yeah you know you + + align:start position:0% +milliseconds which is yeah you know you + + + align:start position:0% +milliseconds which is yeah you know you +you may not even notice or sometimes you + + align:start position:0% +you may not even notice or sometimes you + + + align:start position:0% +you may not even notice or sometimes you +notice it and you go well that's just + + align:start position:0% +notice it and you go well that's just + + + align:start position:0% +notice it and you go well that's just +the internet being the internet you know + + align:start position:0% +the internet being the internet you know + + + align:start position:0% +the internet being the internet you know +sometimes that happens but the fact is + + align:start position:0% +sometimes that happens but the fact is + + + align:start position:0% +sometimes that happens but the fact is +that they were able to you know an ISP + + align:start position:0% +that they were able to you know an ISP + + + align:start position:0% +that they were able to you know an ISP +was able to ESS divert a large fraction + + align:start position:0% +was able to ESS divert a large fraction + + + align:start position:0% +was able to ESS divert a large fraction +of the world's traffic and both these + + align:start position:0% +of the world's traffic and both these + + + align:start position:0% +of the world's traffic and both these +attacks fundamentally stem from the + + align:start position:0% +attacks fundamentally stem from the + + + align:start position:0% +attacks fundamentally stem from the +following problem which is that at the + + align:start position:0% +following problem which is that at the + + + align:start position:0% +following problem which is that at the +end of the day despite all of this + + align:start position:0% +end of the day despite all of this + + + align:start position:0% +end of the day despite all of this +investment into the internet and the + + align:start position:0% +investment into the internet and the + + + align:start position:0% +investment into the internet and the +importance of the internet and the the + + align:start position:0% +importance of the internet and the the + + + align:start position:0% +importance of the internet and the the +amount of money in it uh internet + + align:start position:0% +amount of money in it uh internet + + + align:start position:0% +amount of money in it uh internet +routing works because of essentially an + + align:start position:0% +routing works because of essentially an + + + align:start position:0% +routing works because of essentially an +honor code it's like isps at some level + + align:start position:0% +honor code it's like isps at some level + + + align:start position:0% +honor code it's like isps at some level +internet service providers and + + align:start position:0% +internet service providers and + + + align:start position:0% +internet service providers and +organizations trust each other and + + align:start position:0% +organizations trust each other and + + + align:start position:0% +organizations trust each other and +there's this transitive trust which is I + + align:start position:0% +there's this transitive trust which is I + + + align:start position:0% +there's this transitive trust which is I +might trust you and you might trust her + + align:start position:0% +might trust you and you might trust her + + + align:start position:0% +might trust you and you might trust her +and implicitly the way routing works is + + align:start position:0% +and implicitly the way routing works is + + + align:start position:0% +and implicitly the way routing works is +that ends up in me trusting her because + + align:start position:0% +that ends up in me trusting her because + + + align:start position:0% +that ends up in me trusting her because +I trust everything you tell me and you + + align:start position:0% +I trust everything you tell me and you + + + align:start position:0% +I trust everything you tell me and you +happen to trust everything she tells you + + align:start position:0% +happen to trust everything she tells you + + + align:start position:0% +happen to trust everything she tells you +which means that if she were to make a + + align:start position:0% +which means that if she were to make a + + + align:start position:0% +which means that if she were to make a +mistake and you were to believe it then + + align:start position:0% +mistake and you were to believe it then + + + align:start position:0% +mistake and you were to believe it then +in a sense everybody else in the world + + align:start position:0% +in a sense everybody else in the world + + + align:start position:0% +in a sense everybody else in the world +is vulnerable to this + + align:start position:0% +is vulnerable to this + + + align:start position:0% +is vulnerable to this +problem so let me explain what happened + + align:start position:0% +problem so let me explain what happened + + + align:start position:0% +problem so let me explain what happened +in the case of + + align:start position:0% +in the case of + + + align:start position:0% +in the case of +YouTube because it's reflective of how + + align:start position:0% +YouTube because it's reflective of how + + + align:start position:0% +YouTube because it's reflective of how +things really work so here's this little + + align:start position:0% +things really work so here's this little + + + align:start position:0% +things really work so here's this little +ISP called Pakistan + + align:start position:0% + + + + align:start position:0% + +Telecom okay tiny tiny ISP you know + + align:start position:0% +Telecom okay tiny tiny ISP you know + + + align:start position:0% +Telecom okay tiny tiny ISP you know +hardly anyone uses it outs I mean + + align:start position:0% +hardly anyone uses it outs I mean + + + align:start position:0% +hardly anyone uses it outs I mean +everyone in Pakistan probably uses it + + align:start position:0% +everyone in Pakistan probably uses it + + + align:start position:0% +everyone in Pakistan probably uses it +but in the grand scale of things it's + + align:start position:0% +but in the grand scale of things it's + + + align:start position:0% +but in the grand scale of things it's +it's completely tiny so they end up + + align:start position:0% +it's completely tiny so they end up + + + align:start position:0% +it's completely tiny so they end up +connecting to a bunch of people outside + + align:start position:0% +connecting to a bunch of people outside + + + align:start position:0% +connecting to a bunch of people outside +in different parts of the world and one + + align:start position:0% +in different parts of the world and one + + + align:start position:0% +in different parts of the world and one +of the people they ended up connecting + + align:start position:0% +of the people they ended up connecting + + + align:start position:0% +of the people they ended up connecting +to was another ISP out in Hong Kong + + align:start position:0% +to was another ISP out in Hong Kong + + + align:start position:0% +to was another ISP out in Hong Kong +called + + align:start position:0% + + + + align:start position:0% + +pccw and these guys connect to the rest + + align:start position:0% +pccw and these guys connect to the rest + + + align:start position:0% +pccw and these guys connect to the rest +of the internet um and presumably pakist + + align:start position:0% +of the internet um and presumably pakist + + + align:start position:0% +of the internet um and presumably pakist +Telecom connects to other people I I I + + align:start position:0% +Telecom connects to other people I I I + + + align:start position:0% +Telecom connects to other people I I I +don't know now here's what happened so + + align:start position:0% +don't know now here's what happened so + + + align:start position:0% +don't know now here's what happened so +where do YouTube fit into all this you + + align:start position:0% +where do YouTube fit into all this you + + + align:start position:0% +where do YouTube fit into all this you +know YouTube is sitting somewhere over + + align:start position:0% + + + + align:start position:0% + +here and presumably it's not directly I + + align:start position:0% +here and presumably it's not directly I + + + align:start position:0% +here and presumably it's not directly I +mean these guys have nothing to do with + + align:start position:0% +mean these guys have nothing to do with + + + align:start position:0% +mean these guys have nothing to do with +each other this this these guys are + + align:start position:0% +each other this this these guys are + + + align:start position:0% +each other this this these guys are +connected to some other big isps and + + align:start position:0% +connected to some other big isps and + + + align:start position:0% +connected to some other big isps and +small isps and eventually there's a set + + align:start position:0% +small isps and eventually there's a set + + + align:start position:0% +small isps and eventually there's a set +of internet service providers that + + align:start position:0% +of internet service providers that + + + align:start position:0% +of internet service providers that +somehow you + + align:start position:0% +somehow you + + + align:start position:0% +somehow you +know constitute the internet + + align:start position:0% +know constitute the internet + + + align:start position:0% +know constitute the internet +and each of these is independent each of + + align:start position:0% +and each of these is independent each of + + + align:start position:0% +and each of these is independent each of +these is known as an autonomous system + + align:start position:0% +these is known as an autonomous system + + + align:start position:0% +these is known as an autonomous system +or + + align:start position:0% +or + + + align:start position:0% +or +as and each of these autonomous systems + + align:start position:0% +as and each of these autonomous systems + + + align:start position:0% +as and each of these autonomous systems +has a number a 16bit number MIT is an + + align:start position:0% +has a number a 16bit number MIT is an + + + align:start position:0% +has a number a 16bit number MIT is an +autonomous system and because MIT was + + align:start position:0% +autonomous system and because MIT was + + + align:start position:0% +autonomous system and because MIT was +very early in the internet mit's + + align:start position:0% +very early in the internet mit's + + + align:start position:0% +very early in the internet mit's +autonomous system number is + + align:start position:0% +autonomous system number is + + + align:start position:0% +autonomous system number is +three but right now there are many many + + align:start position:0% +three but right now there are many many + + + align:start position:0% +three but right now there are many many +isps you know right now you know you can + + align:start position:0% +isps you know right now you know you can + + + align:start position:0% +isps you know right now you know you can +have + + align:start position:0% +have + + + align:start position:0% +have +is there are tens of thousands of + + align:start position:0% +is there are tens of thousands of + + + align:start position:0% +is there are tens of thousands of +autonomous systems I don't know 35 40 + + align:start position:0% +autonomous systems I don't know 35 40 + + + align:start position:0% +autonomous systems I don't know 35 40 +45,000 something like that we're number + + align:start position:0% +45,000 something like that we're number + + + align:start position:0% +45,000 something like that we're number +three so anyway um uh who's number one + + align:start position:0% +three so anyway um uh who's number one + + + align:start position:0% +three so anyway um uh who's number one +BBN bbnn I don't know who what as2 is + + align:start position:0% +BBN bbnn I don't know who what as2 is + + + align:start position:0% +BBN bbnn I don't know who what as2 is +bbnn of course is number one but + + align:start position:0% +bbnn of course is number one but + + + align:start position:0% +bbnn of course is number one but +actually that number is owned by + + align:start position:0% +actually that number is owned by + + + align:start position:0% +actually that number is owned by +somebody who acquired bbnn who acquired + + align:start position:0% +somebody who acquired bbnn who acquired + + + align:start position:0% +somebody who acquired bbnn who acquired +you know so sort of somebody acquires it + + align:start position:0% +you know so sort of somebody acquires it + + + align:start position:0% +you know so sort of somebody acquires it +now here's an interesting thing that's + + align:start position:0% +now here's an interesting thing that's + + + align:start position:0% +now here's an interesting thing that's +happening you these autonomous system + + align:start position:0% +happening you these autonomous system + + + align:start position:0% +happening you these autonomous system +numbers I remember I was a very young + + align:start position:0% +numbers I remember I was a very young + + + align:start position:0% +numbers I remember I was a very young +graduate student when people were + + align:start position:0% +graduate student when people were + + + align:start position:0% +graduate student when people were +talking about these autonomous system + + align:start position:0% +talking about these autonomous system + + + align:start position:0% +talking about these autonomous system +numbers and I remember these mailing + + align:start position:0% +numbers and I remember these mailing + + + align:start position:0% +numbers and I remember these mailing +lless discussions I wasn't working on + + align:start position:0% +lless discussions I wasn't working on + + + align:start position:0% +lless discussions I wasn't working on +this problem then I worked on it much + + align:start position:0% +this problem then I worked on it much + + + align:start position:0% +this problem then I worked on it much +later but people were saying yeah 16 + + align:start position:0% +later but people were saying yeah 16 + + + align:start position:0% +later but people were saying yeah 16 +bits is plenty enough for an autonomous + + align:start position:0% +bits is plenty enough for an autonomous + + + align:start position:0% +bits is plenty enough for an autonomous +system identifier because remember + + align:start position:0% +system identifier because remember + + + align:start position:0% +system identifier because remember +nsfnet was one there was one internet + + align:start position:0% +nsfnet was one there was one internet + + + align:start position:0% +nsfnet was one there was one internet +service provider in the early '90s um + + align:start position:0% +service provider in the early '90s um + + + align:start position:0% +service provider in the early '90s um +mid90s people were talking about isps + + align:start position:0% +mid90s people were talking about isps + + + align:start position:0% +mid90s people were talking about isps +and they said H 16 bits is plenty and I + + align:start position:0% +and they said H 16 bits is plenty and I + + + align:start position:0% +and they said H 16 bits is plenty and I +remember there were some people actually + + align:start position:0% +remember there were some people actually + + + align:start position:0% +remember there were some people actually +graduate students who were saying maybe + + align:start position:0% +graduate students who were saying maybe + + + align:start position:0% +graduate students who were saying maybe +we should make it 32 bits because we you + + align:start position:0% +we should make it 32 bits because we you + + + align:start position:0% +we should make it 32 bits because we you +know people remembered that you know the + + align:start position:0% +know people remembered that you know the + + + align:start position:0% +know people remembered that you know the +internet started you remember those old + + align:start position:0% +internet started you remember those old + + + align:start position:0% +internet started you remember those old +things of the internet where uh you know + + align:start position:0% +things of the internet where uh you know + + + align:start position:0% +things of the internet where uh you know +people said eight networks or eight bits + + align:start position:0% +people said eight networks or eight bits + + + align:start position:0% +people said eight networks or eight bits +for a network identifier are plenty + + align:start position:0% +for a network identifier are plenty + + + align:start position:0% +for a network identifier are plenty +enough and of course they got you know + + align:start position:0% +enough and of course they got you know + + + align:start position:0% +enough and of course they got you know +screwed so anyway what's happening now + + align:start position:0% +screwed so anyway what's happening now + + + align:start position:0% +screwed so anyway what's happening now +of course is the the older guys where 16 + + align:start position:0% +of course is the the older guys where 16 + + + align:start position:0% +of course is the the older guys where 16 +bits is plenty enough because you know + + align:start position:0% +bits is plenty enough because you know + + + align:start position:0% +bits is plenty enough because you know +we don't want to have too much overhead + + align:start position:0% +we don't want to have too much overhead + + + align:start position:0% +we don't want to have too much overhead +on packets and get they put in you know + + align:start position:0% +on packets and get they put in you know + + + align:start position:0% +on packets and get they put in you know +16 bits and now we're at 45,000 or + + align:start position:0% +16 bits and now we're at 45,000 or + + + align:start position:0% +16 bits and now we're at 45,000 or +50,000 and guess what there's a proposal + + align:start position:0% +50,000 and guess what there's a proposal + + + align:start position:0% +50,000 and guess what there's a proposal +on now on how do you how the heck do you + + align:start position:0% +on now on how do you how the heck do you + + + align:start position:0% +on now on how do you how the heck do you +extend this to you know more than two + + align:start position:0% +extend this to you know more than two + + + align:start position:0% +extend this to you know more than two +two to the 16 autonomous systems because + + align:start position:0% +two to the 16 autonomous systems because + + + align:start position:0% +two to the 16 autonomous systems because +now the internet is growing so you know + + align:start position:0% +now the internet is growing so you know + + + align:start position:0% +now the internet is growing so you know +whenever if ever you're given an + + align:start position:0% +whenever if ever you're given an + + + align:start position:0% +whenever if ever you're given an +opportunity to design the number of bits + + align:start position:0% +opportunity to design the number of bits + + + align:start position:0% +opportunity to design the number of bits +for something and you will always have + + align:start position:0% +for something and you will always have + + + align:start position:0% +for something and you will always have +to do something just pick something much + + align:start position:0% +to do something just pick something much + + + align:start position:0% +to do something just pick something much +much bigger than you imagine and then + + align:start position:0% +much bigger than you imagine and then + + + align:start position:0% +much bigger than you imagine and then +double + + align:start position:0% +double + + + align:start position:0% +double +it because it's always you'll never get + + align:start position:0% +it because it's always you'll never get + + + align:start position:0% +it because it's always you'll never get +it right so anyway um each of these + + align:start position:0% +it right so anyway um each of these + + + align:start position:0% +it right so anyway um each of these +autonomous systems has an identifier in + + align:start position:0% +autonomous systems has an identifier in + + + align:start position:0% +autonomous systems has an identifier in +it okay and each of these guys when they + + align:start position:0% +it okay and each of these guys when they + + + align:start position:0% +it okay and each of these guys when they +make an announcement in the routing + + align:start position:0% +make an announcement in the routing + + + align:start position:0% +make an announcement in the routing +system the way it works is that you + + align:start position:0% +system the way it works is that you + + + align:start position:0% +system the way it works is that you +create your your identifier and then you + + align:start position:0% +create your your identifier and then you + + + align:start position:0% +create your your identifier and then you +tell people all of the IP prefixes that + + align:start position:0% +tell people all of the IP prefixes that + + + align:start position:0% +tell people all of the IP prefixes that +you own okay so when I create my + + align:start position:0% +you own okay so when I create my + + + align:start position:0% +you own okay so when I create my +distance vector or in this case a path + + align:start position:0% +distance vector or in this case a path + + + align:start position:0% +distance vector or in this case a path +Vector advertisement if I'm autonomous + + align:start position:0% +Vector advertisement if I'm autonomous + + + align:start position:0% +Vector advertisement if I'm autonomous +system three I have a set of IP + + align:start position:0% +system three I have a set of IP + + + align:start position:0% +system three I have a set of IP +addresses so MIT might have 18. whatever + + align:start position:0% +addresses so MIT might have 18. whatever + + + align:start position:0% +addresses so MIT might have 18. whatever +sl8 uh MIT has you know 128. something/ + + align:start position:0% +sl8 uh MIT has you know 128. something/ + + + align:start position:0% +sl8 uh MIT has you know 128. something/ +let's say 19 MIT has a whole slew of + + align:start position:0% +let's say 19 MIT has a whole slew of + + + align:start position:0% +let's say 19 MIT has a whole slew of +these IP addresses that they've Acquired + + align:start position:0% +these IP addresses that they've Acquired + + + align:start position:0% +these IP addresses that they've Acquired +and what they're going to say is I'm + + align:start position:0% +and what they're going to say is I'm + + + align:start position:0% +and what they're going to say is I'm +autonomous system three and I know how + + align:start position:0% +autonomous system three and I know how + + + align:start position:0% +autonomous system three and I know how +to get to these guys because I own these + + align:start position:0% +to get to these guys because I own these + + + align:start position:0% +to get to these guys because I own these +guys this is the origin announcement and + + align:start position:0% +guys this is the origin announcement and + + + align:start position:0% +guys this is the origin announcement and +then other people you know MIT might + + align:start position:0% +then other people you know MIT might + + + align:start position:0% +then other people you know MIT might +this is as3 MIT sends it to its isps and + + align:start position:0% +this is as3 MIT sends it to its isps and + + + align:start position:0% +this is as3 MIT sends it to its isps and +they send it to their isps and every + + align:start position:0% +they send it to their isps and every + + + align:start position:0% +they send it to their isps and every +time an autonomous system receives + + align:start position:0% +time an autonomous system receives + + + align:start position:0% +time an autonomous system receives +multiple advertisements along different + + align:start position:0% +multiple advertisements along different + + + align:start position:0% +multiple advertisements along different +paths for the same prefix they pick one + + align:start position:0% +paths for the same prefix they pick one + + + align:start position:0% +paths for the same prefix they pick one +they they select among them they have + + align:start position:0% +they they select among them they have + + + align:start position:0% +they they select among them they have +some rules to select among them and + + align:start position:0% +some rules to select among them and + + + align:start position:0% +some rules to select among them and +these rules have to do with the length + + align:start position:0% +these rules have to do with the length + + + align:start position:0% +these rules have to do with the length +of the path between autonomous system + + align:start position:0% +of the path between autonomous system + + + align:start position:0% +of the path between autonomous system +they have to do with how much you're + + align:start position:0% +they have to do with how much you're + + + align:start position:0% +they have to do with how much you're +paying so for example MIT might be + + align:start position:0% +paying so for example MIT might be + + + align:start position:0% +paying so for example MIT might be +getting a better deal from cogent than + + align:start position:0% +getting a better deal from cogent than + + + align:start position:0% +getting a better deal from cogent than +from level three and so it would want + + align:start position:0% +from level three and so it would want + + + align:start position:0% +from level three and so it would want +more of its traffic to come from Cent + + align:start position:0% +more of its traffic to come from Cent + + + align:start position:0% +more of its traffic to come from Cent +and therefore it would decide that it + + align:start position:0% +and therefore it would decide that it + + + align:start position:0% +and therefore it would decide that it +would uh only advertise C + + align:start position:0% +would uh only advertise C + + + align:start position:0% +would uh only advertise C +of its addresses on certain path there's + + align:start position:0% +of its addresses on certain path there's + + + align:start position:0% +of its addresses on certain path there's +lots of policy it's very very + + align:start position:0% +lots of policy it's very very + + + align:start position:0% +lots of policy it's very very +complicated but yet you know some + + align:start position:0% +complicated but yet you know some + + + align:start position:0% +complicated but yet you know some +miracle miracle the whole thing works so + + align:start position:0% +miracle miracle the whole thing works so + + + align:start position:0% +miracle miracle the whole thing works so +anyway these things go through from + + align:start position:0% +anyway these things go through from + + + align:start position:0% +anyway these things go through from +autonomous system to autonomous system + + align:start position:0% +autonomous system to autonomous system + + + align:start position:0% +autonomous system to autonomous system +so what's this path Vector right + + align:start position:0% +so what's this path Vector right + + + align:start position:0% +so what's this path Vector right +remember I told you about the path + + align:start position:0% +remember I told you about the path + + + align:start position:0% +remember I told you about the path +Vector the path Vector is a sequence of + + align:start position:0% +Vector the path Vector is a sequence of + + + align:start position:0% +Vector the path Vector is a sequence of +paths so it could be 3 17 26 and so + + align:start position:0% +paths so it could be 3 17 26 and so + + + align:start position:0% +paths so it could be 3 17 26 and so +forth so I have an animation of this + + align:start position:0% +forth so I have an animation of this + + + align:start position:0% +forth so I have an animation of this +thing so I want to show that to you + + align:start position:0% +thing so I want to show that to you + + + align:start position:0% +thing so I want to show that to you +because it's totally interesting so what + + align:start position:0% +because it's totally interesting so what + + + align:start position:0% +because it's totally interesting so what +there's this website called bgp play if + + align:start position:0% +there's this website called bgp play if + + + align:start position:0% +there's this website called bgp play if +I can find it so there's a way to get + + align:start position:0% +I can find it so there's a way to get + + + align:start position:0% +I can find it so there's a way to get +mit's uh route advertisements over the + + align:start position:0% +mit's uh route advertisements over the + + + align:start position:0% +mit's uh route advertisements over the +past month and you can kind of see how + + align:start position:0% +past month and you can kind of see how + + + align:start position:0% +past month and you can kind of see how +these stats change so anyway what + + align:start position:0% +these stats change so anyway what + + + align:start position:0% +these stats change so anyway what +happened to YouTube what what happened + + align:start position:0% +happened to YouTube what what happened + + + align:start position:0% +happened to YouTube what what happened +to YouTube was the the government of + + align:start position:0% +to YouTube was the the government of + + + align:start position:0% +to YouTube was the the government of +Pakistan decided that what they would + + align:start position:0% +Pakistan decided that what they would + + + align:start position:0% +Pakistan decided that what they would +tell Pakistan Telecom was to not allow + + align:start position:0% +tell Pakistan Telecom was to not allow + + + align:start position:0% +tell Pakistan Telecom was to not allow +their users to go to YouTube so what + + align:start position:0% +their users to go to YouTube so what + + + align:start position:0% +their users to go to YouTube so what +they did was rather than simply drop + + align:start position:0% +they did was rather than simply drop + + + align:start position:0% +they did was rather than simply drop +those requests they wanted to get + + align:start position:0% +those requests they wanted to get + + + align:start position:0% +those requests they wanted to get +Pakistan Telecom when somebody clicked + + align:start position:0% +Pakistan Telecom when somebody clicked + + + align:start position:0% +Pakistan Telecom when somebody clicked +on a YouTube link to go to a website + + align:start position:0% +on a YouTube link to go to a website + + + align:start position:0% +on a YouTube link to go to a website +that Pakistan Telecom would run that + + align:start position:0% +that Pakistan Telecom would run that + + + align:start position:0% +that Pakistan Telecom would run that +basically said you're not allowed to use + + align:start position:0% +basically said you're not allowed to use + + + align:start position:0% +basically said you're not allowed to use +YouTube but would you like to see + + align:start position:0% +YouTube but would you like to see + + + align:start position:0% +YouTube but would you like to see +something + + align:start position:0% +something + + + align:start position:0% +something +else okay so the way they did that was + + align:start position:0% +else okay so the way they did that was + + + align:start position:0% +else okay so the way they did that was +they decided YouTube has some address + + align:start position:0% +they decided YouTube has some address + + + align:start position:0% +they decided YouTube has some address +let me call YouTube's address y + + align:start position:0% +let me call YouTube's address y + + + align:start position:0% +let me call YouTube's address y +something something let me just call it + + align:start position:0% +something something let me just call it + + + align:start position:0% +something something let me just call it +y right Y is a is a set of IP addresses + + align:start position:0% +y right Y is a is a set of IP addresses + + + align:start position:0% +y right Y is a is a set of IP addresses +that correspond to YouTube it's not one + + align:start position:0% +that correspond to YouTube it's not one + + + align:start position:0% +that correspond to YouTube it's not one +they have many machines so what these + + align:start position:0% +they have many machines so what these + + + align:start position:0% +they have many machines so what these +guys did was they did something they + + align:start position:0% +guys did was they did something they + + + align:start position:0% +guys did was they did something they +thought was very clever they have a + + align:start position:0% +thought was very clever they have a + + + align:start position:0% +thought was very clever they have a +whole network of users there they + + align:start position:0% +whole network of users there they + + + align:start position:0% +whole network of users there they +decided they would + + align:start position:0% +decided they would + + + align:start position:0% +decided they would +advertise a route for Destination y + + align:start position:0% +advertise a route for Destination y + + + align:start position:0% +advertise a route for Destination y +inside their network but rather than + + align:start position:0% +inside their network but rather than + + + align:start position:0% +inside their network but rather than +use um the actual route advertisement + + align:start position:0% +use um the actual route advertisement + + + align:start position:0% +use um the actual route advertisement +for y they would actually send it to + + align:start position:0% +for y they would actually send it to + + + align:start position:0% +for y they would actually send it to +their own machine so remember they + + align:start position:0% +their own machine so remember they + + + align:start position:0% +their own machine so remember they +changed the routing now they're telling + + align:start position:0% +changed the routing now they're telling + + + align:start position:0% +changed the routing now they're telling +their users they're hijacking the route + + align:start position:0% +their users they're hijacking the route + + + align:start position:0% +their users they're hijacking the route +they're telling their users that to go + + align:start position:0% +they're telling their users that to go + + + align:start position:0% +they're telling their users that to go +to YouTube you should not use the actual + + align:start position:0% +to YouTube you should not use the actual + + + align:start position:0% +to YouTube you should not use the actual +link that I'm telling you to use but + + align:start position:0% +link that I'm telling you to use but + + + align:start position:0% +link that I'm telling you to use but +instead go to this other place inside my + + align:start position:0% +instead go to this other place inside my + + + align:start position:0% +instead go to this other place inside my +network where I can show you this other + + align:start position:0% +network where I can show you this other + + + align:start position:0% +network where I can show you this other +website you know maybe pretend it's + + align:start position:0% +website you know maybe pretend it's + + + align:start position:0% +website you know maybe pretend it's +YouTube or whatever now everything is so + + align:start position:0% +YouTube or whatever now everything is so + + + align:start position:0% +YouTube or whatever now everything is so +far so good right I mean people do this + + align:start position:0% +far so good right I mean people do this + + + align:start position:0% +far so good right I mean people do this +all the time you know when you go to a + + align:start position:0% +all the time you know when you go to a + + + align:start position:0% +all the time you know when you go to a +hotel or any internet kiosk internet + + align:start position:0% +hotel or any internet kiosk internet + + + align:start position:0% +hotel or any internet kiosk internet +place you take your laptop and you go to + + align:start position:0% +place you take your laptop and you go to + + + align:start position:0% +place you take your laptop and you go to +you know CNN.com and the thing next + + align:start position:0% +you know CNN.com and the thing next + + + align:start position:0% +you know CNN.com and the thing next +thing you see is would you like to sign + + align:start position:0% +thing you see is would you like to sign + + + align:start position:0% +thing you see is would you like to sign +in how does that work well that works + + align:start position:0% +in how does that work well that works + + + align:start position:0% +in how does that work well that works +because they essentially hijack the + + align:start position:0% +because they essentially hijack the + + + align:start position:0% +because they essentially hijack the +route they make it look like you're + + align:start position:0% +route they make it look like you're + + + align:start position:0% +route they make it look like you're +going to CNN but in fact you're going + + align:start position:0% +going to CNN but in fact you're going + + + align:start position:0% +going to CNN but in fact you're going +somewhere else right after all your + + align:start position:0% +somewhere else right after all your + + + align:start position:0% +somewhere else right after all your +computer wrote to go to CNN and the IP + + align:start position:0% +computer wrote to go to CNN and the IP + + + align:start position:0% +computer wrote to go to CNN and the IP +address used was presume the CNN but + + align:start position:0% +address used was presume the CNN but + + + align:start position:0% +address used was presume the CNN but +then they made a mistake somewh here + + align:start position:0% +then they made a mistake somewh here + + + align:start position:0% +then they made a mistake somewh here +probably he was too tired set up a + + align:start position:0% +probably he was too tired set up a + + + align:start position:0% +probably he was too tired set up a +configuration so so he advertised his + + align:start position:0% +configuration so so he advertised his + + + align:start position:0% +configuration so so he advertised his +new route to Y that he created out to + + align:start position:0% + + + + align:start position:0% + +pccw now pccw was to some degree at + + align:start position:0% +pccw now pccw was to some degree at + + + align:start position:0% +pccw now pccw was to some degree at +fault because pccw should have known to + + align:start position:0% +fault because pccw should have known to + + + align:start position:0% +fault because pccw should have known to +some degree what actual IP addresses + + align:start position:0% +some degree what actual IP addresses + + + align:start position:0% +some degree what actual IP addresses +Pakistan Telecom owns and only owner + + align:start position:0% +Pakistan Telecom owns and only owner + + + align:start position:0% +Pakistan Telecom owns and only owner +route requests route advertisements + + align:start position:0% +route requests route advertisements + + + align:start position:0% +route requests route advertisements +coming from those things right pccw + + align:start position:0% +coming from those things right pccw + + + align:start position:0% +coming from those things right pccw +needs to know how to go how to send + + align:start position:0% +needs to know how to go how to send + + + align:start position:0% +needs to know how to go how to send +packets to nodes inside of Pakistan + + align:start position:0% +packets to nodes inside of Pakistan + + + align:start position:0% +packets to nodes inside of Pakistan +Telecom but clearly this guy has nothing + + align:start position:0% +Telecom but clearly this guy has nothing + + + align:start position:0% +Telecom but clearly this guy has nothing +useful to say about how to send packets + + align:start position:0% +useful to say about how to send packets + + + align:start position:0% +useful to say about how to send packets +to YouTube but yet this guy honored this + + align:start position:0% +to YouTube but yet this guy honored this + + + align:start position:0% +to YouTube but yet this guy honored this +message so there were two mistakes here + + align:start position:0% +message so there were two mistakes here + + + align:start position:0% +message so there were two mistakes here +actually there were many mistakes but + + align:start position:0% +actually there were many mistakes but + + + align:start position:0% +actually there were many mistakes but +the two big ones were there was a + + align:start position:0% +the two big ones were there was a + + + align:start position:0% +the two big ones were there was a +mistake made here sending something out + + align:start position:0% +mistake made here sending something out + + + align:start position:0% +mistake made here sending something out +there was a mistake made here honoring + + align:start position:0% +there was a mistake made here honoring + + + align:start position:0% +there was a mistake made here honoring +this request by this time you have + + align:start position:0% +this request by this time you have + + + align:start position:0% +this request by this time you have +transitive trust because pccw would find + + align:start position:0% +transitive trust because pccw would find + + + align:start position:0% +transitive trust because pccw would find +and what they also did was they made + + align:start position:0% +and what they also did was they made + + + align:start position:0% +and what they also did was they made +this a more specific prefix so YouTube + + align:start position:0% +this a more specific prefix so YouTube + + + align:start position:0% +this a more specific prefix so YouTube +is advertising a slash I believe a SL2 + + align:start position:0% +is advertising a slash I believe a SL2 + + + align:start position:0% +is advertising a slash I believe a SL2 +one which meant it was many many bits in + + align:start position:0% +one which meant it was many many bits in + + + align:start position:0% +one which meant it was many many bits in +the prefix 11 bits in common and there + + align:start position:0% +the prefix 11 bits in common and there + + + align:start position:0% +the prefix 11 bits in common and there +were uh it was sorry 21 bits in common + + align:start position:0% +were uh it was sorry 21 bits in common + + + align:start position:0% +were uh it was sorry 21 bits in common +sl21 but these guys advertised to + + align:start position:0% +sl21 but these guys advertised to + + + align:start position:0% +sl21 but these guys advertised to +guarantee that all traffic would come in + + align:start position:0% +guarantee that all traffic would come in + + + align:start position:0% +guarantee that all traffic would come in +they advertised a + + align:start position:0% +they advertised a + + + align:start position:0% +they advertised a +sl24 so it's more specific so what + + align:start position:0% +sl24 so it's more specific so what + + + align:start position:0% +sl24 so it's more specific so what +happened was pccw believed that and they + + align:start position:0% +happened was pccw believed that and they + + + align:start position:0% +happened was pccw believed that and they +read advertised that to their isps and + + align:start position:0% +read advertised that to their isps and + + + align:start position:0% +read advertised that to their isps and +to their isps and so forth now the + + align:start position:0% +to their isps and so forth now the + + + align:start position:0% +to their isps and so forth now the +reason why this really got all of the + + align:start position:0% +reason why this really got all of the + + + align:start position:0% +reason why this really got all of the +internet's traffic was sent toward this + + align:start position:0% +internet's traffic was sent toward this + + + align:start position:0% +internet's traffic was sent toward this +poor guy in Pakistan + + align:start position:0% +poor guy in Pakistan + + + align:start position:0% +poor guy in Pakistan +was because everybody is doing this + + align:start position:0% +was because everybody is doing this + + + align:start position:0% +was because everybody is doing this +longest prefix match and it's true that + + align:start position:0% +longest prefix match and it's true that + + + align:start position:0% +longest prefix match and it's true that +there's a legitimate route to YouTube in + + align:start position:0% +there's a legitimate route to YouTube in + + + align:start position:0% +there's a legitimate route to YouTube in +those routers but they're ignoring it + + align:start position:0% +those routers but they're ignoring it + + + align:start position:0% +those routers but they're ignoring it +because they find a more specific route + + align:start position:0% +because they find a more specific route + + + align:start position:0% +because they find a more specific route +that somebody had advertised so if you + + align:start position:0% +that somebody had advertised so if you + + + align:start position:0% +that somebody had advertised so if you +want to get traffic sent to Google + + align:start position:0% +want to get traffic sent to Google + + + align:start position:0% +want to get traffic sent to Google +figure out a way to convince some bigger + + align:start position:0% +figure out a way to convince some bigger + + + align:start position:0% +figure out a way to convince some bigger +ISP to take your route to a more + + align:start position:0% +ISP to take your route to a more + + + align:start position:0% +ISP to take your route to a more +specific prefix that you know is owned + + align:start position:0% +specific prefix that you know is owned + + + align:start position:0% +specific prefix that you know is owned +by Google and just advertise it out okay + + align:start position:0% +by Google and just advertise it out okay + + + align:start position:0% +by Google and just advertise it out okay +you're probably going to get a lot of + + align:start position:0% +you're probably going to get a lot of + + + align:start position:0% +you're probably going to get a lot of +traffic now you know you may not want + + align:start position:0% +traffic now you know you may not want + + + align:start position:0% +traffic now you know you may not want +all that traffic but you get it + + align:start position:0% +all that traffic but you get it + + + align:start position:0% +all that traffic but you get it +so you see how the stuff spread right + + align:start position:0% +so you see how the stuff spread right + + + align:start position:0% +so you see how the stuff spread right +how do you solve this problem all right + + align:start position:0% +how do you solve this problem all right + + + align:start position:0% +how do you solve this problem all right +this is going on and then people are not + + align:start position:0% +this is going on and then people are not + + + align:start position:0% +this is going on and then people are not +able to see their cats and you know they + + align:start position:0% +able to see their cats and you know they + + + align:start position:0% +able to see their cats and you know they +they they're scrambling I mean this is + + align:start position:0% +they they're scrambling I mean this is + + + align:start position:0% +they they're scrambling I mean this is +literally the whole internet uh wasn't + + align:start position:0% +literally the whole internet uh wasn't + + + align:start position:0% +literally the whole internet uh wasn't +able to get to YouTube which you know + + align:start position:0% +able to get to YouTube which you know + + + align:start position:0% +able to get to YouTube which you know +admittedly is not the biggest problem in + + align:start position:0% +admittedly is not the biggest problem in + + + align:start position:0% +admittedly is not the biggest problem in +the world but still if you on YouTube + + align:start position:0% +the world but still if you on YouTube + + + align:start position:0% +the world but still if you on YouTube +this is a big problem so how do you + + align:start position:0% +this is a big problem so how do you + + + align:start position:0% +this is a big problem so how do you +solve this problem what do you actually + + align:start position:0% +solve this problem what do you actually + + + align:start position:0% +solve this problem what do you actually +do the whole world has this now this bad + + align:start position:0% +do the whole world has this now this bad + + + align:start position:0% +do the whole world has this now this bad +entry in the routing table now there's + + align:start position:0% +entry in the routing table now there's + + + align:start position:0% +entry in the routing table now there's +this long-term solution which is of + + align:start position:0% +this long-term solution which is of + + + align:start position:0% +this long-term solution which is of +course let's figure out a way to + + align:start position:0% +course let's figure out a way to + + + align:start position:0% +course let's figure out a way to +authenticate the vertisements and use + + align:start position:0% +authenticate the vertisements and use + + + align:start position:0% +authenticate the vertisements and use +some public key and this and that and + + align:start position:0% +some public key and this and that and + + + align:start position:0% +some public key and this and that and +you'll study this in 6829 and other + + align:start position:0% +you'll study this in 6829 and other + + + align:start position:0% +you'll study this in 6829 and other +courses but today we don't have that and + + align:start position:0% +courses but today we don't have that and + + + align:start position:0% +courses but today we don't have that and +this problem exists so how do we ever + + align:start position:0% +this problem exists so how do we ever + + + align:start position:0% +this problem exists so how do we ever +come out of + + align:start position:0% +come out of + + + align:start position:0% +come out of +it yeah actually you know it's + + align:start position:0% +it yeah actually you know it's + + + align:start position:0% +it yeah actually you know it's +interesting you and I I mean you + + align:start position:0% +interesting you and I I mean you + + + align:start position:0% +interesting you and I I mean you +certainly thought about this in 30 + + align:start position:0% +certainly thought about this in 30 + + + align:start position:0% +certainly thought about this in 30 +seconds but for YouTube actually did it + + align:start position:0% +seconds but for YouTube actually did it + + + align:start position:0% +seconds but for YouTube actually did it +took them a while to figure out what was + + align:start position:0% +took them a while to figure out what was + + + align:start position:0% +took them a while to figure out what was +really going on because one of the + + align:start position:0% +really going on because one of the + + + align:start position:0% +really going on because one of the +problems is you don't want to do + + align:start position:0% +problems is you don't want to do + + + align:start position:0% +problems is you don't want to do +something like that without knowing for + + align:start position:0% +something like that without knowing for + + + align:start position:0% +something like that without knowing for +sure but eventually they did exactly + + align:start position:0% +sure but eventually they did exactly + + + align:start position:0% +sure but eventually they did exactly +this they figured out the prefixes that + + align:start position:0% +this they figured out the prefixes that + + + align:start position:0% +this they figured out the prefixes that +were being advertised and that took a + + align:start position:0% +were being advertised and that took a + + + align:start position:0% +were being advertised and that took a +while because you don't know somebody + + align:start position:0% +while because you don't know somebody + + + align:start position:0% +while because you don't know somebody +else's what's in your routing table I + + align:start position:0% +else's what's in your routing table I + + + align:start position:0% +else's what's in your routing table I +don't know I have to pick up the phone + + align:start position:0% +don't know I have to pick up the phone + + + align:start position:0% +don't know I have to pick up the phone +or email and you know email may not work + + align:start position:0% +or email and you know email may not work + + + align:start position:0% +or email and you know email may not work +because com back to YouTube but whatever + + align:start position:0% +because com back to YouTube but whatever + + + align:start position:0% +because com back to YouTube but whatever +there's a way there's a way to figure + + align:start position:0% +there's a way there's a way to figure + + + align:start position:0% +there's a way there's a way to figure +this out right phone and yeah you have + + align:start position:0% +this out right phone and yeah you have + + + align:start position:0% +this out right phone and yeah you have +use your Gmail or something and then + + align:start position:0% +use your Gmail or something and then + + + align:start position:0% +use your Gmail or something and then +they they figured out what it was and + + align:start position:0% +they they figured out what it was and + + + align:start position:0% +they they figured out what it was and +then they inserted SL 25s that were more + + align:start position:0% +then they inserted SL 25s that were more + + + align:start position:0% +then they inserted SL 25s that were more +specific and then once the problem kind + + align:start position:0% +specific and then once the problem kind + + + align:start position:0% +specific and then once the problem kind +of resolved itself they got out of it so + + align:start position:0% +of resolved itself they got out of it so + + + align:start position:0% +of resolved itself they got out of it so +uh let me jump on move on give me two + + align:start position:0% +uh let me jump on move on give me two + + + align:start position:0% +uh let me jump on move on give me two +more minutes and I'll finish uh finish + + align:start position:0% +more minutes and I'll finish uh finish + + + align:start position:0% +more minutes and I'll finish uh finish +up + + align:start position:0% +up + + + align:start position:0% +up +uh a similar problem happened with China + + align:start position:0% +uh a similar problem happened with China + + + align:start position:0% +uh a similar problem happened with China +Telecom they didn't advertise a more + + align:start position:0% +Telecom they didn't advertise a more + + + align:start position:0% +Telecom they didn't advertise a more +specific route so they only got about + + align:start position:0% +specific route so they only got about + + + align:start position:0% +specific route so they only got about +15% of the internet and they were nice + + align:start position:0% +15% of the internet and they were nice + + + align:start position:0% +15% of the internet and they were nice +enough to forward it around to the to + + align:start position:0% +enough to forward it around to the to + + + align:start position:0% +enough to forward it around to the to +the actual destinations but uh this was + + align:start position:0% +the actual destinations but uh this was + + + align:start position:0% +the actual destinations but uh this was +a problem I'm going to skip through the + + align:start position:0% +a problem I'm going to skip through the + + + align:start position:0% +a problem I'm going to skip through the +decade ahead because you know what + + align:start position:0% +decade ahead because you know what + + + align:start position:0% +decade ahead because you know what +you'll find it soon + + align:start position:0% +you'll find it soon + + + align:start position:0% +you'll find it soon +enough all right what I do want to do is + + align:start position:0% +enough all right what I do want to do is + + + align:start position:0% +enough all right what I do want to do is +to summarize 602 in one + + align:start position:0% +to summarize 602 in one + + + align:start position:0% +to summarize 602 in one +slide this course was about how to + + align:start position:0% +slide this course was about how to + + + align:start position:0% +slide this course was about how to +design digital communication networks + + align:start position:0% +design digital communication networks + + + align:start position:0% +design digital communication networks +right I'm sure you all kind of know that + + align:start position:0% +right I'm sure you all kind of know that + + + align:start position:0% +right I'm sure you all kind of know that +we did this with three layers of + + align:start position:0% +we did this with three layers of + + + align:start position:0% +we did this with three layers of +abstraction very simple story bits + + align:start position:0% +abstraction very simple story bits + + + align:start position:0% +abstraction very simple story bits +signals and packets and I think as far + + align:start position:0% +signals and packets and I think as far + + + align:start position:0% +signals and packets and I think as far +as these kinds of courses go across uh + + align:start position:0% +as these kinds of courses go across uh + + + align:start position:0% +as these kinds of courses go across uh +the world it's a pretty unique storyline + + align:start position:0% +the world it's a pretty unique storyline + + + align:start position:0% +the world it's a pretty unique storyline +there aren't very many courses that we + + align:start position:0% +there aren't very many courses that we + + + align:start position:0% +there aren't very many courses that we +know of which have this vertical study + + align:start position:0% +know of which have this vertical study + + + align:start position:0% +know of which have this vertical study +across all the layers and um there are + + align:start position:0% +across all the layers and um there are + + + align:start position:0% +across all the layers and um there are +some schools now starting to adopt that + + align:start position:0% +some schools now starting to adopt that + + + align:start position:0% +some schools now starting to adopt that +we know of that are starting to adopt + + align:start position:0% +we know of that are starting to adopt + + + align:start position:0% +we know of that are starting to adopt +this idea and we feel like this is a + + align:start position:0% +this idea and we feel like this is a + + + align:start position:0% +this idea and we feel like this is a +pretty unique way in which to teach this + + align:start position:0% +pretty unique way in which to teach this + + + align:start position:0% +pretty unique way in which to teach this +because it demystifies all of the layers + + align:start position:0% +because it demystifies all of the layers + + + align:start position:0% +because it demystifies all of the layers +so we didn't cover anything with we + + align:start position:0% +so we didn't cover anything with we + + + align:start position:0% +so we didn't cover anything with we +didn't tell you 15 ways to solve any + + align:start position:0% +didn't tell you 15 ways to solve any + + + align:start position:0% +didn't tell you 15 ways to solve any +given problem but we told you one good + + align:start position:0% +given problem but we told you one good + + + align:start position:0% +given problem but we told you one good +way to solve each of the problems that + + align:start position:0% +way to solve each of the problems that + + + align:start position:0% +way to solve each of the problems that +you will see so we went from point + + align:start position:0% +you will see so we went from point + + + align:start position:0% +you will see so we went from point +to-point links to multihop communication + + align:start position:0% +to-point links to multihop communication + + + align:start position:0% +to-point links to multihop communication +networks and across these different + + align:start position:0% +networks and across these different + + + align:start position:0% +networks and across these different +topics and you can see that you know we + + align:start position:0% +topics and you can see that you know we + + + align:start position:0% +topics and you can see that you know we +studied these different topics the two + + align:start position:0% +studied these different topics the two + + + align:start position:0% +studied these different topics the two +big themes that I want to leave you with + + align:start position:0% +big themes that I want to leave you with + + + align:start position:0% +big themes that I want to leave you with +are reliability and sharing because + + align:start position:0% +are reliability and sharing because + + + align:start position:0% +are reliability and sharing because +that's really what makes our + + align:start position:0% +that's really what makes our + + + align:start position:0% +that's really what makes our +communication systems work how do you + + align:start position:0% +communication systems work how do you + + + align:start position:0% +communication systems work how do you +make it reliable we don't have a + + align:start position:0% +make it reliable we don't have a + + + align:start position:0% +make it reliable we don't have a +perfectly reliable communication medium + + align:start position:0% +perfectly reliable communication medium + + + align:start position:0% +perfectly reliable communication medium +at any layer so how you make things + + align:start position:0% +at any layer so how you make things + + + align:start position:0% +at any layer so how you make things +reliable is important we studied this + + align:start position:0% +reliable is important we studied this + + + align:start position:0% +reliable is important we studied this +over and over again and how do you share + + align:start position:0% +over and over again and how do you share + + + align:start position:0% +over and over again and how do you share +those are the two big uh topics \ No newline at end of file diff --git a/RWPfOV0CV5Y.txt b/RWPfOV0CV5Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..dfd16f8baca48379627ef9a237818ab59ab22682 --- /dev/null +++ b/RWPfOV0CV5Y.txt @@ -0,0 +1,1227 @@ +align:start position:0% + +so my comments comments first one if the + + align:start position:0% +so my comments comments first one if the + + + align:start position:0% +so my comments comments first one if the +sy n of T can be chosen to be real the + + align:start position:0% +sy n of T can be chosen to be real the + + + align:start position:0% +sy n of T can be chosen to be real the +geometric face vanishes so why is that + + align:start position:0% +geometric face vanishes so why is that + + + align:start position:0% +geometric face vanishes so why is that +the geometric face is remember the + + align:start position:0% +the geometric face is remember the + + + align:start position:0% +the geometric face is remember the +integral of this new factor which was I + + align:start position:0% +integral of this new factor which was I + + + align:start position:0% +integral of this new factor which was I +sy n of T psi n 3 dot you had to + + align:start position:0% +sy n of T psi n 3 dot you had to + + + align:start position:0% +sy n of T psi n 3 dot you had to +integrate that thing to get the + + align:start position:0% +integrate that thing to get the + + + align:start position:0% +integrate that thing to get the +geometric phase we explained that this + + align:start position:0% +geometric phase we explained that this + + + align:start position:0% +geometric phase we explained that this +quantity in general is well in general + + align:start position:0% +quantity in general is well in general + + + align:start position:0% +quantity in general is well in general +it's always imaginary this quantity and + + align:start position:0% +it's always imaginary this quantity and + + + align:start position:0% +it's always imaginary this quantity and +then with an eye this is a real quantity + + align:start position:0% +then with an eye this is a real quantity + + + align:start position:0% +then with an eye this is a real quantity +which we've been using but if this is + + align:start position:0% +which we've been using but if this is + + + align:start position:0% +which we've been using but if this is +imaginary look at this this is imaginary + + align:start position:0% +imaginary look at this this is imaginary + + + align:start position:0% +imaginary look at this this is imaginary +how could it be imaginary + + align:start position:0% +how could it be imaginary + + + align:start position:0% +how could it be imaginary +if sy is real it can't be if sighs we + + align:start position:0% +if sy is real it can't be if sighs we + + + align:start position:0% +if sy is real it can't be if sighs we +all imagined doing that integral cannot + + align:start position:0% +all imagined doing that integral cannot + + + align:start position:0% +all imagined doing that integral cannot +be imagined so it has to be zero if size + + align:start position:0% +be imagined so it has to be zero if size + + + align:start position:0% +be imagined so it has to be zero if size +is real yes + + align:start position:0% + + + + align:start position:0% + +we proved this was imaginary this we did + + align:start position:0% +we proved this was imaginary this we did + + + align:start position:0% +we proved this was imaginary this we did +calculate the derivative with respect to + + align:start position:0% +calculate the derivative with respect to + + + align:start position:0% +calculate the derivative with respect to +time of sigh with sigh and we proved + + align:start position:0% +time of sigh with sigh and we proved + + + align:start position:0% +time of sigh with sigh and we proved +that this was imaginary and now I'm + + align:start position:0% +that this was imaginary and now I'm + + + align:start position:0% +that this was imaginary and now I'm +saying if this was imaginary + + align:start position:0% +saying if this was imaginary + + + align:start position:0% +saying if this was imaginary +but if sorry is real the only + + align:start position:0% +but if sorry is real the only + + + align:start position:0% +but if sorry is real the only +possibility is that this is zero but you + + align:start position:0% +possibility is that this is zero but you + + + align:start position:0% +possibility is that this is zero but you +can prove in fact that this is 0 if this + + align:start position:0% +can prove in fact that this is 0 if this + + + align:start position:0% +can prove in fact that this is 0 if this +is real like I can do it in a second + + align:start position:0% +is real like I can do it in a second + + + align:start position:0% +is real like I can do it in a second +it's I integral sy n of P because it's + + align:start position:0% +it's I integral sy n of P because it's + + + align:start position:0% +it's I integral sy n of P because it's +real DVT of sy n of T out put an X here + + align:start position:0% +real DVT of sy n of T out put an X here + + + align:start position:0% +real DVT of sy n of T out put an X here +and if it's B X that's what it is if sy + + align:start position:0% +and if it's B X that's what it is if sy + + + align:start position:0% +and if it's B X that's what it is if sy +is real I otherwise there would be a + + align:start position:0% +is real I otherwise there would be a + + + align:start position:0% +is real I otherwise there would be a +star here but if it's real there's no + + align:start position:0% +star here but if it's real there's no + + + align:start position:0% +star here but if it's real there's no +star but this is just the integral of + + align:start position:0% +star but this is just the integral of + + + align:start position:0% +star but this is just the integral of +1/2 of DDT of sy of X and T squared the + + align:start position:0% +1/2 of DDT of sy of X and T squared the + + + align:start position:0% +1/2 of DDT of sy of X and T squared the +X the DDT is that and then the deity + + align:start position:0% +X the DDT is that and then the deity + + + align:start position:0% +X the DDT is that and then the deity +goes out of the end to grow so this is I + + align:start position:0% +goes out of the end to grow so this is I + + + align:start position:0% +goes out of the end to grow so this is I +over to D DT of the integral of size + + align:start position:0% +over to D DT of the integral of size + + + align:start position:0% +over to D DT of the integral of size +squared of x + 3 DX but that integral is + + align:start position:0% +squared of x + 3 DX but that integral is + + + align:start position:0% +squared of x + 3 DX but that integral is +1 so the derivative is 0 so there's no + + align:start position:0% +1 so the derivative is 0 so there's no + + + align:start position:0% +1 so the derivative is 0 so there's no +geometric face so if you have real + + align:start position:0% +geometric face so if you have real + + + align:start position:0% +geometric face so if you have real +instantaneous eigenstate don't even + + align:start position:0% +instantaneous eigenstate don't even + + + align:start position:0% +instantaneous eigenstate don't even +think of Barry's face there's another + + align:start position:0% +think of Barry's face there's another + + + align:start position:0% +think of Barry's face there's another +case where you don't get a Barry's face + + align:start position:0% +case where you don't get a Barry's face + + + align:start position:0% +case where you don't get a Barry's face +of so when I'm speaking of Barry's face + + align:start position:0% +of so when I'm speaking of Barry's face + + + align:start position:0% +of so when I'm speaking of Barry's face +at this moment I mean the Barry's face + + align:start position:0% +at this moment I mean the Barry's face + + + align:start position:0% +at this moment I mean the Barry's face +from a closed path in configuration + + align:start position:0% +from a closed path in configuration + + + align:start position:0% +from a closed path in configuration +space so if the configuration space is + + align:start position:0% +space so if the configuration space is + + + align:start position:0% +space so if the configuration space is +one dimensional the Bary face vanishes + + align:start position:0% +one dimensional the Bary face vanishes + + + align:start position:0% +one dimensional the Bary face vanishes +Barry's face + + align:start position:0% +Barry's face + + + align:start position:0% +Barry's face +his face vanishes for 1/v configuration + + align:start position:0% +his face vanishes for 1/v configuration + + + align:start position:0% +his face vanishes for 1/v configuration +space why is that well what do we have + + align:start position:0% +space why is that well what do we have + + + align:start position:0% +space why is that well what do we have +to do the Berry's face will be the + + align:start position:0% +to do the Berry's face will be the + + + align:start position:0% +to do the Berry's face will be the +integral over the closed path in the + + align:start position:0% +integral over the closed path in the + + + align:start position:0% +integral over the closed path in the +configuration space sigh of our ddr + + align:start position:0% +configuration space sigh of our ddr + + + align:start position:0% +configuration space sigh of our ddr +because there's just one side of our dr + + align:start position:0% +because there's just one side of our dr + + + align:start position:0% +because there's just one side of our dr +you have to integrate that thing that is + + align:start position:0% +you have to integrate that thing that is + + + align:start position:0% +you have to integrate that thing that is +the berry face is the integral of the + + align:start position:0% +the berry face is the integral of the + + + align:start position:0% +the berry face is the integral of the +berry connection over this is capital R + + align:start position:0% +berry connection over this is capital R + + + align:start position:0% +berry connection over this is capital R +over the space but now if this + + align:start position:0% +over the space but now if this + + + align:start position:0% +over the space but now if this +configuration space is one dimensional + + align:start position:0% +configuration space is one dimensional + + + align:start position:0% +configuration space is one dimensional +this is our a closed path is a path that + + align:start position:0% +this is our a closed path is a path that + + + align:start position:0% +this is our a closed path is a path that +goes like this and back it retraces + + align:start position:0% +goes like this and back it retraces + + + align:start position:0% +goes like this and back it retraces +itself so it integrates this quantity + + align:start position:0% +itself so it integrates this quantity + + + align:start position:0% +itself so it integrates this quantity +with increasing R and then it integrates + + align:start position:0% +with increasing R and then it integrates + + + align:start position:0% +with increasing R and then it integrates +the same quantity with decreasing our + + align:start position:0% +the same quantity with decreasing our + + + align:start position:0% +the same quantity with decreasing our +and the two cancel and this face is + + align:start position:0% +and the two cancel and this face is + + + align:start position:0% +and the two cancel and this face is +equal to zero so you cannot get a + + align:start position:0% +equal to zero so you cannot get a + + + align:start position:0% +equal to zero so you cannot get a +Berry's face if you have one dimension + + align:start position:0% +Berry's face if you have one dimension + + + align:start position:0% +Berry's face if you have one dimension +you cannot get a Berry's face if you + + align:start position:0% +you cannot get a Berry's face if you + + + align:start position:0% +you cannot get a Berry's face if you +have real instantaneous eigenstates but + + align:start position:0% +have real instantaneous eigenstates but + + + align:start position:0% +have real instantaneous eigenstates but +you can't get a berry face in two + + align:start position:0% +you can't get a berry face in two + + + align:start position:0% +you can't get a berry face in two +dimensions in three dimensions and there + + align:start position:0% +dimensions in three dimensions and there + + + align:start position:0% +dimensions in three dimensions and there +are several examples I'll mention one + + align:start position:0% +are several examples I'll mention one + + + align:start position:0% +are several examples I'll mention one +example and and then leave the Berry's + + align:start position:0% +example and and then leave the Berry's + + + align:start position:0% +example and and then leave the Berry's +face for some exercises so in in 3d for + + align:start position:0% +face for some exercises so in in 3d for + + + align:start position:0% +face for some exercises so in in 3d for +example 3ds kind of nice a 3d + + align:start position:0% +example 3ds kind of nice a 3d + + + align:start position:0% +example 3ds kind of nice a 3d +configuration space is the perfect place + + align:start position:0% +configuration space is the perfect place + + + align:start position:0% +configuration space is the perfect place +to confuse yourself because you have + + align:start position:0% +to confuse yourself because you have + + + align:start position:0% +to confuse yourself because you have +three dimensions of configuration and + + align:start position:0% +three dimensions of configuration and + + + align:start position:0% +three dimensions of configuration and +three dimensions of space so nice + + align:start position:0% +three dimensions of space so nice + + + align:start position:0% +three dimensions of space so nice +interplay between them r1r + + align:start position:0% +interplay between them r1r + + + align:start position:0% +interplay between them r1r +two or three and then you have an + + align:start position:0% +two or three and then you have an + + + align:start position:0% +two or three and then you have an +integral the barre faces an integral + + align:start position:0% +integral the barre faces an integral + + + align:start position:0% +integral the barre faces an integral +over a closed path here so let's call + + align:start position:0% +over a closed path here so let's call + + + align:start position:0% +over a closed path here so let's call +gamma and it's called this surface s + + align:start position:0% +gamma and it's called this surface s + + + align:start position:0% +gamma and it's called this surface s +whose boundaries gamma so what is the + + align:start position:0% +whose boundaries gamma so what is the + + + align:start position:0% +whose boundaries gamma so what is the +barre face the barre face is the + + align:start position:0% +barre face the barre face is the + + + align:start position:0% +barre face the barre face is the +integral over gamma of the Bary + + align:start position:0% +integral over gamma of the Bary + + + align:start position:0% +integral over gamma of the Bary +connection dr but what is that that is + + align:start position:0% +connection dr but what is that that is + + + align:start position:0% +connection dr but what is that that is +by Stokes theorem the integral over the + + align:start position:0% +by Stokes theorem the integral over the + + + align:start position:0% +by Stokes theorem the integral over the +surface of the curl of the berry + + align:start position:0% +surface of the curl of the berry + + + align:start position:0% +surface of the curl of the berry +connection times the area times the the + + align:start position:0% +connection times the area times the the + + + align:start position:0% +connection times the area times the the +area on that surface Stokes theorem + + align:start position:0% +area on that surface Stokes theorem + + + align:start position:0% +area on that surface Stokes theorem +remember in E&M so here was a vector + + align:start position:0% +remember in E&M so here was a vector + + + align:start position:0% +remember in E&M so here was a vector +potential gives you a magnetic field so + + align:start position:0% +potential gives you a magnetic field so + + + align:start position:0% +potential gives you a magnetic field so +the integral of a along a loop was equal + + align:start position:0% +the integral of a along a loop was equal + + + align:start position:0% +the integral of a along a loop was equal +to the flux of the magnetic field + + align:start position:0% +to the flux of the magnetic field + + + align:start position:0% +to the flux of the magnetic field +through the surface and now the very + + align:start position:0% +through the surface and now the very + + + align:start position:0% +through the surface and now the very +face along the loop is equal to the + + align:start position:0% +face along the loop is equal to the + + + align:start position:0% +face along the loop is equal to the +integral of the we should call it very + + align:start position:0% +integral of the we should call it very + + + align:start position:0% +integral of the we should call it very +magnetic field down people like Barry's + + align:start position:0% +magnetic field down people like Barry's + + + align:start position:0% +magnetic field down people like Barry's +curvature as in the sense that the + + align:start position:0% +curvature as in the sense that the + + + align:start position:0% +curvature as in the sense that the +magnetic field is the curvature of a + + align:start position:0% +magnetic field is the curvature of a + + + align:start position:0% +magnetic field is the curvature of a +connection so this is called the Barry's + + align:start position:0% +connection so this is called the Barry's + + + align:start position:0% +connection so this is called the Barry's +curvature but you think about magnetic + + align:start position:0% +curvature but you think about magnetic + + + align:start position:0% +curvature but you think about magnetic +field varies curvature so the very scary + + align:start position:0% +field varies curvature so the very scary + + + align:start position:0% +field varies curvature so the very scary +people go with B is the curl sub R of + + align:start position:0% +people go with B is the curl sub R of + + + align:start position:0% +people go with B is the curl sub R of +the Bary connection a FR it's kind of + + align:start position:0% +the Bary connection a FR it's kind of + + + align:start position:0% +the Bary connection a FR it's kind of +the magnetic field so is the integral of + + align:start position:0% +the magnetic field so is the integral of + + + align:start position:0% +the magnetic field so is the integral of +D over that surface so there are nice + + align:start position:0% +D over that surface so there are nice + + + align:start position:0% +D over that surface so there are nice +analogies + + align:start position:0% + + + + align:start position:0% + +so one example you will do recitation I + + align:start position:0% +so one example you will do recitation I + + + align:start position:0% +so one example you will do recitation I +hope you have a max over there is the + + align:start position:0% +hope you have a max over there is the + + + align:start position:0% +hope you have a max over there is the +classic example of a spin in a magnetic + + align:start position:0% +classic example of a spin in a magnetic + + + align:start position:0% +classic example of a spin in a magnetic +field so I will just say a couple of + + align:start position:0% +field so I will just say a couple of + + + align:start position:0% +field so I will just say a couple of +words as an introduction but it's a very + + align:start position:0% +words as an introduction but it's a very + + + align:start position:0% +words as an introduction but it's a very +nice computation it's a great exercise + + align:start position:0% +nice computation it's a great exercise + + + align:start position:0% +nice computation it's a great exercise +to figure out if you kind of understand + + align:start position:0% +to figure out if you kind of understand + + + align:start position:0% +to figure out if you kind of understand +all these things if I such a good it's + + align:start position:0% +all these things if I such a good it's + + + align:start position:0% +all these things if I such a good it's +it's done in griffiths explicitly in + + align:start position:0% +it's done in griffiths explicitly in + + + align:start position:0% +it's done in griffiths explicitly in +some ways and it's a great thing to + + align:start position:0% +some ways and it's a great thing to + + + align:start position:0% +some ways and it's a great thing to +practice so if you want a little + + align:start position:0% +practice so if you want a little + + + align:start position:0% +practice so if you want a little +challenge I know you're busy with papers + + align:start position:0% +challenge I know you're busy with papers + + + align:start position:0% +challenge I know you're busy with papers +and other things but the idea is that + + align:start position:0% +and other things but the idea is that + + + align:start position:0% +and other things but the idea is that +you have a magnetic field the constant + + align:start position:0% +you have a magnetic field the constant + + + align:start position:0% +you have a magnetic field the constant +magnetic field B naught and along some + + align:start position:0% +magnetic field B naught and along some + + + align:start position:0% +magnetic field B naught and along some +direction and and you have a spin 1/2 + + align:start position:0% +direction and and you have a spin 1/2 + + + align:start position:0% +direction and and you have a spin 1/2 +particle pointing in that direction and + + align:start position:0% +particle pointing in that direction and + + + align:start position:0% +particle pointing in that direction and +but then you start letting it vary in + + align:start position:0% +but then you start letting it vary in + + + align:start position:0% +but then you start letting it vary in +time that unit vector so this unit + + align:start position:0% +time that unit vector so this unit + + + align:start position:0% +time that unit vector so this unit +vector varies in time and traces a path + + align:start position:0% + + + + align:start position:0% + +and if it's adiabatic process the spin + + align:start position:0% +and if it's adiabatic process the spin + + + align:start position:0% +and if it's adiabatic process the spin +will remain in the instantaneous energy + + align:start position:0% +will remain in the instantaneous energy + + + align:start position:0% +will remain in the instantaneous energy +eigenstate which is spin up in this + + align:start position:0% +eigenstate which is spin up in this + + + align:start position:0% +eigenstate which is spin up in this +direction and it will track the magnetic + + align:start position:0% +direction and it will track the magnetic + + + align:start position:0% +direction and it will track the magnetic +field basically there will be some small + + align:start position:0% +field basically there will be some small + + + align:start position:0% +field basically there will be some small +probability it flips but it's small and + + align:start position:0% +probability it flips but it's small and + + + align:start position:0% +probability it flips but it's small and +if this is an adiabatic process that + + align:start position:0% +if this is an adiabatic process that + + + align:start position:0% +if this is an adiabatic process that +error can be small so as you move around + + align:start position:0% +error can be small so as you move around + + + align:start position:0% +error can be small so as you move around +here there will be a geometric phase and + + align:start position:0% +here there will be a geometric phase and + + + align:start position:0% +here there will be a geometric phase and +the geometric phase is quite nice so for + + align:start position:0% +the geometric phase is quite nice so for + + + align:start position:0% +the geometric phase is quite nice so for +the spin up state and plus state if it + + align:start position:0% +the spin up state and plus state if it + + + align:start position:0% +the spin up state and plus state if it +follows this thing that the geometric + + align:start position:0% +follows this thing that the geometric + + + align:start position:0% +follows this thing that the geometric +phase for the spin up state in this + + align:start position:0% +phase for the spin up state in this + + + align:start position:0% +phase for the spin up state in this +closed path in configuration space this + + align:start position:0% +closed path in configuration space this + + + align:start position:0% +closed path in configuration space this +is the configuration space of the + + align:start position:0% +is the configuration space of the + + + align:start position:0% +is the configuration space of the +magnetic field will just be given by + + align:start position:0% +magnetic field will just be given by + + + align:start position:0% +magnetic field will just be given by +minus 1/2 this comes from spin 1/2 times + + align:start position:0% +minus 1/2 this comes from spin 1/2 times + + + align:start position:0% +minus 1/2 this comes from spin 1/2 times +an invariant of this loop which is the + + align:start position:0% +an invariant of this loop which is the + + + align:start position:0% +an invariant of this loop which is the +solid angle trace by this loop so the + + align:start position:0% +solid angle trace by this loop so the + + + align:start position:0% +solid angle trace by this loop so the +geometric phase that you acquire by this + + align:start position:0% +geometric phase that you acquire by this + + + align:start position:0% +geometric phase that you acquire by this +motion is proportional just to the solid + + align:start position:0% +motion is proportional just to the solid + + + align:start position:0% +motion is proportional just to the solid +angle of this loop would so very nice + + align:start position:0% +angle of this loop would so very nice + + + align:start position:0% +angle of this loop would so very nice +result shows how geometric everything is \ No newline at end of file diff --git a/RcDErxzZpcs.txt b/RcDErxzZpcs.txt new file mode 100644 index 0000000000000000000000000000000000000000..20406babfb511d74667390566665b5040b8cef09 --- /dev/null +++ b/RcDErxzZpcs.txt @@ -0,0 +1,13811 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a creative common license. Your support + + align:start position:0% +a creative common license. Your support + + + align:start position:0% +a creative common license. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +Some content in this audio is not + + align:start position:0% +Some content in this audio is not + + + align:start position:0% +Some content in this audio is not +covered under our creative common + + align:start position:0% +covered under our creative common + + + align:start position:0% +covered under our creative common +license. For more information, see the + + align:start position:0% +license. For more information, see the + + + align:start position:0% +license. For more information, see the +course materials on the MIT Open + + align:start position:0% +course materials on the MIT Open + + + align:start position:0% +course materials on the MIT Open +Courseware website. + + align:start position:0% +Courseware website. + + + align:start position:0% +Courseware website. +>> All right. So, so uh this of course does + + align:start position:0% +>> All right. So, so uh this of course does + + + align:start position:0% +>> All right. So, so uh this of course does +not actually mean that you have more + + align:start position:0% +not actually mean that you have more + + + align:start position:0% +not actually mean that you have more +time for assignment three. In fact, it + + align:start position:0% +time for assignment three. In fact, it + + + align:start position:0% +time for assignment three. In fact, it +needs a little bit more time than for + + align:start position:0% +needs a little bit more time than for + + + align:start position:0% +needs a little bit more time than for +assignment three. Sorry about that. But + + align:start position:0% +assignment three. Sorry about that. But + + + align:start position:0% +assignment three. Sorry about that. But +I think this is a net game for everyone. + + align:start position:0% +I think this is a net game for everyone. + + + align:start position:0% +I think this is a net game for everyone. +Um all right, that with that out of the + + align:start position:0% +Um all right, that with that out of the + + + align:start position:0% +Um all right, that with that out of the +way. Um Konamo actually a lot of you + + align:start position:0% +way. Um Konamo actually a lot of you + + + align:start position:0% +way. Um Konamo actually a lot of you +probably are already familiar. You might + + align:start position:0% +probably are already familiar. You might + + + align:start position:0% +probably are already familiar. You might +have taken any of her classes. She's uh + + align:start position:0% +have taken any of her classes. She's uh + + + align:start position:0% +have taken any of her classes. She's uh +uh she's a visiting uh lecturer, + + align:start position:0% +uh she's a visiting uh lecturer, + + + align:start position:0% +uh she's a visiting uh lecturer, +visiting professor. Visiting professor. + + align:start position:0% +visiting professor. Visiting professor. + + + align:start position:0% +visiting professor. Visiting professor. +>> Um uh here at Gambit uh and um + + align:start position:0% +>> Um uh here at Gambit uh and um + + + align:start position:0% +>> Um uh here at Gambit uh and um +>> are you doing something? + + align:start position:0% +>> are you doing something? + + + align:start position:0% +>> are you doing something? +>> Yes. Cheating and ethics and games. + + align:start position:0% +>> Yes. Cheating and ethics and games. + + + align:start position:0% +>> Yes. Cheating and ethics and games. +>> So this + + align:start position:0% +>> So this + + + align:start position:0% +>> So this +>> Brian can tell you all about it. + + align:start position:0% +>> Brian can tell you all about it. + + + align:start position:0% +>> Brian can tell you all about it. +>> You can take this as a the sneak + + align:start position:0% +>> You can take this as a the sneak + + + align:start position:0% +>> You can take this as a the sneak +preview. + + align:start position:0% +preview. + + + align:start position:0% +preview. +>> Yes. This is the taster of it. + + align:start position:0% +>> Yes. This is the taster of it. + + + align:start position:0% +>> Yes. This is the taster of it. +>> Thanks. + + align:start position:0% +>> Thanks. + + + align:start position:0% +>> Thanks. +Okay. Um, so it sounds like you all have + + align:start position:0% +Okay. Um, so it sounds like you all have + + + align:start position:0% +Okay. Um, so it sounds like you all have +lots of opinions, + + align:start position:0% +lots of opinions, + + + align:start position:0% +lots of opinions, +which will be good. So to get started, + + align:start position:0% +which will be good. So to get started, + + + align:start position:0% +which will be good. So to get started, +and actually I don't like the term + + align:start position:0% +and actually I don't like the term + + + align:start position:0% +and actually I don't like the term +lecture because I don't actually lecture + + align:start position:0% +lecture because I don't actually lecture + + + align:start position:0% +lecture because I don't actually lecture +very much. Um, I'm going to start by + + align:start position:0% +very much. Um, I'm going to start by + + + align:start position:0% +very much. Um, I'm going to start by +handing around some online index cards, + + align:start position:0% +handing around some online index cards, + + + align:start position:0% +handing around some online index cards, +and I want you to take a few minutes and + + align:start position:0% +and I want you to take a few minutes and + + + align:start position:0% +and I want you to take a few minutes and +generate some examples of uh ethical + + align:start position:0% +generate some examples of uh ethical + + + align:start position:0% +generate some examples of uh ethical +elements, procedures, episodes, games. + + align:start position:0% +elements, procedures, episodes, games. + + + align:start position:0% +elements, procedures, episodes, games. +The more specific you can be, the + + align:start position:0% +The more specific you can be, the + + + align:start position:0% +The more specific you can be, the +better. And I'm actually going to + + align:start position:0% +better. And I'm actually going to + + + align:start position:0% +better. And I'm actually going to +collect these at the end um because as + + align:start position:0% +collect these at the end um because as + + + align:start position:0% +collect these at the end um because as +Philip mentioned, I'm teaching this + + align:start position:0% +Philip mentioned, I'm teaching this + + + align:start position:0% +Philip mentioned, I'm teaching this +ethics and games class and I want to + + align:start position:0% +ethics and games class and I want to + + + align:start position:0% +ethics and games class and I want to +bring in more examples and stuff. So + + align:start position:0% +bring in more examples and stuff. So + + + align:start position:0% +bring in more examples and stuff. So +this will actually be useful for me. So + + align:start position:0% +this will actually be useful for me. So + + + align:start position:0% +this will actually be useful for me. So +>> talking about in games. + + align:start position:0% +>> talking about in games. + + + align:start position:0% +>> talking about in games. +>> Yeah. So you like we were just talking + + align:start position:0% +>> Yeah. So you like we were just talking + + + align:start position:0% +>> Yeah. So you like we were just talking +about Fable. Um, but like if you can + + align:start position:0% +about Fable. Um, but like if you can + + + align:start position:0% +about Fable. Um, but like if you can +think of a more specific example from + + align:start position:0% +think of a more specific example from + + + align:start position:0% +think of a more specific example from +it, a level, um, different choices that + + align:start position:0% +it, a level, um, different choices that + + + align:start position:0% +it, a level, um, different choices that +you get with characters in certain + + align:start position:0% +you get with characters in certain + + + align:start position:0% +you get with characters in certain +games, + + align:start position:0% +games, + + + align:start position:0% +games, +whatever you can come up with in terms + + align:start position:0% +whatever you can come up with in terms + + + align:start position:0% +whatever you can come up with in terms +of like are there interesting ethical + + align:start position:0% +of like are there interesting ethical + + + align:start position:0% +of like are there interesting ethical +dilemmas, + + align:start position:0% + + + + align:start position:0% + +situations? + + align:start position:0% +situations? + + + align:start position:0% +situations? +>> Wait, is this within the context of the + + align:start position:0% +>> Wait, is this within the context of the + + + align:start position:0% +>> Wait, is this within the context of the +game or are we talking about like in a + + align:start position:0% +game or are we talking about like in a + + + align:start position:0% +game or are we talking about like in a +multiplayer game, your conduct towards + + align:start position:0% +multiplayer game, your conduct towards + + + align:start position:0% +multiplayer game, your conduct towards +other players and this kind of thing? + + align:start position:0% +other players and this kind of thing? + + + align:start position:0% +other players and this kind of thing? +>> Or when I was in Owen's office, whether + + align:start position:0% +>> Or when I was in Owen's office, whether + + + align:start position:0% +>> Or when I was in Owen's office, whether +or not they steal the swag. um within + + align:start position:0% +or not they steal the swag. um within + + + align:start position:0% +or not they steal the swag. um within +you can do within MMOs as well or you + + align:start position:0% +you can do within MMOs as well or you + + + align:start position:0% +you can do within MMOs as well or you +know multiplayer game + + align:start position:0% + + + + align:start position:0% + +>> you can continue to write examples for + + align:start position:0% +>> you can continue to write examples for + + + align:start position:0% +>> you can continue to write examples for +hand uh if you can think of them but + + align:start position:0% +hand uh if you can think of them but + + + align:start position:0% +hand uh if you can think of them but +just to get started um + + align:start position:0% +just to get started um + + + align:start position:0% +just to get started um +you're going to stand behind me + + align:start position:0% +you're going to stand behind me + + + align:start position:0% +you're going to stand behind me +>> well then you can start by giving me an + + align:start position:0% +>> well then you can start by giving me an + + + align:start position:0% +>> well then you can start by giving me an +example + + align:start position:0% +example + + + align:start position:0% +example +>> sure um okay so I have a couple um names + + align:start position:0% +>> sure um okay so I have a couple um names + + + align:start position:0% +>> sure um okay so I have a couple um names +obviously um there's there's always kind + + align:start position:0% +obviously um there's there's always kind + + + align:start position:0% +obviously um there's there's always kind +of questions and debate about whether + + align:start position:0% +of questions and debate about whether + + + align:start position:0% +of questions and debate about whether +something it's cheap or viable or should + + align:start position:0% +something it's cheap or viable or should + + + align:start position:0% +something it's cheap or viable or should +you be allowed to do it? + + align:start position:0% +you be allowed to do it? + + + align:start position:0% +you be allowed to do it? +>> Oh + + align:start position:0% +>> Oh + + + align:start position:0% +>> Oh +>> yeah. So like if maybe um + + align:start position:0% +>> yeah. So like if maybe um + + + align:start position:0% +>> yeah. So like if maybe um +I'm trying to think how to describe it. + + align:start position:0% +I'm trying to think how to describe it. + + + align:start position:0% +I'm trying to think how to describe it. +So people who play casually will tend to + + align:start position:0% +So people who play casually will tend to + + + align:start position:0% +So people who play casually will tend to +say um oh if you do this with this + + align:start position:0% +say um oh if you do this with this + + + align:start position:0% +say um oh if you do this with this +character that's cheap and you shouldn't + + align:start position:0% +character that's cheap and you shouldn't + + + align:start position:0% +character that's cheap and you shouldn't +do that. Whereas the you know the + + align:start position:0% +do that. Whereas the you know the + + + align:start position:0% +do that. Whereas the you know the +community at large and people who play + + align:start position:0% +community at large and people who play + + + align:start position:0% +community at large and people who play +seriously tend to say well if you can do + + align:start position:0% +seriously tend to say well if you can do + + + align:start position:0% +seriously tend to say well if you can do +something you can't do something you + + align:start position:0% +something you can't do something you + + + align:start position:0% +something you can't do something you +should be allowed to do it and if you + + align:start position:0% +should be allowed to do it and if you + + + align:start position:0% +should be allowed to do it and if you +can't overcome it that's your own fault. + + align:start position:0% +can't overcome it that's your own fault. + + + align:start position:0% +can't overcome it that's your own fault. +>> Okay. is like violating a community + + align:start position:0% +>> Okay. is like violating a community + + + align:start position:0% +>> Okay. is like violating a community +norm. + + align:start position:0% +norm. + + + align:start position:0% +norm. +>> Yeah, kind + + align:start position:0% +>> Yeah, kind + + + align:start position:0% +>> Yeah, kind +>> like it's allowed in the rules, + + align:start position:0% +>> like it's allowed in the rules, + + + align:start position:0% +>> like it's allowed in the rules, +>> but it's like against like the community + + align:start position:0% +>> but it's like against like the community + + + align:start position:0% +>> but it's like against like the community +norm + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% + + + + align:start position:0% + +Evan Owen + + align:start position:0% +Evan Owen + + + align:start position:0% +Evan Owen +>> Owen sorry + + align:start position:0% +>> Owen sorry + + + align:start position:0% +>> Owen sorry +>> so I have a bunch of stuff which is + + align:start position:0% +>> so I have a bunch of stuff which is + + + align:start position:0% +>> so I have a bunch of stuff which is +related to griefing just generally um so + + align:start position:0% +related to griefing just generally um so + + + align:start position:0% +related to griefing just generally um so +let's just go for the one which is one + + align:start position:0% +let's just go for the one which is one + + + align:start position:0% +let's just go for the one which is one +of my favorites + + align:start position:0% +of my favorites + + + align:start position:0% +of my favorites +um so this is griefing for comic effects + + align:start position:0% +um so this is griefing for comic effects + + + align:start position:0% +um so this is griefing for comic effects +or role playing griefing but doing it in + + align:start position:0% +or role playing griefing but doing it in + + + align:start position:0% +or role playing griefing but doing it in +a way which you are then going to write + + align:start position:0% +a way which you are then going to write + + + align:start position:0% +a way which you are then going to write +a blog about and from your character's + + align:start position:0% +a blog about and from your character's + + + align:start position:0% +a blog about and from your character's +perspective. Um the griefing makes + + align:start position:0% +perspective. Um the griefing makes + + + align:start position:0% +perspective. Um the griefing makes +sense. Uh so there is a there is a + + align:start position:0% +sense. Uh so there is a there is a + + + align:start position:0% +sense. Uh so there is a there is a +particular player that played EverQuest. + + align:start position:0% +particular player that played EverQuest. + + + align:start position:0% +particular player that played EverQuest. +His name is Fancy the Famous Bard. Um he + + align:start position:0% +His name is Fancy the Famous Bard. Um he + + + align:start position:0% +His name is Fancy the Famous Bard. Um he +was on the good team side + + align:start position:0% +was on the good team side + + + align:start position:0% +was on the good team side +and um he he griefed evil because evil + + align:start position:0% +and um he he griefed evil because evil + + + align:start position:0% +and um he he griefed evil because evil +is bad. + + align:start position:0% +is bad. + + + align:start position:0% +is bad. +So people who would play evil + + align:start position:0% +So people who would play evil + + + align:start position:0% +So people who would play evil +characters, he would run around and + + align:start position:0% +characters, he would run around and + + + align:start position:0% +characters, he would run around and +annoy in a really frustrating way, which + + align:start position:0% +annoy in a really frustrating way, which + + + align:start position:0% +annoy in a really frustrating way, which +eventually caused the makers of + + align:start position:0% +eventually caused the makers of + + + align:start position:0% +eventually caused the makers of +EverQuest to change the rules of the + + align:start position:0% +EverQuest to change the rules of the + + + align:start position:0% +EverQuest to change the rules of the +server so that bad people could kill + + align:start position:0% +server so that bad people could kill + + + align:start position:0% +server so that bad people could kill +him, whereas previously they weren't + + align:start position:0% +him, whereas previously they weren't + + + align:start position:0% +him, whereas previously they weren't +allowed. They weren't able to. + + align:start position:0% +allowed. They weren't able to. + + + align:start position:0% +allowed. They weren't able to. +>> What did he do? + + align:start position:0% +>> What did he do? + + + align:start position:0% +>> What did he do? +>> Um, so there was this thing there was + + align:start position:0% +>> Um, so there was this thing there was + + + align:start position:0% +>> Um, so there was this thing there was +this mechanic in EverQuest where if you + + align:start position:0% +this mechanic in EverQuest where if you + + + align:start position:0% +this mechanic in EverQuest where if you +were close to a monster, it became + + align:start position:0% +were close to a monster, it became + + + align:start position:0% +were close to a monster, it became +aggressive and attacked you. + + align:start position:0% +aggressive and attacked you. + + + align:start position:0% +aggressive and attacked you. +>> Yeah. Um, so he had a lowle character + + align:start position:0% +>> Yeah. Um, so he had a lowle character + + + align:start position:0% +>> Yeah. Um, so he had a lowle character +that was able to run really fast and + + align:start position:0% +that was able to run really fast and + + + align:start position:0% +that was able to run really fast and +>> I've heard of him + + align:start position:0% +>> I've heard of him + + + align:start position:0% +>> I've heard of him +>> would run around and then run over the + + align:start position:0% +>> would run around and then run over the + + + align:start position:0% +>> would run around and then run over the +top of evil people and then the the + + align:start position:0% +top of evil people and then the the + + + align:start position:0% +top of evil people and then the the +monsters would detach from him and then + + align:start position:0% +monsters would detach from him and then + + + align:start position:0% +monsters would detach from him and then +kill them. + + align:start position:0% +kill them. + + + align:start position:0% +kill them. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> But Oh, yeah. And the the catch was that + + align:start position:0% +>> But Oh, yeah. And the the catch was that + + + align:start position:0% +>> But Oh, yeah. And the the catch was that +um the the server was a no rules server. + + align:start position:0% +um the the server was a no rules server. + + + align:start position:0% +um the the server was a no rules server. +Aside from that is like so you can't + + align:start position:0% +Aside from that is like so you can't + + + align:start position:0% +Aside from that is like so you can't +complain to GMs about player + + align:start position:0% +complain to GMs about player + + + align:start position:0% +complain to GMs about player +misbehavior. + + align:start position:0% +misbehavior. + + + align:start position:0% +misbehavior. +Aside from there was a built-in + + align:start position:0% +Aside from there was a built-in + + + align:start position:0% +Aside from there was a built-in +protection for players so that if + + align:start position:0% +protection for players so that if + + + align:start position:0% +protection for players so that if +they're like level four or below, so + + align:start position:0% +they're like level four or below, so + + + align:start position:0% +they're like level four or below, so +very low level, they can't be killed by + + align:start position:0% +very low level, they can't be killed by + + + align:start position:0% +very low level, they can't be killed by +higher level players. Um, and so he just + + align:start position:0% +higher level players. Um, and so he just + + + align:start position:0% +higher level players. Um, and so he just +sat on the cusp of that yet was still + + align:start position:0% +sat on the cusp of that yet was still + + + align:start position:0% +sat on the cusp of that yet was still +able to use his ability to go around and + + align:start position:0% +able to use his ability to go around and + + + align:start position:0% +able to use his ability to go around and +people who are much higher level. And it + + align:start position:0% +people who are much higher level. And it + + + align:start position:0% +people who are much higher level. And it +was it was pretty great. And he did it + + align:start position:0% +was it was pretty great. And he did it + + + align:start position:0% +was it was pretty great. And he did it +all totally in character as well, which + + align:start position:0% +all totally in character as well, which + + + align:start position:0% +all totally in character as well, which +is what makes it super good. + + align:start position:0% + + + + align:start position:0% + +Is that me? Okay. Uh I thought of I + + align:start position:0% +Is that me? Okay. Uh I thought of I + + + align:start position:0% +Is that me? Okay. Uh I thought of I +think of portal when they ask you to use + + align:start position:0% +think of portal when they ask you to use + + + align:start position:0% +think of portal when they ask you to use +them as your portal. + + align:start position:0% + + + + align:start position:0% + +>> You have to burn up the cube. + + align:start position:0% +>> You have to burn up the cube. + + + align:start position:0% +>> You have to burn up the cube. +>> Yeah. You don't want to and they make + + align:start position:0% +>> Yeah. You don't want to and they make + + + align:start position:0% +>> Yeah. You don't want to and they make +you and you try to like leave without it + + align:start position:0% +you and you try to like leave without it + + + align:start position:0% +you and you try to like leave without it +for a few times and you try to break. It + + align:start position:0% +for a few times and you try to break. It + + + align:start position:0% +for a few times and you try to break. It +doesn't work. + + align:start position:0% +doesn't work. + + + align:start position:0% +doesn't work. +>> It's very sad. + + align:start position:0% +>> It's very sad. + + + align:start position:0% +>> It's very sad. +>> I didn't want to do it. + + align:start position:0% +>> I didn't want to do it. + + + align:start position:0% +>> I didn't want to do it. +I thought of uh Jason Roer's Sleep is + + align:start position:0% +I thought of uh Jason Roer's Sleep is + + + align:start position:0% +I thought of uh Jason Roer's Sleep is +Dead. + + align:start position:0% +Dead. + + + align:start position:0% +Dead. +>> Um + + align:start position:0% +>> Um + + + align:start position:0% +>> Um +what was that one? + + align:start position:0% +what was that one? + + + align:start position:0% +what was that one? +>> It's more of like a storytelling tool + + align:start position:0% +>> It's more of like a storytelling tool + + + align:start position:0% +>> It's more of like a storytelling tool +where you have one player can control + + align:start position:0% +where you have one player can control + + + align:start position:0% +where you have one player can control +like the the 2D world and then you have + + align:start position:0% +like the the 2D world and then you have + + + align:start position:0% +like the the 2D world and then you have +one player who is the player and they + + align:start position:0% +one player who is the player and they + + + align:start position:0% +one player who is the player and they +can interact with it. + + align:start position:0% +can interact with it. + + + align:start position:0% +can interact with it. +>> Oh. + + align:start position:0% +>> Oh. + + + align:start position:0% +>> Oh. +>> And each player has like 30 seconds to + + align:start position:0% +>> And each player has like 30 seconds to + + + align:start position:0% +>> And each player has like 30 seconds to +make some kind of action and then you + + align:start position:0% +make some kind of action and then you + + + align:start position:0% +make some kind of action and then you +make a story going back and forth. And + + align:start position:0% +make a story going back and forth. And + + + align:start position:0% +make a story going back and forth. And +um what happens is you can play online + + align:start position:0% +um what happens is you can play online + + + align:start position:0% +um what happens is you can play online +with people and uh like the controller + + align:start position:0% +with people and uh like the controller + + + align:start position:0% +with people and uh like the controller +character will or player will have some + + align:start position:0% +character will or player will have some + + + align:start position:0% +character will or player will have some +kind of story that they want to tell and + + align:start position:0% +kind of story that they want to tell and + + + align:start position:0% +kind of story that they want to tell and +so it's up to the player whether or not + + align:start position:0% +so it's up to the player whether or not + + + align:start position:0% +so it's up to the player whether or not +they want to go along with the story and + + align:start position:0% +they want to go along with the story and + + + align:start position:0% +they want to go along with the story and +act like a character in their world or + + align:start position:0% +act like a character in their world or + + + align:start position:0% +act like a character in their world or +like try and break the story. + + align:start position:0% +like try and break the story. + + + align:start position:0% +like try and break the story. +>> Okay. What's the name of it again? + + align:start position:0% +>> Okay. What's the name of it again? + + + align:start position:0% +>> Okay. What's the name of it again? +>> Sleep is dead. + + align:start position:0% + + + + align:start position:0% + +>> So actually or brief you say + + align:start position:0% +>> So actually or brief you say + + + align:start position:0% +>> So actually or brief you say +>> kind of. + + align:start position:0% + + + + align:start position:0% + +>> Is that the same person as passing? + + align:start position:0% +>> Is that the same person as passing? + + + align:start position:0% +>> Is that the same person as passing? +>> Yes. + + align:start position:0% +>> Yes. + + + align:start position:0% +>> Yes. +>> Okay. + + align:start position:0% +>> Okay. + + + align:start position:0% +>> Okay. +>> Um, in Ocarina of Time, there's the + + align:start position:0% +>> Um, in Ocarina of Time, there's the + + + align:start position:0% +>> Um, in Ocarina of Time, there's the +treasure box gambling game. You can + + align:start position:0% +treasure box gambling game. You can + + + align:start position:0% +treasure box gambling game. You can +actually cheat if you use the lens of + + align:start position:0% +actually cheat if you use the lens of + + + align:start position:0% +actually cheat if you use the lens of +truth through boxes. So, it's a built-in + + align:start position:0% +truth through boxes. So, it's a built-in + + + align:start position:0% +truth through boxes. So, it's a built-in +mechanic, but that sort of allows you to + + align:start position:0% +mechanic, but that sort of allows you to + + + align:start position:0% +mechanic, but that sort of allows you to +cheat. + + align:start position:0% + + + + align:start position:0% + +>> You just got to do that legit. + + align:start position:0% +>> You just got to do that legit. + + + align:start position:0% +>> You just got to do that legit. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +You can get money easily anyway. It's + + align:start position:0% +You can get money easily anyway. It's + + + align:start position:0% +You can get money easily anyway. It's +not really good. + + align:start position:0% +not really good. + + + align:start position:0% +not really good. +>> I do that. + + align:start position:0% +>> I do that. + + + align:start position:0% +>> I do that. +>> I do that completely chip. + + align:start position:0% + + + + align:start position:0% + +>> Lucky man. + + align:start position:0% +>> Lucky man. + + + align:start position:0% +>> Lucky man. +>> So in the sip hord there's a + + align:start position:0% +>> So in the sip hord there's a + + + align:start position:0% +>> So in the sip hord there's a +pretty much every sip there's some sort + + align:start position:0% +pretty much every sip there's some sort + + + align:start position:0% +pretty much every sip there's some sort +of slavery mechanic. But I guess in S + + align:start position:0% +of slavery mechanic. But I guess in S + + + align:start position:0% +of slavery mechanic. But I guess in S +force example I know uh many players + + align:start position:0% +force example I know uh many players + + + align:start position:0% +force example I know uh many players +don't seem to mind the fact that we + + align:start position:0% +don't seem to mind the fact that we + + + align:start position:0% +don't seem to mind the fact that we +would all consider that slavery is + + align:start position:0% +would all consider that slavery is + + + align:start position:0% +would all consider that slavery is +ethically wrong. But in in game it's + + align:start position:0% +ethically wrong. But in in game it's + + + align:start position:0% +ethically wrong. But in in game it's +actually affectionately called whipping + + align:start position:0% +actually affectionately called whipping + + + align:start position:0% +actually affectionately called whipping +and is considered a very efficient way + + align:start position:0% +and is considered a very efficient way + + + align:start position:0% +and is considered a very efficient way +of converting food into + + align:start position:0% +of converting food into + + + align:start position:0% +of converting food into +>> whipping whipping + + align:start position:0% + + + + align:start position:0% + +unit. + + align:start position:0% + + + + align:start position:0% + +>> Okay. So it's efficient but it's + + align:start position:0% +>> Okay. So it's efficient but it's + + + align:start position:0% +>> Okay. So it's efficient but it's +slavery. But you combine it, you use + + align:start position:0% +slavery. But you combine it, you use + + + align:start position:0% +slavery. But you combine it, you use +granaries to offset the population loss. + + align:start position:0% +granaries to offset the population loss. + + + align:start position:0% +granaries to offset the population loss. +And if you spam farms, it becomes a very + + align:start position:0% +And if you spam farms, it becomes a very + + + align:start position:0% +And if you spam farms, it becomes a very +effective way to uh produce, especially + + align:start position:0% +effective way to uh produce, especially + + + align:start position:0% +effective way to uh produce, especially +in hell for your + + align:start position:0% +in hell for your + + + align:start position:0% +in hell for your +>> usually used to exploit a lot of people + + align:start position:0% +>> usually used to exploit a lot of people + + + align:start position:0% +>> usually used to exploit a lot of people +that way. + + align:start position:0% + + + + align:start position:0% + +>> Anyh who, + + align:start position:0% +>> Anyh who, + + + align:start position:0% +>> Anyh who, +>> um so in Sims, my friend used to do this + + align:start position:0% +>> um so in Sims, my friend used to do this + + + align:start position:0% +>> um so in Sims, my friend used to do this +all the time. You just like off your + + align:start position:0% +all the time. You just like off your + + + align:start position:0% +all the time. You just like off your +characters by putting them in a lot of + + align:start position:0% +characters by putting them in a lot of + + + align:start position:0% +characters by putting them in a lot of +like the pool and then + + align:start position:0% + + + + align:start position:0% + +>> but you have to watch them flail around + + align:start position:0% +>> but you have to watch them flail around + + + align:start position:0% +>> but you have to watch them flail around +and die + + align:start position:0% +and die + + + align:start position:0% +and die +>> and get tired and + + align:start position:0% + + + + align:start position:0% + +>> um I have a few I guess a more obscure + + align:start position:0% +>> um I have a few I guess a more obscure + + + align:start position:0% +>> um I have a few I guess a more obscure +example that kind of goes along the + + align:start position:0% +example that kind of goes along the + + + align:start position:0% +example that kind of goes along the +lines of briefing is uh discussions over + + align:start position:0% +lines of briefing is uh discussions over + + + align:start position:0% +lines of briefing is uh discussions over +the point of the game in communities in + + align:start position:0% +the point of the game in communities in + + + align:start position:0% +the point of the game in communities in +MMOs. Uh specifically, there was + + align:start position:0% +MMOs. Uh specifically, there was + + + align:start position:0% +MMOs. Uh specifically, there was +apparently a + + align:start position:0% +apparently a + + + align:start position:0% +apparently a +huge problem in an obscure mode called + + align:start position:0% +huge problem in an obscure mode called + + + align:start position:0% +huge problem in an obscure mode called +Skys where a large community of the + + align:start position:0% +Skys where a large community of the + + + align:start position:0% +Skys where a large community of the +players was there to basically + + align:start position:0% +players was there to basically + + + align:start position:0% +players was there to basically +anthropomorphic RP and a large community + + align:start position:0% +anthropomorphic RP and a large community + + + align:start position:0% +anthropomorphic RP and a large community +of the players there was there to play + + align:start position:0% +of the players there was there to play + + + align:start position:0% +of the players there was there to play +to win because it had a large combat + + align:start position:0% +to win because it had a large combat + + + align:start position:0% +to win because it had a large combat +economy system. Um, and this effectively + + align:start position:0% +economy system. Um, and this effectively + + + align:start position:0% +economy system. Um, and this effectively +almost tore the game apart because it + + align:start position:0% +almost tore the game apart because it + + + align:start position:0% +almost tore the game apart because it +was such a small number of people um + + align:start position:0% +was such a small number of people um + + + align:start position:0% +was such a small number of people um +over what should be the point of this + + align:start position:0% +over what should be the point of this + + + align:start position:0% +over what should be the point of this +game when mechanically so many things + + align:start position:0% +game when mechanically so many things + + + align:start position:0% +game when mechanically so many things +are bad. + + align:start position:0% +are bad. + + + align:start position:0% +are bad. +>> Uh, also in Cal Hard you can roll up + + align:start position:0% +>> Uh, also in Cal Hard you can roll up + + + align:start position:0% +>> Uh, also in Cal Hard you can roll up +people + + align:start position:0% +people + + + align:start position:0% +people +and then a star. It was traumatizing. + + align:start position:0% + + + + align:start position:0% + +>> Yeah, but they're in a giant ball of + + align:start position:0% +>> Yeah, but they're in a giant ball of + + + align:start position:0% +>> Yeah, but they're in a giant ball of +awesome. That's true. + + align:start position:0% +awesome. That's true. + + + align:start position:0% +awesome. That's true. +It's not really murder. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +>> They don't suffocate on the inside of + + align:start position:0% +>> They don't suffocate on the inside of + + + align:start position:0% +>> They don't suffocate on the inside of +the cavary first. + + align:start position:0% + + + + align:start position:0% + +>> It's like a gour. Once you're in there, + + align:start position:0% +>> It's like a gour. Once you're in there, + + + align:start position:0% +>> It's like a gour. Once you're in there, +you know, it's a better way. + + align:start position:0% +you know, it's a better way. + + + align:start position:0% +you know, it's a better way. +>> You're grateful. + + align:start position:0% +>> You're grateful. + + + align:start position:0% +>> You're grateful. +Um, so in fear there's um there's a nail + + align:start position:0% +Um, so in fear there's um there's a nail + + + align:start position:0% +Um, so in fear there's um there's a nail +gun + + align:start position:0% +gun + + + align:start position:0% +gun +and when + + align:start position:0% +and when + + + align:start position:0% +and when +>> can't end well + + align:start position:0% +>> can't end well + + + align:start position:0% +>> can't end well +>> and when you kill people with it, uh, + + align:start position:0% +>> and when you kill people with it, uh, + + + align:start position:0% +>> and when you kill people with it, uh, +the game does a really good job of + + align:start position:0% +the game does a really good job of + + + align:start position:0% +the game does a really good job of +spectacularly nailing them to surfaces + + align:start position:0% +spectacularly nailing them to surfaces + + + align:start position:0% +spectacularly nailing them to surfaces +in the environment. So if you if like + + align:start position:0% +in the environment. So if you if like + + + align:start position:0% +in the environment. So if you if like +someone jumps and then you shoot them in + + align:start position:0% +someone jumps and then you shoot them in + + + align:start position:0% +someone jumps and then you shoot them in +the shoulder, you'll like you can like + + align:start position:0% +the shoulder, you'll like you can like + + + align:start position:0% +the shoulder, you'll like you can like +nail them up to the ceiling. And if you + + align:start position:0% +nail them up to the ceiling. And if you + + + align:start position:0% +nail them up to the ceiling. And if you +nail them multiple times, you can have + + align:start position:0% +nail them multiple times, you can have + + + align:start position:0% +nail them multiple times, you can have +them like hanging by hand and by their + + align:start position:0% +them like hanging by hand and by their + + + align:start position:0% +them like hanging by hand and by their +head and by a foot from the ceiling or + + align:start position:0% +head and by a foot from the ceiling or + + + align:start position:0% +head and by a foot from the ceiling or +something or from the wall. Anyway, + + align:start position:0% +something or from the wall. Anyway, + + + align:start position:0% +something or from the wall. Anyway, +>> on awesome. Yeah, on forums there were + + align:start position:0% +>> on awesome. Yeah, on forums there were + + + align:start position:0% +>> on awesome. Yeah, on forums there were +entire threads devoted devoted to + + align:start position:0% +entire threads devoted devoted to + + + align:start position:0% +entire threads devoted devoted to +sharing + + align:start position:0% +sharing + + + align:start position:0% +sharing +screenshots of your most spectacular + + align:start position:0% +screenshots of your most spectacular + + + align:start position:0% +screenshots of your most spectacular +nails like like you know just like the + + align:start position:0% +nails like like you know just like the + + + align:start position:0% +nails like like you know just like the +absolutely most gruesome like you know + + align:start position:0% +absolutely most gruesome like you know + + + align:start position:0% +absolutely most gruesome like you know +five nails to the eye suspending a guy + + align:start position:0% +five nails to the eye suspending a guy + + + align:start position:0% +five nails to the eye suspending a guy +from a pole kind of thing. And + + align:start position:0% + + + + align:start position:0% + +um anyway, and there was just a lot of + + align:start position:0% +um anyway, and there was just a lot of + + + align:start position:0% +um anyway, and there was just a lot of +debate on these threads cuz most people + + align:start position:0% +debate on these threads cuz most people + + + align:start position:0% +debate on these threads cuz most people +be like, "Yeah, look at this picture. + + align:start position:0% +be like, "Yeah, look at this picture. + + + align:start position:0% +be like, "Yeah, look at this picture. +This one's awesome." And thinking, you + + align:start position:0% +This one's awesome." And thinking, you + + + align:start position:0% +This one's awesome." And thinking, you +know, has blood splatters everywhere and + + align:start position:0% +know, has blood splatters everywhere and + + + align:start position:0% +know, has blood splatters everywhere and +all that, but every like third or fourth + + align:start position:0% +all that, but every like third or fourth + + + align:start position:0% +all that, but every like third or fourth +post it be like, "You guys are so messed + + align:start position:0% +post it be like, "You guys are so messed + + + align:start position:0% +post it be like, "You guys are so messed +up." You know, this is like this is + + align:start position:0% +up." You know, this is like this is + + + align:start position:0% +up." You know, this is like this is +wrong. And it was and it was it's not + + align:start position:0% +wrong. And it was and it was it's not + + + align:start position:0% +wrong. And it was and it was it's not +real, you idiot. You know, like but it + + align:start position:0% +real, you idiot. You know, like but it + + + align:start position:0% +real, you idiot. You know, like but it +but but the fact that you like it is + + align:start position:0% +but but the fact that you like it is + + + align:start position:0% +but but the fact that you like it is +still real. Well, then people would + + align:start position:0% +still real. Well, then people would + + + align:start position:0% +still real. Well, then people would +argue at, you know, at great lengths + + align:start position:0% +argue at, you know, at great lengths + + + align:start position:0% +argue at, you know, at great lengths +over this. I just remember chanting upon + + align:start position:0% +over this. I just remember chanting upon + + + align:start position:0% +over this. I just remember chanting upon +these forms and being like, "Is this + + align:start position:0% +these forms and being like, "Is this + + + align:start position:0% +these forms and being like, "Is this +messed up?" I'm not sure. + + align:start position:0% +messed up?" I'm not sure. + + + align:start position:0% +messed up?" I'm not sure. +>> So, is it more + + align:start position:0% +>> So, is it more + + + align:start position:0% +>> So, is it more +efficient in the game to use the nail + + align:start position:0% +efficient in the game to use the nail + + + align:start position:0% +efficient in the game to use the nail +gun to kill people than other + + align:start position:0% +gun to kill people than other + + + align:start position:0% +gun to kill people than other +>> It's a hell of a lot more fun. + + align:start position:0% +>> It's a hell of a lot more fun. + + + align:start position:0% +>> It's a hell of a lot more fun. +>> Okay. + + align:start position:0% +>> Okay. + + + align:start position:0% +>> Okay. +>> Um, + + align:start position:0% +>> Um, + + + align:start position:0% +>> Um, +>> but it's not like the game forces you to + + align:start position:0% +>> but it's not like the game forces you to + + + align:start position:0% +>> but it's not like the game forces you to +do it if you would not want to. + + align:start position:0% +do it if you would not want to. + + + align:start position:0% +do it if you would not want to. +>> No, it doesn't. You could use other + + align:start position:0% +>> No, it doesn't. You could use other + + + align:start position:0% +>> No, it doesn't. You could use other +guns, but at some point, you know, if + + align:start position:0% +guns, but at some point, you know, if + + + align:start position:0% +guns, but at some point, you know, if +you don't have enough ammo for other + + align:start position:0% +you don't have enough ammo for other + + + align:start position:0% +you don't have enough ammo for other +guns, you do you would switch to nail + + align:start position:0% +guns, you do you would switch to nail + + + align:start position:0% +guns, you do you would switch to nail +gun, I guess. It's a good gun. Shotgun's + + align:start position:0% +gun, I guess. It's a good gun. Shotgun's + + + align:start position:0% +gun, I guess. It's a good gun. Shotgun's +kind of fun, too. It disintegrates + + align:start position:0% +kind of fun, too. It disintegrates + + + align:start position:0% +kind of fun, too. It disintegrates +people at short range. + + align:start position:0% +people at short range. + + + align:start position:0% +people at short range. +>> Okay. + + align:start position:0% + + + + align:start position:0% + +>> A gun that turns people into skeletons. + + align:start position:0% +>> A gun that turns people into skeletons. + + + align:start position:0% +>> A gun that turns people into skeletons. +>> Yes, that one was in the expansion. + + align:start position:0% +>> Yes, that one was in the expansion. + + + align:start position:0% +>> Yes, that one was in the expansion. +>> Yes. No, it wasn't the original. The + + align:start position:0% +>> Yes. No, it wasn't the original. The + + + align:start position:0% +>> Yes. No, it wasn't the original. The +sniper rifle was a rail gun that shoots + + align:start position:0% +sniper rifle was a rail gun that shoots + + + align:start position:0% +sniper rifle was a rail gun that shoots +a beam of electricity and turns people + + align:start position:0% +a beam of electricity and turns people + + + align:start position:0% +a beam of electricity and turns people +vaporizes the flesh off other opponents. + + align:start position:0% + + + + align:start position:0% + +What? + + align:start position:0% +What? + + + align:start position:0% +What? +>> Um, Grand Theft Auto, you can get a + + align:start position:0% +>> Um, Grand Theft Auto, you can get a + + + align:start position:0% +>> Um, Grand Theft Auto, you can get a +prostitute for money, get health, and + + align:start position:0% +prostitute for money, get health, and + + + align:start position:0% +prostitute for money, get health, and +then potentially kill the prostitute and + + align:start position:0% +then potentially kill the prostitute and + + + align:start position:0% +then potentially kill the prostitute and +get your money back. + + align:start position:0% +get your money back. + + + align:start position:0% +get your money back. +>> The hook or cheat. + + align:start position:0% +>> The hook or cheat. + + + align:start position:0% +>> The hook or cheat. +>> Yeah. Um, and then like some of the ones + + align:start position:0% +>> Yeah. Um, and then like some of the ones + + + align:start position:0% +>> Yeah. Um, and then like some of the ones +related to that is like Bioshock where + + align:start position:0% +related to that is like Bioshock where + + + align:start position:0% +related to that is like Bioshock where +like you can either kill the little + + align:start position:0% +like you can either kill the little + + + align:start position:0% +like you can either kill the little +sisters or and harvest them for like + + align:start position:0% +sisters or and harvest them for like + + + align:start position:0% +sisters or and harvest them for like +lots of good or like lots of points + + align:start position:0% +lots of good or like lots of points + + + align:start position:0% +lots of good or like lots of points +rather or like save them and get a + + align:start position:0% +rather or like save them and get a + + + align:start position:0% +rather or like save them and get a +smaller amount of points but like you + + align:start position:0% +smaller amount of points but like you + + + align:start position:0% +smaller amount of points but like you +feel better about yourself which + + align:start position:0% +feel better about yourself which + + + align:start position:0% +feel better about yourself which +actually in the end ends up being the + + align:start position:0% +actually in the end ends up being the + + + align:start position:0% +actually in the end ends up being the +better way to go. But + + align:start position:0% +better way to go. But + + + align:start position:0% +better way to go. But +>> yeah, you get more. It's like you get + + align:start position:0% +>> yeah, you get more. It's like you get + + + align:start position:0% +>> yeah, you get more. It's like you get +more to save. + + align:start position:0% +more to save. + + + align:start position:0% +more to save. +>> Yeah, cuz well cuz like at like you get + + align:start position:0% +>> Yeah, cuz well cuz like at like you get + + + align:start position:0% +>> Yeah, cuz well cuz like at like you get +small like if you kill them and harvest + + align:start position:0% +small like if you kill them and harvest + + + align:start position:0% +small like if you kill them and harvest +them you get like 10 points let's say. + + align:start position:0% +them you get like 10 points let's say. + + + align:start position:0% +them you get like 10 points let's say. +If you save them, you get like five + + align:start position:0% +If you save them, you get like five + + + align:start position:0% +If you save them, you get like five +points, but then after like 10 saves, + + align:start position:0% +points, but then after like 10 saves, + + + align:start position:0% +points, but then after like 10 saves, +you get like a bonus of like 100 points. + + align:start position:0% +you get like a bonus of like 100 points. + + + align:start position:0% +you get like a bonus of like 100 points. +So, it ends up being like more efficient + + align:start position:0% +So, it ends up being like more efficient + + + align:start position:0% +So, it ends up being like more efficient +or not like more efficient in the long + + align:start position:0% +or not like more efficient in the long + + + align:start position:0% +or not like more efficient in the long +run to save them. More efficient in the + + align:start position:0% +run to save them. More efficient in the + + + align:start position:0% +run to save them. More efficient in the +short run to kill them. + + align:start position:0% +short run to kill them. + + + align:start position:0% +short run to kill them. +>> And also, if you're going to kill them, + + align:start position:0% +>> And also, if you're going to kill them, + + + align:start position:0% +>> And also, if you're going to kill them, +you should kill them all, + + align:start position:0% +you should kill them all, + + + align:start position:0% +you should kill them all, +>> right? + + align:start position:0% +>> right? + + + align:start position:0% +>> right? +>> Don't just knock off one. + + align:start position:0% +>> Don't just knock off one. + + + align:start position:0% +>> Don't just knock off one. +>> Yeah. Yeah. + + align:start position:0% +>> Yeah. Yeah. + + + align:start position:0% +>> Yeah. Yeah. +>> Yeah. Okay. Uh in Age of Empires 3, + + align:start position:0% +>> Yeah. Okay. Uh in Age of Empires 3, + + + align:start position:0% +>> Yeah. Okay. Uh in Age of Empires 3, +there's uh when you're colonizing your + + align:start position:0% +there's uh when you're colonizing your + + + align:start position:0% +there's uh when you're colonizing your +colony, you have the option of + + align:start position:0% +colony, you have the option of + + + align:start position:0% +colony, you have the option of +expediting the native people. So like to + + align:start position:0% +expediting the native people. So like to + + + align:start position:0% +expediting the native people. So like to +help you uh fight like basically to help + + align:start position:0% +help you uh fight like basically to help + + + align:start position:0% +help you uh fight like basically to help +you fight. + + align:start position:0% +you fight. + + + align:start position:0% +you fight. +>> How do you how is this presented to like + + align:start position:0% +>> How do you how is this presented to like + + + align:start position:0% +>> How do you how is this presented to like +explain? + + align:start position:0% +explain? + + + align:start position:0% +explain? +>> No, I mean you like present them. You + + align:start position:0% +>> No, I mean you like present them. You + + + align:start position:0% +>> No, I mean you like present them. You +establish an outpost inside of their um + + align:start position:0% +establish an outpost inside of their um + + + align:start position:0% +establish an outpost inside of their um +residence area and you supposedly trade + + align:start position:0% +residence area and you supposedly trade + + + align:start position:0% +residence area and you supposedly trade +with them, but I mean there's nothing + + align:start position:0% +with them, but I mean there's nothing + + + align:start position:0% +with them, but I mean there's nothing +really there in the game. You just + + align:start position:0% +really there in the game. You just + + + align:start position:0% +really there in the game. You just +literally just put a house of yours + + align:start position:0% +literally just put a house of yours + + + align:start position:0% +literally just put a house of yours +inside of their colony. + + align:start position:0% +inside of their colony. + + + align:start position:0% +inside of their colony. +>> Nice. + + align:start position:0% +>> Nice. + + + align:start position:0% +>> Nice. +>> Also, Microsoft's selling that for 10 + + align:start position:0% +>> Also, Microsoft's selling that for 10 + + + align:start position:0% +>> Also, Microsoft's selling that for 10 +cents. + + align:start position:0% +cents. + + + align:start position:0% +cents. +>> Yeah. inverse. + + align:start position:0% +>> Yeah. inverse. + + + align:start position:0% +>> Yeah. inverse. +>> Yeah. Yeah. + + align:start position:0% +>> Yeah. Yeah. + + + align:start position:0% +>> Yeah. Yeah. +>> I think it was just yesterday. + + align:start position:0% +>> I think it was just yesterday. + + + align:start position:0% +>> I think it was just yesterday. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> I'm not sure. + + align:start position:0% +>> I'm not sure. + + + align:start position:0% +>> I'm not sure. +>> Um I guess infamous you can choose + + align:start position:0% +>> Um I guess infamous you can choose + + + align:start position:0% +>> Um I guess infamous you can choose +whether to be bad or good like go around + + align:start position:0% +whether to be bad or good like go around + + + align:start position:0% +whether to be bad or good like go around +killing people or to help them survive + + align:start position:0% +killing people or to help them survive + + + align:start position:0% +killing people or to help them survive +postapocalyptic world. + + align:start position:0% +postapocalyptic world. + + + align:start position:0% +postapocalyptic world. +>> And I guess you can kind of do the same + + align:start position:0% +>> And I guess you can kind of do the same + + + align:start position:0% +>> And I guess you can kind of do the same +thing in Fallout. + + align:start position:0% +thing in Fallout. + + + align:start position:0% +thing in Fallout. +Well, also, um, Infamous forces you more + + align:start position:0% +Well, also, um, Infamous forces you more + + + align:start position:0% +Well, also, um, Infamous forces you more +to choose. Remember Ash was playing that + + align:start position:0% +to choose. Remember Ash was playing that + + + align:start position:0% +to choose. Remember Ash was playing that +in our class and she said like you + + align:start position:0% +in our class and she said like you + + + align:start position:0% +in our class and she said like you +really had to go one way or the other to + + align:start position:0% +really had to go one way or the other to + + + align:start position:0% +really had to go one way or the other to +get, you know, it's like on either end + + align:start position:0% +get, you know, it's like on either end + + + align:start position:0% +get, you know, it's like on either end +of the spectrum there were special + + align:start position:0% +of the spectrum there were special + + + align:start position:0% +of the spectrum there were special +abilities. If you stay in the middle, + + align:start position:0% +abilities. If you stay in the middle, + + + align:start position:0% +abilities. If you stay in the middle, +you got nothing. + + align:start position:0% +you got nothing. + + + align:start position:0% +you got nothing. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Really note + + align:start position:0% +>> Really note + + + align:start position:0% +>> Really note +>> follow. I just follow I mean there are + + align:start position:0% +>> follow. I just follow I mean there are + + + align:start position:0% +>> follow. I just follow I mean there are +certain things you can build off. So + + align:start position:0% +certain things you can build off. So + + + align:start position:0% +certain things you can build off. So +there's also like in Fallout you can + + align:start position:0% +there's also like in Fallout you can + + + align:start position:0% +there's also like in Fallout you can +gain like people that travel with you + + align:start position:0% +gain like people that travel with you + + + align:start position:0% +gain like people that travel with you +like based off neutral + + align:start position:0% +like based off neutral + + + align:start position:0% +like based off neutral +>> oh sorry um I was going to say in + + align:start position:0% +>> oh sorry um I was going to say in + + + align:start position:0% +>> oh sorry um I was going to say in +Fallout as well like in in Fallout 3 + + align:start position:0% +Fallout as well like in in Fallout 3 + + + align:start position:0% +Fallout as well like in in Fallout 3 +there's one particular really good + + align:start position:0% +there's one particular really good + + + align:start position:0% +there's one particular really good +example um where you get trapped in like + + align:start position:0% +example um where you get trapped in like + + + align:start position:0% +example um where you get trapped in like +this dream world that this guy is + + align:start position:0% +this dream world that this guy is + + + align:start position:0% +this dream world that this guy is +creating for you and a bunch of other + + align:start position:0% +creating for you and a bunch of other + + + align:start position:0% +creating for you and a bunch of other +people um which you don't know that it's + + align:start position:0% +people um which you don't know that it's + + + align:start position:0% +people um which you don't know that it's +a dream world at first like you know + + align:start position:0% +a dream world at first like you know + + + align:start position:0% +a dream world at first like you know +it's a dream or something but you don't + + align:start position:0% +it's a dream or something but you don't + + + align:start position:0% +it's a dream or something but you don't +know that these are real people in the + + align:start position:0% +know that these are real people in the + + + align:start position:0% +know that these are real people in the +dream with you and he tells you to kill + + align:start position:0% +dream with you and he tells you to kill + + + align:start position:0% +dream with you and he tells you to kill +the other people in the dream in order + + align:start position:0% +the other people in the dream in order + + + align:start position:0% +the other people in the dream in order +to like let you get out cuz he's in + + align:start position:0% +to like let you get out cuz he's in + + + align:start position:0% +to like let you get out cuz he's in +complete control of it. Um, and you can + + align:start position:0% +complete control of it. Um, and you can + + + align:start position:0% +complete control of it. Um, and you can +kill them and you'll get out fine. All + + align:start position:0% +kill them and you'll get out fine. All + + + align:start position:0% +kill them and you'll get out fine. All +the people will be dead. Um, or there's + + align:start position:0% +the people will be dead. Um, or there's + + + align:start position:0% +the people will be dead. Um, or there's +ways that aren't like you're not told, + + align:start position:0% +ways that aren't like you're not told, + + + align:start position:0% +ways that aren't like you're not told, +but there's there are ways to like just + + align:start position:0% +but there's there are ways to like just + + + align:start position:0% +but there's there are ways to like just +go around all of it and just get out + + align:start position:0% +go around all of it and just get out + + + align:start position:0% +go around all of it and just get out +without killing anyone. + + align:start position:0% +without killing anyone. + + + align:start position:0% +without killing anyone. +>> They stole that from I guess in Balders + + align:start position:0% +>> They stole that from I guess in Balders + + + align:start position:0% +>> They stole that from I guess in Balders +2. There's the similar thing. was + + align:start position:0% +2. There's the similar thing. was + + + align:start position:0% +2. There's the similar thing. was +actually going to talk. + + align:start position:0% + + + + align:start position:0% + +>> Y + + align:start position:0% + + + + align:start position:0% + +>> So I guess the first thing I'll mention + + align:start position:0% +>> So I guess the first thing I'll mention + + + align:start position:0% +>> So I guess the first thing I'll mention +is uh items but + + align:start position:0% +is uh items but + + + align:start position:0% +is uh items but +>> just watching. + + align:start position:0% +>> just watching. + + + align:start position:0% +>> just watching. +>> Yeah, just uh go out of all of them. how + + align:start position:0% +>> Yeah, just uh go out of all of them. how + + + align:start position:0% +>> Yeah, just uh go out of all of them. how +so many times you'll be fighting + + align:start position:0% +so many times you'll be fighting + + + align:start position:0% +so many times you'll be fighting +monsters and all of a sudden a bunch of + + align:start position:0% +monsters and all of a sudden a bunch of + + + align:start position:0% +monsters and all of a sudden a bunch of +civilians come by and you can just let + + align:start position:0% +civilians come by and you can just let + + + align:start position:0% +civilians come by and you can just let +them go, but there's no fun that if you + + align:start position:0% +them go, but there's no fun that if you + + + align:start position:0% +them go, but there's no fun that if you +kill them, you get life and experience. + + align:start position:0% +kill them, you get life and experience. + + + align:start position:0% +kill them, you get life and experience. +So, it's better to reward you for + + align:start position:0% +So, it's better to reward you for + + + align:start position:0% +So, it's better to reward you for +killing them. + + align:start position:0% +killing them. + + + align:start position:0% +killing them. +>> Yeah, + + align:start position:0% +>> Yeah, + + + align:start position:0% +>> Yeah, +>> you get you get some life back. Maybe + + align:start position:0% +>> you get you get some life back. Maybe + + + align:start position:0% +>> you get you get some life back. Maybe +some usually do that in the story, + + align:start position:0% +some usually do that in the story, + + + align:start position:0% +some usually do that in the story, +>> huh? + + align:start position:0% +>> huh? + + + align:start position:0% +>> huh? +>> You're Kratos. + + align:start position:0% +>> You're Kratos. + + + align:start position:0% +>> You're Kratos. +>> Kratos. + + align:start position:0% +>> Kratos. + + + align:start position:0% +>> Kratos. +>> You are the god of war. Well, you become + + align:start position:0% +>> You are the god of war. Well, you become + + + align:start position:0% +>> You are the god of war. Well, you become +the god, but pretty much you just go + + align:start position:0% +the god, but pretty much you just go + + + align:start position:0% +the god, but pretty much you just go +around kill hackers and slashing + + align:start position:0% +around kill hackers and slashing + + + align:start position:0% +around kill hackers and slashing +everything up. + + align:start position:0% +everything up. + + + align:start position:0% +everything up. +>> Okay. So, you get these are just in + + align:start position:0% +>> Okay. So, you get these are just in + + + align:start position:0% +>> Okay. So, you get these are just in +civilians who are doing nothing. + + align:start position:0% +civilians who are doing nothing. + + + align:start position:0% +civilians who are doing nothing. +>> Yeah. Who do they're just running + + align:start position:0% +>> Yeah. Who do they're just running + + + align:start position:0% +>> Yeah. Who do they're just running +running for their lives from scary + + align:start position:0% +running for their lives from scary + + + align:start position:0% +running for their lives from scary +monsters and then you come and just like + + align:start position:0% +monsters and then you come and just like + + + align:start position:0% +monsters and then you come and just like +hack them all into pieces. + + align:start position:0% +hack them all into pieces. + + + align:start position:0% +hack them all into pieces. +>> Well, also there's in the in the game + + align:start position:0% +>> Well, also there's in the in the game + + + align:start position:0% +>> Well, also there's in the in the game +you could there's like the second one in + + align:start position:0% +you could there's like the second one in + + + align:start position:0% +you could there's like the second one in +order to pass on you have to translate + + align:start position:0% +order to pass on you have to translate + + + align:start position:0% +order to pass on you have to translate +something and then translate it you get + + align:start position:0% +something and then translate it you get + + + align:start position:0% +something and then translate it you get +a priest. You smash your head to it and + + align:start position:0% +a priest. You smash your head to it and + + + align:start position:0% +a priest. You smash your head to it and +then they say they have to sacrifice in + + align:start position:0% +then they say they have to sacrifice in + + + align:start position:0% +then they say they have to sacrifice in +blood. So you just smash them into + + align:start position:0% +blood. So you just smash them into + + + align:start position:0% +blood. So you just smash them into +pieces until the the blood sacrifice. + + align:start position:0% +pieces until the the blood sacrifice. + + + align:start position:0% +pieces until the the blood sacrifice. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> This feels so good. + + align:start position:0% +>> This feels so good. + + + align:start position:0% +>> This feels so good. +>> Do you happen to do that? + + align:start position:0% +>> Do you happen to do that? + + + align:start position:0% +>> Do you happen to do that? +>> Yeah. Oh, okay. + + align:start position:0% +>> Yeah. Oh, okay. + + + align:start position:0% +>> Yeah. Oh, okay. +In Indigo Prophecy, uh you switch + + align:start position:0% +In Indigo Prophecy, uh you switch + + + align:start position:0% +In Indigo Prophecy, uh you switch +between different sets of characters. + + align:start position:0% +between different sets of characters. + + + align:start position:0% +between different sets of characters. +One of them is a guy who committed a + + align:start position:0% +One of them is a guy who committed a + + + align:start position:0% +One of them is a guy who committed a +murder and then you switch to the cops + + align:start position:0% +murder and then you switch to the cops + + + align:start position:0% +murder and then you switch to the cops +who are trying to catch him. And so in + + align:start position:0% +who are trying to catch him. And so in + + + align:start position:0% +who are trying to catch him. And so in +one of the earlier scenes you play as + + align:start position:0% +one of the earlier scenes you play as + + + align:start position:0% +one of the earlier scenes you play as +the cops, you bring in a witness and you + + align:start position:0% +the cops, you bring in a witness and you + + + align:start position:0% +the cops, you bring in a witness and you +um you're trying to make up the artist + + align:start position:0% +um you're trying to make up the artist + + + align:start position:0% +um you're trying to make up the artist +rendering of what the murderer looks + + align:start position:0% +rendering of what the murderer looks + + + align:start position:0% +rendering of what the murderer looks +like. And so you can choose whether or + + align:start position:0% +like. And so you can choose whether or + + + align:start position:0% +like. And so you can choose whether or +not to make a faithful rendering and + + align:start position:0% +not to make a faithful rendering and + + + align:start position:0% +not to make a faithful rendering and +bring the cops closer to catching him or + + align:start position:0% +bring the cops closer to catching him or + + + align:start position:0% +bring the cops closer to catching him or +to make one that looks not nothing like + + align:start position:0% +to make one that looks not nothing like + + + align:start position:0% +to make one that looks not nothing like +him so you can like evade them when you + + align:start position:0% +him so you can like evade them when you + + + align:start position:0% +him so you can like evade them when you +play as the other guy. + + align:start position:0% +play as the other guy. + + + align:start position:0% +play as the other guy. +>> Interesting. + + align:start position:0% +>> Interesting. + + + align:start position:0% +>> Interesting. +>> If you uh make it not look like you as + + align:start position:0% +>> If you uh make it not look like you as + + + align:start position:0% +>> If you uh make it not look like you as +killer + + align:start position:0% +killer + + + align:start position:0% +killer +I think he just there are other clues he + + align:start position:0% +I think he just there are other clues he + + + align:start position:0% +I think he just there are other clues he +has to find in order to finally track + + align:start position:0% +has to find in order to finally track + + + align:start position:0% +has to find in order to finally track +him down. + + align:start position:0% +him down. + + + align:start position:0% +him down. +>> Can you + + align:start position:0% +>> Can you + + + align:start position:0% +>> Can you +win this game? + + align:start position:0% +win this game? + + + align:start position:0% +win this game? +>> Yeah. + + align:start position:0% + + + + align:start position:0% + +>> Yeah. + + align:start position:0% + + + + align:start position:0% + +>> I mean, is the goal to catch the killer + + align:start position:0% +>> I mean, is the goal to catch the killer + + + align:start position:0% +>> I mean, is the goal to catch the killer +for the killer to get away or is + + align:start position:0% +for the killer to get away or is + + + align:start position:0% +for the killer to get away or is +>> it's actually an adventure game. So, the + + align:start position:0% +>> it's actually an adventure game. So, the + + + align:start position:0% +>> it's actually an adventure game. So, the +goal is to get the story. + + align:start position:0% + + + + align:start position:0% + +Hello. + + align:start position:0% +Hello. + + + align:start position:0% +Hello. +>> Um, so in the LAR that I played a long + + align:start position:0% +>> Um, so in the LAR that I played a long + + + align:start position:0% +>> Um, so in the LAR that I played a long +time ago, I was allowed to draw one item + + align:start position:0% +time ago, I was allowed to draw one item + + + align:start position:0% +time ago, I was allowed to draw one item +from a location every hour. The game ran + + align:start position:0% +from a location every hour. The game ran + + + align:start position:0% +from a location every hour. The game ran +from noon to midnight on three different + + align:start position:0% +from noon to midnight on three different + + + align:start position:0% +from noon to midnight on three different +days. Um, but I couldn't play before 2 + + align:start position:0% +days. Um, but I couldn't play before 2 + + + align:start position:0% +days. Um, but I couldn't play before 2 +p.m. So, I come in at 2 p.m. How many + + align:start position:0% +p.m. So, I come in at 2 p.m. How many + + + align:start position:0% +p.m. So, I come in at 2 p.m. How many +items am I was I allowed to draw at the + + align:start position:0% +items am I was I allowed to draw at the + + + align:start position:0% +items am I was I allowed to draw at the +be when I came in the game? Um, given + + align:start position:0% +be when I came in the game? Um, given + + + align:start position:0% +be when I came in the game? Um, given +that I only missed two hours of game. + + align:start position:0% +that I only missed two hours of game. + + + align:start position:0% +that I only missed two hours of game. +And what happens? And if the answer is, + + align:start position:0% +And what happens? And if the answer is, + + + align:start position:0% +And what happens? And if the answer is, +well, I can make that up. And what + + align:start position:0% +well, I can make that up. And what + + + align:start position:0% +well, I can make that up. And what +happens if I miss an hour halfway + + align:start position:0% +happens if I miss an hour halfway + + + align:start position:0% +happens if I miss an hour halfway +through and if I forget? Um, so yeah, no + + align:start position:0% +through and if I forget? Um, so yeah, no + + + align:start position:0% +through and if I forget? Um, so yeah, no +one's looking. + + align:start position:0% +one's looking. + + + align:start position:0% +one's looking. +>> Oh, what did you do? + + align:start position:0% +>> Oh, what did you do? + + + align:start position:0% +>> Oh, what did you do? +>> What did I do? + + align:start position:0% +>> What did I do? + + + align:start position:0% +>> What did I do? +>> Yes. + + align:start position:0% +>> Yes. + + + align:start position:0% +>> Yes. +>> What did I do? I think I threw more than + + align:start position:0% +>> What did I do? I think I threw more than + + + align:start position:0% +>> What did I do? I think I threw more than +one item at the beginning. Okay. + + align:start position:0% +one item at the beginning. Okay. + + + align:start position:0% +one item at the beginning. Okay. +>> And I made sure I never forgot. + + align:start position:0% +>> And I made sure I never forgot. + + + align:start position:0% +>> And I made sure I never forgot. +>> So, honor system. A lot of are based on + + align:start position:0% +>> So, honor system. A lot of are based on + + + align:start position:0% +>> So, honor system. A lot of are based on +honor system. + + align:start position:0% + + + + align:start position:0% + +So, in uh Final Fantasy 7, uh like a lot + + align:start position:0% +So, in uh Final Fantasy 7, uh like a lot + + + align:start position:0% +So, in uh Final Fantasy 7, uh like a lot +of Japanese RPGs, you get used to the + + align:start position:0% +of Japanese RPGs, you get used to the + + + align:start position:0% +of Japanese RPGs, you get used to the +idea of walking into people's houses and + + align:start position:0% +idea of walking into people's houses and + + + align:start position:0% +idea of walking into people's houses and +just leaving any items you find. + + align:start position:0% +just leaving any items you find. + + + align:start position:0% +just leaving any items you find. +>> Except in FF7, they actually mix it up a + + align:start position:0% +>> Except in FF7, they actually mix it up a + + + align:start position:0% +>> Except in FF7, they actually mix it up a +couple times. There are a couple + + align:start position:0% +couple times. There are a couple + + + align:start position:0% +couple times. There are a couple +instances where you go in there and do + + align:start position:0% +instances where you go in there and do + + + align:start position:0% +instances where you go in there and do +that and the item is fairly + + align:start position:0% +that and the item is fairly + + + align:start position:0% +that and the item is fairly +insignificant. Like, you could buy it + + align:start position:0% +insignificant. Like, you could buy it + + + align:start position:0% +insignificant. Like, you could buy it +easily, like a couple pieces of gold or + + align:start position:0% +easily, like a couple pieces of gold or + + + align:start position:0% +easily, like a couple pieces of gold or +gill or whatever it is, and then the + + align:start position:0% +gill or whatever it is, and then the + + + align:start position:0% +gill or whatever it is, and then the +person walks out of their kitchen or + + align:start position:0% +person walks out of their kitchen or + + + align:start position:0% +person walks out of their kitchen or +something. It's like, did did you just + + align:start position:0% +something. It's like, did did you just + + + align:start position:0% +something. It's like, did did you just +take my item? And you have the option of + + align:start position:0% +take my item? And you have the option of + + + align:start position:0% +take my item? And you have the option of +saying yes or no. And if you say no, + + align:start position:0% +saying yes or no. And if you say no, + + + align:start position:0% +saying yes or no. And if you say no, +then you get to keep it. But if you say + + align:start position:0% +then you get to keep it. But if you say + + + align:start position:0% +then you get to keep it. But if you say +yes, they're like, "What the hell? Give + + align:start position:0% +yes, they're like, "What the hell? Give + + + align:start position:0% +yes, they're like, "What the hell? Give +it back." + + align:start position:0% + + + + align:start position:0% + +>> That was interesting. + + align:start position:0% +>> That was interesting. + + + align:start position:0% +>> That was interesting. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> I had something that hasn't really been + + align:start position:0% +>> I had something that hasn't really been + + + align:start position:0% +>> I had something that hasn't really been +touched on. + + align:start position:0% +touched on. + + + align:start position:0% +touched on. +>> Okay. + + align:start position:0% +>> Okay. + + + align:start position:0% +>> Okay. +>> So, when you're running a very large + + align:start position:0% +>> So, when you're running a very large + + + align:start position:0% +>> So, when you're running a very large +scale guild in an MMO, you reach a point + + align:start position:0% +scale guild in an MMO, you reach a point + + + align:start position:0% +scale guild in an MMO, you reach a point +where you need to distribute loot from + + align:start position:0% +where you need to distribute loot from + + + align:start position:0% +where you need to distribute loot from +these high-end rating things. Like the + + align:start position:0% +these high-end rating things. Like the + + + align:start position:0% +these high-end rating things. Like the +kind of community optimal thing to do is + + align:start position:0% +kind of community optimal thing to do is + + + align:start position:0% +kind of community optimal thing to do is +for the people who are in charge of the + + align:start position:0% +for the people who are in charge of the + + + align:start position:0% +for the people who are in charge of the +guild to allocate who gets what so that + + align:start position:0% +guild to allocate who gets what so that + + + align:start position:0% +guild to allocate who gets what so that +you can for instance like kit out the + + align:start position:0% +you can for instance like kit out the + + + align:start position:0% +you can for instance like kit out the +characters that it's most important for + + align:start position:0% +characters that it's most important for + + + align:start position:0% +characters that it's most important for +the guild to have for gear to progress. + + align:start position:0% +the guild to have for gear to progress. + + + align:start position:0% +the guild to have for gear to progress. +But for the most part actual members of + + align:start position:0% +But for the most part actual members of + + + align:start position:0% +But for the most part actual members of +the guild don't really like that because + + align:start position:0% +the guild don't really like that because + + + align:start position:0% +the guild don't really like that because +you kind of wouldn't like to receive + + align:start position:0% +you kind of wouldn't like to receive + + + align:start position:0% +you kind of wouldn't like to receive +some kind of reward for having put in + + align:start position:0% +some kind of reward for having put in + + + align:start position:0% +some kind of reward for having put in +time for the guild and going a long time + + align:start position:0% +time for the guild and going a long time + + + align:start position:0% +time for the guild and going a long time +without ever having gotten anything is + + align:start position:0% +without ever having gotten anything is + + + align:start position:0% +without ever having gotten anything is +really frustrating. So people come up + + align:start position:0% +really frustrating. So people come up + + + align:start position:0% +really frustrating. So people come up +with these intricate systems + + align:start position:0% +with these intricate systems + + + align:start position:0% +with these intricate systems +>> DK + + align:start position:0% +>> DK + + + align:start position:0% +>> DK +>> for DKP. + + align:start position:0% +>> for DKP. + + + align:start position:0% +>> for DKP. +>> Yeah. For distributing your um resources + + align:start position:0% +>> Yeah. For distributing your um resources + + + align:start position:0% +>> Yeah. For distributing your um resources +essentially to try to balance the + + align:start position:0% +essentially to try to balance the + + + align:start position:0% +essentially to try to balance the +interests of the individual and the + + align:start position:0% +interests of the individual and the + + + align:start position:0% +interests of the individual and the +interests of the community. + + align:start position:0% +interests of the community. + + + align:start position:0% +interests of the community. +>> How many of you are unsure what DKP is + + align:start position:0% +>> How many of you are unsure what DKP is + + + align:start position:0% +>> How many of you are unsure what DKP is +driving kill points? + + align:start position:0% +driving kill points? + + + align:start position:0% +driving kill points? +There are these sometimes elaborate + + align:start position:0% +There are these sometimes elaborate + + + align:start position:0% +There are these sometimes elaborate +schemes for if you participate in these + + align:start position:0% +schemes for if you participate in these + + + align:start position:0% +schemes for if you participate in these +raids, you get so many points. Um, and + + align:start position:0% +raids, you get so many points. Um, and + + + align:start position:0% +raids, you get so many points. Um, and +the idea is like the guild claims + + align:start position:0% +the idea is like the guild claims + + + align:start position:0% +the idea is like the guild claims +everything that drops supposedly and uh + + align:start position:0% +everything that drops supposedly and uh + + + align:start position:0% +everything that drops supposedly and uh +you build up points and at some point + + align:start position:0% +you build up points and at some point + + + align:start position:0% +you build up points and at some point +you have enough to buy, you know, a + + align:start position:0% +you have enough to buy, you know, a + + + align:start position:0% +you have enough to buy, you know, a +certain item. So, like let's say you're + + align:start position:0% +certain item. So, like let's say you're + + + align:start position:0% +certain item. So, like let's say you're +on a raid and you just got something + + align:start position:0% +on a raid and you just got something + + + align:start position:0% +on a raid and you just got something +really cool last time and something + + align:start position:0% +really cool last time and something + + + align:start position:0% +really cool last time and something +drops this time that you could really + + align:start position:0% +drops this time that you could really + + + align:start position:0% +drops this time that you could really +use even though you're there, you don't + + align:start position:0% +use even though you're there, you don't + + + align:start position:0% +use even though you're there, you don't +necessarily get it because you just + + align:start position:0% +necessarily get it because you just + + + align:start position:0% +necessarily get it because you just +spent all your decrim + + align:start position:0% + + + + align:start position:0% + +primary source of your problem. + + align:start position:0% +primary source of your problem. + + + align:start position:0% +primary source of your problem. +>> People play. + + align:start position:0% + + + + align:start position:0% + +>> You learn that by going on raids and + + align:start position:0% +>> You learn that by going on raids and + + + align:start position:0% +>> You learn that by going on raids and +then catch them in practice. + + align:start position:0% +then catch them in practice. + + + align:start position:0% +then catch them in practice. +>> And they're a blockout day, too. + + align:start position:0% +>> And they're a blockout day, too. + + + align:start position:0% +>> And they're a blockout day, too. +>> So, running one of these things is + + align:start position:0% +>> So, running one of these things is + + + align:start position:0% +>> So, running one of these things is +actually surprisingly complicated and + + align:start position:0% +actually surprisingly complicated and + + + align:start position:0% +actually surprisingly complicated and +hard. Um, particularly, so my little + + align:start position:0% +hard. Um, particularly, so my little + + + align:start position:0% +hard. Um, particularly, so my little +experience, I ran a guild which which + + align:start position:0% +experience, I ran a guild which which + + + align:start position:0% +experience, I ran a guild which which +incorporated this. Um, one problem that + + align:start position:0% +incorporated this. Um, one problem that + + + align:start position:0% +incorporated this. Um, one problem that +happens is that if you have fixed prices + + align:start position:0% +happens is that if you have fixed prices + + + align:start position:0% +happens is that if you have fixed prices +for things, then you kind of get DKP + + align:start position:0% +for things, then you kind of get DKP + + + align:start position:0% +for things, then you kind of get DKP +inflation as prices change and what + + align:start position:0% +inflation as prices change and what + + + align:start position:0% +inflation as prices change and what +happens at whatever you and it's + + align:start position:0% +happens at whatever you and it's + + + align:start position:0% +happens at whatever you and it's +incredibly complicated to work out and + + align:start position:0% +incredibly complicated to work out and + + + align:start position:0% +incredibly complicated to work out and +you got to repric everything constantly. + + align:start position:0% +you got to repric everything constantly. + + + align:start position:0% +you got to repric everything constantly. +So instead, we went for a auction based + + align:start position:0% +So instead, we went for a auction based + + + align:start position:0% +So instead, we went for a auction based +system where people kind of bid on + + align:start position:0% +system where people kind of bid on + + + align:start position:0% +system where people kind of bid on +things and then prices correct + + align:start position:0% +things and then prices correct + + + align:start position:0% +things and then prices correct +themselves. However, people can collude + + align:start position:0% +themselves. However, people can collude + + + align:start position:0% +themselves. However, people can collude +in auctions in auctions which then + + align:start position:0% +in auctions in auctions which then + + + align:start position:0% +in auctions in auctions which then +causes a resentment in people who aren't + + align:start position:0% +causes a resentment in people who aren't + + + align:start position:0% +causes a resentment in people who aren't +in on the collusion and the whole thing + + align:start position:0% +in on the collusion and the whole thing + + + align:start position:0% +in on the collusion and the whole thing +is just a nightmare. + + align:start position:0% +is just a nightmare. + + + align:start position:0% +is just a nightmare. +And no, I don't run a guild anymore. I'm + + align:start position:0% +And no, I don't run a guild anymore. I'm + + + align:start position:0% +And no, I don't run a guild anymore. I'm +really happy. + + align:start position:0% +really happy. + + + align:start position:0% +really happy. +>> Okay. + + align:start position:0% +>> Okay. + + + align:start position:0% +>> Okay. +>> Um, in games like Pokemon or Animal + + align:start position:0% +>> Um, in games like Pokemon or Animal + + + align:start position:0% +>> Um, in games like Pokemon or Animal +Crossing, uh, you can decide whether or + + align:start position:0% +Crossing, uh, you can decide whether or + + + align:start position:0% +Crossing, uh, you can decide whether or +not to change the time on your DS or + + align:start position:0% +not to change the time on your DS or + + + align:start position:0% +not to change the time on your DS or +GameCube. + + align:start position:0% +GameCube. + + + align:start position:0% +GameCube. +Like when Pokemon Gold and Silver came + + align:start position:0% +Like when Pokemon Gold and Silver came + + + align:start position:0% +Like when Pokemon Gold and Silver came +out, I was like 10. I had a bedtime. I + + align:start position:0% +out, I was like 10. I had a bedtime. I + + + align:start position:0% +out, I was like 10. I had a bedtime. I +didn't have a lot of time to catch all + + align:start position:0% +didn't have a lot of time to catch all + + + align:start position:0% +didn't have a lot of time to catch all +the nighttime Pokemon. + + align:start position:0% +the nighttime Pokemon. + + + align:start position:0% +the nighttime Pokemon. +>> You can do that to manipulate the RNG + + align:start position:0% +>> You can do that to manipulate the RNG + + + align:start position:0% +>> You can do that to manipulate the RNG +and uh, get the stats you want. Perfect. + + align:start position:0% +and uh, get the stats you want. Perfect. + + + align:start position:0% +and uh, get the stats you want. Perfect. +>> There's also uh times whenever you do + + align:start position:0% +>> There's also uh times whenever you do + + + align:start position:0% +>> There's also uh times whenever you do +the um random number generator hacks in + + align:start position:0% +the um random number generator hacks in + + + align:start position:0% +the um random number generator hacks in +games in order to get in order to get a + + align:start position:0% +games in order to get in order to get a + + + align:start position:0% +games in order to get in order to get a +certain drop that's normally like 1% but + + align:start position:0% +certain drop that's normally like 1% but + + + align:start position:0% +certain drop that's normally like 1% but +you can increase it up to like almost + + align:start position:0% +you can increase it up to like almost + + + align:start position:0% +you can increase it up to like almost +100. + + align:start position:0% +100. + + + align:start position:0% +100. +But what I was going to say was that + + align:start position:0% +But what I was going to say was that + + + align:start position:0% +But what I was going to say was that +Fallout 3 u so in Fallout 3 you can + + align:start position:0% +Fallout 3 u so in Fallout 3 you can + + + align:start position:0% +Fallout 3 u so in Fallout 3 you can +pickpocket people and something you do + + align:start position:0% +pickpocket people and something you do + + + align:start position:0% +pickpocket people and something you do +when you pickpocket as long as you don't + + align:start position:0% +when you pickpocket as long as you don't + + + align:start position:0% +when you pickpocket as long as you don't +get caught. You can take a grenade from + + align:start position:0% +get caught. You can take a grenade from + + + align:start position:0% +get caught. You can take a grenade from +your inventory and place it in their + + align:start position:0% +your inventory and place it in their + + + align:start position:0% +your inventory and place it in their +pocket and all of a sudden they be like, + + align:start position:0% +pocket and all of a sudden they be like, + + + align:start position:0% +pocket and all of a sudden they be like, +"Oh my god, there's a grenade. Run + + align:start position:0% +"Oh my god, there's a grenade. Run + + + align:start position:0% +"Oh my god, there's a grenade. Run +away." And it will blow up inside their + + align:start position:0% +away." And it will blow up inside their + + + align:start position:0% +away." And it will blow up inside their +pocket and they will blow. + + align:start position:0% +pocket and they will blow. + + + align:start position:0% +pocket and they will blow. +>> What game? + + align:start position:0% +>> What game? + + + align:start position:0% +>> What game? +>> Fall. + + align:start position:0% +>> Fall. + + + align:start position:0% +>> Fall. +>> Fall asleep. It's also And the funny + + align:start position:0% +>> Fall asleep. It's also And the funny + + + align:start position:0% +>> Fall asleep. It's also And the funny +thing is that's that's actually an + + align:start position:0% +thing is that's that's actually an + + + align:start position:0% +thing is that's that's actually an +achievement to blow someone up. + + align:start position:0% +achievement to blow someone up. + + + align:start position:0% +achievement to blow someone up. +So you get other than the joy and + + align:start position:0% +So you get other than the joy and + + + align:start position:0% +So you get other than the joy and +giggles and + + align:start position:0% +giggles and + + + align:start position:0% +giggles and +>> well you can also you get you you they + + align:start position:0% +>> well you can also you get you you they + + + align:start position:0% +>> well you can also you get you you they +start from the joy and giggles + + align:start position:0% +start from the joy and giggles + + + align:start position:0% +start from the joy and giggles +>> you get that you can well yeah you can + + align:start position:0% +>> you get that you can well yeah you can + + + align:start position:0% +>> you get that you can well yeah you can +pick their pocket so you can whatever + + align:start position:0% +pick their pocket so you can whatever + + + align:start position:0% +pick their pocket so you can whatever +they have in their pocket you can get + + align:start position:0% +they have in their pocket you can get + + + align:start position:0% +they have in their pocket you can get +>> that is still left. + + align:start position:0% +>> that is still left. + + + align:start position:0% +>> that is still left. +>> Yeah. Well no I mean you take it out you + + align:start position:0% +>> Yeah. Well no I mean you take it out you + + + align:start position:0% +>> Yeah. Well no I mean you take it out you +take it out as you're putting the + + align:start position:0% +take it out as you're putting the + + + align:start position:0% +take it out as you're putting the +grenade in. + + align:start position:0% +grenade in. + + + align:start position:0% +grenade in. +>> Uh + + align:start position:0% +>> Uh + + + align:start position:0% +>> Uh +>> you wouldn't want that boot to be + + align:start position:0% +>> you wouldn't want that boot to be + + + align:start position:0% +>> you wouldn't want that boot to be +damaged by the grenade. + + align:start position:0% +damaged by the grenade. + + + align:start position:0% +damaged by the grenade. +>> Put the grenade after + + align:start position:0% +>> Put the grenade after + + + align:start position:0% +>> Put the grenade after +>> you're just hiding the evidence. + + align:start position:0% +>> you're just hiding the evidence. + + + align:start position:0% +>> you're just hiding the evidence. +>> Yeah. You're just putting them in at the + + align:start position:0% +>> Yeah. You're just putting them in at the + + + align:start position:0% +>> Yeah. You're just putting them in at the +same time simultaneously. + + align:start position:0% +same time simultaneously. + + + align:start position:0% +same time simultaneously. +And it can be traded + + align:start position:0% + + + + align:start position:0% + +examples we haven't touched on. + + align:start position:0% +examples we haven't touched on. + + + align:start position:0% +examples we haven't touched on. +>> So I used to play a lot of Ultima online + + align:start position:0% +>> So I used to play a lot of Ultima online + + + align:start position:0% +>> So I used to play a lot of Ultima online +and they had a bunch of really + + align:start position:0% +and they had a bunch of really + + + align:start position:0% +and they had a bunch of really +sophisticated rules that applied in + + align:start position:0% +sophisticated rules that applied in + + + align:start position:0% +sophisticated rules that applied in +certain situations and didn't apply in + + align:start position:0% +certain situations and didn't apply in + + + align:start position:0% +certain situations and didn't apply in +situations. So uh there were a lot of + + align:start position:0% +situations. So uh there were a lot of + + + align:start position:0% +situations. So uh there were a lot of +times in the game you just flat out lie + + align:start position:0% +times in the game you just flat out lie + + + align:start position:0% +times in the game you just flat out lie +to people and have them go into + + align:start position:0% +to people and have them go into + + + align:start position:0% +to people and have them go into +situations that were unsafe for them. + + align:start position:0% +situations that were unsafe for them. + + + align:start position:0% +situations that were unsafe for them. +For example, if people were in your + + align:start position:0% +For example, if people were in your + + + align:start position:0% +For example, if people were in your +house uh In an early version of the + + align:start position:0% +house uh In an early version of the + + + align:start position:0% +house uh In an early version of the +game, if people are inside of your + + align:start position:0% +game, if people are inside of your + + + align:start position:0% +game, if people are inside of your +house, they're automatically flagged as + + align:start position:0% +house, they're automatically flagged as + + + align:start position:0% +house, they're automatically flagged as +like attackable by you because they're + + align:start position:0% +like attackable by you because they're + + + align:start position:0% +like attackable by you because they're +because they're in your house and you + + align:start position:0% +because they're in your house and you + + + align:start position:0% +because they're in your house and you +might not have let them in. And they can + + align:start position:0% +might not have let them in. And they can + + + align:start position:0% +might not have let them in. And they can +like run outside their house and they'll + + align:start position:0% +like run outside their house and they'll + + + align:start position:0% +like run outside their house and they'll +be unattackable by you. But you can also + + align:start position:0% +be unattackable by you. But you can also + + + align:start position:0% +be unattackable by you. But you can also +like put a trash barrel in front of your + + align:start position:0% +like put a trash barrel in front of your + + + align:start position:0% +like put a trash barrel in front of your +door, which only you can destroy and + + align:start position:0% +door, which only you can destroy and + + + align:start position:0% +door, which only you can destroy and +nobody else can destroy and they can't + + align:start position:0% +nobody else can destroy and they can't + + + align:start position:0% +nobody else can destroy and they can't +run through that. So you like invite + + align:start position:0% +run through that. So you like invite + + + align:start position:0% +run through that. So you like invite +them in to like trade them something or + + align:start position:0% +them in to like trade them something or + + + align:start position:0% +them in to like trade them something or +join your guild and they're in your + + align:start position:0% +join your guild and they're in your + + + align:start position:0% +join your guild and they're in your +house and then you put a trash barrel + + align:start position:0% +house and then you put a trash barrel + + + align:start position:0% +house and then you put a trash barrel +there so they can never leave and you + + align:start position:0% +there so they can never leave and you + + + align:start position:0% +there so they can never leave and you +just kill them + + align:start position:0% +just kill them + + + align:start position:0% +just kill them +>> or like + + align:start position:0% +>> or like + + + align:start position:0% +>> or like +>> or just leave them there, right? or just + + align:start position:0% +>> or just leave them there, right? or just + + + align:start position:0% +>> or just leave them there, right? or just +leave it. There were there were tons and + + align:start position:0% +leave it. There were there were tons and + + + align:start position:0% +leave it. There were there were tons and +tons of ways. + + align:start position:0% +tons of ways. + + + align:start position:0% +tons of ways. +>> Was so cool with this stuff. It's + + align:start position:0% +>> Was so cool with this stuff. It's + + + align:start position:0% +>> Was so cool with this stuff. It's +>> Oh, it's really bad. It's really bad. I + + align:start position:0% +>> Oh, it's really bad. It's really bad. I + + + align:start position:0% +>> Oh, it's really bad. It's really bad. I +was part of a guild that that did this + + align:start position:0% +was part of a guild that that did this + + + align:start position:0% +was part of a guild that that did this +to me and then like I told them that I + + align:start position:0% +to me and then like I told them that I + + + align:start position:0% +to me and then like I told them that I +had a couple other things. I was like + + align:start position:0% +had a couple other things. I was like + + + align:start position:0% +had a couple other things. I was like +10. It's pretty sick. A bunch of ways to + + align:start position:0% +10. It's pretty sick. A bunch of ways to + + + align:start position:0% +10. It's pretty sick. A bunch of ways to +like steal tons and tons of money from + + align:start position:0% +like steal tons and tons of money from + + + align:start position:0% +like steal tons and tons of money from +people and they didn't realize they + + align:start position:0% +people and they didn't realize they + + + align:start position:0% +people and they didn't realize they +could do it. + + align:start position:0% +could do it. + + + align:start position:0% +could do it. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> But I feel like just blatantly lying to + + align:start position:0% +>> But I feel like just blatantly lying to + + + align:start position:0% +>> But I feel like just blatantly lying to +people as a as a tactic instead of just + + align:start position:0% +people as a as a tactic instead of just + + + align:start position:0% +people as a as a tactic instead of just +being mean to them. Okay. + + align:start position:0% +being mean to them. Okay. + + + align:start position:0% +being mean to them. Okay. +Yeah. + + align:start position:0% +Yeah. + + + align:start position:0% +Yeah. +>> Uh the question of uh real world play + + align:start position:0% +>> Uh the question of uh real world play + + + align:start position:0% +>> Uh the question of uh real world play +for in game items especially in + + align:start position:0% +for in game items especially in + + + align:start position:0% +for in game items especially in +competitive games + + align:start position:0% +competitive games + + + align:start position:0% +competitive games +>> um whether or not it's allowed by the + + align:start position:0% +>> um whether or not it's allowed by the + + + align:start position:0% +>> um whether or not it's allowed by the +GMs. + + align:start position:0% +GMs. + + + align:start position:0% +GMs. +>> Well, + + align:start position:0% +>> Well, + + + align:start position:0% +>> Well, +>> I mean those are two different + + align:start position:0% +>> I mean those are two different + + + align:start position:0% +>> I mean those are two different +questions. One is ethical question from + + align:start position:0% +questions. One is ethical question from + + + align:start position:0% +questions. One is ethical question from +a player standpoint and the other is + + align:start position:0% +a player standpoint and the other is + + + align:start position:0% +a player standpoint and the other is +what does it mean in terms of + + align:start position:0% +what does it mean in terms of + + + align:start position:0% +what does it mean in terms of +>> the player character relation + + align:start position:0% +>> the player character relation + + + align:start position:0% +>> the player character relation +>> in the game. + + align:start position:0% +>> in the game. + + + align:start position:0% +>> in the game. +>> Okay. + + align:start position:0% +>> Okay. + + + align:start position:0% +>> Okay. +>> Oh yeah. I was going to say one thing + + align:start position:0% +>> Oh yeah. I was going to say one thing + + + align:start position:0% +>> Oh yeah. I was going to say one thing +that comes up in um especially in board + + align:start position:0% +that comes up in um especially in board + + + align:start position:0% +that comes up in um especially in board +games they have um a lot of positive + + align:start position:0% +games they have um a lot of positive + + + align:start position:0% +games they have um a lot of positive +feedbacks called kingmaking and um good + + align:start position:0% +feedbacks called kingmaking and um good + + + align:start position:0% +feedbacks called kingmaking and um good +examples are like in Monopoly or + + align:start position:0% +examples are like in Monopoly or + + + align:start position:0% +examples are like in Monopoly or +Settlers or Munchkin and how it works is + + align:start position:0% +Settlers or Munchkin and how it works is + + + align:start position:0% +Settlers or Munchkin and how it works is +like let's say you know you and Owen and + + align:start position:0% +like let's say you know you and Owen and + + + align:start position:0% +like let's say you know you and Owen and +I are playing Settlers and uh typically + + align:start position:0% +I are playing Settlers and uh typically + + + align:start position:0% +I are playing Settlers and uh typically +what'll happen is say Owen is winning + + align:start position:0% +what'll happen is say Owen is winning + + + align:start position:0% +what'll happen is say Owen is winning +but I'm typically really far behind or + + align:start position:0% +but I'm typically really far behind or + + + align:start position:0% +but I'm typically really far behind or +someone is going to be in a position + + align:start position:0% +someone is going to be in a position + + + align:start position:0% +someone is going to be in a position +where they have no chance of winning. So + + align:start position:0% +where they have no chance of winning. So + + + align:start position:0% +where they have no chance of winning. So +hypothetically like he's winning you're + + align:start position:0% +hypothetically like he's winning you're + + + align:start position:0% +hypothetically like he's winning you're +close second and I'm distant third. What + + align:start position:0% +close second and I'm distant third. What + + + align:start position:0% +close second and I'm distant third. What +people do is say, "Hey, Mia, I will give + + align:start position:0% +people do is say, "Hey, Mia, I will give + + + align:start position:0% +people do is say, "Hey, Mia, I will give +you everything for your one level card + + align:start position:0% +you everything for your one level card + + + align:start position:0% +you everything for your one level card +and then you can win because I'm mad at + + align:start position:0% +and then you can win because I'm mad at + + + align:start position:0% +and then you can win because I'm mad at +all." Right. And that comes up, like you + + align:start position:0% +all." Right. And that comes up, like you + + + align:start position:0% +all." Right. And that comes up, like you +said, in Monopoly and there's this + + align:start position:0% +said, in Monopoly and there's this + + + align:start position:0% +said, in Monopoly and there's this +question of like, is that a really jerky + + align:start position:0% +question of like, is that a really jerky + + + align:start position:0% +question of like, is that a really jerky +thing to do? You know, the rules don't + + align:start position:0% +thing to do? You know, the rules don't + + + align:start position:0% +thing to do? You know, the rules don't +disallow it. + + align:start position:0% +disallow it. + + + align:start position:0% +disallow it. +>> That's kind of an ongoing debate. + + align:start position:0% +>> That's kind of an ongoing debate. + + + align:start position:0% +>> That's kind of an ongoing debate. +>> Yes, it is a jerk. + + align:start position:0% + + + + align:start position:0% + +>> Similarly, Monopoly rules don't + + align:start position:0% +>> Similarly, Monopoly rules don't + + + align:start position:0% +>> Similarly, Monopoly rules don't +specifically allow like if I have two + + align:start position:0% +specifically allow like if I have two + + + align:start position:0% +specifically allow like if I have two +orange, we'll like exchange them and + + align:start position:0% +orange, we'll like exchange them and + + + align:start position:0% +orange, we'll like exchange them and +promise each other immunity. properties + + align:start position:0% +promise each other immunity. properties + + + align:start position:0% +promise each other immunity. properties +or like something that you're not + + align:start position:0% +or like something that you're not + + + align:start position:0% +or like something that you're not +allowed to actually promise each other + + align:start position:0% +allowed to actually promise each other + + + align:start position:0% +allowed to actually promise each other +or if you have two reds. I have a red + + align:start position:0% +or if you have two reds. I have a red + + + align:start position:0% +or if you have two reds. I have a red +I'll give it to you and you promise me + + align:start position:0% +I'll give it to you and you promise me + + + align:start position:0% +I'll give it to you and you promise me +half the profits or something like that + + align:start position:0% +half the profits or something like that + + + align:start position:0% +half the profits or something like that +where clearly the third person is now + + align:start position:0% +where clearly the third person is now + + + align:start position:0% +where clearly the third person is now +shut out of the game and can't win + + align:start position:0% +shut out of the game and can't win + + + align:start position:0% +shut out of the game and can't win +because we have an early advantage even + + align:start position:0% +because we have an early advantage even + + + align:start position:0% +because we have an early advantage even +though we're like agreeing to things + + align:start position:0% +though we're like agreeing to things + + + align:start position:0% +though we're like agreeing to things +that aren't explicitly allowed. + + align:start position:0% +that aren't explicitly allowed. + + + align:start position:0% +that aren't explicitly allowed. +>> Maybe you play Dragon Age. + + align:start position:0% +>> Maybe you play Dragon Age. + + + align:start position:0% +>> Maybe you play Dragon Age. +>> You see + + align:start position:0% +>> You see + + + align:start position:0% +>> You see +>> I've seen a play. + + align:start position:0% +>> I've seen a play. + + + align:start position:0% +>> I've seen a play. +>> Okay. I've just I'm playing for it right + + align:start position:0% +>> Okay. I've just I'm playing for it right + + + align:start position:0% +>> Okay. I've just I'm playing for it right +now. I've been thinking about these + + align:start position:0% +now. I've been thinking about these + + + align:start position:0% +now. I've been thinking about these +issues a lot. Actually, on my first + + align:start position:0% +issues a lot. Actually, on my first + + + align:start position:0% +issues a lot. Actually, on my first +playthrough, there's like scene where + + align:start position:0% +playthrough, there's like scene where + + + align:start position:0% +playthrough, there's like scene where +there's a kid possessed by a demon. You + + align:start position:0% +there's a kid possessed by a demon. You + + + align:start position:0% +there's a kid possessed by a demon. You +have the choice whether to kill him or + + align:start position:0% +have the choice whether to kill him or + + + align:start position:0% +have the choice whether to kill him or +not. First time I killed him, + + align:start position:0% +not. First time I killed him, + + + align:start position:0% +not. First time I killed him, +>> I thought everybody did. + + align:start position:0% +>> I thought everybody did. + + + align:start position:0% +>> I thought everybody did. +>> I had no compulsion about it. Like, + + align:start position:0% +>> I had no compulsion about it. Like, + + + align:start position:0% +>> I had no compulsion about it. Like, +yeah, he's demon. + + align:start position:0% + + + + align:start position:0% + +Turns out everybody really hated that, + + align:start position:0% +Turns out everybody really hated that, + + + align:start position:0% +Turns out everybody really hated that, +you know, all the other characters, my + + align:start position:0% +you know, all the other characters, my + + + align:start position:0% +you know, all the other characters, my +companions. And this this play time + + align:start position:0% +companions. And this this play time + + + align:start position:0% +companions. And this this play time +through, I was like, ah, try it. It's + + align:start position:0% +through, I was like, ah, try it. It's + + + align:start position:0% +through, I was like, ah, try it. It's +like all this extra work involved. And + + align:start position:0% +like all this extra work involved. And + + + align:start position:0% +like all this extra work involved. And +um but it seems like in the game um + + align:start position:0% +um but it seems like in the game um + + + align:start position:0% +um but it seems like in the game um +whether you want to do the good thing or + + align:start position:0% +whether you want to do the good thing or + + + align:start position:0% +whether you want to do the good thing or +not, it generally works to your + + align:start position:0% +not, it generally works to your + + + align:start position:0% +not, it generally works to your +advantage to do the good thing because + + align:start position:0% +advantage to do the good thing because + + + align:start position:0% +advantage to do the good thing because +you get like more stuff either better + + align:start position:0% +you get like more stuff either better + + + align:start position:0% +you get like more stuff either better +approval ratings from your companions + + align:start position:0% +approval ratings from your companions + + + align:start position:0% +approval ratings from your companions +who then like unlock bonuses or um you + + align:start position:0% +who then like unlock bonuses or um you + + + align:start position:0% +who then like unlock bonuses or um you +get stuff. Whereas, you know, being the + + align:start position:0% +get stuff. Whereas, you know, being the + + + align:start position:0% +get stuff. Whereas, you know, being the +jerk + + align:start position:0% +jerk + + + align:start position:0% +jerk +>> kind of depends on who your companions + + align:start position:0% +>> kind of depends on who your companions + + + align:start position:0% +>> kind of depends on who your companions +are. + + align:start position:0% +are. + + + align:start position:0% +are. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Does it approves? Um, people like the + + align:start position:0% +>> Does it approves? Um, people like the + + + align:start position:0% +>> Does it approves? Um, people like the +the like elven assassin. I can't + + align:start position:0% +the like elven assassin. I can't + + + align:start position:0% +the like elven assassin. I can't +remember what his name is. + + align:start position:0% +remember what his name is. + + + align:start position:0% +remember what his name is. +>> Oh, I'm pretty sure approves as well. He + + align:start position:0% +>> Oh, I'm pretty sure approves as well. He + + + align:start position:0% +>> Oh, I'm pretty sure approves as well. He +likes all the jerky things. + + align:start position:0% +likes all the jerky things. + + + align:start position:0% +likes all the jerky things. +>> I didn't have the first play through. + + align:start position:0% +>> I didn't have the first play through. + + + align:start position:0% +>> I didn't have the first play through. +>> Also, um, that one guy, the berserker + + align:start position:0% +>> Also, um, that one guy, the berserker + + + align:start position:0% +>> Also, um, that one guy, the berserker +guy, um, that you can spot. No, no, + + align:start position:0% +guy, um, that you can spot. No, no, + + + align:start position:0% +guy, um, that you can spot. No, no, +another guy. Um, I think you can get him + + align:start position:0% +another guy. Um, I think you can get him + + + align:start position:0% +another guy. Um, I think you can get him +on your team at least. He's in the + + align:start position:0% +on your team at least. He's in the + + + align:start position:0% +on your team at least. He's in the +temple where there's that big dragon and + + align:start position:0% +temple where there's that big dragon and + + + align:start position:0% +temple where there's that big dragon and +where you're like doing some ash quest + + align:start position:0% +where you're like doing some ash quest + + + align:start position:0% +where you're like doing some ash quest +or something. Um, and like he wants you + + align:start position:0% +or something. Um, and like he wants you + + + align:start position:0% +or something. Um, and like he wants you +to pour dragon blood on the ashes or + + align:start position:0% +to pour dragon blood on the ashes or + + + align:start position:0% +to pour dragon blood on the ashes or +something. I'm pretty sure you can get + + align:start position:0% +something. I'm pretty sure you can get + + + align:start position:0% +something. I'm pretty sure you can get +them on your team. Am I right or am I + + align:start position:0% +them on your team. Am I right or am I + + + align:start position:0% +them on your team. Am I right or am I +wrong? + + align:start position:0% +wrong? + + + align:start position:0% +wrong? +>> But I know you can get them as part of + + align:start position:0% +>> But I know you can get them as part of + + + align:start position:0% +>> But I know you can get them as part of +your final army and they're pretty good + + align:start position:0% +your final army and they're pretty good + + + align:start position:0% +your final army and they're pretty good +>> and they're bad. + + align:start position:0% +>> and they're bad. + + + align:start position:0% +>> and they're bad. +>> Okay. + + align:start position:0% +>> Okay. + + + align:start position:0% +>> Okay. +>> Yeah, + + align:start position:0% +>> Yeah, + + + align:start position:0% +>> Yeah, +>> I just chose poorly my companions like + + align:start position:0% +>> I just chose poorly my companions like + + + align:start position:0% +>> I just chose poorly my companions like +moralistic ones. I kill a kid. + + align:start position:0% +moralistic ones. I kill a kid. + + + align:start position:0% +moralistic ones. I kill a kid. +>> Yeah. Okay. + + align:start position:0% +>> Yeah. Okay. + + + align:start position:0% +>> Yeah. Okay. +In the reading that you did, um, Seart + + align:start position:0% +In the reading that you did, um, Seart + + + align:start position:0% +In the reading that you did, um, Seart +talks about, you know, different + + align:start position:0% +talks about, you know, different + + + align:start position:0% +talks about, you know, different +choices, um, and and the way that game + + align:start position:0% +choices, um, and and the way that game + + + align:start position:0% +choices, um, and and the way that game +designers are are putting these + + align:start position:0% +designers are are putting these + + + align:start position:0% +designers are are putting these +together. And he talks about two + + align:start position:0% +together. And he talks about two + + + align:start position:0% +together. And he talks about two +different categories, the open and the + + align:start position:0% +different categories, the open and the + + + align:start position:0% +different categories, the open and the +closed ethical systems. + + align:start position:0% +closed ethical systems. + + + align:start position:0% +closed ethical systems. +And, um, the open was, you know, more + + align:start position:0% +And, um, the open was, you know, more + + + align:start position:0% +And, um, the open was, you know, more +letting players kind of determine for + + align:start position:0% +letting players kind of determine for + + + align:start position:0% +letting players kind of determine for +themselves the stance that they want to + + align:start position:0% +themselves the stance that they want to + + + align:start position:0% +themselves the stance that they want to +take and kind of seeing how that goes + + align:start position:0% +take and kind of seeing how that goes + + + align:start position:0% +take and kind of seeing how that goes +through. whereas the closed is the + + align:start position:0% +through. whereas the closed is the + + + align:start position:0% +through. whereas the closed is the +system kind of you know forces a + + align:start position:0% +system kind of you know forces a + + + align:start position:0% +system kind of you know forces a +particular way of playing upon you. And + + align:start position:0% +particular way of playing upon you. And + + + align:start position:0% +particular way of playing upon you. And +so just kind of going through these + + align:start position:0% +so just kind of going through these + + + align:start position:0% +so just kind of going through these +here, where do you see them falling in + + align:start position:0% +here, where do you see them falling in + + + align:start position:0% +here, where do you see them falling in +terms of closed and open? + + align:start position:0% + + + + align:start position:0% + +>> Um I'm confused what closed means. So + + align:start position:0% +>> Um I'm confused what closed means. So + + + align:start position:0% +>> Um I'm confused what closed means. So +you said open means that you have the + + align:start position:0% +you said open means that you have the + + + align:start position:0% +you said open means that you have the +decision like on how to value your + + align:start position:0% +decision like on how to value your + + + align:start position:0% +decision like on how to value your +actions and what or what to do. Um both + + align:start position:0% +actions and what or what to do. Um both + + + align:start position:0% +actions and what or what to do. Um both +well like he says for example, you know, + + align:start position:0% +well like he says for example, you know, + + + align:start position:0% +well like he says for example, you know, +in the Sims with drowning, um he + + align:start position:0% +in the Sims with drowning, um he + + + align:start position:0% +in the Sims with drowning, um he +mentions The Sims as an open game + + align:start position:0% +mentions The Sims as an open game + + + align:start position:0% +mentions The Sims as an open game +>> where you can do what you want and uh + + align:start position:0% +>> where you can do what you want and uh + + + align:start position:0% +>> where you can do what you want and uh +kind of think about what happens. + + align:start position:0% +kind of think about what happens. + + + align:start position:0% +kind of think about what happens. +>> I have a definite closed example. It's + + align:start position:0% +>> I have a definite closed example. It's + + + align:start position:0% +>> I have a definite closed example. It's +not up there. There might be a closed + + align:start position:0% +not up there. There might be a closed + + + align:start position:0% +not up there. There might be a closed +example up there. I'm just missing. But + + align:start position:0% +example up there. I'm just missing. But + + + align:start position:0% +example up there. I'm just missing. But +um in the first Modern Warfare game, + + align:start position:0% +um in the first Modern Warfare game, + + + align:start position:0% +um in the first Modern Warfare game, +they have a flashback uh sequence where + + align:start position:0% +they have a flashback uh sequence where + + + align:start position:0% +they have a flashback uh sequence where +you have to snipe + + align:start position:0% +you have to snipe + + + align:start position:0% +you have to snipe +>> the future bad guy Zakayv. And even + + align:start position:0% +>> the future bad guy Zakayv. And even + + + align:start position:0% +>> the future bad guy Zakayv. And even +though in the game story he survives + + align:start position:0% +though in the game story he survives + + + align:start position:0% +though in the game story he survives +your attempt to kill him, if you don't + + align:start position:0% +your attempt to kill him, if you don't + + + align:start position:0% +your attempt to kill him, if you don't +actually hit him with the bullet, the + + align:start position:0% +actually hit him with the bullet, the + + + align:start position:0% +actually hit him with the bullet, the +game won't let you progress. + + align:start position:0% +game won't let you progress. + + + align:start position:0% +game won't let you progress. +>> So you have to go and basically snipe + + align:start position:0% +>> So you have to go and basically snipe + + + align:start position:0% +>> So you have to go and basically snipe +this dude no matter what. The game won't + + align:start position:0% +this dude no matter what. The game won't + + + align:start position:0% +this dude no matter what. The game won't +won't let you do it. And that's just + + align:start position:0% +won't let you do it. And that's just + + + align:start position:0% +won't let you do it. And that's just +part of the story. That's how it works. + + align:start position:0% +part of the story. That's how it works. + + + align:start position:0% +part of the story. That's how it works. +And it's dubiously moral that you should + + align:start position:0% +And it's dubiously moral that you should + + + align:start position:0% +And it's dubiously moral that you should +be meddling in such affairs. But you + + align:start position:0% +be meddling in such affairs. But you + + + align:start position:0% +be meddling in such affairs. But you +know, + + align:start position:0% +know, + + + align:start position:0% +know, +>> and it actually comes back to bite you + + align:start position:0% +>> and it actually comes back to bite you + + + align:start position:0% +>> and it actually comes back to bite you +later in the game because well, you're + + align:start position:0% +later in the game because well, you're + + + align:start position:0% +later in the game because well, you're +at this you're at the place where it's + + align:start position:0% +at this you're at the place where it's + + + align:start position:0% +at this you're at the place where it's +causing problems for you. The fact that + + align:start position:0% +causing problems for you. The fact that + + + align:start position:0% +causing problems for you. The fact that +you tried to save this guy and then they + + align:start position:0% +you tried to save this guy and then they + + + align:start position:0% +you tried to save this guy and then they +play the flashback in which you have to + + align:start position:0% +play the flashback in which you have to + + + align:start position:0% +play the flashback in which you have to +do it. Um and it's all directed, you + + align:start position:0% +do it. Um and it's all directed, you + + + align:start position:0% +do it. Um and it's all directed, you +know, you didn't close this. + + align:start position:0% +know, you didn't close this. + + + align:start position:0% +know, you didn't close this. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Isn't like the Q murder close as well? + + align:start position:0% +>> Isn't like the Q murder close as well? + + + align:start position:0% +>> Isn't like the Q murder close as well? +Cuz like you don't have a choice like + + align:start position:0% +Cuz like you don't have a choice like + + + align:start position:0% +Cuz like you don't have a choice like +that you have to kill them to move on. + + align:start position:0% +that you have to kill them to move on. + + + align:start position:0% +that you have to kill them to move on. +The what? + + align:start position:0% +The what? + + + align:start position:0% +The what? +>> The cube murder like in uh + + align:start position:0% +>> The cube murder like in uh + + + align:start position:0% +>> The cube murder like in uh +>> Oh, the + + align:start position:0% +>> Oh, the + + + align:start position:0% +>> Oh, the +>> Oh, the cube. + + align:start position:0% +>> Oh, the cube. + + + align:start position:0% +>> Oh, the cube. +>> Yeah, + + align:start position:0% +>> Yeah, + + + align:start position:0% +>> Yeah, +>> I'm thinking cube. + + align:start position:0% +>> I'm thinking cube. + + + align:start position:0% +>> I'm thinking cube. +>> Yeah. Yeah, that would be close because + + align:start position:0% +>> Yeah. Yeah, that would be close because + + + align:start position:0% +>> Yeah. Yeah, that would be close because +you you simply can't move on. You just + + align:start position:0% +you you simply can't move on. You just + + + align:start position:0% +you you simply can't move on. You just +have to deal with your + + align:start position:0% +have to deal with your + + + align:start position:0% +have to deal with your +>> joke. Yeah. Yeah. No, exactly. + + align:start position:0% + + + + align:start position:0% + +>> Start vacation is currently closed. + + align:start position:0% +>> Start vacation is currently closed. + + + align:start position:0% +>> Start vacation is currently closed. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> You feel bad about those people. You + + align:start position:0% +>> You feel bad about those people. You + + + align:start position:0% +>> You feel bad about those people. You +just can't play Tamari. I'm sorry. Uh + + align:start position:0% + + + + align:start position:0% + +I have a question actually about um + + align:start position:0% +I have a question actually about um + + + align:start position:0% +I have a question actually about um +probably when we asked like the steepest + + align:start position:0% +probably when we asked like the steepest + + + align:start position:0% +probably when we asked like the steepest +death briefing. It seems to me that was + + align:start position:0% +death briefing. It seems to me that was + + + align:start position:0% +death briefing. It seems to me that was +intended by design + + align:start position:0% +intended by design + + + align:start position:0% +intended by design +briefing briefing directly in the cube. + + align:start position:0% +briefing briefing directly in the cube. + + + align:start position:0% +briefing briefing directly in the cube. +Like the idea that I'm a GM, you're a + + align:start position:0% +Like the idea that I'm a GM, you're a + + + align:start position:0% +Like the idea that I'm a GM, you're a +player and part of the challenge of the + + align:start position:0% +player and part of the challenge of the + + + align:start position:0% +player and part of the challenge of the +GM is not knowing whether your player is + + align:start position:0% +GM is not knowing whether your player is + + + align:start position:0% +GM is not knowing whether your player is +going to play along with you, but that's + + align:start position:0% +going to play along with you, but that's + + + align:start position:0% +going to play along with you, but that's +part of the game. So I don't know if + + align:start position:0% +part of the game. So I don't know if + + + align:start position:0% +part of the game. So I don't know if +that's something + + align:start position:0% + + + + align:start position:0% + +That tension is intended. + + align:start position:0% +That tension is intended. + + + align:start position:0% +That tension is intended. +>> I don't know. + + align:start position:0% +>> I don't know. + + + align:start position:0% +>> I don't know. +>> Well, I mean, + + align:start position:0% +>> Well, I mean, + + + align:start position:0% +>> Well, I mean, +>> it's still open, right? + + align:start position:0% +>> it's still open, right? + + + align:start position:0% +>> it's still open, right? +>> I would say this one is open, I guess, + + align:start position:0% +>> I would say this one is open, I guess, + + + align:start position:0% +>> I would say this one is open, I guess, +>> because you are allowed to do what you + + align:start position:0% +>> because you are allowed to do what you + + + align:start position:0% +>> because you are allowed to do what you +want. + + align:start position:0% +want. + + + align:start position:0% +want. +>> I mean, the example he gives for + + align:start position:0% +>> I mean, the example he gives for + + + align:start position:0% +>> I mean, the example he gives for +closedended is one of them is manhunt, + + align:start position:0% +closedended is one of them is manhunt, + + + align:start position:0% +closedended is one of them is manhunt, +>> where you have to kill people and you + + align:start position:0% +>> where you have to kill people and you + + + align:start position:0% +>> where you have to kill people and you +know, the more grizzly you kill them, + + align:start position:0% +know, the more grizzly you kill them, + + + align:start position:0% +know, the more grizzly you kill them, +the better. And so like if you don't + + align:start position:0% +the better. And so like if you don't + + + align:start position:0% +the better. And so like if you don't +like it, you know, there's just no way + + align:start position:0% +like it, you know, there's just no way + + + align:start position:0% +like it, you know, there's just no way +to get through the game. And the other + + align:start position:0% +to get through the game. And the other + + + align:start position:0% +to get through the game. And the other +example he also gives is um Shadow of + + align:start position:0% +example he also gives is um Shadow of + + + align:start position:0% +example he also gives is um Shadow of +the Colossus. + + align:start position:0% +the Colossus. + + + align:start position:0% +the Colossus. +>> And that one especially where it's sort + + align:start position:0% +>> And that one especially where it's sort + + + align:start position:0% +>> And that one especially where it's sort +of not really it's ambiguous in terms of + + align:start position:0% +of not really it's ambiguous in terms of + + + align:start position:0% +of not really it's ambiguous in terms of +like, okay, I have to kill these things. + + align:start position:0% +like, okay, I have to kill these things. + + + align:start position:0% +like, okay, I have to kill these things. +And you know, if you play through you + + align:start position:0% +And you know, if you play through you + + + align:start position:0% +And you know, if you play through you +realize like, well, wait a minute, + + align:start position:0% +realize like, well, wait a minute, + + + align:start position:0% +realize like, well, wait a minute, +they're just sort of hanging out. + + align:start position:0% +they're just sort of hanging out. + + + align:start position:0% +they're just sort of hanging out. +They're not really doing anything + + align:start position:0% +They're not really doing anything + + + align:start position:0% +They're not really doing anything +necessarily bad, but I have to keep + + align:start position:0% +necessarily bad, but I have to keep + + + align:start position:0% +necessarily bad, but I have to keep +killing them anyhow. Then you can start + + align:start position:0% +killing them anyhow. Then you can start + + + align:start position:0% +killing them anyhow. Then you can start +to feel sort of guilty, but it's what + + align:start position:0% +to feel sort of guilty, but it's what + + + align:start position:0% +to feel sort of guilty, but it's what +you have to do to play the game. So you + + align:start position:0% +you have to do to play the game. So you + + + align:start position:0% +you have to do to play the game. So you +would say that's that's a closed system. + + align:start position:0% + + + + align:start position:0% + +So uh let's see I would almost say + + align:start position:0% +So uh let's see I would almost say + + + align:start position:0% +So uh let's see I would almost say +Indigo Prophecy might be closed because + + align:start position:0% +Indigo Prophecy might be closed because + + + align:start position:0% +Indigo Prophecy might be closed because +you have to go on with the story which + + align:start position:0% +you have to go on with the story which + + + align:start position:0% +you have to go on with the story which +in order you have to make decisions and + + align:start position:0% +in order you have to make decisions and + + + align:start position:0% +in order you have to make decisions and +such in order to go progress on I feel + + align:start position:0% +such in order to go progress on I feel + + + align:start position:0% +such in order to go progress on I feel +like isn't is that right? + + align:start position:0% +like isn't is that right? + + + align:start position:0% +like isn't is that right? +>> I think the idea is that close would be + + align:start position:0% +>> I think the idea is that close would be + + + align:start position:0% +>> I think the idea is that close would be +you don't have to make decisions like + + align:start position:0% +you don't have to make decisions like + + + align:start position:0% +you don't have to make decisions like +close is like if you want to play the + + align:start position:0% +close is like if you want to play the + + + align:start position:0% +close is like if you want to play the +game you have to make this moral + + align:start position:0% +game you have to make this moral + + + align:start position:0% +game you have to make this moral +decision. You don't have a choice in the + + align:start position:0% +decision. You don't have a choice in the + + + align:start position:0% +decision. You don't have a choice in the +moral decision. You have to be evil or + + align:start position:0% +moral decision. You have to be evil or + + + align:start position:0% +moral decision. You have to be evil or +like and that that's that's one thing. + + align:start position:0% +like and that that's that's one thing. + + + align:start position:0% +like and that that's that's one thing. +And another game could be you have to be + + align:start position:0% +And another game could be you have to be + + + align:start position:0% +And another game could be you have to be +good. But if you have the decision + + align:start position:0% +good. But if you have the decision + + + align:start position:0% +good. But if you have the decision +between both paths and that's open, I + + align:start position:0% +between both paths and that's open, I + + + align:start position:0% +between both paths and that's open, I +believe. Right. + + align:start position:0% +believe. Right. + + + align:start position:0% +believe. Right. +>> The premise behind Indigo Prophecy was + + align:start position:0% +>> The premise behind Indigo Prophecy was + + + align:start position:0% +>> The premise behind Indigo Prophecy was +that like you could choose to do any + + align:start position:0% +that like you could choose to do any + + + align:start position:0% +that like you could choose to do any +action and the game would just have a + + align:start position:0% +action and the game would just have a + + + align:start position:0% +action and the game would just have a +different ending as a result. Though I + + align:start position:0% +different ending as a result. Though I + + + align:start position:0% +different ending as a result. Though I +think in practice it only had a few + + align:start position:0% +think in practice it only had a few + + + align:start position:0% +think in practice it only had a few +endings, but the premise was sort of + + align:start position:0% +endings, but the premise was sort of + + + align:start position:0% +endings, but the premise was sort of +that it would have like countless + + align:start position:0% +that it would have like countless + + + align:start position:0% +that it would have like countless +endings depending on your actions. + + align:start position:0% + + + + align:start position:0% + +pretty sure that Age of Empires 3 is + + align:start position:0% +pretty sure that Age of Empires 3 is + + + align:start position:0% +pretty sure that Age of Empires 3 is +going to have some closed + + align:start position:0% +going to have some closed + + + align:start position:0% +going to have some closed +>> um + + align:start position:0% +>> um + + + align:start position:0% +>> um +>> native exploitation because for the + + align:start position:0% +>> native exploitation because for the + + + align:start position:0% +>> native exploitation because for the +campaigns at least I'm pretty sure there + + align:start position:0% +campaigns at least I'm pretty sure there + + + align:start position:0% +campaigns at least I'm pretty sure there +are like + + align:start position:0% +are like + + + align:start position:0% +are like +>> conditions for completing a scenario + + align:start position:0% +>> conditions for completing a scenario + + + align:start position:0% +>> conditions for completing a scenario +which + + align:start position:0% +which + + + align:start position:0% +which +is pretty + + align:start position:0% + + + + align:start position:0% + +>> the hooker sheet is open + + align:start position:0% + + + + align:start position:0% + +>> most of the mess are open + + align:start position:0% +>> most of the mess are open + + + align:start position:0% +>> most of the mess are open +>> yeah follow through is definitely + + align:start position:0% +>> yeah follow through is definitely + + + align:start position:0% +>> yeah follow through is definitely +>> the western style one. + + align:start position:0% +>> the western style one. + + + align:start position:0% +>> the western style one. +>> The fear nail gun is is actually + + align:start position:0% +>> The fear nail gun is is actually + + + align:start position:0% +>> The fear nail gun is is actually +>> the nail gun is what? + + align:start position:0% +>> the nail gun is what? + + + align:start position:0% +>> the nail gun is what? +>> I don't know anyone who's gotten through + + align:start position:0% +>> I don't know anyone who's gotten through + + + align:start position:0% +>> I don't know anyone who's gotten through +fear without killing someone with a nail + + align:start position:0% +fear without killing someone with a nail + + + align:start position:0% +fear without killing someone with a nail +gun at some point. + + align:start position:0% +gun at some point. + + + align:start position:0% +gun at some point. +>> I mean, + + align:start position:0% + + + + align:start position:0% + +>> I'm wondering actually like you can run + + align:start position:0% +>> I'm wondering actually like you can run + + + align:start position:0% +>> I'm wondering actually like you can run +out of ammo and everything else. + + align:start position:0% +out of ammo and everything else. + + + align:start position:0% +out of ammo and everything else. +>> Yeah. Can you punch things? + + align:start position:0% +>> Yeah. Can you punch things? + + + align:start position:0% +>> Yeah. Can you punch things? +>> Yeah, you can. Yeah, + + align:start position:0% +>> Yeah, you can. Yeah, + + + align:start position:0% +>> Yeah, you can. Yeah, +>> you can't run out of ammo. You can + + align:start position:0% +>> you can't run out of ammo. You can + + + align:start position:0% +>> you can't run out of ammo. You can +actually kung fu kick things which is + + align:start position:0% +actually kung fu kick things which is + + + align:start position:0% +actually kung fu kick things which is +pretty cool. + + align:start position:0% +pretty cool. + + + align:start position:0% +pretty cool. +>> Nice + + align:start position:0% +>> Nice + + + align:start position:0% +>> Nice +>> in slow. + + align:start position:0% +>> in slow. + + + align:start position:0% +>> in slow. +>> In fact, I would almost say all the rest + + align:start position:0% +>> In fact, I would almost say all the rest + + + align:start position:0% +>> In fact, I would almost say all the rest +of them seem open. + + align:start position:0% +of them seem open. + + + align:start position:0% +of them seem open. +>> Pretty open. + + align:start position:0% +>> Pretty open. + + + align:start position:0% +>> Pretty open. +>> One of my favorite things. + + align:start position:0% +>> One of my favorite things. + + + align:start position:0% +>> One of my favorite things. +>> You don't have to do this at any point, + + align:start position:0% +>> You don't have to do this at any point, + + + align:start position:0% +>> You don't have to do this at any point, +do you? + + align:start position:0% + + + + align:start position:0% + +>> Okay. So, most of these What did we say + + align:start position:0% +>> Okay. So, most of these What did we say + + + align:start position:0% +>> Okay. So, most of these What did we say +about? + + align:start position:0% +about? + + + align:start position:0% +about? +>> Oh, + + align:start position:0% +>> Oh, + + + align:start position:0% +>> Oh, +>> okay. + + align:start position:0% +>> okay. + + + align:start position:0% +>> okay. +So, + + align:start position:0% + + + + align:start position:0% + +>> regarding Bioshock, + + align:start position:0% +>> regarding Bioshock, + + + align:start position:0% +>> regarding Bioshock, +>> would that be open or closed? + + align:start position:0% +>> would that be open or closed? + + + align:start position:0% +>> would that be open or closed? +>> I mean, there's you have a choice, but + + align:start position:0% +>> I mean, there's you have a choice, but + + + align:start position:0% +>> I mean, there's you have a choice, but +it's in your best interest to do one or + + align:start position:0% +it's in your best interest to do one or + + + align:start position:0% +it's in your best interest to do one or +the other. + + align:start position:0% +the other. + + + align:start position:0% +the other. +>> Mhm. + + align:start position:0% +>> Mhm. + + + align:start position:0% +>> Mhm. +>> Well, is it really? + + align:start position:0% +>> Well, is it really? + + + align:start position:0% +>> Well, is it really? +>> So, if you have one only one thing you + + align:start position:0% +>> So, if you have one only one thing you + + + align:start position:0% +>> So, if you have one only one thing you +can do, it's clearly closed. If you have + + align:start position:0% +can do, it's clearly closed. If you have + + + align:start position:0% +can do, it's clearly closed. If you have +only two things you can do that are very + + align:start position:0% +only two things you can do that are very + + + align:start position:0% +only two things you can do that are very +clearly defined, is it really an open + + align:start position:0% +clearly defined, is it really an open + + + align:start position:0% +clearly defined, is it really an open +system or is it just a closed system + + align:start position:0% +system or is it just a closed system + + + align:start position:0% +system or is it just a closed system +with two paths? + + align:start position:0% +with two paths? + + + align:start position:0% +with two paths? +impressionist arguing was closed. + + align:start position:0% +impressionist arguing was closed. + + + align:start position:0% +impressionist arguing was closed. +>> Yeah, + + align:start position:0% +>> Yeah, + + + align:start position:0% +>> Yeah, +>> because you weren't self-evaluating the + + align:start position:0% +>> because you weren't self-evaluating the + + + align:start position:0% +>> because you weren't self-evaluating the +system was determining whether what you + + align:start position:0% +system was determining whether what you + + + align:start position:0% +system was determining whether what you +were doing was good or bad. + + align:start position:0% +were doing was good or bad. + + + align:start position:0% +were doing was good or bad. +>> I was thinking so like I thought + + align:start position:0% +>> I was thinking so like I thought + + + align:start position:0% +>> I was thinking so like I thought +infamous like the goods would also be + + align:start position:0% +infamous like the goods would also be + + + align:start position:0% +infamous like the goods would also be +closed. + + align:start position:0% + + + + align:start position:0% + +>> Some of them I think there's a + + align:start position:0% +>> Some of them I think there's a + + + align:start position:0% +>> Some of them I think there's a +difference between only having one + + align:start position:0% +difference between only having one + + + align:start position:0% +difference between only having one +option the system telling you which + + align:start position:0% +option the system telling you which + + + align:start position:0% +option the system telling you which +option is the right option. + + align:start position:0% + + + + align:start position:0% + +So in that case, some of these turned + + align:start position:0% +So in that case, some of these turned + + + align:start position:0% +So in that case, some of these turned +from open to + + align:start position:0% +from open to + + + align:start position:0% +from open to +>> Bioshock, + + align:start position:0% +>> Bioshock, + + + align:start position:0% +>> Bioshock, +>> like Bioshock would then be closed. Like + + align:start position:0% +>> like Bioshock would then be closed. Like + + + align:start position:0% +>> like Bioshock would then be closed. Like +Fallout 3, the Dreamland would then be + + align:start position:0% +Fallout 3, the Dreamland would then be + + + align:start position:0% +Fallout 3, the Dreamland would then be +closed. + + align:start position:0% +closed. + + + align:start position:0% +closed. +>> Like telling you what was the right + + align:start position:0% +>> Like telling you what was the right + + + align:start position:0% +>> Like telling you what was the right +optionally + + align:start position:0% +optionally + + + align:start position:0% +optionally +acceptable option. + + align:start position:0% +acceptable option. + + + align:start position:0% +acceptable option. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> What do you think? Do you think um he's + + align:start position:0% +>> What do you think? Do you think um he's + + + align:start position:0% +>> What do you think? Do you think um he's +saying I know what you're saying because + + align:start position:0% +saying I know what you're saying because + + + align:start position:0% +saying I know what you're saying because +he also mentioned the Old Republic as a + + align:start position:0% +he also mentioned the Old Republic as a + + + align:start position:0% +he also mentioned the Old Republic as a +closed option. + + align:start position:0% +closed option. + + + align:start position:0% +closed option. +>> Um + + align:start position:0% +>> Um + + + align:start position:0% +>> Um +Is it that there are two discreet like + + align:start position:0% +Is it that there are two discreet like + + + align:start position:0% +Is it that there are two discreet like +like good or evil you know the lights + + align:start position:0% +like good or evil you know the lights + + + align:start position:0% +like good or evil you know the lights +the Jedi or the nar path? Um is Fallout + + align:start position:0% +the Jedi or the nar path? Um is Fallout + + + align:start position:0% +the Jedi or the nar path? Um is Fallout +that concrete follow three? I mean like + + align:start position:0% +that concrete follow three? I mean like + + + align:start position:0% +that concrete follow three? I mean like +I know uh so + + align:start position:0% +I know uh so + + + align:start position:0% +I know uh so +>> Infamous is you know you're either going + + align:start position:0% +>> Infamous is you know you're either going + + + align:start position:0% +>> Infamous is you know you're either going +one way or the other. Um but I'm not as + + align:start position:0% +one way or the other. Um but I'm not as + + + align:start position:0% +one way or the other. Um but I'm not as +sure and I'm just asking people who + + align:start position:0% +sure and I'm just asking people who + + + align:start position:0% +sure and I'm just asking people who +played it. Is Fallout 3 that particular + + align:start position:0% +played it. Is Fallout 3 that particular + + + align:start position:0% +played it. Is Fallout 3 that particular +in how it's kind of is it setting up a + + align:start position:0% +in how it's kind of is it setting up a + + + align:start position:0% +in how it's kind of is it setting up a +dichotomy of like the good character + + align:start position:0% +dichotomy of like the good character + + + align:start position:0% +dichotomy of like the good character +versus evil or is it much + + align:start position:0% +versus evil or is it much + + + align:start position:0% +versus evil or is it much +>> it's much more of a gradient + + align:start position:0% +>> it's much more of a gradient + + + align:start position:0% +>> it's much more of a gradient +>> yeah + + align:start position:0% +>> yeah + + + align:start position:0% +>> yeah +more emphasis + + align:start position:0% +more emphasis + + + align:start position:0% +more emphasis +>> in Boulders Gate it's weird because + + align:start position:0% +>> in Boulders Gate it's weird because + + + align:start position:0% +>> in Boulders Gate it's weird because +there's two things there's your + + align:start position:0% +there's two things there's your + + + align:start position:0% +there's two things there's your +alignment which you pick at the + + align:start position:0% +alignment which you pick at the + + + align:start position:0% +alignment which you pick at the +beginning of the game + + align:start position:0% +beginning of the game + + + align:start position:0% +beginning of the game +>> uh D&D style that is just fixed but then + + align:start position:0% +>> uh D&D style that is just fixed but then + + + align:start position:0% +>> uh D&D style that is just fixed but then +there's this thing that's your + + align:start position:0% +there's this thing that's your + + + align:start position:0% +there's this thing that's your +reputation which can be decreased if you + + align:start position:0% +reputation which can be decreased if you + + + align:start position:0% +reputation which can be decreased if you +do certain things from the game's point + + align:start position:0% +do certain things from the game's point + + + align:start position:0% +do certain things from the game's point +of view in view of others. So, you can + + align:start position:0% +of view in view of others. So, you can + + + align:start position:0% +of view in view of others. So, you can +get away with doing bad stuff sometimes + + align:start position:0% +get away with doing bad stuff sometimes + + + align:start position:0% +get away with doing bad stuff sometimes +without actually decreasing your + + align:start position:0% +without actually decreasing your + + + align:start position:0% +without actually decreasing your +reputation. You can also just pick a + + align:start position:0% +reputation. You can also just pick a + + + align:start position:0% +reputation. You can also just pick a +like chaotic evil alignment and then do + + align:start position:0% +like chaotic evil alignment and then do + + + align:start position:0% +like chaotic evil alignment and then do +only good things and then it's just very + + align:start position:0% +only good things and then it's just very + + + align:start position:0% +only good things and then it's just very +weird. Um, so I don't exactly remember + + align:start position:0% +weird. Um, so I don't exactly remember + + + align:start position:0% +weird. Um, so I don't exactly remember +it how the alignment really factors in + + align:start position:0% +it how the alignment really factors in + + + align:start position:0% +it how the alignment really factors in +the game play. But there's a moment, for + + align:start position:0% +the game play. But there's a moment, for + + + align:start position:0% +the game play. But there's a moment, for +example, in the game there's a big story + + align:start position:0% +example, in the game there's a big story + + + align:start position:0% +example, in the game there's a big story +for sort of rejoins that afterwards, but + + align:start position:0% +for sort of rejoins that afterwards, but + + + align:start position:0% +for sort of rejoins that afterwards, but +you have to, you know, ally yourself + + align:start position:0% +you have to, you know, ally yourself + + + align:start position:0% +you have to, you know, ally yourself +with either the thieves guild or the + + align:start position:0% +with either the thieves guild or the + + + align:start position:0% +with either the thieves guild or the +vampires in a in a town who are sort of + + align:start position:0% +vampires in a in a town who are sort of + + + align:start position:0% +vampires in a in a town who are sort of +competing factions. Sort of weird, the + + align:start position:0% +competing factions. Sort of weird, the + + + align:start position:0% +competing factions. Sort of weird, the +thieves against the vampire because the + + align:start position:0% +thieves against the vampire because the + + + align:start position:0% +thieves against the vampire because the +thieves against the vampires, you got to + + align:start position:0% +thieves against the vampires, you got to + + + align:start position:0% +thieves against the vampires, you got to +pick one uh to help you raid a certain + + align:start position:0% +pick one uh to help you raid a certain + + + align:start position:0% +pick one uh to help you raid a certain +area. Um, and you don't really have + + align:start position:0% +area. Um, and you don't really have + + + align:start position:0% +area. Um, and you don't really have +other choices and there's no there's not + + align:start position:0% +other choices and there's no there's not + + + align:start position:0% +other choices and there's no there's not +one is not + + align:start position:0% +one is not + + + align:start position:0% +one is not +>> does it make you gooder or evil? They're + + align:start position:0% +>> does it make you gooder or evil? They're + + + align:start position:0% +>> does it make you gooder or evil? They're +both kind of bad, but you have to do it + + align:start position:0% +both kind of bad, but you have to do it + + + align:start position:0% +both kind of bad, but you have to do it +to kind of find the person that you're + + align:start position:0% +to kind of find the person that you're + + + align:start position:0% +to kind of find the person that you're +trying to get. + + align:start position:0% +trying to get. + + + align:start position:0% +trying to get. +>> That's kind of closed. + + align:start position:0% +>> That's kind of closed. + + + align:start position:0% +>> That's kind of closed. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> So, in terms of Boulders Gate 2, I would + + align:start position:0% +>> So, in terms of Boulders Gate 2, I would + + + align:start position:0% +>> So, in terms of Boulders Gate 2, I would +say one there's like the reputation + + align:start position:0% +say one there's like the reputation + + + align:start position:0% +say one there's like the reputation +stat, which I found never really into, + + align:start position:0% +stat, which I found never really into, + + + align:start position:0% +stat, which I found never really into, +which is some type of metric for your + + align:start position:0% +which is some type of metric for your + + + align:start position:0% +which is some type of metric for your +That's not true. If you kill everyone, + + align:start position:0% +That's not true. If you kill everyone, + + + align:start position:0% +That's not true. If you kill everyone, +then you have to go and start attacking + + align:start position:0% +then you have to go and start attacking + + + align:start position:0% +then you have to go and start attacking +them. Do that. + + align:start position:0% +them. Do that. + + + align:start position:0% +them. Do that. +>> People in your party can duel you for + + align:start position:0% +>> People in your party can duel you for + + + align:start position:0% +>> People in your party can duel you for +your honor if they get upset at you. + + align:start position:0% +your honor if they get upset at you. + + + align:start position:0% +your honor if they get upset at you. +Kellorn duled me, left my party, and + + align:start position:0% +Kellorn duled me, left my party, and + + + align:start position:0% +Kellorn duled me, left my party, and +then tried to attack because I was too + + align:start position:0% +then tried to attack because I was too + + + align:start position:0% +then tried to attack because I was too +evil. + + align:start position:0% +evil. + + + align:start position:0% +evil. +>> Anyway, so that's uh like very very + + align:start position:0% +>> Anyway, so that's uh like very very + + + align:start position:0% +>> Anyway, so that's uh like very very +specific actions that will affect your + + align:start position:0% +specific actions that will affect your + + + align:start position:0% +specific actions that will affect your +alignment. And there aren't very many of + + align:start position:0% +alignment. And there aren't very many of + + + align:start position:0% +alignment. And there aren't very many of +those. In addition, you have kind of + + align:start position:0% +those. In addition, you have kind of + + + align:start position:0% +those. In addition, you have kind of +like these scene type decisions which + + align:start position:0% +like these scene type decisions which + + + align:start position:0% +like these scene type decisions which +are also very black or white, good or + + align:start position:0% +are also very black or white, good or + + + align:start position:0% +are also very black or white, good or +equal. I would say there's a lot of + + align:start position:0% +equal. I would say there's a lot of + + + align:start position:0% +equal. I would say there's a lot of +decisions in the game that don't impact + + align:start position:0% +decisions in the game that don't impact + + + align:start position:0% +decisions in the game that don't impact +both of those to have both an ethical + + align:start position:0% +both of those to have both an ethical + + + align:start position:0% +both of those to have both an ethical +choice but not nearly as much of a + + align:start position:0% +choice but not nearly as much of a + + + align:start position:0% +choice but not nearly as much of a +mechanical + + align:start position:0% +mechanical + + + align:start position:0% +mechanical +impact. + + align:start position:0% +impact. + + + align:start position:0% +impact. +>> One of the things he also mentions in + + align:start position:0% +>> One of the things he also mentions in + + + align:start position:0% +>> One of the things he also mentions in +relation to the open system like going + + align:start position:0% +relation to the open system like going + + + align:start position:0% +relation to the open system like going +back to the Sims is that um + + align:start position:0% +back to the Sims is that um + + + align:start position:0% +back to the Sims is that um +you can do what you want and the game + + align:start position:0% +you can do what you want and the game + + + align:start position:0% +you can do what you want and the game +doesn't necessarily punish you. you + + align:start position:0% +doesn't necessarily punish you. you + + + align:start position:0% +doesn't necessarily punish you. you +know, like you can murder, you know, you + + align:start position:0% +know, like you can murder, you know, you + + + align:start position:0% +know, like you can murder, you know, you +you can drown your Sims and the rest of + + align:start position:0% +you can drown your Sims and the rest of + + + align:start position:0% +you can drown your Sims and the rest of +the Sims in the house like joy in fear + + align:start position:0% +the Sims in the house like joy in fear + + + align:start position:0% +the Sims in the house like joy in fear +or, you know, like disapprove of their + + align:start position:0% +or, you know, like disapprove of their + + + align:start position:0% +or, you know, like disapprove of their +action. + + align:start position:0% +action. + + + align:start position:0% +action. +>> Um, it's just sort of up to you like + + align:start position:0% +>> Um, it's just sort of up to you like + + + align:start position:0% +>> Um, it's just sort of up to you like +whether you want to feel bad about it or + + align:start position:0% +whether you want to feel bad about it or + + + align:start position:0% +whether you want to feel bad about it or +not or or you know, the game has no + + align:start position:0% +not or or you know, the game has no + + + align:start position:0% +not or or you know, the game has no +larger response other than uh light the + + align:start position:0% +larger response other than uh light the + + + align:start position:0% +larger response other than uh light the +Sim die once because I let him set the + + align:start position:0% +Sim die once because I let him set the + + + align:start position:0% +Sim die once because I let him set the +stone on fire and I foolishly mold for + + align:start position:0% +stone on fire and I foolishly mold for + + + align:start position:0% +stone on fire and I foolishly mold for +his life and got his zombie back. Turns + + align:start position:0% +his life and got his zombie back. Turns + + + align:start position:0% +his life and got his zombie back. Turns +out the only way zombie is happy in the + + align:start position:0% +out the only way zombie is happy in the + + + align:start position:0% +out the only way zombie is happy in the +game is if he makes everybody else + + align:start position:0% +game is if he makes everybody else + + + align:start position:0% +game is if he makes everybody else +unhappy. So then I had to kill zombie. + + align:start position:0% +unhappy. So then I had to kill zombie. + + + align:start position:0% +unhappy. So then I had to kill zombie. +But + + align:start position:0% +But + + + align:start position:0% +But +so that was another kind of element to + + align:start position:0% +so that was another kind of element to + + + align:start position:0% +so that was another kind of element to +it. One of the things that he talks + + align:start position:0% +it. One of the things that he talks + + + align:start position:0% +it. One of the things that he talks +about in general in relation to all of + + align:start position:0% +about in general in relation to all of + + + align:start position:0% +about in general in relation to all of +this and a lot of these kind of fit is + + align:start position:0% +this and a lot of these kind of fit is + + + align:start position:0% +this and a lot of these kind of fit is +like ethics through statistics. You like + + align:start position:0% +like ethics through statistics. You like + + + align:start position:0% +like ethics through statistics. You like +that somehow ethical systems are on this + + align:start position:0% +that somehow ethical systems are on this + + + align:start position:0% +that somehow ethical systems are on this +point or sliding scale and that you know + + align:start position:0% +point or sliding scale and that you know + + + align:start position:0% +point or sliding scale and that you know +you're heading towards good or you're + + align:start position:0% +you're heading towards good or you're + + + align:start position:0% +you're heading towards good or you're +heading towards evil. We were even + + align:start position:0% +heading towards evil. We were even + + + align:start position:0% +heading towards evil. We were even +mentioning this before class started + + align:start position:0% +mentioning this before class started + + + align:start position:0% +mentioning this before class started +that, you know, you can blow up an + + align:start position:0% +that, you know, you can blow up an + + + align:start position:0% +that, you know, you can blow up an +entire town, but then if you know, like + + align:start position:0% +entire town, but then if you know, like + + + align:start position:0% +entire town, but then if you know, like +you give like three beggars 50 cents + + align:start position:0% +you give like three beggars 50 cents + + + align:start position:0% +you give like three beggars 50 cents +each, suddenly, you know, you're back at + + align:start position:0% +each, suddenly, you know, you're back at + + + align:start position:0% +each, suddenly, you know, you're back at +neutral because of the way that these + + align:start position:0% +neutral because of the way that these + + + align:start position:0% +neutral because of the way that these +lighting systems work, you know, in + + align:start position:0% +lighting systems work, you know, in + + + align:start position:0% +lighting systems work, you know, in +bizarrely mechanical. + + align:start position:0% +bizarrely mechanical. + + + align:start position:0% +bizarrely mechanical. +>> Yeah, you you can buy reputation back by + + align:start position:0% +>> Yeah, you you can buy reputation back by + + + align:start position:0% +>> Yeah, you you can buy reputation back by +donating to temples. + + align:start position:0% +donating to temples. + + + align:start position:0% +donating to temples. +>> It's like indulgences. + + align:start position:0% +>> It's like indulgences. + + + align:start position:0% +>> It's like indulgences. +>> Yeah, it is exactly like + + align:start position:0% +>> Yeah, it is exactly like + + + align:start position:0% +>> Yeah, it is exactly like +>> I want that not going to happen. + + align:start position:0% +>> I want that not going to happen. + + + align:start position:0% +>> I want that not going to happen. +I have to close this now because I'm + + align:start position:0% +I have to close this now because I'm + + + align:start position:0% +I have to close this now because I'm +getting high off of the microphones. I + + align:start position:0% +getting high off of the microphones. I + + + align:start position:0% +getting high off of the microphones. I +wanted to show you an example um of one + + align:start position:0% +wanted to show you an example um of one + + + align:start position:0% +wanted to show you an example um of one +that we haven't talked about yet. + + align:start position:0% +that we haven't talked about yet. + + + align:start position:0% +that we haven't talked about yet. +Somebody mentioned Call of Duty. This is + + align:start position:0% +Somebody mentioned Call of Duty. This is + + + align:start position:0% +Somebody mentioned Call of Duty. This is +actually from last year. It's not + + align:start position:0% +actually from last year. It's not + + + align:start position:0% +actually from last year. It's not +Castro, which is the new one. Um but + + align:start position:0% +Castro, which is the new one. Um but + + + align:start position:0% +Castro, which is the new one. Um but +>> is it the Russian hostage thing? + + align:start position:0% +>> is it the Russian hostage thing? + + + align:start position:0% +>> is it the Russian hostage thing? +>> Yeah, it's the no Russian level + + align:start position:0% + + + + align:start position:0% + +>> from Modern Warfare 2. + + align:start position:0% + + + + align:start position:0% + +>> It's like a competition. + + align:start position:0% +>> It's like a competition. + + + align:start position:0% +>> It's like a competition. +This is um so this was last year's + + align:start position:0% +This is um so this was last year's + + + align:start position:0% +This is um so this was last year's +modern uh Call of Duty and this was the + + align:start position:0% +modern uh Call of Duty and this was the + + + align:start position:0% +modern uh Call of Duty and this was the +optional level. You did not have to play + + align:start position:0% +optional level. You did not have to play + + + align:start position:0% +optional level. You did not have to play +it and of course it caused a big storm + + align:start position:0% +it and of course it caused a big storm + + + align:start position:0% +it and of course it caused a big storm +when it was released. Um I'm just going + + align:start position:0% +when it was released. Um I'm just going + + + align:start position:0% +when it was released. Um I'm just going +to play it and then we can talk about it + + align:start position:0% +to play it and then we can talk about it + + + align:start position:0% +to play it and then we can talk about it +after. + + align:start position:0% +after. + + + align:start position:0% +after. +>> So what's has anyone played this? + + align:start position:0% +>> So what's has anyone played this? + + + align:start position:0% +>> So what's has anyone played this? +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Want to um provide a little context or + + align:start position:0% +>> Want to um provide a little context or + + + align:start position:0% +>> Want to um provide a little context or +explain the a little bit more? + + align:start position:0% +explain the a little bit more? + + + align:start position:0% +explain the a little bit more? +So the convoluted plot is that this is a + + align:start position:0% +So the convoluted plot is that this is a + + + align:start position:0% +So the convoluted plot is that this is a +false flag attack which is staged by a + + align:start position:0% +false flag attack which is staged by a + + + align:start position:0% +false flag attack which is staged by a +terrorist organization which is meant to + + align:start position:0% +terrorist organization which is meant to + + + align:start position:0% +terrorist organization which is meant to +frame the CIA to start a war between + + align:start position:0% +frame the CIA to start a war between + + + align:start position:0% +frame the CIA to start a war between +Russia and the US. And so the idea here + + align:start position:0% +Russia and the US. And so the idea here + + + align:start position:0% +Russia and the US. And so the idea here +is that you are playing a character who + + align:start position:0% +is that you are playing a character who + + + align:start position:0% +is that you are playing a character who +is undercover as part of the CIA who was + + align:start position:0% +is undercover as part of the CIA who was + + + align:start position:0% +is undercover as part of the CIA who was +part of this terrorist organization. + + align:start position:0% +part of this terrorist organization. + + + align:start position:0% +part of this terrorist organization. +And then you end up being double crossed + + align:start position:0% +And then you end up being double crossed + + + align:start position:0% +And then you end up being double crossed +because they as it was just revealed at + + align:start position:0% +because they as it was just revealed at + + + align:start position:0% +because they as it was just revealed at +the end they knew that you were a CIA + + align:start position:0% +the end they knew that you were a CIA + + + align:start position:0% +the end they knew that you were a CIA +agent and they're trying to pin the + + align:start position:0% +agent and they're trying to pin the + + + align:start position:0% +agent and they're trying to pin the +attack on America. + + align:start position:0% +attack on America. + + + align:start position:0% +attack on America. +>> So that's that's you have the option + + align:start position:0% +>> So that's that's you have the option + + + align:start position:0% +>> So that's that's you have the option +>> story context. the option of shooting + + align:start position:0% +>> story context. the option of shooting + + + align:start position:0% +>> story context. the option of shooting +Makarov in the back or + + align:start position:0% +Makarov in the back or + + + align:start position:0% +Makarov in the back or +>> if you try and shoot Makarov then the + + align:start position:0% +>> if you try and shoot Makarov then the + + + align:start position:0% +>> if you try and shoot Makarov then the +game then the level ends with a fail + + align:start position:0% +game then the level ends with a fail + + + align:start position:0% +game then the level ends with a fail +>> um and can't progress in the game. If + + align:start position:0% +>> um and can't progress in the game. If + + + align:start position:0% +>> um and can't progress in the game. If +you try and get through the level + + align:start position:0% +you try and get through the level + + + align:start position:0% +you try and get through the level +without shooting any civilians the level + + align:start position:0% +without shooting any civilians the level + + + align:start position:0% +without shooting any civilians the level +also ends off discover decides that + + align:start position:0% +also ends off discover decides that + + + align:start position:0% +also ends off discover decides that +you're a traitor and shoots you + + align:start position:0% +you're a traitor and shoots you + + + align:start position:0% +you're a traitor and shoots you +before doing anything else + + align:start position:0% +before doing anything else + + + align:start position:0% +before doing anything else +>> before he's supposed to shoot you + + align:start position:0% +>> before he's supposed to shoot you + + + align:start position:0% +>> before he's supposed to shoot you +>> before he's supposed to shoot you. I + + align:start position:0% +>> before he's supposed to shoot you. I + + + align:start position:0% +>> before he's supposed to shoot you. I +seem to remember. + + align:start position:0% +seem to remember. + + + align:start position:0% +seem to remember. +>> I I think you can get through the + + align:start position:0% +>> I I think you can get through the + + + align:start position:0% +>> I I think you can get through the +mission by not shooting any civilians, + + align:start position:0% +mission by not shooting any civilians, + + + align:start position:0% +mission by not shooting any civilians, +but you can't get through without + + align:start position:0% +but you can't get through without + + + align:start position:0% +but you can't get through without +shooting any of the cops. + + align:start position:0% +shooting any of the cops. + + + align:start position:0% +shooting any of the cops. +>> Yeah. Like something + + align:start position:0% +>> Yeah. Like something + + + align:start position:0% +>> Yeah. Like something +>> if you don't shoot the cops, I think you + + align:start position:0% +>> if you don't shoot the cops, I think you + + + align:start position:0% +>> if you don't shoot the cops, I think you +can. + + align:start position:0% +can. + + + align:start position:0% +can. +>> Yeah. You still have to shoot civilians. + + align:start position:0% +>> Yeah. You still have to shoot civilians. + + + align:start position:0% +>> Yeah. You still have to shoot civilians. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> Maybe different difficulty settings as + + align:start position:0% +>> Maybe different difficulty settings as + + + align:start position:0% +>> Maybe different difficulty settings as +well. + + align:start position:0% +well. + + + align:start position:0% +well. +>> Yeah. I don't know. Also, that guy was + + align:start position:0% +>> Yeah. I don't know. Also, that guy was + + + align:start position:0% +>> Yeah. I don't know. Also, that guy was +incredibly diligent about killing + + align:start position:0% +incredibly diligent about killing + + + align:start position:0% +incredibly diligent about killing +civilians. + + align:start position:0% +civilians. + + + align:start position:0% +civilians. +>> I mean, I I was I was impressed. I did + + align:start position:0% +>> I mean, I I was I was impressed. I did + + + align:start position:0% +>> I mean, I I was I was impressed. I did +not play that level that way. Oh, I + + align:start position:0% +not play that level that way. Oh, I + + + align:start position:0% +not play that level that way. Oh, I +think + + align:start position:0% + + + + align:start position:0% + +that's + + align:start position:0% +that's + + + align:start position:0% +that's +>> Yeah, that was uh that guy took his work + + align:start position:0% +>> Yeah, that was uh that guy took his work + + + align:start position:0% +>> Yeah, that was uh that guy took his work +to heart. Like + + align:start position:0% +to heart. Like + + + align:start position:0% +to heart. Like +>> I don't think that I would have like + + align:start position:0% +>> I don't think that I would have like + + + align:start position:0% +>> I don't think that I would have like +like Owen says if I was I haven't played + + align:start position:0% +like Owen says if I was I haven't played + + + align:start position:0% +like Owen says if I was I haven't played +Modern Warfare 2 yet, but or Black Ops + + align:start position:0% +Modern Warfare 2 yet, but or Black Ops + + + align:start position:0% +Modern Warfare 2 yet, but or Black Ops +for that matter, but don't feel like it + + align:start position:0% +for that matter, but don't feel like it + + + align:start position:0% +for that matter, but don't feel like it +would it would come to me that it was + + align:start position:0% +would it would come to me that it was + + + align:start position:0% +would it would come to me that it was +really necessary to just hunt down every + + align:start position:0% +really necessary to just hunt down every + + + align:start position:0% +really necessary to just hunt down every +last + + align:start position:0% +last + + + align:start position:0% +last +>> thorough. It was very thorough. + + align:start position:0% +>> thorough. It was very thorough. + + + align:start position:0% +>> thorough. It was very thorough. +>> Yeah, blend in. And but you know it's + + align:start position:0% +>> Yeah, blend in. And but you know it's + + + align:start position:0% +>> Yeah, blend in. And but you know it's +also interesting that you're the dupe in + + align:start position:0% +also interesting that you're the dupe in + + + align:start position:0% +also interesting that you're the dupe in +this, right? You think, well, I'm + + align:start position:0% +this, right? You think, well, I'm + + + align:start position:0% +this, right? You think, well, I'm +killing all of these people + + align:start position:0% +killing all of these people + + + align:start position:0% +killing all of these people +>> so that I can then kill him probably or + + align:start position:0% +>> so that I can then kill him probably or + + + align:start position:0% +>> so that I can then kill him probably or +something, + + align:start position:0% +something, + + + align:start position:0% +something, +>> right? Or it's for a greater good, + + align:start position:0% +>> right? Or it's for a greater good, + + + align:start position:0% +>> right? Or it's for a greater good, +right? That you know, I'm going to get + + align:start position:0% +right? That you know, I'm going to get + + + align:start position:0% +right? That you know, I'm going to get +in with this group and and help bring + + align:start position:0% +in with this group and and help bring + + + align:start position:0% +in with this group and and help bring +down this terrorist cell or haha, you + + align:start position:0% +down this terrorist cell or haha, you + + + align:start position:0% +down this terrorist cell or haha, you +know, not so much. + + align:start position:0% +know, not so much. + + + align:start position:0% +know, not so much. +>> And I mean, Call of Duty like has anyone + + align:start position:0% +>> And I mean, Call of Duty like has anyone + + + align:start position:0% +>> And I mean, Call of Duty like has anyone +played Black Ops? + + align:start position:0% +played Black Ops? + + + align:start position:0% +played Black Ops? +There's the scene in it, another uh + + align:start position:0% +There's the scene in it, another uh + + + align:start position:0% +There's the scene in it, another uh +level where you can assassinate Castro + + align:start position:0% +level where you can assassinate Castro + + + align:start position:0% +level where you can assassinate Castro +>> and um I was just watching it off Castro + + align:start position:0% +>> and um I was just watching it off Castro + + + align:start position:0% +>> and um I was just watching it off Castro +>> this morning and uh + + align:start position:0% +>> this morning and uh + + + align:start position:0% +>> this morning and uh +>> is it they they + + align:start position:0% +>> is it they they + + + align:start position:0% +>> is it they they +Russian uh Cuba objected + + align:start position:0% +Russian uh Cuba objected + + + align:start position:0% +Russian uh Cuba objected +>> um to to the video game. + + align:start position:0% +>> um to to the video game. + + + align:start position:0% +>> um to to the video game. +But um I watched that level. It's not + + align:start position:0% +But um I watched that level. It's not + + + align:start position:0% +But um I watched that level. It's not +nearly as exciting as this one. Um + + align:start position:0% +nearly as exciting as this one. Um + + + align:start position:0% +nearly as exciting as this one. Um +although it's interesting in that you uh + + align:start position:0% +although it's interesting in that you uh + + + align:start position:0% +although it's interesting in that you uh +he's you infiltrate his compound, you + + align:start position:0% +he's you infiltrate his compound, you + + + align:start position:0% +he's you infiltrate his compound, you +know, you get up to he's like in his + + align:start position:0% +know, you get up to he's like in his + + + align:start position:0% +know, you get up to he's like in his +bedroom with his or whatever she is and + + align:start position:0% +bedroom with his or whatever she is and + + + align:start position:0% +bedroom with his or whatever she is and +um you shoot him and in this uh clip the + + align:start position:0% +um you shoot him and in this uh clip the + + + align:start position:0% +um you shoot him and in this uh clip the +guy shot him in the head and it's it + + align:start position:0% +guy shot him in the head and it's it + + + align:start position:0% +guy shot him in the head and it's it +slows down to bullet time actually and + + align:start position:0% +slows down to bullet time actually and + + + align:start position:0% +slows down to bullet time actually and +you see it enter his forehead and he + + align:start position:0% +you see it enter his forehead and he + + + align:start position:0% +you see it enter his forehead and he +falls over and and then the enraged + + align:start position:0% +falls over and and then the enraged + + + align:start position:0% +falls over and and then the enraged +lover grabs the machine gun and starts + + align:start position:0% +lover grabs the machine gun and starts + + + align:start position:0% +lover grabs the machine gun and starts +firing at you in her negligence so you + + align:start position:0% +firing at you in her negligence so you + + + align:start position:0% +firing at you in her negligence so you +have to kill her too. And yeah, Cuba is + + align:start position:0% +have to kill her too. And yeah, Cuba is + + + align:start position:0% +have to kill her too. And yeah, Cuba is +outraged, + + align:start position:0% +outraged, + + + align:start position:0% +outraged, +but I I don't think it takes a lot to + + align:start position:0% +but I I don't think it takes a lot to + + + align:start position:0% +but I I don't think it takes a lot to +get Cuba mad anyway. + + align:start position:0% +get Cuba mad anyway. + + + align:start position:0% +get Cuba mad anyway. +>> Can you score statistics? + + align:start position:0% +>> Can you score statistics? + + + align:start position:0% +>> Can you score statistics? +>> Don't like statistics. + + align:start position:0% +>> Don't like statistics. + + + align:start position:0% +>> Don't like statistics. +>> 495 likes, 85 dislikes. + + align:start position:0% +>> 495 likes, 85 dislikes. + + + align:start position:0% +>> 495 likes, 85 dislikes. +>> It's pretty high for dislikes. + + align:start position:0% +>> It's pretty high for dislikes. + + + align:start position:0% +>> It's pretty high for dislikes. +>> For something that's not like video, + + align:start position:0% +>> For something that's not like video, + + + align:start position:0% +>> For something that's not like video, +>> um + + align:start position:0% +>> um + + + align:start position:0% +>> um +I I No. Yes. I I in the previous Modern + + align:start position:0% +I I No. Yes. I I in the previous Modern + + + align:start position:0% +I I No. Yes. I I in the previous Modern +Warfare game, there's actually It + + align:start position:0% +Warfare game, there's actually It + + + align:start position:0% +Warfare game, there's actually It +it it I haven't seen anyone draw this + + align:start position:0% +it it I haven't seen anyone draw this + + + align:start position:0% +it it I haven't seen anyone draw this +parallel, but there is a level where you + + align:start position:0% +parallel, but there is a level where you + + + align:start position:0% +parallel, but there is a level where you +are in the middle of a firefight, a US + + align:start position:0% +are in the middle of a firefight, a US + + + align:start position:0% +are in the middle of a firefight, a US +marine in some Middle Eastern wars, + + align:start position:0% +marine in some Middle Eastern wars, + + + align:start position:0% +marine in some Middle Eastern wars, +and you're told to shoot at enemies who + + align:start position:0% +and you're told to shoot at enemies who + + + align:start position:0% +and you're told to shoot at enemies who +are coming on the on your center, but + + align:start position:0% +are coming on the on your center, but + + + align:start position:0% +are coming on the on your center, but +they're at such a range that you cannot + + align:start position:0% +they're at such a range that you cannot + + + align:start position:0% +they're at such a range that you cannot +tell friend. there's you're absolutely + + align:start position:0% +tell friend. there's you're absolutely + + + align:start position:0% +tell friend. there's you're absolutely +certain that whatever you're shooting + + align:start position:0% +certain that whatever you're shooting + + + align:start position:0% +certain that whatever you're shooting +at, there's a 50% chance that there's + + align:start position:0% +at, there's a 50% chance that there's + + + align:start position:0% +at, there's a 50% chance that there's +actually some one one of the allies. + + align:start position:0% +actually some one one of the allies. + + + align:start position:0% +actually some one one of the allies. +>> There there's also the really creepy um + + align:start position:0% +>> There there's also the really creepy um + + + align:start position:0% +>> There there's also the really creepy um +>> that's the gunship sequence. the gunship + + align:start position:0% +>> that's the gunship sequence. the gunship + + + align:start position:0% +>> that's the gunship sequence. the gunship +>> which is which is which is uh which gets + + align:start position:0% +>> which is which is which is uh which gets + + + align:start position:0% +>> which is which is which is uh which gets +most of the attention but I I I but but + + align:start position:0% +most of the attention but I I I but but + + + align:start position:0% +most of the attention but I I I but but +the I was surprised by the subtlety of + + align:start position:0% +the I was surprised by the subtlety of + + + align:start position:0% +the I was surprised by the subtlety of +the the the sequence where you are just + + align:start position:0% +the the the sequence where you are just + + + align:start position:0% +the the the sequence where you are just +in the middle of a firefight in in + + align:start position:0% +in the middle of a firefight in in + + + align:start position:0% +in the middle of a firefight in in +Modern Warfare one because it has that + + align:start position:0% +Modern Warfare one because it has that + + + align:start position:0% +Modern Warfare one because it has that +situation of the you are being told to + + align:start position:0% +situation of the you are being told to + + + align:start position:0% +situation of the you are being told to +kill but you + + align:start position:0% +kill but you + + + align:start position:0% +kill but you +may not even though everyone on on um + + align:start position:0% +may not even though everyone on on um + + + align:start position:0% +may not even though everyone on on um +that you might be shooting at is a + + align:start position:0% +that you might be shooting at is a + + + align:start position:0% +that you might be shooting at is a +combatant you may not want to shoot + + align:start position:0% +combatant you may not want to shoot + + + align:start position:0% +combatant you may not want to shoot +everyone. in this space, you know, maybe + + align:start position:0% +everyone. in this space, you know, maybe + + + align:start position:0% +everyone. in this space, you know, maybe +I felt that actually made a more + + align:start position:0% +I felt that actually made a more + + + align:start position:0% +I felt that actually made a more +interesting subtle point of well, + + align:start position:0% +interesting subtle point of well, + + + align:start position:0% +interesting subtle point of well, +actually that's kind of what the + + align:start position:0% +actually that's kind of what the + + + align:start position:0% +actually that's kind of what the +situation of being in the Middle East + + align:start position:0% +situation of being in the Middle East + + + align:start position:0% +situation of being in the Middle East +right now is like it's hard to tell + + align:start position:0% +right now is like it's hard to tell + + + align:start position:0% +right now is like it's hard to tell +where + + align:start position:0% +where + + + align:start position:0% +where +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +Um, I was thinking about this because I + + align:start position:0% +Um, I was thinking about this because I + + + align:start position:0% +Um, I was thinking about this because I +actually um I did an interview last week + + align:start position:0% +actually um I did an interview last week + + + align:start position:0% +actually um I did an interview last week +or two weeks ago with some radio people + + align:start position:0% +or two weeks ago with some radio people + + + align:start position:0% +or two weeks ago with some radio people +and it was about Black Ops being + + align:start position:0% +and it was about Black Ops being + + + align:start position:0% +and it was about Black Ops being +released because it's like the best + + align:start position:0% +released because it's like the best + + + align:start position:0% +released because it's like the best +selling entertainment video ever and uh + + align:start position:0% +selling entertainment video ever and uh + + + align:start position:0% +selling entertainment video ever and uh +they introduced it of course on the + + align:start position:0% +they introduced it of course on the + + + align:start position:0% +they introduced it of course on the +segment as the ultraviolent video game + + align:start position:0% +segment as the ultraviolent video game + + + align:start position:0% +segment as the ultraviolent video game +>> Call of Duty. + + align:start position:0% +>> Call of Duty. + + + align:start position:0% +>> Call of Duty. +>> H + + align:start position:0% +>> H + + + align:start position:0% +>> H +>> that's pretty accurate. It is, but it's + + align:start position:0% +>> that's pretty accurate. It is, but it's + + + align:start position:0% +>> that's pretty accurate. It is, but it's +and one of the thing, one of the + + align:start position:0% +and one of the thing, one of the + + + align:start position:0% +and one of the thing, one of the +questions that they asked that each + + align:start position:0% +questions that they asked that each + + + align:start position:0% +questions that they asked that each +affiliate asked over and over is, you + + align:start position:0% +affiliate asked over and over is, you + + + align:start position:0% +affiliate asked over and over is, you +know, they mentioned the caster level. + + align:start position:0% +know, they mentioned the caster level. + + + align:start position:0% +know, they mentioned the caster level. +They said the video games gone too far. + + align:start position:0% +They said the video games gone too far. + + + align:start position:0% +They said the video games gone too far. +You know, is there is there a line that + + align:start position:0% +You know, is there is there a line that + + + align:start position:0% +You know, is there is there a line that +that shouldn't be crossed? And I'm sure + + align:start position:0% +that shouldn't be crossed? And I'm sure + + + align:start position:0% +that shouldn't be crossed? And I'm sure +if they had I mean, none of these people + + align:start position:0% +if they had I mean, none of these people + + + align:start position:0% +if they had I mean, none of these people +actually played video games, so you + + align:start position:0% +actually played video games, so you + + + align:start position:0% +actually played video games, so you +know, they had they were just reading + + align:start position:0% +know, they had they were just reading + + + align:start position:0% +know, they had they were just reading +their script. + + align:start position:0% +their script. + + + align:start position:0% +their script. +This might have even fit even better, + + align:start position:0% +This might have even fit even better, + + + align:start position:0% +This might have even fit even better, +you know, in terms of how + + align:start position:0% +you know, in terms of how + + + align:start position:0% +you know, in terms of how +>> this is pretty I'm surprised this got + + align:start position:0% +>> this is pretty I'm surprised this got + + + align:start position:0% +>> this is pretty I'm surprised this got +through. + + align:start position:0% +through. + + + align:start position:0% +through. +>> Well, it's an optional level, + + align:start position:0% +>> Well, it's an optional level, + + + align:start position:0% +>> Well, it's an optional level, +>> right? + + align:start position:0% +>> right? + + + align:start position:0% +>> right? +>> You know, you don't have to do it. + + align:start position:0% +>> You know, you don't have to do it. + + + align:start position:0% +>> You know, you don't have to do it. +Interesting comment right there. You + + align:start position:0% +Interesting comment right there. You + + + align:start position:0% +Interesting comment right there. You +know, JFK airport US citizens. + + align:start position:0% +know, JFK airport US citizens. + + + align:start position:0% +know, JFK airport US citizens. +>> But, you know, leaving aside the just + + align:start position:0% +>> But, you know, leaving aside the just + + + align:start position:0% +>> But, you know, leaving aside the just +like the the knee-jerk kind of gamer + + align:start position:0% +like the the knee-jerk kind of gamer + + + align:start position:0% +like the the knee-jerk kind of gamer +defense, well, it's just for fun or it's + + align:start position:0% +defense, well, it's just for fun or it's + + + align:start position:0% +defense, well, it's just for fun or it's +just a video game. I mean, how do you + + align:start position:0% +just a video game. I mean, how do you + + + align:start position:0% +just a video game. I mean, how do you +answer that question? I mean, I know + + align:start position:0% +answer that question? I mean, I know + + + align:start position:0% +answer that question? I mean, I know +what I spew to them, but I'm just + + align:start position:0% +what I spew to them, but I'm just + + + align:start position:0% +what I spew to them, but I'm just +curious in terms of like what is what + + align:start position:0% +curious in terms of like what is what + + + align:start position:0% +curious in terms of like what is what +does it mean and beyond just like games + + align:start position:0% +does it mean and beyond just like games + + + align:start position:0% +does it mean and beyond just like games +as like statistics for like the good or + + align:start position:0% +as like statistics for like the good or + + + align:start position:0% +as like statistics for like the good or +the dark side? Um, you know, is there a + + align:start position:0% +the dark side? Um, you know, is there a + + + align:start position:0% +the dark side? Um, you know, is there a +point you think where it can go too far + + align:start position:0% +point you think where it can go too far + + + align:start position:0% +point you think where it can go too far +with the game? What um what's the + + align:start position:0% +with the game? What um what's the + + + align:start position:0% +with the game? What um what's the +assumption behind that question? + + align:start position:0% +assumption behind that question? + + + align:start position:0% +assumption behind that question? +this really + + align:start position:0% +this really + + + align:start position:0% +this really +disturbing news report I was reading + + align:start position:0% +disturbing news report I was reading + + + align:start position:0% +disturbing news report I was reading +about this Japanese game called Wave + + align:start position:0% +about this Japanese game called Wave + + + align:start position:0% +about this Japanese game called Wave +Play. + + align:start position:0% +Play. + + + align:start position:0% +Play. +>> Oh yeah. + + align:start position:0% +>> Oh yeah. + + + align:start position:0% +>> Oh yeah. +>> And the disturbing for me it was clear + + align:start position:0% +>> And the disturbing for me it was clear + + + align:start position:0% +>> And the disturbing for me it was clear +like this is totally messed up. Can't + + align:start position:0% +like this is totally messed up. Can't + + + align:start position:0% +like this is totally messed up. Can't +believe that this is like this exists. + + align:start position:0% +believe that this is like this exists. + + + align:start position:0% +believe that this is like this exists. +But the part that was disturbing was the + + align:start position:0% +But the part that was disturbing was the + + + align:start position:0% +But the part that was disturbing was the +the defense put forth by the developers + + align:start position:0% +the defense put forth by the developers + + + align:start position:0% +the defense put forth by the developers +and they were say who are you guys to be + + align:start position:0% +and they were say who are you guys to be + + + align:start position:0% +and they were say who are you guys to be +telling us this is messed up. You + + align:start position:0% +telling us this is messed up. You + + + align:start position:0% +telling us this is messed up. You +Americans, you make games all the time + + align:start position:0% +Americans, you make games all the time + + + align:start position:0% +Americans, you make games all the time +where you have to kill people. Murder is + + align:start position:0% +where you have to kill people. Murder is + + + align:start position:0% +where you have to kill people. Murder is +a much worse crime than rape. Our game + + align:start position:0% +a much worse crime than rape. Our game + + + align:start position:0% +a much worse crime than rape. Our game +is not nearly as bad as for say this. + + align:start position:0% +is not nearly as bad as for say this. + + + align:start position:0% +is not nearly as bad as for say this. +And I was just like, wait, no, but but + + align:start position:0% +And I was just like, wait, no, but but + + + align:start position:0% +And I was just like, wait, no, but but +that's more messed up. But but what and + + align:start position:0% +that's more messed up. But but what and + + + align:start position:0% +that's more messed up. But but what and +and I don't know what what to think of + + align:start position:0% +and I don't know what what to think of + + + align:start position:0% +and I don't know what what to think of +it. Um South Park. + + align:start position:0% +it. Um South Park. + + + align:start position:0% +it. Um South Park. +>> What? + + align:start position:0% +>> What? + + + align:start position:0% +>> What? +>> South Park episode that addresses South + + align:start position:0% +>> South Park episode that addresses South + + + align:start position:0% +>> South Park episode that addresses South +Park. + + align:start position:0% +Park. + + + align:start position:0% +Park. +>> Not seen that South Park + + align:start position:0% +>> Not seen that South Park + + + align:start position:0% +>> Not seen that South Park +actually. Um just on that on that game + + align:start position:0% +actually. Um just on that on that game + + + align:start position:0% +actually. Um just on that on that game +in particular, there was a lot of + + align:start position:0% +in particular, there was a lot of + + + align:start position:0% +in particular, there was a lot of +backlash I heard in Japan about um + + align:start position:0% +backlash I heard in Japan about um + + + align:start position:0% +backlash I heard in Japan about um +Replay. Mainly because the game had been + + align:start position:0% +Replay. Mainly because the game had been + + + align:start position:0% +Replay. Mainly because the game had been +out for maybe 2 years and gone + + align:start position:0% +out for maybe 2 years and gone + + + align:start position:0% +out for maybe 2 years and gone +completely unnoticed until basically the + + align:start position:0% +completely unnoticed until basically the + + + align:start position:0% +completely unnoticed until basically the +West heard about it, America and Europe, + + align:start position:0% +West heard about it, America and Europe, + + + align:start position:0% +West heard about it, America and Europe, +because I think it showed up on like + + align:start position:0% +because I think it showed up on like + + + align:start position:0% +because I think it showed up on like +Amazon.com or something at some point. + + align:start position:0% +Amazon.com or something at some point. + + + align:start position:0% +Amazon.com or something at some point. +And of course there was a gigantic + + align:start position:0% +And of course there was a gigantic + + + align:start position:0% +And of course there was a gigantic +controversy and the media blew it up + + align:start position:0% +controversy and the media blew it up + + + align:start position:0% +controversy and the media blew it up +completely. And so then in Japan I think + + align:start position:0% +completely. And so then in Japan I think + + + align:start position:0% +completely. And so then in Japan I think +I think it was it banned in Japan I + + align:start position:0% +I think it was it banned in Japan I + + + align:start position:0% +I think it was it banned in Japan I +think. + + align:start position:0% +think. + + + align:start position:0% +think. +>> No. + + align:start position:0% +>> No. + + + align:start position:0% +>> No. +>> So something like Japanese politicians + + align:start position:0% +>> So something like Japanese politicians + + + align:start position:0% +>> So something like Japanese politicians +out for a while like negative attention + + align:start position:0% +out for a while like negative attention + + + align:start position:0% +out for a while like negative attention +all the time. + + align:start position:0% +all the time. + + + align:start position:0% +all the time. +>> Apparently like Japanese politicians + + align:start position:0% +>> Apparently like Japanese politicians + + + align:start position:0% +>> Apparently like Japanese politicians +started cracking down on these types of + + align:start position:0% +started cracking down on these types of + + + align:start position:0% +started cracking down on these types of +games and a lot of fans got like really + + align:start position:0% +games and a lot of fans got like really + + + align:start position:0% +games and a lot of fans got like really +angry and they said well this is just + + align:start position:0% +angry and they said well this is just + + + align:start position:0% +angry and they said well this is just +like your western eur eurosentric view. + + align:start position:0% +like your western eur eurosentric view. + + + align:start position:0% +like your western eur eurosentric view. +It's like and why is this backlashing + + align:start position:0% +It's like and why is this backlashing + + + align:start position:0% +It's like and why is this backlashing +onto us kind of thing. The only reason + + align:start position:0% +onto us kind of thing. The only reason + + + align:start position:0% +onto us kind of thing. The only reason +why there was a backlash was because of + + align:start position:0% +why there was a backlash was because of + + + align:start position:0% +why there was a backlash was because of +political attention, not necessarily + + align:start position:0% +political attention, not necessarily + + + align:start position:0% +political attention, not necessarily +because of moral. + + align:start position:0% +because of moral. + + + align:start position:0% +because of moral. +>> Well, I mean, a lot of our moral + + align:start position:0% +>> Well, I mean, a lot of our moral + + + align:start position:0% +>> Well, I mean, a lot of our moral +framework is sort of Judeo-Christian in + + align:start position:0% +framework is sort of Judeo-Christian in + + + align:start position:0% +framework is sort of Judeo-Christian in +nature. + + align:start position:0% +nature. + + + align:start position:0% +nature. +And I was I read an entire entire + + align:start position:0% +And I was I read an entire entire + + + align:start position:0% +And I was I read an entire entire +Wikipedia article on such things + + align:start position:0% +Wikipedia article on such things + + + align:start position:0% +Wikipedia article on such things +afterwards. Uh, child pornography + + align:start position:0% +afterwards. Uh, child pornography + + + align:start position:0% +afterwards. Uh, child pornography +as as long as it doesn't actually use + + align:start position:0% +as as long as it doesn't actually use + + + align:start position:0% +as as long as it doesn't actually use +child actors. So like representations, + + align:start position:0% +child actors. So like representations, + + + align:start position:0% +child actors. So like representations, +animated, 3D, whatever, is not illegal + + align:start position:0% +animated, 3D, whatever, is not illegal + + + align:start position:0% +animated, 3D, whatever, is not illegal +in Japan. U and and there's no real + + align:start position:0% +in Japan. U and and there's no real + + + align:start position:0% +in Japan. U and and there's no real +political pressure either to make it + + align:start position:0% +political pressure either to make it + + + align:start position:0% +political pressure either to make it +illegal. It's just not part of the + + align:start position:0% +illegal. It's just not part of the + + + align:start position:0% +illegal. It's just not part of the +public consciousness that's something + + align:start position:0% +public consciousness that's something + + + align:start position:0% +public consciousness that's something +that needs to be made illegal. Um + + align:start position:0% +that needs to be made illegal. Um + + + align:start position:0% +that needs to be made illegal. Um +and and the point is not a a weird point + + align:start position:0% +and and the point is not a a weird point + + + align:start position:0% +and and the point is not a a weird point +like completely crazy that that you know + + align:start position:0% +like completely crazy that that you know + + + align:start position:0% +like completely crazy that that you know +killing people is probably the worst + + align:start position:0% +killing people is probably the worst + + + align:start position:0% +killing people is probably the worst +crime and and you know and the West + + align:start position:0% +crime and and you know and the West + + + align:start position:0% +crime and and you know and the West +makes games advocate that all the time. + + align:start position:0% + + + + align:start position:0% + +>> So the question + + align:start position:0% +>> So the question + + + align:start position:0% +>> So the question +Well, in the radio interview with that + + align:start position:0% +Well, in the radio interview with that + + + align:start position:0% +Well, in the radio interview with that +answer + + align:start position:0% +answer + + + align:start position:0% +answer +question in terms of like the question + + align:start position:0% +question in terms of like the question + + + align:start position:0% +question in terms of like the question +of uh whether or not a game crosses a + + align:start position:0% +of uh whether or not a game crosses a + + + align:start position:0% +of uh whether or not a game crosses a +line first assumes that there is a line + + align:start position:0% +line first assumes that there is a line + + + align:start position:0% +line first assumes that there is a line +to be crossed and + + align:start position:0% +to be crossed and + + + align:start position:0% +to be crossed and +>> I guess second I guess my answer would + + align:start position:0% +>> I guess second I guess my answer would + + + align:start position:0% +>> I guess second I guess my answer would +be yes there is a line but that line is + + align:start position:0% +be yes there is a line but that line is + + + align:start position:0% +be yes there is a line but that line is +basically whether or not people buy the + + align:start position:0% +basically whether or not people buy the + + + align:start position:0% +basically whether or not people buy the +game. If people buy the game, the game + + align:start position:0% +game. If people buy the game, the game + + + align:start position:0% +game. If people buy the game, the game +hasn't really crossed the line. + + align:start position:0% +hasn't really crossed the line. + + + align:start position:0% +hasn't really crossed the line. +>> So, see this image reminds me of like + + align:start position:0% +>> So, see this image reminds me of like + + + align:start position:0% +>> So, see this image reminds me of like +the video reminds me of remember the + + align:start position:0% +the video reminds me of remember the + + + align:start position:0% +the video reminds me of remember the +game of 9/11 where you are a person on + + align:start position:0% +game of 9/11 where you are a person on + + + align:start position:0% +game of 9/11 where you are a person on +one of the top floors. + + align:start position:0% +one of the top floors. + + + align:start position:0% +one of the top floors. +>> Oh, you can jump. + + align:start position:0% +>> Oh, you can jump. + + + align:start position:0% +>> Oh, you can jump. +>> Yeah. Well, that's the only way to end + + align:start position:0% +>> Yeah. Well, that's the only way to end + + + align:start position:0% +>> Yeah. Well, that's the only way to end +the game. You can go anywhere you want, + + align:start position:0% +the game. You can go anywhere you want, + + + align:start position:0% +the game. You can go anywhere you want, +but there's no escape. And so, the only + + align:start position:0% +but there's no escape. And so, the only + + + align:start position:0% +but there's no escape. And so, the only +way to end the game is to jump out of + + align:start position:0% +way to end the game is to jump out of + + + align:start position:0% +way to end the game is to jump out of +window. + + align:start position:0% +window. + + + align:start position:0% +window. +>> And that that had the same response. I + + align:start position:0% +>> And that that had the same response. I + + + align:start position:0% +>> And that that had the same response. I +think + + align:start position:0% +think + + + align:start position:0% +think +>> I was just going to say back on the + + align:start position:0% +>> I was just going to say back on the + + + align:start position:0% +>> I was just going to say back on the +point of like is there a line or not? I + + align:start position:0% +point of like is there a line or not? I + + + align:start position:0% +point of like is there a line or not? I +think the line is not a line on whether + + align:start position:0% +think the line is not a line on whether + + + align:start position:0% +think the line is not a line on whether +like it becomes okay or not. It's a line + + align:start position:0% +like it becomes okay or not. It's a line + + + align:start position:0% +like it becomes okay or not. It's a line +between I know we've mentioned this + + align:start position:0% +between I know we've mentioned this + + + align:start position:0% +between I know we've mentioned this +before, but like between like + + align:start position:0% +before, but like between like + + + align:start position:0% +before, but like between like +pornography and art. Like like there's a + + align:start position:0% +pornography and art. Like like there's a + + + align:start position:0% +pornography and art. Like like there's a +line like if you're you know there's + + align:start position:0% +line like if you're you know there's + + + align:start position:0% +line like if you're you know there's +there's ways to like take pictures of + + align:start position:0% +there's ways to like take pictures of + + + align:start position:0% +there's ways to like take pictures of +like naked human bodies and like it's + + align:start position:0% +like naked human bodies and like it's + + + align:start position:0% +like naked human bodies and like it's +artful like people respect it and all + + align:start position:0% +artful like people respect it and all + + + align:start position:0% +artful like people respect it and all +that. And like there's there's ways in + + align:start position:0% +that. And like there's there's ways in + + + align:start position:0% +that. And like there's there's ways in +games to represent killing and rape and + + align:start position:0% +games to represent killing and rape and + + + align:start position:0% +games to represent killing and rape and +all that kind of stuff in a way that + + align:start position:0% +all that kind of stuff in a way that + + + align:start position:0% +all that kind of stuff in a way that +provides a message within this framework + + align:start position:0% +provides a message within this framework + + + align:start position:0% +provides a message within this framework +that makes it okay. And there were + + align:start position:0% +that makes it okay. And there were + + + align:start position:0% +that makes it okay. And there were +there's like there's games where like + + align:start position:0% +there's like there's games where like + + + align:start position:0% +there's like there's games where like +you know I think Manhunt was one of + + align:start position:0% +you know I think Manhunt was one of + + + align:start position:0% +you know I think Manhunt was one of +these where it's like there's no real + + align:start position:0% +these where it's like there's no real + + + align:start position:0% +these where it's like there's no real +like point other than just like + + align:start position:0% +like point other than just like + + + align:start position:0% +like point other than just like +displaying just terrible terrible images + + align:start position:0% +displaying just terrible terrible images + + + align:start position:0% +displaying just terrible terrible images +for the sake of displaying them. And + + align:start position:0% +for the sake of displaying them. And + + + align:start position:0% +for the sake of displaying them. And +like in my mind it's very very similar + + align:start position:0% +like in my mind it's very very similar + + + align:start position:0% +like in my mind it's very very similar +to like the discussion of like is that + + align:start position:0% +to like the discussion of like is that + + + align:start position:0% +to like the discussion of like is that +image like pornography art and so I + + align:start position:0% +image like pornography art and so I + + + align:start position:0% +image like pornography art and so I +think that's that's the right way to go + + align:start position:0% +think that's that's the right way to go + + + align:start position:0% +think that's that's the right way to go +with this kind of thing in particular. + + align:start position:0% +with this kind of thing in particular. + + + align:start position:0% +with this kind of thing in particular. +Like I feel that there's this question + + align:start position:0% +Like I feel that there's this question + + + align:start position:0% +Like I feel that there's this question +of like is it doing anything meaningful + + align:start position:0% +of like is it doing anything meaningful + + + align:start position:0% +of like is it doing anything meaningful +in the game other than just being + + align:start position:0% +in the game other than just being + + + align:start position:0% +in the game other than just being +virtuous and in this case it's + + align:start position:0% +virtuous and in this case it's + + + align:start position:0% +virtuous and in this case it's +definitely yes like it progresses the + + align:start position:0% +definitely yes like it progresses the + + + align:start position:0% +definitely yes like it progresses the +plot um kind of + + align:start position:0% +plot um kind of + + + align:start position:0% +plot um kind of +makes you think I guess a bit about the + + align:start position:0% +makes you think I guess a bit about the + + + align:start position:0% +makes you think I guess a bit about the +characters that are involved like + + align:start position:0% +characters that are involved like + + + align:start position:0% +characters that are involved like +there's there's actual there's character + + align:start position:0% +there's there's actual there's character + + + align:start position:0% +there's there's actual there's character +development of Marov of Marov here. Um + + align:start position:0% +development of Marov of Marov here. Um + + + align:start position:0% +development of Marov of Marov here. Um +it's showing the shady dealings of the + + align:start position:0% +it's showing the shady dealings of the + + + align:start position:0% +it's showing the shady dealings of the +CIA and all this kind of business. So + + align:start position:0% +CIA and all this kind of business. So + + + align:start position:0% +CIA and all this kind of business. So +like it's also making a political + + align:start position:0% +like it's also making a political + + + align:start position:0% +like it's also making a political +statement at the same time. Um so yeah, + + align:start position:0% +statement at the same time. Um so yeah, + + + align:start position:0% +statement at the same time. Um so yeah, +I mean it's it's not just nailing + + align:start position:0% +I mean it's it's not just nailing + + + align:start position:0% +I mean it's it's not just nailing +people's eyes to the ceiling or what + + align:start position:0% +people's eyes to the ceiling or what + + + align:start position:0% +people's eyes to the ceiling or what +have you. + + align:start position:0% +have you. + + + align:start position:0% +have you. +>> I definitely feel like there I I was + + align:start position:0% +>> I definitely feel like there I I was + + + align:start position:0% +>> I definitely feel like there I I was +thinking like are there any games that + + align:start position:0% +thinking like are there any games that + + + align:start position:0% +thinking like are there any games that +are over the line? I definitely imagine + + align:start position:0% +are over the line? I definitely imagine + + + align:start position:0% +are over the line? I definitely imagine +a game would be over the line. Like you + + align:start position:0% +a game would be over the line. Like you + + + align:start position:0% +a game would be over the line. Like you +could imagine if like in Rafe or + + align:start position:0% +could imagine if like in Rafe or + + + align:start position:0% +could imagine if like in Rafe or +whatever it's called there were like a + + align:start position:0% +whatever it's called there were like a + + + align:start position:0% +whatever it's called there were like a +customizable character thing advertised + + align:start position:0% +customizable character thing advertised + + + align:start position:0% +customizable character thing advertised +like rape your neighbors or something + + align:start position:0% +like rape your neighbors or something + + + align:start position:0% +like rape your neighbors or something +like that. I would be uncomfortable with + + align:start position:0% +like that. I would be uncomfortable with + + + align:start position:0% +like that. I would be uncomfortable with +something like that. + + align:start position:0% +something like that. + + + align:start position:0% +something like that. +So I feel like I I almost wanted to say + + align:start position:0% +So I feel like I I almost wanted to say + + + align:start position:0% +So I feel like I I almost wanted to say +that there is no line to make people buy + + align:start position:0% +that there is no line to make people buy + + + align:start position:0% +that there is no line to make people buy +it, but I feel like there are some + + align:start position:0% +it, but I feel like there are some + + + align:start position:0% +it, but I feel like there are some +things where like they would be over the + + align:start position:0% +things where like they would be over the + + + align:start position:0% +things where like they would be over the +line regardless of whether people buy + + align:start position:0% +line regardless of whether people buy + + + align:start position:0% +line regardless of whether people buy +them. + + align:start position:0% +them. + + + align:start position:0% +them. +>> People might even buy them because they + + align:start position:0% +>> People might even buy them because they + + + align:start position:0% +>> People might even buy them because they +are over this line. + + align:start position:0% +are over this line. + + + align:start position:0% +are over this line. +>> Oh yeah, of course. That's why you would + + align:start position:0% +>> Oh yeah, of course. That's why you would + + + align:start position:0% +>> Oh yeah, of course. That's why you would +buy that. + + align:start position:0% +buy that. + + + align:start position:0% +buy that. +>> What about how many of you have uh + + align:start position:0% +>> What about how many of you have uh + + + align:start position:0% +>> What about how many of you have uh +played or seen Super Combine Master RPG? + + align:start position:0% +played or seen Super Combine Master RPG? + + + align:start position:0% +played or seen Super Combine Master RPG? +How many of you have heard of it? + + align:start position:0% +How many of you have heard of it? + + + align:start position:0% +How many of you have heard of it? +>> Okay. I mean, does that game cross a + + align:start position:0% +>> Okay. I mean, does that game cross a + + + align:start position:0% +>> Okay. I mean, does that game cross a +line? + + align:start position:0% +line? + + + align:start position:0% +line? +Can somebody describe this? + + align:start position:0% +Can somebody describe this? + + + align:start position:0% +Can somebody describe this? +>> I mean, I get an idea from the title. + + align:start position:0% + + + + align:start position:0% + +>> Attent it's it's kind of a Super + + align:start position:0% +>> Attent it's it's kind of a Super + + + align:start position:0% +>> Attent it's it's kind of a Super +Nintendo era styled RPG. It's it it has + + align:start position:0% +Nintendo era styled RPG. It's it it has + + + align:start position:0% +Nintendo era styled RPG. It's it it has +you walking around in a sort of Final + + align:start position:0% +you walking around in a sort of Final + + + align:start position:0% +you walking around in a sort of Final +Fantasy Nintendo + + align:start position:0% +Fantasy Nintendo + + + align:start position:0% +Fantasy Nintendo +era kind of graphics with quotes and + + align:start position:0% +era kind of graphics with quotes and + + + align:start position:0% +era kind of graphics with quotes and +dialogue that have been + + align:start position:0% +dialogue that have been + + + align:start position:0% +dialogue that have been +um that have been collected from the + + align:start position:0% +um that have been collected from the + + + align:start position:0% +um that have been collected from the +actual news reports uh or and you know + + align:start position:0% +actual news reports uh or and you know + + + align:start position:0% +actual news reports uh or and you know +the the deliverables um uh diaries and + + align:start position:0% +the the deliverables um uh diaries and + + + align:start position:0% +the the deliverables um uh diaries and +stuff like that + + align:start position:0% +stuff like that + + + align:start position:0% +stuff like that +and uh and yeah it it it it is largely + + align:start position:0% +and uh and yeah it it it it is largely + + + align:start position:0% +and uh and yeah it it it it is largely +about the events leading up to and the + + align:start position:0% +about the events leading up to and the + + + align:start position:0% +about the events leading up to and the +massacre itself and yes you do go around + + align:start position:0% +massacre itself and yes you do go around + + + align:start position:0% +massacre itself and yes you do go around +and I I can't remember whether you + + align:start position:0% +and I I can't remember whether you + + + align:start position:0% +and I I can't remember whether you +actually + + align:start position:0% +actually + + + align:start position:0% +actually +>> you do everything + + align:start position:0% +>> you do everything + + + align:start position:0% +>> you do everything +>> yeah you you shoot + + align:start position:0% +>> yeah you you shoot + + + align:start position:0% +>> yeah you you shoot +You have to plant you you have to sneak + + align:start position:0% +You have to plant you you have to sneak + + + align:start position:0% +You have to plant you you have to sneak +into the school. I forget which one you + + align:start position:0% +into the school. I forget which one you + + + align:start position:0% +into the school. I forget which one you +start off as either, you know, gold or + + align:start position:0% +start off as either, you know, gold or + + + align:start position:0% +start off as either, you know, gold or +Harris, but you you pick up your friend. + + align:start position:0% +Harris, but you you pick up your friend. + + + align:start position:0% +Harris, but you you pick up your friend. +It's very RPG-ish in the beginning where + + align:start position:0% +It's very RPG-ish in the beginning where + + + align:start position:0% +It's very RPG-ish in the beginning where +you're in your room because you touch + + align:start position:0% +you're in your room because you touch + + + align:start position:0% +you're in your room because you touch +objects and it gives flashbacks to like + + align:start position:0% +objects and it gives flashbacks to like + + + align:start position:0% +objects and it gives flashbacks to like +your friendship with this guy like + + align:start position:0% +your friendship with this guy like + + + align:start position:0% +your friendship with this guy like +learning how to make pipe bombs behind + + align:start position:0% +learning how to make pipe bombs behind + + + align:start position:0% +learning how to make pipe bombs behind +the convenience store and you pick them + + align:start position:0% +the convenience store and you pick them + + + align:start position:0% +the convenience store and you pick them +up, you go to the school, you have to + + align:start position:0% +up, you go to the school, you have to + + + align:start position:0% +up, you go to the school, you have to +sneak in and plant some bombs and after + + align:start position:0% +sneak in and plant some bombs and after + + + align:start position:0% +sneak in and plant some bombs and after +those go off and you move through the + + align:start position:0% +those go off and you move through the + + + align:start position:0% +those go off and you move through the +school and you're shooting and um it's + + align:start position:0% +school and you're shooting and um it's + + + align:start position:0% +school and you're shooting and um it's +interesting. Brian fire this five times + + align:start position:0% +interesting. Brian fire this five times + + + align:start position:0% +interesting. Brian fire this five times +now, but I showed it to a class once uh + + align:start position:0% +now, but I showed it to a class once uh + + + align:start position:0% +now, but I showed it to a class once uh +in Ohio, my old school, and + + align:start position:0% +in Ohio, my old school, and + + + align:start position:0% +in Ohio, my old school, and +we're I'm like sneaking into the school, + + align:start position:0% +we're I'm like sneaking into the school, + + + align:start position:0% +we're I'm like sneaking into the school, +right? And there are security cameras + + align:start position:0% +right? And there are security cameras + + + align:start position:0% +right? And there are security cameras +you have to avoid and uh students who + + align:start position:0% +you have to avoid and uh students who + + + align:start position:0% +you have to avoid and uh students who +can't be seen by them either. And + + align:start position:0% +can't be seen by them either. And + + + align:start position:0% +can't be seen by them either. And +there's a point where, you know, I'm + + align:start position:0% +there's a point where, you know, I'm + + + align:start position:0% +there's a point where, you know, I'm +trying to manipulate the character and + + align:start position:0% +trying to manipulate the character and + + + align:start position:0% +trying to manipulate the character and +and everyone class like, "Oh, that way, + + align:start position:0% +and everyone class like, "Oh, that way, + + + align:start position:0% +and everyone class like, "Oh, that way, +that way, that way. Oh, oh, you know, + + align:start position:0% +that way, that way. Oh, oh, you know, + + + align:start position:0% +that way, that way. Oh, oh, you know, +you blew it. You got seen. You got + + align:start position:0% +you blew it. You got seen. You got + + + align:start position:0% +you blew it. You got seen. You got +kicked out. You get it." And it was like + + align:start position:0% +kicked out. You get it." And it was like + + + align:start position:0% +kicked out. You get it." And it was like +this moment of like typical gaming. Ah, + + align:start position:0% +this moment of like typical gaming. Ah, + + + align:start position:0% +this moment of like typical gaming. Ah, +I did it. And then you realize like I + + align:start position:0% +I did it. And then you realize like I + + + align:start position:0% +I did it. And then you realize like I +got kicked out of the school because I + + align:start position:0% +got kicked out of the school because I + + + align:start position:0% +got kicked out of the school because I +was trying to plant a bomb. This was + + align:start position:0% +was trying to plant a bomb. This was + + + align:start position:0% +was trying to plant a bomb. This was +based on something that really happened. + + align:start position:0% +based on something that really happened. + + + align:start position:0% +based on something that really happened. +And it was that moment of like you were + + align:start position:0% +And it was that moment of like you were + + + align:start position:0% +And it was that moment of like you were +saying with the friendly fire and not, + + align:start position:0% +saying with the friendly fire and not, + + + align:start position:0% +saying with the friendly fire and not, +you know, not sure who you're shooting. + + align:start position:0% +you know, not sure who you're shooting. + + + align:start position:0% +you know, not sure who you're shooting. +And it was like, wow. + + align:start position:0% +And it was like, wow. + + + align:start position:0% +And it was like, wow. +>> You know, this is something that made me + + align:start position:0% +>> You know, this is something that made me + + + align:start position:0% +>> You know, this is something that made me +think about what about all those other + + align:start position:0% +think about what about all those other + + + align:start position:0% +think about what about all those other +games where I'm happy to kill people and + + align:start position:0% +games where I'm happy to kill people and + + + align:start position:0% +games where I'm happy to kill people and +I don't really think about the + + align:start position:0% +I don't really think about the + + + align:start position:0% +I don't really think about the +consequences. And this is a game where + + align:start position:0% +consequences. And this is a game where + + + align:start position:0% +consequences. And this is a game where +you were forced to. say I think there's + + align:start position:0% +you were forced to. say I think there's + + + align:start position:0% +you were forced to. say I think there's +a really interesting parallel in a film + + align:start position:0% +a really interesting parallel in a film + + + align:start position:0% +a really interesting parallel in a film +um that I can think of with the battle + + align:start position:0% +um that I can think of with the battle + + + align:start position:0% +um that I can think of with the battle +of Alers. I don't know if you've seen + + align:start position:0% +of Alers. I don't know if you've seen + + + align:start position:0% +of Alers. I don't know if you've seen +this, but so there's this scene where + + align:start position:0% +this, but so there's this scene where + + + align:start position:0% +this, but so there's this scene where +you're following um the insurgents who + + align:start position:0% +you're following um the insurgents who + + + align:start position:0% +you're following um the insurgents who +are these two women who've managed to + + align:start position:0% +are these two women who've managed to + + + align:start position:0% +are these two women who've managed to +smuggle bombs into a cafe which is + + align:start position:0% +smuggle bombs into a cafe which is + + + align:start position:0% +smuggle bombs into a cafe which is +basically just a a civilian hangout + + align:start position:0% +basically just a a civilian hangout + + + align:start position:0% +basically just a a civilian hangout +which is largely um frequented by the + + align:start position:0% +which is largely um frequented by the + + + align:start position:0% +which is largely um frequented by the +the ruling French um section of society + + align:start position:0% +the ruling French um section of society + + + align:start position:0% +the ruling French um section of society +there. And there's this incredibly tense + + align:start position:0% +there. And there's this incredibly tense + + + align:start position:0% +there. And there's this incredibly tense +scene where they're trying to like leave + + align:start position:0% +scene where they're trying to like leave + + + align:start position:0% +scene where they're trying to like leave +their bombs + + align:start position:0% +their bombs + + + align:start position:0% +their bombs +in the cafe without being detected and + + align:start position:0% +in the cafe without being detected and + + + align:start position:0% +in the cafe without being detected and +get out of there. And you're like, "Oh + + align:start position:0% +get out of there. And you're like, "Oh + + + align:start position:0% +get out of there. And you're like, "Oh +my god, + + align:start position:0% +my god, + + + align:start position:0% +my god, +are they going to be able to make it? I + + align:start position:0% +are they going to be able to make it? I + + + align:start position:0% +are they going to be able to make it? I +hope that they can bomb this cafe." And + + align:start position:0% +hope that they can bomb this cafe." And + + + align:start position:0% +hope that they can bomb this cafe." And +you're like, + + align:start position:0% +you're like, + + + align:start position:0% +you're like, +>> "What are they thinking? This is + + align:start position:0% +>> "What are they thinking? This is + + + align:start position:0% +>> "What are they thinking? This is +terrible." + + align:start position:0% +terrible." + + + align:start position:0% +terrible." +And it definitely you definitely have + + align:start position:0% +And it definitely you definitely have + + + align:start position:0% +And it definitely you definitely have +that same kind of tension though. Yeah. + + align:start position:0% +that same kind of tension though. Yeah. + + + align:start position:0% +that same kind of tension though. Yeah. +I feel like people spend devote too much + + align:start position:0% +I feel like people spend devote too much + + + align:start position:0% +I feel like people spend devote too much +emotional energy into getting offended. + + align:start position:0% +emotional energy into getting offended. + + + align:start position:0% +emotional energy into getting offended. +Um people really pour their heart and + + align:start position:0% +Um people really pour their heart and + + + align:start position:0% +Um people really pour their heart and +souls into getting offended by things. + + align:start position:0% +souls into getting offended by things. + + + align:start position:0% +souls into getting offended by things. +Um and the the line for me is is it does + + align:start position:0% +Um and the the line for me is is it does + + + align:start position:0% +Um and the the line for me is is it does +it advocate and is it instructional? + + align:start position:0% +it advocate and is it instructional? + + + align:start position:0% +it advocate and is it instructional? +If it's not either of those two things, + + align:start position:0% +If it's not either of those two things, + + + align:start position:0% +If it's not either of those two things, +it doesn't affect me really. And if you + + align:start position:0% +it doesn't affect me really. And if you + + + align:start position:0% +it doesn't affect me really. And if you +really want to go out and play some + + align:start position:0% +really want to go out and play some + + + align:start position:0% +really want to go out and play some +messed up it's not my none of my + + align:start position:0% +messed up it's not my none of my + + + align:start position:0% +messed up it's not my none of my +business. + + align:start position:0% +business. + + + align:start position:0% +business. +and my line is not going to be the same + + align:start position:0% +and my line is not going to be the same + + + align:start position:0% +and my line is not going to be the same +as your line. It's not going to be the + + align:start position:0% +as your line. It's not going to be the + + + align:start position:0% +as your line. It's not going to be the +same as someone else's line. And because + + align:start position:0% +same as someone else's line. And because + + + align:start position:0% +same as someone else's line. And because +there is no easily definable line, it + + align:start position:0% +there is no easily definable line, it + + + align:start position:0% +there is no easily definable line, it +really scares me that someone could + + align:start position:0% +really scares me that someone could + + + align:start position:0% +really scares me that someone could +define a line. And since since I don't + + align:start position:0% +define a line. And since since I don't + + + align:start position:0% +define a line. And since since I don't +like that idea, I'd rather say that as + + align:start position:0% +like that idea, I'd rather say that as + + + align:start position:0% +like that idea, I'd rather say that as +long as it's not advoc, + + align:start position:0% + + + + align:start position:0% + +you know, my attitudes are so liberal + + align:start position:0% +you know, my attitudes are so liberal + + + align:start position:0% +you know, my attitudes are so liberal +and someone else's attitudes might be so + + align:start position:0% +and someone else's attitudes might be so + + + align:start position:0% +and someone else's attitudes might be so +conservative and oh god, someone else's + + align:start position:0% +conservative and oh god, someone else's + + + align:start position:0% +conservative and oh god, someone else's +attitudes might be even more liberal + + align:start position:0% +attitudes might be even more liberal + + + align:start position:0% +attitudes might be even more liberal +than mine. and be okay with things that + + align:start position:0% +than mine. and be okay with things that + + + align:start position:0% +than mine. and be okay with things that +I wouldn't feel comfortable with. If I + + align:start position:0% +I wouldn't feel comfortable with. If I + + + align:start position:0% +I wouldn't feel comfortable with. If I +was allowed to draw a line, someone else + + align:start position:0% +was allowed to draw a line, someone else + + + align:start position:0% +was allowed to draw a line, someone else +could draw it somewhere, you know, + + align:start position:0% +could draw it somewhere, you know, + + + align:start position:0% +could draw it somewhere, you know, +either before or after, and that would + + align:start position:0% +either before or after, and that would + + + align:start position:0% +either before or after, and that would +just mess everything up. And and so, you + + align:start position:0% +just mess everything up. And and so, you + + + align:start position:0% +just mess everything up. And and so, you +know, that that that's how I kind of + + align:start position:0% +know, that that that's how I kind of + + + align:start position:0% +know, that that that's how I kind of +feel about it. And I think that the + + align:start position:0% +feel about it. And I think that the + + + align:start position:0% +feel about it. And I think that the +environment right now kind of is tends + + align:start position:0% +environment right now kind of is tends + + + align:start position:0% +environment right now kind of is tends +towards that. Um, in that + + align:start position:0% +towards that. Um, in that + + + align:start position:0% +towards that. Um, in that +>> what + + align:start position:0% +>> what + + + align:start position:0% +>> what +>> the the line drawing the + + align:start position:0% +>> the the line drawing the + + + align:start position:0% +>> the the line drawing the +>> tends towards line drawing. + + align:start position:0% +>> tends towards line drawing. + + + align:start position:0% +>> tends towards line drawing. +>> Yeah. People in general are not people + + align:start position:0% +>> Yeah. People in general are not people + + + align:start position:0% +>> Yeah. People in general are not people +who make games are not intrinsically on + + align:start position:0% +who make games are not intrinsically on + + + align:start position:0% +who make games are not intrinsically on +average really messed up and so tend to + + align:start position:0% +average really messed up and so tend to + + + align:start position:0% +average really messed up and so tend to +make stuff that they feel generally + + align:start position:0% +make stuff that they feel generally + + + align:start position:0% +make stuff that they feel generally +comfortable with. Uh and those who are + + align:start position:0% +comfortable with. Uh and those who are + + + align:start position:0% +comfortable with. Uh and those who are +messed up, you know, I mean you just + + align:start position:0% +messed up, you know, I mean you just + + + align:start position:0% +messed up, you know, I mean you just +draw attention to them really by giving + + align:start position:0% +draw attention to them really by giving + + + align:start position:0% +draw attention to them really by giving +them publicity anyway. But but uh for + + align:start position:0% +them publicity anyway. But but uh for + + + align:start position:0% +them publicity anyway. But but uh for +every person who says that that you know + + align:start position:0% +every person who says that that you know + + + align:start position:0% +every person who says that that you know +what what game like Diablo II got an M + + align:start position:0% +what what game like Diablo II got an M + + + align:start position:0% +what what game like Diablo II got an M +rating because of violence. Now if you + + align:start position:0% +rating because of violence. Now if you + + + align:start position:0% +rating because of violence. Now if you +look at it today, it's like little + + align:start position:0% +look at it today, it's like little + + + align:start position:0% +look at it today, it's like little +sprites whacking at each other, you + + align:start position:0% +sprites whacking at each other, you + + + align:start position:0% +sprites whacking at each other, you +know, but that was the line back then. + + align:start position:0% +know, but that was the line back then. + + + align:start position:0% +know, but that was the line back then. +and and if that's the line today then + + align:start position:0% +and and if that's the line today then + + + align:start position:0% +and and if that's the line today then +that this stuff is is just absolutely + + align:start position:0% +that this stuff is is just absolutely + + + align:start position:0% +that this stuff is is just absolutely +horrendous and should not be + + align:start position:0% +horrendous and should not be + + + align:start position:0% +horrendous and should not be +disseminated. I think it should be and + + align:start position:0% +disseminated. I think it should be and + + + align:start position:0% +disseminated. I think it should be and +someone else might think that what I + + align:start position:0% +someone else might think that what I + + + align:start position:0% +someone else might think that what I +think is okay is not okay and it's just + + align:start position:0% +think is okay is not okay and it's just + + + align:start position:0% +think is okay is not okay and it's just +going to be what I think is not okay is + + align:start position:0% +going to be what I think is not okay is + + + align:start position:0% +going to be what I think is not okay is +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +it's very complicated. + + align:start position:0% +it's very complicated. + + + align:start position:0% +it's very complicated. +>> Just got to get death threats. + + align:start position:0% +>> Just got to get death threats. + + + align:start position:0% +>> Just got to get death threats. +>> Yeah. + + align:start position:0% +>> Yeah. + + + align:start position:0% +>> Yeah. +>> For releasing this game. I I strongly + + align:start position:0% +>> For releasing this game. I I strongly + + + align:start position:0% +>> For releasing this game. I I strongly +like to + + align:start position:0% +like to + + + align:start position:0% +like to +uh to to agree with the a lot of effort + + align:start position:0% +uh to to agree with the a lot of effort + + + align:start position:0% +uh to to agree with the a lot of effort +being put into the line drawing u and + + align:start position:0% +being put into the line drawing u and + + + align:start position:0% +being put into the line drawing u and +especially public discussion + + align:start position:0% +especially public discussion + + + align:start position:0% +especially public discussion +uh the the the public display of hand + + align:start position:0% +uh the the the public display of hand + + + align:start position:0% +uh the the the public display of hand +drawing the line here mostly by + + align:start position:0% +drawing the line here mostly by + + + align:start position:0% +drawing the line here mostly by +politicians but people with with some + + align:start position:0% +politicians but people with with some + + + align:start position:0% +politicians but people with with some +sort of u + + align:start position:0% +sort of u + + + align:start position:0% +sort of u +>> possibly self often self-interested + + align:start position:0% +>> possibly self often self-interested + + + align:start position:0% +>> possibly self often self-interested +agenda you know it's like for um both + + align:start position:0% +agenda you know it's like for um both + + + align:start position:0% +agenda you know it's like for um both +and both by the game industry and + + align:start position:0% +and both by the game industry and + + + align:start position:0% +and both by the game industry and +It seems it seems like there's more + + align:start position:0% +It seems it seems like there's more + + + align:start position:0% +It seems it seems like there's more +effort + + align:start position:0% +effort + + + align:start position:0% +effort +either being used to figure out what is + + align:start position:0% +either being used to figure out what is + + + align:start position:0% +either being used to figure out what is +offensive and what is not offensive than + + align:start position:0% +offensive and what is not offensive than + + + align:start position:0% +offensive and what is not offensive than +to possibly + + align:start position:0% +to possibly + + + align:start position:0% +to possibly +uh to discuss the the the need that some + + align:start position:0% +uh to discuss the the the need that some + + + align:start position:0% +uh to discuss the the the need that some +things can should be able to offend. + + align:start position:0% +things can should be able to offend. + + + align:start position:0% +things can should be able to offend. +Then we should have stuff that allow + + align:start position:0% +Then we should have stuff that allow + + + align:start position:0% +Then we should have stuff that allow +that that that needs to exist. Well, + + align:start position:0% +that that that needs to exist. Well, + + + align:start position:0% +that that that needs to exist. Well, +then because it's so hard to actually + + align:start position:0% +then because it's so hard to actually + + + align:start position:0% +then because it's so hard to actually +figure out where the line is. It's like + + align:start position:0% +figure out where the line is. It's like + + + align:start position:0% +figure out where the line is. It's like +then then there needs to be some stuff + + align:start position:0% +then then there needs to be some stuff + + + align:start position:0% +then then there needs to be some stuff +that crosses because maybe the line you + + align:start position:0% +that crosses because maybe the line you + + + align:start position:0% +that crosses because maybe the line you +can't draw. + + align:start position:0% +can't draw. + + + align:start position:0% +can't draw. +>> Yeah. And it's a method to desensitize + + align:start position:0% +>> Yeah. And it's a method to desensitize + + + align:start position:0% +>> Yeah. And it's a method to desensitize +adults to violence. There's so much + + align:start position:0% +adults to violence. There's so much + + + align:start position:0% +adults to violence. There's so much +violence these days. Be better if you + + align:start position:0% +violence these days. Be better if you + + + align:start position:0% +violence these days. Be better if you +didn't freak out at every level. + + align:start position:0% +didn't freak out at every level. + + + align:start position:0% +didn't freak out at every level. +>> I think it's totally okay to be freaked + + align:start position:0% +>> I think it's totally okay to be freaked + + + align:start position:0% +>> I think it's totally okay to be freaked +out at things. I think that you should + + align:start position:0% +out at things. I think that you should + + + align:start position:0% +out at things. I think that you should +definitely say when you're offended by + + align:start position:0% +definitely say when you're offended by + + + align:start position:0% +definitely say when you're offended by +something and I think that should be + + align:start position:0% +something and I think that should be + + + align:start position:0% +something and I think that should be +open to debate like whether something is + + align:start position:0% +open to debate like whether something is + + + align:start position:0% +open to debate like whether something is +like a decent artistic expression or + + align:start position:0% +like a decent artistic expression or + + + align:start position:0% +like a decent artistic expression or +>> but I mean + + align:start position:0% +>> but I mean + + + align:start position:0% +>> but I mean +>> I mean like so there's there's a + + align:start position:0% +>> I mean like so there's there's a + + + align:start position:0% +>> I mean like so there's there's a +difference between + + align:start position:0% +difference between + + + align:start position:0% +difference between +stating that you find something + + align:start position:0% +stating that you find something + + + align:start position:0% +stating that you find something +offensive and attempting to have these + + align:start position:0% +offensive and attempting to have these + + + align:start position:0% +offensive and attempting to have these +things banned or right so + + align:start position:0% +things banned or right so + + + align:start position:0% +things banned or right so +>> I agree and I'm totally fine with people + + align:start position:0% +>> I agree and I'm totally fine with people + + + align:start position:0% +>> I agree and I'm totally fine with people +wasting words on on saying whether it's + + align:start position:0% +wasting words on on saying whether it's + + + align:start position:0% +wasting words on on saying whether it's +like + + align:start position:0% +like + + + align:start position:0% +like +>> no clearly But as long as because you + + align:start position:0% +>> no clearly But as long as because you + + + align:start position:0% +>> no clearly But as long as because you +are offended, you think I shouldn't be + + align:start position:0% +are offended, you think I shouldn't be + + + align:start position:0% +are offended, you think I shouldn't be +able to look at it. That's that's the + + align:start position:0% +able to look at it. That's that's the + + + align:start position:0% +able to look at it. That's that's the +problem. + + align:start position:0% +problem. + + + align:start position:0% +problem. +>> Okay. + + align:start position:0% +>> Okay. + + + align:start position:0% +>> Okay. +>> Or even or even better, if by by being + + align:start position:0% +>> Or even or even better, if by by being + + + align:start position:0% +>> Or even or even better, if by by being +offended, you get to now make your + + align:start position:0% +offended, you get to now make your + + + align:start position:0% +offended, you get to now make your +point. You know, it's like, you know, + + align:start position:0% +point. You know, it's like, you know, + + + align:start position:0% +point. You know, it's like, you know, +this is this is why this offends me and + + align:start position:0% +this is this is why this offends me and + + + align:start position:0% +this is this is why this offends me and +this is these are my reasons for it + + align:start position:0% +this is these are my reasons for it + + + align:start position:0% +this is these are my reasons for it +might be more informative and actually + + align:start position:0% +might be more informative and actually + + + align:start position:0% +might be more informative and actually +better for society to get that those + + align:start position:0% +better for society to get that those + + + align:start position:0% +better for society to get that those +ideas in the open. + + align:start position:0% +ideas in the open. + + + align:start position:0% +ideas in the open. +>> People also get offended by proxy. This + + align:start position:0% +>> People also get offended by proxy. This + + + align:start position:0% +>> People also get offended by proxy. This +doesn't offend me, but I can see how it + + align:start position:0% +doesn't offend me, but I can see how it + + + align:start position:0% +doesn't offend me, but I can see how it +would affect other + + align:start position:0% +would affect other + + + align:start position:0% +would affect other +>> well and people are I think there's also + + align:start position:0% +>> well and people are I think there's also + + + align:start position:0% +>> well and people are I think there's also +a conflation of of taking offense and + + align:start position:0% +a conflation of of taking offense and + + + align:start position:0% +a conflation of of taking offense and +discomfort. Um because you know playing + + align:start position:0% +discomfort. Um because you know playing + + + align:start position:0% +discomfort. Um because you know playing +these games might be uncomfortable. Um + + align:start position:0% +these games might be uncomfortable. Um + + + align:start position:0% +these games might be uncomfortable. Um +and I don't think that's necessarily a + + align:start position:0% +and I don't think that's necessarily a + + + align:start position:0% +and I don't think that's necessarily a +bad thing, you know, if makes you think + + align:start position:0% +bad thing, you know, if makes you think + + + align:start position:0% +bad thing, you know, if makes you think +about like what Ellen is saying or like + + align:start position:0% +about like what Ellen is saying or like + + + align:start position:0% +about like what Ellen is saying or like +this game combat massacre if it makes + + align:start position:0% +this game combat massacre if it makes + + + align:start position:0% +this game combat massacre if it makes +you think about things in a different + + align:start position:0% +you think about things in a different + + + align:start position:0% +you think about things in a different +way or like that film. I mean, and + + align:start position:0% +way or like that film. I mean, and + + + align:start position:0% +way or like that film. I mean, and +especially games have the ability to + + align:start position:0% +especially games have the ability to + + + align:start position:0% +especially games have the ability to +kind of provoke that in you to make you + + align:start position:0% +kind of provoke that in you to make you + + + align:start position:0% +kind of provoke that in you to make you +think because you're the one, especially + + align:start position:0% +think because you're the one, especially + + + align:start position:0% +think because you're the one, especially +these games that force you to do certain + + align:start position:0% +these games that force you to do certain + + + align:start position:0% +these games that force you to do certain +things. It's like, well, and I mean, + + align:start position:0% +things. It's like, well, and I mean, + + + align:start position:0% +things. It's like, well, and I mean, +think about is there a game that you + + align:start position:0% +think about is there a game that you + + + align:start position:0% +think about is there a game that you +absolutely refuse to play because, you + + align:start position:0% +absolutely refuse to play because, you + + + align:start position:0% +absolutely refuse to play because, you +know, there was something in it that you + + align:start position:0% +know, there was something in it that you + + + align:start position:0% +know, there was something in it that you +just really did not want to do. + + align:start position:0% +just really did not want to do. + + + align:start position:0% +just really did not want to do. +>> So, that's fine. Yeah, I think we'll end + + align:start position:0% +>> So, that's fine. Yeah, I think we'll end + + + align:start position:0% +>> So, that's fine. Yeah, I think we'll end +there. \ No newline at end of file diff --git a/Roj7FVjl-gw.txt b/Roj7FVjl-gw.txt new file mode 100644 index 0000000000000000000000000000000000000000..95765a7c873fe0ac26744a5d1b74b5d53c72996f --- /dev/null +++ b/Roj7FVjl-gw.txt @@ -0,0 +1,9744 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or to view additional + + align:start position:0% +to make a donation or to view additional + + + align:start position:0% +to make a donation or to view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +so what are we going to do today so + + align:start position:0% +so what are we going to do today so + + + align:start position:0% +so what are we going to do today so +today we are going to continue the + + align:start position:0% +today we are going to continue the + + + align:start position:0% +today we are going to continue the +discussion of based on what we have + + align:start position:0% +discussion of based on what we have + + + align:start position:0% +discussion of based on what we have +learned from the diffraction and and + + align:start position:0% +learned from the diffraction and and + + + align:start position:0% +learned from the diffraction and and +also interesting phenomena and we are + + align:start position:0% +also interesting phenomena and we are + + + align:start position:0% +also interesting phenomena and we are +going to make connections to content + + align:start position:0% +going to make connections to content + + + align:start position:0% +going to make connections to content +mechanics and discussion in greater + + align:start position:0% +mechanics and discussion in greater + + + align:start position:0% +mechanics and discussion in greater +detail about this connection and those + + align:start position:0% +detail about this connection and those + + + align:start position:0% +detail about this connection and those +so if time the Lao we are going to cover + + align:start position:0% +so if time the Lao we are going to cover + + + align:start position:0% +so if time the Lao we are going to cover +a few results a few information about + + align:start position:0% +a few results a few information about + + + align:start position:0% +a few results a few information about +gravitational waves as well so last time + + align:start position:0% +gravitational waves as well so last time + + + align:start position:0% +gravitational waves as well so last time +we have discussed diffraction pattern + + align:start position:0% +we have discussed diffraction pattern + + + align:start position:0% +we have discussed diffraction pattern +coming from a laser beam and we + + align:start position:0% +coming from a laser beam and we + + + align:start position:0% +coming from a laser beam and we +discussed about resolution you can see + + align:start position:0% +discussed about resolution you can see + + + align:start position:0% +discussed about resolution you can see +that this is the graph we see last time + + align:start position:0% +that this is the graph we see last time + + + align:start position:0% +that this is the graph we see last time +already in the lecture basically all the + + align:start position:0% +already in the lecture basically all the + + + align:start position:0% +already in the lecture basically all the +point like source coming through a + + align:start position:0% +point like source coming through a + + + align:start position:0% +point like source coming through a +single slit is going to be doing + + align:start position:0% +single slit is going to be doing + + + align:start position:0% +single slit is going to be doing +interference to each other I so + + align:start position:0% +interference to each other I so + + + align:start position:0% +interference to each other I so +basically you see interesting pattern + + align:start position:0% +basically you see interesting pattern + + + align:start position:0% +basically you see interesting pattern +which you have a central peak and and + + align:start position:0% +which you have a central peak and and + + + align:start position:0% +which you have a central peak and and +the constructive the total constructive + + align:start position:0% +the constructive the total constructive + + + align:start position:0% +the constructive the total constructive +interference happens at the center of + + align:start position:0% +interference happens at the center of + + + align:start position:0% +interference happens at the center of +the screen and at some point you have a + + align:start position:0% +the screen and at some point you have a + + + align:start position:0% +the screen and at some point you have a +deep which is actually where destructive + + align:start position:0% +deep which is actually where destructive + + + align:start position:0% +deep which is actually where destructive +total destructive interference actually + + align:start position:0% +total destructive interference actually + + + align:start position:0% +total destructive interference actually +happened and we were able to understand + + align:start position:0% +happened and we were able to understand + + + align:start position:0% +happened and we were able to understand +this with mathematics which we learn by + + align:start position:0% +this with mathematics which we learn by + + + align:start position:0% +this with mathematics which we learn by +Austria another interesting result we + + align:start position:0% +Austria another interesting result we + + + align:start position:0% +Austria another interesting result we +found is that if we shoot a laser beam + + align:start position:0% +found is that if we shoot a laser beam + + + align:start position:0% +found is that if we shoot a laser beam +to the moon all right by now you should + + align:start position:0% +to the moon all right by now you should + + + align:start position:0% +to the moon all right by now you should +be able to conclude that it's not going + + align:start position:0% +be able to conclude that it's not going + + + align:start position:0% +be able to conclude that it's not going +to be a point on the moon instead it's + + align:start position:0% +to be a point on the moon instead it's + + + align:start position:0% +to be a point on the moon instead it's +going to be a spot as large as the whole + + align:start position:0% +going to be a spot as large as the whole + + + align:start position:0% +going to be a spot as large as the whole +mystery state all right so that's + + align:start position:0% +mystery state all right so that's + + + align:start position:0% +mystery state all right so that's +actually another interesting result we + + align:start position:0% +actually another interesting result we + + + align:start position:0% +actually another interesting result we +found from from the discussion last time + + align:start position:0% +found from from the discussion last time + + + align:start position:0% +found from from the discussion last time +and finally we are able to put together + + align:start position:0% +and finally we are able to put together + + + align:start position:0% +and finally we are able to put together +all the things we have learned from the + + align:start position:0% +all the things we have learned from the + + + align:start position:0% +all the things we have learned from the +last few lectures basically you can have + + align:start position:0% +last few lectures basically you can have + + + align:start position:0% +last few lectures basically you can have +at the same time the effect of motifs + + align:start position:0% +at the same time the effect of motifs + + + align:start position:0% +at the same time the effect of motifs +lead + + align:start position:0% +lead + + + align:start position:0% +lead +diffraction interference and also the + + align:start position:0% +diffraction interference and also the + + + align:start position:0% +diffraction interference and also the +the effect of a single slit diffraction + + align:start position:0% +the effect of a single slit diffraction + + + align:start position:0% +the effect of a single slit diffraction +of then put together then you have this + + align:start position:0% +of then put together then you have this + + + align:start position:0% +of then put together then you have this +complicated but also beautiful pattern + + align:start position:0% +complicated but also beautiful pattern + + + align:start position:0% +complicated but also beautiful pattern +which you will be able to observe on the + + align:start position:0% +which you will be able to observe on the + + + align:start position:0% +which you will be able to observe on the +screen and basically the point is that + + align:start position:0% +screen and basically the point is that + + + align:start position:0% +screen and basically the point is that +you are going to have for example in + + align:start position:0% +you are going to have for example in + + + align:start position:0% +you are going to have for example in +this case face the interference pattern + + align:start position:0% +this case face the interference pattern + + + align:start position:0% +this case face the interference pattern +but that is actually modulated the end + + align:start position:0% +but that is actually modulated the end + + + align:start position:0% +but that is actually modulated the end +the intensity is actually modulated by + + align:start position:0% +the intensity is actually modulated by + + + align:start position:0% +the intensity is actually modulated by +the pattern from a single slit + + align:start position:0% +the pattern from a single slit + + + align:start position:0% +the pattern from a single slit +diffraction okay so that is actually + + align:start position:0% +diffraction okay so that is actually + + + align:start position:0% +diffraction okay so that is actually +what we have learned from the last + + align:start position:0% +what we have learned from the last + + + align:start position:0% +what we have learned from the last +lecture coming back to the original + + align:start position:0% +lecture coming back to the original + + + align:start position:0% +lecture coming back to the original +question why do we study al 3 right the + + align:start position:0% +question why do we study al 3 right the + + + align:start position:0% +question why do we study al 3 right the +reason is that we would like to + + align:start position:0% +reason is that we would like to + + + align:start position:0% +reason is that we would like to +understand we would like to hear from + + align:start position:0% +understand we would like to hear from + + + align:start position:0% +understand we would like to hear from +the universe right so we cannot even + + align:start position:0% +the universe right so we cannot even + + + align:start position:0% +the universe right so we cannot even +recognize the universe without using + + align:start position:0% +recognize the universe without using + + + align:start position:0% +recognize the universe without using +waves and vibrations so that's the cool + + align:start position:0% +waves and vibrations so that's the cool + + + align:start position:0% +waves and vibrations so that's the cool +thing which we which we have been doing + + align:start position:0% +thing which we which we have been doing + + + align:start position:0% +thing which we which we have been doing +here and we have seen waves of matters + + align:start position:0% +here and we have seen waves of matters + + + align:start position:0% +here and we have seen waves of matters +right so for example here we have this + + align:start position:0% +right so for example here we have this + + + align:start position:0% +right so for example here we have this +water wave generator you can see water + + align:start position:0% +water wave generator you can see water + + + align:start position:0% +water wave generator you can see water +waves we have this pair lab machine + + align:start position:0% +waves we have this pair lab machine + + + align:start position:0% +waves we have this pair lab machine +which you can see the coupled oscillator + + align:start position:0% +which you can see the coupled oscillator + + + align:start position:0% +which you can see the coupled oscillator +multiple coupled oscillator and they are + + align:start position:0% +multiple coupled oscillator and they are + + + align:start position:0% +multiple coupled oscillator and they are +doing their job together to form + + align:start position:0% +doing their job together to form + + + align:start position:0% +doing their job together to form +beautiful waves and you can see those + + align:start position:0% +beautiful waves and you can see those + + + align:start position:0% +beautiful waves and you can see those +beautiful results from there last time + + align:start position:0% +beautiful results from there last time + + + align:start position:0% +beautiful results from there last time +we also and also the including the last + + align:start position:0% +we also and also the including the last + + + align:start position:0% +we also and also the including the last +few lectures we have been using this + + align:start position:0% +few lectures we have been using this + + + align:start position:0% +few lectures we have been using this +laser to produce interesting + + align:start position:0% +laser to produce interesting + + + align:start position:0% +laser to produce interesting +interference pattern in the diffraction + + align:start position:0% +interference pattern in the diffraction + + + align:start position:0% +interference pattern in the diffraction +pattern okay so that's the second kind + + align:start position:0% +pattern okay so that's the second kind + + + align:start position:0% +pattern okay so that's the second kind +of wave which we actually encounter the + + align:start position:0% +of wave which we actually encounter the + + + align:start position:0% +of wave which we actually encounter the +first kind is the waves of matters the + + align:start position:0% +first kind is the waves of matters the + + + align:start position:0% +first kind is the waves of matters the +second kind is waves of what waves of + + align:start position:0% +second kind is waves of what waves of + + + align:start position:0% +second kind is waves of what waves of +vector field right it's not matter + + align:start position:0% +vector field right it's not matter + + + align:start position:0% +vector field right it's not matter +anymore because this fear this + + align:start position:0% +anymore because this fear this + + + align:start position:0% +anymore because this fear this +oscillation of fear can also travel + + align:start position:0% +oscillation of fear can also travel + + + align:start position:0% +oscillation of fear can also travel +through vacuum right so that is actually + + align:start position:0% +through vacuum right so that is actually + + + align:start position:0% +through vacuum right so that is actually +a second kind of wave which way I should + + align:start position:0% +a second kind of wave which way I should + + + align:start position:0% +a second kind of wave which way I should +learn from history they provide a + + align:start position:0% +learn from history they provide a + + + align:start position:0% +learn from history they provide a +completely adequate description of the + + align:start position:0% +completely adequate description of the + + + align:start position:0% +completely adequate description of the +nature a description of the phenomena + + align:start position:0% +nature a description of the phenomena + + + align:start position:0% +nature a description of the phenomena +which we can as you measure can see from + + align:start position:0% +which we can as you measure can see from + + + align:start position:0% +which we can as you measure can see from +the experiment from the experiment we + + align:start position:0% +the experiment from the experiment we + + + align:start position:0% +the experiment from the experiment we +went over so what I would like to say in + + align:start position:0% +went over so what I would like to say in + + + align:start position:0% +went over so what I would like to say in +the lecture today is that there are two + + align:start position:0% +the lecture today is that there are two + + + align:start position:0% +the lecture today is that there are two +kinds of completely different waves + + align:start position:0% +kinds of completely different waves + + + align:start position:0% +kinds of completely different waves +which we haven't talked about the first + + align:start position:0% +which we haven't talked about the first + + + align:start position:0% +which we haven't talked about the first +one is the probability density wave + + align:start position:0% +one is the probability density wave + + + align:start position:0% +one is the probability density wave +which I will cover that in a few moment + + align:start position:0% +which I will cover that in a few moment + + + align:start position:0% +which I will cover that in a few moment +the second one is gravitational waves + + align:start position:0% +the second one is gravitational waves + + + align:start position:0% +the second one is gravitational waves +this is actually a spacetime distortion + + align:start position:0% +this is actually a spacetime distortion + + + align:start position:0% +this is actually a spacetime distortion +coming from the motion of massive + + align:start position:0% +coming from the motion of massive + + + align:start position:0% +coming from the motion of massive +objects and we would like to see what we + + align:start position:0% +objects and we would like to see what we + + + align:start position:0% +objects and we would like to see what we +can also learn from there using the + + align:start position:0% +can also learn from there using the + + + align:start position:0% +can also learn from there using the +existing knowledge which we have learned + + align:start position:0% +existing knowledge which we have learned + + + align:start position:0% +existing knowledge which we have learned +from metal wave and the vector field + + align:start position:0% +from metal wave and the vector field + + + align:start position:0% +from metal wave and the vector field +waves and that they are actually pretty + + align:start position:0% +waves and that they are actually pretty + + + align:start position:0% +waves and that they are actually pretty +similar to each other if you don't get + + align:start position:0% +similar to each other if you don't get + + + align:start position:0% +similar to each other if you don't get +their behavior so the first thing which + + align:start position:0% +their behavior so the first thing which + + + align:start position:0% +their behavior so the first thing which +I would like to discuss is light so far + + align:start position:0% +I would like to discuss is light so far + + + align:start position:0% +I would like to discuss is light so far +what is light light is like + + align:start position:0% +what is light light is like + + + align:start position:0% +what is light light is like +electromagnetic waves right so that's + + align:start position:0% +electromagnetic waves right so that's + + + align:start position:0% +electromagnetic waves right so that's +essentially what we have learned so far + + align:start position:0% +essentially what we have learned so far + + + align:start position:0% +essentially what we have learned so far +from AO 2 and L 3 so they are like waves + + align:start position:0% +from AO 2 and L 3 so they are like waves + + + align:start position:0% +from AO 2 and L 3 so they are like waves +their waves all right + + align:start position:0% +their waves all right + + + align:start position:0% +their waves all right +on the other hand in the 20th century + + align:start position:0% +on the other hand in the 20th century + + + align:start position:0% +on the other hand in the 20th century +there are many many crises going on okay + + align:start position:0% +there are many many crises going on okay + + + align:start position:0% +there are many many crises going on okay +so so the first thing which is happening + + align:start position:0% +so so the first thing which is happening + + + align:start position:0% +so so the first thing which is happening +is photo electric effect so this + + align:start position:0% +is photo electric effect so this + + + align:start position:0% +is photo electric effect so this +experimental result was actually first + + align:start position:0% +experimental result was actually first + + + align:start position:0% +experimental result was actually first +cub discovered by Hertz so he found that + + align:start position:0% +cub discovered by Hertz so he found that + + + align:start position:0% +cub discovered by Hertz so he found that +if you want to kick one electron out of + + align:start position:0% +if you want to kick one electron out of + + + align:start position:0% +if you want to kick one electron out of +some material or some charge the + + align:start position:0% +some material or some charge the + + + align:start position:0% +some material or some charge the +material it is easy + + align:start position:0% +material it is easy + + + align:start position:0% +material it is easy +if you use a high-frequency light + + align:start position:0% +if you use a high-frequency light + + + align:start position:0% +if you use a high-frequency light +compared to low frequency light okay so + + align:start position:0% +compared to low frequency light okay so + + + align:start position:0% +compared to low frequency light okay so +that's really really strange right + + align:start position:0% +that's really really strange right + + + align:start position:0% +that's really really strange right +because based on waves and also the + + align:start position:0% +because based on waves and also the + + + align:start position:0% +because based on waves and also the +intensity formula what we really care + + align:start position:0% +intensity formula what we really care + + + align:start position:0% +intensity formula what we really care +right intensity is proportional to the + + align:start position:0% +right intensity is proportional to the + + + align:start position:0% +right intensity is proportional to the +square of the electric field amplitude + + align:start position:0% +square of the electric field amplitude + + + align:start position:0% +square of the electric field amplitude +right so that's a 2 what we I should + + align:start position:0% +right so that's a 2 what we I should + + + align:start position:0% +right so that's a 2 what we I should +learn from the previous lectures but + + align:start position:0% +learn from the previous lectures but + + + align:start position:0% +learn from the previous lectures but +what hers was saying is that the + + align:start position:0% +what hers was saying is that the + + + align:start position:0% +what hers was saying is that the +frequency also matters ok so that's + + align:start position:0% +frequency also matters ok so that's + + + align:start position:0% +frequency also matters ok so that's +really a big really strange and Einstein + + align:start position:0% +really a big really strange and Einstein + + + align:start position:0% +really a big really strange and Einstein +is accounting and explain his photo + + align:start position:0% +is accounting and explain his photo + + + align:start position:0% +is accounting and explain his photo +electric effect okay so what he found is + + align:start position:0% +electric effect okay so what he found is + + + align:start position:0% +electric effect okay so what he found is +that this effect can be explained by + + align:start position:0% +that this effect can be explained by + + + align:start position:0% +that this effect can be explained by +viewing the flight as smoke want us ok + + align:start position:0% +viewing the flight as smoke want us ok + + + align:start position:0% +viewing the flight as smoke want us ok +and the light is actually not like waves + + align:start position:0% +and the light is actually not like waves + + + align:start position:0% +and the light is actually not like waves +anymore but like contests + + align:start position:0% +anymore but like contests + + + align:start position:0% +anymore but like contests +small contest discrete ones with energy + + align:start position:0% +small contest discrete ones with energy + + + align:start position:0% +small contest discrete ones with energy +proportional to the frequency all right + + align:start position:0% +proportional to the frequency all right + + + align:start position:0% +proportional to the frequency all right +the and basically the elect the energy + + align:start position:0% +the and basically the elect the energy + + + align:start position:0% +the and basically the elect the energy +of those little canta or say we now call + + align:start position:0% +of those little canta or say we now call + + + align:start position:0% +of those little canta or say we now call +them photon is actually equal to H which + + align:start position:0% +them photon is actually equal to H which + + + align:start position:0% +them photon is actually equal to H which +is constant it's or some constant relate + + align:start position:0% +is constant it's or some constant relate + + + align:start position:0% +is constant it's or some constant relate +the frequency and the energy of the + + align:start position:0% +the frequency and the energy of the + + + align:start position:0% +the frequency and the energy of the +contact ok and with this explanation + + align:start position:0% +contact ok and with this explanation + + + align:start position:0% +contact ok and with this explanation +the the view is that the photons are + + align:start position:0% +the the view is that the photons are + + + align:start position:0% +the the view is that the photons are +like particles and therefore he can + + align:start position:0% +like particles and therefore he can + + + align:start position:0% +like particles and therefore he can +actually explain that ok if I measure + + align:start position:0% +actually explain that ok if I measure + + + align:start position:0% +actually explain that ok if I measure +the kinetic energy the maximum kinetic + + align:start position:0% +the kinetic energy the maximum kinetic + + + align:start position:0% +the kinetic energy the maximum kinetic +energy of the of the electron which + + align:start position:0% + + + + align:start position:0% + +electrons which are kicked out from this + + align:start position:0% +electrons which are kicked out from this + + + align:start position:0% +electrons which are kicked out from this +photo electric effect experiment ok I + + align:start position:0% +photo electric effect experiment ok I + + + align:start position:0% +photo electric effect experiment ok I +call it + + align:start position:0% +call it + + + align:start position:0% +call it +max what what are you do what you are + + align:start position:0% +max what what are you do what you are + + + align:start position:0% +max what what are you do what you are +going to get is a formula like this the + + align:start position:0% +going to get is a formula like this the + + + align:start position:0% +going to get is a formula like this the +Maxima kinetic energy of electron will + + align:start position:0% +Maxima kinetic energy of electron will + + + align:start position:0% +Maxima kinetic energy of electron will +be equal to H bar nu minus Phi Phi's H + + align:start position:0% +be equal to H bar nu minus Phi Phi's H + + + align:start position:0% +be equal to H bar nu minus Phi Phi's H +is some kind of stray show which you + + align:start position:0% +is some kind of stray show which you + + + align:start position:0% +is some kind of stray show which you +need over say some kind of energy which + + align:start position:0% +need over say some kind of energy which + + + align:start position:0% +need over say some kind of energy which +you need to overcome to kick one + + align:start position:0% +you need to overcome to kick one + + + align:start position:0% +you need to overcome to kick one +electron out of there the material okay + + align:start position:0% +electron out of there the material okay + + + align:start position:0% +electron out of there the material okay +so you can see from here that if the if + + align:start position:0% +so you can see from here that if the if + + + align:start position:0% +so you can see from here that if the if +the frequency of the light is too low + + align:start position:0% +the frequency of the light is too low + + + align:start position:0% +the frequency of the light is too low +then this will never work because the + + align:start position:0% +then this will never work because the + + + align:start position:0% +then this will never work because the +kinetic energy the Maxima can actually + + align:start position:0% +kinetic energy the Maxima can actually + + + align:start position:0% +kinetic energy the Maxima can actually +energy will be below zero therefore you + + align:start position:0% +energy will be below zero therefore you + + + align:start position:0% +energy will be below zero therefore you +cannot kick out of electron all right + + align:start position:0% +cannot kick out of electron all right + + + align:start position:0% +cannot kick out of electron all right +but if the frequency is high as shown by + + align:start position:0% +but if the frequency is high as shown by + + + align:start position:0% +but if the frequency is high as shown by +hertz experiment it is possible and also + + align:start position:0% +hertz experiment it is possible and also + + + align:start position:0% +hertz experiment it is possible and also +you can create energetic kinetic energy + + align:start position:0% +you can create energetic kinetic energy + + + align:start position:0% +you can create energetic kinetic energy +of electron have been kicked out of the + + align:start position:0% +of electron have been kicked out of the + + + align:start position:0% +of electron have been kicked out of the +material okay and this is actually + + align:start position:0% +material okay and this is actually + + + align:start position:0% +material okay and this is actually +verified by experiment and that is + + align:start position:0% +verified by experiment and that is + + + align:start position:0% +verified by experiment and that is +actually why Einstein I should get a + + align:start position:0% +actually why Einstein I should get a + + + align:start position:0% +actually why Einstein I should get a +Nobel Prize in 1921 so let me tell you + + align:start position:0% +Nobel Prize in 1921 so let me tell you + + + align:start position:0% +Nobel Prize in 1921 so let me tell you +what the fitting here the fitting here + + align:start position:0% +what the fitting here the fitting here + + + align:start position:0% +what the fitting here the fitting here +is that now things are really becoming + + align:start position:0% +is that now things are really becoming + + + align:start position:0% +is that now things are really becoming +more and more interesting because first + + align:start position:0% +more and more interesting because first + + + align:start position:0% +more and more interesting because first +of all we see really well that the + + align:start position:0% +of all we see really well that the + + + align:start position:0% +of all we see really well that the +electromagnetic waves describe the + + align:start position:0% +electromagnetic waves describe the + + + align:start position:0% +electromagnetic waves describe the +behavior of light with this DC + + align:start position:0% +behavior of light with this DC + + + align:start position:0% +behavior of light with this DC +diffraction we see interference + + align:start position:0% +diffraction we see interference + + + align:start position:0% +diffraction we see interference +all those things can be explained by the + + align:start position:0% +all those things can be explained by the + + + align:start position:0% +all those things can be explained by the +beautiful mathematics which we have been + + align:start position:0% +beautiful mathematics which we have been + + + align:start position:0% +beautiful mathematics which we have been +employing to explain all those results + + align:start position:0% +employing to explain all those results + + + align:start position:0% +employing to explain all those results +but here you can see that at the same + + align:start position:0% +but here you can see that at the same + + + align:start position:0% +but here you can see that at the same +time the photons are very good tour or + + align:start position:0% +time the photons are very good tour or + + + align:start position:0% +time the photons are very good tour or +very good viewpoint to explain the + + align:start position:0% +very good viewpoint to explain the + + + align:start position:0% +very good viewpoint to explain the +photoelectric feel fat so that can + + align:start position:0% +photoelectric feel fat so that can + + + align:start position:0% +photoelectric feel fat so that can +actually last a should be really + + align:start position:0% +actually last a should be really + + + align:start position:0% +actually last a should be really +surprising because that means you have + + align:start position:0% +surprising because that means you have + + + align:start position:0% +surprising because that means you have +suddenly post kind of explanation of the + + align:start position:0% +suddenly post kind of explanation of the + + + align:start position:0% +suddenly post kind of explanation of the +light + + align:start position:0% +light + + + align:start position:0% +light +which should be only to be described in + + align:start position:0% +which should be only to be described in + + + align:start position:0% +which should be only to be described in +the sensing right so now you are one one + + align:start position:0% +the sensing right so now you are one one + + + align:start position:0% +the sensing right so now you are one one +one idea is to take focus is quite learn + + align:start position:0% +one idea is to take focus is quite learn + + + align:start position:0% +one idea is to take focus is quite learn +by waves the other the ideas to describe + + align:start position:0% +by waves the other the ideas to describe + + + align:start position:0% +by waves the other the ideas to describe +them by particles and also at the same + + align:start position:0% +them by particles and also at the same + + + align:start position:0% +them by particles and also at the same +time as we actually discussed in the + + align:start position:0% +time as we actually discussed in the + + + align:start position:0% +time as we actually discussed in the +previous lecture we can do a to sleet + + align:start position:0% +previous lecture we can do a to sleet + + + align:start position:0% +previous lecture we can do a to sleet +interfere a two-slit experiment with PD + + align:start position:0% +interfere a two-slit experiment with PD + + + align:start position:0% +interfere a two-slit experiment with PD +abort or I will put it suppose we do + + align:start position:0% +abort or I will put it suppose we do + + + align:start position:0% +abort or I will put it suppose we do +this experiment we fire the pause or put + + align:start position:0% +this experiment we fire the pause or put + + + align:start position:0% +this experiment we fire the pause or put +it through some source and we have some + + align:start position:0% +it through some source and we have some + + + align:start position:0% +it through some source and we have some +kind of to sleep setup here okay so that + + align:start position:0% +kind of to sleep setup here okay so that + + + align:start position:0% +kind of to sleep setup here okay so that +the Buddha tour report can actually pass + + align:start position:0% +the Buddha tour report can actually pass + + + align:start position:0% +the Buddha tour report can actually pass +through and then we will wonder the what + + align:start position:0% +through and then we will wonder the what + + + align:start position:0% +through and then we will wonder the what +would be the pattern which we see from + + align:start position:0% +would be the pattern which we see from + + + align:start position:0% +would be the pattern which we see from +the detector in the right hand side then + + align:start position:0% +the detector in the right hand side then + + + align:start position:0% +the detector in the right hand side then +basically what we see is the following + + align:start position:0% +basically what we see is the following + + + align:start position:0% +basically what we see is the following +so basically we have a distribution of + + align:start position:0% +so basically we have a distribution of + + + align:start position:0% +so basically we have a distribution of +the pause from come in France lead + + align:start position:0% +the pause from come in France lead + + + align:start position:0% +the pause from come in France lead +number one and we have another + + align:start position:0% +number one and we have another + + + align:start position:0% +number one and we have another +distribution of both which is actually + + align:start position:0% +distribution of both which is actually + + + align:start position:0% +distribution of both which is actually +coming from three number two and I can + + align:start position:0% +coming from three number two and I can + + + align:start position:0% +coming from three number two and I can +call it p1 and p2 which is actually the + + align:start position:0% +call it p1 and p2 which is actually the + + + align:start position:0% +call it p1 and p2 which is actually the +probability density distribution of the + + align:start position:0% +probability density distribution of the + + + align:start position:0% +probability density distribution of the +experimental result and if the the final + + align:start position:0% +experimental result and if the the final + + + align:start position:0% +experimental result and if the the final +result or say if you just look at the + + align:start position:0% +result or say if you just look at the + + + align:start position:0% +result or say if you just look at the +distribution of balls without separating + + align:start position:0% +distribution of balls without separating + + + align:start position:0% +distribution of balls without separating +from this from the mean the post from + + align:start position:0% +from this from the mean the post from + + + align:start position:0% +from this from the mean the post from +its dilemma whence the number two + + align:start position:0% +its dilemma whence the number two + + + align:start position:0% +its dilemma whence the number two +basically you get some distribution like + + align:start position:0% +basically you get some distribution like + + + align:start position:0% +basically you get some distribution like +this which is a superposition of p1 and + + align:start position:0% +this which is a superposition of p1 and + + + align:start position:0% +this which is a superposition of p1 and +p2 distributions okay all these things + + align:start position:0% +p2 distributions okay all these things + + + align:start position:0% +p2 distributions okay all these things +doesn't surprise anybody right the + + align:start position:0% +doesn't surprise anybody right the + + + align:start position:0% +doesn't surprise anybody right the +experiment the experiment one which we + + align:start position:0% +experiment the experiment one which we + + + align:start position:0% +experiment the experiment one which we +perform with now instead of PD opposed + + align:start position:0% +perform with now instead of PD opposed + + + align:start position:0% +perform with now instead of PD opposed +now we perform the same experiment it + + align:start position:0% +now we perform the same experiment it + + + align:start position:0% +now we perform the same experiment it +with electrons + + align:start position:0% +with electrons + + + align:start position:0% +with electrons +and again we have all those electrons + + align:start position:0% +and again we have all those electrons + + + align:start position:0% +and again we have all those electrons +pass through this to sleep in to sleet + + align:start position:0% +pass through this to sleep in to sleet + + + align:start position:0% +pass through this to sleep in to sleet +experiment as we actually see before + + align:start position:0% +experiment as we actually see before + + + align:start position:0% +experiment as we actually see before +basically again we can actually separate + + align:start position:0% +basically again we can actually separate + + + align:start position:0% +basically again we can actually separate +electrons from the first lead which I + + align:start position:0% +electrons from the first lead which I + + + align:start position:0% +electrons from the first lead which I +call it I won and the electrons coming + + align:start position:0% +call it I won and the electrons coming + + + align:start position:0% +call it I won and the electrons coming +from the intensity of electrons coming + + align:start position:0% +from the intensity of electrons coming + + + align:start position:0% +from the intensity of electrons coming +from the second lead okay which I call + + align:start position:0% +from the second lead okay which I call + + + align:start position:0% +from the second lead okay which I call +it I to them basically if you can + + align:start position:0% +it I to them basically if you can + + + align:start position:0% +it I to them basically if you can +identify and make sure that the electron + + align:start position:0% +identify and make sure that the electron + + + align:start position:0% +identify and make sure that the electron +is coming from one of this lead you are + + align:start position:0% +is coming from one of this lead you are + + + align:start position:0% +is coming from one of this lead you are +going to get distribution like this okay + + align:start position:0% +going to get distribution like this okay + + + align:start position:0% +going to get distribution like this okay +and of course I can always write this I + + align:start position:0% +and of course I can always write this I + + + align:start position:0% +and of course I can always write this I +want as some wave function Phi 1 squared + + align:start position:0% +want as some wave function Phi 1 squared + + + align:start position:0% +want as some wave function Phi 1 squared +right and I can always write this I 2 + + align:start position:0% +right and I can always write this I 2 + + + align:start position:0% +right and I can always write this I 2 +which is the intensity as a function of + + align:start position:0% +which is the intensity as a function of + + + align:start position:0% +which is the intensity as a function of +position of the electron coming from the + + align:start position:0% +position of the electron coming from the + + + align:start position:0% +position of the electron coming from the +second sleet okay I can always write it + + align:start position:0% +second sleet okay I can always write it + + + align:start position:0% +second sleet okay I can always write it +down as side two square okay in in in + + align:start position:0% +down as side two square okay in in in + + + align:start position:0% +down as side two square okay in in in +the case of light it's actually just + + align:start position:0% +the case of light it's actually just + + + align:start position:0% +the case of light it's actually just +proportional to lay electric field right + + align:start position:0% +proportional to lay electric field right + + + align:start position:0% +proportional to lay electric field right +okay so if you accept this and now you + + align:start position:0% +okay so if you accept this and now you + + + align:start position:0% +okay so if you accept this and now you +actually don't measure where the + + align:start position:0% +actually don't measure where the + + + align:start position:0% +actually don't measure where the +electron actually pass through when the + + align:start position:0% +electron actually pass through when the + + + align:start position:0% +electron actually pass through when the +electron the from the source pass + + align:start position:0% +electron the from the source pass + + + align:start position:0% +electron the from the source pass +through this experiment okay we now + + align:start position:0% +through this experiment okay we now + + + align:start position:0% +through this experiment okay we now +don't measure if I pass through one or + + align:start position:0% +don't measure if I pass through one or + + + align:start position:0% +don't measure if I pass through one or +two then the pattern becomes like this + + align:start position:0% +two then the pattern becomes like this + + + align:start position:0% +two then the pattern becomes like this +you have something like this which is + + align:start position:0% +you have something like this which is + + + align:start position:0% +you have something like this which is +actually very very similar to the two + + align:start position:0% +actually very very similar to the two + + + align:start position:0% +actually very very similar to the two +slit interference experimental result of + + align:start position:0% +slit interference experimental result of + + + align:start position:0% +slit interference experimental result of +the of the laser experiment as you can + + align:start position:0% +the of the laser experiment as you can + + + align:start position:0% +the of the laser experiment as you can +as you see from this experimental result + + align:start position:0% +as you see from this experimental result + + + align:start position:0% +as you see from this experimental result +you see some kind of pattern you have a + + align:start position:0% +you see some kind of pattern you have a + + + align:start position:0% +you see some kind of pattern you have a +peak you have the belly as a function of + + align:start position:0% +peak you have the belly as a function of + + + align:start position:0% +peak you have the belly as a function of +position in + + align:start position:0% +position in + + + align:start position:0% +position in +tatata and we can actually code this I 1 + + align:start position:0% +tatata and we can actually code this I 1 + + + align:start position:0% +tatata and we can actually code this I 1 +2 which is actually when you don't + + align:start position:0% +2 which is actually when you don't + + + align:start position:0% +2 which is actually when you don't +matter or say - you don't identify which + + align:start position:0% +matter or say - you don't identify which + + + align:start position:0% +matter or say - you don't identify which +need the electron count goes through + + align:start position:0% +need the electron count goes through + + + align:start position:0% +need the electron count goes through +then you have the intensity which is + + align:start position:0% +then you have the intensity which is + + + align:start position:0% +then you have the intensity which is +actually code I want to and what we + + align:start position:0% +actually code I want to and what we + + + align:start position:0% +actually code I want to and what we +actually found is that I 1 2 is actually + + align:start position:0% +actually found is that I 1 2 is actually + + + align:start position:0% +actually found is that I 1 2 is actually +not i1 + i2 + + align:start position:0% +not i1 + i2 + + + align:start position:0% +not i1 + i2 +okay what we found is that I 1 2 is a + + align:start position:0% +okay what we found is that I 1 2 is a + + + align:start position:0% +okay what we found is that I 1 2 is a +shoddy psy 1 plus I 2 squared okay so + + align:start position:0% +shoddy psy 1 plus I 2 squared okay so + + + align:start position:0% +shoddy psy 1 plus I 2 squared okay so +basically we see interference pattern + + align:start position:0% +basically we see interference pattern + + + align:start position:0% +basically we see interference pattern +and this will be equal to i1 plus i2 + + align:start position:0% +and this will be equal to i1 plus i2 + + + align:start position:0% +and this will be equal to i1 plus i2 +plus 2 square root of I 1 plus I 2 and + + align:start position:0% +plus 2 square root of I 1 plus I 2 and + + + align:start position:0% +plus 2 square root of I 1 plus I 2 and +the cosine there where the theta is + + align:start position:0% +the cosine there where the theta is + + + align:start position:0% +the cosine there where the theta is +coming from the path length difference + + align:start position:0% +coming from the path length difference + + + align:start position:0% +coming from the path length difference +okay so based on this experimental + + align:start position:0% +okay so based on this experimental + + + align:start position:0% +okay so based on this experimental +result this is actually really + + align:start position:0% +result this is actually really + + + align:start position:0% +result this is actually really +surprising + + align:start position:0% +surprising + + + align:start position:0% +surprising +first of all electrons arriving like a + + align:start position:0% +first of all electrons arriving like a + + + align:start position:0% +first of all electrons arriving like a +particle right because we can see from + + align:start position:0% +particle right because we can see from + + + align:start position:0% +particle right because we can see from +from this slide okay if you look at the + + align:start position:0% +from this slide okay if you look at the + + + align:start position:0% +from this slide okay if you look at the +upper lab figure you see - - - every + + align:start position:0% +upper lab figure you see - - - every + + + align:start position:0% +upper lab figure you see - - - every +time you have something hitting the + + align:start position:0% +time you have something hitting the + + + align:start position:0% +time you have something hitting the +screen and you what this is real app + + align:start position:0% +screen and you what this is real app + + + align:start position:0% +screen and you what this is real app +uber is a single heat on the screen + + align:start position:0% +uber is a single heat on the screen + + + align:start position:0% +uber is a single heat on the screen +right therefore the electrons are + + align:start position:0% +right therefore the electrons are + + + align:start position:0% +right therefore the electrons are +arriving like a particle all right + + align:start position:0% +arriving like a particle all right + + + align:start position:0% +arriving like a particle all right +producing a heat in the detector on the + + align:start position:0% +producing a heat in the detector on the + + + align:start position:0% +producing a heat in the detector on the +other hand what we are saying here is + + align:start position:0% +other hand what we are saying here is + + + align:start position:0% +other hand what we are saying here is +that before they hit before they hit the + + align:start position:0% +that before they hit before they hit the + + + align:start position:0% +that before they hit before they hit the +screen okay they are behaving like a + + align:start position:0% +screen okay they are behaving like a + + + align:start position:0% +screen okay they are behaving like a +wave he has interference with itself + + align:start position:0% +wave he has interference with itself + + + align:start position:0% +wave he has interference with itself +like a wave all right so is electron a + + align:start position:0% +like a wave all right so is electron a + + + align:start position:0% +like a wave all right so is electron a +particle or is the electron + + align:start position:0% +particle or is the electron + + + align:start position:0% +particle or is the electron +wave strange + + align:start position:0% +wave strange + + + align:start position:0% +wave strange +the answer is electron is as neither of + + align:start position:0% +the answer is electron is as neither of + + + align:start position:0% +the answer is electron is as neither of +that in reality okay so how about we + + align:start position:0% +that in reality okay so how about we + + + align:start position:0% +that in reality okay so how about we +actually do some more experiment to + + align:start position:0% +actually do some more experiment to + + + align:start position:0% +actually do some more experiment to +convince ourselves what is actually + + align:start position:0% +convince ourselves what is actually + + + align:start position:0% +convince ourselves what is actually +really going up so what we could do as I + + align:start position:0% +really going up so what we could do as I + + + align:start position:0% +really going up so what we could do as I +actually mentioned I can still have the + + align:start position:0% +actually mentioned I can still have the + + + align:start position:0% +actually mentioned I can still have the +electron gun I have electron source in + + align:start position:0% +electron gun I have electron source in + + + align:start position:0% +electron gun I have electron source in +elapids I again I have this two slit + + align:start position:0% +elapids I again I have this two slit + + + align:start position:0% +elapids I again I have this two slit +experiment you okay then what I'm going + + align:start position:0% +experiment you okay then what I'm going + + + align:start position:0% +experiment you okay then what I'm going +to do is to have produce a light source + + align:start position:0% +to do is to have produce a light source + + + align:start position:0% +to do is to have produce a light source +here okay I put a light source there + + align:start position:0% +here okay I put a light source there + + + align:start position:0% +here okay I put a light source there +okay to shine the whole experiment okay + + align:start position:0% +okay to shine the whole experiment okay + + + align:start position:0% +okay to shine the whole experiment okay +then we I was wondering what is going to + + align:start position:0% +then we I was wondering what is going to + + + align:start position:0% +then we I was wondering what is going to +happen to the distribution so if I first + + align:start position:0% +happen to the distribution so if I first + + + align:start position:0% +happen to the distribution so if I first +close the lower sleet see number two and + + align:start position:0% +close the lower sleet see number two and + + + align:start position:0% +close the lower sleet see number two and +only measure the intensity coming from + + align:start position:0% +only measure the intensity coming from + + + align:start position:0% +only measure the intensity coming from +street number one then this is a + + align:start position:0% +street number one then this is a + + + align:start position:0% +street number one then this is a +distribution I get which is i1 if I + + align:start position:0% +distribution I get which is i1 if I + + + align:start position:0% +distribution I get which is i1 if I +close the upper one and open only the + + align:start position:0% +close the upper one and open only the + + + align:start position:0% +close the upper one and open only the +lower one I get a distribution which is + + align:start position:0% +lower one I get a distribution which is + + + align:start position:0% +lower one I get a distribution which is +i2 okay + + align:start position:0% +i2 okay + + + align:start position:0% +i2 okay +and this light source is actually + + align:start position:0% +and this light source is actually + + + align:start position:0% +and this light source is actually +interacting with the electron when + + align:start position:0% +interacting with the electron when + + + align:start position:0% +interacting with the electron when +electron pass through this to eat what + + align:start position:0% +electron pass through this to eat what + + + align:start position:0% +electron pass through this to eat what +is going to happen is that you will see + + align:start position:0% +is going to happen is that you will see + + + align:start position:0% +is going to happen is that you will see +some scattered a light coming from last + + align:start position:0% +some scattered a light coming from last + + + align:start position:0% +some scattered a light coming from last +lead therefore you can know which slit + + align:start position:0% +lead therefore you can know which slit + + + align:start position:0% +lead therefore you can know which slit +the electronic pass through okay + + align:start position:0% +the electronic pass through okay + + + align:start position:0% +the electronic pass through okay +and we if I do this experimental result + + align:start position:0% +and we if I do this experimental result + + + align:start position:0% +and we if I do this experimental result +if I pluck one of the this lead this is + + align:start position:0% +if I pluck one of the this lead this is + + + align:start position:0% +if I pluck one of the this lead this is +a distribution I 1 and I 2 and now I'm + + align:start position:0% +a distribution I 1 and I 2 and now I'm + + + align:start position:0% +a distribution I 1 and I 2 and now I'm +going to open post sleet and + + align:start position:0% +going to open post sleet and + + + align:start position:0% +going to open post sleet and +you see light coming out of the street + + align:start position:0% +you see light coming out of the street + + + align:start position:0% +you see light coming out of the street +when the electron passed + + align:start position:0% +when the electron passed + + + align:start position:0% +when the electron passed +Sudama wine or cinema - okay you can + + align:start position:0% +Sudama wine or cinema - okay you can + + + align:start position:0% +Sudama wine or cinema - okay you can +identify which need for all the electron + + align:start position:0% +identify which need for all the electron + + + align:start position:0% +identify which need for all the electron +passing through this experiment and the + + align:start position:0% +passing through this experiment and the + + + align:start position:0% +passing through this experiment and the +resulting distribution of electrons on + + align:start position:0% +resulting distribution of electrons on + + + align:start position:0% +resulting distribution of electrons on +the screen is actually like this as I + + align:start position:0% +the screen is actually like this as I + + + align:start position:0% +the screen is actually like this as I +said like I 1 plus I 2 there will be no + + align:start position:0% +said like I 1 plus I 2 there will be no + + + align:start position:0% +said like I 1 plus I 2 there will be no +interference why is that that is because + + align:start position:0% +interference why is that that is because + + + align:start position:0% +interference why is that that is because +you know very precisely which slit the + + align:start position:0% +you know very precisely which slit the + + + align:start position:0% +you know very precisely which slit the +electron as you pass through this + + align:start position:0% +electron as you pass through this + + + align:start position:0% +electron as you pass through this +experiment okay and also say we can say + + align:start position:0% +experiment okay and also say we can say + + + align:start position:0% +experiment okay and also say we can say +that ha the electrons are actually + + align:start position:0% +that ha the electrons are actually + + + align:start position:0% +that ha the electrons are actually +disturbed right therefore they now + + align:start position:0% +disturbed right therefore they now + + + align:start position:0% +disturbed right therefore they now +behave like would it work like a video + + align:start position:0% +behave like would it work like a video + + + align:start position:0% +behave like would it work like a video +pours okay so this is actually a bit + + align:start position:0% +pours okay so this is actually a bit + + + align:start position:0% +pours okay so this is actually a bit +strange right maybe it is because the + + align:start position:0% +strange right maybe it is because the + + + align:start position:0% +strange right maybe it is because the +intensity of the light is too large + + align:start position:0% +intensity of the light is too large + + + align:start position:0% +intensity of the light is too large +therefore is changing the behavior of + + align:start position:0% +therefore is changing the behavior of + + + align:start position:0% +therefore is changing the behavior of +the electron okay so what I we're going + + align:start position:0% +the electron okay so what I we're going + + + align:start position:0% +the electron okay so what I we're going +to do now experimental result number 3 + + align:start position:0% +to do now experimental result number 3 + + + align:start position:0% +to do now experimental result number 3 +is to lower the intensity of the light + + align:start position:0% + + + + align:start position:0% + +so what will happen if I'd lower the + + align:start position:0% +so what will happen if I'd lower the + + + align:start position:0% +so what will happen if I'd lower the +instant intensity of the light source so + + align:start position:0% +instant intensity of the light source so + + + align:start position:0% +instant intensity of the light source so +that we would like to see the behavior + + align:start position:0% +that we would like to see the behavior + + + align:start position:0% +that we would like to see the behavior +as a function of intensity okay + + align:start position:0% +as a function of intensity okay + + + align:start position:0% +as a function of intensity okay +so at some point we'll find that some of + + align:start position:0% +so at some point we'll find that some of + + + align:start position:0% +so at some point we'll find that some of +the electrons are not heated by photon + + align:start position:0% +the electrons are not heated by photon + + + align:start position:0% +the electrons are not heated by photon +or say there will be no scattered light + + align:start position:0% +or say there will be no scattered light + + + align:start position:0% +or say there will be no scattered light +of the electron when he passed through + + align:start position:0% +of the electron when he passed through + + + align:start position:0% +of the electron when he passed through +the experiment because the intensity of + + align:start position:0% +the experiment because the intensity of + + + align:start position:0% +the experiment because the intensity of +the light is too small okay and we + + align:start position:0% +the light is too small okay and we + + + align:start position:0% +the light is too small okay and we +already know of + + align:start position:0% +already know of + + + align:start position:0% +already know of +from photoelectric experiment light is + + align:start position:0% +from photoelectric experiment light is + + + align:start position:0% +from photoelectric experiment light is +actually also like quanta right so when + + align:start position:0% +actually also like quanta right so when + + + align:start position:0% +actually also like quanta right so when +the intensity is low enough the + + align:start position:0% +the intensity is low enough the + + + align:start position:0% +the intensity is low enough the +effectiveness of the light source + + align:start position:0% +effectiveness of the light source + + + align:start position:0% +effectiveness of the light source +decrease okay then the experimental + + align:start position:0% +decrease okay then the experimental + + + align:start position:0% +decrease okay then the experimental +result will be like what can somebody + + align:start position:0% +result will be like what can somebody + + + align:start position:0% +result will be like what can somebody +actually keep gas is that going to be + + align:start position:0% +actually keep gas is that going to be + + + align:start position:0% +actually keep gas is that going to be +like experimental result number one or + + align:start position:0% +like experimental result number one or + + + align:start position:0% +like experimental result number one or +is that going to be like experimental + + align:start position:0% +is that going to be like experimental + + + align:start position:0% +is that going to be like experimental +result number two anybody want to get + + align:start position:0% + + + + align:start position:0% + +very good so the result as I mentioned + + align:start position:0% +very good so the result as I mentioned + + + align:start position:0% +very good so the result as I mentioned +before sometimes the electrons are + + align:start position:0% +before sometimes the electrons are + + + align:start position:0% +before sometimes the electrons are +detected okay by the light source + + align:start position:0% +detected okay by the light source + + + align:start position:0% +detected okay by the light source +sometimes the electrons are lucky they + + align:start position:0% +sometimes the electrons are lucky they + + + align:start position:0% +sometimes the electrons are lucky they +pass through without get hit by a photon + + align:start position:0% +pass through without get hit by a photon + + + align:start position:0% +pass through without get hit by a photon +therefore you cannot know which lead + + align:start position:0% +therefore you cannot know which lead + + + align:start position:0% +therefore you cannot know which lead +actually this electron went through + + align:start position:0% +actually this electron went through + + + align:start position:0% +actually this electron went through +therefore the experimental results if I + + align:start position:0% +therefore the experimental results if I + + + align:start position:0% +therefore the experimental results if I +just lower the intensity of the light + + align:start position:0% +just lower the intensity of the light + + + align:start position:0% +just lower the intensity of the light +source then what I'm going to get is a + + align:start position:0% +source then what I'm going to get is a + + + align:start position:0% +source then what I'm going to get is a +mixture of experimental result number + + align:start position:0% +mixture of experimental result number + + + align:start position:0% +mixture of experimental result number +one and experimental result number two + + align:start position:0% +one and experimental result number two + + + align:start position:0% +one and experimental result number two +when I have the intensity is low enough + + align:start position:0% +when I have the intensity is low enough + + + align:start position:0% +when I have the intensity is low enough +going to really really low intensity + + align:start position:0% +going to really really low intensity + + + align:start position:0% +going to really really low intensity +limit the result will become + + align:start position:0% +limit the result will become + + + align:start position:0% +limit the result will become +experimental result number one because + + align:start position:0% +experimental result number one because + + + align:start position:0% +experimental result number one because +then you are not really detecting the + + align:start position:0% +then you are not really detecting the + + + align:start position:0% +then you are not really detecting the +position of the electrons okay + + align:start position:0% +position of the electrons okay + + + align:start position:0% +position of the electrons okay +finally you can actually also suggest + + align:start position:0% +finally you can actually also suggest + + + align:start position:0% +finally you can actually also suggest +something else right so okay now I have + + align:start position:0% +something else right so okay now I have + + + align:start position:0% +something else right so okay now I have +no intensity of light one way to lower + + align:start position:0% +no intensity of light one way to lower + + + align:start position:0% +no intensity of light one way to lower +the intensity is like what I was saying + + align:start position:0% +the intensity is like what I was saying + + + align:start position:0% +the intensity is like what I was saying +right the rate of the photon emission I + + align:start position:0% +right the rate of the photon emission I + + + align:start position:0% +right the rate of the photon emission I +can make it lower and lower all right + + align:start position:0% +can make it lower and lower all right + + + align:start position:0% +can make it lower and lower all right +there is another way + + align:start position:0% + + + + align:start position:0% + +to do this experimental number four and + + align:start position:0% +to do this experimental number four and + + + align:start position:0% +to do this experimental number four and +its mere mental result number four so + + align:start position:0% +its mere mental result number four so + + + align:start position:0% +its mere mental result number four so +what will happen if I use this formula e + + align:start position:0% +what will happen if I use this formula e + + + align:start position:0% +what will happen if I use this formula e +equal to H bar nu equal to HC divided by + + align:start position:0% +equal to H bar nu equal to HC divided by + + + align:start position:0% +equal to H bar nu equal to HC divided by +lambda right because new is a just C + + align:start position:0% +lambda right because new is a just C + + + align:start position:0% +lambda right because new is a just C +over lambda what will happen if I + + align:start position:0% +over lambda what will happen if I + + + align:start position:0% +over lambda what will happen if I +instead of you know lowering the rate of + + align:start position:0% +instead of you know lowering the rate of + + + align:start position:0% +instead of you know lowering the rate of +photon emission I know where the energy + + align:start position:0% +photon emission I know where the energy + + + align:start position:0% +photon emission I know where the energy +of individual photon how do I do that + + align:start position:0% +of individual photon how do I do that + + + align:start position:0% +of individual photon how do I do that +what I could do is to lower the + + align:start position:0% +what I could do is to lower the + + + align:start position:0% +what I could do is to lower the +frequency of the electromagnetic wave of + + align:start position:0% +frequency of the electromagnetic wave of + + + align:start position:0% +frequency of the electromagnetic wave of +the light source or say increase the + + align:start position:0% +the light source or say increase the + + + align:start position:0% +the light source or say increase the +wavelength of the light source + + align:start position:0% +wavelength of the light source + + + align:start position:0% +wavelength of the light source +okay I can now this is really nice + + align:start position:0% +okay I can now this is really nice + + + align:start position:0% +okay I can now this is really nice +because now I can keep the same rate so + + align:start position:0% +because now I can keep the same rate so + + + align:start position:0% +because now I can keep the same rate so +that I make sure all the electrons are + + align:start position:0% +that I make sure all the electrons are + + + align:start position:0% +that I make sure all the electrons are +bothered by the pile of photon right + + align:start position:0% +bothered by the pile of photon right + + + align:start position:0% +bothered by the pile of photon right +because I can emit very high rate but at + + align:start position:0% +because I can emit very high rate but at + + + align:start position:0% +because I can emit very high rate but at +the same time I can also lower the + + align:start position:0% +the same time I can also lower the + + + align:start position:0% +the same time I can also lower the +intensity so that the intensity is very + + align:start position:0% +intensity so that the intensity is very + + + align:start position:0% +intensity so that the intensity is very +very low can anybody guess what is going + + align:start position:0% +very low can anybody guess what is going + + + align:start position:0% +very low can anybody guess what is going +to happen where the result like + + align:start position:0% +to happen where the result like + + + align:start position:0% +to happen where the result like +experimental result number one when I go + + align:start position:0% +experimental result number one when I go + + + align:start position:0% +experimental result number one when I go +to extremely low intensity or my result + + align:start position:0% +to extremely low intensity or my result + + + align:start position:0% +to extremely low intensity or my result +will be like experimental result number + + align:start position:0% +will be like experimental result number + + + align:start position:0% +will be like experimental result number +two because each electrons are bothered + + align:start position:0% +two because each electrons are bothered + + + align:start position:0% +two because each electrons are bothered +are heated by the light light source by + + align:start position:0% +are heated by the light light source by + + + align:start position:0% +are heated by the light light source by +by the light source the emission from + + align:start position:0% +by the light source the emission from + + + align:start position:0% +by the light source the emission from +the light source anybody want to try + + align:start position:0% +the light source anybody want to try + + + align:start position:0% +the light source anybody want to try +just get us know what I know to for a + + align:start position:0% +just get us know what I know to for a + + + align:start position:0% +just get us know what I know to for a +mixture of them + + align:start position:0% + + + + align:start position:0% + +the gas is that it is going to be like + + align:start position:0% +the gas is that it is going to be like + + + align:start position:0% +the gas is that it is going to be like +to which is essentially well-motivated + + align:start position:0% +to which is essentially well-motivated + + + align:start position:0% +to which is essentially well-motivated +very good try what this actually happen + + align:start position:0% +very good try what this actually happen + + + align:start position:0% +very good try what this actually happen +is that okay I can say who each electron + + align:start position:0% +is that okay I can say who each electron + + + align:start position:0% +is that okay I can say who each electron +apotres by like many many photons right + + align:start position:0% +apotres by like many many photons right + + + align:start position:0% +apotres by like many many photons right +so so okay + + align:start position:0% +so so okay + + + align:start position:0% +so so okay +those are disturbed therefore it has to + + align:start position:0% +those are disturbed therefore it has to + + + align:start position:0% +those are disturbed therefore it has to +look like experimental we block number + + align:start position:0% +look like experimental we block number + + + align:start position:0% +look like experimental we block number +two the answer may surprise you + + align:start position:0% +two the answer may surprise you + + + align:start position:0% +two the answer may surprise you +the answer is that if I have the deme + + align:start position:0% +the answer is that if I have the deme + + + align:start position:0% +the answer is that if I have the deme +lambda goes to infinity nu goes to zero + + align:start position:0% +lambda goes to infinity nu goes to zero + + + align:start position:0% +lambda goes to infinity nu goes to zero +what is going to happen is that no + + align:start position:0% +what is going to happen is that no + + + align:start position:0% +what is going to happen is that no +matter how high frequency of photon + + align:start position:0% +matter how high frequency of photon + + + align:start position:0% +matter how high frequency of photon +emission I have I am going to get the + + align:start position:0% +emission I have I am going to get the + + + align:start position:0% +emission I have I am going to get the +result of experimental number one why is + + align:start position:0% +result of experimental number one why is + + + align:start position:0% +result of experimental number one why is +that that is because when the + + align:start position:0% +that that is because when the + + + align:start position:0% +that that is because when the +wavelengths of the electromagnetic wave + + align:start position:0% +wavelengths of the electromagnetic wave + + + align:start position:0% +wavelengths of the electromagnetic wave +or the photon is going to infinity that + + align:start position:0% +or the photon is going to infinity that + + + align:start position:0% +or the photon is going to infinity that +means you cannot resolve which electron + + align:start position:0% +means you cannot resolve which electron + + + align:start position:0% +means you cannot resolve which electron +which sleet issue in the electron goes + + align:start position:0% +which sleet issue in the electron goes + + + align:start position:0% +which sleet issue in the electron goes +through right because if I I draw the + + align:start position:0% +through right because if I I draw the + + + align:start position:0% +through right because if I I draw the +wave lens here it's going to be like + + align:start position:0% +wave lens here it's going to be like + + + align:start position:0% +wave lens here it's going to be like +this okay + + align:start position:0% +this okay + + + align:start position:0% +this okay +if you observe some kind of light + + align:start position:0% +if you observe some kind of light + + + align:start position:0% +if you observe some kind of light +emission scattered light from the + + align:start position:0% +emission scattered light from the + + + align:start position:0% +emission scattered light from the +electron okay it could come from both + + align:start position:0% +electron okay it could come from both + + + align:start position:0% +electron okay it could come from both +sleet because the wavelength is too long + + align:start position:0% +sleet because the wavelength is too long + + + align:start position:0% +sleet because the wavelength is too long +right so if you go to infinity then it's + + align:start position:0% +right so if you go to infinity then it's + + + align:start position:0% +right so if you go to infinity then it's +like you have a constant electric field + + align:start position:0% +like you have a constant electric field + + + align:start position:0% +like you have a constant electric field +there is that already I should help you + + align:start position:0% +there is that already I should help you + + + align:start position:0% +there is that already I should help you +to identify which sleet the electron as + + align:start position:0% +to identify which sleet the electron as + + + align:start position:0% +to identify which sleet the electron as +you pass through okay + + align:start position:0% +you pass through okay + + + align:start position:0% +you pass through okay +so therefore the interference pattern + + align:start position:0% +so therefore the interference pattern + + + align:start position:0% +so therefore the interference pattern +reappear so this is really crazy thing + + align:start position:0% +reappear so this is really crazy thing + + + align:start position:0% +reappear so this is really crazy thing +if you look at all this for experimental + + align:start position:0% +if you look at all this for experimental + + + align:start position:0% +if you look at all this for experimental +result + + align:start position:0% +result + + + align:start position:0% +result +the conclusion from this for imaginary + + align:start position:0% +the conclusion from this for imaginary + + + align:start position:0% +the conclusion from this for imaginary +experiment is that it is not yet + + align:start position:0% +experiment is that it is not yet + + + align:start position:0% +experiment is that it is not yet +possible to tell the position of the + + align:start position:0% +possible to tell the position of the + + + align:start position:0% +possible to tell the position of the +electron and also at the same time do + + align:start position:0% +electron and also at the same time do + + + align:start position:0% +electron and also at the same time do +not disturb it okay if you would able to + + align:start position:0% +not disturb it okay if you would able to + + + align:start position:0% +not disturb it okay if you would able to +tell the position of the electron then + + align:start position:0% +tell the position of the electron then + + + align:start position:0% +tell the position of the electron then +there will be no interference pattern on + + align:start position:0% +there will be no interference pattern on + + + align:start position:0% +there will be no interference pattern on +the other hand if you our experimental + + align:start position:0% +the other hand if you our experimental + + + align:start position:0% +the other hand if you our experimental +setup have no ability at all to tell if + + align:start position:0% +setup have no ability at all to tell if + + + align:start position:0% +setup have no ability at all to tell if +the electron is coming from three number + + align:start position:0% +the electron is coming from three number + + + align:start position:0% +the electron is coming from three number +one compared to see number two then you + + align:start position:0% +one compared to see number two then you + + + align:start position:0% +one compared to see number two then you +are going to get interference there's + + align:start position:0% +are going to get interference there's + + + align:start position:0% +are going to get interference there's +another thing which I would like to make + + align:start position:0% +another thing which I would like to make + + + align:start position:0% +another thing which I would like to make +connection to the uncertainty principle + + align:start position:0% +connection to the uncertainty principle + + + align:start position:0% +connection to the uncertainty principle +which we should learn from wave and + + align:start position:0% +which we should learn from wave and + + + align:start position:0% +which we should learn from wave and +vibrations so we have learned that + + align:start position:0% +vibrations so we have learned that + + + align:start position:0% +vibrations so we have learned that +Heisenberg's uncertainty principle this + + align:start position:0% +Heisenberg's uncertainty principle this + + + align:start position:0% +Heisenberg's uncertainty principle this +is actually purely coming from the + + align:start position:0% +is actually purely coming from the + + + align:start position:0% +is actually purely coming from the +property of the wave if you actually + + align:start position:0% +property of the wave if you actually + + + align:start position:0% +property of the wave if you actually +remember the deviation which we have + + align:start position:0% +remember the deviation which we have + + + align:start position:0% +remember the deviation which we have +done in the previous lecture so what is + + align:start position:0% +done in the previous lecture so what is + + + align:start position:0% +done in the previous lecture so what is +this uncertainty principle telling us is + + align:start position:0% +this uncertainty principle telling us is + + + align:start position:0% +this uncertainty principle telling us is +that the standard deviation of the + + align:start position:0% +that the standard deviation of the + + + align:start position:0% +that the standard deviation of the +position times the standard deviation of + + align:start position:0% +position times the standard deviation of + + + align:start position:0% +position times the standard deviation of +the momentum okay it's going to be + + align:start position:0% +the momentum okay it's going to be + + + align:start position:0% +the momentum okay it's going to be +greater or equal to H bar over to some + + align:start position:0% +greater or equal to H bar over to some + + + align:start position:0% +greater or equal to H bar over to some +constant and how do we actually + + align:start position:0% +constant and how do we actually + + + align:start position:0% +constant and how do we actually +understand this from the electrons as + + align:start position:0% +understand this from the electrons as + + + align:start position:0% +understand this from the electrons as +experiment that is actually highly + + align:start position:0% +experiment that is actually highly + + + align:start position:0% +experiment that is actually highly +related to the single slit experiment + + align:start position:0% +related to the single slit experiment + + + align:start position:0% +related to the single slit experiment +with electron so what we could do now is + + align:start position:0% +with electron so what we could do now is + + + align:start position:0% +with electron so what we could do now is +to have + + align:start position:0% +to have + + + align:start position:0% +to have +a fifth experiment I have electron + + align:start position:0% +a fifth experiment I have electron + + + align:start position:0% +a fifth experiment I have electron +source here and I have a single sleet + + align:start position:0% +source here and I have a single sleet + + + align:start position:0% +source here and I have a single sleet +and the wheels of this lead is capital P + + align:start position:0% +and the wheels of this lead is capital P + + + align:start position:0% +and the wheels of this lead is capital P +and we were wondering what is going to + + align:start position:0% +and we were wondering what is going to + + + align:start position:0% +and we were wondering what is going to +happen what will be recorded by the + + align:start position:0% +happen what will be recorded by the + + + align:start position:0% +happen what will be recorded by the +smoke detector in the right hand side + + align:start position:0% +smoke detector in the right hand side + + + align:start position:0% +smoke detector in the right hand side +and by now you should not surprise you + + align:start position:0% +and by now you should not surprise you + + + align:start position:0% +and by now you should not surprise you +that this will give you some kind of + + align:start position:0% +that this will give you some kind of + + + align:start position:0% +that this will give you some kind of +diffraction pattern which is actually + + align:start position:0% +diffraction pattern which is actually + + + align:start position:0% +diffraction pattern which is actually +very similar to what we actually observe + + align:start position:0% +very similar to what we actually observe + + + align:start position:0% +very similar to what we actually observe +with laser experiment okay so you can + + align:start position:0% +with laser experiment okay so you can + + + align:start position:0% +with laser experiment okay so you can +see that the electron the momentum now I + + align:start position:0% +see that the electron the momentum now I + + + align:start position:0% +see that the electron the momentum now I +would like to actually define my + + align:start position:0% +would like to actually define my + + + align:start position:0% +would like to actually define my +coordinate system the the the vertical + + align:start position:0% +coordinate system the the the vertical + + + align:start position:0% +coordinate system the the the vertical +direction pointing up where is my X + + align:start position:0% +direction pointing up where is my X + + + align:start position:0% +direction pointing up where is my X +direction okay so now if I have take a + + align:start position:0% +direction okay so now if I have take a + + + align:start position:0% +direction okay so now if I have take a +look at this experimental result so what + + align:start position:0% +look at this experimental result so what + + + align:start position:0% +look at this experimental result so what +this is actually telling us is the + + align:start position:0% +this is actually telling us is the + + + align:start position:0% +this is actually telling us is the +following we know the position of the + + align:start position:0% +following we know the position of the + + + align:start position:0% +following we know the position of the +electron to accuracy to accuracy of the + + align:start position:0% +electron to accuracy to accuracy of the + + + align:start position:0% +electron to accuracy to accuracy of the +width of this sleeve okay which is deep + + align:start position:0% +width of this sleeve okay which is deep + + + align:start position:0% +width of this sleeve okay which is deep +okay so that is actually telling you + + align:start position:0% +okay so that is actually telling you + + + align:start position:0% +okay so that is actually telling you +about the uncertainty in the of the + + align:start position:0% +about the uncertainty in the of the + + + align:start position:0% +about the uncertainty in the of the +position in the X direction okay now + + align:start position:0% +position in the X direction okay now + + + align:start position:0% +position in the X direction okay now +this electron goes through and they + + align:start position:0% +this electron goes through and they + + + align:start position:0% +this electron goes through and they +actually hit the screen and the each + + align:start position:0% +actually hit the screen and the each + + + align:start position:0% +actually hit the screen and the each +electron is having a single pass okay if + + align:start position:0% +electron is having a single pass okay if + + + align:start position:0% +electron is having a single pass okay if +I do get one of the past the upper one + + align:start position:0% +I do get one of the past the upper one + + + align:start position:0% +I do get one of the past the upper one +okay what I am getting is that there + + align:start position:0% +okay what I am getting is that there + + + align:start position:0% +okay what I am getting is that there +must be a momentum which is actually in + + align:start position:0% +must be a momentum which is actually in + + + align:start position:0% +must be a momentum which is actually in +the X direction when this electron pop + + align:start position:0% +the X direction when this electron pop + + + align:start position:0% +the X direction when this electron pop +goes through the slit and hit the screen + + align:start position:0% +goes through the slit and hit the screen + + + align:start position:0% +goes through the slit and hit the screen +okay one interesting thing we learned + + align:start position:0% +okay one interesting thing we learned + + + align:start position:0% +okay one interesting thing we learned +from the deviation from last time is + + align:start position:0% +from the deviation from last time is + + + align:start position:0% +from the deviation from last time is +that if I let's look at the slide here + + align:start position:0% +that if I let's look at the slide here + + + align:start position:0% +that if I let's look at the slide here +if I do get a laugh and sigh slide if I + + align:start position:0% +if I do get a laugh and sigh slide if I + + + align:start position:0% +if I do get a laugh and sigh slide if I +have a very small sleet okay P is small + + align:start position:0% +have a very small sleet okay P is small + + + align:start position:0% +have a very small sleet okay P is small +okay what does that correspond to lark + + align:start position:0% +okay what does that correspond to lark + + + align:start position:0% +okay what does that correspond to lark +corresponds to Delta X goes to very + + align:start position:0% +corresponds to Delta X goes to very + + + align:start position:0% +corresponds to Delta X goes to very +small value case okay we have a very + + align:start position:0% +small value case okay we have a very + + + align:start position:0% +small value case okay we have a very +small Delta X values you are really sure + + align:start position:0% +small Delta X values you are really sure + + + align:start position:0% +small Delta X values you are really sure +where is the electron at some instant of + + align:start position:0% +where is the electron at some instant of + + + align:start position:0% +where is the electron at some instant of +time when it passes through the + + align:start position:0% + + + + align:start position:0% + +experiment okay then what is going to + + align:start position:0% +experiment okay then what is going to + + + align:start position:0% +experiment okay then what is going to +happen if you look at the right hand + + align:start position:0% +happen if you look at the right hand + + + align:start position:0% +happen if you look at the right hand +side the distribution on the screen you + + align:start position:0% +side the distribution on the screen you + + + align:start position:0% +side the distribution on the screen you +will have a wide distribution of the + + align:start position:0% +will have a wide distribution of the + + + align:start position:0% +will have a wide distribution of the +central maxima peak will be very wide + + align:start position:0% +central maxima peak will be very wide + + + align:start position:0% +central maxima peak will be very wide +right so what does that mean that means + + align:start position:0% +right so what does that mean that means + + + align:start position:0% +right so what does that mean that means +you have a wide distribution of momentum + + align:start position:0% +you have a wide distribution of momentum + + + align:start position:0% +you have a wide distribution of momentum +in the X direction right therefore that + + align:start position:0% +in the X direction right therefore that + + + align:start position:0% +in the X direction right therefore that +will give you essentially consistent + + align:start position:0% +will give you essentially consistent + + + align:start position:0% +will give you essentially consistent +with what is actually written here - + + align:start position:0% +with what is actually written here - + + + align:start position:0% +with what is actually written here - +first principle Delta x times Delta P + + align:start position:0% +first principle Delta x times Delta P + + + align:start position:0% +first principle Delta x times Delta P +will be greater or equal to some value + + align:start position:0% +will be greater or equal to some value + + + align:start position:0% +will be greater or equal to some value +on the other hand if I increase the + + align:start position:0% +on the other hand if I increase the + + + align:start position:0% +on the other hand if I increase the +width of the speed the T is now large as + + align:start position:0% +width of the speed the T is now large as + + + align:start position:0% +width of the speed the T is now large as +you are making a T larger and larger + + align:start position:0% +you are making a T larger and larger + + + align:start position:0% +you are making a T larger and larger +what is happening is that the central + + align:start position:0% +what is happening is that the central + + + align:start position:0% +what is happening is that the central +peak the Wiis is actually going to be + + align:start position:0% +peak the Wiis is actually going to be + + + align:start position:0% +peak the Wiis is actually going to be +narrower and narrower right + + align:start position:0% +narrower and narrower right + + + align:start position:0% +narrower and narrower right +that is actually also consistent with + + align:start position:0% +that is actually also consistent with + + + align:start position:0% +that is actually also consistent with +what we have learned from high schools + + align:start position:0% +what we have learned from high schools + + + align:start position:0% +what we have learned from high schools +Heisenberg's uncertainty principle when + + align:start position:0% +Heisenberg's uncertainty principle when + + + align:start position:0% +Heisenberg's uncertainty principle when +Delta X becoming larger okay then the + + align:start position:0% +Delta X becoming larger okay then the + + + align:start position:0% +Delta X becoming larger okay then the +uncertainty or say the distribution of + + align:start position:0% +uncertainty or say the distribution of + + + align:start position:0% +uncertainty or say the distribution of +the momentum in the X Direction becomes + + align:start position:0% +the momentum in the X Direction becomes + + + align:start position:0% +the momentum in the X Direction becomes +smaller okay so now we actually also + + align:start position:0% +smaller okay so now we actually also + + + align:start position:0% +smaller okay so now we actually also +understand will be more + + align:start position:0% +understand will be more + + + align:start position:0% +understand will be more +about what is the single diffraction as + + align:start position:0% +about what is the single diffraction as + + + align:start position:0% +about what is the single diffraction as +you mean and the easiest is really + + align:start position:0% +you mean and the easiest is really + + + align:start position:0% +you mean and the easiest is really +closely connected to the uncertainty + + align:start position:0% +closely connected to the uncertainty + + + align:start position:0% +closely connected to the uncertainty +principle hi separation proposed and if + + align:start position:0% +principle hi separation proposed and if + + + align:start position:0% +principle hi separation proposed and if +we use the mathematics which we learn + + align:start position:0% +we use the mathematics which we learn + + + align:start position:0% +we use the mathematics which we learn +from last time the C function is going + + align:start position:0% +from last time the C function is going + + + align:start position:0% +from last time the C function is going +to be proportional to integration from + + align:start position:0% +to be proportional to integration from + + + align:start position:0% +to be proportional to integration from +minus T over 2 to T over 2 DX + + align:start position:0% +minus T over 2 to T over 2 DX + + + align:start position:0% +minus T over 2 to T over 2 DX +exponential and I KX times X and if I + + align:start position:0% +exponential and I KX times X and if I + + + align:start position:0% +exponential and I KX times X and if I +have T equals to infinity which means + + align:start position:0% +have T equals to infinity which means + + + align:start position:0% +have T equals to infinity which means +that you have an infinitely wide to eat + + align:start position:0% +that you have an infinitely wide to eat + + + align:start position:0% +that you have an infinitely wide to eat +okay based on the formula which we have + + align:start position:0% +okay based on the formula which we have + + + align:start position:0% +okay based on the formula which we have +derived last time basically we will see + + align:start position:0% +derived last time basically we will see + + + align:start position:0% +derived last time basically we will see +that C function as a function of K X is + + align:start position:0% +that C function as a function of K X is + + + align:start position:0% +that C function as a function of K X is +going to be become a delta function and + + align:start position:0% +going to be become a delta function and + + + align:start position:0% +going to be become a delta function and +this Delta function is Delta K X all + + align:start position:0% +this Delta function is Delta K X all + + + align:start position:0% +this Delta function is Delta K X all +right so that means if you have + + align:start position:0% +right so that means if you have + + + align:start position:0% +right so that means if you have +absolutely no idea about the position of + + align:start position:0% +absolutely no idea about the position of + + + align:start position:0% +absolutely no idea about the position of +the electron all right + + align:start position:0% +the electron all right + + + align:start position:0% +the electron all right +you are going to get very very precise + + align:start position:0% +you are going to get very very precise + + + align:start position:0% +you are going to get very very precise +information about the momentum in the X + + align:start position:0% +information about the momentum in the X + + + align:start position:0% +information about the momentum in the X +direction he says you're going to be + + align:start position:0% +direction he says you're going to be + + + align:start position:0% +direction he says you're going to be +equal to 0 + + align:start position:0% +equal to 0 + + + align:start position:0% +equal to 0 +because it's a delta function it's only + + align:start position:0% +because it's a delta function it's only + + + align:start position:0% +because it's a delta function it's only +nonzero at KX which is the direction of + + align:start position:0% +nonzero at KX which is the direction of + + + align:start position:0% +nonzero at KX which is the direction of +propagation equal to 0 any questions so + + align:start position:0% +propagation equal to 0 any questions so + + + align:start position:0% +propagation equal to 0 any questions so +far + + align:start position:0% + + + + align:start position:0% + +ok so from those experimental result we + + align:start position:0% +ok so from those experimental result we + + + align:start position:0% +ok so from those experimental result we +found that the probability okay the + + align:start position:0% +found that the probability okay the + + + align:start position:0% +found that the probability okay the +probability of getting heat on the + + align:start position:0% +probability of getting heat on the + + + align:start position:0% +probability of getting heat on the +screen is proportional to Phi 1 square + + align:start position:0% +screen is proportional to Phi 1 square + + + align:start position:0% +screen is proportional to Phi 1 square +if I only have the first lead there okay + + align:start position:0% +if I only have the first lead there okay + + + align:start position:0% +if I only have the first lead there okay +that means the probability P is + + align:start position:0% +that means the probability P is + + + align:start position:0% +that means the probability P is +proportional to + + align:start position:0% +proportional to + + + align:start position:0% +proportional to +sighs Square and this is actually + + align:start position:0% +sighs Square and this is actually + + + align:start position:0% +sighs Square and this is actually +probably one of the most crazy result in + + align:start position:0% +probably one of the most crazy result in + + + align:start position:0% +probably one of the most crazy result in +the physics we learned so far in some + + align:start position:0% +the physics we learned so far in some + + + align:start position:0% +the physics we learned so far in some +sense it's kind of sad as well why is + + align:start position:0% +sense it's kind of sad as well why is + + + align:start position:0% +sense it's kind of sad as well why is +that + + align:start position:0% +that + + + align:start position:0% +that +this means that okay I can calculate + + align:start position:0% +this means that okay I can calculate + + + align:start position:0% +this means that okay I can calculate +those wave functions and the probability + + align:start position:0% +those wave functions and the probability + + + align:start position:0% +those wave functions and the probability +of Catina + + align:start position:0% +of Catina + + + align:start position:0% +of Catina +alka at a specific position is + + align:start position:0% +alka at a specific position is + + + align:start position:0% +alka at a specific position is +proportional to this wave function + + align:start position:0% +proportional to this wave function + + + align:start position:0% +proportional to this wave function +squared okay but I feel maybe demo D + + align:start position:0% +squared okay but I feel maybe demo D + + + align:start position:0% +squared okay but I feel maybe demo D +right because originally we are like God + + align:start position:0% +right because originally we are like God + + + align:start position:0% +right because originally we are like God +you know you can read it okay I have + + align:start position:0% +you know you can read it okay I have + + + align:start position:0% +you know you can read it okay I have +this scene this object and I have force + + align:start position:0% +this scene this object and I have force + + + align:start position:0% +this scene this object and I have force +and then it goes like oh like this way I + + align:start position:0% +and then it goes like oh like this way I + + + align:start position:0% +and then it goes like oh like this way I +can calculate the trajectory of the the + + align:start position:0% +can calculate the trajectory of the the + + + align:start position:0% +can calculate the trajectory of the the +discharge seen over the place as a + + align:start position:0% +discharge seen over the place as a + + + align:start position:0% +discharge seen over the place as a +function of time and I know what is + + align:start position:0% +function of time and I know what is + + + align:start position:0% +function of time and I know what is +going to happen I have the full control + + align:start position:0% +going to happen I have the full control + + + align:start position:0% +going to happen I have the full control +of all that objects which I have in my + + align:start position:0% +of all that objects which I have in my + + + align:start position:0% +of all that objects which I have in my +hand in my experiment right but now + + align:start position:0% +hand in my experiment right but now + + + align:start position:0% +hand in my experiment right but now +quantum mechanics or this experimental + + align:start position:0% +quantum mechanics or this experimental + + + align:start position:0% +quantum mechanics or this experimental +result tells me that we can only predict + + align:start position:0% +result tells me that we can only predict + + + align:start position:0% +result tells me that we can only predict +the probability the odd right instead of + + align:start position:0% +the probability the odd right instead of + + + align:start position:0% +the probability the odd right instead of +the outcome you see my point + + align:start position:0% +the outcome you see my point + + + align:start position:0% +the outcome you see my point +I can only predict the wave function the + + align:start position:0% +I can only predict the wave function the + + + align:start position:0% +I can only predict the wave function the +distribution of the wave function and + + align:start position:0% +distribution of the wave function and + + + align:start position:0% +distribution of the wave function and +the probability of getting a result here + + align:start position:0% +the probability of getting a result here + + + align:start position:0% +the probability of getting a result here +is proportional to the wave function + + align:start position:0% +is proportional to the wave function + + + align:start position:0% +is proportional to the wave function +squared but I cannot pretty the outcome + + align:start position:0% +squared but I cannot pretty the outcome + + + align:start position:0% +squared but I cannot pretty the outcome +before I do the experiment that's really + + align:start position:0% +before I do the experiment that's really + + + align:start position:0% +before I do the experiment that's really +a big change in your view or si in our + + align:start position:0% +a big change in your view or si in our + + + align:start position:0% +a big change in your view or si in our +current understanding of the physics + + align:start position:0% + + + + align:start position:0% + +you can say that maybe well maybe angie + + align:start position:0% +you can say that maybe well maybe angie + + + align:start position:0% +you can say that maybe well maybe angie +is not working hard enough maybe all + + align:start position:0% +is not working hard enough maybe all + + + align:start position:0% +is not working hard enough maybe all +those electrons which are emitted from + + align:start position:0% +those electrons which are emitted from + + + align:start position:0% +those electrons which are emitted from +the light source sorry from the electron + + align:start position:0% +the light source sorry from the electron + + + align:start position:0% +the light source sorry from the electron +source already made up their mind where + + align:start position:0% +source already made up their mind where + + + align:start position:0% +source already made up their mind where +this electron is going to for example + + align:start position:0% +this electron is going to for example + + + align:start position:0% +this electron is going to for example +electron number Y is doing this mm-hmm + + align:start position:0% +electron number Y is doing this mm-hmm + + + align:start position:0% +electron number Y is doing this mm-hmm +here an electron number 2 I already make + + align:start position:0% +here an electron number 2 I already make + + + align:start position:0% +here an electron number 2 I already make +up this minus 2 equal to 2 this and the + + align:start position:0% +up this minus 2 equal to 2 this and the + + + align:start position:0% +up this minus 2 equal to 2 this and the +electron number 3 is maybe to this and + + align:start position:0% +electron number 3 is maybe to this and + + + align:start position:0% +electron number 3 is maybe to this and +then all those trajectories are already + + align:start position:0% +then all those trajectories are already + + + align:start position:0% +then all those trajectories are already +determined and they are hidden variables + + align:start position:0% +determined and they are hidden variables + + + align:start position:0% +determined and they are hidden variables +which E&G to that No therefore he screw + + align:start position:0% +which E&G to that No therefore he screw + + + align:start position:0% +which E&G to that No therefore he screw +this up and said oh come on you can we + + align:start position:0% +this up and said oh come on you can we + + + align:start position:0% +this up and said oh come on you can we +can only predict the probability right + + align:start position:0% +can only predict the probability right + + + align:start position:0% +can only predict the probability right +but the thing is that from the + + align:start position:0% +but the thing is that from the + + + align:start position:0% +but the thing is that from the +experimental result number to + + align:start position:0% +experimental result number to + + + align:start position:0% +experimental result number to +experimental result and number 4 you can + + align:start position:0% +experimental result and number 4 you can + + + align:start position:0% +experimental result and number 4 you can +see that the electrons cannot make up + + align:start position:0% +see that the electrons cannot make up + + + align:start position:0% +see that the electrons cannot make up +their mind when they are emitted right + + align:start position:0% +their mind when they are emitted right + + + align:start position:0% +their mind when they are emitted right +because when they got hit by the light + + align:start position:0% +because when they got hit by the light + + + align:start position:0% +because when they got hit by the light +the electrons cannot know in advance + + align:start position:0% +the electrons cannot know in advance + + + align:start position:0% +the electrons cannot know in advance +that it is going to be hit by a light + + align:start position:0% +that it is going to be hit by a light + + + align:start position:0% +that it is going to be hit by a light +right and the light in the light can be + + align:start position:0% +right and the light in the light can be + + + align:start position:0% +right and the light in the light can be +a very very mild very very small energy + + align:start position:0% +a very very mild very very small energy + + + align:start position:0% +a very very mild very very small energy +so that you should not affect the + + align:start position:0% +so that you should not affect the + + + align:start position:0% +so that you should not affect the +predetermined path of the electron to + + align:start position:0% +predetermined path of the electron to + + + align:start position:0% +predetermined path of the electron to +get this right so that doesn't make + + align:start position:0% +get this right so that doesn't make + + + align:start position:0% +get this right so that doesn't make +sense + + align:start position:0% +sense + + + align:start position:0% +sense +so it is not because youngji is not is + + align:start position:0% +so it is not because youngji is not is + + + align:start position:0% +so it is not because youngji is not is +tried not trying hard it is really + + align:start position:0% +tried not trying hard it is really + + + align:start position:0% +tried not trying hard it is really +because nobody can really tell before + + align:start position:0% +because nobody can really tell before + + + align:start position:0% +because nobody can really tell before +the experimental result is actually Sean + + align:start position:0% +the experimental result is actually Sean + + + align:start position:0% +the experimental result is actually Sean +or the measurement is already done okay + + align:start position:0% +or the measurement is already done okay + + + align:start position:0% +or the measurement is already done okay +if you can + + align:start position:0% +if you can + + + align:start position:0% +if you can +in any case all right you know maybe we + + align:start position:0% +in any case all right you know maybe we + + + align:start position:0% +in any case all right you know maybe we +will win another 100 Nobel Prize because + + align:start position:0% +will win another 100 Nobel Prize because + + + align:start position:0% +will win another 100 Nobel Prize because +you are showing that the whole + + align:start position:0% +you are showing that the whole + + + align:start position:0% +you are showing that the whole +understanding of quantum mechanics is + + align:start position:0% +understanding of quantum mechanics is + + + align:start position:0% +understanding of quantum mechanics is +not correct + + align:start position:0% +not correct + + + align:start position:0% +not correct +really okay please tell me when you + + align:start position:0% +really okay please tell me when you + + + align:start position:0% +really okay please tell me when you +actually have done this experiment I + + align:start position:0% +actually have done this experiment I + + + align:start position:0% +actually have done this experiment I +would be very proud of you for sure + + align:start position:0% +would be very proud of you for sure + + + align:start position:0% +would be very proud of you for sure +all right so now we are entering a + + align:start position:0% +all right so now we are entering a + + + align:start position:0% +all right so now we are entering a +position to discuss this result so now + + align:start position:0% +position to discuss this result so now + + + align:start position:0% +position to discuss this result so now +actually we can also make use of this + + align:start position:0% +actually we can also make use of this + + + align:start position:0% +actually we can also make use of this +understanding and the printed what would + + align:start position:0% +understanding and the printed what would + + + align:start position:0% +understanding and the printed what would +be the particle probability distribution + + align:start position:0% +be the particle probability distribution + + + align:start position:0% +be the particle probability distribution +in potential well suppose I have an + + align:start position:0% +in potential well suppose I have an + + + align:start position:0% +in potential well suppose I have an +experiment which I have well where I + + align:start position:0% +experiment which I have well where I + + + align:start position:0% +experiment which I have well where I +have potential goes to infinity in the + + align:start position:0% +have potential goes to infinity in the + + + align:start position:0% +have potential goes to infinity in the +lab and side or right hand side edge of + + align:start position:0% +lab and side or right hand side edge of + + + align:start position:0% +lab and side or right hand side edge of +this world and I will define my + + align:start position:0% +this world and I will define my + + + align:start position:0% +this world and I will define my +coordinate system so that the well is as + + align:start position:0% +coordinate system so that the well is as + + + align:start position:0% +coordinate system so that the well is as +you add X equal to 0 or X equal to L all + + align:start position:0% +you add X equal to 0 or X equal to L all + + + align:start position:0% +you add X equal to 0 or X equal to L all +right so by now you when you see this + + align:start position:0% +right so by now you when you see this + + + align:start position:0% +right so by now you when you see this +this is really looks really familiar to + + align:start position:0% +this is really looks really familiar to + + + align:start position:0% +this is really looks really familiar to +you in the center part you have some + + align:start position:0% +you in the center part you have some + + + align:start position:0% +you in the center part you have some +kind of translation see symmetry and at + + align:start position:0% +kind of translation see symmetry and at + + + align:start position:0% +kind of translation see symmetry and at +the boundary those are forbidden region + + align:start position:0% +the boundary those are forbidden region + + + align:start position:0% +the boundary those are forbidden region +you can eyes you they have particle + + align:start position:0% +you can eyes you they have particle + + + align:start position:0% +you can eyes you they have particle +there because the potential is infinity + + align:start position:0% +there because the potential is infinity + + + align:start position:0% +there because the potential is infinity +right therefore this is actually giving + + align:start position:0% +right therefore this is actually giving + + + align:start position:0% +right therefore this is actually giving +you boundary conditions of the wave + + align:start position:0% +you boundary conditions of the wave + + + align:start position:0% +you boundary conditions of the wave +function describing the stay of the + + align:start position:0% +function describing the stay of the + + + align:start position:0% +function describing the stay of the +particle inside these parts so the + + align:start position:0% +particle inside these parts so the + + + align:start position:0% +particle inside these parts so the +boundary condition will be size 0 will + + align:start position:0% +boundary condition will be size 0 will + + + align:start position:0% +boundary condition will be size 0 will +be equal to 0 because this energy at the + + align:start position:0% +be equal to 0 because this energy at the + + + align:start position:0% +be equal to 0 because this energy at the +lapin side edge of the well where you + + align:start position:0% +lapin side edge of the well where you + + + align:start position:0% +lapin side edge of the well where you +have infinitely potential and also you + + align:start position:0% +have infinitely potential and also you + + + align:start position:0% +have infinitely potential and also you +can have side L this will be equal to 0 + + align:start position:0% +can have side L this will be equal to 0 + + + align:start position:0% +can have side L this will be equal to 0 +right because the + + align:start position:0% +right because the + + + align:start position:0% +right because the +the right hand side edge you also have + + align:start position:0% +the right hand side edge you also have + + + align:start position:0% +the right hand side edge you also have +infinitely a man of put of Infini the + + align:start position:0% +infinitely a man of put of Infini the + + + align:start position:0% +infinitely a man of put of Infini the +high potential right therefore when you + + align:start position:0% +high potential right therefore when you + + + align:start position:0% +high potential right therefore when you +see this you were the immediate reaction + + align:start position:0% +see this you were the immediate reaction + + + align:start position:0% +see this you were the immediate reaction +will be + + align:start position:0% +will be + + + align:start position:0% +will be +I know what is this this is a sigh and + + align:start position:0% +I know what is this this is a sigh and + + + align:start position:0% +I know what is this this is a sigh and +the solution to this problem must be + + align:start position:0% +the solution to this problem must be + + + align:start position:0% +the solution to this problem must be +something like sy n of X should be the + + align:start position:0% +something like sy n of X should be the + + + align:start position:0% +something like sy n of X should be the +normal more of this system and it's + + align:start position:0% +normal more of this system and it's + + + align:start position:0% +normal more of this system and it's +going to be a n sine k MX where K n will + + align:start position:0% +going to be a n sine k MX where K n will + + + align:start position:0% +going to be a n sine k MX where K n will +be equal to M pi divided by L where n is + + align:start position:0% +be equal to M pi divided by L where n is + + + align:start position:0% +be equal to M pi divided by L where n is +a number can be 1 2 3 goes to infinity + + align:start position:0% +a number can be 1 2 3 goes to infinity + + + align:start position:0% +a number can be 1 2 3 goes to infinity +right by far you have actually learned + + align:start position:0% +right by far you have actually learned + + + align:start position:0% +right by far you have actually learned +all these practical calculations from + + align:start position:0% +all these practical calculations from + + + align:start position:0% +all these practical calculations from +the previous examples we have therefore + + align:start position:0% +the previous examples we have therefore + + + align:start position:0% +the previous examples we have therefore +what would be the sigh and X as a + + align:start position:0% +what would be the sigh and X as a + + + align:start position:0% +what would be the sigh and X as a +function of time then what I'm going to + + align:start position:0% +function of time then what I'm going to + + + align:start position:0% +function of time then what I'm going to +get is a M sine K M X exponential minus + + align:start position:0% +get is a M sine K M X exponential minus + + + align:start position:0% +get is a M sine K M X exponential minus +I Omega M of course we can also really + + align:start position:0% +I Omega M of course we can also really + + + align:start position:0% +I Omega M of course we can also really +Pratt of those results so for example n + + align:start position:0% +Pratt of those results so for example n + + + align:start position:0% +Pratt of those results so for example n +is equal to 1 basically what you are + + align:start position:0% +is equal to 1 basically what you are + + + align:start position:0% +is equal to 1 basically what you are +getting is like this doesn't surprise + + align:start position:0% +getting is like this doesn't surprise + + + align:start position:0% +getting is like this doesn't surprise +you all right this is as you sigh as a + + align:start position:0% +you all right this is as you sigh as a + + + align:start position:0% +you all right this is as you sigh as a +function of X and n equal to 2 this will + + align:start position:0% +function of X and n equal to 2 this will + + + align:start position:0% +function of X and n equal to 2 this will +correspond toward the situation where + + align:start position:0% +correspond toward the situation where + + + align:start position:0% +correspond toward the situation where +you have one note in the middle right + + align:start position:0% +you have one note in the middle right + + + align:start position:0% +you have one note in the middle right +shì shì you can have many many higher + + align:start position:0% +shì shì you can have many many higher + + + align:start position:0% +shì shì you can have many many higher +math and value solutions and the one + + align:start position:0% +math and value solutions and the one + + + align:start position:0% +math and value solutions and the one +would be the probability to find the + + align:start position:0% +would be the probability to find the + + + align:start position:0% +would be the probability to find the +particle in a specific location as I we + + align:start position:0% +particle in a specific location as I we + + + align:start position:0% +particle in a specific location as I we +mentioned before the probability is + + align:start position:0% +mentioned before the probability is + + + align:start position:0% +mentioned before the probability is +proportional to wave function squared + + align:start position:0% +proportional to wave function squared + + + align:start position:0% +proportional to wave function squared +therefore the probability will be + + align:start position:0% +therefore the probability will be + + + align:start position:0% +therefore the probability will be +proportional to sine square and and one + + align:start position:0% +proportional to sine square and and one + + + align:start position:0% +proportional to sine square and and one +that we are going to get is like this if + + align:start position:0% +that we are going to get is like this if + + + align:start position:0% +that we are going to get is like this if +I prat m equal to 1 is P as a function + + align:start position:0% +I prat m equal to 1 is P as a function + + + align:start position:0% +I prat m equal to 1 is P as a function +of X the probability of getting particle + + align:start position:0% +of X the probability of getting particle + + + align:start position:0% +of X the probability of getting particle +at a specific price if we are looking at + + align:start position:0% +at a specific price if we are looking at + + + align:start position:0% +at a specific price if we are looking at +the situation in normal more number 1 + + align:start position:0% +the situation in normal more number 1 + + + align:start position:0% +the situation in normal more number 1 +that is like this you are much more + + align:start position:0% +that is like this you are much more + + + align:start position:0% +that is like this you are much more +likely to find a particle in the middle + + align:start position:0% +likely to find a particle in the middle + + + align:start position:0% +likely to find a particle in the middle +of the box the other hand we can also + + align:start position:0% +of the box the other hand we can also + + + align:start position:0% +of the box the other hand we can also +plot the probability as functional x for + + align:start position:0% +plot the probability as functional x for + + + align:start position:0% +plot the probability as functional x for +n equal to 2 case if we are actually + + align:start position:0% +n equal to 2 case if we are actually + + + align:start position:0% +n equal to 2 case if we are actually +operating and you know second normal + + align:start position:0% +operating and you know second normal + + + align:start position:0% +operating and you know second normal +mode then basically you have some + + align:start position:0% +mode then basically you have some + + + align:start position:0% +mode then basically you have some +distribution looks like this in this + + align:start position:0% +distribution looks like this in this + + + align:start position:0% +distribution looks like this in this +situation it is forbidden or say there's + + align:start position:0% +situation it is forbidden or say there's + + + align:start position:0% +situation it is forbidden or say there's +no general probability you will find the + + align:start position:0% +no general probability you will find the + + + align:start position:0% +no general probability you will find the +particle in the middle of the box etc + + align:start position:0% +particle in the middle of the box etc + + + align:start position:0% +particle in the middle of the box etc +etc you can easily calculate all those + + align:start position:0% +etc you can easily calculate all those + + + align:start position:0% +etc you can easily calculate all those +corresponding probability a distribution + + align:start position:0% +corresponding probability a distribution + + + align:start position:0% +corresponding probability a distribution +as a function of n value and as a + + align:start position:0% +as a function of n value and as a + + + align:start position:0% +as a function of n value and as a +function of position ok sounds like a + + align:start position:0% +function of position ok sounds like a + + + align:start position:0% +function of position ok sounds like a +very good story but there is something + + align:start position:0% +very good story but there is something + + + align:start position:0% +very good story but there is something +missing right what is actually missing + + align:start position:0% +missing right what is actually missing + + + align:start position:0% +missing right what is actually missing +you have the normal mode you have the kN + + align:start position:0% +you have the normal mode you have the kN + + + align:start position:0% +you have the normal mode you have the kN +what is missing is the wave equation + + align:start position:0% +what is missing is the wave equation + + + align:start position:0% +what is missing is the wave equation +right the wave equation is missing right + + align:start position:0% +right the wave equation is missing right + + + align:start position:0% +right the wave equation is missing right +you don't have the dispersion relation + + align:start position:0% +you don't have the dispersion relation + + + align:start position:0% +you don't have the dispersion relation +this solution is incomplete you don't + + align:start position:0% +this solution is incomplete you don't + + + align:start position:0% +this solution is incomplete you don't +know what is actually the Omega value + + align:start position:0% +know what is actually the Omega value + + + align:start position:0% +know what is actually the Omega value +right because you don't have dispersion + + align:start position:0% +right because you don't have dispersion + + + align:start position:0% +right because you don't have dispersion +relation so what is actually the wave + + align:start position:0% +relation so what is actually the wave + + + align:start position:0% +relation so what is actually the wave +equation for the quantum mechanics so it + + align:start position:0% +equation for the quantum mechanics so it + + + align:start position:0% +equation for the quantum mechanics so it +is actually Schrodinger's equation so + + align:start position:0% +is actually Schrodinger's equation so + + + align:start position:0% +is actually Schrodinger's equation so +Feynman once commented on the origin of + + align:start position:0% +Feynman once commented on the origin of + + + align:start position:0% +Feynman once commented on the origin of +the Schrodinger's equation from where is + + align:start position:0% +the Schrodinger's equation from where is + + + align:start position:0% +the Schrodinger's equation from where is +not possible to derive it from anything + + align:start position:0% +not possible to derive it from anything + + + align:start position:0% +not possible to derive it from anything +you know it's just coming out of the + + align:start position:0% +you know it's just coming out of the + + + align:start position:0% +you know it's just coming out of the +might of surrounding er so there's no + + align:start position:0% +might of surrounding er so there's no + + + align:start position:0% +might of surrounding er so there's no +reason and that it works that's the + + align:start position:0% +reason and that it works that's the + + + align:start position:0% +reason and that it works that's the +beautiful part so what is this with this + + align:start position:0% +beautiful part so what is this with this + + + align:start position:0% +beautiful part so what is this with this +equation so this is the equation + + align:start position:0% +equation so this is the equation + + + align:start position:0% +equation so this is the equation +Schrodinger I should write down it's + + align:start position:0% +Schrodinger I should write down it's + + + align:start position:0% +Schrodinger I should write down it's +like I h-bar from front constant partial + + align:start position:0% +like I h-bar from front constant partial + + + align:start position:0% +like I h-bar from front constant partial +party sy XT and this will be equal to + + align:start position:0% +party sy XT and this will be equal to + + + align:start position:0% +party sy XT and this will be equal to +minus H bar squared over 2m partial + + align:start position:0% +minus H bar squared over 2m partial + + + align:start position:0% +minus H bar squared over 2m partial +square partial x squared plus V XT side + + align:start position:0% +square partial x squared plus V XT side + + + align:start position:0% +square partial x squared plus V XT side +okay so this is really nice and it works + + align:start position:0% +okay so this is really nice and it works + + + align:start position:0% +okay so this is really nice and it works +in the matches with experimental result + + align:start position:0% +in the matches with experimental result + + + align:start position:0% +in the matches with experimental result +and now I have already done or my mouth + + align:start position:0% +and now I have already done or my mouth + + + align:start position:0% +and now I have already done or my mouth +I can practically into this equation to + + align:start position:0% +I can practically into this equation to + + + align:start position:0% +I can practically into this equation to +see what I can actually learn from there + + align:start position:0% +see what I can actually learn from there + + + align:start position:0% +see what I can actually learn from there +so what I'm going to do is to plot in sy + + align:start position:0% +so what I'm going to do is to plot in sy + + + align:start position:0% +so what I'm going to do is to plot in sy +n xt into this equation to get the + + align:start position:0% +n xt into this equation to get the + + + align:start position:0% +n xt into this equation to get the +dispersion relation so what is actually + + align:start position:0% +dispersion relation so what is actually + + + align:start position:0% +dispersion relation so what is actually +the dispersion relation so here i have + + align:start position:0% +the dispersion relation so here i have + + + align:start position:0% +the dispersion relation so here i have +partial partial T so I extract one Omega + + align:start position:0% +partial partial T so I extract one Omega + + + align:start position:0% +partial partial T so I extract one Omega +minus I Omega out of this then basically + + align:start position:0% +minus I Omega out of this then basically + + + align:start position:0% +minus I Omega out of this then basically +I get h-bar Omega n sy n X + + align:start position:0% +I get h-bar Omega n sy n X + + + align:start position:0% +I get h-bar Omega n sy n X +alabanza okay I'm plugging in sigh and + + align:start position:0% +alabanza okay I'm plugging in sigh and + + + align:start position:0% +alabanza okay I'm plugging in sigh and +into this equation and see what happened + + align:start position:0% +into this equation and see what happened + + + align:start position:0% +into this equation and see what happened +then this would be equal to I also know + + align:start position:0% +then this would be equal to I also know + + + align:start position:0% +then this would be equal to I also know +that in the middle of the box okay B is + + align:start position:0% +that in the middle of the box okay B is + + + align:start position:0% +that in the middle of the box okay B is +actually the potential okay + + align:start position:0% +actually the potential okay + + + align:start position:0% +actually the potential okay +the potential is zero inside the box the + + align:start position:0% +the potential is zero inside the box the + + + align:start position:0% +the potential is zero inside the box the +potential is infinity at the edge of the + + align:start position:0% +potential is infinity at the edge of the + + + align:start position:0% +potential is infinity at the edge of the +box okay + + align:start position:0% +box okay + + + align:start position:0% +box okay +therefore I can safely ignore this term + + align:start position:0% +therefore I can safely ignore this term + + + align:start position:0% +therefore I can safely ignore this term +to be equal to zero so you have a free + + align:start position:0% +to be equal to zero so you have a free + + + align:start position:0% +to be equal to zero so you have a free +particle inside a box and what is + + align:start position:0% +particle inside a box and what is + + + align:start position:0% +particle inside a box and what is +actually this term this term will give + + align:start position:0% +actually this term this term will give + + + align:start position:0% +actually this term this term will give +you minus H bar squared over 2m okay I + + align:start position:0% +you minus H bar squared over 2m okay I + + + align:start position:0% +you minus H bar squared over 2m okay I +have a double differential of X and + + align:start position:0% +have a double differential of X and + + + align:start position:0% +have a double differential of X and +therefore I get basically minus km + + align:start position:0% +therefore I get basically minus km + + + align:start position:0% +therefore I get basically minus km +squared right because the sine theta + + align:start position:0% +squared right because the sine theta + + + align:start position:0% +squared right because the sine theta +right so basically I get minus K squared + + align:start position:0% +right so basically I get minus K squared + + + align:start position:0% +right so basically I get minus K squared +so therefore I cancel this this is a + + align:start position:0% +so therefore I cancel this this is a + + + align:start position:0% +so therefore I cancel this this is a +minus sign I have K and square out of + + align:start position:0% +minus sign I have K and square out of + + + align:start position:0% +minus sign I have K and square out of +this calculation and I still have cyan + + align:start position:0% +this calculation and I still have cyan + + + align:start position:0% +this calculation and I still have cyan +XT okay cancel this tool then what I'm + + align:start position:0% +XT okay cancel this tool then what I'm + + + align:start position:0% +XT okay cancel this tool then what I'm +getting is that Omega and is equal to KN + + align:start position:0% +getting is that Omega and is equal to KN + + + align:start position:0% +getting is that Omega and is equal to KN +squared H bar that I cancel one of the X + + align:start position:0% +squared H bar that I cancel one of the X + + + align:start position:0% +squared H bar that I cancel one of the X +bar H bar here all right / - well this + + align:start position:0% +bar H bar here all right / - well this + + + align:start position:0% +bar H bar here all right / - well this +is actually the dispersion relation of + + align:start position:0% +is actually the dispersion relation of + + + align:start position:0% +is actually the dispersion relation of +the wave function + + align:start position:0% + + + + align:start position:0% + +d-boy proposed the wavelengths of the + + align:start position:0% +d-boy proposed the wavelengths of the + + + align:start position:0% +d-boy proposed the wavelengths of the +the the wavelengths of the metal wave is + + align:start position:0% +the the wavelengths of the metal wave is + + + align:start position:0% +the the wavelengths of the metal wave is +they should be hided related to the + + align:start position:0% +they should be hided related to the + + + align:start position:0% +they should be hided related to the +momentum of the matter so basically he + + align:start position:0% +momentum of the matter so basically he + + + align:start position:0% +momentum of the matter so basically he +proposed that P the momentum of the + + align:start position:0% +proposed that P the momentum of the + + + align:start position:0% +proposed that P the momentum of the +particle is actually equal to H Bar K + + align:start position:0% +particle is actually equal to H Bar K + + + align:start position:0% +particle is actually equal to H Bar K +where K is the wave number of the metal + + align:start position:0% +where K is the wave number of the metal + + + align:start position:0% +where K is the wave number of the metal +wave okay if you accept the bra is + + align:start position:0% +wave okay if you accept the bra is + + + align:start position:0% +wave okay if you accept the bra is +interpretation basically what we are + + align:start position:0% +interpretation basically what we are + + + align:start position:0% +interpretation basically what we are +getting is something really really + + align:start position:0% +getting is something really really + + + align:start position:0% +getting is something really really +interesting if we put together this + + align:start position:0% +interesting if we put together this + + + align:start position:0% +interesting if we put together this +dispersion relation and the deploys + + align:start position:0% +dispersion relation and the deploys + + + align:start position:0% +dispersion relation and the deploys +interpretation of metal weight what I'm + + align:start position:0% +interpretation of metal weight what I'm + + + align:start position:0% +interpretation of metal weight what I'm +going to do is to calculate the group + + align:start position:0% +going to do is to calculate the group + + + align:start position:0% +going to do is to calculate the group +velocity of this dispersion relation so + + align:start position:0% +velocity of this dispersion relation so + + + align:start position:0% +velocity of this dispersion relation so +I can now calculate group velocity VG + + align:start position:0% +I can now calculate group velocity VG + + + align:start position:0% +I can now calculate group velocity VG +will be equal to D Omega DK right and I + + align:start position:0% +will be equal to D Omega DK right and I + + + align:start position:0% +will be equal to D Omega DK right and I +know that Omega is equal to H Bar K + + align:start position:0% +know that Omega is equal to H Bar K + + + align:start position:0% +know that Omega is equal to H Bar K +square divided by 2 m right this is a + + align:start position:0% +square divided by 2 m right this is a + + + align:start position:0% +square divided by 2 m right this is a +should be equal to H Bar K divided by n + + align:start position:0% +should be equal to H Bar K divided by n + + + align:start position:0% +should be equal to H Bar K divided by n +right everybody's following okay and + + align:start position:0% +right everybody's following okay and + + + align:start position:0% +right everybody's following okay and +this is equal to what this is equal to P + + align:start position:0% +this is equal to what this is equal to P + + + align:start position:0% +this is equal to what this is equal to P +divided by M if I use the browser metal + + align:start position:0% +divided by M if I use the browser metal + + + align:start position:0% +divided by M if I use the browser metal +wave okay therefore you have P equal to + + align:start position:0% +wave okay therefore you have P equal to + + + align:start position:0% +wave okay therefore you have P equal to +n times and gee wow look at this what + + align:start position:0% +n times and gee wow look at this what + + + align:start position:0% +n times and gee wow look at this what +are we getting here what we are getting + + align:start position:0% +are we getting here what we are getting + + + align:start position:0% +are we getting here what we are getting +here is that the group velocity of the + + align:start position:0% +here is that the group velocity of the + + + align:start position:0% +here is that the group velocity of the +wave equation okay the waves it's + + align:start position:0% +wave equation okay the waves it's + + + align:start position:0% +wave equation okay the waves it's +actually the classical velocity + + align:start position:0% +actually the classical velocity + + + align:start position:0% +actually the classical velocity +P equal to n times B now everything is + + align:start position:0% +P equal to n times B now everything is + + + align:start position:0% +P equal to n times B now everything is +becoming more and more clear we know and + + align:start position:0% +becoming more and more clear we know and + + + align:start position:0% +becoming more and more clear we know and +we learned already from a oh three what + + align:start position:0% +we learned already from a oh three what + + + align:start position:0% +we learned already from a oh three what +is a the meaning of group velocity the + + align:start position:0% +is a the meaning of group velocity the + + + align:start position:0% +is a the meaning of group velocity the +meaning of the group velocity is the + + align:start position:0% +meaning of the group velocity is the + + + align:start position:0% +meaning of the group velocity is the +speed of propagation of a wave package + + align:start position:0% +speed of propagation of a wave package + + + align:start position:0% +speed of propagation of a wave package +right remember our discussion before + + align:start position:0% +right remember our discussion before + + + align:start position:0% +right remember our discussion before +about a and radio right so what is issue + + align:start position:0% +about a and radio right so what is issue + + + align:start position:0% +about a and radio right so what is issue +the speed of propagation of the wave + + align:start position:0% +the speed of propagation of the wave + + + align:start position:0% +the speed of propagation of the wave +packet is the group velocity so now we + + align:start position:0% +packet is the group velocity so now we + + + align:start position:0% +packet is the group velocity so now we +have solved the problem why electron can + + align:start position:0% +have solved the problem why electron can + + + align:start position:0% +have solved the problem why electron can +be a particle at the same time also like + + align:start position:0% +be a particle at the same time also like + + + align:start position:0% +be a particle at the same time also like +waves it essentially described by wave + + align:start position:0% +waves it essentially described by wave + + + align:start position:0% +waves it essentially described by wave +functions the classical behavior we see + + align:start position:0% +functions the classical behavior we see + + + align:start position:0% +functions the classical behavior we see +an electron is because it is as we + + align:start position:0% +an electron is because it is as we + + + align:start position:0% +an electron is because it is as we +described by these web packages is + + align:start position:0% +described by these web packages is + + + align:start position:0% +described by these web packages is +pretty localized and it the motion of + + align:start position:0% +pretty localized and it the motion of + + + align:start position:0% +pretty localized and it the motion of +this web package in a free space is + + align:start position:0% +this web package in a free space is + + + align:start position:0% +this web package in a free space is +actually the speed of the propagation is + + align:start position:0% +actually the speed of the propagation is + + + align:start position:0% +actually the speed of the propagation is +the group velocity therefore there is no + + align:start position:0% +the group velocity therefore there is no + + + align:start position:0% +the group velocity therefore there is no +contradiction about me between the + + align:start position:0% +contradiction about me between the + + + align:start position:0% +contradiction about me between the +classical calculation and the wave + + align:start position:0% +classical calculation and the wave + + + align:start position:0% +classical calculation and the wave +interpretation of the electron so that + + align:start position:0% +interpretation of the electron so that + + + align:start position:0% +interpretation of the electron so that +really surprised me really very much and + + align:start position:0% +really surprised me really very much and + + + align:start position:0% +really surprised me really very much and +you can see that given the dispersion + + align:start position:0% +you can see that given the dispersion + + + align:start position:0% +you can see that given the dispersion +relation you can see also this is a + + align:start position:0% +relation you can see also this is a + + + align:start position:0% +relation you can see also this is a +rather domenico result the wave function + + align:start position:0% +rather domenico result the wave function + + + align:start position:0% +rather domenico result the wave function +the real part of wave function is a + + align:start position:0% +the real part of wave function is a + + + align:start position:0% +the real part of wave function is a +should be blue and the imaginary apart + + align:start position:0% +should be blue and the imaginary apart + + + align:start position:0% +should be blue and the imaginary apart +is actually red is actually oscillating + + align:start position:0% +is actually red is actually oscillating + + + align:start position:0% +is actually red is actually oscillating +up and down and the + + align:start position:0% +up and down and the + + + align:start position:0% +up and down and the +oscillation frequency by now you know + + align:start position:0% +oscillation frequency by now you know + + + align:start position:0% +oscillation frequency by now you know +it's covered by that dispersion relation + + align:start position:0% +it's covered by that dispersion relation + + + align:start position:0% +it's covered by that dispersion relation +okay now actually everything seems to + + align:start position:0% +okay now actually everything seems to + + + align:start position:0% +okay now actually everything seems to +make sense now really really very cool + + align:start position:0% +make sense now really really very cool + + + align:start position:0% +make sense now really really very cool +so on the other hand we also have to + + align:start position:0% +so on the other hand we also have to + + + align:start position:0% +so on the other hand we also have to +live with probability density right so + + align:start position:0% +live with probability density right so + + + align:start position:0% +live with probability density right so +you cannot tell the exact position of a + + align:start position:0% +you cannot tell the exact position of a + + + align:start position:0% +you cannot tell the exact position of a +particle anymore + + align:start position:0% +particle anymore + + + align:start position:0% +particle anymore +you cannot tell the exact outcome of an + + align:start position:0% +you cannot tell the exact outcome of an + + + align:start position:0% +you cannot tell the exact outcome of an +experiment anymore and that is actually + + align:start position:0% +experiment anymore and that is actually + + + align:start position:0% +experiment anymore and that is actually +to do with this interpretation and all + + align:start position:0% +to do with this interpretation and all + + + align:start position:0% +to do with this interpretation and all +those phenomena it's memories very small + + align:start position:0% +those phenomena it's memories very small + + + align:start position:0% +those phenomena it's memories very small +scale is as you described by quantum + + align:start position:0% +scale is as you described by quantum + + + align:start position:0% +scale is as you described by quantum +mechanics which we will learn some 104 + + align:start position:0% +mechanics which we will learn some 104 + + + align:start position:0% +mechanics which we will learn some 104 +and also few in the future you will be + + align:start position:0% +and also few in the future you will be + + + align:start position:0% +and also few in the future you will be +governed by the quantum field theory + + align:start position:0% +governed by the quantum field theory + + + align:start position:0% +governed by the quantum field theory +which is actually father future and what + + align:start position:0% +which is actually father future and what + + + align:start position:0% +which is actually father future and what +is actually the life living with content + + align:start position:0% +is actually the life living with content + + + align:start position:0% +is actually the life living with content +mechanics and quantum field theory so + + align:start position:0% +mechanics and quantum field theory so + + + align:start position:0% +mechanics and quantum field theory so +this is a very simple like a range of + + align:start position:0% +this is a very simple like a range of + + + align:start position:0% +this is a very simple like a range of +the standard model right and it + + align:start position:0% +the standard model right and it + + + align:start position:0% +the standard model right and it +described everything except the gravity + + align:start position:0% +described everything except the gravity + + + align:start position:0% +described everything except the gravity +okay and it's really simple is called + + align:start position:0% +okay and it's really simple is called + + + align:start position:0% +okay and it's really simple is called +standard model right and look at this + + align:start position:0% +standard model right and look at this + + + align:start position:0% +standard model right and look at this +part this is governing the Higgs decay + + align:start position:0% +part this is governing the Higgs decay + + + align:start position:0% +part this is governing the Higgs decay +to Z boson all right and without + + align:start position:0% +to Z boson all right and without + + + align:start position:0% +to Z boson all right and without +experimental result we don't really know + + align:start position:0% +experimental result we don't really know + + + align:start position:0% +experimental result we don't really know +what is actually the mass of the Higgs + + align:start position:0% +what is actually the mass of the Higgs + + + align:start position:0% +what is actually the mass of the Higgs +is a missing observable before and on + + align:start position:0% +is a missing observable before and on + + + align:start position:0% +is a missing observable before and on +the other hand as a particle physicist + + align:start position:0% +the other hand as a particle physicist + + + align:start position:0% +the other hand as a particle physicist +or as a high-energy nuclear physicist I + + align:start position:0% +or as a high-energy nuclear physicist I + + + align:start position:0% +or as a high-energy nuclear physicist I +have no idea about what will happen in + + align:start position:0% +have no idea about what will happen in + + + align:start position:0% +have no idea about what will happen in +the next collision why is that you know + + align:start position:0% +the next collision why is that you know + + + align:start position:0% +the next collision why is that you know +there is a reason now right because we + + align:start position:0% +there is a reason now right because we + + + align:start position:0% +there is a reason now right because we +cannot predict the exact outcome of an + + align:start position:0% +cannot predict the exact outcome of an + + + align:start position:0% +cannot predict the exact outcome of an +experiment it's all governed by wave + + align:start position:0% +experiment it's all governed by wave + + + align:start position:0% +experiment it's all governed by wave +function + + align:start position:0% +function + + + align:start position:0% +function +therefore what we are doing is the + + align:start position:0% +therefore what we are doing is the + + + align:start position:0% +therefore what we are doing is the +following we are doing the poo force so + + align:start position:0% +following we are doing the poo force so + + + align:start position:0% +following we are doing the poo force so +we called light like crazy collide + + align:start position:0% +we called light like crazy collide + + + align:start position:0% +we called light like crazy collide +collide collide collide like crazy until + + align:start position:0% +collide collide collide like crazy until + + + align:start position:0% +collide collide collide like crazy until +something interesting pop out that's + + align:start position:0% +something interesting pop out that's + + + align:start position:0% +something interesting pop out that's +actually what we're really doing okay as + + align:start position:0% +actually what we're really doing okay as + + + align:start position:0% +actually what we're really doing okay as +a particle physicist and this is you a + + align:start position:0% +a particle physicist and this is you a + + + align:start position:0% +a particle physicist and this is you a +beautiful event from proton-proton + + align:start position:0% +beautiful event from proton-proton + + + align:start position:0% +beautiful event from proton-proton +collisions as a large health on collider + + align:start position:0% +collisions as a large health on collider + + + align:start position:0% +collisions as a large health on collider +is a Higgs to to Z boson event and the + + align:start position:0% +is a Higgs to to Z boson event and the + + + align:start position:0% +is a Higgs to to Z boson event and the +one of the Z boson become the to red red + + align:start position:0% +one of the Z boson become the to red red + + + align:start position:0% +one of the Z boson become the to red red +light light on line three is actually + + align:start position:0% +light light on line three is actually + + + align:start position:0% +light light on line three is actually +the to me ones and the other one decays + + align:start position:0% +the to me ones and the other one decays + + + align:start position:0% +the to me ones and the other one decays +to two electrons which are detected by + + align:start position:0% +to two electrons which are detected by + + + align:start position:0% +to two electrons which are detected by +the kilometer as the two blue thinks + + align:start position:0% +the kilometer as the two blue thinks + + + align:start position:0% +the kilometer as the two blue thinks +them as a high-energy + + align:start position:0% +them as a high-energy + + + align:start position:0% +them as a high-energy +nuclear physicist I am interested in the + + align:start position:0% +nuclear physicist I am interested in the + + + align:start position:0% +nuclear physicist I am interested in the +production of quark one Proxima from let + + align:start position:0% +production of quark one Proxima from let + + + align:start position:0% +production of quark one Proxima from let +I am collision so I am now putting + + align:start position:0% +I am collision so I am now putting + + + align:start position:0% +I am collision so I am now putting +together two ions have been collide and + + align:start position:0% +together two ions have been collide and + + + align:start position:0% +together two ions have been collide and +I hope that by chance I can be passing a + + align:start position:0% +I hope that by chance I can be passing a + + + align:start position:0% +I hope that by chance I can be passing a +huge amount of energy in a very small + + align:start position:0% +huge amount of energy in a very small + + + align:start position:0% +huge amount of energy in a very small +volume and then I would like to see this + + align:start position:0% +volume and then I would like to see this + + + align:start position:0% +volume and then I would like to see this +crazy matter actually gradually expand + + align:start position:0% +crazy matter actually gradually expand + + + align:start position:0% +crazy matter actually gradually expand +and become a lot of particles and I + + align:start position:0% +and become a lot of particles and I + + + align:start position:0% +and become a lot of particles and I +study those particles to understand what + + align:start position:0% +study those particles to understand what + + + align:start position:0% +study those particles to understand what +would be the nature of this material + + align:start position:0% +would be the nature of this material + + + align:start position:0% +would be the nature of this material +which sought to exist in the very early + + align:start position:0% +which sought to exist in the very early + + + align:start position:0% +which sought to exist in the very early +part of the whole universe history just + + align:start position:0% +part of the whole universe history just + + + align:start position:0% +part of the whole universe history just +one micro second after the Big Bang we + + align:start position:0% +one micro second after the Big Bang we + + + align:start position:0% +one micro second after the Big Bang we +are having the whole universe filled by + + align:start position:0% +are having the whole universe filled by + + + align:start position:0% +are having the whole universe filled by +this crazy material and we are creating + + align:start position:0% +this crazy material and we are creating + + + align:start position:0% +this crazy material and we are creating +this in the experiment and we will only + + align:start position:0% +this in the experiment and we will only + + + align:start position:0% +this in the experiment and we will only +be able to hope that okay by chance I + + align:start position:0% +be able to hope that okay by chance I + + + align:start position:0% +be able to hope that okay by chance I +have the collision happen by chance I + + align:start position:0% +have the collision happen by chance I + + + align:start position:0% +have the collision happen by chance I +have a very high density environment + + align:start position:0% +have a very high density environment + + + align:start position:0% +have a very high density environment +somehow multiple contact decide to + + align:start position:0% +somehow multiple contact decide to + + + align:start position:0% +somehow multiple contact decide to +scatter from each other and they deposit + + align:start position:0% +scatter from each other and they deposit + + + align:start position:0% +scatter from each other and they deposit +energy in a very small volume and we + + align:start position:0% +energy in a very small volume and we + + + align:start position:0% +energy in a very small volume and we +collect all those spectacular events to + + align:start position:0% +collect all those spectacular events to + + + align:start position:0% +collect all those spectacular events to +start + + align:start position:0% +start + + + align:start position:0% +start +the property of all those little people + + align:start position:0% +the property of all those little people + + + align:start position:0% +the property of all those little people +so that is actually the consequence of + + align:start position:0% +so that is actually the consequence of + + + align:start position:0% +so that is actually the consequence of +this wave function interpretation so now + + align:start position:0% +this wave function interpretation so now + + + align:start position:0% +this wave function interpretation so now +coming back to this standard model this + + align:start position:0% +coming back to this standard model this + + + align:start position:0% +coming back to this standard model this +really simple one you can see that is a + + align:start position:0% +really simple one you can see that is a + + + align:start position:0% +really simple one you can see that is a +theory of almost everything but the + + align:start position:0% +theory of almost everything but the + + + align:start position:0% +theory of almost everything but the +accept the gravity really sad so if you + + align:start position:0% +accept the gravity really sad so if you + + + align:start position:0% +accept the gravity really sad so if you +can actually put them all together then + + align:start position:0% +can actually put them all together then + + + align:start position:0% +can actually put them all together then +you also win a Nobel Prize and giving + + align:start position:0% +you also win a Nobel Prize and giving + + + align:start position:0% +you also win a Nobel Prize and giving +you all those ideas so that I can have a + + align:start position:0% +you all those ideas so that I can have a + + + align:start position:0% +you all those ideas so that I can have a +very good student we mean a whole Nobel + + align:start position:0% +very good student we mean a whole Nobel + + + align:start position:0% +very good student we mean a whole Nobel +Prize of course you were and now I would + + align:start position:0% +Prize of course you were and now I would + + + align:start position:0% +Prize of course you were and now I would +like to discuss and use the remaining + + align:start position:0% +like to discuss and use the remaining + + + align:start position:0% +like to discuss and use the remaining +maybe ten minutes to discuss with you + + align:start position:0% +maybe ten minutes to discuss with you + + + align:start position:0% +maybe ten minutes to discuss with you +the gravity so here this HD is something + + align:start position:0% +the gravity so here this HD is something + + + align:start position:0% +the gravity so here this HD is something +related to gravity so Einstein actually + + align:start position:0% +related to gravity so Einstein actually + + + align:start position:0% +related to gravity so Einstein actually +predicted that the distortion of the way + + align:start position:0% +predicted that the distortion of the way + + + align:start position:0% +predicted that the distortion of the way +of the space-time generated by objects + + align:start position:0% +of the space-time generated by objects + + + align:start position:0% +of the space-time generated by objects +can travel through the space okay + + align:start position:0% +can travel through the space okay + + + align:start position:0% +can travel through the space okay +I don't have the deviation here because + + align:start position:0% +I don't have the deviation here because + + + align:start position:0% +I don't have the deviation here because +you would take another maybe two hours + + align:start position:0% +you would take another maybe two hours + + + align:start position:0% +you would take another maybe two hours +to do this but I would like to ask you + + align:start position:0% +to do this but I would like to ask you + + + align:start position:0% +to do this but I would like to ask you +to trust me this is actually a result + + align:start position:0% +to trust me this is actually a result + + + align:start position:0% +to trust me this is actually a result +coming from general relativity and you + + align:start position:0% +coming from general relativity and you + + + align:start position:0% +coming from general relativity and you +can see that when we can actually + + align:start position:0% +can see that when we can actually + + + align:start position:0% +can see that when we can actually +generate gravitational waves and I can + + align:start position:0% +generate gravitational waves and I can + + + align:start position:0% +generate gravitational waves and I can +issue to the generation here right this + + align:start position:0% +issue to the generation here right this + + + align:start position:0% +issue to the generation here right this +I'm rotating and generating + + align:start position:0% +I'm rotating and generating + + + align:start position:0% +I'm rotating and generating +gravitational wave and the student in + + align:start position:0% +gravitational wave and the student in + + + align:start position:0% +gravitational wave and the student in +the back is also generating yes you are + + align:start position:0% +the back is also generating yes you are + + + align:start position:0% +the back is also generating yes you are +you're generating everybody is + + align:start position:0% +you're generating everybody is + + + align:start position:0% +you're generating everybody is +generating you are also generating yeah + + align:start position:0% +generating you are also generating yeah + + + align:start position:0% +generating you are also generating yeah +very good but the problem is that the + + align:start position:0% +very good but the problem is that the + + + align:start position:0% +very good but the problem is that the +space-time distortion is really small + + align:start position:0% +space-time distortion is really small + + + align:start position:0% +space-time distortion is really small +for people who are not very massive like + + align:start position:0% +for people who are not very massive like + + + align:start position:0% +for people who are not very massive like +me right so that's a problem so I can + + align:start position:0% +me right so that's a problem so I can + + + align:start position:0% +me right so that's a problem so I can +generate I'm doing the demo here but the + + align:start position:0% +generate I'm doing the demo here but the + + + align:start position:0% +generate I'm doing the demo here but the +help + + align:start position:0% +help + + + align:start position:0% +help +cannot you cannot really detect them and + + align:start position:0% +cannot you cannot really detect them and + + + align:start position:0% +cannot you cannot really detect them and +even Einstein himself think is + + align:start position:0% +even Einstein himself think is + + + align:start position:0% +even Einstein himself think is +impossible to detect + + align:start position:0% +impossible to detect + + + align:start position:0% +impossible to detect +maybe in our lifetime right and what + + align:start position:0% +maybe in our lifetime right and what + + + align:start position:0% +maybe in our lifetime right and what +would be the outcome of the calculation + + align:start position:0% +would be the outcome of the calculation + + + align:start position:0% +would be the outcome of the calculation +the uncountable calculation if you have + + align:start position:0% +the uncountable calculation if you have + + + align:start position:0% +the uncountable calculation if you have +quite a tional wave passing to where you + + align:start position:0% +quite a tional wave passing to where you + + + align:start position:0% +quite a tional wave passing to where you +okay so what is it does is the following + + align:start position:0% +okay so what is it does is the following + + + align:start position:0% +okay so what is it does is the following +so basically the space that the space is + + align:start position:0% +so basically the space that the space is + + + align:start position:0% +so basically the space that the space is +distort it in a way such that if first + + align:start position:0% +distort it in a way such that if first + + + align:start position:0% +distort it in a way such that if first +expand in this direction and then expand + + align:start position:0% +expand in this direction and then expand + + + align:start position:0% +expand in this direction and then expand +in the other direction perpendicular to + + align:start position:0% +in the other direction perpendicular to + + + align:start position:0% +in the other direction perpendicular to +the original distortion and if you put a + + align:start position:0% +the original distortion and if you put a + + + align:start position:0% +the original distortion and if you put a +ray of particles the circular array of + + align:start position:0% +ray of particles the circular array of + + + align:start position:0% +ray of particles the circular array of +particle and look at what is going on + + align:start position:0% +particle and look at what is going on + + + align:start position:0% +particle and look at what is going on +when the gravitational wave pass through + + align:start position:0% +when the gravitational wave pass through + + + align:start position:0% +when the gravitational wave pass through +it you pass through the array in this + + align:start position:0% +it you pass through the array in this + + + align:start position:0% +it you pass through the array in this +direction what you are going to get is a + + align:start position:0% +direction what you are going to get is a + + + align:start position:0% +direction what you are going to get is a +fad like that okay + + align:start position:0% +fad like that okay + + + align:start position:0% +fad like that okay +of course this is actually highly + + align:start position:0% +of course this is actually highly + + + align:start position:0% +of course this is actually highly +exaggerated in this setup you don't + + align:start position:0% +exaggerated in this setup you don't + + + align:start position:0% +exaggerated in this setup you don't +really see this kind of sizable + + align:start position:0% +really see this kind of sizable + + + align:start position:0% +really see this kind of sizable +distortion when Eng is dancing around + + align:start position:0% +distortion when Eng is dancing around + + + align:start position:0% +distortion when Eng is dancing around +all right + + align:start position:0% +all right + + + align:start position:0% +all right +okay so how about we actually visualize + + align:start position:0% +okay so how about we actually visualize + + + align:start position:0% +okay so how about we actually visualize +this thing the problem is that we cannot + + align:start position:0% +this thing the problem is that we cannot + + + align:start position:0% +this thing the problem is that we cannot +really see the space distortion but what + + align:start position:0% +really see the space distortion but what + + + align:start position:0% +really see the space distortion but what +we can as you see is the light which way + + align:start position:0% +we can as you see is the light which way + + + align:start position:0% +we can as you see is the light which way +should I pass through those little + + align:start position:0% +should I pass through those little + + + align:start position:0% +should I pass through those little +distortion so this is a stimulation from + + align:start position:0% +distortion so this is a stimulation from + + + align:start position:0% +distortion so this is a stimulation from +LIGO collaboration they are simulating + + align:start position:0% +LIGO collaboration they are simulating + + + align:start position:0% +LIGO collaboration they are simulating +the merging of the two + + align:start position:0% +the merging of the two + + + align:start position:0% +the merging of the two +massive black holes and you can see that + + align:start position:0% +massive black holes and you can see that + + + align:start position:0% +massive black holes and you can see that +they are rotating to each other to each + + align:start position:0% +they are rotating to each other to each + + + align:start position:0% +they are rotating to each other to each +other they are radiating energy out of + + align:start position:0% +other they are radiating energy out of + + + align:start position:0% +other they are radiating energy out of +the out of this two party system let's + + align:start position:0% +the out of this two party system let's + + + align:start position:0% +the out of this two party system let's +take a look at this again so this is + + align:start position:0% +take a look at this again so this is + + + align:start position:0% +take a look at this again so this is +actually a simulation of the event + + align:start position:0% +actually a simulation of the event + + + align:start position:0% +actually a simulation of the event +observed by LIGO + + align:start position:0% +observed by LIGO + + + align:start position:0% +observed by LIGO +so both Bracco have a mass roughly 30 + + align:start position:0% +so both Bracco have a mass roughly 30 + + + align:start position:0% +so both Bracco have a mass roughly 30 +times of the our son + + align:start position:0% +times of the our son + + + align:start position:0% +times of the our son +okay it's very massive and they are + + align:start position:0% +okay it's very massive and they are + + + align:start position:0% +okay it's very massive and they are +rotating we just read to each other and + + align:start position:0% +rotating we just read to each other and + + + align:start position:0% +rotating we just read to each other and +the trend array space-time distortion + + align:start position:0% +the trend array space-time distortion + + + align:start position:0% +the trend array space-time distortion +and you can see that the space-time + + align:start position:0% +and you can see that the space-time + + + align:start position:0% +and you can see that the space-time +distortion stopped when after they match + + align:start position:0% +distortion stopped when after they match + + + align:start position:0% +distortion stopped when after they match +each other and we were hoping that we + + align:start position:0% +each other and we were hoping that we + + + align:start position:0% +each other and we were hoping that we +can detect those how crazy is that + + align:start position:0% +can detect those how crazy is that + + + align:start position:0% +can detect those how crazy is that +okay so how do we detect them actually + + align:start position:0% +okay so how do we detect them actually + + + align:start position:0% +okay so how do we detect them actually +you already have the knowledge to design + + align:start position:0% +you already have the knowledge to design + + + align:start position:0% +you already have the knowledge to design +the experiment to detect this kind of + + align:start position:0% +the experiment to detect this kind of + + + align:start position:0% +the experiment to detect this kind of +effect so remember the effect of the + + align:start position:0% +effect so remember the effect of the + + + align:start position:0% +effect so remember the effect of the +gravitational wave is like this so you + + align:start position:0% +gravitational wave is like this so you + + + align:start position:0% +gravitational wave is like this so you +have distortion like this right + + align:start position:0% +have distortion like this right + + + align:start position:0% +have distortion like this right +while we issue the issue nit and the + + align:start position:0% +while we issue the issue nit and the + + + align:start position:0% +while we issue the issue nit and the +Kaltag and the many other collaborator + + align:start position:0% +Kaltag and the many other collaborator + + + align:start position:0% +Kaltag and the many other collaborator +designed the LIGO experiment so what is + + align:start position:0% +designed the LIGO experiment so what is + + + align:start position:0% +designed the LIGO experiment so what is +as you like is a laser interferometer + + align:start position:0% +as you like is a laser interferometer + + + align:start position:0% +as you like is a laser interferometer +gravitational-wave Observatory it is + + align:start position:0% +gravitational-wave Observatory it is + + + align:start position:0% +gravitational-wave Observatory it is +actually always good to have a very good + + align:start position:0% +actually always good to have a very good + + + align:start position:0% +actually always good to have a very good +man experiment right so at this issue + + align:start position:0% +man experiment right so at this issue + + + align:start position:0% +man experiment right so at this issue +like oh so what actually it does is the + + align:start position:0% +like oh so what actually it does is the + + + align:start position:0% +like oh so what actually it does is the +following so basically it emit a laser + + align:start position:0% +following so basically it emit a laser + + + align:start position:0% +following so basically it emit a laser +and is pretty laser into two pieces and + + align:start position:0% +and is pretty laser into two pieces and + + + align:start position:0% +and is pretty laser into two pieces and +there were mirrors in the verify and + + align:start position:0% +there were mirrors in the verify and + + + align:start position:0% +there were mirrors in the verify and +refract those laser and they come + + align:start position:0% +refract those laser and they come + + + align:start position:0% +refract those laser and they come +together and there is a detector photo + + align:start position:0% +together and there is a detector photo + + + align:start position:0% +together and there is a detector photo +detector which detect the interference + + align:start position:0% +detector which detect the interference + + + align:start position:0% +detector which detect the interference +pattern of these two optical pestilence + + align:start position:0% +pattern of these two optical pestilence + + + align:start position:0% +pattern of these two optical pestilence +Wow + + align:start position:0% +Wow + + + align:start position:0% +Wow +sounds familiar to you right you already + + align:start position:0% +sounds familiar to you right you already + + + align:start position:0% +sounds familiar to you right you already +know how to explain this to your friends + + align:start position:0% +know how to explain this to your friends + + + align:start position:0% +know how to explain this to your friends +already really cool and in order to have + + align:start position:0% +already really cool and in order to have + + + align:start position:0% +already really cool and in order to have +redundant management for example if you + + align:start position:0% +redundant management for example if you + + + align:start position:0% +redundant management for example if you +only have a single experiment maybe one + + align:start position:0% +only have a single experiment maybe one + + + align:start position:0% +only have a single experiment maybe one +graduate students who twin dancing next + + align:start position:0% +graduate students who twin dancing next + + + align:start position:0% +graduate students who twin dancing next +to a detector then you see sound fake + + align:start position:0% +to a detector then you see sound fake + + + align:start position:0% +to a detector then you see sound fake +signal right and that's not going to be + + align:start position:0% +signal right and that's not going to be + + + align:start position:0% +signal right and that's not going to be +helpful right so what it does is that + + align:start position:0% +helpful right so what it does is that + + + align:start position:0% +helpful right so what it does is that +basically we have to experiment one is + + align:start position:0% +basically we have to experiment one is + + + align:start position:0% +basically we have to experiment one is +this actually in a hand fort the other + + align:start position:0% +this actually in a hand fort the other + + + align:start position:0% +this actually in a hand fort the other +one is actually in Livingston and they + + align:start position:0% +one is actually in Livingston and they + + + align:start position:0% +one is actually in Livingston and they +are HD 3000 kilometer away from each + + align:start position:0% +are HD 3000 kilometer away from each + + + align:start position:0% +are HD 3000 kilometer away from each +other so that there + + align:start position:0% +other so that there + + + align:start position:0% +other so that there +there should not be any correlation + + align:start position:0% +there should not be any correlation + + + align:start position:0% +there should not be any correlation +between the signal coming from + + align:start position:0% +between the signal coming from + + + align:start position:0% +between the signal coming from +earthquake or dancing of the graduate + + align:start position:0% +earthquake or dancing of the graduate + + + align:start position:0% +earthquake or dancing of the graduate +students whatever right so they can + + align:start position:0% +students whatever right so they can + + + align:start position:0% +students whatever right so they can +actually use that to suppress any + + align:start position:0% +actually use that to suppress any + + + align:start position:0% +actually use that to suppress any +current sentence which is actually not + + align:start position:0% +current sentence which is actually not + + + align:start position:0% +current sentence which is actually not +related to gravitational waves so what + + align:start position:0% +related to gravitational waves so what + + + align:start position:0% +related to gravitational waves so what +does this - alright so now we have the + + align:start position:0% +does this - alright so now we have the + + + align:start position:0% +does this - alright so now we have the +older knowledge to actually explain this + + align:start position:0% +older knowledge to actually explain this + + + align:start position:0% +older knowledge to actually explain this +phenomena so what this does is define so + + align:start position:0% +phenomena so what this does is define so + + + align:start position:0% +phenomena so what this does is define so +you meet the laser and when the + + align:start position:0% +you meet the laser and when the + + + align:start position:0% +you meet the laser and when the +gravitational waves comes in then it + + align:start position:0% +gravitational waves comes in then it + + + align:start position:0% +gravitational waves comes in then it +does this space-time distortion and then + + align:start position:0% +does this space-time distortion and then + + + align:start position:0% +does this space-time distortion and then +the interference pattern of the waves + + align:start position:0% +the interference pattern of the waves + + + align:start position:0% +the interference pattern of the waves +going through different optical path + + align:start position:0% +going through different optical path + + + align:start position:0% +going through different optical path +length is going to change so you can see + + align:start position:0% +length is going to change so you can see + + + align:start position:0% +length is going to change so you can see +that originally the the experiments + + align:start position:0% +that originally the the experiments + + + align:start position:0% +that originally the the experiments +designed so that you have complete + + align:start position:0% +designed so that you have complete + + + align:start position:0% +designed so that you have complete +cancellation but when the electro that + + align:start position:0% +cancellation but when the electro that + + + align:start position:0% +cancellation but when the electro that +when the gravitational waves is hitting + + align:start position:0% +when the gravitational waves is hitting + + + align:start position:0% +when the gravitational waves is hitting +the site you will be able to see that + + align:start position:0% +the site you will be able to see that + + + align:start position:0% +the site you will be able to see that +really you have constructive + + align:start position:0% +really you have constructive + + + align:start position:0% +really you have constructive +interference at some point because of + + align:start position:0% +interference at some point because of + + + align:start position:0% +interference at some point because of +the movement of the the mirrors and + + align:start position:0% +the movement of the the mirrors and + + + align:start position:0% +the movement of the the mirrors and +those mirrors are really really far away + + align:start position:0% +those mirrors are really really far away + + + align:start position:0% +those mirrors are really really far away +from the sources like each of them is a + + align:start position:0% +from the sources like each of them is a + + + align:start position:0% +from the sources like each of them is a +she like 4 kilometer away from the + + align:start position:0% +she like 4 kilometer away from the + + + align:start position:0% +she like 4 kilometer away from the +mirror and due to the incredible + + align:start position:0% +mirror and due to the incredible + + + align:start position:0% +mirror and due to the incredible +precision which were achieved by this + + align:start position:0% +precision which were achieved by this + + + align:start position:0% +precision which were achieved by this +experiment we will be able to detect + + align:start position:0% +experiment we will be able to detect + + + align:start position:0% +experiment we will be able to detect +this the signal of gravitational waves + + align:start position:0% +this the signal of gravitational waves + + + align:start position:0% +this the signal of gravitational waves +so you can see again from here right so + + align:start position:0% +so you can see again from here right so + + + align:start position:0% +so you can see again from here right so +basically when the gravitational wave + + align:start position:0% +basically when the gravitational wave + + + align:start position:0% +basically when the gravitational wave +comes in the first you split the the + + align:start position:0% +comes in the first you split the the + + + align:start position:0% +comes in the first you split the the +light source into two pieces have then + + align:start position:0% +light source into two pieces have then + + + align:start position:0% +light source into two pieces have then +hit the mirror which is a four kilometer + + align:start position:0% +hit the mirror which is a four kilometer + + + align:start position:0% +hit the mirror which is a four kilometer +far away from each other and they come + + align:start position:0% +far away from each other and they come + + + align:start position:0% +far away from each other and they come +back and initially the experiment is + + align:start position:0% +back and initially the experiment is + + + align:start position:0% +back and initially the experiment is +designed so that very precisely + + align:start position:0% +designed so that very precisely + + + align:start position:0% +designed so that very precisely +there will be no amplitude + + align:start position:0% +there will be no amplitude + + + align:start position:0% +there will be no amplitude +detected by the photo detector and when + + align:start position:0% +detected by the photo detector and when + + + align:start position:0% +detected by the photo detector and when +the gravitational waves can see they + + align:start position:0% +the gravitational waves can see they + + + align:start position:0% +the gravitational waves can see they +should be changed the really change the + + align:start position:0% +should be changed the really change the + + + align:start position:0% +should be changed the really change the +lens right between the splitter and the + + align:start position:0% +lens right between the splitter and the + + + align:start position:0% +lens right between the splitter and the +mirror therefore you will see light + + align:start position:0% +mirror therefore you will see light + + + align:start position:0% +mirror therefore you will see light +constructive interference even from the + + align:start position:0% +constructive interference even from the + + + align:start position:0% +constructive interference even from the +photo detector so that is really cool + + align:start position:0% +photo detector so that is really cool + + + align:start position:0% +photo detector so that is really cool +and this is actually the experimental + + align:start position:0% +and this is actually the experimental + + + align:start position:0% +and this is actually the experimental +result look at this you actually can see + + align:start position:0% +result look at this you actually can see + + + align:start position:0% +result look at this you actually can see +that like actually achieved the the + + align:start position:0% +that like actually achieved the the + + + align:start position:0% +that like actually achieved the the +sensitivity the gravitational wave is + + align:start position:0% +sensitivity the gravitational wave is + + + align:start position:0% +sensitivity the gravitational wave is +was first observed on September 14th + + align:start position:0% +was first observed on September 14th + + + align:start position:0% +was first observed on September 14th + + align:start position:0% + + + align:start position:0% +and the LIGO is actually announcing that + + align:start position:0% +and the LIGO is actually announcing that + + + align:start position:0% +and the LIGO is actually announcing that +in the February 11th earlier this year + + align:start position:0% +in the February 11th earlier this year + + + align:start position:0% +in the February 11th earlier this year +right and what we actually see from here + + align:start position:0% +right and what we actually see from here + + + align:start position:0% +right and what we actually see from here +is that this is actually as I mentioned + + align:start position:0% +is that this is actually as I mentioned + + + align:start position:0% +is that this is actually as I mentioned +to you there are two measurements to + + align:start position:0% +to you there are two measurements to + + + align:start position:0% +to you there are two measurements to +cite the laughing sight is a should the + + align:start position:0% +cite the laughing sight is a should the + + + align:start position:0% +cite the laughing sight is a should the +measurement from Hanford and the other + + align:start position:0% +measurement from Hanford and the other + + + align:start position:0% +measurement from Hanford and the other +one is actually the measurement from + + align:start position:0% +one is actually the measurement from + + + align:start position:0% +one is actually the measurement from +Livingston okay so there are two + + align:start position:0% +Livingston okay so there are two + + + align:start position:0% +Livingston okay so there are two +different curves and they all have + + align:start position:0% +different curves and they all have + + + align:start position:0% +different curves and they all have +exactly the same almost exactly the same + + align:start position:0% +exactly the same almost exactly the same + + + align:start position:0% +exactly the same almost exactly the same +pattern of course the tiny size shifted + + align:start position:0% +pattern of course the tiny size shifted + + + align:start position:0% +pattern of course the tiny size shifted +because they are in different praise of + + align:start position:0% +because they are in different praise of + + + align:start position:0% +because they are in different praise of +the under earth the three thousand + + align:start position:0% +the under earth the three thousand + + + align:start position:0% +the under earth the three thousand +kilometer apart so therefore there will + + align:start position:0% +kilometer apart so therefore there will + + + align:start position:0% +kilometer apart so therefore there will +be a shift in time and this is actually + + align:start position:0% +be a shift in time and this is actually + + + align:start position:0% +be a shift in time and this is actually +time shifted result and you can see also + + align:start position:0% +time shifted result and you can see also + + + align:start position:0% +time shifted result and you can see also +the calculation below which is actually + + align:start position:0% +the calculation below which is actually + + + align:start position:0% +the calculation below which is actually +what you should expect if you have the + + align:start position:0% +what you should expect if you have the + + + align:start position:0% +what you should expect if you have the +merger of the the two massive holes you + + align:start position:0% +merger of the the two massive holes you + + + align:start position:0% +merger of the the two massive holes you +can see that they are actually rotating + + align:start position:0% +can see that they are actually rotating + + + align:start position:0% +can see that they are actually rotating +which is fed to each other one obtained + + align:start position:0% +which is fed to each other one obtained + + + align:start position:0% +which is fed to each other one obtained +is actually 29 times larger than the + + align:start position:0% +is actually 29 times larger than the + + + align:start position:0% +is actually 29 times larger than the +mass of the Sun and the other one is 36 + + align:start position:0% +mass of the Sun and the other one is 36 + + + align:start position:0% +mass of the Sun and the other one is 36 +times larger than the + + align:start position:0% +times larger than the + + + align:start position:0% +times larger than the +it's not precision okay and the general + + align:start position:0% +it's not precision okay and the general + + + align:start position:0% +it's not precision okay and the general +a theoretical D this kind of pattern and + + align:start position:0% +a theoretical D this kind of pattern and + + + align:start position:0% +a theoretical D this kind of pattern and +this is actually really detected by + + align:start position:0% +this is actually really detected by + + + align:start position:0% +this is actually really detected by +posts like or experiment which they are + + align:start position:0% +posts like or experiment which they are + + + align:start position:0% +posts like or experiment which they are +three thousand kilometer apart from each + + align:start position:0% +three thousand kilometer apart from each + + + align:start position:0% +three thousand kilometer apart from each +other okay so I think this is really a + + align:start position:0% +other okay so I think this is really a + + + align:start position:0% +other okay so I think this is really a +historical moment that we actually were + + align:start position:0% +historical moment that we actually were + + + align:start position:0% +historical moment that we actually were +very lucky to live in this moment what + + align:start position:0% +very lucky to live in this moment what + + + align:start position:0% +very lucky to live in this moment what +does that mean that means we have a new + + align:start position:0% +does that mean that means we have a new + + + align:start position:0% +does that mean that means we have a new +way to really hear about what the + + align:start position:0% +way to really hear about what the + + + align:start position:0% +way to really hear about what the +universe is actually trying to tell us + + align:start position:0% +universe is actually trying to tell us + + + align:start position:0% +universe is actually trying to tell us +we have a new way to detect phenomena + + align:start position:0% +we have a new way to detect phenomena + + + align:start position:0% +we have a new way to detect phenomena +which is as usual if happening very very + + align:start position:0% +which is as usual if happening very very + + + align:start position:0% +which is as usual if happening very very +far away from the earth how far is + + align:start position:0% +far away from the earth how far is + + + align:start position:0% +far away from the earth how far is +actually this event this event according + + align:start position:0% +actually this event this event according + + + align:start position:0% +actually this event this event according +to calculation essentially something + + align:start position:0% +to calculation essentially something + + + align:start position:0% +to calculation essentially something +like two PD and like 11.3 PD now like + + align:start position:0% +like two PD and like 11.3 PD now like + + + align:start position:0% +like two PD and like 11.3 PD now like +year away from the earth and we can + + align:start position:0% +year away from the earth and we can + + + align:start position:0% +year away from the earth and we can +detect them we even know the mass of the + + align:start position:0% +detect them we even know the mass of the + + + align:start position:0% +detect them we even know the mass of the +two procore Wow + + align:start position:0% +two procore Wow + + + align:start position:0% +two procore Wow +what does that mean this is really crazy + + align:start position:0% +what does that mean this is really crazy + + + align:start position:0% +what does that mean this is really crazy +to me and really exciting because we are + + align:start position:0% +to me and really exciting because we are + + + align:start position:0% +to me and really exciting because we are +opening up okay I have two years and + + align:start position:0% +opening up okay I have two years and + + + align:start position:0% +opening up okay I have two years and +it's opening up a more another year my + + align:start position:0% +it's opening up a more another year my + + + align:start position:0% +it's opening up a more another year my +friend and that is actually the way to + + align:start position:0% +friend and that is actually the way to + + + align:start position:0% +friend and that is actually the way to +here the gravitational wave with the + + align:start position:0% +here the gravitational wave with the + + + align:start position:0% +here the gravitational wave with the +experiment we've performed on hers okay + + align:start position:0% +experiment we've performed on hers okay + + + align:start position:0% +experiment we've performed on hers okay +so I hope until now I have convinced you + + align:start position:0% +so I hope until now I have convinced you + + + align:start position:0% +so I hope until now I have convinced you +that this is really not the end of + + align:start position:0% +that this is really not the end of + + + align:start position:0% +that this is really not the end of +vibration of waves which is actually the + + align:start position:0% +vibration of waves which is actually the + + + align:start position:0% +vibration of waves which is actually the +Nano ao3 instead this is actually just + + align:start position:0% +Nano ao3 instead this is actually just + + + align:start position:0% +Nano ao3 instead this is actually just +the beginning you have a lot more to + + align:start position:0% +the beginning you have a lot more to + + + align:start position:0% +the beginning you have a lot more to +explore when you take general or special + + align:start position:0% +explore when you take general or special + + + align:start position:0% +explore when you take general or special +relativity course you have a lot ready + + align:start position:0% +relativity course you have a lot ready + + + align:start position:0% +relativity course you have a lot ready +more to explore when you take Ponton + + align:start position:0% +more to explore when you take Ponton + + + align:start position:0% +more to explore when you take Ponton +mechanics and I hope you really enjoy + + align:start position:0% +mechanics and I hope you really enjoy + + + align:start position:0% +mechanics and I hope you really enjoy +enjoy the content of + + align:start position:0% +enjoy the content of + + + align:start position:0% +enjoy the content of +of course personally I really enjoy that + + align:start position:0% +of course personally I really enjoy that + + + align:start position:0% +of course personally I really enjoy that +very much I love this course and I hope + + align:start position:0% +very much I love this course and I hope + + + align:start position:0% +very much I love this course and I hope +you also love it and understand + + align:start position:0% +you also love it and understand + + + align:start position:0% +you also love it and understand +something from a lecture and thank you + + align:start position:0% +something from a lecture and thank you + + + align:start position:0% +something from a lecture and thank you +very much and the next time we are going + + align:start position:0% +very much and the next time we are going + + + align:start position:0% +very much and the next time we are going +to have a review of all concepts we have + + align:start position:0% +to have a review of all concepts we have + + + align:start position:0% +to have a review of all concepts we have +learned from AOC next Tuesday thank you + + align:start position:0% +learned from AOC next Tuesday thank you + + + align:start position:0% +learned from AOC next Tuesday thank you +[Applause] + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/SCpzazvhXaU.txt b/SCpzazvhXaU.txt new file mode 100644 index 0000000000000000000000000000000000000000..7d65e4c3243d36d667030a66ef1d71301cd98bdc --- /dev/null +++ b/SCpzazvhXaU.txt @@ -0,0 +1,10971 @@ +align:start position:0% + +just one one brief announcement um hkn + + align:start position:0% +just one one brief announcement um hkn + + + align:start position:0% +just one one brief announcement um hkn +reviews are going to be done in class + + align:start position:0% +reviews are going to be done in class + + + align:start position:0% +reviews are going to be done in class +next Monday so you guys should make sure + + align:start position:0% +next Monday so you guys should make sure + + + align:start position:0% +next Monday so you guys should make sure +you come give us your feedback let us + + align:start position:0% +you come give us your feedback let us + + + align:start position:0% +you come give us your feedback let us +know what you like what you don't like + + align:start position:0% +know what you like what you don't like + + + align:start position:0% +know what you like what you don't like +um and with that we'll start talking + + align:start position:0% +um and with that we'll start talking + + + align:start position:0% +um and with that we'll start talking +about protection + + align:start position:0% + + + + align:start position:0% + +so protection + + align:start position:0% +so protection + + + align:start position:0% +so protection +is like fault tolerance and + + align:start position:0% +is like fault tolerance and + + + align:start position:0% +is like fault tolerance and +recoverability one of these properties + + align:start position:0% +recoverability one of these properties + + + align:start position:0% +recoverability one of these properties +of systems or building secure and + + align:start position:0% +of systems or building secure and + + + align:start position:0% +of systems or building secure and +protected systems + + align:start position:0% +protected systems + + + align:start position:0% +protected systems +has has implications for the entire + + align:start position:0% +has has implications for the entire + + + align:start position:0% +has has implications for the entire +design of the system and it's going to + + align:start position:0% +design of the system and it's going to + + + align:start position:0% +design of the system and it's going to +be sort of a set of crosscutting issues + + align:start position:0% +be sort of a set of crosscutting issues + + + align:start position:0% +be sort of a set of crosscutting issues +that is going to affect the way that for + + align:start position:0% +that is going to affect the way that for + + + align:start position:0% +that is going to affect the way that for +example the networking Protocols are + + align:start position:0% +example the networking Protocols are + + + align:start position:0% +example the networking Protocols are +designed or that the sort of modules + + align:start position:0% +designed or that the sort of modules + + + align:start position:0% +designed or that the sort of modules +that are a part that make up your big + + align:start position:0% +that are a part that make up your big + + + align:start position:0% +that are a part that make up your big +computer system are designed so it's + + align:start position:0% +computer system are designed so it's + + + align:start position:0% +computer system are designed so it's +going to be a whole set of issues that + + align:start position:0% +going to be a whole set of issues that + + + align:start position:0% +going to be a whole set of issues that +we're going to look at through the + + align:start position:0% +we're going to look at through the + + + align:start position:0% +we're going to look at through the +course of this discussion about uh + + align:start position:0% +course of this discussion about uh + + + align:start position:0% +course of this discussion about uh +protection that are going to affect the + + align:start position:0% +protection that are going to affect the + + + align:start position:0% +protection that are going to affect the +system at all + + align:start position:0% +system at all + + + align:start position:0% +system at all +levels in 6033 we use the word + + align:start position:0% +levels in 6033 we use the word + + + align:start position:0% +levels in 6033 we use the word +protection and security essentially + + align:start position:0% +protection and security essentially + + + align:start position:0% +protection and security essentially +synonymously so times we'll talk about a + + align:start position:0% +synonymously so times we'll talk about a + + + align:start position:0% +synonymously so times we'll talk about a +secure system or a system that has + + align:start position:0% +secure system or a system that has + + + align:start position:0% +secure system or a system that has +security uh or certain uh security goals + + align:start position:0% +security uh or certain uh security goals + + + align:start position:0% +security uh or certain uh security goals +that we have um so we're going to use + + align:start position:0% +that we have um so we're going to use + + + align:start position:0% +that we have um so we're going to use +those two words + + align:start position:0% +those two words + + + align:start position:0% +those two words +interchangeably + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +so you guys security is one of these + + align:start position:0% +so you guys security is one of these + + + align:start position:0% +so you guys security is one of these +topics that you guys are familiar with + + align:start position:0% +topics that you guys are familiar with + + + align:start position:0% +topics that you guys are familiar with +to some extent already you've all heard + + align:start position:0% +to some extent already you've all heard + + + align:start position:0% +to some extent already you've all heard +about uh various things on the internet + + align:start position:0% +about uh various things on the internet + + + align:start position:0% +about uh various things on the internet +going on where people your people's + + align:start position:0% +going on where people your people's + + + align:start position:0% +going on where people your people's +information has been stolen from laptops + + align:start position:0% +information has been stolen from laptops + + + align:start position:0% +information has been stolen from laptops +or you know a website has been cracked + + align:start position:0% +or you know a website has been cracked + + + align:start position:0% +or you know a website has been cracked +into or um some worm or you know new + + align:start position:0% +into or um some worm or you know new + + + align:start position:0% +into or um some worm or you know new +virus new I love you virus is spreading + + align:start position:0% +virus new I love you virus is spreading + + + align:start position:0% +virus new I love you virus is spreading +around and infecting people's computers + + align:start position:0% +around and infecting people's computers + + + align:start position:0% +around and infecting people's computers +so you guys are sort of familiar with it + + align:start position:0% +so you guys are sort of familiar with it + + + align:start position:0% +so you guys are sort of familiar with it +on a a colloquial sort of way I'm I'm + + align:start position:0% +on a a colloquial sort of way I'm I'm + + + align:start position:0% +on a a colloquial sort of way I'm I'm +sure um you also are familiar with many + + align:start position:0% +sure um you also are familiar with many + + + align:start position:0% +sure um you also are familiar with many +of the tools that we're going to talk + + align:start position:0% +of the tools that we're going to talk + + + align:start position:0% +of the tools that we're going to talk +about uh so the the the applied versions + + align:start position:0% +about uh so the the the applied versions + + + align:start position:0% +about uh so the the the applied versions +of many of the tools that we're going to + + align:start position:0% +of many of the tools that we're going to + + + align:start position:0% +of many of the tools that we're going to +talk about so you've you've all used a + + align:start position:0% +talk about so you've you've all used a + + + align:start position:0% +talk about so you've you've all used a +password to log into a computer before + + align:start position:0% +password to log into a computer before + + + align:start position:0% +password to log into a computer before +or you've used uh a website that uses + + align:start position:0% +or you've used uh a website that uses + + + align:start position:0% +or you've used uh a website that uses +SSL to crypt the communication with uh + + align:start position:0% +SSL to crypt the communication with uh + + + align:start position:0% +SSL to crypt the communication with uh +some other website so um you're going to + + align:start position:0% +some other website so um you're going to + + + align:start position:0% +some other website so um you're going to +be familiar with sort of many of the + + align:start position:0% +be familiar with sort of many of the + + + align:start position:0% +be familiar with sort of many of the +highle instances of the tools that we'll + + align:start position:0% +highle instances of the tools that we'll + + + align:start position:0% +highle instances of the tools that we'll +talk through in this section but what + + align:start position:0% +talk through in this section but what + + + align:start position:0% +talk through in this section but what +we're going to try and delve down into + + align:start position:0% +we're going to try and delve down into + + + align:start position:0% +we're going to try and delve down into +in 6033 is how those systems are + + align:start position:0% +in 6033 is how those systems are + + + align:start position:0% +in 6033 is how those systems are +actually put together what the design + + align:start position:0% +actually put together what the design + + + align:start position:0% +actually put together what the design +principles are behind building these + + align:start position:0% +principles are behind building these + + + align:start position:0% +principles are behind building these +secure + + align:start position:0% +secure + + + align:start position:0% +secure +systems so as I said you guys are all + + align:start position:0% +systems so as I said you guys are all + + + align:start position:0% +systems so as I said you guys are all +presumably very familiar with uh various + + align:start position:0% +presumably very familiar with uh various + + + align:start position:0% +presumably very familiar with uh various +you've all heard about these various + + align:start position:0% +you've all heard about these various + + + align:start position:0% +you've all heard about these various +kinds of attacks uh that are going on + + align:start position:0% +kinds of attacks uh that are going on + + + align:start position:0% +kinds of attacks uh that are going on +and um one of the things that has has + + align:start position:0% +and um one of the things that has has + + + align:start position:0% +and um one of the things that has has +happened in the last few years years as + + align:start position:0% +happened in the last few years years as + + + align:start position:0% +happened in the last few years years as +the internet has become more and more + + align:start position:0% +the internet has become more and more + + + align:start position:0% +the internet has become more and more +commercial and larger and larger so is + + align:start position:0% +commercial and larger and larger so is + + + align:start position:0% +commercial and larger and larger so is +that it's meant + + align:start position:0% +that it's meant + + + align:start position:0% +that it's meant +that + + align:start position:0% +that + + + align:start position:0% +that +security of computers has become much + + align:start position:0% +security of computers has become much + + + align:start position:0% +security of computers has become much +much more of a problem so the growth of + + align:start position:0% +much more of a problem so the growth of + + + align:start position:0% +much more of a problem so the growth of +the internet has spawned you know uh + + align:start position:0% + + + + align:start position:0% + +in additional + + align:start position:0% +in additional + + + align:start position:0% +in additional +attacks okay so if you go look at a + + align:start position:0% +attacks okay so if you go look at a + + + align:start position:0% +attacks okay so if you go look at a +website for example uh there's several + + align:start position:0% +website for example uh there's several + + + align:start position:0% +website for example uh there's several +security websites that track recent + + align:start position:0% +security websites that track recent + + + align:start position:0% +security websites that track recent +security breaches this is one example + + align:start position:0% +security breaches this is one example + + + align:start position:0% +security breaches this is one example +it's called uh it's called security + + align:start position:0% +it's called uh it's called security + + + align:start position:0% +it's called uh it's called security +focus.com I if you can see these but + + align:start position:0% +focus.com I if you can see these but + + + align:start position:0% +focus.com I if you can see these but +this is just a list of things that have + + align:start position:0% +this is just a list of things that have + + + align:start position:0% +this is just a list of things that have +happened in the last just few days on + + align:start position:0% +happened in the last just few days on + + + align:start position:0% +happened in the last just few days on +the internet so web server somebody's + + align:start position:0% +the internet so web server somebody's + + + align:start position:0% +the internet so web server somebody's +reporting that web server hacks were up + + align:start position:0% +reporting that web server hacks were up + + + align:start position:0% +reporting that web server hacks were up +by a third some it conference had its + + align:start position:0% +by a third some it conference had its + + + align:start position:0% +by a third some it conference had its +was hacked Windows says Windows is still + + align:start position:0% +was hacked Windows says Windows is still + + + align:start position:0% +was hacked Windows says Windows is still +trusted Windows is still coming + + align:start position:0% +trusted Windows is still coming + + + align:start position:0% +trusted Windows is still coming +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +um so there's it just goes on and on + + align:start position:0% +um so there's it just goes on and on + + + align:start position:0% +um so there's it just goes on and on +with you know these are things that have + + align:start position:0% +with you know these are things that have + + + align:start position:0% +with you know these are things that have +happened in the last few days there's + + align:start position:0% +happened in the last few days there's + + + align:start position:0% +happened in the last few days there's +this huge number of things you may have + + align:start position:0% +this huge number of things you may have + + + align:start position:0% +this huge number of things you may have +heard recent about how um you know large + + align:start position:0% +heard recent about how um you know large + + + align:start position:0% +heard recent about how um you know large +number there have been several large + + align:start position:0% +number there have been several large + + + align:start position:0% +number there have been several large +companies recently that had big privacy + + align:start position:0% +companies recently that had big privacy + + + align:start position:0% +companies recently that had big privacy +problems where databases of customer + + align:start position:0% +problems where databases of customer + + + align:start position:0% +problems where databases of customer +information have been stolen a merit + + align:start position:0% +information have been stolen a merit + + + align:start position:0% +information have been stolen a merit +trade just had this happen the + + align:start position:0% +trade just had this happen the + + + align:start position:0% +trade just had this happen the +University of California at Berkeley had + + align:start position:0% +University of California at Berkeley had + + + align:start position:0% +University of California at Berkeley had +something like uh several hundred + + align:start position:0% +something like uh several hundred + + + align:start position:0% +something like uh several hundred +thousand applications and graduate + + align:start position:0% +thousand applications and graduate + + + align:start position:0% +thousand applications and graduate +student records were on a laptop that + + align:start position:0% +student records were on a laptop that + + + align:start position:0% +student records were on a laptop that +was stolen so these are the kinds of + + align:start position:0% +was stolen so these are the kinds of + + + align:start position:0% +was stolen so these are the kinds of +things the kinds of attacks that + + align:start position:0% +things the kinds of attacks that + + + align:start position:0% +things the kinds of attacks that +um happen happen in the happen in the + + align:start position:0% +um happen happen in the happen in the + + + align:start position:0% +um happen happen in the happen in the +world um and these are the kinds of + + align:start position:0% +world um and these are the kinds of + + + align:start position:0% +world um and these are the kinds of +things that we're going to talk about + + align:start position:0% +things that we're going to talk about + + + align:start position:0% +things that we're going to talk about +how you mitigate so + + align:start position:0% + + + + align:start position:0% + +um the objective really of security um + + align:start position:0% +um the objective really of security um + + + align:start position:0% +um the objective really of security um +one one simple way to look at an + + align:start position:0% +one one simple way to look at an + + + align:start position:0% +one one simple way to look at an +objective of security is that we want to + + align:start position:0% +objective of security is that we want to + + + align:start position:0% +objective of security is that we want to +sort of + + align:start position:0% +sort of + + + align:start position:0% +sort of +protect our computer from the from bad + + align:start position:0% +protect our computer from the from bad + + + align:start position:0% +protect our computer from the from bad +guys + + align:start position:0% +guys + + + align:start position:0% +guys +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +uh definition a bad guy it depends on on + + align:start position:0% +uh definition a bad guy it depends on on + + + align:start position:0% +uh definition a bad guy it depends on on +what you mean it could be the + + align:start position:0% +what you mean it could be the + + + align:start position:0% +what you mean it could be the +16-year-old kid in his dorm room hacking + + align:start position:0% +16-year-old kid in his dorm room hacking + + + align:start position:0% +16-year-old kid in his dorm room hacking +into people's computers it could be you + + align:start position:0% +into people's computers it could be you + + + align:start position:0% +into people's computers it could be you +know somebody out to steal hundreds of + + align:start position:0% +know somebody out to steal hundreds of + + + align:start position:0% +know somebody out to steal hundreds of +thousand dollars hundreds of thousands + + align:start position:0% +thousand dollars hundreds of thousands + + + align:start position:0% +thousand dollars hundreds of thousands +of dollars from a corporation but let's + + align:start position:0% +of dollars from a corporation but let's + + + align:start position:0% +of dollars from a corporation but let's +assume that there are some bad people + + align:start position:0% +assume that there are some bad people + + + align:start position:0% +assume that there are some bad people +out there who want to sort of uh take + + align:start position:0% +out there who want to sort of uh take + + + align:start position:0% +out there who want to sort of uh take +take over your computer but at the same + + align:start position:0% +take over your computer but at the same + + + align:start position:0% +take over your computer but at the same +time the objective of security is also + + align:start position:0% +time the objective of security is also + + + align:start position:0% +time the objective of security is also +to allow + + align:start position:0% +to allow + + + align:start position:0% +to allow +access to the good guys okay + + align:start position:0% + + + + align:start position:0% + +so so one way to make sure that the bad + + align:start position:0% +so so one way to make sure that the bad + + + align:start position:0% +so so one way to make sure that the bad +guys don't get at your data is simply to + + align:start position:0% +guys don't get at your data is simply to + + + align:start position:0% +guys don't get at your data is simply to +turn your computer off right but that's + + align:start position:0% +turn your computer off right but that's + + + align:start position:0% +turn your computer off right but that's +not not that's not really a good option + + align:start position:0% +not not that's not really a good option + + + align:start position:0% +not not that's not really a good option +either we want the data to be available + + align:start position:0% +either we want the data to be available + + + align:start position:0% +either we want the data to be available +to the people who need the need the data + + align:start position:0% +to the people who need the need the data + + + align:start position:0% +to the people who need the need the data +and have the rights to access the + + align:start position:0% +and have the rights to access the + + + align:start position:0% +and have the rights to access the +data + + align:start position:0% +data + + + align:start position:0% +data +so often times we uh can sort of frame + + align:start position:0% +so often times we uh can sort of frame + + + align:start position:0% +so often times we uh can sort of frame +our discussion of that we can say that + + align:start position:0% +our discussion of that we can say that + + + align:start position:0% +our discussion of that we can say that +what we're trying to protect we have + + align:start position:0% +what we're trying to protect we have + + + align:start position:0% +what we're trying to protect we have +some set of information that we want to + + align:start position:0% +some set of information that we want to + + + align:start position:0% +some set of information that we want to +keep private so one of the sort of a + + align:start position:0% +keep private so one of the sort of a + + + align:start position:0% +keep private so one of the sort of a +goal of uh a secure system in some sense + + align:start position:0% +goal of uh a secure system in some sense + + + align:start position:0% +goal of uh a secure system in some sense +is + + align:start position:0% + + + + align:start position:0% + +providing uh privacy okay so we have + + align:start position:0% +providing uh privacy okay so we have + + + align:start position:0% +providing uh privacy okay so we have +some set of data that's on our computer + + align:start position:0% +some set of data that's on our computer + + + align:start position:0% +some set of data that's on our computer +system or that's being transmitted over + + align:start position:0% +system or that's being transmitted over + + + align:start position:0% +system or that's being transmitted over +the network that we want to keep private + + align:start position:0% +the network that we want to keep private + + + align:start position:0% +the network that we want to keep private +we want to keep other people from being + + align:start position:0% +we want to keep other people from being + + + align:start position:0% +we want to keep other people from being +able to have access to or tamper with + + align:start position:0% +able to have access to or tamper with + + + align:start position:0% +able to have access to or tamper with +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um and throughout the the sort of notion + + align:start position:0% +um and throughout the the sort of notion + + + align:start position:0% +um and throughout the the sort of notion +of what it means for a computer system + + align:start position:0% +of what it means for a computer system + + + align:start position:0% +of what it means for a computer system +to be secure is um sort of application + + align:start position:0% +to be secure is um sort of application + + + align:start position:0% +to be secure is um sort of application +dependent it depends very much on what + + align:start position:0% +dependent it depends very much on what + + + align:start position:0% +dependent it depends very much on what +the computer system we're talking about + + align:start position:0% +the computer system we're talking about + + + align:start position:0% +the computer system we're talking about +is so it may be the case that in your + + align:start position:0% +is so it may be the case that in your + + + align:start position:0% +is so it may be the case that in your +you know file system you have a set of + + align:start position:0% +you know file system you have a set of + + + align:start position:0% +you know file system you have a set of +files that you want the entire world to + + align:start position:0% +files that you want the entire world to + + + align:start position:0% +files that you want the entire world to +have access to stuff that's on your web + + align:start position:0% +have access to stuff that's on your web + + + align:start position:0% +have access to stuff that's on your web +page that you're willing to make public + + align:start position:0% +page that you're willing to make public + + + align:start position:0% +page that you're willing to make public +you don't have any real security + + align:start position:0% +you don't have any real security + + + align:start position:0% +you don't have any real security +concerns about who can read it you don't + + align:start position:0% +concerns about who can read it you don't + + + align:start position:0% +concerns about who can read it you don't +um but at the same time you know you + + align:start position:0% +um but at the same time you know you + + + align:start position:0% +um but at the same time you know you +might have banking data that you really + + align:start position:0% +might have banking data that you really + + + align:start position:0% +might have banking data that you really +don't want people in the outside world + + align:start position:0% +don't want people in the outside world + + + align:start position:0% +don't want people in the outside world +to be able to access so you have a set + + align:start position:0% +to be able to access so you have a set + + + align:start position:0% +to be able to access so you have a set +of policies that Define in your head + + align:start position:0% +of policies that Define in your head + + + align:start position:0% +of policies that Define in your head +some sort of set of policies or rules + + align:start position:0% +some sort of set of policies or rules + + + align:start position:0% +some sort of set of policies or rules +about what it is that you would like + + align:start position:0% +about what it is that you would like + + + align:start position:0% +about what it is that you would like +users to be able to access so almost any + + align:start position:0% +users to be able to access so almost any + + + align:start position:0% +users to be able to access so almost any +any system has a set of has some + + align:start position:0% +any system has a set of has some + + + align:start position:0% +any system has a set of has some +policies associated with what data + + align:start position:0% +policies associated with what data + + + align:start position:0% +policies associated with what data +should be accessed by other people some + + align:start position:0% +should be accessed by other people some + + + align:start position:0% +should be accessed by other people some +notion of what data they want to keep + + align:start position:0% +notion of what data they want to keep + + + align:start position:0% +notion of what data they want to keep +private that can be sort of translated + + align:start position:0% +private that can be sort of translated + + + align:start position:0% +private that can be sort of translated +into into this set of policies so in + + align:start position:0% +into into this set of policies so in + + + align:start position:0% +into into this set of policies so in +6033 it's sort of it's hard to study in + + align:start position:0% +6033 it's sort of it's hard to study in + + + align:start position:0% +6033 it's sort of it's hard to study in +a systematic way um different types of + + align:start position:0% +a systematic way um different types of + + + align:start position:0% +a systematic way um different types of +policy right policy is something that um + + align:start position:0% +policy right policy is something that um + + + align:start position:0% +policy right policy is something that um +we're not going to have uh we could we + + align:start position:0% +we're not going to have uh we could we + + + align:start position:0% +we're not going to have uh we could we +could sit around and have a informal + + align:start position:0% +could sit around and have a informal + + + align:start position:0% +could sit around and have a informal +discussion about different possible + + align:start position:0% +discussion about different possible + + + align:start position:0% +discussion about different possible +policies that you might want but instead + + align:start position:0% +policies that you might want but instead + + + align:start position:0% +policies that you might want but instead +in 6033 what we're going to do as we've + + align:start position:0% +in 6033 what we're going to do as we've + + + align:start position:0% +in 6033 what we're going to do as we've +done in much of the rest of the class is + + align:start position:0% +done in much of the rest of the class is + + + align:start position:0% +done in much of the rest of the class is +talk about + + align:start position:0% + + + + align:start position:0% + +mechanisms that we can use to enforce + + align:start position:0% +mechanisms that we can use to enforce + + + align:start position:0% +mechanisms that we can use to enforce +these different security policies that + + align:start position:0% +these different security policies that + + + align:start position:0% +these different security policies that +someone might have so this is we're + + align:start position:0% +someone might have so this is we're + + + align:start position:0% +someone might have so this is we're +going to talk about the tools that we + + align:start position:0% +going to talk about the tools that we + + + align:start position:0% +going to talk about the tools that we +use to protect + + align:start position:0% +use to protect + + + align:start position:0% +use to protect +data okay so in thinking about + + align:start position:0% +data okay so in thinking about + + + align:start position:0% +data okay so in thinking about +security and I think about these + + align:start position:0% +security and I think about these + + + align:start position:0% +security and I think about these +mechanisms it's a little bit it's useful + + align:start position:0% +mechanisms it's a little bit it's useful + + + align:start position:0% +mechanisms it's a little bit it's useful +to start off maybe by thinking about + + align:start position:0% +to start off maybe by thinking about + + + align:start position:0% +to start off maybe by thinking about +what we mean by security and protection + + align:start position:0% +what we mean by security and protection + + + align:start position:0% +what we mean by security and protection +in the real world and sort of compare + + align:start position:0% +in the real world and sort of compare + + + align:start position:0% +in the real world and sort of compare +the mechanisms that we have in the real + + align:start position:0% +the mechanisms that we have in the real + + + align:start position:0% +the mechanisms that we have in the real +world for protecting data from say + + align:start position:0% +world for protecting data from say + + + align:start position:0% +world for protecting data from say +mechanisms that we have on the computer + + align:start position:0% + + + + align:start position:0% + +so from the point of view of what we + + align:start position:0% +so from the point of view of what we + + + align:start position:0% +so from the point of view of what we +might want to accomplish with a Compu + + align:start position:0% +might want to accomplish with a Compu + + + align:start position:0% +might want to accomplish with a Compu +with a secure computer system some of + + align:start position:0% +with a secure computer system some of + + + align:start position:0% +with a secure computer system some of +the goals and uh objectives are similar + + align:start position:0% +the goals and uh objectives are similar + + + align:start position:0% +the goals and uh objectives are similar +to what we have in the real world + + align:start position:0% +to what we have in the real world + + + align:start position:0% +to what we have in the real world +so clearly we want to um we have this + + align:start position:0% +so clearly we want to um we have this + + + align:start position:0% +so clearly we want to um we have this +this same objective which is to protect + + align:start position:0% +this same objective which is to protect + + + align:start position:0% +this same objective which is to protect +data so + + align:start position:0% +data so + + + align:start position:0% +data so +um we can say you know just like in the + + align:start position:0% +um we can say you know just like in the + + + align:start position:0% +um we can say you know just like in the +real world we have say a lock on a door + + align:start position:0% +real world we have say a lock on a door + + + align:start position:0% +real world we have say a lock on a door +that protects somebody from getting + + align:start position:0% +that protects somebody from getting + + + align:start position:0% +that protects somebody from getting +access to something we don't want them + + align:start position:0% +access to something we don't want them + + + align:start position:0% +access to something we don't want them +to have access to um in this in the + + align:start position:0% +to have access to um in this in the + + + align:start position:0% +to have access to um in this in the +world of computers we have we can + + align:start position:0% +world of computers we have we can + + + align:start position:0% +world of computers we have we can +encrypt data um in order to make it so + + align:start position:0% +encrypt data um in order to make it so + + + align:start position:0% +encrypt data um in order to make it so +somebody who we don't want to have + + align:start position:0% +somebody who we don't want to have + + + align:start position:0% +somebody who we don't want to have +access to the data who access to our + + align:start position:0% +access to the data who access to our + + + align:start position:0% +access to the data who access to our +data doesn't have access to that + + align:start position:0% +data doesn't have access to that + + + align:start position:0% +data doesn't have access to that +data okay um similarly there there are + + align:start position:0% +data okay um similarly there there are + + + align:start position:0% +data okay um similarly there there are +also say for example in the real world + + align:start position:0% +also say for example in the real world + + + align:start position:0% +also say for example in the real world +are a set of laws that regulate who can + + align:start position:0% +are a set of laws that regulate who can + + + align:start position:0% +are a set of laws that regulate who can +access what data or what's legal and + + align:start position:0% +access what data or what's legal and + + + align:start position:0% +access what data or what's legal and +what's not legal so it's not legal for + + align:start position:0% +what's not legal so it's not legal for + + + align:start position:0% +what's not legal so it's not legal for +me to break into your house and take + + align:start position:0% +me to break into your house and take + + + align:start position:0% +me to break into your house and take +something from it similarly it's not + + align:start position:0% +something from it similarly it's not + + + align:start position:0% +something from it similarly it's not +legal for somebody to hack into a + + align:start position:0% +legal for somebody to hack into a + + + align:start position:0% +legal for somebody to hack into a +computer and steal a bunch of + + align:start position:0% +computer and steal a bunch of + + + align:start position:0% +computer and steal a bunch of +files there are also some differences + + align:start position:0% + + + + align:start position:0% + +okay so the obvious one is one that's + + align:start position:0% +okay so the obvious one is one that's + + + align:start position:0% +okay so the obvious one is one that's +been true of almost all of our + + align:start position:0% +been true of almost all of our + + + align:start position:0% +been true of almost all of our +comparisons with uh exist the between + + align:start position:0% +comparisons with uh exist the between + + + align:start position:0% +comparisons with uh exist the between +the real world that say real engine + + align:start position:0% +the real world that say real engine + + + align:start position:0% +the real world that say real engine +normal engineering disciplines that + + align:start position:0% +normal engineering disciplines that + + + align:start position:0% +normal engineering disciplines that +involve Building Bridges and buildings + + align:start position:0% +involve Building Bridges and buildings + + + align:start position:0% +involve Building Bridges and buildings +um and computer systems and that's this + + align:start position:0% +um and computer systems and that's this + + + align:start position:0% +um and computer systems and that's this +issue that computer systems have a very + + align:start position:0% +issue that computer systems have a very + + + align:start position:0% +issue that computer systems have a very +high dtec over DT okay so the computer + + align:start position:0% +high dtec over DT okay so the computer + + + align:start position:0% +high dtec over DT okay so the computer +systems change quickly and that means + + align:start position:0% +systems change quickly and that means + + + align:start position:0% +systems change quickly and that means +there's always new uh both new ways in + + align:start position:0% +there's always new uh both new ways in + + + align:start position:0% +there's always new uh both new ways in +which computer systems are connected to + + align:start position:0% +which computer systems are connected to + + + align:start position:0% +which computer systems are connected to +the world there are new and faster + + align:start position:0% +the world there are new and faster + + + align:start position:0% +the world there are new and faster +computers that are capable of breaking + + align:start position:0% +computers that are capable of breaking + + + align:start position:0% +computers that are capable of breaking +encryption algorithms that maybe we + + align:start position:0% +encryption algorithms that maybe we + + + align:start position:0% +encryption algorithms that maybe we +didn't think could be broken before + + align:start position:0% +didn't think could be broken before + + + align:start position:0% +didn't think could be broken before +there are new algorithms being developed + + align:start position:0% +there are new algorithms being developed + + + align:start position:0% +there are new algorithms being developed +both for protecting data and there are + + align:start position:0% +both for protecting data and there are + + + align:start position:0% +both for protecting data and there are +new strategies that people are adopting + + align:start position:0% +new strategies that people are adopting + + + align:start position:0% +new strategies that people are adopting +to sort of attack computers so in the + + align:start position:0% +to sort of attack computers so in the + + + align:start position:0% +to sort of attack computers so in the +recent years we've seen this thing where + + align:start position:0% +recent years we've seen this thing where + + + align:start position:0% +recent years we've seen this thing where +people are doing what they call fishing + + align:start position:0% +people are doing what they call fishing + + + align:start position:0% +people are doing what they call fishing +p i sh i n g where people are putting up + + align:start position:0% +p i sh i n g where people are putting up + + + align:start position:0% +p i sh i n g where people are putting up +fake websites that look like real + + align:start position:0% +fake websites that look like real + + + align:start position:0% +fake websites that look like real +websites so all these emails that you + + align:start position:0% +websites so all these emails that you + + + align:start position:0% +websites so all these emails that you +get from uh you know bank one or whoever + + align:start position:0% +get from uh you know bank one or whoever + + + align:start position:0% +get from uh you know bank one or whoever +it is saying come to our website click + + align:start position:0% +it is saying come to our website click + + + align:start position:0% +it is saying come to our website click +on it and you know give us your social + + align:start position:0% +on it and you know give us your social + + + align:start position:0% +on it and you know give us your social +security number and your credit card + + align:start position:0% +security number and your credit card + + + align:start position:0% +security number and your credit card +number I hope you guys aren't responding + + align:start position:0% +number I hope you guys aren't responding + + + align:start position:0% +number I hope you guys aren't responding +to those those are fake websit ites and + + align:start position:0% +to those those are fake websit ites and + + + align:start position:0% +to those those are fake websit ites and +people trying to steal your information + + align:start position:0% +people trying to steal your information + + + align:start position:0% +people trying to steal your information +okay so we see new attacks emerging over + + align:start position:0% +okay so we see new attacks emerging over + + + align:start position:0% +okay so we see new attacks emerging over +time + + align:start position:0% +time + + + align:start position:0% +time +um we uh the the other so the other + + align:start position:0% +um we uh the the other so the other + + + align:start position:0% +um we uh the the other so the other +kinds of things that we see that are + + align:start position:0% +kinds of things that we see that are + + + align:start position:0% +kinds of things that we see that are +different um clearly computer systems + + align:start position:0% +different um clearly computer systems + + + align:start position:0% +different um clearly computer systems +are attacks and computer systems can be + + align:start position:0% +are attacks and computer systems can be + + + align:start position:0% +are attacks and computer systems can be +both very + + align:start position:0% +both very + + + align:start position:0% +both very +fast and they can be cheap okay so + + align:start position:0% +fast and they can be cheap okay so + + + align:start position:0% +fast and they can be cheap okay so +unlike in the real world in a computer + + align:start position:0% +unlike in the real world in a computer + + + align:start position:0% +unlike in the real world in a computer +system you don't have to break into + + align:start position:0% +system you don't have to break into + + + align:start position:0% +system you don't have to break into +somebody you don't have to physically + + align:start position:0% +somebody you don't have to physically + + + align:start position:0% +somebody you don't have to physically +break into something you can do this + + align:start position:0% +break into something you can do this + + + align:start position:0% +break into something you can do this +very quickly over a computer system so + + align:start position:0% +very quickly over a computer system so + + + align:start position:0% +very quickly over a computer system so +you see for example with some of these + + align:start position:0% +you see for example with some of these + + + align:start position:0% +you see for example with some of these +worms and viruses these things spread + + align:start position:0% +worms and viruses these things spread + + + align:start position:0% +worms and viruses these things spread +literally across tens of thousands of + + align:start position:0% +literally across tens of thousands of + + + align:start position:0% +literally across tens of thousands of +computers in the matter of seconds okay + + align:start position:0% +computers in the matter of seconds okay + + + align:start position:0% +computers in the matter of seconds okay +so these are very efficient and + + align:start position:0% +so these are very efficient and + + + align:start position:0% +so these are very efficient and +effective attacks that can take over a + + align:start position:0% +effective attacks that can take over a + + + align:start position:0% +effective attacks that can take over a +huge number of computers in a very short + + align:start position:0% +huge number of computers in a very short + + + align:start position:0% +huge number of computers in a very short +period of time um and that that leads to + + align:start position:0% +period of time um and that that leads to + + + align:start position:0% +period of time um and that that leads to +us wanting to have a different set of + + align:start position:0% +us wanting to have a different set of + + + align:start position:0% +us wanting to have a different set of +sort of mechanisms for dealing with + + align:start position:0% +sort of mechanisms for dealing with + + + align:start position:0% +sort of mechanisms for dealing with +these kinds of + + align:start position:0% +these kinds of + + + align:start position:0% +these kinds of +problems okay and then finally + + align:start position:0% + + + + align:start position:0% + +um it is also the case that in computer + + align:start position:0% +um it is also the case that in computer + + + align:start position:0% +um it is also the case that in computer +that there's there are some differences + + align:start position:0% +that there's there are some differences + + + align:start position:0% +that there's there are some differences +in in between laws in computer systems + + align:start position:0% +in in between laws in computer systems + + + align:start position:0% +in in between laws in computer systems +and in uh the real world so in + + align:start position:0% +and in uh the real world so in + + + align:start position:0% +and in uh the real world so in +particular because the computer systems + + align:start position:0% +particular because the computer systems + + + align:start position:0% +particular because the computer systems +change so fast because new technologies + + align:start position:0% +change so fast because new technologies + + + align:start position:0% +change so fast because new technologies +develop so fast the legal system tends + + align:start position:0% +develop so fast the legal system tends + + + align:start position:0% +develop so fast the legal system tends +to lag significantly behind the + + align:start position:0% +to lag significantly behind the + + + align:start position:0% +to lag significantly behind the +state-of-the-art and technology so the + + align:start position:0% +state-of-the-art and technology so the + + + align:start position:0% +state-of-the-art and technology so the +legal system often doesn't have + + align:start position:0% +legal system often doesn't have + + + align:start position:0% +legal system often doesn't have +regulations or rules that specifically + + align:start position:0% +regulations or rules that specifically + + + align:start position:0% +regulations or rules that specifically +govern whether or not something is okay + + align:start position:0% +govern whether or not something is okay + + + align:start position:0% +govern whether or not something is okay +or is not okay um and that means + + align:start position:0% +or is not okay um and that means + + + align:start position:0% +or is not okay um and that means +sometimes it's unclear whether it's + + align:start position:0% +sometimes it's unclear whether it's + + + align:start position:0% +sometimes it's unclear whether it's +legal to do something so for example + + align:start position:0% +legal to do something so for example + + + align:start position:0% +legal to do something so for example +right now it's not legal for it's not + + align:start position:0% +right now it's not legal for it's not + + + align:start position:0% +right now it's not legal for it's not +clear whether it's legal for you to take + + align:start position:0% +clear whether it's legal for you to take + + + align:start position:0% +clear whether it's legal for you to take +your laptop out into the of Cambridge + + align:start position:0% +your laptop out into the of Cambridge + + + align:start position:0% +your laptop out into the of Cambridge +open it up and try and connect to + + align:start position:0% +open it up and try and connect to + + + align:start position:0% +open it up and try and connect to +somebody's open wireless network um + + align:start position:0% +somebody's open wireless network um + + + align:start position:0% +somebody's open wireless network um +certainly you can do that it's very easy + + align:start position:0% +certainly you can do that it's very easy + + + align:start position:0% +certainly you can do that it's very easy +to do probably many of us have done this + + align:start position:0% +to do probably many of us have done this + + + align:start position:0% +to do probably many of us have done this +right but it's not clear legally from a + + align:start position:0% +right but it's not clear legally from a + + + align:start position:0% +right but it's not clear legally from a +legal standpoint there's still some + + align:start position:0% +legal standpoint there's still some + + + align:start position:0% +legal standpoint there's still some +debate as to whether this is okay or not + + align:start position:0% +debate as to whether this is okay or not + + + align:start position:0% +debate as to whether this is okay or not +um what this suggests the fact that laws + + align:start position:0% +um what this suggests the fact that laws + + + align:start position:0% +um what this suggests the fact that laws +are often unclear ambiguous or simply + + align:start position:0% +are often unclear ambiguous or simply + + + align:start position:0% +are often unclear ambiguous or simply +unspecified about a particular thing is + + align:start position:0% +unspecified about a particular thing is + + + align:start position:0% +unspecified about a particular thing is +that we're going to need additional sort + + align:start position:0% +that we're going to need additional sort + + + align:start position:0% +that we're going to need additional sort +of sets of if if you really want to make + + align:start position:0% +of sets of if if you really want to make + + + align:start position:0% +of sets of if if you really want to make +sure your data is secure if you want to + + align:start position:0% +sure your data is secure if you want to + + + align:start position:0% +sure your data is secure if you want to +enforce a particular security policy + + align:start position:0% +enforce a particular security policy + + + align:start position:0% +enforce a particular security policy +you're going to need to rely more on + + align:start position:0% +you're going to need to rely more on + + + align:start position:0% +you're going to need to rely more on +mechanis more on sort of real mechanisms + + align:start position:0% +mechanis more on sort of real mechanisms + + + align:start position:0% +mechanis more on sort of real mechanisms +at the in the computer software to do + + align:start position:0% +at the in the computer software to do + + + align:start position:0% +at the in the computer software to do +this rather than on the legal system to + + align:start position:0% +this rather than on the legal system to + + + align:start position:0% +this rather than on the legal system to +say for example protect you from some + + align:start position:0% +say for example protect you from some + + + align:start position:0% +say for example protect you from some +thing that might be happening in the + + align:start position:0% +thing that might be happening in the + + + align:start position:0% +thing that might be happening in the +outside + + align:start position:0% + + + + align:start position:0% + +world okay + + align:start position:0% + + + + align:start position:0% + +so designing computer systems is hard + + align:start position:0% +so designing computer systems is hard + + + align:start position:0% +so designing computer systems is hard +designing secure computer systems is + + align:start position:0% +designing secure computer systems is + + + align:start position:0% +designing secure computer systems is +hard um in particular and the reason for + + align:start position:0% +hard um in particular and the reason for + + + align:start position:0% +hard um in particular and the reason for +that is that security often times the + + align:start position:0% +that is that security often times the + + + align:start position:0% +that is that security often times the +things that we want to do with security + + align:start position:0% +things that we want to do with security + + + align:start position:0% +things that we want to do with security +in in Secure systems are so the things + + align:start position:0% +in in Secure systems are so the things + + + align:start position:0% +in in Secure systems are so the things +we want to enforce are so-called + + align:start position:0% +we want to enforce are so-called + + + align:start position:0% +we want to enforce are so-called +negative goals okay so what do I mean by + + align:start position:0% + + + + align:start position:0% + +that so an example of a positive goal um + + align:start position:0% +that so an example of a positive goal um + + + align:start position:0% +that so an example of a positive goal um +is for example I might say + + align:start position:0% +is for example I might say + + + align:start position:0% +is for example I might say +Sam can + + align:start position:0% + + + + align:start position:0% + +access file F okay so if I have a that + + align:start position:0% +access file F okay so if I have a that + + + align:start position:0% +access file F okay so if I have a that +that presumably is something that's + + align:start position:0% +that presumably is something that's + + + align:start position:0% +that presumably is something that's +relatively easy to verify that that's + + align:start position:0% +relatively easy to verify that that's + + + align:start position:0% +relatively easy to verify that that's +true right I can log on to my computer + + align:start position:0% +true right I can log on to my computer + + + align:start position:0% +true right I can log on to my computer +system and if I can access the file this + + align:start position:0% +system and if I can access the file this + + + align:start position:0% +system and if I can access the file this +file F then well great I can access the + + align:start position:0% +file F then well great I can access the + + + align:start position:0% +file F then well great I can access the +file F we know that's true and that was + + align:start position:0% +file F we know that's true and that was + + + align:start position:0% +file F we know that's true and that was +easy to check + + align:start position:0% +easy to check + + + align:start position:0% +easy to check +okay furthermore if I can't access the + + align:start position:0% +okay furthermore if I can't access the + + + align:start position:0% +okay furthermore if I can't access the +file it's very and I think that I should + + align:start position:0% +file it's very and I think that I should + + + align:start position:0% +file it's very and I think that I should +have the rights to access it I'm going + + align:start position:0% +have the rights to access it I'm going + + + align:start position:0% +have the rights to access it I'm going +to email my system administrator and say + + align:start position:0% +to email my system administrator and say + + + align:start position:0% +to email my system administrator and say +hey I think I should be able to access + + align:start position:0% +hey I think I should be able to access + + + align:start position:0% +hey I think I should be able to access +this file why can't I will you please + + align:start position:0% +this file why can't I will you please + + + align:start position:0% +this file why can't I will you please +give me access to it okay a neg example + + align:start position:0% +give me access to it okay a neg example + + + align:start position:0% +give me access to it okay a neg example +of a negative goal is that + + align:start position:0% + + + + align:start position:0% + +Sam shouldn't be + + align:start position:0% +Sam shouldn't be + + + align:start position:0% +Sam shouldn't be +able to + + align:start position:0% +able to + + + align:start position:0% +able to +access F okay so at first it may seem + + align:start position:0% +access F okay so at first it may seem + + + align:start position:0% +access F okay so at first it may seem +that this is just the same problem as + + align:start position:0% +that this is just the same problem as + + + align:start position:0% +that this is just the same problem as +saying that Sam is just the inverse of + + align:start position:0% +saying that Sam is just the inverse of + + + align:start position:0% +saying that Sam is just the inverse of +saying Sam can't access Heaven it seems + + align:start position:0% +saying Sam can't access Heaven it seems + + + align:start position:0% +saying Sam can't access Heaven it seems +like it should be just as easy or hard + + align:start position:0% +like it should be just as easy or hard + + + align:start position:0% +like it should be just as easy or hard +to verify but it turns out that when + + align:start position:0% +to verify but it turns out that when + + + align:start position:0% +to verify but it turns out that when +you're thinking about computer systems + + align:start position:0% +you're thinking about computer systems + + + align:start position:0% +you're thinking about computer systems +this sort of a problem is very hard to + + align:start position:0% +this sort of a problem is very hard to + + + align:start position:0% +this sort of a problem is very hard to +verify because well it may be true that + + align:start position:0% +verify because well it may be true that + + + align:start position:0% +verify because well it may be true that +when I try and open open the file and I + + align:start position:0% +when I try and open open the file and I + + + align:start position:0% +when I try and open open the file and I +log into my machine and I connect to + + align:start position:0% +log into my machine and I connect to + + + align:start position:0% +log into my machine and I connect to +some remote machine and try and access + + align:start position:0% +some remote machine and try and access + + + align:start position:0% +some remote machine and try and access +that file maybe the case that the file + + align:start position:0% +that file maybe the case that the file + + + align:start position:0% +that file maybe the case that the file +system denies me access to that file but + + align:start position:0% +system denies me access to that file but + + + align:start position:0% +system denies me access to that file but +I may have many other avenues for + + align:start position:0% +I may have many other avenues for + + + align:start position:0% +I may have many other avenues for +obtaining access to that file so for + + align:start position:0% +obtaining access to that file so for + + + align:start position:0% +obtaining access to that file so for +example suppose I have a a key to the + + align:start position:0% +example suppose I have a a key to the + + + align:start position:0% +example suppose I have a a key to the +the room in which the server that hosts + + align:start position:0% +the room in which the server that hosts + + + align:start position:0% +the room in which the server that hosts +that file is stored I can walk into that + + align:start position:0% +that file is stored I can walk into that + + + align:start position:0% +that file is stored I can walk into that +room and I may be able to sit down in + + align:start position:0% +room and I may be able to sit down in + + + align:start position:0% +room and I may be able to sit down in +front of the console on this machine and + + align:start position:0% +front of the console on this machine and + + + align:start position:0% +front of the console on this machine and +get obtained super user root access to + + align:start position:0% +get obtained super user root access to + + + align:start position:0% +get obtained super user root access to +that machine or I may be able to pull + + align:start position:0% +that machine or I may be able to pull + + + align:start position:0% +that machine or I may be able to pull +the hard drive off of the machine and + + align:start position:0% +the hard drive off of the machine and + + + align:start position:0% +the hard drive off of the machine and +put it into my computer and read files + + align:start position:0% +put it into my computer and read files + + + align:start position:0% +put it into my computer and read files +off of it right or I may be able to + + align:start position:0% +off of it right or I may be able to + + + align:start position:0% +off of it right or I may be able to +bribe my system administrator and you + + align:start position:0% +bribe my system administrator and you + + + align:start position:0% +bribe my system administrator and you +know give him $100 in exchange for him + + align:start position:0% +know give him $100 in exchange for him + + + align:start position:0% +know give him $100 in exchange for him +letting me have access to this file + + align:start position:0% +letting me have access to this file + + + align:start position:0% +letting me have access to this file +right so there's lots and lots of ways + + align:start position:0% +right so there's lots and lots of ways + + + align:start position:0% +right so there's lots and lots of ways +in which users can get unauthorized or + + align:start position:0% +in which users can get unauthorized or + + + align:start position:0% +in which users can get unauthorized or +unintended access to files or other + + align:start position:0% +unintended access to files or other + + + align:start position:0% +unintended access to files or other +information in computer systems and + + align:start position:0% +information in computer systems and + + + align:start position:0% +information in computer systems and +verifying that none of those Avenues are + + align:start position:0% +verifying that none of those Avenues are + + + align:start position:0% +verifying that none of those Avenues are +available to a particular user is very + + align:start position:0% +available to a particular user is very + + + align:start position:0% +available to a particular user is very +hard worse or similarly it's this is + + align:start position:0% +hard worse or similarly it's this is + + + align:start position:0% +hard worse or similarly it's this is +hard because it's very unlikely that a + + align:start position:0% +hard because it's very unlikely that a + + + align:start position:0% +hard because it's very unlikely that a +user is going to complain about having + + align:start position:0% +user is going to complain about having + + + align:start position:0% +user is going to complain about having +access to some file that they shouldn't + + align:start position:0% +access to some file that they shouldn't + + + align:start position:0% +access to some file that they shouldn't +have access to right so I'm not going to + + align:start position:0% +have access to right so I'm not going to + + + align:start position:0% +have access to right so I'm not going to +call out my system administrator and say + + align:start position:0% +call out my system administrator and say + + + align:start position:0% +call out my system administrator and say +hey I have access to this file I don't + + align:start position:0% +hey I have access to this file I don't + + + align:start position:0% +hey I have access to this file I don't +think I should have access to it right + + align:start position:0% +think I should have access to it right + + + align:start position:0% +think I should have access to it right +nobody's going to do that so even though + + align:start position:0% +nobody's going to do that so even though + + + align:start position:0% +nobody's going to do that so even though +I'm not a malicious user I don't really + + align:start position:0% +I'm not a malicious user I don't really + + + align:start position:0% +I'm not a malicious user I don't really +have any incentive to go to my system + + align:start position:0% +have any incentive to go to my system + + + align:start position:0% +have any incentive to go to my system +administrator and tell them that there's + + align:start position:0% +administrator and tell them that there's + + + align:start position:0% +administrator and tell them that there's +this problem with the way that things + + align:start position:0% +this problem with the way that things + + + align:start position:0% +this problem with the way that things +are configured on the computer um and + + align:start position:0% +are configured on the computer um and + + + align:start position:0% +are configured on the computer um and +that extends also to people who in fact + + align:start position:0% +that extends also to people who in fact + + + align:start position:0% +that extends also to people who in fact +are malicious users right when somebody + + align:start position:0% +are malicious users right when somebody + + + align:start position:0% +are malicious users right when somebody +breaks into a computer system they don't + + align:start position:0% +breaks into a computer system they don't + + + align:start position:0% +breaks into a computer system they don't +typically usually they don't send out an + + align:start position:0% +typically usually they don't send out an + + + align:start position:0% +typically usually they don't send out an +advertisement to everybody in the world + + align:start position:0% +advertisement to everybody in the world + + + align:start position:0% +advertisement to everybody in the world +saying hey by the way I got access to + + align:start position:0% +saying hey by the way I got access to + + + align:start position:0% +saying hey by the way I got access to +this file that I shouldn't have access + + align:start position:0% +this file that I shouldn't have access + + + align:start position:0% +this file that I shouldn't have access +to right it's possible for them to log + + align:start position:0% +to right it's possible for them to log + + + align:start position:0% +to right it's possible for them to log +in read the file log out and nobody + + align:start position:0% +in read the file log out and nobody + + + align:start position:0% +in read the file log out and nobody +would be any any the wiser okay so um + + align:start position:0% +would be any any the wiser okay so um + + + align:start position:0% +would be any any the wiser okay so um +often times so many many of our security + + align:start position:0% +often times so many many of our security + + + align:start position:0% +often times so many many of our security +goals are negative and that means + + align:start position:0% +goals are negative and that means + + + align:start position:0% +goals are negative and that means +building computer systems secure + + align:start position:0% +building computer systems secure + + + align:start position:0% +building computer systems secure +computer systems is + + align:start position:0% + + + + align:start position:0% + +hard okay so what we're going to do in + + align:start position:0% +hard okay so what we're going to do in + + + align:start position:0% +hard okay so what we're going to do in +6033 in in order to get at this is look + + align:start position:0% +6033 in in order to get at this is look + + + align:start position:0% +6033 in in order to get at this is look +at um get at sort of building security + + align:start position:0% +at um get at sort of building security + + + align:start position:0% +at um get at sort of building security +secure systems in face of these goal + + align:start position:0% +secure systems in face of these goal + + + align:start position:0% +secure systems in face of these goal +these negative goals is look at um a set + + align:start position:0% +these negative goals is look at um a set + + + align:start position:0% +these negative goals is look at um a set +of sort of principled security functions + + align:start position:0% +of sort of principled security functions + + + align:start position:0% +of sort of principled security functions +that or a a set of different security + + align:start position:0% +that or a a set of different security + + + align:start position:0% +that or a a set of different security +functions that we can use to protect + + align:start position:0% +functions that we can use to protect + + + align:start position:0% +functions that we can use to protect +information in different and access to + + align:start position:0% +information in different and access to + + + align:start position:0% +information in different and access to +computers in different sorts of ways um + + align:start position:0% +computers in different sorts of ways um + + + align:start position:0% +computers in different sorts of ways um +and we're typically going to talk about + + align:start position:0% +and we're typically going to talk about + + + align:start position:0% +and we're typically going to talk about +uh throughout throughout this we're + + align:start position:0% +uh throughout throughout this we're + + + align:start position:0% +uh throughout throughout this we're +going to talk about we're going to talk + + align:start position:0% +going to talk about we're going to talk + + + align:start position:0% +going to talk about we're going to talk +about a client server sort of a system + + align:start position:0% +about a client server sort of a system + + + align:start position:0% +about a client server sort of a system +where you have some client and some + + align:start position:0% +where you have some client and some + + + align:start position:0% +where you have some client and some +server that are separated say you + + align:start position:0% +server that are separated say you + + + align:start position:0% +server that are separated say you +typically over the internet that are + + align:start position:0% +typically over the internet that are + + + align:start position:0% +typically over the internet that are +sort of trying to uh exchange + + align:start position:0% +sort of trying to uh exchange + + + align:start position:0% +sort of trying to uh exchange +information or obtain information from + + align:start position:0% +information or obtain information from + + + align:start position:0% +information or obtain information from +each other in a way that such that that + + align:start position:0% +each other in a way that such that that + + + align:start position:0% +each other in a way that such that that +information exchange is protected and + + align:start position:0% +information exchange is protected and + + + align:start position:0% +information exchange is protected and +secure and uh so on so we have a client + + align:start position:0% +secure and uh so on so we have a client + + + align:start position:0% +secure and uh so on so we have a client +suppose we have a client sending some + + align:start position:0% +suppose we have a client sending some + + + align:start position:0% +suppose we have a client sending some +information out over the + + align:start position:0% +information out over the + + + align:start position:0% +information out over the +internet to some + + align:start position:0% +internet to some + + + align:start position:0% +internet to some +server okay so what are the kinds of + + align:start position:0% +server okay so what are the kinds of + + + align:start position:0% +server okay so what are the kinds of +things that we we want to make sure what + + align:start position:0% +things that we we want to make sure what + + + align:start position:0% +things that we we want to make sure what +are the the sorts of security goals that + + align:start position:0% +are the the sorts of security goals that + + + align:start position:0% +are the the sorts of security goals that +we might want to enforce um in this + + align:start position:0% +we might want to enforce um in this + + + align:start position:0% +we might want to enforce um in this +environment so one thing we might want + + align:start position:0% +environment so one thing we might want + + + align:start position:0% +environment so one thing we might want +to do is + + align:start position:0% +to do is + + + align:start position:0% +to do is +um + + align:start position:0% +um + + + align:start position:0% +um +authenticate the client okay so the + + align:start position:0% +authenticate the client okay so the + + + align:start position:0% +authenticate the client okay so the +server might like to know for sure that + + align:start position:0% +server might like to know for sure that + + + align:start position:0% +server might like to know for sure that +the person who issued this request is in + + align:start position:0% +the person who issued this request is in + + + align:start position:0% +the person who issued this request is in +fact the client they' like to have some + + align:start position:0% +fact the client they' like to have some + + + align:start position:0% +fact the client they' like to have some +way of knowing that the the client + + align:start position:0% +way of knowing that the the client + + + align:start position:0% +way of knowing that the the client +issued this request and that the uh + + align:start position:0% +issued this request and that the uh + + + align:start position:0% +issued this request and that the uh +request that was sent is in fact what + + align:start position:0% +request that was sent is in fact what + + + align:start position:0% +request that was sent is in fact what +the client intended to be sent so for + + align:start position:0% +the client intended to be sent so for + + + align:start position:0% +the client intended to be sent so for +example that somebody didn't intercept + + align:start position:0% +example that somebody didn't intercept + + + align:start position:0% +example that somebody didn't intercept +this message as it was being transmitted + + align:start position:0% +this message as it was being transmitted + + + align:start position:0% +this message as it was being transmitted +over the network change it a little bit + + align:start position:0% +over the network change it a little bit + + + align:start position:0% +over the network change it a little bit +and then send it on making it look as + + align:start position:0% +and then send it on making it look as + + + align:start position:0% +and then send it on making it look as +though it came from the client okay so + + align:start position:0% +though it came from the client okay so + + + align:start position:0% +though it came from the client okay so +there might be different kinds of + + align:start position:0% +there might be different kinds of + + + align:start position:0% +there might be different kinds of +attackers that are sitting in this + + align:start position:0% +attackers that are sitting in this + + + align:start position:0% +attackers that are sitting in this +internet for example there might be you + + align:start position:0% +internet for example there might be you + + + align:start position:0% +internet for example there might be you +know say a intermediate router along the + + align:start position:0% +know say a intermediate router along the + + + align:start position:0% +know say a intermediate router along the +path between the client and the server + + align:start position:0% +path between the client and the server + + + align:start position:0% +path between the client and the server +where uh the system administrator of the + + align:start position:0% +where uh the system administrator of the + + + align:start position:0% +where uh the system administrator of the +router is + + align:start position:0% +router is + + + align:start position:0% +router is +malicious so uh the often times in the + + align:start position:0% +malicious so uh the often times in the + + + align:start position:0% +malicious so uh the often times in the +security literature there are these + + align:start position:0% +security literature there are these + + + align:start position:0% +security literature there are these +funny names that are attached to the + + align:start position:0% +funny names that are attached to the + + + align:start position:0% +funny names that are attached to the +different people the different places so + + align:start position:0% +different people the different places so + + + align:start position:0% +different people the different places so +often times the client is called Alice + + align:start position:0% +often times the client is called Alice + + + align:start position:0% +often times the client is called Alice +and the the server is called bob the + + align:start position:0% +and the the server is called bob the + + + align:start position:0% +and the the server is called bob the +person receiving the request we talk + + align:start position:0% +person receiving the request we talk + + + align:start position:0% +person receiving the request we talk +about two different attackers we talk + + align:start position:0% +about two different attackers we talk + + + align:start position:0% +about two different attackers we talk +about Eve Who's an evees dropper who + + align:start position:0% +about Eve Who's an evees dropper who + + + align:start position:0% +about Eve Who's an evees dropper who +listens listens to the listens to what's + + align:start position:0% +listens listens to the listens to what's + + + align:start position:0% +listens listens to the listens to what's +going on and tries to acquire + + align:start position:0% +going on and tries to acquire + + + align:start position:0% +going on and tries to acquire +information that she's not authorized to + + align:start position:0% +information that she's not authorized to + + + align:start position:0% +information that she's not authorized to +have and we talk about Lucifer who's the + + align:start position:0% +have and we talk about Lucifer who's the + + + align:start position:0% +have and we talk about Lucifer who's the +bad guy who not only is trying to + + align:start position:0% +bad guy who not only is trying to + + + align:start position:0% +bad guy who not only is trying to +overhear information but may do + + align:start position:0% +overhear information but may do + + + align:start position:0% +overhear information but may do +arbitrarily bad things okay so he's + + align:start position:0% +arbitrarily bad things okay so he's + + + align:start position:0% +arbitrarily bad things okay so he's +trying to take over the take over the + + align:start position:0% +trying to take over the take over the + + + align:start position:0% +trying to take over the take over the +data corrupt it in any way he possibly + + align:start position:0% +data corrupt it in any way he possibly + + + align:start position:0% +data corrupt it in any way he possibly +can + + align:start position:0% +can + + + align:start position:0% +can +okay um so one one goal is that we want + + align:start position:0% +okay um so one one goal is that we want + + + align:start position:0% +okay um so one one goal is that we want +to prevent uh say for example Lucifer + + align:start position:0% +to prevent uh say for example Lucifer + + + align:start position:0% +to prevent uh say for example Lucifer +from being able to interfere with + + align:start position:0% +from being able to interfere with + + + align:start position:0% +from being able to interfere with +packets coming from Alice to Bob and + + align:start position:0% +packets coming from Alice to Bob and + + + align:start position:0% +packets coming from Alice to Bob and +make sure that those so that we want to + + align:start position:0% +make sure that those so that we want to + + + align:start position:0% +make sure that those so that we want to +make sure that packets that the server + + align:start position:0% +make sure that packets that the server + + + align:start position:0% +make sure that packets that the server +receives actually originated from Alice + + align:start position:0% +receives actually originated from Alice + + + align:start position:0% +receives actually originated from Alice +and were the original requests that + + align:start position:0% +and were the original requests that + + + align:start position:0% +and were the original requests that +Alice sent so that's + + align:start position:0% +Alice sent so that's + + + align:start position:0% +Alice sent so that's +authentication we also also might want + + align:start position:0% +authentication we also also might want + + + align:start position:0% +authentication we also also might want +to + + align:start position:0% +to + + + align:start position:0% +to +authorize that that at the server that + + align:start position:0% +authorize that that at the server that + + + align:start position:0% +authorize that that at the server that +Alice is in fact allowed to access the + + align:start position:0% +Alice is in fact allowed to access the + + + align:start position:0% +Alice is in fact allowed to access the +things that she is trying to access okay + + align:start position:0% +things that she is trying to access okay + + + align:start position:0% +things that she is trying to access okay +so if Alice tries to read a file we need + + align:start position:0% +so if Alice tries to read a file we need + + + align:start position:0% +so if Alice tries to read a file we need +some way of understanding whether Alice + + align:start position:0% +some way of understanding whether Alice + + + align:start position:0% +some way of understanding whether Alice +is allowed to access this file or + + align:start position:0% + + + + align:start position:0% + +not + + align:start position:0% + + + + align:start position:0% + +um we also need to keep some information + + align:start position:0% + + + + align:start position:0% + +confidential okay so we may want it to + + align:start position:0% +confidential okay so we may want it to + + + align:start position:0% +confidential okay so we may want it to +be the case that Eve so the we may want + + align:start position:0% +be the case that Eve so the we may want + + + align:start position:0% +be the case that Eve so the we may want +it to be the case that Eve who overhears + + align:start position:0% +it to be the case that Eve who overhears + + + align:start position:0% +it to be the case that Eve who overhears +a packet can't tell what the contents of + + align:start position:0% +a packet can't tell what the contents of + + + align:start position:0% +a packet can't tell what the contents of +that packet are right we may want to be + + align:start position:0% +that packet are right we may want to be + + + align:start position:0% +that packet are right we may want to be +able to protect the contents of that + + align:start position:0% +able to protect the contents of that + + + align:start position:0% +able to protect the contents of that +thing so that Eve can't even see what's + + align:start position:0% +thing so that Eve can't even see what's + + + align:start position:0% +thing so that Eve can't even see what's +going over the network so notice that + + align:start position:0% +going over the network so notice that + + + align:start position:0% +going over the network so notice that +this is a little bit different than + + align:start position:0% +this is a little bit different than + + + align:start position:0% +this is a little bit different than +authenticating authenticating says we + + align:start position:0% +authenticating authenticating says we + + + align:start position:0% +authenticating authenticating says we +just want to make sure the packet in + + align:start position:0% +just want to make sure the packet in + + + align:start position:0% +just want to make sure the packet in +fact came from the client but we're not + + align:start position:0% +fact came from the client but we're not + + + align:start position:0% +fact came from the client but we're not +saying anything about whether or not + + align:start position:0% +saying anything about whether or not + + + align:start position:0% +saying anything about whether or not +somebody else can see the contents of + + align:start position:0% +somebody else can see the contents of + + + align:start position:0% +somebody else can see the contents of +that packet keeping confidential says we + + align:start position:0% +that packet keeping confidential says we + + + align:start position:0% +that packet keeping confidential says we +want to make sure that nobody except for + + align:start position:0% +want to make sure that nobody except for + + + align:start position:0% +want to make sure that nobody except for +the intended recipients can in fact see + + align:start position:0% +the intended recipients can in fact see + + + align:start position:0% +the intended recipients can in fact see +the contents of + + align:start position:0% +the contents of + + + align:start position:0% +the contents of +this there's a couple of other + + align:start position:0% +this there's a couple of other + + + align:start position:0% +this there's a couple of other +properties that we we want as well one + + align:start position:0% +properties that we we want as well one + + + align:start position:0% +properties that we we want as well one +thing we might want is accountability + + align:start position:0% + + + + align:start position:0% + +so this says this we're going to talk + + align:start position:0% +so this says this we're going to talk + + + align:start position:0% +so this says this we're going to talk +about this a little bit more this says + + align:start position:0% +about this a little bit more this says + + + align:start position:0% +about this a little bit more this says +we need to assume that people who are + + align:start position:0% +we need to assume that people who are + + + align:start position:0% +we need to assume that people who are +it's always possible that something + + align:start position:0% +it's always possible that something + + + align:start position:0% +it's always possible that something +could go wrong right it's always + + align:start position:0% +could go wrong right it's always + + + align:start position:0% +could go wrong right it's always +possible that you know I might have + + align:start position:0% +possible that you know I might have + + + align:start position:0% +possible that you know I might have +bribed my system administrator and he + + align:start position:0% +bribed my system administrator and he + + + align:start position:0% +bribed my system administrator and he +might have given me access to the + + align:start position:0% +might have given me access to the + + + align:start position:0% +might have given me access to the +computer and in the end there's not much + + align:start position:0% +computer and in the end there's not much + + + align:start position:0% +computer and in the end there's not much +you're going to be able to do about that + + align:start position:0% +you're going to be able to do about that + + + align:start position:0% +you're going to be able to do about that +what you want to do is make sure that + + align:start position:0% +what you want to do is make sure that + + + align:start position:0% +what you want to do is make sure that +when systems like when situations like + + align:start position:0% +when systems like when situations like + + + align:start position:0% +when systems like when situations like +that occur that there's some log of what + + align:start position:0% +that occur that there's some log of what + + + align:start position:0% +that occur that there's some log of what +happened that you have some way of + + align:start position:0% +happened that you have some way of + + + align:start position:0% +happened that you have some way of +understanding what it was that happened + + align:start position:0% +understanding what it was that happened + + + align:start position:0% +understanding what it was that happened +why it happened and how it happened so + + align:start position:0% +why it happened and how it happened so + + + align:start position:0% +why it happened and how it happened so +you can try and prevent it later so you + + align:start position:0% +you can try and prevent it later so you + + + align:start position:0% +you can try and prevent it later so you +want to make sure that you do uh you you + + align:start position:0% +want to make sure that you do uh you you + + + align:start position:0% +want to make sure that you do uh you you +you keep you do accounting you keep + + align:start position:0% +you keep you do accounting you keep + + + align:start position:0% +you keep you do accounting you keep +track of what's been going on and + + align:start position:0% +track of what's been going on and + + + align:start position:0% +track of what's been going on and +finally you might want + + align:start position:0% + + + + align:start position:0% + +availability okay so this is uh you + + align:start position:0% +availability okay so this is uh you + + + align:start position:0% +availability okay so this is uh you +might want to make sure that lufer who's + + align:start position:0% +might want to make sure that lufer who's + + + align:start position:0% +might want to make sure that lufer who's +sitting here between the client and the + + align:start position:0% +sitting here between the client and the + + + align:start position:0% +sitting here between the client and the +server can't uh for example send a huge + + align:start position:0% +server can't uh for example send a huge + + + align:start position:0% +server can't uh for example send a huge +number of packets at the server and make + + align:start position:0% +number of packets at the server and make + + + align:start position:0% +number of packets at the server and make +it unavailable just swamp it with a + + align:start position:0% +it unavailable just swamp it with a + + + align:start position:0% +it unavailable just swamp it with a +denial of service attack okay so + + align:start position:0% +denial of service attack okay so + + + align:start position:0% +denial of service attack okay so +availability means that this system in + + align:start position:0% +availability means that this system in + + + align:start position:0% +availability means that this system in +fact functions and provides the + + align:start position:0% +fact functions and provides the + + + align:start position:0% +fact functions and provides the +functionality that's intended uh that it + + align:start position:0% +functionality that's intended uh that it + + + align:start position:0% +functionality that's intended uh that it +was intended to provide to the client + + align:start position:0% + + + + align:start position:0% + +okay so we're going to spend a while in + + align:start position:0% +okay so we're going to spend a while in + + + align:start position:0% +okay so we're going to spend a while in +6033 especially focusing on these first + + align:start position:0% +6033 especially focusing on these first + + + align:start position:0% +6033 especially focusing on these first +three techniques essentially the next + + align:start position:0% +three techniques essentially the next + + + align:start position:0% +three techniques essentially the next +three lectures are going to be talking + + align:start position:0% +three lectures are going to be talking + + + align:start position:0% +three lectures are going to be talking +about how we guarantee and how how we + + align:start position:0% +about how we guarantee and how how we + + + align:start position:0% +about how we guarantee and how how we +protect how we uh authenticate and + + align:start position:0% +protect how we uh authenticate and + + + align:start position:0% +protect how we uh authenticate and +authorize users and how we keep + + align:start position:0% +authorize users and how we keep + + + align:start position:0% +authorize users and how we keep +information confidential and + + align:start position:0% +information confidential and + + + align:start position:0% +information confidential and +private um + + align:start position:0% +private um + + + align:start position:0% +private um +but all of these goals together uh these + + align:start position:0% +but all of these goals together uh these + + + align:start position:0% +but all of these goals together uh these +These are these are simply there's a set + + align:start position:0% +These are these are simply there's a set + + + align:start position:0% +These are these are simply there's a set +of technical techniques that we can talk + + align:start position:0% +of technical techniques that we can talk + + + align:start position:0% +of technical techniques that we can talk +about for trying to provide each one of + + align:start position:0% +about for trying to provide each one of + + + align:start position:0% +about for trying to provide each one of +these things but when you think about + + align:start position:0% +these things but when you think about + + + align:start position:0% +these things but when you think about +building a secure system it's not enough + + align:start position:0% +building a secure system it's not enough + + + align:start position:0% +building a secure system it's not enough +to Simply uh say we're going to employ + + align:start position:0% +to Simply uh say we're going to employ + + + align:start position:0% +to Simply uh say we're going to employ +you know we I employ authentication to + + align:start position:0% +you know we I employ authentication to + + + align:start position:0% +you know we I employ authentication to +make sure that you know Alice is in fact + + align:start position:0% +make sure that you know Alice is in fact + + + align:start position:0% +make sure that you know Alice is in fact +Alice when she talks to Bob what you + + align:start position:0% +Alice when she talks to Bob what you + + + align:start position:0% +Alice when she talks to Bob what you +might want to do what you want to do + + align:start position:0% +might want to do what you want to do + + + align:start position:0% +might want to do what you want to do +when you build a secure system is think + + align:start position:0% +when you build a secure system is think + + + align:start position:0% +when you build a secure system is think +about sort of how to you you want to get + + align:start position:0% +about sort of how to you you want to get + + + align:start position:0% +about sort of how to you you want to get +your mindset around building a sort of + + align:start position:0% +your mindset around building a sort of + + + align:start position:0% +your mindset around building a sort of +the general ideas behind building a + + align:start position:0% +the general ideas behind building a + + + align:start position:0% +the general ideas behind building a +secure system and so in 6033 we have + + align:start position:0% +secure system and so in 6033 we have + + + align:start position:0% +secure system and so in 6033 we have +this set of principles that we Advocate + + align:start position:0% +this set of principles that we Advocate + + + align:start position:0% +this set of principles that we Advocate +um called the safety net approach the + + align:start position:0% +um called the safety net approach the + + + align:start position:0% +um called the safety net approach the +idea is the safety net approach is a way + + align:start position:0% +idea is the safety net approach is a way + + + align:start position:0% +idea is the safety net approach is a way +to help you sort of in general think + + align:start position:0% +to help you sort of in general think + + + align:start position:0% +to help you sort of in general think +about building a secure system as + + align:start position:0% +about building a secure system as + + + align:start position:0% +about building a secure system as +opposed to uh these specific techniques + + align:start position:0% +opposed to uh these specific techniques + + + align:start position:0% +opposed to uh these specific techniques +that we're going to see how to apply + + align:start position:0% +that we're going to see how to apply + + + align:start position:0% +that we're going to see how to apply +later + + align:start position:0% + + + + align:start position:0% + +on so the safety net approach Advocates + + align:start position:0% +on so the safety net approach Advocates + + + align:start position:0% +on so the safety net approach Advocates +uh sort of set of ways of thinking about + + align:start position:0% +uh sort of set of ways of thinking about + + + align:start position:0% +uh sort of set of ways of thinking about +your + + align:start position:0% +your + + + align:start position:0% +your +system the first one is paranoid okay so + + align:start position:0% +system the first one is paranoid okay so + + + align:start position:0% +system the first one is paranoid okay so +this says assume that things that this + + align:start position:0% +this says assume that things that this + + + align:start position:0% +this says assume that things that this +sort of uh this says this is sort of the + + align:start position:0% +sort of uh this says this is sort of the + + + align:start position:0% +sort of uh this says this is sort of the +Murphy's Law of security it says assume + + align:start position:0% +Murphy's Law of security it says assume + + + align:start position:0% +Murphy's Law of security it says assume +that anything that can go wrong will go + + align:start position:0% +that anything that can go wrong will go + + + align:start position:0% +that anything that can go wrong will go +wrong right don't just assume that + + align:start position:0% +wrong right don't just assume that + + + align:start position:0% +wrong right don't just assume that +because you have uh you know that + + align:start position:0% +because you have uh you know that + + + align:start position:0% +because you have uh you know that +because you have installed a um because + + align:start position:0% +because you have installed a um because + + + align:start position:0% +because you have installed a um because +you're authenticating the communication + + align:start position:0% +you're authenticating the communication + + + align:start position:0% +you're authenticating the communication +between uh Alice and Bob that there is + + align:start position:0% +between uh Alice and Bob that there is + + + align:start position:0% +between uh Alice and Bob that there is +no way that somebody else will pretend + + align:start position:0% +no way that somebody else will pretend + + + align:start position:0% +no way that somebody else will pretend +to be Alice you should always have + + align:start position:0% +to be Alice you should always have + + + align:start position:0% +to be Alice you should always have +something uh a a a safety net something + + align:start position:0% +something uh a a a safety net something + + + align:start position:0% +something uh a a a safety net something +some backup to make sure that your + + align:start position:0% +some backup to make sure that your + + + align:start position:0% +some backup to make sure that your +system is really secure so um good + + align:start position:0% +system is really secure so um good + + + align:start position:0% +system is really secure so um good +examples of being paranoid and applying + + align:start position:0% +examples of being paranoid and applying + + + align:start position:0% +examples of being paranoid and applying +the safety net approach are things like + + align:start position:0% +the safety net approach are things like + + + align:start position:0% +the safety net approach are things like +um you know suppose that + + align:start position:0% +um you know suppose that + + + align:start position:0% +um you know suppose that +your um router has a firewall on it + + align:start position:0% +your um router has a firewall on it + + + align:start position:0% +your um router has a firewall on it +right so suppose you're your your home + + align:start position:0% +right so suppose you're your your home + + + align:start position:0% +right so suppose you're your your home +your home router has a firewall that's + + align:start position:0% +your home router has a firewall that's + + + align:start position:0% +your home router has a firewall that's +supposed to prevent unauthorized users + + align:start position:0% +supposed to prevent unauthorized users + + + align:start position:0% +supposed to prevent unauthorized users +from being able to access your computer + + align:start position:0% +from being able to access your computer + + + align:start position:0% +from being able to access your computer +does that mean that you should then you + + align:start position:0% +does that mean that you should then you + + + align:start position:0% +does that mean that you should then you +know turn off all password protection on + + align:start position:0% +know turn off all password protection on + + + align:start position:0% +know turn off all password protection on +your computer so that anybody can log in + + align:start position:0% +your computer so that anybody can log in + + + align:start position:0% +your computer so that anybody can log in +no right you're not going to do that + + align:start position:0% +no right you're not going to do that + + + align:start position:0% +no right you're not going to do that +you're going to continue to protect the + + align:start position:0% +you're going to continue to protect the + + + align:start position:0% +you're going to continue to protect the +information on your computer with a + + align:start position:0% +information on your computer with a + + + align:start position:0% +information on your computer with a +password because you may not always be + + align:start position:0% +password because you may not always be + + + align:start position:0% +password because you may not always be +using your you know you may have a + + align:start position:0% +using your you know you may have a + + + align:start position:0% +using your you know you may have a +laptop and you may not be using it from + + align:start position:0% +laptop and you may not be using it from + + + align:start position:0% +laptop and you may not be using it from +home or you know you may be worried + + align:start position:0% +home or you know you may be worried + + + align:start position:0% +home or you know you may be worried +about somebody breaking into your + + align:start position:0% +about somebody breaking into your + + + align:start position:0% +about somebody breaking into your +computer uh from inside of your house + + align:start position:0% +computer uh from inside of your house + + + align:start position:0% +computer uh from inside of your house +say perhaps um so that's an example of + + align:start position:0% +say perhaps um so that's an example of + + + align:start position:0% +say perhaps um so that's an example of +sort of thinking about of the safety net + + align:start position:0% +sort of thinking about of the safety net + + + align:start position:0% +sort of thinking about of the safety net +approach you have multiple layers of + + align:start position:0% +approach you have multiple layers of + + + align:start position:0% +approach you have multiple layers of +protection for your + + align:start position:0% +protection for your + + + align:start position:0% +protection for your +information um so there's some sort of + + align:start position:0% +information um so there's some sort of + + + align:start position:0% +information um so there's some sort of +sub approaches uh there's some sort of + + align:start position:0% +sub approaches uh there's some sort of + + + align:start position:0% +sub approaches uh there's some sort of +sub techniques that we can talk about in + + align:start position:0% +sub techniques that we can talk about in + + + align:start position:0% +sub techniques that we can talk about in +the context of being prepared um one of + + align:start position:0% +the context of being prepared um one of + + + align:start position:0% +the context of being prepared um one of +them is accept feedback from users so if + + align:start position:0% +them is accept feedback from users so if + + + align:start position:0% +them is accept feedback from users so if +you're designing a big computer system + + align:start position:0% +you're designing a big computer system + + + align:start position:0% +you're designing a big computer system +um and somebody tells you that something + + align:start position:0% +um and somebody tells you that something + + + align:start position:0% +um and somebody tells you that something +is is secure or that there's a problem + + align:start position:0% +is is secure or that there's a problem + + + align:start position:0% +is is secure or that there's a problem +you know be prepared to accept that + + align:start position:0% +you know be prepared to accept that + + + align:start position:0% +you know be prepared to accept that +feedback have a way to accept that + + align:start position:0% +feedback have a way to accept that + + + align:start position:0% +feedback have a way to accept that +feedback and respond to that feedback so + + align:start position:0% +feedback and respond to that feedback so + + + align:start position:0% +feedback and respond to that feedback so +don't simply say oh you know that's not + + align:start position:0% +don't simply say oh you know that's not + + + align:start position:0% +don't simply say oh you know that's not +a real security problem that's not a + + align:start position:0% +a real security problem that's not a + + + align:start position:0% +a real security problem that's not a +concern or uh don't for example keep + + align:start position:0% +concern or uh don't for example keep + + + align:start position:0% +concern or uh don't for example keep +this make make it so that users don't + + align:start position:0% +this make make it so that users don't + + + align:start position:0% +this make make it so that users don't +have a way to give you + + align:start position:0% +have a way to give you + + + align:start position:0% +have a way to give you +information um defend in depth so this + + align:start position:0% +information um defend in depth so this + + + align:start position:0% +information um defend in depth so this +is have multiple multiple security + + align:start position:0% +is have multiple multiple security + + + align:start position:0% +is have multiple multiple security +interfac like passwords plus a + + align:start position:0% +interfac like passwords plus a + + + align:start position:0% +interfac like passwords plus a +firewall and + + align:start position:0% + + + + align:start position:0% + +finally minimize what is + + align:start position:0% + + + + align:start position:0% + +trusted so you want to make sure that + + align:start position:0% +trusted so you want to make sure that + + + align:start position:0% +trusted so you want to make sure that +the this this and this is sort of a good + + align:start position:0% +the this this and this is sort of a good + + + align:start position:0% +the this this and this is sort of a good +example we've talked about this as an + + align:start position:0% +example we've talked about this as an + + + align:start position:0% +example we've talked about this as an +example of system design before we want + + align:start position:0% +example of system design before we want + + + align:start position:0% +example of system design before we want +to try and keep things as simple as + + align:start position:0% +to try and keep things as simple as + + + align:start position:0% +to try and keep things as simple as +possible but this was really important + + align:start position:0% +possible but this was really important + + + align:start position:0% +possible but this was really important +in the context of security because you + + align:start position:0% +in the context of security because you + + + align:start position:0% +in the context of security because you +want to make sure for example that the + + align:start position:0% +want to make sure for example that the + + + align:start position:0% +want to make sure for example that the +prot OLS that you you that you try and + + align:start position:0% +prot OLS that you you that you try and + + + align:start position:0% +prot OLS that you you that you try and +keep the the protocols that you use to + + align:start position:0% +keep the the protocols that you use to + + + align:start position:0% +keep the the protocols that you use to +interact with people from the outside + + align:start position:0% +interact with people from the outside + + + align:start position:0% +interact with people from the outside +world as simple as possible Right the + + align:start position:0% +world as simple as possible Right the + + + align:start position:0% +world as simple as possible Right the +more interfaces that you have with the + + align:start position:0% +more interfaces that you have with the + + + align:start position:0% +more interfaces that you have with the +outside world that users can connect to + + align:start position:0% +outside world that users can connect to + + + align:start position:0% +outside world that users can connect to +your computer over the more places you + + align:start position:0% +your computer over the more places you + + + align:start position:0% +your computer over the more places you +have where your computer system is + + align:start position:0% +have where your computer system is + + + align:start position:0% +have where your computer system is +vulnerable okay so you want to try and + + align:start position:0% +vulnerable okay so you want to try and + + + align:start position:0% +vulnerable okay so you want to try and +minimize make it so that your computer + + align:start position:0% +minimize make it so that your computer + + + align:start position:0% +minimize make it so that your computer +system has as few sort of openings in + + align:start position:0% +system has as few sort of openings in + + + align:start position:0% +system has as few sort of openings in +that that can that you have to verify + + align:start position:0% +that that can that you have to verify + + + align:start position:0% +that that can that you have to verify +are secure as + + align:start position:0% +are secure as + + + align:start position:0% +are secure as +possible okay so other examples of the + + align:start position:0% +possible okay so other examples of the + + + align:start position:0% +possible okay so other examples of the +safety net approach um you need to + + align:start position:0% +safety net approach um you need to + + + align:start position:0% +safety net approach um you need to +consider the environment okay + + align:start position:0% + + + + align:start position:0% + +so this just means it's not enough you + + align:start position:0% +so this just means it's not enough you + + + align:start position:0% +so this just means it's not enough you +know suppose that I have this connection + + align:start position:0% +know suppose that I have this connection + + + align:start position:0% +know suppose that I have this connection +here this this connection over the + + align:start position:0% +here this this connection over the + + + align:start position:0% +here this this connection over the +Internet between Alice and Bob I may + + align:start position:0% +Internet between Alice and Bob I may + + + align:start position:0% +Internet between Alice and Bob I may +assume that you I'm only worried about + + align:start position:0% +assume that you I'm only worried about + + + align:start position:0% +assume that you I'm only worried about +attackers who are coming in uh say for + + align:start position:0% +attackers who are coming in uh say for + + + align:start position:0% +attackers who are coming in uh say for +example um over the internet but if + + align:start position:0% +example um over the internet but if + + + align:start position:0% +example um over the internet but if +you're a server you know the server may + + align:start position:0% +you're a server you know the server may + + + align:start position:0% +you're a server you know the server may +have other connections available to it + + align:start position:0% +have other connections available to it + + + align:start position:0% +have other connections available to it +right so it may be the fact it may be + + align:start position:0% +right so it may be the fact it may be + + + align:start position:0% +right so it may be the fact it may be +the case that this is a server inside of + + align:start position:0% +the case that this is a server inside of + + + align:start position:0% +the case that this is a server inside of +some corporate environment and this + + align:start position:0% +some corporate environment and this + + + align:start position:0% +some corporate environment and this +server has a dialup modem connected to + + align:start position:0% +server has a dialup modem connected to + + + align:start position:0% +server has a dialup modem connected to +it right so especially nowadays this is + + align:start position:0% +it right so especially nowadays this is + + + align:start position:0% +it right so especially nowadays this is +less common but it used to be the case + + align:start position:0% +less common but it used to be the case + + + align:start position:0% +less common but it used to be the case +that you know almost all companies had a + + align:start position:0% +that you know almost all companies had a + + + align:start position:0% +that you know almost all companies had a +way that you could dial in and get + + align:start position:0% +way that you could dial in and get + + + align:start position:0% +way that you could dial in and get +access to a computer when you didn't + + align:start position:0% +access to a computer when you didn't + + + align:start position:0% +access to a computer when you didn't +have a wired Internet connection + + align:start position:0% +have a wired Internet connection + + + align:start position:0% +have a wired Internet connection +available to you and oftentimes this + + align:start position:0% +available to you and oftentimes this + + + align:start position:0% +available to you and oftentimes this +dial in Access was a separate place + + align:start position:0% +dial in Access was a separate place + + + align:start position:0% +dial in Access was a separate place +where people could connect so it was for + + align:start position:0% +where people could connect so it was for + + + align:start position:0% +where people could connect so it was for +example we didn't have the same + + align:start position:0% +example we didn't have the same + + + align:start position:0% +example we didn't have the same +interface as the sort of main connection + + align:start position:0% +interface as the sort of main connection + + + align:start position:0% +interface as the sort of main connection +to the internet and that meant that um + + align:start position:0% +to the internet and that meant that um + + + align:start position:0% +to the internet and that meant that um +there was a sort of a side Channel + + align:start position:0% +there was a sort of a side Channel + + + align:start position:0% +there was a sort of a side Channel +through which people could uh in the + + align:start position:0% +through which people could uh in the + + + align:start position:0% +through which people could uh in the +environment which people could use to + + align:start position:0% +environment which people could use to + + + align:start position:0% +environment which people could use to +get access to the computer similarly + + align:start position:0% +get access to the computer similarly + + + align:start position:0% +get access to the computer similarly +this means you should think about all + + align:start position:0% +this means you should think about all + + + align:start position:0% +this means you should think about all +the people who have access to the + + align:start position:0% +the people who have access to the + + + align:start position:0% +the people who have access to the +computer is it the case maybe that + + align:start position:0% +computer is it the case maybe that + + + align:start position:0% +computer is it the case maybe that +you're uh you know this is a computer in + + align:start position:0% +you're uh you know this is a computer in + + + align:start position:0% +you're uh you know this is a computer in +your office and the janitor who works in + + align:start position:0% +your office and the janitor who works in + + + align:start position:0% +your office and the janitor who works in +your office has uh you know comes in the + + align:start position:0% +your office has uh you know comes in the + + + align:start position:0% +your office has uh you know comes in the +office every night would would he or she + + align:start position:0% +office every night would would he or she + + + align:start position:0% +office every night would would he or she +be able to sit down in front of your + + align:start position:0% +be able to sit down in front of your + + + align:start position:0% +be able to sit down in front of your +computer and get access to the system + + align:start position:0% +computer and get access to the system + + + align:start position:0% +computer and get access to the system +when they shouldn't be able to um and + + align:start position:0% +when they shouldn't be able to um and + + + align:start position:0% +when they shouldn't be able to um and +this you know this may sound paranoid it + + align:start position:0% +this you know this may sound paranoid it + + + align:start position:0% +this you know this may sound paranoid it +is being paranoid but if you really want + + align:start position:0% +is being paranoid but if you really want + + + align:start position:0% +is being paranoid but if you really want +to build a computer a secure computer + + align:start position:0% +to build a computer a secure computer + + + align:start position:0% +to build a computer a secure computer +system you need to sort of keep all + + align:start position:0% +system you need to sort of keep all + + + align:start position:0% +system you need to sort of keep all +these things in + + align:start position:0% +these things in + + + align:start position:0% +these things in +mind + + align:start position:0% +mind + + + align:start position:0% +mind +um need to plan for iteration + + align:start position:0% +um need to plan for iteration + + + align:start position:0% +um need to plan for iteration +this is again just a good system design + + align:start position:0% +this is again just a good system design + + + align:start position:0% +this is again just a good system design +principle but it's especially true here + + align:start position:0% +principle but it's especially true here + + + align:start position:0% +principle but it's especially true here +assume that there will be security + + align:start position:0% +assume that there will be security + + + align:start position:0% +assume that there will be security +violations in your computer system + + align:start position:0% +violations in your computer system + + + align:start position:0% +violations in your computer system +assume there will be security problems + + align:start position:0% +assume there will be security problems + + + align:start position:0% +assume there will be security problems +and plan to be able to address those + + align:start position:0% +and plan to be able to address those + + + align:start position:0% +and plan to be able to address those +problems and also have a way to verify + + align:start position:0% +problems and also have a way to verify + + + align:start position:0% +problems and also have a way to verify +that once you've addressed those + + align:start position:0% +that once you've addressed those + + + align:start position:0% +that once you've addressed those +problems the other parts of your system + + align:start position:0% +problems the other parts of your system + + + align:start position:0% +problems the other parts of your system +that are supposed to be secure continue + + align:start position:0% +that are supposed to be secure continue + + + align:start position:0% +that are supposed to be secure continue +to be + + align:start position:0% +to be + + + align:start position:0% +to be +secure and + + align:start position:0% +secure and + + + align:start position:0% +secure and +finally um keep audit + + align:start position:0% + + + + align:start position:0% + +Trails okay so this this gets at uh our + + align:start position:0% +Trails okay so this this gets at uh our + + + align:start position:0% +Trails okay so this this gets at uh our +goal of accountability this just means + + align:start position:0% +goal of accountability this just means + + + align:start position:0% +goal of accountability this just means +keep track of everything all of the + + align:start position:0% +keep track of everything all of the + + + align:start position:0% +keep track of everything all of the +authentication and authorization request + + align:start position:0% +authentication and authorization request + + + align:start position:0% +authentication and authorization request +that you made in a computer in your in + + align:start position:0% +that you made in a computer in your in + + + align:start position:0% +that you made in a computer in your in +your system when a user logs in keep + + align:start position:0% +your system when a user logs in keep + + + align:start position:0% +your system when a user logs in keep +track of who that you where they logged + + align:start position:0% +track of who that you where they logged + + + align:start position:0% +track of who that you where they logged +into maybe even keep track of what they + + align:start position:0% +into maybe even keep track of what they + + + align:start position:0% +into maybe even keep track of what they +did so that you can come back at a late + + align:start position:0% +did so that you can come back at a late + + + align:start position:0% +did so that you can come back at a late +if if it turns out that this person was + + align:start position:0% +if if it turns out that this person was + + + align:start position:0% +if if it turns out that this person was +unauthorized you later discover that + + align:start position:0% +unauthorized you later discover that + + + align:start position:0% +unauthorized you later discover that +they were up to no good you can come + + align:start position:0% +they were up to no good you can come + + + align:start position:0% +they were up to no good you can come +back and understand what it is that they + + align:start position:0% + + + + align:start position:0% + +did okay so what all this sort of this + + align:start position:0% +did okay so what all this sort of this + + + align:start position:0% +did okay so what all this sort of this +discussion esecially this discussion + + align:start position:0% +discussion esecially this discussion + + + align:start position:0% +discussion esecially this discussion +about the safety net approach uh + + align:start position:0% +about the safety net approach uh + + + align:start position:0% +about the safety net approach uh +illustrates or gets at is that there's + + align:start position:0% +illustrates or gets at is that there's + + + align:start position:0% +illustrates or gets at is that there's +lots of these issues that we're talking + + align:start position:0% +lots of these issues that we're talking + + + align:start position:0% +lots of these issues that we're talking +about so for example the janitor + + align:start position:0% +about so for example the janitor + + + align:start position:0% +about so for example the janitor +breaking into our computer or me bribing + + align:start position:0% +breaking into our computer or me bribing + + + align:start position:0% +breaking into our computer or me bribing +my system administrator that aren't + + align:start position:0% +my system administrator that aren't + + + align:start position:0% +my system administrator that aren't +really computer system issues right + + align:start position:0% +really computer system issues right + + + align:start position:0% +really computer system issues right +these are human issues these are things + + align:start position:0% +these are human issues these are things + + + align:start position:0% +these are human issues these are things +that you know I'm I'm bypassing any sort + + align:start position:0% +that you know I'm I'm bypassing any sort + + + align:start position:0% +that you know I'm I'm bypassing any sort +of authentication I might have in the + + align:start position:0% +of authentication I might have in the + + + align:start position:0% +of authentication I might have in the +computer or any kind of you know + + align:start position:0% +computer or any kind of you know + + + align:start position:0% +computer or any kind of you know +security that I might have built into + + align:start position:0% +security that I might have built into + + + align:start position:0% +security that I might have built into +the computer by uh because you know for + + align:start position:0% +the computer by uh because you know for + + + align:start position:0% +the computer by uh because you know for +example my system administrator is + + align:start position:0% +example my system administrator is + + + align:start position:0% +example my system administrator is +authorized to access anything on the + + align:start position:0% +authorized to access anything on the + + + align:start position:0% +authorized to access anything on the +computer he wants to and so I've you + + align:start position:0% +computer he wants to and so I've you + + + align:start position:0% +computer he wants to and so I've you +know essentially from the computer + + align:start position:0% +know essentially from the computer + + + align:start position:0% +know essentially from the computer +systems point of view made it look like + + align:start position:0% +systems point of view made it look like + + + align:start position:0% +systems point of view made it look like +I have rights to get it anything I want + + align:start position:0% +I have rights to get it anything I want + + + align:start position:0% +I have rights to get it anything I want +to if I can bribe the system + + align:start position:0% +to if I can bribe the system + + + align:start position:0% +to if I can bribe the system +administrator so this suggests that sort + + align:start position:0% +administrator so this suggests that sort + + + align:start position:0% +administrator so this suggests that sort +of in many computer + + align:start position:0% +of in many computer + + + align:start position:0% +of in many computer +systems um humans are the weak link okay + + align:start position:0% + + + + align:start position:0% + +so people not only are people bribable + + align:start position:0% +so people not only are people bribable + + + align:start position:0% +so people not only are people bribable +but people make mistakes people don't + + align:start position:0% +but people make mistakes people don't + + + align:start position:0% +but people make mistakes people don't +read dialog boxes people uh are do + + align:start position:0% +read dialog boxes people uh are do + + + align:start position:0% +read dialog boxes people uh are do +things hastily people don't pay + + align:start position:0% +things hastily people don't pay + + + align:start position:0% +things hastily people don't pay +attention right the reason that these + + align:start position:0% +attention right the reason that these + + + align:start position:0% +attention right the reason that these +fishing atts work where somebody + + align:start position:0% +fishing atts work where somebody + + + align:start position:0% +fishing atts work where somebody +pretends to be Washington Mutual or eBay + + align:start position:0% +pretends to be Washington Mutual or eBay + + + align:start position:0% +pretends to be Washington Mutual or eBay +and sends you an account that it asks + + align:start position:0% +and sends you an account that it asks + + + align:start position:0% +and sends you an account that it asks +you to log in and type in your your + + align:start position:0% +you to log in and type in your your + + + align:start position:0% +you to log in and type in your your +social security number is that you know + + align:start position:0% +social security number is that you know + + + align:start position:0% +social security number is that you know +people don't think they just you know + + align:start position:0% +people don't think they just you know + + + align:start position:0% +people don't think they just you know +say see this email and they say oh I + + align:start position:0% +say see this email and they say oh I + + + align:start position:0% +say see this email and they say oh I +guess eBay wants me to you know give + + align:start position:0% +guess eBay wants me to you know give + + + align:start position:0% +guess eBay wants me to you know give +them their social security number okay + + align:start position:0% +them their social security number okay + + + align:start position:0% +them their social security number okay +right people make mistakes and this is + + align:start position:0% +right people make mistakes and this is + + + align:start position:0% +right people make mistakes and this is +the way that many many security + + align:start position:0% +the way that many many security + + + align:start position:0% +the way that many many security +vulnerabilities uh security problems + + align:start position:0% +vulnerabilities uh security problems + + + align:start position:0% +vulnerabilities uh security problems +happen is through people mistakes okay + + align:start position:0% +happen is through people mistakes okay + + + align:start position:0% +happen is through people mistakes okay +so we're going to talk in most of 6033 + + align:start position:0% +so we're going to talk in most of 6033 + + + align:start position:0% +so we're going to talk in most of 6033 +about Technical Solutions to security + + align:start position:0% +about Technical Solutions to security + + + align:start position:0% +about Technical Solutions to security +problems s but when you're actually out + + align:start position:0% +problems s but when you're actually out + + + align:start position:0% +problems s but when you're actually out +in the world building a system you need + + align:start position:0% +in the world building a system you need + + + align:start position:0% +in the world building a system you need +to be thinking about the people who are + + align:start position:0% +to be thinking about the people who are + + + align:start position:0% +to be thinking about the people who are +going to be using the system almost as + + align:start position:0% +going to be using the system almost as + + + align:start position:0% +going to be using the system almost as +much as you're thinking about the sort + + align:start position:0% +much as you're thinking about the sort + + + align:start position:0% +much as you're thinking about the sort +of security cryptographic protocols that + + align:start position:0% +of security cryptographic protocols that + + + align:start position:0% +of security cryptographic protocols that +um you design so that means for example + + align:start position:0% +um you design so that means for example + + + align:start position:0% +um you design so that means for example +you should think about the user + + align:start position:0% +you should think about the user + + + align:start position:0% +you should think about the user +interface in your system it does the + + align:start position:0% +interface in your system it does the + + + align:start position:0% +interface in your system it does the +user interface promote uh sort of users + + align:start position:0% +user interface promote uh sort of users + + + align:start position:0% +user interface promote uh sort of users +thinking securely right so the classic + + align:start position:0% +thinking securely right so the classic + + + align:start position:0% +thinking securely right so the classic +example of sort of a bad user interface + + align:start position:0% +example of sort of a bad user interface + + + align:start position:0% +example of sort of a bad user interface +is the your uh web browser popping up + + align:start position:0% +is the your uh web browser popping up + + + align:start position:0% +is the your uh web browser popping up +this dialogue that dialog box every time + + align:start position:0% +this dialogue that dialog box every time + + + align:start position:0% +this dialogue that dialog box every time +you access a site that doesn't isn't uh + + align:start position:0% +you access a site that doesn't isn't uh + + + align:start position:0% +you access a site that doesn't isn't uh +SSL in saying this website isn't SSL + + align:start position:0% +SSL in saying this website isn't SSL + + + align:start position:0% +SSL in saying this website isn't SSL +encrypted are you sure you wish to + + align:start position:0% +encrypted are you sure you wish to + + + align:start position:0% +encrypted are you sure you wish to +continue you know and after it's done + + align:start position:0% +continue you know and after it's done + + + align:start position:0% +continue you know and after it's done +this about 10 times and you know these + + align:start position:0% +this about 10 times and you know these + + + align:start position:0% +this about 10 times and you know these +are sites that you know and believe are + + align:start position:0% +are sites that you know and believe are + + + align:start position:0% +are sites that you know and believe are +safe like almost any site on the + + align:start position:0% +safe like almost any site on the + + + align:start position:0% +safe like almost any site on the +internet you just click the by dialogue + + align:start position:0% +internet you just click the by dialogue + + + align:start position:0% +internet you just click the by dialogue +box that says never show me this alert + + align:start position:0% +box that says never show me this alert + + + align:start position:0% +box that says never show me this alert +again right because there's there's + + align:start position:0% +again right because there's there's + + + align:start position:0% +again right because there's there's +almost no useful information that the + + align:start position:0% +almost no useful information that the + + + align:start position:0% +almost no useful information that the +system is giving you by complaining in + + align:start position:0% +system is giving you by complaining in + + + align:start position:0% +system is giving you by complaining in +that way okay um other examples of uh + + align:start position:0% +that way okay um other examples of uh + + + align:start position:0% +that way okay um other examples of uh +things that you want to make sure you do + + align:start position:0% +things that you want to make sure you do + + + align:start position:0% +things that you want to make sure you do +is have good defaults + + align:start position:0% + + + + align:start position:0% + +okay so in particular don't default to a + + align:start position:0% +okay so in particular don't default to a + + + align:start position:0% +okay so in particular don't default to a +state where the system is open right + + align:start position:0% +state where the system is open right + + + align:start position:0% +state where the system is open right +don't the when when an error occurs + + align:start position:0% +don't the when when an error occurs + + + align:start position:0% +don't the when when an error occurs +don't leave the system in some state + + align:start position:0% +don't leave the system in some state + + + align:start position:0% +don't leave the system in some state +where anybody can have access to + + align:start position:0% +where anybody can have access to + + + align:start position:0% +where anybody can have access to +anything that they want to right instead + + align:start position:0% +anything that they want to right instead + + + align:start position:0% +anything that they want to right instead +default to a state where people don't + + align:start position:0% +default to a state where people don't + + + align:start position:0% +default to a state where people don't +have access to things so that you're not + + align:start position:0% +have access to things so that you're not + + + align:start position:0% +have access to things so that you're not +exposing the system to to failures right + + align:start position:0% +exposing the system to to failures right + + + align:start position:0% +exposing the system to to failures right +don't default to you know a password + + align:start position:0% +don't default to you know a password + + + align:start position:0% +don't default to you know a password +that is anybody can guess right don't + + align:start position:0% +that is anybody can guess right don't + + + align:start position:0% +that is anybody can guess right don't +you know when you create a new user for + + align:start position:0% +you know when you create a new user for + + + align:start position:0% +you know when you create a new user for +your system don't make the the default + + align:start position:0% +your system don't make the the default + + + align:start position:0% +your system don't make the the default +password password okay that's a bad idea + + align:start position:0% +password password okay that's a bad idea + + + align:start position:0% +password password okay that's a bad idea +make it some random string that you + + align:start position:0% +make it some random string that you + + + align:start position:0% +make it some random string that you +email to the user so that they have to + + align:start position:0% +email to the user so that they have to + + + align:start position:0% +email to the user so that they have to +come back and type it + + align:start position:0% +come back and type it + + + align:start position:0% +come back and type it +in + + align:start position:0% +in + + + align:start position:0% +in +um finally use least give users least + + align:start position:0% +um finally use least give users least + + + align:start position:0% +um finally use least give users least +privilege needed to do whatever it is + + align:start position:0% +privilege needed to do whatever it is + + + align:start position:0% +privilege needed to do whatever it is +they need to do okay so um this means + + align:start position:0% +they need to do okay so um this means + + + align:start position:0% +they need to do okay so um this means +don't don't by default make users + + align:start position:0% +don't don't by default make users + + + align:start position:0% +don't don't by default make users +administrators of the system right if + + align:start position:0% +administrators of the system right if + + + align:start position:0% +administrators of the system right if +user doesn't need to be an administrator + + align:start position:0% +user doesn't need to be an administrator + + + align:start position:0% +user doesn't need to be an administrator +of the system they shouldn't have + + align:start position:0% +of the system they shouldn't have + + + align:start position:0% +of the system they shouldn't have +administrative access they shouldn't be + + align:start position:0% +administrative access they shouldn't be + + + align:start position:0% +administrative access they shouldn't be +able to change anything that they want + + align:start position:0% +able to change anything that they want + + + align:start position:0% +able to change anything that they want +okay so a good example of lease + + align:start position:0% +okay so a good example of lease + + + align:start position:0% +okay so a good example of lease +privilege being violated is many + + align:start position:0% +privilege being violated is many + + + align:start position:0% +privilege being violated is many +versions of Microsoft Windows uh by + + align:start position:0% +versions of Microsoft Windows uh by + + + align:start position:0% +versions of Microsoft Windows uh by +default make the first user who's + + align:start position:0% +default make the first user who's + + + align:start position:0% +default make the first user who's +created an administrator user who has + + align:start position:0% +created an administrator user who has + + + align:start position:0% +created an administrator user who has +access to everything okay and this is a + + align:start position:0% +access to everything okay and this is a + + + align:start position:0% +access to everything okay and this is a +problem because now when somebody you + + align:start position:0% +problem because now when somebody you + + + align:start position:0% +problem because now when somebody you +know breaks into that user's account + + align:start position:0% +know breaks into that user's account + + + align:start position:0% +know breaks into that user's account +they now have access to everything on + + align:start position:0% +they now have access to everything on + + + align:start position:0% +they now have access to everything on +the machine as opposed to Simply Having + + align:start position:0% +the machine as opposed to Simply Having + + + align:start position:0% +the machine as opposed to Simply Having +access to just that user's files + + align:start position:0% + + + + align:start position:0% + +okay so in general what this just means + + align:start position:0% +okay so in general what this just means + + + align:start position:0% +okay so in general what this just means +is you know keep your systems simple + + align:start position:0% +is you know keep your systems simple + + + align:start position:0% +is you know keep your systems simple +keep them understandable keep the + + align:start position:0% +keep them understandable keep the + + + align:start position:0% +keep them understandable keep the +complexity down okay and that's sort of + + align:start position:0% +complexity down okay and that's sort of + + + align:start position:0% +complexity down okay and that's sort of +the safety net so so there's these two + + align:start position:0% +the safety net so so there's these two + + + align:start position:0% +the safety net so so there's these two +sort of principles that you want to + + align:start position:0% +sort of principles that you want to + + + align:start position:0% +sort of principles that you want to +think about one sort of be paranoid + + align:start position:0% +think about one sort of be paranoid + + + align:start position:0% +think about one sort of be paranoid +apply this notion of having a safety net + + align:start position:0% +apply this notion of having a safety net + + + align:start position:0% +apply this notion of having a safety net +in computer system and two don't just + + align:start position:0% +in computer system and two don't just + + + align:start position:0% +in computer system and two don't just +think about the technical protocols that + + align:start position:0% +think about the technical protocols that + + + align:start position:0% +think about the technical protocols that +you're going to use to enforce access to + + align:start position:0% +you're going to use to enforce access to + + + align:start position:0% +you're going to use to enforce access to +the computer but think about um sort of + + align:start position:0% +the computer but think about um sort of + + + align:start position:0% +the computer but think about um sort of +who's using the system think about + + align:start position:0% +who's using the system think about + + + align:start position:0% +who's using the system think about +humans who have access to it and think + + align:start position:0% +humans who have access to it and think + + + align:start position:0% +humans who have access to it and think +about how to prevent those humans from + + align:start position:0% +about how to prevent those humans from + + + align:start position:0% +about how to prevent those humans from +being able to do stupid things that + + align:start position:0% +being able to do stupid things that + + + align:start position:0% +being able to do stupid things that +break the computer that that break your + + align:start position:0% +break the computer that that break your + + + align:start position:0% +break the computer that that break your +security goals for your system okay + + align:start position:0% + + + + align:start position:0% + +so this was a very sort of high level + + align:start position:0% +so this was a very sort of high level + + + align:start position:0% +so this was a very sort of high level +fuzzy discussion about security Now what + + align:start position:0% +fuzzy discussion about security Now what + + + align:start position:0% +fuzzy discussion about security Now what +we're going to do is we're going to + + align:start position:0% +we're going to do is we're going to + + + align:start position:0% +we're going to do is we're going to +drill in on some of these uh more + + align:start position:0% +drill in on some of these uh more + + + align:start position:0% +drill in on some of these uh more +specific technical protocols and today + + align:start position:0% +specific technical protocols and today + + + align:start position:0% +specific technical protocols and today +we're going to start looking at we're + + align:start position:0% +we're going to start looking at we're + + + align:start position:0% +we're going to start looking at we're +going to look at sort of security has + + align:start position:0% +going to look at sort of security has + + + align:start position:0% +going to look at sort of security has +there's there's a way in which security + + align:start position:0% +there's there's a way in which security + + + align:start position:0% +there's there's a way in which security +is uh you can think of security as being + + align:start position:0% +is uh you can think of security as being + + + align:start position:0% +is uh you can think of security as being +architect at most secure systems as + + align:start position:0% +architect at most secure systems as + + + align:start position:0% +architect at most secure systems as +consisting of a set of layers those + + align:start position:0% +consisting of a set of layers those + + + align:start position:0% +consisting of a set of layers those +layers are basically um as follows we + + align:start position:0% +layers are basically um as follows we + + + align:start position:0% +layers are basically um as follows we +have at the top some + + align:start position:0% +have at the top some + + + align:start position:0% +have at the top some +application which we want to secure um + + align:start position:0% +application which we want to secure um + + + align:start position:0% +application which we want to secure um +and then underneath this + + align:start position:0% +and then underneath this + + + align:start position:0% +and then underneath this +application we can talk about three + + align:start position:0% + + + + align:start position:0% + +layers okay so um we + + align:start position:0% + + + + align:start position:0% + +have some kind of functionality that we + + align:start position:0% +have some kind of functionality that we + + + align:start position:0% +have some kind of functionality that we +want to provide um we have some set of + + align:start position:0% +want to provide um we have some set of + + + align:start position:0% +want to provide um we have some set of +Primitives that we're going to use to + + align:start position:0% +Primitives that we're going to use to + + + align:start position:0% +Primitives that we're going to use to +provide + + align:start position:0% +provide + + + align:start position:0% +provide +that okay and then at the very bottom we + + align:start position:0% +that okay and then at the very bottom we + + + align:start position:0% +that okay and then at the very bottom we +have cryptography which is + + align:start position:0% + + + + align:start position:0% + +the set of sort of mathematics and + + align:start position:0% +the set of sort of mathematics and + + + align:start position:0% +the set of sort of mathematics and +algorithms that we're going to use to + + align:start position:0% +algorithms that we're going to use to + + + align:start position:0% +algorithms that we're going to use to +actually make sure that that that we + + align:start position:0% +actually make sure that that that we + + + align:start position:0% +actually make sure that that that we +generally in modern computer systems use + + align:start position:0% +generally in modern computer systems use + + + align:start position:0% +generally in modern computer systems use +to make sure that the computer system is + + align:start position:0% +to make sure that the computer system is + + + align:start position:0% +to make sure that the computer system is +secure okay um so the application may + + align:start position:0% +secure okay um so the application may + + + align:start position:0% +secure okay um so the application may +have has its high level functions that + + align:start position:0% +have has its high level functions that + + + align:start position:0% +have has its high level functions that +correspond to these things over here so + + align:start position:0% +correspond to these things over here so + + + align:start position:0% +correspond to these things over here so +we may want um to be able to + + align:start position:0% +we may want um to be able to + + + align:start position:0% +we may want um to be able to +authenticate + + align:start position:0% +authenticate + + + align:start position:0% +authenticate +users okay or we may be able to we may + + align:start position:0% +users okay or we may be able to we may + + + align:start position:0% +users okay or we may be able to we may +want to be able to authorize that users + + align:start position:0% +want to be able to authorize that users + + + align:start position:0% +want to be able to authorize that users +have access to + + align:start position:0% +have access to + + + align:start position:0% +have access to +something or we may be may want to + + align:start position:0% +something or we may be may want to + + + align:start position:0% +something or we may be may want to +provide uh + + align:start position:0% +provide uh + + + align:start position:0% +provide uh +confidentiality okay so we may be able + + align:start position:0% +confidentiality okay so we may be able + + + align:start position:0% +confidentiality okay so we may be able +to want may want to be able to uh make + + align:start position:0% +to want may want to be able to uh make + + + align:start position:0% +to want may want to be able to uh make +sure that nobody can read information + + align:start position:0% +sure that nobody can read information + + + align:start position:0% +sure that nobody can read information +they don't have access + + align:start position:0% +they don't have access + + + align:start position:0% +they don't have access +to um so we're going to have a set of + + align:start position:0% +to um so we're going to have a set of + + + align:start position:0% +to um so we're going to have a set of +Primitives for doing these different + + align:start position:0% +Primitives for doing these different + + + align:start position:0% +Primitives for doing these different +different things so uh for + + align:start position:0% +different things so uh for + + + align:start position:0% +different things so uh for +authentication um we're going to talk + + align:start position:0% +authentication um we're going to talk + + + align:start position:0% +authentication um we're going to talk +about something called an access control + + align:start position:0% +about something called an access control + + + align:start position:0% +about something called an access control +list um for authorization we're going to + + align:start position:0% +list um for authorization we're going to + + + align:start position:0% +list um for authorization we're going to +talk about Primitives called sign and + + align:start position:0% +talk about Primitives called sign and + + + align:start position:0% +talk about Primitives called sign and +verify um and for confidentiality we'll + + align:start position:0% +verify um and for confidentiality we'll + + + align:start position:0% +verify um and for confidentiality we'll +talk about these Primitives called um + + align:start position:0% +talk about these Primitives called um + + + align:start position:0% +talk about these Primitives called um +encrypt and decrypt + + align:start position:0% + + + + align:start position:0% + +okay um and these topics the stuff + + align:start position:0% +okay um and these topics the stuff + + + align:start position:0% +okay um and these topics the stuff +that's in this middle set of Primitives + + align:start position:0% +that's in this middle set of Primitives + + + align:start position:0% +that's in this middle set of Primitives +we're going to describe these in more + + align:start position:0% +we're going to describe these in more + + + align:start position:0% +we're going to describe these in more +detail in later lectures so what I want + + align:start position:0% +detail in later lectures so what I want + + + align:start position:0% +detail in later lectures so what I want +to do with the rest of the lecture today + + align:start position:0% +to do with the rest of the lecture today + + + align:start position:0% +to do with the rest of the lecture today +is to talk about this bottom layer this + + align:start position:0% +is to talk about this bottom layer this + + + align:start position:0% +is to talk about this bottom layer this +cryptography + + align:start position:0% + + + + align:start position:0% + +layer so we have some set of + + align:start position:0% +layer so we have some set of + + + align:start position:0% +layer so we have some set of +cryptographic ciphers and + + align:start position:0% +cryptographic ciphers and + + + align:start position:0% +cryptographic ciphers and +hashes so a cipher is just something + + align:start position:0% +hashes so a cipher is just something + + + align:start position:0% +hashes so a cipher is just something +that uh takes in in a say message that + + align:start position:0% +that uh takes in in a say message that + + + align:start position:0% +that uh takes in in a say message that +dieser wants to send that's not + + align:start position:0% +dieser wants to send that's not + + + align:start position:0% +dieser wants to send that's not +protected at all and it flips the bits + + align:start position:0% +protected at all and it flips the bits + + + align:start position:0% +protected at all and it flips the bits +in that message around in order to + + align:start position:0% +in that message around in order to + + + align:start position:0% +in that message around in order to +create something that um is sort of not + + align:start position:0% +create something that um is sort of not + + + align:start position:0% +create something that um is sort of not +understandable unless you have some + + align:start position:0% +understandable unless you have some + + + align:start position:0% +understandable unless you have some +piece of information that allows you to + + align:start position:0% +piece of information that allows you to + + + align:start position:0% +piece of information that allows you to +say d decipher that uh message so you + + align:start position:0% +say d decipher that uh message so you + + + align:start position:0% +say d decipher that uh message so you +can say you know ciphering and + + align:start position:0% +can say you know ciphering and + + + align:start position:0% +can say you know ciphering and +deciphering is sort of like it's + + align:start position:0% +deciphering is sort of like it's + + + align:start position:0% +deciphering is sort of like it's +encrypting and decrypting is words you + + align:start position:0% +encrypting and decrypting is words you + + + align:start position:0% +encrypting and decrypting is words you +may be familiar with we also talk about + + align:start position:0% +may be familiar with we also talk about + + + align:start position:0% +may be familiar with we also talk about +hashes and hashes we're going to use to + + align:start position:0% +hashes and hashes we're going to use to + + + align:start position:0% +hashes and hashes we're going to use to +authenticate uh or to authoriz to + + align:start position:0% +authenticate uh or to authoriz to + + + align:start position:0% +authenticate uh or to authoriz to +authorize a particular message to make + + align:start position:0% +authorize a particular message to make + + + align:start position:0% +authorize a particular message to make +sure that a message is um oops I'm sorry + + align:start position:0% +sure that a message is um oops I'm sorry + + + align:start position:0% +sure that a message is um oops I'm sorry +just to for your notes I got these + + align:start position:0% +just to for your notes I got these + + + align:start position:0% +just to for your notes I got these +backwards this should be uh authenticate + + align:start position:0% +backwards this should be uh authenticate + + + align:start position:0% +backwards this should be uh authenticate +we we authenticate with uh sign and + + align:start position:0% + + + + align:start position:0% + +verify and we authorize with ACL so + + align:start position:0% +verify and we authorize with ACL so + + + align:start position:0% +verify and we authorize with ACL so +we'll talk about these things these + + align:start position:0% +we'll talk about these things these + + + align:start position:0% +we'll talk about these things these +things more in a minute but um it's just + + align:start position:0% +things more in a minute but um it's just + + + align:start position:0% +things more in a minute but um it's just +confusion over two words that start with + + align:start position:0% +confusion over two words that start with + + + align:start position:0% +confusion over two words that start with +o um okay so we're going to use hashes + + align:start position:0% +o um okay so we're going to use hashes + + + align:start position:0% +o um okay so we're going to use hashes +to basically authenticate that a user is + + align:start position:0% +to basically authenticate that a user is + + + align:start position:0% +to basically authenticate that a user is +in fact who they claimed that they were + + align:start position:0% +in fact who they claimed that they were + + + align:start position:0% +in fact who they claimed that they were +and again we'll see in more detail how + + align:start position:0% +and again we'll see in more detail how + + + align:start position:0% +and again we'll see in more detail how +this how this works um over the next + + align:start position:0% +this how this works um over the next + + + align:start position:0% +this how this works um over the next +couple + + align:start position:0% + + + + align:start position:0% + +days okay so + + align:start position:0% +days okay so + + + align:start position:0% +days okay so +um early cryptographic systems relied on + + align:start position:0% +um early cryptographic systems relied on + + + align:start position:0% +um early cryptographic systems relied on +this idea or early cryptography relied + + align:start position:0% +this idea or early cryptography relied + + + align:start position:0% +this idea or early cryptography relied +on this idea that um we're going to try + + align:start position:0% +on this idea that um we're going to try + + + align:start position:0% +on this idea that um we're going to try +and keep the protocol that's used for uh + + align:start position:0% +and keep the protocol that's used for uh + + + align:start position:0% +and keep the protocol that's used for uh +encoding the information we're going to + + align:start position:0% +encoding the information we're going to + + + align:start position:0% +encoding the information we're going to +try and keep that secret right so a + + align:start position:0% +try and keep that secret right so a + + + align:start position:0% +try and keep that secret right so a +simple example of an early uh encryption + + align:start position:0% +simple example of an early uh encryption + + + align:start position:0% +simple example of an early uh encryption +method might be um something that you + + align:start position:0% +method might be um something that you + + + align:start position:0% +method might be um something that you +guys probably many of you played with + + align:start position:0% +guys probably many of you played with + + + align:start position:0% +guys probably many of you played with +when you were kids where you transpose + + align:start position:0% +when you were kids where you transpose + + + align:start position:0% +when you were kids where you transpose +all the letters so you have some map + + align:start position:0% +all the letters so you have some map + + + align:start position:0% +all the letters so you have some map +where you map you know a maps to C and B + + align:start position:0% +where you map you know a maps to C and B + + + align:start position:0% +where you map you know a maps to C and B +maps to F and you know so on some + + align:start position:0% +maps to F and you know so on some + + + align:start position:0% +maps to F and you know so on some +mapping like that and you use that to + + align:start position:0% +mapping like that and you use that to + + + align:start position:0% +mapping like that and you use that to +encrypt it and there's you know there's + + align:start position:0% +encrypt it and there's you know there's + + + align:start position:0% +encrypt it and there's you know there's +these puzzles where you get to you get + + align:start position:0% +these puzzles where you get to you get + + + align:start position:0% +these puzzles where you get to you get +told a few of the letters and you try + + align:start position:0% +told a few of the letters and you try + + + align:start position:0% +told a few of the letters and you try +and guess what the other letters are and + + align:start position:0% +and guess what the other letters are and + + + align:start position:0% +and guess what the other letters are and +you know decode a message right that's + + align:start position:0% +you know decode a message right that's + + + align:start position:0% +you know decode a message right that's +in a simple example of a kind of + + align:start position:0% +in a simple example of a kind of + + + align:start position:0% +in a simple example of a kind of +encryption that you might apply okay and + + align:start position:0% +encryption that you might apply okay and + + + align:start position:0% +encryption that you might apply okay and +that encryption relies on the fact that + + align:start position:0% +that encryption relies on the fact that + + + align:start position:0% +that encryption relies on the fact that +this transform is essentially secret + + align:start position:0% +this transform is essentially secret + + + align:start position:0% +this transform is essentially secret +right that if you know the transform + + align:start position:0% +right that if you know the transform + + + align:start position:0% +right that if you know the transform +obviously you can decrypt the + + align:start position:0% +obviously you can decrypt the + + + align:start position:0% +obviously you can decrypt the +message so + + align:start position:0% +message so + + + align:start position:0% +message so +um these schemes are called are often + + align:start position:0% +um these schemes are called are often + + + align:start position:0% +um these schemes are called are often +called closed + + align:start position:0% +called closed + + + align:start position:0% +called closed +design crypto schemes okay and there + + align:start position:0% +design crypto schemes okay and there + + + align:start position:0% +design crypto schemes okay and there +there are the the idea is that um you + + align:start position:0% +there are the the idea is that um you + + + align:start position:0% +there are the the idea is that um you +know because the attacker doesn't know + + align:start position:0% +know because the attacker doesn't know + + + align:start position:0% +know because the attacker doesn't know +what scheme was used to encode the + + align:start position:0% +what scheme was used to encode the + + + align:start position:0% +what scheme was used to encode the +information can be very very hard for + + align:start position:0% +information can be very very hard for + + + align:start position:0% +information can be very very hard for +them to go about decoding it um so for + + align:start position:0% +them to go about decoding it um so for + + + align:start position:0% +them to go about decoding it um so for +example you might the architecture for + + align:start position:0% +example you might the architecture for + + + align:start position:0% +example you might the architecture for +this might look like message goes into + + align:start position:0% +this might look like message goes into + + + align:start position:0% +this might look like message goes into +some encryption box which is secured + + align:start position:0% +some encryption box which is secured + + + align:start position:0% +some encryption box which is secured +from the outside world nobody which just + + align:start position:0% +from the outside world nobody which just + + + align:start position:0% +from the outside world nobody which just +hidden from the outside world nobody + + align:start position:0% +hidden from the outside world nobody + + + align:start position:0% +hidden from the outside world nobody +else knows what that is um then this + + align:start position:0% +else knows what that is um then this + + + align:start position:0% +else knows what that is um then this +goes over the + + align:start position:0% +goes over the + + + align:start position:0% +goes over the +internet to some other decryption box + + align:start position:0% +internet to some other decryption box + + + align:start position:0% +internet to some other decryption box +which then comes out on the other end as + + align:start position:0% +which then comes out on the other end as + + + align:start position:0% +which then comes out on the other end as +message okay so this is a closed a + + align:start position:0% +message okay so this is a closed a + + + align:start position:0% +message okay so this is a closed a +closed design and um these designs in + + align:start position:0% +closed design and um these designs in + + + align:start position:0% +closed design and um these designs in +general are sort of turn out not to be a + + align:start position:0% +general are sort of turn out not to be a + + + align:start position:0% +general are sort of turn out not to be a +very good idea because the problem is + + align:start position:0% +very good idea because the problem is + + + align:start position:0% +very good idea because the problem is +that once you have once this if somebody + + align:start position:0% +that once you have once this if somebody + + + align:start position:0% +that once you have once this if somebody +does discover what this function is + + align:start position:0% +does discover what this function is + + + align:start position:0% +does discover what this function is +right now you're in trouble now this + + align:start position:0% +right now you're in trouble now this + + + align:start position:0% +right now you're in trouble now this +this whole system is no longer secure + + align:start position:0% +this whole system is no longer secure + + + align:start position:0% +this whole system is no longer secure +right and worse than that when you make + + align:start position:0% +right and worse than that when you make + + + align:start position:0% +right and worse than that when you make +these things secure it sort of is now if + + align:start position:0% +these things secure it sort of is now if + + + align:start position:0% +these things secure it sort of is now if +you suppose now you're going to put this + + align:start position:0% +you suppose now you're going to put this + + + align:start position:0% +you suppose now you're going to put this +system out in the world with a hidden + + align:start position:0% +system out in the world with a hidden + + + align:start position:0% +system out in the world with a hidden +protocol that nobody can understand + + align:start position:0% +protocol that nobody can understand + + + align:start position:0% +protocol that nobody can understand +nobody knows in the world now it's sort + + align:start position:0% +nobody knows in the world now it's sort + + + align:start position:0% +nobody knows in the world now it's sort +of you against the whole world right + + align:start position:0% +of you against the whole world right + + + align:start position:0% +of you against the whole world right +whereas if you had told everybody what + + align:start position:0% +whereas if you had told everybody what + + + align:start position:0% +whereas if you had told everybody what +the protocol was to begin with and said + + align:start position:0% +the protocol was to begin with and said + + + align:start position:0% +the protocol was to begin with and said +this is the protocol um and there's this + + align:start position:0% +this is the protocol um and there's this + + + align:start position:0% +this is the protocol um and there's this +little bit of information that we keep + + align:start position:0% +little bit of information that we keep + + + align:start position:0% +little bit of information that we keep +secret within the protocol the two + + align:start position:0% +secret within the protocol the two + + + align:start position:0% +secret within the protocol the two +parties in the protocol keep secret but + + align:start position:0% +parties in the protocol keep secret but + + + align:start position:0% +parties in the protocol keep secret but +here's the sort of algorithm that's in + + align:start position:0% +here's the sort of algorithm that's in + + + align:start position:0% +here's the sort of algorithm that's in +the protocol let's let the entire world + + align:start position:0% +the protocol let's let the entire world + + + align:start position:0% +the protocol let's let the entire world +verify whether this protocol is in fact + + align:start position:0% +verify whether this protocol is in fact + + + align:start position:0% +verify whether this protocol is in fact +secure or not you'd have a much better + + align:start position:0% +secure or not you'd have a much better + + + align:start position:0% +secure or not you'd have a much better +chance of developing something that was + + align:start position:0% +chance of developing something that was + + + align:start position:0% +chance of developing something that was +Secure so it's sort of his accepted + + align:start position:0% +Secure so it's sort of his accepted + + + align:start position:0% +Secure so it's sort of his accepted +wisdom that these kinds of closed Design + + align:start position:0% +wisdom that these kinds of closed Design + + + align:start position:0% +wisdom that these kinds of closed Design +Systems tend not to be um they're + + align:start position:0% +Systems tend not to be um they're + + + align:start position:0% +Systems tend not to be um they're +they're not widely used anymore and the + + align:start position:0% +they're not widely used anymore and the + + + align:start position:0% +they're not widely used anymore and the +systems that we're going to talk about + + align:start position:0% +systems that we're going to talk about + + + align:start position:0% +systems that we're going to talk about +uh sort of for the rest of this this + + align:start position:0% +uh sort of for the rest of this this + + + align:start position:0% +uh sort of for the rest of this this +talk today are going to be so-called + + align:start position:0% +talk today are going to be so-called + + + align:start position:0% +talk today are going to be so-called +open Design Systems of course there are + + align:start position:0% +open Design Systems of course there are + + + align:start position:0% +open Design Systems of course there are +many many systems that were designed + + align:start position:0% +many many systems that were designed + + + align:start position:0% +many many systems that were designed +with this in and there are many many + + align:start position:0% +with this in and there are many many + + + align:start position:0% +with this in and there are many many +closed cryptography systems and in some + + align:start position:0% +closed cryptography systems and in some + + + align:start position:0% +closed cryptography systems and in some +ways they're sort of the most natural + + align:start position:0% +ways they're sort of the most natural + + + align:start position:0% +ways they're sort of the most natural +ones and the things you think of first + + align:start position:0% +ones and the things you think of first + + + align:start position:0% +ones and the things you think of first +and um they've been very effective + + align:start position:0% +and um they've been very effective + + + align:start position:0% +and um they've been very effective +throughout history it's just the case + + align:start position:0% +throughout history it's just the case + + + align:start position:0% +throughout history it's just the case +that modern cryptography typically + + align:start position:0% +that modern cryptography typically + + + align:start position:0% +that modern cryptography typically +doesn't rely on + + align:start position:0% +doesn't rely on + + + align:start position:0% +doesn't rely on +it okay + + align:start position:0% +it okay + + + align:start position:0% +it okay +so open Design + + align:start position:0% +so open Design + + + align:start position:0% +so open Design +Systems move to a different + + align:start position:0% + + + + align:start position:0% + +board so open Design + + align:start position:0% + + + + align:start position:0% + +Systems have an architecture that + + align:start position:0% +Systems have an architecture that + + + align:start position:0% +Systems have an architecture that +typically looks as follows it's pretty + + align:start position:0% +typically looks as follows it's pretty + + + align:start position:0% +typically looks as follows it's pretty +similar to um + + align:start position:0% +similar to um + + + align:start position:0% +similar to um +what we showed before we have m going + + align:start position:0% +what we showed before we have m going + + + align:start position:0% +what we showed before we have m going +into e but this time this protocol e is + + align:start position:0% +into e but this time this protocol e is + + + align:start position:0% +into e but this time this protocol e is +this this algorithm e is the world knows + + align:start position:0% +this this algorithm e is the world knows + + + align:start position:0% +this this algorithm e is the world knows +what the algorithm e is and instead this + + align:start position:0% +what the algorithm e is and instead this + + + align:start position:0% +what the algorithm e is and instead this +e has some piece of secret information + + align:start position:0% +e has some piece of secret information + + + align:start position:0% +e has some piece of secret information +coming into it a key K okay and this is + + align:start position:0% +coming into it a key K okay and this is + + + align:start position:0% +coming into it a key K okay and this is +this this key uh usually won't be may + + align:start position:0% +this this key uh usually won't be may + + + align:start position:0% +this this key uh usually won't be may +may or may not this this key is usually + + align:start position:0% +may or may not this this key is usually + + + align:start position:0% +may or may not this this key is usually +not known to the world okay um and now + + align:start position:0% +not known to the world okay um and now + + + align:start position:0% +not known to the world okay um and now +we go through the internet say for + + align:start position:0% +we go through the internet say for + + + align:start position:0% +we go through the internet say for +example we come out to a decryption box + + align:start position:0% +example we come out to a decryption box + + + align:start position:0% +example we come out to a decryption box +which also has a key going into it and + + align:start position:0% +which also has a key going into it and + + + align:start position:0% +which also has a key going into it and +these Keys may or may not be the same on + + align:start position:0% +these Keys may or may not be the same on + + + align:start position:0% +these Keys may or may not be the same on +the two on the two boxes and we'll talk + + align:start position:0% +the two on the two boxes and we'll talk + + + align:start position:0% +the two on the two boxes and we'll talk +about um the difference between making + + align:start position:0% +about um the difference between making + + + align:start position:0% +about um the difference between making +them the same or not making them the + + align:start position:0% +them the same or not making them the + + + align:start position:0% +them the same or not making them the +same now we have this message comes out + + align:start position:0% +same now we have this message comes out + + + align:start position:0% +same now we have this message comes out +okay so um message comes in gets + + align:start position:0% +okay so um message comes in gets + + + align:start position:0% +okay so um message comes in gets +encrypted goes to goes over the Internet + + align:start position:0% +encrypted goes to goes over the Internet + + + align:start position:0% +encrypted goes to goes over the Internet +goes into the decryption box and gets + + align:start position:0% +goes into the decryption box and gets + + + align:start position:0% +goes into the decryption box and gets +decrypted okay so if + + align:start position:0% +decrypted okay so if + + + align:start position:0% +decrypted okay so if +K1 is equal to + + align:start position:0% +K1 is equal to + + + align:start position:0% +K1 is equal to +K2 um we say that this system is a + + align:start position:0% +K2 um we say that this system is a + + + align:start position:0% +K2 um we say that this system is a +uh shared + + align:start position:0% +uh shared + + + align:start position:0% +uh shared +system okay and if + + align:start position:0% +system okay and if + + + align:start position:0% +system okay and if +K1 is not equal to K2 we say that this + + align:start position:0% +K1 is not equal to K2 we say that this + + + align:start position:0% +K1 is not equal to K2 we say that this +is a public Key + + align:start position:0% + + + + align:start position:0% + +System okay so in K1 is equal to K2 this + + align:start position:0% +System okay so in K1 is equal to K2 this + + + align:start position:0% +System okay so in K1 is equal to K2 this +is uh these two keys are the same and + + align:start position:0% +is uh these two keys are the same and + + + align:start position:0% +is uh these two keys are the same and +say Alice and Bob on the two ends of + + align:start position:0% +say Alice and Bob on the two ends of + + + align:start position:0% +say Alice and Bob on the two ends of +this have exchanged information about + + align:start position:0% +this have exchanged information about + + + align:start position:0% +this have exchanged information about +what this key is before the sort of + + align:start position:0% +what this key is before the sort of + + + align:start position:0% +what this key is before the sort of +protocol started okay so Alice called up + + align:start position:0% +protocol started okay so Alice called up + + + align:start position:0% +protocol started okay so Alice called up +Bob on the phone or saw Bob in the + + align:start position:0% +Bob on the phone or saw Bob in the + + + align:start position:0% +Bob on the phone or saw Bob in the +hallway and said hey the key is X okay + + align:start position:0% +hallway and said hey the key is X okay + + + align:start position:0% +hallway and said hey the key is X okay +and they agreed on this beforehand and + + align:start position:0% +and they agreed on this beforehand and + + + align:start position:0% +and they agreed on this beforehand and +now that they've agreed on what this key + + align:start position:0% +now that they've agreed on what this key + + + align:start position:0% +now that they've agreed on what this key +is they can exchange information in a + + align:start position:0% +is they can exchange information in a + + + align:start position:0% +is they can exchange information in a +public key information in a public Key + + align:start position:0% +public key information in a public Key + + + align:start position:0% +public key information in a public Key +System um we'll see the design of how + + align:start position:0% +System um we'll see the design of how + + + align:start position:0% +System um we'll see the design of how +one public key system works in a little + + align:start position:0% +one public key system works in a little + + + align:start position:0% +one public key system works in a little +bit more detail but uh typically it's + + align:start position:0% +bit more detail but uh typically it's + + + align:start position:0% +bit more detail but uh typically it's +it's the case that for example uh the + + align:start position:0% +it's the case that for example uh the + + + align:start position:0% +it's the case that for example uh the +person who's sending the message has a + + align:start position:0% +person who's sending the message has a + + + align:start position:0% +person who's sending the message has a +private key um which they nobody else + + align:start position:0% +private key um which they nobody else + + + align:start position:0% +private key um which they nobody else +knows only they know and then there's a + + align:start position:0% +knows only they know and then there's a + + + align:start position:0% +knows only they know and then there's a +public key which everybody else in the + + align:start position:0% +public key which everybody else in the + + + align:start position:0% +public key which everybody else in the +world knows and is sort of distributed + + align:start position:0% +world knows and is sort of distributed + + + align:start position:0% +world knows and is sort of distributed +publicly and these two keys aren't equal + + align:start position:0% +publicly and these two keys aren't equal + + + align:start position:0% +publicly and these two keys aren't equal +but there's some math matical operation + + align:start position:0% +but there's some math matical operation + + + align:start position:0% +but there's some math matical operation +that you can apply uh that sort of given + + align:start position:0% +that you can apply uh that sort of given + + + align:start position:0% +that you can apply uh that sort of given +something that's been encrypted with K1 + + align:start position:0% +something that's been encrypted with K1 + + + align:start position:0% +something that's been encrypted with K1 +you can later decrypt it with K2 and + + align:start position:0% +you can later decrypt it with K2 and + + + align:start position:0% +you can later decrypt it with K2 and +we'll look at one one example of one of + + align:start position:0% +we'll look at one one example of one of + + + align:start position:0% +we'll look at one one example of one of +those mathematical + + align:start position:0% + + + + align:start position:0% + +functions okay so the so so the point + + align:start position:0% +functions okay so the so so the point + + + align:start position:0% +functions okay so the so so the point +here is closed design says the algorithm + + align:start position:0% +here is closed design says the algorithm + + + align:start position:0% +here is closed design says the algorithm +itself is uh unknown to the world what + + align:start position:0% +itself is uh unknown to the world what + + + align:start position:0% +itself is uh unknown to the world what +shared secret simply says is that + + align:start position:0% +shared secret simply says is that + + + align:start position:0% +shared secret simply says is that +there's some little bit of information a + + align:start position:0% +there's some little bit of information a + + + align:start position:0% +there's some little bit of information a +little key like a a number that we've + + align:start position:0% +little key like a a number that we've + + + align:start position:0% +little key like a a number that we've +exchanged right but it's not that + + align:start position:0% +exchanged right but it's not that + + + align:start position:0% +exchanged right but it's not that +algorithm it's not the it's not the it's + + align:start position:0% +algorithm it's not the it's not the it's + + + align:start position:0% +algorithm it's not the it's not the it's +not the protocol it's just this one + + align:start position:0% +not the protocol it's just this one + + + align:start position:0% +not the protocol it's just this one +little bit of say you know 100 several + + align:start position:0% +little bit of say you know 100 several + + + align:start position:0% +little bit of say you know 100 several +hundred bits of key information that we + + align:start position:0% +hundred bits of key information that we + + + align:start position:0% +hundred bits of key information that we +established beforehand okay but it still + + align:start position:0% +established beforehand okay but it still + + + align:start position:0% +established beforehand okay but it still +is the case that say for example system + + align:start position:0% +is the case that say for example system + + + align:start position:0% +is the case that say for example system +attack uh that you know this this + + align:start position:0% +attack uh that you know this this + + + align:start position:0% +attack uh that you know this this +protocol in in in a uh shared secret + + align:start position:0% +protocol in in in a uh shared secret + + + align:start position:0% +protocol in in in a uh shared secret +system is published and so people can go + + align:start position:0% +system is published and so people can go + + + align:start position:0% +system is published and so people can go +and try and uh you know analyze the + + align:start position:0% +and try and uh you know analyze the + + + align:start position:0% +and try and uh you know analyze the +security of this thing right so the + + align:start position:0% +security of this thing right so the + + + align:start position:0% +security of this thing right so the +community can look at what the what the + + align:start position:0% +community can look at what the what the + + + align:start position:0% +community can look at what the what the +math is that's going on + + align:start position:0% +math is that's going on + + + align:start position:0% +math is that's going on +okay um + + align:start position:0% +okay um + + + align:start position:0% +okay um +okay so let's look at a simple example + + align:start position:0% +okay so let's look at a simple example + + + align:start position:0% +okay so let's look at a simple example +of a + + align:start position:0% + + + + align:start position:0% + +um shared Key + + align:start position:0% + + + + align:start position:0% + +System this is a system this is an + + align:start position:0% +System this is a system this is an + + + align:start position:0% +System this is a system this is an +approach called a one-time + + align:start position:0% + + + + align:start position:0% + +pad so onetime pad is a very ex a very + + align:start position:0% +pad so onetime pad is a very ex a very + + + align:start position:0% +pad so onetime pad is a very ex a very +simple example of an encryption protocol + + align:start position:0% +simple example of an encryption protocol + + + align:start position:0% +simple example of an encryption protocol +that + + align:start position:0% +that + + + align:start position:0% +that +is essentially is sort of it's + + align:start position:0% +is essentially is sort of it's + + + align:start position:0% +is essentially is sort of it's +cryptographically unbreakable that is it + + align:start position:0% +cryptographically unbreakable that is it + + + align:start position:0% +cryptographically unbreakable that is it +may be possible to break it through + + align:start position:0% +may be possible to break it through + + + align:start position:0% +may be possible to break it through +other means but it's not it's sort of + + align:start position:0% +other means but it's not it's sort of + + + align:start position:0% +other means but it's not it's sort of +provably not possible to break this + + align:start position:0% +provably not possible to break this + + + align:start position:0% +provably not possible to break this +through some sort of mathematical + + align:start position:0% +through some sort of mathematical + + + align:start position:0% +through some sort of mathematical +analysis attack okay um onetime pad + + align:start position:0% +analysis attack okay um onetime pad + + + align:start position:0% +analysis attack okay um onetime pad +depends on the ability of a source of + + align:start position:0% +depends on the ability of a source of + + + align:start position:0% +depends on the ability of a source of +truly random bits okay so I need some + + align:start position:0% +truly random bits okay so I need some + + + align:start position:0% +truly random bits okay so I need some +way to generate a set of bits which are + + align:start position:0% +way to generate a set of bits which are + + + align:start position:0% +way to generate a set of bits which are +uh sort of completely random and doing + + align:start position:0% +uh sort of completely random and doing + + + align:start position:0% +uh sort of completely random and doing +that is tricky but let's suppose that we + + align:start position:0% +that is tricky but let's suppose that we + + + align:start position:0% +that is tricky but let's suppose that we +can do it um so at one time pad says and + + align:start position:0% +can do it um so at one time pad says and + + + align:start position:0% +can do it um so at one time pad says and +so we're going to call this sequence a + + align:start position:0% +so we're going to call this sequence a + + + align:start position:0% +so we're going to call this sequence a +bits K that's going to be our key and + + align:start position:0% +bits K that's going to be our key and + + + align:start position:0% +bits K that's going to be our key and +this key key in the onetime pad approach + + align:start position:0% +this key key in the onetime pad approach + + + align:start position:0% +this key key in the onetime pad approach +is not going to be short this key is + + align:start position:0% +is not going to be short this key is + + + align:start position:0% +is not going to be short this key is +going to be very very long it's going to + + align:start position:0% +going to be very very long it's going to + + + align:start position:0% +going to be very very long it's going to +be as long as all the messages that we + + align:start position:0% +be as long as all the messages that we + + + align:start position:0% +be as long as all the messages that we +possibly want to send over all of time + + align:start position:0% +possibly want to send over all of time + + + align:start position:0% +possibly want to send over all of time +okay so this is suppose that Alice and + + align:start position:0% +okay so this is suppose that Alice and + + + align:start position:0% +okay so this is suppose that Alice and +Bob the way they generate this is Alice + + align:start position:0% +Bob the way they generate this is Alice + + + align:start position:0% +Bob the way they generate this is Alice +writes a set of random bits onto a CD + + align:start position:0% +writes a set of random bits onto a CD + + + align:start position:0% +writes a set of random bits onto a CD +and hand you know write 650 megabytes of + + align:start position:0% +and hand you know write 650 megabytes of + + + align:start position:0% +and hand you know write 650 megabytes of +random bits onto a CD and gives that to + + align:start position:0% +random bits onto a CD and gives that to + + + align:start position:0% +random bits onto a CD and gives that to +Bob and they agree that this is the key + + align:start position:0% +Bob and they agree that this is the key + + + align:start position:0% +Bob and they agree that this is the key +that they're going to use over time okay + + align:start position:0% +that they're going to use over time okay + + + align:start position:0% +that they're going to use over time okay +so we've got M and + + align:start position:0% +so we've got M and + + + align:start position:0% +so we've got M and +K coming + + align:start position:0% +K coming + + + align:start position:0% +K coming +in um they're being combined together + + align:start position:0% +in um they're being combined together + + + align:start position:0% +in um they're being combined together +and being transmitted over the + + align:start position:0% +and being transmitted over the + + + align:start position:0% +and being transmitted over the +Internet um and then on the other + + align:start position:0% +Internet um and then on the other + + + align:start position:0% +Internet um and then on the other +side they're being + + align:start position:0% +side they're being + + + align:start position:0% +side they're being +um decoded also with K where K these two + + align:start position:0% +um decoded also with K where K these two + + + align:start position:0% +um decoded also with K where K these two +Ks are equal in this case and we've got + + align:start position:0% +Ks are equal in this case and we've got + + + align:start position:0% +Ks are equal in this case and we've got +M coming out okay this plus operation + + align:start position:0% +M coming out okay this plus operation + + + align:start position:0% +M coming out okay this plus operation +here is an exor okay this plus with a + + align:start position:0% +here is an exor okay this plus with a + + + align:start position:0% +here is an exor okay this plus with a +circle it's exor so if you would + + align:start position:0% +circle it's exor so if you would + + + align:start position:0% +circle it's exor so if you would +remember what exor does is the the + + align:start position:0% +remember what exor does is the the + + + align:start position:0% +remember what exor does is the the +definition of exor is given two bits um + + align:start position:0% +definition of exor is given two bits um + + + align:start position:0% +definition of exor is given two bits um +0 one if two things that we're xoring + + align:start position:0% +0 one if two things that we're xoring + + + align:start position:0% +0 one if two things that we're xoring +together two bits they're either zero or + + align:start position:0% +together two bits they're either zero or + + + align:start position:0% +together two bits they're either zero or +one um the exor of two zeros is zero the + + align:start position:0% +one um the exor of two zeros is zero the + + + align:start position:0% +one um the exor of two zeros is zero the +xor of zero and one is one um and the + + align:start position:0% +xor of zero and one is one um and the + + + align:start position:0% +xor of zero and one is one um and the +exor of two ones is zero okay so uh exor + + align:start position:0% +exor of two ones is zero okay so uh exor + + + align:start position:0% +exor of two ones is zero okay so uh exor +has this nice property that um so this + + align:start position:0% +has this nice property that um so this + + + align:start position:0% +has this nice property that um so this +this exor is a this is a bitwise + + align:start position:0% +this exor is a this is a bitwise + + + align:start position:0% +this exor is a this is a bitwise +operation so this says every one bit in + + align:start position:0% +operation so this says every one bit in + + + align:start position:0% +operation so this says every one bit in +the first bit in K is exord with the + + align:start position:0% +the first bit in K is exord with the + + + align:start position:0% +the first bit in K is exord with the +first bit in m and the second bit in K + + align:start position:0% +first bit in m and the second bit in K + + + align:start position:0% +first bit in m and the second bit in K +is exord with the second bit in m and so + + align:start position:0% +is exord with the second bit in m and so + + + align:start position:0% +is exord with the second bit in m and so +on the same thing happens over here xor + + align:start position:0% +on the same thing happens over here xor + + + align:start position:0% +on the same thing happens over here xor +has the nice property that M uh X or + + align:start position:0% +has the nice property that M uh X or + + + align:start position:0% +has the nice property that M uh X or +k x or k is equal to M okay so you can + + align:start position:0% +k x or k is equal to M okay so you can + + + align:start position:0% +k x or k is equal to M okay so you can +verify that that's true if you look at + + align:start position:0% +verify that that's true if you look at + + + align:start position:0% +verify that that's true if you look at +look at a simple example but this means + + align:start position:0% +look at a simple example but this means + + + align:start position:0% +look at a simple example but this means +that so what happens is when this bit + + align:start position:0% +that so what happens is when this bit + + + align:start position:0% +that so what happens is when this bit +when thisam M comes in and gets exord + + align:start position:0% +when thisam M comes in and gets exord + + + align:start position:0% +when thisam M comes in and gets exord +with K the encrypted message that's + + align:start position:0% +with K the encrypted message that's + + + align:start position:0% +with K the encrypted message that's +traveling over here essentially looks + + align:start position:0% +traveling over here essentially looks + + + align:start position:0% +traveling over here essentially looks +like a random bit string because K is a + + align:start position:0% +like a random bit string because K is a + + + align:start position:0% +like a random bit string because K is a +random bit string and sort of this M + + align:start position:0% +random bit string and sort of this M + + + align:start position:0% +random bit string and sort of this M +which is also no matter what m is when + + align:start position:0% +which is also no matter what m is when + + + align:start position:0% +which is also no matter what m is when +it's exord with a random bit string + + align:start position:0% +it's exord with a random bit string + + + align:start position:0% +it's exord with a random bit string +you're going to get something that looks + + align:start position:0% +you're going to get something that looks + + + align:start position:0% +you're going to get something that looks +like a random bit string coming out and + + align:start position:0% +like a random bit string coming out and + + + align:start position:0% +like a random bit string coming out and +then on this other side though we also + + align:start position:0% +then on this other side though we also + + + align:start position:0% +then on this other side though we also +we have access to the same bit string + + align:start position:0% +we have access to the same bit string + + + align:start position:0% +we have access to the same bit string +that was used and now we can decrypt the + + align:start position:0% +that was used and now we can decrypt the + + + align:start position:0% +that was used and now we can decrypt the +message okay so only if somebody knows + + align:start position:0% +message okay so only if somebody knows + + + align:start position:0% +message okay so only if somebody knows +exactly what K is can they decrypt the + + align:start position:0% +exactly what K is can they decrypt the + + + align:start position:0% +exactly what K is can they decrypt the +message this approach is hard to make + + align:start position:0% +message this approach is hard to make + + + align:start position:0% +message this approach is hard to make +work in practice because it requires the + + align:start position:0% +work in practice because it requires the + + + align:start position:0% +work in practice because it requires the +availability of a large amount of random + + align:start position:0% +availability of a large amount of random + + + align:start position:0% +availability of a large amount of random +data um so one thing that you can do is + + align:start position:0% +data um so one thing that you can do is + + + align:start position:0% +data um so one thing that you can do is +use a random number generator that's + + align:start position:0% +use a random number generator that's + + + align:start position:0% +use a random number generator that's +seated with some number and then use + + align:start position:0% +seated with some number and then use + + + align:start position:0% +seated with some number and then use +that random number generator to begin to + + align:start position:0% +that random number generator to begin to + + + align:start position:0% +that random number generator to begin to +to uh sort of generate the sequence of + + align:start position:0% +to uh sort of generate the sequence of + + + align:start position:0% +to uh sort of generate the sequence of +bits um of course that has the problem + + align:start position:0% +bits um of course that has the problem + + + align:start position:0% +bits um of course that has the problem +now which is somebody can discover the + + align:start position:0% +now which is somebody can discover the + + + align:start position:0% +now which is somebody can discover the +seed or somebody can guess which seed + + align:start position:0% +seed or somebody can guess which seed + + + align:start position:0% +seed or somebody can guess which seed +you use because the random number + + align:start position:0% +you use because the random number + + + align:start position:0% +you use because the random number +generator use isn't very good they may + + align:start position:0% +generator use isn't very good they may + + + align:start position:0% +generator use isn't very good they may +be able to break your protocol but one + + align:start position:0% +be able to break your protocol but one + + + align:start position:0% +be able to break your protocol but one +time pad is a nice example of something + + align:start position:0% +time pad is a nice example of something + + + align:start position:0% +time pad is a nice example of something +which is sort of a cryptographic + + align:start position:0% +which is sort of a cryptographic + + + align:start position:0% +which is sort of a cryptographic +protocol that is known to work pretty + + align:start position:0% +protocol that is known to work pretty + + + align:start position:0% +protocol that is known to work pretty +well + + align:start position:0% +well + + + align:start position:0% +well +um okay + + align:start position:0% +um okay + + + align:start position:0% +um okay +so what I want to do just with the last + + align:start position:0% +so what I want to do just with the last + + + align:start position:0% +so what I want to do just with the last +five minutes I want to talk about um + + align:start position:0% +five minutes I want to talk about um + + + align:start position:0% +five minutes I want to talk about um +one specific cryptographic protocol um + + align:start position:0% +one specific cryptographic protocol um + + + align:start position:0% +one specific cryptographic protocol um +which is called the RSA protocol and we + + align:start position:0% +which is called the RSA protocol and we + + + align:start position:0% +which is called the RSA protocol and we +probably um won't have time to go + + align:start position:0% +probably um won't have time to go + + + align:start position:0% +probably um won't have time to go +through the details of how RSA actually + + align:start position:0% +through the details of how RSA actually + + + align:start position:0% +through the details of how RSA actually +works + + align:start position:0% +works + + + align:start position:0% +works +um but RSA is + + align:start position:0% +um but RSA is + + + align:start position:0% +um but RSA is +a a public + + align:start position:0% +a a public + + + align:start position:0% +a a public +key + + align:start position:0% + + + + align:start position:0% + +protocol um and it works let let's just + + align:start position:0% +protocol um and it works let let's just + + + align:start position:0% +protocol um and it works let let's just +quickly let me just quickly show you you + + align:start position:0% +quickly let me just quickly show you you + + + align:start position:0% +quickly let me just quickly show you you +um what RSA uses and then uh we'll skip + + align:start position:0% +um what RSA uses and then uh we'll skip + + + align:start position:0% +um what RSA uses and then uh we'll skip +over Dees + + align:start position:0% + + + + align:start position:0% + +here um so what RSA does is it says + + align:start position:0% +here um so what RSA does is it says + + + align:start position:0% +here um so what RSA does is it says +we're going to take two numbers p and Q + + align:start position:0% +we're going to take two numbers p and Q + + + align:start position:0% +we're going to take two numbers p and Q +which are prime this protocol is in the + + align:start position:0% +which are prime this protocol is in the + + + align:start position:0% +which are prime this protocol is in the +book so if you guys don't need to it's + + align:start position:0% +book so if you guys don't need to it's + + + align:start position:0% +book so if you guys don't need to it's +in the uh the appendix one of chapter of + + align:start position:0% +in the uh the appendix one of chapter of + + + align:start position:0% +in the uh the appendix one of chapter of +the chapter so you don't need to copy it + + align:start position:0% +the chapter so you don't need to copy it + + + align:start position:0% +the chapter so you don't need to copy it +down word for word if you don't want to + + align:start position:0% +down word for word if you don't want to + + + align:start position:0% +down word for word if you don't want to +um so if you have p and Q or primes we + + align:start position:0% +um so if you have p and Q or primes we + + + align:start position:0% +um so if you have p and Q or primes we +pick two numbers p and Q which are prime + + align:start position:0% +pick two numbers p and Q which are prime + + + align:start position:0% +pick two numbers p and Q which are prime +um and then we generate some number n + + align:start position:0% +um and then we generate some number n + + + align:start position:0% +um and then we generate some number n +which is equal to p and * q and another + + align:start position:0% +which is equal to p and * q and another + + + align:start position:0% +which is equal to p and * q and another +number Z which is equal to P - 1 * Q -1 + + align:start position:0% +number Z which is equal to P - 1 * Q -1 + + + align:start position:0% +number Z which is equal to P - 1 * Q -1 +okay and then pick another number e + + align:start position:0% +okay and then pick another number e + + + align:start position:0% +okay and then pick another number e +which is relatively prime to Z so that + + align:start position:0% +which is relatively prime to Z so that + + + align:start position:0% +which is relatively prime to Z so that +relatively prime just means uh that e + + align:start position:0% +relatively prime just means uh that e + + + align:start position:0% +relatively prime just means uh that e +doesn't divide Z evenly okay so Z is not + + align:start position:0% +doesn't divide Z evenly okay so Z is not + + + align:start position:0% +doesn't divide Z evenly okay so Z is not +divisible by e um and we pick a number D + + align:start position:0% +divisible by e um and we pick a number D + + + align:start position:0% +divisible by e um and we pick a number D +such that e * D is equal to one um as + + align:start position:0% +such that e * D is equal to one um as + + + align:start position:0% +such that e * D is equal to one um as +long as the product of mod modulo Z + + align:start position:0% +long as the product of mod modulo Z + + + align:start position:0% +long as the product of mod modulo Z +right so take the product so e * d uh if + + align:start position:0% +right so take the product so e * d uh if + + + align:start position:0% +right so take the product so e * d uh if +you take e time D and you take the + + align:start position:0% +you take e time D and you take the + + + align:start position:0% +you take e time D and you take the +modulus with Z the value should be one + + align:start position:0% +modulus with Z the value should be one + + + align:start position:0% +modulus with Z the value should be one +okay um so if you pick a set of numbers + + align:start position:0% +okay um so if you pick a set of numbers + + + align:start position:0% +okay um so if you pick a set of numbers +that satisfy this property then we can + + align:start position:0% +that satisfy this property then we can + + + align:start position:0% +that satisfy this property then we can +Define the public key to be e comma n + + align:start position:0% +Define the public key to be e comma n + + + align:start position:0% +Define the public key to be e comma n +and the private key to be D comma n okay + + align:start position:0% +and the private key to be D comma n okay + + + align:start position:0% +and the private key to be D comma n okay +and these numbers have this magic + + align:start position:0% +and these numbers have this magic + + + align:start position:0% +and these numbers have this magic +property um so and then we're going to + + align:start position:0% +property um so and then we're going to + + + align:start position:0% +property um so and then we're going to +be able to with this encrypt any message + + align:start position:0% +be able to with this encrypt any message + + + align:start position:0% +be able to with this encrypt any message +that's up to n in length Okay so n is in + + align:start position:0% +that's up to n in length Okay so n is in + + + align:start position:0% +that's up to n in length Okay so n is in +general we're going to want n and p and + + align:start position:0% +general we're going to want n and p and + + + align:start position:0% +general we're going to want n and p and +Q to be some set of very large numbers + + align:start position:0% +Q to be some set of very large numbers + + + align:start position:0% +Q to be some set of very large numbers +right like hundred they're going to be + + align:start position:0% +right like hundred they're going to be + + + align:start position:0% +right like hundred they're going to be +hundreds of bits long okay so we're + + align:start position:0% +hundreds of bits long okay so we're + + + align:start position:0% +hundreds of bits long okay so we're +going to be able to encrypt any message + + align:start position:0% +going to be able to encrypt any message + + + align:start position:0% +going to be able to encrypt any message +that's up to end bit it's long it's it's + + align:start position:0% +that's up to end bit it's long it's it's + + + align:start position:0% +that's up to end bit it's long it's it's +up to the size of n um and if it's uh so + + align:start position:0% +up to the size of n um and if it's uh so + + + align:start position:0% +up to the size of n um and if it's uh so +we may have to break the messages up + + align:start position:0% +we may have to break the messages up + + + align:start position:0% +we may have to break the messages up +into chunks that are smaller that are + + align:start position:0% +into chunks that are smaller that are + + + align:start position:0% +into chunks that are smaller that are +that are size n or smaller this has this + + align:start position:0% +that are size n or smaller this has this + + + align:start position:0% +that are size n or smaller this has this +magic property now that if we encrypt + + align:start position:0% +magic property now that if we encrypt + + + align:start position:0% +magic property now that if we encrypt +the data with uh in this in the + + align:start position:0% +the data with uh in this in the + + + align:start position:0% +the data with uh in this in the +following way we take the message to + + align:start position:0% +following way we take the message to + + + align:start position:0% +following way we take the message to +encrypt a message we take m to the power + + align:start position:0% +encrypt a message we take m to the power + + + align:start position:0% +encrypt a message we take m to the power +of E then take the whole thing module n + + align:start position:0% +of E then take the whole thing module n + + + align:start position:0% +of E then take the whole thing module n +now transmit that message C across the + + align:start position:0% +now transmit that message C across the + + + align:start position:0% +now transmit that message C across the +network now to decrypt we take the that + + align:start position:0% +network now to decrypt we take the that + + + align:start position:0% +network now to decrypt we take the that +that encrypted thing and take it to the + + align:start position:0% +that encrypted thing and take it to the + + + align:start position:0% +that encrypted thing and take it to the +power D and then take the whole thing + + align:start position:0% +power D and then take the whole thing + + + align:start position:0% +power D and then take the whole thing +modulo n we get the the original message + + align:start position:0% +modulo n we get the the original message + + + align:start position:0% +modulo n we get the the original message +out at the end okay um so the + + align:start position:0% +out at the end okay um so the + + + align:start position:0% +out at the end okay um so the +mathematics of understanding why this + + align:start position:0% +mathematics of understanding why this + + + align:start position:0% +mathematics of understanding why this +work turn out to be fairly subtle and + + align:start position:0% +work turn out to be fairly subtle and + + + align:start position:0% +work turn out to be fairly subtle and +sophisticated there's a brief outline of + + align:start position:0% +sophisticated there's a brief outline of + + + align:start position:0% +sophisticated there's a brief outline of +it in the paper but if you really want + + align:start position:0% +it in the paper but if you really want + + + align:start position:0% +it in the paper but if you really want +to understand this is the kind of thing + + align:start position:0% +to understand this is the kind of thing + + + align:start position:0% +to understand this is the kind of thing +that requires an additional course in + + align:start position:0% +that requires an additional course in + + + align:start position:0% +that requires an additional course in +cryptography so we're not going to go + + align:start position:0% +cryptography so we're not going to go + + + align:start position:0% +cryptography so we're not going to go +into the details of the mathematics but + + align:start position:0% +into the details of the mathematics but + + + align:start position:0% +into the details of the mathematics but +the idea is suppose we pick P to be 47 + + align:start position:0% +the idea is suppose we pick P to be 47 + + + align:start position:0% +the idea is suppose we pick P to be 47 +and Q to be 49 two prime numbers + + align:start position:0% +and Q to be 49 two prime numbers + + + align:start position:0% +and Q to be 49 two prime numbers +generate n to be 2773 just the product + + align:start position:0% +generate n to be 2773 just the product + + + align:start position:0% +generate n to be 2773 just the product +of those Z then is + + align:start position:0% +of those Z then is + + + align:start position:0% +of those Z then is +2668 um and now we pick two numbers e + + align:start position:0% +2668 um and now we pick two numbers e + + + align:start position:0% +2668 um and now we pick two numbers e +and D so we pick these numbers just by + + align:start position:0% +and D so we pick these numbers just by + + + align:start position:0% +and D so we pick these numbers just by +using some search uh searching for these + + align:start position:0% +using some search uh searching for these + + + align:start position:0% +using some search uh searching for these +numbers somehow over the set of you know + + align:start position:0% +numbers somehow over the set of you know + + + align:start position:0% +numbers somehow over the set of you know +all possible numbers we could have + + align:start position:0% +all possible numbers we could have + + + align:start position:0% +all possible numbers we could have +picked so we have these two numbers e + + align:start position:0% +picked so we have these two numbers e + + + align:start position:0% +picked so we have these two numbers e +and D which satisfy this property um + + align:start position:0% +and D which satisfy this property um + + + align:start position:0% +and D which satisfy this property um +that is 2668 is not divisible by 17 and + + align:start position:0% +that is 2668 is not divisible by 17 and + + + align:start position:0% +that is 2668 is not divisible by 17 and +uh 17 * + + align:start position:0% +uh 17 * + + + align:start position:0% +uh 17 * +157 uh modulo Z modulo 2668 is equal to + + align:start position:0% +157 uh modulo Z modulo 2668 is equal to + + + align:start position:0% +157 uh modulo Z modulo 2668 is equal to +one you have to trust me that that's + + align:start position:0% +one you have to trust me that that's + + + align:start position:0% +one you have to trust me that that's +true um now suppose we have our message + + align:start position:0% +true um now suppose we have our message + + + align:start position:0% +true um now suppose we have our message +is equal to 31 okay so if we compute now + + align:start position:0% +is equal to 31 okay so if we compute now + + + align:start position:0% +is equal to 31 okay so if we compute now +C is equal to this thing 31 to the 17th + + align:start position:0% +C is equal to this thing 31 to the 17th + + + align:start position:0% +C is equal to this thing 31 to the 17th +modulo 2773 we get 587 and then sort of + + align:start position:0% +modulo 2773 we get 587 and then sort of + + + align:start position:0% +modulo 2773 we get 587 and then sort of +magically at the end uh we reverse this + + align:start position:0% +magically at the end uh we reverse this + + + align:start position:0% +magically at the end uh we reverse this +thing and out pops out our message okay + + align:start position:0% +thing and out pops out our message okay + + + align:start position:0% +thing and out pops out our message okay +so um this protocol uh what what we see + + align:start position:0% +so um this protocol uh what what we see + + + align:start position:0% +so um this protocol uh what what we see +here is so this is this is the a public + + align:start position:0% +here is so this is this is the a public + + + align:start position:0% +here is so this is this is the a public +key protocol what we say here is the + + align:start position:0% +key protocol what we say here is the + + + align:start position:0% +key protocol what we say here is the +public key is equal to this combination + + align:start position:0% +public key is equal to this combination + + + align:start position:0% +public key is equal to this combination +of e and n and the private key is equal + + align:start position:0% +of e and n and the private key is equal + + + align:start position:0% +of e and n and the private key is equal +to this combination is equal to this + + align:start position:0% +to this combination is equal to this + + + align:start position:0% +to this combination is equal to this +combination of d and n so suppose that + + align:start position:0% +combination of d and n so suppose that + + + align:start position:0% +combination of d and n so suppose that +Alice only Alice knows the private key + + align:start position:0% +Alice only Alice knows the private key + + + align:start position:0% +Alice only Alice knows the private key +and that Bob know knows the public key + + align:start position:0% +and that Bob know knows the public key + + + align:start position:0% +and that Bob know knows the public key +and everybody else in the world for + + align:start position:0% +and everybody else in the world for + + + align:start position:0% +and everybody else in the world for +example knows what the public key is now + + align:start position:0% +example knows what the public key is now + + + align:start position:0% +example knows what the public key is now +what we can do is Alice can encrypt the + + align:start position:0% +what we can do is Alice can encrypt the + + + align:start position:0% +what we can do is Alice can encrypt the +message with the private with her + + align:start position:0% +message with the private with her + + + align:start position:0% +message with the private with her +private key right which nobody else + + align:start position:0% +private key right which nobody else + + + align:start position:0% +private key right which nobody else +knows and then uh using the public key + + align:start position:0% +knows and then uh using the public key + + + align:start position:0% +knows and then uh using the public key +everybody else can go ahead and decrypt + + align:start position:0% +everybody else can go ahead and decrypt + + + align:start position:0% +everybody else can go ahead and decrypt +that message and by decrypting that + + align:start position:0% +that message and by decrypting that + + + align:start position:0% +that message and by decrypting that +message um they they can be assured that + + align:start position:0% +message um they they can be assured that + + + align:start position:0% +message um they they can be assured that +the only person that could have had the + + align:start position:0% +the only person that could have had the + + + align:start position:0% +the only person that could have had the +me that could have had the that could + + align:start position:0% +me that could have had the that could + + + align:start position:0% +me that could have had the that could +have actually created this message to + + align:start position:0% +have actually created this message to + + + align:start position:0% +have actually created this message to +begin with is somebody who had had + + align:start position:0% +begin with is somebody who had had + + + align:start position:0% +begin with is somebody who had had +access to Alice's private key okay so + + align:start position:0% +access to Alice's private key okay so + + + align:start position:0% +access to Alice's private key okay so +they can authenticate that this message + + align:start position:0% +they can authenticate that this message + + + align:start position:0% +they can authenticate that this message +came from + + align:start position:0% +came from + + + align:start position:0% +came from +Alice uh this protocol also has a nice + + align:start position:0% +Alice uh this protocol also has a nice + + + align:start position:0% +Alice uh this protocol also has a nice +side effect which is that it's it's it's + + align:start position:0% +side effect which is that it's it's it's + + + align:start position:0% +side effect which is that it's it's it's +reversible so if I so uh I can also if + + align:start position:0% +reversible so if I so uh I can also if + + + align:start position:0% +reversible so if I so uh I can also if +Bob encrypts a message using Alice's + + align:start position:0% +Bob encrypts a message using Alice's + + + align:start position:0% +Bob encrypts a message using Alice's +public key he can decrypt if Alice can + + align:start position:0% +public key he can decrypt if Alice can + + + align:start position:0% +public key he can decrypt if Alice can +decrypt that message and only Alice can + + align:start position:0% +decrypt that message and only Alice can + + + align:start position:0% +decrypt that message and only Alice can +decrypt that message using her private + + align:start position:0% +decrypt that message using her private + + + align:start position:0% +decrypt that message using her private +key so we'll talk more about these + + align:start position:0% +key so we'll talk more about these + + + align:start position:0% +key so we'll talk more about these +properties next time um and uh take care \ No newline at end of file diff --git a/T1K4pkhtad8.txt b/T1K4pkhtad8.txt new file mode 100644 index 0000000000000000000000000000000000000000..ff6897294fb6e2ecba2456bcf80e714269aac345 --- /dev/null +++ b/T1K4pkhtad8.txt @@ -0,0 +1,12272 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT + + align:start position:0% +hundreds of MIT courses visit MIT + + + align:start position:0% +hundreds of MIT courses visit MIT +opencourseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay well this is uh this is + + align:start position:0% +ocw.mit.edu okay well this is uh this is + + + align:start position:0% +ocw.mit.edu okay well this is uh this is +literally for most of you the start of + + align:start position:0% +literally for most of you the start of + + + align:start position:0% +literally for most of you the start of +your lean Journey because we've seen the + + align:start position:0% +your lean Journey because we've seen the + + + align:start position:0% +your lean Journey because we've seen the +value data and we know that for many of + + align:start position:0% +value data and we know that for many of + + + align:start position:0% +value data and we know that for many of +you these this whole subject matter is + + align:start position:0% +you these this whole subject matter is + + + align:start position:0% +you these this whole subject matter is +something you've hardly heard about and + + align:start position:0% +something you've hardly heard about and + + + align:start position:0% +something you've hardly heard about and +that's perfect because that's what this + + align:start position:0% +that's perfect because that's what this + + + align:start position:0% +that's perfect because that's what this +course is designed for so welcome so at + + align:start position:0% +course is designed for so welcome so at + + + align:start position:0% +course is designed for so welcome so at +the end of this + + align:start position:0% +the end of this + + + align:start position:0% +the end of this +module we hope you'll be able to explain + + align:start position:0% +module we hope you'll be able to explain + + + align:start position:0% +module we hope you'll be able to explain +the origins of lean and Six + + align:start position:0% +the origins of lean and Six + + + align:start position:0% +the origins of lean and Six +Sigma explain the lean 6s tool you're + + align:start position:0% +Sigma explain the lean 6s tool you're + + + align:start position:0% +Sigma explain the lean 6s tool you're +going to learn your first lean tool here + + align:start position:0% +going to learn your first lean tool here + + + align:start position:0% +going to learn your first lean tool here +you're going to be able to Define what + + align:start position:0% +you're going to be able to Define what + + + align:start position:0% +you're going to be able to Define what +is lean what's a lean Enterprise and + + align:start position:0% +is lean what's a lean Enterprise and + + + align:start position:0% +is lean what's a lean Enterprise and +what are stake who are stakeholders of + + align:start position:0% +what are stake who are stakeholders of + + + align:start position:0% +what are stake who are stakeholders of +the lean + + align:start position:0% +the lean + + + align:start position:0% +the lean +Enterprise you'll recognize why lean + + align:start position:0% +Enterprise you'll recognize why lean + + + align:start position:0% +Enterprise you'll recognize why lean +Sigma principles are being implemented + + align:start position:0% +Sigma principles are being implemented + + + align:start position:0% +Sigma principles are being implemented +in Aerospace Healthcare and other + + align:start position:0% +in Aerospace Healthcare and other + + + align:start position:0% +in Aerospace Healthcare and other +sectors we're going to talk about why + + align:start position:0% +sectors we're going to talk about why + + + align:start position:0% +sectors we're going to talk about why +these sectors are moving in this + + align:start position:0% +these sectors are moving in this + + + align:start position:0% +these sectors are moving in this +direction and you'll be able to explain + + align:start position:0% +direction and you'll be able to explain + + + align:start position:0% +direction and you'll be able to explain +that lean is a journey it's not a state + + align:start position:0% +that lean is a journey it's not a state + + + align:start position:0% +that lean is a journey it's not a state +you never are lean you're always trying + + align:start position:0% +you never are lean you're always trying + + + align:start position:0% +you never are lean you're always trying +to become lean and we'll talk a little + + align:start position:0% +to become lean and we'll talk a little + + + align:start position:0% +to become lean and we'll talk a little +bit about + + align:start position:0% + + + + align:start position:0% + +that so this this subject matter comes + + align:start position:0% +that so this this subject matter comes + + + align:start position:0% +that so this this subject matter comes +out of the Japanese automotive industry + + align:start position:0% +out of the Japanese automotive industry + + + align:start position:0% +out of the Japanese automotive industry +and + + align:start position:0% +and + + + align:start position:0% +and +unlike um aerospace + + align:start position:0% +unlike um aerospace + + + align:start position:0% +unlike um aerospace +engineering and structures and controls + + align:start position:0% +engineering and structures and controls + + + align:start position:0% +engineering and structures and controls +and + + align:start position:0% +and + + + align:start position:0% +and +aerodynamics where you can go to the + + align:start position:0% +aerodynamics where you can go to the + + + align:start position:0% +aerodynamics where you can go to the +laboratory and see what's happening and + + align:start position:0% +laboratory and see what's happening and + + + align:start position:0% +laboratory and see what's happening and +do experiments and things in this field + + align:start position:0% +do experiments and things in this field + + + align:start position:0% +do experiments and things in this field +you have to go to where where it's + + align:start position:0% +you have to go to where where it's + + + align:start position:0% +you have to go to where where it's +actually being practiced because that's + + align:start position:0% +actually being practiced because that's + + + align:start position:0% +actually being practiced because that's +the body of knowledge comes from that + + align:start position:0% +the body of knowledge comes from that + + + align:start position:0% +the body of knowledge comes from that +field so this all kind of came to the + + align:start position:0% +field so this all kind of came to the + + + align:start position:0% +field so this all kind of came to the +surface in 1990 when MIT published a + + align:start position:0% +surface in 1990 when MIT published a + + + align:start position:0% +surface in 1990 when MIT published a +book called the machine that changed the + + align:start position:0% +book called the machine that changed the + + + align:start position:0% +book called the machine that changed the +world there was a study of the Japanese + + align:start position:0% +world there was a study of the Japanese + + + align:start position:0% +world there was a study of the Japanese +North American and European Automotive + + align:start position:0% +North American and European Automotive + + + align:start position:0% +North American and European Automotive +manufacturing and this is a plot given + + align:start position:0% +manufacturing and this is a plot given + + + align:start position:0% +manufacturing and this is a plot given +then of production of cars these are all + + align:start position:0% +then of production of cars these are all + + + align:start position:0% +then of production of cars these are all +the + + align:start position:0% +the + + + align:start position:0% +the +US car manufacturers and here's + + align:start position:0% +US car manufacturers and here's + + + align:start position:0% +US car manufacturers and here's +Japan and what do you see in that chart + + align:start position:0% +Japan and what do you see in that chart + + + align:start position:0% +Japan and what do you see in that chart +what what jumps out at + + align:start position:0% + + + + align:start position:0% + +you what's the first thing you see uh + + align:start position:0% +you what's the first thing you see uh + + + align:start position:0% +you what's the first thing you see uh +Japan + + align:start position:0% +Japan + + + align:start position:0% +Japan +increasing a lot faster than us + + align:start position:0% + + + + align:start position:0% + +passes going so that's one thing Japan + + align:start position:0% +passes going so that's one thing Japan + + + align:start position:0% +passes going so that's one thing Japan +has just steady growth what's the next + + align:start position:0% +has just steady growth what's the next + + + align:start position:0% +has just steady growth what's the next +thing you + + align:start position:0% +thing you + + + align:start position:0% +thing you +see consistent inconsistent + + align:start position:0% +see consistent inconsistent + + + align:start position:0% +see consistent inconsistent +right this is the the typical us thing + + align:start position:0% +right this is the the typical us thing + + + align:start position:0% +right this is the the typical us thing +you know you kind of overproduce + + align:start position:0% +you know you kind of overproduce + + + align:start position:0% +you know you kind of overproduce +underproduce overproduce and the + + align:start position:0% +underproduce overproduce and the + + + align:start position:0% +underproduce overproduce and the +Japanese are nice smooth and steady + + align:start position:0% +Japanese are nice smooth and steady + + + align:start position:0% +Japanese are nice smooth and steady +there's a lot of data in the machine + + align:start position:0% +there's a lot of data in the machine + + + align:start position:0% +there's a lot of data in the machine +that changed the world and we're not + + align:start position:0% +that changed the world and we're not + + + align:start position:0% +that changed the world and we're not +going to go through all this but I want + + align:start position:0% +going to go through all this but I want + + + align:start position:0% +going to go through all this but I want +to make a couple points first of all the + + align:start position:0% +to make a couple points first of all the + + + align:start position:0% +to make a couple points first of all the +data in this this chart is product + + align:start position:0% +data in this this chart is product + + + align:start position:0% +data in this this chart is product +development and Manufacturing now a big + + align:start position:0% +development and Manufacturing now a big + + + align:start position:0% +development and Manufacturing now a big +mistake a lot of us companies made when + + align:start position:0% +mistake a lot of us companies made when + + + align:start position:0% +mistake a lot of us companies made when +they read this book was that leans a + + align:start position:0% +they read this book was that leans a + + + align:start position:0% +they read this book was that leans a +manufacturing Paradigm it's a + + align:start position:0% +manufacturing Paradigm it's a + + + align:start position:0% +manufacturing Paradigm it's a +manufacturing system in fact most of my + + align:start position:0% +manufacturing system in fact most of my + + + align:start position:0% +manufacturing system in fact most of my +friends when they talk to me say oh + + align:start position:0% +friends when they talk to me say oh + + + align:start position:0% +friends when they talk to me say oh +you're in lean manufacturing okay the + + align:start position:0% +you're in lean manufacturing okay the + + + align:start position:0% +you're in lean manufacturing okay the +Japanese never saw it that way they they + + align:start position:0% +Japanese never saw it that way they they + + + align:start position:0% +Japanese never saw it that way they they +Implement lean right back in engineering + + align:start position:0% +Implement lean right back in engineering + + + align:start position:0% +Implement lean right back in engineering +and product development okay so in + + align:start position:0% +and product development okay so in + + + align:start position:0% +and product development okay so in +product development for instance the uh + + align:start position:0% +product development for instance the uh + + + align:start position:0% +product development for instance the uh +average engineering hours in a new car + + align:start position:0% +average engineering hours in a new car + + + align:start position:0% +average engineering hours in a new car +1.7 million for Japanese 3.1 million for + + align:start position:0% +1.7 million for Japanese 3.1 million for + + + align:start position:0% +1.7 million for Japanese 3.1 million for +us almost twice the number of + + align:start position:0% +us almost twice the number of + + + align:start position:0% +us almost twice the number of +engineering hours for the same + + align:start position:0% +engineering hours for the same + + + align:start position:0% +engineering hours for the same +car uh supplier share of engineering how + + align:start position:0% +car uh supplier share of engineering how + + + align:start position:0% +car uh supplier share of engineering how +many of the suppliers are actually doing + + align:start position:0% +many of the suppliers are actually doing + + + align:start position:0% +many of the suppliers are actually doing +engineering compared to just supplying + + align:start position:0% +engineering compared to just supplying + + + align:start position:0% +engineering compared to just supplying +Parts 51% in Japan 14% in us so we're + + align:start position:0% +Parts 51% in Japan 14% in us so we're + + + align:start position:0% +Parts 51% in Japan 14% in us so we're +going to be talking about that tomorrow + + align:start position:0% +going to be talking about that tomorrow + + + align:start position:0% +going to be talking about that tomorrow +in the engineering + + align:start position:0% +in the engineering + + + align:start position:0% +in the engineering +section uh this that's that's design + + align:start position:0% +section uh this that's that's design + + + align:start position:0% +section uh this that's that's design +here here's production uh let's just get + + align:start position:0% +here here's production uh let's just get + + + align:start position:0% +here here's production uh let's just get +a couple numbers + + align:start position:0% +a couple numbers + + + align:start position:0% +a couple numbers +uh quality defects per 100 Vehicles 60 + + align:start position:0% +uh quality defects per 100 Vehicles 60 + + + align:start position:0% +uh quality defects per 100 Vehicles 60 +for Japanese 82 for us uh training hours + + align:start position:0% +for Japanese 82 for us uh training hours + + + align:start position:0% +for Japanese 82 for us uh training hours +of new workers 380 for Japan + + align:start position:0% +of new workers 380 for Japan + + + align:start position:0% +of new workers 380 for Japan +46 for us that's probably not because + + align:start position:0% +46 for us that's probably not because + + + align:start position:0% +46 for us that's probably not because +the Japanese need more training it's + + align:start position:0% +the Japanese need more training it's + + + align:start position:0% +the Japanese need more training it's +probably because Japan invests more in + + align:start position:0% +probably because Japan invests more in + + + align:start position:0% +probably because Japan invests more in +training okay so this is what started uh + + align:start position:0% +training okay so this is what started uh + + + align:start position:0% +training okay so this is what started uh +the whole lean uh activity around the + + align:start position:0% +the whole lean uh activity around the + + + align:start position:0% +the whole lean uh activity around the +world in in the US now how does lean + + align:start position:0% +world in in the US now how does lean + + + align:start position:0% +world in in the US now how does lean +compare what are the fundamental + + align:start position:0% +compare what are the fundamental + + + align:start position:0% +compare what are the fundamental +comparisons of lean with what we already + + align:start position:0% +comparisons of lean with what we already + + + align:start position:0% +comparisons of lean with what we already +know well we have here lean + + align:start position:0% +know well we have here lean + + + align:start position:0% +know well we have here lean +thinking mass production and craft + + align:start position:0% +thinking mass production and craft + + + align:start position:0% +thinking mass production and craft +production as sort of three paradigms + + align:start position:0% +production as sort of three paradigms + + + align:start position:0% +production as sort of three paradigms +let's just we're going to spend a little + + align:start position:0% +let's just we're going to spend a little + + + align:start position:0% +let's just we're going to spend a little +bit of time on this chart because this + + align:start position:0% +bit of time on this chart because this + + + align:start position:0% +bit of time on this chart because this +is going to set your your thoughts for + + align:start position:0% +is going to set your your thoughts for + + + align:start position:0% +is going to set your your thoughts for +the whole course so let's look at the + + align:start position:0% +the whole course so let's look at the + + + align:start position:0% +the whole course so let's look at the +the these are different Focus areas so + + align:start position:0% +the these are different Focus areas so + + + align:start position:0% +the these are different Focus areas so +in operations in craft thing person's + + align:start position:0% +in operations in craft thing person's + + + align:start position:0% +in operations in craft thing person's +working on a single item in mass + + align:start position:0% +working on a single item in mass + + + align:start position:0% +working on a single item in mass +production the the idea was you make a + + align:start position:0% +production the the idea was you make a + + + align:start position:0% +production the the idea was you make a +lot of them and you put them in a queue + + align:start position:0% +lot of them and you put them in a queue + + + align:start position:0% +lot of them and you put them in a queue +you make more and you put them in a + + align:start position:0% +you make more and you put them in a + + + align:start position:0% +you make more and you put them in a +queue in lean thinking it's all flow + + align:start position:0% +queue in lean thinking it's all flow + + + align:start position:0% +queue in lean thinking it's all flow +everything is Flowing very smoothly and + + align:start position:0% +everything is Flowing very smoothly and + + + align:start position:0% +everything is Flowing very smoothly and +synchronized and we're going to talk a + + align:start position:0% +synchronized and we're going to talk a + + + align:start position:0% +synchronized and we're going to talk a +lot about flow what's the overall + + align:start position:0% +lot about flow what's the overall + + + align:start position:0% +lot about flow what's the overall +aim in craft it was the Mastery of the + + align:start position:0% +aim in craft it was the Mastery of the + + + align:start position:0% +aim in craft it was the Mastery of the +craft in mass production it's reduced + + align:start position:0% +craft in mass production it's reduced + + + align:start position:0% +craft in mass production it's reduced +unit cost and increase + + align:start position:0% +unit cost and increase + + + align:start position:0% +unit cost and increase +efficiency in lean it's eliminating all + + align:start position:0% +efficiency in lean it's eliminating all + + + align:start position:0% +efficiency in lean it's eliminating all +waste and only doing value added + + align:start position:0% +waste and only doing value added + + + align:start position:0% +waste and only doing value added +activities you're going to be hearing a + + align:start position:0% +activities you're going to be hearing a + + + align:start position:0% +activities you're going to be hearing a +lot about this by the way most of the + + align:start position:0% +lot about this by the way most of the + + + align:start position:0% +lot about this by the way most of the +things that we talk about today we're + + align:start position:0% +things that we talk about today we're + + + align:start position:0% +things that we talk about today we're +going to come back and talk about + + align:start position:0% +going to come back and talk about + + + align:start position:0% +going to come back and talk about +tomorrow and then we're going to come + + align:start position:0% +tomorrow and then we're going to come + + + align:start position:0% +tomorrow and then we're going to come +back and talk about on Wednesday so if + + align:start position:0% +back and talk about on Wednesday so if + + + align:start position:0% +back and talk about on Wednesday so if +something goes by you today and you go + + align:start position:0% +something goes by you today and you go + + + align:start position:0% +something goes by you today and you go +home and say I don't think I really got + + align:start position:0% +home and say I don't think I really got + + + align:start position:0% +home and say I don't think I really got +it that's good because tomorrow you're + + align:start position:0% +it that's good because tomorrow you're + + + align:start position:0% +it that's good because tomorrow you're +going to get it again probably okay so + + align:start position:0% +going to get it again probably okay so + + + align:start position:0% +going to get it again probably okay so +we're going to be talking about all + + align:start position:0% +we're going to be talking about all + + + align:start position:0% +we're going to be talking about all +these things + + align:start position:0% +these things + + + align:start position:0% +these things +quality in mass in craft production it + + align:start position:0% +quality in mass in craft production it + + + align:start position:0% +quality in mass in craft production it +was just part of how they did things it + + align:start position:0% +was just part of how they did things it + + + align:start position:0% +was just part of how they did things it +was integrated into their whole system + + align:start position:0% +was integrated into their whole system + + + align:start position:0% +was integrated into their whole system +in mass production quality was treated + + align:start position:0% +in mass production quality was treated + + + align:start position:0% +in mass production quality was treated +as a second step we inspect and we + + align:start position:0% +as a second step we inspect and we + + + align:start position:0% +as a second step we inspect and we +correct in lean thinking it's built is + + align:start position:0% +correct in lean thinking it's built is + + + align:start position:0% +correct in lean thinking it's built is +the quality is built in at every step of + + align:start position:0% +the quality is built in at every step of + + + align:start position:0% +the quality is built in at every step of +the whole activity from engineering + + align:start position:0% +the whole activity from engineering + + + align:start position:0% +the whole activity from engineering +right through production and one of the + + align:start position:0% +right through production and one of the + + + align:start position:0% +right through production and one of the +conf things that was so hard for + + align:start position:0% +conf things that was so hard for + + + align:start position:0% +conf things that was so hard for +westerners to grasp was most westerners + + align:start position:0% +westerners to grasp was most westerners + + + align:start position:0% +westerners to grasp was most westerners +thought I'll give you a quality output + + align:start position:0% +thought I'll give you a quality output + + + align:start position:0% +thought I'll give you a quality output +but it's going to cost you more money + + align:start position:0% +but it's going to cost you more money + + + align:start position:0% +but it's going to cost you more money +and what the Japanese found was I'll + + align:start position:0% +and what the Japanese found was I'll + + + align:start position:0% +and what the Japanese found was I'll +give you a quality output and it costs + + align:start position:0% +give you a quality output and it costs + + + align:start position:0% +give you a quality output and it costs +less money okay quality and this is + + align:start position:0% +less money okay quality and this is + + + align:start position:0% +less money okay quality and this is +really important in healthcare is really + + align:start position:0% +really important in healthcare is really + + + align:start position:0% +really important in healthcare is really +important in healthare focusing on + + align:start position:0% +important in healthare focusing on + + + align:start position:0% +important in healthare focusing on +quality will drive down cost okay it + + align:start position:0% +quality will drive down cost okay it + + + align:start position:0% +quality will drive down cost okay it +always has business strategy here was + + align:start position:0% +always has business strategy here was + + + align:start position:0% +always has business strategy here was +customization here it's economies of + + align:start position:0% +customization here it's economies of + + + align:start position:0% +customization here it's economies of +scale automation here it's being + + align:start position:0% +scale automation here it's being + + + align:start position:0% +scale automation here it's being +flexible and adaptable to the changing + + align:start position:0% +flexible and adaptable to the changing + + + align:start position:0% +flexible and adaptable to the changing +customer + + align:start position:0% +customer + + + align:start position:0% +customer +demands and I think this is the really + + align:start position:0% +demands and I think this is the really + + + align:start position:0% +demands and I think this is the really +the heart of leing this last one in in + + align:start position:0% +the heart of leing this last one in in + + + align:start position:0% +the heart of leing this last one in in +the craft who who does the Improvement + + align:start position:0% +the craft who who does the Improvement + + + align:start position:0% +the craft who who does the Improvement +in the + + align:start position:0% +in the + + + align:start position:0% +in the +craft uh world it was the master driven + + align:start position:0% +craft uh world it was the master driven + + + align:start position:0% +craft uh world it was the master driven +continuous Improvement in the mass + + align:start position:0% +continuous Improvement in the mass + + + align:start position:0% +continuous Improvement in the mass +production World there was the expert + + align:start position:0% +production World there was the expert + + + align:start position:0% +production World there was the expert +driven periodic Improvement we bring in + + align:start position:0% +driven periodic Improvement we bring in + + + align:start position:0% +driven periodic Improvement we bring in +the consulting company they tell us how + + align:start position:0% +the consulting company they tell us how + + + align:start position:0% +the consulting company they tell us how +to improve here it's the worker does the + + align:start position:0% +to improve here it's the worker does the + + + align:start position:0% +to improve here it's the worker does the +Improvement in a continuous way the + + align:start position:0% +Improvement in a continuous way the + + + align:start position:0% +Improvement in a continuous way the +worker is Contin Problem Solver so this + + align:start position:0% +worker is Contin Problem Solver so this + + + align:start position:0% +worker is Contin Problem Solver so this +I spent a lot of time on that chart + + align:start position:0% +I spent a lot of time on that chart + + + align:start position:0% +I spent a lot of time on that chart +because this this really sets up the + + align:start position:0% +because this this really sets up the + + + align:start position:0% +because this this really sets up the +whole course + + align:start position:0% +whole course + + + align:start position:0% +whole course +and when we wrote a book on this we + + align:start position:0% +and when we wrote a book on this we + + + align:start position:0% +and when we wrote a book on this we +struggled with how we Define lean and + + align:start position:0% +struggled with how we Define lean and + + + align:start position:0% +struggled with how we Define lean and +here's the term we came up with lean + + align:start position:0% +here's the term we came up with lean + + + align:start position:0% +here's the term we came up with lean +thinking is the dynamic knowledge driven + + align:start position:0% +thinking is the dynamic knowledge driven + + + align:start position:0% +thinking is the dynamic knowledge driven +customer focused process through which + + align:start position:0% +customer focused process through which + + + align:start position:0% +customer focused process through which +all people in an Enterprise continuously + + align:start position:0% +all people in an Enterprise continuously + + + align:start position:0% +all people in an Enterprise continuously +eliminate waste and create value so you + + align:start position:0% +eliminate waste and create value so you + + + align:start position:0% +eliminate waste and create value so you +guys are actually little Enterprises for + + align:start position:0% +guys are actually little Enterprises for + + + align:start position:0% +guys are actually little Enterprises for +this course you guys are going to be + + align:start position:0% +this course you guys are going to be + + + align:start position:0% +this course you guys are going to be +airplane manufact facturing Enterprises + + align:start position:0% +airplane manufact facturing Enterprises + + + align:start position:0% +airplane manufact facturing Enterprises +and you guys are going to be clinics + + align:start position:0% +and you guys are going to be clinics + + + align:start position:0% +and you guys are going to be clinics +okay and tomorrow when we do our Lego + + align:start position:0% +okay and tomorrow when we do our Lego + + + align:start position:0% +okay and tomorrow when we do our Lego +simulations you're going to be applying + + align:start position:0% +simulations you're going to be applying + + + align:start position:0% +simulations you're going to be applying +these principles in your + + align:start position:0% + + + + align:start position:0% + +Enterprises okay so what about lean and + + align:start position:0% +Enterprises okay so what about lean and + + + align:start position:0% +Enterprises okay so what about lean and +Six Sigma they're they're very + + align:start position:0% +Six Sigma they're they're very + + + align:start position:0% +Six Sigma they're they're very +interrelated they came from somewhat + + align:start position:0% +interrelated they came from somewhat + + + align:start position:0% +interrelated they came from somewhat +different background Six Sigma was + + align:start position:0% +different background Six Sigma was + + + align:start position:0% +different background Six Sigma was +developed by Motorola in the 1980s when + + align:start position:0% +developed by Motorola in the 1980s when + + + align:start position:0% +developed by Motorola in the 1980s when +they decided that the big problem they + + align:start position:0% +they decided that the big problem they + + + align:start position:0% +they decided that the big problem they +had was that all their processes had too + + align:start position:0% +had was that all their processes had too + + + align:start position:0% +had was that all their processes had too +much variation so when they were built + + align:start position:0% +much variation so when they were built + + + align:start position:0% +much variation so when they were built +something they weren't sure what the + + align:start position:0% +something they weren't sure what the + + + align:start position:0% +something they weren't sure what the +output was going to be and so they + + align:start position:0% +output was going to be and so they + + + align:start position:0% +output was going to be and so they +didn't have very good what you might + + align:start position:0% +didn't have very good what you might + + + align:start position:0% +didn't have very good what you might +call yield they had a lot of scrap and + + align:start position:0% +call yield they had a lot of scrap and + + + align:start position:0% +call yield they had a lot of scrap and +not just in production but in office + + align:start position:0% +not just in production but in office + + + align:start position:0% +not just in production but in office +processes and everything so so Motorola + + align:start position:0% +processes and everything so so Motorola + + + align:start position:0% +processes and everything so so Motorola +focused on reducing the variation of + + align:start position:0% +focused on reducing the variation of + + + align:start position:0% +focused on reducing the variation of +every process so that every process + + align:start position:0% +every process so that every process + + + align:start position:0% +every process so that every process +would have a predictable output to + + align:start position:0% +would have a predictable output to + + + align:start position:0% +would have a predictable output to +deliver value to their customers it was + + align:start position:0% +deliver value to their customers it was + + + align:start position:0% +deliver value to their customers it was +very problem + + align:start position:0% +very problem + + + align:start position:0% +very problem +focused and the assumption is you got a + + align:start position:0% +focused and the assumption is you got a + + + align:start position:0% +focused and the assumption is you got a +the process isn't working so you go in + + align:start position:0% +the process isn't working so you go in + + + align:start position:0% +the process isn't working so you go in +you do a very kind of quantitative + + align:start position:0% +you do a very kind of quantitative + + + align:start position:0% +you do a very kind of quantitative +analysis and fix that process and get + + align:start position:0% +analysis and fix that process and get + + + align:start position:0% +analysis and fix that process and get +the variation down lean has the same end + + align:start position:0% +the variation down lean has the same end + + + align:start position:0% +the variation down lean has the same end +objective of delivering value to the + + align:start position:0% +objective of delivering value to the + + + align:start position:0% +objective of delivering value to the +customer but its focus is to reduce + + align:start position:0% +customer but its focus is to reduce + + + align:start position:0% +customer but its focus is to reduce +waste to get all the waste out of the + + align:start position:0% +waste to get all the waste out of the + + + align:start position:0% +waste to get all the waste out of the +system and we'll find out that most the + + align:start position:0% +system and we'll find out that most the + + + align:start position:0% +system and we'll find out that most the +thing most the inefficiency is not the + + align:start position:0% +thing most the inefficiency is not the + + + align:start position:0% +thing most the inefficiency is not the +people it's the system in which the + + align:start position:0% +people it's the system in which the + + + align:start position:0% +people it's the system in which the +people are working is wasteful and it's + + align:start position:0% +people are working is wasteful and it's + + + align:start position:0% +people are working is wasteful and it's +focused on keeping everything flowing + + align:start position:0% +focused on keeping everything flowing + + + align:start position:0% +focused on keeping everything flowing +and so the assumption is that waste + + align:start position:0% +and so the assumption is that waste + + + align:start position:0% +and so the assumption is that waste +removal will improve businesses and that + + align:start position:0% +removal will improve businesses and that + + + align:start position:0% +removal will improve businesses and that +many small improvements are better than + + align:start position:0% +many small improvements are better than + + + align:start position:0% +many small improvements are better than +a big giant step so lean is very much a + + align:start position:0% +a big giant step so lean is very much a + + + align:start position:0% +a big giant step so lean is very much a +process of starting where you are taking + + align:start position:0% +process of starting where you are taking + + + align:start position:0% +process of starting where you are taking +whatever system you have making a little + + align:start position:0% +whatever system you have making a little + + + align:start position:0% +whatever system you have making a little +bit better or a lot better and then + + align:start position:0% +bit better or a lot better and then + + + align:start position:0% +bit better or a lot better and then +making it a lot better and then making a + + align:start position:0% +making it a lot better and then making a + + + align:start position:0% +making it a lot better and then making a +lot better and just continually trying + + align:start position:0% +lot better and just continually trying + + + align:start position:0% +lot better and just continually trying +to improve it and that's why it's a + + align:start position:0% + + + + align:start position:0% + +journey now what's happened over the + + align:start position:0% +journey now what's happened over the + + + align:start position:0% +journey now what's happened over the +past 10 15 years is + + align:start position:0% +past 10 15 years is + + + align:start position:0% +past 10 15 years is +that is that well let me back up and say + + align:start position:0% +that is that well let me back up and say + + + align:start position:0% +that is that well let me back up and say +15 years ago there were people say oh + + align:start position:0% +15 years ago there were people say oh + + + align:start position:0% +15 years ago there were people say oh +I'm doing Six Sigma or I'm doing lean it + + align:start position:0% +I'm doing Six Sigma or I'm doing lean it + + + align:start position:0% +I'm doing Six Sigma or I'm doing lean it +was like there were two camps and + + align:start position:0% +was like there were two camps and + + + align:start position:0% +was like there were two camps and +luckily that eventually we got past that + + align:start position:0% +luckily that eventually we got past that + + + align:start position:0% +luckily that eventually we got past that +and and most organizations now pick some + + align:start position:0% +and and most organizations now pick some + + + align:start position:0% +and and most organizations now pick some +portions of lean some portions of Six + + align:start position:0% +portions of lean some portions of Six + + + align:start position:0% +portions of lean some portions of Six +Sigma uh and bring bring them together + + align:start position:0% +Sigma uh and bring bring them together + + + align:start position:0% +Sigma uh and bring bring them together +they we think of lean is sort of + + align:start position:0% +they we think of lean is sort of + + + align:start position:0% +they we think of lean is sort of +optimizing flow and Sig Sig Sigma is + + align:start position:0% +optimizing flow and Sig Sig Sigma is + + + align:start position:0% +optimizing flow and Sig Sig Sigma is +reducing + + align:start position:0% +reducing + + + align:start position:0% +reducing +variation and they the body of + + align:start position:0% +variation and they the body of + + + align:start position:0% +variation and they the body of +knowledges have come together into + + align:start position:0% +knowledges have come together into + + + align:start position:0% +knowledges have come together into +something is generally called lean Six + + align:start position:0% +something is generally called lean Six + + + align:start position:0% +something is generally called lean Six +Sigma there there books you can buy + + align:start position:0% +Sigma there there books you can buy + + + align:start position:0% +Sigma there there books you can buy +called lean Six Sigma and what happens + + align:start position:0% +called lean Six Sigma and what happens + + + align:start position:0% +called lean Six Sigma and what happens +is an Enterprise + + align:start position:0% +is an Enterprise + + + align:start position:0% +is an Enterprise +will look at these principles they will + + align:start position:0% +will look at these principles they will + + + align:start position:0% +will look at these principles they will +tailor their own version of it they will + + align:start position:0% +tailor their own version of it they will + + + align:start position:0% +tailor their own version of it they will +name it and brand it and it becomes + + align:start position:0% +name it and brand it and it becomes + + + align:start position:0% +name it and brand it and it becomes +their operating strategy or their + + align:start position:0% +their operating strategy or their + + + align:start position:0% +their operating strategy or their +Improvement strategy so Textron calls + + align:start position:0% +Improvement strategy so Textron calls + + + align:start position:0% +Improvement strategy so Textron calls +their Textron 6 Sigma Virginia Mason + + align:start position:0% +their Textron 6 Sigma Virginia Mason + + + align:start position:0% +their Textron 6 Sigma Virginia Mason +Medical Center calls it the Virginia + + align:start position:0% +Medical Center calls it the Virginia + + + align:start position:0% +Medical Center calls it the Virginia +Mason production system some of you are + + align:start position:0% +Mason production system some of you are + + + align:start position:0% +Mason production system some of you are +either going to work or been working at + + align:start position:0% +either going to work or been working at + + + align:start position:0% +either going to work or been working at +Boeing they call theirs lean plus + + align:start position:0% +Boeing they call theirs lean plus + + + align:start position:0% +Boeing they call theirs lean plus +now and I was talking with Susan a + + align:start position:0% +now and I was talking with Susan a + + + align:start position:0% +now and I was talking with Susan a +little earlier Dart which is a real + + align:start position:0% +little earlier Dart which is a real + + + align:start position:0% +little earlier Dart which is a real +leader in this area doesn't even call it + + align:start position:0% +leader in this area doesn't even call it + + + align:start position:0% +leader in this area doesn't even call it +lean at all okay and that doesn't matter + + align:start position:0% +lean at all okay and that doesn't matter + + + align:start position:0% +lean at all okay and that doesn't matter +it it's it's that the organization + + align:start position:0% +it it's it's that the organization + + + align:start position:0% +it it's it's that the organization +understands their process Improvement + + align:start position:0% +understands their process Improvement + + + align:start position:0% +understands their process Improvement +and identifies with it and takes + + align:start position:0% +and identifies with it and takes + + + align:start position:0% +and identifies with it and takes +ownership of it and doesn't get hung up + + align:start position:0% +ownership of it and doesn't get hung up + + + align:start position:0% +ownership of it and doesn't get hung up +on what the name is so our course is + + align:start position:0% +on what the name is so our course is + + + align:start position:0% +on what the name is so our course is +going to cover all the principles that + + align:start position:0% +going to cover all the principles that + + + align:start position:0% +going to cover all the principles that +underly all these things if you were + + align:start position:0% +underly all these things if you were + + + align:start position:0% +underly all these things if you were +going if you were in a company or a + + align:start position:0% +going if you were in a company or a + + + align:start position:0% +going if you were in a company or a +hospital and went to their training they + + align:start position:0% +hospital and went to their training they + + + align:start position:0% +hospital and went to their training they +would give you specific training on + + align:start position:0% +would give you specific training on + + + align:start position:0% +would give you specific training on +their system because you're working for + + align:start position:0% +their system because you're working for + + + align:start position:0% +their system because you're working for +them but you're all going to go + + align:start position:0% +them but you're all going to go + + + align:start position:0% +them but you're all going to go +somewhere else different places so what + + align:start position:0% +somewhere else different places so what + + + align:start position:0% +somewhere else different places so what +we give you the fundamentals that apply + + align:start position:0% +we give you the fundamentals that apply + + + align:start position:0% +we give you the fundamentals that apply +to any of those + + align:start position:0% +to any of those + + + align:start position:0% +to any of those +systems let's wind up the first part of + + align:start position:0% +systems let's wind up the first part of + + + align:start position:0% +systems let's wind up the first part of +this module with this slide that shows + + align:start position:0% +this module with this slide that shows + + + align:start position:0% +this module with this slide that shows +how important people are in implementing + + align:start position:0% +how important people are in implementing + + + align:start position:0% +how important people are in implementing +continuous Improvement I often hear that + + align:start position:0% +continuous Improvement I often hear that + + + align:start position:0% +continuous Improvement I often hear that +there are two jobs we all have one job + + align:start position:0% +there are two jobs we all have one job + + + align:start position:0% +there are two jobs we all have one job +is the work we do and the other job is + + align:start position:0% +is the work we do and the other job is + + + align:start position:0% +is the work we do and the other job is +improving how we do our work and we're + + align:start position:0% +improving how we do our work and we're + + + align:start position:0% +improving how we do our work and we're +going to emphasize the importance of + + align:start position:0% +going to emphasize the importance of + + + align:start position:0% +going to emphasize the importance of +people and implementing lean thinking + + align:start position:0% +people and implementing lean thinking + + + align:start position:0% +people and implementing lean thinking +throughout the whole course and we'll + + align:start position:0% +throughout the whole course and we'll + + + align:start position:0% +throughout the whole course and we'll +even get a hint of it in this exercise + + align:start position:0% +even get a hint of it in this exercise + + + align:start position:0% +even get a hint of it in this exercise +we're now going to do + + align:start position:0% +we're now going to do + + + align:start position:0% +we're now going to do +that's the background now let's let's + + align:start position:0% +that's the background now let's let's + + + align:start position:0% +that's the background now let's let's +get some something specific on the right + + align:start position:0% +get some something specific on the right + + + align:start position:0% +get some something specific on the right +hand side of your folder is a exercise + + align:start position:0% +hand side of your folder is a exercise + + + align:start position:0% +hand side of your folder is a exercise +that looks like this and take it out and + + align:start position:0% +that looks like this and take it out and + + + align:start position:0% +that looks like this and take it out and +don't open it up yet just put it in + + align:start position:0% +don't open it up yet just put it in + + + align:start position:0% +don't open it up yet just put it in +front of + + align:start position:0% + + + + align:start position:0% + +you okay this is called 6s now there are + + align:start position:0% +you okay this is called 6s now there are + + + align:start position:0% +you okay this is called 6s now there are +two versions of this out there there + + align:start position:0% +two versions of this out there there + + + align:start position:0% +two versions of this out there there +there multiple versions there's 5s and + + align:start position:0% +there multiple versions there's 5s and + + + align:start position:0% +there multiple versions there's 5s and +6s so + + align:start position:0% +6s so + + + align:start position:0% +6s so +5S came from the Japanese they were + + align:start position:0% +5S came from the Japanese they were + + + align:start position:0% +5S came from the Japanese they were +Japanese words which I don't remember + + align:start position:0% +Japanese words which I don't remember + + + align:start position:0% +Japanese words which I don't remember +but they've been + + align:start position:0% +but they've been + + + align:start position:0% +but they've been +translated into basically s short + + align:start position:0% +translated into basically s short + + + align:start position:0% +translated into basically s short +straighten scrub standardize and sustain + + align:start position:0% +straighten scrub standardize and sustain + + + align:start position:0% +straighten scrub standardize and sustain +and this is a way of improving your work + + align:start position:0% +and this is a way of improving your work + + + align:start position:0% +and this is a way of improving your work +environment very simple and we'll talk a + + align:start position:0% +environment very simple and we'll talk a + + + align:start position:0% +environment very simple and we'll talk a +little bit about it now what happened + + align:start position:0% +little bit about it now what happened + + + align:start position:0% +little bit about it now what happened +when this came to the Western World the + + align:start position:0% +when this came to the Western World the + + + align:start position:0% +when this came to the Western World the +Western World said ah safety that starts + + align:start position:0% +Western World said ah safety that starts + + + align:start position:0% +Western World said ah safety that starts +with an S too and safety is very + + align:start position:0% +with an S too and safety is very + + + align:start position:0% +with an S too and safety is very +important so we'll make it sucess and + + align:start position:0% +important so we'll make it sucess and + + + align:start position:0% +important so we'll make it sucess and +we'll add safety onto the + + align:start position:0% +we'll add safety onto the + + + align:start position:0% +we'll add safety onto the +list and when we put this is the only + + align:start position:0% +list and when we put this is the only + + + align:start position:0% +list and when we put this is the only +place in the course where we've actually + + align:start position:0% +place in the course where we've actually + + + align:start position:0% +place in the course where we've actually +taken something that we didn't observe + + align:start position:0% +taken something that we didn't observe + + + align:start position:0% +taken something that we didn't observe +in the field when we did this we thought + + align:start position:0% +in the field when we did this we thought + + + align:start position:0% +in the field when we did this we thought +that's kind of an afterthought just to + + align:start position:0% +that's kind of an afterthought just to + + + align:start position:0% +that's kind of an afterthought just to +put safety at the end of the list and + + align:start position:0% +put safety at the end of the list and + + + align:start position:0% +put safety at the end of the list and +safety is more important than that so + + align:start position:0% +safety is more important than that so + + + align:start position:0% +safety is more important than that so +either if you either leave it off or if + + align:start position:0% +either if you either leave it off or if + + + align:start position:0% +either if you either leave it off or if +you're going to integrate it integrate + + align:start position:0% +you're going to integrate it integrate + + + align:start position:0% +you're going to integrate it integrate +it and so we put it as the second s and + + align:start position:0% +it and so we put it as the second s and + + + align:start position:0% +it and so we put it as the second s and +we call it safe which is an action verb + + align:start position:0% +we call it safe which is an action verb + + + align:start position:0% +we call it safe which is an action verb +this is probably the only place you'll + + align:start position:0% +this is probably the only place you'll + + + align:start position:0% +this is probably the only place you'll +see this version of 6s but that's okay + + align:start position:0% +see this version of 6s but that's okay + + + align:start position:0% +see this version of 6s but that's okay +don't worry about that so what we're + + align:start position:0% +don't worry about that so what we're + + + align:start position:0% +don't worry about that so what we're +going to do is we're going to do a + + align:start position:0% +going to do is we're going to do a + + + align:start position:0% +going to do is we're going to do a +little exercise and this is your + + align:start position:0% +little exercise and this is your + + + align:start position:0% +little exercise and this is your +workplace for right now this is your + + align:start position:0% +workplace for right now this is your + + + align:start position:0% +workplace for right now this is your +work environment and we're going to try + + align:start position:0% +work environment and we're going to try + + + align:start position:0% +work environment and we're going to try +to improve it applying the basic + + align:start position:0% +to improve it applying the basic + + + align:start position:0% +to improve it applying the basic +principles of 6s and we're going to do + + align:start position:0% +principles of 6s and we're going to do + + + align:start position:0% +principles of 6s and we're going to do +it in 202 rounds you can think of each + + align:start position:0% +it in 202 rounds you can think of each + + + align:start position:0% +it in 202 rounds you can think of each +22nd round as maybe a work shift or + + align:start position:0% +22nd round as maybe a work shift or + + + align:start position:0% +22nd round as maybe a work shift or +something like that and you have a bunch + + align:start position:0% +something like that and you have a bunch + + + align:start position:0% +something like that and you have a bunch +of supplies and this is in the medical + + align:start position:0% +of supplies and this is in the medical + + + align:start position:0% +of supplies and this is in the medical +context but we could do it otherwise you + + align:start position:0% +context but we could do it otherwise you + + + align:start position:0% +context but we could do it otherwise you +have some instruments some bandages and + + align:start position:0% +have some instruments some bandages and + + + align:start position:0% +have some instruments some bandages and +some medications and you're going to + + align:start position:0% +some medications and you're going to + + + align:start position:0% +some medications and you're going to +each of your work uh shifts you're going + + align:start position:0% +each of your work uh shifts you're going + + + align:start position:0% +each of your work uh shifts you're going +to be asked + + align:start position:0% +to be asked + + + align:start position:0% +to be asked +to fetch some of these supplies from + + align:start position:0% +to fetch some of these supplies from + + + align:start position:0% +to fetch some of these supplies from +your store + + align:start position:0% +your store + + + align:start position:0% +your store +room and don't turn it over yet but the + + align:start position:0% +room and don't turn it over yet but the + + + align:start position:0% +room and don't turn it over yet but the +first page represents your current work + + align:start position:0% +first page represents your current work + + + align:start position:0% +first page represents your current work +environment and then each + + align:start position:0% +environment and then each + + + align:start position:0% +environment and then each +next slide will show you what you have + + align:start position:0% +next slide will show you what you have + + + align:start position:0% +next slide will show you what you have +to fetch in your first workshift and + + align:start position:0% +to fetch in your first workshift and + + + align:start position:0% +to fetch in your first workshift and +when you fetch it so what you're going + + align:start position:0% +when you fetch it so what you're going + + + align:start position:0% +when you fetch it so what you're going +to do is just put an X through whatever + + align:start position:0% +to do is just put an X through whatever + + + align:start position:0% +to do is just put an X through whatever +you fetch or if you want to Circle it + + align:start position:0% +you fetch or if you want to Circle it + + + align:start position:0% +you fetch or if you want to Circle it +you could do that too I don't care okay + + align:start position:0% +you could do that too I don't care okay + + + align:start position:0% +you could do that too I don't care okay +so here's what we're going to need to + + align:start position:0% +so here's what we're going to need to + + + align:start position:0% +so here's what we're going to need to +get on the first + + align:start position:0% +get on the first + + + align:start position:0% +get on the first +round you're going to have to find five + + align:start position:0% +round you're going to have to find five + + + align:start position:0% +round you're going to have to find five +syringes five of these Band-Aids five + + align:start position:0% +syringes five of these Band-Aids five + + + align:start position:0% +syringes five of these Band-Aids five +scissors and five of the medication twos + + align:start position:0% +scissors and five of the medication twos + + + align:start position:0% +scissors and five of the medication twos +so when don't do it yet when I say go + + align:start position:0% +so when don't do it yet when I say go + + + align:start position:0% +so when don't do it yet when I say go +you're going to flip the page cross off + + align:start position:0% +you're going to flip the page cross off + + + align:start position:0% +you're going to flip the page cross off +five of each these until I say stop and + + align:start position:0% +five of each these until I say stop and + + + align:start position:0% +five of each these until I say stop and +that's the end of the + + align:start position:0% +that's the end of the + + + align:start position:0% +that's the end of the +shift okay any questions on the + + align:start position:0% +shift okay any questions on the + + + align:start position:0% +shift okay any questions on the +mechanics of + + align:start position:0% +mechanics of + + + align:start position:0% +mechanics of +it okay so we'll do Ready set + + align:start position:0% + + + + align:start position:0% + +go + + align:start position:0% + + + + align:start position:0% + +stop shift is over time to go home okay + + align:start position:0% +stop shift is over time to go home okay + + + align:start position:0% +stop shift is over time to go home okay +okay so now count up the number of of + + align:start position:0% +okay so now count up the number of of + + + align:start position:0% +okay so now count up the number of of +items toal number of items you got I + + align:start position:0% +items toal number of items you got I + + + align:start position:0% +items toal number of items you got I +don't need to know items by category + + align:start position:0% +don't need to know items by category + + + align:start position:0% +don't need to know items by category +just the total number of items okay + + align:start position:0% +just the total number of items okay + + + align:start position:0% +just the total number of items okay +super okay how many are kind of around 8 + + align:start position:0% +super okay how many are kind of around 8 + + + align:start position:0% +super okay how many are kind of around 8 +n + + align:start position:0% +n + + + align:start position:0% +n +10 okay probably 10 is roughly about the + + align:start position:0% +10 okay probably 10 is roughly about the + + + align:start position:0% +10 okay probably 10 is roughly about the +middle we don't have to be too careful + + align:start position:0% +middle we don't have to be too careful + + + align:start position:0% +middle we don't have to be too careful +but so's so this is kind of + + align:start position:0% +but so's so this is kind of + + + align:start position:0% +but so's so this is kind of +our our workplace well what do we see + + align:start position:0% +our our workplace well what do we see + + + align:start position:0% +our our workplace well what do we see +okay we didn't get the job done and + + align:start position:0% +okay we didn't get the job done and + + + align:start position:0% +okay we didn't get the job done and +there's High + + align:start position:0% +there's High + + + align:start position:0% +there's High +variability okay we got uh we have about + + align:start position:0% +variability okay we got uh we have about + + + align:start position:0% +variability okay we got uh we have about +uh see six we have about 25 28 workers + + align:start position:0% +uh see six we have about 25 28 workers + + + align:start position:0% +uh see six we have about 25 28 workers +here in our plant and we get quite a + + align:start position:0% +here in our plant and we get quite a + + + align:start position:0% +here in our plant and we get quite a +variable outcome this is the kind of + + align:start position:0% +variable outcome this is the kind of + + + align:start position:0% +variable outcome this is the kind of +thing Six Sigma was worried about high + + align:start position:0% +thing Six Sigma was worried about high + + + align:start position:0% +thing Six Sigma was worried about high +variability okay so that's that's where + + align:start position:0% +variability okay so that's that's where + + + align:start position:0% +variability okay so that's that's where +we're + + align:start position:0% +we're + + + align:start position:0% +we're +starting now our first first S is to + + align:start position:0% +starting now our first first S is to + + + align:start position:0% +starting now our first first S is to +sort and you probably saw in your + + align:start position:0% +sort and you probably saw in your + + + align:start position:0% +sort and you probably saw in your +workplace there's a lot of stuff there + + align:start position:0% +workplace there's a lot of stuff there + + + align:start position:0% +workplace there's a lot of stuff there +that you don't have to go collect + + align:start position:0% +that you don't have to go collect + + + align:start position:0% +that you don't have to go collect +there's some old equipment that's in + + align:start position:0% +there's some old equipment that's in + + + align:start position:0% +there's some old equipment that's in +your store room there may be some un you + + align:start position:0% +your store room there may be some un you + + + align:start position:0% +your store room there may be some un you +know medications that have been there + + align:start position:0% +know medications that have been there + + + align:start position:0% +know medications that have been there +you know when this first started a lot + + align:start position:0% +you know when this first started a lot + + + align:start position:0% +you know when this first started a lot +of these companies go into this store + + align:start position:0% +of these companies go into this store + + + align:start position:0% +of these companies go into this store +room and they find out that somebody in + + align:start position:0% +room and they find out that somebody in + + + align:start position:0% +room and they find out that somebody in +purchasing got a good deal sometime on + + align:start position:0% +purchasing got a good deal sometime on + + + align:start position:0% +purchasing got a good deal sometime on +some piece of some some equipment or + + align:start position:0% +some piece of some some equipment or + + + align:start position:0% +some piece of some some equipment or +Supply they got a volume discount they + + align:start position:0% +Supply they got a volume discount they + + + align:start position:0% +Supply they got a volume discount they +bought 10 years worth of it and a year + + align:start position:0% +bought 10 years worth of it and a year + + + align:start position:0% +bought 10 years worth of it and a year +later they stopped using that stuff and + + align:start position:0% +later they stopped using that stuff and + + + align:start position:0% +later they stopped using that stuff and +then other nine years are still in the + + align:start position:0% +then other nine years are still in the + + + align:start position:0% +then other nine years are still in the +store room okay that's waste okay so + + align:start position:0% +store room okay that's waste okay so + + + align:start position:0% +store room okay that's waste okay so +what we're going to do is we're just + + align:start position:0% +what we're going to do is we're just + + + align:start position:0% +what we're going to do is we're just +going to go through and clean up get get + + align:start position:0% +going to go through and clean up get get + + + align:start position:0% +going to go through and clean up get get +everything out of the workplace that + + align:start position:0% +everything out of the workplace that + + + align:start position:0% +everything out of the workplace that +we're not looking for and then we're + + align:start position:0% +we're not looking for and then we're + + + align:start position:0% +we're not looking for and then we're +going to redo this so it's the same + + align:start position:0% +going to redo this so it's the same + + + align:start position:0% +going to redo this so it's the same +thing but now we've gotten rid of all + + align:start position:0% +thing but now we've gotten rid of all + + + align:start position:0% +thing but now we've gotten rid of all +the Clutter but we're going to get just + + align:start position:0% +the Clutter but we're going to get just + + + align:start position:0% +the Clutter but we're going to get just +so we take the learning out we're going + + align:start position:0% +so we take the learning out we're going + + + align:start position:0% +so we take the learning out we're going +to get now five tape rolls five + + align:start position:0% +to get now five tape rolls five + + + align:start position:0% +to get now five tape rolls five +Band-Aids five tweezers and five + + align:start position:0% +Band-Aids five tweezers and five + + + align:start position:0% +Band-Aids five tweezers and five +medication + + align:start position:0% +medication + + + align:start position:0% +medication +threes okay ready set + + align:start position:0% + + + + align:start position:0% + +go + + align:start position:0% +go + + + align:start position:0% +go +stop okay now we count them up again and + + align:start position:0% +stop okay now we count them up again and + + + align:start position:0% +stop okay now we count them up again and +then we'll see where + + align:start position:0% +then we'll see where + + + align:start position:0% +then we'll see where +we're yeah okay anybody get all + + align:start position:0% +we're yeah okay anybody get all + + + align:start position:0% +we're yeah okay anybody get all +20 19 + + align:start position:0% +20 19 + + + align:start position:0% +20 19 + + align:start position:0% + + + + align:start position:0% + +okay okay uh how many how many are + + align:start position:0% +okay okay uh how many how many are + + + align:start position:0% +okay okay uh how many how many are +around 15 + + align:start position:0% +around 15 + + + align:start position:0% +around 15 +15 okay that's that's good enough + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +25 so you made a You made a we're we're + + align:start position:0% +25 so you made a You made a we're we're + + + align:start position:0% +25 so you made a You made a we're we're +going to talk a lot + + align:start position:0% + + + + align:start position:0% + +so I + + align:start position:0% +so I + + + align:start position:0% +so I +uh just a heads up one of the things + + align:start position:0% +uh just a heads up one of the things + + + align:start position:0% +uh just a heads up one of the things +about lean is you're trying to meet your + + align:start position:0% +about lean is you're trying to meet your + + + align:start position:0% +about lean is you're trying to meet your +customer's demand and you exceeded + + align:start position:0% +customer's demand and you exceeded + + + align:start position:0% +customer's demand and you exceeded +customer demand okay sometime the + + align:start position:0% +customer demand okay sometime the + + + align:start position:0% +customer demand okay sometime the +customer won't pay you for it but this + + align:start position:0% +customer won't pay you for it but this + + + align:start position:0% +customer won't pay you for it but this +time is probably okay how many got look + + align:start position:0% +time is probably okay how many got look + + + align:start position:0% +time is probably okay how many got look +at your medications did everybody did + + align:start position:0% +at your medications did everybody did + + + align:start position:0% +at your medications did everybody did +anybody get a medication one or a + + align:start position:0% +anybody get a medication one or a + + + align:start position:0% +anybody get a medication one or a +medication + + align:start position:0% + + + + align:start position:0% + +two ah + + align:start position:0% + + + + align:start position:0% + +okay okay okay so now we're going to + + align:start position:0% +okay okay okay so now we're going to + + + align:start position:0% +okay okay okay so now we're going to +save getting the wrong medications is a + + align:start position:0% +save getting the wrong medications is a + + + align:start position:0% +save getting the wrong medications is a +big problem so that's an example why we + + align:start position:0% +big problem so that's an example why we + + + align:start position:0% +big problem so that's an example why we +set it up for that's why we put safe + + align:start position:0% +set it up for that's why we put safe + + + align:start position:0% +set it up for that's why we put safe +here so safe is just making the + + align:start position:0% +here so safe is just making the + + + align:start position:0% +here so safe is just making the +workplace safe G you know if your + + align:start position:0% +workplace safe G you know if your + + + align:start position:0% +workplace safe G you know if your +workers get injured or if the customers + + align:start position:0% +workers get injured or if the customers + + + align:start position:0% +workers get injured or if the customers +get injured or suppliers get injured + + align:start position:0% +get injured or suppliers get injured + + + align:start position:0% +get injured or suppliers get injured +that's pure waste that's lost + + align:start position:0% +that's pure waste that's lost + + + align:start position:0% +that's pure waste that's lost +time that they can't contribute to your + + align:start position:0% +time that they can't contribute to your + + + align:start position:0% +time that they can't contribute to your +Enterprise so safety is + + align:start position:0% +Enterprise so safety is + + + align:start position:0% +Enterprise so safety is +not good safety is important for many + + align:start position:0% +not good safety is important for many + + + align:start position:0% +not good safety is important for many +reasons but it's it's it's very much a + + align:start position:0% +reasons but it's it's it's very much a + + + align:start position:0% +reasons but it's it's it's very much a +lean principle you don't want anything + + align:start position:0% +lean principle you don't want anything + + + align:start position:0% +lean principle you don't want anything +that well I've already said accidents or + + align:start position:0% +that well I've already said accidents or + + + align:start position:0% +that well I've already said accidents or +waste so we we've we've gone in and + + align:start position:0% +waste so we we've we've gone in and + + + align:start position:0% +waste so we we've we've gone in and +we've made our workplace a little safe + + align:start position:0% +we've made our workplace a little safe + + + align:start position:0% +we've made our workplace a little safe +now we've um we've put sheet on our + + align:start position:0% +now we've um we've put sheet on our + + + align:start position:0% +now we've um we've put sheet on our +syringes we've made the medications + + align:start position:0% +syringes we've made the medications + + + align:start position:0% +syringes we've made the medications +different shapes we've closed the + + align:start position:0% +different shapes we've closed the + + + align:start position:0% +different shapes we've closed the +scissors and so we're going to do the + + align:start position:0% +scissors and so we're going to do the + + + align:start position:0% +scissors and so we're going to do the +same thing get 20 um items and Ready Set + + align:start position:0% +same thing get 20 um items and Ready Set + + + align:start position:0% +same thing get 20 um items and Ready Set +Go + + align:start position:0% + + + + align:start position:0% + +stop I think everybody's got the + + align:start position:0% +stop I think everybody's got the + + + align:start position:0% +stop I think everybody's got the +mechanics down + + align:start position:0% +mechanics down + + + align:start position:0% +mechanics down +so okay anybody at 10 or less than 10 + + align:start position:0% +so okay anybody at 10 or less than 10 + + + align:start position:0% +so okay anybody at 10 or less than 10 + + align:start position:0% + + + align:start position:0% +11 11 11 11 12 okay had a little bit of + + align:start position:0% +11 11 11 11 12 okay had a little bit of + + + align:start position:0% +11 11 11 11 12 okay had a little bit of +improvement + + align:start position:0% +improvement + + + align:start position:0% +improvement +here anybody get all + + align:start position:0% +here anybody get all + + + align:start position:0% +here anybody get all + + align:start position:0% + + + align:start position:0% + + align:start position:0% + + + align:start position:0% +19 19 + + align:start position:0% +19 19 + + + align:start position:0% +19 19 +okay okay how about 16 + + align:start position:0% +okay okay how about 16 + + + align:start position:0% +okay okay how about 16 + + align:start position:0% + + + align:start position:0% + + align:start position:0% + + + align:start position:0% + + align:start position:0% + + + align:start position:0% +14 okay it's kind of hard to see I think + + align:start position:0% +14 okay it's kind of hard to see I think + + + align:start position:0% +14 okay it's kind of hard to see I think +we're still we're maybe a little bit + + align:start position:0% +we're still we're maybe a little bit + + + align:start position:0% +we're still we're maybe a little bit +better than before + + align:start position:0% +better than before + + + align:start position:0% +better than before +but about the same so we we we've closed + + align:start position:0% +but about the same so we we we've closed + + + align:start position:0% +but about the same so we we we've closed +down the variation a little bit we + + align:start position:0% +down the variation a little bit we + + + align:start position:0% +down the variation a little bit we +didn't expect to get too much improv + + align:start position:0% +didn't expect to get too much improv + + + align:start position:0% +didn't expect to get too much improv +Improvement in productivity because all + + align:start position:0% +Improvement in productivity because all + + + align:start position:0% +Improvement in productivity because all +we did was we made the environment safe + + align:start position:0% +we did was we made the environment safe + + + align:start position:0% +we did was we made the environment safe +we didn't really do any + + align:start position:0% +we didn't really do any + + + align:start position:0% +we didn't really do any +reorganization okay now we're going to + + align:start position:0% +reorganization okay now we're going to + + + align:start position:0% +reorganization okay now we're going to +uh straighten now that we've gotten all + + align:start position:0% +uh straighten now that we've gotten all + + + align:start position:0% +uh straighten now that we've gotten all +the Clutter out we've made things safe + + align:start position:0% +the Clutter out we've made things safe + + + align:start position:0% +the Clutter out we've made things safe +now let's get our workplace a little bit + + align:start position:0% +now let's get our workplace a little bit + + + align:start position:0% +now let's get our workplace a little bit +better organized so it's not so hter + + align:start position:0% +better organized so it's not so hter + + + align:start position:0% +better organized so it's not so hter +Skelter so we're going to straighten + + align:start position:0% +Skelter so we're going to straighten + + + align:start position:0% +Skelter so we're going to straighten +things so we've installed some racks in + + align:start position:0% +things so we've installed some racks in + + + align:start position:0% +things so we've installed some racks in +our store room because uh management + + align:start position:0% +our store room because uh management + + + align:start position:0% +our store room because uh management +seen this great increase in + + align:start position:0% +seen this great increase in + + + align:start position:0% +seen this great increase in +productivity they're going to ask for + + align:start position:0% +productivity they're going to ask for + + + align:start position:0% +productivity they're going to ask for +more now in the shift they want + + align:start position:0% +more now in the shift they want + + + align:start position:0% +more now in the shift they want +25 want 25 things found okay so you can + + align:start position:0% +25 want 25 things found okay so you can + + + align:start position:0% +25 want 25 things found okay so you can +see the list up there okay Ready set + + align:start position:0% + + + + align:start position:0% + +go + + align:start position:0% +go + + + align:start position:0% +go +stop okay anybody 15 or + + align:start position:0% +stop okay anybody 15 or + + + align:start position:0% +stop okay anybody 15 or +less how many 14 14 okay 14 + + align:start position:0% +less how many 14 14 okay 14 + + + align:start position:0% +less how many 14 14 okay 14 +okay yeah you got 15 but she got 14 what + + align:start position:0% +okay yeah you got 15 but she got 14 what + + + align:start position:0% +okay yeah you got 15 but she got 14 what +you 15 okay anybody get + + align:start position:0% +you 15 okay anybody get + + + align:start position:0% +you 15 okay anybody get +25 24 23 23 okay + + align:start position:0% +25 24 23 23 okay + + + align:start position:0% +25 24 23 23 okay +and how many + + align:start position:0% +and how many + + + align:start position:0% +and how many +are8 19 20 + + align:start position:0% +are8 19 20 + + + align:start position:0% +are8 19 20 +21 okay it looks like we're about in the + + align:start position:0% +21 okay it looks like we're about in the + + + align:start position:0% +21 okay it looks like we're about in the +middle + + align:start position:0% +middle + + + align:start position:0% +middle +here okay well we see the increase in + + align:start position:0% +here okay well we see the increase in + + + align:start position:0% +here okay well we see the increase in +productivity there okay now the next the + + align:start position:0% +productivity there okay now the next the + + + align:start position:0% +productivity there okay now the next the +next ass is to is basically clean things + + align:start position:0% +next ass is to is basically clean things + + + align:start position:0% +next ass is to is basically clean things +up to scrub by the way in these charts + + align:start position:0% +up to scrub by the way in these charts + + + align:start position:0% +up to scrub by the way in these charts +there there are multiple translations of + + align:start position:0% +there there are multiple translations of + + + align:start position:0% +there there are multiple translations of +the uh Japanese word and we've given + + align:start position:0% +the uh Japanese word and we've given + + + align:start position:0% +the uh Japanese word and we've given +them all here so for scrub it's scrub + + align:start position:0% +them all here so for scrub it's scrub + + + align:start position:0% +them all here so for scrub it's scrub +shine or sweep you might find in a + + align:start position:0% +shine or sweep you might find in a + + + align:start position:0% +shine or sweep you might find in a +particular five or 6s incarnation and + + align:start position:0% +particular five or 6s incarnation and + + + align:start position:0% +particular five or 6s incarnation and +that's pretty important in a of course + + align:start position:0% +that's pretty important in a of course + + + align:start position:0% +that's pretty important in a of course +in a healthcare environment it's + + align:start position:0% +in a healthcare environment it's + + + align:start position:0% +in a healthcare environment it's +critical for for all sorts of reasons + + align:start position:0% +critical for for all sorts of reasons + + + align:start position:0% +critical for for all sorts of reasons +but in a Aerospace environment or a + + align:start position:0% +but in a Aerospace environment or a + + + align:start position:0% +but in a Aerospace environment or a +production environment you can walk a + + align:start position:0% +production environment you can walk a + + + align:start position:0% +production environment you can walk a +lean Factory you can walk into you can + + align:start position:0% +lean Factory you can walk into you can + + + align:start position:0% +lean Factory you can walk into you can +eat off the floor I mean we'll see we're + + align:start position:0% +eat off the floor I mean we'll see we're + + + align:start position:0% +eat off the floor I mean we'll see we're +going to have a a a balanc video of new + + align:start position:0% +going to have a a a balanc video of new + + + align:start position:0% +going to have a a a balanc video of new +Balan shoe and you'll see when we get + + align:start position:0% +Balan shoe and you'll see when we get + + + align:start position:0% +Balan shoe and you'll see when we get +into that factory how clean it is well + + align:start position:0% +into that factory how clean it is well + + + align:start position:0% +into that factory how clean it is well +lit everything's clean uh it's just it's + + align:start position:0% +lit everything's clean uh it's just it's + + + align:start position:0% +lit everything's clean uh it's just it's +just a a way of thinking so keeping your + + align:start position:0% +just a a way of thinking so keeping your + + + align:start position:0% +just a a way of thinking so keeping your +workplace tidy and neat is just part of + + align:start position:0% +workplace tidy and neat is just part of + + + align:start position:0% +workplace tidy and neat is just part of +it we can't find a good way to do that + + align:start position:0% +it we can't find a good way to do that + + + align:start position:0% +it we can't find a good way to do that +exercise here so we're going to skip + + align:start position:0% +exercise here so we're going to skip + + + align:start position:0% +exercise here so we're going to skip +this s and move on to + + align:start position:0% +this s and move on to + + + align:start position:0% +this s and move on to +standardize so now we want to make it + + align:start position:0% +standardize so now we want to make it + + + align:start position:0% +standardize so now we want to make it +now we got everything straightened up + + align:start position:0% +now we got everything straightened up + + + align:start position:0% +now we got everything straightened up +now we make make it really easy to find + + align:start position:0% +now we make make it really easy to find + + + align:start position:0% +now we make make it really easy to find +things so we got three clinics here okay + + align:start position:0% +things so we got three clinics here okay + + + align:start position:0% +things so we got three clinics here okay +be nice if each Clinic had its own way + + align:start position:0% +be nice if each Clinic had its own way + + + align:start position:0% +be nice if each Clinic had its own way +of storing things okay and we're going + + align:start position:0% +of storing things okay and we're going + + + align:start position:0% +of storing things okay and we're going +to talk about that tomorrow in our + + align:start position:0% +to talk about that tomorrow in our + + + align:start position:0% +to talk about that tomorrow in our +simulation or we got two production + + align:start position:0% +simulation or we got two production + + + align:start position:0% +simulation or we got two production +facilities here it' be nice that in the + + align:start position:0% +facilities here it' be nice that in the + + + align:start position:0% +facilities here it' be nice that in the +two production facilities maybe of the + + align:start position:0% +two production facilities maybe of the + + + align:start position:0% +two production facilities maybe of the +same company you have the same same way + + align:start position:0% +same company you have the same same way + + + align:start position:0% +same company you have the same same way +of storing things so you can go from one + + align:start position:0% +of storing things so you can go from one + + + align:start position:0% +of storing things so you can go from one +to the other and not have to be trained + + align:start position:0% +to the other and not have to be trained + + + align:start position:0% +to the other and not have to be trained +so we're now going to we've done a good + + align:start position:0% +so we're now going to we've done a good + + + align:start position:0% +so we're now going to we've done a good +job of that we standardized this is an + + align:start position:0% +job of that we standardized this is an + + + align:start position:0% +job of that we standardized this is an +example it's hard to see but these are a + + align:start position:0% +example it's hard to see but these are a + + + align:start position:0% +example it's hard to see but these are a +bunch of binders and they just put + + align:start position:0% +bunch of binders and they just put + + + align:start position:0% +bunch of binders and they just put +little tags on them so you can + + align:start position:0% +little tags on them so you can + + + align:start position:0% +little tags on them so you can +immediately see which binder is missing + + align:start position:0% +immediately see which binder is missing + + + align:start position:0% +immediately see which binder is missing +because it's out of + + align:start position:0% +because it's out of + + + align:start position:0% +because it's out of +sequence okay well now we're up to 30 + + align:start position:0% +sequence okay well now we're up to 30 + + + align:start position:0% +sequence okay well now we're up to 30 +okay we want to get 30 items on this + + align:start position:0% +okay we want to get 30 items on this + + + align:start position:0% +okay we want to get 30 items on this +round it's the last shift of the week + + align:start position:0% +round it's the last shift of the week + + + align:start position:0% +round it's the last shift of the week +you're going to have the weekend off + + align:start position:0% +you're going to have the weekend off + + + align:start position:0% +you're going to have the weekend off +after + + align:start position:0% +after + + + align:start position:0% +after +this Ready Set Go + + align:start position:0% + + + + align:start position:0% + +stop okay anybody get + + align:start position:0% +stop okay anybody get + + + align:start position:0% +stop okay anybody get +30 look at that + + align:start position:0% +30 look at that + + + align:start position:0% +30 look at that +wow anybody get 25 or less how many + + align:start position:0% +wow anybody get 25 or less how many + + + align:start position:0% +wow anybody get 25 or less how many +25 okay and how many got 30 let's see + + align:start position:0% +25 okay and how many got 30 let's see + + + align:start position:0% +25 okay and how many got 30 let's see +your hands again + + align:start position:0% +your hands again + + + align:start position:0% +your hands again +29 I mean we're it's like this okay + + align:start position:0% +29 I mean we're it's like this okay + + + align:start position:0% +29 I mean we're it's like this okay +okay well let's look at this chart so + + align:start position:0% +okay well let's look at this chart so + + + align:start position:0% +okay well let's look at this chart so +we've gone from A system that has high + + align:start position:0% +we've gone from A system that has high + + + align:start position:0% +we've gone from A system that has high +variability and low productivity to A + + align:start position:0% +variability and low productivity to A + + + align:start position:0% +variability and low productivity to A +system that has high productivity and + + align:start position:0% +system that has high productivity and + + + align:start position:0% +system that has high productivity and +low + + align:start position:0% + + + + align:start position:0% + +variability how many of you would how + + align:start position:0% +variability how many of you would how + + + align:start position:0% +variability how many of you would how +many how many of you found this + + align:start position:0% +many how many of you found this + + + align:start position:0% +many how many of you found this +environment where you produce so much so + + align:start position:0% +environment where you produce so much so + + + align:start position:0% +environment where you produce so much so +much more to be more stressful to work + + align:start position:0% +much more to be more stressful to work + + + align:start position:0% +much more to be more stressful to work +in than this + + align:start position:0% +in than this + + + align:start position:0% +in than this +environment nobody right okay that's + + align:start position:0% +environment nobody right okay that's + + + align:start position:0% +environment nobody right okay that's +what lean's about okay lean is about + + align:start position:0% +what lean's about okay lean is about + + + align:start position:0% +what lean's about okay lean is about +doing Simple Things to improve your + + align:start position:0% +doing Simple Things to improve your + + + align:start position:0% +doing Simple Things to improve your +workplace that when I toured the corsky + + align:start position:0% +workplace that when I toured the corsky + + + align:start position:0% +workplace that when I toured the corsky +plant where they make the Blackhawk + + align:start position:0% +plant where they make the Blackhawk + + + align:start position:0% +plant where they make the Blackhawk +helicopter the plant manager said Earl + + align:start position:0% +helicopter the plant manager said Earl + + + align:start position:0% +helicopter the plant manager said Earl +lean is the focused application of + + align:start position:0% +lean is the focused application of + + + align:start position:0% +lean is the focused application of +Common Sense okay this is not + + align:start position:0% +Common Sense okay this is not + + + align:start position:0% +Common Sense okay this is not +complicated stuff okay uh and lean is + + align:start position:0% +complicated stuff okay uh and lean is + + + align:start position:0% +complicated stuff okay uh and lean is +not about making the worker work harder + + align:start position:0% +not about making the worker work harder + + + align:start position:0% +not about making the worker work harder +lean is about making putting the worker + + align:start position:0% +lean is about making putting the worker + + + align:start position:0% +lean is about making putting the worker +in a an environment where they can be + + align:start position:0% +in a an environment where they can be + + + align:start position:0% +in a an environment where they can be +more productive and happier okay so this + + align:start position:0% +more productive and happier okay so this + + + align:start position:0% +more productive and happier okay so this +is what lean's about most + + align:start position:0% +is what lean's about most + + + align:start position:0% +is what lean's about most +organizations start with 5S as their + + align:start position:0% +organizations start with 5S as their + + + align:start position:0% +organizations start with 5S as their +first first thing let me just share just + + align:start position:0% +first first thing let me just share just + + + align:start position:0% +first first thing let me just share just +to underline share you an example I live + + align:start position:0% +to underline share you an example I live + + + align:start position:0% +to underline share you an example I live +in a small town of 9,000 people the + + align:start position:0% +in a small town of 9,000 people the + + + align:start position:0% +in a small town of 9,000 people the +whole County only has 30,000 people it's + + align:start position:0% +whole County only has 30,000 people it's + + + align:start position:0% +whole County only has 30,000 people it's +a rural community our Hospital started + + align:start position:0% +a rural community our Hospital started + + + align:start position:0% +a rural community our Hospital started +adopting lean the very first thing they + + align:start position:0% +adopting lean the very first thing they + + + align:start position:0% +adopting lean the very first thing they +did was they went into the hospital + + align:start position:0% +did was they went into the hospital + + + align:start position:0% +did was they went into the hospital +laundry in plied 5S the laundry was so + + align:start position:0% +laundry in plied 5S the laundry was so + + + align:start position:0% +laundry in plied 5S the laundry was so +dysfunctional they had high turnover + + align:start position:0% +dysfunctional they had high turnover + + + align:start position:0% +dysfunctional they had high turnover +employees the Linens and gowns were not + + align:start position:0% +employees the Linens and gowns were not + + + align:start position:0% +employees the Linens and gowns were not +on the floors when they needed to be the + + align:start position:0% +on the floors when they needed to be the + + + align:start position:0% +on the floors when they needed to be the +laundry bin they did didn't get to the + + align:start position:0% +laundry bin they did didn't get to the + + + align:start position:0% +laundry bin they did didn't get to the +bottom of it each day dirty laundry so + + align:start position:0% +bottom of it each day dirty laundry so + + + align:start position:0% +bottom of it each day dirty laundry so +the next day more laundry was on top so + + align:start position:0% +the next day more laundry was on top so + + + align:start position:0% +the next day more laundry was on top so +on in one + + align:start position:0% +on in one + + + align:start position:0% +on in one +week the women in the laundry who + + align:start position:0% +week the women in the laundry who + + + align:start position:0% +week the women in the laundry who +operate the laundry took 5s with a + + align:start position:0% +operate the laundry took 5s with a + + + align:start position:0% +operate the laundry took 5s with a +facilitator and a coach they reorganized + + align:start position:0% +facilitator and a coach they reorganized + + + align:start position:0% +facilitator and a coach they reorganized +their laundry and it went from that to + + align:start position:0% +their laundry and it went from that to + + + align:start position:0% +their laundry and it went from that to +now they get all the in all the laundry + + align:start position:0% +now they get all the in all the laundry + + + align:start position:0% +now they get all the in all the laundry +done every day I've been in this laundry + + align:start position:0% +done every day I've been in this laundry + + + align:start position:0% +done every day I've been in this laundry +the women are so happy they just can't + + align:start position:0% +the women are so happy they just can't + + + align:start position:0% +the women are so happy they just can't +they just want to tell you about their + + align:start position:0% +they just want to tell you about their + + + align:start position:0% +they just want to tell you about their +workplace they've have no turnover since + + align:start position:0% +workplace they've have no turnover since + + + align:start position:0% +workplace they've have no turnover since +they did this and everybody in the + + align:start position:0% +they did this and everybody in the + + + align:start position:0% +they did this and everybody in the +hospital is affected by the laundry and + + align:start position:0% +hospital is affected by the laundry and + + + align:start position:0% +hospital is affected by the laundry and +they all knew it was a success so if you + + align:start position:0% +they all knew it was a success so if you + + + align:start position:0% +they all knew it was a success so if you +want to start in a hospital start in the + + align:start position:0% +want to start in a hospital start in the + + + align:start position:0% +want to start in a hospital start in the +laundry okay with 5S okay the last S is + + align:start position:0% +laundry okay with 5S okay the last S is + + + align:start position:0% +laundry okay with 5S okay the last S is +to sustain often the hardest part um I + + align:start position:0% +to sustain often the hardest part um I + + + align:start position:0% +to sustain often the hardest part um I +like the Virginia Mason version of it + + align:start position:0% +like the Virginia Mason version of it + + + align:start position:0% +like the Virginia Mason version of it +self-discipline uh sustainment should be + + align:start position:0% +self-discipline uh sustainment should be + + + align:start position:0% +self-discipline uh sustainment should be +the the Trap is you do this one week + + align:start position:0% +the the Trap is you do this one week + + + align:start position:0% +the the Trap is you do this one week +event like I mentioned in the laundry + + align:start position:0% +event like I mentioned in the laundry + + + align:start position:0% +event like I mentioned in the laundry +and then you know you drift back into + + align:start position:0% +and then you know you drift back into + + + align:start position:0% +and then you know you drift back into +Old Habits so the hard part is is + + align:start position:0% +Old Habits so the hard part is is + + + align:start position:0% +Old Habits so the hard part is is +keeping this as a + + align:start position:0% +keeping this as a + + + align:start position:0% +keeping this as a +mindset sometimes you have to have a + + align:start position:0% +mindset sometimes you have to have a + + + align:start position:0% +mindset sometimes you have to have a +chart but usually you should just be + + align:start position:0% +chart but usually you should just be + + + align:start position:0% +chart but usually you should just be +able to do it okay so that's your first + + align:start position:0% +able to do it okay so that's your first + + + align:start position:0% +able to do it okay so that's your first +lean experience uh let's now talk about + + align:start position:0% +lean experience uh let's now talk about + + + align:start position:0% +lean experience uh let's now talk about +why lean is being applied in these in + + align:start position:0% +why lean is being applied in these in + + + align:start position:0% +why lean is being applied in these in +these areas okay we're going to look at + + align:start position:0% +these areas okay we're going to look at + + + align:start position:0% +these areas okay we're going to look at +Aerospace Healthcare and we're going to + + align:start position:0% +Aerospace Healthcare and we're going to + + + align:start position:0% +Aerospace Healthcare and we're going to +look also at New Balance shoes just for + + align:start position:0% +look also at New Balance shoes just for + + + align:start position:0% +look also at New Balance shoes just for +three comparisons so Aerospace is a + + align:start position:0% +three comparisons so Aerospace is a + + + align:start position:0% +three comparisons so Aerospace is a +really interesting industry it's it's a + + align:start position:0% +really interesting industry it's it's a + + + align:start position:0% +really interesting industry it's it's a +flagship industry of the of the United + + align:start position:0% +flagship industry of the of the United + + + align:start position:0% +flagship industry of the of the United +States it's one of these things that + + align:start position:0% +States it's one of these things that + + + align:start position:0% +States it's one of these things that +goes with the image of the country it + + align:start position:0% +goes with the image of the country it + + + align:start position:0% +goes with the image of the country it +enables a movement of people in + + align:start position:0% +enables a movement of people in + + + align:start position:0% +enables a movement of people in +Goods uh we enables communication it + + align:start position:0% +Goods uh we enables communication it + + + align:start position:0% +Goods uh we enables communication it +it's critical to National Security + + align:start position:0% +it's critical to National Security + + + align:start position:0% +it's critical to National Security +and it's a source of inspiration uh for + + align:start position:0% +and it's a source of inspiration uh for + + + align:start position:0% +and it's a source of inspiration uh for +many people for exploration now here's + + align:start position:0% +many people for exploration now here's + + + align:start position:0% +many people for exploration now here's +what why did Aerospace turn to adopting + + align:start position:0% +what why did Aerospace turn to adopting + + + align:start position:0% +what why did Aerospace turn to adopting +lean here's an industry + + align:start position:0% +lean here's an industry + + + align:start position:0% +lean here's an industry +where we think we're the world's leader + + align:start position:0% +where we think we're the world's leader + + + align:start position:0% +where we think we're the world's leader +and I pause because we may not be but we + + align:start position:0% +and I pause because we may not be but we + + + align:start position:0% +and I pause because we may not be but we +think we are but why do we turn to lean + + align:start position:0% +think we are but why do we turn to lean + + + align:start position:0% +think we are but why do we turn to lean +well here's why this is a study that + + align:start position:0% +well here's why this is a study that + + + align:start position:0% +well here's why this is a study that +came out of the Sloan school by Jim + + align:start position:0% +came out of the Sloan school by Jim + + + align:start position:0% +came out of the Sloan school by Jim +Utterback that shows the natural + + align:start position:0% +Utterback that shows the natural + + + align:start position:0% +Utterback that shows the natural +progression of many different + + align:start position:0% +progression of many different + + + align:start position:0% +progression of many different +Industries plotted by the number of + + align:start position:0% +Industries plotted by the number of + + + align:start position:0% +Industries plotted by the number of +companies + + align:start position:0% +companies + + + align:start position:0% +companies +in a particular industry so this is the + + align:start position:0% +in a particular industry so this is the + + + align:start position:0% +in a particular industry so this is the +typewriter industry so it started in the + + align:start position:0% +typewriter industry so it started in the + + + align:start position:0% +typewriter industry so it started in the +late + + align:start position:0% +late + + + align:start position:0% +late +1870s and companies came in they reached + + align:start position:0% +1870s and companies came in they reached + + + align:start position:0% +1870s and companies came in they reached +a peak of about 80 companies and then + + align:start position:0% +a peak of about 80 companies and then + + + align:start position:0% +a peak of about 80 companies and then +somewhere they reached a peak around + + align:start position:0% +somewhere they reached a peak around + + + align:start position:0% +somewhere they reached a peak around +1910 and then the number of companies + + align:start position:0% +1910 and then the number of companies + + + align:start position:0% +1910 and then the number of companies +started declining and of course there's + + align:start position:0% +started declining and of course there's + + + align:start position:0% +started declining and of course there's +probably no typewriter companies now + + align:start position:0% +probably no typewriter companies now + + + align:start position:0% +probably no typewriter companies now +okay what happens well in this phase + + align:start position:0% +okay what happens well in this phase + + + align:start position:0% +okay what happens well in this phase +this is where the product architecture + + align:start position:0% +this is where the product architecture + + + align:start position:0% +this is where the product architecture +and product characteristics are not set + + align:start position:0% +and product characteristics are not set + + + align:start position:0% +and product characteristics are not set +so many inventors come up with new ways + + align:start position:0% +so many inventors come up with new ways + + + align:start position:0% +so many inventors come up with new ways +of doing things eventually somehow the + + align:start position:0% +of doing things eventually somehow the + + + align:start position:0% +of doing things eventually somehow the +best design emerges and that's where the + + align:start position:0% +best design emerges and that's where the + + + align:start position:0% +best design emerges and that's where the +market consolidates around and then + + align:start position:0% +market consolidates around and then + + + align:start position:0% +market consolidates around and then +instead there's not really real + + align:start position:0% +instead there's not really real + + + align:start position:0% +instead there's not really real +opportunities for new companies what + + align:start position:0% +opportunities for new companies what + + + align:start position:0% +opportunities for new companies what +happens is companies buy up other + + align:start position:0% +happens is companies buy up other + + + align:start position:0% +happens is companies buy up other +companies emerge and at this point it's + + align:start position:0% +companies emerge and at this point it's + + + align:start position:0% +companies emerge and at this point it's +very hard to change the product + + align:start position:0% +very hard to change the product + + + align:start position:0% +very hard to change the product +architecture this keyboard we all use + + align:start position:0% +architecture this keyboard we all use + + + align:start position:0% +architecture this keyboard we all use +came out of this + + align:start position:0% +came out of this + + + align:start position:0% +came out of this +era it's pretty well known that there's + + align:start position:0% +era it's pretty well known that there's + + + align:start position:0% +era it's pretty well known that there's +more efficient keyboard layouts okay but + + align:start position:0% +more efficient keyboard layouts okay but + + + align:start position:0% +more efficient keyboard layouts okay but +it's impossible to change that now it's + + align:start position:0% +it's impossible to change that now it's + + + align:start position:0% +it's impossible to change that now it's +just it's impossible to change it + + align:start position:0% +just it's impossible to change it + + + align:start position:0% +just it's impossible to change it +because it's a standard okay here's the + + align:start position:0% +because it's a standard okay here's the + + + align:start position:0% +because it's a standard okay here's the +automobile + + align:start position:0% +automobile + + + align:start position:0% +automobile +industry say same kind of thing here the + + align:start position:0% +industry say same kind of thing here the + + + align:start position:0% +industry say same kind of thing here the +the main product architecture was the + + align:start position:0% +the main product architecture was the + + + align:start position:0% +the main product architecture was the +enclosed steel body okay here's + + align:start position:0% +enclosed steel body okay here's + + + align:start position:0% +enclosed steel body okay here's +Aerospace now this this is + + align:start position:0% +Aerospace now this this is + + + align:start position:0% +Aerospace now this this is +representative Aerospace it's probably + + align:start position:0% +representative Aerospace it's probably + + + align:start position:0% +representative Aerospace it's probably +it's just some of the major companies + + align:start position:0% +it's just some of the major companies + + + align:start position:0% +it's just some of the major companies +but throughout the 1900s up to about + + align:start position:0% +but throughout the 1900s up to about + + + align:start position:0% +but throughout the 1900s up to about +1960 we had a a growth in the number of + + align:start position:0% +1960 we had a a growth in the number of + + + align:start position:0% +1960 we had a a growth in the number of +companies then Along Came something + + align:start position:0% +companies then Along Came something + + + align:start position:0% +companies then Along Came something +looks like a + + align:start position:0% +looks like a + + + align:start position:0% +looks like a +74777 okay and other things and we sort + + align:start position:0% +74777 okay and other things and we sort + + + align:start position:0% +74777 okay and other things and we sort +of reached the product architecture and + + align:start position:0% +of reached the product architecture and + + + align:start position:0% +of reached the product architecture and +then we would have gone on this + + align:start position:0% +then we would have gone on this + + + align:start position:0% +then we would have gone on this +decline just as companies Buy but we get + + align:start position:0% +decline just as companies Buy but we get + + + align:start position:0% +decline just as companies Buy but we get +to this point here and there's a plateau + + align:start position:0% +to this point here and there's a plateau + + + align:start position:0% +to this point here and there's a plateau +we're in the Cold War okay and the + + align:start position:0% +we're in the Cold War okay and the + + + align:start position:0% +we're in the Cold War okay and the +government for strategic reasons wanted + + align:start position:0% +government for strategic reasons wanted + + + align:start position:0% +government for strategic reasons wanted +to keep a big industrial base so they + + align:start position:0% +to keep a big industrial base so they + + + align:start position:0% +to keep a big industrial base so they +invested in that industrial base when + + align:start position:0% +invested in that industrial base when + + + align:start position:0% +invested in that industrial base when +the Cold War was over the Secretary of + + align:start position:0% +the Cold War was over the Secretary of + + + align:start position:0% +the Cold War was over the Secretary of +Defense invited all the CEOs of the + + align:start position:0% +Defense invited all the CEOs of the + + + align:start position:0% +Defense invited all the CEOs of the +major aerospace companies to dinner it's + + align:start position:0% +major aerospace companies to dinner it's + + + align:start position:0% +major aerospace companies to dinner it's +called The Last Supper and he said we + + align:start position:0% +called The Last Supper and he said we + + + align:start position:0% +called The Last Supper and he said we +don't need this many companies and so + + align:start position:0% +don't need this many companies and so + + + align:start position:0% +don't need this many companies and so +we're not going to have as many but it's + + align:start position:0% +we're not going to have as many but it's + + + align:start position:0% +we're not going to have as many but it's +up to you to sort it out we'll let the + + align:start position:0% +up to you to sort it out we'll let the + + + align:start position:0% +up to you to sort it out we'll let the +marketplace sort it out so you know + + align:start position:0% +marketplace sort it out so you know + + + align:start position:0% +marketplace sort it out so you know +boing buys McDonald Douglas you know so + + align:start position:0% +boing buys McDonald Douglas you know so + + + align:start position:0% +boing buys McDonald Douglas you know so +on so forth and we have now + + align:start position:0% +on so forth and we have now + + + align:start position:0% +on so forth and we have now +consolidation in fewer aerospace + + align:start position:0% +consolidation in fewer aerospace + + + align:start position:0% +consolidation in fewer aerospace +companies had we not had the Cold War we + + align:start position:0% +companies had we not had the Cold War we + + + align:start position:0% +companies had we not had the Cold War we +probably would have done this okay but + + align:start position:0% +probably would have done this okay but + + + align:start position:0% +probably would have done this okay but +here's where aerosp here's where Lai + + align:start position:0% +here's where aerosp here's where Lai + + + align:start position:0% +here's where aerosp here's where Lai +started + + align:start position:0% +started + + + align:start position:0% +started +okay uh we had an industry which was + + align:start position:0% +okay uh we had an industry which was + + + align:start position:0% +okay uh we had an industry which was +inefficient and couldn't survive in the + + align:start position:0% +inefficient and couldn't survive in the + + + align:start position:0% +inefficient and couldn't survive in the +new world okay and so they turned to + + align:start position:0% +new world okay and so they turned to + + + align:start position:0% +new world okay and so they turned to +lean so we had a company with companies + + align:start position:0% +lean so we had a company with companies + + + align:start position:0% +lean so we had a company with companies +that have mature products can't survive + + align:start position:0% +that have mature products can't survive + + + align:start position:0% +that have mature products can't survive +on a business strategy that's designed + + align:start position:0% +on a business strategy that's designed + + + align:start position:0% +on a business strategy that's designed +for early + + align:start position:0% +for early + + + align:start position:0% +for early +growth here's one of the things that + + align:start position:0% +growth here's one of the things that + + + align:start position:0% +growth here's one of the things that +happens in an early phase when there's + + align:start position:0% +happens in an early phase when there's + + + align:start position:0% +happens in an early phase when there's +not when the competition really hasn't + + align:start position:0% +not when the competition really hasn't + + + align:start position:0% +not when the competition really hasn't +developed you can charge what you + + align:start position:0% +developed you can charge what you + + + align:start position:0% +developed you can charge what you +want you know you can charge what you + + align:start position:0% +want you know you can charge what you + + + align:start position:0% +want you know you can charge what you +want for a new device okay and and then + + align:start position:0% +want for a new device okay and and then + + + align:start position:0% +want for a new device okay and and then +you subtract your costs and you get + + align:start position:0% +you subtract your costs and you get + + + align:start position:0% +you subtract your costs and you get +whatever profit competition builds up or + + align:start position:0% +whatever profit competition builds up or + + + align:start position:0% +whatever profit competition builds up or +the government says we're not going to + + align:start position:0% +the government says we're not going to + + + align:start position:0% +the government says we're not going to +pay as much for airplanes anymore okay + + align:start position:0% +pay as much for airplanes anymore okay + + + align:start position:0% +pay as much for airplanes anymore okay +the customer sets the price the only way + + align:start position:0% +the customer sets the price the only way + + + align:start position:0% +the customer sets the price the only way +for you to make a profit is is to reduce + + align:start position:0% +for you to make a profit is is to reduce + + + align:start position:0% +for you to make a profit is is to reduce +your cost okay so you have to you have + + align:start position:0% +your cost okay so you have to you have + + + align:start position:0% +your cost okay so you have to you have +to become more efficient it's just the + + align:start position:0% +to become more efficient it's just the + + + align:start position:0% +to become more efficient it's just the +way it is or you don't + + align:start position:0% +way it is or you don't + + + align:start position:0% +way it is or you don't +survive here's an example of some of the + + align:start position:0% +survive here's an example of some of the + + + align:start position:0% +survive here's an example of some of the +problems in the Aerospace industry uh + + align:start position:0% +problems in the Aerospace industry uh + + + align:start position:0% +problems in the Aerospace industry uh +here are three programs the second block + + align:start position:0% +here are three programs the second block + + + align:start position:0% +here are three programs the second block +of the GPS satellites The Joint Strike + + align:start position:0% +of the GPS satellites The Joint Strike + + + align:start position:0% +of the GPS satellites The Joint Strike +Fighter Boeing 787 these are new + + align:start position:0% +Fighter Boeing 787 these are new + + + align:start position:0% +Fighter Boeing 787 these are new +airplanes years behind schedule 1 two 3 + + align:start position:0% +airplanes years behind schedule 1 two 3 + + + align:start position:0% +airplanes years behind schedule 1 two 3 +four + + align:start position:0% +four + + + align:start position:0% +four +okay billion dollars overrun 12 billion + + align:start position:0% +okay billion dollars overrun 12 billion + + + align:start position:0% +okay billion dollars overrun 12 billion +dollar over Beyond development cost 90 + + align:start position:0% +dollar over Beyond development cost 90 + + + align:start position:0% +dollar over Beyond development cost 90 +the the price per unit they're going to + + align:start position:0% +the the price per unit they're going to + + + align:start position:0% +the the price per unit they're going to +buy a lot of f-35s the price has doubled + + align:start position:0% +buy a lot of f-35s the price has doubled + + + align:start position:0% +buy a lot of f-35s the price has doubled +okay and it's still in trouble other + + align:start position:0% +okay and it's still in trouble other + + + align:start position:0% +okay and it's still in trouble other +programs where their cost and schedules + + align:start position:0% +programs where their cost and schedules + + + align:start position:0% +programs where their cost and schedules +overruns the F22 and so on the A340 + + align:start position:0% +overruns the F22 and so on the A340 + + + align:start position:0% +overruns the F22 and so on the A340 +A380 so on this is what's called The + + align:start position:0% +A380 so on this is what's called The + + + align:start position:0% +A380 so on this is what's called The +Burning platform okay most the Paradigm + + align:start position:0% +Burning platform okay most the Paradigm + + + align:start position:0% +Burning platform okay most the Paradigm +here is people adopt lean when the + + align:start position:0% +here is people adopt lean when the + + + align:start position:0% +here is people adopt lean when the +platform they're staying on is burning + + align:start position:0% +platform they're staying on is burning + + + align:start position:0% +platform they're staying on is burning +and if they don't do something they're + + align:start position:0% +and if they don't do something they're + + + align:start position:0% +and if they don't do something they're +going to disappear okay now there are + + align:start position:0% +going to disappear okay now there are + + + align:start position:0% +going to disappear okay now there are +also many Aerospace programs which are + + align:start position:0% +also many Aerospace programs which are + + + align:start position:0% +also many Aerospace programs which are +executed very well okay and we've + + align:start position:0% +executed very well okay and we've + + + align:start position:0% +executed very well okay and we've +learned a lot from studying those so I + + align:start position:0% +learned a lot from studying those so I + + + align:start position:0% +learned a lot from studying those so I +don't want to say the Aerospace can't do + + align:start position:0% +don't want to say the Aerospace can't do + + + align:start position:0% +don't want to say the Aerospace can't do +anything but there are a lot of problems + + align:start position:0% +anything but there are a lot of problems + + + align:start position:0% +anything but there are a lot of problems +with the Aerospace programs + + align:start position:0% +with the Aerospace programs + + + align:start position:0% +with the Aerospace programs +Healthcare it's a book published in 2003 + + align:start position:0% +Healthcare it's a book published in 2003 + + + align:start position:0% +Healthcare it's a book published in 2003 +called crossing the quality Chasm it's + + align:start position:0% +called crossing the quality Chasm it's + + + align:start position:0% +called crossing the quality Chasm it's +published by The Institute of medicine + + align:start position:0% +published by The Institute of medicine + + + align:start position:0% +published by The Institute of medicine +and the Paradigm here was this is the + + align:start position:0% +and the Paradigm here was this is the + + + align:start position:0% +and the Paradigm here was this is the +health care we're delivering this is the + + align:start position:0% +health care we're delivering this is the + + + align:start position:0% +health care we're delivering this is the +health care we know how to deliver and + + align:start position:0% +health care we know how to deliver and + + + align:start position:0% +health care we know how to deliver and +there's such a wide Gap in quality of + + align:start position:0% +there's such a wide Gap in quality of + + + align:start position:0% +there's such a wide Gap in quality of +Health Care that we have a big Chasm + + align:start position:0% +Health Care that we have a big Chasm + + + align:start position:0% +Health Care that we have a big Chasm +between what we're doing what we should + + align:start position:0% +between what we're doing what we should + + + align:start position:0% +between what we're doing what we should +be doing and they outlined what the + + align:start position:0% +be doing and they outlined what the + + + align:start position:0% +be doing and they outlined what the +objectives of Health Care are and that + + align:start position:0% +objectives of Health Care are and that + + + align:start position:0% +objectives of Health Care are and that +these are not new aims these are aims + + align:start position:0% +these are not new aims these are aims + + + align:start position:0% +these are not new aims these are aims +that have been there for many years and + + align:start position:0% +that have been there for many years and + + + align:start position:0% +that have been there for many years and +most people go into health care because + + align:start position:0% +most people go into health care because + + + align:start position:0% +most people go into health care because +they want to do this you know probably + + align:start position:0% +they want to do this you know probably + + + align:start position:0% +they want to do this you know probably +all of you guys are going in healthare + + align:start position:0% +all of you guys are going in healthare + + + align:start position:0% +all of you guys are going in healthare +because you you don't want you don't + + align:start position:0% +because you you don't want you don't + + + align:start position:0% +because you you don't want you don't +want you probably didn't say I picked + + align:start position:0% +want you probably didn't say I picked + + + align:start position:0% +want you probably didn't say I picked +healthare because it's inefficient + + align:start position:0% +healthare because it's inefficient + + + align:start position:0% +healthare because it's inefficient +system I can work in right you picked + + align:start position:0% +system I can work in right you picked + + + align:start position:0% +system I can work in right you picked +healthare because you want to help + + align:start position:0% +healthare because you want to help + + + align:start position:0% +healthare because you want to help +people and do things so we need to we + + align:start position:0% +people and do things so we need to we + + + align:start position:0% +people and do things so we need to we +need to do that okay but what are some + + align:start position:0% +need to do that okay but what are some + + + align:start position:0% +need to do that okay but what are some +signs well I think we've all heard about + + align:start position:0% +signs well I think we've all heard about + + + align:start position:0% +signs well I think we've all heard about +the cost of healthc care uh uh there + + align:start position:0% +the cost of healthc care uh uh there + + + align:start position:0% +the cost of healthc care uh uh there +different metrics here uh I don't think + + align:start position:0% +different metrics here uh I don't think + + + align:start position:0% +different metrics here uh I don't think +we have to go through those in detail + + align:start position:0% +we have to go through those in detail + + + align:start position:0% +we have to go through those in detail +there quality issues this is the one + + align:start position:0% +there quality issues this is the one + + + align:start position:0% +there quality issues this is the one +that is was staggering to me the study + + align:start position:0% +that is was staggering to me the study + + + align:start position:0% +that is was staggering to me the study +done in + + align:start position:0% +done in + + + align:start position:0% +done in +1999 that between about 50 and 100,000 + + align:start position:0% +1999 that between about 50 and 100,000 + + + align:start position:0% +1999 that between about 50 and 100,000 +people a year in our country die from + + align:start position:0% +people a year in our country die from + + + align:start position:0% +people a year in our country die from +perfectly preventable medical mistakes + + align:start position:0% +perfectly preventable medical mistakes + + + align:start position:0% +perfectly preventable medical mistakes +okay that's more people than die on the + + align:start position:0% +okay that's more people than die on the + + + align:start position:0% +okay that's more people than die on the +highway um and by the way that number + + align:start position:0% +highway um and by the way that number + + + align:start position:0% +highway um and by the way that number +still has not changed too much it's + + align:start position:0% +still has not changed too much it's + + + align:start position:0% +still has not changed too much it's +gotten a little bit better maybe but not + + align:start position:0% +gotten a little bit better maybe but not + + + align:start position:0% +gotten a little bit better maybe but not +changed many people don't have access to + + align:start position:0% +changed many people don't have access to + + + align:start position:0% +changed many people don't have access to +healthc care + + align:start position:0% +healthc care + + + align:start position:0% +healthc care +uh that's this slide's a little bit out + + align:start position:0% +uh that's this slide's a little bit out + + + align:start position:0% +uh that's this slide's a little bit out +of date because of the Affordable Health + + align:start position:0% +of date because of the Affordable Health + + + align:start position:0% +of date because of the Affordable Health +Care + + align:start position:0% +Care + + + align:start position:0% +Care +Act and you know 60% of the doctors in + + align:start position:0% +Act and you know 60% of the doctors in + + + align:start position:0% +Act and you know 60% of the doctors in +the survey said they wouldn't recommend + + align:start position:0% +the survey said they wouldn't recommend + + + align:start position:0% +the survey said they wouldn't recommend +going into healthc care to their + + align:start position:0% +going into healthc care to their + + + align:start position:0% +going into healthc care to their +children here we got Bose in emergency + + align:start position:0% +children here we got Bose in emergency + + + align:start position:0% +children here we got Bose in emergency +doctor emergency medicine doctor is 50% + + align:start position:0% +doctor emergency medicine doctor is 50% + + + align:start position:0% +doctor emergency medicine doctor is 50% +of your time spent on tap + + align:start position:0% +of your time spent on tap + + + align:start position:0% +of your time spent on tap +paperwork was day on a good day 50% of + + align:start position:0% +paperwork was day on a good day 50% of + + + align:start position:0% +paperwork was day on a good day 50% of +his waste and Susan's a nurse uh many + + align:start position:0% +his waste and Susan's a nurse uh many + + + align:start position:0% +his waste and Susan's a nurse uh many +Studies have showed we have a big + + align:start position:0% +Studies have showed we have a big + + + align:start position:0% +Studies have showed we have a big +shortage of nurses coming up here okay + + align:start position:0% +shortage of nurses coming up here okay + + + align:start position:0% +shortage of nurses coming up here okay +so we got some problems that you all + + align:start position:0% +so we got some problems that you all + + + align:start position:0% +so we got some problems that you all +know about so basically what we say in + + align:start position:0% +know about so basically what we say in + + + align:start position:0% +know about so basically what we say in +healthcare is there's a value crisis + + align:start position:0% +healthcare is there's a value crisis + + + align:start position:0% +healthcare is there's a value crisis +values Define is what you deliver and + + align:start position:0% +values Define is what you deliver and + + + align:start position:0% +values Define is what you deliver and +what divided by what you pay for it and + + align:start position:0% +what divided by what you pay for it and + + + align:start position:0% +what divided by what you pay for it and +roughly about half the health care we + + align:start position:0% +roughly about half the health care we + + + align:start position:0% +roughly about half the health care we +know how to deliver to the patient gets + + align:start position:0% +know how to deliver to the patient gets + + + align:start position:0% +know how to deliver to the patient gets +delivered and the cost this is the + + align:start position:0% +delivered and the cost this is the + + + align:start position:0% +delivered and the cost this is the +percent of U GDP in 2007 we were + + align:start position:0% +percent of U GDP in 2007 we were + + + align:start position:0% +percent of U GDP in 2007 we were +spending 16% of our gross domestic + + align:start position:0% +spending 16% of our gross domestic + + + align:start position:0% +spending 16% of our gross domestic +product on Healthcare in 2050 is + + align:start position:0% +product on Healthcare in 2050 is + + + align:start position:0% +product on Healthcare in 2050 is +supposed to be 37% that's just un + + align:start position:0% +supposed to be 37% that's just un + + + align:start position:0% +supposed to be 37% that's just un +sustainable and the same with + + align:start position:0% +sustainable and the same with + + + align:start position:0% +sustainable and the same with +Medicare so we hope that lean thinking + + align:start position:0% +Medicare so we hope that lean thinking + + + align:start position:0% +Medicare so we hope that lean thinking +can be one piece of a puzzle of + + align:start position:0% +can be one piece of a puzzle of + + + align:start position:0% +can be one piece of a puzzle of +improving Healthcare it's it's a + + align:start position:0% +improving Healthcare it's it's a + + + align:start position:0% +improving Healthcare it's it's a +complicated it's a complicated field and + + align:start position:0% +complicated it's a complicated field and + + + align:start position:0% +complicated it's a complicated field and +there's no simple solution but lean can + + align:start position:0% +there's no simple solution but lean can + + + align:start position:0% +there's no simple solution but lean can +help Okay so those are two industries as + + align:start position:0% +help Okay so those are two industries as + + + align:start position:0% +help Okay so those are two industries as +to why they're applying lean now let's + + align:start position:0% +to why they're applying lean now let's + + + align:start position:0% +to why they're applying lean now let's +talk a little bit about what is an + + align:start position:0% +talk a little bit about what is an + + + align:start position:0% +talk a little bit about what is an +Enterprise because in this course we + + align:start position:0% +Enterprise because in this course we + + + align:start position:0% +Enterprise because in this course we +very much focus on applying lean across + + align:start position:0% +very much focus on applying lean across + + + align:start position:0% +very much focus on applying lean across +an Enterprise not just a manufacturing + + align:start position:0% +an Enterprise not just a manufacturing + + + align:start position:0% +an Enterprise not just a manufacturing +or clinic thing so an Enterprise is a + + align:start position:0% +or clinic thing so an Enterprise is a + + + align:start position:0% +or clinic thing so an Enterprise is a +broadly defined as one or more + + align:start position:0% +broadly defined as one or more + + + align:start position:0% +broadly defined as one or more +organizations having related activities + + align:start position:0% +organizations having related activities + + + align:start position:0% +organizations having related activities +a unified operation and a common + + align:start position:0% +a unified operation and a common + + + align:start position:0% +a unified operation and a common +business + + align:start position:0% +business + + + align:start position:0% +business +purpose and so you might have in an + + align:start position:0% +purpose and so you might have in an + + + align:start position:0% +purpose and so you might have in an +engineering Enterprise + + align:start position:0% +engineering Enterprise + + + align:start position:0% +engineering Enterprise +customers engineering products uh + + align:start position:0% +customers engineering products uh + + + align:start position:0% +customers engineering products uh +product development or engineering + + align:start position:0% +product development or engineering + + + align:start position:0% +product development or engineering +manufacturing + + align:start position:0% +manufacturing + + + align:start position:0% +manufacturing +suppliers finance and so on and + + align:start position:0% +suppliers finance and so on and + + + align:start position:0% +suppliers finance and so on and +support okay and Enterprises can be + + align:start position:0% +support okay and Enterprises can be + + + align:start position:0% +support okay and Enterprises can be +pretty + + align:start position:0% +pretty + + + align:start position:0% +pretty +complex so it's hard to define the + + align:start position:0% +complex so it's hard to define the + + + align:start position:0% +complex so it's hard to define the +boundaries of an Enterprise uh soone + + align:start position:0% +boundaries of an Enterprise uh soone + + + align:start position:0% +boundaries of an Enterprise uh soone +contextual you might draw it around your + + align:start position:0% +contextual you might draw it around your + + + align:start position:0% +contextual you might draw it around your +table here as an + + align:start position:0% +table here as an + + + align:start position:0% +table here as an +Enterprise uh but most Enterprises have + + align:start position:0% +Enterprise uh but most Enterprises have + + + align:start position:0% +Enterprise uh but most Enterprises have +partners that they have closely close + + align:start position:0% +partners that they have closely close + + + align:start position:0% +partners that they have closely close +operating agreements with and so we call + + align:start position:0% +operating agreements with and so we call + + + align:start position:0% +operating agreements with and so we call +the core + + align:start position:0% +the core + + + align:start position:0% +the core +Enterprise the organization plus its + + align:start position:0% +Enterprise the organization plus its + + + align:start position:0% +Enterprise the organization plus its +most closely related + + align:start position:0% +most closely related + + + align:start position:0% +most closely related +partners and + + align:start position:0% +partners and + + + align:start position:0% +partners and +uh uh that work with them and then + + align:start position:0% +uh uh that work with them and then + + + align:start position:0% +uh uh that work with them and then +beyond that there's an extended + + align:start position:0% +beyond that there's an extended + + + align:start position:0% +beyond that there's an extended +Enterprise which is all their suppliers + + align:start position:0% +Enterprise which is all their suppliers + + + align:start position:0% +Enterprise which is all their suppliers +and actually their customers too and and + + align:start position:0% +and actually their customers too and and + + + align:start position:0% +and actually their customers too and and +also their community and Regulatory + + align:start position:0% +also their community and Regulatory + + + align:start position:0% +also their community and Regulatory +Agencies and things like that all can + + align:start position:0% +Agencies and things like that all can + + + align:start position:0% +Agencies and things like that all can +affect their Enterprise okay so a a + + align:start position:0% +affect their Enterprise okay so a a + + + align:start position:0% +affect their Enterprise okay so a a +company like Boeing has maybe 2,000 + + align:start position:0% +company like Boeing has maybe 2,000 + + + align:start position:0% +company like Boeing has maybe 2,000 +suppliers okay + + align:start position:0% +suppliers okay + + + align:start position:0% +suppliers okay +that's by the way those 2,000 suppliers + + align:start position:0% +that's by the way those 2,000 suppliers + + + align:start position:0% +that's by the way those 2,000 suppliers +are suppliers to Airbus and embri a and + + align:start position:0% +are suppliers to Airbus and embri a and + + + align:start position:0% +are suppliers to Airbus and embri a and +so this gets very complicated okay okay + + align:start position:0% +so this gets very complicated okay okay + + + align:start position:0% +so this gets very complicated okay okay +so who are the stakeholders of an + + align:start position:0% +so who are the stakeholders of an + + + align:start position:0% +so who are the stakeholders of an +Enterprise there any group or individual + + align:start position:0% +Enterprise there any group or individual + + + align:start position:0% +Enterprise there any group or individual +who can affect or is affected by the + + align:start position:0% +who can affect or is affected by the + + + align:start position:0% +who can affect or is affected by the +organizational objectiv so you have your + + align:start position:0% +organizational objectiv so you have your + + + align:start position:0% +organizational objectiv so you have your +employees Partners suppliers + + align:start position:0% +employees Partners suppliers + + + align:start position:0% +employees Partners suppliers +unions uh customers shareholders these + + align:start position:0% +unions uh customers shareholders these + + + align:start position:0% +unions uh customers shareholders these +are all stakeholders who can affect or + + align:start position:0% +are all stakeholders who can affect or + + + align:start position:0% +are all stakeholders who can affect or +are affected by your + + align:start position:0% +are affected by your + + + align:start position:0% +are affected by your +Enterprise Jennifer at Boston Medical + + align:start position:0% +Enterprise Jennifer at Boston Medical + + + align:start position:0% +Enterprise Jennifer at Boston Medical +Center do you have any I don't know how + + align:start position:0% +Center do you have any I don't know how + + + align:start position:0% +Center do you have any I don't know how +long you've been at Boston Medical + + align:start position:0% +long you've been at Boston Medical + + + align:start position:0% +long you've been at Boston Medical +Center and whether you you know do any + + align:start position:0% +Center and whether you you know do any + + + align:start position:0% +Center and whether you you know do any +of these kind of things with you in + + align:start position:0% +of these kind of things with you in + + + align:start position:0% +of these kind of things with you in +terms of who your stakeholders are there + + align:start position:0% +terms of who your stakeholders are there + + + align:start position:0% +terms of who your stakeholders are there +what what depart you're in Radiology + + align:start position:0% +what what depart you're in Radiology + + + align:start position:0% +what what depart you're in Radiology +I've been there for five years so okay + + align:start position:0% +I've been there for five years so okay + + + align:start position:0% +I've been there for five years so okay +hope I know a little bit so you have + + align:start position:0% +hope I know a little bit so you have + + + align:start position:0% +hope I know a little bit so you have +some suppliers of CAT scans and all this + + align:start position:0% +some suppliers of CAT scans and all this + + + align:start position:0% +some suppliers of CAT scans and all this +kind of stuff oh sure okay sure I mean I + + align:start position:0% +kind of stuff oh sure okay sure I mean I + + + align:start position:0% +kind of stuff oh sure okay sure I mean I +was actually thinking of it in a broader + + align:start position:0% +was actually thinking of it in a broader + + + align:start position:0% +was actually thinking of it in a broader +sense in terms of we have the community + + align:start position:0% +sense in terms of we have the community + + + align:start position:0% +sense in terms of we have the community +health centers who sent so we you know + + align:start position:0% +health centers who sent so we you know + + + align:start position:0% +health centers who sent so we you know +for instance serve the emergency room we + + align:start position:0% +for instance serve the emergency room we + + + align:start position:0% +for instance serve the emergency room we +serve the inpatients we serve our own + + align:start position:0% +serve the inpatients we serve our own + + + align:start position:0% +serve the inpatients we serve our own +BMC out patients then we also serve a + + align:start position:0% +BMC out patients then we also serve a + + + align:start position:0% +BMC out patients then we also serve a +very large network of Community Health + + align:start position:0% +very large network of Community Health + + + align:start position:0% +very large network of Community Health +centers who send all of their patients + + align:start position:0% +centers who send all of their patients + + + align:start position:0% +centers who send all of their patients +to us for for Imaging that they can't + + align:start position:0% +to us for for Imaging that they can't + + + align:start position:0% +to us for for Imaging that they can't +provide uh then there's the technical + + align:start position:0% +provide uh then there's the technical + + + align:start position:0% +provide uh then there's the technical +Arena of all of the um G provides most + + align:start position:0% +Arena of all of the um G provides most + + + align:start position:0% +Arena of all of the um G provides most +of our um our equipment um but we have + + align:start position:0% +of our um our equipment um but we have + + + align:start position:0% +of our um our equipment um but we have +different suppliers for our MRIs and our + + align:start position:0% +different suppliers for our MRIs and our + + + align:start position:0% +different suppliers for our MRIs and our +CTS and our Ultras soundes are all + + align:start position:0% +CTS and our Ultras soundes are all + + + align:start position:0% +CTS and our Ultras soundes are all +different corporations and then they all + + align:start position:0% +different corporations and then they all + + + align:start position:0% +different corporations and then they all +have their own Technical Support + + align:start position:0% +have their own Technical Support + + + align:start position:0% +have their own Technical Support +Services I think you made the point + + align:start position:0% +Services I think you made the point + + + align:start position:0% +Services I think you made the point +yeah so there are a lot of stakeholders + + align:start position:0% +yeah so there are a lot of stakeholders + + + align:start position:0% +yeah so there are a lot of stakeholders +and each of these stakeholders + + align:start position:0% + + + + align:start position:0% + +this is a very high level definition of + + align:start position:0% +this is a very high level definition of + + + align:start position:0% +this is a very high level definition of +value we're going to come in the next + + align:start position:0% +value we're going to come in the next + + + align:start position:0% +value we're going to come in the next +module to a much more specific + + align:start position:0% +module to a much more specific + + + align:start position:0% +module to a much more specific +definition of value this is a very high + + align:start position:0% +definition of value this is a very high + + + align:start position:0% +definition of value this is a very high +level but every one of these + + align:start position:0% +level but every one of these + + + align:start position:0% +level but every one of these +stakeholders expect some value from the + + align:start position:0% +stakeholders expect some value from the + + + align:start position:0% +stakeholders expect some value from the +Enterprise just like Jennifer just + + align:start position:0% +Enterprise just like Jennifer just + + + align:start position:0% +Enterprise just like Jennifer just +outlined okay and in return they + + align:start position:0% +outlined okay and in return they + + + align:start position:0% +outlined okay and in return they +supposed to contribute some value to + + align:start position:0% +supposed to contribute some value to + + + align:start position:0% +supposed to contribute some value to +that Enterprise okay so there's a kind + + align:start position:0% +that Enterprise okay so there's a kind + + + align:start position:0% +that Enterprise okay so there's a kind +of a value proposition here you know + + align:start position:0% +of a value proposition here you know + + + align:start position:0% +of a value proposition here you know +values how various stakeholders find + + align:start position:0% +values how various stakeholders find + + + align:start position:0% +values how various stakeholders find +worth utility or benefit reward in + + align:start position:0% +worth utility or benefit reward in + + + align:start position:0% +worth utility or benefit reward in +exchange for their respective contra + + align:start position:0% +exchange for their respective contra + + + align:start position:0% +exchange for their respective contra +contribution to the Enterprise so + + align:start position:0% +contribution to the Enterprise so + + + align:start position:0% +contribution to the Enterprise so +there's this kind of + + align:start position:0% +there's this kind of + + + align:start position:0% +there's this kind of +value relationship going on here in an + + align:start position:0% +value relationship going on here in an + + + align:start position:0% +value relationship going on here in an +Enterprise and now what's a lean + + align:start position:0% +Enterprise and now what's a lean + + + align:start position:0% +Enterprise and now what's a lean +Enterprise when we started this work + + align:start position:0% +Enterprise when we started this work + + + align:start position:0% +Enterprise when we started this work +said this is a lean Enterprise course or + + align:start position:0% +said this is a lean Enterprise course or + + + align:start position:0% +said this is a lean Enterprise course or +lean Enterprise initiative people said + + align:start position:0% +lean Enterprise initiative people said + + + align:start position:0% +lean Enterprise initiative people said +well what is lean Enterprise turns out + + align:start position:0% +well what is lean Enterprise turns out + + + align:start position:0% +well what is lean Enterprise turns out +that's a good question and here's our + + align:start position:0% +that's a good question and here's our + + + align:start position:0% +that's a good question and here's our +definition it's an Enterprise of an it's + + align:start position:0% +definition it's an Enterprise of an it's + + + align:start position:0% +definition it's an Enterprise of an it's +an integrated entity that efficiently + + align:start position:0% +an integrated entity that efficiently + + + align:start position:0% +an integrated entity that efficiently +creates value for its multiple + + align:start position:0% +creates value for its multiple + + + align:start position:0% +creates value for its multiple +stakeholders by employing the principles + + align:start position:0% +stakeholders by employing the principles + + + align:start position:0% +stakeholders by employing the principles +and practices we're going to cover in + + align:start position:0% +and practices we're going to cover in + + + align:start position:0% +and practices we're going to cover in +this this + + align:start position:0% +this this + + + align:start position:0% +this this +course + + align:start position:0% +course + + + align:start position:0% +course +okay now these principles apply across + + align:start position:0% +okay now these principles apply across + + + align:start position:0% +okay now these principles apply across +the entire Enterprise so in a in an + + align:start position:0% +the entire Enterprise so in a in an + + + align:start position:0% +the entire Enterprise so in a in an +engineering Enterprise you have + + align:start position:0% +engineering Enterprise you have + + + align:start position:0% +engineering Enterprise you have +generally What's called the product life + + align:start position:0% +generally What's called the product life + + + align:start position:0% +generally What's called the product life +cycle from the you know the + + align:start position:0% +cycle from the you know the + + + align:start position:0% +cycle from the you know the +initial concept of a product like this + + align:start position:0% +initial concept of a product like this + + + align:start position:0% +initial concept of a product like this +through the + + align:start position:0% +through the + + + align:start position:0% +through the +design definition design gain the supply + + align:start position:0% +design definition design gain the supply + + + align:start position:0% +design definition design gain the supply +chain lineup production distribution of + + align:start position:0% +chain lineup production distribution of + + + align:start position:0% +chain lineup production distribution of +support that's what generates money for + + align:start position:0% +support that's what generates money for + + + align:start position:0% +support that's what generates money for +the Enterprise okay selling this product + + align:start position:0% +the Enterprise okay selling this product + + + align:start position:0% +the Enterprise okay selling this product +but it also has + + align:start position:0% + + + + align:start position:0% + +Finance Information Technology Human + + align:start position:0% +Finance Information Technology Human + + + align:start position:0% +Finance Information Technology Human +Resources various support functions + + align:start position:0% +Resources various support functions + + + align:start position:0% +Resources various support functions +which are needed and and Leadership + + align:start position:0% +which are needed and and Leadership + + + align:start position:0% +which are needed and and Leadership +processes and the point is lean a prize + + align:start position:0% +processes and the point is lean a prize + + + align:start position:0% +processes and the point is lean a prize +to all these it doesn't apply just to + + align:start position:0% +to all these it doesn't apply just to + + + align:start position:0% +to all these it doesn't apply just to +manufacturing it applies across the + + align:start position:0% +manufacturing it applies across the + + + align:start position:0% +manufacturing it applies across the +whole Enterprise and we'll show you some + + align:start position:0% +whole Enterprise and we'll show you some + + + align:start position:0% +whole Enterprise and we'll show you some +an example of that in a minute in + + align:start position:0% +an example of that in a minute in + + + align:start position:0% +an example of that in a minute in +healthcare it's very much the same + + align:start position:0% +healthcare it's very much the same + + + align:start position:0% +healthcare it's very much the same +instead of having the product life cycle + + align:start position:0% +instead of having the product life cycle + + + align:start position:0% +instead of having the product life cycle +you have the patient life cycle okay the + + align:start position:0% +you have the patient life cycle okay the + + + align:start position:0% +you have the patient life cycle okay the +lean doesn't apply just to treatment you + + align:start position:0% +lean doesn't apply just to treatment you + + + align:start position:0% +lean doesn't apply just to treatment you +know it applies to from preventive uh + + align:start position:0% +know it applies to from preventive uh + + + align:start position:0% +know it applies to from preventive uh +monitoring through Long-Term Care + + align:start position:0% +monitoring through Long-Term Care + + + align:start position:0% +monitoring through Long-Term Care +Management if you have we should really + + align:start position:0% +Management if you have we should really + + + align:start position:0% +Management if you have we should really +be thinking in fact there are people who + + align:start position:0% +be thinking in fact there are people who + + + align:start position:0% +be thinking in fact there are people who +feel that the Health Care System should + + align:start position:0% +feel that the Health Care System should + + + align:start position:0% +feel that the Health Care System should +be reorganized along along uh you know + + align:start position:0% +be reorganized along along uh you know + + + align:start position:0% +be reorganized along along uh you know +let's call disease Pathways or something + + align:start position:0% +let's call disease Pathways or something + + + align:start position:0% +let's call disease Pathways or something +like that you know instead of segmented + + align:start position:0% +like that you know instead of segmented + + + align:start position:0% +like that you know instead of segmented +into Imaging and so on okay and again + + align:start position:0% +into Imaging and so on okay and again + + + align:start position:0% +into Imaging and so on okay and again +you have the same supporting functions + + align:start position:0% +you have the same supporting functions + + + align:start position:0% +you have the same supporting functions +and I'm really glad that a couple of our + + align:start position:0% +and I'm really glad that a couple of our + + + align:start position:0% +and I'm really glad that a couple of our +students here in healthcare are + + align:start position:0% +students here in healthcare are + + + align:start position:0% +students here in healthcare are +administrative fellows uh looking into + + align:start position:0% +administrative fellows uh looking into + + + align:start position:0% +administrative fellows uh looking into +healthcare administration it's really + + align:start position:0% +healthcare administration it's really + + + align:start position:0% +healthcare administration it's really +important + + align:start position:0% +important + + + align:start position:0% +important +okay so it does it + + align:start position:0% +okay so it does it + + + align:start position:0% +okay so it does it +work well I told you how lii got started + + align:start position:0% +work well I told you how lii got started + + + align:start position:0% +work well I told you how lii got started +in 1992 and it took us 10 years to + + align:start position:0% +in 1992 and it took us 10 years to + + + align:start position:0% +in 1992 and it took us 10 years to +respond to the general with a book we + + align:start position:0% +respond to the general with a book we + + + align:start position:0% +respond to the general with a book we +wrote and we said after 10 years we said + + align:start position:0% +wrote and we said after 10 years we said + + + align:start position:0% +wrote and we said after 10 years we said +to the general he didn't by then we'd + + align:start position:0% +to the general he didn't by then we'd + + + align:start position:0% +to the general he didn't by then we'd +been through three or four generals uh + + align:start position:0% +been through three or four generals uh + + + align:start position:0% +been through three or four generals uh +and we said yes lean does + + align:start position:0% +and we said yes lean does + + + align:start position:0% +and we said yes lean does +apply to Aerospace if we take it at the + + align:start position:0% +apply to Aerospace if we take it at the + + + align:start position:0% +apply to Aerospace if we take it at the +Enterprise level if it's applied to all + + align:start position:0% +Enterprise level if it's applied to all + + + align:start position:0% +Enterprise level if it's applied to all +the functions of Aerospace not just to + + align:start position:0% + + + + align:start position:0% + +manufacturing okay here's an here's a a + + align:start position:0% +manufacturing okay here's an here's a a + + + align:start position:0% +manufacturing okay here's an here's a a +really good example of the the F-18 + + align:start position:0% +really good example of the the F-18 + + + align:start position:0% +really good example of the the F-18 +aircraft uh this is a fighter aircraft + + align:start position:0% +aircraft uh this is a fighter aircraft + + + align:start position:0% +aircraft uh this is a fighter aircraft +for the the Navy uh they were going + + align:start position:0% +for the the Navy uh they were going + + + align:start position:0% +for the the Navy uh they were going +through an upgrade to the model EF it + + align:start position:0% +through an upgrade to the model EF it + + + align:start position:0% +through an upgrade to the model EF it +was a upgrade but it was actually a + + align:start position:0% +was a upgrade but it was actually a + + + align:start position:0% +was a upgrade but it was actually a +completely new aircraft it was 25% + + align:start position:0% +completely new aircraft it was 25% + + + align:start position:0% +completely new aircraft it was 25% +bigger but it was sold to Congress as an + + align:start position:0% +bigger but it was sold to Congress as an + + + align:start position:0% +bigger but it was sold to Congress as an +upgrade $5 billion budget eight and a + + align:start position:0% +upgrade $5 billion budget eight and a + + + align:start position:0% +upgrade $5 billion budget eight and a +half years to do the uh engineering and + + align:start position:0% +half years to do the uh engineering and + + + align:start position:0% +half years to do the uh engineering and +UPG design the program per performed on + + align:start position:0% +UPG design the program per performed on + + + align:start position:0% +UPG design the program per performed on +schedule within cost met all technical + + align:start position:0% +schedule within cost met all technical + + + align:start position:0% +schedule within cost met all technical +requirements very unusual compared to + + align:start position:0% +requirements very unusual compared to + + + align:start position:0% +requirements very unusual compared to +those burning platform programs I showed + + align:start position:0% +those burning platform programs I showed + + + align:start position:0% +those burning platform programs I showed +you when we went in and studied it and + + align:start position:0% +you when we went in and studied it and + + + align:start position:0% +you when we went in and studied it and +looked at what they had done with what + + align:start position:0% +looked at what they had done with what + + + align:start position:0% +looked at what they had done with what +the lean principles are they were lean + + align:start position:0% +the lean principles are they were lean + + + align:start position:0% +the lean principles are they were lean +Enterprise they didn't call themselves + + align:start position:0% +Enterprise they didn't call themselves + + + align:start position:0% +Enterprise they didn't call themselves +lean Enterprise but they had done this + + align:start position:0% +lean Enterprise but they had done this + + + align:start position:0% +lean Enterprise but they had done this +and in fact uh we went and gave them + + align:start position:0% +and in fact uh we went and gave them + + + align:start position:0% +and in fact uh we went and gave them +this briefing and we said to them we've + + align:start position:0% +this briefing and we said to them we've + + + align:start position:0% +this briefing and we said to them we've +concluded you're a lean Enterprise and + + align:start position:0% +concluded you're a lean Enterprise and + + + align:start position:0% +concluded you're a lean Enterprise and +they said + + align:start position:0% +they said + + + align:start position:0% +they said +whoa no we're not we have so much more + + align:start position:0% +whoa no we're not we have so much more + + + align:start position:0% +whoa no we're not we have so much more +to do don't tell us we're in lean + + align:start position:0% +to do don't tell us we're in lean + + + align:start position:0% +to do don't tell us we're in lean +Enterprise that's the attitude you want + + align:start position:0% +Enterprise that's the attitude you want + + + align:start position:0% +Enterprise that's the attitude you want +want + + align:start position:0% +want + + + align:start position:0% +want +okay wonderful program here here's U + + align:start position:0% +okay wonderful program here here's U + + + align:start position:0% +okay wonderful program here here's U +completely different area Electronics + + align:start position:0% +completely different area Electronics + + + align:start position:0% +completely different area Electronics +Rockwell Collins we're going to come + + align:start position:0% +Rockwell Collins we're going to come + + + align:start position:0% +Rockwell Collins we're going to come +back to them on on uh Thursday with a + + align:start position:0% +back to them on on uh Thursday with a + + + align:start position:0% +back to them on on uh Thursday with a +case study of Rockwell + + align:start position:0% +case study of Rockwell + + + align:start position:0% +case study of Rockwell +Collins but they applied lean thinking + + align:start position:0% +Collins but they applied lean thinking + + + align:start position:0% +Collins but they applied lean thinking +across their whole company in the office + + align:start position:0% +across their whole company in the office + + + align:start position:0% +across their whole company in the office +environment as well as in the factory uh + + align:start position:0% +environment as well as in the factory uh + + + align:start position:0% +environment as well as in the factory uh +and the great results and we'll see data + + align:start position:0% +and the great results and we'll see data + + + align:start position:0% +and the great results and we'll see data +from them on their operating performance + + align:start position:0% +from them on their operating performance + + + align:start position:0% +from them on their operating performance +tomorrow Healthcare many examples in + + align:start position:0% +tomorrow Healthcare many examples in + + + align:start position:0% +tomorrow Healthcare many examples in +healthcare and Susan will give you a lot + + align:start position:0% +healthcare and Susan will give you a lot + + + align:start position:0% +healthcare and Susan will give you a lot +more when she talks on uh on Thursday + + align:start position:0% +more when she talks on uh on Thursday + + + align:start position:0% +more when she talks on uh on Thursday +but just here a few there's number of + + align:start position:0% +but just here a few there's number of + + + align:start position:0% +but just here a few there's number of +books out now uh Theta Care in Wisconsin + + align:start position:0% +books out now uh Theta Care in Wisconsin + + + align:start position:0% +books out now uh Theta Care in Wisconsin +waiting time from when you first call to + + align:start position:0% +waiting time from when you first call to + + + align:start position:0% +waiting time from when you first call to +when you get scheduled for orthopedic + + align:start position:0% +when you get scheduled for orthopedic + + + align:start position:0% +when you get scheduled for orthopedic +surgery went from 14 weeks to 31 hours + + align:start position:0% +surgery went from 14 weeks to 31 hours + + + align:start position:0% +surgery went from 14 weeks to 31 hours +okay uh here's a hospital in + + align:start position:0% +okay uh here's a hospital in + + + align:start position:0% +okay uh here's a hospital in +Pennsylvania where they reduced the + + align:start position:0% +Pennsylvania where they reduced the + + + align:start position:0% +Pennsylvania where they reduced the +readmission rate for COPD patients um + + align:start position:0% +readmission rate for COPD patients um + + + align:start position:0% +readmission rate for COPD patients um +Troll's Hospital in Seattle reduced its + + align:start position:0% +Troll's Hospital in Seattle reduced its + + + align:start position:0% +Troll's Hospital in Seattle reduced its +capital expenditures by 180 million by + + align:start position:0% +capital expenditures by 180 million by + + + align:start position:0% +capital expenditures by 180 million by +using lean improvements and Susan + + align:start position:0% +using lean improvements and Susan + + + align:start position:0% +using lean improvements and Susan +mentioned about architecture that's + + align:start position:0% +mentioned about architecture that's + + + align:start position:0% +mentioned about architecture that's +becoming a big area for Capital Saving + + align:start position:0% +becoming a big area for Capital Saving + + + align:start position:0% +becoming a big area for Capital Saving +and Capital Improvements and here's a + + align:start position:0% +and Capital Improvements and here's a + + + align:start position:0% +and Capital Improvements and here's a +hospital in in Nebraska where reduce the + + align:start position:0% +hospital in in Nebraska where reduce the + + + align:start position:0% +hospital in in Nebraska where reduce the +time it took to turn around the lab + + align:start position:0% +time it took to turn around the lab + + + align:start position:0% +time it took to turn around the lab +results uh over a six-year period by 72% + + align:start position:0% +results uh over a six-year period by 72% + + + align:start position:0% +results uh over a six-year period by 72% +by using the same people in the same + + align:start position:0% +by using the same people in the same + + + align:start position:0% +by using the same people in the same +facilities + + align:start position:0% +facilities + + + align:start position:0% +facilities +okay okay here's the New Balance story + + align:start position:0% +okay okay here's the New Balance story + + + align:start position:0% +okay okay here's the New Balance story +we're going to see a video on this um + + align:start position:0% +we're going to see a video on this um + + + align:start position:0% +we're going to see a video on this um +shortly but uh they're a shoe company + + align:start position:0% +shortly but uh they're a shoe company + + + align:start position:0% +shortly but uh they're a shoe company +they're the only company that + + align:start position:0% +they're the only company that + + + align:start position:0% +they're the only company that +manufactures athletic shoes in United + + align:start position:0% +manufactures athletic shoes in United + + + align:start position:0% +manufactures athletic shoes in United +States okay used to take them eight days + + align:start position:0% +States okay used to take them eight days + + + align:start position:0% +States okay used to take them eight days +to make a pair of shoes now it takes + + align:start position:0% +to make a pair of shoes now it takes + + + align:start position:0% +to make a pair of shoes now it takes +three hours okay uh they're actually + + align:start position:0% +three hours okay uh they're actually + + + align:start position:0% +three hours okay uh they're actually +doing the same amount of work so here + + align:start position:0% +doing the same amount of work so here + + + align:start position:0% +doing the same amount of work so here +they were only of the eight days only + + align:start position:0% +they were only of the eight days only + + + align:start position:0% +they were only of the eight days only +two two10 of a percent of the time where + + align:start position:0% +two two10 of a percent of the time where + + + align:start position:0% +two two10 of a percent of the time where +they doing anything useful on the + + align:start position:0% +they doing anything useful on the + + + align:start position:0% +they doing anything useful on the +shoe uh number of items they have to + + align:start position:0% +shoe uh number of items they have to + + + align:start position:0% +shoe uh number of items they have to +have an inventory went from uh well the + + align:start position:0% +have an inventory went from uh well the + + + align:start position:0% +have an inventory went from uh well the +inventory turn is the number of number + + align:start position:0% +inventory turn is the number of number + + + align:start position:0% +inventory turn is the number of number +of times you turn over the inventory + + align:start position:0% +of times you turn over the inventory + + + align:start position:0% +of times you turn over the inventory +here it took from 3.5 to 13 they can + + align:start position:0% +here it took from 3.5 to 13 they can + + + align:start position:0% +here it took from 3.5 to 13 they can +make a pair of shoes they get a call say + + align:start position:0% +make a pair of shoes they get a call say + + + align:start position:0% +make a pair of shoes they get a call say +we need some more shoes they can strip + + align:start position:0% +we need some more shoes they can strip + + + align:start position:0% +we need some more shoes they can strip +it in three + + align:start position:0% +it in three + + + align:start position:0% +it in three +days floor space reduced production went + + align:start position:0% +days floor space reduced production went + + + align:start position:0% +days floor space reduced production went +up and so on uh let's let's just talk + + align:start position:0% +up and so on uh let's let's just talk + + + align:start position:0% +up and so on uh let's let's just talk +about this kbon Japanese word who's + + align:start position:0% +about this kbon Japanese word who's + + + align:start position:0% +about this kbon Japanese word who's +heard who's ever heard the word + + align:start position:0% +heard who's ever heard the word + + + align:start position:0% +heard who's ever heard the word +kban one Katherine's heard kbon okay + + align:start position:0% +kban one Katherine's heard kbon okay + + + align:start position:0% +kban one Katherine's heard kbon okay +kind of a strange word isn't it who's + + align:start position:0% +kind of a strange word isn't it who's + + + align:start position:0% +kind of a strange word isn't it who's +how many of you at home keep a shopping + + align:start position:0% +how many of you at home keep a shopping + + + align:start position:0% +how many of you at home keep a shopping +list + + align:start position:0% +list + + + align:start position:0% +list +okay so tell me what how how do you make + + align:start position:0% +okay so tell me what how how do you make + + + align:start position:0% +okay so tell me what how how do you make +your shopping list + + align:start position:0% +your shopping list + + + align:start position:0% +your shopping list +Whitney like in terms of which ones I + + align:start position:0% +Whitney like in terms of which ones I + + + align:start position:0% +Whitney like in terms of which ones I +well now I use an app for everything + + align:start position:0% +well now I use an app for everything + + + align:start position:0% +well now I use an app for everything +so on the weekends we'll kind of pick + + align:start position:0% +so on the weekends we'll kind of pick + + + align:start position:0% +so on the weekends we'll kind of pick +what things I'm going to do and then PS + + align:start position:0% +what things I'm going to do and then PS + + + align:start position:0% +what things I'm going to do and then PS +a list for me so I carry it around so + + align:start position:0% +a list for me so I carry it around so + + + align:start position:0% +a list for me so I carry it around so +you and how do you make that list of + + align:start position:0% +you and how do you make that list of + + + align:start position:0% +you and how do you make that list of +things you well let's say grocery + + align:start position:0% +things you well let's say grocery + + + align:start position:0% +things you well let's say grocery +shopping just to make simple so grocery + + align:start position:0% +shopping just to make simple so grocery + + + align:start position:0% +shopping just to make simple so grocery +shopping what do you put on your list I + + align:start position:0% +shopping what do you put on your list I + + + align:start position:0% +shopping what do you put on your list I +pick the recipes and uh create the list + + align:start position:0% +pick the recipes and uh create the list + + + align:start position:0% +pick the recipes and uh create the list +okay so you pick what you need okay + + align:start position:0% +okay so you pick what you need okay + + + align:start position:0% +okay so you pick what you need okay +anybody else how you how do you do your + + align:start position:0% +anybody else how you how do you do your + + + align:start position:0% +anybody else how you how do you do your +shopping list Telly I I go to my fridge + + align:start position:0% +shopping list Telly I I go to my fridge + + + align:start position:0% +shopping list Telly I I go to my fridge +and I look at what is missing I go to + + align:start position:0% +and I look at what is missing I go to + + + align:start position:0% +and I look at what is missing I go to +the um my my cboard and see if there are + + align:start position:0% +the um my my cboard and see if there are + + + align:start position:0% +the um my my cboard and see if there are +things that are missing I need to + + align:start position:0% +things that are missing I need to + + + align:start position:0% +things that are missing I need to +replace and I down the L so he's got 5S + + align:start position:0% +replace and I down the L so he's got 5S + + + align:start position:0% +replace and I down the L so he's got 5S +word he can look at his cupboard and see + + align:start position:0% +word he can look at his cupboard and see + + + align:start position:0% +word he can look at his cupboard and see +he's missing something right okay you + + align:start position:0% +he's missing something right okay you + + + align:start position:0% +he's missing something right okay you +have some kind of standardized way of + + align:start position:0% +have some kind of standardized way of + + + align:start position:0% +have some kind of standardized way of +storing things in your cupboard yeah + + align:start position:0% +storing things in your cupboard yeah + + + align:start position:0% +storing things in your cupboard yeah +okay you spot what you're missing you + + align:start position:0% +okay you spot what you're missing you + + + align:start position:0% +okay you spot what you're missing you +put it on your list those are con bonds + + align:start position:0% +put it on your list those are con bonds + + + align:start position:0% +put it on your list those are con bonds +okay con bond is nothing more then a + + align:start position:0% +okay con bond is nothing more then a + + + align:start position:0% +okay con bond is nothing more then a +queuing system a visual system to + + align:start position:0% +queuing system a visual system to + + + align:start position:0% +queuing system a visual system to +indicate what material parts or other + + align:start position:0% +indicate what material parts or other + + + align:start position:0% +indicate what material parts or other +information you need to keep going okay + + align:start position:0% +information you need to keep going okay + + + align:start position:0% +information you need to keep going okay +in a factory environment typically it's + + align:start position:0% +in a factory environment typically it's + + + align:start position:0% +in a factory environment typically it's +a card a barcoded card of some kind and + + align:start position:0% +a card a barcoded card of some kind and + + + align:start position:0% +a card a barcoded card of some kind and +uh at some + + align:start position:0% +uh at some + + + align:start position:0% +uh at some +station + + align:start position:0% +station + + + align:start position:0% +station +uh where they're manufacturing something + + align:start position:0% +uh where they're manufacturing something + + + align:start position:0% +uh where they're manufacturing something +or in a healthcare environment where + + align:start position:0% +or in a healthcare environment where + + + align:start position:0% +or in a healthcare environment where +they need some + + align:start position:0% +they need some + + + align:start position:0% +they need some +supplies um they need more of that and + + align:start position:0% +supplies um they need more of that and + + + align:start position:0% +supplies um they need more of that and +so they they make system and then + + align:start position:0% +so they they make system and then + + + align:start position:0% +so they they make system and then +someone delivers it okay now the the + + align:start position:0% +someone delivers it okay now the the + + + align:start position:0% +someone delivers it okay now the the +opposite is instead of instead of + + align:start position:0% +opposite is instead of instead of + + + align:start position:0% +opposite is instead of instead of +deciding what recipes you have and what + + align:start position:0% +deciding what recipes you have and what + + + align:start position:0% +deciding what recipes you have and what +you're going to buy you go to the store + + align:start position:0% +you're going to buy you go to the store + + + align:start position:0% +you're going to buy you go to the store +you say oh this is unsp special I'm + + align:start position:0% +you say oh this is unsp special I'm + + + align:start position:0% +you say oh this is unsp special I'm +going to load up on whatever you know + + align:start position:0% +going to load up on whatever you know + + + align:start position:0% +going to load up on whatever you know +Hamburger toilet paper catsup okay what + + align:start position:0% +Hamburger toilet paper catsup okay what + + + align:start position:0% +Hamburger toilet paper catsup okay what +you're doing is you're buying because + + align:start position:0% +you're doing is you're buying because + + + align:start position:0% +you're doing is you're buying because +you're getting volume discount but you + + align:start position:0% +you're getting volume discount but you + + + align:start position:0% +you're getting volume discount but you +may not need it so a con Bond system is + + align:start position:0% +may not need it so a con Bond system is + + + align:start position:0% +may not need it so a con Bond system is +one where you only deliver what's needed + + align:start position:0% +one where you only deliver what's needed + + + align:start position:0% +one where you only deliver what's needed +to whoever is doing the work and um and + + align:start position:0% +to whoever is doing the work and um and + + + align:start position:0% +to whoever is doing the work and um and +there's some cue usually visual cue it + + align:start position:0% +there's some cue usually visual cue it + + + align:start position:0% +there's some cue usually visual cue it +can be a a barcoded car could be a bin + + align:start position:0% +can be a a barcoded car could be a bin + + + align:start position:0% +can be a a barcoded car could be a bin +that's empty some space on the floor + + align:start position:0% +that's empty some space on the floor + + + align:start position:0% +that's empty some space on the floor +that's you know they need a new delivery + + align:start position:0% +that's you know they need a new delivery + + + align:start position:0% +that's you know they need a new delivery +there in an engineering environment or + + align:start position:0% +there in an engineering environment or + + + align:start position:0% +there in an engineering environment or +work office environment it might be an + + align:start position:0% +work office environment it might be an + + + align:start position:0% +work office environment it might be an +empty inbox I'll tell you an interesting + + align:start position:0% +empty inbox I'll tell you an interesting + + + align:start position:0% +empty inbox I'll tell you an interesting +conon I saw uh this is a factory at + + align:start position:0% +conon I saw uh this is a factory at + + + align:start position:0% +conon I saw uh this is a factory at +McDonald Douglas in East St Louis and + + align:start position:0% +McDonald Douglas in East St Louis and + + + align:start position:0% +McDonald Douglas in East St Louis and +they have supplies something coming from + + align:start position:0% +they have supplies something coming from + + + align:start position:0% +they have supplies something coming from +a company in California they make a + + align:start position:0% +a company in California they make a + + + align:start position:0% +a company in California they make a +packaging container that this product + + align:start position:0% +packaging container that this product + + + align:start position:0% +packaging container that this product +went into and so the companies in + + align:start position:0% +went into and so the companies in + + + align:start position:0% +went into and so the companies in +California the factories in East St + + align:start position:0% +California the factories in East St + + + align:start position:0% +California the factories in East St +Louis and on the + + align:start position:0% +Louis and on the + + + align:start position:0% +Louis and on the +ceiling is a camera looking down at the + + align:start position:0% +ceiling is a camera looking down at the + + + align:start position:0% +ceiling is a camera looking down at the +number of these boxes that are there and + + align:start position:0% +number of these boxes that are there and + + + align:start position:0% +number of these boxes that are there and +when the company in California sees they + + align:start position:0% +when the company in California sees they + + + align:start position:0% +when the company in California sees they +need more boxes they ship them okay + + align:start position:0% +need more boxes they ship them okay + + + align:start position:0% +need more boxes they ship them okay +that's a conon okay so Toyota + + align:start position:0% +that's a conon okay so Toyota + + + align:start position:0% +that's a conon okay so Toyota +implemented conon in their production + + align:start position:0% +implemented conon in their production + + + align:start position:0% +implemented conon in their production +system took them 20 + + align:start position:0% +system took them 20 + + + align:start position:0% +system took them 20 +years you wouldn't think it would take + + align:start position:0% +years you wouldn't think it would take + + + align:start position:0% +years you wouldn't think it would take +that long okay when they first started + + align:start position:0% +that long okay when they first started + + + align:start position:0% +that long okay when they first started +doing it they actually came to the + + align:start position:0% +doing it they actually came to the + + + align:start position:0% +doing it they actually came to the +United States and saw the supermarkets + + align:start position:0% +United States and saw the supermarkets + + + align:start position:0% +United States and saw the supermarkets +and then Supermarket you know the potato + + align:start position:0% +and then Supermarket you know the potato + + + align:start position:0% +and then Supermarket you know the potato +chips uh you buy potato chips and the + + align:start position:0% +chips uh you buy potato chips and the + + + align:start position:0% +chips uh you buy potato chips and the +Shelf looks empty so the potato chip guy + + align:start position:0% +Shelf looks empty so the potato chip guy + + + align:start position:0% +Shelf looks empty so the potato chip guy +comes and sees you need more potato + + align:start position:0% +comes and sees you need more potato + + + align:start position:0% +comes and sees you need more potato +chips that's where it came from + + align:start position:0% +chips that's where it came from + + + align:start position:0% +chips that's where it came from +supermarkets so they introduced it took + + align:start position:0% +supermarkets so they introduced it took + + + align:start position:0% +supermarkets so they introduced it took +them 10 years after they did the + + align:start position:0% +them 10 years after they did the + + + align:start position:0% +them 10 years after they did the +experiments to make it across the whole + + align:start position:0% +experiments to make it across the whole + + + align:start position:0% +experiments to make it across the whole +company and another 10 years to make it + + align:start position:0% +company and another 10 years to make it + + + align:start position:0% +company and another 10 years to make it +across their suppliers okay and they + + align:start position:0% +across their suppliers okay and they + + + align:start position:0% +across their suppliers okay and they +continued to work on so now think a + + align:start position:0% +continued to work on so now think a + + + align:start position:0% +continued to work on so now think a +little bit about what every Enterprise + + align:start position:0% +little bit about what every Enterprise + + + align:start position:0% +little bit about what every Enterprise +you might think about uh get out your + + align:start position:0% +you might think about uh get out your + + + align:start position:0% +you might think about uh get out your +colored cards here think about you know + + align:start position:0% +colored cards here think about you know + + + align:start position:0% +colored cards here think about you know +in where you've had some experiences how + + align:start position:0% +in where you've had some experiences how + + + align:start position:0% +in where you've had some experiences how +long do you think it would take to + + align:start position:0% +long do you think it would take to + + + align:start position:0% +long do you think it would take to +implement lean in some environment you + + align:start position:0% +implement lean in some environment you + + + align:start position:0% +implement lean in some environment you +could think about your company or your + + align:start position:0% +could think about your company or your + + + align:start position:0% +could think about your company or your +department at MIT think about lean + + align:start position:0% +department at MIT think about lean + + + align:start position:0% +department at MIT think about lean +thinking in your + + align:start position:0% +thinking in your + + + align:start position:0% +thinking in your +department um think about your parents + + align:start position:0% +department um think about your parents + + + align:start position:0% +department um think about your parents +work environment just to pick some work + + align:start position:0% +work environment just to pick some work + + + align:start position:0% +work environment just to pick some work +environment knowing that all that we + + align:start position:0% +environment knowing that all that we + + + align:start position:0% +environment knowing that all that we +could teach you in 3 days how long do + + align:start position:0% +could teach you in 3 days how long do + + + align:start position:0% +could teach you in 3 days how long do +you think it might take to implement + + align:start position:0% +you think it might take to implement + + + align:start position:0% +you think it might take to implement +lean in whatever work environment you're + + align:start position:0% +lean in whatever work environment you're + + + align:start position:0% +lean in whatever work environment you're +thinking about and then hold up the + + align:start position:0% +thinking about and then hold up the + + + align:start position:0% +thinking about and then hold up the +colored hard when you make up your + + align:start position:0% + + + + align:start position:0% + +mind okay I don't see any blues I see a + + align:start position:0% +mind okay I don't see any blues I see a + + + align:start position:0% +mind okay I don't see any blues I see a +lot of yellows a lot of greens that's + + align:start position:0% +lot of yellows a lot of greens that's + + + align:start position:0% +lot of yellows a lot of greens that's +good some Reds okay so it's going to + + align:start position:0% +good some Reds okay so it's going to + + + align:start position:0% +good some Reds okay so it's going to +take a little while maybe looks like I'd + + align:start position:0% +take a little while maybe looks like I'd + + + align:start position:0% +take a little while maybe looks like I'd +say the the bulk of the numbers I have + + align:start position:0% +say the the bulk of the numbers I have + + + align:start position:0% +say the the bulk of the numbers I have +up here are five years Susan you work + + align:start position:0% +up here are five years Susan you work + + + align:start position:0% +up here are five years Susan you work +with a lot of healthcare organizations + + align:start position:0% +with a lot of healthcare organizations + + + align:start position:0% +with a lot of healthcare organizations +you said you've been doing this for five + + align:start position:0% +you said you've been doing this for five + + + align:start position:0% +you said you've been doing this for five +years what kind of how long are you + + align:start position:0% +years what kind of how long are you + + + align:start position:0% +years what kind of how long are you +seeing that a typical healthc Care + + align:start position:0% +seeing that a typical healthc Care + + + align:start position:0% +seeing that a typical healthc Care +Organization most of the hospitals + + align:start position:0% +Organization most of the hospitals + + + align:start position:0% +Organization most of the hospitals +you've worked would take at least 5 + + align:start position:0% +you've worked would take at least 5 + + + align:start position:0% +you've worked would take at least 5 +years if not more because you really + + align:start position:0% +years if not more because you really + + + align:start position:0% +years if not more because you really +have to spread it throughout the + + align:start position:0% +have to spread it throughout the + + + align:start position:0% +have to spread it throughout the +organization and it takes that long you + + align:start position:0% +organization and it takes that long you + + + align:start position:0% +organization and it takes that long you +can't just teach five people and say + + align:start position:0% +can't just teach five people and say + + + align:start position:0% +can't just teach five people and say +okay we're Le so it's at least five + + align:start position:0% +okay we're Le so it's at least five + + + align:start position:0% +okay we're Le so it's at least five +years if not more and that's with an + + align:start position:0% +years if not more and that's with an + + + align:start position:0% +years if not more and that's with an +allout effort least five years with an + + align:start position:0% +allout effort least five years with an + + + align:start position:0% +allout effort least five years with an +allout effort not a half harded effort + + align:start position:0% +allout effort not a half harded effort + + + align:start position:0% +allout effort not a half harded effort +okay okay so this is a big commitment + + align:start position:0% +okay okay so this is a big commitment + + + align:start position:0% +okay okay so this is a big commitment +for an organization to implement lean + + align:start position:0% +for an organization to implement lean + + + align:start position:0% +for an organization to implement lean +okay they're not going to see + + align:start position:0% +okay they're not going to see + + + align:start position:0% +okay they're not going to see +quarterly bottom line profit changes + + align:start position:0% +quarterly bottom line profit changes + + + align:start position:0% +quarterly bottom line profit changes +which their shareholders may be looking + + align:start position:0% +which their shareholders may be looking + + + align:start position:0% +which their shareholders may be looking +for what are some questions that uh this + + align:start position:0% +for what are some questions that uh this + + + align:start position:0% +for what are some questions that uh this +introductory module kind of brings up in + + align:start position:0% +introductory module kind of brings up in + + + align:start position:0% +introductory module kind of brings up in +your mind or do you have comments you'd + + align:start position:0% +your mind or do you have comments you'd + + + align:start position:0% +your mind or do you have comments you'd +like to make or suggest or yeah um for + + align:start position:0% +like to make or suggest or yeah um for + + + align:start position:0% +like to make or suggest or yeah um for +the 6s activity if you had asked me to + + align:start position:0% +the 6s activity if you had asked me to + + + align:start position:0% +the 6s activity if you had asked me to +sort that stuff in the very beginning I + + align:start position:0% +sort that stuff in the very beginning I + + + align:start position:0% +sort that stuff in the very beginning I +probably would have ended at the end + + align:start position:0% +probably would have ended at the end + + + align:start position:0% +probably would have ended at the end +page first with everything in if you + + align:start position:0% +page first with everything in if you + + + align:start position:0% +page first with everything in if you +just had sort these things it would have + + align:start position:0% +just had sort these things it would have + + + align:start position:0% +just had sort these things it would have +been Super Sub selected which might just + + align:start position:0% +been Super Sub selected which might just + + + align:start position:0% +been Super Sub selected which might just +be my own personality when somebody says + + align:start position:0% +be my own personality when somebody says + + + align:start position:0% +be my own personality when somebody says +sort so I'm a little um unclear on what + + align:start position:0% +sort so I'm a little um unclear on what + + + align:start position:0% +sort so I'm a little um unclear on what +the difference between sort standard um + + align:start position:0% +the difference between sort standard um + + + align:start position:0% +the difference between sort standard um +straight and standardized are in that + + align:start position:0% +straight and standardized are in that + + + align:start position:0% +straight and standardized are in that +respect that's a good question you know + + align:start position:0% +respect that's a good question you know + + + align:start position:0% +respect that's a good question you know +I I I think the sort one is first of all + + align:start position:0% +I I I think the sort one is first of all + + + align:start position:0% +I I I think the sort one is first of all +just get rid of stuff that shouldn't be + + align:start position:0% +just get rid of stuff that shouldn't be + + + align:start position:0% +just get rid of stuff that shouldn't be +there okay and uh I I have slides from a + + align:start position:0% +there okay and uh I I have slides from a + + + align:start position:0% +there okay and uh I I have slides from a +lot of different examples of store rooms + + align:start position:0% +lot of different examples of store rooms + + + align:start position:0% +lot of different examples of store rooms +that had you know totally obsolete + + align:start position:0% +that had you know totally obsolete + + + align:start position:0% +that had you know totally obsolete +equipment in them and people were + + align:start position:0% +equipment in them and people were + + + align:start position:0% +equipment in them and people were +spending lots of time looking for + + align:start position:0% +spending lots of time looking for + + + align:start position:0% +spending lots of time looking for +something that was not all that obsolete + + align:start position:0% +something that was not all that obsolete + + + align:start position:0% +something that was not all that obsolete +equipment so I think the sort part is + + align:start position:0% +equipment so I think the sort part is + + + align:start position:0% +equipment so I think the sort part is +pretty quick now the the straighten and + + align:start position:0% +pretty quick now the the straighten and + + + align:start position:0% +pretty quick now the the straighten and +standardize I think might be done as a + + align:start position:0% +standardize I think might be done as a + + + align:start position:0% +standardize I think might be done as a +single step okay uh but + + align:start position:0% +single step okay uh but + + + align:start position:0% +single step okay uh but +it I'm not going to I think it's you're + + align:start position:0% +it I'm not going to I think it's you're + + + align:start position:0% +it I'm not going to I think it's you're +fine it's a good comment but what's + + align:start position:0% +fine it's a good comment but what's + + + align:start position:0% +fine it's a good comment but what's +amazing to me is how often an + + align:start position:0% +amazing to me is how often an + + + align:start position:0% +amazing to me is how often an +organization starts with 5S I mean you + + align:start position:0% +organization starts with 5S I mean you + + + align:start position:0% +organization starts with 5S I mean you +would think why isn't anybody doing it + + align:start position:0% +would think why isn't anybody doing it + + + align:start position:0% +would think why isn't anybody doing it +this way it's it's because and we hear + + align:start position:0% +this way it's it's because and we hear + + + align:start position:0% +this way it's it's because and we hear +this term all the time it's the way + + align:start position:0% +this term all the time it's the way + + + align:start position:0% +this term all the time it's the way +we've always done it it's what we always + + align:start position:0% +we've always done it it's what we always + + + align:start position:0% +we've always done it it's what we always +hear because it's the way we and + + align:start position:0% +hear because it's the way we and + + + align:start position:0% +hear because it's the way we and +workarounds and doovers have been built + + align:start position:0% +workarounds and doovers have been built + + + align:start position:0% +workarounds and doovers have been built +into the system so nobody even + + align:start position:0% +into the system so nobody even + + + align:start position:0% +into the system so nobody even +recognizes that they're doing it + + align:start position:0% +recognizes that they're doing it + + + align:start position:0% +recognizes that they're doing it +just becomes part of the daily work you + + align:start position:0% +just becomes part of the daily work you + + + align:start position:0% +just becomes part of the daily work you +have a question Monica yeah I was just + + align:start position:0% +have a question Monica yeah I was just + + + align:start position:0% +have a question Monica yeah I was just +wondering you said that the average time + + align:start position:0% +wondering you said that the average time + + + align:start position:0% +wondering you said that the average time +is 5 years so I just wondering in our + + align:start position:0% +is 5 years so I just wondering in our + + + align:start position:0% +is 5 years so I just wondering in our +culture of immediate + + align:start position:0% +culture of immediate + + + align:start position:0% +culture of immediate +response time and response to crisis how + + align:start position:0% +response time and response to crisis how + + + align:start position:0% +response time and response to crisis how +do you sustain an organization's + + align:start position:0% +do you sustain an organization's + + + align:start position:0% +do you sustain an organization's +interest that's a really really good + + align:start position:0% +interest that's a really really good + + + align:start position:0% +interest that's a really really good +question + + align:start position:0% +question + + + align:start position:0% +question +uh I'll answer what I can and Bo and Sue + + align:start position:0% +uh I'll answer what I can and Bo and Sue + + + align:start position:0% +uh I'll answer what I can and Bo and Sue +and others can pipe in first of all you + + align:start position:0% +and others can pipe in first of all you + + + align:start position:0% +and others can pipe in first of all you +have to have this so-called burning + + align:start position:0% +have to have this so-called burning + + + align:start position:0% +have to have this so-called burning +platform that is there's sort of no + + align:start position:0% +platform that is there's sort of no + + + align:start position:0% +platform that is there's sort of no +other option either we do it or we go + + align:start position:0% +other option either we do it or we go + + + align:start position:0% +other option either we do it or we go +out of business okay so it's very hard + + align:start position:0% +out of business okay so it's very hard + + + align:start position:0% +out of business okay so it's very hard +for an organization that's doing + + align:start position:0% +for an organization that's doing + + + align:start position:0% +for an organization that's doing +extremely well to adopt something like + + align:start position:0% +extremely well to adopt something like + + + align:start position:0% +extremely well to adopt something like +this + + align:start position:0% +this + + + align:start position:0% +this +um secondly it takes leadership you know + + align:start position:0% +um secondly it takes leadership you know + + + align:start position:0% +um secondly it takes leadership you know +it it has to be that the the the + + align:start position:0% +it it has to be that the the the + + + align:start position:0% +it it has to be that the the the +organizational leadership says this is + + align:start position:0% +organizational leadership says this is + + + align:start position:0% +organizational leadership says this is +important and we're going to have + + align:start position:0% +important and we're going to have + + + align:start position:0% +important and we're going to have +constancy of purpose and sustain this + + align:start position:0% +constancy of purpose and sustain this + + + align:start position:0% +constancy of purpose and sustain this +we're going to start this and do it and + + align:start position:0% +we're going to start this and do it and + + + align:start position:0% +we're going to start this and do it and +stay with it and then third it has to + + align:start position:0% +stay with it and then third it has to + + + align:start position:0% +stay with it and then third it has to +align with the strategy the organization + + align:start position:0% +align with the strategy the organization + + + align:start position:0% +align with the strategy the organization +that is has to be built into what the + + align:start position:0% +that is has to be built into what the + + + align:start position:0% +that is has to be built into what the +organization is trying to do it can't be + + align:start position:0% +organization is trying to do it can't be + + + align:start position:0% +organization is trying to do it can't be +something separate we're trying to do + + align:start position:0% +something separate we're trying to do + + + align:start position:0% +something separate we're trying to do +this and Meanwhile we're going to do + + align:start position:0% +this and Meanwhile we're going to do + + + align:start position:0% +this and Meanwhile we're going to do +lean the two have to be together and uh + + align:start position:0% +lean the two have to be together and uh + + + align:start position:0% +lean the two have to be together and uh +frankly many organizations can't do it + + align:start position:0% +frankly many organizations can't do it + + + align:start position:0% +frankly many organizations can't do it +yeah I can answer that too it's all it's + + align:start position:0% +yeah I can answer that too it's all it's + + + align:start position:0% +yeah I can answer that too it's all it's +also a series of incremental changes so + + align:start position:0% +also a series of incremental changes so + + + align:start position:0% +also a series of incremental changes so +if something happens like a medication + + align:start position:0% +if something happens like a medication + + + align:start position:0% +if something happens like a medication +error that's disastrous you can + + align:start position:0% +error that's disastrous you can + + + align:start position:0% +error that's disastrous you can +certainly start with that and as you + + align:start position:0% +certainly start with that and as you + + + align:start position:0% +certainly start with that and as you +have improvements you celebrate those + + align:start position:0% +have improvements you celebrate those + + + align:start position:0% +have improvements you celebrate those +improvements and distribute that + + align:start position:0% +improvements and distribute that + + + align:start position:0% +improvements and distribute that +information so that it's a continuous + + align:start position:0% +information so that it's a continuous + + + align:start position:0% +information so that it's a continuous +Improvement and it can happen over time + + align:start position:0% +Improvement and it can happen over time + + + align:start position:0% +Improvement and it can happen over time +with really good things happening along + + align:start position:0% +with really good things happening along + + + align:start position:0% +with really good things happening along +the way but to roll it out to an entire + + align:start position:0% +the way but to roll it out to an entire + + + align:start position:0% +the way but to roll it out to an entire +organization takes a long time but we + + align:start position:0% +organization takes a long time but we + + + align:start position:0% +organization takes a long time but we +tell people you have to start somewhere + + align:start position:0% +tell people you have to start somewhere + + + align:start position:0% +tell people you have to start somewhere +and it's not like it's going to alter + + align:start position:0% +and it's not like it's going to alter + + + align:start position:0% +and it's not like it's going to alter +your whole organization overnight it's + + align:start position:0% +your whole organization overnight it's + + + align:start position:0% +your whole organization overnight it's +celebrating those incremental things + + align:start position:0% +celebrating those incremental things + + + align:start position:0% +celebrating those incremental things +that you do looking at your data looking + + align:start position:0% +that you do looking at your data looking + + + align:start position:0% +that you do looking at your data looking +at your outcomes looking at your step + + align:start position:0% +at your outcomes looking at your step + + + align:start position:0% +at your outcomes looking at your step +turnover and and using that to build + + align:start position:0% +turnover and and using that to build + + + align:start position:0% +turnover and and using that to build +your lean program so it takes time but + + align:start position:0% +your lean program so it takes time but + + + align:start position:0% +your lean program so it takes time but +you can celebrate things along the way + + align:start position:0% +you can celebrate things along the way + + + align:start position:0% +you can celebrate things along the way +the biggest I think the biggest + + align:start position:0% +the biggest I think the biggest + + + align:start position:0% +the biggest I think the biggest +um barrier to this is if there's a + + align:start position:0% +um barrier to this is if there's a + + + align:start position:0% +um barrier to this is if there's a +change in the leadership at the top and + + align:start position:0% +change in the leadership at the top and + + + align:start position:0% +change in the leadership at the top and +the new person doesn't really understand + + align:start position:0% +the new person doesn't really understand + + + align:start position:0% +the new person doesn't really understand +it and then you know the whole thing can + + align:start position:0% +it and then you know the whole thing can + + + align:start position:0% +it and then you know the whole thing can +crash both I think as well it's + + align:start position:0% +crash both I think as well it's + + + align:start position:0% +crash both I think as well it's +important that you have a vision that + + align:start position:0% +important that you have a vision that + + + align:start position:0% +important that you have a vision that +your organization has a vision and that + + align:start position:0% +your organization has a vision and that + + + align:start position:0% +your organization has a vision and that +everybody knows what that vision is and + + align:start position:0% +everybody knows what that vision is and + + + align:start position:0% +everybody knows what that vision is and +then the beginning is the hardest but in + + align:start position:0% +then the beginning is the hardest but in + + + align:start position:0% +then the beginning is the hardest but in +reality we all want to do value added + + align:start position:0% +reality we all want to do value added + + + align:start position:0% +reality we all want to do value added +work we want to do the work that we're + + align:start position:0% +work we want to do the work that we're + + + align:start position:0% +work we want to do the work that we're +actually employed to do people they + + align:start position:0% +actually employed to do people they + + + align:start position:0% +actually employed to do people they +enjoy that when they can see with the + + align:start position:0% +enjoy that when they can see with the + + + align:start position:0% +enjoy that when they can see with the +first steps that the waste that they + + align:start position:0% +first steps that the waste that they + + + align:start position:0% +first steps that the waste that they +that were sucked into every day that + + align:start position:0% +that were sucked into every day that + + + align:start position:0% +that were sucked into every day that +that goes away and you're more + + align:start position:0% +that goes away and you're more + + + align:start position:0% +that goes away and you're more +productive that's nice people they enjoy + + align:start position:0% +productive that's nice people they enjoy + + + align:start position:0% +productive that's nice people they enjoy +that what are good what what are some + + align:start position:0% +that what are good what what are some + + + align:start position:0% +that what are good what what are some +questions that come from from the uh + + align:start position:0% +questions that come from from the uh + + + align:start position:0% +questions that come from from the uh +from the engineering folks here yeah + + align:start position:0% +from the engineering folks here yeah + + + align:start position:0% +from the engineering folks here yeah +real so at some point you pointed out + + align:start position:0% +real so at some point you pointed out + + + align:start position:0% +real so at some point you pointed out +the disparity between how many hours of + + align:start position:0% +the disparity between how many hours of + + + align:start position:0% +the disparity between how many hours of +training both um United States and + + align:start position:0% +training both um United States and + + + align:start position:0% +training both um United States and +exactly inter workers and this might be + + align:start position:0% +exactly inter workers and this might be + + + align:start position:0% +exactly inter workers and this might be +silly but it seems that the people are + + align:start position:0% +silly but it seems that the people are + + + align:start position:0% +silly but it seems that the people are +what pretty much Mak the company Rong so + + align:start position:0% +what pretty much Mak the company Rong so + + + align:start position:0% +what pretty much Mak the company Rong so +if they're spending so much time + + align:start position:0% +if they're spending so much time + + + align:start position:0% +if they're spending so much time +training their um workers and getting so + + align:start position:0% +training their um workers and getting so + + + align:start position:0% +training their um workers and getting so +much profit off it how in the world are + + align:start position:0% +much profit off it how in the world are + + + align:start position:0% +much profit off it how in the world are +how are we not doing the same + + align:start position:0% +how are we not doing the same + + + align:start position:0% +how are we not doing the same +thing so it's a question is a question + + align:start position:0% +thing so it's a question is a question + + + align:start position:0% +thing so it's a question is a question +does training detect from the productive + + align:start position:0% +does training detect from the productive + + + align:start position:0% +does training detect from the productive +no my question is why aren't we + + align:start position:0% +no my question is why aren't we + + + align:start position:0% +no my question is why aren't we +investing more into training yeah so + + align:start position:0% +investing more into training yeah so + + + align:start position:0% +investing more into training yeah so +that that's been a real change in the US + + align:start position:0% +that that's been a real change in the US + + + align:start position:0% +that that's been a real change in the US +companies as they've adopted these as + + align:start position:0% +companies as they've adopted these as + + + align:start position:0% +companies as they've adopted these as +they they've come to realize the + + align:start position:0% +they they've come to realize the + + + align:start position:0% +they they've come to realize the +importance of training they do invest a + + align:start position:0% +importance of training they do invest a + + + align:start position:0% +importance of training they do invest a +lot in + + align:start position:0% +lot in + + + align:start position:0% +lot in +training uh the typical company that I + + align:start position:0% +training uh the typical company that I + + + align:start position:0% +training uh the typical company that I +know of in the US will invest at least + + align:start position:0% +know of in the US will invest at least + + + align:start position:0% +know of in the US will invest at least +40 hours a week for every employee to be + + align:start position:0% +40 hours a week for every employee to be + + + align:start position:0% +40 hours a week for every employee to be +trained during the year and training can + + align:start position:0% +trained during the year and training can + + + align:start position:0% +trained during the year and training can +be broad it can be it could be specific + + align:start position:0% +be broad it can be it could be specific + + + align:start position:0% +be broad it can be it could be specific +to that particular job but it be much + + align:start position:0% +to that particular job but it be much + + + align:start position:0% +to that particular job but it be much +broader just communication skills + + align:start position:0% +broader just communication skills + + + align:start position:0% +broader just communication skills +or sometimes even just awareness about + + align:start position:0% +or sometimes even just awareness about + + + align:start position:0% +or sometimes even just awareness about +their culture of the customers in other + + align:start position:0% +their culture of the customers in other + + + align:start position:0% +their culture of the customers in other +countries do you think the difference is + + align:start position:0% +countries do you think the difference is + + + align:start position:0% +countries do you think the difference is +not in training hours anymore but in the + + align:start position:0% +not in training hours anymore but in the + + + align:start position:0% +not in training hours anymore but in the +workers + + align:start position:0% +workers + + + align:start position:0% +workers +themselves well I don't know I'm not + + align:start position:0% +themselves well I don't know I'm not + + + align:start position:0% +themselves well I don't know I'm not +sure I can answer I can say that they + + align:start position:0% +sure I can answer I can say that they + + + align:start position:0% +sure I can answer I can say that they +are investing more in training hours + + align:start position:0% +are investing more in training hours + + + align:start position:0% +are investing more in training hours +whether it's because the workers are + + align:start position:0% +whether it's because the workers are + + + align:start position:0% +whether it's because the workers are +different I don't know yeah there may be + + align:start position:0% +different I don't know yeah there may be + + + align:start position:0% +different I don't know yeah there may be +a chicken and egg situation there one + + align:start position:0% +a chicken and egg situation there one + + + align:start position:0% +a chicken and egg situation there one +take question here and then we'll come + + align:start position:0% +take question here and then we'll come + + + align:start position:0% +take question here and then we'll come +back okay so you you mentioned that a + + align:start position:0% +back okay so you you mentioned that a + + + align:start position:0% +back okay so you you mentioned that a +lean Enterprise creates value to + + align:start position:0% +lean Enterprise creates value to + + + align:start position:0% +lean Enterprise creates value to +multiple stakeholders yeah right so what + + align:start position:0% +multiple stakeholders yeah right so what + + + align:start position:0% +multiple stakeholders yeah right so what +happen if those values are not necessar + + align:start position:0% +happen if those values are not necessar + + + align:start position:0% +happen if those values are not necessar +align + + align:start position:0% +align + + + align:start position:0% +align +align I'm thinking sometimes you you + + align:start position:0% +align I'm thinking sometimes you you + + + align:start position:0% +align I'm thinking sometimes you you +have the shareholders they might be + + align:start position:0% +have the shareholders they might be + + + align:start position:0% +have the shareholders they might be +willing to move the Enterprise transform + + align:start position:0% +willing to move the Enterprise transform + + + align:start position:0% +willing to move the Enterprise transform +the Enterprise to One Direction yeah you + + align:start position:0% +the Enterprise to One Direction yeah you + + + align:start position:0% +the Enterprise to One Direction yeah you +can have the employees they don't want + + align:start position:0% +can have the employees they don't want + + + align:start position:0% +can have the employees they don't want +change because they're comfortable in + + align:start position:0% +change because they're comfortable in + + + align:start position:0% +change because they're comfortable in +that sitation I don't know it's a great + + align:start position:0% +that sitation I don't know it's a great + + + align:start position:0% +that sitation I don't know it's a great +question yeah + + align:start position:0% +question yeah + + + align:start position:0% +question yeah +is the shareholders values are are not + + align:start position:0% +is the shareholders values are are not + + + align:start position:0% +is the shareholders values are are not +always will will normally not be aligned + + align:start position:0% +always will will normally not be aligned + + + align:start position:0% +always will will normally not be aligned +completely okay so you have to do the + + align:start position:0% +completely okay so you have to do the + + + align:start position:0% +completely okay so you have to do the +best you can okay I mean you're you you + + align:start position:0% +best you can okay I mean you're you you + + + align:start position:0% +best you can okay I mean you're you you +have to find something I mean the ideal + + align:start position:0% +have to find something I mean the ideal + + + align:start position:0% +have to find something I mean the ideal +is if you could find something where + + align:start position:0% +is if you could find something where + + + align:start position:0% +is if you could find something where +every stakeholder gains something maybe + + align:start position:0% +every stakeholder gains something maybe + + + align:start position:0% +every stakeholder gains something maybe +they don't gain everything they want but + + align:start position:0% +they don't gain everything they want but + + + align:start position:0% +they don't gain everything they want but +they gain something something's better + + align:start position:0% +they gain something something's better + + + align:start position:0% +they gain something something's better +than before okay so let me take an + + align:start position:0% +than before okay so let me take an + + + align:start position:0% +than before okay so let me take an +employee thing + + align:start position:0% + + + + align:start position:0% + +um I think one of the the question + + align:start position:0% +um I think one of the the question + + + align:start position:0% +um I think one of the the question +Monica asked relates to that too one of + + align:start position:0% +Monica asked relates to that too one of + + + align:start position:0% +Monica asked relates to that too one of +the things that one of the things that + + align:start position:0% +the things that one of the things that + + + align:start position:0% +the things that one of the things that +successful organizations do the + + align:start position:0% +successful organizations do the + + + align:start position:0% +successful organizations do the +Implement lean is they they make it + + align:start position:0% +Implement lean is they they make it + + + align:start position:0% +Implement lean is they they make it +known to their employees that nobody's + + align:start position:0% +known to their employees that nobody's + + + align:start position:0% +known to their employees that nobody's +going to lose their job because of + + align:start position:0% +going to lose their job because of + + + align:start position:0% +going to lose their job because of +increas in + + align:start position:0% +increas in + + + align:start position:0% +increas in +productivity okay so it's very hard if + + align:start position:0% +productivity okay so it's very hard if + + + align:start position:0% +productivity okay so it's very hard if +you go into an organization and say + + align:start position:0% +you go into an organization and say + + + align:start position:0% +you go into an organization and say +Emily I want you to help improve us and + + align:start position:0% +Emily I want you to help improve us and + + + align:start position:0% +Emily I want you to help improve us and +by the way we probably won't need you + + align:start position:0% +by the way we probably won't need you + + + align:start position:0% +by the way we probably won't need you +when we're finished okay your heart's + + align:start position:0% +when we're finished okay your heart's + + + align:start position:0% +when we're finished okay your heart's +not going to be in in that so so instead + + align:start position:0% +not going to be in in that so so instead + + + align:start position:0% +not going to be in in that so so instead +you say Emily + + align:start position:0% +you say Emily + + + align:start position:0% +you say Emily +we want to have a better organization + + align:start position:0% +we want to have a better organization + + + align:start position:0% +we want to have a better organization +and you're going to be part of it you + + align:start position:0% +and you're going to be part of it you + + + align:start position:0% +and you're going to be part of it you +may not be doing the same thing you were + + align:start position:0% +may not be doing the same thing you were + + + align:start position:0% +may not be doing the same thing you were +doing before we may have to train you to + + align:start position:0% +doing before we may have to train you to + + + align:start position:0% +doing before we may have to train you to +do something else or we may have to do + + align:start position:0% +do something else or we may have to do + + + align:start position:0% +do something else or we may have to do +something but but you're valuable to us + + align:start position:0% +something but but you're valuable to us + + + align:start position:0% +something but but you're valuable to us +and we want you here and now we want you + + align:start position:0% +and we want you here and now we want you + + + align:start position:0% +and we want you here and now we want you +to help us improve so Emily is going to + + align:start position:0% +to help us improve so Emily is going to + + + align:start position:0% +to help us improve so Emily is going to +come out she'll probably be happier when + + align:start position:0% +come out she'll probably be happier when + + + align:start position:0% +come out she'll probably be happier when +she's done because she's probably not + + align:start position:0% +she's done because she's probably not + + + align:start position:0% +she's done because she's probably not +completely satisfied with her job and + + align:start position:0% +completely satisfied with her job and + + + align:start position:0% +completely satisfied with her job and +they'll be more productive and maybe + + align:start position:0% +they'll be more productive and maybe + + + align:start position:0% +they'll be more productive and maybe +they end up Outsourcing stuff uh but + + align:start position:0% +they end up Outsourcing stuff uh but + + + align:start position:0% +they end up Outsourcing stuff uh but +they'll find a place for Emily in the + + align:start position:0% +they'll find a place for Emily in the + + + align:start position:0% +they'll find a place for Emily in the +organization so you want to make sure + + align:start position:0% +organization so you want to make sure + + + align:start position:0% +organization so you want to make sure +it's as much of a win-win as you can and + + align:start position:0% +it's as much of a win-win as you can and + + + align:start position:0% +it's as much of a win-win as you can and +that's a challenge I mean sometimes you + + align:start position:0% +that's a challenge I mean sometimes you + + + align:start position:0% +that's a challenge I mean sometimes you +you + + align:start position:0% +you + + + align:start position:0% +you +know sometimes it's hard and and and it + + align:start position:0% +know sometimes it's hard and and and it + + + align:start position:0% +know sometimes it's hard and and and it +unfortunately the short-term focus of + + align:start position:0% +unfortunately the short-term focus of + + + align:start position:0% +unfortunately the short-term focus of +our financial + + align:start position:0% +our financial + + + align:start position:0% +our financial +system is a barrier for some of these + + align:start position:0% +system is a barrier for some of these + + + align:start position:0% +system is a barrier for some of these +long-term commitments so it takes a lot + + align:start position:0% +long-term commitments so it takes a lot + + + align:start position:0% +long-term commitments so it takes a lot +of strong leadership to overcome that + + align:start position:0% +of strong leadership to overcome that + + + align:start position:0% +of strong leadership to overcome that +and I think Susan's good you want to + + align:start position:0% +and I think Susan's good you want to + + + align:start position:0% +and I think Susan's good you want to +show show incremental + + align:start position:0% +show show incremental + + + align:start position:0% +show show incremental +Improvement want to try to get better + + align:start position:0% +Improvement want to try to get better + + + align:start position:0% +Improvement want to try to get better +and better and better + + align:start position:0% +and better and better + + + align:start position:0% +and better and better +I also think that the equation in + + align:start position:0% +I also think that the equation in + + + align:start position:0% +I also think that the equation in +healthc care traditionally has been that + + align:start position:0% +healthc care traditionally has been that + + + align:start position:0% +healthc care traditionally has been that +employees were on the expense side of + + align:start position:0% +employees were on the expense side of + + + align:start position:0% +employees were on the expense side of +the + + align:start position:0% +the + + + align:start position:0% +the +equation and so when they needed to cut + + align:start position:0% +equation and so when they needed to cut + + + align:start position:0% +equation and so when they needed to cut +cost they cut positions and what Toyota + + align:start position:0% +cost they cut positions and what Toyota + + + align:start position:0% +cost they cut positions and what Toyota +does is their employees are on the value + + align:start position:0% +does is their employees are on the value + + + align:start position:0% +does is their employees are on the value +side of the equation and so they value + + align:start position:0% +side of the equation and so they value + + + align:start position:0% +side of the equation and so they value +those employees and that makes the + + align:start position:0% +those employees and that makes the + + + align:start position:0% +those employees and that makes the +difference in the expense side as well + + align:start position:0% +difference in the expense side as well + + + align:start position:0% +difference in the expense side as well +and I think that makes a difference + + align:start position:0% +and I think that makes a difference + + + align:start position:0% +and I think that makes a difference +because Toyota expects their employees + + align:start position:0% +because Toyota expects their employees + + + align:start position:0% +because Toyota expects their employees +to make suggestions and they Implement + + align:start position:0% +to make suggestions and they Implement + + + align:start position:0% +to make suggestions and they Implement +their suggestions we in healthcare we + + align:start position:0% +their suggestions we in healthcare we + + + align:start position:0% +their suggestions we in healthcare we +haven't done a good job at doing that + + align:start position:0% +haven't done a good job at doing that + + + align:start position:0% +haven't done a good job at doing that +employees were just employees and now + + align:start position:0% +employees were just employees and now + + + align:start position:0% +employees were just employees and now +they're starting to see that employees + + align:start position:0% +they're starting to see that employees + + + align:start position:0% +they're starting to see that employees +are the experts at what they do and so + + align:start position:0% +are the experts at what they do and so + + + align:start position:0% +are the experts at what they do and so +we need to start listening to them and I + + align:start position:0% +we need to start listening to them and I + + + align:start position:0% +we need to start listening to them and I +have an example I was doing work at a + + align:start position:0% +have an example I was doing work at a + + + align:start position:0% +have an example I was doing work at a +small rural Hospital in Northern New + + align:start position:0% +small rural Hospital in Northern New + + + align:start position:0% +small rural Hospital in Northern New +England 50 bed hospital and this class I + + align:start position:0% +England 50 bed hospital and this class I + + + align:start position:0% +England 50 bed hospital and this class I +did two classes of 16 people and they + + align:start position:0% +did two classes of 16 people and they + + + align:start position:0% +did two classes of 16 people and they +were working on some productivity kinds + + align:start position:0% +were working on some productivity kinds + + + align:start position:0% +were working on some productivity kinds +of issues and they came up with $3 + + align:start position:0% +of issues and they came up with $3 + + + align:start position:0% +of issues and they came up with $3 +million in savings for delayed o start + + align:start position:0% +million in savings for delayed o start + + + align:start position:0% +million in savings for delayed o start +time + + align:start position:0% +time + + + align:start position:0% +time +and and canceled Imaging tests and all + + align:start position:0% +and and canceled Imaging tests and all + + + align:start position:0% +and and canceled Imaging tests and all +those kinds of things and they really + + align:start position:0% +those kinds of things and they really + + + align:start position:0% +those kinds of things and they really +did a beautiful job with their projects + + align:start position:0% +did a beautiful job with their projects + + + align:start position:0% +did a beautiful job with their projects +and the last day at report out the CEO + + align:start position:0% +and the last day at report out the CEO + + + align:start position:0% +and the last day at report out the CEO +was there he didn't hire us it was a + + align:start position:0% +was there he didn't hire us it was a + + + align:start position:0% +was there he didn't hire us it was a +grant through the state so they did this + + align:start position:0% +grant through the state so they did this + + + align:start position:0% +grant through the state so they did this +report out and talked about what they + + align:start position:0% +report out and talked about what they + + + align:start position:0% +report out and talked about what they +found and at the end he said this really + + align:start position:0% +found and at the end he said this really + + + align:start position:0% +found and at the end he said this really +makes me look + + align:start position:0% +makes me look + + + align:start position:0% +makes me look +bad and I said excuse me and he said I + + align:start position:0% +bad and I said excuse me and he said I + + + align:start position:0% +bad and I said excuse me and he said I +should have fixed these + + align:start position:0% + + + + align:start position:0% + +things it was just it was the old + + align:start position:0% +things it was just it was the old + + + align:start position:0% +things it was just it was the old +traditional model of the high I tell you + + align:start position:0% +traditional model of the high I tell you + + + align:start position:0% +traditional model of the high I tell you +what to do and you do it if I tell you + + align:start position:0% +what to do and you do it if I tell you + + + align:start position:0% +what to do and you do it if I tell you +to cut 10% off your budget you do it not + + align:start position:0% +to cut 10% off your budget you do it not + + + align:start position:0% +to cut 10% off your budget you do it not +show me how you can increase throughput + + align:start position:0% +show me how you can increase throughput + + + align:start position:0% +show me how you can increase throughput +and revenue so we need to just change + + align:start position:0% +and revenue so we need to just change + + + align:start position:0% +and revenue so we need to just change +our thinking in healthcare and it's + + align:start position:0% +our thinking in healthcare and it's + + + align:start position:0% +our thinking in healthcare and it's +happening but very slowly and valuing + + align:start position:0% +happening but very slowly and valuing + + + align:start position:0% +happening but very slowly and valuing +the employee is the most important thing + + align:start position:0% +the employee is the most important thing + + + align:start position:0% +the employee is the most important thing +we need to do and unfortunately the term + + align:start position:0% +we need to do and unfortunately the term + + + align:start position:0% +we need to do and unfortunately the term +lean gives people the absolute fear that + + align:start position:0% +lean gives people the absolute fear that + + + align:start position:0% +lean gives people the absolute fear that +we're going to cut positions that's what + + align:start position:0% +we're going to cut positions that's what + + + align:start position:0% +we're going to cut positions that's what +they immediately think when you say + + align:start position:0% +they immediately think when you say + + + align:start position:0% +they immediately think when you say +we're coming in to do the the word too + + align:start position:0% +we're coming in to do the the word too + + + align:start position:0% +we're coming in to do the the word too +bad the lean became word it's like exact + + align:start position:0% +bad the lean became word it's like exact + + + align:start position:0% +bad the lean became word it's like exact +it's like the you know evolution of + + align:start position:0% +it's like the you know evolution of + + + align:start position:0% +it's like the you know evolution of +Industry I showed you we can't change + + align:start position:0% +Industry I showed you we can't change + + + align:start position:0% +Industry I showed you we can't change +the word now it's it's just become part + + align:start position:0% +the word now it's it's just become part + + + align:start position:0% +the word now it's it's just become part +of it it it came actually from a MIT + + align:start position:0% +of it it it came actually from a MIT + + + align:start position:0% +of it it it came actually from a MIT +graduate student in a research seminar + + align:start position:0% +graduate student in a research seminar + + + align:start position:0% +graduate student in a research seminar +one day when they were talking about + + align:start position:0% +one day when they were talking about + + + align:start position:0% +one day when they were talking about +this things they were learning about the + + align:start position:0% +this things they were learning about the + + + align:start position:0% +this things they were learning about the +Japanese + + align:start position:0% +Japanese + + + align:start position:0% +Japanese +automotive industry and and and they + + align:start position:0% +automotive industry and and and they + + + align:start position:0% +automotive industry and and and they +said what are we going to call this and + + align:start position:0% +said what are we going to call this and + + + align:start position:0% +said what are we going to call this and +he said well let's call it lean because + + align:start position:0% +he said well let's call it lean because + + + align:start position:0% +he said well let's call it lean because +we're doing more with less and it's + + align:start position:0% +we're doing more with less and it's + + + align:start position:0% +we're doing more with less and it's +stuck but it's unfortunately has a + + align:start position:0% +stuck but it's unfortunately has a + + + align:start position:0% +stuck but it's unfortunately has a +negative sound to it lean and mean and + + align:start position:0% +negative sound to it lean and mean and + + + align:start position:0% +negative sound to it lean and mean and +all that kind of stuff so we have time + + align:start position:0% +all that kind of stuff so we have time + + + align:start position:0% +all that kind of stuff so we have time +for one more question did you have a + + align:start position:0% +for one more question did you have a + + + align:start position:0% +for one more question did you have a +question uh yeah also I'm going to play + + align:start position:0% +question uh yeah also I'm going to play + + + align:start position:0% +question uh yeah also I'm going to play +the skeptic a little bit how do you + + align:start position:0% +the skeptic a little bit how do you + + + align:start position:0% +the skeptic a little bit how do you +establish causation between these + + align:start position:0% +establish causation between these + + + align:start position:0% +establish causation between these +methods and and you how is it not just + + align:start position:0% +methods and and you how is it not just + + + align:start position:0% +methods and and you how is it not just +an improvement in employee I want to + + align:start position:0% +an improvement in employee I want to + + + align:start position:0% +an improvement in employee I want to +have company supped to just sit back and + + align:start position:0% +have company supped to just sit back and + + + align:start position:0% +have company supped to just sit back and +that's a really good question how can we + + align:start position:0% +that's a really good question how can we + + + align:start position:0% +that's a really good question how can we +show that the kind of results we showed + + align:start position:0% +show that the kind of results we showed + + + align:start position:0% +show that the kind of results we showed +here come from lean because there are a + + align:start position:0% +here come from lean because there are a + + + align:start position:0% +here come from lean because there are a +lot of confounding factors going on + + align:start position:0% +lot of confounding factors going on + + + align:start position:0% +lot of confounding factors going on +there's a changing business environment + + align:start position:0% +there's a changing business environment + + + align:start position:0% +there's a changing business environment +there may be other things going on and + + align:start position:0% +there may be other things going on and + + + align:start position:0% +there may be other things going on and +uh + + align:start position:0% + + + + align:start position:0% + +I guess in a scientific sense it might + + align:start position:0% +I guess in a scientific sense it might + + + align:start position:0% +I guess in a scientific sense it might +be very hard to do that but you know + + align:start position:0% +be very hard to do that but you know + + + align:start position:0% +be very hard to do that but you know +when you go and look at organization + + align:start position:0% +when you go and look at organization + + + align:start position:0% +when you go and look at organization +after organization after organization + + align:start position:0% +after organization after organization + + + align:start position:0% +after organization after organization +that adopts this and sees Improvement + + align:start position:0% +that adopts this and sees Improvement + + + align:start position:0% +that adopts this and sees Improvement +there's a correlation there that you + + align:start position:0% +there's a correlation there that you + + + align:start position:0% +there's a correlation there that you +know adopting lean thinking in the way + + align:start position:0% +know adopting lean thinking in the way + + + align:start position:0% +know adopting lean thinking in the way +we teach it here not the one of the + + align:start position:0% +we teach it here not the one of the + + + align:start position:0% +we teach it here not the one of the +pitfalls in adopting lean thinking is + + align:start position:0% +pitfalls in adopting lean thinking is + + + align:start position:0% +pitfalls in adopting lean thinking is +and let's take the 5S or 6s a lot of + + align:start position:0% +and let's take the 5S or 6s a lot of + + + align:start position:0% +and let's take the 5S or 6s a lot of +people think lean's a + + align:start position:0% +people think lean's a + + + align:start position:0% +people think lean's a +tool oh okay now I know how to do 5S I + + align:start position:0% +tool oh okay now I know how to do 5S I + + + align:start position:0% +tool oh okay now I know how to do 5S I +can fix it that's not what lean lean is + + align:start position:0% +can fix it that's not what lean lean is + + + align:start position:0% +can fix it that's not what lean lean is +this change in culture that in the way + + align:start position:0% +this change in culture that in the way + + + align:start position:0% +this change in culture that in the way +of thinking that that Susan mentioned + + align:start position:0% +of thinking that that Susan mentioned + + + align:start position:0% +of thinking that that Susan mentioned +and that that takes some + + align:start position:0% + + + + align:start position:0% + +time for \ No newline at end of file diff --git a/TPeKtQykujI.txt b/TPeKtQykujI.txt new file mode 100644 index 0000000000000000000000000000000000000000..d1c77df167e4287731115655f97c65215a4f3396 --- /dev/null +++ b/TPeKtQykujI.txt @@ -0,0 +1,10099 @@ +align:start position:0% + +so in casee you're uh all worried that + + align:start position:0% +so in casee you're uh all worried that + + + align:start position:0% +so in casee you're uh all worried that +you may not be in the in the right class + + align:start position:0% +you may not be in the in the right class + + + align:start position:0% +you may not be in the in the right class +you are still in 6033 um and if you're + + align:start position:0% +you are still in 6033 um and if you're + + + align:start position:0% +you are still in 6033 um and if you're +wondering what happened to the Indian + + align:start position:0% +wondering what happened to the Indian + + + align:start position:0% +wondering what happened to the Indian +guy who normally lectures he's sitting + + align:start position:0% +guy who normally lectures he's sitting + + + align:start position:0% +guy who normally lectures he's sitting +right over there um we're trading off + + align:start position:0% +right over there um we're trading off + + + align:start position:0% +right over there um we're trading off +lectures for uh the next uh through + + align:start position:0% +lectures for uh the next uh through + + + align:start position:0% +lectures for uh the next uh through +throughout the class I'm going to do + + align:start position:0% +throughout the class I'm going to do + + + align:start position:0% +throughout the class I'm going to do +about the next eight lectures up until + + align:start position:0% +about the next eight lectures up until + + + align:start position:0% +about the next eight lectures up until +spring break and then uh har will be + + align:start position:0% +spring break and then uh har will be + + + align:start position:0% +spring break and then uh har will be +back so my name is Sam and um feel free + + align:start position:0% +back so my name is Sam and um feel free + + + align:start position:0% +back so my name is Sam and um feel free +to address any questions about the + + align:start position:0% +to address any questions about the + + + align:start position:0% +to address any questions about the +lecture to me so um we're going to keep + + align:start position:0% +lecture to me so um we're going to keep + + + align:start position:0% +lecture to me so um we're going to keep +today we're going to keep talking about + + align:start position:0% +today we're going to keep talking about + + + align:start position:0% +today we're going to keep talking about +this concept of enforcing modularity + + align:start position:0% +this concept of enforcing modularity + + + align:start position:0% +this concept of enforcing modularity +that we started talking about last + + align:start position:0% + + + + align:start position:0% + +time so last time we saw how we can use + + align:start position:0% +time so last time we saw how we can use + + + align:start position:0% +time so last time we saw how we can use +this uh notion of the client service + + align:start position:0% +this uh notion of the client service + + + align:start position:0% +this uh notion of the client service +model in order to separate two uh in + + align:start position:0% +model in order to separate two uh in + + + align:start position:0% +model in order to separate two uh in +order to separate the separate two + + align:start position:0% +order to separate the separate two + + + align:start position:0% +order to separate the separate two +modules from each other so the idea was + + align:start position:0% +modules from each other so the idea was + + + align:start position:0% +modules from each other so the idea was +that we could have uh we could by + + align:start position:0% +that we could have uh we could by + + + align:start position:0% +that we could have uh we could by +running the client and the service on + + align:start position:0% +running the client and the service on + + + align:start position:0% +running the client and the service on +separate machines we can isolate these + + align:start position:0% +separate machines we can isolate these + + + align:start position:0% +separate machines we can isolate these +two things from each other so we can + + align:start position:0% +two things from each other so we can + + + align:start position:0% +two things from each other so we can +make it so that the uh for example when + + align:start position:0% +make it so that the uh for example when + + + align:start position:0% +make it so that the uh for example when +the client wants to uh invoke some + + align:start position:0% +the client wants to uh invoke some + + + align:start position:0% +the client wants to uh invoke some +operation on the server that the server + + align:start position:0% +operation on the server that the server + + + align:start position:0% +operation on the server that the server +is uh can verify can uh verify the + + align:start position:0% +is uh can verify can uh verify the + + + align:start position:0% +is uh can verify can uh verify the +request that the uh client makes and + + align:start position:0% +request that the uh client makes and + + + align:start position:0% +request that the uh client makes and +make sure that the client isn't asking + + align:start position:0% +make sure that the client isn't asking + + + align:start position:0% +make sure that the client isn't asking +to do something malicious uh similarly + + align:start position:0% +to do something malicious uh similarly + + + align:start position:0% +to do something malicious uh similarly +we can um so this is what we saw last + + align:start position:0% +we can um so this is what we saw last + + + align:start position:0% +we can um so this is what we saw last +time was this client service model + + align:start position:0% +time was this client service model + + + align:start position:0% +time was this client service model +um and this had the so the other benefit + + align:start position:0% +um and this had the so the other benefit + + + align:start position:0% +um and this had the so the other benefit +of the client service model was ad meant + + align:start position:0% +of the client service model was ad meant + + + align:start position:0% +of the client service model was ad meant +that we could decouple the client from + + align:start position:0% +that we could decouple the client from + + + align:start position:0% +that we could decouple the client from +the from the service so it meant that + + align:start position:0% +the from the service so it meant that + + + align:start position:0% +the from the service so it meant that +when the client issued a request against + + align:start position:0% +when the client issued a request against + + + align:start position:0% +when the client issued a request against +the service uh it was possible for the + + align:start position:0% +the service uh it was possible for the + + + align:start position:0% +the service uh it was possible for the +uh it it didn't necessarily mean that uh + + align:start position:0% +uh it it didn't necessarily mean that uh + + + align:start position:0% +uh it it didn't necessarily mean that uh +the client if the service failed when + + align:start position:0% +the client if the service failed when + + + align:start position:0% +the client if the service failed when +the client issued the request it wasn't + + align:start position:0% +the client issued the request it wasn't + + + align:start position:0% +the client issued the request it wasn't +necessarily the case that the client + + align:start position:0% +necessarily the case that the client + + + align:start position:0% +necessarily the case that the client +would also fail so the server uh could + + align:start position:0% +would also fail so the server uh could + + + align:start position:0% +would also fail so the server uh could +might might crash executing the request + + align:start position:0% +might might crash executing the request + + + align:start position:0% +might might crash executing the request +and then the client would get a timeout + + align:start position:0% +and then the client would get a timeout + + + align:start position:0% +and then the client would get a timeout +and would be able to retry um and + + align:start position:0% +and would be able to retry um and + + + align:start position:0% +and would be able to retry um and +similarly if the uh server failed if the + + align:start position:0% +similarly if the uh server failed if the + + + align:start position:0% +similarly if the uh server failed if the +if the client failed the server could + + align:start position:0% +if the client failed the server could + + + align:start position:0% +if the client failed the server could +continue handling requests on the behalf + + align:start position:0% +continue handling requests on the behalf + + + align:start position:0% +continue handling requests on the behalf +of other clients okay so that was a nice + + align:start position:0% +of other clients okay so that was a nice + + + align:start position:0% +of other clients okay so that was a nice +separation the ability to split the + + align:start position:0% +separation the ability to split the + + + align:start position:0% +separation the ability to split the +client from the and the server apart + + align:start position:0% +client from the and the server apart + + + align:start position:0% +client from the and the server apart +from each other uh that that was that's + + align:start position:0% +from each other uh that that was that's + + + align:start position:0% +from each other uh that that was that's +a good thing but the problem with this + + align:start position:0% +a good thing but the problem with this + + + align:start position:0% +a good thing but the problem with this +approach is that we had to have two + + align:start position:0% +approach is that we had to have two + + + align:start position:0% +approach is that we had to have two +separate machines right the way we + + align:start position:0% +separate machines right the way we + + + align:start position:0% +separate machines right the way we +presented this was that the client was + + align:start position:0% +presented this was that the client was + + + align:start position:0% +presented this was that the client was +running on one computer and the server + + align:start position:0% +running on one computer and the server + + + align:start position:0% +running on one computer and the server +was running on another computer um and + + align:start position:0% +was running on another computer um and + + + align:start position:0% +was running on another computer um and +this is a little bit if you think about + + align:start position:0% +this is a little bit if you think about + + + align:start position:0% +this is a little bit if you think about +this this is this isn't exactly what we + + align:start position:0% +this this is this isn't exactly what we + + + align:start position:0% +this this is this isn't exactly what we +want right because that means suppose we + + align:start position:0% +want right because that means suppose we + + + align:start position:0% +want right because that means suppose we +want to build up a big complicated + + align:start position:0% +want to build up a big complicated + + + align:start position:0% +want to build up a big complicated +computer system that's composed of + + align:start position:0% +computer system that's composed of + + + align:start position:0% +computer system that's composed of +multiple multiple different modules uh + + align:start position:0% +multiple multiple different modules uh + + + align:start position:0% +multiple multiple different modules uh +if we have to run each one of those + + align:start position:0% +if we have to run each one of those + + + align:start position:0% +if we have to run each one of those +modules on a separate computer that's uh + + align:start position:0% +modules on a separate computer that's uh + + + align:start position:0% +modules on a separate computer that's uh +not really very ideal right it's going + + align:start position:0% +not really very ideal right it's going + + + align:start position:0% +not really very ideal right it's going +to mean that if we to build up a big + + align:start position:0% +to mean that if we to build up a big + + + align:start position:0% +to mean that if we to build up a big +service we're going to need a whole lot + + align:start position:0% +service we're going to need a whole lot + + + align:start position:0% +service we're going to need a whole lot +of computers and clearly that's not the + + align:start position:0% +of computers and clearly that's not the + + + align:start position:0% +of computers and clearly that's not the +way that computer systems that we + + align:start position:0% +way that computer systems that we + + + align:start position:0% +way that computer systems that we +actually interact with work um so what + + align:start position:0% +actually interact with work um so what + + + align:start position:0% +actually interact with work um so what +we've seen so far is this notion we have + + align:start position:0% +we've seen so far is this notion we have + + + align:start position:0% +we've seen so far is this notion we have +a + + align:start position:0% + + + + align:start position:0% + +module per + + align:start position:0% +module per + + + align:start position:0% +module per +computer okay and what we're going to do + + align:start position:0% +computer okay and what we're going to do + + + align:start position:0% +computer okay and what we're going to do +today is we're going to see how we can + + align:start position:0% +today is we're going to see how we can + + + align:start position:0% +today is we're going to see how we can +uh generalize this so that instead of + + align:start position:0% +uh generalize this so that instead of + + + align:start position:0% +uh generalize this so that instead of +having one module per computer we can + + align:start position:0% +having one module per computer we can + + + align:start position:0% +having one module per computer we can +instead have multiple modules running + + align:start position:0% +instead have multiple modules running + + + align:start position:0% +instead have multiple modules running +with within a single computer but when + + align:start position:0% +with within a single computer but when + + + align:start position:0% +with within a single computer but when +we do that we still want to maintain + + align:start position:0% +we do that we still want to maintain + + + align:start position:0% +we do that we still want to maintain +these nice these nice sort of protection + + align:start position:0% +these nice these nice sort of protection + + + align:start position:0% +these nice these nice sort of protection +benefits that we had between the client + + align:start position:0% +benefits that we had between the client + + + align:start position:0% +benefits that we had between the client +and service when these two things were + + align:start position:0% +and service when these two things were + + + align:start position:0% +and service when these two things were +running on separate computers okay so + + align:start position:0% +running on separate computers okay so + + + align:start position:0% +running on separate computers okay so +the way that we're going to do that is + + align:start position:0% +the way that we're going to do that is + + + align:start position:0% +the way that we're going to do that is +by + + align:start position:0% +by + + + align:start position:0% +by +uh do creating something we call a + + align:start position:0% +uh do creating something we call a + + + align:start position:0% +uh do creating something we call a +virtual computer + + align:start position:0% + + + + align:start position:0% + +so what we're going to do is is we're + + align:start position:0% +so what we're going to do is is we're + + + align:start position:0% +so what we're going to do is is we're +going to create this notion of a virtual + + align:start position:0% +going to create this notion of a virtual + + + align:start position:0% +going to create this notion of a virtual +multiple virtual computers that're all + + align:start position:0% +multiple virtual computers that're all + + + align:start position:0% +multiple virtual computers that're all +running on one single computer and then + + align:start position:0% +running on one single computer and then + + + align:start position:0% +running on one single computer and then +we're going to run each one of these + + align:start position:0% +we're going to run each one of these + + + align:start position:0% +we're going to run each one of these +modules within a virtual computer okay + + align:start position:0% +modules within a virtual computer okay + + + align:start position:0% +modules within a virtual computer okay +and I'll talk about more about what I + + align:start position:0% +and I'll talk about more about what I + + + align:start position:0% +and I'll talk about more about what I +mean by a virtual computer uh throughout + + align:start position:0% +mean by a virtual computer uh throughout + + + align:start position:0% +mean by a virtual computer uh throughout +the next couple of lectures but the idea + + align:start position:0% +the next couple of lectures but the idea + + + align:start position:0% +the next couple of lectures but the idea +is that a virtual computer has the sort + + align:start position:0% +is that a virtual computer has the sort + + + align:start position:0% +is that a virtual computer has the sort +of exactly the same uh to to the to a + + align:start position:0% +of exactly the same uh to to the to a + + + align:start position:0% +of exactly the same uh to to the to a +program that's running on it a virtual + + align:start position:0% +program that's running on it a virtual + + + align:start position:0% +program that's running on it a virtual +computer looks just like one of these + + align:start position:0% +computer looks just like one of these + + + align:start position:0% +computer looks just like one of these +client or server computers might have + + align:start position:0% +client or server computers might have + + + align:start position:0% +client or server computers might have +looked um and in particular a virtual + + align:start position:0% +looked um and in particular a virtual + + + align:start position:0% +looked um and in particular a virtual +computer has the same uh sorts of + + align:start position:0% +computer has the same uh sorts of + + + align:start position:0% +computer has the same uh sorts of +abstractions that we studied in the + + align:start position:0% +abstractions that we studied in the + + + align:start position:0% +abstractions that we studied in the +previous lectures available to it that a + + align:start position:0% +previous lectures available to it that a + + + align:start position:0% +previous lectures available to it that a +real computer has so a virtual computer + + align:start position:0% +real computer has so a virtual computer + + + align:start position:0% +real computer has so a virtual computer +has a virtual + + align:start position:0% + + + + align:start position:0% + +memory and a virtual + + align:start position:0% + + + + align:start position:0% + +processor + + align:start position:0% +processor + + + align:start position:0% +processor +so today what we're going to talk about + + align:start position:0% +so today what we're going to talk about + + + align:start position:0% +so today what we're going to talk about +is this notion of a virtual memory um + + align:start position:0% +is this notion of a virtual memory um + + + align:start position:0% +is this notion of a virtual memory um +and this virtual so you've already you + + align:start position:0% +and this virtual so you've already you + + + align:start position:0% +and this virtual so you've already you +guys have already probably seen the term + + align:start position:0% +guys have already probably seen the term + + + align:start position:0% +guys have already probably seen the term +virtual memory in 64 so the words should + + align:start position:0% +virtual memory in 64 so the words should + + + align:start position:0% +virtual memory in 64 so the words should +be familiar to you and we're going to + + align:start position:0% +be familiar to you and we're going to + + + align:start position:0% +be familiar to you and we're going to +use exactly the same abstraction that we + + align:start position:0% +use exactly the same abstraction that we + + + align:start position:0% +use exactly the same abstraction that we +used in 64 so we're just going to show + + align:start position:0% +used in 64 so we're just going to show + + + align:start position:0% +used in 64 so we're just going to show +how this abstraction can be used to + + align:start position:0% +how this abstraction can be used to + + + align:start position:0% +how this abstraction can be used to +provide this protection between the + + align:start position:0% +provide this protection between the + + + align:start position:0% +provide this protection between the +client and server that we want okay + + align:start position:0% +client and server that we want okay + + + align:start position:0% +client and server that we want okay +we're also going to introduce today this + + align:start position:0% +we're also going to introduce today this + + + align:start position:0% +we're also going to introduce today this +notion of something called a kernel um + + align:start position:0% +notion of something called a kernel um + + + align:start position:0% +notion of something called a kernel um +and a kernel is something that's in + + align:start position:0% +and a kernel is something that's in + + + align:start position:0% +and a kernel is something that's in +charge basically of managing all of + + align:start position:0% +charge basically of managing all of + + + align:start position:0% +charge basically of managing all of +these different virtual computers that + + align:start position:0% +these different virtual computers that + + + align:start position:0% +these different virtual computers that +are running on our one uh physical + + align:start position:0% +are running on our one uh physical + + + align:start position:0% +are running on our one uh physical +computer so the kernel is going to be + + align:start position:0% +computer so the kernel is going to be + + + align:start position:0% +computer so the kernel is going to be +the sort of system that knows about it's + + align:start position:0% +the sort of system that knows about it's + + + align:start position:0% +the sort of system that knows about it's +going to be the piece of the system that + + align:start position:0% +going to be the piece of the system that + + + align:start position:0% +going to be the piece of the system that +actually knows that there are multiple + + align:start position:0% +actually knows that there are multiple + + + align:start position:0% +actually knows that there are multiple +virtual computers running on this + + align:start position:0% +virtual computers running on this + + + align:start position:0% +virtual computers running on this +system okay so + + align:start position:0% +system okay so + + + align:start position:0% +system okay so +um I want to start off by first just + + align:start position:0% +um I want to start off by first just + + + align:start position:0% +um I want to start off by first just +talking about why we want a virtualize + + align:start position:0% +talking about why we want a virtualize + + + align:start position:0% +talking about why we want a virtualize +memory why virtualizing memory is a good + + align:start position:0% +memory why virtualizing memory is a good + + + align:start position:0% +memory why virtualizing memory is a good +thing + + align:start position:0% + + + + align:start position:0% + +so I'm going abbreviate virtual memory + + align:start position:0% +so I'm going abbreviate virtual memory + + + align:start position:0% +so I'm going abbreviate virtual memory +as VM so um why would we want to + + align:start position:0% +as VM so um why would we want to + + + align:start position:0% +as VM so um why would we want to +virtualize memory well so let's see what + + align:start position:0% +virtualize memory well so let's see what + + + align:start position:0% +virtualize memory well so let's see what +let's let's see what might happen if we + + align:start position:0% +let's let's see what might happen if we + + + align:start position:0% +let's let's see what might happen if we +built a computer system with multiple + + align:start position:0% +built a computer system with multiple + + + align:start position:0% +built a computer system with multiple +modules running on at the same time uh + + align:start position:0% +modules running on at the same time uh + + + align:start position:0% +modules running on at the same time uh +that didn't have a virtualized + + align:start position:0% +that didn't have a virtualized + + + align:start position:0% +that didn't have a virtualized +memory so suppose we have some + + align:start position:0% +memory so suppose we have some + + + align:start position:0% +memory so suppose we have some +microprocessor uh and we have some + + align:start position:0% + + + + align:start position:0% + +memory and within this memory um we have + + align:start position:0% +memory and within this memory um we have + + + align:start position:0% +memory and within this memory um we have +the data for a couple of the code and + + align:start position:0% +the data for a couple of the code and + + + align:start position:0% +the data for a couple of the code and +data for a couple of different modules + + align:start position:0% +data for a couple of different modules + + + align:start position:0% +data for a couple of different modules +is stored so we have say module a and + + align:start position:0% +is stored so we have say module a and + + + align:start position:0% +is stored so we have say module a and +module + + align:start position:0% +module + + + align:start position:0% +module +B and this is the data this this is the + + align:start position:0% +B and this is the data this this is the + + + align:start position:0% +B and this is the data this this is the +things like the code + + align:start position:0% +things like the code + + + align:start position:0% +things like the code +and the uh data that these modules are + + align:start position:0% +and the uh data that these modules are + + + align:start position:0% +and the uh data that these modules are +using to currently execute so uh in this + + align:start position:0% +using to currently execute so uh in this + + + align:start position:0% +using to currently execute so uh in this +environment we have suppose a module a + + align:start position:0% +environment we have suppose a module a + + + align:start position:0% +environment we have suppose a module a +executes some instruction + + align:start position:0% +executes some instruction + + + align:start position:0% +executes some instruction +um so so let's these if this if you + + align:start position:0% +um so so let's these if this if you + + + align:start position:0% +um so so let's these if this if you +think of this as memory uh let's say + + align:start position:0% +think of this as memory uh let's say + + + align:start position:0% +think of this as memory uh let's say +that module a uh begins at address a + + align:start position:0% +that module a uh begins at address a + + + align:start position:0% +that module a uh begins at address a +here and module B begins at address B + + align:start position:0% +here and module B begins at address B + + + align:start position:0% +here and module B begins at address B +here um so suppose that module a + + align:start position:0% +here um so suppose that module a + + + align:start position:0% +here um so suppose that module a +executes some instruction like uh store + + align:start position:0% +executes some instruction like uh store + + + align:start position:0% +executes some instruction like uh store +um some value + + align:start position:0% +um some value + + + align:start position:0% +um some value +R1 in memory address B okay so uh module + + align:start position:0% +R1 in memory address B okay so uh module + + + align:start position:0% +R1 in memory address B okay so uh module +a writes into memory address B here so + + align:start position:0% +a writes into memory address B here so + + + align:start position:0% +a writes into memory address B here so +this is this can be a problematic thing + + align:start position:0% +this is this can be a problematic thing + + + align:start position:0% +this is this can be a problematic thing +right because the microprocessor if the + + align:start position:0% +right because the microprocessor if the + + + align:start position:0% +right because the microprocessor if the +microprocessor just allows this to + + align:start position:0% +microprocessor just allows this to + + + align:start position:0% +microprocessor just allows this to +happen if it just allows uh a to write + + align:start position:0% +happen if it just allows uh a to write + + + align:start position:0% +happen if it just allows uh a to write +into module B's memory then module B has + + align:start position:0% +into module B's memory then module B has + + + align:start position:0% +into module B's memory then module B has +no way of being isolated from module a + + align:start position:0% +no way of being isolated from module a + + + align:start position:0% +no way of being isolated from module a +at all right uh module a can for example + + align:start position:0% +at all right uh module a can for example + + + align:start position:0% +at all right uh module a can for example +uh write some sort of garbage into the + + align:start position:0% +uh write some sort of garbage into the + + + align:start position:0% +uh write some sort of garbage into the +memory of module B then when module B + + align:start position:0% +memory of module B then when module B + + + align:start position:0% +memory of module B then when module B +tries to load in that the tries to read + + align:start position:0% +tries to load in that the tries to read + + + align:start position:0% +tries to load in that the tries to read +from that memory address it will either + + align:start position:0% +from that memory address it will either + + + align:start position:0% +from that memory address it will either +say try and execute an illegal + + align:start position:0% +say try and execute an illegal + + + align:start position:0% +say try and execute an illegal +instruction or it'll read in some data + + align:start position:0% +instruction or it'll read in some data + + + align:start position:0% +instruction or it'll read in some data +that doesn't make any sense so um it's + + align:start position:0% +that doesn't make any sense so um it's + + + align:start position:0% +that doesn't make any sense so um it's +this is this we we we've lost the + + align:start position:0% +this is this we we we've lost the + + + align:start position:0% +this is this we we we've lost the +separation the isolation that we had + + align:start position:0% +separation the isolation that we had + + + align:start position:0% +separation the isolation that we had +between if module a and module B are a + + align:start position:0% +between if module a and module B are a + + + align:start position:0% +between if module a and module B are a +client and a service uh trying to + + align:start position:0% +client and a service uh trying to + + + align:start position:0% +client and a service uh trying to +interact with each other we've lost this + + align:start position:0% +interact with each other we've lost this + + + align:start position:0% +interact with each other we've lost this +sort of ability to uh they they now uh + + align:start position:0% +sort of ability to uh they they now uh + + + align:start position:0% +sort of ability to uh they they now uh +we we've lost this ability to separate + + align:start position:0% +we we've lost this ability to separate + + + align:start position:0% +we we've lost this ability to separate +and isolate each other isolate them from + + align:start position:0% +and isolate each other isolate them from + + + align:start position:0% +and isolate each other isolate them from +each other that we had when they were + + align:start position:0% +each other that we had when they were + + + align:start position:0% +each other that we had when they were +running on separate computers um + + align:start position:0% +running on separate computers um + + + align:start position:0% +running on separate computers um +furthermore this uh this sort of + + align:start position:0% +furthermore this uh this sort of + + + align:start position:0% +furthermore this uh this sort of +arrangement of virtual memory um so one + + align:start position:0% +arrangement of virtual memory um so one + + + align:start position:0% +arrangement of virtual memory um so one +problem with this is a + + align:start position:0% + + + + align:start position:0% + +can + + align:start position:0% +can + + + align:start position:0% +can +overwrite B's + + align:start position:0% +overwrite B's + + + align:start position:0% +overwrite B's +memory but we have another problem which + + align:start position:0% +memory but we have another problem which + + + align:start position:0% +memory but we have another problem which +is that um this sort of arrangement also + + align:start position:0% +is that um this sort of arrangement also + + + align:start position:0% +is that um this sort of arrangement also +is very very difficult to debug so uh + + align:start position:0% +is very very difficult to debug so uh + + + align:start position:0% +is very very difficult to debug so uh +these kinds of bugs can be very hard to + + align:start position:0% +these kinds of bugs can be very hard to + + + align:start position:0% +these kinds of bugs can be very hard to +track down and we really when we're + + align:start position:0% +track down and we really when we're + + + align:start position:0% +track down and we really when we're +building computer systems we'd like to + + align:start position:0% +building computer systems we'd like to + + + align:start position:0% +building computer systems we'd like to +get rid of them so for example suppose + + align:start position:0% +get rid of them so for example suppose + + + align:start position:0% +get rid of them so for example suppose +that a stores into B's memory some it + + align:start position:0% +that a stores into B's memory some it + + + align:start position:0% +that a stores into B's memory some it +overwrites an instruction that's + + align:start position:0% +overwrites an instruction that's + + + align:start position:0% +overwrites an instruction that's +somewhere sort of arbitrarily within B's + + align:start position:0% +somewhere sort of arbitrarily within B's + + + align:start position:0% +somewhere sort of arbitrarily within B's +memory and then 10,000 instructions + + align:start position:0% +memory and then 10,000 instructions + + + align:start position:0% +memory and then 10,000 instructions +later B tries to load in that memory + + align:start position:0% +later B tries to load in that memory + + + align:start position:0% +later B tries to load in that memory +address and execute that instruction and + + align:start position:0% +address and execute that instruction and + + + align:start position:0% +address and execute that instruction and +it gets an illegal instruction now + + align:start position:0% +it gets an illegal instruction now + + + align:start position:0% +it gets an illegal instruction now +imagine that you have to debug this + + align:start position:0% +imagine that you have to debug this + + + align:start position:0% +imagine that you have to debug this +program so you uh sort of are sitting + + align:start position:0% +program so you uh sort of are sitting + + + align:start position:0% +program so you uh sort of are sitting +there and you're you're running you run + + align:start position:0% +there and you're you're running you run + + + align:start position:0% +there and you're you're running you run +so you run application B and it works + + align:start position:0% +so you run application B and it works + + + align:start position:0% +so you run application B and it works +just fine and then you try and run + + align:start position:0% +just fine and then you try and run + + + align:start position:0% +just fine and then you try and run +applica you run and then you run + + align:start position:0% +applica you run and then you run + + + align:start position:0% +applica you run and then you run +application a and a overwrites part of + + align:start position:0% +application a and a overwrites part of + + + align:start position:0% +application a and a overwrites part of +B's memory and now when a program B runs + + align:start position:0% +B's memory and now when a program B runs + + + align:start position:0% +B's memory and now when a program B runs +sometime long after program a perhaps + + align:start position:0% +sometime long after program a perhaps + + + align:start position:0% +sometime long after program a perhaps +has already terminated B mysteriously + + align:start position:0% +has already terminated B mysteriously + + + align:start position:0% +has already terminated B mysteriously +crashes on you so how are you going to + + align:start position:0% +crashes on you so how are you going to + + + align:start position:0% +crashes on you so how are you going to +track down this problem it's very tricky + + align:start position:0% +track down this problem it's very tricky + + + align:start position:0% +track down this problem it's very tricky +and it's the kind of problem that's just + + align:start position:0% +and it's the kind of problem that's just + + + align:start position:0% +and it's the kind of problem that's just +it's extremely hard to debug these kinds + + align:start position:0% +it's extremely hard to debug these kinds + + + align:start position:0% +it's extremely hard to debug these kinds +of issues and so we really would like to + + align:start position:0% +of issues and so we really would like to + + + align:start position:0% +of issues and so we really would like to +make it so that a isn't able to Simply + + align:start position:0% +make it so that a isn't able to Simply + + + align:start position:0% +make it so that a isn't able to Simply +overwrite arbitrary things into B's + + align:start position:0% +overwrite arbitrary things into B's + + + align:start position:0% +overwrite arbitrary things into B's +memory we' like to protect a from B okay + + align:start position:0% +memory we' like to protect a from B okay + + + align:start position:0% +memory we' like to protect a from B okay +and that's what this virtual memory + + align:start position:0% +and that's what this virtual memory + + + align:start position:0% +and that's what this virtual memory +abstraction that we're going to talk + + align:start position:0% +abstraction that we're going to talk + + + align:start position:0% +abstraction that we're going to talk +about today is going to do for us so uh + + align:start position:0% +about today is going to do for us so uh + + + align:start position:0% +about today is going to do for us so uh +if you think about how you might protect + + align:start position:0% +if you think about how you might protect + + + align:start position:0% +if you think about how you might protect +a from B uh + + align:start position:0% +a from B uh + + + align:start position:0% +a from B uh +the solution that you sort of come up + + align:start position:0% +the solution that you sort of come up + + + align:start position:0% +the solution that you sort of come up +with after thinking about this and + + align:start position:0% +with after thinking about this and + + + align:start position:0% +with after thinking about this and +staring at this for a little bit is that + + align:start position:0% +staring at this for a little bit is that + + + align:start position:0% +staring at this for a little bit is that +you want to verify that all of the the + + align:start position:0% +you want to verify that all of the the + + + align:start position:0% +you want to verify that all of the the +memory accesses that a does are actually + + align:start position:0% +memory accesses that a does are actually + + + align:start position:0% +memory accesses that a does are actually +uh valid memory accesses that a should + + align:start position:0% +uh valid memory accesses that a should + + + align:start position:0% +uh valid memory accesses that a should +be allowed to make so for example that + + align:start position:0% +be allowed to make so for example that + + + align:start position:0% +be allowed to make so for example that +refer to objects that are actually in uh + + align:start position:0% +refer to objects that are actually in uh + + + align:start position:0% +refer to objects that are actually in uh +that a has allocated or that a owns okay + + align:start position:0% +that a has allocated or that a owns okay + + + align:start position:0% +that a has allocated or that a owns okay +so in order to do that um what we're + + align:start position:0% +so in order to do that um what we're + + + align:start position:0% +so in order to do that um what we're +going to need to do is to interpose some + + align:start position:0% +going to need to do is to interpose some + + + align:start position:0% +going to need to do is to interpose some +sort of software in between uh the + + align:start position:0% +sort of software in between uh the + + + align:start position:0% +sort of software in between uh the +memory axises that each module makes um + + align:start position:0% +memory axises that each module makes um + + + align:start position:0% +memory axises that each module makes um +and the uh and and the actual memory + + align:start position:0% +and the uh and and the actual memory + + + align:start position:0% +and the uh and and the actual memory +access so the idea + + align:start position:0% +access so the idea + + + align:start position:0% +access so the idea +is as follows so this is the virtual + + align:start position:0% +is as follows so this is the virtual + + + align:start position:0% +is as follows so this is the virtual +memory + + align:start position:0% + + + + align:start position:0% + +abstraction okay so the idea is as + + align:start position:0% +abstraction okay so the idea is as + + + align:start position:0% +abstraction okay so the idea is as +follows we're going + + align:start position:0% +follows we're going + + + align:start position:0% +follows we're going +to for each one of our + + align:start position:0% +to for each one of our + + + align:start position:0% +to for each one of our +modules say A and B we're going to + + align:start position:0% +modules say A and B we're going to + + + align:start position:0% +modules say A and B we're going to +create what's known as uh an address + + align:start position:0% +create what's known as uh an address + + + align:start position:0% +create what's known as uh an address +space okay + + align:start position:0% + + + + align:start position:0% + +and this address space is going to be a + + align:start position:0% +and this address space is going to be a + + + align:start position:0% +and this address space is going to be a +uh for example on a 32-bit + + align:start position:0% + + + + align:start position:0% + +computer it's 2 32 minus one it's going + + align:start position:0% +computer it's 2 32 minus one it's going + + + align:start position:0% +computer it's 2 32 minus one it's going +to be a 32bit uh me memory space so + + align:start position:0% +to be a 32bit uh me memory space so + + + align:start position:0% +to be a 32bit uh me memory space so +these are going to be this is the uh the + + align:start position:0% +these are going to be this is the uh the + + + align:start position:0% +these are going to be this is the uh the +the virtual address space of say a + + align:start position:0% +the virtual address space of say a + + + align:start position:0% +the virtual address space of say a +process a so process a can use memory + + align:start position:0% +process a so process a can use memory + + + align:start position:0% +process a so process a can use memory +any memory address that's in this 0 to 2 + + align:start position:0% +any memory address that's in this 0 to 2 + + + align:start position:0% +any memory address that's in this 0 to 2 +to 32-bit range + + align:start position:0% +to 32-bit range + + + align:start position:0% +to 32-bit range +okay um but this is going to be a + + align:start position:0% +okay um but this is going to be a + + + align:start position:0% +okay um but this is going to be a +virtual uh a virtual address space what + + align:start position:0% +virtual uh a virtual address space what + + + align:start position:0% +virtual uh a virtual address space what +I mean by that is that um when a when + + align:start position:0% +I mean by that is that um when a when + + + align:start position:0% +I mean by that is that um when a when +process a refers to some address + + align:start position:0% +process a refers to some address + + + align:start position:0% +process a refers to some address +uh refers to some address within its + + align:start position:0% +uh refers to some address within its + + + align:start position:0% +uh refers to some address within its +memory space um call it virtual a + + align:start position:0% +memory space um call it virtual a + + + align:start position:0% +memory space um call it virtual a +virtual address VA that's going that + + align:start position:0% +virtual address VA that's going that + + + align:start position:0% +virtual address VA that's going that +address is going to be mapped by some + + align:start position:0% +address is going to be mapped by some + + + align:start position:0% +address is going to be mapped by some +the virtual memory system um into a + + align:start position:0% +the virtual memory system um into a + + + align:start position:0% +the virtual memory system um into a +physical address okay + + align:start position:0% + + + + align:start position:0% + +so this virtual address here is going to + + align:start position:0% +so this virtual address here is going to + + + align:start position:0% +so this virtual address here is going to +be mapped into some physical + + align:start position:0% + + + + align:start position:0% + +address somewhere within the uh memory + + align:start position:0% +address somewhere within the uh memory + + + align:start position:0% +address somewhere within the uh memory +the the actual physical memory of the + + align:start position:0% +the the actual physical memory of the + + + align:start position:0% +the the actual physical memory of the +system okay so this physical memory of + + align:start position:0% +system okay so this physical memory of + + + align:start position:0% +system okay so this physical memory of +the system is also a 32-bit uh a 32-bit + + align:start position:0% +the system is also a 32-bit uh a 32-bit + + + align:start position:0% +the system is also a 32-bit uh a 32-bit +space um and but what but the uh but the + + align:start position:0% +space um and but what but the uh but the + + + align:start position:0% +space um and but what but the uh but the +sort of mapping from this virtual + + align:start position:0% +sort of mapping from this virtual + + + align:start position:0% +sort of mapping from this virtual +address in A's memory into this physical + + align:start position:0% +address in A's memory into this physical + + + align:start position:0% +address in A's memory into this physical +address space um is going to be is going + + align:start position:0% +address space um is going to be is going + + + align:start position:0% +address space um is going to be is going +to be handled by this this virtual + + align:start position:0% +to be handled by this this virtual + + + align:start position:0% +to be handled by this this virtual +memory system so um now the idea is that + + align:start position:0% +memory system so um now the idea is that + + + align:start position:0% +memory system so um now the idea is that +each thing that say a process A or B + + align:start position:0% +each thing that say a process A or B + + + align:start position:0% +each thing that say a process A or B +might want to reference is going to be + + align:start position:0% +might want to reference is going to be + + + align:start position:0% +might want to reference is going to be +mapped into some different location + + align:start position:0% +mapped into some different location + + + align:start position:0% +mapped into some different location +within this memory so for example uh the + + align:start position:0% +within this memory so for example uh the + + + align:start position:0% +within this memory so for example uh the +code from process a uh or from from + + align:start position:0% +code from process a uh or from from + + + align:start position:0% +code from process a uh or from from +module a is going to be mapped into one + + align:start position:0% +module a is going to be mapped into one + + + align:start position:0% +module a is going to be mapped into one +location um and the code from module B + + align:start position:0% +location um and the code from module B + + + align:start position:0% +location um and the code from module B +is going to be mapped into a different + + align:start position:0% +is going to be mapped into a different + + + align:start position:0% +is going to be mapped into a different +location in the physical address + + align:start position:0% +location in the physical address + + + align:start position:0% +location in the physical address +space okay so we have this notion of + + align:start position:0% +space okay so we have this notion of + + + align:start position:0% +space okay so we have this notion of +address spaces each module that's + + align:start position:0% +address spaces each module that's + + + align:start position:0% +address spaces each module that's +running on the system and the virtual + + align:start position:0% +running on the system and the virtual + + + align:start position:0% +running on the system and the virtual +memory system is going to be allocated + + align:start position:0% +memory system is going to be allocated + + + align:start position:0% +memory system is going to be allocated +one of these address spaces okay this + + align:start position:0% +one of these address spaces okay this + + + align:start position:0% +one of these address spaces okay this +address space is going to uh be a and + + align:start position:0% +address space is going to uh be a and + + + align:start position:0% +address space is going to uh be a and +this address space is virtual in the + + align:start position:0% +this address space is virtual in the + + + align:start position:0% +this address space is virtual in the +sense that um it's the these uh these + + align:start position:0% +sense that um it's the these uh these + + + align:start position:0% +sense that um it's the these uh these +addresses are only valid in the context + + align:start position:0% +addresses are only valid in the context + + + align:start position:0% +addresses are only valid in the context +of this given module okay and they + + align:start position:0% +of this given module okay and they + + + align:start position:0% +of this given module okay and they +translate into some under each each of + + align:start position:0% +translate into some under each each of + + + align:start position:0% +translate into some under each each of +address in the virtual space uh + + align:start position:0% +address in the virtual space uh + + + align:start position:0% +address in the virtual space uh +translates into some address in the + + align:start position:0% +translates into some address in the + + + align:start position:0% +translates into some address in the +physical space now if you look at this + + align:start position:0% +physical space now if you look at this + + + align:start position:0% +physical space now if you look at this +for a minute you might think well this + + align:start position:0% +for a minute you might think well this + + + align:start position:0% +for a minute you might think well this +is kind of confusing because now b and a + + align:start position:0% +is kind of confusing because now b and a + + + align:start position:0% +is kind of confusing because now b and a +both have a 32-bit address space and the + + align:start position:0% +both have a 32-bit address space and the + + + align:start position:0% +both have a 32-bit address space and the +computer itself only has a 32-bit + + align:start position:0% +computer itself only has a 32-bit + + + align:start position:0% +computer itself only has a 32-bit +address space so uh there are sort of + + align:start position:0% +address space so uh there are sort of + + + align:start position:0% +address space so uh there are sort of +more addresses between all the modules + + align:start position:0% +more addresses between all the modules + + + align:start position:0% +more addresses between all the modules +than the computer itself physically has + + align:start position:0% +than the computer itself physically has + + + align:start position:0% +than the computer itself physically has +and if you remember back from 64 the + + align:start position:0% +and if you remember back from 64 the + + + align:start position:0% +and if you remember back from 64 the +story that we told you about that was + + align:start position:0% +story that we told you about that was + + + align:start position:0% +story that we told you about that was +that well some of these virtual + + align:start position:0% +that well some of these virtual + + + align:start position:0% +that well some of these virtual +addresses can actually be mapped into + + align:start position:0% +addresses can actually be mapped into + + + align:start position:0% +addresses can actually be mapped into +the dis on the computer so in 64 virtual + + align:start position:0% +the dis on the computer so in 64 virtual + + + align:start position:0% +the dis on the computer so in 64 virtual +memory was presented as a way to create + + align:start position:0% +memory was presented as a way to create + + + align:start position:0% +memory was presented as a way to create +a computer that appeared to have more + + align:start position:0% +a computer that appeared to have more + + + align:start position:0% +a computer that appeared to have more +physical memory uh than it in fact did + + align:start position:0% +physical memory uh than it in fact did + + + align:start position:0% +physical memory uh than it in fact did +and the way that that was done was to + + align:start position:0% +and the way that that was done was to + + + align:start position:0% +and the way that that was done was to +map some of these addresses uh onto + + align:start position:0% + + + + align:start position:0% + +disk so you might have addresses from B + + align:start position:0% +disk so you might have addresses from B + + + align:start position:0% +disk so you might have addresses from B +mapped onto disk and then when B tries + + align:start position:0% +mapped onto disk and then when B tries + + + align:start position:0% +mapped onto disk and then when B tries +to reference an address that's mapped + + align:start position:0% +to reference an address that's mapped + + + align:start position:0% +to reference an address that's mapped +onto disk uh the system would load that + + align:start position:0% +onto disk uh the system would load that + + + align:start position:0% +onto disk uh the system would load that +address from memory would load that data + + align:start position:0% +address from memory would load that data + + + align:start position:0% +address from memory would load that data +from memory uh load that data from dis + + align:start position:0% +from memory uh load that data from dis + + + align:start position:0% +from memory uh load that data from dis +and into memory so we're not going to + + align:start position:0% +and into memory so we're not going to + + + align:start position:0% +and into memory so we're not going to +talk about that aspect of virtual memory + + align:start position:0% +talk about that aspect of virtual memory + + + align:start position:0% +talk about that aspect of virtual memory +very much today um the thing to remember + + align:start position:0% +very much today um the thing to remember + + + align:start position:0% +very much today um the thing to remember +is just that these virtual address + + align:start position:0% +is just that these virtual address + + + align:start position:0% +is just that these virtual address +spaces there may be things there may be + + align:start position:0% +spaces there may be things there may be + + + align:start position:0% +spaces there may be things there may be +parts of this virtual address space in + + align:start position:0% +parts of this virtual address space in + + + align:start position:0% +parts of this virtual address space in +each of the modules that isn't actually + + align:start position:0% +each of the modules that isn't actually + + + align:start position:0% +each of the modules that isn't actually +mapped into any physical address space + + align:start position:0% +mapped into any physical address space + + + align:start position:0% +mapped into any physical address space +so if one of these modules tries to use + + align:start position:0% +so if one of these modules tries to use + + + align:start position:0% +so if one of these modules tries to use +this unmapped physical uh one of these + + align:start position:0% +this unmapped physical uh one of these + + + align:start position:0% +this unmapped physical uh one of these +unmapped virtual address spaces it it's + + align:start position:0% +unmapped virtual address spaces it it's + + + align:start position:0% +unmapped virtual address spaces it it's +not allowed to do that this virtual + + align:start position:0% +not allowed to do that this virtual + + + align:start position:0% +not allowed to do that this virtual +memory system will signal an error when + + align:start position:0% +memory system will signal an error when + + + align:start position:0% +memory system will signal an error when +it tries to do that and in on your + + align:start position:0% +it tries to do that and in on your + + + align:start position:0% +it tries to do that and in on your +computer sometimes you'll see programs + + align:start position:0% +computer sometimes you'll see programs + + + align:start position:0% +computer sometimes you'll see programs +will mysteriously crash um with things + + align:start position:0% +will mysteriously crash um with things + + + align:start position:0% +will mysteriously crash um with things +that say things like you know tried to + + align:start position:0% +that say things like you know tried to + + + align:start position:0% +that say things like you know tried to +access an illegal uh an illegal memory + + align:start position:0% +access an illegal uh an illegal memory + + + align:start position:0% +access an illegal uh an illegal memory +address when it does that that's because + + align:start position:0% +address when it does that that's because + + + align:start position:0% +address when it does that that's because +the virtual the the program tried to + + align:start position:0% +the virtual the the program tried to + + + align:start position:0% +the virtual the the program tried to +address access some memory location that + + align:start position:0% +address access some memory location that + + + align:start position:0% +address access some memory location that +wasn't mapped by the virtual memory + + align:start position:0% + + + + align:start position:0% + +system okay so let's see um now let's + + align:start position:0% +system okay so let's see um now let's + + + align:start position:0% +system okay so let's see um now let's +let's dive a little bit more into + + align:start position:0% +let's dive a little bit more into + + + align:start position:0% +let's dive a little bit more into +actually how this virtual memory + + align:start position:0% +actually how this virtual memory + + + align:start position:0% +actually how this virtual memory +abstraction works so we can try to + + align:start position:0% +abstraction works so we can try to + + + align:start position:0% +abstraction works so we can try to +understand a little bit more about + + align:start position:0% +understand a little bit more about + + + align:start position:0% +understand a little bit more about +what's going on so um this is going to + + align:start position:0% +what's going on so um this is going to + + + align:start position:0% +what's going on so um this is going to +be a + + align:start position:0% + + + + align:start position:0% + +simplified + + align:start position:0% +simplified + + + align:start position:0% +simplified +VM Hardware + + align:start position:0% + + + + align:start position:0% + +okay this is a simplified version a + + align:start position:0% +okay this is a simplified version a + + + align:start position:0% +okay this is a simplified version a +little bit simplified even from what you + + align:start position:0% +little bit simplified even from what you + + + align:start position:0% +little bit simplified even from what you +learned about in six4 So the idea in + + align:start position:0% +learned about in six4 So the idea in + + + align:start position:0% +learned about in six4 So the idea in +this simplified Hardware is that uh we + + align:start position:0% +this simplified Hardware is that uh we + + + align:start position:0% +this simplified Hardware is that uh we +have our + + align:start position:0% +have our + + + align:start position:0% +have our +processor okay um and then we're going + + align:start position:0% +processor okay um and then we're going + + + align:start position:0% +processor okay um and then we're going +to have this VM system um which is + + align:start position:0% +to have this VM system um which is + + + align:start position:0% +to have this VM system um which is +sometimes called a memory management + + align:start position:0% +sometimes called a memory management + + + align:start position:0% +sometimes called a memory management +unit mmu and this is a piece of Hardware + + align:start position:0% +unit mmu and this is a piece of Hardware + + + align:start position:0% +unit mmu and this is a piece of Hardware +that's going to help us to do this + + align:start position:0% +that's going to help us to do this + + + align:start position:0% +that's going to help us to do this +mapping from these logical addresses in + + align:start position:0% +mapping from these logical addresses in + + + align:start position:0% +mapping from these logical addresses in +the in the modules that address spaces + + align:start position:0% +the in the modules that address spaces + + + align:start position:0% +the in the modules that address spaces +into the physical memory and then we're + + align:start position:0% +into the physical memory and then we're + + + align:start position:0% +into the physical memory and then we're +going to have the physical memory + + align:start position:0% + + + + align:start position:0% + +okay now the idea is that um when a + + align:start position:0% +okay now the idea is that um when a + + + align:start position:0% +okay now the idea is that um when a +instruction tries to access some virtual + + align:start position:0% +instruction tries to access some virtual + + + align:start position:0% +instruction tries to access some virtual +address so for example suppose we + + align:start position:0% +address so for example suppose we + + + align:start position:0% +address so for example suppose we +execute an instruction + + align:start position:0% + + + + align:start position:0% + +load some virtual address uh load into + + align:start position:0% +load some virtual address uh load into + + + align:start position:0% +load some virtual address uh load into +R1 some virtual address okay what's + + align:start position:0% +R1 some virtual address okay what's + + + align:start position:0% +R1 some virtual address okay what's +going to happen when we do that is that + + align:start position:0% +going to happen when we do that is that + + + align:start position:0% +going to happen when we do that is that +the microprocessor is going to send this + + align:start position:0% +the microprocessor is going to send this + + + align:start position:0% +the microprocessor is going to send this +vir address to the to the VM system and + + align:start position:0% +vir address to the to the VM system and + + + align:start position:0% +vir address to the to the VM system and +then the VM system is going to translate + + align:start position:0% +then the VM system is going to translate + + + align:start position:0% +then the VM system is going to translate +that into some physical address that is + + align:start position:0% +that into some physical address that is + + + align:start position:0% +that into some physical address that is +can be resolved within the memory itself + + align:start position:0% +can be resolved within the memory itself + + + align:start position:0% +can be resolved within the memory itself +okay and the way that the virtual memory + + align:start position:0% +okay and the way that the virtual memory + + + align:start position:0% +okay and the way that the virtual memory +system is going to decide which he's + + align:start position:0% +system is going to decide which he's + + + align:start position:0% +system is going to decide which he's +going to decide this mapping between a + + align:start position:0% +going to decide this mapping between a + + + align:start position:0% +going to decide this mapping between a +virtual address and a physical address + + align:start position:0% +virtual address and a physical address + + + align:start position:0% +virtual address and a physical address +is by using something that um that we + + align:start position:0% +is by using something that um that we + + + align:start position:0% +is by using something that um that we +call a page map okay so + + align:start position:0% + + + + align:start position:0% + +okay so this table is is an example this + + align:start position:0% +okay so this table is is an example this + + + align:start position:0% +okay so this table is is an example this +is this is a this so this is a page map + + align:start position:0% +is this is a this so this is a page map + + + align:start position:0% +is this is a this so this is a page map +and what a page map basically has is + + align:start position:0% +and what a page map basically has is + + + align:start position:0% +and what a page map basically has is +it's just a table of virtual address to + + align:start position:0% +it's just a table of virtual address to + + + align:start position:0% +it's just a table of virtual address to +physical address mappings so this is + + align:start position:0% +physical address mappings so this is + + + align:start position:0% +physical address mappings so this is +virtual address to physical address so + + align:start position:0% +virtual address to physical address so + + + align:start position:0% +virtual address to physical address so +the idea is that when some virtual + + align:start position:0% +the idea is that when some virtual + + + align:start position:0% +the idea is that when some virtual +address comes in here the virtual memory + + align:start position:0% +address comes in here the virtual memory + + + align:start position:0% +address comes in here the virtual memory +manager looks up that virtual address in + + align:start position:0% +manager looks up that virtual address in + + + align:start position:0% +manager looks up that virtual address in +this page map finds the corresponding + + align:start position:0% +this page map finds the corresponding + + + align:start position:0% +this page map finds the corresponding +physical address and then looks that + + align:start position:0% +physical address and then looks that + + + align:start position:0% +physical address and then looks that +physical address up in the actual memory + + align:start position:0% +physical address up in the actual memory + + + align:start position:0% +physical address up in the actual memory +okay so uh now there's one more detail + + align:start position:0% +okay so uh now there's one more detail + + + align:start position:0% +okay so uh now there's one more detail +that we need right so we so what this + + align:start position:0% +that we need right so we so what this + + + align:start position:0% +that we need right so we so what this +gives us is uh we have this notion of a + + align:start position:0% +gives us is uh we have this notion of a + + + align:start position:0% +gives us is uh we have this notion of a +page map that does this mapping for us + + align:start position:0% +page map that does this mapping for us + + + align:start position:0% +page map that does this mapping for us +but we're missing a detail which is okay + + align:start position:0% +but we're missing a detail which is okay + + + align:start position:0% +but we're missing a detail which is okay +what we wanted was for each one of these + + align:start position:0% +what we wanted was for each one of these + + + align:start position:0% +what we wanted was for each one of these +uh different modules that's running in + + align:start position:0% +uh different modules that's running in + + + align:start position:0% +uh different modules that's running in +the system to have a different uh + + align:start position:0% +the system to have a different uh + + + align:start position:0% +the system to have a different uh +address space associated with it so what + + align:start position:0% +address space associated with it so what + + + align:start position:0% +address space associated with it so what +we want is we want to have separate page + + align:start position:0% +we want is we want to have separate page + + + align:start position:0% +we want is we want to have separate page +maps for each of these different modules + + align:start position:0% +maps for each of these different modules + + + align:start position:0% +maps for each of these different modules +so for A and B okay we're going to have + + align:start position:0% +so for A and B okay we're going to have + + + align:start position:0% +so for A and B okay we're going to have +a different page map and this different + + align:start position:0% +a different page map and this different + + + align:start position:0% +a different page map and this different +page so and we're going to have the sort + + align:start position:0% +page so and we're going to have the sort + + + align:start position:0% +page so and we're going to have the sort +of same we might have multiple copies of + + align:start position:0% +of same we might have multiple copies of + + + align:start position:0% +of same we might have multiple copies of +the same of a particular virtual address + + align:start position:0% +the same of a particular virtual address + + + align:start position:0% +the same of a particular virtual address +in each one of these page Maps um and + + align:start position:0% +in each one of these page Maps um and + + + align:start position:0% +in each one of these page Maps um and +then what we're going to do is we're + + align:start position:0% +then what we're going to do is we're + + + align:start position:0% +then what we're going to do is we're +going to allocate a special register on + + align:start position:0% +going to allocate a special register on + + + align:start position:0% +going to allocate a special register on +the hardware we're going to on the + + align:start position:0% +the hardware we're going to on the + + + align:start position:0% +the hardware we're going to on the +processor we're going to add uh a little + + align:start position:0% +processor we're going to add uh a little + + + align:start position:0% +processor we're going to add uh a little +uh register that's can allow us to keep + + align:start position:0% +uh register that's can allow us to keep + + + align:start position:0% +uh register that's can allow us to keep +track of which one of these page Maps + + align:start position:0% +track of which one of these page Maps + + + align:start position:0% +track of which one of these page Maps +we're currently looking at okay so this + + align:start position:0% +we're currently looking at okay so this + + + align:start position:0% +we're currently looking at okay so this +thing is called the + + align:start position:0% +thing is called the + + + align:start position:0% +thing is called the +PM or the page map address register + + align:start position:0% + + + + align:start position:0% + +okay and the page map address register + + align:start position:0% +okay and the page map address register + + + align:start position:0% +okay and the page map address register +simply points at one of these page Maps + + align:start position:0% +simply points at one of these page Maps + + + align:start position:0% +simply points at one of these page Maps +Okay so what happens is that the uh the + + align:start position:0% +Okay so what happens is that the uh the + + + align:start position:0% +Okay so what happens is that the uh the +virtual memory system when it wants to + + align:start position:0% +virtual memory system when it wants to + + + align:start position:0% +virtual memory system when it wants to +resolve a virtual address looks at this + + align:start position:0% +resolve a virtual address looks at this + + + align:start position:0% +resolve a virtual address looks at this +page map address register and uses that + + align:start position:0% +page map address register and uses that + + + align:start position:0% +page map address register and uses that +to find a pointer to the beginning of + + align:start position:0% +to find a pointer to the beginning of + + + align:start position:0% +to find a pointer to the beginning of +the page map it's to to the to the page + + align:start position:0% +the page map it's to to the to the page + + + align:start position:0% +the page map it's to to the to the page +map that's currently in use and then it + + align:start position:0% +map that's currently in use and then it + + + align:start position:0% +map that's currently in use and then it +uses the page map that's currently in + + align:start position:0% +uses the page map that's currently in + + + align:start position:0% +uses the page map that's currently in +use to resolve the current phys to to + + align:start position:0% +use to resolve the current phys to to + + + align:start position:0% +use to resolve the current phys to to +get what what physical address + + align:start position:0% +get what what physical address + + + align:start position:0% +get what what physical address +corresponds to this logical address okay + + align:start position:0% +corresponds to this logical address okay + + + align:start position:0% +corresponds to this logical address okay +so this is really the core concept from + + align:start position:0% +so this is really the core concept from + + + align:start position:0% +so this is really the core concept from +virtual memory so what we have now is we + + align:start position:0% +virtual memory so what we have now is we + + + align:start position:0% +virtual memory so what we have now is we +have this page map address register that + + align:start position:0% +have this page map address register that + + + align:start position:0% +have this page map address register that +can be used to select which one of these + + align:start position:0% +can be used to select which one of these + + + align:start position:0% +can be used to select which one of these +address spaces we are currently using + + align:start position:0% +address spaces we are currently using + + + align:start position:0% +address spaces we are currently using +okay so and when we have selected for + + align:start position:0% +okay so and when we have selected for + + + align:start position:0% +okay so and when we have selected for +example the page map for uh for for + + align:start position:0% +example the page map for uh for for + + + align:start position:0% +example the page map for uh for for +module a then module a can only refer to + + align:start position:0% +module a then module a can only refer to + + + align:start position:0% +module a then module a can only refer to +Virtual addresses uh that are in its + + align:start position:0% +Virtual addresses uh that are in its + + + align:start position:0% +Virtual addresses uh that are in its +page map and those virtual addresses can + + align:start position:0% +page map and those virtual addresses can + + + align:start position:0% +page map and those virtual addresses can +only map into physic only map into + + align:start position:0% +only map into physic only map into + + + align:start position:0% +only map into physic only map into +certain physical addresses so for + + align:start position:0% +certain physical addresses so for + + + align:start position:0% +certain physical addresses so for +example suppose this block here is the + + align:start position:0% +example suppose this block here is the + + + align:start position:0% +example suppose this block here is the +set of virtual addresses uh the set of + + align:start position:0% +set of virtual addresses uh the set of + + + align:start position:0% +set of virtual addresses uh the set of +physical addresses that correspond to + + align:start position:0% +physical addresses that correspond to + + + align:start position:0% +physical addresses that correspond to +the virtual addresses in A's page map + + align:start position:0% +the virtual addresses in A's page map + + + align:start position:0% +the virtual addresses in A's page map +okay these are the only physical + + align:start position:0% +okay these are the only physical + + + align:start position:0% +okay these are the only physical +addresses that a can talk about so if we + + align:start position:0% +addresses that a can talk about so if we + + + align:start position:0% +addresses that a can talk about so if we +for example have a different block of + + align:start position:0% +for example have a different block of + + + align:start position:0% +for example have a different block of +memory addresses that correspond to to + + align:start position:0% +memory addresses that correspond to to + + + align:start position:0% +memory addresses that correspond to to +the virtual addresses that B can + + align:start position:0% +the virtual addresses that B can + + + align:start position:0% +the virtual addresses that B can +reference we can see that there's no way + + align:start position:0% +reference we can see that there's no way + + + align:start position:0% +reference we can see that there's no way +for a for module a to be able to + + align:start position:0% +for a for module a to be able to + + + align:start position:0% +for a for module a to be able to +reference some of the memor for any of + + align:start position:0% +reference some of the memor for any of + + + align:start position:0% +reference some of the memor for any of +the memory that b uses so we're able to + + align:start position:0% +the memory that b uses so we're able to + + + align:start position:0% +the memory that b uses so we're able to +totally separate the physical memory + + align:start position:0% +totally separate the physical memory + + + align:start position:0% +totally separate the physical memory +pieces of physical memory that A and B + + align:start position:0% +pieces of physical memory that A and B + + + align:start position:0% +pieces of physical memory that A and B +can talk about by interposing this uh by + + align:start position:0% +can talk about by interposing this uh by + + + align:start position:0% +can talk about by interposing this uh by +by using this page map mechanism that + + align:start position:0% +by using this page map mechanism that + + + align:start position:0% +by using this page map mechanism that +virtual memory gives us so what we so + + align:start position:0% +virtual memory gives us so what we so + + + align:start position:0% +virtual memory gives us so what we so +basically what we've done is we've sort + + align:start position:0% +basically what we've done is we've sort + + + align:start position:0% +basically what we've done is we've sort +of added this extra layer of indirection + + align:start position:0% +of added this extra layer of indirection + + + align:start position:0% +of added this extra layer of indirection +this virtual memory system that is look + + align:start position:0% +this virtual memory system that is look + + + align:start position:0% +this virtual memory system that is look +that that gets to uh gets to map virtual + + align:start position:0% +that that gets to uh gets to map virtual + + + align:start position:0% +that that gets to uh gets to map virtual +addresses into phys physical + + align:start position:0% +addresses into phys physical + + + align:start position:0% +addresses into phys physical +addresses um so the rest of this lecture + + align:start position:0% +addresses um so the rest of this lecture + + + align:start position:0% +addresses um so the rest of this lecture +is really going to be details about how + + align:start position:0% +is really going to be details about how + + + align:start position:0% +is really going to be details about how +we actually make this work about how we + + align:start position:0% +we actually make this work about how we + + + align:start position:0% +we actually make this work about how we +do things like how we actually decide + + align:start position:0% +do things like how we actually decide + + + align:start position:0% +do things like how we actually decide +when to change the how how we decide to + + align:start position:0% +when to change the how how we decide to + + + align:start position:0% +when to change the how how we decide to +change this how we assign this P this PM + + align:start position:0% +change this how we assign this P this PM + + + align:start position:0% +change this how we assign this P this PM +register based on which one of the + + align:start position:0% +register based on which one of the + + + align:start position:0% +register based on which one of the +modules is currently executing about + + align:start position:0% +modules is currently executing about + + + align:start position:0% +modules is currently executing about +things like what the format of this page + + align:start position:0% +things like what the format of this page + + + align:start position:0% +things like what the format of this page +map table is going to look like okay so + + align:start position:0% +map table is going to look like okay so + + + align:start position:0% +map table is going to look like okay so +this is this is really the key + + align:start position:0% + + + + align:start position:0% + +concept so + + align:start position:0% +concept so + + + align:start position:0% +concept so +if you think so what I want to do now is + + align:start position:0% +if you think so what I want to do now is + + + align:start position:0% +if you think so what I want to do now is +sort of turn to this first question the + + align:start position:0% +sort of turn to this first question the + + + align:start position:0% +sort of turn to this first question the +second question I asked which is what + + align:start position:0% +second question I asked which is what + + + align:start position:0% +second question I asked which is what +how does this page map thing actually + + align:start position:0% +how does this page map thing actually + + + align:start position:0% +how does this page map thing actually +work what does it actually look how how + + align:start position:0% +work what does it actually look how how + + + align:start position:0% +work what does it actually look how how +is it actually represented so one very + + align:start position:0% +is it actually represented so one very + + + align:start position:0% +is it actually represented so one very +simple representation of a page map + + align:start position:0% +simple representation of a page map + + + align:start position:0% +simple representation of a page map +might be that uh it's simply is a + + align:start position:0% +might be that uh it's simply is a + + + align:start position:0% +might be that uh it's simply is a +pointer to the the page map just says + + align:start position:0% +pointer to the the page map just says + + + align:start position:0% +pointer to the the page map just says +where A's memory begins on the processor + + align:start position:0% +where A's memory begins on the processor + + + align:start position:0% +where A's memory begins on the processor +right so it's just one value it says A's + + align:start position:0% +right so it's just one value it says A's + + + align:start position:0% +right so it's just one value it says A's +memory begins at this location in the + + align:start position:0% +memory begins at this location in the + + + align:start position:0% +memory begins at this location in the +physical memory and all uh virtual + + align:start position:0% +physical memory and all uh virtual + + + align:start position:0% +physical memory and all uh virtual +addresses should be uh resolved relative + + align:start position:0% +addresses should be uh resolved relative + + + align:start position:0% +addresses should be uh resolved relative +to this beginning location of a memory + + align:start position:0% +to this beginning location of a memory + + + align:start position:0% +to this beginning location of a memory +um the problem with the the problem with + + align:start position:0% +um the problem with the the problem with + + + align:start position:0% +um the problem with the the problem with +that representation is that uh it it's + + align:start position:0% +that representation is that uh it it's + + + align:start position:0% +that representation is that uh it it's +not very flexible so um for example it + + align:start position:0% +not very flexible so um for example it + + + align:start position:0% +not very flexible so um for example it +means that if suppose that I have + + align:start position:0% +means that if suppose that I have + + + align:start position:0% +means that if suppose that I have +suppose that A and B are suppose there's + + align:start position:0% +suppose that A and B are suppose there's + + + align:start position:0% +suppose that A and B are suppose there's +a third process a third module C which + + align:start position:0% +a third process a third module C which + + + align:start position:0% +a third process a third module C which +is uh laid out in memory very right + + align:start position:0% +is uh laid out in memory very right + + + align:start position:0% +is uh laid out in memory very right +right next to a so its storage is is + + align:start position:0% +right next to a so its storage is is + + + align:start position:0% +right next to a so its storage is is +placed right next to a in memory and now + + align:start position:0% +placed right next to a in memory and now + + + align:start position:0% +placed right next to a in memory and now +suppose that a wants to allocate some + + align:start position:0% +suppose that a wants to allocate some + + + align:start position:0% +suppose that a wants to allocate some +additional memory memory that it can use + + align:start position:0% +additional memory memory that it can use + + + align:start position:0% +additional memory memory that it can use +um now in order to do that we're with if + + align:start position:0% +um now in order to do that we're with if + + + align:start position:0% +um now in order to do that we're with if +if these virtual address if the the page + + align:start position:0% +if these virtual address if the the page + + + align:start position:0% +if these virtual address if the the page +map is simply a single pointer to the + + align:start position:0% +map is simply a single pointer to the + + + align:start position:0% +map is simply a single pointer to the +beginning of A's address space we're + + align:start position:0% +beginning of A's address space we're + + + align:start position:0% +beginning of A's address space we're +kind of in trouble we can't just add + + align:start position:0% +kind of in trouble we can't just add + + + align:start position:0% +kind of in trouble we can't just add +memory onto the bottom because then we + + align:start position:0% +memory onto the bottom because then we + + + align:start position:0% +memory onto the bottom because then we +would overlap C's we would overlap C so + + align:start position:0% +would overlap C's we would overlap C so + + + align:start position:0% +would overlap C's we would overlap C so +we're going to have to sort of move all + + align:start position:0% +we're going to have to sort of move all + + + align:start position:0% +we're going to have to sort of move all +of A's memory around in order to be able + + align:start position:0% +of A's memory around in order to be able + + + align:start position:0% +of A's memory around in order to be able +to make space for this okay so that this + + align:start position:0% +to make space for this okay so that this + + + align:start position:0% +to make space for this okay so that this +seems like a little bit problematic to + + align:start position:0% +seems like a little bit problematic to + + + align:start position:0% +seems like a little bit problematic to +Simply have it be a pointer the other + + align:start position:0% +Simply have it be a pointer the other + + + align:start position:0% +Simply have it be a pointer the other +thing we could do is that we could + + align:start position:0% +thing we could do is that we could + + + align:start position:0% +thing we could do is that we could +suppose we could instead have a + + align:start position:0% +suppose we could instead have a + + + align:start position:0% +suppose we could instead have a +different uh option where we could say + + align:start position:0% +different uh option where we could say + + + align:start position:0% +different uh option where we could say +for example for every virtual address in + + align:start position:0% +for example for every virtual address in + + + align:start position:0% +for example for every virtual address in +in uh A's address space um so for each + + align:start position:0% +in uh A's address space um so for each + + + align:start position:0% +in uh A's address space um so for each +32-bit uh for each 322 bit value that a + + align:start position:0% +32-bit uh for each 322 bit value that a + + + align:start position:0% +32-bit uh for each 322 bit value that a +wants to resolve there might be an entry + + align:start position:0% +wants to resolve there might be an entry + + + align:start position:0% +wants to resolve there might be an entry +in this page map table right so we could + + align:start position:0% +in this page map table right so we could + + + align:start position:0% +in this page map table right so we could +for every 32-bit virtual address there + + align:start position:0% +for every 32-bit virtual address there + + + align:start position:0% +for every 32-bit virtual address there +would be a corresponding uh 32-bit uh + + align:start position:0% +would be a corresponding uh 32-bit uh + + + align:start position:0% +would be a corresponding uh 32-bit uh +physical address and there would just be + + align:start position:0% +physical address and there would just be + + + align:start position:0% +physical address and there would just be +a one to one mapping between all these + + align:start position:0% +a one to one mapping between all these + + + align:start position:0% +a one to one mapping between all these +things so if a could reference a million + + align:start position:0% +things so if a could reference a million + + + align:start position:0% +things so if a could reference a million +blocks of memory there would be a + + align:start position:0% +blocks of memory there would be a + + + align:start position:0% +blocks of memory there would be a +million entries in this page map table + + align:start position:0% +million entries in this page map table + + + align:start position:0% +million entries in this page map table +um so if you think about this for a + + align:start position:0% +um so if you think about this for a + + + align:start position:0% +um so if you think about this for a +minute that that sounds like kind of a + + align:start position:0% +minute that that sounds like kind of a + + + align:start position:0% +minute that that sounds like kind of a +bad idea too because now these tables + + align:start position:0% +bad idea too because now these tables + + + align:start position:0% +bad idea too because now these tables +are totally huge right and in fact + + align:start position:0% +are totally huge right and in fact + + + align:start position:0% +are totally huge right and in fact +they're is almost as big as they're + + align:start position:0% +they're is almost as big as they're + + + align:start position:0% +they're is almost as big as they're +they're as big as the memory itself + + align:start position:0% +they're as big as the memory itself + + + align:start position:0% +they're as big as the memory itself +right because if I have a million + + align:start position:0% +right because if I have a million + + + align:start position:0% +right because if I have a million +entries in the table if a can reference + + align:start position:0% +entries in the table if a can reference + + + align:start position:0% +entries in the table if a can reference +a million blocks then I'm going to need + + align:start position:0% +a million blocks then I'm going to need + + + align:start position:0% +a million blocks then I'm going to need +a million entries in the table so the + + align:start position:0% +a million entries in the table so the + + + align:start position:0% +a million entries in the table so the +table becomes just as big as the memory + + align:start position:0% +table becomes just as big as the memory + + + align:start position:0% +table becomes just as big as the memory +itself so we need some in between sort + + align:start position:0% +itself so we need some in between sort + + + align:start position:0% +itself so we need some in between sort +of alternative hybrid between these two + + align:start position:0% +of alternative hybrid between these two + + + align:start position:0% +of alternative hybrid between these two +uh extremes and the idea is again is + + align:start position:0% +uh extremes and the idea is again is + + + align:start position:0% +uh extremes and the idea is again is +very simple and you uh saw it in 64 so + + align:start position:0% +very simple and you uh saw it in 64 so + + + align:start position:0% +very simple and you uh saw it in 64 so +the idea is to take this 32-bit virtual + + align:start position:0% + + + + align:start position:0% + +address so suppose this is our 32bit + + align:start position:0% +address so suppose this is our 32bit + + + align:start position:0% +address so suppose this is our 32bit +virtual address now what we're going to + + align:start position:0% +virtual address now what we're going to + + + align:start position:0% +virtual address now what we're going to +do is we're going to split it up into + + align:start position:0% +do is we're going to split it up into + + + align:start position:0% +do is we're going to split it up into +two + + align:start position:0% +two + + + align:start position:0% +two +pieces a page + + align:start position:0% +pieces a page + + + align:start position:0% +pieces a page +number and an + + align:start position:0% +number and an + + + align:start position:0% +number and an +offset okay um we're going to choose + + align:start position:0% +offset okay um we're going to choose + + + align:start position:0% +offset okay um we're going to choose +some size for these two things um for + + align:start position:0% +some size for these two things um for + + + align:start position:0% +some size for these two things um for +now I'll just arbitrarily pick a 20 a 20 + + align:start position:0% +now I'll just arbitrarily pick a 20 a 20 + + + align:start position:0% +now I'll just arbitrarily pick a 20 a 20 +bit page number uh and a 12bit + + align:start position:0% +bit page number uh and a 12bit + + + align:start position:0% +bit page number uh and a 12bit +offset okay so um what this page so what + + align:start position:0% +offset okay so um what this page so what + + + align:start position:0% +offset okay so um what this page so what +this is going to do so now what we're + + align:start position:0% +this is going to do so now what we're + + + align:start position:0% +this is going to do so now what we're +going to do is instead of storing uh a + + align:start position:0% +going to do is instead of storing uh a + + + align:start position:0% +going to do is instead of storing uh a +single uh a single word of memory at + + align:start position:0% +single uh a single word of memory at + + + align:start position:0% +single uh a single word of memory at +each entry in this table we're going to + + align:start position:0% +each entry in this table we're going to + + + align:start position:0% +each entry in this table we're going to +store a page of memory at each entry in + + align:start position:0% +store a page of memory at each entry in + + + align:start position:0% +store a page of memory at each entry in +this table so um + + align:start position:0% + + + + align:start position:0% + +so this table is going to look like a + + align:start position:0% +so this table is going to look like a + + + align:start position:0% +so this table is going to look like a +mapping between a page and a physical + + align:start position:0% +mapping between a page and a physical + + + align:start position:0% +mapping between a page and a physical +address okay so what a page is so so uh + + align:start position:0% +address okay so what a page is so so uh + + + align:start position:0% +address okay so what a page is so so uh +if so if the the page number is 20 bits + + align:start position:0% +if so if the the page number is 20 bits + + + align:start position:0% +if so if the the page number is 20 bits +long then that means that the each page + + align:start position:0% +long then that means that the each page + + + align:start position:0% +long then that means that the each page +is going to be uh 2 to the 12 bits big + + align:start position:0% +is going to be uh 2 to the 12 bits big + + + align:start position:0% +is going to be uh 2 to the 12 bits big +which is equal to say + + align:start position:0% +which is equal to say + + + align:start position:0% +which is equal to say +4,096 uh words okay + + align:start position:0% +4,096 uh words okay + + + align:start position:0% +4,096 uh words okay +um so the idea is that we're going to + + align:start position:0% +um so the idea is that we're going to + + + align:start position:0% +um so the idea is that we're going to +have + + align:start position:0% +have + + + align:start position:0% +have +two to the 20th Pages within each + + align:start position:0% +two to the 20th Pages within each + + + align:start position:0% +two to the 20th Pages within each +address space um and each page is going + + align:start position:0% +address space um and each page is going + + + align:start position:0% +address space um and each page is going +to map to one of these 496 byte blocks + + align:start position:0% +to map to one of these 496 byte blocks + + + align:start position:0% +to map to one of these 496 byte blocks +okay so + + align:start position:0% + + + + align:start position:0% + +um if we have our memory here uh this + + align:start position:0% +um if we have our memory here uh this + + + align:start position:0% +um if we have our memory here uh this +phys this page say page one is going to + + align:start position:0% +phys this page say page one is going to + + + align:start position:0% +phys this page say page one is going to +map into some physical address and page + + align:start position:0% +map into some physical address and page + + + align:start position:0% +map into some physical address and page +two is going to map into some other + + align:start position:0% +two is going to map into some other + + + align:start position:0% +two is going to map into some other +physical block okay so each one of these + + align:start position:0% +physical block okay so each one of these + + + align:start position:0% +physical block okay so each one of these +things is now + + align:start position:0% +things is now + + + align:start position:0% +things is now +4,096 + + align:start position:0% +4,096 + + + align:start position:0% +4,096 +bytes each block here okay um and so uh + + align:start position:0% +bytes each block here okay um and so uh + + + align:start position:0% +bytes each block here okay um and so uh +this let's just expand this so this is + + align:start position:0% +this let's just expand this so this is + + + align:start position:0% +this let's just expand this so this is +now a page um and this offset this 12bit + + align:start position:0% +now a page um and this offset this 12bit + + + align:start position:0% +now a page um and this offset this 12bit +offset is going to be used in order to + + align:start position:0% +offset is going to be used in order to + + + align:start position:0% +offset is going to be used in order to +look up the word that we want to + + align:start position:0% +look up the word that we want to + + + align:start position:0% +look up the word that we want to +actually look up in this page so um if + + align:start position:0% +actually look up in this page so um if + + + align:start position:0% +actually look up in this page so um if +the uh if if the if the virtual address + + align:start position:0% +the uh if if the if the virtual address + + + align:start position:0% +the uh if if the if the virtual address +is say for example uh page one um offset + + align:start position:0% +is say for example uh page one um offset + + + align:start position:0% +is say for example uh page one um offset +zero what that's going to do is we're + + align:start position:0% +zero what that's going to do is we're + + + align:start position:0% +zero what that's going to do is we're +going to look in P we're going to look + + align:start position:0% +going to look in P we're going to look + + + align:start position:0% +going to look in P we're going to look +up in the page map we're going to find + + align:start position:0% +up in the page map we're going to find + + + align:start position:0% +up in the page map we're going to find +uh the page number that corresponds to + + align:start position:0% +uh the page number that corresponds to + + + align:start position:0% +uh the page number that corresponds to +uh we're going to find page number one + + align:start position:0% +uh we're going to find page number one + + + align:start position:0% +uh we're going to find page number one +we're going to find the physical address + + align:start position:0% +we're going to find the physical address + + + align:start position:0% +we're going to find the physical address +that corresponds to it we're going to + + align:start position:0% +that corresponds to it we're going to + + + align:start position:0% +that corresponds to it we're going to +come down here and look in this physical + + align:start position:0% +come down here and look in this physical + + + align:start position:0% +come down here and look in this physical +address uh and look at this block of + + align:start position:0% +address uh and look at this block of + + + align:start position:0% +address uh and look at this block of +memory and then within this 496 block of + + align:start position:0% +memory and then within this 496 block of + + + align:start position:0% +memory and then within this 496 block of +memory we're going to take the uh + + align:start position:0% +memory we're going to take the uh + + + align:start position:0% +memory we're going to take the uh +address zero the the the first word + + align:start position:0% +address zero the the the first word + + + align:start position:0% +address zero the the the first word +within that thing okay so um now we + + align:start position:0% +within that thing okay so um now we + + + align:start position:0% +within that thing okay so um now we +don't need to have now the size of these + + align:start position:0% +don't need to have now the size of these + + + align:start position:0% +don't need to have now the size of these +page tables is much smaller right + + align:start position:0% +page tables is much smaller right + + + align:start position:0% +page tables is much smaller right +they're no longer 2 to the 30th bits now + + align:start position:0% +they're no longer 2 to the 30th bits now + + + align:start position:0% +they're no longer 2 to the 30th bits now +they're to the 20th bits which is uh + + align:start position:0% +they're to the 20th bits which is uh + + + align:start position:0% +they're to the 20th bits which is uh +some small number of megabytes big um + + align:start position:0% +some small number of megabytes big um + + + align:start position:0% +some small number of megabytes big um +and they uh and but we still have this + + align:start position:0% +and they uh and but we still have this + + + align:start position:0% +and they uh and but we still have this +this we've avoided this problem that we + + align:start position:0% +this we've avoided this problem that we + + + align:start position:0% +this we've avoided this problem that we +had before we have some flexibility in + + align:start position:0% +had before we have some flexibility in + + + align:start position:0% +had before we have some flexibility in +terms of where how these physical how + + align:start position:0% +terms of where how these physical how + + + align:start position:0% +terms of where how these physical how +each page Maps into the physical memory + + align:start position:0% +each page Maps into the physical memory + + + align:start position:0% +each page Maps into the physical memory +so I can create a third page here I can + + align:start position:0% +so I can create a third page here I can + + + align:start position:0% +so I can create a third page here I can +allocate a third page uh to a a process + + align:start position:0% +allocate a third page uh to a a process + + + align:start position:0% +allocate a third page uh to a a process +and I can map that into any 496 block a + + align:start position:0% +and I can map that into any 496 block a + + + align:start position:0% +and I can map that into any 496 block a +BTE block that's in memory that's + + align:start position:0% +BTE block that's in memory that's + + + align:start position:0% +BTE block that's in memory that's +currently unused okay so I have + + align:start position:0% +currently unused okay so I have + + + align:start position:0% +currently unused okay so I have +flexibility I don't have this problem + + align:start position:0% +flexibility I don't have this problem + + + align:start position:0% +flexibility I don't have this problem +say with a where A and C were colliding + + align:start position:0% +say with a where A and C were colliding + + + align:start position:0% +say with a where A and C were colliding +with each + + align:start position:0% +with each + + + align:start position:0% +with each +other + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so this is sort of the outline of how + + align:start position:0% +so this is sort of the outline of how + + + align:start position:0% +so this is sort of the outline of how +virtual memory works but what I haven't + + align:start position:0% +virtual memory works but what I haven't + + + align:start position:0% +virtual memory works but what I haven't +yet described to you is how it is that + + align:start position:0% +yet described to you is how it is that + + + align:start position:0% +yet described to you is how it is that +we can actually go about creating these + + align:start position:0% +we can actually go about creating these + + + align:start position:0% +we can actually go about creating these +uh these different address spaces that + + align:start position:0% +uh these different address spaces that + + + align:start position:0% +uh these different address spaces that +are allocated to the different modules + + align:start position:0% +are allocated to the different modules + + + align:start position:0% +are allocated to the different modules +and how we can switch between different + + align:start position:0% +and how we can switch between different + + + align:start position:0% +and how we can switch between different +modules using this this PM register so + + align:start position:0% +modules using this this PM register so + + + align:start position:0% +modules using this this PM register so +um I sort of described this as though + + align:start position:0% +um I sort of described this as though + + + align:start position:0% +um I sort of described this as though +these things you know suppose that these + + align:start position:0% +these things you know suppose that these + + + align:start position:0% +these things you know suppose that these +these data structures exist now here's + + align:start position:0% +these data structures exist now here's + + + align:start position:0% +these data structures exist now here's +how we can use them but I haven't told + + align:start position:0% +how we can use them but I haven't told + + + align:start position:0% +how we can use them but I haven't told +you how these data structures all get + + align:start position:0% +you how these data structures all get + + + align:start position:0% +you how these data structures all get +put together and created and set up to + + align:start position:0% +put together and created and set up to + + + align:start position:0% +put together and created and set up to +begin with um and I hinted at this at + + align:start position:0% +begin with um and I hinted at this at + + + align:start position:0% +begin with um and I hinted at this at +the beginning but in order to do this + + align:start position:0% +the beginning but in order to do this + + + align:start position:0% +the beginning but in order to do this +what we're going to need is some sort of + + align:start position:0% +what we're going to need is some sort of + + + align:start position:0% +what we're going to need is some sort of +a uh special supervisory module that's + + align:start position:0% +a uh special supervisory module that's + + + align:start position:0% +a uh special supervisory module that's +able to look at the page maps for all of + + align:start position:0% +able to look at the page maps for all of + + + align:start position:0% +able to look at the page maps for all of +these different that's able to create + + align:start position:0% +these different that's able to create + + + align:start position:0% +these different that's able to create +new page Maps and look at the page maps + + align:start position:0% +new page Maps and look at the page maps + + + align:start position:0% +new page Maps and look at the page maps +for all of the different modules that + + align:start position:0% +for all of the different modules that + + + align:start position:0% +for all of the different modules that +are within the system um and this + + align:start position:0% +are within the system um and this + + + align:start position:0% +are within the system um and this +supervisory module is going to be able + + align:start position:0% +supervisory module is going to be able + + + align:start position:0% +supervisory module is going to be able +to do things like add new memory to a + + align:start position:0% +to do things like add new memory to a + + + align:start position:0% +to do things like add new memory to a +page map or be able to do or be able to + + align:start position:0% +page map or be able to do or be able to + + + align:start position:0% +page map or be able to do or be able to +uh destroy delete uh a a particular + + align:start position:0% +uh destroy delete uh a a particular + + + align:start position:0% +uh destroy delete uh a a particular +module and its Associated page map so we + + align:start position:0% +module and its Associated page map so we + + + align:start position:0% +module and its Associated page map so we +need some sort of a thing that can + + align:start position:0% +need some sort of a thing that can + + + align:start position:0% +need some sort of a thing that can +manage all of this infrastructure um so + + align:start position:0% +manage all of this infrastructure um so + + + align:start position:0% +manage all of this infrastructure um so +this supervisory + + align:start position:0% + + + + align:start position:0% + +module it's called the + + align:start position:0% +module it's called the + + + align:start position:0% +module it's called the +kernel okay + + align:start position:0% +kernel okay + + + align:start position:0% +kernel okay +and the kernel is really uh it's it's + + align:start position:0% +and the kernel is really uh it's it's + + + align:start position:0% +and the kernel is really uh it's it's +going to be the thing that's going to be + + align:start position:0% +going to be the thing that's going to be + + + align:start position:0% +going to be the thing that's going to be +in charge of managing all these data + + align:start position:0% +in charge of managing all these data + + + align:start position:0% +in charge of managing all these data +structures for us so + + align:start position:0% + + + + align:start position:0% + +um so + + align:start position:0% +um so + + + align:start position:0% +um so +so here's our microprocessor with its PM + + align:start position:0% +so here's our microprocessor with its PM + + + align:start position:0% +so here's our microprocessor with its PM +register on it um and what we're going + + align:start position:0% +register on it um and what we're going + + + align:start position:0% +register on it um and what we're going +to do is we're going to extend the micro + + align:start position:0% +to do is we're going to extend the micro + + + align:start position:0% +to do is we're going to extend the micro +processor with one additional uh piece + + align:start position:0% +processor with one additional uh piece + + + align:start position:0% +processor with one additional uh piece +of one additional piece of hardware and + + align:start position:0% +of one additional piece of hardware and + + + align:start position:0% +of one additional piece of hardware and +this is the uh + + align:start position:0% +this is the uh + + + align:start position:0% +this is the uh +user + + align:start position:0% +user + + + align:start position:0% +user +uh kernel bit okay so this is just a bit + + align:start position:0% +uh kernel bit okay so this is just a bit + + + align:start position:0% +uh kernel bit okay so this is just a bit +that specifies whether we're whether + + align:start position:0% +that specifies whether we're whether + + + align:start position:0% +that specifies whether we're whether +we're currently running a user module + + align:start position:0% +we're currently running a user module + + + align:start position:0% +we're currently running a user module +that is one of these just just a program + + align:start position:0% +that is one of these just just a program + + + align:start position:0% +that is one of these just just a program +that's running on your computer or + + align:start position:0% +that's running on your computer or + + + align:start position:0% +that's running on your computer or +whether uh the kernel is currently + + align:start position:0% +whether uh the kernel is currently + + + align:start position:0% +whether uh the kernel is currently +executed + + align:start position:0% +executed + + + align:start position:0% +executed +okay and the idea with this kernel bit + + align:start position:0% +okay and the idea with this kernel bit + + + align:start position:0% +okay and the idea with this kernel bit +is that when this kernel bit is set the + + align:start position:0% +is that when this kernel bit is set the + + + align:start position:0% +is that when this kernel bit is set the +uh code that's going to that is running + + align:start position:0% +uh code that's going to that is running + + + align:start position:0% +uh code that's going to that is running +is going to have special privileges it's + + align:start position:0% +is going to have special privileges it's + + + align:start position:0% +is going to have special privileges it's +going to be able to do it's going to be + + align:start position:0% +going to be able to do it's going to be + + + align:start position:0% +going to be able to do it's going to be +able to manipulate uh special things + + align:start position:0% +able to manipulate uh special things + + + align:start position:0% +able to manipulate uh special things +about the uh hardware and the processor + + align:start position:0% +about the uh hardware and the processor + + + align:start position:0% +about the uh hardware and the processor +and in particular um we're going to have + + align:start position:0% +and in particular um we're going to have + + + align:start position:0% +and in particular um we're going to have +a rule that says that + + align:start position:0% +a rule that says that + + + align:start position:0% +a rule that says that +only + + align:start position:0% +only + + + align:start position:0% +only +uh the + + align:start position:0% +uh the + + + align:start position:0% +uh the +kernel can change the PM okay + + align:start position:0% + + + + align:start position:0% + +so the PM is the thing that specifies + + align:start position:0% +so the PM is the thing that specifies + + + align:start position:0% +so the PM is the thing that specifies +which process is currently running um + + align:start position:0% +which process is currently running um + + + align:start position:0% +which process is currently running um +and which selects which address space we + + align:start position:0% +and which selects which address space we + + + align:start position:0% +and which selects which address space we +want to be currently using um and what + + align:start position:0% +want to be currently using um and what + + + align:start position:0% +want to be currently using um and what +we're going to use is we're going to use + + align:start position:0% +we're going to use is we're going to use + + + align:start position:0% +we're going to use is we're going to use +we're and but so what we want what we're + + align:start position:0% +we're and but so what we want what we're + + + align:start position:0% +we're and but so what we want what we're +going to do is have the kernel be the + + align:start position:0% +going to do is have the kernel be the + + + align:start position:0% +going to do is have the kernel be the +thing that's in charge of manipulating + + align:start position:0% +thing that's in charge of manipulating + + + align:start position:0% +thing that's in charge of manipulating +the value of this PM register to select + + align:start position:0% +the value of this PM register to select + + + align:start position:0% +the value of this PM register to select +which thing is currently being executed + + align:start position:0% +which thing is currently being executed + + + align:start position:0% +which thing is currently being executed +um and we want to make it so that only + + align:start position:0% +um and we want to make it so that only + + + align:start position:0% +um and we want to make it so that only +the kernel can do this because if we for + + align:start position:0% +the kernel can do this because if we for + + + align:start position:0% +the kernel can do this because if we for +example allowed one of these other + + align:start position:0% +example allowed one of these other + + + align:start position:0% +example allowed one of these other +programs to be able to manipulate the PM + + align:start position:0% +programs to be able to manipulate the PM + + + align:start position:0% +programs to be able to manipulate the PM +right then that other program might be + + align:start position:0% +right then that other program might be + + + align:start position:0% +right then that other program might be +able to do something unpleasant to the + + align:start position:0% +able to do something unpleasant to the + + + align:start position:0% +able to do something unpleasant to the +computer right it changes the PM to + + align:start position:0% +computer right it changes the PM to + + + align:start position:0% +computer right it changes the PM to +point at some other program's memory um + + align:start position:0% +point at some other program's memory um + + + align:start position:0% +point at some other program's memory um +and now suddenly all the memory + + align:start position:0% +and now suddenly all the memory + + + align:start position:0% +and now suddenly all the memory +addresses in the system are going to be + + align:start position:0% +addresses in the system are going to be + + + align:start position:0% +addresses in the system are going to be +being resolved uh then suddenly we're + + align:start position:0% +being resolved uh then suddenly we're + + + align:start position:0% +being resolved uh then suddenly we're +going to be sort of resolving memory + + align:start position:0% +going to be sort of resolving memory + + + align:start position:0% +going to be sort of resolving memory +addresses relative to some other + + align:start position:0% +addresses relative to some other + + + align:start position:0% +addresses relative to some other +module's uh page map and that's likely + + align:start position:0% +module's uh page map and that's likely + + + align:start position:0% +module's uh page map and that's likely +to be a problematic thing it's likely to + + align:start position:0% +to be a problematic thing it's likely to + + + align:start position:0% +to be a problematic thing it's likely to +cause that other module to crash for + + align:start position:0% +cause that other module to crash for + + + align:start position:0% +cause that other module to crash for +example because the processor is set up + + align:start position:0% +example because the processor is set up + + + align:start position:0% +example because the processor is set up +to be executing um instructions from the + + align:start position:0% +to be executing um instructions from the + + + align:start position:0% +to be executing um instructions from the +current program so we want to make sure + + align:start position:0% +current program so we want to make sure + + + align:start position:0% +current program so we want to make sure +that only uh something this kernel can + + align:start position:0% +that only uh something this kernel can + + + align:start position:0% +that only uh something this kernel can +change the PM and this kernel is going + + align:start position:0% +change the PM and this kernel is going + + + align:start position:0% +change the PM and this kernel is going +to be this sort of supervisory module + + align:start position:0% +to be this sort of supervisory module + + + align:start position:0% +to be this sort of supervisory module +that all of the other modules are going + + align:start position:0% +that all of the other modules are going + + + align:start position:0% +that all of the other modules are going +to have to trust to kind of do the right + + align:start position:0% +to have to trust to kind of do the right + + + align:start position:0% +to have to trust to kind of do the right +thing and manage the computer's + + align:start position:0% +thing and manage the computer's + + + align:start position:0% +thing and manage the computer's +execution for you um and this kernel in + + align:start position:0% +execution for you um and this kernel in + + + align:start position:0% +execution for you um and this kernel in +except for this one difference that the + + align:start position:0% +except for this one difference that the + + + align:start position:0% +except for this one difference that the +kernel can change the PM the kernel is + + align:start position:0% +kernel can change the PM the kernel is + + + align:start position:0% +kernel can change the PM the kernel is +in all other respects uh essentially + + align:start position:0% +in all other respects uh essentially + + + align:start position:0% +in all other respects uh essentially +just going to be another module that's + + align:start position:0% +just going to be another module that's + + + align:start position:0% +just going to be another module that's +running in the computer system so the + + align:start position:0% +running in the computer system so the + + + align:start position:0% +running in the computer system so the +kernel in particular the kernel is also + + align:start position:0% +kernel in particular the kernel is also + + + align:start position:0% +kernel in particular the kernel is also +going to have one of these 32-bit + + align:start position:0% +going to have one of these 32-bit + + + align:start position:0% +going to have one of these 32-bit +virtual address spaces associated with + + align:start position:0% +virtual address spaces associated with + + + align:start position:0% +virtual address spaces associated with +it okay um and we're going to but what + + align:start position:0% +it okay um and we're going to but what + + + align:start position:0% +it okay um and we're going to but what +we're going to do is we're going to say + + align:start position:0% +we're going to do is we're going to say + + + align:start position:0% +we're going to do is we're going to say +that the kernel within its address space + + align:start position:0% +that the kernel within its address space + + + align:start position:0% +that the kernel within its address space +um has all of the page maps of all the + + align:start position:0% +um has all of the page maps of all the + + + align:start position:0% +um has all of the page maps of all the +other programs that are currently + + align:start position:0% +other programs that are currently + + + align:start position:0% +other programs that are currently +running on the system mapped into its + + align:start position:0% +running on the system mapped into its + + + align:start position:0% +running on the system mapped into its +address space okay so this is a little + + align:start position:0% +address space okay so this is a little + + + align:start position:0% +address space okay so this is a little +bit tricky because I presented this as + + align:start position:0% +bit tricky because I presented this as + + + align:start position:0% +bit tricky because I presented this as +though you know A and B's memory a a and + + align:start position:0% +though you know A and B's memory a a and + + + align:start position:0% +though you know A and B's memory a a and +b reference totally different uh pieces + + align:start position:0% +b reference totally different uh pieces + + + align:start position:0% +b reference totally different uh pieces +of memory so I sort of have told you so + + align:start position:0% +of memory so I sort of have told you so + + + align:start position:0% +of memory so I sort of have told you so +far only about modules that are uh + + align:start position:0% +far only about modules that are uh + + + align:start position:0% +far only about modules that are uh +referencing disjoint sets of memory but + + align:start position:0% +referencing disjoint sets of memory but + + + align:start position:0% +referencing disjoint sets of memory but +in fact these page Maps right they just + + align:start position:0% +in fact these page Maps right they just + + + align:start position:0% +in fact these page Maps right they just +reside in memory somewhere um and the it + + align:start position:0% +reside in memory somewhere um and the it + + + align:start position:0% +reside in memory somewhere um and the it +it's just fine if I for example have + + align:start position:0% +it's just fine if I for example have + + + align:start position:0% +it's just fine if I for example have +multiple modules uh that are all ma that + + align:start position:0% +multiple modules uh that are all ma that + + + align:start position:0% +multiple modules uh that are all ma that +that are able to reference that have the + + align:start position:0% +that are able to reference that have the + + + align:start position:0% +that are able to reference that have the +same physical addresses mapped into + + align:start position:0% +same physical addresses mapped into + + + align:start position:0% +same physical addresses mapped into +their uh in into their virtual address + + align:start position:0% +their uh in into their virtual address + + + align:start position:0% +their uh in into their virtual address +space so I may you know it's very likely + + align:start position:0% +space so I may you know it's very likely + + + align:start position:0% +space so I may you know it's very likely +that I might want to have some down here + + align:start position:0% +that I might want to have some down here + + + align:start position:0% +that I might want to have some down here +at the bottom that both A and B can + + align:start position:0% +at the bottom that both A and B can + + + align:start position:0% +at the bottom that both A and B can +access so this might be stuff that + + align:start position:0% +access so this might be stuff that + + + align:start position:0% +access so this might be stuff that +shared between A and B I can map that + + align:start position:0% +shared between A and B I can map that + + + align:start position:0% +shared between A and B I can map that +into both A and B's memory um in the + + align:start position:0% +into both A and B's memory um in the + + + align:start position:0% +into both A and B's memory um in the +same way what I'm going to do is I'm + + align:start position:0% +same way what I'm going to do is I'm + + + align:start position:0% +same way what I'm going to do is I'm +going to map these page Maps which are + + align:start position:0% +going to map these page Maps which are + + + align:start position:0% +going to map these page Maps which are +also stored in memory into the all of + + align:start position:0% +also stored in memory into the all of + + + align:start position:0% +also stored in memory into the all of +the page Maps into the Kernel's address + + align:start position:0% +the page Maps into the Kernel's address + + + align:start position:0% +the page Maps into the Kernel's address +space so the kernel is going to be able + + align:start position:0% +space so the kernel is going to be able + + + align:start position:0% +space so the kernel is going to be able +to reference uh all the the address + + align:start position:0% +to reference uh all the the address + + + align:start position:0% +to reference uh all the the address +spaces of all the modules um and the + + align:start position:0% +spaces of all the modules um and the + + + align:start position:0% +spaces of all the modules um and the +kernel is also going to keep a little + + align:start position:0% +kernel is also going to keep a little + + + align:start position:0% +kernel is also going to keep a little +table of all the page maps that are for + + align:start position:0% +table of all the page maps that are for + + + align:start position:0% +table of all the page maps that are for +all of the currently running programs on + + align:start position:0% +all of the currently running programs on + + + align:start position:0% +all of the currently running programs on +the system + + align:start position:0% +the system + + + align:start position:0% +the system +so these are for example page maps for a + + align:start position:0% +so these are for example page maps for a + + + align:start position:0% +so these are for example page maps for a +and b um and this is a list of all the + + align:start position:0% +and b um and this is a list of all the + + + align:start position:0% +and b um and this is a list of all the +maps that are currently running in the + + align:start position:0% +maps that are currently running in the + + + align:start position:0% +maps that are currently running in the +system so uh what's going to happen is + + align:start position:0% +system so uh what's going to happen is + + + align:start position:0% +system so uh what's going to happen is +so now what can happen is that the + + align:start position:0% +so now what can happen is that the + + + align:start position:0% +so now what can happen is that the +kernel because the kernel is allowed to + + align:start position:0% +kernel because the kernel is allowed to + + + align:start position:0% +kernel because the kernel is allowed to +change the PM and because it knows about + + align:start position:0% +change the PM and because it knows about + + + align:start position:0% +change the PM and because it knows about +the the location of all the other + + align:start position:0% +the the location of all the other + + + align:start position:0% +the the location of all the other +address spaces that are in the system it + + align:start position:0% +address spaces that are in the system it + + + align:start position:0% +address spaces that are in the system it +can when it wants to start running one + + align:start position:0% +can when it wants to start running one + + + align:start position:0% +can when it wants to start running one +of these programs that's running in the + + align:start position:0% +of these programs that's running in the + + + align:start position:0% +of these programs that's running in the +system it can change the value of the PM + + align:start position:0% +system it can change the value of the PM + + + align:start position:0% +system it can change the value of the PM +to be sort of the the the PM for a or + + align:start position:0% +to be sort of the the the PM for a or + + + align:start position:0% +to be sort of the the the PM for a or +the PM Tob and it can manipulate the all + + align:start position:0% +the PM Tob and it can manipulate the all + + + align:start position:0% +the PM Tob and it can manipulate the all +the values of the registers on the + + align:start position:0% +the values of the registers on the + + + align:start position:0% +the values of the registers on the +system so that you can start executing + + align:start position:0% +system so that you can start executing + + + align:start position:0% +system so that you can start executing +code for one of these you can switch + + align:start position:0% +code for one of these you can switch + + + align:start position:0% +code for one of these you can switch +between one of these these two modules + + align:start position:0% +between one of these these two modules + + + align:start position:0% +between one of these these two modules +so the actual process of switching + + align:start position:0% +so the actual process of switching + + + align:start position:0% +so the actual process of switching +between which module is currently + + align:start position:0% +between which module is currently + + + align:start position:0% +between which module is currently +running we're going to focus on that + + align:start position:0% +running we're going to focus on that + + + align:start position:0% +running we're going to focus on that +more next time so don't worry too much + + align:start position:0% +more next time so don't worry too much + + + align:start position:0% +more next time so don't worry too much +if you don't understand the details of + + align:start position:0% +if you don't understand the details of + + + align:start position:0% +if you don't understand the details of +how you actually switch from executing + + align:start position:0% +how you actually switch from executing + + + align:start position:0% +how you actually switch from executing +one program to another program but you + + align:start position:0% +one program to another program but you + + + align:start position:0% +one program to another program but you +can see that the kernel can switch which + + align:start position:0% +can see that the kernel can switch which + + + align:start position:0% +can see that the kernel can switch which +sort of which me which address space is + + align:start position:0% +sort of which me which address space is + + + align:start position:0% +sort of which me which address space is +currently active by simply manipulating + + align:start position:0% +currently active by simply manipulating + + + align:start position:0% +currently active by simply manipulating +ating the value of this PM register + + align:start position:0% +ating the value of this PM register + + + align:start position:0% +ating the value of this PM register +furthermore the the kernel can do things + + align:start position:0% +furthermore the the kernel can do things + + + align:start position:0% +furthermore the the kernel can do things +like uh it can create a new map right so + + align:start position:0% +like uh it can create a new map right so + + + align:start position:0% +like uh it can create a new map right so +the kernel can simply allocate one of + + align:start position:0% +the kernel can simply allocate one of + + + align:start position:0% +the kernel can simply allocate one of +these new tables and it can set up a + + align:start position:0% +these new tables and it can set up a + + + align:start position:0% +these new tables and it can set up a +mapping from a set of uh set of virtual + + align:start position:0% +mapping from a set of uh set of virtual + + + align:start position:0% +mapping from a set of uh set of virtual +addresses to a set of physical addresses + + align:start position:0% +addresses to a set of physical addresses + + + align:start position:0% +addresses to a set of physical addresses +so that you can create a new address + + align:start position:0% +so that you can create a new address + + + align:start position:0% +so that you can create a new address +space that a new module can start + + align:start position:0% +space that a new module can start + + + align:start position:0% +space that a new module can start +executing within similarly the kernel + + align:start position:0% +executing within similarly the kernel + + + align:start position:0% +executing within similarly the kernel +can do things like allocate new memory + + align:start position:0% +can do things like allocate new memory + + + align:start position:0% +can do things like allocate new memory +into one of these addresses so it can + + align:start position:0% +into one of these addresses so it can + + + align:start position:0% +into one of these addresses so it can +map some additional it can map some + + align:start position:0% +map some additional it can map some + + + align:start position:0% +map some additional it can map some +additional physical uh some it can map + + align:start position:0% +additional physical uh some it can map + + + align:start position:0% +additional physical uh some it can map +some additional virtual addresses uh + + align:start position:0% +some additional virtual addresses uh + + + align:start position:0% +some additional virtual addresses uh +into real physical memory so that one of + + align:start position:0% +into real physical memory so that one of + + + align:start position:0% +into real physical memory so that one of +these when one of these modules say for + + align:start position:0% +these when one of these modules say for + + + align:start position:0% +these when one of these modules say for +example requests additional memory to + + align:start position:0% +example requests additional memory to + + + align:start position:0% +example requests additional memory to +execute the kernel can uh add that + + align:start position:0% +execute the kernel can uh add that + + + align:start position:0% +execute the kernel can uh add that +memory into they can add an entry into + + align:start position:0% +memory into they can add an entry into + + + align:start position:0% +memory into they can add an entry into +the table so that that new memory that + + align:start position:0% +the table so that that new memory that + + + align:start position:0% +the table so that that new memory that +the program has requested actually Maps + + align:start position:0% +the program has requested actually Maps + + + align:start position:0% +the program has requested actually Maps +into a valid physical + + align:start position:0% + + + + align:start position:0% + +address okay so + + align:start position:0% +address okay so + + + align:start position:0% +address okay so +um the question of course then is so + + align:start position:0% +um the question of course then is so + + + align:start position:0% +um the question of course then is so +this is this so you can see the value of + + align:start position:0% +this is this so you can see the value of + + + align:start position:0% +this is this so you can see the value of +having this kernel module but the + + align:start position:0% +having this kernel module but the + + + align:start position:0% +having this kernel module but the +question is how do we communicate + + align:start position:0% +question is how do we communicate + + + align:start position:0% +question is how do we communicate +between these modules that are running + + align:start position:0% +between these modules that are running + + + align:start position:0% +between these modules that are running +these user level modules that are + + align:start position:0% +these user level modules that are + + + align:start position:0% +these user level modules that are +running uh and the kernel module uh that + + align:start position:0% +running uh and the kernel module uh that + + + align:start position:0% +running uh and the kernel module uh that +needs that that the user modules need to + + align:start position:0% +needs that that the user modules need to + + + align:start position:0% +needs that that the user modules need to +invoke for example to request new memory + + align:start position:0% +invoke for example to request new memory + + + align:start position:0% +invoke for example to request new memory +um so the way that we're going to do + + align:start position:0% +um so the way that we're going to do + + + align:start position:0% +um so the way that we're going to do +this + + align:start position:0% +this + + + align:start position:0% +this +is just like we've done everything else + + align:start position:0% +is just like we've done everything else + + + align:start position:0% +is just like we've done everything else +in this lecture so far by adding uh a + + align:start position:0% +in this lecture so far by adding uh a + + + align:start position:0% +in this lecture so far by adding uh a +little bit of extra by changing the + + align:start position:0% +little bit of extra by changing the + + + align:start position:0% +little bit of extra by changing the +processor just a little bit so in + + align:start position:0% +processor just a little bit so in + + + align:start position:0% +processor just a little bit so in +particular what we're going to do + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +what we're going to do is to uh add this + + align:start position:0% +what we're going to do is to uh add this + + + align:start position:0% +what we're going to do is to uh add this +notion of a supervisor + + align:start position:0% + + + + align:start position:0% + +call call that SVC so a supervisor call + + align:start position:0% +call call that SVC so a supervisor call + + + align:start position:0% +call call that SVC so a supervisor call +is simply a special instruction uh that + + align:start position:0% +is simply a special instruction uh that + + + align:start position:0% +is simply a special instruction uh that +is on the processor that invokes the + + align:start position:0% +is on the processor that invokes the + + + align:start position:0% +is on the processor that invokes the +kernel so when this supervisor call + + align:start position:0% +kernel so when this supervisor call + + + align:start position:0% +kernel so when this supervisor call +instruction gets executed uh it's going + + align:start position:0% +instruction gets executed uh it's going + + + align:start position:0% +instruction gets executed uh it's going +to set up the uh the state of these pm + + align:start position:0% +to set up the uh the state of these pm + + + align:start position:0% +to set up the uh the state of these pm +and user kernel bit instructions so that + + align:start position:0% +and user kernel bit instructions so that + + + align:start position:0% +and user kernel bit instructions so that +the uh Colonel can begin executing um + + align:start position:0% +the uh Colonel can begin executing um + + + align:start position:0% +the uh Colonel can begin executing um +the supervisor call is also going to uh + + align:start position:0% +the supervisor call is also going to uh + + + align:start position:0% +the supervisor call is also going to uh +but when the supervisor call instruction + + align:start position:0% +but when the supervisor call instruction + + + align:start position:0% +but when the supervisor call instruction +is executed uh we need to be a little + + align:start position:0% +is executed uh we need to be a little + + + align:start position:0% +is executed uh we need to be a little +bit careful because we also need to + + align:start position:0% +bit careful because we also need to + + + align:start position:0% +bit careful because we also need to +decide uh somehow which code within the + + align:start position:0% +decide uh somehow which code within the + + + align:start position:0% +decide uh somehow which code within the +kernel we want to begin executing when + + align:start position:0% +kernel we want to begin executing when + + + align:start position:0% +kernel we want to begin executing when +the supervisor call instruction gets + + align:start position:0% +the supervisor call instruction gets + + + align:start position:0% +the supervisor call instruction gets +executed right so um the supervisor what + + align:start position:0% +executed right so um the supervisor what + + + align:start position:0% +executed right so um the supervisor what +so what the supervisor call instruction + + align:start position:0% +so what the supervisor call instruction + + + align:start position:0% +so what the supervisor call instruction +does is it uh accepts a parameter um + + align:start position:0% +does is it uh accepts a parameter um + + + align:start position:0% +does is it uh accepts a parameter um +which is uh a so this the name of a of a + + align:start position:0% +which is uh a so this the name of a of a + + + align:start position:0% +which is uh a so this the name of a of a +so-called gate function so a gate + + align:start position:0% +so-called gate function so a gate + + + align:start position:0% +so-called gate function so a gate +function is a uh well- defined entry + + align:start position:0% +function is a uh well- defined entry + + + align:start position:0% +function is a uh well- defined entry +point um into another module that uh + + align:start position:0% +point um into another module that uh + + + align:start position:0% +point um into another module that uh +that that can be used uh to to invoke a + + align:start position:0% +that that can be used uh to to invoke a + + + align:start position:0% +that that can be used uh to to invoke a +piece of code in that other module so + + align:start position:0% +piece of code in that other module so + + + align:start position:0% +piece of code in that other module so +for example the kernel is going to have + + align:start position:0% +for example the kernel is going to have + + + align:start position:0% +for example the kernel is going to have +a particular gate function which + + align:start position:0% +a particular gate function which + + + align:start position:0% +a particular gate function which +corresponds to uh allocating a + + align:start position:0% +corresponds to uh allocating a + + + align:start position:0% +corresponds to uh allocating a +additional memory for a module so um the + + align:start position:0% +additional memory for a module so um the + + + align:start position:0% +additional memory for a module so um the +when when a user program executes an + + align:start position:0% +when when a user program executes an + + + align:start position:0% +when when a user program executes an +instruction uh uh supervisor call to + + align:start position:0% +instruction uh uh supervisor call to + + + align:start position:0% +instruction uh uh supervisor call to +gate say for example uh this might + + align:start position:0% +gate say for example uh this might + + + align:start position:0% +gate say for example uh this might +be uh the the the memory allocation Co + + align:start position:0% +be uh the the the memory allocation Co + + + align:start position:0% +be uh the the the memory allocation Co +some some memory allocation code um this + + align:start position:0% +some some memory allocation code um this + + + align:start position:0% +some some memory allocation code um this +special instruction is going to uh do + + align:start position:0% +special instruction is going to uh do + + + align:start position:0% +special instruction is going to uh do +the following things first it's going + + align:start position:0% +the following things first it's going + + + align:start position:0% +the following things first it's going +to set the user kernel bit to Kernel + + align:start position:0% +to set the user kernel bit to Kernel + + + align:start position:0% +to set the user kernel bit to Kernel +then it's going to uh set the value of + + align:start position:0% +then it's going to uh set the value of + + + align:start position:0% +then it's going to uh set the value of +the + + align:start position:0% +the + + + align:start position:0% +the +PM register to the + + align:start position:0% + + + + align:start position:0% + +kernel page + + align:start position:0% +kernel page + + + align:start position:0% +kernel page +map + + align:start position:0% +map + + + align:start position:0% +map +um it's going to save the program + + align:start position:0% +um it's going to save the program + + + align:start position:0% +um it's going to save the program +counter for the currently executing + + align:start position:0% +counter for the currently executing + + + align:start position:0% +counter for the currently executing +instruction um and then it's going to + + align:start position:0% +instruction um and then it's going to + + + align:start position:0% +instruction um and then it's going to +set the program counter to be the + + align:start position:0% +set the program counter to be the + + + align:start position:0% +set the program counter to be the +address of the gate function okay so + + align:start position:0% +address of the gate function okay so + + + align:start position:0% +address of the gate function okay so +there's this special we've introduced a + + align:start position:0% +there's this special we've introduced a + + + align:start position:0% +there's this special we've introduced a +special new processor instruction that + + align:start position:0% +special new processor instruction that + + + align:start position:0% +special new processor instruction that +uh takes these these special step that + + align:start position:0% +uh takes these these special step that + + + align:start position:0% +uh takes these these special step that +that takes these steps so when this + + align:start position:0% +that takes these steps so when this + + + align:start position:0% +that takes these steps so when this +instruction is executed we are + + align:start position:0% +instruction is executed we are + + + align:start position:0% +instruction is executed we are +essentially switch into uh executing uh + + align:start position:0% +essentially switch into uh executing uh + + + align:start position:0% +essentially switch into uh executing uh +within the Kernel's address space okay + + align:start position:0% +within the Kernel's address space okay + + + align:start position:0% +within the Kernel's address space okay +um and this kernel and we begin + + align:start position:0% +um and this kernel and we begin + + + align:start position:0% +um and this kernel and we begin +executing within the kernel address + + align:start position:0% +executing within the kernel address + + + align:start position:0% +executing within the kernel address +space at the uh address of this G gate + + align:start position:0% +space at the uh address of this G gate + + + align:start position:0% +space at the uh address of this G gate +function within the within the kernels + + align:start position:0% +function within the within the kernels + + + align:start position:0% +function within the within the kernels +address space okay so uh what this has + + align:start position:0% +address space okay so uh what this has + + + align:start position:0% +address space okay so uh what this has +done is it means so this is a sort of a + + align:start position:0% +done is it means so this is a sort of a + + + align:start position:0% +done is it means so this is a sort of a +well this is a well defined entry point + + align:start position:0% +well this is a well defined entry point + + + align:start position:0% +well this is a well defined entry point +if this instruction if the if the + + align:start position:0% +if this instruction if the if the + + + align:start position:0% +if this instruction if the if the +program tries to execute this + + align:start position:0% +program tries to execute this + + + align:start position:0% +program tries to execute this +instruction with the name of a gate + + align:start position:0% +instruction with the name of a gate + + + align:start position:0% +instruction with the name of a gate +function that doesn't exist then there + + align:start position:0% +function that doesn't exist then there + + + align:start position:0% +function that doesn't exist then there +that program is going to get an error + + align:start position:0% +that program is going to get an error + + + align:start position:0% +that program is going to get an error +when it tries to do that so the program + + align:start position:0% +when it tries to do that so the program + + + align:start position:0% +when it tries to do that so the program +can only name gate functions that + + align:start position:0% +can only name gate functions that + + + align:start position:0% +can only name gate functions that +actually correspond to real things that + + align:start position:0% +actually correspond to real things that + + + align:start position:0% +actually correspond to real things that +the operating system can do um the colel + + align:start position:0% +the operating system can do um the colel + + + align:start position:0% +the operating system can do um the colel +can do and when the colel get and so the + + align:start position:0% +can do and when the colel get and so the + + + align:start position:0% +can do and when the colel get and so the +the colel is then going to be invoked + + align:start position:0% +the colel is then going to be invoked + + + align:start position:0% +the colel is then going to be invoked +and take that that action that was + + align:start position:0% +and take that that action that was + + + align:start position:0% +and take that that action that was +requested of it + + align:start position:0% +requested of it + + + align:start position:0% +requested of it +um on return essentially we're just + + align:start position:0% +um on return essentially we're just + + + align:start position:0% +um on return essentially we're just +going to so when the colonel finishes + + align:start position:0% +going to so when the colonel finishes + + + align:start position:0% +going to so when the colonel finishes +executing this process when it finishes + + align:start position:0% +executing this process when it finishes + + + align:start position:0% +executing this process when it finishes +executing this say memory allocation + + align:start position:0% +executing this say memory allocation + + + align:start position:0% +executing this say memory allocation +instruction we're just going to reverse + + align:start position:0% +instruction we're just going to reverse + + + align:start position:0% +instruction we're just going to reverse +this step so uh we're just going to set + + align:start position:0% +this step so uh we're just going to set + + + align:start position:0% +this step so uh we're just going to set +the PM to be we're going to set the set + + align:start position:0% +the PM to be we're going to set the set + + + align:start position:0% +the PM to be we're going to set the set +the PM back to the to to the users + + align:start position:0% +the PM back to the to to the users + + + align:start position:0% +the PM back to the to to the users +program um we're going to set the user + + align:start position:0% +program um we're going to set the user + + + align:start position:0% +program um we're going to set the user +kernel bit back into user mode and then + + align:start position:0% +kernel bit back into user mode and then + + + align:start position:0% +kernel bit back into user mode and then +we're going to jump back to the the + + align:start position:0% +we're going to jump back to the the + + + align:start position:0% +we're going to jump back to the the +saved return address this that we saved + + align:start position:0% +saved return address this that we saved + + + align:start position:0% +saved return address this that we saved +here the save program counter address uh + + align:start position:0% +here the save program counter address uh + + + align:start position:0% +here the save program counter address uh +from the from the user program so when + + align:start position:0% +from the from the user program so when + + + align:start position:0% +from the from the user program so when +the the program finishes when the kernel + + align:start position:0% +the the program finishes when the kernel + + + align:start position:0% +the the program finishes when the kernel +finishes EX + + align:start position:0% +finishes EX + + + align:start position:0% +finishes EX +uh this service instruction the control + + align:start position:0% +uh this service instruction the control + + + align:start position:0% +uh this service instruction the control +will just return back to the program in + + align:start position:0% +will just return back to the program in + + + align:start position:0% +will just return back to the program in +the place where the the program needs to + + align:start position:0% +the place where the the program needs to + + + align:start position:0% +the place where the the program needs to +begin + + align:start position:0% +begin + + + align:start position:0% +begin +executing okay so now using this uh + + align:start position:0% +executing okay so now using this uh + + + align:start position:0% +executing okay so now using this uh +using this gate of so using this notion + + align:start position:0% +using this gate of so using this notion + + + align:start position:0% +using this gate of so using this notion +of a uh this uh so what we've seen so + + align:start position:0% +of a uh this uh so what we've seen so + + + align:start position:0% +of a uh this uh so what we've seen so +far now is the ability for uh + + align:start position:0% +far now is the ability for uh + + + align:start position:0% +far now is the ability for uh +the we we can use the virtual memory the + + align:start position:0% +the we we can use the virtual memory the + + + align:start position:0% +the we we can use the virtual memory the +virtual memory abstraction in order to + + align:start position:0% +virtual memory abstraction in order to + + + align:start position:0% +virtual memory abstraction in order to +protect uh the memory references of two + + align:start position:0% +protect uh the memory references of two + + + align:start position:0% +protect uh the memory references of two +modules from each other and we' SE we + + align:start position:0% +modules from each other and we' SE we + + + align:start position:0% +modules from each other and we' SE we +have this notion of the Cur Journal that + + align:start position:0% +have this notion of the Cur Journal that + + + align:start position:0% +have this notion of the Cur Journal that +can be uh used to for example uh create + + align:start position:0% +can be uh used to for example uh create + + + align:start position:0% +can be uh used to for example uh create +new that can be used to manage these + + align:start position:0% +new that can be used to manage these + + + align:start position:0% +new that can be used to manage these +address spaces to allocate new memory to + + align:start position:0% +address spaces to allocate new memory to + + + align:start position:0% +address spaces to allocate new memory to +these address spaces um and in general + + align:start position:0% +these address spaces um and in general + + + align:start position:0% +these address spaces um and in general +to sort of uh manage the uh the the cre + + align:start position:0% +to sort of uh manage the uh the the cre + + + align:start position:0% +to sort of uh manage the uh the the cre +manage these address spes so + + align:start position:0% +manage these address spes so + + + align:start position:0% +manage these address spes so +um this kernel though is also going to + + align:start position:0% +um this kernel though is also going to + + + align:start position:0% +um this kernel though is also going to +allow us to do uh + + align:start position:0% +allow us to do uh + + + align:start position:0% +allow us to do uh +exactly what what we set out trying to + + align:start position:0% +exactly what what we set out trying to + + + align:start position:0% +exactly what what we set out trying to +do which is to um act as the uh a + + align:start position:0% +do which is to um act as the uh a + + + align:start position:0% +do which is to um act as the uh a +so-called trusted intermediary + + align:start position:0% + + + + align:start position:0% + +between say for example a client and a + + align:start position:0% +between say for example a client and a + + + align:start position:0% +between say for example a client and a +server running on the same + + align:start position:0% + + + + align:start position:0% + +machine okay so a trusted intermediary + + align:start position:0% +machine okay so a trusted intermediary + + + align:start position:0% +machine okay so a trusted intermediary +is just a piece of code that uh so + + align:start position:0% +is just a piece of code that uh so + + + align:start position:0% +is just a piece of code that uh so +suppose we have a client and a server + + align:start position:0% +suppose we have a client and a server + + + align:start position:0% +suppose we have a client and a server +right and these are two pieces of code + + align:start position:0% +right and these are two pieces of code + + + align:start position:0% +right and these are two pieces of code +written by two different developers + + align:start position:0% +written by two different developers + + + align:start position:0% +written by two different developers +maybe the two developers don't + + align:start position:0% +maybe the two developers don't + + + align:start position:0% +maybe the two developers don't +necessarily trust that the other + + align:start position:0% +necessarily trust that the other + + + align:start position:0% +necessarily trust that the other +developer has written a piece of code + + align:start position:0% +developer has written a piece of code + + + align:start position:0% +developer has written a piece of code +that's 100% foolproof or that doesn't + + align:start position:0% +that's 100% foolproof or that doesn't + + + align:start position:0% +that's 100% foolproof or that doesn't +have any bugs but they may be both of + + align:start position:0% +have any bugs but they may be both of + + + align:start position:0% +have any bugs but they may be both of +those developers may be willing to say + + align:start position:0% +those developers may be willing to say + + + align:start position:0% +those developers may be willing to say +that they'll trust that the kernel is is + + align:start position:0% +that they'll trust that the kernel is is + + + align:start position:0% +that they'll trust that the kernel is is +properly written and doesn't have any + + align:start position:0% +properly written and doesn't have any + + + align:start position:0% +properly written and doesn't have any +bugs in it and so they're willing to + + align:start position:0% +bugs in it and so they're willing to + + + align:start position:0% +bugs in it and so they're willing to +allow the colonel to sit in between + + align:start position:0% +allow the colonel to sit in between + + + align:start position:0% +allow the colonel to sit in between +those two programs and make sure that + + align:start position:0% +those two programs and make sure that + + + align:start position:0% +those two programs and make sure that +neither of them uh that both of them are + + align:start position:0% +neither of them uh that both of them are + + + align:start position:0% +neither of them uh that both of them are +able to that that neither of them has + + align:start position:0% +able to that that neither of them has + + + align:start position:0% +able to that that neither of them has +any bad interactions with each other so + + align:start position:0% +any bad interactions with each other so + + + align:start position:0% +any bad interactions with each other so +let's see how we can use this kernel uh + + align:start position:0% +let's see how we can use this kernel uh + + + align:start position:0% +let's see how we can use this kernel uh +the kernel combined with virtual memory + + align:start position:0% +the kernel combined with virtual memory + + + align:start position:0% +the kernel combined with virtual memory +in order to be able to do this so + + align:start position:0% +in order to be able to do this so + + + align:start position:0% +in order to be able to do this so +um suppose this is our kernel + + align:start position:0% +um suppose this is our kernel + + + align:start position:0% +um suppose this is our kernel +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +um so the idea is that this kernel has + + align:start position:0% +um so the idea is that this kernel has + + + align:start position:0% +um so the idea is that this kernel has +running has so suppose we have two + + align:start position:0% +running has so suppose we have two + + + align:start position:0% +running has so suppose we have two +processes A and B that want to + + align:start position:0% +processes A and B that want to + + + align:start position:0% +processes A and B that want to +communicate with each other in some way + + align:start position:0% +communicate with each other in some way + + + align:start position:0% +communicate with each other in some way +and we've already said that we don't + + align:start position:0% +and we've already said that we don't + + + align:start position:0% +and we've already said that we don't +want these two processes to be able to + + align:start position:0% +want these two processes to be able to + + + align:start position:0% +want these two processes to be able to +directly reference into each other's + + align:start position:0% +directly reference into each other's + + + align:start position:0% +directly reference into each other's +memory because that makes them dependent + + align:start position:0% +memory because that makes them dependent + + + align:start position:0% +memory because that makes them dependent +on each other it means that if there's a + + align:start position:0% +on each other it means that if there's a + + + align:start position:0% +on each other it means that if there's a +bug in a that a can you know overwrite + + align:start position:0% +bug in a that a can you know overwrite + + + align:start position:0% +bug in a that a can you know overwrite +some memory in B's address space and + + align:start position:0% +some memory in B's address space and + + + align:start position:0% +some memory in B's address space and +cause B to C so that's a bad thing so + + align:start position:0% +cause B to C so that's a bad thing so + + + align:start position:0% +cause B to C so that's a bad thing so +instead what we're going to do is we're + + align:start position:0% +instead what we're going to do is we're + + + align:start position:0% +instead what we're going to do is we're +going to create + + align:start position:0% +going to create + + + align:start position:0% +going to create +uh a special we one thing we can do is + + align:start position:0% +uh a special we one thing we can do is + + + align:start position:0% +uh a special we one thing we can do is +to create a special uh set of these + + align:start position:0% +to create a special uh set of these + + + align:start position:0% +to create a special uh set of these +supervisor calls that these two modules + + align:start position:0% +supervisor calls that these two modules + + + align:start position:0% +supervisor calls that these two modules +can be can use to interact with each + + align:start position:0% +can be can use to interact with each + + + align:start position:0% +can be can use to interact with each +other so um in particular we might + + align:start position:0% +other so um in particular we might + + + align:start position:0% +other so um in particular we might +within the kernel maintain a little a + + align:start position:0% +within the kernel maintain a little a + + + align:start position:0% +within the kernel maintain a little a +cue of messages that these two programs + + align:start position:0% +cue of messages that these two programs + + + align:start position:0% +cue of messages that these two programs +are exchanging with each other a list + + align:start position:0% +are exchanging with each other a list + + + align:start position:0% +are exchanging with each other a list +list of messages that they're exchanging + + align:start position:0% +list of messages that they're exchanging + + + align:start position:0% +list of messages that they're exchanging +I and suppose a uh and suppose a is + + align:start position:0% +I and suppose a uh and suppose a is + + + align:start position:0% +I and suppose a uh and suppose a is +we're going to call this guy that a is a + + align:start position:0% +we're going to call this guy that a is a + + + align:start position:0% +we're going to call this guy that a is a +producer he's he's creating messages and + + align:start position:0% +producer he's he's creating messages and + + + align:start position:0% +producer he's he's creating messages and +B is a + + align:start position:0% +B is a + + + align:start position:0% +B is a +consumer um + + align:start position:0% +consumer um + + + align:start position:0% +consumer um +a can call some function like put which + + align:start position:0% +a can call some function like put which + + + align:start position:0% +a can call some function like put which +will uh a supervisor call like put which + + align:start position:0% +will uh a supervisor call like put which + + + align:start position:0% +will uh a supervisor call like put which +will cause a new instruction it will + + align:start position:0% +will cause a new instruction it will + + + align:start position:0% +will cause a new instruction it will +cause a data item to be put on this que + + align:start position:0% +cause a data item to be put on this que + + + align:start position:0% +cause a data item to be put on this que +um and then sometime later B can call + + align:start position:0% +um and then sometime later B can call + + + align:start position:0% +um and then sometime later B can call +the supervisor call git and pull this + + align:start position:0% +the supervisor call git and pull this + + + align:start position:0% +the supervisor call git and pull this +instruction out and and pull this value + + align:start position:0% +instruction out and and pull this value + + + align:start position:0% +instruction out and and pull this value +out of the que okay so in this way the + + align:start position:0% +out of the que okay so in this way the + + + align:start position:0% +out of the que okay so in this way the +producer and the consumer can interact + + align:start position:0% +producer and the consumer can interact + + + align:start position:0% +producer and the consumer can interact +with each other they can exchange data + + align:start position:0% +with each other they can exchange data + + + align:start position:0% +with each other they can exchange data +with each other um and because we have + + align:start position:0% +with each other um and because we have + + + align:start position:0% +with each other um and because we have +this gate interface this well- defined + + align:start position:0% +this gate interface this well- defined + + + align:start position:0% +this gate interface this well- defined +gate interface with these put and git + + align:start position:0% +gate interface with these put and git + + + align:start position:0% +gate interface with these put and git +calls being invoked by the the kernel + + align:start position:0% +calls being invoked by the the kernel + + + align:start position:0% +calls being invoked by the the kernel +the kernel can be very careful just just + + align:start position:0% +the kernel can be very careful just just + + + align:start position:0% +the kernel can be very careful just just +like in the case of the of the client + + align:start position:0% +like in the case of the of the client + + + align:start position:0% +like in the case of the of the client +and server running on two different + + align:start position:0% +and server running on two different + + + align:start position:0% +and server running on two different +machines in this case the kernel can + + align:start position:0% +machines in this case the kernel can + + + align:start position:0% +machines in this case the kernel can +carefully verify that these put and get + + align:start position:0% +carefully verify that these put and get + + + align:start position:0% +carefully verify that these put and get +commands that these procedures that + + align:start position:0% +commands that these procedures that + + + align:start position:0% +commands that these procedures that +these two different modules are calling + + align:start position:0% +these two different modules are calling + + + align:start position:0% +these two different modules are calling +actually are correctly formed that they + + align:start position:0% +actually are correctly formed that they + + + align:start position:0% +actually are correctly formed that they +have good par that the parameters are + + align:start position:0% +have good par that the parameters are + + + align:start position:0% +have good par that the parameters are +valid that they're referring to valid + + align:start position:0% +valid that they're referring to valid + + + align:start position:0% +valid that they're referring to valid +locations in memory um and therefore the + + align:start position:0% +locations in memory um and therefore the + + + align:start position:0% +locations in memory um and therefore the +colonel can uh sort of ensure that these + + align:start position:0% +colonel can uh sort of ensure that these + + + align:start position:0% +colonel can uh sort of ensure that these +two modules uh don't do malicious things + + align:start position:0% +two modules uh don't do malicious things + + + align:start position:0% +two modules uh don't do malicious things +to each other or cause each other to + + align:start position:0% +to each other or cause each other to + + + align:start position:0% +to each other or cause each other to +Break um so this is an example here of + + align:start position:0% +Break um so this is an example here of + + + align:start position:0% +Break um so this is an example here of +something that's like uh an inter + + align:start position:0% +something that's like uh an inter + + + align:start position:0% +something that's like uh an inter +process interprocess communication so + + align:start position:0% +process interprocess communication so + + + align:start position:0% +process interprocess communication so +you saw uh for example you've seen + + align:start position:0% +you saw uh for example you've seen + + + align:start position:0% +you saw uh for example you've seen +you've seen an instance of interprocess + + align:start position:0% +you've seen an instance of interprocess + + + align:start position:0% +you've seen an instance of interprocess +communication when you studied the Unix + + align:start position:0% +communication when you studied the Unix + + + align:start position:0% +communication when you studied the Unix +paper we talked about pipes and the pipe + + align:start position:0% +paper we talked about pipes and the pipe + + + align:start position:0% +paper we talked about pipes and the pipe +abstraction and how that works well + + align:start position:0% +abstraction and how that works well + + + align:start position:0% +abstraction and how that works well +pipes are sort of something that's + + align:start position:0% +pipes are sort of something that's + + + align:start position:0% +pipes are sort of something that's +implemented uh as a by the kernel in in + + align:start position:0% +implemented uh as a by the kernel in in + + + align:start position:0% +implemented uh as a by the kernel in in +Unix as a way to for two programs to + + align:start position:0% +Unix as a way to for two programs to + + + align:start position:0% +Unix as a way to for two programs to +Interchange to exchange data with each + + align:start position:0% +Interchange to exchange data with each + + + align:start position:0% +Interchange to exchange data with each +other um and there's lots of these kinds + + align:start position:0% +other um and there's lots of these kinds + + + align:start position:0% +other um and there's lots of these kinds +of services that are people tend to push + + align:start position:0% +of services that are people tend to push + + + align:start position:0% +of services that are people tend to push +into the kernel that the kernel provides + + align:start position:0% +into the kernel that the kernel provides + + + align:start position:0% +into the kernel that the kernel provides +to the other applications that are the + + align:start position:0% +to the other applications that are the + + + align:start position:0% +to the other applications that are the +modules that are running so that these + + align:start position:0% +modules that are running so that these + + + align:start position:0% +modules that are running so that these +modules can for example interact with + + align:start position:0% +modules can for example interact with + + + align:start position:0% +modules can for example interact with +Hardware or interact with each other so + + align:start position:0% +Hardware or interact with each other so + + + align:start position:0% +Hardware or interact with each other so +commonly within a kernel you'd find + + align:start position:0% +commonly within a kernel you'd find + + + align:start position:0% +commonly within a kernel you'd find +things like a file system um an + + align:start position:0% +things like a file system um an + + + align:start position:0% +things like a file system um an +interface to the network um and you + + align:start position:0% +interface to the network um and you + + + align:start position:0% +interface to the network um and you +might for example find things like an + + align:start position:0% +might for example find things like an + + + align:start position:0% +might for example find things like an +interface + + align:start position:0% +interface + + + align:start position:0% +interface +to the graphics Hardware okay there's + + align:start position:0% +to the graphics Hardware okay there's + + + align:start position:0% +to the graphics Hardware okay there's +some sort of uh you can so if you if you + + align:start position:0% +some sort of uh you can so if you if you + + + align:start position:0% +some sort of uh you can so if you if you +look at what's actually within a kernel + + align:start position:0% +look at what's actually within a kernel + + + align:start position:0% +look at what's actually within a kernel +there's a huge amount of code that's + + align:start position:0% +there's a huge amount of code that's + + + align:start position:0% +there's a huge amount of code that's +going into these kernels so I think we + + align:start position:0% +going into these kernels so I think we + + + align:start position:0% +going into these kernels so I think we +we talked earlier about how the Linux + + align:start position:0% +we talked earlier about how the Linux + + + align:start position:0% +we talked earlier about how the Linux +operating system is many millions of + + align:start position:0% +operating system is many millions of + + + align:start position:0% +operating system is many millions of +lines of code if you go look at the + + align:start position:0% +lines of code if you go look at the + + + align:start position:0% +lines of code if you go look at the +Linux kernel uh the Linux kernel is uh + + align:start position:0% +Linux kernel uh the Linux kernel is uh + + + align:start position:0% +Linux kernel uh the Linux kernel is uh +about probably today on the order of + + align:start position:0% +about probably today on the order of + + + align:start position:0% +about probably today on the order of +five million lines of code um most of + + align:start position:0% +five million lines of code um most of + + + align:start position:0% +five million lines of code um most of +which say two-thirds of which is related + + align:start position:0% +which say two-thirds of which is related + + + align:start position:0% +which say two-thirds of which is related +to these so-called device drivers that + + align:start position:0% +to these so-called device drivers that + + + align:start position:0% +to these so-called device drivers that +manage this low-level Hardware um so + + align:start position:0% +manage this low-level Hardware um so + + + align:start position:0% +manage this low-level Hardware um so +there's this kernel has gotten quite + + align:start position:0% +there's this kernel has gotten quite + + + align:start position:0% +there's this kernel has gotten quite +large and one of the sort of side + + align:start position:0% +large and one of the sort of side + + + align:start position:0% +large and one of the sort of side +effects of the kernel getting large is + + align:start position:0% +effects of the kernel getting large is + + + align:start position:0% +effects of the kernel getting large is +that well maybe it's harder to trust it + + align:start position:0% +that well maybe it's harder to trust it + + + align:start position:0% +that well maybe it's harder to trust it +right maybe you sort of have le less + + align:start position:0% +right maybe you sort of have le less + + + align:start position:0% +right maybe you sort of have le less +confidence that the the code in the + + align:start position:0% +confidence that the the code in the + + + align:start position:0% +confidence that the the code in the +kernel is actually correct you can + + align:start position:0% +kernel is actually correct you can + + + align:start position:0% +kernel is actually correct you can +imagine if you don't trust the kernel + + align:start position:0% +imagine if you don't trust the kernel + + + align:start position:0% +imagine if you don't trust the kernel +then the program the computer is going + + align:start position:0% +then the program the computer is going + + + align:start position:0% +then the program the computer is going +to be uh is sort of going to CRA the + + align:start position:0% +to be uh is sort of going to CRA the + + + align:start position:0% +to be uh is sort of going to CRA the +computer is not going to be as stable as + + align:start position:0% +computer is not going to be as stable as + + + align:start position:0% +computer is not going to be as stable as +you would like it to be and this is you + + align:start position:0% +you would like it to be and this is you + + + align:start position:0% +you would like it to be and this is you +know one argument for why Windows + + align:start position:0% +know one argument for why Windows + + + align:start position:0% +know one argument for why Windows +crashes all the time as well because it + + align:start position:0% +crashes all the time as well because it + + + align:start position:0% +crashes all the time as well because it +has all these drivers in it and these + + align:start position:0% +has all these drivers in it and these + + + align:start position:0% +has all these drivers in it and these +drivers uh aren't necessarily all + + align:start position:0% +drivers uh aren't necessarily all + + + align:start position:0% +drivers uh aren't necessarily all +perfectly written there are tens of + + align:start position:0% +perfectly written there are tens of + + + align:start position:0% +perfectly written there are tens of +millions of lines of code in Windows and + + align:start position:0% +millions of lines of code in Windows and + + + align:start position:0% +millions of lines of code in Windows and +some of them crash some of the time that + + align:start position:0% +some of them crash some of the time that + + + align:start position:0% +some of them crash some of the time that +causes the whole computer to come down + + align:start position:0% +causes the whole computer to come down + + + align:start position:0% +causes the whole computer to come down +so there's a tension in the operating + + align:start position:0% +so there's a tension in the operating + + + align:start position:0% +so there's a tension in the operating +systems Community about whether you + + align:start position:0% +systems Community about whether you + + + align:start position:0% +systems Community about whether you +should execute these things like the F + + align:start position:0% +should execute these things like the F + + + align:start position:0% +should execute these things like the F +you should keep these things like the + + align:start position:0% +you should keep these things like the + + + align:start position:0% +you should keep these things like the +file system or the graphic system within + + align:start position:0% +file system or the graphic system within + + + align:start position:0% +file system or the graphic system within +the kernel or whether you should move + + align:start position:0% +the kernel or whether you should move + + + align:start position:0% +the kernel or whether you should move +them outside as separate + + align:start position:0% +them outside as separate + + + align:start position:0% +them outside as separate +Services um which can be invoked in the + + align:start position:0% +Services um which can be invoked in the + + + align:start position:0% +Services um which can be invoked in the +same way for example that A and B + + align:start position:0% +same way for example that A and B + + + align:start position:0% +same way for example that A and B +interact with each other by having some + + align:start position:0% +interact with each other by having some + + + align:start position:0% +interact with each other by having some +uh data structure that's stored within + + align:start position:0% +uh data structure that's stored within + + + align:start position:0% +uh data structure that's stored within +the kernel that buffers the requests + + align:start position:0% +the kernel that buffers the requests + + + align:start position:0% +the kernel that buffers the requests +between say the service and uh and the + + align:start position:0% +between say the service and uh and the + + + align:start position:0% +between say the service and uh and the +the the S this say for example the + + align:start position:0% +the the S this say for example the + + + align:start position:0% +the the S this say for example the +graphic service and the uh users + + align:start position:0% +graphic service and the uh users + + + align:start position:0% +graphic service and the uh users +programs that want to interact with + + align:start position:0% +programs that want to interact with + + + align:start position:0% +programs that want to interact with +it okay so um that's basically it for + + align:start position:0% +it okay so um that's basically it for + + + align:start position:0% +it okay so um that's basically it for +today what I've shown you is um well + + align:start position:0% +today what I've shown you is um well + + + align:start position:0% +today what I've shown you is um well +actually we have a few more minutes + + align:start position:0% +actually we have a few more minutes + + + align:start position:0% +actually we have a few more minutes +sorry I know you're all getting up to + + align:start position:0% +sorry I know you're all getting up to + + + align:start position:0% +sorry I know you're all getting up to +leave but um okay so I just want to + + align:start position:0% +leave but um okay so I just want to + + + align:start position:0% +leave but um okay so I just want to +quickly + + align:start position:0% +quickly + + + align:start position:0% +quickly +um I want to quickly touch on uh on one + + align:start position:0% +um I want to quickly touch on uh on one + + + align:start position:0% +um I want to quickly touch on uh on one +last topic + + align:start position:0% +last topic + + + align:start position:0% +last topic +um which is that uh that one of so what + + align:start position:0% +um which is that uh that one of so what + + + align:start position:0% +um which is that uh that one of so what +I've shown you so far is this um how we + + align:start position:0% +I've shown you so far is this um how we + + + align:start position:0% +I've shown you so far is this um how we +can use + + align:start position:0% +can use + + + align:start position:0% +can use +the notion of virtual memory in order to + + align:start position:0% +the notion of virtual memory in order to + + + align:start position:0% +the notion of virtual memory in order to +protect the the data that two things + + align:start position:0% +protect the the data that two things + + + align:start position:0% +protect the the data that two things +that two programs + + align:start position:0% +that two programs + + + align:start position:0% +that two programs +uh that that protect two programs from + + align:start position:0% +uh that that protect two programs from + + + align:start position:0% +uh that that protect two programs from +each other so that they can't + + align:start position:0% +each other so that they can't + + + align:start position:0% +each other so that they can't +necessarily interact with each other's + + align:start position:0% +necessarily interact with each other's + + + align:start position:0% +necessarily interact with each other's +data but there's some situations in + + align:start position:0% +data but there's some situations in + + + align:start position:0% +data but there's some situations in +which we might actually want to have two + + align:start position:0% +which we might actually want to have two + + + align:start position:0% +which we might actually want to have two +programs able to share some data with + + align:start position:0% +programs able to share some data with + + + align:start position:0% +programs able to share some data with +each other so I don't know if you guys + + align:start position:0% +each other so I don't know if you guys + + + align:start position:0% +each other so I don't know if you guys +remember but when Harry was lecturing + + align:start position:0% +remember but when Harry was lecturing + + + align:start position:0% +remember but when Harry was lecturing +earlier he talked about how you have Li + + align:start position:0% +earlier he talked about how you have Li + + + align:start position:0% +earlier he talked about how you have Li +how there are libraries that get linked + + align:start position:0% +how there are libraries that get linked + + + align:start position:0% +how there are libraries that get linked +into programs um and one of the sort of + + align:start position:0% +into programs um and one of the sort of + + + align:start position:0% +into programs um and one of the sort of +common ways that libraries are uh + + align:start position:0% +common ways that libraries are uh + + + align:start position:0% +common ways that libraries are uh +structured these days are so-called + + align:start position:0% +structured these days are so-called + + + align:start position:0% +structured these days are so-called +shared libraries so an example so a + + align:start position:0% +shared libraries so an example so a + + + align:start position:0% +shared libraries so an example so a +shared library is something that is uh + + align:start position:0% +shared library is something that is uh + + + align:start position:0% +shared library is something that is uh +it's only it's only stored in one + + align:start position:0% +it's only it's only stored in one + + + align:start position:0% +it's only it's only stored in one +location in physical memory um but + + align:start position:0% +location in physical memory um but + + + align:start position:0% +location in physical memory um but +multiple different modules that are + + align:start position:0% +multiple different modules that are + + + align:start position:0% +multiple different modules that are +executing on that system can call + + align:start position:0% +executing on that system can call + + + align:start position:0% +executing on that system can call +functions can call functions within that + + align:start position:0% +functions can call functions within that + + + align:start position:0% +functions can call functions within that +shared Library um so in order to make + + align:start position:0% +shared Library um so in order to make + + + align:start position:0% +shared Library um so in order to make +this work right we need to uh have + + align:start position:0% +this work right we need to uh have + + + align:start position:0% +this work right we need to uh have +mapped the memory for this shared + + align:start position:0% +mapped the memory for this shared + + + align:start position:0% +mapped the memory for this shared +library that has all the functions that + + align:start position:0% +library that has all the functions that + + + align:start position:0% +library that has all the functions that +these other modules want to call um into + + align:start position:0% +these other modules want to call um into + + + align:start position:0% +these other modules want to call um into +the address spaces for both of these + + align:start position:0% +the address spaces for both of these + + + align:start position:0% +the address spaces for both of these +modules so that they can actually + + align:start position:0% +modules so that they can actually + + + align:start position:0% +modules so that they can actually +execute the code that's there so um the + + align:start position:0% +execute the code that's there so um the + + + align:start position:0% +execute the code that's there so um the +virtual memory system makes it very + + align:start position:0% +virtual memory system makes it very + + + align:start position:0% +virtual memory system makes it very +trivial to do this so uh suppose I have + + align:start position:0% +trivial to do this so uh suppose I have + + + align:start position:0% +trivial to do this so uh suppose I have +my address space for some function a and + + align:start position:0% +my address space for some function a and + + + align:start position:0% +my address space for some function a and +I have my address space for some + + align:start position:0% +I have my address space for some + + + align:start position:0% +I have my address space for some +function + + align:start position:0% +function + + + align:start position:0% +function +B um and suppose that function a + + align:start position:0% +B um and suppose that function a + + + align:start position:0% +B um and suppose that function a +references Library 1 and function a + + align:start position:0% +references Library 1 and function a + + + align:start position:0% +references Library 1 and function a +module B references libraries uh one and + + align:start position:0% +module B references libraries uh one and + + + align:start position:0% +module B references libraries uh one and +two okay so + + align:start position:0% +two okay so + + + align:start position:0% +two okay so +um using the virtual memory system we + + align:start position:0% +um using the virtual memory system we + + + align:start position:0% +um using the virtual memory system we +can suppose we have so this is our + + align:start position:0% +can suppose we have so this is our + + + align:start position:0% +can suppose we have so this is our +physical + + align:start position:0% +physical + + + align:start position:0% +physical +memory um so suppose that module one + + align:start position:0% +memory um so suppose that module one + + + align:start position:0% +memory um so suppose that module one +module a uh program a is loaded and when + + align:start position:0% +module a uh program a is loaded and when + + + align:start position:0% +module a uh program a is loaded and when +it's loaded the shared Library the the + + align:start position:0% +it's loaded the shared Library the the + + + align:start position:0% +it's loaded the shared Library the the +the uh the program that runs the the + + align:start position:0% +the uh the program that runs the the + + + align:start position:0% +the uh the program that runs the the +program that runs other programs the + + align:start position:0% +program that runs other programs the + + + align:start position:0% +program that runs other programs the +loader in this case is going to load + + align:start position:0% +loader in this case is going to load + + + align:start position:0% +loader in this case is going to load +this shared Library one in as it loads + + align:start position:0% +this shared Library one in as it loads + + + align:start position:0% +this shared Library one in as it loads +in the code for add for program a so + + align:start position:0% +in the code for add for program a so + + + align:start position:0% +in the code for add for program a so +it's going to first load the code for a + + align:start position:0% +it's going to first load the code for a + + + align:start position:0% +it's going to first load the code for a +um and then it's going to load the code + + align:start position:0% +um and then it's going to load the code + + + align:start position:0% +um and then it's going to load the code +for one and these things are going to be + + align:start position:0% +for one and these things are going to be + + + align:start position:0% +for one and these things are going to be +sitting in memory somewhere um So within + + align:start position:0% +sitting in memory somewhere um So within + + + align:start position:0% +sitting in memory somewhere um So within +A's address space oops sorry within A's + + align:start position:0% +A's address space oops sorry within A's + + + align:start position:0% +A's address space oops sorry within A's +address space we're going to have the + + align:start position:0% +address space we're going to have the + + + align:start position:0% +address space we're going to have the +code for a is going to be mapped and the + + align:start position:0% +code for a is going to be mapped and the + + + align:start position:0% +code for a is going to be mapped and the +code for one is going to be mapped um + + align:start position:0% +code for one is going to be mapped um + + + align:start position:0% +code for one is going to be mapped um +now when B executes right we don't what + + align:start position:0% +now when B executes right we don't what + + + align:start position:0% +now when B executes right we don't what +we want to avoid so one the whole + + align:start position:0% +we want to avoid so one the whole + + + align:start position:0% +we want to avoid so one the whole +purpose of shared libraries is to make + + align:start position:0% +purpose of shared libraries is to make + + + align:start position:0% +purpose of shared libraries is to make +it so that uh when two programs are + + align:start position:0% +it so that uh when two programs are + + + align:start position:0% +it so that uh when two programs are +running and they both use the same + + align:start position:0% +running and they both use the same + + + align:start position:0% +running and they both use the same +Library there aren't two copies of that + + align:start position:0% +Library there aren't two copies of that + + + align:start position:0% +Library there aren't two copies of that +Library they in memory using twice as + + align:start position:0% +Library they in memory using twice as + + + align:start position:0% +Library they in memory using twice as +much of the memory up right because + + align:start position:0% +much of the memory up right because + + + align:start position:0% +much of the memory up right because +there's all these libraries that all the + + align:start position:0% +there's all these libraries that all the + + + align:start position:0% +there's all these libraries that all the +that all uh computer programs share um + + align:start position:0% +that all uh computer programs share um + + + align:start position:0% +that all uh computer programs share um +for example the you know uh on Linux + + align:start position:0% +for example the you know uh on Linux + + + align:start position:0% +for example the you know uh on Linux +it's there's the libc library that + + align:start position:0% +it's there's the libc library that + + + align:start position:0% +it's there's the libc library that +implements all of the standard functions + + align:start position:0% +implements all of the standard functions + + + align:start position:0% +implements all of the standard functions +that people use in C in C programs and + + align:start position:0% +that people use in C in C programs and + + + align:start position:0% +that people use in C in C programs and +we don't want to have you know if + + align:start position:0% +we don't want to have you know if + + + align:start position:0% +we don't want to have you know if +there's 50 c program 50 programs written + + align:start position:0% +there's 50 c program 50 programs written + + + align:start position:0% +there's 50 c program 50 programs written +in C on your Linux machine you don't + + align:start position:0% +in C on your Linux machine you don't + + + align:start position:0% +in C on your Linux machine you don't +have 50 copies of this libc library and + + align:start position:0% +have 50 copies of this libc library and + + + align:start position:0% +have 50 copies of this libc library and +memory you want to have just one so um + + align:start position:0% +memory you want to have just one so um + + + align:start position:0% +memory you want to have just one so um +so what we want is that when when module + + align:start position:0% +so what we want is that when when module + + + align:start position:0% +so what we want is that when when module +b gets loaded we want it to uh map this + + align:start position:0% +b gets loaded we want it to uh map this + + + align:start position:0% +b gets loaded we want it to uh map this +code that's already been mapped into the + + align:start position:0% +code that's already been mapped into the + + + align:start position:0% +code that's already been mapped into the +address space of a into its memory as + + align:start position:0% +address space of a into its memory as + + + align:start position:0% +address space of a into its memory as +well okay um and then of course we're + + align:start position:0% +well okay um and then of course we're + + + align:start position:0% +well okay um and then of course we're +going to have to load additional memory + + align:start position:0% +going to have to load additional memory + + + align:start position:0% +going to have to load additional memory +for B + + align:start position:0% +for B + + + align:start position:0% +for B +itself and for the uh Library 2 which a + + align:start position:0% +itself and for the uh Library 2 which a + + + align:start position:0% +itself and for the uh Library 2 which a +hasn't already loaded so now those are + + align:start position:0% +hasn't already loaded so now those are + + + align:start position:0% +hasn't already loaded so now those are +going to be loaded into some additional + + align:start position:0% +going to be loaded into some additional + + + align:start position:0% +going to be loaded into some additional +locations in A's in B's memory or going + + align:start position:0% +locations in A's in B's memory or going + + + align:start position:0% +locations in A's in B's memory or going +to be loaded into some additional + + align:start position:0% +to be loaded into some additional + + + align:start position:0% +to be loaded into some additional +locations in the physical memory and + + align:start position:0% +locations in the physical memory and + + + align:start position:0% +locations in the physical memory and +then mapped into A's memory okay so um + + align:start position:0% +then mapped into A's memory okay so um + + + align:start position:0% +then mapped into A's memory okay so um +this is just showing that we can + + align:start position:0% +this is just showing that we can + + + align:start position:0% +this is just showing that we can +actually use this notion of address + + align:start position:0% +actually use this notion of address + + + align:start position:0% +actually use this notion of address +spaces to map uh in addition to using it + + align:start position:0% +spaces to map uh in addition to using it + + + align:start position:0% +spaces to map uh in addition to using it +to isolate two two modules from each + + align:start position:0% +to isolate two two modules from each + + + align:start position:0% +to isolate two two modules from each +other so they can't refer to each + + align:start position:0% +other so they can't refer to each + + + align:start position:0% +other so they can't refer to each +other's memory we can also use it as a + + align:start position:0% +other's memory we can also use it as a + + + align:start position:0% +other's memory we can also use it as a +way to allow two modules to share uh + + align:start position:0% +way to allow two modules to share uh + + + align:start position:0% +way to allow two modules to share uh +things with each other and in particular + + align:start position:0% +things with each other and in particular + + + align:start position:0% +things with each other and in particular +this is a good idea in the case of these + + align:start position:0% +this is a good idea in the case of these + + + align:start position:0% +this is a good idea in the case of these +um in the in the case of things like + + align:start position:0% +um in the in the case of things like + + + align:start position:0% +um in the in the case of things like +shared libraries where we have two + + align:start position:0% +shared libraries where we have two + + + align:start position:0% +shared libraries where we have two +things the both programs need to be able + + align:start position:0% +things the both programs need to be able + + + align:start position:0% +things the both programs need to be able +to read the same data so they can they + + align:start position:0% +to read the same data so they can they + + + align:start position:0% +to read the same data so they can they +can use this to do that okay so what we + + align:start position:0% +can use this to do that okay so what we + + + align:start position:0% +can use this to do that okay so what we +saw today was this notion of virtual + + align:start position:0% +saw today was this notion of virtual + + + align:start position:0% +saw today was this notion of virtual +memory and address spaces um we saw how + + align:start position:0% +memory and address spaces um we saw how + + + align:start position:0% +memory and address spaces um we saw how +we have the kernel that's a trusted + + align:start position:0% +we have the kernel that's a trusted + + + align:start position:0% +we have the kernel that's a trusted +intermediary between two applications + + align:start position:0% +intermediary between two applications + + + align:start position:0% +intermediary between two applications +what we're going to see next time is how + + align:start position:0% +what we're going to see next time is how + + + align:start position:0% +what we're going to see next time is how +we can take this not notion of uh + + align:start position:0% +we can take this not notion of uh + + + align:start position:0% +we can take this not notion of uh +virtualizing a computer we saw how to + + align:start position:0% +virtualizing a computer we saw how to + + + align:start position:0% +virtualizing a computer we saw how to +virtualize the memory today next time + + align:start position:0% +virtualize the memory today next time + + + align:start position:0% +virtualize the memory today next time +we're going to see how we virtualize the + + align:start position:0% +we're going to see how we virtualize the + + + align:start position:0% +we're going to see how we virtualize the +processor in order to create the + + align:start position:0% +processor in order to create the + + + align:start position:0% +processor in order to create the +abstraction of multiple processors + + align:start position:0% +abstraction of multiple processors + + + align:start position:0% +abstraction of multiple processors +running on just one single physical + + align:start position:0% +running on just one single physical + + + align:start position:0% +running on just one single physical +piece of Hardware so I'll see you + + align:start position:0% +piece of Hardware so I'll see you + + + align:start position:0% +piece of Hardware so I'll see you +tomorrow \ No newline at end of file diff --git a/UBGcs9r4U40.txt b/UBGcs9r4U40.txt new file mode 100644 index 0000000000000000000000000000000000000000..742acc124263e2705b4df7c13a3de632caa77f84 --- /dev/null +++ b/UBGcs9r4U40.txt @@ -0,0 +1,1035 @@ +align:start position:0% + +why does this matter i'm going to give + + align:start position:0% +why does this matter i'm going to give + + + align:start position:0% +why does this matter i'm going to give +you a brief why this matters + + align:start position:0% +you a brief why this matters + + + align:start position:0% +you a brief why this matters +and you know we've been talking about + + align:start position:0% +and you know we've been talking about + + + align:start position:0% +and you know we've been talking about +the quantum nature of things + + align:start position:0% +the quantum nature of things + + + align:start position:0% +the quantum nature of things +right quantum is this quantum are these + + align:start position:0% +right quantum is this quantum are these + + + align:start position:0% +right quantum is this quantum are these +differences + + align:start position:0% +differences + + + align:start position:0% +differences +it's this probability it's quantization + + align:start position:0% +it's this probability it's quantization + + + align:start position:0% +it's this probability it's quantization +of energies + + align:start position:0% +of energies + + + align:start position:0% +of energies +what does that mean right well last time + + align:start position:0% +what does that mean right well last time + + + align:start position:0% +what does that mean right well last time +i told you + + align:start position:0% +i told you + + + align:start position:0% +i told you +that you know by electrons being quantum + + align:start position:0% +that you know by electrons being quantum + + + align:start position:0% +that you know by electrons being quantum +and having wave-like character we were + + align:start position:0% +and having wave-like character we were + + + align:start position:0% +and having wave-like character we were +able to use them to see things + + align:start position:0% +able to use them to see things + + + align:start position:0% +able to use them to see things +and it started the nanotechnology + + align:start position:0% +and it started the nanotechnology + + + align:start position:0% +and it started the nanotechnology +revolution about 30 years ago + + align:start position:0% +revolution about 30 years ago + + + align:start position:0% +revolution about 30 years ago +and today i want to give you an example + + align:start position:0% +and today i want to give you an example + + + align:start position:0% +and today i want to give you an example +of that in my why this matters + + align:start position:0% +of that in my why this matters + + + align:start position:0% +of that in my why this matters +um and and it has to do with quantum + + align:start position:0% +um and and it has to do with quantum + + + align:start position:0% +um and and it has to do with quantum +domination + + align:start position:0% +domination + + + align:start position:0% +domination +which should be the title of a movie or + + align:start position:0% +which should be the title of a movie or + + + align:start position:0% +which should be the title of a movie or +a book + + align:start position:0% +a book + + + align:start position:0% +a book +um and here's the example take a piece + + align:start position:0% +um and here's the example take a piece + + + align:start position:0% +um and here's the example take a piece +of bulk + + align:start position:0% +of bulk + + + align:start position:0% +of bulk +material take a piece of silicon okay + + align:start position:0% +material take a piece of silicon okay + + + align:start position:0% +material take a piece of silicon okay +and if you look at the silicon + + align:start position:0% +and if you look at the silicon + + + align:start position:0% +and if you look at the silicon +it's kind of boring to look at optically + + align:start position:0% +it's kind of boring to look at optically + + + align:start position:0% +it's kind of boring to look at optically +it's not very interesting + + align:start position:0% +it's not very interesting + + + align:start position:0% +it's not very interesting +you know don't tell that to your iphone + + align:start position:0% +you know don't tell that to your iphone + + + align:start position:0% +you know don't tell that to your iphone +which has a lot of it in there + + align:start position:0% +which has a lot of it in there + + + align:start position:0% +which has a lot of it in there +but it's it's boring but now take out + + align:start position:0% +but it's it's boring but now take out + + + align:start position:0% +but it's it's boring but now take out +your little nano + + align:start position:0% +your little nano + + + align:start position:0% +your little nano +ice cream scooper which you all have and + + align:start position:0% +ice cream scooper which you all have and + + + align:start position:0% +ice cream scooper which you all have and +you take a little tiny piece of it + + align:start position:0% +you take a little tiny piece of it + + + align:start position:0% +you take a little tiny piece of it +we call that a quantum dot why + + align:start position:0% +we call that a quantum dot why + + + align:start position:0% +we call that a quantum dot why +we call it a quantum dot because it kind + + align:start position:0% +we call it a quantum dot because it kind + + + align:start position:0% +we call it a quantum dot because it kind +of looks like a dot + + align:start position:0% +of looks like a dot + + + align:start position:0% +of looks like a dot +small ish but we call it that because + + align:start position:0% +small ish but we call it that because + + + align:start position:0% +small ish but we call it that because +quantum mechanics + + align:start position:0% +quantum mechanics + + + align:start position:0% +quantum mechanics +takes over the properties here's an + + align:start position:0% +takes over the properties here's an + + + align:start position:0% +takes over the properties here's an +example shine light + + align:start position:0% +example shine light + + + align:start position:0% +example shine light +on this thing or have it glow and all of + + align:start position:0% +on this thing or have it glow and all of + + + align:start position:0% +on this thing or have it glow and all of +a sudden instead of being + + align:start position:0% +a sudden instead of being + + + align:start position:0% +a sudden instead of being +boring it can be any color you want why + + align:start position:0% +boring it can be any color you want why + + + align:start position:0% +boring it can be any color you want why +because if i shine light and here's a + + align:start position:0% +because if i shine light and here's a + + + align:start position:0% +because if i shine light and here's a +very sophisticated + + align:start position:0% +very sophisticated + + + align:start position:0% +very sophisticated +uh picture of a laser you can tell i had + + align:start position:0% +uh picture of a laser you can tell i had + + + align:start position:0% +uh picture of a laser you can tell i had +trouble making transparent + + align:start position:0% +trouble making transparent + + + align:start position:0% +trouble making transparent +um and so you you shine a laser on this + + align:start position:0% +um and so you you shine a laser on this + + + align:start position:0% +um and so you you shine a laser on this +piece + + align:start position:0% +piece + + + align:start position:0% +piece +we know already light excites charge + + align:start position:0% +we know already light excites charge + + + align:start position:0% +we know already light excites charge +in an atom it does the same in solids so + + align:start position:0% +in an atom it does the same in solids so + + + align:start position:0% +in an atom it does the same in solids so +here's my stomach here's my piece of + + align:start position:0% +here's my stomach here's my piece of + + + align:start position:0% +here's my stomach here's my piece of +silicon + + align:start position:0% +silicon + + + align:start position:0% +silicon +and what that does is it sends an + + align:start position:0% +and what that does is it sends an + + + align:start position:0% +and what that does is it sends an +electron up in energy levels + + align:start position:0% +electron up in energy levels + + + align:start position:0% +electron up in energy levels +yeah but the electron is up in an energy + + align:start position:0% +yeah but the electron is up in an energy + + + align:start position:0% +yeah but the electron is up in an energy +level and it left behind + + align:start position:0% +level and it left behind + + + align:start position:0% +level and it left behind +a hole which is something we'll talk + + align:start position:0% +a hole which is something we'll talk + + + align:start position:0% +a hole which is something we'll talk +about later when we talk about + + align:start position:0% +about later when we talk about + + + align:start position:0% +about later when we talk about +semiconductors + + align:start position:0% +semiconductors + + + align:start position:0% +semiconductors +a hole is just a positive charge and it + + align:start position:0% +a hole is just a positive charge and it + + + align:start position:0% +a hole is just a positive charge and it +turns out that that electron and that + + align:start position:0% +turns out that that electron and that + + + align:start position:0% +turns out that that electron and that +hole + + align:start position:0% +hole + + + align:start position:0% +hole +are attracted to each other but not they + + align:start position:0% +are attracted to each other but not they + + + align:start position:0% +are attracted to each other but not they +can't get too close + + align:start position:0% +can't get too close + + + align:start position:0% +can't get too close +but they want to kind of hang out at a + + align:start position:0% +but they want to kind of hang out at a + + + align:start position:0% +but they want to kind of hang out at a +certain distance where + + align:start position:0% +certain distance where + + + align:start position:0% +certain distance where +how far yeah quantum mechanics + + align:start position:0% +how far yeah quantum mechanics + + + align:start position:0% +how far yeah quantum mechanics +n two three four tells us it tells us + + align:start position:0% +n two three four tells us it tells us + + + align:start position:0% +n two three four tells us it tells us +how far + + align:start position:0% +how far + + + align:start position:0% +how far +right i don't wanna hang out this far + + align:start position:0% +right i don't wanna hang out this far + + + align:start position:0% +right i don't wanna hang out this far +and then all of a sudden i've nano + + align:start position:0% +and then all of a sudden i've nano + + + align:start position:0% +and then all of a sudden i've nano +scooped them out + + align:start position:0% +scooped them out + + + align:start position:0% +scooped them out +and i've made a quantum dot but if i try + + align:start position:0% +and i've made a quantum dot but if i try + + + align:start position:0% +and i've made a quantum dot but if i try +to do the same thing there + + align:start position:0% +to do the same thing there + + + align:start position:0% +to do the same thing there +that's how far they want it to be and + + align:start position:0% +that's how far they want it to be and + + + align:start position:0% +that's how far they want it to be and +they can't be they literally + + align:start position:0% +they can't be they literally + + + align:start position:0% +they can't be they literally +ran out of real estate they ran out of + + align:start position:0% +ran out of real estate they ran out of + + + align:start position:0% +ran out of real estate they ran out of +atoms + + align:start position:0% +atoms + + + align:start position:0% +atoms +they cannot be out here because there's + + align:start position:0% +they cannot be out here because there's + + + align:start position:0% +they cannot be out here because there's +no stuff out here so they get squeezed + + align:start position:0% +no stuff out here so they get squeezed + + + align:start position:0% +no stuff out here so they get squeezed +i am squeezing these quantum mechanical + + align:start position:0% +i am squeezing these quantum mechanical + + + align:start position:0% +i am squeezing these quantum mechanical +objects this electron in this hole + + align:start position:0% +objects this electron in this hole + + + align:start position:0% +objects this electron in this hole +and by squeezing them i'm changing + + align:start position:0% +and by squeezing them i'm changing + + + align:start position:0% +and by squeezing them i'm changing +the way they interact with light i'm + + align:start position:0% +the way they interact with light i'm + + + align:start position:0% +the way they interact with light i'm +changing the color + + align:start position:0% +changing the color + + + align:start position:0% +changing the color +right oh it's all stuff we've learned + + align:start position:0% +right oh it's all stuff we've learned + + + align:start position:0% +right oh it's all stuff we've learned +that explains something revolutionary + + align:start position:0% +that explains something revolutionary + + + align:start position:0% +that explains something revolutionary +by the way if you buy a qled tv is it as + + align:start position:0% +by the way if you buy a qled tv is it as + + + align:start position:0% +by the way if you buy a qled tv is it as +good as oled + + align:start position:0% +good as oled + + + align:start position:0% +good as oled +no but is it better than led yeah + + align:start position:0% +no but is it better than led yeah + + + align:start position:0% +no but is it better than led yeah +a little bit that's what the qled + + align:start position:0% +a little bit that's what the qled + + + align:start position:0% +a little bit that's what the qled +quantum is quantum dots + + align:start position:0% +quantum is quantum dots + + + align:start position:0% +quantum is quantum dots +they have coded the led emitters with + + align:start position:0% +they have coded the led emitters with + + + align:start position:0% +they have coded the led emitters with +quantum dots + + align:start position:0% +quantum dots + + + align:start position:0% +quantum dots +to give you better color now + + align:start position:0% +to give you better color now + + + align:start position:0% +to give you better color now +um what this means why this matters + + align:start position:0% +um what this means why this matters + + + align:start position:0% +um what this means why this matters +is nothing less than the periodic table + + align:start position:0% +is nothing less than the periodic table + + + align:start position:0% +is nothing less than the periodic table +itself because + + align:start position:0% +itself because + + + align:start position:0% +itself because +you know i think i showed you this kind + + align:start position:0% +you know i think i showed you this kind + + + align:start position:0% +you know i think i showed you this kind +of you know we're living in these + + align:start position:0% +of you know we're living in these + + + align:start position:0% +of you know we're living in these +different ages which i love + + align:start position:0% +different ages which i love + + + align:start position:0% +different ages which i love +we have the periodic table that has the + + align:start position:0% +we have the periodic table that has the + + + align:start position:0% +we have the periodic table that has the +ability to work with it + + align:start position:0% +ability to work with it + + + align:start position:0% +ability to work with it +is what's brought us to the age of + + align:start position:0% +is what's brought us to the age of + + + align:start position:0% +is what's brought us to the age of +materials design right + + align:start position:0% +materials design right + + + align:start position:0% +materials design right +but see um now + + align:start position:0% +but see um now + + + align:start position:0% +but see um now +i've literally just told you that by + + align:start position:0% +i've literally just told you that by + + + align:start position:0% +i've literally just told you that by +changing the size nothing more than the + + align:start position:0% +changing the size nothing more than the + + + align:start position:0% +changing the size nothing more than the +size + + align:start position:0% +size + + + align:start position:0% +size +i can tune a property because of quantum + + align:start position:0% +i can tune a property because of quantum + + + align:start position:0% +i can tune a property because of quantum +mechanics + + align:start position:0% +mechanics + + + align:start position:0% +mechanics +because i'm changing its quantum + + align:start position:0% +because i'm changing its quantum + + + align:start position:0% +because i'm changing its quantum +mechanical interactions it would be like + + align:start position:0% +mechanical interactions it would be like + + + align:start position:0% +mechanical interactions it would be like +saying + + align:start position:0% +saying + + + align:start position:0% +saying +i can take a piece of this table i can + + align:start position:0% +i can take a piece of this table i can + + + align:start position:0% +i can take a piece of this table i can +break a piece of this table + + align:start position:0% +break a piece of this table + + + align:start position:0% +break a piece of this table +and it's now going to be red that's + + align:start position:0% +and it's now going to be red that's + + + align:start position:0% +and it's now going to be red that's +that's exactly what we're doing but at a + + align:start position:0% +that's exactly what we're doing but at a + + + align:start position:0% +that's exactly what we're doing but at a +very + + align:start position:0% +very + + + align:start position:0% +very +tiny size that is as if we are taking + + align:start position:0% +tiny size that is as if we are taking + + + align:start position:0% +tiny size that is as if we are taking +this periodic table and giving it + + align:start position:0% +this periodic table and giving it + + + align:start position:0% +this periodic table and giving it +a whole another dimension every element + + align:start position:0% +a whole another dimension every element + + + align:start position:0% +a whole another dimension every element +now + + align:start position:0% +now + + + align:start position:0% +now +can do more things than we thought + + align:start position:0% +can do more things than we thought + + + align:start position:0% +can do more things than we thought +possible because + + align:start position:0% +possible because + + + align:start position:0% +possible because +we can tune these properties related to + + align:start position:0% +we can tune these properties related to + + + align:start position:0% +we can tune these properties related to +quantum mechanics + + align:start position:0% +quantum mechanics + + + align:start position:0% +quantum mechanics +right so that's a big deal that's a very + + align:start position:0% +right so that's a big deal that's a very + + + align:start position:0% +right so that's a big deal that's a very +big deal \ No newline at end of file diff --git a/UE-O9TiKOw0.txt b/UE-O9TiKOw0.txt new file mode 100644 index 0000000000000000000000000000000000000000..67eec9fdd315887c7570d13d7afc5680c0702607 --- /dev/null +++ b/UE-O9TiKOw0.txt @@ -0,0 +1,1051 @@ +align:start position:0% + +we would now like to look at + + align:start position:0% +we would now like to look at + + + align:start position:0% +we would now like to look at +two-dimensional collisions and what we + + align:start position:0% +two-dimensional collisions and what we + + + align:start position:0% +two-dimensional collisions and what we +like to look at is in the laboratory + + align:start position:0% +like to look at is in the laboratory + + + align:start position:0% +like to look at is in the laboratory +frame so I'll call that the lab frame in + + align:start position:0% +frame so I'll call that the lab frame in + + + align:start position:0% +frame so I'll call that the lab frame in +which we have a target particle which + + align:start position:0% +which we have a target particle which + + + align:start position:0% +which we have a target particle which +I'm going to call two and an incoming + + align:start position:0% +I'm going to call two and an incoming + + + align:start position:0% +I'm going to call two and an incoming +particle one which is coming in with + + align:start position:0% +particle one which is coming in with + + + align:start position:0% +particle one which is coming in with +some initial velocity after the + + align:start position:0% +some initial velocity after the + + + align:start position:0% +some initial velocity after the +collision the target let's imagine that + + align:start position:0% +collision the target let's imagine that + + + align:start position:0% +collision the target let's imagine that +the target particle is going out at a + + align:start position:0% +the target particle is going out at a + + + align:start position:0% +the target particle is going out at a +certain direction so we'll call that two + + align:start position:0% +certain direction so we'll call that two + + + align:start position:0% +certain direction so we'll call that two +and the target particle has a velocity V + + align:start position:0% +and the target particle has a velocity V + + + align:start position:0% +and the target particle has a velocity V +two final and the initial particle at + + align:start position:0% +two final and the initial particle at + + + align:start position:0% +two final and the initial particle at +going in this direction we'll call that + + align:start position:0% +going in this direction we'll call that + + + align:start position:0% +going in this direction we'll call that +one and that is its outcoming velocity + + align:start position:0% +one and that is its outcoming velocity + + + align:start position:0% +one and that is its outcoming velocity +now in this collision we want to ask + + align:start position:0% +now in this collision we want to ask + + + align:start position:0% +now in this collision we want to ask +ourselves first what quantities are + + align:start position:0% +ourselves first what quantities are + + + align:start position:0% +ourselves first what quantities are +constants of the motion well let's + + align:start position:0% +constants of the motion well let's + + + align:start position:0% +constants of the motion well let's +assume no external forces therefore + + align:start position:0% +assume no external forces therefore + + + align:start position:0% +assume no external forces therefore +momentum is constant and we can write + + align:start position:0% +momentum is constant and we can write + + + align:start position:0% +momentum is constant and we can write +our momentum equation as m1 v1 initial + + align:start position:0% +our momentum equation as m1 v1 initial + + + align:start position:0% +our momentum equation as m1 v1 initial +equals m1 v1 final plus m2 the two final + + align:start position:0% +equals m1 v1 final plus m2 the two final + + + align:start position:0% +equals m1 v1 final plus m2 the two final +now recall that momentum is a vector and + + align:start position:0% +now recall that momentum is a vector and + + + align:start position:0% +now recall that momentum is a vector and +so what we have here are two the + + align:start position:0% +so what we have here are two the + + + align:start position:0% +so what we have here are two the +unknowns here are our two outcoming + + align:start position:0% +unknowns here are our two outcoming + + + align:start position:0% +unknowns here are our two outcoming +vectors v1 final and v2 final and a + + align:start position:0% +vectors v1 final and v2 final and a + + + align:start position:0% +vectors v1 final and v2 final and a +vector in two dimensions has two + + align:start position:0% +vector in two dimensions has two + + + align:start position:0% +vector in two dimensions has two +quantities it can we can discuss we can + + align:start position:0% +quantities it can we can discuss we can + + + align:start position:0% +quantities it can we can discuss we can +write that as components or we can write + + align:start position:0% +write that as components or we can write + + + align:start position:0% +write that as components or we can write +it in terms of magnitudes and directions + + align:start position:0% +it in terms of magnitudes and directions + + + align:start position:0% +it in terms of magnitudes and directions +now experimentally we often will measure + + align:start position:0% +now experimentally we often will measure + + + align:start position:0% +now experimentally we often will measure +the directions of the outcoming + + align:start position:0% +the directions of the outcoming + + + align:start position:0% +the directions of the outcoming +particles which I will now indicate by + + align:start position:0% +particles which I will now indicate by + + + align:start position:0% +particles which I will now indicate by +theta to final and theta1 final and so + + align:start position:0% +theta to final and theta1 final and so + + + align:start position:0% +theta to final and theta1 final and so +when we write our two momentum equations + + align:start position:0% +when we write our two momentum equations + + + align:start position:0% +when we write our two momentum equations +we can either write it as components or + + align:start position:0% +we can either write it as components or + + + align:start position:0% +we can either write it as components or +we can write it in terms of magnitudes + + align:start position:0% +we can write it in terms of magnitudes + + + align:start position:0% +we can write it in terms of magnitudes +and directions and do vector + + align:start position:0% +and directions and do vector + + + align:start position:0% +and directions and do vector +decomposition now because we measure the + + align:start position:0% +decomposition now because we measure the + + + align:start position:0% +decomposition now because we measure the +outcoming directions we're going to + + align:start position:0% +outcoming directions we're going to + + + align:start position:0% +outcoming directions we're going to +choose to do magnitudes and directions + + align:start position:0% +choose to do magnitudes and directions + + + align:start position:0% +choose to do magnitudes and directions +so let's indicate a little notation + + align:start position:0% +so let's indicate a little notation + + + align:start position:0% +so let's indicate a little notation +we'll say that the magnitude of V one + + align:start position:0% +we'll say that the magnitude of V one + + + align:start position:0% +we'll say that the magnitude of V one +initial is v1 I and the magnitude + + align:start position:0% +initial is v1 I and the magnitude + + + align:start position:0% +initial is v1 I and the magnitude +of the two final is b2 final and the + + align:start position:0% +of the two final is b2 final and the + + + align:start position:0% +of the two final is b2 final and the +magnitude of the one final is v1 final + + align:start position:0% +magnitude of the one final is v1 final + + + align:start position:0% +magnitude of the one final is v1 final +and so now when we look at our two + + align:start position:0% +and so now when we look at our two + + + align:start position:0% +and so now when we look at our two +momentum conditions we can we now also + + align:start position:0% +momentum conditions we can we now also + + + align:start position:0% +momentum conditions we can we now also +have to introduce unit vectors for + + align:start position:0% +have to introduce unit vectors for + + + align:start position:0% +have to introduce unit vectors for +directions so let's call I hat that way + + align:start position:0% +directions so let's call I hat that way + + + align:start position:0% +directions so let's call I hat that way +and J hat in this direction and in our I + + align:start position:0% +and J hat in this direction and in our I + + + align:start position:0% +and J hat in this direction and in our I +hat direction we have only the incoming + + align:start position:0% +hat direction we have only the incoming + + + align:start position:0% +hat direction we have only the incoming +momentum and we can write that as m1 v1 + + align:start position:0% +momentum and we can write that as m1 v1 + + + align:start position:0% +momentum and we can write that as m1 v1 +initial it's positive because we've + + align:start position:0% +initial it's positive because we've + + + align:start position:0% +initial it's positive because we've +chosen the forward direction as our I + + align:start position:0% +chosen the forward direction as our I + + + align:start position:0% +chosen the forward direction as our I +hat direction now in terms of the + + align:start position:0% +hat direction now in terms of the + + + align:start position:0% +hat direction now in terms of the +outgoing momentum in the I hat direction + + align:start position:0% +outgoing momentum in the I hat direction + + + align:start position:0% +outgoing momentum in the I hat direction +we have to do vector decomposition of + + align:start position:0% +we have to do vector decomposition of + + + align:start position:0% +we have to do vector decomposition of +both of these vectors and they're both + + align:start position:0% +both of these vectors and they're both + + + align:start position:0% +both of these vectors and they're both +have positive components so we have m1 + + align:start position:0% +have positive components so we have m1 + + + align:start position:0% +have positive components so we have m1 +v1 + + align:start position:0% +v1 + + + align:start position:0% +v1 +final that's the magnitude cosine theta + + align:start position:0% +final that's the magnitude cosine theta + + + align:start position:0% +final that's the magnitude cosine theta +1 final plus positive sign because + + align:start position:0% +1 final plus positive sign because + + + align:start position:0% +1 final plus positive sign because +they're both in the positive direction + + align:start position:0% +they're both in the positive direction + + + align:start position:0% +they're both in the positive direction +the two final magnitude times we need + + align:start position:0% +the two final magnitude times we need + + + align:start position:0% +the two final magnitude times we need +that little m to the two final cosine + + align:start position:0% +that little m to the two final cosine + + + align:start position:0% +that little m to the two final cosine +theta two final and that is our I hat + + align:start position:0% +theta two final and that is our I hat + + + align:start position:0% +theta two final and that is our I hat +direction now the J hat direction + + align:start position:0% +direction now the J hat direction + + + align:start position:0% +direction now the J hat direction +remember we have to be careful because + + align:start position:0% +remember we have to be careful because + + + align:start position:0% +remember we have to be careful because +we're taking positive J head up so our + + align:start position:0% +we're taking positive J head up so our + + + align:start position:0% +we're taking positive J head up so our +particle two has a positive component in + + align:start position:0% +particle two has a positive component in + + + align:start position:0% +particle two has a positive component in +the J direction and our particle one has + + align:start position:0% +the J direction and our particle one has + + + align:start position:0% +the J direction and our particle one has +a negative component in the J direction + + align:start position:0% +a negative component in the J direction + + + align:start position:0% +a negative component in the J direction +the incoming momentum there's no + + align:start position:0% +the incoming momentum there's no + + + align:start position:0% +the incoming momentum there's no +momentum in the J direction so we have a + + align:start position:0% +momentum in the J direction so we have a + + + align:start position:0% +momentum in the J direction so we have a +zero and that's equal to positive m to + + align:start position:0% +zero and that's equal to positive m to + + + align:start position:0% +zero and that's equal to positive m to +be two final and that's a sine theta two + + align:start position:0% +be two final and that's a sine theta two + + + align:start position:0% +be two final and that's a sine theta two +final now here's where we have to be + + align:start position:0% +final now here's where we have to be + + + align:start position:0% +final now here's where we have to be +careful because this one is negative the + + align:start position:0% +careful because this one is negative the + + + align:start position:0% +careful because this one is negative the +component is in the negative J hat + + align:start position:0% +component is in the negative J hat + + + align:start position:0% +component is in the negative J hat +direction and we have m1 v1 final sine + + align:start position:0% +direction and we have m1 v1 final sine + + + align:start position:0% +direction and we have m1 v1 final sine +theta one final and these two represent + + align:start position:0% +theta one final and these two represent + + + align:start position:0% +theta one final and these two represent +our momentum equations now we also have + + align:start position:0% +our momentum equations now we also have + + + align:start position:0% +our momentum equations now we also have +to think let's think about energy again + + align:start position:0% +to think let's think about energy again + + + align:start position:0% +to think let's think about energy again +we have to know something about this + + align:start position:0% +we have to know something about this + + + align:start position:0% +we have to know something about this +collision and our assumption will be + + align:start position:0% +collision and our assumption will be + + + align:start position:0% +collision and our assumption will be +that this particular collision is + + align:start position:0% +that this particular collision is + + + align:start position:0% +that this particular collision is +elastic and that means the initial + + align:start position:0% +elastic and that means the initial + + + align:start position:0% +elastic and that means the initial +kinetic energy + + align:start position:0% +kinetic energy + + + align:start position:0% +kinetic energy +is equal to the final kinetic energy + + align:start position:0% +is equal to the final kinetic energy + + + align:start position:0% +is equal to the final kinetic energy +energy is a scalar we've been describing + + align:start position:0% +energy is a scalar we've been describing + + + align:start position:0% +energy is a scalar we've been describing +our incoming velocity vectors in terms + + align:start position:0% +our incoming velocity vectors in terms + + + align:start position:0% +our incoming velocity vectors in terms +of magnitudes so we can write our + + align:start position:0% +of magnitudes so we can write our + + + align:start position:0% +of magnitudes so we can write our +elastic energy condition as the incoming + + align:start position:0% +elastic energy condition as the incoming + + + align:start position:0% +elastic energy condition as the incoming +kinetic energy squared that's the + + align:start position:0% +kinetic energy squared that's the + + + align:start position:0% +kinetic energy squared that's the +kinetic energy incoming is equal to + + align:start position:0% +kinetic energy incoming is equal to + + + align:start position:0% +kinetic energy incoming is equal to +one-half m1 the one final squared plus + + align:start position:0% +one-half m1 the one final squared plus + + + align:start position:0% +one-half m1 the one final squared plus +one-half m2 v2 final squared and that is + + align:start position:0% +one-half m2 v2 final squared and that is + + + align:start position:0% +one-half m2 v2 final squared and that is +our kinetic energy condition let's label + + align:start position:0% +our kinetic energy condition let's label + + + align:start position:0% +our kinetic energy condition let's label +this equation one and equation two now + + align:start position:0% +this equation one and equation two now + + + align:start position:0% +this equation one and equation two now +it's very important to realize what + + align:start position:0% +it's very important to realize what + + + align:start position:0% +it's very important to realize what +quantities are given and which we need + + align:start position:0% +quantities are given and which we need + + + align:start position:0% +quantities are given and which we need +to solve for so in this problem because + + align:start position:0% +to solve for so in this problem because + + + align:start position:0% +to solve for so in this problem because +the two outcoming velocities unknowns we + + align:start position:0% +the two outcoming velocities unknowns we + + + align:start position:0% +the two outcoming velocities unknowns we +have four unknowns those unknowns can be + + align:start position:0% +have four unknowns those unknowns can be + + + align:start position:0% +have four unknowns those unknowns can be +written in terms of the two velocity + + align:start position:0% +written in terms of the two velocity + + + align:start position:0% +written in terms of the two velocity +final plot and the other one the two + + align:start position:0% +final plot and the other one the two + + + align:start position:0% +final plot and the other one the two +final those are our vector quantities + + align:start position:0% +final those are our vector quantities + + + align:start position:0% +final those are our vector quantities +but recall in terms of the scalar + + align:start position:0% +but recall in terms of the scalar + + + align:start position:0% +but recall in terms of the scalar +magnitudes we have that v1 final and + + align:start position:0% +magnitudes we have that v1 final and + + + align:start position:0% +magnitudes we have that v1 final and +I'll just write the other ones down the + + align:start position:0% +I'll just write the other ones down the + + + align:start position:0% +I'll just write the other ones down the +two final and the two outgoing + + align:start position:0% +two final and the two outgoing + + + align:start position:0% +two final and the two outgoing +directions theta1 final and theta2 final + + align:start position:0% +directions theta1 final and theta2 final + + + align:start position:0% +directions theta1 final and theta2 final +so these are our four unknown quantities + + align:start position:0% +so these are our four unknown quantities + + + align:start position:0% +so these are our four unknown quantities +but you can see we only have three + + align:start position:0% +but you can see we only have three + + + align:start position:0% +but you can see we only have three +equations and therefore if we want to + + align:start position:0% +equations and therefore if we want to + + + align:start position:0% +equations and therefore if we want to +determine the outcomes we need to + + align:start position:0% +determine the outcomes we need to + + + align:start position:0% +determine the outcomes we need to +measure one additional quantity now + + align:start position:0% +measure one additional quantity now + + + align:start position:0% +measure one additional quantity now +that's very useful when doing problem + + align:start position:0% +that's very useful when doing problem + + + align:start position:0% +that's very useful when doing problem +solving because when you start to read a + + align:start position:0% +solving because when you start to read a + + + align:start position:0% +solving because when you start to read a +problem and you look at what's being + + align:start position:0% +problem and you look at what's being + + + align:start position:0% +problem and you look at what's being +measured you can right away determine + + align:start position:0% +measured you can right away determine + + + align:start position:0% +measured you can right away determine +which of the four quantities has been + + align:start position:0% +which of the four quantities has been + + + align:start position:0% +which of the four quantities has been +given you may be given an outgoing + + align:start position:0% +given you may be given an outgoing + + + align:start position:0% +given you may be given an outgoing +magnitude or you may of the velocity or + + align:start position:0% +magnitude or you may of the velocity or + + + align:start position:0% +magnitude or you may of the velocity or +you may be given one of these scattering + + align:start position:0% +you may be given one of these scattering + + + align:start position:0% +you may be given one of these scattering +angles and so that's how we approach + + align:start position:0% +angles and so that's how we approach + + + align:start position:0% +angles and so that's how we approach +two-dimensional a stick collision of + + align:start position:0% +two-dimensional a stick collision of + + + align:start position:0% +two-dimensional a stick collision of +course there's algebra now to solve for + + align:start position:0% +course there's algebra now to solve for + + + align:start position:0% +course there's algebra now to solve for +any particular quantity that you're + + align:start position:0% +any particular quantity that you're + + + align:start position:0% +any particular quantity that you're +interested in provided you have this + + align:start position:0% +interested in provided you have this + + + align:start position:0% +interested in provided you have this +extra additional information \ No newline at end of file diff --git a/WB8r7CU7clk.txt b/WB8r7CU7clk.txt new file mode 100644 index 0000000000000000000000000000000000000000..88d2c9354c5c912d6ebed2b84015c4ab4df863a2 --- /dev/null +++ b/WB8r7CU7clk.txt @@ -0,0 +1,13483 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu in the back of the room uh + + align:start position:0% +ocw.mit.edu in the back of the room uh + + + align:start position:0% +ocw.mit.edu in the back of the room uh +this course is being taped it may appear + + align:start position:0% +this course is being taped it may appear + + + align:start position:0% +this course is being taped it may appear +in the future on adex or mitx it'll + + align:start position:0% +in the future on adex or mitx it'll + + + align:start position:0% +in the future on adex or mitx it'll +appear on open course whereare so that + + align:start position:0% +appear on open course whereare so that + + + align:start position:0% +appear on open course whereare so that +means that by just sitting in the + + align:start position:0% +means that by just sitting in the + + + align:start position:0% +means that by just sitting in the +classroom you're choosing to participate + + align:start position:0% +classroom you're choosing to participate + + + align:start position:0% +classroom you're choosing to participate +in this adventure of having the course + + align:start position:0% +in this adventure of having the course + + + align:start position:0% +in this adventure of having the course +videotape if you want to hide you can + + align:start position:0% +videotape if you want to hide you can + + + align:start position:0% +videotape if you want to hide you can +sit in the back row if you want to you + + align:start position:0% +sit in the back row if you want to you + + + align:start position:0% +sit in the back row if you want to you +want to be part of the uh part of the + + align:start position:0% +want to be part of the uh part of the + + + align:start position:0% +want to be part of the uh part of the +part if you want to be famous sit in the + + align:start position:0% +part if you want to be famous sit in the + + + align:start position:0% +part if you want to be famous sit in the +front + + align:start position:0% + + + + align:start position:0% + +row so I handed out the syllabus and + + align:start position:0% +row so I handed out the syllabus and + + + align:start position:0% +row so I handed out the syllabus and +I'll just go through some of the things + + align:start position:0% +I'll just go through some of the things + + + align:start position:0% +I'll just go through some of the things +on here so as a prerequisite so at MIT + + align:start position:0% +on here so as a prerequisite so at MIT + + + align:start position:0% +on here so as a prerequisite so at MIT +we have three field Theory courses 1 2 3 + + align:start position:0% +we have three field Theory courses 1 2 3 + + + align:start position:0% +we have three field Theory courses 1 2 3 +as a prerequisite I've listed Quantum + + align:start position:0% +as a prerequisite I've listed Quantum + + + align:start position:0% +as a prerequisite I've listed Quantum +field Theory 2 I don't want to stop + + align:start position:0% +field Theory 2 I don't want to stop + + + align:start position:0% +field Theory 2 I don't want to stop +people that are taking Quantum field + + align:start position:0% +people that are taking Quantum field + + + align:start position:0% +people that are taking Quantum field +Theory 3 this term from also registering + + align:start position:0% +Theory 3 this term from also registering + + + align:start position:0% +Theory 3 this term from also registering +for this course but some of the things + + align:start position:0% +for this course but some of the things + + + align:start position:0% +for this course but some of the things +that you usually see in Quantum field + + align:start position:0% +that you usually see in Quantum field + + + align:start position:0% +that you usually see in Quantum field +Theory 3 are kind of important + + align:start position:0% +Theory 3 are kind of important + + + align:start position:0% +Theory 3 are kind of important +background things for this course so + + align:start position:0% +background things for this course so + + + align:start position:0% +background things for this course so +what I've done is I've posted on the on + + align:start position:0% +what I've done is I've posted on the on + + + align:start position:0% +what I've done is I've posted on the on +the website for the course my lecture + + align:start position:0% +the website for the course my lecture + + + align:start position:0% +the website for the course my lecture +notes from when I talk Quantum field + + align:start position:0% +notes from when I talk Quantum field + + + align:start position:0% +notes from when I talk Quantum field +Theory 3 last year so you can look at + + align:start position:0% +Theory 3 last year so you can look at + + + align:start position:0% +Theory 3 last year so you can look at +that and I'll assign some reading for + + align:start position:0% +that and I'll assign some reading for + + + align:start position:0% +that and I'll assign some reading for +that as background material for this + + align:start position:0% +that as background material for this + + + align:start position:0% +that as background material for this +uh some things actually were taught in + + align:start position:0% +uh some things actually were taught in + + + align:start position:0% +uh some things actually were taught in +Quantum field Theory too last term so + + align:start position:0% +Quantum field Theory too last term so + + + align:start position:0% +Quantum field Theory too last term so +some things like for example the beta + + align:start position:0% +some things like for example the beta + + + align:start position:0% +some things like for example the beta +function of qcd for normalization group + + align:start position:0% +function of qcd for normalization group + + + align:start position:0% +function of qcd for normalization group +so those things are going to be + + align:start position:0% +so those things are going to be + + + align:start position:0% +so those things are going to be +important prerequisites for this course + + align:start position:0% +important prerequisites for this course + + + align:start position:0% +important prerequisites for this course +uh and I'll assign some background + + align:start position:0% +uh and I'll assign some background + + + align:start position:0% +uh and I'll assign some background +reading so that you can remind yourself + + align:start position:0% +reading so that you can remind yourself + + + align:start position:0% +reading so that you can remind yourself +about about those things if you have any + + align:start position:0% +about about those things if you have any + + + align:start position:0% +about about those things if you have any +concerns about your preparation please + + align:start position:0% +concerns about your preparation please + + + align:start position:0% +concerns about your preparation please +feel free to talk to me in terms of + + align:start position:0% +feel free to talk to me in terms of + + + align:start position:0% +feel free to talk to me in terms of +grading this is pretty low-key we have + + align:start position:0% +grading this is pretty low-key we have + + + align:start position:0% +grading this is pretty low-key we have +five problem sets uh that will be + + align:start position:0% +five problem sets uh that will be + + + align:start position:0% +five problem sets uh that will be +roughly every two weeks we won't start + + align:start position:0% +roughly every two weeks we won't start + + + align:start position:0% +roughly every two weeks we won't start +the first problem set until next week um + + align:start position:0% +the first problem set until next week um + + + align:start position:0% +the first problem set until next week um +and then there'll be a presentation at + + align:start position:0% +and then there'll be a presentation at + + + align:start position:0% +and then there'll be a presentation at +the end of the course there's no exams + + align:start position:0% +the end of the course there's no exams + + + align:start position:0% +the end of the course there's no exams +no tests uh the purpose of the + + align:start position:0% +no tests uh the purpose of the + + + align:start position:0% +no tests uh the purpose of the +presentation is basically effective + + align:start position:0% +presentation is basically effective + + + align:start position:0% +presentation is basically effective +field theory is a very broad topic and + + align:start position:0% +field theory is a very broad topic and + + + align:start position:0% +field theory is a very broad topic and +there's no chance we'll be able to cover + + align:start position:0% +there's no chance we'll be able to cover + + + align:start position:0% +there's no chance we'll be able to cover +every possible thing about effective + + align:start position:0% +every possible thing about effective + + + align:start position:0% +every possible thing about effective +field theory in this course in + + align:start position:0% +field theory in this course in + + + align:start position:0% +field theory in this course in +particular a lot of applications will + + align:start position:0% +particular a lot of applications will + + + align:start position:0% +particular a lot of applications will +have to be brief on so or or we won't + + align:start position:0% +have to be brief on so or or we won't + + + align:start position:0% +have to be brief on so or or we won't +touch on at all so if you look at the + + align:start position:0% +touch on at all so if you look at the + + + align:start position:0% +touch on at all so if you look at the +syllabus on page three + + align:start position:0% +syllabus on page three + + + align:start position:0% +syllabus on page three +there's a list of possible presentation + + align:start position:0% +there's a list of possible presentation + + + align:start position:0% +there's a list of possible presentation +topics each one of you will pick a each + + align:start position:0% +topics each one of you will pick a each + + + align:start position:0% +topics each one of you will pick a each +one of you that registers for the course + + align:start position:0% +one of you that registers for the course + + + align:start position:0% +one of you that registers for the course +and wants to give a presentation we'll + + align:start position:0% +and wants to give a presentation we'll + + + align:start position:0% +and wants to give a presentation we'll +give a presentation at the end on one of + + align:start position:0% +give a presentation at the end on one of + + + align:start position:0% +give a presentation at the end on one of +these topics prepare it and stand up and + + align:start position:0% +these topics prepare it and stand up and + + + align:start position:0% +these topics prepare it and stand up and +lecture to the class and the idea is + + align:start position:0% +lecture to the class and the idea is + + + align:start position:0% +lecture to the class and the idea is +that basically you will teach the class + + align:start position:0% +that basically you will teach the class + + + align:start position:0% +that basically you will teach the class +for half an hour or so about one of + + align:start position:0% +for half an hour or so about one of + + + align:start position:0% +for half an hour or so about one of +these topics and in that way we will + + align:start position:0% +these topics and in that way we will + + + align:start position:0% +these topics and in that way we will +broaden the scope of things that we'll + + align:start position:0% +broaden the scope of things that we'll + + + align:start position:0% +broaden the scope of things that we'll +be able to + + align:start position:0% +be able to + + + align:start position:0% +be able to +cover this list is even this long list + + align:start position:0% +cover this list is even this long list + + + align:start position:0% +cover this list is even this long list +is not complete uh and you can also pick + + align:start position:0% +is not complete uh and you can also pick + + + align:start position:0% +is not complete uh and you can also pick +a topic that's not on this list if you + + align:start position:0% +a topic that's not on this list if you + + + align:start position:0% +a topic that's not on this list if you +talk to me about it so I'll broad a + + align:start position:0% +talk to me about it so I'll broad a + + + align:start position:0% +talk to me about it so I'll broad a +little later I'll also give you some + + align:start position:0% +little later I'll also give you some + + + align:start position:0% +little later I'll also give you some +suggested references for reading about + + align:start position:0% +suggested references for reading about + + + align:start position:0% +suggested references for reading about +this I just at this point give you the + + align:start position:0% +this I just at this point give you the + + + align:start position:0% +this I just at this point give you the +the list and we'll talk about where you + + align:start position:0% +the list and we'll talk about where you + + + align:start position:0% +the list and we'll talk about where you +might read about these things later on + + align:start position:0% +might read about these things later on + + + align:start position:0% +might read about these things later on +I'll give you a more detailed + + align:start position:0% +I'll give you a more detailed + + + align:start position:0% +I'll give you a more detailed +handout uh so even if you just look at + + align:start position:0% +handout uh so even if you just look at + + + align:start position:0% +handout uh so even if you just look at +this list you kind of see the breadth of + + align:start position:0% +this list you kind of see the breadth of + + + align:start position:0% +this list you kind of see the breadth of +the idea of effective field Theory how + + align:start position:0% +the idea of effective field Theory how + + + align:start position:0% +the idea of effective field Theory how +broadly it + + align:start position:0% +broadly it + + + align:start position:0% +broadly it +impacts uh physics when particle physics + + align:start position:0% +impacts uh physics when particle physics + + + align:start position:0% +impacts uh physics when particle physics +in particular so you know everything + + align:start position:0% +in particular so you know everything + + + align:start position:0% +in particular so you know everything +from finite temperature qcd finite + + align:start position:0% +from finite temperature qcd finite + + + align:start position:0% +from finite temperature qcd finite +density effective field theories of + + align:start position:0% +density effective field theories of + + + align:start position:0% +density effective field theories of +inflation popular these days effective + + align:start position:0% +inflation popular these days effective + + + align:start position:0% +inflation popular these days effective +field theories of cold atoms also very + + align:start position:0% +field theories of cold atoms also very + + + align:start position:0% +field theories of cold atoms also very +popular these days non-relativistic qcd + + align:start position:0% +popular these days non-relativistic qcd + + + align:start position:0% +popular these days non-relativistic qcd +production of coronia both in medium out + + align:start position:0% +production of coronia both in medium out + + + align:start position:0% +production of coronia both in medium out +of medium relativistic superfluids + + align:start position:0% +of medium relativistic superfluids + + + align:start position:0% +of medium relativistic superfluids +conformal effective field theories the + + align:start position:0% +conformal effective field theories the + + + align:start position:0% +conformal effective field theories the +list goes on and on lattice effective + + align:start position:0% +list goes on and on lattice effective + + + align:start position:0% +list goes on and on lattice effective +field theories so it's a very broad + + align:start position:0% +field theories so it's a very broad + + + align:start position:0% +field theories so it's a very broad +topic and what I'm going to do in this + + align:start position:0% +topic and what I'm going to do in this + + + align:start position:0% +topic and what I'm going to do in this +course is I'm going to start out with + + align:start position:0% +course is I'm going to start out with + + + align:start position:0% +course is I'm going to start out with +the first half of the course teaching + + align:start position:0% +the first half of the course teaching + + + align:start position:0% +the first half of the course teaching +you about the ideas of effective field + + align:start position:0% +you about the ideas of effective field + + + align:start position:0% +you about the ideas of effective field +Theory so some of the basic ingredients + + align:start position:0% +Theory so some of the basic ingredients + + + align:start position:0% +Theory so some of the basic ingredients +that go into all effective field + + align:start position:0% +that go into all effective field + + + align:start position:0% +that go into all effective field +theories and and some more technical + + align:start position:0% +theories and and some more technical + + + align:start position:0% +theories and and some more technical +things that should only show up in some + + align:start position:0% +things that should only show up in some + + + align:start position:0% +things that should only show up in some +effective field theories but that are + + align:start position:0% +effective field theories but that are + + + align:start position:0% +effective field theories but that are +kind of providing you with lessons if + + align:start position:0% +kind of providing you with lessons if + + + align:start position:0% +kind of providing you with lessons if +you had to ever construct your own + + align:start position:0% +you had to ever construct your own + + + align:start position:0% +you had to ever construct your own +effective field Theory that's the idea + + align:start position:0% +effective field Theory that's the idea + + + align:start position:0% +effective field Theory that's the idea +of the first half of the course the + + align:start position:0% +of the first half of the course the + + + align:start position:0% +of the first half of the course the +second half of the course I'm going to + + align:start position:0% +second half of the course I'm going to + + + align:start position:0% +second half of the course I'm going to +focus on a particular effective field + + align:start position:0% +focus on a particular effective field + + + align:start position:0% +focus on a particular effective field +Theory Soft cinear effective field + + align:start position:0% +Theory Soft cinear effective field + + + align:start position:0% +Theory Soft cinear effective field +Theory which is an effective field + + align:start position:0% +Theory which is an effective field + + + align:start position:0% +Theory which is an effective field +Theory that's close to my + + align:start position:0% +Theory that's close to my + + + align:start position:0% +Theory that's close to my +heart uh but that's uh exciting these + + align:start position:0% +heart uh but that's uh exciting these + + + align:start position:0% +heart uh but that's uh exciting these +days because of its applications to Jet + + align:start position:0% +days because of its applications to Jet + + + align:start position:0% +days because of its applications to Jet +physics and the LHC + + align:start position:0% +physics and the LHC + + + align:start position:0% +physics and the LHC +so we'll we'll talk about that as the + + align:start position:0% +so we'll we'll talk about that as the + + + align:start position:0% +so we'll we'll talk about that as the +second half of the + + align:start position:0% + + + + align:start position:0% + +course + + align:start position:0% +course + + + align:start position:0% +course +okay so as I say on the outline there's + + align:start position:0% +okay so as I say on the outline there's + + + align:start position:0% +okay so as I say on the outline there's +not really a textbook for this + + align:start position:0% +not really a textbook for this + + + align:start position:0% +not really a textbook for this +course uh I suggest some text that may + + align:start position:0% +course uh I suggest some text that may + + + align:start position:0% +course uh I suggest some text that may +be useful but they're not not not any + + align:start position:0% +be useful but they're not not not any + + + align:start position:0% +be useful but they're not not not any +one of them will be useful for more than + + align:start position:0% +one of them will be useful for more than + + + align:start position:0% +one of them will be useful for more than +20% of the material many of them for + + align:start position:0% +20% of the material many of them for + + + align:start position:0% +20% of the material many of them for +less than 10% of the material so I don't + + align:start position:0% +less than 10% of the material so I don't + + + align:start position:0% +less than 10% of the material so I don't +necessarily recommend that you go out + + align:start position:0% +necessarily recommend that you go out + + + align:start position:0% +necessarily recommend that you go out +and buy all of them or buy any of them I + + align:start position:0% +and buy all of them or buy any of them I + + + align:start position:0% +and buy all of them or buy any of them I +will try to post chapters of things when + + align:start position:0% +will try to post chapters of things when + + + align:start position:0% +will try to post chapters of things when +on the on the website when when it's + + align:start position:0% +on the on the website when when it's + + + align:start position:0% +on the on the website when when it's +required reading and these books will be + + align:start position:0% +required reading and these books will be + + + align:start position:0% +required reading and these books will be +available in the reading room so you can + + align:start position:0% +available in the reading room so you can + + + align:start position:0% +available in the reading room so you can +do it that way if you + + align:start position:0% +do it that way if you + + + align:start position:0% +do it that way if you +like if you're really serious about if + + align:start position:0% +like if you're really serious about if + + + align:start position:0% +like if you're really serious about if +you're really serious about + + align:start position:0% +you're really serious about + + + align:start position:0% +you're really serious about +phenomenology of course you should own + + align:start position:0% +phenomenology of course you should own + + + align:start position:0% +phenomenology of course you should own +all these books + + align:start position:0% + + + + align:start position:0% + +so so on the course outline I also + + align:start position:0% +so so on the course outline I also + + + align:start position:0% +so so on the course outline I also +listed office hours and I will adjust + + align:start position:0% +listed office hours and I will adjust + + + align:start position:0% +listed office hours and I will adjust +those when I find out all your + + align:start position:0% +those when I find out all your + + + align:start position:0% +those when I find out all your +schedules um and I also that Yoni who's + + align:start position:0% +schedules um and I also that Yoni who's + + + align:start position:0% +schedules um and I also that Yoni who's +sitting in the back is a 10% ta for the + + align:start position:0% +sitting in the back is a 10% ta for the + + + align:start position:0% +sitting in the back is a 10% ta for the +course he'll be doing some grading for + + align:start position:0% +course he'll be doing some grading for + + + align:start position:0% +course he'll be doing some grading for +us he won't have office + + align:start position:0% + + + + align:start position:0% + +hours thank you + + align:start position:0% + + + + align:start position:0% + +yeah so I know that some of you have + + align:start position:0% +yeah so I know that some of you have + + + align:start position:0% +yeah so I know that some of you have +registered for the course and some of + + align:start position:0% +registered for the course and some of + + + align:start position:0% +registered for the course and some of +you are here as listeners if you are + + align:start position:0% +you are here as listeners if you are + + + align:start position:0% +you are here as listeners if you are +here as a listener I have an ad form and + + align:start position:0% +here as a listener I have an ad form and + + + align:start position:0% +here as a listener I have an ad form and +I want you to add it as a listener just + + align:start position:0% +I want you to add it as a listener just + + + align:start position:0% +I want you to add it as a listener just +so that we have a record of you partly + + align:start position:0% +so that we have a record of you partly + + + align:start position:0% +so that we have a record of you partly +because that affects + + align:start position:0% +because that affects + + + align:start position:0% +because that affects +the ability to offer this course in the + + align:start position:0% +the ability to offer this course in the + + + align:start position:0% +the ability to offer this course in the +future also because we're going to use + + align:start position:0% +future also because we're going to use + + + align:start position:0% +future also because we're going to use +online tools and we may even use some + + align:start position:0% +online tools and we may even use some + + + align:start position:0% +online tools and we may even use some +online mitx tools if I find out that + + align:start position:0% +online mitx tools if I find out that + + + align:start position:0% +online mitx tools if I find out that +they're very useful for the course so I + + align:start position:0% +they're very useful for the course so I + + + align:start position:0% +they're very useful for the course so I +want you to be in the system and I want + + align:start position:0% +want you to be in the system and I want + + + align:start position:0% +want you to be in the system and I want +you to be able to access that + + align:start position:0% +you to be able to access that + + + align:start position:0% +you to be able to access that +information if we if we end up going + + align:start position:0% +information if we if we end up going + + + align:start position:0% +information if we if we end up going +that + + align:start position:0% + + + + align:start position:0% + +way okay so I think that's it so as far + + align:start position:0% +way okay so I think that's it so as far + + + align:start position:0% +way okay so I think that's it so as far +as Preamble does anybody have any + + align:start position:0% +as Preamble does anybody have any + + + align:start position:0% +as Preamble does anybody have any +questions + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so all right so let's + + align:start position:0% +so all right so let's + + + align:start position:0% +so all right so let's +start so let's start with the big + + align:start position:0% +start so let's start with the big + + + align:start position:0% +start so let's start with the big +picture + + align:start position:0% + + + + align:start position:0% + +I like to say that the big picture is + + align:start position:0% +I like to say that the big picture is + + + align:start position:0% +I like to say that the big picture is +that there's interesting physics at all + + align:start position:0% + + + + align:start position:0% + +scales what effective field Theory lets + + align:start position:0% +scales what effective field Theory lets + + + align:start position:0% +scales what effective field Theory lets +you do is you lets you tease out this + + align:start position:0% +you do is you lets you tease out this + + + align:start position:0% +you do is you lets you tease out this +interesting physics at all scales so you + + align:start position:0% +interesting physics at all scales so you + + + align:start position:0% +interesting physics at all scales so you +can in particular you can focus on on a + + align:start position:0% +can in particular you can focus on on a + + + align:start position:0% +can in particular you can focus on on a +particular scale and find the + + align:start position:0% +particular scale and find the + + + align:start position:0% +particular scale and find the +interesting physics there using the + + align:start position:0% +interesting physics there using the + + + align:start position:0% +interesting physics there using the +tools of effective field Theory + + align:start position:0% +tools of effective field Theory + + + align:start position:0% +tools of effective field Theory +now that's a little different than how + + align:start position:0% +now that's a little different than how + + + align:start position:0% +now that's a little different than how +we teach physics if you think about + + align:start position:0% +we teach physics if you think about + + + align:start position:0% +we teach physics if you think about +drawing a diagram from you know your + + align:start position:0% +drawing a diagram from you know your + + + align:start position:0% +drawing a diagram from you know your +freshman year to you know now many of + + align:start position:0% +freshman year to you know now many of + + + align:start position:0% +freshman year to you know now many of +you in Graduate Studies about how you + + align:start position:0% +you in Graduate Studies about how you + + + align:start position:0% +you in Graduate Studies about how you +learn physics it was not by kind of + + align:start position:0% +learn physics it was not by kind of + + + align:start position:0% +learn physics it was not by kind of +focusing in on individual particular + + align:start position:0% +focusing in on individual particular + + + align:start position:0% +focusing in on individual particular +scales but more from a kind of bottom up + + align:start position:0% +scales but more from a kind of bottom up + + + align:start position:0% +scales but more from a kind of bottom up +point of view so I would draw it picture + + align:start position:0% +point of view so I would draw it picture + + + align:start position:0% +point of view so I would draw it picture +of how we teach physics in the following + + align:start position:0% +of how we teach physics in the following + + + align:start position:0% +of how we teach physics in the following +way so you start out as a fresh freshman + + align:start position:0% +way so you start out as a fresh freshman + + + align:start position:0% +way so you start out as a fresh freshman +you learned classical mechanics + + align:start position:0% + + + + align:start position:0% + +you learn en and M classical + + align:start position:0% + + + + align:start position:0% + +enm you you learn Newtonian + + align:start position:0% + + + + align:start position:0% + +gravity and then you build on these + + align:start position:0% +gravity and then you build on these + + + align:start position:0% +gravity and then you build on these +things these things are your starting + + align:start position:0% +things these things are your starting + + + align:start position:0% +things these things are your starting +point and then you build on them so you + + align:start position:0% +point and then you build on them so you + + + align:start position:0% +point and then you build on them so you +learn quantum mechanics + + align:start position:0% + + + + align:start position:0% + +and that builds on classical + + align:start position:0% +and that builds on classical + + + align:start position:0% +and that builds on classical +mechanics you learn special + + align:start position:0% + + + + align:start position:0% + +relativity which is building on both + + align:start position:0% +relativity which is building on both + + + align:start position:0% +relativity which is building on both +classical mechanics and + + align:start position:0% + + + + align:start position:0% + +electromagnetism at some point you learn + + align:start position:0% +electromagnetism at some point you learn + + + align:start position:0% +electromagnetism at some point you learn +general relativity + + align:start position:0% + + + + align:start position:0% + +and Quantum field + + align:start position:0% + + + + align:start position:0% + +Theory and Quantum field Theory + + align:start position:0% +Theory and Quantum field Theory + + + align:start position:0% +Theory and Quantum field Theory +synthesizing quantum mechanics and + + align:start position:0% +synthesizing quantum mechanics and + + + align:start position:0% +synthesizing quantum mechanics and +special + + align:start position:0% +special + + + align:start position:0% +special +relativity and then these two here + + align:start position:0% + + + + align:start position:0% + +so you think about learning physics from + + align:start position:0% +so you think about learning physics from + + + align:start position:0% +so you think about learning physics from +the bottom up some in this picture from + + align:start position:0% +the bottom up some in this picture from + + + align:start position:0% +the bottom up some in this picture from +you learn these things first and then + + align:start position:0% +you learn these things first and then + + + align:start position:0% +you learn these things first and then +you learn these things and you sort of + + align:start position:0% +you learn these things and you sort of + + + align:start position:0% +you learn these things and you sort of +keep synthesizing keep putting things + + align:start position:0% +keep synthesizing keep putting things + + + align:start position:0% +keep synthesizing keep putting things +together we're going to be doing in this + + align:start position:0% +together we're going to be doing in this + + + align:start position:0% +together we're going to be doing in this +course the exact opposite of that we're + + align:start position:0% +course the exact opposite of that we're + + + align:start position:0% +course the exact opposite of that we're +going to be taking one of these blobs in + + align:start position:0% +going to be taking one of these blobs in + + + align:start position:0% +going to be taking one of these blobs in +particular this one and we're going to + + align:start position:0% +particular this one and we're going to + + + align:start position:0% +particular this one and we're going to +be looking deep inside it trying to make + + align:start position:0% +be looking deep inside it trying to make + + + align:start position:0% +be looking deep inside it trying to make +more and more specific field theories + + align:start position:0% + + + + align:start position:0% + +so if you like if you want to draw it as + + align:start position:0% +so if you like if you want to draw it as + + + align:start position:0% +so if you like if you want to draw it as +a blob we'll be taking Quantum field + + align:start position:0% +a blob we'll be taking Quantum field + + + align:start position:0% +a blob we'll be taking Quantum field +Theory and we'll be looking for + + align:start position:0% +Theory and we'll be looking for + + + align:start position:0% +Theory and we'll be looking for +derivatives of it or perhaps derivatives + + align:start position:0% +derivatives of it or perhaps derivatives + + + align:start position:0% +derivatives of it or perhaps derivatives +of derivatives of it like this and + + align:start position:0% +of derivatives of it like this and + + + align:start position:0% +of derivatives of it like this and +figuring out how to take a very general + + align:start position:0% +figuring out how to take a very general + + + align:start position:0% +figuring out how to take a very general +theory like Quantum field theory for the + + align:start position:0% +theory like Quantum field theory for the + + + align:start position:0% +theory like Quantum field theory for the +standard model and finding things that + + align:start position:0% +standard model and finding things that + + + align:start position:0% +standard model and finding things that +are more specific and More in some ways + + align:start position:0% +are more specific and More in some ways + + + align:start position:0% +are more specific and More in some ways +more powerful than just having + + align:start position:0% +more powerful than just having + + + align:start position:0% +more powerful than just having +the original Theory we we started with + + align:start position:0% +the original Theory we we started with + + + align:start position:0% +the original Theory we we started with +more powerful in the sense of being able + + align:start position:0% +more powerful in the sense of being able + + + align:start position:0% +more powerful in the sense of being able +to do calculations + + align:start position:0% + + + + align:start position:0% + +so why do we want to do + + align:start position:0% + + + + align:start position:0% + +that there's a couple of different + + align:start position:0% +that there's a couple of different + + + align:start position:0% +that there's a couple of different +reasons or why do we do that since as + + align:start position:0% +reasons or why do we do that since as + + + align:start position:0% +reasons or why do we do that since as +I've tried to convince you with the + + align:start position:0% +I've tried to convince you with the + + + align:start position:0% +I've tried to convince you with the +outline of the course and some of the + + align:start position:0% +outline of the course and some of the + + + align:start position:0% +outline of the course and some of the +presentation topics that this is + + align:start position:0% +presentation topics that this is + + + align:start position:0% +presentation topics that this is +something that happens all over the + + align:start position:0% + + + + align:start position:0% + +place so as you go up in this chart it + + align:start position:0% +place so as you go up in this chart it + + + align:start position:0% +place so as you go up in this chart it +actually becomes even though you have a + + align:start position:0% +actually becomes even though you have a + + + align:start position:0% +actually becomes even though you have a +more general theory and it becomes more + + align:start position:0% +more general theory and it becomes more + + + align:start position:0% +more general theory and it becomes more +beautiful and you can write down + + align:start position:0% +beautiful and you can write down + + + align:start position:0% +beautiful and you can write down +synthesis of physics and fewer lines it + + align:start position:0% +synthesis of physics and fewer lines it + + + align:start position:0% +synthesis of physics and fewer lines it +also becomes harder to compute + + align:start position:0% + + + + align:start position:0% + +things so just as an + + align:start position:0% +things so just as an + + + align:start position:0% +things so just as an +example if you just wanted to compute + + align:start position:0% +example if you just wanted to compute + + + align:start position:0% +example if you just wanted to compute +the energy spectrum of + + align:start position:0% + + + + align:start position:0% + +hydrogen and you you know very well that + + align:start position:0% +hydrogen and you you know very well that + + + align:start position:0% +hydrogen and you you know very well that +you can do that in quantum mechanics and + + align:start position:0% +you can do that in quantum mechanics and + + + align:start position:0% +you can do that in quantum mechanics and +it's particularly it's a classic example + + align:start position:0% +it's particularly it's a classic example + + + align:start position:0% +it's particularly it's a classic example +and fairly easy if you try to do that in + + align:start position:0% +and fairly easy if you try to do that in + + + align:start position:0% +and fairly easy if you try to do that in +Quantum field Theory it's much harder + + align:start position:0% +Quantum field Theory it's much harder + + + align:start position:0% +Quantum field Theory it's much harder +because Quantum field theory in some + + align:start position:0% +because Quantum field theory in some + + + align:start position:0% +because Quantum field theory in some +sense has too much for that problem so + + align:start position:0% +sense has too much for that problem so + + + align:start position:0% +sense has too much for that problem so +that's one + + align:start position:0% + + + + align:start position:0% + +example another is the elliptic orbits + + align:start position:0% +example another is the elliptic orbits + + + align:start position:0% +example another is the elliptic orbits +of the planets which are easier in + + align:start position:0% +of the planets which are easier in + + + align:start position:0% +of the planets which are easier in +Newtonian gravity than in general + + align:start position:0% + + + + align:start position:0% + +relativity and these are just two + + align:start position:0% +relativity and these are just two + + + align:start position:0% +relativity and these are just two +examples there's many more where the + + align:start position:0% +examples there's many more where the + + + align:start position:0% +examples there's many more where the +field that one of these blobs may be too + + align:start position:0% +field that one of these blobs may be too + + + align:start position:0% +field that one of these blobs may be too +general for actually tackling the + + align:start position:0% +general for actually tackling the + + + align:start position:0% +general for actually tackling the +problem that you want to deal + + align:start position:0% +problem that you want to deal + + + align:start position:0% +problem that you want to deal +with and by focusing in as which is what + + align:start position:0% +with and by focusing in as which is what + + + align:start position:0% +with and by focusing in as which is what +effective field Theory allows you to do + + align:start position:0% +effective field Theory allows you to do + + + align:start position:0% +effective field Theory allows you to do +you can get more uh ability to compute + + align:start position:0% +you can get more uh ability to compute + + + align:start position:0% +you can get more uh ability to compute +more accurately and in a simpler + + align:start position:0% + + + + align:start position:0% + +fashion so what we want when we think + + align:start position:0% +fashion so what we want when we think + + + align:start position:0% +fashion so what we want when we think +about effective field Theory + + align:start position:0% + + + + align:start position:0% + +is we want the simplest framework that + + align:start position:0% +is we want the simplest framework that + + + align:start position:0% +is we want the simplest framework that +captures the essential + + align:start position:0% + + + + align:start position:0% + +physics we don't want to carry along for + + align:start position:0% +physics we don't want to carry along for + + + align:start position:0% +physics we don't want to carry along for +the ride a whole bunch of Superfluous + + align:start position:0% +the ride a whole bunch of Superfluous + + + align:start position:0% +the ride a whole bunch of Superfluous +things that are not important for the + + align:start position:0% +things that are not important for the + + + align:start position:0% +things that are not important for the +problem we're trying to deal + + align:start position:0% +problem we're trying to deal + + + align:start position:0% +problem we're trying to deal +with but we also don't want to give up + + align:start position:0% +with but we also don't want to give up + + + align:start position:0% +with but we also don't want to give up +anything so we're very + + align:start position:0% + + + + align:start position:0% + +demanding so even if we're giving up + + align:start position:0% +demanding so even if we're giving up + + + align:start position:0% +demanding so even if we're giving up +something in our leading order + + align:start position:0% +something in our leading order + + + align:start position:0% +something in our leading order +description we want the to retain the + + align:start position:0% +description we want the to retain the + + + align:start position:0% +description we want the to retain the +ability to correct that leading order + + align:start position:0% +ability to correct that leading order + + + align:start position:0% +ability to correct that leading order +description order by order in some + + align:start position:0% +description order by order in some + + + align:start position:0% +description order by order in some +expansions so that we can make it as + + align:start position:0% +expansions so that we can make it as + + + align:start position:0% +expansions so that we can make it as +precise as we + + align:start position:0% + + + + align:start position:0% + +desire so I'll say that we can correct + + align:start position:0% +desire so I'll say that we can correct + + + align:start position:0% +desire so I'll say that we can correct +it in + + align:start position:0% +it in + + + align:start position:0% +it in +principle to arbitrary + + align:start position:0% + + + + align:start position:0% + +Precision so if you like what we're + + align:start position:0% +Precision so if you like what we're + + + align:start position:0% +Precision so if you like what we're +doing is we're taking Quantum field + + align:start position:0% +doing is we're taking Quantum field + + + align:start position:0% +doing is we're taking Quantum field +Theory and we're expanding it and we're + + align:start position:0% +Theory and we're expanding it and we're + + + align:start position:0% +Theory and we're expanding it and we're +the lowest order to termine that + + align:start position:0% +the lowest order to termine that + + + align:start position:0% +the lowest order to termine that +description is effective field Theory + + align:start position:0% +description is effective field Theory + + + align:start position:0% +description is effective field Theory +and that effective field field Theory + + align:start position:0% +and that effective field field Theory + + + align:start position:0% +and that effective field field Theory +may have different fields it may have + + align:start position:0% +may have different fields it may have + + + align:start position:0% +may have different fields it may have +different + + align:start position:0% +different + + + align:start position:0% +different +symmetries um and it will certainly have + + align:start position:0% +symmetries um and it will certainly have + + + align:start position:0% +symmetries um and it will certainly have +ability to calculate in a different + + align:start position:0% +ability to calculate in a different + + + align:start position:0% +ability to calculate in a different +fashion than the original Theory but we + + align:start position:0% +fashion than the original Theory but we + + + align:start position:0% +fashion than the original Theory but we +will keep higher order terms in that + + align:start position:0% +will keep higher order terms in that + + + align:start position:0% +will keep higher order terms in that +expansion and therefore we'll be able to + + align:start position:0% +expansion and therefore we'll be able to + + + align:start position:0% +expansion and therefore we'll be able to +correct it to arbitrary Precision just + + align:start position:0% +correct it to arbitrary Precision just + + + align:start position:0% +correct it to arbitrary Precision just +by uh expanding to higher and higher + + align:start position:0% +by uh expanding to higher and higher + + + align:start position:0% +by uh expanding to higher and higher +order so examples of this that even are + + align:start position:0% +order so examples of this that even are + + + align:start position:0% +order so examples of this that even are +familiar here non-relativistic expansion + + align:start position:0% +familiar here non-relativistic expansion + + + align:start position:0% +familiar here non-relativistic expansion +getting back to non- relative + + align:start position:0% +getting back to non- relative + + + align:start position:0% +getting back to non- relative +quantum mechanics or doing a post + + align:start position:0% +quantum mechanics or doing a post + + + align:start position:0% +quantum mechanics or doing a post +neonian expansion in general relativity + + align:start position:0% +neonian expansion in general relativity + + + align:start position:0% +neonian expansion in general relativity +to go back towards Newtonian gravity you + + align:start position:0% +to go back towards Newtonian gravity you + + + align:start position:0% +to go back towards Newtonian gravity you +don't have to stop at the first term you + + align:start position:0% +don't have to stop at the first term you + + + align:start position:0% +don't have to stop at the first term you +can keep higher order terms and in that + + align:start position:0% +can keep higher order terms and in that + + + align:start position:0% +can keep higher order terms and in that +way you could calculate for example + + align:start position:0% +way you could calculate for example + + + align:start position:0% +way you could calculate for example +energy levels in hydrogen using a + + align:start position:0% +energy levels in hydrogen using a + + + align:start position:0% +energy levels in hydrogen using a +non-relativistic framework that encodes + + align:start position:0% +non-relativistic framework that encodes + + + align:start position:0% +non-relativistic framework that encodes +all the ingredients of quantum field + + align:start position:0% +all the ingredients of quantum field + + + align:start position:0% +all the ingredients of quantum field +Theory or you could use you know you + + align:start position:0% +Theory or you could use you know you + + + align:start position:0% +Theory or you could use you know you +could look at the orbit of planets and + + align:start position:0% +could look at the orbit of planets and + + + align:start position:0% +could look at the orbit of planets and +relativistic Corrections and General + + align:start position:0% +relativistic Corrections and General + + + align:start position:0% +relativistic Corrections and General +relativistic corrections by expanding + + align:start position:0% +relativistic corrections by expanding + + + align:start position:0% +relativistic corrections by expanding +this + + align:start position:0% +this + + + align:start position:0% +this +Theory so those are two examples + + align:start position:0% + + + + align:start position:0% + +so most of the examples that I've listed + + align:start position:0% +so most of the examples that I've listed + + + align:start position:0% +so most of the examples that I've listed +on the project list are of the type of + + align:start position:0% +on the project list are of the type of + + + align:start position:0% +on the project list are of the type of +taking Quantum field theory for the + + align:start position:0% +taking Quantum field theory for the + + + align:start position:0% +taking Quantum field theory for the +standard + + align:start position:0% +standard + + + align:start position:0% +standard +model some of them involve gravity but + + align:start position:0% +model some of them involve gravity but + + + align:start position:0% +model some of them involve gravity but +most of them involve the standard + + align:start position:0% +most of them involve the standard + + + align:start position:0% +most of them involve the standard +model and expanding + + align:start position:0% +model and expanding + + + align:start position:0% +model and expanding +it and focusing in on particular degrees + + align:start position:0% +it and focusing in on particular degrees + + + align:start position:0% +it and focusing in on particular degrees +of + + align:start position:0% +of + + + align:start position:0% +of +freedom so let's say that we've picked a + + align:start position:0% +freedom so let's say that we've picked a + + + align:start position:0% +freedom so let's say that we've picked a +physical system and we want to describe + + align:start position:0% +physical system and we want to describe + + + align:start position:0% +physical system and we want to describe +it what are the things that we should do + + align:start position:0% +it what are the things that we should do + + + align:start position:0% +it what are the things that we should do +in order to develop an effective field + + align:start position:0% + + + + align:start position:0% + +Theory what are the + + align:start position:0% + + + + align:start position:0% + +steps I should say that I'm going to + + align:start position:0% +steps I should say that I'm going to + + + align:start position:0% +steps I should say that I'm going to +post my lecture notes so if you don't + + align:start position:0% +post my lecture notes so if you don't + + + align:start position:0% +post my lecture notes so if you don't +want to take notes you don't have to if + + align:start position:0% +want to take notes you don't have to if + + + align:start position:0% +want to take notes you don't have to if +you like to take notes feel + + align:start position:0% +you like to take notes feel + + + align:start position:0% +you like to take notes feel +free but I will scan and post by + + align:start position:0% + + + + align:start position:0% + +notes so the first thing you need to do + + align:start position:0% +notes so the first thing you need to do + + + align:start position:0% +notes so the first thing you need to do +is figure out what the relevant degrees + + align:start position:0% +is figure out what the relevant degrees + + + align:start position:0% +is figure out what the relevant degrees +of freedom are + + align:start position:0% + + + + align:start position:0% + +what are the things that actually matter + + align:start position:0% +what are the things that actually matter + + + align:start position:0% +what are the things that actually matter +for the problem you want to + + align:start position:0% +for the problem you want to + + + align:start position:0% +for the problem you want to +study sometimes that that is easier than + + align:start position:0% +study sometimes that that is easier than + + + align:start position:0% +study sometimes that that is easier than +other times sometimes it's completely + + align:start position:0% +other times sometimes it's completely + + + align:start position:0% +other times sometimes it's completely +obvious you want to study some low + + align:start position:0% +obvious you want to study some low + + + align:start position:0% +obvious you want to study some low +energy properties of the standard model + + align:start position:0% +energy properties of the standard model + + + align:start position:0% +energy properties of the standard model +you get rid of the heavy particles you + + align:start position:0% +you get rid of the heavy particles you + + + align:start position:0% +you get rid of the heavy particles you +keep the light ones fairly + + align:start position:0% +keep the light ones fairly + + + align:start position:0% +keep the light ones fairly +straightforward other times it may be + + align:start position:0% +straightforward other times it may be + + + align:start position:0% +straightforward other times it may be +tricky to actually determine what the + + align:start position:0% +tricky to actually determine what the + + + align:start position:0% +tricky to actually determine what the +relevant degrees of freedom are and + + align:start position:0% +relevant degrees of freedom are and + + + align:start position:0% +relevant degrees of freedom are and +people in the field may even argue about + + align:start position:0% +people in the field may even argue about + + + align:start position:0% +people in the field may even argue about +what they are so we'll talk about + + align:start position:0% +what they are so we'll talk about + + + align:start position:0% +what they are so we'll talk about +examples of both types + + align:start position:0% +examples of both types + + + align:start position:0% +examples of both types +here throughout the course + + align:start position:0% +here throughout the course + + + align:start position:0% +here throughout the course +so it sounds trivial but it may not be + + align:start position:0% +so it sounds trivial but it may not be + + + align:start position:0% +so it sounds trivial but it may not be +you also want to think about the + + align:start position:0% +you also want to think about the + + + align:start position:0% +you also want to think about the +symmetries sometimes that guides you in + + align:start position:0% +symmetries sometimes that guides you in + + + align:start position:0% +symmetries sometimes that guides you in +thinking about the relevant degrees of + + align:start position:0% +thinking about the relevant degrees of + + + align:start position:0% +thinking about the relevant degrees of +freedom sometimes these things go hand + + align:start position:0% +freedom sometimes these things go hand + + + align:start position:0% +freedom sometimes these things go hand +in hand um but that's a certainly an + + align:start position:0% +in hand um but that's a certainly an + + + align:start position:0% +in hand um but that's a certainly an +important ingredient in in + + align:start position:0% +important ingredient in in + + + align:start position:0% +important ingredient in in +developing the effective field + + align:start position:0% +developing the effective field + + + align:start position:0% +developing the effective field +Theory and you also have to be careful + + align:start position:0% +Theory and you also have to be careful + + + align:start position:0% +Theory and you also have to be careful +here because sometimes you might have uh + + align:start position:0% +here because sometimes you might have uh + + + align:start position:0% +here because sometimes you might have uh +a theory that has no symmetry or doesn't + + align:start position:0% +a theory that has no symmetry or doesn't + + + align:start position:0% +a theory that has no symmetry or doesn't +have an apparent symmetry but when you + + align:start position:0% +have an apparent symmetry but when you + + + align:start position:0% +have an apparent symmetry but when you +start expanding which is what I've + + align:start position:0% +start expanding which is what I've + + + align:start position:0% +start expanding which is what I've +argued you're going to be doing when you + + align:start position:0% +argued you're going to be doing when you + + + align:start position:0% +argued you're going to be doing when you +start expanding ing you may have it a + + align:start position:0% +start expanding ing you may have it a + + + align:start position:0% +start expanding ing you may have it a +symmetry suddenly appear and we'll + + align:start position:0% +symmetry suddenly appear and we'll + + + align:start position:0% +symmetry suddenly appear and we'll +actually talk about several examples of + + align:start position:0% +actually talk about several examples of + + + align:start position:0% +actually talk about several examples of +that happening uh throughout the course + + align:start position:0% +that happening uh throughout the course + + + align:start position:0% +that happening uh throughout the course +as + + align:start position:0% +as + + + align:start position:0% +as +well so your effective field Theory may + + align:start position:0% +well so your effective field Theory may + + + align:start position:0% +well so your effective field Theory may +have more symmetry than the theory you + + align:start position:0% +have more symmetry than the theory you + + + align:start position:0% +have more symmetry than the theory you +started with because you've neglected + + align:start position:0% +started with because you've neglected + + + align:start position:0% +started with because you've neglected +something you could have more + + align:start position:0% + + + + align:start position:0% + +Symmetry and the other important thing + + align:start position:0% +Symmetry and the other important thing + + + align:start position:0% +Symmetry and the other important thing +is to figure out what you're expanding + + align:start position:0% + + + + align:start position:0% + +in and at the the same time what the + + align:start position:0% +in and at the the same time what the + + + align:start position:0% +in and at the the same time what the +leading order description of the theory + + align:start position:0% +leading order description of the theory + + + align:start position:0% +leading order description of the theory +is what is the lowest order + + align:start position:0% +is what is the lowest order + + + align:start position:0% +is what is the lowest order +lran and basically these are the things + + align:start position:0% +lran and basically these are the things + + + align:start position:0% +lran and basically these are the things +you have to do to get + + align:start position:0% +you have to do to get + + + align:start position:0% +you have to do to get +started if this is truly actually + + align:start position:0% +started if this is truly actually + + + align:start position:0% +started if this is truly actually +independent of kind of what theory + + align:start position:0% +independent of kind of what theory + + + align:start position:0% +independent of kind of what theory +you're talking about if you're doing + + align:start position:0% +you're talking about if you're doing + + + align:start position:0% +you're talking about if you're doing +Quantum field Theory what this first one + + align:start position:0% +Quantum field Theory what this first one + + + align:start position:0% +Quantum field Theory what this first one +means is figuring out what Fields you're + + align:start position:0% +means is figuring out what Fields you're + + + align:start position:0% +means is figuring out what Fields you're +going to be + + align:start position:0% + + + + align:start position:0% + +using the Symmetry is basically is + + align:start position:0% +using the Symmetry is basically is + + + align:start position:0% +using the Symmetry is basically is +guiding you about the interactions + + align:start position:0% + + + + align:start position:0% + +if you have gauge symmetry then of + + align:start position:0% +if you have gauge symmetry then of + + + align:start position:0% +if you have gauge symmetry then of +course you're going to write down + + align:start position:0% +course you're going to write down + + + align:start position:0% +course you're going to write down +something that respects that symmetry + + align:start position:0% +something that respects that symmetry + + + align:start position:0% +something that respects that symmetry +that's going to tell you something about + + align:start position:0% +that's going to tell you something about + + + align:start position:0% +that's going to tell you something about +the interaction + + align:start position:0% +the interaction + + + align:start position:0% +the interaction +terms and then finally this expansion + + align:start position:0% +terms and then finally this expansion + + + align:start position:0% +terms and then finally this expansion +parameters goes under the rubric of what + + align:start position:0% +parameters goes under the rubric of what + + + align:start position:0% +parameters goes under the rubric of what +is called Power Counting + + align:start position:0% + + + + align:start position:0% + +and if you take those three things + + align:start position:0% +and if you take those three things + + + align:start position:0% +and if you take those three things +together and you figure out the leading + + align:start position:0% +together and you figure out the leading + + + align:start position:0% +together and you figure out the leading +order description then you have an + + align:start position:0% +order description then you have an + + + align:start position:0% +order description then you have an +effective field Theory you write down a + + align:start position:0% +effective field Theory you write down a + + + align:start position:0% +effective field Theory you write down a +lran for + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +it should try to use some color + + align:start position:0% + + + + align:start position:0% + +so if you thought about regular Quantum + + align:start position:0% +so if you thought about regular Quantum + + + align:start position:0% +so if you thought about regular Quantum +field theory for example for the + + align:start position:0% +field theory for example for the + + + align:start position:0% +field theory for example for the +standard model you'd also do these first + + align:start position:0% +standard model you'd also do these first + + + align:start position:0% +standard model you'd also do these first +two things you figure out what the + + align:start position:0% +two things you figure out what the + + + align:start position:0% +two things you figure out what the +fields are you figure out what the + + align:start position:0% +fields are you figure out what the + + + align:start position:0% +fields are you figure out what the +interactions are but you don't think + + align:start position:0% +interactions are but you don't think + + + align:start position:0% +interactions are but you don't think +about too much about this question about + + align:start position:0% +about too much about this question about + + + align:start position:0% +about too much about this question about +the power + + align:start position:0% +the power + + + align:start position:0% +the power +counting and actually more broadly in + + align:start position:0% +counting and actually more broadly in + + + align:start position:0% +counting and actually more broadly in +the field of effective field Theory this + + align:start position:0% +the field of effective field Theory this + + + align:start position:0% +the field of effective field Theory this +idea here of power counting is very + + align:start position:0% +idea here of power counting is very + + + align:start position:0% +idea here of power counting is very +important it's as important as something + + align:start position:0% +important it's as important as something + + + align:start position:0% +important it's as important as something +like gauge symmetry okay it's really a + + align:start position:0% +like gauge symmetry okay it's really a + + + align:start position:0% +like gauge symmetry okay it's really a +fundamental thing about the whole + + align:start position:0% +fundamental thing about the whole + + + align:start position:0% +fundamental thing about the whole +framework that you're doing + + align:start position:0% + + + + align:start position:0% + +so in an effective field + + align:start position:0% + + + + align:start position:0% + +Theory power + + align:start position:0% + + + + align:start position:0% + +counting is just as important as + + align:start position:0% +counting is just as important as + + + align:start position:0% +counting is just as important as +figuring out things like + + align:start position:0% +figuring out things like + + + align:start position:0% +figuring out things like +symmetries and in particular just to + + align:start position:0% +symmetries and in particular just to + + + align:start position:0% +symmetries and in particular just to +make it sort of clear that it's + + align:start position:0% +make it sort of clear that it's + + + align:start position:0% +make it sort of clear that it's +important I'll compare it to gauge + + align:start position:0% + + + + align:start position:0% + +it's really a fundamental ingredient in + + align:start position:0% +it's really a fundamental ingredient in + + + align:start position:0% +it's really a fundamental ingredient in +what you're doing and in the whole + + align:start position:0% +what you're doing and in the whole + + + align:start position:0% +what you're doing and in the whole +Theory because the power counting being + + align:start position:0% +Theory because the power counting being + + + align:start position:0% +Theory because the power counting being +consistent is actually necessary for the + + align:start position:0% +consistent is actually necessary for the + + + align:start position:0% +consistent is actually necessary for the +whole field Theory effective field + + align:start position:0% +whole field Theory effective field + + + align:start position:0% +whole field Theory effective field +Theory to make + + align:start position:0% + + + + align:start position:0% + +sense okay so what's the key + + align:start position:0% + + + + align:start position:0% + +principle well there's a key principle + + align:start position:0% +principle well there's a key principle + + + align:start position:0% +principle well there's a key principle +of quantum field theory that we're using + + align:start position:0% +of quantum field theory that we're using + + + align:start position:0% +of quantum field theory that we're using +when we design effective field + + align:start position:0% +when we design effective field + + + align:start position:0% +when we design effective field +theories and and that is that we're + + align:start position:0% +theories and and that is that we're + + + align:start position:0% +theories and and that is that we're +insensitive to physics at higher energy + + align:start position:0% + + + + align:start position:0% + +scales so going back to + + align:start position:0% + + + + align:start position:0% + +Wilson if we're interested in describing + + align:start position:0% +Wilson if we're interested in describing + + + align:start position:0% +Wilson if we're interested in describing +the physics at some scale + + align:start position:0% + + + + align:start position:0% + +m^2 we don't need to know the details of + + align:start position:0% +m^2 we don't need to know the details of + + + align:start position:0% +m^2 we don't need to know the details of +physics at higher energy + + align:start position:0% + + + + align:start position:0% + +so it scales Lambda + + align:start position:0% +so it scales Lambda + + + align:start position:0% +so it scales Lambda +squ that are much bigger than m s we + + align:start position:0% +squ that are much bigger than m s we + + + align:start position:0% +squ that are much bigger than m s we +don't really need to know the details of + + align:start position:0% +don't really need to know the details of + + + align:start position:0% +don't really need to know the details of +the Dynamics that is going on there we + + align:start position:0% +the Dynamics that is going on there we + + + align:start position:0% +the Dynamics that is going on there we +don't need to know the field content + + align:start position:0% +don't need to know the field content + + + align:start position:0% +don't need to know the field content +necessarily at those + + align:start position:0% +necessarily at those + + + align:start position:0% +necessarily at those +scales or anything else about the + + align:start position:0% + + + + align:start position:0% + +Dynamics and that is in some sense a key + + align:start position:0% +Dynamics and that is in some sense a key + + + align:start position:0% +Dynamics and that is in some sense a key +idea that makes the whole idea of + + align:start position:0% +idea that makes the whole idea of + + + align:start position:0% +idea that makes the whole idea of +effective field the + + align:start position:0% + + + + align:start position:0% + +possible I want you to make to make sure + + align:start position:0% +possible I want you to make to make sure + + + align:start position:0% +possible I want you to make to make sure +that you don't think of this too + + align:start position:0% +that you don't think of this too + + + align:start position:0% +that you don't think of this too +narrowly and the way that I've written + + align:start position:0% +narrowly and the way that I've written + + + align:start position:0% +narrowly and the way that I've written +it's actually a little bit too narrow + + align:start position:0% +it's actually a little bit too narrow + + + align:start position:0% +it's actually a little bit too narrow +because I said that I've described it in + + align:start position:0% +because I said that I've described it in + + + align:start position:0% +because I said that I've described it in +terms of mass scale so I've kind of + + align:start position:0% +terms of mass scale so I've kind of + + + align:start position:0% +terms of mass scale so I've kind of +inted in your mind something like a z + + align:start position:0% +inted in your mind something like a z + + + align:start position:0% +inted in your mind something like a z +BOS on or a w BOS on which is a heavy + + align:start position:0% +BOS on or a w BOS on which is a heavy + + + align:start position:0% +BOS on or a w BOS on which is a heavy +particle from some perspective and maybe + + align:start position:0% +particle from some perspective and maybe + + + align:start position:0% +particle from some perspective and maybe +they treat that as a heavy particle and + + align:start position:0% +they treat that as a heavy particle and + + + align:start position:0% +they treat that as a heavy particle and +I'm interested uh and I'm let me say it + + align:start position:0% +I'm interested uh and I'm let me say it + + + align:start position:0% +I'm interested uh and I'm let me say it +differently say I'm interested in a + + align:start position:0% +differently say I'm interested in a + + + align:start position:0% +differently say I'm interested in a +light particle like the bottom Quark + + align:start position:0% +light particle like the bottom Quark + + + align:start position:0% +light particle like the bottom Quark +then I can get rid of physics at a heavy + + align:start position:0% +then I can get rid of physics at a heavy + + + align:start position:0% +then I can get rid of physics at a heavy +scale like the W mass or if I think + + align:start position:0% +scale like the W mass or if I think + + + align:start position:0% +scale like the W mass or if I think +about how new physics impacts Precision + + align:start position:0% +about how new physics impacts Precision + + + align:start position:0% +about how new physics impacts Precision +Electro week data and that new physics + + align:start position:0% +Electro week data and that new physics + + + align:start position:0% +Electro week data and that new physics +is heavy then I can think about + + align:start position:0% +is heavy then I can think about + + + align:start position:0% +is heavy then I can think about +effective operators that's kind of the + + align:start position:0% +effective operators that's kind of the + + + align:start position:0% +effective operators that's kind of the +the intuition I've given you with the + + align:start position:0% +the intuition I've given you with the + + + align:start position:0% +the intuition I've given you with the +sentence that I've written here but it's + + align:start position:0% +sentence that I've written here but it's + + + align:start position:0% +sentence that I've written here but it's +actually not that's not quite General + + align:start position:0% +actually not that's not quite General + + + align:start position:0% +actually not that's not quite General +enough and the reason it's not quite + + align:start position:0% +enough and the reason it's not quite + + + align:start position:0% +enough and the reason it's not quite +General enough is that this mentality + + align:start position:0% +General enough is that this mentality + + + align:start position:0% +General enough is that this mentality +doesn't always apply just strictly to + + align:start position:0% +doesn't always apply just strictly to + + + align:start position:0% +doesn't always apply just strictly to +mass + + align:start position:0% +mass + + + align:start position:0% +mass +scales if I say this m^2 much less than + + align:start position:0% +scales if I say this m^2 much less than + + + align:start position:0% +scales if I say this m^2 much less than +Lambda squ then you immediately think + + align:start position:0% +Lambda squ then you immediately think + + + align:start position:0% +Lambda squ then you immediately think +that you're expanding an m^2 over Lambda + + align:start position:0% +that you're expanding an m^2 over Lambda + + + align:start position:0% +that you're expanding an m^2 over Lambda +squ and that of classic effective field + + align:start position:0% +squ and that of classic effective field + + + align:start position:0% +squ and that of classic effective field +Theory that's exactly what you do you + + align:start position:0% +Theory that's exactly what you do you + + + align:start position:0% +Theory that's exactly what you do you +expand in light scales divided by scales + + align:start position:0% +expand in light scales divided by scales + + + align:start position:0% +expand in light scales divided by scales +their Mass scales their invariant masses + + align:start position:0% +their Mass scales their invariant masses + + + align:start position:0% +their Mass scales their invariant masses +their Lorent invariant quantities that's + + align:start position:0% +their Lorent invariant quantities that's + + + align:start position:0% +their Lorent invariant quantities that's +the most common thing that you do we're + + align:start position:0% +the most common thing that you do we're + + + align:start position:0% +the most common thing that you do we're +going to be doing much more than that in + + align:start position:0% +going to be doing much more than that in + + + align:start position:0% +going to be doing much more than that in +this course we'll be doing we'll be + + align:start position:0% +this course we'll be doing we'll be + + + align:start position:0% +this course we'll be doing we'll be +talking about cases where the power + + align:start position:0% +talking about cases where the power + + + align:start position:0% +talking about cases where the power +counting is in situations that are not + + align:start position:0% +counting is in situations that are not + + + align:start position:0% +counting is in situations that are not +simply M squ much less than Lambda squar + + align:start position:0% +simply M squ much less than Lambda squar + + + align:start position:0% +simply M squ much less than Lambda squar +but other things dimensionless + + align:start position:0% +but other things dimensionless + + + align:start position:0% +but other things dimensionless +parameters so sometimes it will become + + align:start position:0% +parameters so sometimes it will become + + + align:start position:0% +parameters so sometimes it will become +more complicated but still this guiding + + align:start position:0% +more complicated but still this guiding + + + align:start position:0% +more complicated but still this guiding +principle that there's physics that's + + align:start position:0% +principle that there's physics that's + + + align:start position:0% +principle that there's physics that's +far away in some sense from the physics + + align:start position:0% +far away in some sense from the physics + + + align:start position:0% +far away in some sense from the physics +that you're interested in that it can be + + align:start position:0% +that you're interested in that it can be + + + align:start position:0% +that you're interested in that it can be +removed + + align:start position:0% +removed + + + align:start position:0% +removed +from the theory when you're just talking + + align:start position:0% +from the theory when you're just talking + + + align:start position:0% +from the theory when you're just talking +about it in that sense this is more + + align:start position:0% +about it in that sense this is more + + + align:start position:0% +about it in that sense this is more +General that it's really not just a + + align:start position:0% +General that it's really not just a + + + align:start position:0% +General that it's really not just a +strictly one-dimensional thing as it + + align:start position:0% +strictly one-dimensional thing as it + + + align:start position:0% +strictly one-dimensional thing as it +would be if I describe it in terms of + + align:start position:0% +would be if I describe it in terms of + + + align:start position:0% +would be if I describe it in terms of +mass scales but a more General principle + + align:start position:0% +mass scales but a more General principle + + + align:start position:0% +mass scales but a more General principle +and I think that'll become clearer when + + align:start position:0% +and I think that'll become clearer when + + + align:start position:0% +and I think that'll become clearer when +we actually do examples where it's not + + align:start position:0% +we actually do examples where it's not + + + align:start position:0% +we actually do examples where it's not +simply Mass scales we'll of course start + + align:start position:0% +simply Mass scales we'll of course start + + + align:start position:0% +simply Mass scales we'll of course start +out by talking about Mass scales since + + align:start position:0% +out by talking about Mass scales since + + + align:start position:0% +out by talking about Mass scales since +that's the the classic thing that most + + align:start position:0% +that's the the classic thing that most + + + align:start position:0% +that's the the classic thing that most +people think of when they think of + + align:start position:0% +people think of when they think of + + + align:start position:0% +people think of when they think of +effective field + + align:start position:0% +effective field + + + align:start position:0% +effective field +Theory so can anyone give me an example + + align:start position:0% +Theory so can anyone give me an example + + + align:start position:0% +Theory so can anyone give me an example +just try to get the class engaged here + + align:start position:0% +just try to get the class engaged here + + + align:start position:0% +just try to get the class engaged here +can every anyone give me an example of + + align:start position:0% +can every anyone give me an example of + + + align:start position:0% +can every anyone give me an example of +an effective field theory that doesn't + + align:start position:0% +an effective field theory that doesn't + + + align:start position:0% +an effective field theory that doesn't +involve expanding strictly in Mass + + align:start position:0% +involve expanding strictly in Mass + + + align:start position:0% +involve expanding strictly in Mass +scales that involve some other type of + + align:start position:0% +scales that involve some other type of + + + align:start position:0% +scales that involve some other type of +expansion yeah + + align:start position:0% +expansion yeah + + + align:start position:0% +expansion yeah +well okay HQ you can say is just an + + align:start position:0% +well okay HQ you can say is just an + + + align:start position:0% +well okay HQ you can say is just an +expansion in Lambda qcd over MB or MC so + + align:start position:0% +expansion in Lambda qcd over MB or MC so + + + align:start position:0% +expansion in Lambda qcd over MB or MC so +not + + align:start position:0% +not + + + align:start position:0% +not +quite SC scat + + align:start position:0% +quite SC scat + + + align:start position:0% +quite SC scat +well you've studied + + align:start position:0% +well you've studied + + + align:start position:0% +well you've studied +it but correct + + align:start position:0% +it but correct + + + align:start position:0% +it but correct +answer any other + + align:start position:0% +answer any other + + + align:start position:0% +answer any other +thoughts so another example would be + + align:start position:0% +thoughts so another example would be + + + align:start position:0% +thoughts so another example would be +something like non-relativistic QED if + + align:start position:0% +something like non-relativistic QED if + + + align:start position:0% +something like non-relativistic QED if +you do non-relativistic QED you're + + align:start position:0% +you do non-relativistic QED you're + + + align:start position:0% +you do non-relativistic QED you're +actually expanding in the velocity not + + align:start position:0% +actually expanding in the velocity not + + + align:start position:0% +actually expanding in the velocity not +in strictly in the ratio of mass scale + + align:start position:0% +in strictly in the ratio of mass scale + + + align:start position:0% +in strictly in the ratio of mass scale +so though they you would think for + + align:start position:0% +so though they you would think for + + + align:start position:0% +so though they you would think for +example non-relativistic QED would be + + align:start position:0% +example non-relativistic QED would be + + + align:start position:0% +example non-relativistic QED would be +for a heavy electron which is true a + + align:start position:0% +for a heavy electron which is true a + + + align:start position:0% +for a heavy electron which is true a +heavy massive particle that's not what + + align:start position:0% +heavy massive particle that's not what + + + align:start position:0% +heavy massive particle that's not what +the power counting expansion is in it'll + + align:start position:0% +the power counting expansion is in it'll + + + align:start position:0% +the power counting expansion is in it'll +actually be in the velocity being much + + align:start position:0% +actually be in the velocity being much + + + align:start position:0% +actually be in the velocity being much +less than the speed of light and that + + align:start position:0% +less than the speed of light and that + + + align:start position:0% +less than the speed of light and that +actually plays an important role in + + align:start position:0% +actually plays an important role in + + + align:start position:0% +actually plays an important role in +designing the effective field Theory + + align:start position:0% +designing the effective field Theory + + + align:start position:0% +designing the effective field Theory +determining what the leading operators + + align:start position:0% +determining what the leading operators + + + align:start position:0% +determining what the leading operators +are so even something as simple as going + + align:start position:0% +are so even something as simple as going + + + align:start position:0% +are so even something as simple as going +to higher order Corrections in hydrogen + + align:start position:0% +to higher order Corrections in hydrogen + + + align:start position:0% +to higher order Corrections in hydrogen +involves thinking about Thinking Beyond + + align:start position:0% +involves thinking about Thinking Beyond + + + align:start position:0% +involves thinking about Thinking Beyond +this simple statement + + align:start position:0% + + + + align:start position:0% + +here well since we're on the topic of + + align:start position:0% +here well since we're on the topic of + + + align:start position:0% +here well since we're on the topic of +hydrogen let me go into a little more + + align:start position:0% +hydrogen let me go into a little more + + + align:start position:0% +hydrogen let me go into a little more +detail there + + align:start position:0% + + + + align:start position:0% + +so just to flesh this out a + + align:start position:0% +so just to flesh this out a + + + align:start position:0% +so just to flesh this out a +bit and to talk + + align:start position:0% +bit and to talk + + + align:start position:0% +bit and to talk +about some of the things you have to be + + align:start position:0% +about some of the things you have to be + + + align:start position:0% +about some of the things you have to be +careful + + align:start position:0% + + + + align:start position:0% + +about I'll phrase an example of this + + align:start position:0% +about I'll phrase an example of this + + + align:start position:0% +about I'll phrase an example of this +statement as the fact that we don't need + + align:start position:0% +statement as the fact that we don't need + + + align:start position:0% +statement as the fact that we don't need +to know about bottom quirks to describe + + align:start position:0% +to know about bottom quirks to describe + + + align:start position:0% +to know about bottom quirks to describe +hydrogen + + align:start position:0% + + + + align:start position:0% + +well that's good when you took quantum + + align:start position:0% +well that's good when you took quantum + + + align:start position:0% +well that's good when you took quantum +mechanics as an undergraduate you didn't + + align:start position:0% +mechanics as an undergraduate you didn't + + + align:start position:0% +mechanics as an undergraduate you didn't +have bottom quirks in your description + + align:start position:0% +have bottom quirks in your description + + + align:start position:0% +have bottom quirks in your description +so if you did need them you would have + + align:start position:0% +so if you did need them you would have + + + align:start position:0% +so if you did need them you would have +missed + + align:start position:0% + + + + align:start position:0% + +something what did you have in your + + align:start position:0% +something what did you have in your + + + align:start position:0% +something what did you have in your +description well in a Quantum field + + align:start position:0% +description well in a Quantum field + + + align:start position:0% +description well in a Quantum field +Theory language you had this diagram you + + align:start position:0% +Theory language you had this diagram you + + + align:start position:0% +Theory language you had this diagram you +had an electron and a proton with Photon + + align:start position:0% + + + + align:start position:0% + +exchange and you also when you thought + + align:start position:0% +exchange and you also when you thought + + + align:start position:0% +exchange and you also when you thought +about The Binding energy if we work in + + align:start position:0% +about The Binding energy if we work in + + + align:start position:0% +about The Binding energy if we work in +units where H bar and C is one which I + + align:start position:0% +units where H bar and C is one which I + + + align:start position:0% +units where H bar and C is one which I +will always do then The Binding energy + + align:start position:0% +will always do then The Binding energy + + + align:start position:0% +will always do then The Binding energy +is a half me Alpha squ and if you ask + + align:start position:0% +is a half me Alpha squ and if you ask + + + align:start position:0% +is a half me Alpha squ and if you ask +about the bottom quirks the reason that + + align:start position:0% +about the bottom quirks the reason that + + + align:start position:0% +about the bottom quirks the reason that +you didn't need them is because they + + align:start position:0% +you didn't need them is because they + + + align:start position:0% +you didn't need them is because they +were suppressed they were giving they + + align:start position:0% +were suppressed they were giving they + + + align:start position:0% +were suppressed they were giving they +weren't negligible completely negligible + + align:start position:0% +weren't negligible completely negligible + + + align:start position:0% +weren't negligible completely negligible +at least at the level of how accurately + + align:start position:0% +at least at the level of how accurately + + + align:start position:0% +at least at the level of how accurately +we can measure this thing well they're + + align:start position:0% +we can measure this thing well they're + + + align:start position:0% +we can measure this thing well they're +pretty small they're at the 10us 8 + + align:start position:0% + + + + align:start position:0% + +level okay and that's because they come + + align:start position:0% +level okay and that's because they come + + + align:start position:0% +level okay and that's because they come +in suppressed by the mass of the + + align:start position:0% +in suppressed by the mass of the + + + align:start position:0% +in suppressed by the mass of the +electron squar over the mass of the + + align:start position:0% +electron squar over the mass of the + + + align:start position:0% +electron squar over the mass of the +bottom qu + + align:start position:0% + + + + align:start position:0% + +squared so how would you think of them + + align:start position:0% +squared so how would you think of them + + + align:start position:0% +squared so how would you think of them +coming in well You' think of them coming + + align:start position:0% +coming in well You' think of them coming + + + align:start position:0% +coming in well You' think of them coming +in through some diagram for example + + align:start position:0% +in through some diagram for example + + + align:start position:0% +in through some diagram for example +where the bottom + + align:start position:0% + + + + align:start position:0% + +Quirk couples to the photon through a + + align:start position:0% +Quirk couples to the photon through a + + + align:start position:0% +Quirk couples to the photon through a +ver vacuum polarization like + + align:start position:0% +ver vacuum polarization like + + + align:start position:0% +ver vacuum polarization like +that and this diagram indeed will give + + align:start position:0% +that and this diagram indeed will give + + + align:start position:0% +that and this diagram indeed will give +you Corrections of this + + align:start position:0% +you Corrections of this + + + align:start position:0% +you Corrections of this +type now it's a bit more subtle than + + align:start position:0% +type now it's a bit more subtle than + + + align:start position:0% +type now it's a bit more subtle than +that and that's because a diagram like + + align:start position:0% +that and that's because a diagram like + + + align:start position:0% +that and that's because a diagram like +this also has other contributions + + align:start position:0% +this also has other contributions + + + align:start position:0% +this also has other contributions +besides just these ones that I mentioned + + align:start position:0% + + + + align:start position:0% + +here so the basic picture is indeed + + align:start position:0% +here so the basic picture is indeed + + + align:start position:0% +here so the basic picture is indeed +correct that we can neglect the bottom + + align:start position:0% +correct that we can neglect the bottom + + + align:start position:0% +correct that we can neglect the bottom +cork because it's giving small + + align:start position:0% +cork because it's giving small + + + align:start position:0% +cork because it's giving small +corrections but there is one subtlety + + align:start position:0% +corrections but there is one subtlety + + + align:start position:0% +corrections but there is one subtlety +and that has to do with the fact that we + + align:start position:0% +and that has to do with the fact that we + + + align:start position:0% +and that has to do with the fact that we +have to decide what we mean by this + + align:start position:0% + + + + align:start position:0% + +coupling okay + + align:start position:0% + + + + align:start position:0% + +so from your previous courses in quum + + align:start position:0% +so from your previous courses in quum + + + align:start position:0% +so from your previous courses in quum +field Theory when you learned about + + align:start position:0% +field Theory when you learned about + + + align:start position:0% +field Theory when you learned about +running + + align:start position:0% +running + + + align:start position:0% +running +couplings you learned that diagrams like + + align:start position:0% +couplings you learned that diagrams like + + + align:start position:0% +couplings you learned that diagrams like +that wouldn't contribute to running + + align:start position:0% + + + + align:start position:0% + +couplings and so the beark therefore can + + align:start position:0% +couplings and so the beark therefore can + + + align:start position:0% +couplings and so the beark therefore can +affect the + + align:start position:0% +affect the + + + align:start position:0% +affect the +coupling if you worked in for example + + align:start position:0% +coupling if you worked in for example + + + align:start position:0% +coupling if you worked in for example +the msar + + align:start position:0% +the msar + + + align:start position:0% +the msar +scheme since it contributes to the + + align:start position:0% +scheme since it contributes to the + + + align:start position:0% +scheme since it contributes to the +running of the + + align:start position:0% + + + + align:start position:0% + +coupling and in + + align:start position:0% +coupling and in + + + align:start position:0% +coupling and in +particular you know for the + + align:start position:0% +particular you know for the + + + align:start position:0% +particular you know for the +electromagnetic coupling if you ask + + align:start position:0% +electromagnetic coupling if you ask + + + align:start position:0% +electromagnetic coupling if you ask +about what that coupling is it has a + + align:start position:0% +about what that coupling is it has a + + + align:start position:0% +about what that coupling is it has a +different value because it runs if you + + align:start position:0% +different value because it runs if you + + + align:start position:0% +different value because it runs if you +evaluate it at a scale like the W mass + + align:start position:0% +evaluate it at a scale like the W mass + + + align:start position:0% +evaluate it at a scale like the W mass +then it's like 1 over + + align:start position:0% +then it's like 1 over + + + align:start position:0% +then it's like 1 over +128 versus if you evaluate it at a very + + align:start position:0% +128 versus if you evaluate it at a very + + + align:start position:0% +128 versus if you evaluate it at a very +low energy the electron Mass are below + + align:start position:0% +low energy the electron Mass are below + + + align:start position:0% +low energy the electron Mass are below +then it's the classic 1 over + + align:start position:0% +then it's the classic 1 over + + + align:start position:0% +then it's the classic 1 over +137.0 + + align:start position:0% +137.0 + + + align:start position:0% +137.0 +36 okay so there's some change and the + + align:start position:0% +36 okay so there's some change and the + + + align:start position:0% +36 okay so there's some change and the +bottom Quirk is part of what contributes + + align:start position:0% +bottom Quirk is part of what contributes + + + align:start position:0% +bottom Quirk is part of what contributes +to that change of course other particles + + align:start position:0% +to that change of course other particles + + + align:start position:0% +to that change of course other particles +are contributing too + + align:start position:0% + + + + align:start position:0% + +so if we want to say this this statement + + align:start position:0% +so if we want to say this this statement + + + align:start position:0% +so if we want to say this this statement +about bottom + + align:start position:0% +about bottom + + + align:start position:0% +about bottom +quarks and we want to State the + + align:start position:0% +quarks and we want to State the + + + align:start position:0% +quarks and we want to State the +conclusions more + + align:start position:0% +conclusions more + + + align:start position:0% +conclusions more +precisely then we would do it this way + + align:start position:0% +precisely then we would do it this way + + + align:start position:0% +precisely then we would do it this way +we would say if Alpha is a parameter of + + align:start position:0% +we would say if Alpha is a parameter of + + + align:start position:0% +we would say if Alpha is a parameter of +the standard model + + align:start position:0% + + + + align:start position:0% + +and we imagine that we fix it at high + + align:start position:0% +and we imagine that we fix it at high + + + align:start position:0% +and we imagine that we fix it at high +energy so we could imagine that we fixed + + align:start position:0% +energy so we could imagine that we fixed + + + align:start position:0% +energy so we could imagine that we fixed +it by doing zos on physics in an e plus + + align:start position:0% +it by doing zos on physics in an e plus + + + align:start position:0% +it by doing zos on physics in an e plus +e minus collider but some process that's + + align:start position:0% +e minus collider but some process that's + + + align:start position:0% +e minus collider but some process that's +a high energy process we determine say + + align:start position:0% +a high energy process we determine say + + + align:start position:0% +a high energy process we determine say +for example this + + align:start position:0% + + + + align:start position:0% + +value if we take that attitude as how we + + align:start position:0% +value if we take that attitude as how we + + + align:start position:0% +value if we take that attitude as how we +Define the parameter then the parameter + + align:start position:0% +Define the parameter then the parameter + + + align:start position:0% +Define the parameter then the parameter +that actually matters for hydrogen which + + align:start position:0% +that actually matters for hydrogen which + + + align:start position:0% +that actually matters for hydrogen which +is this parameter at the low scale does + + align:start position:0% +is this parameter at the low scale does + + + align:start position:0% +is this parameter at the low scale does +depend on the bottom + + align:start position:0% + + + + align:start position:0% + +Quirk because how we get from the high + + align:start position:0% +Quirk because how we get from the high + + + align:start position:0% +Quirk because how we get from the high +scale to the low scale depends on the + + align:start position:0% +scale to the low scale depends on the + + + align:start position:0% +scale to the low scale depends on the +fact that the bottom Quirk + + align:start position:0% + + + + align:start position:0% + +exists but we could also take a + + align:start position:0% +exists but we could also take a + + + align:start position:0% +exists but we could also take a +different + + align:start position:0% +different + + + align:start position:0% +different +attitude and that is we could take a low + + align:start position:0% +attitude and that is we could take a low + + + align:start position:0% +attitude and that is we could take a low +energy attitude + + align:start position:0% + + + + align:start position:0% + +so we could say let's forget about doing + + align:start position:0% +so we could say let's forget about doing + + + align:start position:0% +so we could say let's forget about doing +high energy physics let's just do low + + align:start position:0% +high energy physics let's just do low + + + align:start position:0% +high energy physics let's just do low +energy physics and extract Alpha of + + align:start position:0% +energy physics and extract Alpha of + + + align:start position:0% +energy physics and extract Alpha of +Zero from some low energy Atomic + + align:start position:0% +Zero from some low energy Atomic + + + align:start position:0% +Zero from some low energy Atomic +experiments + + align:start position:0% + + + + align:start position:0% + +and if that's the way that we Define the + + align:start position:0% + + + + align:start position:0% + +parameter then the value can be used in + + align:start position:0% +parameter then the value can be used in + + + align:start position:0% +parameter then the value can be used in +other experiments and we never had to + + align:start position:0% +other experiments and we never had to + + + align:start position:0% +other experiments and we never had to +know anything about + + align:start position:0% + + + + align:start position:0% + +MB so we didn't really have to know + + align:start position:0% +MB so we didn't really have to know + + + align:start position:0% +MB so we didn't really have to know +about the high energy + + align:start position:0% +about the high energy + + + align:start position:0% +about the high energy +uh about the higher higher energy Theory + + align:start position:0% +uh about the higher higher energy Theory + + + align:start position:0% +uh about the higher higher energy Theory +unless we actually were doing some + + align:start position:0% +unless we actually were doing some + + + align:start position:0% +unless we actually were doing some +experiments up + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +there is there any questions about + + align:start position:0% +there is there any questions about + + + align:start position:0% +there is there any questions about +that + + align:start position:0% + + + + align:start position:0% + +good so if we want to write an equation + + align:start position:0% +good so if we want to write an equation + + + align:start position:0% +good so if we want to write an equation +for + + align:start position:0% +for + + + align:start position:0% +for +that what it means is that when you + + align:start position:0% +that what it means is that when you + + + align:start position:0% +that what it means is that when you +integrate out particles like the B Quark + + align:start position:0% +integrate out particles like the B Quark + + + align:start position:0% +integrate out particles like the B Quark +remove them from your theory stop + + align:start position:0% +remove them from your theory stop + + + align:start position:0% +remove them from your theory stop +considering them + + align:start position:0% +considering them + + + align:start position:0% +considering them +that it's not simply the + + align:start position:0% +that it's not simply the + + + align:start position:0% +that it's not simply the +casee that you generate higher order + + align:start position:0% +casee that you generate higher order + + + align:start position:0% +casee that you generate higher order +terms in the series you can also affect + + align:start position:0% +terms in the series you can also affect + + + align:start position:0% +terms in the series you can also affect +what you mean by the leading order term + + align:start position:0% +what you mean by the leading order term + + + align:start position:0% +what you mean by the leading order term +in the sense of changing what you mean + + align:start position:0% +in the sense of changing what you mean + + + align:start position:0% +in the sense of changing what you mean +by the + + align:start position:0% +by the + + + align:start position:0% +by the +[Applause] + + align:start position:0% + + + + align:start position:0% + +coupling so if I write it in terms of + + align:start position:0% +coupling so if I write it in terms of + + + align:start position:0% +coupling so if I write it in terms of +lran I would say that lran for + + align:start position:0% +lran I would say that lran for + + + align:start position:0% +lran I would say that lran for +hydrogen if we include the B Quark well + + align:start position:0% +hydrogen if we include the B Quark well + + + align:start position:0% +hydrogen if we include the B Quark well +it's got our proton electron and Photon + + align:start position:0% +it's got our proton electron and Photon + + + align:start position:0% +it's got our proton electron and Photon +and let's keep the B + + align:start position:0% +and let's keep the B + + + align:start position:0% +and let's keep the B +Quark Alpha and MB are + + align:start position:0% + + + + align:start position:0% + +parameters if we drop the B Quark + + align:start position:0% +parameters if we drop the B Quark + + + align:start position:0% +parameters if we drop the B Quark +because it's giving small + + align:start position:0% +because it's giving small + + + align:start position:0% +because it's giving small +effects we just have these fields proton + + align:start position:0% +effects we just have these fields proton + + + align:start position:0% +effects we just have these fields proton +electron and + + align:start position:0% +electron and + + + align:start position:0% +electron and +Photon we get a different + + align:start position:0% + + + + align:start position:0% + +coupling in in practice in + + align:start position:0% +coupling in in practice in + + + align:start position:0% +coupling in in practice in +principle okay so you think of this as + + align:start position:0% +principle okay so you think of this as + + + align:start position:0% +principle okay so you think of this as +being a higher energy coupling and over + + align:start position:0% +being a higher energy coupling and over + + + align:start position:0% +being a higher energy coupling and over +there Alpha being the low energy + + align:start position:0% +there Alpha being the low energy + + + align:start position:0% +there Alpha being the low energy +coupling there's a lot of other things + + align:start position:0% +coupling there's a lot of other things + + + align:start position:0% +coupling there's a lot of other things +actually that if you think about + + align:start position:0% +actually that if you think about + + + align:start position:0% +actually that if you think about +hydrogen for a minute there's a lot of + + align:start position:0% +hydrogen for a minute there's a lot of + + + align:start position:0% +hydrogen for a minute there's a lot of +other expansions that you've done + + align:start position:0% +other expansions that you've done + + + align:start position:0% +other expansions that you've done +hydrogen is a very fertile ground for + + align:start position:0% +hydrogen is a very fertile ground for + + + align:start position:0% +hydrogen is a very fertile ground for +Effective field Theory so let's do that + + align:start position:0% +Effective field Theory so let's do that + + + align:start position:0% +Effective field Theory so let's do that +let's make a little list of what we + + align:start position:0% +let's make a little list of what we + + + align:start position:0% +let's make a little list of what we +dropped when we thought about hydrogen + + align:start position:0% +dropped when we thought about hydrogen + + + align:start position:0% +dropped when we thought about hydrogen +how much did we lie to you when we first + + align:start position:0% +how much did we lie to you when we first + + + align:start position:0% +how much did we lie to you when we first +taught you the hydrogen atom and in a + + align:start position:0% +taught you the hydrogen atom and in a + + + align:start position:0% +taught you the hydrogen atom and in a +quantum mechanics course well we didn't + + align:start position:0% +quantum mechanics course well we didn't + + + align:start position:0% +quantum mechanics course well we didn't +teach you about quarks + + align:start position:0% + + + + align:start position:0% + +why didn't we teach you about + + align:start position:0% + + + + align:start position:0% + +quarks and the reason we didn't teach + + align:start position:0% +quarks and the reason we didn't teach + + + align:start position:0% +quarks and the reason we didn't teach +you about quarks is because if you think + + align:start position:0% +you about quarks is because if you think + + + align:start position:0% +you about quarks is because if you think +about the typical momentum transfer in + + align:start position:0% +about the typical momentum transfer in + + + align:start position:0% +about the typical momentum transfer in +hydrogen three momentum transfer it's + + align:start position:0% +hydrogen three momentum transfer it's + + + align:start position:0% +hydrogen three momentum transfer it's +avoided the mass of the electron times + + align:start position:0% +avoided the mass of the electron times + + + align:start position:0% +avoided the mass of the electron times +the fine structure constant and that's + + align:start position:0% +the fine structure constant and that's + + + align:start position:0% +the fine structure constant and that's +much less than the proton + + align:start position:0% +much less than the proton + + + align:start position:0% +much less than the proton +size so the typical photons that are + + align:start position:0% +size so the typical photons that are + + + align:start position:0% +size so the typical photons that are +involved in Binding Together the + + align:start position:0% +involved in Binding Together the + + + align:start position:0% +involved in Binding Together the +hydrogen + + align:start position:0% +hydrogen + + + align:start position:0% +hydrogen +atom just have much lower energy + + align:start position:0% +atom just have much lower energy + + + align:start position:0% +atom just have much lower energy +and they can't see inside the proton + + align:start position:0% +and they can't see inside the proton + + + align:start position:0% +and they can't see inside the proton +they just see it as one overall object + + align:start position:0% +they just see it as one overall object + + + align:start position:0% +they just see it as one overall object +and so we don't need to know about the + + align:start position:0% +and so we don't need to know about the + + + align:start position:0% +and so we don't need to know about the +quarks inside the pro + + align:start position:0% +quarks inside the pro + + + align:start position:0% +quarks inside the pro +proton so that was an + + align:start position:0% + + + + align:start position:0% + +expansion it's also in insensitive to + + align:start position:0% +expansion it's also in insensitive to + + + align:start position:0% +expansion it's also in insensitive to +the proton + + align:start position:0% + + + + align:start position:0% + +Mass + + align:start position:0% +Mass + + + align:start position:0% +Mass +itself so the proton we keep as an + + align:start position:0% +itself so the proton we keep as an + + + align:start position:0% +itself so the proton we keep as an +object but the mass of the again the + + align:start position:0% +object but the mass of the again the + + + align:start position:0% +object but the mass of the again the +momentum transfer me + + align:start position:0% +momentum transfer me + + + align:start position:0% +momentum transfer me +Alpha is much less than the mass of the + + align:start position:0% +Alpha is much less than the mass of the + + + align:start position:0% +Alpha is much less than the mass of the +proton which is of order of + + align:start position:0% + + + + align:start position:0% + +GV and so we expand in our treatment of + + align:start position:0% +GV and so we expand in our treatment of + + + align:start position:0% +GV and so we expand in our treatment of +the proton as well and basically what + + align:start position:0% +the proton as well and basically what + + + align:start position:0% +the proton as well and basically what +this means is that the + + align:start position:0% + + + + align:start position:0% + +proton acts like a + + align:start position:0% +proton acts like a + + + align:start position:0% +proton acts like a +static charge + + align:start position:0% + + + + align:start position:0% + +okay with proton Mass wasn't showing up + + align:start position:0% +okay with proton Mass wasn't showing up + + + align:start position:0% +okay with proton Mass wasn't showing up +in our lowest order description of the + + align:start position:0% +in our lowest order description of the + + + align:start position:0% +in our lowest order description of the +energy here it would show up in higher + + align:start position:0% +energy here it would show up in higher + + + align:start position:0% +energy here it would show up in higher +order Corrections that we + + align:start position:0% + + + + align:start position:0% + +neglect and again it's because we're + + align:start position:0% +neglect and again it's because we're + + + align:start position:0% +neglect and again it's because we're +expanding and that actually effects when + + align:start position:0% +expanding and that actually effects when + + + align:start position:0% +expanding and that actually effects when +we designed an effective field theory + + align:start position:0% +we designed an effective field theory + + + align:start position:0% +we designed an effective field theory +for this situation how we would treat + + align:start position:0% +for this situation how we would treat + + + align:start position:0% +for this situation how we would treat +the proton what type of lran we would + + align:start position:0% +the proton what type of lran we would + + + align:start position:0% +the proton what type of lran we would +write down for + + align:start position:0% +write down for + + + align:start position:0% +write down for +it and that will be one of our our + + align:start position:0% +it and that will be one of our our + + + align:start position:0% +it and that will be one of our our +topics is to figure out how we treat + + align:start position:0% +topics is to figure out how we treat + + + align:start position:0% +topics is to figure out how we treat +heavy particles like a proton in this + + align:start position:0% +heavy particles like a proton in this + + + align:start position:0% +heavy particles like a proton in this +case + + align:start position:0% + + + + align:start position:0% + +another expansion that we did is we used + + align:start position:0% +another expansion that we did is we used + + + align:start position:0% +another expansion that we did is we used +the fact that the momentum transfer is + + align:start position:0% +the fact that the momentum transfer is + + + align:start position:0% +the fact that the momentum transfer is +much less than the electron Mass not + + align:start position:0% +much less than the electron Mass not + + + align:start position:0% +much less than the electron Mass not +just the proton mass and + + align:start position:0% +just the proton mass and + + + align:start position:0% +just the proton mass and +that meant that the theory is + + align:start position:0% +that meant that the theory is + + + align:start position:0% +that meant that the theory is +non-relativistic and that's why we did + + align:start position:0% +non-relativistic and that's why we did + + + align:start position:0% +non-relativistic and that's why we did +non-relativistic quantum + + align:start position:0% +non-relativistic quantum + + + align:start position:0% +non-relativistic quantum +mechanics if we wanted to do it as a + + align:start position:0% +mechanics if we wanted to do it as a + + + align:start position:0% +mechanics if we wanted to do it as a +Quantum field Theory we would do a + + align:start position:0% +Quantum field Theory we would do a + + + align:start position:0% +Quantum field Theory we would do a +non-relativistic Quantum field + + align:start position:0% + + + + align:start position:0% + +Theory so already in something as le as + + align:start position:0% +Theory so already in something as le as + + + align:start position:0% +Theory so already in something as le as +hydrogen we have here three expansions + + align:start position:0% +hydrogen we have here three expansions + + + align:start position:0% +hydrogen we have here three expansions +plus many more thinking about the + + align:start position:0% +plus many more thinking about the + + + align:start position:0% +plus many more thinking about the +particles that we neglected in the + + align:start position:0% + + + + align:start position:0% + +description so the second point you alha + + align:start position:0% +description so the second point you alha + + + align:start position:0% +description so the second point you alha +yeah how do you know it's not just a + + align:start position:0% +yeah how do you know it's not just a + + + align:start position:0% +yeah how do you know it's not just a +ratio of MP + + align:start position:0% +ratio of MP + + + align:start position:0% +ratio of MP +rather + + align:start position:0% +rather + + + align:start position:0% +rather +um + + align:start position:0% +um + + + align:start position:0% +um +yeah g that's right so absolutely so in + + align:start position:0% +yeah g that's right so absolutely so in + + + align:start position:0% +yeah g that's right so absolutely so in +some sense I could have written meem + + align:start position:0% +some sense I could have written meem + + + align:start position:0% +some sense I could have written meem +here and that would have been fine um if + + align:start position:0% +here and that would have been fine um if + + + align:start position:0% +here and that would have been fine um if +you take these together then of course + + align:start position:0% +you take these together then of course + + + align:start position:0% +you take these together then of course +you could take a ratio and get me over M + + align:start position:0% +you could take a ratio and get me over M + + + align:start position:0% +you could take a ratio and get me over M +proton uh the reason I wrote me Alpha is + + align:start position:0% +proton uh the reason I wrote me Alpha is + + + align:start position:0% +proton uh the reason I wrote me Alpha is +I was really thinking about the probe + + align:start position:0% +I was really thinking about the probe + + + align:start position:0% +I was really thinking about the probe +the momentum sort of the non-static + + align:start position:0% +the momentum sort of the non-static + + + align:start position:0% +the momentum sort of the non-static +properties the Dynamics and the momentum + + align:start position:0% +properties the Dynamics and the momentum + + + align:start position:0% +properties the Dynamics and the momentum +of the photons the largest energy is + + align:start position:0% +of the photons the largest energy is + + + align:start position:0% +of the photons the largest energy is +this that's why I was thinking about it + + align:start position:0% +this that's why I was thinking about it + + + align:start position:0% +this that's why I was thinking about it +but you're right that I should write me + + align:start position:0% +but you're right that I should write me + + + align:start position:0% +but you're right that I should write me +over M proton as + + align:start position:0% +over M proton as + + + align:start position:0% +over M proton as +well any + + align:start position:0% +well any + + + align:start position:0% +well any +other comments questions + + align:start position:0% +other comments questions + + + align:start position:0% + +[Applause] + + align:start position:0% + + + + align:start position:0% + +so another point that I just want to + + align:start position:0% +so another point that I just want to + + + align:start position:0% +so another point that I just want to +briefly comment which has to be the true + + align:start position:0% +briefly comment which has to be the true + + + align:start position:0% +briefly comment which has to be the true +if everything I'm telling you is Right + + align:start position:0% +if everything I'm telling you is Right + + + align:start position:0% +if everything I'm telling you is Right +which is has to be true because it's + + align:start position:0% +which is has to be true because it's + + + align:start position:0% +which is has to be true because it's +what we taught you + + align:start position:0% +what we taught you + + + align:start position:0% +what we taught you +right is that this whole description is + + align:start position:0% +right is that this whole description is + + + align:start position:0% +right is that this whole description is +true even though there's ultraviolet + + align:start position:0% +true even though there's ultraviolet + + + align:start position:0% +true even though there's ultraviolet +diversity es when you start doing + + align:start position:0% +diversity es when you start doing + + + align:start position:0% +diversity es when you start doing +Quantum field Theory even if you do + + align:start position:0% +Quantum field Theory even if you do + + + align:start position:0% +Quantum field Theory even if you do +Quantum field theory in this case for + + align:start position:0% +Quantum field theory in this case for + + + align:start position:0% +Quantum field theory in this case for +the hydrogen atom you run into + + align:start position:0% +the hydrogen atom you run into + + + align:start position:0% +the hydrogen atom you run into +ultraviolet divergences where things are + + align:start position:0% +ultraviolet divergences where things are + + + align:start position:0% +ultraviolet divergences where things are +blowing up actually even this diagram + + align:start position:0% +blowing up actually even this diagram + + + align:start position:0% +blowing up actually even this diagram +has ultraviolet + + align:start position:0% + + + + align:start position:0% + +divergences so before you regulate the + + align:start position:0% +divergences so before you regulate the + + + align:start position:0% +divergences so before you regulate the +theory the bottom Quirk Loop is infinity + + align:start position:0% +theory the bottom Quirk Loop is infinity + + + align:start position:0% +theory the bottom Quirk Loop is infinity +once you regulate the theory it's well + + align:start position:0% +once you regulate the theory it's well + + + align:start position:0% +once you regulate the theory it's well +defined and you can make everything well + + align:start position:0% +defined and you can make everything well + + + align:start position:0% +defined and you can make everything well +defined but you may worry that this + + align:start position:0% +defined but you may worry that this + + + align:start position:0% +defined but you may worry that this +diagram is seems to be contributing an + + align:start position:0% +diagram is seems to be contributing an + + + align:start position:0% +diagram is seems to be contributing an +infinite amount rather than a finite + + align:start position:0% +infinite amount rather than a finite + + + align:start position:0% +infinite amount rather than a finite +amount and the whole story goes through + + align:start position:0% +amount and the whole story goes through + + + align:start position:0% +amount and the whole story goes through +even in the context of having + + align:start position:0% +even in the context of having + + + align:start position:0% +even in the context of having +ultraviolet + + align:start position:0% + + + + align:start position:0% + +divergences that better be true because + + align:start position:0% +divergences that better be true because + + + align:start position:0% +divergences that better be true because +for example if we had graviton Loops + + align:start position:0% +for example if we had graviton Loops + + + align:start position:0% +for example if we had graviton Loops +they would also lead ultraviolet + + align:start position:0% +they would also lead ultraviolet + + + align:start position:0% +they would also lead ultraviolet +divergences and + + align:start position:0% + + + + align:start position:0% + +so we neglecting gravity so it better be + + align:start position:0% +so we neglecting gravity so it better be + + + align:start position:0% +so we neglecting gravity so it better be +that these ideas of effective field + + align:start position:0% +that these ideas of effective field + + + align:start position:0% +that these ideas of effective field +Theory are not changed by having ultrai + + align:start position:0% +Theory are not changed by having ultrai + + + align:start position:0% +Theory are not changed by having ultrai +divergences + + align:start position:0% +divergences + + + align:start position:0% +divergences +and we'll encounter that in our + + align:start position:0% +and we'll encounter that in our + + + align:start position:0% +and we'll encounter that in our +discussion later + + align:start position:0% + + + + align:start position:0% + +on okay so that gives you a bit of a + + align:start position:0% +on okay so that gives you a bit of a + + + align:start position:0% +on okay so that gives you a bit of a +sense for how these ideas of effective + + align:start position:0% +sense for how these ideas of effective + + + align:start position:0% +sense for how these ideas of effective +field Theory you've been using them all + + align:start position:0% +field Theory you've been using them all + + + align:start position:0% +field Theory you've been using them all +along whether or not you knew + + align:start position:0% + + + + align:start position:0% + +it and we will in this course flesh out + + align:start position:0% +it and we will in this course flesh out + + + align:start position:0% +it and we will in this course flesh out +how we figure out some of these + + align:start position:0% +how we figure out some of these + + + align:start position:0% +how we figure out some of these +Corrections how we would actually + + align:start position:0% +Corrections how we would actually + + + align:start position:0% +Corrections how we would actually +compute them how we would actually + + align:start position:0% +compute them how we would actually + + + align:start position:0% +compute them how we would actually +figure out how to even the Le meting + + align:start position:0% +figure out how to even the Le meting + + + align:start position:0% +figure out how to even the Le meting +order what the meeting order description + + align:start position:0% +order what the meeting order description + + + align:start position:0% +order what the meeting order description +of a theory is in cases where we may not + + align:start position:0% +of a theory is in cases where we may not + + + align:start position:0% +of a theory is in cases where we may not +know it or someone else hasn't figured + + align:start position:0% +know it or someone else hasn't figured + + + align:start position:0% +know it or someone else hasn't figured +it out yet those are the type of things + + align:start position:0% +it out yet those are the type of things + + + align:start position:0% +it out yet those are the type of things +we're + + align:start position:0% + + + + align:start position:0% + +after now if you talk about the + + align:start position:0% +after now if you talk about the + + + align:start position:0% +after now if you talk about the +categories of effective field theories + + align:start position:0% +categories of effective field theories + + + align:start position:0% +categories of effective field theories +if you look at the list that I handed + + align:start position:0% +if you look at the list that I handed + + + align:start position:0% +if you look at the list that I handed +out to you or the list of things we're + + align:start position:0% +out to you or the list of things we're + + + align:start position:0% +out to you or the list of things we're +going to do in the course then there's + + align:start position:0% +going to do in the course then there's + + + align:start position:0% +going to do in the course then there's +really in general two ways that + + align:start position:0% +really in general two ways that + + + align:start position:0% +really in general two ways that +effective field theories are used + + align:start position:0% +effective field theories are used + + + align:start position:0% +effective field theories are used +[Applause] + + align:start position:0% + + + + align:start position:0% + +so the two ways are from the top down or + + align:start position:0% +so the two ways are from the top down or + + + align:start position:0% +so the two ways are from the top down or +from the bottom + + align:start position:0% +from the bottom + + + align:start position:0% +from the bottom +up so we'll start with the top + + align:start position:0% + + + + align:start position:0% + +down so in the top down + + align:start position:0% +down so in the top down + + + align:start position:0% +down so in the top down +situation you know what the high energy + + align:start position:0% +situation you know what the high energy + + + align:start position:0% +situation you know what the high energy +theory is I'm going to keep using this + + align:start position:0% +theory is I'm going to keep using this + + + align:start position:0% +theory is I'm going to keep using this +language of masses where I have a high + + align:start position:0% +language of masses where I have a high + + + align:start position:0% +language of masses where I have a high +energy and low energy Theory and we'll + + align:start position:0% +energy and low energy Theory and we'll + + + align:start position:0% +energy and low energy Theory and we'll +think about it more generally when we + + align:start position:0% +think about it more generally when we + + + align:start position:0% +think about it more generally when we +come to examples where we need to think + + align:start position:0% +come to examples where we need to think + + + align:start position:0% +come to examples where we need to think +about it more + + align:start position:0% +about it more + + + align:start position:0% +about it more +generally so in this top down case we + + align:start position:0% +generally so in this top down case we + + + align:start position:0% +generally so in this top down case we +have a high energy Theory say the + + align:start position:0% +have a high energy Theory say the + + + align:start position:0% +have a high energy Theory say the +standard model and that theory is + + align:start position:0% +standard model and that theory is + + + align:start position:0% +standard model and that theory is +understood in the sense that we can + + align:start position:0% +understood in the sense that we can + + + align:start position:0% +understood in the sense that we can +write down the lran for + + align:start position:0% +write down the lran for + + + align:start position:0% +write down the lran for +it but we're not satisfied with + + align:start position:0% +it but we're not satisfied with + + + align:start position:0% +it but we're not satisfied with +that we find it + + align:start position:0% +that we find it + + + align:start position:0% +that we find it +useful to have a simpler Theory + + align:start position:0% + + + + align:start position:0% + +to do some low energy + + align:start position:0% + + + + align:start position:0% + +physics or even to do some high energy + + align:start position:0% +physics or even to do some high energy + + + align:start position:0% +physics or even to do some high energy +physics where not all the degrees of + + align:start position:0% +physics where not all the degrees of + + + align:start position:0% +physics where not all the degrees of +freedom of this of this high energy + + align:start position:0% +freedom of this of this high energy + + + align:start position:0% +freedom of this of this high energy +Theory are + + align:start position:0% + + + + align:start position:0% + +relevant so we're in a situation where + + align:start position:0% +relevant so we're in a situation where + + + align:start position:0% +relevant so we're in a situation where +we have some Theory which I'll call + + align:start position:0% +we have some Theory which I'll call + + + align:start position:0% +we have some Theory which I'll call +Theory one which is this high energy + + align:start position:0% +Theory one which is this high energy + + + align:start position:0% +Theory one which is this high energy +theory that we understand it that we can + + align:start position:0% +theory that we understand it that we can + + + align:start position:0% +theory that we understand it that we can +think about doing calculations in it but + + align:start position:0% +think about doing calculations in it but + + + align:start position:0% +think about doing calculations in it but +we want to go over to some other Theory + + align:start position:0% +we want to go over to some other Theory + + + align:start position:0% +we want to go over to some other Theory +which I'll call Theory + + align:start position:0% +which I'll call Theory + + + align:start position:0% +which I'll call Theory +2 which has less degrees of freedom and + + align:start position:0% +2 which has less degrees of freedom and + + + align:start position:0% +2 which has less degrees of freedom and +we're making expansions and that's a low + + align:start position:0% +we're making expansions and that's a low + + + align:start position:0% +we're making expansions and that's a low +energy Theory this is the high + + align:start position:0% +energy Theory this is the high + + + align:start position:0% +energy Theory this is the high +Theory this is the low + + align:start position:0% +Theory this is the low + + + align:start position:0% +Theory this is the low +Theory so that that's what we are in + + align:start position:0% +Theory so that that's what we are in + + + align:start position:0% +Theory so that that's what we are in +this situation of what we call top down + + align:start position:0% +this situation of what we call top down + + + align:start position:0% +this situation of what we call top down +coming from the top from high energy + + align:start position:0% +coming from the top from high energy + + + align:start position:0% +coming from the top from high energy +down so what do we do well in this case + + align:start position:0% +down so what do we do well in this case + + + align:start position:0% +down so what do we do well in this case +it's kind of nice because we can + + align:start position:0% +it's kind of nice because we can + + + align:start position:0% +it's kind of nice because we can +actually use the fact that we know this + + align:start position:0% +actually use the fact that we know this + + + align:start position:0% +actually use the fact that we know this +Theory one and can do calculation in + + align:start position:0% +Theory one and can do calculation in + + + align:start position:0% +Theory one and can do calculation in +that theory one to even think about + + align:start position:0% +that theory one to even think about + + + align:start position:0% +that theory one to even think about +constructing Theory + + align:start position:0% + + + + align:start position:0% + +2 so what we can do is we can just start + + align:start position:0% +2 so what we can do is we can just start + + + align:start position:0% +2 so what we can do is we can just start +calculating things in theory + + align:start position:0% +calculating things in theory + + + align:start position:0% +calculating things in theory +one + + align:start position:0% +one + + + align:start position:0% +one +and integrate out IE + + align:start position:0% +and integrate out IE + + + align:start position:0% +and integrate out IE +remove the heavier particles + + align:start position:0% + + + + align:start position:0% + +and in in doing that we can do what's + + align:start position:0% +and in in doing that we can do what's + + + align:start position:0% +and in in doing that we can do what's +called + + align:start position:0% + + + + align:start position:0% + +matching onto the low energy + + align:start position:0% + + + + align:start position:0% + +theory that means we can use this + + align:start position:0% +theory that means we can use this + + + align:start position:0% +theory that means we can use this +ability to do calculations in the high + + align:start position:0% +ability to do calculations in the high + + + align:start position:0% +ability to do calculations in the high +energy + + align:start position:0% +energy + + + align:start position:0% +energy +Theory to find what the operators are of + + align:start position:0% +Theory to find what the operators are of + + + align:start position:0% +Theory to find what the operators are of +the low energy Theory + + align:start position:0% +the low energy Theory + + + align:start position:0% +the low energy Theory +just by direct + + align:start position:0% +just by direct + + + align:start position:0% +just by direct +calculation and also if there's new low + + align:start position:0% +calculation and also if there's new low + + + align:start position:0% +calculation and also if there's new low +energy constants that show up we can + + align:start position:0% +energy constants that show up we can + + + align:start position:0% +energy constants that show up we can +calculate the values of those constants + + align:start position:0% +calculate the values of those constants + + + align:start position:0% +calculate the values of those constants +by using information and connecting them + + align:start position:0% +by using information and connecting them + + + align:start position:0% +by using information and connecting them +to the high energy + + align:start position:0% +to the high energy + + + align:start position:0% +to the high energy +Theory so in this case we're able to use + + align:start position:0% +Theory so in this case we're able to use + + + align:start position:0% +Theory so in this case we're able to use +calculations really to construct the low + + align:start position:0% +calculations really to construct the low + + + align:start position:0% +calculations really to construct the low +energy + + align:start position:0% + + + + align:start position:0% + +Theory so just schematically I start + + align:start position:0% +Theory so just schematically I start + + + align:start position:0% +Theory so just schematically I start +with some high energy + + align:start position:0% + + + + align:start position:0% + +lran and I go over to + + align:start position:0% +lran and I go over to + + + align:start position:0% +lran and I go over to +some low energy + + align:start position:0% +some low energy + + + align:start position:0% +some low energy +Lans where there's an infinite series + + align:start position:0% +Lans where there's an infinite series + + + align:start position:0% +Lans where there's an infinite series +which I've index by n and that index is + + align:start position:0% +which I've index by n and that index is + + + align:start position:0% +which I've index by n and that index is +to denote higher order terms that are + + align:start position:0% +to denote higher order terms that are + + + align:start position:0% +to denote higher order terms that are +less relevant in whatever expansion + + align:start position:0% +less relevant in whatever expansion + + + align:start position:0% +less relevant in whatever expansion +you're + + align:start position:0% + + + + align:start position:0% + +doing so just to be General I'll say + + align:start position:0% +doing so just to be General I'll say + + + align:start position:0% +doing so just to be General I'll say +it's an expansion in decreasing + + align:start position:0% +it's an expansion in decreasing + + + align:start position:0% +it's an expansion in decreasing +relevance of the kep + + align:start position:0% + + + + align:start position:0% + +terms so if you're in this situation + + align:start position:0% +terms so if you're in this situation + + + align:start position:0% +terms so if you're in this situation +then these two theories are in some + + align:start position:0% +then these two theories are in some + + + align:start position:0% +then these two theories are in some +sense describing common things the high + + align:start position:0% +sense describing common things the high + + + align:start position:0% +sense describing common things the high +energy Theory describes more than the + + align:start position:0% +energy Theory describes more than the + + + align:start position:0% +energy Theory describes more than the +low energy Theory because you've removed + + align:start position:0% +low energy Theory because you've removed + + + align:start position:0% +low energy Theory because you've removed +something in constructing the low energy + + align:start position:0% +something in constructing the low energy + + + align:start position:0% +something in constructing the low energy +Theory but the two theories have to at + + align:start position:0% +Theory but the two theories have to at + + + align:start position:0% +Theory but the two theories have to at +least age where they + + align:start position:0% +least age where they + + + align:start position:0% +least age where they +overlap and so they have to agree on + + align:start position:0% +overlap and so they have to agree on + + + align:start position:0% +overlap and so they have to agree on +certain + + align:start position:0% +certain + + + align:start position:0% +certain +infrared observables + + align:start position:0% + + + + align:start position:0% + +which I will also often denote as IR for + + align:start position:0% +which I will also often denote as IR for + + + align:start position:0% +which I will also often denote as IR for +infrared the place where they differ is + + align:start position:0% +infrared the place where they differ is + + + align:start position:0% +infrared the place where they differ is +in the + + align:start position:0% +in the + + + align:start position:0% +in the +ultraviolet so they might have different + + align:start position:0% +ultraviolet so they might have different + + + align:start position:0% +ultraviolet so they might have different +ultraviolet divergences often most often + + align:start position:0% +ultraviolet divergences often most often + + + align:start position:0% +ultraviolet divergences often most often +they will have different ultraviolet + + align:start position:0% +they will have different ultraviolet + + + align:start position:0% +they will have different ultraviolet +divergences they don't have to agree in + + align:start position:0% +divergences they don't have to agree in + + + align:start position:0% +divergences they don't have to agree in +the + + align:start position:0% +the + + + align:start position:0% +the +ultraviolet and actually you exploit + + align:start position:0% +ultraviolet and actually you exploit + + + align:start position:0% +ultraviolet and actually you exploit +that to do things with the effective + + align:start position:0% +that to do things with the effective + + + align:start position:0% +that to do things with the effective +theory that you would be hard to do with + + align:start position:0% +theory that you would be hard to do with + + + align:start position:0% +theory that you would be hard to do with +the full Theory we'll talk about how we + + align:start position:0% +the full Theory we'll talk about how we + + + align:start position:0% +the full Theory we'll talk about how we +do that later on so the fact that they + + align:start position:0% +do that later on so the fact that they + + + align:start position:0% +do that later on so the fact that they +differ is actually not necessarily a + + align:start position:0% +differ is actually not necessarily a + + + align:start position:0% +differ is actually not necessarily a +negative thing it can be a bonus + + align:start position:0% + + + + align:start position:0% + +and finally you have to ask about this + + align:start position:0% +and finally you have to ask about this + + + align:start position:0% +and finally you have to ask about this +sum Over N well this sum Over N is + + align:start position:0% +sum Over N well this sum Over N is + + + align:start position:0% +sum Over N well this sum Over N is +infinite goes on forever and so you have + + align:start position:0% +infinite goes on forever and so you have + + + align:start position:0% +infinite goes on forever and so you have +to ask the question when should I + + align:start position:0% +to ask the question when should I + + + align:start position:0% +to ask the question when should I +stop and therefore you have to look to + + align:start position:0% +stop and therefore you have to look to + + + align:start position:0% +stop and therefore you have to look to +experiment and see how precise they are + + align:start position:0% +experiment and see how precise they are + + + align:start position:0% +experiment and see how precise they are +or just to your + + align:start position:0% +or just to your + + + align:start position:0% +or just to your +own perseverance and and figure out what + + align:start position:0% +own perseverance and and figure out what + + + align:start position:0% +own perseverance and and figure out what +level do you want what Precision do you + + align:start position:0% +level do you want what Precision do you + + + align:start position:0% +level do you want what Precision do you +want in your + + align:start position:0% +want in your + + + align:start position:0% +want in your +description so what nend do you want to + + align:start position:0% +description so what nend do you want to + + + align:start position:0% +description so what nend do you want to +stop + + align:start position:0% +stop + + + align:start position:0% +stop +at sometimes experiment tells you only + + align:start position:0% +at sometimes experiment tells you only + + + align:start position:0% +at sometimes experiment tells you only +to do the first two ends sometimes you + + align:start position:0% +to do the first two ends sometimes you + + + align:start position:0% +to do the first two ends sometimes you +have to decide maybe I only want the + + align:start position:0% +have to decide maybe I only want the + + + align:start position:0% +have to decide maybe I only want the +first one if you're doing it for the + + align:start position:0% +first one if you're doing it for the + + + align:start position:0% +first one if you're doing it for the +first time I suggest you start stop at + + align:start position:0% +first time I suggest you start stop at + + + align:start position:0% +first time I suggest you start stop at +the beginning and let someone else do + + align:start position:0% +the beginning and let someone else do + + + align:start position:0% +the beginning and let someone else do +this do the + + align:start position:0% + + + + align:start position:0% + +corrections this is this idea of doing + + align:start position:0% +corrections this is this idea of doing + + + align:start position:0% +corrections this is this idea of doing +this can be important for separating + + align:start position:0% +this can be important for separating + + + align:start position:0% +this can be important for separating +physics of the high energy Theory one + + align:start position:0% +physics of the high energy Theory one + + + align:start position:0% +physics of the high energy Theory one +example of this is in qcd if you take + + align:start position:0% +example of this is in qcd if you take + + + align:start position:0% +example of this is in qcd if you take +qcd for just about any process there'll + + align:start position:0% +qcd for just about any process there'll + + + align:start position:0% +qcd for just about any process there'll +be some parts of it which we're + + align:start position:0% +be some parts of it which we're + + + align:start position:0% +be some parts of it which we're +perturbative and some parts of it that + + align:start position:0% +perturbative and some parts of it that + + + align:start position:0% +perturbative and some parts of it that +are + + align:start position:0% +are + + + align:start position:0% +are +non-perturbative and by doing this kind + + align:start position:0% +non-perturbative and by doing this kind + + + align:start position:0% +non-perturbative and by doing this kind +of thing where you expand you could + + align:start position:0% +of thing where you expand you could + + + align:start position:0% +of thing where you expand you could +construct a low energy theory that only + + align:start position:0% +construct a low energy theory that only + + + align:start position:0% +construct a low energy theory that only +has the non-perturbative scale in it and + + align:start position:0% +has the non-perturbative scale in it and + + + align:start position:0% +has the non-perturbative scale in it and +removes all the perturbative scales if + + align:start position:0% +removes all the perturbative scales if + + + align:start position:0% +removes all the perturbative scales if +you did that then just doing this + + align:start position:0% +you did that then just doing this + + + align:start position:0% +you did that then just doing this +procedure would allow you to figure out + + align:start position:0% +procedure would allow you to figure out + + + align:start position:0% +procedure would allow you to figure out +what is the non-perturbative physics and + + align:start position:0% +what is the non-perturbative physics and + + + align:start position:0% +what is the non-perturbative physics and +what is the perturbative physics you'd + + align:start position:0% +what is the perturbative physics you'd + + + align:start position:0% +what is the perturbative physics you'd +separate out in that case into operators + + align:start position:0% +separate out in that case into operators + + + align:start position:0% +separate out in that case into operators +you'd separate out the infrared physics + + align:start position:0% +you'd separate out the infrared physics + + + align:start position:0% +you'd separate out the infrared physics +you'd have operators built out of the + + align:start position:0% +you'd have operators built out of the + + + align:start position:0% +you'd have operators built out of the +infrared fields and those operators + + align:start position:0% +infrared fields and those operators + + + align:start position:0% +infrared fields and those operators +would describe the non-curative physics + + align:start position:0% +would describe the non-curative physics + + + align:start position:0% +would describe the non-curative physics +and you'd have some new low energy + + align:start position:0% +and you'd have some new low energy + + + align:start position:0% +and you'd have some new low energy +constants which would describe the + + align:start position:0% +constants which would describe the + + + align:start position:0% +constants which would describe the +perturbative physics and some of the + + align:start position:0% +perturbative physics and some of the + + + align:start position:0% +perturbative physics and some of the +examples that we'll + + align:start position:0% +examples that we'll + + + align:start position:0% +examples that we'll +do we'll make use of + + align:start position:0% +do we'll make use of + + + align:start position:0% +do we'll make use of +that + + align:start position:0% + + + + align:start position:0% + +probably so that's kind of a + + align:start position:0% +probably so that's kind of a + + + align:start position:0% +probably so that's kind of a +motivation actually + + align:start position:0% + + + + align:start position:0% + +for for some of the examples in the + + align:start position:0% +for for some of the examples in the + + + align:start position:0% +for for some of the examples in the +standard model so if you think about for + + align:start position:0% +standard model so if you think about for + + + align:start position:0% +standard model so if you think about for +example integrating out heavy particles + + align:start position:0% + + + + align:start position:0% + +like the W or the Z or the top + + align:start position:0% +like the W or the Z or the top + + + align:start position:0% +like the W or the Z or the top +quk one of the motivations is sometimes + + align:start position:0% +quk one of the motivations is sometimes + + + align:start position:0% +quk one of the motivations is sometimes +what I just said to separate out + + align:start position:0% +what I just said to separate out + + + align:start position:0% +what I just said to separate out +perturbative and non-perturbative + + align:start position:0% +perturbative and non-perturbative + + + align:start position:0% +perturbative and non-perturbative +physics so that's one + + align:start position:0% +physics so that's one + + + align:start position:0% +physics so that's one +example heavy Quark effective theory is + + align:start position:0% +example heavy Quark effective theory is + + + align:start position:0% +example heavy Quark effective theory is +also an example of this top + + align:start position:0% + + + + align:start position:0% + +down effective field theory in heavy + + align:start position:0% +down effective field theory in heavy + + + align:start position:0% +down effective field theory in heavy +Quark effective field Theory you have a + + align:start position:0% +Quark effective field Theory you have a + + + align:start position:0% +Quark effective field Theory you have a +field theory for the B Quark or for the + + align:start position:0% +field theory for the B Quark or for the + + + align:start position:0% +field theory for the B Quark or for the +charm quark + + align:start position:0% +charm quark + + + align:start position:0% +charm quark +but you want to describe things like the + + align:start position:0% +but you want to describe things like the + + + align:start position:0% +but you want to describe things like the +b meeson or bottom or or the or a charm + + align:start position:0% + + + + align:start position:0% + +meons and those are objects have + + align:start position:0% +meons and those are objects have + + + align:start position:0% +meons and those are objects have +non-perturbative physics as well as + + align:start position:0% +non-perturbative physics as well as + + + align:start position:0% +non-perturbative physics as well as +perturbative have mostly + + align:start position:0% +perturbative have mostly + + + align:start position:0% +perturbative have mostly +non-perturbative physics and in order to + + align:start position:0% +non-perturbative physics and in order to + + + align:start position:0% +non-perturbative physics and in order to +do that you want to actually integrate + + align:start position:0% +do that you want to actually integrate + + + align:start position:0% +do that you want to actually integrate +out the mass scale of the charm Quark or + + align:start position:0% +out the mass scale of the charm Quark or + + + align:start position:0% +out the mass scale of the charm Quark or +the bottom quk if you integrate out the + + align:start position:0% +the bottom quk if you integrate out the + + + align:start position:0% +the bottom quk if you integrate out the +mass of the charm Quirk or the bottom + + align:start position:0% +mass of the charm Quirk or the bottom + + + align:start position:0% +mass of the charm Quirk or the bottom +Quirk you go over to something called + + align:start position:0% +Quirk you go over to something called + + + align:start position:0% +Quirk you go over to something called +heavy quk effective field Theory but it + + align:start position:0% +heavy quk effective field Theory but it + + + align:start position:0% +heavy quk effective field Theory but it +can be done in exactly this way that I + + align:start position:0% +can be done in exactly this way that I + + + align:start position:0% +can be done in exactly this way that I +described to you where you start with + + align:start position:0% +described to you where you start with + + + align:start position:0% +described to you where you start with +the Theory with the full B Quark + + align:start position:0% +the Theory with the full B Quark + + + align:start position:0% +the Theory with the full B Quark +relativistic description and you + + align:start position:0% +relativistic description and you + + + align:start position:0% +relativistic description and you +actually just expand and figure out what + + align:start position:0% +actually just expand and figure out what + + + align:start position:0% +actually just expand and figure out what +the heavy Quark effective theory + + align:start position:0% + + + + align:start position:0% + +is so non-relativistic + + align:start position:0% + + + + align:start position:0% + +QED and non-relativistic + + align:start position:0% +QED and non-relativistic + + + align:start position:0% +QED and non-relativistic +qcd are also examples here and soft + + align:start position:0% +qcd are also examples here and soft + + + align:start position:0% +qcd are also examples here and soft +cinear effective Theory one of our main + + align:start position:0% +cinear effective Theory one of our main + + + align:start position:0% +cinear effective Theory one of our main +subjects is also an example of this type + + align:start position:0% +subjects is also an example of this type + + + align:start position:0% +subjects is also an example of this type +where we can just start in qcd + + align:start position:0% +where we can just start in qcd + + + align:start position:0% +where we can just start in qcd +do an expansion and get the effective + + align:start position:0% +do an expansion and get the effective + + + align:start position:0% +do an expansion and get the effective +field + + align:start position:0% + + + + align:start position:0% + +Theory so what's the other category so + + align:start position:0% +Theory so what's the other category so + + + align:start position:0% +Theory so what's the other category so +the other category is from the bottom + + align:start position:0% +the other category is from the bottom + + + align:start position:0% +the other category is from the bottom +up and typically in this case you're + + align:start position:0% +up and typically in this case you're + + + align:start position:0% +up and typically in this case you're +interested in using effective the theory + + align:start position:0% +interested in using effective the theory + + + align:start position:0% +interested in using effective the theory +logic but maybe you don't know the high + + align:start position:0% +logic but maybe you don't know the high + + + align:start position:0% +logic but maybe you don't know the high +energy + + align:start position:0% +energy + + + align:start position:0% +energy +Theory you don't really know anything + + align:start position:0% +Theory you don't really know anything + + + align:start position:0% +Theory you don't really know anything +about it maybe we've never proved it + + align:start position:0% +about it maybe we've never proved it + + + align:start position:0% +about it maybe we've never proved it +that's one way in which bottom up + + align:start position:0% +that's one way in which bottom up + + + align:start position:0% +that's one way in which bottom up +effective field Theory shows + + align:start position:0% +effective field Theory shows + + + align:start position:0% +effective field Theory shows +up or it could be that the high energy + + align:start position:0% +up or it could be that the high energy + + + align:start position:0% +up or it could be that the high energy +theory is known but actually doing the + + align:start position:0% +theory is known but actually doing the + + + align:start position:0% +theory is known but actually doing the +matching calculations to integrate out + + align:start position:0% +matching calculations to integrate out + + + align:start position:0% +matching calculations to integrate out +the degrees of freedom to do those + + align:start position:0% +the degrees of freedom to do those + + + align:start position:0% +the degrees of freedom to do those +calculations explicitly could be just + + align:start position:0% +calculations explicitly could be just + + + align:start position:0% +calculations explicitly could be just +very very + + align:start position:0% + + + + align:start position:0% + +difficult maybe it would be + + align:start position:0% +difficult maybe it would be + + + align:start position:0% +difficult maybe it would be +non-perturbative for + + align:start position:0% +non-perturbative for + + + align:start position:0% +non-perturbative for +example so if the matching is too + + align:start position:0% +example so if the matching is too + + + align:start position:0% +example so if the matching is too +difficult then you may also be want to + + align:start position:0% +difficult then you may also be want to + + + align:start position:0% +difficult then you may also be want to +be thinking in this bottom up framework + + align:start position:0% +be thinking in this bottom up framework + + + align:start position:0% +be thinking in this bottom up framework +where you really just start by thinking + + align:start position:0% +where you really just start by thinking + + + align:start position:0% +where you really just start by thinking +about the low energy Theory without + + align:start position:0% +about the low energy Theory without + + + align:start position:0% +about the low energy Theory without +worrying about what the high energy + + align:start position:0% +worrying about what the high energy + + + align:start position:0% +worrying about what the high energy +theory + + align:start position:0% +theory + + + align:start position:0% +theory +was or without thinking too hard about + + align:start position:0% +was or without thinking too hard about + + + align:start position:0% +was or without thinking too hard about +the high energy Theory and in particular + + align:start position:0% +the high energy Theory and in particular + + + align:start position:0% +the high energy Theory and in particular +without doing calculations in the high + + align:start position:0% +without doing calculations in the high + + + align:start position:0% +without doing calculations in the high +energy theory in order + + align:start position:0% +energy theory in order + + + align:start position:0% +energy theory in order +to motivate the low energy Theory you + + align:start position:0% +to motivate the low energy Theory you + + + align:start position:0% +to motivate the low energy Theory you +may not have to need need to know some + + align:start position:0% +may not have to need need to know some + + + align:start position:0% +may not have to need need to know some +things about the high energy Theory like + + align:start position:0% +things about the high energy Theory like + + + align:start position:0% +things about the high energy Theory like +you need may need to know that it's + + align:start position:0% +you need may need to know that it's + + + align:start position:0% +you need may need to know that it's +Loren invariant that it has certain + + align:start position:0% +Loren invariant that it has certain + + + align:start position:0% +Loren invariant that it has certain +gauge symmetry + + align:start position:0% +gauge symmetry + + + align:start position:0% +gauge symmetry +that it's not totally + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +crazy but you don't need to know it at + + align:start position:0% +crazy but you don't need to know it at + + + align:start position:0% +crazy but you don't need to know it at +the level where you would actually carry + + align:start position:0% +the level where you would actually carry + + + align:start position:0% +the level where you would actually carry +out calculations with it in order to + + align:start position:0% +out calculations with it in order to + + + align:start position:0% +out calculations with it in order to +construct the low energy Theory instead + + align:start position:0% +construct the low energy Theory instead + + + align:start position:0% +construct the low energy Theory instead +you think about the low energy Theory + + align:start position:0% +you think about the low energy Theory + + + align:start position:0% +you think about the low energy Theory +from the bottom up where you can just + + align:start position:0% +from the bottom up where you can just + + + align:start position:0% +from the bottom up where you can just +divise + + align:start position:0% +divise + + + align:start position:0% +divise +it based on the symmetries based on your + + align:start position:0% +it based on the symmetries based on your + + + align:start position:0% +it based on the symmetries based on your +power counting and based on identifying + + align:start position:0% +power counting and based on identifying + + + align:start position:0% +power counting and based on identifying +the degrees of + + align:start position:0% + + + + align:start position:0% + +freedom so + + align:start position:0% + + + + align:start position:0% + +construct this + + align:start position:0% + + + + align:start position:0% + +series simply by writing + + align:start position:0% +series simply by writing + + + align:start position:0% +series simply by writing +down the most General operators that we + + align:start position:0% +down the most General operators that we + + + align:start position:0% +down the most General operators that we +can think up + + align:start position:0% + + + + align:start position:0% + +consistent with whatever degrees of + + align:start position:0% +consistent with whatever degrees of + + + align:start position:0% +consistent with whatever degrees of +freedom we + + align:start position:0% +freedom we + + + align:start position:0% +freedom we +have and of course consistent with the + + align:start position:0% +have and of course consistent with the + + + align:start position:0% +have and of course consistent with the +symmetries that we're + + align:start position:0% + + + + align:start position:0% + +imposing okay so the picture is that you + + align:start position:0% +imposing okay so the picture is that you + + + align:start position:0% +imposing okay so the picture is that you +don't know or you want to remain + + align:start position:0% +don't know or you want to remain + + + align:start position:0% +don't know or you want to remain +agnostic about Theory one but you still + + align:start position:0% +agnostic about Theory one but you still + + + align:start position:0% +agnostic about Theory one but you still +are interested in constructing Theory 2 + + align:start position:0% + + + + align:start position:0% + +if you do this then unlike the other + + align:start position:0% +if you do this then unlike the other + + + align:start position:0% +if you do this then unlike the other +case the couplings that you have when + + align:start position:0% +case the couplings that you have when + + + align:start position:0% +case the couplings that you have when +you write down these operators they all + + align:start position:0% +you write down these operators they all + + + align:start position:0% +you write down these operators they all +are multiplied by some couplings if + + align:start position:0% +are multiplied by some couplings if + + + align:start position:0% +are multiplied by some couplings if +they're higher Dimension + + align:start position:0% +they're higher Dimension + + + align:start position:0% +they're higher Dimension +operators and they're not constrained by + + align:start position:0% +operators and they're not constrained by + + + align:start position:0% +operators and they're not constrained by +gauge + + align:start position:0% +gauge + + + align:start position:0% +gauge +symmetry then all of those couplings are + + align:start position:0% +symmetry then all of those couplings are + + + align:start position:0% +symmetry then all of those couplings are +unknown but you can fit them to + + align:start position:0% + + + + align:start position:0% + +experiment so the effective Theory may + + align:start position:0% +experiment so the effective Theory may + + + align:start position:0% +experiment so the effective Theory may +still be + + align:start position:0% +still be + + + align:start position:0% +still be +powerful because you can make more than + + align:start position:0% +powerful because you can make more than + + + align:start position:0% +powerful because you can make more than +more predictions than the number of + + align:start position:0% +more predictions than the number of + + + align:start position:0% +more predictions than the number of +parameters that you + + align:start position:0% +parameters that you + + + align:start position:0% +parameters that you +have like for + + align:start position:0% +have like for + + + align:start position:0% +have like for +hydrogen where we have very few + + align:start position:0% +hydrogen where we have very few + + + align:start position:0% +hydrogen where we have very few +parameters in the the effective Theory + + align:start position:0% +parameters in the the effective Theory + + + align:start position:0% +parameters in the the effective Theory +but we can make lots of predictions from + + align:start position:0% +but we can make lots of predictions from + + + align:start position:0% +but we can make lots of predictions from +non-realistic quantum + + align:start position:0% +non-realistic quantum + + + align:start position:0% +non-realistic quantum +mechanics or it could be in the case + + align:start position:0% +mechanics or it could be in the case + + + align:start position:0% +mechanics or it could be in the case +where you matching is too difficult that + + align:start position:0% +where you matching is too difficult that + + + align:start position:0% +where you matching is too difficult that +maybe you have to carry out the matching + + align:start position:0% +maybe you have to carry out the matching + + + align:start position:0% +maybe you have to carry out the matching +numerically like with Lattis + + align:start position:0% +numerically like with Lattis + + + align:start position:0% +numerically like with Lattis +qcd um and so that would be another + + align:start position:0% +qcd um and so that would be another + + + align:start position:0% +qcd um and so that would be another +possible way of determining + + align:start position:0% +possible way of determining + + + align:start position:0% +possible way of determining +couplings and again the desired + + align:start position:0% +couplings and again the desired + + + align:start position:0% +couplings and again the desired +Precision tells us when to stop + + align:start position:0% +Precision tells us when to stop + + + align:start position:0% +Precision tells us when to stop +so it's important that we have a power + + align:start position:0% +so it's important that we have a power + + + align:start position:0% +so it's important that we have a power +counting for this theory that that power + + align:start position:0% +counting for this theory that that power + + + align:start position:0% +counting for this theory that that power +counting is in some sense defined + + align:start position:0% +counting is in some sense defined + + + align:start position:0% +counting is in some sense defined +irrespective of what the full theory was + + align:start position:0% +irrespective of what the full theory was + + + align:start position:0% +irrespective of what the full theory was +so that we can stop even in this in the + + align:start position:0% +so that we can stop even in this in the + + + align:start position:0% +so that we can stop even in this in the +bottom uh bottom up + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +case so what are examples here well the + + align:start position:0% +case so what are examples here well the + + + align:start position:0% +case so what are examples here well the +classic example of this type is Carl + + align:start position:0% +classic example of this type is Carl + + + align:start position:0% +classic example of this type is Carl +pration + + align:start position:0% +pration + + + align:start position:0% +pration +Theory where you're thinking about a + + align:start position:0% +Theory where you're thinking about a + + + align:start position:0% +Theory where you're thinking about a +field theory for + + align:start position:0% +field theory for + + + align:start position:0% +field theory for +chons and + + align:start position:0% + + + + align:start position:0% + +pons and doing the matching onto chons + + align:start position:0% +pons and doing the matching onto chons + + + align:start position:0% +pons and doing the matching onto chons +and + + align:start position:0% +and + + + align:start position:0% +and +P from qcd is a non perative process so + + align:start position:0% +P from qcd is a non perative process so + + + align:start position:0% +P from qcd is a non perative process so +you think about constructing the + + align:start position:0% +you think about constructing the + + + align:start position:0% +you think about constructing the +effective Theory just from low energy + + align:start position:0% +effective Theory just from low energy + + + align:start position:0% +effective Theory just from low energy +and from symmetries knowing the Symmetry + + align:start position:0% +and from symmetries knowing the Symmetry + + + align:start position:0% +and from symmetries knowing the Symmetry +breaking pattern in particular uh then + + align:start position:0% +breaking pattern in particular uh then + + + align:start position:0% +breaking pattern in particular uh then +you construct the K pration Theory + + align:start position:0% +you construct the K pration Theory + + + align:start position:0% +you construct the K pration Theory +without thinking about doing the + + align:start position:0% +without thinking about doing the + + + align:start position:0% +without thinking about doing the +matching + + align:start position:0% +matching + + + align:start position:0% +matching +explicitly so that's one + + align:start position:0% +explicitly so that's one + + + align:start position:0% +explicitly so that's one +example another example of this type is + + align:start position:0% +example another example of this type is + + + align:start position:0% +example another example of this type is +actually the standard model itself + + align:start position:0% + + + + align:start position:0% + +self if you think about the logic that + + align:start position:0% +self if you think about the logic that + + + align:start position:0% +self if you think about the logic that +we used when we construct the standard + + align:start position:0% +we used when we construct the standard + + + align:start position:0% +we used when we construct the standard +model it was exactly this effective + + align:start position:0% +model it was exactly this effective + + + align:start position:0% +model it was exactly this effective +field Theory logic he said what are the + + align:start position:0% +field Theory logic he said what are the + + + align:start position:0% +field Theory logic he said what are the +relevant degrees of freedom electron + + align:start position:0% +relevant degrees of freedom electron + + + align:start position:0% +relevant degrees of freedom electron +quarks W bons listed them we wrote down + + align:start position:0% +quarks W bons listed them we wrote down + + + align:start position:0% +quarks W bons listed them we wrote down +we said what are the important guiding + + align:start position:0% +we said what are the important guiding + + + align:start position:0% +we said what are the important guiding +principles gauge + + align:start position:0% +principles gauge + + + align:start position:0% +principles gauge +symmetry how and then we wrote down the + + align:start position:0% +symmetry how and then we wrote down the + + + align:start position:0% +symmetry how and then we wrote down the +most General lran that we could think of + + align:start position:0% +most General lran that we could think of + + + align:start position:0% +most General lran that we could think of +that was the standard + + align:start position:0% +that was the standard + + + align:start position:0% +that was the standard +model okay so it's an ex example of a + + align:start position:0% +model okay so it's an ex example of a + + + align:start position:0% +model okay so it's an ex example of a +bottom up effective field Theory we + + align:start position:0% +bottom up effective field Theory we + + + align:start position:0% +bottom up effective field Theory we +don't ask questions about what's higher + + align:start position:0% +don't ask questions about what's higher + + + align:start position:0% +don't ask questions about what's higher +up when we write down the leading order + + align:start position:0% +up when we write down the leading order + + + align:start position:0% +up when we write down the leading order +lran and we can actually construct + + align:start position:0% +lran and we can actually construct + + + align:start position:0% +lran and we can actually construct +higher order terms in the standard model + + align:start position:0% +higher order terms in the standard model + + + align:start position:0% +higher order terms in the standard model +expanding in the idea that there's + + align:start position:0% +expanding in the idea that there's + + + align:start position:0% +expanding in the idea that there's +physics above the scales of the standard + + align:start position:0% +physics above the scales of the standard + + + align:start position:0% +physics above the scales of the standard +model and write down higher Dimension + + align:start position:0% +model and write down higher Dimension + + + align:start position:0% +model and write down higher Dimension +operators and have a real standard model + + align:start position:0% +operators and have a real standard model + + + align:start position:0% +operators and have a real standard model +that has an infinite series okay so the + + align:start position:0% +that has an infinite series okay so the + + + align:start position:0% +that has an infinite series okay so the +standard model is an effective field + + align:start position:0% +standard model is an effective field + + + align:start position:0% +standard model is an effective field +theory that has an infinite number of + + align:start position:0% +theory that has an infinite number of + + + align:start position:0% +theory that has an infinite number of +operators and we'll talk about that + + align:start position:0% +operators and we'll talk about that + + + align:start position:0% +operators and we'll talk about that +momentarily and as well next time so + + align:start position:0% +momentarily and as well next time so + + + align:start position:0% +momentarily and as well next time so +that be that'll be the first example we + + align:start position:0% +that be that'll be the first example we + + + align:start position:0% +that be that'll be the first example we +actually treat is the standard model is + + align:start position:0% +actually treat is the standard model is + + + align:start position:0% +actually treat is the standard model is +in effective field + + align:start position:0% + + + + align:start position:0% + +Theory another example is quantum + + align:start position:0% + + + + align:start position:0% + +gravity if you take Einstein gravity and + + align:start position:0% +gravity if you take Einstein gravity and + + + align:start position:0% +gravity if you take Einstein gravity and +you make it quantum and you allow + + align:start position:0% +you make it quantum and you allow + + + align:start position:0% +you make it quantum and you allow +yourself to expand I.E you say you're + + align:start position:0% +yourself to expand I.E you say you're + + + align:start position:0% +yourself to expand I.E you say you're +only interested in low energy physics so + + align:start position:0% +only interested in low energy physics so + + + align:start position:0% +only interested in low energy physics so +so you allow yourself to write down an + + align:start position:0% +so you allow yourself to write down an + + + align:start position:0% +so you allow yourself to write down an +infinite number of + + align:start position:0% +infinite number of + + + align:start position:0% +infinite number of +operators then you can also re normalize + + align:start position:0% +operators then you can also re normalize + + + align:start position:0% +operators then you can also re normalize +that theory order by order in those + + align:start position:0% +that theory order by order in those + + + align:start position:0% +that theory order by order in those +those infinite number of operators and + + align:start position:0% +those infinite number of operators and + + + align:start position:0% +those infinite number of operators and +so it's also an example of something + + align:start position:0% +so it's also an example of something + + + align:start position:0% +so it's also an example of something +that you can treat from this effective + + align:start position:0% +that you can treat from this effective + + + align:start position:0% +that you can treat from this effective +field Theory + + align:start position:0% + + + + align:start position:0% + +Paradigm that was the last topic that I + + align:start position:0% +Paradigm that was the last topic that I + + + align:start position:0% +Paradigm that was the last topic that I +would actually cover in this if we had + + align:start position:0% +would actually cover in this if we had + + + align:start position:0% +would actually cover in this if we had +like a couple extra weeks of lectures I + + align:start position:0% +like a couple extra weeks of lectures I + + + align:start position:0% +like a couple extra weeks of lectures I +would get to this but probably we want + + align:start position:0% +would get to this but probably we want + + + align:start position:0% +would get to this but probably we want +so that's a topic somebody might pick + + align:start position:0% +so that's a topic somebody might pick + + + align:start position:0% +so that's a topic somebody might pick +for their project at the end for their + + align:start position:0% +for their project at the end for their + + + align:start position:0% +for their project at the end for their +presentation + + align:start position:0% +presentation + + + align:start position:0% +presentation +okay so important + + align:start position:0% + + + + align:start position:0% + +stuff is there any question about + + align:start position:0% + + + + align:start position:0% + +that sits well with everybody makes them + + align:start position:0% +that sits well with everybody makes them + + + align:start position:0% +that sits well with everybody makes them +feel good + + align:start position:0% +feel good + + + align:start position:0% +feel good +inside + + align:start position:0% + + + + align:start position:0% + +okay so so far when we've been talking + + align:start position:0% +okay so so far when we've been talking + + + align:start position:0% +okay so so far when we've been talking +about this sum Over N we've been really + + align:start position:0% +about this sum Over N we've been really + + + align:start position:0% +about this sum Over N we've been really +thinking about expansions and + + align:start position:0% +thinking about expansions and + + + align:start position:0% +thinking about expansions and +Powers some Mass scale divided by some + + align:start position:0% +Powers some Mass scale divided by some + + + align:start position:0% +Powers some Mass scale divided by some +other scale being much less than one + + align:start position:0% +other scale being much less than one + + + align:start position:0% +other scale being much less than one +okay that's what we've meant by + + align:start position:0% + + + + align:start position:0% + +it but when you have two scales like + + align:start position:0% +it but when you have two scales like + + + align:start position:0% +it but when you have two scales like +this m and Lambda you also get + + align:start position:0% + + + + align:start position:0% + +logarithms so it's not always Powers + + align:start position:0% +logarithms so it's not always Powers + + + align:start position:0% +logarithms so it's not always Powers +there's also log that show + + align:start position:0% + + + + align:start position:0% + +up and this comment I meant about that I + + align:start position:0% +up and this comment I meant about that I + + + align:start position:0% +up and this comment I meant about that I +made about ultraviolet + + align:start position:0% +made about ultraviolet + + + align:start position:0% +made about ultraviolet +divergences in the low energy Theory it + + align:start position:0% +divergences in the low energy Theory it + + + align:start position:0% +divergences in the low energy Theory it +can actually help you to understand + + align:start position:0% +can actually help you to understand + + + align:start position:0% +can actually help you to understand +those + + align:start position:0% + + + + align:start position:0% + +logarithms continue over + + align:start position:0% +logarithms continue over + + + align:start position:0% +logarithms continue over +here so when you treat the re + + align:start position:0% +here so when you treat the re + + + align:start position:0% +here so when you treat the re +normalization of the low energy + + align:start position:0% + + + + align:start position:0% + +Theory as you know from Quantum field + + align:start position:0% +Theory as you know from Quantum field + + + align:start position:0% +Theory as you know from Quantum field +the + + align:start position:0% + + + + align:start position:0% + +there's you have different types of + + align:start position:0% +there's you have different types of + + + align:start position:0% +there's you have different types of +divergences power Divergence is but the + + align:start position:0% +divergences power Divergence is but the + + + align:start position:0% +divergences power Divergence is but the +logarithmic divergences in particular + + align:start position:0% +logarithmic divergences in particular + + + align:start position:0% +logarithmic divergences in particular +are things that are playing an important + + align:start position:0% +are things that are playing an important + + + align:start position:0% +are things that are playing an important +role often in Quantum field Theory and + + align:start position:0% +role often in Quantum field Theory and + + + align:start position:0% +role often in Quantum field Theory and +in effective field Theory it's the same + + align:start position:0% +in effective field Theory it's the same + + + align:start position:0% +in effective field Theory it's the same +thing logarithms can be tied to the + + align:start position:0% +thing logarithms can be tied to the + + + align:start position:0% +thing logarithms can be tied to the +renormalization of the low energy + + align:start position:0% +renormalization of the low energy + + + align:start position:0% +renormalization of the low energy +effective + + align:start position:0% + + + + align:start position:0% + +Theory + + align:start position:0% +Theory + + + align:start position:0% +Theory +and allow us to sum infinite series of + + align:start position:0% +and allow us to sum infinite series of + + + align:start position:0% +and allow us to sum infinite series of +those logarithms + + align:start position:0% + + + + align:start position:0% + +so often just the power counting and the + + align:start position:0% +so often just the power counting and the + + + align:start position:0% +so often just the power counting and the +re normalization of the low energy + + align:start position:0% +re normalization of the low energy + + + align:start position:0% +re normalization of the low energy +Theory I'll actually allow us not only + + align:start position:0% +Theory I'll actually allow us not only + + + align:start position:0% +Theory I'll actually allow us not only +to calculate the logarithms but to think + + align:start position:0% +to calculate the logarithms but to think + + + align:start position:0% +to calculate the logarithms but to think +about summing up infinite series of of + + align:start position:0% +about summing up infinite series of of + + + align:start position:0% +about summing up infinite series of of +those + + align:start position:0% + + + + align:start position:0% + +logarithms okay so that was kind of just + + align:start position:0% +logarithms okay so that was kind of just + + + align:start position:0% +logarithms okay so that was kind of just +elaborating on the point I made earlier + + align:start position:0% +elaborating on the point I made earlier + + + align:start position:0% +elaborating on the point I made earlier +and again I should say here that I've + + align:start position:0% +and again I should say here that I've + + + align:start position:0% +and again I should say here that I've +said this in the language of there being + + align:start position:0% +said this in the language of there being + + + align:start position:0% +said this in the language of there being +two masses M1 and M2 and W over MB but + + align:start position:0% +two masses M1 and M2 and W over MB but + + + align:start position:0% +two masses M1 and M2 and W over MB but +this is actually true more generally + + align:start position:0% +this is actually true more generally + + + align:start position:0% +this is actually true more generally +again so I actually make a claim that + + align:start position:0% +again so I actually make a claim that + + + align:start position:0% +again so I actually make a claim that +there's not any log that you've seen in + + align:start position:0% +there's not any log that you've seen in + + + align:start position:0% +there's not any log that you've seen in +Quantum field theory that shouldn't be + + align:start position:0% +Quantum field theory that shouldn't be + + + align:start position:0% +Quantum field theory that shouldn't be +possible to figure out an effective + + align:start position:0% +possible to figure out an effective + + + align:start position:0% +possible to figure out an effective +field theory that allows you to + + align:start position:0% +field theory that allows you to + + + align:start position:0% +field theory that allows you to +understand those logs and predict + + align:start position:0% +understand those logs and predict + + + align:start position:0% +understand those logs and predict +logarithms at higher orders in peration + + align:start position:0% +logarithms at higher orders in peration + + + align:start position:0% +logarithms at higher orders in peration +theory there's not there's not an + + align:start position:0% +theory there's not there's not an + + + align:start position:0% +theory there's not there's not an +example in Quantum field theory that + + align:start position:0% +example in Quantum field theory that + + + align:start position:0% +example in Quantum field theory that +I've met that hasn't fallen into that + + align:start position:0% +I've met that hasn't fallen into that + + + align:start position:0% +I've met that hasn't fallen into that +rubric where some effective field Theory + + align:start position:0% +rubric where some effective field Theory + + + align:start position:0% +rubric where some effective field Theory +description allows you to understand the + + align:start position:0% +description allows you to understand the + + + align:start position:0% +description allows you to understand the +logarithms + + align:start position:0% +logarithms + + + align:start position:0% +logarithms +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +okay so that's kind of a bonus it's not + + align:start position:0% +okay so that's kind of a bonus it's not + + + align:start position:0% +okay so that's kind of a bonus it's not +the guiding principle it's not what + + align:start position:0% +the guiding principle it's not what + + + align:start position:0% +the guiding principle it's not what +we're doing when we're expanding in + + align:start position:0% +we're doing when we're expanding in + + + align:start position:0% +we're doing when we're expanding in +Powers but it's something that we get + + align:start position:0% +Powers but it's something that we get + + + align:start position:0% +Powers but it's something that we get +along for the + + align:start position:0% +along for the + + + align:start position:0% +along for the +ride and maybe it would be the + + align:start position:0% +ride and maybe it would be the + + + align:start position:0% +ride and maybe it would be the +motivation if you if you see some + + align:start position:0% +motivation if you if you see some + + + align:start position:0% +motivation if you if you see some +logarithms and some process and you want + + align:start position:0% +logarithms and some process and you want + + + align:start position:0% +logarithms and some process and you want +to understand them and maybe say well + + align:start position:0% +to understand them and maybe say well + + + align:start position:0% +to understand them and maybe say well +I'd like to understand what effective + + align:start position:0% +I'd like to understand what effective + + + align:start position:0% +I'd like to understand what effective +field Theory would give rise to a + + align:start position:0% +field Theory would give rise to a + + + align:start position:0% +field Theory would give rise to a +description where I could understand + + align:start position:0% +description where I could understand + + + align:start position:0% +description where I could understand +those logarithms from a renormalization + + align:start position:0% +those logarithms from a renormalization + + + align:start position:0% +those logarithms from a renormalization +perspective and sometimes that's very + + align:start position:0% +perspective and sometimes that's very + + + align:start position:0% +perspective and sometimes that's very +useful because maybe those logarithms + + align:start position:0% +useful because maybe those logarithms + + + align:start position:0% +useful because maybe those logarithms +are phenologically important and you + + align:start position:0% +are phenologically important and you + + + align:start position:0% +are phenologically important and you +want to make predictions about higher + + align:start position:0% +want to make predictions about higher + + + align:start position:0% +want to make predictions about higher +order logarithms or maybe there's + + align:start position:0% +order logarithms or maybe there's + + + align:start position:0% +order logarithms or maybe there's +controversy when I was a graduate when I + + align:start position:0% +controversy when I was a graduate when I + + + align:start position:0% +controversy when I was a graduate when I +was a postto there was some controversy + + align:start position:0% +was a postto there was some controversy + + + align:start position:0% +was a postto there was some controversy +about a term that was Alpha to the + + align:start position:0% +about a term that was Alpha to the + + + align:start position:0% +about a term that was Alpha to the +8 log cubed Alpha in hydrogen energy + + align:start position:0% +8 log cubed Alpha in hydrogen energy + + + align:start position:0% +8 log cubed Alpha in hydrogen energy +levels okay Eight Powers of alpha three + + align:start position:0% +levels okay Eight Powers of alpha three + + + align:start position:0% +levels okay Eight Powers of alpha three +powers of logs there was four groups two + + align:start position:0% +powers of logs there was four groups two + + + align:start position:0% +powers of logs there was four groups two +of them had got one answer two of them + + align:start position:0% +of them had got one answer two of them + + + align:start position:0% +of them had got one answer two of them +had got another answer and using the + + align:start position:0% +had got another answer and using the + + + align:start position:0% +had got another answer and using the +ideas of effective field Theory we were + + align:start position:0% +ideas of effective field Theory we were + + + align:start position:0% +ideas of effective field Theory we were +able to figure out that one of those + + align:start position:0% +able to figure out that one of those + + + align:start position:0% +able to figure out that one of those +groups was right the other was wrong + + align:start position:0% +groups was right the other was wrong + + + align:start position:0% +groups was right the other was wrong +very clearly because you could connect + + align:start position:0% +very clearly because you could connect + + + align:start position:0% +very clearly because you could connect +these + + align:start position:0% +these + + + align:start position:0% +these +logarithms uh to an effective field + + align:start position:0% +logarithms uh to an effective field + + + align:start position:0% +logarithms uh to an effective field +Theory and then the whole consistency of + + align:start position:0% +Theory and then the whole consistency of + + + align:start position:0% +Theory and then the whole consistency of +that effective field Theory really + + align:start position:0% +that effective field Theory really + + + align:start position:0% +that effective field Theory really +allows you to to connect this logarithm + + align:start position:0% +allows you to to connect this logarithm + + + align:start position:0% +allows you to to connect this logarithm +to other logarithms and really to build + + align:start position:0% +to other logarithms and really to build + + + align:start position:0% +to other logarithms and really to build +a uh a picture for what's going on with + + align:start position:0% +a uh a picture for what's going on with + + + align:start position:0% +a uh a picture for what's going on with +the physics that makes it totally clear + + align:start position:0% +the physics that makes it totally clear + + + align:start position:0% +the physics that makes it totally clear +what the answer must + + align:start position:0% +what the answer must + + + align:start position:0% +what the answer must +be okay so just to give you an example + + align:start position:0% +be okay so just to give you an example + + + align:start position:0% +be okay so just to give you an example +from my own past + + align:start position:0% + + + + align:start position:0% + +okay so let's now turn to this question + + align:start position:0% +okay so let's now turn to this question + + + align:start position:0% +okay so let's now turn to this question +of the standard model as an effective + + align:start position:0% +of the standard model as an effective + + + align:start position:0% +of the standard model as an effective +field + + align:start position:0% + + + + align:start position:0% + +Theory so we have some over n we're + + align:start position:0% +Theory so we have some over n we're + + + align:start position:0% +Theory so we have some over n we're +treating this from the bottom up so + + align:start position:0% +treating this from the bottom up so + + + align:start position:0% +treating this from the bottom up so +we're going to just talk about what the + + align:start position:0% +we're going to just talk about what the + + + align:start position:0% +we're going to just talk about what the +degrees of freedom are and then + + align:start position:0% +degrees of freedom are and then + + + align:start position:0% +degrees of freedom are and then +think about constructing + + align:start position:0% + + + + align:start position:0% + +operators and part of the job has + + align:start position:0% +operators and part of the job has + + + align:start position:0% +operators and part of the job has +already been done for us because I'm + + align:start position:0% +already been done for us because I'm + + + align:start position:0% +already been done for us because I'm +assuming you have a background in the + + align:start position:0% +assuming you have a background in the + + + align:start position:0% +assuming you have a background in the +standard model at the least at the level + + align:start position:0% +standard model at the least at the level + + + align:start position:0% +standard model at the least at the level +of knowing what the lran is and if you + + align:start position:0% +of knowing what the lran is and if you + + + align:start position:0% +of knowing what the lran is and if you +haven't then you should look at the + + align:start position:0% +haven't then you should look at the + + + align:start position:0% +haven't then you should look at the +quantum field Theory 3 lecture + + align:start position:0% +quantum field Theory 3 lecture + + + align:start position:0% +quantum field Theory 3 lecture +notes so the l0 here is the standard + + align:start position:0% +notes so the l0 here is the standard + + + align:start position:0% +notes so the l0 here is the standard +model as taught in Quantum field Theory + + align:start position:0% + + + + align:start position:0% + +3 so what one most we be interested in + + align:start position:0% +3 so what one most we be interested in + + + align:start position:0% +3 so what one most we be interested in +is the higher order + + align:start position:0% + + + + align:start position:0% + +terms but let me nevertheless remind you + + align:start position:0% +terms but let me nevertheless remind you + + + align:start position:0% +terms but let me nevertheless remind you +of what the degrees of freedom were in + + align:start position:0% +of what the degrees of freedom were in + + + align:start position:0% +of what the degrees of freedom were in +the standard + + align:start position:0% + + + + align:start position:0% + +model so you at least know what the + + align:start position:0% +model so you at least know what the + + + align:start position:0% +model so you at least know what the +players are when we go to talk about + + align:start position:0% + + + + align:start position:0% + +L1 so it's a gauge Theory + + align:start position:0% + + + + align:start position:0% + +so we have + + align:start position:0% +so we have + + + align:start position:0% +so we have +color cross su2 + + align:start position:0% + + + + align:start position:0% + +weak cross the U1 of + + align:start position:0% +weak cross the U1 of + + + align:start position:0% +weak cross the U1 of +hypercharge and so we have eight gluons + + align:start position:0% +hypercharge and so we have eight gluons + + + align:start position:0% +hypercharge and so we have eight gluons +here three weak bons + + align:start position:0% + + + + align:start position:0% + +here and + + align:start position:0% +here and + + + align:start position:0% +here and +one guy here + + align:start position:0% + + + + align:start position:0% + +so just to introduce some notation for + + align:start position:0% +so just to introduce some notation for + + + align:start position:0% +so just to introduce some notation for +Fields I'll call these guys with a index + + align:start position:0% +Fields I'll call these guys with a index + + + align:start position:0% +Fields I'll call these guys with a index +capital a running from 1 to eight these + + align:start position:0% +capital a running from 1 to eight these + + + align:start position:0% +capital a running from 1 to eight these +guys with an index lower a running from + + align:start position:0% +guys with an index lower a running from + + + align:start position:0% +guys with an index lower a running from +1 to three and B here would be + + align:start position:0% +1 to three and B here would be + + + align:start position:0% +1 to three and B here would be +the analog of a photon field for U1 of + + align:start position:0% +the analog of a photon field for U1 of + + + align:start position:0% +the analog of a photon field for U1 of +electromagnetism but this is the U1 of + + align:start position:0% +electromagnetism but this is the U1 of + + + align:start position:0% +electromagnetism but this is the U1 of +hypercharge So it's b b mu so we have + + align:start position:0% +hypercharge So it's b b mu so we have + + + align:start position:0% +hypercharge So it's b b mu so we have +gauge + + align:start position:0% +gauge + + + align:start position:0% +gauge +bosons we have + + align:start position:0% +bosons we have + + + align:start position:0% +bosons we have +Fons let me do the f on over + + align:start position:0% + + + + align:start position:0% + +here so an important thing in thinking + + align:start position:0% +here so an important thing in thinking + + + align:start position:0% +here so an important thing in thinking +about this as an effective field theory + + align:start position:0% +about this as an effective field theory + + + align:start position:0% +about this as an effective field theory +is to note what the mass scales + + align:start position:0% + + + + align:start position:0% + +are so maybe I should do that already + + align:start position:0% +are so maybe I should do that already + + + align:start position:0% +are so maybe I should do that already +here photons are massless that's one + + align:start position:0% +here photons are massless that's one + + + align:start position:0% +here photons are massless that's one +combination of the weak and U1 bow + + align:start position:0% +combination of the weak and U1 bow + + + align:start position:0% +combination of the weak and U1 bow +on gluons are + + align:start position:0% +on gluons are + + + align:start position:0% +on gluons are +massless that's these guys + + align:start position:0% +massless that's these guys + + + align:start position:0% +massless that's these guys +and then there's the mass of the + + align:start position:0% +and then there's the mass of the + + + align:start position:0% +and then there's the mass of the +W 8.42 + + align:start position:0% +W 8.42 + + + align:start position:0% +W 8.42 +GV mass in Z + + align:start position:0% + + + + align:start position:0% + +9119 and for the first time in me + + align:start position:0% +9119 and for the first time in me + + + align:start position:0% +9119 and for the first time in me +teaching this course we also know what + + align:start position:0% +teaching this course we also know what + + + align:start position:0% +teaching this course we also know what +the mass of the higs is so let me just + + align:start position:0% +the mass of the higs is so let me just + + + align:start position:0% +the mass of the higs is so let me just +that's not part of the gauge Theory but + + align:start position:0% +that's not part of the gauge Theory but + + + align:start position:0% +that's not part of the gauge Theory but +I'll just list it there as well since it + + align:start position:0% +I'll just list it there as well since it + + + align:start position:0% +I'll just list it there as well since it +doesn't fit in with the Fons + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% + + + + align:start position:0% + +Fons so you can see that these scales + + align:start position:0% +Fons so you can see that these scales + + + align:start position:0% +Fons so you can see that these scales +here are kind of similar for the firion + + align:start position:0% +here are kind of similar for the firion + + + align:start position:0% +here are kind of similar for the firion +there's a broad spectrum of scales and + + align:start position:0% +there's a broad spectrum of scales and + + + align:start position:0% +there's a broad spectrum of scales and +that's why I wanted to put them all in + + align:start position:0% +that's why I wanted to put them all in + + + align:start position:0% +that's why I wanted to put them all in +one + + align:start position:0% + + + + align:start position:0% + +board so + + align:start position:0% +board so + + + align:start position:0% +board so +quarks up + + align:start position:0% +quarks up + + + align:start position:0% +quarks up +quirks down quirks strange quarks they + + align:start position:0% +quirks down quirks strange quarks they + + + align:start position:0% +quirks down quirks strange quarks they +all come in left and right-handed + + align:start position:0% +all come in left and right-handed + + + align:start position:0% +all come in left and right-handed +guys and the gauge couplings are + + align:start position:0% +guys and the gauge couplings are + + + align:start position:0% +guys and the gauge couplings are +different for left and + + align:start position:0% +different for left and + + + align:start position:0% +different for left and +right-handed for the electro we and U1 + + align:start position:0% +right-handed for the electro we and U1 + + + align:start position:0% +right-handed for the electro we and U1 +parts of the gauge + + align:start position:0% + + + + align:start position:0% + +group so there's six different + + align:start position:0% +group so there's six different + + + align:start position:0% +group so there's six different +flavors and both right and + + align:start position:0% +flavors and both right and + + + align:start position:0% +flavors and both right and +left-handed what masses do we have up + + align:start position:0% +left-handed what masses do we have up + + + align:start position:0% +left-handed what masses do we have up +quirks and down quarks are rather + + align:start position:0% + + + + align:start position:0% + +light but of couple of me + + align:start position:0% + + + + align:start position:0% + +it's hard to measure the light + + align:start position:0% + + + + align:start position:0% + +ones it's a little easier to measure + + align:start position:0% +ones it's a little easier to measure + + + align:start position:0% +ones it's a little easier to measure +everything's going to be in me I'm going + + align:start position:0% +everything's going to be in me I'm going + + + align:start position:0% +everything's going to be in me I'm going +to stop writing + + align:start position:0% +to stop writing + + + align:start position:0% +to stop writing +me oh that's not true I switched to + + align:start position:0% +me oh that's not true I switched to + + + align:start position:0% +me oh that's not true I switched to +G + + align:start position:0% + + + + align:start position:0% + +sorry everything's going to be in + + align:start position:0% + + + + align:start position:0% + +GV oh sorry that's top + + align:start position:0% + + + + align:start position:0% + +cork okay so there's a pretty wide range + + align:start position:0% +cork okay so there's a pretty wide range + + + align:start position:0% +cork okay so there's a pretty wide range +of scales here from an me to 100 + + align:start position:0% +of scales here from an me to 100 + + + align:start position:0% +of scales here from an me to 100 +G let's just the + + align:start position:0% +G let's just the + + + align:start position:0% +G let's just the +quarks then we also have the leptons + + align:start position:0% + + + + align:start position:0% + +three types of charge + + align:start position:0% +three types of charge + + + align:start position:0% +three types of charge +leptons again with a fairly wide range + + align:start position:0% +leptons again with a fairly wide range + + + align:start position:0% +leptons again with a fairly wide range +of + + align:start position:0% + + + + align:start position:0% + +scales so I'm now I'm switching back to + + align:start position:0% +scales so I'm now I'm switching back to + + + align:start position:0% +scales so I'm now I'm switching back to +me just to keep you on your + + align:start position:0% + + + + align:start position:0% + +toes + + align:start position:0% + + + + align:start position:0% + +oops have + + align:start position:0% +oops have + + + align:start position:0% +oops have +neutrinos the left-handed ones we've + + align:start position:0% +neutrinos the left-handed ones we've + + + align:start position:0% +neutrinos the left-handed ones we've +studied much more than anything + + align:start position:0% +studied much more than anything + + + align:start position:0% +studied much more than anything +else and in particular what we know most + + align:start position:0% +else and in particular what we know most + + + align:start position:0% +else and in particular what we know most +about the left-handed guys is Mass + + align:start position:0% +about the left-handed guys is Mass + + + align:start position:0% +about the left-handed guys is Mass +splittings from neutrino + + align:start position:0% +splittings from neutrino + + + align:start position:0% +splittings from neutrino +oscillations these are pretty small + + align:start position:0% + + + + align:start position:0% + +numbers we also know that overall these + + align:start position:0% +numbers we also know that overall these + + + align:start position:0% +numbers we also know that overall these +things are quite + + align:start position:0% +things are quite + + + align:start position:0% +things are quite +light from cosmological constraints and + + align:start position:0% +light from cosmological constraints and + + + align:start position:0% +light from cosmological constraints and +otherwise + + align:start position:0% + + + + align:start position:0% + +and we don't really + + align:start position:0% +and we don't really + + + align:start position:0% +and we don't really +know about anything like a sterile + + align:start position:0% +know about anything like a sterile + + + align:start position:0% +know about anything like a sterile +nutrino that we could put bounds on its + + align:start position:0% +nutrino that we could put bounds on its + + + align:start position:0% +nutrino that we could put bounds on its +mass so even within the standard model + + align:start position:0% +mass so even within the standard model + + + align:start position:0% +mass so even within the standard model +there's a lot of different + + align:start position:0% +there's a lot of different + + + align:start position:0% +there's a lot of different +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +scales and if you think about it from an + + align:start position:0% +scales and if you think about it from an + + + align:start position:0% +scales and if you think about it from an +effective field Theory point of view and + + align:start position:0% +effective field Theory point of view and + + + align:start position:0% +effective field Theory point of view and +you think about it from the top down the + + align:start position:0% +you think about it from the top down the + + + align:start position:0% +you think about it from the top down the +first thing you'd get rid of would be + + align:start position:0% +first thing you'd get rid of would be + + + align:start position:0% +first thing you'd get rid of would be +the top Quirk and then you'd get rid of + + align:start position:0% +the top Quirk and then you'd get rid of + + + align:start position:0% +the top Quirk and then you'd get rid of +the W and the Z and the + + align:start position:0% +the W and the Z and the + + + align:start position:0% +the W and the Z and the +higs and then you would proceed down the + + align:start position:0% +higs and then you would proceed down the + + + align:start position:0% +higs and then you would proceed down the +the next thing to go would be the bottom + + align:start position:0% +the next thing to go would be the bottom + + + align:start position:0% +the next thing to go would be the bottom +cork + + align:start position:0% +cork + + + align:start position:0% +cork +Etc and you could think about + + align:start position:0% +Etc and you could think about + + + align:start position:0% +Etc and you could think about +constructing an effective field Theory + + align:start position:0% +constructing an effective field Theory + + + align:start position:0% +constructing an effective field Theory +by integrating out one at a time getting + + align:start position:0% +by integrating out one at a time getting + + + align:start position:0% +by integrating out one at a time getting +a new effective field Theory every time + + align:start position:0% +a new effective field Theory every time + + + align:start position:0% +a new effective field Theory every time +you remove a degree of Freedom uh you + + align:start position:0% +you remove a degree of Freedom uh you + + + align:start position:0% +you remove a degree of Freedom uh you +could take the standard model and expand + + align:start position:0% +could take the standard model and expand + + + align:start position:0% +could take the standard model and expand +in that fashion that's not the sense in + + align:start position:0% +in that fashion that's not the sense in + + + align:start position:0% +in that fashion that's not the sense in +which we we are thinking about it that + + align:start position:0% +which we we are thinking about it that + + + align:start position:0% +which we we are thinking about it that +would be the top down sense of taking + + align:start position:0% +would be the top down sense of taking + + + align:start position:0% +would be the top down sense of taking +the standard model and deriving + + align:start position:0% +the standard model and deriving + + + align:start position:0% +the standard model and deriving +something else we're thinking of it here + + align:start position:0% +something else we're thinking of it here + + + align:start position:0% +something else we're thinking of it here +in a different context where we have all + + align:start position:0% +in a different context where we have all + + + align:start position:0% +in a different context where we have all +this stuff and we're actually interested + + align:start position:0% +this stuff and we're actually interested + + + align:start position:0% +this stuff and we're actually interested +in thinking about physics at higher + + align:start position:0% +in thinking about physics at higher + + + align:start position:0% +in thinking about physics at higher +energy scale beyond the scale the weak + + align:start position:0% +energy scale beyond the scale the weak + + + align:start position:0% +energy scale beyond the scale the weak +bons beyond the scale the top cork the + + align:start position:0% +bons beyond the scale the top cork the + + + align:start position:0% +bons beyond the scale the top cork the +things we're trying to figure out from + + align:start position:0% +things we're trying to figure out from + + + align:start position:0% +things we're trying to figure out from +the at the + + align:start position:0% +the at the + + + align:start position:0% +the at the +LHC scales we're trying to + + align:start position:0% + + + + align:start position:0% + +probe that's the attitude in this bottom + + align:start position:0% +probe that's the attitude in this bottom + + + align:start position:0% +probe that's the attitude in this bottom +up + + align:start position:0% + + + + align:start position:0% + +approach okay so the lowest order lran + + align:start position:0% +approach okay so the lowest order lran + + + align:start position:0% +approach okay so the lowest order lran +would be the gauge sector the fironic LR + + align:start position:0% +would be the gauge sector the fironic LR + + + align:start position:0% +would be the gauge sector the fironic LR +the higs lran and if we have + + align:start position:0% +the higs lran and if we have + + + align:start position:0% +the higs lran and if we have +right-handed neutrinos we need a lran + + align:start position:0% +right-handed neutrinos we need a lran + + + align:start position:0% +right-handed neutrinos we need a lran +for them + + align:start position:0% +for them + + + align:start position:0% +for them +[Applause] + + align:start position:0% + + + + align:start position:0% + +too so you know these are the topic + + align:start position:0% +too so you know these are the topic + + + align:start position:0% +too so you know these are the topic +these are topics that come up in in qf3 + + align:start position:0% +these are topics that come up in in qf3 + + + align:start position:0% +these are topics that come up in in qf3 +I'm not even going + + align:start position:0% +I'm not even going + + + align:start position:0% +I'm not even going +to touch + + align:start position:0% +to touch + + + align:start position:0% +to touch +them at the + + align:start position:0% +them at the + + + align:start position:0% +them at the +moment I can't give you a complete + + align:start position:0% + + + + align:start position:0% + +review but but just a + + align:start position:0% +review but but just a + + + align:start position:0% +review but but just a +taste emphasizing things that are + + align:start position:0% +taste emphasizing things that are + + + align:start position:0% +taste emphasizing things that are +important so to give you a taste I just + + align:start position:0% +important so to give you a taste I just + + + align:start position:0% +important so to give you a taste I just +write the other two + + align:start position:0% + + + + align:start position:0% + +down which are the prettier Parts + + align:start position:0% + + + + align:start position:0% + +anyway so we have field strengths for + + align:start position:0% +anyway so we have field strengths for + + + align:start position:0% +anyway so we have field strengths for +the kinetic terms for our gauge bosons + + align:start position:0% + + + + align:start position:0% + +and the fironic + + align:start position:0% +and the fironic + + + align:start position:0% +and the fironic +lran I can write it as a sum over the + + align:start position:0% +lran I can write it as a sum over the + + + align:start position:0% +lran I can write it as a sum over the +left-handed + + align:start position:0% +left-handed + + + align:start position:0% +left-handed +Fields Fon coant derivative + + align:start position:0% +Fields Fon coant derivative + + + align:start position:0% +Fields Fon coant derivative +Fon and a sum of right-handed + + align:start position:0% +Fon and a sum of right-handed + + + align:start position:0% +Fon and a sum of right-handed +fields from on covariant + + align:start position:0% +fields from on covariant + + + align:start position:0% +fields from on covariant +derivative from + + align:start position:0% +derivative from + + + align:start position:0% +derivative from +on where this coant derivative is a + + align:start position:0% +on where this coant derivative is a + + + align:start position:0% +on where this coant derivative is a +coant derivative with these gauge + + align:start position:0% +coant derivative with these gauge + + + align:start position:0% +coant derivative with these gauge +Fields so there's some + + align:start position:0% +Fields so there's some + + + align:start position:0% +Fields so there's some +gauge coupling G1 for + + align:start position:0% +gauge coupling G1 for + + + align:start position:0% +gauge coupling G1 for +hypercharge some gauge coupling + + align:start position:0% +hypercharge some gauge coupling + + + align:start position:0% +hypercharge some gauge coupling +G2 for su2 week and some gauge coupling + + align:start position:0% +G2 for su2 week and some gauge coupling + + + align:start position:0% +G2 for su2 week and some gauge coupling +G for + + align:start position:0% + + + + align:start position:0% + +qcd so what is the power + + align:start position:0% +qcd so what is the power + + + align:start position:0% +qcd so what is the power +counting so we've just + + align:start position:0% +counting so we've just + + + align:start position:0% +counting so we've just +said what the degrees of freedom are and + + align:start position:0% +said what the degrees of freedom are and + + + align:start position:0% +said what the degrees of freedom are and +what kind of some of the guiding + + align:start position:0% +what kind of some of the guiding + + + align:start position:0% +what kind of some of the guiding +principles are the symmetries the gauge + + align:start position:0% +principles are the symmetries the gauge + + + align:start position:0% +principles are the symmetries the gauge +symmetry you learn much more about + + align:start position:0% +symmetry you learn much more about + + + align:start position:0% +symmetry you learn much more about +symmetries in Quantum field 33 so I'm + + align:start position:0% +symmetries in Quantum field 33 so I'm + + + align:start position:0% +symmetries in Quantum field 33 so I'm +not going to go into that but those are + + align:start position:0% +not going to go into that but those are + + + align:start position:0% +not going to go into that but those are +basically The Guiding principles in + + align:start position:0% +basically The Guiding principles in + + + align:start position:0% +basically The Guiding principles in +figuring out this L zero what is it that + + align:start position:0% +figuring out this L zero what is it that + + + align:start position:0% +figuring out this L zero what is it that +we would do a Power counting in + + align:start position:0% +we would do a Power counting in + + + align:start position:0% +we would do a Power counting in +here so the power counting in this + + align:start position:0% +here so the power counting in this + + + align:start position:0% +here so the power counting in this +bottom up approach is related to what we + + align:start position:0% +bottom up approach is related to what we + + + align:start position:0% +bottom up approach is related to what we +left out + + align:start position:0% + + + + align:start position:0% + +so we're expanding an Epsilon here where + + align:start position:0% +so we're expanding an Epsilon here where + + + align:start position:0% +so we're expanding an Epsilon here where +Epsilon is mass scales in the standard + + align:start position:0% +Epsilon is mass scales in the standard + + + align:start position:0% +Epsilon is mass scales in the standard +model divided by things that we've left + + align:start position:0% +model divided by things that we've left + + + align:start position:0% +model divided by things that we've left +out of our + + align:start position:0% +out of our + + + align:start position:0% +out of our +description so in the numerator would be + + align:start position:0% +description so in the numerator would be + + + align:start position:0% +description so in the numerator would be +things like the topc mass the W Mass Z + + align:start position:0% +things like the topc mass the W Mass Z + + + align:start position:0% +things like the topc mass the W Mass Z +mass higs mass all the mass scales of + + align:start position:0% +mass higs mass all the mass scales of + + + align:start position:0% +mass higs mass all the mass scales of +the standard model in the denominator + + align:start position:0% +the standard model in the denominator + + + align:start position:0% +the standard model in the denominator +well certainly something like M plank is + + align:start position:0% +well certainly something like M plank is + + + align:start position:0% +well certainly something like M plank is +left out of our description here + + align:start position:0% +left out of our description here + + + align:start position:0% +left out of our description here +if we had some Grand unified theory that + + align:start position:0% +if we had some Grand unified theory that + + + align:start position:0% +if we had some Grand unified theory that +goes in the denominator if we had super + + align:start position:0% +goes in the denominator if we had super + + + align:start position:0% +goes in the denominator if we had super +Symmetry and we broke it that would go + + align:start position:0% +Symmetry and we broke it that would go + + + align:start position:0% +Symmetry and we broke it that would go +in the denominator so from this + + align:start position:0% +in the denominator so from this + + + align:start position:0% +in the denominator so from this +effective field Theory point of view any + + align:start position:0% +effective field Theory point of view any + + + align:start position:0% +effective field Theory point of view any +physics that we've left out of the + + align:start position:0% +physics that we've left out of the + + + align:start position:0% +physics that we've left out of the +standard model description is anything + + align:start position:0% +standard model description is anything + + + align:start position:0% +standard model description is anything +that generates a higher energy scale + + align:start position:0% +that generates a higher energy scale + + + align:start position:0% +that generates a higher energy scale +that goes in the + + align:start position:0% + + + + align:start position:0% + +denominator and this is what we expanded + + align:start position:0% +denominator and this is what we expanded + + + align:start position:0% +denominator and this is what we expanded +so even not knowing something about what + + align:start position:0% +so even not knowing something about what + + + align:start position:0% +so even not knowing something about what +this physics is we can come up with a + + align:start position:0% +this physics is we can come up with a + + + align:start position:0% +this physics is we can come up with a +universal description a universal L1 + + align:start position:0% +universal description a universal L1 + + + align:start position:0% +universal description a universal L1 +that describes Corrections beyond the + + align:start position:0% +that describes Corrections beyond the + + + align:start position:0% +that describes Corrections beyond the +standard + + align:start position:0% + + + + align:start position:0% + +model and what we'll be describing that + + align:start position:0% +model and what we'll be describing that + + + align:start position:0% +model and what we'll be describing that +physics is higher Dimension operators + + align:start position:0% +physics is higher Dimension operators + + + align:start position:0% +physics is higher Dimension operators +operators Beyond Dimension + + align:start position:0% + + + + align:start position:0% + +four but they'll be built out of + + align:start position:0% +four but they'll be built out of + + + align:start position:0% +four but they'll be built out of +standard model + + align:start position:0% + + + + align:start position:0% + +Fields so kind of from your teaching of + + align:start position:0% +Fields so kind of from your teaching of + + + align:start position:0% +Fields so kind of from your teaching of +quantum field Theory it + + align:start position:0% +quantum field Theory it + + + align:start position:0% +quantum field Theory it +maybe Perhaps Perhaps the idea that + + align:start position:0% +maybe Perhaps Perhaps the idea that + + + align:start position:0% +maybe Perhaps Perhaps the idea that +these two things are connected may be + + align:start position:0% +these two things are connected may be + + + align:start position:0% +these two things are connected may be +clear to you but it's something that we + + align:start position:0% +clear to you but it's something that we + + + align:start position:0% +clear to you but it's something that we +will actually + + align:start position:0% + + + + align:start position:0% + +cover mostly next class actually + + align:start position:0% +cover mostly next class actually + + + align:start position:0% +cover mostly next class actually +some some part of the beginning of next + + align:start position:0% +some some part of the beginning of next + + + align:start position:0% +some some part of the beginning of next +class we'll make this connection between + + align:start position:0% +class we'll make this connection between + + + align:start position:0% +class we'll make this connection between +the fact that we want to expand in that + + align:start position:0% +the fact that we want to expand in that + + + align:start position:0% +the fact that we want to expand in that +Epsilon and the fact that we will do in + + align:start position:0% +Epsilon and the fact that we will do in + + + align:start position:0% +Epsilon and the fact that we will do in +doing so we get higher Dimension + + align:start position:0% +doing so we get higher Dimension + + + align:start position:0% +doing so we get higher Dimension +operators will make that absolutely + + align:start position:0% +operators will make that absolutely + + + align:start position:0% +operators will make that absolutely +clear that'll come next + + align:start position:0% +clear that'll come next + + + align:start position:0% +clear that'll come next +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +time so in the remainder of today let me + + align:start position:0% +time so in the remainder of today let me + + + align:start position:0% +time so in the remainder of today let me +just address one final + + align:start position:0% + + + + align:start position:0% + +point and that is the idea of what it + + align:start position:0% +point and that is the idea of what it + + + align:start position:0% +point and that is the idea of what it +means to have a renormalizable field + + align:start position:0% +means to have a renormalizable field + + + align:start position:0% +means to have a renormalizable field +Theory so in our description of the + + align:start position:0% +Theory so in our description of the + + + align:start position:0% +Theory so in our description of the +standard model that I gave here I + + align:start position:0% +standard model that I gave here I + + + align:start position:0% +standard model that I gave here I +mentioned symmetries I mentioned degrees + + align:start position:0% +mentioned symmetries I mentioned degrees + + + align:start position:0% +mentioned symmetries I mentioned degrees +of freedom I didn't mention + + align:start position:0% +of freedom I didn't mention + + + align:start position:0% +of freedom I didn't mention +renormalizability + + align:start position:0% + + + + align:start position:0% + +so what does renormalizable mean so the + + align:start position:0% +so what does renormalizable mean so the + + + align:start position:0% +so what does renormalizable mean so the +traditional definition of what + + align:start position:0% +traditional definition of what + + + align:start position:0% +traditional definition of what +renormalizable mean would be the + + align:start position:0% +renormalizable mean would be the + + + align:start position:0% +renormalizable mean would be the +following you would say a theory is re + + align:start position:0% +following you would say a theory is re + + + align:start position:0% +following you would say a theory is re +normalizable + + align:start position:0% + + + + align:start position:0% + +if at any order in pration + + align:start position:0% + + + + align:start position:0% + +theory in this Quantum field + + align:start position:0% + + + + align:start position:0% + +Theory the UV + + align:start position:0% + + + + align:start position:0% + +divergences can be absorbed so there's + + align:start position:0% +divergences can be absorbed so there's + + + align:start position:0% +divergences can be absorbed so there's +UV divergences from Loop + + align:start position:0% +UV divergences from Loop + + + align:start position:0% +UV divergences from Loop +integrals if they can always be absorbed + + align:start position:0% +integrals if they can always be absorbed + + + align:start position:0% +integrals if they can always be absorbed +into a finite number of parameters then + + align:start position:0% +into a finite number of parameters then + + + align:start position:0% +into a finite number of parameters then +you'd say the theory is re + + align:start position:0% + + + + align:start position:0% + +normalizable but that's a traditional + + align:start position:0% +normalizable but that's a traditional + + + align:start position:0% +normalizable but that's a traditional +definition and we will use a more + + align:start position:0% +definition and we will use a more + + + align:start position:0% +definition and we will use a more +general definition + + align:start position:0% + + + + align:start position:0% + +here certainly this was a guiding + + align:start position:0% +here certainly this was a guiding + + + align:start position:0% +here certainly this was a guiding +principle when people constructed this + + align:start position:0% +principle when people constructed this + + + align:start position:0% +principle when people constructed this +manner + + align:start position:0% + + + + align:start position:0% + +model what is the effective field theory + + align:start position:0% +model what is the effective field theory + + + align:start position:0% +model what is the effective field theory +definition of this + + align:start position:0% +definition of this + + + align:start position:0% +definition of this +it's a little more + + align:start position:0% + + + + align:start position:0% + +General because it brings in the idea of + + align:start position:0% +General because it brings in the idea of + + + align:start position:0% +General because it brings in the idea of +doing power + + align:start position:0% + + + + align:start position:0% + +counting so the effective field Theory's + + align:start position:0% +counting so the effective field Theory's + + + align:start position:0% +counting so the effective field Theory's +definition allows for the possibility of + + align:start position:0% +definition allows for the possibility of + + + align:start position:0% +definition allows for the possibility of +having an infinite number of + + align:start position:0% +having an infinite number of + + + align:start position:0% +having an infinite number of +parameters but at any order that you + + align:start position:0% +parameters but at any order that you + + + align:start position:0% +parameters but at any order that you +truncate the theory there should only be + + align:start position:0% +truncate the theory there should only be + + + align:start position:0% +truncate the theory there should only be +a finite + + align:start position:0% + + + + align:start position:0% + +number so it + + align:start position:0% +number so it + + + align:start position:0% +number so it +says that a theory must be + + align:start position:0% +says that a theory must be + + + align:start position:0% +says that a theory must be +renormalizable order by order + + align:start position:0% +renormalizable order by order + + + align:start position:0% +renormalizable order by order +in its expansion + + align:start position:0% + + + + align:start position:0% + +parameter or if there's more than one + + align:start position:0% +parameter or if there's more than one + + + align:start position:0% +parameter or if there's more than one +it's expansion + + align:start position:0% + + + + align:start position:0% + +parameters so even just this sentence + + align:start position:0% +parameters so even just this sentence + + + align:start position:0% +parameters so even just this sentence +alone tells you why power counting is + + align:start position:0% +alone tells you why power counting is + + + align:start position:0% +alone tells you why power counting is +such an important part of the effective + + align:start position:0% +such an important part of the effective + + + align:start position:0% +such an important part of the effective +Theory because the effective Theory to + + align:start position:0% +Theory because the effective Theory to + + + align:start position:0% +Theory because the effective Theory to +make sense as a normalizable Quantum + + align:start position:0% +make sense as a normalizable Quantum + + + align:start position:0% +make sense as a normalizable Quantum +field Theory needs to know about its + + align:start position:0% +field Theory needs to know about its + + + align:start position:0% +field Theory needs to know about its +expansion parameter saying that it's a + + align:start position:0% +expansion parameter saying that it's a + + + align:start position:0% +expansion parameter saying that it's a +we're normalizable that we can make + + align:start position:0% +we're normalizable that we can make + + + align:start position:0% +we're normalizable that we can make +sense of the theory absorb all the + + align:start position:0% +sense of the theory absorb all the + + + align:start position:0% +sense of the theory absorb all the +Infinities only order by order in + + align:start position:0% +Infinities only order by order in + + + align:start position:0% +Infinities only order by order in +expansion + + align:start position:0% +expansion + + + align:start position:0% +expansion +parameters in + + align:start position:0% + + + + align:start position:0% + +general so it could be that you do some + + align:start position:0% +general so it could be that you do some + + + align:start position:0% +general so it could be that you do some +calculation you en counter some + + align:start position:0% +calculation you en counter some + + + align:start position:0% +calculation you en counter some +divergences but if they're higher order + + align:start position:0% +divergences but if they're higher order + + + align:start position:0% +divergences but if they're higher order +in the expansion than what you need and + + align:start position:0% +in the expansion than what you need and + + + align:start position:0% +in the expansion than what you need and +you have a power counting that tells you + + align:start position:0% +you have a power counting that tells you + + + align:start position:0% +you have a power counting that tells you +that they would be absorbable into some + + align:start position:0% +that they would be absorbable into some + + + align:start position:0% +that they would be absorbable into some +operators that you haven't even written + + align:start position:0% +operators that you haven't even written + + + align:start position:0% +operators that you haven't even written +down you can just drop them + + align:start position:0% + + + + align:start position:0% + +so this definition + + align:start position:0% + + + + align:start position:0% + +allows for an infinite + + align:start position:0% + + + + align:start position:0% + +number of + + align:start position:0% +number of + + + align:start position:0% +number of +parameters that are needed for example + + align:start position:0% +parameters that are needed for example + + + align:start position:0% +parameters that are needed for example +for normalizability + + align:start position:0% +for normalizability + + + align:start position:0% +for normalizability +but only a finite + + align:start position:0% + + + + align:start position:0% + +number at some fixed order + + align:start position:0% + + + + align:start position:0% + +now if you take this logic that I just + + align:start position:0% +now if you take this logic that I just + + + align:start position:0% +now if you take this logic that I just +said to you that you could think about + + align:start position:0% +said to you that you could think about + + + align:start position:0% +said to you that you could think about +things more generally then you can ask + + align:start position:0% +things more generally then you can ask + + + align:start position:0% +things more generally then you can ask +well what was the point of thinking + + align:start position:0% +well what was the point of thinking + + + align:start position:0% +well what was the point of thinking +about the standard model where the + + align:start position:0% +about the standard model where the + + + align:start position:0% +about the standard model where the +theory turned out to be renormalizable + + align:start position:0% +theory turned out to be renormalizable + + + align:start position:0% +theory turned out to be renormalizable +in the traditional sense how does this + + align:start position:0% +in the traditional sense how does this + + + align:start position:0% +in the traditional sense how does this +fact which you know is just a subset of + + align:start position:0% +fact which you know is just a subset of + + + align:start position:0% +fact which you know is just a subset of +this case but an important one how does + + align:start position:0% +this case but an important one how does + + + align:start position:0% +this case but an important one how does +it fit into this rubric from an + + align:start position:0% +it fit into this rubric from an + + + align:start position:0% +it fit into this rubric from an +effective field Theory point of + + align:start position:0% +effective field Theory point of + + + align:start position:0% +effective field Theory point of +view and so the way that that fits in is + + align:start position:0% +view and so the way that that fits in is + + + align:start position:0% +view and so the way that that fits in is +as + + align:start position:0% +as + + + align:start position:0% +as +follows it could turn out that your l0 + + align:start position:0% +follows it could turn out that your l0 + + + align:start position:0% +follows it could turn out that your l0 +in your + + align:start position:0% +in your + + + align:start position:0% +in your +expansion is renormalizable in the + + align:start position:0% +expansion is renormalizable in the + + + align:start position:0% +expansion is renormalizable in the +traditional sense rather than this more + + align:start position:0% +traditional sense rather than this more + + + align:start position:0% +traditional sense rather than this more +General + + align:start position:0% + + + + align:start position:0% + +sense and if that's true what it means + + align:start position:0% +sense and if that's true what it means + + + align:start position:0% +sense and if that's true what it means +is that you don't + + align:start position:0% +is that you don't + + + align:start position:0% +is that you don't +see the higher energy + + align:start position:0% +see the higher energy + + + align:start position:0% +see the higher energy +scales from your lowest order lran + + align:start position:0% + + + + align:start position:0% + +so we do not + + align:start position:0% + + + + align:start position:0% + +know + + align:start position:0% + + + + align:start position:0% + +directly + + align:start position:0% +directly + + + align:start position:0% +directly +about Lambda + + align:start position:0% +about Lambda + + + align:start position:0% +about Lambda +new from just looking at L + + align:start position:0% +new from just looking at L + + + align:start position:0% +new from just looking at L +Zer and that's what happens in the + + align:start position:0% +Zer and that's what happens in the + + + align:start position:0% +Zer and that's what happens in the +standard model we don't really know + + align:start position:0% +standard model we don't really know + + + align:start position:0% +standard model we don't really know +precisely what the high energy scale + + align:start position:0% +precisely what the high energy scale + + + align:start position:0% +precisely what the high energy scale +should be just from studying the effect + + align:start position:0% +should be just from studying the effect + + + align:start position:0% +should be just from studying the effect +from studying the leading orium this + + align:start position:0% +from studying the leading orium this + + + align:start position:0% +from studying the leading orium this +will not always be the case sometimes + + align:start position:0% +will not always be the case sometimes + + + align:start position:0% +will not always be the case sometimes +we'll be in a situation where when we + + align:start position:0% +we'll be in a situation where when we + + + align:start position:0% +we'll be in a situation where when we +study the effective Theory at lowest + + align:start position:0% +study the effective Theory at lowest + + + align:start position:0% +study the effective Theory at lowest +order lran we really find that even in + + align:start position:0% +order lran we really find that even in + + + align:start position:0% +order lran we really find that even in +order to make sense of that as a Quantum + + align:start position:0% +order to make sense of that as a Quantum + + + align:start position:0% +order to make sense of that as a Quantum +field theory that we need to that + + align:start position:0% +field theory that we need to that + + + align:start position:0% +field theory that we need to that +there's a scale that gets generated and + + align:start position:0% +there's a scale that gets generated and + + + align:start position:0% +there's a scale that gets generated and +it's part of our expansion and there's + + align:start position:0% +it's part of our expansion and there's + + + align:start position:0% +it's part of our expansion and there's +some terms that we calculate with L Zer + + align:start position:0% +some terms that we calculate with L Zer + + + align:start position:0% +some terms that we calculate with L Zer +that end up being higher order in our + + align:start position:0% +that end up being higher order in our + + + align:start position:0% +that end up being higher order in our +expansion and and we can't renormalize + + align:start position:0% +expansion and and we can't renormalize + + + align:start position:0% +expansion and and we can't renormalize +the theory unless we actually uh include + + align:start position:0% +the theory unless we actually uh include + + + align:start position:0% +the theory unless we actually uh include +higher Dimension off operators KY + + align:start position:0% +higher Dimension off operators KY + + + align:start position:0% +higher Dimension off operators KY +pration theory is an example of that + + align:start position:0% +pration theory is an example of that + + + align:start position:0% +pration theory is an example of that +type and that's an example that we'll + + align:start position:0% +type and that's an example that we'll + + + align:start position:0% +type and that's an example that we'll +treat so it's not always the case in the + + align:start position:0% +treat so it's not always the case in the + + + align:start position:0% +treat so it's not always the case in the +standard model where it's normalizable + + align:start position:0% +standard model where it's normalizable + + + align:start position:0% +standard model where it's normalizable +in a traditional sense that's a special + + align:start position:0% +in a traditional sense that's a special + + + align:start position:0% +in a traditional sense that's a special +case though it's an important + + align:start position:0% +case though it's an important + + + align:start position:0% +case though it's an important +one so + + align:start position:0% + + + + align:start position:0% + +questions okay so hopefully this has + + align:start position:0% +questions okay so hopefully this has + + + align:start position:0% +questions okay so hopefully this has +been partly a review of some things that + + align:start position:0% +been partly a review of some things that + + + align:start position:0% +been partly a review of some things that +you've thought of of before but putting + + align:start position:0% +you've thought of of before but putting + + + align:start position:0% +you've thought of of before but putting +them together perhaps in a nicer package + + align:start position:0% +them together perhaps in a nicer package + + + align:start position:0% +them together perhaps in a nicer package +and we'll continue next time talking + + align:start position:0% +and we'll continue next time talking + + + align:start position:0% +and we'll continue next time talking +about the standard model as an effective + + align:start position:0% +about the standard model as an effective + + + align:start position:0% +about the standard model as an effective +field Theory what can be gained from + + align:start position:0% +field Theory what can be gained from + + + align:start position:0% +field Theory what can be gained from +that how do we construct The + + align:start position:0% +that how do we construct The + + + align:start position:0% +that how do we construct The +Operators we'll keep going from there \ No newline at end of file diff --git a/WkYdi40yNwY.txt b/WkYdi40yNwY.txt new file mode 100644 index 0000000000000000000000000000000000000000..7f15c1315650f4cb1b8243d76f2a86dfb7580c5a --- /dev/null +++ b/WkYdi40yNwY.txt @@ -0,0 +1,1243 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu and so again we go here back + + align:start position:0% +ocw.mit.edu and so again we go here back + + + align:start position:0% +ocw.mit.edu and so again we go here back +up to the + + align:start position:0% +up to the + + + align:start position:0% +up to the +examples + + align:start position:0% +examples + + + align:start position:0% +examples +intro group Theory + + align:start position:0% +intro group Theory + + + align:start position:0% +intro group Theory +start it + + align:start position:0% + + + + align:start position:0% + +up all right and then our first example + + align:start position:0% +up all right and then our first example + + + align:start position:0% +up all right and then our first example +is group Theory one and it just goes + + align:start position:0% +is group Theory one and it just goes + + + align:start position:0% +is group Theory one and it just goes +through and basically I sort of came up + + align:start position:0% +through and basically I sort of came up + + + align:start position:0% +through and basically I sort of came up +with a way and a spreadsheet to define + + align:start position:0% +with a way and a spreadsheet to define + + + align:start position:0% +with a way and a spreadsheet to define +the functions I was looking at and then + + align:start position:0% +the functions I was looking at and then + + + align:start position:0% +the functions I was looking at and then +start create combinations of them and + + align:start position:0% +start create combinations of them and + + + align:start position:0% +start create combinations of them and +then do very simple tests on + + align:start position:0% +then do very simple tests on + + + align:start position:0% +then do very simple tests on +associativity and and and and distribut + + align:start position:0% +associativity and and and and distribut + + + align:start position:0% +associativity and and and and distribut +and all that stuff if you actually look + + align:start position:0% +and all that stuff if you actually look + + + align:start position:0% +and all that stuff if you actually look +at the tests I do you might be like you + + align:start position:0% +at the tests I do you might be like you + + + align:start position:0% +at the tests I do you might be like you +might blanch and be like really you said + + align:start position:0% +might blanch and be like really you said + + + align:start position:0% +might blanch and be like really you said +that you you you you declared that it + + align:start position:0% +that you you you you declared that it + + + align:start position:0% +that you you you you declared that it +was fully associative it's not like I + + align:start position:0% +was fully associative it's not like I + + + align:start position:0% +was fully associative it's not like I +went and and did formal proofs for every + + align:start position:0% +went and and did formal proofs for every + + + align:start position:0% +went and and did formal proofs for every +these things I just sort of did some + + align:start position:0% +these things I just sort of did some + + + align:start position:0% +these things I just sort of did some +very quick a numerical test uh the semi- + + align:start position:0% +very quick a numerical test uh the semi- + + + align:start position:0% +very quick a numerical test uh the semi- +ring uh test is actually takes a while + + align:start position:0% +ring uh test is actually takes a while + + + align:start position:0% +ring uh test is actually takes a while +here um as you can as you can + + align:start position:0% +here um as you can as you can + + + align:start position:0% +here um as you can as you can +see um and this will take a minute here + + align:start position:0% +see um and this will take a minute here + + + align:start position:0% +see um and this will take a minute here +and + + align:start position:0% +and + + + align:start position:0% +and +it + + align:start position:0% +it + + + align:start position:0% +it +even appears to be hanging oh no it's + + align:start position:0% +even appears to be hanging oh no it's + + + align:start position:0% +even appears to be hanging oh no it's +not good okay we'll let it go through + + align:start position:0% +not good okay we'll let it go through + + + align:start position:0% +not good okay we'll let it go through +that so in fact while it does that we + + align:start position:0% +that so in fact while it does that we + + + align:start position:0% +that so in fact while it does that we +can look at + + align:start position:0% +can look at + + + align:start position:0% +can look at +here look at so basically these were + + align:start position:0% + + + + align:start position:0% + +inputs + + align:start position:0% + + + + align:start position:0% + +that so basically I have kind of my + + align:start position:0% +that so basically I have kind of my + + + align:start position:0% +that so basically I have kind of my +different what I call the sort of the + + align:start position:0% +different what I call the sort of the + + + align:start position:0% +different what I call the sort of the +key function I have Union and + + align:start position:0% +key function I have Union and + + + align:start position:0% +key function I have Union and +intersection and then I have the sort of + + align:start position:0% +intersection and then I have the sort of + + + align:start position:0% +intersection and then I have the sort of +the three possible conditions V1 less + + align:start position:0% +the three possible conditions V1 less + + + align:start position:0% +the three possible conditions V1 less +than V2 V1 equal to V2 V1 greater than + + align:start position:0% +than V2 V1 equal to V2 V1 greater than + + + align:start position:0% +than V2 V1 equal to V2 V1 greater than +V2 and then essentially the different + + align:start position:0% +V2 and then essentially the different + + + align:start position:0% +V2 and then essentially the different +types of of operators you know the + + align:start position:0% +types of of operators you know the + + + align:start position:0% +types of of operators you know the +results that can occur from those and so + + align:start position:0% +results that can occur from those and so + + + align:start position:0% +results that can occur from those and so +this is a CSV file and we read it in as + + align:start position:0% +this is a CSV file and we read it in as + + + align:start position:0% +this is a CSV file and we read it in as +a sociate array and so you know looks + + align:start position:0% +a sociate array and so you know looks + + + align:start position:0% +a sociate array and so you know looks +like a spreadsheet and I can actually + + align:start position:0% +like a spreadsheet and I can actually + + + align:start position:0% +like a spreadsheet and I can actually +have columns named V1 less than V2 you + + align:start position:0% +have columns named V1 less than V2 you + + + align:start position:0% +have columns named V1 less than V2 you +know very powerful and in fact I'm even + + align:start position:0% +know very powerful and in fact I'm even + + + align:start position:0% +know very powerful and in fact I'm even +able to pass that column into the mat + + align:start position:0% +able to pass that column into the mat + + + align:start position:0% +able to pass that column into the mat +lab eval function and have it actually + + align:start position:0% +lab eval function and have it actually + + + align:start position:0% +lab eval function and have it actually +executed which is nice so I can use you + + align:start position:0% +executed which is nice so I can use you + + + align:start position:0% +executed which is nice so I can use you +know I can actually have code in my + + align:start position:0% +know I can actually have code in my + + + align:start position:0% +know I can actually have code in my +column or row names and then have you + + align:start position:0% +column or row names and then have you + + + align:start position:0% +column or row names and then have you +know operations performed based on that + + align:start position:0% +know operations performed based on that + + + align:start position:0% +know operations performed based on that +which is I think a nice thing that you + + align:start position:0% +which is I think a nice thing that you + + + align:start position:0% +which is I think a nice thing that you +can do when you have you know rows when + + align:start position:0% +can do when you have you know rows when + + + align:start position:0% +can do when you have you know rows when +you allow strings to be in your set + + align:start position:0% +you allow strings to be in your set + + + align:start position:0% +you allow strings to be in your set +likewise mat lab will formally parse Nan + + align:start position:0% +likewise mat lab will formally parse Nan + + + align:start position:0% +likewise mat lab will formally parse Nan +as Nan and plus minus infas minus INF + + align:start position:0% +as Nan and plus minus infas minus INF + + + align:start position:0% +as Nan and plus minus infas minus INF +and so I can get all that functionality + + align:start position:0% +and so I can get all that functionality + + + align:start position:0% +and so I can get all that functionality +out of there which is very nice + + align:start position:0% + + + + align:start position:0% + +oops all right and then it goes through + + align:start position:0% +oops all right and then it goes through + + + align:start position:0% +oops all right and then it goes through +let's see here + + align:start position:0% + + + + align:start position:0% + +right and these are just different tests + + align:start position:0% +right and these are just different tests + + + align:start position:0% +right and these are just different tests +that we do on + + align:start position:0% +that we do on + + + align:start position:0% +that we do on +those see how we doing + + align:start position:0% +those see how we doing + + + align:start position:0% +those see how we doing +here almost + + align:start position:0% + + + + align:start position:0% + +done man special + + align:start position:0% +done man special + + + align:start position:0% +done man special +character not a number I sort of yeah I + + align:start position:0% +character not a number I sort of yeah I + + + align:start position:0% +character not a number I sort of yeah I +kind of I like I use that as kind of + + align:start position:0% +kind of I like I use that as kind of + + + align:start position:0% +kind of I like I use that as kind of +like it has a lot of the properties of + + align:start position:0% +like it has a lot of the properties of + + + align:start position:0% +like it has a lot of the properties of +null when you add it to different + + align:start position:0% +null when you add it to different + + + align:start position:0% +null when you add it to different +functions so I kind of I'm just I'm like + + align:start position:0% +functions so I kind of I'm just I'm like + + + align:start position:0% +functions so I kind of I'm just I'm like +yeah I'm using that for that and it and + + align:start position:0% +yeah I'm using that for that and it and + + + align:start position:0% +yeah I'm using that for that and it and +it works out pretty well so it's it's i + + align:start position:0% +it works out pretty well so it's it's i + + + align:start position:0% +it works out pretty well so it's it's i +e failure State modes or whatever it's + + align:start position:0% +e failure State modes or whatever it's + + + align:start position:0% +e failure State modes or whatever it's +how it's supposed to be it it appears + + align:start position:0% +how it's supposed to be it it appears + + + align:start position:0% +how it's supposed to be it it appears +like that you know I can't remember if + + align:start position:0% +like that you know I can't remember if + + + align:start position:0% +like that you know I can't remember if +there's a plus Nan and a negative Nan as + + align:start position:0% +there's a plus Nan and a negative Nan as + + + align:start position:0% +there's a plus Nan and a negative Nan as +well no no it's just Nan yeah yeah yeah + + align:start position:0% +well no no it's just Nan yeah yeah yeah + + + align:start position:0% +well no no it's just Nan yeah yeah yeah +yeah yeah and then actually it goes + + align:start position:0% +yeah yeah and then actually it goes + + + align:start position:0% +yeah yeah and then actually it goes +through here and I + + align:start position:0% +through here and I + + + align:start position:0% +through here and I +think see we doing yeah these just these + + align:start position:0% +think see we doing yeah these just these + + + align:start position:0% +think see we doing yeah these just these +are just various little ways of + + align:start position:0% +are just various little ways of + + + align:start position:0% +are just various little ways of +inputting these are just different + + align:start position:0% +inputting these are just different + + + align:start position:0% +inputting these are just different +values just different little + + align:start position:0% +values just different little + + + align:start position:0% +values just different little +spreadsheets that that you can make for + + align:start position:0% +spreadsheets that that you can make for + + + align:start position:0% +spreadsheets that that you can make for +exploring these different types of + + align:start position:0% +exploring these different types of + + + align:start position:0% +exploring these different types of +things and you can just write them as + + align:start position:0% +things and you can just write them as + + + align:start position:0% +things and you can just write them as +little CSV files very useful construct + + align:start position:0% +little CSV files very useful construct + + + align:start position:0% +little CSV files very useful construct +here I do apologize for the length of + + align:start position:0% +here I do apologize for the length of + + + align:start position:0% +here I do apologize for the length of +time is taking I think um um having the + + align:start position:0% +time is taking I think um um having the + + + align:start position:0% +time is taking I think um um having the +QuickTime video recording going at the + + align:start position:0% +QuickTime video recording going at the + + + align:start position:0% +QuickTime video recording going at the +same time is is causing the poor + + align:start position:0% +same time is is causing the poor + + + align:start position:0% +same time is is causing the poor +computer to to sweat a little bit more + + align:start position:0% +computer to to sweat a little bit more + + + align:start position:0% +computer to to sweat a little bit more +than I than it does normally usually + + align:start position:0% +than I than it does normally usually + + + align:start position:0% +than I than it does normally usually +doesn't take this long so + + align:start position:0% + + + + align:start position:0% + +the outputs that it comes up with so + + align:start position:0% +the outputs that it comes up with so + + + align:start position:0% +the outputs that it comes up with so +these are all it basically writes all + + align:start position:0% +these are all it basically writes all + + + align:start position:0% +these are all it basically writes all +these out + + align:start position:0% + + + + align:start position:0% + +so look at + + align:start position:0% +so look at + + + align:start position:0% +so look at +here this shows I ask it to + + align:start position:0% +here this shows I ask it to + + + align:start position:0% +here this shows I ask it to +basically you + + align:start position:0% +basically you + + + align:start position:0% +basically you +know generate all those 200 pairs so it + + align:start position:0% +know generate all those 200 pairs so it + + + align:start position:0% +know generate all those 200 pairs so it +will do for different each key and every + + align:start position:0% +will do for different each key and every + + + align:start position:0% +will do for different each key and every +whatever it can go and just generate + + align:start position:0% +whatever it can go and just generate + + + align:start position:0% +whatever it can go and just generate +those for me so I just create this + + align:start position:0% +those for me so I just create this + + + align:start position:0% +those for me so I just create this +little thing and it goes through and + + align:start position:0% +little thing and it goes through and + + + align:start position:0% +little thing and it goes through and +just sort of creates this whole function + + align:start position:0% +just sort of creates this whole function + + + align:start position:0% +just sort of creates this whole function +and then writes that out as a CSV itself + + align:start position:0% +and then writes that out as a CSV itself + + + align:start position:0% +and then writes that out as a CSV itself +which is very convenient again these are + + align:start position:0% +which is very convenient again these are + + + align:start position:0% +which is very convenient again these are +things you can do I think this is the + + align:start position:0% +things you can do I think this is the + + + align:start position:0% +things you can do I think this is the +one where we came up with all the felds + + align:start position:0% +one where we came up with all the felds + + + align:start position:0% +one where we came up with all the felds +yeah it doesn't + + align:start position:0% +yeah it doesn't + + + align:start position:0% +yeah it doesn't +really fit there but you can see these + + align:start position:0% +really fit there but you can see these + + + align:start position:0% +really fit there but you can see these +are the pairs that it found and it shows + + align:start position:0% +are the pairs that it found and it shows + + + align:start position:0% +are the pairs that it found and it shows +this is the zero operator and again this + + align:start position:0% +this is the zero operator and again this + + + align:start position:0% +this is the zero operator and again this +is all done with d4m kinds of values + + align:start position:0% +is all done with d4m kinds of values + + + align:start position:0% +is all done with d4m kinds of values +that it can store you know different + + align:start position:0% +that it can store you know different + + + align:start position:0% +that it can store you know different +types of things this is how we made all + + align:start position:0% +types of things this is how we made all + + + align:start position:0% +types of things this is how we made all +the tables that are in the uh there oh + + align:start position:0% +the tables that are in the uh there oh + + + align:start position:0% +the tables that are in the uh there oh +it's writing out results that means it's + + align:start position:0% + + + + align:start position:0% + +done there we go and so the main one I + + align:start position:0% +done there we go and so the main one I + + + align:start position:0% +done there we go and so the main one I +just want to show you is that you we + + align:start position:0% +just want to show you is that you we + + + align:start position:0% +just want to show you is that you we +read in that function Funk range and we + + align:start position:0% +read in that function Funk range and we + + + align:start position:0% +read in that function Funk range and we +permuted it and if we do display full a + + align:start position:0% + + + + align:start position:0% + +funk you can see there's the full + + align:start position:0% +funk you can see there's the full + + + align:start position:0% +funk you can see there's the full +combination of values as we saw there so + + align:start position:0% +combination of values as we saw there so + + + align:start position:0% +combination of values as we saw there so +there's really nothing here for you it's + + align:start position:0% +there's really nothing here for you it's + + + align:start position:0% +there's really nothing here for you it's +not I expect you to go using um d4m to + + align:start position:0% +not I expect you to go using um d4m to + + + align:start position:0% +not I expect you to go using um d4m to +do group Theory things so there's not + + align:start position:0% +do group Theory things so there's not + + + align:start position:0% +do group Theory things so there's not +really the point of these examples I I + + align:start position:0% +really the point of these examples I I + + + align:start position:0% +really the point of these examples I I +did it's more just showing that you can + + align:start position:0% +did it's more just showing that you can + + + align:start position:0% +did it's more just showing that you can +you know when you when you go into this + + align:start position:0% +you know when you when you go into this + + + align:start position:0% +you know when you when you go into this +larger space problems that you might not + + align:start position:0% +larger space problems that you might not + + + align:start position:0% +larger space problems that you might not +solve linear algebraically all of a + + align:start position:0% +solve linear algebraically all of a + + + align:start position:0% +solve linear algebraically all of a +sudden it's like oh yeah I you know if I + + align:start position:0% +sudden it's like oh yeah I you know if I + + + align:start position:0% +sudden it's like oh yeah I you know if I +have strings and other types of things + + align:start position:0% +have strings and other types of things + + + align:start position:0% +have strings and other types of things +it really opens up the flexibility and I + + align:start position:0% +it really opens up the flexibility and I + + + align:start position:0% +it really opens up the flexibility and I +thought that was very neat that you + + align:start position:0% +thought that was very neat that you + + + align:start position:0% +thought that was very neat that you +could do this and it it just handled the + + align:start position:0% +could do this and it it just handled the + + + align:start position:0% +could do this and it it just handled the +data very nicely and without any any + + align:start position:0% +data very nicely and without any any + + + align:start position:0% +data very nicely and without any any +real uh any real difficulty so um so + + align:start position:0% +real uh any real difficulty so um so + + + align:start position:0% +real uh any real difficulty so um so +with that that's the end of this lecture + + align:start position:0% +with that that's the end of this lecture + + + align:start position:0% +with that that's the end of this lecture +um I don't know if there's any CL final + + align:start position:0% +um I don't know if there's any CL final + + + align:start position:0% +um I don't know if there's any CL final +question questions before we proceed all + + align:start position:0% +question questions before we proceed all + + + align:start position:0% +question questions before we proceed all +right very good and please if you + + align:start position:0% +right very good and please if you + + + align:start position:0% +right very good and please if you +haven't signed up on the sheet please + + align:start position:0% +haven't signed up on the sheet please + + + align:start position:0% +haven't signed up on the sheet please +please do please do so thank you very + + align:start position:0% +please do please do so thank you very + + + align:start position:0% +please do please do so thank you very +much \ No newline at end of file diff --git a/X-krLprDrOI.txt b/X-krLprDrOI.txt new file mode 100644 index 0000000000000000000000000000000000000000..f8ba6c52dfa29993f9595d5623f84bb7aec2982d --- /dev/null +++ b/X-krLprDrOI.txt @@ -0,0 +1,1115 @@ +align:start position:0% + +in all of the examples that we have seen + + align:start position:0% +in all of the examples that we have seen + + + align:start position:0% +in all of the examples that we have seen +so far we have calculated the + + align:start position:0% +so far we have calculated the + + + align:start position:0% +so far we have calculated the +distribution of a random variable Y + + align:start position:0% +distribution of a random variable Y + + + align:start position:0% +distribution of a random variable Y +which is defined as a function of + + align:start position:0% +which is defined as a function of + + + align:start position:0% +which is defined as a function of +another random variable X what about the + + align:start position:0% +another random variable X what about the + + + align:start position:0% +another random variable X what about the +case where we define a random variable Z + + align:start position:0% +case where we define a random variable Z + + + align:start position:0% +case where we define a random variable Z +as a function of multiple random + + align:start position:0% +as a function of multiple random + + + align:start position:0% +as a function of multiple random +variables for example as here as a + + align:start position:0% +variables for example as here as a + + + align:start position:0% +variables for example as here as a +function of two random variables how can + + align:start position:0% +function of two random variables how can + + + align:start position:0% +function of two random variables how can +we find the distribution of Z the + + align:start position:0% +we find the distribution of Z the + + + align:start position:0% +we find the distribution of Z the +general methodology is exactly the same + + align:start position:0% +general methodology is exactly the same + + + align:start position:0% +general methodology is exactly the same +we somehow calculate the CDF of the + + align:start position:0% +we somehow calculate the CDF of the + + + align:start position:0% +we somehow calculate the CDF of the +random variable Z and then differentiate + + align:start position:0% +random variable Z and then differentiate + + + align:start position:0% +random variable Z and then differentiate +to find its PDF let us illustrate this + + align:start position:0% +to find its PDF let us illustrate this + + + align:start position:0% +to find its PDF let us illustrate this +methodology with a simple example so + + align:start position:0% +methodology with a simple example so + + + align:start position:0% +methodology with a simple example so +suppose that x and y are independent + + align:start position:0% +suppose that x and y are independent + + + align:start position:0% +suppose that x and y are independent +random variables and each one of them is + + align:start position:0% +random variables and each one of them is + + + align:start position:0% +random variables and each one of them is +uniform on the unit interval so their + + align:start position:0% +uniform on the unit interval so their + + + align:start position:0% +uniform on the unit interval so their +Joint Distribution is going to be a + + align:start position:0% +Joint Distribution is going to be a + + + align:start position:0% +Joint Distribution is going to be a +uniform PDF on the unit square we are + + align:start position:0% +uniform PDF on the unit square we are + + + align:start position:0% +uniform PDF on the unit square we are +interested in the random variable which + + align:start position:0% +interested in the random variable which + + + align:start position:0% +interested in the random variable which +is defined as the ratio of Y divided by + + align:start position:0% +is defined as the ratio of Y divided by + + + align:start position:0% +is defined as the ratio of Y divided by +X so we will now calculate the CDF of Z + + align:start position:0% +X so we will now calculate the CDF of Z + + + align:start position:0% +X so we will now calculate the CDF of Z +and then differentiate it is useful to + + align:start position:0% +and then differentiate it is useful to + + + align:start position:0% +and then differentiate it is useful to +work in terms of a diagram this is + + align:start position:0% +work in terms of a diagram this is + + + align:start position:0% +work in terms of a diagram this is +essentially our sample space the unit + + align:start position:0% +essentially our sample space the unit + + + align:start position:0% +essentially our sample space the unit +square the PDF of X is 1 on the unit + + align:start position:0% +square the PDF of X is 1 on the unit + + + align:start position:0% +square the PDF of X is 1 on the unit +interval the PDF of y is 1 on the unit + + align:start position:0% +interval the PDF of y is 1 on the unit + + + align:start position:0% +interval the PDF of y is 1 on the unit +interval because of independence the + + align:start position:0% +interval because of independence the + + + align:start position:0% +interval because of independence the +joint PDF is the product of their + + align:start position:0% +joint PDF is the product of their + + + align:start position:0% +joint PDF is the product of their +individual PDFs so the joint PDF is + + align:start position:0% +individual PDFs so the joint PDF is + + + align:start position:0% +individual PDFs so the joint PDF is +equal to 1 throughout this unit square + + align:start position:0% +equal to 1 throughout this unit square + + + align:start position:0% +equal to 1 throughout this unit square +so now let us write an expression for + + align:start position:0% +so now let us write an expression for + + + align:start position:0% +so now let us write an expression for +the CDF of Z which by definition is the + + align:start position:0% +the CDF of Z which by definition is the + + + align:start position:0% +the CDF of Z which by definition is the +probability that the random variable Z + + align:start position:0% +probability that the random variable Z + + + align:start position:0% +probability that the random variable Z +which in our case is Y divided by X is + + align:start position:0% +which in our case is Y divided by X is + + + align:start position:0% +which in our case is Y divided by X is +less than or equal than a certain number + + align:start position:0% +less than or equal than a certain number + + + align:start position:0% +less than or equal than a certain number +little Z what is the probability of this + + align:start position:0% +little Z what is the probability of this + + + align:start position:0% +little Z what is the probability of this +event + + align:start position:0% +event + + + align:start position:0% +event +let us consider a few different cases + + align:start position:0% +let us consider a few different cases + + + align:start position:0% +let us consider a few different cases +suppose that Z is negative what is the + + align:start position:0% +suppose that Z is negative what is the + + + align:start position:0% +suppose that Z is negative what is the +probability that this ratio is negative + + align:start position:0% +probability that this ratio is negative + + + align:start position:0% +probability that this ratio is negative +well since x and y are non-negative + + align:start position:0% +well since x and y are non-negative + + + align:start position:0% +well since x and y are non-negative +numbers there is no way that the ratio + + align:start position:0% +numbers there is no way that the ratio + + + align:start position:0% +numbers there is no way that the ratio +is going to be negative so if Z little Z + + align:start position:0% +is going to be negative so if Z little Z + + + align:start position:0% +is going to be negative so if Z little Z +is a negative number the probability of + + align:start position:0% +is a negative number the probability of + + + align:start position:0% +is a negative number the probability of +this event is going to be equal to 0 + + align:start position:0% +this event is going to be equal to 0 + + + align:start position:0% +this event is going to be equal to 0 +this is the easier case now suppose that + + align:start position:0% +this is the easier case now suppose that + + + align:start position:0% +this is the easier case now suppose that +Z is a positive number let us draw a + + align:start position:0% +Z is a positive number let us draw a + + + align:start position:0% +Z is a positive number let us draw a +line that has a slope of little Z Y over + + align:start position:0% +line that has a slope of little Z Y over + + + align:start position:0% +line that has a slope of little Z Y over +X being less than or equal to little Z + + align:start position:0% +X being less than or equal to little Z + + + align:start position:0% +X being less than or equal to little Z +is the same as saying that Y is less + + align:start position:0% +is the same as saying that Y is less + + + align:start position:0% +is the same as saying that Y is less +than or equal to little Z times X this + + align:start position:0% +than or equal to little Z times X this + + + align:start position:0% +than or equal to little Z times X this +is the line on which Y is equal to Z + + align:start position:0% +is the line on which Y is equal to Z + + + align:start position:0% +is the line on which Y is equal to Z +times X so below that line y is going to + + align:start position:0% +times X so below that line y is going to + + + align:start position:0% +times X so below that line y is going to +be less than or equal to Z times X so + + align:start position:0% +be less than or equal to Z times X so + + + align:start position:0% +be less than or equal to Z times X so +the event of interest is actually this + + align:start position:0% +the event of interest is actually this + + + align:start position:0% +the event of interest is actually this +triangle here and the probability of + + align:start position:0% +triangle here and the probability of + + + align:start position:0% +triangle here and the probability of +this event since we're dealing with a + + align:start position:0% +this event since we're dealing with a + + + align:start position:0% +this event since we're dealing with a +uniform distribution on the unit square + + align:start position:0% +uniform distribution on the unit square + + + align:start position:0% +uniform distribution on the unit square +is just the area of this triangle now + + align:start position:0% +is just the area of this triangle now + + + align:start position:0% +is just the area of this triangle now +since this line rises at slope Z this + + align:start position:0% +since this line rises at slope Z this + + + align:start position:0% +since this line rises at slope Z this +point here this intercept is at Z and so + + align:start position:0% +point here this intercept is at Z and so + + + align:start position:0% +point here this intercept is at Z and so +these sides of the triangle are 1 and Z + + align:start position:0% +these sides of the triangle are 1 and Z + + + align:start position:0% +these sides of the triangle are 1 and Z +and so this formula here gives us the + + align:start position:0% +and so this formula here gives us the + + + align:start position:0% +and so this formula here gives us the +value of the CDF for the case where + + align:start position:0% +value of the CDF for the case where + + + align:start position:0% +value of the CDF for the case where +little Z is positive and the same + + align:start position:0% +little Z is positive and the same + + + align:start position:0% +little Z is positive and the same +formula would also be true if Z also + + align:start position:0% +formula would also be true if Z also + + + align:start position:0% +formula would also be true if Z also +were equal to 0 in which case we get + + align:start position:0% +were equal to 0 in which case we get + + + align:start position:0% +were equal to 0 in which case we get +zero probability but is this correct for + + align:start position:0% +zero probability but is this correct for + + + align:start position:0% +zero probability but is this correct for +all positive Z's well not really this + + align:start position:0% +all positive Z's well not really this + + + align:start position:0% +all positive Z's well not really this +calculation was based on this picture + + align:start position:0% +calculation was based on this picture + + + align:start position:0% +calculation was based on this picture +and in this picture this line + + align:start position:0% +and in this picture this line + + + align:start position:0% +and in this picture this line +intercepted this side of the unit Square + + align:start position:0% +intercepted this side of the unit Square + + + align:start position:0% +intercepted this side of the unit Square +and for that to happen this slope must + + align:start position:0% +and for that to happen this slope must + + + align:start position:0% +and for that to happen this slope must +be less than or equal to one so this + + align:start position:0% +be less than or equal to one so this + + + align:start position:0% +be less than or equal to one so this +formula is only correct in the case + + align:start position:0% +formula is only correct in the case + + + align:start position:0% +formula is only correct in the case +where we have a slope of less than or + + align:start position:0% +where we have a slope of less than or + + + align:start position:0% +where we have a slope of less than or +equal to one and now we need to deal + + align:start position:0% +equal to one and now we need to deal + + + align:start position:0% +equal to one and now we need to deal +with the remaining case in which little + + align:start position:0% +with the remaining case in which little + + + align:start position:0% +with the remaining case in which little +Z is strictly larger than one in this + + align:start position:0% +Z is strictly larger than one in this + + + align:start position:0% +Z is strictly larger than one in this +case we get a somewhat different picture + + align:start position:0% +case we get a somewhat different picture + + + align:start position:0% +case we get a somewhat different picture +if we draw a line with slope again + + align:start position:0% +if we draw a line with slope again + + + align:start position:0% +if we draw a line with slope again +little Z because little Z is bigger than + + align:start position:0% +little Z because little Z is bigger than + + + align:start position:0% +little Z because little Z is bigger than +1 it's going to intercept this side of + + align:start position:0% +1 it's going to intercept this side of + + + align:start position:0% +1 it's going to intercept this side of +the rectum + + align:start position:0% +the rectum + + + align:start position:0% +the rectum +now the event that y over X is less than + + align:start position:0% +now the event that y over X is less than + + + align:start position:0% +now the event that y over X is less than +or equal to little Z is again the event + + align:start position:0% +or equal to little Z is again the event + + + align:start position:0% +or equal to little Z is again the event +that the pair XY lies below this line + + align:start position:0% +that the pair XY lies below this line + + + align:start position:0% +that the pair XY lies below this line +that has a slope of Z so all we need is + + align:start position:0% +that has a slope of Z so all we need is + + + align:start position:0% +that has a slope of Z so all we need is +to find the area of this region one way + + align:start position:0% +to find the area of this region one way + + + align:start position:0% +to find the area of this region one way +of finding the area of this region is to + + align:start position:0% +of finding the area of this region is to + + + align:start position:0% +of finding the area of this region is to +take the area of the entire unit square + + align:start position:0% +take the area of the entire unit square + + + align:start position:0% +take the area of the entire unit square +which is equal to one and subtract the + + align:start position:0% +which is equal to one and subtract the + + + align:start position:0% +which is equal to one and subtract the +area of this triangle what is the area + + align:start position:0% +area of this triangle what is the area + + + align:start position:0% +area of this triangle what is the area +of this triangle well since this line + + align:start position:0% +of this triangle well since this line + + + align:start position:0% +of this triangle well since this line +has a slope of Z in order for it to rise + + align:start position:0% +has a slope of Z in order for it to rise + + + align:start position:0% +has a slope of Z in order for it to rise +to a value of 1 X must be equal to 1 + + align:start position:0% +to a value of 1 X must be equal to 1 + + + align:start position:0% +to a value of 1 X must be equal to 1 +over little Z therefore this side of the + + align:start position:0% +over little Z therefore this side of the + + + align:start position:0% +over little Z therefore this side of the +triangle is 1 over Z and therefore the + + align:start position:0% +triangle is 1 over Z and therefore the + + + align:start position:0% +triangle is 1 over Z and therefore the +area of the triangle is 1/2 times 1 over + + align:start position:0% +area of the triangle is 1/2 times 1 over + + + align:start position:0% +area of the triangle is 1/2 times 1 over +Z which is this expression here and so + + align:start position:0% +Z which is this expression here and so + + + align:start position:0% +Z which is this expression here and so +we have found the value of the CDF for + + align:start position:0% +we have found the value of the CDF for + + + align:start position:0% +we have found the value of the CDF for +all possible choices of little Z we can + + align:start position:0% +all possible choices of little Z we can + + + align:start position:0% +all possible choices of little Z we can +draw the CDF + + align:start position:0% + + + + align:start position:0% + +and the picture is as follows for zi- + + align:start position:0% +and the picture is as follows for zi- + + + align:start position:0% +and the picture is as follows for zi- +the CDF is equal to 0 for Z between 0 & + + align:start position:0% +the CDF is equal to 0 for Z between 0 & + + + align:start position:0% +the CDF is equal to 0 for Z between 0 & +1 the CDF Rises linearly at the slope of + + align:start position:0% +1 the CDF Rises linearly at the slope of + + + align:start position:0% +1 the CDF Rises linearly at the slope of +1/2 and so when Z is equal to 1 the CDF + + align:start position:0% +1/2 and so when Z is equal to 1 the CDF + + + align:start position:0% +1/2 and so when Z is equal to 1 the CDF +has reason to value of 1/2 and then as Z + + align:start position:0% +has reason to value of 1/2 and then as Z + + + align:start position:0% +has reason to value of 1/2 and then as Z +goes to infinity this term disappears + + align:start position:0% +goes to infinity this term disappears + + + align:start position:0% +goes to infinity this term disappears +and the CDF will converge to 1 so it + + align:start position:0% +and the CDF will converge to 1 so it + + + align:start position:0% +and the CDF will converge to 1 so it +converges to 1 monotonically but in a + + align:start position:0% +converges to 1 monotonically but in a + + + align:start position:0% +converges to 1 monotonically but in a +nonlinear fashion so we get a picture of + + align:start position:0% +nonlinear fashion so we get a picture of + + + align:start position:0% +nonlinear fashion so we get a picture of +this type the next step the final step + + align:start position:0% +this type the next step the final step + + + align:start position:0% +this type the next step the final step +is to differentiate the CDF and obtain + + align:start position:0% +is to differentiate the CDF and obtain + + + align:start position:0% +is to differentiate the CDF and obtain +the PDF + + align:start position:0% + + + + align:start position:0% + +in this region the CDF is constant so + + align:start position:0% +in this region the CDF is constant so + + + align:start position:0% +in this region the CDF is constant so +it's derivative is going to be equal to + + align:start position:0% +it's derivative is going to be equal to + + + align:start position:0% +it's derivative is going to be equal to +zero in this region the CDF is linear so + + align:start position:0% +zero in this region the CDF is linear so + + + align:start position:0% +zero in this region the CDF is linear so +it's derivative is equal to this factor + + align:start position:0% +it's derivative is equal to this factor + + + align:start position:0% +it's derivative is equal to this factor +of one-half so the CDF is equal to + + align:start position:0% +of one-half so the CDF is equal to + + + align:start position:0% +of one-half so the CDF is equal to +one-half for these between 0 and 1 and + + align:start position:0% +one-half for these between 0 and 1 and + + + align:start position:0% +one-half for these between 0 and 1 and +finally in this region this is the + + align:start position:0% +finally in this region this is the + + + align:start position:0% +finally in this region this is the +formula for the CDF when we take the + + align:start position:0% +formula for the CDF when we take the + + + align:start position:0% +formula for the CDF when we take the +derivative we get the expression 1 over + + align:start position:0% +derivative we get the expression 1 over + + + align:start position:0% +derivative we get the expression 1 over +2 Z squared which is a function that + + align:start position:0% +2 Z squared which is a function that + + + align:start position:0% +2 Z squared which is a function that +decreases as Z goes to infinity so it + + align:start position:0% +decreases as Z goes to infinity so it + + + align:start position:0% +decreases as Z goes to infinity so it +has a shape like this one so we have + + align:start position:0% +has a shape like this one so we have + + + align:start position:0% +has a shape like this one so we have +completed the solution to this problem + + align:start position:0% +completed the solution to this problem + + + align:start position:0% +completed the solution to this problem +we found the CDF and we found the + + align:start position:0% +we found the CDF and we found the + + + align:start position:0% +we found the CDF and we found the +corresponding PDF this methodology works + + align:start position:0% +corresponding PDF this methodology works + + + align:start position:0% +corresponding PDF this methodology works +more generally for more complicated + + align:start position:0% +more generally for more complicated + + + align:start position:0% +more generally for more complicated +functions of x and y and for more + + align:start position:0% +functions of x and y and for more + + + align:start position:0% +functions of x and y and for more +complicated distributions for x and y of + + align:start position:0% +complicated distributions for x and y of + + + align:start position:0% +complicated distributions for x and y of +course when the functions or the + + align:start position:0% +course when the functions or the + + + align:start position:0% +course when the functions or the +distributions are more complicated the + + align:start position:0% +distributions are more complicated the + + + align:start position:0% +distributions are more complicated the +calculus involved in the geometry may + + align:start position:0% +calculus involved in the geometry may + + + align:start position:0% +calculus involved in the geometry may +require a lot more work but conceptually + + align:start position:0% +require a lot more work but conceptually + + + align:start position:0% +require a lot more work but conceptually +the methodology is exactly the same \ No newline at end of file diff --git a/X5ch4xZf3LE.txt b/X5ch4xZf3LE.txt new file mode 100644 index 0000000000000000000000000000000000000000..8d55fe9e69e8b52bab616199d21d12fa32297180 --- /dev/null +++ b/X5ch4xZf3LE.txt @@ -0,0 +1,640 @@ +Hi. + +In this problem, we have an +absent-minded professor who + +will inadvertently give us some +practice with exponential + +random variables. + +So the professor has made two +appointments with two students + +and inadvertently made them +at the same time. + +And what we do is we model the +duration of these appointments + +with an exponential +random variable. + +So remember, an exponential +random variable is a + +continuous random variable that +takes on non-negative + +values, and it's parametrized +by a rate parameter, lambda. + +And the exponential random +variable is often used to + +model durations of time-- so +time until something happens, + +so for example, in this case, +time until the student leaves + +or the appointment is over. + +Or sometimes you will also use +it to be as a model of time + +until something fails. + + + +And one thing that will be +useful is the CDF of this + +exponential random variable. + +So the probability that it's +less than or equal to some + +value, little t, is equal to 1 +minus e to the minus lambda t. + +So this is, of course, valid +only when t is non-negative. + +The other useful property is +that the expected value of an + +exponential random variable +is just 1 over + +the parameter lambda. + +And the last thing that we'll +use specifically in this + +problem is the memory +list property of + +exponential random variables. + +And so recall that that just +means that if you pop in the + +middle of an exponential +random variable, the + +distribution for that random +variable going forward from + +the point where you popped in +is exactly the same as if it + +had just started over. + +So that's why we call it the +memory list property. + +Basically, the past doesn't +really matter, and going + +forward from whatever point +that you observe it at, it + +looks as if it had just +started over afresh. + +And last thing we'll use, which +is a review of a concept + +from earlier, is total +expectation. + +So let's actually model +this problem + +with two random variables. + +Let's let T1 be the time that +the first student takes in the + +appointment and T2 be the time +that the second student takes. + +And what we're told in the +problem is that they're both + +exponential with mean +30 minutes. + +So remember the mean being 30 +minutes means that the lambda + +is 1 over the mean. + +And so the lambda in this +case would be 1/30. + +And importantly, we're also +told that they are + +independent. + +So how long the first person +takes is independent of how + +long the second person takes. + +So the first student arrives on +time and take some random + +amount of time, T1. + +The second student arrives +exactly five minutes late. + +And whatever the second person +meets with the professor, that + +student will then take some +random amount of time, T2. + +What we're asked to do is find +the expected time between when + +the first student arrives-- + +so we can just call +that time 0-- + +and when the second +student leaves. + +Now you may say, well we're +dealing with expectations, so + +it's easier. + +And in this case, it probably is +just the expectation of how + +long the first student takes +plus the expectation of how + +long the second student takes. + +So it should be about 60 minutes +or exactly 60 minutes. + +Now, why is that not +exactly right? + +It's because there is a small +wrinkle, that the students may + +not go exactly back to back. + +So let's actually draw out a +time frame of what might + +actually happen. + +So here's time 0, when the +first student arrives. + +And the first will go for some +amount of time and leave. + +And now let's consider +two scenarios. + +One scenario is that the first +student takes more than five + +minutes to complete. + +Well then the second student +will have arrived at 5 minutes + +and then will be already waiting +whenever this first + +student leaves. + +So then the second student will + +immediately pick up and continue. + +And in that case, we do have two +exponentials back to back. + +But there could be another +situation. + +Suppose that the first student +didn't take very long at all + +and finished within five +minutes, in which case the + +second student hasn't +arrived yet. + +So this professor is idle +in between here. + +And so we actually don't +necessarily have two of them + +going back to back. + +So there's an empty period in +between that we have to + +account for. + +So with that in mind, we see +that we have two scenarios. + +And so what does that +beg to use? + +Well, we can split them up into +the two scenarios and + +then calculate expectations +with each one and then use + +total expectation to +find the overall + +expected length of time. + +OK, so let's begin with +the first scenario. + + + +The first scenario is that, +let's say, the first student + +finished within five minutes. + +So what does that mean in terms +of the definitions that + +we've used? + +That means T1 is less +than or equal to 5. + +So if the first student took +less than five minutes, then + +what happens? + +Then we know that the +amount of time that + +you'd need to take-- + + + +let's call that something +else. + +Let's call that X. So X is the +random variable that we're + +interested in, the time between +when the first student + +comes and the second +student leaves. + +This is the value that +we want to find. + +Well we know that we're +guaranteed that there will be + +a five-minute interval. + +So first student will come, +and then the second person + +will take over. + +So we're guaranteed that the +first five minutes will be the + +difference between when time +starts and when the second + +student arrives. + +And then, after that, it's just +however long the second + +student takes, which is just +the expected value of T2. + +And T2 is a exponential random +variable with mean 30. + +So in this case, it's just 35. + + + +So the first student doesn't +take very long. + +Then we just get the five +minutes, that little buffer, + +plus however long the second +student takes, which, on + +average, is 30 minutes. + +Now what is the probability +of this happening? + +The probability of this +happening is the probability + +that the first student takes +less than five minutes. + +And here is where we use the CDF +that we wrote out earlier. + +It's going to be 1 minus e +to the minus lambda t. + +So in this case, t is five +and lambda is 1/30. + +So it's minus 5/30 is +the probability. + +All right, now let's consider +the second case. + +The second case is that the +first student actually takes + +longer than five minutes. + +OK, so what happens +in that case? + +Here's five minutes. + +The first student came +to five minutes. + +The second student arrived, +and the first + +student is still going. + +So he goes for some +amount of time. + +And then whenever he finishes, +the second student continues. + +So now the question is, what +is the total amount of + +time in this case? + +Well, you can think +of it as using + +the memory list property. + +This is where it comes in. + +So the first five minutes, we +know that it was already taken + +because we're considering the +second scenario, which we're + +given that T1 is +greater than 5. + +And so the question now is, if +we know that, how much longer + +does it take? + +How much longer past the +five-minute mark does the + +first student take? + +And by the member list property, +we know that it's as + +if the first student +started over. + +So there was no memory of the +first five minutes, and it's + +as if the first student just +arrived also at the + +five-minute mark and met +with the professor. + +So past the five-minute mark, +it's as if you have a new + +exponential random variable, +still with mean 30. + +And so what we get is that, +in this case, you get the + +guaranteed five minutes, and +then you get the memory list + +continuation of the first +student's appointment. + +So you get another 30 minutes +on average because of the + +memory list property. + +And then whenever the first +student finally does finish + +up, the second student will +immediately take over because + +he has already arrived. + +It's past the five-minute +mark. + +And then that second student +will take, again, on average, + +30 more minutes. + +So what you get is, in this +case, the appointment lasts 65 + +minutes on average. + +Now what is the probability +of this case? + +The probability of this case is +the probability that T1 is + +greater than 5. + +And now we know that that is +just the complement of this, 1 + +minus that. + +So it's just e to +the minus 5/30. + + + +So now we have both scenarios. + +We have the probabilities of +each scenario, and we have the + +expectation under +each scenario. + +Now all that remains now is to +combine them using total + +expectation. + + + +So I really should have written +expectation of X given + +T1 is less than or +equal to 5 here. + +And this is expectation +of X given that T1 is + +greater than 5. + +So expectation of X overall is +the probability that T1 is + +less than or equal to 5 times +the expectation of X given + +that T1 is less than or equal to +5 plus the probability that + +T1 is greater than 5 times the +expectation of X given that T1 + +is greater than 5. + +And we have all four of +these pieces here. + +so it's 35 times 1 minus e to +the minus 5/30 plus 65 times e + +to the minus 5 5/30. + +And it turns out that this +is approximately + +equal to 60.394 minutes. + +All right, so what +have we found? + +We found that the original guess +that we had, if we just + +had two meetings back to back, +was on average it would take + +60 minutes. + +It turns out that, because of +the way that things are set + +up, because of the five minute +thing, it actually takes a + +little longer than 60 +minutes on average. + +And why is that? + +It's because the five sometimes +adds an extra + +buffer, adds a little bit of +extra amount, because it would + +have been shorter in this +scenario because, if the both + +students had arrived on time, +then the second student would + +have been able to pick up +right here immediately. + +And so both appointments would +have ended sooner. + +But because the second student +didn't arrive until five + +minutes, there was some empty +space that was wasted. + +And that's where you get you the +little bit of extra time. + +So this is a nice problem just +to get some more exercise with + +exponential random variables +and also nicely illustrates + +the memory list property, which +was a key points in + +order to solve this. + +And it also is nice because we +get to review a useful tool + +that we've been using all course +long, which is to split + +things into different scenarios +and then solve the + +simpler problems and then +combine them up, for example + +using total expectation. + +So I hope that was helpful, +and see you next time. \ No newline at end of file diff --git a/YjUOaNbLnn0.txt b/YjUOaNbLnn0.txt new file mode 100644 index 0000000000000000000000000000000000000000..b9ef8a115f25d476699d6e76eb7d5ec63e90eaac --- /dev/null +++ b/YjUOaNbLnn0.txt @@ -0,0 +1,8611 @@ +align:start position:0% + +getting into the lecture proper I just + + align:start position:0% +getting into the lecture proper I just + + + align:start position:0% +getting into the lecture proper I just +wanted to say a few words about the quiz + + align:start position:0% +wanted to say a few words about the quiz + + + align:start position:0% +wanted to say a few words about the quiz +and then talk a little bit about where + + align:start position:0% +and then talk a little bit about where + + + align:start position:0% +and then talk a little bit about where +we were last time uh you probably don't + + align:start position:0% +we were last time uh you probably don't + + + align:start position:0% +we were last time uh you probably don't +want to talk about the quiz it's okay um + + align:start position:0% +want to talk about the quiz it's okay um + + + align:start position:0% +want to talk about the quiz it's okay um +so uh this time Joe B won out uh not + + align:start position:0% +so uh this time Joe B won out uh not + + + align:start position:0% +so uh this time Joe B won out uh not +completely but did perhaps a bit better + + align:start position:0% +completely but did perhaps a bit better + + + align:start position:0% +completely but did perhaps a bit better +than class average uh and historically + + align:start position:0% +than class average uh and historically + + + align:start position:0% +than class average uh and historically +that's exactly as it's always been in + + align:start position:0% +that's exactly as it's always been in + + + align:start position:0% +that's exactly as it's always been in +this quiz that you like pretty much + + align:start position:0% +this quiz that you like pretty much + + + align:start position:0% +this quiz that you like pretty much +every UniFi class before you was able to + + align:start position:0% +every UniFi class before you was able to + + + align:start position:0% +every UniFi class before you was able to +do the routine application of beam + + align:start position:0% +do the routine application of beam + + + align:start position:0% +do the routine application of beam +Theory quite well uh but your level of + + align:start position:0% +Theory quite well uh but your level of + + + align:start position:0% +Theory quite well uh but your level of +conceptual understanding of the + + align:start position:0% +conceptual understanding of the + + + align:start position:0% +conceptual understanding of the +limitations of it of how to go about + + align:start position:0% +limitations of it of how to go about + + + align:start position:0% +limitations of it of how to go about +analyzing a non-standard structure one + + align:start position:0% +analyzing a non-standard structure one + + + align:start position:0% +analyzing a non-standard structure one +that you hadn't seen before was + + align:start position:0% +that you hadn't seen before was + + + align:start position:0% +that you hadn't seen before was +considerably more shaky um that's + + align:start position:0% +considerably more shaky um that's + + + align:start position:0% +considerably more shaky um that's +perhaps not surprising because we've + + align:start position:0% +perhaps not surprising because we've + + + align:start position:0% +perhaps not surprising because we've +really only had that that quiz was on uh + + align:start position:0% +really only had that that quiz was on uh + + + align:start position:0% +really only had that that quiz was on uh +less than 10 lectures worth of material + + align:start position:0% +less than 10 lectures worth of material + + + align:start position:0% +less than 10 lectures worth of material +and you you haven't had enough time for + + align:start position:0% +and you you haven't had enough time for + + + align:start position:0% +and you you haven't had enough time for +it to sort of embed in your your core + + align:start position:0% +it to sort of embed in your your core + + + align:start position:0% +it to sort of embed in your your core +Consciousness + + align:start position:0% +Consciousness + + + align:start position:0% +Consciousness +um so uh I I don't get down on + + align:start position:0% +um so uh I I don't get down on + + + align:start position:0% +um so uh I I don't get down on +yourselves about it because feeling this + + align:start position:0% +yourselves about it because feeling this + + + align:start position:0% +yourselves about it because feeling this +is something you really should know uh + + align:start position:0% +is something you really should know uh + + + align:start position:0% +is something you really should know uh +you should but it may take a little bit + + align:start position:0% +you should but it may take a little bit + + + align:start position:0% +you should but it may take a little bit +longer and the quiz is a feedback + + align:start position:0% +longer and the quiz is a feedback + + + align:start position:0% +longer and the quiz is a feedback +mechanism to help that I'll be around in + + align:start position:0% +mechanism to help that I'll be around in + + + align:start position:0% +mechanism to help that I'll be around in +office hours uh this afternoon and if + + align:start position:0% +office hours uh this afternoon and if + + + align:start position:0% +office hours uh this afternoon and if +you know you feel strongly about it do + + align:start position:0% +you know you feel strongly about it do + + + align:start position:0% +you know you feel strongly about it do +come and make an appointment come and + + align:start position:0% +come and make an appointment come and + + + align:start position:0% +come and make an appointment come and +see me uh outside office house that + + align:start position:0% +see me uh outside office house that + + + align:start position:0% +see me uh outside office house that +would be + + align:start position:0% +would be + + + align:start position:0% +would be +fine uh last time we concluded talking + + align:start position:0% +fine uh last time we concluded talking + + + align:start position:0% +fine uh last time we concluded talking +about buckling and this is also uh + + align:start position:0% +about buckling and this is also uh + + + align:start position:0% +about buckling and this is also uh +concluding our treatment of uh + + align:start position:0% +concluding our treatment of uh + + + align:start position:0% +concluding our treatment of uh +structural analysis so buckling uh an + + align:start position:0% +structural analysis so buckling uh an + + + align:start position:0% +structural analysis so buckling uh an +elastic an example one of many examples + + align:start position:0% +elastic an example one of many examples + + + align:start position:0% +elastic an example one of many examples +of an elastic instability where if we + + align:start position:0% +of an elastic instability where if we + + + align:start position:0% +of an elastic instability where if we +actually load a in the simple case we're + + align:start position:0% +actually load a in the simple case we're + + + align:start position:0% +actually load a in the simple case we're +considering a initially nearly straight + + align:start position:0% +considering a initially nearly straight + + + align:start position:0% +considering a initially nearly straight +column we see that it loads up + + align:start position:0% +column we see that it loads up + + + align:start position:0% +column we see that it loads up +elastically and then bang it goes + + align:start position:0% +elastically and then bang it goes + + + align:start position:0% +elastically and then bang it goes +unstable on us uh if this was a + + align:start position:0% +unstable on us uh if this was a + + + align:start position:0% +unstable on us uh if this was a +Structure would represent a dramatic + + align:start position:0% +Structure would represent a dramatic + + + align:start position:0% +Structure would represent a dramatic +loss of load carrying capacity + + align:start position:0% +loss of load carrying capacity + + + align:start position:0% +loss of load carrying capacity +we can understand this and last time + + align:start position:0% +we can understand this and last time + + + align:start position:0% +we can understand this and last time +particularly we looked at the effects of + + align:start position:0% +particularly we looked at the effects of + + + align:start position:0% +particularly we looked at the effects of +imperfections on that behavior and + + align:start position:0% +imperfections on that behavior and + + + align:start position:0% +imperfections on that behavior and +there's no such thing as a perfect + + align:start position:0% +there's no such thing as a perfect + + + align:start position:0% +there's no such thing as a perfect +column a perfectly straight perfectly + + align:start position:0% +column a perfectly straight perfectly + + + align:start position:0% +column a perfectly straight perfectly +aely loaded column so the this is the + + align:start position:0% +aely loaded column so the this is the + + + align:start position:0% +aely loaded column so the this is the +general case where we found that just as + + align:start position:0% +general case where we found that just as + + + align:start position:0% +general case where we found that just as +we found for a perfectly straight column + + align:start position:0% +we found for a perfectly straight column + + + align:start position:0% +we found for a perfectly straight column +the governing equation is + + align:start position:0% +the governing equation is + + + align:start position:0% +the governing equation is +still uh that the lateral deflection W + + align:start position:0% +still uh that the lateral deflection W + + + align:start position:0% +still uh that the lateral deflection W +as a function of X goes as this + + align:start position:0% +as a function of X goes as this + + + align:start position:0% +as a function of X goes as this +combination of s and cosine and linear + + align:start position:0% +combination of s and cosine and linear + + + align:start position:0% +combination of s and cosine and linear +and constant terms but now unlike the + + align:start position:0% +and constant terms but now unlike the + + + align:start position:0% +and constant terms but now unlike the +case when we had a perfectly straight + + align:start position:0% +case when we had a perfectly straight + + + align:start position:0% +case when we had a perfectly straight +perfectly ax loaded uh column these + + align:start position:0% +perfectly ax loaded uh column these + + + align:start position:0% +perfectly ax loaded uh column these +constants a b c and d are actually + + align:start position:0% +constants a b c and d are actually + + + align:start position:0% +constants a b c and d are actually +satisfied take on + + align:start position:0% +satisfied take on + + + align:start position:0% +satisfied take on +nonzero uh + + align:start position:0% +nonzero uh + + + align:start position:0% +nonzero uh +values according to whatever the + + align:start position:0% +values according to whatever the + + + align:start position:0% +values according to whatever the +boundary conditions are and if we plot + + align:start position:0% +boundary conditions are and if we plot + + + align:start position:0% +boundary conditions are and if we plot +out the uh sorry + + align:start position:0% + + + + align:start position:0% + +that's the lateral displacement say of + + align:start position:0% +that's the lateral displacement say of + + + align:start position:0% +that's the lateral displacement say of +the midpoint + + align:start position:0% +the midpoint + + + align:start position:0% +the midpoint +versus the load that we're applying as + + align:start position:0% +versus the load that we're applying as + + + align:start position:0% +versus the load that we're applying as +we get increasing imperfection so as + + align:start position:0% +we get increasing imperfection so as + + + align:start position:0% +we get increasing imperfection so as +this load e uh as this load p is applied + + align:start position:0% +this load e uh as this load p is applied + + + align:start position:0% +this load e uh as this load p is applied +an increasing distance away from the + + align:start position:0% +an increasing distance away from the + + + align:start position:0% +an increasing distance away from the +midline we get further and further away + + align:start position:0% +midline we get further and further away + + + align:start position:0% +midline we get further and further away +from the ideal + + align:start position:0% + + + + align:start position:0% + +bicationic loaded our column is uh we'll + + align:start position:0% +bicationic loaded our column is uh we'll + + + align:start position:0% +bicationic loaded our column is uh we'll +get a larger and larger deflection at a + + align:start position:0% +get a larger and larger deflection at a + + + align:start position:0% +get a larger and larger deflection at a +lower and lower load but the bation + + align:start position:0% +lower and lower load but the bation + + + align:start position:0% +lower and lower load but the bation +behavior still represents an ASM toote + + align:start position:0% +behavior still represents an ASM toote + + + align:start position:0% +behavior still represents an ASM toote +the for the simply supported case with + + align:start position:0% +the for the simply supported case with + + + align:start position:0% +the for the simply supported case with +pin and roller at each end the critical + + align:start position:0% +pin and roller at each end the critical + + + align:start position:0% +pin and roller at each end the critical +load asmp tootes but never quite reaches + + align:start position:0% +load asmp tootes but never quite reaches + + + align:start position:0% +load asmp tootes but never quite reaches +Pi s EI over + + align:start position:0% +Pi s EI over + + + align:start position:0% +Pi s EI over +l^2 um and so uh in the absence of any + + align:start position:0% +l^2 um and so uh in the absence of any + + + align:start position:0% +l^2 um and so uh in the absence of any +information about the imperfection we + + align:start position:0% +information about the imperfection we + + + align:start position:0% +information about the imperfection we +might have in the actual structure this + + align:start position:0% +might have in the actual structure this + + + align:start position:0% +might have in the actual structure this +provides at least some estimate of when + + align:start position:0% +provides at least some estimate of when + + + align:start position:0% +provides at least some estimate of when +uh this elastic instability will + + align:start position:0% +uh this elastic instability will + + + align:start position:0% +uh this elastic instability will +occur I mentioned something else in + + align:start position:0% +occur I mentioned something else in + + + align:start position:0% +occur I mentioned something else in +passing and I think I managed to confuse + + align:start position:0% +passing and I think I managed to confuse + + + align:start position:0% +passing and I think I managed to confuse +you that I I said that in general for a + + align:start position:0% +you that I I said that in general for a + + + align:start position:0% +you that I I said that in general for a +perfect column the critical load goes as + + align:start position:0% +perfect column the critical load goes as + + + align:start position:0% +perfect column the critical load goes as +some factor C times pi squ di I over l s + + align:start position:0% +some factor C times pi squ di I over l s + + + align:start position:0% +some factor C times pi squ di I over l s +the the critical load for a perfectly uh + + align:start position:0% +the the critical load for a perfectly uh + + + align:start position:0% +the the critical load for a perfectly uh +straight perfectly loaded elastic column + + align:start position:0% +straight perfectly loaded elastic column + + + align:start position:0% +straight perfectly loaded elastic column +where this constant C I tried to appeal + + align:start position:0% +where this constant C I tried to appeal + + + align:start position:0% +where this constant C I tried to appeal +to your intuition about what it might + + align:start position:0% +to your intuition about what it might + + + align:start position:0% +to your intuition about what it might +look like for a couple of cases and and + + align:start position:0% +look like for a couple of cases and and + + + align:start position:0% +look like for a couple of cases and and +that was probably the wrong way to go + + align:start position:0% +that was probably the wrong way to go + + + align:start position:0% +that was probably the wrong way to go +about doing + + align:start position:0% +about doing + + + align:start position:0% +about doing +it to avoid the confusion or to redress + + align:start position:0% +it to avoid the confusion or to redress + + + align:start position:0% +it to avoid the confusion or to redress +address the confusion in in the muddy + + align:start position:0% +address the confusion in in the muddy + + + align:start position:0% +address the confusion in in the muddy +cards uh if you solve or or assume that + + align:start position:0% +cards uh if you solve or or assume that + + + align:start position:0% +cards uh if you solve or or assume that +this was the solution for some arbitrary + + align:start position:0% +this was the solution for some arbitrary + + + align:start position:0% +this was the solution for some arbitrary +uh set of boundary conditions you would + + align:start position:0% +uh set of boundary conditions you would + + + align:start position:0% +uh set of boundary conditions you would +solve it and this constant C would uh + + align:start position:0% +solve it and this constant C would uh + + + align:start position:0% +solve it and this constant C would uh +just come out of that solution uh + + align:start position:0% +just come out of that solution uh + + + align:start position:0% +just come out of that solution uh +naturally and you wouldn't have to be + + align:start position:0% +naturally and you wouldn't have to be + + + align:start position:0% +naturally and you wouldn't have to be +assuming anything other than uh that + + align:start position:0% +assuming anything other than uh that + + + align:start position:0% +assuming anything other than uh that +solutions to the governing differential + + align:start position:0% +solutions to the governing differential + + + align:start position:0% +solutions to the governing differential +equation or of this + + align:start position:0% +equation or of this + + + align:start position:0% +equation or of this +form so C is just a function of the + + align:start position:0% +form so C is just a function of the + + + align:start position:0% +form so C is just a function of the +boundary conditions and the geometry of + + align:start position:0% +boundary conditions and the geometry of + + + align:start position:0% +boundary conditions and the geometry of +the problem uh perhaps forget if it + + align:start position:0% +the problem uh perhaps forget if it + + + align:start position:0% +the problem uh perhaps forget if it +didn't make any sense to you uh the + + align:start position:0% +didn't make any sense to you uh the + + + align:start position:0% +didn't make any sense to you uh the +intuition I was appealing to because I + + align:start position:0% +intuition I was appealing to because I + + + align:start position:0% +intuition I was appealing to because I +think From the Muddy cards for many of + + align:start position:0% +think From the Muddy cards for many of + + + align:start position:0% +think From the Muddy cards for many of +you it wasn't good intuition it wasn't a + + align:start position:0% +you it wasn't good intuition it wasn't a + + + align:start position:0% +you it wasn't good intuition it wasn't a +good assumption on my part any are there + + align:start position:0% +good assumption on my part any are there + + + align:start position:0% +good assumption on my part any are there +any questions about buckling uh + + align:start position:0% +any questions about buckling uh + + + align:start position:0% +any questions about buckling uh +effective imperfections on buckling + + align:start position:0% +effective imperfections on buckling + + + align:start position:0% +effective imperfections on buckling +before we move on to the next topic + + align:start position:0% + + + + align:start position:0% + +yes what is the word after + + align:start position:0% +yes what is the word after + + + align:start position:0% +yes what is the word after +solution oh sorry still thank you yes + + align:start position:0% +solution oh sorry still thank you yes + + + align:start position:0% +solution oh sorry still thank you yes +the handwriting is not getting any + + align:start position:0% +the handwriting is not getting any + + + align:start position:0% +the handwriting is not getting any +better any other + + align:start position:0% + + + + align:start position:0% + +questions okay um what we're going to do + + align:start position:0% +questions okay um what we're going to do + + + align:start position:0% +questions okay um what we're going to do +then is move on to the next uh and final + + align:start position:0% +then is move on to the next uh and final + + + align:start position:0% +then is move on to the next uh and final +topical area for uh you in in unified + + align:start position:0% +topical area for uh you in in unified + + + align:start position:0% +topical area for uh you in in unified +materials and + + align:start position:0% +materials and + + + align:start position:0% +materials and +structures and that's to look at uh or + + align:start position:0% +structures and that's to look at uh or + + + align:start position:0% +structures and that's to look at uh or +to tie together what we've done on + + align:start position:0% +to tie together what we've done on + + + align:start position:0% +to tie together what we've done on +structural analysis and start so from + + align:start position:0% +structural analysis and start so from + + + align:start position:0% +structural analysis and start so from +what you've done on structural analysis + + align:start position:0% +what you've done on structural analysis + + + align:start position:0% +what you've done on structural analysis +you in principle for the simple + + align:start position:0% +you in principle for the simple + + + align:start position:0% +you in principle for the simple +structural members axial bars or rods + + align:start position:0% +structural members axial bars or rods + + + align:start position:0% +structural members axial bars or rods +beams shafts carrying torsion now uh + + align:start position:0% +beams shafts carrying torsion now uh + + + align:start position:0% +beams shafts carrying torsion now uh +beam columns buckling you can say + + align:start position:0% +beam columns buckling you can say + + + align:start position:0% +beam columns buckling you can say +something about the stresses stress + + align:start position:0% +something about the stresses stress + + + align:start position:0% +something about the stresses stress +distribution the maximum value of stress + + align:start position:0% +distribution the maximum value of stress + + + align:start position:0% +distribution the maximum value of stress +and for that matter the deoration of the + + align:start position:0% +and for that matter the deoration of the + + + align:start position:0% +and for that matter the deoration of the +structure + + align:start position:0% +structure + + + align:start position:0% +structure +but you don't actually have anything to + + align:start position:0% +but you don't actually have anything to + + + align:start position:0% +but you don't actually have anything to +equate that to so how much stress is too + + align:start position:0% +equate that to so how much stress is too + + + align:start position:0% +equate that to so how much stress is too +much how much defamation is too much and + + align:start position:0% +much how much defamation is too much and + + + align:start position:0% +much how much defamation is too much and +what we're going to try and do in the + + align:start position:0% +what we're going to try and do in the + + + align:start position:0% +what we're going to try and do in the +last six lectures or so is tie this or + + align:start position:0% +last six lectures or so is tie this or + + + align:start position:0% +last six lectures or so is tie this or +or bring in the the material element uh + + align:start position:0% +or bring in the the material element uh + + + align:start position:0% +or bring in the the material element uh +understand what governs uh structural + + align:start position:0% +understand what governs uh structural + + + align:start position:0% +understand what governs uh structural +Integrity of our simple structures we've + + align:start position:0% +Integrity of our simple structures we've + + + align:start position:0% +Integrity of our simple structures we've +analyzed from the material point of view + + align:start position:0% +analyzed from the material point of view + + + align:start position:0% +analyzed from the material point of view +how the material contributes to that + + align:start position:0% +how the material contributes to that + + + align:start position:0% +how the material contributes to that +that so before going any further let's + + align:start position:0% +that so before going any further let's + + + align:start position:0% +that so before going any further let's +just uh do a PRS concept question um and + + align:start position:0% +just uh do a PRS concept question um and + + + align:start position:0% +just uh do a PRS concept question um and +see if we can uh recall what we actually + + align:start position:0% +see if we can uh recall what we actually + + + align:start position:0% +see if we can uh recall what we actually +mean by structural + + align:start position:0% + + + + align:start position:0% + +integrity and + + align:start position:0% + + + + align:start position:0% + +yeah so it's about stiffness failure + + align:start position:0% +yeah so it's about stiffness failure + + + align:start position:0% +yeah so it's about stiffness failure +longevity cost stiffness failure safety + + align:start position:0% +longevity cost stiffness failure safety + + + align:start position:0% +longevity cost stiffness failure safety +cost + + align:start position:0% +cost + + + align:start position:0% +cost +failure failure longevity cost longevity + + align:start position:0% +failure failure longevity cost longevity + + + align:start position:0% +failure failure longevity cost longevity +stiffness and safety some other answer + + align:start position:0% +stiffness and safety some other answer + + + align:start position:0% +stiffness and safety some other answer +do not know do not understand so just to + + align:start position:0% +do not know do not understand so just to + + + align:start position:0% +do not know do not understand so just to +get us warmed up on on this topic what + + align:start position:0% +get us warmed up on on this topic what + + + align:start position:0% +get us warmed up on on this topic what +we're thinking about + + align:start position:0% + + + + align:start position:0% + +just in case I'm not strong + + align:start position:0% + + + + align:start position:0% + +enough how are we doing + + align:start position:0% + + + + align:start position:0% + +anyone need more time guess you either + + align:start position:0% +anyone need more time guess you either + + + align:start position:0% +anyone need more time guess you either +know this or + + align:start position:0% +know this or + + + align:start position:0% +know this or +don't 5 4 3 2 1 + + align:start position:0% +don't 5 4 3 2 1 + + + align:start position:0% +don't 5 4 3 2 1 +cut what do we + + align:start position:0% + + + + align:start position:0% + +think yeah okay so the majority think + + align:start position:0% +think yeah okay so the majority think + + + align:start position:0% +think yeah okay so the majority think +it's about stiffness failure longevity + + align:start position:0% +it's about stiffness failure longevity + + + align:start position:0% +it's about stiffness failure longevity +and some of you have some residual + + align:start position:0% +and some of you have some residual + + + align:start position:0% +and some of you have some residual +memory that safety should be in there uh + + align:start position:0% +memory that safety should be in there uh + + + align:start position:0% +memory that safety should be in there uh +it really is just structural integrity + + align:start position:0% +it really is just structural integrity + + + align:start position:0% +it really is just structural integrity +it's not the design objective which if + + align:start position:0% +it's not the design objective which if + + + align:start position:0% +it's not the design objective which if +you remember the design objective for + + align:start position:0% +you remember the design objective for + + + align:start position:0% +you remember the design objective for +structural design has some mention of + + align:start position:0% +structural design has some mention of + + + align:start position:0% +structural design has some mention of +cost it doesn't have a mention of safety + + align:start position:0% +cost it doesn't have a mention of safety + + + align:start position:0% +cost it doesn't have a mention of safety +it's achieving structural Integrity + + align:start position:0% +it's achieving structural Integrity + + + align:start position:0% +it's achieving structural Integrity +while minimizing cost structural + + align:start position:0% +while minimizing cost structural + + + align:start position:0% +while minimizing cost structural +Integrity is the if you like the + + align:start position:0% +Integrity is the if you like the + + + align:start position:0% +Integrity is the if you like the +technical part of this it's how much + + align:start position:0% +technical part of this it's how much + + + align:start position:0% +technical part of this it's how much +deflection are we going to get for the + + align:start position:0% +deflection are we going to get for the + + + align:start position:0% +deflection are we going to get for the +loads we're being asked to carry asking + + align:start position:0% +loads we're being asked to carry asking + + + align:start position:0% +loads we're being asked to carry asking +our structure to carry so that's about + + align:start position:0% +our structure to carry so that's about + + + align:start position:0% +our structure to carry so that's about +stiffness we obviously don't want our + + align:start position:0% +stiffness we obviously don't want our + + + align:start position:0% +stiffness we obviously don't want our +structure to break into two pieces or to + + align:start position:0% +structure to break into two pieces or to + + + align:start position:0% +structure to break into two pieces or to +collapse on us it's about resisting + + align:start position:0% +collapse on us it's about resisting + + + align:start position:0% +collapse on us it's about resisting +failure + + align:start position:0% +failure + + + align:start position:0% +failure +and we want it to last uh a decent + + align:start position:0% +and we want it to last uh a decent + + + align:start position:0% +and we want it to last uh a decent +economic length of time we want it to + + align:start position:0% +economic length of time we want it to + + + align:start position:0% +economic length of time we want it to +have certain longevity so the correct + + align:start position:0% +have certain longevity so the correct + + + align:start position:0% +have certain longevity so the correct +answer is number one any + + align:start position:0% +answer is number one any + + + align:start position:0% +answer is number one any +questions particularly those of you who + + align:start position:0% +questions particularly those of you who + + + align:start position:0% +questions particularly those of you who +had safety in there safety is an + + align:start position:0% +had safety in there safety is an + + + align:start position:0% +had safety in there safety is an +economic consideration + + align:start position:0% +economic consideration + + + align:start position:0% +economic consideration +remember hard to take I know but we've + + align:start position:0% +remember hard to take I know but we've + + + align:start position:0% +remember hard to take I know but we've +debated at length yes Scott oh no I'm + + align:start position:0% +debated at length yes Scott oh no I'm + + + align:start position:0% +debated at length yes Scott oh no I'm +just going to ask don't you sometimes + + align:start position:0% +just going to ask don't you sometimes + + + align:start position:0% +just going to ask don't you sometimes +design structure TR fail at a certain + + align:start position:0% +design structure TR fail at a certain + + + align:start position:0% +design structure TR fail at a certain +point yes uh in in a sense that uh you + + align:start position:0% +point yes uh in in a sense that uh you + + + align:start position:0% +point yes uh in in a sense that uh you +certainly don't want a structure to + + align:start position:0% +certainly don't want a structure to + + + align:start position:0% +certainly don't want a structure to +carry to to have unnecessary strength + + align:start position:0% +carry to to have unnecessary strength + + + align:start position:0% +carry to to have unnecessary strength +because by and large additional strength + + align:start position:0% +because by and large additional strength + + + align:start position:0% +because by and large additional strength +means additional material additional + + align:start position:0% +means additional material additional + + + align:start position:0% +means additional material additional +weight to the structure and if it's a + + align:start position:0% +weight to the structure and if it's a + + + align:start position:0% +weight to the structure and if it's a +flight structure you're going to pay an + + align:start position:0% +flight structure you're going to pay an + + + align:start position:0% +flight structure you're going to pay an +economic penalty for that additional + + align:start position:0% +economic penalty for that additional + + + align:start position:0% +economic penalty for that additional +weight so uh you want it to hit its + + align:start position:0% +weight so uh you want it to hit its + + + align:start position:0% +weight so uh you want it to hit its +design + + align:start position:0% +design + + + align:start position:0% +design +loads with maybe some small margin of + + align:start position:0% +loads with maybe some small margin of + + + align:start position:0% +loads with maybe some small margin of +safety and that's a technical term the + + align:start position:0% +safety and that's a technical term the + + + align:start position:0% +safety and that's a technical term the +margin is what the designer builds in to + + align:start position:0% +margin is what the designer builds in to + + + align:start position:0% +margin is what the designer builds in to +exceed the requirement so that if he's + + align:start position:0% +exceed the requirement so that if he's + + + align:start position:0% +exceed the requirement so that if he's +made or she's made some error that it's + + align:start position:0% +made or she's made some error that it's + + + align:start position:0% +made or she's made some error that it's +accounted for uh but no more than maybe + + align:start position:0% +accounted for uh but no more than maybe + + + align:start position:0% +accounted for uh but no more than maybe +5% on the the ultimate load that you're + + align:start position:0% +5% on the the ultimate load that you're + + + align:start position:0% +5% on the the ultimate load that you're +asking your structure to carry it's a + + align:start position:0% +asking your structure to carry it's a + + + align:start position:0% +asking your structure to carry it's a +important question other + + align:start position:0% +important question other + + + align:start position:0% +important question other +questions Okay so we've talked about the + + align:start position:0% +questions Okay so we've talked about the + + + align:start position:0% +questions Okay so we've talked about the +first of these last term we've talked + + align:start position:0% +first of these last term we've talked + + + align:start position:0% +first of these last term we've talked +about elastic behavior of materials so + + align:start position:0% +about elastic behavior of materials so + + + align:start position:0% +about elastic behavior of materials so +you you know at least where the Young's + + align:start position:0% +you you know at least where the Young's + + + align:start position:0% +you you know at least where the Young's +modulus or uh Young's modulus G modulus + + align:start position:0% +modulus or uh Young's modulus G modulus + + + align:start position:0% +modulus or uh Young's modulus G modulus +plus ratio come from which are going to + + align:start position:0% +plus ratio come from which are going to + + + align:start position:0% +plus ratio come from which are going to +govern the deflections uh extensions of + + align:start position:0% +govern the deflections uh extensions of + + + align:start position:0% +govern the deflections uh extensions of +bars and rods and deflections of beams + + align:start position:0% +bars and rods and deflections of beams + + + align:start position:0% +bars and rods and deflections of beams +and angles of twist of shafts what we're + + align:start position:0% +and angles of twist of shafts what we're + + + align:start position:0% +and angles of twist of shafts what we're +going to talk about now are the + + align:start position:0% +going to talk about now are the + + + align:start position:0% +going to talk about now are the +uh materials aspects the constitutive + + align:start position:0% +uh materials aspects the constitutive + + + align:start position:0% +uh materials aspects the constitutive +behaviors that relate to these other two + + align:start position:0% +behaviors that relate to these other two + + + align:start position:0% +behaviors that relate to these other two +uh aspects of structural Integrity + + align:start position:0% +uh aspects of structural Integrity + + + align:start position:0% +uh aspects of structural Integrity +namely failure and and + + align:start position:0% +namely failure and and + + + align:start position:0% +namely failure and and +Longevity and just as we + + align:start position:0% +Longevity and just as we + + + align:start position:0% +Longevity and just as we +had last time uh that there are three + + align:start position:0% +had last time uh that there are three + + + align:start position:0% +had last time uh that there are three +objectives and these are the same three + + align:start position:0% +objectives and these are the same three + + + align:start position:0% +objectives and these are the same three +objectives as we had at the end of last + + align:start position:0% +objectives as we had at the end of last + + + align:start position:0% +objectives as we had at the end of last +term when we talked about elasticity uh + + align:start position:0% +term when we talked about elasticity uh + + + align:start position:0% +term when we talked about elasticity uh +the first one we've already mentioned is + + align:start position:0% +the first one we've already mentioned is + + + align:start position:0% +the first one we've already mentioned is +to allow you to understand what are what + + align:start position:0% +to allow you to understand what are what + + + align:start position:0% +to allow you to understand what are what +places the limits on the loads the + + align:start position:0% +places the limits on the loads the + + + align:start position:0% +places the limits on the loads the +stresses a structure can carry uh how + + align:start position:0% +stresses a structure can carry uh how + + + align:start position:0% +stresses a structure can carry uh how +the material um God brilliant uh how the + + align:start position:0% +the material um God brilliant uh how the + + + align:start position:0% +the material um God brilliant uh how the +material plays into that then to allow + + align:start position:0% +material plays into that then to allow + + + align:start position:0% +material plays into that then to allow +you to understand the origins and limits + + align:start position:0% +you to understand the origins and limits + + + align:start position:0% +you to understand the origins and limits +of the strength of the material so just + + align:start position:0% +of the strength of the material so just + + + align:start position:0% +of the strength of the material so just +as we looked at atomic structure cryst + + align:start position:0% +as we looked at atomic structure cryst + + + align:start position:0% +as we looked at atomic structure cryst +packing Atomic bonding to look at the + + align:start position:0% +packing Atomic bonding to look at the + + + align:start position:0% +packing Atomic bonding to look at the +origins of Young's modulus we're now + + align:start position:0% +origins of Young's modulus we're now + + + align:start position:0% +origins of Young's modulus we're now +going to do the same thing but where + + align:start position:0% +going to do the same thing but where + + + align:start position:0% +going to do the same thing but where +strength comes from and then finally uh + + align:start position:0% +strength comes from and then finally uh + + + align:start position:0% +strength comes from and then finally uh +to allow you to select materials uh for + + align:start position:0% +to allow you to select materials uh for + + + align:start position:0% +to allow you to select materials uh for +a specific application that we've looked + + align:start position:0% +a specific application that we've looked + + + align:start position:0% +a specific application that we've looked +at for a a a loaded Rod we might want + + align:start position:0% +at for a a a loaded Rod we might want + + + align:start position:0% +at for a a a loaded Rod we might want +for maximum stiffness uh young High + + align:start position:0% +for maximum stiffness uh young High + + + align:start position:0% +for maximum stiffness uh young High +young modulus over density uh but for a + + align:start position:0% +young modulus over density uh but for a + + + align:start position:0% +young modulus over density uh but for a +beam in + + align:start position:0% +beam in + + + align:start position:0% +beam in +bending we want a a high value Young's + + align:start position:0% +bending we want a a high value Young's + + + align:start position:0% +bending we want a a high value Young's +modulus square root of Young's modulus + + align:start position:0% +modulus square root of Young's modulus + + + align:start position:0% +modulus square root of Young's modulus +over density and we're going to explore + + align:start position:0% +over density and we're going to explore + + + align:start position:0% +over density and we're going to explore +those same relations for strength and + + align:start position:0% +those same relations for strength and + + + align:start position:0% +those same relations for strength and +also to prevent fracture occurring but + + align:start position:0% +also to prevent fracture occurring but + + + align:start position:0% +also to prevent fracture occurring but +before we get sorry one final thing just + + align:start position:0% +before we get sorry one final thing just + + + align:start position:0% +before we get sorry one final thing just +be a little bit careful that uh and this + + align:start position:0% +be a little bit careful that uh and this + + + align:start position:0% +be a little bit careful that uh and this +sort of ties back to the quiz that uh or + + align:start position:0% +sort of ties back to the quiz that uh or + + + align:start position:0% +sort of ties back to the quiz that uh or +part of the quiz that when we Define we + + align:start position:0% +part of the quiz that when we Define we + + + align:start position:0% +part of the quiz that when we Define we +need to distinguish between the material + + align:start position:0% +need to distinguish between the material + + + align:start position:0% +need to distinguish between the material +response and the structural response if + + align:start position:0% +response and the structural response if + + + align:start position:0% +response and the structural response if +we're designing an airplane or a launch + + align:start position:0% +we're designing an airplane or a launch + + + align:start position:0% +we're designing an airplane or a launch +vehicle uh satellite whatever + + align:start position:0% +vehicle uh satellite whatever + + + align:start position:0% +vehicle uh satellite whatever +uh we're really ultimately interested in + + align:start position:0% +uh we're really ultimately interested in + + + align:start position:0% +uh we're really ultimately interested in +structural performance and we're + + align:start position:0% +structural performance and we're + + + align:start position:0% +structural performance and we're +interested not so much in uh material + + align:start position:0% +interested not so much in uh material + + + align:start position:0% +interested not so much in uh material +failing or the material being stiff + + align:start position:0% +failing or the material being stiff + + + align:start position:0% +failing or the material being stiff +enough we're interested in the structure + + align:start position:0% +enough we're interested in the structure + + + align:start position:0% +enough we're interested in the structure +failing or the structure being stiff + + align:start position:0% +failing or the structure being stiff + + + align:start position:0% +failing or the structure being stiff +enough failure of a structure may have + + align:start position:0% +enough failure of a structure may have + + + align:start position:0% +enough failure of a structure may have +nothing to do with the the material that + + align:start position:0% +nothing to do with the the material that + + + align:start position:0% +nothing to do with the the material that +it's made of um and a good example of + + align:start position:0% +it's made of um and a good example of + + + align:start position:0% +it's made of um and a good example of +this is is buckling which is a is a + + align:start position:0% +this is is buckling which is a is a + + + align:start position:0% +this is is buckling which is a is a +collapse of the structure but it owes uh + + align:start position:0% +collapse of the structure but it owes uh + + + align:start position:0% +collapse of the structure but it owes uh +something to the stiffness of the + + align:start position:0% +something to the stiffness of the + + + align:start position:0% +something to the stiffness of the +material but a lot more to the geometry + + align:start position:0% +material but a lot more to the geometry + + + align:start position:0% +material but a lot more to the geometry +the length the cross-sectional + + align:start position:0% +the length the cross-sectional + + + align:start position:0% +the length the cross-sectional +dimensions of the structure so when we + + align:start position:0% +dimensions of the structure so when we + + + align:start position:0% +dimensions of the structure so when we +talk about failure it's failure to meet + + align:start position:0% +talk about failure it's failure to meet + + + align:start position:0% +talk about failure it's failure to meet +a structural design purpose not + + align:start position:0% +a structural design purpose not + + + align:start position:0% +a structural design purpose not +necessarily just a material failure + + align:start position:0% +necessarily just a material failure + + + align:start position:0% +necessarily just a material failure +although that's often part of it so + + align:start position:0% +although that's often part of it so + + + align:start position:0% +although that's often part of it so +before we start talking about + + align:start position:0% +before we start talking about + + + align:start position:0% +before we start talking about +failure and sort of uh developing + + align:start position:0% +failure and sort of uh developing + + + align:start position:0% +failure and sort of uh developing +analytical models for it wanted to just + + align:start position:0% +analytical models for it wanted to just + + + align:start position:0% +analytical models for it wanted to just +look at the uh phenomen phenomenology of + + align:start position:0% +look at the uh phenomen phenomenology of + + + align:start position:0% +look at the uh phenomen phenomenology of +failure um of of metals particularly + + align:start position:0% +failure um of of metals particularly + + + align:start position:0% +failure um of of metals particularly +which is mainly what we're going to + + align:start position:0% +which is mainly what we're going to + + + align:start position:0% +which is mainly what we're going to +concentrate on here and just note that + + align:start position:0% +concentrate on here and just note that + + + align:start position:0% +concentrate on here and just note that +depending on what we do to it a material + + align:start position:0% +depending on what we do to it a material + + + align:start position:0% +depending on what we do to it a material +May behave in different ways and you + + align:start position:0% +May behave in different ways and you + + + align:start position:0% +May behave in different ways and you +sort of know this already here's a + + align:start position:0% +sort of know this already here's a + + + align:start position:0% +sort of know this already here's a +paperclip uh it behaves elastically I + + align:start position:0% +paperclip uh it behaves elastically I + + + align:start position:0% +paperclip uh it behaves elastically I +can use this paper clip over and over + + align:start position:0% +can use this paper clip over and over + + + align:start position:0% +can use this paper clip over and over +again uh you know it it it just provides + + align:start position:0% +again uh you know it it it just provides + + + align:start position:0% +again uh you know it it it just provides +a little bit of spring stiffness holds + + align:start position:0% +a little bit of spring stiffness holds + + + align:start position:0% +a little bit of spring stiffness holds +the papers together but we've all done + + align:start position:0% +the papers together but we've all done + + + align:start position:0% +the papers together but we've all done +it in our idle moments we pull it apart + + align:start position:0% +it in our idle moments we pull it apart + + + align:start position:0% +it in our idle moments we pull it apart +and it deforms plastically which is a + + align:start position:0% +and it deforms plastically which is a + + + align:start position:0% +and it deforms plastically which is a +permanent deformation so that I've + + align:start position:0% +permanent deformation so that I've + + + align:start position:0% +permanent deformation so that I've +opened it up and and you know I can try + + align:start position:0% +opened it up and and you know I can try + + + align:start position:0% +opened it up and and you know I can try +and get it back but it's never quite the + + align:start position:0% +and get it back but it's never quite the + + + align:start position:0% +and get it back but it's never quite the +same again you bend a piece of metal + + align:start position:0% +same again you bend a piece of metal + + + align:start position:0% +same again you bend a piece of metal +Beyond its elastic limit it's + + align:start position:0% +Beyond its elastic limit it's + + + align:start position:0% +Beyond its elastic limit it's +permanently + + align:start position:0% +permanently + + + align:start position:0% +permanently +deformed it's failed at least for this + + align:start position:0% +deformed it's failed at least for this + + + align:start position:0% +deformed it's failed at least for this +purpose and then I get mad at it and I + + align:start position:0% +purpose and then I get mad at it and I + + + align:start position:0% +purpose and then I get mad at it and I +do some cyclic loading on it and yeah at + + align:start position:0% +do some cyclic loading on it and yeah at + + + align:start position:0% +do some cyclic loading on it and yeah at +a few Cycles just bending it backwards + + align:start position:0% +a few Cycles just bending it backwards + + + align:start position:0% +a few Cycles just bending it backwards +and forwards it breaks into two and + + align:start position:0% +and forwards it breaks into two and + + + align:start position:0% +and forwards it breaks into two and +that's a fatigue failure a failure under + + align:start position:0% +that's a fatigue failure a failure under + + + align:start position:0% +that's a fatigue failure a failure under +a repeated cyclic load so same bit of + + align:start position:0% +a repeated cyclic load so same bit of + + + align:start position:0% +a repeated cyclic load so same bit of +metal that was performing quite happily + + align:start position:0% +metal that was performing quite happily + + + align:start position:0% +metal that was performing quite happily +elastically holding my papers + + align:start position:0% +elastically holding my papers + + + align:start position:0% +elastically holding my papers +together overloaded plastically deformed + + align:start position:0% +together overloaded plastically deformed + + + align:start position:0% +together overloaded plastically deformed +and then repeated cycling it failed uh + + align:start position:0% +and then repeated cycling it failed uh + + + align:start position:0% +and then repeated cycling it failed uh +that's the essence of what we're going + + align:start position:0% +that's the essence of what we're going + + + align:start position:0% +that's the essence of what we're going +to be looking at what governs those + + align:start position:0% +to be looking at what governs those + + + align:start position:0% +to be looking at what governs those +different failure + + align:start position:0% +different failure + + + align:start position:0% +different failure +processes uh couple of other examples um + + align:start position:0% +processes uh couple of other examples um + + + align:start position:0% +processes uh couple of other examples um +just tied into the + + align:start position:0% +just tied into the + + + align:start position:0% +just tied into the +uh the little bit of modeling we're + + align:start position:0% +uh the little bit of modeling we're + + + align:start position:0% +uh the little bit of modeling we're +going to do um this may or may not work + + align:start position:0% +going to do um this may or may not work + + + align:start position:0% +going to do um this may or may not work +depending on how strong I'm feeling + + align:start position:0% +depending on how strong I'm feeling + + + align:start position:0% +depending on how strong I'm feeling +today here's a bit of metal um there are + + align:start position:0% +today here's a bit of metal um there are + + + align:start position:0% +today here's a bit of metal um there are +not many bits of metal I can do this + + align:start position:0% +not many bits of metal I can do this + + + align:start position:0% +not many bits of metal I can do this +with but this happens to be a bit of + + align:start position:0% +with but this happens to be a bit of + + + align:start position:0% +with but this happens to be a bit of +solder and what I'm going to do is a is + + align:start position:0% +solder and what I'm going to do is a is + + + align:start position:0% +solder and what I'm going to do is a is +an impromptu utensile test actually Carl + + align:start position:0% +an impromptu utensile test actually Carl + + + align:start position:0% +an impromptu utensile test actually Carl +can + + align:start position:0% +can + + + align:start position:0% +can +you better still uh we hold it low so + + align:start position:0% +you better still uh we hold it low so + + + align:start position:0% +you better still uh we hold it low so +it's actually if you uh yeah okay so + + align:start position:0% +it's actually if you uh yeah okay so + + + align:start position:0% +it's actually if you uh yeah okay so +we're going to pull and going to try + + align:start position:0% +we're going to pull and going to try + + + align:start position:0% +we're going to pull and going to try +and break + + align:start position:0% + + + + align:start position:0% + +it is it slipping at your end + + align:start position:0% + + + + align:start position:0% + +Carl okay + + align:start position:0% + + + + align:start position:0% + +okay that was worth it that was worth it + + align:start position:0% +okay that was worth it that was worth it + + + align:start position:0% +okay that was worth it that was worth it +okay if we if we put it down look what's + + align:start position:0% +okay if we if we put it down look what's + + + align:start position:0% +okay if we if we put it down look what's +happened this initially this is lead + + align:start position:0% +happened this initially this is lead + + + align:start position:0% +happened this initially this is lead +free s uh sorry about that no but look + + align:start position:0% +free s uh sorry about that no but look + + + align:start position:0% +free s uh sorry about that no but look +what look what it's done to the notch in + + align:start position:0% +what look what it's done to the notch in + + + align:start position:0% +what look what it's done to the notch in +my hat okay what you what you can see is + + align:start position:0% +my hat okay what you what you can see is + + + align:start position:0% +my hat okay what you what you can see is +or I hope you can see just hold it there + + align:start position:0% +or I hope you can see just hold it there + + + align:start position:0% +or I hope you can see just hold it there +a second is that as this has failed that + + align:start position:0% +a second is that as this has failed that + + + align:start position:0% +a second is that as this has failed that +the solder has thinned all the way down + + align:start position:0% +the solder has thinned all the way down + + + align:start position:0% +the solder has thinned all the way down +uh to nearly to a point it's that + + align:start position:0% +uh to nearly to a point it's that + + + align:start position:0% +uh to nearly to a point it's that +process we're going to uh has a + + align:start position:0% +process we're going to uh has a + + + align:start position:0% +process we're going to uh has a +technical name of + + align:start position:0% +technical name of + + + align:start position:0% +technical name of +necking + + align:start position:0% +necking + + + align:start position:0% +necking +um that's what I didn't want to do okay + + align:start position:0% +um that's what I didn't want to do okay + + + align:start position:0% +um that's what I didn't want to do okay +and you'll say well this was just a soft + + align:start position:0% +and you'll say well this was just a soft + + + align:start position:0% +and you'll say well this was just a soft +solder uh so it's not representative but + + align:start position:0% +solder uh so it's not representative but + + + align:start position:0% +solder uh so it's not representative but +if we took a piece of Steel and I'll + + align:start position:0% +if we took a piece of Steel and I'll + + + align:start position:0% +if we took a piece of Steel and I'll +pass this round um you'll see a very + + align:start position:0% +pass this round um you'll see a very + + + align:start position:0% +pass this round um you'll see a very +similar thing that uh okay you can + + align:start position:0% +similar thing that uh okay you can + + + align:start position:0% +similar thing that uh okay you can +thanks uh that yeah that hurt me + + align:start position:0% +thanks uh that yeah that hurt me + + + align:start position:0% +thanks uh that yeah that hurt me +too action and reaction comes in there + + align:start position:0% +too action and reaction comes in there + + + align:start position:0% +too action and reaction comes in there +so at Le our pain was equal um you see a + + align:start position:0% +so at Le our pain was equal um you see a + + + align:start position:0% +so at Le our pain was equal um you see a +piece of Steel which was pulled in a T + + align:start position:0% +piece of Steel which was pulled in a T + + + align:start position:0% +piece of Steel which was pulled in a T +Cell test T in machine has also necked + + align:start position:0% +Cell test T in machine has also necked + + + align:start position:0% +Cell test T in machine has also necked +down significantly maybe not to a point + + align:start position:0% +down significantly maybe not to a point + + + align:start position:0% +down significantly maybe not to a point +but but still a significant reduction in + + align:start position:0% +but but still a significant reduction in + + + align:start position:0% +but but still a significant reduction in +area around the point where it's + + align:start position:0% + + + + align:start position:0% + +failed going to do another T Cell test + + align:start position:0% +failed going to do another T Cell test + + + align:start position:0% +failed going to do another T Cell test +but this time on a piece of aluminum or + + align:start position:0% +but this time on a piece of aluminum or + + + align:start position:0% +but this time on a piece of aluminum or +aluminium where I come + + align:start position:0% +aluminium where I come + + + align:start position:0% +aluminium where I come +from um and I think I can manage this + + align:start position:0% +from um and I think I can manage this + + + align:start position:0% +from um and I think I can manage this +one on my own uh I'm going to pull this + + align:start position:0% +one on my own uh I'm going to pull this + + + align:start position:0% +one on my own uh I'm going to pull this +and you can see oops that's actually not + + align:start position:0% +and you can see oops that's actually not + + + align:start position:0% +and you can see oops that's actually not +necking that's uh + + align:start position:0% +necking that's uh + + + align:start position:0% +necking that's uh +oh right okay there it goes always fails + + align:start position:0% +oh right okay there it goes always fails + + + align:start position:0% +oh right okay there it goes always fails +near the grips uh that it it bent up on + + align:start position:0% +near the grips uh that it it bent up on + + + align:start position:0% +near the grips uh that it it bent up on +me because I wasn't holding it flat but + + align:start position:0% +me because I wasn't holding it flat but + + + align:start position:0% +me because I wasn't holding it flat but +you'll see that actually this time it it + + align:start position:0% +you'll see that actually this time it it + + + align:start position:0% +you'll see that actually this time it it +failed in a pretty brittle manner that + + align:start position:0% +failed in a pretty brittle manner that + + + align:start position:0% +failed in a pretty brittle manner that +there was no appreciable reduction in + + align:start position:0% +there was no appreciable reduction in + + + align:start position:0% +there was no appreciable reduction in +area at least in in the the width of the + + align:start position:0% +area at least in in the the width of the + + + align:start position:0% +area at least in in the the width of the +specimen it just failed suddenly + + align:start position:0% +specimen it just failed suddenly + + + align:start position:0% +specimen it just failed suddenly +straight across as opposed to the the + + align:start position:0% +straight across as opposed to the the + + + align:start position:0% +straight across as opposed to the the +solder that + + align:start position:0% +solder that + + + align:start position:0% +solder that +uh uh necked down and and and then + + align:start position:0% +uh uh necked down and and and then + + + align:start position:0% +uh uh necked down and and and then +failed mly quite catastrophically for + + align:start position:0% +failed mly quite catastrophically for + + + align:start position:0% +failed mly quite catastrophically for +Carl and me so + + align:start position:0% +Carl and me so + + + align:start position:0% +Carl and me so +this is aluminum this is the material we + + align:start position:0% +this is aluminum this is the material we + + + align:start position:0% +this is aluminum this is the material we +build aircraft out of admittedly very + + align:start position:0% +build aircraft out of admittedly very + + + align:start position:0% +build aircraft out of admittedly very +thin but it's essentially the same + + align:start position:0% +thin but it's essentially the same + + + align:start position:0% +thin but it's essentially the same +material uh probably not as strong an + + align:start position:0% +material uh probably not as strong an + + + align:start position:0% +material uh probably not as strong an +alloy as we used to make aircraft + + align:start position:0% +alloy as we used to make aircraft + + + align:start position:0% +alloy as we used to make aircraft +aircraft out of so how come this steel + + align:start position:0% +aircraft out of so how come this steel + + + align:start position:0% +aircraft out of so how come this steel +is and the solder is quite ductile it + + align:start position:0% +is and the solder is quite ductile it + + + align:start position:0% +is and the solder is quite ductile it +necks down it deforms whereas the + + align:start position:0% +necks down it deforms whereas the + + + align:start position:0% +necks down it deforms whereas the +aluminum fails by a fracture process uh + + align:start position:0% +aluminum fails by a fracture process uh + + + align:start position:0% +aluminum fails by a fracture process uh +couple more just if you didn't see what + + align:start position:0% +couple more just if you didn't see what + + + align:start position:0% +couple more just if you didn't see what +what I did then um + + align:start position:0% + + + + align:start position:0% + +this is a modeling clay and I'll try and + + align:start position:0% +this is a modeling clay and I'll try and + + + align:start position:0% +this is a modeling clay and I'll try and +load it just so you get the idea of + + align:start position:0% +load it just so you get the idea of + + + align:start position:0% +load it just so you get the idea of +what's going on you see it's thinning + + align:start position:0% +what's going on you see it's thinning + + + align:start position:0% +what's going on you see it's thinning +down it's plastically deforming and oops + + align:start position:0% +down it's plastically deforming and oops + + + align:start position:0% +down it's plastically deforming and oops +it always does that + + align:start position:0% +it always does that + + + align:start position:0% +it always does that +ah + + align:start position:0% +ah + + + align:start position:0% +ah +yeah and it and it necks down nearly to + + align:start position:0% +yeah and it and it necks down nearly to + + + align:start position:0% +yeah and it and it necks down nearly to +a point as we're drawing out material + + align:start position:0% +a point as we're drawing out material + + + align:start position:0% +a point as we're drawing out material +this is actually a plastic instability + + align:start position:0% +this is actually a plastic instability + + + align:start position:0% +this is actually a plastic instability +and we'll talk more about that by the + + align:start position:0% +and we'll talk more about that by the + + + align:start position:0% +and we'll talk more about that by the +end of the lecture so there are + + align:start position:0% +end of the lecture so there are + + + align:start position:0% +end of the lecture so there are +different material behaviors here + + align:start position:0% +different material behaviors here + + + align:start position:0% +different material behaviors here +there's this sort of plastic response + + align:start position:0% +there's this sort of plastic response + + + align:start position:0% +there's this sort of plastic response +and then there's a a brittle response + + align:start position:0% +and then there's a a brittle response + + + align:start position:0% +and then there's a a brittle response +going to do one more uh example to + + align:start position:0% +going to do one more uh example to + + + align:start position:0% +going to do one more uh example to +concentrate the + + align:start position:0% +concentrate the + + + align:start position:0% +concentrate the +mind + + align:start position:0% + + + + align:start position:0% + +uh I should have I've got a slight cold + + align:start position:0% +uh I should have I've got a slight cold + + + align:start position:0% +uh I should have I've got a slight cold +so this + + align:start position:0% + + + + align:start position:0% + +may if I'm looking red it's just the + + align:start position:0% +may if I'm looking red it's just the + + + align:start position:0% +may if I'm looking red it's just the +reflection of this + + align:start position:0% + + + + align:start position:0% + +okay but it's got a leak I'll swear to + + align:start position:0% +okay but it's got a leak I'll swear to + + + align:start position:0% +okay but it's got a leak I'll swear to +it that's + + align:start position:0% +it that's + + + align:start position:0% +it that's +enough uh + + align:start position:0% + + + + align:start position:0% + +this despite what you may be thinking is + + align:start position:0% +this despite what you may be thinking is + + + align:start position:0% +this despite what you may be thinking is +not a balloon okay you got to use your + + align:start position:0% +not a balloon okay you got to use your + + + align:start position:0% +not a balloon okay you got to use your +imagination what do you what do you see + + align:start position:0% +imagination what do you what do you see + + + align:start position:0% +imagination what do you what do you see +here pressure vessel a pressure vessel + + align:start position:0% +here pressure vessel a pressure vessel + + + align:start position:0% +here pressure vessel a pressure vessel +okay that that's that's good you could + + align:start position:0% +okay that that's that's good you could + + + align:start position:0% +okay that that's that's good you could +be a mechanical engineer what do you see + + align:start position:0% +be a mechanical engineer what do you see + + + align:start position:0% +be a mechanical engineer what do you see +here fuel tank fuel tank yeah cryogenic + + align:start position:0% +here fuel tank fuel tank yeah cryogenic + + + align:start position:0% +here fuel tank fuel tank yeah cryogenic +fuel tank maybe you pressurized we + + align:start position:0% +fuel tank maybe you pressurized we + + + align:start position:0% +fuel tank maybe you pressurized we +talked about that last time uh so that's + + align:start position:0% +talked about that last time uh so that's + + + align:start position:0% +talked about that last time uh so that's +the sort of space launch vehicle person + + align:start position:0% +the sort of space launch vehicle person + + + align:start position:0% +the sort of space launch vehicle person +what about humans in space what do you + + align:start position:0% +what about humans in space what do you + + + align:start position:0% +what about humans in space what do you +see + + align:start position:0% +see + + + align:start position:0% +see +here you see a pressure + + align:start position:0% + + + + align:start position:0% + +vessel I see the International Space + + align:start position:0% +vessel I see the International Space + + + align:start position:0% +vessel I see the International Space +Station + + align:start position:0% +Station + + + align:start position:0% +Station +okay and and what do I see + + align:start position:0% +okay and and what do I see + + + align:start position:0% +okay and and what do I see +here me yeah now now you're going with + + align:start position:0% +here me yeah now now you're going with + + + align:start position:0% +here me yeah now now you're going with +it so a very thin walled fuel uh sorry + + align:start position:0% +it so a very thin walled fuel uh sorry + + + align:start position:0% +it so a very thin walled fuel uh sorry +very thin walled pressure vessel and + + align:start position:0% +very thin walled pressure vessel and + + + align:start position:0% +very thin walled pressure vessel and +something that's going to approach it at + + align:start position:0% +something that's going to approach it at + + + align:start position:0% +something that's going to approach it at +high velocity and I don't even need to + + align:start position:0% +high velocity and I don't even need to + + + align:start position:0% +high velocity and I don't even need to +do this + + align:start position:0% +do this + + + align:start position:0% +do this +right or or I see a an aircraft fuselage + + align:start position:0% +right or or I see a an aircraft fuselage + + + align:start position:0% +right or or I see a an aircraft fuselage +which is also pressurized when you're at + + align:start position:0% +which is also pressurized when you're at + + + align:start position:0% +which is also pressurized when you're at +altitude uh and by the way an aircraft + + align:start position:0% +altitude uh and by the way an aircraft + + + align:start position:0% +altitude uh and by the way an aircraft +fuselage and for that matter the + + align:start position:0% +fuselage and for that matter the + + + align:start position:0% +fuselage and for that matter the +International Space Station has a + + align:start position:0% +International Space Station has a + + + align:start position:0% +International Space Station has a +thinner wall compared to its + + align:start position:0% +thinner wall compared to its + + + align:start position:0% +thinner wall compared to its +diameter uh than this balloon does is + + align:start position:0% +diameter uh than this balloon does is + + + align:start position:0% +diameter uh than this balloon does is +I've got it pressurized here comforting + + align:start position:0% +I've got it pressurized here comforting + + + align:start position:0% +I've got it pressurized here comforting +thought next time you go up in an + + align:start position:0% +thought next time you go up in an + + + align:start position:0% +thought next time you go up in an +aircraft uh you hope it's you they have + + align:start position:0% +aircraft uh you hope it's you they have + + + align:start position:0% +aircraft uh you hope it's you they have +been properly designed so this isn't + + align:start position:0% +been properly designed so this isn't + + + align:start position:0% +been properly designed so this isn't +going to happen but in that case uh + + align:start position:0% +going to happen but in that case uh + + + align:start position:0% +going to happen but in that case uh +aircraft fuselage turbine blade or or in + + align:start position:0% +aircraft fuselage turbine blade or or in + + + align:start position:0% +aircraft fuselage turbine blade or or in +fact a fan blade or uh compressor blade + + align:start position:0% +fact a fan blade or uh compressor blade + + + align:start position:0% +fact a fan blade or uh compressor blade +that + + align:start position:0% +that + + + align:start position:0% +that +gets thrown out from the disc an + + align:start position:0% +gets thrown out from the disc an + + + align:start position:0% +gets thrown out from the disc an +uncontained disc burst and it + + align:start position:0% +uncontained disc burst and it + + + align:start position:0% +uncontained disc burst and it +goes and you'd really rather that didn't + + align:start position:0% +goes and you'd really rather that didn't + + + align:start position:0% +goes and you'd really rather that didn't +happen if you're an astronaut in the + + align:start position:0% +happen if you're an astronaut in the + + + align:start position:0% +happen if you're an astronaut in the +international space station passenger in + + align:start position:0% +international space station passenger in + + + align:start position:0% +international space station passenger in +row + + align:start position:0% +row + + + align:start position:0% +row +13A uh which is the blade out row in a + + align:start position:0% +13A uh which is the blade out row in a + + + align:start position:0% +13A uh which is the blade out row in a +in a 7 in a 737 or uh if you're sitting + + align:start position:0% +in a 7 in a 737 or uh if you're sitting + + + align:start position:0% +in a 7 in a 737 or uh if you're sitting +on top of a a satin 5 launch vehicle why + + align:start position:0% +on top of a a satin 5 launch vehicle why + + + align:start position:0% +on top of a a satin 5 launch vehicle why +did that happen I just put a little hole + + align:start position:0% +did that happen I just put a little hole + + + align:start position:0% +did that happen I just put a little hole +in it and bang I got a a very + + align:start position:0% +in it and bang I got a a very + + + align:start position:0% +in it and bang I got a a very +catastrophic failure uh it ties back to + + align:start position:0% +catastrophic failure uh it ties back to + + + align:start position:0% +catastrophic failure uh it ties back to +what was going on with this piece of + + align:start position:0% +what was going on with this piece of + + + align:start position:0% +what was going on with this piece of +aluminum that it just went bang it + + align:start position:0% +aluminum that it just went bang it + + + align:start position:0% +aluminum that it just went bang it +failed straight across it's a fracture + + align:start position:0% +failed straight across it's a fracture + + + align:start position:0% +failed straight across it's a fracture +process as as opposed to the uh the + + align:start position:0% +process as as opposed to the uh the + + + align:start position:0% +process as as opposed to the uh the +steel or the the the modeling clay which + + align:start position:0% +steel or the the the modeling clay which + + + align:start position:0% +steel or the the the modeling clay which +is our prototypical metal uh or model + + align:start position:0% +is our prototypical metal uh or model + + + align:start position:0% +is our prototypical metal uh or model +for a metal which had this ductile + + align:start position:0% +for a metal which had this ductile + + + align:start position:0% +for a metal which had this ductile +response that they neck down they uh + + align:start position:0% +response that they neck down they uh + + + align:start position:0% +response that they neck down they uh +undergo permanent deformation before + + align:start position:0% +undergo permanent deformation before + + + align:start position:0% +undergo permanent deformation before +they break into two pieces so that's + + align:start position:0% +they break into two pieces so that's + + + align:start position:0% +they break into two pieces so that's +what we're going to look at and it's + + align:start position:0% +what we're going to look at and it's + + + align:start position:0% +what we're going to look at and it's +very important to understand that there + + align:start position:0% +very important to understand that there + + + align:start position:0% +very important to understand that there +may be different failure mechanisms + + align:start position:0% +may be different failure mechanisms + + + align:start position:0% +may be different failure mechanisms +depending on what material we're looking + + align:start position:0% +depending on what material we're looking + + + align:start position:0% +depending on what material we're looking +at and also we need to know uh + + align:start position:0% +at and also we need to know uh + + + align:start position:0% +at and also we need to know uh +what we can do about preventing those + + align:start position:0% +what we can do about preventing those + + + align:start position:0% +what we can do about preventing those +failure modes or from a material point + + align:start position:0% +failure modes or from a material point + + + align:start position:0% +failure modes or from a material point +of view how to what extent can we make + + align:start position:0% +of view how to what extent can we make + + + align:start position:0% +of view how to what extent can we make +material stronger uh more resistant to + + align:start position:0% +material stronger uh more resistant to + + + align:start position:0% +material stronger uh more resistant to +failure and uh we'll move on and talk + + align:start position:0% +failure and uh we'll move on and talk + + + align:start position:0% +failure and uh we'll move on and talk +about uh uh fatigue in in due + + align:start position:0% +about uh uh fatigue in in due + + + align:start position:0% +about uh uh fatigue in in due +course any + + align:start position:0% + + + + align:start position:0% + +questions as curiosity um would a plane + + align:start position:0% +questions as curiosity um would a plane + + + align:start position:0% +questions as curiosity um would a plane +actually play like that or is it more + + align:start position:0% +actually play like that or is it more + + + align:start position:0% +actually play like that or is it more +likely to be the way the movies + + align:start position:0% + + + + align:start position:0% + +ah time for one of my favorite + + align:start position:0% +ah time for one of my favorite + + + align:start position:0% +ah time for one of my favorite +anecdotes um so uh aircraft by and large + + align:start position:0% +anecdotes um so uh aircraft by and large + + + align:start position:0% +anecdotes um so uh aircraft by and large +are designed not to blow up like that + + align:start position:0% +are designed not to blow up like that + + + align:start position:0% +are designed not to blow up like that +aircraft are designed not to blow up + + align:start position:0% +aircraft are designed not to blow up + + + align:start position:0% +aircraft are designed not to blow up +like that okay + + align:start position:0% +like that okay + + + align:start position:0% +like that okay +just uh and it's it's what's known as a + + align:start position:0% +just uh and it's it's what's known as a + + + align:start position:0% +just uh and it's it's what's known as a +damage tolerant design approach and in + + align:start position:0% +damage tolerant design approach and in + + + align:start position:0% +damage tolerant design approach and in +particular it's design for that specific + + align:start position:0% +particular it's design for that specific + + + align:start position:0% +particular it's design for that specific +or one of the design criteria is that uh + + align:start position:0% +or one of the design criteria is that uh + + + align:start position:0% +or one of the design criteria is that uh +the fuse large could get punctured with + + align:start position:0% +the fuse large could get punctured with + + + align:start position:0% +the fuse large could get punctured with +a pretty large puncture for instance due + + align:start position:0% +a pretty large puncture for instance due + + + align:start position:0% +a pretty large puncture for instance due +to a blade out or a fatigue crack that's + + align:start position:0% +to a blade out or a fatigue crack that's + + + align:start position:0% +to a blade out or a fatigue crack that's +grown we'll talk about fatigue later so + + align:start position:0% +grown we'll talk about fatigue later so + + + align:start position:0% +grown we'll talk about fatigue later so +uh you have ribs that go round uh uh + + align:start position:0% +uh you have ribs that go round uh uh + + + align:start position:0% +uh you have ribs that go round uh uh +circumferentially down the fuselage and + + align:start position:0% +circumferentially down the fuselage and + + + align:start position:0% +circumferentially down the fuselage and +they provide uh overall stiffness but + + align:start position:0% +they provide uh overall stiffness but + + + align:start position:0% +they provide uh overall stiffness but +they also very importantly provide uh a + + align:start position:0% +they also very importantly provide uh a + + + align:start position:0% +they also very importantly provide uh a +barrier Beyond which a crack shouldn't + + align:start position:0% +barrier Beyond which a crack shouldn't + + + align:start position:0% +barrier Beyond which a crack shouldn't +grow + + align:start position:0% +grow + + + align:start position:0% +grow +catastrophically uh but you can still + + align:start position:0% +catastrophically uh but you can still + + + align:start position:0% +catastrophically uh but you can still +get cracks and you still occasionally + + align:start position:0% +get cracks and you still occasionally + + + align:start position:0% +get cracks and you still occasionally +very occasionally get an unconstrained + + align:start position:0% +very occasionally get an unconstrained + + + align:start position:0% +very occasionally get an unconstrained +blade out and there was a case of a dc9 + + align:start position:0% +blade out and there was a case of a dc9 + + + align:start position:0% +blade out and there was a case of a dc9 +I believe it was this this isn't my + + align:start position:0% +I believe it was this this isn't my + + + align:start position:0% +I believe it was this this isn't my +story I'll give credit to Alan Epstein + + align:start position:0% +story I'll give credit to Alan Epstein + + + align:start position:0% +story I'll give credit to Alan Epstein +who told me about it um which was uh + + align:start position:0% +who told me about it um which was uh + + + align:start position:0% +who told me about it um which was uh +flying domestically around the states + + align:start position:0% +flying domestically around the states + + + align:start position:0% +flying domestically around the states +and uh it suffered an engine a disc + + align:start position:0% +and uh it suffered an engine a disc + + + align:start position:0% +and uh it suffered an engine a disc +burst in in the engine and dc9 has the + + align:start position:0% +burst in in the engine and dc9 has the + + + align:start position:0% +burst in in the engine and dc9 has the +engines at the back and it shot one of + + align:start position:0% +engines at the back and it shot one of + + + align:start position:0% +engines at the back and it shot one of +its uh I guess fan blades through the uh + + align:start position:0% +its uh I guess fan blades through the uh + + + align:start position:0% +its uh I guess fan blades through the uh +fuselage and uh + + align:start position:0% +fuselage and uh + + + align:start position:0% +fuselage and uh +uh you know you lose pressure but it it + + align:start position:0% +uh you know you lose pressure but it it + + + align:start position:0% +uh you know you lose pressure but it it +wasn't a catastrophic failure and uh uh + + align:start position:0% +wasn't a catastrophic failure and uh uh + + + align:start position:0% +wasn't a catastrophic failure and uh uh +got down to low altitude and uh you know + + align:start position:0% +got down to low altitude and uh you know + + + align:start position:0% +got down to low altitude and uh you know +did an emergency landing but it was + + align:start position:0% +did an emergency landing but it was + + + align:start position:0% +did an emergency landing but it was +basically fine then the this was this + + align:start position:0% +basically fine then the this was this + + + align:start position:0% +basically fine then the this was this +was a while ago before they were quite + + align:start position:0% +was a while ago before they were quite + + + align:start position:0% +was a while ago before they were quite +so uh uh uh disciplined about counting + + align:start position:0% +so uh uh uh disciplined about counting + + + align:start position:0% +so uh uh uh disciplined about counting +everyone on the plane and uh the the + + align:start position:0% +everyone on the plane and uh the the + + + align:start position:0% +everyone on the plane and uh the the +flight attendent saying well wasn't + + align:start position:0% +flight attendent saying well wasn't + + + align:start position:0% +flight attendent saying well wasn't +there someone in that that row 28 wasn't + + align:start position:0% +there someone in that that row 28 wasn't + + + align:start position:0% +there someone in that that row 28 wasn't +there someone in 28h + + align:start position:0% +there someone in 28h + + + align:start position:0% +there someone in 28h +and they they scratching their heads and + + align:start position:0% +and they they scratching their heads and + + + align:start position:0% +and they they scratching their heads and +they couldn't quite remember and it was + + align:start position:0% +they couldn't quite remember and it was + + + align:start position:0% +they couldn't quite remember and it was +only when they got to the Manifest that + + align:start position:0% +only when they got to the Manifest that + + + align:start position:0% +only when they got to the Manifest that +there had indeed been someone sitting in + + align:start position:0% +there had indeed been someone sitting in + + + align:start position:0% +there had indeed been someone sitting in +that row and uh uh they were close + + align:start position:0% +that row and uh uh they were close + + + align:start position:0% +that row and uh uh they were close +enough to where the blade went through + + align:start position:0% +enough to where the blade went through + + + align:start position:0% +enough to where the blade went through +that uh their moral remains got sucked + + align:start position:0% +that uh their moral remains got sucked + + + align:start position:0% +that uh their moral remains got sucked +out somewhere over the Midwest uh which + + align:start position:0% +out somewhere over the Midwest uh which + + + align:start position:0% +out somewhere over the Midwest uh which +is not a very nice thought but + + align:start position:0% +is not a very nice thought but + + + align:start position:0% +is not a very nice thought but +anyway thank you for asking that + + align:start position:0% +anyway thank you for asking that + + + align:start position:0% +anyway thank you for asking that +question any other questions curiosity + + align:start position:0% +question any other questions curiosity + + + align:start position:0% +question any other questions curiosity +is good yes + + align:start position:0% +is good yes + + + align:start position:0% +is good yes +Ben where the the airpl off ah no that's + + align:start position:0% +Ben where the the airpl off ah no that's + + + align:start position:0% +Ben where the the airpl off ah no that's +not a + + align:start position:0% +not a + + + align:start position:0% +not a +movie uh we we will talk about this + + align:start position:0% +movie uh we we will talk about this + + + align:start position:0% +movie uh we we will talk about this +particular case and it's actually a + + align:start position:0% +particular case and it's actually a + + + align:start position:0% +particular case and it's actually a +success story that uh Boeing 737 flown + + align:start position:0% +success story that uh Boeing 737 flown + + + align:start position:0% +success story that uh Boeing 737 flown +by Aloha Airlines I think it was in 1990 + + align:start position:0% +by Aloha Airlines I think it was in 1990 + + + align:start position:0% +by Aloha Airlines I think it was in 1990 +uh became the world's first + + align:start position:0% +uh became the world's first + + + align:start position:0% +uh became the world's first +convertiable uh commercial jet as it + + align:start position:0% +convertiable uh commercial jet as it + + + align:start position:0% +convertiable uh commercial jet as it +lost a large part of its upper fuselage + + align:start position:0% +lost a large part of its upper fuselage + + + align:start position:0% +lost a large part of its upper fuselage +uh forward of the Wings and I'll bring + + align:start position:0% +uh forward of the Wings and I'll bring + + + align:start position:0% +uh forward of the Wings and I'll bring +in pictures when we talk about fatigue + + align:start position:0% +in pictures when we talk about fatigue + + + align:start position:0% +in pictures when we talk about fatigue +it was accumulated fatigue cracks that + + align:start position:0% +it was accumulated fatigue cracks that + + + align:start position:0% +it was accumulated fatigue cracks that +basically caused perforations around the + + align:start position:0% +basically caused perforations around the + + + align:start position:0% +basically caused perforations around the +fuselage and the uh the upper fuselage + + align:start position:0% +fuselage and the uh the upper fuselage + + + align:start position:0% +fuselage and the uh the upper fuselage +uh got ripped off but miraculously even + + align:start position:0% +uh got ripped off but miraculously even + + + align:start position:0% +uh got ripped off but miraculously even +though it was lose it had lost nearly + + align:start position:0% +though it was lose it had lost nearly + + + align:start position:0% +though it was lose it had lost nearly +half of the circumference of the + + align:start position:0% +half of the circumference of the + + + align:start position:0% +half of the circumference of the +fuselage in that region the plane still + + align:start position:0% +fuselage in that region the plane still + + + align:start position:0% +fuselage in that region the plane still +was able to get down and land safely + + align:start position:0% +was able to get down and land safely + + + align:start position:0% +was able to get down and land safely +there was one casualty uh of a flight + + align:start position:0% +there was one casualty uh of a flight + + + align:start position:0% +there was one casualty uh of a flight +attendant who was standing up uh and got + + align:start position:0% +attendant who was standing up uh and got + + + align:start position:0% +attendant who was standing up uh and got +whisked out 20,000 ft but everyone else + + align:start position:0% +whisked out 20,000 ft but everyone else + + + align:start position:0% +whisked out 20,000 ft but everyone else +survived and it really is a remarkable + + align:start position:0% +survived and it really is a remarkable + + + align:start position:0% +survived and it really is a remarkable +story of of very solid structural design + + align:start position:0% +story of of very solid structural design + + + align:start position:0% +story of of very solid structural design +that that that was able to happen I mean + + align:start position:0% +that that that was able to happen I mean + + + align:start position:0% +that that that was able to happen I mean +I'll show you pictures of this you + + align:start position:0% +I'll show you pictures of this you + + + align:start position:0% +I'll show you pictures of this you +you'll be amazed but it's not a movie + + align:start position:0% +you'll be amazed but it's not a movie + + + align:start position:0% +you'll be amazed but it's not a movie +that was + + align:start position:0% +that was + + + align:start position:0% +that was +real okay let's uh uh move on and talk a + + align:start position:0% +real okay let's uh uh move on and talk a + + + align:start position:0% +real okay let's uh uh move on and talk a +little bit about + + align:start position:0% +little bit about + + + align:start position:0% +little bit about +uh the first of these failure modes + + align:start position:0% +uh the first of these failure modes + + + align:start position:0% +uh the first of these failure modes +we're going to examine that of yield and + + align:start position:0% +we're going to examine that of yield and + + + align:start position:0% +we're going to examine that of yield and +and + + align:start position:0% +and + + + align:start position:0% +and +plasticity um and it's the failure mode + + align:start position:0% +plasticity um and it's the failure mode + + + align:start position:0% +plasticity um and it's the failure mode +we saw when we looked looked at a piece + + align:start position:0% +we saw when we looked looked at a piece + + + align:start position:0% +we saw when we looked looked at a piece +of Steel a piece of plexiglass sorry a + + align:start position:0% +of Steel a piece of plexiglass sorry a + + + align:start position:0% +of Steel a piece of plexiglass sorry a +piece of modeling clay and uh this piece + + align:start position:0% +piece of modeling clay and uh this piece + + + align:start position:0% +piece of modeling clay and uh this piece +of solder uh deforming necking + + align:start position:0% +of solder uh deforming necking + + + align:start position:0% +of solder uh deforming necking +down uh undergoing permanent uh plastic + + align:start position:0% +down uh undergoing permanent uh plastic + + + align:start position:0% +down uh undergoing permanent uh plastic +deformation before + + align:start position:0% +deformation before + + + align:start position:0% +deformation before +failing so this is lecture M15 and it's + + align:start position:0% +failing so this is lecture M15 and it's + + + align:start position:0% +failing so this is lecture M15 and it's +yield and + + align:start position:0% + + + + align:start position:0% + +plasticity and + + align:start position:0% + + + + align:start position:0% + +going to do a little bit of naming of + + align:start position:0% +going to do a little bit of naming of + + + align:start position:0% +going to do a little bit of naming of +parts and I I wish that you had uh an + + align:start position:0% +parts and I I wish that you had uh an + + + align:start position:0% +parts and I I wish that you had uh an +opportunity to actually go down into the + + align:start position:0% +opportunity to actually go down into the + + + align:start position:0% +opportunity to actually go down into the +lab and and uh do some T cell testing on + + align:start position:0% +lab and and uh do some T cell testing on + + + align:start position:0% +lab and and uh do some T cell testing on +some pieces of material we've done this + + align:start position:0% +some pieces of material we've done this + + + align:start position:0% +some pieces of material we've done this +in previous years um unfortunately we + + align:start position:0% +in previous years um unfortunately we + + + align:start position:0% +in previous years um unfortunately we +don't have time in the systems problem + + align:start position:0% +don't have time in the systems problem + + + align:start position:0% +don't have time in the systems problem +schedule to do it this year but if you + + align:start position:0% +schedule to do it this year but if you + + + align:start position:0% +schedule to do it this year but if you +ever get a chance don't take my word for + + align:start position:0% +ever get a chance don't take my word for + + + align:start position:0% +ever get a chance don't take my word for +this actually do a mechanical test + + align:start position:0% +this actually do a mechanical test + + + align:start position:0% +this actually do a mechanical test +yourself on a piece of material uh as + + align:start position:0% +yourself on a piece of material uh as + + + align:start position:0% +yourself on a piece of material uh as +always I'm just presenting a model uh + + align:start position:0% +always I'm just presenting a model uh + + + align:start position:0% +always I'm just presenting a model uh +you should always question it so the + + align:start position:0% +you should always question it so the + + + align:start position:0% +you should always question it so the +typical test we'll do is what in a more + + align:start position:0% +typical test we'll do is what in a more + + + align:start position:0% +typical test we'll do is what in a more +instrumented + + align:start position:0% + + + + align:start position:0% + +way what Carl and I did over the + + align:start position:0% +way what Carl and I did over the + + + align:start position:0% +way what Carl and I did over the +overhead projector we have + + align:start position:0% + + + + align:start position:0% + +some material uh a rod of material some + + align:start position:0% +some material uh a rod of material some + + + align:start position:0% +some material uh a rod of material some +cross-sectional area a + + align:start position:0% +cross-sectional area a + + + align:start position:0% +cross-sectional area a +uh some length L and in fact I'm going + + align:start position:0% +uh some length L and in fact I'm going + + + align:start position:0% +uh some length L and in fact I'm going +to call this + + align:start position:0% +to call this + + + align:start position:0% +to call this +a0 and l0 because well we'll see why in + + align:start position:0% +a0 and l0 because well we'll see why in + + + align:start position:0% +a0 and l0 because well we'll see why in +a minute um and I can that allows us + + align:start position:0% +a minute um and I can that allows us + + + align:start position:0% +a minute um and I can that allows us +just as it always has to define a stress + + align:start position:0% +just as it always has to define a stress + + + align:start position:0% +just as it always has to define a stress +some stress which is force over area and + + align:start position:0% +some stress which is force over area and + + + align:start position:0% +some stress which is force over area and +some strain which is Delta L over + + align:start position:0% + + + + align:start position:0% + +L and I'm going to give these slightly + + align:start position:0% +L and I'm going to give these slightly + + + align:start position:0% +L and I'm going to give these slightly +different uh names so some stress that's + + align:start position:0% +different uh names so some stress that's + + + align:start position:0% +different uh names so some stress that's +I'm going to call Sigma nominal uh which + + align:start position:0% +I'm going to call Sigma nominal uh which + + + align:start position:0% +I'm going to call Sigma nominal uh which +is Sigma n force over area + + align:start position:0% +is Sigma n force over area + + + align:start position:0% +is Sigma n force over area +and + + align:start position:0% +and + + + align:start position:0% +and +some + + align:start position:0% + + + + align:start position:0% + +strain which is the change in length + + align:start position:0% +strain which is the change in length + + + align:start position:0% +strain which is the change in length +over the original length and what we're + + align:start position:0% +over the original length and what we're + + + align:start position:0% +over the original length and what we're +going to typically see for a + + align:start position:0% +going to typically see for a + + + align:start position:0% +going to typically see for a +metal is that there's some region in + + align:start position:0% +metal is that there's some region in + + + align:start position:0% +metal is that there's some region in +which it's + + align:start position:0% + + + + align:start position:0% + +elastic with Young's modulus + + align:start position:0% + + + + align:start position:0% + +e then we hit a region where we get + + align:start position:0% +e then we hit a region where we get + + + align:start position:0% +e then we hit a region where we get +plastic deformation we get yield the + + align:start position:0% +plastic deformation we get yield the + + + align:start position:0% +plastic deformation we get yield the +so-called yield stress Sigma + + align:start position:0% +so-called yield stress Sigma + + + align:start position:0% +so-called yield stress Sigma +Y and after that + + align:start position:0% +Y and after that + + + align:start position:0% +Y and after that +point we'll get a nonlinear increase of + + align:start position:0% +point we'll get a nonlinear increase of + + + align:start position:0% +point we'll get a nonlinear increase of +stress with strain but with a slope + + align:start position:0% +stress with strain but with a slope + + + align:start position:0% +stress with strain but with a slope +that's significantly less than the + + align:start position:0% +that's significantly less than the + + + align:start position:0% +that's significantly less than the +Young's + + align:start position:0% +Young's + + + align:start position:0% +Young's +modulus and then at some + + align:start position:0% +modulus and then at some + + + align:start position:0% +modulus and then at some +point we'll find that + + align:start position:0% +point we'll find that + + + align:start position:0% +point we'll find that +uh we get a maximum in the in the stress + + align:start position:0% +uh we get a maximum in the in the stress + + + align:start position:0% +uh we get a maximum in the in the stress +strain + + align:start position:0% + + + + align:start position:0% + +response usually called the tensile + + align:start position:0% +response usually called the tensile + + + align:start position:0% +response usually called the tensile +strength so Sigma subscript TS so that's + + align:start position:0% +strength so Sigma subscript TS so that's + + + align:start position:0% +strength so Sigma subscript TS so that's +the maximum stress the material can + + align:start position:0% +the maximum stress the material can + + + align:start position:0% +the maximum stress the material can +carry at which point we'll talk more + + align:start position:0% +carry at which point we'll talk more + + + align:start position:0% +carry at which point we'll talk more +about + + align:start position:0% + + + + align:start position:0% + +this we see this necking phenomenon this + + align:start position:0% +this we see this necking phenomenon this + + + align:start position:0% +this we see this necking phenomenon this +this reduction in a cross-sectional area + + align:start position:0% +this reduction in a cross-sectional area + + + align:start position:0% +this reduction in a cross-sectional area +in a very dutile material down to a near + + align:start position:0% +in a very dutile material down to a near + + + align:start position:0% +in a very dutile material down to a near +point and then somewhere after that we + + align:start position:0% +point and then somewhere after that we + + + align:start position:0% +point and then somewhere after that we +get failure breaking into two halves + + align:start position:0% + + + + align:start position:0% + +which again we see in all those cases up + + align:start position:0% +which again we see in all those cases up + + + align:start position:0% +which again we see in all those cases up +there so that's the the basic phenomenon + + align:start position:0% +there so that's the the basic phenomenon + + + align:start position:0% +there so that's the the basic phenomenon +if we just took a a piece of aluminum or + + align:start position:0% +if we just took a a piece of aluminum or + + + align:start position:0% +if we just took a a piece of aluminum or +or steel and loaded it up we'd go + + align:start position:0% +or steel and loaded it up we'd go + + + align:start position:0% +or steel and loaded it up we'd go +through these + + align:start position:0% +through these + + + align:start position:0% +through these +uh through these + + align:start position:0% +uh through these + + + align:start position:0% +uh through these +uh conditions there's one other thing + + align:start position:0% +uh conditions there's one other thing + + + align:start position:0% +uh conditions there's one other thing +you should be aware of which is if we + + align:start position:0% +you should be aware of which is if we + + + align:start position:0% +you should be aware of which is if we +load this up but don't go to uh failure + + align:start position:0% +load this up but don't go to uh failure + + + align:start position:0% +load this up but don't go to uh failure +we don't go past the point where we get + + align:start position:0% +we don't go past the point where we get + + + align:start position:0% +we don't go past the point where we get +necking if we uh unload it from here and + + align:start position:0% +necking if we uh unload it from here and + + + align:start position:0% +necking if we uh unload it from here and +I'll just draw + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% + + + + align:start position:0% + +oops we go up past yield to some strain + + align:start position:0% +oops we go up past yield to some strain + + + align:start position:0% +oops we go up past yield to some strain +and some stress and we + + align:start position:0% + + + + align:start position:0% + +unload we unload with the Young's + + align:start position:0% +unload we unload with the Young's + + + align:start position:0% +unload we unload with the Young's +modulus + + align:start position:0% +modulus + + + align:start position:0% +modulus +that we started with and we get some + + align:start position:0% +that we started with and we get some + + + align:start position:0% +that we started with and we get some +plastic permanent + + align:start position:0% +plastic permanent + + + align:start position:0% +plastic permanent +strain resulting and then if we reloaded + + align:start position:0% +strain resulting and then if we reloaded + + + align:start position:0% +strain resulting and then if we reloaded +this + + align:start position:0% +this + + + align:start position:0% +this +up or went back up here we would reload + + align:start position:0% +up or went back up here we would reload + + + align:start position:0% +up or went back up here we would reload +again with the uh same modulus of that + + align:start position:0% +again with the uh same modulus of that + + + align:start position:0% +again with the uh same modulus of that +material the modulus doesn't change + + align:start position:0% +material the modulus doesn't change + + + align:start position:0% +material the modulus doesn't change +because of this uh plastic deoration um + + align:start position:0% +because of this uh plastic deoration um + + + align:start position:0% +because of this uh plastic deoration um +until we hit this yield stress this new + + align:start position:0% +until we hit this yield stress this new + + + align:start position:0% +until we hit this yield stress this new +yield stress the material has apparently + + align:start position:0% +yield stress the material has apparently + + + align:start position:0% +yield stress the material has apparently +got stronger because we've done this + + align:start position:0% +got stronger because we've done this + + + align:start position:0% +got stronger because we've done this +defamation to it and would continue on + + align:start position:0% +defamation to it and would continue on + + + align:start position:0% +defamation to it and would continue on +uh until we get uh T Cell failure yes + + align:start position:0% + + + + align:start position:0% + +then no it's + + align:start position:0% +then no it's + + + align:start position:0% +then no it's +actually to the + + align:start position:0% +actually to the + + + align:start position:0% +actually to the +nth significant figure true that uh and + + align:start position:0% +nth significant figure true that uh and + + + align:start position:0% +nth significant figure true that uh and +it's because as we'll see that we aren't + + align:start position:0% +it's because as we'll see that we aren't + + + align:start position:0% +it's because as we'll see that we aren't +fundamentally changing the crystal + + align:start position:0% +fundamentally changing the crystal + + + align:start position:0% +fundamentally changing the crystal +structure or the atomic bonding the + + align:start position:0% +structure or the atomic bonding the + + + align:start position:0% +structure or the atomic bonding the +things that control the young modulus + + align:start position:0% +things that control the young modulus + + + align:start position:0% +things that control the young modulus +we're just rearranging where those bonds + + align:start position:0% +we're just rearranging where those bonds + + + align:start position:0% +we're just rearranging where those bonds +are as we do this and we'll look at the + + align:start position:0% +are as we do this and we'll look at the + + + align:start position:0% +are as we do this and we'll look at the +mechanisms that underly that yes what's + + align:start position:0% +mechanisms that underly that yes what's + + + align:start position:0% +mechanisms that underly that yes what's +the subscript of the + + align:start position:0% + + + + align:start position:0% + +sigma I I'll will just do a little bit + + align:start position:0% +sigma I I'll will just do a little bit + + + align:start position:0% +sigma I I'll will just do a little bit +of naming of Parts here uh on the + + align:start position:0% +of naming of Parts here uh on the + + + align:start position:0% +of naming of Parts here uh on the +screen uh so so there's + + align:start position:0% +screen uh so so there's + + + align:start position:0% +screen uh so so there's +the stress strain curve that I + + align:start position:0% + + + + align:start position:0% + +uh sketched and these are in the notes + + align:start position:0% +uh sketched and these are in the notes + + + align:start position:0% +uh sketched and these are in the notes +um and we have yield strength Sigma Y T + + align:start position:0% +um and we have yield strength Sigma Y T + + + align:start position:0% +um and we have yield strength Sigma Y T +Cell strength Sigma subscrip TS there's + + align:start position:0% +Cell strength Sigma subscrip TS there's + + + align:start position:0% +Cell strength Sigma subscrip TS there's +some permanent strain after unloading so + + align:start position:0% +some permanent strain after unloading so + + + align:start position:0% +some permanent strain after unloading so +some plastic strain and unloading and + + align:start position:0% +some plastic strain and unloading and + + + align:start position:0% +some plastic strain and unloading and +reloading is a linear elastic behavior + + align:start position:0% +reloading is a linear elastic behavior + + + align:start position:0% +reloading is a linear elastic behavior +and then uh once we go beyond yield + + align:start position:0% +and then uh once we go beyond yield + + + align:start position:0% +and then uh once we go beyond yield +initially we get this + + align:start position:0% +initially we get this + + + align:start position:0% +initially we get this +increasing + + align:start position:0% +increasing + + + align:start position:0% +increasing +strength with more deformation and this + + align:start position:0% +strength with more deformation and this + + + align:start position:0% +strength with more deformation and this +is socalled work hardening so increasing + + align:start position:0% +is socalled work hardening so increasing + + + align:start position:0% +is socalled work hardening so increasing +yield stress with increasing plastic + + align:start position:0% +yield stress with increasing plastic + + + align:start position:0% +yield stress with increasing plastic +strength any + + align:start position:0% + + + + align:start position:0% + +questions everyone buy that yes D well + + align:start position:0% +questions everyone buy that yes D well + + + align:start position:0% +questions everyone buy that yes D well +is it ever the case in manufacturing + + align:start position:0% +is it ever the case in manufacturing + + + align:start position:0% +is it ever the case in manufacturing +that someone might purposely stress + + align:start position:0% +that someone might purposely stress + + + align:start position:0% +that someone might purposely stress +something past yield and make it a + + align:start position:0% +something past yield and make it a + + + align:start position:0% +something past yield and make it a +strong + + align:start position:0% +strong + + + align:start position:0% +strong +absolutely absolutely and in fact uh + + align:start position:0% +absolutely absolutely and in fact uh + + + align:start position:0% +absolutely absolutely and in fact uh +there's no metal that you're going to + + align:start position:0% +there's no metal that you're going to + + + align:start position:0% +there's no metal that you're going to +use as an engineer that hasn't been + + align:start position:0% +use as an engineer that hasn't been + + + align:start position:0% +use as an engineer that hasn't been +deliberately work hardened in order to + + align:start position:0% +deliberately work hardened in order to + + + align:start position:0% +deliberately work hardened in order to +get a certain yield stress uh what are + + align:start position:0% +get a certain yield stress uh what are + + + align:start position:0% +get a certain yield stress uh what are +examples of this what what might you do + + align:start position:0% +examples of this what what might you do + + + align:start position:0% +examples of this what what might you do +to work harden a a piece of steel or + + align:start position:0% +to work harden a a piece of steel or + + + align:start position:0% +to work harden a a piece of steel or +even a even this foil has been work + + align:start position:0% + + + + align:start position:0% + +hardened what what how do you make foil + + align:start position:0% +hardened what what how do you make foil + + + align:start position:0% +hardened what what how do you make foil +anyone just basically roll it into + + align:start position:0% +anyone just basically roll it into + + + align:start position:0% +anyone just basically roll it into +sheets you just basically roll it into + + align:start position:0% +sheets you just basically roll it into + + + align:start position:0% +sheets you just basically roll it into +sheets but the the deformation you're + + align:start position:0% +sheets but the the deformation you're + + + align:start position:0% +sheets but the the deformation you're +doing is plastic defamation because you + + align:start position:0% +doing is plastic defamation because you + + + align:start position:0% +doing is plastic defamation because you +don't want it to Spring back elastically + + align:start position:0% +don't want it to Spring back elastically + + + align:start position:0% +don't want it to Spring back elastically +you want to permanently reduce its + + align:start position:0% +you want to permanently reduce its + + + align:start position:0% +you want to permanently reduce its +thickness so this has seen a lot of + + align:start position:0% +thickness so this has seen a lot of + + + align:start position:0% +thickness so this has seen a lot of +plastic deformation in fact you more or + + align:start position:0% +plastic deformation in fact you more or + + + align:start position:0% +plastic deformation in fact you more or +less reduce it all the way up to this + + align:start position:0% +less reduce it all the way up to this + + + align:start position:0% +less reduce it all the way up to this +point which also explains why there + + align:start position:0% +point which also explains why there + + + align:start position:0% +point which also explains why there +isn't much additional defamation when I + + align:start position:0% +isn't much additional defamation when I + + + align:start position:0% +isn't much additional defamation when I +pulled on this foil it it it broke in a + + align:start position:0% +pulled on this foil it it it broke in a + + + align:start position:0% +pulled on this foil it it it broke in a +pretty brittle manner without much uh + + align:start position:0% +pretty brittle manner without much uh + + + align:start position:0% +pretty brittle manner without much uh +additional plastic defamation occurring + + align:start position:0% +additional plastic defamation occurring + + + align:start position:0% +additional plastic defamation occurring +uh + + align:start position:0% +uh + + + align:start position:0% +uh +how else might you do um work + + align:start position:0% + + + + align:start position:0% + +hardening how who are the first metal + + align:start position:0% +hardening how who are the first metal + + + align:start position:0% +hardening how who are the first metal +workers + + align:start position:0% +workers + + + align:start position:0% +workers +blacksmiths when you hit things what + + align:start position:0% +blacksmiths when you hit things what + + + align:start position:0% +blacksmiths when you hit things what +you're doing what you're whacking the + + align:start position:0% +you're doing what you're whacking the + + + align:start position:0% +you're doing what you're whacking the +the metal is is increasing its strength + + align:start position:0% +the metal is is increasing its strength + + + align:start position:0% +the metal is is increasing its strength +you're turning it into a shape sure but + + align:start position:0% +you're turning it into a shape sure but + + + align:start position:0% +you're turning it into a shape sure but +the difference between doing it hot and + + align:start position:0% +the difference between doing it hot and + + + align:start position:0% +the difference between doing it hot and +doing it cold we'll understand in a few + + align:start position:0% +doing it cold we'll understand in a few + + + align:start position:0% +doing it cold we'll understand in a few +lectures time but hitting it whilst it's + + align:start position:0% +lectures time but hitting it whilst it's + + + align:start position:0% +lectures time but hitting it whilst it's +cold will push up the strength obviously + + align:start position:0% +cold will push up the strength obviously + + + align:start position:0% +cold will push up the strength obviously +there's a tradeoff you don't want to + + align:start position:0% +there's a tradeoff you don't want to + + + align:start position:0% +there's a tradeoff you don't want to +make it so brittle that you know it it + + align:start position:0% +make it so brittle that you know it it + + + align:start position:0% +make it so brittle that you know it it +it shatters uh if if the horse you know + + align:start position:0% +it shatters uh if if the horse you know + + + align:start position:0% +it shatters uh if if the horse you know +gallops its foot onto a stone but uh you + + align:start position:0% +gallops its foot onto a stone but uh you + + + align:start position:0% +gallops its foot onto a stone but uh you +know it's so that's the blacksmith's art + + align:start position:0% +know it's so that's the blacksmith's art + + + align:start position:0% +know it's so that's the blacksmith's art +tempering there's some other things + + align:start position:0% +tempering there's some other things + + + align:start position:0% +tempering there's some other things +going on in in metal working steel the + + align:start position:0% +going on in in metal working steel the + + + align:start position:0% +going on in in metal working steel the +there are phase Transformations which + + align:start position:0% +there are phase Transformations which + + + align:start position:0% +there are phase Transformations which +we're not particularly going to talk + + align:start position:0% +we're not particularly going to talk + + + align:start position:0% +we're not particularly going to talk +about here uh yeah + + align:start position:0% +about here uh yeah + + + align:start position:0% +about here uh yeah +Ben I was curious about why the curve DS + + align:start position:0% +Ben I was curious about why the curve DS + + + align:start position:0% +Ben I was curious about why the curve DS +down after the yes we'll come on to + + align:start position:0% + + + + align:start position:0% + +that basically it's run out of work + + align:start position:0% +that basically it's run out of work + + + align:start position:0% +that basically it's run out of work +hardening capability it can't you can't + + align:start position:0% +hardening capability it can't you can't + + + align:start position:0% +hardening capability it can't you can't +make it any stronger um that so failure + + align:start position:0% +make it any stronger um that so failure + + + align:start position:0% +make it any stronger um that so failure +starts to occur we'll we'll look at that + + align:start position:0% +starts to occur we'll we'll look at that + + + align:start position:0% +starts to occur we'll we'll look at that +hopefully before the end of this + + align:start position:0% +hopefully before the end of this + + + align:start position:0% +hopefully before the end of this +lecture + + align:start position:0% +lecture + + + align:start position:0% +lecture +um up to now we haven't really + + align:start position:0% +um up to now we haven't really + + + align:start position:0% +um up to now we haven't really +distinguished + + align:start position:0% +distinguished + + + align:start position:0% +distinguished +between uh tensile and compressive + + align:start position:0% +between uh tensile and compressive + + + align:start position:0% +between uh tensile and compressive +Behavior but we're going to need to um + + align:start position:0% +Behavior but we're going to need to um + + + align:start position:0% +Behavior but we're going to need to um +for reasons I'll hopefully demonstrate + + align:start position:0% +for reasons I'll hopefully demonstrate + + + align:start position:0% +for reasons I'll hopefully demonstrate +here + + align:start position:0% + + + + align:start position:0% + +that if I take now + + align:start position:0% + + + + align:start position:0% + +a piece of material that I'm going to + + align:start position:0% +a piece of material that I'm going to + + + align:start position:0% +a piece of material that I'm going to +load in + + align:start position:0% +load in + + + align:start position:0% +load in +compression uh I can only do this once + + align:start position:0% +compression uh I can only do this once + + + align:start position:0% +compression uh I can only do this once +uh so two blocks of metal I'm going to + + align:start position:0% +uh so two blocks of metal I'm going to + + + align:start position:0% +uh so two blocks of metal I'm going to +start pushing what + + align:start position:0% +start pushing what + + + align:start position:0% +start pushing what +happens what are you seeing happen this + + align:start position:0% +happens what are you seeing happen this + + + align:start position:0% +happens what are you seeing happen this +is it's + + align:start position:0% +is it's + + + align:start position:0% +is it's +expanding and it's going to continue to + + align:start position:0% +expanding and it's going to continue to + + + align:start position:0% +expanding and it's going to continue to +expand and I can go so far but at some + + align:start position:0% +expand and I can go so far but at some + + + align:start position:0% +expand and I can go so far but at some +point I just can't continue to to + + align:start position:0% +point I just can't continue to to + + + align:start position:0% +point I just can't continue to to +compress this it's it's it's barreling + + align:start position:0% +compress this it's it's it's barreling + + + align:start position:0% +compress this it's it's it's barreling +out and it's extruding upward uh as I've + + align:start position:0% +out and it's extruding upward uh as I've + + + align:start position:0% +out and it's extruding upward uh as I've +uh do this plastic deformation it's + + align:start position:0% +uh do this plastic deformation it's + + + align:start position:0% +uh do this plastic deformation it's +fundamentally a different behavior from + + align:start position:0% +fundamentally a different behavior from + + + align:start position:0% +fundamentally a different behavior from +what I've got here where I don't see + + align:start position:0% +what I've got here where I don't see + + + align:start position:0% +what I've got here where I don't see +this necking down in compression and why + + align:start position:0% +this necking down in compression and why + + + align:start position:0% +this necking down in compression and why +not why don't I see this this necking + + align:start position:0% +not why don't I see this this necking + + + align:start position:0% +not why don't I see this this necking +Behavior + + align:start position:0% +Behavior + + + align:start position:0% +Behavior +when I load in compression what's + + align:start position:0% +when I load in compression what's + + + align:start position:0% +when I load in compression what's +happening as I deform in in + + align:start position:0% +happening as I deform in in + + + align:start position:0% +happening as I deform in in +compression that area what's it + + align:start position:0% + + + + align:start position:0% + +doing the air is increasing so if I had + + align:start position:0% +doing the air is increasing so if I had + + + align:start position:0% +doing the air is increasing so if I had +this Behavior the load I have to carry + + align:start position:0% +this Behavior the load I have to carry + + + align:start position:0% +this Behavior the load I have to carry +is continually increasing only because + + align:start position:0% +is continually increasing only because + + + align:start position:0% +is continually increasing only because +the air is increasing + + align:start position:0% +the air is increasing + + + align:start position:0% +the air is increasing +so it's not that the material is + + align:start position:0% +so it's not that the material is + + + align:start position:0% +so it's not that the material is +necessarily behaving any different + + align:start position:0% +necessarily behaving any different + + + align:start position:0% +necessarily behaving any different +intention + + align:start position:0% +intention + + + align:start position:0% +intention +compression it's that the way we've + + align:start position:0% +compression it's that the way we've + + + align:start position:0% +compression it's that the way we've +defined stress and strain is no longer + + align:start position:0% +defined stress and strain is no longer + + + align:start position:0% +defined stress and strain is no longer +adequate um why not what's the limit on + + align:start position:0% +adequate um why not what's the limit on + + + align:start position:0% +adequate um why not what's the limit on +our definitions of stress and strain up + + align:start position:0% +our definitions of stress and strain up + + + align:start position:0% +our definitions of stress and strain up +to + + align:start position:0% +to + + + align:start position:0% +to +now what's one of the key limitations + + align:start position:0% +now what's one of the key limitations + + + align:start position:0% +now what's one of the key limitations +where our model for uh strain and + + align:start position:0% +where our model for uh strain and + + + align:start position:0% +where our model for uh strain and +displacement depends + + align:start position:0% +displacement depends + + + align:start position:0% +displacement depends +on uh Jonathan got be a long be it's got + + align:start position:0% +on uh Jonathan got be a long be it's got + + + align:start position:0% +on uh Jonathan got be a long be it's got +to be a long be no that we were looking + + align:start position:0% +to be a long be no that we were looking + + + align:start position:0% +to be a long be no that we were looking +we remember we Define small uh we + + align:start position:0% +we remember we Define small uh we + + + align:start position:0% +we remember we Define small uh we +defined strain displacement relations uh + + align:start position:0% +defined strain displacement relations uh + + + align:start position:0% +defined strain displacement relations uh +for this infinitesimal cube of material + + align:start position:0% +for this infinitesimal cube of material + + + align:start position:0% +for this infinitesimal cube of material +or Square of material say + + align:start position:0% +or Square of material say + + + align:start position:0% +or Square of material say +small FL yes so long as we're dealing + + align:start position:0% +small FL yes so long as we're dealing + + + align:start position:0% +small FL yes so long as we're dealing +with small deformations sort of less + + align:start position:0% +with small deformations sort of less + + + align:start position:0% +with small deformations sort of less +than 10% ideally less than maybe a + + align:start position:0% +than 10% ideally less than maybe a + + + align:start position:0% +than 10% ideally less than maybe a +couple of percent strain and what's the + + align:start position:0% +couple of percent strain and what's the + + + align:start position:0% +couple of percent strain and what's the +strain here what strain did I put this + + align:start position:0% +strain here what strain did I put this + + + align:start position:0% +strain here what strain did I put this +through + + align:start position:0% + + + + align:start position:0% + +well what change how what fraction did + + align:start position:0% +well what change how what fraction did + + + align:start position:0% +well what change how what fraction did +the length change by by a factor half so + + align:start position:0% +the length change by by a factor half so + + + align:start position:0% +the length change by by a factor half so +you know went to 50% strain or if I did + + align:start position:0% +you know went to 50% strain or if I did + + + align:start position:0% +you know went to 50% strain or if I did +it in reverse it would be 100% strain so + + align:start position:0% +it in reverse it would be 100% strain so + + + align:start position:0% +it in reverse it would be 100% strain so +strains of 0.5 or one or two those are + + align:start position:0% +strains of 0.5 or one or two those are + + + align:start position:0% +strains of 0.5 or one or two those are +big strains so we have to be a little + + align:start position:0% +big strains so we have to be a little + + + align:start position:0% +big strains so we have to be a little +bit careful about how we uh Define our + + align:start position:0% +bit careful about how we uh Define our + + + align:start position:0% +bit careful about how we uh Define our +reference for uh the length and just + + align:start position:0% +reference for uh the length and just + + + align:start position:0% +reference for uh the length and just +plotting Delta L over l0 and for that + + align:start position:0% +plotting Delta L over l0 and for that + + + align:start position:0% +plotting Delta L over l0 and for that +matter force or stress in terms of force + + align:start position:0% +matter force or stress in terms of force + + + align:start position:0% +matter force or stress in terms of force +over a area is not quite enough so um + + align:start position:0% +over a area is not quite enough so um + + + align:start position:0% +over a area is not quite enough so um +the way we get around this or or just + + align:start position:0% +the way we get around this or or just + + + align:start position:0% +the way we get around this or or just +deal with this is just to uh refine our + + align:start position:0% +deal with this is just to uh refine our + + + align:start position:0% +deal with this is just to uh refine our +definition of of + + align:start position:0% + + + + align:start position:0% + +strain and introduce the idea of a a + + align:start position:0% +strain and introduce the idea of a a + + + align:start position:0% +strain and introduce the idea of a a +true stress and a true strain + + align:start position:0% + + + + align:start position:0% + +as opposed to what I had here which are + + align:start position:0% +as opposed to what I had here which are + + + align:start position:0% +as opposed to what I had here which are +the nominal stress and + + align:start position:0% + + + + align:start position:0% + +strain and it really couldn't be simpler + + align:start position:0% +strain and it really couldn't be simpler + + + align:start position:0% +strain and it really couldn't be simpler +that the true stress is the actual force + + align:start position:0% +that the true stress is the actual force + + + align:start position:0% +that the true stress is the actual force +over the + + align:start position:0% +over the + + + align:start position:0% +over the +area at that uh amount of + + align:start position:0% +area at that uh amount of + + + align:start position:0% +area at that uh amount of +deformation + + align:start position:0% + + + + align:start position:0% + +so + + align:start position:0% +so + + + align:start position:0% +so +and the true + + align:start position:0% + + + + align:start position:0% + +strain is Def find the is + + align:start position:0% +strain is Def find the is + + + align:start position:0% +strain is Def find the is +a differential quantity it's the change + + align:start position:0% +a differential quantity it's the change + + + align:start position:0% +a differential quantity it's the change +in differential change in length with + + align:start position:0% +in differential change in length with + + + align:start position:0% +in differential change in length with +respect to the current + + align:start position:0% +respect to the current + + + align:start position:0% +respect to the current +length which is is it's no the + + align:start position:0% +length which is is it's no the + + + align:start position:0% +length which is is it's no the +definitions are just the same as we had + + align:start position:0% +definitions are just the same as we had + + + align:start position:0% +definitions are just the same as we had +before it's just that the + + align:start position:0% +before it's just that the + + + align:start position:0% +before it's just that the +uh cross-sectional area and the uh + + align:start position:0% +uh cross-sectional area and the uh + + + align:start position:0% +uh cross-sectional area and the uh +length are continually changing or + + align:start position:0% +length are continually changing or + + + align:start position:0% +length are continually changing or +potentially continually changing as we + + align:start position:0% +potentially continually changing as we + + + align:start position:0% +potentially continually changing as we +do these large deformation uh operations + + align:start position:0% +do these large deformation uh operations + + + align:start position:0% +do these large deformation uh operations +on our material elastically most of the + + align:start position:0% +on our material elastically most of the + + + align:start position:0% +on our material elastically most of the +materials we're going to be looking at + + align:start position:0% +materials we're going to be looking at + + + align:start position:0% +materials we're going to be looking at +don't go through large deformations but + + align:start position:0% +don't go through large deformations but + + + align:start position:0% +don't go through large deformations but +in plastic deformation they do and this + + align:start position:0% +in plastic deformation they do and this + + + align:start position:0% +in plastic deformation they do and this +allows us to uh account for + + align:start position:0% + + + + align:start position:0% + +that uh just to sort of reinforce how + + align:start position:0% +that uh just to sort of reinforce how + + + align:start position:0% +that uh just to sort of reinforce how +this this works that uh if we're + + align:start position:0% +this this works that uh if we're + + + align:start position:0% +this this works that uh if we're +deforming material from an initial + + align:start position:0% +deforming material from an initial + + + align:start position:0% +deforming material from an initial +length l0 to some current length L then + + align:start position:0% +length l0 to some current length L then + + + align:start position:0% +length l0 to some current length L then +we're going to need to integrate up all + + align:start position:0% +we're going to need to integrate up all + + + align:start position:0% +we're going to need to integrate up all +the deformation we're + + align:start position:0% +the deformation we're + + + align:start position:0% +the deformation we're +[Applause] + + align:start position:0% + + + + align:start position:0% + +doing ah sorry excuse me that this is + + align:start position:0% +doing ah sorry excuse me that this is + + + align:start position:0% +doing ah sorry excuse me that this is +the increment of true strain is DL over + + align:start position:0% +the increment of true strain is DL over + + + align:start position:0% +the increment of true strain is DL over +l so the true strain is therefore the + + align:start position:0% + + + + align:start position:0% + +integral from wherever we started + + align:start position:0% +integral from wherever we started + + + align:start position:0% +integral from wherever we started +whatever our initial length was to our + + align:start position:0% +whatever our initial length was to our + + + align:start position:0% +whatever our initial length was to our +current length and that gives + + align:start position:0% + + + + align:start position:0% + +us a logarithmic dependence on the ratio + + align:start position:0% +us a logarithmic dependence on the ratio + + + align:start position:0% +us a logarithmic dependence on the ratio +of the current length to the initial + + align:start position:0% +of the current length to the initial + + + align:start position:0% +of the current length to the initial +length and sometimes true strain is + + align:start position:0% +length and sometimes true strain is + + + align:start position:0% +length and sometimes true strain is +called logarithmic strain uh because of + + align:start position:0% +called logarithmic strain uh because of + + + align:start position:0% +called logarithmic strain uh because of +that one further thing we can do to tie + + align:start position:0% +that one further thing we can do to tie + + + align:start position:0% +that one further thing we can do to tie +these two uh ideas together is to note + + align:start position:0% +these two uh ideas together is to note + + + align:start position:0% +these two uh ideas together is to note +that in plastic deformation unlike + + align:start position:0% +that in plastic deformation unlike + + + align:start position:0% +that in plastic deformation unlike +elastic deformation in plastic + + align:start position:0% +elastic deformation in plastic + + + align:start position:0% +elastic deformation in plastic +deformation volume is + + align:start position:0% +deformation volume is + + + align:start position:0% +deformation volume is +conserved that uh the Leng change in + + align:start position:0% +conserved that uh the Leng change in + + + align:start position:0% +conserved that uh the Leng change in +length and the change in area are + + align:start position:0% +length and the change in area are + + + align:start position:0% +length and the change in area are +related because volume is conserved so + + align:start position:0% +related because volume is conserved so + + + align:start position:0% +related because volume is conserved so +we can + + align:start position:0% +we can + + + align:start position:0% +we can +uh in defining the uh true strain the + + align:start position:0% +uh in defining the uh true strain the + + + align:start position:0% +uh in defining the uh true strain the +the the current length we also know that + + align:start position:0% +the the current length we also know that + + + align:start position:0% +the the current length we also know that +the current area must be uh scaling with + + align:start position:0% +the current area must be uh scaling with + + + align:start position:0% +the current area must be uh scaling with +that + + align:start position:0% + + + + align:start position:0% + +and so if we just uh manipulate the + + align:start position:0% + + + + align:start position:0% + +uh the equations uh these fairly simple + + align:start position:0% +uh the equations uh these fairly simple + + + align:start position:0% +uh the equations uh these fairly simple +equations + + align:start position:0% +equations + + + align:start position:0% +equations +oh who made that nasty mess on the + + align:start position:0% +oh who made that nasty mess on the + + + align:start position:0% +oh who made that nasty mess on the +screen + + align:start position:0% + + + + align:start position:0% + +uh we can get Expressions that link the + + align:start position:0% +uh we can get Expressions that link the + + + align:start position:0% +uh we can get Expressions that link the +nominal and True Values of stress and + + align:start position:0% +nominal and True Values of stress and + + + align:start position:0% +nominal and True Values of stress and +strain that the True Value true stress + + align:start position:0% +strain that the True Value true stress + + + align:start position:0% +strain that the True Value true stress +is the nominal stress times one plus the + + align:start position:0% +is the nominal stress times one plus the + + + align:start position:0% +is the nominal stress times one plus the +nominal strain the true strain is the + + align:start position:0% +nominal strain the true strain is the + + + align:start position:0% +nominal strain the true strain is the +log natural log of one plus the nominal + + align:start position:0% +log natural log of one plus the nominal + + + align:start position:0% +log natural log of one plus the nominal +strain just by substituting in these + + align:start position:0% +strain just by substituting in these + + + align:start position:0% +strain just by substituting in these +Expressions uh for True stress true + + align:start position:0% +Expressions uh for True stress true + + + align:start position:0% +Expressions uh for True stress true +strain and the fact that volume is + + align:start position:0% +strain and the fact that volume is + + + align:start position:0% +strain and the fact that volume is +conserved any + + align:start position:0% + + + + align:start position:0% + +questions if we do that if we plot true + + align:start position:0% +questions if we do that if we plot true + + + align:start position:0% +questions if we do that if we plot true +stress against true strain + + align:start position:0% + + + + align:start position:0% + +we find that materials + + align:start position:0% +we find that materials + + + align:start position:0% +we find that materials +look more or less uh isotropic between + + align:start position:0% +look more or less uh isotropic between + + + align:start position:0% +look more or less uh isotropic between +tension and compression there are some + + align:start position:0% +tension and compression there are some + + + align:start position:0% +tension and compression there are some +uh except important exceptions to + + align:start position:0% + + + + align:start position:0% + +this but we won't + + align:start position:0% + + + + align:start position:0% + +and what's happening here is that we're + + align:start position:0% +and what's happening here is that we're + + + align:start position:0% +and what's happening here is that we're +just uh continuing to increase the force + + align:start position:0% +just uh continuing to increase the force + + + align:start position:0% +just uh continuing to increase the force +Contin to increase the area but we're + + align:start position:0% +Contin to increase the area but we're + + + align:start position:0% +Contin to increase the area but we're +not increasing the stress uh and we're + + align:start position:0% +not increasing the stress uh and we're + + + align:start position:0% +not increasing the stress uh and we're +not increasing the + + align:start position:0% +not increasing the + + + align:start position:0% +not increasing the +strain any + + align:start position:0% + + + + align:start position:0% + +questions okay + + align:start position:0% +questions okay + + + align:start position:0% +questions okay +uh suppose we did this test suppose + + align:start position:0% +uh suppose we did this test suppose + + + align:start position:0% +uh suppose we did this test suppose +we applied tensional compression + + align:start position:0% +we applied tensional compression + + + align:start position:0% +we applied tensional compression +compression loading to + + align:start position:0% +compression loading to + + + align:start position:0% +compression loading to +uh a circular cylinder circular + + align:start position:0% +uh a circular cylinder circular + + + align:start position:0% +uh a circular cylinder circular +cross-section cylinder + + align:start position:0% +cross-section cylinder + + + align:start position:0% +cross-section cylinder +uh what would be the work we' have to do + + align:start position:0% +uh what would be the work we' have to do + + + align:start position:0% +uh what would be the work we' have to do +in order + + align:start position:0% +in order + + + align:start position:0% +in order +to deform this cylinder uh to some + + align:start position:0% + + + + align:start position:0% + +stress and + + align:start position:0% +stress and + + + align:start position:0% +stress and +strain uh on our true stress true strain + + align:start position:0% +strain uh on our true stress true strain + + + align:start position:0% +strain uh on our true stress true strain +curve so a metal cylinder is loaded by + + align:start position:0% +curve so a metal cylinder is loaded by + + + align:start position:0% +curve so a metal cylinder is loaded by +uni axial + + align:start position:0% +uni axial + + + align:start position:0% +uni axial +tension past its yield point so we're + + align:start position:0% +tension past its yield point so we're + + + align:start position:0% +tension past its yield point so we're +we're somewhere up Beyond this elastic + + align:start position:0% +we're somewhere up Beyond this elastic + + + align:start position:0% +we're somewhere up Beyond this elastic +region how much work did we have to + + align:start position:0% + + + + align:start position:0% + +do and uh choices it's the area under + + align:start position:0% +do and uh choices it's the area under + + + align:start position:0% +do and uh choices it's the area under +this stress strain curve the area under + + align:start position:0% +this stress strain curve the area under + + + align:start position:0% +this stress strain curve the area under +the the stress strain curve multiplied + + align:start position:0% +the the stress strain curve multiplied + + + align:start position:0% +the the stress strain curve multiplied +by the volume of the cylinder the stress + + align:start position:0% +by the volume of the cylinder the stress + + + align:start position:0% +by the volume of the cylinder the stress +times The Strain times the length of the + + align:start position:0% +times The Strain times the length of the + + + align:start position:0% +times The Strain times the length of the +cylinder strain time the stress times + + align:start position:0% +cylinder strain time the stress times + + + align:start position:0% +cylinder strain time the stress times +the cross-sectional area of the bar the + + align:start position:0% +the cross-sectional area of the bar the + + + align:start position:0% +the cross-sectional area of the bar the +maximum stress times the area time the + + align:start position:0% +maximum stress times the area time the + + + align:start position:0% +maximum stress times the area time the +strain times the length of the bar some + + align:start position:0% +strain times the length of the bar some + + + align:start position:0% +strain times the length of the bar some +other answer and you've lost + + align:start position:0% + + + + align:start position:0% + +me for + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +Lou no I mean the + + align:start position:0% + + + + align:start position:0% + +what do we + + align:start position:0% +what do we + + + align:start position:0% +what do we +think so the majority think yes okay the + + align:start position:0% +think so the majority think yes okay the + + + align:start position:0% +think so the majority think yes okay the +majority think the area under the stress + + align:start position:0% +majority think the area under the stress + + + align:start position:0% +majority think the area under the stress +strain curve multiplied by the volume of + + align:start position:0% +strain curve multiplied by the volume of + + + align:start position:0% +strain curve multiplied by the volume of +the cylinder which is absolutely right + + align:start position:0% +the cylinder which is absolutely right + + + align:start position:0% +the cylinder which is absolutely right +that uh if + + align:start position:0% +that uh if + + + align:start position:0% +that uh if +you took this area which of course + + align:start position:0% +you took this area which of course + + + align:start position:0% +you took this area which of course +is the integral of stress D strain + + align:start position:0% +is the integral of stress D strain + + + align:start position:0% +is the integral of stress D strain +that's the the Vol sorry that's the + + align:start position:0% +that's the the Vol sorry that's the + + + align:start position:0% +that's the the Vol sorry that's the +energy or work done per unit + + align:start position:0% +energy or work done per unit + + + align:start position:0% +energy or work done per unit +volume just by dimensional analysis you + + align:start position:0% +volume just by dimensional analysis you + + + align:start position:0% +volume just by dimensional analysis you +can see that look you're considering the + + align:start position:0% +can see that look you're considering the + + + align:start position:0% +can see that look you're considering the +units of stress and strain so in order + + align:start position:0% +units of stress and strain so in order + + + align:start position:0% +units of stress and strain so in order +to get the total work done you'd need to + + align:start position:0% +to get the total work done you'd need to + + + align:start position:0% +to get the total work done you'd need to +multiply this by the volume of the + + align:start position:0% +multiply this by the volume of the + + + align:start position:0% +multiply this by the volume of the +cylinder and it doesn't really matter uh + + align:start position:0% +cylinder and it doesn't really matter uh + + + align:start position:0% +cylinder and it doesn't really matter uh +what the length is and what the area is + + align:start position:0% +what the length is and what the area is + + + align:start position:0% +what the length is and what the area is +because we've said that the plastic + + align:start position:0% +because we've said that the plastic + + + align:start position:0% +because we've said that the plastic +deformation uh is occurring at constant + + align:start position:0% +deformation uh is occurring at constant + + + align:start position:0% +deformation uh is occurring at constant +volume so the volume isn't changing as + + align:start position:0% +volume so the volume isn't changing as + + + align:start position:0% +volume so the volume isn't changing as +we do this um and this is the + + align:start position:0% +we do this um and this is the + + + align:start position:0% +we do this um and this is the +explanation of uh and this is an + + align:start position:0% +explanation of uh and this is an + + + align:start position:0% +explanation of uh and this is an +irreversible process + + align:start position:0% +irreversible process + + + align:start position:0% +irreversible process +thermodynamically uh unlike elasticity + + align:start position:0% +thermodynamically uh unlike elasticity + + + align:start position:0% +thermodynamically uh unlike elasticity +which is reversible plasticity you're + + align:start position:0% +which is reversible plasticity you're + + + align:start position:0% +which is reversible plasticity you're +having to do + + align:start position:0% + + + + align:start position:0% + +work it's being dissipated as heat it's + + align:start position:0% +work it's being dissipated as heat it's + + + align:start position:0% +work it's being dissipated as heat it's +not recoverable and this is why if you + + align:start position:0% +not recoverable and this is why if you + + + align:start position:0% +not recoverable and this is why if you +do a a rolling operation if you just do + + align:start position:0% +do a a rolling operation if you just do + + + align:start position:0% +do a a rolling operation if you just do +frictional contact between surfaces + + align:start position:0% +frictional contact between surfaces + + + align:start position:0% +frictional contact between surfaces +which has lots of little uh uh + + align:start position:0% +which has lots of little uh uh + + + align:start position:0% +which has lots of little uh uh +asperities on the metal surfaces + + align:start position:0% +asperities on the metal surfaces + + + align:start position:0% +asperities on the metal surfaces +deforming plastically uh the Metal's + + align:start position:0% +deforming plastically uh the Metal's + + + align:start position:0% +deforming plastically uh the Metal's +going to heat up by this amount and the + + align:start position:0% +going to heat up by this amount and the + + + align:start position:0% +going to heat up by this amount and the +thermal conductivity of the material any + + align:start position:0% + + + + align:start position:0% + +questions we'll come back to this idea + + align:start position:0% +questions we'll come back to this idea + + + align:start position:0% +questions we'll come back to this idea +of energy uh energy of deformation uh in + + align:start position:0% +of energy uh energy of deformation uh in + + + align:start position:0% +of energy uh energy of deformation uh in +due course and particularly when we look + + align:start position:0% +due course and particularly when we look + + + align:start position:0% +due course and particularly when we look +at fracture I'm just going to skip + + align:start position:0% +at fracture I'm just going to skip + + + align:start position:0% +at fracture I'm just going to skip +slightly in the notes um but just to set + + align:start position:0% +slightly in the notes um but just to set + + + align:start position:0% +slightly in the notes um but just to set +up where we're going to go next + + align:start position:0% +up where we're going to go next + + + align:start position:0% +up where we're going to go next +so the the two material properties uh + + align:start position:0% +so the the two material properties uh + + + align:start position:0% +so the the two material properties uh +that I'd like you to take away from this + + align:start position:0% +that I'd like you to take away from this + + + align:start position:0% +that I'd like you to take away from this +lecture are the yield stress and the + + align:start position:0% +lecture are the yield stress and the + + + align:start position:0% +lecture are the yield stress and the +tensile + + align:start position:0% +tensile + + + align:start position:0% +tensile +strength generally for Aerospace design + + align:start position:0% +strength generally for Aerospace design + + + align:start position:0% +strength generally for Aerospace design +we're going to try and design well we + + align:start position:0% +we're going to try and design well we + + + align:start position:0% +we're going to try and design well we +are going to design so our material + + align:start position:0% +are going to design so our material + + + align:start position:0% +are going to design so our material +remains pretty much everywhere below its + + align:start position:0% +remains pretty much everywhere below its + + + align:start position:0% +remains pretty much everywhere below its +yield strength and we're going to rely + + align:start position:0% +yield strength and we're going to rely + + + align:start position:0% +yield strength and we're going to rely +on the fact that there's some T Cell + + align:start position:0% +on the fact that there's some T Cell + + + align:start position:0% +on the fact that there's some T Cell +strength that's a higher quantity that + + align:start position:0% +strength that's a higher quantity that + + + align:start position:0% +strength that's a higher quantity that +is there to to bail us out if we got an + + align:start position:0% +is there to to bail us out if we got an + + + align:start position:0% +is there to to bail us out if we got an +unexpected overload um and we'll come on + + align:start position:0% +unexpected overload um and we'll come on + + + align:start position:0% +unexpected overload um and we'll come on +to talk about the concepts of limit and + + align:start position:0% +to talk about the concepts of limit and + + + align:start position:0% +to talk about the concepts of limit and +ultimate load on a structure in due + + align:start position:0% +ultimate load on a structure in due + + + align:start position:0% +ultimate load on a structure in due +course this is + + align:start position:0% + + + + align:start position:0% + +uh a uh plot of strength versus density + + align:start position:0% +uh a uh plot of strength versus density + + + align:start position:0% +uh a uh plot of strength versus density +from uh ashb material selection book + + align:start position:0% +from uh ashb material selection book + + + align:start position:0% +from uh ashb material selection book +and what I want you to get out of this + + align:start position:0% +and what I want you to get out of this + + + align:start position:0% +and what I want you to get out of this +is a couple of things my laser pointer + + align:start position:0% +is a couple of things my laser pointer + + + align:start position:0% +is a couple of things my laser pointer +isn't working so + + align:start position:0% + + + + align:start position:0% + +um strength and megap Pascal's density + + align:start position:0% +um strength and megap Pascal's density + + + align:start position:0% +um strength and megap Pascal's density +uh strength spanning several orders of + + align:start position:0% +uh strength spanning several orders of + + + align:start position:0% +uh strength spanning several orders of +magnitude here here are metals + + align:start position:0% +magnitude here here are metals + + + align:start position:0% +magnitude here here are metals +Composites polymers Ceramics in a dotted + + align:start position:0% +Composites polymers Ceramics in a dotted + + + align:start position:0% +Composites polymers Ceramics in a dotted +dashed line because generally yield or + + align:start position:0% +dashed line because generally yield or + + + align:start position:0% +dashed line because generally yield or +or failure uh won't get to these uh uh + + align:start position:0% +or failure uh won't get to these uh uh + + + align:start position:0% +or failure uh won't get to these uh uh +levels because intention at least will + + align:start position:0% +levels because intention at least will + + + align:start position:0% +levels because intention at least will +get fractur before we'll talk more about + + align:start position:0% +get fractur before we'll talk more about + + + align:start position:0% +get fractur before we'll talk more about +that but a couple of things to notice + + align:start position:0% +that but a couple of things to notice + + + align:start position:0% +that but a couple of things to notice +that unlike uh for elastic the Young's + + align:start position:0% +that unlike uh for elastic the Young's + + + align:start position:0% +that unlike uh for elastic the Young's +modulus uh elastic responsive materials + + align:start position:0% +modulus uh elastic responsive materials + + + align:start position:0% +modulus uh elastic responsive materials +uh an individual material titanium steel + + align:start position:0% +uh an individual material titanium steel + + + align:start position:0% +uh an individual material titanium steel +aluminum Alloys span a big range more + + align:start position:0% +aluminum Alloys span a big range more + + + align:start position:0% +aluminum Alloys span a big range more +than an order of magnitude in each case + + align:start position:0% +than an order of magnitude in each case + + + align:start position:0% +than an order of magnitude in each case +in the strength of the material either + + align:start position:0% +in the strength of the material either + + + align:start position:0% +in the strength of the material either +the ultimate T Cell strength or the + + align:start position:0% +the ultimate T Cell strength or the + + + align:start position:0% +the ultimate T Cell strength or the +yield strength we have a lot more + + align:start position:0% +yield strength we have a lot more + + + align:start position:0% +yield strength we have a lot more +ability to change the strength of a + + align:start position:0% +ability to change the strength of a + + + align:start position:0% +ability to change the strength of a +material by changing its composition and + + align:start position:0% +material by changing its composition and + + + align:start position:0% +material by changing its composition and +its micr structure in strength and we + + align:start position:0% +its micr structure in strength and we + + + align:start position:0% +its micr structure in strength and we +did in in stiffness and secondly that + + align:start position:0% +did in in stiffness and secondly that + + + align:start position:0% +did in in stiffness and secondly that +just as before uh metals tend to group + + align:start position:0% +just as before uh metals tend to group + + + align:start position:0% +just as before uh metals tend to group +Composites tend to group polymers tend + + align:start position:0% +Composites tend to group polymers tend + + + align:start position:0% +Composites tend to group polymers tend +to group so by understanding the sort of + + align:start position:0% +to group so by understanding the sort of + + + align:start position:0% +to group so by understanding the sort of +prototypical behavior of one material we + + align:start position:0% +prototypical behavior of one material we + + + align:start position:0% +prototypical behavior of one material we +get an idea of what's going on in the + + align:start position:0% +get an idea of what's going on in the + + + align:start position:0% +get an idea of what's going on in the +whole class of material and that's what + + align:start position:0% +whole class of material and that's what + + + align:start position:0% +whole class of material and that's what +we're going to move on to next time + + align:start position:0% +we're going to move on to next time + + + align:start position:0% +we're going to move on to next time +looking at how this works looking at + + align:start position:0% +looking at how this works looking at + + + align:start position:0% +looking at how this works looking at +what the different strengthening + + align:start position:0% +what the different strengthening + + + align:start position:0% +what the different strengthening +mechanisms are that get us from a steel + + align:start position:0% +mechanisms are that get us from a steel + + + align:start position:0% +mechanisms are that get us from a steel +that uh has a strength of maybe just + + align:start position:0% +that uh has a strength of maybe just + + + align:start position:0% +that uh has a strength of maybe just +over 100 megap pascals a mile mild steel + + align:start position:0% +over 100 megap pascals a mile mild steel + + + align:start position:0% +over 100 megap pascals a mile mild steel +uh structural steel up to a high tensile + + align:start position:0% +uh structural steel up to a high tensile + + + align:start position:0% +uh structural steel up to a high tensile +steel which might be 2 gigap Pascal or + + align:start position:0% +steel which might be 2 gigap Pascal or + + + align:start position:0% +steel which might be 2 gigap Pascal or +perhaps of more importance to us how we + + align:start position:0% +perhaps of more importance to us how we + + + align:start position:0% +perhaps of more importance to us how we +get aluminum from uh 50 or 60 megap + + align:start position:0% +get aluminum from uh 50 or 60 megap + + + align:start position:0% +get aluminum from uh 50 or 60 megap +pascals up to nearly 700 uh megap Pascal + + align:start position:0% +pascals up to nearly 700 uh megap Pascal + + + align:start position:0% +pascals up to nearly 700 uh megap Pascal +strength in the the high strength Alloys + + align:start position:0% +strength in the the high strength Alloys + + + align:start position:0% +strength in the the high strength Alloys +is commonly used in airf frames so + + align:start position:0% +is commonly used in airf frames so + + + align:start position:0% +is commonly used in airf frames so +that's what we're going to move on to + + align:start position:0% +that's what we're going to move on to + + + align:start position:0% +that's what we're going to move on to +next time as well as just finishing off + + align:start position:0% +next time as well as just finishing off + + + align:start position:0% +next time as well as just finishing off +a few thoughts on this uh as you fill + + align:start position:0% +a few thoughts on this uh as you fill + + + align:start position:0% +a few thoughts on this uh as you fill +out your muddy cards are there any + + align:start position:0% +out your muddy cards are there any + + + align:start position:0% +out your muddy cards are there any +questions yes + + align:start position:0% +questions yes + + + align:start position:0% +questions yes +Jack that's a a failure stress um so for + + align:start position:0% +Jack that's a a failure stress um so for + + + align:start position:0% +Jack that's a a failure stress um so for +a for a metal it's uh usually the + + align:start position:0% +a for a metal it's uh usually the + + + align:start position:0% +a for a metal it's uh usually the +ultimate T Cell strength this number for + + align:start position:0% +ultimate T Cell strength this number for + + + align:start position:0% +ultimate T Cell strength this number for +a ceramic or a brittle material it it's + + align:start position:0% +a ceramic or a brittle material it it's + + + align:start position:0% +a ceramic or a brittle material it it's +the strength that which fast fracture + + align:start position:0% +the strength that which fast fracture + + + align:start position:0% +the strength that which fast fracture +occurs and we'll we'll understand a + + align:start position:0% +occurs and we'll we'll understand a + + + align:start position:0% +occurs and we'll we'll understand a +little bit that distinction uh in about + + align:start position:0% +little bit that distinction uh in about + + + align:start position:0% +little bit that distinction uh in about +three lectures time okay please give me + + align:start position:0% +three lectures time okay please give me + + + align:start position:0% +three lectures time okay please give me +your muddy cards and uh I will see you + + align:start position:0% +your muddy cards and uh I will see you + + + align:start position:0% +your muddy cards and uh I will see you +the same time tomorrow \ No newline at end of file diff --git a/ZD2sKqPxPIk.txt b/ZD2sKqPxPIk.txt new file mode 100644 index 0000000000000000000000000000000000000000..9720ee67b00ecaeace4b741854374dfcee3e50d8 --- /dev/null +++ b/ZD2sKqPxPIk.txt @@ -0,0 +1,3573 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So, what I'll talk +about here is how to actually + +understand the performance of +your application, and what are + +some of the things you can do +to actually improve your + +performance. + +You're going to hear more about +automated optimizations, + +compile the optimizations +on Monday. + +There will be two +talks on that. + +You'll get some cell-specific +optimizations that you can do, + +so some cell-specific tricks on +Tuesday in the recitation. + +So here, this is meant to be a +more general purpose talk on + +how can you debug performance +anomalies and performance + +problems. Then what are some +way that you can actually + +improve the performance. + +Where do you look after you've +done your parallelization. + +So just to review the key +concepts to parallelism. + +Coverage -- how much parallelism +do you have in + +your application. + +All of you know, because +you all had perfect + +scores on the last quiz. + +So that means if you take a look +at your program, you find + +the parallel parts and that +tells you how much parallelism + +that you have. If you don't +have more than a certain + +fraction, there's really nothing +else you can do with + +parallelism. + +So the rest of the talk will +help you address the question + +of well, where do you go +for last frontier. + +The granularity. + +We talked about how the +granularity of your work and + +how much work are you doing on +each processor affects your + +load balancing, and how it +actually affects your + +communication costs. + +If you have a lot of things +colocate on a single + +processor, then you don't have +to do a whole lot of + +communication across processors, +but if you + +distribute things at a finer +level, then you're doing a + +whole lot of communication. + +So we'll look at the +communication costs again and + +some tricks that you can +apply to optimize that. + +Then the last thing that we had +talked about in one of the + +previous lectures is locality, +in locality of communication + +versus computation, and both +of those are critical. + +So we'll have some +examples of that. + +So just to review the +communication cost model, so I + +had flashed up on the screen a +while ago this equation that + +captures all the factors that +go into figuring out how + +expensive is it to actually send +data from one processor + +to the other. + +Or this could even apply on +a single machine where a + +processor is talking +to the memory -- + +you know, loads and stores. + +The same cost model really +applies there. + +If you look at how +processors -- + +a uniprocessor tries to improve +communication, and + +some of the things we've +mentioned really early on in + +the course for improving +communication costs, what we + +focused on is this overlap. + +There are things you can do, +for example, sending fewer + +messages, optimizing how you're +packing data into your + +messages, reducing the cost of +the network in terms of the + +latency, using architecture +support, increasing the + +bandwidth and so on. + +But really the biggest impact +that you can get is really + +just from overlap because you +have direct control over that, + +especially in parallel +programming. + +So let's look at a small review +-- you know, what did + +it mean to overlap. + +So we had some synchronization +point or some point in the + +execution and then +we get data. + +Then once the data's arrived, +we compute on that data. + +So this could be +a uniprocessor. + +A CPU issues a load, it goes +out to memory, memory sends + +back the data, and then the +CU can continue operating. + +But the uniprocessors +can pipeline. + +They allow you to have +multiple loads + +going out to memory. + +So you can get the effect of +hiding over overlapping a lot + +of that communication latency. + +But there are limits to the +communication, to the + +pipelining effects. + +If the work that you're doing is +really equal to the amount + +of data that you're +fetching, then you + +have really good overlap. + +So we went over this in the +recitation and we showed you + +an example of where pipelining +doesn't have any performance + +effects and so you might not +want to do it because it + +doesn't give you the performance +bang for the + +complexity you invest in it. + +So, if things are really nicely +matched you get good + +overlap, here you only get god +overlap -- sorry, these, for + +some reason, should be +shifted over one. + +So where else do you look +for performance? + +So there are two kinds +of communication. + +There's inherent communication +and your algorithm, and this + +is a result of how you actually +partition your data + +and how you partitioned +your computation. + +Then there's artifacts that come +up because of the way you + +actually do the implementation +and how you map it to the + +architecture. + +So, if you have poor +distribution of data across + +memory, then you might +unnecessarily end up fetching + +data that you don't need. + +So, you might also have +redundant data fetchers. + +So let's talk about that +in more detail. + +The way I'm going to do this +is to draw from wisdom in + +uniprocessors. + +So in uniprocessors, CPUs +communicate with memory, and + +really conceptually, I think +that's no different than + +multiple processors talking +to multiple processors. + +It's really all about where the +data is flowing and how + +the memories are structured. + +So, loads and stores are the +uniprocessor as what and what + +are to distributed memory. + +So if you think of Cell, what +would go in those two blanks? + +Can you get this? + +I heard the answer there. + +You get input. + +So, DMA get and DMA put. + +That's really just the +load and a store. + +It's just doing, instead of +loading one particular data + +element, you're loading a +whole chunk of memory. + +So, on a uniprocessor, how do +you overlap communication? + +Well, architecture, the memory +system is designed in a way to + +exploit two properties that +have been observed in + +computation. + +Spacial locality and temporal +locality, and I'll look at + +each one separately. + +So in spacial locality, +CPU asks for a + +data address of 1,000. + +What the memory does, it'll send +data address of 1,000, + +plus a whole bunch of other data +that's neighboring to it, + +so 1,000 to 1,064. + +Really, how much data you +actually send, you know, what + +is the granularity of +communication depends on + +architectural parameters. + +So in common architecture it's +really the block side. + +So if you have a cache where the +organization says you have + +a block side to 32 words, 32 +bytes, then this is how much + +you transfer from main +memory to the caches. + +So this works well when the CPU +actually uses that data. + +If I send you 64 data bytes and +I only use one of them, + +then what have I done? + +I've wasted bandwidth. + +Plus, I need to store all that +extra data in the cache so + +I've wasted my cache capacity. + +So that's bad and you +want to avoid it. + +Temporal locality is +a clustering of + +references in time. + +So if you access some particular +data element, then + +what the memory assumes is +you're going reuse that data + +over and over and over again, so +it stores it in the cache. + +So your memory hierarchy has +the main memory at the top + +level, and that's your +slowest memory + +but the biggest capacity. + +Then as you get closer and +closer to the processor, you + +end up with smaller caches -- +these are local, smaller + +storage, but they're faster. + +So, if you reuse a data element +then it gets cached at + +the lowest data level, and so +the assumption there is that + +you're gonna reuse it over +and over and over again. + +If you do that, then what +you've done is you've + +amortized the cost of bringing +in that data over many, many + +references. + +So that works out really well. + +But if you don't reuse that +particular data elements over + +and over again, then you've +wasted cache capacity. + +You still need to fetch the data +because the CPU asks for + +it, but you might not have had +the cache, so that would have + +created more space in your cache +to have something else + +in there that might have +been more useful. + +So in the multiprocessor case, +how do you reduce these + +artifactual costs in +communication. + +So, DCMA gets inputs on the +cell, or just in just message + +passing, you're exchanging +messages. + +Typically, you're communicating +over a course or + +large blocks of data. + +What you're usually getting is +a continuous chunk of memory, + +although you could do some +things in software or in + +hardware to gather data from +different memory locations and + +pack them into contiguous +locations. + +The reason you pack them into +contiguous locations again to + +export spatial locality when +you store the data locally. + +So to exploit the spatial +locality characteristics, what + +you want to make sure is that +you actually are going to have + +good spatial locality in your +actual computation. + +So you want things that are +iterating over loops with + +well-defined indices with +indices that go over very + +short ranges, or they're very +sequential or have fixed + +striped patterns where you're +not wasting a lot of the data + +that you have brought in. + +Otherwise, you have to +essentially just increase your + +communication because every +fetch is getting you only a + +small fraction of what +you actually need. + +So, intuitively this +should make sense. + +Temporal locality just says I +brought in some data and so I + +want to maximize this utility. + +So if I have any computation in +a parallel system, I might + +be able to reorder my tasks in +a way that I have explicit + +control over the scheduling -- +which stripe executes when. + +Then you want to make sure that +all the computation that + +needs that particular data +happens adjacent in time or in + +some short time window so that +you can amortize the cost. + +Are those two concepts clear? + +Any questions on this? + +So, you've done all of that. + +You've parallelized your code, +you've taken care of your + +communication costs, you've +tried to reduce + +it as much as possible. + +Where else can you look for +performance -- things just + +don't look like they're +performing as + +well as they could? + +So, the last frontier is +perhaps single thread + +performance, so I'm going +to talk about that. + +So what is really +a single thread. + +So if you think of what you're +doing with parallel + +programming, you're taking a +bunch of tasks -- this is the + +work that you have to do -- and +you group them together + +into threads or the equivalent +of threads, and some threads + +will run on individual cores. + +So essentially you have one +thread running on a core, and + +if that performance goes fast, +then your overall execution + +can also benefit from that. + +So, that's single thread +performance. + +So if you look at a timeline, +here you have sequential code + +going on, then we hit some +parallel part of the + +computation. + +We have multiple executions +going on. + +Each one of these is a +thread of execution. + +Really, my finish line depends +on who's the longest thread, + +who's the slowest one to +complete, and that's going to + +essentially control +my speed up. + +So I can improve this by doing +better load balancing. + +If I distribute the +work [? so that ?] + +everybody's doing equivalent +amount of work, then I can + +shift that finish line +earlier in time. + +That can work reasonably well. + +So we talked about load +balancing before. + +We can also make execution +on each processor faster. + +If each one of these threads +finishes faster or I've done + +the load balancing and now I +can even squeeze out more + +performance by shrinking each +one of those lines, then I can + +get performance improvement +there as well. + +So that's improving single +thread performance. + +But how do we actually +understand what's going on? + +How do I know where +to optimize? + +How do I know how long each +thread is taking? + +How do I know how long +my program is taking? + +Where are the problems? + +So, there are performance +monitoring tools that hard + +designed to help you do that. + +So what's the most +coarse-grained way of figuring + +out how long your +program took? + +You have some sample piece of +code shown over here, you + +might compile it, and then you +might just use time -- + +standard units command say run +this program and tell me how + +much time it took to run. + +So you get some alpha back from +time that said you took + +about two seconds of user time, +this is actual code, you + +took some small amount of time +in system code, and this is + +your overall execution, this is +how much of the processor + +you actually use. + +So, a 95% utilization. + +Then you might apply +some optimization. + +So here we'll use the compiler, +we'll change the + +optimization level, compile +the same code, run it, and + +we'll see wow, performance +improved. + +So we increased 99% utilization, +my running time + +went down by a small chunk. + +But did we really learn +anything about + +what's going on here? + +There's some code going on, +there's a loop here, there's a + +loop here, there's some +functions with more loops. + +So where is the actual +computation time going? + +So how would I actually go +about understanding this? + +So what are some tricks you +might have used in trying to + +figure out how long something +took in your computation? + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: Right. + +So you might have a timer, you +record the time here, you + +compute and then you stop the +timer and then you might + +printout or record how +long that particular + +block of code took. + +Then you might have a histogram +of them and then you + +might analyze the histogram to +find out the distribution. + +You might repeat this over and +over again for many different + +loops or many different +parts that are code. + +If you have a preconceived +notion of where the problem is + +then you instrument that +and see if your + +hypothesis is correct. + +That can help you identify the +problems. But increasingly you + +can actually get more accurate +measurements. + +So, in the previous routine, +you're using the time, you + +were looking at how much time +has elapsed in seconds or in + +small increments. + +But you can actually use +hardware counters today to + +actually measure clock +cycles, clock ticks. + +That might be more useful. + +Actually, it's more useful +because you can measure a lot + +more events than just +clock ticks. + +The counters in modern +architectures are really + +specialized registers that count +up events and then you + +can go in there and probe and +ask what is the value in this + +register, and you can +use that as part of + +your performance tuning. + +You use them much in the same +way as you would have done to + +start a regular timer or +stop a regular timer. + +There are specialized +libraries that run. + +Unfortunately, these are very + +architecture-specific at this point. + +There's not really a common +standard that says grab a + +timer at each different +architecture in a uniform way, + +although that's getting +better with some + +standards coming out from--. + +I'll talk about that in +just a few slides. + +You can use this to, for +example, measure your + +communication to computation +cost. So you can wrap your DMA + +get and DMA put by timer calls, +and you can measure + +your actual work by timer calls, +and figuring out how + +much overlap can you get from +overlap in communication and + +communication computation and +is that really worthwhile to + +do pipelining. + +But this really requires +manual changes to code. + +You have to go in there +and start the timers. + +You have to have maybe an idea +of where the problem is, and + +you have the Heisenberg +effect. + +If you have a loop and you want +to measure code within + +the loop because you have a +nested loop inside of that, + +then now you're effecting the +performance of the outer loop. + +That can be problematic. + +So it has a better effect +because you can't really make + +an accurate measurement on the +thing you're inspecting. + +So there's a slightly better +approach, dynamic profiling. + +Dynamic profiling is really +there's an event-based + +profiling and time-based +profiling. + +Conceptually they do +the same thing. + +What's going on here is your +program is running and you're + +going to say I'm interested in +events such as cache misses. + +Whenever n number of cache +misses happen, let's say + +1,000, let me know. + +So you get an interrupt +whenever 1,000 + +cache misses happen. + +Then you can update a counter +or use that to trigger some + +optimizations or analysis. + +This works really nicely because +you don't have to + +touch your code. + +You essentially run your program +as you normally do + +with just one modification +that includes running the + +dynamic profiler, as well as +your actual computation. + +As far as multiple languages +because all it does is just + +takes your binary so you can +program in any language, any + +programming model. + +It's quite efficient to actually +use these dynamic + +profiling tools. + +The sampling frequencies are +reasonably small, you can make + +them reasonably small and still +have it be efficient. + +So some counter examples. + +Clock cycles, so you can +measure clock ticks. + +Pipeline stalls. + +This might be interesting if +you want to optimize your + +instruction schedule -- you'll +actually see this in the + +recitation next week. + +Cache hits, cache misses -- you +can get an idea of how bad + +your cache performance is and +how much time you're spending + +in the memory system. + +Number of instructions, loads, +stores, floating + +point ops and so on. + +Then you can derive some useful +measures from that. + +So I can get an idea of +processor utilization -- + +divide cycles by time and that +gives me utilization. + +I can derive some other things +and maybe some of the more + +interesting things like +memory of traffic. + +So how much data am I actually +sending between a CPU and a + +processor, or how much data am +I communicating from one + +processor to the other. + +So I can just grab the counters +for number of loads + +and number of stores, figure out +what the cache line size + +is -- usually those are +documented or there are + +calibration tools you can run +to get that value, and you + +figure out memory of traffic. + +Another one would be +bandwidth consumed. + +So bandwidth is memory of +traffic per second. + +So how would you measure that? + +It's just the traffic divided +by the wall clock time. + +There's some others that +you can calculate. + +So these can be really useful +in helping you figure out + +where are the things you +should go focus in on. + +I'm going to show you +some examples. + +The way these tools work is +you have your application + +source code, you compile +it down to a binary. + +You take your binary and you +run it, and then that can + +generate some profile that +stores locally on your disk. + +Then you can take that profile +and analyze it by some sort of + +interpreter, and some cases you +can actually analyze the + +binary as well, and reannotate +your source code. + +That can actually be very useful +because it'll tell you + +this particular line of your +code is the one where you're + +spending most of your +time computing. + +So some tools -- have any +of you used these tools? + +Anybody use Gprof, +for example? + +Good. + +So, you might have an idea of +how these could be used. + +There are others. + +HPCToolkit, which I commonly +use from Rice. + +Pappy is very common because it +has a very nice interface + +for grabbing all kinds +of counters. + +VTune from Intel, and there's +others that work in different + +ways and so there are binary +instrumenters that do the same + +things and do it slightly more +efficiently and actually give + +you the ability to compile +your code at run time and + +optimize it, taking advantage +of the profiling information + +you've collected. + +So here's a sample +of running Gprof. + +Gprof should be available on +any Linux system, it's even + +available on Cygwin, +if you see Cygwin. + +I've compiled some code -- +this is MPEG 2D code, a + +reference implementation. + +I specify some parameters +to run it. + +Here I add this dash Rflag which +says use a particular + +kind of inverse DCDT that's a +floating point precise that + +uses double precision for +the floating point + +computations in DCT -- + +inverse DCT rather. + +So you can see actually where +most of the time is being + +spent in the computation. + +So here's a time per function, +so each row + +represents a function. + +So this is the percent of the +time, this is the actual time + +in seconds, how many times I +actually called this function, + +and some other useful things. + +So the second function that's +used here that happens is MPEG + +intrablock decoding and here +you're doing some spatial + +decomposition, restoring +spatial pictures by 5%. + +So if you were optimize this +particular code, where would + +you go look? + +You would look in the +reference DCT. + +So, MPEG has two versions +of DCT -- + +one that uses floating point, +another that just uses some + +numerical tricks to operate over +integers for a loss of + +precision, but they find that +acceptable as part of this + +application. + +So you omit the Rflag, it +actually uses a different + +function for doing the DCT. + +Now you see the distribution of +where the time is spent in + +your computation changes. + +Now there's a new function +that's become the bottleneck + +and it's called Form Component +Prediction. + +Then IDCT column, which +actually is the main + +replacement of the previous +code, this one, is now about + +1/3 of the actual computation. + +So, this could be useful because +you can Gprof your + +application, figure out where +the bottlenecks are in terms + +of performance, and you might +go in there and tweak the + +algorithm completely. + +You might go in there and sort +of look at some problems that + +might be implementation bugs +or performance bugs and be + +able to fix those. + +Any questions on that? + +You can do sort of more +accurate things. + +So, Gprof largely uses one +mechanism, HPCToolkit uses the + +performance counters to actually +give you more finer + +grade measurements +if you want them. + +So, in the HPCToolkit, you run +your program in the same way. + +You have MPEG 2D code, dash dash +just says this is where + +the parameters are to impact +2D code following that dash + +dash, and you can add some +parameters in there that say + +these are counters I'm +interested in measuring. + +So the first one is +total cycles. + +The second one is the L1, so +primary cache load misses. + +Then you might want to count +the floating point + +instructions and the +total instructions. + +As you run your program you +actually get a profiling + +output, and then you can process +that file and it'll + +spit out some summaries +for you. + +So it'll tell you this is the +total number of cycles, 698 + +samples with this frequency. + +So if you multiply the two +together, you an idea of how + +many cycles your computation +took. + +How many load misses? + +So it's 27 samples at +this frequency. + +So remember what's going on +here is the counter is + +measuring events, and when the +event reaches a particular + +threshold it let's you know. + +So here the sampling threshold +is 32,000. + +So whenever 32,000 floating +point instructions occur you + +get a sample. + +So you're just counting how many +interrupts you're getting + +or how many samples. + +So you multiply the two +together you can + +get the final counts. + +It can do things like Gprof, +it'll tell you where your time + +is and where you spent +most of your time. + +Actually breaks it down +into your module. + +So, MPEG calls some standard +libraries, libsi. + +I could break it down by +functions, break it down by + +line number. + +You can even annotate +your source code. + +So here's just a simple example +that I used earlier, + +and each one of these columns +represent one of the metrics + +that we measured, and you can +see most of my time is spent + +here, 36% at this particular +statement. + +So that can be very useful. + +You can go in there and +say, I want to do some + +[? dization ?], I can maybe +reduce this overhead in some + +way to get better performance. + +Any questions on that? + +Yup. + +AUDIENCE: [INAUDIBLE PHRASE]? + +PROFESSOR: I don't know. + +Unfortunately, I don't know +the answer to that. + +There's some nice gooies for +some of these tools. + +So VTune has a nice interface. + +I use HPCViewer. + +I use HPCToolkit, which provides +HPCViewer, so I just + +grab the screenshot from one +of the tutorials on this. + +You have your source code. + +It shows you some of the same +information I had on a + +previous slide, but in a +nicer graphical format. + +So, now I have all this +information, how do I actually + +improve the performance? + +Well, if you look at what is +the performance time on a + +uniprocessor, it's time spent +computing plus the time spent + +waiting for data or +waiting for some + +other things to complete. + +You have instructional level +parallels, which is really + +critical for uniprocessors, +and architect that sort of + +spent massive amounts of effort +in providing multiple + +functional units, +deeply pipeline + +the instruction pipeline. + +Doing things like speculation, +prediction to keep that + +instructional level of +parallelism number high so you + +can get really good +performance. + +You can do things like looking +at the assembly code and + +re-ordering instructions to +avoid instruction hazards in + +the pipeline. + +You might look at a register +allocation. + +But that's really very +low-hanging fruit. + +You have to reach really high +to grab that kind of fruit. + +You'll actually, unfortunately, +get the + +experience that is part of +the next recitation. + +So apologies in advance. + +But you'll see that -- +well I'm not going + +to talk about that. + +Instead I'm going to focus about +some things that are + +perhaps lower-hanging fruit. + +So data level parallelism. + +So we've used SIMD in +some of recitations. + +I'm giving you a short +example of that. + +Here, I'm going to talk about +how you actually get data + +level parallelism or how do you +actually find the SIMD in + +your computation so you can +get that added advantage. + +Some nice things about data +level parallelism in the form + +of short vector instructions +is that the harder really + +becomes simpler. + +You issue one instruction and +that same instruction operates + +over multiple data elements +and you get + +better instruction bandwidth. + +I just have to fetch one +instruction and if my vector + +lens is 10, than that +effectively does 10 + +instructions for me. + +The architecture can get +simpler, reduces the + +complexity. + +So it has some nice +advantages. + +The thing to go after is +the memory hierarchy. + +This is because of that speed +gap that we showed earlier on + +in the course between memory +speed and processor speed, and + +if you optimize a performance +usually it's like 1% + +performance and your cache +registry gives you some + +significant performance +improvement in + +your overall execution. + +So you want to go after that +because that's the biggest + +beast in the room. + +A brief overview of SIMD and +then some detailed examples as + +to how you actually go about +extracting short vector + +instructions. + +So, here we have an example +of scaleacode. + +We're iterating in a loop from +zero to n, and we're just + +adding some array elements a to +b and storing results in c. + +So in the scaler mode, we just +have one add, each value of a + +and b is one register. + +We add those together, +we write the value + +to a separate register. + +In the vector mode, we can pack +multiple data elements, + +so here let's assume our vector +lens is four, I can + +pack four of these data values +into one vector register. + +You can pack four of these data +elements into another + +vector register, and now my +single vector instruction has + +the effect of doing four ads +at th same time, and it can + +store results into four +elements of c. + +Any questions on that? + +AUDIENCE: [UNINTELLIGIBLE] + +PROFESSOR: No. + +We'll get to that. + +So, let's look at those to sort +of give you a more lower + +level feel for this. + +Same code, I've just shown +data dependence graph. + +I've omitted things like the +increment of the loop and the + +branch, just focusing on +the main computation. + +So I have two loads, one brings +a sub i, the other + +brings b sub i. + +I do the add and I get c sub i +and then I can store that. + +So that might be sort of a +generic op code sequence that + +you have. If you're scheduling +that, then in the first slot I + +can do those two loads in +parallel, second cycle I can + +do the add, third cycle +I can do the store. + +I can further improve +this performance. + +If you took 6.035 you might see +software pipelining, you + +can actually overlap some +of these operations. + +Not really that important +here. + +So, what would the cycle or the +schedule look like on a + +cycle-by-cycle basis if this +was defector output? + +In the scaler case, you have +n iterations, right? + +Each iteration's taking three +cycles so that's your overall + +execution on time -- +n times 3 cycles. + +In the vector case, each load +is bringing you four data + +elements, so a sub i +to a sub i plus 3. + +Similarly for b. + +Then you add those together. + +So the schedule would look +essentially the same. + +The op codes are different, +and here what your overall + +execution time be? + +Well, what I've done is each +iteration is now doing four + +additions for me. + +So if you notice, the loop +bounds have changed. + +Instead of going from i to n +by increments of 1, now I'm + +going by increments of 4. + +So, overall, instead of having +n iterations, I can get by + +with n over 4 iterations. + +That make sense? + +So, what would my speed +up be in this case? + +4. + +So you can get more and more +speed up if your vector lens + +is longer, because then I can +cut down on the number of + +iterations that I need. + +Depending on the length of my +vector register and the data + +types that I have, that +effectively gives me different + +kinds of vector lens for +different data types. + +So you saw on Cell you have 128 +bit registers and you can + +pack those with bytes, +characters, bytes, shorts, + +integers, floats or doubles. + +So each one of those gives you +different kinds of a different + +vector lens. + +SIMD is really now, SIMD +extensions are + +increasingly popular. + +They're available on +a lot of ISAs. + +Alt of x, MMX, SSE +are available + +on a lot x86 machines. + +And, of course, in Cell, in +fact, on the SPU, all your + +instructions are SIMD +instruction, and when you're + +doing a scaler instruction, +you're actually using just one + +chunk of your vector register +and your vector pipeline. + +So how do you actually use +these SIMD instructions? + +Unfortunately, it's library +calls or using inline assembly + +or using intrinsics. + +You'll get hands-on experience +with this with Cell, so you + +might complain about that +when you actually do it. + +Compile technology is actually +getting better, and you'll see + +that one of the reasons we're +using an XLC compiler is + +because it has these vector data +types, which also latest + +versions of GCC have that allow +you to express data + +types as vector data types, +and the compiler can more + +easily or more naturally get the +parallelism for you, SIMD + +parallelism with you having to +go in there and do it by hand. + +But if you were to do it by +hand, or, in fact, what the + +compilers are trying to +automate are different + +techniques for looking for where +the SIMD parallelism is. + +There was some work done here +about six years ago by Sam + +Larson, who is now graduated, +on super word level + +parallelism. + +so I'm going to focus the rest +of this talk on this concept + +of SIMDization because I think +it's probably the one that's + +most useful for extracting +parallelism in some of the + +codes that you're doing. + +So this is really ideal for +SIMD where you have really + +short vector lens, 2 to 8. + +What you're looking for is +SIMDization that exists within + +a basic block. + +So within a code block, within +a body of a loop or within + +some control flow even. + +You can uncover this with simple +analysis, and this + +really has pushed the boundary +on what automatic + +compilers can do. + +Some of work that's gone on +at IMB, what they call the + +octipiler, has eventually been +transferred to the XLC + +compiler do a lot of defecniques +that build on SLP + +and expand in various ways to +broaden the scope of what you + +can automatically parallize. + +So here's an example of how +you might actually derive + +SIMDization or opportunities +for SIMDization. + +So you have some code, let's +say you're doing RGB + +computations where you're just +adding the r elements, that's + +a red, green and blue. + +So this might be in a loop, and +what you might notice it + +well I can pack the RGB elements +into one register. + +I can pack these into another +register, and I can pack these + +literals into a third +register. + +So that gives me a way to pack +data together into SIMD + +registers, and now I can replace +this scaler code with + +instructions that pack +the vector register. + +I can do the computations +in parallel and + +I can unpack them. + +We'll talk about that with a +little bit more illustration + +in a second. + +Any questions on this? + +Perhaps the biggest improvement +that you can get + +from SIMDization is by looking +at adjacent memory references. + +Rather than doing one load you +can do a vector load, which + +really gives you a bigger +bandwidth to memory. + +So in this case, I have a load +from I1, I2, and since these + +memory locations are continuous, +I can replace them + +by one vector load that brings +in all these data + +elements in one shot. + +That essentially eliminates +three load instructions, which + +are potentially most heavy +weight for one ligher weight + +instruction because it amortizes +bandwidth and + +exploits things like +spatial locality. + +Another one, vectorizable +loops. + +So this is probably one of +the most advanced ways of + +exploiting SIMDization, +especially in really long + +vector codes, so traditional +supercomputers like the Cray, + +and you'll probably hear Simmon +talk about this in the + +next lecture. + +So I have some loop +and I hvae this + +particular statement here. + +So how can I get SIMD +code out of this? + +Anybody have any ideas? + +Anybody know about +loop unrolling? + +So if I unroll this loop, I +essentially -- that same trick + +that I had shown earlier, +although I didn't + +quite do it this way. + +I change a loop bound +from n to -- + +the increment from -- rather +than stepping through one at a + +time, stepping through +four at a time. + +Now the loop body, rather than +doing one addition at a time, + +I'm doing four additions +at a time. + +So now this is very natural for +a vectorization, right? + +Vector load, vector load, vector +store plus the vector + +add in the middle. + +Is that intuitive? + +So this gives you another way +of extracting parallelism. + +Looking at traditional loops, +seeing whether you can + +actually unroll it in different +ways, be able to get + +that SIMD parallelization. + +The last one I'll talk about +is about partial + +vectorization. + +Either it might be some things +where you have a mix of + +statements. + +So here I have a loop where I +have some load and then I'm + +doing some computation here. + +So what could I do here? + +It's not as symmetric +as the other loop. + +AUDIENCE: There's no vector +and [INAUDIBLE PHRASE]. + +PROFESSOR: Right. + +So you might omit that. + +But could you do anything +about the subtraction? + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: If I can unroll +this again, right? + +Now there's no dependencies +between this instruction and + +this instruction, so I can +really move these together, + +and once I've moved these +together then these loads + +become contiguous. + +These loads are contiguous so I +can replace these by vector + +codes, vector equivalents. + +So now the vector load bring +in L0, L1, I have the + +addition, that brings in those +two elements in a vector, and + +then I can do my scaler +additions. + +But what do I do about the +value getting out of this + +vector register into this scaler +register that I need + +for the absolute values. + +So this is where the benefits +versus cost of + +SIMDization come in. + +So the benefits are great +because you can replace + +multiple instructions by one +instruction, or you can just + +cut down the number of +instructions by specific + +factor, your vector lens. + +Low stores can be replaced by +one wide memory operation, and + +this is probably the biggest +opportunity for performance + +improvements. + +But the cost is that you have +to pack data into the data + +registers an you have to unpack +it out so that you can + +have those kinds of +communications between this + +vector register here and the +value here, this value here + +and this value here. + +Often you can't simply access +vector values without doing + +this packing and unpacking. + +So how do you actually do +the packing, unpacking? + +This is predominantly where a +lot of the complexity goes. + +So the value of a here is +initialized by some function + +and the value of b here is +initialized by some function, + +and these might not be +things that I can + +SIMdize very easily. + +So what I need to do is move +that value into the first + +element of vector register, and +move the second value into + +the second element of +the vector register. + +So if I have a four-way vector +register, then I have to do + +four of these moves, and that +essentially is the packing. + +Then I could do my vector +computation, which is really + +these two statements here. + +Then eventually I have to do my +unpacking because I have to + +get the values out to do this +operation and this operation. + +So there's an extraction +that has to happen + +out of my SIMD register. + +But you can amortize the cost +of the packing and unpacking + +by just reusing your +vector registers. + +So these are like register +allocation techniques. + +So if I pack things into a +vector register, I find all + +cases where I can actually reuse +that vector register and + +I try to find opportunities +for extra SIMDization. + +So in the other case then, I +pack one then I can reuse that + +same vector register. + +So what are some ways I can look +for to amortize the cost? + +The interesting thing about +memory operations is while + +there are many different ways +you can pack scaler values + +into a vector register, there's +really only one way + +you can pack loads coming in +from memory into a vector + +register is because you want +the loads to be sequential, + +you want to exploit the +spatial locality. + +So one vector load really gives +you specific ordering. + +So, that really constrains +you in various ways. + +So you might bend over backwards +in some cases to + +actually get your code to +be able to you reuse the + +wide-word load without having +to do too much packing or + +unpacking because that'll start + +eating into your benefits. + +So simple example of how +you might find the SLP + +parallelism. + +So the first thing you want to +do is start with are the + +instructions that give you the +most benefit, so it's memory + +references. + +So here there are two +memory references. + +They happen to be adjacent, so +I'm accessing a contiguous + +memory chunks, so I can +parallelized that. + +That would be my first step. + +I can do a vector load and +that assignment can + +become a and b. + +I can look for opportunities +where I can propagate this + +vector values within the +vector register that's + +holding a and b. + +So the way I do that is I look +for uses of a and b. + +In this case, there are +these two statements. + +So I can look for opportunities + +to vectorize that. + +So in this case, both of these +instructions are also + +vectorizable. + +Now I have a vector subtraction, +and I have a + +vector register holding +new values h and j. + +So I follow that chain again +of where data's flowing. + +I find these operations and I +can vectorize that as well. + +So, sign up with a vectorizable +loop where all my + +instructions, all my scale +instructions are now in SIMD + +instructions. + +I can cut down on loop +iterations of total number of + +instructions that I issue. + +But I've made some implicit +assumption here. + +Anybody know what it is? + +AUDIENCE: Do you actually +need that many + +iterations of the loop? + +PROFESSOR: Well, so you can +factor down the cost. so here + +I've vectorized by 2, so I would +cut down the number of + +iterations by 2. + +AUDIENCE: You could have an +odd number of iterations? + +PROFESSOR: Right, so you could +have an odd number of + +iterations. + +What do you do about the +remaining iterations. + +You might have to do scaler +code for that. + +What are some other +assumptions? + +Maybe it will be clear here. + +So in vectorizing this, what +have I assumed about + +relationships between +these statements? + +I've essentially reorganized +all the statements so that + +assumes I have this liberty to +move instructions around. + +Yup? + +AUDIENCE: [UNINTELLIGIBLE] +a and b don't change + +[INAUDIBLE PHRASE]. + +PROFESSOR: Right. + +So there's nothing in here +that's changing the values. + +There's no dependencies between +these statements -- no + +flow dependencies and no other +kind of constraints that limit + +this kind of movement. + +So in real code it's not +actually the case. + +You end up with patterns of +computation where you can get + +really a nice case of classic +cases you can vectorize those + +really nicely. + +In a lot of other codes you +have a mix of vectorizable + +code and scaler code and there's +a lot of communication + +between the two. + +So the cost is really something +significant that you + +have to consider. + +This was, as I mentioned, done +in somebody's Masters thesis + +and eventually led to some +additional work that was his + +PhD thesis. + +So in some of the early work, +what he did was he looked at a + +bunch of benchmarks and looked +at how much available + +parallelism you have in terms +of this kind of short vector + +parallelism, or rather SLP +where you're looking for + +vectorizable code within basic +blocks, which really differed + +from a classic way of people +looking for vectorization. + +[? And you ?] have +well-structured loops and + +doing kinds of transformations +you'll hear about next week. + +So for different kinds of vector +registers, so these are + +your vector lens. + +So going from 128 bits to 1,024 +bits, you can actually + +reduce a whole lot +of instructions. + +So what I'm showing here +is the percent dynamic + +instruction reduction. + +So if I take my baseline +application and just compile + +it in a normal way and I run it +again an instruction count. + +I apply this SLP technique that +find the SIMDization and + +then run my application again, +use the performance counters + +to count the number +of instructions + +and compare the two. + +I can get 60%, 50%, 40%. + +In some cases I can completely +eliminate almost 90% or more + +of the instructions. + +So it's a lot of opportunity for +performance improvements + +that might be apparent. + +One because I'm reducing the +instruction bandwidth, I'm + +reducing the amount of space I +need in my instruction cache, + +I have fewer instructions so I +can fit more instructions into + +my instruction cache, you reduce +the number of branches. + +You get better bandwidth to the +memory, better use of the + +memory bandwidth. + +Overall, you're running fewer +iterations, so you're getting + +lots of potential +for performance. + +So, I actually ran this +on the AltiVec. + +This was one of the earliest +generations of AltiVec, which + +SIMD instructions didn't have +I believe double precision + +floating point, so not all the +benchmarks you see on the + +previsou slide are here, only +the ones that could run + +reasonably accurately +with a single + +precision floating point. + +What they measure is the +actual speed up. + +Doing this SIMDization versus +not doing a SIMDization, how + +much performance you can get. + +The thing to take away is in +some cases where you have + +nicely structured loops and some +nice patterns, you can + +get up to 7x speed up +on some benchmarks. + +What might be the maximum speed +up that you can get + +depends on the vector lens, +so 8, for example on some + +architectures depending +on the data type. + +Is there any questions +on that? + +So as part of the next +recitation, you'll actually + +get an exercise of going through +and SIMDizing for + +Cell, and whether that actually +means SIMDize + +instructions for Cell might take +statements and sort of + +replace them by intrinsic +functions, which eventually + +map down to actually assembly +op codes that you'll need. + +So you don't actually have to +program at the assembly level, + +although in effect, you're +probably doing the same thing. + +Last thing we'll talk about +today is optimizing for the + +memeory hierarchy. + +In addition to data level +parallelism, looking for + +performance enhancements in the +memory system gives you + +the best opportunities because +of this big gap in performance + +between memory access latencies +and what the CPU + +efficiency is. + +So exploiting locality in +a memroy system is key. + +So these concepts of temporal +and spatial locality. + +So let's look at an example. + +Let's say I have a loop and in +this loop I have some code + +that's embodied in some function +a, some code embodied + +in some function b, and some +code in some function c. + +The values produced by a are +consumed by the function b, + +and similarly the values +consumed by b + +are consumed by c. + +So this is a general data flow +graph that you might have for + +this function. + +Let's say that all the data +could go into a small array + +that then I can communicate +between functions. + +So if I look at my actual cache +size and how the working + +set of each of these functions +is, so let's say this is my + +cache size -- this is how +many instructions I can + +pack into the cache. + +Looking at the collective number +of instructions in each + +one of these functions, +I overflow that. + +I have more instructions +I can fit into my + +cache any one time. + +So what does that mean for my +actual cash performance? + +So when I run a, what do I +expect the cache hit and miss + +rate behavior to be like? + +So in the first iteration, I +need the instructions for a. + +I've never seen a before so I +have to fetch that data from + +memory and put in the cache. + +So, the attachments. + +So what about b? + +Then c? + +Same thing. + +So now I'm back at the +top of my loop. + +So if everything fit in +the cache then I would + +expect a to be a what? + +You'll be a hit. + +But since I've constrained this +problem such that the + +working set doesn't really fit +in the cache, what that means + +is that I have to fetch some +new instructions for a. + +So let's say I have +to fetch all the + +instructions for a again. + +That leads me to another miss. + +Now, bringing a again into my +cache kicks out some extra + +instructions because I need to +make room in a finite memory + +so I kick out b. + +Bring in b and I end +up kicking out c. + +So you end up with a pattern +where everything is a miss. + +This is a problem because the +way the loop is structured, + +collectively I just can't pack +all those instructions into + +the cache, so I end up taking +a lot of cache misses and + +that's bad for performance. + +But I can look at an +alternative way + +of doing this loop. + +I can split up this loop into +three where in one loop I do + +all the a instructions, in the +second loop I do all the b's, + +and the third loop +I do all the c's. + +Now my working set +is really small. + +So the instructions for a fit in +the cache, instructions for + +b fit in the cache, and +instructions for + +c fit in the cache. + +So what do I expect for the +first time I see a? + +Miss. + +Then second time? + +It'll be hit, because I've +brought in a, I haven't run b + +or c yet, the number of +instructions I need for a is + +smaller than what I +can fit into the + +cache, so that's great. + +Nothing gets kicked out. + +So every one of those +iterations + +for a becomes a hit. + +So that's good. + +I've improved performance. + +For b I have the same pattern. + +First time I see b it's a miss, +every time after that + +it's a hit. + +Similarly for c. + +So my cache miss rate goes from +being one, everything's a + +miss, to decreasing to 1 over +n where n is essentially how + +much I can run the loop. + +So we call that full scaling +because we've taken the loop + +where we've distributed, and +we've scaled every one of + +those smaller loops to the +maximum that we could get. + +Now what about the data? + +So we have the same example. + +Here we saw that the instruction +working set is + +big, but what about the data? + +So let's say in this case +I'm sending just a + +small amount of data. + +Then the behavior +is really good. + +It's a small amount of data +that I need to communicate + +from a to b. + +A small amount of +data you need to + +communicate from b to c. + +So it's great. + +No problems with +the data cache. + +What happens in full +scaling case? + +AUDIENCE: It's not correct to +communicate from a to b. + +PROFESSOR: What do you mean +it's not correct? + +AUDIENCE: Oh, it's not + +communicating at the same time. + +PROFESSOR: Yeah, it's not +at the same time. + +In fact, just assume +this is sequential. + +So I run a, I store some data, +and then when I run + +b I grab that data. + +This is in sequential. + +AUDIENCE: How do you know that +the transmission's valid then? + +We could use some +global variable. + +PROFESSOR: Simple case. + +There's no global variables. + +All the data that b needs +comes from a. + +So if I run a I produce +all the data and + +that's all that b needs. + +So in the full scaling case, +what do I expect to + +happen for the data? + +Remember, in the full scaling +case, all the working sets for + +the instructions are small so +they all fit in the cache. + +But now I'm running a for a lot +longer so I have to store + +a lot more data for b. + +Similarly, I'm running b for a +lot longer so I have to store + +a lot more data for c. + +So what do I expect to happen +with the working set here? + +Instructions are still good, +but the data might be bad + +because I've run a for a lot +more iterations at one shot. + +So now I have to buffer all +this data for a to b. + +Similarly, I've run b for a long +time so I have to buffer + +a whole lot data for b to c. + +Is that clear? + +AUDIENCE: No. + +PROFESSOR: So let's say every +time a runs it produces one + +data element. + +So now in this case, +every iteration + +produces one data element. + +That's fine. + +That's clear? + +Here I run a n times, so I +produce n data elements. + +And b let's say produces +one data element. + +So if my cache can only hold +let's say n by 2 data + +elements, then there's +an overflow. + +So what that means is not +everything's in the cache, and + +that's bad because of the same +reasons we saw for the + +instructions. + +When I need those data I have +to go out to memory and get + +them again, so it's extra +communication, extra + +redundancy. + +AUDIENCE: In this case where you +don't need to store the a + +variables +[UNINTELLIGIBLE PHRASE]. + +PROFESSOR: But notice these were +sequential simple case. + +I need all the data from a to +run all the iterations for b. + +Then, yeah, this goes away. + +So let's say this goes away, +but still b produces n + +elements and that overflows +the cache. + +So there's a third example where +I don't fully distribute + +everything, I partially +distribute some of the loops. + +I can fully scale a and b +because I can fit those + +instructions in the cache. + +That gets me around this +problem, because now a and b + +are just communicating +one day data element. + +But c is still a problem because +I still have to run b + +n times in the end before I can +run c so there are n data + +elements in flight. + +So the data for b still becomes +a problem in terms of + +its locality. + +Is that clear? + +So, any ideas on how +I can improve this? + +AUDIENCE: assuming you have the +wrong cache line and you + +have to do one or two memory +acceses to get the cache back. + +PROFESSOR: So, programs +typically have really good + +instruction locality just +because the nature of the way + +we run them. + +We have small loops and they +iterate over and over again. + +Data is actually where you spend +most of your time in the + +memory system. + +It's fetching data. + +So I didn't actually understand +why you think data + +is less expensive than +instructions. + +AUDIENCE: What I'm saying say +you want to read an array, + +read the first, say, 8 +elements to 8 words + +in the cache box. + +Well then you'd get 7 hits, so +every 8 iterations you have to + +do a rewrite. + +PROFESSOR: Right. + +So that assumes that you have +really good spatial locality, + +because you've assumed that I've +brought in 8 elements and + +I'm going to use every +one of them. + +So if that's the case you have +really good spatial locality + +and that's, in fact, +what you want. + +It's the same kind of thing +that I showed for the + +instruction cache. + +The first thing is a miss, +the rest are hits. + +The reason data is more +expensive, you simply have a + +lot more data reads than +you have instructions. + +Typically you have small +loops, hundreds of + +instructions and they might +access really big arrays that + +are millions of data +references. + +So that becomes a problem. + +So ideas on how to +improve this? + +AUDIENCE: That's a loop? + +PROFESSOR: That's a loop. + +So what would you do in +the smaller loop? + +AUDIENCE: [INAUDIBLE PHRASE]. + +PROFESSOR: Something +like that? + +AUDIENCE: Yeah. + +PROFESSOR: OK. + +So in a nested loop, you have +a smaller loop that has a + +small number of iterations, +so 64. + +So, 64 might be just as much as +I can buffer for the data + +in the cache. + +Then I wrap that loop with one +outer loop that completes the + +whole number of iterations. + +So if I had to do n, then +I divide n by 64. + +So that can work out +really well. + +So there's different kinds of +blocking techniques that you + +can use on getting your data to +fit into your local store + +or into your cache to exploit +these spatial and temporal + +properties. + +Question? + +AUDIENCE: Would it not be +better to use a small + +[UNINTELLIGIBLE] size so +you could run a, b, c + +sequentially? + +PROFESSOR: You could +do that as well. + +But the problem with running a, +b, c sequentially is that + +if they're in the same +loop, you end up with + +instructions being bad. + +That would really, this case -- +so even if you change this + +number you don't get around +the instructions. + +So you're going to see more +optimizations that do more of + +these loop tricks. + +I talk about unrolling without +really defining what unrolling + +is or going into a +lot of details. + +Loop distribution, loop fision, +some of the things, + +like loop tiling, +loop blocking. + +I think Simmon's going to cover +some of these next week. + +So this was implemented, this +was done by another Master + +student at MIT who graduated +about two years ago, to show + +that if you factor in cache +constraints versus ignoring + +cache constraints, how much +performance you can get. + +This was done in the context +of StreamIt. + +So, in fact, some of you might +have recognized a to b to c as + +being interconnected as +pipeline filters. + +We ran it on different +processors, so the StrongARM + +processor's really small. + +InOrder processor has no L1 +cache in this particular model + +that we used. + +But it had a really +long latency -- + +sorry, it had no L2 cache. + +It had really long latency +to memory. + +Pentium, an x86 processor. + +Reasonably fast. It had a +complicated memory system and + +a lot, a lot of memory overlap +in terms of references. + +Then the Itanium processor, +which had a huge L2 cache at + +its disposal. + +So what you can see is that +lower bars indicate + +bigger speed ups. + +This is normalized run time. + +So on the processor where you +don't actually have caches to + +save you, and the memory +communication is really + +expensive, you can get a lot +of benefit from doing the + +cache aware scaling, that loop +nesting to take advantage of + +packing instructions instead of +instruction cache, packing + +data into data cache and not +having to go out to memory if + +you don't to. + +So you can reduce run time to +about 1/3 of what it was with + +this kind of cache +optimization. + +On the Pentium3 where you have +a cache to help you out, the + +benefits are there, but you +don't get as big a benefit + +from ignoring the cache +constraints versus being aware + +of the cache constraints. + +So here you're actually doing +some of that middle column + +whereas here we're doing +third columns, + +the cache aware fusion. + +In a Itanium you really get no +benefits between the two. + +Yep? + +AUDIENCE: Can you explain what +the left columns are? + +PROFESSOR: These? + +AUDIENCE: Yeah. + +PROFESSOR: So this is tricky. + +So the left columns +are doing this. + +AUDIENCE: OK, sort of assuming +that icache is there. + +PROFESSOR: Right, and the third +column is doing this. + +So you want to do this because +the icache locality is the + +best. So you always want to go +to full or maximum scaling. + +I'm actually fudging a little +just for sake of clarity. + +Here you're actually doing this +nesting to improve both + +the instruction and +the data locality. + +So you can get really good +performance improvement. + +So what does that mean for +your Cell projects or for + +Cell, we'll talk about that next +week at the recitation. + +Yeah? + +AUDIENCE: Is there +some big reasons + +[UNINTELLIGIBLE PHRASE]. + +PROFESSOR: Well it just means +that if you have caches to + +save you, and they're really big +caches and they're really + +efficient, the law of +diminishing returns. + +That's where profiling +comes in. + +So you look at the profiling +results, you look at your + +cache misses, how many cache +misses are you taking. + +If it's really significant, +then you look at ways to + +improve it. + +If your cache misses are really +low, you missed rate is + +really low, then it doesn't make +sense to spend time and + +energy focusing on that. + +Good question. + +So, any other questions? + +So summarizing the gamut of +programming for performance. + +So you tune to parallelism +first, because if you can't + +find the concurrency, your +Amdahl's law, you're not going + +to a get a whole lot +of speed up. + +But then once you figured out +what the parallelism is, then + +what you want to do is really +get the performance on each + +processor, the single track +performance to be really good. + +You shouldn't ignore that. + +The modern processors +are complex. + +You need instructional level +parallelism, you need data + +level parallelism, you +need memory hierarchy + +optimizations, and so you +should consider those + +optimizations. + +Here, profiling tools could +really help you figure out + +where the biggest benefits to +performance will come from. + +You may have to, in fact, +change everything. + +You may have to change your +algorithm, your data + +structures, your program +structure. + +So in the MPEG decoder case, for +example, I showed you that + +if you change the flag that +says don't use double + +precision inverse DCT, use a +numerical hack, then you can + +get performance improvements +but you're changing your + +algorithm really. + +You really want to focus on just +the biggest nuggets -- + +where is most of the performance +coming in, or + +where's the biggest performance +bottleneck, and + +that's the thing you +want optimize. + +So remember the law of +diminishing returns. + +Don't spend your time on doing +things that aren't going to + +get you anything significant +in return. + +That's it. + +Any questions? + +OK. + +How are you guys doing +with the projects? + +So, one of the added benefits of +the central CBS repository + +is I get notifications too +when you submit things. + +So I know of only two projects +that have been submitting + +things regularly. + +So, I hope that'll +pick up soon. + +I guess a few minutes to finish +the quiz and then we'll + +see you next week. + +Have a good weekend. \ No newline at end of file diff --git a/_GT4SZibf5E.txt b/_GT4SZibf5E.txt new file mode 100644 index 0000000000000000000000000000000000000000..92dd8029833df181a48d9ddd12b3c7b1a74303af --- /dev/null +++ b/_GT4SZibf5E.txt @@ -0,0 +1,1519 @@ +align:start position:0% + +hi everyone I'm Dave now today I'd like + + align:start position:0% +hi everyone I'm Dave now today I'd like + + + align:start position:0% +hi everyone I'm Dave now today I'd like +to tackle a problem in orthogonal + + align:start position:0% +to tackle a problem in orthogonal + + + align:start position:0% +to tackle a problem in orthogonal +subspaces so the problem we'd like to + + align:start position:0% +subspaces so the problem we'd like to + + + align:start position:0% +subspaces so the problem we'd like to +tackle uh given a Subspace s and suppose + + align:start position:0% +tackle uh given a Subspace s and suppose + + + align:start position:0% +tackle uh given a Subspace s and suppose +s is spanned by two vectors 1 2 2 3 and + + align:start position:0% +s is spanned by two vectors 1 2 2 3 and + + + align:start position:0% +s is spanned by two vectors 1 2 2 3 and +1 3 + + align:start position:0% +1 3 + + + align:start position:0% +1 3 +32 uh we have a question here which is + + align:start position:0% +32 uh we have a question here which is + + + align:start position:0% +32 uh we have a question here which is +to find a basis for S per s per is + + align:start position:0% +to find a basis for S per s per is + + + align:start position:0% +to find a basis for S per s per is +another sub space which is orthogonal to + + align:start position:0% +another sub space which is orthogonal to + + + align:start position:0% +another sub space which is orthogonal to +S and then secondly can every Vector in + + align:start position:0% +S and then secondly can every Vector in + + + align:start position:0% +S and then secondly can every Vector in +R4 be uniquely written in terms of S and + + align:start position:0% +R4 be uniquely written in terms of S and + + + align:start position:0% +R4 be uniquely written in terms of S and +S per so I'll let you think about this + + align:start position:0% +S per so I'll let you think about this + + + align:start position:0% +S per so I'll let you think about this +for now and I'll come back in a + + align:start position:0% + + + + align:start position:0% + +minute hi everyone welcome back okay so + + align:start position:0% +minute hi everyone welcome back okay so + + + align:start position:0% +minute hi everyone welcome back okay so +why don't we tackle this + + align:start position:0% +why don't we tackle this + + + align:start position:0% +why don't we tackle this +problem + + align:start position:0% + + + + align:start position:0% + +okay so first off what does it mean for + + align:start position:0% +okay so first off what does it mean for + + + align:start position:0% +okay so first off what does it mean for +a vector to be an S per + + align:start position:0% +a vector to be an S per + + + align:start position:0% +a vector to be an S per +well if I have a vector + + align:start position:0% + + + + align:start position:0% + +X and S per and X is in s per what this + + align:start position:0% +X and S per and X is in s per what this + + + align:start position:0% +X and S per and X is in s per what this +means is X is going to be orthogonal to + + align:start position:0% +means is X is going to be orthogonal to + + + align:start position:0% +means is X is going to be orthogonal to +every Vector in s now specifically s is + + align:start position:0% +every Vector in s now specifically s is + + + align:start position:0% +every Vector in s now specifically s is +spanned by these two vectors so it's + + align:start position:0% +spanned by these two vectors so it's + + + align:start position:0% +spanned by these two vectors so it's +sufficient that X be perpendic to the + + align:start position:0% +sufficient that X be perpendic to the + + + align:start position:0% +sufficient that X be perpendic to the +two uh basis vectors in s so + + align:start position:0% +two uh basis vectors in s so + + + align:start position:0% +two uh basis vectors in s so +specifically I can take 1 2 2 + + align:start position:0% + + + + align:start position:0% + +3 and Dot it with + + align:start position:0% + + + + align:start position:0% + +X and it's going to be zero so I'm + + align:start position:0% +X and it's going to be zero so I'm + + + align:start position:0% +X and it's going to be zero so I'm +writing I'm treating X as a column + + align:start position:0% +writing I'm treating X as a column + + + align:start position:0% +writing I'm treating X as a column +Vector + + align:start position:0% +Vector + + + align:start position:0% +Vector +here in + + align:start position:0% + + + + align:start position:0% + +addition X must also be orthogonal to + + align:start position:0% +addition X must also be orthogonal to + + + align:start position:0% +addition X must also be orthogonal to + + align:start position:0% + + + + align:start position:0% + +so any Vector X that's in s per must be + + align:start position:0% +so any Vector X that's in s per must be + + + align:start position:0% +so any Vector X that's in s per must be +orthogonal to both of these + + align:start position:0% +orthogonal to both of these + + + align:start position:0% +orthogonal to both of these +vectors so what we can do is we can + + align:start position:0% +vectors so what we can do is we can + + + align:start position:0% +vectors so what we can do is we can +write this as a matrix + + align:start position:0% + + + + align:start position:0% + +equation and we do this by combining + + align:start position:0% +equation and we do this by combining + + + align:start position:0% +equation and we do this by combining +these two vectors as rows of The + + align:start position:0% + + + + align:start position:0% + +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +so if we step back and take a look at + + align:start position:0% +so if we step back and take a look at + + + align:start position:0% +so if we step back and take a look at +this equation we see that what we're + + align:start position:0% +this equation we see that what we're + + + align:start position:0% +this equation we see that what we're +really asking is to find all X that are + + align:start position:0% +really asking is to find all X that are + + + align:start position:0% +really asking is to find all X that are +in the null space of this + + align:start position:0% +in the null space of this + + + align:start position:0% +in the null space of this +Matrix so how do we find X in the null + + align:start position:0% +Matrix so how do we find X in the null + + + align:start position:0% +Matrix so how do we find X in the null +space of a matrix well what we can do is + + align:start position:0% +space of a matrix well what we can do is + + + align:start position:0% +space of a matrix well what we can do is +we can row reduce this Matrix and try + + align:start position:0% +we can row reduce this Matrix and try + + + align:start position:0% +we can row reduce this Matrix and try +and find a basis for the null space so + + align:start position:0% +and find a basis for the null space so + + + align:start position:0% +and find a basis for the null space so +I'm going to just row reduce this Matrix + + align:start position:0% +I'm going to just row reduce this Matrix + + + align:start position:0% +I'm going to just row reduce this Matrix +and notice that by row reduction we + + align:start position:0% +and notice that by row reduction we + + + align:start position:0% +and notice that by row reduction we +don't actually change the null space of + + align:start position:0% +don't actually change the null space of + + + align:start position:0% +don't actually change the null space of +a + + align:start position:0% +a + + + align:start position:0% +a +matrix so if I'm only interested in the + + align:start position:0% +matrix so if I'm only interested in the + + + align:start position:0% +matrix so if I'm only interested in the +null space + + align:start position:0% +null space + + + align:start position:0% +null space +this system is going to be equivalent to + + align:start position:0% +this system is going to be equivalent to + + + align:start position:0% +this system is going to be equivalent to +I can keep the top row the + + align:start position:0% + + + + align:start position:0% + +same and then just to simplify Our Lives + + align:start position:0% +same and then just to simplify Our Lives + + + align:start position:0% +same and then just to simplify Our Lives +we can take the second row and subtract + + align:start position:0% +we can take the second row and subtract + + + align:start position:0% +we can take the second row and subtract +one copy of the first + + align:start position:0% + + + + align:start position:0% + +row now if I do that I obtain 0 1 1 + + align:start position:0% +row now if I do that I obtain 0 1 1 + + + align:start position:0% +row now if I do that I obtain 0 1 1 +minus + + align:start position:0% + + + + align:start position:0% + +one okay now to parameterize the null + + align:start position:0% +one okay now to parameterize the null + + + align:start position:0% +one okay now to parameterize the null +space what I'm going to do is I'm going + + align:start position:0% +space what I'm going to do is I'm going + + + align:start position:0% +space what I'm going to do is I'm going +to write X out as + + align:start position:0% +to write X out as + + + align:start position:0% +to write X out as +components so if I write + + align:start position:0% +components so if I write + + + align:start position:0% +components so if I write +x with components X1 + + align:start position:0% +x with components X1 + + + align:start position:0% +x with components X1 +X2 X3 and + + align:start position:0% + + + + align:start position:0% + +X4 we see here that this Matrix has a + + align:start position:0% +X4 we see here that this Matrix has a + + + align:start position:0% +X4 we see here that this Matrix has a +rank of + + align:start position:0% +rank of + + + align:start position:0% +rank of +two now we we're looking uh at vectors + + align:start position:0% +two now we we're looking uh at vectors + + + align:start position:0% +two now we we're looking uh at vectors +which live in R4 so we know that the + + align:start position:0% +which live in R4 so we know that the + + + align:start position:0% +which live in R4 so we know that the +null space is going to have a dimension + + align:start position:0% +null space is going to have a dimension + + + align:start position:0% +null space is going to have a dimension +which is 4 minus 2 so that means there + + align:start position:0% +which is 4 minus 2 so that means there + + + align:start position:0% +which is 4 minus 2 so that means there +should be two vectors in the null space + + align:start position:0% +should be two vectors in the null space + + + align:start position:0% +should be two vectors in the null space +of this + + align:start position:0% +of this + + + align:start position:0% +of this +Matrix to parameterize uh these two + + align:start position:0% +Matrix to parameterize uh these two + + + align:start position:0% +Matrix to parameterize uh these two +dimensional vectors what I'm going to do + + align:start position:0% +dimensional vectors what I'm going to do + + + align:start position:0% +dimensional vectors what I'm going to do +is I'm going to let X4 equal some + + align:start position:0% +is I'm going to let X4 equal some + + + align:start position:0% +is I'm going to let X4 equal some +constant and X3 equal another + + align:start position:0% +constant and X3 equal another + + + align:start position:0% +constant and X3 equal another +constant so specifically I'm going to + + align:start position:0% +constant so specifically I'm going to + + + align:start position:0% +constant so specifically I'm going to +let + + align:start position:0% +let + + + align:start position:0% +let +X4 equal + + align:start position:0% +X4 equal + + + align:start position:0% +X4 equal +B and X3 equal + + align:start position:0% + + + + align:start position:0% + +a now what + + align:start position:0% +a now what + + + align:start position:0% +a now what +we do is we take a look at these two + + align:start position:0% +we do is we take a look at these two + + + align:start position:0% +we do is we take a look at these two +equations and this bottom equation will + + align:start position:0% +equations and this bottom equation will + + + align:start position:0% +equations and this bottom equation will +say that + + align:start position:0% +say that + + + align:start position:0% +say that +X2 is equal + + align:start position:0% +X2 is equal + + + align:start position:0% +X2 is equal +to X3 + + + align:start position:0% + + + + align:start position:0% + +X4 which is going to equal negative + + align:start position:0% +X4 which is going to equal negative + + + align:start position:0% +X4 which is going to equal negative +a + + align:start position:0% +a + + + align:start position:0% +a +X4 plus + + align:start position:0% + + + + align:start position:0% + +b and then the top equation says that + + align:start position:0% +b and then the top equation says that + + + align:start position:0% +b and then the top equation says that +X1 is equal to -2 + + align:start position:0% +X1 is equal to -2 + + + align:start position:0% +X1 is equal to -2 +X2 - 2 + + align:start position:0% +X2 - 2 + + + align:start position:0% +X2 - 2 +X3 + 3 X4 sorry - 3 + + align:start position:0% + + + + align:start position:0% + +X4 and if I substitute + + align:start position:0% + + + + align:start position:0% + +in X2 is minus a plus + + align:start position:0% + + + + align:start position:0% + +b X3 is + + align:start position:0% +b X3 is + + + align:start position:0% +b X3 is +a and X4 is + + align:start position:0% +a and X4 is + + + align:start position:0% +a and X4 is +B so when the dust settles the A's + + align:start position:0% +B so when the dust settles the A's + + + align:start position:0% +B so when the dust settles the A's +cancel and I'm left with minus + + align:start position:0% + + + + align:start position:0% + +5B okay so we can combine everything + + align:start position:0% +5B okay so we can combine everything + + + align:start position:0% +5B okay so we can combine everything +together and we end + + align:start position:0% +together and we end + + + align:start position:0% +together and we end +up + + align:start position:0% +up + + + align:start position:0% +up +obtaining X1 X2 + + align:start position:0% +obtaining X1 X2 + + + align:start position:0% +obtaining X1 X2 +X3 + + align:start position:0% + + + + align:start position:0% + +X4 + + align:start position:0% +X4 + + + align:start position:0% +X4 +equals - + + align:start position:0% +equals - + + + align:start position:0% +equals - +5B X2 is - A plus b + + align:start position:0% + + + + align:start position:0% + +X3 is + + align:start position:0% +X3 is + + + align:start position:0% +X3 is +a and X4 is + + align:start position:0% +a and X4 is + + + align:start position:0% +a and X4 is +B and now what we can do is we can take + + align:start position:0% +B and now what we can do is we can take + + + align:start position:0% +B and now what we can do is we can take +this vector and we can decompose it into + + align:start position:0% +this vector and we can decompose it into + + + align:start position:0% +this vector and we can decompose it into +pieces which are a multiplied by a + + align:start position:0% +pieces which are a multiplied by a + + + align:start position:0% +pieces which are a multiplied by a +vector and B multiplied by a + + align:start position:0% +vector and B multiplied by a + + + align:start position:0% +vector and B multiplied by a +vector so you'll note that this is + + align:start position:0% +vector so you'll note that this is + + + align:start position:0% +vector so you'll note that this is +actually + + align:start position:0% +actually + + + align:start position:0% +actually +a * 0 - 1 1 + + align:start position:0% +a * 0 - 1 1 + + + align:start position:0% +a * 0 - 1 1 +0 + B + + align:start position:0% +0 + B + + + align:start position:0% +0 + B +* - + + align:start position:0% +* - + + + align:start position:0% +* - +5 1 0 + + align:start position:0% + + + + align:start position:0% + + + align:start position:0% + + + align:start position:0% +okay so we have successfully achieved a + + align:start position:0% +okay so we have successfully achieved a + + + align:start position:0% +okay so we have successfully achieved a +parameterization of the null space of + + align:start position:0% +parameterization of the null space of + + + align:start position:0% +parameterization of the null space of +this Matrix as some constant a time a + + align:start position:0% +this Matrix as some constant a time a + + + align:start position:0% +this Matrix as some constant a time a +vector 0 - 1 1 0 plus b * a vector minus + + align:start position:0% +vector 0 - 1 1 0 plus b * a vector minus + + + align:start position:0% +vector 0 - 1 1 0 plus b * a vector minus +5 1 0 + + align:start position:0% +5 1 0 + + + align:start position:0% +5 1 0 +1 and now we claim that this is the + + align:start position:0% +1 and now we claim that this is the + + + align:start position:0% +1 and now we claim that this is the +entire space s + + align:start position:0% + + + + align:start position:0% + +per so s per is going to be spanned by + + align:start position:0% +per so s per is going to be spanned by + + + align:start position:0% +per so s per is going to be spanned by +this vector and this + + align:start position:0% +this vector and this + + + align:start position:0% +this vector and this +Vector now notice + + align:start position:0% +Vector now notice + + + align:start position:0% +Vector now notice +how uh if I were to take either of these + + align:start position:0% +how uh if I were to take either of these + + + align:start position:0% +how uh if I were to take either of these +two vectors in s and Dot it with any + + align:start position:0% +two vectors in s and Dot it with any + + + align:start position:0% +two vectors in s and Dot it with any +Vector uh in the null Space by + + align:start position:0% +Vector uh in the null Space by + + + align:start position:0% +Vector uh in the null Space by +construction it automatically + + align:start position:0% +construction it automatically + + + align:start position:0% +construction it automatically +vanishes okay so this concludes part + + align:start position:0% +vanishes okay so this concludes part + + + align:start position:0% +vanishes okay so this concludes part +one now for part two + + align:start position:0% +one now for part two + + + align:start position:0% +one now for part two +can every vector v and R4 be written + + align:start position:0% +can every vector v and R4 be written + + + align:start position:0% +can every vector v and R4 be written +uniquely in terms of S and S per the + + align:start position:0% +uniquely in terms of S and S per the + + + align:start position:0% +uniquely in terms of S and S per the +answer is + + align:start position:0% + + + + align:start position:0% + +yes so how do we see this well if I have + + align:start position:0% +yes so how do we see this well if I have + + + align:start position:0% +yes so how do we see this well if I have +a vector v what I can do is I can try + + align:start position:0% +a vector v what I can do is I can try + + + align:start position:0% +a vector v what I can do is I can try +and write it as some constant + + align:start position:0% +and write it as some constant + + + align:start position:0% +and write it as some constant +C1 times the vector 1 22 + + align:start position:0% +C1 times the vector 1 22 + + + align:start position:0% +C1 times the vector 1 22 +3 plus C2 + + align:start position:0% + + + + align:start position:0% + +times a vector + + align:start position:0% + + + + align:start position:0% + +1332 plus a vector + + align:start position:0% +1332 plus a vector + + + align:start position:0% +1332 plus a vector +C4 sorry + + align:start position:0% + + + + align:start position:0% + +C3 0 - 1 1 + + align:start position:0% +C3 0 - 1 1 + + + align:start position:0% +C3 0 - 1 1 +0 plus + + align:start position:0% +0 plus + + + align:start position:0% +0 plus +C4 - 5 1 0 + + align:start position:0% +C4 - 5 1 0 + + + align:start position:0% +C4 - 5 1 0 +1 okay so C1 uh and C2 are multiplying + + align:start position:0% +1 okay so C1 uh and C2 are multiplying + + + align:start position:0% +1 okay so C1 uh and C2 are multiplying +the vectors in s and C3 and C4 are + + align:start position:0% +the vectors in s and C3 and C4 are + + + align:start position:0% +the vectors in s and C3 and C4 are +multiplying the vectors in s per so the + + align:start position:0% +multiplying the vectors in s per so the + + + align:start position:0% +multiplying the vectors in s per so the +question is given any V can I find + + align:start position:0% +question is given any V can I find + + + align:start position:0% +question is given any V can I find +constants C1 C2 C3 C4 such that uh this + + align:start position:0% +constants C1 C2 C3 C4 such that uh this + + + align:start position:0% +constants C1 C2 C3 C4 such that uh this +equation holds and the answer is yes now + + align:start position:0% +equation holds and the answer is yes now + + + align:start position:0% +equation holds and the answer is yes now +notice how uh just to see just to see + + align:start position:0% +notice how uh just to see just to see + + + align:start position:0% +notice how uh just to see just to see +why it's yes what we can do is we can + + align:start position:0% +why it's yes what we can do is we can + + + align:start position:0% +why it's yes what we can do is we can +rewrite this in a matrix + + align:start position:0% +rewrite this in a matrix + + + align:start position:0% +rewrite this in a matrix +notation and there's kind of a handy + + align:start position:0% + + + + align:start position:0% + +trick + + align:start position:0% + + + + align:start position:0% + +what I can do is I can take these uh + + align:start position:0% +what I can do is I can take these uh + + + align:start position:0% +what I can do is I can take these uh +columns and write them as Columns of a + + align:start position:0% + + + + align:start position:0% + +matrix and this whole expression is + + align:start position:0% +matrix and this whole expression is + + + align:start position:0% +matrix and this whole expression is +actually equivalent + + align:start position:0% +actually equivalent + + + align:start position:0% +actually equivalent +to this Matrix multiplied by the + + align:start position:0% +to this Matrix multiplied by the + + + align:start position:0% +to this Matrix multiplied by the +constant C1 C2 C3 + + align:start position:0% +constant C1 C2 C3 + + + align:start position:0% +constant C1 C2 C3 +C4 and on the right hand side we have + + align:start position:0% +C4 and on the right hand side we have + + + align:start position:0% +C4 and on the right hand side we have +the vector + + align:start position:0% +the vector + + + align:start position:0% +the vector +v Now by + + align:start position:0% +v Now by + + + align:start position:0% +v Now by +construction these vectors are linearly + + align:start position:0% +construction these vectors are linearly + + + align:start position:0% +construction these vectors are linearly +independent and we know from linear + + align:start position:0% +independent and we know from linear + + + align:start position:0% +independent and we know from linear +algebra that if we have a matrix with + + align:start position:0% +algebra that if we have a matrix with + + + align:start position:0% +algebra that if we have a matrix with +linearly independent columns The Matrix + + align:start position:0% +linearly independent columns The Matrix + + + align:start position:0% +linearly independent columns The Matrix +is + + align:start position:0% +is + + + align:start position:0% +is +invertible what this means is for any V + + align:start position:0% +invertible what this means is for any V + + + align:start position:0% +invertible what this means is for any V +on the right hand side we can invert + + align:start position:0% +on the right hand side we can invert + + + align:start position:0% +on the right hand side we can invert +this Matrix and obtain unique + + align:start position:0% +this Matrix and obtain unique + + + align:start position:0% +this Matrix and obtain unique +coefficients C1 C2 C3 + + align:start position:0% +coefficients C1 C2 C3 + + + align:start position:0% +coefficients C1 C2 C3 +C4 this then gives us a unique Decon + + align:start position:0% +C4 this then gives us a unique Decon + + + align:start position:0% +C4 this then gives us a unique Decon +composition for v in terms of a piece + + align:start position:0% +composition for v in terms of a piece + + + align:start position:0% +composition for v in terms of a piece +which is in + + align:start position:0% +which is in + + + align:start position:0% +which is in +s and a piece which is in s + + align:start position:0% + + + + align:start position:0% + +per and in general this can be done for + + align:start position:0% +per and in general this can be done for + + + align:start position:0% +per and in general this can be done for +any Vector + + align:start position:0% +any Vector + + + align:start position:0% +any Vector +space well I'd like to conclude this uh + + align:start position:0% +space well I'd like to conclude this uh + + + align:start position:0% +space well I'd like to conclude this uh +problem now and I hope you had a good + + align:start position:0% +problem now and I hope you had a good + + + align:start position:0% +problem now and I hope you had a good +time \ No newline at end of file diff --git a/a2mMA4M-V9M.txt b/a2mMA4M-V9M.txt new file mode 100644 index 0000000000000000000000000000000000000000..c287916387e062337840ea148f2ce6ddc6818dbe --- /dev/null +++ b/a2mMA4M-V9M.txt @@ -0,0 +1,12144 @@ +align:start position:0% + +and let us + + align:start position:0% +and let us + + + align:start position:0% +and let us +start first uh uh I forgot to mention + + align:start position:0% +start first uh uh I forgot to mention + + + align:start position:0% +start first uh uh I forgot to mention +last time I will always use the matric + + align:start position:0% +last time I will always use the matric + + + align:start position:0% +last time I will always use the matric +convention for MOSI space time to be it + + align:start position:0% +convention for MOSI space time to be it + + + align:start position:0% +convention for MOSI space time to be it +to be given by this one so the time + + align:start position:0% +to be given by this one so the time + + + align:start position:0% +to be given by this one so the time +component have minus one and then the + + align:start position:0% +component have minus one and then the + + + align:start position:0% +component have minus one and then the +spatial component this positive + + align:start position:0% + + + + align:start position:0% + +one and uh yeah so so also let me just + + align:start position:0% +one and uh yeah so so also let me just + + + align:start position:0% +one and uh yeah so so also let me just +first remind you what we did in last + + align:start position:0% +first remind you what we did in last + + + align:start position:0% +first remind you what we did in last +lecture so um in last lecture we talk + + align:start position:0% +lecture so um in last lecture we talk + + + align:start position:0% +lecture so um in last lecture we talk +about principle of + + align:start position:0% + + + + align:start position:0% + +locality which is a powerful + + align:start position:0% +locality which is a powerful + + + align:start position:0% +locality which is a powerful +principle and uh so this naturally leads + + align:start position:0% +principle and uh so this naturally leads + + + align:start position:0% +principle and uh so this naturally leads +to the concept of + + align:start position:0% + + + + align:start position:0% + +fields and we generally Deo Fields say + + align:start position:0% +fields and we generally Deo Fields say + + + align:start position:0% +fields and we generally Deo Fields say +using this kind of rotation yeah in the + + align:start position:0% +using this kind of rotation yeah in the + + + align:start position:0% +using this kind of rotation yeah in the +uh when we talk about fields abstractly + + align:start position:0% +uh when we talk about fields abstractly + + + align:start position:0% +uh when we talk about fields abstractly +we will use this kind of loation and so + + align:start position:0% +we will use this kind of loation and so + + + align:start position:0% +we will use this kind of loation and so +five just and a just na for for + + align:start position:0% +five just and a just na for for + + + align:start position:0% +five just and a just na for for +different fields and also so the fields + + align:start position:0% +different fields and also so the fields + + + align:start position:0% +different fields and also so the fields +depend on spatial coordinate and also + + align:start position:0% +depend on spatial coordinate and also + + + align:start position:0% +depend on spatial coordinate and also +depend on + + align:start position:0% +depend on + + + align:start position:0% +depend on +time so the physical you can syn this + + align:start position:0% +time so the physical you can syn this + + + align:start position:0% +time so the physical you can syn this +spal dependence as the label for the uh + + align:start position:0% +spal dependence as the label for the uh + + + align:start position:0% +spal dependence as the label for the uh +for the fields uh for the degree Freedom + + align:start position:0% +for the fields uh for the degree Freedom + + + align:start position:0% +for the fields uh for the degree Freedom +so at each spatial point there deg + + align:start position:0% +so at each spatial point there deg + + + align:start position:0% +so at each spatial point there deg +freedom and the time describe its + + align:start position:0% +freedom and the time describe its + + + align:start position:0% +freedom and the time describe its +Evolution + + align:start position:0% +Evolution + + + align:start position:0% +Evolution +okay so essentially this is + + align:start position:0% +okay so essentially this is + + + align:start position:0% +okay so essentially this is +like so so classical field is like + + align:start position:0% +like so so classical field is like + + + align:start position:0% +like so so classical field is like +classical mechanics to freedom but now + + align:start position:0% +classical mechanics to freedom but now + + + align:start position:0% +classical mechanics to freedom but now +with the infinite number de Freedom okay + + align:start position:0% +with the infinite number de Freedom okay + + + align:start position:0% +with the infinite number de Freedom okay +so the so the classical field theory is + + align:start position:0% +so the so the classical field theory is + + + align:start position:0% +so the so the classical field theory is +like a classical mechanics but now it's + + align:start position:0% +like a classical mechanics but now it's + + + align:start position:0% +like a classical mechanics but now it's +infinite number of degre + + align:start position:0% +infinite number of degre + + + align:start position:0% +infinite number of degre +f because now you have + + align:start position:0% +f because now you have + + + align:start position:0% +f because now you have +some finite number to Freed them for for + + align:start position:0% +some finite number to Freed them for for + + + align:start position:0% +some finite number to Freed them for for +each point in space time + + align:start position:0% + + + + align:start position:0% + +okay and the principal locality also + + align:start position:0% +okay and the principal locality also + + + align:start position:0% +okay and the principal locality also +implies that the action for such kind + + align:start position:0% +implies that the action for such kind + + + align:start position:0% +implies that the action for such kind +dynamical variables so the fields are + + align:start position:0% +dynamical variables so the fields are + + + align:start position:0% +dynamical variables so the fields are +our dynamical variables and also implies + + align:start position:0% +our dynamical variables and also implies + + + align:start position:0% +our dynamical variables and also implies +that the action has a very has a local + + align:start position:0% + + + + align:start position:0% + +form so that the action have the form + + align:start position:0% +form so that the action have the form + + + align:start position:0% +form so that the action have the form +that is always a single SpaceTime + + align:start position:0% +that is always a single SpaceTime + + + align:start position:0% +that is always a single SpaceTime +integral and some function which is + + align:start position:0% +integral and some function which is + + + align:start position:0% +integral and some function which is +called a + + align:start position:0% +called a + + + align:start position:0% +called a +intensity which is a function of the + + align:start position:0% +intensity which is a function of the + + + align:start position:0% +intensity which is a function of the +field say five at some point at the + + align:start position:0% +field say five at some point at the + + + align:start position:0% +field say five at some point at the +point x which and then all also its + + align:start position:0% + + + + align:start position:0% + +derivatives okay and uh so because of + + align:start position:0% +derivatives okay and uh so because of + + + align:start position:0% +derivatives okay and uh so because of +locality then action has a very simple + + align:start position:0% +locality then action has a very simple + + + align:start position:0% +locality then action has a very simple +form okay and then you can uh as in + + align:start position:0% +form okay and then you can uh as in + + + align:start position:0% +form okay and then you can uh as in +classical mechanics you can introduce + + align:start position:0% +classical mechanics you can introduce + + + align:start position:0% +classical mechanics you can introduce +canonical momentum conjugate to your + + align:start position:0% +canonical momentum conjugate to your + + + align:start position:0% +canonical momentum conjugate to your +dynamical variable so so we have uh um + + align:start position:0% +dynamical variable so so we have uh um + + + align:start position:0% +dynamical variable so so we have uh um +momentum density say conjugate to five a + + align:start position:0% +momentum density say conjugate to five a + + + align:start position:0% +momentum density say conjugate to five a +at each + + align:start position:0% + + + + align:start position:0% + +point okay so so this is the Five Dot + + align:start position:0% +point okay so so this is the Five Dot + + + align:start position:0% +point okay so so this is the Five Dot +which is the time derivative + + align:start position:0% +which is the time derivative + + + align:start position:0% +which is the time derivative +five and then you can also introduce the + + align:start position:0% +five and then you can also introduce the + + + align:start position:0% +five and then you can also introduce the +honin + + align:start position:0% +honin + + + align:start position:0% +honin +density which is the pi + + align:start position:0% +density which is the pi + + + align:start position:0% +density which is the pi +a by dot a so a is sumed and the minus + + align:start position:0% +a by dot a so a is sumed and the minus + + + align:start position:0% +a by dot a so a is sumed and the minus +L and the hon is obtained by integrate + + align:start position:0% +L and the hon is obtained by integrate + + + align:start position:0% +L and the hon is obtained by integrate +this over + + align:start position:0% +this over + + + align:start position:0% +this over +space uh yeah and also the equation + + align:start position:0% +space uh yeah and also the equation + + + align:start position:0% +space uh yeah and also the equation +motion when you do the variation of the + + align:start position:0% +motion when you do the variation of the + + + align:start position:0% +motion when you do the variation of the +action and you find the equation motion + + align:start position:0% +action and you find the equation motion + + + align:start position:0% +action and you find the equation motion +is given by the the following general + + align:start position:0% + + + + align:start position:0% + +form okay so the equation motion is + + align:start position:0% +form okay so the equation motion is + + + align:start position:0% +form okay so the equation motion is +given by this general + + align:start position:0% +given by this general + + + align:start position:0% +given by this general +form and when we study field + + align:start position:0% +form and when we study field + + + align:start position:0% +form and when we study field +Theory as we study say any other subject + + align:start position:0% +Theory as we study say any other subject + + + align:start position:0% +Theory as we study say any other subject +we always start with simply examples + + align:start position:0% +we always start with simply examples + + + align:start position:0% +we always start with simply examples +okay and the simplest example would be + + align:start position:0% +okay and the simplest example would be + + + align:start position:0% +okay and the simplest example would be +say a single single scal + + align:start position:0% +say a single single scal + + + align:start position:0% +say a single single scal +field okay if you can see the single + + align:start position:0% +field okay if you can see the single + + + align:start position:0% +field okay if you can see the single +scal of + + align:start position:0% + + + + align:start position:0% + +field which you have low index we just + + align:start position:0% +field which you have low index we just + + + align:start position:0% +field which you have low index we just +have five not depend on SpaceTime point + + align:start position:0% +have five not depend on SpaceTime point + + + align:start position:0% +have five not depend on SpaceTime point +x and then the simplicit action for such + + align:start position:0% +x and then the simplicit action for such + + + align:start position:0% +x and then the simplicit action for such +a scaler field you can just write down + + align:start position:0% +a scaler field you can just write down + + + align:start position:0% +a scaler field you can just write down +based + + align:start position:0% +based + + + align:start position:0% +based +on uh a general principle say + + align:start position:0% +on uh a general principle say + + + align:start position:0% +on uh a general principle say +um yeah so so you can have this form so + + align:start position:0% +um yeah so so you can have this form so + + + align:start position:0% +um yeah so so you can have this form so +we discussed last time the simplest + + align:start position:0% +we discussed last time the simplest + + + align:start position:0% +we discussed last time the simplest +action for scaler field have the + + align:start position:0% +action for scaler field have the + + + align:start position:0% +action for scaler field have the +following form partial mu5 paral + + align:start position:0% +following form partial mu5 paral + + + align:start position:0% +following form partial mu5 paral +mu5 and plus m s pi square and the sign + + align:start position:0% +mu5 and plus m s pi square and the sign + + + align:start position:0% +mu5 and plus m s pi square and the sign +here is determined because of the MATC + + align:start position:0% +here is determined because of the MATC + + + align:start position:0% +here is determined because of the MATC +convention okay so this is the simplest + + align:start position:0% +convention okay so this is the simplest + + + align:start position:0% +convention okay so this is the simplest +say scalar field Theory we can write + + align:start position:0% +say scalar field Theory we can write + + + align:start position:0% +say scalar field Theory we can write +down okay so here I have written here a + + align:start position:0% +down okay so here I have written here a + + + align:start position:0% +down okay so here I have written here a +quadratic uh function for five which we + + align:start position:0% +quadratic uh function for five which we + + + align:start position:0% +quadratic uh function for five which we +wrote as a general function last time + + align:start position:0% +wrote as a general function last time + + + align:start position:0% +wrote as a general function last time +and here is from here the ktic term come + + align:start position:0% +and here is from here the ktic term come + + + align:start position:0% +and here is from here the ktic term come +from the lent symmetry so this is the + + align:start position:0% +from the lent symmetry so this is the + + + align:start position:0% +from the lent symmetry so this is the +simplest derivative term you can write + + align:start position:0% +simplest derivative term you can write + + + align:start position:0% +simplest derivative term you can write +down which respect Len symmetry you can + + align:start position:0% +down which respect Len symmetry you can + + + align:start position:0% +down which respect Len symmetry you can +have more complicated terms you can have + + align:start position:0% +have more complicated terms you can have + + + align:start position:0% +have more complicated terms you can have +this term for example Square okay but + + align:start position:0% +this term for example Square okay but + + + align:start position:0% +this term for example Square okay but +that will be more complicated so so this + + align:start position:0% +that will be more complicated so so this + + + align:start position:0% +that will be more complicated so so this +is the simplest one + + align:start position:0% + + + + align:start position:0% + +and so this will be the simplest field + + align:start position:0% +and so this will be the simplest field + + + align:start position:0% +and so this will be the simplest field +Ser we we will study first okay and uh + + align:start position:0% +Ser we we will study first okay and uh + + + align:start position:0% +Ser we we will study first okay and uh +um yeah so in this + + align:start position:0% +um yeah so in this + + + align:start position:0% +um yeah so in this +case for for this example the uh the the + + align:start position:0% +case for for this example the uh the the + + + align:start position:0% +case for for this example the uh the the +momentum density just equal to F + + align:start position:0% +momentum density just equal to F + + + align:start position:0% +momentum density just equal to F +dot that's time derivative five and then + + align:start position:0% +dot that's time derivative five and then + + + align:start position:0% +dot that's time derivative five and then +the equation + + align:start position:0% +the equation + + + align:start position:0% +the equation +motion is given by a linear equation + + align:start position:0% +motion is given by a linear equation + + + align:start position:0% +motion is given by a linear equation +five + + align:start position:0% +five + + + align:start position:0% +five +it's given by + + align:start position:0% + + + + align:start position:0% + +that so this is a very simple Theory + + align:start position:0% +that so this is a very simple Theory + + + align:start position:0% +that so this is a very simple Theory +it's very simple equation motion and uh + + align:start position:0% +it's very simple equation motion and uh + + + align:start position:0% +it's very simple equation motion and uh +but later we will see actually will uh + + align:start position:0% +but later we will see actually will uh + + + align:start position:0% +but later we will see actually will uh +teach us a lot about General field + + align:start position:0% +teach us a lot about General field + + + align:start position:0% +teach us a lot about General field +the so so that's it's a very quick + + align:start position:0% +the so so that's it's a very quick + + + align:start position:0% +the so so that's it's a very quick +summary of some of the main points of + + align:start position:0% +summary of some of the main points of + + + align:start position:0% +summary of some of the main points of +last lecture do you have any + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% + + + + align:start position:0% + +yes right so five here is a real field + + align:start position:0% +yes right so five here is a real field + + + align:start position:0% +yes right so five here is a real field +yeah yeah so so five just take a real + + align:start position:0% +yeah yeah so so five just take a real + + + align:start position:0% +yeah yeah so so five just take a real +value + + align:start position:0% + + + + align:start position:0% + +yeah other + + align:start position:0% + + + + align:start position:0% + +questions good + + align:start position:0% +questions good + + + align:start position:0% +questions good +okay + + align:start position:0% + + + + align:start position:0% + +so now we + + align:start position:0% +so now we + + + align:start position:0% +so now we +um talk about the second topic related + + align:start position:0% +um talk about the second topic related + + + align:start position:0% +um talk about the second topic related +to our discussion of classical field + + align:start position:0% +to our discussion of classical field + + + align:start position:0% +to our discussion of classical field +Theory + + align:start position:0% + + + + align:start position:0% + +symmetries inovation + + align:start position:0% + + + + align:start position:0% + +rules so when we have a the say we such + + align:start position:0% +rules so when we have a the say we such + + + align:start position:0% +rules so when we have a the say we such +action we say the theory has a + + align:start position:0% +action we say the theory has a + + + align:start position:0% +action we say the theory has a +symmetry so the definition of the + + align:start position:0% +symmetry so the definition of the + + + align:start position:0% +symmetry so the definition of the +Symmetry is the + + align:start position:0% + + + + align:start position:0% + +following so symmetry is some + + align:start position:0% + + + + align:start position:0% + +transformation of each field F A + + align:start position:0% +transformation of each field F A + + + align:start position:0% +transformation of each field F A +into say some function of + + align:start position:0% +into say some function of + + + align:start position:0% +into say some function of +F so so this uh uh this new f a can can + + align:start position:0% +F so so this uh uh this new f a can can + + + align:start position:0% +F so so this uh uh this new f a can can +say depend + + align:start position:0% +say depend + + + align:start position:0% +say depend +on all possible Fields okay and so some + + align:start position:0% +on all possible Fields okay and so some + + + align:start position:0% +on all possible Fields okay and so some +transformation of your dynamical + + align:start position:0% +transformation of your dynamical + + + align:start position:0% +transformation of your dynamical +variables so here Prime just means a + + align:start position:0% +variables so here Prime just means a + + + align:start position:0% +variables so here Prime just means a +different function does not mean + + align:start position:0% +different function does not mean + + + align:start position:0% +different function does not mean +derivatives okay which + + align:start position:0% +derivatives okay which + + + align:start position:0% +derivatives okay which +leaves the action + + align:start position:0% + + + + align:start position:0% + +varant + + align:start position:0% + + + + align:start position:0% + +okay so so whenever happens and uh um we + + align:start position:0% +okay so so whenever happens and uh um we + + + align:start position:0% +okay so so whenever happens and uh um we +say this is a + + align:start position:0% +say this is a + + + align:start position:0% +say this is a +symmetry so um so for example in + + align:start position:0% +symmetry so um so for example in + + + align:start position:0% +symmetry so um so for example in +this in this + + align:start position:0% +this in this + + + align:start position:0% +this in this +example okay in this + + align:start position:0% +example okay in this + + + align:start position:0% +example okay in this +example uh um yeah let me give you a + + align:start position:0% +example uh um yeah let me give you a + + + align:start position:0% +example uh um yeah let me give you a +label label to this equation let me call + + align:start position:0% +label label to this equation let me call + + + align:start position:0% +label label to this equation let me call +this equation + + align:start position:0% +this equation + + + align:start position:0% +this equation +star so in the uh uh so in the um in the + + align:start position:0% +star so in the uh uh so in the um in the + + + align:start position:0% +star so in the uh uh so in the um in the +example of + + align:start position:0% +example of + + + align:start position:0% +example of +star say for example the Symmetry + + align:start position:0% +star say for example the Symmetry + + + align:start position:0% +star say for example the Symmetry +includes say + + align:start position:0% + + + + align:start position:0% + +translation okay so so if you + + align:start position:0% + + + + align:start position:0% + +imagine we take a coordinate + + align:start position:0% +imagine we take a coordinate + + + align:start position:0% +imagine we take a coordinate +transformation uh uh we do a shift in + + align:start position:0% + + + + align:start position:0% + +coordinate by a constant + + align:start position:0% +coordinate by a constant + + + align:start position:0% +coordinate by a constant +shift okay let's imagine we do a + + align:start position:0% +shift okay let's imagine we do a + + + align:start position:0% +shift okay let's imagine we do a +constant shift of the + + align:start position:0% +constant shift of the + + + align:start position:0% +constant shift of the +coordinates and a mu is a constant so a + + align:start position:0% +coordinates and a mu is a constant so a + + + align:start position:0% +coordinates and a mu is a constant so a +mu are + + align:start position:0% + + + + align:start position:0% + +constants okay so it's a constant vector + + align:start position:0% +constants okay so it's a constant vector + + + align:start position:0% +constants okay so it's a constant vector +and now if we assume that the five + + align:start position:0% +and now if we assume that the five + + + align:start position:0% +and now if we assume that the five +transform as a following + + align:start position:0% +transform as a following + + + align:start position:0% +transform as a following +so when you change the coordinates it + + align:start position:0% +so when you change the coordinates it + + + align:start position:0% +so when you change the coordinates it +essentially just change the label okay + + align:start position:0% +essentially just change the label okay + + + align:start position:0% +essentially just change the label okay +change the label on the field so but the + + align:start position:0% +change the label on the field so but the + + + align:start position:0% +change the label on the field so but the +value of the field should not change so + + align:start position:0% +value of the field should not change so + + + align:start position:0% +value of the field should not change so +that + + align:start position:0% +that + + + align:start position:0% +that +means that the F evaluated at the + + align:start position:0% +means that the F evaluated at the + + + align:start position:0% +means that the F evaluated at the +original point should be the same so + + align:start position:0% +original point should be the same so + + + align:start position:0% +original point should be the same so +that means the new transformed F + + align:start position:0% +that means the new transformed F + + + align:start position:0% +that means the new transformed F +evaluated at the new + + align:start position:0% +evaluated at the new + + + align:start position:0% +evaluated at the new +Point okay a new X Prime point should be + + align:start position:0% +Point okay a new X Prime point should be + + + align:start position:0% +Point okay a new X Prime point should be +the same as the value at the original + + align:start position:0% +the same as the value at the original + + + align:start position:0% +the same as the value at the original +point okay so this is the uh um yeah so + + align:start position:0% +point okay so this is the uh um yeah so + + + align:start position:0% +point okay so this is the uh um yeah so +so suppose the file transform like this + + align:start position:0% +so suppose the file transform like this + + + align:start position:0% +so suppose the file transform like this +so the so scaler + + align:start position:0% + + + + align:start position:0% + +field should transform as + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% + + + + align:start position:0% + +under General so this is the example of + + align:start position:0% +under General so this is the example of + + + align:start position:0% +under General so this is the example of +a space-time transformation okay and the + + align:start position:0% +a space-time transformation okay and the + + + align:start position:0% +a space-time transformation okay and the +general SpaceTime + + align:start position:0% + + + + align:start position:0% + +transformation + + align:start position:0% + + + + align:start position:0% + +s say this equation okay so the so you + + align:start position:0% +s say this equation okay so the so you + + + align:start position:0% +s say this equation okay so the so you +change the label but the value of five + + align:start position:0% +change the label but the value of five + + + align:start position:0% +change the label but the value of five +should not change okay so so the new + + align:start position:0% +should not change okay so so the new + + + align:start position:0% +should not change okay so so the new +five Val that the new location should be + + align:start position:0% +five Val that the new location should be + + + align:start position:0% +five Val that the new location should be +the same as the value of five the + + align:start position:0% +the same as the value of five the + + + align:start position:0% +the same as the value of five the +original location + + align:start position:0% +original location + + + align:start position:0% +original location +okay and so you can easily check + + align:start position:0% +okay and so you can easily check + + + align:start position:0% +okay and so you can easily check +yourself okay okay so you can easily + + align:start position:0% +yourself okay okay so you can easily + + + align:start position:0% +yourself okay okay so you can easily +check yourself I will not do it here so + + align:start position:0% +check yourself I will not do it here so + + + align:start position:0% +check yourself I will not do it here so +so this exercise for yourself that + + align:start position:0% +so this exercise for yourself that + + + align:start position:0% +so this exercise for yourself that +actually this action is in warant under + + align:start position:0% +actually this action is in warant under + + + align:start position:0% +actually this action is in warant under +this trans uh is inir on this + + align:start position:0% +this trans uh is inir on this + + + align:start position:0% +this trans uh is inir on this +transformation with this with this + + align:start position:0% +transformation with this with this + + + align:start position:0% +transformation with this with this +change of X + + align:start position:0% +change of X + + + align:start position:0% +change of X +okay any questions on + + align:start position:0% + + + + align:start position:0% + +this so second transformation which this + + align:start position:0% +this so second transformation which this + + + align:start position:0% +this so second transformation which this +is in + + align:start position:0% +is in + + + align:start position:0% +is in +warant is aant + + align:start position:0% +warant is aant + + + align:start position:0% +warant is aant +symmetry + + align:start position:0% + + + + align:start position:0% + +so low range transformation is another + + align:start position:0% +so low range transformation is another + + + align:start position:0% +so low range transformation is another +kind of space-time transformation on the + + align:start position:0% +kind of space-time transformation on the + + + align:start position:0% +kind of space-time transformation on the +SpaceTime coordinates is you take X + + align:start position:0% +SpaceTime coordinates is you take X + + + align:start position:0% +SpaceTime coordinates is you take X +mu to X mu + + align:start position:0% +mu to X mu + + + align:start position:0% +mu to X mu +Prime equal to Lambda mu + + align:start position:0% +Prime equal to Lambda mu + + + align:start position:0% +Prime equal to Lambda mu +new X + + align:start position:0% +new X + + + align:start position:0% +new X +new so so so Lambda new + + align:start position:0% +new so so so Lambda new + + + align:start position:0% +new so so so Lambda new +new is the + + align:start position:0% + + + + align:start position:0% + +constant no rent transformation matrix + + align:start position:0% +constant no rent transformation matrix + + + align:start position:0% +constant no rent transformation matrix +okay + + align:start position:0% + + + + align:start position:0% + +okay the constant orang transformation + + align:start position:0% +okay the constant orang transformation + + + align:start position:0% +okay the constant orang transformation +matrix and again under such a coordinate + + align:start position:0% +matrix and again under such a coordinate + + + align:start position:0% +matrix and again under such a coordinate +transformation file will will transform + + align:start position:0% +transformation file will will transform + + + align:start position:0% +transformation file will will transform +this way file should transform this way + + align:start position:0% +this way file should transform this way + + + align:start position:0% +this way file should transform this way +and now and now you can check + + align:start position:0% +and now and now you can check + + + align:start position:0% +and now and now you can check +yourself okay and uh and because of this + + align:start position:0% +yourself okay and uh and because of this + + + align:start position:0% +yourself okay and uh and because of this +contraction of partial mu partial mu and + + align:start position:0% +contraction of partial mu partial mu and + + + align:start position:0% +contraction of partial mu partial mu and +this is actually a symmetry okay again + + align:start position:0% +this is actually a symmetry okay again + + + align:start position:0% +this is actually a symmetry okay again +this is s as exercise for yourself and + + align:start position:0% +this is s as exercise for yourself and + + + align:start position:0% +this is s as exercise for yourself and +in fact I think in your pide problem you + + align:start position:0% +in fact I think in your pide problem you + + + align:start position:0% +in fact I think in your pide problem you +do something + + align:start position:0% + + + + align:start position:0% + +similar any questions on + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% + + + + align:start position:0% + +good so um examples like this kind of + + align:start position:0% +good so um examples like this kind of + + + align:start position:0% +good so um examples like this kind of +transformation for translation and for + + align:start position:0% +transformation for translation and for + + + align:start position:0% +transformation for translation and for +range transformation so this is what we + + align:start position:0% +range transformation so this is what we + + + align:start position:0% +range transformation so this is what we +called the continual + + align:start position:0% + + + + align:start position:0% + +symmetries so uh so continous symmetries + + align:start position:0% + + + + align:start position:0% + +okay so so these are the + + align:start position:0% + + + + align:start position:0% + +Transformations I should also give a + + align:start position:0% +Transformations I should also give a + + + align:start position:0% +Transformations I should also give a +label to this equation so let me call it + + align:start position:0% +label to this equation so let me call it + + + align:start position:0% +label to this equation so let me call it +just star star star so so continuous + + align:start position:0% +just star star star so so continuous + + + align:start position:0% +just star star star so so continuous +symmetries are + + align:start position:0% +symmetries are + + + align:start position:0% +symmetries are +transformations + + align:start position:0% + + + + align:start position:0% + +like star star + + align:start position:0% +like star star + + + align:start position:0% +like star star +star + + align:start position:0% + + + + align:start position:0% + +involving + + align:start position:0% + + + + align:start position:0% + +continuous + + align:start position:0% + + + + align:start position:0% + +parameters + + align:start position:0% +parameters + + + align:start position:0% +parameters +okay and so both one and + + align:start position:0% +okay and so both one and + + + align:start position:0% +okay and so both one and +two uh um + + align:start position:0% + + + + align:start position:0% + +and the two are + + align:start position:0% +and the two are + + + align:start position:0% +and the two are +clearly continuous + + align:start position:0% + + + + align:start position:0% + +symmetries yeah they are continous + + align:start position:0% + + + + align:start position:0% + +symmetries so you can easily see from + + align:start position:0% +symmetries so you can easily see from + + + align:start position:0% +symmetries so you can easily see from +here so here the transformation is a and + + align:start position:0% +here so here the transformation is a and + + + align:start position:0% +here so here the transformation is a and +a is four numbers okay it's a vector + + align:start position:0% +a is four numbers okay it's a vector + + + align:start position:0% +a is four numbers okay it's a vector +it's a four VOR factor and a can be arit + + align:start position:0% +it's a four VOR factor and a can be arit + + + align:start position:0% +it's a four VOR factor and a can be arit +changed so it's a continuous parameter + + align:start position:0% +changed so it's a continuous parameter + + + align:start position:0% +changed so it's a continuous parameter +okay you can take it to be zero you can + + align:start position:0% +okay you can take it to be zero you can + + + align:start position:0% +okay you can take it to be zero you can +take it to be point1 in all directions + + align:start position:0% +take it to be point1 in all directions + + + align:start position:0% +take it to be point1 in all directions +Etc so something can be continuous + + align:start position:0% +Etc so something can be continuous + + + align:start position:0% +Etc so something can be continuous +changed and + + align:start position:0% +changed and + + + align:start position:0% +changed and +similarly the load range + + align:start position:0% +similarly the load range + + + align:start position:0% +similarly the load range +transformation contains continuous + + align:start position:0% +transformation contains continuous + + + align:start position:0% +transformation contains continuous +parameters so do you remember how many + + align:start position:0% +parameters so do you remember how many + + + align:start position:0% +parameters so do you remember how many +continuous parameters does the Len + + align:start position:0% +continuous parameters does the Len + + + align:start position:0% +continuous parameters does the Len +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +contain in four dimensions + + align:start position:0% +contain in four dimensions + + + align:start position:0% +contain in four dimensions +yes h + + align:start position:0% + + + + align:start position:0% + +no yes yeah six uh it's because you have + + align:start position:0% +no yes yeah six uh it's because you have + + + align:start position:0% +no yes yeah six uh it's because you have +three rotations because you have three + + align:start position:0% +three rotations because you have three + + + align:start position:0% +three rotations because you have three +Direction three spatial directions you + + align:start position:0% +Direction three spatial directions you + + + align:start position:0% +Direction three spatial directions you +have three rotations and then you also + + align:start position:0% +have three rotations and then you also + + + align:start position:0% +have three rotations and then you also +have three boosts yeah so together six + + align:start position:0% +have three boosts yeah so together six + + + align:start position:0% +have three boosts yeah so together six +so here there's six continuous + + align:start position:0% + + + + align:start position:0% + +parameters and here there's + + align:start position:0% +parameters and here there's + + + align:start position:0% +parameters and here there's +four okay so here this four so both are + + align:start position:0% +four okay so here this four so both are + + + align:start position:0% +four okay so here this four so both are +Contin symmetries + + align:start position:0% +Contin symmetries + + + align:start position:0% +Contin symmetries +okay and in + + align:start position:0% + + + + align:start position:0% + +contrast this Lan have this action has a + + align:start position:0% +contrast this Lan have this action has a + + + align:start position:0% +contrast this Lan have this action has a +lot of + + align:start position:0% +lot of + + + align:start position:0% +lot of +symmetry uh which is not + + align:start position:0% +symmetry uh which is not + + + align:start position:0% +symmetry uh which is not +continuous can you say what that + + align:start position:0% +continuous can you say what that + + + align:start position:0% +continuous can you say what that +symmetry + + align:start position:0% + + + + align:start position:0% + +is good uh parity is a good it's a it's + + align:start position:0% +is good uh parity is a good it's a it's + + + align:start position:0% +is good uh parity is a good it's a it's +a good uh it's a good answer yeah uh but + + align:start position:0% +a good uh it's a good answer yeah uh but + + + align:start position:0% +a good uh it's a good answer yeah uh but +but there still something sightly Sim + + align:start position:0% +but there still something sightly Sim + + + align:start position:0% +but there still something sightly Sim +simpler + + align:start position:0% + + + + align:start position:0% + +yeah so so notice that here it's all + + align:start position:0% +yeah so so notice that here it's all + + + align:start position:0% +yeah so so notice that here it's all +quadratic in + + align:start position:0% +quadratic in + + + align:start position:0% +quadratic in +five and uh and what do You + + align:start position:0% + + + + align:start position:0% + +observe so so here there's a symmetry A + + align:start position:0% +observe so so here there's a symmetry A + + + align:start position:0% +observe so so here there's a symmetry A +lot of + + align:start position:0% + + + + align:start position:0% + +symmetry this five goes to Minus 5 okay + + align:start position:0% +symmetry this five goes to Minus 5 okay + + + align:start position:0% +symmetry this five goes to Minus 5 okay +because it's quadratic in five and also + + align:start position:0% +because it's quadratic in five and also + + + align:start position:0% +because it's quadratic in five and also +of course there's a symmetry called the + + align:start position:0% + + + + align:start position:0% + +parity which in the case X goes to minus + + align:start position:0% +parity which in the case X goes to minus + + + align:start position:0% +parity which in the case X goes to minus +X so the spatial Direction X goes to + + align:start position:0% +X so the spatial Direction X goes to + + + align:start position:0% +X so the spatial Direction X goes to +minus X and then five again transform as + + align:start position:0% +minus X and then five again transform as + + + align:start position:0% +minus X and then five again transform as +this okay and you can also check this is + + align:start position:0% +this okay and you can also check this is + + + align:start position:0% +this okay and you can also check this is +also symmetry so in both of these cases + + align:start position:0% +also symmetry so in both of these cases + + + align:start position:0% +also symmetry so in both of these cases +they don't involve continuous + + align:start position:0% +they don't involve continuous + + + align:start position:0% +they don't involve continuous +parameters and so these are called + + align:start position:0% +parameters and so these are called + + + align:start position:0% +parameters and so these are called +discrete + + align:start position:0% +discrete + + + align:start position:0% +discrete +symmetries + + align:start position:0% + + + + align:start position:0% + +okay so there's no continuous + + align:start position:0% +okay so there's no continuous + + + align:start position:0% +okay so there's no continuous +parameters and uh yeah in this case both + + align:start position:0% +parameters and uh yeah in this case both + + + align:start position:0% +parameters and uh yeah in this case both +of them are called + + align:start position:0% +of them are called + + + align:start position:0% +of them are called +Z2 in this Z2 means that if you do the + + align:start position:0% +Z2 in this Z2 means that if you do the + + + align:start position:0% +Z2 in this Z2 means that if you do the +transformation once they go back to the + + align:start position:0% +transformation once they go back to the + + + align:start position:0% +transformation once they go back to the +identity okay so here if you do the uh + + align:start position:0% +identity okay so here if you do the uh + + + align:start position:0% +identity okay so here if you do the uh +uh twice yeah if you do it twice go back + + align:start position:0% +uh twice yeah if you do it twice go back + + + align:start position:0% +uh twice yeah if you do it twice go back +to if you do it twice go back to + + align:start position:0% +to if you do it twice go back to + + + align:start position:0% +to if you do it twice go back to +Identity this is the + + align:start position:0% +Identity this is the + + + align:start position:0% +Identity this is the +same so here is a Z2 + + align:start position:0% +same so here is a Z2 + + + align:start position:0% +same so here is a Z2 +transformation also symmetries can be Al + + align:start position:0% +transformation also symmetries can be Al + + + align:start position:0% +transformation also symmetries can be Al +separated into say symmetries can be + + align:start position:0% +separated into say symmetries can be + + + align:start position:0% +separated into say symmetries can be +separated into continous + + align:start position:0% +separated into continous + + + align:start position:0% +separated into continous +symmetry or discrete symmetries depend + + align:start position:0% +symmetry or discrete symmetries depend + + + align:start position:0% +symmetry or discrete symmetries depend +on whether you have continuous + + align:start position:0% +on whether you have continuous + + + align:start position:0% +on whether you have continuous +parameters or not but symmetries can + + align:start position:0% +parameters or not but symmetries can + + + align:start position:0% +parameters or not but symmetries can +also be separated + + align:start position:0% +also be separated + + + align:start position:0% +also be separated +into other different uh there's another + + align:start position:0% +into other different uh there's another + + + align:start position:0% +into other different uh there's another +classification of the Symmetry it's + + align:start position:0% +classification of the Symmetry it's + + + align:start position:0% +classification of the Symmetry it's +called the gaug Symmetry and Global + + align:start position:0% +called the gaug Symmetry and Global + + + align:start position:0% +called the gaug Symmetry and Global +symmetries so they are Global + + align:start position:0% + + + + align:start position:0% + +symmetries + + align:start position:0% + + + + align:start position:0% + +corresponding to the transformation + + align:start position:0% + + + + align:start position:0% + +parameters are SpaceTime + + align:start position:0% + + + + align:start position:0% + +independent okay so both of these are + + align:start position:0% +independent okay so both of these are + + + align:start position:0% +independent okay so both of these are +examples + + align:start position:0% +examples + + + align:start position:0% +examples +of global symmetries because because + + align:start position:0% +of global symmetries because because + + + align:start position:0% +of global symmetries because because +they're just constant okay they don't + + align:start position:0% +they're just constant okay they don't + + + align:start position:0% +they're just constant okay they don't +don't depend on space time and the + + align:start position:0% +don't depend on space time and the + + + align:start position:0% +don't depend on space time and the +Lambda don't depend on space time okay + + align:start position:0% +Lambda don't depend on space time okay + + + align:start position:0% +Lambda don't depend on space time okay +and uh you can also have local + + align:start position:0% + + + + align:start position:0% + +symmetries which in which case the + + align:start position:0% +symmetries which in which case the + + + align:start position:0% +symmetries which in which case the +transformation + + align:start position:0% + + + + align:start position:0% + +parameters the transformation + + align:start position:0% +parameters the transformation + + + align:start position:0% +parameters the transformation +parameters + + align:start position:0% + + + + align:start position:0% + +are space time dependent + + align:start position:0% + + + + align:start position:0% + +okay so so example of the local + + align:start position:0% +okay so so example of the local + + + align:start position:0% +okay so so example of the local +transformation which you may + + align:start position:0% +transformation which you may + + + align:start position:0% +transformation which you may +remember is the uh so-call guge + + align:start position:0% +remember is the uh so-call guge + + + align:start position:0% +remember is the uh so-call guge +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +inm so M you can uh um yeah anyway so + + align:start position:0% +inm so M you can uh um yeah anyway so + + + align:start position:0% +inm so M you can uh um yeah anyway so +later we will see example we will go + + align:start position:0% +later we will see example we will go + + + align:start position:0% +later we will see example we will go +back to and M again and you will see + + align:start position:0% +back to and M again and you will see + + + align:start position:0% +back to and M again and you will see +examples of this local + + align:start position:0% + + + + align:start position:0% + +IM any + + align:start position:0% +IM any + + + align:start position:0% +IM any +questions + + align:start position:0% +questions + + + align:start position:0% +questions +yes changes the action but doesn't + + align:start position:0% +yes changes the action but doesn't + + + align:start position:0% +yes changes the action but doesn't +change the equation of motion is that so + + align:start position:0% +change the equation of motion is that so + + + align:start position:0% +change the equation of motion is that so +symm oh yeah yeah as far as the action + + align:start position:0% +symm oh yeah yeah as far as the action + + + align:start position:0% +symm oh yeah yeah as far as the action +uh uh yeah that's a very good question + + align:start position:0% +uh uh yeah that's a very good question + + + align:start position:0% +uh uh yeah that's a very good question +so so uh uh by + + align:start position:0% +so so uh uh by + + + align:start position:0% +so so uh uh by +definition uh uh if it's leave the + + align:start position:0% +definition uh uh if it's leave the + + + align:start position:0% +definition uh uh if it's leave the +action envirment we say it's a symmetry + + align:start position:0% +action envirment we say it's a symmetry + + + align:start position:0% +action envirment we say it's a symmetry +and in general actually almost always if + + align:start position:0% +and in general actually almost always if + + + align:start position:0% +and in general actually almost always if +it's leaves the action envirment + + align:start position:0% +it's leaves the action envirment + + + align:start position:0% +it's leaves the action envirment +actually also leaves equation motion + + align:start position:0% +actually also leaves equation motion + + + align:start position:0% +actually also leaves equation motion +environment yeah yeah but it's not + + align:start position:0% +environment yeah yeah but it's not + + + align:start position:0% +environment yeah yeah but it's not +guaranteed yeah just purely from + + align:start position:0% +guaranteed yeah just purely from + + + align:start position:0% +guaranteed yeah just purely from +mathematical point of view is not + + align:start position:0% +mathematical point of view is not + + + align:start position:0% +mathematical point of view is not +guaranteed but for all physical examples + + align:start position:0% +guaranteed but for all physical examples + + + align:start position:0% +guaranteed but for all physical examples +uh it's almost always the + + align:start position:0% +uh it's almost always the + + + align:start position:0% +uh it's almost always the +same other + + align:start position:0% + + + + align:start position:0% + +questions okay + + align:start position:0% +questions okay + + + align:start position:0% +questions okay +good and + + align:start position:0% +good and + + + align:start position:0% +good and +now + + align:start position:0% +now + + + align:start position:0% +now +this a very simple and it's simple but + + align:start position:0% +this a very simple and it's simple but + + + align:start position:0% +this a very simple and it's simple but +but very deep connection between the + + align:start position:0% +but very deep connection between the + + + align:start position:0% +but very deep connection between the +Symmetry and the conservation no so that + + align:start position:0% +Symmetry and the conservation no so that + + + align:start position:0% +Symmetry and the conservation no so that +may you may have already sended in in + + align:start position:0% +may you may have already sended in in + + + align:start position:0% +may you may have already sended in in +yeah actually I forgot when I landed + + align:start position:0% +yeah actually I forgot when I landed + + + align:start position:0% +yeah actually I forgot when I landed +myself so some of them some of you may + + align:start position:0% +myself so some of them some of you may + + + align:start position:0% +myself so some of them some of you may +land in high school some of you may land + + align:start position:0% +land in high school some of you may land + + + align:start position:0% +land in high school some of you may land +it in a ET anyway so so there's a a + + align:start position:0% +it in a ET anyway so so there's a a + + + align:start position:0% +it in a ET anyway so so there's a a +connection between the Symmetry and + + align:start position:0% +connection between the Symmetry and + + + align:start position:0% +connection between the Symmetry and +conservation + + align:start position:0% +conservation + + + align:start position:0% +conservation +nose and uh so any conservation no can + + align:start position:0% +nose and uh so any conservation no can + + + align:start position:0% +nose and uh so any conservation no can +be understood as a consequence of + + align:start position:0% +be understood as a consequence of + + + align:start position:0% +be understood as a consequence of +symmetry so In classical mechanics you + + align:start position:0% +symmetry so In classical mechanics you + + + align:start position:0% +symmetry so In classical mechanics you +may remember that the time + + align:start position:0% + + + + align:start position:0% + +translation this leads to energy + + align:start position:0% + + + + align:start position:0% + +conservation and the uh the spatial + + align:start position:0% +conservation and the uh the spatial + + + align:start position:0% +conservation and the uh the spatial +trans + + align:start position:0% +trans + + + align:start position:0% +trans +acction + + align:start position:0% +acction + + + align:start position:0% +acction +symmetry then this to the momentum + + align:start position:0% + + + + align:start position:0% + +conservation and if it's a rotational + + align:start position:0% + + + + align:start position:0% + +symmetry then Le to the angular momentum + + align:start position:0% + + + + align:start position:0% + +conation + + align:start position:0% + + + + align:start position:0% + +okay so so this is should be something + + align:start position:0% +okay so so this is should be something + + + align:start position:0% +okay so so this is should be something +you already know say from your uh say + + align:start position:0% +you already know say from your uh say + + + align:start position:0% +you already know say from your uh say +from your classical + + align:start position:0% +from your classical + + + align:start position:0% +from your classical +mechanics but in classical field Theory + + align:start position:0% +mechanics but in classical field Theory + + + align:start position:0% +mechanics but in classical field Theory +this can be generalized okay so so + + align:start position:0% +this can be generalized okay so so + + + align:start position:0% +this can be generalized okay so so +here this loer + + align:start position:0% +here this loer + + + align:start position:0% +here this loer +theorem so first disc discovered by I + + align:start position:0% +theorem so first disc discovered by I + + + align:start position:0% +theorem so first disc discovered by I +loer the Lo + + align:start position:0% + + + + align:start position:0% + +theorem he said any continuous Global s + + align:start position:0% + + + + align:start position:0% + +Tre lead two conservation do + + align:start position:0% + + + + align:start position:0% + +okay okay let's do a + + align:start position:0% + + + + align:start position:0% + +conservation and uh so L ma what kind of + + align:start position:0% +conservation and uh so L ma what kind of + + + align:start position:0% +conservation and uh so L ma what kind of +symmetry okay l in addition to those + + align:start position:0% +symmetry okay l in addition to those + + + align:start position:0% +symmetry okay l in addition to those +things you are familiar with but no + + align:start position:0% +things you are familiar with but no + + + align:start position:0% +things you are familiar with but no +matter what kind of symmetry but anytime + + align:start position:0% +matter what kind of symmetry but anytime + + + align:start position:0% +matter what kind of symmetry but anytime +you have a continuous Global symmetry uh + + align:start position:0% +you have a continuous Global symmetry uh + + + align:start position:0% +you have a continuous Global symmetry uh +in your system then you have conserv you + + align:start position:0% +in your system then you have conserv you + + + align:start position:0% +in your system then you have conserv you +have + + align:start position:0% +have + + + align:start position:0% +have +conservation okay so now let me give a + + align:start position:0% +conservation okay so now let me give a + + + align:start position:0% +conservation okay so now let me give a +proof of this no no + + align:start position:0% +proof of this no no + + + align:start position:0% +proof of this no no +theorem okay so before I proove it do + + align:start position:0% +theorem okay so before I proove it do + + + align:start position:0% +theorem okay so before I proove it do +you have any questions regarding it + + align:start position:0% + + + + align:start position:0% + +statement + + align:start position:0% +statement + + + align:start position:0% +statement +yes on like the + + align:start position:0% +yes on like the + + + align:start position:0% +yes on like the +like the definition so you said the + + align:start position:0% +like the definition so you said the + + + align:start position:0% +like the definition so you said the +continuous symmetry is only depends + + align:start position:0% +continuous symmetry is only depends + + + align:start position:0% +continuous symmetry is only depends +continu on on a parameter but if you + + align:start position:0% +continu on on a parameter but if you + + + align:start position:0% +continu on on a parameter but if you +wanted to write out like equation star + + align:start position:0% +wanted to write out like equation star + + + align:start position:0% +wanted to write out like equation star +start in a way that specializes to + + align:start position:0% +start in a way that specializes to + + + align:start position:0% +start in a way that specializes to +continu symetri is there a way to do + + align:start position:0% +continu symetri is there a way to do + + + align:start position:0% +continu symetri is there a way to do +that show like just like how to check + + align:start position:0% +that show like just like how to check + + + align:start position:0% +that show like just like how to check +something as a continu oh yeah yeah you + + align:start position:0% +something as a continu oh yeah yeah you + + + align:start position:0% +something as a continu oh yeah yeah you +just check whether there's a continuous + + align:start position:0% +just check whether there's a continuous + + + align:start position:0% +just check whether there's a continuous +parameter you just check whether there's + + align:start position:0% +parameter you just check whether there's + + + align:start position:0% +parameter you just check whether there's +a + + align:start position:0% + + + + align:start position:0% + +parameter + + align:start position:0% +parameter + + + align:start position:0% +parameter +yeah + + align:start position:0% + + + + align:start position:0% + +Does this answer your + + align:start position:0% +Does this answer your + + + align:start position:0% +Does this answer your +question yeah normally you can just see + + align:start position:0% +question yeah normally you can just see + + + align:start position:0% +question yeah normally you can just see +whether there's a parameter yeah if you + + align:start position:0% +whether there's a parameter yeah if you + + + align:start position:0% +whether there's a parameter yeah if you +write down the transformation explicitly + + align:start position:0% +write down the transformation explicitly + + + align:start position:0% +write down the transformation explicitly +you will be able to just see for example + + align:start position:0% +you will be able to just see for example + + + align:start position:0% +you will be able to just see for example +here there's no transformation parameter + + align:start position:0% +here there's no transformation parameter + + + align:start position:0% +here there's no transformation parameter +you can just see and there for the laen + + align:start position:0% +you can just see and there for the laen + + + align:start position:0% +you can just see and there for the laen +transformation and translation you can + + align:start position:0% +transformation and translation you can + + + align:start position:0% +transformation and translation you can +just see the + + align:start position:0% + + + + align:start position:0% + +explicit + + align:start position:0% +explicit + + + align:start position:0% +explicit +okay so so important aspect + + align:start position:0% +okay so so important aspect + + + align:start position:0% +okay so so important aspect +of a continuous + + align:start position:0% +of a continuous + + + align:start position:0% +of a continuous +symmetry is said because you have a + + align:start position:0% +symmetry is said because you have a + + + align:start position:0% +symmetry is said because you have a +continuous + + align:start position:0% +continuous + + + align:start position:0% +continuous +parameter so you can continuously + + align:start position:0% +parameter so you can continuously + + + align:start position:0% +parameter so you can continuously +related to Identity so so the trivial + + align:start position:0% +related to Identity so so the trivial + + + align:start position:0% +related to Identity so so the trivial +transformation you just you don't + + align:start position:0% +transformation you just you don't + + + align:start position:0% +transformation you just you don't +transform at all right so so in this + + align:start position:0% +transform at all right so so in this + + + align:start position:0% +transform at all right so so in this +case the a mu is equal to zero and so in + + align:start position:0% +case the a mu is equal to zero and so in + + + align:start position:0% +case the a mu is equal to zero and so in +this case the trivial transformation + + align:start position:0% +this case the trivial transformation + + + align:start position:0% +this case the trivial transformation +just the Lambda mu mu is the identity + + align:start position:0% +just the Lambda mu mu is the identity + + + align:start position:0% +just the Lambda mu mu is the identity +Matrix and then you can imagine a + + align:start position:0% + + + + align:start position:0% + +slightly tending on a slight + + align:start position:0% +slightly tending on a slight + + + align:start position:0% +slightly tending on a slight +infinitesimal rotation or infinitesimal + + align:start position:0% +infinitesimal rotation or infinitesimal + + + align:start position:0% +infinitesimal rotation or infinitesimal +boost and then that's corresponding to + + align:start position:0% +boost and then that's corresponding to + + + align:start position:0% +boost and then that's corresponding to +So-Cal infinitesimal transformation okay + + align:start position:0% +So-Cal infinitesimal transformation okay + + + align:start position:0% +So-Cal infinitesimal transformation okay +so here you can also just translate am a + + align:start position:0% +so here you can also just translate am a + + + align:start position:0% +so here you can also just translate am a +little bit okay so very close to the + + align:start position:0% +little bit okay so very close to the + + + align:start position:0% +little bit okay so very close to the +identity and so so essentially for + + align:start position:0% + + + + align:start position:0% + +any okay so for any Global uh continuous + + align:start position:0% + + + + align:start position:0% + +symmetry + + align:start position:0% + + + + align:start position:0% + +it has a infini for + + align:start position:0% + + + + align:start position:0% + +form okay it's just when the parameter + + align:start position:0% +form okay it's just when the parameter + + + align:start position:0% +form okay it's just when the parameter +when transform transformation parameter + + align:start position:0% +when transform transformation parameter + + + align:start position:0% +when transform transformation parameter +is very close to the identity okay very + + align:start position:0% +is very close to the identity okay very + + + align:start position:0% +is very close to the identity okay very +close to the + + align:start position:0% +close to the + + + align:start position:0% +close to the +zero and so so for example uh for + + align:start position:0% +zero and so so for example uh for + + + align:start position:0% +zero and so so for example uh for +General transformation like this if the + + align:start position:0% +General transformation like this if the + + + align:start position:0% +General transformation like this if the +transformation is close to the + + align:start position:0% +transformation is close to the + + + align:start position:0% +transformation is close to the +identity then we can always write it in + + align:start position:0% +identity then we can always write it in + + + align:start position:0% +identity then we can always write it in +the following form 5 a goes to f a + + align:start position:0% +the following form 5 a goes to f a + + + align:start position:0% +the following form 5 a goes to f a +prime which is equal to 5 + + align:start position:0% +prime which is equal to 5 + + + align:start position:0% +prime which is equal to 5 +a and with some parameter small + + align:start position:0% +a and with some parameter small + + + align:start position:0% +a and with some parameter small +parameter + + align:start position:0% +parameter + + + align:start position:0% +parameter +Epsilon and some function fa a and then + + align:start position:0% +Epsilon and some function fa a and then + + + align:start position:0% +Epsilon and some function fa a and then +say I B okay and the derivative of i b + + align:start position:0% +say I B okay and the derivative of i b + + + align:start position:0% +say I B okay and the derivative of i b +ex + + align:start position:0% +ex + + + align:start position:0% +ex +actually okay so this Epsilon + + align:start position:0% + + + + align:start position:0% + +is the infinite tmal transformation + + align:start position:0% + + + + align:start position:0% + +parameter okay so if you have a + + align:start position:0% +parameter okay so if you have a + + + align:start position:0% +parameter okay so if you have a +a continous iMat there's always say + + align:start position:0% +a continous iMat there's always say + + + align:start position:0% +a continous iMat there's always say +infinite mod + + align:start position:0% +infinite mod + + + align:start position:0% +infinite mod +transformation which are close to the + + align:start position:0% +transformation which are close to the + + + align:start position:0% +transformation which are close to the +identity so so this Epsilon + + align:start position:0% +identity so so this Epsilon + + + align:start position:0% +identity so so this Epsilon +corresponding to this case would be for + + align:start position:0% +corresponding to this case would be for + + + align:start position:0% +corresponding to this case would be for +a mu is very + + align:start position:0% +a mu is very + + + align:start position:0% +a mu is very +small or for the low transformation case + + align:start position:0% +small or for the low transformation case + + + align:start position:0% +small or for the low transformation case +corresponding to rotation angle is very + + align:start position:0% +corresponding to rotation angle is very + + + align:start position:0% +corresponding to rotation angle is very +small or the Boost is very small + + align:start position:0% +small or the Boost is very small + + + align:start position:0% +small or the Boost is very small +okay yeah so the Epson can be any of + + align:start position:0% +okay yeah so the Epson can be any of + + + align:start position:0% +okay yeah so the Epson can be any of +those + + align:start position:0% + + + + align:start position:0% + +parameters and then this F can be some + + align:start position:0% +parameters and then this F can be some + + + align:start position:0% +parameters and then this F can be some +arbitary function okay this F can be + + align:start position:0% +arbitary function okay this F can be + + + align:start position:0% +arbitary function okay this F can be +some arbitrary functions of your + + align:start position:0% + + + + align:start position:0% + +field good so so in this case yeah so in + + align:start position:0% +field good so so in this case yeah so in + + + align:start position:0% +field good so so in this case yeah so in +this case the data f + + align:start position:0% +this case the data f + + + align:start position:0% +this case the data f +okay so the um yeah so the Symmetry + + align:start position:0% +okay so the um yeah so the Symmetry + + + align:start position:0% +okay so the um yeah so the Symmetry +transformation so we use rotation that + + align:start position:0% +transformation so we use rotation that + + + align:start position:0% +transformation so we use rotation that +hat by a so this symmetry then given by + + align:start position:0% +hat by a so this symmetry then given by + + + align:start position:0% +hat by a so this symmetry then given by +the Epsilon fa + + align:start position:0% + + + + align:start position:0% + +okay so so so data head here implies a + + align:start position:0% +okay so so so data head here implies a + + + align:start position:0% +okay so so so data head here implies a +symmetry trans infinite tmal symmetry + + align:start position:0% +symmetry trans infinite tmal symmetry + + + align:start position:0% +symmetry trans infinite tmal symmetry +transformation + + align:start position:0% + + + + align:start position:0% + +okay so now let's + + align:start position:0% +okay so now let's + + + align:start position:0% +okay so now let's +consider during a + + align:start position:0% +consider during a + + + align:start position:0% +consider during a +variation of s under this data hat okay + + align:start position:0% +variation of s under this data hat okay + + + align:start position:0% +variation of s under this data hat okay +since the by + + align:start position:0% + + + + align:start position:0% + +definition of the Symmetry because the + + align:start position:0% +definition of the Symmetry because the + + + align:start position:0% +definition of the Symmetry because the +uh this is a + + align:start position:0% +uh this is a + + + align:start position:0% +uh this is a +symmetry that means that data hat s + + align:start position:0% +symmetry that means that data hat s + + + align:start position:0% +symmetry that means that data hat s +should be equal to + + align:start position:0% +should be equal to + + + align:start position:0% +should be equal to +zero okay because the variation of the + + align:start position:0% +zero okay because the variation of the + + + align:start position:0% +zero okay because the variation of the +action should be invariant under the uh + + align:start position:0% +action should be invariant under the uh + + + align:start position:0% +action should be invariant under the uh +the + + align:start position:0% +the + + + align:start position:0% +the +Symmetry and so now let's look at what's + + align:start position:0% +Symmetry and so now let's look at what's + + + align:start position:0% +Symmetry and so now let's look at what's +the consequence of it okay so so now we + + align:start position:0% +the consequence of it okay so so now we + + + align:start position:0% +the consequence of it okay so so now we +can just worry this + + align:start position:0% +can just worry this + + + align:start position:0% +can just worry this +L and the so this + + align:start position:0% +L and the so this + + + align:start position:0% +L and the so this +means that the variation of the l l + + align:start position:0% +means that the variation of the l l + + + align:start position:0% +means that the variation of the l l +density must be a total + + align:start position:0% + + + + align:start position:0% + +derivative okay since all every + + align:start position:0% +derivative okay since all every + + + align:start position:0% +derivative okay since all every +transformation is proportional to EP + + align:start position:0% +transformation is proportional to EP + + + align:start position:0% +transformation is proportional to EP +yeah so Epson is a small parameter + + align:start position:0% +yeah so Epson is a small parameter + + + align:start position:0% +yeah so Epson is a small parameter +so when we do the transformation we only + + align:start position:0% +so when we do the transformation we only + + + align:start position:0% +so when we do the transformation we only +need to keep keep track the order in the + + align:start position:0% +need to keep keep track the order in the + + + align:start position:0% +need to keep keep track the order in the +in epsilon so so the transformation of + + align:start position:0% +in epsilon so so the transformation of + + + align:start position:0% +in epsilon so so the transformation of +the L so so must also be proportional to + + align:start position:0% +the L so so must also be proportional to + + + align:start position:0% +the L so so must also be proportional to +EPS okay so so uh so since this must be + + align:start position:0% +EPS okay so so uh so since this must be + + + align:start position:0% +EPS okay so so uh so since this must be +in warant that means the variation of + + align:start position:0% +in warant that means the variation of + + + align:start position:0% +in warant that means the variation of +the L must be a total derivative so K mu + + align:start position:0% +the L must be a total derivative so K mu + + + align:start position:0% +the L must be a total derivative so K mu +would be just some so for some K mu okay + + align:start position:0% +would be just some so for some K mu okay + + + align:start position:0% +would be just some so for some K mu okay +some K so must exist some K mu and this + + align:start position:0% +some K so must exist some K mu and this + + + align:start position:0% +some K so must exist some K mu and this +K mu can also be zero + + align:start position:0% +K mu can also be zero + + + align:start position:0% +K mu can also be zero +the in that case L density is invariant + + align:start position:0% + + + + align:start position:0% + +yes sorry is Delta the variation under + + align:start position:0% +yes sorry is Delta the variation under + + + align:start position:0% +yes sorry is Delta the variation under +the transformation Del head is a Del + + align:start position:0% +the transformation Del head is a Del + + + align:start position:0% +the transformation Del head is a Del +head just dels such a + + align:start position:0% +head just dels such a + + + align:start position:0% +head just dels such a +transformation just Delo such a + + align:start position:0% +transformation just Delo such a + + + align:start position:0% +transformation just Delo such a +transformation uh this is not the + + align:start position:0% +transformation uh this is not the + + + align:start position:0% +transformation uh this is not the +general trans this is not the general + + align:start position:0% +general trans this is not the general + + + align:start position:0% +general trans this is not the general +variation this is a very specific this + + align:start position:0% +variation this is a very specific this + + + align:start position:0% +variation this is a very specific this +is a symmetric + + align:start position:0% +is a symmetric + + + align:start position:0% +is a symmetric +transformation and so under the + + align:start position:0% +transformation and so under the + + + align:start position:0% +transformation and so under the +symmetric transformation your action + + align:start position:0% +symmetric transformation your action + + + align:start position:0% +symmetric transformation your action +should be in warant by definition + + align:start position:0% +should be in warant by definition + + + align:start position:0% +should be in warant by definition +because this is a symmetry and that in + + align:start position:0% +because this is a symmetry and that in + + + align:start position:0% +because this is a symmetry and that in +turn because the S is the integration of + + align:start position:0% +turn because the S is the integration of + + + align:start position:0% +turn because the S is the integration of +L then that means that the + + align:start position:0% +L then that means that the + + + align:start position:0% +L then that means that the +transformation of L long density must be + + align:start position:0% +transformation of L long density must be + + + align:start position:0% +transformation of L long density must be +a total + + align:start position:0% +a total + + + align:start position:0% +a total +derivative and here we only only keep + + align:start position:0% +derivative and here we only only keep + + + align:start position:0% +derivative and here we only only keep +track everything inine the order in + + align:start position:0% +track everything inine the order in + + + align:start position:0% +track everything inine the order in +epsilon and so this must be proportional + + align:start position:0% +epsilon and so this must be proportional + + + align:start position:0% +epsilon and so this must be proportional +to Epsilon times the total der okay and + + align:start position:0% +to Epsilon times the total der okay and + + + align:start position:0% +to Epsilon times the total der okay and +so so you we must have this structure + + align:start position:0% +so so you we must have this structure + + + align:start position:0% +so so you we must have this structure +yeah for some for some C + + align:start position:0% +yeah for some for some C + + + align:start position:0% +yeah for some for some C +okay which can be + + align:start position:0% + + + + align:start position:0% + +zero which can be + + align:start position:0% +zero which can be + + + align:start position:0% +zero which can be +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay good so now let's look at what's + + align:start position:0% +okay good so now let's look at what's + + + align:start position:0% +okay good so now let's look at what's +the implications of this + + align:start position:0% +the implications of this + + + align:start position:0% +the implications of this +equation okay so this equation is the + + align:start position:0% +equation okay so this equation is the + + + align:start position:0% +equation okay so this equation is the +constraint imposed by the Symmetry okay + + align:start position:0% +constraint imposed by the Symmetry okay + + + align:start position:0% +constraint imposed by the Symmetry okay +now let's look at about the implications + + align:start position:0% +now let's look at about the implications + + + align:start position:0% +now let's look at about the implications +of this + + align:start position:0% + + + + align:start position:0% + +constraint so now we can just do the + + align:start position:0% +constraint so now we can just do the + + + align:start position:0% +constraint so now we can just do the +variation of + + align:start position:0% +variation of + + + align:start position:0% +variation of +L now we can just do the variation of + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +L yeah maybe I will keep that equation + + align:start position:0% +L yeah maybe I will keep that equation + + + align:start position:0% +L yeah maybe I will keep that equation +then I will do this Bo + + align:start position:0% + + + + align:start position:0% + +first yeah show like something symmetry + + align:start position:0% +first yeah show like something symmetry + + + align:start position:0% +first yeah show like something symmetry +of + + align:start position:0% +of + + + align:start position:0% +of +Your Action for the your system would + + align:start position:0% +Your Action for the your system would + + + align:start position:0% +Your Action for the your system would +you like directly vary the thing like + + align:start position:0% +you like directly vary the thing like + + + align:start position:0% +you like directly vary the thing like +parameter and then show that your action + + align:start position:0% +parameter and then show that your action + + + align:start position:0% +parameter and then show that your action +doesn't change or would you do that + + align:start position:0% + + + + align:start position:0% + +um + + align:start position:0% +um + + + align:start position:0% +um +and so we want to right so we want to + + align:start position:0% +and so we want to right so we want to + + + align:start position:0% +and so we want to right so we want to +use the fact that such a trans such a + + align:start position:0% +use the fact that such a trans such a + + + align:start position:0% +use the fact that such a trans such a +transformation + + align:start position:0% +transformation + + + align:start position:0% +transformation +is a symmetry to + + align:start position:0% +is a symmetry to + + + align:start position:0% +is a symmetry to +derive what is the + + align:start position:0% +derive what is the + + + align:start position:0% +derive what is the +constraint on the + + align:start position:0% +constraint on the + + + align:start position:0% +constraint on the +Lin okay what is the constraint on the + + align:start position:0% +Lin okay what is the constraint on the + + + align:start position:0% +Lin okay what is the constraint on the +theory say we assume that somehow the + + align:start position:0% +theory say we assume that somehow the + + + align:start position:0% +theory say we assume that somehow the +theory have a symmetry and then we want + + align:start position:0% +theory have a symmetry and then we want + + + align:start position:0% +theory have a symmetry and then we want +to see what is what is the constraint + + align:start position:0% +to see what is what is the constraint + + + align:start position:0% +to see what is what is the constraint +this put on your + + align:start position:0% +this put on your + + + align:start position:0% +this put on your +Series yeah that's right we're put the L + + align:start position:0% + + + + align:start position:0% + +yeah good and + + align:start position:0% + + + + align:start position:0% + +questions okay so that + + align:start position:0% + + + + align:start position:0% + +equation is the uh is the + + align:start position:0% +equation is the uh is the + + + align:start position:0% +equation is the uh is the +implication is the constraint imposed by + + align:start position:0% +implication is the constraint imposed by + + + align:start position:0% +implication is the constraint imposed by +the Symmetry and we want to see what + + align:start position:0% +the Symmetry and we want to see what + + + align:start position:0% +the Symmetry and we want to see what +this equation tells us + + align:start position:0% +this equation tells us + + + align:start position:0% +this equation tells us +okay and for this purpose we just do the + + align:start position:0% +okay and for this purpose we just do the + + + align:start position:0% +okay and for this purpose we just do the +variation so the do + + align:start position:0% +variation so the do + + + align:start position:0% +variation so the do +hat + + align:start position:0% +hat + + + align:start position:0% +hat +l so because L is just a function or or + + align:start position:0% +l so because L is just a function or or + + + align:start position:0% +l so because L is just a function or or +five and then we have partial L partial + + align:start position:0% +five and then we have partial L partial + + + align:start position:0% +five and then we have partial L partial + + align:start position:0% + + + align:start position:0% +a do a hat 5 + + align:start position:0% +a do a hat 5 + + + align:start position:0% +a do a hat 5 +a and then we have L partial partial mu + + align:start position:0% +a and then we have L partial partial mu + + + align:start position:0% +a and then we have L partial partial mu +by + + align:start position:0% +by + + + align:start position:0% +by +a and then partial mu do head by a + + align:start position:0% +a and then partial mu do head by a + + + align:start position:0% +a and then partial mu do head by a +okay so we just did the + + align:start position:0% + + + + align:start position:0% + +variation and + + align:start position:0% +variation and + + + align:start position:0% +variation and +now okay and uh uh uh uh uh uh so yeah + + align:start position:0% +now okay and uh uh uh uh uh uh so yeah + + + align:start position:0% +now okay and uh uh uh uh uh uh so yeah +and now we are going to use equation + + align:start position:0% +and now we are going to use equation + + + align:start position:0% +and now we are going to use equation +motion okay so so from the equation + + align:start position:0% +motion okay so so from the equation + + + align:start position:0% +motion okay so so from the equation +motion I think I erased yeah from the + + align:start position:0% +motion I think I erased yeah from the + + + align:start position:0% +motion I think I erased yeah from the +equation + + align:start position:0% +equation + + + align:start position:0% +equation +motion then partial L partial 5 a this + + align:start position:0% +motion then partial L partial 5 a this + + + align:start position:0% +motion then partial L partial 5 a this +is just equal to partial + + align:start position:0% +is just equal to partial + + + align:start position:0% +is just equal to partial +mu partial L partial partial mu a okay + + align:start position:0% +mu partial L partial partial mu a okay + + + align:start position:0% +mu partial L partial partial mu a okay +so we just plug in this into here so + + align:start position:0% +so we just plug in this into here so + + + align:start position:0% +so we just plug in this into here so +when you plug in this into here now you + + align:start position:0% +when you plug in this into here now you + + + align:start position:0% +when you plug in this into here now you +notice this become a total + + align:start position:0% + + + + align:start position:0% + +derivative okay so you have parti + + align:start position:0% + + + + align:start position:0% + +l i + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% +a + + + align:start position:0% +a +hat + + align:start position:0% +hat + + + align:start position:0% +hat +a okay so you find after using equation + + align:start position:0% +a okay so you find after using equation + + + align:start position:0% +a okay so you find after using equation +motion this variation of L have the + + align:start position:0% +motion this variation of L have the + + + align:start position:0% +motion this variation of L have the +following form which is the total + + align:start position:0% + + + + align:start position:0% + +derivative and this should be equal to + + align:start position:0% +derivative and this should be equal to + + + align:start position:0% +derivative and this should be equal to +the right hand side + + align:start position:0% +the right hand side + + + align:start position:0% +the right hand side +okay uh should be equal to the right + + align:start position:0% +okay uh should be equal to the right + + + align:start position:0% +okay uh should be equal to the right +hand side yeah so so um yeah so and then + + align:start position:0% +hand side yeah so so um yeah so and then + + + align:start position:0% +hand side yeah so so um yeah so and then +we here we find so this should be equal + + align:start position:0% +we here we find so this should be equal + + + align:start position:0% +we here we find so this should be equal +to Epsilon H mu K + + align:start position:0% +to Epsilon H mu K + + + align:start position:0% +to Epsilon H mu K +mu okay so we combine both sides + + align:start position:0% +mu okay so we combine both sides + + + align:start position:0% +mu okay so we combine both sides +together plug in that this is equal to + + align:start position:0% +together plug in that this is equal to + + + align:start position:0% +together plug in that this is equal to +Epsilon time F and then we + + align:start position:0% +Epsilon time F and then we + + + align:start position:0% +Epsilon time F and then we +conclude okay then we + + align:start position:0% +conclude okay then we + + + align:start position:0% +conclude okay then we +conclude parti mu + + align:start position:0% + + + + align:start position:0% + +parti + + align:start position:0% +parti + + + align:start position:0% +parti +L par par mu + + align:start position:0% +L par par mu + + + align:start position:0% +L par par mu +a then + + align:start position:0% +a then + + + align:start position:0% +a then +fa minus K + + align:start position:0% +fa minus K + + + align:start position:0% +fa minus K +mu re equal to + + align:start position:0% +mu re equal to + + + align:start position:0% +mu re equal to +zero okay so if we call this J + + align:start position:0% + + + + align:start position:0% + +mu and then we have a conservation + + align:start position:0% +mu and then we have a conservation + + + align:start position:0% +mu and then we have a conservation +equation parti mu J mu equal to + + align:start position:0% +equation parti mu J mu equal to + + + align:start position:0% +equation parti mu J mu equal to +zero okay so we have a conation + + align:start position:0% + + + + align:start position:0% + +no so so remember conation no is just to + + align:start position:0% +no so so remember conation no is just to + + + align:start position:0% +no so so remember conation no is just to +to have a VOR which satisfy this + + align:start position:0% +to have a VOR which satisfy this + + + align:start position:0% +to have a VOR which satisfy this +equation and and then uh um + + align:start position:0% + + + + align:start position:0% + +yeah so so more explicitly yeah so the J + + align:start position:0% +yeah so so more explicitly yeah so the J + + + align:start position:0% +yeah so so more explicitly yeah so the J +mu just this combination okay J mu just + + align:start position:0% +mu just this combination okay J mu just + + + align:start position:0% +mu just this combination okay J mu just +this combination so any questions on + + align:start position:0% +this combination so any questions on + + + align:start position:0% +this combination so any questions on +this yes this quite a stct because it's + + align:start position:0% +this yes this quite a stct because it's + + + align:start position:0% +this yes this quite a stct because it's +the with respect to space time is but + + align:start position:0% +the with respect to space time is but + + + align:start position:0% +the with respect to space time is but +you have a conservation thetive with + + align:start position:0% +you have a conservation thetive with + + + align:start position:0% +you have a conservation thetive with +respect to time but not space yeah yeah + + align:start position:0% +respect to time but not space yeah yeah + + + align:start position:0% +respect to time but not space yeah yeah +I will yeah yeah this is the stronger + + align:start position:0% +I will yeah yeah this is the stronger + + + align:start position:0% +I will yeah yeah this is the stronger +version than your + + align:start position:0% +version than your + + + align:start position:0% +version than your +normally yeah so this is the SpaceTime + + align:start position:0% +normally yeah so this is the SpaceTime + + + align:start position:0% +normally yeah so this is the SpaceTime +version of the conation LA from your + + align:start position:0% +version of the conation LA from your + + + align:start position:0% +version of the conation LA from your +normally classical mechanics yeah so + + align:start position:0% +normally classical mechanics yeah so + + + align:start position:0% +normally classical mechanics yeah so +this is a field series version of that + + align:start position:0% +this is a field series version of that + + + align:start position:0% +this is a field series version of that +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +yeah I will elaborate that equation a + + align:start position:0% +yeah I will elaborate that equation a + + + align:start position:0% +yeah I will elaborate that equation a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +yeah yes so + + align:start position:0% +yeah yes so + + + align:start position:0% +yeah yes so +if you + + align:start position:0% + + + + align:start position:0% + +only + + align:start position:0% + + + + align:start position:0% + +yeah say it again + + align:start position:0% + + + + align:start position:0% + +IUD + + align:start position:0% + + + + align:start position:0% + +fuding + + align:start position:0% +fuding + + + align:start position:0% +fuding +trans coordinates so so here uh yeah + + align:start position:0% +trans coordinates so so here uh yeah + + + align:start position:0% +trans coordinates so so here uh yeah +yeah so here is a general + + align:start position:0% +yeah so here is a general + + + align:start position:0% +yeah so here is a general +formulation so this transformation can + + align:start position:0% +formulation so this transformation can + + + align:start position:0% +formulation so this transformation can +be General doesn't have to be say A + + align:start position:0% +be General doesn't have to be say A + + + align:start position:0% +be General doesn't have to be say A +Spacetime transformation we said earlier + + align:start position:0% +Spacetime transformation we said earlier + + + align:start position:0% +Spacetime transformation we said earlier +uh this just some abstract symmetry just + + align:start position:0% +uh this just some abstract symmetry just + + + align:start position:0% +uh this just some abstract symmetry just +some arbory + + align:start position:0% + + + + align:start position:0% + +Transformations symmetries that change + + align:start position:0% +Transformations symmetries that change + + + align:start position:0% +Transformations symmetries that change +the + + align:start position:0% + + + + align:start position:0% + +field + + align:start position:0% +field + + + align:start position:0% +field +yeah because because space time variable + + align:start position:0% +yeah because because space time variable + + + align:start position:0% +yeah because because space time variable +is a Dom variable in the action you can + + align:start position:0% +is a Dom variable in the action you can + + + align:start position:0% +is a Dom variable in the action you can +always get rid of + + align:start position:0% +always get rid of + + + align:start position:0% +always get rid of +that the Xchange X is just a DI variable + + align:start position:0% +that the Xchange X is just a DI variable + + + align:start position:0% +that the Xchange X is just a DI variable +in your in your + + align:start position:0% +in your in your + + + align:start position:0% +in your in your +action because you integrate over over X + + align:start position:0% + + + + align:start position:0% + +yeah yeah yeah that that can include the + + align:start position:0% +yeah yeah yeah that that can include the + + + align:start position:0% +yeah yeah yeah that that can include the +normally uh uh yeah you can you can in + + align:start position:0% +normally uh uh yeah you can you can in + + + align:start position:0% +normally uh uh yeah you can you can in +principle have as many derives as you + + align:start position:0% +principle have as many derives as you + + + align:start position:0% +principle have as many derives as you +want but normally we if we have action + + align:start position:0% +want but normally we if we have action + + + align:start position:0% +want but normally we if we have action +which only contain first derivatives and + + align:start position:0% +which only contain first derivatives and + + + align:start position:0% +which only contain first derivatives and +your your symmetry transformation only + + align:start position:0% +your your symmetry transformation only + + + align:start position:0% +your your symmetry transformation only +involve first + + align:start position:0% + + + + align:start position:0% + +derivatives + + align:start position:0% +derivatives + + + align:start position:0% +derivatives +um yeah yeah in principle you can have + + align:start position:0% +um yeah yeah in principle you can have + + + align:start position:0% +um yeah yeah in principle you can have +it you can principle you can have it + + align:start position:0% +it you can principle you can have it + + + align:start position:0% +it you can principle you can have it +just uh uh yeah I'm just writing this + + align:start position:0% +just uh uh yeah I'm just writing this + + + align:start position:0% +just uh uh yeah I'm just writing this +for Simplicity + + align:start position:0% + + + + align:start position:0% + +yeah yeah good maybe you can ask after + + align:start position:0% +yeah yeah good maybe you can ask after + + + align:start position:0% +yeah yeah good maybe you can ask after +the class yeah if it's not clear other + + align:start position:0% +the class yeah if it's not clear other + + + align:start position:0% +the class yeah if it's not clear other +questions okay good so so let me + + align:start position:0% +questions okay good so so let me + + + align:start position:0% +questions okay good so so let me +elaborate a little bit on this equation + + align:start position:0% +elaborate a little bit on this equation + + + align:start position:0% +elaborate a little bit on this equation +so this equation you may have seen in + + align:start position:0% +so this equation you may have seen in + + + align:start position:0% +so this equation you may have seen in +the in m so uh which you often call the + + align:start position:0% +the in m so uh which you often call the + + + align:start position:0% +the in m so uh which you often call the +Contin continuity equation uh if you if + + align:start position:0% +Contin continuity equation uh if you if + + + align:start position:0% +Contin continuity equation uh if you if +you write this equation + + align:start position:0% +you write this equation + + + align:start position:0% +you write this equation +separately has the following form + + align:start position:0% +separately has the following form + + + align:start position:0% +separately has the following form +partial 0 j0 plus partial + + align:start position:0% +partial 0 j0 plus partial + + + align:start position:0% +partial 0 j0 plus partial +I or or or the Divergence of the spatial + + align:start position:0% +I or or or the Divergence of the spatial + + + align:start position:0% +I or or or the Divergence of the spatial +component so J mu if we write it in + + align:start position:0% +component so J mu if we write it in + + + align:start position:0% +component so J mu if we write it in +terms of + + align:start position:0% +terms of + + + align:start position:0% +terms of +the okay uh explicitly then you have + + align:start position:0% +the okay uh explicitly then you have + + + align:start position:0% +the okay uh explicitly then you have +this + + align:start position:0% + + + + align:start position:0% + +form so so this is so-called the + + align:start position:0% +form so so this is so-called the + + + align:start position:0% +form so so this is so-called the +continuity equation just the the uh the + + align:start position:0% +continuity equation just the the uh the + + + align:start position:0% +continuity equation just the the uh the +time variation of the density okay the + + align:start position:0% +time variation of the density okay the + + + align:start position:0% +time variation of the density okay the +zero component they considered some kind + + align:start position:0% +zero component they considered some kind + + + align:start position:0% +zero component they considered some kind +of density it's the same as Divergence + + align:start position:0% +of density it's the same as Divergence + + + align:start position:0% +of density it's the same as Divergence +of the current okay and in particular + + align:start position:0% +of the current okay and in particular + + + align:start position:0% +of the current okay and in particular +you can define a charge which is the + + align:start position:0% +you can define a charge which is the + + + align:start position:0% +you can define a charge which is the +total spatial + + align:start position:0% +total spatial + + + align:start position:0% +total spatial +integration of J + + align:start position:0% +integration of J + + + align:start position:0% +integration of J +Zer okay so if you integrate both sides + + align:start position:0% +Zer okay so if you integrate both sides + + + align:start position:0% +Zer okay so if you integrate both sides +by over the total volume and then this + + align:start position:0% +by over the total volume and then this + + + align:start position:0% +by over the total volume and then this +just become partial zero + + align:start position:0% +just become partial zero + + + align:start position:0% +just become partial zero +q and and this term become a total + + align:start position:0% +q and and this term become a total + + + align:start position:0% +q and and this term become a total +derivative and uh and then you can + + align:start position:0% +derivative and uh and then you can + + + align:start position:0% +derivative and uh and then you can +convert it into a boundary term using + + align:start position:0% +convert it into a boundary term using + + + align:start position:0% +convert it into a boundary term using +the G Law and uh and then normally the + + align:start position:0% +the G Law and uh and then normally the + + + align:start position:0% +the G Law and uh and then normally the +current vanish is at infinity and then + + align:start position:0% +current vanish is at infinity and then + + + align:start position:0% +current vanish is at infinity and then +you just have the charge + + align:start position:0% + + + + align:start position:0% + +conation just have charge + + align:start position:0% +conation just have charge + + + align:start position:0% +conation just have charge +comination okay and uh um yeah so so + + align:start position:0% +comination okay and uh um yeah so so + + + align:start position:0% +comination okay and uh um yeah so so +this is like the field SL In classical + + align:start position:0% +this is like the field SL In classical + + + align:start position:0% +this is like the field SL In classical +mechanics you just have this + + align:start position:0% +mechanics you just have this + + + align:start position:0% +mechanics you just have this +equation okay and this is the field + + align:start position:0% +equation okay and this is the field + + + align:start position:0% +equation okay and this is the field +series version of your + + align:start position:0% + + + + align:start position:0% + +conservation + + align:start position:0% + + + + align:start position:0% + +yes what it is sorry is toate what + + align:start position:0% +yes what it is sorry is toate what + + + align:start position:0% +yes what it is sorry is toate what +represents J J represent yeah represent + + align:start position:0% +represents J J represent yeah represent + + + align:start position:0% +represents J J represent yeah represent +yeah yeah yeah if I give you a specific + + align:start position:0% +yeah yeah yeah if I give you a specific + + + align:start position:0% +yeah yeah yeah if I give you a specific +yeah you will do it in your P set so if + + align:start position:0% +yeah you will do it in your P set so if + + + align:start position:0% +yeah you will do it in your P set so if +I give you a specific like + + align:start position:0% +I give you a specific like + + + align:start position:0% +I give you a specific like +ranging if you start a specific + + align:start position:0% +ranging if you start a specific + + + align:start position:0% +ranging if you start a specific +transformation and then you will be able + + align:start position:0% +transformation and then you will be able + + + align:start position:0% +transformation and then you will be able +to find all the those quantities exp you + + align:start position:0% +to find all the those quantities exp you + + + align:start position:0% +to find all the those quantities exp you +will be able to find the K explicitly + + align:start position:0% +will be able to find the K explicitly + + + align:start position:0% +will be able to find the K explicitly +and you will be able to find all those + + align:start position:0% +and you will be able to find all those + + + align:start position:0% +and you will be able to find all those +quantity explicitly then you can find + + align:start position:0% +quantity explicitly then you can find + + + align:start position:0% +quantity explicitly then you can find +the J + + align:start position:0% + + + + align:start position:0% + +yeah other + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% + + + + align:start position:0% + +yes right it's because the because if we + + align:start position:0% +yes right it's because the because if we + + + align:start position:0% +yes right it's because the because if we +have + + align:start position:0% +have + + + align:start position:0% +have +here so if we here if we have s equal to + + align:start position:0% +here so if we here if we have s equal to + + + align:start position:0% +here so if we here if we have s equal to +zero and then and then you can just put + + align:start position:0% +zero and then and then you can just put + + + align:start position:0% +zero and then and then you can just put +the data + + align:start position:0% +the data + + + align:start position:0% +the data +in and then this quantity then it's + + align:start position:0% +in and then this quantity then it's + + + align:start position:0% +in and then this quantity then it's +integrated over that if this is zero + + align:start position:0% +integrated over that if this is zero + + + align:start position:0% +integrated over that if this is zero +then this has to be a total + + align:start position:0% + + + + align:start position:0% + +derivative other + + align:start position:0% + + + + align:start position:0% + +questions + + align:start position:0% +questions + + + align:start position:0% +questions +yes it's not a global symmetry argument + + align:start position:0% +yes it's not a global symmetry argument + + + align:start position:0% +yes it's not a global symmetry argument +right yeah good good good ide this is a + + align:start position:0% +right yeah good good good ide this is a + + + align:start position:0% +right yeah good good good ide this is a +very um good question so so yeah so I + + align:start position:0% +very um good question so so yeah so I + + + align:start position:0% +very um good question so so yeah so I +will not have time to go into here let + + align:start position:0% +will not have time to go into here let + + + align:start position:0% +will not have time to go into here let +me just very quickly mention so this is + + align:start position:0% +me just very quickly mention so this is + + + align:start position:0% +me just very quickly mention so this is +called the first loer theorem and uh + + align:start position:0% +called the first loer theorem and uh + + + align:start position:0% +called the first loer theorem and uh +when Epsilon is spacetime + + align:start position:0% +when Epsilon is spacetime + + + align:start position:0% +when Epsilon is spacetime +independent and so so Epsilon is not + + align:start position:0% +independent and so so Epsilon is not + + + align:start position:0% +independent and so so Epsilon is not +space-time dependent and then story is a + + align:start position:0% +space-time dependent and then story is a + + + align:start position:0% +space-time dependent and then story is a +little bit more communicated so the + + align:start position:0% +little bit more communicated so the + + + align:start position:0% +little bit more communicated so the +Epsilon will be inside the Epsilon will + + align:start position:0% +Epsilon will be inside the Epsilon will + + + align:start position:0% +Epsilon will be inside the Epsilon will +be inside this total der you cannot take + + align:start position:0% +be inside this total der you cannot take + + + align:start position:0% +be inside this total der you cannot take +it out ex and then the story change a + + align:start position:0% +it out ex and then the story change a + + + align:start position:0% +it out ex and then the story change a +little bit and then and then there's + + align:start position:0% +little bit and then and then there's + + + align:start position:0% +little bit and then and then there's +something called second loss of theorem + + align:start position:0% +something called second loss of theorem + + + align:start position:0% +something called second loss of theorem +and actually in that case when you have + + align:start position:0% +and actually in that case when you have + + + align:start position:0% +and actually in that case when you have +local symmetries when EPS depend on + + align:start position:0% +local symmetries when EPS depend on + + + align:start position:0% +local symmetries when EPS depend on +space time instead of finding + + align:start position:0% +space time instead of finding + + + align:start position:0% +space time instead of finding +conservation La you find that the your + + align:start position:0% +conservation La you find that the your + + + align:start position:0% +conservation La you find that the your +equation motion not all uh you find some + + align:start position:0% +equation motion not all uh you find some + + + align:start position:0% +equation motion not all uh you find some +part of the equation motion are + + align:start position:0% +part of the equation motion are + + + align:start position:0% +part of the equation motion are +redundant + + align:start position:0% +redundant + + + align:start position:0% +redundant +yeah yeah and if you it's not difficult + + align:start position:0% +yeah yeah and if you it's not difficult + + + align:start position:0% +yeah yeah and if you it's not difficult +but actually uh um in principle I can + + align:start position:0% +but actually uh um in principle I can + + + align:start position:0% +but actually uh um in principle I can +put it in the pide problem uh if people + + align:start position:0% +put it in the pide problem uh if people + + + align:start position:0% +put it in the pide problem uh if people +really want to see it + + align:start position:0% + + + + align:start position:0% + +yes what happens + + align:start position:0% + + + + align:start position:0% + +to good good good so so this is a q + + align:start position:0% +to good good good so so this is a q + + + align:start position:0% +to good good good so so this is a q +Beauty a q key beauty of physics which + + align:start position:0% +Beauty a q key beauty of physics which + + + align:start position:0% +Beauty a q key beauty of physics which +you may already have seen in quantum + + align:start position:0% +you may already have seen in quantum + + + align:start position:0% +you may already have seen in quantum +mechanics so whenever we see a + + align:start position:0% +mechanics so whenever we see a + + + align:start position:0% +mechanics so whenever we see a +symmetry no matter how complicated that + + align:start position:0% +symmetry no matter how complicated that + + + align:start position:0% +symmetry no matter how complicated that +symmetry is say say some continuous + + align:start position:0% +symmetry is say say some continuous + + + align:start position:0% +symmetry is say say some continuous +symmetry it's enough just to understand + + align:start position:0% +symmetry it's enough just to understand + + + align:start position:0% +symmetry it's enough just to understand +that symmetry near the identity near to + + align:start position:0% +that symmetry near the identity near to + + + align:start position:0% +that symmetry near the identity near to +be the infal transformation it's because + + align:start position:0% +be the infal transformation it's because + + + align:start position:0% +be the infal transformation it's because +any finite transformation you can build + + align:start position:0% +any finite transformation you can build + + + align:start position:0% +any finite transformation you can build +up from from just adding up the infal + + align:start position:0% +up from from just adding up the infal + + + align:start position:0% +up from from just adding up the infal +Transformations so once you know the + + align:start position:0% +Transformations so once you know the + + + align:start position:0% +Transformations so once you know the +infal transformation actually + + align:start position:0% +infal transformation actually + + + align:start position:0% +infal transformation actually +essentially up to some Global + + align:start position:0% +essentially up to some Global + + + align:start position:0% +essentially up to some Global +topological structure essentially + + align:start position:0% +topological structure essentially + + + align:start position:0% +topological structure essentially +determine the full fight + + align:start position:0% +determine the full fight + + + align:start position:0% +determine the full fight +transformation yeah + + align:start position:0% + + + + align:start position:0% + +uh no no it's always a symmetry right + + align:start position:0% +uh no no it's always a symmetry right + + + align:start position:0% +uh no no it's always a symmetry right +because because each step is a symmetry + + align:start position:0% +because because each step is a symmetry + + + align:start position:0% +because because each step is a symmetry +and so you add them you add them up + + align:start position:0% +and so you add them you add them up + + + align:start position:0% +and so you add them you add them up +still a + + align:start position:0% +still a + + + align:start position:0% +still a +symmetry okay but a sequence of + + align:start position:0% +symmetry okay but a sequence of + + + align:start position:0% +symmetry okay but a sequence of +different Sy oh if you do different yeah + + align:start position:0% +different Sy oh if you do different yeah + + + align:start position:0% +different Sy oh if you do different yeah +there still a symmetry yeah because by + + align:start position:0% +there still a symmetry yeah because by + + + align:start position:0% +there still a symmetry yeah because by +definition uh uh if something something + + align:start position:0% +definition uh uh if something something + + + align:start position:0% +definition uh uh if something something +transform is in Warr you do a lot of + + align:start position:0% +transform is in Warr you do a lot of + + + align:start position:0% +transform is in Warr you do a lot of +transformation still + + align:start position:0% + + + + align:start position:0% + +enironment good other questions yes + + align:start position:0% +enironment good other questions yes + + + align:start position:0% +enironment good other questions yes +symmetry we don't have can do something + + align:start position:0% +symmetry we don't have can do something + + + align:start position:0% +symmetry we don't have can do something +similar sorry for discr symmetry for + + align:start position:0% +similar sorry for discr symmetry for + + + align:start position:0% +similar sorry for discr symmetry for +discrete symmetry have this do something + + align:start position:0% +discrete symmetry have this do something + + + align:start position:0% +discrete symmetry have this do something +similar uh yeah in general for the + + align:start position:0% +similar uh yeah in general for the + + + align:start position:0% +similar uh yeah in general for the +symmetries you don't have such a + + align:start position:0% +symmetries you don't have such a + + + align:start position:0% +symmetries you don't have such a +conservational uh you don't have such a + + align:start position:0% +conservational uh you don't have such a + + + align:start position:0% +conservational uh you don't have such a +conservation or you can still sometimes + + align:start position:0% +conservation or you can still sometimes + + + align:start position:0% +conservation or you can still sometimes +you can still Define some discreete + + align:start position:0% +you can still Define some discreete + + + align:start position:0% +you can still Define some discreete +quantum number which is conserved like + + align:start position:0% +quantum number which is conserved like + + + align:start position:0% +quantum number which is conserved like +the parity which in the parity case and + + align:start position:0% +the parity which in the parity case and + + + align:start position:0% +the parity which in the parity case and +uh but but you don't have a current okay + + align:start position:0% +uh but but you don't have a current okay + + + align:start position:0% +uh but but you don't have a current okay +so here JMU is called the conserved + + align:start position:0% +so here JMU is called the conserved + + + align:start position:0% +so here JMU is called the conserved +current so uh but you won't have a + + align:start position:0% + + + + align:start position:0% + +current good good so so this + + align:start position:0% +current good good so so this + + + align:start position:0% +current good good so so this +concludes our + + align:start position:0% +concludes our + + + align:start position:0% +concludes our +discussion very quick discussion of the + + align:start position:0% +discussion very quick discussion of the + + + align:start position:0% +discussion very quick discussion of the +important features + + align:start position:0% +important features + + + align:start position:0% +important features +of classical field Theory and with this + + align:start position:0% +of classical field Theory and with this + + + align:start position:0% +of classical field Theory and with this +preparation and now we can start talking + + align:start position:0% +preparation and now we can start talking + + + align:start position:0% +preparation and now we can start talking +about uh start thinking about going to + + align:start position:0% +about uh start thinking about going to + + + align:start position:0% +about uh start thinking about going to +Quantum Mechanics talking about the + + align:start position:0% +Quantum Mechanics talking about the + + + align:start position:0% +Quantum Mechanics talking about the +quantum Fields okay and so so here is a + + align:start position:0% +quantum Fields okay and so so here is a + + + align:start position:0% +quantum Fields okay and so so here is a +good place to pause a little bit from + + align:start position:0% +good place to pause a little bit from + + + align:start position:0% +good place to pause a little bit from +what we said uh uh from what we already + + align:start position:0% +what we said uh uh from what we already + + + align:start position:0% +what we said uh uh from what we already +said about classical field Theory to to + + align:start position:0% +said about classical field Theory to to + + + align:start position:0% +said about classical field Theory to to +anticipate a little bit about the uh uh + + align:start position:0% +anticipate a little bit about the uh uh + + + align:start position:0% +anticipate a little bit about the uh uh +Quantum field the okay so so here we + + align:start position:0% +Quantum field the okay so so here we + + + align:start position:0% +Quantum field the okay so so here we +restate our + + align:start position:0% +restate our + + + align:start position:0% +restate our +goal for uh for for Quantum field + + align:start position:0% +goal for uh for for Quantum field + + + align:start position:0% +goal for uh for for Quantum field +Theory which I said a little + + align:start position:0% +Theory which I said a little + + + align:start position:0% +Theory which I said a little +bit in the in the last lecture + + align:start position:0% +bit in the in the last lecture + + + align:start position:0% +bit in the in the last lecture +okay so now we have seen the classical + + align:start position:0% +okay so now we have seen the classical + + + align:start position:0% +okay so now we have seen the classical +fields and our goal is to understand the + + align:start position:0% +fields and our goal is to understand the + + + align:start position:0% +fields and our goal is to understand the +quantum version of this story okay so so + + align:start position:0% +quantum version of this story okay so so + + + align:start position:0% +quantum version of this story okay so so +classical field theory is the classical + + align:start position:0% +classical field theory is the classical + + + align:start position:0% +classical field theory is the classical +mechanics with infinite number freom and + + align:start position:0% +mechanics with infinite number freom and + + + align:start position:0% +mechanics with infinite number freom and +now we want to quantize this Infinite L + + align:start position:0% +now we want to quantize this Infinite L + + + align:start position:0% +now we want to quantize this Infinite L +freedom and now this become Quantum + + align:start position:0% +freedom and now this become Quantum + + + align:start position:0% +freedom and now this become Quantum +field Ser okay and now we want to + + align:start position:0% +field Ser okay and now we want to + + + align:start position:0% +field Ser okay and now we want to +understand the quantum dynamics of such + + align:start position:0% +understand the quantum dynamics of such + + + align:start position:0% +understand the quantum dynamics of such +a field such kind of five Fields okay + + align:start position:0% +a field such kind of five Fields okay + + + align:start position:0% +a field such kind of five Fields okay +and for example example is the + + align:start position:0% +and for example example is the + + + align:start position:0% +and for example example is the +m you have Electric magnetic field okay + + align:start position:0% +m you have Electric magnetic field okay + + + align:start position:0% +m you have Electric magnetic field okay +and uh uh you know the max whe equations + + align:start position:0% +and uh uh you know the max whe equations + + + align:start position:0% +and uh uh you know the max whe equations +you can solve the Marx equations + + align:start position:0% +you can solve the Marx equations + + + align:start position:0% +you can solve the Marx equations +and so let's defines the classical field + + align:start position:0% +and so let's defines the classical field + + + align:start position:0% +and so let's defines the classical field +the and uh and then then we will tell + + align:start position:0% +the and uh and then then we will tell + + + align:start position:0% +the and uh and then then we will tell +you how to actually quantize such a + + align:start position:0% +you how to actually quantize such a + + + align:start position:0% +you how to actually quantize such a +system to understand electric field and + + align:start position:0% +system to understand electric field and + + + align:start position:0% +system to understand electric field and +magnetic field quantum + + align:start position:0% + + + + align:start position:0% + +mechanical good and uh and that actually + + align:start position:0% +mechanical good and uh and that actually + + + align:start position:0% +mechanical good and uh and that actually +would be the our goal okay so we will + + align:start position:0% +would be the our goal okay so we will + + + align:start position:0% +would be the our goal okay so we will +start the simplest field Theory just the + + align:start position:0% +start the simplest field Theory just the + + + align:start position:0% +start the simplest field Theory just the +Scala field the and then we go to the uh + + align:start position:0% +Scala field the and then we go to the uh + + + align:start position:0% +Scala field the and then we go to the uh +the rock theory which describes the + + align:start position:0% +the rock theory which describes the + + + align:start position:0% +the rock theory which describes the +electron and then eventually we will go + + align:start position:0% +electron and then eventually we will go + + + align:start position:0% +electron and then eventually we will go +to the theory which describe the + + align:start position:0% +to the theory which describe the + + + align:start position:0% +to the theory which describe the +electromagnetic field so this is called + + align:start position:0% +electromagnetic field so this is called + + + align:start position:0% +electromagnetic field so this is called +QED okay Quantum Electro Dynamics so + + align:start position:0% +QED okay Quantum Electro Dynamics so + + + align:start position:0% +QED okay Quantum Electro Dynamics so +that will be the end point of of this + + align:start position:0% +that will be the end point of of this + + + align:start position:0% +that will be the end point of of this +course + + align:start position:0% +course + + + align:start position:0% +course +um okay so so + + align:start position:0% + + + + align:start position:0% + +now let's say a little bit how we go to + + align:start position:0% +now let's say a little bit how we go to + + + align:start position:0% +now let's say a little bit how we go to +this classical field Theory to to + + align:start position:0% +this classical field Theory to to + + + align:start position:0% +this classical field Theory to to +Quantum field the okay so so some just + + align:start position:0% +Quantum field the okay so so some just + + + align:start position:0% +Quantum field the okay so so some just +some general remarks so before doing + + align:start position:0% +some general remarks so before doing + + + align:start position:0% +some general remarks so before doing +that let's think a little bit how we go + + align:start position:0% +that let's think a little bit how we go + + + align:start position:0% +that let's think a little bit how we go +to from classical mechanics which a + + align:start position:0% +to from classical mechanics which a + + + align:start position:0% +to from classical mechanics which a +small number how how you go to Quantum + + align:start position:0% +small number how how you go to Quantum + + + align:start position:0% +small number how how you go to Quantum +Mechanics okay so + + align:start position:0% +Mechanics okay so + + + align:start position:0% +Mechanics okay so +um so so let's + + align:start position:0% + + + + align:start position:0% + +recall So In classical + + align:start position:0% + + + + align:start position:0% + +mechanics so let's just consider the + + align:start position:0% +mechanics so let's just consider the + + + align:start position:0% +mechanics so let's just consider the +simplest you just have a single deg + + align:start position:0% +simplest you just have a single deg + + + align:start position:0% +simplest you just have a single deg +Freedom say + + align:start position:0% +Freedom say + + + align:start position:0% +Freedom say +XT okay just one dimensional particle + + align:start position:0% +XT okay just one dimensional particle + + + align:start position:0% +XT okay just one dimensional particle +whose motion just describe the + + align:start position:0% +whose motion just describe the + + + align:start position:0% +whose motion just describe the +XT and then and then then of course the + + align:start position:0% +XT and then and then then of course the + + + align:start position:0% +XT and then and then then of course the +goal of classical mechanic is just to + + align:start position:0% +goal of classical mechanic is just to + + + align:start position:0% +goal of classical mechanic is just to +solve the equation motion over XT okay + + align:start position:0% +solve the equation motion over XT okay + + + align:start position:0% +solve the equation motion over XT okay +so if I write down the equation for XT + + align:start position:0% +so if I write down the equation for XT + + + align:start position:0% +so if I write down the equation for XT +and I solve it then I'm done okay I'm + + align:start position:0% +and I solve it then I'm done okay I'm + + + align:start position:0% +and I solve it then I'm done okay I'm +done uh uh uh I solve the classical + + align:start position:0% +done uh uh uh I solve the classical + + + align:start position:0% +done uh uh uh I solve the classical +mechanics so when we go to quantum + + align:start position:0% + + + + align:start position:0% + +mechanics what you do so this XT then + + align:start position:0% +mechanics what you do so this XT then + + + align:start position:0% +mechanics what you do so this XT then +become + + align:start position:0% + + + + align:start position:0% + +operator okay so become an operator so + + align:start position:0% +operator okay so become an operator so + + + align:start position:0% +operator okay so become an operator so +the classical dynamical variable now + + align:start position:0% +the classical dynamical variable now + + + align:start position:0% +the classical dynamical variable now +become a Quantum + + align:start position:0% +become a Quantum + + + align:start position:0% +become a Quantum +operator and the equation motion of XT + + align:start position:0% +operator and the equation motion of XT + + + align:start position:0% +operator and the equation motion of XT +if you + + align:start position:0% +if you + + + align:start position:0% +if you +remember then do you remember what it + + align:start position:0% + + + + align:start position:0% + +becomes + + align:start position:0% + + + + align:start position:0% + +yeah exactly become the Heisenberg + + align:start position:0% + + + + align:start position:0% + +equation so become a Heisenberg + + align:start position:0% + + + + align:start position:0% + +equation for XT for this operate XT now + + align:start position:0% +equation for XT for this operate XT now + + + align:start position:0% +equation for XT for this operate XT now +okay yeah so so in quantum mechanics + + align:start position:0% +okay yeah so so in quantum mechanics + + + align:start position:0% +okay yeah so so in quantum mechanics +there are two no normally two way to + + align:start position:0% +there are two no normally two way to + + + align:start position:0% +there are two no normally two way to +describe it so first is the shinger + + align:start position:0% +describe it so first is the shinger + + + align:start position:0% +describe it so first is the shinger +picture + + align:start position:0% + + + + align:start position:0% + +in this case you have a wave equ uh you + + align:start position:0% +in this case you have a wave equ uh you + + + align:start position:0% +in this case you have a wave equ uh you +have a wave + + align:start position:0% + + + + align:start position:0% + +function which is function of x and t + + align:start position:0% +function which is function of x and t + + + align:start position:0% +function which is function of x and t +and then you have operator which is X + + align:start position:0% +and then you have operator which is X + + + align:start position:0% +and then you have operator which is X +okay and then of course you also have + + align:start position:0% +okay and then of course you also have + + + align:start position:0% +okay and then of course you also have +conjugate + + align:start position:0% +conjugate + + + align:start position:0% +conjugate +momentum sat which is defined to be a x + + align:start position:0% +momentum sat which is defined to be a x + + + align:start position:0% +momentum sat which is defined to be a x +dot + + align:start position:0% +dot + + + align:start position:0% +dot +okay and so so the wave function + + align:start position:0% +okay and so so the wave function + + + align:start position:0% +okay and so so the wave function +is a function of Theon values + + align:start position:0% +is a function of Theon values + + + align:start position:0% +is a function of Theon values +of so X here should be understood as + + align:start position:0% +of so X here should be understood as + + + align:start position:0% +of so X here should be understood as +agon + + align:start position:0% +agon + + + align:start position:0% +agon +values of this operator X hat + + align:start position:0% +values of this operator X hat + + + align:start position:0% +values of this operator X hat +okay is Theon value of x hat so in the + + align:start position:0% +okay is Theon value of x hat so in the + + + align:start position:0% +okay is Theon value of x hat so in the +Shing a picture you solve the Evolution + + align:start position:0% +Shing a picture you solve the Evolution + + + align:start position:0% +Shing a picture you solve the Evolution +for for p you solve the equation for + + align:start position:0% +for for p you solve the equation for + + + align:start position:0% +for for p you solve the equation for +p and once you find P you can calculate + + align:start position:0% +p and once you find P you can calculate + + + align:start position:0% +p and once you find P you can calculate +any quantities you want okay you can + + align:start position:0% +any quantities you want okay you can + + + align:start position:0% +any quantities you want okay you can +calculate any expectation + + align:start position:0% +calculate any expectation + + + align:start position:0% +calculate any expectation +values any amplitude EXC but the second + + align:start position:0% +values any amplitude EXC but the second + + + align:start position:0% +values any amplitude EXC but the second +way of approach it is the Heisenberg + + align:start position:0% + + + + align:start position:0% + +picture in in this case + + align:start position:0% +picture in in this case + + + align:start position:0% +picture in in this case +you the the dynamical quantity is your + + align:start position:0% +you the the dynamical quantity is your + + + align:start position:0% +you the the dynamical quantity is your +operator now you assume the operator + + align:start position:0% +operator now you assume the operator + + + align:start position:0% +operator now you assume the operator +depend on time so in the shorting of + + align:start position:0% +depend on time so in the shorting of + + + align:start position:0% +depend on time so in the shorting of +picture your X is just some constant + + align:start position:0% +picture your X is just some constant + + + align:start position:0% +picture your X is just some constant +does not depend on time but in the + + align:start position:0% +does not depend on time but in the + + + align:start position:0% +does not depend on time but in the +Heisenberg picture now now your operator + + align:start position:0% +Heisenberg picture now now your operator + + + align:start position:0% +Heisenberg picture now now your operator +now become time + + align:start position:0% +now become time + + + align:start position:0% +now become time +dependent okay and the equation motion + + align:start position:0% +dependent okay and the equation motion + + + align:start position:0% +dependent okay and the equation motion +and and you solve the Heisenberg + + align:start position:0% +and and you solve the Heisenberg + + + align:start position:0% +and and you solve the Heisenberg +equation okay and then the state is in + + align:start position:0% +equation okay and then the state is in + + + align:start position:0% +equation okay and then the state is in +warrant okay state does not evolve is + + align:start position:0% +warrant okay state does not evolve is + + + align:start position:0% +warrant okay state does not evolve is +time + + align:start position:0% +time + + + align:start position:0% +time +okay so so you solve the Heisenberg + + align:start position:0% +okay so so you solve the Heisenberg + + + align:start position:0% +okay so so you solve the Heisenberg +equation for those operators and once + + align:start position:0% +equation for those operators and once + + + align:start position:0% +equation for those operators and once +you solve the Heisenberg equation and + + align:start position:0% +you solve the Heisenberg equation and + + + align:start position:0% +you solve the Heisenberg equation and +then you can evaluate again your your + + align:start position:0% +then you can evaluate again your your + + + align:start position:0% +then you can evaluate again your your +expectation value in any states you're + + align:start position:0% +expectation value in any states you're + + + align:start position:0% +expectation value in any states you're +interested + + align:start position:0% +interested + + + align:start position:0% +interested +ex + + align:start position:0% +ex + + + align:start position:0% +ex +okay so any questions on this so this is + + align:start position:0% +okay so any questions on this so this is + + + align:start position:0% +okay so any questions on this so this is +a very quick review what you did to go + + align:start position:0% +a very quick review what you did to go + + + align:start position:0% +a very quick review what you did to go +from classical mechanics to Quantum + + align:start position:0% +from classical mechanics to Quantum + + + align:start position:0% +from classical mechanics to Quantum +Mechanics okay so now in field + + align:start position:0% + + + + align:start position:0% + +Theory okay in fi the we do the same + + align:start position:0% +Theory okay in fi the we do the same + + + align:start position:0% +Theory okay in fi the we do the same +similar + + align:start position:0% +similar + + + align:start position:0% +similar +thing the + + align:start position:0% + + + + align:start position:0% + +similarly in field + + align:start position:0% +similarly in field + + + align:start position:0% +similarly in field +series we have + + align:start position:0% +series we have + + + align:start position:0% +series we have +classical + + align:start position:0% +classical + + + align:start position:0% +classical +Fields okay we have classical + + align:start position:0% +Fields okay we have classical + + + align:start position:0% +Fields okay we have classical +fields and then when you go to + + align:start position:0% + + + + align:start position:0% + +Quantum this become Quantum + + align:start position:0% + + + + align:start position:0% + +operators okay so this is now Quantum + + align:start position:0% +operators okay so this is now Quantum + + + align:start position:0% +operators okay so this is now Quantum +operators remember in field the this x + + align:start position:0% +operators remember in field the this x + + + align:start position:0% +operators remember in field the this x +is always just labels of the space Point + + align:start position:0% +is always just labels of the space Point + + + align:start position:0% +is always just labels of the space Point +okay uh it's not a dynamical war iable + + align:start position:0% +okay uh it's not a dynamical war iable + + + align:start position:0% +okay uh it's not a dynamical war iable +okay the rotation is a little + + align:start position:0% +okay the rotation is a little + + + align:start position:0% +okay the rotation is a little +bit Yeah here the In classical mechanic + + align:start position:0% +bit Yeah here the In classical mechanic + + + align:start position:0% +bit Yeah here the In classical mechanic +this is dynamic variable but in field + + align:start position:0% +this is dynamic variable but in field + + + align:start position:0% +this is dynamic variable but in field +Series this is just labels okay so so + + align:start position:0% +Series this is just labels okay so so + + + align:start position:0% +Series this is just labels okay so so +they're not dynamic dynamic variable F + + align:start position:0% +they're not dynamic dynamic variable F + + + align:start position:0% +they're not dynamic dynamic variable F +itself so so F become an operator + + align:start position:0% +itself so so F become an operator + + + align:start position:0% +itself so so F become an operator +okay and then now the classical equation + + align:start position:0% +okay and then now the classical equation + + + align:start position:0% +okay and then now the classical equation +motion + + align:start position:0% + + + + align:start position:0% + +for of five which be derived and then + + align:start position:0% +for of five which be derived and then + + + align:start position:0% +for of five which be derived and then +become the Heisenberg equation + + align:start position:0% + + + + align:start position:0% + +F hat okay for f + + align:start position:0% +F hat okay for f + + + align:start position:0% +F hat okay for f +hat so so again here you + + align:start position:0% +hat so so again here you + + + align:start position:0% +hat so so again here you +can do two picture you can do the + + align:start position:0% +can do two picture you can do the + + + align:start position:0% +can do two picture you can do the +shorting of picture you can do a + + align:start position:0% +shorting of picture you can do a + + + align:start position:0% +shorting of picture you can do a +Heisenberg + + align:start position:0% + + + + align:start position:0% + +picture so so for + + align:start position:0% + + + + align:start position:0% + +qft the shorting of + + align:start position:0% +qft the shorting of + + + align:start position:0% +qft the shorting of +picture again you look at the wave + + align:start position:0% +picture again you look at the wave + + + align:start position:0% +picture again you look at the wave +functions of your dynamical + + align:start position:0% +functions of your dynamical + + + align:start position:0% +functions of your dynamical +variables the ion value of dyal + + align:start position:0% + + + + align:start position:0% + +variables so so what's the generation of + + align:start position:0% +variables so so what's the generation of + + + align:start position:0% +variables so so what's the generation of +this P + + align:start position:0% +this P + + + align:start position:0% +this P +XT so remember here p is a function of + + align:start position:0% +XT so remember here p is a function of + + + align:start position:0% +XT so remember here p is a function of +agon + + align:start position:0% +agon + + + align:start position:0% +agon +value of your dynamical variables + + align:start position:0% +value of your dynamical variables + + + align:start position:0% +value of your dynamical variables +okay so now if we push this analog first + + align:start position:0% +okay so now if we push this analog first + + + align:start position:0% +okay so now if we push this analog first +when you go to Quantum field Ser in the + + align:start position:0% +when you go to Quantum field Ser in the + + + align:start position:0% +when you go to Quantum field Ser in the +Shing a picture now the wave + + align:start position:0% +Shing a picture now the wave + + + align:start position:0% +Shing a picture now the wave +function should + + align:start position:0% +function should + + + align:start position:0% +function should +be a function of + + align:start position:0% +be a function of + + + align:start position:0% +be a function of +5x and a + + align:start position:0% +5x and a + + + align:start position:0% +5x and a +t Okay so this + + align:start position:0% +t Okay so this + + + align:start position:0% +t Okay so this +5x are addon + + align:start position:0% + + + + align:start position:0% + +values of f hat + + align:start position:0% +values of f hat + + + align:start position:0% +values of f hat +X okay so so in the shorting of picture + + align:start position:0% +X okay so so in the shorting of picture + + + align:start position:0% +X okay so so in the shorting of picture +F hat does not evolve this + + align:start position:0% +F hat does not evolve this + + + align:start position:0% +F hat does not evolve this +time and uh and so you have the wave + + align:start position:0% +time and uh and so you have the wave + + + align:start position:0% +time and uh and so you have the wave +function which is the + + align:start position:0% +function which is the + + + align:start position:0% +function which is the +function uh now become a functional bit + + align:start position:0% +function uh now become a functional bit + + + align:start position:0% +function uh now become a functional bit +because this itself is a function of + + align:start position:0% +because this itself is a function of + + + align:start position:0% +because this itself is a function of +space okay + + align:start position:0% +space okay + + + align:start position:0% +space okay +and + + align:start position:0% +and + + + align:start position:0% +and +yeah and you solve the shorting equation + + align:start position:0% +yeah and you solve the shorting equation + + + align:start position:0% +yeah and you solve the shorting equation +for this and then you have the uh uh the + + align:start position:0% + + + + align:start position:0% + +operator and then you have the operator + + align:start position:0% +operator and then you have the operator + + + align:start position:0% +operator and then you have the operator +yeah and so you have and the dynamic and + + align:start position:0% +yeah and so you have and the dynamic and + + + align:start position:0% +yeah and so you have and the dynamic and +then you have operator five + + align:start position:0% +then you have operator five + + + align:start position:0% +then you have operator five +x okay so so that's what you do in the + + align:start position:0% +x okay so so that's what you do in the + + + align:start position:0% +x okay so so that's what you do in the +shinger + + align:start position:0% +shinger + + + align:start position:0% +shinger +picture in the shinger + + align:start position:0% +picture in the shinger + + + align:start position:0% +picture in the shinger +picture and in the Heisenberg + + align:start position:0% + + + + align:start position:0% + +picture if you forget about the wave + + align:start position:0% +picture if you forget about the wave + + + align:start position:0% +picture if you forget about the wave +function okay you look at the evolution + + align:start position:0% +function okay you look at the evolution + + + align:start position:0% +function okay you look at the evolution +of + + align:start position:0% +of + + + align:start position:0% +of +[Applause] + + align:start position:0% + + + + align:start position:0% + +operators + + align:start position:0% + + + + align:start position:0% + +so so the Heisenberg for the field + + align:start position:0% + + + + align:start position:0% + +the yeah Heisenberg picture for the + + align:start position:0% +the yeah Heisenberg picture for the + + + align:start position:0% +the yeah Heisenberg picture for the +field + + align:start position:0% +field + + + align:start position:0% +field +three is that you look at the + + align:start position:0% +three is that you look at the + + + align:start position:0% +three is that you look at the +evolution of x and T so now this just + + align:start position:0% +evolution of x and T so now this just + + + align:start position:0% +evolution of x and T so now this just +obeys the Heisenberg equations which is + + align:start position:0% +obeys the Heisenberg equations which is + + + align:start position:0% +obeys the Heisenberg equations which is +just is the classic just the quantum + + align:start position:0% +just is the classic just the quantum + + + align:start position:0% +just is the classic just the quantum +version of the classical equation for + + align:start position:0% +version of the classical equation for + + + align:start position:0% +version of the classical equation for +five so you have the high you look at + + align:start position:0% +five so you have the high you look at + + + align:start position:0% +five so you have the high you look at +the evolution of this and then the state + + align:start position:0% +the evolution of this and then the state + + + align:start position:0% +the evolution of this and then the state +does not change with time okay the state + + align:start position:0% +does not change with time okay the state + + + align:start position:0% +does not change with time okay the state +does not change each + + align:start position:0% + + + + align:start position:0% + +time good any questions on + + align:start position:0% + + + + align:start position:0% + +this + + align:start position:0% + + + + align:start position:0% + +yes + + align:start position:0% + + + + align:start position:0% + +yeah so in the sh of picture so remember + + align:start position:0% +yeah so in the sh of picture so remember + + + align:start position:0% +yeah so in the sh of picture so remember +the X X is a label of for + + align:start position:0% +the X X is a label of for + + + align:start position:0% +the X X is a label of for +five but time is it's Evolution but in + + align:start position:0% +five but time is it's Evolution but in + + + align:start position:0% +five but time is it's Evolution but in +the shorting of picture the operator + + align:start position:0% +the shorting of picture the operator + + + align:start position:0% +the shorting of picture the operator +don't evolve and so there's no time here + + align:start position:0% +don't evolve and so there's no time here + + + align:start position:0% +don't evolve and so there's no time here +so we don't have time here and we just + + align:start position:0% +so we don't have time here and we just + + + align:start position:0% +so we don't have time here and we just +have the just the analog of the X here + + align:start position:0% +have the just the analog of the X here + + + align:start position:0% +have the just the analog of the X here +in the Shing a picture uh for the uh for + + align:start position:0% +in the Shing a picture uh for the uh for + + + align:start position:0% +in the Shing a picture uh for the uh for +the classical yeah yeah for quantum + + align:start position:0% +the classical yeah yeah for quantum + + + align:start position:0% +the classical yeah yeah for quantum +mechanics and then and then the and then + + align:start position:0% +mechanics and then and then the and then + + + align:start position:0% +mechanics and then and then the and then +the time dependence is in your wave + + align:start position:0% +the time dependence is in your wave + + + align:start position:0% +the time dependence is in your wave +function so the wave function is a + + align:start position:0% +function so the wave function is a + + + align:start position:0% +function so the wave function is a +function of possible values ion values + + align:start position:0% +function of possible values ion values + + + align:start position:0% +function of possible values ion values +of + + align:start position:0% +of + + + align:start position:0% +of +this operat + + align:start position:0% + + + + align:start position:0% + +file okay and then the Heisenberg pure + + align:start position:0% +file okay and then the Heisenberg pure + + + align:start position:0% +file okay and then the Heisenberg pure +again then you just focus on the Opera + + align:start position:0% +again then you just focus on the Opera + + + align:start position:0% +again then you just focus on the Opera +equations and once you solve the Opera + + align:start position:0% +equations and once you solve the Opera + + + align:start position:0% +equations and once you solve the Opera +equations and then and then you can + + align:start position:0% +equations and then and then you can + + + align:start position:0% +equations and then and then you can +calculate the say expectation values in + + align:start position:0% +calculate the say expectation values in + + + align:start position:0% +calculate the say expectation values in +any state you want + + align:start position:0% +any state you want + + + align:start position:0% +any state you want +okay so now you can already maybe see a + + align:start position:0% +okay so now you can already maybe see a + + + align:start position:0% +okay so now you can already maybe see a +difference a little bit so if you do the + + align:start position:0% +difference a little bit so if you do the + + + align:start position:0% +difference a little bit so if you do the +shorting a + + align:start position:0% +shorting a + + + align:start position:0% +shorting a +picture you have to deal with this pie + + align:start position:0% +picture you have to deal with this pie + + + align:start position:0% +picture you have to deal with this pie +okay which is the wave functional of all + + align:start position:0% +okay which is the wave functional of all + + + align:start position:0% +okay which is the wave functional of all +possible values of some function in + + align:start position:0% +possible values of some function in + + + align:start position:0% +possible values of some function in +space okay and if you have multiple + + align:start position:0% +space okay and if you have multiple + + + align:start position:0% +space okay and if you have multiple +field then this is a hugely complicated + + align:start position:0% +field then this is a hugely complicated + + + align:start position:0% +field then this is a hugely complicated +thing and you need to write down the + + align:start position:0% +thing and you need to write down the + + + align:start position:0% +thing and you need to write down the +Shoring equation for it Etc okay but + + align:start position:0% +Shoring equation for it Etc okay but + + + align:start position:0% +Shoring equation for it Etc okay but +here but in the Heisenberg picture we + + align:start position:0% +here but in the Heisenberg picture we + + + align:start position:0% +here but in the Heisenberg picture we +just + + align:start position:0% +just + + + align:start position:0% +just +solve the analog of the classical + + align:start position:0% +solve the analog of the classical + + + align:start position:0% +solve the analog of the classical +equation motion which we have already + + align:start position:0% +equation motion which we have already + + + align:start position:0% +equation motion which we have already +written down and it just now interpreted + + align:start position:0% +written down and it just now interpreted + + + align:start position:0% +written down and it just now interpreted +as a Quantum operator equation so which + + align:start position:0% +as a Quantum operator equation so which + + + align:start position:0% +as a Quantum operator equation so which +one you think it's + + align:start position:0% + + + + align:start position:0% + +simpler so so so that's why in Quantum + + align:start position:0% +simpler so so so that's why in Quantum + + + align:start position:0% +simpler so so so that's why in Quantum +filter we almost always use Heisenberg + + align:start position:0% +filter we almost always use Heisenberg + + + align:start position:0% +filter we almost always use Heisenberg +picture okay we always use Heisenberg + + align:start position:0% +picture okay we always use Heisenberg + + + align:start position:0% +picture okay we always use Heisenberg +picture and uh and we don't even uh + + align:start position:0% +picture and uh and we don't even uh + + + align:start position:0% +picture and uh and we don't even uh +rarely think about the wave function but + + align:start position:0% +rarely think about the wave function but + + + align:start position:0% +rarely think about the wave function but +even though sometimes this can be useful + + align:start position:0% +even though sometimes this can be useful + + + align:start position:0% +even though sometimes this can be useful +in in some problems but for the most of + + align:start position:0% +in in some problems but for the most of + + + align:start position:0% +in in some problems but for the most of +the time this is much easier okay so + + align:start position:0% +the time this is much easier okay so + + + align:start position:0% +the time this is much easier okay so +that's what we are going to do okay and + + align:start position:0% +that's what we are going to do okay and + + + align:start position:0% +that's what we are going to do okay and +so in Quantum field we will just use the + + align:start position:0% +so in Quantum field we will just use the + + + align:start position:0% +so in Quantum field we will just use the +Heisenberg picture almost all the time + + align:start position:0% +Heisenberg picture almost all the time + + + align:start position:0% +Heisenberg picture almost all the time +okay from now on I will not talk about + + align:start position:0% +okay from now on I will not talk about + + + align:start position:0% +okay from now on I will not talk about +shorting a picture + + align:start position:0% + + + + align:start position:0% + +okay good so so it's very important you + + align:start position:0% +okay good so so it's very important you + + + align:start position:0% +okay good so so it's very important you +remind + + align:start position:0% +remind + + + align:start position:0% +remind +yourself about quantum mechanics in the + + align:start position:0% +yourself about quantum mechanics in the + + + align:start position:0% +yourself about quantum mechanics in the +Heisenberg picture okay okay and because + + align:start position:0% +Heisenberg picture okay okay and because + + + align:start position:0% +Heisenberg picture okay okay and because +most of the quantum mechanical uh + + align:start position:0% +most of the quantum mechanical uh + + + align:start position:0% +most of the quantum mechanical uh +classes before maybe it's all in the + + align:start position:0% +classes before maybe it's all in the + + + align:start position:0% +classes before maybe it's all in the +Shing a picture solving the wave uh + + align:start position:0% +Shing a picture solving the wave uh + + + align:start position:0% +Shing a picture solving the wave uh +solving the shinger equations Etc but + + align:start position:0% +solving the shinger equations Etc but + + + align:start position:0% +solving the shinger equations Etc but +now you have to change the perspective + + align:start position:0% +now you have to change the perspective + + + align:start position:0% +now you have to change the perspective +to think everything in terms of the + + align:start position:0% +to think everything in terms of the + + + align:start position:0% +to think everything in terms of the +Heisenberg picture and then that will + + align:start position:0% +Heisenberg picture and then that will + + + align:start position:0% +Heisenberg picture and then that will +make you then in Quantum fil much easier + + align:start position:0% + + + + align:start position:0% + +okay good any questions on + + align:start position:0% +okay good any questions on + + + align:start position:0% +okay good any questions on +this + + align:start position:0% + + + + align:start position:0% + +yes so in the Heisenberg picture if + + align:start position:0% +yes so in the Heisenberg picture if + + + align:start position:0% +yes so in the Heisenberg picture if +we're not concerned about the wave + + align:start position:0% +we're not concerned about the wave + + + align:start position:0% +we're not concerned about the wave +function and all then how how do we + + align:start position:0% +function and all then how how do we + + + align:start position:0% +function and all then how how do we +determine like for example the + + align:start position:0% +determine like for example the + + + align:start position:0% +determine like for example the +probability or the expectation value of + + align:start position:0% +probability or the expectation value of + + + align:start position:0% +probability or the expectation value of +where X is at some point the momentum + + align:start position:0% +where X is at some point the momentum + + + align:start position:0% +where X is at some point the momentum +good good good that's a very good + + align:start position:0% +good good good that's a very good + + + align:start position:0% +good good good that's a very good +question so so this is actually also + + align:start position:0% +question so so this is actually also + + + align:start position:0% +question so so this is actually also +related to the kind of + + align:start position:0% +related to the kind of + + + align:start position:0% +related to the kind of +kind of questions we want to solve in in + + align:start position:0% +kind of questions we want to solve in in + + + align:start position:0% +kind of questions we want to solve in in +Quantum field Theory so in Quantum field + + align:start position:0% +Quantum field Theory so in Quantum field + + + align:start position:0% +Quantum field Theory so in Quantum field +Theory we often work with the vacuum + + align:start position:0% +Theory we often work with the vacuum + + + align:start position:0% +Theory we often work with the vacuum +state so so for example uh + + align:start position:0% +state so so for example uh + + + align:start position:0% +state so so for example uh +here yeah so when you consider the QED + + align:start position:0% +here yeah so when you consider the QED + + + align:start position:0% +here yeah so when you consider the QED +most of the + + align:start position:0% +most of the + + + align:start position:0% +most of the +time in the in the quantum electrical + + align:start position:0% +time in the in the quantum electrical + + + align:start position:0% +time in the in the quantum electrical +magnetic field they in the vacuum State + + align:start position:0% +magnetic field they in the vacuum State + + + align:start position:0% +magnetic field they in the vacuum State +and so so so we just consider the in the + + align:start position:0% +and so so so we just consider the in the + + + align:start position:0% +and so so so we just consider the in the +vacuum State and so we don't have to + + align:start position:0% +vacuum State and so we don't have to + + + align:start position:0% +vacuum State and so we don't have to +consider yeah right yeah s in Quant they + + align:start position:0% +consider yeah right yeah s in Quant they + + + align:start position:0% +consider yeah right yeah s in Quant they +preferred States we are interested + + align:start position:0% + + + + align:start position:0% + +in that's a lot of Reason uh that the + + align:start position:0% +in that's a lot of Reason uh that the + + + align:start position:0% +in that's a lot of Reason uh that the +Heisenberg picture is convenient yeah + + align:start position:0% +Heisenberg picture is convenient yeah + + + align:start position:0% +Heisenberg picture is convenient yeah +you don't have to consider General State + + align:start position:0% +you don't have to consider General State + + + align:start position:0% +you don't have to consider General State +in general + + align:start position:0% + + + + align:start position:0% + +yes sorry what is a phical meaning of oh + + align:start position:0% +yes sorry what is a phical meaning of oh + + + align:start position:0% +yes sorry what is a phical meaning of oh +oh this is just some State you + + align:start position:0% +oh this is just some State you + + + align:start position:0% +oh this is just some State you +interested in see you have a h space but + + align:start position:0% +interested in see you have a h space but + + + align:start position:0% +interested in see you have a h space but +now you just don't when you study the + + align:start position:0% +now you just don't when you study the + + + align:start position:0% +now you just don't when you study the +evolution you you only evolve operator + + align:start position:0% +evolution you you only evolve operator + + + align:start position:0% +evolution you you only evolve operator +don't Evol States yeah that so that's + + align:start position:0% +don't Evol States yeah that so that's + + + align:start position:0% +don't Evol States yeah that so that's +the difference between the Shing + + align:start position:0% +the difference between the Shing + + + align:start position:0% +the difference between the Shing +and for + + align:start position:0% + + + + align:start position:0% + +example values of some operators with + + align:start position:0% +example values of some operators with + + + align:start position:0% +example values of some operators with +respect and we get like like + + align:start position:0% +respect and we get like like + + + align:start position:0% +respect and we get like like +measurements result and + + align:start position:0% +measurements result and + + + align:start position:0% +measurements result and +stff yeah it's the same thing yeah same + + align:start position:0% +stff yeah it's the same thing yeah same + + + align:start position:0% +stff yeah it's the same thing yeah same +thing yeah at this level there's no + + align:start position:0% +thing yeah at this level there's no + + + align:start position:0% +thing yeah at this level there's no +difference between Quantum fil and + + align:start position:0% +difference between Quantum fil and + + + align:start position:0% +difference between Quantum fil and +quantum mechanics yeah just think about + + align:start position:0% +quantum mechanics yeah just think about + + + align:start position:0% +quantum mechanics yeah just think about +quantum mechanics in terms of Heisenberg + + align:start position:0% +quantum mechanics in terms of Heisenberg + + + align:start position:0% +quantum mechanics in terms of Heisenberg +picture translate everything you learn + + align:start position:0% +picture translate everything you learn + + + align:start position:0% +picture translate everything you learn +about the Shoring or Evolution Etc in + + align:start position:0% +about the Shoring or Evolution Etc in + + + align:start position:0% +about the Shoring or Evolution Etc in +terms of Pyon BG + + align:start position:0% +terms of Pyon BG + + + align:start position:0% +terms of Pyon BG +picture + + align:start position:0% + + + + align:start position:0% + +yes yeah that's right that's right yeah + + align:start position:0% +yes yeah that's right that's right yeah + + + align:start position:0% +yes yeah that's right that's right yeah +yes the state we interested inally the + + align:start position:0% +yes the state we interested inally the + + + align:start position:0% +yes the state we interested inally the +vacuum State and like what what sorts of + + align:start position:0% +vacuum State and like what what sorts of + + + align:start position:0% +vacuum State and like what what sorts of +measurements yeah so + + align:start position:0% +measurements yeah so + + + align:start position:0% +measurements yeah so +it's a it's a again + + align:start position:0% +it's a it's a again + + + align:start position:0% +it's a it's a again +so yeah it's a very good question uh + + align:start position:0% +so yeah it's a very good question uh + + + align:start position:0% +so yeah it's a very good question uh +what I should have said is that what the + + align:start position:0% +what I should have said is that what the + + + align:start position:0% +what I should have said is that what the +state we are interested in are state + + align:start position:0% +state we are interested in are state + + + align:start position:0% +state we are interested in are state +which are close to the vacuum state so + + align:start position:0% +which are close to the vacuum state so + + + align:start position:0% +which are close to the vacuum state so +so so you excite the vacuum a little bit + + align:start position:0% +so so you excite the vacuum a little bit + + + align:start position:0% +so so you excite the vacuum a little bit +and uh yeah uh uh it's not yeah of + + align:start position:0% +and uh yeah uh uh it's not yeah of + + + align:start position:0% +and uh yeah uh uh it's not yeah of +course in the vacuum you don't have + + align:start position:0% +course in the vacuum you don't have + + + align:start position:0% +course in the vacuum you don't have +anything and we are since close to the + + align:start position:0% +anything and we are since close to the + + + align:start position:0% +anything and we are since close to the +vacuum State yeah and later when we + + align:start position:0% +vacuum State yeah and later when we + + + align:start position:0% +vacuum State yeah and later when we +discuss things you will see + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +good good + + align:start position:0% + + + + align:start position:0% + +okay so before going + + align:start position:0% + + + + align:start position:0% + +to Quantum field + + align:start position:0% + + + + align:start position:0% + +Theory let's also make some + + align:start position:0% +Theory let's also make some + + + align:start position:0% +Theory let's also make some +remarks have a short discussion on right + + align:start position:0% +remarks have a short discussion on right + + + align:start position:0% +remarks have a short discussion on right +visic quantum + + align:start position:0% +visic quantum + + + align:start position:0% +visic quantum +mechanics okay + + align:start position:0% + + + + align:start position:0% + +so so naively if you have special + + align:start position:0% + + + + align:start position:0% + +relativity plus quantum + + align:start position:0% +relativity plus quantum + + + align:start position:0% +relativity plus quantum +mechanics so if you want to generalize + + align:start position:0% +mechanics so if you want to generalize + + + align:start position:0% +mechanics so if you want to generalize +so most of quantum mechanics you learn + + align:start position:0% +so most of quantum mechanics you learn + + + align:start position:0% +so most of quantum mechanics you learn +is the long non relativistic quantum + + align:start position:0% +is the long non relativistic quantum + + + align:start position:0% +is the long non relativistic quantum +mechanics okay but now if you want to + + align:start position:0% +mechanics okay but now if you want to + + + align:start position:0% +mechanics okay but now if you want to +incorporate special you want to combine + + align:start position:0% +incorporate special you want to combine + + + align:start position:0% +incorporate special you want to combine +the special relativity with mechanics + + align:start position:0% +the special relativity with mechanics + + + align:start position:0% +the special relativity with mechanics +and then what should you + + align:start position:0% +and then what should you + + + align:start position:0% +and then what should you +get what do you think you should + + align:start position:0% + + + + align:start position:0% + +get + + align:start position:0% +get + + + align:start position:0% +get +H I + + align:start position:0% +H I + + + align:start position:0% +H I +expect yeah just just whatever come to + + align:start position:0% +expect yeah just just whatever come to + + + align:start position:0% +expect yeah just just whatever come to +your + + align:start position:0% +your + + + align:start position:0% +your +mind + + align:start position:0% + + + + align:start position:0% + +H that's the right + + align:start position:0% +H that's the right + + + align:start position:0% +H that's the right +answer that's the correct answer but but + + align:start position:0% +answer that's the correct answer but but + + + align:start position:0% +answer that's the correct answer but but +I was hoping some of you will say it's + + align:start position:0% +I was hoping some of you will say it's + + + align:start position:0% +I was hoping some of you will say it's +right this Quant + + align:start position:0% +right this Quant + + + align:start position:0% +right this Quant +mechanics + + align:start position:0% +mechanics + + + align:start position:0% +mechanics +okay so + + align:start position:0% + + + + align:start position:0% + +liely when you combine these two in + + align:start position:0% +liely when you combine these two in + + + align:start position:0% +liely when you combine these two in +particular if you read some old quantum + + align:start position:0% +particular if you read some old quantum + + + align:start position:0% +particular if you read some old quantum +mechanics books they do disc they do + + align:start position:0% +mechanics books they do disc they do + + + align:start position:0% +mechanics books they do disc they do +discuss ristic quantum mechanics okay so + + align:start position:0% +discuss ristic quantum mechanics okay so + + + align:start position:0% +discuss ristic quantum mechanics okay so +liity that's what you get okay when you + + align:start position:0% +liity that's what you get okay when you + + + align:start position:0% +liity that's what you get okay when you +combine these two and you say oh we just + + align:start position:0% +combine these two and you say oh we just + + + align:start position:0% +combine these two and you say oh we just +get WR V mechanics + + align:start position:0% +get WR V mechanics + + + align:start position:0% +get WR V mechanics +okay but that's actually not correct + + align:start position:0% +okay but that's actually not correct + + + align:start position:0% +okay but that's actually not correct +statement actually right strictly + + align:start position:0% +statement actually right strictly + + + align:start position:0% +statement actually right strictly +speaking the reason now you don't + + align:start position:0% +speaking the reason now you don't + + + align:start position:0% +speaking the reason now you don't +actually learn much about the right + + align:start position:0% +actually learn much about the right + + + align:start position:0% +actually learn much about the right +Quantum mechanic because strictly + + align:start position:0% +Quantum mechanic because strictly + + + align:start position:0% +Quantum mechanic because strictly +speaking right quantum mechanics does + + align:start position:0% +speaking right quantum mechanics does + + + align:start position:0% +speaking right quantum mechanics does +not exist okay and whenever if you want + + align:start position:0% +not exist okay and whenever if you want + + + align:start position:0% +not exist okay and whenever if you want +to combine quantum + + align:start position:0% +to combine quantum + + + align:start position:0% +to combine quantum +mechanics with special + + align:start position:0% +mechanics with special + + + align:start position:0% +mechanics with special +relativity actually you get the quantum + + align:start position:0% +relativity actually you get the quantum + + + align:start position:0% +relativity actually you get the quantum +F so the quantum f is actually forced on + + align:start position:0% +F so the quantum f is actually forced on + + + align:start position:0% +F so the quantum f is actually forced on +us if you want to unify spal relativity + + align:start position:0% +us if you want to unify spal relativity + + + align:start position:0% +us if you want to unify spal relativity +and mechanics okay and even even if you + + align:start position:0% +and mechanics okay and even even if you + + + align:start position:0% +and mechanics okay and even even if you +don't want to talk about Fields okay + + align:start position:0% +don't want to talk about Fields okay + + + align:start position:0% +don't want to talk about Fields okay +even if you don't want to talk about + + align:start position:0% +even if you don't want to talk about + + + align:start position:0% +even if you don't want to talk about +field if you just want to talk about + + align:start position:0% +field if you just want to talk about + + + align:start position:0% +field if you just want to talk about +particles still if you want to unify + + align:start position:0% +particles still if you want to unify + + + align:start position:0% +particles still if you want to unify +this two then you actually automatically + + align:start position:0% +this two then you actually automatically + + + align:start position:0% +this two then you actually automatically +Le to qu field three so now let me just + + align:start position:0% +Le to qu field three so now let me just + + + align:start position:0% +Le to qu field three so now let me just +explain why this is the case Okay so + + align:start position:0% +explain why this is the case Okay so + + + align:start position:0% +explain why this is the case Okay so +that the you have some uh better + + align:start position:0% +that the you have some uh better + + + align:start position:0% +that the you have some uh better +appreciation of the quantum fi + + align:start position:0% +appreciation of the quantum fi + + + align:start position:0% +appreciation of the quantum fi +stre good so so let's try to to apply + + align:start position:0% +stre good so so let's try to to apply + + + align:start position:0% +stre good so so let's try to to apply +what you did for for long ristic quantum + + align:start position:0% +what you did for for long ristic quantum + + + align:start position:0% +what you did for for long ristic quantum +mechanics try to generalize it to to + + align:start position:0% +mechanics try to generalize it to to + + + align:start position:0% +mechanics try to generalize it to to +derive some ristic quantum mechanics + + align:start position:0% +derive some ristic quantum mechanics + + + align:start position:0% +derive some ristic quantum mechanics +okay suppose you are the the people in + + align:start position:0% +okay suppose you are the the people in + + + align:start position:0% +okay suppose you are the the people in +the 1926 okay quantum mechanics just was + + align:start position:0% +the 1926 okay quantum mechanics just was + + + align:start position:0% +the 1926 okay quantum mechanics just was +discovered and you say all people have + + align:start position:0% +discovered and you say all people have + + + align:start position:0% +discovered and you say all people have +understood nortiv Quant mechanics now + + align:start position:0% +understood nortiv Quant mechanics now + + + align:start position:0% +understood nortiv Quant mechanics now +let's generalize to special + + align:start position:0% +let's generalize to special + + + align:start position:0% +let's generalize to special +relativity okay so so you narrativ + + align:start position:0% + + + + align:start position:0% + +istic + + align:start position:0% + + + + align:start position:0% + +mechanics how do we derive the shorting + + align:start position:0% +mechanics how do we derive the shorting + + + align:start position:0% +mechanics how do we derive the shorting +equation the way we do this is we + + align:start position:0% +equation the way we do this is we + + + align:start position:0% +equation the way we do this is we +start with a dispersion + + align:start position:0% +start with a dispersion + + + align:start position:0% +start with a dispersion +relation okay for long ristic + + align:start position:0% +relation okay for long ristic + + + align:start position:0% +relation okay for long ristic +particle and then we say this takes e to + + align:start position:0% +particle and then we say this takes e to + + + align:start position:0% +particle and then we say this takes e to +i paral + + align:start position:0% +i paral + + + align:start position:0% +i paral +t Okay P so say if you can have a vector + + align:start position:0% +t Okay P so say if you can have a vector + + + align:start position:0% +t Okay P so say if you can have a vector +become + + align:start position:0% +become + + + align:start position:0% +become +yeah so let me forget about H bar P then + + align:start position:0% +yeah so let me forget about H bar P then + + + align:start position:0% +yeah so let me forget about H bar P then +become special derivatives and then this + + align:start position:0% +become special derivatives and then this + + + align:start position:0% +become special derivatives and then this +equation just become the Shing equation + + align:start position:0% +equation just become the Shing equation + + + align:start position:0% +equation just become the Shing equation +for the three + + align:start position:0% + + + + align:start position:0% + +particles okay so this become the + + align:start position:0% +particles okay so this become the + + + align:start position:0% +particles okay so this become the +shorting equation for for fre long + + align:start position:0% +shorting equation for for fre long + + + align:start position:0% +shorting equation for for fre long +ristic part because then you can add the + + align:start position:0% +ristic part because then you can add the + + + align:start position:0% +ristic part because then you can add the +potential okay so that's how you derive + + align:start position:0% +potential okay so that's how you derive + + + align:start position:0% +potential okay so that's how you derive +you're shoting equation for long right + + align:start position:0% +you're shoting equation for long right + + + align:start position:0% +you're shoting equation for long right +bastic quantum + + align:start position:0% +bastic quantum + + + align:start position:0% +bastic quantum +mechanics so but if you are someone say + + align:start position:0% +mechanics so but if you are someone say + + + align:start position:0% +mechanics so but if you are someone say +uh in the early days of Quant mechanics + + align:start position:0% +uh in the early days of Quant mechanics + + + align:start position:0% +uh in the early days of Quant mechanics +say now let's try to generalize it to to + + align:start position:0% +say now let's try to generalize it to to + + + align:start position:0% +say now let's try to generalize it to to +special + + align:start position:0% +special + + + align:start position:0% +special +relativity and then it's easy to + + align:start position:0% +relativity and then it's easy to + + + align:start position:0% +relativity and then it's easy to +do then in the ristic + + align:start position:0% + + + + align:start position:0% + +case then you have we just start with + + align:start position:0% +case then you have we just start with + + + align:start position:0% +case then you have we just start with +relativistic a dispersion relation + + align:start position:0% + + + + align:start position:0% + +okay you say let's do the same + + align:start position:0% +okay you say let's do the same + + + align:start position:0% +okay you say let's do the same +thing okay let's do the same thing so + + align:start position:0% +thing okay let's do the same thing so + + + align:start position:0% +thing okay let's do the same thing so +this become I part T and this P become + + align:start position:0% +this become I part T and this P become + + + align:start position:0% +this become I part T and this P become +this one and then then we can just write + + align:start position:0% +this one and then then we can just write + + + align:start position:0% +this one and then then we can just write +this + + align:start position:0% + + + + align:start position:0% + +equation + + align:start position:0% +equation + + + align:start position:0% +equation +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so now let's combine this derivative + + align:start position:0% +so now let's combine this derivative + + + align:start position:0% +so now let's combine this derivative +together or put all this on the same + + align:start position:0% +together or put all this on the same + + + align:start position:0% +together or put all this on the same +side and then what you find is parti mu + + align:start position:0% +side and then what you find is parti mu + + + align:start position:0% +side and then what you find is parti mu +parti + + align:start position:0% + + + + align:start position:0% + +mu okay that's what you get so does this + + align:start position:0% +mu okay that's what you get so does this + + + align:start position:0% +mu okay that's what you get so does this +equation look + + align:start position:0% + + + + align:start position:0% + +familiar okay so this is the simplest + + align:start position:0% +familiar okay so this is the simplest + + + align:start position:0% +familiar okay so this is the simplest +Scala field theory equation motion we + + align:start position:0% +Scala field theory equation motion we + + + align:start position:0% +Scala field theory equation motion we +have written down but here the + + align:start position:0% +have written down but here the + + + align:start position:0% +have written down but here the +interpretation is very different okay so + + align:start position:0% +interpretation is very different okay so + + + align:start position:0% +interpretation is very different okay so +earlier we wrote down this equation we + + align:start position:0% +earlier we wrote down this equation we + + + align:start position:0% +earlier we wrote down this equation we +say this is cling golden + + align:start position:0% + + + + align:start position:0% + +equation this is the Cent golden + + align:start position:0% +equation this is the Cent golden + + + align:start position:0% +equation this is the Cent golden +equation okay so this is the equation + + align:start position:0% +equation okay so this is the equation + + + align:start position:0% +equation okay so this is the equation +motion for the simplest free field scal + + align:start position:0% +motion for the simplest free field scal + + + align:start position:0% +motion for the simplest free field scal +field we roll down before but here the + + align:start position:0% +field we roll down before but here the + + + align:start position:0% +field we roll down before but here the +interpretation is very + + align:start position:0% +interpretation is very + + + align:start position:0% +interpretation is very +different so remember the is not a field + + align:start position:0% +different so remember the is not a field + + + align:start position:0% +different so remember the is not a field +in Quantum mechanic it's a wave function + + align:start position:0% +in Quantum mechanic it's a wave function + + + align:start position:0% +in Quantum mechanic it's a wave function +for single particle sitting uh so so the + + align:start position:0% +for single particle sitting uh so so the + + + align:start position:0% +for single particle sitting uh so so the +is the amplitude for + + align:start position:0% + + + + align:start position:0% + +particle at special location X at time t + + align:start position:0% +particle at special location X at time t + + + align:start position:0% +particle at special location X at time t +Okay so this is and it's Square then its + + align:start position:0% +Okay so this is and it's Square then its + + + align:start position:0% +Okay so this is and it's Square then its +probability okay and this does not + + align:start position:0% +probability okay and this does not + + + align:start position:0% +probability okay and this does not +describe a field okay this is the wave + + align:start position:0% +describe a field okay this is the wave + + + align:start position:0% +describe a field okay this is the wave +function of a single particle okay even + + align:start position:0% +function of a single particle okay even + + + align:start position:0% +function of a single particle okay even +though they have the same equation as + + align:start position:0% +though they have the same equation as + + + align:start position:0% +though they have the same equation as +the field the we uh uh uh we wrote down + + align:start position:0% +the field the we uh uh uh we wrote down + + + align:start position:0% +the field the we uh uh uh we wrote down +earlier and + + align:start position:0% +earlier and + + + align:start position:0% +earlier and +so the so that's what client Gordon did + + align:start position:0% +so the so that's what client Gordon did + + + align:start position:0% +so the so that's what client Gordon did +okay so the client Gordon they tried to + + align:start position:0% +okay so the client Gordon they tried to + + + align:start position:0% +okay so the client Gordon they tried to +generalize long Bic Quant mechanics + + align:start position:0% +generalize long Bic Quant mechanics + + + align:start position:0% +generalize long Bic Quant mechanics +write this quantum mechanics then they + + align:start position:0% +write this quantum mechanics then they + + + align:start position:0% +write this quantum mechanics then they +wrote down this equation they say ah now + + align:start position:0% +wrote down this equation they say ah now + + + align:start position:0% +wrote down this equation they say ah now +we are Immortal okay because we wrote + + align:start position:0% +we are Immortal okay because we wrote + + + align:start position:0% +we are Immortal okay because we wrote +down the the first equation for for for + + align:start position:0% +down the the first equation for for for + + + align:start position:0% +down the the first equation for for for +for relativistic quantum + + align:start position:0% + + + + align:start position:0% + +mechanics and then then soon + + align:start position:0% +mechanics and then then soon + + + align:start position:0% +mechanics and then then soon +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +realize so realize actually this + + align:start position:0% +realize so realize actually this + + + align:start position:0% +realize so realize actually this +equation if you want to interpret it as + + align:start position:0% +equation if you want to interpret it as + + + align:start position:0% +equation if you want to interpret it as +a + + align:start position:0% +a + + + align:start position:0% +a +right equation for the wave + + align:start position:0% +right equation for the wave + + + align:start position:0% +right equation for the wave +function there actually lots of + + align:start position:0% +function there actually lots of + + + align:start position:0% +function there actually lots of +problems there one is problems yeah but + + align:start position:0% +problems there one is problems yeah but + + + align:start position:0% +problems there one is problems yeah but +by saying lot of it maybe it's a little + + align:start position:0% +by saying lot of it maybe it's a little + + + align:start position:0% +by saying lot of it maybe it's a little +accuration there there are various + + align:start position:0% +accuration there there are various + + + align:start position:0% +accuration there there are various +problems so + + align:start position:0% + + + + align:start position:0% + +um yeah so so some yeah let me call this + + align:start position:0% +um yeah so so some yeah let me call this + + + align:start position:0% +um yeah so so some yeah let me call this +equation I think I I have used up + + align:start position:0% +equation I think I I have used up + + + align:start position:0% +equation I think I I have used up +my my uh uh my stars I think to have a + + align:start position:0% +my my uh uh my stars I think to have a + + + align:start position:0% +my my uh uh my stars I think to have a +four star is a little bit too too much + + align:start position:0% +four star is a little bit too too much + + + align:start position:0% +four star is a little bit too too much +let's just call this equation one uh for + + align:start position:0% +let's just call this equation one uh for + + + align:start position:0% +let's just call this equation one uh for +this + + align:start position:0% +this + + + align:start position:0% +this +section so so some immediate + + align:start position:0% + + + + align:start position:0% + +difficulties + + align:start position:0% +difficulties + + + align:start position:0% +difficulties +of + + align:start position:0% + + + + align:start position:0% + +interpreting one as a wave equation + + align:start position:0% + + + + align:start position:0% + +okay as a wave + + align:start position:0% + + + + align:start position:0% + +equation for ristic + + align:start position:0% + + + + align:start position:0% + +particle yeah let me just save + + align:start position:0% +particle yeah let me just save + + + align:start position:0% +particle yeah let me just save +time okay so so this is the wave fation + + align:start position:0% +time okay so so this is the wave fation + + + align:start position:0% +time okay so so this is the wave fation +for long r buiness particle if you want + + align:start position:0% +for long r buiness particle if you want + + + align:start position:0% +for long r buiness particle if you want +to generalize the quantum mechanics + + align:start position:0% +to generalize the quantum mechanics + + + align:start position:0% +to generalize the quantum mechanics +right this Quantum mechanic then you + + align:start position:0% +right this Quantum mechanic then you + + + align:start position:0% +right this Quantum mechanic then you +would interpret this as a wave equation + + align:start position:0% +would interpret this as a wave equation + + + align:start position:0% +would interpret this as a wave equation +for for for single right vtic particle + + align:start position:0% +for for for single right vtic particle + + + align:start position:0% +for for for single right vtic particle +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +um so + + align:start position:0% + + + + align:start position:0% + +first so + + align:start position:0% +first so + + + align:start position:0% +first so +first is that so if you + + align:start position:0% +first is that so if you + + + align:start position:0% +first is that so if you +remember so in this + + align:start position:0% +remember so in this + + + align:start position:0% +remember so in this +equation okay for + + align:start position:0% +equation okay for + + + align:start position:0% +equation okay for +if you go back to early days of + + align:start position:0% +if you go back to early days of + + + align:start position:0% +if you go back to early days of +this long right B quantum mechanics so + + align:start position:0% +this long right B quantum mechanics so + + + align:start position:0% +this long right B quantum mechanics so +you remember from this equation you can + + align:start position:0% +you remember from this equation you can + + + align:start position:0% +you remember from this equation you can +der you can + + align:start position:0% +der you can + + + align:start position:0% +der you can +derive a equation for the conserved + + align:start position:0% +derive a equation for the conserved + + + align:start position:0% +derive a equation for the conserved +probability okay uh conserv probability + + align:start position:0% +probability okay uh conserv probability + + + align:start position:0% +probability okay uh conserv probability +and and that equation tells + + align:start position:0% +and and that equation tells + + + align:start position:0% +and and that equation tells +you that square should have the + + align:start position:0% +you that square should have the + + + align:start position:0% +you that square should have the +interpretation of the + + align:start position:0% +interpretation of the + + + align:start position:0% +interpretation of the +probability + + align:start position:0% +probability + + + align:start position:0% +probability +Okay so + + align:start position:0% + + + + align:start position:0% + +but but for uh for that equation you can + + align:start position:0% +but but for uh for that equation you can + + + align:start position:0% +but but for uh for that equation you can +show there's no + + align:start position:0% + + + + align:start position:0% + +quantity has can be there's no quantity + + align:start position:0% +quantity has can be there's no quantity + + + align:start position:0% +quantity has can be there's no quantity +can be + + align:start position:0% + + + + align:start position:0% + +used + + align:start position:0% +used + + + align:start position:0% +used +as probability + + align:start position:0% +as probability + + + align:start position:0% +as probability +density + + align:start position:0% + + + + align:start position:0% + +okay so probability bity by by + + align:start position:0% +okay so probability bity by by + + + align:start position:0% +okay so probability bity by by +definition should satisfy two conditions + + align:start position:0% +definition should satisfy two conditions + + + align:start position:0% +definition should satisfy two conditions +so the first condition is that it's non + + align:start position:0% + + + + align:start position:0% + +negative and the second condition is + + align:start position:0% +negative and the second condition is + + + align:start position:0% +negative and the second condition is +that it should be conserved okay the + + align:start position:0% +that it should be conserved okay the + + + align:start position:0% +that it should be conserved okay the +probability should conserved otherwise + + align:start position:0% +probability should conserved otherwise + + + align:start position:0% +probability should conserved otherwise +you violate the um yeah + + align:start position:0% +you violate the um yeah + + + align:start position:0% +you violate the um yeah +so so you can show that this equation + + align:start position:0% +so so you can show that this equation + + + align:start position:0% +so so you can show that this equation +actually does not + + align:start position:0% +actually does not + + + align:start position:0% +actually does not +allow this equation allows such a + + align:start position:0% +allow this equation allows such a + + + align:start position:0% +allow this equation allows such a +quantity but this equation does not + + align:start position:0% +quantity but this equation does not + + + align:start position:0% +quantity but this equation does not +allow okay and I will not go through + + align:start position:0% +allow okay and I will not go through + + + align:start position:0% +allow okay and I will not go through +that myself I think that will be in your + + align:start position:0% +that myself I think that will be in your + + + align:start position:0% +that myself I think that will be in your +P side two okay that would be your p 2 + + align:start position:0% +P side two okay that would be your p 2 + + + align:start position:0% +P side two okay that would be your p 2 +you will show it + + align:start position:0% + + + + align:start position:0% + +yourself and the second + + align:start position:0% + + + + align:start position:0% + +difficulty you say if you square that if + + align:start position:0% +difficulty you say if you square that if + + + align:start position:0% +difficulty you say if you square that if +you find the + + align:start position:0% +you find the + + + align:start position:0% +you find the +energy so the energy if you take the + + align:start position:0% +energy so the energy if you take the + + + align:start position:0% +energy so the energy if you take the +square root then the energy in principle + + align:start position:0% +square root then the energy in principle + + + align:start position:0% +square root then the energy in principle +can + + align:start position:0% + + + + align:start position:0% + +be say plus minus you have two + + align:start position:0% +be say plus minus you have two + + + align:start position:0% +be say plus minus you have two +solutions okay e equal to plus minus + + align:start position:0% +solutions okay e equal to plus minus + + + align:start position:0% +solutions okay e equal to plus minus +this + + align:start position:0% +this + + + align:start position:0% +this +quantity so in contrast to that equation + + align:start position:0% +quantity so in contrast to that equation + + + align:start position:0% +quantity so in contrast to that equation +there's only positive energy okay long + + align:start position:0% +there's only positive energy okay long + + + align:start position:0% +there's only positive energy okay long +just have positive energy so classically + + align:start position:0% +just have positive energy so classically + + + align:start position:0% +just have positive energy so classically +you can just say let's throw away the + + align:start position:0% +you can just say let's throw away the + + + align:start position:0% +you can just say let's throw away the +second branch + + align:start position:0% +second branch + + + align:start position:0% +second branch +okay uh uh uh we can just throw away the + + align:start position:0% +okay uh uh uh we can just throw away the + + + align:start position:0% +okay uh uh uh we can just throw away the +second Branch by hand okay classically + + align:start position:0% +second Branch by hand okay classically + + + align:start position:0% +second Branch by hand okay classically +but Quantum + + align:start position:0% +but Quantum + + + align:start position:0% +but Quantum +mechanically okay so + + align:start position:0% + + + + align:start position:0% + +classically just ignore the second + + align:start position:0% + + + + align:start position:0% + +Branch the lactive + + align:start position:0% + + + + align:start position:0% + +branch okay but but the quantum mechanic + + align:start position:0% +branch okay but but the quantum mechanic + + + align:start position:0% +branch okay but but the quantum mechanic +this is not + + align:start position:0% +this is not + + + align:start position:0% +this is not +possible okay because you have the + + align:start position:0% +possible okay because you have the + + + align:start position:0% +possible okay because you have the +equation there then you automatically + + align:start position:0% +equation there then you automatically + + + align:start position:0% +equation there then you automatically +have the lative solutions okay so so + + align:start position:0% +have the lative solutions okay so so + + + align:start position:0% +have the lative solutions okay so so +Quantum mechanically and then you have + + align:start position:0% +Quantum mechanically and then you have + + + align:start position:0% +Quantum mechanically and then you have +dispersion relation like + + align:start position:0% +dispersion relation like + + + align:start position:0% +dispersion relation like +this so that dispersion relation have + + align:start position:0% +this so that dispersion relation have + + + align:start position:0% +this so that dispersion relation have +the following form is say e as a + + align:start position:0% +the following form is say e as a + + + align:start position:0% +the following form is say e as a +function of + + align:start position:0% +function of + + + align:start position:0% +function of +P okay so you have positive Branch then + + align:start position:0% +P okay so you have positive Branch then + + + align:start position:0% +P okay so you have positive Branch then +you have a netive + + align:start position:0% +you have a netive + + + align:start position:0% +you have a netive +branch and then you remember in quantum + + align:start position:0% +branch and then you remember in quantum + + + align:start position:0% +branch and then you remember in quantum +mechanics you can have the uh then you + + align:start position:0% +mechanics you can have the uh then you + + + align:start position:0% +mechanics you can have the uh then you +have energy + + align:start position:0% +have energy + + + align:start position:0% +have energy +levels and you have energy level + + align:start position:0% + + + + align:start position:0% + +and such particle a particle here they + + align:start position:0% +and such particle a particle here they + + + align:start position:0% +and such particle a particle here they +have a high energy than particle here + + align:start position:0% +have a high energy than particle here + + + align:start position:0% +have a high energy than particle here +okay and so so here the energy level is + + align:start position:0% +okay and so so here the energy level is + + + align:start position:0% +okay and so so here the energy level is +higher than energy level here and + + align:start position:0% +higher than energy level here and + + + align:start position:0% +higher than energy level here and +there's always a long zero probability + + align:start position:0% +there's always a long zero probability + + + align:start position:0% +there's always a long zero probability +Quantum mechanically for particle to to + + align:start position:0% +Quantum mechanically for particle to to + + + align:start position:0% +Quantum mechanically for particle to to +go from some higher energy level to the + + align:start position:0% +go from some higher energy level to the + + + align:start position:0% +go from some higher energy level to the +lower energy level okay just like in the + + align:start position:0% +lower energy level okay just like in the + + + align:start position:0% +lower energy level okay just like in the +hydrogen atom if you excited and they + + align:start position:0% +hydrogen atom if you excited and they + + + align:start position:0% +hydrogen atom if you excited and they +always go to the lower uh energy level + + align:start position:0% +always go to the lower uh energy level + + + align:start position:0% +always go to the lower uh energy level +so in Quant mechanically such thing + + align:start position:0% +so in Quant mechanically such thing + + + align:start position:0% +so in Quant mechanically such thing +cannot be avoided + + align:start position:0% +cannot be avoided + + + align:start position:0% +cannot be avoided +okay so you cannot just throw this + + align:start position:0% +okay so you cannot just throw this + + + align:start position:0% +okay so you cannot just throw this +Branch away okay and so and so this will + + align:start position:0% +Branch away okay and so and so this will + + + align:start position:0% +Branch away okay and so and so this will +lead to + + align:start position:0% + + + + align:start position:0% + +instability because the because the uh + + align:start position:0% +instability because the because the uh + + + align:start position:0% +instability because the because the uh +because the energy can be infinitely + + align:start position:0% +because the energy can be infinitely + + + align:start position:0% +because the energy can be infinitely +negative okay can be infinite negative + + align:start position:0% +negative okay can be infinite negative + + + align:start position:0% +negative okay can be infinite negative +and then and then all your particles we + + align:start position:0% +and then and then all your particles we + + + align:start position:0% +and then and then all your particles we +all go to infinite negative energies and + + align:start position:0% +all go to infinite negative energies and + + + align:start position:0% +all go to infinite negative energies and +then uh then your system will be a big + + align:start position:0% +then uh then your system will be a big + + + align:start position:0% +then uh then your system will be a big +problem + + align:start position:0% +problem + + + align:start position:0% +problem +okay so so so these are the + + align:start position:0% +okay so so so these are the + + + align:start position:0% +okay so so so these are the +two so these are the two uh + + align:start position:0% + + + + align:start position:0% + +um the the most prominent problems and + + align:start position:0% +um the the most prominent problems and + + + align:start position:0% +um the the most prominent problems and +then people uh tried many different ways + + align:start position:0% +then people uh tried many different ways + + + align:start position:0% +then people uh tried many different ways +try to avoid them Etc including some + + align:start position:0% +try to avoid them Etc including some + + + align:start position:0% +try to avoid them Etc including some +very ingenious Solutions Etc so we will + + align:start position:0% +very ingenious Solutions Etc so we will + + + align:start position:0% +very ingenious Solutions Etc so we will +not going into + + align:start position:0% +not going into + + + align:start position:0% +not going into +them but let me just mention this + + align:start position:0% +them but let me just mention this + + + align:start position:0% +them but let me just mention this +actually even if you can address those + + align:start position:0% +actually even if you can address those + + + align:start position:0% +actually even if you can address those +problems still the uh the the ristic + + align:start position:0% +problems still the uh the the ristic + + + align:start position:0% +problems still the uh the the ristic +quantum mechanics will not make sense + + align:start position:0% +quantum mechanics will not make sense + + + align:start position:0% +quantum mechanics will not make sense +for very fundamental reason okay so so + + align:start position:0% +for very fundamental reason okay so so + + + align:start position:0% +for very fundamental reason okay so so +these are the more like superficial + + align:start position:0% +these are the more like superficial + + + align:start position:0% +these are the more like superficial +reason why that equation does not quite + + align:start position:0% +reason why that equation does not quite + + + align:start position:0% +reason why that equation does not quite +work okay but there actually more + + align:start position:0% +work okay but there actually more + + + align:start position:0% +work okay but there actually more +fundamental + + align:start position:0% +fundamental + + + align:start position:0% +fundamental +reason + + align:start position:0% + + + + align:start position:0% + +right right this quantum mechanics even + + align:start position:0% +right right this quantum mechanics even + + + align:start position:0% +right right this quantum mechanics even +as a concept does not make sense + + align:start position:0% + + + + align:start position:0% + +okay so so by definition + + align:start position:0% +okay so so by definition + + + align:start position:0% +okay so so by definition +by definition if you want to interpret + + align:start position:0% +by definition if you want to interpret + + + align:start position:0% +by definition if you want to interpret +this kind of thing as a wave function + + align:start position:0% +this kind of thing as a wave function + + + align:start position:0% +this kind of thing as a wave function +okay so what's the interpretation of the + + align:start position:0% +okay so what's the interpretation of the + + + align:start position:0% +okay so what's the interpretation of the +wave function which we already set so + + align:start position:0% +wave function which we already set so + + + align:start position:0% +wave function which we already set so +this is the pro describe the amplitude + + align:start position:0% +this is the pro describe the amplitude + + + align:start position:0% +this is the pro describe the amplitude +for single particle at some point + + align:start position:0% +for single particle at some point + + + align:start position:0% +for single particle at some point +okay at some point + + align:start position:0% +okay at some point + + + align:start position:0% +okay at some point +x at time T but now if you have two + + align:start position:0% +x at time T but now if you have two + + + align:start position:0% +x at time T but now if you have two +particles what do you do you introduce + + align:start position:0% +particles what do you do you introduce + + + align:start position:0% +particles what do you do you introduce +the location for particle one and + + align:start position:0% +the location for particle one and + + + align:start position:0% +the location for particle one and +particle two and the t Okay so this + + align:start position:0% +particle two and the t Okay so this + + + align:start position:0% +particle two and the t Okay so this +describe two particles and if you want + + align:start position:0% +describe two particles and if you want + + + align:start position:0% +describe two particles and if you want +to describe three particles then you + + align:start position:0% +to describe three particles then you + + + align:start position:0% +to describe three particles then you +have to introduce more X okay remember + + align:start position:0% +have to introduce more X okay remember + + + align:start position:0% +have to introduce more X okay remember +that's what you did in nonr B quantum + + align:start position:0% +that's what you did in nonr B quantum + + + align:start position:0% +that's what you did in nonr B quantum +mechanics so in nonr B quantum mechanics + + align:start position:0% +mechanics so in nonr B quantum mechanics + + + align:start position:0% +mechanics so in nonr B quantum mechanics +this makes sense okay you can just + + align:start position:0% +this makes sense okay you can just + + + align:start position:0% +this makes sense okay you can just +because there's no mixing between the + + align:start position:0% +because there's no mixing between the + + + align:start position:0% +because there's no mixing between the +different branches say single particle + + align:start position:0% +different branches say single particle + + + align:start position:0% +different branches say single particle +two particles because particle cannot be + + align:start position:0% +two particles because particle cannot be + + + align:start position:0% +two particles because particle cannot be +created and destroyed in Long right + + align:start position:0% +created and destroyed in Long right + + + align:start position:0% +created and destroyed in Long right +visic system but in relativistic system + + align:start position:0% +visic system but in relativistic system + + + align:start position:0% +visic system but in relativistic system +you can always create particles okay if + + align:start position:0% +you can always create particles okay if + + + align:start position:0% +you can always create particles okay if +you have enough uh energy you can create + + align:start position:0% +you have enough uh energy you can create + + + align:start position:0% +you have enough uh energy you can create +new particles PA create electrons okay + + align:start position:0% +new particles PA create electrons okay + + + align:start position:0% +new particles PA create electrons okay +happens in the accelerator all the time + + align:start position:0% +happens in the accelerator all the time + + + align:start position:0% +happens in the accelerator all the time +all electrons they can allate into + + align:start position:0% +all electrons they can allate into + + + align:start position:0% +all electrons they can allate into +photons okay so so so so the particles + + align:start position:0% +photons okay so so so so the particles + + + align:start position:0% +photons okay so so so so the particles +are lot conserved okay lot conserved so + + align:start position:0% +are lot conserved okay lot conserved so + + + align:start position:0% +are lot conserved okay lot conserved so +so this kind of wave function concept + + align:start position:0% +so this kind of wave function concept + + + align:start position:0% +so this kind of wave function concept +don't even make sense so if you want to + + align:start position:0% +don't even make sense so if you want to + + + align:start position:0% +don't even make sense so if you want to +describe so that means whenever you have + + align:start position:0% +describe so that means whenever you have + + + align:start position:0% +describe so that means whenever you have +special relativity and the quantum + + align:start position:0% +special relativity and the quantum + + + align:start position:0% +special relativity and the quantum +mechanics + + align:start position:0% +mechanics + + + align:start position:0% +mechanics +together you must have a + + align:start position:0% +together you must have a + + + align:start position:0% +together you must have a +framework which can describe arbitrary L + + align:start position:0% +framework which can describe arbitrary L + + + align:start position:0% +framework which can describe arbitrary L +of + + align:start position:0% +of + + + align:start position:0% +of +particles at the same time okay because + + align:start position:0% +particles at the same time okay because + + + align:start position:0% +particles at the same time okay because +particle numbers can change all the time + + align:start position:0% +particle numbers can change all the time + + + align:start position:0% +particle numbers can change all the time +okay because of liation and creation + + align:start position:0% +okay because of liation and creation + + + align:start position:0% +okay because of liation and creation +effect and that cannot be achieved by by + + align:start position:0% +effect and that cannot be achieved by by + + + align:start position:0% +effect and that cannot be achieved by by +this kind of concept like wave function + + align:start position:0% +this kind of concept like wave function + + + align:start position:0% +this kind of concept like wave function +okay cannot be achieved by wave function + + align:start position:0% +okay cannot be achieved by wave function + + + align:start position:0% +okay cannot be achieved by wave function +it turns out miraculously that can be + + align:start position:0% +it turns out miraculously that can be + + + align:start position:0% +it turns out miraculously that can be +achieved by field theory that the field + + align:start position:0% +achieved by field theory that the field + + + align:start position:0% +achieved by field theory that the field +the once you quantize + + align:start position:0% +the once you quantize + + + align:start position:0% +the once you quantize +it + + align:start position:0% +it + + + align:start position:0% +it +automatically give you a framework to + + align:start position:0% +automatically give you a framework to + + + align:start position:0% +automatically give you a framework to +describe arbitrary number of particles + + align:start position:0% +describe arbitrary number of particles + + + align:start position:0% +describe arbitrary number of particles +okay in the in the unified manner okay + + align:start position:0% +okay in the in the unified manner okay + + + align:start position:0% +okay in the in the unified manner okay +single particle two particles up number + + align:start position:0% +single particle two particles up number + + + align:start position:0% +single particle two particles up number +particles and so this is one of the + + align:start position:0% +particles and so this is one of the + + + align:start position:0% +particles and so this is one of the +magic of field the so that's why the + + align:start position:0% +magic of field the so that's why the + + + align:start position:0% +magic of field the so that's why the +field Theory plays such important role + + align:start position:0% +field Theory plays such important role + + + align:start position:0% +field Theory plays such important role +in particle physics is because the + + align:start position:0% +in particle physics is because the + + + align:start position:0% +in particle physics is because the +excitations of + + align:start position:0% +excitations of + + + align:start position:0% +excitations of +fields automatically provide the + + align:start position:0% +fields automatically provide the + + + align:start position:0% +fields automatically provide the +mechanism to describe arbitary L of + + align:start position:0% +mechanism to describe arbitary L of + + + align:start position:0% +mechanism to describe arbitary L of +particles okay so we will stop here + + align:start position:0% + + + + align:start position:0% + +today \ No newline at end of file diff --git a/anA3P9McG5Y.txt b/anA3P9McG5Y.txt new file mode 100644 index 0000000000000000000000000000000000000000..d7de88cf04396c87afec686b492f77449a08b0c9 --- /dev/null +++ b/anA3P9McG5Y.txt @@ -0,0 +1,6680 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free to make a donation or view + + align:start position:0% +for free to make a donation or view + + + align:start position:0% +for free to make a donation or view +additional materials from hundreds of + + align:start position:0% +additional materials from hundreds of + + + align:start position:0% +additional materials from hundreds of +MIT courses visit MIT opencourseware at + + align:start position:0% +MIT courses visit MIT opencourseware at + + + align:start position:0% +MIT courses visit MIT opencourseware at +ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +hi welcome to our lecture today in + + align:start position:0% +hi welcome to our lecture today in + + + align:start position:0% +hi welcome to our lecture today in +calculus revisited and our topic is + + align:start position:0% +calculus revisited and our topic is + + + align:start position:0% +calculus revisited and our topic is +going to be the dot product and by way + + align:start position:0% +going to be the dot product and by way + + + align:start position:0% +going to be the dot product and by way +of a preamble let me point out that in + + align:start position:0% +of a preamble let me point out that in + + + align:start position:0% +of a preamble let me point out that in +the in our development our vector spaces + + align:start position:0% +the in our development our vector spaces + + + align:start position:0% +the in our development our vector spaces +in this block up until now we have + + align:start position:0% +in this block up until now we have + + + align:start position:0% +in this block up until now we have +deliberately not mentioned the concept + + align:start position:0% +deliberately not mentioned the concept + + + align:start position:0% +deliberately not mentioned the concept +of the dot product even though dot + + align:start position:0% +of the dot product even though dot + + + align:start position:0% +of the dot product even though dot +product plays a very prominent role in + + align:start position:0% +product plays a very prominent role in + + + align:start position:0% +product plays a very prominent role in +the usual vector algebra of two and + + align:start position:0% +the usual vector algebra of two and + + + align:start position:0% +the usual vector algebra of two and +three dimensional space and the reason + + align:start position:0% +three dimensional space and the reason + + + align:start position:0% +three dimensional space and the reason +for this is that we wanted to emphasize + + align:start position:0% +for this is that we wanted to emphasize + + + align:start position:0% +for this is that we wanted to emphasize +the structure of a vector space and a + + align:start position:0% +the structure of a vector space and a + + + align:start position:0% +the structure of a vector space and a +matter of manner of speaking + + align:start position:0% +matter of manner of speaking + + + align:start position:0% +matter of manner of speaking +mathematical structures are pretty much + + align:start position:0% +mathematical structures are pretty much + + + align:start position:0% +mathematical structures are pretty much +like an Anatomy type course that one + + align:start position:0% +like an Anatomy type course that one + + + align:start position:0% +like an Anatomy type course that one +starts with a basic structure exploits + + align:start position:0% +starts with a basic structure exploits + + + align:start position:0% +starts with a basic structure exploits +it sees what ramifications it has and + + align:start position:0% +it sees what ramifications it has and + + + align:start position:0% +it sees what ramifications it has and +then gradually adds on more + + align:start position:0% +then gradually adds on more + + + align:start position:0% +then gradually adds on more +sophisticated layers of nerves nerve + + align:start position:0% +sophisticated layers of nerves nerve + + + align:start position:0% +sophisticated layers of nerves nerve +centers skin grafts and what-have-you + + align:start position:0% +centers skin grafts and what-have-you + + + align:start position:0% +centers skin grafts and what-have-you +and ultimately builds up a super + + align:start position:0% +and ultimately builds up a super + + + align:start position:0% +and ultimately builds up a super +structure based on top of an underlying + + align:start position:0% +structure based on top of an underlying + + + align:start position:0% +structure based on top of an underlying +basic fundamental model now without + + align:start position:0% +basic fundamental model now without + + + align:start position:0% +basic fundamental model now without +going into that in more detail right now + + align:start position:0% +going into that in more detail right now + + + align:start position:0% +going into that in more detail right now +well it suffice to say that I call + + align:start position:0% +well it suffice to say that I call + + + align:start position:0% +well it suffice to say that I call +today's lecture dot products and by way + + align:start position:0% +today's lecture dot products and by way + + + align:start position:0% +today's lecture dot products and by way +of review notice that in the usual two + + align:start position:0% +of review notice that in the usual two + + + align:start position:0% +of review notice that in the usual two +and three dimensional case by the dot + + align:start position:0% +and three dimensional case by the dot + + + align:start position:0% +and three dimensional case by the dot +product of two vectors we mean a real + + align:start position:0% +product of two vectors we mean a real + + + align:start position:0% +product of two vectors we mean a real +number and if we want to keep this thing + + align:start position:0% +number and if we want to keep this thing + + + align:start position:0% +number and if we want to keep this thing +vague and not indicate the cosine of the + + align:start position:0% +vague and not indicate the cosine of the + + + align:start position:0% +vague and not indicate the cosine of the +angle between two vectors etc one + + align:start position:0% +angle between two vectors etc one + + + align:start position:0% +angle between two vectors etc one +usually says that a dot product is a + + align:start position:0% +usually says that a dot product is a + + + align:start position:0% +usually says that a dot product is a +mapping that carries ordered pairs of + + align:start position:0% +mapping that carries ordered pairs of + + + align:start position:0% +mapping that carries ordered pairs of +vectors into the real numbers this is + + align:start position:0% +vectors into the real numbers this is + + + align:start position:0% +vectors into the real numbers this is +the mathematical way of talking about + + align:start position:0% +the mathematical way of talking about + + + align:start position:0% +the mathematical way of talking about +what a dot product is without referring + + align:start position:0% +what a dot product is without referring + + + align:start position:0% +what a dot product is without referring +to angles or lines it's a function which + + align:start position:0% +to angles or lines it's a function which + + + align:start position:0% +to angles or lines it's a function which +Maps ordered pairs of vectors into real + + align:start position:0% +Maps ordered pairs of vectors into real + + + align:start position:0% +Maps ordered pairs of vectors into real +numbers in particular the mapping must + + align:start position:0% +numbers in particular the mapping must + + + align:start position:0% +numbers in particular the mapping must +have certain properties to be called the + + align:start position:0% +have certain properties to be called the + + + align:start position:0% +have certain properties to be called the +dot product and again emphasizing + + align:start position:0% +dot product and again emphasizing + + + align:start position:0% +dot product and again emphasizing +mathematical structure based on what we + + align:start position:0% +mathematical structure based on what we + + + align:start position:0% +mathematical structure based on what we +already know is the case from the two + + align:start position:0% +already know is the case from the two + + + align:start position:0% +already know is the case from the two +and three dimensional situation what + + align:start position:0% +and three dimensional situation what + + + align:start position:0% +and three dimensional situation what +properties do we want the dot product to + + align:start position:0% +properties do we want the dot product to + + + align:start position:0% +properties do we want the dot product to +have well we would like alpha dot beta + + align:start position:0% +have well we would like alpha dot beta + + + align:start position:0% +have well we would like alpha dot beta +to we'll be the DAAD alpha because that + + align:start position:0% +to we'll be the DAAD alpha because that + + + align:start position:0% +to we'll be the DAAD alpha because that +certainly happened in the tuna and + + align:start position:0% +certainly happened in the tuna and + + + align:start position:0% +certainly happened in the tuna and +three-dimensional case we would like + + align:start position:0% +three-dimensional case we would like + + + align:start position:0% +three-dimensional case we would like +alpha dot beta plus gamma to be alpha + + align:start position:0% +alpha dot beta plus gamma to be alpha + + + align:start position:0% +alpha dot beta plus gamma to be alpha +dot beta plus alpha alpha gamma and if + + align:start position:0% +dot beta plus alpha alpha gamma and if + + + align:start position:0% +dot beta plus alpha alpha gamma and if +we have a scalar multiple of alpha + + align:start position:0% +we have a scalar multiple of alpha + + + align:start position:0% +we have a scalar multiple of alpha +dotted with beta we would like that to + + align:start position:0% +dotted with beta we would like that to + + + align:start position:0% +dotted with beta we would like that to +be the scalar C times the number alpha + + align:start position:0% +be the scalar C times the number alpha + + + align:start position:0% +be the scalar C times the number alpha +dot beta or if we wanted to rewrite this + + align:start position:0% +dot beta or if we wanted to rewrite this + + + align:start position:0% +dot beta or if we wanted to rewrite this +in vector form that the C could also be + + align:start position:0% +in vector form that the C could also be + + + align:start position:0% +in vector form that the C could also be +used as the scalar multiple of beta that + + align:start position:0% +used as the scalar multiple of beta that + + + align:start position:0% +used as the scalar multiple of beta that +C alpha dot beta is the same as alpha + + align:start position:0% +C alpha dot beta is the same as alpha + + + align:start position:0% +C alpha dot beta is the same as alpha +dot C beta and whether these three rules + + align:start position:0% +dot C beta and whether these three rules + + + align:start position:0% +dot C beta and whether these three rules +come from they came from the properties + + align:start position:0% +come from they came from the properties + + + align:start position:0% +come from they came from the properties +that the ordinary dot product has by the + + align:start position:0% +that the ordinary dot product has by the + + + align:start position:0% +that the ordinary dot product has by the +way a dot product becomes known as a + + align:start position:0% +way a dot product becomes known as a + + + align:start position:0% +way a dot product becomes known as a +Euclidean dot product if in addition to + + align:start position:0% +Euclidean dot product if in addition to + + + align:start position:0% +Euclidean dot product if in addition to +the given three properties we also know + + align:start position:0% +the given three properties we also know + + + align:start position:0% +the given three properties we also know +that the dot product of a vector and + + align:start position:0% +that the dot product of a vector and + + + align:start position:0% +that the dot product of a vector and +itself alpha dot alpha is a non-negative + + align:start position:0% +itself alpha dot alpha is a non-negative + + + align:start position:0% +itself alpha dot alpha is a non-negative +real number and that in particular alpha + + align:start position:0% +real number and that in particular alpha + + + align:start position:0% +real number and that in particular alpha +alpha can equal zero if and only if + + align:start position:0% +alpha can equal zero if and only if + + + align:start position:0% +alpha can equal zero if and only if +alpha equals zero by the way let me + + align:start position:0% +alpha equals zero by the way let me + + + align:start position:0% +alpha equals zero by the way let me +point out that this fourth condition is + + align:start position:0% +point out that this fourth condition is + + + align:start position:0% +point out that this fourth condition is +independent of the other three that when + + align:start position:0% +independent of the other three that when + + + align:start position:0% +independent of the other three that when +one studies vector spaces in more + + align:start position:0% +one studies vector spaces in more + + + align:start position:0% +one studies vector spaces in more +abstract detail one usually defines a + + align:start position:0% +abstract detail one usually defines a + + + align:start position:0% +abstract detail one usually defines a +dot product to have just the first three + + align:start position:0% +dot product to have just the first three + + + align:start position:0% +dot product to have just the first three +properties that we talked about and if + + align:start position:0% +properties that we talked about and if + + + align:start position:0% +properties that we talked about and if +the fourth property happens to be + + align:start position:0% +the fourth property happens to be + + + align:start position:0% +the fourth property happens to be +present then one talks about a positive + + align:start position:0% +present then one talks about a positive + + + align:start position:0% +present then one talks about a positive +definite dot product but not every dot + + align:start position:0% +definite dot product but not every dot + + + align:start position:0% +definite dot product but not every dot +product has to be positive definite + + align:start position:0% +product has to be positive definite + + + align:start position:0% +product has to be positive definite +except that if we're trying to imitate + + align:start position:0% +except that if we're trying to imitate + + + align:start position:0% +except that if we're trying to imitate +the distance property of real vector + + align:start position:0% +the distance property of real vector + + + align:start position:0% +the distance property of real vector +spaces then we add the positive definite + + align:start position:0% +spaces then we add the positive definite + + + align:start position:0% +spaces then we add the positive definite +criterion and that's explained in more + + align:start position:0% +criterion and that's explained in more + + + align:start position:0% +criterion and that's explained in more +detail in the study guide as we do the + + align:start position:0% +detail in the study guide as we do the + + + align:start position:0% +detail in the study guide as we do the +exercises but I did want to simply point + + align:start position:0% +exercises but I did want to simply point + + + align:start position:0% +exercises but I did want to simply point +out that once you know that you have a + + align:start position:0% +out that once you know that you have a + + + align:start position:0% +out that once you know that you have a +positive definite form that alpha alpha + + align:start position:0% +positive definite form that alpha alpha + + + align:start position:0% +positive definite form that alpha alpha +is non-negative then it makes sense to + + align:start position:0% +is non-negative then it makes sense to + + + align:start position:0% +is non-negative then it makes sense to +abstractly define the norm or the length + + align:start position:0% +abstractly define the norm or the length + + + align:start position:0% +abstractly define the norm or the length +of alpha to be the positive square root + + align:start position:0% +of alpha to be the positive square root + + + align:start position:0% +of alpha to be the positive square root +of alpha dot alpha you see this makes + + align:start position:0% +of alpha dot alpha you see this makes + + + align:start position:0% +of alpha dot alpha you see this makes +sense because you know that alpha dot + + align:start position:0% +sense because you know that alpha dot + + + align:start position:0% +sense because you know that alpha dot +alpha is a non-negative real number + + align:start position:0% +alpha is a non-negative real number + + + align:start position:0% +alpha is a non-negative real number +hence it has a unique positive square + + align:start position:0% +hence it has a unique positive square + + + align:start position:0% +hence it has a unique positive square +root and this is how we abstract the + + align:start position:0% +root and this is how we abstract the + + + align:start position:0% +root and this is how we abstract the +usual distance function at any rate to + + align:start position:0% +usual distance function at any rate to + + + align:start position:0% +usual distance function at any rate to +show you how this works an app tract + + align:start position:0% +show you how this works an app tract + + + align:start position:0% +show you how this works an app tract +form let's take a three dimensional case + + align:start position:0% +form let's take a three dimensional case + + + align:start position:0% +form let's take a three dimensional case +let's suppose V is a three dimensional + + align:start position:0% +let's suppose V is a three dimensional + + + align:start position:0% +let's suppose V is a three dimensional +vector space that a particularly chosen + + align:start position:0% +vector space that a particularly chosen + + + align:start position:0% +vector space that a particularly chosen +basis for V is u1 u2 and u3 and let's + + align:start position:0% +basis for V is u1 u2 and u3 and let's + + + align:start position:0% +basis for V is u1 u2 and u3 and let's +suppose that we have a positive definite + + align:start position:0% +suppose that we have a positive definite + + + align:start position:0% +suppose that we have a positive definite +dot product and I'll just make this up + + align:start position:0% +dot product and I'll just make this up + + + align:start position:0% +dot product and I'll just make this up +at random or semi random here let's + + align:start position:0% +at random or semi random here let's + + + align:start position:0% +at random or semi random here let's +suppose that I know what the dot product + + align:start position:0% +suppose that I know what the dot product + + + align:start position:0% +suppose that I know what the dot product +looks like on all of the pairs of basis + + align:start position:0% +looks like on all of the pairs of basis + + + align:start position:0% +looks like on all of the pairs of basis +elements in other words I know what u 1 + + align:start position:0% +elements in other words I know what u 1 + + + align:start position:0% +elements in other words I know what u 1 +dot u1 is what u 2 dot u1 is what u 3 + + align:start position:0% +dot u1 is what u 2 dot u1 is what u 3 + + + align:start position:0% +dot u1 is what u 2 dot u1 is what u 3 +dot u 1 is and by the way by the + + align:start position:0% +dot u 1 is and by the way by the + + + align:start position:0% +dot u 1 is and by the way by the +property that u 2 dot u 1 must equal u 1 + + align:start position:0% +property that u 2 dot u 1 must equal u 1 + + + align:start position:0% +property that u 2 dot u 1 must equal u 1 +u 2 etc by the commutative property + + align:start position:0% +u 2 etc by the commutative property + + + align:start position:0% +u 2 etc by the commutative property +notice that once I know what u 2 dot u1 + + align:start position:0% +notice that once I know what u 2 dot u1 + + + align:start position:0% +notice that once I know what u 2 dot u1 +is I also know what u 1 dot u2 is once I + + align:start position:0% +is I also know what u 1 dot u2 is once I + + + align:start position:0% +is I also know what u 1 dot u2 is once I +know what you three dot u1 is I know + + align:start position:0% +know what you three dot u1 is I know + + + align:start position:0% +know what you three dot u1 is I know +what u 1 dot u 3 is etc at any rate + + align:start position:0% +what u 1 dot u 3 is etc at any rate + + + align:start position:0% +what u 1 dot u 3 is etc at any rate +there are nine possible combinations + + align:start position:0% +there are nine possible combinations + + + align:start position:0% +there are nine possible combinations +here and just try to fix these in your + + align:start position:0% +here and just try to fix these in your + + + align:start position:0% +here and just try to fix these in your +mind because I'll be referring to these + + align:start position:0% +mind because I'll be referring to these + + + align:start position:0% +mind because I'll be referring to these +as we go along u 1 dot u 1 is 3 u 1 dot + + align:start position:0% +as we go along u 1 dot u 1 is 3 u 1 dot + + + align:start position:0% +as we go along u 1 dot u 1 is 3 u 1 dot +u 2 is 4 u 1 dot u 3 is 5 u 2 dot u 2 is + + align:start position:0% +u 2 is 4 u 1 dot u 3 is 5 u 2 dot u 2 is + + + align:start position:0% +u 2 is 4 u 1 dot u 3 is 5 u 2 dot u 2 is +6 u 2 dot u 3 is 7 & u 3 dot u 3 is 9 + + align:start position:0% +6 u 2 dot u 3 is 7 & u 3 dot u 3 is 9 + + + align:start position:0% +6 u 2 dot u 3 is 7 & u 3 dot u 3 is 9 +okay I just happen to know that + + align:start position:0% +okay I just happen to know that + + + align:start position:0% +okay I just happen to know that +particular amount let's also suppose + + align:start position:0% +particular amount let's also suppose + + + align:start position:0% +particular amount let's also suppose +that I now want to find the dot product + + align:start position:0% +that I now want to find the dot product + + + align:start position:0% +that I now want to find the dot product +of any two vectors in my space V my + + align:start position:0% +of any two vectors in my space V my + + + align:start position:0% +of any two vectors in my space V my +first claim is and again this is an + + align:start position:0% +first claim is and again this is an + + + align:start position:0% +first claim is and again this is an +overview I'll do this in more abstract + + align:start position:0% +overview I'll do this in more abstract + + + align:start position:0% +overview I'll do this in more abstract +detail in the exercises in the study + + align:start position:0% +detail in the exercises in the study + + + align:start position:0% +detail in the exercises in the study +guide my first point though is that once + + align:start position:0% +guide my first point though is that once + + + align:start position:0% +guide my first point though is that once +we know what the dot product is for each + + align:start position:0% +we know what the dot product is for each + + + align:start position:0% +we know what the dot product is for each +pair of basis vectors we know what the + + align:start position:0% +pair of basis vectors we know what the + + + align:start position:0% +pair of basis vectors we know what the +dot product is for all vectors in pairs + + align:start position:0% +dot product is for all vectors in pairs + + + align:start position:0% +dot product is for all vectors in pairs +of vectors in the space that in + + align:start position:0% +of vectors in the space that in + + + align:start position:0% +of vectors in the space that in +particular the four rules actually the + + align:start position:0% +particular the four rules actually the + + + align:start position:0% +particular the four rules actually the +three rules that we have from up for + + align:start position:0% +three rules that we have from up for + + + align:start position:0% +three rules that we have from up for +defining a dot product tells us how to + + align:start position:0% +defining a dot product tells us how to + + + align:start position:0% +defining a dot product tells us how to +compute the dot product for any two + + align:start position:0% +compute the dot product for any two + + + align:start position:0% +compute the dot product for any two +elements for example suppose I have one + + align:start position:0% +elements for example suppose I have one + + + align:start position:0% +elements for example suppose I have one +three tuple in other words it suppose I + + align:start position:0% +three tuple in other words it suppose I + + + align:start position:0% +three tuple in other words it suppose I +have two vectors x 1 u 1 plus X 2 u 2 + + align:start position:0% +have two vectors x 1 u 1 plus X 2 u 2 + + + align:start position:0% +have two vectors x 1 u 1 plus X 2 u 2 +plus X 3 u 3 and Y 1 u 1 plus y 2 u 2 + + align:start position:0% +plus X 3 u 3 and Y 1 u 1 plus y 2 u 2 + + + align:start position:0% +plus X 3 u 3 and Y 1 u 1 plus y 2 u 2 +plus y 3 u 3 let's suppose I want to + + align:start position:0% +plus y 3 u 3 let's suppose I want to + + + align:start position:0% +plus y 3 u 3 let's suppose I want to +find that dot product notice that my + + align:start position:0% +find that dot product notice that my + + + align:start position:0% +find that dot product notice that my +distributive rule for multiplication + + align:start position:0% +distributive rule for multiplication + + + align:start position:0% +distributive rule for multiplication +coupled with the commutative properties + + align:start position:0% +coupled with the commutative properties + + + align:start position:0% +coupled with the commutative properties +and how I can factor scalar multiples + + align:start position:0% +and how I can factor scalar multiples + + + align:start position:0% +and how I can factor scalar multiples +tells me that I multiply these two + + align:start position:0% +tells me that I multiply these two + + + align:start position:0% +tells me that I multiply these two +trinomials the same way as I would have + + align:start position:0% +trinomials the same way as I would have + + + align:start position:0% +trinomials the same way as I would have +had these been algebraic expressions in + + align:start position:0% +had these been algebraic expressions in + + + align:start position:0% +had these been algebraic expressions in +other words I dot X one new one with + + align:start position:0% +other words I dot X one new one with + + + align:start position:0% +other words I dot X one new one with +each of these three terms I dot X to you + + align:start position:0% +each of these three terms I dot X to you + + + align:start position:0% +each of these three terms I dot X to you +two with each of these three terms and I + + align:start position:0% +two with each of these three terms and I + + + align:start position:0% +two with each of these three terms and I +dot X 3 you three with each of these + + align:start position:0% +dot X 3 you three with each of these + + + align:start position:0% +dot X 3 you three with each of these +three terms for example this will give + + align:start position:0% +three terms for example this will give + + + align:start position:0% +three terms for example this will give +me X 1 y 1 x u 1 dot u 1 but if you + + align:start position:0% +me X 1 y 1 x u 1 dot u 1 but if you + + + align:start position:0% +me X 1 y 1 x u 1 dot u 1 but if you +recall I said that u 1 dot u 1 is 3 so + + align:start position:0% +recall I said that u 1 dot u 1 is 3 so + + + align:start position:0% +recall I said that u 1 dot u 1 is 3 so +this becomes 3 x 1 y 1 and in a similar + + align:start position:0% +this becomes 3 x 1 y 1 and in a similar + + + align:start position:0% +this becomes 3 x 1 y 1 and in a similar +way when I dot X 1 new one with Y 2 u 2 + + align:start position:0% +way when I dot X 1 new one with Y 2 u 2 + + + align:start position:0% +way when I dot X 1 new one with Y 2 u 2 +I get X 1 Y 2 u 1 dot u 2 but I gave the + + align:start position:0% +I get X 1 Y 2 u 1 dot u 2 but I gave the + + + align:start position:0% +I get X 1 Y 2 u 1 dot u 2 but I gave the +fact that u 1 dot u 2 was 4 so this term + + align:start position:0% +fact that u 1 dot u 2 was 4 so this term + + + align:start position:0% +fact that u 1 dot u 2 was 4 so this term +becomes 4 X 1 y 2 and in a similar way + + align:start position:0% +becomes 4 X 1 y 2 and in a similar way + + + align:start position:0% +becomes 4 X 1 y 2 and in a similar way +going through this I get a term will be + + align:start position:0% +going through this I get a term will be + + + align:start position:0% +going through this I get a term will be +5 X 1 Y 3 then dotting X 2 u 2 with each + + align:start position:0% +5 X 1 Y 3 then dotting X 2 u 2 with each + + + align:start position:0% +5 X 1 Y 3 then dotting X 2 u 2 with each +of these three terms I get three more + + align:start position:0% +of these three terms I get three more + + + align:start position:0% +of these three terms I get three more +terms for X 2 y 1 plus 6 X 2 y 2 plus 7 + + align:start position:0% +terms for X 2 y 1 plus 6 X 2 y 2 plus 7 + + + align:start position:0% +terms for X 2 y 1 plus 6 X 2 y 2 plus 7 +X 2 y 3 + + align:start position:0% +X 2 y 3 + + + align:start position:0% +X 2 y 3 +then I dot X 3 u 3 with each of these + + align:start position:0% +then I dot X 3 u 3 with each of these + + + align:start position:0% +then I dot X 3 u 3 with each of these +three terms again just do this thing + + align:start position:0% +three terms again just do this thing + + + align:start position:0% +three terms again just do this thing +quickly X 3 u 3 dotted with Y 1 u 1 is X + + align:start position:0% +quickly X 3 u 3 dotted with Y 1 u 1 is X + + + align:start position:0% +quickly X 3 u 3 dotted with Y 1 u 1 is X +3 y 1 times u 3 dotted with u 1 & u 3 + + align:start position:0% +3 y 1 times u 3 dotted with u 1 & u 3 + + + align:start position:0% +3 y 1 times u 3 dotted with u 1 & u 3 +dotted with u 1 was given to be 5 in + + align:start position:0% +dotted with u 1 was given to be 5 in + + + align:start position:0% +dotted with u 1 was given to be 5 in +fact it was the same as u 1 dotted with + + align:start position:0% +fact it was the same as u 1 dotted with + + + align:start position:0% +fact it was the same as u 1 dotted with +u 3 by karma tivity you see which was + + align:start position:0% +u 3 by karma tivity you see which was + + + align:start position:0% +u 3 by karma tivity you see which was +also v at any rate I get what 5 X 3 y 1 + + align:start position:0% +also v at any rate I get what 5 X 3 y 1 + + + align:start position:0% +also v at any rate I get what 5 X 3 y 1 +plus 7 X 3 y 2 plus 9 X 3 y 3 by the way + + align:start position:0% +plus 7 X 3 y 2 plus 9 X 3 y 3 by the way + + + align:start position:0% +plus 7 X 3 y 2 plus 9 X 3 y 3 by the way +at this particular stage I would like to + + align:start position:0% +at this particular stage I would like to + + + align:start position:0% +at this particular stage I would like to +pause for a moment and some of you may + + align:start position:0% +pause for a moment and some of you may + + + align:start position:0% +pause for a moment and some of you may +have picked this up better than others + + align:start position:0% +have picked this up better than others + + + align:start position:0% +have picked this up better than others +but at this stage of the game maybe + + align:start position:0% +but at this stage of the game maybe + + + align:start position:0% +but at this stage of the game maybe +you've already learned how to look at a + + align:start position:0% +you've already learned how to look at a + + + align:start position:0% +you've already learned how to look at a +system like this and write it in matrix + + align:start position:0% +system like this and write it in matrix + + + align:start position:0% +system like this and write it in matrix +form there was notice that these are + + align:start position:0% +form there was notice that these are + + + align:start position:0% +form there was notice that these are +what we call quadratic forms each term + + align:start position:0% +what we call quadratic forms each term + + + align:start position:0% +what we call quadratic forms each term +involves an X x a y I've written this so + + align:start position:0% +involves an X x a y I've written this so + + + align:start position:0% +involves an X x a y I've written this so +that the X's are always the left side + + align:start position:0% +that the X's are always the left side + + + align:start position:0% +that the X's are always the left side +factor and the Y's are always on the + + align:start position:0% +factor and the Y's are always on the + + + align:start position:0% +factor and the Y's are always on the +right notice that there is a matrix of + + align:start position:0% +right notice that there is a matrix of + + + align:start position:0% +right notice that there is a matrix of +coefficients namely three four five four + + align:start position:0% +coefficients namely three four five four + + + align:start position:0% +coefficients namely three four five four +six seven five seven nine and that + + align:start position:0% +six seven five seven nine and that + + + align:start position:0% +six seven five seven nine and that +consequently I can write this array of + + align:start position:0% +consequently I can write this array of + + + align:start position:0% +consequently I can write this array of +nine terms simply as the following + + align:start position:0% +nine terms simply as the following + + + align:start position:0% +nine terms simply as the following +product I write the row matrix x1 x2 x3 + + align:start position:0% +product I write the row matrix x1 x2 x3 + + + align:start position:0% +product I write the row matrix x1 x2 x3 +multiply that by the 3x3 matrix three + + align:start position:0% +multiply that by the 3x3 matrix three + + + align:start position:0% +multiply that by the 3x3 matrix three +four five four six seven five seven nine + + align:start position:0% +four five four six seven five seven nine + + + align:start position:0% +four five four six seven five seven nine +and multiply that in turn by the column + + align:start position:0% +and multiply that in turn by the column + + + align:start position:0% +and multiply that in turn by the column +matrix y1 y2 y3 as a quick check notice + + align:start position:0% +matrix y1 y2 y3 as a quick check notice + + + align:start position:0% +matrix y1 y2 y3 as a quick check notice +that this is a one by three matrix this + + align:start position:0% +that this is a one by three matrix this + + + align:start position:0% +that this is a one by three matrix this +is three by three this is three by one + + align:start position:0% +is three by three this is three by one + + + align:start position:0% +is three by three this is three by one +and + + align:start position:0% +and + + + align:start position:0% +and +consequently this will be a one by one + + align:start position:0% +consequently this will be a one by one + + + align:start position:0% +consequently this will be a one by one +matrix or a number what number will it + + align:start position:0% +matrix or a number what number will it + + + align:start position:0% +matrix or a number what number will it +be it'll be this number here and notice + + align:start position:0% +be it'll be this number here and notice + + + align:start position:0% +be it'll be this number here and notice +what I'm saying that X 1 X 2 X 3 y 1 y 2 + + align:start position:0% +what I'm saying that X 1 X 2 X 3 y 1 y 2 + + + align:start position:0% +what I'm saying that X 1 X 2 X 3 y 1 y 2 +y 3 are given numbers and + + align:start position:0% +y 3 are given numbers and + + + align:start position:0% +y 3 are given numbers and +consequently the dot product in question + + align:start position:0% +consequently the dot product in question + + + align:start position:0% +consequently the dot product in question +is determined as soon as I know these + + align:start position:0% +is determined as soon as I know these + + + align:start position:0% +is determined as soon as I know these +coefficients which happen to be the dot + + align:start position:0% +coefficients which happen to be the dot + + + align:start position:0% +coefficients which happen to be the dot +products of the basis elements with one + + align:start position:0% +products of the basis elements with one + + + align:start position:0% +products of the basis elements with one +another so this shows two things one how + + align:start position:0% +another so this shows two things one how + + + align:start position:0% +another so this shows two things one how +we write this in matrix form and two how + + align:start position:0% +we write this in matrix form and two how + + + align:start position:0% +we write this in matrix form and two how +the dot product of each two vectors in V + + align:start position:0% +the dot product of each two vectors in V + + + align:start position:0% +the dot product of each two vectors in V +is determined by just knowing what + + align:start position:0% +is determined by just knowing what + + + align:start position:0% +is determined by just knowing what +happens to the pairs of basis vectors + + align:start position:0% +happens to the pairs of basis vectors + + + align:start position:0% +happens to the pairs of basis vectors +when we got them and this gives us still + + align:start position:0% +when we got them and this gives us still + + + align:start position:0% +when we got them and this gives us still +another way of seeing how matrices are + + align:start position:0% +another way of seeing how matrices are + + + align:start position:0% +another way of seeing how matrices are +used as a coding system in other words + + align:start position:0% +used as a coding system in other words + + + align:start position:0% +used as a coding system in other words +every symmetric remember what symmetric + + align:start position:0% +every symmetric remember what symmetric + + + align:start position:0% +every symmetric remember what symmetric +means you get the same matrix when you + + align:start position:0% +means you get the same matrix when you + + + align:start position:0% +means you get the same matrix when you +interchange rows and columns every + + align:start position:0% +interchange rows and columns every + + + align:start position:0% +interchange rows and columns every +symmetric n by n matrix codes a dot + + align:start position:0% +symmetric n by n matrix codes a dot + + + align:start position:0% +symmetric n by n matrix codes a dot +product and conversely every dot product + + align:start position:0% +product and conversely every dot product + + + align:start position:0% +product and conversely every dot product +is coded by a symmetric n by n matrix + + align:start position:0% +is coded by a symmetric n by n matrix + + + align:start position:0% +is coded by a symmetric n by n matrix +you see what does this matrix tell me + + align:start position:0% +you see what does this matrix tell me + + + align:start position:0% +you see what does this matrix tell me +this is the entry in the eye the entry + + align:start position:0% +this is the entry in the eye the entry + + + align:start position:0% +this is the entry in the eye the entry +in the I throw J column is what happens + + align:start position:0% +in the I throw J column is what happens + + + align:start position:0% +in the I throw J column is what happens +when you sub I is dotted with u sub j + + align:start position:0% +when you sub I is dotted with u sub j + + + align:start position:0% +when you sub I is dotted with u sub j +without meaning to belabor this point + + align:start position:0% +without meaning to belabor this point + + + align:start position:0% +without meaning to belabor this point +let us notice that the array here 3 4 5 + + align:start position:0% +let us notice that the array here 3 4 5 + + + align:start position:0% +let us notice that the array here 3 4 5 +4 6 7 5 7 9 is precisely the array that + + align:start position:0% +4 6 7 5 7 9 is precisely the array that + + + align:start position:0% +4 6 7 5 7 9 is precisely the array that +we had over here 3 4 5 4 seven five + + align:start position:0% +we had over here 3 4 5 4 seven five + + + align:start position:0% +we had over here 3 4 5 4 seven five +seven nine this is what we mean when we + + align:start position:0% +seven nine this is what we mean when we + + + align:start position:0% +seven nine this is what we mean when we +talk about the matrix of the dot product + + align:start position:0% +talk about the matrix of the dot product + + + align:start position:0% +talk about the matrix of the dot product +it's the array of how the basis vectors + + align:start position:0% +it's the array of how the basis vectors + + + align:start position:0% +it's the array of how the basis vectors +look when you dot them with one another + + align:start position:0% +look when you dot them with one another + + + align:start position:0% +look when you dot them with one another +by the way as another aside we agreed + + align:start position:0% +by the way as another aside we agreed + + + align:start position:0% +by the way as another aside we agreed +that when you dot a vector with itself + + align:start position:0% +that when you dot a vector with itself + + + align:start position:0% +that when you dot a vector with itself +that can be identified in a way with the + + align:start position:0% +that can be identified in a way with the + + + align:start position:0% +that can be identified in a way with the +length of the vector in particular going + + align:start position:0% +length of the vector in particular going + + + align:start position:0% +length of the vector in particular going +back to this example here if the X's and + + align:start position:0% +back to this example here if the X's and + + + align:start position:0% +back to this example here if the X's and +the Y's are chosen to be equal if I let + + align:start position:0% +the Y's are chosen to be equal if I let + + + align:start position:0% +the Y's are chosen to be equal if I let +x1 equal y1 x2 equal Y 2 and X 3 equals + + align:start position:0% +x1 equal y1 x2 equal Y 2 and X 3 equals + + + align:start position:0% +x1 equal y1 x2 equal Y 2 and X 3 equals +y 3 this problem here reduces to this + + align:start position:0% +y 3 this problem here reduces to this + + + align:start position:0% +y 3 this problem here reduces to this +problem which in turn just combining + + align:start position:0% +problem which in turn just combining + + + align:start position:0% +problem which in turn just combining +what I had above in other words with the + + align:start position:0% +what I had above in other words with the + + + align:start position:0% +what I had above in other words with the +X's and the Y's equal gives me that + + align:start position:0% +X's and the Y's equal gives me that + + + align:start position:0% +X's and the Y's equal gives me that +define the square of the length of a + + align:start position:0% +define the square of the length of a + + + align:start position:0% +define the square of the length of a +matrix of a vector I have to solve this + + align:start position:0% +matrix of a vector I have to solve this + + + align:start position:0% +matrix of a vector I have to solve this +particular algebraic equation and this + + align:start position:0% +particular algebraic equation and this + + + align:start position:0% +particular algebraic equation and this +algebraic equation is called a quadratic + + align:start position:0% +algebraic equation is called a quadratic + + + align:start position:0% +algebraic equation is called a quadratic +form you see notice that each of the + + align:start position:0% +form you see notice that each of the + + + align:start position:0% +form you see notice that each of the +variables x1 x2 x3 appears in each term + + align:start position:0% +variables x1 x2 x3 appears in each term + + + align:start position:0% +variables x1 x2 x3 appears in each term +here as a second degree variable see + + align:start position:0% +here as a second degree variable see + + + align:start position:0% +here as a second degree variable see +here's an x1 squared his x1 times x2 you + + align:start position:0% +here's an x1 squared his x1 times x2 you + + + align:start position:0% +here's an x1 squared his x1 times x2 you +see two factors x1 times x3 and what I'm + + align:start position:0% +see two factors x1 times x3 and what I'm + + + align:start position:0% +see two factors x1 times x3 and what I'm +driving at again is aside from any other + + align:start position:0% +driving at again is aside from any other + + + align:start position:0% +driving at again is aside from any other +connections notice that to solve for the + + align:start position:0% +connections notice that to solve for the + + + align:start position:0% +connections notice that to solve for the +length of a particular vector one has to + + align:start position:0% +length of a particular vector one has to + + + align:start position:0% +length of a particular vector one has to +wind up solving what we call quadratic + + align:start position:0% +wind up solving what we call quadratic + + + align:start position:0% +wind up solving what we call quadratic +forms and these for 2 & 3 dimensions can + + align:start position:0% +forms and these for 2 & 3 dimensions can + + + align:start position:0% +forms and these for 2 & 3 dimensions can +be identified with certain curves in two + + align:start position:0% +be identified with certain curves in two + + + align:start position:0% +be identified with certain curves in two +or three dimensional space but I don't + + align:start position:0% +or three dimensional space but I don't + + + align:start position:0% +or three dimensional space but I don't +want to belabor that point too much here + + align:start position:0% +want to belabor that point too much here + + + align:start position:0% +want to belabor that point too much here +either I just want you to get a Buckshot + + align:start position:0% +either I just want you to get a Buckshot + + + align:start position:0% +either I just want you to get a Buckshot +overview of how one works abstractly + + align:start position:0% +overview of how one works abstractly + + + align:start position:0% +overview of how one works abstractly +with the dot product idea by the way + + align:start position:0% +with the dot product idea by the way + + + align:start position:0% +with the dot product idea by the way +some new terminology if V is an + + align:start position:0% +some new terminology if V is an + + + align:start position:0% +some new terminology if V is an +n-dimensional vector space with basis u1 + + align:start position:0% +n-dimensional vector space with basis u1 + + + align:start position:0% +n-dimensional vector space with basis u1 +up to u n we call the basis u1 up to u N + + align:start position:0% +up to u n we call the basis u1 up to u N + + + align:start position:0% +up to u n we call the basis u1 up to u N +and orthogonal basis relative to a given + + align:start position:0% +and orthogonal basis relative to a given + + + align:start position:0% +and orthogonal basis relative to a given +dot product if the dot product of any + + align:start position:0% +dot product if the dot product of any + + + align:start position:0% +dot product if the dot product of any +two different members of the basis is 0 + + align:start position:0% +two different members of the basis is 0 + + + align:start position:0% +two different members of the basis is 0 +in other words if u sub I dot u sub J is + + align:start position:0% +in other words if u sub I dot u sub J is + + + align:start position:0% +in other words if u sub I dot u sub J is +0 for all I on equal to J we call this + + align:start position:0% +0 for all I on equal to J we call this + + + align:start position:0% +0 for all I on equal to J we call this +an orthogonal basis + + align:start position:0% +an orthogonal basis + + + align:start position:0% +an orthogonal basis +for the usual reason of what our thuggin + + align:start position:0% +for the usual reason of what our thuggin + + + align:start position:0% +for the usual reason of what our thuggin +all means when the dot product of two + + align:start position:0% +all means when the dot product of two + + + align:start position:0% +all means when the dot product of two +arrows was zero we said the arrows were + + align:start position:0% +arrows was zero we said the arrows were + + + align:start position:0% +arrows was zero we said the arrows were +perpendicular etc this is just a + + align:start position:0% +perpendicular etc this is just a + + + align:start position:0% +perpendicular etc this is just a +carryover from that in particular if in + + align:start position:0% +carryover from that in particular if in + + + align:start position:0% +carryover from that in particular if in +addition the dot product of any vector + + align:start position:0% +addition the dot product of any vector + + + align:start position:0% +addition the dot product of any vector +with itself happens to be one then the + + align:start position:0% +with itself happens to be one then the + + + align:start position:0% +with itself happens to be one then the +basis is called an ortho normal basis + + align:start position:0% +basis is called an ortho normal basis + + + align:start position:0% +basis is called an ortho normal basis +and this whole idea is moderate modeled + + align:start position:0% +and this whole idea is moderate modeled + + + align:start position:0% +and this whole idea is moderate modeled +after the usual example that in + + align:start position:0% +after the usual example that in + + + align:start position:0% +after the usual example that in +three-dimensional space IJ K forms an + + align:start position:0% +three-dimensional space IJ K forms an + + + align:start position:0% +three-dimensional space IJ K forms an +orthonormal basis relative to the usual + + align:start position:0% +orthonormal basis relative to the usual + + + align:start position:0% +orthonormal basis relative to the usual +dot product in other words i dot j i dot + + align:start position:0% +dot product in other words i dot j i dot + + + align:start position:0% +dot product in other words i dot j i dot +k and j dot k are all + + align:start position:0% +k and j dot k are all + + + align:start position:0% +k and j dot k are all +around zero but i dot i J dot J and K + + align:start position:0% +around zero but i dot i J dot J and K + + + align:start position:0% +around zero but i dot i J dot J and K +dot k are all 1 now the interesting + + align:start position:0% +dot k are all 1 now the interesting + + + align:start position:0% +dot k are all 1 now the interesting +point is that in most textbooks one + + align:start position:0% +point is that in most textbooks one + + + align:start position:0% +point is that in most textbooks one +always defines the dot product in much + + align:start position:0% +always defines the dot product in much + + + align:start position:0% +always defines the dot product in much +the same way as we do I J and K one + + align:start position:0% +the same way as we do I J and K one + + + align:start position:0% +the same way as we do I J and K one +always assumes that somehow or other we + + align:start position:0% +always assumes that somehow or other we + + + align:start position:0% +always assumes that somehow or other we +have an orthonormal basis now obviously + + align:start position:0% +have an orthonormal basis now obviously + + + align:start position:0% +have an orthonormal basis now obviously +in the example I'm motivating today's + + align:start position:0% +in the example I'm motivating today's + + + align:start position:0% +in the example I'm motivating today's +lecture on we don't have an orthonormal + + align:start position:0% +lecture on we don't have an orthonormal + + + align:start position:0% +lecture on we don't have an orthonormal +basis remember we had something like u 1 + + align:start position:0% +basis remember we had something like u 1 + + + align:start position:0% +basis remember we had something like u 1 +dot u 2 was 4 what's it to be + + align:start position:0% +dot u 2 was 4 what's it to be + + + align:start position:0% +dot u 2 was 4 what's it to be +orthonormal u 1 dot u 2 first of all + + align:start position:0% +orthonormal u 1 dot u 2 first of all + + + align:start position:0% +orthonormal u 1 dot u 2 first of all +would have to be 0 and u 1 dot u 1 would + + align:start position:0% +would have to be 0 and u 1 dot u 1 would + + + align:start position:0% +would have to be 0 and u 1 dot u 1 would +have to be 1 but in our example u 1 dot + + align:start position:0% +have to be 1 but in our example u 1 dot + + + align:start position:0% +have to be 1 but in our example u 1 dot +u 1 is 3 so the question that comes up + + align:start position:0% +u 1 is 3 so the question that comes up + + + align:start position:0% +u 1 is 3 so the question that comes up +is do we always have an orthonormal + + align:start position:0% +is do we always have an orthonormal + + + align:start position:0% +is do we always have an orthonormal +basis and the answer is yes and in fact + + align:start position:0% +basis and the answer is yes and in fact + + + align:start position:0% +basis and the answer is yes and in fact +if you like big words the process by + + align:start position:0% +if you like big words the process by + + + align:start position:0% +if you like big words the process by +which we construct an orthonormal + + align:start position:0% +which we construct an orthonormal + + + align:start position:0% +which we construct an orthonormal +basis in fact the process is easier than + + align:start position:0% +basis in fact the process is easier than + + + align:start position:0% +basis in fact the process is easier than +the name the name is called the + + align:start position:0% +the name the name is called the + + + align:start position:0% +the name the name is called the +gram-schmidt orthogonalization process + + align:start position:0% +gram-schmidt orthogonalization process + + + align:start position:0% +gram-schmidt orthogonalization process +and geometrically what the method boils + + align:start position:0% +and geometrically what the method boils + + + align:start position:0% +and geometrically what the method boils +down to is that if I'm given two + + align:start position:0% +down to is that if I'm given two + + + align:start position:0% +down to is that if I'm given two +non-parallel vectors u 1 and u 2 to find + + align:start position:0% +non-parallel vectors u 1 and u 2 to find + + + align:start position:0% +non-parallel vectors u 1 and u 2 to find +the space spanned by u1 and u2 i can + + align:start position:0% +the space spanned by u1 and u2 i can + + + align:start position:0% +the space spanned by u1 and u2 i can +replace you two by the component of u 2 + + align:start position:0% +replace you two by the component of u 2 + + + align:start position:0% +replace you two by the component of u 2 +which is perpendicular to u 1 let's call + + align:start position:0% +which is perpendicular to u 1 let's call + + + align:start position:0% +which is perpendicular to u 1 let's call +that component u 2 star what I'm saying + + align:start position:0% +that component u 2 star what I'm saying + + + align:start position:0% +that component u 2 star what I'm saying +is that u 1 and u 2 star span the same + + align:start position:0% +is that u 1 and u 2 star span the same + + + align:start position:0% +is that u 1 and u 2 star span the same +space as u 1 and u 2 but obviously + + align:start position:0% +space as u 1 and u 2 but obviously + + + align:start position:0% +space as u 1 and u 2 but obviously +geometrically it's easy to see that u 1 + + align:start position:0% +geometrically it's easy to see that u 1 + + + align:start position:0% +geometrically it's easy to see that u 1 +and u 2 star are orthogonal now the + + align:start position:0% +and u 2 star are orthogonal now the + + + align:start position:0% +and u 2 star are orthogonal now the +question is how could we get the same + + align:start position:0% +question is how could we get the same + + + align:start position:0% +question is how could we get the same +result without having to rely on + + align:start position:0% +result without having to rely on + + + align:start position:0% +result without having to rely on +geometry and the answer is we say look + + align:start position:0% +geometry and the answer is we say look + + + align:start position:0% +geometry and the answer is we say look +at we know already in our cost that in + + align:start position:0% +at we know already in our cost that in + + + align:start position:0% +at we know already in our cost that in +terms of spanning vectors if you replace + + align:start position:0% +terms of spanning vectors if you replace + + + align:start position:0% +terms of spanning vectors if you replace +a vector by a by itself plus or minus a + + align:start position:0% +a vector by a by itself plus or minus a + + + align:start position:0% +a vector by a by itself plus or minus a +scalar multiple of another you don't + + align:start position:0% +scalar multiple of another you don't + + + align:start position:0% +scalar multiple of another you don't +change the space spanned by the given + + align:start position:0% +change the space spanned by the given + + + align:start position:0% +change the space spanned by the given +set of vectors so why not write you to + + align:start position:0% +set of vectors so why not write you to + + + align:start position:0% +set of vectors so why not write you to +star to be you to minus some suitable + + align:start position:0% +star to be you to minus some suitable + + + align:start position:0% +star to be you to minus some suitable +multiple of u1 to u2 minus x u1 where + + align:start position:0% +multiple of u1 to u2 minus x u1 where + + + align:start position:0% +multiple of u1 to u2 minus x u1 where +we'll try to determine X in such a way + + align:start position:0% +we'll try to determine X in such a way + + + align:start position:0% +we'll try to determine X in such a way +that you to star dotted with u 1 will be + + align:start position:0% +that you to star dotted with u 1 will be + + + align:start position:0% +that you to star dotted with u 1 will be +0 you see what we're going to try to do + + align:start position:0% +0 you see what we're going to try to do + + + align:start position:0% +0 you see what we're going to try to do +is replace u2 by an equivalent vector + + align:start position:0% +is replace u2 by an equivalent vector + + + align:start position:0% +is replace u2 by an equivalent vector +meaning that u 1 and u 2 star will span + + align:start position:0% +meaning that u 1 and u 2 star will span + + + align:start position:0% +meaning that u 1 and u 2 star will span +the same space as u 1 and u 2 but with + + align:start position:0% +the same space as u 1 and u 2 but with + + + align:start position:0% +the same space as u 1 and u 2 but with +the additional property that u 1 and u 2 + + align:start position:0% +the additional property that u 1 and u 2 + + + align:start position:0% +the additional property that u 1 and u 2 +star will be your Thugga know where as u + + align:start position:0% +star will be your Thugga know where as u + + + align:start position:0% +star will be your Thugga know where as u +1 and u 2 might not have been orthogonal + + align:start position:0% +1 and u 2 might not have been orthogonal + + + align:start position:0% +1 and u 2 might not have been orthogonal +and now you see we can proceed + + align:start position:0% +and now you see we can proceed + + + align:start position:0% +and now you see we can proceed +axiomatically namely we say ok what we + + align:start position:0% +axiomatically namely we say ok what we + + + align:start position:0% +axiomatically namely we say ok what we +want to look at is u 2 star dot u 1 so + + align:start position:0% +want to look at is u 2 star dot u 1 so + + + align:start position:0% +want to look at is u 2 star dot u 1 so +let's start both sides of this equation + + align:start position:0% +let's start both sides of this equation + + + align:start position:0% +let's start both sides of this equation +with u 1 you see the left-hand side will + + align:start position:0% +with u 1 you see the left-hand side will + + + align:start position:0% +with u 1 you see the left-hand side will +become u 2 u 1 the right-hand side + + align:start position:0% +become u 2 u 1 the right-hand side + + + align:start position:0% +become u 2 u 1 the right-hand side +becomes u 2 minus x u 1 dotted with u 1 + + align:start position:0% +becomes u 2 minus x u 1 dotted with u 1 + + + align:start position:0% +becomes u 2 minus x u 1 dotted with u 1 +but by our distributive property this is + + align:start position:0% +but by our distributive property this is + + + align:start position:0% +but by our distributive property this is +the same as u 2 dot u 1 minus x u 1 got + + align:start position:0% +the same as u 2 dot u 1 minus x u 1 got + + + align:start position:0% +the same as u 2 dot u 1 minus x u 1 got +you one now we didn't want X to be any + + align:start position:0% +you one now we didn't want X to be any + + + align:start position:0% +you one now we didn't want X to be any +old number we wanted X to be that number + + align:start position:0% +old number we wanted X to be that number + + + align:start position:0% +old number we wanted X to be that number +if one exists that makes u 2 star dot u + + align:start position:0% +if one exists that makes u 2 star dot u + + + align:start position:0% +if one exists that makes u 2 star dot u +1 equal to 0 remember u 2 dot u 1 and u + + align:start position:0% +1 equal to 0 remember u 2 dot u 1 and u + + + align:start position:0% +1 equal to 0 remember u 2 dot u 1 and u +1 dot u 1 are numbers + + align:start position:0% +1 dot u 1 are numbers + + + align:start position:0% +1 dot u 1 are numbers +consequently I treat this as an ordinary + + align:start position:0% +consequently I treat this as an ordinary + + + align:start position:0% +consequently I treat this as an ordinary +algebraic equation namely this is a + + align:start position:0% +algebraic equation namely this is a + + + align:start position:0% +algebraic equation namely this is a +number this is a number I equate this to + + align:start position:0% +number this is a number I equate this to + + + align:start position:0% +number this is a number I equate this to +0 and solve for X in other words X's u 2 + + align:start position:0% +0 and solve for X in other words X's u 2 + + + align:start position:0% +0 and solve for X in other words X's u 2 +dot u 1 divided by u 1 dot u 1 and by + + align:start position:0% +dot u 1 divided by u 1 dot u 1 and by + + + align:start position:0% +dot u 1 divided by u 1 dot u 1 and by +the way just as an aside many + + align:start position:0% +the way just as an aside many + + + align:start position:0% +the way just as an aside many +mathematicians as an abbreviation when + + align:start position:0% +mathematicians as an abbreviation when + + + align:start position:0% +mathematicians as an abbreviation when +they want to write the dot product of a + + align:start position:0% +they want to write the dot product of a + + + align:start position:0% +they want to write the dot product of a +vector and itself they write it as the + + align:start position:0% +vector and itself they write it as the + + + align:start position:0% +vector and itself they write it as the +square of the given vector obviously + + align:start position:0% +square of the given vector obviously + + + align:start position:0% +square of the given vector obviously +this cannot mean the usual squaring + + align:start position:0% +this cannot mean the usual squaring + + + align:start position:0% +this cannot mean the usual squaring +operation + + align:start position:0% +operation + + + align:start position:0% +operation +because we don't multiply vectors by + + align:start position:0% +because we don't multiply vectors by + + + align:start position:0% +because we don't multiply vectors by +themselves this obviously refers to the + + align:start position:0% +themselves this obviously refers to the + + + align:start position:0% +themselves this obviously refers to the +dot product and I mentioned this in + + align:start position:0% +dot product and I mentioned this in + + + align:start position:0% +dot product and I mentioned this in +passing simply so that if you see this + + align:start position:0% +passing simply so that if you see this + + + align:start position:0% +passing simply so that if you see this +in the literature you will not be + + align:start position:0% +in the literature you will not be + + + align:start position:0% +in the literature you will not be +confused by it I prefer to write u 1 dot + + align:start position:0% +confused by it I prefer to write u 1 dot + + + align:start position:0% +confused by it I prefer to write u 1 dot +u 1 rather than u 1 squared but would + + align:start position:0% +u 1 rather than u 1 squared but would + + + align:start position:0% +u 1 rather than u 1 squared but would +like you to see this notation anyway at + + align:start position:0% +like you to see this notation anyway at + + + align:start position:0% +like you to see this notation anyway at +any rate now knowing what X is I replace + + align:start position:0% +any rate now knowing what X is I replace + + + align:start position:0% +any rate now knowing what X is I replace +X here + + align:start position:0% +X here + + + align:start position:0% +X here +into this equation and I wind up with + + align:start position:0% +into this equation and I wind up with + + + align:start position:0% +into this equation and I wind up with +that u 2 star is u 2 minus u 2 dot u 1 + + align:start position:0% +that u 2 star is u 2 minus u 2 dot u 1 + + + align:start position:0% +that u 2 star is u 2 minus u 2 dot u 1 +over u 1 dot u 1 times you want and if + + align:start position:0% +over u 1 dot u 1 times you want and if + + + align:start position:0% +over u 1 dot u 1 times you want and if +you want to check this thing + + align:start position:0% +you want to check this thing + + + align:start position:0% +you want to check this thing +geometrically the u2 started I've + + align:start position:0% +geometrically the u2 started I've + + + align:start position:0% +geometrically the u2 started I've +computed this way is precisely the u 2 + + align:start position:0% +computed this way is precisely the u 2 + + + align:start position:0% +computed this way is precisely the u 2 +star that I get geometrically the beauty + + align:start position:0% +star that I get geometrically the beauty + + + align:start position:0% +star that I get geometrically the beauty +of this technique is that it did not + + align:start position:0% +of this technique is that it did not + + + align:start position:0% +of this technique is that it did not +require geometry and consequently + + align:start position:0% +require geometry and consequently + + + align:start position:0% +require geometry and consequently +structurally I should be able to use + + align:start position:0% +structurally I should be able to use + + + align:start position:0% +structurally I should be able to use +this in higher dimensions and that's + + align:start position:0% +this in higher dimensions and that's + + + align:start position:0% +this in higher dimensions and that's +exactly what the gram-schmidt + + align:start position:0% +exactly what the gram-schmidt + + + align:start position:0% +exactly what the gram-schmidt +orthogonalization process is what you do + + align:start position:0% +orthogonalization process is what you do + + + align:start position:0% +orthogonalization process is what you do +is is you start with a basis okay you + + align:start position:0% +is is you start with a basis okay you + + + align:start position:0% +is is you start with a basis okay you +take the first vector in that basis and + + align:start position:0% +take the first vector in that basis and + + + align:start position:0% +take the first vector in that basis and +doll it with the second vector if the if + + align:start position:0% +doll it with the second vector if the if + + + align:start position:0% +doll it with the second vector if the if +that dot product is 0 those two vectors + + align:start position:0% +that dot product is 0 those two vectors + + + align:start position:0% +that dot product is 0 those two vectors +are both eligible to be part of an + + align:start position:0% +are both eligible to be part of an + + + align:start position:0% +are both eligible to be part of an +orthogonal basis now if that dot product + + align:start position:0% +orthogonal basis now if that dot product + + + align:start position:0% +orthogonal basis now if that dot product +isn't 0 you use the gram-schmidt + + align:start position:0% +isn't 0 you use the gram-schmidt + + + align:start position:0% +isn't 0 you use the gram-schmidt +orthogonalization process to replace the + + align:start position:0% +orthogonalization process to replace the + + + align:start position:0% +orthogonalization process to replace the +second vector u 2 by u 2 star where u 1 + + align:start position:0% +second vector u 2 by u 2 star where u 1 + + + align:start position:0% +second vector u 2 by u 2 star where u 1 +dot u 2 star is 0 now you take that new + + align:start position:0% +dot u 2 star is 0 now you take that new + + + align:start position:0% +dot u 2 star is 0 now you take that new +basis which spans the same space as the + + align:start position:0% +basis which spans the same space as the + + + align:start position:0% +basis which spans the same space as the +original u 1 and u 2 and compare that or + + align:start position:0% +original u 1 and u 2 and compare that or + + + align:start position:0% +original u 1 and u 2 and compare that or +take that in connection with u 3 and see + + align:start position:0% +take that in connection with u 3 and see + + + align:start position:0% +take that in connection with u 3 and see +if those three vectors form an + + align:start position:0% +if those three vectors form an + + + align:start position:0% +if those three vectors form an +orthogonal basis our our Authority + + align:start position:0% +orthogonal basis our our Authority + + + align:start position:0% +orthogonal basis our our Authority +meaning their dot product of different + + align:start position:0% +meaning their dot product of different + + + align:start position:0% +meaning their dot product of different +ones is 0 and if it is fine and if it + + align:start position:0% +ones is 0 and if it is fine and if it + + + align:start position:0% +ones is 0 and if it is fine and if it +isn't you just inductively keep using + + align:start position:0% +isn't you just inductively keep using + + + align:start position:0% +isn't you just inductively keep using +the gram-schmidt orthogonalization + + align:start position:0% +the gram-schmidt orthogonalization + + + align:start position:0% +the gram-schmidt orthogonalization +process now to show you what this means + + align:start position:0% +process now to show you what this means + + + align:start position:0% +process now to show you what this means +in a specific case let's suppose I have + + align:start position:0% +in a specific case let's suppose I have + + + align:start position:0% +in a specific case let's suppose I have +the following situation let's suppose I + + align:start position:0% +the following situation let's suppose I + + + align:start position:0% +the following situation let's suppose I +have a 4 dimensional vector space for + + align:start position:0% +have a 4 dimensional vector space for + + + align:start position:0% +have a 4 dimensional vector space for +which a basis is u1 u2 u3 and u4 + + align:start position:0% +which a basis is u1 u2 u3 and u4 + + + align:start position:0% +which a basis is u1 u2 u3 and u4 +suppose I also know that u 1 u 2 & u 3 + + align:start position:0% +suppose I also know that u 1 u 2 & u 3 + + + align:start position:0% +suppose I also know that u 1 u 2 & u 3 +form an orthogonal set that means I know + + align:start position:0% +form an orthogonal set that means I know + + + align:start position:0% +form an orthogonal set that means I know +that u 1 u 2 u 1 dot u 3 and u 2 dot u 3 + + align:start position:0% +that u 1 u 2 u 1 dot u 3 and u 2 dot u 3 + + + align:start position:0% +that u 1 u 2 u 1 dot u 3 and u 2 dot u 3 +are all 0 but I don't know that you for + + align:start position:0% +are all 0 but I don't know that you for + + + align:start position:0% +are all 0 but I don't know that you for +dot u 1 you for dot u 2 u for dot u 3 + + align:start position:0% +dot u 1 you for dot u 2 u for dot u 3 + + + align:start position:0% +dot u 1 you for dot u 2 u for dot u 3 +are 0 or anything like this and the + + align:start position:0% +are 0 or anything like this and the + + + align:start position:0% +are 0 or anything like this and the +question that comes up now is I would + + align:start position:0% +question that comes up now is I would + + + align:start position:0% +question that comes up now is I would +like to replace you for by an equivalent + + align:start position:0% +like to replace you for by an equivalent + + + align:start position:0% +like to replace you for by an equivalent +vector which I'll call u sub 4 star such + + align:start position:0% +vector which I'll call u sub 4 star such + + + align:start position:0% +vector which I'll call u sub 4 star such +that u 1 u 2 u 3 and u sub 4 star spend + + align:start position:0% +that u 1 u 2 u 3 and u sub 4 star spend + + + align:start position:0% +that u 1 u 2 u 3 and u sub 4 star spend +the same space V but that now with you 4 + + align:start position:0% +the same space V but that now with you 4 + + + align:start position:0% +the same space V but that now with you 4 +replaced by u 4 star this becomes an + + align:start position:0% +replaced by u 4 star this becomes an + + + align:start position:0% +replaced by u 4 star this becomes an +orthogonal basis + + align:start position:0% +orthogonal basis + + + align:start position:0% +orthogonal basis +well the way I proceed is I use the fact + + align:start position:0% +well the way I proceed is I use the fact + + + align:start position:0% +well the way I proceed is I use the fact +that whenever I replace a vector by + + align:start position:0% +that whenever I replace a vector by + + + align:start position:0% +that whenever I replace a vector by +itself plus or minus a linear + + align:start position:0% +itself plus or minus a linear + + + align:start position:0% +itself plus or minus a linear +combination of the other vectors I don't + + align:start position:0% +combination of the other vectors I don't + + + align:start position:0% +combination of the other vectors I don't +change the space spanned by the vectors + + align:start position:0% +change the space spanned by the vectors + + + align:start position:0% +change the space spanned by the vectors +so what I say is let u 4 star be u 4 + + align:start position:0% +so what I say is let u 4 star be u 4 + + + align:start position:0% +so what I say is let u 4 star be u 4 +minus X 1 u 1 minus X 2 u 2 minus X 3 u + + align:start position:0% +minus X 1 u 1 minus X 2 u 2 minus X 3 u + + + align:start position:0% +minus X 1 u 1 minus X 2 u 2 minus X 3 u +3 you see I'm modeling this after what I + + align:start position:0% +3 you see I'm modeling this after what I + + + align:start position:0% +3 you see I'm modeling this after what I +did in the two dimensional case what I + + align:start position:0% +did in the two dimensional case what I + + + align:start position:0% +did in the two dimensional case what I +want to do is determine X 1 X 2 and X 3 + + align:start position:0% +want to do is determine X 1 X 2 and X 3 + + + align:start position:0% +want to do is determine X 1 X 2 and X 3 +such that u 4 star dot u 1 u 4 star dot + + align:start position:0% +such that u 4 star dot u 1 u 4 star dot + + + align:start position:0% +such that u 4 star dot u 1 u 4 star dot +u 2 & u 4 star dot you 3 will all be 0 + + align:start position:0% +u 2 & u 4 star dot you 3 will all be 0 + + + align:start position:0% +u 2 & u 4 star dot you 3 will all be 0 +and the trick is simply this let me + + align:start position:0% +and the trick is simply this let me + + + align:start position:0% +and the trick is simply this let me +focus my attention on one of these + + align:start position:0% +focus my attention on one of these + + + align:start position:0% +focus my attention on one of these +coefficients because the technique is + + align:start position:0% +coefficients because the technique is + + + align:start position:0% +coefficients because the technique is +the same for all the others let's + + align:start position:0% +the same for all the others let's + + + align:start position:0% +the same for all the others let's +suppose I want to find out what X 3 is + + align:start position:0% +suppose I want to find out what X 3 is + + + align:start position:0% +suppose I want to find out what X 3 is +the trick is I dot both sides of this + + align:start position:0% +the trick is I dot both sides of this + + + align:start position:0% +the trick is I dot both sides of this +equation with you 3 now why do I do that + + align:start position:0% +equation with you 3 now why do I do that + + + align:start position:0% +equation with you 3 now why do I do that +remember u1 u2 and u3 are an orthogonal + + align:start position:0% +remember u1 u2 and u3 are an orthogonal + + + align:start position:0% +remember u1 u2 and u3 are an orthogonal +set consequently when I dot u 1 with u 3 + + align:start position:0% +set consequently when I dot u 1 with u 3 + + + align:start position:0% +set consequently when I dot u 1 with u 3 +and u2 with u3 those terms will be 0 and + + align:start position:0% +and u2 with u3 those terms will be 0 and + + + align:start position:0% +and u2 with u3 those terms will be 0 and +they will drop out in other words + + align:start position:0% +they will drop out in other words + + + align:start position:0% +they will drop out in other words +dotting both sides of this equation with + + align:start position:0% +dotting both sides of this equation with + + + align:start position:0% +dotting both sides of this equation with +u 3 and using the fact that the dot + + align:start position:0% +u 3 and using the fact that the dot + + + align:start position:0% +u 3 and using the fact that the dot +product is distributive I get u force + + align:start position:0% +product is distributive I get u force + + + align:start position:0% +product is distributive I get u force +dot u 3 is U for dot u 3 minus X 1 u 1 + + align:start position:0% +dot u 3 is U for dot u 3 minus X 1 u 1 + + + align:start position:0% +dot u 3 is U for dot u 3 minus X 1 u 1 +dot u 3 minus X 2 u 2 dot u 3 minus X 3 + + align:start position:0% +dot u 3 minus X 2 u 2 dot u 3 minus X 3 + + + align:start position:0% +dot u 3 minus X 2 u 2 dot u 3 minus X 3 +u 3 dot u 3 and the key point is that by + + align:start position:0% +u 3 dot u 3 and the key point is that by + + + align:start position:0% +u 3 dot u 3 and the key point is that by +orthogonality + + align:start position:0% +orthogonality + + + align:start position:0% +orthogonality +these two things here are 0 + + align:start position:0% +these two things here are 0 + + + align:start position:0% +these two things here are 0 +consequently you forced out you three is + + align:start position:0% +consequently you forced out you three is + + + align:start position:0% +consequently you forced out you three is +you for dot u 3 minus X 3 you three got + + align:start position:0% +you for dot u 3 minus X 3 you three got + + + align:start position:0% +you for dot u 3 minus X 3 you three got +you three remember these are numbers I + + align:start position:0% +you three remember these are numbers I + + + align:start position:0% +you three remember these are numbers I +would like you for star dot u3 to be + + align:start position:0% +would like you for star dot u3 to be + + + align:start position:0% +would like you for star dot u3 to be +zero so all I have to do now is solve + + align:start position:0% +zero so all I have to do now is solve + + + align:start position:0% +zero so all I have to do now is solve +this algebraic equation for x 3 and + + align:start position:0% +this algebraic equation for x 3 and + + + align:start position:0% +this algebraic equation for x 3 and +notice that X 3 algebraically simply + + align:start position:0% +notice that X 3 algebraically simply + + + align:start position:0% +notice that X 3 algebraically simply +turns out to be u 4 dot u 3 over u 3 u 3 + + align:start position:0% +turns out to be u 4 dot u 3 over u 3 u 3 + + + align:start position:0% +turns out to be u 4 dot u 3 over u 3 u 3 +again the only thing I have to be + + align:start position:0% +again the only thing I have to be + + + align:start position:0% +again the only thing I have to be +careful about is that the denominator + + align:start position:0% +careful about is that the denominator + + + align:start position:0% +careful about is that the denominator +not be 0 and notice that by positive + + align:start position:0% +not be 0 and notice that by positive + + + align:start position:0% +not be 0 and notice that by positive +definiteness u 3 dot u 3 can only equal + + align:start position:0% +definiteness u 3 dot u 3 can only equal + + + align:start position:0% +definiteness u 3 dot u 3 can only equal +0 if if u 3 is the zero vector + + align:start position:0% +0 if if u 3 is the zero vector + + + align:start position:0% +0 if if u 3 is the zero vector +but if you three had been the 0 vector + + align:start position:0% +but if you three had been the 0 vector + + + align:start position:0% +but if you three had been the 0 vector +it couldn't be part of a basis so you + + align:start position:0% +it couldn't be part of a basis so you + + + align:start position:0% +it couldn't be part of a basis so you +get the idea of how this works this is + + align:start position:0% +get the idea of how this works this is + + + align:start position:0% +get the idea of how this works this is +the same gram-schmidt orthogonalization + + align:start position:0% +the same gram-schmidt orthogonalization + + + align:start position:0% +the same gram-schmidt orthogonalization +process that we used in two dimensions + + align:start position:0% +process that we used in two dimensions + + + align:start position:0% +process that we used in two dimensions +because once we know that all the + + align:start position:0% +because once we know that all the + + + align:start position:0% +because once we know that all the +vectors up to use up for our orthogonal + + align:start position:0% +vectors up to use up for our orthogonal + + + align:start position:0% +vectors up to use up for our orthogonal +whenever we got one of them with the + + align:start position:0% +whenever we got one of them with the + + + align:start position:0% +whenever we got one of them with the +other three we essentially reduce this + + align:start position:0% +other three we essentially reduce this + + + align:start position:0% +other three we essentially reduce this +to a do dimensional product problem + + align:start position:0% +to a do dimensional product problem + + + align:start position:0% +to a do dimensional product problem +because all the other dot products drop + + align:start position:0% +because all the other dot products drop + + + align:start position:0% +because all the other dot products drop +out in a similar way you see I could + + align:start position:0% +out in a similar way you see I could + + + align:start position:0% +out in a similar way you see I could +have found X sub 2 and X sub 1 leaving + + align:start position:0% +have found X sub 2 and X sub 1 leaving + + + align:start position:0% +have found X sub 2 and X sub 1 leaving +the details to you the easiest way to + + align:start position:0% +the details to you the easiest way to + + + align:start position:0% +the details to you the easiest way to +remember this is every place I see a + + align:start position:0% +remember this is every place I see a + + + align:start position:0% +remember this is every place I see a +subscript 3 over here let me replace it + + align:start position:0% +subscript 3 over here let me replace it + + + align:start position:0% +subscript 3 over here let me replace it +by a tool or and then every place I see + + align:start position:0% +by a tool or and then every place I see + + + align:start position:0% +by a tool or and then every place I see +the 3 let me replace it by a 1 and what + + align:start position:0% +the 3 let me replace it by a 1 and what + + + align:start position:0% +the 3 let me replace it by a 1 and what +I get is that you for star is u 4 and + + align:start position:0% +I get is that you for star is u 4 and + + + align:start position:0% +I get is that you for star is u 4 and +then I subtract off these scalar + + align:start position:0% +then I subtract off these scalar + + + align:start position:0% +then I subtract off these scalar +multiples what scalar multiples are they + + align:start position:0% +multiples what scalar multiples are they + + + align:start position:0% +multiples what scalar multiples are they +notice that it's what the coefficient of + + align:start position:0% +notice that it's what the coefficient of + + + align:start position:0% +notice that it's what the coefficient of +U 1 is U 4 dot u 1 over u 1 dot u 1 the + + align:start position:0% +U 1 is U 4 dot u 1 over u 1 dot u 1 the + + + align:start position:0% +U 1 is U 4 dot u 1 over u 1 dot u 1 the +coefficient of U to has as its + + align:start position:0% +coefficient of U to has as its + + + align:start position:0% +coefficient of U to has as its +denominator u 2 dot u 2 the numerator is + + align:start position:0% +denominator u 2 dot u 2 the numerator is + + + align:start position:0% +denominator u 2 dot u 2 the numerator is +you four dotted with u 2 in other words + + align:start position:0% +you four dotted with u 2 in other words + + + align:start position:0% +you four dotted with u 2 in other words +in a sense it's like the projection of U + + align:start position:0% +in a sense it's like the projection of U + + + align:start position:0% +in a sense it's like the projection of U +4 onto u 2 and the coefficient of U 3 + + align:start position:0% +4 onto u 2 and the coefficient of U 3 + + + align:start position:0% +4 onto u 2 and the coefficient of U 3 +has as its denominator u 3 u 3 and its + + align:start position:0% +has as its denominator u 3 u 3 and its + + + align:start position:0% +has as its denominator u 3 u 3 and its +denominator is u 4 . u 3 now to show you + + align:start position:0% +denominator is u 4 . u 3 now to show you + + + align:start position:0% +denominator is u 4 . u 3 now to show you +how this works let's come back to our + + align:start position:0% +how this works let's come back to our + + + align:start position:0% +how this works let's come back to our +original problem which I've reproduced + + align:start position:0% +original problem which I've reproduced + + + align:start position:0% +original problem which I've reproduced +over here remember what we had we had + + align:start position:0% +over here remember what we had we had + + + align:start position:0% +over here remember what we had we had +that u 1 dot u 1 is 3 u 1 u 2 is 4 u 1 + + align:start position:0% +that u 1 dot u 1 is 3 u 1 u 2 is 4 u 1 + + + align:start position:0% +that u 1 dot u 1 is 3 u 1 u 2 is 4 u 1 +dot u 3 is 5 etc I'll refer to this as I + + align:start position:0% +dot u 3 is 5 etc I'll refer to this as I + + + align:start position:0% +dot u 3 is 5 etc I'll refer to this as I +need it let me show you how the + + align:start position:0% +need it let me show you how the + + + align:start position:0% +need it let me show you how the +gram-schmidt process allows me to find + + align:start position:0% +gram-schmidt process allows me to find + + + align:start position:0% +gram-schmidt process allows me to find +from this an orthogonal basis the first + + align:start position:0% +from this an orthogonal basis the first + + + align:start position:0% +from this an orthogonal basis the first +thing is that obviously u1 is not the + + align:start position:0% +thing is that obviously u1 is not the + + + align:start position:0% +thing is that obviously u1 is not the +zero vector because if it were the zero + + align:start position:0% +zero vector because if it were the zero + + + align:start position:0% +zero vector because if it were the zero +vector u 1 dot u one would be zero not + + align:start position:0% +vector u 1 dot u one would be zero not + + + align:start position:0% +vector u 1 dot u one would be zero not +three so the first vector in my + + align:start position:0% +three so the first vector in my + + + align:start position:0% +three so the first vector in my +orthogonal basis which I'll call you one + + align:start position:0% +orthogonal basis which I'll call you one + + + align:start position:0% +orthogonal basis which I'll call you one +star can be u 1 itself how do I find the + + align:start position:0% +star can be u 1 itself how do I find the + + + align:start position:0% +star can be u 1 itself how do I find the +second vector according to the + + align:start position:0% +second vector according to the + + + align:start position:0% +second vector according to the +gram-schmidt orthogonalization process i + + align:start position:0% +gram-schmidt orthogonalization process i + + + align:start position:0% +gram-schmidt orthogonalization process i +replace u 2 by u 2 minus a suitable + + align:start position:0% +replace u 2 by u 2 minus a suitable + + + align:start position:0% +replace u 2 by u 2 minus a suitable +scalar multiple of u 1 star and what + + align:start position:0% +scalar multiple of u 1 star and what + + + align:start position:0% +scalar multiple of u 1 star and what +scalar multiple is that the denominator + + align:start position:0% +scalar multiple is that the denominator + + + align:start position:0% +scalar multiple is that the denominator +will be u 1 star u 1 star and the + + align:start position:0% +will be u 1 star u 1 star and the + + + align:start position:0% +will be u 1 star u 1 star and the +numerator will be u 2 dot u 1 star well + + align:start position:0% +numerator will be u 2 dot u 1 star well + + + align:start position:0% +numerator will be u 2 dot u 1 star well +remember u 1 star is equal to u 1 so + + align:start position:0% +remember u 1 star is equal to u 1 so + + + align:start position:0% +remember u 1 star is equal to u 1 so +right from this array here what do I + + align:start position:0% +right from this array here what do I + + + align:start position:0% +right from this array here what do I +have u 2 dot u 1 star is u 2 dot u 1 u 2 + + align:start position:0% +have u 2 dot u 1 star is u 2 dot u 1 u 2 + + + align:start position:0% +have u 2 dot u 1 star is u 2 dot u 1 u 2 +dot u 1 is for u 1 star dot u 1 star is + + align:start position:0% +dot u 1 is for u 1 star dot u 1 star is + + + align:start position:0% +dot u 1 is for u 1 star dot u 1 star is +u 1 dot u 1 u 1 dot u 1 is 3 so this is + + align:start position:0% +u 1 dot u 1 u 1 dot u 1 is 3 so this is + + + align:start position:0% +u 1 dot u 1 u 1 dot u 1 is 3 so this is +simply what minus 4 over 3 times u 1 in + + align:start position:0% +simply what minus 4 over 3 times u 1 in + + + align:start position:0% +simply what minus 4 over 3 times u 1 in +other words u 2 star is simply u 2 minus + + align:start position:0% +other words u 2 star is simply u 2 minus + + + align:start position:0% +other words u 2 star is simply u 2 minus +4/3 u 1 and by the way as a check what + + align:start position:0% +4/3 u 1 and by the way as a check what + + + align:start position:0% +4/3 u 1 and by the way as a check what +was this supposed to do if I replace u 2 + + align:start position:0% +was this supposed to do if I replace u 2 + + + align:start position:0% +was this supposed to do if I replace u 2 +by u 2 star these two vectors here + + align:start position:0% +by u 2 star these two vectors here + + + align:start position:0% +by u 2 star these two vectors here +should now be orthogonal are they let's + + align:start position:0% +should now be orthogonal are they let's + + + align:start position:0% +should now be orthogonal are they let's +dot them if i dot these two i get what + + align:start position:0% +dot them if i dot these two i get what + + + align:start position:0% +dot them if i dot these two i get what +you 1 dot u 2 minus 4/3 u 1 dot u 1 + + align:start position:0% +you 1 dot u 2 minus 4/3 u 1 dot u 1 + + + align:start position:0% +you 1 dot u 2 minus 4/3 u 1 dot u 1 +notice that u 1 dot u 2 is 4 u 1 dot u 1 + + align:start position:0% +notice that u 1 dot u 2 is 4 u 1 dot u 1 + + + align:start position:0% +notice that u 1 dot u 2 is 4 u 1 dot u 1 +is 3 so coming down here is a check u 1 + + align:start position:0% +is 3 so coming down here is a check u 1 + + + align:start position:0% +is 3 so coming down here is a check u 1 +star dot u 2 star is u 1 minus u 2 which + + align:start position:0% +star dot u 2 star is u 1 minus u 2 which + + + align:start position:0% +star dot u 2 star is u 1 minus u 2 which +is 4 minus 4/3 u 1 dot u 1 which is 3 + + align:start position:0% +is 4 minus 4/3 u 1 dot u 1 which is 3 + + + align:start position:0% +is 4 minus 4/3 u 1 dot u 1 which is 3 +the 3s cancel 4 minus 4 is 0 this checks + + align:start position:0% +the 3s cancel 4 minus 4 is 0 this checks + + + align:start position:0% +the 3s cancel 4 minus 4 is 0 this checks +out fine + + align:start position:0% +out fine + + + align:start position:0% +out fine +how do I find u 3 star well i subtract + + align:start position:0% +how do I find u 3 star well i subtract + + + align:start position:0% +how do I find u 3 star well i subtract +from from u 3 suitable scalar multiples + + align:start position:0% +from from u 3 suitable scalar multiples + + + align:start position:0% +from from u 3 suitable scalar multiples +of u 1 star and u 2 star you see what + + align:start position:0% +of u 1 star and u 2 star you see what + + + align:start position:0% +of u 1 star and u 2 star you see what +I've done I orthogonalize 1 vector at a + + align:start position:0% +I've done I orthogonalize 1 vector at a + + + align:start position:0% +I've done I orthogonalize 1 vector at a +time see first I got u 2 star now I know + + align:start position:0% +time see first I got u 2 star now I know + + + align:start position:0% +time see first I got u 2 star now I know +that u 1 star in u 2 star orthogonal + + align:start position:0% +that u 1 star in u 2 star orthogonal + + + align:start position:0% +that u 1 star in u 2 star orthogonal +using you once new to star the multiples + + align:start position:0% +using you once new to star the multiples + + + align:start position:0% +using you once new to star the multiples +that I subtract from you three are what + + align:start position:0% +that I subtract from you three are what + + + align:start position:0% +that I subtract from you three are what +for you one star my denominator is you + + align:start position:0% +for you one star my denominator is you + + + align:start position:0% +for you one star my denominator is you +one star dot u 1 star and my numerator + + align:start position:0% +one star dot u 1 star and my numerator + + + align:start position:0% +one star dot u 1 star and my numerator +is u 3 dot u 1 star and for you to star + + align:start position:0% +is u 3 dot u 1 star and for you to star + + + align:start position:0% +is u 3 dot u 1 star and for you to star +my denominator is u 2 star you 2 star + + align:start position:0% +my denominator is u 2 star you 2 star + + + align:start position:0% +my denominator is u 2 star you 2 star +and my numerator is u 3 dot u 2 star and + + align:start position:0% +and my numerator is u 3 dot u 2 star and + + + align:start position:0% +and my numerator is u 3 dot u 2 star and +now how do I evaluate what this thing + + align:start position:0% +now how do I evaluate what this thing + + + align:start position:0% +now how do I evaluate what this thing +really means well first of all I know + + align:start position:0% +really means well first of all I know + + + align:start position:0% +really means well first of all I know +what you three dot u 1 star is that's + + align:start position:0% +what you three dot u 1 star is that's + + + align:start position:0% +what you three dot u 1 star is that's +just you 3 dot u 1 which happens to be 5 + + align:start position:0% +just you 3 dot u 1 which happens to be 5 + + + align:start position:0% +just you 3 dot u 1 which happens to be 5 +and I also know what u 1 star dot u 1 + + align:start position:0% +and I also know what u 1 star dot u 1 + + + align:start position:0% +and I also know what u 1 star dot u 1 +star is that u 1 dot u 1 which is 3 I + + align:start position:0% +star is that u 1 dot u 1 which is 3 I + + + align:start position:0% +star is that u 1 dot u 1 which is 3 I +now have to compute what u 3 dot u 2 + + align:start position:0% +now have to compute what u 3 dot u 2 + + + align:start position:0% +now have to compute what u 3 dot u 2 +star and I have to compute u 2 dot u 2 + + align:start position:0% +star and I have to compute u 2 dot u 2 + + + align:start position:0% +star and I have to compute u 2 dot u 2 +star keep in mind that I've already + + align:start position:0% +star keep in mind that I've already + + + align:start position:0% +star keep in mind that I've already +computed that u 2 star is u 2 minus 4/3 + + align:start position:0% +computed that u 2 star is u 2 minus 4/3 + + + align:start position:0% +computed that u 2 star is u 2 minus 4/3 +u1 consequently u 3 u 2 star is u 3 dot + + align:start position:0% +u1 consequently u 3 u 2 star is u 3 dot + + + align:start position:0% +u1 consequently u 3 u 2 star is u 3 dot +u 2 minus 4/3 you want and now you see + + align:start position:0% +u 2 minus 4/3 you want and now you see + + + align:start position:0% +u 2 minus 4/3 you want and now you see +the mechanical algebra takes over again + + align:start position:0% +the mechanical algebra takes over again + + + align:start position:0% +the mechanical algebra takes over again +I know what my axioms for dot products + + align:start position:0% +I know what my axioms for dot products + + + align:start position:0% +I know what my axioms for dot products +are this gives me u 3 dot u 2 minus 4/3 + + align:start position:0% +are this gives me u 3 dot u 2 minus 4/3 + + + align:start position:0% +are this gives me u 3 dot u 2 minus 4/3 +u 3 dot u 1 I'm given that u 3 dot u 2 + + align:start position:0% +u 3 dot u 1 I'm given that u 3 dot u 2 + + + align:start position:0% +u 3 dot u 1 I'm given that u 3 dot u 2 +is 7 I'm given that u 3 dot u 1 is 5 so + + align:start position:0% +is 7 I'm given that u 3 dot u 1 is 5 so + + + align:start position:0% +is 7 I'm given that u 3 dot u 1 is 5 so +u 3 dot u 2 star is 7 minus 4/3 of 5 + + align:start position:0% +u 3 dot u 2 star is 7 minus 4/3 of 5 + + + align:start position:0% +u 3 dot u 2 star is 7 minus 4/3 of 5 +that's 1/3 21 minus 20 over 3 which is + + align:start position:0% +that's 1/3 21 minus 20 over 3 which is + + + align:start position:0% +that's 1/3 21 minus 20 over 3 which is +1/3 so let's see what I know now I know + + align:start position:0% +1/3 so let's see what I know now I know + + + align:start position:0% +1/3 so let's see what I know now I know +now how to handle this numerator u 3 dot + + align:start position:0% +now how to handle this numerator u 3 dot + + + align:start position:0% +now how to handle this numerator u 3 dot +u 2 star is 1/3 how do I handle u 2 star + + align:start position:0% +u 2 star is 1/3 how do I handle u 2 star + + + align:start position:0% +u 2 star is 1/3 how do I handle u 2 star +dot u 2 star u 2 star is u 2 minus 4/3 + + align:start position:0% +dot u 2 star u 2 star is u 2 minus 4/3 + + + align:start position:0% +dot u 2 star u 2 star is u 2 minus 4/3 +u1 so to find u 2 star dot u 2 star I + + align:start position:0% +u1 so to find u 2 star dot u 2 star I + + + align:start position:0% +u1 so to find u 2 star dot u 2 star I +have to dot u 2 minus 4/3 u 1 with + + align:start position:0% +have to dot u 2 minus 4/3 u 1 with + + + align:start position:0% +have to dot u 2 minus 4/3 u 1 with +itself if I do that and again notice how + + align:start position:0% +itself if I do that and again notice how + + + align:start position:0% +itself if I do that and again notice how +these rules work the same way as for + + align:start position:0% +these rules work the same way as for + + + align:start position:0% +these rules work the same way as for +ordinary algebra I get u 2 u 2 minus 8/3 + + align:start position:0% +ordinary algebra I get u 2 u 2 minus 8/3 + + + align:start position:0% +ordinary algebra I get u 2 u 2 minus 8/3 +u 1 dot u 2 plus 16 ninths u 1 dot u 1 + + align:start position:0% +u 1 dot u 2 plus 16 ninths u 1 dot u 1 + + + align:start position:0% +u 1 dot u 2 plus 16 ninths u 1 dot u 1 +well I know + + align:start position:0% +well I know + + + align:start position:0% +well I know +you too dot you two is six that was + + align:start position:0% +you too dot you two is six that was + + + align:start position:0% +you too dot you two is six that was +given I know that u 1 dot you u 2 dot u + + align:start position:0% +given I know that u 1 dot you u 2 dot u + + + align:start position:0% +given I know that u 1 dot you u 2 dot u +2 is 6 u 1 dot u 2 is 4 and nu 1 dot u 1 + + align:start position:0% +2 is 6 u 1 dot u 2 is 4 and nu 1 dot u 1 + + + align:start position:0% +2 is 6 u 1 dot u 2 is 4 and nu 1 dot u 1 +is 3 so evaluating this I wind up with + + align:start position:0% +is 3 so evaluating this I wind up with + + + align:start position:0% +is 3 so evaluating this I wind up with +the fact that u 2 star you 2 star is 6 + + align:start position:0% +the fact that u 2 star you 2 star is 6 + + + align:start position:0% +the fact that u 2 star you 2 star is 6 +minus 16 thirds or 2/3 + + align:start position:0% +minus 16 thirds or 2/3 + + + align:start position:0% +minus 16 thirds or 2/3 +consequently going back here you see my + + align:start position:0% +consequently going back here you see my + + + align:start position:0% +consequently going back here you see my +numerator is 1/3 my denominator is 2/3 + + align:start position:0% +numerator is 1/3 my denominator is 2/3 + + + align:start position:0% +numerator is 1/3 my denominator is 2/3 +so the fraction is 1/2 in other words + + align:start position:0% +so the fraction is 1/2 in other words + + + align:start position:0% +so the fraction is 1/2 in other words +substituting into here I get that you 3 + + align:start position:0% +substituting into here I get that you 3 + + + align:start position:0% +substituting into here I get that you 3 +star is u 3 minus 5/3 u 1 minus 1/2 u 2 + + align:start position:0% +star is u 3 minus 5/3 u 1 minus 1/2 u 2 + + + align:start position:0% +star is u 3 minus 5/3 u 1 minus 1/2 u 2 +minus 4/3 u 1 and re Cabul ating my + + align:start position:0% +minus 4/3 u 1 and re Cabul ating my + + + align:start position:0% +minus 4/3 u 1 and re Cabul ating my +results to write them in the usual order + + align:start position:0% +results to write them in the usual order + + + align:start position:0% +results to write them in the usual order +of U 1 u 2 & u 3 components notice that + + align:start position:0% +of U 1 u 2 & u 3 components notice that + + + align:start position:0% +of U 1 u 2 & u 3 components notice that +u 1 star is u 1 + + align:start position:0% +u 1 star is u 1 + + + align:start position:0% +u 1 star is u 1 +u 2 star is minus 4/3 u 1 plus u 2 u 3 + + align:start position:0% +u 2 star is minus 4/3 u 1 plus u 2 u 3 + + + align:start position:0% +u 2 star is minus 4/3 u 1 plus u 2 u 3 +star is minus u 1 minus 1/2 u 2 plus u 3 + + align:start position:0% +star is minus u 1 minus 1/2 u 2 plus u 3 + + + align:start position:0% +star is minus u 1 minus 1/2 u 2 plus u 3 +now what property does this set of + + align:start position:0% +now what property does this set of + + + align:start position:0% +now what property does this set of +vectors have first of all my claim is + + align:start position:0% +vectors have first of all my claim is + + + align:start position:0% +vectors have first of all my claim is +that there are Thugga no and secondly + + align:start position:0% +that there are Thugga no and secondly + + + align:start position:0% +that there are Thugga no and secondly +they span the same space as u1 u2 and u3 + + align:start position:0% +they span the same space as u1 u2 and u3 + + + align:start position:0% +they span the same space as u1 u2 and u3 +and it's clear why they span the same + + align:start position:0% +and it's clear why they span the same + + + align:start position:0% +and it's clear why they span the same +space as u1 u2 and u3 namely they're + + align:start position:0% +space as u1 u2 and u3 namely they're + + + align:start position:0% +space as u1 u2 and u3 namely they're +essentially suitable scalar multiples of + + align:start position:0% +essentially suitable scalar multiples of + + + align:start position:0% +essentially suitable scalar multiples of +u1 u2 linear combinations of scalar + + align:start position:0% +u1 u2 linear combinations of scalar + + + align:start position:0% +u1 u2 linear combinations of scalar +multiples of u1 u2 and u3 as a quick + + align:start position:0% +multiples of u1 u2 and u3 as a quick + + + align:start position:0% +multiples of u1 u2 and u3 as a quick +check and I'll leave some of the other + + align:start position:0% +check and I'll leave some of the other + + + align:start position:0% +check and I'll leave some of the other +details to you let's actually check that + + align:start position:0% +details to you let's actually check that + + + align:start position:0% +details to you let's actually check that +u 1 star dot u 3 star is really 0 if I + + align:start position:0% +u 1 star dot u 3 star is really 0 if I + + + align:start position:0% +u 1 star dot u 3 star is really 0 if I +dot u 1 star with u 3 star look at what + + align:start position:0% +dot u 1 star with u 3 star look at what + + + align:start position:0% +dot u 1 star with u 3 star look at what +I get I get minus u 1 dot u 1 minus 1/2 + + align:start position:0% +I get I get minus u 1 dot u 1 minus 1/2 + + + align:start position:0% +I get I get minus u 1 dot u 1 minus 1/2 +u 1 dot u 2 Plus u 1 dot u 3 u 1 dot u 1 + + align:start position:0% +u 1 dot u 2 Plus u 1 dot u 3 u 1 dot u 1 + + + align:start position:0% +u 1 dot u 2 Plus u 1 dot u 3 u 1 dot u 1 +is 3 u 1 dot u 2 is 4 so this is minus 3 + + align:start position:0% +is 3 u 1 dot u 2 is 4 so this is minus 3 + + + align:start position:0% +is 3 u 1 dot u 2 is 4 so this is minus 3 +minus 1/2 R 4 that's minus 2 u 1 dot u 3 + + align:start position:0% +minus 1/2 R 4 that's minus 2 u 1 dot u 3 + + + align:start position:0% +minus 1/2 R 4 that's minus 2 u 1 dot u 3 +is 5 minus 3 minus 2 plus 5 is 0 a + + align:start position:0% +is 5 minus 3 minus 2 plus 5 is 0 a + + + align:start position:0% +is 5 minus 3 minus 2 plus 5 is 0 a +similar check will show that u 2 star 3 + + align:start position:0% +similar check will show that u 2 star 3 + + + align:start position:0% +similar check will show that u 2 star 3 +star is 0 + + align:start position:0% +star is 0 + + + align:start position:0% +star is 0 +we should also check to see what the + + align:start position:0% +we should also check to see what the + + + align:start position:0% +we should also check to see what the +lengths of u 1 star u 2 star and u 3 + + align:start position:0% +lengths of u 1 star u 2 star and u 3 + + + align:start position:0% +lengths of u 1 star u 2 star and u 3 +star are in other words u 1 star dot u 1 + + align:start position:0% +star are in other words u 1 star dot u 1 + + + align:start position:0% +star are in other words u 1 star dot u 1 +star + + align:start position:0% +star + + + align:start position:0% +star +what that's u 1 dot u 1 which is 3 u 2 + + align:start position:0% +what that's u 1 dot u 1 which is 3 u 2 + + + align:start position:0% +what that's u 1 dot u 1 which is 3 u 2 +star you 2 star well we just found that + + align:start position:0% +star you 2 star well we just found that + + + align:start position:0% +star you 2 star well we just found that +over here that's 2/3 u 3 star dot u 3 + + align:start position:0% +over here that's 2/3 u 3 star dot u 3 + + + align:start position:0% +over here that's 2/3 u 3 star dot u 3 +star well you three star was minus u 1 + + align:start position:0% +star well you three star was minus u 1 + + + align:start position:0% +star well you three star was minus u 1 +minus 1/2 u 2 Plus u 3 dotting that with + + align:start position:0% +minus 1/2 u 2 Plus u 3 dotting that with + + + align:start position:0% +minus 1/2 u 2 Plus u 3 dotting that with +itself and notice I use the square + + align:start position:0% +itself and notice I use the square + + + align:start position:0% +itself and notice I use the square +notation here to save space and not have + + align:start position:0% +notation here to save space and not have + + + align:start position:0% +notation here to save space and not have +this run too long but dotting this the + + align:start position:0% +this run too long but dotting this the + + + align:start position:0% +this run too long but dotting this the +same as I would the square of any + + align:start position:0% +same as I would the square of any + + + align:start position:0% +same as I would the square of any +trinomial I get what you 1 dot u 1 plus + + align:start position:0% +trinomial I get what you 1 dot u 1 plus + + + align:start position:0% +trinomial I get what you 1 dot u 1 plus +1/4 u 2 u 2 plus u 3 u 3 plus u 1 dot u + + align:start position:0% +1/4 u 2 u 2 plus u 3 u 3 plus u 1 dot u + + + align:start position:0% +1/4 u 2 u 2 plus u 3 u 3 plus u 1 dot u +2 minus twice u 1 dot u 3 minus u 2 dot + + align:start position:0% +2 minus twice u 1 dot u 3 minus u 2 dot + + + align:start position:0% +2 minus twice u 1 dot u 3 minus u 2 dot +u 3 putting in the values for u 1 dot u + + align:start position:0% +u 3 putting in the values for u 1 dot u + + + align:start position:0% +u 3 putting in the values for u 1 dot u +1 for you to dot u 2 u 3 dot u 3 u 1 dot + + align:start position:0% +1 for you to dot u 2 u 3 dot u 3 u 1 dot + + + align:start position:0% +1 for you to dot u 2 u 3 dot u 3 u 1 dot +u 2 u 1 dot u 3 and u 2 dot u 3 putting + + align:start position:0% +u 2 u 1 dot u 3 and u 2 dot u 3 putting + + + align:start position:0% +u 2 u 1 dot u 3 and u 2 dot u 3 putting +in these values I find that u 3 star u 3 + + align:start position:0% +in these values I find that u 3 star u 3 + + + align:start position:0% +in these values I find that u 3 star u 3 +star is one-half so I have an orthogonal + + align:start position:0% +star is one-half so I have an orthogonal + + + align:start position:0% +star is one-half so I have an orthogonal +basis it's not orthonormal but notice + + align:start position:0% +basis it's not orthonormal but notice + + + align:start position:0% +basis it's not orthonormal but notice +that it's easy to fix up or the + + align:start position:0% +that it's easy to fix up or the + + + align:start position:0% +that it's easy to fix up or the +normality part because all I have to do + + align:start position:0% +normality part because all I have to do + + + align:start position:0% +normality part because all I have to do +is divide each of these vectors by the + + align:start position:0% +is divide each of these vectors by the + + + align:start position:0% +is divide each of these vectors by the +square root of this number and that will + + align:start position:0% +square root of this number and that will + + + align:start position:0% +square root of this number and that will +make the dot product one for example if + + align:start position:0% +make the dot product one for example if + + + align:start position:0% +make the dot product one for example if +I were to replace u 1 star by u 1 star + + align:start position:0% +I were to replace u 1 star by u 1 star + + + align:start position:0% +I were to replace u 1 star by u 1 star +over the square root of 3 then when I + + align:start position:0% +over the square root of 3 then when I + + + align:start position:0% +over the square root of 3 then when I +dotted these two vectors I would have 3 + + align:start position:0% +dotted these two vectors I would have 3 + + + align:start position:0% +dotted these two vectors I would have 3 +divided by the square root of 3 times + + align:start position:0% +divided by the square root of 3 times + + + align:start position:0% +divided by the square root of 3 times +the square root of 3 which is 3 and 3 + + align:start position:0% +the square root of 3 which is 3 and 3 + + + align:start position:0% +the square root of 3 which is 3 and 3 +over 3 is 1 so getting the lengths to be + + align:start position:0% +over 3 is 1 so getting the lengths to be + + + align:start position:0% +over 3 is 1 so getting the lengths to be +1 is quite easy the hotpot is thus + + align:start position:0% +1 is quite easy the hotpot is thus + + + align:start position:0% +1 is quite easy the hotpot is thus +gram-schmidt orthogonalization process + + align:start position:0% +gram-schmidt orthogonalization process + + + align:start position:0% +gram-schmidt orthogonalization process +to normalize what's going to + + align:start position:0% +to normalize what's going to + + + align:start position:0% +to normalize what's going to +orthogonalize what's going on now you + + align:start position:0% +orthogonalize what's going on now you + + + align:start position:0% +orthogonalize what's going on now you +know this may seem rather complicated + + align:start position:0% +know this may seem rather complicated + + + align:start position:0% +know this may seem rather complicated +but it's really one long piece of + + align:start position:0% +but it's really one long piece of + + + align:start position:0% +but it's really one long piece of +computation we'll do this more slowly in + + align:start position:0% +computation we'll do this more slowly in + + + align:start position:0% +computation we'll do this more slowly in +the exercises but the whole idea is what + + align:start position:0% +the exercises but the whole idea is what + + + align:start position:0% +the exercises but the whole idea is what +i successively use the gram-schmidt + + align:start position:0% +i successively use the gram-schmidt + + + align:start position:0% +i successively use the gram-schmidt +orthogonalization process to replace + + align:start position:0% +orthogonalization process to replace + + + align:start position:0% +orthogonalization process to replace +each vector by a suitable linear + + align:start position:0% +each vector by a suitable linear + + + align:start position:0% +each vector by a suitable linear +combination of itself and the preceding + + align:start position:0% +combination of itself and the preceding + + + align:start position:0% +combination of itself and the preceding +ones to make sure that the new + + align:start position:0% +ones to make sure that the new + + + align:start position:0% +ones to make sure that the new +replacement is orthogonal to the + + align:start position:0% +replacement is orthogonal to the + + + align:start position:0% +replacement is orthogonal to the +remaining ones and that doesn't change + + align:start position:0% +remaining ones and that doesn't change + + + align:start position:0% +remaining ones and that doesn't change +the space that i already have by the way + + align:start position:0% +the space that i already have by the way + + + align:start position:0% +the space that i already have by the way +if you want to see what means in terms + + align:start position:0% +if you want to see what means in terms + + + align:start position:0% +if you want to see what means in terms +of matrix multiplication + + align:start position:0% +of matrix multiplication + + + align:start position:0% +of matrix multiplication +notice that we saw earlier that to dot a + + align:start position:0% +notice that we saw earlier that to dot a + + + align:start position:0% +notice that we saw earlier that to dot a +vector with itself you write the vector + + align:start position:0% +vector with itself you write the vector + + + align:start position:0% +vector with itself you write the vector +as a row vector then write down the + + align:start position:0% +as a row vector then write down the + + + align:start position:0% +as a row vector then write down the +matrix of coefficients for the basis + + align:start position:0% +matrix of coefficients for the basis + + + align:start position:0% +matrix of coefficients for the basis +elements then write down that same + + align:start position:0% +elements then write down that same + + + align:start position:0% +elements then write down that same +vector as a column vector the fact that + + align:start position:0% +vector as a column vector the fact that + + + align:start position:0% +vector as a column vector the fact that +u 1 star is U 1 + 0 u 2 + 0 u 3 means + + align:start position:0% +u 1 star is U 1 + 0 u 2 + 0 u 3 means + + + align:start position:0% +u 1 star is U 1 + 0 u 2 + 0 u 3 means +that as a three tuple it would be 1 0 0 + + align:start position:0% +that as a three tuple it would be 1 0 0 + + + align:start position:0% +that as a three tuple it would be 1 0 0 +its transpose would be 1 0 0 the column + + align:start position:0% +its transpose would be 1 0 0 the column + + + align:start position:0% +its transpose would be 1 0 0 the column +vector and so when we take this vector + + align:start position:0% +vector and so when we take this vector + + + align:start position:0% +vector and so when we take this vector +and dot it with this vector that should + + align:start position:0% +and dot it with this vector that should + + + align:start position:0% +and dot it with this vector that should +be the entry u 1 dot u 1 in this + + align:start position:0% +be the entry u 1 dot u 1 in this + + + align:start position:0% +be the entry u 1 dot u 1 in this +particular matrix here if we take this + + align:start position:0% +particular matrix here if we take this + + + align:start position:0% +particular matrix here if we take this +times this this should be u 1 star + + align:start position:0% +times this this should be u 1 star + + + align:start position:0% +times this this should be u 1 star +dotted with u 2 star and since u 1 star + + align:start position:0% +dotted with u 2 star and since u 1 star + + + align:start position:0% +dotted with u 2 star and since u 1 star +on u 2 star or a thuggin oh that had + + align:start position:0% +on u 2 star or a thuggin oh that had + + + align:start position:0% +on u 2 star or a thuggin oh that had +better come out to be 0 and going on in + + align:start position:0% +better come out to be 0 and going on in + + + align:start position:0% +better come out to be 0 and going on in +this way what I claim is if you now + + align:start position:0% +this way what I claim is if you now + + + align:start position:0% +this way what I claim is if you now +replace u 1 star u 2 star and u 3 star + + align:start position:0% +replace u 1 star u 2 star and u 3 star + + + align:start position:0% +replace u 1 star u 2 star and u 3 star +by what three tuples they are then also + + align:start position:0% +by what three tuples they are then also + + + align:start position:0% +by what three tuples they are then also +replace them as column vectors here you + + align:start position:0% +replace them as column vectors here you + + + align:start position:0% +replace them as column vectors here you +will get a new 3 by 3 matrix which will + + align:start position:0% +will get a new 3 by 3 matrix which will + + + align:start position:0% +will get a new 3 by 3 matrix which will +be diagonal in other words if we change + + align:start position:0% +be diagonal in other words if we change + + + align:start position:0% +be diagonal in other words if we change +our basis from u1 u2 and u3 if we change + + align:start position:0% +our basis from u1 u2 and u3 if we change + + + align:start position:0% +our basis from u1 u2 and u3 if we change +that basis to u 1 star u 2 star u 3 star + + align:start position:0% +that basis to u 1 star u 2 star u 3 star + + + align:start position:0% +that basis to u 1 star u 2 star u 3 star +notice that the new matrix that we get + + align:start position:0% +notice that the new matrix that we get + + + align:start position:0% +notice that the new matrix that we get +is a diagonal matrix it's our way of + + align:start position:0% +is a diagonal matrix it's our way of + + + align:start position:0% +is a diagonal matrix it's our way of +saying that when u dot 2 different + + align:start position:0% +saying that when u dot 2 different + + + align:start position:0% +saying that when u dot 2 different +vectors the dot product is 0 the + + align:start position:0% +vectors the dot product is 0 the + + + align:start position:0% +vectors the dot product is 0 the +diagonal elements tell you what u 1 star + + align:start position:0% +diagonal elements tell you what u 1 star + + + align:start position:0% +diagonal elements tell you what u 1 star +dot u 1 star R u 2 star you 2 star u 3 + + align:start position:0% +dot u 1 star R u 2 star you 2 star u 3 + + + align:start position:0% +dot u 1 star R u 2 star you 2 star u 3 +star dot u 3 star that you see by using + + align:start position:0% +star dot u 3 star that you see by using + + + align:start position:0% +star dot u 3 star that you see by using +the diagonal matrix over here this is a + + align:start position:0% +the diagonal matrix over here this is a + + + align:start position:0% +the diagonal matrix over here this is a +much simpler model to use u 1 star u 2 + + align:start position:0% +much simpler model to use u 1 star u 2 + + + align:start position:0% +much simpler model to use u 1 star u 2 +star you 3 star is a much nicer basis to + + align:start position:0% +star you 3 star is a much nicer basis to + + + align:start position:0% +star you 3 star is a much nicer basis to +use the new 1 u 2 & u 3 in order to + + align:start position:0% +use the new 1 u 2 & u 3 in order to + + + align:start position:0% +use the new 1 u 2 & u 3 in order to +determine what thought products are I'll + + align:start position:0% +determine what thought products are I'll + + + align:start position:0% +determine what thought products are I'll +emphasize that in more detail later let + + align:start position:0% +emphasize that in more detail later let + + + align:start position:0% +emphasize that in more detail later let +me make one remark before I get to our + + align:start position:0% +me make one remark before I get to our + + + align:start position:0% +me make one remark before I get to our +concluding remarks and that is have you + + align:start position:0% +concluding remarks and that is have you + + + align:start position:0% +concluding remarks and that is have you +begun to notice how complicated matrices + + align:start position:0% +begun to notice how complicated matrices + + + align:start position:0% +begun to notice how complicated matrices +are from the point of view that they are + + align:start position:0% +are from the point of view that they are + + + align:start position:0% +are from the point of view that they are +such a wonderful coding device that we + + align:start position:0% +such a wonderful coding device that we + + + align:start position:0% +such a wonderful coding device that we +use them to code many different things + + align:start position:0% +use them to code many different things + + + align:start position:0% +use them to code many different things +for example we have used matrices to + + align:start position:0% +for example we have used matrices to + + + align:start position:0% +for example we have used matrices to +code a linear transformation relative to + + align:start position:0% +code a linear transformation relative to + + + align:start position:0% +code a linear transformation relative to +various bases we're now using linear + + align:start position:0% +various bases we're now using linear + + + align:start position:0% +various bases we're now using linear +we're now using matrices to code the + + align:start position:0% +we're now using matrices to code the + + + align:start position:0% +we're now using matrices to code the +same dot product relative to different + + align:start position:0% +same dot product relative to different + + + align:start position:0% +same dot product relative to different +bases we have used matrices to code + + align:start position:0% +bases we have used matrices to code + + + align:start position:0% +bases we have used matrices to code +equivalent row reduced bases as basis + + align:start position:0% +equivalent row reduced bases as basis + + + align:start position:0% +equivalent row reduced bases as basis +for the same vector space that at the + + align:start position:0% +for the same vector space that at the + + + align:start position:0% +for the same vector space that at the +end of this unit what I will do is try + + align:start position:0% +end of this unit what I will do is try + + + align:start position:0% +end of this unit what I will do is try +to give you a summary in the study guide + + align:start position:0% +to give you a summary in the study guide + + + align:start position:0% +to give you a summary in the study guide +of the different kinds of matrix + + align:start position:0% +of the different kinds of matrix + + + align:start position:0% +of the different kinds of matrix +equivalence and where they use because + + align:start position:0% +equivalence and where they use because + + + align:start position:0% +equivalence and where they use because +after a while you tend to get mixed up + + align:start position:0% +after a while you tend to get mixed up + + + align:start position:0% +after a while you tend to get mixed up +if we don't see these pieces one bit at + + align:start position:0% +if we don't see these pieces one bit at + + + align:start position:0% +if we don't see these pieces one bit at +a time but to help you see what all this + + align:start position:0% +a time but to help you see what all this + + + align:start position:0% +a time but to help you see what all this +problem means I have cheated that the + + align:start position:0% +problem means I have cheated that the + + + align:start position:0% +problem means I have cheated that the +place I got the data from for the u1 u2 + + align:start position:0% +place I got the data from for the u1 u2 + + + align:start position:0% +place I got the data from for the u1 u2 +and u3 in this problem was that I + + align:start position:0% +and u3 in this problem was that I + + + align:start position:0% +and u3 in this problem was that I +thought of the following three vectors I + + align:start position:0% +thought of the following three vectors I + + + align:start position:0% +thought of the following three vectors I +plus J plus K 2 I plus J plus K 2 I plus + + align:start position:0% +plus J plus K 2 I plus J plus K 2 I plus + + + align:start position:0% +plus J plus K 2 I plus J plus K 2 I plus +J plus 2 K and used this to make up the + + align:start position:0% +J plus 2 K and used this to make up the + + + align:start position:0% +J plus 2 K and used this to make up the +data for u1 u2 and u3 that was in this + + align:start position:0% +data for u1 u2 and u3 that was in this + + + align:start position:0% +data for u1 u2 and u3 that was in this +exercise what you may be in which you + + align:start position:0% +exercise what you may be in which you + + + align:start position:0% +exercise what you may be in which you +may find informative and what I will do + + align:start position:0% +may find informative and what I will do + + + align:start position:0% +may find informative and what I will do +as a learning exercise is have you go + + align:start position:0% +as a learning exercise is have you go + + + align:start position:0% +as a learning exercise is have you go +through the same exercise that we have + + align:start position:0% +through the same exercise that we have + + + align:start position:0% +through the same exercise that we have +just done as today's lesson and have you + + align:start position:0% +just done as today's lesson and have you + + + align:start position:0% +just done as today's lesson and have you +verify that this checks out with the + + align:start position:0% +verify that this checks out with the + + + align:start position:0% +verify that this checks out with the +equivalent geometric construction that + + align:start position:0% +equivalent geometric construction that + + + align:start position:0% +equivalent geometric construction that +one of the exercises in the homework + + align:start position:0% +one of the exercises in the homework + + + align:start position:0% +one of the exercises in the homework +will be to show what the gram-schmidt + + align:start position:0% +will be to show what the gram-schmidt + + + align:start position:0% +will be to show what the gram-schmidt +orthogonalization process means + + align:start position:0% +orthogonalization process means + + + align:start position:0% +orthogonalization process means +geometrically for these three vectors by + + align:start position:0% +geometrically for these three vectors by + + + align:start position:0% +geometrically for these three vectors by +the way rather than to belabor that + + align:start position:0% +the way rather than to belabor that + + + align:start position:0% +the way rather than to belabor that +point for now let me make one other + + align:start position:0% +point for now let me make one other + + + align:start position:0% +point for now let me make one other +aside and that is I had mentioned before + + align:start position:0% +aside and that is I had mentioned before + + + align:start position:0% +aside and that is I had mentioned before +that to find the dot product of two + + align:start position:0% +that to find the dot product of two + + + align:start position:0% +that to find the dot product of two +vectors it may be more advantageous to + + align:start position:0% +vectors it may be more advantageous to + + + align:start position:0% +vectors it may be more advantageous to +use one basis rather than another + + align:start position:0% +use one basis rather than another + + + align:start position:0% +use one basis rather than another +remember when we wanted to dot a vector + + align:start position:0% +remember when we wanted to dot a vector + + + align:start position:0% +remember when we wanted to dot a vector +with itself using u1 u2 and u3 as a + + align:start position:0% +with itself using u1 u2 and u3 as a + + + align:start position:0% +with itself using u1 u2 and u3 as a +basis remember we got six different + + align:start position:0% +basis remember we got six different + + + align:start position:0% +basis remember we got six different +terms we had a an x1 squared x2 squared + + align:start position:0% +terms we had a an x1 squared x2 squared + + + align:start position:0% +terms we had a an x1 squared x2 squared +x3 squared an X 1 X 2 X 1 X 3 and X 2 X + + align:start position:0% +x3 squared an X 1 X 2 X 1 X 3 and X 2 X + + + align:start position:0% +x3 squared an X 1 X 2 X 1 X 3 and X 2 X + + align:start position:0% + + + align:start position:0% +notice that when you pick an orthogonal + + align:start position:0% +notice that when you pick an orthogonal + + + align:start position:0% +notice that when you pick an orthogonal +basis you only get three terms because + + align:start position:0% +basis you only get three terms because + + + align:start position:0% +basis you only get three terms because +once the basis is orthogonal all you + + align:start position:0% +once the basis is orthogonal all you + + + align:start position:0% +once the basis is orthogonal all you +have to do is dot corresponding entries + + align:start position:0% +have to do is dot corresponding entries + + + align:start position:0% +have to do is dot corresponding entries +because you see if I dot u 1 star with a + + align:start position:0% +because you see if I dot u 1 star with a + + + align:start position:0% +because you see if I dot u 1 star with a +term involving u 2 star or u 3 star that + + align:start position:0% +term involving u 2 star or u 3 star that + + + align:start position:0% +term involving u 2 star or u 3 star that +will be 0 by orthogonality if I didn't + + align:start position:0% +will be 0 by orthogonality if I didn't + + + align:start position:0% +will be 0 by orthogonality if I didn't +have an orthogonal basis I couldn't + + align:start position:0% +have an orthogonal basis I couldn't + + + align:start position:0% +have an orthogonal basis I couldn't +neglect those terms so for example to + + align:start position:0% +neglect those terms so for example to + + + align:start position:0% +neglect those terms so for example to +dot a vector with itself in this + + align:start position:0% +dot a vector with itself in this + + + align:start position:0% +dot a vector with itself in this +particular example using u 1 star u 2 + + align:start position:0% +particular example using u 1 star u 2 + + + align:start position:0% +particular example using u 1 star u 2 +star & u 3 star as a basis notice that + + align:start position:0% +star & u 3 star as a basis notice that + + + align:start position:0% +star & u 3 star as a basis notice that +when I wind up with is what X 1 times X + + align:start position:0% +when I wind up with is what X 1 times X + + + align:start position:0% +when I wind up with is what X 1 times X +1 X 1 squared times u 1 star dot u 1 + + align:start position:0% +1 X 1 squared times u 1 star dot u 1 + + + align:start position:0% +1 X 1 squared times u 1 star dot u 1 +star which is 3 etc meaning 3 X 1 + + align:start position:0% +star which is 3 etc meaning 3 X 1 + + + align:start position:0% +star which is 3 etc meaning 3 X 1 +squared plus 2/3 X 2 squared plus 1/2 X + + align:start position:0% +squared plus 2/3 X 2 squared plus 1/2 X + + + align:start position:0% +squared plus 2/3 X 2 squared plus 1/2 X +3 squared which is the square of the + + align:start position:0% +3 squared which is the square of the + + + align:start position:0% +3 squared which is the square of the +length of the vector that I'm looking + + align:start position:0% +length of the vector that I'm looking + + + align:start position:0% +length of the vector that I'm looking +for if I put everything over a common + + align:start position:0% +for if I put everything over a common + + + align:start position:0% +for if I put everything over a common +denominator I get a very nice equation + + align:start position:0% +denominator I get a very nice equation + + + align:start position:0% +denominator I get a very nice equation +for an ellipsoid over here you see a + + align:start position:0% +for an ellipsoid over here you see a + + + align:start position:0% +for an ellipsoid over here you see a +very nice equation with no mixed terms + + align:start position:0% +very nice equation with no mixed terms + + + align:start position:0% +very nice equation with no mixed terms +just perfect squares appearing over here + + align:start position:0% +just perfect squares appearing over here + + + align:start position:0% +just perfect squares appearing over here +the mixed terms drop out and that's one + + align:start position:0% +the mixed terms drop out and that's one + + + align:start position:0% +the mixed terms drop out and that's one +reason why we like orthogonal basis + + align:start position:0% +reason why we like orthogonal basis + + + align:start position:0% +reason why we like orthogonal basis +still another reason that we like + + align:start position:0% +still another reason that we like + + + align:start position:0% +still another reason that we like +orthogonal basis and I'll conclude with + + align:start position:0% +orthogonal basis and I'll conclude with + + + align:start position:0% +orthogonal basis and I'll conclude with +this example is that if we know that the + + align:start position:0% +this example is that if we know that the + + + align:start position:0% +this example is that if we know that the +vectors u1 up to u n are orthonormal say + + align:start position:0% +vectors u1 up to u n are orthonormal say + + + align:start position:0% +vectors u1 up to u n are orthonormal say +and that X 1 u 1 plus etcetera xn u n is + + align:start position:0% +and that X 1 u 1 plus etcetera xn u n is + + + align:start position:0% +and that X 1 u 1 plus etcetera xn u n is +0 then we automatically know that the + + align:start position:0% +0 then we automatically know that the + + + align:start position:0% +0 then we automatically know that the +user that x1 up to xn are 0 that these + + align:start position:0% +user that x1 up to xn are 0 that these + + + align:start position:0% +user that x1 up to xn are 0 that these +are linearly independent and the proof + + align:start position:0% +are linearly independent and the proof + + + align:start position:0% +are linearly independent and the proof +is quite simple namely all we do is we + + align:start position:0% +is quite simple namely all we do is we + + + align:start position:0% +is quite simple namely all we do is we +dot both sides of this equation with for + + align:start position:0% +dot both sides of this equation with for + + + align:start position:0% +dot both sides of this equation with for +example u sub 1 we could have used any + + align:start position:0% +example u sub 1 we could have used any + + + align:start position:0% +example u sub 1 we could have used any +one of the use that we wanted but using + + align:start position:0% +one of the use that we wanted but using + + + align:start position:0% +one of the use that we wanted but using +u sub 1 we dot u sub 1 with both sides + + align:start position:0% +u sub 1 we dot u sub 1 with both sides + + + align:start position:0% +u sub 1 we dot u sub 1 with both sides +of this equation notice that this term + + align:start position:0% +of this equation notice that this term + + + align:start position:0% +of this equation notice that this term +gives me X 1 u 1 dot u 1 the next terms + + align:start position:0% +gives me X 1 u 1 dot u 1 the next terms + + + align:start position:0% +gives me X 1 u 1 dot u 1 the next terms +are what u 1 dot u 2 up to u 1 dot u n + + align:start position:0% +are what u 1 dot u 2 up to u 1 dot u n + + + align:start position:0% +are what u 1 dot u 2 up to u 1 dot u n +by the property of being orthogonal all + + align:start position:0% +by the property of being orthogonal all + + + align:start position:0% +by the property of being orthogonal all +of these products are 0 consequently + + align:start position:0% +of these products are 0 consequently + + + align:start position:0% +of these products are 0 consequently +this scalar times X 1 must be 0 + + align:start position:0% +this scalar times X 1 must be 0 + + + align:start position:0% +this scalar times X 1 must be 0 +consequently X 1 itself must be 0 I've + + align:start position:0% +consequently X 1 itself must be 0 I've + + + align:start position:0% +consequently X 1 itself must be 0 I've +deliberately gone very rapidly here to + + align:start position:0% +deliberately gone very rapidly here to + + + align:start position:0% +deliberately gone very rapidly here to +give you an overview and to also have + + align:start position:0% +give you an overview and to also have + + + align:start position:0% +give you an overview and to also have +you see as I'm talking + + align:start position:0% +you see as I'm talking + + + align:start position:0% +you see as I'm talking +what these computations look like I + + align:start position:0% +what these computations look like I + + + align:start position:0% +what these computations look like I +think by hearing this as complicated as + + align:start position:0% +think by hearing this as complicated as + + + align:start position:0% +think by hearing this as complicated as +it may sound I think when you now read + + align:start position:0% +it may sound I think when you now read + + + align:start position:0% +it may sound I think when you now read +the solutions to the exercises you will + + align:start position:0% +the solutions to the exercises you will + + + align:start position:0% +the solutions to the exercises you will +have a better feeling for what's going + + align:start position:0% +have a better feeling for what's going + + + align:start position:0% +have a better feeling for what's going +on in as I say in the exercises I will + + align:start position:0% +on in as I say in the exercises I will + + + align:start position:0% +on in as I say in the exercises I will +develop these topics much more slowly + + align:start position:0% +develop these topics much more slowly + + + align:start position:0% +develop these topics much more slowly +and you can read these solutions as we + + align:start position:0% +and you can read these solutions as we + + + align:start position:0% +and you can read these solutions as we +go along at any rate this presents our + + align:start position:0% +go along at any rate this presents our + + + align:start position:0% +go along at any rate this presents our +overview of dot products and so until + + align:start position:0% +overview of dot products and so until + + + align:start position:0% +overview of dot products and so until +next time then goodbye + + align:start position:0% + + + + align:start position:0% + +funding for the publication of this + + align:start position:0% +funding for the publication of this + + + align:start position:0% +funding for the publication of this +video was provided by the Gabriella and + + align:start position:0% +video was provided by the Gabriella and + + + align:start position:0% +video was provided by the Gabriella and +Paul Rosenbaum foundation + + align:start position:0% +Paul Rosenbaum foundation + + + align:start position:0% +Paul Rosenbaum foundation +help ocw continue to provide free and + + align:start position:0% +help ocw continue to provide free and + + + align:start position:0% +help ocw continue to provide free and +open access to MIT courses by making a + + align:start position:0% +open access to MIT courses by making a + + + align:start position:0% +open access to MIT courses by making a +donation at ocw.mit.edu/donate \ No newline at end of file diff --git a/bElQTlIWCr8.txt b/bElQTlIWCr8.txt new file mode 100644 index 0000000000000000000000000000000000000000..fe150c86d91e62013ae2d7322b9b65089065c491 --- /dev/null +++ b/bElQTlIWCr8.txt @@ -0,0 +1,7419 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free to make a donation or to view + + align:start position:0% +for free to make a donation or to view + + + align:start position:0% +for free to make a donation or to view +additional materials from hundreds of + + align:start position:0% +additional materials from hundreds of + + + align:start position:0% +additional materials from hundreds of +MIT courses visit MIT opencourseware at + + align:start position:0% +MIT courses visit MIT opencourseware at + + + align:start position:0% +MIT courses visit MIT opencourseware at +ocw.mit.edu + + align:start position:0% +ocw.mit.edu + + + align:start position:0% +ocw.mit.edu +ok + + align:start position:0% +ok + + + align:start position:0% +ok +so I thought I'd quickly list the four + + align:start position:0% +so I thought I'd quickly list the four + + + align:start position:0% +so I thought I'd quickly list the four +topics for central topics for the + + align:start position:0% +topics for central topics for the + + + align:start position:0% +topics for central topics for the +Fourier part of the course and I would + + align:start position:0% +Fourier part of the course and I would + + + align:start position:0% +Fourier part of the course and I would +guess that there'll be a question on + + align:start position:0% +guess that there'll be a question on + + + align:start position:0% +guess that there'll be a question on +each of those four in the final a quiz + + align:start position:0% +each of those four in the final a quiz + + + align:start position:0% +each of those four in the final a quiz +final exam and we covered 4.1 Fourier + + align:start position:0% +final exam and we covered 4.1 Fourier + + + align:start position:0% +final exam and we covered 4.1 Fourier +series I don't plan to do + + align:start position:0% +series I don't plan to do + + + align:start position:0% +series I don't plan to do +discussion in 4.2 of other series like + + align:start position:0% +discussion in 4.2 of other series like + + + align:start position:0% +discussion in 4.2 of other series like +vessel and Legendre and so on okay if I + + align:start position:0% +vessel and Legendre and so on okay if I + + + align:start position:0% +vessel and Legendre and so on okay if I +can I'll come back to those in the very + + align:start position:0% +can I'll come back to those in the very + + + align:start position:0% +can I'll come back to those in the very +last lectures but I + + align:start position:0% +last lectures but I + + + align:start position:0% +last lectures but I +want to pick up now on the second + + align:start position:0% +want to pick up now on the second + + + align:start position:0% +want to pick up now on the second +key example which is the discrete + + align:start position:0% +key example which is the discrete + + + align:start position:0% +key example which is the discrete +Fourier series that has only n terms + + align:start position:0% +Fourier series that has only n terms + + + align:start position:0% +Fourier series that has only n terms +instead of this series as you're looking + + align:start position:0% +instead of this series as you're looking + + + align:start position:0% +instead of this series as you're looking +at it has infinitely many terms but I'm + + align:start position:0% +at it has infinitely many terms but I'm + + + align:start position:0% +at it has infinitely many terms but I'm +going to cut back to n terms + + align:start position:0% +going to cut back to n terms + + + align:start position:0% +going to cut back to n terms +so this this K well I can go 1 to N but + + align:start position:0% +so this this K well I can go 1 to N but + + + align:start position:0% +so this this K well I can go 1 to N but +the best way is 0 to n minus 1 + + align:start position:0% +the best way is 0 to n minus 1 + + + align:start position:0% +the best way is 0 to n minus 1 +so so that's that's going to be that's + + align:start position:0% +so so that's that's going to be that's + + + align:start position:0% +so so that's that's going to be that's +the discrete series we're going to be + + align:start position:0% +the discrete series we're going to be + + + align:start position:0% +the discrete series we're going to be +dealing with a vector C 0 up to C n + + align:start position:0% +dealing with a vector C 0 up to C n + + + align:start position:0% +dealing with a vector C 0 up to C n +minus 1 and a vector of of function + + align:start position:0% +minus 1 and a vector of of function + + + align:start position:0% +minus 1 and a vector of of function +values + + align:start position:0% +values + + + align:start position:0% +values +vector to vector so a matrix is going to + + align:start position:0% +vector to vector so a matrix is going to + + + align:start position:0% +vector to vector so a matrix is going to +be the key to everything here an N by n + + align:start position:0% +be the key to everything here an N by n + + + align:start position:0% +be the key to everything here an N by n +matrix so that's what's coming then + + align:start position:0% +matrix so that's what's coming then + + + align:start position:0% +matrix so that's what's coming then +after that probably the by Friday will + + align:start position:0% +after that probably the by Friday will + + + align:start position:0% +after that probably the by Friday will +be the integral transform and early next + + align:start position:0% +be the integral transform and early next + + + align:start position:0% +be the integral transform and early next +week and after a little after + + align:start position:0% +week and after a little after + + + align:start position:0% +week and after a little after +Thanksgiving will be this key idea of + + align:start position:0% +Thanksgiving will be this key idea of + + + align:start position:0% +Thanksgiving will be this key idea of +convolution which is really important in + + align:start position:0% +convolution which is really important in + + + align:start position:0% +convolution which is really important in +so many applications and needs to be + + align:start position:0% +so many applications and needs to be + + + align:start position:0% +so many applications and needs to be +raided out the convolution will apply to + + align:start position:0% +raided out the convolution will apply to + + + align:start position:0% +raided out the convolution will apply to +all of these and + + align:start position:0% +all of these and + + + align:start position:0% +all of these and +you'll see the point there okay ready + + align:start position:0% +you'll see the point there okay ready + + + align:start position:0% +you'll see the point there okay ready +for the idea of the discrete one okay so + + align:start position:0% +for the idea of the discrete one okay so + + + align:start position:0% +for the idea of the discrete one okay so +the key idea is we only have n terms so + + align:start position:0% +the key idea is we only have n terms so + + + align:start position:0% +the key idea is we only have n terms so +I can't expect to reproduce a whole + + align:start position:0% +I can't expect to reproduce a whole + + + align:start position:0% +I can't expect to reproduce a whole +function I can get n function values so + + align:start position:0% +function I can get n function values so + + + align:start position:0% +function I can get n function values so +I'll get this at n different points and + + align:start position:0% +I'll get this at n different points and + + + align:start position:0% +I'll get this at n different points and +if I'm thinking of my f of X on let me + + align:start position:0% +if I'm thinking of my f of X on let me + + + align:start position:0% +if I'm thinking of my f of X on let me +take 0 to 2pi now and I'm tanging again + + align:start position:0% +take 0 to 2pi now and I'm tanging again + + + align:start position:0% +take 0 to 2pi now and I'm tanging again +of an f of X it's periodic so it it goes + + align:start position:0% +of an f of X it's periodic so it it goes + + + align:start position:0% +of an f of X it's periodic so it it goes +you know does whatever if it was like + + align:start position:0% +you know does whatever if it was like + + + align:start position:0% +you know does whatever if it was like +that if that was my f of X it just to + + align:start position:0% +that if that was my f of X it just to + + + align:start position:0% +that if that was my f of X it just to +remember about Fourier series what could + + align:start position:0% +remember about Fourier series what could + + + align:start position:0% +remember about Fourier series what could +you tell me about the Fourier series for + + align:start position:0% +you tell me about the Fourier series for + + + align:start position:0% +you tell me about the Fourier series for +that f of X well when I continue + + align:start position:0% +that f of X well when I continue + + + align:start position:0% +that f of X well when I continue +periodically am I going to see a jump + + align:start position:0% +periodically am I going to see a jump + + + align:start position:0% +periodically am I going to see a jump +yes there will be a jump at + + align:start position:0% +yes there will be a jump at + + + align:start position:0% +yes there will be a jump at +every + + align:start position:0% +every + + + align:start position:0% +every +2 pi so the part of the underlying + + align:start position:0% +2 pi so the part of the underlying + + + align:start position:0% +2 pi so the part of the underlying +function is not continuous has a jump + + align:start position:0% +function is not continuous has a jump + + + align:start position:0% +function is not continuous has a jump +and and the + + align:start position:0% +and and the + + + align:start position:0% +and and the +so that our special + + align:start position:0% +so that our special + + + align:start position:0% +so that our special +examples + + align:start position:0% +examples + + + align:start position:0% +examples +with jumps and slow decay 1 over K decay + + align:start position:0% +with jumps and slow decay 1 over K decay + + + align:start position:0% +with jumps and slow decay 1 over K decay +rate for the Fourier coefficients would + + align:start position:0% +rate for the Fourier coefficients would + + + align:start position:0% +rate for the Fourier coefficients would +apply here ok that's remembering Fourier + + align:start position:0% +apply here ok that's remembering Fourier + + + align:start position:0% +apply here ok that's remembering Fourier +series now Fourier integrals I'm just + + align:start position:0% +series now Fourier integrals I'm just + + + align:start position:0% +series now Fourier integrals I'm just +going to take let me just take n equal 4 + + align:start position:0% +going to take let me just take n equal 4 + + + align:start position:0% +going to take let me just take n equal 4 +so I'll take this point you know what + + align:start position:0% +so I'll take this point you know what + + + align:start position:0% +so I'll take this point you know what +what four points am I going to take I'm + + align:start position:0% +what four points am I going to take I'm + + + align:start position:0% +what four points am I going to take I'm +not gonna repeat ah + + align:start position:0% +not gonna repeat ah + + + align:start position:0% +not gonna repeat ah +let's make it let's just for this for + + align:start position:0% +let's make it let's just for this for + + + align:start position:0% +let's make it let's just for this for +the heck of it get it make it look + + align:start position:0% +the heck of it get it make it look + + + align:start position:0% +the heck of it get it make it look +periodic yeah let's make it look + + align:start position:0% +periodic yeah let's make it look + + + align:start position:0% +periodic yeah let's make it look +periodic I never should have done it + + align:start position:0% +periodic I never should have done it + + + align:start position:0% +periodic I never should have done it +otherwise okay but okay so there's one + + align:start position:0% +otherwise okay but okay so there's one + + + align:start position:0% +otherwise okay but okay so there's one +point I'm just going to take four + + align:start position:0% +point I'm just going to take four + + + align:start position:0% +point I'm just going to take four +equally spaced equally spaced being key + + align:start position:0% +equally spaced equally spaced being key + + + align:start position:0% +equally spaced equally spaced being key +0 1 2 3 so n minus 1 is 3 and + + align:start position:0% +0 1 2 3 so n minus 1 is 3 and + + + align:start position:0% +0 1 2 3 so n minus 1 is 3 and +these values + + align:start position:0% + + + + align:start position:0% + +for values I can get right so those are + + align:start position:0% +for values I can get right so those are + + + align:start position:0% +for values I can get right so those are +my four X's the four X's that I'm going + + align:start position:0% +my four X's the four X's that I'm going + + + align:start position:0% +my four X's the four X's that I'm going +to take + + align:start position:0% +to take + + + align:start position:0% +to take +so this is x equals zero of course and + + align:start position:0% +so this is x equals zero of course and + + + align:start position:0% +so this is x equals zero of course and +this one is what's the X there X is two + + align:start position:0% +this one is what's the X there X is two + + + align:start position:0% +this one is what's the X there X is two +pi the whole deal the whole interval but + + align:start position:0% +pi the whole deal the whole interval but + + + align:start position:0% +pi the whole deal the whole interval but +it's divided into n pieces so 2 PI over + + align:start position:0% +it's divided into n pieces so 2 PI over + + + align:start position:0% +it's divided into n pieces so 2 PI over +N + + align:start position:0% +N + + + align:start position:0% +N +so we are going to see a lot of + + align:start position:0% +so we are going to see a lot of + + + align:start position:0% +so we are going to see a lot of +fractions involving PI over N or 2 PI + + align:start position:0% +fractions involving PI over N or 2 PI + + + align:start position:0% +fractions involving PI over N or 2 PI +over N there they just going to come up + + align:start position:0% +over N there they just going to come up + + + align:start position:0% +over N there they just going to come up +everywhere because that's the Delta X + + align:start position:0% +everywhere because that's the Delta X + + + align:start position:0% +everywhere because that's the Delta X +the Delta the H the the the step in in + + align:start position:0% +the Delta the H the the the step in in + + + align:start position:0% +the Delta the H the the the step in in +the discrete form ok so that so those + + align:start position:0% +the discrete form ok so that so those + + + align:start position:0% +the discrete form ok so that so those +are the X's so I'm only going to get + + align:start position:0% +are the X's so I'm only going to get + + + align:start position:0% +are the X's so I'm only going to get +this at x equals 0 to PI over n 4 PI + + align:start position:0% +this at x equals 0 to PI over n 4 PI + + + align:start position:0% +this at x equals 0 to PI over n 4 PI +over n up to oh whatever it comes out to + + align:start position:0% +over n up to oh whatever it comes out to + + + align:start position:0% +over n up to oh whatever it comes out to +n minus 1/2 PI over N it's you know that + + align:start position:0% +n minus 1/2 PI over N it's you know that + + + align:start position:0% +n minus 1/2 PI over N it's you know that +doesn't look elegant so we probably will + + align:start position:0% +doesn't look elegant so we probably will + + + align:start position:0% +doesn't look elegant so we probably will +try to avoid writing that again but + + align:start position:0% +try to avoid writing that again but + + + align:start position:0% +try to avoid writing that again but +those are this was the 3 times 2 PI over + + align:start position:0% +those are this was the 3 times 2 PI over + + + align:start position:0% +those are this was the 3 times 2 PI over +4 that got us to there so that's this is + + align:start position:0% +4 that got us to there so that's this is + + + align:start position:0% +4 that got us to there so that's this is +this is 2 PI over 8 PI over 4 sorry 2 PI + + align:start position:0% +this is 2 PI over 8 PI over 4 sorry 2 PI + + + align:start position:0% +this is 2 PI over 8 PI over 4 sorry 2 PI +over 4 4 PI over 4 6 5 oh okay so that's + + align:start position:0% +over 4 4 PI over 4 6 5 oh okay so that's + + + align:start position:0% +over 4 4 PI over 4 6 5 oh okay so that's +we're only gonna get equality at those + + align:start position:0% +we're only gonna get equality at those + + + align:start position:0% +we're only gonna get equality at those +X's so it's those X's that I should plug + + align:start position:0% +X's so it's those X's that I should plug + + + align:start position:0% +X's so it's those X's that I should plug +in here okay so let me do that let me + + align:start position:0% +in here okay so let me do that let me + + + align:start position:0% +in here okay so let me do that let me +plug in what does this series look like + + align:start position:0% +plug in what does this series look like + + + align:start position:0% +plug in what does this series look like +at these 4 points yeah let me see what + + align:start position:0% +at these 4 points yeah let me see what + + + align:start position:0% +at these 4 points yeah let me see what +so so what so writing out all four + + align:start position:0% +so so what so writing out all four + + + align:start position:0% +so so what so writing out all four +equations F F at 0 is going to match the + + align:start position:0% +equations F F at 0 is going to match the + + + align:start position:0% +equations F F at 0 is going to match the +right side at 0 because 0 is one of my + + align:start position:0% +right side at 0 because 0 is one of my + + + align:start position:0% +right side at 0 because 0 is one of my +points so I get C 0 plus C 1 plus C 2 + + align:start position:0% +points so I get C 0 plus C 1 plus C 2 + + + align:start position:0% +points so I get C 0 plus C 1 plus C 2 +plus C 3 + + align:start position:0% +plus C 3 + + + align:start position:0% +plus C 3 +well at x equals 0 right all the e to + + align:start position:0% +well at x equals 0 right all the e to + + + align:start position:0% +well at x equals 0 right all the e to +these whatever's were 1 now at the next + + align:start position:0% +these whatever's were 1 now at the next + + + align:start position:0% +these whatever's were 1 now at the next +X two pi over n + + align:start position:0% + + + + align:start position:0% + +now I'm matching the series with a + + align:start position:0% +now I'm matching the series with a + + + align:start position:0% +now I'm matching the series with a +function at that value they're two PI + + align:start position:0% +function at that value they're two PI + + + align:start position:0% +function at that value they're two PI +over N so now I have K equals 0 so what + + align:start position:0% +over N so now I have K equals 0 so what + + + align:start position:0% +over N so now I have K equals 0 so what +does K equal 0 will give me + + align:start position:0% +does K equal 0 will give me + + + align:start position:0% +does K equal 0 will give me +when K is 0 what's what's my term look + + align:start position:0% +when K is 0 what's what's my term look + + + align:start position:0% +when K is 0 what's what's my term look +like + + align:start position:0% +like + + + align:start position:0% +like +it's just C 0 times + + align:start position:0% +it's just C 0 times + + + align:start position:0% +it's just C 0 times +1 because if K is 0 e to the whatever is + + align:start position:0% +1 because if K is 0 e to the whatever is + + + align:start position:0% +1 because if K is 0 e to the whatever is +again 1 so this is just C 0 now here's + + align:start position:0% +again 1 so this is just C 0 now here's + + + align:start position:0% +again 1 so this is just C 0 now here's +the key + + align:start position:0% +the key + + + align:start position:0% +the key +what is + + align:start position:0% +what is + + + align:start position:0% +what is +that business there at X equal to PI + + align:start position:0% +that business there at X equal to PI + + + align:start position:0% +that business there at X equal to PI +over n here comes the important number + + align:start position:0% +over n here comes the important number + + + align:start position:0% +over n here comes the important number +in this whole business the important + + align:start position:0% +in this whole business the important + + + align:start position:0% +in this whole business the important +number in this whole business is I'll + + align:start position:0% +number in this whole business is I'll + + + align:start position:0% +number in this whole business is I'll +call it W is e to the 2 pi I over m + + align:start position:0% +call it W is e to the 2 pi I over m + + + align:start position:0% +call it W is e to the 2 pi I over m +that's a complex number and + + align:start position:0% + + + + align:start position:0% + +we'll we'll place it in the in the + + align:start position:0% +we'll we'll place it in the in the + + + align:start position:0% +we'll we'll place it in the in the +complex plane so you you must get to + + align:start position:0% +complex plane so you you must get to + + + align:start position:0% +complex plane so you you must get to +know that number W because when I plug + + align:start position:0% +know that number W because when I plug + + + align:start position:0% +know that number W because when I plug +in X equal K is now 1 here so I have C 1 + + align:start position:0% +in X equal K is now 1 here so I have C 1 + + + align:start position:0% +in X equal K is now 1 here so I have C 1 +times this e to the I 1 2 pi over n what + + align:start position:0% +times this e to the I 1 2 pi over n what + + + align:start position:0% +times this e to the I 1 2 pi over n what +is that + + align:start position:0% +is that + + + align:start position:0% +is that +W so it's wc1 and + + align:start position:0% +W so it's wc1 and + + + align:start position:0% +W so it's wc1 and +what do I get from the next term in this + + align:start position:0% +what do I get from the next term in this + + + align:start position:0% +what do I get from the next term in this +series I have C 2 e to the I 2 X X is 2 + + align:start position:0% +series I have C 2 e to the I 2 X X is 2 + + + align:start position:0% +series I have C 2 e to the I 2 X X is 2 +pi over n do you see what's happening + + align:start position:0% +pi over n do you see what's happening + + + align:start position:0% +pi over n do you see what's happening +e to the you know W squared is e to the + + align:start position:0% +e to the you know W squared is e to the + + + align:start position:0% +e to the you know W squared is e to the +4 PI over n + + align:start position:0% +4 PI over n + + + align:start position:0% +4 PI over n +we're using the beauty of Exponential's + + align:start position:0% +we're using the beauty of Exponential's + + + align:start position:0% +we're using the beauty of Exponential's +that's what make making everything go + + align:start position:0% +that's what make making everything go + + + align:start position:0% +that's what make making everything go +it's W squared and this guy will be W + + align:start position:0% +it's W squared and this guy will be W + + + align:start position:0% +it's W squared and this guy will be W +cubed C 3 + + align:start position:0% + + + + align:start position:0% + +that's the series at our point and and + + align:start position:0% +that's the series at our point and and + + + align:start position:0% +that's the series at our point and and +and I'll write so this this is like + + align:start position:0% +and I'll write so this this is like + + + align:start position:0% +and I'll write so this this is like +we'll just see this once what were we + + align:start position:0% +we'll just see this once what were we + + + align:start position:0% +we'll just see this once what were we +doing but this is what we're going to + + align:start position:0% +doing but this is what we're going to + + + align:start position:0% +doing but this is what we're going to +live with here so I'll rewrite it all in + + align:start position:0% +live with here so I'll rewrite it all in + + + align:start position:0% +live with here so I'll rewrite it all in +terms of W so so you so you just got the + + align:start position:0% +terms of W so so you so you just got the + + + align:start position:0% +terms of W so so you so you just got the +idea of what are we doing we're matching + + align:start position:0% +idea of what are we doing we're matching + + + align:start position:0% +idea of what are we doing we're matching +at endpoints and now we get the good + + align:start position:0% +at endpoints and now we get the good + + + align:start position:0% +at endpoints and now we get the good +notation W ok and that the next point + + align:start position:0% +notation W ok and that the next point + + + align:start position:0% +notation W ok and that the next point +for PI over N well again k equals 0 term + + align:start position:0% +for PI over N well again k equals 0 term + + + align:start position:0% +for PI over N well again k equals 0 term +it's just c0 the k equal 1 term yeah can + + align:start position:0% +it's just c0 the k equal 1 term yeah can + + + align:start position:0% +it's just c0 the k equal 1 term yeah can +you tell me what what I get from K is 1 + + align:start position:0% +you tell me what what I get from K is 1 + + + align:start position:0% +you tell me what what I get from K is 1 +I have something up some something times + + align:start position:0% +I have something up some something times + + + align:start position:0% +I have something up some something times +c1 it's e to the I 1 + + align:start position:0% +c1 it's e to the I 1 + + + align:start position:0% +c1 it's e to the I 1 +4 PI over N what's that + + align:start position:0% +4 PI over N what's that + + + align:start position:0% +4 PI over N what's that +w squared e to the I 4 PI over N is w + + align:start position:0% +w squared e to the I 4 PI over N is w + + + align:start position:0% +w squared e to the I 4 PI over N is w +squared look this matrix is coming out + + align:start position:0% +squared look this matrix is coming out + + + align:start position:0% +squared look this matrix is coming out +symmetric and this will be W to the + + align:start position:0% +symmetric and this will be W to the + + + align:start position:0% +symmetric and this will be W to the +fourth and that'll turn out to be W to + + align:start position:0% +fourth and that'll turn out to be W to + + + align:start position:0% +fourth and that'll turn out to be W to +the 6 and then the last row of the + + align:start position:0% +the 6 and then the last row of the + + + align:start position:0% +the 6 and then the last row of the +matrix is going to come from matching at + + align:start position:0% +matrix is going to come from matching at + + + align:start position:0% +matrix is going to come from matching at +6 PI over N and + + align:start position:0% +6 PI over N and + + + align:start position:0% +6 PI over N and +it will turn out to be C 0 and it'll be + + align:start position:0% +it will turn out to be C 0 and it'll be + + + align:start position:0% +it will turn out to be C 0 and it'll be +W cubed + + align:start position:0% +W cubed + + + align:start position:0% +W cubed +w2 6 and + + align:start position:0% +w2 6 and + + + align:start position:0% +w2 6 and +W to the ninth + + align:start position:0% + + + + align:start position:0% + +so I did the last row or to a bit fast + + align:start position:0% +so I did the last row or to a bit fast + + + align:start position:0% +so I did the last row or to a bit fast +just because the patterns there and + + align:start position:0% +just because the patterns there and + + + align:start position:0% +just because the patterns there and +you'll connect you'll spot it now I want + + align:start position:0% +you'll connect you'll spot it now I want + + + align:start position:0% +you'll connect you'll spot it now I want +to + + align:start position:0% +to + + + align:start position:0% +to +pull out of that + + align:start position:0% +pull out of that + + + align:start position:0% +pull out of that +the matrix the Fourier matrix the 4x4 + + align:start position:0% +the matrix the Fourier matrix the 4x4 + + + align:start position:0% +the matrix the Fourier matrix the 4x4 +Fourier matrix that multiplies the C's + + align:start position:0% +Fourier matrix that multiplies the C's + + + align:start position:0% +Fourier matrix that multiplies the C's +and gives me the FS let me call these + + align:start position:0% +and gives me the FS let me call these + + + align:start position:0% +and gives me the FS let me call these +numbers y0 y1 + + align:start position:0% +numbers y0 y1 + + + align:start position:0% +numbers y0 y1 +y2 and y3 just to have up so it's a + + align:start position:0% +y2 and y3 just to have up so it's a + + + align:start position:0% +y2 and y3 just to have up so it's a +vector of values of the function and + + align:start position:0% +vector of values of the function and + + + align:start position:0% +vector of values of the function and +this is a vector of coefficients so it's + + align:start position:0% +this is a vector of coefficients so it's + + + align:start position:0% +this is a vector of coefficients so it's +wise to the Fourier transform is goes + + align:start position:0% +wise to the Fourier transform is goes + + + align:start position:0% +wise to the Fourier transform is goes +between wise and C's and wives + + align:start position:0% +between wise and C's and wives + + + align:start position:0% +between wise and C's and wives +right + + align:start position:0% + + + + align:start position:0% + +connects a vector and all these guys + + align:start position:0% +connects a vector and all these guys + + + align:start position:0% +connects a vector and all these guys +this is and values and function values + + align:start position:0% +this is and values and function values + + + align:start position:0% +this is and values and function values +in + + align:start position:0% +in + + + align:start position:0% +in +physical space these are n coefficients + + align:start position:0% +physical space these are n coefficients + + + align:start position:0% +physical space these are n coefficients +in frequency space and one way is the + + align:start position:0% +in frequency space and one way is the + + + align:start position:0% +in frequency space and one way is the +discrete Fourier transform and the other + + align:start position:0% +discrete Fourier transform and the other + + + align:start position:0% +discrete Fourier transform and the other +way is the inverse discrete Fourier + + align:start position:0% +way is the inverse discrete Fourier + + + align:start position:0% +way is the inverse discrete Fourier +transform so it's a little bit confused + + align:start position:0% +transform so it's a little bit confused + + + align:start position:0% +transform so it's a little bit confused +which is which actually there was no + + align:start position:0% +which is which actually there was no + + + align:start position:0% +which is which actually there was no +question with Fourier series it was easy + + align:start position:0% +question with Fourier series it was easy + + + align:start position:0% +question with Fourier series it was easy +to tell the function from the + + align:start position:0% +to tell the function from the + + + align:start position:0% +to tell the function from the +coefficients because the function was f + + align:start position:0% +coefficients because the function was f + + + align:start position:0% +coefficients because the function was f +of X and the coefficients were a bunch + + align:start position:0% +of X and the coefficients were a bunch + + + align:start position:0% +of X and the coefficients were a bunch +of numbers here we only have n numbers N + + align:start position:0% +of numbers here we only have n numbers N + + + align:start position:0% +of numbers here we only have n numbers N +and wise and NCS and we're transforming + + align:start position:0% +and wise and NCS and we're transforming + + + align:start position:0% +and wise and NCS and we're transforming +back and forth but I'm so I'm finally + + align:start position:0% +back and forth but I'm so I'm finally + + + align:start position:0% +back and forth but I'm so I'm finally +right now the matrix this Fourier matrix + + align:start position:0% +right now the matrix this Fourier matrix + + + align:start position:0% +right now the matrix this Fourier matrix +is going to take this C's and give me + + align:start position:0% +is going to take this C's and give me + + + align:start position:0% +is going to take this C's and give me +the Y so I'm talking here about the + + align:start position:0% +the Y so I'm talking here about the + + + align:start position:0% +the Y so I'm talking here about the +matrix F and let's see what F is can can + + align:start position:0% +matrix F and let's see what F is can can + + + align:start position:0% +matrix F and let's see what F is can can +you can you just see what that was why Y + + align:start position:0% +you can you just see what that was why Y + + + align:start position:0% +you can you just see what that was why Y +0 to Y 3 + + align:start position:0% +0 to Y 3 + + + align:start position:0% +0 to Y 3 +equals this matrix F the 4x4 matrix + + align:start position:0% +equals this matrix F the 4x4 matrix + + + align:start position:0% +equals this matrix F the 4x4 matrix +times C 0 to C 3 + + align:start position:0% +times C 0 to C 3 + + + align:start position:0% +times C 0 to C 3 +this is really the inverse + + align:start position:0% +this is really the inverse + + + align:start position:0% +this is really the inverse +DFT + + align:start position:0% +DFT + + + align:start position:0% +DFT +it's + + align:start position:0% +it's + + + align:start position:0% +it's +reconstruct + + align:start position:0% +reconstruct + + + align:start position:0% +reconstruct +it reconstruct the wise + + align:start position:0% +it reconstruct the wise + + + align:start position:0% +it reconstruct the wise +from the C's or easier way to say that + + align:start position:0% +from the C's or easier way to say that + + + align:start position:0% +from the C's or easier way to say that +is add up add up this series + + align:start position:0% + + + + align:start position:0% + +so that's the + + align:start position:0% +so that's the + + + align:start position:0% +so that's the +the usual DFT is taking us starting with + + align:start position:0% +the usual DFT is taking us starting with + + + align:start position:0% +the usual DFT is taking us starting with +the Y's and giving us the C's so that we + + align:start position:0% +the Y's and giving us the C's so that we + + + align:start position:0% +the Y's and giving us the C's so that we +have to this would be the this would be + + align:start position:0% +have to this would be the this would be + + + align:start position:0% +have to this would be the this would be +the discrete Fourier transform take a + + align:start position:0% +the discrete Fourier transform take a + + + align:start position:0% +the discrete Fourier transform take a +function produce its coefficients the + + align:start position:0% +function produce its coefficients the + + + align:start position:0% +function produce its coefficients the +SEC the reverse step is take the + + align:start position:0% +SEC the reverse step is take the + + + align:start position:0% +SEC the reverse step is take the +coefficients add back add up the series + + align:start position:0% +coefficients add back add up the series + + + align:start position:0% +coefficients add back add up the series +get the function so that's and that's + + align:start position:0% +get the function so that's and that's + + + align:start position:0% +get the function so that's and that's +what F does + + align:start position:0% +what F does + + + align:start position:0% +what F does +so I'm gonna focus on F which is the one + + align:start position:0% +so I'm gonna focus on F which is the one + + + align:start position:0% +so I'm gonna focus on F which is the one +that involves this W guy ok can you read + + align:start position:0% +that involves this W guy ok can you read + + + align:start position:0% +that involves this W guy ok can you read +off peel off from here what the matrix F + + align:start position:0% +off peel off from here what the matrix F + + + align:start position:0% +off peel off from here what the matrix F +is the Fourier matrix its first row is + + align:start position:0% +is the Fourier matrix its first row is + + + align:start position:0% +is the Fourier matrix its first row is +all + + align:start position:0% +all + + + align:start position:0% +all +one's + + align:start position:0% +one's + + + align:start position:0% +one's +its first its first column is all ones + + align:start position:0% +its first its first column is all ones + + + align:start position:0% +its first its first column is all ones +and then it's one w w squared W cubed W + + align:start position:0% +and then it's one w w squared W cubed W + + + align:start position:0% +and then it's one w w squared W cubed W +square w 4w + + align:start position:0% +square w 4w + + + align:start position:0% +square w 4w +6w q w6 + w 9 to the 9th power + + align:start position:0% +6w q w6 + w 9 to the 9th power + + + align:start position:0% +6w q w6 + w 9 to the 9th power +okay so it's made up of these powers of + + align:start position:0% +okay so it's made up of these powers of + + + align:start position:0% +okay so it's made up of these powers of +W the 0 first second and third power and + + align:start position:0% +W the 0 first second and third power and + + + align:start position:0% +W the 0 first second and third power and +then higher powers + + align:start position:0% +then higher powers + + + align:start position:0% +then higher powers +but higher powers are all and let's + + align:start position:0% +but higher powers are all and let's + + + align:start position:0% +but higher powers are all and let's +let's draw a picture where is W so I + + align:start position:0% +let's draw a picture where is W so I + + + align:start position:0% +let's draw a picture where is W so I +this is the the complex plane here's the + + align:start position:0% +this is the the complex plane here's the + + + align:start position:0% +this is the the complex plane here's the +real and here's the imaginary direction + + align:start position:0% +real and here's the imaginary direction + + + align:start position:0% +real and here's the imaginary direction +and let me take n to be here n was for + + align:start position:0% +and let me take n to be here n was for + + + align:start position:0% +and let me take n to be here n was for +let me take n to be 8 in my picture just + + align:start position:0% +let me take n to be 8 in my picture just + + + align:start position:0% +let me take n to be 8 in my picture just +to have some + + align:start position:0% +to have some + + + align:start position:0% +to have some +then I'll be able to spot the fours and + + align:start position:0% +then I'll be able to spot the fours and + + + align:start position:0% +then I'll be able to spot the fours and +and the 8 if n is 8 where would w 8 be + + align:start position:0% +and the 8 if n is 8 where would w 8 be + + + align:start position:0% +and the 8 if n is 8 where would w 8 be +so w 8 is meant to be the + + align:start position:0% +so w 8 is meant to be the + + + align:start position:0% +so w 8 is meant to be the +the e + + align:start position:0% +the e + + + align:start position:0% +the e +to the 2 pi + + align:start position:0% +to the 2 pi + + + align:start position:0% +to the 2 pi +over 8 now + + align:start position:0% + + + + align:start position:0% + +where's that + + align:start position:0% +where's that + + + align:start position:0% +where's that +where's that number in that picture + + align:start position:0% +where's that number in that picture + + + align:start position:0% +where's that number in that picture +it's + + align:start position:0% +it's + + + align:start position:0% +it's +is it on the circle + + align:start position:0% +is it on the circle + + + align:start position:0% +is it on the circle +absolutely + + align:start position:0% +absolutely + + + align:start position:0% +absolutely +come this discrete Fourier transform + + align:start position:0% +come this discrete Fourier transform + + + align:start position:0% +come this discrete Fourier transform +never gets off this circle and in fact + + align:start position:0% +never gets off this circle and in fact + + + align:start position:0% +never gets off this circle and in fact +it never gets off 8 points on the circle + + align:start position:0% +it never gets off 8 points on the circle + + + align:start position:0% +it never gets off 8 points on the circle +which are the eight equally spaced + + align:start position:0% +which are the eight equally spaced + + + align:start position:0% +which are the eight equally spaced +points this says go 1/8 of the way of + + align:start position:0% +points this says go 1/8 of the way of + + + align:start position:0% +points this says go 1/8 of the way of +the whole way around which will be here + + align:start position:0% +the whole way around which will be here + + + align:start position:0% +the whole way around which will be here +so there's w 8 + + align:start position:0% + + + + align:start position:0% + +when I square it what's the square of w + + align:start position:0% +when I square it what's the square of w + + + align:start position:0% +when I square it what's the square of w +8 the angle what happens to the angle + + align:start position:0% +8 the angle what happens to the angle + + + align:start position:0% +8 the angle what happens to the angle +when i when i multiply numbers i add the + + align:start position:0% +when i when i multiply numbers i add the + + + align:start position:0% +when i when i multiply numbers i add the +exponents here if I'm multiplying by + + align:start position:0% +exponents here if I'm multiplying by + + + align:start position:0% +exponents here if I'm multiplying by +itself it'll double the exponent double + + align:start position:0% +itself it'll double the exponent double + + + align:start position:0% +itself it'll double the exponent double +the angle it'll be there's W 2 there's w + + align:start position:0% +the angle it'll be there's W 2 there's w + + + align:start position:0% +the angle it'll be there's W 2 there's w +8 squared so that point is + + align:start position:0% +8 squared so that point is + + + align:start position:0% +8 squared so that point is +w8 squared and it's the same as w-4 + + align:start position:0% +w8 squared and it's the same as w-4 + + + align:start position:0% +w8 squared and it's the same as w-4 +because it's 1/4 the way round and what + + align:start position:0% +because it's 1/4 the way round and what + + + align:start position:0% +because it's 1/4 the way round and what +is that number in ordinary language I + + align:start position:0% + + + + align:start position:0% + +it's i right it's one it's the on the + + align:start position:0% +it's i right it's one it's the on the + + + align:start position:0% +it's i right it's one it's the on the +unit circle at ninety degrees and it's + + align:start position:0% +unit circle at ninety degrees and it's + + + align:start position:0% +unit circle at ninety degrees and it's +on the imaginary axis it's just I so + + align:start position:0% +on the imaginary axis it's just I so + + + align:start position:0% +on the imaginary axis it's just I so +this all this here was I I squared I + + align:start position:0% +this all this here was I I squared I + + + align:start position:0% +this all this here was I I squared I +cubed I squared I fourth I 6i q by 6i9 + + align:start position:0% +cubed I squared I fourth I 6i q by 6i9 + + + align:start position:0% +cubed I squared I fourth I 6i q by 6i9 +the the four by four Fourier matrix it's + + align:start position:0% +the the four by four Fourier matrix it's + + + align:start position:0% +the the four by four Fourier matrix it's +just powers of I and the N by n the + + align:start position:0% +just powers of I and the N by n the + + + align:start position:0% +just powers of I and the N by n the +eight by eight for a matrix is powers of + + align:start position:0% +eight by eight for a matrix is powers of + + + align:start position:0% +eight by eight for a matrix is powers of +W eight and let's find all the rest of + + align:start position:0% +W eight and let's find all the rest of + + + align:start position:0% +W eight and let's find all the rest of +the powers so there's w8 w8 squared + + align:start position:0% +the powers so there's w8 w8 squared + + + align:start position:0% +the powers so there's w8 w8 squared +where's W 8 cubed here I multiplied + + align:start position:0% +where's W 8 cubed here I multiplied + + + align:start position:0% +where's W 8 cubed here I multiplied +those guys I add the angle I'm out to + + align:start position:0% +those guys I add the angle I'm out to + + + align:start position:0% +those guys I add the angle I'm out to +here here's the fourth power here's the + + align:start position:0% +here here's the fourth power here's the + + + align:start position:0% +here here's the fourth power here's the +fifth power sixth power seventh power + + align:start position:0% +fifth power sixth power seventh power + + + align:start position:0% +fifth power sixth power seventh power +and finally we get to + + align:start position:0% +and finally we get to + + + align:start position:0% +and finally we get to +W eight to the 8th power which is + + align:start position:0% +W eight to the 8th power which is + + + align:start position:0% +W eight to the 8th power which is +one because if I take the 8th power here + + align:start position:0% +one because if I take the 8th power here + + + align:start position:0% +one because if I take the 8th power here +I've got e to the 2 pi and that's 1 so + + align:start position:0% +I've got e to the 2 pi and that's 1 so + + + align:start position:0% +I've got e to the 2 pi and that's 1 so +so that's the picture to remember + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +while looking at that picture + + align:start position:0% +while looking at that picture + + + align:start position:0% +while looking at that picture +could you tell me the + + align:start position:0% +could you tell me the + + + align:start position:0% +could you tell me the +sum of those eight numbers what do those + + align:start position:0% +sum of those eight numbers what do those + + + align:start position:0% +sum of those eight numbers what do those +eight numbers add up to so so I'm just + + align:start position:0% +eight numbers add up to so so I'm just + + + align:start position:0% +eight numbers add up to so so I'm just +want to ask what do W 1 plus 1 plus W up + + align:start position:0% +want to ask what do W 1 plus 1 plus W up + + + align:start position:0% +want to ask what do W 1 plus 1 plus W up +to W to the seventh what I'm doing the + + align:start position:0% +to W to the seventh what I'm doing the + + + align:start position:0% +to W to the seventh what I'm doing the +eighth guy adds up to + + align:start position:0% +eighth guy adds up to + + + align:start position:0% +eighth guy adds up to +so there's some of those eight numbers + + align:start position:0% +so there's some of those eight numbers + + + align:start position:0% +so there's some of those eight numbers +well I wouldn't ask the question if it + + align:start position:0% +well I wouldn't ask the question if it + + + align:start position:0% +well I wouldn't ask the question if it +didn't have a nice answer 0 that's of + + align:start position:0% +didn't have a nice answer 0 that's of + + + align:start position:0% +didn't have a nice answer 0 that's of +course the usual answer in math + + align:start position:0% +course the usual answer in math + + + align:start position:0% +course the usual answer in math +we we do all this work and we get 0 + + align:start position:0% + + + + align:start position:0% + +but now of course the real math is why I + + align:start position:0% +but now of course the real math is why I + + + align:start position:0% +but now of course the real math is why I +mean that's I'm sorry that yeah so math + + align:start position:0% +mean that's I'm sorry that yeah so math + + + align:start position:0% +mean that's I'm sorry that yeah so math +is you had equations but then always is + + align:start position:0% +is you had equations but then always is + + + align:start position:0% +is you had equations but then always is +a kicker why and why is why do they add + + align:start position:0% +a kicker why and why is why do they add + + + align:start position:0% +a kicker why and why is why do they add +up to zero here + + align:start position:0% + + + + align:start position:0% + +can you see that + + align:start position:0% +can you see that + + + align:start position:0% +can you see that +why those eight numbers would add to + + align:start position:0% +why those eight numbers would add to + + + align:start position:0% +why those eight numbers would add to +zero + + align:start position:0% + + + + align:start position:0% + +well yeah + + align:start position:0% +well yeah + + + align:start position:0% +well yeah +so what do these add up to just those + + align:start position:0% +so what do these add up to just those + + + align:start position:0% +so what do these add up to just those +two guys + + align:start position:0% +two guys + + + align:start position:0% +two guys +one and minus one add to zero that and + + align:start position:0% +one and minus one add to zero that and + + + align:start position:0% +one and minus one add to zero that and +that add to zero I can pair them off + + align:start position:0% +that add to zero I can pair them off + + + align:start position:0% +that add to zero I can pair them off +this and this add to zero that in that + + align:start position:0% +this and this add to zero that in that + + + align:start position:0% +this and this add to zero that in that +add to zero yeah so that's one way of + + align:start position:0% +add to zero yeah so that's one way of + + + align:start position:0% +add to zero yeah so that's one way of +seeing it but actually even if n was 3 + + align:start position:0% +seeing it but actually even if n was 3 + + + align:start position:0% +seeing it but actually even if n was 3 +or 5 or some odd number and I had so + + align:start position:0% +or 5 or some odd number and I had so + + + align:start position:0% +or 5 or some odd number and I had so +should I do the picture for n equal 3 + + align:start position:0% +should I do the picture for n equal 3 + + + align:start position:0% +should I do the picture for n equal 3 +just a little doesn't need a very big + + align:start position:0% +just a little doesn't need a very big + + + align:start position:0% +just a little doesn't need a very big +picture for n equal 3 so where would the + + align:start position:0% +picture for n equal 3 so where would the + + + align:start position:0% +picture for n equal 3 so where would the +roots be for n equal 3 one of them is + + align:start position:0% +roots be for n equal 3 one of them is + + + align:start position:0% +roots be for n equal 3 one of them is +always 1 these are the 3 cube roots of 1 + + align:start position:0% +always 1 these are the 3 cube roots of 1 + + + align:start position:0% +always 1 these are the 3 cube roots of 1 +that I'm going to draw + + align:start position:0% +that I'm going to draw + + + align:start position:0% +that I'm going to draw +the those were the + + align:start position:0% +the those were the + + + align:start position:0% +the those were the +8/8 roots of 1 because if I take any one + + align:start position:0% +8/8 roots of 1 because if I take any one + + + align:start position:0% +8/8 roots of 1 because if I take any one +of those numbers its 8th power brings me + + align:start position:0% +of those numbers its 8th power brings me + + + align:start position:0% +of those numbers its 8th power brings me +back to + + align:start position:0% +back to + + + align:start position:0% +back to +2 1 so where are these guys were so this + + align:start position:0% +2 1 so where are these guys were so this + + + align:start position:0% +2 1 so where are these guys were so this +is three numbers equally spaced around + + align:start position:0% +is three numbers equally spaced around + + + align:start position:0% +is three numbers equally spaced around +the circle where where do you think they + + align:start position:0% +the circle where where do you think they + + + align:start position:0% +the circle where where do you think they +are well it's got to be at 120 degrees + + align:start position:0% +are well it's got to be at 120 degrees + + + align:start position:0% +are well it's got to be at 120 degrees +240 degrees and 360 + + align:start position:0% +240 degrees and 360 + + + align:start position:0% +240 degrees and 360 +yeah and again those will add to 0 yeah + + align:start position:0% +yeah and again those will add to 0 yeah + + + align:start position:0% +yeah and again those will add to 0 yeah +yeah you can't pair them off because we + + align:start position:0% +yeah you can't pair them off because we + + + align:start position:0% +yeah you can't pair them off because we +got an odd number but it's safely 0 we + + align:start position:0% +got an odd number but it's safely 0 we + + + align:start position:0% +got an odd number but it's safely 0 we +could see why + + align:start position:0% + + + + align:start position:0% + +okay so this + + align:start position:0% +okay so this + + + align:start position:0% +okay so this +section this topic is + + align:start position:0% +section this topic is + + + align:start position:0% +section this topic is +all about that matrix + + align:start position:0% +all about that matrix + + + align:start position:0% +all about that matrix +it's all about that 4 by 4 n by n matrix + + align:start position:0% +it's all about that 4 by 4 n by n matrix + + + align:start position:0% +it's all about that 4 by 4 n by n matrix +which has powers of W notice that the + + align:start position:0% +which has powers of W notice that the + + + align:start position:0% +which has powers of W notice that the +matrix is hasn't got any zeros + + align:start position:0% +matrix is hasn't got any zeros + + + align:start position:0% +matrix is hasn't got any zeros +hasn't even caused anything close to 0 + + align:start position:0% +hasn't even caused anything close to 0 + + + align:start position:0% +hasn't even caused anything close to 0 +they're all those numbers are on the + + align:start position:0% +they're all those numbers are on the + + + align:start position:0% +they're all those numbers are on the +unit circle + + align:start position:0% +unit circle + + + align:start position:0% +unit circle +so + + align:start position:0% + + + + align:start position:0% + +multiplying by that matrix + + align:start position:0% +multiplying by that matrix + + + align:start position:0% +multiplying by that matrix +which is the same as adding up the + + align:start position:0% +which is the same as adding up the + + + align:start position:0% +which is the same as adding up the +Fourier series at the four points + + align:start position:0% +Fourier series at the four points + + + align:start position:0% +Fourier series at the four points +multiplied doing this calculation + + align:start position:0% + + + + align:start position:0% + +finding these Y's from this C's + + align:start position:0% +finding these Y's from this C's + + + align:start position:0% +finding these Y's from this C's +reconstructing the Y's given the + + align:start position:0% +reconstructing the Y's given the + + + align:start position:0% +reconstructing the Y's given the +coefficients + + align:start position:0% +coefficients + + + align:start position:0% +coefficients +has 16 terms right every either the + + align:start position:0% +has 16 terms right every either the + + + align:start position:0% +has 16 terms right every either the +matrix has got 16 entries all these all + + align:start position:0% +matrix has got 16 entries all these all + + + align:start position:0% +matrix has got 16 entries all these all +the entries in the matrix are showing up + + align:start position:0% +the entries in the matrix are showing up + + + align:start position:0% +the entries in the matrix are showing up +here in powers of W we've got 16 + + align:start position:0% +here in powers of W we've got 16 + + + align:start position:0% +here in powers of W we've got 16 +multiplications well maybe a couple of + + align:start position:0% +multiplications well maybe a couple of + + + align:start position:0% +multiplications well maybe a couple of +them were easy but basically 16 + + align:start position:0% +them were easy but basically 16 + + + align:start position:0% +them were easy but basically 16 +multiplications and additions + + align:start position:0% +multiplications and additions + + + align:start position:0% +multiplications and additions +pretty much n squared work N squared + + align:start position:0% +pretty much n squared work N squared + + + align:start position:0% +pretty much n squared work N squared +work and that + + align:start position:0% + + + + align:start position:0% + +you know that's not bad + + align:start position:0% + + + + align:start position:0% + +except if you want to do it a million + + align:start position:0% +except if you want to do it a million + + + align:start position:0% +except if you want to do it a million +times + + align:start position:0% +times + + + align:start position:0% +times +right suppose we have a typical n might + + align:start position:0% +right suppose we have a typical n might + + + align:start position:0% +right suppose we have a typical n might +be a thousand 24 + + align:start position:0% +be a thousand 24 + + + align:start position:0% +be a thousand 24 +so the matrix has then got is a thousand + + align:start position:0% +so the matrix has then got is a thousand + + + align:start position:0% +so the matrix has then got is a thousand +24 squared numbers which is about a + + align:start position:0% +24 squared numbers which is about a + + + align:start position:0% +24 squared numbers which is about a +million so if we have a matrix with a + + align:start position:0% +million so if we have a matrix with a + + + align:start position:0% +million so if we have a matrix with a +million entries million operations to do + + align:start position:0% +million entries million operations to do + + + align:start position:0% +million entries million operations to do +and then we do in a million times then + + align:start position:0% +and then we do in a million times then + + + align:start position:0% +and then we do in a million times then +where you know it's getting up to + + align:start position:0% +where you know it's getting up to + + + align:start position:0% +where you know it's getting up to +money that Congress would give to the + + align:start position:0% +money that Congress would give to the + + + align:start position:0% +money that Congress would give to the +bank's yeah whatever anyway serious + + align:start position:0% +bank's yeah whatever anyway serious + + + align:start position:0% +bank's yeah whatever anyway serious +money + + align:start position:0% +money + + + align:start position:0% +money +serious computing time and + + align:start position:0% + + + + align:start position:0% + +the wonderful thing is that there is a + + align:start position:0% +the wonderful thing is that there is a + + + align:start position:0% +the wonderful thing is that there is a +faster way than + + align:start position:0% +faster way than + + + align:start position:0% +faster way than +N squared there's a faster way to do + + align:start position:0% +N squared there's a faster way to do + + + align:start position:0% +N squared there's a faster way to do +these 16 terms than the obvious way you + + align:start position:0% +these 16 terms than the obvious way you + + + align:start position:0% +these 16 terms than the obvious way you +might say well they're pretty nice and + + align:start position:0% +might say well they're pretty nice and + + + align:start position:0% +might say well they're pretty nice and +they are but they're nicer than you can + + align:start position:0% +they are but they're nicer than you can + + + align:start position:0% +they are but they're nicer than you can +know I mean nicer then you can see + + align:start position:0% +know I mean nicer then you can see + + + align:start position:0% +know I mean nicer then you can see +immediately this matrix will + + align:start position:0% +immediately this matrix will + + + align:start position:0% +immediately this matrix will +break up into + + align:start position:0% + + + + align:start position:0% + +simple steps with lots of zeros in each + + align:start position:0% +simple steps with lots of zeros in each + + + align:start position:0% +simple steps with lots of zeros in each +step and the final result is that + + align:start position:0% +step and the final result is that + + + align:start position:0% +step and the final result is that +instead of instead of N squared sorry + + align:start position:0% +instead of instead of N squared sorry + + + align:start position:0% +instead of instead of N squared sorry +capital N squared which is done the + + align:start position:0% +capital N squared which is done the + + + align:start position:0% +capital N squared which is done the +old-fashioned way let's say that that is + + align:start position:0% +old-fashioned way let's say that that is + + + align:start position:0% +old-fashioned way let's say that that is +there's a fast Fourier transform so the + + align:start position:0% +there's a fast Fourier transform so the + + + align:start position:0% +there's a fast Fourier transform so the +FFT I + + align:start position:0% +FFT I + + + align:start position:0% +FFT I +should maybe find a better space it's + + align:start position:0% +should maybe find a better space it's + + + align:start position:0% +should maybe find a better space it's +it's the most important algorithm in the + + align:start position:0% +it's the most important algorithm in the + + + align:start position:0% +it's the most important algorithm in the +last hundred years and here it is + + align:start position:0% +last hundred years and here it is + + + align:start position:0% +last hundred years and here it is +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +well I guess my son my goal one goal for + + align:start position:0% +well I guess my son my goal one goal for + + + align:start position:0% +well I guess my son my goal one goal for +Wednesday will be to give you some + + align:start position:0% +Wednesday will be to give you some + + + align:start position:0% +Wednesday will be to give you some +insight into the FFT but here I'm just + + align:start position:0% +insight into the FFT but here I'm just + + + align:start position:0% +insight into the FFT but here I'm just +looking at the result the number of + + align:start position:0% +looking at the result the number of + + + align:start position:0% +looking at the result the number of +computations is instead of N squared + + align:start position:0% +computations is instead of N squared + + + align:start position:0% +computations is instead of N squared +it's n times log in + + align:start position:0% +it's n times log in + + + align:start position:0% +it's n times log in +and it's log to the base 2 or maybe 1/2 + + align:start position:0% +and it's log to the base 2 or maybe 1/2 + + + align:start position:0% +and it's log to the base 2 or maybe 1/2 +in log n so let me erase some of the + + align:start position:0% +in log n so let me erase some of the + + + align:start position:0% +in log n so let me erase some of the +other things + + align:start position:0% + + + + align:start position:0% + +so that where N squared was if n was a + + align:start position:0% +so that where N squared was if n was a + + + align:start position:0% +so that where N squared was if n was a +thousand N squared was a million + + align:start position:0% +thousand N squared was a million + + + align:start position:0% +thousand N squared was a million +if N is a thousand this is a thousand + + align:start position:0% +if N is a thousand this is a thousand + + + align:start position:0% +if N is a thousand this is a thousand +and what's the logarithm of a thousand + + align:start position:0% +and what's the logarithm of a thousand + + + align:start position:0% +and what's the logarithm of a thousand +to the base two that's the tenth right + + align:start position:0% +to the base two that's the tenth right + + + align:start position:0% +to the base two that's the tenth right +that 2 to the tenth gave us that + + align:start position:0% +that 2 to the tenth gave us that + + + align:start position:0% +that 2 to the tenth gave us that +thousand and 24 so this is 10 to the + + align:start position:0% +thousand and 24 so this is 10 to the + + + align:start position:0% +thousand and 24 so this is 10 to the +fourth + + align:start position:0% +fourth + + + align:start position:0% +fourth +so n is 10 cubed the logarithm or a + + align:start position:0% +so n is 10 cubed the logarithm or a + + + align:start position:0% +so n is 10 cubed the logarithm or a +thousand 24 gigs more exactly the + + align:start position:0% +thousand 24 gigs more exactly the + + + align:start position:0% +thousand 24 gigs more exactly the +logarithm is 10 so we're ten to the + + align:start position:0% +logarithm is 10 so we're ten to the + + + align:start position:0% +logarithm is 10 so we're ten to the +fourth instead of 10 to the sixth and + + align:start position:0% +fourth instead of 10 to the sixth and + + + align:start position:0% +fourth instead of 10 to the sixth and +that's so that's a saving of a factor of + + align:start position:0% +that's so that's a saving of a factor of + + + align:start position:0% +that's so that's a saving of a factor of +100 that's true I mean it just comes + + align:start position:0% +100 that's true I mean it just comes + + + align:start position:0% +100 that's true I mean it just comes +from doing the addition and + + align:start position:0% +from doing the addition and + + + align:start position:0% +from doing the addition and +multiplication the right in the right + + align:start position:0% +multiplication the right in the right + + + align:start position:0% +multiplication the right in the right +order you get this incredible saving and + + align:start position:0% +order you get this incredible saving and + + + align:start position:0% +order you get this incredible saving and +it sort of makes whole calculations that + + align:start position:0% +it sort of makes whole calculations that + + + align:start position:0% +it sort of makes whole calculations that +were previously impossible or now + + align:start position:0% +were previously impossible or now + + + align:start position:0% +were previously impossible or now +possible because you know instead of + + align:start position:0% + + + + align:start position:0% + +where it might have been a hundred + + align:start position:0% +where it might have been a hundred + + + align:start position:0% +where it might have been a hundred +minutes it's now one minute + + align:start position:0% +minutes it's now one minute + + + align:start position:0% +minutes it's now one minute +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so what everything focuses on this + + align:start position:0% +so what everything focuses on this + + + align:start position:0% +so what everything focuses on this +fourier matrix and its inverse which we + + align:start position:0% +fourier matrix and its inverse which we + + + align:start position:0% +fourier matrix and its inverse which we +still have to find but it'll come out + + align:start position:0% +still have to find but it'll come out + + + align:start position:0% +still have to find but it'll come out +beautifully in + + align:start position:0% +beautifully in + + + align:start position:0% +beautifully in +fact I could tell you what how what F + + align:start position:0% +fact I could tell you what how what F + + + align:start position:0% +fact I could tell you what how what F +inverse just so you like see it coming F + + align:start position:0% +inverse just so you like see it coming F + + + align:start position:0% +inverse just so you like see it coming F +inverse will so what happened to W that + + align:start position:0% +inverse will so what happened to W that + + + align:start position:0% +inverse will so what happened to W that +all-important number W well + + align:start position:0% +all-important number W well + + + align:start position:0% +all-important number W well +let me repeat what W is + + align:start position:0% +let me repeat what W is + + + align:start position:0% +let me repeat what W is +okay + + align:start position:0% + + + + align:start position:0% + +just I'll put it on this board F has + + align:start position:0% +just I'll put it on this board F has + + + align:start position:0% +just I'll put it on this board F has +powers of W W is e to the 2 pi I over N + + align:start position:0% +powers of W W is e to the 2 pi I over N + + + align:start position:0% +powers of W W is e to the 2 pi I over N +and + + align:start position:0% +and + + + align:start position:0% +and +what power has it got in the j k + + align:start position:0% +what power has it got in the j k + + + align:start position:0% +what power has it got in the j k +position all right so now you're good to + + align:start position:0% +position all right so now you're good to + + + align:start position:0% +position all right so now you're good to +see formula for these entries + + align:start position:0% +see formula for these entries + + + align:start position:0% +see formula for these entries +only you have to let me start the count + + align:start position:0% +only you have to let me start the count + + + align:start position:0% +only you have to let me start the count +at J and K equals 0 this is a zero based + + align:start position:0% +at J and K equals 0 this is a zero based + + + align:start position:0% +at J and K equals 0 this is a zero based +where MATLAB is one based and to do this + + align:start position:0% +where MATLAB is one based and to do this + + + align:start position:0% +where MATLAB is one based and to do this +stuff you always have to shift things by + + align:start position:0% +stuff you always have to shift things by + + + align:start position:0% +stuff you always have to shift things by +one some other more recent software like + + align:start position:0% +one some other more recent software like + + + align:start position:0% +one some other more recent software like +Python is zero based because this is so + + align:start position:0% +Python is zero based because this is so + + + align:start position:0% +Python is zero based because this is so +common so so these ones for J here's the + + align:start position:0% +common so so these ones for J here's the + + + align:start position:0% +common so so these ones for J here's the +formula it's W to the power J times K + + align:start position:0% +formula it's W to the power J times K + + + align:start position:0% +formula it's W to the power J times K +that's neat that's what goes into the + + align:start position:0% +that's neat that's what goes into the + + + align:start position:0% +that's neat that's what goes into the +matrix F into this is this is here is + + align:start position:0% +matrix F into this is this is here is + + + align:start position:0% +matrix F into this is this is here is +Row three it looks like Row 4 but I'm + + align:start position:0% +Row three it looks like Row 4 but I'm + + + align:start position:0% +Row three it looks like Row 4 but I'm +starting with zero so that's Row three + + align:start position:0% +starting with zero so that's Row three + + + align:start position:0% +starting with zero so that's Row three +that's column three this is W three + + align:start position:0% +that's column three this is W three + + + align:start position:0% +that's column three this is W three +times + + align:start position:0% +times + + + align:start position:0% +times +3w the ninth which by the way is the + + align:start position:0% +3w the ninth which by the way is the + + + align:start position:0% +3w the ninth which by the way is the +same as what what what is if W excuse me + + align:start position:0% +same as what what what is if W excuse me + + + align:start position:0% +same as what what what is if W excuse me +of W is I in this 4x4 it is w is I + + align:start position:0% +of W is I in this 4x4 it is w is I + + + align:start position:0% +of W is I in this 4x4 it is w is I +what's w to the ninth was I to the ninth + + align:start position:0% +what's w to the ninth was I to the ninth + + + align:start position:0% +what's w to the ninth was I to the ninth +power + + align:start position:0% + + + + align:start position:0% + +same as + + align:start position:0% +same as + + + align:start position:0% +same as +can you do I to the ninth in your head + + align:start position:0% +can you do I to the ninth in your head + + + align:start position:0% +can you do I to the ninth in your head +sure because you're starting here you're + + align:start position:0% +sure because you're starting here you're + + + align:start position:0% +sure because you're starting here you're +taking its ninth power so one one two + + align:start position:0% +taking its ninth power so one one two + + + align:start position:0% +taking its ninth power so one one two +three four you're back to one I to the + + align:start position:0% +three four you're back to one I to the + + + align:start position:0% +three four you're back to one I to the +fourth is 1 one two three four more I to + + align:start position:0% +fourth is 1 one two three four more I to + + + align:start position:0% +fourth is 1 one two three four more I to +the eighth is one I to the ninth that + + align:start position:0% +the eighth is one I to the ninth that + + + align:start position:0% +the eighth is one I to the ninth that +that will actually be just I I + + align:start position:0% +that will actually be just I I + + + align:start position:0% +that will actually be just I I +to the ninth so they're all powers of I + + align:start position:0% +to the ninth so they're all powers of I + + + align:start position:0% +to the ninth so they're all powers of I +but this is the good way to see it it's + + align:start position:0% +but this is the good way to see it it's + + + align:start position:0% +but this is the good way to see it it's +3 times 3 because it's in and this of + + align:start position:0% +3 times 3 because it's in and this of + + + align:start position:0% +3 times 3 because it's in and this of +course is 3 times 2 and 2 times 2 and 3 + + align:start position:0% +course is 3 times 2 and 2 times 2 and 3 + + + align:start position:0% +course is 3 times 2 and 2 times 2 and 3 +times 1 you see the entries of F yeah so + + align:start position:0% +times 1 you see the entries of F yeah so + + + align:start position:0% +times 1 you see the entries of F yeah so +so now I better write down I promise to + + align:start position:0% +so now I better write down I promise to + + + align:start position:0% +so now I better write down I promise to +write this formula in a better form + + align:start position:0% +write this formula in a better form + + + align:start position:0% +write this formula in a better form +though all those formulas in a better + + align:start position:0% +though all those formulas in a better + + + align:start position:0% +though all those formulas in a better +yeah yeah that's nobody is going to + + align:start position:0% +yeah yeah that's nobody is going to + + + align:start position:0% +yeah yeah that's nobody is going to +write this out for matrix of order + + align:start position:0% +write this out for matrix of order + + + align:start position:0% +write this out for matrix of order +thousand right so we've got a right to + + align:start position:0% +thousand right so we've got a right to + + + align:start position:0% +thousand right so we've got a right to +decent formula + + align:start position:0% +decent formula + + + align:start position:0% +decent formula +so the decent formula is that the Jase + + align:start position:0% +so the decent formula is that the Jase + + + align:start position:0% +so the decent formula is that the Jase +why because it's going to come in + + align:start position:0% +why because it's going to come in + + + align:start position:0% +why because it's going to come in +equation number J will be the sum 1 K + + align:start position:0% +equation number J will be the sum 1 K + + + align:start position:0% +equation number J will be the sum 1 K +equals 0 to n minus 1 of + + align:start position:0% +equals 0 to n minus 1 of + + + align:start position:0% +equals 0 to n minus 1 of +C K times W to the J ok + + align:start position:0% +C K times W to the J ok + + + align:start position:0% +C K times W to the J ok +those are the entries that's those are + + align:start position:0% +those are the entries that's those are + + + align:start position:0% +those are the entries that's those are +the seeds that are it multiplies and the + + align:start position:0% +the seeds that are it multiplies and the + + + align:start position:0% +the seeds that are it multiplies and the +Y's that's a gift this is just what + + align:start position:0% +Y's that's a gift this is just what + + + align:start position:0% +Y's that's a gift this is just what +vector wise this is y equal after see + + align:start position:0% +vector wise this is y equal after see + + + align:start position:0% +vector wise this is y equal after see +yeah now we finally got a good notation + + align:start position:0% +yeah now we finally got a good notation + + + align:start position:0% +yeah now we finally got a good notation +so this was like horrible notation I + + align:start position:0% +so this was like horrible notation I + + + align:start position:0% +so this was like horrible notation I +mean that's like exhausting this shows + + align:start position:0% +mean that's like exhausting this shows + + + align:start position:0% +mean that's like exhausting this shows +you the algebra but you have to be sort + + align:start position:0% +you the algebra but you have to be sort + + + align:start position:0% +you the algebra but you have to be sort +of prepared well that the information is + + align:start position:0% +of prepared well that the information is + + + align:start position:0% +of prepared well that the information is +here because this is telling you what + + align:start position:0% +here because this is telling you what + + + align:start position:0% +here because this is telling you what +the entries of F of the matrix are but + + align:start position:0% +the entries of F of the matrix are but + + + align:start position:0% +the entries of F of the matrix are but +like this is with indices and this is + + align:start position:0% +like this is with indices and this is + + + align:start position:0% +like this is with indices and this is +with hole vectors right + + align:start position:0% +with hole vectors right + + + align:start position:0% +with hole vectors right +so I would that would be why in MATLAB + + align:start position:0% +so I would that would be why in MATLAB + + + align:start position:0% +so I would that would be why in MATLAB +that would be the inverse fast Fourier + + align:start position:0% +that would be the inverse fast Fourier + + + align:start position:0% +that would be the inverse fast Fourier +transform of C + + align:start position:0% + + + + align:start position:0% + +so you see that that's our matrix okay + + align:start position:0% +so you see that that's our matrix okay + + + align:start position:0% +so you see that that's our matrix okay +now I was going to say before I + + align:start position:0% +now I was going to say before I + + + align:start position:0% +now I was going to say before I +show why I was going to say what about + + align:start position:0% +show why I was going to say what about + + + align:start position:0% +show why I was going to say what about +the inverse because if the FFT gave us a + + align:start position:0% +the inverse because if the FFT gave us a + + + align:start position:0% +the inverse because if the FFT gave us a +fast way to multiply by F + + align:start position:0% +fast way to multiply by F + + + align:start position:0% +fast way to multiply by F +we wanted also to give us a fast way to + + align:start position:0% +we wanted also to give us a fast way to + + + align:start position:0% +we wanted also to give us a fast way to +do the inverse right we have to go both + + align:start position:0% +do the inverse right we have to go both + + + align:start position:0% +do the inverse right we have to go both +ways here + + align:start position:0% +ways here + + + align:start position:0% +ways here +we get our data we put it into frequency + + align:start position:0% +we get our data we put it into frequency + + + align:start position:0% +we get our data we put it into frequency +space we look at it in frequency space + + align:start position:0% +space we look at it in frequency space + + + align:start position:0% +space we look at it in frequency space +we understand what's going on by + + align:start position:0% +we understand what's going on by + + + align:start position:0% +we understand what's going on by +separating out the frequencies we may be + + align:start position:0% +separating out the frequencies we may be + + + align:start position:0% +separating out the frequencies we may be +smooth it we may be convolve it whatever + + align:start position:0% +smooth it we may be convolve it whatever + + + align:start position:0% +smooth it we may be convolve it whatever +we do compress it and then we got to go + + align:start position:0% +we do compress it and then we got to go + + + align:start position:0% +we do compress it and then we got to go +back to physical space so we have to go + + align:start position:0% +back to physical space so we have to go + + + align:start position:0% +back to physical space so we have to go +both ways and + + align:start position:0% +both ways and + + + align:start position:0% +both ways and +the question is what about F inverse and + + align:start position:0% +the question is what about F inverse and + + + align:start position:0% +the question is what about F inverse and +let me just say + + align:start position:0% +let me just say + + + align:start position:0% +let me just say +what it what goes into F inverse + + align:start position:0% + + + + align:start position:0% + +the point is that the number that goes + + align:start position:0% +the point is that the number that goes + + + align:start position:0% +the point is that the number that goes +into F inverse is just like W + + align:start position:0% +into F inverse is just like W + + + align:start position:0% +into F inverse is just like W +but it's the complex conjugate and I'll + + align:start position:0% +but it's the complex conjugate and I'll + + + align:start position:0% +but it's the complex conjugate and I'll +call it W bar and that's e to the minus + + align:start position:0% +call it W bar and that's e to the minus + + + align:start position:0% +call it W bar and that's e to the minus +2 pi I over N + + align:start position:0% +2 pi I over N + + + align:start position:0% +2 pi I over N +so the thing that that's going to go + + align:start position:0% +so the thing that that's going to go + + + align:start position:0% +so the thing that that's going to go +into the inverse matrix is the powers of + + align:start position:0% +into the inverse matrix is the powers of + + + align:start position:0% +into the inverse matrix is the powers of +W bar the complex conjugate JK + + align:start position:0% + + + + align:start position:0% + +let me just say right away + + align:start position:0% +let me just say right away + + + align:start position:0% +let me just say right away +that just as there were two pies in the + + align:start position:0% +that just as there were two pies in the + + + align:start position:0% +that just as there were two pies in the +Fourier series world you know that got + + align:start position:0% +Fourier series world you know that got + + + align:start position:0% +Fourier series world you know that got +in our way and + + align:start position:0% +in our way and + + + align:start position:0% +in our way and +physicists + + align:start position:0% +physicists + + + align:start position:0% +physicists +can't stand those two pies they try to + + align:start position:0% +can't stand those two pies they try to + + + align:start position:0% +can't stand those two pies they try to +get rid of them of course they can't + + align:start position:0% +get rid of them of course they can't + + + align:start position:0% +get rid of them of course they can't +they're there but they so they put it up + + align:start position:0% +they're there but they so they put it up + + + align:start position:0% +they're there but they so they put it up +into the exponent well I guess maybe + + align:start position:0% +into the exponent well I guess maybe + + + align:start position:0% +into the exponent well I guess maybe +physicists I've done it too I've put the + + align:start position:0% +physicists I've done it too I've put the + + + align:start position:0% +physicists I've done it too I've put the +2 pi up there for the Fourier series + + align:start position:0% +2 pi up there for the Fourier series + + + align:start position:0% +2 pi up there for the Fourier series +anyway whatever to pies are all in your + + align:start position:0% +anyway whatever to pies are all in your + + + align:start position:0% +anyway whatever to pies are all in your +hair in the Fourier series and in this + + align:start position:0% +hair in the Fourier series and in this + + + align:start position:0% +hair in the Fourier series and in this +for the discrete one the corresponding + + align:start position:0% +for the discrete one the corresponding + + + align:start position:0% +for the discrete one the corresponding +thing is an end there's a factor n that + + align:start position:0% +thing is an end there's a factor n that + + + align:start position:0% +thing is an end there's a factor n that +I have to deal with because look + + align:start position:0% +I have to deal with because look + + + align:start position:0% +I have to deal with because look +yeah here's what I'm saying hey let me + + align:start position:0% +yeah here's what I'm saying hey let me + + + align:start position:0% +yeah here's what I'm saying hey let me +multiply F by F inverse okay say 1 1 1 1 + + align:start position:0% +multiply F by F inverse okay say 1 1 1 1 + + + align:start position:0% +multiply F by F inverse okay say 1 1 1 1 +1 I I squared I cube this is my F right + + align:start position:0% +1 I I squared I cube this is my F right + + + align:start position:0% +1 I I squared I cube this is my F right +whoops + + align:start position:0% + + + + align:start position:0% + +squared 4 6 I cube by 6 I 9 + + align:start position:0% +squared 4 6 I cube by 6 I 9 + + + align:start position:0% +squared 4 6 I cube by 6 I 9 +now my claim is that F inverse is going + + align:start position:0% +now my claim is that F inverse is going + + + align:start position:0% +now my claim is that F inverse is going +to involve the complex conjugate W bar I + + align:start position:0% +to involve the complex conjugate W bar I + + + align:start position:0% +to involve the complex conjugate W bar I +bar what is the complex conjugate of I + + align:start position:0% +bar what is the complex conjugate of I + + + align:start position:0% +bar what is the complex conjugate of I +you see that we really have to use + + align:start position:0% +you see that we really have to use + + + align:start position:0% +you see that we really have to use +complex numbers here and and there's but + + align:start position:0% +complex numbers here and and there's but + + + align:start position:0% +complex numbers here and and there's but +there on the unit circle you couldn't + + align:start position:0% +there on the unit circle you couldn't + + + align:start position:0% +there on the unit circle you couldn't +ask for better ones what's the complex + + align:start position:0% +ask for better ones what's the complex + + + align:start position:0% +ask for better ones what's the complex +conjugate that's going to go into f + + align:start position:0% +conjugate that's going to go into f + + + align:start position:0% +conjugate that's going to go into f +inverse + + align:start position:0% +inverse + + + align:start position:0% +inverse +if I take I and I + + align:start position:0% +if I take I and I + + + align:start position:0% +if I take I and I +take its conjugate what does that mean + + align:start position:0% +take its conjugate what does that mean + + + align:start position:0% +take its conjugate what does that mean +so the conjugate of that is just flip it + + align:start position:0% +so the conjugate of that is just flip it + + + align:start position:0% +so the conjugate of that is just flip it +across the real axis + + align:start position:0% +across the real axis + + + align:start position:0% +across the real axis +to the other one yeah you see it's great + + align:start position:0% +to the other one yeah you see it's great + + + align:start position:0% +to the other one yeah you see it's great +that conjugate the complex comes out of + + align:start position:0% +that conjugate the complex comes out of + + + align:start position:0% +that conjugate the complex comes out of +I is minus I the complex conjugate here + + align:start position:0% +I is minus I the complex conjugate here + + + align:start position:0% +I is minus I the complex conjugate here +is W bar 8 + + align:start position:0% + + + + align:start position:0% + +it's just across the axis so it still + + align:start position:0% +it's just across the axis so it still + + + align:start position:0% +it's just across the axis so it still +has + + align:start position:0% +has + + + align:start position:0% +has +size 1 and of course it's e to the this + + align:start position:0% +size 1 and of course it's e to the this + + + align:start position:0% +size 1 and of course it's e to the this +angle which is just minus this angle so + + align:start position:0% +angle which is just minus this angle so + + + align:start position:0% +angle which is just minus this angle so +that's why we get this - because when I + + align:start position:0% +that's why we get this - because when I + + + align:start position:0% +that's why we get this - because when I +flip it across I changes to minus i + + align:start position:0% +flip it across I changes to minus i + + + align:start position:0% +flip it across I changes to minus i +angles changes to minus angle and + + align:start position:0% +angles changes to minus angle and + + + align:start position:0% +angles changes to minus angle and +finally I was going to do this + + align:start position:0% +finally I was going to do this + + + align:start position:0% +finally I was going to do this +multiplication just to see so now I'm + + align:start position:0% +multiplication just to see so now I'm + + + align:start position:0% +multiplication just to see so now I'm +claiming that this is 1 1 1 1 1 1 1 + + align:start position:0% +claiming that this is 1 1 1 1 1 1 1 + + + align:start position:0% +claiming that this is 1 1 1 1 1 1 1 +minus I minus I squared minus IQ so on + + align:start position:0% +minus I minus I squared minus IQ so on + + + align:start position:0% +minus I minus I squared minus IQ so on +minus I squared minus I cubed + + align:start position:0% +minus I squared minus I cubed + + + align:start position:0% +minus I squared minus I cubed +for 6 + + align:start position:0% +for 6 + + + align:start position:0% +for 6 +six and nine + + align:start position:0% +six and nine + + + align:start position:0% +six and nine +and now if you do that multiplication + + align:start position:0% +and now if you do that multiplication + + + align:start position:0% +and now if you do that multiplication +you will get the identity matrix that's + + align:start position:0% +you will get the identity matrix that's + + + align:start position:0% +you will get the identity matrix that's +the great thing you'll get the identity + + align:start position:0% +the great thing you'll get the identity + + + align:start position:0% +the great thing you'll get the identity +1 1 1 1 + + align:start position:0% +1 1 1 1 + + + align:start position:0% +1 1 1 1 +except for a factor + + align:start position:0% +except for a factor + + + align:start position:0% +except for a factor +and now what's what what happens when I + + align:start position:0% +and now what's what what happens when I + + + align:start position:0% +and now what's what what happens when I +do you see that coming when I multiply + + align:start position:0% +do you see that coming when I multiply + + + align:start position:0% +do you see that coming when I multiply +this by this what do I get + + align:start position:0% +this by this what do I get + + + align:start position:0% +this by this what do I get +for if + + align:start position:0% +for if + + + align:start position:0% +for if +they were n by n I'd have n ones against + + align:start position:0% +they were n by n I'd have n ones against + + + align:start position:0% +they were n by n I'd have n ones against +N 1 so I'd have to expect an M there + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so F times F inverse well F times F n + + align:start position:0% +so F times F inverse well F times F n + + + align:start position:0% +so F times F inverse well F times F n +inverse so in other words if I want to + + align:start position:0% +inverse so in other words if I want to + + + align:start position:0% +inverse so in other words if I want to +get the identity I better + + align:start position:0% +get the identity I better + + + align:start position:0% +get the identity I better +divide these divide this by n so now I + + align:start position:0% +divide these divide this by n so now I + + + align:start position:0% +divide these divide this by n so now I +have that's F F inverse equal I so f + + align:start position:0% +have that's F F inverse equal I so f + + + align:start position:0% +have that's F F inverse equal I so f +inverse is just like F + + align:start position:0% +inverse is just like F + + + align:start position:0% +inverse is just like F +except complex conjugate and divided by + + align:start position:0% +except complex conjugate and divided by + + + align:start position:0% +except complex conjugate and divided by +n so if I want this formula to be really + + align:start position:0% +n so if I want this formula to be really + + + align:start position:0% +n so if I want this formula to be really +correct I have to divide by n + + align:start position:0% +correct I have to divide by n + + + align:start position:0% +correct I have to divide by n +okay so and that's what W and W bar is + + align:start position:0% +okay so and that's what W and W bar is + + + align:start position:0% +okay so and that's what W and W bar is +and and another letter that often gets + + align:start position:0% +and and another letter that often gets + + + align:start position:0% +and and another letter that often gets +used in this topic is Omega and I figure + + align:start position:0% +used in this topic is Omega and I figure + + + align:start position:0% +used in this topic is Omega and I figure +good that's a good way to + + align:start position:0% +good that's a good way to + + + align:start position:0% +good that's a good way to +separate out the complex conjugate + + align:start position:0% +separate out the complex conjugate + + + align:start position:0% +separate out the complex conjugate +that's called the call this guy W and + + align:start position:0% +that's called the call this guy W and + + + align:start position:0% +that's called the call this guy W and +call this guy Omega so this is W and + + align:start position:0% +call this guy Omega so this is W and + + + align:start position:0% +call this guy Omega so this is W and +here's Omega I don't know if that helps + + align:start position:0% +here's Omega I don't know if that helps + + + align:start position:0% +here's Omega I don't know if that helps +but you do have to keep straight + + align:start position:0% +but you do have to keep straight + + + align:start position:0% +but you do have to keep straight +whether you're talking about this number + + align:start position:0% +whether you're talking about this number + + + align:start position:0% +whether you're talking about this number +or that number and and many and and this + + align:start position:0% +or that number and and many and and this + + + align:start position:0% +or that number and and many and and this +number could be called W in a because + + align:start position:0% +number could be called W in a because + + + align:start position:0% +number could be called W in a because +Omega wouldn't be easy to type so so + + align:start position:0% +Omega wouldn't be easy to type so so + + + align:start position:0% +Omega wouldn't be easy to type so so +just you have to say you have to pay + + align:start position:0% +just you have to say you have to pay + + + align:start position:0% +just you have to say you have to pay +attention which one you're doing and + + align:start position:0% +attention which one you're doing and + + + align:start position:0% +attention which one you're doing and +when somewhere you have to divide by n + + align:start position:0% +when somewhere you have to divide by n + + + align:start position:0% +when somewhere you have to divide by n +but otherwise it's fantastic it's just + + align:start position:0% +but otherwise it's fantastic it's just + + + align:start position:0% +but otherwise it's fantastic it's just +beautiful so so if I write out the the + + align:start position:0% +beautiful so so if I write out the the + + + align:start position:0% +beautiful so so if I write out the the +yeah I have to do that yeah + + align:start position:0% +yeah I have to do that yeah + + + align:start position:0% +yeah I have to do that yeah +can we do that multiplication + + align:start position:0% +can we do that multiplication + + + align:start position:0% +can we do that multiplication +just to see that it really works + + align:start position:0% +just to see that it really works + + + align:start position:0% +just to see that it really works +well the ones worked fine what about the + + align:start position:0% +well the ones worked fine what about the + + + align:start position:0% +well the ones worked fine what about the +ones times what about or what about what + + align:start position:0% +ones times what about or what about what + + + align:start position:0% +ones times what about or what about what +about the yeah what about the ones times + + align:start position:0% +about the yeah what about the ones times + + + align:start position:0% +about the yeah what about the ones times +that column so + + align:start position:0% + + + + align:start position:0% + +I'm looking at the one two entry in this + + align:start position:0% +I'm looking at the one two entry in this + + + align:start position:0% +I'm looking at the one two entry in this +multiplication or things rather than + + align:start position:0% +multiplication or things rather than + + + align:start position:0% +multiplication or things rather than +zero one entry I should say this is the + + align:start position:0% +zero one entry I should say this is the + + + align:start position:0% +zero one entry I should say this is the +zeroth row and this is the row number + + align:start position:0% +zeroth row and this is the row number + + + align:start position:0% +zeroth row and this is the row number +one and what do I get out of that + + align:start position:0% +one and what do I get out of that + + + align:start position:0% +one and what do I get out of that +zero right that's that's this is that + + align:start position:0% +zero right that's that's this is that + + + align:start position:0% +zero right that's that's this is that +was my point that that this is adding up + + align:start position:0% +was my point that that this is adding up + + + align:start position:0% +was my point that that this is adding up +oh well going the other way round + + align:start position:0% +oh well going the other way round + + + align:start position:0% +oh well going the other way round +because it's the complex conjugate but + + align:start position:0% +because it's the complex conjugate but + + + align:start position:0% +because it's the complex conjugate but +it's adding up the four same four + + align:start position:0% +it's adding up the four same four + + + align:start position:0% +it's adding up the four same four +numbers and giving me that zero + + align:start position:0% +numbers and giving me that zero + + + align:start position:0% +numbers and giving me that zero +and now how about the ones on the + + align:start position:0% +and now how about the ones on the + + + align:start position:0% +and now how about the ones on the +diagonal when I do this times this so + + align:start position:0% +diagonal when I do this times this so + + + align:start position:0% +diagonal when I do this times this so +this is the the same the row times + + align:start position:0% +this is the the same the row times + + + align:start position:0% +this is the the same the row times +itself what am I seeing there + + align:start position:0% +itself what am I seeing there + + + align:start position:0% +itself what am I seeing there +what what does what what are these terms + + align:start position:0% +what what does what what are these terms + + + align:start position:0% +what what does what what are these terms +that's certainly one what is I times + + align:start position:0% +that's certainly one what is I times + + + align:start position:0% +that's certainly one what is I times +minus I I + + align:start position:0% +minus I I + + + align:start position:0% +minus I I +times minus I is one again numbers + + align:start position:0% +times minus I is one again numbers + + + align:start position:0% +times minus I is one again numbers +getting multiplied by its conjugate that + + align:start position:0% +getting multiplied by its conjugate that + + + align:start position:0% +getting multiplied by its conjugate that +gives you something real and positive + + align:start position:0% +gives you something real and positive + + + align:start position:0% +gives you something real and positive +when you multiply a number by its + + align:start position:0% +when you multiply a number by its + + + align:start position:0% +when you multiply a number by its +conjugate a number by its conjugate in + + align:start position:0% +conjugate a number by its conjugate in + + + align:start position:0% +conjugate a number by its conjugate in +fact we get one every time so we get + + align:start position:0% +fact we get one every time so we get + + + align:start position:0% +fact we get one every time so we get +four ones we divide by four and we we + + align:start position:0% +four ones we divide by four and we we + + + align:start position:0% +four ones we divide by four and we we +get that + + align:start position:0% + + + + align:start position:0% + +maybe you actually see here just so just + + align:start position:0% +maybe you actually see here just so just + + + align:start position:0% +maybe you actually see here just so just +so we remember + + align:start position:0% +so we remember + + + align:start position:0% +so we remember +so F F inverse is + + align:start position:0% +so F F inverse is + + + align:start position:0% +so F F inverse is +I'm concluding that F sorry F F inverse + + align:start position:0% +I'm concluding that F sorry F F inverse + + + align:start position:0% +I'm concluding that F sorry F F inverse +I'm looking now what is F inverse its F + + align:start position:0% +I'm looking now what is F inverse its F + + + align:start position:0% +I'm looking now what is F inverse its F +conjugate divided by this + + align:start position:0% +conjugate divided by this + + + align:start position:0% +conjugate divided by this +nuisance number n I could put square + + align:start position:0% +nuisance number n I could put square + + + align:start position:0% +nuisance number n I could put square +root of n with with F and then square + + align:start position:0% +root of n with with F and then square + + + align:start position:0% +root of n with with F and then square +root of n would show up with F inverse + + align:start position:0% +root of n would show up with F inverse + + + align:start position:0% +root of n would show up with F inverse +just the way I could have done square + + align:start position:0% +just the way I could have done square + + + align:start position:0% +just the way I could have done square +root of 2pi with 1 and square root of + + align:start position:0% +root of 2pi with 1 and square root of + + + align:start position:0% +root of 2pi with 1 and square root of +2pi with the other but let's leave it + + align:start position:0% +2pi with the other but let's leave it + + + align:start position:0% +2pi with the other but let's leave it +like so + + align:start position:0% + + + + align:start position:0% + +yeah so that's not proved in a way just + + align:start position:0% +yeah so that's not proved in a way just + + + align:start position:0% +yeah so that's not proved in a way just +just + + align:start position:0% +just + + + align:start position:0% +just +checked for a + + align:start position:0% +checked for a + + + align:start position:0% +checked for a +couple of cases within equal four but it + + align:start position:0% +couple of cases within equal four but it + + + align:start position:0% +couple of cases within equal four but it +always works so that's the beauty in + + align:start position:0% +always works so that's the beauty in + + + align:start position:0% +always works so that's the beauty in +other words the the invert the two + + align:start position:0% +other words the the invert the two + + + align:start position:0% +other words the the invert the two +directions the y2 C and the C 2 y + + align:start position:0% +directions the y2 C and the C 2 y + + + align:start position:0% +directions the y2 C and the C 2 y +are both going to be speeded up by the + + align:start position:0% +are both going to be speeded up by the + + + align:start position:0% +are both going to be speeded up by the +FFT the FFT if whatever it did whatever + + align:start position:0% +FFT the FFT if whatever it did whatever + + + align:start position:0% +FFT the FFT if whatever it did whatever +it could do with W and powers of W it + + align:start position:0% +it could do with W and powers of W it + + + align:start position:0% +it could do with W and powers of W it +can do the same with W bar and powers of + + align:start position:0% +can do the same with W bar and powers of + + + align:start position:0% +can do the same with W bar and powers of +W bar if the FFT is a fast waiting to + + align:start position:0% +W bar if the FFT is a fast waiting to + + + align:start position:0% +W bar if the FFT is a fast waiting to +multiply by that it'll also give me a + + align:start position:0% +multiply by that it'll also give me a + + + align:start position:0% +multiply by that it'll also give me a +fast way to multiply to Trenton to do + + align:start position:0% +fast way to multiply to Trenton to do + + + align:start position:0% +fast way to multiply to Trenton to do +the other transform yeah so + + align:start position:0% +the other transform yeah so + + + align:start position:0% +the other transform yeah so +the FFT is what makes everything this + + align:start position:0% +the FFT is what makes everything this + + + align:start position:0% +the FFT is what makes everything this +would all be important if the FFT didn't + + align:start position:0% +would all be important if the FFT didn't + + + align:start position:0% +would all be important if the FFT didn't +exist and of course actually Fourier + + align:start position:0% +exist and of course actually Fourier + + + align:start position:0% +exist and of course actually Fourier +didn't notice it gauss kind of had + + align:start position:0% +didn't notice it gauss kind of had + + + align:start position:0% +didn't notice it gauss kind of had +again had the idea but he had so many + + align:start position:0% +again had the idea but he had so many + + + align:start position:0% +again had the idea but he had so many +ideas that didn't like wasn't very clear + + align:start position:0% +ideas that didn't like wasn't very clear + + + align:start position:0% +ideas that didn't like wasn't very clear +in his notes + + align:start position:0% +in his notes + + + align:start position:0% +in his notes +the fft idea but Cooley and kooky + + align:start position:0% +the fft idea but Cooley and kooky + + + align:start position:0% +the fft idea but Cooley and kooky +guys at Bell Labs in + + align:start position:0% +guys at Bell Labs in + + + align:start position:0% +guys at Bell Labs in +1950s + + align:start position:0% +1950s + + + align:start position:0% +1950s +discovered it in a small paper I don't + + align:start position:0% +discovered it in a small paper I don't + + + align:start position:0% +discovered it in a small paper I don't +think they had any idea + + align:start position:0% +think they had any idea + + + align:start position:0% +think they had any idea +how important it would be but they + + align:start position:0% +how important it would be but they + + + align:start position:0% +how important it would be but they +published their paper and people + + align:start position:0% +published their paper and people + + + align:start position:0% +published their paper and people +got you saw what was happening and + + align:start position:0% +got you saw what was happening and + + + align:start position:0% +got you saw what was happening and +realized that they should that that gave + + align:start position:0% +realized that they should that that gave + + + align:start position:0% +realized that they should that that gave +the right way to do the transforms okay + + align:start position:0% +the right way to do the transforms okay + + + align:start position:0% +the right way to do the transforms okay +I was going to say here + + align:start position:0% +I was going to say here + + + align:start position:0% +I was going to say here +do you notice that this one + + align:start position:0% +do you notice that this one + + + align:start position:0% +do you notice that this one +when I take a + + align:start position:0% +when I take a + + + align:start position:0% +when I take a +vector you know that vector and it's + + align:start position:0% +vector you know that vector and it's + + + align:start position:0% +vector you know that vector and it's +complex conjugate what am I getting + + align:start position:0% +complex conjugate what am I getting + + + align:start position:0% +complex conjugate what am I getting +I'm getting the length squared I'm + + align:start position:0% +I'm getting the length squared I'm + + + align:start position:0% +I'm getting the length squared I'm +getting the right inner product this is + + align:start position:0% +getting the right inner product this is + + + align:start position:0% +getting the right inner product this is +the right inner product when things are + + align:start position:0% +the right inner product when things are + + + align:start position:0% +the right inner product when things are +complex something times its conjugate I + + align:start position:0% +complex something times its conjugate I + + + align:start position:0% +complex something times its conjugate I +just reminding you that that the inner + + align:start position:0% +just reminding you that that the inner + + + align:start position:0% +just reminding you that that the inner +product of two vectors u V u dot V or u + + align:start position:0% +product of two vectors u V u dot V or u + + + align:start position:0% +product of two vectors u V u dot V or u +comma V should now be the sum you should + + align:start position:0% +comma V should now be the sum you should + + + align:start position:0% +comma V should now be the sum you should +used to be the sum of UI via + + align:start position:0% +used to be the sum of UI via + + + align:start position:0% +used to be the sum of UI via +but now we're in the complex case so we + + align:start position:0% +but now we're in the complex case so we + + + align:start position:0% +but now we're in the complex case so we +should take the conjugate of one of them + + align:start position:0% +should take the conjugate of one of them + + + align:start position:0% +should take the conjugate of one of them +and + + align:start position:0% +and + + + align:start position:0% +and +here I guess that's the V and this is + + align:start position:0% +here I guess that's the V and this is + + + align:start position:0% +here I guess that's the V and this is +the U and it so the point is + + align:start position:0% +the U and it so the point is + + + align:start position:0% +the U and it so the point is +that we're taking the right + + align:start position:0% +that we're taking the right + + + align:start position:0% +that we're taking the right +yeah we + + align:start position:0% +yeah we + + + align:start position:0% +yeah we +we have or oh yeah let me just say it + + align:start position:0% +we have or oh yeah let me just say it + + + align:start position:0% +we have or oh yeah let me just say it +this way the columns these columns are + + align:start position:0% +this way the columns these columns are + + + align:start position:0% +this way the columns these columns are +orthogonal those four columns the + + align:start position:0% +orthogonal those four columns the + + + align:start position:0% +orthogonal those four columns the +columns of the Fourier matrix are + + align:start position:0% +columns of the Fourier matrix are + + + align:start position:0% +columns of the Fourier matrix are +orthogonal in other words we have an + + align:start position:0% +orthogonal in other words we have an + + + align:start position:0% +orthogonal in other words we have an +orthogonal basis + + align:start position:0% +orthogonal basis + + + align:start position:0% +orthogonal basis +and it's those four columns that's the + + align:start position:0% +and it's those four columns that's the + + + align:start position:0% +and it's those four columns that's the +yeah I almost missed saying that but you + + align:start position:0% +yeah I almost missed saying that but you + + + align:start position:0% +yeah I almost missed saying that but you +you remember from last week the whole + + align:start position:0% +you remember from last week the whole + + + align:start position:0% +you remember from last week the whole +point about sines and cosines and + + align:start position:0% +point about sines and cosines and + + + align:start position:0% +point about sines and cosines and +Exponential's in the in the function + + align:start position:0% +Exponential's in the in the function + + + align:start position:0% +Exponential's in the in the function +case was orthogonal that's what made + + align:start position:0% +case was orthogonal that's what made + + + align:start position:0% +case was orthogonal that's what made +everything work and it makes everything + + align:start position:0% +everything work and it makes everything + + + align:start position:0% +everything work and it makes everything +work here here here we have vectors not + + align:start position:0% +work here here here we have vectors not + + + align:start position:0% +work here here here we have vectors not +functions + + align:start position:0% +functions + + + align:start position:0% +functions +orthogonal just means dot products are 0 + + align:start position:0% +orthogonal just means dot products are 0 + + + align:start position:0% +orthogonal just means dot products are 0 +but they're complex so that in the dot + + align:start position:0% +but they're complex so that in the dot + + + align:start position:0% +but they're complex so that in the dot +product one of the one factor or the + + align:start position:0% +product one of the one factor or the + + + align:start position:0% +product one of the one factor or the +other has to get conjugated anyway + + align:start position:0% +other has to get conjugated anyway + + + align:start position:0% +other has to get conjugated anyway +that's an orthogonal matrix + + align:start position:0% +that's an orthogonal matrix + + + align:start position:0% +that's an orthogonal matrix +apart from the if I apart from this end + + align:start position:0% +apart from the if I apart from this end + + + align:start position:0% +apart from the if I apart from this end +this capital M thing so that's if I + + align:start position:0% +this capital M thing so that's if I + + + align:start position:0% +this capital M thing so that's if I +normalize it if I take out one over + + align:start position:0% +normalize it if I take out one over + + + align:start position:0% +normalize it if I take out one over +square root of n now the length of every + + align:start position:0% +square root of n now the length of every + + + align:start position:0% +square root of n now the length of every +column is one so now I have orthonormal + + align:start position:0% +column is one so now I have orthonormal + + + align:start position:0% +column is one so now I have orthonormal +columns 1 squared 1 squared 1 squared 1 + + align:start position:0% +columns 1 squared 1 squared 1 squared 1 + + + align:start position:0% +columns 1 squared 1 squared 1 squared 1 +squared is 4 divided by 4 is 1 and + + align:start position:0% +squared is 4 divided by 4 is 1 and + + + align:start position:0% +squared is 4 divided by 4 is 1 and +every column has length is a is a vector + + align:start position:0% +every column has length is a is a vector + + + align:start position:0% +every column has length is a is a vector +in a vector in four-dimensional complex + + align:start position:0% +in a vector in four-dimensional complex + + + align:start position:0% +in a vector in four-dimensional complex +space of length 1 and + + align:start position:0% +space of length 1 and + + + align:start position:0% +space of length 1 and +orthogonal so that may means orthonormal + + align:start position:0% +orthogonal so that may means orthonormal + + + align:start position:0% +orthogonal so that may means orthonormal +it's a fantastic matrix that's the the + + align:start position:0% +it's a fantastic matrix that's the the + + + align:start position:0% +it's a fantastic matrix that's the the +best basis will ever have for complex + + align:start position:0% +best basis will ever have for complex + + + align:start position:0% +best basis will ever have for complex +four-dimensional space that that basis + + align:start position:0% + + + + align:start position:0% + +well actually when I say the best basis + + align:start position:0% +well actually when I say the best basis + + + align:start position:0% +well actually when I say the best basis +I will ever have I realize I wrote a + + align:start position:0% +I will ever have I realize I wrote a + + + align:start position:0% +I will ever have I realize I wrote a +book about wavelets and the idea of + + align:start position:0% +book about wavelets and the idea of + + + align:start position:0% +book about wavelets and the idea of +wavelets is there's another basis a + + align:start position:0% +wavelets is there's another basis a + + + align:start position:0% +wavelets is there's another basis a +wavelet basis and I hope to tell you + + align:start position:0% +wavelet basis and I hope to tell you + + + align:start position:0% +wavelet basis and I hope to tell you +about that at the very end of the + + align:start position:0% +about that at the very end of the + + + align:start position:0% +about that at the very end of the +semester + + align:start position:0% +semester + + + align:start position:0% +semester +so wavelets would be another basis would + + align:start position:0% +so wavelets would be another basis would + + + align:start position:0% +so wavelets would be another basis would +you like to know the wavelet basis + + align:start position:0% +you like to know the wavelet basis + + + align:start position:0% +you like to know the wavelet basis +have we got + + align:start position:0% +have we got + + + align:start position:0% +have we got +yeah it just in case the end of the + + align:start position:0% +yeah it just in case the end of the + + + align:start position:0% +yeah it just in case the end of the +semester doesn't come + + align:start position:0% + + + + align:start position:0% + +can I write down here the wavelet basis + + align:start position:0% +can I write down here the wavelet basis + + + align:start position:0% +can I write down here the wavelet basis +ok and you can you can suicide you maybe + + align:start position:0% +ok and you can you can suicide you maybe + + + align:start position:0% +ok and you can you can suicide you maybe +like to do you like it better so the + + align:start position:0% +like to do you like it better so the + + + align:start position:0% +like to do you like it better so the +four-by-four wavelet basis all right so + + align:start position:0% +four-by-four wavelet basis all right so + + + align:start position:0% +four-by-four wavelet basis all right so +this will be the wavelet matrix + + align:start position:0% +this will be the wavelet matrix + + + align:start position:0% +this will be the wavelet matrix +well this is this was too good to lose + + align:start position:0% +well this is this was too good to lose + + + align:start position:0% +well this is this was too good to lose +right that's a terrific vector all ones + + align:start position:0% +right that's a terrific vector all ones + + + align:start position:0% +right that's a terrific vector all ones +constant vector + + align:start position:0% +constant vector + + + align:start position:0% +constant vector +it's the same that gives us the average + + align:start position:0% +it's the same that gives us the average + + + align:start position:0% +it's the same that gives us the average +this C naught is going to again be the + + align:start position:0% +this C naught is going to again be the + + + align:start position:0% +this C naught is going to again be the +average of the Y's + + align:start position:0% + + + + align:start position:0% + +yeah it's just yeah how do I get that + + align:start position:0% +yeah it's just yeah how do I get that + + + align:start position:0% +yeah it's just yeah how do I get that +average yeah when I this yeah somehow + + align:start position:0% +average yeah when I this yeah somehow + + + align:start position:0% +average yeah when I this yeah somehow +I'm doing the the C naught the constant + + align:start position:0% +I'm doing the the C naught the constant + + + align:start position:0% +I'm doing the the C naught the constant +term is again I'm going to take one of + + align:start position:0% +term is again I'm going to take one of + + + align:start position:0% +term is again I'm going to take one of +everything and I'll divide by 4 and I'll + + align:start position:0% +everything and I'll divide by 4 and I'll + + + align:start position:0% +everything and I'll divide by 4 and I'll +have the average so I like that vector + + align:start position:0% +have the average so I like that vector + + + align:start position:0% +have the average so I like that vector +that's the DC vector if I'm talking + + align:start position:0% +that's the DC vector if I'm talking + + + align:start position:0% +that's the DC vector if I'm talking +about direct current vector if I'm + + align:start position:0% +about direct current vector if I'm + + + align:start position:0% +about direct current vector if I'm +talking about networks it's the + + align:start position:0% +talking about networks it's the + + + align:start position:0% +talking about networks it's the +in an image it would be the whole the + + align:start position:0% +in an image it would be the whole the + + + align:start position:0% +in an image it would be the whole the +black it's that you could call it the + + align:start position:0% +black it's that you could call it the + + + align:start position:0% +black it's that you could call it the +blackboard vector the whole the whole + + align:start position:0% +blackboard vector the whole the whole + + + align:start position:0% +blackboard vector the whole the whole +image of a empty blackboard would be + + align:start position:0% +image of a empty blackboard would be + + + align:start position:0% +image of a empty blackboard would be +constants okay so that's too good to + + align:start position:0% +constants okay so that's too good to + + + align:start position:0% +constants okay so that's too good to +lose now the obvious thing orthogonal to + + align:start position:0% +lose now the obvious thing orthogonal to + + + align:start position:0% +lose now the obvious thing orthogonal to +that would be one one minus one minus + + align:start position:0% +that would be one one minus one minus + + + align:start position:0% +that would be one one minus one minus +one + + align:start position:0% +one + + + align:start position:0% +one +right those now I've got two orthogonal + + align:start position:0% +right those now I've got two orthogonal + + + align:start position:0% +right those now I've got two orthogonal +columns and + + align:start position:0% +columns and + + + align:start position:0% +columns and +probably that's pretty close to + + align:start position:0% +probably that's pretty close to + + + align:start position:0% +probably that's pretty close to +something I have over here now the + + align:start position:0% +something I have over here now the + + + align:start position:0% +something I have over here now the +here's the point about wavelets you'll + + align:start position:0% +here's the point about wavelets you'll + + + align:start position:0% +here's the point about wavelets you'll +see it with an ex guy the next one you + + align:start position:0% +see it with an ex guy the next one you + + + align:start position:0% +see it with an ex guy the next one you +saw that those two are orthogonal and + + align:start position:0% +saw that those two are orthogonal and + + + align:start position:0% +saw that those two are orthogonal and +real and simple nice numbers now the + + align:start position:0% +real and simple nice numbers now the + + + align:start position:0% +real and simple nice numbers now the +next one will be 1 minus 1 0 0 + + align:start position:0% + + + + align:start position:0% + +do you see that that's orthogonal + + align:start position:0% +do you see that that's orthogonal + + + align:start position:0% +do you see that that's orthogonal +obviously because it's dot product with + + align:start position:0% +obviously because it's dot product with + + + align:start position:0% +obviously because it's dot product with +that is 0 and that is 0 and you want to + + align:start position:0% +that is 0 and that is 0 and you want to + + + align:start position:0% +that is 0 and that is 0 and you want to +tell me the last column of the way but + + align:start position:0% +tell me the last column of the way but + + + align:start position:0% +tell me the last column of the way but +of the simple wavelet matrix this is + + align:start position:0% +of the simple wavelet matrix this is + + + align:start position:0% +of the simple wavelet matrix this is +this would be the HAR named after har + + align:start position:0% +this would be the HAR named after har + + + align:start position:0% +this would be the HAR named after har +the haar wavelets + + align:start position:0% + + + + align:start position:0% + +the whole point about wavelets was a new + + align:start position:0% +the whole point about wavelets was a new + + + align:start position:0% +the whole point about wavelets was a new +basis somebody realized well actually + + align:start position:0% +basis somebody realized well actually + + + align:start position:0% +basis somebody realized well actually +har lived a long time ago but but they + + align:start position:0% +har lived a long time ago but but they + + + align:start position:0% +har lived a long time ago but but they +got improved and improved but here's the + + align:start position:0% +got improved and improved but here's the + + + align:start position:0% +got improved and improved but here's the +simplest one what's the what's the good + + align:start position:0% +simplest one what's the what's the good + + + align:start position:0% +simplest one what's the what's the good +4th column 4th + + align:start position:0% +4th column 4th + + + align:start position:0% +4th column 4th +orthogonal vector here + + align:start position:0% +orthogonal vector here + + + align:start position:0% +orthogonal vector here +chali what shall I start with zeros and + + align:start position:0% +chali what shall I start with zeros and + + + align:start position:0% +chali what shall I start with zeros and +then I'll put + + align:start position:0% + + + + align:start position:0% + +1 minus 1 + + align:start position:0% + + + + align:start position:0% + +so the beauty of wavelets is I've got + + align:start position:0% +so the beauty of wavelets is I've got + + + align:start position:0% +so the beauty of wavelets is I've got +this averaging + + align:start position:0% +this averaging + + + align:start position:0% +this averaging +vector and then I've got this difference + + align:start position:0% +vector and then I've got this difference + + + align:start position:0% +vector and then I've got this difference +sort of on a big scale and then I've got + + align:start position:0% +sort of on a big scale and then I've got + + + align:start position:0% +sort of on a big scale and then I've got +differences on a little scale with it + + align:start position:0% +differences on a little scale with it + + + align:start position:0% +differences on a little scale with it +with zero differences here with zeros so + + align:start position:0% +with zero differences here with zeros so + + + align:start position:0% +with zero differences here with zeros so +the as I keep going I could do 8 by 8 16 + + align:start position:0% +the as I keep going I could do 8 by 8 16 + + + align:start position:0% +the as I keep going I could do 8 by 8 16 +by 16 it would I get the averaging guy + + align:start position:0% +by 16 it would I get the averaging guy + + + align:start position:0% +by 16 it would I get the averaging guy +and then I get differencing on I get + + align:start position:0% +and then I get differencing on I get + + + align:start position:0% +and then I get differencing on I get +large scale differences and then I get + + align:start position:0% +large scale differences and then I get + + + align:start position:0% +large scale differences and then I get +finer differences so worse differences + + align:start position:0% +finer differences so worse differences + + + align:start position:0% +finer differences so worse differences +finer differences finer finer + + align:start position:0% +finer differences finer finer + + + align:start position:0% +finer differences finer finer +differences and + + align:start position:0% +differences and + + + align:start position:0% +differences and +that's a really good way to + + align:start position:0% + + + + align:start position:0% + +if your function if your signal has + + align:start position:0% +if your function if your signal has + + + align:start position:0% +if your function if your signal has +jumps we saw that Fourier + + align:start position:0% +jumps we saw that Fourier + + + align:start position:0% +jumps we saw that Fourier +wasn't perfect right and a lot of + + align:start position:0% +wasn't perfect right and a lot of + + + align:start position:0% +wasn't perfect right and a lot of +signals have jumps right if your shocks + + align:start position:0% +signals have jumps right if your shocks + + + align:start position:0% +signals have jumps right if your shocks +whatever you're trying to represent + + align:start position:0% +whatever you're trying to represent + + + align:start position:0% +whatever you're trying to represent +this is a better basis to represent a + + align:start position:0% +this is a better basis to represent a + + + align:start position:0% +this is a better basis to represent a +jimp a jump a discontinuity than Fourier + + align:start position:0% +jimp a jump a discontinuity than Fourier + + + align:start position:0% +jimp a jump a discontinuity than Fourier +because Fourier at a discontinuity does + + align:start position:0% +because Fourier at a discontinuity does + + + align:start position:0% +because Fourier at a discontinuity does +its best but it's a it's not a local + + align:start position:0% +its best but it's a it's not a local + + + align:start position:0% +its best but it's a it's not a local +basis it can't like specially focus on + + align:start position:0% +basis it can't like specially focus on + + + align:start position:0% +basis it can't like specially focus on +that jump point and and the result is + + align:start position:0% +that jump point and and the result is + + + align:start position:0% +that jump point and and the result is +the coefficients decay very slowly and + + align:start position:0% +the coefficients decay very slowly and + + + align:start position:0% +the coefficients decay very slowly and +it's hard to compute with whereas the + + align:start position:0% +it's hard to compute with whereas the + + + align:start position:0% +it's hard to compute with whereas the +wavelet is great for signals that have + + align:start position:0% +wavelet is great for signals that have + + + align:start position:0% +wavelet is great for signals that have +jumps that something happens suddenly at + + align:start position:0% +jumps that something happens suddenly at + + + align:start position:0% +jumps that something happens suddenly at +a certain time anyway that that would be + + align:start position:0% +a certain time anyway that that would be + + + align:start position:0% +a certain time anyway that that would be +another and of course I haven't made + + align:start position:0% +another and of course I haven't made + + + align:start position:0% +another and of course I haven't made +these unit vectors I'd have to divide + + align:start position:0% +these unit vectors I'd have to divide + + + align:start position:0% +these unit vectors I'd have to divide +that by the square root of four and + + align:start position:0% +that by the square root of four and + + + align:start position:0% +that by the square root of four and +divide these guys by the square root of + + align:start position:0% +divide these guys by the square root of + + + align:start position:0% +divide these guys by the square root of +two just to normalize them but + + align:start position:0% +two just to normalize them but + + + align:start position:0% +two just to normalize them but +normalizing isn't important orthogonal + + align:start position:0% +normalizing isn't important orthogonal + + + align:start position:0% +normalizing isn't important orthogonal +is what is important yeah okay so that's + + align:start position:0% +is what is important yeah okay so that's + + + align:start position:0% +is what is important yeah okay so that's +the that's that's the + + align:start position:0% + + + + align:start position:0% + +competition you could say that's the + + align:start position:0% +competition you could say that's the + + + align:start position:0% +competition you could say that's the +competition okay back to + + align:start position:0% +competition okay back to + + + align:start position:0% +competition okay back to +the main guy what's the so this is the + + align:start position:0% +the main guy what's the so this is the + + + align:start position:0% +the main guy what's the so this is the +famous formula that gives the wise from + + align:start position:0% +famous formula that gives the wise from + + + align:start position:0% +famous formula that gives the wise from +the C's and what's the other formula + + align:start position:0% +the C's and what's the other formula + + + align:start position:0% +the C's and what's the other formula +that gives the C's from the wise + + align:start position:0% + + + + align:start position:0% + +so now this is this is the transform in + + align:start position:0% +so now this is this is the transform in + + + align:start position:0% +so now this is this is the transform in +the other direction so it's going to be + + align:start position:0% +the other direction so it's going to be + + + align:start position:0% +the other direction so it's going to be +a sum from J equals 0 to n minus 1 + + align:start position:0% + + + + align:start position:0% + +and what's going to go in there + + align:start position:0% +and what's going to go in there + + + align:start position:0% +and what's going to go in there +have you got the idea of the two + + align:start position:0% +have you got the idea of the two + + + align:start position:0% +have you got the idea of the two +transforms + + align:start position:0% +transforms + + + align:start position:0% +transforms +in one direction it's this is e to the I + + align:start position:0% +in one direction it's this is e to the I + + + align:start position:0% +in one direction it's this is e to the I +you see why we don't want to write it + + align:start position:0% +you see why we don't want to write it + + + align:start position:0% +you see why we don't want to write it +that is that number is e + + align:start position:0% +that is that number is e + + + align:start position:0% +that is that number is e +to the 2 pi IJ + + align:start position:0% +to the 2 pi IJ + + + align:start position:0% +to the 2 pi IJ +K over N that's what that number is in + + align:start position:0% +K over N that's what that number is in + + + align:start position:0% +K over N that's what that number is in +in the Fourier matrix + + align:start position:0% +in the Fourier matrix + + + align:start position:0% +in the Fourier matrix +so you see using W makes it much cleaner + + align:start position:0% +so you see using W makes it much cleaner + + + align:start position:0% +so you see using W makes it much cleaner +ok what goes there + + align:start position:0% +ok what goes there + + + align:start position:0% +ok what goes there +W bar + + align:start position:0% +W bar + + + align:start position:0% +W bar +there complex conjugant e to the minus + + align:start position:0% +there complex conjugant e to the minus + + + align:start position:0% +there complex conjugant e to the minus +all that stuff W bar to the same power + + align:start position:0% +all that stuff W bar to the same power + + + align:start position:0% +all that stuff W bar to the same power +JK and then I have to remember to divide + + align:start position:0% +JK and then I have to remember to divide + + + align:start position:0% +JK and then I have to remember to divide +by n somewhere I can put it here I can + + align:start position:0% +by n somewhere I can put it here I can + + + align:start position:0% +by n somewhere I can put it here I can +put it there but I have a I the the all + + align:start position:0% +put it there but I have a I the the all + + + align:start position:0% +put it there but I have a I the the all +ones vector has length squared equal to + + align:start position:0% +ones vector has length squared equal to + + + align:start position:0% +ones vector has length squared equal to +n and I've got a + + align:start position:0% +n and I've got a + + + align:start position:0% +n and I've got a +divided by an end somewhere okay those + + align:start position:0% +divided by an end somewhere okay those + + + align:start position:0% +divided by an end somewhere okay those +are the two formulas that many people + + align:start position:0% +are the two formulas that many people + + + align:start position:0% +are the two formulas that many people +would just remember that for them that's + + align:start position:0% +would just remember that for them that's + + + align:start position:0% +would just remember that for them that's +the discrete Fourier transform and the + + align:start position:0% +the discrete Fourier transform and the + + + align:start position:0% +the discrete Fourier transform and the +inverse and maybe they would put the N + + align:start position:0% +inverse and maybe they would put the N + + + align:start position:0% +inverse and maybe they would put the N +over there probably that would be more + + align:start position:0% +over there probably that would be more + + + align:start position:0% +over there probably that would be more +common i I got started with the Fourier + + align:start position:0% +common i I got started with the Fourier + + + align:start position:0% +common i I got started with the Fourier +matrix with this side and then + + align:start position:0% +matrix with this side and then + + + align:start position:0% +matrix with this side and then +the the DFT matrix comes here and I + + align:start position:0% +the the DFT matrix comes here and I + + + align:start position:0% +the the DFT matrix comes here and I +needed the end is that so those are the + + align:start position:0% +needed the end is that so those are the + + + align:start position:0% +needed the end is that so those are the +formulas I don't know how you prefer to + + align:start position:0% +formulas I don't know how you prefer to + + + align:start position:0% +formulas I don't know how you prefer to +remember these I mean somehow you have + + align:start position:0% +remember these I mean somehow you have + + + align:start position:0% +remember these I mean somehow you have +to commit something to memory here + + align:start position:0% +to commit something to memory here + + + align:start position:0% +to commit something to memory here +certainly what W is and the fact that + + align:start position:0% +certainly what W is and the fact that + + + align:start position:0% +certainly what W is and the fact that +it's W and W bar and the fact that the + + align:start position:0% +it's W and W bar and the fact that the + + + align:start position:0% +it's W and W bar and the fact that the +sum start at zero and the fact that you + + align:start position:0% +sum start at zero and the fact that you + + + align:start position:0% +sum start at zero and the fact that you +have just these simple expressions for + + align:start position:0% +have just these simple expressions for + + + align:start position:0% +have just these simple expressions for +the entries in the matrix and this then + + align:start position:0% +the entries in the matrix and this then + + + align:start position:0% +the entries in the matrix and this then +would be C equals F inverse Y that's + + align:start position:0% +would be C equals F inverse Y that's + + + align:start position:0% +would be C equals F inverse Y that's +what that's what I've written down there + + align:start position:0% +what that's what I've written down there + + + align:start position:0% +what that's what I've written down there +in detail + + align:start position:0% +in detail + + + align:start position:0% +in detail +okay so that's + + align:start position:0% +okay so that's + + + align:start position:0% +okay so that's +that's the discrete Fourier transform + + align:start position:0% +that's the discrete Fourier transform + + + align:start position:0% +that's the discrete Fourier transform +and I think we're out of time I've got + + align:start position:0% +and I think we're out of time I've got + + + align:start position:0% +and I think we're out of time I've got +more to say and a little bit about the + + align:start position:0% +more to say and a little bit about the + + + align:start position:0% +more to say and a little bit about the +FFT how that works \ No newline at end of file diff --git a/bJ1nqEC3i0A.txt b/bJ1nqEC3i0A.txt new file mode 100644 index 0000000000000000000000000000000000000000..c01f9dda1e213784371211ea8032b506cf99a431 --- /dev/null +++ b/bJ1nqEC3i0A.txt @@ -0,0 +1,9043 @@ +align:start position:0% + +so just to remind you from the last + + align:start position:0% +so just to remind you from the last + + + align:start position:0% +so just to remind you from the last +lecture we talked about the notion the + + align:start position:0% +lecture we talked about the notion the + + + align:start position:0% +lecture we talked about the notion the +difference between sort of a a linear + + align:start position:0% +difference between sort of a a linear + + + align:start position:0% +difference between sort of a a linear +power supply and a switching power + + align:start position:0% +power supply and a switching power + + + align:start position:0% +power supply and a switching power +supply and we're talking about in this + + align:start position:0% +supply and we're talking about in this + + + align:start position:0% +supply and we're talking about in this +case DC to DC conversion but the same + + align:start position:0% +case DC to DC conversion but the same + + + align:start position:0% +case DC to DC conversion but the same +thing is true actually of RF amplifiers + + align:start position:0% +thing is true actually of RF amplifiers + + + align:start position:0% +thing is true actually of RF amplifiers +and other areas where you can have + + align:start position:0% +and other areas where you can have + + + align:start position:0% +and other areas where you can have +switching amplifiers and linear + + align:start position:0% +switching amplifiers and linear + + + align:start position:0% +switching amplifiers and linear +amplifiers and we said the notion of a + + align:start position:0% +amplifiers and we said the notion of a + + + align:start position:0% +amplifiers and we said the notion of a +linear amplifier was simply that you + + align:start position:0% +linear amplifier was simply that you + + + align:start position:0% +linear amplifier was simply that you +know I have some input source + + align:start position:0% +know I have some input source + + + align:start position:0% +know I have some input source +VN I'll use a + + align:start position:0% + + + + align:start position:0% + +transistor and you know here's my load + + align:start position:0% +transistor and you know here's my load + + + align:start position:0% +transistor and you know here's my load +resistance so here's V + + align:start position:0% +resistance so here's V + + + align:start position:0% +resistance so here's V +out and what we'll do is we'll have a + + align:start position:0% +out and what we'll do is we'll have a + + + align:start position:0% +out and what we'll do is we'll have a +reference + + align:start position:0% + + + + align:start position:0% + +voltage and we'll feed back the output + + align:start position:0% +voltage and we'll feed back the output + + + align:start position:0% +voltage and we'll feed back the output +voltage and control the base or the Gate + + align:start position:0% +voltage and control the base or the Gate + + + align:start position:0% +voltage and control the base or the Gate +of our transistor so that we get some + + align:start position:0% +of our transistor so that we get some + + + align:start position:0% +of our transistor so that we get some +drop I'll call it VD here uh so that + + align:start position:0% +drop I'll call it VD here uh so that + + + align:start position:0% +drop I'll call it VD here uh so that +this + + align:start position:0% + + + + align:start position:0% + +essentially looks like some variable + + align:start position:0% +essentially looks like some variable + + + align:start position:0% +essentially looks like some variable +resistor that we do a resistor divider + + align:start position:0% +resistor that we do a resistor divider + + + align:start position:0% +resistor that we do a resistor divider +and we get our output voltage from our + + align:start position:0% +and we get our output voltage from our + + + align:start position:0% +and we get our output voltage from our +input voltage and we said the real + + align:start position:0% +input voltage and we said the real + + + align:start position:0% +input voltage and we said the real +problem with this was okay I have my + + align:start position:0% +problem with this was okay I have my + + + align:start position:0% +problem with this was okay I have my +voltage drop VD and whatever current is + + align:start position:0% +voltage drop VD and whatever current is + + + align:start position:0% +voltage drop VD and whatever current is +coming from the + + align:start position:0% +coming from the + + + align:start position:0% +coming from the +source and that's the same thing as the + + align:start position:0% +source and that's the same thing as the + + + align:start position:0% +source and that's the same thing as the +load current it's right it coming out of + + align:start position:0% +load current it's right it coming out of + + + align:start position:0% +load current it's right it coming out of +the source coming through this pass + + align:start position:0% +the source coming through this pass + + + align:start position:0% +the source coming through this pass +transistor and going to the load and so + + align:start position:0% +transistor and going to the load and so + + + align:start position:0% +transistor and going to the load and so +if I ask what the power dissipation was + + align:start position:0% +if I ask what the power dissipation was + + + align:start position:0% +if I ask what the power dissipation was +the instantaneous power dissipation in + + align:start position:0% +the instantaneous power dissipation in + + + align:start position:0% +the instantaneous power dissipation in +this transistor is equal + + align:start position:0% +this transistor is equal + + + align:start position:0% +this transistor is equal +to uh VD * + + align:start position:0% +to uh VD * + + + align:start position:0% +to uh VD * +I if I said what's the average power + + align:start position:0% +I if I said what's the average power + + + align:start position:0% +I if I said what's the average power +dissipation it's the average of that and + + align:start position:0% +dissipation it's the average of that and + + + align:start position:0% +dissipation it's the average of that and +it's not equal to zero right so + + align:start position:0% +it's not equal to zero right so + + + align:start position:0% +it's not equal to zero right so +essentially if I have a variable + + align:start position:0% +essentially if I have a variable + + + align:start position:0% +essentially if I have a variable +resistor I'm dumping energy into that + + align:start position:0% +resistor I'm dumping energy into that + + + align:start position:0% +resistor I'm dumping energy into that +variable resistor and especially when I + + align:start position:0% +variable resistor and especially when I + + + align:start position:0% +variable resistor and especially when I +have large conversion ratios that gets + + align:start position:0% +have large conversion ratios that gets + + + align:start position:0% +have large conversion ratios that gets +really + + align:start position:0% +really + + + align:start position:0% +really +bad so we said is okay we can be way + + align:start position:0% +bad so we said is okay we can be way + + + align:start position:0% +bad so we said is okay we can be way +more clever than that and we can go + + align:start position:0% +more clever than that and we can go + + + align:start position:0% +more clever than that and we can go +build a switching converter and the idea + + align:start position:0% +build a switching converter and the idea + + + align:start position:0% +build a switching converter and the idea +would be this right we'd have + + align:start position:0% +would be this right we'd have + + + align:start position:0% +would be this right we'd have +VN will have a switch and this will be a + + align:start position:0% +VN will have a switch and this will be a + + + align:start position:0% +VN will have a switch and this will be a +built out of semiconductor + + align:start position:0% +built out of semiconductor + + + align:start position:0% +built out of semiconductor +switches you know Q of T is equal to 1 Q + + align:start position:0% +switches you know Q of T is equal to 1 Q + + + align:start position:0% +switches you know Q of T is equal to 1 Q +of T is equal to + + align:start position:0% +of T is equal to + + + align:start position:0% +of T is equal to +zero right and then we + + align:start position:0% +zero right and then we + + + align:start position:0% +zero right and then we +will take this output and we'll run it + + align:start position:0% +will take this output and we'll run it + + + align:start position:0% +will take this output and we'll run it +through some lossless LC filter and then + + align:start position:0% +through some lossless LC filter and then + + + align:start position:0% +through some lossless LC filter and then +I'll have my output + + align:start position:0% + + + + align:start position:0% + +here okay and the notion is by chopping + + align:start position:0% +here okay and the notion is by chopping + + + align:start position:0% +here okay and the notion is by chopping +this back and + + align:start position:0% +this back and + + + align:start position:0% +this back and +forth like + + align:start position:0% +forth like + + + align:start position:0% +forth like +this okay so I have some switching + + align:start position:0% +this okay so I have some switching + + + align:start position:0% +this okay so I have some switching +function Q of T is equal to one and zero + + align:start position:0% +function Q of T is equal to one and zero + + + align:start position:0% +function Q of T is equal to one and zero +and I'll control this with some + + align:start position:0% +and I'll control this with some + + + align:start position:0% +and I'll control this with some +switching period and some Duty ratio + + align:start position:0% +switching period and some Duty ratio + + + align:start position:0% +switching period and some Duty ratio +okay that's a pulsewidth modulation this + + align:start position:0% +okay that's a pulsewidth modulation this + + + align:start position:0% +okay that's a pulsewidth modulation this +is Q of + + align:start position:0% +is Q of + + + align:start position:0% +is Q of +T right then I can have this voltage + + align:start position:0% +T right then I can have this voltage + + + align:start position:0% +T right then I can have this voltage +that I'll call + + align:start position:0% +that I'll call + + + align:start position:0% +that I'll call +VX which is sort of a copy of that when + + align:start position:0% +VX which is sort of a copy of that when + + + align:start position:0% +VX which is sort of a copy of that when +Q of T is One VX is VN when Q of T is + + align:start position:0% +Q of T is One VX is VN when Q of T is + + + align:start position:0% +Q of T is One VX is VN when Q of T is +zero VX is zero and I get a pulsed + + align:start position:0% +zero VX is zero and I get a pulsed + + + align:start position:0% +zero VX is zero and I get a pulsed +waveform that looks like this this is + + align:start position:0% +waveform that looks like this this is + + + align:start position:0% +waveform that looks like this this is +VX + + align:start position:0% +VX + + + align:start position:0% +VX +okay and so + + align:start position:0% + + + + align:start position:0% + +forth and when I filter + + align:start position:0% +forth and when I filter + + + align:start position:0% +forth and when I filter +VX right the idea is this acts as a low + + align:start position:0% +VX right the idea is this acts as a low + + + align:start position:0% +VX right the idea is this acts as a low +pass filter and it basically extracts + + align:start position:0% +pass filter and it basically extracts + + + align:start position:0% +pass filter and it basically extracts +the DC component of that and so then I + + align:start position:0% +the DC component of that and so then I + + + align:start position:0% +the DC component of that and so then I +get an output voltage V + + align:start position:0% + + + + align:start position:0% + +out that is basically approximately + + align:start position:0% +out that is basically approximately + + + align:start position:0% +out that is basically approximately +equal + + align:start position:0% + + + + align:start position:0% + +to V out is approximately equal to D * + + align:start position:0% +to V out is approximately equal to D * + + + align:start position:0% +to V out is approximately equal to D * +VN okay so by controlling timing by + + align:start position:0% +VN okay so by controlling timing by + + + align:start position:0% +VN okay so by controlling timing by +controlling the width of the pulse in + + align:start position:0% +controlling the width of the pulse in + + + align:start position:0% +controlling the width of the pulse in +the cycle I control the average voltage + + align:start position:0% +the cycle I control the average voltage + + + align:start position:0% +the cycle I control the average voltage +at the output and the beauty is as we + + align:start position:0% +at the output and the beauty is as we + + + align:start position:0% +at the output and the beauty is as we +argued switches are ideally lossless + + align:start position:0% +argued switches are ideally lossless + + + align:start position:0% +argued switches are ideally lossless +inductors are ideally lossless + + align:start position:0% +inductors are ideally lossless + + + align:start position:0% +inductors are ideally lossless +capacitors are ideally lossless so the + + align:start position:0% +capacitors are ideally lossless so the + + + align:start position:0% +capacitors are ideally lossless so the +efficiency of this whole box can in + + align:start position:0% +efficiency of this whole box can in + + + align:start position:0% +efficiency of this whole box can in +theory approach + + align:start position:0% +theory approach + + + align:start position:0% +theory approach +100% okay so that's that's sort of the + + align:start position:0% +100% okay so that's that's sort of the + + + align:start position:0% +100% okay so that's that's sort of the +fundamental com concept we're going to + + align:start position:0% +fundamental com concept we're going to + + + align:start position:0% +fundamental com concept we're going to +have switching we're going to have + + align:start position:0% +have switching we're going to have + + + align:start position:0% +have switching we're going to have +energy storage and we're going to take + + align:start position:0% +energy storage and we're going to take + + + align:start position:0% +energy storage and we're going to take +energy from an input to an output and + + align:start position:0% +energy from an input to an output and + + + align:start position:0% +energy from an input to an output and +we're going to operate cyclically okay + + align:start position:0% +we're going to operate cyclically okay + + + align:start position:0% +we're going to operate cyclically okay +now things are a lot more you know + + align:start position:0% +now things are a lot more you know + + + align:start position:0% +now things are a lot more you know +there's a lot more to it than just that + + align:start position:0% +there's a lot more to it than just that + + + align:start position:0% +there's a lot more to it than just that +there's many design considerations in + + align:start position:0% +there's many design considerations in + + + align:start position:0% +there's many design considerations in +all this first of all how do you design + + align:start position:0% +all this first of all how do you design + + + align:start position:0% +all this first of all how do you design +these inductors how do you pick a + + align:start position:0% +these inductors how do you pick a + + + align:start position:0% +these inductors how do you pick a +topology what can it do how do you + + align:start position:0% +topology what can it do how do you + + + align:start position:0% +topology what can it do how do you +control it what are the Dynamics all + + align:start position:0% +control it what are the Dynamics all + + + align:start position:0% +control it what are the Dynamics all +these kinds of questions we're going to + + align:start position:0% +these kinds of questions we're going to + + + align:start position:0% +these kinds of questions we're going to +answer in this term okay but that's the + + align:start position:0% +answer in this term okay but that's the + + + align:start position:0% +answer in this term okay but that's the +basic concept so before I get on to the + + align:start position:0% +basic concept so before I get on to the + + + align:start position:0% +basic concept so before I get on to the +material today are there any questions + + align:start position:0% +material today are there any questions + + + align:start position:0% +material today are there any questions +just about the basic idea here + + align:start position:0% + + + + align:start position:0% + +okay so what I'd like to start doing + + align:start position:0% +okay so what I'd like to start doing + + + align:start position:0% +okay so what I'd like to start doing +today is giving us some of the tools to + + align:start position:0% +today is giving us some of the tools to + + + align:start position:0% +today is giving us some of the tools to +analyze these kinds of + + align:start position:0% +analyze these kinds of + + + align:start position:0% +analyze these kinds of +systems okay and what we're going to see + + align:start position:0% +systems okay and what we're going to see + + + align:start position:0% +systems okay and what we're going to see +is we're going to do a lot of our + + align:start position:0% +is we're going to do a lot of our + + + align:start position:0% +is we're going to do a lot of our +analysis in the time domain because it + + align:start position:0% +analysis in the time domain because it + + + align:start position:0% +analysis in the time domain because it +turns out that our circuits tend to be + + align:start position:0% +turns out that our circuits tend to be + + + align:start position:0% +turns out that our circuits tend to be +either nonlinear or time varying + + align:start position:0% +either nonlinear or time varying + + + align:start position:0% +either nonlinear or time varying +depending upon how you wanted to look at + + align:start position:0% +depending upon how you wanted to look at + + + align:start position:0% +depending upon how you wanted to look at +it um and time domain Anis is a really + + align:start position:0% +it um and time domain Anis is a really + + + align:start position:0% +it um and time domain Anis is a really +good way to look at these things okay + + align:start position:0% +good way to look at these things okay + + + align:start position:0% +good way to look at these things okay +and what we would like is some tools to + + align:start position:0% +and what we would like is some tools to + + + align:start position:0% +and what we would like is some tools to +figure out what's going on I'm going to + + align:start position:0% +figure out what's going on I'm going to + + + align:start position:0% +figure out what's going on I'm going to +introduce you two concepts today that + + align:start position:0% +introduce you two concepts today that + + + align:start position:0% +introduce you two concepts today that +we're going to come back to again and + + align:start position:0% +we're going to come back to again and + + + align:start position:0% +we're going to come back to again and +again and the notion is that the first + + align:start position:0% +again and the notion is that the first + + + align:start position:0% +again and the notion is that the first +thing I'd like to talk about uh relates + + align:start position:0% +thing I'd like to talk about uh relates + + + align:start position:0% +thing I'd like to talk about uh relates +to the switches themselves right I + + align:start position:0% +to the switches themselves right I + + + align:start position:0% +to the switches themselves right I +haven't said how we're going to + + align:start position:0% +haven't said how we're going to + + + align:start position:0% +haven't said how we're going to +implement the single pole double throw + + align:start position:0% +implement the single pole double throw + + + align:start position:0% +implement the single pole double throw +switch okay and what the switching + + align:start position:0% +switch okay and what the switching + + + align:start position:0% +switch okay and what the switching +configuration looks like varies from + + align:start position:0% +configuration looks like varies from + + + align:start position:0% +configuration looks like varies from +circuit to Circuit okay okay but usually + + align:start position:0% +circuit to Circuit okay okay but usually + + + align:start position:0% +circuit to Circuit okay okay but usually +we're going to implement those with + + align:start position:0% +we're going to implement those with + + + align:start position:0% +we're going to implement those with +semiconductor + + align:start position:0% +semiconductor + + + align:start position:0% +semiconductor +switches now you can imagine + + align:start position:0% +switches now you can imagine + + + align:start position:0% +switches now you can imagine +semiconductor switches that are fully + + align:start position:0% +semiconductor switches that are fully + + + align:start position:0% +semiconductor switches that are fully +controlled I tell them when to turn on + + align:start position:0% +controlled I tell them when to turn on + + + align:start position:0% +controlled I tell them when to turn on +and off but more often than not the + + align:start position:0% +and off but more often than not the + + + align:start position:0% +and off but more often than not the +switch some aspects of your switch may + + align:start position:0% +switch some aspects of your switch may + + + align:start position:0% +switch some aspects of your switch may +be either semi-controlled or + + align:start position:0% +be either semi-controlled or + + + align:start position:0% +be either semi-controlled or +uncontrolled that is external circuit + + align:start position:0% +uncontrolled that is external circuit + + + align:start position:0% +uncontrolled that is external circuit +events will dictate when the device + + align:start position:0% +events will dictate when the device + + + align:start position:0% +events will dictate when the device +turns on and off and so one of the + + align:start position:0% +turns on and off and so one of the + + + align:start position:0% +turns on and off and so one of the +things you'll need to do if you're going + + align:start position:0% +things you'll need to do if you're going + + + align:start position:0% +things you'll need to do if you're going +to analyze some circuit is figure out + + align:start position:0% +to analyze some circuit is figure out + + + align:start position:0% +to analyze some circuit is figure out +when do these uncontrolled devices turn + + align:start position:0% +when do these uncontrolled devices turn + + + align:start position:0% +when do these uncontrolled devices turn +on and turn off as part of figuring out + + align:start position:0% +on and turn off as part of figuring out + + + align:start position:0% +on and turn off as part of figuring out +what for example some circuit topology + + align:start position:0% +what for example some circuit topology + + + align:start position:0% +what for example some circuit topology +will do or can do for example all right + + align:start position:0% +will do or can do for example all right + + + align:start position:0% +will do or can do for example all right +so let me give you the basic approach + + align:start position:0% +so let me give you the basic approach + + + align:start position:0% +so let me give you the basic approach +that we use to do that and I'm going to + + align:start position:0% +that we use to do that and I'm going to + + + align:start position:0% +that we use to do that and I'm going to +start with you know this some people + + align:start position:0% +start with you know this some people + + + align:start position:0% +start with you know this some people +might think this this is known as a + + align:start position:0% +might think this this is known as a + + + align:start position:0% +might think this this is known as a +operated this way is known as a buck + + align:start position:0% +operated this way is known as a buck + + + align:start position:0% +operated this way is known as a buck +converter it's a a relatively simple + + align:start position:0% +converter it's a a relatively simple + + + align:start position:0% +converter it's a a relatively simple +power converter I'm going to go to + + align:start position:0% +power converter I'm going to go to + + + align:start position:0% +power converter I'm going to go to +perhaps the simplest power converter you + + align:start position:0% +perhaps the simplest power converter you + + + align:start position:0% +perhaps the simplest power converter you +can think of um + + align:start position:0% +can think of um + + + align:start position:0% +can think of um +and it just simply looks like this and + + align:start position:0% +and it just simply looks like this and + + + align:start position:0% +and it just simply looks like this and +this is just by way of illustration okay + + align:start position:0% +this is just by way of illustration okay + + + align:start position:0% +this is just by way of illustration okay +so suppose I have VSS sin Omega + + align:start position:0% +so suppose I have VSS sin Omega + + + align:start position:0% +so suppose I have VSS sin Omega +T some AC Source okay and I'm going to + + align:start position:0% +T some AC Source okay and I'm going to + + + align:start position:0% +T some AC Source okay and I'm going to +put a diode here which is you know my + + align:start position:0% +put a diode here which is you know my + + + align:start position:0% +put a diode here which is you know my +canonical un completely uncontrolled + + align:start position:0% +canonical un completely uncontrolled + + + align:start position:0% +canonical un completely uncontrolled +switch a diode turns on and + + align:start position:0% +switch a diode turns on and + + + align:start position:0% +switch a diode turns on and +off when the external circuit tells it + + align:start position:0% +off when the external circuit tells it + + + align:start position:0% +off when the external circuit tells it +to turn on and off we can have also + + align:start position:0% +to turn on and off we can have also + + + align:start position:0% +to turn on and off we can have also +devices that are semic controlled maybe + + align:start position:0% +devices that are semic controlled maybe + + + align:start position:0% +devices that are semic controlled maybe +we only turn them tell them when to turn + + align:start position:0% +we only turn them tell them when to turn + + + align:start position:0% +we only turn them tell them when to turn +on or maybe we only control when they're + + align:start position:0% +on or maybe we only control when they're + + + align:start position:0% +on or maybe we only control when they're +turning on and off under some conditions + + align:start position:0% +turning on and off under some conditions + + + align:start position:0% +turning on and off under some conditions +and we'll see that in much more detail + + align:start position:0% +and we'll see that in much more detail + + + align:start position:0% +and we'll see that in much more detail +uh but suppose I have this + + align:start position:0% +uh but suppose I have this + + + align:start position:0% +uh but suppose I have this +circuit okay and maybe I have some you + + align:start position:0% +circuit okay and maybe I have some you + + + align:start position:0% +circuit okay and maybe I have some you +know the the interesting thing I'm + + align:start position:0% +know the the interesting thing I'm + + + align:start position:0% +know the the interesting thing I'm +interested in getting here is uh V out + + align:start position:0% +interested in getting here is uh V out + + + align:start position:0% +interested in getting here is uh V out +okay and maybe this is just some value R + + align:start position:0% +okay and maybe this is just some value R + + + align:start position:0% +okay and maybe this is just some value R +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and we have uh some current that's going + + align:start position:0% +and we have uh some current that's going + + + align:start position:0% +and we have uh some current that's going +to come here and let me call this + + align:start position:0% + + + + align:start position:0% + +ID and we will also have some voltage uh + + align:start position:0% + + + + align:start position:0% + +VD + + align:start position:0% +VD + + + align:start position:0% +VD +okay now uh let's talk about diodes for + + align:start position:0% +okay now uh let's talk about diodes for + + + align:start position:0% +okay now uh let's talk about diodes for +a second okay now every people have + + align:start position:0% +a second okay now every people have + + + align:start position:0% +a second okay now every people have +about semiconductor classes you know a + + align:start position:0% +about semiconductor classes you know a + + + align:start position:0% +about semiconductor classes you know a +diode has an exponential characteristic + + align:start position:0% +diode has an exponential characteristic + + + align:start position:0% +diode has an exponential characteristic +but for basic analysis if we're going to + + align:start position:0% +but for basic analysis if we're going to + + + align:start position:0% +but for basic analysis if we're going to +treat things as switches we can really + + align:start position:0% +treat things as switches we can really + + + align:start position:0% +treat things as switches we can really +simplify that so we often think about + + align:start position:0% +simplify that so we often think about + + + align:start position:0% +simplify that so we often think about +what we will call an ideal diode right + + align:start position:0% +what we will call an ideal diode right + + + align:start position:0% +what we will call an ideal diode right +what does an ideal diode do an ideal + + align:start position:0% + + + + align:start position:0% + +diode has the following IV + + align:start position:0% +diode has the following IV + + + align:start position:0% +diode has the following IV +characteristic okay so here's ID and + + align:start position:0% +characteristic okay so here's ID and + + + align:start position:0% +characteristic okay so here's ID and +VD okay and + + align:start position:0% +VD okay and + + + align:start position:0% +VD okay and +and I might have a situation where the + + align:start position:0% +and I might have a situation where the + + + align:start position:0% +and I might have a situation where the +diode's on so you know this is when the + + align:start position:0% +diode's on so you know this is when the + + + align:start position:0% +diode's on so you know this is when the +diode is + + align:start position:0% + + + + align:start position:0% + +on that is it has no forward drop but it + + align:start position:0% +on that is it has no forward drop but it + + + align:start position:0% +on that is it has no forward drop but it +can carry as much current as you want + + align:start position:0% +can carry as much current as you want + + + align:start position:0% +can carry as much current as you want +okay I might also have a case where I + + align:start position:0% +okay I might also have a case where I + + + align:start position:0% +okay I might also have a case where I +have the diode being + + align:start position:0% +have the diode being + + + align:start position:0% +have the diode being +off and so here's the off state of the + + align:start position:0% +off and so here's the off state of the + + + align:start position:0% +off and so here's the off state of the +diode + + align:start position:0% + + + + align:start position:0% + +okay so if I'm + + align:start position:0% +okay so if I'm + + + align:start position:0% +okay so if I'm +off basically I'm thinking of VD and ID + + align:start position:0% +off basically I'm thinking of VD and ID + + + align:start position:0% +off basically I'm thinking of VD and ID +like this here's + + align:start position:0% +like this here's + + + align:start position:0% +like this here's +VD and + + align:start position:0% +VD and + + + align:start position:0% +VD and +ID right VD is whatever it wants to be + + align:start position:0% +ID right VD is whatever it wants to be + + + align:start position:0% +ID right VD is whatever it wants to be +as long as it's negative and + + align:start position:0% +as long as it's negative and + + + align:start position:0% +as long as it's negative and +ID is zero because this is an open + + align:start position:0% +ID is zero because this is an open + + + align:start position:0% +ID is zero because this is an open +circuit right and I'm I should just be + + align:start position:0% +circuit right and I'm I should just be + + + align:start position:0% +circuit right and I'm I should just be +clear I'm talking about an ideal diode + + align:start position:0% +clear I'm talking about an ideal diode + + + align:start position:0% +clear I'm talking about an ideal diode +looking like + + align:start position:0% +looking like + + + align:start position:0% +looking like +this + + align:start position:0% +this + + + align:start position:0% +this +okay and if I'm on what I'm assuming is + + align:start position:0% +okay and if I'm on what I'm assuming is + + + align:start position:0% +okay and if I'm on what I'm assuming is +that essentially VD is + + align:start position:0% + + + + align:start position:0% + +zero and I have some positive + + align:start position:0% +zero and I have some positive + + + align:start position:0% +zero and I have some positive +ID okay so I can essentially treating it + + align:start position:0% +ID okay so I can essentially treating it + + + align:start position:0% +ID okay so I can essentially treating it +like a switch I'm either treating it + + align:start position:0% +like a switch I'm either treating it + + + align:start position:0% +like a switch I'm either treating it +like a perfectly closed switch which + + align:start position:0% +like a perfectly closed switch which + + + align:start position:0% +like a perfectly closed switch which +happens in this part of the IV plane or + + align:start position:0% +happens in this part of the IV plane or + + + align:start position:0% +happens in this part of the IV plane or +I think of it as a perfectly open switch + + align:start position:0% +I think of it as a perfectly open switch + + + align:start position:0% +I think of it as a perfectly open switch +in which case it happens in this part of + + align:start position:0% +in which case it happens in this part of + + + align:start position:0% +in which case it happens in this part of +the IV plane all right so that's how we + + align:start position:0% +the IV plane all right so that's how we + + + align:start position:0% +the IV plane all right so that's how we +will think of as a diode right and yes a + + align:start position:0% +will think of as a diode right and yes a + + + align:start position:0% +will think of as a diode right and yes a +real diode would have some exponential + + align:start position:0% +real diode would have some exponential + + + align:start position:0% +real diode would have some exponential +characteristic but for analysis is much + + align:start position:0% +characteristic but for analysis is much + + + align:start position:0% +characteristic but for analysis is much +simpler to treat it this way and then + + align:start position:0% +simpler to treat it this way and then + + + align:start position:0% +simpler to treat it this way and then +add in nonidealities + + align:start position:0% +add in nonidealities + + + align:start position:0% +add in nonidealities +later + + align:start position:0% +later + + + align:start position:0% +later +okay so a diode's an uncontrolled + + align:start position:0% +okay so a diode's an uncontrolled + + + align:start position:0% +okay so a diode's an uncontrolled +switch okay what controls it switching + + align:start position:0% +switch okay what controls it switching + + + align:start position:0% +switch okay what controls it switching +well the right way to think about + + align:start position:0% +well the right way to think about + + + align:start position:0% +well the right way to think about +this is based on what a diode cannot do + + align:start position:0% +this is based on what a diode cannot do + + + align:start position:0% +this is based on what a diode cannot do +right notice that the there's no + + align:start position:0% +right notice that the there's no + + + align:start position:0% +right notice that the there's no +characteristic down here with ID + + align:start position:0% +characteristic down here with ID + + + align:start position:0% +characteristic down here with ID +negative so a diode cannot support a + + align:start position:0% +negative so a diode cannot support a + + + align:start position:0% +negative so a diode cannot support a +negative + + align:start position:0% + + + + align:start position:0% + +current and no positive voltage + + align:start position:0% + + + + align:start position:0% + +this should be ID and VD right so it + + align:start position:0% +this should be ID and VD right so it + + + align:start position:0% +this should be ID and VD right so it +cannot have a positive voltage because + + align:start position:0% +cannot have a positive voltage because + + + align:start position:0% +cannot have a positive voltage because +it'll turn on it cannot have a negative + + align:start position:0% +it'll turn on it cannot have a negative + + + align:start position:0% +it'll turn on it cannot have a negative +current because it'll turn off all right + + align:start position:0% +current because it'll turn off all right + + + align:start position:0% +current because it'll turn off all right +and so in figuring out in our circuit + + align:start position:0% +and so in figuring out in our circuit + + + align:start position:0% +and so in figuring out in our circuit +what a diode is doing we often figure + + align:start position:0% +what a diode is doing we often figure + + + align:start position:0% +what a diode is doing we often figure +out it out based on what it can't do + + align:start position:0% +out it out based on what it can't do + + + align:start position:0% +out it out based on what it can't do +rather than what it can do okay and and + + align:start position:0% +rather than what it can do okay and and + + + align:start position:0% +rather than what it can do okay and and +I'll get to what I mean by that in a + + align:start position:0% +I'll get to what I mean by that in a + + + align:start position:0% +I'll get to what I mean by that in a +moment okay so um let's think about this + + align:start position:0% +moment okay so um let's think about this + + + align:start position:0% +moment okay so um let's think about this +circuit How Will I analyze it suppose I + + align:start position:0% +circuit How Will I analyze it suppose I + + + align:start position:0% +circuit How Will I analyze it suppose I +have a + + align:start position:0% +have a + + + align:start position:0% +have a +circuit like this for example with one + + align:start position:0% +circuit like this for example with one + + + align:start position:0% +circuit like this for example with one +or more diodes in it and and this + + align:start position:0% +or more diodes in it and and this + + + align:start position:0% +or more diodes in it and and this +circuit's trivial it has one diode but + + align:start position:0% +circuit's trivial it has one diode but + + + align:start position:0% +circuit's trivial it has one diode but +you can actually find power converter + + align:start position:0% +you can actually find power converter + + + align:start position:0% +you can actually find power converter +circuits for high power that have 48 + + align:start position:0% +circuits for high power that have 48 + + + align:start position:0% +circuits for high power that have 48 +diodes in them right and so then you get + + align:start position:0% +diodes in them right and so then you get + + + align:start position:0% +diodes in them right and so then you get +part of your job is they're turning on + + align:start position:0% +part of your job is they're turning on + + + align:start position:0% +part of your job is they're turning on +and off and you got to figure out what's + + align:start position:0% +and off and you got to figure out what's + + + align:start position:0% +and off and you got to figure out what's +going on + + align:start position:0% +going on + + + align:start position:0% +going on +okay what would I do here well what we + + align:start position:0% +okay what would I do here well what we + + + align:start position:0% +okay what would I do here well what we +would tend to use is something known as + + align:start position:0% +would tend to use is something known as + + + align:start position:0% +would tend to use is something known as +the method of assume state + + align:start position:0% +the method of assume state + + + align:start position:0% +the method of assume state +okay and here's the method of assume + + align:start position:0% +okay and here's the method of assume + + + align:start position:0% +okay and here's the method of assume +States or Mas as I'd call it + + align:start position:0% +States or Mas as I'd call it + + + align:start position:0% +States or Mas as I'd call it +one assume a state for each + + align:start position:0% + + + + align:start position:0% + +switch okay so you know some switches + + align:start position:0% +switch okay so you know some switches + + + align:start position:0% +switch okay so you know some switches +you know if you fully control the switch + + align:start position:0% +you know if you fully control the switch + + + align:start position:0% +you know if you fully control the switch +you know when it's on and off because + + align:start position:0% +you know when it's on and off because + + + align:start position:0% +you know when it's on and off because +you're telling it to turn on off but but + + align:start position:0% +you're telling it to turn on off but but + + + align:start position:0% +you're telling it to turn on off but but +if you don't know if you have diodes for + + align:start position:0% +if you don't know if you have diodes for + + + align:start position:0% +if you don't know if you have diodes for +example in your + + align:start position:0% +example in your + + + align:start position:0% +example in your +circuit guess assume it's on or off at a + + align:start position:0% +circuit guess assume it's on or off at a + + + align:start position:0% +circuit guess assume it's on or off at a +given point in time okay what you would + + align:start position:0% +given point in time okay what you would + + + align:start position:0% +given point in time okay what you would +then do is say okay take that diod and + + align:start position:0% +then do is say okay take that diod and + + + align:start position:0% +then do is say okay take that diod and +replace it either with a short circuit + + align:start position:0% +replace it either with a short circuit + + + align:start position:0% +replace it either with a short circuit +if I've assumed it's on or an open + + align:start position:0% +if I've assumed it's on or an open + + + align:start position:0% +if I've assumed it's on or an open +circuit if I've assumed it's off okay + + align:start position:0% +circuit if I've assumed it's off okay + + + align:start position:0% +circuit if I've assumed it's off okay +and now I've replaced things with + + align:start position:0% +and now I've replaced things with + + + align:start position:0% +and now I've replaced things with +shortens opens and so now my circuit's + + align:start position:0% +shortens opens and so now my circuit's + + + align:start position:0% +shortens opens and so now my circuit's +simpler so I've assumed a state + + align:start position:0% +simpler so I've assumed a state + + + align:start position:0% +simpler so I've assumed a state +substitut it in then I analyze + + align:start position:0% + + + + align:start position:0% + +the v's and the I's in the circuit right + + align:start position:0% +the v's and the I's in the circuit right + + + align:start position:0% +the v's and the I's in the circuit right +now if what I have is switches inductors + + align:start position:0% +now if what I have is switches inductors + + + align:start position:0% +now if what I have is switches inductors +capacitors resistors that kind of thing + + align:start position:0% +capacitors resistors that kind of thing + + + align:start position:0% +capacitors resistors that kind of thing +then that just becomes a linear circuit + + align:start position:0% +then that just becomes a linear circuit + + + align:start position:0% +then that just becomes a linear circuit +problem that's straightforward to solve + + align:start position:0% +problem that's straightforward to solve + + + align:start position:0% +problem that's straightforward to solve +right so analyzing the v's and I in that + + align:start position:0% +right so analyzing the v's and I in that + + + align:start position:0% +right so analyzing the v's and I in that +case is pretty easy whereas if I want + + align:start position:0% +case is pretty easy whereas if I want + + + align:start position:0% +case is pretty easy whereas if I want +exponentials in there then it gets a + + align:start position:0% +exponentials in there then it gets a + + + align:start position:0% +exponentials in there then it gets a +little + + align:start position:0% +little + + + align:start position:0% +little +ugly okay the next thing I do and this + + align:start position:0% +ugly okay the next thing I do and this + + + align:start position:0% +ugly okay the next thing I do and this +is the key thing + + align:start position:0% +is the key thing + + + align:start position:0% +is the key thing +check if switch conditions are violated + + align:start position:0% + + + + align:start position:0% + +okay so what I'm really going to do is + + align:start position:0% +okay so what I'm really going to do is + + + align:start position:0% +okay so what I'm really going to do is +I'm going to go say oh I've assumed my + + align:start position:0% +I'm going to go say oh I've assumed my + + + align:start position:0% +I'm going to go say oh I've assumed my +switch is on so I've replaced it with a + + align:start position:0% +switch is on so I've replaced it with a + + + align:start position:0% +switch is on so I've replaced it with a +short circuit did the dioda current end + + align:start position:0% +short circuit did the dioda current end + + + align:start position:0% +short circuit did the dioda current end +up being negative if it did I know it + + align:start position:0% +up being negative if it did I know it + + + align:start position:0% +up being negative if it did I know it +can't do that because diodes can't do + + align:start position:0% +can't do that because diodes can't do + + + align:start position:0% +can't do that because diodes can't do +that if I've assumed it's off the + + align:start position:0% +that if I've assumed it's off the + + + align:start position:0% +that if I've assumed it's off the +question I have to ask myself is that + + align:start position:0% +question I have to ask myself is that + + + align:start position:0% +question I have to ask myself is that +did the diode voltage end up being + + align:start position:0% +did the diode voltage end up being + + + align:start position:0% +did the diode voltage end up being +positive right so what I'm going to do + + align:start position:0% +positive right so what I'm going to do + + + align:start position:0% +positive right so what I'm going to do +is I'm going to assume something I'm + + align:start position:0% +is I'm going to assume something I'm + + + align:start position:0% +is I'm going to assume something I'm +going to assume it's a Shor or an open + + align:start position:0% +going to assume it's a Shor or an open + + + align:start position:0% +going to assume it's a Shor or an open +and then check if the other condition is + + align:start position:0% +and then check if the other condition is + + + align:start position:0% +and then check if the other condition is +violated and the reason I have to do it + + align:start position:0% +violated and the reason I have to do it + + + align:start position:0% +violated and the reason I have to do it +that way is because if I've assumed it's + + align:start position:0% +that way is because if I've assumed it's + + + align:start position:0% +that way is because if I've assumed it's +a short then I can't check its voltage + + align:start position:0% +a short then I can't check its voltage + + + align:start position:0% +a short then I can't check its voltage +because I've already assumed its voltage + + align:start position:0% +because I've already assumed its voltage + + + align:start position:0% +because I've already assumed its voltage +is zero I got to check the other + + align:start position:0% +is zero I got to check the other + + + align:start position:0% +is zero I got to check the other +terminal condition + + align:start position:0% +terminal condition + + + align:start position:0% +terminal condition +okay so all right + + align:start position:0% +okay so all right + + + align:start position:0% +okay so all right +four if + + align:start position:0% +four if + + + align:start position:0% +four if +not right we're happy keep going in time + + align:start position:0% + + + + align:start position:0% + +time if + + align:start position:0% + + + + align:start position:0% + +violated I have to make a new set of + + align:start position:0% +violated I have to make a new set of + + + align:start position:0% +violated I have to make a new set of +assumptions and come up here right so + + align:start position:0% +assumptions and come up here right so + + + align:start position:0% +assumptions and come up here right so +guess again what I might do is if I + + align:start position:0% +guess again what I might do is if I + + + align:start position:0% +guess again what I might do is if I +found a device condition violated maybe + + align:start position:0% +found a device condition violated maybe + + + align:start position:0% +found a device condition violated maybe +I'll switch switch the the condition + + align:start position:0% +I'll switch switch the the condition + + + align:start position:0% +I'll switch switch the the condition +state of that assume state of that Di + + align:start position:0% +state of that assume state of that Di + + + align:start position:0% +state of that assume state of that Di +and go back and do it over again right + + align:start position:0% +and go back and do it over again right + + + align:start position:0% +and go back and do it over again right +so I can sort of start to guess at a + + align:start position:0% +so I can sort of start to guess at a + + + align:start position:0% +so I can sort of start to guess at a +given point in time time what the state + + align:start position:0% +given point in time time what the state + + + align:start position:0% +given point in time time what the state +of the uncontrolled switches is and then + + align:start position:0% +of the uncontrolled switches is and then + + + align:start position:0% +of the uncontrolled switches is and then +check if I'm wrong and keep iterating + + align:start position:0% +check if I'm wrong and keep iterating + + + align:start position:0% +check if I'm wrong and keep iterating +that until I figured out I'm right + + align:start position:0% +that until I figured out I'm right + + + align:start position:0% +that until I figured out I'm right +okay so let me + + align:start position:0% +okay so let me + + + align:start position:0% +okay so let me +just illustrate that for a very simple + + align:start position:0% +just illustrate that for a very simple + + + align:start position:0% +just illustrate that for a very simple +condition okay in this particular + + align:start position:0% +condition okay in this particular + + + align:start position:0% +condition okay in this particular +circuit right I have two possibilities + + align:start position:0% +circuit right I have two possibilities + + + align:start position:0% +circuit right I have two possibilities +if the diode's + + align:start position:0% + + + + align:start position:0% + +on and this is why this is this world + + align:start position:0% +on and this is why this is this world + + + align:start position:0% +on and this is why this is this world +simple as circuit if I've assumed the + + align:start position:0% +simple as circuit if I've assumed the + + + align:start position:0% +simple as circuit if I've assumed the +Di's + + align:start position:0% +Di's + + + align:start position:0% +Di's +on right then I've got V out + + align:start position:0% +on right then I've got V out + + + align:start position:0% +on right then I've got V out +here is just equal to the input voltage + + align:start position:0% +here is just equal to the input voltage + + + align:start position:0% +here is just equal to the input voltage +and I ought to look + + align:start position:0% +and I ought to look + + + align:start position:0% +and I ought to look +at this current to check whether I'm + + align:start position:0% +at this current to check whether I'm + + + align:start position:0% +at this current to check whether I'm +making an + + align:start position:0% +making an + + + align:start position:0% +making an +error + + align:start position:0% +error + + + align:start position:0% +error +and if I've assumed it's + + align:start position:0% + + + + align:start position:0% + +off right then what I would need to look + + align:start position:0% +off right then what I would need to look + + + align:start position:0% +off right then what I would need to look +at + + align:start position:0% + + + + align:start position:0% + +I would + + align:start position:0% + + + + align:start position:0% + +have be out like this and I would need + + align:start position:0% +have be out like this and I would need + + + align:start position:0% +have be out like this and I would need +to look at the diode + + align:start position:0% + + + + align:start position:0% + +voltage to see if it's gone + + align:start position:0% +voltage to see if it's gone + + + align:start position:0% +voltage to see if it's gone +positive all right so let's just apply + + align:start position:0% +positive all right so let's just apply + + + align:start position:0% +positive all right so let's just apply +this and yes I I grant you you've long + + align:start position:0% +this and yes I I grant you you've long + + + align:start position:0% +this and yes I I grant you you've long +since figured out what this circuit's + + align:start position:0% +since figured out what this circuit's + + + align:start position:0% +since figured out what this circuit's +doing in your head but it's not so + + align:start position:0% +doing in your head but it's not so + + + align:start position:0% +doing in your head but it's not so +simple if you have a whole pile of + + align:start position:0% +simple if you have a whole pile of + + + align:start position:0% +simple if you have a whole pile of +uncontrolled devices or a more comp + + align:start position:0% +uncontrolled devices or a more comp + + + align:start position:0% +uncontrolled devices or a more comp +complicated circuit as we'll see okay so + + align:start position:0% +complicated circuit as we'll see okay so + + + align:start position:0% +complicated circuit as we'll see okay so +let's just look at this example so here + + align:start position:0% +let's just look at this example so here + + + align:start position:0% +let's just look at this example so here +we go I've got my input + + align:start position:0% +we go I've got my input + + + align:start position:0% +we go I've got my input +source BS sin Omega T so it looks like + + align:start position:0% +source BS sin Omega T so it looks like + + + align:start position:0% +source BS sin Omega T so it looks like +some sine + + align:start position:0% +some sine + + + align:start position:0% +some sine +wave right here's Omega T okay and I + + align:start position:0% +wave right here's Omega T okay and I + + + align:start position:0% +wave right here's Omega T okay and I +want to know what for example is the + + align:start position:0% +want to know what for example is the + + + align:start position:0% +want to know what for example is the +output voltage doing there okay well + + align:start position:0% +output voltage doing there okay well + + + align:start position:0% +output voltage doing there okay well +let's assume let's let's start let me + + align:start position:0% +let's assume let's let's start let me + + + align:start position:0% +let's assume let's let's start let me +just start at tal 0 + + align:start position:0% +just start at tal 0 + + + align:start position:0% +just start at tal 0 +plus like right + + align:start position:0% +plus like right + + + align:start position:0% +plus like right +here okay + + align:start position:0% +here okay + + + align:start position:0% +here okay +or Omega t 0 plus well if I assumed the + + align:start position:0% +or Omega t 0 plus well if I assumed the + + + align:start position:0% +or Omega t 0 plus well if I assumed the +diode was off I'd + + align:start position:0% +diode was off I'd + + + align:start position:0% +diode was off I'd +have this picture + + align:start position:0% +have this picture + + + align:start position:0% +have this picture +here right if I assume the died off I'd + + align:start position:0% +here right if I assume the died off I'd + + + align:start position:0% +here right if I assume the died off I'd +have this picture here but if this is + + align:start position:0% +have this picture here but if this is + + + align:start position:0% +have this picture here but if this is +open the diode current zero so there's + + align:start position:0% +open the diode current zero so there's + + + align:start position:0% +open the diode current zero so there's +no current through the resistor so + + align:start position:0% +no current through the resistor so + + + align:start position:0% +no current through the resistor so +there's no voltage here so in that case + + align:start position:0% +there's no voltage here so in that case + + + align:start position:0% +there's no voltage here so in that case +VD would equal vs Sin Omega T right and + + align:start position:0% +VD would equal vs Sin Omega T right and + + + align:start position:0% +VD would equal vs Sin Omega T right and +if I just told you that vs Sin Omega T + + align:start position:0% +if I just told you that vs Sin Omega T + + + align:start position:0% +if I just told you that vs Sin Omega T +is + + align:start position:0% +is + + + align:start position:0% +is +positive well that would mean that the + + align:start position:0% +positive well that would mean that the + + + align:start position:0% +positive well that would mean that the +diode voltage is positive and hence this + + align:start position:0% +diode voltage is positive and hence this + + + align:start position:0% +diode voltage is positive and hence this +violates this assumption and so it can't + + align:start position:0% +violates this assumption and so it can't + + + align:start position:0% +violates this assumption and so it can't +be true this cannot be the state if vs + + align:start position:0% +be true this cannot be the state if vs + + + align:start position:0% +be true this cannot be the state if vs +Sin Omega T is positive right so what + + align:start position:0% +Sin Omega T is positive right so what + + + align:start position:0% +Sin Omega T is positive right so what +that would tell me is that + + align:start position:0% +that would tell me is that + + + align:start position:0% +that would tell me is that +G I must have at least in this + + align:start position:0% +G I must have at least in this + + + align:start position:0% +G I must have at least in this +range the diode has to be on for at + + align:start position:0% +range the diode has to be on for at + + + align:start position:0% +range the diode has to be on for at +least this + + align:start position:0% +least this + + + align:start position:0% +least this +range and so I would get V out looking + + align:start position:0% +range and so I would get V out looking + + + align:start position:0% +range and so I would get V out looking +like exactly like VD because I if I look + + align:start position:0% +like exactly like VD because I if I look + + + align:start position:0% +like exactly like VD because I if I look +at the top assume circuit vs Sin Omega T + + align:start position:0% +at the top assume circuit vs Sin Omega T + + + align:start position:0% +at the top assume circuit vs Sin Omega T +is applied directly across V out and it + + align:start position:0% +is applied directly across V out and it + + + align:start position:0% +is applied directly across V out and it +looks like + + align:start position:0% +looks like + + + align:start position:0% +looks like +this right here's V + + align:start position:0% +this right here's V + + + align:start position:0% +this right here's V +out and what would the diode current + + align:start position:0% +out and what would the diode current + + + align:start position:0% +out and what would the diode current +look like ID well ID is just vs over R + + align:start position:0% +look like ID well ID is just vs over R + + + align:start position:0% +look like ID well ID is just vs over R +so it would do something like + + align:start position:0% +so it would do something like + + + align:start position:0% +so it would do something like +this + + align:start position:0% +this + + + align:start position:0% +this +right okay well what happens + + align:start position:0% +right okay well what happens + + + align:start position:0% +right okay well what happens +when I cross this + + align:start position:0% +when I cross this + + + align:start position:0% +when I cross this +boundary if I continue to assume I was + + align:start position:0% +boundary if I continue to assume I was + + + align:start position:0% +boundary if I continue to assume I was +in the same state where the where the + + align:start position:0% +in the same state where the where the + + + align:start position:0% +in the same state where the where the +diode is + + align:start position:0% +diode is + + + align:start position:0% +diode is +on then I would have ID + + align:start position:0% +on then I would have ID + + + align:start position:0% +on then I would have ID +here go negative right here but we know + + align:start position:0% +here go negative right here but we know + + + align:start position:0% +here go negative right here but we know +it can't do that so what do I know I + + align:start position:0% +it can't do that so what do I know I + + + align:start position:0% +it can't do that so what do I know I +know my assumption that the diode was on + + align:start position:0% +know my assumption that the diode was on + + + align:start position:0% +know my assumption that the diode was on +must be off and so in this part of the + + align:start position:0% +must be off and so in this part of the + + + align:start position:0% +must be off and so in this part of the +cycle the diode must be off + + align:start position:0% +cycle the diode must be off + + + align:start position:0% +cycle the diode must be off +okay so pretty simple if the diode's off + + align:start position:0% +okay so pretty simple if the diode's off + + + align:start position:0% +okay so pretty simple if the diode's off +then ID is + + align:start position:0% +then ID is + + + align:start position:0% +then ID is +zero and VD is zero and V out is zero + + align:start position:0% +zero and VD is zero and V out is zero + + + align:start position:0% +zero and VD is zero and V out is zero +and this is the waveform I get and it + + align:start position:0% +and this is the waveform I get and it + + + align:start position:0% +and this is the waveform I get and it +would look like this okay so we've sort + + align:start position:0% +would look like this okay so we've sort + + + align:start position:0% +would look like this okay so we've sort +of + + align:start position:0% +of + + + align:start position:0% +of +analyzed the circuit took a lot of time + + align:start position:0% +analyzed the circuit took a lot of time + + + align:start position:0% +analyzed the circuit took a lot of time +to do it which is you know just by way + + align:start position:0% +to do it which is you know just by way + + + align:start position:0% +to do it which is you know just by way +of illustration but that's the notion of + + align:start position:0% +of illustration but that's the notion of + + + align:start position:0% +of illustration but that's the notion of +assume States I assume a state for the + + align:start position:0% +assume States I assume a state for the + + + align:start position:0% +assume States I assume a state for the +device I calculate along and then I see + + align:start position:0% +device I calculate along and then I see + + + align:start position:0% +device I calculate along and then I see +if I'm wrong at any point about what the + + align:start position:0% +if I'm wrong at any point about what the + + + align:start position:0% +if I'm wrong at any point about what the +diode can and can't do + + align:start position:0% +diode can and can't do + + + align:start position:0% +diode can and can't do +okay let me stop there and just ask if + + align:start position:0% +okay let me stop there and just ask if + + + align:start position:0% +okay let me stop there and just ask if +there's any questions about the + + align:start position:0% + + + + align:start position:0% + +concept yeah are you always are you g + + align:start position:0% +concept yeah are you always are you g + + + align:start position:0% +concept yeah are you always are you g +get a uni + + align:start position:0% +get a uni + + + align:start position:0% +get a uni +answer very good question are you going + + align:start position:0% +answer very good question are you going + + + align:start position:0% +answer very good question are you going +to get a unique answer and the an and + + align:start position:0% +to get a unique answer and the an and + + + align:start position:0% +to get a unique answer and the an and +the answer to that is uh so long + + align:start position:0% +the answer to that is uh so long + + + align:start position:0% +the answer to that is uh so long +as + + align:start position:0% +as + + + align:start position:0% +as +um it gets more complicated when you + + align:start position:0% +um it gets more complicated when you + + + align:start position:0% +um it gets more complicated when you +have controlled and uncontrolled devices + + align:start position:0% +have controlled and uncontrolled devices + + + align:start position:0% +have controlled and uncontrolled devices +but if I know an initial state it will + + align:start position:0% +but if I know an initial state it will + + + align:start position:0% +but if I know an initial state it will +do a it will do a unique thing I could + + align:start position:0% +do a it will do a unique thing I could + + + align:start position:0% +do a it will do a unique thing I could +give you something where I didn't tell + + align:start position:0% +give you something where I didn't tell + + + align:start position:0% +give you something where I didn't tell +you the state variables in the circuit + + align:start position:0% +you the state variables in the circuit + + + align:start position:0% +you the state variables in the circuit +and then you wouldn't know what the + + align:start position:0% +and then you wouldn't know what the + + + align:start position:0% +and then you wouldn't know what the +state of the devices were okay but + + align:start position:0% +state of the devices were okay but + + + align:start position:0% +state of the devices were okay but +generally yes and I should say by the + + align:start position:0% +generally yes and I should say by the + + + align:start position:0% +generally yes and I should say by the +way that this notion of making some + + align:start position:0% +way that this notion of making some + + + align:start position:0% +way that this notion of making some +assumption and calculating there's a lot + + align:start position:0% +assumption and calculating there's a lot + + + align:start position:0% +assumption and calculating there's a lot +of circuit simulators fast simulators + + align:start position:0% +of circuit simulators fast simulators + + + align:start position:0% +of circuit simulators fast simulators +for say switching circuits that's + + align:start position:0% +for say switching circuits that's + + + align:start position:0% +for say switching circuits that's +exactly how they operate and they go + + align:start position:0% +exactly how they operate and they go + + + align:start position:0% +exactly how they operate and they go +through and then they change States and + + align:start position:0% +through and then they change States and + + + align:start position:0% +through and then they change States and +they keep keep going and so so you can + + align:start position:0% +they keep keep going and so so you can + + + align:start position:0% +they keep keep going and so so you can +do this and you will get an + + align:start position:0% +do this and you will get an + + + align:start position:0% +do this and you will get an +answer you know those who are oldtimers + + align:start position:0% +answer you know those who are oldtimers + + + align:start position:0% +answer you know those who are oldtimers +in the field like myself at one point or + + align:start position:0% +in the field like myself at one point or + + + align:start position:0% +in the field like myself at one point or +another have written a simulator that + + align:start position:0% +another have written a simulator that + + + align:start position:0% +another have written a simulator that +works that way to simulate some circuit + + align:start position:0% +works that way to simulate some circuit + + + align:start position:0% +works that way to simulate some circuit +these days these circuit simulators the + + align:start position:0% +these days these circuit simulators the + + + align:start position:0% +these days these circuit simulators the +general purpose ones are so good that + + align:start position:0% +general purpose ones are so good that + + + align:start position:0% +general purpose ones are so good that +you'd never bother writing your own uh + + align:start position:0% +you'd never bother writing your own uh + + + align:start position:0% +you'd never bother writing your own uh +but nonetheless it turns out to be very + + align:start position:0% +but nonetheless it turns out to be very + + + align:start position:0% +but nonetheless it turns out to be very +useful to analyze a circuit so yes + + align:start position:0% +useful to analyze a circuit so yes + + + align:start position:0% +useful to analyze a circuit so yes +generally you'll get a unique solution + + align:start position:0% +generally you'll get a unique solution + + + align:start position:0% +generally you'll get a unique solution +assuming you know all the state + + align:start position:0% +assuming you know all the state + + + align:start position:0% +assuming you know all the state +variables and you can think of that as + + align:start position:0% +variables and you can think of that as + + + align:start position:0% +variables and you can think of that as +you know if you built the thing it had + + align:start position:0% +you know if you built the thing it had + + + align:start position:0% +you know if you built the thing it had +to do something right and it can only do + + align:start position:0% +to do something right and it can only do + + + align:start position:0% +to do something right and it can only do +one + + align:start position:0% +one + + + align:start position:0% +one +thing okay so that's the method of + + align:start position:0% +thing okay so that's the method of + + + align:start position:0% +thing okay so that's the method of +assume States and we'll come back to + + align:start position:0% +assume States and we'll come back to + + + align:start position:0% +assume States and we'll come back to +this um with more much more complicated + + align:start position:0% +this um with more much more complicated + + + align:start position:0% +this um with more much more complicated +circuits but I wanted to give you the + + align:start position:0% +circuits but I wanted to give you the + + + align:start position:0% +circuits but I wanted to give you the +notion of when you have an uncontrolled + + align:start position:0% +notion of when you have an uncontrolled + + + align:start position:0% +notion of when you have an uncontrolled +device what do you + + align:start position:0% +device what do you + + + align:start position:0% +device what do you +do there is another topic I'd like to + + align:start position:0% +do there is another topic I'd like to + + + align:start position:0% +do there is another topic I'd like to +cover + + align:start position:0% +cover + + + align:start position:0% +cover +today that relates to how we generalize + + align:start position:0% +today that relates to how we generalize + + + align:start position:0% +today that relates to how we generalize +generally analyze power converter + + align:start position:0% +generally analyze power converter + + + align:start position:0% +generally analyze power converter +circuits and we said well um you know + + align:start position:0% +circuits and we said well um you know + + + align:start position:0% +circuits and we said well um you know +I'm going to do something and there's + + align:start position:0% +I'm going to do something and there's + + + align:start position:0% +I'm going to do something and there's +all kinds of power converter circuits + + align:start position:0% +all kinds of power converter circuits + + + align:start position:0% +all kinds of power converter circuits +but generally I'm going to do something + + align:start position:0% +but generally I'm going to do something + + + align:start position:0% +but generally I'm going to do something +like this where typically I'm going to + + align:start position:0% +like this where typically I'm going to + + + align:start position:0% +like this where typically I'm going to +operate something periodically + + align:start position:0% +operate something periodically + + + align:start position:0% +operate something periodically +right and then I want to analyze what + + align:start position:0% +right and then I want to analyze what + + + align:start position:0% +right and then I want to analyze what +its behavior is okay and because we're + + align:start position:0% +its behavior is okay and because we're + + + align:start position:0% +its behavior is okay and because we're +operating things periodically we can + + align:start position:0% +operating things periodically we can + + + align:start position:0% +operating things periodically we can +often end up with a + + align:start position:0% +often end up with a + + + align:start position:0% +often end up with a +a an operating regime that we will call + + align:start position:0% +a an operating regime that we will call + + + align:start position:0% +a an operating regime that we will call +periodic stady steady state okay or uh + + align:start position:0% +periodic stady steady state okay or uh + + + align:start position:0% +periodic stady steady state okay or uh +we abbreviate periodic steady state as + + align:start position:0% +we abbreviate periodic steady state as + + + align:start position:0% +we abbreviate periodic steady state as +PSS okay now the notion of periodic + + align:start position:0% +PSS okay now the notion of periodic + + + align:start position:0% +PSS okay now the notion of periodic +steady state is a little bit like the + + align:start position:0% +steady state is a little bit like the + + + align:start position:0% +steady state is a little bit like the +notion of sinusoidal steady state which + + align:start position:0% +notion of sinusoidal steady state which + + + align:start position:0% +notion of sinusoidal steady state which +you would have studied in linear + + align:start position:0% +you would have studied in linear + + + align:start position:0% +you would have studied in linear +circuits except that we don't typically + + align:start position:0% +circuits except that we don't typically + + + align:start position:0% +circuits except that we don't typically +have all our waveforms being sinusoidal + + align:start position:0% +have all our waveforms being sinusoidal + + + align:start position:0% +have all our waveforms being sinusoidal +right because we have some kind of + + align:start position:0% +right because we have some kind of + + + align:start position:0% +right because we have some kind of +nonlinear circuit going on um but it's + + align:start position:0% +nonlinear circuit going on um but it's + + + align:start position:0% +nonlinear circuit going on um but it's +it's a related concept and the idea is + + align:start position:0% +it's a related concept and the idea is + + + align:start position:0% +it's a related concept and the idea is +this we're operating cyclically + + align:start position:0% +this we're operating cyclically + + + align:start position:0% +this we're operating cyclically +eventually what we expect is for every + + align:start position:0% +eventually what we expect is for every + + + align:start position:0% +eventually what we expect is for every +cycle the circuit to do the same thing + + align:start position:0% +cycle the circuit to do the same thing + + + align:start position:0% +cycle the circuit to do the same thing +so periodic steady state + + align:start position:0% +so periodic steady state + + + align:start position:0% +so periodic steady state +operation is something like this uh + + align:start position:0% +operation is something like this uh + + + align:start position:0% +operation is something like this uh +every so suppose I have some operating + + align:start position:0% +every so suppose I have some operating + + + align:start position:0% +every so suppose I have some operating +period T 2T + + align:start position:0% +period T 2T + + + align:start position:0% +period T 2T +3T Etc okay I would be in periodic + + align:start position:0% +3T Etc okay I would be in periodic + + + align:start position:0% +3T Etc okay I would be in periodic +steady state operation if every + + align:start position:0% +steady state operation if every + + + align:start position:0% +steady state operation if every +operating cycle was some carbon copy so + + align:start position:0% +operating cycle was some carbon copy so + + + align:start position:0% +operating cycle was some carbon copy so +if I looked at all the waveforms you + + align:start position:0% +if I looked at all the waveforms you + + + align:start position:0% +if I looked at all the waveforms you +know maybe it would do if it did + + align:start position:0% +know maybe it would do if it did + + + align:start position:0% +know maybe it would do if it did +something in this cycle it would do the + + align:start position:0% +something in this cycle it would do the + + + align:start position:0% +something in this cycle it would do the +precise same thing in the next cycle the + + align:start position:0% +precise same thing in the next cycle the + + + align:start position:0% +precise same thing in the next cycle the +third cycle would be a carbon copy of + + align:start position:0% +third cycle would be a carbon copy of + + + align:start position:0% +third cycle would be a carbon copy of +that that's periodic steady state + + align:start position:0% +that that's periodic steady state + + + align:start position:0% +that that's periodic steady state +operation okay and what I mean is + + align:start position:0% +operation okay and what I mean is + + + align:start position:0% +operation okay and what I mean is +generally about all the waveforms in the + + align:start position:0% +generally about all the waveforms in the + + + align:start position:0% +generally about all the waveforms in the +circuit like what I'm saying is + + align:start position:0% +circuit like what I'm saying is + + + align:start position:0% +circuit like what I'm saying is +this if I just shift it back of cycle + + align:start position:0% +this if I just shift it back of cycle + + + align:start position:0% +this if I just shift it back of cycle +just + + align:start position:0% +just + + + align:start position:0% +just +repeating okay do we have to check all + + align:start position:0% +repeating okay do we have to check all + + + align:start position:0% +repeating okay do we have to check all +the waveforms in the circuit well if we + + align:start position:0% +the waveforms in the circuit well if we + + + align:start position:0% +the waveforms in the circuit well if we +if we check the state + + align:start position:0% +if we check the state + + + align:start position:0% +if we check the state +variables then we sort of know what the + + align:start position:0% +variables then we sort of know what the + + + align:start position:0% +variables then we sort of know what the +rest of the variables in the circuit are + + align:start position:0% +rest of the variables in the circuit are + + + align:start position:0% +rest of the variables in the circuit are +going to do so I only really have to + + align:start position:0% +going to do so I only really have to + + + align:start position:0% +going to do so I only really have to +think about State variables and + + align:start position:0% +think about State variables and + + + align:start position:0% +think about State variables and +generally we could often just say look + + align:start position:0% +generally we could often just say look + + + align:start position:0% +generally we could often just say look +at the things of interest and maybe you + + align:start position:0% +at the things of interest and maybe you + + + align:start position:0% +at the things of interest and maybe you +know if it's it if it takes this + + align:start position:0% +know if it's it if it takes this + + + align:start position:0% +know if it's it if it takes this +waveform x whatever it is a voltage or + + align:start position:0% +waveform x whatever it is a voltage or + + + align:start position:0% +waveform x whatever it is a voltage or +current in the circuit takes on some + + align:start position:0% +current in the circuit takes on some + + + align:start position:0% +current in the circuit takes on some +value at the beginning of the cycle and + + align:start position:0% +value at the beginning of the cycle and + + + align:start position:0% +value at the beginning of the cycle and +it returns to the exact same value at + + align:start position:0% +it returns to the exact same value at + + + align:start position:0% +it returns to the exact same value at +the end of the cycle then probably it's + + align:start position:0% +the end of the cycle then probably it's + + + align:start position:0% +the end of the cycle then probably it's +also periodic stady St operation right + + align:start position:0% +also periodic stady St operation right + + + align:start position:0% +also periodic stady St operation right +so sometimes we don't really think about + + align:start position:0% +so sometimes we don't really think about + + + align:start position:0% +so sometimes we don't really think about +looking at every point but we just look + + align:start position:0% +looking at every point but we just look + + + align:start position:0% +looking at every point but we just look +at the beginning of the end of each + + align:start position:0% +at the beginning of the end of each + + + align:start position:0% +at the beginning of the end of each +cycle okay so that's periodic steady + + align:start position:0% +cycle okay so that's periodic steady + + + align:start position:0% +cycle okay so that's periodic steady +state and we're going to see that it's + + align:start position:0% +state and we're going to see that it's + + + align:start position:0% +state and we're going to see that it's +really useful to think about circuits in + + align:start position:0% +really useful to think about circuits in + + + align:start position:0% +really useful to think about circuits in +periodic steady state operation they + + align:start position:0% +periodic steady state operation they + + + align:start position:0% +periodic steady state operation they +don't have have to be even a cyclically + + align:start position:0% +don't have have to be even a cyclically + + + align:start position:0% +don't have have to be even a cyclically +operated circuit may not be in periodic + + align:start position:0% +operated circuit may not be in periodic + + + align:start position:0% +operated circuit may not be in periodic +stady state right you could imagine some + + align:start position:0% +stady state right you could imagine some + + + align:start position:0% +stady state right you could imagine some +operating regime you're going through a + + align:start position:0% +operating regime you're going through a + + + align:start position:0% +operating regime you're going through a +transient we'll see one where maybe you + + align:start position:0% +transient we'll see one where maybe you + + + align:start position:0% +transient we'll see one where maybe you +know in this cycle it did this in this + + align:start position:0% +know in this cycle it did this in this + + + align:start position:0% +know in this cycle it did this in this +cycle it did this and this cycle it did + + align:start position:0% +cycle it did this and this cycle it did + + + align:start position:0% +cycle it did this and this cycle it did +this so you know we're switching things + + align:start position:0% +this so you know we're switching things + + + align:start position:0% +this so you know we're switching things +cyclically but the waveforms are not + + align:start position:0% +cyclically but the waveforms are not + + + align:start position:0% +cyclically but the waveforms are not +repeating right and this would be sort + + align:start position:0% +repeating right and this would be sort + + + align:start position:0% +repeating right and this would be sort +of clearly not + + align:start position:0% +of clearly not + + + align:start position:0% +of clearly not +PSS all + + align:start position:0% +PSS all + + + align:start position:0% +PSS all +right so we want to think about what + + align:start position:0% +right so we want to think about what + + + align:start position:0% +right so we want to think about what +will our circuits do in the steady state + + align:start position:0% +will our circuits do in the steady state + + + align:start position:0% +will our circuits do in the steady state +when they're doing the same thing every + + align:start position:0% +when they're doing the same thing every + + + align:start position:0% +when they're doing the same thing every +cycle we'll also think about these + + align:start position:0% +cycle we'll also think about these + + + align:start position:0% +cycle we'll also think about these +conditions but we often like to start + + align:start position:0% +conditions but we often like to start + + + align:start position:0% +conditions but we often like to start +with this condition okay why is that + + align:start position:0% +with this condition okay why is that + + + align:start position:0% +with this condition okay why is that +because we can say a lot of things about + + align:start position:0% +because we can say a lot of things about + + + align:start position:0% +because we can say a lot of things about +what a circuit will do once it reaches + + align:start position:0% +what a circuit will do once it reaches + + + align:start position:0% +what a circuit will do once it reaches +periodic steady + + align:start position:0% +periodic steady + + + align:start position:0% +periodic steady +state all right let's let's just give an + + align:start position:0% +state all right let's let's just give an + + + align:start position:0% +state all right let's let's just give an +example of + + align:start position:0% +example of + + + align:start position:0% +example of +that uh suppose I have an inductor + + align:start position:0% + + + + align:start position:0% + +right and I have some V subel voltage + + align:start position:0% +right and I have some V subel voltage + + + align:start position:0% +right and I have some V subel voltage +across the inductor and I subel current + + align:start position:0% +across the inductor and I subel current + + + align:start position:0% +across the inductor and I subel current +into the inductor what I know is that V + + align:start position:0% +into the inductor what I know is that V + + + align:start position:0% +into the inductor what I know is that V +subel is equal to l d i l + + align:start position:0% +subel is equal to l d i l + + + align:start position:0% +subel is equal to l d i l +DT okay well suppose I took the + + align:start position:0% +DT okay well suppose I took the + + + align:start position:0% +DT okay well suppose I took the +average of each side of this equation + + align:start position:0% +average of each side of this equation + + + align:start position:0% +average of each side of this equation +right the time average and maybe I'll + + align:start position:0% +right the time average and maybe I'll + + + align:start position:0% +right the time average and maybe I'll +average over all time or maybe I'll + + align:start position:0% +average over all time or maybe I'll + + + align:start position:0% +average over all time or maybe I'll +average over a cycle but let's talk + + align:start position:0% +average over a cycle but let's talk + + + align:start position:0% +average over a cycle but let's talk +about averaging over all time then I + + align:start position:0% +about averaging over all time then I + + + align:start position:0% +about averaging over all time then I +could say okay the average V subel is + + align:start position:0% +could say okay the average V subel is + + + align:start position:0% +could say okay the average V subel is +equal to l time is equal to the + + align:start position:0% +equal to l time is equal to the + + + align:start position:0% +equal to l time is equal to the +average of l d i l + + align:start position:0% +average of l d i l + + + align:start position:0% +average of l d i l +DT which is I could pull this L out of + + align:start position:0% +DT which is I could pull this L out of + + + align:start position:0% +DT which is I could pull this L out of +the average which is the average of V + + align:start position:0% +the average which is the average of V + + + align:start position:0% +the average which is the average of V +subel is equal to l * the average of D + + align:start position:0% +subel is equal to l * the average of D + + + align:start position:0% +subel is equal to l * the average of D +DT + + align:start position:0% +DT + + + align:start position:0% +DT +okay so what does that tell me Well if + + align:start position:0% +okay so what does that tell me Well if + + + align:start position:0% +okay so what does that tell me Well if +look at the periodic steady state + + align:start position:0% +look at the periodic steady state + + + align:start position:0% +look at the periodic steady state +waveform suppose for example I said this + + align:start position:0% +waveform suppose for example I said this + + + align:start position:0% +waveform suppose for example I said this +was some random variable X + + align:start position:0% +was some random variable X + + + align:start position:0% +was some random variable X +suppose X was equal to I + + align:start position:0% +suppose X was equal to I + + + align:start position:0% +suppose X was equal to I +subel right what is the I DT on average + + align:start position:0% +subel right what is the I DT on average + + + align:start position:0% +subel right what is the I DT on average +of this wave form well the current went + + align:start position:0% +of this wave form well the current went + + + align:start position:0% +of this wave form well the current went +up the current came down went up came + + align:start position:0% +up the current came down went up came + + + align:start position:0% +up the current came down went up came +down right on average the current's not + + align:start position:0% +down right on average the current's not + + + align:start position:0% +down right on average the current's not +going anywhere right on average the DT + + align:start position:0% +going anywhere right on average the DT + + + align:start position:0% +going anywhere right on average the DT +is zero I'm just repeating every cycle + + align:start position:0% +is zero I'm just repeating every cycle + + + align:start position:0% +is zero I'm just repeating every cycle +okay so what I can say is that in this + + align:start position:0% +okay so what I can say is that in this + + + align:start position:0% +okay so what I can say is that in this +case in + + align:start position:0% + + + + align:start position:0% + +PSS this is equal to + + align:start position:0% +PSS this is equal to + + + align:start position:0% +PSS this is equal to +zero right if I have an inductor in + + align:start position:0% +zero right if I have an inductor in + + + align:start position:0% +zero right if I have an inductor in +periodic steady state the average + + align:start position:0% +periodic steady state the average + + + align:start position:0% +periodic steady state the average +voltage across it has to be zero because + + align:start position:0% +voltage across it has to be zero because + + + align:start position:0% +voltage across it has to be zero because +on average the current through it's not + + align:start position:0% +on average the current through it's not + + + align:start position:0% +on average the current through it's not +changing it's might be doing something + + align:start position:0% +changing it's might be doing something + + + align:start position:0% +changing it's might be doing something +cyclically but it's just sitting there + + align:start position:0% +cyclically but it's just sitting there + + + align:start position:0% +cyclically but it's just sitting there +on + + align:start position:0% +on + + + align:start position:0% +on +average okay so what we can say is that + + align:start position:0% +average okay so what we can say is that + + + align:start position:0% +average okay so what we can say is that +for + + align:start position:0% + + + + align:start position:0% + +inductors right the average value of the + + align:start position:0% +inductors right the average value of the + + + align:start position:0% +inductors right the average value of the +voltage across an inductor is equal to + + align:start position:0% +voltage across an inductor is equal to + + + align:start position:0% +voltage across an inductor is equal to +zero in PSS + + align:start position:0% +zero in PSS + + + align:start position:0% +zero in PSS +I could have made the same argument + + align:start position:0% +I could have made the same argument + + + align:start position:0% +I could have made the same argument +about + + align:start position:0% + + + + align:start position:0% + +capacitors right the average value of a + + align:start position:0% +capacitors right the average value of a + + + align:start position:0% +capacitors right the average value of a +current through a capacitor is equal to + + align:start position:0% +current through a capacitor is equal to + + + align:start position:0% +current through a capacitor is equal to +zero in + + align:start position:0% +zero in + + + align:start position:0% +zero in +PSS okay so suddenly I can start having + + align:start position:0% +PSS okay so suddenly I can start having + + + align:start position:0% +PSS okay so suddenly I can start having +an + + align:start position:0% +an + + + align:start position:0% +an +understanding of requirements on the + + align:start position:0% +understanding of requirements on the + + + align:start position:0% +understanding of requirements on the +circuit operation if I'm sitting there + + align:start position:0% +circuit operation if I'm sitting there + + + align:start position:0% +circuit operation if I'm sitting there +in periodic steady state operation which + + align:start position:0% +in periodic steady state operation which + + + align:start position:0% +in periodic steady state operation which +is very often where we start our + + align:start position:0% +is very often where we start our + + + align:start position:0% +is very often where we start our +analysis so if I want to know what some + + align:start position:0% +analysis so if I want to know what some + + + align:start position:0% +analysis so if I want to know what some +cyclically operating circuit like this + + align:start position:0% +cyclically operating circuit like this + + + align:start position:0% +cyclically operating circuit like this +is + + align:start position:0% +is + + + align:start position:0% +is +doing + + align:start position:0% +doing + + + align:start position:0% +doing +um I might just start there and in fact + + align:start position:0% +um I might just start there and in fact + + + align:start position:0% +um I might just start there and in fact +I did that subtly when I analyzed the + + align:start position:0% +I did that subtly when I analyzed the + + + align:start position:0% +I did that subtly when I analyzed the +circuit right we said this is a low pass + + align:start position:0% +circuit right we said this is a low pass + + + align:start position:0% +circuit right we said this is a low pass +filter right the output voltage extracts + + align:start position:0% +filter right the output voltage extracts + + + align:start position:0% +filter right the output voltage extracts +the DC component of VX that's precisely + + align:start position:0% +the DC component of VX that's precisely + + + align:start position:0% +the DC component of VX that's precisely +the same thing as saying the average + + align:start position:0% +the same thing as saying the average + + + align:start position:0% +the same thing as saying the average +voltage across this inductor + + align:start position:0% +voltage across this inductor + + + align:start position:0% +voltage across this inductor +zero right so so we actually sort of + + align:start position:0% +zero right so so we actually sort of + + + align:start position:0% +zero right so so we actually sort of +already used that subtly but we just + + align:start position:0% +already used that subtly but we just + + + align:start position:0% +already used that subtly but we just +recognize that that was a low pass + + align:start position:0% +recognize that that was a low pass + + + align:start position:0% +recognize that that was a low pass +filter but it applies to any element in + + align:start position:0% +filter but it applies to any element in + + + align:start position:0% +filter but it applies to any element in +your circuit okay this is very much like + + align:start position:0% +your circuit okay this is very much like + + + align:start position:0% +your circuit okay this is very much like +saying you know the average voltage + + align:start position:0% +saying you know the average voltage + + + align:start position:0% +saying you know the average voltage +across inductors being a zero sort of + + align:start position:0% +across inductors being a zero sort of + + + align:start position:0% +across inductors being a zero sort of +like saying at DC or in steady state + + align:start position:0% +like saying at DC or in steady state + + + align:start position:0% +like saying at DC or in steady state +when nothing's changing an inductor + + align:start position:0% +when nothing's changing an inductor + + + align:start position:0% +when nothing's changing an inductor +looks like a short or in DC or steady + + align:start position:0% +looks like a short or in DC or steady + + + align:start position:0% +looks like a short or in DC or steady +state when nothing's changing a + + align:start position:0% +state when nothing's changing a + + + align:start position:0% +state when nothing's changing a +capacitor looks like an open has no + + align:start position:0% +capacitor looks like an open has no + + + align:start position:0% +capacitor looks like an open has no +current on average okay so that's the + + align:start position:0% +current on average okay so that's the + + + align:start position:0% +current on average okay so that's the +basic idea but what we're going to do + + align:start position:0% +basic idea but what we're going to do + + + align:start position:0% +basic idea but what we're going to do +going forward is we're going to start to + + align:start position:0% +going forward is we're going to start to + + + align:start position:0% +going forward is we're going to start to +figure out how to analyze all kinds of + + align:start position:0% +figure out how to analyze all kinds of + + + align:start position:0% +figure out how to analyze all kinds of +circuits and we're going to this is a + + align:start position:0% +circuits and we're going to this is a + + + align:start position:0% +circuits and we're going to this is a +very useful tool to figure out what they + + align:start position:0% +very useful tool to figure out what they + + + align:start position:0% +very useful tool to figure out what they +do in the periodic state state which is + + align:start position:0% +do in the periodic state state which is + + + align:start position:0% +do in the periodic state state which is +a very good first step to figure out + + align:start position:0% +a very good first step to figure out + + + align:start position:0% +a very good first step to figure out +what they're going to + + align:start position:0% +what they're going to + + + align:start position:0% +what they're going to +do you know in the non periodic stady + + align:start position:0% +do you know in the non periodic stady + + + align:start position:0% +do you know in the non periodic stady +State condition but we're often + + align:start position:0% +State condition but we're often + + + align:start position:0% +State condition but we're often +operating in periodic steady state so + + align:start position:0% +operating in periodic steady state so + + + align:start position:0% +operating in periodic steady state so +that's why we look at it and I should + + align:start position:0% +that's why we look at it and I should + + + align:start position:0% +that's why we look at it and I should +say it's not + + align:start position:0% +say it's not + + + align:start position:0% +say it's not +uncommon you + + align:start position:0% +uncommon you + + + align:start position:0% +uncommon you +know as a consultant for example right + + align:start position:0% +know as a consultant for example right + + + align:start position:0% +know as a consultant for example right +there some problem with their power + + align:start position:0% +there some problem with their power + + + align:start position:0% +there some problem with their power +converter right they ship you up their + + align:start position:0% +converter right they ship you up their + + + align:start position:0% +converter right they ship you up their +documents you know here's this circuit + + align:start position:0% +documents you know here's this circuit + + + align:start position:0% +documents you know here's this circuit +and they tell you nothing else and what + + align:start position:0% +and they tell you nothing else and what + + + align:start position:0% +and they tell you nothing else and what +do you have to do the first thing you + + align:start position:0% +do you have to do the first thing you + + + align:start position:0% +do you have to do the first thing you +have to do is figure + + align:start position:0% +have to do is figure + + + align:start position:0% +have to do is figure +out what will it do how will it operate + + align:start position:0% +out what will it do how will it operate + + + align:start position:0% +out what will it do how will it operate +and the first place to start with that + + align:start position:0% +and the first place to start with that + + + align:start position:0% +and the first place to start with that +is how does it operate in steady state + + align:start position:0% +is how does it operate in steady state + + + align:start position:0% +is how does it operate in steady state +and of course sometimes they'll tell you + + align:start position:0% +and of course sometimes they'll tell you + + + align:start position:0% +and of course sometimes they'll tell you +well let me tell you about how my + + align:start position:0% +well let me tell you about how my + + + align:start position:0% +well let me tell you about how my +circuit operates but of course they + + align:start position:0% +circuit operates but of course they + + + align:start position:0% +circuit operates but of course they +wouldn't be calling you if it did what + + align:start position:0% +wouldn't be calling you if it did what + + + align:start position:0% +wouldn't be calling you if it did what +they thought it did right so um very + + align:start position:0% +they thought it did right so um very + + + align:start position:0% +they thought it did right so um very +often you have to tell them why and + + align:start position:0% +often you have to tell them why and + + + align:start position:0% +often you have to tell them why and +tools like this are very good at + + align:start position:0% +tools like this are very good at + + + align:start position:0% +tools like this are very good at +figuring F out what is it going to do + + align:start position:0% +figuring F out what is it going to do + + + align:start position:0% +figuring F out what is it going to do +and why is it going to do it all + + align:start position:0% +and why is it going to do it all + + + align:start position:0% +and why is it going to do it all +right so let me just give you a super + + align:start position:0% +right so let me just give you a super + + + align:start position:0% +right so let me just give you a super +simple + + align:start position:0% +simple + + + align:start position:0% +simple +example uh of of that and sort of how it + + align:start position:0% +example uh of of that and sort of how it + + + align:start position:0% +example uh of of that and sort of how it +can inform your thinking and here's the + + align:start position:0% +can inform your thinking and here's the + + + align:start position:0% +can inform your thinking and here's the +circuit I'm going to do suppose we came + + align:start position:0% +circuit I'm going to do suppose we came + + + align:start position:0% +circuit I'm going to do suppose we came +back to this + + align:start position:0% +back to this + + + align:start position:0% +back to this +um to this circuit okay and what I got + + align:start position:0% +um to this circuit okay and what I got + + + align:start position:0% +um to this circuit okay and what I got +when I looked at that output voltage + + align:start position:0% +when I looked at that output voltage + + + align:start position:0% +when I looked at that output voltage +right this voltage here + + align:start position:0% + + + + align:start position:0% + +um is sort of a periodic state to state + + align:start position:0% +um is sort of a periodic state to state + + + align:start position:0% +um is sort of a periodic state to state +voltage it actually has a DC component + + align:start position:0% +voltage it actually has a DC component + + + align:start position:0% +voltage it actually has a DC component +so that thing is actually the world's + + align:start position:0% +so that thing is actually the world's + + + align:start position:0% +so that thing is actually the world's +simplest rectifier takes an ac voltage + + align:start position:0% +simplest rectifier takes an ac voltage + + + align:start position:0% +simplest rectifier takes an ac voltage +and generates a an output voltage that + + align:start position:0% +and generates a an output voltage that + + + align:start position:0% +and generates a an output voltage that +has a DC component right that's why I + + align:start position:0% +has a DC component right that's why I + + + align:start position:0% +has a DC component right that's why I +would use a switch I've now taken AC and + + align:start position:0% +would use a switch I've now taken AC and + + + align:start position:0% +would use a switch I've now taken AC and +turned it into DC you can't do that with + + align:start position:0% +turned it into DC you can't do that with + + + align:start position:0% +turned it into DC you can't do that with +a linear circuit element right but a + + align:start position:0% +a linear circuit element right but a + + + align:start position:0% +a linear circuit element right but a +diode you can use to do that so I might + + align:start position:0% +diode you can use to do that so I might + + + align:start position:0% +diode you can use to do that so I might +use this if I had some ac voltage and I + + align:start position:0% +use this if I had some ac voltage and I + + + align:start position:0% +use this if I had some ac voltage and I +wanted an output with a DC + + align:start position:0% +wanted an output with a DC + + + align:start position:0% +wanted an output with a DC +component to it or what I merely might + + align:start position:0% +component to it or what I merely might + + + align:start position:0% +component to it or what I merely might +want is a constant DC + + align:start position:0% +want is a constant DC + + + align:start position:0% +want is a constant DC +output right what did we do last time we + + align:start position:0% +output right what did we do last time we + + + align:start position:0% +output right what did we do last time we +wanted a constant DC output when we when + + align:start position:0% +wanted a constant DC output when we when + + + align:start position:0% +wanted a constant DC output when we when +we last class when we analyzed our + + align:start position:0% +we last class when we analyzed our + + + align:start position:0% +we last class when we analyzed our +converter we kind of generated a pulsing + + align:start position:0% +converter we kind of generated a pulsing + + + align:start position:0% +converter we kind of generated a pulsing +waveform and then we throw a filter on + + align:start position:0% +waveform and then we throw a filter on + + + align:start position:0% +waveform and then we throw a filter on +it maybe I should just throw an + + align:start position:0% +it maybe I should just throw an + + + align:start position:0% +it maybe I should just throw an +inductive filter on this thing and I can + + align:start position:0% +inductive filter on this thing and I can + + + align:start position:0% +inductive filter on this thing and I can +get now constant output which might I + + align:start position:0% +get now constant output which might I + + + align:start position:0% +get now constant output which might I +might want if I'm going to run some DC + + align:start position:0% +might want if I'm going to run some DC + + + align:start position:0% +might want if I'm going to run some DC +load with it okay so let's try that just + + align:start position:0% +load with it okay so let's try that just + + + align:start position:0% +load with it okay so let's try that just +as an examp example and see where we get + + align:start position:0% +as an examp example and see where we get + + + align:start position:0% +as an examp example and see where we get +so here's the circuit I'm going to + + align:start position:0% +so here's the circuit I'm going to + + + align:start position:0% +so here's the circuit I'm going to +propose and we'll take a look at this + + align:start position:0% +propose and we'll take a look at this + + + align:start position:0% +propose and we'll take a look at this +here is vs Sin Omega + + align:start position:0% + + + + align:start position:0% + +T okay here's my + + align:start position:0% +T okay here's my + + + align:start position:0% +T okay here's my +diode I'm just going to now put an + + align:start position:0% +diode I'm just going to now put an + + + align:start position:0% +diode I'm just going to now put an +inductor and here's my + + align:start position:0% +inductor and here's my + + + align:start position:0% +inductor and here's my +output okay so I can look at um some + + align:start position:0% +output okay so I can look at um some + + + align:start position:0% +output okay so I can look at um some +voltage that I'll call uh for + + align:start position:0% +voltage that I'll call uh for + + + align:start position:0% +voltage that I'll call uh for +example + + align:start position:0% +example + + + align:start position:0% +example +um I'll I'll call this + + align:start position:0% +um I'll I'll call this + + + align:start position:0% +um I'll I'll call this +ID okay let me now I have some + + align:start position:0% +ID okay let me now I have some + + + align:start position:0% +ID okay let me now I have some +distinction now between the uh voltage + + align:start position:0% +distinction now between the uh voltage + + + align:start position:0% +distinction now between the uh voltage +here and the voltage at the output but + + align:start position:0% +here and the voltage at the output but + + + align:start position:0% +here and the voltage at the output but +let me do this let me call this voltage + + align:start position:0% + + + + align:start position:0% + +VX and I'll call this voltage V + + align:start position:0% + + + + align:start position:0% + +out okay + + align:start position:0% +out okay + + + align:start position:0% +out okay +and let's think about analyzing this + + align:start position:0% +and let's think about analyzing this + + + align:start position:0% +and let's think about analyzing this +circuit + + align:start position:0% +circuit + + + align:start position:0% +circuit +well my goal was to use this inductor so + + align:start position:0% +well my goal was to use this inductor so + + + align:start position:0% +well my goal was to use this inductor so +that ID which is also I here is smooth + + align:start position:0% +that ID which is also I here is smooth + + + align:start position:0% +that ID which is also I here is smooth +right so maybe the Assumption I could + + align:start position:0% +right so maybe the Assumption I could + + + align:start position:0% +right so maybe the Assumption I could +make is let me just start by assuming + + align:start position:0% +make is let me just start by assuming + + + align:start position:0% +make is let me just start by assuming +this diod just on all the time I'll make + + align:start position:0% +this diod just on all the time I'll make + + + align:start position:0% +this diod just on all the time I'll make +that assumption right we said we're + + align:start position:0% +that assumption right we said we're + + + align:start position:0% +that assumption right we said we're +going to analyze this we'll make some + + align:start position:0% +going to analyze this we'll make some + + + align:start position:0% +going to analyze this we'll make some +assumption about the state let me just + + align:start position:0% +assumption about the state let me just + + + align:start position:0% +assumption about the state let me just +assume the diode's on so in that case I + + align:start position:0% +assume the diode's on so in that case I + + + align:start position:0% +assume the diode's on so in that case I +got VSS sin Omega t + + align:start position:0% +got VSS sin Omega t + + + align:start position:0% +got VSS sin Omega t +uh I'll assume that the diode's always + + align:start position:0% +uh I'll assume that the diode's always + + + align:start position:0% +uh I'll assume that the diode's always +on I'll replace it with a short I have + + align:start position:0% +on I'll replace it with a short I have + + + align:start position:0% +on I'll replace it with a short I have +my inductor and I have my + + align:start position:0% +my inductor and I have my + + + align:start position:0% +my inductor and I have my +output + + align:start position:0% +output + + + align:start position:0% +output +okay and here's my diode current + + align:start position:0% + + + + align:start position:0% + +ID and here's my output voltage V + + align:start position:0% + + + + align:start position:0% + +out let me Analyze This + + align:start position:0% +out let me Analyze This + + + align:start position:0% +out let me Analyze This +circuit okay so I'll just do kvl around + + align:start position:0% +circuit okay so I'll just do kvl around + + + align:start position:0% +circuit okay so I'll just do kvl around +the loop here so I've got s sin Omega + + align:start position:0% + + + + align:start position:0% + +T minus + + align:start position:0% +T minus + + + align:start position:0% +T minus +VL call that + + align:start position:0% +VL call that + + + align:start position:0% +VL call that +VL minus V out is equal to + + align:start position:0% +VL minus V out is equal to + + + align:start position:0% +VL minus V out is equal to +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay well this is a legitimate equation + + align:start position:0% +okay well this is a legitimate equation + + + align:start position:0% +okay well this is a legitimate equation +I could take the average of each side of + + align:start position:0% +I could take the average of each side of + + + align:start position:0% +I could take the average of each side of +this equation right and still a + + align:start position:0% +this equation right and still a + + + align:start position:0% +this equation right and still a +legitimate + + align:start position:0% +legitimate + + + align:start position:0% +legitimate +equation so maybe what I'll do is I'll + + align:start position:0% +equation so maybe what I'll do is I'll + + + align:start position:0% +equation so maybe what I'll do is I'll +take this kvl equation I'll take the + + align:start position:0% +take this kvl equation I'll take the + + + align:start position:0% +take this kvl equation I'll take the +average of the whole thing and that + + align:start position:0% +average of the whole thing and that + + + align:start position:0% +average of the whole thing and that +gives me the average of each individual + + align:start position:0% +gives me the average of each individual + + + align:start position:0% +gives me the average of each individual +component + + align:start position:0% +component + + + align:start position:0% +component +right what's the average of vs Sin Omega + + align:start position:0% + + + + align:start position:0% + +t + + align:start position:0% +t + + + align:start position:0% +t +zero that goes away what is the average + + align:start position:0% +zero that goes away what is the average + + + align:start position:0% +zero that goes away what is the average +of the inductor voltage well I just told + + align:start position:0% +of the inductor voltage well I just told + + + align:start position:0% +of the inductor voltage well I just told +you that if I'm in periodic steady state + + align:start position:0% +you that if I'm in periodic steady state + + + align:start position:0% +you that if I'm in periodic steady state +and I maybe I'm interested in what the + + align:start position:0% +and I maybe I'm interested in what the + + + align:start position:0% +and I maybe I'm interested in what the +circuit does in the periodic steady + + align:start position:0% +circuit does in the periodic steady + + + align:start position:0% +circuit does in the periodic steady +state this is zero in + + align:start position:0% + + + + align:start position:0% + +PSS okay which just gives me then the + + align:start position:0% +PSS okay which just gives me then the + + + align:start position:0% +PSS okay which just gives me then the +average Val voltage of V + + align:start position:0% +average Val voltage of V + + + align:start position:0% +average Val voltage of V +out would be zero in that case right + + align:start position:0% +out would be zero in that case right + + + align:start position:0% +out would be zero in that case right +because the other two terms are zero and + + align:start position:0% +because the other two terms are zero and + + + align:start position:0% +because the other two terms are zero and +this is the only thing + + align:start position:0% +this is the only thing + + + align:start position:0% +this is the only thing +left well something's funny about that + + align:start position:0% +left well something's funny about that + + + align:start position:0% +left well something's funny about that +right I just told you we were building a + + align:start position:0% +right I just told you we were building a + + + align:start position:0% +right I just told you we were building a +rectifier and now I've told you I've got + + align:start position:0% +rectifier and now I've told you I've got + + + align:start position:0% +rectifier and now I've told you I've got +a zero output voltage which isn't + + align:start position:0% +a zero output voltage which isn't + + + align:start position:0% +a zero output voltage which isn't +exactly what a rectifier is supposed to + + align:start position:0% +exactly what a rectifier is supposed to + + + align:start position:0% +exactly what a rectifier is supposed to +do something's funny here what's funny + + align:start position:0% +do something's funny here what's funny + + + align:start position:0% +do something's funny here what's funny +is my assumption stupid right I assume + + align:start position:0% +is my assumption stupid right I assume + + + align:start position:0% +is my assumption stupid right I assume +that this diode was on all the time well + + align:start position:0% +that this diode was on all the time well + + + align:start position:0% +that this diode was on all the time well +if the diode was on all the time I + + align:start position:0% +if the diode was on all the time I + + + align:start position:0% +if the diode was on all the time I +suppose I could have just replaced it + + align:start position:0% +suppose I could have just replaced it + + + align:start position:0% +suppose I could have just replaced it +with a short circuit right but what this + + align:start position:0% +with a short circuit right but what this + + + align:start position:0% +with a short circuit right but what this +voltage being zero in periodic St State + + align:start position:0% +voltage being zero in periodic St State + + + align:start position:0% +voltage being zero in periodic St State +told me is I've made a mistake I've done + + align:start position:0% +told me is I've made a mistake I've done + + + align:start position:0% +told me is I've made a mistake I've done +something perhaps not stupid but I've + + align:start position:0% +something perhaps not stupid but I've + + + align:start position:0% +something perhaps not stupid but I've +just I've gotten over aggressive with my + + align:start position:0% +just I've gotten over aggressive with my + + + align:start position:0% +just I've gotten over aggressive with my +assumption that this diode stays on all + + align:start position:0% +assumption that this diode stays on all + + + align:start position:0% +assumption that this diode stays on all +the + + align:start position:0% +the + + + align:start position:0% +the +time and in fact I can tell that because + + align:start position:0% +time and in fact I can tell that because + + + align:start position:0% +time and in fact I can tell that because +if the average voltage was + + align:start position:0% +if the average voltage was + + + align:start position:0% +if the average voltage was +zero and presumably some of the time + + align:start position:0% +zero and presumably some of the time + + + align:start position:0% +zero and presumably some of the time +this current's positive so I have a + + align:start position:0% +this current's positive so I have a + + + align:start position:0% +this current's positive so I have a +positive voltage and if it's average is + + align:start position:0% +positive voltage and if it's average is + + + align:start position:0% +positive voltage and if it's average is +going to be zero then some of the + + align:start position:0% +going to be zero then some of the + + + align:start position:0% +going to be zero then some of the +voltage must be negative some of the + + align:start position:0% +voltage must be negative some of the + + + align:start position:0% +voltage must be negative some of the +time and if the voltage across the + + align:start position:0% +time and if the voltage across the + + + align:start position:0% +time and if the voltage across the +resistor is negative some of the time + + align:start position:0% +resistor is negative some of the time + + + align:start position:0% +resistor is negative some of the time +the current through the resistor is + + align:start position:0% +the current through the resistor is + + + align:start position:0% +the current through the resistor is +negative some of the time but we already + + align:start position:0% +negative some of the time but we already + + + align:start position:0% +negative some of the time but we already +said this diode can never have a + + align:start position:0% +said this diode can never have a + + + align:start position:0% +said this diode can never have a +negative + + align:start position:0% +negative + + + align:start position:0% +negative +current right so clearly my assumption + + align:start position:0% +current right so clearly my assumption + + + align:start position:0% +current right so clearly my assumption +was bad or you know when I assume that + + align:start position:0% +was bad or you know when I assume that + + + align:start position:0% +was bad or you know when I assume that +this diode was turned on that might be + + align:start position:0% +this diode was turned on that might be + + + align:start position:0% +this diode was turned on that might be +true for some time but it can't be true + + align:start position:0% +true for some time but it can't be true + + + align:start position:0% +true for some time but it can't be true +all the time so my my quest test to use + + align:start position:0% +all the time so my my quest test to use + + + align:start position:0% +all the time so my my quest test to use +this inductor to filter the waveforms + + align:start position:0% +this inductor to filter the waveforms + + + align:start position:0% +this inductor to filter the waveforms +you know maybe can't work out or at + + align:start position:0% +you know maybe can't work out or at + + + align:start position:0% +you know maybe can't work out or at +least as I've done it so far what would + + align:start position:0% +least as I've done it so far what would + + + align:start position:0% +least as I've done it so far what would +I get for waveforms if I did this what + + align:start position:0% +I get for waveforms if I did this what + + + align:start position:0% +I get for waveforms if I did this what +you would see is something like this + + align:start position:0% +you would see is something like this + + + align:start position:0% +you would see is something like this +um with this circuit what I would get is + + align:start position:0% + + + + align:start position:0% + +this right here's my VSS sin Omega t + + align:start position:0% +this right here's my VSS sin Omega t + + + align:start position:0% +this right here's my VSS sin Omega t +I know my diode has to be off some of + + align:start position:0% +I know my diode has to be off some of + + + align:start position:0% +I know my diode has to be off some of +the time right well let me assume that + + align:start position:0% +the time right well let me assume that + + + align:start position:0% +the time right well let me assume that +right where vs Sin Omega T is zero the + + align:start position:0% +right where vs Sin Omega T is zero the + + + align:start position:0% +right where vs Sin Omega T is zero the +diode's + + align:start position:0% +diode's + + + align:start position:0% +diode's +off + + align:start position:0% +off + + + align:start position:0% +off +okay all right so if I assume this Di's + + align:start position:0% +okay all right so if I assume this Di's + + + align:start position:0% +okay all right so if I assume this Di's +off and I replace this with an open + + align:start position:0% +off and I replace this with an open + + + align:start position:0% +off and I replace this with an open +circuit + + align:start position:0% +circuit + + + align:start position:0% +circuit +um so I'll just go do that let me let me + + align:start position:0% +um so I'll just go do that let me let me + + + align:start position:0% +um so I'll just go do that let me let me +just assume you know I just went through + + align:start position:0% +just assume you know I just went through + + + align:start position:0% +just assume you know I just went through +zero it's an open + + align:start position:0% +zero it's an open + + + align:start position:0% +zero it's an open +circuit what do I know well I know that + + align:start position:0% +circuit what do I know well I know that + + + align:start position:0% +circuit what do I know well I know that +if there's no current if this isn't open + + align:start position:0% +if there's no current if this isn't open + + + align:start position:0% +if there's no current if this isn't open +there's no current this way that means + + align:start position:0% +there's no current this way that means + + + align:start position:0% +there's no current this way that means +there's also no + + align:start position:0% +there's also no + + + align:start position:0% +there's also no +didt right which means that the voltage + + align:start position:0% +didt right which means that the voltage + + + align:start position:0% +didt right which means that the voltage +across the inductor is zero because V is + + align:start position:0% +across the inductor is zero because V is + + + align:start position:0% +across the inductor is zero because V is +LD DT voltage across the resistor is + + align:start position:0% +LD DT voltage across the resistor is + + + align:start position:0% +LD DT voltage across the resistor is +zero because the current's zero and that + + align:start position:0% +zero because the current's zero and that + + + align:start position:0% +zero because the current's zero and that +means that this + + align:start position:0% +means that this + + + align:start position:0% +means that this +VD since this is zero voltage and this + + align:start position:0% +VD since this is zero voltage and this + + + align:start position:0% +VD since this is zero voltage and this +is zero voltage VD is the same as vs Sin + + align:start position:0% +is zero voltage VD is the same as vs Sin + + + align:start position:0% +is zero voltage VD is the same as vs Sin +Omega + + align:start position:0% +Omega + + + align:start position:0% +Omega +T all right so what I can tell is that + + align:start position:0% +T all right so what I can tell is that + + + align:start position:0% +T all right so what I can tell is that +gez if the diode was off here and I know + + align:start position:0% +gez if the diode was off here and I know + + + align:start position:0% +gez if the diode was off here and I know +it's off sometime so probably maybe up + + align:start position:0% +it's off sometime so probably maybe up + + + align:start position:0% +it's off sometime so probably maybe up +to some point here the diode's + + align:start position:0% +to some point here the diode's + + + align:start position:0% +to some point here the diode's +off but as soon as I cross zero that + + align:start position:0% +off but as soon as I cross zero that + + + align:start position:0% +off but as soon as I cross zero that +assumption is bad because VD would no + + align:start position:0% +assumption is bad because VD would no + + + align:start position:0% +assumption is bad because VD would no +longer be negative it would be + + align:start position:0% +longer be negative it would be + + + align:start position:0% +longer be negative it would be +positive right so the diode must turn on + + align:start position:0% +positive right so the diode must turn on + + + align:start position:0% +positive right so the diode must turn on +right at t equal Z or Omega T equals + + align:start position:0% +right at t equal Z or Omega T equals + + + align:start position:0% +right at t equal Z or Omega T equals +zero right so the first part of what I + + align:start position:0% +zero right so the first part of what I + + + align:start position:0% +zero right so the first part of what I +did was correct the diode turns on VX + + align:start position:0% +did was correct the diode turns on VX + + + align:start position:0% +did was correct the diode turns on VX +when the diode's + + align:start position:0% +when the diode's + + + align:start position:0% +when the diode's +on is exactly going to + + align:start position:0% +on is exactly going to + + + align:start position:0% +on is exactly going to +follow v f sin Omega t for T greater + + align:start position:0% +follow v f sin Omega t for T greater + + + align:start position:0% +follow v f sin Omega t for T greater +than zero okay so it's going to follow + + align:start position:0% +than zero okay so it's going to follow + + + align:start position:0% +than zero okay so it's going to follow +same argument + + align:start position:0% +same argument + + + align:start position:0% +same argument +okay what's going to happen here though + + align:start position:0% +okay what's going to happen here though + + + align:start position:0% +okay what's going to happen here though +right is is the do going to turn off + + align:start position:0% +right is is the do going to turn off + + + align:start position:0% +right is is the do going to turn off +here well let's think about what this + + align:start position:0% +here well let's think about what this + + + align:start position:0% +here well let's think about what this +current would be I could I could analyze + + align:start position:0% +current would be I could I could analyze + + + align:start position:0% +current would be I could I could analyze +I could say look at tal 0 + + align:start position:0% +I could say look at tal 0 + + + align:start position:0% +I could say look at tal 0 +plus + + align:start position:0% +plus + + + align:start position:0% +plus +ID inductor current 0 + + align:start position:0% +ID inductor current 0 + + + align:start position:0% +ID inductor current 0 +and I've replaced at that point I've + + align:start position:0% +and I've replaced at that point I've + + + align:start position:0% +and I've replaced at that point I've +replaced this switch with a short + + align:start position:0% +replaced this switch with a short + + + align:start position:0% +replaced this switch with a short +circuit I can analyze that circuit right + + align:start position:0% +circuit I can analyze that circuit right + + + align:start position:0% +circuit I can analyze that circuit right +that that circuits uh just + + align:start position:0% +that that circuits uh just + + + align:start position:0% +that that circuits uh just +this + + align:start position:0% + + + + align:start position:0% + +right I can analyze this circuit for the + + align:start position:0% +right I can analyze this circuit for the + + + align:start position:0% +right I can analyze this circuit for the +inductor + + align:start position:0% +inductor + + + align:start position:0% +inductor +current knowing that I of Z is zero and + + align:start position:0% +current knowing that I of Z is zero and + + + align:start position:0% +current knowing that I of Z is zero and +if I plotted that what I would get is + + align:start position:0% +if I plotted that what I would get is + + + align:start position:0% +if I plotted that what I would get is +something that did I don't know + + align:start position:0% +something that did I don't know + + + align:start position:0% +something that did I don't know +something something like this it would + + align:start position:0% +something something like this it would + + + align:start position:0% +something something like this it would +start off very small and it would get + + align:start position:0% +start off very small and it would get + + + align:start position:0% +start off very small and it would get +bigger and then it would you know + + align:start position:0% +bigger and then it would you know + + + align:start position:0% +bigger and then it would you know +eventually it would cross through zero + + align:start position:0% +eventually it would cross through zero + + + align:start position:0% +eventually it would cross through zero +because the voltage would get negative + + align:start position:0% +because the voltage would get negative + + + align:start position:0% +because the voltage would get negative +and negative more and more negative + + align:start position:0% +and negative more and more negative + + + align:start position:0% +and negative more and more negative +right and then it would keep going Etc + + align:start position:0% +right and then it would keep going Etc + + + align:start position:0% +right and then it would keep going Etc +but what do I know I know that I can + + align:start position:0% +but what do I know I know that I can + + + align:start position:0% +but what do I know I know that I can +never go negative because the diode + + align:start position:0% +never go negative because the diode + + + align:start position:0% +never go negative because the diode +current would go + + align:start position:0% +current would go + + + align:start position:0% +current would go +negative so what would happen is if this + + align:start position:0% +negative so what would happen is if this + + + align:start position:0% +negative so what would happen is if this +was + + align:start position:0% + + + + align:start position:0% + +ID the I would stay on as long as ID is + + align:start position:0% +ID the I would stay on as long as ID is + + + align:start position:0% +ID the I would stay on as long as ID is +positive and when I ID tried to go + + align:start position:0% +positive and when I ID tried to go + + + align:start position:0% +positive and when I ID tried to go +negative this would go negative and the + + align:start position:0% +negative this would go negative and the + + + align:start position:0% +negative this would go negative and the +diode would just turn off and ID would + + align:start position:0% +diode would just turn off and ID would + + + align:start position:0% +diode would just turn off and ID would +go to zero it do something like this now + + align:start position:0% +go to zero it do something like this now + + + align:start position:0% +go to zero it do something like this now +what is exactly that solution look + + align:start position:0% +what is exactly that solution look + + + align:start position:0% +what is exactly that solution look +like you know we can calculate that it + + align:start position:0% +like you know we can calculate that it + + + align:start position:0% +like you know we can calculate that it +depends on the parameter values but what + + align:start position:0% +depends on the parameter values but what + + + align:start position:0% +depends on the parameter values but what +we can tell from all this is that at + + align:start position:0% +we can tell from all this is that at + + + align:start position:0% +we can tell from all this is that at +some point this Dow is going to turn off + + align:start position:0% +some point this Dow is going to turn off + + + align:start position:0% +some point this Dow is going to turn off +and it's going to limit the current and + + align:start position:0% +and it's going to limit the current and + + + align:start position:0% +and it's going to limit the current and +the current's not going to be a smooth + + align:start position:0% +the current's not going to be a smooth + + + align:start position:0% +the current's not going to be a smooth +constant current like I might want if I + + align:start position:0% +constant current like I might want if I + + + align:start position:0% +constant current like I might want if I +wanted a purely DC output current and + + align:start position:0% +wanted a purely DC output current and + + + align:start position:0% +wanted a purely DC output current and +voltage + + align:start position:0% + + + + align:start position:0% + +okay just to illustrate + + align:start position:0% +okay just to illustrate + + + align:start position:0% +okay just to illustrate +that I've got a simulation here to show + + align:start position:0% +that I've got a simulation here to show + + + align:start position:0% +that I've got a simulation here to show +you and all I did was go into LST spice + + align:start position:0% +you and all I did was go into LST spice + + + align:start position:0% +you and all I did was go into LST spice +which I encourage you to all down to + + align:start position:0% +which I encourage you to all down to + + + align:start position:0% +which I encourage you to all down to +download + + align:start position:0% +download + + + align:start position:0% +download +um and simulate it so here we have a + + align:start position:0% +um and simulate it so here we have a + + + align:start position:0% +um and simulate it so here we have a +sinusoidal voltage source an almost + + align:start position:0% +sinusoidal voltage source an almost + + + align:start position:0% +sinusoidal voltage source an almost +ideal diode we gave it a small forward + + align:start position:0% +ideal diode we gave it a small forward + + + align:start position:0% +ideal diode we gave it a small forward +drop but if we gave it zero forward drop + + align:start position:0% +drop but if we gave it zero forward drop + + + align:start position:0% +drop but if we gave it zero forward drop +it would be ideal we put in a big + + align:start position:0% +it would be ideal we put in a big + + + align:start position:0% +it would be ideal we put in a big +inductor and a resistor and here you can + + align:start position:0% +inductor and a resistor and here you can + + + align:start position:0% +inductor and a resistor and here you can +see in uh red we on the left axis we + + align:start position:0% +see in uh red we on the left axis we + + + align:start position:0% +see in uh red we on the left axis we +have voltage it's just a signal voltage + + align:start position:0% +have voltage it's just a signal voltage + + + align:start position:0% +have voltage it's just a signal voltage +and the the zero is here okay in the + + align:start position:0% +and the the zero is here okay in the + + + align:start position:0% +and the the zero is here okay in the +right hand axis you can see the diode + + align:start position:0% +right hand axis you can see the diode + + + align:start position:0% +right hand axis you can see the diode +current and what you can see is right + + align:start position:0% +current and what you can see is right + + + align:start position:0% +current and what you can see is right +when just sort of just after um the + + align:start position:0% +when just sort of just after um the + + + align:start position:0% +when just sort of just after um the +voltage crosses 0o positive the diode + + align:start position:0% +voltage crosses 0o positive the diode + + + align:start position:0% +voltage crosses 0o positive the diode +current starts to ramp up it goes up and + + align:start position:0% +current starts to ramp up it goes up and + + + align:start position:0% +current starts to ramp up it goes up and +up and up it hits about just under an + + align:start position:0% +up and up it hits about just under an + + + align:start position:0% +up and up it hits about just under an +amp but then the voltage gets + + align:start position:0% +amp but then the voltage gets + + + align:start position:0% +amp but then the voltage gets +negative and boom turns off okay if I + + align:start position:0% +negative and boom turns off okay if I + + + align:start position:0% +negative and boom turns off okay if I +plotted this voltage as + + align:start position:0% +plotted this voltage as + + + align:start position:0% +plotted this voltage as +well oops I'm not sure it gave me that + + align:start position:0% +well oops I'm not sure it gave me that + + + align:start position:0% +well oops I'm not sure it gave me that +yeah see we can see this thing where the + + align:start position:0% +yeah see we can see this thing where the + + + align:start position:0% +yeah see we can see this thing where the +diode the the voltage here which I + + align:start position:0% +diode the the voltage here which I + + + align:start position:0% +diode the the voltage here which I +plotted in + + align:start position:0% +plotted in + + + align:start position:0% +plotted in +yellow jumps back to zero this + + align:start position:0% +yellow jumps back to zero this + + + align:start position:0% +yellow jumps back to zero this +particular parameters Just Let It Go + + align:start position:0% +particular parameters Just Let It Go + + + align:start position:0% +particular parameters Just Let It Go +much more of the cycle does that make + + align:start position:0% +much more of the cycle does that make + + + align:start position:0% +much more of the cycle does that make +sense + + align:start position:0% +sense + + + align:start position:0% +sense +everybody any questions about + + align:start position:0% + + + + align:start position:0% + +that so what would I do to fix + + align:start position:0% +that so what would I do to fix + + + align:start position:0% +that so what would I do to fix +this right the real problem I have is + + align:start position:0% +this right the real problem I have is + + + align:start position:0% +this right the real problem I have is +what's going on + + align:start position:0% +what's going on + + + align:start position:0% +what's going on +here this voltage went positive diode + + align:start position:0% +here this voltage went positive diode + + + align:start position:0% +here this voltage went positive diode +turns on I start shoving current through + + align:start position:0% +turns on I start shoving current through + + + align:start position:0% +turns on I start shoving current through +the + + align:start position:0% +the + + + align:start position:0% +the +inductor okay voltage goes negative what + + align:start position:0% +inductor okay voltage goes negative what + + + align:start position:0% +inductor okay voltage goes negative what +I wanted to do and what happened over + + align:start position:0% +I wanted to do and what happened over + + + align:start position:0% +I wanted to do and what happened over +here + + align:start position:0% +here + + + align:start position:0% +here +okay was that when the voltage went + + align:start position:0% +okay was that when the voltage went + + + align:start position:0% +okay was that when the voltage went +negative the diode shut off and then I + + align:start position:0% +negative the diode shut off and then I + + + align:start position:0% +negative the diode shut off and then I +got zero which is what I wanted so I had + + align:start position:0% +got zero which is what I wanted so I had + + + align:start position:0% +got zero which is what I wanted so I had +positive the positive part of the sine + + align:start position:0% +positive the positive part of the sine + + + align:start position:0% +positive the positive part of the sine +wave and then zero for the other half + + align:start position:0% +wave and then zero for the other half + + + align:start position:0% +wave and then zero for the other half +and I got an average value here what + + align:start position:0% +and I got an average value here what + + + align:start position:0% +and I got an average value here what +happens is the inductor forces the diode + + align:start position:0% +happens is the inductor forces the diode + + + align:start position:0% +happens is the inductor forces the diode +to stay on and I get this chunk of + + align:start position:0% +to stay on and I get this chunk of + + + align:start position:0% +to stay on and I get this chunk of +negative voltage until the diode voltage + + align:start position:0% +negative voltage until the diode voltage + + + align:start position:0% +negative voltage until the diode voltage +averages to zero I'm sorry until the + + align:start position:0% +averages to zero I'm sorry until the + + + align:start position:0% +averages to zero I'm sorry until the +inductor current averages until the + + align:start position:0% +inductor current averages until the + + + align:start position:0% +inductor current averages until the +inductor voltage averages to zero in + + align:start position:0% +inductor voltage averages to zero in + + + align:start position:0% +inductor voltage averages to zero in +which case the circuit + + align:start position:0% +which case the circuit + + + align:start position:0% +which case the circuit +switches okay what could I do if I + + align:start position:0% +switches okay what could I do if I + + + align:start position:0% +switches okay what could I do if I +wanted it to do something more + + align:start position:0% +wanted it to do something more + + + align:start position:0% +wanted it to do something more +like this waveform but smooth the output + + align:start position:0% +like this waveform but smooth the output + + + align:start position:0% +like this waveform but smooth the output +well if I got clever I might say hey why + + align:start position:0% +well if I got clever I might say hey why + + + align:start position:0% +well if I got clever I might say hey why +don't I build + + align:start position:0% +don't I build + + + align:start position:0% +don't I build +Instead This + + align:start position:0% +Instead This + + + align:start position:0% +Instead This +circuit okay I will build this but + + align:start position:0% +circuit okay I will build this but + + + align:start position:0% +circuit okay I will build this but +instead of just having D let me call + + align:start position:0% +instead of just having D let me call + + + align:start position:0% +instead of just having D let me call +this + + align:start position:0% +this + + + align:start position:0% +this +D1 and I'll call this then id1 + + align:start position:0% + + + + align:start position:0% + +right my problem is that VX is going + + align:start position:0% +right my problem is that VX is going + + + align:start position:0% +right my problem is that VX is going +negative and then that means that you + + align:start position:0% +negative and then that means that you + + + align:start position:0% +negative and then that means that you +know sort of instead of getting this + + align:start position:0% +know sort of instead of getting this + + + align:start position:0% +know sort of instead of getting this +positive bump and then zero I'm getting + + align:start position:0% +positive bump and then zero I'm getting + + + align:start position:0% +positive bump and then zero I'm getting +this negative part because the inductor + + align:start position:0% +this negative part because the inductor + + + align:start position:0% +this negative part because the inductor +current is holding the diode on well + + align:start position:0% +current is holding the diode on well + + + align:start position:0% +current is holding the diode on well +maybe I can just get clever come in and + + align:start position:0% +maybe I can just get clever come in and + + + align:start position:0% +maybe I can just get clever come in and +add a second diode + + align:start position:0% +add a second diode + + + align:start position:0% +add a second diode +here + + align:start position:0% + + + + align:start position:0% + +D2 okay this diode D2 + + align:start position:0% +D2 okay this diode D2 + + + align:start position:0% +D2 okay this diode D2 +can take the inductor current so if I + + align:start position:0% +can take the inductor current so if I + + + align:start position:0% +can take the inductor current so if I +have I sub + + align:start position:0% +have I sub + + + align:start position:0% +have I sub +L now I sub D1 is going to be different + + align:start position:0% +L now I sub D1 is going to be different + + + align:start position:0% +L now I sub D1 is going to be different +than Isabel so I guess I'll have to give + + align:start position:0% +than Isabel so I guess I'll have to give + + + align:start position:0% +than Isabel so I guess I'll have to give +it a different color let me call this + + align:start position:0% +it a different color let me call this + + + align:start position:0% +it a different color let me call this +Isabel if anybody can see + + align:start position:0% +Isabel if anybody can see + + + align:start position:0% +Isabel if anybody can see +that okay so Isabel can now be big it + + align:start position:0% +that okay so Isabel can now be big it + + + align:start position:0% +that okay so Isabel can now be big it +doesn't have to go through D1 instead it + + align:start position:0% +doesn't have to go through D1 instead it + + + align:start position:0% +doesn't have to go through D1 instead it +can go through this diod + + align:start position:0% +can go through this diod + + + align:start position:0% +can go through this diod +D2 all right well how would I analyze + + align:start position:0% +D2 all right well how would I analyze + + + align:start position:0% +D2 all right well how would I analyze +this circuit well can do the method of + + align:start position:0% +this circuit well can do the method of + + + align:start position:0% +this circuit well can do the method of +assume States but now I have two + + align:start position:0% +assume States but now I have two + + + align:start position:0% +assume States but now I have two +switches right which could give me in + + align:start position:0% +switches right which could give me in + + + align:start position:0% +switches right which could give me in +theory up to four possible States right + + align:start position:0% +theory up to four possible States right + + + align:start position:0% +theory up to four possible States right +both off one off one on the other off + + align:start position:0% +both off one off one on the other off + + + align:start position:0% +both off one off one on the other off +the other on both on okay but if I'm + + align:start position:0% +the other on both on okay but if I'm + + + align:start position:0% +the other on both on okay but if I'm +clever maybe I assume that they're not + + align:start position:0% +clever maybe I assume that they're not + + + align:start position:0% +clever maybe I assume that they're not +both on at the same time typically or + + align:start position:0% +both on at the same time typically or + + + align:start position:0% +both on at the same time typically or +off at the same time + + align:start position:0% +off at the same time + + + align:start position:0% +off at the same time +hopefully so what would I do if I + + align:start position:0% +hopefully so what would I do if I + + + align:start position:0% +hopefully so what would I do if I +analyze this circuit and let me just + + align:start position:0% +analyze this circuit and let me just + + + align:start position:0% +analyze this circuit and let me just +assume the inductor is pretty big so + + align:start position:0% +assume the inductor is pretty big so + + + align:start position:0% +assume the inductor is pretty big so +that I is going to be approximately + + align:start position:0% +that I is going to be approximately + + + align:start position:0% +that I is going to be approximately +constant + + align:start position:0% +constant + + + align:start position:0% +constant +okay what would I get in that case I'd + + align:start position:0% +okay what would I get in that case I'd + + + align:start position:0% +okay what would I get in that case I'd +get something like + + align:start position:0% +get something like + + + align:start position:0% +get something like +this here's my sinusal + + align:start position:0% +this here's my sinusal + + + align:start position:0% +this here's my sinusal +voltage all right if my inductor + + align:start position:0% +voltage all right if my inductor + + + align:start position:0% +voltage all right if my inductor +current's + + align:start position:0% +current's + + + align:start position:0% +current's +positive okay suppose D2 was on as soon + + align:start position:0% +positive okay suppose D2 was on as soon + + + align:start position:0% +positive okay suppose D2 was on as soon +as vs Sin Omega T crosses zero + + align:start position:0% +as vs Sin Omega T crosses zero + + + align:start position:0% +as vs Sin Omega T crosses zero +positive if D2 was on this voltage would + + align:start position:0% +positive if D2 was on this voltage would + + + align:start position:0% +positive if D2 was on this voltage would +then get to be positive so I know as + + align:start position:0% +then get to be positive so I know as + + + align:start position:0% +then get to be positive so I know as +soon as I cross Z + + align:start position:0% +soon as I cross Z + + + align:start position:0% +soon as I cross Z +positive d1's going to be + + align:start position:0% +positive d1's going to be + + + align:start position:0% +positive d1's going to be +on in this + + align:start position:0% +on in this + + + align:start position:0% +on in this +range right and I'm going to get a + + align:start position:0% +range right and I'm going to get a + + + align:start position:0% +range right and I'm going to get a +voltage VX that looks like this it's + + align:start position:0% +voltage VX that looks like this it's + + + align:start position:0% +voltage VX that looks like this it's +going to + + align:start position:0% + + + + align:start position:0% + +follow this now what happens when VX + + align:start position:0% +follow this now what happens when VX + + + align:start position:0% +follow this now what happens when VX +goes negative if I assume that D1 is + + align:start position:0% +goes negative if I assume that D1 is + + + align:start position:0% +goes negative if I assume that D1 is +on and vs Sin Omega T goes to becomes + + align:start position:0% +on and vs Sin Omega T goes to becomes + + + align:start position:0% +on and vs Sin Omega T goes to becomes +negative and D was off I'd have this + + align:start position:0% + + + + align:start position:0% + +configuration I'm assuming he's on and + + align:start position:0% +configuration I'm assuming he's on and + + + align:start position:0% +configuration I'm assuming he's on and +I'm assuming he's + + align:start position:0% +I'm assuming he's + + + align:start position:0% +I'm assuming he's +off and you know my inductor current's + + align:start position:0% +off and you know my inductor current's + + + align:start position:0% +off and you know my inductor current's +doing something here + + align:start position:0% +doing something here + + + align:start position:0% +doing something here +right this diode 2 + + align:start position:0% +right this diode 2 + + + align:start position:0% +right this diode 2 +voltage if VSS sin Omega + + align:start position:0% + + + + align:start position:0% + +T becomes negative that means this diode + + align:start position:0% +T becomes negative that means this diode + + + align:start position:0% +T becomes negative that means this diode +voltage would become + + align:start position:0% +voltage would become + + + align:start position:0% +voltage would become +positive can I have a positive diode + + align:start position:0% +positive can I have a positive diode + + + align:start position:0% +positive can I have a positive diode +voltage no that means that this diode + + align:start position:0% +voltage no that means that this diode + + + align:start position:0% +voltage no that means that this diode +must turn on when this voltage goes to + + align:start position:0% +must turn on when this voltage goes to + + + align:start position:0% +must turn on when this voltage goes to +zero so the minimum I know that D2 has + + align:start position:0% +zero so the minimum I know that D2 has + + + align:start position:0% +zero so the minimum I know that D2 has +to be on + + align:start position:0% +to be on + + + align:start position:0% +to be on +here now if I assumed that both D1 and + + align:start position:0% +here now if I assumed that both D1 and + + + align:start position:0% +here now if I assumed that both D1 and +D2 were on here I'd be shorting out the + + align:start position:0% +D2 were on here I'd be shorting out the + + + align:start position:0% +D2 were on here I'd be shorting out the +source so that can't happen so what + + align:start position:0% +source so that can't happen so what + + + align:start position:0% +source so that can't happen so what +happens is it when I cross this point + + align:start position:0% +happens is it when I cross this point + + + align:start position:0% +happens is it when I cross this point +this diode turns on and this diode turns + + align:start position:0% +this diode turns on and this diode turns + + + align:start position:0% +this diode turns on and this diode turns +off and what I will get is when the + + align:start position:0% +off and what I will get is when the + + + align:start position:0% +off and what I will get is when the +bottom diode's on VX is going to be zero + + align:start position:0% +bottom diode's on VX is going to be zero + + + align:start position:0% +bottom diode's on VX is going to be zero +okay and I'm going to get something that + + align:start position:0% +okay and I'm going to get something that + + + align:start position:0% +okay and I'm going to get something that +looks like + + align:start position:0% + + + + align:start position:0% + +this and I get the waveform I had before + + align:start position:0% +this and I get the waveform I had before + + + align:start position:0% +this and I get the waveform I had before +but now what happens I'm applying this + + align:start position:0% +but now what happens I'm applying this + + + align:start position:0% +but now what happens I'm applying this +yellow waveform + + align:start position:0% + + + + align:start position:0% + +vx to this big LR filter well if the L's + + align:start position:0% +vx to this big LR filter well if the L's + + + align:start position:0% +vx to this big LR filter well if the L's +really + + align:start position:0% +really + + + align:start position:0% +really +big it + + align:start position:0% +big it + + + align:start position:0% +big it +extracts this and I get V + + align:start position:0% +extracts this and I get V + + + align:start position:0% +extracts this and I get V +out is equal to the is approximately + + align:start position:0% +out is equal to the is approximately + + + align:start position:0% +out is equal to the is approximately +equal to the average of VX right so the + + align:start position:0% +equal to the average of VX right so the + + + align:start position:0% +equal to the average of VX right so the +average of V + + align:start position:0% + + + + align:start position:0% + +out right well what's the average of + + align:start position:0% +out right well what's the average of + + + align:start position:0% +out right well what's the average of +voltage VX well I would say that the + + align:start position:0% +voltage VX well I would say that the + + + align:start position:0% +voltage VX well I would say that the +average value of VX is simply 1 over 2 + + align:start position:0% +average value of VX is simply 1 over 2 + + + align:start position:0% +average value of VX is simply 1 over 2 +pi the integral + + align:start position:0% +pi the integral + + + align:start position:0% +pi the integral +from 0 to + + align:start position:0% + + + + align:start position:0% + +Pi of vs Sin Omega + + align:start position:0% +Pi of vs Sin Omega + + + align:start position:0% +Pi of vs Sin Omega +t d Omega t because I did everything an + + align:start position:0% +t d Omega t because I did everything an + + + align:start position:0% +t d Omega t because I did everything an +electrical angle here instead of time + + align:start position:0% +electrical angle here instead of time + + + align:start position:0% +electrical angle here instead of time +okay if I take this integral this just + + align:start position:0% +okay if I take this integral this just + + + align:start position:0% +okay if I take this integral this just +ends up being VSS this means being + + align:start position:0% +ends up being VSS this means being + + + align:start position:0% +ends up being VSS this means being +cosine of 0us cosine of pi this just + + align:start position:0% +cosine of 0us cosine of pi this just + + + align:start position:0% +cosine of 0us cosine of pi this just +ends up being vs over + + align:start position:0% +ends up being vs over + + + align:start position:0% +ends up being vs over +PI right so what I can say is the + + align:start position:0% +PI right so what I can say is the + + + align:start position:0% +PI right so what I can say is the +average value of VX + + align:start position:0% +average value of VX + + + align:start position:0% +average value of VX +here is just going to be vs over + + align:start position:0% +here is just going to be vs over + + + align:start position:0% +here is just going to be vs over +pi and because the average value of + + align:start position:0% +pi and because the average value of + + + align:start position:0% +pi and because the average value of +across the inductor zero that means V + + align:start position:0% +across the inductor zero that means V + + + align:start position:0% +across the inductor zero that means V +out has to be approximately vs over pi + + align:start position:0% +out has to be approximately vs over pi + + + align:start position:0% +out has to be approximately vs over pi +Pi so basically V out is going to be + + align:start position:0% +Pi so basically V out is going to be + + + align:start position:0% +Pi so basically V out is going to be +basically vs over pi and now I've got a + + align:start position:0% +basically vs over pi and now I've got a + + + align:start position:0% +basically vs over pi and now I've got a +DC output current and a DC output + + align:start position:0% +DC output current and a DC output + + + align:start position:0% +DC output current and a DC output +voltage which is what I wanted out of + + align:start position:0% +voltage which is what I wanted out of + + + align:start position:0% +voltage which is what I wanted out of +the + + align:start position:0% +the + + + align:start position:0% +the +circuit okay let me just show you that + + align:start position:0% +circuit okay let me just show you that + + + align:start position:0% +circuit okay let me just show you that +really + + align:start position:0% +really + + + align:start position:0% +really +quickly okay if I put down this + + align:start position:0% +quickly okay if I put down this + + + align:start position:0% +quickly okay if I put down this +simulation I'll put up my other + + align:start position:0% +simulation I'll put up my other + + + align:start position:0% +simulation I'll put up my other +simulation all we've done + + align:start position:0% +simulation all we've done + + + align:start position:0% +simulation all we've done +here is I've added a second + + align:start position:0% +here is I've added a second + + + align:start position:0% +here is I've added a second +diode okay this is what's known as a + + align:start position:0% +diode okay this is what's known as a + + + align:start position:0% +diode okay this is what's known as a +halfwave rectifier let me show you two + + align:start position:0% +halfwave rectifier let me show you two + + + align:start position:0% +halfwave rectifier let me show you two +things first of all you can see vs Sin + + align:start position:0% +things first of all you can see vs Sin + + + align:start position:0% +things first of all you can see vs Sin +Omega T here is this red which is on the + + align:start position:0% +Omega T here is this red which is on the + + + align:start position:0% +Omega T here is this red which is on the +left axis I'm sorry this is this is V + + align:start position:0% +left axis I'm sorry this is this is V + + + align:start position:0% +left axis I'm sorry this is this is V +subx I'm sorry this is my yellow + + align:start position:0% +subx I'm sorry this is my yellow + + + align:start position:0% +subx I'm sorry this is my yellow +waveform over here but look at the + + align:start position:0% +waveform over here but look at the + + + align:start position:0% +waveform over here but look at the +inductor + + align:start position:0% +inductor + + + align:start position:0% +inductor +current what do you think's happening + + align:start position:0% +current what do you think's happening + + + align:start position:0% +current what do you think's happening +here this is the inductor current + + align:start position:0% +here this is the inductor current + + + align:start position:0% +here this is the inductor current +building up over time the blue waveform + + align:start position:0% +building up over time the blue waveform + + + align:start position:0% +building up over time the blue waveform +is Isabel starting at some time equals + + align:start position:0% +is Isabel starting at some time equals + + + align:start position:0% +is Isabel starting at some time equals +zero it's it's not constant if I look at + + align:start position:0% +zero it's it's not constant if I look at + + + align:start position:0% +zero it's it's not constant if I look at +this would you say that this blue + + align:start position:0% +this would you say that this blue + + + align:start position:0% +this would you say that this blue +waveform you can see all these Cycles + + align:start position:0% +waveform you can see all these Cycles + + + align:start position:0% +waveform you can see all these Cycles +going on is the blue waveform in + + align:start position:0% +going on is the blue waveform in + + + align:start position:0% +going on is the blue waveform in +periodic steady + + align:start position:0% +periodic steady + + + align:start position:0% +periodic steady +state no it's it's ramping up over time + + align:start position:0% +state no it's it's ramping up over time + + + align:start position:0% +state no it's it's ramping up over time +so anything I might say about steady + + align:start position:0% +so anything I might say about steady + + + align:start position:0% +so anything I might say about steady +state operation is not true down here + + align:start position:0% +state operation is not true down here + + + align:start position:0% +state operation is not true down here +right after I've started this circuit up + + align:start position:0% +right after I've started this circuit up + + + align:start position:0% +right after I've started this circuit up +and it's coming up right real circuits + + align:start position:0% +and it's coming up right real circuits + + + align:start position:0% +and it's coming up right real circuits +have Dynamics it's doing something + + align:start position:0% +have Dynamics it's doing something + + + align:start position:0% +have Dynamics it's doing something +Dynamic but the interesting thing is + + align:start position:0% +Dynamic but the interesting thing is + + + align:start position:0% +Dynamic but the interesting thing is +eventually I get way over here and look + + align:start position:0% +eventually I get way over here and look + + + align:start position:0% +eventually I get way over here and look +at this if I come over here and let me + + align:start position:0% +at this if I come over here and let me + + + align:start position:0% +at this if I come over here and let me +just zoom in on this right hand portion + + align:start position:0% +just zoom in on this right hand portion + + + align:start position:0% +just zoom in on this right hand portion +of the circuit after I've waited for a + + align:start position:0% +of the circuit after I've waited for a + + + align:start position:0% +of the circuit after I've waited for a +while + + align:start position:0% +while + + + align:start position:0% +while +h everything's repeating every cycle + + align:start position:0% +h everything's repeating every cycle + + + align:start position:0% +h everything's repeating every cycle +that's periodic state state operation + + align:start position:0% +that's periodic state state operation + + + align:start position:0% +that's periodic state state operation +and the interesting thing is if I look + + align:start position:0% +and the interesting thing is if I look + + + align:start position:0% +and the interesting thing is if I look +at this + + align:start position:0% +at this + + + align:start position:0% +at this +um if I look + + align:start position:0% +um if I look + + + align:start position:0% +um if I look +at this inductor currence almost + + align:start position:0% +at this inductor currence almost + + + align:start position:0% +at this inductor currence almost +constant okay VX is exactly this + + align:start position:0% +constant okay VX is exactly this + + + align:start position:0% +constant okay VX is exactly this +halfwave rectified + + align:start position:0% +halfwave rectified + + + align:start position:0% +halfwave rectified +waveform if I looked at the voltage here + + align:start position:0% +waveform if I looked at the voltage here + + + align:start position:0% +waveform if I looked at the voltage here +um and I will now look at it it it is um + + align:start position:0% +um and I will now look at it it it is um + + + align:start position:0% +um and I will now look at it it it is um +um almost constant and it's just about + + align:start position:0% +um almost constant and it's just about + + + align:start position:0% +um almost constant and it's just about +1/3 or one over pi times the peak value + + align:start position:0% +1/3 or one over pi times the peak value + + + align:start position:0% +1/3 or one over pi times the peak value +of the sine wave right so we've been + + align:start position:0% +of the sine wave right so we've been + + + align:start position:0% +of the sine wave right so we've been +able to use the fact that I understand + + align:start position:0% +able to use the fact that I understand + + + align:start position:0% +able to use the fact that I understand +the average value across the inductor to + + align:start position:0% +the average value across the inductor to + + + align:start position:0% +the average value across the inductor to +tell us what the output voltage of this + + align:start position:0% +tell us what the output voltage of this + + + align:start position:0% +tell us what the output voltage of this +thing is going to be in periodic steady + + align:start position:0% +thing is going to be in periodic steady + + + align:start position:0% +thing is going to be in periodic steady +state so to conclude what we've got is + + align:start position:0% +state so to conclude what we've got is + + + align:start position:0% +state so to conclude what we've got is +method of assume states to figure out + + align:start position:0% +method of assume states to figure out + + + align:start position:0% +method of assume states to figure out +when our diodes are turning on and off + + align:start position:0% +when our diodes are turning on and off + + + align:start position:0% +when our diodes are turning on and off +and period state state operation where + + align:start position:0% +and period state state operation where + + + align:start position:0% +and period state state operation where +we can use some of those relationships + + align:start position:0% +we can use some of those relationships + + + align:start position:0% +we can use some of those relationships +to start figuring out what voltages and + + align:start position:0% +to start figuring out what voltages and + + + align:start position:0% +to start figuring out what voltages and +currents I'll get in my + + align:start position:0% +currents I'll get in my + + + align:start position:0% +currents I'll get in my +circuit that's all for today I'm I'm + + align:start position:0% +circuit that's all for today I'm I'm + + + align:start position:0% +circuit that's all for today I'm I'm +like a minute over but if there's any + + align:start position:0% +like a minute over but if there's any + + + align:start position:0% +like a minute over but if there's any +last minute question I'll happily take + + align:start position:0% + + + + align:start position:0% + +it okay have a great day I'll see you + + align:start position:0% +it okay have a great day I'll see you + + + align:start position:0% +it okay have a great day I'll see you +next class \ No newline at end of file diff --git a/br3mu-IK9N8.txt b/br3mu-IK9N8.txt new file mode 100644 index 0000000000000000000000000000000000000000..0f2f9755be7b145f8230dd8af0af8bfcd63c01a8 --- /dev/null +++ b/br3mu-IK9N8.txt @@ -0,0 +1,371 @@ +Okay, now that we understand how to build +combinational logic gates using CMOS, let's + +turn our attention to the timing specifications +for the gates. + +Here's a simple circuit consisting of two +CMOS inverters connected in series, which + +we'll use to understand how to characterize +the timing of the inverter on the left. + +It will be helpful to build an electrical +model of what happens when we change V_IN, + +the voltage on the input to the left inverter. + +If V_IN makes a transition from a digital +0 to a digital 1, the PFET switch in the pullup + +turns off and the NFET switch in pulldown +turns on, connecting the output node of the + +left inverter to GROUND. + +The electrical model for this node includes +the distributed resistance and capacitance + +of the physical wire connecting the output +of the left inverter to the input of the right + +inverter. + +And there is also capacitance associated with +the gate terminals of the MOSFETs in the right + +inverter. + +When the output node is connected to GROUND, +the charge on this capacitance will flow towards + +the GROUND connection through the resistance +of the wire and the resistance of the conducting + +channel of the NFET pulldown switch. + +Eventually the voltage on the wire will reach +the potential of the GROUND connection, 0V. + +The process is much the same for falling transitions +on V_IN, which cause the output node to charge + +up to V_DD. + +Now let's look at the voltage waveforms as +a function of time. + +The top plot shows both a rising and, later, +a falling transition for V_IN. + +We see that the output waveform has the characteristic +exponential shape for the voltage of a capacitor + +being discharged or charged though a resistor. + +The exponential is characterized by its associated +R-C time constant, where, in this case, the + +R is the net resistance of the wire and MOSFET +channel, and the C is the net capacitance + +of the wire and MOSFET gate terminals. + +Since neither the input nor output transition +is instantaneous, we have some choices to + +make about how to measure the inverter's propagation +delay. + +Happily, we have just the guidance we need +from our signaling thresholds! + +The propagation delay of a combinational logic +gate is defined to be an upper bound on the + +delay from valid inputs to valid outputs. + +Valid input voltages are defined by the V_IL +and V_IH signaling thresholds, and valid output + +voltages are defined by the V_OL and V_OH +signaling thresholds. + +We've shown these thresholds on the waveform +plots. + +To measure the delay associated with the rising +transition on V_IN, first identify the time + +when the input becomes a valid digital 1, +i.e., the time at which V_IN crosses the V_IH + +threshold. + +Next identify the time when the output becomes +a valid digital 0, i.e., the time at which + +V_OUT crosses the V_OL threshold. + +The interval between these two time points +is the delay for this particular set of input + +and output transitions. + +We can go through the same process to measure +the delay associated with a falling input + +transition. + +First, identify the time at which V_IN cross +the V_IL threshold. + +Then find the time at which V_OUT crosses +the V_OH threshold. + +The resulting interval is the delay we wanted +to measure. + +Since the propagation delay, t_PD, is an upper +bound on the delay associated with *any* input + +transition, we'll choose a value for t_PD +that's greater than or equal to the measurements + +we just made. + +When a manufacturer selects the t_PD specification +for a gate, it must take into account manufacturing + +variations, the effects of different environmental +conditions such as temperature and power-supply + +voltage, and so on. + +It should choose a t_PD that will be an upper +bound on any delay measurements their customers + +might make on actual devices. + +From the designer's point of view, we can +rely on this upper bound for each component + +of a larger digital system and use it to calculate +the system's t_PD without having to repeat + +all the manufacturer's measurements. + +If our goal is to minimize the propagation +delay of our system, then we'll want to keep + +the capacitances and resistances as small +as possible. + +There's an interesting tension here: to make +the effective resistance of a MOSFET switch + +smaller, we would increase its width. + +But that would add additional capacitance +to the switch's gate terminal, slowing down + +transitions on the input node that connects +to the gate! + +It's a fun optimization problem to figure +out transistor sizing that minimizes the overall + +propagation delay. + +Although not strictly required by the static +discipline, it will be useful to define another + +timing specification, called the "contamination +delay". + +It measures how long a gate's previous output +value remains valid after the gate's inputs + +start to change and become invalid. + +Technically, the contamination delay will +be a lower bound on the delay from an invalid + +input to an invalid output. + +We'll make the delay measurements much as +we did for the propagation delay. + +On a rising input transition, the delay starts +when the input is no longer a valid digital + +0, i.e., when V_IN crosses the V_IL threshold. + +And the delay ends when the output becomes +invalid, i.e., when V_OUT crosses the V_OH + +threshold. + +We can make a similar delay measurement for +the falling input transition. + +Since the contamination delay, t_CD, is a +lower bound on the delay associated with *any* + +input transition, we'll choose a value for +t_CD that's less than or equal to the measurements + +we just made. + +Do we really need the contamination delay +specification? + +Usually not. + +And if not's specified, designers should assume +that the t_CD for a combinational device is + +0. + +In other words a conservative assumption is +that the outputs go invalid as soon as the + +inputs go invalid. + +By the way, manufacturers often use the term +"minimum propagation delay" to refer to a + +device's contamination delay. + +That terminology is a bit confusing, but now +you know what it is they're trying to tell + +you. + +So here's a quick summary of the timing specifications +for combinational logic. + +These specifications tell us how the timing +of changes in the output waveform (labeled + +B in this example) are related to the timing +of changes in the input waveform (labeled + +A). + +A combinational device may retain its previous +output value for some interval of time after + +an input transition. + +The contamination delay of the device is a +guarantee on the minimum size of that interval, + +i.e., t_CD is a lower bound on how long the +old output value stays valid. + +As stated in Note 2, a conservative assumption +is that the contamination delay of a device + +is 0, meaning the device's output may change +immediately after an input transition. + +So t_CD gives us information on when B will +start to change. + +Similarly, it would be good to know when B +is guaranteed to be done changing after an + +input transition. + +In other words, how long do we have to wait +for a change in the inputs to reflected in + +an updated value on the outputs? + +This is what t_PD tells us since it is a upper +bound on the time it takes for B to become + +valid and stable after an input transition. + +As Note 1 points out, in general there are +no guarantees on the behavior of the output + +in the interval after t_CD and before t_PD, +as measured from the input transition. + +It would legal for the B output to change +several times in that interval, or even have + +a non-digital voltage for any part of the +interval. + +As we'll see in the last video of this chapter, +we'll be able to offer more insights into + +B's behavior in this interval for a subclass +of combinational devices. + +But in general, a designer should make no +assumptions about B's value in the interval + +between t_CD and t_PD. + +How do we calculate the propagation and contamination +delays of a larger combinational circuit from + +the timing specifications of its components? + +Our example is a circuit of four NAND gates +where each NAND has a t_PD of 4 ns and t_CD + +of 1 ns. + +To find the propagation delay for the larger +circuit, we need to find the maximum delay + +from an input transition on nodes A, B, or +C to a valid and stable value on the output + +Y. + +To do this, consider each possible path from +one of the inputs to Y and compute the path + +delay by summing the t_PDs of the components +along the path. + +Choose the largest such path delay as the +t_PD of the overall circuit. + +In our example, the largest delay is a path +that includes three NAND gates, with a cumulative + +propagation delay of 12 ns. + +In other words, the output Y is guaranteed +be stable and valid within 12 ns of a transition + +on A, B, or C. +To find the contamination delay for the larger + +circuit, we again investigate all paths from +inputs to outputs, but this time we're looking + +for the shortest path from an invalid input +to an invalid output. + +So we sum the t_CDs of the components along +each path and choose the smallest such path + +delay as the t_CD of the overall circuit. + +In our example, the smallest delay is a path +that includes two NAND gates with a cumulative + +contamination delay of 2 ns. + +In other words, the output Y will retain its +previous value for at least 2 ns after one + +of the inputs goes invalid. \ No newline at end of file diff --git a/cQpCPzetm3E.txt b/cQpCPzetm3E.txt new file mode 100644 index 0000000000000000000000000000000000000000..31cd692e5b6fe11a168d8878e05b9bc98b0853c9 --- /dev/null +++ b/cQpCPzetm3E.txt @@ -0,0 +1,11384 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu um so I was just going to be + + align:start position:0% +ocw.mit.edu um so I was just going to be + + + align:start position:0% +ocw.mit.edu um so I was just going to be +here + + align:start position:0% + + + + align:start position:0% + +questions what's the uh that we covering + + align:start position:0% +questions what's the uh that we covering + + + align:start position:0% +questions what's the uh that we covering +the test um so the test covers + + align:start position:0% +the test um so the test covers + + + align:start position:0% +the test um so the test covers +everything up to the end of the part on + + align:start position:0% +everything up to the end of the part on + + + align:start position:0% +everything up to the end of the part on +modeling phones but not the bit on the + + align:start position:0% +modeling phones but not the bit on the + + + align:start position:0% +modeling phones but not the bit on the +performance Industries and the material + + align:start position:0% +performance Industries and the material + + + align:start position:0% +performance Industries and the material +selection charts for + + align:start position:0% +selection charts for + + + align:start position:0% +selection charts for +Foams so I think up to the end of the + + align:start position:0% +Foams so I think up to the end of the + + + align:start position:0% +Foams so I think up to the end of the +fracture toughness of Foams I see okay + + align:start position:0% +fracture toughness of Foams I see okay + + + align:start position:0% +fracture toughness of Foams I see okay +yeah so not covering + + align:start position:0% + + + + align:start position:0% + +the not not covering thermal proper + + align:start position:0% +the not not covering thermal proper + + + align:start position:0% +the not not covering thermal proper +doesn't cover + + align:start position:0% + + + + align:start position:0% + +properties I at the very + + align:start position:0% + + + + align:start position:0% + +back there you + + align:start position:0% +back there you + + + align:start position:0% +back there you +go so you know I got this McVicker award + + align:start position:0% +go so you know I got this McVicker award + + + align:start position:0% +go so you know I got this McVicker award +and we had a lunch on Friday in at the + + align:start position:0% +and we had a lunch on Friday in at the + + + align:start position:0% +and we had a lunch on Friday in at the +Catalyst restaurant and I had to get up + + align:start position:0% +Catalyst restaurant and I had to get up + + + align:start position:0% +Catalyst restaurant and I had to get up +and speak and just as I got up and spoke + + align:start position:0% +and speak and just as I got up and spoke + + + align:start position:0% +and speak and just as I got up and spoke +there was a red tail talk like swoop by + + align:start position:0% +there was a red tail talk like swoop by + + + align:start position:0% +there was a red tail talk like swoop by +the window perfect it's + + align:start position:0% + + + + align:start position:0% + +perfect yeah hi so I'm just I'm just + + align:start position:0% +perfect yeah hi so I'm just I'm just + + + align:start position:0% +perfect yeah hi so I'm just I'm just +here to answer questions so come on + + align:start position:0% +here to answer questions so come on + + + align:start position:0% +here to answer questions so come on +somebody must have questions it's all + + align:start position:0% +somebody must have questions it's all + + + align:start position:0% +somebody must have questions it's all +perfectly + + align:start position:0% +perfectly + + + align:start position:0% +perfectly +clear you want me to do through uh test + + align:start position:0% +clear you want me to do through uh test + + + align:start position:0% +clear you want me to do through uh test +one from last year a little bit you have + + align:start position:0% +one from last year a little bit you have + + + align:start position:0% +one from last year a little bit you have +to give me test one from last year I + + align:start position:0% +to give me test one from last year I + + + align:start position:0% +to give me test one from last year I +didn't bring it with me I just brought + + align:start position:0% +didn't bring it with me I just brought + + + align:start position:0% +didn't bring it with me I just brought +the problem set I have it on my computer + + align:start position:0% +the problem set I have it on my computer + + + align:start position:0% +the problem set I have it on my computer +and I could read you the problems or + + align:start position:0% +and I could read you the problems or + + + align:start position:0% +and I could read you the problems or +just hand you the laptop uh + + align:start position:0% +just hand you the laptop uh + + + align:start position:0% +just hand you the laptop uh +why don't you hand me the laptop and + + align:start position:0% +why don't you hand me the laptop and + + + align:start position:0% +why don't you hand me the laptop and +I'll try to do it is that okay + + align:start position:0% +I'll try to do it is that okay + + + align:start position:0% +I'll try to do it is that okay +y okay so the question is about the test + + align:start position:0% +y okay so the question is about the test + + + align:start position:0% +y okay so the question is about the test +for + + align:start position:0% +for + + + align:start position:0% +for +2014 okay so the first question was + + align:start position:0% +2014 okay so the first question was + + + align:start position:0% +2014 okay so the first question was +describe four processes for making + + align:start position:0% +describe four processes for making + + + align:start position:0% +describe four processes for making +Honeycombs and comment on the type of + + align:start position:0% +Honeycombs and comment on the type of + + + align:start position:0% +Honeycombs and comment on the type of +material usually used for each process + + align:start position:0% +material usually used for each process + + + align:start position:0% +material usually used for each process +so I did post the solutions right did + + align:start position:0% +so I did post the solutions right did + + + align:start position:0% +so I did post the solutions right did +you look at that yeah I looked at them I + + align:start position:0% +you look at that yeah I looked at them I + + + align:start position:0% +you look at that yeah I looked at them I +guess I just feel + + align:start position:0% +guess I just feel + + + align:start position:0% +guess I just feel +like I don't fully understand why + + align:start position:0% +like I don't fully understand why + + + align:start position:0% +like I don't fully understand why +the way there but I can look at it okay + + align:start position:0% +the way there but I can look at it okay + + + align:start position:0% +the way there but I can look at it okay +well I can go over it if you want it's + + align:start position:0% +well I can go over it if you want it's + + + align:start position:0% +well I can go over it if you want it's +just I'll just look at it somewhere no + + align:start position:0% +just I'll just look at it somewhere no + + + align:start position:0% +just I'll just look at it somewhere no +no I can go over it so so four processes + + align:start position:0% +no I can go over it so so four processes + + + align:start position:0% +no I can go over it so so four processes +let's see so there's the expansion + + align:start position:0% +let's see so there's the expansion + + + align:start position:0% +let's see so there's the expansion +process where you take sheets and you + + align:start position:0% +process where you take sheets and you + + + align:start position:0% +process where you take sheets and you +glue the sheets together and then you + + align:start position:0% +glue the sheets together and then you + + + align:start position:0% +glue the sheets together and then you +pull them apart so you can only really + + align:start position:0% +pull them apart so you can only really + + + align:start position:0% +pull them apart so you can only really +use that process for materials that are + + align:start position:0% +use that process for materials that are + + + align:start position:0% +use that process for materials that are +going to have large plastic deformations + + align:start position:0% +going to have large plastic deformations + + + align:start position:0% +going to have large plastic deformations +so you could use it for Metals some + + align:start position:0% +so you could use it for Metals some + + + align:start position:0% +so you could use it for Metals some +polymers but you couldn't really use it + + align:start position:0% +polymers but you couldn't really use it + + + align:start position:0% +polymers but you couldn't really use it +for Ceramics you know you couldn't use + + align:start position:0% +for Ceramics you know you couldn't use + + + align:start position:0% +for Ceramics you know you couldn't use +it for a glass cuz you couldn't as soon + + align:start position:0% +it for a glass cuz you couldn't as soon + + + align:start position:0% +it for a glass cuz you couldn't as soon +as you yanked on it you'd break the + + align:start position:0% +as you yanked on it you'd break the + + + align:start position:0% +as you yanked on it you'd break the +sheets right so is rigid polymers that + + align:start position:0% +sheets right so is rigid polymers that + + + align:start position:0% +sheets right so is rigid polymers that +you can use it for or well something + + align:start position:0% +you can use it for or well something + + + align:start position:0% +you can use it for or well something +like nylon you could use it for you know + + align:start position:0% +like nylon you could use it for you know + + + align:start position:0% +like nylon you could use it for you know +something that's got that'll yield + + align:start position:0% +something that's got that'll yield + + + align:start position:0% +something that's got that'll yield +that'll have some sort of yield Point + + align:start position:0% +that'll have some sort of yield Point + + + align:start position:0% +that'll have some sort of yield Point +not like if you had epoxy you couldn't + + align:start position:0% +not like if you had epoxy you couldn't + + + align:start position:0% +not like if you had epoxy you couldn't +use it for epoxy so okay so that's one + + align:start position:0% +use it for epoxy so okay so that's one + + + align:start position:0% +use it for epoxy so okay so that's one +process another process is a corrugation + + align:start position:0% +process another process is a corrugation + + + align:start position:0% +process another process is a corrugation +process where you have a wheel that has + + align:start position:0% +process where you have a wheel that has + + + align:start position:0% +process where you have a wheel that has +little kind of like gear knobs on it and + + align:start position:0% +little kind of like gear knobs on it and + + + align:start position:0% +little kind of like gear knobs on it and +uh you run your flat sheet through that + + align:start position:0% +uh you run your flat sheet through that + + + align:start position:0% +uh you run your flat sheet through that +and it comes out with the half hexagonal + + align:start position:0% +and it comes out with the half hexagonal + + + align:start position:0% +and it comes out with the half hexagonal +profile and you glue those together so + + align:start position:0% +profile and you glue those together so + + + align:start position:0% +profile and you glue those together so +again you need something that's going to + + align:start position:0% +again you need something that's going to + + + align:start position:0% +again you need something that's going to +yield so that would typically be a metal + + align:start position:0% +yield so that would typically be a metal + + + align:start position:0% +yield so that would typically be a metal +that you would use that with um let's + + align:start position:0% +that you would use that with um let's + + + align:start position:0% +that you would use that with um let's +see another process for making + + align:start position:0% +see another process for making + + + align:start position:0% +see another process for making +Honeycombs is 3D printing you can 3D + + align:start position:0% +Honeycombs is 3D printing you can 3D + + + align:start position:0% +Honeycombs is 3D printing you can 3D +print Honeycombs and there's different + + align:start position:0% +print Honeycombs and there's different + + + align:start position:0% +print Honeycombs and there's different +ways to do it um one way is by having an + + align:start position:0% +ways to do it um one way is by having an + + + align:start position:0% +ways to do it um one way is by having an +ink and so you know if you want to print + + align:start position:0% +ink and so you know if you want to print + + + align:start position:0% +ink and so you know if you want to print +an ink typically that's some sort of + + align:start position:0% +an ink typically that's some sort of + + + align:start position:0% +an ink typically that's some sort of +polymer that you're printing I suppose I + + align:start position:0% +polymer that you're printing I suppose I + + + align:start position:0% +polymer that you're printing I suppose I +mean physically it's possible to print + + align:start position:0% +mean physically it's possible to print + + + align:start position:0% +mean physically it's possible to print +glass or to print a metal but you'd have + + align:start position:0% +glass or to print a metal but you'd have + + + align:start position:0% +glass or to print a metal but you'd have +to have some very high temperature sit + + align:start position:0% +to have some very high temperature sit + + + align:start position:0% +to have some very high temperature sit +set up to do that so typically um a + + align:start position:0% +set up to do that so typically um a + + + align:start position:0% +set up to do that so typically um a +resin of some sort um let's see other + + align:start position:0% +resin of some sort um let's see other + + + align:start position:0% +resin of some sort um let's see other +ways to make Honeycombs you can extrude + + align:start position:0% +ways to make Honeycombs you can extrude + + + align:start position:0% +ways to make Honeycombs you can extrude +Honeycombs so the ceramic Honeycombs we + + align:start position:0% +Honeycombs so the ceramic Honeycombs we + + + align:start position:0% +Honeycombs so the ceramic Honeycombs we +saw were made by extruding a ceramic + + align:start position:0% +saw were made by extruding a ceramic + + + align:start position:0% +saw were made by extruding a ceramic +slurry and typically you would do that + + align:start position:0% +slurry and typically you would do that + + + align:start position:0% +slurry and typically you would do that +with a ceramic that's you know a slurry + + align:start position:0% +with a ceramic that's you know a slurry + + + align:start position:0% +with a ceramic that's you know a slurry +and a powder you wouldn't necessarily do + + align:start position:0% +and a powder you wouldn't necessarily do + + + align:start position:0% +and a powder you wouldn't necessarily do +that with a metal I don't think I've + + align:start position:0% +that with a metal I don't think I've + + + align:start position:0% +that with a metal I don't think I've +seen any metal Honeycombs that are + + align:start position:0% +seen any metal Honeycombs that are + + + align:start position:0% +seen any metal Honeycombs that are +extruded like that okay okay are we good + + align:start position:0% +extruded like that okay okay are we good + + + align:start position:0% +extruded like that okay okay are we good +with number one yeah that makes sense + + align:start position:0% +with number one yeah that makes sense + + + align:start position:0% +with number one yeah that makes sense +okay up we now need your password + + align:start position:0% + + + + align:start position:0% + +sorry yeah so the Extrusion you have a a + + align:start position:0% +sorry yeah so the Extrusion you have a a + + + align:start position:0% +sorry yeah so the Extrusion you have a a +dye and you squeeze the material through + + align:start position:0% +dye and you squeeze the material through + + + align:start position:0% +dye and you squeeze the material through +the die right so Extrusion is kind of + + align:start position:0% +the die right so Extrusion is kind of + + + align:start position:0% +the die right so Extrusion is kind of +like the tooth pasty thing and 3D + + align:start position:0% +like the tooth pasty thing and 3D + + + align:start position:0% +like the tooth pasty thing and 3D +printing you know you can have an ink or + + align:start position:0% +printing you know you can have an ink or + + + align:start position:0% +printing you know you can have an ink or +you can have um you know you can do 3D + + align:start position:0% +you can have um you know you can do 3D + + + align:start position:0% +you can have um you know you can do 3D +printing where you you have um say a + + align:start position:0% +printing where you you have um say a + + + align:start position:0% +printing where you you have um say a +powder and then you print the binder and + + align:start position:0% +powder and then you print the binder and + + + align:start position:0% +powder and then you print the binder and +then you fire like you you heat it up + + align:start position:0% +then you fire like you you heat it up + + + align:start position:0% +then you fire like you you heat it up +some way to get the binder to cure and + + align:start position:0% +some way to get the binder to cure and + + + align:start position:0% +some way to get the binder to cure and +then you get rid of the powder that's + + align:start position:0% +then you get rid of the powder that's + + + align:start position:0% +then you get rid of the powder that's +not bound that's another way to do the + + align:start position:0% +not bound that's another way to do the + + + align:start position:0% +not bound that's another way to do the +3D printing okay okay aold yeah yeah + + align:start position:0% +3D printing okay okay aold yeah yeah + + + align:start position:0% +3D printing okay okay aold yeah yeah +those silicon rubber Honeycombs that I + + align:start position:0% +those silicon rubber Honeycombs that I + + + align:start position:0% +those silicon rubber Honeycombs that I +showed you those are all made by pouring + + align:start position:0% +showed you those are all made by pouring + + + align:start position:0% +showed you those are all made by pouring +rubber like a liquid into a mold and + + align:start position:0% +rubber like a liquid into a mold and + + + align:start position:0% +rubber like a liquid into a mold and +then curing it yeah yeah there's other + + align:start position:0% +then curing it yeah yeah there's other + + + align:start position:0% +then curing it yeah yeah there's other +ways it just asks for four so I randomly + + align:start position:0% +ways it just asks for four so I randomly + + + align:start position:0% +ways it just asks for four so I randomly +thought of four + + align:start position:0% +thought of four + + + align:start position:0% +thought of four +okay okay are we good hello the next one + + align:start position:0% +okay okay are we good hello the next one + + + align:start position:0% +okay okay are we good hello the next one +is a hexagonal titanium alloy honeycomb + + align:start position:0% +is a hexagonal titanium alloy honeycomb + + + align:start position:0% +is a hexagonal titanium alloy honeycomb +has H overl is 2 Theta is 45 and TL is + + align:start position:0% +has H overl is 2 Theta is 45 and TL is + + + align:start position:0% +has H overl is 2 Theta is 45 and TL is +05 it says the N constraint factor for + + align:start position:0% +05 it says the N constraint factor for + + + align:start position:0% +05 it says the N constraint factor for +elastic buckling is n equal + + align:start position:0% +elastic buckling is n equal + + + align:start position:0% +elastic buckling is n equal +806 the titanium has a modulus of 110 + + align:start position:0% +806 the titanium has a modulus of 110 + + + align:start position:0% +806 the titanium has a modulus of 110 +gigap pascals and a yield strength of + + align:start position:0% +gigap pascals and a yield strength of + + + align:start position:0% +gigap pascals and a yield strength of +880 and then you have to calculate some + + align:start position:0% +880 and then you have to calculate some + + + align:start position:0% +880 and then you have to calculate some +properties so would you like me to do + + align:start position:0% +properties so would you like me to do + + + align:start position:0% +properties so would you like me to do +that yeah you would + + align:start position:0% +that yeah you would + + + align:start position:0% +that yeah you would +okay + + align:start position:0% +okay + + + align:start position:0% +okay +yeah I don't see see a lot of other + + align:start position:0% +yeah I don't see see a lot of other + + + align:start position:0% +yeah I don't see see a lot of other +people wanting anything else so I may as + + align:start position:0% +people wanting anything else so I may as + + + align:start position:0% +people wanting anything else so I may as +well do + + align:start position:0% +well do + + + align:start position:0% +well do +that um let's see I would need a piece + + align:start position:0% +that um let's see I would need a piece + + + align:start position:0% +that um let's see I would need a piece +of chalk here we + + align:start position:0% +of chalk here we + + + align:start position:0% +of chalk here we +go okay so it's a + + align:start position:0% + + + + align:start position:0% + +titanium alloy + + align:start position:0% + + + + align:start position:0% + +honeycomb and we're + + align:start position:0% +honeycomb and we're + + + align:start position:0% +honeycomb and we're +told H over L is + + align:start position:0% +told H over L is + + + align:start position:0% +told H over L is +2 Theta is + + align:start position:0% + + + + align:start position:0% + +45 and T overl is 05 5 and we're told + + align:start position:0% +45 and T overl is 05 5 and we're told + + + align:start position:0% +45 and T overl is 05 5 and we're told +that n we going to put the N over here n + + align:start position:0% +that n we going to put the N over here n + + + align:start position:0% +that n we going to put the N over here n +is + + align:start position:0% + + + + align:start position:0% + +0.806 and we're told the modulus of the + + align:start position:0% +0.806 and we're told the modulus of the + + + align:start position:0% +0.806 and we're told the modulus of the +solid is + + align:start position:0% +solid is + + + align:start position:0% +solid is +110 gigap pascals and the heel strength + + align:start position:0% +110 gigap pascals and the heel strength + + + align:start position:0% +110 gigap pascals and the heel strength +of the solid is + + align:start position:0% + + + + align:start position:0% + +880 megap + + align:start position:0% +880 megap + + + align:start position:0% +880 megap +pascals okay so it says calculate the + + align:start position:0% +pascals okay so it says calculate the + + + align:start position:0% +pascals okay so it says calculate the +value of and describe the mechanism of + + align:start position:0% +value of and describe the mechanism of + + + align:start position:0% +value of and describe the mechanism of +deformation and failure for and the + + align:start position:0% +deformation and failure for and the + + + align:start position:0% +deformation and failure for and the +first part is the young modulus in the + + align:start position:0% +first part is the young modulus in the + + + align:start position:0% +first part is the young modulus in the +two direction e 2 okay so I don't + + align:start position:0% +two direction e 2 okay so I don't + + + align:start position:0% +two direction e 2 okay so I don't +remember these formulas either so I need + + align:start position:0% +remember these formulas either so I need + + + align:start position:0% +remember these formulas either so I need +to look at my notes and oh I don't have + + align:start position:0% +to look at my notes and oh I don't have + + + align:start position:0% +to look at my notes and oh I don't have +the formula for E2 in my + + align:start position:0% + + + + align:start position:0% + +notes let me see is it in any of the + + align:start position:0% +notes let me see is it in any of the + + + align:start position:0% +notes let me see is it in any of the +problems you have the formula sheet I + + align:start position:0% +problems you have the formula sheet I + + + align:start position:0% +problems you have the formula sheet I +didn't bring the formula sheet with + + align:start position:0% +didn't bring the formula sheet with + + + align:start position:0% +didn't bring the formula sheet with +me you have it + + align:start position:0% + + + + align:start position:0% + +okay yeah it I think it's there I'm + + align:start position:0% +okay yeah it I think it's there I'm + + + align:start position:0% +okay yeah it I think it's there I'm +pretty sure it's + + align:start position:0% + + + + align:start position:0% + +there okay so this is just like + + align:start position:0% +there okay so this is just like + + + align:start position:0% +there okay so this is just like +substituting and there's nothing + + align:start position:0% +substituting and there's nothing + + + align:start position:0% +substituting and there's nothing +complicated about + + align:start position:0% +complicated about + + + align:start position:0% +complicated about +this so it's equal to + + align:start position:0% +this so it's equal to + + + align:start position:0% +this so it's equal to +es * t l + + align:start position:0% +es * t l + + + align:start position:0% +es * t l +cubed uh time h l + sin + + align:start position:0% +cubed uh time h l + sin + + + align:start position:0% +cubed uh time h l + sin +Theta / cos Cub Theta + + align:start position:0% +Theta / cos Cub Theta + + + align:start position:0% +Theta / cos Cub Theta +so then you just plug everything in so + + align:start position:0% +so then you just plug everything in so + + + align:start position:0% +so then you just plug everything in so +this is 110 gigap pascals and I'm going + + align:start position:0% +this is 110 gigap pascals and I'm going + + + align:start position:0% +this is 110 gigap pascals and I'm going +to put + + align:start position:0% +to put + + + align:start position:0% +to put +110,000 megap pascals because it's + + align:start position:0% +110,000 megap pascals because it's + + + align:start position:0% +110,000 megap pascals because it's +probably going to be less than a gigap + + align:start position:0% +probably going to be less than a gigap + + + align:start position:0% +probably going to be less than a gigap +pascal uh then T over L is 005 so that's + + align:start position:0% +pascal uh then T over L is 005 so that's + + + align:start position:0% +pascal uh then T over L is 005 so that's +05 cubed and then H over L is 2 plus s + + align:start position:0% +05 cubed and then H over L is 2 plus s + + + align:start position:0% +05 cubed and then H over L is 2 plus s +of 45 + + align:start position:0% + + + + align:start position:0% + +707 and then we div div by cos Theta + + align:start position:0% +707 and then we div div by cos Theta + + + align:start position:0% +707 and then we div div by cos Theta +cubed 707 cubed and then I'm not going + + align:start position:0% +cubed 707 cubed and then I'm not going + + + align:start position:0% +cubed 707 cubed and then I'm not going +to work it out but that's okay I assume + + align:start position:0% +to work it out but that's okay I assume + + + align:start position:0% +to work it out but that's okay I assume +that's what's in the solution are we + + align:start position:0% +that's what's in the solution are we + + + align:start position:0% +that's what's in the solution are we +good so it's just substituting that's + + align:start position:0% +good so it's just substituting that's + + + align:start position:0% +good so it's just substituting that's +all it is then the second part okay um + + align:start position:0% +all it is then the second part okay um + + + align:start position:0% +all it is then the second part okay um +you need to do the change the time on + + align:start position:0% +you need to do the change the time on + + + align:start position:0% +you need to do the change the time on +this because it just keeps timing out + + align:start position:0% +this because it just keeps timing out + + + align:start position:0% +this because it just keeps timing out +sorry I don't know + + align:start position:0% +sorry I don't know + + + align:start position:0% +sorry I don't know +to oh is it is it is that what this is + + align:start position:0% +to oh is it is it is that what this is + + + align:start position:0% +to oh is it is it is that what this is +okay this is the test oh this is from + + align:start position:0% + + + + align:start position:0% + +2013 oh the next one we keep going here + + align:start position:0% +2013 oh the next one we keep going here + + + align:start position:0% +2013 oh the next one we keep going here +we go oh he's he's got it so you can + + align:start position:0% +we go oh he's he's got it so you can + + + align:start position:0% +we go oh he's he's got it so you can +take your computer that's that's + + align:start position:0% +take your computer that's that's + + + align:start position:0% +take your computer that's that's +probably better for that's perfect for + + align:start position:0% +probably better for that's perfect for + + + align:start position:0% +probably better for that's perfect for +everybody okay the second part is the + + align:start position:0% +everybody okay the second part is the + + + align:start position:0% +everybody okay the second part is the +PLO stress for loading in the X2 + + align:start position:0% +PLO stress for loading in the X2 + + + align:start position:0% +PLO stress for loading in the X2 +Direction so that's that for loading in + + align:start position:0% +Direction so that's that for loading in + + + align:start position:0% +Direction so that's that for loading in +the X2 Direction it could either be um + + align:start position:0% +the X2 Direction it could either be um + + + align:start position:0% +the X2 Direction it could either be um +an elastic buckling collapse dress or a + + align:start position:0% +an elastic buckling collapse dress or a + + + align:start position:0% +an elastic buckling collapse dress or a +plastic buckling collapse dress so I'm + + align:start position:0% +plastic buckling collapse dress so I'm + + + align:start position:0% +plastic buckling collapse dress so I'm +going to calculate both and then + + align:start position:0% +going to calculate both and then + + + align:start position:0% +going to calculate both and then +whichever one's lower that's the one it + + align:start position:0% +whichever one's lower that's the one it + + + align:start position:0% +whichever one's lower that's the one it +would be um so let's see here so that's + + align:start position:0% +would be um so let's see here so that's + + + align:start position:0% +would be um so let's see here so that's +going to be let me see my formulas + + align:start position:0% +going to be let me see my formulas + + + align:start position:0% +going to be let me see my formulas +again here we are so here's the buckling + + align:start position:0% +again here we are so here's the buckling + + + align:start position:0% +again here we are so here's the buckling +one is n^2 pi^ 2 over + + align:start position:0% +one is n^2 pi^ 2 over + + + align:start position:0% +one is n^2 pi^ 2 over +24 * T cubed over LH 2 * 1 cos + + align:start position:0% +24 * T cubed over LH 2 * 1 cos + + + align:start position:0% +24 * T cubed over LH 2 * 1 cos +Theta so so you'd put 0 806 squared in + + align:start position:0% +Theta so so you'd put 0 806 squared in + + + align:start position:0% +Theta so so you'd put 0 806 squared in +here + + align:start position:0% + + + + align:start position:0% + +pi^ + + align:start position:0% +pi^ + + + align:start position:0% +pi^ + + align:start position:0% + + + align:start position:0% +24 so here you'd go this is T L cubed * + + align:start position:0% +24 so here you'd go this is T L cubed * + + + align:start position:0% +24 so here you'd go this is T L cubed * +h + + align:start position:0% +h + + + align:start position:0% +h +l + + align:start position:0% +l + + + align:start position:0% +l +SAR so that would be + + align:start position:0% +SAR so that would be + + + align:start position:0% +SAR so that would be +05 cubed and that would be 1 over 2 + + align:start position:0% +05 cubed and that would be 1 over 2 + + + align:start position:0% +05 cubed and that would be 1 over 2 +squared uh and then 1 over + + align:start position:0% +squared uh and then 1 over + + + align:start position:0% +squared uh and then 1 over +707 and then whatever that equals okay + + align:start position:0% +707 and then whatever that equals okay + + + align:start position:0% +707 and then whatever that equals okay +are we good with + + align:start position:0% + + + + align:start position:0% + +that and then you'd want to + + align:start position:0% +that and then you'd want to + + + align:start position:0% +that and then you'd want to +calculate Sigma star to + + align:start position:0% + + + + align:start position:0% + +plastic and that's equal to Sigma y + + align:start position:0% +plastic and that's equal to Sigma y + + + align:start position:0% +plastic and that's equal to Sigma y +s t l + + align:start position:0% +s t l + + + align:start position:0% +s t l +s and 1 + + align:start position:0% +s and 1 + + + align:start position:0% +s and 1 +over + + align:start position:0% +over + + + align:start position:0% +over +2 co^ 2 Theta + + align:start position:0% +2 co^ 2 Theta + + + align:start position:0% +2 co^ 2 Theta +all right so then Sigma Ys was + + align:start position:0% +all right so then Sigma Ys was + + + align:start position:0% +all right so then Sigma Ys was +880 megap + + align:start position:0% +880 megap + + + align:start position:0% +880 megap +pascals and T over L was our + + align:start position:0% +pascals and T over L was our + + + align:start position:0% +pascals and T over L was our +05 and that's 1 over 2 * 77 squ whatever + + align:start position:0% +05 and that's 1 over 2 * 77 squ whatever + + + align:start position:0% +05 and that's 1 over 2 * 77 squ whatever +that + + align:start position:0% +that + + + align:start position:0% +that +equals okay and then whichever one of + + align:start position:0% +equals okay and then whichever one of + + + align:start position:0% +equals okay and then whichever one of +those would be + + align:start position:0% +those would be + + + align:start position:0% +those would be +less is the plateau stress so I don't + + align:start position:0% +less is the plateau stress so I don't + + + align:start position:0% +less is the plateau stress so I don't +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so I know I think I made this mistake in + + align:start position:0% +so I know I think I made this mistake in + + + align:start position:0% +so I know I think I made this mistake in +prom set but here uh because it's + + align:start position:0% +prom set but here uh because it's + + + align:start position:0% +prom set but here uh because it's +titanium we don't consider them brle + + align:start position:0% +titanium we don't consider them brle + + + align:start position:0% +titanium we don't consider them brle +right right I I mean you could but you + + align:start position:0% +right right I I mean you could but you + + + align:start position:0% +right right I I mean you could but you +don't need to with Ceramics yeah or if + + align:start position:0% +don't need to with Ceramics yeah or if + + + align:start position:0% +don't need to with Ceramics yeah or if +it was a glass or ceramic or you know + + align:start position:0% +it was a glass or ceramic or you know + + + align:start position:0% +it was a glass or ceramic or you know +maybe like an epoxy something that was + + align:start position:0% +maybe like an epoxy something that was + + + align:start position:0% +maybe like an epoxy something that was +brittle and besides which if you look at + + align:start position:0% +brittle and besides which if you look at + + + align:start position:0% +brittle and besides which if you look at +the question I only give you a yield + + align:start position:0% +the question I only give you a yield + + + align:start position:0% +the question I only give you a yield +strength and a solid modulus so to get + + align:start position:0% +strength and a solid modulus so to get + + + align:start position:0% +strength and a solid modulus so to get +the brittle thing I would have to give + + align:start position:0% +the brittle thing I would have to give + + + align:start position:0% +the brittle thing I would have to give +you a fracture strength + + align:start position:0% +you a fracture strength + + + align:start position:0% +you a fracture strength +[Laughter] + + align:start position:0% +[Laughter] + + + align:start position:0% +[Laughter] +I usually give you what you need + + align:start position:0% +I usually give you what you need + + + align:start position:0% +I usually give you what you need +especially on on the test I'm going to + + align:start position:0% +especially on on the test I'm going to + + + align:start position:0% +especially on on the test I'm going to +give you what you need right you're not + + align:start position:0% +give you what you need right you're not + + + align:start position:0% +give you what you need right you're not +going to be looking things up okay so + + align:start position:0% +going to be looking things up okay so + + + align:start position:0% +going to be looking things up okay so +we're good so + + align:start position:0% +we're good so + + + align:start position:0% +we're good so +far okay let me go back to the + + align:start position:0% +far okay let me go back to the + + + align:start position:0% +far okay let me go back to the +question uh so then the the third one is + + align:start position:0% +question uh so then the the third one is + + + align:start position:0% +question uh so then the the third one is +the out of plane Young's + + align:start position:0% +the out of plane Young's + + + align:start position:0% +the out of plane Young's +modulus in the X3 Direction and that's + + align:start position:0% +modulus in the X3 Direction and that's + + + align:start position:0% +modulus in the X3 Direction and that's +just going to be estimes the relative + + align:start position:0% +just going to be estimes the relative + + + align:start position:0% +just going to be estimes the relative +density and the relative + + align:start position:0% +density and the relative + + + align:start position:0% +density and the relative +density let's see yeah so it's es s + + align:start position:0% +density let's see yeah so it's es s + + + align:start position:0% +density let's see yeah so it's es s +times + + align:start position:0% +times + + + align:start position:0% +times +row star over row s so that's + + align:start position:0% + + + + align:start position:0% + +110,000 Mega pascals and then there's + + align:start position:0% +110,000 Mega pascals and then there's + + + align:start position:0% +110,000 Mega pascals and then there's +also the very first equation on this is + + align:start position:0% +also the very first equation on this is + + + align:start position:0% +also the very first equation on this is +the relative density so it's t + + align:start position:0% +the relative density so it's t + + + align:start position:0% +the relative density so it's t +l * h l + 2 + + align:start position:0% +l * h l + 2 + + + align:start position:0% +l * h l + 2 +/ 2 cos + + align:start position:0% +/ 2 cos + + + align:start position:0% +/ 2 cos +Theta HL plus sin thet so I'm not going + + align:start position:0% +Theta HL plus sin thet so I'm not going + + + align:start position:0% +Theta HL plus sin thet so I'm not going +to substitute everything in okay so that + + align:start position:0% +to substitute everything in okay so that + + + align:start position:0% +to substitute everything in okay so that +that was it that's all it was very chug + + align:start position:0% +that was it that's all it was very chug + + + align:start position:0% +that was it that's all it was very chug +and plug plug and + + align:start position:0% +and plug plug and + + + align:start position:0% +and plug plug and +chug are you good can I ask a question + + align:start position:0% + + + + align:start position:0% + +yeah I'm going to go through the rest of + + align:start position:0% +yeah I'm going to go through the rest of + + + align:start position:0% +yeah I'm going to go through the rest of +them she wants me to do the whole test + + align:start position:0% +them she wants me to do the whole test + + + align:start position:0% +them she wants me to do the whole test +you want me to do the whole test right + + align:start position:0% +you want me to do the whole test right + + + align:start position:0% +you want me to do the whole test right +that would be great but if other people + + align:start position:0% +that would be great but if other people + + + align:start position:0% +that would be great but if other people +have other questions it's fine why don't + + align:start position:0% +have other questions it's fine why don't + + + align:start position:0% +have other questions it's fine why don't +I do the whole test and then there going + + align:start position:0% +I do the whole test and then there going + + + align:start position:0% +I do the whole test and then there going +to be time I think so + + align:start position:0% + + + + align:start position:0% + +let me do the test from last year okay + + align:start position:0% +let me do the test from last year okay + + + align:start position:0% +let me do the test from last year okay +so that's number one or that's one and + + align:start position:0% +so that's number one or that's one and + + + align:start position:0% +so that's number one or that's one and +two and then + + align:start position:0% + + + + align:start position:0% + +three three is a closed cell elastomeric + + align:start position:0% +three three is a closed cell elastomeric + + + align:start position:0% +three three is a closed cell elastomeric +polyethylene foam has a relative density + + align:start position:0% +polyethylene foam has a relative density + + + align:start position:0% +polyethylene foam has a relative density +of 0.05 and a volume fraction of solid + + align:start position:0% +of 0.05 and a volume fraction of solid + + + align:start position:0% +of 0.05 and a volume fraction of solid +in the edges of 6 uh they give you the + + align:start position:0% +in the edges of 6 uh they give you the + + + align:start position:0% +in the edges of 6 uh they give you the +Young's mod of the solid is 2 Gap + + align:start position:0% +Young's mod of the solid is 2 Gap + + + align:start position:0% +Young's mod of the solid is 2 Gap +pascals the pressure within the cell + + align:start position:0% +pascals the pressure within the cell + + + align:start position:0% +pascals the pressure within the cell +walls is atmospheric .1 megapascals and + + align:start position:0% +walls is atmospheric .1 megapascals and + + + align:start position:0% +walls is atmospheric .1 megapascals and +the plus ratio of the foam + + align:start position:0% +the plus ratio of the foam + + + align:start position:0% +the plus ratio of the foam +is3 and you're asked to get the Young's + + align:start position:0% +is3 and you're asked to get the Young's + + + align:start position:0% +is3 and you're asked to get the Young's +modulus of the foam the compressive + + align:start position:0% +modulus of the foam the compressive + + + align:start position:0% +modulus of the foam the compressive +Plateau stress and then uh there's a + + align:start position:0% +Plateau stress and then uh there's a + + + align:start position:0% +Plateau stress and then uh there's a +question about why does the young + + align:start position:0% +question about why does the young + + + align:start position:0% +question about why does the young +modulus depend on the solid modulus in + + align:start position:0% +modulus depend on the solid modulus in + + + align:start position:0% +modulus depend on the solid modulus in +relative density while the pon ratio + + align:start position:0% +relative density while the pon ratio + + + align:start position:0% +relative density while the pon ratio +does not so um let me go through + + align:start position:0% + + + + align:start position:0% + +then so the first one is + + align:start position:0% +then so the first one is + + + align:start position:0% +then so the first one is +what's E star and we're + + align:start position:0% +what's E star and we're + + + align:start position:0% +what's E star and we're +told relative density is + + align:start position:0% +told relative density is + + + align:start position:0% +told relative density is +005 the volume fraction in the edges is + + align:start position:0% +005 the volume fraction in the edges is + + + align:start position:0% +005 the volume fraction in the edges is +6 so remember that was what we called + + align:start position:0% +6 so remember that was what we called + + + align:start position:0% +6 so remember that was what we called +five so five + + align:start position:0% +five so five + + + align:start position:0% +five so five +is6 the young modulus of the solid is + + align:start position:0% + + + + align:start position:0% + +0.2 gigap + + align:start position:0% +0.2 gigap + + + align:start position:0% +0.2 gigap +pascals the initial pressure within the + + align:start position:0% +pascals the initial pressure within the + + + align:start position:0% +pascals the initial pressure within the +cells is .1 megapascal + + align:start position:0% +cells is .1 megapascal + + + align:start position:0% +cells is .1 megapascal +and plus one's ratio for the + + align:start position:0% + + + + align:start position:0% + +foam is + + align:start position:0% + + + + align:start position:0% + +0.3 and it's closed + + align:start position:0% + + + + align:start position:0% + +cell so if you remember oh let's see I + + align:start position:0% +cell so if you remember oh let's see I + + + align:start position:0% +cell so if you remember oh let's see I +think back here was I supposed to I was + + align:start position:0% +think back here was I supposed to I was + + + align:start position:0% +think back here was I supposed to I was +supposed to say something about the + + align:start position:0% +supposed to say something about the + + + align:start position:0% +supposed to say something about the +mechanism of deformation and failure for + + align:start position:0% +mechanism of deformation and failure for + + + align:start position:0% +mechanism of deformation and failure for +the first one so the mechanism of fail + + align:start position:0% +the first one so the mechanism of fail + + + align:start position:0% +the first one so the mechanism of fail +of deoration in the modulus in the two + + align:start position:0% +of deoration in the modulus in the two + + + align:start position:0% +of deoration in the modulus in the two +direction is bending the mechanism of + + align:start position:0% +direction is bending the mechanism of + + + align:start position:0% +direction is bending the mechanism of +failure here is buckling the mechan of + + align:start position:0% +failure here is buckling the mechan of + + + align:start position:0% +failure here is buckling the mechan of +failure here is yielding and the + + align:start position:0% +failure here is yielding and the + + + align:start position:0% +failure here is yielding and the +mechanism of deformation here was axial + + align:start position:0% +mechanism of deformation here was axial + + + align:start position:0% +mechanism of deformation here was axial +deformation okay so I forgot to say that + + align:start position:0% +deformation okay so I forgot to say that + + + align:start position:0% +deformation okay so I forgot to say that +okay let me go back here so for this one + + align:start position:0% +okay let me go back here so for this one + + + align:start position:0% +okay let me go back here so for this one +if it's a closed cell Pham remember + + align:start position:0% +if it's a closed cell Pham remember + + + align:start position:0% +if it's a closed cell Pham remember +there were three terms to the modulus + + align:start position:0% +there were three terms to the modulus + + + align:start position:0% +there were three terms to the modulus +there was one from bending of the edges + + align:start position:0% +there was one from bending of the edges + + + align:start position:0% +there was one from bending of the edges +one from stretching of the faces and one + + align:start position:0% +one from stretching of the faces and one + + + align:start position:0% +one from stretching of the faces and one +from the gas contribution if you've got + + align:start position:0% +from the gas contribution if you've got + + + align:start position:0% +from the gas contribution if you've got +gas inside the cells so again I'm going + + align:start position:0% +gas inside the cells so again I'm going + + + align:start position:0% +gas inside the cells so again I'm going +to have to peek at the + + align:start position:0% + + + + align:start position:0% + +equation Foams Foams here we go foams + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +okay and then this gas + + align:start position:0% + + + + align:start position:0% + +one get rid of that + + align:start position:0% + + + + align:start position:0% + +yeah okay so this one is just the same + + align:start position:0% +yeah okay so this one is just the same + + + align:start position:0% +yeah okay so this one is just the same +kind of thing it's just plug and chug + + align:start position:0% +kind of thing it's just plug and chug + + + align:start position:0% +kind of thing it's just plug and chug +okay do I need to put all the numbers in + + align:start position:0% +okay do I need to put all the numbers in + + + align:start position:0% +okay do I need to put all the numbers in +no okay I + + align:start position:0% +no okay I + + + align:start position:0% +no okay I +guess I guess I'm a little bit confused + + align:start position:0% +guess I guess I'm a little bit confused + + + align:start position:0% +guess I guess I'm a little bit confused +why you need + + align:start position:0% +why you need + + + align:start position:0% +why you need +the pressure term cuz you talked + + align:start position:0% +the pressure term cuz you talked + + + align:start position:0% +the pressure term cuz you talked +about B is bursting ah so if it's the + + align:start position:0% +about B is bursting ah so if it's the + + + align:start position:0% +about B is bursting ah so if it's the +modulus + + align:start position:0% +modulus + + + align:start position:0% +modulus +remember the + + align:start position:0% +remember the + + + align:start position:0% +remember the +modulus um so the question is why do you + + align:start position:0% +modulus um so the question is why do you + + + align:start position:0% +modulus um so the question is why do you +need to worry about the + + align:start position:0% +need to worry about the + + + align:start position:0% +need to worry about the +pressure uh because I talked about the + + align:start position:0% +pressure uh because I talked about the + + + align:start position:0% +pressure uh because I talked about the +fa is bursting and remember the stress + + align:start position:0% +fa is bursting and remember the stress + + + align:start position:0% +fa is bursting and remember the stress +strain curve looks you know something + + align:start position:0% +strain curve looks you know something + + + align:start position:0% +strain curve looks you know something +like that maybe the slope of the curve + + align:start position:0% +like that maybe the slope of the curve + + + align:start position:0% +like that maybe the slope of the curve +is a little bit higher over here U but + + align:start position:0% +is a little bit higher over here U but + + + align:start position:0% +is a little bit higher over here U but +this is the modulus down here right the + + align:start position:0% +this is the modulus down here right the + + + align:start position:0% +this is the modulus down here right the +modulus is related to the initial stress + + align:start position:0% +modulus is related to the initial stress + + + align:start position:0% +modulus is related to the initial stress +strain relationship and initially + + align:start position:0% +strain relationship and initially + + + align:start position:0% +strain relationship and initially +they're not going to burst you'd have to + + align:start position:0% +they're not going to burst you'd have to + + + align:start position:0% +they're not going to burst you'd have to +load it up to some amount of stress + + align:start position:0% +load it up to some amount of stress + + + align:start position:0% +load it up to some amount of stress +before the faces burst right so when + + align:start position:0% +before the faces burst right so when + + + align:start position:0% +before the faces burst right so when +you're down here the faces certainly + + align:start position:0% +you're down here the faces certainly + + + align:start position:0% +you're down here the faces certainly +down at the beginning they're not burst + + align:start position:0% +down at the beginning they're not burst + + + align:start position:0% +down at the beginning they're not burst +right you have to get some stress before + + align:start position:0% +right you have to get some stress before + + + align:start position:0% +right you have to get some stress before +they're going to burst and in some + + align:start position:0% +they're going to burst and in some + + + align:start position:0% +they're going to burst and in some +materials when you get up around here + + align:start position:0% +materials when you get up around here + + + align:start position:0% +materials when you get up around here +around the plateau stress or the let's + + align:start position:0% +around the plateau stress or the let's + + + align:start position:0% +around the plateau stress or the let's +just call that Sigma star um then they + + align:start position:0% +just call that Sigma star um then they + + + align:start position:0% +just call that Sigma star um then they +might burst and then that term would the + + align:start position:0% +might burst and then that term would the + + + align:start position:0% +might burst and then that term would the +pressure term would disappear and the + + align:start position:0% +pressure term would disappear and the + + + align:start position:0% +pressure term would disappear and the +face term would disappear okay so if I + + align:start position:0% +face term would disappear okay so if I + + + align:start position:0% +face term would disappear okay so if I +don't tell you to ignore them you know + + align:start position:0% +don't tell you to ignore them you know + + + align:start position:0% +don't tell you to ignore them you know +if I don't say they're going to burst or + + align:start position:0% +if I don't say they're going to burst or + + + align:start position:0% +if I don't say they're going to burst or +I don't say they're they're negligible I + + align:start position:0% +I don't say they're they're negligible I + + + align:start position:0% +I don't say they're they're negligible I +would calculate them and then if they're + + align:start position:0% +would calculate them and then if they're + + + align:start position:0% +would calculate them and then if they're +small and you can say Well they're + + align:start position:0% +small and you can say Well they're + + + align:start position:0% +small and you can say Well they're +negligible okay are we good with that + + align:start position:0% +negligible okay are we good with that + + + align:start position:0% +negligible okay are we good with that +you're good you're good sart you don't + + align:start position:0% +you're good you're good sart you don't + + + align:start position:0% +you're good you're good sart you don't +need to be + + align:start position:0% +need to be + + + align:start position:0% +need to be +here but you can you can stay if you + + align:start position:0% +here but you can you can stay if you + + + align:start position:0% +here but you can you can stay if you +want but you don't need to be here okay + + align:start position:0% +want but you don't need to be here okay + + + align:start position:0% +want but you don't need to be here okay +are you + + align:start position:0% +are you + + + align:start position:0% +are you +good everybody else good okay uh that + + align:start position:0% +good everybody else good okay uh that + + + align:start position:0% +good everybody else good okay uh that +was a + + align:start position:0% + + + + align:start position:0% + +uh B what's the comess compressive + + align:start position:0% +uh B what's the comess compressive + + + align:start position:0% +uh B what's the comess compressive +Plateau stress of the foam so here um + + align:start position:0% +Plateau stress of the foam so here um + + + align:start position:0% +Plateau stress of the foam so here um +they want to know what Sigma star is + + align:start position:0% +they want to know what Sigma star is + + + align:start position:0% +they want to know what Sigma star is +you're told it's elastomeric so if it's + + align:start position:0% +you're told it's elastomeric so if it's + + + align:start position:0% +you're told it's elastomeric so if it's +elastomeric it's like a rubber right + + align:start position:0% +elastomeric it's like a rubber right + + + align:start position:0% +elastomeric it's like a rubber right +it's rubbery so if it's rubbery it's + + align:start position:0% +it's rubbery so if it's rubbery it's + + + align:start position:0% +it's rubbery so if it's rubbery it's +going to buckle it's not going to yield + + align:start position:0% +going to buckle it's not going to yield + + + align:start position:0% +going to buckle it's not going to yield +it's not going to be brittle so you can + + align:start position:0% +it's not going to be brittle so you can + + + align:start position:0% +it's not going to be brittle so you can +just calculate the + + align:start position:0% +just calculate the + + + align:start position:0% +just calculate the +elastic stress + + align:start position:0% +elastic stress + + + align:start position:0% +elastic stress +here and if we flip over to our handy + + align:start position:0% +here and if we flip over to our handy + + + align:start position:0% +here and if we flip over to our handy +dandy list of equations + + align:start position:0% + + + + align:start position:0% + +uh blah blah blah blah blah oh + + align:start position:0% +uh blah blah blah blah blah oh + + + align:start position:0% +uh blah blah blah blah blah oh +Poo + + align:start position:0% +Poo + + + align:start position:0% +Poo +okay I'm realizing + + align:start position:0% +okay I'm realizing + + + align:start position:0% +okay I'm realizing +ah yeah so I don't I don't have the term + + align:start position:0% +ah yeah so I don't I don't have the term + + + align:start position:0% +ah yeah so I don't I don't have the term +here for the faces or for the gas so + + align:start position:0% +here for the faces or for the gas so + + + align:start position:0% +here for the faces or for the gas so +here we could assume it's going to + + align:start position:0% +here we could assume it's going to + + + align:start position:0% +here we could assume it's going to +rupture okay so let's assume it's going + + align:start position:0% +rupture okay so let's assume it's going + + + align:start position:0% +rupture okay so let's assume it's going +to + + align:start position:0% + + + + align:start position:0% + +rupture so if we assume that it's going + + align:start position:0% +rupture so if we assume that it's going + + + align:start position:0% +rupture so if we assume that it's going +to rub rure it' be just like the um open + + align:start position:0% +to rub rure it' be just like the um open + + + align:start position:0% +to rub rure it' be just like the um open +cell + + align:start position:0% +cell + + + align:start position:0% +cell +Foams + + align:start position:0% + + + + align:start position:0% + +and and you can just use + + align:start position:0% + + + + align:start position:0% + +that and that's been found to work + + align:start position:0% +that and that's been found to work + + + align:start position:0% +that and that's been found to work +fairly well for the open cell and the + + align:start position:0% +fairly well for the open cell and the + + + align:start position:0% +fairly well for the open cell and the +closed cell Foams we assume faces + + align:start position:0% +closed cell Foams we assume faces + + + align:start position:0% +closed cell Foams we assume faces +Rapture yeah because oh well to be + + align:start position:0% +Rapture yeah because oh well to be + + + align:start position:0% +Rapture yeah because oh well to be +honest I can't remember if last year I + + align:start position:0% +honest I can't remember if last year I + + + align:start position:0% +honest I can't remember if last year I +got to this part point in the test and + + align:start position:0% +got to this part point in the test and + + + align:start position:0% +got to this part point in the test and +somebody said we don't have the equation + + align:start position:0% +somebody said we don't have the equation + + + align:start position:0% +somebody said we don't have the equation +and I gave them the equation with the + + align:start position:0% +and I gave them the equation with the + + + align:start position:0% +and I gave them the equation with the +other terms or if we just assume that + + align:start position:0% +other terms or if we just assume that + + + align:start position:0% +other terms or if we just assume that +the face is ruptured I can't remember I + + align:start position:0% +the face is ruptured I can't remember I + + + align:start position:0% +the face is ruptured I can't remember I +to be honest I think probably for an + + align:start position:0% +to be honest I think probably for an + + + align:start position:0% +to be honest I think probably for an +elastomeric foam um you could assume + + align:start position:0% +elastomeric foam um you could assume + + + align:start position:0% +elastomeric foam um you could assume +that they probably don't rupture uh you + + align:start position:0% +that they probably don't rupture uh you + + + align:start position:0% +that they probably don't rupture uh you +know unless they're very very thin so um + + align:start position:0% +know unless they're very very thin so um + + + align:start position:0% +know unless they're very very thin so um +so what kinds of phones do they + + align:start position:0% +so what kinds of phones do they + + + align:start position:0% +so what kinds of phones do they +typically rupture so certainly if you + + align:start position:0% +typically rupture so certainly if you + + + align:start position:0% +typically rupture so certainly if you +had a metal foam they'd probably + + align:start position:0% +had a metal foam they'd probably + + + align:start position:0% +had a metal foam they'd probably +rupture um if you + + align:start position:0% +rupture um if you + + + align:start position:0% +rupture um if you +had uh say a polymer foam that was more + + align:start position:0% +had uh say a polymer foam that was more + + + align:start position:0% +had uh say a polymer foam that was more +rigid like a rigid + + align:start position:0% +rigid like a rigid + + + align:start position:0% +rigid like a rigid +polyurethane so polyurethanes can be + + align:start position:0% +polyurethane so polyurethanes can be + + + align:start position:0% +polyurethane so polyurethanes can be +flexible which means they're made out of + + align:start position:0% +flexible which means they're made out of + + + align:start position:0% +flexible which means they're made out of +an elastomer or they can be rigid and + + align:start position:0% +an elastomer or they can be rigid and + + + align:start position:0% +an elastomer or they can be rigid and +the Foams that are typically used for + + align:start position:0% +the Foams that are typically used for + + + align:start position:0% +the Foams that are typically used for +like you know + + align:start position:0% +like you know + + + align:start position:0% +like you know +insulation thermal insulation are + + align:start position:0% +insulation thermal insulation are + + + align:start position:0% +insulation thermal insulation are +typically Clos cell polyurethane Foams + + align:start position:0% +typically Clos cell polyurethane Foams + + + align:start position:0% +typically Clos cell polyurethane Foams +and those typically have very thin faces + + align:start position:0% +and those typically have very thin faces + + + align:start position:0% +and those typically have very thin faces +and they they would rupture + + align:start position:0% +and they they would rupture + + + align:start position:0% +and they they would rupture +yep are you looking for the + + align:start position:0% +yep are you looking for the + + + align:start position:0% +yep are you looking for the +mod the young modulus was the first part + + align:start position:0% +mod the young modulus was the first part + + + align:start position:0% +mod the young modulus was the first part +right so the part A was the young + + align:start position:0% +right so the part A was the young + + + align:start position:0% +right so the part A was the young +modules in B is the collapse stress the + + align:start position:0% +modules in B is the collapse stress the + + + align:start position:0% +modules in B is the collapse stress the +compressive strength so I think + + align:start position:0% + + + + align:start position:0% + +like + + align:start position:0% +like + + + align:start position:0% +like +yes right if Peanut's bigger than so + + align:start position:0% +yes right if Peanut's bigger than so + + + align:start position:0% +yes right if Peanut's bigger than so +what she's showing me in her notes is I + + align:start position:0% +what she's showing me in her notes is I + + + align:start position:0% +what she's showing me in her notes is I +had a little note in the class in the + + align:start position:0% +had a little note in the class in the + + + align:start position:0% +had a little note in the class in the +lecture that if the initial pressure + + align:start position:0% +lecture that if the initial pressure + + + align:start position:0% +lecture that if the initial pressure +pressure in the cells is greater than + + align:start position:0% +pressure in the cells is greater than + + + align:start position:0% +pressure in the cells is greater than +atmospheric then the cell walls are + + align:start position:0% +atmospheric then the cell walls are + + + align:start position:0% +atmospheric then the cell walls are +pre-stressed and you have to overcome + + align:start position:0% +pre-stressed and you have to overcome + + + align:start position:0% +pre-stressed and you have to overcome +that in the buckling but atph that is + + align:start position:0% +that in the buckling but atph that is + + + align:start position:0% +that in the buckling but atph that is +atmospheric pressure so you don't need + + align:start position:0% +atmospheric pressure so you don't need + + + align:start position:0% +atmospheric pressure so you don't need +the G no + + align:start position:0% +the G no + + + align:start position:0% +the G no +yeah okay + + align:start position:0% +yeah okay + + + align:start position:0% +yeah okay +okay yeah you don't know that that's + + align:start position:0% +okay yeah you don't know that that's + + + align:start position:0% +okay yeah you don't know that that's +atmospheric so do you do you ever do + + align:start position:0% +atmospheric so do you do you ever do + + + align:start position:0% +atmospheric so do you do you ever do +things in + + align:start position:0% +things in + + + align:start position:0% +things in +PSI no you don't because when when I was + + align:start position:0% +PSI no you don't because when when I was + + + align:start position:0% +PSI no you don't because when when I was +a student a long time ago um the thing I + + align:start position:0% +a student a long time ago um the thing I + + + align:start position:0% +a student a long time ago um the thing I +remember learning was atmospheric + + align:start position:0% +remember learning was atmospheric + + + align:start position:0% +remember learning was atmospheric +pressures 14.7 PSI more or less and the + + align:start position:0% +pressures 14.7 PSI more or less and the + + + align:start position:0% +pressures 14.7 PSI more or less and the +conversion between megap pascals and PSI + + align:start position:0% +conversion between megap pascals and PSI + + + align:start position:0% +conversion between megap pascals and PSI +is there's more or less 145 PSI to a + + align:start position:0% +is there's more or less 145 PSI to a + + + align:start position:0% +is there's more or less 145 PSI to a +megapascal so MEAP uh the atmospheric + + align:start position:0% +megapascal so MEAP uh the atmospheric + + + align:start position:0% +megapascal so MEAP uh the atmospheric +pressure is about 0.1 megap pascals yeah + + align:start position:0% +pressure is about 0.1 megap pascals yeah + + + align:start position:0% +pressure is about 0.1 megap pascals yeah +I know this is a silly question but for + + align:start position:0% +I know this is a silly question but for + + + align:start position:0% +I know this is a silly question but for +Part B how do we get from The Young + + align:start position:0% +Part B how do we get from The Young + + + align:start position:0% +Part B how do we get from The Young +modulus and the pH oh sorry sorry sorry + + align:start position:0% +modulus and the pH oh sorry sorry sorry + + + align:start position:0% +modulus and the pH oh sorry sorry sorry +sorry I'm WR the wrong thing down here + + align:start position:0% +sorry I'm WR the wrong thing down here + + + align:start position:0% +sorry I'm WR the wrong thing down here +sorry sorry sorry sorry sorry my mistake + + align:start position:0% +sorry sorry sorry sorry sorry my mistake + + + align:start position:0% +sorry sorry sorry sorry sorry my mistake +okay now you happy sorry + + align:start position:0% + + + + align:start position:0% + +okay should I move on to the next part + + align:start position:0% +okay should I move on to the next part + + + align:start position:0% +okay should I move on to the next part +another question well I had a question + + align:start position:0% +another question well I had a question + + + align:start position:0% +another question well I had a question +about number two but maybe we can come + + align:start position:0% +about number two but maybe we can come + + + align:start position:0% +about number two but maybe we can come +back to that okay let me finish this and + + align:start position:0% +back to that okay let me finish this and + + + align:start position:0% +back to that okay let me finish this and +then we'll do we'll go back to number + + align:start position:0% +then we'll do we'll go back to number + + + align:start position:0% +then we'll do we'll go back to number +two so this one here that the part C is + + align:start position:0% +two so this one here that the part C is + + + align:start position:0% +two so this one here that the part C is +why does the Young's modulus foam depend + + align:start position:0% +why does the Young's modulus foam depend + + + align:start position:0% +why does the Young's modulus foam depend +on the solid modulus and the relative + + align:start position:0% +on the solid modulus and the relative + + + align:start position:0% +on the solid modulus and the relative +density while the poson ratio does not + + align:start position:0% +density while the poson ratio does not + + + align:start position:0% +density while the poson ratio does not +so when I write the equation for the + + align:start position:0% +so when I write the equation for the + + + align:start position:0% +so when I write the equation for the +Young's modulus the solid modulus comes + + align:start position:0% +Young's modulus the solid modulus comes + + + align:start position:0% +Young's modulus the solid modulus comes +into it the relative density comes into + + align:start position:0% +into it the relative density comes into + + + align:start position:0% +into it the relative density comes into +it and you remember when we had the pon + + align:start position:0% +it and you remember when we had the pon + + + align:start position:0% +it and you remember when we had the pon +ratio + + align:start position:0% +ratio + + + align:start position:0% +ratio +it's just a constant that depends on the + + align:start position:0% +it's just a constant that depends on the + + + align:start position:0% +it's just a constant that depends on the +cell geometry so here c new + + align:start position:0% +cell geometry so here c new + + + align:start position:0% +cell geometry so here c new +star uh just is a + + align:start position:0% +star uh just is a + + + align:start position:0% +star uh just is a +constant and that constant just depends + + align:start position:0% +constant and that constant just depends + + + align:start position:0% +constant and that constant just depends +on the cell + + align:start position:0% + + + + align:start position:0% + +geometry so if you think of the pon + + align:start position:0% +geometry so if you think of the pon + + + align:start position:0% +geometry so if you think of the pon +ratio it's the ratio of two strains + + align:start position:0% +ratio it's the ratio of two strains + + + align:start position:0% +ratio it's the ratio of two strains +right so say I say I have my foam here + + align:start position:0% +right so say I say I have my foam here + + + align:start position:0% +right so say I say I have my foam here +so say that's just a block of foam + + align:start position:0% +so say that's just a block of foam + + + align:start position:0% +so say that's just a block of foam +little cells in it here cells um and say + + align:start position:0% +little cells in it here cells um and say + + + align:start position:0% +little cells in it here cells um and say +I press on it this way here and let's + + align:start position:0% +I press on it this way here and let's + + + align:start position:0% +I press on it this way here and let's +call this the One Direction and the two + + align:start position:0% +call this the One Direction and the two + + + align:start position:0% +call this the One Direction and the two +direction if I press it in the two + + align:start position:0% +direction if I press it in the two + + + align:start position:0% +direction if I press it in the two +direction uh the poson ratio is then + + align:start position:0% +direction uh the poson ratio is then + + + align:start position:0% +direction uh the poson ratio is then +just new would be let's see this would + + align:start position:0% +just new would be let's see this would + + + align:start position:0% +just new would be let's see this would +be 21 be the strain in the One Direction + + align:start position:0% +be 21 be the strain in the One Direction + + + align:start position:0% +be 21 be the strain in the One Direction +Over The Strain in the two direction so + + align:start position:0% +Over The Strain in the two direction so + + + align:start position:0% +Over The Strain in the two direction so +it's the ratio of two strains right and + + align:start position:0% +it's the ratio of two strains right and + + + align:start position:0% +it's the ratio of two strains right and +if you think of our model for the + + align:start position:0% +if you think of our model for the + + + align:start position:0% +if you think of our model for the +elastic Behavior of the uh foam each of + + align:start position:0% +elastic Behavior of the uh foam each of + + + align:start position:0% +elastic Behavior of the uh foam each of +those strains is going to be related to + + align:start position:0% +those strains is going to be related to + + + align:start position:0% +those strains is going to be related to +some bending deformation in the cell + + align:start position:0% +some bending deformation in the cell + + + align:start position:0% +some bending deformation in the cell +walls or the cell struts and this strain + + align:start position:0% +walls or the cell struts and this strain + + + align:start position:0% +walls or the cell struts and this strain +here is going to be let me make this + + align:start position:0% +here is going to be let me make this + + + align:start position:0% +here is going to be let me make this +proportional is going to be proportional + + align:start position:0% +proportional is going to be proportional + + + align:start position:0% +proportional is going to be proportional +to a Delta over + + align:start position:0% +to a Delta over + + + align:start position:0% +to a Delta over +L and this one here is going to be + + align:start position:0% +L and this one here is going to be + + + align:start position:0% +L and this one here is going to be +proportional to the Delta over l so this + + align:start position:0% +proportional to the Delta over l so this + + + align:start position:0% +proportional to the Delta over l so this +might be um Delta in the One Direction + + align:start position:0% +might be um Delta in the One Direction + + + align:start position:0% +might be um Delta in the One Direction +and this will be Delta in the two + + align:start position:0% +and this will be Delta in the two + + + align:start position:0% +and this will be Delta in the two +direction but those two things are both + + align:start position:0% +direction but those two things are both + + + align:start position:0% +direction but those two things are both +going to be related to the bending + + align:start position:0% +going to be related to the bending + + + align:start position:0% +going to be related to the bending +deflection of the beams + + align:start position:0% +deflection of the beams + + + align:start position:0% +deflection of the beams +right and since both of those Deltas are + + align:start position:0% +right and since both of those Deltas are + + + align:start position:0% +right and since both of those Deltas are +related to the bending deflection of the + + align:start position:0% +related to the bending deflection of the + + + align:start position:0% +related to the bending deflection of the +beams you know we could we could write + + align:start position:0% +beams you know we could we could write + + + align:start position:0% +beams you know we could we could write +them if you want I could write that as f + + align:start position:0% +them if you want I could write that as f + + + align:start position:0% +them if you want I could write that as f +l cubed over e of the solid * T 4th and + + align:start position:0% +l cubed over e of the solid * T 4th and + + + align:start position:0% +l cubed over e of the solid * T 4th and +then that's * 1 L and then this thing + + align:start position:0% +then that's * 1 L and then this thing + + + align:start position:0% +then that's * 1 L and then this thing +here is also f l cubed oops over e of + + align:start position:0% +here is also f l cubed oops over e of + + + align:start position:0% +here is also f l cubed oops over e of +the solid T 4th 1 L + + align:start position:0% +the solid T 4th 1 L + + + align:start position:0% +the solid T 4th 1 L +so everything cancels out except the + + align:start position:0% +so everything cancels out except the + + + align:start position:0% +so everything cancels out except the +geometrical constant and if you remember + + align:start position:0% +geometrical constant and if you remember + + + align:start position:0% +geometrical constant and if you remember +when we did the Honeycombs it looked + + align:start position:0% +when we did the Honeycombs it looked + + + align:start position:0% +when we did the Honeycombs it looked +exactly the same when we when we when we + + align:start position:0% +exactly the same when we when we when we + + + align:start position:0% +exactly the same when we when we when we +looked at the poson ratio of the + + align:start position:0% +looked at the poson ratio of the + + + align:start position:0% +looked at the poson ratio of the +Honeycombs we had one strain The Strain + + align:start position:0% +Honeycombs we had one strain The Strain + + + align:start position:0% +Honeycombs we had one strain The Strain +in One Direction Over The Strain in + + align:start position:0% +in One Direction Over The Strain in + + + align:start position:0% +in One Direction Over The Strain in +another Direction and each of those + + align:start position:0% +another Direction and each of those + + + align:start position:0% +another Direction and each of those +strains was related to some component of + + align:start position:0% +strains was related to some component of + + + align:start position:0% +strains was related to some component of +Delta there was like a Delta 1 and a + + align:start position:0% +Delta there was like a Delta 1 and a + + + align:start position:0% +Delta there was like a Delta 1 and a +Delta 2 but the Delta you know Delta 1 + + align:start position:0% +Delta 2 but the Delta you know Delta 1 + + + align:start position:0% +Delta 2 but the Delta you know Delta 1 +might be Delta sin Theta and Delta 2 is + + align:start position:0% +might be Delta sin Theta and Delta 2 is + + + align:start position:0% +might be Delta sin Theta and Delta 2 is +Delta Co Theta so if the Deltas are the + + align:start position:0% +Delta Co Theta so if the Deltas are the + + + align:start position:0% +Delta Co Theta so if the Deltas are the +same then it all just cancels out and + + align:start position:0% +same then it all just cancels out and + + + align:start position:0% +same then it all just cancels out and +all you're left with is a geometrical + + align:start position:0% +all you're left with is a geometrical + + + align:start position:0% +all you're left with is a geometrical +constant + + align:start position:0% +constant + + + align:start position:0% +constant +okay you get sort of physically why that + + align:start position:0% +okay you get sort of physically why that + + + align:start position:0% +okay you get sort of physically why that +is yeah sorry to question about this um + + align:start position:0% +is yeah sorry to question about this um + + + align:start position:0% +is yeah sorry to question about this um +because we're given most of the + + align:start position:0% +because we're given most of the + + + align:start position:0% +because we're given most of the +equations that we need um is it only in + + align:start position:0% +equations that we need um is it only in + + + align:start position:0% +equations that we need um is it only in +like conceptual questions that we should + + align:start position:0% +like conceptual questions that we should + + + align:start position:0% +like conceptual questions that we should +know how we actually derive the equation + + align:start position:0% +know how we actually derive the equation + + + align:start position:0% +know how we actually derive the equation +um I'm not going to ask you to derive + + align:start position:0% +um I'm not going to ask you to derive + + + align:start position:0% +um I'm not going to ask you to derive +like that equation for a close cell foam + + align:start position:0% +like that equation for a close cell foam + + + align:start position:0% +like that equation for a close cell foam +I meant this last part like well you + + align:start position:0% +I meant this last part like well you + + + align:start position:0% +I meant this last part like well you +should be yeah you should be able to + + align:start position:0% +should be yeah you should be able to + + + align:start position:0% +should be yeah you should be able to +explain that yeah okay yeah just + + align:start position:0% +explain that yeah okay yeah just + + + align:start position:0% +explain that yeah okay yeah just +but I mean just at this level I mean + + align:start position:0% +but I mean just at this level I mean + + + align:start position:0% +but I mean just at this level I mean +nothing very mathematically + + align:start position:0% +nothing very mathematically + + + align:start position:0% +nothing very mathematically +involved okay yeah okay are we good so + + align:start position:0% +involved okay yeah okay are we good so + + + align:start position:0% +involved okay yeah okay are we good so +so that was the end of the test for the + + align:start position:0% +so that was the end of the test for the + + + align:start position:0% +so that was the end of the test for the +undergraduates okay so and then for The + + align:start position:0% +undergraduates okay so and then for The + + + align:start position:0% +undergraduates okay so and then for The +Graduate students just like the problem + + align:start position:0% +Graduate students just like the problem + + + align:start position:0% +Graduate students just like the problem +sets I just have an extra question and + + align:start position:0% +sets I just have an extra question and + + + align:start position:0% +sets I just have an extra question and +that's what I did this year too so The + + align:start position:0% +that's what I did this year too so The + + + align:start position:0% +that's what I did this year too so The +Graduate students have one extra + + align:start position:0% +Graduate students have one extra + + + align:start position:0% +Graduate students have one extra +question so that's you and you is + + align:start position:0% +question so that's you and you is + + + align:start position:0% +question so that's you and you is +anybody else a graduate student I think + + align:start position:0% +anybody else a graduate student I think + + + align:start position:0% +anybody else a graduate student I think +it's just the two of you you're post + + align:start position:0% +it's just the two of you you're post + + + align:start position:0% +it's just the two of you you're post +postgraduate okay okay um so let's + + align:start position:0% + + + + align:start position:0% + +see so this one says the performance so + + align:start position:0% +see so this one says the performance so + + + align:start position:0% +see so this one says the performance so +this is uh on the performance indices + + align:start position:0% +this is uh on the performance indices + + + align:start position:0% +this is uh on the performance indices +which I told you you didn't need to know + + align:start position:0% +which I told you you didn't need to know + + + align:start position:0% +which I told you you didn't need to know +for this test partly because remember we + + align:start position:0% +for this test partly because remember we + + + align:start position:0% +for this test partly because remember we +missed two lectures we're not exactly in + + align:start position:0% +missed two lectures we're not exactly in + + + align:start position:0% +missed two lectures we're not exactly in +the same spot as we were last year uh + + align:start position:0% +the same spot as we were last year uh + + + align:start position:0% +the same spot as we were last year uh +but I can do it if you want you want me + + align:start position:0% +but I can do it if you want you want me + + + align:start position:0% +but I can do it if you want you want me +to do it or should we do other + + align:start position:0% + + + + align:start position:0% + +questions huh what are the grand + + align:start position:0% +questions huh what are the grand + + + align:start position:0% +questions huh what are the grand +students think you got sure okay so the + + align:start position:0% +students think you got sure okay so the + + + align:start position:0% +students think you got sure okay so the +question is the performance index to + + align:start position:0% +question is the performance index to + + + align:start position:0% +question is the performance index to +minimize the mass of a beam of a giving + + align:start position:0% +minimize the mass of a beam of a giving + + + align:start position:0% +minimize the mass of a beam of a giving +bending stiffness length and square + + align:start position:0% +bending stiffness length and square + + + align:start position:0% +bending stiffness length and square +cross-section is e to the 1/2 over row + + align:start position:0% +cross-section is e to the 1/2 over row + + + align:start position:0% +cross-section is e to the 1/2 over row +so remember we we derived that e to the + + align:start position:0% +so remember we we derived that e to the + + + align:start position:0% +so remember we we derived that e to the +1/2 over row in class in the section on + + align:start position:0% +1/2 over row in class in the section on + + + align:start position:0% +1/2 over row in class in the section on +wood we saw that this performance index + + align:start position:0% +wood we saw that this performance index + + + align:start position:0% +wood we saw that this performance index +for wood is higher than that for the + + align:start position:0% +for wood is higher than that for the + + + align:start position:0% +for wood is higher than that for the +solid cell wall material in Wood + + align:start position:0% +solid cell wall material in Wood + + + align:start position:0% +solid cell wall material in Wood +remember that the e e to the 1/2 over + + align:start position:0% +remember that the e e to the 1/2 over + + + align:start position:0% +remember that the e e to the 1/2 over +row for the wood was I think uh row s + + align:start position:0% +row for the wood was I think uh row s + + + align:start position:0% +row for the wood was I think uh row s +over row star to the2 uh time e s to the + + align:start position:0% +over row star to the2 uh time e s to the + + + align:start position:0% +over row star to the2 uh time e s to the +1 12 over row + + align:start position:0% +1 12 over row + + + align:start position:0% +1 12 over row +s um so explain why wood has a high + + align:start position:0% +s um so explain why wood has a high + + + align:start position:0% +s um so explain why wood has a high +value of e to the 1/2 over row in the + + align:start position:0% +value of e to the 1/2 over row in the + + + align:start position:0% +value of e to the 1/2 over row in the +solid cell wall material and then Part B + + align:start position:0% +solid cell wall material and then Part B + + + align:start position:0% +solid cell wall material and then Part B +is suggest a design for an engineering + + align:start position:0% +is suggest a design for an engineering + + + align:start position:0% +is suggest a design for an engineering +material based on wood that has high + + align:start position:0% +material based on wood that has high + + + align:start position:0% +material based on wood that has high +values of e to the 1/2 over a row okay + + align:start position:0% +values of e to the 1/2 over a row okay + + + align:start position:0% +values of e to the 1/2 over a row okay +so + + align:start position:0% +so + + + align:start position:0% +so +um you know one way to explain + + align:start position:0% + + + + align:start position:0% + +it one way to explain it is to say that + + align:start position:0% +it one way to explain it is to say that + + + align:start position:0% +it one way to explain it is to say that +if you're looking at e to the 12 over + + align:start position:0% +if you're looking at e to the 12 over + + + align:start position:0% +if you're looking at e to the 12 over +row you can say for wood + + align:start position:0% +row you can say for wood + + + align:start position:0% +row you can say for wood +e + + align:start position:0% +e + + + align:start position:0% +e +oops e over e + + align:start position:0% +oops e over e + + + align:start position:0% +oops e over e +s is equal to row star over row s for + + align:start position:0% +s is equal to row star over row s for + + + align:start position:0% +s is equal to row star over row s for +loading in the axial Direction so this + + align:start position:0% + + + + align:start position:0% + +is so this will be for loading actually + + align:start position:0% +is so this will be for loading actually + + + align:start position:0% +is so this will be for loading actually +along the Grain and that's that's what + + align:start position:0% +along the Grain and that's that's what + + + align:start position:0% +along the Grain and that's that's what +we were looking at so that's what I'm + + align:start position:0% +we were looking at so that's what I'm + + + align:start position:0% +we were looking at so that's what I'm +talking about + + align:start position:0% +talking about + + + align:start position:0% +talking about +here so uh + + align:start position:0% + + + + align:start position:0% + +so I think let me just see if this is + + align:start position:0% +so I think let me just see if this is + + + align:start position:0% +so I think let me just see if this is +right yeah so this equation here is + + align:start position:0% +right yeah so this equation here is + + + align:start position:0% +right yeah so this equation here is +exactly the same as that equation there + + align:start position:0% +exactly the same as that equation there + + + align:start position:0% +exactly the same as that equation there +right and this is basically saying that + + align:start position:0% +right and this is basically saying that + + + align:start position:0% +right and this is basically saying that +this is the performance index for the + + align:start position:0% +this is the performance index for the + + + align:start position:0% +this is the performance index for the +wood this is the performance index for + + align:start position:0% +wood this is the performance index for + + + align:start position:0% +wood this is the performance index for +the solid and this Factor here is bigger + + align:start position:0% +the solid and this Factor here is bigger + + + align:start position:0% +the solid and this Factor here is bigger +than one because the solid density is + + align:start position:0% +than one because the solid density is + + + align:start position:0% +than one because the solid density is +higher than the wood density okay so + + align:start position:0% +higher than the wood density okay so + + + align:start position:0% +higher than the wood density okay so +really all all you have to do is say + + align:start position:0% +really all all you have to do is say + + + align:start position:0% +really all all you have to do is say +that um for the wood the modulus in the + + align:start position:0% +that um for the wood the modulus in the + + + align:start position:0% +that um for the wood the modulus in the +longitudinal or the axial Direction + + align:start position:0% +longitudinal or the axial Direction + + + align:start position:0% +longitudinal or the axial Direction +along the grain varies linearly with the + + align:start position:0% +along the grain varies linearly with the + + + align:start position:0% +along the grain varies linearly with the +relative density and it probably would + + align:start position:0% +relative density and it probably would + + + align:start position:0% +relative density and it probably would +be a good idea to say that this is a + + align:start position:0% +be a good idea to say that this is a + + + align:start position:0% +be a good idea to say that this is a +result of the cell walls deforming + + align:start position:0% +result of the cell walls deforming + + + align:start position:0% +result of the cell walls deforming +ax so when you take the cells you know + + align:start position:0% +ax so when you take the cells you know + + + align:start position:0% +ax so when you take the cells you know +if you think of the wood cells as being + + align:start position:0% +if you think of the wood cells as being + + + align:start position:0% +if you think of the wood cells as being +something like + + align:start position:0% +something like + + + align:start position:0% +something like +that and you're loading it this way on + + align:start position:0% +that and you're loading it this way on + + + align:start position:0% +that and you're loading it this way on +the cells just actually shorten and the + + align:start position:0% +the cells just actually shorten and the + + + align:start position:0% +the cells just actually shorten and the +modulus depends on it's just is is the + + align:start position:0% +modulus depends on it's just is is the + + + align:start position:0% +modulus depends on it's just is is the +volume fraction of solid times the + + align:start position:0% +volume fraction of solid times the + + + align:start position:0% +volume fraction of solid times the +modulus of the solid and that's where + + align:start position:0% +modulus of the solid and that's where + + + align:start position:0% +modulus of the solid and that's where +this comes from and once you have this + + align:start position:0% +this comes from and once you have this + + + align:start position:0% +this comes from and once you have this +that basically gives you that okay are + + align:start position:0% +that basically gives you that okay are + + + align:start position:0% +that basically gives you that okay are +we good with that um so that's why it's + + align:start position:0% +we good with that um so that's why it's + + + align:start position:0% +we good with that um so that's why it's +higher + + align:start position:0% +higher + + + align:start position:0% +higher +um you know another way to look at it as + + align:start position:0% +um you know another way to look at it as + + + align:start position:0% +um you know another way to look at it as +sort of more of a handwavy argument is + + align:start position:0% +sort of more of a handwavy argument is + + + align:start position:0% +sort of more of a handwavy argument is +that if you have a certain amount of + + align:start position:0% +that if you have a certain amount of + + + align:start position:0% +that if you have a certain amount of +solid so say you have a certain mass of + + align:start position:0% +solid so say you have a certain mass of + + + align:start position:0% +solid so say you have a certain mass of +solid if it's solid it takes up a + + align:start position:0% +solid if it's solid it takes up a + + + align:start position:0% +solid if it's solid it takes up a +certain cross-sectional area so say your + + align:start position:0% +certain cross-sectional area so say your + + + align:start position:0% +certain cross-sectional area so say your +beam's a certain length it's going to + + align:start position:0% +beam's a certain length it's going to + + + align:start position:0% +beam's a certain length it's going to +have a certain cross-sectional area and + + align:start position:0% +have a certain cross-sectional area and + + + align:start position:0% +have a certain cross-sectional area and +if you have wood if you have a cellular + + align:start position:0% +if you have wood if you have a cellular + + + align:start position:0% +if you have wood if you have a cellular +material if you have the same mass + + align:start position:0% +material if you have the same mass + + + align:start position:0% +material if you have the same mass +you're essentially making the dimensions + + align:start position:0% +you're essentially making the dimensions + + + align:start position:0% +you're essentially making the dimensions +of that piece bigger right so you're + + align:start position:0% +of that piece bigger right so you're + + + align:start position:0% +of that piece bigger right so you're +you're sort of moving the material + + align:start position:0% +you're sort of moving the material + + + align:start position:0% +you're sort of moving the material +further away and as you're making it + + align:start position:0% +further away and as you're making it + + + align:start position:0% +further away and as you're making it +bigger you're increasing the moment of + + align:start position:0% +bigger you're increasing the moment of + + + align:start position:0% +bigger you're increasing the moment of +inertia and so you're increasing sort of + + align:start position:0% +inertia and so you're increasing sort of + + + align:start position:0% +inertia and so you're increasing sort of +the bending resistance of it okay that's + + align:start position:0% +the bending resistance of it okay that's + + + align:start position:0% +the bending resistance of it okay that's +another more hand waving way to talk + + align:start position:0% +another more hand waving way to talk + + + align:start position:0% +another more hand waving way to talk +about + + align:start position:0% +about + + + align:start position:0% +about +it and then the second + + align:start position:0% +it and then the second + + + align:start position:0% +it and then the second +part is to suggest a design for an + + align:start position:0% +part is to suggest a design for an + + + align:start position:0% +part is to suggest a design for an +engineering material based on wood that + + align:start position:0% +engineering material based on wood that + + + align:start position:0% +engineering material based on wood that +would have high values of e to the 1/2 + + align:start position:0% +would have high values of e to the 1/2 + + + align:start position:0% +would have high values of e to the 1/2 +over row so you remember when we looked + + align:start position:0% +over row so you remember when we looked + + + align:start position:0% +over row so you remember when we looked +at those material performance charts we + + align:start position:0% +at those material performance charts we + + + align:start position:0% +at those material performance charts we +said that wood was similar to + + align:start position:0% +said that wood was similar to + + + align:start position:0% +said that wood was similar to +engineering fiber Composites but those + + align:start position:0% +engineering fiber Composites but those + + + align:start position:0% +engineering fiber Composites but those +data for fiber Composites are assuming + + align:start position:0% +data for fiber Composites are assuming + + + align:start position:0% +data for fiber Composites are assuming +that it's solid the fiber Composites a + + align:start position:0% +that it's solid the fiber Composites a + + + align:start position:0% +that it's solid the fiber Composites a +solid so if you could take fiber + + align:start position:0% +solid so if you could take fiber + + + align:start position:0% +solid so if you could take fiber +Composites and make little tubes of + + align:start position:0% +Composites and make little tubes of + + + align:start position:0% +Composites and make little tubes of +fiber Composites and assemble the tubes + + align:start position:0% +fiber Composites and assemble the tubes + + + align:start position:0% +fiber Composites and assemble the tubes +together so it was like wood you would + + align:start position:0% +together so it was like wood you would + + + align:start position:0% +together so it was like wood you would +get something that would be even higher + + align:start position:0% +get something that would be even higher + + + align:start position:0% +get something that would be even higher +so if you could make a say a fiber + + align:start position:0% + + + + align:start position:0% + +composite uh honeycomb material + + align:start position:0% + + + + align:start position:0% + +and you'd want to have the fibers + + align:start position:0% +and you'd want to have the fibers + + + align:start position:0% +and you'd want to have the fibers +aligned along the prism axis of the + + align:start position:0% + + + + align:start position:0% + +honeycomb then you would get higher + + align:start position:0% +honeycomb then you would get higher + + + align:start position:0% +honeycomb then you would get higher +values it' be the same you know be this + + align:start position:0% +values it' be the same you know be this + + + align:start position:0% +values it' be the same you know be this +sort of argument again um but now with a + + align:start position:0% +sort of argument again um but now with a + + + align:start position:0% +sort of argument again um but now with a +fiber composite so you'd want if this + + align:start position:0% +fiber composite so you'd want if this + + + align:start position:0% +fiber composite so you'd want if this +was your kind of fiber composite like + + align:start position:0% + + + + align:start position:0% + +this you'd want the fibers well in Wood + + align:start position:0% +this you'd want the fibers well in Wood + + + align:start position:0% +this you'd want the fibers well in Wood +they're a little bit of an angle but say + + align:start position:0% +they're a little bit of an angle but say + + + align:start position:0% +they're a little bit of an angle but say +they were lined up like + + align:start position:0% +they were lined up like + + + align:start position:0% +they were lined up like +that you'd want through something like + + align:start position:0% +that you'd want through something like + + + align:start position:0% +that you'd want through something like +that if then loading + + align:start position:0% +that if then loading + + + align:start position:0% +that if then loading +it kind of that way on + + align:start position:0% +it kind of that way on + + + align:start position:0% +it kind of that way on +right and if one way to think about + + align:start position:0% +right and if one way to think about + + + align:start position:0% +right and if one way to think about +those charts is if you say we had a plot + + align:start position:0% +those charts is if you say we had a plot + + + align:start position:0% +those charts is if you say we had a plot +um and say this was log of the + + align:start position:0% +um and say this was log of the + + + align:start position:0% +um and say this was log of the +modulus and that was log of the density + + align:start position:0% +modulus and that was log of the density + + + align:start position:0% +modulus and that was log of the density +and I think I'll just draw the envelope + + align:start position:0% +and I think I'll just draw the envelope + + + align:start position:0% +and I think I'll just draw the envelope +so Foams were somewhere down here metals + + align:start position:0% +so Foams were somewhere down here metals + + + align:start position:0% +so Foams were somewhere down here metals +were somewhere over + + align:start position:0% + + + + align:start position:0% + +here gastr were you know somewhere in + + align:start position:0% + + + + align:start position:0% + +here uh I think Ceramics were up + + align:start position:0% +here uh I think Ceramics were up + + + align:start position:0% +here uh I think Ceramics were up +here and then I can't remember exactly + + align:start position:0% +here and then I can't remember exactly + + + align:start position:0% +here and then I can't remember exactly +where where Composites were but + + align:start position:0% +where where Composites were but + + + align:start position:0% +where where Composites were but +Composites were around about here I'll + + align:start position:0% +Composites were around about here I'll + + + align:start position:0% +Composites were around about here I'll +just say F FRC for fiber reinforced + + align:start position:0% +just say F FRC for fiber reinforced + + + align:start position:0% +just say F FRC for fiber reinforced +Composites and I think Woods were kind + + align:start position:0% +Composites and I think Woods were kind + + + align:start position:0% +Composites and I think Woods were kind +of in + + align:start position:0% +of in + + + align:start position:0% +of in +here something like that and then we had + + align:start position:0% +here something like that and then we had + + + align:start position:0% +here something like that and then we had +our performance Index right so remember + + align:start position:0% +our performance Index right so remember + + + align:start position:0% +our performance Index right so remember +there was a like a performance index + + align:start position:0% +there was a like a performance index + + + align:start position:0% +there was a like a performance index +something like that and that the slope + + align:start position:0% +something like that and that the slope + + + align:start position:0% +something like that and that the slope +of that was e to + + align:start position:0% +of that was e to + + + align:start position:0% +of that was e to +the2 over row so every point on that + + align:start position:0% +the2 over row so every point on that + + + align:start position:0% +the2 over row so every point on that +line had the same value of he 1/2 over + + align:start position:0% +line had the same value of he 1/2 over + + + align:start position:0% +line had the same value of he 1/2 over +row and essentially if you had the fiber + + align:start position:0% +row and essentially if you had the fiber + + + align:start position:0% +row and essentially if you had the fiber +composite and you made a honeycomb out + + align:start position:0% +composite and you made a honeycomb out + + + align:start position:0% +composite and you made a honeycomb out +of it you would be taking you know the + + align:start position:0% +of it you would be taking you know the + + + align:start position:0% +of it you would be taking you know the +data from here and shifting them out + + align:start position:0% +data from here and shifting them out + + + align:start position:0% +data from here and shifting them out +that way you know you'd be pushing them + + align:start position:0% +that way you know you'd be pushing them + + + align:start position:0% +that way you know you'd be pushing them +out over here so you get a higher value + + align:start position:0% +out over here so you get a higher value + + + align:start position:0% +out over here so you get a higher value +of that performance + + align:start position:0% +of that performance + + + align:start position:0% +of that performance +index okay so that's that's the test + + align:start position:0% +index okay so that's that's the test + + + align:start position:0% +index okay so that's that's the test +from last year that's the end + + align:start position:0% +from last year that's the end + + + align:start position:0% +from last year that's the end +yeah + + align:start position:0% + + + + align:start position:0% + +R yeah so the thing about the Honeycombs + + align:start position:0% +R yeah so the thing about the Honeycombs + + + align:start position:0% +R yeah so the thing about the Honeycombs +is oppos right actually we it' be worse + + align:start position:0% +is oppos right actually we it' be worse + + + align:start position:0% +is oppos right actually we it' be worse +that's that's true so the thing about + + align:start position:0% +that's that's true so the thing about + + + align:start position:0% +that's that's true so the thing about +the Hy Combs is they're very stiff in + + align:start position:0% +the Hy Combs is they're very stiff in + + + align:start position:0% +the Hy Combs is they're very stiff in +the axial Direction but you pay for that + + align:start position:0% +the axial Direction but you pay for that + + + align:start position:0% +the axial Direction but you pay for that +in the other directions and it's the + + align:start position:0% +in the other directions and it's the + + + align:start position:0% +in the other directions and it's the +same for wood so the wood is very good + + align:start position:0% +same for wood so the wood is very good + + + align:start position:0% +same for wood so the wood is very good +when you load it along the grain but you + + align:start position:0% +when you load it along the grain but you + + + align:start position:0% +when you load it along the grain but you +pay for it the other way but if you + + align:start position:0% +pay for it the other way but if you + + + align:start position:0% +pay for it the other way but if you +think of from the trees point of view + + align:start position:0% +think of from the trees point of view + + + align:start position:0% +think of from the trees point of view +you know if you're a tree so here's my + + align:start position:0% +you know if you're a tree so here's my + + + align:start position:0% +you know if you're a tree so here's my +little tree so here say we have a tree + + align:start position:0% +little tree so here say we have a tree + + + align:start position:0% +little tree so here say we have a tree +trunk and we have some Branch Branch + + align:start position:0% +trunk and we have some Branch Branch + + + align:start position:0% +trunk and we have some Branch Branch +over here branches tree um so the grain + + align:start position:0% +over here branches tree um so the grain + + + align:start position:0% +over here branches tree um so the grain +is you know lined up this way and then + + align:start position:0% +is you know lined up this way and then + + + align:start position:0% +is you know lined up this way and then +when there's a branch the the grain kind + + align:start position:0% +when there's a branch the the grain kind + + + align:start position:0% +when there's a branch the the grain kind +of turns around and goes that way right + + align:start position:0% +of turns around and goes that way right + + + align:start position:0% +of turns around and goes that way right +so if you think of the tree as a hole + + align:start position:0% +so if you think of the tree as a hole + + + align:start position:0% +so if you think of the tree as a hole +you know the whole tree blows in the + + align:start position:0% +you know the whole tree blows in the + + + align:start position:0% +you know the whole tree blows in the +wind like this so it's like a you know + + align:start position:0% +wind like this so it's like a you know + + + align:start position:0% +wind like this so it's like a you know +it's like a column like this and + + align:start position:0% +it's like a column like this and + + + align:start position:0% +it's like a column like this and +everything's lined up that way and + + align:start position:0% +everything's lined up that way and + + + align:start position:0% +everything's lined up that way and +you're loading it this way so that that + + align:start position:0% +you're loading it this way so that that + + + align:start position:0% +you're loading it this way so that that +is the stiff direction right and if + + align:start position:0% +is the stiff direction right and if + + + align:start position:0% +is the stiff direction right and if +you're a branch uh the branches are more + + align:start position:0% +you're a branch uh the branches are more + + + align:start position:0% +you're a branch uh the branches are more +like loaded by gravity so they're kind + + align:start position:0% +like loaded by gravity so they're kind + + + align:start position:0% +like loaded by gravity so they're kind +of loaded that way and then because the + + align:start position:0% +of loaded that way and then because the + + + align:start position:0% +of loaded that way and then because the +fibers you know the the grain turns + + align:start position:0% +fibers you know the the grain turns + + + align:start position:0% +fibers you know the the grain turns +around they're also oriented in the um + + align:start position:0% +around they're also oriented in the um + + + align:start position:0% +around they're also oriented in the um +sort of the good direction so from the + + align:start position:0% +sort of the good direction so from the + + + align:start position:0% +sort of the good direction so from the +trees point of view it it sort of + + align:start position:0% +trees point of view it it sort of + + + align:start position:0% +trees point of view it it sort of +optimized things and you remember when I + + align:start position:0% +optimized things and you remember when I + + + align:start position:0% +optimized things and you remember when I +talked about the old wooden sailing + + align:start position:0% +talked about the old wooden sailing + + + align:start position:0% +talked about the old wooden sailing +ships uh when they when they made the + + align:start position:0% +ships uh when they when they made the + + + align:start position:0% +ships uh when they when they made the +old old wooden Shing sailing ships you + + align:start position:0% +old old wooden Shing sailing ships you + + + align:start position:0% +old old wooden Shing sailing ships you +know if this was the deck here and that + + align:start position:0% +know if this was the deck here and that + + + align:start position:0% +know if this was the deck here and that +was the hull there they would get pieces + + align:start position:0% +was the hull there they would get pieces + + + align:start position:0% +was the hull there they would get pieces +of wood to fit in here that were called + + align:start position:0% +of wood to fit in here that were called + + + align:start position:0% +of wood to fit in here that were called +the knees that was the knee and they + + align:start position:0% +the knees that was the knee and they + + + align:start position:0% +the knees that was the knee and they +would try to get a piece it was from a + + align:start position:0% +would try to get a piece it was from a + + + align:start position:0% +would try to get a piece it was from a +branch like this and they would try to + + align:start position:0% +branch like this and they would try to + + + align:start position:0% +branch like this and they would try to +match you know the of curve of that + + align:start position:0% +match you know the of curve of that + + + align:start position:0% +match you know the of curve of that +joint with the branch with the curve + + align:start position:0% +joint with the branch with the curve + + + align:start position:0% +joint with the branch with the curve +that they needed in here so the grain + + align:start position:0% +that they needed in here so the grain + + + align:start position:0% +that they needed in here so the grain +kind of followed the pattern of what + + align:start position:0% +kind of followed the pattern of what + + + align:start position:0% +kind of followed the pattern of what +they needed for the + + align:start position:0% +they needed for the + + + align:start position:0% +they needed for the +boat okay other + + align:start position:0% + + + + align:start position:0% + +questions not quite sure about the + + align:start position:0% +questions not quite sure about the + + + align:start position:0% +questions not quite sure about the +difference between tangential versus R + + align:start position:0% +difference between tangential versus R + + + align:start position:0% +difference between tangential versus R +oh okay so in the wood you mean yes okay + + align:start position:0% +oh okay so in the wood you mean yes okay + + + align:start position:0% +oh okay so in the wood you mean yes okay +um so can I rub this stuff off we're + + align:start position:0% +um so can I rub this stuff off we're + + + align:start position:0% +um so can I rub this stuff off we're +happy um + + align:start position:0% + + + + align:start position:0% + +uh let's see um say again so oh + + align:start position:0% +uh let's see um say again so oh + + + align:start position:0% +uh let's see um say again so oh +tangential and Radial okay so say the + + align:start position:0% +tangential and Radial okay so say the + + + align:start position:0% +tangential and Radial okay so say the +wood cells look something like + + align:start position:0% +wood cells look something like + + + align:start position:0% +wood cells look something like +this so these would be sort of the fiber + + align:start position:0% +this so these would be sort of the fiber + + + align:start position:0% +this so these would be sort of the fiber +cells of the + + align:start position:0% + + + + align:start position:0% + +trachead and then the Rays typically are + + align:start position:0% +trachead and then the Rays typically are + + + align:start position:0% +trachead and then the Rays typically are +more you know kind of rectangular cells + + align:start position:0% +more you know kind of rectangular cells + + + align:start position:0% +more you know kind of rectangular cells +so they might + + align:start position:0% +so they might + + + align:start position:0% +so they might +look something like that and then there + + align:start position:0% +look something like that and then there + + + align:start position:0% +look something like that and then there +would be you know some + + align:start position:0% +would be you know some + + + align:start position:0% +would be you know some +more fibers or tracheas depending on if + + align:start position:0% +more fibers or tracheas depending on if + + + align:start position:0% +more fibers or tracheas depending on if +it was a softwood or a hard hardwood so + + align:start position:0% +it was a softwood or a hard hardwood so + + + align:start position:0% +it was a softwood or a hard hardwood so +so these would be either + + align:start position:0% +so these would be either + + + align:start position:0% +so these would be either +fibers or tracheids in a in + + align:start position:0% +fibers or tracheids in a in + + + align:start position:0% +fibers or tracheids in a in +a a hardwood or a soft wood and then + + align:start position:0% +a a hardwood or a soft wood and then + + + align:start position:0% +a a hardwood or a soft wood and then +these would be the ray cells in here + + align:start position:0% +these would be the ray cells in here + + + align:start position:0% +these would be the ray cells in here +okay so they have a different structure + + align:start position:0% +okay so they have a different structure + + + align:start position:0% +okay so they have a different structure +they just look different they're + + align:start position:0% +they just look different they're + + + align:start position:0% +they just look different they're +different shape this is the top from the + + align:start position:0% +different shape this is the top from the + + + align:start position:0% +different shape this is the top from the +top yeah this is looking from the top + + align:start position:0% +top yeah this is looking from the top + + + align:start position:0% +top yeah this is looking from the top +down and then if you think of the + + align:start position:0% + + + + align:start position:0% + +tree y uh so the trees is going to have + + align:start position:0% +tree y uh so the trees is going to have + + + align:start position:0% +tree y uh so the trees is going to have +growth rings right so the growth rings + + align:start position:0% +growth rings right so the growth rings + + + align:start position:0% +growth rings right so the growth rings +are going to look obviously I'm not + + align:start position:0% +are going to look obviously I'm not + + + align:start position:0% +are going to look obviously I'm not +making perfect circles but you get the + + align:start position:0% +making perfect circles but you get the + + + align:start position:0% +making perfect circles but you get the +idea something like that and then the + + align:start position:0% +idea something like that and then the + + + align:start position:0% +idea something like that and then the +the Rays go kind of this way they go + + align:start position:0% +the Rays go kind of this way they go + + + align:start position:0% +the Rays go kind of this way they go +radially + + align:start position:0% +radially + + + align:start position:0% +radially +okay so you know this is this would be + + align:start position:0% +okay so you know this is this would be + + + align:start position:0% +okay so you know this is this would be +the radial Direction and then those are + + align:start position:0% +the radial Direction and then those are + + + align:start position:0% +the radial Direction and then those are +the + + align:start position:0% +the + + + align:start position:0% +the +Rays are we good + + align:start position:0% +Rays are we good + + + align:start position:0% +Rays are we good +so the + + align:start position:0% +so the + + + align:start position:0% +so the +TTI uh so the tangential would be this + + align:start position:0% +TTI uh so the tangential would be this + + + align:start position:0% +TTI uh so the tangential would be this +way on okay so if I loaded this way like + + align:start position:0% +way on okay so if I loaded this way like + + + align:start position:0% +way on okay so if I loaded this way like +that that would be loading it in the + + align:start position:0% +that that would be loading it in the + + + align:start position:0% +that that would be loading it in the +tangential Direction + + align:start position:0% +tangential Direction + + + align:start position:0% +tangential Direction +and if I loaded it this way that would + + align:start position:0% +and if I loaded it this way that would + + + align:start position:0% +and if I loaded it this way that would +be loading it in the radial Direction + + align:start position:0% +be loading it in the radial Direction + + + align:start position:0% +be loading it in the radial Direction +the ra the length of the rayor runs in + + align:start position:0% +the ra the length of the rayor runs in + + + align:start position:0% +the ra the length of the rayor runs in +the radial + + align:start position:0% +the radial + + + align:start position:0% +the radial +Direction the like this way + + align:start position:0% + + + + align:start position:0% + +on so this thing here corresponds to one + + align:start position:0% +on so this thing here corresponds to one + + + align:start position:0% +on so this thing here corresponds to one +of these lines I've drawn here + + align:start position:0% +of these lines I've drawn here + + + align:start position:0% +of these lines I've drawn here +right and then you know these guys here + + align:start position:0% +right and then you know these guys here + + + align:start position:0% +right and then you know these guys here +are you know the stuff in between here + + align:start position:0% +are you know the stuff in between here + + + align:start position:0% +are you know the stuff in between here +so how do you how do you how do you know + + align:start position:0% +so how do you how do you how do you know + + + align:start position:0% +so how do you how do you how do you know +like what the + + align:start position:0% +like what the + + + align:start position:0% +like what the +sure uh the young mod is in stiffness is + + align:start position:0% +sure uh the young mod is in stiffness is + + + align:start position:0% +sure uh the young mod is in stiffness is +uh so say so say we were loading it + + align:start position:0% +uh so say so say we were loading it + + + align:start position:0% +uh so say so say we were loading it +tangentially we're loading it like + + align:start position:0% +tangentially we're loading it like + + + align:start position:0% +tangentially we're loading it like +that then + + align:start position:0% +that then + + + align:start position:0% +that then +uh if you have like a tree how do you + + align:start position:0% +uh if you have like a tree how do you + + + align:start position:0% +uh if you have like a tree how do you +apply a tangential load on it oh well + + align:start position:0% +apply a tangential load on it oh well + + + align:start position:0% +apply a tangential load on it oh well +it's not the whole tree right so you you + + align:start position:0% +it's not the whole tree right so you you + + + align:start position:0% +it's not the whole tree right so you you +know say we have a piece of wood that we + + align:start position:0% +know say we have a piece of wood that we + + + align:start position:0% +know say we have a piece of wood that we +cut out like this so say I have that and + + align:start position:0% +cut out like this so say I have that and + + + align:start position:0% +cut out like this so say I have that and +if I loaded it this way on I'd be + + align:start position:0% +if I loaded it this way on I'd be + + + align:start position:0% +if I loaded it this way on I'd be +loading it tangentially you know the + + align:start position:0% +loading it tangentially you know the + + + align:start position:0% +loading it tangentially you know the +trees the tree is Big right so you don't + + align:start position:0% +trees the tree is Big right so you don't + + + align:start position:0% +trees the tree is Big right so you don't +I'm not talking about loading the whole + + align:start position:0% +I'm not talking about loading the whole + + + align:start position:0% +I'm not talking about loading the whole +tree I'm talking about taking a piece of + + align:start position:0% +tree I'm talking about taking a piece of + + + align:start position:0% +tree I'm talking about taking a piece of +wood out of the tree and loading it okay + + align:start position:0% +wood out of the tree and loading it okay + + + align:start position:0% +wood out of the tree and loading it okay +so you can tangentially for the entire + + align:start position:0% +so you can tangentially for the entire + + + align:start position:0% +so you can tangentially for the entire +like a trunk no I'm talking about taking + + align:start position:0% +like a trunk no I'm talking about taking + + + align:start position:0% +like a trunk no I'm talking about taking +a piece out and loading that piece how + + align:start position:0% +a piece out and loading that piece how + + + align:start position:0% +a piece out and loading that piece how +about R do you take so the same thing + + align:start position:0% +about R do you take so the same thing + + + align:start position:0% +about R do you take so the same thing +you'd take you know say this was the + + align:start position:0% +you'd take you know say this was the + + + align:start position:0% +you'd take you know say this was the +piece of wood that you were looking at + + align:start position:0% +piece of wood that you were looking at + + + align:start position:0% +piece of wood that you were looking at +now you would just load it this way + + align:start position:0% +now you would just load it this way + + + align:start position:0% +now you would just load it this way +on okay I think I think um I brought my + + align:start position:0% +on okay I think I think um I brought my + + + align:start position:0% +on okay I think I think um I brought my +thing cuz I had + + align:start position:0% +thing cuz I had + + + align:start position:0% +thing cuz I had +the slides let me see if I can find I + + align:start position:0% +the slides let me see if I can find I + + + align:start position:0% +the slides let me see if I can find I +think there was a slide that showed + + align:start position:0% + + + + align:start position:0% + +this uh + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so okay that was furry + + align:start position:0% +so okay that was furry + + + align:start position:0% +so okay that was furry +Fridays uh that was the wood sculpture + + align:start position:0% +Fridays uh that was the wood sculpture + + + align:start position:0% +Fridays uh that was the wood sculpture +here we + + align:start position:0% +here we + + + align:start position:0% +here we +go okay so imagine that that cube is + + align:start position:0% +go okay so imagine that that cube is + + + align:start position:0% +go okay so imagine that that cube is +your piece of wood that you're loading + + align:start position:0% +your piece of wood that you're loading + + + align:start position:0% +your piece of wood that you're loading +right so imagine this is the you cut a + + align:start position:0% +right so imagine this is the you cut a + + + align:start position:0% +right so imagine this is the you cut a +little piece out + + align:start position:0% +little piece out + + + align:start position:0% +little piece out +then you're loading at tangent can you + + align:start position:0% +then you're loading at tangent can you + + + align:start position:0% +then you're loading at tangent can you +see then you can load at Radio you're + + align:start position:0% +see then you can load at Radio you're + + + align:start position:0% +see then you can load at Radio you're +not loading the whole + + align:start position:0% +not loading the whole + + + align:start position:0% +not loading the whole +tree + + align:start position:0% +tree + + + align:start position:0% +tree +no yeah because then it's yeah I see the + + align:start position:0% +no yeah because then it's yeah I see the + + + align:start position:0% +no yeah because then it's yeah I see the +problem yeah yeah because I could say + + align:start position:0% +problem yeah yeah because I could say + + + align:start position:0% +problem yeah yeah because I could say +well if I was trying to load the whole + + align:start position:0% +well if I was trying to load the whole + + + align:start position:0% +well if I was trying to load the whole +thing say I was loading it from here to + + align:start position:0% +thing say I was loading it from here to + + + align:start position:0% +thing say I was loading it from here to +there well for one if you look at it one + + align:start position:0% +there well for one if you look at it one + + + align:start position:0% +there well for one if you look at it one +way it looks tangential if you look at + + align:start position:0% +way it looks tangential if you look at + + + align:start position:0% +way it looks tangential if you look at +the other way it looks radial so think + + align:start position:0% +the other way it looks radial so think + + + align:start position:0% +the other way it looks radial so think +of cutting a piece out because that is + + align:start position:0% +of cutting a piece out because that is + + + align:start position:0% +of cutting a piece out because that is +what you're going to do you're going to + + align:start position:0% +what you're going to do you're going to + + + align:start position:0% +what you're going to do you're going to +cut a piece out okay + + align:start position:0% +cut a piece out okay + + + align:start position:0% +cut a piece out okay +all right are there other + + align:start position:0% + + + + align:start position:0% + +questions yes sheet do you only get that + + align:start position:0% +questions yes sheet do you only get that + + + align:start position:0% +questions yes sheet do you only get that +formula for theams or also I'm going to + + align:start position:0% +formula for theams or also I'm going to + + + align:start position:0% +formula for theams or also I'm going to +give you um if you look at I think + + align:start position:0% +give you um if you look at I think + + + align:start position:0% +give you um if you look at I think +problem set two I gave you a sheet that + + align:start position:0% +problem set two I gave you a sheet that + + + align:start position:0% +problem set two I gave you a sheet that +had three pages of + + align:start position:0% +had three pages of + + + align:start position:0% +had three pages of +equations and it looked exactly like + + align:start position:0% +equations and it looked exactly like + + + align:start position:0% +equations and it looked exactly like +this so there was one saying properties + + align:start position:0% +this so there was one saying properties + + + align:start position:0% +this so there was one saying properties +of two-dimensional cellular solids + + align:start position:0% +of two-dimensional cellular solids + + + align:start position:0% +of two-dimensional cellular solids +Honeycombs there was a whole thing of + + align:start position:0% +Honeycombs there was a whole thing of + + + align:start position:0% +Honeycombs there was a whole thing of +inplane properties and out of plane + + align:start position:0% +inplane properties and out of plane + + + align:start position:0% +inplane properties and out of plane +properties + + align:start position:0% +properties + + + align:start position:0% +properties +that was one page the next page was + + align:start position:0% +that was one page the next page was + + + align:start position:0% +that was one page the next page was +properties of regular hexagonal + + align:start position:0% +properties of regular hexagonal + + + align:start position:0% +properties of regular hexagonal +Honeycombs and then the next page + + align:start position:0% +Honeycombs and then the next page + + + align:start position:0% +Honeycombs and then the next page +was properties of threedimensional + + align:start position:0% +was properties of threedimensional + + + align:start position:0% +was properties of threedimensional +cellular solids Foams okay excellent + + align:start position:0% +cellular solids Foams okay excellent + + + align:start position:0% +cellular solids Foams okay excellent +thank you okay and like I just said I I + + align:start position:0% +thank you okay and like I just said I I + + + align:start position:0% +thank you okay and like I just said I I +think there's maybe one or two equations + + align:start position:0% +think there's maybe one or two equations + + + align:start position:0% +think there's maybe one or two equations +missing from this but if if there was + + align:start position:0% +missing from this but if if there was + + + align:start position:0% +missing from this but if if there was +something you needed I would give it to + + align:start position:0% +something you needed I would give it to + + + align:start position:0% +something you needed I would give it to +you I would give it to you + + align:start position:0% +you I would give it to you + + + align:start position:0% +you I would give it to you +okay I should have scrolled down what + + align:start position:0% +okay I should have scrolled down what + + + align:start position:0% +okay I should have scrolled down what +you should have scrolled so here like me + + align:start position:0% +you should have scrolled so here like me + + + align:start position:0% +you should have scrolled so here like me +this happens to me all the time I have + + align:start position:0% +this happens to me all the time I have + + + align:start position:0% +this happens to me all the time I have +some website I'm looking at I'm like + + align:start position:0% +some website I'm looking at I'm like + + + align:start position:0% +some website I'm looking at I'm like +okay I got it I think I've got + + align:start position:0% +okay I got it I think I've got + + + align:start position:0% +okay I got it I think I've got +everything and then I realized I was + + align:start position:0% +everything and then I realized I was + + + align:start position:0% +everything and then I realized I was +supposed to you know I missed something + + align:start position:0% +supposed to you know I missed something + + + align:start position:0% +supposed to you know I missed something +because I was supposed to scroll down + + align:start position:0% +because I was supposed to scroll down + + + align:start position:0% +because I was supposed to scroll down +was only honeycom that's why well I + + align:start position:0% +was only honeycom that's why well I + + + align:start position:0% +was only honeycom that's why well I +think that was probably all we covered + + align:start position:0% +think that was probably all we covered + + + align:start position:0% +think that was probably all we covered +was the Honeycombs on that problem set + + align:start position:0% +was the Honeycombs on that problem set + + + align:start position:0% +was the Honeycombs on that problem set +that's why I yeah okay all right yeah so + + align:start position:0% +that's why I yeah okay all right yeah so + + + align:start position:0% +that's why I yeah okay all right yeah so +I'm going to give you this this will be + + align:start position:0% +I'm going to give you this this will be + + + align:start position:0% +I'm going to give you this this will be +attached to the + + align:start position:0% +attached to the + + + align:start position:0% +attached to the +test okay so I think I think on the um + + align:start position:0% +test okay so I think I think on the um + + + align:start position:0% +test okay so I think I think on the um +test that I posted it was attached + + align:start position:0% +test that I posted it was attached + + + align:start position:0% +test that I posted it was attached +wasn't it yeah yeah K do you have a + + align:start position:0% +wasn't it yeah yeah K do you have a + + + align:start position:0% +wasn't it yeah yeah K do you have a +question the two part D I think I don't + + align:start position:0% +question the two part D I think I don't + + + align:start position:0% +question the two part D I think I don't +think we went over that but I was + + align:start position:0% +think we went over that but I was + + + align:start position:0% +think we went over that but I was +confused as to how um I guess is it just + + align:start position:0% +confused as to how um I guess is it just + + + align:start position:0% +confused as to how um I guess is it just +that equil equilateral triangular cells + + align:start position:0% +that equil equilateral triangular cells + + + align:start position:0% +that equil equilateral triangular cells +always have is always like trust behavor + + align:start position:0% +always have is always like trust behavor + + + align:start position:0% +always have is always like trust behavor +um let's see which 2014 T 2014 oh sorry + + align:start position:0% +um let's see which 2014 T 2014 oh sorry + + + align:start position:0% +um let's see which 2014 T 2014 oh sorry +I missed a part sorry um yeah so it says + + align:start position:0% +I missed a part sorry um yeah so it says + + + align:start position:0% +I missed a part sorry um yeah so it says +the same titanium alloy is used to make + + align:start position:0% +the same titanium alloy is used to make + + + align:start position:0% +the same titanium alloy is used to make +a honeycomb with lateral triangular + + align:start position:0% +a honeycomb with lateral triangular + + + align:start position:0% +a honeycomb with lateral triangular +cells and what is the inlan Young's + + align:start position:0% +cells and what is the inlan Young's + + + align:start position:0% +cells and what is the inlan Young's +modulus for loading in the X2 direction + + align:start position:0% +modulus for loading in the X2 direction + + + align:start position:0% +modulus for loading in the X2 direction +of the Triangular honeycomb so + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um so this + + align:start position:0% +um so this + + + align:start position:0% +um so this +is you know say you + + align:start position:0% + + + + align:start position:0% + +have cells that look like that now + + align:start position:0% +have cells that look like that now + + + align:start position:0% +have cells that look like that now +and that's + + align:start position:0% +and that's + + + align:start position:0% +and that's +X1 that's X2 + + align:start position:0% +X1 that's X2 + + + align:start position:0% +X1 that's X2 +um blah blah blah blah blah okay so the + + align:start position:0% +um blah blah blah blah blah okay so the + + + align:start position:0% +um blah blah blah blah blah okay so the +Young's modulus for + + align:start position:0% +Young's modulus for + + + align:start position:0% +Young's modulus for +this um so I happen to remember the + + align:start position:0% +this um so I happen to remember the + + + align:start position:0% +this um so I happen to remember the +formula so I guess I'm thinking you + + align:start position:0% +formula so I guess I'm thinking you + + + align:start position:0% +formula so I guess I'm thinking you +might have put this on your cheat sheets + + align:start position:0% +might have put this on your cheat sheets + + + align:start position:0% +might have put this on your cheat sheets +uh it's 1.15 time + + align:start position:0% +uh it's 1.15 time + + + align:start position:0% +uh it's 1.15 time +es time that times the relative density + + align:start position:0% +es time that times the relative density + + + align:start position:0% +es time that times the relative density +so um I'm trying to remember do I have + + align:start position:0% +so um I'm trying to remember do I have + + + align:start position:0% +so um I'm trying to remember do I have +that on + + align:start position:0% +that on + + + align:start position:0% +that on +here I don't have it on + + align:start position:0% +here I don't have it on + + + align:start position:0% +here I don't have it on +here suppos to + + align:start position:0% + + + + align:start position:0% + +um are we just supposed to well I just + + align:start position:0% +um are we just supposed to well I just + + + align:start position:0% +um are we just supposed to well I just +what I would hope that you would know is + + align:start position:0% +what I would hope that you would know is + + + align:start position:0% +what I would hope that you would know is +maybe not the constant but that it + + align:start position:0% +maybe not the constant but that it + + + align:start position:0% +maybe not the constant but that it +should go as es and linearly with the + + align:start position:0% +should go as es and linearly with the + + + align:start position:0% +should go as es and linearly with the +relative density because it's a trust + + align:start position:0% +relative density because it's a trust + + + align:start position:0% +relative density because it's a trust +and because it deforms actually I don't + + align:start position:0% +and because it deforms actually I don't + + + align:start position:0% +and because it deforms actually I don't +really expect that you would remember + + align:start position:0% +really expect that you would remember + + + align:start position:0% +really expect that you would remember +the + + align:start position:0% +the + + + align:start position:0% +the +1.15 yeah so does that mean for all the + + align:start position:0% +1.15 yeah so does that mean for all the + + + align:start position:0% +1.15 yeah so does that mean for all the +phones of which there are like 10 + + align:start position:0% +phones of which there are like 10 + + + align:start position:0% +phones of which there are like 10 +constants we don't need to write all + + align:start position:0% +constants we don't need to write all + + + align:start position:0% +constants we don't need to write all +down like + + align:start position:0% +down like + + + align:start position:0% +down like +I think I think that's what this thing + + align:start position:0% +I think I think that's what this thing + + + align:start position:0% +I think I think that's what this thing +gives you uh let's see no it gives you + + align:start position:0% +gives you uh let's see no it gives you + + + align:start position:0% +gives you uh let's see no it gives you +all the C's all right then I'll make + + align:start position:0% +all the C's all right then I'll make + + + align:start position:0% +all the C's all right then I'll make +sure I give you the + + align:start position:0% +sure I give you the + + + align:start position:0% +sure I give you the +C's I'll make sure I give you the C's um + + align:start position:0% +C's I'll make sure I give you the C's um + + + align:start position:0% +C's I'll make sure I give you the C's um +but who's got a pen so I can write that + + align:start position:0% +but who's got a pen so I can write that + + + align:start position:0% +but who's got a pen so I can write that +down and make sure that I do + + align:start position:0% + + + + align:start position:0% + +that need somebody got a piece of paper + + align:start position:0% +that need somebody got a piece of paper + + + align:start position:0% +that need somebody got a piece of paper +well I could write it down in here oh + + align:start position:0% +well I could write it down in here oh + + + align:start position:0% +well I could write it down in here oh +here we go I can write it down on this + + align:start position:0% +here we go I can write it down on this + + + align:start position:0% +here we go I can write it down on this +little sticky thing here + + align:start position:0% +little sticky thing here + + + align:start position:0% +little sticky thing here +[Music] + + align:start position:0% + + + + align:start position:0% + +okay so I'll stick that on there so I'll + + align:start position:0% +okay so I'll stick that on there so I'll + + + align:start position:0% +okay so I'll stick that on there so I'll +remember to do + + align:start position:0% +remember to do + + + align:start position:0% +remember to do +that writing what C's because you have + + align:start position:0% +that writing what C's because you have + + + align:start position:0% +that writing what C's because you have +in your equation C1 C2 well I think I + + align:start position:0% +in your equation C1 C2 well I think I + + + align:start position:0% +in your equation C1 C2 well I think I +would say you know say I asked you for I + + align:start position:0% +would say you know say I asked you for I + + + align:start position:0% +would say you know say I asked you for I +don't know the uh yield stress for a + + align:start position:0% +don't know the uh yield stress for a + + + align:start position:0% +don't know the uh yield stress for a +foam and compression that yields + + align:start position:0% +foam and compression that yields + + + align:start position:0% +foam and compression that yields +plastically I would say the constant for + + align:start position:0% +plastically I would say the constant for + + + align:start position:0% +plastically I would say the constant for +that + + align:start position:0% +that + + + align:start position:0% +that +is3 you know I wouldn't I wouldn't give + + align:start position:0% +is3 you know I wouldn't I wouldn't give + + + align:start position:0% +is3 you know I wouldn't I wouldn't give +you C2 like I wouldn't do it by numbers + + align:start position:0% +you C2 like I wouldn't do it by numbers + + + align:start position:0% +you C2 like I wouldn't do it by numbers +I would tell you which what the number + + align:start position:0% +I would tell you which what the number + + + align:start position:0% +I would tell you which what the number +was for the thing you + + align:start position:0% +was for the thing you + + + align:start position:0% +was for the thing you +needed because I mean the way the + + align:start position:0% +needed because I mean the way the + + + align:start position:0% +needed because I mean the way the +numbers are the only reason they're + + align:start position:0% +numbers are the only reason they're + + + align:start position:0% +numbers are the only reason they're +numbered is because that's the number + + align:start position:0% +numbered is because that's the number + + + align:start position:0% +numbered is because that's the number +they are in the book they're just + + align:start position:0% +they are in the book they're just + + + align:start position:0% +they are in the book they're just +ordered sequentially in the book um but + + align:start position:0% +ordered sequentially in the book um but + + + align:start position:0% +ordered sequentially in the book um but +I don't expect you to remember which you + + align:start position:0% +I don't expect you to remember which you + + + align:start position:0% +I don't expect you to remember which you +know if it's C6 or C5 or something yeah + + align:start position:0% +know if it's C6 or C5 or something yeah + + + align:start position:0% +know if it's C6 or C5 or something yeah +so anyone else + + align:start position:0% + + + + align:start position:0% + +can you explain the difference between + + align:start position:0% +can you explain the difference between + + + align:start position:0% +can you explain the difference between +un the axial + + align:start position:0% +un the axial + + + align:start position:0% +un the axial +yield + + align:start position:0% +yield + + + align:start position:0% +yield +plastic oh okay + + align:start position:0% +plastic oh okay + + + align:start position:0% +plastic oh okay +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +um + + align:start position:0% + + + + align:start position:0% + +so so if you have + + align:start position:0% + + + + align:start position:0% + +something and it fails by uniaxial yield + + align:start position:0% +something and it fails by uniaxial yield + + + align:start position:0% +something and it fails by uniaxial yield +so say you have a honeycomb + + align:start position:0% + + + + align:start position:0% + +like + + align:start position:0% +like + + + align:start position:0% +like +this and you're loading it this way on + + align:start position:0% +this and you're loading it this way on + + + align:start position:0% +this and you're loading it this way on +okay so if you're loading it that way on + + align:start position:0% +okay so if you're loading it that way on + + + align:start position:0% +okay so if you're loading it that way on +these walls of the honeycomb are just + + align:start position:0% +these walls of the honeycomb are just + + + align:start position:0% +these walls of the honeycomb are just +actually deforming initially right so + + align:start position:0% +actually deforming initially right so + + + align:start position:0% +actually deforming initially right so +the elastic behaviors they just actually + + align:start position:0% +the elastic behaviors they just actually + + + align:start position:0% +the elastic behaviors they just actually +deform so if if it works out that if + + align:start position:0% +deform so if if it works out that if + + + align:start position:0% +deform so if if it works out that if +these cell walls are very + + align:start position:0% +these cell walls are very + + + align:start position:0% +these cell walls are very +thick then you can reach a yield stress + + align:start position:0% +thick then you can reach a yield stress + + + align:start position:0% +thick then you can reach a yield stress +before any buckling occurs and then the + + align:start position:0% +before any buckling occurs and then the + + + align:start position:0% +before any buckling occurs and then the +strength + + align:start position:0% +strength + + + align:start position:0% +strength +Str would just be that yield stress of + + align:start position:0% +Str would just be that yield stress of + + + align:start position:0% +Str would just be that yield stress of +the cell wall material times the + + align:start position:0% +the cell wall material times the + + + align:start position:0% +the cell wall material times the +relative + + align:start position:0% +relative + + + align:start position:0% +relative +density okay but the cell walls have to + + align:start position:0% +density okay but the cell walls have to + + + align:start position:0% +density okay but the cell walls have to +be thick for that to happen so then + + align:start position:0% +be thick for that to happen so then + + + align:start position:0% +be thick for that to happen so then +imagine that the cell walls aren't thick + + align:start position:0% +imagine that the cell walls aren't thick + + + align:start position:0% +imagine that the cell walls aren't thick +imagine that the cell walls are + + align:start position:0% +imagine that the cell walls are + + + align:start position:0% +imagine that the cell walls are +thin so say I have the same + + align:start position:0% + + + + align:start position:0% + +honeycomb like + + align:start position:0% + + + + align:start position:0% + +this if + + align:start position:0% +this if + + + align:start position:0% +this if +if the walls are thin and say the solid + + align:start position:0% +if the walls are thin and say the solid + + + align:start position:0% +if the walls are thin and say the solid +material itself so this + + align:start position:0% +material itself so this + + + align:start position:0% +material itself so this +is for the solid it has some stress + + align:start position:0% +is for the solid it has some stress + + + align:start position:0% +is for the solid it has some stress +strain curve and it may have a linear + + align:start position:0% +strain curve and it may have a linear + + + align:start position:0% +strain curve and it may have a linear +elastic part and then kind of a yield + + align:start position:0% +elastic part and then kind of a yield + + + align:start position:0% +elastic part and then kind of a yield +thing like that right uh so say this is + + align:start position:0% +thing like that right uh so say this is + + + align:start position:0% +thing like that right uh so say this is +the yield strength + + align:start position:0% +the yield strength + + + align:start position:0% +the yield strength +here um as you say we compress that this + + align:start position:0% +here um as you say we compress that this + + + align:start position:0% +here um as you say we compress that this +way on the same thing in the three + + align:start position:0% +way on the same thing in the three + + + align:start position:0% +way on the same thing in the three +Direction then um if a material's + + align:start position:0% +Direction then um if a material's + + + align:start position:0% +Direction then um if a material's +got a healed point there can be an + + align:start position:0% +got a healed point there can be an + + + align:start position:0% +got a healed point there can be an +interaction between plastic heeling and + + align:start position:0% +interaction between plastic heeling and + + + align:start position:0% +interaction between plastic heeling and +elastic buckling and you can get plastic + + align:start position:0% +elastic buckling and you can get plastic + + + align:start position:0% +elastic buckling and you can get plastic +buckling and the plastic buckling you're + + align:start position:0% +buckling and the plastic buckling you're + + + align:start position:0% +buckling and the plastic buckling you're +going to get kind of wrinkles that go + + align:start position:0% +going to get kind of wrinkles that go + + + align:start position:0% +going to get kind of wrinkles that go +like along the length of it this way + + align:start position:0% +like along the length of it this way + + + align:start position:0% +like along the length of it this way +kind of thing remember I showed you that + + align:start position:0% +kind of thing remember I showed you that + + + align:start position:0% +kind of thing remember I showed you that +tube that kind of collapsed and folded + + align:start position:0% +tube that kind of collapsed and folded + + + align:start position:0% +tube that kind of collapsed and folded +up kind of thing that's plastic buckling + + align:start position:0% +up kind of thing that's plastic buckling + + + align:start position:0% +up kind of thing that's plastic buckling +okay and uh typically people use What's + + align:start position:0% +okay and uh typically people use What's + + + align:start position:0% +okay and uh typically people use What's +called the tangential modulus to + + align:start position:0% +called the tangential modulus to + + + align:start position:0% +called the tangential modulus to +calculate a buckling stress for plastic + + align:start position:0% +calculate a buckling stress for plastic + + + align:start position:0% +calculate a buckling stress for plastic +buckling and the tangential modulus + + align:start position:0% +buckling and the tangential modulus + + + align:start position:0% +buckling and the tangential modulus +would be you know something related to + + align:start position:0% +would be you know something related to + + + align:start position:0% +would be you know something related to +the tangent over there I mean I don't + + align:start position:0% +the tangent over there I mean I don't + + + align:start position:0% +the tangent over there I mean I don't +expect you to you know be able to derive + + align:start position:0% +expect you to you know be able to derive + + + align:start position:0% +expect you to you know be able to derive +plastic buckling + + align:start position:0% +plastic buckling + + + align:start position:0% +plastic buckling +equations but um the plastic + + align:start position:0% +equations but um the plastic + + + align:start position:0% +equations but um the plastic +buckling uh you you know what elastic + + align:start position:0% +buckling uh you you know what elastic + + + align:start position:0% +buckling uh you you know what elastic +buckling is + + align:start position:0% +buckling is + + + align:start position:0% +buckling is +right yeah yeah so you know one way to + + align:start position:0% +right yeah yeah so you know one way to + + + align:start position:0% +right yeah yeah so you know one way to +think about plastic buckling is um + + align:start position:0% +think about plastic buckling is um + + + align:start position:0% +think about plastic buckling is um +if you have uh I'm trying to + + align:start position:0% +if you have uh I'm trying to + + + align:start position:0% +if you have uh I'm trying to +remember uh this is called the + + align:start position:0% +remember uh this is called the + + + align:start position:0% +remember uh this is called the +slenderness + + align:start position:0% + + + + align:start position:0% + +ratio and I'm trying to remember is that + + align:start position:0% +ratio and I'm trying to remember is that + + + align:start position:0% +ratio and I'm trying to remember is that +L over R imagine you had just a circular + + align:start position:0% +L over R imagine you had just a circular + + + align:start position:0% +L over R imagine you had just a circular +crosssection and you had a length l so + + align:start position:0% +crosssection and you had a length l so + + + align:start position:0% +crosssection and you had a length l so +you have a column + + align:start position:0% +you have a column + + + align:start position:0% +you have a column +here and it's got a length + + align:start position:0% +here and it's got a length + + + align:start position:0% +here and it's got a length +L and it's got a radius R like that okay + + align:start position:0% +L and it's got a radius R like that okay + + + align:start position:0% +L and it's got a radius R like that okay +so the longer it gets the more slender + + align:start position:0% +so the longer it gets the more slender + + + align:start position:0% +so the longer it gets the more slender +it is the higher this slenderness ratio + + align:start position:0% +it is the higher this slenderness ratio + + + align:start position:0% +it is the higher this slenderness ratio +is + + align:start position:0% +is + + + align:start position:0% +is +and this I think is some sort of + + align:start position:0% +and this I think is some sort of + + + align:start position:0% +and this I think is some sort of +stress if the Slender is ratio of just a + + align:start position:0% +stress if the Slender is ratio of just a + + + align:start position:0% +stress if the Slender is ratio of just a +single column is short if it's stubby if + + align:start position:0% +single column is short if it's stubby if + + + align:start position:0% +single column is short if it's stubby if +you had a column that looked kind of + + align:start position:0% +you had a column that looked kind of + + + align:start position:0% +you had a column that looked kind of +like that it's not going to buckle it's + + align:start position:0% +like that it's not going to buckle it's + + + align:start position:0% +like that it's not going to buckle it's +going to yield and so if you compress + + align:start position:0% +going to yield and so if you compress + + + align:start position:0% +going to yield and so if you compress +that it would just + + align:start position:0% +that it would just + + + align:start position:0% +that it would just +yield and it's just going to yield at + + align:start position:0% +yield and it's just going to yield at + + + align:start position:0% +yield and it's just going to yield at +the yield stress right just going to + + align:start position:0% +the yield stress right just going to + + + align:start position:0% +the yield stress right just going to +yield it Sigma y of the solid whatever + + align:start position:0% +yield it Sigma y of the solid whatever + + + align:start position:0% +yield it Sigma y of the solid whatever +the solid is if you have a long C column + + align:start position:0% +the solid is if you have a long C column + + + align:start position:0% +the solid is if you have a long C column +um it would Buckle elastically like by + + align:start position:0% +um it would Buckle elastically like by + + + align:start position:0% +um it would Buckle elastically like by +an Oiler buckling and Oiler + + align:start position:0% +an Oiler buckling and Oiler + + + align:start position:0% +an Oiler buckling and Oiler +buckling um let's see I'm going to run + + align:start position:0% +buckling um let's see I'm going to run + + + align:start position:0% +buckling um let's see I'm going to run +out of room + + align:start position:0% + + + + align:start position:0% + +here if you think of it in terms of a + + align:start position:0% +here if you think of it in terms of a + + + align:start position:0% +here if you think of it in terms of a +stress instead of a load it's going to + + align:start position:0% +stress instead of a load it's going to + + + align:start position:0% +stress instead of a load it's going to +be n^2 pi^ 2 e s i let's say I goes as R + + align:start position:0% +be n^2 pi^ 2 e s i let's say I goes as R + + + align:start position:0% +be n^2 pi^ 2 e s i let's say I goes as R +4th and this is going to be + + align:start position:0% +4th and this is going to be + + + align:start position:0% +4th and this is going to be +L2 R 2 right this there going to be a pi + + align:start position:0% +L2 R 2 right this there going to be a pi + + + align:start position:0% +L2 R 2 right this there going to be a pi +in here there's going to be a pi in here + + align:start position:0% +in here there's going to be a pi in here + + + align:start position:0% +in here there's going to be a pi in here +I might have lost a factor of four but + + align:start position:0% +I might have lost a factor of four but + + + align:start position:0% +I might have lost a factor of four but +uh it's going to be let me make this + + align:start position:0% +uh it's going to be let me make this + + + align:start position:0% +uh it's going to be let me make this +proportional + + align:start position:0% +proportional + + + align:start position:0% +proportional +okay so this slenderness ratio this + + align:start position:0% +okay so this slenderness ratio this + + + align:start position:0% +okay so this slenderness ratio this +going to be an L over R squar term here + + align:start position:0% +going to be an L over R squar term here + + + align:start position:0% +going to be an L over R squar term here +so I can cancel out the four there and + + align:start position:0% +so I can cancel out the four there and + + + align:start position:0% +so I can cancel out the four there and +put a + + align:start position:0% +put a + + + align:start position:0% +put a +squared so it goes as Sigma + + align:start position:0% +squared so it goes as Sigma + + + align:start position:0% +squared so it goes as Sigma +Oiler is going to go as e s + + align:start position:0% +Oiler is going to go as e s + + + align:start position:0% +Oiler is going to go as e s +time r + + align:start position:0% +time r + + + align:start position:0% +time r +L squared like that and so this is the + + align:start position:0% +L squared like that and so this is the + + + align:start position:0% +L squared like that and so this is the +oiler buckling stress here okay so this + + align:start position:0% +oiler buckling stress here okay so this + + + align:start position:0% +oiler buckling stress here okay so this +would be + + align:start position:0% + + + + align:start position:0% + +elastic and right here at this little + + align:start position:0% +elastic and right here at this little + + + align:start position:0% +elastic and right here at this little +corner it turns out life isn't quite + + align:start position:0% +corner it turns out life isn't quite + + + align:start position:0% +corner it turns out life isn't quite +that kind of mathematically exact um if + + align:start position:0% +that kind of mathematically exact um if + + + align:start position:0% +that kind of mathematically exact um if +you're near that corner it's not like + + align:start position:0% +you're near that corner it's not like + + + align:start position:0% +you're near that corner it's not like +here it's buckling elastically and here + + align:start position:0% +here it's buckling elastically and here + + + align:start position:0% +here it's buckling elastically and here +it's buckling plastically what happens + + align:start position:0% +it's buckling plastically what happens + + + align:start position:0% +it's buckling plastically what happens +is if you looked at data data might + + align:start position:0% +is if you looked at data data might + + + align:start position:0% +is if you looked at data data might +do something like + + align:start position:0% +do something like + + + align:start position:0% +do something like +that so there's some interaction between + + align:start position:0% +that so there's some interaction between + + + align:start position:0% +that so there's some interaction between +the elastic and the plastic and that's + + align:start position:0% +the elastic and the plastic and that's + + + align:start position:0% +the elastic and the plastic and that's +kind of what's going on with this thing + + align:start position:0% +kind of what's going on with this thing + + + align:start position:0% +kind of what's going on with this thing +here does that make + + align:start position:0% + + + + align:start position:0% + +sense okay so if you if you unload + + align:start position:0% +sense okay so if you if you unload + + + align:start position:0% +sense okay so if you if you unload +plastic buckling you actually get some + + align:start position:0% +plastic buckling you actually get some + + + align:start position:0% +plastic buckling you actually get some +of the nastic part back you're not going + + align:start position:0% +of the nastic part back you're not going + + + align:start position:0% +of the nastic part back you're not going +to get much back not no + + align:start position:0% +to get much back not no + + + align:start position:0% +to get much back not no +because because it's because you know + + align:start position:0% +because because it's because you know + + + align:start position:0% +because because it's because you know +once to get the plastic buckling you're + + align:start position:0% +once to get the plastic buckling you're + + + align:start position:0% +once to get the plastic buckling you're +you're really you're you're very close + + align:start position:0% +you're really you're you're very close + + + align:start position:0% +you're really you're you're very close +to this by the time you get that + + align:start position:0% +to this by the time you get that + + + align:start position:0% +to this by the time you get that +deformation you've got locally it's + + align:start position:0% +deformation you've got locally it's + + + align:start position:0% +deformation you've got locally it's +yielded it's you know it's it's not all + + align:start position:0% +yielded it's you know it's it's not all + + + align:start position:0% +yielded it's you know it's it's not all +elastic everywhere it's going to yield + + align:start position:0% +elastic everywhere it's going to yield + + + align:start position:0% +elastic everywhere it's going to yield +in places and once it starts yielding + + align:start position:0% +in places and once it starts yielding + + + align:start position:0% +in places and once it starts yielding +it's you know it's not like you're um + + align:start position:0% +it's you know it's not like you're um + + + align:start position:0% +it's you know it's not like you're um +you know if you think of these buckles + + align:start position:0% +you know if you think of these buckles + + + align:start position:0% +you know if you think of these buckles +forming it's not like you're at one spot + + align:start position:0% +forming it's not like you're at one spot + + + align:start position:0% +forming it's not like you're at one spot +on this curve throughout the whole thing + + align:start position:0% +on this curve throughout the whole thing + + + align:start position:0% +on this curve throughout the whole thing +right some of it's more deformed and + + align:start position:0% +right some of it's more deformed and + + + align:start position:0% +right some of it's more deformed and +some of it's less deformed let me let me + + align:start position:0% +some of it's less deformed let me let me + + + align:start position:0% +some of it's less deformed let me let me +pull up those buckled plastically + + align:start position:0% +pull up those buckled plastically + + + align:start position:0% +pull up those buckled plastically +buckled columns those + + align:start position:0% +buckled columns those + + + align:start position:0% +buckled columns those +tubes oops get rid of that + + align:start position:0% +tubes oops get rid of that + + + align:start position:0% +tubes oops get rid of that +one uh let me try and remind myself + + align:start position:0% +one uh let me try and remind myself + + + align:start position:0% +one uh let me try and remind myself +where they + + align:start position:0% +where they + + + align:start position:0% +where they +were I + + align:start position:0% +were I + + + align:start position:0% +were I +think Honeycombs I want Honeycombs out + + align:start position:0% +think Honeycombs I want Honeycombs out + + + align:start position:0% +think Honeycombs I want Honeycombs out +of plane that's what I + + align:start position:0% +of plane that's what I + + + align:start position:0% +of plane that's what I +want it was this thing + + align:start position:0% +want it was this thing + + + align:start position:0% +want it was this thing +here so you see when you have like + + align:start position:0% +here so you see when you have like + + + align:start position:0% +here so you see when you have like +that's just one Tu but the whole + + align:start position:0% +that's just one Tu but the whole + + + align:start position:0% +that's just one Tu but the whole +honeycomb would you know imagine that + + align:start position:0% +honeycomb would you know imagine that + + + align:start position:0% +honeycomb would you know imagine that +you have groups of tubes put together + + align:start position:0% +you have groups of tubes put together + + + align:start position:0% +you have groups of tubes put together +they would have to you know fail in some + + align:start position:0% +they would have to you know fail in some + + + align:start position:0% +they would have to you know fail in some +compatible way but you know the the + + align:start position:0% +compatible way but you know the the + + + align:start position:0% +compatible way but you know the the +deformation and the stresses are not + + align:start position:0% +deformation and the stresses are not + + + align:start position:0% +deformation and the stresses are not +going to be uniform through this whole + + align:start position:0% +going to be uniform through this whole + + + align:start position:0% +going to be uniform through this whole +thing right one parts of it going to be + + align:start position:0% +thing right one parts of it going to be + + + align:start position:0% +thing right one parts of it going to be +a one stress and something else is going + + align:start position:0% +a one stress and something else is going + + + align:start position:0% +a one stress and something else is going +to be another stress so parts of it are + + align:start position:0% +to be another stress so parts of it are + + + align:start position:0% +to be another stress so parts of it are +going to yield plastically and that's + + align:start position:0% +going to yield plastically and that's + + + align:start position:0% +going to yield plastically and that's +you're not going to recover + + align:start position:0% +you're not going to recover + + + align:start position:0% +you're not going to recover +that okay so in fact you know they use + + align:start position:0% +that okay so in fact you know they use + + + align:start position:0% +that okay so in fact you know they use +these sorts of things for um energy + + align:start position:0% +these sorts of things for um energy + + + align:start position:0% +these sorts of things for um energy +absorption devices like like in cars and + + align:start position:0% +absorption devices like like in cars and + + + align:start position:0% +absorption devices like like in cars and +things like that uh to absorb the energy + + align:start position:0% +things like that uh to absorb the energy + + + align:start position:0% +things like that uh to absorb the energy +from the + + align:start position:0% +from the + + + align:start position:0% +from the +impact more + + align:start position:0% +impact more + + + align:start position:0% +impact more +questions oh yeah oh well let him have a + + align:start position:0% +questions oh yeah oh well let him have a + + + align:start position:0% +questions oh yeah oh well let him have a +turn I have a question about the + + align:start position:0% +turn I have a question about the + + + align:start position:0% +turn I have a question about the +uh think + + align:start position:0% +uh think + + + align:start position:0% +uh think +203 2013 + + align:start position:0% + + + + align:start position:0% + +okay oh okay so + + align:start position:0% + + + + align:start position:0% + +2013 2013 let me rub some of this stuff + + align:start position:0% +2013 2013 let me rub some of this stuff + + + align:start position:0% +2013 2013 let me rub some of this stuff +off off um + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +um there we + + align:start position:0% +um there we + + + align:start position:0% +um there we +go + + align:start position:0% +go + + + align:start position:0% +go +okay oh we haven't covered this at all + + align:start position:0% +okay oh we haven't covered this at all + + + align:start position:0% +okay oh we haven't covered this at all +so the the last question this one here + + align:start position:0% +so the the last question this one here + + + align:start position:0% +so the the last question this one here +right yeah so this question's on energy + + align:start position:0% +right yeah so this question's on energy + + + align:start position:0% +right yeah so this question's on energy +absorption we haven't got there yet how + + align:start position:0% +absorption we haven't got there yet how + + + align:start position:0% +absorption we haven't got there yet how +about so okay so oh and this the third + + align:start position:0% +about so okay so oh and this the third + + + align:start position:0% +about so okay so oh and this the third +question is on sandwich structure so + + align:start position:0% +question is on sandwich structure so + + + align:start position:0% +question is on sandwich structure so +when I taught the course in 2013 + + align:start position:0% +when I taught the course in 2013 + + + align:start position:0% +when I taught the course in 2013 +I did the topics in a different order so + + align:start position:0% +I did the topics in a different order so + + + align:start position:0% +I did the topics in a different order so +I did Honeycombs and I did Foams and + + align:start position:0% +I did Honeycombs and I did Foams and + + + align:start position:0% +I did Honeycombs and I did Foams and +then I think I did sandwich panels and I + + align:start position:0% +then I think I did sandwich panels and I + + + align:start position:0% +then I think I did sandwich panels and I +did energy absorption and I left the + + align:start position:0% +did energy absorption and I left the + + + align:start position:0% +did energy absorption and I left the +stuff on the wood and the cork to the + + align:start position:0% +stuff on the wood and the cork to the + + + align:start position:0% +stuff on the wood and the cork to the +end so we haven't done that so don't + + align:start position:0% +end so we haven't done that so don't + + + align:start position:0% +end so we haven't done that so don't +panic if you haven't if you can't do + + align:start position:0% +panic if you haven't if you can't do + + + align:start position:0% +panic if you haven't if you can't do +that okay you should have known come on + + align:start position:0% +that okay you should have known come on + + + align:start position:0% +that okay you should have known come on +you should have known that if it talked + + align:start position:0% +you should have known that if it talked + + + align:start position:0% +you should have known that if it talked +about things we haven't covered yet + + align:start position:0% +about things we haven't covered yet + + + align:start position:0% +about things we haven't covered yet +we're not going to I'm not going to do + + align:start position:0% +we're not going to I'm not going to do + + + align:start position:0% +we're not going to I'm not going to do +on the test okay what else yep I'm what + + align:start position:0% +on the test okay what else yep I'm what + + + align:start position:0% +on the test okay what else yep I'm what +a plastic hinge is plastic hinge okay um + + align:start position:0% +a plastic hinge is plastic hinge okay um + + + align:start position:0% +a plastic hinge is plastic hinge okay um +so let's just say we have a + + align:start position:0% +so let's just say we have a + + + align:start position:0% +so let's just say we have a +beam in bending + + align:start position:0% + + + + align:start position:0% + +okay and say it just has a load p in the + + align:start position:0% +okay and say it just has a load p in the + + + align:start position:0% +okay and say it just has a load p in the +middle right are we good so um so if + + align:start position:0% +middle right are we good so um so if + + + align:start position:0% +middle right are we good so um so if +there's a load p in the middle then this + + align:start position:0% +there's a load p in the middle then this + + + align:start position:0% +there's a load p in the middle then this +reaction is p over2 and that reaction is + + align:start position:0% +reaction is p over2 and that reaction is + + + align:start position:0% +reaction is p over2 and that reaction is +p over2 and if I drew the sheer force + + align:start position:0% +p over2 and if I drew the sheer force + + + align:start position:0% +p over2 and if I drew the sheer force +diagram It Go P over2 + + align:start position:0% +diagram It Go P over2 + + + align:start position:0% +diagram It Go P over2 +up go over over go P over2 down like two + + align:start position:0% +up go over over go P over2 down like two + + + align:start position:0% +up go over over go P over2 down like two +P over2 down over and back + + align:start position:0% +P over2 down over and back + + + align:start position:0% +P over2 down over and back +up okay and then if I drew the bending + + align:start position:0% +up okay and then if I drew the bending + + + align:start position:0% +up okay and then if I drew the bending +moment + + align:start position:0% +moment + + + align:start position:0% +moment +diagram it would go up and down like + + align:start position:0% +diagram it would go up and down like + + + align:start position:0% +diagram it would go up and down like +that and that would be zero and that + + align:start position:0% +that and that would be zero and that + + + align:start position:0% +that and that would be zero and that +would be zero this would be p l over + + align:start position:0% + + + + align:start position:0% + +4 okay are + + align:start position:0% + + + + align:start position:0% + +we are we okay with + + align:start position:0% +we are we okay with + + + align:start position:0% +we are we okay with +that well I haven't got to the end of + + align:start position:0% +that well I haven't got to the end of + + + align:start position:0% +that well I haven't got to the end of +the answer + + align:start position:0% +the answer + + + align:start position:0% +the answer +but + + align:start position:0% +but + + + align:start position:0% +but +okay no no no you don't need to do this + + align:start position:0% +okay no no no you don't need to do this + + + align:start position:0% +okay no no no you don't need to do this +I'm just trying to explain it no you + + align:start position:0% +I'm just trying to explain it no you + + + align:start position:0% +I'm just trying to explain it no you +don't need to you don't need to retain + + align:start position:0% +don't need to you don't need to retain + + + align:start position:0% +don't need to you don't need to retain +that information for heaven's sakes no + + align:start position:0% +that information for heaven's sakes no + + + align:start position:0% +that information for heaven's sakes no +come on I'm so + + align:start position:0% +come on I'm so + + + align:start position:0% +come on I'm so +disappointed for the moments yeah is it + + align:start position:0% +disappointed for the moments yeah is it + + + align:start position:0% +disappointed for the moments yeah is it +positive for the counter wise oh so you + + align:start position:0% +positive for the counter wise oh so you + + + align:start position:0% +positive for the counter wise oh so you +remember for the beam bending uh there's + + align:start position:0% +remember for the beam bending uh there's + + + align:start position:0% +remember for the beam bending uh there's +a different convention it's positive if + + align:start position:0% +a different convention it's positive if + + + align:start position:0% +a different convention it's positive if +it's tension on the bottom + + align:start position:0% +it's tension on the bottom + + + align:start position:0% +it's tension on the bottom +are you in mechanical engineering I + + align:start position:0% +are you in mechanical engineering I + + + align:start position:0% +are you in mechanical engineering I +thought you were in mechanical + + align:start position:0% +thought you were in mechanical + + + align:start position:0% +thought you were in mechanical +engineering no I did physics oh you did + + align:start position:0% +engineering no I did physics oh you did + + + align:start position:0% +engineering no I did physics oh you did +physics so it's okay just my all I + + align:start position:0% +physics so it's okay just my all I + + + align:start position:0% +physics so it's okay just my all I +really want to say is the moment's + + align:start position:0% +really want to say is the moment's + + + align:start position:0% +really want to say is the moment's +maximum in the middle okay so let me + + align:start position:0% +maximum in the middle okay so let me + + + align:start position:0% +maximum in the middle okay so let me +just say the moment's maximum in the + + align:start position:0% +just say the moment's maximum in the + + + align:start position:0% +just say the moment's maximum in the +middle okay so then let's look at the + + align:start position:0% +middle okay so then let's look at the + + + align:start position:0% +middle okay so then let's look at the +crosssection + + align:start position:0% + + + + align:start position:0% + +uh so say I look at a cross-section here + + align:start position:0% +uh so say I look at a cross-section here + + + align:start position:0% +uh so say I look at a cross-section here +let's just make it rectangular to make + + align:start position:0% +let's just make it rectangular to make + + + align:start position:0% +let's just make it rectangular to make +it easy for me to draw so it has a width + + align:start position:0% +it easy for me to draw so it has a width + + + align:start position:0% +it easy for me to draw so it has a width +b and a height H okay so this would be h + + align:start position:0% +b and a height H okay so this would be h + + + align:start position:0% +b and a height H okay so this would be h +on this picture over + + align:start position:0% +on this picture over + + + align:start position:0% +on this picture over +here and remember the neutral axis goes + + align:start position:0% +here and remember the neutral axis goes + + + align:start position:0% +here and remember the neutral axis goes +through the middle on the cross-section + + align:start position:0% +through the middle on the cross-section + + + align:start position:0% +through the middle on the cross-section +here and so one half of the beam is in + + align:start position:0% +here and so one half of the beam is in + + + align:start position:0% +here and so one half of the beam is in +tension and the other half of the beam + + align:start position:0% +tension and the other half of the beam + + + align:start position:0% +tension and the other half of the beam +is in compression so for this situation + + align:start position:0% +is in compression so for this situation + + + align:start position:0% +is in compression so for this situation +here this half of the beam is going to + + align:start position:0% +here this half of the beam is going to + + + align:start position:0% +here this half of the beam is going to +see compression and that half of the + + align:start position:0% +see compression and that half of the + + + align:start position:0% +see compression and that half of the +beam is going to see tension okay are we + + align:start position:0% +beam is going to see tension okay are we + + + align:start position:0% +beam is going to see tension okay are we +happy with that we're happy with that + + align:start position:0% +happy with that we're happy with that + + + align:start position:0% +happy with that we're happy with that +okay now let me draw the stress + + align:start position:0% + + + + align:start position:0% + +distribution + + align:start position:0% + + + + align:start position:0% + +so if it's linear elastic and it hasn't + + align:start position:0% +so if it's linear elastic and it hasn't + + + align:start position:0% +so if it's linear elastic and it hasn't +yielded yet the stress distribution is + + align:start position:0% +yielded yet the stress distribution is + + + align:start position:0% +yielded yet the stress distribution is +going to look like this so this is H + + align:start position:0% +going to look like this so this is H + + + align:start position:0% +going to look like this so this is H +again that's the height and now B is + + align:start position:0% +again that's the height and now B is + + + align:start position:0% +again that's the height and now B is +into the + + align:start position:0% + + + + align:start position:0% + +board and I'm plotting the stress this + + align:start position:0% +board and I'm plotting the stress this + + + align:start position:0% +board and I'm plotting the stress this +way so this thing here is my neutral + + align:start position:0% +way so this thing here is my neutral + + + align:start position:0% +way so this thing here is my neutral +axis that had no stress remember there + + align:start position:0% +axis that had no stress remember there + + + align:start position:0% +axis that had no stress remember there +was one plane that has no stress and for + + align:start position:0% +was one plane that has no stress and for + + + align:start position:0% +was one plane that has no stress and for +a rectangular cross-section it goes + + align:start position:0% +a rectangular cross-section it goes + + + align:start position:0% +a rectangular cross-section it goes +through the middle of the cross-section + + align:start position:0% +through the middle of the cross-section + + + align:start position:0% +through the middle of the cross-section +goes through the + + align:start position:0% +goes through the + + + align:start position:0% +goes through the +centroid does this is this ringing a + + align:start position:0% +centroid does this is this ringing a + + + align:start position:0% +centroid does this is this ringing a +bell I'm hoping this is ringing a + + align:start position:0% +bell I'm hoping this is ringing a + + + align:start position:0% +bell I'm hoping this is ringing a +bell come on come on we did I know I + + align:start position:0% +bell come on come on we did I know I + + + align:start position:0% +bell come on come on we did I know I +know we did this in 3032 I know we + + align:start position:0% +know we did this in 3032 I know we + + + align:start position:0% +know we did this in 3032 I know we +did + + align:start position:0% + + + + align:start position:0% + +okay okay so this is all linear elastic + + align:start position:0% + + + + align:start position:0% + +right so at some point so I'm I'm going + + align:start position:0% +right so at some point so I'm I'm going + + + align:start position:0% +right so at some point so I'm I'm going +to get to the plastic hinge at some + + align:start position:0% +to get to the plastic hinge at some + + + align:start position:0% +to get to the plastic hinge at some +point uh if you keep loading it and P + + align:start position:0% +point uh if you keep loading it and P + + + align:start position:0% +point uh if you keep loading it and P +gets bigger and bigger the moment gets + + align:start position:0% +gets bigger and bigger the moment gets + + + align:start position:0% +gets bigger and bigger the moment gets +bigger and bigger the stress gets bigger + + align:start position:0% +bigger and bigger the stress gets bigger + + + align:start position:0% +bigger and bigger the stress gets bigger +and bigger remember the equation here + + align:start position:0% +and bigger remember the equation here + + + align:start position:0% +and bigger remember the equation here +for the stress was it's equal to m y + + align:start position:0% +for the stress was it's equal to m y + + + align:start position:0% +for the stress was it's equal to m y +over I so this moment the maximum moment + + align:start position:0% +over I so this moment the maximum moment + + + align:start position:0% +over I so this moment the maximum moment +is going to be this moment here the + + align:start position:0% +is going to be this moment here the + + + align:start position:0% +is going to be this moment here the +maximum Y is going to be H over 2 the + + align:start position:0% +maximum Y is going to be H over 2 the + + + align:start position:0% +maximum Y is going to be H over 2 the +distance from the neutral axis and I is + + align:start position:0% +distance from the neutral axis and I is + + + align:start position:0% +distance from the neutral axis and I is +going to be BH cubed over 12 for the + + align:start position:0% +going to be BH cubed over 12 for the + + + align:start position:0% +going to be BH cubed over 12 for the +rectangular + + align:start position:0% +rectangular + + + align:start position:0% +rectangular +section so if I keep loading it up at + + align:start position:0% +section so if I keep loading it up at + + + align:start position:0% +section so if I keep loading it up at +some point the maximum stress is going + + align:start position:0% +some point the maximum stress is going + + + align:start position:0% +some point the maximum stress is going +to equal the yield + + align:start position:0% + + + + align:start position:0% + +stress right and in our cellular things + + align:start position:0% +stress right and in our cellular things + + + align:start position:0% +stress right and in our cellular things +it's going to equal the yield stress of + + align:start position:0% +it's going to equal the yield stress of + + + align:start position:0% +it's going to equal the yield stress of +the solid so our beam is kind of one of + + align:start position:0% +the solid so our beam is kind of one of + + + align:start position:0% +the solid so our beam is kind of one of +our uh edges in the foam or struts in + + align:start position:0% +our uh edges in the foam or struts in + + + align:start position:0% +our uh edges in the foam or struts in +the + + align:start position:0% + + + + align:start position:0% + +honeycomb so at some point it's going to + + align:start position:0% +honeycomb so at some point it's going to + + + align:start position:0% +honeycomb so at some point it's going to +equal the yield strength of the solid so + + align:start position:0% +equal the yield strength of the solid so + + + align:start position:0% +equal the yield strength of the solid so +let me draw the stress distribution + + align:start position:0% +let me draw the stress distribution + + + align:start position:0% +let me draw the stress distribution +again where we start to have + + align:start position:0% +again where we start to have + + + align:start position:0% +again where we start to have +plasticity so + + align:start position:0% +plasticity so + + + align:start position:0% +plasticity so +here the stress is equal the yel stress + + align:start position:0% +here the stress is equal the yel stress + + + align:start position:0% +here the stress is equal the yel stress +and it's going to equal the yel stress + + align:start position:0% +and it's going to equal the yel stress + + + align:start position:0% +and it's going to equal the yel stress +at the bottom too because it's all + + align:start position:0% +at the bottom too because it's all + + + align:start position:0% +at the bottom too because it's all +symmetric right and the neutral axis is + + align:start position:0% +symmetric right and the neutral axis is + + + align:start position:0% +symmetric right and the neutral axis is +is still going to be in the middle here + + align:start position:0% +is still going to be in the middle here + + + align:start position:0% +is still going to be in the middle here +so it's going to be zero down there so + + align:start position:0% +so it's going to be zero down there so + + + align:start position:0% +so it's going to be zero down there so +initially when it's just barely reached + + align:start position:0% +initially when it's just barely reached + + + align:start position:0% +initially when it's just barely reached +the yield stress at the outer part of + + align:start position:0% +the yield stress at the outer part of + + + align:start position:0% +the yield stress at the outer part of +the beam then this stress distribution + + align:start position:0% +the beam then this stress distribution + + + align:start position:0% +the beam then this stress distribution +would still be linear in between but + + align:start position:0% +would still be linear in between but + + + align:start position:0% +would still be linear in between but +once you start to um load it more than + + align:start position:0% +once you start to um load it more than + + + align:start position:0% +once you start to um load it more than +that then you the plastic region starts + + align:start position:0% +that then you the plastic region starts + + + align:start position:0% +that then you the plastic region starts +to sort of seep in from the outside + + align:start position:0% +to sort of seep in from the outside + + + align:start position:0% +to sort of seep in from the outside +inwards and what we do here is we assume + + align:start position:0% +inwards and what we do here is we assume + + + align:start position:0% +inwards and what we do here is we assume +that the solid is elastic perfectly + + align:start position:0% + + + + align:start position:0% + +plastic and if you remember when we said + + align:start position:0% +plastic and if you remember when we said + + + align:start position:0% +plastic and if you remember when we said +things were perfectly plastic or if they + + align:start position:0% +things were perfectly plastic or if they + + + align:start position:0% +things were perfectly plastic or if they +were elastic perfectly plastic they look + + align:start position:0% +were elastic perfectly plastic they look + + + align:start position:0% +were elastic perfectly plastic they look +like that the stress strain curve for + + align:start position:0% +like that the stress strain curve for + + + align:start position:0% +like that the stress strain curve for +the solid I'm assuming looks like that + + align:start position:0% +the solid I'm assuming looks like that + + + align:start position:0% +the solid I'm assuming looks like that +so I'm assuming the yield stress in the + + align:start position:0% +so I'm assuming the yield stress in the + + + align:start position:0% +so I'm assuming the yield stress in the +solid is just a constant right that if I + + align:start position:0% +solid is just a constant right that if I + + + align:start position:0% +solid is just a constant right that if I +strain it more I don't there's no work + + align:start position:0% +strain it more I don't there's no work + + + align:start position:0% +strain it more I don't there's no work +hardening I'm neglecting work hardening + + align:start position:0% + + + + align:start position:0% + +in in board + + align:start position:0% +in in board + + + align:start position:0% +in in board +inward + + align:start position:0% +inward + + + align:start position:0% +inward +something inward uh so so this is um + + align:start position:0% +something inward uh so so this is um + + + align:start position:0% +something inward uh so so this is um +let's see I didn't bring a beam with me + + align:start position:0% +let's see I didn't bring a beam with me + + + align:start position:0% +let's see I didn't bring a beam with me +today no beam do we have anything beam + + align:start position:0% +today no beam do we have anything beam + + + align:start position:0% +today no beam do we have anything beam +like ah here we have a beam like thing + + align:start position:0% +like ah here we have a beam like thing + + + align:start position:0% +like ah here we have a beam like thing +okay so say this is my beam and I'm + + align:start position:0% +okay so say this is my beam and I'm + + + align:start position:0% +okay so say this is my beam and I'm +loading it this way on okay and this is + + align:start position:0% +loading it this way on okay and this is + + + align:start position:0% +loading it this way on okay and this is +B and that's H so this picture here is + + align:start position:0% +B and that's H so this picture here is + + + align:start position:0% +B and that's H so this picture here is +looking at it that way on okay + + align:start position:0% +looking at it that way on okay + + + align:start position:0% +looking at it that way on okay +and this picture here i' I've drawn H + + align:start position:0% +and this picture here i' I've drawn H + + + align:start position:0% +and this picture here i' I've drawn H +but now I'm just looking at the stress + + align:start position:0% +but now I'm just looking at the stress + + + align:start position:0% +but now I'm just looking at the stress +distribution across H and B is kind of + + align:start position:0% +distribution across H and B is kind of + + + align:start position:0% +distribution across H and B is kind of +into the + + align:start position:0% +into the + + + align:start position:0% +into the +board is that okay does that answer your + + align:start position:0% +board is that okay does that answer your + + + align:start position:0% +board is that okay does that answer your +question + + align:start position:0% +question + + + align:start position:0% +question +yeah for this + + align:start position:0% +yeah for this + + + align:start position:0% +yeah for this +part okay so this is I'm I'm working up + + align:start position:0% +part okay so this is I'm I'm working up + + + align:start position:0% +part okay so this is I'm I'm working up +I haven't finished it yet um so this is + + align:start position:0% +I haven't finished it yet um so this is + + + align:start position:0% +I haven't finished it yet um so this is +the same kind of view as here I drew it + + align:start position:0% +the same kind of view as here I drew it + + + align:start position:0% +the same kind of view as here I drew it +a little bigger I shouldn't have drawn + + align:start position:0% +a little bigger I shouldn't have drawn + + + align:start position:0% +a little bigger I shouldn't have drawn +it bigger I should have drawn the same + + align:start position:0% +it bigger I should have drawn the same + + + align:start position:0% +it bigger I should have drawn the same +height + + align:start position:0% +height + + + align:start position:0% +height +but it's the same thing + + align:start position:0% +but it's the same thing + + + align:start position:0% +but it's the same thing +okay now so you'll buy that at some + + align:start position:0% +okay now so you'll buy that at some + + + align:start position:0% +okay now so you'll buy that at some +point we reach the yield strength here + + align:start position:0% +point we reach the yield strength here + + + align:start position:0% +point we reach the yield strength here +and if I keep loading it up and I assume + + align:start position:0% +and if I keep loading it up and I assume + + + align:start position:0% +and if I keep loading it up and I assume +that the solid is perfectly plastic that + + align:start position:0% +that the solid is perfectly plastic that + + + align:start position:0% +that the solid is perfectly plastic that +there's no work hardening then the + + align:start position:0% +there's no work hardening then the + + + align:start position:0% +there's no work hardening then the +stress + + align:start position:0% + + + + align:start position:0% + +distribution would look like this okay + + align:start position:0% +distribution would look like this okay + + + align:start position:0% +distribution would look like this okay +and then if it yields more then it's + + align:start position:0% +and then if it yields more then it's + + + align:start position:0% +and then if it yields more then it's +going to look like that and if it yields + + align:start position:0% +going to look like that and if it yields + + + align:start position:0% +going to look like that and if it yields +more eventually I'm going to get to this + + align:start position:0% +more eventually I'm going to get to this + + + align:start position:0% +more eventually I'm going to get to this +stage here where it's this let me redraw + + align:start position:0% +stage here where it's this let me redraw + + + align:start position:0% +stage here where it's this let me redraw +this that would + + align:start position:0% +this that would + + + align:start position:0% +this that would +be you get the idea okay this we go over + + align:start position:0% +be you get the idea okay this we go over + + + align:start position:0% +be you get the idea okay this we go over +here and down here like that + + align:start position:0% +here and down here like that + + + align:start position:0% +here and down here like that +okay + + align:start position:0% +okay + + + align:start position:0% +okay +okay so are we are we happy with this + + align:start position:0% +okay so are we are we happy with this + + + align:start position:0% +okay so are we are we happy with this +stress distribution across the + + align:start position:0% +stress distribution across the + + + align:start position:0% +stress distribution across the +cross-section yeah okay so that's when + + align:start position:0% +cross-section yeah okay so that's when + + + align:start position:0% +cross-section yeah okay so that's when +it forms the plastic hinge so when it + + align:start position:0% +it forms the plastic hinge so when it + + + align:start position:0% +it forms the plastic hinge so when it +forms a plastic hinge + + align:start position:0% + + + + align:start position:0% + +the stress distribution looks like + + align:start position:0% + + + + align:start position:0% + +this okay so these are supposed to be + + align:start position:0% +this okay so these are supposed to be + + + align:start position:0% +this okay so these are supposed to be +the same size they're not + + align:start position:0% + + + + align:start position:0% + +quite and um let's see so one of the + + align:start position:0% +quite and um let's see so one of the + + + align:start position:0% +quite and um let's see so one of the +things I talked about was the plastic + + align:start position:0% +things I talked about was the plastic + + + align:start position:0% +things I talked about was the plastic +moment that kind of characterized that + + align:start position:0% +moment that kind of characterized that + + + align:start position:0% +moment that kind of characterized that +plastic hinge and the plastic moment is + + align:start position:0% +plastic hinge and the plastic moment is + + + align:start position:0% +plastic hinge and the plastic moment is +just the internal amount of moment that + + align:start position:0% +just the internal amount of moment that + + + align:start position:0% +just the internal amount of moment that +the beam can withstand when it's yielded + + align:start position:0% +the beam can withstand when it's yielded + + + align:start position:0% +the beam can withstand when it's yielded +completely across the whole + + align:start position:0% +completely across the whole + + + align:start position:0% +completely across the whole +cross-section so when we're like at this + + align:start position:0% +cross-section so when we're like at this + + + align:start position:0% +cross-section so when we're like at this +point here so you calculate that by + + align:start position:0% +point here so you calculate that by + + + align:start position:0% +point here so you calculate that by +saying that stress there is equivalent + + align:start position:0% +saying that stress there is equivalent + + + align:start position:0% +saying that stress there is equivalent +to a force that stress there's + + align:start position:0% +to a force that stress there's + + + align:start position:0% +to a force that stress there's +equivalent to a force and you get the + + align:start position:0% +equivalent to a force and you get the + + + align:start position:0% +equivalent to a force and you get the +moment by multiplying those forces times + + align:start position:0% +moment by multiplying those forces times + + + align:start position:0% +moment by multiplying those forces times +that distance there okay because you + + align:start position:0% +that distance there okay because you + + + align:start position:0% +that distance there okay because you +think of those two forces as being a + + align:start position:0% +think of those two forces as being a + + + align:start position:0% +think of those two forces as being a +couple and the moments the force times + + align:start position:0% +couple and the moments the force times + + + align:start position:0% +couple and the moments the force times +the distance between them so the plastic + + align:start position:0% +the distance between them so the plastic + + + align:start position:0% +the distance between them so the plastic +moment was Sigma y s and uh + + align:start position:0% +moment was Sigma y s and uh + + + align:start position:0% +moment was Sigma y s and uh +say um say we're talking about our + + align:start position:0% +say um say we're talking about our + + + align:start position:0% +say um say we're talking about our +honeycomb or foam or something that was + + align:start position:0% +honeycomb or foam or something that was + + + align:start position:0% +honeycomb or foam or something that was +our cell wall thickness T so let me call + + align:start position:0% +our cell wall thickness T so let me call + + + align:start position:0% +our cell wall thickness T so let me call +it t instead of H for the Foams and the + + align:start position:0% +it t instead of H for the Foams and the + + + align:start position:0% +it t instead of H for the Foams and the +Honeycombs so this Force + + align:start position:0% +Honeycombs so this Force + + + align:start position:0% +Honeycombs so this Force +here is going to be uh the stress times + + align:start position:0% +here is going to be uh the stress times + + + align:start position:0% +here is going to be uh the stress times +the area over which it acts + + align:start position:0% +the area over which it acts + + + align:start position:0% +the area over which it acts +and let's say we look at it for a + + align:start position:0% + + + + align:start position:0% + +honeycomb then I've got the stress is + + align:start position:0% +honeycomb then I've got the stress is + + + align:start position:0% +honeycomb then I've got the stress is +acting over this distance here and then + + align:start position:0% +acting over this distance here and then + + + align:start position:0% +acting over this distance here and then +times the depth into the page right and + + align:start position:0% +times the depth into the page right and + + + align:start position:0% +times the depth into the page right and +if it's the honeycomb that depth into + + align:start position:0% +if it's the honeycomb that depth into + + + align:start position:0% +if it's the honeycomb that depth into +the page is just B okay and then this + + align:start position:0% +the page is just B okay and then this + + + align:start position:0% +the page is just B okay and then this +moment arm here it's just t over2 as + + align:start position:0% +moment arm here it's just t over2 as + + + align:start position:0% +moment arm here it's just t over2 as +well because that's T over4 and that's T + + align:start position:0% +well because that's T over4 and that's T + + + align:start position:0% +well because that's T over4 and that's T +over4 so it's t over2 again + + align:start position:0% +over4 so it's t over2 again + + + align:start position:0% +over4 so it's t over2 again +so it's Sigma y SB t^2 over + + align:start position:0% + + + + align:start position:0% + +4 of a honeycomb and say we had an open + + align:start position:0% +4 of a honeycomb and say we had an open + + + align:start position:0% +4 of a honeycomb and say we had an open +cell + + align:start position:0% + + + + align:start position:0% + +foam um the edges aren't of thickness B + + align:start position:0% +foam um the edges aren't of thickness B + + + align:start position:0% +foam um the edges aren't of thickness B +they're of thickness T so then it's MP + + align:start position:0% +they're of thickness T so then it's MP + + + align:start position:0% +they're of thickness T so then it's MP +is just Sigma y s t cubed over 4 + + align:start position:0% +is just Sigma y s t cubed over 4 + + + align:start position:0% +is just Sigma y s t cubed over 4 +are we + + align:start position:0% +are we + + + align:start position:0% +are we +happy and really physically what that is + + align:start position:0% +happy and really physically what that is + + + align:start position:0% +happy and really physically what that is +is it it means that the beam can't with + + align:start position:0% +is it it means that the beam can't with + + + align:start position:0% +is it it means that the beam can't with +can't hold any more Force you can't + + align:start position:0% +can't hold any more Force you can't + + + align:start position:0% +can't hold any more Force you can't +apply any more Force to it it's just + + align:start position:0% +apply any more Force to it it's just + + + align:start position:0% +apply any more Force to it it's just +going to kind of rotate like this once + + align:start position:0% +going to kind of rotate like this once + + + align:start position:0% +going to kind of rotate like this once +you've got to that plastic moment that's + + align:start position:0% +you've got to that plastic moment that's + + + align:start position:0% +you've got to that plastic moment that's +why it's called a hinge because it just + + align:start position:0% +why it's called a hinge because it just + + + align:start position:0% +why it's called a hinge because it just +can rotate like a hinge rotates like a + + align:start position:0% +can rotate like a hinge rotates like a + + + align:start position:0% +can rotate like a hinge rotates like a +door hinge + + align:start position:0% + + + + align:start position:0% + +okay how does + + align:start position:0% +okay how does + + + align:start position:0% +okay how does +it well um + + align:start position:0% +it well um + + + align:start position:0% +it well um +where's my original + + align:start position:0% +where's my original + + + align:start position:0% +where's my original +picture so if this was the beam when you + + align:start position:0% +picture so if this was the beam when you + + + align:start position:0% +picture so if this was the beam when you +form the plastic hinge your beam would + + align:start position:0% +form the plastic hinge your beam would + + + align:start position:0% +form the plastic hinge your beam would +just look like that and this would be + + align:start position:0% +just look like that and this would be + + + align:start position:0% +just look like that and this would be +your kind of your hinge + + align:start position:0% +your kind of your hinge + + + align:start position:0% +your kind of your hinge +point in I'm a civil engineer originally + + align:start position:0% +point in I'm a civil engineer originally + + + align:start position:0% +point in I'm a civil engineer originally +we try to avoid + + align:start position:0% +we try to avoid + + + align:start position:0% +we try to avoid +this so I mean that's that's why in the + + align:start position:0% +this so I mean that's that's why in the + + + align:start position:0% +this so I mean that's that's why in the +foam and in the honeycomb that's when it + + align:start position:0% +foam and in the honeycomb that's when it + + + align:start position:0% +foam and in the honeycomb that's when it +fails this when you get that plastic + + align:start position:0% +fails this when you get that plastic + + + align:start position:0% +fails this when you get that plastic +hinge for + + align:start position:0% +hinge for + + + align:start position:0% +hinge for +me + + align:start position:0% +me + + + align:start position:0% +me +okay all right we have a few more + + align:start position:0% +okay all right we have a few more + + + align:start position:0% +okay all right we have a few more +minutes + + align:start position:0% +minutes + + + align:start position:0% +minutes +I plastic well yeah well that's well + + align:start position:0% +I plastic well yeah well that's well + + + align:start position:0% +I plastic well yeah well that's well +it's it's it's not buckling but it's + + align:start position:0% +it's it's it's not buckling but it's + + + align:start position:0% +it's it's it's not buckling but it's +plastic yeah it's + + align:start position:0% +plastic yeah it's + + + align:start position:0% +plastic yeah it's +permanent anyone + + align:start position:0% + + + + align:start position:0% + +else okay no other + + align:start position:0% + + + + align:start position:0% + +questions should we call it a day was + + align:start position:0% +questions should we call it a day was + + + align:start position:0% +questions should we call it a day was +that + + align:start position:0% +that + + + align:start position:0% +that +helpful all right then no + + align:start position:0% +helpful all right then no + + + align:start position:0% +helpful all right then no +it's what I do come on it's what I + + align:start position:0% + + + + align:start position:0% + +do all right so I'll see you + + align:start position:0% +do all right so I'll see you + + + align:start position:0% +do all right so I'll see you +Wednesday and my plan is to grade the + + align:start position:0% +Wednesday and my plan is to grade the + + + align:start position:0% +Wednesday and my plan is to grade the +test before spring break so I shall have + + align:start position:0% +test before spring break so I shall have + + + align:start position:0% +test before spring break so I shall have +it back to you \ No newline at end of file diff --git a/cT3KA-QLEI0.txt b/cT3KA-QLEI0.txt new file mode 100644 index 0000000000000000000000000000000000000000..fe13976c76220bd344bb6773700ded27f084fc6b --- /dev/null +++ b/cT3KA-QLEI0.txt @@ -0,0 +1,1187 @@ +align:start position:0% + +in this video we'll solve our sports + + align:start position:0% +in this video we'll solve our sports + + + align:start position:0% +in this video we'll solve our sports +scheduling problem in libreoffice we can + + align:start position:0% +scheduling problem in libreoffice we can + + + align:start position:0% +scheduling problem in libreoffice we can +use the solver to solve integer + + align:start position:0% +use the solver to solve integer + + + align:start position:0% +use the solver to solve integer +optimization problems using the same + + align:start position:0% +optimization problems using the same + + + align:start position:0% +optimization problems using the same +process as for linear optimization + + align:start position:0% +process as for linear optimization + + + align:start position:0% +process as for linear optimization +problems the only difference is that we + + align:start position:0% +problems the only difference is that we + + + align:start position:0% +problems the only difference is that we +need to add extra constraints to define + + align:start position:0% +need to add extra constraints to define + + + align:start position:0% +need to add extra constraints to define +variables as integer or binary let's go + + align:start position:0% +variables as integer or binary let's go + + + align:start position:0% +variables as integer or binary let's go +ahead and solve our small tournament + + align:start position:0% +ahead and solve our small tournament + + + align:start position:0% +ahead and solve our small tournament +scheduling problem in the LibreOffice or + + align:start position:0% +scheduling problem in the LibreOffice or + + + align:start position:0% +scheduling problem in the LibreOffice or +in the spreadsheet software you're using + + align:start position:0% +in the spreadsheet software you're using + + + align:start position:0% +in the spreadsheet software you're using +go ahead and open the spreadsheet sports + + align:start position:0% +go ahead and open the spreadsheet sports + + + align:start position:0% +go ahead and open the spreadsheet sports +scheduling ODS at the top of the + + align:start position:0% +scheduling ODS at the top of the + + + align:start position:0% +scheduling ODS at the top of the +spreadsheet I've created a spot for our + + align:start position:0% +spreadsheet I've created a spot for our + + + align:start position:0% +spreadsheet I've created a spot for our +decision variables we have a decision + + align:start position:0% +decision variables we have a decision + + + align:start position:0% +decision variables we have a decision +variable for each week weeks one through + + align:start position:0% +variable for each week weeks one through + + + align:start position:0% +variable for each week weeks one through +four and for each team pair a and B and + + align:start position:0% +four and for each team pair a and B and + + + align:start position:0% +four and for each team pair a and B and +C and D B and C B and D and C and D this + + align:start position:0% +C and D B and C B and D and C and D this + + + align:start position:0% +C and D B and C B and D and C and D this +gives us a total of 24 decision + + align:start position:0% +gives us a total of 24 decision + + + align:start position:0% +gives us a total of 24 decision +variables highlighted in yellow below + + align:start position:0% +variables highlighted in yellow below + + + align:start position:0% +variables highlighted in yellow below +the decision variables there's a spot + + align:start position:0% +the decision variables there's a spot + + + align:start position:0% +the decision variables there's a spot +for our objective highlighted in blue + + align:start position:0% +for our objective highlighted in blue + + + align:start position:0% +for our objective highlighted in blue +let's go ahead and construct our + + align:start position:0% +let's go ahead and construct our + + + align:start position:0% +let's go ahead and construct our +objective start by typing an equal sign + + align:start position:0% +objective start by typing an equal sign + + + align:start position:0% +objective start by typing an equal sign +and then we want it to be equal to 1 + + align:start position:0% +and then we want it to be equal to 1 + + + align:start position:0% +and then we want it to be equal to 1 +times the decision variable for a and B + + align:start position:0% +times the decision variable for a and B + + + align:start position:0% +times the decision variable for a and B +in week one plus two times + + align:start position:0% +in week one plus two times + + + align:start position:0% +in week one plus two times +the decision variable for a and B in + + align:start position:0% +the decision variable for a and B in + + + align:start position:0% +the decision variable for a and B in +week two plus four times + + align:start position:0% +week two plus four times + + + align:start position:0% +week two plus four times +the decision variable for a and B in + + align:start position:0% +the decision variable for a and B in + + + align:start position:0% +the decision variable for a and B in +week 3 plus 8 times the decision + + align:start position:0% +week 3 plus 8 times the decision + + + align:start position:0% +week 3 plus 8 times the decision +variable for a and B in week four now we + + align:start position:0% +variable for a and B in week four now we + + + align:start position:0% +variable for a and B in week four now we +want to repeat this for team C and D so + + align:start position:0% +want to repeat this for team C and D so + + + align:start position:0% +want to repeat this for team C and D so +now we have one time's the decision + + align:start position:0% +now we have one time's the decision + + + align:start position:0% +now we have one time's the decision +variable for C and D in week one plus 2 + + align:start position:0% +variable for C and D in week one plus 2 + + + align:start position:0% +variable for C and D in week one plus 2 +times the decision variable for C and D + + align:start position:0% +times the decision variable for C and D + + + align:start position:0% +times the decision variable for C and D +and week 2 plus 4 times the decision + + align:start position:0% +and week 2 plus 4 times the decision + + + align:start position:0% +and week 2 plus 4 times the decision +variable for C and D in week 3 plus 8 + + align:start position:0% +variable for C and D in week 3 plus 8 + + + align:start position:0% +variable for C and D in week 3 plus 8 +times the decision variable for C and D + + align:start position:0% +times the decision variable for C and D + + + align:start position:0% +times the decision variable for C and D +in week four go ahead and hit enter our + + align:start position:0% +in week four go ahead and hit enter our + + + align:start position:0% +in week four go ahead and hit enter our +objective has value 0 for now because we + + align:start position:0% +objective has value 0 for now because we + + + align:start position:0% +objective has value 0 for now because we +haven't filled in our decision variables + + align:start position:0% +haven't filled in our decision variables + + + align:start position:0% +haven't filled in our decision variables +yet + + align:start position:0% +yet + + + align:start position:0% +yet +now let's come + + align:start position:0% +now let's come + + + align:start position:0% +now let's come +director constraints the first + + align:start position:0% +director constraints the first + + + align:start position:0% +director constraints the first +constraint is teams a and B should play + + align:start position:0% +constraint is teams a and B should play + + + align:start position:0% +constraint is teams a and B should play +twice so our left-hand side should be + + align:start position:0% +twice so our left-hand side should be + + + align:start position:0% +twice so our left-hand side should be +equal to the sum will use the sum + + align:start position:0% +equal to the sum will use the sum + + + align:start position:0% +equal to the sum will use the sum +function here which just adds up + + align:start position:0% +function here which just adds up + + + align:start position:0% +function here which just adds up +everything inside the parentheses so + + align:start position:0% +everything inside the parentheses so + + + align:start position:0% +everything inside the parentheses so +type equals sum and then in parentheses + + align:start position:0% +type equals sum and then in parentheses + + + align:start position:0% +type equals sum and then in parentheses +select the for a and B decision + + align:start position:0% +select the for a and B decision + + + align:start position:0% +select the for a and B decision +variables the sign should be equals and + + align:start position:0% +variables the sign should be equals and + + + align:start position:0% +variables the sign should be equals and +the right-hand side should be two now + + align:start position:0% +the right-hand side should be two now + + + align:start position:0% +the right-hand side should be two now +let's just repeat this for team C and D + + align:start position:0% +let's just repeat this for team C and D + + + align:start position:0% +let's just repeat this for team C and D +so the left-hand side is the sum of the + + align:start position:0% +so the left-hand side is the sum of the + + + align:start position:0% +so the left-hand side is the sum of the +C and D decision variables the sine is + + align:start position:0% +C and D decision variables the sine is + + + align:start position:0% +C and D decision variables the sine is +equals and the right-hand side is two + + align:start position:0% +equals and the right-hand side is two + + + align:start position:0% +equals and the right-hand side is two +now we want to add the constraint that + + align:start position:0% +now we want to add the constraint that + + + align:start position:0% +now we want to add the constraint that +teams a and C should play once so this + + align:start position:0% +teams a and C should play once so this + + + align:start position:0% +teams a and C should play once so this +left hand side is very similar it should + + align:start position:0% +left hand side is very similar it should + + + align:start position:0% +left hand side is very similar it should +be the sum of the a and C decision + + align:start position:0% +be the sum of the a and C decision + + + align:start position:0% +be the sum of the a and C decision +variables the sign should be equals and + + align:start position:0% +variables the sign should be equals and + + + align:start position:0% +variables the sign should be equals and +the right hand side here should be one + + align:start position:0% +the right hand side here should be one + + + align:start position:0% +the right hand side here should be one +now let's repeat this for teams a and D + + align:start position:0% +now let's repeat this for teams a and D + + + align:start position:0% +now let's repeat this for teams a and D +the left hand side is the sum of the a + + align:start position:0% +the left hand side is the sum of the a + + + align:start position:0% +the left hand side is the sum of the a +and D decision variables the sine is + + align:start position:0% +and D decision variables the sine is + + + align:start position:0% +and D decision variables the sine is +equals and the right hand side is one + + align:start position:0% +equals and the right hand side is one + + + align:start position:0% +equals and the right hand side is one +we'll repeat it again for team's B and C + + align:start position:0% +we'll repeat it again for team's B and C + + + align:start position:0% +we'll repeat it again for team's B and C +so the left-hand side is the sum of the + + align:start position:0% +so the left-hand side is the sum of the + + + align:start position:0% +so the left-hand side is the sum of the +B and C decision variables the sine is + + align:start position:0% +B and C decision variables the sine is + + + align:start position:0% +B and C decision variables the sine is +equals and the right-hand side is 1 the + + align:start position:0% +equals and the right-hand side is 1 the + + + align:start position:0% +equals and the right-hand side is 1 the +last of this type of constraint is that + + align:start position:0% +last of this type of constraint is that + + + align:start position:0% +last of this type of constraint is that +teams B and D should play once so the + + align:start position:0% +teams B and D should play once so the + + + align:start position:0% +teams B and D should play once so the +left-hand side is the sum of the B and D + + align:start position:0% +left-hand side is the sum of the B and D + + + align:start position:0% +left-hand side is the sum of the B and D +decision variables the sine is equals + + align:start position:0% +decision variables the sine is equals + + + align:start position:0% +decision variables the sine is equals +and the right-hand side is 1 now we want + + align:start position:0% +and the right-hand side is 1 now we want + + + align:start position:0% +and the right-hand side is 1 now we want +to add the constraints that each team + + align:start position:0% +to add the constraints that each team + + + align:start position:0% +to add the constraints that each team +should only play once in each week so + + align:start position:0% +should only play once in each week so + + + align:start position:0% +should only play once in each week so +the first is that team a should play + + align:start position:0% +the first is that team a should play + + + align:start position:0% +the first is that team a should play +once in week 1 so the left-hand side + + align:start position:0% +once in week 1 so the left-hand side + + + align:start position:0% +once in week 1 so the left-hand side +should be the sum of all of the decision + + align:start position:0% +should be the sum of all of the decision + + + align:start position:0% +should be the sum of all of the decision +variables were a plays in week 1 so this + + align:start position:0% +variables were a plays in week 1 so this + + + align:start position:0% +variables were a plays in week 1 so this +should be equal to a plane B in week 1 + + align:start position:0% +should be equal to a plane B in week 1 + + + align:start position:0% +should be equal to a plane B in week 1 +plus a plane C in week 1 plus a playing + + align:start position:0% +plus a plane C in week 1 plus a playing + + + align:start position:0% +plus a plane C in week 1 plus a playing +D in week 1 the sine is equals and the + + align:start position:0% +D in week 1 the sine is equals and the + + + align:start position:0% +D in week 1 the sine is equals and the +right-hand side is again 1 now let's + + align:start position:0% +right-hand side is again 1 now let's + + + align:start position:0% +right-hand side is again 1 now let's +repeat this for week 2 it's + + align:start position:0% +repeat this for week 2 it's + + + align:start position:0% +repeat this for week 2 it's +the left-hand side is equal to a plane B + + align:start position:0% +the left-hand side is equal to a plane B + + + align:start position:0% +the left-hand side is equal to a plane B +in week 2 plus a plane C in week 2 plus + + align:start position:0% +in week 2 plus a plane C in week 2 plus + + + align:start position:0% +in week 2 plus a plane C in week 2 plus +a plane D in week 2 the sine is equals + + align:start position:0% +a plane D in week 2 the sine is equals + + + align:start position:0% +a plane D in week 2 the sine is equals +and the right-hand side is 1 now let's + + align:start position:0% +and the right-hand side is 1 now let's + + + align:start position:0% +and the right-hand side is 1 now let's +repeat this for weeks 3 & 4 so for week + + align:start position:0% +repeat this for weeks 3 & 4 so for week + + + align:start position:0% +repeat this for weeks 3 & 4 so for week +3 the left-hand side is just equal to + + align:start position:0% +3 the left-hand side is just equal to + + + align:start position:0% +3 the left-hand side is just equal to +the variables with a plane with week 3 a + + align:start position:0% +the variables with a plane with week 3 a + + + align:start position:0% +the variables with a plane with week 3 a +and B and C a and D the sine is equals + + align:start position:0% +and B and C a and D the sine is equals + + + align:start position:0% +and B and C a and D the sine is equals +and the right-hand side is 1 for week 4 + + align:start position:0% +and the right-hand side is 1 for week 4 + + + align:start position:0% +and the right-hand side is 1 for week 4 +the left-hand side is just the a + + align:start position:0% +the left-hand side is just the a + + + align:start position:0% +the left-hand side is just the a +variables in week 4 a and B a and C and + + align:start position:0% +variables in week 4 a and B a and C and + + + align:start position:0% +variables in week 4 a and B a and C and +a and D the sign should be equals and + + align:start position:0% +a and D the sign should be equals and + + + align:start position:0% +a and D the sign should be equals and +the right-hand side is 1 I went ahead + + align:start position:0% +the right-hand side is 1 I went ahead + + + align:start position:0% +the right-hand side is 1 I went ahead +and filled in the rest of the + + align:start position:0% +and filled in the rest of the + + + align:start position:0% +and filled in the rest of the +constraints for you since they're just + + align:start position:0% +constraints for you since they're just + + + align:start position:0% +constraints for you since they're just +repeating the same thing for Team B Team + + align:start position:0% +repeating the same thing for Team B Team + + + align:start position:0% +repeating the same thing for Team B Team +C and team D now we're ready to solve + + align:start position:0% +C and team D now we're ready to solve + + + align:start position:0% +C and team D now we're ready to solve +our problem so let's go to the Tools + + align:start position:0% +our problem so let's go to the Tools + + + align:start position:0% +our problem so let's go to the Tools +menu and select solver in the solver + + align:start position:0% +menu and select solver in the solver + + + align:start position:0% +menu and select solver in the solver +window let's first pick our target cell + + align:start position:0% +window let's first pick our target cell + + + align:start position:0% +window let's first pick our target cell +so with the cursor in the target cell + + align:start position:0% +so with the cursor in the target cell + + + align:start position:0% +so with the cursor in the target cell +box go ahead and select the objective + + align:start position:0% +box go ahead and select the objective + + + align:start position:0% +box go ahead and select the objective +cell or the blue cell make sure that + + align:start position:0% +cell or the blue cell make sure that + + + align:start position:0% +cell or the blue cell make sure that +maximum is selected since we're trying + + align:start position:0% +maximum is selected since we're trying + + + align:start position:0% +maximum is selected since we're trying +to maximize preferences then with the + + align:start position:0% +to maximize preferences then with the + + + align:start position:0% +to maximize preferences then with the +cursor in the by changing cells box go + + align:start position:0% +cursor in the by changing cells box go + + + align:start position:0% +cursor in the by changing cells box go +ahead and select all 24 decision + + align:start position:0% +ahead and select all 24 decision + + + align:start position:0% +ahead and select all 24 decision +variables now let's add in our + + align:start position:0% +variables now let's add in our + + + align:start position:0% +variables now let's add in our +constraints since all of our constraints + + align:start position:0% +constraints since all of our constraints + + + align:start position:0% +constraints since all of our constraints +have an equal sign we can add them all + + align:start position:0% +have an equal sign we can add them all + + + align:start position:0% +have an equal sign we can add them all +in together so in the first cell + + align:start position:0% +in together so in the first cell + + + align:start position:0% +in together so in the first cell +reference box go ahead and select all of + + align:start position:0% +reference box go ahead and select all of + + + align:start position:0% +reference box go ahead and select all of +the left-hand sides + + align:start position:0% + + + + align:start position:0% + +in the operator box select equals then + + align:start position:0% +in the operator box select equals then + + + align:start position:0% +in the operator box select equals then +in the value box select all of the + + align:start position:0% +in the value box select all of the + + + align:start position:0% +in the value box select all of the +right-hand sides + + align:start position:0% + + + + align:start position:0% + +since this is an integer optimization + + align:start position:0% +since this is an integer optimization + + + align:start position:0% +since this is an integer optimization +problem there's one more thing we need + + align:start position:0% +problem there's one more thing we need + + + align:start position:0% +problem there's one more thing we need +to do in the constraint area in the cell + + align:start position:0% +to do in the constraint area in the cell + + + align:start position:0% +to do in the constraint area in the cell +reference box go ahead and select all of + + align:start position:0% +reference box go ahead and select all of + + + align:start position:0% +reference box go ahead and select all of +the decision variables then in the + + align:start position:0% +the decision variables then in the + + + align:start position:0% +the decision variables then in the +operator pull down menu select binary + + align:start position:0% +operator pull down menu select binary + + + align:start position:0% +operator pull down menu select binary +this will make all of our decision + + align:start position:0% +this will make all of our decision + + + align:start position:0% +this will make all of our decision +variables binary we don't need to put + + align:start position:0% +variables binary we don't need to put + + + align:start position:0% +variables binary we don't need to put +anything in the value column the last + + align:start position:0% +anything in the value column the last + + + align:start position:0% +anything in the value column the last +thing we need to do is in options make + + align:start position:0% +thing we need to do is in options make + + + align:start position:0% +thing we need to do is in options make +sure that we're using the linear solver + + align:start position:0% +sure that we're using the linear solver + + + align:start position:0% +sure that we're using the linear solver +and click OK + + align:start position:0% +and click OK + + + align:start position:0% +and click OK +now go ahead and hit solve the solving + + align:start position:0% +now go ahead and hit solve the solving + + + align:start position:0% +now go ahead and hit solve the solving +result says solving successfully + + align:start position:0% +result says solving successfully + + + align:start position:0% +result says solving successfully +finished result 24 go ahead and pick + + align:start position:0% +finished result 24 go ahead and pick + + + align:start position:0% +finished result 24 go ahead and pick +keep result and now let's look at our + + align:start position:0% +keep result and now let's look at our + + + align:start position:0% +keep result and now let's look at our +solution we can see that teams a and B + + align:start position:0% +solution we can see that teams a and B + + + align:start position:0% +solution we can see that teams a and B +and teams C and D both play during weeks + + align:start position:0% +and teams C and D both play during weeks + + + align:start position:0% +and teams C and D both play during weeks +three and four this makes sense since + + align:start position:0% +three and four this makes sense since + + + align:start position:0% +three and four this makes sense since +we're trying to maximize preferences and + + align:start position:0% +we're trying to maximize preferences and + + + align:start position:0% +we're trying to maximize preferences and +the preference for teams in the same + + align:start position:0% +the preference for teams in the same + + + align:start position:0% +the preference for teams in the same +division is to play later on in the next + + align:start position:0% +division is to play later on in the next + + + align:start position:0% +division is to play later on in the next +video we'll see the different types of + + align:start position:0% +video we'll see the different types of + + + align:start position:0% +video we'll see the different types of +constraints that we can add to an + + align:start position:0% +constraints that we can add to an + + + align:start position:0% +constraints that we can add to an +integer optimization model \ No newline at end of file diff --git a/ciWpS6SetdY.txt b/ciWpS6SetdY.txt new file mode 100644 index 0000000000000000000000000000000000000000..6e4b65ac9f4c4a2ac01a9ec4c4741e0b1a2457a9 --- /dev/null +++ b/ciWpS6SetdY.txt @@ -0,0 +1,3011 @@ +align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +reaction workup one extracting washing + + align:start position:0% +reaction workup one extracting washing + + + align:start position:0% +reaction workup one extracting washing +and + + align:start position:0% + + + + align:start position:0% + +drying as all chemists quickly learn it + + align:start position:0% +drying as all chemists quickly learn it + + + align:start position:0% +drying as all chemists quickly learn it +is very rare for a chemical reaction to + + align:start position:0% +is very rare for a chemical reaction to + + + align:start position:0% +is very rare for a chemical reaction to +provide only the one compound that + + align:start position:0% +provide only the one compound that + + + align:start position:0% +provide only the one compound that +you're looking for even highly selective + + align:start position:0% +you're looking for even highly selective + + + align:start position:0% +you're looking for even highly selective +reactions generate the desired product + + align:start position:0% +reactions generate the desired product + + + align:start position:0% +reactions generate the desired product +as a crude mixture containing byproducts + + align:start position:0% +as a crude mixture containing byproducts + + + align:start position:0% +as a crude mixture containing byproducts +and unreacted starting materials and + + align:start position:0% +and unreacted starting materials and + + + align:start position:0% +and unreacted starting materials and +reagents liquid liquid extraction is the + + align:start position:0% +reagents liquid liquid extraction is the + + + align:start position:0% +reagents liquid liquid extraction is the +most common technique for separating a + + align:start position:0% +most common technique for separating a + + + align:start position:0% +most common technique for separating a +compound from a comp Lex mixture in an + + align:start position:0% +compound from a comp Lex mixture in an + + + align:start position:0% +compound from a comp Lex mixture in an +extraction you can take advantage of + + align:start position:0% +extraction you can take advantage of + + + align:start position:0% +extraction you can take advantage of +differing solubilities to selectively + + align:start position:0% +differing solubilities to selectively + + + align:start position:0% +differing solubilities to selectively +separate the different + + align:start position:0% +separate the different + + + align:start position:0% +separate the different +components by carefully planning out an + + align:start position:0% +components by carefully planning out an + + + align:start position:0% +components by carefully planning out an +extraction and washing sequence + + align:start position:0% +extraction and washing sequence + + + align:start position:0% +extraction and washing sequence +otherwise known as a + + align:start position:0% +otherwise known as a + + + align:start position:0% +otherwise known as a +workup the desired product can usually + + align:start position:0% +workup the desired product can usually + + + align:start position:0% +workup the desired product can usually +be separated from The Unwanted + + align:start position:0% +be separated from The Unwanted + + + align:start position:0% +be separated from The Unwanted +impurities this video will illustrate + + align:start position:0% +impurities this video will illustrate + + + align:start position:0% +impurities this video will illustrate +the proper technique involved in working + + align:start position:0% +the proper technique involved in working + + + align:start position:0% +the proper technique involved in working +up a + + align:start position:0% + + + + align:start position:0% + +reaction in an Ideal World World each + + align:start position:0% +reaction in an Ideal World World each + + + align:start position:0% +reaction in an Ideal World World each +chemical reaction in the laboratory + + align:start position:0% +chemical reaction in the laboratory + + + align:start position:0% +chemical reaction in the laboratory +would provide only the desired product + + align:start position:0% +would provide only the desired product + + + align:start position:0% +would provide only the desired product +in its pure form in reality the product + + align:start position:0% +in its pure form in reality the product + + + align:start position:0% +in its pure form in reality the product +is almost always generated as part of a + + align:start position:0% +is almost always generated as part of a + + + align:start position:0% +is almost always generated as part of a +messy mixture of byproducts and side + + align:start position:0% +messy mixture of byproducts and side + + + align:start position:0% +messy mixture of byproducts and side +products in short garbage liquid liquid + + align:start position:0% +products in short garbage liquid liquid + + + align:start position:0% +products in short garbage liquid liquid +extraction is a useful technique used to + + align:start position:0% +extraction is a useful technique used to + + + align:start position:0% +extraction is a useful technique used to +isolate the desired compound from a + + align:start position:0% +isolate the desired compound from a + + + align:start position:0% +isolate the desired compound from a +complex mixture in an extraction the + + align:start position:0% +complex mixture in an extraction the + + + align:start position:0% +complex mixture in an extraction the +mixture is partitioned between two imiss + + align:start position:0% +mixture is partitioned between two imiss + + + align:start position:0% +mixture is partitioned between two imiss +solvents in a separatory funnel + + align:start position:0% +solvents in a separatory funnel + + + align:start position:0% +solvents in a separatory funnel +otherwise known as a sep funnel the key + + align:start position:0% +otherwise known as a sep funnel the key + + + align:start position:0% +otherwise known as a sep funnel the key +is that the two solvents are mutually + + align:start position:0% +is that the two solvents are mutually + + + align:start position:0% +is that the two solvents are mutually +insoluble so they form two distinct + + align:start position:0% +insoluble so they form two distinct + + + align:start position:0% +insoluble so they form two distinct +layers one of the solvents is almost + + align:start position:0% +layers one of the solvents is almost + + + align:start position:0% +layers one of the solvents is almost +always water and the other is an organic + + align:start position:0% +always water and the other is an organic + + + align:start position:0% +always water and the other is an organic +solvent of your + + align:start position:0% +solvent of your + + + align:start position:0% +solvent of your +choice the different components of the + + align:start position:0% +choice the different components of the + + + align:start position:0% +choice the different components of the +mixture are selectively distributed in + + align:start position:0% +mixture are selectively distributed in + + + align:start position:0% +mixture are selectively distributed in +one solvent or the other depending on + + align:start position:0% +one solvent or the other depending on + + + align:start position:0% +one solvent or the other depending on +their different + + align:start position:0% +their different + + + align:start position:0% +their different +solubilities in this way you can take + + align:start position:0% +solubilities in this way you can take + + + align:start position:0% +solubilities in this way you can take +advantage of differing solubilities to + + align:start position:0% +advantage of differing solubilities to + + + align:start position:0% +advantage of differing solubilities to +selectively trans Port solutes from one + + align:start position:0% +selectively trans Port solutes from one + + + align:start position:0% +selectively trans Port solutes from one +layer to + + align:start position:0% + + + + align:start position:0% + +another in most cases but not all + + align:start position:0% +another in most cases but not all + + + align:start position:0% +another in most cases but not all +neutral organic molecules prefer the + + align:start position:0% +neutral organic molecules prefer the + + + align:start position:0% +neutral organic molecules prefer the +organic phase while charged molecules + + align:start position:0% +organic phase while charged molecules + + + align:start position:0% +organic phase while charged molecules +and inorganic salts prefer the aquous + + align:start position:0% +and inorganic salts prefer the aquous + + + align:start position:0% +and inorganic salts prefer the aquous +layer by carefully planning out an + + align:start position:0% +layer by carefully planning out an + + + align:start position:0% +layer by carefully planning out an +extraction and washing sequence + + align:start position:0% +extraction and washing sequence + + + align:start position:0% +extraction and washing sequence +otherwise known as a reaction workup the + + align:start position:0% +otherwise known as a reaction workup the + + + align:start position:0% +otherwise known as a reaction workup the +desired compound can usually be + + align:start position:0% +desired compound can usually be + + + align:start position:0% +desired compound can usually be +separated from most of the unwanted + + align:start position:0% +separated from most of the unwanted + + + align:start position:0% +separated from most of the unwanted +impurities this brings up an important + + align:start position:0% +impurities this brings up an important + + + align:start position:0% +impurities this brings up an important +Point what is the difference between an + + align:start position:0% +Point what is the difference between an + + + align:start position:0% +Point what is the difference between an +extraction and a wash these terms + + align:start position:0% +extraction and a wash these terms + + + align:start position:0% +extraction and a wash these terms +describe similar but fundamentally + + align:start position:0% +describe similar but fundamentally + + + align:start position:0% +describe similar but fundamentally +different + + align:start position:0% +different + + + align:start position:0% +different +operations an extraction involves + + align:start position:0% +operations an extraction involves + + + align:start position:0% +operations an extraction involves +pulling the desired compound out of a + + align:start position:0% +pulling the desired compound out of a + + + align:start position:0% +pulling the desired compound out of a +mixture of + + align:start position:0% +mixture of + + + align:start position:0% +mixture of +compounds whereas in a wash you are + + align:start position:0% +compounds whereas in a wash you are + + + align:start position:0% +compounds whereas in a wash you are +pulling unwanted impurities away from + + align:start position:0% +pulling unwanted impurities away from + + + align:start position:0% +pulling unwanted impurities away from +the desired product in other words you + + align:start position:0% +the desired product in other words you + + + align:start position:0% +the desired product in other words you +always keep the extracts and trash the + + align:start position:0% +always keep the extracts and trash the + + + align:start position:0% +always keep the extracts and trash the +washes this might sound confusing but + + align:start position:0% +washes this might sound confusing but + + + align:start position:0% +washes this might sound confusing but +but it will hopefully become clear as we + + align:start position:0% +but it will hopefully become clear as we + + + align:start position:0% +but it will hopefully become clear as we +continue the first step in an extraction + + align:start position:0% +continue the first step in an extraction + + + align:start position:0% +continue the first step in an extraction +and washing sequence once you have + + align:start position:0% +and washing sequence once you have + + + align:start position:0% +and washing sequence once you have +decided on the appropriate solvents of + + align:start position:0% +decided on the appropriate solvents of + + + align:start position:0% +decided on the appropriate solvents of +course is filling the sep bunnel it is a + + align:start position:0% +course is filling the sep bunnel it is a + + + align:start position:0% +course is filling the sep bunnel it is a +good idea to use an iron ring and a nice + + align:start position:0% +good idea to use an iron ring and a nice + + + align:start position:0% +good idea to use an iron ring and a nice +cushy cork ring to safely support the + + align:start position:0% +cushy cork ring to safely support the + + + align:start position:0% +cushy cork ring to safely support the +sep funnel before you add any solvent + + align:start position:0% +sep funnel before you add any solvent + + + align:start position:0% +sep funnel before you add any solvent +close the Stop + + align:start position:0% +close the Stop + + + align:start position:0% +close the Stop +coock and place a clean dry flask under + + align:start position:0% +coock and place a clean dry flask under + + + align:start position:0% +coock and place a clean dry flask under +the sep + + align:start position:0% +the sep + + + align:start position:0% +the sep +funnel this will prevent you from + + align:start position:0% +funnel this will prevent you from + + + align:start position:0% +funnel this will prevent you from +dumping precious material all over the + + align:start position:0% +dumping precious material all over the + + + align:start position:0% +dumping precious material all over the +dirty + + align:start position:0% +dirty + + + align:start position:0% +dirty +bench the flask will save you if the + + align:start position:0% +bench the flask will save you if the + + + align:start position:0% +bench the flask will save you if the +funnel leaks or the stopcock somehow + + align:start position:0% +funnel leaks or the stopcock somehow + + + align:start position:0% +funnel leaks or the stopcock somehow +opened + + align:start position:0% +opened + + + align:start position:0% +opened +itself when the stopcock is safely + + align:start position:0% +itself when the stopcock is safely + + + align:start position:0% +itself when the stopcock is safely +closed and the flask is in place pour + + align:start position:0% +closed and the flask is in place pour + + + align:start position:0% +closed and the flask is in place pour +your two solvents into the sep + + align:start position:0% +your two solvents into the sep + + + align:start position:0% +your two solvents into the sep +funnel use a sep funnel large enough + + align:start position:0% +funnel use a sep funnel large enough + + + align:start position:0% +funnel use a sep funnel large enough +that you don't fill it more than 3/4 + + align:start position:0% +that you don't fill it more than 3/4 + + + align:start position:0% +that you don't fill it more than 3/4 +full if it is too full you won't be able + + align:start position:0% +full if it is too full you won't be able + + + align:start position:0% +full if it is too full you won't be able +to efficiently mix the solvent + + align:start position:0% +to efficiently mix the solvent + + + align:start position:0% +to efficiently mix the solvent +this brings us to The Next Step mixing + + align:start position:0% +this brings us to The Next Step mixing + + + align:start position:0% +this brings us to The Next Step mixing +and venting it is important to mix the + + align:start position:0% +and venting it is important to mix the + + + align:start position:0% +and venting it is important to mix the +two solvents very well this increases + + align:start position:0% +two solvents very well this increases + + + align:start position:0% +two solvents very well this increases +the contact surface area and allows the + + align:start position:0% +the contact surface area and allows the + + + align:start position:0% +the contact surface area and allows the +distribution of solutes to occur very + + align:start position:0% +distribution of solutes to occur very + + + align:start position:0% +distribution of solutes to occur very +rapidly but use caution mixing will + + align:start position:0% +rapidly but use caution mixing will + + + align:start position:0% +rapidly but use caution mixing will +frequently cause pressure to build up + + align:start position:0% +frequently cause pressure to build up + + + align:start position:0% +frequently cause pressure to build up +inside of the sep + + align:start position:0% +inside of the sep + + + align:start position:0% +inside of the sep +funnel pressure buildup is especially + + align:start position:0% +funnel pressure buildup is especially + + + align:start position:0% +funnel pressure buildup is especially +common when you were using particularly + + align:start position:0% +common when you were using particularly + + + align:start position:0% +common when you were using particularly +volatile solvents like diethylether + + align:start position:0% + + + + align:start position:0% + +or compounds that can generate gas like + + align:start position:0% +or compounds that can generate gas like + + + align:start position:0% +or compounds that can generate gas like +sodium + + align:start position:0% + + + + align:start position:0% + +bicarbonate under acidic conditions + + align:start position:0% +bicarbonate under acidic conditions + + + align:start position:0% +bicarbonate under acidic conditions +sodium bicarbonate will release gaseous + + align:start position:0% +sodium bicarbonate will release gaseous + + + align:start position:0% +sodium bicarbonate will release gaseous +carbon + + align:start position:0% +carbon + + + align:start position:0% +carbon +dioxide before any vigorous mixing it is + + align:start position:0% +dioxide before any vigorous mixing it is + + + align:start position:0% +dioxide before any vigorous mixing it is +a good idea to gently swirl and invert + + align:start position:0% +a good idea to gently swirl and invert + + + align:start position:0% +a good idea to gently swirl and invert +the sep + + align:start position:0% +the sep + + + align:start position:0% +the sep +funnel then invert the sep funnel + + align:start position:0% +funnel then invert the sep funnel + + + align:start position:0% +funnel then invert the sep funnel +holding the stopper + + align:start position:0% +holding the stopper + + + align:start position:0% +holding the stopper +tightly allow the liquid to drain away + + align:start position:0% +tightly allow the liquid to drain away + + + align:start position:0% +tightly allow the liquid to drain away +from the stop + + align:start position:0% +from the stop + + + align:start position:0% +from the stop +topcock and point the tip of the set + + align:start position:0% +topcock and point the tip of the set + + + align:start position:0% +topcock and point the tip of the set +funnel away from yourself and other + + align:start position:0% +funnel away from yourself and other + + + align:start position:0% +funnel away from yourself and other +people slowly open the stop coock to + + align:start position:0% +people slowly open the stop coock to + + + align:start position:0% +people slowly open the stop coock to +allow + + align:start position:0% +allow + + + align:start position:0% +allow +venting now you're ready to really mix + + align:start position:0% +venting now you're ready to really mix + + + align:start position:0% +venting now you're ready to really mix +it up hold the SE funnel firmly and + + align:start position:0% +it up hold the SE funnel firmly and + + + align:start position:0% +it up hold the SE funnel firmly and +Shake It vigorously for several seconds + + align:start position:0% +Shake It vigorously for several seconds + + + align:start position:0% +Shake It vigorously for several seconds +once again invert the funnel and vent it + + align:start position:0% +once again invert the funnel and vent it + + + align:start position:0% +once again invert the funnel and vent it +carefully repeat the shaking and venting + + align:start position:0% +carefully repeat the shaking and venting + + + align:start position:0% +carefully repeat the shaking and venting +until you no longer hear gas Escape when + + align:start position:0% +until you no longer hear gas Escape when + + + align:start position:0% +until you no longer hear gas Escape when +you open the stopcock + + align:start position:0% +you open the stopcock + + + align:start position:0% +you open the stopcock +then set your funnel down and let the + + align:start position:0% +then set your funnel down and let the + + + align:start position:0% +then set your funnel down and let the +layers + + align:start position:0% + + + + align:start position:0% + +settle ideally two layers with a nice + + align:start position:0% +settle ideally two layers with a nice + + + align:start position:0% +settle ideally two layers with a nice +clean interface should form very + + align:start position:0% + + + + align:start position:0% + +quickly unfortunately things don't + + align:start position:0% +quickly unfortunately things don't + + + align:start position:0% +quickly unfortunately things don't +always go so + + align:start position:0% + + + + align:start position:0% + +smoothly a thick cloudy layer called an + + align:start position:0% +smoothly a thick cloudy layer called an + + + align:start position:0% +smoothly a thick cloudy layer called an +Emulsion can sometimes form between the + + align:start position:0% +Emulsion can sometimes form between the + + + align:start position:0% +Emulsion can sometimes form between the +two solvent layers an Emulsion is a + + align:start position:0% +two solvent layers an Emulsion is a + + + align:start position:0% +two solvent layers an Emulsion is a +colloidal mix mixture of the two + + align:start position:0% +colloidal mix mixture of the two + + + align:start position:0% +colloidal mix mixture of the two +solvents and is frequently caused by the + + align:start position:0% +solvents and is frequently caused by the + + + align:start position:0% +solvents and is frequently caused by the +presence of fine particles in the + + align:start position:0% +presence of fine particles in the + + + align:start position:0% +presence of fine particles in the +solution getting rid of an emolion can + + align:start position:0% +solution getting rid of an emolion can + + + align:start position:0% +solution getting rid of an emolion can +take some time so if you know that you + + align:start position:0% +take some time so if you know that you + + + align:start position:0% +take some time so if you know that you +are likely to generate one your best bet + + align:start position:0% +are likely to generate one your best bet + + + align:start position:0% +are likely to generate one your best bet +is to take pains to prevent it ahead of + + align:start position:0% +is to take pains to prevent it ahead of + + + align:start position:0% +is to take pains to prevent it ahead of +time for example gently swirling and + + align:start position:0% +time for example gently swirling and + + + align:start position:0% +time for example gently swirling and +inverting your sep bunnel will rarely + + align:start position:0% +inverting your sep bunnel will rarely + + + align:start position:0% +inverting your sep bunnel will rarely +cause an Emulsion to form you will have + + align:start position:0% +cause an Emulsion to form you will have + + + align:start position:0% +cause an Emulsion to form you will have +to spend more time mixing because + + align:start position:0% +to spend more time mixing because + + + align:start position:0% +to spend more time mixing because +swirling is not as efficient as shaking + + align:start position:0% +swirling is not as efficient as shaking + + + align:start position:0% +swirling is not as efficient as shaking +but it may be worth it + + align:start position:0% +but it may be worth it + + + align:start position:0% +but it may be worth it +don't worry if you unwittingly generated + + align:start position:0% +don't worry if you unwittingly generated + + + align:start position:0% +don't worry if you unwittingly generated +a monster Emulsion you still have a few + + align:start position:0% +a monster Emulsion you still have a few + + + align:start position:0% +a monster Emulsion you still have a few +options first you can just sit and wait + + align:start position:0% +options first you can just sit and wait + + + align:start position:0% +options first you can just sit and wait +it might clear itself up even if it + + align:start position:0% +it might clear itself up even if it + + + align:start position:0% +it might clear itself up even if it +takes a few hours if you don't have all + + align:start position:0% +takes a few hours if you don't have all + + + align:start position:0% +takes a few hours if you don't have all +day to finish your extraction try + + align:start position:0% +day to finish your extraction try + + + align:start position:0% +day to finish your extraction try +swirling the mixture gently and stirring + + align:start position:0% +swirling the mixture gently and stirring + + + align:start position:0% +swirling the mixture gently and stirring +the Emulsion with a glass + + align:start position:0% +the Emulsion with a glass + + + align:start position:0% +the Emulsion with a glass +rod if this doesn't work add several + + align:start position:0% +rod if this doesn't work add several + + + align:start position:0% +rod if this doesn't work add several +milliliters of saturated sodium chloride + + align:start position:0% +milliliters of saturated sodium chloride + + + align:start position:0% +milliliters of saturated sodium chloride +solution to the funnel and swirl to mix + + align:start position:0% +solution to the funnel and swirl to mix + + + align:start position:0% +solution to the funnel and swirl to mix +the sodium chloride increases the ionic + + align:start position:0% +the sodium chloride increases the ionic + + + align:start position:0% +the sodium chloride increases the ionic +strength of the aquous layer and + + align:start position:0% +strength of the aquous layer and + + + align:start position:0% +strength of the aquous layer and +decreases the solubility of the organic + + align:start position:0% +decreases the solubility of the organic + + + align:start position:0% +decreases the solubility of the organic +solvent in the water as a last resort + + align:start position:0% +solvent in the water as a last resort + + + align:start position:0% +solvent in the water as a last resort +you may need to use vacuum filtration to + + align:start position:0% +you may need to use vacuum filtration to + + + align:start position:0% +you may need to use vacuum filtration to +filter your entire mixture through a pad + + align:start position:0% +filter your entire mixture through a pad + + + align:start position:0% +filter your entire mixture through a pad +of sea + + align:start position:0% +of sea + + + align:start position:0% +of sea +light when you are carrying out an + + align:start position:0% +light when you are carrying out an + + + align:start position:0% +light when you are carrying out an +extraction and washing sequence it is + + align:start position:0% +extraction and washing sequence it is + + + align:start position:0% +extraction and washing sequence it is +very important that you keep track of + + align:start position:0% +very important that you keep track of + + + align:start position:0% +very important that you keep track of +which layer is which and what compounds + + align:start position:0% +which layer is which and what compounds + + + align:start position:0% +which layer is which and what compounds +are dissolved in each layer this means + + align:start position:0% +are dissolved in each layer this means + + + align:start position:0% +are dissolved in each layer this means +that you constantly need to be asking + + align:start position:0% +that you constantly need to be asking + + + align:start position:0% +that you constantly need to be asking +yourself which layer is on the top which + + align:start position:0% +yourself which layer is on the top which + + + align:start position:0% +yourself which layer is on the top which +layer is on the + + align:start position:0% +layer is on the + + + align:start position:0% +layer is on the +bottom one way to keep track of this is + + align:start position:0% +bottom one way to keep track of this is + + + align:start position:0% +bottom one way to keep track of this is +to know something about the densities of + + align:start position:0% +to know something about the densities of + + + align:start position:0% +to know something about the densities of +the solvents you are using in every case + + align:start position:0% +the solvents you are using in every case + + + align:start position:0% +the solvents you are using in every case +the solvent with the lowest density will + + align:start position:0% +the solvent with the lowest density will + + + align:start position:0% +the solvent with the lowest density will +be on top and the solvent with the + + align:start position:0% +be on top and the solvent with the + + + align:start position:0% +be on top and the solvent with the +highest density will be on the + + align:start position:0% +highest density will be on the + + + align:start position:0% +highest density will be on the +bottom this is helpful because you can + + align:start position:0% +bottom this is helpful because you can + + + align:start position:0% +bottom this is helpful because you can +generally assume that dilute aquous + + align:start position:0% +generally assume that dilute aquous + + + align:start position:0% +generally assume that dilute aquous +Solutions have a density around 1 G per + + align:start position:0% +Solutions have a density around 1 G per + + + align:start position:0% +Solutions have a density around 1 G per +Mill similar to + + align:start position:0% +Mill similar to + + + align:start position:0% +Mill similar to +water the organic solvent will be in the + + align:start position:0% +water the organic solvent will be in the + + + align:start position:0% +water the organic solvent will be in the +top layer if it has a density less than + + align:start position:0% +top layer if it has a density less than + + + align:start position:0% +top layer if it has a density less than +1 gr per milliliter such as hexane + + align:start position:0% +1 gr per milliliter such as hexane + + + align:start position:0% +1 gr per milliliter such as hexane +diethyl ether or ethyl + + align:start position:0% +diethyl ether or ethyl + + + align:start position:0% +diethyl ether or ethyl +acetate the organic solvent will be the + + align:start position:0% +acetate the organic solvent will be the + + + align:start position:0% +acetate the organic solvent will be the +bottom layer if it has a density greater + + align:start position:0% +bottom layer if it has a density greater + + + align:start position:0% +bottom layer if it has a density greater +than 1 gr per milliliter such as + + align:start position:0% +than 1 gr per milliliter such as + + + align:start position:0% +than 1 gr per milliliter such as +methylene chloride or + + align:start position:0% +methylene chloride or + + + align:start position:0% +methylene chloride or +chloroform but be careful high + + align:start position:0% +chloroform but be careful high + + + align:start position:0% +chloroform but be careful high +concentrations of solutes can sometimes + + align:start position:0% +concentrations of solutes can sometimes + + + align:start position:0% +concentrations of solutes can sometimes +drastically affect the density of a + + align:start position:0% +drastically affect the density of a + + + align:start position:0% +drastically affect the density of a +solvent if you're having trouble + + align:start position:0% +solvent if you're having trouble + + + align:start position:0% +solvent if you're having trouble +figuring out which layer is which you + + align:start position:0% +figuring out which layer is which you + + + align:start position:0% +figuring out which layer is which you +may need to perform a quick solubility + + align:start position:0% + + + + align:start position:0% + +test take a couple of drops of the layer + + align:start position:0% +test take a couple of drops of the layer + + + align:start position:0% +test take a couple of drops of the layer +in question and add them to a small + + align:start position:0% +in question and add them to a small + + + align:start position:0% +in question and add them to a small +amount of water in a test + + align:start position:0% + + + + align:start position:0% + +tube if the drops dissolve without + + align:start position:0% +tube if the drops dissolve without + + + align:start position:0% +tube if the drops dissolve without +turning the water cloudy then the drops + + align:start position:0% +turning the water cloudy then the drops + + + align:start position:0% +turning the water cloudy then the drops +were from the aquous layer + + align:start position:0% + + + + align:start position:0% + +if the solution turns cloudy or the + + align:start position:0% +if the solution turns cloudy or the + + + align:start position:0% +if the solution turns cloudy or the +drops form an insoluble layer on the + + align:start position:0% +drops form an insoluble layer on the + + + align:start position:0% +drops form an insoluble layer on the +bottom or an insoluble layer on the top + + align:start position:0% +bottom or an insoluble layer on the top + + + align:start position:0% +bottom or an insoluble layer on the top +then the drops are from the organic + + align:start position:0% + + + + align:start position:0% + +layer but even if you think you know + + align:start position:0% +layer but even if you think you know + + + align:start position:0% +layer but even if you think you know +which layer is which do not discard any + + align:start position:0% +which layer is which do not discard any + + + align:start position:0% +which layer is which do not discard any +of the layers until you are absolutely + + align:start position:0% +of the layers until you are absolutely + + + align:start position:0% +of the layers until you are absolutely +sure that you have isolated all of the + + align:start position:0% + + + + align:start position:0% + +material once you have a good idea of + + align:start position:0% +material once you have a good idea of + + + align:start position:0% +material once you have a good idea of +where your material is it's time to + + align:start position:0% +where your material is it's time to + + + align:start position:0% +where your material is it's time to +separate the layers before you do + + align:start position:0% +separate the layers before you do + + + align:start position:0% +separate the layers before you do +anything place a clean dry labeled + + align:start position:0% +anything place a clean dry labeled + + + align:start position:0% +anything place a clean dry labeled +Beaker under the step funnel and remove + + align:start position:0% +Beaker under the step funnel and remove + + + align:start position:0% +Beaker under the step funnel and remove +the + + align:start position:0% + + + + align:start position:0% + +stopper if you don't do this you'll have + + align:start position:0% +stopper if you don't do this you'll have + + + align:start position:0% +stopper if you don't do this you'll have +some trouble getting any liquid to + + align:start position:0% + + + + align:start position:0% + +drain with the stopper off open the + + align:start position:0% +drain with the stopper off open the + + + align:start position:0% +drain with the stopper off open the +stopcock and allow the bottom layer to + + align:start position:0% +stopcock and allow the bottom layer to + + + align:start position:0% +stopcock and allow the bottom layer to +drain into the beaker + + align:start position:0% + + + + align:start position:0% + +take it slow when you get near the + + align:start position:0% +take it slow when you get near the + + + align:start position:0% +take it slow when you get near the +interface so that you can close the + + align:start position:0% +interface so that you can close the + + + align:start position:0% +interface so that you can close the +valve precisely in between the two + + align:start position:0% + + + + align:start position:0% + +layers once you have drained the bottom + + align:start position:0% +layers once you have drained the bottom + + + align:start position:0% +layers once you have drained the bottom +layer you have a few options if you + + align:start position:0% +layer you have a few options if you + + + align:start position:0% +layer you have a few options if you +still need to perform a wash or an + + align:start position:0% +still need to perform a wash or an + + + align:start position:0% +still need to perform a wash or an +extraction with the top layer then leave + + align:start position:0% +extraction with the top layer then leave + + + align:start position:0% +extraction with the top layer then leave +it in the funnel pour in the second + + align:start position:0% +it in the funnel pour in the second + + + align:start position:0% +it in the funnel pour in the second +solvent and proceed to mix and + + align:start position:0% +solvent and proceed to mix and + + + align:start position:0% +solvent and proceed to mix and +vent if you are done with the top layer + + align:start position:0% +vent if you are done with the top layer + + + align:start position:0% +vent if you are done with the top layer +then pick up the funnel and pour it into + + align:start position:0% +then pick up the funnel and pour it into + + + align:start position:0% +then pick up the funnel and pour it into +a second clean dry labeled + + align:start position:0% + + + + align:start position:0% + +Beaker here is a little bit of sep + + align:start position:0% +Beaker here is a little bit of sep + + + align:start position:0% +Beaker here is a little bit of sep +funnel etiquette to follow when you are + + align:start position:0% +funnel etiquette to follow when you are + + + align:start position:0% +funnel etiquette to follow when you are +separating the layers always drain the + + align:start position:0% +separating the layers always drain the + + + align:start position:0% +separating the layers always drain the +bottom layer through the stopcock and + + align:start position:0% +bottom layer through the stopcock and + + + align:start position:0% +bottom layer through the stopcock and +pour the top layer through the top this + + align:start position:0% +pour the top layer through the top this + + + align:start position:0% +pour the top layer through the top this +will minimize recontamination of your + + align:start position:0% + + + + align:start position:0% + +material before we move on to proper + + align:start position:0% +material before we move on to proper + + + align:start position:0% +material before we move on to proper +post extraction procedures + + align:start position:0% +post extraction procedures + + + align:start position:0% +post extraction procedures +let's walk through a sample reaction + + align:start position:0% +let's walk through a sample reaction + + + align:start position:0% +let's walk through a sample reaction +workup similar to one you might use in + + align:start position:0% +workup similar to one you might use in + + + align:start position:0% +workup similar to one you might use in +the + + align:start position:0% +the + + + align:start position:0% +the +laboratory let's say that you performed + + align:start position:0% +laboratory let's say that you performed + + + align:start position:0% +laboratory let's say that you performed +an isolation reaction to generate feny + + align:start position:0% +an isolation reaction to generate feny + + + align:start position:0% +an isolation reaction to generate feny +acetate at the end of the reaction you + + align:start position:0% +acetate at the end of the reaction you + + + align:start position:0% +acetate at the end of the reaction you +were left with a solution containing a + + align:start position:0% +were left with a solution containing a + + + align:start position:0% +were left with a solution containing a +lot more than the material you were + + align:start position:0% +lot more than the material you were + + + align:start position:0% +lot more than the material you were +looking for so what do you do first you + + align:start position:0% +looking for so what do you do first you + + + align:start position:0% +looking for so what do you do first you +know that feny acetate is soluble in + + align:start position:0% +know that feny acetate is soluble in + + + align:start position:0% +know that feny acetate is soluble in +diethyl ether and that diethyl ether is + + align:start position:0% +diethyl ether and that diethyl ether is + + + align:start position:0% +diethyl ether and that diethyl ether is +insoluble in water therefore in your + + align:start position:0% +insoluble in water therefore in your + + + align:start position:0% +insoluble in water therefore in your +workup you will use diyl ether as the + + align:start position:0% +workup you will use diyl ether as the + + + align:start position:0% +workup you will use diyl ether as the +organic layer and wash it with different + + align:start position:0% +organic layer and wash it with different + + + align:start position:0% +organic layer and wash it with different +aquous solutions to remove the + + align:start position:0% +aquous solutions to remove the + + + align:start position:0% +aquous solutions to remove the +impurities now it is time to plan out + + align:start position:0% +impurities now it is time to plan out + + + align:start position:0% +impurities now it is time to plan out +the washes it is important that you use + + align:start position:0% +the washes it is important that you use + + + align:start position:0% +the washes it is important that you use +what you know about the impurities to + + align:start position:0% +what you know about the impurities to + + + align:start position:0% +what you know about the impurities to +decide on appropriate aquous washes for + + align:start position:0% +decide on appropriate aquous washes for + + + align:start position:0% +decide on appropriate aquous washes for +your + + align:start position:0% +your + + + align:start position:0% +your +mixture keep in mind that the washes + + align:start position:0% +mixture keep in mind that the washes + + + align:start position:0% +mixture keep in mind that the washes +should only be 10 to 50% of the volume + + align:start position:0% +should only be 10 to 50% of the volume + + + align:start position:0% +should only be 10 to 50% of the volume +of the solution that you are washing and + + align:start position:0% +of the solution that you are washing and + + + align:start position:0% +of the solution that you are washing and +make sure to repeat each wash two or + + align:start position:0% +make sure to repeat each wash two or + + + align:start position:0% +make sure to repeat each wash two or +three times to wash away as much of the + + align:start position:0% +three times to wash away as much of the + + + align:start position:0% +three times to wash away as much of the +impurities as + + align:start position:0% + + + + align:start position:0% + +possible your crude mixture contains + + align:start position:0% +possible your crude mixture contains + + + align:start position:0% +possible your crude mixture contains +acetic acid a fairly strong acid and two + + align:start position:0% +acetic acid a fairly strong acid and two + + + align:start position:0% +acetic acid a fairly strong acid and two +weak bases triethylamine and + + align:start position:0% +weak bases triethylamine and + + + align:start position:0% +weak bases triethylamine and +dmap to get rid of the acetic acid you + + align:start position:0% +dmap to get rid of the acetic acid you + + + align:start position:0% +dmap to get rid of the acetic acid you +need to wash the solution with a mild + + align:start position:0% +need to wash the solution with a mild + + + align:start position:0% +need to wash the solution with a mild +base that will deprotonate the acid and + + align:start position:0% +base that will deprotonate the acid and + + + align:start position:0% +base that will deprotonate the acid and +pull the charged acetate ion into the + + align:start position:0% +pull the charged acetate ion into the + + + align:start position:0% +pull the charged acetate ion into the +aquous layer saturated sodium + + align:start position:0% +aquous layer saturated sodium + + + align:start position:0% +aquous layer saturated sodium +bicarbonate works very well for this + + align:start position:0% +bicarbonate works very well for this + + + align:start position:0% +bicarbonate works very well for this +purpose add the sodium bicarbonate + + align:start position:0% +purpose add the sodium bicarbonate + + + align:start position:0% +purpose add the sodium bicarbonate +solution and mix well make sure that you + + align:start position:0% +solution and mix well make sure that you + + + align:start position:0% +solution and mix well make sure that you +vent frequently to release the carbon + + align:start position:0% +vent frequently to release the carbon + + + align:start position:0% +vent frequently to release the carbon +dioxide gas that is generated finally + + align:start position:0% +dioxide gas that is generated finally + + + align:start position:0% +dioxide gas that is generated finally +drain away the aquous solution that now + + align:start position:0% +drain away the aquous solution that now + + + align:start position:0% +drain away the aquous solution that now +contains the sodium acetate and repeat + + align:start position:0% +contains the sodium acetate and repeat + + + align:start position:0% +contains the sodium acetate and repeat +the wash two more + + align:start position:0% + + + + align:start position:0% + +times to get rid of the weak bases + + align:start position:0% +times to get rid of the weak bases + + + align:start position:0% +times to get rid of the weak bases +triethylamine and dmap you need to wash + + align:start position:0% +triethylamine and dmap you need to wash + + + align:start position:0% +triethylamine and dmap you need to wash +with a dilute solution of a strong acid + + align:start position:0% +with a dilute solution of a strong acid + + + align:start position:0% +with a dilute solution of a strong acid +that will protonate the bases and pull + + align:start position:0% +that will protonate the bases and pull + + + align:start position:0% +that will protonate the bases and pull +them into the aquous layer a 10% aquous + + align:start position:0% +them into the aquous layer a 10% aquous + + + align:start position:0% +them into the aquous layer a 10% aquous +solution of HCL works well for this once + + align:start position:0% +solution of HCL works well for this once + + + align:start position:0% +solution of HCL works well for this once +again add the wash and mix and vent + + align:start position:0% +again add the wash and mix and vent + + + align:start position:0% +again add the wash and mix and vent +well drain the aquous layer containing + + align:start position:0% +well drain the aquous layer containing + + + align:start position:0% +well drain the aquous layer containing +the protonated amines and repeat two + + align:start position:0% +the protonated amines and repeat two + + + align:start position:0% +the protonated amines and repeat two +more + + align:start position:0% + + + + align:start position:0% + +times so far this looks like a pretty + + align:start position:0% +times so far this looks like a pretty + + + align:start position:0% +times so far this looks like a pretty +effective reaction workup but there is + + align:start position:0% +effective reaction workup but there is + + + align:start position:0% +effective reaction workup but there is +one more thing to keep in mind water is + + align:start position:0% +one more thing to keep in mind water is + + + align:start position:0% +one more thing to keep in mind water is +slightly soluble in ether not to a large + + align:start position:0% +slightly soluble in ether not to a large + + + align:start position:0% +slightly soluble in ether not to a large +extent but there is some water hanging + + align:start position:0% +extent but there is some water hanging + + + align:start position:0% +extent but there is some water hanging +around in the organic layer one way to + + align:start position:0% +around in the organic layer one way to + + + align:start position:0% +around in the organic layer one way to +pull some of the water out is to wash it + + align:start position:0% +pull some of the water out is to wash it + + + align:start position:0% +pull some of the water out is to wash it +with saturated sodium chloride otherwise + + align:start position:0% +with saturated sodium chloride otherwise + + + align:start position:0% +with saturated sodium chloride otherwise +known as brine the high ionic strength + + align:start position:0% +known as brine the high ionic strength + + + align:start position:0% +known as brine the high ionic strength +of the salt solution decreases the + + align:start position:0% +of the salt solution decreases the + + + align:start position:0% +of the salt solution decreases the +solubility of the aquous layer in The + + align:start position:0% +solubility of the aquous layer in The + + + align:start position:0% +solubility of the aquous layer in The +Ether effectively washing away some of + + align:start position:0% +Ether effectively washing away some of + + + align:start position:0% +Ether effectively washing away some of +the water + + align:start position:0% + + + + align:start position:0% + +voila now that you have done all you can + + align:start position:0% +voila now that you have done all you can + + + align:start position:0% +voila now that you have done all you can +with your sep funnel it's time to dry + + align:start position:0% +with your sep funnel it's time to dry + + + align:start position:0% +with your sep funnel it's time to dry +your organic layer even more with a + + align:start position:0% +your organic layer even more with a + + + align:start position:0% +your organic layer even more with a +drying + + align:start position:0% + + + + align:start position:0% + +agent magnesium sulfate is one popular + + align:start position:0% +agent magnesium sulfate is one popular + + + align:start position:0% +agent magnesium sulfate is one popular +drying agent because it is quick and + + align:start position:0% +drying agent because it is quick and + + + align:start position:0% +drying agent because it is quick and +effective it is also a very fine powder + + align:start position:0% +effective it is also a very fine powder + + + align:start position:0% +effective it is also a very fine powder +so take care that you don't leave any of + + align:start position:0% +so take care that you don't leave any of + + + align:start position:0% +so take care that you don't leave any of +your desired material absorbed onto the + + align:start position:0% +your desired material absorbed onto the + + + align:start position:0% +your desired material absorbed onto the +surface when you discard it keep in mind + + align:start position:0% +surface when you discard it keep in mind + + + align:start position:0% +surface when you discard it keep in mind +that magnesium sulfate is also slightly + + align:start position:0% +that magnesium sulfate is also slightly + + + align:start position:0% +that magnesium sulfate is also slightly +acidic so it may not be suitable for use + + align:start position:0% +acidic so it may not be suitable for use + + + align:start position:0% +acidic so it may not be suitable for use +with compounds that are sensitive to + + align:start position:0% +with compounds that are sensitive to + + + align:start position:0% +with compounds that are sensitive to +acid to dry the organic layer with + + align:start position:0% +acid to dry the organic layer with + + + align:start position:0% +acid to dry the organic layer with +magnesium sulfate add a small amount of + + align:start position:0% +magnesium sulfate add a small amount of + + + align:start position:0% +magnesium sulfate add a small amount of +the powder and + + align:start position:0% +the powder and + + + align:start position:0% +the powder and +swirl incrementally add more drying + + align:start position:0% +swirl incrementally add more drying + + + align:start position:0% +swirl incrementally add more drying +agent and swirl until you get the snow + + align:start position:0% +agent and swirl until you get the snow + + + align:start position:0% +agent and swirl until you get the snow +globe + + align:start position:0% +globe + + + align:start position:0% +globe +effect there should be free unclump + + align:start position:0% +effect there should be free unclump + + + align:start position:0% +effect there should be free unclump +powder in the flask even after letting + + align:start position:0% +powder in the flask even after letting + + + align:start position:0% +powder in the flask even after letting +it sit for a few minutes + + align:start position:0% + + + + align:start position:0% + +sodium sulfate is another common drying + + align:start position:0% +sodium sulfate is another common drying + + + align:start position:0% +sodium sulfate is another common drying +agent although it is slower than + + align:start position:0% +agent although it is slower than + + + align:start position:0% +agent although it is slower than +magnesium sulfate it is effectively + + align:start position:0% +magnesium sulfate it is effectively + + + align:start position:0% +magnesium sulfate it is effectively +neutral and in its granular form will + + align:start position:0% +neutral and in its granular form will + + + align:start position:0% +neutral and in its granular form will +absorb less of your desired material + + align:start position:0% +absorb less of your desired material + + + align:start position:0% +absorb less of your desired material +onto its + + align:start position:0% +onto its + + + align:start position:0% +onto its +surface drying the organic layer with + + align:start position:0% +surface drying the organic layer with + + + align:start position:0% +surface drying the organic layer with +sodium sulfate is similar to using + + align:start position:0% +sodium sulfate is similar to using + + + align:start position:0% +sodium sulfate is similar to using +magnesium sulfate except you may need to + + align:start position:0% +magnesium sulfate except you may need to + + + align:start position:0% +magnesium sulfate except you may need to +look a bit closer to see whether there + + align:start position:0% +look a bit closer to see whether there + + + align:start position:0% +look a bit closer to see whether there +is free unclump drying agent in the + + align:start position:0% +is free unclump drying agent in the + + + align:start position:0% +is free unclump drying agent in the +flask it is also a good idea to let the + + align:start position:0% +flask it is also a good idea to let the + + + align:start position:0% +flask it is also a good idea to let the +solution dry for 5 or 10 minutes before + + align:start position:0% +solution dry for 5 or 10 minutes before + + + align:start position:0% +solution dry for 5 or 10 minutes before +removing the drying + + align:start position:0% +removing the drying + + + align:start position:0% +removing the drying +agent to remove the drying agent perform + + align:start position:0% +agent to remove the drying agent perform + + + align:start position:0% +agent to remove the drying agent perform +a gravity filtration with fluted filter + + align:start position:0% +a gravity filtration with fluted filter + + + align:start position:0% +a gravity filtration with fluted filter +paper once you have filtered the entire + + align:start position:0% +paper once you have filtered the entire + + + align:start position:0% +paper once you have filtered the entire +solution be sure to rinse the drying + + align:start position:0% +solution be sure to rinse the drying + + + align:start position:0% +solution be sure to rinse the drying +agent very well so that you don't leave + + align:start position:0% +agent very well so that you don't leave + + + align:start position:0% +agent very well so that you don't leave +any product stuck to the surface it is a + + align:start position:0% +any product stuck to the surface it is a + + + align:start position:0% +any product stuck to the surface it is a +good idea to rinse the drying agent + + align:start position:0% +good idea to rinse the drying agent + + + align:start position:0% +good idea to rinse the drying agent +three times with clean dry solvent + + align:start position:0% +three times with clean dry solvent + + + align:start position:0% +three times with clean dry solvent +adding each of these rinses to the flat + + align:start position:0% + + + + align:start position:0% + +once you are confident that you have + + align:start position:0% +once you are confident that you have + + + align:start position:0% +once you are confident that you have +transferred all of the desired material + + align:start position:0% +transferred all of the desired material + + + align:start position:0% +transferred all of the desired material +to the round bottom flask you are ready + + align:start position:0% +to the round bottom flask you are ready + + + align:start position:0% +to the round bottom flask you are ready +to proceed to the rotovap and + + align:start position:0% +to proceed to the rotovap and + + + align:start position:0% +to proceed to the rotovap and +concentrate the solution in vacuo for + + align:start position:0% +concentrate the solution in vacuo for + + + align:start position:0% +concentrate the solution in vacuo for +detailed information on proper use of + + align:start position:0% +detailed information on proper use of + + + align:start position:0% +detailed information on proper use of +the rotovap you can watch the second + + align:start position:0% +the rotovap you can watch the second + + + align:start position:0% +the rotovap you can watch the second +reaction workup + + align:start position:0% + + + + align:start position:0% + +video remember this video is intended to + + align:start position:0% +video remember this video is intended to + + + align:start position:0% +video remember this video is intended to +help you prepare for lab by providing a + + align:start position:0% +help you prepare for lab by providing a + + + align:start position:0% +help you prepare for lab by providing a +demonstration of the proper experimental + + align:start position:0% +demonstration of the proper experimental + + + align:start position:0% +demonstration of the proper experimental +technique it is not intended as a + + align:start position:0% +technique it is not intended as a + + + align:start position:0% +technique it is not intended as a +replacement for reading your lab manual + + align:start position:0% +replacement for reading your lab manual + + + align:start position:0% +replacement for reading your lab manual +or the supplementary material in order + + align:start position:0% +or the supplementary material in order + + + align:start position:0% +or the supplementary material in order +to become a great experimentalist it is + + align:start position:0% +to become a great experimentalist it is + + + align:start position:0% +to become a great experimentalist it is +important that you understand both + + align:start position:0% +important that you understand both + + + align:start position:0% +important that you understand both +Theory and technique now it's your turn + + align:start position:0% +Theory and technique now it's your turn + + + align:start position:0% +Theory and technique now it's your turn +good luck + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/dARl_gGrS4o.txt b/dARl_gGrS4o.txt new file mode 100644 index 0000000000000000000000000000000000000000..90d14f785d4c84db1579e72c1cdfa3b4ba99723b --- /dev/null +++ b/dARl_gGrS4o.txt @@ -0,0 +1,8219 @@ +align:start position:0% + +it's too bad in a way that we can't + + align:start position:0% +it's too bad in a way that we can't + + + align:start position:0% +it's too bad in a way that we can't +paint everything black because this map + + align:start position:0% +paint everything black because this map + + + align:start position:0% +paint everything black because this map +coloring problem + + align:start position:0% +coloring problem + + + align:start position:0% +coloring problem +sure would be a lot easier + + align:start position:0% +sure would be a lot easier + + + align:start position:0% +sure would be a lot easier +so uh i don't know what we're going to + + align:start position:0% +so uh i don't know what we're going to + + + align:start position:0% +so uh i don't know what we're going to +do about that the problem is + + align:start position:0% +do about that the problem is + + + align:start position:0% +do about that the problem is +well how long is this going to take + + align:start position:0% +well how long is this going to take + + + align:start position:0% +well how long is this going to take +maybe we should here's what i'm going to + + align:start position:0% +maybe we should here's what i'm going to + + + align:start position:0% +maybe we should here's what i'm going to +do we're going to wait till either all + + align:start position:0% +do we're going to wait till either all + + + align:start position:0% +do we're going to wait till either all +the laptops are closed or this program + + align:start position:0% +the laptops are closed or this program + + + align:start position:0% +the laptops are closed or this program +terminates + + align:start position:0% +terminates + + + align:start position:0% +terminates +whichever comes first + + align:start position:0% + + + + align:start position:0% + +so how long is this going to take i + + align:start position:0% +so how long is this going to take i + + + align:start position:0% +so how long is this going to take i +actually don't know i + + align:start position:0% +actually don't know i + + + align:start position:0% +actually don't know i +i think it'll take more than a lifetime + + align:start position:0% +i think it'll take more than a lifetime + + + align:start position:0% +i think it'll take more than a lifetime +of the universe but i'm not sure + + align:start position:0% +of the universe but i'm not sure + + + align:start position:0% +of the universe but i'm not sure +so let's take a little bit let's take a + + align:start position:0% +so let's take a little bit let's take a + + + align:start position:0% +so let's take a little bit let's take a +look at a slightly easier + + align:start position:0% +look at a slightly easier + + + align:start position:0% +look at a slightly easier +map coloring problem we'll stop this one + + align:start position:0% +map coloring problem we'll stop this one + + + align:start position:0% +map coloring problem we'll stop this one +and change the map to something i call + + align:start position:0% +and change the map to something i call + + + align:start position:0% +and change the map to something i call +simplicia + + align:start position:0% +simplicia + + + align:start position:0% +simplicia +there's 26 states one for each letter in + + align:start position:0% +there's 26 states one for each letter in + + + align:start position:0% +there's 26 states one for each letter in +the alphabet + + align:start position:0% +the alphabet + + + align:start position:0% +the alphabet +and what we're going to do is we're + + align:start position:0% +and what we're going to do is we're + + + align:start position:0% +and what we're going to do is we're +going to do a depth first + + align:start position:0% +going to do a depth first + + + align:start position:0% +going to do a depth first +search for a suitable coloring of this + + align:start position:0% +search for a suitable coloring of this + + + align:start position:0% +search for a suitable coloring of this +map + + align:start position:0% +map + + + align:start position:0% +map +we're going to go in order a b c d e and + + align:start position:0% +we're going to go in order a b c d e and + + + align:start position:0% +we're going to go in order a b c d e and +as i've suggested here + + align:start position:0% +as i've suggested here + + + align:start position:0% +as i've suggested here +at each level we're going to rotate the + + align:start position:0% +at each level we're going to rotate the + + + align:start position:0% +at each level we're going to rotate the +color choices so we don't overuse any + + align:start position:0% +color choices so we don't overuse any + + + align:start position:0% +color choices so we don't overuse any +one color + + align:start position:0% +one color + + + align:start position:0% +one color +so if we launch this particular search + + align:start position:0% +so if we launch this particular search + + + align:start position:0% +so if we launch this particular search +this depth first attempt to + + align:start position:0% +this depth first attempt to + + + align:start position:0% +this depth first attempt to +color this map there it goes and maybe + + align:start position:0% +color this map there it goes and maybe + + + align:start position:0% +color this map there it goes and maybe +we should wait until it terminates + + align:start position:0% +we should wait until it terminates + + + align:start position:0% +we should wait until it terminates +or maybe we just let it run and + + align:start position:0% +or maybe we just let it run and + + + align:start position:0% +or maybe we just let it run and +it'll terminate perhaps sometime within + + align:start position:0% +it'll terminate perhaps sometime within + + + align:start position:0% +it'll terminate perhaps sometime within +the lecture or + + align:start position:0% +the lecture or + + + align:start position:0% +the lecture or +maybe we should just let it run over the + + align:start position:0% +maybe we should just let it run over the + + + align:start position:0% +maybe we should just let it run over the +weekend + + align:start position:0% +weekend + + + align:start position:0% +weekend +or how long do you think we'd have to + + align:start position:0% +or how long do you think we'd have to + + + align:start position:0% +or how long do you think we'd have to +wait if we want to come back and watch + + align:start position:0% +wait if we want to come back and watch + + + align:start position:0% +wait if we want to come back and watch +it terminate + + align:start position:0% +it terminate + + + align:start position:0% +it terminate +roughly 30 frames a second on + + align:start position:0% +roughly 30 frames a second on + + + align:start position:0% +roughly 30 frames a second on +calculating it all in my head + + align:start position:0% +calculating it all in my head + + + align:start position:0% +calculating it all in my head +i don't want to bet my life on it but i + + align:start position:0% +i don't want to bet my life on it but i + + + align:start position:0% +i don't want to bet my life on it but i +think about 5 + + align:start position:0% +think about 5 + + + align:start position:0% +think about 5 +000 years and if you want to use + + align:start position:0% +000 years and if you want to use + + + align:start position:0% +000 years and if you want to use +as many states as there are in the + + align:start position:0% +as many states as there are in the + + + align:start position:0% +as many states as there are in the +united states + + align:start position:0% +united states + + + align:start position:0% +united states +in this demonstration you get up to + + align:start position:0% +in this demonstration you get up to + + + align:start position:0% +in this demonstration you get up to +numbers like + + align:start position:0% +numbers like + + + align:start position:0% +numbers like +10 to the 17th years + + align:start position:0% +10 to the 17th years + + + align:start position:0% +10 to the 17th years +17th 18th 16th i'm not exactly sure i + + align:start position:0% +17th 18th 16th i'm not exactly sure i + + + align:start position:0% +17th 18th 16th i'm not exactly sure i +did a rough calculation + + align:start position:0% +did a rough calculation + + + align:start position:0% +did a rough calculation +and of course you could do some + + align:start position:0% +and of course you could do some + + + align:start position:0% +and of course you could do some +parallels into that and it's not as bad + + align:start position:0% +parallels into that and it's not as bad + + + align:start position:0% +parallels into that and it's not as bad +as chess where you need all the atoms in + + align:start position:0% +as chess where you need all the atoms in + + + align:start position:0% +as chess where you need all the atoms in +the universe you still can't do it and + + align:start position:0% +the universe you still can't do it and + + + align:start position:0% +the universe you still can't do it and +things like that + + align:start position:0% +things like that + + + align:start position:0% +things like that +acting as computers but still it's + + align:start position:0% +acting as computers but still it's + + + align:start position:0% +acting as computers but still it's +pretty horrendous and the problem + + align:start position:0% +pretty horrendous and the problem + + + align:start position:0% +pretty horrendous and the problem +the problem is well the problem is + + align:start position:0% +the problem is well the problem is + + + align:start position:0% +the problem is well the problem is +the problem is illustrated by this + + align:start position:0% +the problem is illustrated by this + + + align:start position:0% +the problem is illustrated by this +diagram i put in back of me + + align:start position:0% +diagram i put in back of me + + + align:start position:0% +diagram i put in back of me +if you do a depth first search + + align:start position:0% +if you do a depth first search + + + align:start position:0% +if you do a depth first search +and you have a a problem like + + align:start position:0% +and you have a a problem like + + + align:start position:0% +and you have a a problem like +texas if you label + + align:start position:0% +texas if you label + + + align:start position:0% +texas if you label +if you assign a color to arizona + + align:start position:0% +if you assign a color to arizona + + + align:start position:0% +if you assign a color to arizona +oklahoma arkansas and louisiana + + align:start position:0% +oklahoma arkansas and louisiana + + + align:start position:0% +oklahoma arkansas and louisiana +first and then wait around to do texas + + align:start position:0% +first and then wait around to do texas + + + align:start position:0% +first and then wait around to do texas +last + + align:start position:0% +last + + + align:start position:0% +last +then you get yourself into a bind + + align:start position:0% +then you get yourself into a bind + + + align:start position:0% +then you get yourself into a bind +by your fourth choice that you don't + + align:start position:0% +by your fourth choice that you don't + + + align:start position:0% +by your fourth choice that you don't +discover until your 48th choice + + align:start position:0% +discover until your 48th choice + + + align:start position:0% +discover until your 48th choice +so what happens then is that you start + + align:start position:0% +so what happens then is that you start + + + align:start position:0% +so what happens then is that you start +developing this tree like this + + align:start position:0% +developing this tree like this + + + align:start position:0% +developing this tree like this +you get to those states surrounding + + align:start position:0% +you get to those states surrounding + + + align:start position:0% +you get to those states surrounding +texas + + align:start position:0% +texas + + + align:start position:0% +texas +texas is the last state assigned a color + + align:start position:0% +texas is the last state assigned a color + + + align:start position:0% +texas is the last state assigned a color +and there's nothing left for it + + align:start position:0% +and there's nothing left for it + + + align:start position:0% +and there's nothing left for it +and that problem was there on the fourth + + align:start position:0% +and that problem was there on the fourth + + + align:start position:0% +and that problem was there on the fourth +choice you don't discover it until your + + align:start position:0% +choice you don't discover it until your + + + align:start position:0% +choice you don't discover it until your +50th choice + + align:start position:0% +50th choice + + + align:start position:0% +50th choice +so you develop a horrendous impossible + + align:start position:0% +so you develop a horrendous impossible + + + align:start position:0% +so you develop a horrendous impossible +impossible search + + align:start position:0% +impossible search + + + align:start position:0% +impossible search +so you simply can't do it that way + + align:start position:0% +so you simply can't do it that way + + + align:start position:0% +so you simply can't do it that way +but now not to worry we now have + + align:start position:0% +but now not to worry we now have + + + align:start position:0% +but now not to worry we now have +come equipped with the idea of + + align:start position:0% +come equipped with the idea of + + + align:start position:0% +come equipped with the idea of +constraint propagation + + align:start position:0% +constraint propagation + + + align:start position:0% +constraint propagation +so we could just take a country with + + align:start position:0% +so we could just take a country with + + + align:start position:0% +so we could just take a country with +four states like this + + align:start position:0% +four states like this + + + align:start position:0% +four states like this +each can be labeled red green blue and + + align:start position:0% +each can be labeled red green blue and + + + align:start position:0% +each can be labeled red green blue and +yellow + + align:start position:0% +yellow + + + align:start position:0% +yellow +so just like in a case of line drawings + + align:start position:0% +so just like in a case of line drawings + + + align:start position:0% +so just like in a case of line drawings +we'll pile up all the possible things + + align:start position:0% +we'll pile up all the possible things + + + align:start position:0% +we'll pile up all the possible things +that the + + align:start position:0% +that the + + + align:start position:0% +that the +value can be red green blue and yellow + + align:start position:0% +value can be red green blue and yellow + + + align:start position:0% +value can be red green blue and yellow +red green blue and yellow red + + align:start position:0% +red green blue and yellow red + + + align:start position:0% +red green blue and yellow red +green blue and yellow and we start up + + align:start position:0% +green blue and yellow and we start up + + + align:start position:0% +green blue and yellow and we start up +constraint propagation + + align:start position:0% +constraint propagation + + + align:start position:0% +constraint propagation +so we say for the upper left hand corner + + align:start position:0% +so we say for the upper left hand corner + + + align:start position:0% +so we say for the upper left hand corner +state + + align:start position:0% +state + + + align:start position:0% +state +is there any reason to believe that r is + + align:start position:0% +is there any reason to believe that r is + + + align:start position:0% +is there any reason to believe that r is +impossible + + align:start position:0% +impossible + + + align:start position:0% +impossible +well we look at our neighbors and see + + align:start position:0% +well we look at our neighbors and see + + + align:start position:0% +well we look at our neighbors and see +what kind of constraint flows in from + + align:start position:0% +what kind of constraint flows in from + + + align:start position:0% +what kind of constraint flows in from +them + + align:start position:0% +them + + + align:start position:0% +them +and sure this guy could be green and + + align:start position:0% +and sure this guy could be green and + + + align:start position:0% +and sure this guy could be green and +this guy can be blue + + align:start position:0% +this guy can be blue + + + align:start position:0% +this guy can be blue +they don't have to be red so there's no + + align:start position:0% +they don't have to be red so there's no + + + align:start position:0% +they don't have to be red so there's no +nothing that rules out red and there's + + align:start position:0% +nothing that rules out red and there's + + + align:start position:0% +nothing that rules out red and there's +nothing that rules out blue + + align:start position:0% +nothing that rules out blue + + + align:start position:0% +nothing that rules out blue +and there's nothing that rolls out + + align:start position:0% +and there's nothing that rolls out + + + align:start position:0% +and there's nothing that rolls out +yellow and there's nothing + + align:start position:0% +yellow and there's nothing + + + align:start position:0% +yellow and there's nothing +rolls out green so constraint + + align:start position:0% +rolls out green so constraint + + + align:start position:0% +rolls out green so constraint +propagation just sits there + + align:start position:0% +propagation just sits there + + + align:start position:0% +propagation just sits there +with its finger up its nose doing + + align:start position:0% +with its finger up its nose doing + + + align:start position:0% +with its finger up its nose doing +nothing + + align:start position:0% +nothing + + + align:start position:0% +nothing +so it doesn't look like we can use + + align:start position:0% +so it doesn't look like we can use + + + align:start position:0% +so it doesn't look like we can use +either + + align:start position:0% +either + + + align:start position:0% +either +depth first search + + align:start position:0% + + + + align:start position:0% + +or constraint propagation so we could + + align:start position:0% +or constraint propagation so we could + + + align:start position:0% +or constraint propagation so we could +just + + align:start position:0% +just + + + align:start position:0% +just +give up and cry but maybe there's some + + align:start position:0% +give up and cry but maybe there's some + + + align:start position:0% +give up and cry but maybe there's some +other approach that will help + + align:start position:0% +other approach that will help + + + align:start position:0% +other approach that will help +so let me actually work the texas + + align:start position:0% +so let me actually work the texas + + + align:start position:0% +so let me actually work the texas +problem + + align:start position:0% +problem + + + align:start position:0% +problem +so with apologies to houston + + align:start position:0% +so with apologies to houston + + + align:start position:0% +so with apologies to houston +and tyler here's the map of texas + + align:start position:0% +and tyler here's the map of texas + + + align:start position:0% +and tyler here's the map of texas +there we are and here's uh roughly + + align:start position:0% +there we are and here's uh roughly + + + align:start position:0% +there we are and here's uh roughly +speaking arizona + + align:start position:0% +speaking arizona + + + align:start position:0% +speaking arizona +is over here somewhere and we've got + + align:start position:0% +is over here somewhere and we've got + + + align:start position:0% +is over here somewhere and we've got +oklahoma in there + + align:start position:0% +oklahoma in there + + + align:start position:0% +oklahoma in there +and uh old bill clinton's state arkansas + + align:start position:0% +and uh old bill clinton's state arkansas + + + align:start position:0% +and uh old bill clinton's state arkansas +and then louisiana sticks out there a + + align:start position:0% +and then louisiana sticks out there a + + + align:start position:0% +and then louisiana sticks out there a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +so there's our map of + + align:start position:0% +so there's our map of + + + align:start position:0% +so there's our map of +that particular part of the country so + + align:start position:0% +that particular part of the country so + + + align:start position:0% +that particular part of the country so +we've got arizona here + + align:start position:0% +we've got arizona here + + + align:start position:0% +we've got arizona here +oklahoma here arkansas here + + align:start position:0% +oklahoma here arkansas here + + + align:start position:0% +oklahoma here arkansas here +and louisiana here and texas here + + align:start position:0% +and louisiana here and texas here + + + align:start position:0% +and louisiana here and texas here +and we have elected to assign colors to + + align:start position:0% +and we have elected to assign colors to + + + align:start position:0% +and we have elected to assign colors to +these states + + align:start position:0% +these states + + + align:start position:0% +these states +in that order so this is one two + + align:start position:0% +in that order so this is one two + + + align:start position:0% +in that order so this is one two +three four + + align:start position:0% + + + + align:start position:0% + +and we're going to do that and we're + + align:start position:0% +and we're going to do that and we're + + + align:start position:0% +and we're going to do that and we're +going to rotate our color choices just + + align:start position:0% +going to rotate our color choices just + + + align:start position:0% +going to rotate our color choices just +so we don't overuse any one color + + align:start position:0% + + + + align:start position:0% + +but we're going to also have a look at + + align:start position:0% +but we're going to also have a look at + + + align:start position:0% +but we're going to also have a look at +texas as we go around because texas is a + + align:start position:0% +texas as we go around because texas is a + + + align:start position:0% +texas as we go around because texas is a +state that borders on the + + align:start position:0% +state that borders on the + + + align:start position:0% +state that borders on the +states that we're choosing colors for + + align:start position:0% + + + + align:start position:0% + +so the only possible colors that texas + + align:start position:0% +so the only possible colors that texas + + + align:start position:0% +so the only possible colors that texas +could be are red + + align:start position:0% +could be are red + + + align:start position:0% +could be are red +green blue and yellow + + align:start position:0% + + + + align:start position:0% + +so as we make our choices around here + + align:start position:0% +so as we make our choices around here + + + align:start position:0% +so as we make our choices around here +we'll say that + + align:start position:0% +we'll say that + + + align:start position:0% +we'll say that +i don't know we don't have to adhere to + + align:start position:0% +i don't know we don't have to adhere to + + + align:start position:0% +i don't know we don't have to adhere to +any particular style we can say that + + align:start position:0% +any particular style we can say that + + + align:start position:0% +any particular style we can say that +arizona is going to get colored red + + align:start position:0% +arizona is going to get colored red + + + align:start position:0% +arizona is going to get colored red +our that's going to rule out our over + + align:start position:0% +our that's going to rule out our over + + + align:start position:0% +our that's going to rule out our over +here for texas + + align:start position:0% +here for texas + + + align:start position:0% +here for texas +because no adjacent states can have the + + align:start position:0% +because no adjacent states can have the + + + align:start position:0% +because no adjacent states can have the +same color + + align:start position:0% +same color + + + align:start position:0% +same color +then we go over to oklahoma and we're + + align:start position:0% +then we go over to oklahoma and we're + + + align:start position:0% +then we go over to oklahoma and we're +rotating our color choices so we'll say + + align:start position:0% +rotating our color choices so we'll say + + + align:start position:0% +rotating our color choices so we'll say +that can be green + + align:start position:0% +that can be green + + + align:start position:0% +that can be green +and that's fine because it's consistent + + align:start position:0% +and that's fine because it's consistent + + + align:start position:0% +and that's fine because it's consistent +with the red here but it rules out the + + align:start position:0% +with the red here but it rules out the + + + align:start position:0% +with the red here but it rules out the +possibility that texas can be green + + align:start position:0% +possibility that texas can be green + + + align:start position:0% +possibility that texas can be green +and then we go over here to arkansas red + + align:start position:0% +and then we go over here to arkansas red + + + align:start position:0% +and then we go over here to arkansas red +green + + align:start position:0% +green + + + align:start position:0% +green +blue that's fine that's consistent with + + align:start position:0% +blue that's fine that's consistent with + + + align:start position:0% +blue that's fine that's consistent with +the green on oklahoma + + align:start position:0% +the green on oklahoma + + + align:start position:0% +the green on oklahoma +but if we look at its neighbors we know + + align:start position:0% +but if we look at its neighbors we know + + + align:start position:0% +but if we look at its neighbors we know +that texas is + + align:start position:0% +that texas is + + + align:start position:0% +that texas is +forever forbidden to be blue now + + align:start position:0% +forever forbidden to be blue now + + + align:start position:0% +forever forbidden to be blue now +so now we go over to louisiana and + + align:start position:0% +so now we go over to louisiana and + + + align:start position:0% +so now we go over to louisiana and +remember we're rotating our color + + align:start position:0% +remember we're rotating our color + + + align:start position:0% +remember we're rotating our color +choices because we don't + + align:start position:0% +choices because we don't + + + align:start position:0% +choices because we don't +want to overuse them so this means that + + align:start position:0% +want to overuse them so this means that + + + align:start position:0% +want to overuse them so this means that +the first choice we're going to make + + align:start position:0% +the first choice we're going to make + + + align:start position:0% +the first choice we're going to make +here for louisiana + + align:start position:0% +here for louisiana + + + align:start position:0% +here for louisiana +is yellow + + align:start position:0% + + + + align:start position:0% + +and that's fine because it's consistent + + align:start position:0% +and that's fine because it's consistent + + + align:start position:0% +and that's fine because it's consistent +with arkansas but it's not so fine + + align:start position:0% +with arkansas but it's not so fine + + + align:start position:0% +with arkansas but it's not so fine +because it's now ruled out the last + + align:start position:0% +because it's now ruled out the last + + + align:start position:0% +because it's now ruled out the last +possibility + + align:start position:0% +possibility + + + align:start position:0% +possibility +for texas so even though texas is going + + align:start position:0% +for texas so even though texas is going + + + align:start position:0% +for texas so even though texas is going +to be the 50th + + align:start position:0% +to be the 50th + + + align:start position:0% +to be the 50th +48th 48th state that we color + + align:start position:0% +48th 48th state that we color + + + align:start position:0% +48th 48th state that we color +we're going to say at this point there's + + align:start position:0% +we're going to say at this point there's + + + align:start position:0% +we're going to say at this point there's +no need in going on + + align:start position:0% +no need in going on + + + align:start position:0% +no need in going on +we'd better back up because there's + + align:start position:0% +we'd better back up because there's + + + align:start position:0% +we'd better back up because there's +nothing left for texas when we get + + align:start position:0% +nothing left for texas when we get + + + align:start position:0% +nothing left for texas when we get +around to coloring it + + align:start position:0% +around to coloring it + + + align:start position:0% +around to coloring it +so that means that this yellow is ruled + + align:start position:0% +so that means that this yellow is ruled + + + align:start position:0% +so that means that this yellow is ruled +out here + + align:start position:0% +out here + + + align:start position:0% +out here +this yellow reappears we select the next + + align:start position:0% +this yellow reappears we select the next + + + align:start position:0% +this yellow reappears we select the next +color in line for louisiana which + + align:start position:0% +color in line for louisiana which + + + align:start position:0% +color in line for louisiana which +happens to be red + + align:start position:0% +happens to be red + + + align:start position:0% +happens to be red +and now that's consistent with this + + align:start position:0% +and now that's consistent with this + + + align:start position:0% +and now that's consistent with this +yellow that's still left for texas and + + align:start position:0% +yellow that's still left for texas and + + + align:start position:0% +yellow that's still left for texas and +it's also consistent with the blue + + align:start position:0% +it's also consistent with the blue + + + align:start position:0% +it's also consistent with the blue +that's up here for arkansas + + align:start position:0% +that's up here for arkansas + + + align:start position:0% +that's up here for arkansas +so that's cool i wonder if we maybe we + + align:start position:0% +so that's cool i wonder if we maybe we + + + align:start position:0% +so that's cool i wonder if we maybe we +can make an algorithm out of that + + align:start position:0% +can make an algorithm out of that + + + align:start position:0% +can make an algorithm out of that +and solve problems like this we see sort + + align:start position:0% +and solve problems like this we see sort + + + align:start position:0% +and solve problems like this we see sort +of the intuition of what we're doing + + align:start position:0% +of the intuition of what we're doing + + + align:start position:0% +of the intuition of what we're doing +we're actually using the martial arts + + align:start position:0% +we're actually using the martial arts + + + align:start position:0% +we're actually using the martial arts +principle again because the whole + + align:start position:0% +principle again because the whole + + + align:start position:0% +principle again because the whole +problem + + align:start position:0% +problem + + + align:start position:0% +problem +is that local constraints undiscovered + + align:start position:0% +is that local constraints undiscovered + + + align:start position:0% +is that local constraints undiscovered +local constraints are causing downstream + + align:start position:0% +local constraints are causing downstream + + + align:start position:0% +local constraints are causing downstream +problems + + align:start position:0% +problems + + + align:start position:0% +problems +so we're going to use the enemy's powers + + align:start position:0% +so we're going to use the enemy's powers + + + align:start position:0% +so we're going to use the enemy's powers +against them and we're going to look at + + align:start position:0% +against them and we're going to look at + + + align:start position:0% +against them and we're going to look at +those local constraints as we go + + align:start position:0% +those local constraints as we go + + + align:start position:0% +those local constraints as we go +and make sure they're not going to get + + align:start position:0% +and make sure they're not going to get + + + align:start position:0% +and make sure they're not going to get +us downstream not going to get us later + + align:start position:0% +us downstream not going to get us later + + + align:start position:0% +us downstream not going to get us later +on + + align:start position:0% +on + + + align:start position:0% +on +so now i'm going to i'm going to get i'm + + align:start position:0% +so now i'm going to i'm going to get i'm + + + align:start position:0% +so now i'm going to i'm going to get i'm +going to look like i'm getting a little + + align:start position:0% +going to look like i'm getting a little + + + align:start position:0% +going to look like i'm getting a little +formal + + align:start position:0% +formal + + + align:start position:0% +formal +but i'm just getting a little bit more + + align:start position:0% +but i'm just getting a little bit more + + + align:start position:0% +but i'm just getting a little bit more +formal because i want to have a language + + align:start position:0% +formal because i want to have a language + + + align:start position:0% +formal because i want to have a language +have some language that i can use to + + align:start position:0% +have some language that i can use to + + + align:start position:0% +have some language that i can use to +describe what's going on so it's clear + + align:start position:0% +describe what's going on so it's clear + + + align:start position:0% +describe what's going on so it's clear +what the choices are + + align:start position:0% +what the choices are + + + align:start position:0% +what the choices are +so to start off with we're going to have + + align:start position:0% +so to start off with we're going to have + + + align:start position:0% +so to start off with we're going to have +to have some vocabulary + + align:start position:0% +to have some vocabulary + + + align:start position:0% +to have some vocabulary +so let's start up our vocabulary here + + align:start position:0% +so let's start up our vocabulary here + + + align:start position:0% +so let's start up our vocabulary here +we're going to have a notion of a + + align:start position:0% +we're going to have a notion of a + + + align:start position:0% +we're going to have a notion of a +variable + + align:start position:0% + + + + align:start position:0% + +v and that's something that can have an + + align:start position:0% +v and that's something that can have an + + + align:start position:0% +v and that's something that can have an +assignment + + align:start position:0% + + + + align:start position:0% + +yeah just you know + + align:start position:0% +yeah just you know + + + align:start position:0% +yeah just you know +yeah there's nothing complicated about + + align:start position:0% +yeah there's nothing complicated about + + + align:start position:0% +yeah there's nothing complicated about +that and a value + + align:start position:0% + + + + align:start position:0% + +a value x is something that can + + align:start position:0% +a value x is something that can + + + align:start position:0% +a value x is something that can +be an assignment + + align:start position:0% + + + + align:start position:0% + +a little bit circular but we're all + + align:start position:0% +a little bit circular but we're all + + + align:start position:0% +a little bit circular but we're all +computer scientists you know what i mean + + align:start position:0% +computer scientists you know what i mean + + + align:start position:0% +computer scientists you know what i mean +so the next thing is a little slightly + + align:start position:0% +so the next thing is a little slightly + + + align:start position:0% +so the next thing is a little slightly +less + + align:start position:0% +less + + + align:start position:0% +less +obvious and that's a notion of a domain + + align:start position:0% + + + + align:start position:0% + +d and that's going to be a bag + + align:start position:0% +d and that's going to be a bag + + + align:start position:0% +d and that's going to be a bag +of values + + align:start position:0% + + + + align:start position:0% + +okay so one more thing a constraint + + align:start position:0% + + + + align:start position:0% + +that's a constraint c is a + + align:start position:0% +that's a constraint c is a + + + align:start position:0% +that's a constraint c is a +limit on + + align:start position:0% +limit on + + + align:start position:0% +limit on +well in our examples it's mostly going + + align:start position:0% +well in our examples it's mostly going + + + align:start position:0% +well in our examples it's mostly going +to be pairs of variables + + align:start position:0% +to be pairs of variables + + + align:start position:0% +to be pairs of variables +pairs of variable values but in general + + align:start position:0% +pairs of variable values but in general + + + align:start position:0% +pairs of variable values but in general +it could be variable values + + align:start position:0% +it could be variable values + + + align:start position:0% +it could be variable values +so if we go back here to texas we can + + align:start position:0% +so if we go back here to texas we can + + + align:start position:0% +so if we go back here to texas we can +say okay + + align:start position:0% +say okay + + + align:start position:0% +say okay +how does that vocabulary drape itself + + align:start position:0% +how does that vocabulary drape itself + + + align:start position:0% +how does that vocabulary drape itself +over that configuration + + align:start position:0% +over that configuration + + + align:start position:0% +over that configuration +and the answer is the states have the + + align:start position:0% +and the answer is the states have the + + + align:start position:0% +and the answer is the states have the +role + + align:start position:0% +role + + + align:start position:0% +role +of variables the colors have the role + + align:start position:0% +of variables the colors have the role + + + align:start position:0% +of variables the colors have the role +of values + + align:start position:0% +of values + + + align:start position:0% +of values +and the domains are the remaining color + + align:start position:0% +and the domains are the remaining color + + + align:start position:0% +and the domains are the remaining color +possibilities + + align:start position:0% +possibilities + + + align:start position:0% +possibilities +that we can still use on a particular + + align:start position:0% +that we can still use on a particular + + + align:start position:0% +that we can still use on a particular +state and the constraint in this case is + + align:start position:0% +state and the constraint in this case is + + + align:start position:0% +state and the constraint in this case is +the simple map coloring constraint that + + align:start position:0% +the simple map coloring constraint that + + + align:start position:0% +the simple map coloring constraint that +no + + align:start position:0% +no + + + align:start position:0% +no +states that share a boundary can have + + align:start position:0% +states that share a boundary can have + + + align:start position:0% +states that share a boundary can have +the same color + + align:start position:0% +the same color + + + align:start position:0% +the same color +so states are variables colors are + + align:start position:0% +so states are variables colors are + + + align:start position:0% +so states are variables colors are +values + + align:start position:0% +values + + + align:start position:0% +values +domains are bags of colors and + + align:start position:0% +domains are bags of colors and + + + align:start position:0% +domains are bags of colors and +constraints + + align:start position:0% +constraints + + + align:start position:0% +constraints +there's only one json states can't have + + align:start position:0% +there's only one json states can't have + + + align:start position:0% +there's only one json states can't have +the same + + align:start position:0% +the same + + + align:start position:0% +the same +color so that's how it fits with this + + align:start position:0% +color so that's how it fits with this + + + align:start position:0% +color so that's how it fits with this +vocabulary + + align:start position:0% +vocabulary + + + align:start position:0% +vocabulary +so now what did i actually do here well + + align:start position:0% +so now what did i actually do here well + + + align:start position:0% +so now what did i actually do here well +what i actually did here i'm going to + + align:start position:0% +what i actually did here i'm going to + + + align:start position:0% +what i actually did here i'm going to +now + + align:start position:0% +now + + + align:start position:0% +now +formalize a little bit by writing it + + align:start position:0% +formalize a little bit by writing it + + + align:start position:0% +formalize a little bit by writing it +down in a in pseudocode + + align:start position:0% +down in a in pseudocode + + + align:start position:0% +down in a in pseudocode +so here we are we're going to have a + + align:start position:0% +so here we are we're going to have a + + + align:start position:0% +so here we are we're going to have a +look at what we did here intuit with our + + align:start position:0% +look at what we did here intuit with our + + + align:start position:0% +look at what we did here intuit with our +intuition + + align:start position:0% +intuition + + + align:start position:0% +intuition +and we're going to reduce it to a + + align:start position:0% +and we're going to reduce it to a + + + align:start position:0% +and we're going to reduce it to a +procedure and here's the procedure + + align:start position:0% +procedure and here's the procedure + + + align:start position:0% +procedure and here's the procedure +remember we're doing depth first search + + align:start position:0% +remember we're doing depth first search + + + align:start position:0% +remember we're doing depth first search +on this stuff i did a depth first search + + align:start position:0% +on this stuff i did a depth first search + + + align:start position:0% +on this stuff i did a depth first search +we're going to do a depth first search + + align:start position:0% +we're going to do a depth first search + + + align:start position:0% +we're going to do a depth first search +and for each + + align:start position:0% + + + + align:start position:0% + +depth first search + + align:start position:0% +depth first search + + + align:start position:0% +depth first search +assignment + + align:start position:0% + + + + align:start position:0% + +okay so here i am i'm labeling arizona + + align:start position:0% +okay so here i am i'm labeling arizona + + + align:start position:0% +okay so here i am i'm labeling arizona +and then oklahoma and arkansas and then + + align:start position:0% +and then oklahoma and arkansas and then + + + align:start position:0% +and then oklahoma and arkansas and then +louisiana + + align:start position:0% +louisiana + + + align:start position:0% +louisiana +when i lay when i give each one of those + + align:start position:0% +when i lay when i give each one of those + + + align:start position:0% +when i lay when i give each one of those +a label a color + + align:start position:0% +a label a color + + + align:start position:0% +a label a color +i'm gonna i'm gonna do this procedure + + align:start position:0% +i'm gonna i'm gonna do this procedure + + + align:start position:0% +i'm gonna i'm gonna do this procedure +every time i make one of those + + align:start position:0% +every time i make one of those + + + align:start position:0% +every time i make one of those +assignments the last one was + + align:start position:0% +assignments the last one was + + + align:start position:0% +assignments the last one was +the last one that caused trouble was + + align:start position:0% +the last one that caused trouble was + + + align:start position:0% +the last one that caused trouble was +coloring louisiana yellow each time i + + align:start position:0% +coloring louisiana yellow each time i + + + align:start position:0% +coloring louisiana yellow each time i +put one of those colors down each time i + + align:start position:0% +put one of those colors down each time i + + + align:start position:0% +put one of those colors down each time i +make an assignment i'm going to do this + + align:start position:0% +make an assignment i'm going to do this + + + align:start position:0% +make an assignment i'm going to do this +procedure so for each step first + + align:start position:0% +procedure so for each step first + + + align:start position:0% +procedure so for each step first +assignment for each + + align:start position:0% + + + + align:start position:0% + +variable + + align:start position:0% +variable + + + align:start position:0% +variable +v considered + + align:start position:0% + + + + align:start position:0% + +now i don't know what i mean by you + + align:start position:0% +now i don't know what i mean by you + + + align:start position:0% +now i don't know what i mean by you +don't know what i mean by considered but + + align:start position:0% +don't know what i mean by considered but + + + align:start position:0% +don't know what i mean by considered but +when i + + align:start position:0% +when i + + + align:start position:0% +when i +put a label when i put a value i + + align:start position:0% +put a label when i put a value i + + + align:start position:0% +put a label when i put a value i +chose something as a color for louisiana + + align:start position:0% +chose something as a color for louisiana + + + align:start position:0% +chose something as a color for louisiana +i thought about texas so i was + + align:start position:0% +i thought about texas so i was + + + align:start position:0% +i thought about texas so i was +considering the variable texas + + align:start position:0% +considering the variable texas + + + align:start position:0% +considering the variable texas +when i made the assignment for louisiana + + align:start position:0% +when i made the assignment for louisiana + + + align:start position:0% +when i made the assignment for louisiana +i'm going to be a little bit vague about + + align:start position:0% +i'm going to be a little bit vague about + + + align:start position:0% +i'm going to be a little bit vague about +what i mean by considered right now + + align:start position:0% +what i mean by considered right now + + + align:start position:0% +what i mean by considered right now +because there are lots of choices about + + align:start position:0% +because there are lots of choices about + + + align:start position:0% +because there are lots of choices about +how much stuff you actually consider + + align:start position:0% +how much stuff you actually consider + + + align:start position:0% +how much stuff you actually consider +so let me just say consider and then + + align:start position:0% +so let me just say consider and then + + + align:start position:0% +so let me just say consider and then +we'll open that up and talk about the + + align:start position:0% +we'll open that up and talk about the + + + align:start position:0% +we'll open that up and talk about the +options in a moment + + align:start position:0% +options in a moment + + + align:start position:0% +options in a moment +so for each variable v considered + + align:start position:0% +so for each variable v considered + + + align:start position:0% +so for each variable v considered +for let's call that variable + + align:start position:0% +for let's call that variable + + + align:start position:0% +for let's call that variable +v sub i for each + + align:start position:0% + + + + align:start position:0% + +x sum i for each value in + + align:start position:0% +x sum i for each value in + + + align:start position:0% +x sum i for each value in +the domain of that variable + + align:start position:0% +the domain of that variable + + + align:start position:0% +the domain of that variable +i'm going to consider each of the things + + align:start position:0% +i'm going to consider each of the things + + + align:start position:0% +i'm going to consider each of the things +that's still surviving + + align:start position:0% +that's still surviving + + + align:start position:0% +that's still surviving +for each of those for + + align:start position:0% +for each of those for + + + align:start position:0% +for each of those for +each constraint + + align:start position:0% + + + + align:start position:0% + +c that's between x sub i + + align:start position:0% +c that's between x sub i + + + align:start position:0% +c that's between x sub i +and some x sub j + + align:start position:0% +and some x sub j + + + align:start position:0% +and some x sub j +where + + align:start position:0% + + + + align:start position:0% + +x sub j is an element of the domain + + align:start position:0% +x sub j is an element of the domain + + + align:start position:0% +x sub j is an element of the domain +of j oh that sounds awfully fancy but + + align:start position:0% +of j oh that sounds awfully fancy but + + + align:start position:0% +of j oh that sounds awfully fancy but +that just says + + align:start position:0% +that just says + + + align:start position:0% +that just says +in the case of texas up there whenever i + + align:start position:0% +in the case of texas up there whenever i + + + align:start position:0% +in the case of texas up there whenever i +consider one of the values that's + + align:start position:0% +consider one of the values that's + + + align:start position:0% +consider one of the values that's +still remaining as a choice for texas i + + align:start position:0% +still remaining as a choice for texas i + + + align:start position:0% +still remaining as a choice for texas i +want to consider + + align:start position:0% +want to consider + + + align:start position:0% +want to consider +all of the constraints between that + + align:start position:0% +all of the constraints between that + + + align:start position:0% +all of the constraints between that +variable and and the adjacent value and + + align:start position:0% +variable and and the adjacent value and + + + align:start position:0% +variable and and the adjacent value and +the adjacent states + + align:start position:0% +the adjacent states + + + align:start position:0% +the adjacent states +and i want to be sure that anything i + + align:start position:0% +and i want to be sure that anything i + + + align:start position:0% +and i want to be sure that anything i +leave in the domain + + align:start position:0% +leave in the domain + + + align:start position:0% +leave in the domain +is okay for some selection in the other + + align:start position:0% +is okay for some selection in the other + + + align:start position:0% +is okay for some selection in the other +states + + align:start position:0% +states + + + align:start position:0% +states +some remaining choices in the other + + align:start position:0% +some remaining choices in the other + + + align:start position:0% +some remaining choices in the other +states so that's why + + align:start position:0% +states so that's why + + + align:start position:0% +states so that's why +we're getting pretty nested here but + + align:start position:0% +we're getting pretty nested here but + + + align:start position:0% +we're getting pretty nested here but +we're doing depth first search + + align:start position:0% +we're doing depth first search + + + align:start position:0% +we're doing depth first search +we are considering the variables in a + + align:start position:0% +we are considering the variables in a + + + align:start position:0% +we are considering the variables in a +certain collection + + align:start position:0% +certain collection + + + align:start position:0% +certain collection +of a certain collection of variables + + align:start position:0% +of a certain collection of variables + + + align:start position:0% +of a certain collection of variables +for each one of those we're considering + + align:start position:0% +for each one of those we're considering + + + align:start position:0% +for each one of those we're considering +all the values that still remain + + align:start position:0% +all the values that still remain + + + align:start position:0% +all the values that still remain +in the domains of those variables and + + align:start position:0% +in the domains of those variables and + + + align:start position:0% +in the domains of those variables and +then for each of those values we're + + align:start position:0% +then for each of those values we're + + + align:start position:0% +then for each of those values we're +checking to see if it satisfies that + + align:start position:0% +checking to see if it satisfies that + + + align:start position:0% +checking to see if it satisfies that +some constraint + + align:start position:0% +some constraint + + + align:start position:0% +some constraint +satisfies the constraint that are placed + + align:start position:0% +satisfies the constraint that are placed + + + align:start position:0% +satisfies the constraint that are placed +upon it + + align:start position:0% +upon it + + + align:start position:0% +upon it +so for each of these constraints + + align:start position:0% +so for each of these constraints + + + align:start position:0% +so for each of these constraints +if there does not exist + + align:start position:0% +if there does not exist + + + align:start position:0% +if there does not exist +an x sub j such that + + align:start position:0% +an x sub j such that + + + align:start position:0% +an x sub j such that +the constraint between x sub i and x sub + + align:start position:0% +the constraint between x sub i and x sub + + + align:start position:0% +the constraint between x sub i and x sub +j + + align:start position:0% +j + + + align:start position:0% +j +is satisfied + + align:start position:0% + + + + align:start position:0% + +well if in that adjacent place there's + + align:start position:0% +well if in that adjacent place there's + + + align:start position:0% +well if in that adjacent place there's +no nothing that is consistent with + + align:start position:0% +no nothing that is consistent with + + + align:start position:0% +no nothing that is consistent with +a value then we've got to get rid of it + + align:start position:0% +a value then we've got to get rid of it + + + align:start position:0% +a value then we've got to get rid of it +if it if that's true if there does not + + align:start position:0% +if it if that's true if there does not + + + align:start position:0% +if it if that's true if there does not +exist some + + align:start position:0% +exist some + + + align:start position:0% +exist some +some value in an adjacent variable such + + align:start position:0% +some value in an adjacent variable such + + + align:start position:0% +some value in an adjacent variable such +that that constraint is satisfied we + + align:start position:0% +that that constraint is satisfied we + + + align:start position:0% +that that constraint is satisfied we +we're hosed we got to get we got to get + + align:start position:0% +we're hosed we got to get we got to get + + + align:start position:0% +we're hosed we got to get we got to get +rid of that value so we're going to + + align:start position:0% +rid of that value so we're going to + + + align:start position:0% +rid of that value so we're going to +remove + + align:start position:0% + + + + align:start position:0% + +x sub i from + + align:start position:0% +x sub i from + + + align:start position:0% +x sub i from +d sub i + + align:start position:0% + + + + align:start position:0% + +okay now that that's fine that's sort of + + align:start position:0% +okay now that that's fine that's sort of + + + align:start position:0% +okay now that that's fine that's sort of +what i did with texas i + + align:start position:0% +what i did with texas i + + + align:start position:0% +what i did with texas i +as soon as i plopped down a value for + + align:start position:0% +as soon as i plopped down a value for + + + align:start position:0% +as soon as i plopped down a value for +louisiana + + align:start position:0% +louisiana + + + align:start position:0% +louisiana +i said well what are what are the + + align:start position:0% +i said well what are what are the + + + align:start position:0% +i said well what are what are the +possible values in texas red green blue + + align:start position:0% +possible values in texas red green blue + + + align:start position:0% +possible values in texas red green blue +and yellow + + align:start position:0% +and yellow + + + align:start position:0% +and yellow +let's consider red let's consider the + + align:start position:0% +let's consider red let's consider the + + + align:start position:0% +let's consider red let's consider the +constraints between texas and all the + + align:start position:0% +constraints between texas and all the + + + align:start position:0% +constraints between texas and all the +adjacent states + + align:start position:0% +adjacent states + + + align:start position:0% +adjacent states +one of those constraints says it can't + + align:start position:0% +one of those constraints says it can't + + + align:start position:0% +one of those constraints says it can't +be the same color as arizona + + align:start position:0% +be the same color as arizona + + + align:start position:0% +be the same color as arizona +the only color i've got available for + + align:start position:0% +the only color i've got available for + + + align:start position:0% +the only color i've got available for +arizona since i've already made the + + align:start position:0% +arizona since i've already made the + + + align:start position:0% +arizona since i've already made the +assignment is red + + align:start position:0% +assignment is red + + + align:start position:0% +assignment is red +red is not consistent with red so i've + + align:start position:0% +red is not consistent with red so i've + + + align:start position:0% +red is not consistent with red so i've +got to get rid of it + + align:start position:0% +got to get rid of it + + + align:start position:0% +got to get rid of it +so it looks complicated but it's just + + align:start position:0% +so it looks complicated but it's just + + + align:start position:0% +so it looks complicated but it's just +intuition + + align:start position:0% +intuition + + + align:start position:0% +intuition +so what do we do if we get to a + + align:start position:0% +so what do we do if we get to a + + + align:start position:0% +so what do we do if we get to a +situation where the domain is empty + + align:start position:0% +situation where the domain is empty + + + align:start position:0% +situation where the domain is empty +that means whenever we get around to + + align:start position:0% +that means whenever we get around to + + + align:start position:0% +that means whenever we get around to +making an assignment to it there won't + + align:start position:0% +making an assignment to it there won't + + + align:start position:0% +making an assignment to it there won't +be anything left + + align:start position:0% +be anything left + + + align:start position:0% +be anything left +so if that ever happens if + + align:start position:0% +so if that ever happens if + + + align:start position:0% +so if that ever happens if +the domain ever becomes empty + + align:start position:0% + + + + align:start position:0% + +then what do we do we got to back up + + align:start position:0% + + + + align:start position:0% + +all right so the intuition is clear this + + align:start position:0% +all right so the intuition is clear this + + + align:start position:0% +all right so the intuition is clear this +is the algorithm + + align:start position:0% +is the algorithm + + + align:start position:0% +is the algorithm +the algorithm when you work through it + + align:start position:0% +the algorithm when you work through it + + + align:start position:0% +the algorithm when you work through it +think about whether it makes sense and + + align:start position:0% +think about whether it makes sense and + + + align:start position:0% +think about whether it makes sense and +whatnot how it fits with texas yeah it + + align:start position:0% +whatnot how it fits with texas yeah it + + + align:start position:0% +whatnot how it fits with texas yeah it +sure does all we're doing + + align:start position:0% +sure does all we're doing + + + align:start position:0% +sure does all we're doing +is we're making these depth first + + align:start position:0% +is we're making these depth first + + + align:start position:0% +is we're making these depth first +assignments and in the neighborhood of + + align:start position:0% +assignments and in the neighborhood of + + + align:start position:0% +assignments and in the neighborhood of +those depth first assignments + + align:start position:0% +those depth first assignments + + + align:start position:0% +those depth first assignments +we're looking around to see if the + + align:start position:0% +we're looking around to see if the + + + align:start position:0% +we're looking around to see if the +values that are possible + + align:start position:0% +values that are possible + + + align:start position:0% +values that are possible +include something and if they don't + + align:start position:0% +include something and if they don't + + + align:start position:0% +include something and if they don't +include anything we know we made + + align:start position:0% +include anything we know we made + + + align:start position:0% +include anything we know we made +an irrevocable blunder and we have to + + align:start position:0% +an irrevocable blunder and we have to + + + align:start position:0% +an irrevocable blunder and we have to +back up + + align:start position:0% +back up + + + align:start position:0% +back up +so that's the essence of the idea + + align:start position:0% + + + + align:start position:0% + +now how well does it work well it + + align:start position:0% +now how well does it work well it + + + align:start position:0% +now how well does it work well it +depends on + + align:start position:0% +depends on + + + align:start position:0% +depends on +a little bit depends on what we choose + + align:start position:0% +a little bit depends on what we choose + + + align:start position:0% +a little bit depends on what we choose +for + + align:start position:0% +for + + + align:start position:0% +for +considered there are lots of choices for + + align:start position:0% +considered there are lots of choices for + + + align:start position:0% +considered there are lots of choices for +what we consider + + align:start position:0% + + + + align:start position:0% + +so let me enumerate some of those + + align:start position:0% +so let me enumerate some of those + + + align:start position:0% +so let me enumerate some of those +choices and then we'll work it out on uh + + align:start position:0% +choices and then we'll work it out on uh + + + align:start position:0% +choices and then we'll work it out on uh +we'll have a look and see what they do + + align:start position:0% + + + + align:start position:0% + +oh i i guess one possibility to consider + + align:start position:0% + + + + align:start position:0% + +nothing + + align:start position:0% + + + + align:start position:0% + +let's try it out + + align:start position:0% + + + + align:start position:0% + +so our type of search is going to be no + + align:start position:0% +so our type of search is going to be no + + + align:start position:0% +so our type of search is going to be no +checks + + align:start position:0% +checks + + + align:start position:0% +checks +what do you think is going to happen + + align:start position:0% + + + + align:start position:0% + +we're not even checking the assignment + + align:start position:0% +we're not even checking the assignment + + + align:start position:0% +we're not even checking the assignment +well that's pretty fast unfortunately + + align:start position:0% +well that's pretty fast unfortunately + + + align:start position:0% +well that's pretty fast unfortunately +since we haven't even checked the most + + align:start position:0% +since we haven't even checked the most + + + align:start position:0% +since we haven't even checked the most +recent assignment we get lots of places + + align:start position:0% +recent assignment we get lots of places + + + align:start position:0% +recent assignment we get lots of places +where they're + + align:start position:0% +where they're + + + align:start position:0% +where they're +states that are adjacent to each other + + align:start position:0% +states that are adjacent to each other + + + align:start position:0% +states that are adjacent to each other +that have the same color + + align:start position:0% +that have the same color + + + align:start position:0% +that have the same color +that's no good + + align:start position:0% + + + + align:start position:0% + +so another thing we can do is + + align:start position:0% +so another thing we can do is + + + align:start position:0% +so another thing we can do is +consider every everything + + align:start position:0% + + + + align:start position:0% + +that's no good because that would say as + + align:start position:0% +that's no good because that would say as + + + align:start position:0% +that's no good because that would say as +soon as we color our first state + + align:start position:0% +soon as we color our first state + + + align:start position:0% +soon as we color our first state +we check to make sure that every other + + align:start position:0% +we check to make sure that every other + + + align:start position:0% +we check to make sure that every other +you know all 47 other states can be + + align:start position:0% +you know all 47 other states can be + + + align:start position:0% +you know all 47 other states can be +colored + + align:start position:0% +colored + + + align:start position:0% +colored +that seems like overdoing it a little + + align:start position:0% +that seems like overdoing it a little + + + align:start position:0% +that seems like overdoing it a little +bit + + align:start position:0% +bit + + + align:start position:0% +bit +but in any case at least we want to + + align:start position:0% +but in any case at least we want to + + + align:start position:0% +but in any case at least we want to +check + + align:start position:0% +check + + + align:start position:0% +check +the assignment + + align:start position:0% + + + + align:start position:0% + +so if we go back here and check the + + align:start position:0% +so if we go back here and check the + + + align:start position:0% +so if we go back here and check the +assignment + + align:start position:0% +assignment + + + align:start position:0% +assignment +let's see what happens + + align:start position:0% + + + + align:start position:0% + +assignments only boom all that geez + + align:start position:0% +assignments only boom all that geez + + + align:start position:0% +assignments only boom all that geez +that's + + align:start position:0% +that's + + + align:start position:0% +that's +that's what i got in trouble before this + + align:start position:0% +that's what i got in trouble before this + + + align:start position:0% +that's what i got in trouble before this +is the thing that's going to run + + align:start position:0% +is the thing that's going to run + + + align:start position:0% +is the thing that's going to run +for uh + + align:start position:0% +for uh + + + align:start position:0% +for uh +17 billion years at nanosecond you know + + align:start position:0% +17 billion years at nanosecond you know + + + align:start position:0% +17 billion years at nanosecond you know +something like that + + align:start position:0% +something like that + + + align:start position:0% +something like that +well it's only a billion years if you + + align:start position:0% +well it's only a billion years if you + + + align:start position:0% +well it's only a billion years if you +run it at nanosecond speed so i guess + + align:start position:0% +run it at nanosecond speed so i guess + + + align:start position:0% +run it at nanosecond speed so i guess +maybe you could + + align:start position:0% +maybe you could + + + align:start position:0% +maybe you could +do that have a fast computer but this + + align:start position:0% +do that have a fast computer but this + + + align:start position:0% +do that have a fast computer but this +isn't going to work because of our + + align:start position:0% +isn't going to work because of our + + + align:start position:0% +isn't going to work because of our +unfortunate choice of texas as the + + align:start position:0% +unfortunate choice of texas as the + + + align:start position:0% +unfortunate choice of texas as the +as the last state to be considered + + align:start position:0% +as the last state to be considered + + + align:start position:0% +as the last state to be considered +and the unfortunate coloring of the four + + align:start position:0% +and the unfortunate coloring of the four + + + align:start position:0% +and the unfortunate coloring of the four +surrounding states right up front + + align:start position:0% +surrounding states right up front + + + align:start position:0% +surrounding states right up front +and our unfortunate decision to rotate + + align:start position:0% +and our unfortunate decision to rotate + + + align:start position:0% +and our unfortunate decision to rotate +the colors so as to avoid + + align:start position:0% +the colors so as to avoid + + + align:start position:0% +the colors so as to avoid +overdoing any one color + + align:start position:0% + + + + align:start position:0% + +so this doesn't work but you know we + + align:start position:0% +so this doesn't work but you know we + + + align:start position:0% +so this doesn't work but you know we +went to the trouble of working out + + align:start position:0% +went to the trouble of working out + + + align:start position:0% +went to the trouble of working out +the the business with um with texas + + align:start position:0% +the the business with um with texas + + + align:start position:0% +the the business with um with texas +by hand using the domain reduction + + align:start position:0% +by hand using the domain reduction + + + align:start position:0% +by hand using the domain reduction +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +better make a note that this is the + + align:start position:0% +better make a note that this is the + + + align:start position:0% +better make a note that this is the +domain reduction algorithm + + align:start position:0% + + + + align:start position:0% + +and what we're going to do is we're + + align:start position:0% +and what we're going to do is we're + + + align:start position:0% +and what we're going to do is we're +going to check the neighbors of the + + align:start position:0% +going to check the neighbors of the + + + align:start position:0% +going to check the neighbors of the +assignments + + align:start position:0% +assignments + + + align:start position:0% +assignments +just like we did here we checked texas + + align:start position:0% +just like we did here we checked texas + + + align:start position:0% +just like we did here we checked texas +each time we made one of those four + + align:start position:0% +each time we made one of those four + + + align:start position:0% +each time we made one of those four +choices + + align:start position:0% +choices + + + align:start position:0% +choices +because it's a neighbor of all of the + + align:start position:0% +because it's a neighbor of all of the + + + align:start position:0% +because it's a neighbor of all of the +choices of the states that we made + + align:start position:0% +choices of the states that we made + + + align:start position:0% +choices of the states that we made +so one thing to do is check neighbors + + align:start position:0% + + + + align:start position:0% + +so this is one two three now let's see + + align:start position:0% +so this is one two three now let's see + + + align:start position:0% +so this is one two three now let's see +what happens + + align:start position:0% + + + + align:start position:0% + +check neighbors only go + + align:start position:0% + + + + align:start position:0% + +shoot i don't know it's okay with texas + + align:start position:0% +shoot i don't know it's okay with texas + + + align:start position:0% +shoot i don't know it's okay with texas +right + + align:start position:0% +right + + + align:start position:0% +right +because um it didn't color the states + + align:start position:0% +because um it didn't color the states + + + align:start position:0% +because um it didn't color the states +around texas + + align:start position:0% +around texas + + + align:start position:0% +around texas +uh with all four color choices + + align:start position:0% +uh with all four color choices + + + align:start position:0% +uh with all four color choices +but it's still getting in trouble uh in + + align:start position:0% +but it's still getting in trouble uh in + + + align:start position:0% +but it's still getting in trouble uh in +other places + + align:start position:0% +other places + + + align:start position:0% +other places +uh like all like the states like + + align:start position:0% +uh like all like the states like + + + align:start position:0% +uh like all like the states like +missouri kentucky + + align:start position:0% +missouri kentucky + + + align:start position:0% +missouri kentucky +virginia tennessee states with lots of + + align:start position:0% +virginia tennessee states with lots of + + + align:start position:0% +virginia tennessee states with lots of +lots of + + align:start position:0% +lots of + + + align:start position:0% +lots of +boundaries so i don't know + + align:start position:0% +boundaries so i don't know + + + align:start position:0% +boundaries so i don't know +whether this is gonna oh there it + + align:start position:0% +whether this is gonna oh there it + + + align:start position:0% +whether this is gonna oh there it +finally worked + + align:start position:0% +finally worked + + + align:start position:0% +finally worked +phew did a lot of went through a lot of + + align:start position:0% +phew did a lot of went through a lot of + + + align:start position:0% +phew did a lot of went through a lot of +effort though + + align:start position:0% +effort though + + + align:start position:0% +effort though +i know for the sake of comparison we + + align:start position:0% +i know for the sake of comparison we + + + align:start position:0% +i know for the sake of comparison we +might make a note that it ran into + + align:start position:0% +might make a note that it ran into + + + align:start position:0% +might make a note that it ran into +9139 dead ends + + align:start position:0% + + + + align:start position:0% + +so um but uh it did do some good it + + align:start position:0% +so um but uh it did do some good it + + + align:start position:0% +so um but uh it did do some good it +didn't take + + align:start position:0% +didn't take + + + align:start position:0% +didn't take +a length of time longer than the + + align:start position:0% +a length of time longer than the + + + align:start position:0% +a length of time longer than the +remaining part of the universe + + align:start position:0% +remaining part of the universe + + + align:start position:0% +remaining part of the universe +but if it's a good idea to check the + + align:start position:0% +but if it's a good idea to check the + + + align:start position:0% +but if it's a good idea to check the +neighbors + + align:start position:0% +neighbors + + + align:start position:0% +neighbors +if we make a change to the neighbors + + align:start position:0% +if we make a change to the neighbors + + + align:start position:0% +if we make a change to the neighbors +what might that suggest that we do in + + align:start position:0% +what might that suggest that we do in + + + align:start position:0% +what might that suggest that we do in +addition + + align:start position:0% +addition + + + align:start position:0% +addition +well it might suggest that if we make a + + align:start position:0% +well it might suggest that if we make a + + + align:start position:0% +well it might suggest that if we make a +change to a neighbor that we + + align:start position:0% +change to a neighbor that we + + + align:start position:0% +change to a neighbor that we +check its neighbors too make sure + + align:start position:0% +check its neighbors too make sure + + + align:start position:0% +check its neighbors too make sure +they're all right + + align:start position:0% +they're all right + + + align:start position:0% +they're all right +so a another choice + + align:start position:0% +so a another choice + + + align:start position:0% +so a another choice +is to propagate + + align:start position:0% + + + + align:start position:0% + +so propagate through variables with + + align:start position:0% +so propagate through variables with + + + align:start position:0% +so propagate through variables with +reduced + + align:start position:0% +reduced + + + align:start position:0% +reduced +domains let's see how that works + + align:start position:0% + + + + align:start position:0% + +well wait a minute um + + align:start position:0% +well wait a minute um + + + align:start position:0% +well wait a minute um +i must have made a mistake let's try + + align:start position:0% +i must have made a mistake let's try + + + align:start position:0% +i must have made a mistake let's try +that again + + align:start position:0% +that again + + + align:start position:0% +that again +oh maybe we better slow it down + + align:start position:0% +oh maybe we better slow it down + + + align:start position:0% +oh maybe we better slow it down +all that gray stuff is showing the limit + + align:start position:0% +all that gray stuff is showing the limit + + + align:start position:0% +all that gray stuff is showing the limit +of the of the propagation + + align:start position:0% + + + + align:start position:0% + +man it's um see it for a second + + align:start position:0% +man it's um see it for a second + + + align:start position:0% +man it's um see it for a second +of 40 that's about 10 seconds + + align:start position:0% + + + + align:start position:0% + +boom not bad zero dead ends + + align:start position:0% +boom not bad zero dead ends + + + align:start position:0% +boom not bad zero dead ends +and it was a lot faster i didn't happen + + align:start position:0% +and it was a lot faster i didn't happen + + + align:start position:0% +and it was a lot faster i didn't happen +to notice how many constraints were + + align:start position:0% +to notice how many constraints were + + + align:start position:0% +to notice how many constraints were +checked + + align:start position:0% +checked + + + align:start position:0% +checked +another thing i think was around twenty + + align:start position:0% +another thing i think was around twenty + + + align:start position:0% +another thing i think was around twenty +thousand or so this is a lot less + + align:start position:0% +thousand or so this is a lot less + + + align:start position:0% +thousand or so this is a lot less +so this looks like a good idea but why + + align:start position:0% +so this looks like a good idea but why + + + align:start position:0% +so this looks like a good idea but why +do they + + align:start position:0% +do they + + + align:start position:0% +do they +why do they label it number five well + + align:start position:0% +why do they label it number five well + + + align:start position:0% +why do they label it number five well +because there's something between this + + align:start position:0% +because there's something between this + + + align:start position:0% +because there's something between this +and number three + + align:start position:0% +and number three + + + align:start position:0% +and number three +so number four is + + align:start position:0% +so number four is + + + align:start position:0% +so number four is +through v with d + + align:start position:0% +through v with d + + + align:start position:0% +through v with d +reduced + + align:start position:0% + + + + align:start position:0% + +to one value + + align:start position:0% + + + + align:start position:0% + +so we're not going to propagate through + + align:start position:0% +so we're not going to propagate through + + + align:start position:0% +so we're not going to propagate through +all of the variables who have that which + + align:start position:0% +all of the variables who have that which + + + align:start position:0% +all of the variables who have that which +have their domains + + align:start position:0% +have their domains + + + align:start position:0% +have their domains +shrunk a little bit we're only going to + + align:start position:0% +shrunk a little bit we're only going to + + + align:start position:0% +shrunk a little bit we're only going to +propagate through those that have the + + align:start position:0% +propagate through those that have the + + + align:start position:0% +propagate through those that have the +greater shrinkage all the way down to a + + align:start position:0% +greater shrinkage all the way down to a + + + align:start position:0% +greater shrinkage all the way down to a +single value + + align:start position:0% +single value + + + align:start position:0% +single value +all right so let's see how that might + + align:start position:0% + + + + align:start position:0% + +work + + align:start position:0% + + + + align:start position:0% + +anybody want to place any bets on this + + align:start position:0% +anybody want to place any bets on this + + + align:start position:0% +anybody want to place any bets on this +one + + align:start position:0% +one + + + align:start position:0% +one +let's see we checked 2623 constraints + + align:start position:0% +let's see we checked 2623 constraints + + + align:start position:0% +let's see we checked 2623 constraints +last time + + align:start position:0% +last time + + + align:start position:0% +last time +let's see what happens this time + + align:start position:0% +let's see what happens this time + + + align:start position:0% +let's see what happens this time +you you can see that the extent of the + + align:start position:0% +you you can see that the extent of the + + + align:start position:0% +you you can see that the extent of the +gray is less because it's not + + align:start position:0% +gray is less because it's not + + + align:start position:0% +gray is less because it's not +propagating so far + + align:start position:0% +propagating so far + + + align:start position:0% +propagating so far +and as we breathfully await the answer + + align:start position:0% + + + + align:start position:0% + +we see we found our winner this is does + + align:start position:0% +we see we found our winner this is does + + + align:start position:0% +we see we found our winner this is does +a couple of dead ends but the number of + + align:start position:0% +a couple of dead ends but the number of + + + align:start position:0% +a couple of dead ends but the number of +constraints checked is less than a + + align:start position:0% +constraints checked is less than a + + + align:start position:0% +constraints checked is less than a +thousand + + align:start position:0% +thousand + + + align:start position:0% +thousand +so in general with problems like this + + align:start position:0% +so in general with problems like this + + + align:start position:0% +so in general with problems like this +you have all of these choices for what + + align:start position:0% +you have all of these choices for what + + + align:start position:0% +you have all of these choices for what +you consider + + align:start position:0% +you consider + + + align:start position:0% +you consider +you don't want to consider nothing + + align:start position:0% +you don't want to consider nothing + + + align:start position:0% +you don't want to consider nothing +because then you're not honoring your + + align:start position:0% +because then you're not honoring your + + + align:start position:0% +because then you're not honoring your +constraints + + align:start position:0% +constraints + + + align:start position:0% +constraints +you'll certainly want to consider the + + align:start position:0% +you'll certainly want to consider the + + + align:start position:0% +you'll certainly want to consider the +things you've just made assignments for + + align:start position:0% +things you've just made assignments for + + + align:start position:0% +things you've just made assignments for +because otherwise you'll + + align:start position:0% +because otherwise you'll + + + align:start position:0% +because otherwise you'll +pre-date giving you'll construct a + + align:start position:0% +pre-date giving you'll construct a + + + align:start position:0% +pre-date giving you'll construct a +solution that + + align:start position:0% +solution that + + + align:start position:0% +solution that +violates a constraint you do want don't + + align:start position:0% +violates a constraint you do want don't + + + align:start position:0% +violates a constraint you do want don't +want to do + + align:start position:0% +want to do + + + align:start position:0% +want to do +everything because that's excessive work + + align:start position:0% +everything because that's excessive work + + + align:start position:0% +everything because that's excessive work +and so these two i'm sorry + + align:start position:0% +and so these two i'm sorry + + + align:start position:0% +and so these two i'm sorry +checking the neighbors is a good idea + + align:start position:0% +checking the neighbors is a good idea + + + align:start position:0% +checking the neighbors is a good idea +but it's always better in practice + + align:start position:0% +but it's always better in practice + + + align:start position:0% +but it's always better in practice +in practice inevitably it's the case + + align:start position:0% +in practice inevitably it's the case + + + align:start position:0% +in practice inevitably it's the case +that it's better to do some propagation + + align:start position:0% +that it's better to do some propagation + + + align:start position:0% +that it's better to do some propagation +through the things that you've changed + + align:start position:0% +through the things that you've changed + + + align:start position:0% +through the things that you've changed +how much propagation it doesn't seem to + + align:start position:0% +how much propagation it doesn't seem to + + + align:start position:0% +how much propagation it doesn't seem to +do much good to propagate through things + + align:start position:0% +do much good to propagate through things + + + align:start position:0% +do much good to propagate through things +that are just changed + + align:start position:0% +that are just changed + + + align:start position:0% +that are just changed +but it does seem to do some good to + + align:start position:0% +but it does seem to do some good to + + + align:start position:0% +but it does seem to do some good to +propagate through things that have + + align:start position:0% +propagate through things that have + + + align:start position:0% +propagate through things that have +changed and been reduced to a single + + align:start position:0% +changed and been reduced to a single + + + align:start position:0% +changed and been reduced to a single +value + + align:start position:0% +value + + + align:start position:0% +value +so as soon as you've got a neighbor of + + align:start position:0% +so as soon as you've got a neighbor of + + + align:start position:0% +so as soon as you've got a neighbor of +some assignment you just made + + align:start position:0% +some assignment you just made + + + align:start position:0% +some assignment you just made +that has its domain reduced to a single + + align:start position:0% +that has its domain reduced to a single + + + align:start position:0% +that has its domain reduced to a single +value then you check its neighbors too + + align:start position:0% +value then you check its neighbors too + + + align:start position:0% +value then you check its neighbors too +so you check the neighbors of the + + align:start position:0% +so you check the neighbors of the + + + align:start position:0% +so you check the neighbors of the +neighbors of the neighbors of the + + align:start position:0% +neighbors of the neighbors of the + + + align:start position:0% +neighbors of the neighbors of the +neighbors + + align:start position:0% +neighbors + + + align:start position:0% +neighbors +on and on and on as long as you've found + + align:start position:0% +on and on and on as long as you've found + + + align:start position:0% +on and on and on as long as you've found +a domain being reduced and not only + + align:start position:0% +a domain being reduced and not only + + + align:start position:0% +a domain being reduced and not only +being reduced but reduced to a single + + align:start position:0% +being reduced but reduced to a single + + + align:start position:0% +being reduced but reduced to a single +value + + align:start position:0% +value + + + align:start position:0% +value +all right so that's the domain reduction + + align:start position:0% +all right so that's the domain reduction + + + align:start position:0% +all right so that's the domain reduction +algorithm and i guarantee we're going to + + align:start position:0% +algorithm and i guarantee we're going to + + + align:start position:0% +algorithm and i guarantee we're going to +give you a problem like that + + align:start position:0% +give you a problem like that + + + align:start position:0% +give you a problem like that +and i know you don't know how to work + + align:start position:0% +and i know you don't know how to work + + + align:start position:0% +and i know you don't know how to work +those problems yet + + align:start position:0% +those problems yet + + + align:start position:0% +those problems yet +because this is a little bit abstract + + align:start position:0% +because this is a little bit abstract + + + align:start position:0% +because this is a little bit abstract +and to work these + + align:start position:0% +and to work these + + + align:start position:0% +and to work these +problems in the exam setting you need to + + align:start position:0% +problems in the exam setting you need to + + + align:start position:0% +problems in the exam setting you need to +know a little bit + + align:start position:0% +know a little bit + + + align:start position:0% +know a little bit +about how to keep track of the variable + + align:start position:0% +about how to keep track of the variable + + + align:start position:0% +about how to keep track of the variable +values and remain in the domains + + align:start position:0% +values and remain in the domains + + + align:start position:0% +values and remain in the domains +and that sort of thing and and you'll + + align:start position:0% +and that sort of thing and and you'll + + + align:start position:0% +and that sort of thing and and you'll +learn more about that in your + + align:start position:0% +learn more about that in your + + + align:start position:0% +learn more about that in your +recitations and in this mega recitation + + align:start position:0% +recitations and in this mega recitation + + + align:start position:0% +recitations and in this mega recitation +and + + align:start position:0% +and + + + align:start position:0% +and +tutorials so we could go home + + align:start position:0% +tutorials so we could go home + + + align:start position:0% +tutorials so we could go home +except that there are few little + + align:start position:0% +except that there are few little + + + align:start position:0% +except that there are few little +flourishes to deal with here + + align:start position:0% +flourishes to deal with here + + + align:start position:0% +flourishes to deal with here +and those flourishes + + align:start position:0% + + + + align:start position:0% + +those flourishes include some + + align:start position:0% +those flourishes include some + + + align:start position:0% +those flourishes include some +dirty filthy little secrets + + align:start position:0% +dirty filthy little secrets + + + align:start position:0% +dirty filthy little secrets +for example i've chosen as my classroom + + align:start position:0% +for example i've chosen as my classroom + + + align:start position:0% +for example i've chosen as my classroom +example + + align:start position:0% +example + + + align:start position:0% +example +to pick on texas and arrange for this + + align:start position:0% +to pick on texas and arrange for this + + + align:start position:0% +to pick on texas and arrange for this +situation to be + + align:start position:0% +situation to be + + + align:start position:0% +situation to be +especially ugly so i i could + + align:start position:0% +especially ugly so i i could + + + align:start position:0% +especially ugly so i i could +arrange the states in a different way uh + + align:start position:0% +arrange the states in a different way uh + + + align:start position:0% +arrange the states in a different way uh +we have highly constrained states we + + align:start position:0% +we have highly constrained states we + + + align:start position:0% +we have highly constrained states we +have a lot of bordering states around + + align:start position:0% +have a lot of bordering states around + + + align:start position:0% +have a lot of bordering states around +them + + align:start position:0% +them + + + align:start position:0% +them +and we have other states like maine + + align:start position:0% +and we have other states like maine + + + align:start position:0% +and we have other states like maine +up there that has only one as only + + align:start position:0% +up there that has only one as only + + + align:start position:0% +up there that has only one as only +borders on one other state + + align:start position:0% +borders on one other state + + + align:start position:0% +borders on one other state +so i don't know will + + align:start position:0% +so i don't know will + + + align:start position:0% +so i don't know will +what do you think should we um + + align:start position:0% + + + + align:start position:0% + +should we arrange the states in for our + + align:start position:0% +should we arrange the states in for our + + + align:start position:0% +should we arrange the states in for our +depth first search + + align:start position:0% +depth first search + + + align:start position:0% +depth first search +in the order of least constrained to + + align:start position:0% +in the order of least constrained to + + + align:start position:0% +in the order of least constrained to +most constrained or most constrained to + + align:start position:0% +most constrained or most constrained to + + + align:start position:0% +most constrained or most constrained to +lease constraint + + align:start position:0% + + + + align:start position:0% + +in other words should we start with + + align:start position:0% +in other words should we start with + + + align:start position:0% +in other words should we start with +missouri or tennessee or + + align:start position:0% +missouri or tennessee or + + + align:start position:0% +missouri or tennessee or +kentucky or something like that or + + align:start position:0% +kentucky or something like that or + + + align:start position:0% +kentucky or something like that or +should we start with maine + + align:start position:0% +should we start with maine + + + align:start position:0% +should we start with maine +what do you think you have a 50 chance + + align:start position:0% +what do you think you have a 50 chance + + + align:start position:0% +what do you think you have a 50 chance +of getting it right just by + + align:start position:0% +of getting it right just by + + + align:start position:0% +of getting it right just by +flipping a coin + + align:start position:0% + + + + align:start position:0% + +he thinks we should start with the most + + align:start position:0% +he thinks we should start with the most + + + align:start position:0% +he thinks we should start with the most +constraint first + + align:start position:0% +constraint first + + + align:start position:0% +constraint first +do we have a volunteer who wants to + + align:start position:0% +do we have a volunteer who wants to + + + align:start position:0% +do we have a volunteer who wants to +suggest that we start with the lease + + align:start position:0% +suggest that we start with the lease + + + align:start position:0% +suggest that we start with the lease +constraint first + + align:start position:0% +constraint first + + + align:start position:0% +constraint first +that's the way i always uh that's the + + align:start position:0% +that's the way i always uh that's the + + + align:start position:0% +that's the way i always uh that's the +way i always work on stuff i + + align:start position:0% +way i always work on stuff i + + + align:start position:0% +way i always work on stuff i +you know i'm working on a book or + + align:start position:0% +you know i'm working on a book or + + + align:start position:0% +you know i'm working on a book or +something i have 500 things to fix i'll + + align:start position:0% +something i have 500 things to fix i'll + + + align:start position:0% +something i have 500 things to fix i'll +always choose to work on the easiest + + align:start position:0% +always choose to work on the easiest + + + align:start position:0% +always choose to work on the easiest +stuff first so that i feel like i'm + + align:start position:0% +stuff first so that i feel like i'm + + + align:start position:0% +stuff first so that i feel like i'm +making the list a lot smaller + + align:start position:0% +making the list a lot smaller + + + align:start position:0% +making the list a lot smaller +leave the hardest things to last but we + + align:start position:0% +leave the hardest things to last but we + + + align:start position:0% +leave the hardest things to last but we +don't have any volunteers do you want to + + align:start position:0% +don't have any volunteers do you want to + + + align:start position:0% +don't have any volunteers do you want to +want to bet on on that idea least + + align:start position:0% +want to bet on on that idea least + + + align:start position:0% +want to bet on on that idea least +constraint first + + align:start position:0% +constraint first + + + align:start position:0% +constraint first +okay jason wants to suggest that we + + align:start position:0% +okay jason wants to suggest that we + + + align:start position:0% +okay jason wants to suggest that we +should + + align:start position:0% +should + + + align:start position:0% +should +work on the least constraint first well + + align:start position:0% +work on the least constraint first well + + + align:start position:0% +work on the least constraint first well +we have ground truth because we can just + + align:start position:0% +we have ground truth because we can just + + + align:start position:0% +we have ground truth because we can just +try it out + + align:start position:0% + + + + align:start position:0% + +i guess we'll stick with our shrinking + + align:start position:0% +i guess we'll stick with our shrinking + + + align:start position:0% +i guess we'll stick with our shrinking +to one value thing here + + align:start position:0% +to one value thing here + + + align:start position:0% +to one value thing here +but we will reorder things so that we + + align:start position:0% +but we will reorder things so that we + + + align:start position:0% +but we will reorder things so that we +have the + + align:start position:0% +have the + + + align:start position:0% +have the +least constrained first + + align:start position:0% + + + + align:start position:0% + +so that we right away we got a color for + + align:start position:0% +so that we right away we got a color for + + + align:start position:0% +so that we right away we got a color for +uh for maine + + align:start position:0% + + + + align:start position:0% + +maybe we ought to speed this up a little + + align:start position:0% +maybe we ought to speed this up a little + + + align:start position:0% +maybe we ought to speed this up a little +bit + + align:start position:0% + + + + align:start position:0% + +okay well that's a good idea uh jason + + align:start position:0% +okay well that's a good idea uh jason + + + align:start position:0% +okay well that's a good idea uh jason +suggested this and + + align:start position:0% +suggested this and + + + align:start position:0% +suggested this and +we only checked 1732 constraints and we + + align:start position:0% +we only checked 1732 constraints and we + + + align:start position:0% +we only checked 1732 constraints and we +had 59 dead ends so let's try the other + + align:start position:0% +had 59 dead ends so let's try the other + + + align:start position:0% +had 59 dead ends so let's try the other +way around + + align:start position:0% + + + + align:start position:0% + +and we'll go back to four frames a + + align:start position:0% +and we'll go back to four frames a + + + align:start position:0% +and we'll go back to four frames a +second + + align:start position:0% + + + + align:start position:0% + +so we're working kind of from the middle + + align:start position:0% +so we're working kind of from the middle + + + align:start position:0% +so we're working kind of from the middle +of the country out with this one + + align:start position:0% +of the country out with this one + + + align:start position:0% +of the country out with this one +we're going to deal with maine i guess + + align:start position:0% +we're going to deal with maine i guess + + + align:start position:0% +we're going to deal with maine i guess +last + + align:start position:0% + + + + align:start position:0% + +yeah which is better + + align:start position:0% +yeah which is better + + + align:start position:0% +yeah which is better +too bad i think it looks like this is + + align:start position:0% +too bad i think it looks like this is + + + align:start position:0% +too bad i think it looks like this is +better + + align:start position:0% +better + + + align:start position:0% +better +in fact let's not be so aggressive with + + align:start position:0% +in fact let's not be so aggressive with + + + align:start position:0% +in fact let's not be so aggressive with +the use of constraint propagation + + align:start position:0% +the use of constraint propagation + + + align:start position:0% +the use of constraint propagation +let's just check the assignments only if + + align:start position:0% +let's just check the assignments only if + + + align:start position:0% +let's just check the assignments only if +we go back to + + align:start position:0% +we go back to + + + align:start position:0% +we go back to +an arrangement where we have least + + align:start position:0% +an arrangement where we have least + + + align:start position:0% +an arrangement where we have least +constrain first + + align:start position:0% +constrain first + + + align:start position:0% +constrain first +and we'll crank up the speed + + align:start position:0% + + + + align:start position:0% + +well actually we'd have to crank it up + + align:start position:0% +well actually we'd have to crank it up + + + align:start position:0% +well actually we'd have to crank it up +pretty big because uh + + align:start position:0% +pretty big because uh + + + align:start position:0% +pretty big because uh +the st states like missouri tennessee + + align:start position:0% +the st states like missouri tennessee + + + align:start position:0% +the st states like missouri tennessee +kentucky they're gonna they're gonna be + + align:start position:0% +kentucky they're gonna they're gonna be + + + align:start position:0% +kentucky they're gonna they're gonna be +like texas + + align:start position:0% + + + + align:start position:0% + +and so we're kind of back to the length + + align:start position:0% +and so we're kind of back to the length + + + align:start position:0% +and so we're kind of back to the length +of the universe type problem here with + + align:start position:0% +of the universe type problem here with + + + align:start position:0% +of the universe type problem here with +the least constrained first and + + align:start position:0% +the least constrained first and + + + align:start position:0% +the least constrained first and +no constrain and no use of constraints + + align:start position:0% +no constrain and no use of constraints + + + align:start position:0% +no constrain and no use of constraints +other than to check the + + align:start position:0% +other than to check the + + + align:start position:0% +other than to check the +the current assignment + + align:start position:0% + + + + align:start position:0% + +so let's uh stop that though and + + align:start position:0% +so let's uh stop that though and + + + align:start position:0% +so let's uh stop that though and +check the most constrained first + + align:start position:0% +check the most constrained first + + + align:start position:0% +check the most constrained first +assignments only + + align:start position:0% +assignments only + + + align:start position:0% +assignments only +i don't know how long was this going to + + align:start position:0% +i don't know how long was this going to + + + align:start position:0% +i don't know how long was this going to +take + + align:start position:0% + + + + align:start position:0% + +that's the dirty little secret if we had + + align:start position:0% +that's the dirty little secret if we had + + + align:start position:0% +that's the dirty little secret if we had +arranged our states + + align:start position:0% +arranged our states + + + align:start position:0% +arranged our states +from most constraint to least + + align:start position:0% +from most constraint to least + + + align:start position:0% +from most constraint to least +constrained ordinary depth first search + + align:start position:0% +constrained ordinary depth first search + + + align:start position:0% +constrained ordinary depth first search +with none of this stuff we talked about + + align:start position:0% +with none of this stuff we talked about + + + align:start position:0% +with none of this stuff we talked about +today would work just fine + + align:start position:0% + + + + align:start position:0% + +all right + + align:start position:0% + + + + align:start position:0% + +so uh it's a little bit like uh like + + align:start position:0% +so uh it's a little bit like uh like + + + align:start position:0% +so uh it's a little bit like uh like +games do you use progressive deepening + + align:start position:0% +games do you use progressive deepening + + + align:start position:0% +games do you use progressive deepening +or do you use alpha beta and the answer + + align:start position:0% +or do you use alpha beta and the answer + + + align:start position:0% +or do you use alpha beta and the answer +is both + + align:start position:0% +is both + + + align:start position:0% +is both +you use everything you got to uh to to + + align:start position:0% +you use everything you got to uh to to + + + align:start position:0% +you use everything you got to uh to to +to deal with + + align:start position:0% +to deal with + + + align:start position:0% +to deal with +with the problems and depending on the + + align:start position:0% +with the problems and depending on the + + + align:start position:0% +with the problems and depending on the +problem + + align:start position:0% +problem + + + align:start position:0% +problem +one or another of the things you + + align:start position:0% +one or another of the things you + + + align:start position:0% +one or another of the things you +incorporate into your approach will work + + align:start position:0% +incorporate into your approach will work + + + align:start position:0% +incorporate into your approach will work +just great + + align:start position:0% +just great + + + align:start position:0% +just great +if you're lucky so now + + align:start position:0% +if you're lucky so now + + + align:start position:0% +if you're lucky so now +i promise that this is not useful not + + align:start position:0% +i promise that this is not useful not + + + align:start position:0% +i promise that this is not useful not +only for people who want to color maps + + align:start position:0% +only for people who want to color maps + + + align:start position:0% +only for people who want to color maps +god who wants to do that we know it can + + align:start position:0% +god who wants to do that we know it can + + + align:start position:0% +god who wants to do that we know it can +be done with four colors but it's also + + align:start position:0% +be done with four colors but it's also + + + align:start position:0% +be done with four colors but it's also +useful for doing all kinds of resource + + align:start position:0% +useful for doing all kinds of resource + + + align:start position:0% +useful for doing all kinds of resource +planning + + align:start position:0% +planning + + + align:start position:0% +planning +problems so when i want to show you a + + align:start position:0% +problems so when i want to show you a + + + align:start position:0% +problems so when i want to show you a +resource planning problem and i want you + + align:start position:0% +resource planning problem and i want you + + + align:start position:0% +resource planning problem and i want you +to think about while i'm doing it + + align:start position:0% +to think about while i'm doing it + + + align:start position:0% +to think about while i'm doing it +think about whether it's actually + + align:start position:0% +think about whether it's actually + + + align:start position:0% +think about whether it's actually +analogous to the map coloring problem + + align:start position:0% +analogous to the map coloring problem + + + align:start position:0% +analogous to the map coloring problem +all right + + align:start position:0% +all right + + + align:start position:0% +all right +so here's the deal you have just landed + + align:start position:0% +so here's the deal you have just landed + + + align:start position:0% +so here's the deal you have just landed +a summer job + + align:start position:0% +a summer job + + + align:start position:0% +a summer job +with jet green a new airline + + align:start position:0% +with jet green a new airline + + + align:start position:0% +with jet green a new airline +and jet green is a is a + + align:start position:0% +and jet green is a is a + + + align:start position:0% +and jet green is a is a +low-cost no frills + + align:start position:0% +low-cost no frills + + + align:start position:0% +low-cost no frills +hardly any maintenance type of airline + + align:start position:0% +hardly any maintenance type of airline + + + align:start position:0% +hardly any maintenance type of airline +and they want to fly mostly between + + align:start position:0% +and they want to fly mostly between + + + align:start position:0% +and they want to fly mostly between +boston and new york + + align:start position:0% +boston and new york + + + align:start position:0% +boston and new york +occasionally they want to fly to los + + align:start position:0% +occasionally they want to fly to los + + + align:start position:0% +occasionally they want to fly to los +angeles and they're trying to get by + + align:start position:0% +angeles and they're trying to get by + + + align:start position:0% +angeles and they're trying to get by +with the smallest number of airplanes + + align:start position:0% +with the smallest number of airplanes + + + align:start position:0% +with the smallest number of airplanes +so that's why we have a kind of resource + + align:start position:0% +so that's why we have a kind of resource + + + align:start position:0% +so that's why we have a kind of resource +allocation problem + + align:start position:0% +allocation problem + + + align:start position:0% +allocation problem +jet green so i'm going to write down + + align:start position:0% +jet green so i'm going to write down + + + align:start position:0% +jet green so i'm going to write down +what their schedule looks like they have + + align:start position:0% +what their schedule looks like they have + + + align:start position:0% +what their schedule looks like they have +one flight + + align:start position:0% +one flight + + + align:start position:0% +one flight +f1 that goes from boston + + align:start position:0% +f1 that goes from boston + + + align:start position:0% +f1 that goes from boston +to uh los angeles to uh jfk + + align:start position:0% +to uh los angeles to uh jfk + + + align:start position:0% +to uh los angeles to uh jfk +like so it's a early in the day flight + + align:start position:0% +like so it's a early in the day flight + + + align:start position:0% +like so it's a early in the day flight +then they want to have another one f2 + + align:start position:0% +then they want to have another one f2 + + + align:start position:0% +then they want to have another one f2 +that flies from + + align:start position:0% +that flies from + + + align:start position:0% +that flies from +jfk to boston + + align:start position:0% + + + + align:start position:0% + +and then they want to have another + + align:start position:0% +and then they want to have another + + + align:start position:0% +and then they want to have another +flight a little later in the day + + align:start position:0% +flight a little later in the day + + + align:start position:0% +flight a little later in the day +that flies from boston to jfk + + align:start position:0% + + + + align:start position:0% + +and a little later than that they want + + align:start position:0% +and a little later than that they want + + + align:start position:0% +and a little later than that they want +to have another flight that goes from + + align:start position:0% +to have another flight that goes from + + + align:start position:0% +to have another flight that goes from +jfk to boston + + align:start position:0% +jfk to boston + + + align:start position:0% +jfk to boston +they're going to start off mostly as a + + align:start position:0% +they're going to start off mostly as a + + + align:start position:0% +they're going to start off mostly as a +shuttle airline in the beginning so + + align:start position:0% +shuttle airline in the beginning so + + + align:start position:0% +shuttle airline in the beginning so +that's + + align:start position:0% +that's + + + align:start position:0% +that's +f1 f2 f3 + + align:start position:0% +f1 f2 f3 + + + align:start position:0% +f1 f2 f3 +and f4 and they have a fifth flight + + align:start position:0% +and f4 and they have a fifth flight + + + align:start position:0% +and f4 and they have a fifth flight +f5 that goes from boston to los angeles + + align:start position:0% +f5 that goes from boston to los angeles + + + align:start position:0% +f5 that goes from boston to los angeles +that takes a long time + + align:start position:0% +that takes a long time + + + align:start position:0% +that takes a long time +so it looks uh like this on on the + + align:start position:0% +so it looks uh like this on on the + + + align:start position:0% +so it looks uh like this on on the +schedule of course we have time going + + align:start position:0% +schedule of course we have time going + + + align:start position:0% +schedule of course we have time going +that way + + align:start position:0% +that way + + + align:start position:0% +that way +so that's boston to + + align:start position:0% + + + + align:start position:0% + +lax + + align:start position:0% +lax + + + align:start position:0% +lax +now your job is to determine if they can + + align:start position:0% +now your job is to determine if they can + + + align:start position:0% +now your job is to determine if they can +fly this schedule with four aircraft + + align:start position:0% +fly this schedule with four aircraft + + + align:start position:0% +fly this schedule with four aircraft +and naturally you don't want to overuse + + align:start position:0% +and naturally you don't want to overuse + + + align:start position:0% +and naturally you don't want to overuse +any one aircraft because you like to + + align:start position:0% +any one aircraft because you like to + + + align:start position:0% +any one aircraft because you like to +have + + align:start position:0% +have + + + align:start position:0% +have +kind of even even wear on them right so + + align:start position:0% +kind of even even wear on them right so + + + align:start position:0% +kind of even even wear on them right so +as you make your choices + + align:start position:0% +as you make your choices + + + align:start position:0% +as you make your choices +you'll rotate the aircraft so you'll + + align:start position:0% +you'll rotate the aircraft so you'll + + + align:start position:0% +you'll rotate the aircraft so you'll +assign + + align:start position:0% +assign + + + align:start position:0% +assign +this one to a1 aircraft number one + + align:start position:0% +this one to a1 aircraft number one + + + align:start position:0% +this one to a1 aircraft number one +this one will be a2 this one will be a3 + + align:start position:0% +this one will be a2 this one will be a3 + + + align:start position:0% +this one will be a2 this one will be a3 +and this one will be a4 and + + align:start position:0% +and this one will be a4 and + + + align:start position:0% +and this one will be a4 and +oops uh there's no aircraft left for the + + align:start position:0% +oops uh there's no aircraft left for the + + + align:start position:0% +oops uh there's no aircraft left for the +flight to los angeles + + align:start position:0% +flight to los angeles + + + align:start position:0% +flight to los angeles +because i have four so it's obvious + + align:start position:0% +because i have four so it's obvious + + + align:start position:0% +because i have four so it's obvious +right this is + + align:start position:0% +right this is + + + align:start position:0% +right this is +100 exactly the map coloring problem + + align:start position:0% +100 exactly the map coloring problem + + + align:start position:0% +100 exactly the map coloring problem +even down to the four choices because + + align:start position:0% +even down to the four choices because + + + align:start position:0% +even down to the four choices because +you have the constraint the no single + + align:start position:0% +you have the constraint the no single + + + align:start position:0% +you have the constraint the no single +physical aircraft + + align:start position:0% +physical aircraft + + + align:start position:0% +physical aircraft +can fly on fly two flights at the same + + align:start position:0% +can fly on fly two flights at the same + + + align:start position:0% +can fly on fly two flights at the same +time just like no two adjacent states + + align:start position:0% +time just like no two adjacent states + + + align:start position:0% +time just like no two adjacent states +can be colored the same + + align:start position:0% +can be colored the same + + + align:start position:0% +can be colored the same +so there's a no same no same time + + align:start position:0% +so there's a no same no same time + + + align:start position:0% +so there's a no same no same time +constraint like so + + align:start position:0% +constraint like so + + + align:start position:0% +constraint like so +so if you were assigning flight aircraft + + align:start position:0% +so if you were assigning flight aircraft + + + align:start position:0% +so if you were assigning flight aircraft +to these flights + + align:start position:0% +to these flights + + + align:start position:0% +to these flights +you get down to f4 the fourth flight + + align:start position:0% +you get down to f4 the fourth flight + + + align:start position:0% +you get down to f4 the fourth flight +and you'd say well let's see + + align:start position:0% + + + + align:start position:0% + +this guy down here can be a1 a2 a3 or a4 + + align:start position:0% +this guy down here can be a1 a2 a3 or a4 + + + align:start position:0% +this guy down here can be a1 a2 a3 or a4 +but if i choose + + align:start position:0% +but if i choose + + + align:start position:0% +but if i choose +a4 for that fourth flight then there'll + + align:start position:0% +a4 for that fourth flight then there'll + + + align:start position:0% +a4 for that fourth flight then there'll +be nothing left in its domain + + align:start position:0% + + + + align:start position:0% + +so you've thus + + align:start position:0% +so you've thus + + + align:start position:0% +so you've thus +set the problem up to be identical to + + align:start position:0% +set the problem up to be identical to + + + align:start position:0% +set the problem up to be identical to +the map coloring problem and of course + + align:start position:0% +the map coloring problem and of course + + + align:start position:0% +the map coloring problem and of course +you you can enrich it with other kinds + + align:start position:0% +you you can enrich it with other kinds + + + align:start position:0% +you you can enrich it with other kinds +of constraints + + align:start position:0% +of constraints + + + align:start position:0% +of constraints +so for example you might have this is a + + align:start position:0% +so for example you might have this is a + + + align:start position:0% +so for example you might have this is a +not same time constraint + + align:start position:0% + + + + align:start position:0% + +and these + + align:start position:0% + + + + align:start position:0% + +i mean this is at jfk and it flies out + + align:start position:0% +i mean this is at jfk and it flies out + + + align:start position:0% +i mean this is at jfk and it flies out +of jfk so + + align:start position:0% +of jfk so + + + align:start position:0% +of jfk so +maybe you can use those maybe use the + + align:start position:0% +maybe you can use those maybe use the + + + align:start position:0% +maybe you can use those maybe use the +same aircraft for those + + align:start position:0% +same aircraft for those + + + align:start position:0% +same aircraft for those +but not if they're right up against each + + align:start position:0% +but not if they're right up against each + + + align:start position:0% +but not if they're right up against each +other because you have a minimum ground + + align:start position:0% +other because you have a minimum ground + + + align:start position:0% +other because you have a minimum ground +time rule + + align:start position:0% +time rule + + + align:start position:0% +time rule +so there's a minimum ground time + + align:start position:0% +so there's a minimum ground time + + + align:start position:0% +so there's a minimum ground time +constraint here + + align:start position:0% + + + + align:start position:0% + +and there's a minimum ground time + + align:start position:0% +and there's a minimum ground time + + + align:start position:0% +and there's a minimum ground time +constraint here + + align:start position:0% +constraint here + + + align:start position:0% +constraint here +there's a minimum ground time constraint + + align:start position:0% +there's a minimum ground time constraint + + + align:start position:0% +there's a minimum ground time constraint +here + + align:start position:0% + + + + align:start position:0% + +and if these aren't the same city then + + align:start position:0% +and if these aren't the same city then + + + align:start position:0% +and if these aren't the same city then +you've got to allow enough time for them + + align:start position:0% +you've got to allow enough time for them + + + align:start position:0% +you've got to allow enough time for them +to fly between the two cities that are + + align:start position:0% +to fly between the two cities that are + + + align:start position:0% +to fly between the two cities that are +involved + + align:start position:0% +involved + + + align:start position:0% +involved +so the constraints can get a little bit + + align:start position:0% +so the constraints can get a little bit + + + align:start position:0% +so the constraints can get a little bit +more complicated but the idea is the + + align:start position:0% +more complicated but the idea is the + + + align:start position:0% +more complicated but the idea is the +same + + align:start position:0% +same + + + align:start position:0% +same +so you say to me i don't trust you show + + align:start position:0% +so you say to me i don't trust you show + + + align:start position:0% +so you say to me i don't trust you show +me + + align:start position:0% +me + + + align:start position:0% +me +okay so let me show you + + align:start position:0% + + + + align:start position:0% + +oh by the way there's one more way to + + align:start position:0% +oh by the way there's one more way to + + + align:start position:0% +oh by the way there's one more way to +make this map coloring problem easier + + align:start position:0% +make this map coloring problem easier + + + align:start position:0% +make this map coloring problem easier +right + + align:start position:0% + + + + align:start position:0% + +let's see the arrangement is going to be + + align:start position:0% +let's see the arrangement is going to be + + + align:start position:0% +let's see the arrangement is going to be +alphabetical + + align:start position:0% +alphabetical + + + align:start position:0% +alphabetical +the type is going to be assignments only + + align:start position:0% +the type is going to be assignments only + + + align:start position:0% +the type is going to be assignments only +and we know that's a loser but not if we + + align:start position:0% +and we know that's a loser but not if we + + + align:start position:0% +and we know that's a loser but not if we +use a whole lot of colors + + align:start position:0% + + + + align:start position:0% + +so it's the use of four colors that got + + align:start position:0% +so it's the use of four colors that got + + + align:start position:0% +so it's the use of four colors that got +us into trouble + + align:start position:0% +us into trouble + + + align:start position:0% +us into trouble +oh that's an aside but it will be coming + + align:start position:0% +oh that's an aside but it will be coming + + + align:start position:0% +oh that's an aside but it will be coming +back in a moment or two + + align:start position:0% +back in a moment or two + + + align:start position:0% +back in a moment or two +scheduling here's that problem + + align:start position:0% +scheduling here's that problem + + + align:start position:0% +scheduling here's that problem +boom yep you can almost see it working + + align:start position:0% +boom yep you can almost see it working + + + align:start position:0% +boom yep you can almost see it working +just like a map coloring thing + + align:start position:0% +just like a map coloring thing + + + align:start position:0% +just like a map coloring thing +but that's maybe too easy + + align:start position:0% +but that's maybe too easy + + + align:start position:0% +but that's maybe too easy +let's do this one + + align:start position:0% + + + + align:start position:0% + +see this is just like uh this is like + + align:start position:0% +see this is just like uh this is like + + + align:start position:0% +see this is just like uh this is like +simplicia we we've + + align:start position:0% +simplicia we we've + + + align:start position:0% +simplicia we we've +kind of got a a goofy arrangement here + + align:start position:0% +kind of got a a goofy arrangement here + + + align:start position:0% +kind of got a a goofy arrangement here +that's guaranteed + + align:start position:0% +that's guaranteed + + + align:start position:0% +that's guaranteed +to lose at the bottom because of choices + + align:start position:0% +to lose at the bottom because of choices + + + align:start position:0% +to lose at the bottom because of choices +made at the top + + align:start position:0% +made at the top + + + align:start position:0% +made at the top +but that's okay we can we can stop this + + align:start position:0% +but that's okay we can we can stop this + + + align:start position:0% +but that's okay we can we can stop this +and we can do we can change to + + align:start position:0% +and we can do we can change to + + + align:start position:0% +and we can do we can change to +check neighbors only and boom there it + + align:start position:0% +check neighbors only and boom there it + + + align:start position:0% +check neighbors only and boom there it +goes + + align:start position:0% + + + + align:start position:0% + +all right or alternatively let me see if + + align:start position:0% +all right or alternatively let me see if + + + align:start position:0% +all right or alternatively let me see if +i can do it this way most constrained + + align:start position:0% +i can do it this way most constrained + + + align:start position:0% +i can do it this way most constrained +first + + align:start position:0% +first + + + align:start position:0% +first +type will be assignments only boom + + align:start position:0% +type will be assignments only boom + + + align:start position:0% +type will be assignments only boom +that worked fine too + + align:start position:0% + + + + align:start position:0% + +so you might choose to have a slightly + + align:start position:0% +so you might choose to have a slightly + + + align:start position:0% +so you might choose to have a slightly +harder problem + + align:start position:0% +harder problem + + + align:start position:0% +harder problem +i don't know like this and we can + + align:start position:0% +i don't know like this and we can + + + align:start position:0% +i don't know like this and we can +search away + + align:start position:0% + + + + align:start position:0% + +actually i don't know if this will + + align:start position:0% +actually i don't know if this will + + + align:start position:0% +actually i don't know if this will +complete or not this is a randomly + + align:start position:0% +complete or not this is a randomly + + + align:start position:0% +complete or not this is a randomly +generated example + + align:start position:0% +generated example + + + align:start position:0% +generated example +but deal you know you're going to lose + + align:start position:0% +but deal you know you're going to lose + + + align:start position:0% +but deal you know you're going to lose +your summer job if you can't figure out + + align:start position:0% +your summer job if you can't figure out + + + align:start position:0% +your summer job if you can't figure out +whether you can do this or not + + align:start position:0% +whether you can do this or not + + + align:start position:0% +whether you can do this or not +so what are you going to do + + align:start position:0% + + + + align:start position:0% + +elliot you got your thoughts about how + + align:start position:0% +elliot you got your thoughts about how + + + align:start position:0% +elliot you got your thoughts about how +you're going to save your job + + align:start position:0% + + + + align:start position:0% + +so here's the question you've been asked + + align:start position:0% +so here's the question you've been asked + + + align:start position:0% +so here's the question you've been asked +how many + + align:start position:0% +how many + + + align:start position:0% +how many +airplanes does jet green need + + align:start position:0% + + + + align:start position:0% + +and you decide well four seemed to work + + align:start position:0% +and you decide well four seemed to work + + + align:start position:0% +and you decide well four seemed to work +before + + align:start position:0% +before + + + align:start position:0% +before +so we'll try four here and you're not + + align:start position:0% +so we'll try four here and you're not + + + align:start position:0% +so we'll try four here and you're not +sure if it's going to terminate or not + + align:start position:0% +sure if it's going to terminate or not + + + align:start position:0% +sure if it's going to terminate or not +i mean in your in your in your lifetime + + align:start position:0% +i mean in your in your in your lifetime + + + align:start position:0% +i mean in your in your in your lifetime +let alone in your summer job + + align:start position:0% +let alone in your summer job + + + align:start position:0% +let alone in your summer job +elliot let me give you a hint look at + + align:start position:0% +elliot let me give you a hint look at + + + align:start position:0% +elliot let me give you a hint look at +the outline + + align:start position:0% + + + + align:start position:0% + +the outline up here on the board the + + align:start position:0% +the outline up here on the board the + + + align:start position:0% +the outline up here on the board the +last item + + align:start position:0% +last item + + + align:start position:0% +last item +now what's that mean + + align:start position:0% +now what's that mean + + + align:start position:0% +now what's that mean +how many what's the maximum number of + + align:start position:0% +how many what's the maximum number of + + + align:start position:0% +how many what's the maximum number of +airplanes we're going to need + + align:start position:0% +airplanes we're going to need + + + align:start position:0% +airplanes we're going to need +suppose we've got five flights + + align:start position:0% +suppose we've got five flights + + + align:start position:0% +suppose we've got five flights +what's the maximum number of airplanes + + align:start position:0% +what's the maximum number of airplanes + + + align:start position:0% +what's the maximum number of airplanes +would ever need five + + align:start position:0% +would ever need five + + + align:start position:0% +would ever need five +what's the minimum number of airplanes + + align:start position:0% +what's the minimum number of airplanes + + + align:start position:0% +what's the minimum number of airplanes +we'll need one + + align:start position:0% +we'll need one + + + align:start position:0% +we'll need one +so let's try let's try it with a small + + align:start position:0% +so let's try let's try it with a small + + + align:start position:0% +so let's try let's try it with a small +number of airplanes and a large number + + align:start position:0% +number of airplanes and a large number + + + align:start position:0% +number of airplanes and a large number +of airplanes + + align:start position:0% +of airplanes + + + align:start position:0% +of airplanes +so that showed us very fast that we + + align:start position:0% +so that showed us very fast that we + + + align:start position:0% +so that showed us very fast that we +can't do it with one airplane + + align:start position:0% +can't do it with one airplane + + + align:start position:0% +can't do it with one airplane +that showed us very fast we could do it + + align:start position:0% +that showed us very fast we could do it + + + align:start position:0% +that showed us very fast we could do it +with 10 airplanes + + align:start position:0% + + + + align:start position:0% + +what are we going to do to find the + + align:start position:0% +what are we going to do to find the + + + align:start position:0% +what are we going to do to find the +actual number as fast as possible + + align:start position:0% +actual number as fast as possible + + + align:start position:0% +actual number as fast as possible +and at least give our boss a reasonable + + align:start position:0% +and at least give our boss a reasonable + + + align:start position:0% +and at least give our boss a reasonable +answer + + align:start position:0% +answer + + + align:start position:0% +answer +even if not necessarily the exact number + + align:start position:0% +even if not necessarily the exact number + + + align:start position:0% +even if not necessarily the exact number +very fast + + align:start position:0% +very fast + + + align:start position:0% +very fast +it's just it's easy right we're gonna + + align:start position:0% +it's just it's easy right we're gonna + + + align:start position:0% +it's just it's easy right we're gonna +start up here with one computer + + align:start position:0% +start up here with one computer + + + align:start position:0% +start up here with one computer +and we're gonna start down here with + + align:start position:0% +and we're gonna start down here with + + + align:start position:0% +and we're gonna start down here with +another computer + + align:start position:0% +another computer + + + align:start position:0% +another computer +and see what happens so let's see + + align:start position:0% +and see what happens so let's see + + + align:start position:0% +and see what happens so let's see +if we can do it with nine + + align:start position:0% + + + + align:start position:0% + +let's see if we can do it with eight + + align:start position:0% + + + + align:start position:0% + +let's see if we can do it with seven + + align:start position:0% +let's see if we can do it with seven + + + align:start position:0% +let's see if we can do it with seven +these take almost zero time right + + align:start position:0% +these take almost zero time right + + + align:start position:0% +these take almost zero time right +because they're under constrained + + align:start position:0% + + + + align:start position:0% + +now that's good seven let's try six + + align:start position:0% +now that's good seven let's try six + + + align:start position:0% +now that's good seven let's try six +actually let's try two + + align:start position:0% +actually let's try two + + + align:start position:0% +actually let's try two +it loses fast let's try three + + align:start position:0% +it loses fast let's try three + + + align:start position:0% +it loses fast let's try three +don't know maybe if you let it run long + + align:start position:0% +don't know maybe if you let it run long + + + align:start position:0% +don't know maybe if you let it run long +enough three will work + + align:start position:0% +enough three will work + + + align:start position:0% +enough three will work +i doubt it while we're at it though we + + align:start position:0% +i doubt it while we're at it though we + + + align:start position:0% +i doubt it while we're at it though we +might as well + + align:start position:0% +might as well + + + align:start position:0% +might as well +go back here and try it with six + + align:start position:0% +go back here and try it with six + + + align:start position:0% +go back here and try it with six +remember seven worked real fast + + align:start position:0% + + + + align:start position:0% + +oh she's six so that was six right yeah + + align:start position:0% +oh she's six so that was six right yeah + + + align:start position:0% +oh she's six so that was six right yeah +so let's try it with five + + align:start position:0% + + + + align:start position:0% + +okay so it runs real fast with five it + + align:start position:0% +okay so it runs real fast with five it + + + align:start position:0% +okay so it runs real fast with five it +terminates real quick with + + align:start position:0% +terminates real quick with + + + align:start position:0% +terminates real quick with +two so we've got three and four left + + align:start position:0% +two so we've got three and four left + + + align:start position:0% +two so we've got three and four left +so we can tell our boss a la anytime + + align:start position:0% +so we can tell our boss a la anytime + + + align:start position:0% +so we can tell our boss a la anytime +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +that you're not real sure but you know + + align:start position:0% +that you're not real sure but you know + + + align:start position:0% +that you're not real sure but you know +it's going to be either three or four + + align:start position:0% +it's going to be either three or four + + + align:start position:0% +it's going to be either three or four +and then you got two computers you can + + align:start position:0% +and then you got two computers you can + + + align:start position:0% +and then you got two computers you can +let both run and see if either one + + align:start position:0% +let both run and see if either one + + + align:start position:0% +let both run and see if either one +terminate + + align:start position:0% +terminate + + + align:start position:0% +terminate +so you three and four my guess is that + + align:start position:0% +so you three and four my guess is that + + + align:start position:0% +so you three and four my guess is that +three + + align:start position:0% +three + + + align:start position:0% +three +will eventually give up but of course uh + + align:start position:0% +will eventually give up but of course uh + + + align:start position:0% +will eventually give up but of course uh +there's another little problem here we + + align:start position:0% +there's another little problem here we + + + align:start position:0% +there's another little problem here we +haven't used the most constraint first + + align:start position:0% +haven't used the most constraint first + + + align:start position:0% +haven't used the most constraint first +if we did that we might be able to do it + + align:start position:0% +if we did that we might be able to do it + + + align:start position:0% +if we did that we might be able to do it +even faster actually i don't think i can + + align:start position:0% +even faster actually i don't think i can + + + align:start position:0% +even faster actually i don't think i can +make that switch without getting another + + align:start position:0% +make that switch without getting another + + + align:start position:0% +make that switch without getting another +random assignment but + + align:start position:0% +random assignment but + + + align:start position:0% +random assignment but +let's see what happens maybe so + + align:start position:0% + + + + align:start position:0% + +i already had most constraint first okay + + align:start position:0% +i already had most constraint first okay + + + align:start position:0% +i already had most constraint first okay +so it didn't it didn't help to actually + + align:start position:0% +so it didn't it didn't help to actually + + + align:start position:0% +so it didn't it didn't help to actually +switch and i got it i got to think i've + + align:start position:0% +switch and i got it i got to think i've + + + align:start position:0% +switch and i got it i got to think i've +got a new schedule to work here + + align:start position:0% +got a new schedule to work here + + + align:start position:0% +got a new schedule to work here +so that's the that's the that's the end + + align:start position:0% +so that's the that's the that's the end + + + align:start position:0% +so that's the that's the that's the end +of the story you can do + + align:start position:0% +of the story you can do + + + align:start position:0% +of the story you can do +good resource allocation if you do + + align:start position:0% +good resource allocation if you do + + + align:start position:0% +good resource allocation if you do +several things all at once + + align:start position:0% +several things all at once + + + align:start position:0% +several things all at once +number one you always want to use most + + align:start position:0% +number one you always want to use most + + + align:start position:0% +number one you always want to use most +constraints first number two you want to + + align:start position:0% +constraints first number two you want to + + + align:start position:0% +constraints first number two you want to +propagate through domains reduced to a + + align:start position:0% +propagate through domains reduced to a + + + align:start position:0% +propagate through domains reduced to a +single algorithm + + align:start position:0% +single algorithm + + + align:start position:0% +single algorithm +and number three if you're really trying + + align:start position:0% +and number three if you're really trying + + + align:start position:0% +and number three if you're really trying +to figure out what the minimum number of + + align:start position:0% +to figure out what the minimum number of + + + align:start position:0% +to figure out what the minimum number of +resources needed is you do this under + + align:start position:0% +resources needed is you do this under + + + align:start position:0% +resources needed is you do this under +over + + align:start position:0% +over + + + align:start position:0% +over +business and you can quickly converge on + + align:start position:0% +business and you can quickly converge on + + + align:start position:0% +business and you can quickly converge on +a narrow range where the search is + + align:start position:0% +a narrow range where the search is + + + align:start position:0% +a narrow range where the search is +taking a long time and be sure that it + + align:start position:0% +taking a long time and be sure that it + + + align:start position:0% +taking a long time and be sure that it +lies within that + + align:start position:0% +lies within that + + + align:start position:0% +lies within that +narrow range because when you over + + align:start position:0% +narrow range because when you over + + + align:start position:0% +narrow range because when you over +source it's fast and when + + align:start position:0% +source it's fast and when + + + align:start position:0% +source it's fast and when +fast to complete and when you under + + align:start position:0% +fast to complete and when you under + + + align:start position:0% +fast to complete and when you under +resource it's + + align:start position:0% +resource it's + + + align:start position:0% +resource it's +fast to terminate and so you can just + + align:start position:0% +fast to terminate and so you can just + + + align:start position:0% +fast to terminate and so you can just +squeeze it right down into a very small + + align:start position:0% +squeeze it right down into a very small + + + align:start position:0% +squeeze it right down into a very small +range + + align:start position:0% +range + + + align:start position:0% +range +and that is the end of the story enjoy + + align:start position:0% +and that is the end of the story enjoy + + + align:start position:0% +and that is the end of the story enjoy +your holiday on monday + + align:start position:0% +your holiday on monday + + + align:start position:0% +your holiday on monday +we'll have two classes next week on + + align:start position:0% +we'll have two classes next week on + + + align:start position:0% +we'll have two classes next week on +wednesday + + align:start position:0% +wednesday + + + align:start position:0% +wednesday +and friday as advertised + + align:start position:0% +and friday as advertised + + + align:start position:0% +and friday as advertised +you \ No newline at end of file diff --git a/dHveJh0UbY8.txt b/dHveJh0UbY8.txt new file mode 100644 index 0000000000000000000000000000000000000000..96b9f3981b794046fc9dd0b56c8bf48f439bb94c --- /dev/null +++ b/dHveJh0UbY8.txt @@ -0,0 +1,6589 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +in the last lecture we considered the + + align:start position:0% +in the last lecture we considered the + + + align:start position:0% +in the last lecture we considered the +frequency response of linear shift and + + align:start position:0% +frequency response of linear shift and + + + align:start position:0% +frequency response of linear shift and +variance + + align:start position:0% +variance + + + align:start position:0% +variance +systems in this lecture what I would + + align:start position:0% +systems in this lecture what I would + + + align:start position:0% +systems in this lecture what I would +like to do is extend some of those ideas + + align:start position:0% +like to do is extend some of those ideas + + + align:start position:0% +like to do is extend some of those ideas +to the notion of the forier + + align:start position:0% +to the notion of the forier + + + align:start position:0% +to the notion of the forier +transform which I'll refer to as the + + align:start position:0% +transform which I'll refer to as the + + + align:start position:0% +transform which I'll refer to as the +discreete time forier + + align:start position:0% +discreete time forier + + + align:start position:0% +discreete time forier +transform so let me Begin by reminding + + align:start position:0% +transform so let me Begin by reminding + + + align:start position:0% +transform so let me Begin by reminding +you of one of the key results from last + + align:start position:0% +you of one of the key results from last + + + align:start position:0% +you of one of the key results from last +time namely the notion of the frequency + + align:start position:0% +time namely the notion of the frequency + + + align:start position:0% +time namely the notion of the frequency +response of a linear shift and variance + + align:start position:0% +response of a linear shift and variance + + + align:start position:0% +response of a linear shift and variance +system for a linear shift and variance + + align:start position:0% +system for a linear shift and variance + + + align:start position:0% +system for a linear shift and variance +system we saw last time that one of the + + align:start position:0% +system we saw last time that one of the + + + align:start position:0% +system we saw last time that one of the +Key Properties was that for a complex + + align:start position:0% +Key Properties was that for a complex + + + align:start position:0% +Key Properties was that for a complex +exponential input the output is a + + align:start position:0% +exponential input the output is a + + + align:start position:0% +exponential input the output is a +complex exponential + + align:start position:0% +complex exponential + + + align:start position:0% +complex exponential +sequence with the same complex frequency + + align:start position:0% +sequence with the same complex frequency + + + align:start position:0% +sequence with the same complex frequency +but with a change in + + align:start position:0% +but with a change in + + + align:start position:0% +but with a change in +amplitude and the change in amplitude + + align:start position:0% +amplitude and the change in amplitude + + + align:start position:0% +amplitude and the change in amplitude +that is the function h of e to the J + + align:start position:0% +that is the function h of e to the J + + + align:start position:0% +that is the function h of e to the J +Omega we refer to as the frequency + + align:start position:0% +Omega we refer to as the frequency + + + align:start position:0% +Omega we refer to as the frequency +response of the system + + align:start position:0% +response of the system + + + align:start position:0% +response of the system +the expression that we had for the + + align:start position:0% +the expression that we had for the + + + align:start position:0% +the expression that we had for the +frequency response in terms of the unit + + align:start position:0% +frequency response in terms of the unit + + + align:start position:0% +frequency response in terms of the unit +sample response was that the frequency + + align:start position:0% +sample response was that the frequency + + + align:start position:0% +sample response was that the frequency +response h of e to the J Omega is given + + align:start position:0% +response h of e to the J Omega is given + + + align:start position:0% +response h of e to the J Omega is given +by the sum of H of n the unit sample + + align:start position:0% +by the sum of H of n the unit sample + + + align:start position:0% +by the sum of H of n the unit sample +response of the system multiplied by E + + align:start position:0% +response of the system multiplied by E + + + align:start position:0% +response of the system multiplied by E +to Theus J Omega n so this is a + + align:start position:0% +to Theus J Omega n so this is a + + + align:start position:0% +to Theus J Omega n so this is a +relationship that tells us in terms of + + align:start position:0% +relationship that tells us in terms of + + + align:start position:0% +relationship that tells us in terms of +the unit sample response of the system + + align:start position:0% +the unit sample response of the system + + + align:start position:0% +the unit sample response of the system +how to get the frequency response + + align:start position:0% +how to get the frequency response + + + align:start position:0% +how to get the frequency response +there were two properties of the + + align:start position:0% +there were two properties of the + + + align:start position:0% +there were two properties of the +frequency response that I stressed last + + align:start position:0% +frequency response that I stressed last + + + align:start position:0% +frequency response that I stressed last +time one of them was the fact that the + + align:start position:0% +time one of them was the fact that the + + + align:start position:0% +time one of them was the fact that the +frequency response is a function of a + + align:start position:0% +frequency response is a function of a + + + align:start position:0% +frequency response is a function of a +continuous variable Omega that is + + align:start position:0% +continuous variable Omega that is + + + align:start position:0% +continuous variable Omega that is +complex exponential + + align:start position:0% +complex exponential + + + align:start position:0% +complex exponential +inputs can have the frequency variable + + align:start position:0% +inputs can have the frequency variable + + + align:start position:0% +inputs can have the frequency variable +Omega vary continuously Omega is a + + align:start position:0% +Omega vary continuously Omega is a + + + align:start position:0% +Omega vary continuously Omega is a +continuous variable whereas n is the + + align:start position:0% +continuous variable whereas n is the + + + align:start position:0% +continuous variable whereas n is the +discrete + + align:start position:0% +discrete + + + align:start position:0% +discrete +variable so this was one important + + align:start position:0% +variable so this was one important + + + align:start position:0% +variable so this was one important +property the second important property + + align:start position:0% +property the second important property + + + align:start position:0% +property the second important property +is that the frequency response is a + + align:start position:0% +is that the frequency response is a + + + align:start position:0% +is that the frequency response is a +periodic function of Omega and the + + align:start position:0% +periodic function of Omega and the + + + align:start position:0% +periodic function of Omega and the +period is equal to 2 + + align:start position:0% +period is equal to 2 + + + align:start position:0% +period is equal to 2 +pi h of e to the J Omega is equal to H + + align:start position:0% +pi h of e to the J Omega is equal to H + + + align:start position:0% +pi h of e to the J Omega is equal to H +of e to the J Omega plus 2 pi K where K + + align:start position:0% +of e to the J Omega plus 2 pi K where K + + + align:start position:0% +of e to the J Omega plus 2 pi K where K +is any integer now one of the sort of + + align:start position:0% +is any integer now one of the sort of + + + align:start position:0% +is any integer now one of the sort of +Uris explanations or justifications for + + align:start position:0% +Uris explanations or justifications for + + + align:start position:0% +Uris explanations or justifications for +why the frequency response is periodic + + align:start position:0% +why the frequency response is periodic + + + align:start position:0% +why the frequency response is periodic +as I've tried to indicate in several + + align:start position:0% +as I've tried to indicate in several + + + align:start position:0% +as I've tried to indicate in several +lectures is basically tied to the fact + + align:start position:0% +lectures is basically tied to the fact + + + align:start position:0% +lectures is basically tied to the fact +that complex exponentials or sinusoidal + + align:start position:0% +that complex exponentials or sinusoidal + + + align:start position:0% +that complex exponentials or sinusoidal +inputs are periodic veryy periodically + + align:start position:0% +inputs are periodic veryy periodically + + + align:start position:0% +inputs are periodic veryy periodically +with + + align:start position:0% +with + + + align:start position:0% +with +frequency over an interval 0 to 2 pi + + align:start position:0% +frequency over an interval 0 to 2 pi + + + align:start position:0% +frequency over an interval 0 to 2 pi +that is once we've looked at them for + + align:start position:0% +that is once we've looked at them for + + + align:start position:0% +that is once we've looked at them for +Omega between 0 and 2 pi + + align:start position:0% +Omega between 0 and 2 pi + + + align:start position:0% +Omega between 0 and 2 pi +if we go further than that in frequency + + align:start position:0% +if we go further than that in frequency + + + align:start position:0% +if we go further than that in frequency +all we see are the same complex + + align:start position:0% +all we see are the same complex + + + align:start position:0% +all we see are the same complex +exponentials or the same sinusoids over + + align:start position:0% +exponentials or the same sinusoids over + + + align:start position:0% +exponentials or the same sinusoids over +again so that in essence is the reason + + align:start position:0% +again so that in essence is the reason + + + align:start position:0% +again so that in essence is the reason +why the frequency response is a periodic + + align:start position:0% +why the frequency response is a periodic + + + align:start position:0% +why the frequency response is a periodic +function of + + align:start position:0% +function of + + + align:start position:0% +function of +Omega well one of the things we'd like + + align:start position:0% +Omega well one of the things we'd like + + + align:start position:0% +Omega well one of the things we'd like +to do is develop an inverse + + align:start position:0% +to do is develop an inverse + + + align:start position:0% +to do is develop an inverse +relationship which permits us to get the + + align:start position:0% +relationship which permits us to get the + + + align:start position:0% +relationship which permits us to get the +unit sample response from the frequency + + align:start position:0% +unit sample response from the frequency + + + align:start position:0% +unit sample response from the frequency +response one + + align:start position:0% +response one + + + align:start position:0% +response one +ursic notion or style of developing such + + align:start position:0% +ursic notion or style of developing such + + + align:start position:0% +ursic notion or style of developing such +an inverse relationship we can get by + + align:start position:0% +an inverse relationship we can get by + + + align:start position:0% +an inverse relationship we can get by +observing that since the frequency + + align:start position:0% +observing that since the frequency + + + align:start position:0% +observing that since the frequency +response is a function of a continuous + + align:start position:0% +response is a function of a continuous + + + align:start position:0% +response is a function of a continuous +variable Omega and in fact it's a + + align:start position:0% +variable Omega and in fact it's a + + + align:start position:0% +variable Omega and in fact it's a +periodic function of Omega then it + + align:start position:0% +periodic function of Omega then it + + + align:start position:0% +periodic function of Omega then it +should have a 4A series representation + + align:start position:0% +should have a 4A series representation + + + align:start position:0% +should have a 4A series representation +that is it's a continuous periodic + + align:start position:0% +that is it's a continuous periodic + + + align:start position:0% +that is it's a continuous periodic +function a continuous periodic function + + align:start position:0% +function a continuous periodic function + + + align:start position:0% +function a continuous periodic function +has a 4A series + + align:start position:0% +has a 4A series + + + align:start position:0% +has a 4A series +representation well in fact if we look + + align:start position:0% +representation well in fact if we look + + + align:start position:0% +representation well in fact if we look +at this + + align:start position:0% +at this + + + align:start position:0% +at this +expression we see that indeed what this + + align:start position:0% +expression we see that indeed what this + + + align:start position:0% +expression we see that indeed what this +is is a fora series expansion of this + + align:start position:0% +is is a fora series expansion of this + + + align:start position:0% +is is a fora series expansion of this +periodic + + align:start position:0% +periodic + + + align:start position:0% +periodic +function in terms of a complex fora + + align:start position:0% +function in terms of a complex fora + + + align:start position:0% +function in terms of a complex fora +series The fora series expressed in + + align:start position:0% +series The fora series expressed in + + + align:start position:0% +series The fora series expressed in +terms of complex + + align:start position:0% +terms of complex + + + align:start position:0% +terms of complex +exponentials well what are the 4A series + + align:start position:0% +exponentials well what are the 4A series + + + align:start position:0% +exponentials well what are the 4A series +coefficients the fora series + + align:start position:0% +coefficients the fora series + + + align:start position:0% +coefficients the fora series +coefficients are the values of the unit + + align:start position:0% +coefficients are the values of the unit + + + align:start position:0% +coefficients are the values of the unit +sample response in other words the + + align:start position:0% +sample response in other words the + + + align:start position:0% +sample response in other words the +values h of n so in fact this has the + + align:start position:0% +values h of n so in fact this has the + + + align:start position:0% +values h of n so in fact this has the +form of a 4A series that means that + + align:start position:0% +form of a 4A series that means that + + + align:start position:0% +form of a 4A series that means that +these are the 4ier coefficients that + + align:start position:0% +these are the 4ier coefficients that + + + align:start position:0% +these are the 4ier coefficients that +means that we can get these 4ier + + align:start position:0% +means that we can get these 4ier + + + align:start position:0% +means that we can get these 4ier +coefficients in terms of H to the J + + align:start position:0% +coefficients in terms of H to the J + + + align:start position:0% +coefficients in terms of H to the J +Omega the way we always get 4A series + + align:start position:0% +Omega the way we always get 4A series + + + align:start position:0% +Omega the way we always get 4A series +coefficients in terms of a periodic + + align:start position:0% +coefficients in terms of a periodic + + + align:start position:0% +coefficients in terms of a periodic +continuous + + align:start position:0% +continuous + + + align:start position:0% +continuous +function well the resulting expression + + align:start position:0% +function well the resulting expression + + + align:start position:0% +function well the resulting expression +then is is that the forier series + + align:start position:0% +then is is that the forier series + + + align:start position:0% +then is is that the forier series +coefficients or equivalently the unit + + align:start position:0% +coefficients or equivalently the unit + + + align:start position:0% +coefficients or equivalently the unit +sample response is equal to 1 over 2 pi + + align:start position:0% +sample response is equal to 1 over 2 pi + + + align:start position:0% +sample response is equal to 1 over 2 pi +times the integral over a period which + + align:start position:0% +times the integral over a period which + + + align:start position:0% +times the integral over a period which +I've taken as minus pi to plus pi of H + + align:start position:0% +I've taken as minus pi to plus pi of H + + + align:start position:0% +I've taken as minus pi to plus pi of H +of e to the J Omega e to the J Omega n d + + align:start position:0% +of e to the J Omega e to the J Omega n d + + + align:start position:0% +of e to the J Omega e to the J Omega n d +Omega this is just simply the expression + + align:start position:0% +Omega this is just simply the expression + + + align:start position:0% +Omega this is just simply the expression +for 4A series coefficients in terms of + + align:start position:0% +for 4A series coefficients in terms of + + + align:start position:0% +for 4A series coefficients in terms of +the continuous periodic function that + + align:start position:0% +the continuous periodic function that + + + align:start position:0% +the continuous periodic function that +we're dealing with + + align:start position:0% +we're dealing with + + + align:start position:0% +we're dealing with +well that's in a sense a Uris derivation + + align:start position:0% +well that's in a sense a Uris derivation + + + align:start position:0% +well that's in a sense a Uris derivation +we can in fact verify that this + + align:start position:0% +we can in fact verify that this + + + align:start position:0% +we can in fact verify that this +expression is valid simply by + + align:start position:0% +expression is valid simply by + + + align:start position:0% +expression is valid simply by +substituting into the integral the + + align:start position:0% +substituting into the integral the + + + align:start position:0% +substituting into the integral the +expression expression for H of e to the + + align:start position:0% +expression expression for H of e to the + + + align:start position:0% +expression expression for H of e to the +J + + align:start position:0% +J + + + align:start position:0% +J +Omega and if we do that we end up with + + align:start position:0% +Omega and if we do that we end up with + + + align:start position:0% +Omega and if we do that we end up with +for the expression for H of e to the J + + align:start position:0% +for the expression for H of e to the J + + + align:start position:0% +for the expression for H of e to the J +Omega we have the sum of H of k e to the + + align:start position:0% +Omega we have the sum of H of k e to the + + + align:start position:0% +Omega we have the sum of H of k e to the +minus J Omega GA + + align:start position:0% +minus J Omega GA + + + align:start position:0% +minus J Omega GA +K substituting + + align:start position:0% +K substituting + + + align:start position:0% +K substituting +in the result is this + + align:start position:0% +in the result is this + + + align:start position:0% +in the result is this +integral if we interchange the order of + + align:start position:0% +integral if we interchange the order of + + + align:start position:0% +integral if we interchange the order of +summation and + + align:start position:0% +summation and + + + align:start position:0% +summation and +integration then the resulting + + align:start position:0% +integration then the resulting + + + align:start position:0% +integration then the resulting +expression is shown here and we can + + align:start position:0% +expression is shown here and we can + + + align:start position:0% +expression is shown here and we can +observe that this + + align:start position:0% +observe that this + + + align:start position:0% +observe that this +integral first of all let's consider it + + align:start position:0% +integral first of all let's consider it + + + align:start position:0% +integral first of all let's consider it +for n not equal to + + align:start position:0% +for n not equal to + + + align:start position:0% +for n not equal to +K if n is not equal to K this is just + + align:start position:0% +K if n is not equal to K this is just + + + align:start position:0% +K if n is not equal to K this is just +simply the integral over a period of 2 + + align:start position:0% +simply the integral over a period of 2 + + + align:start position:0% +simply the integral over a period of 2 +pi of a complex exponential whose period + + align:start position:0% +pi of a complex exponential whose period + + + align:start position:0% +pi of a complex exponential whose period +is 2 + + align:start position:0% +is 2 + + + align:start position:0% +is 2 +pi the integral of the real part is the + + align:start position:0% +pi the integral of the real part is the + + + align:start position:0% +pi the integral of the real part is the +integral of a cosine over an integral + + align:start position:0% +integral of a cosine over an integral + + + align:start position:0% +integral of a cosine over an integral +number of periods and the integral of + + align:start position:0% +number of periods and the integral of + + + align:start position:0% +number of periods and the integral of +the imaginary part is the integral of + + align:start position:0% +the imaginary part is the integral of + + + align:start position:0% +the imaginary part is the integral of +the sign over an integral number of + + align:start position:0% +the sign over an integral number of + + + align:start position:0% +the sign over an integral number of +periods obviously then this integral if + + align:start position:0% +periods obviously then this integral if + + + align:start position:0% +periods obviously then this integral if +n is not equal to K is going to be zero + + align:start position:0% +n is not equal to K is going to be zero + + + align:start position:0% +n is not equal to K is going to be zero +so for n not equal to to K the value of + + align:start position:0% +so for n not equal to to K the value of + + + align:start position:0% +so for n not equal to to K the value of +this integral is zero whereas for n + + align:start position:0% +this integral is zero whereas for n + + + align:start position:0% +this integral is zero whereas for n +equal to + + align:start position:0% + + + + align:start position:0% + +K this exponent is zero the exponential + + align:start position:0% +K this exponent is zero the exponential + + + align:start position:0% +K this exponent is zero the exponential +is Unity Unity integrated from minus pi + + align:start position:0% +is Unity Unity integrated from minus pi + + + align:start position:0% +is Unity Unity integrated from minus pi +to Pi is equal to 2 pi so for n equal to + + align:start position:0% +to Pi is equal to 2 pi so for n equal to + + + align:start position:0% +to Pi is equal to 2 pi so for n equal to +K the value of the integral is equal to + + align:start position:0% +K the value of the integral is equal to + + + align:start position:0% +K the value of the integral is equal to + + align:start position:0% + + + align:start position:0% +pi well that means that the only term in + + align:start position:0% +pi well that means that the only term in + + + align:start position:0% +pi well that means that the only term in +this sum that is going to contribute to + + align:start position:0% +this sum that is going to contribute to + + + align:start position:0% +this sum that is going to contribute to +the answer is the term for k equal to n + + align:start position:0% +the answer is the term for k equal to n + + + align:start position:0% +the answer is the term for k equal to n +because for all the others the integral + + align:start position:0% +because for all the others the integral + + + align:start position:0% +because for all the others the integral +is zero so for k equal to n that's the + + align:start position:0% +is zero so for k equal to n that's the + + + align:start position:0% +is zero so for k equal to n that's the +only nonzero term for k equal to n the + + align:start position:0% +only nonzero term for k equal to n the + + + align:start position:0% +only nonzero term for k equal to n the +value of this integral is 2 pi which + + align:start position:0% +value of this integral is 2 pi which + + + align:start position:0% +value of this integral is 2 pi which +will cancel out this one over 2 pi and + + align:start position:0% +will cancel out this one over 2 pi and + + + align:start position:0% +will cancel out this one over 2 pi and +consequently we get H of n all right so + + align:start position:0% +consequently we get H of n all right so + + + align:start position:0% +consequently we get H of n all right so +this is in a sense a + + align:start position:0% +this is in a sense a + + + align:start position:0% +this is in a sense a +formal justification for the fact that + + align:start position:0% +formal justification for the fact that + + + align:start position:0% +formal justification for the fact that +indeed this is the inverse relationship + + align:start position:0% +indeed this is the inverse relationship + + + align:start position:0% +indeed this is the inverse relationship +to express H ofn in terms of the + + align:start position:0% +to express H ofn in terms of the + + + align:start position:0% +to express H ofn in terms of the +frequency + + align:start position:0% +frequency + + + align:start position:0% +frequency +response although in fact it's more + + align:start position:0% +response although in fact it's more + + + align:start position:0% +response although in fact it's more +useful in terms of insight to think of + + align:start position:0% +useful in terms of insight to think of + + + align:start position:0% +useful in terms of insight to think of +it as the 4A series coefficients of a + + align:start position:0% +it as the 4A series coefficients of a + + + align:start position:0% +it as the 4A series coefficients of a +function a periodic function of the + + align:start position:0% +function a periodic function of the + + + align:start position:0% +function a periodic function of the +continuous variable + + align:start position:0% +continuous variable + + + align:start position:0% +continuous variable +Omega now this in essence is a forier + + align:start position:0% +Omega now this in essence is a forier + + + align:start position:0% +Omega now this in essence is a forier +domain represent ation for the unit + + align:start position:0% +domain represent ation for the unit + + + align:start position:0% +domain represent ation for the unit +sample response of a system and in fact + + align:start position:0% +sample response of a system and in fact + + + align:start position:0% +sample response of a system and in fact +we can think of this as a 4A transform + + align:start position:0% +we can think of this as a 4A transform + + + align:start position:0% +we can think of this as a 4A transform +or a Time domain 48 domain transform + + align:start position:0% +or a Time domain 48 domain transform + + + align:start position:0% +or a Time domain 48 domain transform +pair relating the unit sample response + + align:start position:0% +pair relating the unit sample response + + + align:start position:0% +pair relating the unit sample response +of a system and the frequency response + + align:start position:0% +of a system and the frequency response + + + align:start position:0% +of a system and the frequency response +of the system and we can go back and + + align:start position:0% +of the system and we can go back and + + + align:start position:0% +of the system and we can go back and +forth now one of the obvious facts is + + align:start position:0% +forth now one of the obvious facts is + + + align:start position:0% +forth now one of the obvious facts is +that any sequence if we wanted to we + + align:start position:0% +that any sequence if we wanted to we + + + align:start position:0% +that any sequence if we wanted to we +could think of as the unit sample + + align:start position:0% +could think of as the unit sample + + + align:start position:0% +could think of as the unit sample +response of a + + align:start position:0% +response of a + + + align:start position:0% +response of a +system well that suggests then that this + + align:start position:0% +system well that suggests then that this + + + align:start position:0% +system well that suggests then that this +transform pair isn't restricted to just + + align:start position:0% +transform pair isn't restricted to just + + + align:start position:0% +transform pair isn't restricted to just +sequences that we explicitly identify as + + align:start position:0% +sequences that we explicitly identify as + + + align:start position:0% +sequences that we explicitly identify as +the unit sampled response of a system it + + align:start position:0% +the unit sampled response of a system it + + + align:start position:0% +the unit sampled response of a system it +in fact permits the representation of an + + align:start position:0% +in fact permits the representation of an + + + align:start position:0% +in fact permits the representation of an +arbitrary not quite arbitrary as we'll + + align:start position:0% +arbitrary not quite arbitrary as we'll + + + align:start position:0% +arbitrary not quite arbitrary as we'll +see in a while but a the representation + + align:start position:0% +see in a while but a the representation + + + align:start position:0% +see in a while but a the representation +of a more General class of sequences + + align:start position:0% +of a more General class of sequences + + + align:start position:0% +of a more General class of sequences +than just the ones that we explicitly + + align:start position:0% +than just the ones that we explicitly + + + align:start position:0% +than just the ones that we explicitly +identify as the unit sample response of + + align:start position:0% +identify as the unit sample response of + + + align:start position:0% +identify as the unit sample response of +a system that is we can generalize this + + align:start position:0% +a system that is we can generalize this + + + align:start position:0% +a system that is we can generalize this +set of ideas to the forier + + align:start position:0% +set of ideas to the forier + + + align:start position:0% +set of ideas to the forier +transform which is a frequency domain + + align:start position:0% +transform which is a frequency domain + + + align:start position:0% +transform which is a frequency domain +representation of an arbitrary again not + + align:start position:0% +representation of an arbitrary again not + + + align:start position:0% +representation of an arbitrary again not +quite arbitrary but for the time being + + align:start position:0% +quite arbitrary but for the time being + + + align:start position:0% +quite arbitrary but for the time being +we'll consider arbitrary sequence X of + + align:start position:0% +we'll consider arbitrary sequence X of + + + align:start position:0% +we'll consider arbitrary sequence X of +n well the forier transform then is + + align:start position:0% +n well the forier transform then is + + + align:start position:0% +n well the forier transform then is +defined as X of e to the J Omega which + + align:start position:0% +defined as X of e to the J Omega which + + + align:start position:0% +defined as X of e to the J Omega which +is the sum of X of n e to the minus J + + align:start position:0% +is the sum of X of n e to the minus J + + + align:start position:0% +is the sum of X of n e to the minus J +Omega + + align:start position:0% +Omega + + + align:start position:0% +Omega +n the 4A transform X of e to the J Omega + + align:start position:0% +n the 4A transform X of e to the J Omega + + + align:start position:0% +n the 4A transform X of e to the J Omega +of a system of of a sequence X of n is + + align:start position:0% +of a system of of a sequence X of n is + + + align:start position:0% +of a system of of a sequence X of n is +essentially the frequency response of a + + align:start position:0% +essentially the frequency response of a + + + align:start position:0% +essentially the frequency response of a +system whose unit sample response would + + align:start position:0% +system whose unit sample response would + + + align:start position:0% +system whose unit sample response would +be X of n so then obviously from what we + + align:start position:0% +be X of n so then obviously from what we + + + align:start position:0% +be X of n so then obviously from what we +previous just finished the discussing we + + align:start position:0% +previous just finished the discussing we + + + align:start position:0% +previous just finished the discussing we +have an inverse relationship that tells + + align:start position:0% +have an inverse relationship that tells + + + align:start position:0% +have an inverse relationship that tells +us what x of n is in terms of X of e to + + align:start position:0% +us what x of n is in terms of X of e to + + + align:start position:0% +us what x of n is in terms of X of e to +the J Omega and that then is this + + align:start position:0% + + + + align:start position:0% + +relationship well this then + + align:start position:0% +relationship well this then + + + align:start position:0% +relationship well this then +provides + + align:start position:0% +provides + + + align:start position:0% +provides +a transform pair or a frequency domain + + align:start position:0% +a transform pair or a frequency domain + + + align:start position:0% +a transform pair or a frequency domain +time domain relationship between + + align:start position:0% +time domain relationship between + + + align:start position:0% +time domain relationship between +sequences and frequency domain functions + + align:start position:0% +sequences and frequency domain functions + + + align:start position:0% +sequences and frequency domain functions +and it's useful in fact to interpret + + align:start position:0% +and it's useful in fact to interpret + + + align:start position:0% +and it's useful in fact to interpret +this + + align:start position:0% +this + + + align:start position:0% +this +expression somewhat Uris again as + + align:start position:0% +expression somewhat Uris again as + + + align:start position:0% +expression somewhat Uris again as +basically corresponding to a + + align:start position:0% +basically corresponding to a + + + align:start position:0% +basically corresponding to a +decomposition of a sequence X of n in + + align:start position:0% +decomposition of a sequence X of n in + + + align:start position:0% +decomposition of a sequence X of n in +terms of complex + + align:start position:0% +terms of complex + + + align:start position:0% +terms of complex +exponentials with incremental amplitude + + align:start position:0% +exponentials with incremental amplitude + + + align:start position:0% +exponentials with incremental amplitude +this is basically an expression that + + align:start position:0% +this is basically an expression that + + + align:start position:0% +this is basically an expression that +says that X of N is a sum except that + + align:start position:0% +says that X of N is a sum except that + + + align:start position:0% +says that X of N is a sum except that +it's a sum sort of in the limit which + + align:start position:0% +it's a sum sort of in the limit which + + + align:start position:0% +it's a sum sort of in the limit which +correspond respond to an integral of a + + align:start position:0% +correspond respond to an integral of a + + + align:start position:0% +correspond respond to an integral of a +set of complex exponentials with + + align:start position:0% +set of complex exponentials with + + + align:start position:0% +set of complex exponentials with +amplitudes that are essentially given by + + align:start position:0% +amplitudes that are essentially given by + + + align:start position:0% +amplitudes that are essentially given by +the 4A transform X of e to the J Omega + + align:start position:0% +the 4A transform X of e to the J Omega + + + align:start position:0% +the 4A transform X of e to the J Omega +well in fact you can see this a little + + align:start position:0% +well in fact you can see this a little + + + align:start position:0% +well in fact you can see this a little +more explicitly if we consider this + + align:start position:0% +more explicitly if we consider this + + + align:start position:0% +more explicitly if we consider this +integral as the limiting form of a sum + + align:start position:0% +integral as the limiting form of a sum + + + align:start position:0% +integral as the limiting form of a sum +the limit as Delta Omega goes to zero of + + align:start position:0% +the limit as Delta Omega goes to zero of + + + align:start position:0% +the limit as Delta Omega goes to zero of +the sum of X of e to the J K Delta Omega + + align:start position:0% +the sum of X of e to the J K Delta Omega + + + align:start position:0% +the sum of X of e to the J K Delta Omega +time Delta Omega 2 pi e to J K Delta + + align:start position:0% +time Delta Omega 2 pi e to J K Delta + + + align:start position:0% +time Delta Omega 2 pi e to J K Delta +Omega + + align:start position:0% +Omega + + + align:start position:0% +Omega +n this limit is by definition what this + + align:start position:0% +n this limit is by definition what this + + + align:start position:0% +n this limit is by definition what this +integral is so an important point to + + align:start position:0% +integral is so an important point to + + + align:start position:0% +integral is so an important point to +keep in mind is that basically the + + align:start position:0% +keep in mind is that basically the + + + align:start position:0% +keep in mind is that basically the +forier + + align:start position:0% +forier + + + align:start position:0% +forier +transform corresponds to a decomposition + + align:start position:0% +transform corresponds to a decomposition + + + align:start position:0% +transform corresponds to a decomposition +of a sequence in terms of a linear + + align:start position:0% +of a sequence in terms of a linear + + + align:start position:0% +of a sequence in terms of a linear +combination of complex exponentials with + + align:start position:0% +combination of complex exponentials with + + + align:start position:0% +combination of complex exponentials with +incremental amplitudes + + align:start position:0% +incremental amplitudes + + + align:start position:0% +incremental amplitudes +there are a number of reasons why that's + + align:start position:0% +there are a number of reasons why that's + + + align:start position:0% +there are a number of reasons why that's +an important point of view one of the + + align:start position:0% +an important point of view one of the + + + align:start position:0% +an important point of view one of the +reasons is that it leads to a very + + align:start position:0% +reasons is that it leads to a very + + + align:start position:0% +reasons is that it leads to a very +important property of linear shift and + + align:start position:0% +important property of linear shift and + + + align:start position:0% +important property of linear shift and +variance systems which I refer to as the + + align:start position:0% +variance systems which I refer to as the + + + align:start position:0% +variance systems which I refer to as the +convolution + + align:start position:0% +convolution + + + align:start position:0% +convolution +property and which states + + align:start position:0% +property and which states + + + align:start position:0% +property and which states +that if I + + align:start position:0% +that if I + + + align:start position:0% +that if I +have the convolution + + align:start position:0% +have the convolution + + + align:start position:0% +have the convolution +of two sequences X of n and y of + + align:start position:0% +of two sequences X of n and y of + + + align:start position:0% +of two sequences X of n and y of +n then the forier transform of those is + + align:start position:0% +n then the forier transform of those is + + + align:start position:0% +n then the forier transform of those is +the product of their forier transforms + + align:start position:0% +the product of their forier transforms + + + align:start position:0% +the product of their forier transforms +and this of course shouldn't be an H it + + align:start position:0% +and this of course shouldn't be an H it + + + align:start position:0% +and this of course shouldn't be an H it +should be a + + align:start position:0% +should be a + + + align:start position:0% +should be a +y or this shouldn't be a y it should be + + align:start position:0% +y or this shouldn't be a y it should be + + + align:start position:0% +y or this shouldn't be a y it should be +an H the important property is that the + + align:start position:0% +an H the important property is that the + + + align:start position:0% +an H the important property is that the +convolution of two sequences has as a 48 + + align:start position:0% +convolution of two sequences has as a 48 + + + align:start position:0% +convolution of two sequences has as a 48 +transform the product of the for of the + + align:start position:0% +transform the product of the for of the + + + align:start position:0% +transform the product of the for of the + + align:start position:0% + + + align:start position:0% +transforms well let's look at uh again + + align:start position:0% +transforms well let's look at uh again + + + align:start position:0% +transforms well let's look at uh again +somewhat + + align:start position:0% +somewhat + + + align:start position:0% +somewhat +Uris an argument that at least justifies + + align:start position:0% +Uris an argument that at least justifies + + + align:start position:0% +Uris an argument that at least justifies +this uh keeping in mind that we could go + + align:start position:0% +this uh keeping in mind that we could go + + + align:start position:0% +this uh keeping in mind that we could go +through this more formally plugging sums + + align:start position:0% +through this more formally plugging sums + + + align:start position:0% +through this more formally plugging sums +into integrals and integrals into sums + + align:start position:0% +into integrals and integrals into sums + + + align:start position:0% +into integrals and integrals into sums +but let's not do that let's look at this + + align:start position:0% +but let's not do that let's look at this + + + align:start position:0% +but let's not do that let's look at this +from a somewhat Uris point of + + align:start position:0% +from a somewhat Uris point of + + + align:start position:0% +from a somewhat Uris point of +view first of all we have + + align:start position:0% +view first of all we have + + + align:start position:0% +view first of all we have +that again a property that we began the + + align:start position:0% +that again a property that we began the + + + align:start position:0% +that again a property that we began the +lecture with that for a linear shift and + + align:start position:0% +lecture with that for a linear shift and + + + align:start position:0% +lecture with that for a linear shift and +variance + + align:start position:0% +variance + + + align:start position:0% +variance +system a complex exponential input gives + + align:start position:0% +system a complex exponential input gives + + + align:start position:0% +system a complex exponential input gives +us at the output the same complex + + align:start position:0% +us at the output the same complex + + + align:start position:0% +us at the output the same complex +exponential that is the same frequency + + align:start position:0% +exponential that is the same frequency + + + align:start position:0% +exponential that is the same frequency +and only one of them multiplied by h of + + align:start position:0% +and only one of them multiplied by h of + + + align:start position:0% +and only one of them multiplied by h of +e to the J Omega + + align:start position:0% +e to the J Omega + + + align:start position:0% +e to the J Omega +0 that's a consequence of linearity and + + align:start position:0% +0 that's a consequence of linearity and + + + align:start position:0% +0 that's a consequence of linearity and +shift in + + align:start position:0% +shift in + + + align:start position:0% +shift in +variance we know also that because of + + align:start position:0% +variance we know also that because of + + + align:start position:0% +variance we know also that because of +the fact that the system is + + align:start position:0% +the fact that the system is + + + align:start position:0% +the fact that the system is +linear if we have a linear combination + + align:start position:0% +linear if we have a linear combination + + + align:start position:0% +linear if we have a linear combination +of complex + + align:start position:0% +of complex + + + align:start position:0% +of complex +exponentials then the output of the + + align:start position:0% +exponentials then the output of the + + + align:start position:0% +exponentials then the output of the +system is going to be the same linear + + align:start position:0% +system is going to be the same linear + + + align:start position:0% +system is going to be the same linear +combination of complex exponentials with + + align:start position:0% +combination of complex exponentials with + + + align:start position:0% +combination of complex exponentials with +the amplitudes multiplied by h of e to J + + align:start position:0% +the amplitudes multiplied by h of e to J + + + align:start position:0% +the amplitudes multiplied by h of e to J +Omega K in other words each each of + + align:start position:0% +Omega K in other words each each of + + + align:start position:0% +Omega K in other words each each of +these exponentials has as an output a + + align:start position:0% +these exponentials has as an output a + + + align:start position:0% +these exponentials has as an output a +sub K * h of e j Omega sub k e to J + + align:start position:0% +sub K * h of e j Omega sub k e to J + + + align:start position:0% +sub K * h of e j Omega sub k e to J +Omega sub k + + align:start position:0% +Omega sub k + + + align:start position:0% +Omega sub k +n a sum of those at the input gives us a + + align:start position:0% +n a sum of those at the input gives us a + + + align:start position:0% +n a sum of those at the input gives us a +sum at the output because of the fact + + align:start position:0% +sum at the output because of the fact + + + align:start position:0% +sum at the output because of the fact +that the system is + + align:start position:0% +that the system is + + + align:start position:0% +that the system is +linear all right so let's take an input + + align:start position:0% +linear all right so let's take an input + + + align:start position:0% +linear all right so let's take an input +which is an arbitrary input more or less + + align:start position:0% +which is an arbitrary input more or less + + + align:start position:0% +which is an arbitrary input more or less +arbitrary an input X of + + align:start position:0% +arbitrary an input X of + + + align:start position:0% +arbitrary an input X of +n which I can express + + align:start position:0% +n which I can express + + + align:start position:0% +n which I can express +in terms of its fora + + align:start position:0% +in terms of its fora + + + align:start position:0% +in terms of its fora +transform in terms of this inverse fora + + align:start position:0% +transform in terms of this inverse fora + + + align:start position:0% +transform in terms of this inverse fora +transform + + align:start position:0% +transform + + + align:start position:0% +transform +relationship all right now this as I + + align:start position:0% +relationship all right now this as I + + + align:start position:0% +relationship all right now this as I +emphasized just a minute ago is a + + align:start position:0% +emphasized just a minute ago is a + + + align:start position:0% +emphasized just a minute ago is a +decomposition of X of + + align:start position:0% +decomposition of X of + + + align:start position:0% +decomposition of X of +n as a linear combination of complex + + align:start position:0% +n as a linear combination of complex + + + align:start position:0% +n as a linear combination of complex +exponentials this is a linear + + align:start position:0% +exponentials this is a linear + + + align:start position:0% +exponentials this is a linear +combination of complex exponentials at + + align:start position:0% +combination of complex exponentials at + + + align:start position:0% +combination of complex exponentials at +the input so what's the output well the + + align:start position:0% +the input so what's the output well the + + + align:start position:0% +the input so what's the output well the +output is then going to be a linear + + align:start position:0% +output is then going to be a linear + + + align:start position:0% +output is then going to be a linear +combination of complex + + align:start position:0% +combination of complex + + + align:start position:0% +combination of complex +exponentials with the amplitude of each + + align:start position:0% +exponentials with the amplitude of each + + + align:start position:0% +exponentials with the amplitude of each +one of the input exponentials multiplied + + align:start position:0% +one of the input exponentials multiplied + + + align:start position:0% +one of the input exponentials multiplied +by the frequency response of the system + + align:start position:0% +by the frequency response of the system + + + align:start position:0% +by the frequency response of the system +at that frequency so the result is that + + align:start position:0% +at that frequency so the result is that + + + align:start position:0% +at that frequency so the result is that +with this is the + + align:start position:0% +with this is the + + + align:start position:0% +with this is the +input what we have to get at the + + align:start position:0% + + + + align:start position:0% + +output is is + + align:start position:0% +output is is + + + align:start position:0% +output is is +this the same linear combination the + + align:start position:0% +this the same linear combination the + + + align:start position:0% +this the same linear combination the +only change being that the complex + + align:start position:0% +only change being that the complex + + + align:start position:0% +only change being that the complex +amplitudes of the in input are + + align:start position:0% +amplitudes of the in input are + + + align:start position:0% +amplitudes of the in input are +multiplied by h of e to the J + + align:start position:0% +multiplied by h of e to the J + + + align:start position:0% +multiplied by h of e to the J +Omega well this of course is the + + align:start position:0% +Omega well this of course is the + + + align:start position:0% +Omega well this of course is the +expression for the output we put in X of + + align:start position:0% +expression for the output we put in X of + + + align:start position:0% +expression for the output we put in X of +n we know that we're getting out y of + + align:start position:0% +n we know that we're getting out y of + + + align:start position:0% +n we know that we're getting out y of +n so obviously this then must be the + + align:start position:0% +n so obviously this then must be the + + + align:start position:0% +n so obviously this then must be the +fora + + align:start position:0% +fora + + + align:start position:0% +fora +transform of the output of the system so + + align:start position:0% +transform of the output of the system so + + + align:start position:0% +transform of the output of the system so +what this says then is that the forier + + align:start position:0% +what this says then is that the forier + + + align:start position:0% +what this says then is that the forier +transform of the output y of e to the J + + align:start position:0% +transform of the output y of e to the J + + + align:start position:0% +transform of the output y of e to the J +Omega has to be + + align:start position:0% +Omega has to be + + + align:start position:0% +Omega has to be +this it has to be X of e to the J Omega + + align:start position:0% +this it has to be X of e to the J Omega + + + align:start position:0% +this it has to be X of e to the J Omega +times h of e to the J + + align:start position:0% +times h of e to the J + + + align:start position:0% +times h of e to the J +Omega and basically well and we know + + align:start position:0% +Omega and basically well and we know + + + align:start position:0% +Omega and basically well and we know +also that that y of n is going to be + + align:start position:0% +also that that y of n is going to be + + + align:start position:0% +also that that y of n is going to be +equal to X of n involved with h of n so + + align:start position:0% +equal to X of n involved with h of n so + + + align:start position:0% +equal to X of n involved with h of n so +basically this justifies the convolution + + align:start position:0% +basically this justifies the convolution + + + align:start position:0% +basically this justifies the convolution +property that is the convolution of two + + align:start position:0% +property that is the convolution of two + + + align:start position:0% +property that is the convolution of two +sequences has as its forier transform + + align:start position:0% +sequences has as its forier transform + + + align:start position:0% +sequences has as its forier transform +the product of the forier transform of + + align:start position:0% +the product of the forier transform of + + + align:start position:0% +the product of the forier transform of +each of the individual sequences very + + align:start position:0% +each of the individual sequences very + + + align:start position:0% +each of the individual sequences very +important property and although we can + + align:start position:0% +important property and although we can + + + align:start position:0% +important property and although we can +go through a formal derivation of this + + align:start position:0% +go through a formal derivation of this + + + align:start position:0% +go through a formal derivation of this +in fact the basic reason for it is tied + + align:start position:0% +in fact the basic reason for it is tied + + + align:start position:0% +in fact the basic reason for it is tied +to the arguments that I've outlined here + + align:start position:0% +to the arguments that I've outlined here + + + align:start position:0% +to the arguments that I've outlined here +and in terms of insight I feel that it's + + align:start position:0% +and in terms of insight I feel that it's + + + align:start position:0% +and in terms of insight I feel that it's +more important to understand this way of + + align:start position:0% +more important to understand this way of + + + align:start position:0% +more important to understand this way of +looking at it than to understand a + + align:start position:0% +looking at it than to understand a + + + align:start position:0% +looking at it than to understand a +formal + + align:start position:0% +formal + + + align:start position:0% +formal +derivation well this is interesting also + + align:start position:0% +derivation well this is interesting also + + + align:start position:0% +derivation well this is interesting also +important and also should be familiar to + + align:start position:0% +important and also should be familiar to + + + align:start position:0% +important and also should be familiar to +you in terms of things that you're used + + align:start position:0% +you in terms of things that you're used + + + align:start position:0% +you in terms of things that you're used +to thinking about for continuous time + + align:start position:0% +to thinking about for continuous time + + + align:start position:0% +to thinking about for continuous time +systems obviously in continuous time + + align:start position:0% +systems obviously in continuous time + + + align:start position:0% +systems obviously in continuous time +systems the same type of property holds + + align:start position:0% +systems the same type of property holds + + + align:start position:0% +systems the same type of property holds +that is is that the forier transform + + align:start position:0% +that is is that the forier transform + + + align:start position:0% +that is is that the forier transform +changes multiplication uh convolution to + + align:start position:0% +changes multiplication uh convolution to + + + align:start position:0% +changes multiplication uh convolution to +multiplication and in fact it permits + + align:start position:0% +multiplication and in fact it permits + + + align:start position:0% +multiplication and in fact it permits +the description of a linear shift inv + + align:start position:0% +the description of a linear shift inv + + + align:start position:0% +the description of a linear shift inv +variance + + align:start position:0% +variance + + + align:start position:0% +variance +system to be in terms of multiplication + + align:start position:0% +system to be in terms of multiplication + + + align:start position:0% +system to be in terms of multiplication +rather than in terms of convolution and + + align:start position:0% +rather than in terms of convolution and + + + align:start position:0% +rather than in terms of convolution and +as we'll see in a number of lectures + + align:start position:0% +as we'll see in a number of lectures + + + align:start position:0% +as we'll see in a number of lectures +that's basically the basis for the + + align:start position:0% +that's basically the basis for the + + + align:start position:0% +that's basically the basis for the +Notions of filtering uh and some other + + align:start position:0% +Notions of filtering uh and some other + + + align:start position:0% +Notions of filtering uh and some other +very important Notions the Notions of + + align:start position:0% +very important Notions the Notions of + + + align:start position:0% +very important Notions the Notions of +modulation + + align:start position:0% +modulation + + + align:start position:0% +modulation +Etc okay key property this is a key + + align:start position:0% +Etc okay key property this is a key + + + align:start position:0% +Etc okay key property this is a key +property of linear shift and variance + + align:start position:0% +property of linear shift and variance + + + align:start position:0% +property of linear shift and variance +systems and the forier + + align:start position:0% +systems and the forier + + + align:start position:0% +systems and the forier +transform there are of course lots of + + align:start position:0% +transform there are of course lots of + + + align:start position:0% +transform there are of course lots of +other properties of linear shift and + + align:start position:0% +other properties of linear shift and + + + align:start position:0% +other properties of linear shift and +variance systems uh I'm sorry other + + align:start position:0% +variance systems uh I'm sorry other + + + align:start position:0% +variance systems uh I'm sorry other +properties there are other properties + + align:start position:0% +properties there are other properties + + + align:start position:0% +properties there are other properties +obviously of linear shift and variance + + align:start position:0% +obviously of linear shift and variance + + + align:start position:0% +obviously of linear shift and variance +systems there are other properties of + + align:start position:0% +systems there are other properties of + + + align:start position:0% +systems there are other properties of +forier transforms that are important + + align:start position:0% +forier transforms that are important + + + align:start position:0% +forier transforms that are important +both in terms of interpreting forier + + align:start position:0% +both in terms of interpreting forier + + + align:start position:0% +both in terms of interpreting forier +transforms and in terms of computing + + align:start position:0% +transforms and in terms of computing + + + align:start position:0% +transforms and in terms of computing +forier transforms of a variety of + + align:start position:0% +forier transforms of a variety of + + + align:start position:0% +forier transforms of a variety of +sequences a lot of these properties will + + align:start position:0% +sequences a lot of these properties will + + + align:start position:0% +sequences a lot of these properties will +be developed in the text and also in the + + align:start position:0% +be developed in the text and also in the + + + align:start position:0% +be developed in the text and also in the +study guide so you'll have to do the + + align:start position:0% +study guide so you'll have to do the + + + align:start position:0% +study guide so you'll have to do the +work rather than me but let me just + + align:start position:0% +work rather than me but let me just + + + align:start position:0% +work rather than me but let me just +indicate one class of properties that + + align:start position:0% +indicate one class of properties that + + + align:start position:0% +indicate one class of properties that +again should be very familiar to you if + + align:start position:0% +again should be very familiar to you if + + + align:start position:0% +again should be very familiar to you if +you relate your thinking back to Contin + + align:start position:0% +you relate your thinking back to Contin + + + align:start position:0% +you relate your thinking back to Contin +ous time forier transforms and that is + + align:start position:0% +ous time forier transforms and that is + + + align:start position:0% +ous time forier transforms and that is +the class of symmetry properties for the + + align:start position:0% +the class of symmetry properties for the + + + align:start position:0% +the class of symmetry properties for the +special case in which the sequences that + + align:start position:0% +special case in which the sequences that + + + align:start position:0% +special case in which the sequences that +we're talking about are real + + align:start position:0% +we're talking about are real + + + align:start position:0% +we're talking about are real +sequences well the basic symmetry + + align:start position:0% +sequences well the basic symmetry + + + align:start position:0% +sequences well the basic symmetry +property is that for X of n real the + + align:start position:0% +property is that for X of n real the + + + align:start position:0% +property is that for X of n real the +forier transform is a conjugate + + align:start position:0% +forier transform is a conjugate + + + align:start position:0% +forier transform is a conjugate +symmetric + + align:start position:0% +symmetric + + + align:start position:0% +symmetric +function X of e the J Omega is equal to + + align:start position:0% +function X of e the J Omega is equal to + + + align:start position:0% +function X of e the J Omega is equal to +X conjugate of e to the minus J + + align:start position:0% +X conjugate of e to the minus J + + + align:start position:0% +X conjugate of e to the minus J +Omega and we can see that essentially in + + align:start position:0% +Omega and we can see that essentially in + + + align:start position:0% +Omega and we can see that essentially in +a straightforward way that is the + + align:start position:0% +a straightforward way that is the + + + align:start position:0% +a straightforward way that is the +derivation is effectively + + align:start position:0% +derivation is effectively + + + align:start position:0% +derivation is effectively +straightforward here's X of e to the J + + align:start position:0% +straightforward here's X of e to the J + + + align:start position:0% +straightforward here's X of e to the J +Omega the sum of X of n e to the minus J + + align:start position:0% +Omega the sum of X of n e to the minus J + + + align:start position:0% +Omega the sum of X of n e to the minus J +Omega + + align:start position:0% +Omega + + + align:start position:0% +Omega +n here is X of e to the minus J Omega + + align:start position:0% +n here is X of e to the minus J Omega + + + align:start position:0% +n here is X of e to the minus J Omega +well the only difference between that + + align:start position:0% +well the only difference between that + + + align:start position:0% +well the only difference between that +and that is that we replace Omega by + + align:start position:0% +and that is that we replace Omega by + + + align:start position:0% +and that is that we replace Omega by +minus Omega so this becomes a plus sign + + align:start position:0% +minus Omega so this becomes a plus sign + + + align:start position:0% +minus Omega so this becomes a plus sign +of course it's not this that we + + align:start position:0% +of course it's not this that we + + + align:start position:0% +of course it's not this that we +want from this expression it's the + + align:start position:0% +want from this expression it's the + + + align:start position:0% +want from this expression it's the +conjugate of that so we want to complex + + align:start position:0% +conjugate of that so we want to complex + + + align:start position:0% +conjugate of that so we want to complex +conjugate + + align:start position:0% +conjugate + + + align:start position:0% +conjugate +this well we would do the same on the + + align:start position:0% +this well we would do the same on the + + + align:start position:0% +this well we would do the same on the +left hand side on the right hand + + align:start position:0% +left hand side on the right hand + + + align:start position:0% +left hand side on the right hand +side and so we would conjugate + + align:start position:0% +side and so we would conjugate + + + align:start position:0% +side and so we would conjugate +that and conjugate this which replaces + + align:start position:0% +that and conjugate this which replaces + + + align:start position:0% +that and conjugate this which replaces +this plus sign with a minus + + align:start position:0% +this plus sign with a minus + + + align:start position:0% +this plus sign with a minus +sign but we're talking about a real + + align:start position:0% +sign but we're talking about a real + + + align:start position:0% +sign but we're talking about a real +sequence X of n so X conjugate of n is + + align:start position:0% +sequence X of n so X conjugate of n is + + + align:start position:0% +sequence X of n so X conjugate of n is +just X of n in other words this is just + + align:start position:0% +just X of n in other words this is just + + + align:start position:0% +just X of n in other words this is just +X of n all over again and so we have + + align:start position:0% +X of n all over again and so we have + + + align:start position:0% +X of n all over again and so we have +that X conjugate of e the minus J Omega + + align:start position:0% +that X conjugate of e the minus J Omega + + + align:start position:0% +that X conjugate of e the minus J Omega +is the sum of X of n e to the minus J + + align:start position:0% +is the sum of X of n e to the minus J + + + align:start position:0% +is the sum of X of n e to the minus J +Omega n which is just what we have up + + align:start position:0% +Omega n which is just what we have up + + + align:start position:0% +Omega n which is just what we have up +here so obviously then these two are + + align:start position:0% +here so obviously then these two are + + + align:start position:0% +here so obviously then these two are +equal so for a real + + align:start position:0% +equal so for a real + + + align:start position:0% +equal so for a real +sequence the forier transform is a + + align:start position:0% +sequence the forier transform is a + + + align:start position:0% +sequence the forier transform is a +conjugate symmetric function this is + + align:start position:0% +conjugate symmetric function this is + + + align:start position:0% +conjugate symmetric function this is +what we'll call conjugate + + align:start position:0% +what we'll call conjugate + + + align:start position:0% +what we'll call conjugate +symmetric well let's press that a little + + align:start position:0% +symmetric well let's press that a little + + + align:start position:0% +symmetric well let's press that a little +further we have X of e to the J Omega + + align:start position:0% +further we have X of e to the J Omega + + + align:start position:0% +further we have X of e to the J Omega +which I can represent in terms of its + + align:start position:0% +which I can represent in terms of its + + + align:start position:0% +which I can represent in terms of its +real part and its imaginary part as + + align:start position:0% +real part and its imaginary part as + + + align:start position:0% +real part and its imaginary part as +obviously X real X subr of e to the J + + align:start position:0% +obviously X real X subr of e to the J + + + align:start position:0% +obviously X real X subr of e to the J +Omega plus J * X subi of e to the J + + align:start position:0% +Omega plus J * X subi of e to the J + + + align:start position:0% +Omega plus J * X subi of e to the J +Omega and the conjugate + + align:start position:0% +Omega and the conjugate + + + align:start position:0% +Omega and the conjugate +symmetric + + align:start position:0% +symmetric + + + align:start position:0% +symmetric +counterpart + + align:start position:0% +counterpart + + + align:start position:0% +counterpart +is this with Omega replaced by minus + + align:start position:0% +is this with Omega replaced by minus + + + align:start position:0% +is this with Omega replaced by minus +Omega and the expression conjugated so + + align:start position:0% +Omega and the expression conjugated so + + + align:start position:0% +Omega and the expression conjugated so +we have xar of e the minus J Omega minus + + align:start position:0% +we have xar of e the minus J Omega minus + + + align:start position:0% +we have xar of e the minus J Omega minus +J * + + align:start position:0% +J * + + + align:start position:0% +J * +XI of eus J Omega and we know that these + + align:start position:0% +XI of eus J Omega and we know that these + + + align:start position:0% +XI of eus J Omega and we know that these +two are equal well if these two are + + align:start position:0% +two are equal well if these two are + + + align:start position:0% +two are equal well if these two are +equal then these two are equal and so + + align:start position:0% +equal then these two are equal and so + + + align:start position:0% +equal then these two are equal and so +are + + align:start position:0% +are + + + align:start position:0% +are +these the real part of X of the J Omega + + align:start position:0% +these the real part of X of the J Omega + + + align:start position:0% +these the real part of X of the J Omega +must be equal to the real part of X of e + + align:start position:0% +must be equal to the real part of X of e + + + align:start position:0% +must be equal to the real part of X of e +to the minus J Omega in other words the + + align:start position:0% +to the minus J Omega in other words the + + + align:start position:0% +to the minus J Omega in other words the +real part has to be the same if Omega is + + align:start position:0% +real part has to be the same if Omega is + + + align:start position:0% +real part has to be the same if Omega is +replaced by minus + + align:start position:0% +replaced by minus + + + align:start position:0% +replaced by minus +Omega that means then that the real part + + align:start position:0% +Omega that means then that the real part + + + align:start position:0% +Omega that means then that the real part +of the forier transform is an even + + align:start position:0% +of the forier transform is an even + + + align:start position:0% +of the forier transform is an even +function of Omega meaning that if we + + align:start position:0% +function of Omega meaning that if we + + + align:start position:0% +function of Omega meaning that if we +replace Omega by minus Omega then the + + align:start position:0% +replace Omega by minus Omega then the + + + align:start position:0% +replace Omega by minus Omega then the +real part doesn't + + align:start position:0% +real part doesn't + + + align:start position:0% +real part doesn't +change the imaginary part on the other + + align:start position:0% +change the imaginary part on the other + + + align:start position:0% +change the imaginary part on the other +hand does in + + align:start position:0% +hand does in + + + align:start position:0% +hand does in +particular on the basis of what we're + + align:start position:0% +particular on the basis of what we're + + + align:start position:0% +particular on the basis of what we're +saying here and the equality of these + + align:start position:0% +saying here and the equality of these + + + align:start position:0% +saying here and the equality of these +the imaginary part X of I of e the J + + align:start position:0% +the imaginary part X of I of e the J + + + align:start position:0% +the imaginary part X of I of e the J +Omega must be equal to minus don't + + align:start position:0% +Omega must be equal to minus don't + + + align:start position:0% +Omega must be equal to minus don't +forget the minus sign minus X ofi of eus + + align:start position:0% +forget the minus sign minus X ofi of eus + + + align:start position:0% +forget the minus sign minus X ofi of eus +J Omega and that says then that if we + + align:start position:0% +J Omega and that says then that if we + + + align:start position:0% +J Omega and that says then that if we +replace Omega by minus Omega then the + + align:start position:0% +replace Omega by minus Omega then the + + + align:start position:0% +replace Omega by minus Omega then the +sign of the imaginary part changes so + + align:start position:0% +sign of the imaginary part changes so + + + align:start position:0% +sign of the imaginary part changes so +the imaginary part in fact is an odd + + align:start position:0% +the imaginary part in fact is an odd + + + align:start position:0% +the imaginary part in fact is an odd +function of Omega the real part is an + + align:start position:0% +function of Omega the real part is an + + + align:start position:0% +function of Omega the real part is an +even function of Omega + + align:start position:0% +even function of Omega + + + align:start position:0% +even function of Omega +well from this or from this we can also + + align:start position:0% +well from this or from this we can also + + + align:start position:0% +well from this or from this we can also +show that the magnitude of the 4A + + align:start position:0% +show that the magnitude of the 4A + + + align:start position:0% +show that the magnitude of the 4A +transform is an even function of + + align:start position:0% +transform is an even function of + + + align:start position:0% +transform is an even function of +Omega and the angle of the fora + + align:start position:0% +Omega and the angle of the fora + + + align:start position:0% +Omega and the angle of the fora +transform + + align:start position:0% +transform + + + align:start position:0% +transform +is an odd function of Omega and those of + + align:start position:0% +is an odd function of Omega and those of + + + align:start position:0% +is an odd function of Omega and those of +course are identical to what we know is + + align:start position:0% +course are identical to what we know is + + + align:start position:0% +course are identical to what we know is +true true for the continuous time forier + + align:start position:0% +true true for the continuous time forier + + + align:start position:0% +true true for the continuous time forier +transform remember however again that + + align:start position:0% +transform remember however again that + + + align:start position:0% +transform remember however again that +these are periodic functions whereas in + + align:start position:0% +these are periodic functions whereas in + + + align:start position:0% +these are periodic functions whereas in +the continuous time case they're + + align:start position:0% +the continuous time case they're + + + align:start position:0% +the continuous time case they're +not all right well this is an + + align:start position:0% +not all right well this is an + + + align:start position:0% +not all right well this is an +introduction to the forier + + align:start position:0% + + + + align:start position:0% + +transform one of the things that we've + + align:start position:0% +transform one of the things that we've + + + align:start position:0% +transform one of the things that we've +refrain from doing in all of these + + align:start position:0% +refrain from doing in all of these + + + align:start position:0% +refrain from doing in all of these +lectures is tying our development too + + align:start position:0% +lectures is tying our development too + + + align:start position:0% +lectures is tying our development too +closely to the notion of continuous time + + align:start position:0% +closely to the notion of continuous time + + + align:start position:0% +closely to the notion of continuous time +signals uh and in particular avoiding to + + align:start position:0% +signals uh and in particular avoiding to + + + align:start position:0% +signals uh and in particular avoiding to +some extent the notion of interpreting + + align:start position:0% +some extent the notion of interpreting + + + align:start position:0% +some extent the notion of interpreting +discrete time signals as just simply + + align:start position:0% +discrete time signals as just simply + + + align:start position:0% +discrete time signals as just simply +sampled replicas of continuous time + + align:start position:0% +sampled replicas of continuous time + + + align:start position:0% +sampled replicas of continuous time +signals and we'll continue to do that + + align:start position:0% +signals and we'll continue to do that + + + align:start position:0% +signals and we'll continue to do that +throughout this set of lectures but in + + align:start position:0% +throughout this set of lectures but in + + + align:start position:0% +throughout this set of lectures but in +particular for the forier + + align:start position:0% +particular for the forier + + + align:start position:0% +particular for the forier +transform I think that it's instructive + + align:start position:0% +transform I think that it's instructive + + + align:start position:0% +transform I think that it's instructive +to + + align:start position:0% +to + + + align:start position:0% +to +tie the + + align:start position:0% +tie the + + + align:start position:0% +tie the +together at least in terms of some + + align:start position:0% +together at least in terms of some + + + align:start position:0% +together at least in terms of some +insight into the + + align:start position:0% +insight into the + + + align:start position:0% +insight into the +relationship The Continuous time forier + + align:start position:0% +relationship The Continuous time forier + + + align:start position:0% +relationship The Continuous time forier +transform of obviously a continuous time + + align:start position:0% +transform of obviously a continuous time + + + align:start position:0% +transform of obviously a continuous time +signal and the discrete time forier + + align:start position:0% +signal and the discrete time forier + + + align:start position:0% +signal and the discrete time forier +transform for a sequence that's obtained + + align:start position:0% +transform for a sequence that's obtained + + + align:start position:0% +transform for a sequence that's obtained +by periodic sampling that is equally + + align:start position:0% +by periodic sampling that is equally + + + align:start position:0% +by periodic sampling that is equally +space sampling of the continuous time + + align:start position:0% +space sampling of the continuous time + + + align:start position:0% +space sampling of the continuous time +signal so what I'd like to do now is + + align:start position:0% +signal so what I'd like to do now is + + + align:start position:0% +signal so what I'd like to do now is +focus on + + align:start position:0% +focus on + + + align:start position:0% +focus on +relationship emphasizing again that not + + align:start position:0% +relationship emphasizing again that not + + + align:start position:0% +relationship emphasizing again that not +all sequences arise by periodic sampling + + align:start position:0% +all sequences arise by periodic sampling + + + align:start position:0% +all sequences arise by periodic sampling +of continuous time signals but for the + + align:start position:0% +of continuous time signals but for the + + + align:start position:0% +of continuous time signals but for the +cases in which they do the relationship + + align:start position:0% +cases in which they do the relationship + + + align:start position:0% +cases in which they do the relationship +between the continuous time and discreet + + align:start position:0% +between the continuous time and discreet + + + align:start position:0% +between the continuous time and discreet +time 4A transform is instructive so + + align:start position:0% +time 4A transform is instructive so + + + align:start position:0% +time 4A transform is instructive so +let's take a + + align:start position:0% +let's take a + + + align:start position:0% +let's take a +look + + align:start position:0% +look + + + align:start position:0% +look +at the + + align:start position:0% +at the + + + align:start position:0% +at the +relationship + + align:start position:0% +relationship + + + align:start position:0% +relationship +between some continuous time and + + align:start position:0% +between some continuous time and + + + align:start position:0% +between some continuous time and +discrete time forier + + align:start position:0% +discrete time forier + + + align:start position:0% +discrete time forier +transforms when we obtain the discrete + + align:start position:0% +transforms when we obtain the discrete + + + align:start position:0% +transforms when we obtain the discrete +time signal by sampling a continuous + + align:start position:0% +time signal by sampling a continuous + + + align:start position:0% +time signal by sampling a continuous +time + + align:start position:0% +time + + + align:start position:0% +time +signal well we begin of course with A + + align:start position:0% +signal well we begin of course with A + + + align:start position:0% +signal well we begin of course with A +continuous time uh time function which I + + align:start position:0% +continuous time uh time function which I + + + align:start position:0% +continuous time uh time function which I +denote by x sub a of t a sort of meaning + + align:start position:0% +denote by x sub a of t a sort of meaning + + + align:start position:0% +denote by x sub a of t a sort of meaning +analog and the steps that we would go + + align:start position:0% +analog and the steps that we would go + + + align:start position:0% +analog and the steps that we would go +through to convert that to a + + align:start position:0% +through to convert that to a + + + align:start position:0% +through to convert that to a +sequence are first of all to go through + + align:start position:0% +sequence are first of all to go through + + + align:start position:0% +sequence are first of all to go through +a + + align:start position:0% +a + + + align:start position:0% +a +sampler which I've indicated here and + + align:start position:0% +sampler which I've indicated here and + + + align:start position:0% +sampler which I've indicated here and +the output of the sampler is then a + + align:start position:0% +the output of the sampler is then a + + + align:start position:0% +the output of the sampler is then a +sampled continuous time version of this + + align:start position:0% +sampled continuous time version of this + + + align:start position:0% +sampled continuous time version of this +signal this essentially is the input + + align:start position:0% +signal this essentially is the input + + + align:start position:0% +signal this essentially is the input +signal multiplied by an Impulse + + align:start position:0% +signal multiplied by an Impulse + + + align:start position:0% +signal multiplied by an Impulse +train so I've indicated that here here's + + align:start position:0% +train so I've indicated that here here's + + + align:start position:0% +train so I've indicated that here here's +the Contin continuous time input here is + + align:start position:0% +the Contin continuous time input here is + + + align:start position:0% +the Contin continuous time input here is +the continuous time output of the + + align:start position:0% +the continuous time output of the + + + align:start position:0% +the continuous time output of the +sampler which is an Impulse train with + + align:start position:0% +sampler which is an Impulse train with + + + align:start position:0% +sampler which is an Impulse train with +the envelope of the impulse train being + + align:start position:0% +the envelope of the impulse train being + + + align:start position:0% +the envelope of the impulse train being +the continuous time function xub a of + + align:start position:0% +the continuous time function xub a of + + + align:start position:0% +the continuous time function xub a of +T all right well this isn't a sequence + + align:start position:0% +T all right well this isn't a sequence + + + align:start position:0% +T all right well this isn't a sequence +this is just simply an Impulse train to + + align:start position:0% +this is just simply an Impulse train to + + + align:start position:0% +this is just simply an Impulse train to +turn this into a sequence we need to go + + align:start position:0% +turn this into a sequence we need to go + + + align:start position:0% +turn this into a sequence we need to go +into a box which I've labeled uh c/d + + align:start position:0% +into a box which I've labeled uh c/d + + + align:start position:0% +into a box which I've labeled uh c/d +meaning continuous time to discrete time + + align:start position:0% +meaning continuous time to discrete time + + + align:start position:0% +meaning continuous time to discrete time +converter and the output then is a + + align:start position:0% +converter and the output then is a + + + align:start position:0% +converter and the output then is a +sequence X of n the sequence values + + align:start position:0% +sequence X of n the sequence values + + + align:start position:0% +sequence X of n the sequence values +being samples of X of a of T at the + + align:start position:0% +being samples of X of a of T at the + + + align:start position:0% +being samples of X of a of T at the +sampling instance instances n * capital + + align:start position:0% +sampling instance instances n * capital + + + align:start position:0% +sampling instance instances n * capital +T in other words it's + + align:start position:0% +T in other words it's + + + align:start position:0% +T in other words it's +converting the areas of these impulses + + align:start position:0% +converting the areas of these impulses + + + align:start position:0% +converting the areas of these impulses +into sequence + + align:start position:0% +into sequence + + + align:start position:0% +into sequence +values now I've Illustrated it here for + + align:start position:0% +values now I've Illustrated it here for + + + align:start position:0% +values now I've Illustrated it here for +one choice for the sampling interval + + align:start position:0% +one choice for the sampling interval + + + align:start position:0% +one choice for the sampling interval +capital + + align:start position:0% +capital + + + align:start position:0% +capital +T let's down here Illustrated for a + + align:start position:0% +T let's down here Illustrated for a + + + align:start position:0% +T let's down here Illustrated for a +sampling interval that's twice as long + + align:start position:0% +sampling interval that's twice as long + + + align:start position:0% +sampling interval that's twice as long +well of course we have the same + + align:start position:0% +well of course we have the same + + + align:start position:0% +well of course we have the same +continuous time + + align:start position:0% +continuous time + + + align:start position:0% +continuous time +input the sampled output X of a Tilda of + + align:start position:0% +input the sampled output X of a Tilda of + + + align:start position:0% +input the sampled output X of a Tilda of +T has the same envelope but the spacing + + align:start position:0% +T has the same envelope but the spacing + + + align:start position:0% +T has the same envelope but the spacing +of the impulses is twice what it is here + + align:start position:0% +of the impulses is twice what it is here + + + align:start position:0% +of the impulses is twice what it is here +and that I've indicated the envelope of + + align:start position:0% +and that I've indicated the envelope of + + + align:start position:0% +and that I've indicated the envelope of +course is the + + align:start position:0% +course is the + + + align:start position:0% +course is the +same but at the output of the continuous + + align:start position:0% +same but at the output of the continuous + + + align:start position:0% +same but at the output of the continuous +time to discrete time converter what do + + align:start position:0% +time to discrete time converter what do + + + align:start position:0% +time to discrete time converter what do +we have well we have the areas of these + + align:start position:0% +we have well we have the areas of these + + + align:start position:0% +we have well we have the areas of these +impulses lined up along this axis again + + align:start position:0% +impulses lined up along this axis again + + + align:start position:0% +impulses lined up along this axis again +at integer values of + + align:start position:0% +at integer values of + + + align:start position:0% +at integer values of +n that is the spacing of the lines when + + align:start position:0% +n that is the spacing of the lines when + + + align:start position:0% +n that is the spacing of the lines when +we look at the sequence here must be + + align:start position:0% +we look at the sequence here must be + + + align:start position:0% +we look at the sequence here must be +exact the same as the spacing of the + + align:start position:0% +exact the same as the spacing of the + + + align:start position:0% +exact the same as the spacing of the +lines here it's just that the values are + + align:start position:0% +lines here it's just that the values are + + + align:start position:0% +lines here it's just that the values are +different because we picked out samples + + align:start position:0% +different because we picked out samples + + + align:start position:0% +different because we picked out samples +at different instance so in fact the + + align:start position:0% +at different instance so in fact the + + + align:start position:0% +at different instance so in fact the +envelope + + align:start position:0% +envelope + + + align:start position:0% +envelope +here is indeed a compressed version of + + align:start position:0% +here is indeed a compressed version of + + + align:start position:0% +here is indeed a compressed version of +the envelope that we had here very + + align:start position:0% +the envelope that we had here very + + + align:start position:0% +the envelope that we had here very +important point the point being that no + + align:start position:0% +important point the point being that no + + + align:start position:0% +important point the point being that no +matter what the sampling rate is the + + align:start position:0% +matter what the sampling rate is the + + + align:start position:0% +matter what the sampling rate is the +sequence values when we line them up as + + align:start position:0% +sequence values when we line them up as + + + align:start position:0% +sequence values when we line them up as +a sequence are going to call at integer + + align:start position:0% +a sequence are going to call at integer + + + align:start position:0% +a sequence are going to call at integer +values along this argument n always at + + align:start position:0% +values along this argument n always at + + + align:start position:0% +values along this argument n always at +intervals that correspond to one whereas + + align:start position:0% +intervals that correspond to one whereas + + + align:start position:0% +intervals that correspond to one whereas +the output of the sampler had impulses + + align:start position:0% +the output of the sampler had impulses + + + align:start position:0% +the output of the sampler had impulses +occurring at a spacing of capital T + + align:start position:0% +occurring at a spacing of capital T + + + align:start position:0% +occurring at a spacing of capital T +which in this case was Capital T1 and in + + align:start position:0% +which in this case was Capital T1 and in + + + align:start position:0% +which in this case was Capital T1 and in +this case is capital + + align:start position:0% +this case is capital + + + align:start position:0% +this case is capital +T2 all right well this is essentially + + align:start position:0% +T2 all right well this is essentially + + + align:start position:0% +T2 all right well this is essentially +the sampling process plus the conversion + + align:start position:0% +the sampling process plus the conversion + + + align:start position:0% +the sampling process plus the conversion +to a discrete time signal and now let's + + align:start position:0% +to a discrete time signal and now let's + + + align:start position:0% +to a discrete time signal and now let's +take a look at what this means in terms + + align:start position:0% +take a look at what this means in terms + + + align:start position:0% +take a look at what this means in terms +of the forier + + align:start position:0% +of the forier + + + align:start position:0% +of the forier +transform of the discrete time signal as + + align:start position:0% +transform of the discrete time signal as + + + align:start position:0% +transform of the discrete time signal as +compared with the fora transform of the + + align:start position:0% +compared with the fora transform of the + + + align:start position:0% +compared with the fora transform of the +continuous time + + align:start position:0% +continuous time + + + align:start position:0% +continuous time +signal let's do this in two + + align:start position:0% +signal let's do this in two + + + align:start position:0% +signal let's do this in two +steps first of all we have the sampler + + align:start position:0% +steps first of all we have the sampler + + + align:start position:0% +steps first of all we have the sampler +here's the input xub of T continuous + + align:start position:0% +here's the input xub of T continuous + + + align:start position:0% +here's the input xub of T continuous +time function here's the output X till + + align:start position:0% +time function here's the output X till + + + align:start position:0% +time function here's the output X till +Del of T A continuous time function and + + align:start position:0% +Del of T A continuous time function and + + + align:start position:0% +Del of T A continuous time function and +the output of the sampler is the input + + align:start position:0% +the output of the sampler is the input + + + align:start position:0% +the output of the sampler is the input +to the sampler multiplied by an Impulse + + align:start position:0% +to the sampler multiplied by an Impulse + + + align:start position:0% +to the sampler multiplied by an Impulse +train or equivalently it's an Impulse + + align:start position:0% +train or equivalently it's an Impulse + + + align:start position:0% +train or equivalently it's an Impulse +train with the areas of the impulses + + align:start position:0% +train with the areas of the impulses + + + align:start position:0% +train with the areas of the impulses +given by the values of x sub B of T at + + align:start position:0% +given by the values of x sub B of T at + + + align:start position:0% +given by the values of x sub B of T at +the times that the impulses occur this + + align:start position:0% +the times that the impulses occur this + + + align:start position:0% +the times that the impulses occur this +you not by the way is what I'm using as + + align:start position:0% +you not by the way is what I'm using as + + + align:start position:0% +you not by the way is what I'm using as +the notation to designate a unit impulse + + align:start position:0% +the notation to designate a unit impulse + + + align:start position:0% +the notation to designate a unit impulse +unit continuous time impulse now in the + + align:start position:0% +unit continuous time impulse now in the + + + align:start position:0% +unit continuous time impulse now in the +forier transform domain then the + + align:start position:0% +forier transform domain then the + + + align:start position:0% +forier transform domain then the +continuous time forier + + align:start position:0% +continuous time forier + + + align:start position:0% +continuous time forier +transform is the + + align:start position:0% +transform is the + + + align:start position:0% +transform is the +convolution of the continuous time + + align:start position:0% +convolution of the continuous time + + + align:start position:0% +convolution of the continuous time +forier transform of xub of t convolved + + align:start position:0% +forier transform of xub of t convolved + + + align:start position:0% +forier transform of xub of t convolved +with the forier transform of the impulse + + align:start position:0% +with the forier transform of the impulse + + + align:start position:0% +with the forier transform of the impulse +train which is an Impulse train in the + + align:start position:0% +train which is an Impulse train in the + + + align:start position:0% +train which is an Impulse train in the +frequency domain that's a result that + + align:start position:0% +frequency domain that's a result that + + + align:start position:0% +frequency domain that's a result that +you should be familiar with with for + + align:start position:0% +you should be familiar with with for + + + align:start position:0% +you should be familiar with with for +discret for continuous time signals or + + align:start position:0% +discret for continuous time signals or + + + align:start position:0% +discret for continuous time signals or +equivalently it's given by 1/t times the + + align:start position:0% +equivalently it's given by 1/t times the + + + align:start position:0% +equivalently it's given by 1/t times the +sum of x sub a of J Omega plus J 2i R + + align:start position:0% +sum of x sub a of J Omega plus J 2i R + + + align:start position:0% +sum of x sub a of J Omega plus J 2i R +over capital T basically what that means + + align:start position:0% +over capital T basically what that means + + + align:start position:0% +over capital T basically what that means +is that the forier transform of this + + align:start position:0% +is that the forier transform of this + + + align:start position:0% +is that the forier transform of this +continuous time + + align:start position:0% +continuous time + + + align:start position:0% +continuous time +signal is equal to the forier transform + + align:start position:0% +signal is equal to the forier transform + + + align:start position:0% +signal is equal to the forier transform +of this continuous time signal but + + align:start position:0% +of this continuous time signal but + + + align:start position:0% +of this continuous time signal but +repeated over and over again in + + align:start position:0% +repeated over and over again in + + + align:start position:0% +repeated over and over again in +frequency at intervals of 2 pi over + + align:start position:0% +frequency at intervals of 2 pi over + + + align:start position:0% +frequency at intervals of 2 pi over +capital T So th this is sort of a + + align:start position:0% +capital T So th this is sort of a + + + align:start position:0% +capital T So th this is sort of a +standard sampling theorem kind of result + + align:start position:0% +standard sampling theorem kind of result + + + align:start position:0% +standard sampling theorem kind of result +in the continuous time case and a result + + align:start position:0% +in the continuous time case and a result + + + align:start position:0% +in the continuous time case and a result +that you should be more or less familiar + + align:start position:0% +that you should be more or less familiar + + + align:start position:0% +that you should be more or less familiar +with let's look at this now from a + + align:start position:0% +with let's look at this now from a + + + align:start position:0% +with let's look at this now from a +different point of view again looking at + + align:start position:0% +different point of view again looking at + + + align:start position:0% +different point of view again looking at +ex Tilda of J Omega well xab Tilda of J + + align:start position:0% +ex Tilda of J Omega well xab Tilda of J + + + align:start position:0% +ex Tilda of J Omega well xab Tilda of J +Omega is the integral of xab Tilda of t + + align:start position:0% +Omega is the integral of xab Tilda of t + + + align:start position:0% +Omega is the integral of xab Tilda of t +T eus J Omega T + + align:start position:0% +T eus J Omega T + + + align:start position:0% +T eus J Omega T +DT substitute in for X Tilda of T the + + align:start position:0% +DT substitute in for X Tilda of T the + + + align:start position:0% +DT substitute in for X Tilda of T the +relationship in terms of an Impulse + + align:start position:0% +relationship in terms of an Impulse + + + align:start position:0% +relationship in terms of an Impulse +train and interchange summation and + + align:start position:0% +train and interchange summation and + + + align:start position:0% +train and interchange summation and +integration and I think you can verify + + align:start position:0% +integration and I think you can verify + + + align:start position:0% +integration and I think you can verify +in a very straightforward way that what + + align:start position:0% +in a very straightforward way that what + + + align:start position:0% +in a very straightforward way that what +you end up with is an expression for the + + align:start position:0% +you end up with is an expression for the + + + align:start position:0% +you end up with is an expression for the +4A transform at the output of the + + align:start position:0% +4A transform at the output of the + + + align:start position:0% +4A transform at the output of the +sampler as given by the sampling values + + align:start position:0% +sampler as given by the sampling values + + + align:start position:0% +sampler as given by the sampling values +times e to minus JN Capital Omega T + + align:start position:0% +times e to minus JN Capital Omega T + + + align:start position:0% +times e to minus JN Capital Omega T +Capital Omega is a continuous frequency + + align:start position:0% +Capital Omega is a continuous frequency + + + align:start position:0% +Capital Omega is a continuous frequency +variable now we want to look at the + + align:start position:0% +variable now we want to look at the + + + align:start position:0% +variable now we want to look at the +relationship between the forier + + align:start position:0% +relationship between the forier + + + align:start position:0% +relationship between the forier +transform continuous time of x sub a of + + align:start position:0% +transform continuous time of x sub a of + + + align:start position:0% +transform continuous time of x sub a of +T and the discrete time fora transform + + align:start position:0% +T and the discrete time fora transform + + + align:start position:0% +T and the discrete time fora transform +of X of n so we have the next step which + + align:start position:0% +of X of n so we have the next step which + + + align:start position:0% +of X of n so we have the next step which +is to put this impulse train into the + + align:start position:0% +is to put this impulse train into the + + + align:start position:0% +is to put this impulse train into the +continuous to discrete time + + align:start position:0% +continuous to discrete time + + + align:start position:0% +continuous to discrete time +converter and I remind you that we just + + align:start position:0% +converter and I remind you that we just + + + align:start position:0% +converter and I remind you that we just +developed two results one result was + + align:start position:0% +developed two results one result was + + + align:start position:0% +developed two results one result was +that xate Tilda of J Omega was given by + + align:start position:0% +that xate Tilda of J Omega was given by + + + align:start position:0% +that xate Tilda of J Omega was given by +this + + align:start position:0% +this + + + align:start position:0% +this +expression also we developed that it was + + align:start position:0% +expression also we developed that it was + + + align:start position:0% +expression also we developed that it was +given by this + + align:start position:0% +given by this + + + align:start position:0% +given by this +expression well what's the forier + + align:start position:0% +expression well what's the forier + + + align:start position:0% +expression well what's the forier +transform of the output of the + + align:start position:0% +transform of the output of the + + + align:start position:0% +transform of the output of the +continuous to discrete time converter + + align:start position:0% +continuous to discrete time converter + + + align:start position:0% +continuous to discrete time converter +well it's just simply X of e to the J + + align:start position:0% +well it's just simply X of e to the J + + + align:start position:0% +well it's just simply X of e to the J +Omega our discrete time for 4 a + + align:start position:0% +Omega our discrete time for 4 a + + + align:start position:0% +Omega our discrete time for 4 a +transform which is equal to the sum on + + align:start position:0% +transform which is equal to the sum on + + + align:start position:0% +transform which is equal to the sum on +N of X of n but X of N is xub a of n + + align:start position:0% +N of X of n but X of N is xub a of n + + + align:start position:0% +N of X of n but X of N is xub a of n +capital T so we have x sub a of n + + align:start position:0% +capital T so we have x sub a of n + + + align:start position:0% +capital T so we have x sub a of n +capital T time eus J Omega + + align:start position:0% +capital T time eus J Omega + + + align:start position:0% +capital T time eus J Omega +n well let's compare this with this we + + align:start position:0% +n well let's compare this with this we + + + align:start position:0% +n well let's compare this with this we +see that they're exactly the same + + align:start position:0% +see that they're exactly the same + + + align:start position:0% +see that they're exactly the same +except that for Omega little Omega here + + align:start position:0% +except that for Omega little Omega here + + + align:start position:0% +except that for Omega little Omega here +we have Capital Omega time capital T + + align:start position:0% +we have Capital Omega time capital T + + + align:start position:0% +we have Capital Omega time capital T +there consequently we can say that the + + align:start position:0% +there consequently we can say that the + + + align:start position:0% +there consequently we can say that the +discrete time 4A + + align:start position:0% +discrete time 4A + + + align:start position:0% +discrete time 4A +transform is equal to the forier + + align:start position:0% +transform is equal to the forier + + + align:start position:0% +transform is equal to the forier +transform of the impulse Train The + + align:start position:0% +transform of the impulse Train The + + + align:start position:0% +transform of the impulse Train The +Continuous time forier transform of the + + align:start position:0% +Continuous time forier transform of the + + + align:start position:0% +Continuous time forier transform of the +impulse train with Omega * capital t + + align:start position:0% +impulse train with Omega * capital t + + + align:start position:0% +impulse train with Omega * capital t +equal to little + + align:start position:0% + + + + align:start position:0% + +Omega and and we had another expression + + align:start position:0% +Omega and and we had another expression + + + align:start position:0% +Omega and and we had another expression +for the fora transform of the impulse + + align:start position:0% +for the fora transform of the impulse + + + align:start position:0% +for the fora transform of the impulse +train which we derived here consequently + + align:start position:0% +train which we derived here consequently + + + align:start position:0% +train which we derived here consequently +the final result that we end up with is + + align:start position:0% +the final result that we end up with is + + + align:start position:0% +the final result that we end up with is +that the fora transform of the discrete + + align:start position:0% +that the fora transform of the discrete + + + align:start position:0% +that the fora transform of the discrete +time sequence is equal to 1 / T time the + + align:start position:0% +time sequence is equal to 1 / T time the + + + align:start position:0% +time sequence is equal to 1 / T time the +sum of x sub a of J Omega plus J 2i R + + align:start position:0% +sum of x sub a of J Omega plus J 2i R + + + align:start position:0% +sum of x sub a of J Omega plus J 2i R +over capital T with Omega + + align:start position:0% +over capital T with Omega + + + align:start position:0% +over capital T with Omega +replaced by little Omega ided capital T + + align:start position:0% +replaced by little Omega ided capital T + + + align:start position:0% +replaced by little Omega ided capital T +in other words we had the expression + + align:start position:0% +in other words we had the expression + + + align:start position:0% +in other words we had the expression +that Capital Omega * capital t is equal + + align:start position:0% +that Capital Omega * capital t is equal + + + align:start position:0% +that Capital Omega * capital t is equal +to little Omega and this then tells us + + align:start position:0% +to little Omega and this then tells us + + + align:start position:0% +to little Omega and this then tells us +what the 48 + + align:start position:0% +what the 48 + + + align:start position:0% +what the 48 +transform of the sequence is in terms of + + align:start position:0% +transform of the sequence is in terms of + + + align:start position:0% +transform of the sequence is in terms of +the fora transform of the + + align:start position:0% +the fora transform of the + + + align:start position:0% +the fora transform of the +output well this is just equations let's + + align:start position:0% +output well this is just equations let's + + + align:start position:0% +output well this is just equations let's +take a look at what this looks like + + align:start position:0% + + + + align:start position:0% + +graphically I've + + align:start position:0% +graphically I've + + + align:start position:0% +graphically I've +depicted + + align:start position:0% +depicted + + + align:start position:0% +depicted +here the continuous time fora + + align:start position:0% +here the continuous time fora + + + align:start position:0% +here the continuous time fora +transform of uh some sequence uh some + + align:start position:0% +transform of uh some sequence uh some + + + align:start position:0% +transform of uh some sequence uh some +time function and I've picked the 4A + + align:start position:0% +time function and I've picked the 4A + + + align:start position:0% +time function and I've picked the 4A +transform that looks like a rectang uh + + align:start position:0% +transform that looks like a rectang uh + + + align:start position:0% +transform that looks like a rectang uh +looks like a + + align:start position:0% +looks like a + + + align:start position:0% +looks like a +triangle well well first of all we + + align:start position:0% +triangle well well first of all we + + + align:start position:0% +triangle well well first of all we +derived the fact that the impulse train + + align:start position:0% +derived the fact that the impulse train + + + align:start position:0% +derived the fact that the impulse train +that results from sampling Little X of T + + align:start position:0% +that results from sampling Little X of T + + + align:start position:0% +that results from sampling Little X of T +has a fora transform which is this + + align:start position:0% +has a fora transform which is this + + + align:start position:0% +has a fora transform which is this +periodically repeated in + + align:start position:0% +periodically repeated in + + + align:start position:0% +periodically repeated in +frequency with a period in frequency + + align:start position:0% +frequency with a period in frequency + + + align:start position:0% +frequency with a period in frequency +equal to 2 Pi / Capital 1 where Capital + + align:start position:0% +equal to 2 Pi / Capital 1 where Capital + + + align:start position:0% +equal to 2 Pi / Capital 1 where Capital +1 is the sampling + + align:start position:0% +1 is the sampling + + + align:start position:0% +1 is the sampling +rate and on the basis of the expression + + align:start position:0% +rate and on the basis of the expression + + + align:start position:0% +rate and on the basis of the expression +that we derived relating the discrete + + align:start position:0% +that we derived relating the discrete + + + align:start position:0% +that we derived relating the discrete +time 4A transform and the continuous + + align:start position:0% +time 4A transform and the continuous + + + align:start position:0% +time 4A transform and the continuous +time 4ier + + align:start position:0% +time 4ier + + + align:start position:0% +time 4ier +transform the discrete time fora + + align:start position:0% +transform the discrete time fora + + + align:start position:0% +transform the discrete time fora +transform looks exactly like this but + + align:start position:0% +transform looks exactly like this but + + + align:start position:0% +transform looks exactly like this but +with a renormalization of the frequency + + align:start position:0% +with a renormalization of the frequency + + + align:start position:0% +with a renormalization of the frequency +axis because Capital Omega time capital + + align:start position:0% +axis because Capital Omega time capital + + + align:start position:0% +axis because Capital Omega time capital +t is equal to little Omega or yes + + align:start position:0% +t is equal to little Omega or yes + + + align:start position:0% +t is equal to little Omega or yes +Capital Omega * capital t is equal to + + align:start position:0% +Capital Omega * capital t is equal to + + + align:start position:0% +Capital Omega * capital t is equal to +little Omega so where capit Omega is + + align:start position:0% +little Omega so where capit Omega is + + + align:start position:0% +little Omega so where capit Omega is +equal to 2 piun / capital + + align:start position:0% +equal to 2 piun / capital + + + align:start position:0% +equal to 2 piun / capital +T little Omega is equal to 2 pi so this + + align:start position:0% +T little Omega is equal to 2 pi so this + + + align:start position:0% +T little Omega is equal to 2 pi so this +point which was at pi over capital T + + align:start position:0% +point which was at pi over capital T + + + align:start position:0% +point which was at pi over capital T +ends up on the Omega little Omega axis + + align:start position:0% +ends up on the Omega little Omega axis + + + align:start position:0% +ends up on the Omega little Omega axis +at Pi so this picture just simply gets + + align:start position:0% +at Pi so this picture just simply gets + + + align:start position:0% +at Pi so this picture just simply gets +scaled according to the relationship + + align:start position:0% +scaled according to the relationship + + + align:start position:0% +scaled according to the relationship +that Capital Omega time capital t is + + align:start position:0% +that Capital Omega time capital t is + + + align:start position:0% +that Capital Omega time capital t is +equal to little + + align:start position:0% +equal to little + + + align:start position:0% +equal to little +Omega + + align:start position:0% +Omega + + + align:start position:0% +Omega +well this is for one choice of the + + align:start position:0% +well this is for one choice of the + + + align:start position:0% +well this is for one choice of the +sampling period obviously if capital T + + align:start position:0% +sampling period obviously if capital T + + + align:start position:0% +sampling period obviously if capital T +was large enough so that 2 pi over T1 + + align:start position:0% +was large enough so that 2 pi over T1 + + + align:start position:0% +was large enough so that 2 pi over T1 +was small enough then each of these + + align:start position:0% +was small enough then each of these + + + align:start position:0% +was small enough then each of these +individual replicas of the frequency + + align:start position:0% +individual replicas of the frequency + + + align:start position:0% +individual replicas of the frequency +response would + + align:start position:0% +response would + + + align:start position:0% +response would +interact and we wouldn't have just a + + align:start position:0% +interact and we wouldn't have just a + + + align:start position:0% +interact and we wouldn't have just a +simple separation of the Spectra as we + + align:start position:0% +simple separation of the Spectra as we + + + align:start position:0% +simple separation of the Spectra as we +have here we'd have an + + align:start position:0% +have here we'd have an + + + align:start position:0% +have here we'd have an +interaction which of course is is the + + align:start position:0% +interaction which of course is is the + + + align:start position:0% +interaction which of course is is the +interaction and the relationship between + + align:start position:0% +interaction and the relationship between + + + align:start position:0% +interaction and the relationship between +when that interaction occurs and capital + + align:start position:0% +when that interaction occurs and capital + + + align:start position:0% +when that interaction occurs and capital +t is the basis for this for the + + align:start position:0% +t is the basis for this for the + + + align:start position:0% +t is the basis for this for the +well-known and hopefully uh theorem that + + align:start position:0% +well-known and hopefully uh theorem that + + + align:start position:0% +well-known and hopefully uh theorem that +you're familiar with namely the sampling + + align:start position:0% +you're familiar with namely the sampling + + + align:start position:0% +you're familiar with namely the sampling +theorem well to illustrate that if we + + align:start position:0% +theorem well to illustrate that if we + + + align:start position:0% +theorem well to illustrate that if we +had a different sampling rate say twice + + align:start position:0% +had a different sampling rate say twice + + + align:start position:0% +had a different sampling rate say twice +the sampling rate that we have over here + + align:start position:0% +the sampling rate that we have over here + + + align:start position:0% +the sampling rate that we have over here +so that capital t is equal to 2 * + + align:start position:0% +so that capital t is equal to 2 * + + + align:start position:0% +so that capital t is equal to 2 * +Capital + + align:start position:0% +Capital + + + align:start position:0% +Capital +T1 then and starting with the same + + align:start position:0% +T1 then and starting with the same + + + align:start position:0% +T1 then and starting with the same +continuous time Spectrum what we have + + align:start position:0% +continuous time Spectrum what we have + + + align:start position:0% +continuous time Spectrum what we have +now is the + + align:start position:0% +now is the + + + align:start position:0% +now is the +Spectra again periodically repeated with + + align:start position:0% +Spectra again periodically repeated with + + + align:start position:0% +Spectra again periodically repeated with +a period again which is 2 pi over + + align:start position:0% +a period again which is 2 pi over + + + align:start position:0% +a period again which is 2 pi over +capital T which in this case is 2 pi + + align:start position:0% +capital T which in this case is 2 pi + + + align:start position:0% +capital T which in this case is 2 pi +over Capital + + align:start position:0% +over Capital + + + align:start position:0% +over Capital +T2 but now they interact and of course + + align:start position:0% +T2 but now they interact and of course + + + align:start position:0% +T2 but now they interact and of course +we have to add these up that was the + + align:start position:0% +we have to add these up that was the + + + align:start position:0% +we have to add these up that was the +expression that we just arrived so in + + align:start position:0% +expression that we just arrived so in + + + align:start position:0% +expression that we just arrived so in +that case we get some interaction or + + align:start position:0% +that case we get some interaction or + + + align:start position:0% +that case we get some interaction or +aliasing as it referred to and due to + + align:start position:0% +aliasing as it referred to and due to + + + align:start position:0% +aliasing as it referred to and due to +this aliasing the periodic one period of + + align:start position:0% +this aliasing the periodic one period of + + + align:start position:0% +this aliasing the periodic one period of +this periodic Spectrum no longer + + align:start position:0% +this periodic Spectrum no longer + + + align:start position:0% +this periodic Spectrum no longer +resembles the original + + align:start position:0% +resembles the original + + + align:start position:0% +resembles the original +Spectrum this is the fora transform for + + align:start position:0% +Spectrum this is the fora transform for + + + align:start position:0% +Spectrum this is the fora transform for +the sampled continuous time function + + align:start position:0% +the sampled continuous time function + + + align:start position:0% +the sampled continuous time function +that is this is the forier transform for + + align:start position:0% +that is this is the forier transform for + + + align:start position:0% +that is this is the forier transform for +the impulse train and now if we + + align:start position:0% +the impulse train and now if we + + + align:start position:0% +the impulse train and now if we +renormalize the frequency axis so that + + align:start position:0% +renormalize the frequency axis so that + + + align:start position:0% +renormalize the frequency axis so that +we express this in terms of the discrete + + align:start position:0% +we express this in terms of the discrete + + + align:start position:0% +we express this in terms of the discrete +time frequency variable little Omega + + align:start position:0% +time frequency variable little Omega + + + align:start position:0% +time frequency variable little Omega +then we simply scale this picture so + + align:start position:0% +then we simply scale this picture so + + + align:start position:0% +then we simply scale this picture so +that we end up with 2 pi over capital T + + align:start position:0% +that we end up with 2 pi over capital T + + + align:start position:0% +that we end up with 2 pi over capital T +corresponding to 2 pi in little + + align:start position:0% +corresponding to 2 pi in little + + + align:start position:0% +corresponding to 2 pi in little +Omega pi over capital T corresponding to + + align:start position:0% +Omega pi over capital T corresponding to + + + align:start position:0% +Omega pi over capital T corresponding to +Pi and we see in fact as we better see + + align:start position:0% +Pi and we see in fact as we better see + + + align:start position:0% +Pi and we see in fact as we better see +that is it better turn out this way that + + align:start position:0% +that is it better turn out this way that + + + align:start position:0% +that is it better turn out this way that +the Spectrum in the discreet time case + + align:start position:0% +the Spectrum in the discreet time case + + + align:start position:0% +the Spectrum in the discreet time case +is a periodic function of Omega in other + + align:start position:0% +is a periodic function of Omega in other + + + align:start position:0% +is a periodic function of Omega in other +words it's periodic furthermore the + + align:start position:0% +words it's periodic furthermore the + + + align:start position:0% +words it's periodic furthermore the +period is given by 2 pi whereas here the + + align:start position:0% +period is given by 2 pi whereas here the + + + align:start position:0% +period is given by 2 pi whereas here the +period was 2 pi ided by capital + + align:start position:0% +period was 2 pi ided by capital + + + align:start position:0% +period was 2 pi ided by capital +T all right this perhaps takes a little + + align:start position:0% +T all right this perhaps takes a little + + + align:start position:0% +T all right this perhaps takes a little +digesting and you'll have some chance to + + align:start position:0% +digesting and you'll have some chance to + + + align:start position:0% +digesting and you'll have some chance to +do that as + + align:start position:0% +do that as + + + align:start position:0% +do that as +we uh work some problems we meaning you + + align:start position:0% +we uh work some problems we meaning you + + + align:start position:0% +we uh work some problems we meaning you +as we as you work some problems in the + + align:start position:0% +as we as you work some problems in the + + + align:start position:0% +as we as you work some problems in the +study guide and uh digest this a little + + align:start position:0% +study guide and uh digest this a little + + + align:start position:0% +study guide and uh digest this a little +while you're reading the text but it's + + align:start position:0% +while you're reading the text but it's + + + align:start position:0% +while you're reading the text but it's +an important relationship that uh and + + align:start position:0% +an important relationship that uh and + + + align:start position:0% +an important relationship that uh and +it's important to understand + + align:start position:0% +it's important to understand + + + align:start position:0% +it's important to understand +it now this is basically the forier + + align:start position:0% +it now this is basically the forier + + + align:start position:0% +it now this is basically the forier +transform the relationship between the + + align:start position:0% +transform the relationship between the + + + align:start position:0% +transform the relationship between the +discrete time and continuous time forier + + align:start position:0% +discrete time and continuous time forier + + + align:start position:0% +discrete time and continuous time forier +transform one of the difficulties with + + align:start position:0% +transform one of the difficulties with + + + align:start position:0% +transform one of the difficulties with +the forier + + align:start position:0% +the forier + + + align:start position:0% +the forier +transform which I've avoided + + align:start position:0% +transform which I've avoided + + + align:start position:0% +transform which I've avoided +illustrating explicit ly in this lecture + + align:start position:0% +illustrating explicit ly in this lecture + + + align:start position:0% +illustrating explicit ly in this lecture +is that the fora transform doesn't exist + + align:start position:0% +is that the fora transform doesn't exist + + + align:start position:0% +is that the fora transform doesn't exist +for all sequences in particular it + + align:start position:0% +for all sequences in particular it + + + align:start position:0% +for all sequences in particular it +doesn't converge for all + + align:start position:0% +doesn't converge for all + + + align:start position:0% +doesn't converge for all +sequences and this is a problem which we + + align:start position:0% +sequences and this is a problem which we + + + align:start position:0% +sequences and this is a problem which we +can get around by generalizing the + + align:start position:0% +can get around by generalizing the + + + align:start position:0% +can get around by generalizing the +notion of the forier transform to what + + align:start position:0% +notion of the forier transform to what + + + align:start position:0% +notion of the forier transform to what +we'll call the Z transform and the Z + + align:start position:0% +we'll call the Z transform and the Z + + + align:start position:0% +we'll call the Z transform and the Z +transform as you'll observe is like in + + align:start position:0% +transform as you'll observe is like in + + + align:start position:0% +transform as you'll observe is like in +the continuous time case the + + align:start position:0% +the continuous time case the + + + align:start position:0% +the continuous time case the +transform and this is what we'll go on + + align:start position:0% +transform and this is what we'll go on + + + align:start position:0% +transform and this is what we'll go on +to in the next lecture + + align:start position:0% + + + + align:start position:0% + +thanks \ No newline at end of file diff --git a/dLjCy6RmBN4.txt b/dLjCy6RmBN4.txt new file mode 100644 index 0000000000000000000000000000000000000000..e1221afd32db18b936d614a632796963276a85fb --- /dev/null +++ b/dLjCy6RmBN4.txt @@ -0,0 +1,4691 @@ +PROFESSOR: I'm excited +about today's lecture + +because there's so +many fun topics. + +This is like many fun +things all in one lecture. + +We're going to start with a +cool little problem, which + +is about unfolding +and re-folding. + +You could think +of them-- they're + +kind of like hinged +dissections although they're + +from between surfaces +of polyhedra. + +You can also think of +them as common unfoldings. + +So general idea is, +you have over here + +in the left team you have +unfoldings-- polygons, + +let's say. + +Possible things that +could fold into polyhedra. + +And we'll think convex again. + +And when we were +thinking about unfolding, + +we we're thinking about +going this direction. + +When we were thinking +about folding, + +we were thinking +about this direction. + +But what if we do +both repeatedly? + +So I start, say, with a cube. + +And then I unfold it +and then I re-fold it. + +That's sort of what the +metamorphosis of the cube + +was about. + +And then I unfold +that and I re-fold it, + +and I unfold and I re-fold +and I unfold and re-fold. + +This is a fun tour to take. + +Is this space connected? + +Can I get from any +polyhedral surface + +to any other-- say, convex-- +by unfolding and re-folding? + +We have no idea. + +So while each of +these operations + +we know a fair amount about-- +we know how to generally unfold + +convex polyhedra, +we know how to find + +all of the gluings of a polygon +into a polyhedron-- repeating + +those processes, +we could explore + +but actually no ones' every +tried that algorithmically. + +It'd be fun to see what +crazy things you get. + +But we have lots of examples +and partial progress + +towards this question. + +So here's the first example. + +This appears in the book. + +It's by Hirata from 2000. + +He was one of the guys who +implemented a gluing algorithm. + +And this is an unfolding-- +a common unfolding-- + +of a cube-- ah, not quite-- +and a regular tetrahedron. + +So it's actually +a box not a cube. + +One of the big open +questions in this area + +is, can you find +a common unfolding + +of a perfect cube and a regular +tetrahedron that's open? + +Marty posed that +question I think + +in 1998, in the good old days of +the beginning of folding stuff. + +And this is almost an answer +but it's not quite a cube, + +as a result. + +You could see-- I think +it's pretty easy to see + +how to fold it into a box just +with extending all the lines. + +And the dotted lines +show how to fold + +into a regular tetrahedron. + +That's one example. + +You can also fold-- this thing +makes both a regular octahedron + +instead of a regular tetrahedron +and some kind of tetrahedra. + +It's not regular. + +We call it a tetramonohedron, +meaning each of the sides + +are the same. + +So it's just one type of side, +but there's four of them. + +And I guess the red lines +are folding into that, + +the green lines fold into +a regular tetrahedron. + +I feel like I'm +getting forgetful. + +I don't even remember where +this example comes from. + +But it's in the book, it's +not attributed to anyone + +so I assume Joe invented it. + +But recently, like +just this year, + +inspired a whole bunch of +examples by these guys. + +I just saw the talk +last week in China-- + +that's where I was traveling, +it was a geometry conference. + +And Horiyama and Uehara +talked about a bunch + +of different common unfoldings. + +This is, again, of +a regular octahedron + +and a tetramonohedron. + +But a different example. + +But they kept going. + +Said all right, let's do +all the platonic solids. + +So this is a common unfolding +of a cube and a tetramonohedron. + +Cube-- actually two of them. + +You can see how it makes a cube. + +That's obvious. + +But the tetramonohedron +are the blue lines. + +Then I have the octahedron, +we have the icosahedron. + +I don't think they +have a dodecahedron yet + +because all of these +approaches are actually + +based on dissection +techniques where + +you take a tiling of-- here +are equilateral triangles + +for the icosahedron, +and you take + +a tiling of some +triangle that's going + +to make the tetramonohedron, +and you align them + +so that things work out nicely. + +And that's not +always well defined, + +but it often leads +to good dissections, + +often hinged dissections. + +It's the way, for +example, you show + +you can hinge +dissect a rectangle + +into any other rectangle. + +You take tilings of +different rectangles + +and overlay them appropriately. + +Here, same approach, +but with a dodecahedron, + +regular pentagons +don't tile so it's + +very hard to use that approach. + +So this is as far +as they've gotten. + +Here they've measured +the proportions + +of the tetramonohedron +to give you an idea. + +It's close to regular. + +But again, open question, +can any two platonic solids-- + +do any two have a +common unfolding? + +They proved in this paper, +if you restrict one of them + +to be an edge unfolding +and the other one + +can be a general unfolding +then it's not possible. + +But if they're both general +unfoldings, who knows. + +Here you see it's edge +unfolding for the icosahedron, + +but general unfolding +for the other. + +Cool. + +But very recently, +this is, like, + +hasn't even been released yet. + +This is the premier +of the following, + +I'll call it conjecture. + +I think it's not yet +approved or explicitly-- it's + +not certain that it's correct. + +But the claim is this gray +shape, taken to the limit-- + +so this is the first +iteration of the fractal, + +this is the second iteration +of the fractal-- in the limit, + +will fold both to a regular +tetrahedron and a cube. + +This would be an +amazing breakthrough. + +Still, the conjecture +is that it is not + +possible to go from +a regular tetrahedron + +to a cube with a regular-- +like a normal polygon + +with a finite number of sides. + +But with an infinite number of +sides, it seems to be possible. + +Which is awesome. + +This is-- I haven't +met this guy yet. + +He's a professional puzzler +in Japan, Toshihiro Shirakawa. + +So stay tuned for maybe a proof +of that theorem, that claim. + +The next topic-- +this started back + +in '99, inspired +by this question. + +We thought well, +what about boxes? + +And this is a common unfolding +of two different size boxes + +which is cool. + +And it's generated in +a fairly intuitive way. + +You start with an +unfolding of a box. + +This makes a one +by one by three box + +if you think about it +for a little while. + +Just wrap around-- this +is like one top side, 1 + +by 3 rectangle and wrap around. + +And then you-- you +draw the gluing-- here + +I've labeled which edges +glue to which edges. + +And for every letter, +like the two Gs + +here, I could imagine adding a +triangle here and removing it + +from here. + +That will still fold to +the same thing, right? + +So I get to choose +for each letter which + +guy goes in, which guy goes out. + +Then I get this shape as +a result of that process. + +And if I do it right, +when I rotate 45 degrees, + +I get a different orthogonal +unfolding of some other box. + +So here, if I started +with a root 2 by root 2 + +by three root 2 box, I +get a 1 by 2 by 4 box. + +So this is a common +unfolding of both. + +I guess here is like the +center core of the 1 by 2 by 4 + +and you wrap around again. + +Or this is probably center core. + +So that's pretty cool. + +This is an idea by Timothy Chan. + +Of course, natural +question is, do I + +need to do this rotation trick +or could I get away without it? + +And you can get away without it. + +This is an idea +of Therese Biedl. + +This is my Waterloo days. + +We had an open problem +session, kind of like the one + +we have in this class. + +It was the very +first one that I ran. + +I ran it with Therese. + +And she came up with this idea. + +This is a-- it's not obvious +exactly how this works + +or where she came up with this. + +It was kind of magical. + +But this the same polygon, +different creases, you + +make two different size boxes. + +Now they're going to be integers +because they're orthogonal + +aligned on the grid. + +Pretty cool. + +And for a long time, this +was the only example of this + +that we had. + +There's still an open question +which I give you A by C by-- A + +by B by C box and a D by E +by F box, is this possible? + +When is this possible? + +But at least now-- +oh, here's, sorry. + +There are two examples. + +Of course, the surface +areas have to match. + +So the sum of A plus B plus +C equals D plus E plus F. + +I think that's right. + +Or no. + +It's more complicated. + +It's like A times +B plus-- and so on. + +Pairwise products. + +Now we know that +there are actually + +infinitely many examples. + +This is another fairly +new result by Uehara, + +again in 2008. + +This is-- Uehara translated +our textbook to Japanese, + +by the way. + +Another connection. + +He does a lot of +fun folding stuff. + +Just saw him last week. + +So this is an +example of taking a 1 + +by 5 by 2k box and a common +unfolding of that with a 1 + +by 1 by 6k plus 2 box. + +Which has a very +regular pattern. + +And this one, little more +complicated to copy and paste + +but it makes 1 by 1 by 8k +plus 11 box and a 1 by 3 + +by 4k plus 5 box. + +Which is pretty cool. + +I haven't studied +these carefully, + +but there's two different +ways to fold each. + +So now we know +there are infinitely + +many of these examples. + +It's still not known +when it's possible, + +but also in this +paper Uehara came up + +with a sort of random +generation algorithm + +where he would take a +box, randomly unfold + +it, try to fold it +into other boxes. + +And he has now over 250,000 +examples of this process. + +And I think these are maybe +inspired by his random search. + +I'm not sure, but this +is theory obviously. + +One particularly fun +example, this one + +actually tiles the plane. + +So it'd be efficient +if you're cutting it + +out of sheet material. + +You can make a common unfolding +of 1 by 2 by 5 box and a 1 + +by 1 by 8 box. + +I think this one he +made into a puzzle + +with a paper manufacturer. + +I'm getting ahead of myself. + +Big open question +here that he asked is, + +are there-- is there a common +unfolding of three boxes? + +That remains open. + +And he feels like he's +very close to finding one + +with his random search +but hasn't yet found one. + +It's like it almost +folds into the third box. + +But it's strange how +hard it is to find them. + +Maybe they don't exist. + +That would be surprising. + +All right. + +Next example on this theme, +common unfoldings, is this toy. + +So this is a 1 by 1 by 4 box, +also known as the-- as a tetra + +cubes, four cubes +joined edge to edge. + +And-- oh, I should +have practiced. + +You can unfold it. + +This is a commercially +produced toy. + +It's called Cubigami. + +And it's one net, one unfolding. + +But it can fold into +all tetra cubes. + +So that was the tube and, let's +see, what else can I make here? + +I should have practiced. + +Interesting. + +It's fun. + +You can play with it later. + +Oh, that looks interesting. + +Almost. + +Not quite. + +It's almost-- it looks +like a Tetris piece, right? + +Except I didn't quite +cover it right at the end. + +It's a good puzzle. + +Obviously. + +Maybe if I do it like-- +that doesn't work. + +Wow. + +All right. + +You're going to have to +play with it yourself. + +I lose. + +But you can make all of +the four cube joinings + +except-- except for this one. + +See, the problem +with this example + +is it doesn't have the same +surface areas the rest. + +And you have to +conserve surface area. + +But if you think about +all the other four + +cubes-- like I was trying to +make this guy or this guy-- + +it's like Tetris +pieces-- but also things + +like-- I can draw +better than I can + +solve the puzzle apparently. + +Like this. + +This is the one non-planar one. + +All right? + +So you've got all the Tetris +pieces except this guy. + +It's the wrong surface area. + +So, in general, it's +all the tree shape ones. + +No cycles. + +Can make all of them. + +This is an example found by +Donald Knuth, famous computer + +scientist. + +He sort of accidentally +at a cocktail party heard + +about this problem from George +Miller who's a toy designer-- + +or puzzle designer. + +And so then Knuth +went back and he + +wrote a program to numerate +all unfoldings of these things + +and found there are a whole +bunch of common unfoldings. + +But it's found by +exhaustive search. + +This was the one that sort of +had the smallest bounding box, + +I believe, in terms of area. + +And so it's a nice +compact thing. + +And then there are various +manufacturing's of it. + +This is the latest one that's +sort of relatively easy + +to build I guess. + +So, play with that later. + +That's four cubes. + +What about five cubes? + +Well, that was the subject +of a paper also presented + +last week in China. + +And it turns out, there +is no common unfolding + +of all 24 pentacubes. + +That's five cubes +joined together. + +But there is a common unfolding +of 23 out of 24 of them. + +So this is the paper. + +There was a bunch of authors. + +There were basically +three teams that + +worked on this, two of +which were writing code. + +I was on one of +the coding teams. + +And the third one +was trying to think + +about the problem +using mathematics. + +And for a long time, the +thinkers were leading. + +But then, of course, +eventually the computers + +win because after a couple days +of just solid computation on I + +don't know now how many cores +with each of the groups, + +we numerated all +these unfoldings. + +And so now there's, I think, +over one trillion unfoldings + +of the 1 by 1 by 5 tube. + +But one trillions not that bad. + +Now, we could not +do this for six. + +But for five it wasn't so bad. + +And this is-- there's a bunch +of unfoldings of 23 out of 24. + +But that's the max you can get. + +Little disappointing. + +AUDIENCE: Which pentacube lost? + +PROFESSOR: I don't know +which pentacube lost. + +I should find out. + +That's a good question. + +But I do have some +other answers. + +So in some sense, +the hard ones I think + +are the non-planar guys. + +Like this guy. + +So they're planar +if all the cubes + +lie in a thickened +plane, thickened by one. + +This guy will fold into +all the non-planar cubes + +and also fold into +most of the pentacubes. + +There are only 24 total +so it's only missing two. + +And this'll fold into +all the non-planar guys. + +And what's cool is +this one is unique. + +There's only one common +unfolding of those guys. + +AUDIENCE: How many +non-planar [INAUDIBLE]? + +PROFESSOR: How many +non-planar are there? + +I don't remember. + +Maybe 10. + +I think it's a minority. + +But there are still +a bunch of them. + +And I think this would +make a good puzzle. + +If you're going to +manufacture-- if you guys want + +to do a start up, here you go. + +Freely available. + +If you want to do +the planar pentacubes + +there are a lot of common +unfoldings of them. + +This is one of the +fairly compact ones. + +And this one, I have +an animation of. + +Or, actually, not +this particular + +unfolding, but this concept. + +And that is here. + +Yes, I trust myself. + +So here is unfolding +and re-folding + +of that particular shape. + +And then I hit +Space bar and it's + +the same unfolding but +a different polycube. + +And this is going to go +through all of the flat ones. + +And that animation is +done heuristically. + +I don't have any theory +that that's always possible. + +But always keeping +the same unfolding, + +just changing where +the creases are. + +That's so cool. + +It's funny, actually. + +The person who implemented this +was the guy who was thinking, + +not the coder-- coder teams. + +I guess he had free time. + +This is by [? Karim ?] +[INAUDIBLE]. + +I guess you can count them +and then subtract from 24 + +and you'll get how many +non-planar ones there are. + +But I've lost track +of where we are. + +Always same unfolding. + +This is a fairly nice, +simple unfolding. + +It's mostly one dimensional. + +All right. + +You get the idea, right? + +Pretty fun. + +All right. + +So, right. + +Do I have anymore? + +I think that was the +end of my slides. + +I do have one more example in +the notes which is, if you just + +want to make the flat +guys-- so just the two + +dimensional +examples-- so we know + +we could do that with five, +but you can also do with six. + +We wrote another +program that looks + +at a very special +kind of unfolding. + +And in that special class, +it's possible to fold + +all planar six +cubes-- hexacubes. + +But that class does not work +for septacubes-- seven cubes. + +Open question, is there +a common unfolding + +of all planar seven cubes or +all non-planar seven cubes? + +Or how many can you make? + +There it was beyond exhaustion, +and we have to actually think. + +Unless you come up with +a good class and then + +you can exhaust +it in that class. + +One nice open question here +is, if you go to large N, + +are there some two polycubes +that have no common unfolding? + +At the moment, it +could be every pair + +of polycubes has a +common unfolding. + +Certainly there +are-- for example, + +in this class there +are four polycubes that + +do not have a common unfolding. + +I think we're not +sure about three. + +For size five. + +Of course, we don't even +know whether there's + +any polycube that +has no unfolding. + +I think there should be one. + +But at the moment, it +could be every polycube + +has an unfolding. + +But to make it a little harder, +what about two polycubes + +at once you want a +common unfolding? + +All these questions are open. + +All right. + +This is common unfolding. + +We're going to stick +with unfolding stuff + +but change around the +problem a little bit. + +So let me ask you a question. + +Can have a vote for those who +haven't read the notes already + +and know the answer. + +So let's say, +orthogonal polyhedron. + +We talk a lot about +orthogonal polyhedra. + +See all this polycube +stuff is in that genre. + +And so way back when we +talked about grid unfolding + +of orthogonal polyhedra. + +It's not known whether +that's possible, + +but we have epsilon +unfolding where + +you cut exponentially +many times and so on. + +But how do you define +orthogonal polyhedra? + +There are two +natural definitions. + +One is that the +angles are right. + +Right angles, let's +say, in the faces. + +The other natural definition +is that you look at two faces + +and the angles between +those should be right. + +So I guess right +dihedral angles. + +Right face angles or +right dihedral angles. + +The question is, are +these the same thing? + +Who thinks yes? + +Who thinks no? + +Yeah. + +I kind of set it up. + +Everyone thinks no. + +They're not the same. + +But for genus zero +polyhedra, they are the same. + +That's maybe the +surprising thing. + +This is a genus +eight polyhedron. + +No, seven. + +It's always a little +tricky to measure genus. + +If it just had one triangular +face that would be-- well, + +anyway, that's genus seven. + +I'm not going to +try to convince you. + +This is an unfolding +of the thing. + +So you can see, +in the unfolding, + +it looks like it's an +orthogonal polyhedron. + +All the angles are right. + +It looks perfect. + +And yet, it folds into +this non-orthogonal thing. + +Kind of a thickened octahedron. + +It's kind of critical that it +has a genus more than zero. + +In this paper-- this +is the original paper + +that considered this problem-- +there's a lower bound of one. + +The genus 0 is not enough. + +Then we came along-- I don't +have the author list here. + +It's with the Waterloo gang, it +was Therese Biedl and others. + +And this is a smaller genus, +a genus six polyhedron. + +This guy. + +So it's almost the same +example turned inside out. + +So this like to half +octahedra and then joined + +in this cubicle frame +and then you put caps + +on the cubicle frame to make +there not be holes out there. + +And then you have +slightly smaller genus + +because you can go +around the backside. + +So that's the best known, +is a genus six example. + +We proved that you need +genus at least three + +in order for such +an example to exist. + +I have a little sketch +of the proof in the notes + +if you want to read it. + +It's a fun little boot +strapping argument but I would-- + +I'm going to go on +to other fun topics + +here rather than prove this. + +Is that a good plan? + +I think that's good plan. + +OK. + +So this is a fun +kind of-- unfoldings + +can be orthogonal while the +three dimensional versions are + +not orthogonal. + +All right. + +Next topic. + +I'm going to go back to +Alexandrov's theorem. + +Turns out there is a +smooth version of that. + +So now we're going +to segue a little bit + +into smooth foldings +and smooth unfoldings. + +So instead of thinking of +polyhedron objects-- polygons + +and convex polyhedra-- I want +to think about smooth bodies. + +So, for example, suppose +I take a smooth convex + +shape like an +ellipse or something + +and I picked two +perimeter antipodes + +and I do perimeter having +gluing where this is defines-- + +as I walk along the +perimeter in both directions + +it-- I obviously +didn't do it perfectly, + +they should meet at +exactly the same time. + +This defines a gluing. + +For every point there +is a corresponding point + +it gets glued to. + +This is a way to make what is +locally like a convex surface + +because at any point, at +most 360 degrees of material + +is glued there because +this thing was convex. + +And the same way as +for convex polygons, + +does this make a convex +something in three dimensions? + +It's not going to make +a polyhedron because it + +has this curve, +but indeed it does + +make a convex smooth surface. + +So every convex metric +that's topologically a sphere + +is realized by a +unique convex surface. + +So Alexandrov's theorem was +identical to this statement + +except it also had +polyhedral up here, + +that there were finite number +of points of nonzero curvature. + +Now we have +infinitely many points + +of slightly positive +curvature because, again, this + +is supposed to sum to 4 pi. + +That's still true. + +But it's now an integral +instead of a sum. + +So each of these things sort of +has an infinitesimal curvature + +and if you integrate +them it adds up to 4 pi. + +You can check that. + +So this will make something. + +I encourage you to try +this out, again, with tape. + +You're going to +approximate it because tape + +is going to be polygonal. + +But it works. + +It will make something. + +I particularly-- I should +mention the idea of this proof + +is just to take limits +of regular Alexandrov. + +Take closer and closer +polyhedral approximations. + +In the polyhedral world +we can use that induction + +that we talked about. + +In the smooth case, you +can't, but the smooth case + +is the limit of the polyhedral +case so it works out. + +This is proved by a student +of Alexandrov Pogorelov + +in the '70s, whereas he +proved his theorem in the '40s + +or '50s. + +One really fun thing you +could do with this theorem + +is, instead of using +just one convex shape, + +you could use two convex shapes +and zip them to each other. + +And this is called a D-form. + +It was invented by an +artist, Tony Wills. + +So here I've taken +two-- in this case, + +two identical +convect shapes-- they + +don't have to be identical-- +picked two points to glue them + +to each other and then you +just zip around the perimeter. + +And again, because you're always +gluing convex angles to convex + +angles-- the smooth +convex angles-- + +but they're still less than +180, so you glue them together, + +it's less than 360. + +And in this case, it's-- we +could actually figure out + +and think about what 3D shape +you get so we could build that + +in Mathematica. + +But in general, you get +some weird convex shape. + +For a while there were +some examples of this + +but no one knew exactly +what they looked like. + +Then, I think it was a +project in this class + +or it came out of the problem +session in this class three + +years ago, Greg +Price and I proved + +that these things +are nice in the sense + +that the only place +you get creases + +is along the seam, +the pink stuff. + +Both for-- these +are called D-forms, + +these have another-- I +think these are pita-forms, + +if I recall, where you take one +convex shape instead of two. + +Here you only get-- +you can get the creases + +along the seam and +one extra crease, + +if I recall correctly here. + +And here you don't +get any extra creases. + +It's always smooth +except at the seam. + +And also, if you just take +the seam-- the pink part-- + +and take the convex hull of that +thing, you get the same thing. + +So it doesn't go outside. + +It's really tightly +wrapped around wherever + +the seam happens to go. + +Remember, this thing is +unique by Pogorelov's theorem. + +So it's kind of nice to +know that structurally these + +are pretty nice and smooth. + +If your original shapes +are smooth convex bodies, + +you will get a +nice, smooth shape + +at the end that only has +creases at the seams. + +Cool. + +Again, please try to it at home. + +It's lots of fun. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Let's see. + +This point should glue to here. + +I mean, it's +perfectly symmetric. + +AUDIENCE: I'm looking +at the 3D form. + +PROFESSOR: The 3D form. + +So one of the two shapes +is here and the other one + +is here and goes around +the back to there. + +And it's, again, symmetric. + +This is a nice example because +we have those parallel lines. + +Usually you wouldn't have that. + +And they're harder to +draw, is the challenge. + +Here, obviously, +we're doing sort + +of a polygonal approximation. + +You see all the lines. + +All right. + +This is a smooth version of +folding-- a smooth version + +of Alexandrov's theorem. + +We can also think about +smooth versions of unfolding. + +So here there is +exactly one paper + +by Nadia Benbernou whose in +the front row and Heather-- + +AUDIENCE: Patricia. + +PROFESSOR: Patricia +Khan and Joe O'Rourke. + +So this is a prismatoid. + +It's a little hard to +see the bottom face + +but there's a convex polygon on +the bottom, a parallel convex + +polygon on the top. + +You take the convex hull-- +sorry, they're not polygons. + +They're smooth convex bodies. + +So you've got one in the floor +plane, one in a parallel plane + +up top. + +You take the convex hull, you +get this nice smooth thing + +around the outside. + +Now, we have to generalize +our notion of unfolding + +because normally with +unfolding this would take + +an infinite number of cuts +to-- we have to cut everywhere + +there's curvature. + +Which means we're going +to have to cut along + +all those black lines. + +Which means we slice the thing +into very infinitesimal pieces. + +But if you think +of it as a limit + +of regular polyhedral things-- +here I have a little example. + +Let's think about the limit in +a simpler example to start with. + +So imagine you want +to take a pyramid-- + +so the top poly-- the top +convex shape is just a point. + +I guess it looks like +a cone but down here + +it could be anything, could be +an ellipse or any convex shape. + +Well, we can think of this as +a polyhedral approximation. + +So, for example, we take +a hexagon on the bottom, + +we want to unfold that. + +And in particular, we +thought about these-- + +these are the +pyramids-- and we-- + +one of the unfoldings of +them is the volcano unfolding + +if you remember back to +the unfolding lecture. + +Looks like that. + +All these triangles just fold +out, get all those parts. + +That never overlaps, +it's sort of trivial. + +You take the limit of that. + +In the limit, the floor becomes +whatever the convex shape. + +Maybe-- let's think about the +simple case where it's a disk. + +And in the limit you're getting +lots of really tiny triangles. + +You take that all the way to +limit, what you're getting + +is actually a concentric +circle around there. + +So really, these +become segments. + +Now, what's funny about +this limit is, normally-- + +before you get to the end, you +see there's these big gaps. + +A lot of the area's missing. + +These things are getting +infinitesimally small + +and yet they have to +spread over this big range. + +So most of this area +is actually absent. + +When you take the limit you +can't really see that anymore. + +It just becomes filled in. + +And so in this unfolding, +the area of the green stuff, + +if you just took that area +measured on the floor, + +it's going to be larger +than the area in the pink. + +So this is not an area +preserving unfolding + +which makes it a little weird. + +But it's still well defined. + +I mean, you wouldn't +actually-- well, + +for example-- we're going +to get to this in a moment-- + +if you actually took material +like this out of, say, + +tin foil, something +that can crinkle, + +then you should be able to +crinkle it into this shape. + +I'll talk about +how to prove that. + +That's actually most of +the rest of the lecture, + +is about that kind +of notion of folding. + +It's more like origami, +though, than unfolding + +because you're sort of +over covering stuff. + +And here-- actually, +here the hard part + +is not so much to show +these ribs don't intersect, + +although they don't and +it's not totally obvious + +because here they're kind +of going towards each other. + +But they won't actually +intersect in the unfolding. + +One of the tricky parts is to +show that the top face actually + +can fit somewhere, +so you actually + +get an unfolding of this thing. + +And I forget, this is choosing +some kind of extreme rib + +and putting it out there. + +It's a nice line of +separation if I recall. + +This is funny because here we +have a limit of some process. + +Now, for pyramids we know +the volcano unfolding works. + +For prismatoids, +regular prismatoids + +are when you take +some convex polygon + +and some other parallel convex +polygon, take the convex hull. + +We don't know whether +these have edge unfoldings. + +Still an open problem. + +And yet, for the +smooth case, we do. + +Kind of magical. + +I know why that's true. + +It's somehow the edge +constraint is harder. + +If you're not just worried +about edge unfoldings, + +we do know how to +unfold those obviously. + +You can do star unfolding, +source unfolding. + +Here, edge unfolding-- +well, we have + +to cut along all those +infinitely many edges. + +That makes it easier, +much smoother. + +But it's funny when the +smooth case is actually + +easier than the discrete case. + +All right. + +The next problem I want to +talk about is chocolate. + +I have here a bunch of +spherical chocolates. + +The most-- apparently the only +perfectly spherical chocolate, + +at least according +to the advertisement, + +is this thing called +the Mozart Kugel. + +Now, Mozart Kugel-- how many +people have eaten them before. + +Just a couple. + +Good stuff. + +It's, I guess, more +a European thing. + +It's from Austria. + +It's invented in early +1900s, I forget exactly when. + +It was a big thing at the +time because making chocolate + +perfectly spherical is not easy. + +It's like, how do +you hold it and not + +get little indentations? + +This thing is +perfectly spherical. + +Here I'll show you. + +But, really, the question I +wonder, because as an origamist + +you wonder, how do +you wrap this thing? + +Oh, I ripped it. + +I'll try to do this +more carefully. + +It's not how you usually +eat chocolate, is it? + +Open very carefully. + +It's OK. + +I have more in case I fail. + +More chocolate. + +Not enough for you, I'm afraid. + +So ignore the chocolate. + +It's not the Droid +you're looking for. + +It's not the chocolate. + +So it's a rectangle. + +I didn't do a perfect job. + +There's a few +little tears there. + +But they fold-- Mirabell. + +Mirabell makes the most +Mozart Kugel in the world. + +Mozart Kugel is very +cool because it's + +built in-- built up +in concentric spheres. + +You have the marzipan layer, +then the milk chocolate layer, + +then the nougat layer, then +the dark chocolate layer, + +if I recall. + +Each brand has a +different recipe, + +but they're always +spherical on the outside. + +It's kind of like +glassblowing actually. + +It's kind of fun. + +And each company has a +slightly different way-- well, + +I've studied only +two main companies. + +Mirabell makes the most of them +but they are not the original. + +They are called the +echta which is-- + +AUDIENCE: The real. + +PROFESSOR: The real. + +The authentic. + +But-- now, these +are hard to come by. + +These are brought to me by +my student, [INAUDIBLE], + +some of you know. + +Architecture. + +This is the-- oh, +it says in English. + +It's kind of easy. + +The original Salzburger +Mozart Kugel. + +Mozart was-- lived +in Salzburg, I guess. + +And so this is named after him. + +Oh, 1884. + +Wow. + +So that's when they started. + +Now, these guys-- +I think I've only + +had like one of +these in my life. + +I'm really excited. + +The Mirabell's are +OK, but this stuff? + +Wow. + +Oh, it's so much +easier to unfold. + +I like-- this is, I +think, probably handmade. + +Much more handmade. + +In fact, you can kind of tell +it's not perfectly spherical. + +It has a little nub at the top. + +So this is probably more how +they were originally made. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: What, are +you getting hungry? + +Now, Furst-- Furst +is the company + +who made the first Mozart +Kugel-- they use squares. + +I claim they're a +little bit better. + +But interesting question is, +which uses more material? + +Something to think about. + +Meanwhile-- I won't +torture you more by eating. + +All right. + +So this is a Mozart +Kugel problem. + +This paper started when-- I +think we are in New Orleans. + +Some part of the gang +was in New Orleans + +and there was this +deadline the next day + +and it was for this workshop +on computational geometry-- + +the European workshop-- +and it happened + +to be in Austria that +year-- that coming year. + +We're like, what +paper could we write? + +And we're sitting there +in the little cafe eating + +these beignets of +doughnuts and thinking, + +what could we write +a paper about? + +It's like, how about food? + +And what does Austria have? + +Well, [SPEAKING GERMAN] +Well, how about Mozart Kugel? + +So-- this is how +research happens. + +But it's really cool. + +It's really cool because +this is not your-- + +this is not the origami you +grew up with in this class. + +Because you can't fold a +sphere out of a square paper. + +And yet, this was a square +folded into a sphere. + +Somehow that was done using +a finite amount of effort. + +Whereas if you use regular +paper to fold something + +that has positive +curvature everywhere, + +you need infinitely +many creases. + +And yet this is fairly +practical to do. + +This is hand wrapped. + +In theory, I could re-wrap this. + +I've never actually tried. + +But something like this. + +It works pretty well. + +I even covered the tip. + +How did I do that +in finite effort? + +Well, of course it's +not a perfect sphere. + +But we need to model +this mathematically. + +It's annoying to +take approximations. + +I would like a model of +folding that actually + +does make it possible +to fold a sphere. + +So this is the idea of +contractive folding. + +We haven't been super rigorous +about defining origami, + +but I always say you +take a piece of paper, + +you can't stretch the paper, +you can't tear the paper, + +and you can't self-intersect. + +We're going to relax the +you can't stretch the paper. + +You still can't +stretch the paper, + +but now the paper can contract. + +So it can't get longer +but it can get shorter. + +It's like cables from +tensegrity theory. + +So you take any pair of points. + +There's some distance as +measured on the piece of paper. + +When you fold this thing +into your awesome sphere, + +you take the two points, +you measure the distance + +along the surface of +the piece of paper. + +Now, I'll-- normally +with origami, + +these two distances +should be equal. + +That's isometry. + +That's regular origami. + +But if I say that this one-- +so write equal that way. + +If this one can be smaller, +then this is contractive. + +And that is paper that can +shrink but not stretch. + +So pairwise distances +don't increase. + +So they could stay the same. + +We could still do +regular origami. + +But we can also contract. + +And then it is possible +to fold a sphere. + +Now, intuitively, +what's going on + +is, when you fold out of +tinfoil, you can crinkle. + +And that lets you not have +to worry about-- I mean, + +this is pretty good +approximation to a sphere + +especially when I have +a good base underneath + +to approximate against. + +I'm doing lots of little +tiny creases in order + +to approximate that contractive +mapping, contractive folding. + +So, conveniently, +there's a theorem + +that tells us this +is always possible. + +I'll tell you the theorem. + +This is another theorem +by Burago and Zalgallar + +who proved the other +theorem that if you + +have any polyhedral +metric you can turn it + +into some polyhedron, +not necessarily convex. + +So they solved that problem +plus they solved this problem. + +If you take a contractive-- they +only solved the smooth case. + +I imagine this works +for piecewise smooth. + +You take a contractive +C2 immersion-- + +it's just some fancy +word for folding, + +it has some extra constraints +but let's not worry about it. + +So C2 means continuous up +to the second derivative. + +So nice and smooth. + +Spheres are valid, for example. + +Then any one of those +things has a C0-- + +I'll just call it +polyhedral approximation. + +And this is approximation +in the Hausdorff sense + +meaning you want +to fold the sphere. + +If you just thicken that +sphere by some epsilon, + +then you can sort of stay within +that epsilon thickened sphere + +and do some kind of wiggling. + +You'll be polyhedral +and you'll only + +have finitely many creases. + +So there-- if you have a nice, +smooth contracted folded state, + +you could turn it into a regular +origami isometry folded state + +that's arbitrarily +close to the sphere. + +So for any epsilon. + +So that's a convenient +theorem from 1996. + +So that's the model. + +Now we can think about, how +do I optimally wrap a sphere? + +Now, there are +many possible goals + +you might want to optimize +in wrapping a sphere. + +Presumably, you want your +shape to tile the plane. + +So you can cut out a +whole bunch of these out + +of one sheet of tinfoil. + +Obviously Mirabell +likes rectangles, + +Furst likes squares. + +Are those the +right things to do? + +What about triangles? + +What about other shapes? + +These are the sorts of +questions we consider. + +We don't have a complete +answer to this question. + +But we have a lot of +fun-- fun things to do. + +What should I tell +you about first? + +I'm getting hungry. + +Maybe I'll have the +rest of that Mirabell. + +It's just sitting there. + +Half a Mozart Kugel, +can't have that. + +All right. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: Yes. + +Question? + +AUDIENCE: I was wondering-- + +PROFESSOR: You can have any. + +AUDIENCE: Because of +the fact that you've + +got this contracting +that occurs, + +I was wondering-- it's obvious +that because of contracting + +you need more than 4 pi +r surface area of paper + +to wrap a sphere-- +a one unit sphere. + +I'm wondering, do you +know exactly how much + +paper do you require due to +the fact that [INAUDIBLE]? + +PROFESSOR: Good question. + +How much paper do you require? + +Area is not being +preserved here. + +Just like the continuous +unfolding stuff, + +you don't preserve area. + +This is really the same thing. + +I think you can prove +this is a contractive map. + +So if you had this +as a piece of paper, + +you really could fold +that smooth pyramid. + +But you lose material when +you do a contractive mapping. + +And in the inverse, when you're +unfolding, you gain material. + +How much material +do I have to gain? + +Think about it. + +You should be able to +answer that question. + +I'm going to tell you about some +stuff while you think about it. + +That was the original +question we started with. + +What's the minimum area +wrapping of a unit sphere? + +The surface area of a +sphere is 4 pi, FYI. + +How much more do you need? + +All right. + +To describe these unfoldings, +I guess they are, or wrappings, + +whichever way you're +thinking about going, + +it's useful to have +some structure, kind + +of a backbone to the unfolding. + +So we came up with this +idea of stretched path. + +And you can show that any +kind of optimal wrapping + +will have at least +one stretch path. + +And our idea is +actually-- let me tell you + +what a stretch path is. + +This is a, let's say, a +path between two vertices + +whose length does not decrease. + +So it actually is +preserved in the folding. + +So I have my sphere, +I have two points, + +take the shortest +path between them. + +That shortest path +is exactly what + +it is in the unfolding, +exactly the same length. + +So that's what we +call a stretch path. + +There's no crinkling +along that path. + +There maybe crinkling on +either side of the path, + +but not on it. + +Our idea is-- OK, that gives +you some kind of structure. + +Our idea is to completely +cover the surface + +of the sphere with +stretched paths. + +There's a lot of +ways you can do that. + +Some of them will be valid, +some of them won't be. + +The simplest one is +the source unfolding. + +Or I guess you could call +it the source wrapping. + +Wrapping somehow means +contractive I guess. + +Which is, you take your +sphere, take some point x, + +you take all the +shortest paths around x-- + +it's a little tricky to draw. + +In other words, the Voronoi +diagram at that point. + +Just like we did with +source unfolding. + +And you call all of these edges, +all those straight lines-- + +geodesics, whatever-- they go to +this opposite south pole here. + +All of those lines you +call stretch paths. + +That determines an unfolding. + +And it happens to +be contractive. + +The unfolding will be a +big disk because you'll + +have the center-- call this x. + +This is 3D, this is 2D, +in case it wasn't clear. + +They both look the same. + +But now all those +paths are straight. + +And it's clear what the +lengths of these paths are. + +Each one of them is +half the circumference. + +Circumference? + +Is that what you call it? + +Half of an equator +of the sphere. + +Which for a unit sphere is pi. + +So this is radius pi, which +means the area of this thing + +is pi r squared. + +Sorry, the area is pi cubed. + +Interesting. + +But pi cubed, you can +compute, is more than 4pi. + +Pi squared is +almost-- is over nine. + +It's over nine times pi. + +We want four times pi. + +This is an example of +not preserving area. + +What's happening is +there's lots of crinkling + +between these lines. + +Now, there are infinitely +many of these lines. + +Every point is covered by +one of these stretched paths. + +But again, when I +unfold them, if I + +did a limiting approximation, +there'd be lots of holes here. + +But in the limit +there are no holes + +and that's where +I waste material + +and that's where +I get contraction. + +Make sense? + +I actually brought a +sphere, a couple spheres. + +I brought some chocolate +spheres, but slightly bigger + +sphere so we can +think about this. + +In this case, we're making +stretch paths all around + +from the north pole +down to the south pole + +and kind of cutting +at the south pole. + +And that's it. + +All right. + +Has anyone solved the problem +of what the minimum area + +wrapping of the sphere is? + +Yeah? + +You solved it? + +Janine. + +Or an idea. + +AUDIENCE: I think +it's 4pi plus epsilon. + +PROFESSOR: 4pi plus +epsilon is correct. + +How do you want to do it? + +Exactly. + +AUDIENCE: An apple +core-- or peeling. + +PROFESSOR: Apple peeling, yes. + +Or I prefer to think +of it as lecturer-- + +I don't know which one-- +the one about strip folding. + +AUDIENCE: Oh, yeah. + +PROFESSOR: Yes. + +Exactly. + +So we had this result +about strip folding + +if you remember way back in +the folding anything lecture. + +We talked about this +and then orgamizer. + +This was the inefficient method. + +But if you started with a +very long rectangle of paper, + +we could show that the +area of that piece of paper + +is arbitrary-- could +be made arbitrarily + +close to the area +of your polyhedron. + +So that area plus some epsilon. + +And you can make +epsilon as small + +as you wanted just by +making this polygon longer. + +If you take a polyhedral +approximation of a sphere + +and apply this theorem, you'll +get very close to the surface + +area of that approximation which +is very close to the surface + +area of the sphere, +which is 4pi. + +And then, if you take +an outer approximation, + +then you can just sort of +crinkle all those vertices down + +against the sphere. + +And you'll do-- it's +maybe not totally obvious, + +but it's not that hard. + +You get a contractive map that +actually wraps the sphere using + +not much more surface +area than what you had. + +The same as what you +had, which was not + +much more than the sphere. + +So you can get 4pi plus epsilon. + +So it turns out, minimizing +the area of your wrapping + +is not that interesting +a question by itself + +because there's kind of +this cheating solution. + +Obviously, you don't +want to manufacture that. + +I don't think. + +Maybe she built a robot, did +the inverse orange peeling, + +it would be pretty cool. + +But if you're trying to sell +this idea to confectioners + +around the world, I +wouldn't recommend + +attempting strip folding. + +So we would like +something that's + +reasonably nice but-- yeah. + +OK. + +AUDIENCE: So if +you're trying sell + +wrapper companies [INAUDIBLE] +square or rectangular amounts + +would these be 4pi squared? + +Because you're basically +producing something + +that maybe would expand +the circumference and-- + +PROFESSOR: Well, OK, an +interesting question is, + +what is the surface +area of these wrappings? + +These actually have +pretty special properties, + +the rectangle and +the-- I'm getting + +hungry-- and the square. + +Have you thought about which +of these has more surface area? + +The rectangle has more? + +Who thinks the +rectangle has more? + +Who thinks the square has more? + +Who thinks they're the same? + +Seed you with that idea. + +Well, they're actually the same. + +I'll explain why +in a little bit. + +It's crazy, I know. + +I prefer the square because +it has less perimeter. + +There are obviously many +things you might not + +like about this strip folding. + +It has high aspect +ratio, but in particular, + +one way to characterize +why this is nasty, + +it says high perimeter. + +Perimeter is annoying +because-- for a few reasons. + +Intuitively, if you +started with the sphere + +and you wanted to +cut it open, then you + +need a lot of cutting +because the perimeter is + +the amount that you cut. + +Or it's twice that. + +So conversely, when you're +trying to wrap a surface, + +if you have high +perimeter, there's + +a lot to worry about, lots of +things that have to match up. + +So you've got to be very +careful in your crinkling. + +Whereas I really didn't +have to be very careful + +wrapping with the square +because it has low perimeter. + +Another sense in which +perimeter is annoying + +is you're going to +have some error. + +So in fact, you can't just +perfectly wrap a sphere. + +Like, if I took a disk +of exactly this size, + +I probably couldn't +wrap a sphere with it + +because I'm going to +lose just some epsilon + +and then there'll +be a little point + +around the south +pole that's missing. + +If you're really going to +build confectionery-- build + +confectionery-- if you're really +going to wrap confectionery, + +you probably make this +a little bit bigger. + +How much area do +you lose when you + +make your thing a +little bit bigger? + +Well, it's roughly the +perimeter times epsilon. + +It's a little bit different from +that, but basically perimeter + +times epsilon. + +So if you minimize +perimeter, then + +your area wastage from +double coverage will go down. + +So really what I +want is something + +that's low area +and low perimeter. + +That's our new goal. + +And that's why I like +Furst better than Mirabell, + +not just because +they taste better. + +I really should verify +that they taste better. + +Oh, yeah. + +Now, they're very +different insides. + +Oh, but it's so good. + +Oh, much better chocolate. + +All right. + +Maybe I should have a +lottery for eating the rest. + +Petal wrapping. + +This is going to be +another way to put stretch + +paths on the sphere and +get an unfolding-- get + +a contractive +wrapping from that. + +Which actually +corresponds to this toy. + +I don't know if you +ever played with this. + +The Frisbee that's also a ball. + +These-- you see those cuts? + +Those are the shortest +paths from the north + +pole to the south pole. + +But we're not-- +before we were sort + +of using-- kind of slicing +along but also preserving-- + +that's kind of confusing-- +all of them, infinitely many. + +Now I want to do +with finitely many. + +Here I only have six. + +Six? + +Yes, six. + +Doesn't have to be six. + +Could be any number k. + +So I'm going to look at k +stretch paths from north pole + +to south pole. + +So I have my sphere, +here is my north pole. + +I do some constant number. + +Here I've done five. + +This is equally spaced +angular around the north pole, + +they all go to the south +pole on the bottom. + +Something like that. + +It's going to start +getting messy. + +These are going to +be stretch paths. + +I have to fill these orange +slices in between them. + +How should I fill them? + +Here's an idea. + +It's kind of like +the Voronoi diagram. + +Voronoi diagram is you grow from +many objects simultaneously. + +With this sphere wrapping +we grew from a single point + +in all directions. + +That was it. + +Now, I've drawn these paths. + +What if I grew from all of these +finite stretch paths at once? + +What I would get, these +would at some point converge. + +They would converge at +the angular bisector here. + +Along the way, +what's happening is + +each of these points is kind of +tracing along a straight line, + +so to speak, a +great circular arc + +until it reaches that point. + +I'm going to make +these stretched paths, + +and these are also stretched +pads, and basically cutting + +along the dotted line. + +OK. + +I won't draw all of them. + +But you get the idea. + +When you unfold this thing, you +have these kind of wish bones. + +These guys meet sort +of perpendicularly. + +So when you unfold you +preserve those angles. + +Remember these are +stretched paths. + +These lengths are preserved. + +The stuff in between, +it's really a curved thing + +and it gets slightly +larger in this thing. + +We call this thing a petal. + +But this is an +unfolding of this sort + +of one fifth of the sphere. + +This is the center line and +these are the two sides. + +So that's the idea +of petal wrapping. + +Now, there's different ways +to join these petals together. + +One idea is join them +all at the north pole. + +So then what you get-- +it's a little hard + +to imagine that these things +don't intersect each other, + +especially when I've +drawn them so fat. + +For five, it's going to +look something like this. + +I'm drawing it perfectly. + +They won't actually +intersect in the center + +because the total amount +of material at the center + +is only 360 degrees. + +And this will actually have-- +the tangents will actually + +match up here. + +So they will perfectly +mean in the center + +without self-intersection. + +So it's only sort of +a vertex unfolding. + +Because they're only +connected at the single point. + +But that's maybe necessary. + +I don't know. + +And again, these are +the stretched paths. + +It's a neat way to +think about unfolding. + +You can draw these-- +ignore the yellow for now. + +That's if you might want +to actually cut these out. + +So we have the three +petal unfolding, the four + +petal unfolding, five +petal unfolding, six petal, + +you can go arbitrarily high. + +In the limit, the +area of the blue stuff + +will converge to 4pi. + +This is another way to +get arbitrarily close. + +Because the smaller +these things are, + +the less you're distorting. + +So this is two +families of wrappings. + +We call these-- the blue +stuff is the petal unfolding, + +the yellow is the convex +hull of the petal unfoldings. + +Not quite, actually. + +So in the case of k equals 3, +we could think about a convex + +hull, but what I've drawn +here is the smallest + +enclosing equilateral triangle. + +Now this is the first +class of unfoldings + +we came up with after +the obvious sphere-- + +or circular one which +had pi cubed over 9pi. + +One thing we wondered +is that triangle, + +is it better than the +Mozart Kugel wrappings? + +Or is it worse? + +One way or the +other, presumably. + +Or maybe it's the same again. + +Who knows. + +Let's see. + +Yeah. + +Let me tell you, at this point-- +so I need more techniques + +to cover both of +those unfoldings, + +but that square is +the first wrapping. + +This one. + +I'll have to unfold another +one just so you can see. + +All right. + +So you see-- I mean, +I did a few times + +so maybe you already know. + +Here I have four corners, +four right angles. + +They meet at the top. + +So that is-- that's +where the four + +corners of the +square which are also + +the four corners of the +petal come together. + +And then it's just +everything-- these lines + +are stretched paths. + +There's no distortion around +them, they just kind of unfold. + +The stuff in the middle is-- +it's like undressing here. + +It's so tantalizing. + +The stuff in the middle +is getting contracted. + +So if-- I don't know if you +could see, maybe in the video + +you'll be able to see. + +Look closely at here. + +Along this path there +isn't so much crinkling. + +In between there's a +lot more crinkling. + +It's like here there's +a lot of crinkling. + +When I unfold it, +a lot more stuff + +happens in between +the four top paths. + +OK? + +Now, they wanted to +cut very simple shapes. + +In particular, shapes +that tiled the plane. + +So they ended up using squares +instead of the sort of optimal + +with that stretched paths +which are those four petals. + +So they used the yellow, +whereas you could just + +get away with the blue. + +Of course, you want to add +a little bit of material + +in the center so it +doesn't fall apart. + +And you need to thicken +the edges a little bit. + +So they care about that little +yellow minus blue savings? + +I'm not sure. + +But what about the triangle? + +We spend a lot of time +computing these shapes. + +It's some weird trigonometry. + +It's in the notes. + +Arc sine of sine over square +root of 1 over sine squared + +minus cos squared of +various parameters + +is the description of +one of these curves. + +So we did all this +computation and then + +we integrated it to compute +what these areas were and then-- + +or figure out exactly what these +shapes were, take the tangents, + +say, well, is the smallest +enclosing triangle better + +or worse than the square? + +It turns out it's +better by 0.1%. + +Now, I think-- millions +of Mozart Kugel + +are made every year. + +0.1% could equate +to huge savings. + +Dollars. + +But just think of +the material wastage + +that Furst is committing +by using the square. + +If they used the +triangle instead, + +I mean, this could +solve global warming. + +This could solve +chocolate melting. + +We actually talk about global +warming in the paper as a joke. + +It's a very funny paper. + +Very silly paper, I should say. + +Right. + +Let me tell you +another wrapping. + +Chalk. + +The comb wrapping. + +Comb wrapping, we're going +to use the same idea. + +Again-- do I really +want to draw this again? + +I'm going to draw those petals, +but instead of connecting them + +at the north pole, we're +going to connect them + +along the equator. + +This is actually what +happens-- oh, no. + +This is not-- this connects +them at the north pole I guess, + +and it folds them in half. + +Whatever. + +But I have the equator +nicely denoted here. + +So I want to keep the equator +as a new stretched path. + +I want that to unfold straight. + +But then attached to +it perpendicularly + +are all these +petals which unfold. + +So the result looks like this. + +Here's the equatorial stretched +path and here are the petals. + +Petals are exactly the +same shapes as before, + +so we still have stretched +pads perpendicular like that. + +But it's a new way +to cover every point + +on the sphere with +stretched paths. + +It leads to the blue unfoldings. + +You can take the smallest +enclosing rectangle + +and you get the yellow. + +What do I want to +say about these? + +They're the same +area, of course. + +They look a lot like these +old cartograms, cartographs-- + +whatever you call them-- +unfoldings of the earth. + +I thought I brought an earth. + +Maybe we didn't bring the earth. + +A globe, that is. + +You've seen pictures +maybe like this. + +They're not unfolded +in the same way. + +They don't have stretched +paths that are perpendicular. + +They use some other +projection, so their petals + +are a different shape. + +And I'm not sure that +they're contractive-- + +or inverse contractive maps. + +But same spirit anyway. + +Let's see. + +This one is the +Mirabell unfolding. + +Should I unfold another +just to illustrate? + +Going through chocolate +like crazy here. + +This is the really +hard one to unfold. + +So here's one corner-- +a little hard to see. + +Where's the equator going to be? + +I think the equator +is around here. + +That make sense? + +No. + +Actually it should be +perpendicular to that. + +Around here. + +This is a little harder to see. + +Here's a corner, actually. + +Tucked inside. + +I've been really curious +what kind of robots + +they have to do this. + +All right. + +Here's the equator. + +Now I can see it. + +So this-- the long +edge of the rectangle + +is wrapped around the equator. + +See it come off? + +And then the corners +are wrapped up + +against-- so there's +two-- well, yeah, + +these guys go on one side, +these guys go on the other. + +That's the short edge +of the rectangle. + +Now we can actually compute how +big these things are, right? + +So the-- where's the-- I +have a page about this. + +Not much. + +The vertical length, +that is one half equator. + +So that's pi. + +The horizontal length is 2pi. + +So this is Mirabell +rectangle, pi by 2pi. + +And we talked about +the Furst wrapping + +which, let's see, this length-- +so this goes like this. + +So this is 2pi, right? + +The diagonal is 2pi. + +So that means this edge +length is root 2pi. + +By root 2pi. + +And magically-- I don't +really have a great reason why + +this should be the case +but-- well, maybe I + +do-- but these +have the same area. + +Both 2pi squared. + +Which is like 6pi. + +So better than 9ish pi, but +still not quite as good as + +4ish pi. + +I have some exact numbers. + +More exact numbers? + +Oh, I have the perimeters. + +So the first wrapping, the +perimeter is 5.7 times pi. + +And the Mirabell +wrapping is 6 times pi. + +So reasonable +savings in perimeter. + +2pi squared. + +The equilateral +triangle wrapping-- + +that one in the top left-- +instead of 2pi squared, + +it has area 1.9983pi squared. + +That's the 0.1% improvement. + +Amazing. + +This was a surprise. + +We thought it'd be a fair +amount better or worse + +or the same or something. + +But almost the same. + +It's not what we expected. + +Let's see. + +I want to go to packing. + +What if you want to do better +than those simple convex + +shapes? + +Yeah, equilateral triangles and +squares and rectangles pack. + +But what if I tried to-- what +if I allowed non-convex shapes? + +I still want to tile +the plane, so I'm + +going to lose some +material for that. + +I could add some of this +material to the blue guy, some + +to the purple, some to the red. + +You can compute the +area of this thing + +and it does a lot better than +the equilateral triangle even. + +So now we're getting down there. + +The perimeter goes up a +little bit, but not by much. + +Packing three petals gives +1.6 times pi squared. + +Getting better. + +By the way, 4pi-- because I'm +going to speak in pi squareds + +now-- 4pi is about +1.27pi squared. + +OK. + +So what we want +is 1.27pi squared. + +At this point, we're at +1.6033 times pi squared. + +The comb does better. + +In the limit, you don't +lose zero here in the limit, + +but you lose quite little. + +In the limit you get +1.333 times pi squared. + +Versus 1.27. + +That's pretty good. + +I think this is-- this is +what we should manufacture. + +Maybe. + +Of course, the perimeter +goes to infinity also. + +Slight problem. + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: You don't +lose zero in the limit. + +For awhile we thought we did. + +You'll have to think about it. + +It's not obvious. + +Really, we have this +two dimensional space. + +It's called the +Pareto curve or-- it's + +a plot of perimeter on +the x-axis versus area + +on the y-axis. + +We want both to be small. + +So two-source +wrapping, for example, + +is pretty good in both metrics. + +That's where you take the +Voronoi diagram, both the north + +and south pole. + +So you actually +have two disks-- one + +for the southern hemisphere, one +for the northern hemisphere-- + +you get two disks and you +just attach them side by side. + +Although-- yeah. + +Let's see. + +What's this one? + +There's the Furst wrapping. + +So they're really good +in terms of perimeter. + +In fact, one of the +best perimeters we know. + +It's an open problem +how far left you can go. + +The stars are convex +hull of petal wrappings. + +Because the square was a convex +hull of a four petal wrapping. + +This is the convex of +the three petal wrapping. + +Now, that doesn't +actually tile, but it + +has the smallest +perimeter we now. + +So it's where you +take the three petals, + +but instead of completing +it to a triangle, + +you actually make the sharp +turn around the petal. + +So we have three +petals like this. + +And so the convex hull +is some tangent here. + +And then you follow +the petal for awhile. + +And then you take a +tangent, and then you + +follow the petal for a while, +and then you take a tangent. + +So that's the smallest +perimeter unfolding of a sphere + +that we know. + +Open problem. + +Can you do better? + +Can you get arbitrarily small? + +Probably not. + +Some isoperimetry problem. + +You can get arbitrarily +low area, arbitrarily + +close to the optimal of 4pi. + +That's like the strip wrapping. + +Let's see. + +So that's one limit. + +That corresponds to the limit +of petal or comb wrappings. + +Petal and comb wrappings, +if you don't take any hulls + +or anything, they are the same +area and the same perimeter. + +So I think out of +that you should + +be able to see why, in the +special case of the square + +and the rectangle, you +get the same stuff. + +There's a bijection +between all the parts. + +Not totally obvious. + +You have to dissect +a little bit. + +Mirabell wrappings, +they're not so good. + +What are those? + +The convex hull +of comb wrappings. + +So they're way out here. + +Clearly Furst is better. + +Here's the equilateral +triangle, which you can't tell, + +but it's slightly +below that dashed line. + +And pretty good perimeter but +not quite as good as Furst. + +So actually, probably, you +don't want to use the triangles. + +You prefer the lower perimeter. + +But this guy is interesting. + +Anyway, this is a fun space. + +What we kind of really +care about is-- this + +is called the Pareto curve. + +It's the, if I give you some +bound on perimeter, what's + +the smallest area I can get? + +This is the best +bound we know so far. + +And we know the Pareto +curves below this thing, + +but can you go lower? + +We don't know. + +So these are some fun examples, +but actually, the big questions + +are still pretty +much unsolved here. + +Even if you restrict +to-- I think + +it's fair to restrict to +wrappings of the sphere + +where every point +on the sphere gets + +covered by a stretched path. + +That seems like a nice, +natural class to think about. + +But we have no idea what +that hull space looks like. + +Can you do better than +these particular attempts? + +Looks like we're +doing pretty good, + +but we don't even know +how far left you can go. + +So a pretty neat question. + +And that is Mozart Kugel. + +Any questions? + +Other than, can I have some? + +AUDIENCE: Where can we get some? + +PROFESSOR: Where +can you get some. + +That's a good question. + +Most European airports +sell Mirabell. + +So if you're flying through +Europe, it's the place to go. + +Does anyone know if you +can get them locally? + +I think maybe. + +AUDIENCE: I think Cardullo's. + +PROFESSOR: Cardullo's +that's a good place. + +In Harvard Square. + +They have a lot of +imported chocolates. + +So, yeah, I think +they have Mirabell. + +AUDIENCE: [INAUDIBLE]. + +There's a lot of imported +chocolates and confectioneries + +in the Pru. + +PROFESSOR: In the +Prudential Center. + +All right. + +These I think you have +to go to Salzburg. + +Even in Austria +they're hard to get. + +So these are very special. + +I'll give Marty my second one. + +All right. + +That's all for today. + +Hey, there's one thing I forgot +to talk about in lecture which + +I think is really +cool so I'm going + +to add a little bit to +what we were talking about. + +We have all these +wrappings of the sphere + +but I never proved to that +they're actually contractive. + +How do you prove that all those +wrappings are contractive? + +Well, there's a cool theorem we +proved just for this purpose. + +I'll call it the Cauchy Arm +Lemma on a growing sphere. + +It's a nice little connection +to Cauchy's Arm Lemma + +which we talked about in the +context of Cauchy's rigidity + +theorem for polyhedral. + +Now, remember, +Cauchy's Arm Lemma + +is about you have +some convex chain-- + +and actually it applies both +on the plane and the sphere. + +So we're thinking +of an open chain + +but we had the property that +even if you add the closing + +edge it's convex. + +And then we looked at +a flex of the chain + +where all of the +angles increased + +and we said, if all +the angles increase, + +then this distance +increases, the endpoint-- + +the distance between +the endpoints increases. + +That's regular +Cauchy's Arm Lemma. + +But now I want to look at +not growing the angles, + +but growing the sphere +that the linkage lives on. + +So think of this in +the spherical case, + +which we'll-- imagine this +thing is on a sphere and now I + +transform it by taking a +larger sphere, larger radius, + +and drawing exactly the same +edge lengths and angles. + +Here, I'll draw it +a little bit curved + +because in reality these +edges are great circular arcs. + +So this edge length here +matches this length, + +this angle matches this +angle, this edge length + +matches this edge +length, and so on. + +But I draw it on +a bigger sphere. + +This theorem says, that the +distance between the endpoints + +will increase also in that case. + +So that's kind of neat. + +And in the limit, if you take a +ginormous sphere, all the way-- + +if you take a really, really +big sphere, it becomes a plane. + +So if I take +something on a sphere + +and then I actually draw it on +the plane with the same angle-- + +so this planar angle +matches this spherical angle + +and this length matches this +spherical length-- then, + +in particular, this +distance will increase. + +And in the reverse, if I +take a planar convex chain + +and I redraw it on some +sphere, the distance + +will go down provided +this thing is also convex. + +So that's the Lemma. + +Now, let me show you +how to use that to prove + +that all those wrappings +are contractive. + +It's really easy once +you have this Lemma. + +Let's start with +the source wrapping. + +So remember, we had a +sphere, the north pole, + +and we took all these shortest +paths from the north pole + +to the south pole. + +All of those lines-- I want +to claim that-- and when + +you unfold this you get a really +big disk and all those lines + +become straight. + +So what I need to show is that +between every pair of points, + +the distance decreases when +I go from flat to sphere. + +Which is exactly what +happened over here. + +I went from flat to the sphere, +this distance decreased. + +So that's how it's +going to be useful. + +If I take two points, like, +say, this point and this point. + +Any two points. + +They live on one of these +spokes that goes to the center. + +So draw those two +segments to the center + +which was the north pole here. + +So if I take the corresponding +two points up here, + +I'm looking at that +path and that path. + +Well, that's a convex chain +and the distance between them-- + +between those two points that +I started with, say, x and y, + +is exactly the closing +distance of that convex chain. + +So here's a convex chain, +it matches the angles + +and the lengths of this +convex chain and the plane. + +Therefore, this distance is +larger than this distance. + +And so this is a +contractive map because it + +works for any two +points x and y. + +So that's the source wrapping. + +With slightly more effort, +slightly more interesting + +example, is the petal wrappings. + +So think about one petal. + +So let's say I just take-- in +fact, just think about half + +of a petal. + +So we had a petal look +something like that + +going to the south pole here. + +And so we bisected this thing +and then we took lots of ribs + +like that. + +So that's one half petal. + +So when you unfold, +it looks like this. + +Take any two points +on the half petal. + +I'll show, first of all, that +the half petal is contractive. + +So I take two points, say, +this one and this one, + +call them x and y. + +Now I take this rib, +this rib and this rib. + +Those are the +stretched paths again. + +They map to whatever up here. + +Again, it's a +convex chain and so + +this distance increases +when you go to the sphere + +because it's convex +in both scenarios. + +So that's half petals. + +Now, when you worry +about a full petal + +and you want to show the +whole wrapping is expansive, + +you actually use a +different method. + +So let's say we take +a whole petal here. + +And I want to show not +only any pair of points + +within a single half petal +contract but, in fact, + +any two vertices, any +two points contract. + +So I'm going to take x +and some other point. + +Now I'll call it z. + +If I did the-- just looked +at the stretched paths, + +that's no longer convex. + +I can't use the same trick. + +But here's a new trick. + +I take a straight line, a +shortest path from x to z, + +which gives me a new +point y in the middle. + +Now I know that this +distance contracts + +because that's within +a single half petal. + +So by the previous +argument, and by looking + +at that little chain, I +know by this Arm Lemma + +that distance contracts, I know +that this distance contracts. + +So what about the +whole distance? + +Well, if I look at the +distance from x to z-- + +that's what I care about-- +let's say, in the plane, + +this equals the sum +of those distances. + +Because we drew a +straight line, it + +equals the distance from x to y +plus the distance from y to z. + +Now, I mapped these +onto the sphere, + +call that d prime is +the spherical distance. + +I know that when I look +at d prime I contract. + +So d prime of xy is going +to be smaller for xy, + +it's going to be smaller for yz. + +What I really care +about is the distance + +of the sphere between x and z. + +But this is the +triangle inequality. + +If you have a triangle xyz, +the distance from x to z + +is always, at most, +the distance from x + +to y plus the +distance from y to z. + +That holds in any metric space. + +So, in particular, it +holds on the sphere. + +So this is sort of trivial. + +This is triangle inequality. + +And this was the contractiveness +that we already prove. + +And this is just equal. + +And so we get that +the new distance + +is a contraction of +the old distance. + +So that works on a full petal. + +It actually-- this +exact same technique + +works if you have a +full petal unfolding. + +Maybe you have +something like this. + +And you take-- finish it off-- +you take two points anywhere + +on any two petals, +like here and here, you + +take the shortest +path between them + +and again, you +could argue, well, + +this is going to contract +because it is in a single half + +petal, this is going to +contract because it's + +in a single have petal. + +Therefore, that sum +will also contract + +by exactly the same argument. + +And you can use that for +the comb wrapping too. + +This is kind of neat +with this little Lemma + +about growing spheres and +showing the distances increase, + +you get to prove that all of +these wrappings are contractive + +and therefore all these +things I was claiming + +were working really do work. + +You can formalize that +in a simple little way. \ No newline at end of file diff --git a/dxNyJxI_2eI.txt b/dxNyJxI_2eI.txt new file mode 100644 index 0000000000000000000000000000000000000000..28db84482dcdfda229b03f55e6a7b5494abd515b --- /dev/null +++ b/dxNyJxI_2eI.txt @@ -0,0 +1,8125 @@ +align:start position:0% + +the following content is provided by MIT + + align:start position:0% +the following content is provided by MIT + + + align:start position:0% +the following content is provided by MIT +open courseware under a Creative Commons + + align:start position:0% +open courseware under a Creative Commons + + + align:start position:0% +open courseware under a Creative Commons +license additional information about our + + align:start position:0% +license additional information about our + + + align:start position:0% +license additional information about our +license and MIT open courseware in + + align:start position:0% +license and MIT open courseware in + + + align:start position:0% +license and MIT open courseware in +general is available at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay so I'll I'll start now + + align:start position:0% +ocw.mit.edu okay so I'll I'll start now + + + align:start position:0% +ocw.mit.edu okay so I'll I'll start now +with the third + + align:start position:0% +with the third + + + align:start position:0% +with the third +lecture and we're into partial + + align:start position:0% +lecture and we're into partial + + + align:start position:0% +lecture and we're into partial +differential equations so we had two on + + align:start position:0% +differential equations so we had two on + + + align:start position:0% +differential equations so we had two on +ordinary differential equations and the + + align:start position:0% +ordinary differential equations and the + + + align:start position:0% +ordinary differential equations and the +idea of stability came up and the Order + + align:start position:0% +idea of stability came up and the Order + + + align:start position:0% +idea of stability came up and the Order +of accuracy came up and those will be + + align:start position:0% +of accuracy came up and those will be + + + align:start position:0% +of accuracy came up and those will be +the key questions + + align:start position:0% +the key questions + + + align:start position:0% +the key questions +today accuracy and + + align:start position:0% +today accuracy and + + + align:start position:0% +today accuracy and +stability we do get beyond that actually + + align:start position:0% +stability we do get beyond that actually + + + align:start position:0% +stability we do get beyond that actually +actually to I mean to look at the uh + + align:start position:0% +actually to I mean to look at the uh + + + align:start position:0% +actually to I mean to look at the uh +Contour at the at the output from uh a + + align:start position:0% +Contour at the at the output from uh a + + + align:start position:0% +Contour at the at the output from uh a +difference method once you've decided + + align:start position:0% +difference method once you've decided + + + align:start position:0% +difference method once you've decided +yes it's stable yes it's accurate you + + align:start position:0% +yes it's stable yes it's accurate you + + + align:start position:0% +yes it's stable yes it's accurate you +still have to look at the output could + + align:start position:0% +still have to look at the output could + + + align:start position:0% +still have to look at the output could +and see you know how good is it where is + + align:start position:0% +and see you know how good is it where is + + + align:start position:0% +and see you know how good is it where is +it weak where is it where is it On + + align:start position:0% +it weak where is it where is it On + + + align:start position:0% +it weak where is it where is it On +Target but uh first come the accuracy + + align:start position:0% +Target but uh first come the accuracy + + + align:start position:0% +Target but uh first come the accuracy +and stability questions and beginning + + align:start position:0% +and stability questions and beginning + + + align:start position:0% +and stability questions and beginning +with this equation so this will be the + + align:start position:0% +with this equation so this will be the + + + align:start position:0% +with this equation so this will be the +simplest initial value problem we can + + align:start position:0% +simplest initial value problem we can + + + align:start position:0% +simplest initial value problem we can +think + + align:start position:0% +think + + + align:start position:0% +think +of uh I call it a one-way wave equation + + align:start position:0% +of uh I call it a one-way wave equation + + + align:start position:0% +of uh I call it a one-way wave equation +notice that the the the two-way wave + + align:start position:0% +notice that the the the two-way wave + + + align:start position:0% +notice that the the the two-way wave +equation which will get to would have + + align:start position:0% +equation which will get to would have + + + align:start position:0% +equation which will get to would have +second derivatives + + align:start position:0% +second derivatives + + + align:start position:0% +second derivatives +there and that will send waves in both + + align:start position:0% +there and that will send waves in both + + + align:start position:0% +there and that will send waves in both +directions this will'll see sends a wave + + align:start position:0% +directions this will'll see sends a wave + + + align:start position:0% +directions this will'll see sends a wave +only in One Direction so it's a nice + + align:start position:0% +only in One Direction so it's a nice + + + align:start position:0% +only in One Direction so it's a nice +scalar problem first order constant + + align:start position:0% +scalar problem first order constant + + + align:start position:0% +scalar problem first order constant +coefficient that's the velocity perfect + + align:start position:0% +coefficient that's the velocity perfect + + + align:start position:0% +coefficient that's the velocity perfect +as as the model problem for uh for the + + align:start position:0% +as as the model problem for uh for the + + + align:start position:0% +as as the model problem for uh for the +for wave + + align:start position:0% +for wave + + + align:start position:0% +for wave +equations and of course it begins with + + align:start position:0% +equations and of course it begins with + + + align:start position:0% +equations and of course it begins with +because it's just first order I only I + + align:start position:0% +because it's just first order I only I + + + align:start position:0% +because it's just first order I only I +have to I just begin it with the + + align:start position:0% +have to I just begin it with the + + + align:start position:0% +have to I just begin it with the +function + + align:start position:0% +function + + + align:start position:0% +function +at time + + align:start position:0% +at time + + + align:start position:0% +at time +zero so I'm looking for the solution at + + align:start position:0% +zero so I'm looking for the solution at + + + align:start position:0% +zero so I'm looking for the solution at +time T to this equation okay so that + + align:start position:0% +time T to this equation okay so that + + + align:start position:0% +time T to this equation okay so that +will not be hard to find and I want to + + align:start position:0% +will not be hard to find and I want to + + + align:start position:0% +will not be hard to find and I want to +do it first + + align:start position:0% +do it first + + + align:start position:0% +do it first +for uh pure exponentials When U of X Zer + + align:start position:0% +for uh pure exponentials When U of X Zer + + + align:start position:0% +for uh pure exponentials When U of X Zer +the initial function + + align:start position:0% +the initial function + + + align:start position:0% +the initial function +is a pure exponential e to the ikx + + align:start position:0% +is a pure exponential e to the ikx + + + align:start position:0% +is a pure exponential e to the ikx +because it really pays to get to Fier is + + align:start position:0% +because it really pays to get to Fier is + + + align:start position:0% +because it really pays to get to Fier is +always around and uh to see what happens + + align:start position:0% +always around and uh to see what happens + + + align:start position:0% +always around and uh to see what happens +suppose this is given for example so + + align:start position:0% +suppose this is given for example so + + + align:start position:0% +suppose this is given for example so +this will be my example e to the I + + align:start position:0% +this will be my example e to the I + + + align:start position:0% +this will be my example e to the I +KX Okay now what's special about e to + + align:start position:0% +KX Okay now what's special about e to + + + align:start position:0% +KX Okay now what's special about e to +the + + align:start position:0% +the + + + align:start position:0% +the +IX the special thing is that with + + align:start position:0% +IX the special thing is that with + + + align:start position:0% +IX the special thing is that with +constant coefficients and no No + + align:start position:0% +constant coefficients and no No + + + align:start position:0% +constant coefficients and no No +Boundaries the solution will be a + + align:start position:0% +Boundaries the solution will be a + + + align:start position:0% +Boundaries the solution will be a +multiple of e to the + + align:start position:0% +multiple of e to the + + + align:start position:0% +multiple of e to the +ikx in other words we can separate + + align:start position:0% +ikx in other words we can separate + + + align:start position:0% +ikx in other words we can separate +variables I can look for I'll maybe I'll + + align:start position:0% +variables I can look for I'll maybe I'll + + + align:start position:0% +variables I can look for I'll maybe I'll +put it here I can then look + + align:start position:0% + + + + align:start position:0% + +for the solution U to be a + + align:start position:0% +for the solution U to be a + + + align:start position:0% +for the solution U to be a +function times or or a number really but + + align:start position:0% +function times or or a number really but + + + align:start position:0% +function times or or a number really but +it will depend on the time on the + + align:start position:0% +it will depend on the time on the + + + align:start position:0% +it will depend on the time on the +frequency k and the time ttimes e to the + + align:start position:0% +frequency k and the time ttimes e to the + + + align:start position:0% +frequency k and the time ttimes e to the +IX you see how that's separated + + align:start position:0% +IX you see how that's separated + + + align:start position:0% +IX you see how that's separated +variables X is separated from + + align:start position:0% +variables X is separated from + + + align:start position:0% +variables X is separated from +T and the + + align:start position:0% +T and the + + + align:start position:0% +T and the +frequency uh controls what this growth + + align:start position:0% +frequency uh controls what this growth + + + align:start position:0% +frequency uh controls what this growth +factor will + + align:start position:0% +factor will + + + align:start position:0% +factor will +be so this growth factor is a key + + align:start position:0% +be so this growth factor is a key + + + align:start position:0% +be so this growth factor is a key +quantity to + + align:start position:0% +quantity to + + + align:start position:0% +quantity to +compute and we compute it just by + + align:start position:0% +compute and we compute it just by + + + align:start position:0% +compute and we compute it just by +substituting that hoped for solution + + align:start position:0% +substituting that hoped for solution + + + align:start position:0% +substituting that hoped for solution +into the equation + + align:start position:0% +into the equation + + + align:start position:0% +into the equation +and getting an equation for G because e + + align:start position:0% +and getting an equation for G because e + + + align:start position:0% +and getting an equation for G because e +to the I KX will cancel that's the + + align:start position:0% +to the I KX will cancel that's the + + + align:start position:0% +to the I KX will cancel that's the +that's the key point that that + + align:start position:0% +that's the key point that that + + + align:start position:0% +that's the key point that that +everything remains a pure harmonic with + + align:start position:0% +everything remains a pure harmonic with + + + align:start position:0% +everything remains a pure harmonic with +that single frequency K so if I plug it + + align:start position:0% +that single frequency K so if I plug it + + + align:start position:0% +that single frequency K so if I plug it +in I get + + align:start position:0% + + + + align:start position:0% + +dgdt I'm taking the time derivative of + + align:start position:0% +dgdt I'm taking the time derivative of + + + align:start position:0% +dgdt I'm taking the time derivative of +of U time e to the I KX right that's DT + + align:start position:0% +of U time e to the I KX right that's DT + + + align:start position:0% +of U time e to the I KX right that's DT +because T was separate from X that's + + align:start position:0% +because T was separate from X that's + + + align:start position:0% +because T was separate from X that's +what I get when I plug in this U so I'm + + align:start position:0% +what I get when I plug in this U so I'm + + + align:start position:0% +what I get when I plug in this U so I'm +always plugging in this U what do I get + + align:start position:0% +always plugging in this U what do I get + + + align:start position:0% +always plugging in this U what do I get +on the right hand side C the X + + align:start position:0% +on the right hand side C the X + + + align:start position:0% +on the right hand side C the X +derivative so that's just G the X + + align:start position:0% +derivative so that's just G the X + + + align:start position:0% +derivative so that's just G the X +derivative will bring down i k e to the + + align:start position:0% + + + + align:start position:0% + +ikx no surprise that I can cancel e to + + align:start position:0% +ikx no surprise that I can cancel e to + + + align:start position:0% +ikx no surprise that I can cancel e to +the IX which is never zero and I have a + + align:start position:0% +the IX which is never zero and I have a + + + align:start position:0% +the IX which is never zero and I have a +simple equ equation for + + align:start position:0% +simple equ equation for + + + align:start position:0% +simple equ equation for +G linear constant coefficients but the + + align:start position:0% +G linear constant coefficients but the + + + align:start position:0% +G linear constant coefficients but the +coefficient depends on K of course the + + align:start position:0% +coefficient depends on K of course the + + + align:start position:0% +coefficient depends on K of course the +coefficient is i k and of course the + + align:start position:0% +coefficient is i k and of course the + + + align:start position:0% +coefficient is i k and of course the +solution + + align:start position:0% +solution + + + align:start position:0% +solution +is G is equal to well this is our we're + + align:start position:0% +is G is equal to well this is our we're + + + align:start position:0% +is G is equal to well this is our we're +back to our simplest model of an + + align:start position:0% +back to our simplest model of an + + + align:start position:0% +back to our simplest model of an +ordinary differential equation with the + + align:start position:0% +ordinary differential equation with the + + + align:start position:0% +ordinary differential equation with the +now the coefficient a is now ikc so it's + + align:start position:0% +now the coefficient a is now ikc so it's + + + align:start position:0% +now the coefficient a is now ikc so it's +e to the ik K CT + + align:start position:0% + + + + align:start position:0% + +right that shows us what happens to the + + align:start position:0% +right that shows us what happens to the + + + align:start position:0% +right that shows us what happens to the +to the e to the I KX so now I'll put + + align:start position:0% +to the e to the I KX so now I'll put + + + align:start position:0% +to the e to the I KX so now I'll put +that here because now we know it so it's + + align:start position:0% +that here because now we know it so it's + + + align:start position:0% +that here because now we know it so it's +we have all together e to the i k CT and + + align:start position:0% +we have all together e to the i k CT and + + + align:start position:0% +we have all together e to the i k CT and +here's an X so let's put those together + + align:start position:0% +here's an X so let's put those together + + + align:start position:0% +here's an X so let's put those together +as X Plus CT because + + align:start position:0% +as X Plus CT because + + + align:start position:0% +as X Plus CT because +that's a GU a guide to what's coming so + + align:start position:0% +that's a GU a guide to what's coming so + + + align:start position:0% +that's a GU a guide to what's coming so +that's the solution separate ated + + align:start position:0% +that's the solution separate ated + + + align:start position:0% +that's the solution separate ated +variables looked for the growth factor + + align:start position:0% +variables looked for the growth factor + + + align:start position:0% +variables looked for the growth factor +tried an exponential and we'll do + + align:start position:0% +tried an exponential and we'll do + + + align:start position:0% +tried an exponential and we'll do +exactly the same thing for difference + + align:start position:0% +exactly the same thing for difference + + + align:start position:0% +exactly the same thing for difference +methods so this was Von neyman's + + align:start position:0% +methods so this was Von neyman's + + + align:start position:0% +methods so this was Von neyman's +brilliant idea watch exponentials watch + + align:start position:0% +brilliant idea watch exponentials watch + + + align:start position:0% +brilliant idea watch exponentials watch +every frequency and see what happens to + + align:start position:0% +every frequency and see what happens to + + + align:start position:0% +every frequency and see what happens to +the to the multiple of e to the ikx now + + align:start position:0% +the to the multiple of e to the ikx now + + + align:start position:0% +the to the multiple of e to the ikx now +here is very special because all + + align:start position:0% +here is very special because all + + + align:start position:0% +here is very special because all +frequencies are producing this + + align:start position:0% +frequencies are producing this + + + align:start position:0% +frequencies are producing this +combination X plus c + + align:start position:0% +combination X plus c + + + align:start position:0% +combination X plus c +T so when we combine + + align:start position:0% +T so when we combine + + + align:start position:0% +T so when we combine +frequencies that's what forier said take + + align:start position:0% +frequencies that's what forier said take + + + align:start position:0% +frequencies that's what forier said take +combinations of these + + align:start position:0% +combinations of these + + + align:start position:0% +combinations of these +things the solution will be a + + align:start position:0% +things the solution will be a + + + align:start position:0% +things the solution will be a +combination of these + + align:start position:0% +combination of these + + + align:start position:0% +combination of these +things and what do we get we if our + + align:start position:0% +things and what do we get we if our + + + align:start position:0% +things and what do we get we if our +original function was U of X and zero + + align:start position:0% +original function was U of X and zero + + + align:start position:0% +original function was U of X and zero +It's a combination of these e to the + + align:start position:0% +It's a combination of these e to the + + + align:start position:0% +It's a combination of these e to the +ix's and then what then the at lat time + + align:start position:0% +ix's and then what then the at lat time + + + align:start position:0% +ix's and then what then the at lat time +we have the same combination by + + align:start position:0% +we have the same combination by + + + align:start position:0% +we have the same combination by +linearity of these + + align:start position:0% + + + + align:start position:0% + +guys all all that's happening + + align:start position:0% +guys all all that's happening + + + align:start position:0% +guys all all that's happening +is X is getting changed to X Plus + + align:start position:0% +is X is getting changed to X Plus + + + align:start position:0% +is X is getting changed to X Plus +CT U of X so so I'm getting the answer U + + align:start position:0% +CT U of X so so I'm getting the answer U + + + align:start position:0% +CT U of X so so I'm getting the answer U +of X and so I here here was the answer + + align:start position:0% +of X and so I here here was the answer + + + align:start position:0% +of X and so I here here was the answer +here was the answer for for one + + align:start position:0% +here was the answer for for one + + + align:start position:0% +here was the answer for for one +exponential but now I'm going to do the + + align:start position:0% +exponential but now I'm going to do the + + + align:start position:0% +exponential but now I'm going to do the +answer for a general U and it's it's + + align:start position:0% +answer for a general U and it's it's + + + align:start position:0% +answer for a general U and it's it's +going to be easy to pick off it's just + + align:start position:0% +going to be easy to pick off it's just + + + align:start position:0% +going to be easy to pick off it's just +like picking off this X Plus CT it'll be + + align:start position:0% +like picking off this X Plus CT it'll be + + + align:start position:0% +like picking off this X Plus CT it'll be +U at X+ + + align:start position:0% +U at X+ + + + align:start position:0% +U at X+ +CT at time zero that's the + + align:start position:0% +CT at time zero that's the + + + align:start position:0% +CT at time zero that's the +solution for every U not just for the + + align:start position:0% +solution for every U not just for the + + + align:start position:0% +solution for every U not just for the +exponentials but for all combinations of + + align:start position:0% +exponentials but for all combinations of + + + align:start position:0% +exponentials but for all combinations of +them which give us any U of X and zero + + align:start position:0% +them which give us any U of X and zero + + + align:start position:0% +them which give us any U of X and zero +so U of x and z is a combination of the + + align:start position:0% +so U of x and z is a combination of the + + + align:start position:0% +so U of x and z is a combination of the +e to the + + align:start position:0% +e to the + + + align:start position:0% +e to the +IX and then and the solution is the same + + align:start position:0% +IX and then and the solution is the same + + + align:start position:0% +IX and then and the solution is the same +combination of these guys well we + + align:start position:0% +combination of these guys well we + + + align:start position:0% +combination of these guys well we +can understand what that solution + + align:start position:0% +can understand what that solution + + + align:start position:0% +can understand what that solution +is it's what I call a one-way wave let + + align:start position:0% +is it's what I call a one-way wave let + + + align:start position:0% +is it's what I call a one-way wave let +let + + align:start position:0% +let + + + align:start position:0% +let +me understand what's happening here here + + align:start position:0% +me understand what's happening here here + + + align:start position:0% +me understand what's happening here here +so here's the key picture now the key + + align:start position:0% +so here's the key picture now the key + + + align:start position:0% +so here's the key picture now the key +picture in let's see boards + + align:start position:0% +picture in let's see boards + + + align:start position:0% +picture in let's see boards +there I want to draw a + + align:start position:0% +there I want to draw a + + + align:start position:0% +there I want to draw a +picture in the XT place so this I'm not + + align:start position:0% +picture in the XT place so this I'm not + + + align:start position:0% +picture in the XT place so this I'm not +graphing you here this is a picture in + + align:start position:0% +graphing you here this is a picture in + + + align:start position:0% +graphing you here this is a picture in +the XT plane + + align:start position:0% +the XT plane + + + align:start position:0% +the XT plane +of that that will show us what this + + align:start position:0% +of that that will show us what this + + + align:start position:0% +of that that will show us what this +formula means because this is the this + + align:start position:0% +formula means because this is the this + + + align:start position:0% +formula means because this is the this +is the solution that we then want to + + align:start position:0% +is the solution that we then want to + + + align:start position:0% +is the solution that we then want to +approximate by difference method okay so + + align:start position:0% +approximate by difference method okay so + + + align:start position:0% +approximate by difference method okay so +what does this + + align:start position:0% +what does this + + + align:start position:0% +what does this +mean this means that the value for + + align:start position:0% +mean this means that the value for + + + align:start position:0% +mean this means that the value for +example U of 0 0 so there's the point 0 + + align:start position:0% +example U of 0 0 so there's the point 0 + + + align:start position:0% +example U of 0 0 so there's the point 0 + + align:start position:0% + + + align:start position:0% +U of Z + + align:start position:0% +U of Z + + + align:start position:0% +U of Z +0 at a late at a later time here here's + + align:start position:0% +0 at a late at a later time here here's + + + align:start position:0% +0 at a late at a later time here here's +what's happening at a later time say up + + align:start position:0% +what's happening at a later time say up + + + align:start position:0% +what's happening at a later time say up +here some later time the value of U this + + align:start position:0% +here some later time the value of U this + + + align:start position:0% +here some later time the value of U this +is this is this is the + + align:start position:0% +is this is this is the + + + align:start position:0% +is this is this is the +line x + ctal + + align:start position:0% +line x + ctal + + + align:start position:0% +line x + ctal +0 X Plus CT = zero along that + + align:start position:0% +0 X Plus CT = zero along that + + + align:start position:0% +0 X Plus CT = zero along that +line and what's the point on that line + + align:start position:0% +line and what's the point on that line + + + align:start position:0% +line and what's the point on that line +solution is the same all the way along + + align:start position:0% +solution is the same all the way along + + + align:start position:0% +solution is the same all the way along +so whatever the initial value is here + + align:start position:0% +so whatever the initial value is here + + + align:start position:0% +so whatever the initial value is here +it it + + align:start position:0% +it it + + + align:start position:0% +it it +travels so the U at this point is U at + + align:start position:0% +travels so the U at this point is U at + + + align:start position:0% +travels so the U at this point is U at +this point so let me call that point p + + align:start position:0% +this point so let me call that point p + + + align:start position:0% +this point so let me call that point p +and and and say what I mean now I mean + + align:start position:0% +and and and say what I mean now I mean + + + align:start position:0% +and and and say what I mean now I mean +that U at p is the same as U at + + align:start position:0% +that U at p is the same as U at + + + align:start position:0% +that U at p is the same as U at + + align:start position:0% + + + align:start position:0% +because X Plus CT is the same here and + + align:start position:0% +because X Plus CT is the same here and + + + align:start position:0% +because X Plus CT is the same here and +here uh + + align:start position:0% +here uh + + + align:start position:0% +here uh +so and let me take another Point another + + align:start position:0% +so and let me take another Point another + + + align:start position:0% +so and let me take another Point another +Point let's say + + align:start position:0% +Point let's say + + + align:start position:0% +Point let's say +x0 another initial value then again + + align:start position:0% +x0 another initial value then again + + + align:start position:0% +x0 another initial value then again +along a line like this this will be the + + align:start position:0% +along a line like this this will be the + + + align:start position:0% +along a line like this this will be the +line X+ CT equals capital x because it + + align:start position:0% +line X+ CT equals capital x because it + + + align:start position:0% +line X+ CT equals capital x because it +it's the line where X Plus CT is a + + align:start position:0% +it's the line where X Plus CT is a + + + align:start position:0% +it's the line where X Plus CT is a +constant and it's the L and and the + + align:start position:0% +constant and it's the L and and the + + + align:start position:0% +constant and it's the L and and the +constant is chosen so that it starts at + + align:start position:0% +constant is chosen so that it starts at + + + align:start position:0% +constant is chosen so that it starts at +this point at T equals 0 x is Big X so + + align:start position:0% +this point at T equals 0 x is Big X so + + + align:start position:0% +this point at T equals 0 x is Big X so +now let's see I better make clear that + + align:start position:0% +now let's see I better make clear that + + + align:start position:0% +now let's see I better make clear that +this + + align:start position:0% +this + + + align:start position:0% +this +line carries this initial value this + + align:start position:0% +line carries this initial value this + + + align:start position:0% +line carries this initial value this +line carries this initial value so the + + align:start position:0% +line carries this initial value so the + + + align:start position:0% +line carries this initial value so the +values do you see it the value of U all + + align:start position:0% +values do you see it the value of U all + + + align:start position:0% +values do you see it the value of U all +along this line is this is the value it + + align:start position:0% +along this line is this is the value it + + + align:start position:0% +along this line is this is the value it +started with right there and do you know + + align:start position:0% +started with right there and do you know + + + align:start position:0% +started with right there and do you know +the name for those + + align:start position:0% +the name for those + + + align:start position:0% +the name for those +lines so these SE are + + align:start position:0% +lines so these SE are + + + align:start position:0% +lines so these SE are +lines they happen to be straight here + + align:start position:0% +lines they happen to be straight here + + + align:start position:0% +lines they happen to be straight here +because we got constant + + align:start position:0% +because we got constant + + + align:start position:0% +because we got constant +coefficients straight and even + + align:start position:0% +coefficients straight and even + + + align:start position:0% +coefficients straight and even +parallel and they're the lines on which + + align:start position:0% +parallel and they're the lines on which + + + align:start position:0% +parallel and they're the lines on which +the information travels whatever the + + align:start position:0% +the information travels whatever the + + + align:start position:0% +the information travels whatever the +information was at time + + align:start position:0% +information was at time + + + align:start position:0% +information was at time +Z by information I mean the value of U + + align:start position:0% +Z by information I mean the value of U + + + align:start position:0% +Z by information I mean the value of U +at Z 0 or the value of U at this point + + align:start position:0% +at Z 0 or the value of U at this point + + + align:start position:0% +at Z 0 or the value of U at this point +that information travels along that line + + align:start position:0% +that information travels along that line + + + align:start position:0% +that information travels along that line +to give the solution all on the line and + + align:start position:0% +to give the solution all on the line and + + + align:start position:0% +to give the solution all on the line and +the name of the line anybody know it + + align:start position:0% +the name of the line anybody know it + + + align:start position:0% +the name of the line anybody know it +characteristic so this is a this is a + + align:start position:0% +characteristic so this is a this is a + + + align:start position:0% +characteristic so this is a this is a +characteristic + + align:start position:0% + + + + align:start position:0% + +line they + + align:start position:0% + + + + align:start position:0% + +all this two all these lines are + + align:start position:0% +all this two all these lines are + + + align:start position:0% +all this two all these lines are +characteristic lines can you read + + align:start position:0% +characteristic lines can you read + + + align:start position:0% +characteristic lines can you read +characteristic should have written it a + + align:start position:0% +characteristic should have written it a + + + align:start position:0% +characteristic should have written it a +little + + align:start position:0% +little + + + align:start position:0% +little +better so this is like a + + align:start position:0% +better so this is like a + + + align:start position:0% +better so this is like a +feature a key key feature of wave + + align:start position:0% +feature a key key feature of wave + + + align:start position:0% +feature a key key feature of wave +equations it's a key feature of wave + + align:start position:0% +equations it's a key feature of wave + + + align:start position:0% +equations it's a key feature of wave +equations that we will not see for heat + + align:start position:0% +equations that we will not see for heat + + + align:start position:0% +equations that we will not see for heat +equation and uh so let me just say it + + align:start position:0% +equation and uh so let me just say it + + + align:start position:0% +equation and uh so let me just say it +again because it will it will bear also + + align:start position:0% +again because it will it will bear also + + + align:start position:0% +again because it will it will bear also +on the stability question for difference + + align:start position:0% +on the stability question for difference + + + align:start position:0% +on the stability question for difference +equations the information the true + + align:start position:0% +equations the information the true + + + align:start position:0% +equations the information the true +information for the true solution + + align:start position:0% +information for the true solution + + + align:start position:0% +information for the true solution +travels along characteristic + + align:start position:0% +travels along characteristic + + + align:start position:0% +travels along characteristic +lines + + align:start position:0% +lines + + + align:start position:0% +lines +that we're in one dimension here and + + align:start position:0% +that we're in one dimension here and + + + align:start position:0% +that we're in one dimension here and +which is a ma major simplification in + + align:start position:0% +which is a ma major simplification in + + + align:start position:0% +which is a ma major simplification in +two Dimensions will have characteristic + + align:start position:0% +two Dimensions will have characteristic + + + align:start position:0% +two Dimensions will have characteristic +cones or three dimensions certainly we + + align:start position:0% +cones or three dimensions certainly we + + + align:start position:0% +cones or three dimensions certainly we +would call it a cone and actually I + + align:start position:0% +would call it a cone and actually I + + + align:start position:0% +would call it a cone and actually I +guess what I'm saying is that if I speak + + align:start position:0% +guess what I'm saying is that if I speak + + + align:start position:0% +guess what I'm saying is that if I speak +a + + align:start position:0% +a + + + align:start position:0% +a +word if if you know my voice or the + + align:start position:0% +word if if you know my voice or the + + + align:start position:0% +word if if you know my voice or the +sound waves solve the 3D wave equation + + align:start position:0% +sound waves solve the 3D wave equation + + + align:start position:0% +sound waves solve the 3D wave equation +equation so when I snap my + + align:start position:0% +equation so when I snap my + + + align:start position:0% +equation so when I snap my +fingers that sound travels from this + + align:start position:0% +fingers that sound travels from this + + + align:start position:0% +fingers that sound travels from this +point out uh in along along + + align:start position:0% + + + + align:start position:0% + +characteristics and of course it travels + + align:start position:0% +characteristics and of course it travels + + + align:start position:0% +characteristics and of course it travels +in all directions so we've + + align:start position:0% +in all directions so we've + + + align:start position:0% +in all directions so we've +got a more interesting more complicated + + align:start position:0% +got a more interesting more complicated + + + align:start position:0% +got a more interesting more complicated +picture in higher Dimensions but we + + align:start position:0% +picture in higher Dimensions but we + + + align:start position:0% +picture in higher Dimensions but we +really see it here in one dimension okay + + align:start position:0% +really see it here in one dimension okay + + + align:start position:0% +really see it here in one dimension okay +now + + align:start position:0% +now + + + align:start position:0% +now +uh now I should also include a graph of + + align:start position:0% +uh now I should also include a graph of + + + align:start position:0% +uh now I should also include a graph of +the solution what does the solution look + + align:start position:0% +the solution what does the solution look + + + align:start position:0% +the solution what does the solution look +like maybe I'll find a spot here for + + align:start position:0% +like maybe I'll find a spot here for + + + align:start position:0% +like maybe I'll find a spot here for +that + + align:start position:0% +that + + + align:start position:0% +that +graph suppose the initial function now + + align:start position:0% +graph suppose the initial function now + + + align:start position:0% +graph suppose the initial function now +now I'm going to graph + + align:start position:0% +now I'm going to graph + + + align:start position:0% +now I'm going to graph +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +you this is still X so I'll graph you at + + align:start position:0% +you this is still X so I'll graph you at + + + align:start position:0% +you this is still X so I'll graph you at +maybe two different times so the + + align:start position:0% +maybe two different times so the + + + align:start position:0% +maybe two different times so the +starting time suppose we have a wall of + + align:start position:0% +starting time suppose we have a wall of + + + align:start position:0% +starting time suppose we have a wall of +water suppose this is so so this will be + + align:start position:0% +water suppose this is so so this will be + + + align:start position:0% +water suppose this is so so this will be +U of X and zero a step function maybe + + align:start position:0% +U of X and zero a step function maybe + + + align:start position:0% +U of X and zero a step function maybe +maybe at + + align:start position:0% +maybe at + + + align:start position:0% +maybe at +zero so U of x and z is one and then + + align:start position:0% +zero so U of x and z is one and then + + + align:start position:0% +zero so U of x and z is one and then +zero + + align:start position:0% +zero + + + align:start position:0% +zero +okay so there's a there's a typical + + align:start position:0% +okay so there's a there's a typical + + + align:start position:0% +okay so there's a there's a typical +starting initial value + + align:start position:0% +starting initial value + + + align:start position:0% +starting initial value +value uh well I don't know if it's + + align:start position:0% +value uh well I don't know if it's + + + align:start position:0% +value uh well I don't know if it's +typical pretty special to have one and + + align:start position:0% +typical pretty special to have one and + + + align:start position:0% +typical pretty special to have one and +then zero perfect step function but this + + align:start position:0% +then zero perfect step function but this + + + align:start position:0% +then zero perfect step function but this +will illustrate what's now I want to ask + + align:start position:0% +will illustrate what's now I want to ask + + + align:start position:0% +will illustrate what's now I want to ask +what's the solution to the equation what + + align:start position:0% +what's the solution to the equation what + + + align:start position:0% +what's the solution to the equation what +is you of x and t + + align:start position:0% +is you of x and t + + + align:start position:0% +is you of x and t +now I want to graph U of x and t what + + align:start position:0% +now I want to graph U of x and t what + + + align:start position:0% +now I want to graph U of x and t what +what happens do you you have to assemble + + align:start position:0% +what happens do you you have to assemble + + + align:start position:0% +what happens do you you have to assemble +sort of this picture which is in the XT + + align:start position:0% +sort of this picture which is in the XT + + + align:start position:0% +sort of this picture which is in the XT +plane now I into a graph here of U of x + + align:start position:0% +plane now I into a graph here of U of x + + + align:start position:0% +plane now I into a graph here of U of x +and t What Happens well all these zero + + align:start position:0% +and t What Happens well all these zero + + + align:start position:0% +and t What Happens well all these zero +starting values travel along + + align:start position:0% +starting values travel along + + + align:start position:0% +starting values travel along +characteristics and tell us that U is + + align:start position:0% +characteristics and tell us that U is + + + align:start position:0% +characteristics and tell us that U is +zero along all these character so along + + align:start position:0% +zero along all these character so along + + + align:start position:0% +zero along all these character so along +all these + + align:start position:0% +all these + + + align:start position:0% +all these +characteristics U is + + align:start position:0% +characteristics U is + + + align:start position:0% +characteristics U is +zero this here the starting value is one + + align:start position:0% +zero this here the starting value is one + + + align:start position:0% +zero this here the starting value is one +so along these + + align:start position:0% + + + + align:start position:0% + +characteristics we're starting with a + + align:start position:0% +characteristics we're starting with a + + + align:start position:0% +characteristics we're starting with a +one the we end with a one do you see + + align:start position:0% +one the we end with a one do you see + + + align:start position:0% +one the we end with a one do you see +what happens the the uh how do I graph + + align:start position:0% +what happens the the uh how do I graph + + + align:start position:0% +what happens the the uh how do I graph +it the wave is moving the wall of water + + align:start position:0% +it the wave is moving the wall of water + + + align:start position:0% +it the wave is moving the wall of water +is moving that way moving to the left + + align:start position:0% +is moving that way moving to the left + + + align:start position:0% +is moving that way moving to the left +because I'm taking C to be a positive + + align:start position:0% +because I'm taking C to be a positive + + + align:start position:0% +because I'm taking C to be a positive +number so so U of x and t is a wall a + + align:start position:0% +number so so U of x and t is a wall a + + + align:start position:0% +number so so U of x and t is a wall a +wave or a wave you could say + + align:start position:0% +wave or a wave you could say + + + align:start position:0% +wave or a wave you could say +moving + + align:start position:0% +moving + + + align:start position:0% +moving +left + + align:start position:0% +left + + + align:start position:0% +left +with + + align:start position:0% +with + + + align:start position:0% +with +speed + + align:start position:0% +speed + + + align:start position:0% +speed +C every every solution to the equation + + align:start position:0% +C every every solution to the equation + + + align:start position:0% +C every every solution to the equation +is doing this and in this particular + + align:start position:0% +is doing this and in this particular + + + align:start position:0% +is doing this and in this particular +case it's a wall of water and it stays a + + align:start position:0% +case it's a wall of water and it stays a + + + align:start position:0% +case it's a wall of water and it stays a +wall of water that that's the point + + align:start position:0% +wall of water that that's the point + + + align:start position:0% +wall of water that that's the point +shapes are not uh changed as we go + + align:start position:0% +shapes are not uh changed as we go + + + align:start position:0% +shapes are not uh changed as we go +there's + + align:start position:0% +there's + + + align:start position:0% +there's +no dispersion would be the right word I + + align:start position:0% +no dispersion would be the right word I + + + align:start position:0% +no dispersion would be the right word I +think uh we would expect in a general + + align:start position:0% +think uh we would expect in a general + + + align:start position:0% +think uh we would expect in a general +equation that the shape of the wave + + align:start position:0% +equation that the shape of the wave + + + align:start position:0% +equation that the shape of the wave +would change a little as it + + align:start position:0% +would change a little as it + + + align:start position:0% +would change a little as it +travels in this equation it doesn't + + align:start position:0% +travels in this equation it doesn't + + + align:start position:0% +travels in this equation it doesn't +change the shape stays the same and the + + align:start position:0% +change the shape stays the same and the + + + align:start position:0% +change the shape stays the same and the +and all frequencies see again I'm + + align:start position:0% +and all frequencies see again I'm + + + align:start position:0% +and all frequencies see again I'm +thinking of this wave as a combination + + align:start position:0% +thinking of this wave as a combination + + + align:start position:0% +thinking of this wave as a combination +of pure exponentials and they all travel + + align:start position:0% +of pure exponentials and they all travel + + + align:start position:0% +of pure exponentials and they all travel +with the same speed C so the whole wave + + align:start position:0% +with the same speed C so the whole wave + + + align:start position:0% +with the same speed C so the whole wave +travels with speed C and I at a later + + align:start position:0% +travels with speed C and I at a later + + + align:start position:0% +travels with speed C and I at a later +time that's what uh that's the graph of + + align:start position:0% +time that's what uh that's the graph of + + + align:start position:0% +time that's what uh that's the graph of +the + + align:start position:0% +the + + + align:start position:0% +the +solution + + align:start position:0% +solution + + + align:start position:0% +solution +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so that that that much + + align:start position:0% +so that that that much + + + align:start position:0% +so that that that much +is all we have to do all we can do + + align:start position:0% +is all we have to do all we can do + + + align:start position:0% +is all we have to do all we can do +really in solving the differential + + align:start position:0% + + + + align:start position:0% + +equation it's a simple model certainly + + align:start position:0% +equation it's a simple model certainly + + + align:start position:0% +equation it's a simple model certainly +but now I come to the difference + + align:start position:0% +but now I come to the difference + + + align:start position:0% +but now I come to the difference +equation well when I say the difference + + align:start position:0% +equation well when I say the difference + + + align:start position:0% +equation well when I say the difference +equation I should say + + align:start position:0% +equation I should say + + + align:start position:0% +equation I should say +equations plural because here I've + + align:start position:0% +equations plural because here I've + + + align:start position:0% +equations plural because here I've +written four + + align:start position:0% + + + + align:start position:0% + +possibilities um three of them are + + align:start position:0% +possibilities um three of them are + + + align:start position:0% +possibilities um three of them are +actually + + align:start position:0% +actually + + + align:start position:0% +actually +used and one is a + + align:start position:0% +used and one is a + + + align:start position:0% +used and one is a +disaster so we have and there + + align:start position:0% +disaster so we have and there + + + align:start position:0% +disaster so we have and there +and but no none of the none of the four + + align:start position:0% +and but no none of the none of the four + + + align:start position:0% +and but no none of the none of the four +is perfect uh most people would say LAX + + align:start position:0% +is perfect uh most people would say LAX + + + align:start position:0% +is perfect uh most people would say LAX +wend is the best of these + + align:start position:0% +wend is the best of these + + + align:start position:0% +wend is the best of these +four because it has one extra order of + + align:start position:0% +four because it has one extra order of + + + align:start position:0% +four because it has one extra order of +accuracy and and we've seen that to move + + align:start position:0% +accuracy and and we've seen that to move + + + align:start position:0% +accuracy and and we've seen that to move +the these oh yeah yeah I guess these all + + align:start position:0% +the these oh yeah yeah I guess these all + + + align:start position:0% +the these oh yeah yeah I guess these all +have only first order + + align:start position:0% + + + + align:start position:0% + +accuracy but LAX wend moves up to Second + + align:start position:0% +accuracy but LAX wend moves up to Second + + + align:start position:0% +accuracy but LAX wend moves up to Second +so that's a kind of a key it's a method + + align:start position:0% +so that's a kind of a key it's a method + + + align:start position:0% +so that's a kind of a key it's a method +everybody knows because it gets up to + + align:start position:0% +everybody knows because it gets up to + + + align:start position:0% +everybody knows because it gets up to +say but actually up when up when is the + + align:start position:0% +say but actually up when up when is the + + + align:start position:0% +say but actually up when up when is the +first one to start with let let me start + + align:start position:0% +first one to start with let let me start + + + align:start position:0% +first one to start with let let me start +with that one okay so I've multiplied up + + align:start position:0% +with that one okay so I've multiplied up + + + align:start position:0% +with that one okay so I've multiplied up +by the delta T that should be in the + + align:start position:0% +by the delta T that should be in the + + + align:start position:0% +by the delta T that should be in the +denominator there so that especially so + + align:start position:0% +denominator there so that especially so + + + align:start position:0% +denominator there so that especially so +that you would see so upwind or forward + + align:start position:0% +that you would see so upwind or forward + + + align:start position:0% +that you would see so upwind or forward +difference I'm taking the standard + + align:start position:0% +difference I'm taking the standard + + + align:start position:0% +difference I'm taking the standard +forward difference in time all these + + align:start position:0% +forward difference in time all these + + + align:start position:0% +forward difference in time all these +methods are going to be + + align:start position:0% +methods are going to be + + + align:start position:0% +methods are going to be +explicit so they're all going to be + + align:start position:0% +explicit so they're all going to be + + + align:start position:0% +explicit so they're all going to be +solvable able simp in a simple way for + + align:start position:0% +solvable able simp in a simple way for + + + align:start position:0% +solvable able simp in a simple way for +you at the new time so a forward + + align:start position:0% +you at the new time so a forward + + + align:start position:0% +you at the new time so a forward +difference in time for + + align:start position:0% +difference in time for + + + align:start position:0% +difference in time for +dudt and c times a forward difference in + + align:start position:0% +dudt and c times a forward difference in + + + align:start position:0% +dudt and c times a forward difference in +space for dudx so that's the first idea + + align:start position:0% +space for dudx so that's the first idea + + + align:start position:0% +space for dudx so that's the first idea +that would occur to you and it's pretty + + align:start position:0% +that would occur to you and it's pretty + + + align:start position:0% +that would occur to you and it's pretty +reasonable we we can check its accuracy + + align:start position:0% +reasonable we we can check its accuracy + + + align:start position:0% +reasonable we we can check its accuracy +but you can guess what it will be what + + align:start position:0% +but you can guess what it will be what + + + align:start position:0% +but you can guess what it will be what +what's your guess on the accuracy of + + align:start position:0% +what's your guess on the accuracy of + + + align:start position:0% +what's your guess on the accuracy of +this + + align:start position:0% +this + + + align:start position:0% +this +method + + align:start position:0% +method + + + align:start position:0% +method +you're seeing a forward difference in + + align:start position:0% +you're seeing a forward difference in + + + align:start position:0% +you're seeing a forward difference in +time a forward difference in Space the + + align:start position:0% +time a forward difference in Space the + + + align:start position:0% +time a forward difference in Space the +odds are those finite differences give + + align:start position:0% +odds are those finite differences give + + + align:start position:0% +odds are those finite differences give +you a accuracy P if we use p as the + + align:start position:0% +you a accuracy P if we use p as the + + + align:start position:0% +you a accuracy P if we use p as the +measure of accuracy which would be + + align:start position:0% + + + + align:start position:0% + +probably one first order AC so we'll + + align:start position:0% +probably one first order AC so we'll + + + align:start position:0% +probably one first order AC so we'll +we'll we'll see the accuracy as only P + + align:start position:0% +we'll we'll see the accuracy as only P + + + align:start position:0% +we'll we'll see the accuracy as only P +equal to one here + + align:start position:0% +equal to one here + + + align:start position:0% +equal to one here +okay what about the + + align:start position:0% +okay what about the + + + align:start position:0% +okay what about the +stability I'm looking at this first + + align:start position:0% +stability I'm looking at this first + + + align:start position:0% +stability I'm looking at this first +method because there so one comment + + align:start position:0% +method because there so one comment + + + align:start position:0% +method because there so one comment +about the method is that this ratio C + + align:start position:0% +about the method is that this ratio C + + + align:start position:0% +about the method is that this ratio C +delta T over Delta X let me call it + + align:start position:0% + + + + align:start position:0% + +R that's a key + + align:start position:0% +R that's a key + + + align:start position:0% +R that's a key +number it's called the Quant + + align:start position:0% + + + + align:start position:0% + +number by su + + align:start position:0% + + + + align:start position:0% + +so in the literature you might see the + + align:start position:0% +so in the literature you might see the + + + align:start position:0% +so in the literature you might see the +the phrase Quant number for that ratio + + align:start position:0% +the phrase Quant number for that ratio + + + align:start position:0% +the phrase Quant number for that ratio +R and maybe my first point is stability + + align:start position:0% +R and maybe my first point is stability + + + align:start position:0% +R and maybe my first point is stability +is going to put a bound on + + align:start position:0% +is going to put a bound on + + + align:start position:0% +is going to put a bound on +R we can tell right away for this + + align:start position:0% +R we can tell right away for this + + + align:start position:0% +R we can tell right away for this +explicit method and for any explicit + + align:start position:0% +explicit method and for any explicit + + + align:start position:0% +explicit method and for any explicit +method that R can't + + align:start position:0% +method that R can't + + + align:start position:0% +method that R can't +be + + align:start position:0% +be + + + align:start position:0% +be +Unlimited there's going going to be a a + + align:start position:0% +Unlimited there's going going to be a a + + + align:start position:0% +Unlimited there's going going to be a a +bound on R which means a bound which it + + align:start position:0% +bound on R which means a bound which it + + + align:start position:0% +bound on R which means a bound which it +means a bound on delta T it means it's + + align:start position:0% +means a bound on delta T it means it's + + + align:start position:0% +means a bound on delta T it means it's +telling us that delta T has to be less + + align:start position:0% +telling us that delta T has to be less + + + align:start position:0% +telling us that delta T has to be less +than some constant times Delta + + align:start position:0% +than some constant times Delta + + + align:start position:0% +than some constant times Delta +X and and stability is the job find that + + align:start position:0% +X and and stability is the job find that + + + align:start position:0% +X and and stability is the job find that +constant how small does delta T have to + + align:start position:0% +constant how small does delta T have to + + + align:start position:0% +constant how small does delta T have to +be now let me sort of understand this + + align:start position:0% +be now let me sort of understand this + + + align:start position:0% +be now let me sort of understand this +this forward difference method in this + + align:start position:0% +this forward difference method in this + + + align:start position:0% +this forward difference method in this +picture + + align:start position:0% +picture + + + align:start position:0% +picture +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so I I'm I'm going to do the forward + + align:start position:0% +so I I'm I'm going to do the forward + + + align:start position:0% +so I I'm I'm going to do the forward +differences there you know delta T of U + + align:start position:0% +differences there you know delta T of U + + + align:start position:0% +differences there you know delta T of U +equals that ratio times the forward + + align:start position:0% +equals that ratio times the forward + + + align:start position:0% +equals that ratio times the forward +difference of U the space difference so + + align:start position:0% +difference of U the space difference so + + + align:start position:0% +difference of U the space difference so +time difference is that ratio times the + + align:start position:0% +time difference is that ratio times the + + + align:start position:0% +time difference is that ratio times the +space difference okay it's method + + align:start position:0% +space difference okay it's method + + + align:start position:0% +space difference okay it's method +one + + align:start position:0% +one + + + align:start position:0% +one +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so I guess somehow you want to see see + + align:start position:0% +so I guess somehow you want to see see + + + align:start position:0% +so I guess somehow you want to see see +that the you want to see a picture like + + align:start position:0% +that the you want to see a picture like + + + align:start position:0% +that the you want to see a picture like +this for the difference equation so the + + align:start position:0% +this for the difference equation so the + + + align:start position:0% +this for the difference equation so the +difference + + align:start position:0% +difference + + + align:start position:0% +difference +equation we + + align:start position:0% +equation we + + + align:start position:0% +equation we +imagine we've got steps Delta Delta + + align:start position:0% +imagine we've got steps Delta Delta + + + align:start position:0% +imagine we've got steps Delta Delta +X all these all these steps are Delta X + + align:start position:0% +X all these all these steps are Delta X + + + align:start position:0% +X all these all these steps are Delta X +let's suppose that's + + align:start position:0% +let's suppose that's + + + align:start position:0% +let's suppose that's +zero okay so what's happening now in + + align:start position:0% +zero okay so what's happening now in + + + align:start position:0% +zero okay so what's happening now in +time going this way and I'm solving this + + align:start position:0% +time going this way and I'm solving this + + + align:start position:0% +time going this way and I'm solving this +equation what's happening + + align:start position:0% +equation what's happening + + + align:start position:0% +equation what's happening +here + + align:start position:0% + + + + align:start position:0% + +well if I look at this let me let me + + align:start position:0% +well if I look at this let me let me + + + align:start position:0% +well if I look at this let me let me +copy this method + + align:start position:0% +copy this method + + + align:start position:0% +copy this method +you at a position J so this this might + + align:start position:0% +you at a position J so this this might + + + align:start position:0% +you at a position J so this this might +be the point J Delta + + align:start position:0% +be the point J Delta + + + align:start position:0% +be the point J Delta +X at time n + 1 is I I want to write + + align:start position:0% +X at time n + 1 is I I want to write + + + align:start position:0% +X at time n + 1 is I I want to write +this equation as always in the most + + align:start position:0% +this equation as always in the most + + + align:start position:0% +this equation as always in the most +convenient way so what am I going to do + + align:start position:0% +convenient way so what am I going to do + + + align:start position:0% +convenient way so what am I going to do +I'm going to take this U of x and t and + + align:start position:0% +I'm going to take this U of x and t and + + + align:start position:0% +I'm going to take this U of x and t and +put it on the right hand + + align:start position:0% +put it on the right hand + + + align:start position:0% +put it on the right hand +side so then my equation looks like that + + align:start position:0% +side so then my equation looks like that + + + align:start position:0% +side so then my equation looks like that +ratio R time U at J + 1 at time n that's + + align:start position:0% +ratio R time U at J + 1 at time n that's + + + align:start position:0% +ratio R time U at J + 1 at time n that's +this I'm one position over but I'm at + + align:start position:0% +this I'm one position over but I'm at + + + align:start position:0% +this I'm one position over but I'm at +the starting the the given time and then + + align:start position:0% +the starting the the given time and then + + + align:start position:0% +the starting the the given time and then +what's the coefficient of + + align:start position:0% +what's the coefficient of + + + align:start position:0% +what's the coefficient of +UJ + + align:start position:0% +UJ + + + align:start position:0% +UJ +n so can you just tell me what do I put + + align:start position:0% +n so can you just tell me what do I put + + + align:start position:0% +n so can you just tell me what do I put +in there so this will be the nice way to + + align:start position:0% +in there so this will be the nice way to + + + align:start position:0% +in there so this will be the nice way to +look at our difference equation each new + + align:start position:0% +look at our difference equation each new + + + align:start position:0% +look at our difference equation each new +value is a combination of two old values + + align:start position:0% +value is a combination of two old values + + + align:start position:0% +value is a combination of two old values +R times the times the guy here so in + + align:start position:0% +R times the times the guy here so in + + + align:start position:0% +R times the times the guy here so in +other words here's my little + + align:start position:0% + + + + align:start position:0% + +molecule this is the new value it comes + + align:start position:0% +molecule this is the new value it comes + + + align:start position:0% +molecule this is the new value it comes +from R time this plus what you have to + + align:start position:0% +from R time this plus what you have to + + + align:start position:0% +from R time this plus what you have to +tell me what multiplies this U at this + + align:start position:0% +tell me what multiplies this U at this + + + align:start position:0% +tell me what multiplies this U at this +point so here's UJ n + 1 here's u j + 1 + + align:start position:0% +point so here's UJ n + 1 here's u j + 1 + + + align:start position:0% +point so here's UJ n + 1 here's u j + 1 +n and here is ujn and what goes in + + align:start position:0% +n and here is ujn and what goes in + + + align:start position:0% +n and here is ujn and what goes in +parentheses one minus + + align:start position:0% +parentheses one minus + + + align:start position:0% +parentheses one minus +r because I get the one when that flips + + align:start position:0% +r because I get the one when that flips + + + align:start position:0% +r because I get the one when that flips +over to the other side good so it's just + + align:start position:0% +over to the other side good so it's just + + + align:start position:0% +over to the other side good so it's just +a + + align:start position:0% +a + + + align:start position:0% +a +combination the new value is a + + align:start position:0% +combination the new value is a + + + align:start position:0% +combination the new value is a +combination of those + + align:start position:0% + + + + align:start position:0% + +two and I guess what I want to + + align:start position:0% + + + + align:start position:0% + +show is + + align:start position:0% +show is + + + align:start position:0% +show is +that it could not possibly be + + align:start position:0% + + + + align:start position:0% + +stable unless R is less or equal to one + + align:start position:0% +stable unless R is less or equal to one + + + align:start position:0% +stable unless R is less or equal to one +so this will be the kurant condition the + + align:start position:0% +so this will be the kurant condition the + + + align:start position:0% +so this will be the kurant condition the +condition on the kurant number so the + + align:start position:0% +condition on the kurant number so the + + + align:start position:0% +condition on the kurant number so the +the kurant condition so the or the C f + + align:start position:0% +the kurant condition so the or the C f + + + align:start position:0% +the kurant condition so the or the C f +l that's a really + + align:start position:0% +l that's a really + + + align:start position:0% +l that's a really +better + + align:start position:0% + + + + align:start position:0% + +condition will be let me say what it is + + align:start position:0% +condition will be let me say what it is + + + align:start position:0% +condition will be let me say what it is +the CFL condition is R less or equal to + + align:start position:0% +the CFL condition is R less or equal to + + + align:start position:0% +the CFL condition is R less or equal to +one that's a + + align:start position:0% +one that's a + + + align:start position:0% +one that's a +condition for stability or + + align:start position:0% +condition for stability or + + + align:start position:0% +condition for stability or +convergence that comes to us from this + + align:start position:0% +convergence that comes to us from this + + + align:start position:0% +convergence that comes to us from this +from comparing the characteristics the + + align:start position:0% +from comparing the characteristics the + + + align:start position:0% +from comparing the characteristics the +real characteristics with the with the + + align:start position:0% +real characteristics with the with the + + + align:start position:0% +real characteristics with the with the +finite difference + + align:start position:0% +finite difference + + + align:start position:0% +finite difference +picture okay so what's CFL C is corant + + align:start position:0% +picture okay so what's CFL C is corant + + + align:start position:0% +picture okay so what's CFL C is corant +still so the this came from a really + + align:start position:0% +still so the this came from a really + + + align:start position:0% +still so the this came from a really +early paper and I think actually Ley the + + align:start position:0% +early paper and I think actually Ley the + + + align:start position:0% +early paper and I think actually Ley the +L stand that's kurant that's friedricks + + align:start position:0% +L stand that's kurant that's friedricks + + + align:start position:0% +L stand that's kurant that's friedricks +they were close friends that's Ley all + + align:start position:0% +they were close friends that's Ley all + + + align:start position:0% +they were close friends that's Ley all +three were friends actually and I think + + align:start position:0% +three were friends actually and I think + + + align:start position:0% +three were friends actually and I think +it was actually Ley who realized that + + align:start position:0% +it was actually Ley who realized that + + + align:start position:0% +it was actually Ley who realized that +there was a who who who who spotted what + + align:start position:0% +there was a who who who who spotted what + + + align:start position:0% +there was a who who who who spotted what +we're just going to do right now the + + align:start position:0% +we're just going to do right now the + + + align:start position:0% +we're just going to do right now the +requirement that R had to be less or + + align:start position:0% +requirement that R had to be less or + + + align:start position:0% +requirement that R had to be less or +equal + + align:start position:0% + + + + align:start position:0% + +one now let me just make + + align:start position:0% +one now let me just make + + + align:start position:0% +one now let me just make +clear that this current Frick's Ley + + align:start position:0% +clear that this current Frick's Ley + + + align:start position:0% +clear that this current Frick's Ley +condition is going to come it's going to + + align:start position:0% +condition is going to come it's going to + + + align:start position:0% +condition is going to come it's going to +be a necessary condition it has to hold + + align:start position:0% +be a necessary condition it has to hold + + + align:start position:0% +be a necessary condition it has to hold +or there's no + + align:start position:0% +or there's no + + + align:start position:0% +or there's no +hope but it's not + + align:start position:0% +hope but it's not + + + align:start position:0% +hope but it's not +enough it's not a sufficient + + align:start position:0% +enough it's not a sufficient + + + align:start position:0% +enough it's not a sufficient +condition this we can't guarantee that a + + align:start position:0% +condition this we can't guarantee that a + + + align:start position:0% +condition this we can't guarantee that a +method is stable just because the + + align:start position:0% +method is stable just because the + + + align:start position:0% +method is stable just because the +current conditions satisfy the current + + align:start position:0% +current conditions satisfy the current + + + align:start position:0% +current conditions satisfy the current +condition will tell us something about + + align:start position:0% +condition will tell us something about + + + align:start position:0% +condition will tell us something about +the position of characteristics we'll + + align:start position:0% +the position of characteristics we'll + + + align:start position:0% +the position of characteristics we'll +see it in a second but it doesn't for + + align:start position:0% +see it in a second but it doesn't for + + + align:start position:0% +see it in a second but it doesn't for +example this centered + + align:start position:0% +example this centered + + + align:start position:0% +example this centered +one is + + align:start position:0% +one is + + + align:start position:0% +one is +unstable this this guy when the right + + align:start position:0% +unstable this this guy when the right + + + align:start position:0% +unstable this this guy when the right +hand side you might say oh this is a + + align:start position:0% +hand side you might say oh this is a + + + align:start position:0% +hand side you might say oh this is a +better + + align:start position:0% +better + + + align:start position:0% +better +method always better to take a center + + align:start position:0% +method always better to take a center + + + align:start position:0% +method always better to take a center +difference for dudx than a one-sided but + + align:start position:0% +difference for dudx than a one-sided but + + + align:start position:0% +difference for dudx than a one-sided but +not not now the one-sided one is okay + + align:start position:0% +not not now the one-sided one is okay + + + align:start position:0% +not not now the one-sided one is okay +the centered one is going to be totally + + align:start position:0% + + + + align:start position:0% + +unstable for all + + align:start position:0% +unstable for all + + + align:start position:0% +unstable for all +R is centered + + align:start position:0% +R is centered + + + align:start position:0% +R is centered +one and we'll identify + + align:start position:0% +one and we'll identify + + + align:start position:0% +one and we'll identify +that not from Cent Frederick's Levy + + align:start position:0% +that not from Cent Frederick's Levy + + + align:start position:0% +that not from Cent Frederick's Levy +their paper wouldn't have spotted the + + align:start position:0% +their paper wouldn't have spotted the + + + align:start position:0% +their paper wouldn't have spotted the +difference between one and two but V + + align:start position:0% +difference between one and two but V + + + align:start position:0% +difference between one and two but V +noyman did Van noyman quickly noticed + + align:start position:0% +noyman did Van noyman quickly noticed + + + align:start position:0% +noyman did Van noyman quickly noticed +that if + + align:start position:0% +that if + + + align:start position:0% +that if +you use an exponential so we'll do + + align:start position:0% +you use an exponential so we'll do + + + align:start position:0% +you use an exponential so we'll do +vanoyan in a moment if you plug in an + + align:start position:0% +vanoyan in a moment if you plug in an + + + align:start position:0% +vanoyan in a moment if you plug in an +exponential to number two this Center + + align:start position:0% +exponential to number two this Center + + + align:start position:0% +exponential to number two this Center +difference it takes + + align:start position:0% +difference it takes + + + align:start position:0% +difference it takes +off and uh it's unstable even if delta T + + align:start position:0% +off and uh it's unstable even if delta T + + + align:start position:0% +off and uh it's unstable even if delta T +is small okay now what is this CFL coron + + align:start position:0% +is small okay now what is this CFL coron + + + align:start position:0% +is small okay now what is this CFL coron +Frick's Ley condition where does that + + align:start position:0% +Frick's Ley condition where does that + + + align:start position:0% +Frick's Ley condition where does that +come from + + align:start position:0% + + + + align:start position:0% + +it comes + + align:start position:0% +it comes + + + align:start position:0% +it comes +from just thinking about the + + align:start position:0% +from just thinking about the + + + align:start position:0% +from just thinking about the +information + + align:start position:0% +information + + + align:start position:0% +information +suppose so so I I have to write down the + + align:start position:0% +suppose so so I I have to write down the + + + align:start position:0% +suppose so so I I have to write down the +thinking now that goes into the Quran + + align:start position:0% +thinking now that goes into the Quran + + + align:start position:0% +thinking now that goes into the Quran +fredi's Ley + + align:start position:0% +fredi's Ley + + + align:start position:0% +fredi's Ley +condition okay the CFL + + align:start position:0% + + + + align:start position:0% + +condition + + align:start position:0% +condition + + + align:start position:0% +condition +okay it's + + align:start position:0% +okay it's + + + align:start position:0% +okay it's +straightforward I have to + + align:start position:0% +straightforward I have to + + + align:start position:0% +straightforward I have to +think at a at a time T at time + + align:start position:0% +think at a at a time T at time + + + align:start position:0% +think at a at a time T at time +T at time let's say t equal n delta T + + align:start position:0% +T at time let's say t equal n delta T + + + align:start position:0% +T at time let's say t equal n delta T +suppose I've taken n time + + align:start position:0% + + + + align:start position:0% + +steps then the + + align:start position:0% +steps then the + + + align:start position:0% +steps then the +true the + + align:start position:0% +true the + + + align:start position:0% +true the +true U at let's say zero and that time t + + align:start position:0% +true U at let's say zero and that time t + + + align:start position:0% +true U at let's say zero and that time t +is or at x and t we because we know the + + align:start position:0% +is or at x and t we because we know the + + + align:start position:0% +is or at x and t we because we know the +true solution the true U at x and + + align:start position:0% +true solution the true U at x and + + + align:start position:0% +true solution the true U at x and +t is as we + + align:start position:0% +t is as we + + + align:start position:0% +t is as we +know the initial + + align:start position:0% +know the initial + + + align:start position:0% +know the initial +function X+ + + align:start position:0% +function X+ + + + align:start position:0% +function X+ +CT at at the point X Plus + + align:start position:0% +CT at at the point X Plus + + + align:start position:0% +CT at at the point X Plus +CT so that's what that's the solution we + + align:start position:0% +CT so that's what that's the solution we + + + align:start position:0% +CT so that's what that's the solution we +we that's the correct + + align:start position:0% +we that's the correct + + + align:start position:0% +we that's the correct +solution and corant Frederick's Levy are + + align:start position:0% +solution and corant Frederick's Levy are + + + align:start position:0% +solution and corant Frederick's Levy are +just saying that you better use this + + align:start position:0% +just saying that you better use this + + + align:start position:0% +just saying that you better use this +number in the finite difference + + align:start position:0% +number in the finite difference + + + align:start position:0% +number in the finite difference +method or or you don't have a + + align:start position:0% +method or or you don't have a + + + align:start position:0% +method or or you don't have a +chance right that makes sense that if so + + align:start position:0% +chance right that makes sense that if so + + + align:start position:0% +chance right that makes sense that if so +the so what number what do I mean by use + + align:start position:0% +the so what number what do I mean by use + + + align:start position:0% +the so what number what do I mean by use +this number okay so let me draw the so U + + align:start position:0% +this number okay so let me draw the so U + + + align:start position:0% +this number okay so let me draw the so U +at x and t at some point here this is at + + align:start position:0% +at x and t at some point here this is at + + + align:start position:0% +at x and t at some point here this is at +the point x and t this used these two + + align:start position:0% +the point x and t this used these two + + + align:start position:0% +the point x and t this used these two +values they used these three values they + + align:start position:0% +values they used these three values they + + + align:start position:0% +values they used these three values they +used this one used the that one that one + + align:start position:0% +used this one used the that one that one + + + align:start position:0% +used this one used the that one that one +that one this one used those two those + + align:start position:0% +that one this one used those two those + + + align:start position:0% +that one this one used those two those +for use these five + + align:start position:0% +for use these five + + + align:start position:0% +for use these five +values + + align:start position:0% +values + + + align:start position:0% +values +right so this is a sort of + + align:start position:0% + + + + align:start position:0% + +a see the difference method is not + + align:start position:0% +a see the difference method is not + + + align:start position:0% +a see the difference method is not +propagating the information entirely on + + align:start position:0% +propagating the information entirely on + + + align:start position:0% +propagating the information entirely on +that line it's really taking values over + + align:start position:0% +that line it's really taking values over + + + align:start position:0% +that line it's really taking values over +that whole interval with some + + align:start position:0% +that whole interval with some + + + align:start position:0% +that whole interval with some +combinations of R and 1 minus r and in + + align:start position:0% +combinations of R and 1 minus r and in + + + align:start position:0% +combinations of R and 1 minus r and in +the end after five time steps it's + + align:start position:0% +the end after five time steps it's + + + align:start position:0% +the end after five time steps it's +giving us this value up + + align:start position:0% +giving us this value up + + + align:start position:0% +giving us this value up +there but the point is that if this + + align:start position:0% +there but the point is that if this + + + align:start position:0% +there but the point is that if this +point X Plus CT were out + + align:start position:0% + + + + align:start position:0% + +here then refining Delta X and refining + + align:start position:0% +here then refining Delta X and refining + + + align:start position:0% +here then refining Delta X and refining +delta T and using more and more points + + align:start position:0% +delta T and using more and more points + + + align:start position:0% +delta T and using more and more points +and filling in and using more of these + + align:start position:0% +and filling in and using more of these + + + align:start position:0% +and filling in and using more of these +but not getting out here would get you + + align:start position:0% +but not getting out here would get you + + + align:start position:0% +but not getting out here would get you +nowhere you wouldn't have a chance so + + align:start position:0% +nowhere you wouldn't have a chance so + + + align:start position:0% +nowhere you wouldn't have a chance so +that's the current freedrick Ley + + align:start position:0% +that's the current freedrick Ley + + + align:start position:0% +that's the current freedrick Ley +condition how how far out is this this + + align:start position:0% +condition how how far out is this this + + + align:start position:0% +condition how how far out is this this +is n Delta X's I + + align:start position:0% +is n Delta X's I + + + align:start position:0% +is n Delta X's I +guess and how well if this is X this is + + align:start position:0% +guess and how well if this is X this is + + + align:start position:0% +guess and how well if this is X this is +n Delta X is away and this is X+ + + align:start position:0% +n Delta X is away and this is X+ + + + align:start position:0% +n Delta X is away and this is X+ +CT and C is n Delta + + align:start position:0% + + + + align:start position:0% + +T's right T is n delta + + align:start position:0% + + + + align:start position:0% + +T are you with me that the forward + + align:start position:0% +T are you with me that the forward + + + align:start position:0% +T are you with me that the forward +difference + + align:start position:0% +difference + + + align:start position:0% +difference +method however I as I keep delta T over + + align:start position:0% +method however I as I keep delta T over + + + align:start position:0% +method however I as I keep delta T over +Delta X the ratio R fixed and use more + + align:start position:0% +Delta X the ratio R fixed and use more + + + align:start position:0% +Delta X the ratio R fixed and use more +and more points I'm filling up the + + align:start position:0% +and more points I'm filling up the + + + align:start position:0% +and more points I'm filling up the +filling up this interval with used with + + align:start position:0% +filling up this interval with used with + + + align:start position:0% +filling up this interval with used with +points that I + + align:start position:0% +points that I + + + align:start position:0% +points that I +use but I'm never going to get to a + + align:start position:0% +use but I'm never going to get to a + + + align:start position:0% +use but I'm never going to get to a +point there so it's so the idea is then + + align:start position:0% +point there so it's so the idea is then + + + align:start position:0% +point there so it's so the idea is then +unstable couldn't converge couldn't + + align:start position:0% + + + + align:start position:0% + +work + + align:start position:0% +work + + + align:start position:0% +work +if that if if if the distance reached + + align:start position:0% +if that if if if the distance reached + + + align:start position:0% +if that if if if the distance reached +here n Delta X is smaller than CN delta + + align:start position:0% +here n Delta X is smaller than CN delta + + + align:start position:0% +here n Delta X is smaller than CN delta +T it couldn't + + align:start position:0% +T it couldn't + + + align:start position:0% +T it couldn't +work + + align:start position:0% +work + + + align:start position:0% +work +okay so I'm taking a negative point of + + align:start position:0% +okay so I'm taking a negative point of + + + align:start position:0% +okay so I'm taking a negative point of +view here can't work in this case I I I + + align:start position:0% +view here can't work in this case I I I + + + align:start position:0% +view here can't work in this case I I I +can't the reason I take that negative + + align:start position:0% +can't the reason I take that negative + + + align:start position:0% +can't the reason I take that negative +point of view is I'm not able to say it + + align:start position:0% +point of view is I'm not able to say it + + + align:start position:0% +point of view is I'm not able to say it +does + + align:start position:0% +does + + + align:start position:0% +does +work in the case when Delta X is big + + align:start position:0% +work in the case when Delta X is big + + + align:start position:0% +work in the case when Delta X is big +enough compared to delta T and and I + + align:start position:0% +enough compared to delta T and and I + + + align:start position:0% +enough compared to delta T and and I +include that point I can't be sure but I + + align:start position:0% +include that point I can't be sure but I + + + align:start position:0% +include that point I can't be sure but I +can be sure that if I don't include that + + align:start position:0% +can be sure that if I don't include that + + + align:start position:0% +can be sure that if I don't include that +neighborhood of where the true U is + + align:start position:0% +neighborhood of where the true U is + + + align:start position:0% +neighborhood of where the true U is +produced it can't have a chance so let + + align:start position:0% +produced it can't have a chance so let + + + align:start position:0% +produced it can't have a chance so let +me just cancel n divide by Delta X and I + + align:start position:0% +me just cancel n divide by Delta X and I + + + align:start position:0% +me just cancel n divide by Delta X and I +I say + + align:start position:0% +I say + + + align:start position:0% +I say +fail if one is smaller than C delta T + + align:start position:0% +fail if one is smaller than C delta T + + + align:start position:0% +fail if one is smaller than C delta T +over Delta X which is + + align:start position:0% +over Delta X which is + + + align:start position:0% +over Delta X which is +R it fails if one is less if R is bigger + + align:start position:0% +R it fails if one is less if R is bigger + + + align:start position:0% +R it fails if one is less if R is bigger +than + + align:start position:0% +than + + + align:start position:0% +than +one by this reasoning of + + align:start position:0% + + + + align:start position:0% + +characteristics + + align:start position:0% +characteristics + + + align:start position:0% +characteristics +um there are two more cases that worth + + align:start position:0% +um there are two more cases that worth + + + align:start position:0% +um there are two more cases that worth +thinking about + + align:start position:0% +thinking about + + + align:start position:0% +thinking about +suppose + + align:start position:0% +suppose + + + align:start position:0% +suppose +uh suppose the method was + + align:start position:0% +uh suppose the method was + + + align:start position:0% +uh suppose the method was +downwind so this is this is upwind + + align:start position:0% +downwind so this is this is upwind + + + align:start position:0% +downwind so this is this is upwind +because I take a forward difference the + + align:start position:0% +because I take a forward difference the + + + align:start position:0% +because I take a forward difference the +the wind is blowing this way right + + align:start position:0% +the wind is blowing this way right + + + align:start position:0% +the wind is blowing this way right +forgive me for such + + align:start position:0% +forgive me for such + + + align:start position:0% +forgive me for such +a + + align:start position:0% +a + + + align:start position:0% +a +incomplete use of the word wind who I + + align:start position:0% +incomplete use of the word wind who I + + + align:start position:0% +incomplete use of the word wind who I +don't know what it means but one way or + + align:start position:0% +don't know what it means but one way or + + + align:start position:0% +don't know what it means but one way or +another whatever the wind is blowing + + align:start position:0% +another whatever the wind is blowing + + + align:start position:0% +another whatever the wind is blowing +this way the values are coming from the + + align:start position:0% +this way the values are coming from the + + + align:start position:0% +this way the values are coming from the +upwind + + align:start position:0% +upwind + + + align:start position:0% +upwind +direction and that's good because the + + align:start position:0% +direction and that's good because the + + + align:start position:0% +direction and that's good because the +True Value comes from the upwind + + align:start position:0% +True Value comes from the upwind + + + align:start position:0% +True Value comes from the upwind +Direction that's what we saw in + + align:start position:0% +Direction that's what we saw in + + + align:start position:0% +Direction that's what we saw in +characteristics the values are blowing + + align:start position:0% +characteristics the values are blowing + + + align:start position:0% +characteristics the values are blowing +down wind so if we what would happen if + + align:start position:0% +down wind so if we what would happen if + + + align:start position:0% +down wind so if we what would happen if +I use a backward difference here so I'm + + align:start position:0% +I use a backward difference here so I'm + + + align:start position:0% +I use a backward difference here so I'm +I I didn't write that bad idea but it's + + align:start position:0% +I I didn't write that bad idea but it's + + + align:start position:0% +I I didn't write that bad idea but it's +important to re realize that that that's + + align:start position:0% +important to re realize that that that's + + + align:start position:0% +important to re realize that that that's +method 1 + + align:start position:0% +method 1 + + + align:start position:0% +method 1 +a of bad idea is to use a backward + + align:start position:0% +a of bad idea is to use a backward + + + align:start position:0% +a of bad idea is to use a backward +difference here I should maybe call it + + align:start position:0% +difference here I should maybe call it + + + align:start position:0% +difference here I should maybe call it +1B for + + align:start position:0% +1B for + + + align:start position:0% +1B for +backward you see that it would fail if I + + align:start position:0% +backward you see that it would fail if I + + + align:start position:0% +backward you see that it would fail if I +used a backward difference what would + + align:start position:0% +used a backward difference what would + + + align:start position:0% +used a backward difference what would +happen to this picture this value would + + align:start position:0% +happen to this picture this value would + + + align:start position:0% +happen to this picture this value would +come from stuff on the left it would + + align:start position:0% +come from stuff on the left it would + + + align:start position:0% +come from stuff on the left it would +totally have no chance to use the + + align:start position:0% +totally have no chance to use the + + + align:start position:0% +totally have no chance to use the +correct value initial value so a + + align:start position:0% +correct value initial value so a + + + align:start position:0% +correct value initial value so a +backward difference is an immediate + + align:start position:0% +backward difference is an immediate + + + align:start position:0% +backward difference is an immediate +failure so R has to be + + align:start position:0% + + + + align:start position:0% + +uh if R is it will also + + align:start position:0% +uh if R is it will also + + + align:start position:0% +uh if R is it will also +fail if uh well I was going to say R + + align:start position:0% +fail if uh well I was going to say R + + + align:start position:0% +fail if uh well I was going to say R +less than zero I don't know what can I + + align:start position:0% +less than zero I don't know what can I + + + align:start position:0% +less than zero I don't know what can I +say that R less than zero the way R + + align:start position:0% +say that R less than zero the way R + + + align:start position:0% +say that R less than zero the way R +could be less than zero would be the + + align:start position:0% +could be less than zero would be the + + + align:start position:0% +could be less than zero would be the +Delta X being negative and that's what I + + align:start position:0% +Delta X being negative and that's what I + + + align:start position:0% +Delta X being negative and that's what I +mean by the the downwind method where + + align:start position:0% +mean by the the downwind method where + + + align:start position:0% +mean by the the downwind method where +I'm where I'm looking for looking for + + align:start position:0% +I'm where I'm looking for looking for + + + align:start position:0% +I'm where I'm looking for looking for +the value here and of course I'm not + + align:start position:0% +the value here and of course I'm not + + + align:start position:0% +the value here and of course I'm not +finding it + + align:start position:0% +finding it + + + align:start position:0% +finding it +okay so I guess I'm saying that uh Kuran + + align:start position:0% +okay so I guess I'm saying that uh Kuran + + + align:start position:0% +okay so I guess I'm saying that uh Kuran +Frederick's Levy tell us right away that + + align:start position:0% +Frederick's Levy tell us right away that + + + align:start position:0% +Frederick's Levy tell us right away that +this method will only have a + + align:start position:0% +this method will only have a + + + align:start position:0% +this method will only have a +chance so it only has a chance if R is + + align:start position:0% +chance so it only has a chance if R is + + + align:start position:0% +chance so it only has a chance if R is +is so so uh + + align:start position:0% +is so so uh + + + align:start position:0% +is so so uh +possible and in fact this is the + + align:start position:0% +possible and in fact this is the + + + align:start position:0% +possible and in fact this is the +stability condition so let me write that + + align:start position:0% +stability condition so let me write that + + + align:start position:0% +stability condition so let me write that +fact but we haven't proved it yet it's + + align:start position:0% +fact but we haven't proved it yet it's + + + align:start position:0% +fact but we haven't proved it yet it's +stable for R between 0 and 1 that's the + + align:start position:0% +stable for R between 0 and 1 that's the + + + align:start position:0% +stable for R between 0 and 1 that's the +stability + + align:start position:0% +stability + + + align:start position:0% +stability +condition which limits delta + + align:start position:0% +condition which limits delta + + + align:start position:0% +condition which limits delta +T because R is R is delta T over Delta + + align:start position:0% +T because R is R is delta T over Delta + + + align:start position:0% +T because R is R is delta T over Delta +X and this says that delta T can't be + + align:start position:0% +X and this says that delta T can't be + + + align:start position:0% +X and this says that delta T can't be +small can't be larger than the multiple + + align:start position:0% +small can't be larger than the multiple + + + align:start position:0% +small can't be larger than the multiple +of Delta X okay you you might + + align:start position:0% +of Delta X okay you you might + + + align:start position:0% +of Delta X okay you you might +say that sounds like delta T is too + + align:start position:0% +say that sounds like delta T is too + + + align:start position:0% +say that sounds like delta T is too +small stability is stability too + + align:start position:0% +small stability is stability too + + + align:start position:0% +small stability is stability too +restrictive well it's restrictive + + align:start position:0% +restrictive well it's restrictive + + + align:start position:0% +restrictive well it's restrictive +certainly because it limits delta T but + + align:start position:0% +certainly because it limits delta T but + + + align:start position:0% +certainly because it limits delta T but +actually for these + + align:start position:0% + + + + align:start position:0% + +methods accuracy also limits delta T if + + align:start position:0% +methods accuracy also limits delta T if + + + align:start position:0% +methods accuracy also limits delta T if +if I look for an implicit + + align:start position:0% +if I look for an implicit + + + align:start position:0% +if I look for an implicit +method that would allow + + align:start position:0% +method that would allow + + + align:start position:0% +method that would allow +me uh if I look for a method if if I + + align:start position:0% +me uh if I look for a method if if I + + + align:start position:0% +me uh if I look for a method if if I +look for a method that allowed a bigger + + align:start position:0% +look for a method that allowed a bigger + + + align:start position:0% +look for a method that allowed a bigger +delta + + align:start position:0% +delta + + + align:start position:0% +delta +T then that delta T might the error of + + align:start position:0% +T then that delta T might the error of + + + align:start position:0% +T then that delta T might the error of +that in that method proportional to + + align:start position:0% +that in that method proportional to + + + align:start position:0% +that in that method proportional to +delta T would be too big in other words + + align:start position:0% +delta T would be too big in other words + + + align:start position:0% +delta T would be too big in other words +accuracy as well as stability is keeping + + align:start position:0% +accuracy as well as stability is keeping + + + align:start position:0% +accuracy as well as stability is keeping +delta T of the order of Delta X accuracy + + align:start position:0% +delta T of the order of Delta X accuracy + + + align:start position:0% +delta T of the order of Delta X accuracy +as well as stability is keeping + + align:start position:0% +as well as stability is keeping + + + align:start position:0% +as well as stability is keeping +R within brain within a bound and + + align:start position:0% +R within brain within a bound and + + + align:start position:0% +R within brain within a bound and +stability is keeping it within those + + align:start position:0% +stability is keeping it within those + + + align:start position:0% +stability is keeping it within those +bounds okay so I still have to show that + + align:start position:0% +bounds okay so I still have to show that + + + align:start position:0% +bounds okay so I still have to show that +the that the method is stable + + align:start position:0% +the that the method is stable + + + align:start position:0% +the that the method is stable +the Coran fredi's Ley condition just + + align:start position:0% +the Coran fredi's Ley condition just + + + align:start position:0% +the Coran fredi's Ley condition just +helps to eliminate + + align:start position:0% +helps to eliminate + + + align:start position:0% +helps to eliminate +impossible ratios okay one more + + align:start position:0% +impossible ratios okay one more + + + align:start position:0% +impossible ratios okay one more +point which of course everybody notices + + align:start position:0% +point which of course everybody notices + + + align:start position:0% +point which of course everybody notices +in solving + + align:start position:0% +in solving + + + align:start position:0% +in solving +the the difference equation suppose R is + + align:start position:0% +the the difference equation suppose R is + + + align:start position:0% +the the difference equation suppose R is +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +one think about the case when R is + + align:start position:0% +one think about the case when R is + + + align:start position:0% +one think about the case when R is +exactly + + align:start position:0% +exactly + + + align:start position:0% +exactly +one + + align:start position:0% +one + + + align:start position:0% +one +or remember that's C delta T over Delta + + align:start position:0% + + + + align:start position:0% + +X suppose R is exactly one then what + + align:start position:0% +X suppose R is exactly one then what + + + align:start position:0% +X suppose R is exactly one then what +does the method + + align:start position:0% +does the method + + + align:start position:0% +does the method +do the method takes the new value R is + + align:start position:0% +do the method takes the new value R is + + + align:start position:0% +do the method takes the new value R is +one this is zero now so the new value is + + align:start position:0% +one this is zero now so the new value is + + + align:start position:0% +one this is zero now so the new value is +then when R is one is that old value in + + align:start position:0% +then when R is one is that old value in + + + align:start position:0% +then when R is one is that old value in +this picture when R is one this value is + + align:start position:0% +this picture when R is one this value is + + + align:start position:0% +this picture when R is one this value is +this + + align:start position:0% +this + + + align:start position:0% +this +one the values are + + align:start position:0% +one the values are + + + align:start position:0% +one the values are +traveling as along a line I'm not using + + align:start position:0% +traveling as along a line I'm not using + + + align:start position:0% +traveling as along a line I'm not using +these you see because if R is exactly + + align:start position:0% +these you see because if R is exactly + + + align:start position:0% +these you see because if R is exactly +one these are exactly + + align:start position:0% +one these are exactly + + + align:start position:0% +one these are exactly +zero now is that + + align:start position:0% +zero now is that + + + align:start position:0% +zero now is that +good actually it's + + align:start position:0% +good actually it's + + + align:start position:0% +good actually it's +terrific because that line when R is one + + align:start position:0% +terrific because that line when R is one + + + align:start position:0% +terrific because that line when R is one +is the correct characteristic line if R + + align:start position:0% +is the correct characteristic line if R + + + align:start position:0% +is the correct characteristic line if R +is one + + align:start position:0% +is one + + + align:start position:0% +is one +if C delta T equals Delta X I'm going up + + align:start position:0% +if C delta T equals Delta X I'm going up + + + align:start position:0% +if C delta T equals Delta X I'm going up +exactly with that slope that I that that + + align:start position:0% +exactly with that slope that I that that + + + align:start position:0% +exactly with that slope that I that that +the true line does in other words the + + align:start position:0% +the true line does in other words the + + + align:start position:0% +the true line does in other words the +difference equation is + + align:start position:0% +difference equation is + + + align:start position:0% +difference equation is +exactly gives exactly the solution to + + align:start position:0% +exactly gives exactly the solution to + + + align:start position:0% +exactly gives exactly the solution to +the differential equation because + + align:start position:0% +the differential equation because + + + align:start position:0% +the differential equation because +because it's so simple of course + + align:start position:0% +because it's so simple of course + + + align:start position:0% +because it's so simple of course +couldn't do it well that's the point we + + align:start position:0% +couldn't do it well that's the point we + + + align:start position:0% +couldn't do it well that's the point we +can't do it for big problems because in + + align:start position:0% +can't do it for big problems because in + + + align:start position:0% +can't do it for big problems because in +a big problem C is going to be + + align:start position:0% +a big problem C is going to be + + + align:start position:0% +a big problem C is going to be +variable maybe the problem C may depend + + align:start position:0% +variable maybe the problem C may depend + + + align:start position:0% +variable maybe the problem C may depend +on the position or the time or it might + + align:start position:0% +on the position or the time or it might + + + align:start position:0% +on the position or the time or it might +be or it might depend on the solution + + align:start position:0% +be or it might depend on the solution + + + align:start position:0% +be or it might depend on the solution +you in a nonlinear problem those are + + align:start position:0% +you in a nonlinear problem those are + + + align:start position:0% +you in a nonlinear problem those are +ahead of us but this possibility in + + align:start position:0% +ahead of us but this possibility in + + + align:start position:0% +ahead of us but this possibility in +1D it's only a really a one-dimensional + + align:start position:0% +1D it's only a really a one-dimensional + + + align:start position:0% +1D it's only a really a one-dimensional +possibility where where the true + + align:start position:0% +possibility where where the true + + + align:start position:0% +possibility where where the true +information travels on a line and we + + align:start position:0% +information travels on a line and we + + + align:start position:0% +information travels on a line and we +could just hope to stay close to that + + align:start position:0% +could just hope to stay close to that + + + align:start position:0% +could just hope to stay close to that +characteristic line + + align:start position:0% + + + + align:start position:0% + +okay now I'm ready to tackle for other + + align:start position:0% +okay now I'm ready to tackle for other + + + align:start position:0% +okay now I'm ready to tackle for other +for any method the and and uh let me get + + align:start position:0% +for any method the and and uh let me get + + + align:start position:0% +for any method the and and uh let me get +these guys up + + align:start position:0% +these guys up + + + align:start position:0% +these guys up +again those four so first I want to see + + align:start position:0% +again those four so first I want to see + + + align:start position:0% +again those four so first I want to see +why is upwind stable and why is centered + + align:start position:0% +why is upwind stable and why is centered + + + align:start position:0% +why is upwind stable and why is centered +unstable okay shall I start with the + + align:start position:0% +unstable okay shall I start with the + + + align:start position:0% +unstable okay shall I start with the +stability question rather than the + + align:start position:0% +stability question rather than the + + + align:start position:0% +stability question rather than the +accuracy question the accuracy we could + + align:start position:0% +accuracy question the accuracy we could + + + align:start position:0% +accuracy question the accuracy we could +guess was first order + + align:start position:0% +guess was first order + + + align:start position:0% +guess was first order +until we get to LAX wend so let me so + + align:start position:0% +until we get to LAX wend so let me so + + + align:start position:0% +until we get to LAX wend so let me so +accuracy is going to come next time let + + align:start position:0% +accuracy is going to come next time let + + + align:start position:0% +accuracy is going to come next time let +me finish + + align:start position:0% +me finish + + + align:start position:0% +me finish +with we've had kurant take on + + align:start position:0% +with we've had kurant take on + + + align:start position:0% +with we've had kurant take on +stability the CFL condition but now I'm + + align:start position:0% +stability the CFL condition but now I'm + + + align:start position:0% +stability the CFL condition but now I'm +ready for + + align:start position:0% +ready for + + + align:start position:0% +ready for +vanoyan deeper uh Insight okay so how + + align:start position:0% +vanoyan deeper uh Insight okay so how + + + align:start position:0% +vanoyan deeper uh Insight okay so how +does van noyman study stability he + + align:start position:0% +does van noyman study stability he + + + align:start position:0% +does van noyman study stability he +watches every e to the + + align:start position:0% +watches every e to the + + + align:start position:0% +watches every e to the +ikx so that the vman's test is going to + + align:start position:0% +ikx so that the vman's test is going to + + + align:start position:0% +ikx so that the vman's test is going to +be each e to the ikx should have a + + align:start position:0% +be each e to the ikx should have a + + + align:start position:0% +be each e to the ikx should have a +growth factor in the difference + + align:start position:0% +growth factor in the difference + + + align:start position:0% +growth factor in the difference +equation smaller than + + align:start position:0% +equation smaller than + + + align:start position:0% +equation smaller than +one the growth factor in the + + align:start position:0% +one the growth factor in the + + + align:start position:0% +one the growth factor in the +differential equation of course was + + align:start position:0% +differential equation of course was + + + align:start position:0% +differential equation of course was +right + + align:start position:0% +right + + + align:start position:0% +right +on this has this has magnitude one + + align:start position:0% +on this has this has magnitude one + + + align:start position:0% +on this has this has magnitude one +exactly one + + align:start position:0% +exactly one + + + align:start position:0% +exactly one +so wave equations are not giving us any + + align:start position:0% +so wave equations are not giving us any + + + align:start position:0% +so wave equations are not giving us any +space to work + + align:start position:0% +space to work + + + align:start position:0% +space to work +in because we want the growth factor in + + align:start position:0% +in because we want the growth factor in + + + align:start position:0% +in because we want the growth factor in +the difference equation we want it to be + + align:start position:0% +the difference equation we want it to be + + + align:start position:0% +the difference equation we want it to be +close to the real one and at the same + + align:start position:0% +close to the real one and at the same + + + align:start position:0% +close to the real one and at the same +time we it better be not the real one + + align:start position:0% +time we it better be not the real one + + + align:start position:0% +time we it better be not the real one +having absolute value exactly one on the + + align:start position:0% +having absolute value exactly one on the + + + align:start position:0% +having absolute value exactly one on the +unit + + align:start position:0% +unit + + + align:start position:0% +unit +circle but the difference equation is + + align:start position:0% +circle but the difference equation is + + + align:start position:0% +circle but the difference equation is +allowed to go into the unit circle but + + align:start position:0% +allowed to go into the unit circle but + + + align:start position:0% +allowed to go into the unit circle but +not to go out okay that will separate + + align:start position:0% +not to go out okay that will separate + + + align:start position:0% +not to go out okay that will separate +the good ones from the bad okay let me + + align:start position:0% +the good ones from the bad okay let me + + + align:start position:0% +the good ones from the bad okay let me +work here + + align:start position:0% +work here + + + align:start position:0% +work here +on + + align:start position:0% +on + + + align:start position:0% +on +um I'll copy can I copy this the + + align:start position:0% +um I'll copy can I copy this the + + + align:start position:0% +um I'll copy can I copy this the +equation UJ n + 1 is equal to r u j + 1 + + align:start position:0% +equation UJ n + 1 is equal to r u j + 1 + + + align:start position:0% +equation UJ n + 1 is equal to r u j + 1 +n and 1 - r u j + + align:start position:0% +n and 1 - r u j + + + align:start position:0% +n and 1 - r u j +n Okay now what's + + align:start position:0% +n Okay now what's + + + align:start position:0% +n Okay now what's +now I'm going to do an exponential again + + align:start position:0% +now I'm going to do an exponential again + + + align:start position:0% +now I'm going to do an exponential again +so I'm going to have + + align:start position:0% +so I'm going to have + + + align:start position:0% +so I'm going to have +U + + align:start position:0% +U + + + align:start position:0% +U +say 0 + + align:start position:0% + + + + align:start position:0% + +n i I + + align:start position:0% +n i I + + + align:start position:0% +n i I +want uh I'm going to start from e to the + + align:start position:0% +want uh I'm going to start from e to the + + + align:start position:0% +want uh I'm going to start from e to the +I + + align:start position:0% + + + + align:start position:0% + +KX so X + + align:start position:0% + + + + align:start position:0% + +sorry let me say yeah uh position so + + align:start position:0% +sorry let me say yeah uh position so + + + align:start position:0% +sorry let me say yeah uh position so +time zero and position n will be e to + + align:start position:0% +time zero and position n will be e to + + + align:start position:0% +time zero and position n will be e to +the i k n Delta + + align:start position:0% +the i k n Delta + + + align:start position:0% +the i k n Delta +X right that's my + + align:start position:0% +X right that's my + + + align:start position:0% +X right that's my +initial e to the I KX that's my pure + + align:start position:0% +initial e to the I KX that's my pure + + + align:start position:0% +initial e to the I KX that's my pure +frequency I plug that in to the oh not n + + align:start position:0% +frequency I plug that in to the oh not n + + + align:start position:0% +frequency I plug that in to the oh not n +but J J is measuring how many sorry + + align:start position:0% +but J J is measuring how many sorry + + + align:start position:0% +but J J is measuring how many sorry +let's get it right J is is measuring how + + align:start position:0% +let's get it right J is is measuring how + + + align:start position:0% +let's get it right J is is measuring how +many Delta X's I'm going across n is + + align:start position:0% +many Delta X's I'm going across n is + + + align:start position:0% +many Delta X's I'm going across n is +measuring how many Delta T's I'm going + + align:start position:0% +measuring how many Delta T's I'm going + + + align:start position:0% +measuring how many Delta T's I'm going +up so this is the key here's + + align:start position:0% +up so this is the key here's + + + align:start position:0% +up so this is the key here's +onea + + align:start position:0% +onea + + + align:start position:0% +onea +onea try a pure exponential plug it + + align:start position:0% +onea try a pure exponential plug it + + + align:start position:0% +onea try a pure exponential plug it +in again it's going to work because we + + align:start position:0% +in again it's going to work because we + + + align:start position:0% +in again it's going to work because we +have constant coefficients so what do I + + align:start position:0% +have constant coefficients so what do I + + + align:start position:0% +have constant coefficients so what do I +get on the right hand side I get R times + + align:start position:0% +get on the right hand side I get R times + + + align:start position:0% +get on the right hand side I get R times +this guy at level J + 1 e to the i + + align:start position:0% +this guy at level J + 1 e to the i + + + align:start position:0% +this guy at level J + 1 e to the i +k j + 1 Delta + + align:start position:0% +k j + 1 Delta + + + align:start position:0% +k j + 1 Delta +x times the + + align:start position:0% +x times the + + + align:start position:0% +x times the +exponential can I save the exponential + + align:start position:0% +exponential can I save the exponential + + + align:start position:0% +exponential can I save the exponential +because it's going to factor out I'm + + align:start position:0% +because it's going to factor out I'm + + + align:start position:0% +because it's going to factor out I'm +going to have a I'm G to plus a 1 minus + + align:start position:0% +going to have a I'm G to plus a 1 minus + + + align:start position:0% +going to have a I'm G to plus a 1 minus +r times the exponential itself and + + align:start position:0% +r times the exponential itself and + + + align:start position:0% +r times the exponential itself and +here's the exponential e to the i k j + + align:start position:0% +here's the exponential e to the i k j + + + align:start position:0% +here's the exponential e to the i k j +Delta X this will be one + + align:start position:0% +Delta X this will be one + + + align:start position:0% +Delta X this will be one +step I could say U J1 coming + + align:start position:0% + + + + align:start position:0% + +from Level zero to level + + align:start position:0% +from Level zero to level + + + align:start position:0% +from Level zero to level +one + + align:start position:0% +one + + + align:start position:0% +one +sorry e the ikj deltax so I don't need + + align:start position:0% +sorry e the ikj deltax so I don't need + + + align:start position:0% +sorry e the ikj deltax so I don't need +it here do do you see what I'm sorry I + + align:start position:0% +it here do do you see what I'm sorry I + + + align:start position:0% +it here do do you see what I'm sorry I +did it wrong that e to the ik Delta e to + + align:start position:0% +did it wrong that e to the ik Delta e to + + + align:start position:0% +did it wrong that e to the ik Delta e to +the i j +1 Delta X factors into e to the + + align:start position:0% +the i j +1 Delta X factors into e to the + + + align:start position:0% +the i j +1 Delta X factors into e to the +i k Delta X from the one one and an e to + + align:start position:0% +i k Delta X from the one one and an e to + + + align:start position:0% +i k Delta X from the one one and an e to +the i k j Delta X which is over there so + + align:start position:0% +the i k j Delta X which is over there so + + + align:start position:0% +the i k j Delta X which is over there so +I only wanted this + + align:start position:0% + + + + align:start position:0% + +much + + align:start position:0% + + + + align:start position:0% + +okay sorry that's on the permanent tape + + align:start position:0% +okay sorry that's on the permanent tape + + + align:start position:0% +okay sorry that's on the permanent tape +but maybe it's okay because it makes us + + align:start position:0% +but maybe it's okay because it makes us + + + align:start position:0% +but maybe it's okay because it makes us +think through what's + + align:start position:0% +think through what's + + + align:start position:0% +think through what's +the result from a pure exponential and + + align:start position:0% +the result from a pure exponential and + + + align:start position:0% +the result from a pure exponential and +again the result is pure exponential in + + align:start position:0% +again the result is pure exponential in + + + align:start position:0% +again the result is pure exponential in +pure exponential out but multiplied by + + align:start position:0% +pure exponential out but multiplied by + + + align:start position:0% +pure exponential out but multiplied by +some finite difference growth factor G + + align:start position:0% +some finite difference growth factor G + + + align:start position:0% +some finite difference growth factor G +that depends on the + + align:start position:0% +that depends on the + + + align:start position:0% +that depends on the +frequency and it depends on Delta X it + + align:start position:0% +frequency and it depends on Delta X it + + + align:start position:0% +frequency and it depends on Delta X it +depends on Delta X and it depends on + + align:start position:0% + + + + align:start position:0% + +R well actually it depends on K Delta X + + align:start position:0% +R well actually it depends on K Delta X + + + align:start position:0% +R well actually it depends on K Delta X +together so I could put that together + + align:start position:0% + + + + align:start position:0% + +what what's van Norman's question + + align:start position:0% +what what's van Norman's question + + + align:start position:0% +what what's van Norman's question +now he wants to know is this number it's + + align:start position:0% +now he wants to know is this number it's + + + align:start position:0% +now he wants to know is this number it's +a complex number of course because it's + + align:start position:0% +a complex number of course because it's + + + align:start position:0% +a complex number of course because it's +got this coine of K Delta X plus I sin + + align:start position:0% +got this coine of K Delta X plus I sin + + + align:start position:0% +got this coine of K Delta X plus I sin +of K Delta X he wants to know is it + + align:start position:0% +of K Delta X he wants to know is it + + + align:start position:0% +of K Delta X he wants to know is it +magnitude does the magnitude get bigger + + align:start position:0% +magnitude does the magnitude get bigger + + + align:start position:0% +magnitude does the magnitude get bigger +than + + align:start position:0% +than + + + align:start position:0% +than +one if + + align:start position:0% +one if + + + align:start position:0% +one if +so n steps will give the nth power of + + align:start position:0% +so n steps will give the nth power of + + + align:start position:0% +so n steps will give the nth power of +the thing and it'll blow up or does the + + align:start position:0% +the thing and it'll blow up or does the + + + align:start position:0% +the thing and it'll blow up or does the +magnitude stay less or equal to one in + + align:start position:0% +magnitude stay less or equal to one in + + + align:start position:0% +magnitude stay less or equal to one in +which + + align:start position:0% +which + + + align:start position:0% +which +case it won't blow up in which case we + + align:start position:0% +case it won't blow up in which case we + + + align:start position:0% +case it won't blow up in which case we +have + + align:start position:0% +have + + + align:start position:0% +have +stability of + + align:start position:0% +stability of + + + align:start position:0% +stability of +course it would be great if the + + align:start position:0% +course it would be great if the + + + align:start position:0% +course it would be great if the +magnitude was always exactly one it + + align:start position:0% +magnitude was always exactly one it + + + align:start position:0% +magnitude was always exactly one it +would be great that because that's what + + align:start position:0% +would be great that because that's what + + + align:start position:0% +would be great that because that's what +the true solution has but I that's only + + align:start position:0% +the true solution has but I that's only + + + align:start position:0% +the true solution has but I that's only +going to happen in this special special + + align:start position:0% +going to happen in this special special + + + align:start position:0% +going to happen in this special special +case when R equals 1 and I'm going just + + align:start position:0% +case when R equals 1 and I'm going just + + + align:start position:0% +case when R equals 1 and I'm going just +right on the characteristic when R is + + align:start position:0% +right on the characteristic when R is + + + align:start position:0% +right on the characteristic when R is +exactly one that's the case when that's + + align:start position:0% +exactly one that's the case when that's + + + align:start position:0% +exactly one that's the case when that's +gone this is a one and that has + + align:start position:0% +gone this is a one and that has + + + align:start position:0% +gone this is a one and that has +magnitude exactly one but normally uh R + + align:start position:0% +magnitude exactly one but normally uh R + + + align:start position:0% +magnitude exactly one but normally uh R +is going to be I'm going to be on the + + align:start position:0% +is going to be I'm going to be on the + + + align:start position:0% +is going to be I'm going to be on the +safe side R will be less than one and I + + align:start position:0% +safe side R will be less than one and I + + + align:start position:0% +safe side R will be less than one and I +just want to draw this + + align:start position:0% +just want to draw this + + + align:start position:0% +just want to draw this +voman amplification Factor + + align:start position:0% +voman amplification Factor + + + align:start position:0% +voman amplification Factor +I I'll often use the word growth factor + + align:start position:0% +I I'll often use the word growth factor + + + align:start position:0% +I I'll often use the word growth factor +just because it's shorter but another + + align:start position:0% +just because it's shorter but another + + + align:start position:0% +just because it's shorter but another +word is amplification Factor what does + + align:start position:0% +word is amplification Factor what does + + + align:start position:0% +word is amplification Factor what does +an exponential get Amplified by can you + + align:start position:0% +an exponential get Amplified by can you + + + align:start position:0% +an exponential get Amplified by can you +identify this number in the complex + + align:start position:0% +identify this number in the complex + + + align:start position:0% +identify this number in the complex +plane of course the big question is + + align:start position:0% +plane of course the big question is + + + align:start position:0% +plane of course the big question is +where is it with respect to the unit + + align:start position:0% +where is it with respect to the unit + + + align:start position:0% +where is it with respect to the unit +circle okay take k equals Zer zero + + align:start position:0% +circle okay take k equals Zer zero + + + align:start position:0% +circle okay take k equals Zer zero +frequency the DC term a constant start + + align:start position:0% +frequency the DC term a constant start + + + align:start position:0% +frequency the DC term a constant start +what does that number + + align:start position:0% +what does that number + + + align:start position:0% +what does that number +equal when K is + + align:start position:0% + + + + align:start position:0% + +zero one so that's normal at k equals + + align:start position:0% +zero one so that's normal at k equals + + + align:start position:0% +zero one so that's normal at k equals +z we're right at the position one that's + + align:start position:0% +z we're right at the position one that's + + + align:start position:0% +z we're right at the position one that's +just telling us that a constant initial + + align:start position:0% +just telling us that a constant initial + + + align:start position:0% +just telling us that a constant initial +value stays stays + + align:start position:0% +value stays stays + + + align:start position:0% +value stays stays +unchanged the true growth factor and the + + align:start position:0% +unchanged the true growth factor and the + + + align:start position:0% +unchanged the true growth factor and the +vment amplification Factor both one but + + align:start position:0% +vment amplification Factor both one but + + + align:start position:0% +vment amplification Factor both one but +now let K be none + + align:start position:0% +now let K be none + + + align:start position:0% +now let K be none +Z where is this complex number and now + + align:start position:0% +Z where is this complex number and now + + + align:start position:0% +Z where is this complex number and now +I'm going to impose the condition that R + + align:start position:0% +I'm going to impose the condition that R + + + align:start position:0% +I'm going to impose the condition that R +is between zero and + + align:start position:0% + + + + align:start position:0% + +one because that's I'm I'm I I know that + + align:start position:0% +one because that's I'm I'm I I know that + + + align:start position:0% +one because that's I'm I'm I I know that +from corant that that is going to be + + align:start position:0% +from corant that that is going to be + + + align:start position:0% +from corant that that is going to be +required what's the point here okay then + + align:start position:0% +required what's the point here okay then + + + align:start position:0% +required what's the point here okay then +you see here's a one minus + + align:start position:0% +you see here's a one minus + + + align:start position:0% +you see here's a one minus +r so R is one minus so there's one one + + align:start position:0% +r so R is one minus so there's one one + + + align:start position:0% +r so R is one minus so there's one one +minus r will be a little bit in here and + + align:start position:0% +minus r will be a little bit in here and + + + align:start position:0% +minus r will be a little bit in here and +then what happens when I add on this + + align:start position:0% +then what happens when I add on this + + + align:start position:0% +then what happens when I add on this +number so the one minus r I've done it + + align:start position:0% +number so the one minus r I've done it + + + align:start position:0% +number so the one minus r I've done it +put me here it was real but this number + + align:start position:0% +put me here it was real but this number + + + align:start position:0% +put me here it was real but this number +is not real this this number is R times + + align:start position:0% +is not real this this number is R times + + + align:start position:0% +is not real this this number is R times +some complex number but what do I know I + + align:start position:0% +some complex number but what do I know I + + + align:start position:0% +some complex number but what do I know I +do know something critical here what do + + align:start position:0% +do know something critical here what do + + + align:start position:0% +do know something critical here what do +I know about this + + align:start position:0% +I know about this + + + align:start position:0% +I know about this +number I know its absolute value is one + + align:start position:0% +number I know its absolute value is one + + + align:start position:0% +number I know its absolute value is one +so that it gets multiplied by an R look + + align:start position:0% +so that it gets multiplied by an R look + + + align:start position:0% +so that it gets multiplied by an R look +look look + + align:start position:0% +look look + + + align:start position:0% +look look +look I start with a 1 minus r so I go to + + align:start position:0% +look I start with a 1 minus r so I go to + + + align:start position:0% +look I start with a 1 minus r so I go to +one back to R and now I add in this part + + align:start position:0% +one back to R and now I add in this part + + + align:start position:0% +one back to R and now I add in this part +which is somewhere on a circle of radius + + align:start position:0% +which is somewhere on a circle of radius + + + align:start position:0% +which is somewhere on a circle of radius +R that's that's everything in this + + align:start position:0% +R that's that's everything in this + + + align:start position:0% +R that's that's everything in this +problem there that's a circle of radius + + align:start position:0% +problem there that's a circle of radius + + + align:start position:0% +problem there that's a circle of radius +R around the point one minus + + align:start position:0% +R around the point one minus + + + align:start position:0% +R around the point one minus +r and the of + + align:start position:0% +r and the of + + + align:start position:0% +r and the of +course I I'm inside the circle oh and + + align:start position:0% +course I I'm inside the circle oh and + + + align:start position:0% +course I I'm inside the circle oh and +you could say well you could have seen + + align:start position:0% +you could say well you could have seen + + + align:start position:0% +you could say well you could have seen +that clearly by just using the triangle + + align:start position:0% +that clearly by just using the triangle + + + align:start position:0% +that clearly by just using the triangle +inequality the magnitude of this it + + align:start position:0% +inequality the magnitude of this it + + + align:start position:0% +inequality the magnitude of this it +can't be bigger than the magnitude of + + align:start position:0% +can't be bigger than the magnitude of + + + align:start position:0% +can't be bigger than the magnitude of +that which is + + align:start position:0% +that which is + + + align:start position:0% +that which is +what R plus the magnitude of that which + + align:start position:0% +what R plus the magnitude of that which + + + align:start position:0% +what R plus the magnitude of that which +is + + align:start position:0% +is + + + align:start position:0% +is +what 1 minus r so the magnitude by the + + align:start position:0% +what 1 minus r so the magnitude by the + + + align:start position:0% +what 1 minus r so the magnitude by the +triangle inequality can't be more than r + + align:start position:0% +triangle inequality can't be more than r + + + align:start position:0% +triangle inequality can't be more than r ++ 1 - R which is 1 + + align:start position:0% ++ 1 - R which is 1 + + + align:start position:0% ++ 1 - R which is 1 +but now wait a minute where did I use + + align:start position:0% +but now wait a minute where did I use + + + align:start position:0% +but now wait a minute where did I use +the the the Quant + + align:start position:0% +the the the Quant + + + align:start position:0% +the the the Quant +condition the way I said that there + + align:start position:0% +condition the way I said that there + + + align:start position:0% +condition the way I said that there +sounded like it would always work this + + align:start position:0% +sounded like it would always work this + + + align:start position:0% +sounded like it would always work this +has magnitude + + align:start position:0% +has magnitude + + + align:start position:0% +has magnitude +R this has oh no what's going on here + + align:start position:0% +R this has oh no what's going on here + + + align:start position:0% +R this has oh no what's going on here +suppose R is bigger than one what what's + + align:start position:0% +suppose R is bigger than one what what's + + + align:start position:0% +suppose R is bigger than one what what's +going wrong here in fact what's the + + align:start position:0% +going wrong here in fact what's the + + + align:start position:0% +going wrong here in fact what's the +picture if R is bigger than + + align:start position:0% +picture if R is bigger than + + + align:start position:0% +picture if R is bigger than +one if R is bigger than one then my 1 - + + align:start position:0% +one if R is bigger than one then my 1 - + + + align:start position:0% +one if R is bigger than one then my 1 - +R is out here + + align:start position:0% +R is out here + + + align:start position:0% +R is out here +somewhere and my circle so this is the + + align:start position:0% +somewhere and my circle so this is the + + + align:start position:0% +somewhere and my circle so this is the +unstable case 1 - R and then a circle of + + align:start position:0% +unstable case 1 - R and then a circle of + + + align:start position:0% +unstable case 1 - R and then a circle of +radius R bad news + + align:start position:0% +radius R bad news + + + align:start position:0% +radius R bad news +right every frequency is unstable in + + align:start position:0% +right every frequency is unstable in + + + align:start position:0% +right every frequency is unstable in +fact when I'm when I'm reaching too far + + align:start position:0% +fact when I'm when I'm reaching too far + + + align:start position:0% +fact when I'm when I'm reaching too far +and that's just telling me I'm not using + + align:start position:0% +and that's just telling me I'm not using + + + align:start position:0% +and that's just telling me I'm not using +the information I need I don't have a + + align:start position:0% +the information I need I don't have a + + + align:start position:0% +the information I need I don't have a +chance for uh of keeping controlling any + + align:start position:0% +chance for uh of keeping controlling any + + + align:start position:0% +chance for uh of keeping controlling any +uh frequency okay I've got just + + align:start position:0% +uh frequency okay I've got just + + + align:start position:0% +uh frequency okay I've got just +time to show how bad this second method + + align:start position:0% +time to show how bad this second method + + + align:start position:0% +time to show how bad this second method +is so nobody's name is one nobody wanted + + align:start position:0% +is so nobody's name is one nobody wanted + + + align:start position:0% +is so nobody's name is one nobody wanted +his name associated with that second + + align:start position:0% +his name associated with that second + + + align:start position:0% +his name associated with that second +method why is that so what's the + + align:start position:0% +method why is that so what's the + + + align:start position:0% +method why is that so what's the +vanan quantity for the second method + + align:start position:0% +vanan quantity for the second method + + + align:start position:0% +vanan quantity for the second method +okay just space here to write so this is + + align:start position:0% +okay just space here to write so this is + + + align:start position:0% +okay just space here to write so this is +now I I want to know the number for that + + align:start position:0% +now I I want to know the number for that + + + align:start position:0% +now I I want to know the number for that +second method so now the method is + + align:start position:0% +second method so now the method is + + + align:start position:0% +second method so now the method is +uj+ UJ n + + align:start position:0% +uj+ UJ n + + + align:start position:0% +uj+ UJ n ++1 is + + align:start position:0% ++1 is + + + align:start position:0% ++1 is +ujn from the time difference plus r * UJ + + align:start position:0% +ujn from the time difference plus r * UJ + + + align:start position:0% +ujn from the time difference plus r * UJ +oh over 2 u j + 1 n + + align:start position:0% +oh over 2 u j + 1 n + + + align:start position:0% +oh over 2 u j + 1 n +minus no plus is + + align:start position:0% +minus no plus is + + + align:start position:0% +minus no plus is +it it's minus u j minus one + + align:start position:0% +it it's minus u j minus one + + + align:start position:0% +it it's minus u j minus one +n is that this is going to be the bad + + align:start position:0% +n is that this is going to be the bad + + + align:start position:0% +n is that this is going to be the bad +method it it looks good because the + + align:start position:0% +method it it looks good because the + + + align:start position:0% +method it it looks good because the +center + + align:start position:0% +center + + + align:start position:0% +center +difference is more accurate than a + + align:start position:0% +difference is more accurate than a + + + align:start position:0% +difference is more accurate than a +one-sided + + align:start position:0% +one-sided + + + align:start position:0% +one-sided +difference but it's also unstable here + + align:start position:0% +difference but it's also unstable here + + + align:start position:0% +difference but it's also unstable here +can you can you look at that and see + + align:start position:0% +can you can you look at that and see + + + align:start position:0% +can you can you look at that and see +what the an number G is going to + + align:start position:0% +what the an number G is going to + + + align:start position:0% +what the an number G is going to +be think of an exponential going in what + + align:start position:0% +be think of an exponential going in what + + + align:start position:0% +be think of an exponential going in what +exponential comes out it so + + align:start position:0% +exponential comes out it so + + + align:start position:0% +exponential comes out it so +G is a one from this + + align:start position:0% +G is a one from this + + + align:start position:0% +G is a one from this +now this is our guy that's shifted over + + align:start position:0% +now this is our guy that's shifted over + + + align:start position:0% +now this is our guy that's shifted over +so that will be an R over 2 e to the i k + + align:start position:0% +so that will be an R over 2 e to the i k + + + align:start position:0% +so that will be an R over 2 e to the i k +Delta X just just as it was + + align:start position:0% +Delta X just just as it was + + + align:start position:0% +Delta X just just as it was +before and this one will be a minus r + + align:start position:0% +before and this one will be a minus r + + + align:start position:0% +before and this one will be a minus r +over2 times e to + + align:start position:0% + + + + align:start position:0% + +the so it's back back one step so + + align:start position:0% +the so it's back back one step so + + + align:start position:0% +the so it's back back one step so +there'll be an e to the minus i k Delta + + align:start position:0% +there'll be an e to the minus i k Delta + + + align:start position:0% +there'll be an e to the minus i k Delta +X + + align:start position:0% +X + + + align:start position:0% +X +so what's with this + + align:start position:0% + + + + align:start position:0% + +now G is 1 plus this quantity R over 2 * + + align:start position:0% +now G is 1 plus this quantity R over 2 * + + + align:start position:0% +now G is 1 plus this quantity R over 2 * +e to the IX minus eus + + align:start position:0% +e to the IX minus eus + + + align:start position:0% +e to the IX minus eus +IX what am I seeing + + align:start position:0% +IX what am I seeing + + + align:start position:0% +IX what am I seeing +there I'm seeing 1 + + + align:start position:0% +there I'm seeing 1 + + + + align:start position:0% +there I'm seeing 1 + +r and everybody recognizes this minus + + align:start position:0% +r and everybody recognizes this minus + + + align:start position:0% +r and everybody recognizes this minus +this over two + + align:start position:0% + + + + align:start position:0% + +as I + + align:start position:0% +as I + + + align:start position:0% +as I +s i sin K Delta + + align:start position:0% + + + + align:start position:0% + +X that's the amplification factor and is + + align:start position:0% +X that's the amplification factor and is + + + align:start position:0% +X that's the amplification factor and is +it smaller than + + align:start position:0% + + + + align:start position:0% + +one no way no way let me raise it up + + align:start position:0% +one no way no way let me raise it up + + + align:start position:0% +one no way no way let me raise it up +here so I don't care whether R is less + + align:start position:0% +here so I don't care whether R is less + + + align:start position:0% +here so I don't care whether R is less +than one or not I'm lost because the + + align:start position:0% +than one or not I'm lost because the + + + align:start position:0% +than one or not I'm lost because the +amplification Factor here is this is a + + align:start position:0% +amplification Factor here is this is a + + + align:start position:0% +amplification Factor here is this is a +pure imaginary number number this is a + + align:start position:0% +pure imaginary number number this is a + + + align:start position:0% +pure imaginary number number this is a +real number so I have the sum of squares + + align:start position:0% +real number so I have the sum of squares + + + align:start position:0% +real number so I have the sum of squares +to get the magnitude it'll be the square + + align:start position:0% +to get the magnitude it'll be the square + + + align:start position:0% +to get the magnitude it'll be the square +root of 1 plus r sin K Delta x^2 so if I + + align:start position:0% +root of 1 plus r sin K Delta x^2 so if I + + + align:start position:0% +root of 1 plus r sin K Delta x^2 so if I +draw the bad picture + + align:start position:0% +draw the bad picture + + + align:start position:0% +draw the bad picture +then what's the bad picture is now it + + align:start position:0% +then what's the bad picture is now it + + + align:start position:0% +then what's the bad picture is now it +goes to one and then it goes way up the + + align:start position:0% +goes to one and then it goes way up the + + + align:start position:0% +goes to one and then it goes way up the +imaginary + + align:start position:0% +imaginary + + + align:start position:0% +imaginary +axis well maybe not way up but + + align:start position:0% +axis well maybe not way up but + + + align:start position:0% +axis well maybe not way up but +up sorry I didn't make shouldn't have + + align:start position:0% +up sorry I didn't make shouldn't have + + + align:start position:0% +up sorry I didn't make shouldn't have +made it quite as bad as it was if I + + align:start position:0% +made it quite as bad as it was if I + + + align:start position:0% +made it quite as bad as it was if I +reduce r i don't go so far up but no + + align:start position:0% +reduce r i don't go so far up but no + + + align:start position:0% +reduce r i don't go so far up but no +hope so do you see why that one is bad + + align:start position:0% +hope so do you see why that one is bad + + + align:start position:0% +hope so do you see why that one is bad +because the the amplification factor of + + align:start position:0% +because the the amplification factor of + + + align:start position:0% +because the the amplification factor of +annoyment tells us what Quran did not + + align:start position:0% +annoyment tells us what Quran did not + + + align:start position:0% +annoyment tells us what Quran did not +tell us that the amplification Factor + + align:start position:0% +tell us that the amplification Factor + + + align:start position:0% +tell us that the amplification Factor +here has magnitude bigger than one it's + + align:start position:0% +here has magnitude bigger than one it's + + + align:start position:0% +here has magnitude bigger than one it's +outside the + + align:start position:0% +outside the + + + align:start position:0% +outside the +circle and uh every exponential is + + align:start position:0% +circle and uh every exponential is + + + align:start position:0% +circle and uh every exponential is +growing and there's no hope okay so the + + align:start position:0% +growing and there's no hope okay so the + + + align:start position:0% +growing and there's no hope okay so the +second lecture on this section 52 of the + + align:start position:0% +second lecture on this section 52 of the + + + align:start position:0% +second lecture on this section 52 of the +notes will + + align:start position:0% +notes will + + + align:start position:0% +notes will +be about LAX friedr and LAX wend order + + align:start position:0% +be about LAX friedr and LAX wend order + + + align:start position:0% +be about LAX friedr and LAX wend order +of accuracy stability and actual + + align:start position:0% +of accuracy stability and actual + + + align:start position:0% +of accuracy stability and actual +behavior in + + align:start position:0% +behavior in + + + align:start position:0% +behavior in +practice okay see you Wednesday + + align:start position:0% +practice okay see you Wednesday + + + align:start position:0% +practice okay see you Wednesday +thanks \ No newline at end of file diff --git a/e2WwaVi6VwA.txt b/e2WwaVi6VwA.txt new file mode 100644 index 0000000000000000000000000000000000000000..66f6425877df1864956bb9172f8db7ca3deee4af --- /dev/null +++ b/e2WwaVi6VwA.txt @@ -0,0 +1,3075 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay so I'm Ed Schultz and + + align:start position:0% +ocw.mit.edu okay so I'm Ed Schultz and + + + align:start position:0% +ocw.mit.edu okay so I'm Ed Schultz and +this is Mike fitgerald and we work on a + + align:start position:0% +this is Mike fitgerald and we work on a + + + align:start position:0% +this is Mike fitgerald and we work on a +backhand + + align:start position:0% +backhand + + + align:start position:0% +backhand +compter and to start off let's see show + + align:start position:0% +compter and to start off let's see show + + + align:start position:0% +compter and to start off let's see show +hands who here knows how to play back + + align:start position:0% +hands who here knows how to play back + + + align:start position:0% +hands who here knows how to play back +gam okay a few so to give you an idea of + + align:start position:0% +gam okay a few so to give you an idea of + + + align:start position:0% +gam okay a few so to give you an idea of +how it works um it involves both uh + + align:start position:0% +how it works um it involves both uh + + + align:start position:0% +how it works um it involves both uh +skill and luck and it's a two-player + + align:start position:0% +skill and luck and it's a two-player + + + align:start position:0% +skill and luck and it's a two-player +game and the object is to move all your + + align:start position:0% +game and the object is to move all your + + + align:start position:0% +game and the object is to move all your +pieces past your opponent's pieces and + + align:start position:0% +pieces past your opponent's pieces and + + + align:start position:0% +pieces past your opponent's pieces and +off the board so White's trying to move + + align:start position:0% +off the board so White's trying to move + + + align:start position:0% +off the board so White's trying to move +his pieces this way down and across and + + align:start position:0% +his pieces this way down and across and + + + align:start position:0% +his pieces this way down and across and +Brown's trying to move his pieces the + + align:start position:0% +Brown's trying to move his pieces the + + + align:start position:0% +Brown's trying to move his pieces the +other way and you move by rolling the + + align:start position:0% +other way and you move by rolling the + + + align:start position:0% +other way and you move by rolling the +dice some important rules are that you + + align:start position:0% +dice some important rules are that you + + + align:start position:0% +dice some important rules are that you +cannot land on a point on which your + + align:start position:0% +cannot land on a point on which your + + + align:start position:0% +cannot land on a point on which your +opponent has two or more pieces and if + + align:start position:0% +opponent has two or more pieces and if + + + align:start position:0% +opponent has two or more pieces and if +your opponent only has a single uh piece + + align:start position:0% +your opponent only has a single uh piece + + + align:start position:0% +your opponent only has a single uh piece +there you can land on it and send it + + align:start position:0% +there you can land on it and send it + + + align:start position:0% +there you can land on it and send it +back to the + + align:start position:0% + + + + align:start position:0% + +beginning so the goals of this project + + align:start position:0% +beginning so the goals of this project + + + align:start position:0% +beginning so the goals of this project +when we started off were first of all + + align:start position:0% +when we started off were first of all + + + align:start position:0% +when we started off were first of all +they implement the rules of backham and + + align:start position:0% +they implement the rules of backham and + + + align:start position:0% +they implement the rules of backham and +get the game going and that took a good + + align:start position:0% +get the game going and that took a good + + + align:start position:0% +get the game going and that took a good +amount of work the next we wanted to + + align:start position:0% +amount of work the next we wanted to + + + align:start position:0% +amount of work the next we wanted to +create or find the function that + + align:start position:0% +create or find the function that + + + align:start position:0% +create or find the function that +evaluates or says how good a given board + + align:start position:0% +evaluates or says how good a given board + + + align:start position:0% +evaluates or says how good a given board +is and and then we wanted to be able to + + align:start position:0% +is and and then we wanted to be able to + + + align:start position:0% +is and and then we wanted to be able to +look into the future uh in in order to + + align:start position:0% +look into the future uh in in order to + + + align:start position:0% +look into the future uh in in order to +better determine what move to choose now + + align:start position:0% +better determine what move to choose now + + + align:start position:0% +better determine what move to choose now +and this is the part of the um program + + align:start position:0% +and this is the part of the um program + + + align:start position:0% +and this is the part of the um program +that we + + align:start position:0% +that we + + + align:start position:0% +that we +parallelized and finally our last goal + + align:start position:0% +parallelized and finally our last goal + + + align:start position:0% +parallelized and finally our last goal +was to try to teach the player um teach + + align:start position:0% +was to try to teach the player um teach + + + align:start position:0% +was to try to teach the player um teach +the player how to improve by suggesting + + align:start position:0% +the player how to improve by suggesting + + + align:start position:0% +the player how to improve by suggesting +why one move might be better than + + align:start position:0% +why one move might be better than + + + align:start position:0% +why one move might be better than +another in + + align:start position:0% + + + + align:start position:0% + +English so to start with um the two + + align:start position:0% +English so to start with um the two + + + align:start position:0% +English so to start with um the two +basic cons of board evaluation are just + + align:start position:0% +basic cons of board evaluation are just + + + align:start position:0% +basic cons of board evaluation are just +a static evaluator and a noral net and + + align:start position:0% +a static evaluator and a noral net and + + + align:start position:0% +a static evaluator and a noral net and +the static evalu static evaluator works + + align:start position:0% +the static evalu static evaluator works + + + align:start position:0% +the static evalu static evaluator works +by looking at features of the board and + + align:start position:0% +by looking at features of the board and + + + align:start position:0% +by looking at features of the board and +creating a score based on that feature + + align:start position:0% +creating a score based on that feature + + + align:start position:0% +creating a score based on that feature +and then multiplying it by weight based + + align:start position:0% +and then multiplying it by weight based + + + align:start position:0% +and then multiplying it by weight based +on how important that feature is and + + align:start position:0% +on how important that feature is and + + + align:start position:0% +on how important that feature is and +summing them up so a program like this + + align:start position:0% +summing them up so a program like this + + + align:start position:0% +summing them up so a program like this +was created by Hans Berliner at CMU in + + align:start position:0% +was created by Hans Berliner at CMU in + + + align:start position:0% +was created by Hans Berliner at CMU in +1979 and it was actually the first + + align:start position:0% +1979 and it was actually the first + + + align:start position:0% +1979 and it was actually the first +program to beat a ruling world champion + + align:start position:0% +program to beat a ruling world champion + + + align:start position:0% +program to beat a ruling world champion +and they said the program got a little + + align:start position:0% +and they said the program got a little + + + align:start position:0% +and they said the program got a little +lucky but it did win and one of the + + align:start position:0% +lucky but it did win and one of the + + + align:start position:0% +lucky but it did win and one of the +important features was it adjusted the + + align:start position:0% +important features was it adjusted the + + + align:start position:0% +important features was it adjusted the +weights as the game went on because + + align:start position:0% +weights as the game went on because + + + align:start position:0% +weights as the game went on because +certain features became less important + + align:start position:0% +certain features became less important + + + align:start position:0% +certain features became less important +as the game progressed and other + + align:start position:0% +as the game progressed and other + + + align:start position:0% +as the game progressed and other +features became more + + align:start position:0% +features became more + + + align:start position:0% +features became more +important so the next approach that + + align:start position:0% +important so the next approach that + + + align:start position:0% +important so the next approach that +people have used is um training neural + + align:start position:0% +people have used is um training neural + + + align:start position:0% +people have used is um training neural +Nets um to determine how good a board is + + align:start position:0% +Nets um to determine how good a board is + + + align:start position:0% +Nets um to determine how good a board is +and these have been really successful + + align:start position:0% +and these have been really successful + + + align:start position:0% +and these have been really successful +they work by basically playing hundreds + + align:start position:0% +they work by basically playing hundreds + + + align:start position:0% +they work by basically playing hundreds +of thousands if not millions of games uh + + align:start position:0% +of thousands if not millions of games uh + + + align:start position:0% +of thousands if not millions of games uh +against itself + + align:start position:0% + + + + align:start position:0% + +and so it improves this way and after + + align:start position:0% +and so it improves this way and after + + + align:start position:0% +and so it improves this way and after +about a million and a half games it + + align:start position:0% +about a million and a half games it + + + align:start position:0% +about a million and a half games it +reaches um its maximum + + align:start position:0% +reaches um its maximum + + + align:start position:0% +reaches um its maximum +performance and one such evalu uh board + + align:start position:0% +performance and one such evalu uh board + + + align:start position:0% +performance and one such evalu uh board +evaluator is poal which was released by + + align:start position:0% +evaluator is poal which was released by + + + align:start position:0% +evaluator is poal which was released by +Jerry Torro in + + align:start position:0% +Jerry Torro in + + + align:start position:0% +Jerry Torro in +1993 and this is the evaluation function + + align:start position:0% +1993 and this is the evaluation function + + + align:start position:0% +1993 and this is the evaluation function +that we use for our + + align:start position:0% +that we use for our + + + align:start position:0% +that we use for our +program looks like we lost network + + align:start position:0% +program looks like we lost network + + + align:start position:0% +program looks like we lost network +connection this is the evaluation + + align:start position:0% +connection this is the evaluation + + + align:start position:0% +connection this is the evaluation +function that we use for our program and + + align:start position:0% +function that we use for our program and + + + align:start position:0% +function that we use for our program and +he sort of released this as a benchmark + + align:start position:0% +he sort of released this as a benchmark + + + align:start position:0% +he sort of released this as a benchmark +evaluator so that other people in the + + align:start position:0% +evaluator so that other people in the + + + align:start position:0% +evaluator so that other people in the +development commu Community could have + + align:start position:0% +development commu Community could have + + + align:start position:0% +development commu Community could have +something to compare their evaluators + + align:start position:0% +something to compare their evaluators + + + align:start position:0% +something to compare their evaluators +against and it plays a intermediate + + align:start position:0% +against and it plays a intermediate + + + align:start position:0% +against and it plays a intermediate +level if not a pretty strong + + align:start position:0% + + + + align:start position:0% + +level so our next goal was to implement + + align:start position:0% +level so our next goal was to implement + + + align:start position:0% +level so our next goal was to implement +the search that looks into the future in + + align:start position:0% +the search that looks into the future in + + + align:start position:0% +the search that looks into the future in +order to help choose the best move now + + align:start position:0% +order to help choose the best move now + + + align:start position:0% +order to help choose the best move now +one of the challenges of this is that + + align:start position:0% +one of the challenges of this is that + + + align:start position:0% +one of the challenges of this is that +the branching factor is so large because + + align:start position:0% +the branching factor is so large because + + + align:start position:0% +the branching factor is so large because +you don't know what the dice roles are + + align:start position:0% +you don't know what the dice roles are + + + align:start position:0% +you don't know what the dice roles are +going to be be in the + + align:start position:0% +going to be be in the + + + align:start position:0% +going to be be in the +future and like in checkers the BR the + + align:start position:0% +future and like in checkers the BR the + + + align:start position:0% +future and like in checkers the BR the +branching factor is 10 in chess is 35 to + + align:start position:0% +branching factor is 10 in chess is 35 to + + + align:start position:0% +branching factor is 10 in chess is 35 to +40 but in back G and for a turn it's + + align:start position:0% +40 but in back G and for a turn it's + + + align:start position:0% +40 but in back G and for a turn it's +around + + align:start position:0% +around + + + align:start position:0% +around +400 another challenge that we faced in + + align:start position:0% +400 another challenge that we faced in + + + align:start position:0% +400 another challenge that we faced in +the search was was that um the Pu Val + + align:start position:0% +the search was was that um the Pu Val + + + align:start position:0% +the search was was that um the Pu Val +function that we use is not Zero Sum so + + align:start position:0% +function that we use is not Zero Sum so + + + align:start position:0% +function that we use is not Zero Sum so +that produced some challenges that + + align:start position:0% +that produced some challenges that + + + align:start position:0% +that produced some challenges that +you'll see and also there's the question + + align:start position:0% +you'll see and also there's the question + + + align:start position:0% +you'll see and also there's the question +of whether seing searching deeper + + align:start position:0% +of whether seing searching deeper + + + align:start position:0% +of whether seing searching deeper +actually does produce better play + + align:start position:0% +actually does produce better play + + + align:start position:0% +actually does produce better play +and most papers say that the board + + align:start position:0% +and most papers say that the board + + + align:start position:0% +and most papers say that the board +evaluator is more important than the + + align:start position:0% +evaluator is more important than the + + + align:start position:0% +evaluator is more important than the +searching deeper but they do say that + + align:start position:0% +searching deeper but they do say that + + + align:start position:0% +searching deeper but they do say that +searching into the future uh does + + align:start position:0% +searching into the future uh does + + + align:start position:0% +searching into the future uh does +improve play and especially when you're + + align:start position:0% +improve play and especially when you're + + + align:start position:0% +improve play and especially when you're +already at a pretty high level of play + + align:start position:0% +already at a pretty high level of play + + + align:start position:0% +already at a pretty high level of play +where everyone's near the same and + + align:start position:0% +where everyone's near the same and + + + align:start position:0% +where everyone's near the same and +playing really well a slight perform a + + align:start position:0% +playing really well a slight perform a + + + align:start position:0% +playing really well a slight perform a +slight increase in performance could + + align:start position:0% +slight increase in performance could + + + align:start position:0% +slight increase in performance could +make a big + + align:start position:0% + + + + align:start position:0% + +difference so here's a an illustration + + align:start position:0% +difference so here's a an illustration + + + align:start position:0% +difference so here's a an illustration +of the search tree to give you a better + + align:start position:0% +of the search tree to give you a better + + + align:start position:0% +of the search tree to give you a better +idea of how it works so say it's X's + + align:start position:0% +idea of how it works so say it's X's + + + align:start position:0% +idea of how it works so say it's X's +turn there might be 20 or so moves that + + align:start position:0% +turn there might be 20 or so moves that + + + align:start position:0% +turn there might be 20 or so moves that +um he can commit now these are series of + + align:start position:0% +um he can commit now these are series of + + + align:start position:0% +um he can commit now these are series of +moves so you roll the two dice and if + + align:start position:0% +moves so you roll the two dice and if + + + align:start position:0% +moves so you roll the two dice and if +they're doubles you get four moves um + + align:start position:0% +they're doubles you get four moves um + + + align:start position:0% +they're doubles you get four moves um +certain turns you may not be able to + + align:start position:0% +certain turns you may not be able to + + + align:start position:0% +certain turns you may not be able to +move at all so you might not have any + + align:start position:0% +move at all so you might not have any + + + align:start position:0% +move at all so you might not have any +moves so that really + + align:start position:0% +moves so that really + + + align:start position:0% +moves so that really +varies so after those 20 moves O's the + + align:start position:0% +varies so after those 20 moves O's the + + + align:start position:0% +varies so after those 20 moves O's the +other player o is going to roll and + + align:start position:0% +other player o is going to roll and + + + align:start position:0% +other player o is going to roll and +there's 21 different dice com ations he + + align:start position:0% +there's 21 different dice com ations he + + + align:start position:0% +there's 21 different dice com ations he +can have and then for each of those + + align:start position:0% +can have and then for each of those + + + align:start position:0% +can have and then for each of those +there's about 20 moves and then it's X's + + align:start position:0% +there's about 20 moves and then it's X's + + + align:start position:0% +there's about 20 moves and then it's X's +role and once again he has 21 dice + + align:start position:0% +role and once again he has 21 dice + + + align:start position:0% +role and once again he has 21 dice +combinations and then X's move so this + + align:start position:0% +combinations and then X's move so this + + + align:start position:0% +combinations and then X's move so this +is looking uh two moves into the + + align:start position:0% +is looking uh two moves into the + + + align:start position:0% +is looking uh two moves into the +future so the idea is to build this + + align:start position:0% +future so the idea is to build this + + + align:start position:0% +future so the idea is to build this +search tray and then at this point we're + + align:start position:0% +search tray and then at this point we're + + + align:start position:0% +search tray and then at this point we're +already up to 3.5 million + + align:start position:0% +already up to 3.5 million + + + align:start position:0% +already up to 3.5 million +boards and so you have all these Leaf + + align:start position:0% +boards and so you have all these Leaf + + + align:start position:0% +boards and so you have all these Leaf +nodes that represent your board boards + + align:start position:0% +nodes that represent your board boards + + + align:start position:0% +nodes that represent your board boards +and you're going to evaluate them with + + align:start position:0% +and you're going to evaluate them with + + + align:start position:0% +and you're going to evaluate them with +your evaluation function to determine + + align:start position:0% +your evaluation function to determine + + + align:start position:0% +your evaluation function to determine +how good they are since it's not Zero + + align:start position:0% +how good they are since it's not Zero + + + align:start position:0% +how good they are since it's not Zero +Sum you have to evaluate it for both + + align:start position:0% +Sum you have to evaluate it for both + + + align:start position:0% +Sum you have to evaluate it for both +player and these both these values need + + align:start position:0% +player and these both these values need + + + align:start position:0% +player and these both these values need +to get passed up um as you're going to + + align:start position:0% +to get passed up um as you're going to + + + align:start position:0% +to get passed up um as you're going to +move back up the tree to determine the + + align:start position:0% +move back up the tree to determine the + + + align:start position:0% +move back up the tree to determine the +best + + align:start position:0% + + + + align:start position:0% + +move so you start at the bottom and you + + align:start position:0% +move so you start at the bottom and you + + + align:start position:0% +move so you start at the bottom and you +say that since his X is move he's going + + align:start position:0% +say that since his X is move he's going + + + align:start position:0% +say that since his X is move he's going +to choose the best possible move given + + align:start position:0% +to choose the best possible move given + + + align:start position:0% +to choose the best possible move given +that + + align:start position:0% +that + + + align:start position:0% +that +role and and in order to move up further + + align:start position:0% +role and and in order to move up further + + + align:start position:0% +role and and in order to move up further +and calculate the value for the parent + + align:start position:0% +and calculate the value for the parent + + + align:start position:0% +and calculate the value for the parent +node you say it's equal to the + + align:start position:0% +node you say it's equal to the + + + align:start position:0% +node you say it's equal to the +probability of the dice roll for the + + align:start position:0% +probability of the dice roll for the + + + align:start position:0% +probability of the dice roll for the +child node times um the value that's + + align:start position:0% +child node times um the value that's + + + align:start position:0% +child node times um the value that's +stored in that child + + align:start position:0% + + + + align:start position:0% + +node and then you keep doing this and + + align:start position:0% +node and then you keep doing this and + + + align:start position:0% +node and then you keep doing this and +repeating this o picks his best move and + + align:start position:0% +repeating this o picks his best move and + + + align:start position:0% +repeating this o picks his best move and +sort of sums the expected value and then + + align:start position:0% +sort of sums the expected value and then + + + align:start position:0% +sort of sums the expected value and then +you get back up to the top and X picks + + align:start position:0% +you get back up to the top and X picks + + + align:start position:0% +you get back up to the top and X picks +his best + + align:start position:0% +his best + + + align:start position:0% +his best +move so now I'm going to hand it over to + + align:start position:0% +move so now I'm going to hand it over to + + + align:start position:0% +move so now I'm going to hand it over to +Mike who's going to talk about the part + + align:start position:0% +Mike who's going to talk about the part + + + align:start position:0% +Mike who's going to talk about the part +of code that we + + align:start position:0% +of code that we + + + align:start position:0% +of code that we +parallelized and there's a question + + align:start position:0% +parallelized and there's a question + + + align:start position:0% +parallelized and there's a question +quick question can you use Alpha Beta + + align:start position:0% +quick question can you use Alpha Beta + + + align:start position:0% +quick question can you use Alpha Beta +pruning do you know about Alpha Beta + + align:start position:0% +pruning do you know about Alpha Beta + + + align:start position:0% +pruning do you know about Alpha Beta +pruning uh yeah people have used that + + align:start position:0% +pruning uh yeah people have used that + + + align:start position:0% +pruning uh yeah people have used that +and um just like a beam search of + + align:start position:0% +and um just like a beam search of + + + align:start position:0% +and um just like a beam search of +narrowing it down um typically by you + + align:start position:0% +narrowing it down um typically by you + + + align:start position:0% +narrowing it down um typically by you +know down to the square root of n so you + + align:start position:0% +know down to the square root of n so you + + + align:start position:0% +know down to the square root of n so you +would have a 20 branching Factor rather + + align:start position:0% +would have a 20 branching Factor rather + + + align:start position:0% +would have a 20 branching Factor rather +than a 400 it seems like a real payoff + + align:start position:0% +than a 400 it seems like a real payoff + + + align:start position:0% +than a 400 it seems like a real payoff +if you can make it work here I don't + + align:start position:0% +if you can make it work here I don't + + + align:start position:0% +if you can make it work here I don't +know if there's some reason back why + + align:start position:0% +know if there's some reason back why + + + align:start position:0% +know if there's some reason back why +it's hard um well we we actually didn't + + align:start position:0% +it's hard um well we we actually didn't + + + align:start position:0% +it's hard um well we we actually didn't +get to that point we were just spent a + + align:start position:0% +get to that point we were just spent a + + + align:start position:0% +get to that point we were just spent a +lot of time just implementing the rules + + align:start position:0% +lot of time just implementing the rules + + + align:start position:0% +lot of time just implementing the rules +of the + + align:start position:0% + + + + align:start position:0% + +game all right so um so so the first + + align:start position:0% +game all right so um so so the first + + + align:start position:0% +game all right so um so so the first +thing we we looked at and said um this + + align:start position:0% +thing we we looked at and said um this + + + align:start position:0% +thing we we looked at and said um this +would be perfect for parall + + align:start position:0% +would be perfect for parall + + + align:start position:0% +would be perfect for parall +parallelizing is uh just the Brute Force + + align:start position:0% +parallelizing is uh just the Brute Force + + + align:start position:0% +parallelizing is uh just the Brute Force +evaluation of those you know million of + + align:start position:0% +evaluation of those you know million of + + + align:start position:0% +evaluation of those you know million of +boards that you get down to at the end + + align:start position:0% +boards that you get down to at the end + + + align:start position:0% +boards that you get down to at the end +um which if you want run through on One + + align:start position:0% +um which if you want run through on One + + + align:start position:0% +um which if you want run through on One +processor just takes a while so we + + align:start position:0% +processor just takes a while so we + + + align:start position:0% +processor just takes a while so we +decided to um + + align:start position:0% +decided to um + + + align:start position:0% +decided to um +just generally evaluation of a board + + align:start position:0% +just generally evaluation of a board + + + align:start position:0% +just generally evaluation of a board +regardless of its state takes the same + + align:start position:0% +regardless of its state takes the same + + + align:start position:0% +regardless of its state takes the same +amount of time so we just had to split + + align:start position:0% +amount of time so we just had to split + + + align:start position:0% +amount of time so we just had to split +the number evenly between um + + align:start position:0% +the number evenly between um + + + align:start position:0% +the number evenly between um +spus uh we had to keep it around a + + align:start position:0% +spus uh we had to keep it around a + + + align:start position:0% +spus uh we had to keep it around a +multiple of four just to get um the dma + + align:start position:0% +multiple of four just to get um the dma + + + align:start position:0% +multiple of four just to get um the dma +calls to line up nicely with the floats + + align:start position:0% +calls to line up nicely with the floats + + + align:start position:0% +calls to line up nicely with the floats +that we were returning and things like + + align:start position:0% +that we were returning and things like + + + align:start position:0% +that we were returning and things like +that um so if you're evaluating a + + align:start position:0% +that um so if you're evaluating a + + + align:start position:0% +that um so if you're evaluating a +million boards which was our a million + + align:start position:0% +million boards which was our a million + + + align:start position:0% +million boards which was our a million +was our number for our benchmarks that + + align:start position:0% +was our number for our benchmarks that + + + align:start position:0% +was our number for our benchmarks that +we did um each spu has about 170,000 to + + align:start position:0% +we did um each spu has about 170,000 to + + + align:start position:0% +we did um each spu has about 170,000 to +handle uh and it clearly can't uh take + + align:start position:0% +handle uh and it clearly can't uh take + + + align:start position:0% +handle uh and it clearly can't uh take +all those over at once so each spu knows + + align:start position:0% +all those over at once so each spu knows + + + align:start position:0% +all those over at once so each spu knows +where it's supposed to start and how + + align:start position:0% +where it's supposed to start and how + + + align:start position:0% +where it's supposed to start and how +many it's supposed to do and it knows + + align:start position:0% +many it's supposed to do and it knows + + + align:start position:0% +many it's supposed to do and it knows +how much it can pull over so uh it it + + align:start position:0% +how much it can pull over so uh it it + + + align:start position:0% +how much it can pull over so uh it it +does a dma call the pull in as much as + + align:start position:0% +does a dma call the pull in as much as + + + align:start position:0% +does a dma call the pull in as much as +it can process processes those uh + + align:start position:0% +it can process processes those uh + + + align:start position:0% +it can process processes those uh +evaluates them returns them and and gets + + align:start position:0% +evaluates them returns them and and gets + + + align:start position:0% +evaluates them returns them and and gets +his next Bunch so uh that is what we're + + align:start position:0% +his next Bunch so uh that is what we're + + + align:start position:0% +his next Bunch so uh that is what we're +we're able to implement uh there's also + + align:start position:0% +we're able to implement uh there's also + + + align:start position:0% +we're able to implement uh there's also +clean opportunity for double buffering + + align:start position:0% +clean opportunity for double buffering + + + align:start position:0% +clean opportunity for double buffering +there for pulling them in as it's + + align:start position:0% +there for pulling them in as it's + + + align:start position:0% +there for pulling them in as it's +actually evaluating the previous ones so + + align:start position:0% +actually evaluating the previous ones so + + + align:start position:0% +actually evaluating the previous ones so +that would be actually a pretty easy + + align:start position:0% +that would be actually a pretty easy + + + align:start position:0% +that would be actually a pretty easy +step to do next but each of those six + + align:start position:0% +step to do next but each of those six + + + align:start position:0% +step to do next but each of those six +should roughly finish at the same time + + align:start position:0% +should roughly finish at the same time + + + align:start position:0% +should roughly finish at the same time +and then get back + + align:start position:0% +and then get back + + + align:start position:0% +and then get back +to um the PPU to to evaluate to to run + + align:start position:0% +to um the PPU to to evaluate to to run + + + align:start position:0% +to um the PPU to to evaluate to to run +up that tree and another opportunity to + + align:start position:0% +up that tree and another opportunity to + + + align:start position:0% +up that tree and another opportunity to +make it a bit quicker which we didn't + + align:start position:0% +make it a bit quicker which we didn't + + + align:start position:0% +make it a bit quicker which we didn't +quite get to would be uh siming the + + align:start position:0% +quite get to would be uh siming the + + + align:start position:0% +quite get to would be uh siming the +evaluation function so we could do four + + align:start position:0% +evaluation function so we could do four + + + align:start position:0% +evaluation function so we could do four +boards at once with the Vector + + align:start position:0% +boards at once with the Vector + + + align:start position:0% +boards at once with the Vector +intrinsics instead of just + + align:start position:0% +intrinsics instead of just + + + align:start position:0% +intrinsics instead of just +one so the performance that we got when + + align:start position:0% +one so the performance that we got when + + + align:start position:0% +one so the performance that we got when +looking at uh you know the number of + + align:start position:0% +looking at uh you know the number of + + + align:start position:0% +looking at uh you know the number of +spus we were using was actually + + align:start position:0% +spus we were using was actually + + + align:start position:0% +spus we were using was actually +roughly um in proportional to the number + + align:start position:0% +roughly um in proportional to the number + + + align:start position:0% +roughly um in proportional to the number +of spus we were using it's actually uh + + align:start position:0% +of spus we were using it's actually uh + + + align:start position:0% +of spus we were using it's actually uh +18.18 at the top there so when using two + + align:start position:0% +18.18 at the top there so when using two + + + align:start position:0% +18.18 at the top there so when using two +instead of one we got just about half + + align:start position:0% +instead of one we got just about half + + + align:start position:0% +instead of one we got just about half +when using three instead of one we got + + align:start position:0% +when using three instead of one we got + + + align:start position:0% +when using three instead of one we got +just about a third um if you just look + + align:start position:0% +just about a third um if you just look + + + align:start position:0% +just about a third um if you just look +at this speed up graph it's pretty much + + align:start position:0% +at this speed up graph it's pretty much + + + align:start position:0% +at this speed up graph it's pretty much +one to one from from + + align:start position:0% +one to one from from + + + align:start position:0% +one to one from from +um from the number of SPS we were using + + align:start position:0% +um from the number of SPS we were using + + + align:start position:0% +um from the number of SPS we were using +to the amount of time it took so it was + + align:start position:0% +to the amount of time it took so it was + + + align:start position:0% +to the amount of time it took so it was +a a pretty efficient algorithm for + + align:start position:0% +a a pretty efficient algorithm for + + + align:start position:0% +a a pretty efficient algorithm for +splitting those up and evaluating them + + align:start position:0% +splitting those up and evaluating them + + + align:start position:0% +splitting those up and evaluating them +and pulling them back + + align:start position:0% +and pulling them back + + + align:start position:0% +and pulling them back +together um I'll give you a brief demo + + align:start position:0% +together um I'll give you a brief demo + + + align:start position:0% +together um I'll give you a brief demo +I'll show you quickly uh how it looks we + + align:start position:0% +I'll show you quickly uh how it looks we + + + align:start position:0% +I'll show you quickly uh how it looks we +might have to fudge our network + + align:start position:0% +might have to fudge our network + + + align:start position:0% +might have to fudge our network +connection a little bit + + align:start position:0% +connection a little bit + + + align:start position:0% +connection a little bit +here + + align:start position:0% + + + + align:start position:0% + +but + + align:start position:0% + + + + align:start position:0% + +okay so we used um just an X Windows + + align:start position:0% +okay so we used um just an X Windows + + + align:start position:0% +okay so we used um just an X Windows +setup to um display + + align:start position:0% +setup to um display + + + align:start position:0% +setup to um display +our our gooey that we were + + align:start position:0% + + + + align:start position:0% + +using um + + align:start position:0% +using um + + + align:start position:0% +using um +so I'm just going to play a couple + + align:start position:0% +so I'm just going to play a couple + + + align:start position:0% +so I'm just going to play a couple +rounds with the + + align:start position:0% +rounds with the + + + align:start position:0% +rounds with the +display um let's say against the + + align:start position:0% + + + + align:start position:0% + +computer + + align:start position:0% + + + + align:start position:0% + +so so you can see the computer just took + + align:start position:0% +so so you can see the computer just took + + + align:start position:0% +so so you can see the computer just took +a couple moves there but basically what + + align:start position:0% +a couple moves there but basically what + + + align:start position:0% +a couple moves there but basically what +we get here uh is a print out of a text + + align:start position:0% +we get here uh is a print out of a text + + + align:start position:0% +we get here uh is a print out of a text +representation of the board and then uh + + align:start position:0% +representation of the board and then uh + + + align:start position:0% +representation of the board and then uh +it's my turn I rolled a six and a two + + align:start position:0% +it's my turn I rolled a six and a two + + + align:start position:0% +it's my turn I rolled a six and a two +uh it shows here it does its own + + align:start position:0% +uh it shows here it does its own + + + align:start position:0% +uh it shows here it does its own +evaluation and says this is what the + + align:start position:0% +evaluation and says this is what the + + + align:start position:0% +evaluation and says this is what the +best move combo would be for me at this + + align:start position:0% +best move combo would be for me at this + + + align:start position:0% +best move combo would be for me at this +point + + align:start position:0% +point + + + align:start position:0% +point +um in the ideal tutoring situation we + + align:start position:0% +um in the ideal tutoring situation we + + + align:start position:0% +um in the ideal tutoring situation we +don't let the user pick what they + + align:start position:0% +don't let the user pick what they + + + align:start position:0% +don't let the user pick what they +thought was the best and then tell them + + align:start position:0% +thought was the best and then tell them + + + align:start position:0% +thought was the best and then tell them +why not but right now uh with the time + + align:start position:0% +why not but right now uh with the time + + + align:start position:0% +why not but right now uh with the time +we had this is how we did it so then it + + align:start position:0% +we had this is how we did it so then it + + + align:start position:0% +we had this is how we did it so then it +list all the legal possible moves you + + align:start position:0% +list all the legal possible moves you + + + align:start position:0% +list all the legal possible moves you +can make so say I want to move from 6 + + align:start position:0% +can make so say I want to move from 6 + + + align:start position:0% +can make so say I want to move from 6 +to4 uh moves my piece up there and then + + align:start position:0% +to4 uh moves my piece up there and then + + + align:start position:0% +to4 uh moves my piece up there and then +from eight to two for example and the + + align:start position:0% +from eight to two for example and the + + + align:start position:0% +from eight to two for example and the +computer makes its couple moves so um + + align:start position:0% +computer makes its couple moves so um + + + align:start position:0% +computer makes its couple moves so um +that's the general idea you can run the + + align:start position:0% +that's the general idea you can run the + + + align:start position:0% +that's the general idea you can run the +computer against itself as many times + + align:start position:0% +computer against itself as many times + + + align:start position:0% +computer against itself as many times +just to test different evaluation + + align:start position:0% +just to test different evaluation + + + align:start position:0% +just to test different evaluation +functions against each other you can + + align:start position:0% +functions against each other you can + + + align:start position:0% +functions against each other you can +also do it without the animation on the + + align:start position:0% +also do it without the animation on the + + + align:start position:0% +also do it without the animation on the +gooey so that it runs a lot quicker um + + align:start position:0% +gooey so that it runs a lot quicker um + + + align:start position:0% +gooey so that it runs a lot quicker um +but that's the general + + align:start position:0% +but that's the general + + + align:start position:0% +but that's the general +idea + + align:start position:0% +idea + + + align:start position:0% +idea +um just to wrap + + align:start position:0% +um just to wrap + + + align:start position:0% +um just to wrap +up few more slides quickly uh the way we + + align:start position:0% +up few more slides quickly uh the way we + + + align:start position:0% +up few more slides quickly uh the way we +went about this basically was uh we just + + align:start position:0% +went about this basically was uh we just + + + align:start position:0% +went about this basically was uh we just +got SE sequential code working on just + + align:start position:0% +got SE sequential code working on just + + + align:start position:0% +got SE sequential code working on just +the PPU got the rules of the game worked + + align:start position:0% +the PPU got the rules of the game worked + + + align:start position:0% +the PPU got the rules of the game worked +out um all the weird conditionals and + + align:start position:0% +out um all the weird conditionals and + + + align:start position:0% +out um all the weird conditionals and +and things that can happen in that game + + align:start position:0% +and things that can happen in that game + + + align:start position:0% +and things that can happen in that game +and we fix fix out our bugs and our + + align:start position:0% +and we fix fix out our bugs and our + + + align:start position:0% +and we fix fix out our bugs and our +memory leaks and things like that um we + + align:start position:0% +memory leaks and things like that um we + + + align:start position:0% +memory leaks and things like that um we +just shelled out the parallel code and + + align:start position:0% +just shelled out the parallel code and + + + align:start position:0% +just shelled out the parallel code and +got that working on the PPU then on one + + align:start position:0% +got that working on the PPU then on one + + + align:start position:0% +got that working on the PPU then on one +spu um and then on six so um it was a + + align:start position:0% +spu um and then on six so um it was a + + + align:start position:0% +spu um and then on six so um it was a +pretty clean process of doing and uh we + + align:start position:0% +pretty clean process of doing and uh we + + + align:start position:0% +pretty clean process of doing and uh we +ran into a a few walls we aren't really + + align:start position:0% +ran into a a few walls we aren't really + + + align:start position:0% +ran into a a few walls we aren't really +back gaming experts or even intermediate + + align:start position:0% +back gaming experts or even intermediate + + + align:start position:0% +back gaming experts or even intermediate +players so it's kind of new thing for us + + align:start position:0% +players so it's kind of new thing for us + + + align:start position:0% +players so it's kind of new thing for us +to make sure we had the rules right and + + align:start position:0% +to make sure we had the rules right and + + + align:start position:0% +to make sure we had the rules right and +we were weren't doing stupid things here + + align:start position:0% +we were weren't doing stupid things here + + + align:start position:0% +we were weren't doing stupid things here +and there + + align:start position:0% +and there + + + align:start position:0% +and there +um but also managing the search Tre was + + align:start position:0% +um but also managing the search Tre was + + + align:start position:0% +um but also managing the search Tre was +a big deal and that looking at what what + + align:start position:0% +a big deal and that looking at what what + + + align:start position:0% +a big deal and that looking at what what +the program has to do in running the + + align:start position:0% +the program has to do in running the + + + align:start position:0% +the program has to do in running the +game that's the next thing we'd want to + + align:start position:0% +game that's the next thing we'd want to + + + align:start position:0% +game that's the next thing we'd want to +tackle as far as parallel parallelizing + + align:start position:0% +tackle as far as parallel parallelizing + + + align:start position:0% +tackle as far as parallel parallelizing +goes um it takes a while and it's it's + + align:start position:0% +goes um it takes a while and it's it's + + + align:start position:0% +goes um it takes a while and it's it's +pretty tough so um we ran into some + + align:start position:0% +pretty tough so um we ran into some + + + align:start position:0% +pretty tough so um we ran into some +memory management issues with how we are + + align:start position:0% +memory management issues with how we are + + + align:start position:0% +memory management issues with how we are +representing our boards um we're able to + + align:start position:0% +representing our boards um we're able to + + + align:start position:0% +representing our boards um we're able to +pack them down into I think 24 by + + align:start position:0% +pack them down into I think 24 by + + + align:start position:0% +pack them down into I think 24 by +structure 20 by structure um to be able + + align:start position:0% +structure 20 by structure um to be able + + + align:start position:0% +structure 20 by structure um to be able +to pass more to the spus at one time um + + align:start position:0% + + + + align:start position:0% + +but how the you hand topu sorry I missed + + align:start position:0% +but how the you hand topu sorry I missed + + + align:start position:0% +but how the you hand topu sorry I missed +the beginning of your question because + + align:start position:0% +the beginning of your question because + + + align:start position:0% +the beginning of your question because +it wasn't on speaker phone it of a + + align:start position:0% +it wasn't on speaker phone it of a + + + align:start position:0% +it wasn't on speaker phone it of a +search you have to youru you say do one + + align:start position:0% +search you have to youru you say do one + + + align:start position:0% +search you have to youru you say do one +level one step or some number of steps + + align:start position:0% +level one step or some number of steps + + + align:start position:0% +level one step or some number of steps +you experiment with different number of + + align:start position:0% +you experiment with different number of + + + align:start position:0% +you experiment with different number of +steps so in one sense you can say search + + align:start position:0% +steps so in one sense you can say search + + + align:start position:0% +steps so in one sense you can say search +few steps and then have a lot of search + + align:start position:0% +few steps and then have a lot of search + + + align:start position:0% +few steps and then have a lot of search +in one unit that hands down or you can + + align:start position:0% +in one unit that hands down or you can + + + align:start position:0% +in one unit that hands down or you can +give just do one step at a time just do + + align:start position:0% +give just do one step at a time just do + + + align:start position:0% +give just do one step at a time just do +a do one more evaluation and come back + + align:start position:0% +a do one more evaluation and come back + + + align:start position:0% +a do one more evaluation and come back +so did you look at those regularities so + + align:start position:0% +so did you look at those regularities so + + + align:start position:0% +so did you look at those regularities so +talking about moving into the future are + + align:start position:0% +talking about moving into the future are + + + align:start position:0% +talking about moving into the future are +you talking about looking into the + + align:start position:0% +you talking about looking into the + + + align:start position:0% +you talking about looking into the +future yeah so we we bu the code for + + align:start position:0% +future yeah so we we bu the code for + + + align:start position:0% +future yeah so we we bu the code for +creating that tree and evaluating the + + align:start position:0% +creating that tree and evaluating the + + + align:start position:0% +creating that tree and evaluating the +leaf nodes we didn't quite have time to + + align:start position:0% +leaf nodes we didn't quite have time to + + + align:start position:0% +leaf nodes we didn't quite have time to +finish up um I + + align:start position:0% +finish up um I + + + align:start position:0% +finish up um I +can't okay we uh we created the code for + + align:start position:0% +can't okay we uh we created the code for + + + align:start position:0% +can't okay we uh we created the code for +constructing the tree and evaluating the + + align:start position:0% +constructing the tree and evaluating the + + + align:start position:0% +constructing the tree and evaluating the +leak nodes we haven't quite had time to + + align:start position:0% +leak nodes we haven't quite had time to + + + align:start position:0% +leak nodes we haven't quite had time to +finish up moving back up the tree so at + + align:start position:0% +finish up moving back up the tree so at + + + align:start position:0% +finish up moving back up the tree so at +this point we're not looking ahead more + + align:start position:0% +this point we're not looking ahead more + + + align:start position:0% +this point we're not looking ahead more +than just the moves for now for um like + + align:start position:0% +than just the moves for now for um like + + + align:start position:0% +than just the moves for now for um like +one move + + align:start position:0% +one move + + + align:start position:0% +one move +ahead okay so but we got the parallel + + align:start position:0% +ahead okay so but we got the parallel + + + align:start position:0% +ahead okay so but we got the parallel +code working for actually evaluating the + + align:start position:0% +code working for actually evaluating the + + + align:start position:0% +code working for actually evaluating the +boards it shouldn't be too hard to um + + align:start position:0% +boards it shouldn't be too hard to um + + + align:start position:0% +boards it shouldn't be too hard to um +just extend that tree to extend that to + + align:start position:0% +just extend that tree to extend that to + + + align:start position:0% +just extend that tree to extend that to +move back up the tree and see what the + + align:start position:0% +move back up the tree and see what the + + + align:start position:0% +move back up the tree and see what the +best move is + + align:start position:0% + + + + align:start position:0% + +now um yeah so that's that's basically + + align:start position:0% +now um yeah so that's that's basically + + + align:start position:0% +now um yeah so that's that's basically +as far as um the road blocks we hit were + + align:start position:0% +as far as um the road blocks we hit were + + + align:start position:0% +as far as um the road blocks we hit were +any other + + align:start position:0% + + + + align:start position:0% + +questions there's yeah so just some + + align:start position:0% +questions there's yeah so just some + + + align:start position:0% +questions there's yeah so just some +future ideas um one of the big on + + align:start position:0% +future ideas um one of the big on + + + align:start position:0% +future ideas um one of the big on +is for training um the the evaluation + + align:start position:0% +is for training um the the evaluation + + + align:start position:0% +is for training um the the evaluation +functions using neural Nets that takes a + + align:start position:0% +functions using neural Nets that takes a + + + align:start position:0% +functions using neural Nets that takes a +lot of time um to play hundreds of + + align:start position:0% +lot of time um to play hundreds of + + + align:start position:0% +lot of time um to play hundreds of +thousands millions of games so one of + + align:start position:0% +thousands millions of games so one of + + + align:start position:0% +thousands millions of games so one of +the ideas is to parallelize that um to + + align:start position:0% +the ideas is to parallelize that um to + + + align:start position:0% +the ideas is to parallelize that um to +help speed that + + align:start position:0% +help speed that + + + align:start position:0% +help speed that +up and I think we're about out of time + + align:start position:0% +up and I think we're about out of time + + + align:start position:0% +up and I think we're about out of time +so that concludes it are there any + + align:start position:0% + + + + align:start position:0% + +questions I'm just curious uh you said + + align:start position:0% +questions I'm just curious uh you said + + + align:start position:0% +questions I'm just curious uh you said +looking far into the future doesn't + + align:start position:0% +looking far into the future doesn't + + + align:start position:0% +looking far into the future doesn't +necessarily help us as much as the + + align:start position:0% +necessarily help us as much as the + + + align:start position:0% +necessarily help us as much as the +evaluation function does that mean that + + align:start position:0% +evaluation function does that mean that + + + align:start position:0% +evaluation function does that mean that +I mean AI back gamon is I mean how + + align:start position:0% +I mean AI back gamon is I mean how + + + align:start position:0% +I mean AI back gamon is I mean how +computationally intensive is a good + + align:start position:0% +computationally intensive is a good + + + align:start position:0% +computationally intensive is a good +player I mean is it I is it a + + align:start position:0% +player I mean is it I is it a + + + align:start position:0% +player I mean is it I is it a +computationally intensive problem or I + + align:start position:0% +computationally intensive problem or I + + + align:start position:0% +computationally intensive problem or I +mean do you even I me if would you + + align:start position:0% +mean do you even I me if would you + + + align:start position:0% +mean do you even I me if would you +benefit from the parilis in a practical + + align:start position:0% +benefit from the parilis in a practical + + + align:start position:0% +benefit from the parilis in a practical +setting well um just looking at how long + + align:start position:0% +setting well um just looking at how long + + + align:start position:0% +setting well um just looking at how long +it takes to go through those million + + align:start position:0% +it takes to go through those million + + + align:start position:0% +it takes to go through those million +boards like if you're playing a computer + + align:start position:0% +boards like if you're playing a computer + + + align:start position:0% +boards like if you're playing a computer +you don't want to wait 18 seconds for + + align:start position:0% +you don't want to wait 18 seconds for + + + align:start position:0% +you don't want to wait 18 seconds for +them to make them move as opposed to + + align:start position:0% +them to make them move as opposed to + + + align:start position:0% +them to make them move as opposed to +week that's the time scale of the + + align:start position:0% +week that's the time scale of the + + + align:start position:0% +week that's the time scale of the +absolute if you just ran on a un + + align:start position:0% +absolute if you just ran on a un + + + align:start position:0% +absolute if you just ran on a un +processor you're like 20 seconds kind of + + align:start position:0% +processor you're like 20 seconds kind of + + + align:start position:0% +processor you're like 20 seconds kind of +a thing um yeah when you're doing a + + align:start position:0% +a thing um yeah when you're doing a + + + align:start position:0% +a thing um yeah when you're doing a +million million boards about and also if + + align:start position:0% +million million boards about and also if + + + align:start position:0% +million million boards about and also if +you're on the level of you know + + align:start position:0% +you're on the level of you know + + + align:start position:0% +you're on the level of you know +competing against really good + + align:start position:0% +competing against really good + + + align:start position:0% +competing against really good +competitors like just having a deep + + align:start position:0% +competitors like just having a deep + + + align:start position:0% +competitors like just having a deep +searchy to get that much more Edge would + + align:start position:0% +searchy to get that much more Edge would + + + align:start position:0% +searchy to get that much more Edge would +make a difference um in that + + align:start position:0% + + + + align:start position:0% + +situation anyone + + align:start position:0% +situation anyone + + + align:start position:0% +situation anyone +else great + + align:start position:0% + + + + align:start position:0% + +great \ No newline at end of file diff --git a/eMWG-jTh-GE.txt b/eMWG-jTh-GE.txt new file mode 100644 index 0000000000000000000000000000000000000000..6a498113e38d2ef50032ab1515e8343a88b71073 --- /dev/null +++ b/eMWG-jTh-GE.txt @@ -0,0 +1,1747 @@ +align:start position:0% + +propositional operators play a basic + + align:start position:0% +propositional operators play a basic + + + align:start position:0% +propositional operators play a basic +role in the design of digital circuitry + + align:start position:0% +role in the design of digital circuitry + + + align:start position:0% +role in the design of digital circuitry +and we're going to illustrate that in + + align:start position:0% +and we're going to illustrate that in + + + align:start position:0% +and we're going to illustrate that in +this section by designing a little + + align:start position:0% +this section by designing a little + + + align:start position:0% +this section by designing a little +binary addition circuit so let's begin + + align:start position:0% +binary addition circuit so let's begin + + + align:start position:0% +binary addition circuit so let's begin +with a review of binary notation and + + align:start position:0% +with a review of binary notation and + + + align:start position:0% +with a review of binary notation and +addition and binary so the way binary + + align:start position:0% +addition and binary so the way binary + + + align:start position:0% +addition and binary so the way binary +works is like decimal except instead of + + align:start position:0% +works is like decimal except instead of + + + align:start position:0% +works is like decimal except instead of +using powers of 10 you're using powers + + align:start position:0% +using powers of 10 you're using powers + + + align:start position:0% +using powers of 10 you're using powers +of 2 so here is the binary + + align:start position:0% +of 2 so here is the binary + + + align:start position:0% +of 2 so here is the binary +representation of the number 39 the way + + align:start position:0% +representation of the number 39 the way + + + align:start position:0% +representation of the number 39 the way +to understand that is this is the ones + + align:start position:0% +to understand that is this is the ones + + + align:start position:0% +to understand that is this is the ones +place that's the twos place that's the + + align:start position:0% +place that's the twos place that's the + + + align:start position:0% +place that's the twos place that's the +forest place so at 1 plus 2 plus 4 is 7 + + align:start position:0% +forest place so at 1 plus 2 plus 4 is 7 + + + align:start position:0% +forest place so at 1 plus 2 plus 4 is 7 +then this is the 8th place with nothing + + align:start position:0% +then this is the 8th place with nothing + + + align:start position:0% +then this is the 8th place with nothing +this is the 16th place with something + + align:start position:0% +this is the 16th place with something + + + align:start position:0% +this is the 16th place with something +and this is the 32 place with 1 so we + + align:start position:0% +and this is the 32 place with 1 so we + + + align:start position:0% +and this is the 32 place with 1 so we +add 32 to 7 and get 39 likewise the + + align:start position:0% +add 32 to 7 and get 39 likewise the + + + align:start position:0% +add 32 to 7 and get 39 likewise the +binary representation of 28 is 0 1 1 1 0 + + align:start position:0% +binary representation of 28 is 0 1 1 1 0 + + + align:start position:0% +binary representation of 28 is 0 1 1 1 0 +0 I'll let you check out that works with + + align:start position:0% +0 I'll let you check out that works with + + + align:start position:0% +0 I'll let you check out that works with +contributing 1 2 4 8 16 and 32 and + + align:start position:0% +contributing 1 2 4 8 16 and 32 and + + + align:start position:0% +contributing 1 2 4 8 16 and 32 and +finally let's add these two numbers in + + align:start position:0% +finally let's add these two numbers in + + + align:start position:0% +finally let's add these two numbers in +binary + + align:start position:0% +binary + + + align:start position:0% +binary +now binary addition works just like + + align:start position:0% +now binary addition works just like + + + align:start position:0% +now binary addition works just like +decimal addition except that the only + + align:start position:0% +decimal addition except that the only + + + align:start position:0% +decimal addition except that the only +numbers are ones and zeros so that when + + align:start position:0% +numbers are ones and zeros so that when + + + align:start position:0% +numbers are ones and zeros so that when +you get 1 plus 1 you have to carry one + + align:start position:0% +you get 1 plus 1 you have to carry one + + + align:start position:0% +you get 1 plus 1 you have to carry one +let's do that so 1 plus 0 is 1 that + + align:start position:0% +let's do that so 1 plus 0 is 1 that + + + align:start position:0% +let's do that so 1 plus 0 is 1 that +fills in the first column then we have + + align:start position:0% +fills in the first column then we have + + + align:start position:0% +fills in the first column then we have +another 1 plus 0 is 1 that's fine now we + + align:start position:0% +another 1 plus 0 is 1 that's fine now we + + + align:start position:0% +another 1 plus 0 is 1 that's fine now we +have a 1 plus 1 and that's gonna do a 0 + + align:start position:0% +have a 1 plus 1 and that's gonna do a 0 + + + align:start position:0% +have a 1 plus 1 and that's gonna do a 0 +here and contribute a carry of 1 to the + + align:start position:0% +here and contribute a carry of 1 to the + + + align:start position:0% +here and contribute a carry of 1 to the +next column + + align:start position:0% +next column + + + align:start position:0% +next column +now the next column has two ones so it + + align:start position:0% +now the next column has two ones so it + + + align:start position:0% +now the next column has two ones so it +becomes a 0 and contributes to another + + align:start position:0% +becomes a 0 and contributes to another + + + align:start position:0% +becomes a 0 and contributes to another +carry now we have two ones we get a 0 + + align:start position:0% +carry now we have two ones we get a 0 + + + align:start position:0% +carry now we have two ones we get a 0 +and contribute another carry and now we + + align:start position:0% +and contribute another carry and now we + + + align:start position:0% +and contribute another carry and now we +have two ones and we finally get a 1 0 + + align:start position:0% +have two ones and we finally get a 1 0 + + + align:start position:0% +have two ones and we finally get a 1 0 +so this is the binary representation of + + align:start position:0% +so this is the binary representation of + + + align:start position:0% +so this is the binary representation of +the sum and you can check that this is 1 + + align:start position:0% +the sum and you can check that this is 1 + + + align:start position:0% +the sum and you can check that this is 1 +plus 2 is 3 plus 64 so the answer should + + align:start position:0% +plus 2 is 3 plus 64 so the answer should + + + align:start position:0% +plus 2 is 3 plus 64 so the answer should +be 67 and you can check that it is so + + align:start position:0% +be 67 and you can check that it is so + + + align:start position:0% +be 67 and you can check that it is so +that's how binary addition works now + + align:start position:0% +that's how binary addition works now + + + align:start position:0% +that's how binary addition works now +let's try to design a bit of circuitry + + align:start position:0% +let's try to design a bit of circuitry + + + align:start position:0% +let's try to design a bit of circuitry +using digital logic the signals of 0 & 1 + + align:start position:0% +using digital logic the signals of 0 & 1 + + + align:start position:0% +using digital logic the signals of 0 & 1 +which will do addition and so we're + + align:start position:0% +which will do addition and so we're + + + align:start position:0% +which will do addition and so we're +going to try to design a + + align:start position:0% +going to try to design a + + + align:start position:0% +going to try to design a +little 6 bit binary addition circuits so + + align:start position:0% +little 6 bit binary addition circuits so + + + align:start position:0% +little 6 bit binary addition circuits so +I'm going to have as inputs the six + + align:start position:0% +I'm going to have as inputs the six + + + align:start position:0% +I'm going to have as inputs the six +digits of the first binary number a 5 + + align:start position:0% +digits of the first binary number a 5 + + + align:start position:0% +digits of the first binary number a 5 +down through a zero and then the second + + align:start position:0% +down through a zero and then the second + + + align:start position:0% +down through a zero and then the second +binary number let's call it B zero + + align:start position:0% +binary number let's call it B zero + + + align:start position:0% +binary number let's call it B zero +through B 5 so these are two binary + + align:start position:0% +through B 5 so these are two binary + + + align:start position:0% +through B 5 so these are two binary +numbers six digits long and I'm going to + + align:start position:0% +numbers six digits long and I'm going to + + + align:start position:0% +numbers six digits long and I'm going to +add them up by thinking of a 1 is 0 or 1 + + align:start position:0% +add them up by thinking of a 1 is 0 or 1 + + + align:start position:0% +add them up by thinking of a 1 is 0 or 1 +signal a 0 is a 0 1 signal B 0 is a 0 1 + + align:start position:0% +signal a 0 is a 0 1 signal B 0 is a 0 1 + + + align:start position:0% +signal a 0 is a 0 1 signal B 0 is a 0 1 +signal these can be transmitted down + + align:start position:0% +signal these can be transmitted down + + + align:start position:0% +signal these can be transmitted down +wires into some boxes that contain + + align:start position:0% +wires into some boxes that contain + + + align:start position:0% +wires into some boxes that contain +digital operators that will cause the + + align:start position:0% +digital operators that will cause the + + + align:start position:0% +digital operators that will cause the +right signals to come out and what we + + align:start position:0% +right signals to come out and what we + + + align:start position:0% +right signals to come out and what we +want to come out of here is the possibly + + align:start position:0% +want to come out of here is the possibly + + + align:start position:0% +want to come out of here is the possibly +seven digit representation of their + + align:start position:0% +seven digit representation of their + + + align:start position:0% +seven digit representation of their +binary sum so these 0 is the sum of a 0 + + align:start position:0% +binary sum so these 0 is the sum of a 0 + + + align:start position:0% +binary sum so these 0 is the sum of a 0 +and B 0 the lower did you possibly with + + align:start position:0% +and B 0 the lower did you possibly with + + + align:start position:0% +and B 0 the lower did you possibly with +a carry and so on and then C 5 is if the + + align:start position:0% +a carry and so on and then C 5 is if the + + + align:start position:0% +a carry and so on and then C 5 is if the +number if the sum of two six digit + + align:start position:0% +number if the sum of two six digit + + + align:start position:0% +number if the sum of two six digit +numbers runs to seven digits which it + + align:start position:0% +numbers runs to seven digits which it + + + align:start position:0% +numbers runs to seven digits which it +might as we saw in the previous example + + align:start position:0% +might as we saw in the previous example + + + align:start position:0% +might as we saw in the previous example +and C five would become one of the Y's + + align:start position:0% +and C five would become one of the Y's + + + align:start position:0% +and C five would become one of the Y's +zero so this is the specification I want + + align:start position:0% +zero so this is the specification I want + + + align:start position:0% +zero so this is the specification I want +a and B to come in and I want their + + align:start position:0% +a and B to come in and I want their + + + align:start position:0% +a and B to come in and I want their +binary sum to come out as these with a + + align:start position:0% +binary sum to come out as these with a + + + align:start position:0% +binary sum to come out as these with a +high order seed if need be now the way + + align:start position:0% +high order seed if need be now the way + + + align:start position:0% +high order seed if need be now the way +you're going to do that is it's clear + + align:start position:0% +you're going to do that is it's clear + + + align:start position:0% +you're going to do that is it's clear +that the behavior of the inputs for a + + align:start position:0% +that the behavior of the inputs for a + + + align:start position:0% +that the behavior of the inputs for a +and B which produced a lower digit might + + align:start position:0% +and B which produced a lower digit might + + + align:start position:0% +and B which produced a lower digit might +produce a carry and that carry has to be + + align:start position:0% +produce a carry and that carry has to be + + + align:start position:0% +produce a carry and that carry has to be +transmitted to the next column + + align:start position:0% +transmitted to the next column + + + align:start position:0% +transmitted to the next column +if it exists and so I'm going to need a + + align:start position:0% +if it exists and so I'm going to need a + + + align:start position:0% +if it exists and so I'm going to need a +wire that sends a 0 1 signal from this + + align:start position:0% +wire that sends a 0 1 signal from this + + + align:start position:0% +wire that sends a 0 1 signal from this +box over to that one that can be + + align:start position:0% +box over to that one that can be + + + align:start position:0% +box over to that one that can be +carrying this that carries 0 or 1 and + + align:start position:0% +carrying this that carries 0 or 1 and + + + align:start position:0% +carrying this that carries 0 or 1 and +likewise for all of the others so this + + align:start position:0% +likewise for all of the others so this + + + align:start position:0% +likewise for all of the others so this +is the kind of basic structure of my + + align:start position:0% +is the kind of basic structure of my + + + align:start position:0% +is the kind of basic structure of my +binary additions circuit this is called + + align:start position:0% +binary additions circuit this is called + + + align:start position:0% +binary additions circuit this is called +a ripple carry organization its limiting + + align:start position:0% +a ripple carry organization its limiting + + + align:start position:0% +a ripple carry organization its limiting +its mimicking exactly the way that we + + align:start position:0% +its mimicking exactly the way that we + + + align:start position:0% +its mimicking exactly the way that we +added up the two numbers column by + + align:start position:0% +added up the two numbers column by + + + align:start position:0% +added up the two numbers column by +column possibly propagating a comma + + align:start position:0% +column possibly propagating a comma + + + align:start position:0% +column possibly propagating a comma +column on carry of 0 1 or really a carry + + align:start position:0% +column on carry of 0 1 or really a carry + + + align:start position:0% +column on carry of 0 1 or really a carry +of just 1 to the next column and I've + + align:start position:0% +of just 1 to the next column and I've + + + align:start position:0% +of just 1 to the next column and I've +got all the wires in place that I need + + align:start position:0% +got all the wires in place that I need + + + align:start position:0% +got all the wires in place that I need +what we need to do is design the digital + + align:start position:0% +what we need to do is design the digital + + + align:start position:0% +what we need to do is design the digital +circuitry that's in those boxes well + + align:start position:0% +circuitry that's in those boxes well + + + align:start position:0% +circuitry that's in those boxes well +this box is different from the others + + align:start position:0% +this box is different from the others + + + align:start position:0% +this box is different from the others +because it's only got 2 in + + align:start position:0% +because it's only got 2 in + + + align:start position:0% +because it's only got 2 in +puts all the others have three inputs so + + align:start position:0% +puts all the others have three inputs so + + + align:start position:0% +puts all the others have three inputs so +the three input boxes we'll call full + + align:start position:0% +the three input boxes we'll call full + + + align:start position:0% +the three input boxes we'll call full +adders and the two input boxes a half an + + align:start position:0% +adders and the two input boxes a half an + + + align:start position:0% +adders and the two input boxes a half an +adder and the specification of a half an + + align:start position:0% +adder and the specification of a half an + + + align:start position:0% +adder and the specification of a half an +adder again is that the output is the + + align:start position:0% +adder again is that the output is the + + + align:start position:0% +adder again is that the output is the +binary representation of a 0 plus a 0 + + align:start position:0% +binary representation of a 0 plus a 0 + + + align:start position:0% +binary representation of a 0 plus a 0 +plus B 0 so it's a 2 binary + + align:start position:0% +plus B 0 so it's a 2 binary + + + align:start position:0% +plus B 0 so it's a 2 binary +representation never be bigger than 2 + + align:start position:0% +representation never be bigger than 2 + + + align:start position:0% +representation never be bigger than 2 +because there's only two numbers the + + align:start position:0% +because there's only two numbers the + + + align:start position:0% +because there's only two numbers the +output of a full adder is it gets inputs + + align:start position:0% +output of a full adder is it gets inputs + + + align:start position:0% +output of a full adder is it gets inputs +of 3 inputs in this case B 1 a 1 and the + + align:start position:0% +of 3 inputs in this case B 1 a 1 and the + + + align:start position:0% +of 3 inputs in this case B 1 a 1 and the +carry C 0 and it produces the binary + + align:start position:0% +carry C 0 and it produces the binary + + + align:start position:0% +carry C 0 and it produces the binary +representation of the sum of those three + + align:start position:0% +representation of the sum of those three + + + align:start position:0% +representation of the sum of those three +numbers which is a two digit binary + + align:start position:0% +numbers which is a two digit binary + + + align:start position:0% +numbers which is a two digit binary +representation there might be anything + + align:start position:0% +representation there might be anything + + + align:start position:0% +representation there might be anything +from 0 to 3 ok well let's start with the + + align:start position:0% +from 0 to 3 ok well let's start with the + + + align:start position:0% +from 0 to 3 ok well let's start with the +easy case what's a half adder well a + + align:start position:0% +easy case what's a half adder well a + + + align:start position:0% +easy case what's a half adder well a +half adder again has inputs being a and + + align:start position:0% +half adder again has inputs being a and + + + align:start position:0% +half adder again has inputs being a and +it's supposed to produce as output the + + align:start position:0% +it's supposed to produce as output the + + + align:start position:0% +it's supposed to produce as output the +binary representation of B plus a so B + + align:start position:0% +binary representation of B plus a so B + + + align:start position:0% +binary representation of B plus a so B +is the lower digit in the the 0 or the + + align:start position:0% +is the lower digit in the the 0 or the + + + align:start position:0% +is the lower digit in the the 0 or the +the zeros place and C is the high or + + align:start position:0% +the zeros place and C is the high or + + + align:start position:0% +the zeros place and C is the high or +digit namely the twos place well what + + align:start position:0% +digit namely the twos place well what + + + align:start position:0% +digit namely the twos place well what +does that look like well here's the + + align:start position:0% +does that look like well here's the + + + align:start position:0% +does that look like well here's the +circuit this is the digital designers + + align:start position:0% +circuit this is the digital designers + + + align:start position:0% +circuit this is the digital designers +symbol for a exclusive or gate that + + align:start position:0% +symbol for a exclusive or gate that + + + align:start position:0% +symbol for a exclusive or gate that +returns so D is going to be the + + align:start position:0% +returns so D is going to be the + + + align:start position:0% +returns so D is going to be the +exclusive or of a and B according to + + align:start position:0% +exclusive or of a and B according to + + + align:start position:0% +exclusive or of a and B according to +this pictorial diagnose I am notice I'm + + align:start position:0% +this pictorial diagnose I am notice I'm + + + align:start position:0% +this pictorial diagnose I am notice I'm +using this colon colon equal symbol + + align:start position:0% +using this colon colon equal symbol + + + align:start position:0% +using this colon colon equal symbol +which is convenient as a reminder that + + align:start position:0% +which is convenient as a reminder that + + + align:start position:0% +which is convenient as a reminder that +this is that I'm defining the thing on + + align:start position:0% +this is that I'm defining the thing on + + + align:start position:0% +this is that I'm defining the thing on +the left so this is you can replace it + + align:start position:0% +the left so this is you can replace it + + + align:start position:0% +the left so this is you can replace it +by equal but it's informative to realize + + align:start position:0% +by equal but it's informative to realize + + + align:start position:0% +by equal but it's informative to realize +that it's not an equality that you've + + align:start position:0% +that it's not an equality that you've + + + align:start position:0% +that it's not an equality that you've +proved or if in some derivation the two + + align:start position:0% +proved or if in some derivation the two + + + align:start position:0% +proved or if in some derivation the two +interesting things are proven to be + + align:start position:0% +interesting things are proven to be + + + align:start position:0% +interesting things are proven to be +equal but rather than I'm just defining + + align:start position:0% +equal but rather than I'm just defining + + + align:start position:0% +equal but rather than I'm just defining +what D is so D is Devon this output D is + + align:start position:0% +what D is so D is Devon this output D is + + + align:start position:0% +what D is so D is Devon this output D is +defined to be a XOR B and likewise this + + align:start position:0% +defined to be a XOR B and likewise this + + + align:start position:0% +defined to be a XOR B and likewise this +is a NAND gate so the outputs a is a and + + align:start position:0% +is a NAND gate so the outputs a is a and + + + align:start position:0% +is a NAND gate so the outputs a is a and +B and let's check that the lower two + + align:start position:0% +B and let's check that the lower two + + + align:start position:0% +B and let's check that the lower two +digit is definitely the month to sum the + + align:start position:0% +digit is definitely the month to sum the + + + align:start position:0% +digit is definitely the month to sum the +XOR of a and B and when is there a carry + + align:start position:0% +XOR of a and B and when is there a carry + + + align:start position:0% +XOR of a and B and when is there a carry +well the only way does a carry went is + + align:start position:0% +well the only way does a carry went is + + + align:start position:0% +well the only way does a carry went is +when the value is 2 in which case the + + align:start position:0% +when the value is 2 in which case the + + + align:start position:0% +when the value is 2 in which case the +output C would be 1 and D would be 0 and + + align:start position:0% +output C would be 1 and D would be 0 and + + + align:start position:0% +output C would be 1 and D would be 0 and +that's exactly when both a and B or 1 + + align:start position:0% +that's exactly when both a and B or 1 + + + align:start position:0% +that's exactly when both a and B or 1 +that is C is a and B so that's a half + + align:start position:0% +that is C is a and B so that's a half + + + align:start position:0% +that is C is a and B so that's a half +adder that was easy + + align:start position:0% +adder that was easy + + + align:start position:0% +adder that was easy +well a full adder looks like this it's a + + align:start position:0% +well a full adder looks like this it's a + + + align:start position:0% +well a full adder looks like this it's a +little bit more complicated + + align:start position:0% +little bit more complicated + + + align:start position:0% +little bit more complicated +and I'm gonna write out the equations + + align:start position:0% +and I'm gonna write out the equations + + + align:start position:0% +and I'm gonna write out the equations +without trying to justify them + + align:start position:0% +without trying to justify them + + + align:start position:0% +without trying to justify them +completely but I need a name in order to + + align:start position:0% +completely but I need a name in order to + + + align:start position:0% +completely but I need a name in order to +describe this with with propositional + + align:start position:0% +describe this with with propositional + + + align:start position:0% +describe this with with propositional +operators I need a name for that + + align:start position:0% +operators I need a name for that + + + align:start position:0% +operators I need a name for that +important signal call it s which is what + + align:start position:0% +important signal call it s which is what + + + align:start position:0% +important signal call it s which is what +we we're not calling in the previous one + + align:start position:0% +we we're not calling in the previous one + + + align:start position:0% +we we're not calling in the previous one +but now this is a half adder with inputs + + align:start position:0% +but now this is a half adder with inputs + + + align:start position:0% +but now this is a half adder with inputs +a and B and outputs s which is a XOR B + + align:start position:0% +a and B and outputs s which is a XOR B + + + align:start position:0% +a and B and outputs s which is a XOR B +and another output here in which we know + + align:start position:0% +and another output here in which we know + + + align:start position:0% +and another output here in which we know +is just going to be a and B ok how do i + + align:start position:0% +is just going to be a and B ok how do i + + + align:start position:0% +is just going to be a and B ok how do i +express this set of connections as + + align:start position:0% +express this set of connections as + + + align:start position:0% +express this set of connections as +formulas well first of all s is the + + align:start position:0% +formulas well first of all s is the + + + align:start position:0% +formulas well first of all s is the +output of this first half adder which is + + align:start position:0% +output of this first half adder which is + + + align:start position:0% +output of this first half adder which is +a XOR B okay the output D I get by + + align:start position:0% +a XOR B okay the output D I get by + + + align:start position:0% +a XOR B okay the output D I get by +taking s and it's the first output of + + align:start position:0% +taking s and it's the first output of + + + align:start position:0% +taking s and it's the first output of +the second half adder which means it's + + align:start position:0% +the second half adder which means it's + + + align:start position:0% +the second half adder which means it's +CN XOR s that's easy and what about C + + align:start position:0% +CN XOR s that's easy and what about C + + + align:start position:0% +CN XOR s that's easy and what about C +out well C out is getting and this is an + + align:start position:0% +out well C out is getting and this is an + + + align:start position:0% +out well C out is getting and this is an +or gate by the way so C out is going to + + align:start position:0% +or gate by the way so C out is going to + + + align:start position:0% +or gate by the way so C out is going to +be an or of what comes out of this half + + align:start position:0% +be an or of what comes out of this half + + + align:start position:0% +be an or of what comes out of this half +adder which is C in and C s and or with + + align:start position:0% +adder which is C in and C s and or with + + + align:start position:0% +adder which is C in and C s and or with +the output of this half adder which is + + align:start position:0% +the output of this half adder which is + + + align:start position:0% +the output of this half adder which is +just a and B so there are a bunch of + + align:start position:0% +just a and B so there are a bunch of + + + align:start position:0% +just a and B so there are a bunch of +equations that completely characterize + + align:start position:0% +equations that completely characterize + + + align:start position:0% +equations that completely characterize +the structure of this little bit of + + align:start position:0% +the structure of this little bit of + + + align:start position:0% +the structure of this little bit of +digital logic and how it is wired up and + + align:start position:0% +digital logic and how it is wired up and + + + align:start position:0% +digital logic and how it is wired up and +fits together now let's go back to + + align:start position:0% +fits together now let's go back to + + + align:start position:0% +fits together now let's go back to +describing our ripple-carry circuit of + + align:start position:0% +describing our ripple-carry circuit of + + + align:start position:0% +describing our ripple-carry circuit of +what was going on here now that we have + + align:start position:0% +what was going on here now that we have + + + align:start position:0% +what was going on here now that we have +the equations that characterize the + + align:start position:0% +the equations that characterize the + + + align:start position:0% +the equations that characterize the +behavior of these full adders and half + + align:start position:0% +behavior of these full adders and half + + + align:start position:0% +behavior of these full adders and half +adders I can explain to you what the + + align:start position:0% +adders I can explain to you what the + + + align:start position:0% +adders I can explain to you what the +formulas are for all of these outputs + + align:start position:0% +formulas are for all of these outputs + + + align:start position:0% +formulas are for all of these outputs +the C's and the DS and that goes as + + align:start position:0% +the C's and the DS and that goes as + + + align:start position:0% +the C's and the DS and that goes as +follows so the first one looking at this + + align:start position:0% +follows so the first one looking at this + + + align:start position:0% +follows so the first one looking at this +half adder with a0 b0 coming in and C 0 + + align:start position:0% +half adder with a0 b0 coming in and C 0 + + + align:start position:0% +half adder with a0 b0 coming in and C 0 +D 0 coming out I know that D 0 is a 0 X + + align:start position:0% +D 0 coming out I know that D 0 is a 0 X + + + align:start position:0% +D 0 coming out I know that D 0 is a 0 X +or B 0 and C 0 is a 0 and B 0 that's + + align:start position:0% +or B 0 and C 0 is a 0 and B 0 that's + + + align:start position:0% +or B 0 and C 0 is a 0 and B 0 that's +just the formulas that we have for the + + align:start position:0% +just the formulas that we have for the + + + align:start position:0% +just the formulas that we have for the +half adder when the inputs are a 0 and B + + align:start position:0% +half adder when the inputs are a 0 and B + + + align:start position:0% +half adder when the inputs are a 0 and B +0 and I call the outputs the 0 and C 0 + + align:start position:0% +0 and I call the outputs the 0 and C 0 + + + align:start position:0% +0 and I call the outputs the 0 and C 0 +now the more general case of the full + + align:start position:0% +now the more general case of the full + + + align:start position:0% +now the more general case of the full +adder what's coming in here is an A and + + align:start position:0% +adder what's coming in here is an A and + + + align:start position:0% +adder what's coming in here is an A and +a B with the same subscript AI and bi + + align:start position:0% +a B with the same subscript AI and bi + + + align:start position:0% +a B with the same subscript AI and bi +and + + align:start position:0% +and + + + align:start position:0% +and +coming out is the eighth digit of the + + align:start position:0% +coming out is the eighth digit of the + + + align:start position:0% +coming out is the eighth digit of the +binary some di and the carry CI and I + + align:start position:0% +binary some di and the carry CI and I + + + align:start position:0% +binary some di and the carry CI and I +can describe those just by using the + + align:start position:0% +can describe those just by using the + + + align:start position:0% +can describe those just by using the +formulas for the full adder so what it + + align:start position:0% +formulas for the full adder so what it + + + align:start position:0% +formulas for the full adder so what it +means is that I'm going to introduce a + + align:start position:0% +means is that I'm going to introduce a + + + align:start position:0% +means is that I'm going to introduce a +new convenient variable si which I'm + + align:start position:0% +new convenient variable si which I'm + + + align:start position:0% +new convenient variable si which I'm +going to define to be AI or X or bi di + + align:start position:0% +going to define to be AI or X or bi di + + + align:start position:0% +going to define to be AI or X or bi di +is then going to be CI minus 1 that + + align:start position:0% +is then going to be CI minus 1 that + + + align:start position:0% +is then going to be CI minus 1 that +carry from the previous place ex-ored + + align:start position:0% +carry from the previous place ex-ored + + + align:start position:0% +carry from the previous place ex-ored +with Si and the new carry CI is going to + + align:start position:0% +with Si and the new carry CI is going to + + + align:start position:0% +with Si and the new carry CI is going to +be the out of the output of the second + + align:start position:0% +be the out of the output of the second + + + align:start position:0% +be the out of the output of the second +half adder of the first half adder which + + align:start position:0% +half adder of the first half adder which + + + align:start position:0% +half adder of the first half adder which +is CI minus 1 and si or the output of + + align:start position:0% +is CI minus 1 and si or the output of + + + align:start position:0% +is CI minus 1 and si or the output of +the first half adder which is AI and bi + + align:start position:0% +the first half adder which is AI and bi + + + align:start position:0% +the first half adder which is AI and bi +so the point is that I've just taken the + + align:start position:0% +so the point is that I've just taken the + + + align:start position:0% +so the point is that I've just taken the +the wiring and translated into equations + + align:start position:0% +the wiring and translated into equations + + + align:start position:0% +the wiring and translated into equations +like this and you can see how these + + align:start position:0% +like this and you can see how these + + + align:start position:0% +like this and you can see how these +equations might be more fair to use then + + align:start position:0% +equations might be more fair to use then + + + align:start position:0% +equations might be more fair to use then +the particular way that you drew the + + align:start position:0% +the particular way that you drew the + + + align:start position:0% +the particular way that you drew the +picture with all the wires connected + + align:start position:0% +picture with all the wires connected + + + align:start position:0% +picture with all the wires connected +because the logical behavior of the + + align:start position:0% +because the logical behavior of the + + + align:start position:0% +because the logical behavior of the +circuit doesn't depend on how it's laid + + align:start position:0% +circuit doesn't depend on how it's laid + + + align:start position:0% +circuit doesn't depend on how it's laid +out it just depends on these logical + + align:start position:0% +out it just depends on these logical + + + align:start position:0% +out it just depends on these logical +connectives between the values of these + + align:start position:0% +connectives between the values of these + + + align:start position:0% +connectives between the values of these +different variables \ No newline at end of file diff --git a/e_Hpp8cgeRs.txt b/e_Hpp8cgeRs.txt new file mode 100644 index 0000000000000000000000000000000000000000..e48f8e871b3282a73a1d89dce3ba969d62c38e20 --- /dev/null +++ b/e_Hpp8cgeRs.txt @@ -0,0 +1,11395 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay great so I think it's + + align:start position:0% +ocw.mit.edu okay great so I think it's + + + align:start position:0% +ocw.mit.edu okay great so I think it's +about time to get started so good + + align:start position:0% +about time to get started so good + + + align:start position:0% +about time to get started so good +afternoon so uh let me see uh so what do + + align:start position:0% +afternoon so uh let me see uh so what do + + + align:start position:0% +afternoon so uh let me see uh so what do +you think about genko or jenko I guess + + align:start position:0% +you think about genko or jenko I guess + + + align:start position:0% +you think about genko or jenko I guess +jeno genko I never know was a good talk + + align:start position:0% +jeno genko I never know was a good talk + + + align:start position:0% +jeno genko I never know was a good talk +I enjoyed it do you enjoy it yeah it was + + align:start position:0% +I enjoyed it do you enjoy it yeah it was + + + align:start position:0% +I enjoyed it do you enjoy it yeah it was +interesting so let's talk about the uh + + align:start position:0% +interesting so let's talk about the uh + + + align:start position:0% +interesting so let's talk about the uh +just to kind of refresh our memory and + + align:start position:0% +just to kind of refresh our memory and + + + align:start position:0% +just to kind of refresh our memory and +then we move into the two more things I + + align:start position:0% +then we move into the two more things I + + + align:start position:0% +then we move into the two more things I +want to cover today we want to cover um + + align:start position:0% +want to cover today we want to cover um + + + align:start position:0% +want to cover today we want to cover um +the uh whirpool case study kind of a to + + align:start position:0% +the uh whirpool case study kind of a to + + + align:start position:0% +the uh whirpool case study kind of a to +close this notion of reverse ICS and + + align:start position:0% +close this notion of reverse ICS and + + + align:start position:0% +close this notion of reverse ICS and +Clos Loop Supply chains a little bit uh + + align:start position:0% +Clos Loop Supply chains a little bit uh + + + align:start position:0% +Clos Loop Supply chains a little bit uh +but before we start we read a quick case + + align:start position:0% +but before we start we read a quick case + + + align:start position:0% +but before we start we read a quick case +study on + + align:start position:0% +study on + + + align:start position:0% +study on +recellular uh that was really try to + + align:start position:0% +recellular uh that was really try to + + + align:start position:0% +recellular uh that was really try to +connect with some of the things that we + + align:start position:0% +connect with some of the things that we + + + align:start position:0% +connect with some of the things that we +heard from from from genko jenko + + align:start position:0% +heard from from from genko jenko + + + align:start position:0% +heard from from from genko jenko +jenko and I wanted to know I read the + + align:start position:0% +jenko and I wanted to know I read the + + + align:start position:0% +jenko and I wanted to know I read the +the the responses the homeworks and you + + align:start position:0% +the the responses the homeworks and you + + + align:start position:0% +the the responses the homeworks and you +were split so some of you did think that + + align:start position:0% +were split so some of you did think that + + + align:start position:0% +were split so some of you did think that +recellular had a future and others + + align:start position:0% +recellular had a future and others + + + align:start position:0% +recellular had a future and others +thought thought that they were deemed to + + align:start position:0% +thought thought that they were deemed to + + + align:start position:0% +thought thought that they were deemed to +disappear as a company so who wants to + + align:start position:0% +disappear as a company so who wants to + + + align:start position:0% +disappear as a company so who wants to +be the voice of uh recellular well + + align:start position:0% +be the voice of uh recellular well + + + align:start position:0% +be the voice of uh recellular well +before we + + align:start position:0% +before we + + + align:start position:0% +before we +start uh well since your first time I + + align:start position:0% +start uh well since your first time I + + + align:start position:0% +start uh well since your first time I +see you here so I you were traveling so + + align:start position:0% +see you here so I you were traveling so + + + align:start position:0% +see you here so I you were traveling so +do you remember what is the basic + + align:start position:0% +do you remember what is the basic + + + align:start position:0% +do you remember what is the basic +business model of recellular yeah I did + + align:start position:0% +business model of recellular yeah I did + + + align:start position:0% +business model of recellular yeah I did +I guys for it actually great so what do + + align:start position:0% +I guys for it actually great so what do + + + align:start position:0% +I guys for it actually great so what do +you give us a quick recap of what + + align:start position:0% +you give us a quick recap of what + + + align:start position:0% +you give us a quick recap of what +recellular does just in 10 minutes or + + align:start position:0% +recellular does just in 10 minutes or + + + align:start position:0% +recellular does just in 10 minutes or +less they are uh getting cell phones and + + align:start position:0% +less they are uh getting cell phones and + + + align:start position:0% +less they are uh getting cell phones and +repurposing them and selling them to + + align:start position:0% +repurposing them and selling them to + + + align:start position:0% +repurposing them and selling them to +other markets uh markets that you know + + align:start position:0% +other markets uh markets that you know + + + align:start position:0% +other markets uh markets that you know +may think those sell that still uh give + + align:start position:0% +may think those sell that still uh give + + + align:start position:0% +may think those sell that still uh give +a certain value for those secondhand + + align:start position:0% +a certain value for those secondhand + + + align:start position:0% +a certain value for those secondhand +cell phones and they get them from + + align:start position:0% +cell phones and they get them from + + + align:start position:0% +cell phones and they get them from +various sources uh including the + + align:start position:0% +various sources uh including the + + + align:start position:0% +various sources uh including the +donation bin type sources uh as well as + + align:start position:0% +donation bin type sources uh as well as + + + align:start position:0% +donation bin type sources uh as well as +um uh some higher quality sources okay + + align:start position:0% +um uh some higher quality sources okay + + + align:start position:0% +um uh some higher quality sources okay +great so uh who else was in favor or + + align:start position:0% +great so uh who else was in favor or + + + align:start position:0% +great so uh who else was in favor or +thought that the recellular model had + + align:start position:0% +thought that the recellular model had + + + align:start position:0% +thought that the recellular model had +some + + align:start position:0% + + + + align:start position:0% + +future four so who wants to Mariana you + + align:start position:0% +future four so who wants to Mariana you + + + align:start position:0% +future four so who wants to Mariana you +want to try to do it sure give your + + align:start position:0% +want to try to do it sure give your + + + align:start position:0% +want to try to do it sure give your +pit + + align:start position:0% +pit + + + align:start position:0% +pit +my I think they have a future + + align:start position:0% +my I think they have a future + + + align:start position:0% +my I think they have a future +because people always consume cell + + align:start position:0% +because people always consume cell + + + align:start position:0% +because people always consume cell +phones they might evolve into something + + align:start position:0% +phones they might evolve into something + + + align:start position:0% +phones they might evolve into something +else like they have we have seen it like + + align:start position:0% +else like they have we have seen it like + + + align:start position:0% +else like they have we have seen it like +they will become or something but that + + align:start position:0% +they will become or something but that + + + align:start position:0% +they will become or something but that +same instrument to talk and and serf the + + align:start position:0% +same instrument to talk and and serf the + + + align:start position:0% +same instrument to talk and and serf the +web and what we're doing now with phones + + align:start position:0% +web and what we're doing now with phones + + + align:start position:0% +web and what we're doing now with phones +will evolve and they can C into the + + align:start position:0% +will evolve and they can C into the + + + align:start position:0% +will evolve and they can C into the +industry it might not be cellone but it + + align:start position:0% +industry it might not be cellone but it + + + align:start position:0% +industry it might not be cellone but it +would be something else and they can tap + + align:start position:0% +would be something else and they can tap + + + align:start position:0% +would be something else and they can tap +into that ination as long as they keep + + align:start position:0% +into that ination as long as they keep + + + align:start position:0% +into that ination as long as they keep +up with it which I think by them going + + align:start position:0% +up with it which I think by them going + + + align:start position:0% +up with it which I think by them going +to e-commerce gives him a good sign that + + align:start position:0% +to e-commerce gives him a good sign that + + + align:start position:0% +to e-commerce gives him a good sign that +management is doing a good job on + + align:start position:0% +management is doing a good job on + + + align:start position:0% +management is doing a good job on +keeping up with technology and making it + + align:start position:0% +keeping up with technology and making it + + + align:start position:0% +keeping up with technology and making it +keeping it Global so I think that's why + + align:start position:0% +keeping it Global so I think that's why + + + align:start position:0% +keeping it Global so I think that's why +I see a good future what do you think is + + align:start position:0% +I see a good future what do you think is + + + align:start position:0% +I see a good future what do you think is +the biggest bottleneck of + + align:start position:0% +the biggest bottleneck of + + + align:start position:0% +the biggest bottleneck of +reseller the fast evolution of equipment + + align:start position:0% +reseller the fast evolution of equipment + + + align:start position:0% +reseller the fast evolution of equipment +of the technology thing the other one is + + align:start position:0% +of the technology thing the other one is + + + align:start position:0% +of the technology thing the other one is +the as they say the standards are not + + align:start position:0% +the as they say the standards are not + + + align:start position:0% +the as they say the standards are not +the same in all countries However the + + align:start position:0% +the same in all countries However the + + + align:start position:0% +the same in all countries However the +fact that they have different markets in + + align:start position:0% +fact that they have different markets in + + + align:start position:0% +fact that they have different markets in +these countries also work in that + + align:start position:0% +these countries also work in that + + + align:start position:0% +these countries also work in that +Advantage for example I'm in Latin + + align:start position:0% +Advantage for example I'm in Latin + + + align:start position:0% +Advantage for example I'm in Latin +America you get equipment that is C and + + align:start position:0% +America you get equipment that is C and + + + align:start position:0% +America you get equipment that is C and +it doesn't you know doesn't care it's + + align:start position:0% +it doesn't you know doesn't care it's + + + align:start position:0% +it doesn't you know doesn't care it's +just you have the technology in hand and + + align:start position:0% +just you have the technology in hand and + + + align:start position:0% +just you have the technology in hand and +I'm sure it's the same in third devel in + + align:start position:0% +I'm sure it's the same in third devel in + + + align:start position:0% +I'm sure it's the same in third devel in +developing countries and I see that as + + align:start position:0% +developing countries and I see that as + + + align:start position:0% +developing countries and I see that as +working with C manager as well okay + + align:start position:0% +working with C manager as well okay + + + align:start position:0% +working with C manager as well okay +great so someone that uh doesn't think + + align:start position:0% +great so someone that uh doesn't think + + + align:start position:0% +great so someone that uh doesn't think +reseller has a a + + align:start position:0% +reseller has a a + + + align:start position:0% +reseller has a a +chance I just think that their current + + align:start position:0% +chance I just think that their current + + + align:start position:0% +chance I just think that their current +business model of getting donated cell + + align:start position:0% +business model of getting donated cell + + + align:start position:0% +business model of getting donated cell +phones wasn't viable because you know + + align:start position:0% +phones wasn't viable because you know + + + align:start position:0% +phones wasn't viable because you know +there was a time when you know people + + align:start position:0% +there was a time when you know people + + + align:start position:0% +there was a time when you know people +usually got their cell phone for free + + align:start position:0% +usually got their cell phone for free + + + align:start position:0% +usually got their cell phone for free +and then you know after two years and + + align:start position:0% +and then you know after two years and + + + align:start position:0% +and then you know after two years and +they got another one for free and they + + align:start position:0% +they got another one for free and they + + + align:start position:0% +they got another one for free and they +said okay I don't need this anymore and + + align:start position:0% +said okay I don't need this anymore and + + + align:start position:0% +said okay I don't need this anymore and +they throw a donation but now people pay + + align:start position:0% +they throw a donation but now people pay + + + align:start position:0% +they throw a donation but now people pay +a lot of money for their cell phone and + + align:start position:0% +a lot of money for their cell phone and + + + align:start position:0% +a lot of money for their cell phone and +they want some of that value back or + + align:start position:0% +they want some of that value back or + + + align:start position:0% +they want some of that value back or +they still see the value at the end so + + align:start position:0% +they still see the value at the end so + + + align:start position:0% +they still see the value at the end so +they have to ship their model to + + align:start position:0% +they have to ship their model to + + + align:start position:0% +they have to ship their model to +something where maybe they're actually + + align:start position:0% +something where maybe they're actually + + + align:start position:0% +something where maybe they're actually +paying you know a discount rate for + + align:start position:0% +paying you know a discount rate for + + + align:start position:0% +paying you know a discount rate for +someone's old cell phone which you see + + align:start position:0% +someone's old cell phone which you see + + + align:start position:0% +someone's old cell phone which you see +now + + align:start position:0% +now + + + align:start position:0% +now +like yes H we cannot hear anything at + + align:start position:0% +like yes H we cannot hear anything at + + + align:start position:0% +like yes H we cannot hear anything at +all from here from you can hear me but + + align:start position:0% +all from here from you can hear me but + + + align:start position:0% +all from here from you can hear me but +nobody else yeah I can hear you but we + + align:start position:0% +nobody else yeah I can hear you but we + + + align:start position:0% +nobody else yeah I can hear you but we +cannot hear anybody else so uh Michael + + align:start position:0% +cannot hear anybody else so uh Michael + + + align:start position:0% +cannot hear anybody else so uh Michael +could you uh help us with the uh uh mics + + align:start position:0% +could you uh help us with the uh uh mics + + + align:start position:0% +could you uh help us with the uh uh mics +I'll try to repeat in a sec but keep + + align:start position:0% +I'll try to repeat in a sec but keep + + + align:start position:0% +I'll try to repeat in a sec but keep +going then please B I think they they + + align:start position:0% +going then please B I think they they + + + align:start position:0% +going then please B I think they they +have to shift towards basically you know + + align:start position:0% +have to shift towards basically you know + + + align:start position:0% +have to shift towards basically you know +purchasing these phones on people not + + align:start position:0% +purchasing these phones on people not + + + align:start position:0% +purchasing these phones on people not +relying so much off the third party + + align:start position:0% +relying so much off the third party + + + align:start position:0% +relying so much off the third party +collectors if they want to remain viable + + align:start position:0% +collectors if they want to remain viable + + + align:start position:0% +collectors if they want to remain viable +so your main concern is that the + + align:start position:0% +so your main concern is that the + + + align:start position:0% +so your main concern is that the +shifting um uh business model on cell + + align:start position:0% +shifting um uh business model on cell + + + align:start position:0% +shifting um uh business model on cell +phones or electronics that you're paying + + align:start position:0% +phones or electronics that you're paying + + + align:start position:0% +phones or electronics that you're paying +for them that you don't want to donate + + align:start position:0% +for them that you don't want to donate + + + align:start position:0% +for them that you don't want to donate +it anymore and that's kind of the main + + align:start position:0% +it anymore and that's kind of the main + + + align:start position:0% +it anymore and that's kind of the main +way how resell is trying to make money + + align:start position:0% +way how resell is trying to make money + + + align:start position:0% +way how resell is trying to make money +is by getting them donated and uh trying + + align:start position:0% +is by getting them donated and uh trying + + + align:start position:0% +is by getting them donated and uh trying +to make money out of that donation so + + align:start position:0% +to make money out of that donation so + + + align:start position:0% +to make money out of that donation so +basically you're arguing that there may + + align:start position:0% +basically you're arguing that there may + + + align:start position:0% +basically you're arguing that there may +not be enough residual value to buy a + + align:start position:0% +not be enough residual value to buy a + + + align:start position:0% +not be enough residual value to buy a +phone because they could pay a little + + align:start position:0% +phone because they could pay a little + + + align:start position:0% +phone because they could pay a little +bit for it right and then they will do + + align:start position:0% +bit for it right and then they will do + + + align:start position:0% +bit for it right and then they will do +they can't rely so much as getting it + + align:start position:0% +they can't rely so much as getting it + + + align:start position:0% +they can't rely so much as getting it +from the third party collectors that's + + align:start position:0% +from the third party collectors that's + + + align:start position:0% +from the third party collectors that's +but you you think if they pay for it + + align:start position:0% +but you you think if they pay for it + + + align:start position:0% +but you you think if they pay for it +will that make them viable yes okay + + align:start position:0% +will that make them viable yes okay + + + align:start position:0% +will that make them viable yes okay +somebody does doesn't agree um so just + + align:start position:0% +somebody does doesn't agree um so just + + + align:start position:0% +somebody does doesn't agree um so just +to build on the point of I don't think + + align:start position:0% +to build on the point of I don't think + + + align:start position:0% +to build on the point of I don't think +it'll it'll checking to see if they can + + align:start position:0% +it'll it'll checking to see if they can + + + align:start position:0% +it'll it'll checking to see if they can +see it can they can you hear it now or + + align:start position:0% +see it can they can you hear it now or + + + align:start position:0% +see it can they can you hear it now or +the same as bad + + align:start position:0% +the same as bad + + + align:start position:0% +the same as bad +can you hear better yes okay okay um so + + align:start position:0% +can you hear better yes okay okay um so + + + align:start position:0% +can you hear better yes okay okay um so +I think the business model was more + + align:start position:0% +I think the business model was more + + + align:start position:0% +I think the business model was more +viable at the beginning where the + + align:start position:0% +viable at the beginning where the + + + align:start position:0% +viable at the beginning where the +cellular industry was starting and + + align:start position:0% +cellular industry was starting and + + + align:start position:0% +cellular industry was starting and +product lifetime like was much longer + + align:start position:0% +product lifetime like was much longer + + + align:start position:0% +product lifetime like was much longer +but now you have new models coming all + + align:start position:0% +but now you have new models coming all + + + align:start position:0% +but now you have new models coming all +the time and that significantly + + align:start position:0% +the time and that significantly + + + align:start position:0% +the time and that significantly +decreases the price that you can get for + + align:start position:0% +decreases the price that you can get for + + + align:start position:0% +decreases the price that you can get for +a secondhand phone um so for example + + align:start position:0% +a secondhand phone um so for example + + + align:start position:0% +a secondhand phone um so for example +previously maybe you had I don't know 50 + + align:start position:0% +previously maybe you had I don't know 50 + + + align:start position:0% +previously maybe you had I don't know 50 +mils of cell phones come out in a year + + align:start position:0% +mils of cell phones come out in a year + + + align:start position:0% +mils of cell phones come out in a year +and now you might have 200 I don't know + + align:start position:0% +and now you might have 200 I don't know + + + align:start position:0% +and now you might have 200 I don't know +I'm making the numbers up but you do + + align:start position:0% +I'm making the numbers up but you do + + + align:start position:0% +I'm making the numbers up but you do +have much more more offers right now so + + align:start position:0% +have much more more offers right now so + + + align:start position:0% +have much more more offers right now so +the price you can get is pretty uh I + + align:start position:0% +the price you can get is pretty uh I + + + align:start position:0% +the price you can get is pretty uh I +think it'll Decline and as a result + + align:start position:0% +think it'll Decline and as a result + + + align:start position:0% +think it'll Decline and as a result +you'll have less Revenue so I don't + + align:start position:0% +you'll have less Revenue so I don't + + + align:start position:0% +you'll have less Revenue so I don't +think that it's it's so + + align:start position:0% + + + + align:start position:0% + +valuable I think uh to to add on to the + + align:start position:0% +valuable I think uh to to add on to the + + + align:start position:0% +valuable I think uh to to add on to the +point uh right now I mean we're talking + + align:start position:0% +point uh right now I mean we're talking + + + align:start position:0% +point uh right now I mean we're talking +about enough almost like one to one + + align:start position:0% +about enough almost like one to one + + + align:start position:0% +about enough almost like one to one +ratio of cell phones and people on Earth + + align:start position:0% +ratio of cell phones and people on Earth + + + align:start position:0% +ratio of cell phones and people on Earth +so we're talking about large + + align:start position:0% +so we're talking about large + + + align:start position:0% +so we're talking about large +manufacturing volumes which means that + + align:start position:0% +manufacturing volumes which means that + + + align:start position:0% +manufacturing volumes which means that +the C the price uh has also decreased so + + align:start position:0% +the C the price uh has also decreased so + + + align:start position:0% +the C the price uh has also decreased so +that would decrease the the + + align:start position:0% +that would decrease the the + + + align:start position:0% +that would decrease the the +attractiveness of secondhand phones and + + align:start position:0% +attractiveness of secondhand phones and + + + align:start position:0% +attractiveness of secondhand phones and +also I mean that differential that + + align:start position:0% +also I mean that differential that + + + align:start position:0% +also I mean that differential that +reseller is trying to play on how much + + align:start position:0% +reseller is trying to play on how much + + + align:start position:0% +reseller is trying to play on how much +they buy the phones as compared to how + + align:start position:0% +they buy the phones as compared to how + + + align:start position:0% +they buy the phones as compared to how +much they can sell the + + align:start position:0% +much they can sell the + + + align:start position:0% +much they can sell the +phones so is the shrinking margins that + + align:start position:0% +phones so is the shrinking margins that + + + align:start position:0% +phones so is the shrinking margins that +you think are going to be a problem do + + align:start position:0% +you think are going to be a problem do + + + align:start position:0% +you think are going to be a problem do +you want to go back and say why reseller + + align:start position:0% +you want to go back and say why reseller + + + align:start position:0% +you want to go back and say why reseller +can still make + + align:start position:0% +can still make + + + align:start position:0% +can still make +money + + align:start position:0% +money + + + align:start position:0% +money +and that I think one first thing uh + + align:start position:0% +and that I think one first thing uh + + + align:start position:0% +and that I think one first thing uh +about the prices I don't think that the + + align:start position:0% +about the prices I don't think that the + + + align:start position:0% +about the prices I don't think that the +price going down is bad for the for the + + align:start position:0% +price going down is bad for the for the + + + align:start position:0% +price going down is bad for the for the +customer perspective and what I use is + + align:start position:0% +customer perspective and what I use is + + + align:start position:0% +customer perspective and what I use is +the um technology life cycle model so + + align:start position:0% +the um technology life cycle model so + + + align:start position:0% +the um technology life cycle model so +there are a lot of innovation and and + + align:start position:0% +there are a lot of innovation and and + + + align:start position:0% +there are a lot of innovation and and +there are other adopters and the early + + align:start position:0% +there are other adopters and the early + + + align:start position:0% +there are other adopters and the early +majority but they're also flaggers and + + align:start position:0% +majority but they're also flaggers and + + + align:start position:0% +majority but they're also flaggers and +people who are not adopting the + + align:start position:0% +people who are not adopting the + + + align:start position:0% +people who are not adopting the +technology are not technology oriented + + align:start position:0% +technology are not technology oriented + + + align:start position:0% +technology are not technology oriented +and who are just really happy to have + + align:start position:0% +and who are just really happy to have + + + align:start position:0% +and who are just really happy to have +very low price fund because they value + + align:start position:0% +very low price fund because they value + + + align:start position:0% +very low price fund because they value +more like the price rather than the + + align:start position:0% +more like the price rather than the + + + align:start position:0% +more like the price rather than the +technology and so at least one third or + + align:start position:0% +technology and so at least one third or + + + align:start position:0% +technology and so at least one third or +more of the market that is actually + + align:start position:0% +more of the market that is actually + + + align:start position:0% +more of the market that is actually +asking for those secondary phones + + align:start position:0% +asking for those secondary phones + + + align:start position:0% +asking for those secondary phones +because they don't value as much the + + align:start position:0% +because they don't value as much the + + + align:start position:0% +because they don't value as much the +technology and and they have just more + + align:start position:0% +technology and and they have just more + + + align:start position:0% +technology and and they have just more +choice because there are a lot of + + align:start position:0% +choice because there are a lot of + + + align:start position:0% +choice because there are a lot of +different phones actually that are on + + align:start position:0% +different phones actually that are on + + + align:start position:0% +different phones actually that are on +being um on put on the market and then + + align:start position:0% +being um on put on the market and then + + + align:start position:0% +being um on put on the market and then +Innovation goes so those people have + + align:start position:0% +Innovation goes so those people have + + + align:start position:0% +Innovation goes so those people have +actually largest choice for like um a + + align:start position:0% +actually largest choice for like um a + + + align:start position:0% +actually largest choice for like um a +lower price and from a customer + + align:start position:0% +lower price and from a customer + + + align:start position:0% +lower price and from a customer +perspective and from a demand standpoint + + align:start position:0% +perspective and from a demand standpoint + + + align:start position:0% +perspective and from a demand standpoint +I think this is um a good thing and so + + align:start position:0% +I think this is um a good thing and so + + + align:start position:0% +I think this is um a good thing and so +the business model might have to change + + align:start position:0% +the business model might have to change + + + align:start position:0% +the business model might have to change +a little bit because they would have + + align:start position:0% +a little bit because they would have + + + align:start position:0% +a little bit because they would have +lower margin lower soell but they have + + align:start position:0% +lower margin lower soell but they have + + + align:start position:0% +lower margin lower soell but they have +demand so if they do the right + + align:start position:0% +demand so if they do the right + + + align:start position:0% +demand so if they do the right +adjustments and play on volumes and play + + align:start position:0% +adjustments and play on volumes and play + + + align:start position:0% +adjustments and play on volumes and play +out on quality and play on um the the + + align:start position:0% +out on quality and play on um the the + + + align:start position:0% +out on quality and play on um the the +the quality of phone um offer I think + + align:start position:0% +the quality of phone um offer I think + + + align:start position:0% +the quality of phone um offer I think +there's really a way to make their way + + align:start position:0% +there's really a way to make their way + + + align:start position:0% +there's really a way to make their way +through the secondary market so so the + + align:start position:0% +through the secondary market so so the + + + align:start position:0% +through the secondary market so so the +argument here is that even though the + + align:start position:0% +argument here is that even though the + + + align:start position:0% +argument here is that even though the +margins could shrink over time there's + + align:start position:0% +margins could shrink over time there's + + + align:start position:0% +margins could shrink over time there's +always in in adoption of any technology + + align:start position:0% +always in in adoption of any technology + + + align:start position:0% +always in in adoption of any technology +there's always lards so there's always a + + align:start position:0% +there's always lards so there's always a + + + align:start position:0% +there's always lards so there's always a +market basically yeah the question is uh + + align:start position:0% +market basically yeah the question is uh + + + align:start position:0% +market basically yeah the question is uh +uh well you probably have to be more + + align:start position:0% +uh well you probably have to be more + + + align:start position:0% +uh well you probably have to be more +efficient so the part of the argument is + + align:start position:0% +efficient so the part of the argument is + + + align:start position:0% +efficient so the part of the argument is +they are the first if you're among the + + align:start position:0% +they are the first if you're among the + + + align:start position:0% +they are the first if you're among the +first you can probably get scale and you + + align:start position:0% +first you can probably get scale and you + + + align:start position:0% +first you can probably get scale and you +can be more competitive I don't know + + align:start position:0% +can be more competitive I don't know + + + align:start position:0% +can be more competitive I don't know +part of my reason for thinking they're + + align:start position:0% +part of my reason for thinking they're + + + align:start position:0% +part of my reason for thinking they're +not going to last is that they do one + + align:start position:0% +not going to last is that they do one + + + align:start position:0% +not going to last is that they do one +and only one thing and we find all the + + align:start position:0% +and only one thing and we find all the + + + align:start position:0% +and only one thing and we find all the +time that companies who do one thing + + align:start position:0% +time that companies who do one thing + + + align:start position:0% +time that companies who do one thing +don't survive when the next disruptive + + align:start position:0% +don't survive when the next disruptive + + + align:start position:0% +don't survive when the next disruptive +technology comes along I guess what I'm + + align:start position:0% +technology comes along I guess what I'm + + + align:start position:0% +technology comes along I guess what I'm +saying is I disagree with the + + align:start position:0% +saying is I disagree with the + + + align:start position:0% +saying is I disagree with the +fundamental assumption that they people + + align:start position:0% +fundamental assumption that they people + + + align:start position:0% +fundamental assumption that they people +always have cell phones that's what we + + align:start position:0% +always have cell phones that's what we + + + align:start position:0% +always have cell phones that's what we +said about horses that's what we said + + align:start position:0% +said about horses that's what we said + + + align:start position:0% +said about horses that's what we said +about newspapers things go + + align:start position:0% +about newspapers things go + + + align:start position:0% +about newspapers things go +away I said that they will evolve yeah + + align:start position:0% +away I said that they will evolve yeah + + + align:start position:0% +away I said that they will evolve yeah +so so maybe there is the electronic so + + align:start position:0% +so so maybe there is the electronic so + + + align:start position:0% +so so maybe there is the electronic so +they need to add something else yeah and + + align:start position:0% +they need to add something else yeah and + + + align:start position:0% +they need to add something else yeah and +also um as this SC up they can become + + align:start position:0% +also um as this SC up they can become + + + align:start position:0% +also um as this SC up they can become +more Global emerging countries the cell + + align:start position:0% +more Global emerging countries the cell + + + align:start position:0% +more Global emerging countries the cell +phones are to like a large um Market to + + align:start position:0% +phones are to like a large um Market to + + + align:start position:0% +phones are to like a large um Market to +penetrate and we can see that with + + align:start position:0% +penetrate and we can see that with + + + align:start position:0% +penetrate and we can see that with +Mobile payment people are like just + + align:start position:0% +Mobile payment people are like just + + + align:start position:0% +Mobile payment people are like just +buying phones and there's really they + + align:start position:0% +buying phones and there's really they + + + align:start position:0% +buying phones and there's really they +accessing ways to to pay for those F + + align:start position:0% +accessing ways to to pay for those F + + + align:start position:0% +accessing ways to to pay for those F +because it's also less andess expensive + + align:start position:0% +because it's also less andess expensive + + + align:start position:0% +because it's also less andess expensive +so even if we at some point in the + + align:start position:0% +so even if we at some point in the + + + align:start position:0% +so even if we at some point in the +future don't have phones anymore um they + + align:start position:0% +future don't have phones anymore um they + + + align:start position:0% +future don't have phones anymore um they +can still in the mean time s to other + + align:start position:0% +can still in the mean time s to other + + + align:start position:0% +can still in the mean time s to other +people and what I think is that they can + + align:start position:0% +people and what I think is that they can + + + align:start position:0% +people and what I think is that they can +adapt and if they if you don't have + + align:start position:0% +adapt and if they if you don't have + + + align:start position:0% +adapt and if they if you don't have +phones at one point and you have + + align:start position:0% +phones at one point and you have + + + align:start position:0% +phones at one point and you have +something else then you can sell + + align:start position:0% +something else then you can sell + + + align:start position:0% +something else then you can sell +secondary something else to people + + align:start position:0% +secondary something else to people + + + align:start position:0% +secondary something else to people +afterwards so this mechanism still goes + + align:start position:0% +afterwards so this mechanism still goes + + + align:start position:0% +afterwards so this mechanism still goes +on so let's uh just check with our + + align:start position:0% +on so let's uh just check with our + + + align:start position:0% +on so let's uh just check with our +friends from Saragosa do you hear any of + + align:start position:0% +friends from Saragosa do you hear any of + + + align:start position:0% +friends from Saragosa do you hear any of +that discussion + + align:start position:0% +that discussion + + + align:start position:0% +that discussion +yeah we we heard uh part part of it so + + align:start position:0% +yeah we we heard uh part part of it so + + + align:start position:0% +yeah we we heard uh part part of it so +okay it's okay okay good just want to + + align:start position:0% +okay it's okay okay good just want to + + + align:start position:0% +okay it's okay okay good just want to +double check all right so um so here's + + align:start position:0% +double check all right so um so here's + + + align:start position:0% +double check all right so um so here's +the challenge right so we I am hopeful + + align:start position:0% +the challenge right so we I am hopeful + + + align:start position:0% +the challenge right so we I am hopeful +that uh + + align:start position:0% +that uh + + + align:start position:0% +that uh +recellular can survive or one way or the + + align:start position:0% +recellular can survive or one way or the + + + align:start position:0% +recellular can survive or one way or the +other but the the question is what + + align:start position:0% +other but the the question is what + + + align:start position:0% +other but the the question is what +happens when reseller does not survive + + align:start position:0% +happens when reseller does not survive + + + align:start position:0% +happens when reseller does not survive +if there's not a business uh to be made + + align:start position:0% +if there's not a business uh to be made + + + align:start position:0% +if there's not a business uh to be made +so I will happen with those + + align:start position:0% +so I will happen with those + + + align:start position:0% +so I will happen with those +phones jenko get jenko will get them + + align:start position:0% +phones jenko get jenko will get them + + + align:start position:0% +phones jenko get jenko will get them +yeah so so the we so we heard the + + align:start position:0% +yeah so so the we so we heard the + + + align:start position:0% +yeah so so the we so we heard the +difference is reseller is a specialized + + align:start position:0% +difference is reseller is a specialized + + + align:start position:0% +difference is reseller is a specialized +very Niche reverse Logistics provider uh + + align:start position:0% +very Niche reverse Logistics provider uh + + + align:start position:0% +very Niche reverse Logistics provider uh +jenko was you know completely + + align:start position:0% +jenko was you know completely + + + align:start position:0% +jenko was you know completely +Diversified so they take anything that + + align:start position:0% +Diversified so they take anything that + + + align:start position:0% +Diversified so they take anything that +their customers want in this case the + + align:start position:0% +their customers want in this case the + + + align:start position:0% +their customers want in this case the +customers is the retailers the customers + + align:start position:0% +customers is the retailers the customers + + + align:start position:0% +customers is the retailers the customers +is not us so I think that that's a what + + align:start position:0% +is not us so I think that that's a what + + + align:start position:0% +is not us so I think that that's a what +many of you pointed out that one of the + + align:start position:0% +many of you pointed out that one of the + + + align:start position:0% +many of you pointed out that one of the +big differences is uh jenko's business + + align:start position:0% +big differences is uh jenko's business + + + align:start position:0% +big differences is uh jenko's business +model is more towards um partnership + + align:start position:0% +model is more towards um partnership + + + align:start position:0% +model is more towards um partnership +with the + + align:start position:0% +with the + + + align:start position:0% +with the +retailers that's their + + align:start position:0% +retailers that's their + + + align:start position:0% +retailers that's their +customer um the um reseller on the other + + align:start position:0% +customer um the um reseller on the other + + + align:start position:0% +customer um the um reseller on the other +hand wants to go to the end consumer and + + align:start position:0% +hand wants to go to the end consumer and + + + align:start position:0% +hand wants to go to the end consumer and +wants to get us more engaged one way or + + align:start position:0% +wants to get us more engaged one way or + + + align:start position:0% +wants to get us more engaged one way or +the other of course most of their + + align:start position:0% +the other of course most of their + + + align:start position:0% +the other of course most of their +purchases come from dealers so they have + + align:start position:0% +purchases come from dealers so they have + + + align:start position:0% +purchases come from dealers so they have +another another um another option and + + align:start position:0% +another another um another option and + + + align:start position:0% +another another um another option and +they're trying to grow to in consumers + + align:start position:0% +they're trying to grow to in consumers + + + align:start position:0% +they're trying to grow to in consumers +to try to penetrate the market more but + + align:start position:0% +to try to penetrate the market more but + + + align:start position:0% +to try to penetrate the market more but +is is a challenging it's a challenging + + align:start position:0% +is is a challenging it's a challenging + + + align:start position:0% +is is a challenging it's a challenging +environment uh which get us to + + align:start position:0% +environment uh which get us to + + + align:start position:0% +environment uh which get us to +whpo whpo whpo whpo so what do we do + + align:start position:0% +whpo whpo whpo whpo so what do we do + + + align:start position:0% +whpo whpo whpo whpo so what do we do +with whpo um so the way I would like to + + align:start position:0% +with whpo um so the way I would like to + + + align:start position:0% +with whpo um so the way I would like to +start well any any other comments cannot + + align:start position:0% +start well any any other comments cannot + + + align:start position:0% +start well any any other comments cannot +I'm not sure if they're going to survive + + align:start position:0% +I'm not sure if they're going to survive + + + align:start position:0% +I'm not sure if they're going to survive +or not but every time I fly to Brazil I + + align:start position:0% +or not but every time I fly to Brazil I + + + align:start position:0% +or not but every time I fly to Brazil I +can pay for my ticket by reselling the + + align:start position:0% +can pay for my ticket by reselling the + + + align:start position:0% +can pay for my ticket by reselling the +cell phone that's in my pocket there's + + align:start position:0% +cell phone that's in my pocket there's + + + align:start position:0% +cell phone that's in my pocket there's +definitely a future for + + align:start position:0% +definitely a future for + + + align:start position:0% +definitely a future for +sell hopefully there's enough market and + + align:start position:0% +sell hopefully there's enough market and + + + align:start position:0% +sell hopefully there's enough market and +and I believe there's enough but you + + align:start position:0% +and I believe there's enough but you + + + align:start position:0% +and I believe there's enough but you +know there's lots of pressures to be + + align:start position:0% +know there's lots of pressures to be + + + align:start position:0% +know there's lots of pressures to be +honest as it becomes the margins lower + + align:start position:0% +honest as it becomes the margins lower + + + align:start position:0% +honest as it becomes the margins lower +and lower who knows I was curious I + + align:start position:0% +and lower who knows I was curious I + + + align:start position:0% +and lower who knows I was curious I +didn't see the document when that was oh + + align:start position:0% +didn't see the document when that was oh + + + align:start position:0% +didn't see the document when that was oh +this this case was uh five years ago or + + align:start position:0% +this this case was uh five years ago or + + + align:start position:0% +this this case was uh five years ago or +so so it's a little bit older so + + align:start position:0% +so so it's a little bit older so + + + align:start position:0% +so so it's a little bit older so +reseller is still around + + align:start position:0% +reseller is still around + + + align:start position:0% +reseller is still around +I don't know how good how good are they + + align:start position:0% +I don't know how good how good are they + + + align:start position:0% +I don't know how good how good are they +right now thriving or not um okay good + + align:start position:0% +right now thriving or not um okay good + + + align:start position:0% +right now thriving or not um okay good +so uh let's let's go to + + align:start position:0% +so uh let's let's go to + + + align:start position:0% +so uh let's let's go to +whirpool unless there's any other + + align:start position:0% +whirpool unless there's any other + + + align:start position:0% +whirpool unless there's any other +closing comments or questions about + + align:start position:0% +closing comments or questions about + + + align:start position:0% +closing comments or questions about +recellular or jenko sarosa any comments + + align:start position:0% +recellular or jenko sarosa any comments + + + align:start position:0% +recellular or jenko sarosa any comments +or questions final + + align:start position:0% + + + + align:start position:0% + +thoughts no yeah okay remember wave the + + align:start position:0% +thoughts no yeah okay remember wave the + + + align:start position:0% +thoughts no yeah okay remember wave the +hands otherwise I cannot I cannot see + + align:start position:0% +hands otherwise I cannot I cannot see + + + align:start position:0% +hands otherwise I cannot I cannot see +you all right um so let's go to uh whpo + + align:start position:0% +you all right um so let's go to uh whpo + + + align:start position:0% +you all right um so let's go to uh whpo +and to do whpo we're going to spend a + + align:start position:0% +and to do whpo we're going to spend a + + + align:start position:0% +and to do whpo we're going to spend a +little more time on it and um what we + + align:start position:0% +little more time on it and um what we + + + align:start position:0% +little more time on it and um what we +will start with is who wants to tell + + align:start position:0% +will start with is who wants to tell + + + align:start position:0% +will start with is who wants to tell +me what should whpo + + align:start position:0% +me what should whpo + + + align:start position:0% +me what should whpo +do so what which are the choices of whpo + + align:start position:0% +do so what which are the choices of whpo + + + align:start position:0% +do so what which are the choices of whpo +let's start with here so the choices are + + align:start position:0% +let's start with here so the choices are + + + align:start position:0% +let's start with here so the choices are +to go with the ifo model yeah can you + + align:start position:0% +to go with the ifo model yeah can you + + + align:start position:0% +to go with the ifo model yeah can you +explain what ifo is quickly so the ifo + + align:start position:0% +explain what ifo is quickly so the ifo + + + align:start position:0% +explain what ifo is quickly so the ifo +is the industry for the + + align:start position:0% +is the industry for the + + + align:start position:0% +is the industry for the +organization um in which uh so it's it's + + align:start position:0% +organization um in which uh so it's it's + + + align:start position:0% +organization um in which uh so it's it's +what I understand is it's kind of like + + align:start position:0% +what I understand is it's kind of like + + + align:start position:0% +what I understand is it's kind of like +body that kind of collects you know is + + align:start position:0% +body that kind of collects you know is + + + align:start position:0% +body that kind of collects you know is +formed by all the industry players and + + align:start position:0% +formed by all the industry players and + + + align:start position:0% +formed by all the industry players and +they collect the the appliances and they + + align:start position:0% +they collect the the appliances and they + + + align:start position:0% +they collect the the appliances and they +they deal with it property yeah so we + + align:start position:0% +they deal with it property yeah so we + + + align:start position:0% +they deal with it property yeah so we +put other words like jenko but funded by + + align:start position:0% +put other words like jenko but funded by + + + align:start position:0% +put other words like jenko but funded by +a bunch of same industry players and + + align:start position:0% +a bunch of same industry players and + + + align:start position:0% +a bunch of same industry players and +they all pay jenko and jenko does + + align:start position:0% +they all pay jenko and jenko does + + + align:start position:0% +they all pay jenko and jenko does +everything pretty much the other way is + + align:start position:0% +everything pretty much the other way is + + + align:start position:0% +everything pretty much the other way is +the second method is for um a world pool + + align:start position:0% +the second method is for um a world pool + + + align:start position:0% +the second method is for um a world pool +to be an iPhone on its own or to run a + + align:start position:0% +to be an iPhone on its own or to run a + + + align:start position:0% +to be an iPhone on its own or to run a +closed loop + + align:start position:0% +closed loop + + + align:start position:0% +closed loop +system and collect their own appliances + + align:start position:0% +system and collect their own appliances + + + align:start position:0% +system and collect their own appliances +at the end of life + + align:start position:0% + + + + align:start position:0% + +closed loop system um so in in this + + align:start position:0% +closed loop system um so in in this + + + align:start position:0% +closed loop system um so in in this +context and we probably have not defined + + align:start position:0% +context and we probably have not defined + + + align:start position:0% +context and we probably have not defined +closed loop properly it's just the same + + align:start position:0% +closed loop properly it's just the same + + + align:start position:0% +closed loop properly it's just the same +company that sells the products wants to + + align:start position:0% +company that sells the products wants to + + + align:start position:0% +company that sells the products wants to +get it back and try to keep it within + + align:start position:0% +get it back and try to keep it within + + + align:start position:0% +get it back and try to keep it within +your own system as opposed to uh getting + + align:start position:0% +your own system as opposed to uh getting + + + align:start position:0% +your own system as opposed to uh getting +somebody else to deal with it and take + + align:start position:0% +somebody else to deal with it and take + + + align:start position:0% +somebody else to deal with it and take +care of it and you want to somehow + + align:start position:0% +care of it and you want to somehow + + + align:start position:0% +care of it and you want to somehow +extract value out of that process and + + align:start position:0% +extract value out of that process and + + + align:start position:0% +extract value out of that process and +bring those materials back into your + + align:start position:0% +bring those materials back into your + + + align:start position:0% +bring those materials back into your +same supply chain as best as possible + + align:start position:0% +same supply chain as best as possible + + + align:start position:0% +same supply chain as best as possible +and that's what the option and this + + align:start position:0% +and that's what the option and this + + + align:start position:0% +and that's what the option and this +closed loop is closed loop doing it + + align:start position:0% +closed loop is closed loop doing it + + + align:start position:0% +closed loop is closed loop doing it +alone + + align:start position:0% + + + + align:start position:0% + +a little bit alone at least in Canada + + align:start position:0% +a little bit alone at least in Canada + + + align:start position:0% +a little bit alone at least in Canada +right they're doing by why will they + + align:start position:0% +right they're doing by why will they + + + align:start position:0% +right they're doing by why will they +even there's a third option to do + + align:start position:0% +even there's a third option to do + + + align:start position:0% +even there's a third option to do +nothing third option of + + align:start position:0% +nothing third option of + + + align:start position:0% +nothing third option of +course more than do nothing do nothing + + align:start position:0% +course more than do nothing do nothing + + + align:start position:0% +course more than do nothing do nothing +is no longer an option do nothing was an + + align:start position:0% +is no longer an option do nothing was an + + + align:start position:0% +is no longer an option do nothing was an +option maybe in 2005 for these guys yeah + + align:start position:0% +option maybe in 2005 for these guys yeah + + + align:start position:0% +option maybe in 2005 for these guys yeah +so yeah I know I know what you meant + + align:start position:0% +so yeah I know I know what you meant + + + align:start position:0% +so yeah I know I know what you meant +yeah so third third + + align:start position:0% +yeah so third third + + + align:start position:0% +yeah so third third +option is to oppose the regulation + + align:start position:0% + + + + align:start position:0% + +opposer regulation so let me start doing + + align:start position:0% +opposer regulation so let me start doing + + + align:start position:0% +opposer regulation so let me start doing +with a little show of hands how many + + align:start position:0% +with a little show of hands how many + + + align:start position:0% +with a little show of hands how many +people think that they should go with + + align:start position:0% +people think that they should go with + + + align:start position:0% +people think that they should go with +the industry funded + + align:start position:0% +the industry funded + + + align:start position:0% +the industry funded +option T goes one two anyone there there + + align:start position:0% +option T goes one two anyone there there + + + align:start position:0% +option T goes one two anyone there there +two I two and a half there no no hals + + align:start position:0% +two I two and a half there no no hals + + + align:start position:0% +two I two and a half there no no hals +here I'm I'm going with three and then + + align:start position:0% +here I'm I'm going with three and then + + + align:start position:0% +here I'm I'm going with three and then +one oh okay so if it doesn't work + + align:start position:0% +one oh okay so if it doesn't work + + + align:start position:0% +one oh okay so if it doesn't work +okay + + align:start position:0% +okay + + + align:start position:0% +okay +two how many would like to oppose + + align:start position:0% + + + + align:start position:0% + +regulation one two + + align:start position:0% +regulation one two + + + align:start position:0% +regulation one two +three I see it looks like there's the + + align:start position:0% +three I see it looks like there's the + + + align:start position:0% +three I see it looks like there's the +three so I take the rest of you would + + align:start position:0% +three so I take the rest of you would + + + align:start position:0% +three so I take the rest of you would +like to do it on your + + align:start position:0% +like to do it on your + + + align:start position:0% +like to do it on your +own right so let's start with the so you + + align:start position:0% +own right so let's start with the so you + + + align:start position:0% +own right so let's start with the so you +already SP who else was opposing + + align:start position:0% +already SP who else was opposing + + + align:start position:0% +already SP who else was opposing +regulation why would you oppose + + align:start position:0% +regulation why would you oppose + + + align:start position:0% +regulation why would you oppose +regulation uh well can I also qualified + + align:start position:0% +regulation uh well can I also qualified + + + align:start position:0% +regulation uh well can I also qualified +to say if I had to do one or two I would + + align:start position:0% +to say if I had to do one or two I would + + + align:start position:0% +to say if I had to do one or two I would +pick two but the the idea was that that + + align:start position:0% +pick two but the the idea was that that + + + align:start position:0% +pick two but the the idea was that that +it's not really going to be helpful + + align:start position:0% +it's not really going to be helpful + + + align:start position:0% +it's not really going to be helpful +because a lot of this process is + + align:start position:0% +because a lot of this process is + + + align:start position:0% +because a lot of this process is +self-sufficient to begin with I think + + align:start position:0% +self-sufficient to begin with I think + + + align:start position:0% +self-sufficient to begin with I think +they said like + + align:start position:0% +they said like + + + align:start position:0% +they said like +95% of all of the used products go into + + align:start position:0% +95% of all of the used products go into + + + align:start position:0% +95% of all of the used products go into +the recycling process and hardly any of + + align:start position:0% +the recycling process and hardly any of + + + align:start position:0% +the recycling process and hardly any of +it um goes into landfill just because + + align:start position:0% +it um goes into landfill just because + + + align:start position:0% +it um goes into landfill just because +there's a lot of Commodities that are in + + align:start position:0% +there's a lot of Commodities that are in + + + align:start position:0% +there's a lot of Commodities that are in +these products like aluminum or + + align:start position:0% +these products like aluminum or + + + align:start position:0% +these products like aluminum or +aluminium or uh copper stuff like that + + align:start position:0% +aluminium or uh copper stuff like that + + + align:start position:0% +aluminium or uh copper stuff like that +so all this stuff gets reclaimed so you + + align:start position:0% +so all this stuff gets reclaimed so you + + + align:start position:0% +so all this stuff gets reclaimed so you +don't need + + align:start position:0% +don't need + + + align:start position:0% +don't need +to do something that's going to add a + + align:start position:0% +to do something that's going to add a + + + align:start position:0% +to do something that's going to add a +lot of overhead to people's businesses + + align:start position:0% +lot of overhead to people's businesses + + + align:start position:0% +lot of overhead to people's businesses +to have them do something that is pretty + + align:start position:0% +to have them do something that is pretty + + + align:start position:0% +to have them do something that is pretty +much already happening on its own so it + + align:start position:0% +much already happening on its own so it + + + align:start position:0% +much already happening on its own so it +happens on its own what what were the + + align:start position:0% +happens on its own what what were the + + + align:start position:0% +happens on its own what what were the +rates someone remembers of recycling 95 + + align:start position:0% +rates someone remembers of recycling 95 + + + align:start position:0% +rates someone remembers of recycling 95 +to 99% it's pretty good + + align:start position:0% +to 99% it's pretty good + + + align:start position:0% +to 99% it's pretty good +right those were World + + align:start position:0% +right those were World + + + align:start position:0% +right those were World +numbers oh they're pretty they're pretty + + align:start position:0% +numbers oh they're pretty they're pretty + + + align:start position:0% +numbers oh they're pretty they're pretty +consistent yeah let's trust them let's + + align:start position:0% +consistent yeah let's trust them let's + + + align:start position:0% +consistent yeah let's trust them let's +trust them these are factual numbers so + + align:start position:0% +trust them these are factual numbers so + + + align:start position:0% +trust them these are factual numbers so +95% + + align:start position:0% +95% + + + align:start position:0% +95% +of it is kind of being naturally + + align:start position:0% +of it is kind of being naturally + + + align:start position:0% +of it is kind of being naturally +repurposed recycled in some way or + + align:start position:0% +repurposed recycled in some way or + + + align:start position:0% +repurposed recycled in some way or +another through a normal Network going + + align:start position:0% +another through a normal Network going + + + align:start position:0% +another through a normal Network going +back to we're discussing all the + + align:start position:0% +back to we're discussing all the + + + align:start position:0% +back to we're discussing all the +different products cars and + + align:start position:0% +different products cars and + + + align:start position:0% +different products cars and +t-shirts uh cars have a lot of value + + align:start position:0% +t-shirts uh cars have a lot of value + + + align:start position:0% +t-shirts uh cars have a lot of value +Appliance have a lot of value they're + + align:start position:0% +Appliance have a lot of value they're + + + align:start position:0% +Appliance have a lot of value they're +designed for a very very long time so + + align:start position:0% +designed for a very very long time so + + + align:start position:0% +designed for a very very long time so +someone wants to kind of move that chain + + align:start position:0% +someone wants to kind of move that chain + + + align:start position:0% +someone wants to kind of move that chain +of how much you value having the latest + + align:start position:0% +of how much you value having the latest + + + align:start position:0% +of how much you value having the latest +latest model of refrigerator or not and + + align:start position:0% +latest model of refrigerator or not and + + + align:start position:0% +latest model of refrigerator or not and +eventually when he goes to the bottom of + + align:start position:0% +eventually when he goes to the bottom of + + + align:start position:0% +eventually when he goes to the bottom of +that chain that person also wants to + + align:start position:0% +that chain that person also wants to + + + align:start position:0% +that chain that person also wants to +maybe make the effort to + + align:start position:0% +maybe make the effort to + + + align:start position:0% +maybe make the effort to +to try to get some value and a dealer + + align:start position:0% +to try to get some value and a dealer + + + align:start position:0% +to try to get some value and a dealer +gets in and scraps it and divid it into + + align:start position:0% +gets in and scraps it and divid it into + + + align:start position:0% +gets in and scraps it and divid it into +all the medals and eventually gets done + + align:start position:0% +all the medals and eventually gets done + + + align:start position:0% +all the medals and eventually gets done +I would argue it's more of an effort for + + align:start position:0% +I would argue it's more of an effort for + + + align:start position:0% +I would argue it's more of an effort for +someone to not recycle their old washing + + align:start position:0% +someone to not recycle their old washing + + + align:start position:0% +someone to not recycle their old washing +machine to like pick it up and take it + + align:start position:0% +machine to like pick it up and take it + + + align:start position:0% +machine to like pick it up and take it +to landfill it's not like they're + + align:start position:0% +to landfill it's not like they're + + + align:start position:0% +to landfill it's not like they're +throwing away batteries like I mean most + + align:start position:0% +throwing away batteries like I mean most + + + align:start position:0% +throwing away batteries like I mean most +people get rid of their stuff by putting + + align:start position:0% +people get rid of their stuff by putting + + + align:start position:0% +people get rid of their stuff by putting +it outside in front of their house and + + align:start position:0% +it outside in front of their house and + + + align:start position:0% +it outside in front of their house and +then someone picks it up so if the + + align:start position:0% +then someone picks it up so if the + + + align:start position:0% +then someone picks it up so if the +process already works like those five% + + align:start position:0% +process already works like those five% + + + align:start position:0% +process already works like those five% +that aren't recycling it or whatever + + align:start position:0% +that aren't recycling it or whatever + + + align:start position:0% +that aren't recycling it or whatever +they're probably not going to just + + align:start position:0% +they're probably not going to just + + + align:start position:0% +they're probably not going to just +because warpool came up with a Clos loop + + align:start position:0% +because warpool came up with a Clos loop + + + align:start position:0% +because warpool came up with a Clos loop +system so it's really going to add any + + align:start position:0% +system so it's really going to add any + + + align:start position:0% +system so it's really going to add any +so those 5% have their own landfill so + + align:start position:0% +so those 5% have their own landfill so + + + align:start position:0% +so those 5% have their own landfill so +they will still trash it yeah okay + + align:start position:0% +they will still trash it yeah okay + + + align:start position:0% +they will still trash it yeah okay +they'll leave it there hanging those are + + align:start position:0% +they'll leave it there hanging those are + + + align:start position:0% +they'll leave it there hanging those are +the ones that are not accounted for + + align:start position:0% +the ones that are not accounted for + + + align:start position:0% +the ones that are not accounted for +right those are the ones that are still + + align:start position:0% +right those are the ones that are still + + + align:start position:0% +right those are the ones that are still +in your houses uh landfill somewhere + + align:start position:0% +in your houses uh landfill somewhere + + + align:start position:0% +in your houses uh landfill somewhere +okay good so uh why is yeah you want to + + align:start position:0% +okay good so uh why is yeah you want to + + + align:start position:0% +okay good so uh why is yeah you want to +add something else on yeah I just want + + align:start position:0% +add something else on yeah I just want + + + align:start position:0% +add something else on yeah I just want +to com I think that problem with that + + align:start position:0% +to com I think that problem with that + + + align:start position:0% +to com I think that problem with that +even though it seems to be working is + + align:start position:0% +even though it seems to be working is + + + align:start position:0% +even though it seems to be working is +like perpetuated some mentality that I + + align:start position:0% +like perpetuated some mentality that I + + + align:start position:0% +like perpetuated some mentality that I +can just put something out on my you + + align:start position:0% +can just put something out on my you + + + align:start position:0% +can just put something out on my you +know on my driveway on the sidewalk and + + align:start position:0% +know on my driveway on the sidewalk and + + + align:start position:0% +know on my driveway on the sidewalk and +someone else is going to take care of it + + align:start position:0% +someone else is going to take care of it + + + align:start position:0% +someone else is going to take care of it +and I think that's a big issue + + align:start position:0% + + + + align:start position:0% + +so this is the the the working part is + + align:start position:0% +so this is the the the working part is + + + align:start position:0% +so this is the the the working part is +that not sure the market is but there's + + align:start position:0% +that not sure the market is but there's + + + align:start position:0% +that not sure the market is but there's +something about the overall social norms + + align:start position:0% +something about the overall social norms + + + align:start position:0% +something about the overall social norms +changes that you would like maybe + + align:start position:0% +changes that you would like maybe + + + align:start position:0% +changes that you would like maybe +to so this is part of a trend right so + + align:start position:0% +to so this is part of a trend right so + + + align:start position:0% +to so this is part of a trend right so +it's Canada right we're talking about + + align:start position:0% +it's Canada right we're talking about + + + align:start position:0% +it's Canada right we're talking about +the US here it's Canada so people are + + align:start position:0% +the US here it's Canada so people are + + + align:start position:0% +the US here it's Canada so people are +very conscious they're already doing + + align:start position:0% +very conscious they're already doing + + + align:start position:0% +very conscious they're already doing +lots of recycling there's lots of other + + align:start position:0% +lots of recycling there's lots of other + + + align:start position:0% +lots of recycling there's lots of other +programs going on so this is natural + + align:start position:0% +programs going on so this is natural + + + align:start position:0% +programs going on so this is natural +progression but um a couple of people + + align:start position:0% +progression but um a couple of people + + + align:start position:0% +progression but um a couple of people +that maybe who who thought that the uh + + align:start position:0% +that maybe who who thought that the uh + + + align:start position:0% +that maybe who who thought that the uh +the why regulation is still not enough + + align:start position:0% +the why regulation is still not enough + + + align:start position:0% +the why regulation is still not enough +so the one reason is social which is the + + align:start position:0% +so the one reason is social which is the + + + align:start position:0% +so the one reason is social which is the +other + + align:start position:0% +other + + + align:start position:0% +other +reason well I thought that for now the + + align:start position:0% +reason well I thought that for now the + + + align:start position:0% +reason well I thought that for now the +the prices of all the communities are + + align:start position:0% +the prices of all the communities are + + + align:start position:0% +the prices of all the communities are +pretty high but what happens is at some + + align:start position:0% +pretty high but what happens is at some + + + align:start position:0% +pretty high but what happens is at some +point the prices are not high enough to + + align:start position:0% +point the prices are not high enough to + + + align:start position:0% +point the prices are not high enough to +give incentives to recycl so that was a + + align:start position:0% +give incentives to recycl so that was a + + + align:start position:0% +give incentives to recycl so that was a +second point and also there are some new + + align:start position:0% +second point and also there are some new + + + align:start position:0% +second point and also there are some new +regulations that are that we come up + + align:start position:0% +regulations that are that we come up + + + align:start position:0% +regulations that are that we come up +because um we figure out that + + align:start position:0% +because um we figure out that + + + align:start position:0% +because um we figure out that +this example about Mercury that they + + align:start position:0% +this example about Mercury that they + + + align:start position:0% +this example about Mercury that they +need they need to regulate Mercury how + + align:start position:0% +need they need to regulate Mercury how + + + align:start position:0% +need they need to regulate Mercury how +we did that mercury and how are we sure + + align:start position:0% +we did that mercury and how are we sure + + + align:start position:0% +we did that mercury and how are we sure +that all the Scavengers deal with uh + + align:start position:0% +that all the Scavengers deal with uh + + + align:start position:0% +that all the Scavengers deal with uh +with some of the material correctly um + + align:start position:0% +with some of the material correctly um + + + align:start position:0% +with some of the material correctly um +so that was another questiones + + align:start position:0% +so that was another questiones + + + align:start position:0% +so that was another questiones +refrigerant for example refrigerant so + + align:start position:0% +refrigerant for example refrigerant so + + + align:start position:0% +refrigerant for example refrigerant so +there's a couple of things that uh we + + align:start position:0% +there's a couple of things that uh we + + + align:start position:0% +there's a couple of things that uh we +know that they are + + align:start position:0% +know that they are + + + align:start position:0% +know that they are +recycled uh we know that those materials + + align:start position:0% +recycled uh we know that those materials + + + align:start position:0% +recycled uh we know that those materials +are being somehow + + align:start position:0% +are being somehow + + + align:start position:0% +are being somehow +repurposed a big chunk of them so + + align:start position:0% +repurposed a big chunk of them so + + + align:start position:0% +repurposed a big chunk of them so +the problem is that if the prices change + + align:start position:0% +the problem is that if the prices change + + + align:start position:0% +the problem is that if the prices change +boom this this Market will collapse + + align:start position:0% +boom this this Market will collapse + + + align:start position:0% +boom this this Market will collapse +maybe there's innovation in materials + + align:start position:0% +maybe there's innovation in materials + + + align:start position:0% +maybe there's innovation in materials +and they come with a new material that + + align:start position:0% +and they come with a new material that + + + align:start position:0% +and they come with a new material that +is an alloy plastic who knows that is + + align:start position:0% +is an alloy plastic who knows that is + + + align:start position:0% +is an alloy plastic who knows that is +still as good performing as they need + + align:start position:0% +still as good performing as they need + + + align:start position:0% +still as good performing as they need +for the structure of the refrigerator + + align:start position:0% +for the structure of the refrigerator + + + align:start position:0% +for the structure of the refrigerator +that is not as recyclable or is very + + align:start position:0% +that is not as recyclable or is very + + + align:start position:0% +that is not as recyclable or is very +expensive and then you have much higher + + align:start position:0% +expensive and then you have much higher + + + align:start position:0% +expensive and then you have much higher +waste so there's a little bit of an + + align:start position:0% +waste so there's a little bit of an + + + align:start position:0% +waste so there's a little bit of an +uncertainty Factor then um clearly what + + align:start position:0% +uncertainty Factor then um clearly what + + + align:start position:0% +uncertainty Factor then um clearly what +they're trying to get out of it what is + + align:start position:0% +they're trying to get out of it what is + + + align:start position:0% +they're trying to get out of it what is +the most value and what they know how to + + align:start position:0% +the most value and what they know how to + + + align:start position:0% +the most value and what they know how to +deal with and mercury and refrigerants a + + align:start position:0% +deal with and mercury and refrigerants a + + + align:start position:0% +deal with and mercury and refrigerants a +little bit more tricky and it's unclear + + align:start position:0% +little bit more tricky and it's unclear + + + align:start position:0% +little bit more tricky and it's unclear +to + + align:start position:0% + + + + align:start position:0% + +know if um if they're doing properly so + + align:start position:0% +know if um if they're doing properly so + + + align:start position:0% +know if um if they're doing properly so +there's a little bit of a tricky part + + align:start position:0% +there's a little bit of a tricky part + + + align:start position:0% +there's a little bit of a tricky part +there but there may be other options of + + align:start position:0% +there but there may be other options of + + + align:start position:0% +there but there may be other options of +Regulation instead of this one so this + + align:start position:0% +Regulation instead of this one so this + + + align:start position:0% +Regulation instead of this one so this +is this the regulation that they are + + align:start position:0% +is this the regulation that they are + + + align:start position:0% +is this the regulation that they are +opposing is the the uh extended producer + + align:start position:0% +opposing is the the uh extended producer + + + align:start position:0% +opposing is the the uh extended producer +responsibility the epr + + align:start position:0% +responsibility the epr + + + align:start position:0% +responsibility the epr +responsibility that is worlding to be + + align:start position:0% +responsibility that is worlding to be + + + align:start position:0% +responsibility that is worlding to be +responsible for the whole thing but + + align:start position:0% +responsible for the whole thing but + + + align:start position:0% +responsible for the whole thing but +there are other things that they could + + align:start position:0% +there are other things that they could + + + align:start position:0% +there are other things that they could +do uh just to tackle Mercury and + + align:start position:0% +do uh just to tackle Mercury and + + + align:start position:0% +do uh just to tackle Mercury and +refrigerator for example what could they + + align:start position:0% +refrigerator for example what could they + + + align:start position:0% +refrigerator for example what could they +do if they only want to fix that + + align:start position:0% +do if they only want to fix that + + + align:start position:0% +do if they only want to fix that +problem why would the government what + + align:start position:0% +problem why would the government what + + + align:start position:0% +problem why would the government what +could the government do without doing + + align:start position:0% +could the government do without doing + + + align:start position:0% +could the government do without doing +this whole very complicated process what + + align:start position:0% +this whole very complicated process what + + + align:start position:0% +this whole very complicated process what +they're doing to laptops they just they + + align:start position:0% +they're doing to laptops they just they + + + align:start position:0% +they're doing to laptops they just they +just ban the product or ban the has + + align:start position:0% +just ban the product or ban the has + + + align:start position:0% +just ban the product or ban the has +material of it so some pieces you can + + align:start position:0% +material of it so some pieces you can + + + align:start position:0% +material of it so some pieces you can +ask the manufacturers to phase this out + + align:start position:0% +ask the manufacturers to phase this out + + + align:start position:0% +ask the manufacturers to phase this out +of their products all together right so + + align:start position:0% +of their products all together right so + + + align:start position:0% +of their products all together right so +you work with the manufacturers and you + + align:start position:0% +you work with the manufacturers and you + + + align:start position:0% +you work with the manufacturers and you +do some agreement technology path and + + align:start position:0% +do some agreement technology path and + + + align:start position:0% +do some agreement technology path and +then eventually you can get rid of that + + align:start position:0% +then eventually you can get rid of that + + + align:start position:0% +then eventually you can get rid of that +it's one option any other + + align:start position:0% +it's one option any other + + + align:start position:0% +it's one option any other +options sarosa any other + + align:start position:0% + + + + align:start position:0% + +options they're silent + + align:start position:0% +options they're silent + + + align:start position:0% +options they're silent +today we we have the mic off just uh to + + align:start position:0% +today we we have the mic off just uh to + + + align:start position:0% +today we we have the mic off just uh to +make sure we don't have EO yeah so any + + align:start position:0% +make sure we don't have EO yeah so any + + + align:start position:0% +make sure we don't have EO yeah so any +other + + align:start position:0% +other + + + align:start position:0% +other +options + + align:start position:0% +options + + + align:start position:0% +options +guys no + + align:start position:0% +guys no + + + align:start position:0% +guys no +options the other one is to trade these + + align:start position:0% +options the other one is to trade these + + + align:start position:0% +options the other one is to trade these +dealers maybe right these current + + align:start position:0% +dealers maybe right these current + + + align:start position:0% +dealers maybe right these current +recyclers and train them to do better + + align:start position:0% +recyclers and train them to do better + + + align:start position:0% +recyclers and train them to do better +Mercury management do a whole program + + align:start position:0% +Mercury management do a whole program + + + align:start position:0% +Mercury management do a whole program +right where you can just instead of + + align:start position:0% +right where you can just instead of + + + align:start position:0% +right where you can just instead of +involving everyone you just go to the + + align:start position:0% +involving everyone you just go to the + + + align:start position:0% +involving everyone you just go to the +market directly and do it those are few + + align:start position:0% +market directly and do it those are few + + + align:start position:0% +market directly and do it those are few +things that you could do um instead of + + align:start position:0% +things that you could do um instead of + + + align:start position:0% +things that you could do um instead of +Regulation but let's move to the other + + align:start position:0% +Regulation but let's move to the other + + + align:start position:0% +Regulation but let's move to the other +two + + align:start position:0% +two + + + align:start position:0% +two +options ifo versus Clos + + align:start position:0% +options ifo versus Clos + + + align:start position:0% +options ifo versus Clos +Loop who chose the ifo + + align:start position:0% +Loop who chose the ifo + + + align:start position:0% +Loop who chose the ifo +model so uh no one ins start a go so + + align:start position:0% +model so uh no one ins start a go so + + + align:start position:0% +model so uh no one ins start a go so +maybe I'll give you a chance so why will + + align:start position:0% +maybe I'll give you a chance so why will + + + align:start position:0% +maybe I'll give you a chance so why will +the iPhone model be a good chance for + + align:start position:0% +the iPhone model be a good chance for + + + align:start position:0% +the iPhone model be a good chance for +whpo well I voted that because that + + align:start position:0% +whpo well I voted that because that + + + align:start position:0% +whpo well I voted that because that +gives time and flexibility for the + + align:start position:0% +gives time and flexibility for the + + + align:start position:0% +gives time and flexibility for the +regulation to + + align:start position:0% +regulation to + + + align:start position:0% +regulation to +change uh I said if you go with an ifo + + align:start position:0% +change uh I said if you go with an ifo + + + align:start position:0% +change uh I said if you go with an ifo +give you more time to see how the + + align:start position:0% +give you more time to see how the + + + align:start position:0% +give you more time to see how the +infrastructure really works how um how + + align:start position:0% +infrastructure really works how um how + + + align:start position:0% +infrastructure really works how um how +they can look to see how the loop can be + + align:start position:0% +they can look to see how the loop can be + + + align:start position:0% +they can look to see how the loop can be +designed and + + align:start position:0% + + + + align:start position:0% + +done I I saw it more as a as a temporary + + align:start position:0% +done I I saw it more as a as a temporary + + + align:start position:0% +done I I saw it more as a as a temporary +solution and then based because + + align:start position:0% +solution and then based because + + + align:start position:0% +solution and then based because +is way more expensive right it would + + align:start position:0% +is way more expensive right it would + + + align:start position:0% +is way more expensive right it would +take like three four times according to + + align:start position:0% +take like three four times according to + + + align:start position:0% +take like three four times according to +my + + align:start position:0% +my + + + align:start position:0% +my +calculation so I say do it for a period + + align:start position:0% +calculation so I say do it for a period + + + align:start position:0% +calculation so I say do it for a period +of time and then once you change to + + align:start position:0% +of time and then once you change to + + + align:start position:0% +of time and then once you change to +close loop you can pay back and actually + + align:start position:0% +close loop you can pay back and actually + + + align:start position:0% +close loop you can pay back and actually +meet how the regulation will evolve + + align:start position:0% +meet how the regulation will evolve + + + align:start position:0% +meet how the regulation will evolve +doing so this is like a good safe place + + align:start position:0% +doing so this is like a good safe place + + + align:start position:0% +doing so this is like a good safe place +to start the process and then move ahead + + align:start position:0% +to start the process and then move ahead + + + align:start position:0% +to start the process and then move ahead +either the regulation change or theop + + align:start position:0% +either the regulation change or theop + + + align:start position:0% +either the regulation change or theop +turns out to be more effective than + + align:start position:0% +turns out to be more effective than + + + align:start position:0% +turns out to be more effective than +expected all right so what do you say + + align:start position:0% +expected all right so what do you say + + + align:start position:0% +expected all right so what do you say +about that + + align:start position:0% +about that + + + align:start position:0% +about that +I haven't read the cas I'm still not on + + align:start position:0% +I haven't read the cas I'm still not on + + + align:start position:0% +I haven't read the cas I'm still not on +Stellar oh you still not on Stellar my + + align:start position:0% +Stellar oh you still not on Stellar my + + + align:start position:0% +Stellar oh you still not on Stellar my +first class okay okay all right so + + align:start position:0% +first class okay okay all right so + + + align:start position:0% +first class okay okay all right so +then I said that you should go with the + + align:start position:0% +then I said that you should go with the + + + align:start position:0% +then I said that you should go with the +Clos Loop because I think assuming that + + align:start position:0% +Clos Loop because I think assuming that + + + align:start position:0% +Clos Loop because I think assuming that +you're going to have to get there + + align:start position:0% +you're going to have to get there + + + align:start position:0% +you're going to have to get there +eventually even though it's large + + align:start position:0% +eventually even though it's large + + + align:start position:0% +eventually even though it's large +startup costs putting the time in and + + align:start position:0% +startup costs putting the time in and + + + align:start position:0% +startup costs putting the time in and +getting the jump on it could make them a + + align:start position:0% +getting the jump on it could make them a + + + align:start position:0% +getting the jump on it could make them a +a leader in this um if they know they're + + align:start position:0% +a leader in this um if they know they're + + + align:start position:0% +a leader in this um if they know they're +going to go there and they already have + + align:start position:0% +going to go there and they already have + + + align:start position:0% +going to go there and they already have +started to make their machines more + + align:start position:0% +started to make their machines more + + + align:start position:0% +started to make their machines more +grain and they can stand to benefit from + + align:start position:0% +grain and they can stand to benefit from + + + align:start position:0% +grain and they can stand to benefit from +optimizing their processes and + + align:start position:0% +optimizing their processes and + + + align:start position:0% +optimizing their processes and +Manufacturing their system by continuing + + align:start position:0% +Manufacturing their system by continuing + + + align:start position:0% +Manufacturing their system by continuing +to pay for people who + + align:start position:0% +to pay for people who + + + align:start position:0% +to pay for people who +aren't + + align:start position:0% +aren't + + + align:start position:0% +aren't +um as advanced as they are with + + align:start position:0% +um as advanced as they are with + + + align:start position:0% +um as advanced as they are with +their recycling + + align:start position:0% + + + + align:start position:0% + +technology adding to that we also + + align:start position:0% +technology adding to that we also + + + align:start position:0% +technology adding to that we also +address Customer Loyalty not only are + + align:start position:0% +address Customer Loyalty not only are + + + align:start position:0% +address Customer Loyalty not only are +you there when they start using your + + align:start position:0% +you there when they start using your + + + align:start position:0% +you there when they start using your +Appliance but you take care of their + + align:start position:0% +Appliance but you take care of their + + + align:start position:0% +Appliance but you take care of their +Appliance they don't no longer need it + + align:start position:0% +Appliance they don't no longer need it + + + align:start position:0% +Appliance they don't no longer need it +so that could have a lot of impact + + align:start position:0% + + + + align:start position:0% + +inut the case of the corate culture is + + align:start position:0% +inut the case of the corate culture is + + + align:start position:0% +inut the case of the corate culture is +very inous and they're used to doing + + align:start position:0% +very inous and they're used to doing + + + align:start position:0% +very inous and they're used to doing +their own things so I thought the + + align:start position:0% + + + + align:start position:0% + +CL would basically suffer from Partners + + align:start position:0% +CL would basically suffer from Partners + + + align:start position:0% +CL would basically suffer from Partners +who have a l Green Design and they + + align:start position:0% +who have a l Green Design and they + + + align:start position:0% +who have a l Green Design and they +probably more difficulty than just going + + align:start position:0% +probably more difficulty than just going + + + align:start position:0% +probably more difficulty than just going +with their + + align:start position:0% +with their + + + align:start position:0% +with their +own okay you want to defend your ifo + + align:start position:0% +own okay you want to defend your ifo + + + align:start position:0% +own okay you want to defend your ifo +choice um so basically why I chose IO + + align:start position:0% +choice um so basically why I chose IO + + + align:start position:0% +choice um so basically why I chose IO +was assuming so I worked under the + + align:start position:0% +was assuming so I worked under the + + + align:start position:0% +was assuming so I worked under the +assumption that legislation would pass + + align:start position:0% +assumption that legislation would pass + + + align:start position:0% +assumption that legislation would pass +soon sure um so assuming that legis + + align:start position:0% +soon sure um so assuming that legis + + + align:start position:0% +soon sure um so assuming that legis +legislation passed soon and that there + + align:start position:0% +legislation passed soon and that there + + + align:start position:0% +legislation passed soon and that there +are fines for not complying if you go + + align:start position:0% +are fines for not complying if you go + + + align:start position:0% +are fines for not complying if you go +into closed loop you would have to + + align:start position:0% +into closed loop you would have to + + + align:start position:0% +into closed loop you would have to +develop a logistic system that's really + + align:start position:0% +develop a logistic system that's really + + + align:start position:0% +develop a logistic system that's really +that gets to every part of Canada + + align:start position:0% +that gets to every part of Canada + + + align:start position:0% +that gets to every part of Canada +basically which is a huge country and uh + + align:start position:0% +basically which is a huge country and uh + + + align:start position:0% +basically which is a huge country and uh +and you need to make investments in for + + align:start position:0% +and you need to make investments in for + + + align:start position:0% +and you need to make investments in for +example vehicles to pick up the the + + align:start position:0% +example vehicles to pick up the the + + + align:start position:0% +example vehicles to pick up the the +refrigerators and the ovens or the + + align:start position:0% +refrigerators and the ovens or the + + + align:start position:0% +refrigerators and the ovens or the +washing machines and all of this um so I + + align:start position:0% +washing machines and all of this um so I + + + align:start position:0% +washing machines and all of this um so I +I believe that this was too much of a + + align:start position:0% +I believe that this was too much of a + + + align:start position:0% +I believe that this was too much of a +cost to be to effectively reach all of + + align:start position:0% +cost to be to effectively reach all of + + + align:start position:0% +cost to be to effectively reach all of +the customers that it has + + align:start position:0% +the customers that it has + + + align:start position:0% +the customers that it has +um and that and under the I model since + + align:start position:0% +um and that and under the I model since + + + align:start position:0% +um and that and under the I model since +it was something Consolidated you were + + align:start position:0% +it was something Consolidated you were + + + align:start position:0% +it was something Consolidated you were +taking advantage of the economies of + + align:start position:0% +taking advantage of the economies of + + + align:start position:0% +taking advantage of the economies of +scale of well you reach all the + + align:start position:0% +scale of well you reach all the + + + align:start position:0% +scale of well you reach all the +customers in all of Canada but for not + + align:start position:0% +customers in all of Canada but for not + + + align:start position:0% +customers in all of Canada but for not +just 30% of the market but for the + + align:start position:0% +just 30% of the market but for the + + + align:start position:0% +just 30% of the market but for the +entire 100% of the market and you get + + align:start position:0% +entire 100% of the market and you get + + + align:start position:0% +entire 100% of the market and you get +the economies of scale for of that so if + + align:start position:0% +the economies of scale for of that so if + + + align:start position:0% +the economies of scale for of that so if +I if I makt a bit this argument is well + + align:start position:0% +I if I makt a bit this argument is well + + + align:start position:0% +I if I makt a bit this argument is well +I I can make investment money in many + + align:start position:0% +I I can make investment money in many + + + align:start position:0% +I I can make investment money in many +many places right I could invest them in + + align:start position:0% +many places right I could invest them in + + + align:start position:0% +many places right I could invest them in +better products I can investment in + + align:start position:0% +better products I can investment in + + + align:start position:0% +better products I can investment in +other places + + align:start position:0% +other places + + + align:start position:0% +other places +so why should I put my money in + + align:start position:0% +so why should I put my money in + + + align:start position:0% +so why should I put my money in +developing the new network if I could + + align:start position:0% +developing the new network if I could + + + align:start position:0% +developing the new network if I could +just pull my resources with others and + + align:start position:0% +just pull my resources with others and + + + align:start position:0% +just pull my resources with others and +then try to make pay potentially less + + align:start position:0% +then try to make pay potentially less + + + align:start position:0% +then try to make pay potentially less +we'll talk about the cost later and + + align:start position:0% +we'll talk about the cost later and + + + align:start position:0% +we'll talk about the cost later and +decide what happens so you wanted to add + + align:start position:0% +decide what happens so you wanted to add + + + align:start position:0% +decide what happens so you wanted to add +something to that argument uh just + + align:start position:0% +something to that argument uh just + + + align:start position:0% +something to that argument uh just +speaking of a count scale 95 to around + + align:start position:0% +speaking of a count scale 95 to around + + + align:start position:0% +speaking of a count scale 95 to around +95% of the machines are currently not + + align:start position:0% +95% of the machines are currently not + + + align:start position:0% +95% of the machines are currently not +making their way the L I'm not sure that + + align:start position:0% +making their way the L I'm not sure that + + + align:start position:0% +making their way the L I'm not sure that +there's of scale to justify The Upfront + + align:start position:0% +there's of scale to justify The Upfront + + + align:start position:0% +there's of scale to justify The Upfront +costs for cl loop system so yeah so + + align:start position:0% +costs for cl loop system so yeah so + + + align:start position:0% +costs for cl loop system so yeah so +there there's not even enough uh volume + + align:start position:0% +there there's not even enough uh volume + + + align:start position:0% +there there's not even enough uh volume +even right because people are naturally + + align:start position:0% + + + + align:start position:0% + +recycling ah so here you have your + + align:start position:0% +recycling ah so here you have your + + + align:start position:0% +recycling ah so here you have your +control the costs + + align:start position:0% + + + + align:start position:0% + +here you may get scale maybe maybe right + + align:start position:0% +here you may get scale maybe maybe right + + + align:start position:0% +here you may get scale maybe maybe right +the scale is much more certain here here + + align:start position:0% +the scale is much more certain here here + + + align:start position:0% +the scale is much more certain here here +you control the cost more okay great so + + align:start position:0% +you control the cost more okay great so + + + align:start position:0% +you control the cost more okay great so +those are the options and uh it's hard + + align:start position:0% +those are the options and uh it's hard + + + align:start position:0% +those are the options and uh it's hard +to make a call here without some number + + align:start position:0% +to make a call here without some number + + + align:start position:0% +to make a call here without some number +so who is brave enough to walk us + + align:start position:0% +so who is brave enough to walk us + + + align:start position:0% +so who is brave enough to walk us +through their calculations on how much + + align:start position:0% +through their calculations on how much + + + align:start position:0% +through their calculations on how much +this thing cost for waro let's try to + + align:start position:0% +this thing cost for waro let's try to + + + align:start position:0% +this thing cost for waro let's try to +make a few estimates to see and try to + + align:start position:0% +make a few estimates to see and try to + + + align:start position:0% +make a few estimates to see and try to +make a decision is is really more + + align:start position:0% +make a decision is is really more + + + align:start position:0% +make a decision is is really more +expensive or not from an IND indry u a + + align:start position:0% +expensive or not from an IND indry u a + + + align:start position:0% +expensive or not from an IND indry u a +ifo + + align:start position:0% +ifo + + + align:start position:0% +ifo +versus um the Clos Loop so what I'll do + + align:start position:0% +versus um the Clos Loop so what I'll do + + + align:start position:0% +versus um the Clos Loop so what I'll do +is uh maybe someone is willing to risk + + align:start position:0% +is uh maybe someone is willing to risk + + + align:start position:0% +is uh maybe someone is willing to risk +and tell me how much is the cost per + + align:start position:0% +and tell me how much is the cost per + + + align:start position:0% +and tell me how much is the cost per +ton of doing an ifo + + align:start position:0% +ton of doing an ifo + + + align:start position:0% +ton of doing an ifo +model you remember I I have your + + align:start position:0% +model you remember I I have your + + + align:start position:0% +model you remember I I have your +expresses here so if someone I can open + + align:start position:0% +expresses here so if someone I can open + + + align:start position:0% +expresses here so if someone I can open +it or your document I will be happy to + + align:start position:0% +it or your document I will be happy to + + + align:start position:0% +it or your document I will be happy to +open it so we see uh how do you get to + + align:start position:0% +open it so we see uh how do you get to + + + align:start position:0% +open it so we see uh how do you get to +that number because those are the + + align:start position:0% +that number because those are the + + + align:start position:0% +that number because those are the +numbers you have to do EV ually if you + + align:start position:0% +numbers you have to do EV ually if you + + + align:start position:0% +numbers you have to do EV ually if you +want to analyze the systems so what is + + align:start position:0% +want to analyze the systems so what is + + + align:start position:0% +want to analyze the systems so what is +the cost per ton more or less or per or + + align:start position:0% +the cost per ton more or less or per or + + + align:start position:0% +the cost per ton more or less or per or +per pound I'm sure how you computed to + + align:start position:0% +per pound I'm sure how you computed to + + + align:start position:0% +per pound I'm sure how you computed to +get these numbers let me get mine here + + align:start position:0% +get these numbers let me get mine here + + + align:start position:0% +get these numbers let me get mine here +see more or less what they + + align:start position:0% + + + + align:start position:0% + +were someone remembers how much money + + align:start position:0% +were someone remembers how much money + + + align:start position:0% +were someone remembers how much money +will this cost to whle Total Money you + + align:start position:0% +will this cost to whle Total Money you + + + align:start position:0% +will this cost to whle Total Money you +remember how money 35 million bucks $35 + + align:start position:0% +remember how money 35 million bucks $35 + + + align:start position:0% +remember how money 35 million bucks $35 +million 2008 + + align:start position:0% + + + + align:start position:0% + +I + + align:start position:0% +I + + + align:start position:0% +I +yeah + + align:start position:0% + + + + align:start position:0% + +add that's based on the fact that + + align:start position:0% +add that's based on the fact that + + + align:start position:0% +add that's based on the fact that +there's 100 kiloton of the stuff being + + align:start position:0% +there's 100 kiloton of the stuff being + + + align:start position:0% +there's 100 kiloton of the stuff being +thrown away yeah and they own 30% of it + + align:start position:0% +thrown away yeah and they own 30% of it + + + align:start position:0% +thrown away yeah and they own 30% of it +is war Y and then I found some data + + align:start position:0% +is war Y and then I found some data + + + align:start position:0% +is war Y and then I found some data +somewhere in a case study that had + + align:start position:0% +somewhere in a case study that had + + + align:start position:0% +somewhere in a case study that had +dollar per ton and I applied the + + align:start position:0% +dollar per ton and I applied the + + + align:start position:0% +dollar per ton and I applied the +collection transport and processing + + align:start position:0% +collection transport and processing + + + align:start position:0% +collection transport and processing +numbers that were there yeah so there + + align:start position:0% +numbers that were there yeah so there + + + align:start position:0% +numbers that were there yeah so there +was an exibit that had all these cost + + align:start position:0% +was an exibit that had all these cost + + + align:start position:0% +was an exibit that had all these cost +per ton of collection dollars etc etc + + align:start position:0% +per ton of collection dollars etc etc + + + align:start position:0% +per ton of collection dollars etc etc +and you can apply that if you added up + + align:start position:0% +and you can apply that if you added up + + + align:start position:0% +and you can apply that if you added up +that gives you rough like $1,000 or + + align:start position:0% +that gives you rough like $1,000 or + + + align:start position:0% +that gives you rough like $1,000 or +something of the collection cost yeah I + + align:start position:0% +something of the collection cost yeah I + + + align:start position:0% +something of the collection cost yeah I +assume the most expensive route for the + + align:start position:0% +assume the most expensive route for the + + + align:start position:0% +assume the most expensive route for the +trucks and the full trucks as well mhm + + align:start position:0% +trucks and the full trucks as well mhm + + + align:start position:0% +trucks and the full trucks as well mhm +and I gave you like $35 million to do + + align:start position:0% +and I gave you like $35 million to do + + + align:start position:0% +and I gave you like $35 million to do +ifo for 2008 for 2008 figures I did + + align:start position:0% +ifo for 2008 for 2008 figures I did + + + align:start position:0% +ifo for 2008 for 2008 figures I did +something similar with average numbers + + align:start position:0% +something similar with average numbers + + + align:start position:0% +something similar with average numbers +and ended up same Ball Park 24 million + + align:start position:0% +and ended up same Ball Park 24 million + + + align:start position:0% +and ended up same Ball Park 24 million +24 million 10 million + + align:start position:0% +24 million 10 million + + + align:start position:0% +24 million 10 million +moreck I will + + align:start position:0% + + + + align:start position:0% + +argue but still it's a big b it's a big + + align:start position:0% +argue but still it's a big b it's a big + + + align:start position:0% +argue but still it's a big b it's a big +number a big ballpark someone got a + + align:start position:0% +number a big ballpark someone got a + + + align:start position:0% +number a big ballpark someone got a +different + + align:start position:0% +different + + + align:start position:0% +different +number so that look like like a big + + align:start position:0% +number so that look like like a big + + + align:start position:0% +number so that look like like a big +number but how big is it compared to + + align:start position:0% +number but how big is it compared to + + + align:start position:0% +number but how big is it compared to +what it will cost it's + + align:start position:0% +what it will cost it's + + + align:start position:0% +what it will cost it's +tiny they spend $22 million to ship the + + align:start position:0% +tiny they spend $22 million to ship the + + + align:start position:0% +tiny they spend $22 million to ship the +stuff out to customers how much they + + align:start position:0% +stuff out to customers how much they + + + align:start position:0% +stuff out to customers how much they +spend 200 how do you get that number 220 + + align:start position:0% +spend 200 how do you get that number 220 + + + align:start position:0% +spend 200 how do you get that number 220 +million other + + align:start position:0% +million other + + + align:start position:0% +million other +assumptions + + align:start position:0% +assumptions + + + align:start position:0% +assumptions +uh I assume $40 for appliance delivery + + align:start position:0% +uh I assume $40 for appliance delivery + + + align:start position:0% +uh I assume $40 for appliance delivery +and how much was it $40 $40 for + + align:start position:0% +and how much was it $40 $40 for + + + align:start position:0% +and how much was it $40 $40 for +appliance delivery dely yeah and 5 + + align:start position:0% +appliance delivery dely yeah and 5 + + + align:start position:0% +appliance delivery dely yeah and 5 +million Appliance large appliances + + align:start position:0% +million Appliance large appliances + + + align:start position:0% +million Appliance large appliances +shipped in 2008 okay uh mind you that's + + align:start position:0% +shipped in 2008 okay uh mind you that's + + + align:start position:0% +shipped in 2008 okay uh mind you that's +I didn't take the 30% of that number so + + align:start position:0% +I didn't take the 30% of that number so + + + align:start position:0% +I didn't take the 30% of that number so +it'll be 30% of 202 million so about 70 + + align:start position:0% +it'll be 30% of 202 million so about 70 + + + align:start position:0% +it'll be 30% of 202 million so about 70 +million around 70 million for + + align:start position:0% + + + + align:start position:0% + +uman a littleit about these number give + + align:start position:0% +uman a littleit about these number give + + + align:start position:0% +uman a littleit about these number give +you some I'm sure that number is Bor on + + align:start position:0% +you some I'm sure that number is Bor on + + + align:start position:0% +you some I'm sure that number is Bor on +the customer in terms of a delivery fee + + align:start position:0% +the customer in terms of a delivery fee + + + align:start position:0% +the customer in terms of a delivery fee +it says that it accounts for the costs + + align:start position:0% +it says that it accounts for the costs + + + align:start position:0% +it says that it accounts for the costs +so but it is by it is the customer does + + align:start position:0% +so but it is by it is the customer does + + + align:start position:0% +so but it is by it is the customer does +pay for it you're right deliver Fe right + + align:start position:0% +pay for it you're right deliver Fe right + + + align:start position:0% +pay for it you're right deliver Fe right +now for the retailer but this is the + + align:start position:0% +now for the retailer but this is the + + + align:start position:0% +now for the retailer but this is the +collection piece so yeah but I'm just + + align:start position:0% +collection piece so yeah but I'm just + + + align:start position:0% +collection piece so yeah but I'm just +saying like right now like they haven't + + align:start position:0% +saying like right now like they haven't + + + align:start position:0% +saying like right now like they haven't +their cost for delivery isn't really a + + align:start position:0% +their cost for delivery isn't really a + + + align:start position:0% +their cost for delivery isn't really a +cost to them because they're probably + + align:start position:0% +cost to them because they're probably + + + align:start position:0% +cost to them because they're probably +making money off the delivery you know + + align:start position:0% +making money off the delivery you know + + + align:start position:0% +making money off the delivery you know +they're probably Charing more than + + align:start position:0% +they're probably Charing more than + + + align:start position:0% +they're probably Charing more than +actually costs so I + + align:start position:0% +actually costs so I + + + align:start position:0% +actually costs so I +mean yeah so it's it's uh so uh um to be + + align:start position:0% +mean yeah so it's it's uh so uh um to be + + + align:start position:0% +mean yeah so it's it's uh so uh um to be +able to make this choice we have to make + + align:start position:0% +able to make this choice we have to make + + + align:start position:0% +able to make this choice we have to make +these calculations right so the number I + + align:start position:0% +these calculations right so the number I + + + align:start position:0% +these calculations right so the number I +got although yeah the numbers uh I have + + align:start position:0% +got although yeah the numbers uh I have + + + align:start position:0% +got although yeah the numbers uh I have +are more towards the 35 million but for + + align:start position:0% +are more towards the 35 million but for + + + align:start position:0% +are more towards the 35 million but for +2020 numbers no 208 numbers uh why 2020 + + align:start position:0% +2020 numbers no 208 numbers uh why 2020 + + + align:start position:0% +2020 numbers no 208 numbers uh why 2020 +remember that in some way you only see + + align:start position:0% +remember that in some way you only see + + + align:start position:0% +remember that in some way you only see +things that are discarded the things + + align:start position:0% +things that are discarded the things + + + align:start position:0% +things that are discarded the things +that are kind of naturally progress from + + align:start position:0% +that are kind of naturally progress from + + + align:start position:0% +that are kind of naturally progress from +one place to the other you don't see + + align:start position:0% +one place to the other you don't see + + + align:start position:0% +one place to the other you don't see +those the whle case had a table + + align:start position:0% +those the whle case had a table + + + align:start position:0% +those the whle case had a table +somewhere exhibit 7 and this gives you a + + align:start position:0% +somewhere exhibit 7 and this gives you a + + + align:start position:0% +somewhere exhibit 7 and this gives you a +sense of units discarded in + + align:start position:0% +sense of units discarded in + + + align:start position:0% +sense of units discarded in +2020 so those are the total uh discarded + + align:start position:0% +2020 so those are the total uh discarded + + + align:start position:0% +2020 so those are the total uh discarded +units of different kinds of appliances + + align:start position:0% +units of different kinds of appliances + + + align:start position:0% +units of different kinds of appliances +so you can get there uh refrigerators + + align:start position:0% +so you can get there uh refrigerators + + + align:start position:0% +so you can get there uh refrigerators +freezers dishwashers cooking ranges + + align:start position:0% +freezers dishwashers cooking ranges + + + align:start position:0% +freezers dishwashers cooking ranges +clothes and washers and so forth yeah um + + align:start position:0% +clothes and washers and so forth yeah um + + + align:start position:0% +clothes and washers and so forth yeah um +then there's a table I think on top that + + align:start position:0% +then there's a table I think on top that + + + align:start position:0% +then there's a table I think on top that +has more or less the amount of uh steel + + align:start position:0% +has more or less the amount of uh steel + + + align:start position:0% +has more or less the amount of uh steel +aluminum copper Etc and the weight of + + align:start position:0% +aluminum copper Etc and the weight of + + + align:start position:0% +aluminum copper Etc and the weight of +each of each Appliance you can get the + + align:start position:0% +each of each Appliance you can get the + + + align:start position:0% +each of each Appliance you can get the +total number of appliances times the + + align:start position:0% +total number of appliances times the + + + align:start position:0% +total number of appliances times the +weight of those + + align:start position:0% +weight of those + + + align:start position:0% +weight of those +appliances and that gives you how many + + align:start position:0% +appliances and that gives you how many + + + align:start position:0% +appliances and that gives you how many +tons you have to let's say get back once + + align:start position:0% +tons you have to let's say get back once + + + align:start position:0% +tons you have to let's say get back once +you complete those tons you need to get + + align:start position:0% +you complete those tons you need to get + + + align:start position:0% +you complete those tons you need to get +back um those not all yours right you + + align:start position:0% +back um those not all yours right you + + + align:start position:0% +back um those not all yours right you +only are responsible for your market + + align:start position:0% +only are responsible for your market + + + align:start position:0% +only are responsible for your market +share you said 30% but actually whle do + + align:start position:0% +share you said 30% but actually whle do + + + align:start position:0% +share you said 30% but actually whle do +whle and can more so it's close to 48% + + align:start position:0% +whle and can more so it's close to 48% + + + align:start position:0% +whle and can more so it's close to 48% +more or less of the market uh 48% of the + + align:start position:0% +more or less of the market uh 48% of the + + + align:start position:0% +more or less of the market uh 48% of the +market share and then um you get those + + align:start position:0% +market share and then um you get those + + + align:start position:0% +market share and then um you get those +numbers and that's a total tonage some + + align:start position:0% +numbers and that's a total tonage some + + + align:start position:0% +numbers and that's a total tonage some +of it you sell you make money out of it + + align:start position:0% +of it you sell you make money out of it + + + align:start position:0% +of it you sell you make money out of it +because you can sell it right you get it + + align:start position:0% +because you can sell it right you get it + + + align:start position:0% +because you can sell it right you get it +and you get make money out of it and + + align:start position:0% +and you get make money out of it and + + + align:start position:0% +and you get make money out of it and +then you pay um and that's the the + + align:start position:0% +then you pay um and that's the the + + + align:start position:0% +then you pay um and that's the the +tricky part there's a collection cost on + + align:start position:0% +tricky part there's a collection cost on + + + align:start position:0% +tricky part there's a collection cost on +exhibit 4 it's a collection per ton + + align:start position:0% +exhibit 4 it's a collection per ton + + + align:start position:0% +exhibit 4 it's a collection per ton +that's come from the previous program + + align:start position:0% +that's come from the previous program + + + align:start position:0% +that's come from the previous program +the Wii + + align:start position:0% +the Wii + + + align:start position:0% +the Wii +program and it says roughly you know in + + align:start position:0% +program and it says roughly you know in + + + align:start position:0% +program and it says roughly you know in +the Wei program there's an ifo program + + align:start position:0% +the Wei program there's an ifo program + + + align:start position:0% +the Wei program there's an ifo program +it gives you $165 to collect per ton and + + align:start position:0% +it gives you $165 to collect per ton and + + + align:start position:0% +it gives you $165 to collect per ton and +you can then add all those numbers and + + align:start position:0% +you can then add all those numbers and + + + align:start position:0% +you can then add all those numbers and +it gives you $37 million I I'll put a + + align:start position:0% +it gives you $37 million I I'll put a + + + align:start position:0% +it gives you $37 million I I'll put a +table but it's that those are more or + + align:start position:0% +table but it's that those are more or + + + align:start position:0% +table but it's that those are more or +less a rough numbers that you get and + + align:start position:0% +less a rough numbers that you get and + + + align:start position:0% +less a rough numbers that you get and +that give you $37 million for um the + + align:start position:0% +that give you $37 million for um the + + + align:start position:0% +that give you $37 million for um the +cost for doing this which translates + + align:start position:0% +cost for doing this which translates + + + align:start position:0% +cost for doing this which translates +into a + + align:start position:0% + + + + align:start position:0% + +$47 per + + align:start position:0% +$47 per + + + align:start position:0% +$47 per +unit more or less so the cost of + + align:start position:0% + + + + align:start position:0% + +ifo is equal to + + align:start position:0% +ifo is equal to + + + align:start position:0% +ifo is equal to +47 per + + align:start position:0% +47 per + + + align:start position:0% +47 per +unit + + align:start position:0% +unit + + + align:start position:0% +unit +uh + + align:start position:0% + + + + align:start position:0% + +sold 47 per unit how does that compare + + align:start position:0% +sold 47 per unit how does that compare + + + align:start position:0% +sold 47 per unit how does that compare +to their distribution cost that's how we + + align:start position:0% +to their distribution cost that's how we + + + align:start position:0% +to their distribution cost that's how we +know if this expensive or not how do you + + align:start position:0% +know if this expensive or not how do you + + + align:start position:0% +know if this expensive or not how do you +compute the distribution cost of wh + + align:start position:0% +compute the distribution cost of wh + + + align:start position:0% +compute the distribution cost of wh +someone did that so you we know more or + + align:start position:0% +someone did that so you we know more or + + + align:start position:0% +someone did that so you we know more or +less how to compare how to how they do + + align:start position:0% +less how to compare how to how they do + + + align:start position:0% +less how to compare how to how they do +it that's the reverse part 47 per unit + + align:start position:0% + + + + align:start position:0% + +well I'm noten so I did do it with 30% + + align:start position:0% +well I'm noten so I did do it with 30% + + + align:start position:0% +well I'm noten so I did do it with 30% +of market share not + + align:start position:0% +of market share not + + + align:start position:0% +of market share not +48% but they said that it's approximate + + align:start position:0% +48% but they said that it's approximate + + + align:start position:0% +48% but they said that it's approximate +for the industry standard 10% of their + + align:start position:0% +for the industry standard 10% of their + + + align:start position:0% +for the industry standard 10% of their +sales y + + align:start position:0% +sales y + + + align:start position:0% +sales y +um and so I will say that they were + + align:start position:0% +um and so I will say that they were + + + align:start position:0% +um and so I will say that they were +selling + + align:start position:0% +selling + + + align:start position:0% +selling +2,400,000 units but that's 30% on the + + align:start position:0% +2,400,000 units but that's 30% on the + + + align:start position:0% +2,400,000 units but that's 30% on the +market let me change it to 48 yeah but + + align:start position:0% +market let me change it to 48 yeah but + + + align:start position:0% +market let me change it to 48 yeah but +that's the right number so the up + + align:start position:0% +that's the right number so the up + + + align:start position:0% +that's the right number so the up +approximately the costs are 10% yes so + + align:start position:0% +approximately the costs are 10% yes so + + + align:start position:0% +approximately the costs are 10% yes so +we changing exactly so now there's + + align:start position:0% +we changing exactly so now there's + + + align:start position:0% +we changing exactly so now there's +another number somewhere in the case is + + align:start position:0% +another number somewhere in the case is + + + align:start position:0% +another number somewhere in the case is +$1,000 per unit that's the average + + align:start position:0% +$1,000 per unit that's the average + + + align:start position:0% +$1,000 per unit that's the average +retail price now you can you can also + + align:start position:0% +retail price now you can you can also + + + align:start position:0% +retail price now you can you can also +assume a margin you know a retailer 30% + + align:start position:0% +assume a margin you know a retailer 30% + + + align:start position:0% +assume a margin you know a retailer 30% +margin 25% margin is not uncommon for + + align:start position:0% +margin 25% margin is not uncommon for + + + align:start position:0% +margin 25% margin is not uncommon for +this kind of appliances so I give you + + align:start position:0% +this kind of appliances so I give you + + + align:start position:0% +this kind of appliances so I give you +$700 more or less per the cost of the of + + align:start position:0% +$700 more or less per the cost of the of + + + align:start position:0% +$700 more or less per the cost of the of +the goods so the forward supply chain of + + align:start position:0% +the goods so the forward supply chain of + + + align:start position:0% +the goods so the forward supply chain of +warple is more or less $70 + + align:start position:0% + + + + align:start position:0% + +forward supply + + align:start position:0% + + + + align:start position:0% + +chain so it gives like 70 + + align:start position:0% +chain so it gives like 70 + + + align:start position:0% +chain so it gives like 70 +$70 per + + align:start position:0% +$70 per + + + align:start position:0% +$70 per +unit so it's 10% average sales price + + align:start position:0% +unit so it's 10% average sales price + + + align:start position:0% +unit so it's 10% average sales price +$1,000 30% margin let's suppose of a + + align:start position:0% +$1,000 30% margin let's suppose of a + + + align:start position:0% +$1,000 30% margin let's suppose of a +retailer that give us $700 is the cost + + align:start position:0% +retailer that give us $700 is the cost + + + align:start position:0% +retailer that give us $700 is the cost +of whle of those 10% early distribution + + align:start position:0% +of whle of those 10% early distribution + + + align:start position:0% +of whle of those 10% early distribution +costs so it gives $70 per unit now um + + align:start position:0% +costs so it gives $70 per unit now um + + + align:start position:0% +costs so it gives $70 per unit now um +the ifo cost here this cost includes + + align:start position:0% +the ifo cost here this cost includes + + + align:start position:0% +the ifo cost here this cost includes +selling the scrap metals and recovering + + align:start position:0% +selling the scrap metals and recovering + + + align:start position:0% +selling the scrap metals and recovering +all the value of those Metals if you if + + align:start position:0% +all the value of those Metals if you if + + + align:start position:0% +all the value of those Metals if you if +you get that + + align:start position:0% +you get that + + + align:start position:0% +you get that +out this cost you $80 per + + align:start position:0% +out this cost you $80 per + + + align:start position:0% +out this cost you $80 per +unit if you just look at the direct cost + + align:start position:0% +unit if you just look at the direct cost + + + align:start position:0% +unit if you just look at the direct cost +you know of recovering all this all this + + align:start position:0% +you know of recovering all this all this + + + align:start position:0% +you know of recovering all this all this +material a question um so for the + + align:start position:0% +material a question um so for the + + + align:start position:0% +material a question um so for the +forward supply chain that's the 10% of + + align:start position:0% +forward supply chain that's the 10% of + + + align:start position:0% +forward supply chain that's the 10% of +the cost but that is usually bringing it + + align:start position:0% +the cost but that is usually bringing it + + + align:start position:0% +the cost but that is usually bringing it +to the retailer right absolutely should + + align:start position:0% +to the retailer right absolutely should + + + align:start position:0% +to the retailer right absolutely should +we consider the the fee that is charged + + align:start position:0% +we consider the the fee that is charged + + + align:start position:0% +we consider the the fee that is charged +to customers to get it to their home + + align:start position:0% +to customers to get it to their home + + + align:start position:0% +to customers to get it to their home +because for the reverse supply chain we + + align:start position:0% +because for the reverse supply chain we + + + align:start position:0% +because for the reverse supply chain we +kind of would have to pick them up from + + align:start position:0% +kind of would have to pick them up from + + + align:start position:0% +kind of would have to pick them up from +the home right so uh we we could talk + + align:start position:0% +the home right so uh we we could talk + + + align:start position:0% +the home right so uh we we could talk +about the network design I just want to + + align:start position:0% +about the network design I just want to + + + align:start position:0% +about the network design I just want to +yeah let's talk about the options to try + + align:start position:0% +yeah let's talk about the options to try + + + align:start position:0% +yeah let's talk about the options to try +to get disc cost but to get started + + align:start position:0% +to get disc cost but to get started + + + align:start position:0% +to get disc cost but to get started +these are the two numbers we need to + + align:start position:0% +these are the two numbers we need to + + + align:start position:0% +these are the two numbers we need to +compare so $70 per unit is the cost to + + align:start position:0% +compare so $70 per unit is the cost to + + + align:start position:0% +compare so $70 per unit is the cost to +getting to the dealer to the retailer + + align:start position:0% +getting to the dealer to the retailer + + + align:start position:0% +getting to the dealer to the retailer +sorry the dealer of the of the appliance + + align:start position:0% +sorry the dealer of the of the appliance + + + align:start position:0% +sorry the dealer of the of the appliance +$70 per unit uh to get the back without + + align:start position:0% +$70 per unit uh to get the back without + + + align:start position:0% +$70 per unit uh to get the back without +getting a scrap is $880 per + + align:start position:0% +getting a scrap is $880 per + + + align:start position:0% +getting a scrap is $880 per +unit who what why is this higher you + + align:start position:0% +unit who what why is this higher you + + + align:start position:0% +unit who what why is this higher you +know compared to this + + align:start position:0% +know compared to this + + + align:start position:0% +know compared to this +one centralized distribution centralized + + align:start position:0% +one centralized distribution centralized + + + align:start position:0% +one centralized distribution centralized +distribution right it's just my network + + align:start position:0% +distribution right it's just my network + + + align:start position:0% +distribution right it's just my network +is not designed to collect stuff so + + align:start position:0% +is not designed to collect stuff so + + + align:start position:0% +is not designed to collect stuff so +since it's not designed to collect stuff + + align:start position:0% +since it's not designed to collect stuff + + + align:start position:0% +since it's not designed to collect stuff +the ifo model even if it's the ifo model + + align:start position:0% +the ifo model even if it's the ifo model + + + align:start position:0% +the ifo model even if it's the ifo model +warple is very specialized in forward + + align:start position:0% +warple is very specialized in forward + + + align:start position:0% +warple is very specialized in forward +these numbers even the rough numbers + + align:start position:0% +these numbers even the rough numbers + + + align:start position:0% +these numbers even the rough numbers +this is the kind of of environment that + + align:start position:0% +this is the kind of of environment that + + + align:start position:0% +this is the kind of of environment that +you face the first time you go into any + + align:start position:0% +you face the first time you go into any + + + align:start position:0% +you face the first time you go into any +reverse Logistics cost that maybe the + + align:start position:0% +reverse Logistics cost that maybe the + + + align:start position:0% +reverse Logistics cost that maybe the +numbers are not that big when you look + + align:start position:0% +numbers are not that big when you look + + + align:start position:0% +numbers are not that big when you look +at the whole warpool Corporation but + + align:start position:0% +at the whole warpool Corporation but + + + align:start position:0% +at the whole warpool Corporation but +when you start looking back and try to + + align:start position:0% +when you start looking back and try to + + + align:start position:0% +when you start looking back and try to +nail down and compute your distribution + + align:start position:0% +nail down and compute your distribution + + + align:start position:0% +nail down and compute your distribution +costs this is the more or less situation + + align:start position:0% +costs this is the more or less situation + + + align:start position:0% +costs this is the more or less situation +you will phase the first time around uh + + align:start position:0% +you will phase the first time around uh + + + align:start position:0% +you will phase the first time around uh +your forward costs per unit are 70 your + + align:start position:0% +your forward costs per unit are 70 your + + + align:start position:0% +your forward costs per unit are 70 your +reverse could be higher than that uh + + align:start position:0% +reverse could be higher than that uh + + + align:start position:0% +reverse could be higher than that uh +mainly because you are not using a + + align:start position:0% +mainly because you are not using a + + + align:start position:0% +mainly because you are not using a +optimized welld designed Network which + + align:start position:0% +optimized welld designed Network which + + + align:start position:0% +optimized welld designed Network which +get us to the different options that we + + align:start position:0% +get us to the different options that we + + + align:start position:0% +get us to the different options that we +have to make these $80 down so goes back + + align:start position:0% +have to make these $80 down so goes back + + + align:start position:0% +have to make these $80 down so goes back +to now we can put a little bit more + + align:start position:0% +to now we can put a little bit more + + + align:start position:0% +to now we can put a little bit more +let's say meat to this so if the ifo + + align:start position:0% +let's say meat to this so if the ifo + + + align:start position:0% +let's say meat to this so if the ifo +model assuming our SMS are okay um cost + + align:start position:0% +model assuming our SMS are okay um cost + + + align:start position:0% +model assuming our SMS are okay um cost +us roughly 80 per + + align:start position:0% +us roughly 80 per + + + align:start position:0% +us roughly 80 per +unit and this one cost us + + align:start position:0% +unit and this one cost us + + + align:start position:0% +unit and this one cost us +roughly uh 70 per + + align:start position:0% + + + + align:start position:0% + +unit so if the ifo gets super efficient + + align:start position:0% +unit so if the ifo gets super efficient + + + align:start position:0% +unit so if the ifo gets super efficient +and it really cost me much less well + + align:start position:0% +and it really cost me much less well + + + align:start position:0% +and it really cost me much less well +actually it doesn't cost me really 80 + + align:start position:0% +actually it doesn't cost me really 80 + + + align:start position:0% +actually it doesn't cost me really 80 +per unit it cost me uh 47 but I can also + + align:start position:0% +per unit it cost me uh 47 but I can also + + + align:start position:0% +per unit it cost me uh 47 but I can also +do it here and then sell the scraps + + align:start position:0% +do it here and then sell the scraps + + + align:start position:0% +do it here and then sell the scraps +that's why I'm I'm Computing this one to + + align:start position:0% +that's why I'm I'm Computing this one to + + + align:start position:0% +that's why I'm I'm Computing this one to +the other so if if the ifo pure + + align:start position:0% +the other so if if the ifo pure + + + align:start position:0% +the other so if if the ifo pure +distribution costs get down to much + + align:start position:0% +distribution costs get down to much + + + align:start position:0% +distribution costs get down to much +lower than 70 right maybe it's worth + + align:start position:0% +lower than 70 right maybe it's worth + + + align:start position:0% +lower than 70 right maybe it's worth +doing it with them so if if they can get + + align:start position:0% +doing it with them so if if they can get + + + align:start position:0% +doing it with them so if if they can get +to the + + align:start position:0% +to the + + + align:start position:0% +to the +scale and once they recover the + + align:start position:0% +scale and once they recover the + + + align:start position:0% +scale and once they recover the +Investments that they have the plan it + + align:start position:0% +Investments that they have the plan it + + + align:start position:0% +Investments that they have the plan it +this number gets less than 70 maybe it's + + align:start position:0% +this number gets less than 70 maybe it's + + + align:start position:0% +this number gets less than 70 maybe it's +worth for me to jump there uh on a cost + + align:start position:0% +worth for me to jump there uh on a cost + + + align:start position:0% +worth for me to jump there uh on a cost +pure cost perspective on the other hand + + align:start position:0% +pure cost perspective on the other hand + + + align:start position:0% +pure cost perspective on the other hand +we have some of the other options here + + align:start position:0% +we have some of the other options here + + + align:start position:0% +we have some of the other options here +that will give me value so with that let + + align:start position:0% +that will give me value so with that let + + + align:start position:0% +that will give me value so with that let +me just + + align:start position:0% +me just + + + align:start position:0% +me just +ask how will a Clos Loop how do we want + + align:start position:0% +ask how will a Clos Loop how do we want + + + align:start position:0% +ask how will a Clos Loop how do we want +to compare the actual networks to see + + align:start position:0% +to compare the actual networks to see + + + align:start position:0% +to compare the actual networks to see +how different they are the the ifo + + align:start position:0% +how different they are the the ifo + + + align:start position:0% +how different they are the the ifo +versus the Clos Loop network of whol so + + align:start position:0% +versus the Clos Loop network of whol so + + + align:start position:0% +versus the Clos Loop network of whol so +who wants to draw a diagram of how do + + align:start position:0% +who wants to draw a diagram of how do + + + align:start position:0% +who wants to draw a diagram of how do +you think a warpool Clos Loop supply + + align:start position:0% +you think a warpool Clos Loop supply + + + align:start position:0% +you think a warpool Clos Loop supply +chain could look like someone volunteers + + align:start position:0% +chain could look like someone volunteers + + + align:start position:0% +chain could look like someone volunteers +I'll volunteer + + align:start position:0% +I'll volunteer + + + align:start position:0% +I'll volunteer +someone how is the current supply chain + + align:start position:0% + + + + align:start position:0% + +working go for it you can use that + + align:start position:0% +working go for it you can use that + + + align:start position:0% +working go for it you can use that +one and let's go back to where is a + + align:start position:0% +one and let's go back to where is a + + + align:start position:0% +one and let's go back to where is a +retailer where is the dealer and so + + align:start position:0% +retailer where is the dealer and so + + + align:start position:0% +retailer where is the dealer and so +forth give it a + + align:start position:0% + + + + align:start position:0% + +shot forward supply chain you + + align:start position:0% +shot forward supply chain you + + + align:start position:0% +shot forward supply chain you +have one or one or two factories where + + align:start position:0% +have one or one or two factories where + + + align:start position:0% +have one or one or two factories where +they make the stuff yep go to a series + + align:start position:0% +they make the stuff yep go to a series + + + align:start position:0% +they make the stuff yep go to a series +of regional distribution centers and + + align:start position:0% +of regional distribution centers and + + + align:start position:0% +of regional distribution centers and +each of these in turn goes to the series + + align:start position:0% +each of these in turn goes to the series + + + align:start position:0% +each of these in turn goes to the series +of retailers sure so uh there's actually + + align:start position:0% +of retailers sure so uh there's actually + + + align:start position:0% +of retailers sure so uh there's actually +how many factories this wle has no + + align:start position:0% + + + + align:start position:0% + +remembers I think it was 17 in total oh + + align:start position:0% +remembers I think it was 17 in total oh + + + align:start position:0% +remembers I think it was 17 in total oh +but for Canada for Canada yeah so 17 + + align:start position:0% +but for Canada for Canada yeah so 17 + + + align:start position:0% +but for Canada for Canada yeah so 17 +factories up up there and those go to + + align:start position:0% +factories up up there and those go to + + + align:start position:0% +factories up up there and those go to +how many DCs they have in + + align:start position:0% + + + + align:start position:0% + +Canada someone remembers more or + + align:start position:0% +Canada someone remembers more or + + + align:start position:0% +Canada someone remembers more or +less 30 40 24 24 + + align:start position:0% +less 30 40 24 24 + + + align:start position:0% +less 30 40 24 24 +de 24 deas and how many + + align:start position:0% + + + + align:start position:0% + +retailers th how about 2,400 2,400 + + align:start position:0% +retailers th how about 2,400 2,400 + + + align:start position:0% +retailers th how about 2,400 2,400 +retailers so that's the network 17 + + align:start position:0% +retailers so that's the network 17 + + + align:start position:0% +retailers so that's the network 17 +factories + + align:start position:0% +factories + + + align:start position:0% +factories +24 real distribution centers 2400 uh + + align:start position:0% +24 real distribution centers 2400 uh + + + align:start position:0% +24 real distribution centers 2400 uh +retailers thank you thank you for being + + align:start position:0% +retailers thank you thank you for being + + + align:start position:0% +retailers thank you thank you for being +brave great so uh how is the how would + + align:start position:0% +brave great so uh how is the how would + + + align:start position:0% +brave great so uh how is the how would +be an ifo model look like if I join an + + align:start position:0% +be an ifo model look like if I join an + + + align:start position:0% +be an ifo model look like if I join an +ifo what will + + align:start position:0% +ifo what will + + + align:start position:0% +ifo what will +happen so let me just do a little uh + + align:start position:0% +happen so let me just do a little uh + + + align:start position:0% +happen so let me just do a little uh +change to this so we can add more models + + align:start position:0% +change to this so we can add more models + + + align:start position:0% +change to this so we can add more models +so we have a factory here + + align:start position:0% + + + + align:start position:0% + +and this will go to our regional + + align:start position:0% +and this will go to our regional + + + align:start position:0% +and this will go to our regional +distribution center + + align:start position:0% + + + + align:start position:0% + +right and + + align:start position:0% +right and + + + align:start position:0% +right and +then this goes to a bunch of + + align:start position:0% + + + + align:start position:0% + +different retailers + + align:start position:0% + + + + align:start position:0% + +the same diagram so but we can just grow + + align:start position:0% +the same diagram so but we can just grow + + + align:start position:0% +the same diagram so but we can just grow +on this side so what happens + + align:start position:0% +on this side so what happens + + + align:start position:0% +on this side so what happens +if we decide to join an ifo model if + + align:start position:0% +if we decide to join an ifo model if + + + align:start position:0% +if we decide to join an ifo model if +someone comes with a with an ifo model + + align:start position:0% +someone comes with a with an ifo model + + + align:start position:0% +someone comes with a with an ifo model +what will happen at this point with the + + align:start position:0% +what will happen at this point with the + + + align:start position:0% +what will happen at this point with the +with the goods will I collect them at + + align:start position:0% +with the goods will I collect them at + + + align:start position:0% +with the goods will I collect them at +the customer + + align:start position:0% + + + + align:start position:0% + +side so do you think the industry the + + align:start position:0% +side so do you think the industry the + + + align:start position:0% +side so do you think the industry the +ifo what is extended producer + + align:start position:0% + + + + align:start position:0% + +responsibility so what what walk me + + align:start position:0% +responsibility so what what walk me + + + align:start position:0% +responsibility so what what walk me +through what what does it mean that I + + align:start position:0% +through what what does it mean that I + + + align:start position:0% +through what what does it mean that I +have to be collecting it or have to give + + align:start position:0% +have to be collecting it or have to give + + + align:start position:0% +have to be collecting it or have to give +options to + + align:start position:0% +options to + + + align:start position:0% +options to +dispose what does the legislation say + + align:start position:0% +dispose what does the legislation say + + + align:start position:0% +dispose what does the legislation say +more or less or at least the way it + + align:start position:0% +more or less or at least the way it + + + align:start position:0% +more or less or at least the way it +described here that you're responsible + + align:start position:0% +described here that you're responsible + + + align:start position:0% +described here that you're responsible +for the ultimate disposal of the product + + align:start position:0% +for the ultimate disposal of the product + + + align:start position:0% +for the ultimate disposal of the product +exactly it doesn't say that you know you + + align:start position:0% +exactly it doesn't say that you know you + + + align:start position:0% +exactly it doesn't say that you know you +have to go to your house and pick it up + + align:start position:0% +have to go to your house and pick it up + + + align:start position:0% +have to go to your house and pick it up +right probably is not exactly the way it + + align:start position:0% +right probably is not exactly the way it + + + align:start position:0% +right probably is not exactly the way it +will work the way it will work is that + + align:start position:0% +will work the way it will work is that + + + align:start position:0% +will work the way it will work is that +you will set up some sort of mechanism + + align:start position:0% +you will set up some sort of mechanism + + + align:start position:0% +you will set up some sort of mechanism +to to get those goods + + align:start position:0% +to to get those goods + + + align:start position:0% +to to get those goods +back and that once they get back you are + + align:start position:0% +back and that once they get back you are + + + align:start position:0% +back and that once they get back you are +responsible of properly disposing them + + align:start position:0% +responsible of properly disposing them + + + align:start position:0% +responsible of properly disposing them +and you have to create all the right uh + + align:start position:0% +and you have to create all the right uh + + + align:start position:0% +and you have to create all the right uh +information material and incentives for + + align:start position:0% +information material and incentives for + + + align:start position:0% +information material and incentives for +the consumers to know where and how to + + align:start position:0% +the consumers to know where and how to + + + align:start position:0% +the consumers to know where and how to +dispose these materials it's like + + align:start position:0% +dispose these materials it's like + + + align:start position:0% +dispose these materials it's like +batteries however with the size of stuff + + align:start position:0% +batteries however with the size of stuff + + + align:start position:0% +batteries however with the size of stuff +we're talking about refrigerators and + + align:start position:0% +we're talking about refrigerators and + + + align:start position:0% +we're talking about refrigerators and +whatnot I think the only practical way + + align:start position:0% +whatnot I think the only practical way + + + align:start position:0% +whatnot I think the only practical way +to do it is to go get them for them + + align:start position:0% +to do it is to go get them for them + + + align:start position:0% +to do it is to go get them for them +maybe they have to call and make an + + align:start position:0% +maybe they have to call and make an + + + align:start position:0% +maybe they have to call and make an +appointment several weeks exactly so + + align:start position:0% +appointment several weeks exactly so + + + align:start position:0% +appointment several weeks exactly so +yeah so but but it will not be whle in + + align:start position:0% +yeah so but but it will not be whle in + + + align:start position:0% +yeah so but but it will not be whle in +an ifo model + + align:start position:0% +an ifo model + + + align:start position:0% +an ifo model +more or less the way you will do it is + + align:start position:0% +more or less the way you will do it is + + + align:start position:0% +more or less the way you will do it is +that you will probably get the uh + + align:start position:0% +that you will probably get the uh + + + align:start position:0% +that you will probably get the uh +retailers or another network of dealers + + align:start position:0% +retailers or another network of dealers + + + align:start position:0% +retailers or another network of dealers +probably that's the way you will do it + + align:start position:0% +probably that's the way you will do it + + + align:start position:0% +probably that's the way you will do it +that's the way it works probably today + + align:start position:0% +that's the way it works probably today + + + align:start position:0% +that's the way it works probably today +you have a bunch of dealers here + + align:start position:0% + + + + align:start position:0% + +and then these dealers are the + + align:start position:0% + + + + align:start position:0% + +ones that go to some sort of + + align:start position:0% +ones that go to some sort of + + + align:start position:0% +ones that go to some sort of +processor some entity + + align:start position:0% + + + + align:start position:0% + +here that deals with steel sorry that + + align:start position:0% +here that deals with steel sorry that + + + align:start position:0% +here that deals with steel sorry that +deals with u this compo decomposing + + align:start position:0% +deals with u this compo decomposing + + + align:start position:0% +deals with u this compo decomposing +the + + align:start position:0% +the + + + align:start position:0% +the +uh final you get the raw + + align:start position:0% + + + + align:start position:0% + +materials out of here out of the + + align:start position:0% +materials out of here out of the + + + align:start position:0% +materials out of here out of the +processor so that's more or less how the + + align:start position:0% +processor so that's more or less how the + + + align:start position:0% +processor so that's more or less how the +supply chain will look like if you do + + align:start position:0% +supply chain will look like if you do + + + align:start position:0% +supply chain will look like if you do +some sort of uh of of ifo + + align:start position:0% +some sort of uh of of ifo + + + align:start position:0% +some sort of uh of of ifo +model as someone pointed out one of the + + align:start position:0% +model as someone pointed out one of the + + + align:start position:0% +model as someone pointed out one of the +things that you are missing out is that + + align:start position:0% +things that you are missing out is that + + + align:start position:0% +things that you are missing out is that +you are losing that connection with the + + align:start position:0% +you are losing that connection with the + + + align:start position:0% +you are losing that connection with the +consumer and that's why I wanted to draw + + align:start position:0% +consumer and that's why I wanted to draw + + + align:start position:0% +consumer and that's why I wanted to draw +that diagram so if you go through an + + align:start position:0% +that diagram so if you go through an + + + align:start position:0% +that diagram so if you go through an +model you will effectively uh remove + + align:start position:0% +model you will effectively uh remove + + + align:start position:0% +model you will effectively uh remove +your connection with the dealers maybe + + align:start position:0% +your connection with the dealers maybe + + + align:start position:0% +your connection with the dealers maybe +you want to do that on on that Network + + align:start position:0% +you want to do that on on that Network + + + align:start position:0% +you want to do that on on that Network +your consumer will not have that let's + + align:start position:0% +your consumer will not have that let's + + + align:start position:0% +your consumer will not have that let's +let's talk about practical reasons + + align:start position:0% +let's talk about practical reasons + + + align:start position:0% +let's talk about practical reasons +somebody mentioned this will cost some + + align:start position:0% +somebody mentioned this will cost some + + + align:start position:0% +somebody mentioned this will cost some +money uh to be able to collect those + + align:start position:0% +money uh to be able to collect those + + + align:start position:0% +money uh to be able to collect those +goods from the house of the consumer to + + align:start position:0% +goods from the house of the consumer to + + + align:start position:0% +goods from the house of the consumer to +the dealer how will you recover this + + align:start position:0% +the dealer how will you recover this + + + align:start position:0% +the dealer how will you recover this +money how what happens + + align:start position:0% + + + + align:start position:0% + +today that's exactly the way it works + + align:start position:0% +today that's exactly the way it works + + + align:start position:0% +today that's exactly the way it works +right all of us are paying for this we + + align:start position:0% +right all of us are paying for this we + + + align:start position:0% +right all of us are paying for this we +just do not know + + align:start position:0% +just do not know + + + align:start position:0% +just do not know +no so when there is a realization like + + align:start position:0% +no so when there is a realization like + + + align:start position:0% +no so when there is a realization like +this uh in Europe or even batteries in + + align:start position:0% +this uh in Europe or even batteries in + + + align:start position:0% +this uh in Europe or even batteries in +North America we are pay or or bottles + + align:start position:0% +North America we are pay or or bottles + + + align:start position:0% +North America we are pay or or bottles +or some sort of any kind of uh mandated + + align:start position:0% +or some sort of any kind of uh mandated + + + align:start position:0% +or some sort of any kind of uh mandated +collection we are being charged but we + + align:start position:0% +collection we are being charged but we + + + align:start position:0% +collection we are being charged but we +are is not + + align:start position:0% +are is not + + + align:start position:0% +are is not +itemized and then what happens what + + align:start position:0% +itemized and then what happens what + + + align:start position:0% +itemized and then what happens what +happen with those dealers do you once + + align:start position:0% +happen with those dealers do you once + + + align:start position:0% +happen with those dealers do you once +you get them + + align:start position:0% +you get them + + + align:start position:0% +you get them +collected the dealer says I have a whle + + align:start position:0% +collected the dealer says I have a whle + + + align:start position:0% +collected the dealer says I have a whle +here I take a picture of the whle I scan + + align:start position:0% +here I take a picture of the whle I scan + + + align:start position:0% +here I take a picture of the whle I scan +it I say to warple and whpo give me the + + align:start position:0% +it I say to warple and whpo give me the + + + align:start position:0% +it I say to warple and whpo give me the +money they collected so I can get back + + align:start position:0% +money they collected so I can get back + + + align:start position:0% +money they collected so I can get back +my + + align:start position:0% +my + + + align:start position:0% +my +cost that's how you pay these these + + align:start position:0% +cost that's how you pay these these + + + align:start position:0% +cost that's how you pay these these +situations you don't don't so you don't + + align:start position:0% +situations you don't don't so you don't + + + align:start position:0% +situations you don't don't so you don't +go and charge the consumer for picking + + align:start position:0% +go and charge the consumer for picking + + + align:start position:0% +go and charge the consumer for picking +up but he say Well when you're done call + + align:start position:0% +up but he say Well when you're done call + + + align:start position:0% +up but he say Well when you're done call +one of these authorized dealers 100 + + align:start position:0% +one of these authorized dealers 100 + + + align:start position:0% +one of these authorized dealers 100 +number we'll pick it up for you in an + + align:start position:0% +number we'll pick it up for you in an + + + align:start position:0% +number we'll pick it up for you in an +appointment and then the dealer goes and + + align:start position:0% +appointment and then the dealer goes and + + + align:start position:0% +appointment and then the dealer goes and +picks it up and then the whole process + + align:start position:0% +picks it up and then the whole process + + + align:start position:0% +picks it up and then the whole process +continues that is probably the the most + + align:start position:0% +continues that is probably the the most + + + align:start position:0% +continues that is probably the the most +uh common way that this actually is + + align:start position:0% +uh common way that this actually is + + + align:start position:0% +uh common way that this actually is +implemented in practice so who Bears the + + align:start position:0% +implemented in practice so who Bears the + + + align:start position:0% +implemented in practice so who Bears the +cost ultimately is the consumer is + + align:start position:0% +cost ultimately is the consumer is + + + align:start position:0% +cost ultimately is the consumer is +which creates an interesting dilemma + + align:start position:0% +which creates an interesting dilemma + + + align:start position:0% +which creates an interesting dilemma +right if I'm charging my consumer can I + + align:start position:0% +right if I'm charging my consumer can I + + + align:start position:0% +right if I'm charging my consumer can I +compete on the price I charge my + + align:start position:0% +compete on the price I charge my + + + align:start position:0% +compete on the price I charge my +consumer I + + align:start position:0% +consumer I + + + align:start position:0% +consumer I +can charge less goes back to loyalty and + + align:start position:0% +can charge less goes back to loyalty and + + + align:start position:0% +can charge less goes back to loyalty and +other opportunity to touch the customer + + align:start position:0% +other opportunity to touch the customer + + + align:start position:0% +other opportunity to touch the customer +once you think about the implementation + + align:start position:0% +once you think about the implementation + + + align:start position:0% +once you think about the implementation +of this of these programs that is how uh + + align:start position:0% +of this of these programs that is how uh + + + align:start position:0% +of this of these programs that is how uh +maybe start making sense to try to get + + align:start position:0% +maybe start making sense to try to get + + + align:start position:0% +maybe start making sense to try to get +into it because if I can charge less for + + align:start position:0% +into it because if I can charge less for + + + align:start position:0% +into it because if I can charge less for +this I can actually sell my product for + + align:start position:0% +this I can actually sell my product for + + + align:start position:0% +this I can actually sell my product for +less money from the perspective of the + + align:start position:0% +less money from the perspective of the + + + align:start position:0% +less money from the perspective of the +consumer maybe I can try to do that um + + align:start position:0% +consumer maybe I can try to do that um + + + align:start position:0% +consumer maybe I can try to do that um +how will the network look like if I use + + align:start position:0% +how will the network look like if I use + + + align:start position:0% +how will the network look like if I use +my the the closed loop now it becomes + + align:start position:0% +my the the closed loop now it becomes + + + align:start position:0% +my the the closed loop now it becomes +apparent what I will ask my consumers is + + align:start position:0% +apparent what I will ask my consumers is + + + align:start position:0% +apparent what I will ask my consumers is +whatever you're purchase to computer we + + align:start position:0% +whatever you're purchase to computer we + + + align:start position:0% +whatever you're purchase to computer we +will take it back so I'm moving right + + align:start position:0% +will take it back so I'm moving right + + + align:start position:0% +will take it back so I'm moving right +now so I have all these things that I + + align:start position:0% +now so I have all these things that I + + + align:start position:0% +now so I have all these things that I +buy uh for my new place and uh I go to + + align:start position:0% +buy uh for my new place and uh I go to + + + align:start position:0% +buy uh for my new place and uh I go to +IKEA a lot this last weekend when a lot + + align:start position:0% +IKEA a lot this last weekend when a lot + + + align:start position:0% +IKEA a lot this last weekend when a lot +more times than I wanted to go and + + align:start position:0% +more times than I wanted to go and + + + align:start position:0% +more times than I wanted to go and +there's this + + align:start position:0% +there's this + + + align:start position:0% +there's this +big heart with an Open Hands have you + + align:start position:0% +big heart with an Open Hands have you + + + align:start position:0% +big heart with an Open Hands have you +seen it we'll take it back right so no + + align:start position:0% +seen it we'll take it back right so no + + + align:start position:0% +seen it we'll take it back right so no +matter why you why you buy we will take + + align:start position:0% +matter why you why you buy we will take + + + align:start position:0% +matter why you why you buy we will take +it back so um you can tell your consumer + + align:start position:0% +it back so um you can tell your consumer + + + align:start position:0% +it back so um you can tell your consumer +the same if you bought your refrigerator + + align:start position:0% +the same if you bought your refrigerator + + + align:start position:0% +the same if you bought your refrigerator +from this uh from CRS right or from + + align:start position:0% +from this uh from CRS right or from + + + align:start position:0% +from this uh from CRS right or from +Kmart or from Walmart and it's a warpo + + align:start position:0% +Kmart or from Walmart and it's a warpo + + + align:start position:0% +Kmart or from Walmart and it's a warpo +refrigerator don't worry you can bring + + align:start position:0% +refrigerator don't worry you can bring + + + align:start position:0% +refrigerator don't worry you can bring +it back when you're done with it and we + + align:start position:0% +it back when you're done with it and we + + + align:start position:0% +it back when you're done with it and we +will take it for you and in that + + align:start position:0% +will take it for you and in that + + + align:start position:0% +will take it for you and in that +opportunity I can also use that money to + + align:start position:0% +opportunity I can also use that money to + + + align:start position:0% +opportunity I can also use that money to +give you a new refrigerator so that's + + align:start position:0% +give you a new refrigerator so that's + + + align:start position:0% +give you a new refrigerator so that's +the concept of also engaging the + + align:start position:0% +the concept of also engaging the + + + align:start position:0% +the concept of also engaging the +consumer where you you you go to the + + align:start position:0% +consumer where you you you go to the + + + align:start position:0% +consumer where you you you go to the +same + + align:start position:0% +same + + + align:start position:0% +same +retailer where you purchase the + + align:start position:0% +retailer where you purchase the + + + align:start position:0% +retailer where you purchase the +goods and return that uh + + align:start position:0% +goods and return that uh + + + align:start position:0% +goods and return that uh +refrigerator washer and dryer etc etc + + align:start position:0% +refrigerator washer and dryer etc etc + + + align:start position:0% +refrigerator washer and dryer etc etc +etc the question is how do you get it + + align:start position:0% +etc the question is how do you get it + + + align:start position:0% +etc the question is how do you get it +back from the retailers to the rest of + + align:start position:0% +back from the retailers to the rest of + + + align:start position:0% +back from the retailers to the rest of +your network so one option is which is + + align:start position:0% +your network so one option is which is + + + align:start position:0% +your network so one option is which is +what GCO do pretty much is that you + + align:start position:0% +what GCO do pretty much is that you + + + align:start position:0% +what GCO do pretty much is that you +still keep that connection but you can + + align:start position:0% +still keep that connection but you can + + + align:start position:0% +still keep that connection but you can +still have a separate Network you have + + align:start position:0% +still have a separate Network you have + + + align:start position:0% +still have a separate Network you have +another Network that goes back here + + align:start position:0% +another Network that goes back here + + + align:start position:0% +another Network that goes back here +where you goes back to some sort of + + align:start position:0% +where you goes back to some sort of + + + align:start position:0% +where you goes back to some sort of +collector where you aggregate some of + + align:start position:0% +collector where you aggregate some of + + + align:start position:0% +collector where you aggregate some of +this + + align:start position:0% +this + + + align:start position:0% +this +flows and then you can get it back to a + + align:start position:0% +flows and then you can get it back to a + + + align:start position:0% +flows and then you can get it back to a +processing facility that can takes care + + align:start position:0% +processing facility that can takes care + + + align:start position:0% +processing facility that can takes care +of + + align:start position:0% +of + + + align:start position:0% +of +it this gives you the intimacy with the + + align:start position:0% +it this gives you the intimacy with the + + + align:start position:0% +it this gives you the intimacy with the +consumer without having to deal with the + + align:start position:0% +consumer without having to deal with the + + + align:start position:0% +consumer without having to deal with the +whole network but in that case you will + + align:start position:0% +whole network but in that case you will + + + align:start position:0% +whole network but in that case you will +not get the the cost Advantage you will + + align:start position:0% +not get the the cost Advantage you will + + + align:start position:0% +not get the the cost Advantage you will +have probably higher cost than the if4 + + align:start position:0% +have probably higher cost than the if4 + + + align:start position:0% +have probably higher cost than the if4 +model has because you don't have enough + + align:start position:0% +model has because you don't have enough + + + align:start position:0% +model has because you don't have enough +volume uh where you get the most value + + align:start position:0% +volume uh where you get the most value + + + align:start position:0% +volume uh where you get the most value +is if you somehow use the same flow so + + align:start position:0% +is if you somehow use the same flow so + + + align:start position:0% +is if you somehow use the same flow so +the same + + align:start position:0% +the same + + + align:start position:0% +the same +trucks that collect and deliver your + + align:start position:0% +trucks that collect and deliver your + + + align:start position:0% +trucks that collect and deliver your +goods to the retailer those are the same + + align:start position:0% +goods to the retailer those are the same + + + align:start position:0% +goods to the retailer those are the same +trucks you use you don't have to create + + align:start position:0% +trucks you use you don't have to create + + + align:start position:0% +trucks you use you don't have to create +a new a new set of + + align:start position:0% +a new a new set of + + + align:start position:0% +a new a new set of +trucks they they're coming empty anyways + + align:start position:0% +trucks they they're coming empty anyways + + + align:start position:0% +trucks they they're coming empty anyways +right so why not bring them back uh also + + align:start position:0% +right so why not bring them back uh also + + + align:start position:0% +right so why not bring them back uh also +the return volume is not as high so it's + + align:start position:0% +the return volume is not as high so it's + + + align:start position:0% +the return volume is not as high so it's +not 100% of of the sales so what is the + + align:start position:0% +not 100% of of the sales so what is the + + + align:start position:0% +not 100% of of the sales so what is the +the the main bottleneck then for this to + + align:start position:0% +the the main bottleneck then for this to + + + align:start position:0% +the the main bottleneck then for this to +work if you want to use your retailer + + align:start position:0% +work if you want to use your retailer + + + align:start position:0% +work if you want to use your retailer +and use your own tracks that come empty + + align:start position:0% +and use your own tracks that come empty + + + align:start position:0% +and use your own tracks that come empty +some problems you will find on this + + align:start position:0% +some problems you will find on this + + + align:start position:0% +some problems you will find on this +approach I mean itn't to me so why would + + align:start position:0% +approach I mean itn't to me so why would + + + align:start position:0% +approach I mean itn't to me so why would +I want to do it so that's a big + + align:start position:0% +I want to do it so that's a big + + + align:start position:0% +I want to do it so that's a big +problem you get all this crap I have to + + align:start position:0% +problem you get all this crap I have to + + + align:start position:0% +problem you get all this crap I have to +have it around in my warehouse or in my + + align:start position:0% +have it around in my warehouse or in my + + + align:start position:0% +have it around in my warehouse or in my +floor's place I have to use a sales + + align:start position:0% +floor's place I have to use a sales + + + align:start position:0% +floor's place I have to use a sales +associate to try to uh spend time with + + align:start position:0% +associate to try to uh spend time with + + + align:start position:0% +associate to try to uh spend time with +the customer cons customer and make sure + + align:start position:0% +the customer cons customer and make sure + + + align:start position:0% +the customer cons customer and make sure +that is something I should take any were + + align:start position:0% +that is something I should take any were + + + align:start position:0% +that is something I should take any were +so that's first barrier what's the other + + align:start position:0% +so that's first barrier what's the other + + + align:start position:0% +so that's first barrier what's the other +barrier that one you can fix maybe you + + align:start position:0% +barrier that one you can fix maybe you + + + align:start position:0% +barrier that one you can fix maybe you +can give them some incentive did mention + + align:start position:0% +can give them some incentive did mention + + + align:start position:0% +can give them some incentive did mention +the systems barrier they not able to + + align:start position:0% +the systems barrier they not able to + + + align:start position:0% +the systems barrier they not able to +trace at the seral number level so + + align:start position:0% +trace at the seral number level so + + + align:start position:0% +trace at the seral number level so +figure out when + + align:start position:0% +figure out when + + + align:start position:0% +figure out when +things that's another another thing + + align:start position:0% +things that's another another thing + + + align:start position:0% +things that's another another thing +which is the other + + align:start position:0% +which is the other + + + align:start position:0% +which is the other +one who has ever uh kept the box of your + + align:start position:0% +one who has ever uh kept the box of your + + + align:start position:0% +one who has ever uh kept the box of your +warpool + + align:start position:0% +warpool + + + align:start position:0% +warpool +refrigerator how do you move those + + align:start position:0% +refrigerator how do you move those + + + align:start position:0% +refrigerator how do you move those +things in a truck efficiently luckily is + + align:start position:0% +things in a truck efficiently luckily is + + + align:start position:0% +things in a truck efficiently luckily is +when you go things are very nicely + + align:start position:0% +when you go things are very nicely + + + align:start position:0% +when you go things are very nicely +packed not only because they're + + align:start position:0% +packed not only because they're + + + align:start position:0% +packed not only because they're +beautiful for you but also easier easier + + align:start position:0% +beautiful for you but also easier easier + + + align:start position:0% +beautiful for you but also easier easier +to handle your pallet can know goes to + + align:start position:0% +to handle your pallet can know goes to + + + align:start position:0% +to handle your pallet can know goes to +the bottom put on top of a pallet things + + align:start position:0% +the bottom put on top of a pallet things + + + align:start position:0% +the bottom put on top of a pallet things +do not stick out all over the places the + + align:start position:0% +do not stick out all over the places the + + + align:start position:0% +do not stick out all over the places the +doors do not open and close so just the + + align:start position:0% +doors do not open and close so just the + + + align:start position:0% +doors do not open and close so just the +packaging of this thing yeah is meant to + + align:start position:0% +packaging of this thing yeah is meant to + + + align:start position:0% +packaging of this thing yeah is meant to +be moved but once you return it it's + + align:start position:0% +be moved but once you return it it's + + + align:start position:0% +be moved but once you return it it's +just it's just chaos so that creates + + align:start position:0% +just it's just chaos so that creates + + + align:start position:0% +just it's just chaos so that creates +equipment teror you know eventually you + + align:start position:0% +equipment teror you know eventually you + + + align:start position:0% +equipment teror you know eventually you +have to more labor to put it on top of + + align:start position:0% +have to more labor to put it on top of + + + align:start position:0% +have to more labor to put it on top of +the so all those things are the things + + align:start position:0% +the so all those things are the things + + + align:start position:0% +the so all those things are the things +that make it a little bit more expensive + + align:start position:0% +that make it a little bit more expensive + + + align:start position:0% +that make it a little bit more expensive +but you can come up with some solutions + + align:start position:0% +but you can come up with some solutions + + + align:start position:0% +but you can come up with some solutions +standard wrapping or something yeah but + + align:start position:0% +standard wrapping or something yeah but + + + align:start position:0% +standard wrapping or something yeah but +those are the operational constraints + + align:start position:0% +those are the operational constraints + + + align:start position:0% +those are the operational constraints +that would probably get it once you get + + align:start position:0% +that would probably get it once you get + + + align:start position:0% +that would probably get it once you get +to face that that problem and you get to + + align:start position:0% +to face that that problem and you get to + + + align:start position:0% +to face that that problem and you get to +your RDC you have the same problem that + + align:start position:0% +your RDC you have the same problem that + + + align:start position:0% +your RDC you have the same problem that +they has and that's you don't want to + + align:start position:0% +they has and that's you don't want to + + + align:start position:0% +they has and that's you don't want to +have all this crap in your in your DC + + align:start position:0% +have all this crap in your in your DC + + + align:start position:0% +have all this crap in your in your DC +either so you have to have another area + + align:start position:0% +either so you have to have another area + + + align:start position:0% +either so you have to have another area +of your DC so it doesn't interrupt the + + align:start position:0% +of your DC so it doesn't interrupt the + + + align:start position:0% +of your DC so it doesn't interrupt the +flow so those are the operational + + align:start position:0% +flow so those are the operational + + + align:start position:0% +flow so those are the operational +constraints you have to face to set up + + align:start position:0% +constraints you have to face to set up + + + align:start position:0% +constraints you have to face to set up +your own network and in some ways or + + align:start position:0% +your own network and in some ways or + + + align:start position:0% +your own network and in some ways or +another uh that's what makes the ifo + + align:start position:0% +another uh that's what makes the ifo + + + align:start position:0% +another uh that's what makes the ifo +interesting so even though the cost + + align:start position:0% +interesting so even though the cost + + + align:start position:0% +interesting so even though the cost +could be high all those little barriers + + align:start position:0% +could be high all those little barriers + + + align:start position:0% +could be high all those little barriers +require some really strong collaboration + + align:start position:0% +require some really strong collaboration + + + align:start position:0% +require some really strong collaboration +with all your + + align:start position:0% +with all your + + + align:start position:0% +with all your +partners your your retailers need to be + + align:start position:0% +partners your your retailers need to be + + + align:start position:0% +partners your your retailers need to be +on board you have to give them some + + align:start position:0% +on board you have to give them some + + + align:start position:0% +on board you have to give them some +incentives either on branding + + align:start position:0% +incentives either on branding + + + align:start position:0% +incentives either on branding +or market share some sort of incentive + + align:start position:0% +or market share some sort of incentive + + + align:start position:0% +or market share some sort of incentive +for them to work with you otherwise why + + align:start position:0% +for them to work with you otherwise why + + + align:start position:0% +for them to work with you otherwise why +will they work with you and and after + + align:start position:0% +will they work with you and and after + + + align:start position:0% +will they work with you and and after +that you still have to work with all + + align:start position:0% +that you still have to work with all + + + align:start position:0% +that you still have to work with all +those physical barriers of actually + + align:start position:0% +those physical barriers of actually + + + align:start position:0% +those physical barriers of actually +moving used products back into where + + align:start position:0% +moving used products back into where + + + align:start position:0% +moving used products back into where +they need to be disposed and those + + align:start position:0% +they need to be disposed and those + + + align:start position:0% +they need to be disposed and those +workhouses and DC's are not available + + align:start position:0% +workhouses and DC's are not available + + + align:start position:0% +workhouses and DC's are not available +you need more Investments even if + + align:start position:0% +you need more Investments even if + + + align:start position:0% +you need more Investments even if +they're not huge Capital Investments + + align:start position:0% +they're not huge Capital Investments + + + align:start position:0% +they're not huge Capital Investments +they are big barriers and operational + + align:start position:0% +they are big barriers and operational + + + align:start position:0% +they are big barriers and operational +Investments and that's why companies + + align:start position:0% +Investments and that's why companies + + + align:start position:0% +Investments and that's why companies +like jenko are are very profitable + + align:start position:0% +like jenko are are very profitable + + + align:start position:0% +like jenko are are very profitable +because they still can kind of deal with + + align:start position:0% +because they still can kind of deal with + + + align:start position:0% +because they still can kind of deal with +that complexity and you don't have to + + align:start position:0% +that complexity and you don't have to + + + align:start position:0% +that complexity and you don't have to +think about it in this case whpo has a + + align:start position:0% +think about it in this case whpo has a + + + align:start position:0% +think about it in this case whpo has a +big Advantage market share right 48% + + align:start position:0% +big Advantage market share right 48% + + + align:start position:0% +big Advantage market share right 48% +market share so you got you have the + + align:start position:0% +market share so you got you have the + + + align:start position:0% +market share so you got you have the +scale that you need to work these + + align:start position:0% +scale that you need to work these + + + align:start position:0% +scale that you need to work these +details and if you can somehow include + + align:start position:0% +details and if you can somehow include + + + align:start position:0% +details and if you can somehow include +the the value of the brand into this + + align:start position:0% +the the value of the brand into this + + + align:start position:0% +the the value of the brand into this +whole equation that's where this becomes + + align:start position:0% +whole equation that's where this becomes + + + align:start position:0% +whole equation that's where this becomes +attractive operationally it's a it man + + align:start position:0% +attractive operationally it's a it man + + + align:start position:0% +attractive operationally it's a it man +it's better to send it to + + align:start position:0% +it's better to send it to + + + align:start position:0% +it's better to send it to +jenko once you get certain scale like + + align:start position:0% +jenko once you get certain scale like + + + align:start position:0% +jenko once you get certain scale like +maybe whpo has that's when you can get + + align:start position:0% +maybe whpo has that's when you can get + + + align:start position:0% +maybe whpo has that's when you can get +into uh making worthy Investments plus + + align:start position:0% +into uh making worthy Investments plus + + + align:start position:0% +into uh making worthy Investments plus +if you get connection to the customer + + align:start position:0% +if you get connection to the customer + + + align:start position:0% +if you get connection to the customer +which I think is ultimately just as a + + align:start position:0% +which I think is ultimately just as a + + + align:start position:0% +which I think is ultimately just as a +side note what whpo decided to do whle + + align:start position:0% +side note what whpo decided to do whle + + + align:start position:0% +side note what whpo decided to do whle +in this particular case they actually + + align:start position:0% +in this particular case they actually + + + align:start position:0% +in this particular case they actually +decided to go towards the Clos Loop but + + align:start position:0% +decided to go towards the Clos Loop but + + + align:start position:0% +decided to go towards the Clos Loop but +it was much more expensive than they + + align:start position:0% +it was much more expensive than they + + + align:start position:0% +it was much more expensive than they +thought so it kind of was not did not go + + align:start position:0% +thought so it kind of was not did not go + + + align:start position:0% +thought so it kind of was not did not go +that well for our manager at least the + + align:start position:0% +that well for our manager at least the + + + align:start position:0% +that well for our manager at least the +first + + align:start position:0% +first + + + align:start position:0% +first +trial but on the plus side of that they + + align:start position:0% +trial but on the plus side of that they + + + align:start position:0% +trial but on the plus side of that they +since they did go to it they're probably + + align:start position:0% +since they did go to it they're probably + + + align:start position:0% +since they did go to it they're probably +the first ones maybe maybe they can + + align:start position:0% +the first ones maybe maybe they can + + + align:start position:0% +the first ones maybe maybe they can +become the ifo when everyone else can + + align:start position:0% +become the ifo when everyone else can + + + align:start position:0% +become the ifo when everyone else can +pay them to do it that's exactly what + + align:start position:0% +pay them to do it that's exactly what + + + align:start position:0% +pay them to do it that's exactly what +the thinking the thinking was well maybe + + align:start position:0% +the thinking the thinking was well maybe + + + align:start position:0% +the thinking the thinking was well maybe +we can become the ifo at the end of the + + align:start position:0% +we can become the ifo at the end of the + + + align:start position:0% +we can become the ifo at the end of the +day the legislation says we pick one + + align:start position:0% +day the legislation says we pick one + + + align:start position:0% +day the legislation says we pick one +organization to pick up everyone + + align:start position:0% +organization to pick up everyone + + + align:start position:0% +organization to pick up everyone +everything so if things are not working + + align:start position:0% +everything so if things are not working + + + align:start position:0% +everything so if things are not working +out you could become the io so uh we're + + align:start position:0% +out you could become the io so uh we're + + + align:start position:0% +out you could become the io so uh we're +pulling this particular case they did + + align:start position:0% +pulling this particular case they did + + + align:start position:0% +pulling this particular case they did +decide to to try to close close the loop + + align:start position:0% +decide to to try to close close the loop + + + align:start position:0% +decide to to try to close close the loop +um and they actually talk uh well not + + align:start position:0% +um and they actually talk uh well not + + + align:start position:0% +um and they actually talk uh well not +not in Canada but in general they talk + + align:start position:0% +not in Canada but in general they talk + + + align:start position:0% +not in Canada but in general they talk +widely about these things about how they + + align:start position:0% +widely about these things about how they + + + align:start position:0% +widely about these things about how they +are taking things back and that's part + + align:start position:0% +are taking things back and that's part + + + align:start position:0% +are taking things back and that's part +of their value proposition and they + + align:start position:0% +of their value proposition and they + + + align:start position:0% +of their value proposition and they +believe this is going to give them some + + align:start position:0% +believe this is going to give them some + + + align:start position:0% +believe this is going to give them some +long-term + + align:start position:0% +long-term + + + align:start position:0% +long-term +value all right so that was kind of the + + align:start position:0% +value all right so that was kind of the + + + align:start position:0% +value all right so that was kind of the +underlying whle so this is the way um + + align:start position:0% +underlying whle so this is the way um + + + align:start position:0% +underlying whle so this is the way um +the best data you can get is like the + + align:start position:0% +the best data you can get is like the + + + align:start position:0% +the best data you can get is like the +one was in this case study you can get + + align:start position:0% +one was in this case study you can get + + + align:start position:0% +one was in this case study you can get +rough numbers on how much it costs you + + align:start position:0% +rough numbers on how much it costs you + + + align:start position:0% +rough numbers on how much it costs you +have to look at other initiative like + + align:start position:0% +have to look at other initiative like + + + align:start position:0% +have to look at other initiative like +the Wii initiative in different places + + align:start position:0% +the Wii initiative in different places + + + align:start position:0% +the Wii initiative in different places +of the world they publish these kind of + + align:start position:0% +of the world they publish these kind of + + + align:start position:0% +of the world they publish these kind of +numbers price of steel price of copper + + align:start position:0% +numbers price of steel price of copper + + + align:start position:0% +numbers price of steel price of copper +estimate number of units and rly going + + align:start position:0% +estimate number of units and rly going + + + align:start position:0% +estimate number of units and rly going +those um the mapping of the costs here + + align:start position:0% +those um the mapping of the costs here + + + align:start position:0% +those um the mapping of the costs here +uh was uh uh it's a little bit harder + + align:start position:0% +uh was uh uh it's a little bit harder + + + align:start position:0% +uh was uh uh it's a little bit harder +you need to have the inside information + + align:start position:0% +you need to have the inside information + + + align:start position:0% +you need to have the inside information +so you that's why you use 10% in general + + align:start position:0% +so you that's why you use 10% in general + + + align:start position:0% +so you that's why you use 10% in general +but this is how you probably can think + + align:start position:0% +but this is how you probably can think + + + align:start position:0% +but this is how you probably can think +through understanding what is the right + + align:start position:0% +through understanding what is the right + + + align:start position:0% +through understanding what is the right +tradeoff uh that's always a good + + align:start position:0% +tradeoff uh that's always a good + + + align:start position:0% +tradeoff uh that's always a good +Benchmark try to compute how much it + + align:start position:0% +Benchmark try to compute how much it + + + align:start position:0% +Benchmark try to compute how much it +costs forward versus reverse and that + + align:start position:0% +costs forward versus reverse and that + + + align:start position:0% +costs forward versus reverse and that +give you a sense of well it be don't be + + align:start position:0% +give you a sense of well it be don't be + + + align:start position:0% +give you a sense of well it be don't be +surprised is twice as much 30% as much + + align:start position:0% +surprised is twice as much 30% as much + + + align:start position:0% +surprised is twice as much 30% as much +40% more than your forward because it's + + align:start position:0% +40% more than your forward because it's + + + align:start position:0% +40% more than your forward because it's +not optimized and later it will become + + align:start position:0% +not optimized and later it will become + + + align:start position:0% +not optimized and later it will become +better volumes is here the key uh to do + + align:start position:0% +better volumes is here the key uh to do + + + align:start position:0% +better volumes is here the key uh to do +that on on homogeneous um products like + + align:start position:0% +that on on homogeneous um products like + + + align:start position:0% +that on on homogeneous um products like +the case of warpo uh their boxes big + + align:start position:0% +the case of warpo uh their boxes big + + + align:start position:0% +the case of warpo uh their boxes big +ones were boxes makes it more viable for + + align:start position:0% +ones were boxes makes it more viable for + + + align:start position:0% +ones were boxes makes it more viable for +a retailer that's why their jenko starts + + align:start position:0% +a retailer that's why their jenko starts + + + align:start position:0% +a retailer that's why their jenko starts +with you have shirts and toys and cell + + align:start position:0% +with you have shirts and toys and cell + + + align:start position:0% +with you have shirts and toys and cell +phones everything in one bundle then + + align:start position:0% +phones everything in one bundle then + + + align:start position:0% +phones everything in one bundle then +there's little maybe connecting to your + + align:start position:0% +there's little maybe connecting to your + + + align:start position:0% +there's little maybe connecting to your +forward supply chain is not as easc + + align:start position:0% +forward supply chain is not as easc + + + align:start position:0% +forward supply chain is not as easc +because the box is hard to fit in your + + align:start position:0% +because the box is hard to fit in your + + + align:start position:0% +because the box is hard to fit in your +truck boxes like these ones are easier + + align:start position:0% +truck boxes like these ones are easier + + + align:start position:0% +truck boxes like these ones are easier +all right uh any any other thoughts or + + align:start position:0% +all right uh any any other thoughts or + + + align:start position:0% +all right uh any any other thoughts or +comments on the warple + + align:start position:0% + + + + align:start position:0% + +case Tony or Alex anything I should add + + align:start position:0% +case Tony or Alex anything I should add + + + align:start position:0% +case Tony or Alex anything I should add +great lecture okay great let's keep + + align:start position:0% +great lecture okay great let's keep + + + align:start position:0% +great lecture okay great let's keep +going so let's now I want to talk about + + align:start position:0% +going so let's now I want to talk about + + + align:start position:0% +going so let's now I want to talk about +the final projects so I want each of you + + align:start position:0% +the final projects so I want each of you + + + align:start position:0% +the final projects so I want each of you +to come here in front and quickly uh + + align:start position:0% +to come here in front and quickly uh + + + align:start position:0% +to come here in front and quickly uh +tell the rest of the group what are you + + align:start position:0% +tell the rest of the group what are you + + + align:start position:0% +tell the rest of the group what are you +doing which companies you pick and + + align:start position:0% +doing which companies you pick and + + + align:start position:0% +doing which companies you pick and +that's what I ask for your two + + align:start position:0% +that's what I ask for your two + + + align:start position:0% +that's what I ask for your two +slides great did everyone found a nice + + align:start position:0% +slides great did everyone found a nice + + + align:start position:0% +slides great did everyone found a nice +green area in the website of your + + align:start position:0% +green area in the website of your + + + align:start position:0% +green area in the website of your +companies we with Alexis we joke every + + align:start position:0% +companies we with Alexis we joke every + + + align:start position:0% +companies we with Alexis we joke every +time we look at companies they all they + + align:start position:0% +time we look at companies they all they + + + align:start position:0% +time we look at companies they all they +say it's in our values right it's every + + align:start position:0% +say it's in our values right it's every + + + align:start position:0% +say it's in our values right it's every +it's in our DNA that's the word to use + + align:start position:0% +it's in our DNA that's the word to use + + + align:start position:0% +it's in our DNA that's the word to use +and our DNA yeah so every single company + + align:start position:0% +and our DNA yeah so every single company + + + align:start position:0% +and our DNA yeah so every single company +on website makes the world should be a + + align:start position:0% +on website makes the world should be a + + + align:start position:0% +on website makes the world should be a +better place so the other company is + + align:start position:0% +better place so the other company is + + + align:start position:0% +better place so the other company is +index + + align:start position:0% +index + + + align:start position:0% +index +Sara okay so to you have lots of + + align:start position:0% +Sara okay so to you have lots of + + + align:start position:0% +Sara okay so to you have lots of +questions next class about how to + + align:start position:0% +questions next class about how to + + + align:start position:0% +questions next class about how to +compute carbon footprint of energy and + + align:start position:0% +compute carbon footprint of energy and + + + align:start position:0% +compute carbon footprint of energy and +stores and electricity I think that's + + align:start position:0% +stores and electricity I think that's + + + align:start position:0% +stores and electricity I think that's +going to be something to understand well + + align:start position:0% +going to be something to understand well + + + align:start position:0% +going to be something to understand well +because I'm sure all your companies have + + align:start position:0% +because I'm sure all your companies have + + + align:start position:0% +because I'm sure all your companies have +that highlighted somehow so are + + align:start position:0% +that highlighted somehow so are + + + align:start position:0% +that highlighted somehow so are +they smoker mirrors or they're doing the + + align:start position:0% +they smoker mirrors or they're doing the + + + align:start position:0% +they smoker mirrors or they're doing the +real deal I guess we have to have to see + + align:start position:0% +real deal I guess we have to have to see + + + align:start position:0% +real deal I guess we have to have to see +after no pressure Tony but have more + + align:start position:0% +after no pressure Tony but have more + + + align:start position:0% +after no pressure Tony but have more +questions after your lecture great so + + align:start position:0% +questions after your lecture great so + + + align:start position:0% +questions after your lecture great so +you know that our go our Center is + + align:start position:0% +you know that our go our Center is + + + align:start position:0% +you know that our go our Center is +actually in the same Logistics Park as + + align:start position:0% +actually in the same Logistics Park as + + + align:start position:0% +actually in the same Logistics Park as +Sara largest distribution center in + + align:start position:0% +Sara largest distribution center in + + + align:start position:0% +Sara largest distribution center in +Spain so that's one reason why our + + align:start position:0% +Spain so that's one reason why our + + + align:start position:0% +Spain so that's one reason why our +partner Center is in Saragosa partly uh + + align:start position:0% +partner Center is in Saragosa partly uh + + + align:start position:0% +partner Center is in Saragosa partly uh +collocated with the plaza that is the + + align:start position:0% +collocated with the plaza that is the + + + align:start position:0% +collocated with the plaza that is the +logistics activity zone of Saragosa + + align:start position:0% +logistics activity zone of Saragosa + + + align:start position:0% +logistics activity zone of Saragosa +where the largest distribution center of + + align:start position:0% +where the largest distribution center of + + + align:start position:0% +where the largest distribution center of +Sara is to manage all the global + + align:start position:0% +Sara is to manage all the global + + + align:start position:0% +Sara is to manage all the global +operations they also fly things around + + align:start position:0% +operations they also fly things around + + + align:start position:0% +operations they also fly things around +from there + + align:start position:0% +from there + + + align:start position:0% +from there +okay great thank you so let's uh pick + + align:start position:0% +okay great thank you so let's uh pick + + + align:start position:0% +okay great thank you so let's uh pick +the next one um any questions or + + align:start position:0% +the next one um any questions or + + + align:start position:0% +the next one um any questions or +comments before I move to the + + align:start position:0% +comments before I move to the + + + align:start position:0% +comments before I move to the +next group yep all right let me see so + + align:start position:0% +next group yep all right let me see so + + + align:start position:0% +next group yep all right let me see so +the next one + + align:start position:0% +the next one + + + align:start position:0% +the next one +is H Packard and + + align:start position:0% + + + + align:start position:0% + +Dell so uh thank you I would like to + + align:start position:0% +Dell so uh thank you I would like to + + + align:start position:0% +Dell so uh thank you I would like to +just highlight two between these two + + align:start position:0% +just highlight two between these two + + + align:start position:0% +just highlight two between these two +projects so we look at first these two + + align:start position:0% +projects so we look at first these two + + + align:start position:0% +projects so we look at first these two +Co the two pairs of companies have very + + align:start position:0% +Co the two pairs of companies have very + + + align:start position:0% +Co the two pairs of companies have very +different business models right and I + + align:start position:0% +different business models right and I + + + align:start position:0% +different business models right and I +think Sara has won fast fashion you know + + align:start position:0% +think Sara has won fast fashion you know + + + align:start position:0% +think Sara has won fast fashion you know +lots of designs per year uh Dale goes + + align:start position:0% +lots of designs per year uh Dale goes + + + align:start position:0% +lots of designs per year uh Dale goes +direct to Consumer and I think that + + align:start position:0% +direct to Consumer and I think that + + + align:start position:0% +direct to Consumer and I think that +really has deep implications I think + + align:start position:0% +really has deep implications I think + + + align:start position:0% +really has deep implications I think +both of you highlighted that's important + + align:start position:0% +both of you highlighted that's important + + + align:start position:0% +both of you highlighted that's important +I also want to point out at least the + + align:start position:0% +I also want to point out at least the + + + align:start position:0% +I also want to point out at least the +state of the both Industries in terms of + + align:start position:0% +state of the both Industries in terms of + + + align:start position:0% +state of the both Industries in terms of +environmental practices um electronics + + align:start position:0% +environmental practices um electronics + + + align:start position:0% +environmental practices um electronics +Industry has moved together for a longer + + align:start position:0% +Industry has moved together for a longer + + + align:start position:0% +Industry has moved together for a longer +time let's say there's the Wii directive + + align:start position:0% +time let's say there's the Wii directive + + + align:start position:0% +time let's say there's the Wii directive +in Europe you know that put Electronics + + align:start position:0% +in Europe you know that put Electronics + + + align:start position:0% +in Europe you know that put Electronics +under scrutiny so they're both under + + align:start position:0% +under scrutiny so they're both under + + + align:start position:0% +under scrutiny so they're both under +higher pressure that's where maybe you + + align:start position:0% +higher pressure that's where maybe you + + + align:start position:0% +higher pressure that's where maybe you +see more of the same initiative is like + + align:start position:0% +see more of the same initiative is like + + + align:start position:0% +see more of the same initiative is like +take materials out of certain kind uh + + align:start position:0% +take materials out of certain kind uh + + + align:start position:0% +take materials out of certain kind uh +it's outlawed in some countries right so + + align:start position:0% +it's outlawed in some countries right so + + + align:start position:0% +it's outlawed in some countries right so +you have to do it because you have to do + + align:start position:0% +you have to do it because you have to do + + + align:start position:0% +you have to do it because you have to do +it like so there's a little bit of that + + align:start position:0% +it like so there's a little bit of that + + + align:start position:0% +it like so there's a little bit of that +on one end um um they also tend to be + + align:start position:0% +on one end um um they also tend to be + + + align:start position:0% +on one end um um they also tend to be +more um they collaborate in other + + align:start position:0% +more um they collaborate in other + + + align:start position:0% +more um they collaborate in other +sectors both the aparel industry and the + + align:start position:0% +sectors both the aparel industry and the + + + align:start position:0% +sectors both the aparel industry and the +electronics Industry they collaborate on + + align:start position:0% +electronics Industry they collaborate on + + + align:start position:0% +electronics Industry they collaborate on +social issues on aparel you know for + + align:start position:0% +social issues on aparel you know for + + + align:start position:0% +social issues on aparel you know for +labor um so that brings them together in + + align:start position:0% +labor um so that brings them together in + + + align:start position:0% +labor um so that brings them together in +other forums in electronics they also + + align:start position:0% +other forums in electronics they also + + + align:start position:0% +other forums in electronics they also +get together for technology designs um + + align:start position:0% +get together for technology designs um + + + align:start position:0% +get together for technology designs um +to keep processors and and speed so as + + align:start position:0% +to keep processors and and speed so as + + + align:start position:0% +to keep processors and and speed so as +you go into both of your cases take a + + align:start position:0% +you go into both of your cases take a + + + align:start position:0% +you go into both of your cases take a +look at maybe there's some underline + + align:start position:0% +look at maybe there's some underline + + + align:start position:0% +look at maybe there's some underline +themes that are common to the industry + + align:start position:0% +themes that are common to the industry + + + align:start position:0% +themes that are common to the industry +that have brought because of the + + align:start position:0% +that have brought because of the + + + align:start position:0% +that have brought because of the +industry really and you as a consumer + + align:start position:0% +industry really and you as a consumer + + + align:start position:0% +industry really and you as a consumer +have no idea about these things so you + + align:start position:0% +have no idea about these things so you + + + align:start position:0% +have no idea about these things so you +can for you it looks like every company + + align:start position:0% +can for you it looks like every company + + + align:start position:0% +can for you it looks like every company +is doing the same but it probably comes + + align:start position:0% +is doing the same but it probably comes + + + align:start position:0% +is doing the same but it probably comes +from some other Force so in both cases + + align:start position:0% +from some other Force so in both cases + + + align:start position:0% +from some other Force so in both cases +uh I know especially Electronics Les the + + align:start position:0% +uh I know especially Electronics Les the + + + align:start position:0% +uh I know especially Electronics Les the +apparel are are more on that on that + + align:start position:0% +apparel are are more on that on that + + + align:start position:0% +apparel are are more on that on that +bandwidth so just keep that in mind all + + align:start position:0% +bandwidth so just keep that in mind all + + + align:start position:0% +bandwidth so just keep that in mind all +right good uh let me see who's + + align:start position:0% +right good uh let me see who's + + + align:start position:0% +right good uh let me see who's +next + + align:start position:0% +next + + + align:start position:0% +next +[Music] + + align:start position:0% + + + + align:start position:0% + +uh + + align:start position:0% + + + + align:start position:0% + +BMW yeah so I think that this is thank + + align:start position:0% +BMW yeah so I think that this is thank + + + align:start position:0% +BMW yeah so I think that this is thank +you it's interesting to know that you + + align:start position:0% +you it's interesting to know that you + + + align:start position:0% +you it's interesting to know that you +know the company that started let's say + + align:start position:0% +know the company that started let's say + + + align:start position:0% +know the company that started let's say +the at least brand with the consumer + + align:start position:0% +the at least brand with the consumer + + + align:start position:0% +the at least brand with the consumer +hybrid notion is not the top Raider + + align:start position:0% +hybrid notion is not the top Raider + + + align:start position:0% +hybrid notion is not the top Raider +company you will imagine that uh where + + align:start position:0% +company you will imagine that uh where + + + align:start position:0% +company you will imagine that uh where +the largest emissions are in a car is in + + align:start position:0% +the largest emissions are in a car is in + + + align:start position:0% +the largest emissions are in a car is in +the usage so if you innovated there why + + align:start position:0% +the usage so if you innovated there why + + + align:start position:0% +the usage so if you innovated there why +are you number one for the next 25 years + + align:start position:0% +are you number one for the next 25 years + + + align:start position:0% +are you number one for the next 25 years +but it looks like it's not so I think + + align:start position:0% +but it looks like it's not so I think + + + align:start position:0% +but it looks like it's not so I think +that it's interesting to to know that uh + + align:start position:0% +that it's interesting to to know that uh + + + align:start position:0% +that it's interesting to to know that uh +I also did not mention much about the uh + + align:start position:0% +I also did not mention much about the uh + + + align:start position:0% +I also did not mention much about the uh +uh now the life cycle aspect of it in + + align:start position:0% +uh now the life cycle aspect of it in + + + align:start position:0% +uh now the life cycle aspect of it in +both of these companies it's uh very + + align:start position:0% +both of these companies it's uh very + + + align:start position:0% +both of these companies it's uh very +different and um in textiles Tony I + + align:start position:0% +different and um in textiles Tony I + + + align:start position:0% +different and um in textiles Tony I +don't remember in textiles or Alexis the + + align:start position:0% +don't remember in textiles or Alexis the + + + align:start position:0% +don't remember in textiles or Alexis the +life cycle emissions are not in use + + align:start position:0% +life cycle emissions are not in use + + + align:start position:0% +life cycle emissions are not in use +except if you consider water um energy + + align:start position:0% +except if you consider water um energy + + + align:start position:0% +except if you consider water um energy +used for washing your + + align:start position:0% +used for washing your + + + align:start position:0% +used for washing your +clothes uh that + + align:start position:0% +clothes uh that + + + align:start position:0% +clothes uh that +probably do the other emissions but do + + align:start position:0% +probably do the other emissions but do + + + align:start position:0% +probably do the other emissions but do +you remember Tony the life cycle + + align:start position:0% +you remember Tony the life cycle + + + align:start position:0% +you remember Tony the life cycle +emissions of of Apparel in general for + + align:start position:0% +emissions of of Apparel in general for + + + align:start position:0% +emissions of of Apparel in general for +IND detex yeah it's if it's wash so + + align:start position:0% +IND detex yeah it's if it's wash so + + + align:start position:0% +IND detex yeah it's if it's wash so +don't wash your + + align:start position:0% +don't wash your + + + align:start position:0% +don't wash your +clothes is the electricity high + + align:start position:0% +clothes is the electricity high + + + align:start position:0% +clothes is the electricity high +efficiency high efficiency yeah no don't + + align:start position:0% +efficiency high efficiency yeah no don't + + + align:start position:0% +efficiency high efficiency yeah no don't +wash them uh or use a solar washer + + align:start position:0% +wash them uh or use a solar washer + + + align:start position:0% +wash them uh or use a solar washer +that's what so the uh but this again + + align:start position:0% +that's what so the uh but this again + + + align:start position:0% +that's what so the uh but this again +goes back into the life cycle and which + + align:start position:0% +goes back into the life cycle and which + + + align:start position:0% +goes back into the life cycle and which +pieces you control versus you don't + + align:start position:0% +pieces you control versus you don't + + + align:start position:0% +pieces you control versus you don't +control of that life cycle but um um + + align:start position:0% +control of that life cycle but um um + + + align:start position:0% +control of that life cycle but um um +great thank you uh let's look at the + + align:start position:0% +great thank you uh let's look at the + + + align:start position:0% +great thank you uh let's look at the +other + + align:start position:0% + + + + align:start position:0% + +group Philip Morris + + align:start position:0% + + + + align:start position:0% + +International okay thank you I just um + + align:start position:0% +International okay thank you I just um + + + align:start position:0% +International okay thank you I just um +um want to add the uh it was this + + align:start position:0% +um want to add the uh it was this + + + align:start position:0% +um want to add the uh it was this +comment on on do you work internally in + + align:start position:0% +comment on on do you work internally in + + + align:start position:0% +comment on on do you work internally in +your operations or you do um offsets + + align:start position:0% +your operations or you do um offsets + + + align:start position:0% +your operations or you do um offsets +plant trees or and we'll talk a little + + align:start position:0% +plant trees or and we'll talk a little + + + align:start position:0% +plant trees or and we'll talk a little +bit about that over time but this is I'm + + align:start position:0% +bit about that over time but this is I'm + + + align:start position:0% +bit about that over time but this is I'm +glad that the one of the companies here + + align:start position:0% +glad that the one of the companies here + + + align:start position:0% +glad that the one of the companies here +highlighted offsets as one of the + + align:start position:0% +highlighted offsets as one of the + + + align:start position:0% +highlighted offsets as one of the +strategies they wanted + + align:start position:0% +strategies they wanted + + + align:start position:0% +strategies they wanted +pursue um let me + + align:start position:0% +pursue um let me + + + align:start position:0% +pursue um let me +see um the other one is this one I + + align:start position:0% + + + + align:start position:0% + +skipped so for next class the case study + + align:start position:0% +skipped so for next class the case study + + + align:start position:0% +skipped so for next class the case study +is is is ready the Caron fpr case study + + align:start position:0% +is is is ready the Caron fpr case study + + + align:start position:0% +is is is ready the Caron fpr case study +it's been posted it's pretty simple so + + align:start position:0% +it's been posted it's pretty simple so + + + align:start position:0% +it's been posted it's pretty simple so +hopefully there's any questions about + + align:start position:0% +hopefully there's any questions about + + + align:start position:0% +hopefully there's any questions about +you know what you're actually mechanics + + align:start position:0% +you know what you're actually mechanics + + + align:start position:0% +you know what you're actually mechanics +of doing the calculations Etc you can + + align:start position:0% +of doing the calculations Etc you can + + + align:start position:0% +of doing the calculations Etc you can +email me directly uh you know with those + + align:start position:0% +email me directly uh you know with those + + + align:start position:0% +email me directly uh you know with those +questions but have that filled out and + + align:start position:0% +questions but have that filled out and + + + align:start position:0% +questions but have that filled out and +turned in uh by Wednesday morning + + align:start position:0% +turned in uh by Wednesday morning + + + align:start position:0% +turned in uh by Wednesday morning +because we'll I'm going to collect some + + align:start position:0% +because we'll I'm going to collect some + + + align:start position:0% +because we'll I'm going to collect some +of the data from that and we'll Mo that + + align:start position:0% +of the data from that and we'll Mo that + + + align:start position:0% +of the data from that and we'll Mo that +in discussion during okay and you have + + align:start position:0% +in discussion during okay and you have + + + align:start position:0% +in discussion during okay and you have +to the numbers for that one there's no + + align:start position:0% +to the numbers for that one there's no + + + align:start position:0% +to the numbers for that one there's no +way to escape it there's a bunch of EXC + + align:start position:0% +way to escape it there's a bunch of EXC + + + align:start position:0% +way to escape it there's a bunch of EXC +spreadsheets you have to work on it it + + align:start position:0% +spreadsheets you have to work on it it + + + align:start position:0% +spreadsheets you have to work on it it +requires only basic + + align:start position:0% +requires only basic + + + align:start position:0% +requires only basic +mulation thank you again \ No newline at end of file diff --git a/emrHcqEvXpw.txt b/emrHcqEvXpw.txt new file mode 100644 index 0000000000000000000000000000000000000000..9c97f2c68bf1362378349518512e14f7e9c32546 --- /dev/null +++ b/emrHcqEvXpw.txt @@ -0,0 +1,523 @@ +align:start position:0% + +when we analyzed how the position vector + + align:start position:0% +when we analyzed how the position vector + + + align:start position:0% +when we analyzed how the position vector +changed we know that the velocity for + + align:start position:0% +changed we know that the velocity for + + + align:start position:0% +changed we know that the velocity for +circular motion is given by the radius + + align:start position:0% +circular motion is given by the radius + + + align:start position:0% +circular motion is given by the radius +times the rate that the angle is + + align:start position:0% +times the rate that the angle is + + + align:start position:0% +times the rate that the angle is +changing and it points tangential to the + + align:start position:0% +changing and it points tangential to the + + + align:start position:0% +changing and it points tangential to the +circle so let's draw a few + + align:start position:0% +circle so let's draw a few + + + align:start position:0% +circle so let's draw a few +characteristic arrows to show that at + + align:start position:0% +characteristic arrows to show that at + + + align:start position:0% +characteristic arrows to show that at +this point we'll draw these pictures + + align:start position:0% +this point we'll draw these pictures + + + align:start position:0% +this point we'll draw these pictures +with D theta DT positive so the velocity + + align:start position:0% +with D theta DT positive so the velocity + + + align:start position:0% +with D theta DT positive so the velocity +points like that it points like this + + align:start position:0% +points like that it points like this + + + align:start position:0% +points like that it points like this +points like that and these are all the + + align:start position:0% +points like that and these are all the + + + align:start position:0% +points like that and these are all the +velocity vectors at different times + + align:start position:0% +velocity vectors at different times + + + align:start position:0% +velocity vectors at different times +notice that if we make consider the + + align:start position:0% +notice that if we make consider the + + + align:start position:0% +notice that if we make consider the +special case in which the theta DT is a + + align:start position:0% +special case in which the theta DT is a + + + align:start position:0% +special case in which the theta DT is a +constant in that instance the magnitude + + align:start position:0% +constant in that instance the magnitude + + + align:start position:0% +constant in that instance the magnitude +of the velocity V is given by our + + align:start position:0% +of the velocity V is given by our + + + align:start position:0% +of the velocity V is given by our +magnitude of D theta DT and that is also + + align:start position:0% +magnitude of D theta DT and that is also + + + align:start position:0% +magnitude of D theta DT and that is also +a constant but the velocity vector is + + align:start position:0% +a constant but the velocity vector is + + + align:start position:0% +a constant but the velocity vector is +changing direction and we know by + + align:start position:0% +changing direction and we know by + + + align:start position:0% +changing direction and we know by +definition that the acceleration is the + + align:start position:0% +definition that the acceleration is the + + + align:start position:0% +definition that the acceleration is the +derivative of velocity and so what we + + align:start position:0% +derivative of velocity and so what we + + + align:start position:0% +derivative of velocity and so what we +see here is where we have a vector + + align:start position:0% +see here is where we have a vector + + + align:start position:0% +see here is where we have a vector +that's constant in magnitude but + + align:start position:0% +that's constant in magnitude but + + + align:start position:0% +that's constant in magnitude but +changing direction and we now want to + + align:start position:0% +changing direction and we now want to + + + align:start position:0% +changing direction and we now want to +calculate the derivative in this special + + align:start position:0% +calculate the derivative in this special + + + align:start position:0% +calculate the derivative in this special +case we refer to this case as uniform + + align:start position:0% +case we refer to this case as uniform + + + align:start position:0% +case we refer to this case as uniform +circular motion so this special case is + + align:start position:0% +circular motion so this special case is + + + align:start position:0% +circular motion so this special case is +often called uniform circular motion + + align:start position:0% + + + + align:start position:0% + +okay how do we calculate the derivative + + align:start position:0% +okay how do we calculate the derivative + + + align:start position:0% +okay how do we calculate the derivative +of the velocity well recall that the + + align:start position:0% +of the velocity well recall that the + + + align:start position:0% +of the velocity well recall that the +velocity vector R D theta DT those are + + align:start position:0% +velocity vector R D theta DT those are + + + align:start position:0% +velocity vector R D theta DT those are +all constants because it's in the theta + + align:start position:0% +all constants because it's in the theta + + + align:start position:0% +all constants because it's in the theta +hat direction + + align:start position:0% +hat direction + + + align:start position:0% +hat direction +once again we'll decomposed theta hat + + align:start position:0% +once again we'll decomposed theta hat + + + align:start position:0% +once again we'll decomposed theta hat +into its Cartesian components you see it + + align:start position:0% +into its Cartesian components you see it + + + align:start position:0% +into its Cartesian components you see it +has a - I hat component and a plus J hat + + align:start position:0% +has a - I hat component and a plus J hat + + + align:start position:0% +has a - I hat component and a plus J hat +component the I hat component is + + align:start position:0% +component the I hat component is + + + align:start position:0% +component the I hat component is +opposite the angle so we have minus sine + + align:start position:0% +opposite the angle so we have minus sine + + + align:start position:0% +opposite the angle so we have minus sine +theta of T I have plus cosine theta of T + + align:start position:0% +theta of T I have plus cosine theta of T + + + align:start position:0% +theta of T I have plus cosine theta of T +J hat so when I differentiate the + + align:start position:0% +J hat so when I differentiate the + + + align:start position:0% +J hat so when I differentiate the +velocity in time + + align:start position:0% +velocity in time + + + align:start position:0% +velocity in time +this piece is constant so I'm only again + + align:start position:0% +this piece is constant so I'm only again + + + align:start position:0% +this piece is constant so I'm only again +apply + + align:start position:0% +apply + + + align:start position:0% +apply +the chain rule to these two functions so + + align:start position:0% +the chain rule to these two functions so + + + align:start position:0% +the chain rule to these two functions so +I have our d theta/dt and i + + align:start position:0% +I have our d theta/dt and i + + + align:start position:0% +I have our d theta/dt and i +differentiate sine i get cosine with the + + align:start position:0% +differentiate sine i get cosine with the + + + align:start position:0% +differentiate sine i get cosine with the +minus sign so i have minus cosine theta + + align:start position:0% +minus sign so i have minus cosine theta + + + align:start position:0% +minus sign so i have minus cosine theta +I'll keep the function of T just so that + + align:start position:0% +I'll keep the function of T just so that + + + align:start position:0% +I'll keep the function of T just so that +you can see that D theta DT I had over + + align:start position:0% +you can see that D theta DT I had over + + + align:start position:0% +you can see that D theta DT I had over +here the derivative of cosine is minus + + align:start position:0% +here the derivative of cosine is minus + + + align:start position:0% +here the derivative of cosine is minus +sine D theta DT that's the chain rule + + align:start position:0% +sine D theta DT that's the chain rule + + + align:start position:0% +sine D theta DT that's the chain rule +sine of theta DT D theta DT J hat and + + align:start position:0% +sine of theta DT D theta DT J hat and + + + align:start position:0% +sine of theta DT D theta DT J hat and +now I have this common D theta DT term + + align:start position:0% +now I have this common D theta DT term + + + align:start position:0% +now I have this common D theta DT term +and I can pull it out and I'll square it + + align:start position:0% +and I can pull it out and I'll square it + + + align:start position:0% +and I can pull it out and I'll square it +now whether D theta DT is positive or + + align:start position:0% +now whether D theta DT is positive or + + + align:start position:0% +now whether D theta DT is positive or +negative the square is always positive + + align:start position:0% +negative the square is always positive + + + align:start position:0% +negative the square is always positive +so this quantity is always positive and + + align:start position:0% +so this quantity is always positive and + + + align:start position:0% +so this quantity is always positive and +inside I have I'm also going to pull the + + align:start position:0% +inside I have I'm also going to pull the + + + align:start position:0% +inside I have I'm also going to pull the +minus sign out and I have cosine theta + + align:start position:0% +minus sign out and I have cosine theta + + + align:start position:0% +minus sign out and I have cosine theta +of T I have 2 sine theta of T J hat now + + align:start position:0% +of T I have 2 sine theta of T J hat now + + + align:start position:0% +of T I have 2 sine theta of T J hat now +what we have here is the unit vector R + + align:start position:0% +what we have here is the unit vector R + + + align:start position:0% +what we have here is the unit vector R +hat t our hat has a cosine adjacent in + + align:start position:0% +hat t our hat has a cosine adjacent in + + + align:start position:0% +hat t our hat has a cosine adjacent in +the I hat direction and a sine component + + align:start position:0% +the I hat direction and a sine component + + + align:start position:0% +the I hat direction and a sine component +in the J hat direction so our + + align:start position:0% +in the J hat direction so our + + + align:start position:0% +in the J hat direction so our +acceleration + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/gUrBP6ei4fs.txt b/gUrBP6ei4fs.txt new file mode 100644 index 0000000000000000000000000000000000000000..6908ce8d8903f181f3ce1ec9b7f3bee72853e56e --- /dev/null +++ b/gUrBP6ei4fs.txt @@ -0,0 +1,1251 @@ +align:start position:0% + +why does this matter + + align:start position:0% +why does this matter + + + align:start position:0% +why does this matter +oh we go back to the terror pot + + align:start position:0% +oh we go back to the terror pot + + + align:start position:0% +oh we go back to the terror pot +and by the way i didn't have this link + + align:start position:0% +and by the way i didn't have this link + + + align:start position:0% +and by the way i didn't have this link +and i should have when i showed you the + + align:start position:0% +and i should have when i showed you the + + + align:start position:0% +and i should have when i showed you the +the and this is your goody bag etc right + + align:start position:0% +the and this is your goody bag etc right + + + align:start position:0% +the and this is your goody bag etc right +there's some really nice + + align:start position:0% +there's some really nice + + + align:start position:0% +there's some really nice +articles here that you can find related + + align:start position:0% +articles here that you can find related + + + align:start position:0% +articles here that you can find related +to these experiments and other things + + align:start position:0% +to these experiments and other things + + + align:start position:0% +to these experiments and other things +about ocean acidity + + align:start position:0% +about ocean acidity + + + align:start position:0% +about ocean acidity +in case you're interested um but see + + align:start position:0% +in case you're interested um but see + + + align:start position:0% +in case you're interested um but see +what we + + align:start position:0% +what we + + + align:start position:0% +what we +what i did is was that this was my why + + align:start position:0% +what i did is was that this was my why + + + align:start position:0% +what i did is was that this was my why +this matters on monday + + align:start position:0% +this matters on monday + + + align:start position:0% +this matters on monday +and i wanted to tell you about the + + align:start position:0% +and i wanted to tell you about the + + + align:start position:0% +and i wanted to tell you about the +goodie bag and about + + align:start position:0% +goodie bag and about + + + align:start position:0% +goodie bag and about +the how things dissolve because monday + + align:start position:0% +the how things dissolve because monday + + + align:start position:0% +the how things dissolve because monday +was about + + align:start position:0% +was about + + + align:start position:0% +was about +dissolving right and finding a + + align:start position:0% +dissolving right and finding a + + + align:start position:0% +dissolving right and finding a +saturation point + + align:start position:0% +saturation point + + + align:start position:0% +saturation point +now we can we can get to the next place + + align:start position:0% +now we can we can get to the next place + + + align:start position:0% +now we can we can get to the next place +which is + + align:start position:0% +which is + + + align:start position:0% +which is +why does that matter for the pteropod + + align:start position:0% +why does that matter for the pteropod + + + align:start position:0% +why does that matter for the pteropod +shell + + align:start position:0% +shell + + + align:start position:0% +shell +what is the chemistry that that matters + + align:start position:0% +what is the chemistry that that matters + + + align:start position:0% +what is the chemistry that that matters +there + + align:start position:0% +there + + + align:start position:0% +there +okay so i made the ocean a little more + + align:start position:0% +okay so i made the ocean a little more + + + align:start position:0% +okay so i made the ocean a little more +acidic + + align:start position:0% +acidic + + + align:start position:0% +acidic +why does that matter but you see now + + align:start position:0% +why does that matter but you see now + + + align:start position:0% +why does that matter but you see now +we're armed with the knowledge we need + + align:start position:0% +we're armed with the knowledge we need + + + align:start position:0% +we're armed with the knowledge we need +to answer that question + + align:start position:0% +to answer that question + + + align:start position:0% +to answer that question +now we're armed with it all we need to + + align:start position:0% +now we're armed with it all we need to + + + align:start position:0% +now we're armed with it all we need to +do as always with everything in life + + align:start position:0% +do as always with everything in life + + + align:start position:0% +do as always with everything in life +is look at the chemistry that's it + + align:start position:0% +is look at the chemistry that's it + + + align:start position:0% +is look at the chemistry that's it +say that at the thanksgiving table + + align:start position:0% +say that at the thanksgiving table + + + align:start position:0% +say that at the thanksgiving table +you'll be very popular + + align:start position:0% +you'll be very popular + + + align:start position:0% +you'll be very popular +we said co2 plus h2o + + align:start position:0% +we said co2 plus h2o + + + align:start position:0% +we said co2 plus h2o +this goes oh + + align:start position:0% +this goes oh + + + align:start position:0% +this goes oh +it finds some equilibrium 2h2 + + align:start position:0% +it finds some equilibrium 2h2 + + + align:start position:0% +it finds some equilibrium 2h2 +co3 now this is called carbonic acid + + align:start position:0% +co3 now this is called carbonic acid + + + align:start position:0% +co3 now this is called carbonic acid +this is called carbonic acid there's the + + align:start position:0% +this is called carbonic acid there's the + + + align:start position:0% +this is called carbonic acid there's the +pteropod up there + + align:start position:0% +pteropod up there + + + align:start position:0% +pteropod up there +and there's a reaction that's that's + + align:start position:0% +and there's a reaction that's that's + + + align:start position:0% +and there's a reaction that's that's +really relevant that you'll see from the + + align:start position:0% +really relevant that you'll see from the + + + align:start position:0% +really relevant that you'll see from the +ones we're about to write down why + + align:start position:0% +ones we're about to write down why + + + align:start position:0% +ones we're about to write down why +because the thing is that why what + + align:start position:0% +because the thing is that why what + + + align:start position:0% +because the thing is that why what +happens to carbonic acid + + align:start position:0% +happens to carbonic acid + + + align:start position:0% +happens to carbonic acid +that well carbonic acid also goes + + align:start position:0% +that well carbonic acid also goes + + + align:start position:0% +that well carbonic acid also goes +through + + align:start position:0% +through + + + align:start position:0% +through +a dissolution reaction so carbonic acid + + align:start position:0% +a dissolution reaction so carbonic acid + + + align:start position:0% +a dissolution reaction so carbonic acid +so this is co2 + + align:start position:0% +so this is co2 + + + align:start position:0% +so this is co2 +dissolving in water now we make carbon + + align:start position:0% +dissolving in water now we make carbon + + + align:start position:0% +dissolving in water now we make carbon +so carbonic acid + + align:start position:0% +so carbonic acid + + + align:start position:0% +so carbonic acid +goes like this okay it goes into + + align:start position:0% +goes like this okay it goes into + + + align:start position:0% +goes like this okay it goes into +h co3 minus + + align:start position:0% +h co3 minus + + + align:start position:0% +h co3 minus +plus h plus + + align:start position:0% + + + + align:start position:0% + +now here's the thing okay what is the + + align:start position:0% +now here's the thing okay what is the + + + align:start position:0% +now here's the thing okay what is the +shell made of + + align:start position:0% +shell made of + + + align:start position:0% +shell made of +well the shell that's dissolving in + + align:start position:0% +well the shell that's dissolving in + + + align:start position:0% +well the shell that's dissolving in +in its you know kind of like the core + + align:start position:0% +in its you know kind of like the core + + + align:start position:0% +in its you know kind of like the core +material + + align:start position:0% +material + + + align:start position:0% +material +is calcium carbonate so that's caco3 + + align:start position:0% +is calcium carbonate so that's caco3 + + + align:start position:0% +is calcium carbonate so that's caco3 +that's the shell and the shell also has + + align:start position:0% +that's the shell and the shell also has + + + align:start position:0% +that's the shell and the shell also has +an equilibrium reaction that happens + + align:start position:0% +an equilibrium reaction that happens + + + align:start position:0% +an equilibrium reaction that happens +the shell of of of a sea a creature is + + align:start position:0% +the shell of of of a sea a creature is + + + align:start position:0% +the shell of of of a sea a creature is +in dynamic equilibrium + + align:start position:0% +in dynamic equilibrium + + + align:start position:0% +in dynamic equilibrium +with the ocean and and so it's going + + align:start position:0% +with the ocean and and so it's going + + + align:start position:0% +with the ocean and and so it's going +like this it's going to + + align:start position:0% +like this it's going to + + + align:start position:0% +like this it's going to +uh well okay c a two plus + + align:start position:0% +uh well okay c a two plus + + + align:start position:0% +uh well okay c a two plus +and c o three + + align:start position:0% +and c o three + + + align:start position:0% +and c o three +two minus and and and okay but the thing + + align:start position:0% +two minus and and and okay but the thing + + + align:start position:0% +two minus and and and okay but the thing +is + + align:start position:0% +is + + + align:start position:0% +is +it has an equilibrium constant all these + + align:start position:0% +it has an equilibrium constant all these + + + align:start position:0% +it has an equilibrium constant all these +have equilibrium constants + + align:start position:0% +have equilibrium constants + + + align:start position:0% +have equilibrium constants +so like for example for this one the ksp + + align:start position:0% +so like for example for this one the ksp + + + align:start position:0% +so like for example for this one the ksp +the solubility product constant because + + align:start position:0% +the solubility product constant because + + + align:start position:0% +the solubility product constant because +this is a solid this is a solid shell + + align:start position:0% +this is a solid this is a solid shell + + + align:start position:0% +this is a solid this is a solid shell +solid going to ions in aqueous solution + + align:start position:0% + + + + align:start position:0% + +well so the ksp for that is somewhere + + align:start position:0% +well so the ksp for that is somewhere + + + align:start position:0% +well so the ksp for that is somewhere +around 5 + + align:start position:0% +around 5 + + + align:start position:0% +around 5 +times 10 to the minus 9. + + align:start position:0% +times 10 to the minus 9. + + + align:start position:0% +times 10 to the minus 9. +5 times 10 to the minus 9. yeah but + + align:start position:0% +5 times 10 to the minus 9. yeah but + + + align:start position:0% +5 times 10 to the minus 9. yeah but +here's the thing we just went through + + align:start position:0% +here's the thing we just went through + + + align:start position:0% +here's the thing we just went through +this + + align:start position:0% +this + + + align:start position:0% +this +if i consume one of these or change the + + align:start position:0% +if i consume one of these or change the + + + align:start position:0% +if i consume one of these or change the +concentration of + + align:start position:0% +concentration of + + + align:start position:0% +concentration of +one of these and not the other + + align:start position:0% +one of these and not the other + + + align:start position:0% +one of these and not the other +we just did this if i if i change the + + align:start position:0% +we just did this if i if i change the + + + align:start position:0% +we just did this if i if i change the +concentration if i consume any of these + + align:start position:0% +concentration if i consume any of these + + + align:start position:0% +concentration if i consume any of these +then i might drive the reaction oh and + + align:start position:0% +then i might drive the reaction oh and + + + align:start position:0% +then i might drive the reaction oh and +consume or produce + + align:start position:0% +consume or produce + + + align:start position:0% +consume or produce +if i change any of these independently + + align:start position:0% +if i change any of these independently + + + align:start position:0% +if i change any of these independently +i'm going to drive the reaction + + align:start position:0% +i'm going to drive the reaction + + + align:start position:0% +i'm going to drive the reaction +because that's how we keep to our k + + align:start position:0% +because that's how we keep to our k + + + align:start position:0% +because that's how we keep to our k +that's what le chatelier's principle + + align:start position:0% +that's what le chatelier's principle + + + align:start position:0% +that's what le chatelier's principle +tells us + + align:start position:0% +tells us + + + align:start position:0% +tells us +and so what ends up happening is you've + + align:start position:0% +and so what ends up happening is you've + + + align:start position:0% +and so what ends up happening is you've +got + + align:start position:0% +got + + + align:start position:0% +got +the extra h + + align:start position:0% +the extra h + + + align:start position:0% +the extra h +plus ions so these are ions in solution + + align:start position:0% +plus ions so these are ions in solution + + + align:start position:0% +plus ions so these are ions in solution +where did they come from they came from + + align:start position:0% +where did they come from they came from + + + align:start position:0% +where did they come from they came from +the co2 giving us + + align:start position:0% +the co2 giving us + + + align:start position:0% +the co2 giving us +carbonic acid which then gave us h plus + + align:start position:0% +carbonic acid which then gave us h plus + + + align:start position:0% +carbonic acid which then gave us h plus +those are what i'm talking about + + align:start position:0% +those are what i'm talking about + + + align:start position:0% +those are what i'm talking about +well they react + + align:start position:0% + + + + align:start position:0% + +with the co3 minus + + align:start position:0% +with the co3 minus + + + align:start position:0% +with the co3 minus +3032 minus + + align:start position:0% + + + + align:start position:0% + +this lowers the co32 minus concentration + + align:start position:0% +this lowers the co32 minus concentration + + + align:start position:0% +this lowers the co32 minus concentration +near the shell right because in tight + + align:start position:0% +near the shell right because in tight + + + align:start position:0% +near the shell right because in tight +and if i + + align:start position:0% +and if i + + + align:start position:0% +and if i +lower this because i've taken some of + + align:start position:0% +lower this because i've taken some of + + + align:start position:0% +lower this because i've taken some of +this now and i've reacted it + + align:start position:0% +this now and i've reacted it + + + align:start position:0% +this now and i've reacted it +so now i've got less of it and because + + align:start position:0% +so now i've got less of it and because + + + align:start position:0% +so now i've got less of it and because +of what we just saw if i've got less of + + align:start position:0% +of what we just saw if i've got less of + + + align:start position:0% +of what we just saw if i've got less of +this you're going to drive + + align:start position:0% +this you're going to drive + + + align:start position:0% +this you're going to drive +this way which is going to dissolve + + align:start position:0% +this way which is going to dissolve + + + align:start position:0% +this way which is going to dissolve +more of the shell right that's why this + + align:start position:0% +more of the shell right that's why this + + + align:start position:0% +more of the shell right that's why this +works + + align:start position:0% +works + + + align:start position:0% +works +that's why this this happens + + align:start position:0% +that's why this this happens + + + align:start position:0% +that's why this this happens +works sounds like a positive thing right + + align:start position:0% +works sounds like a positive thing right + + + align:start position:0% +works sounds like a positive thing right +so this lowers + + align:start position:0% + + + + align:start position:0% + +the concentration of co three two minus + + align:start position:0% +the concentration of co three two minus + + + align:start position:0% +the concentration of co three two minus +and that drives + + align:start position:0% + + + + align:start position:0% + +more dissolution + + align:start position:0% +more dissolution + + + align:start position:0% +more dissolution +that is what's happening and we now can + + align:start position:0% +that is what's happening and we now can + + + align:start position:0% +that is what's happening and we now can +understand it + + align:start position:0% +understand it + + + align:start position:0% +understand it +in terms of the concepts that we've just + + align:start position:0% +in terms of the concepts that we've just + + + align:start position:0% +in terms of the concepts that we've just +learned + + align:start position:0% +learned + + + align:start position:0% +learned +historically i mentioned 50 million + + align:start position:0% +historically i mentioned 50 million + + + align:start position:0% +historically i mentioned 50 million +years actually by some accounts it's 300 + + align:start position:0% +years actually by some accounts it's 300 + + + align:start position:0% +years actually by some accounts it's 300 +million + + align:start position:0% +million + + + align:start position:0% +million +it depends on which studies you read + + align:start position:0% +it depends on which studies you read + + + align:start position:0% +it depends on which studies you read +but but for at least 50 and maybe as + + align:start position:0% +but but for at least 50 and maybe as + + + align:start position:0% +but but for at least 50 and maybe as +much as 300 million years the ocean + + align:start position:0% +much as 300 million years the ocean + + + align:start position:0% +much as 300 million years the ocean +has had a ph of 8.18 + + align:start position:0% +has had a ph of 8.18 + + + align:start position:0% +has had a ph of 8.18 +now where's the oh yeah right + + align:start position:0% +now where's the oh yeah right + + + align:start position:0% +now where's the oh yeah right +so let's just say you know + + align:start position:0% +so let's just say you know + + + align:start position:0% +so let's just say you know +last 0 50 to 300 million + + align:start position:0% +last 0 50 to 300 million + + + align:start position:0% +last 0 50 to 300 million +ish years + + align:start position:0% +ish years + + + align:start position:0% +ish years +the ocean ph + + align:start position:0% +the ocean ph + + + align:start position:0% +the ocean ph +was 8.18 and today + + align:start position:0% +was 8.18 and today + + + align:start position:0% +was 8.18 and today +it's uh 8.07 + + align:start position:0% +it's uh 8.07 + + + align:start position:0% +it's uh 8.07 +and the prediction is that in 2100 + + align:start position:0% +and the prediction is that in 2100 + + + align:start position:0% +and the prediction is that in 2100 +it will be 7.8 + + align:start position:0% +it will be 7.8 + + + align:start position:0% +it will be 7.8 +now as we will see in a little bit and + + align:start position:0% +now as we will see in a little bit and + + + align:start position:0% +now as we will see in a little bit and +he said what's ph + + align:start position:0% +he said what's ph + + + align:start position:0% +he said what's ph +well many of you probably already know + + align:start position:0% +well many of you probably already know + + + align:start position:0% +well many of you probably already know +but we i will tell you what it is in a + + align:start position:0% +but we i will tell you what it is in a + + + align:start position:0% +but we i will tell you what it is in a +little bit + + align:start position:0% +little bit + + + align:start position:0% +little bit +but because this is a logarithmic thing + + align:start position:0% +but because this is a logarithmic thing + + + align:start position:0% +but because this is a logarithmic thing +this is a lot + + align:start position:0% +this is a lot + + + align:start position:0% +this is a lot +right today the ocean is 25 percent more + + align:start position:0% +right today the ocean is 25 percent more + + + align:start position:0% +right today the ocean is 25 percent more +acidic than it's been + + align:start position:0% +acidic than it's been + + + align:start position:0% +acidic than it's been +in 300 million ish years and in 2100 it + + align:start position:0% +in 300 million ish years and in 2100 it + + + align:start position:0% +in 300 million ish years and in 2100 it +will be 126 percent + + align:start position:0% +will be 126 percent + + + align:start position:0% +will be 126 percent +more acidic that's why they used 7.8 + + align:start position:0% +more acidic that's why they used 7.8 + + + align:start position:0% +more acidic that's why they used 7.8 +in in the experiments of the pteropots + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/g_HD_17-Msw.txt b/g_HD_17-Msw.txt new file mode 100644 index 0000000000000000000000000000000000000000..fd98c27b2c3bea7cf692e930f408d0be604ab6f2 --- /dev/null +++ b/g_HD_17-Msw.txt @@ -0,0 +1,371 @@ +align:start position:0% + +Faraday's integral law shows how a + + align:start position:0% +Faraday's integral law shows how a + + + align:start position:0% +Faraday's integral law shows how a +voltmeter reading induced by magnetic + + align:start position:0% +voltmeter reading induced by magnetic + + + align:start position:0% +voltmeter reading induced by magnetic +induction at the terminals of a coil + + align:start position:0% +induction at the terminals of a coil + + + align:start position:0% +induction at the terminals of a coil +provides a measurement of the magnetic + + align:start position:0% +provides a measurement of the magnetic + + + align:start position:0% +provides a measurement of the magnetic +flux + + align:start position:0% +flux + + + align:start position:0% +flux +density in this experiment the Contour C + + align:start position:0% +density in this experiment the Contour C + + + align:start position:0% +density in this experiment the Contour C +is traced out by the wire in this coil + + align:start position:0% +is traced out by the wire in this coil + + + align:start position:0% +is traced out by the wire in this coil +so that the surface + + align:start position:0% +so that the surface + + + align:start position:0% +so that the surface +s is the area having the entire length + + align:start position:0% +s is the area having the entire length + + + align:start position:0% +s is the area having the entire length +of coil as its + + align:start position:0% +of coil as its + + + align:start position:0% +of coil as its +Edge in this coil the surface area s is + + align:start position:0% +Edge in this coil the surface area s is + + + align:start position:0% +Edge in this coil the surface area s is +CM by 21 cm multiplied by 20 + + align:start position:0% + + + + align:start position:0% + +turns we will use this coil with + + align:start position:0% +turns we will use this coil with + + + align:start position:0% +turns we will use this coil with +Faraday's law to find the magnetic flux + + align:start position:0% +Faraday's law to find the magnetic flux + + + align:start position:0% +Faraday's law to find the magnetic flux +associated with current in this + + align:start position:0% + + + + align:start position:0% + +wire the upper trace of this + + align:start position:0% +wire the upper trace of this + + + align:start position:0% +wire the upper trace of this +oscilloscope records the electromotive + + align:start position:0% +oscilloscope records the electromotive + + + align:start position:0% +oscilloscope records the electromotive +force of vol at the coil terminals the + + align:start position:0% +force of vol at the coil terminals the + + + align:start position:0% +force of vol at the coil terminals the +lower Trace is the current in the wire + + align:start position:0% +lower Trace is the current in the wire + + + align:start position:0% +lower Trace is the current in the wire +measured by the voltage drop across a 1 + + align:start position:0% +measured by the voltage drop across a 1 + + + align:start position:0% +measured by the voltage drop across a 1 +ohm series + + align:start position:0% + + + + align:start position:0% + +resistor with the coil rotated so that + + align:start position:0% +resistor with the coil rotated so that + + + align:start position:0% +resistor with the coil rotated so that +it links no magnetic + + align:start position:0% +it links no magnetic + + + align:start position:0% +it links no magnetic +flux no voltage is + + align:start position:0% + + + + align:start position:0% + +seen with the coil now plac so that the + + align:start position:0% +seen with the coil now plac so that the + + + align:start position:0% +seen with the coil now plac so that the +magnetic flux passes perpendicularly + + align:start position:0% + + + + align:start position:0% + +through the coil the maximum signal is + + align:start position:0% +through the coil the maximum signal is + + + align:start position:0% +through the coil the maximum signal is +recorded with the coil straddling the + + align:start position:0% + + + + align:start position:0% + +wire the flux passing through the coil + + align:start position:0% +wire the flux passing through the coil + + + align:start position:0% +wire the flux passing through the coil +in the upper + + align:start position:0% +in the upper + + + align:start position:0% +in the upper +section is oppositely directed to the + + align:start position:0% +section is oppositely directed to the + + + align:start position:0% +section is oppositely directed to the +flux through the lower + + align:start position:0% +flux through the lower + + + align:start position:0% +flux through the lower +section with it symmetrically positioned + + align:start position:0% +section with it symmetrically positioned + + + align:start position:0% +section with it symmetrically positioned +the next net flux is zero so the + + align:start position:0% +the next net flux is zero so the + + + align:start position:0% +the next net flux is zero so the +measured voltage is zero the scope + + align:start position:0% +measured voltage is zero the scope + + + align:start position:0% +measured voltage is zero the scope +traces are triggered on the wire current + + align:start position:0% +traces are triggered on the wire current + + + align:start position:0% +traces are triggered on the wire current +the lower Trace so we can see the change + + align:start position:0% +the lower Trace so we can see the change + + + align:start position:0% +the lower Trace so we can see the change +in Phase as the coil is moved from below + + align:start position:0% +in Phase as the coil is moved from below + + + align:start position:0% +in Phase as the coil is moved from below +the wire to above the + + align:start position:0% + + + + align:start position:0% + +wire the lower Trace current is 90° out + + align:start position:0% +wire the lower Trace current is 90° out + + + align:start position:0% +wire the lower Trace current is 90° out +of phase with the upper Trace induced + + align:start position:0% +of phase with the upper Trace induced + + + align:start position:0% +of phase with the upper Trace induced +volage this is because the coil voltage + + align:start position:0% +volage this is because the coil voltage + + + align:start position:0% +volage this is because the coil voltage +is the time rate of change of the + + align:start position:0% +is the time rate of change of the + + + align:start position:0% +is the time rate of change of the +magnetic flux and hence a the time rate + + align:start position:0% +magnetic flux and hence a the time rate + + + align:start position:0% +magnetic flux and hence a the time rate +of change of the + + align:start position:0% + + + + align:start position:0% + +current the coil voltage is 90° out of + + align:start position:0% +current the coil voltage is 90° out of + + + align:start position:0% +current the coil voltage is 90° out of +phase with the current \ No newline at end of file diff --git a/gpMLYEMIw24.txt b/gpMLYEMIw24.txt new file mode 100644 index 0000000000000000000000000000000000000000..74d15444e7ced57cc1f0b507f09efa70281ac905 --- /dev/null +++ b/gpMLYEMIw24.txt @@ -0,0 +1,286 @@ +In this problem, we'll be +looking at an ambulance that + +is traveling back and forth +in interval of size l. + +Say from 0 to l. + +At some point in time, there's +an accident occurring, let's + +say at location x. + +And we'll assume the accident +occurs in a random location so + +that x is uniformly distributed +between 0 and l. + +Now, at this point in time, +let's say the ambulance turns + +out to be at location y. + +Again, we'll assume that y is +a uniform random variable + +between 0 and l, and also that +x and y are independently + +distributed. + +The question we're interested +in answering is how long it + +would take an ambulance to +respond to travel from point y + +to point x. + +Let's call this time T. And in +particular, we want to know + +everything about distribution of +T. For example, what is the + +CDF of T given by the +probability of big T, less + +than or equal to little t, or +the PDF, which is done by + +differentiating the CDF +once we have it. + +Now, to start, we'll express T +you as a function of X and Y. + +Since we know that +the ambulance + +travels at a speed V-- + +V meters or V units of +distance per second-- + +then we can write that big T is +simply equal to Y minus X, + +absolute value the distance +between X and Y, divided by + +the speed at which the ambulance +is traveling at, V. + +So now if we look at the +probability of T less than or + +equal to little t, this is then +equal to the probability + +that Y minus X divided +by V less than or + +equal to little t. + +We now take off the absolute +value by writing the + +expression as negative vt less +equal to Y minus X less equal + +to positive vt. + +Here we multiply v on the other +side of t, and then took + +out the absolute value sign. + +As a final step, we'll also move +X to the other side of + +inequalities by writing this as +X minus vt less equal to y + +less equal to x plus vt. + +To compute this quantity, we'll +define a set A as a set + +of all points that satisfies +this condition right here. + +In particular, it's a pair of +all X and Y such that X minus + +vt less equal to little y less +equal to X plus vt, and also + +that X is within 0 and +l, and so is Y. + +So the set A will be the +set of values we'll + +be integrating over. + +Now that we have A, we can +express the above probability + +as the integral of all X and Y, +this pair within the set A, + +integrating the PDF of f of +X, Y, little x, little y. + + + +Let's now evaluate this +expression right here in a + +graphical way. + +On the right, we're plotting out +what we just illustrated + +here, where the shaded region is +precisely the set A. As we + +can see, this is a set of values +of X and Y where Y is + +sandwiched between two lines, +the upper one being X plus vt + +right here, and the lower line +being X minus vt, right here. + +So these are the values that +correspond to the set A. + +Now that we have A, let's +look f of x, y. + +We know that both x and y are +uniform random variables + +between 0 and l, and therefore, +since they're + +independent, the probability +density of x and y being at + +any point between 0 and l is +precisely 1 over l squared, + +where l squared is the size of +this square box right here. + +So given this picture, all we +need to do is to multiply by 1 + +over l squared the area of the +region A. And depending on the + +value of T, we'll get different + +answers as right here. + +If T is less than 0, obviously, +the area of A + +diminishes to nothing, +so we get 0. + +If T is greater than l over V, +the area of A fills up the + +entire square, and we get 1. + +Now, if T is somewhere in +between 0 and l over v, we + +will have 1 over l squared, +multiply by the area looking + +like something like that right +here-- the shaded region. + +Now, if you wonder how we +arrive at exactly this + +expression right here, here is +a simple way to calculate it. + +What we want is 1 over l squared +times the area A. Now, + +area A can be viewed as the +entire square, l squared, + +minus whatever's not in area +A, which is these two + +triangles right here. + +Now, each triangle has area +1/2, l minus vt squared. + +This multiply 2, and this, after +some algebra, will give + +the answer right here. + +At this point, we have obtained +the probability of + +big T less equal to little t. + +Namely, we have gotten the CDF +for T. And as a final step, we + +can also compute the probability +density function + +for T. We'll call it +little f of t. + +And we do so by simply +differentiating the CDF in + +different regions of T. + +To begin, we'll look at t +between 0 and l over v right + +here at differentiating the +expression right here with + +respect to t. + +And doing so will give +us 2v over l minus 2v + +squared t over L squared. + +And this applies to t greater or +equal to 0, less than l/v. + +Now, any other region, either +t less than 0 or t greater + +than l/v, we have a constant +for the CDF, and hence its + +derivative will be 0. + +So this is for any other t. + +We call it otherwise. + +Now, this completely +characterized the PDF of big + +T, and hence, we've also +finished a problem. \ No newline at end of file diff --git a/grns_GNYWe4.txt b/grns_GNYWe4.txt new file mode 100644 index 0000000000000000000000000000000000000000..9ab71e4b5a24b20e1cdeaac1301f1db4d31315aa --- /dev/null +++ b/grns_GNYWe4.txt @@ -0,0 +1,1275 @@ +align:start position:0% + +welcome back to recitation in this video + + align:start position:0% +welcome back to recitation in this video + + + align:start position:0% +welcome back to recitation in this video +I'd like us to consider the following + + align:start position:0% +I'd like us to consider the following + + + align:start position:0% +I'd like us to consider the following +problem so the question is for what + + align:start position:0% +problem so the question is for what + + + align:start position:0% +problem so the question is for what +simple closed curve C which is oriented + + align:start position:0% +simple closed curve C which is oriented + + + align:start position:0% +simple closed curve C which is oriented +positively around the region it encloses + + align:start position:0% +positively around the region it encloses + + + align:start position:0% +positively around the region it encloses +does the integral over C of minus the + + align:start position:0% +does the integral over C of minus the + + + align:start position:0% +does the integral over C of minus the +quantity x² y + 3x - 2 y + + align:start position:0% +quantity x² y + 3x - 2 y + + + align:start position:0% +quantity x² y + 3x - 2 y +DX + 4 y x - 2x Dy achieve its minimum + + align:start position:0% +DX + 4 y x - 2x Dy achieve its minimum + + + align:start position:0% +DX + 4 y x - 2x Dy achieve its minimum +value so again the point we want to find + + align:start position:0% +value so again the point we want to find + + + align:start position:0% +value so again the point we want to find +the thing we want to find here the point + + align:start position:0% +the thing we want to find here the point + + + align:start position:0% +the thing we want to find here the point +we want to make is that we have this + + align:start position:0% +we want to make is that we have this + + + align:start position:0% +we want to make is that we have this +integral and we're allowed to vary C so + + align:start position:0% +integral and we're allowed to vary C so + + + align:start position:0% +integral and we're allowed to vary C so +we're allowed to change the curve the + + align:start position:0% +we're allowed to change the curve the + + + align:start position:0% +we're allowed to change the curve the +simple closed curve and we want to know + + align:start position:0% +simple closed curve and we want to know + + + align:start position:0% +simple closed curve and we want to know +for what for what curve C does this + + align:start position:0% +for what for what curve C does this + + + align:start position:0% +for what for what curve C does this +integral achieve its minimum value so + + align:start position:0% +integral achieve its minimum value so + + + align:start position:0% +integral achieve its minimum value so +why don't you work on that think about + + align:start position:0% +why don't you work on that think about + + + align:start position:0% +why don't you work on that think about +it pause the video and when you're + + align:start position:0% +it pause the video and when you're + + + align:start position:0% +it pause the video and when you're +feeling like you're ready to see how I + + align:start position:0% +feeling like you're ready to see how I + + + align:start position:0% +feeling like you're ready to see how I +do it bring the video back + + align:start position:0% + + + + align:start position:0% + +up welcome back so again what we would + + align:start position:0% +up welcome back so again what we would + + + align:start position:0% +up welcome back so again what we would +like to do for this problem is we want + + align:start position:0% +like to do for this problem is we want + + + align:start position:0% +like to do for this problem is we want +to take this quantity which is varying + + align:start position:0% +to take this quantity which is varying + + + align:start position:0% +to take this quantity which is varying +in C and we want to figure out a way to + + align:start position:0% +in C and we want to figure out a way to + + + align:start position:0% +in C and we want to figure out a way to +minimize it to find its minimum value + + align:start position:0% +minimize it to find its minimum value + + + align:start position:0% +minimize it to find its minimum value +and actually what's what's interesting + + align:start position:0% +and actually what's what's interesting + + + align:start position:0% +and actually what's what's interesting +to think about before we proceed any + + align:start position:0% +to think about before we proceed any + + + align:start position:0% +to think about before we proceed any +further is you might think you want to + + align:start position:0% +further is you might think you want to + + + align:start position:0% +further is you might think you want to +take the smallest possible simple closed + + align:start position:0% +take the smallest possible simple closed + + + align:start position:0% +take the smallest possible simple closed +curve you can in other words you might + + align:start position:0% +curve you can in other words you might + + + align:start position:0% +curve you can in other words you might +want to shrink it down to nothing but + + align:start position:0% +want to shrink it down to nothing but + + + align:start position:0% +want to shrink it down to nothing but +then you would have that this integral + + align:start position:0% +then you would have that this integral + + + align:start position:0% +then you would have that this integral +would be zero and the question is can we + + align:start position:0% +would be zero and the question is can we + + + align:start position:0% +would be zero and the question is can we +do better because we can have a minimum + + align:start position:0% +do better because we can have a minimum + + + align:start position:0% +do better because we can have a minimum +value of course that's negative and so + + align:start position:0% +value of course that's negative and so + + + align:start position:0% +value of course that's negative and so +we could do better by having a larger + + align:start position:0% +we could do better by having a larger + + + align:start position:0% +we could do better by having a larger +curve put in the right place so I just + + align:start position:0% +curve put in the right place so I just + + + align:start position:0% +curve put in the right place so I just +want to point that out if you were + + align:start position:0% +want to point that out if you were + + + align:start position:0% +want to point that out if you were +thinking well I just make c not actually + + align:start position:0% +thinking well I just make c not actually + + + align:start position:0% +thinking well I just make c not actually +a curve I just shrink it down to nothing + + align:start position:0% +a curve I just shrink it down to nothing + + + align:start position:0% +a curve I just shrink it down to nothing +that won't be the best we can do we can + + align:start position:0% +that won't be the best we can do we can + + + align:start position:0% +that won't be the best we can do we can +actually find a curve that has an + + align:start position:0% +actually find a curve that has an + + + align:start position:0% +actually find a curve that has an +integral that is not zero but is in fact + + align:start position:0% +integral that is not zero but is in fact + + + align:start position:0% +integral that is not zero but is in fact +negative and then we want to make it the + + align:start position:0% +negative and then we want to make it the + + + align:start position:0% +negative and then we want to make it the +most negative we can so that's the idea + + align:start position:0% +most negative we can so that's the idea + + + align:start position:0% +most negative we can so that's the idea +so what we're going to do + + align:start position:0% +so what we're going to do + + + align:start position:0% +so what we're going to do +here is we're going to use Green's + + align:start position:0% +here is we're going to use Green's + + + align:start position:0% +here is we're going to use Green's +theorem to help us and so what we want + + align:start position:0% +theorem to help us and so what we want + + + align:start position:0% +theorem to help us and so what we want +to remember is that if we have the + + align:start position:0% +to remember is that if we have the + + + align:start position:0% +to remember is that if we have the +integral over C of M + + align:start position:0% +integral over C of M + + + align:start position:0% +integral over C of M +DX plus n Dy we want to write that as + + align:start position:0% +DX plus n Dy we want to write that as + + + align:start position:0% +DX plus n Dy we want to write that as +the integral over R of n subx minus m + + align:start position:0% +the integral over R of n subx minus m + + + align:start position:0% +the integral over R of n subx minus m +suby DX Dy right and so what I want to + + align:start position:0% +suby DX Dy right and so what I want to + + + align:start position:0% +suby DX Dy right and so what I want to +point out I'm just going to write down + + align:start position:0% +point out I'm just going to write down + + + align:start position:0% +point out I'm just going to write down +what these are I'm not going to not + + align:start position:0% +what these are I'm not going to not + + + align:start position:0% +what these are I'm not going to not +going to take the derivatives for you + + align:start position:0% +going to take the derivatives for you + + + align:start position:0% +going to take the derivatives for you +I'm just going to show you what they are + + align:start position:0% +I'm just going to show you what they are + + + align:start position:0% +I'm just going to show you what they are +so in this case with the m and n that we + + align:start position:0% +so in this case with the m and n that we + + + align:start position:0% +so in this case with the m and n that we +have we get + + align:start position:0% +have we get + + + align:start position:0% +have we get +exactly this value for the integral we + + align:start position:0% +exactly this value for the integral we + + + align:start position:0% +exactly this value for the integral we +get n subx minus m suby is = to x^2 + 4 + + align:start position:0% +get n subx minus m suby is = to x^2 + 4 + + + align:start position:0% +get n subx minus m suby is = to x^2 + 4 +y^ 2 - 4 + + align:start position:0% +y^ 2 - 4 + + + align:start position:0% +y^ 2 - 4 +DX + + align:start position:0% +DX + + + align:start position:0% +DX +Dy you can obviously compute that + + align:start position:0% +Dy you can obviously compute that + + + align:start position:0% +Dy you can obviously compute that +yourself just take the derivative of n + + align:start position:0% +yourself just take the derivative of n + + + align:start position:0% +yourself just take the derivative of n +with respect to X subtract the + + align:start position:0% +with respect to X subtract the + + + align:start position:0% +with respect to X subtract the +derivative of M with respect to Y you + + align:start position:0% +derivative of M with respect to Y you + + + align:start position:0% +derivative of M with respect to Y you +get a little cancellation and you end up + + align:start position:0% +get a little cancellation and you end up + + + align:start position:0% +get a little cancellation and you end up +with this and so now instead of thinking + + align:start position:0% +with this and so now instead of thinking + + + align:start position:0% +with this and so now instead of thinking +about trying to uh Trying to minimize + + align:start position:0% +about trying to uh Trying to minimize + + + align:start position:0% +about trying to uh Trying to minimize +this quantity over here in terms of a + + align:start position:0% +this quantity over here in terms of a + + + align:start position:0% +this quantity over here in terms of a +curve now we can think about trying to + + align:start position:0% +curve now we can think about trying to + + + align:start position:0% +curve now we can think about trying to +minimize the quantity here in terms of a + + align:start position:0% +minimize the quantity here in terms of a + + + align:start position:0% +minimize the quantity here in terms of a +region right and the goal here is to + + align:start position:0% +region right and the goal here is to + + + align:start position:0% +region right and the goal here is to +make + + align:start position:0% +make + + + align:start position:0% +make +the sum of all of this over the whole + + align:start position:0% +the sum of all of this over the whole + + + align:start position:0% +the sum of all of this over the whole +region we want to make it as negative as + + align:start position:0% +region we want to make it as negative as + + + align:start position:0% +region we want to make it as negative as +we can possibly make it so essentially + + align:start position:0% +we can possibly make it so essentially + + + align:start position:0% +we can possibly make it so essentially +what we want to do is we want that the + + align:start position:0% +what we want to do is we want that the + + + align:start position:0% +what we want to do is we want that the +on the boundary of this region we would + + align:start position:0% +on the boundary of this region we would + + + align:start position:0% +on the boundary of this region we would +like the value here to be zero and on + + align:start position:0% +like the value here to be zero and on + + + align:start position:0% +like the value here to be zero and on +the inside of the region we'd like it to + + align:start position:0% +the inside of the region we'd like it to + + + align:start position:0% +the inside of the region we'd like it to +be negative so let me let me point that + + align:start position:0% +be negative so let me let me point that + + + align:start position:0% +be negative so let me let me point that +out again and just make sure we + + align:start position:0% +out again and just make sure we + + + align:start position:0% +out again and just make sure we +understand this to make this quantity as + + align:start position:0% +understand this to make this quantity as + + + align:start position:0% +understand this to make this quantity as +small as possible what we would like let + + align:start position:0% +small as possible what we would like let + + + align:start position:0% +small as possible what we would like let +me actually just draw a little region so + + align:start position:0% +me actually just draw a little region so + + + align:start position:0% +me actually just draw a little region so +say this is the + + align:start position:0% +say this is the + + + align:start position:0% +say this is the +region to make this integral as small as + + align:start position:0% +region to make this integral as small as + + + align:start position:0% +region to make this integral as small as +possible what we want is that x^2 + 4 + + align:start position:0% +possible what we want is that x^2 + 4 + + + align:start position:0% +possible what we want is that x^2 + 4 +y^2 - 4 is negative inside the region so + + align:start position:0% +y^2 - 4 is negative inside the region so + + + align:start position:0% +y^2 - 4 is negative inside the region so +if this whole quantity is less than zero + + align:start position:0% +if this whole quantity is less than zero + + + align:start position:0% +if this whole quantity is less than zero +inside the region and we want it to on + + align:start position:0% +inside the region and we want it to on + + + align:start position:0% +inside the region and we want it to on +the boundary of the region equal zero + + align:start position:0% +the boundary of the region equal zero + + + align:start position:0% +the boundary of the region equal zero +and why do we want it to equal zero on + + align:start position:0% +and why do we want it to equal zero on + + + align:start position:0% +and why do we want it to equal zero on +the boundary well that's because then + + align:start position:0% +the boundary well that's because then + + + align:start position:0% +the boundary well that's because then +we've gotten all the negative we could + + align:start position:0% +we've gotten all the negative we could + + + align:start position:0% +we've gotten all the negative we could +get and we haven't added in any positive + + align:start position:0% +get and we haven't added in any positive + + + align:start position:0% +get and we haven't added in any positive +and made it brought the value up so + + align:start position:0% +and made it brought the value up so + + + align:start position:0% +and made it brought the value up so +that's really why we want exactly the + + align:start position:0% +that's really why we want exactly the + + + align:start position:0% +that's really why we want exactly the +boundary to be the boundary of the + + align:start position:0% +boundary to be the boundary of the + + + align:start position:0% +boundary to be the boundary of the +region to be exactly where this quantity + + align:start position:0% +region to be exactly where this quantity + + + align:start position:0% +region to be exactly where this quantity +equals zero and so let's think about + + align:start position:0% + + + + align:start position:0% + +geometrically what describes are oops + + align:start position:0% +geometrically what describes are oops + + + align:start position:0% +geometrically what describes are oops +that should have an + + align:start position:0% +that should have an + + + align:start position:0% +that should have an +S what + + align:start position:0% +S what + + + align:start position:0% +S what +describes R + + align:start position:0% +describes R + + + align:start position:0% +describes R +where x^2 + 4 y^ 2 - 4 is less than zero + + align:start position:0% +where x^2 + 4 y^ 2 - 4 is less than zero + + + align:start position:0% +where x^2 + 4 y^ 2 - 4 is less than zero +inside + + align:start position:0% +inside + + + align:start position:0% +inside +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +R + + align:start position:0% +R + + + align:start position:0% +R +and that's the same thing as in our what + + align:start position:0% +and that's the same thing as in our what + + + align:start position:0% +and that's the same thing as in our what +we're interested in x^2 + 4 y^2 - 4 + + align:start position:0% +we're interested in x^2 + 4 y^2 - 4 + + + align:start position:0% +we're interested in x^2 + 4 y^2 - 4 +equal 0 on the boundary of + + align:start position:0% + + + + align:start position:0% + +R and if you if you look at this this is + + align:start position:0% +R and if you if you look at this this is + + + align:start position:0% +R and if you if you look at this this is +really the expression that will probably + + align:start position:0% +really the expression that will probably + + + align:start position:0% +really the expression that will probably +help you right this expression if you + + align:start position:0% +help you right this expression if you + + + align:start position:0% +help you right this expression if you +rewrite it you rewrite it as x^2 + 4 y^2 + + align:start position:0% +rewrite it you rewrite it as x^2 + 4 y^2 + + + align:start position:0% +rewrite it you rewrite it as x^2 + 4 y^2 +is equal to 4 and you see that this is + + align:start position:0% +is equal to 4 and you see that this is + + + align:start position:0% +is equal to 4 and you see that this is +actually the equation that describes an + + align:start position:0% +actually the equation that describes an + + + align:start position:0% +actually the equation that describes an +ellipse okay maybe you see it more often + + align:start position:0% +ellipse okay maybe you see it more often + + + align:start position:0% +ellipse okay maybe you see it more often +if you divide everything by four and so + + align:start position:0% +if you divide everything by four and so + + + align:start position:0% +if you divide everything by four and so +on the right hand side you have a one + + align:start position:0% +on the right hand side you have a one + + + align:start position:0% +on the right hand side you have a one +and your your coefficients are are + + align:start position:0% +and your your coefficients are are + + + align:start position:0% +and your your coefficients are are +fractional potentially there but this is + + align:start position:0% +fractional potentially there but this is + + + align:start position:0% +fractional potentially there but this is +exactly the equation for an ellipse and + + align:start position:0% +exactly the equation for an ellipse and + + + align:start position:0% +exactly the equation for an ellipse and +so the boundary of R is an ellipse + + align:start position:0% +so the boundary of R is an ellipse + + + align:start position:0% +so the boundary of R is an ellipse +described by this equation but the + + align:start position:0% +described by this equation but the + + + align:start position:0% +described by this equation but the +boundary of R is actually just C right + + align:start position:0% +boundary of R is actually just C right + + + align:start position:0% +boundary of R is actually just C right +so C we now know is exactly the curve + + align:start position:0% +so C we now know is exactly the curve + + + align:start position:0% +so C we now know is exactly the curve +that is carved out by this equation on + + align:start position:0% +that is carved out by this equation on + + + align:start position:0% +that is carved out by this equation on +the plane on the XY plane and that's + + align:start position:0% +the plane on the XY plane and that's + + + align:start position:0% +the plane on the XY plane and that's +exactly the that's an that's an ellipse + + align:start position:0% +exactly the that's an that's an ellipse + + + align:start position:0% +exactly the that's an that's an ellipse +okay so just to remind you what we were + + align:start position:0% +okay so just to remind you what we were + + + align:start position:0% +okay so just to remind you what we were +trying to + + align:start position:0% +trying to + + + align:start position:0% +trying to +do if you come back here we were trying + + align:start position:0% +do if you come back here we were trying + + + align:start position:0% +do if you come back here we were trying +to figure out a way to minimize a + + align:start position:0% +to figure out a way to minimize a + + + align:start position:0% +to figure out a way to minimize a +certain integral over a + + align:start position:0% +certain integral over a + + + align:start position:0% +certain integral over a +path and what we did was instead of + + align:start position:0% +path and what we did was instead of + + + align:start position:0% +path and what we did was instead of +trying to look at a bunch of paths and + + align:start position:0% +trying to look at a bunch of paths and + + + align:start position:0% +trying to look at a bunch of paths and +figure out uh what would minimize that + + align:start position:0% +figure out uh what would minimize that + + + align:start position:0% +figure out uh what would minimize that +we tried to see if Green's theorem would + + align:start position:0% +we tried to see if Green's theorem would + + + align:start position:0% +we tried to see if Green's theorem would +help us so Green's theorem allowed us to + + align:start position:0% +help us so Green's theorem allowed us to + + + align:start position:0% +help us so Green's theorem allowed us to +take something that was an integral over + + align:start position:0% +take something that was an integral over + + + align:start position:0% +take something that was an integral over +a path and change it to an integral over + + align:start position:0% +a path and change it to an integral over + + + align:start position:0% +a path and change it to an integral over +a region and then when we look at what + + align:start position:0% +a region and then when we look at what + + + align:start position:0% +a region and then when we look at what +we ended up with we realized that we + + align:start position:0% +we ended up with we realized that we + + + align:start position:0% +we ended up with we realized that we +could make this as small as the most + + align:start position:0% +could make this as small as the most + + + align:start position:0% +could make this as small as the most +minimum if we let this this be on the + + align:start position:0% +minimum if we let this this be on the + + + align:start position:0% +minimum if we let this this be on the +region where it was negative everywhere + + align:start position:0% +region where it was negative everywhere + + + align:start position:0% +region where it was negative everywhere +so we were looking for a region where + + align:start position:0% +so we were looking for a region where + + + align:start position:0% +so we were looking for a region where +this quantity was everywhere negative on + + align:start position:0% +this quantity was everywhere negative on + + + align:start position:0% +this quantity was everywhere negative on +the inside and zero on the boundary and + + align:start position:0% +the inside and zero on the boundary and + + + align:start position:0% +the inside and zero on the boundary and +that's exactly what we did and then we + + align:start position:0% +that's exactly what we did and then we + + + align:start position:0% +that's exactly what we did and then we +see that we get to a where the boundary + + align:start position:0% +see that we get to a where the boundary + + + align:start position:0% +see that we get to a where the boundary +has this equation x^2 + 4 y^2 4 we see + + align:start position:0% +has this equation x^2 + 4 y^2 4 we see + + + align:start position:0% +has this equation x^2 + 4 y^2 4 we see +that the boundar is an ellipse and C is + + align:start position:0% +that the boundar is an ellipse and C is + + + align:start position:0% +that the boundar is an ellipse and C is +indeed the boundary of the region so we + + align:start position:0% +indeed the boundary of the region so we + + + align:start position:0% +indeed the boundary of the region so we +see that c is the ellipse described by + + align:start position:0% +see that c is the ellipse described by + + + align:start position:0% +see that c is the ellipse described by +this equation so that's where all stop \ No newline at end of file diff --git a/gwa-Rh0u6bs.txt b/gwa-Rh0u6bs.txt new file mode 100644 index 0000000000000000000000000000000000000000..9b0c2728ac77cbf064e4d4ba369d64a012abc50c --- /dev/null +++ b/gwa-Rh0u6bs.txt @@ -0,0 +1,7635 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% + + + + align:start position:0% + +hello welcome + + align:start position:0% +hello welcome + + + align:start position:0% +hello welcome +so as you might expect there's yet + + align:start position:0% +so as you might expect there's yet + + + align:start position:0% +so as you might expect there's yet +another announcement so this time exam + + align:start position:0% +another announcement so this time exam + + + align:start position:0% +another announcement so this time exam +three the last of the midterms same + + align:start position:0% +three the last of the midterms same + + + align:start position:0% +three the last of the midterms same +rules everything is roughly the same + + align:start position:0% +rules everything is roughly the same + + + align:start position:0% +rules everything is roughly the same +Walker next Wednesday 7:30 to 9:30 no + + align:start position:0% +Walker next Wednesday 7:30 to 9:30 no + + + align:start position:0% +Walker next Wednesday 7:30 to 9:30 no +recitations on the day of the exam + + align:start position:0% +recitations on the day of the exam + + + align:start position:0% +recitations on the day of the exam +coverage through lecture 18 which is + + align:start position:0% +coverage through lecture 18 which is + + + align:start position:0% +coverage through lecture 18 which is +next lecture coverage through recitation + + align:start position:0% +next lecture coverage through recitation + + + align:start position:0% +next lecture coverage through recitation +16 that's tomorrow homeworks 1 the 10:00 + + align:start position:0% +16 that's tomorrow homeworks 1 the 10:00 + + + align:start position:0% +16 that's tomorrow homeworks 1 the 10:00 +homework 10:00 won't be graded there + + align:start position:0% +homework 10:00 won't be graded there + + + align:start position:0% +homework 10:00 won't be graded there +will be solutions posted three pages + + align:start position:0% +will be solutions posted three pages + + + align:start position:0% +will be solutions posted three pages +year old two plus one no calculators + + align:start position:0% +year old two plus one no calculators + + + align:start position:0% +year old two plus one no calculators +blah blah blah same as last time + + align:start position:0% +blah blah blah same as last time + + + align:start position:0% +blah blah blah same as last time +designed to be one hour two hours to + + align:start position:0% +designed to be one hour two hours to + + + align:start position:0% +designed to be one hour two hours to +complete same as last time + + align:start position:0% +complete same as last time + + + align:start position:0% +complete same as last time +there'll be a review session there'll be + + align:start position:0% +there'll be a review session there'll be + + + align:start position:0% +there'll be a review session there'll be +one on Monday at 3 p.m. in 36 112 and of + + align:start position:0% +one on Monday at 3 p.m. in 36 112 and of + + + align:start position:0% +one on Monday at 3 p.m. in 36 112 and of +course you can ask any review questions + + align:start position:0% +course you can ask any review questions + + + align:start position:0% +course you can ask any review questions +you'd like any of the open office hours + + align:start position:0% +you'd like any of the open office hours + + + align:start position:0% +you'd like any of the open office hours +but there'll be a formal review in 36 + + align:start position:0% +but there'll be a formal review in 36 + + + align:start position:0% +but there'll be a formal review in 36 +112 on Monday at 3:00 prior term exams + + align:start position:0% +112 on Monday at 3:00 prior term exams + + + align:start position:0% +112 on Monday at 3:00 prior term exams +have already been posted and if you have + + align:start position:0% +have already been posted and if you have + + + align:start position:0% +have already been posted and if you have +a conflict please tell me because I have + + align:start position:0% +a conflict please tell me because I have + + + align:start position:0% +a conflict please tell me because I have +to find rooms and a proctor ok questions + + align:start position:0% +to find rooms and a proctor ok questions + + + align:start position:0% +to find rooms and a proctor ok questions +comments completely routine at this + + align:start position:0% +comments completely routine at this + + + align:start position:0% +comments completely routine at this +point right no problems everybody knows + + align:start position:0% +point right no problems everybody knows + + + align:start position:0% +point right no problems everybody knows +what they're doing + + align:start position:0% +what they're doing + + + align:start position:0% +what they're doing +it'll be fun it'll be enjoyable smile + + align:start position:0% + + + + align:start position:0% + +questions comments ok so what I want to + + align:start position:0% +questions comments ok so what I want to + + + align:start position:0% +questions comments ok so what I want to +talk today about is DT signal processing + + align:start position:0% +talk today about is DT signal processing + + + align:start position:0% +talk today about is DT signal processing +so formally I'm going to talk about + + align:start position:0% +so formally I'm going to talk about + + + align:start position:0% +so formally I'm going to talk about +things like DT Fourier series next time + + align:start position:0% +things like DT Fourier series next time + + + align:start position:0% +things like DT Fourier series next time +we'll talk about DT Fourier transform + + align:start position:0% +we'll talk about DT Fourier transform + + + align:start position:0% +we'll talk about DT Fourier transform +but the context for that the reason we + + align:start position:0% +but the context for that the reason we + + + align:start position:0% +but the context for that the reason we +do this is because the discrete-time + + align:start position:0% +do this is because the discrete-time + + + align:start position:0% +do this is because the discrete-time +approaches are so useful for processing + + align:start position:0% +approaches are so useful for processing + + + align:start position:0% +approaches are so useful for processing +signals and I want to motivate that by + + align:start position:0% +signals and I want to motivate that by + + + align:start position:0% +signals and I want to motivate that by +thinking about how signal processing has + + align:start position:0% +thinking about how signal processing has + + + align:start position:0% +thinking about how signal processing has +been viewed historically for over the + + align:start position:0% +been viewed historically for over the + + + align:start position:0% +been viewed historically for over the +past 20 or 30 years there's been + + align:start position:0% +past 20 or 30 years there's been + + + align:start position:0% +past 20 or 30 years there's been +enormous interest in signal processing + + align:start position:0% +enormous interest in signal processing + + + align:start position:0% +enormous interest in signal processing +and most of that interest evolved out of + + align:start position:0% +and most of that interest evolved out of + + + align:start position:0% +and most of that interest evolved out of +CTE applications that we wanted to make + + align:start position:0% +CTE applications that we wanted to make + + + align:start position:0% +CTE applications that we wanted to make +better we wanted to make + + align:start position:0% +better we wanted to make + + + align:start position:0% +better we wanted to make +radio reception better we want to make + + align:start position:0% +radio reception better we want to make + + + align:start position:0% +radio reception better we want to make +telephone reception better we want to + + align:start position:0% +telephone reception better we want to + + + align:start position:0% +telephone reception better we want to +make hi-fi's work better we wanted to + + align:start position:0% +make hi-fi's work better we wanted to + + + align:start position:0% +make hi-fi's work better we wanted to +make television work better photography + + align:start position:0% +make television work better photography + + + align:start position:0% +make television work better photography +x-rays bla bla bla + + align:start position:0% +x-rays bla bla bla + + + align:start position:0% +x-rays bla bla bla +there were lots of reasons why we wanted + + align:start position:0% +there were lots of reasons why we wanted + + + align:start position:0% +there were lots of reasons why we wanted +to be able to alter the signals that + + align:start position:0% +to be able to alter the signals that + + + align:start position:0% +to be able to alter the signals that +were available to us so for example in + + align:start position:0% +were available to us so for example in + + + align:start position:0% +were available to us so for example in +radio how do you alter the signal so as + + align:start position:0% +radio how do you alter the signal so as + + + align:start position:0% +radio how do you alter the signal so as +to reduce static in the early radios + + align:start position:0% +to reduce static in the early radios + + + align:start position:0% +to reduce static in the early radios +there's a big problem with automatic + + align:start position:0% +there's a big problem with automatic + + + align:start position:0% +there's a big problem with automatic +gain control so as you went over the + + align:start position:0% +gain control so as you went over the + + + align:start position:0% +gain control so as you went over the +hills the the line-of-sight to the radio + + align:start position:0% +hills the the line-of-sight to the radio + + + align:start position:0% +hills the the line-of-sight to the radio +station changed and that changed the + + align:start position:0% +station changed and that changed the + + + align:start position:0% +station changed and that changed the +game so there's an interesting + + align:start position:0% +game so there's an interesting + + + align:start position:0% +game so there's an interesting +controlling game so there were lots of + + align:start position:0% +controlling game so there were lots of + + + align:start position:0% +controlling game so there were lots of +applications where we wanted to account + + align:start position:0% +applications where we wanted to account + + + align:start position:0% +applications where we wanted to account +for deficiencies in the hardware and + + align:start position:0% +for deficiencies in the hardware and + + + align:start position:0% +for deficiencies in the hardware and +that gave rise to the notion of signal + + align:start position:0% +that gave rise to the notion of signal + + + align:start position:0% +that gave rise to the notion of signal +processing those signal processing + + align:start position:0% +processing those signal processing + + + align:start position:0% +processing those signal processing +applications were largely in continuous + + align:start position:0% +applications were largely in continuous + + + align:start position:0% +applications were largely in continuous +time because the signals were largely in + + align:start position:0% +time because the signals were largely in + + + align:start position:0% +time because the signals were largely in +continuous time all that's changed now + + align:start position:0% +continuous time all that's changed now + + + align:start position:0% +continuous time all that's changed now +when you say signal processing you + + align:start position:0% +when you say signal processing you + + + align:start position:0% +when you say signal processing you +almost always mean discrete and there's + + align:start position:0% +almost always mean discrete and there's + + + align:start position:0% +almost always mean discrete and there's +a very good reason for it and it's + + align:start position:0% +a very good reason for it and it's + + + align:start position:0% +a very good reason for it and it's +digital electronics digital electronics + + align:start position:0% +digital electronics digital electronics + + + align:start position:0% +digital electronics digital electronics +are very inexpensive and they worked + + align:start position:0% +are very inexpensive and they worked + + + align:start position:0% +are very inexpensive and they worked +very well I want to give just one + + align:start position:0% +very well I want to give just one + + + align:start position:0% +very well I want to give just one +example chosen from my history so like + + align:start position:0% +example chosen from my history so like + + + align:start position:0% +example chosen from my history so like +most teenage people when I was teenage + + align:start position:0% +most teenage people when I was teenage + + + align:start position:0% +most teenage people when I was teenage +once right there was a long time ago but + + align:start position:0% +once right there was a long time ago but + + + align:start position:0% +once right there was a long time ago but +I was one once and like most teenage + + align:start position:0% +I was one once and like most teenage + + + align:start position:0% +I was one once and like most teenage +types even then we got afflicted with + + align:start position:0% +types even then we got afflicted with + + + align:start position:0% +types even then we got afflicted with +the audio HiFi listen to music virus + + align:start position:0% +the audio HiFi listen to music virus + + + align:start position:0% +the audio HiFi listen to music virus +problem I mean the good news is I + + align:start position:0% +problem I mean the good news is I + + + align:start position:0% +problem I mean the good news is I +recover it I'm fully functional it's + + align:start position:0% +recover it I'm fully functional it's + + + align:start position:0% +recover it I'm fully functional it's +gone right so you have every reason to + + align:start position:0% +gone right so you have every reason to + + + align:start position:0% +gone right so you have every reason to +think that you'll recover but that was a + + align:start position:0% +think that you'll recover but that was a + + + align:start position:0% +think that you'll recover but that was a +problem I was interested in hi-fi and + + align:start position:0% +problem I was interested in hi-fi and + + + align:start position:0% +problem I was interested in hi-fi and +it's and that was a hard problem + + align:start position:0% +it's and that was a hard problem + + + align:start position:0% +it's and that was a hard problem +so the idea so if you think about how do + + align:start position:0% +so the idea so if you think about how do + + + align:start position:0% +so the idea so if you think about how do +you make a speaker system one of the + + align:start position:0% +you make a speaker system one of the + + + align:start position:0% +you make a speaker system one of the +problems that you get when you try to + + align:start position:0% +problems that you get when you try to + + + align:start position:0% +problems that you get when you try to +design a speaker system is reproducing + + align:start position:0% +design a speaker system is reproducing + + + align:start position:0% +design a speaker system is reproducing +low frequencies and my guess is that + + align:start position:0% +low frequencies and my guess is that + + + align:start position:0% +low frequencies and my guess is that +you're as interested in low frequencies + + align:start position:0% +you're as interested in low frequencies + + + align:start position:0% +you're as interested in low frequencies +as we were back then the problem with + + align:start position:0% +as we were back then the problem with + + + align:start position:0% +as we were back then the problem with +low frequencies is that if you put us if + + align:start position:0% +low frequencies is that if you put us if + + + align:start position:0% +low frequencies is that if you put us if +you have just a speaker + + align:start position:0% + + + + align:start position:0% + +the speaker has an electromagnet the + + align:start position:0% +the speaker has an electromagnet the + + + align:start position:0% +the speaker has an electromagnet the +electromagnet moves so that it pushes + + align:start position:0% +electromagnet moves so that it pushes + + + align:start position:0% +electromagnet moves so that it pushes +the cone the cone pushes air this way + + align:start position:0% +the cone the cone pushes air this way + + + align:start position:0% +the cone the cone pushes air this way +but if the cones coming out it also + + align:start position:0% +but if the cones coming out it also + + + align:start position:0% +but if the cones coming out it also +pulls air that way so that's a problem + + align:start position:0% +pulls air that way so that's a problem + + + align:start position:0% +pulls air that way so that's a problem +because that means it can do that + + align:start position:0% +because that means it can do that + + + align:start position:0% +because that means it can do that +and the person who's over here hears + + align:start position:0% +and the person who's over here hears + + + align:start position:0% +and the person who's over here hears +nothing that's especially bad at low + + align:start position:0% +nothing that's especially bad at low + + + align:start position:0% +nothing that's especially bad at low +frequencies for reasons I won't go into + + align:start position:0% +frequencies for reasons I won't go into + + + align:start position:0% +frequencies for reasons I won't go into +it because the wavelengths are long but + + align:start position:0% +it because the wavelengths are long but + + + align:start position:0% +it because the wavelengths are long but +that's the problem so what do you do why + + align:start position:0% +that's the problem so what do you do why + + + align:start position:0% +that's the problem so what do you do why +are you putting in a box so you instead + + align:start position:0% +are you putting in a box so you instead + + + align:start position:0% +are you putting in a box so you instead +of having your speaker in space you put + + align:start position:0% +of having your speaker in space you put + + + align:start position:0% +of having your speaker in space you put +the speaker in a box + + align:start position:0% +the speaker in a box + + + align:start position:0% +the speaker in a box +now when the cone goes that way the air + + align:start position:0% +now when the cone goes that way the air + + + align:start position:0% +now when the cone goes that way the air +gets compressed toward the person that's + + align:start position:0% +gets compressed toward the person that's + + + align:start position:0% +gets compressed toward the person that's +our second person and and now the air + + align:start position:0% +our second person and and now the air + + + align:start position:0% +our second person and and now the air +that goes this way is constrained to the + + align:start position:0% +that goes this way is constrained to the + + + align:start position:0% +that goes this way is constrained to the +cavity it constrained to the box so it + + align:start position:0% +cavity it constrained to the box so it + + + align:start position:0% +cavity it constrained to the box so it +doesn't interfere but what's the new + + align:start position:0% +doesn't interfere but what's the new + + + align:start position:0% +doesn't interfere but what's the new +problem so putting in the Box solves one + + align:start position:0% +problem so putting in the Box solves one + + + align:start position:0% +problem so putting in the Box solves one +problem but it introduced a new problem + + align:start position:0% +problem but it introduced a new problem + + + align:start position:0% +problem but it introduced a new problem +what's the new problem box will vibrate + + align:start position:0% +what's the new problem box will vibrate + + + align:start position:0% +what's the new problem box will vibrate +even worse + + align:start position:0% + + + + align:start position:0% + +native pressure so how does that show up + + align:start position:0% +native pressure so how does that show up + + + align:start position:0% +native pressure so how does that show up +as a performance problem that's exactly + + align:start position:0% +as a performance problem that's exactly + + + align:start position:0% +as a performance problem that's exactly +right + + align:start position:0% +right + + + align:start position:0% +right +what's the problem that you that's + + align:start position:0% +what's the problem that you that's + + + align:start position:0% +what's the problem that you that's +generated because of the negative + + align:start position:0% +generated because of the negative + + + align:start position:0% +generated because of the negative +pressure in the box yeah so there's + + align:start position:0% +pressure in the box yeah so there's + + + align:start position:0% +pressure in the box yeah so there's +something to do with gain that's exactly + + align:start position:0% +something to do with gain that's exactly + + + align:start position:0% +something to do with gain that's exactly +right + + align:start position:0% +right + + + align:start position:0% +right +because of the negative pressure what + + align:start position:0% +because of the negative pressure what + + + align:start position:0% +because of the negative pressure what +happens to the speaker cone yeah it + + align:start position:0% +happens to the speaker cone yeah it + + + align:start position:0% +happens to the speaker cone yeah it +can't move you put a load on it if if in + + align:start position:0% +can't move you put a load on it if if in + + + align:start position:0% +can't move you put a load on it if if in +order to move if in order to come out + + align:start position:0% +order to move if in order to come out + + + align:start position:0% +order to move if in order to come out +you have to generate negative pressure + + align:start position:0% +you have to generate negative pressure + + + align:start position:0% +you have to generate negative pressure +but the negative pressure is going to + + align:start position:0% +but the negative pressure is going to + + + align:start position:0% +but the negative pressure is going to +pull it back in so the problem is you + + align:start position:0% +pull it back in so the problem is you + + + align:start position:0% +pull it back in so the problem is you +put the speaker in the Box now you no + + align:start position:0% +put the speaker in the Box now you no + + + align:start position:0% +put the speaker in the Box now you no +longer have the short-circuit of the + + align:start position:0% +longer have the short-circuit of the + + + align:start position:0% +longer have the short-circuit of the +acoustic path however you've now + + align:start position:0% +acoustic path however you've now + + + align:start position:0% +acoustic path however you've now +introduced a load which makes the + + align:start position:0% +introduced a load which makes the + + + align:start position:0% +introduced a load which makes the +speaker much harder to move everyone + + align:start position:0% +speaker much harder to move everyone + + + align:start position:0% +speaker much harder to move everyone +with me so the problem was you put the + + align:start position:0% +with me so the problem was you put the + + + align:start position:0% +with me so the problem was you put the +speaker in the box and now the speaker + + align:start position:0% +speaker in the box and now the speaker + + + align:start position:0% +speaker in the box and now the speaker +which was making a lot of air motion + + align:start position:0% +which was making a lot of air motion + + + align:start position:0% +which was making a lot of air motion +makes very little air motion because of + + align:start position:0% +makes very little air motion because of + + + align:start position:0% +makes very little air motion because of +the box so what do you do next make the + + align:start position:0% +the box so what do you do next make the + + + align:start position:0% +the box so what do you do next make the +Box big okay well that works for a while + + align:start position:0% +Box big okay well that works for a while + + + align:start position:0% +Box big okay well that works for a while +ideally if you were trying to build a + + align:start position:0% +ideally if you were trying to build a + + + align:start position:0% +ideally if you were trying to build a +speaker for this room you would make a + + align:start position:0% +speaker for this room you would make a + + + align:start position:0% +speaker for this room you would make a +box this size well that's kind of an + + align:start position:0% +box this size well that's kind of an + + + align:start position:0% +box this size well that's kind of an +architectural waste so that's not really + + align:start position:0% +architectural waste so that's not really + + + align:start position:0% +architectural waste so that's not really +the right solution so here's a solution + + align:start position:0% +the right solution so here's a solution + + + align:start position:0% +the right solution so here's a solution +here's an acoustic solution that was + + align:start position:0% +here's an acoustic solution that was + + + align:start position:0% +here's an acoustic solution that was +very popular when I was in your age so + + align:start position:0% +very popular when I was in your age so + + + align:start position:0% +very popular when I was in your age so +this is called a reflex port so the idea + + align:start position:0% +this is called a reflex port so the idea + + + align:start position:0% +this is called a reflex port so the idea +is make a hole in the box so if you make + + align:start position:0% +is make a hole in the box so if you make + + + align:start position:0% +is make a hole in the box so if you make +a hole in the box + + align:start position:0% + + + + align:start position:0% + +okay now you're back to the same problem + + align:start position:0% +okay now you're back to the same problem + + + align:start position:0% +okay now you're back to the same problem +that if the speaker comes out this way + + align:start position:0% +that if the speaker comes out this way + + + align:start position:0% +that if the speaker comes out this way +then it sucks air that way that's bad so + + align:start position:0% +then it sucks air that way that's bad so + + + align:start position:0% +then it sucks air that way that's bad so +what you do instead is you put a tube + + align:start position:0% +what you do instead is you put a tube + + + align:start position:0% +what you do instead is you put a tube +and if you make the length of the tube + + align:start position:0% +and if you make the length of the tube + + + align:start position:0% +and if you make the length of the tube +exactly the right size there's mass + + align:start position:0% +exactly the right size there's mass + + + align:start position:0% +exactly the right size there's mass +entrained in the tube and then you have + + align:start position:0% +entrained in the tube and then you have + + + align:start position:0% +entrained in the tube and then you have +a system where the air is springy + + align:start position:0% +a system where the air is springy + + + align:start position:0% +a system where the air is springy +but there's mass in here and you get a + + align:start position:0% +but there's mass in here and you get a + + + align:start position:0% +but there's mass in here and you get a +mass spring dashpot so now when this is + + align:start position:0% +mass spring dashpot so now when this is + + + align:start position:0% +mass spring dashpot so now when this is +going in and out the air goes + + align:start position:0% +going in and out the air goes + + + align:start position:0% +going in and out the air goes +this tube and if you adjust the length + + align:start position:0% +this tube and if you adjust the length + + + align:start position:0% +this tube and if you adjust the length +of the tube so you get the mass right + + align:start position:0% +of the tube so you get the mass right + + + align:start position:0% +of the tube so you get the mass right +you can get them going in phase anyone + + align:start position:0% +you can get them going in phase anyone + + + align:start position:0% +you can get them going in phase anyone +have a clue and I just talked about the + + align:start position:0% +have a clue and I just talked about the + + + align:start position:0% +have a clue and I just talked about the +idea was to use mass spring dashpot + + align:start position:0% +idea was to use mass spring dashpot + + + align:start position:0% +idea was to use mass spring dashpot +resonance theory to change the acoustics + + align:start position:0% +resonance theory to change the acoustics + + + align:start position:0% +resonance theory to change the acoustics +of a speaker box so you get more low + + align:start position:0% +of a speaker box so you get more low + + + align:start position:0% +of a speaker box so you get more low +frequencies out that was the way we + + align:start position:0% +frequencies out that was the way we + + + align:start position:0% +frequencies out that was the way we +thought about speaker design back then + + align:start position:0% +thought about speaker design back then + + + align:start position:0% +thought about speaker design back then +the speakers that I bought were the + + align:start position:0% +the speakers that I bought were the + + + align:start position:0% +the speakers that I bought were the +electric voice interface A's right at + + align:start position:0% +electric voice interface A's right at + + + align:start position:0% +electric voice interface A's right at +that time they cost about $1,500 I was + + align:start position:0% +that time they cost about $1,500 I was + + + align:start position:0% +that time they cost about $1,500 I was +making $600 a month so times have + + align:start position:0% +making $600 a month so times have + + + align:start position:0% +making $600 a month so times have +changed slightly + + align:start position:0% +changed slightly + + + align:start position:0% +changed slightly +so $1500 was then a fortune but I had to + + align:start position:0% +so $1500 was then a fortune but I had to + + + align:start position:0% +so $1500 was then a fortune but I had to +have them right I mean there was any + + align:start position:0% +have them right I mean there was any + + + align:start position:0% +have them right I mean there was any +question and the way these worked was + + align:start position:0% +question and the way these worked was + + + align:start position:0% +question and the way these worked was +like the reflex design so in the reflex + + align:start position:0% +like the reflex design so in the reflex + + + align:start position:0% +like the reflex design so in the reflex +design we had the port that was tuned so + + align:start position:0% +design we had the port that was tuned so + + + align:start position:0% +design we had the port that was tuned so +the mass resonated against the stiffness + + align:start position:0% +the mass resonated against the stiffness + + + align:start position:0% +the mass resonated against the stiffness +of the air here what you did this was + + align:start position:0% +of the air here what you did this was + + + align:start position:0% +of the air here what you did this was +not a speaker this is the speaker and + + align:start position:0% +not a speaker this is the speaker and + + + align:start position:0% +not a speaker this is the speaker and +the idea was that you adjust the mass + + align:start position:0% +the idea was that you adjust the mass + + + align:start position:0% +the idea was that you adjust the mass +and stiffness of this big passive thing + + align:start position:0% +and stiffness of this big passive thing + + + align:start position:0% +and stiffness of this big passive thing +there were no electrical wires hooked up + + align:start position:0% +there were no electrical wires hooked up + + + align:start position:0% +there were no electrical wires hooked up +to that thing that was called a passive + + align:start position:0% +to that thing that was called a passive + + + align:start position:0% +to that thing that was called a passive +resonator it was tuned so that when the + + align:start position:0% +resonator it was tuned so that when the + + + align:start position:0% +resonator it was tuned so that when the +when the eight-inch speaker up here was + + align:start position:0% +when the eight-inch speaker up here was + + + align:start position:0% +when the eight-inch speaker up here was +trying to move it would move in + + align:start position:0% +trying to move it would move in + + + align:start position:0% +trying to move it would move in +resonance so that it was out of phase + + align:start position:0% +resonance so that it was out of phase + + + align:start position:0% +resonance so that it was out of phase +with the 8 inch speaker up on the top so + + align:start position:0% +with the 8 inch speaker up on the top so + + + align:start position:0% +with the 8 inch speaker up on the top so +they were both going in and out at the + + align:start position:0% +they were both going in and out at the + + + align:start position:0% +they were both going in and out at the +same time same sort of ideas the reflex + + align:start position:0% +same time same sort of ideas the reflex + + + align:start position:0% +same time same sort of ideas the reflex +but you could get a bigger motion from + + align:start position:0% +but you could get a bigger motion from + + + align:start position:0% +but you could get a bigger motion from +this passive resonator than you could + + align:start position:0% +this passive resonator than you could + + + align:start position:0% +this passive resonator than you could +with the acoustic reflex so that's not + + align:start position:0% +with the acoustic reflex so that's not + + + align:start position:0% +with the acoustic reflex so that's not +the way we solve it so the next big + + align:start position:0% +the way we solve it so the next big + + + align:start position:0% +the way we solve it so the next big +advance was by amar Bose Bose was here + + align:start position:0% +advance was by amar Bose Bose was here + + + align:start position:0% +advance was by amar Bose Bose was here +at the time he's professor and electro + + align:start position:0% +at the time he's professor and electro + + + align:start position:0% +at the time he's professor and electro +engineering at that time and he invented + + align:start position:0% +engineering at that time and he invented + + + align:start position:0% +engineering at that time and he invented +the Bose 901 s which is something + + align:start position:0% +the Bose 901 s which is something + + + align:start position:0% +the Bose 901 s which is something +everybody had to have what Bose did that + + align:start position:0% +everybody had to have what Bose did that + + + align:start position:0% +everybody had to have what Bose did that +was extraordinarily clever he used + + align:start position:0% +was extraordinarily clever he used + + + align:start position:0% +was extraordinarily clever he used +really chintzy speakers cts speakers 4 + + align:start position:0% +really chintzy speakers cts speakers 4 + + + align:start position:0% +really chintzy speakers cts speakers 4 +inch diameter + + align:start position:0% +inch diameter + + + align:start position:0% +inch diameter +all right they had absolutely crummy + + align:start position:0% +all right they had absolutely crummy + + + align:start position:0% +all right they had absolutely crummy +frequency response flat up to a couple + + align:start position:0% +frequency response flat up to a couple + + + align:start position:0% +frequency response flat up to a couple +of hundred Hertz and then their response + + align:start position:0% +of hundred Hertz and then their response + + + align:start position:0% +of hundred Hertz and then their response +fell roughly with one pole so that by + + align:start position:0% +fell roughly with one pole so that by + + + align:start position:0% +fell roughly with one pole so that by +the time you get out to the highest + + align:start position:0% +the time you get out to the highest + + + align:start position:0% +the time you get out to the highest +frequencies that we can hear the + + align:start position:0% +frequencies that we can hear the + + + align:start position:0% +frequencies that we can hear the +response is greatly attenuated like 40 + + align:start position:0% +response is greatly attenuated like 40 + + + align:start position:0% +response is greatly attenuated like 40 +decibels 40 decibels is a factor of 100 + + align:start position:0% +decibels 40 decibels is a factor of 100 + + + align:start position:0% +decibels 40 decibels is a factor of 100 +and pressure so the problem is that this + + align:start position:0% +and pressure so the problem is that this + + + align:start position:0% +and pressure so the problem is that this +speakers so these speakers had exactly + + align:start position:0% +speakers so these speakers had exactly + + + align:start position:0% +speakers so these speakers had exactly +the same problems that we had in the + + align:start position:0% +the same problems that we had in the + + + align:start position:0% +the same problems that we had in the +riku state reflux problem except they + + align:start position:0% +riku state reflux problem except they + + + align:start position:0% +riku state reflux problem except they +were even worse this was an 8 inch + + align:start position:0% +were even worse this was an 8 inch + + + align:start position:0% +were even worse this was an 8 inch +speaker this is a 4 inch speaker so they + + align:start position:0% +speaker this is a 4 inch speaker so they + + + align:start position:0% +speaker this is a 4 inch speaker so they +were even worse but what Bose did he + + align:start position:0% +were even worse but what Bose did he + + + align:start position:0% +were even worse but what Bose did he +took advantage of electronics he put an + + align:start position:0% +took advantage of electronics he put an + + + align:start position:0% +took advantage of electronics he put an +electronic signal processing box to put + + align:start position:0% +electronic signal processing box to put + + + align:start position:0% +electronic signal processing box to put +the inverse filter so as to so the the + + align:start position:0% +the inverse filter so as to so the the + + + align:start position:0% +the inverse filter so as to so the the +Box pre-process the sound to boost the + + align:start position:0% +Box pre-process the sound to boost the + + + align:start position:0% +Box pre-process the sound to boost the +frequencies that he knew the speaker + + align:start position:0% +frequencies that he knew the speaker + + + align:start position:0% +frequencies that he knew the speaker +would attenuate so this box was filled + + align:start position:0% +would attenuate so this box was filled + + + align:start position:0% +would attenuate so this box was filled +with op amps Gaines buffers all the + + align:start position:0% +with op amps Gaines buffers all the + + + align:start position:0% +with op amps Gaines buffers all the +kinds of things you know about which + + align:start position:0% +kinds of things you know about which + + + align:start position:0% +kinds of things you know about which +were then just barely available that box + + align:start position:0% +were then just barely available that box + + + align:start position:0% +were then just barely available that box +cost a thousand dollars back daddy + + align:start position:0% +cost a thousand dollars back daddy + + + align:start position:0% +cost a thousand dollars back daddy +because that was very state-of-the-art + + align:start position:0% +because that was very state-of-the-art + + + align:start position:0% +because that was very state-of-the-art +so the idea was that he switched the + + align:start position:0% +so the idea was that he switched the + + + align:start position:0% +so the idea was that he switched the +problem from being acoustics problem to + + align:start position:0% +problem from being acoustics problem to + + + align:start position:0% +problem from being acoustics problem to +an electronics problem very clever today + + align:start position:0% +an electronics problem very clever today + + + align:start position:0% +an electronics problem very clever today +we go one more step and we do the signal + + align:start position:0% +we go one more step and we do the signal + + + align:start position:0% +we go one more step and we do the signal +processing digitally so any modern + + align:start position:0% +processing digitally so any modern + + + align:start position:0% +processing digitally so any modern +stereo system has a discrete time filter + + align:start position:0% +stereo system has a discrete time filter + + + align:start position:0% +stereo system has a discrete time filter +in it + + align:start position:0% +in it + + + align:start position:0% +in it +the idea is that you take the signal + + align:start position:0% +the idea is that you take the signal + + + align:start position:0% +the idea is that you take the signal +that's coming off the source like an + + align:start position:0% +that's coming off the source like an + + + align:start position:0% +that's coming off the source like an +MPEG no no like an mp3 sorry you take an + + align:start position:0% +MPEG no no like an mp3 sorry you take an + + + align:start position:0% +MPEG no no like an mp3 sorry you take an +mp3 type source you run it through a + + align:start position:0% +mp3 type source you run it through a + + + align:start position:0% +mp3 type source you run it through a +digital filter this is a filter that + + align:start position:0% +digital filter this is a filter that + + + align:start position:0% +digital filter this is a filter that +works on numbers not on volts and so you + + align:start position:0% +works on numbers not on volts and so you + + + align:start position:0% +works on numbers not on volts and so you +convert the source from the mp3 into a + + align:start position:0% +convert the source from the mp3 into a + + + align:start position:0% +convert the source from the mp3 into a +stream of numbers that get crunched + + align:start position:0% +stream of numbers that get crunched + + + align:start position:0% +stream of numbers that get crunched +digitally giving rise to a different + + align:start position:0% +digitally giving rise to a different + + + align:start position:0% +digitally giving rise to a different +screech stream of numbers which you then + + align:start position:0% +screech stream of numbers which you then + + + align:start position:0% +screech stream of numbers which you then +convert back into an analogue + + align:start position:0% +convert back into an analogue + + + align:start position:0% +convert back into an analogue +signal this is the approach you'll find + + align:start position:0% +signal this is the approach you'll find + + + align:start position:0% +signal this is the approach you'll find +in every modern Cerio system the reason + + align:start position:0% +in every modern Cerio system the reason + + + align:start position:0% +in every modern Cerio system the reason +being that it works so well here's a + + align:start position:0% +being that it works so well here's a + + + align:start position:0% +being that it works so well here's a +chip the Texas Instruments tas 304 which + + align:start position:0% +chip the Texas Instruments tas 304 which + + + align:start position:0% +chip the Texas Instruments tas 304 which +was specifically designed for car + + align:start position:0% +was specifically designed for car + + + align:start position:0% +was specifically designed for car +stereos it's got amazing specs you it + + align:start position:0% +stereos it's got amazing specs you it + + + align:start position:0% +stereos it's got amazing specs you it +has two channels state-of-the-art + + align:start position:0% +has two channels state-of-the-art + + + align:start position:0% +has two channels state-of-the-art +converting rates state-of-the-art + + align:start position:0% +converting rates state-of-the-art + + + align:start position:0% +converting rates state-of-the-art +digitization it it has a processor + + align:start position:0% +digitization it it has a processor + + + align:start position:0% +digitization it it has a processor +internally that runs at 100 mega + + align:start position:0% +internally that runs at 100 mega + + + align:start position:0% +internally that runs at 100 mega +instructions per second it implements + + align:start position:0% +instructions per second it implements + + + align:start position:0% +instructions per second it implements +all the common things treble volume + + align:start position:0% +all the common things treble volume + + + align:start position:0% +all the common things treble volume +loudness everything you can imagine and + + align:start position:0% +loudness everything you can imagine and + + + align:start position:0% +loudness everything you can imagine and +it costs not nine dollars and 63 cents + + align:start position:0% +it costs not nine dollars and 63 cents + + + align:start position:0% +it costs not nine dollars and 63 cents +off digi-key in units of one and if you + + align:start position:0% +off digi-key in units of one and if you + + + align:start position:0% +off digi-key in units of one and if you +buy units of 500 they are five dollars + + align:start position:0% +buy units of 500 they are five dollars + + + align:start position:0% +buy units of 500 they are five dollars +and 20 cents apiece a trivial amount of + + align:start position:0% +and 20 cents apiece a trivial amount of + + + align:start position:0% +and 20 cents apiece a trivial amount of +money by any standard so the idea then + + align:start position:0% +money by any standard so the idea then + + + align:start position:0% +money by any standard so the idea then +is that it's just very effective to do + + align:start position:0% +is that it's just very effective to do + + + align:start position:0% +is that it's just very effective to do +number crunching digitally so that's + + align:start position:0% +number crunching digitally so that's + + + align:start position:0% +number crunching digitally so that's +what we want to talk about we want to + + align:start position:0% +what we want to talk about we want to + + + align:start position:0% +what we want to talk about we want to +talk about the same kinds of Fourier + + align:start position:0% +talk about the same kinds of Fourier + + + align:start position:0% +talk about the same kinds of Fourier +transforms and so for that we've talked + + align:start position:0% +transforms and so for that we've talked + + + align:start position:0% +transforms and so for that we've talked +about with CT signals but we want to new + + align:start position:0% +about with CT signals but we want to new + + + align:start position:0% +about with CT signals but we want to new +that we want to know the new set of + + align:start position:0% +that we want to know the new set of + + + align:start position:0% +that we want to know the new set of +rules that apply when the signals are + + align:start position:0% +rules that apply when the signals are + + + align:start position:0% +rules that apply when the signals are +discrete in time + + align:start position:0% +discrete in time + + + align:start position:0% +discrete in time +okay everybody with me so this is just a + + align:start position:0% +okay everybody with me so this is just a + + + align:start position:0% +okay everybody with me so this is just a +little bit of review you'll remember + + align:start position:0% +little bit of review you'll remember + + + align:start position:0% +little bit of review you'll remember +that we started with discrete time we + + align:start position:0% +that we started with discrete time we + + + align:start position:0% +that we started with discrete time we +did examples in discrete time when we + + align:start position:0% +did examples in discrete time when we + + + align:start position:0% +did examples in discrete time when we +were thinking about feedback then we + + align:start position:0% +were thinking about feedback then we + + + align:start position:0% +were thinking about feedback then we +went on to CT and thought about feedback + + align:start position:0% +went on to CT and thought about feedback + + + align:start position:0% +went on to CT and thought about feedback +systems and so forth then we did CT + + align:start position:0% +systems and so forth then we did CT + + + align:start position:0% +systems and so forth then we did CT +Fourier because I think the Fourier stop + + align:start position:0% +Fourier because I think the Fourier stop + + + align:start position:0% +Fourier because I think the Fourier stop +is easier to see in CTE now we're + + align:start position:0% +is easier to see in CTE now we're + + + align:start position:0% +is easier to see in CTE now we're +folding back to do DT so it's it's been + + align:start position:0% +folding back to do DT so it's it's been + + + align:start position:0% +folding back to do DT so it's it's been +about six weeks since we talked about DT + + align:start position:0% +about six weeks since we talked about DT + + + align:start position:0% +about six weeks since we talked about DT +so a little bit of refresher the first + + align:start position:0% +so a little bit of refresher the first + + + align:start position:0% +so a little bit of refresher the first +thing we're going to we're going to be + + align:start position:0% +thing we're going to we're going to be + + + align:start position:0% +thing we're going to we're going to be +thinking about frequency responses right + + align:start position:0% +thinking about frequency responses right + + + align:start position:0% +thinking about frequency responses right +that was the basis of the Fourier + + align:start position:0% +that was the basis of the Fourier + + + align:start position:0% +that was the basis of the Fourier +transform that's going to be the basis + + align:start position:0% +transform that's going to be the basis + + + align:start position:0% +transform that's going to be the basis +of the Fourier signal processing in + + align:start position:0% +of the Fourier signal processing in + + + align:start position:0% +of the Fourier signal processing in +discrete time and the idea of frequency + + align:start position:0% +discrete time and the idea of frequency + + + align:start position:0% +discrete time and the idea of frequency +analysis starts with the idea of an + + align:start position:0% +analysis starts with the idea of an + + + align:start position:0% +analysis starts with the idea of an +eigenfunction the eigenfunctions for a + + align:start position:0% +eigenfunction the eigenfunctions for a + + + align:start position:0% +eigenfunction the eigenfunctions for a +discrete-time system are very similar to + + align:start position:0% +discrete-time system are very similar to + + + align:start position:0% +discrete-time system are very similar to +the eigen + + align:start position:0% +the eigen + + + align:start position:0% +the eigen +for a discreet for a continuous time but + + align:start position:0% +for a discreet for a continuous time but + + + align:start position:0% +for a discreet for a continuous time but +they're different right the + + align:start position:0% +they're different right the + + + align:start position:0% +they're different right the +eigenfunctions for CG system are complex + + align:start position:0% +eigenfunctions for CG system are complex + + + align:start position:0% +eigenfunctions for CG system are complex +exponentials edst not your head it made + + align:start position:0% +exponentials edst not your head it made + + + align:start position:0% +exponentials edst not your head it made +me feel good to think that you can + + align:start position:0% +me feel good to think that you can + + + align:start position:0% +me feel good to think that you can +remember that we did e to the st at one + + align:start position:0% +remember that we did e to the st at one + + + align:start position:0% +remember that we did e to the st at one +point so the eigenfunctions for CT + + align:start position:0% +point so the eigenfunctions for CT + + + align:start position:0% +point so the eigenfunctions for CT +systems are complex Exponential's e to + + align:start position:0% +systems are complex Exponential's e to + + + align:start position:0% +systems are complex Exponential's e to +the st eigenfunctions for D T systems + + align:start position:0% +the st eigenfunctions for D T systems + + + align:start position:0% +the st eigenfunctions for D T systems +are complex geometrics complex geometric + + align:start position:0% +are complex geometrics complex geometric + + + align:start position:0% +are complex geometrics complex geometric +sin DT play the same role as complex + + align:start position:0% +sin DT play the same role as complex + + + align:start position:0% +sin DT play the same role as complex +Exponential's in CTE and they play that + + align:start position:0% +Exponential's in CTE and they play that + + + align:start position:0% +Exponential's in CTE and they play that +role for exactly the same reason so when + + align:start position:0% +role for exactly the same reason so when + + + align:start position:0% +role for exactly the same reason so when +we wanted to prove that the complex + + align:start position:0% +we wanted to prove that the complex + + + align:start position:0% +we wanted to prove that the complex +Exponential's were eigenfunctions of LTI + + align:start position:0% +Exponential's were eigenfunctions of LTI + + + align:start position:0% +Exponential's were eigenfunctions of LTI +systems we took the complex exponential + + align:start position:0% +systems we took the complex exponential + + + align:start position:0% +systems we took the complex exponential +and week involved it with the impulse + + align:start position:0% +and week involved it with the impulse + + + align:start position:0% +and week involved it with the impulse +response of an LTI system all LTI + + align:start position:0% +response of an LTI system all LTI + + + align:start position:0% +response of an LTI system all LTI +systems can be represented by their + + align:start position:0% +systems can be represented by their + + + align:start position:0% +systems can be represented by their +impulse response if you convolve any + + align:start position:0% +impulse response if you convolve any + + + align:start position:0% +impulse response if you convolve any +real valued function with a complex + + align:start position:0% +real valued function with a complex + + + align:start position:0% +real valued function with a complex +exponential you get back a complex + + align:start position:0% +exponential you get back a complex + + + align:start position:0% +exponential you get back a complex +exponential of the same shape but + + align:start position:0% +exponential of the same shape but + + + align:start position:0% +exponential of the same shape but +possibly different amplitude complex + + align:start position:0% +possibly different amplitude complex + + + align:start position:0% +possibly different amplitude complex +amplitude same thing happens in DT so in + + align:start position:0% +amplitude same thing happens in DT so in + + + align:start position:0% +amplitude same thing happens in DT so in +order to see that that's true we think + + align:start position:0% +order to see that that's true we think + + + align:start position:0% +order to see that that's true we think +about the input to an LTI system being Z + + align:start position:0% +about the input to an LTI system being Z + + + align:start position:0% +about the input to an LTI system being Z +to the N complex exponential so Z is + + align:start position:0% +to the N complex exponential so Z is + + + align:start position:0% +to the N complex exponential so Z is +some complex number Z to the N is the + + align:start position:0% +some complex number Z to the N is the + + + align:start position:0% +some complex number Z to the N is the +evolution of the complex but the complex + + align:start position:0% +evolution of the complex but the complex + + + align:start position:0% +evolution of the complex but the complex +geometric as a function of time we let + + align:start position:0% +geometric as a function of time we let + + + align:start position:0% +geometric as a function of time we let +the system be represented by the + + align:start position:0% +the system be represented by the + + + align:start position:0% +the system be represented by the +unit-sample response the analogous which + + align:start position:0% +unit-sample response the analogous which + + + align:start position:0% +unit-sample response the analogous which +is analogous to the unit impulse + + align:start position:0% +is analogous to the unit impulse + + + align:start position:0% +is analogous to the unit impulse +response and we simply convolve the + + align:start position:0% +response and we simply convolve the + + + align:start position:0% +response and we simply convolve the +impulse the unit sample response with + + align:start position:0% +impulse the unit sample response with + + + align:start position:0% +impulse the unit sample response with +the complex geometric and if you go + + align:start position:0% +the complex geometric and if you go + + + align:start position:0% +the complex geometric and if you go +through the convolution sum it's a sum + + align:start position:0% +through the convolution sum it's a sum + + + align:start position:0% +through the convolution sum it's a sum +now because it's DT you find that the + + align:start position:0% +now because it's DT you find that the + + + align:start position:0% +now because it's DT you find that the +output has the same base Z that the + + align:start position:0% +output has the same base Z that the + + + align:start position:0% +output has the same base Z that the +input did but now the amplitude has been + + align:start position:0% +input did but now the amplitude has been + + + align:start position:0% +input did but now the amplitude has been +modified by the value of the system + + align:start position:0% +modified by the value of the system + + + align:start position:0% +modified by the value of the system +function evaluated at the location Z ok + + align:start position:0% +function evaluated at the location Z ok + + + align:start position:0% +function evaluated at the location Z ok +we did this before this is review + + align:start position:0% + + + + align:start position:0% + +similarly + + align:start position:0% +similarly + + + align:start position:0% +similarly +if you think about representing a + + align:start position:0% +if you think about representing a + + + align:start position:0% +if you think about representing a +discrete-time system in terms of a + + align:start position:0% +discrete-time system in terms of a + + + align:start position:0% +discrete-time system in terms of a +difference equation a linear difference + + align:start position:0% +difference equation a linear difference + + + align:start position:0% +difference equation a linear difference +equation with constant coefficients you + + align:start position:0% +equation with constant coefficients you + + + align:start position:0% +equation with constant coefficients you +can see that that type of system can + + align:start position:0% +can see that that type of system can + + + align:start position:0% +can see that that type of system can +always be represented by the ratio of + + align:start position:0% +always be represented by the ratio of + + + align:start position:0% +always be represented by the ratio of +polynomials in Z the same as with CT we + + align:start position:0% +polynomials in Z the same as with CT we + + + align:start position:0% +polynomials in Z the same as with CT we +had the ratio of polynomials in s here + + align:start position:0% +had the ratio of polynomials in s here + + + align:start position:0% +had the ratio of polynomials in s here +the cEPAL monomials in Z and if we want + + align:start position:0% +the cEPAL monomials in Z and if we want + + + align:start position:0% +the cEPAL monomials in Z and if we want +to evaluate that H of Z thing the system + + align:start position:0% +to evaluate that H of Z thing the system + + + align:start position:0% +to evaluate that H of Z thing the system +function there's a very easy way to do + + align:start position:0% +function there's a very easy way to do + + + align:start position:0% +function there's a very easy way to do +it since it's a polynomial there's + + align:start position:0% +it since it's a polynomial there's + + + align:start position:0% +it since it's a polynomial there's +nothing different about polynomials in Z + + align:start position:0% +nothing different about polynomials in Z + + + align:start position:0% +nothing different about polynomials in Z +and polynomials and ass insofar as there + + align:start position:0% +and polynomials and ass insofar as there + + + align:start position:0% +and polynomials and ass insofar as there +being polynomials the fact that there + + align:start position:0% +being polynomials the fact that there + + + align:start position:0% +being polynomials the fact that there +are polynomial means you can factor the + + align:start position:0% +are polynomial means you can factor the + + + align:start position:0% +are polynomial means you can factor the +numerator you can factor the denominator + + align:start position:0% +numerator you can factor the denominator + + + align:start position:0% +numerator you can factor the denominator +you can think about poles and zeros and + + align:start position:0% +you can think about poles and zeros and + + + align:start position:0% +you can think about poles and zeros and +you can evaluate the system function by + + align:start position:0% +you can evaluate the system function by + + + align:start position:0% +you can evaluate the system function by +after you factor the numerator and the + + align:start position:0% +after you factor the numerator and the + + + align:start position:0% +after you factor the numerator and the +denominator think about each + + align:start position:0% +denominator think about each + + + align:start position:0% +denominator think about each +contribution so Z naught minus Q naught + + align:start position:0% +contribution so Z naught minus Q naught + + + align:start position:0% +contribution so Z naught minus Q naught +so if I have a zero at Q naught and I + + align:start position:0% +so if I have a zero at Q naught and I + + + align:start position:0% +so if I have a zero at Q naught and I +want to know how big is the + + align:start position:0% +want to know how big is the + + + align:start position:0% +want to know how big is the +eigenfunction how big is the eigenvalue + + align:start position:0% +eigenfunction how big is the eigenvalue + + + align:start position:0% +eigenfunction how big is the eigenvalue +at Z naught I think about the arrow that + + align:start position:0% +at Z naught I think about the arrow that + + + align:start position:0% +at Z naught I think about the arrow that +connects the zero to the point of + + align:start position:0% +connects the zero to the point of + + + align:start position:0% +connects the zero to the point of +interest and I can say something about + + align:start position:0% +interest and I can say something about + + + align:start position:0% +interest and I can say something about +magnitude but the length of the arrow + + align:start position:0% +magnitude but the length of the arrow + + + align:start position:0% +magnitude but the length of the arrow +and the phase by the angle of the arrow + + align:start position:0% +and the phase by the angle of the arrow + + + align:start position:0% +and the phase by the angle of the arrow +same as CT and I get the same divide and + + align:start position:0% +same as CT and I get the same divide and + + + align:start position:0% +same as CT and I get the same divide and +conquer idea if I know how one zero + + align:start position:0% +conquer idea if I know how one zero + + + align:start position:0% +conquer idea if I know how one zero +works and if I know how one pole works I + + align:start position:0% +works and if I know how one pole works I + + + align:start position:0% +works and if I know how one pole works I +can combine the responses to the + + align:start position:0% +can combine the responses to the + + + align:start position:0% +can combine the responses to the +numerous poles in a complicated system + + align:start position:0% +numerous poles in a complicated system + + + align:start position:0% +numerous poles in a complicated system +in order to figure out how the + + align:start position:0% +in order to figure out how the + + + align:start position:0% +in order to figure out how the +complicated system works I can think + + align:start position:0% +complicated system works I can think + + + align:start position:0% +complicated system works I can think +about the poles and zeros one at a time + + align:start position:0% +about the poles and zeros one at a time + + + align:start position:0% +about the poles and zeros one at a time +just like I did for CT u so the + + align:start position:0% +just like I did for CT u so the + + + align:start position:0% +just like I did for CT u so the +magnitude is determined by the product + + align:start position:0% +magnitude is determined by the product + + + align:start position:0% +magnitude is determined by the product +and division of all of the factors all + + align:start position:0% +and division of all of the factors all + + + align:start position:0% +and division of all of the factors all +the magnitude factors and the angle is + + align:start position:0% +the magnitude factors and the angle is + + + align:start position:0% +the magnitude factors and the angle is +determined by the sum and difference of + + align:start position:0% +determined by the sum and difference of + + + align:start position:0% +determined by the sum and difference of +all the angle factors ok I'm going over + + align:start position:0% +all the angle factors ok I'm going over + + + align:start position:0% +all the angle factors ok I'm going over +this quickly but that's because I'm + + align:start position:0% +this quickly but that's because I'm + + + align:start position:0% +this quickly but that's because I'm +expecting that you know this you just + + align:start position:0% +expecting that you know this you just + + + align:start position:0% +expecting that you know this you just +need to be reminded if we want to think + + align:start position:0% +need to be reminded if we want to think + + + align:start position:0% +need to be reminded if we want to think +about the frequency response we do the + + align:start position:0% +about the frequency response we do the + + + align:start position:0% +about the frequency response we do the +same thing we did in CT we like complex + + align:start position:0% +same thing we did in CT we like complex + + + align:start position:0% +same thing we did in CT we like complex +geometrics + + align:start position:0% +geometrics + + + align:start position:0% +geometrics +so we try to think about the eternal + + align:start position:0% +so we try to think about the eternal + + + align:start position:0% +so we try to think about the eternal +cosine waves as being expressed in terms + + align:start position:0% +cosine waves as being expressed in terms + + + align:start position:0% +cosine waves as being expressed in terms +of complex geometrics the difference is + + align:start position:0% +of complex geometrics the difference is + + + align:start position:0% +of complex geometrics the difference is +that now we think about we think about + + align:start position:0% +that now we think about we think about + + + align:start position:0% +that now we think about we think about +this e to the J Omega naught n term so + + align:start position:0% +this e to the J Omega naught n term so + + + align:start position:0% +this e to the J Omega naught n term so +we used to think about so we have the + + align:start position:0% +we used to think about so we have the + + + align:start position:0% +we used to think about so we have the +same for me + + align:start position:0% +same for me + + + align:start position:0% +same for me +e to the J Omega naught T we thought + + align:start position:0% +e to the J Omega naught T we thought + + + align:start position:0% +e to the J Omega naught T we thought +about that as a complex exponential with + + align:start position:0% +about that as a complex exponential with + + + align:start position:0% +about that as a complex exponential with +a frequency Omega naught now we're + + align:start position:0% +a frequency Omega naught now we're + + + align:start position:0% +a frequency Omega naught now we're +thinking about e to the J Omega naught + + align:start position:0% +thinking about e to the J Omega naught + + + align:start position:0% +thinking about e to the J Omega naught +and as Z being this e to the J Omega + + align:start position:0% +and as Z being this e to the J Omega + + + align:start position:0% +and as Z being this e to the J Omega +naught thing it's the same thing it's + + align:start position:0% +naught thing it's the same thing it's + + + align:start position:0% +naught thing it's the same thing it's +still oars equation we're just parsing + + align:start position:0% +still oars equation we're just parsing + + + align:start position:0% +still oars equation we're just parsing +it differently we used to think of it as + + align:start position:0% +it differently we used to think of it as + + + align:start position:0% +it differently we used to think of it as +a complex exponential now we think of it + + align:start position:0% +a complex exponential now we think of it + + + align:start position:0% +a complex exponential now we think of it +as a complex geometric that's the only + + align:start position:0% +as a complex geometric that's the only + + + align:start position:0% +as a complex geometric that's the only +difference + + align:start position:0% +difference + + + align:start position:0% +difference +so now what we need to do if we're + + align:start position:0% +so now what we need to do if we're + + + align:start position:0% +so now what we need to do if we're +thinking about the response to the + + align:start position:0% +thinking about the response to the + + + align:start position:0% +thinking about the response to the +cosine of Omega naught and we have to + + align:start position:0% +cosine of Omega naught and we have to + + + align:start position:0% +cosine of Omega naught and we have to +think about adding two complex + + align:start position:0% +think about adding two complex + + + align:start position:0% +think about adding two complex +Exponential's one at Z naught and 1 at Z + + align:start position:0% +Exponential's one at Z naught and 1 at Z + + + align:start position:0% +Exponential's one at Z naught and 1 at Z +one where Z naught is e to the J Omega + + align:start position:0% +one where Z naught is e to the J Omega + + + align:start position:0% +one where Z naught is e to the J Omega +naught then Z 1 is e to the minus J + + align:start position:0% +naught then Z 1 is e to the minus J + + + align:start position:0% +naught then Z 1 is e to the minus J +Omega naught okay + + align:start position:0% + + + + align:start position:0% + +then the response since the Z naught to + + align:start position:0% +then the response since the Z naught to + + + align:start position:0% +then the response since the Z naught to +the N is an eigenfunction the response + + align:start position:0% +the N is an eigenfunction the response + + + align:start position:0% +the N is an eigenfunction the response +the answer is just that same + + align:start position:0% +the answer is just that same + + + align:start position:0% +the answer is just that same +eigenfunction pre multiplied by the + + align:start position:0% +eigenfunction pre multiplied by the + + + align:start position:0% +eigenfunction pre multiplied by the +system function evaluated at Z naught + + align:start position:0% +system function evaluated at Z naught + + + align:start position:0% +system function evaluated at Z naught +and similarly here for Z 1 so we get an + + align:start position:0% +and similarly here for Z 1 so we get an + + + align:start position:0% +and similarly here for Z 1 so we get an +expression here that looks for all the + + align:start position:0% +expression here that looks for all the + + + align:start position:0% +expression here that looks for all the +world except that this is a complex this + + align:start position:0% +world except that this is a complex this + + + align:start position:0% +world except that this is a complex this +is not a geometric this is the base of a + + align:start position:0% +is not a geometric this is the base of a + + + align:start position:0% +is not a geometric this is the base of a +geometric sequence except for that it + + align:start position:0% +geometric sequence except for that it + + + align:start position:0% +geometric sequence except for that it +looks just the same as the CTE example + + align:start position:0% +looks just the same as the CTE example + + + align:start position:0% +looks just the same as the CTE example +from before just like CTE this system + + align:start position:0% +from before just like CTE this system + + + align:start position:0% +from before just like CTE this system +function has conjugate symmetry and in + + align:start position:0% +function has conjugate symmetry and in + + + align:start position:0% +function has conjugate symmetry and in +fact that's for the same reason too so + + align:start position:0% +fact that's for the same reason too so + + + align:start position:0% +fact that's for the same reason too so +you can see that there's coms like + + align:start position:0% +you can see that there's coms like + + + align:start position:0% +you can see that there's coms like +symmetry just by thinking about the + + align:start position:0% +symmetry just by thinking about the + + + align:start position:0% +symmetry just by thinking about the +expansion in terms of the Z transform + + align:start position:0% +expansion in terms of the Z transform + + + align:start position:0% +expansion in terms of the Z transform +and if you think about the fact that the + + align:start position:0% +and if you think about the fact that the + + + align:start position:0% +and if you think about the fact that the +H of ends are all real taking the + + align:start position:0% +H of ends are all real taking the + + + align:start position:0% +H of ends are all real taking the +complex conjugate of this side is the + + align:start position:0% +complex conjugate of this side is the + + + align:start position:0% +complex conjugate of this side is the +same as taking + + align:start position:0% +same as taking + + + align:start position:0% +same as taking +the complex conjugate of that the + + align:start position:0% +the complex conjugate of that the + + + align:start position:0% +the complex conjugate of that the +complex conjugate of a sum is the sum of + + align:start position:0% +complex conjugate of a sum is the sum of + + + align:start position:0% +complex conjugate of a sum is the sum of +the complex conjugates the only thing + + align:start position:0% +the complex conjugates the only thing + + + align:start position:0% +the complex conjugates the only thing +that's imaginary is that so the only + + align:start position:0% +that's imaginary is that so the only + + + align:start position:0% +that's imaginary is that so the only +thing that happens is that the sign + + align:start position:0% +thing that happens is that the sign + + + align:start position:0% +thing that happens is that the sign +changes so it's it's there's complex + + align:start position:0% +changes so it's it's there's complex + + + align:start position:0% +changes so it's it's there's complex +conjugates relationship in DT just the + + align:start position:0% +conjugates relationship in DT just the + + + align:start position:0% +conjugates relationship in DT just the +same as there is in CT for exactly the + + align:start position:0% +same as there is in CT for exactly the + + + align:start position:0% +same as there is in CT for exactly the +same reason and finally we get our final + + align:start position:0% +same reason and finally we get our final + + + align:start position:0% +same reason and finally we get our final +answer which is that if we want to know + + align:start position:0% +answer which is that if we want to know + + + align:start position:0% +answer which is that if we want to know +about the frequency response we + + align:start position:0% +about the frequency response we + + + align:start position:0% +about the frequency response we +therefore think about what was the + + align:start position:0% +therefore think about what was the + + + align:start position:0% +therefore think about what was the +magnitude and angle of the system + + align:start position:0% +magnitude and angle of the system + + + align:start position:0% +magnitude and angle of the system +function we only need to look at one of + + align:start position:0% +function we only need to look at one of + + + align:start position:0% +function we only need to look at one of +the frequencies when since we know the + + align:start position:0% +the frequencies when since we know the + + + align:start position:0% +the frequencies when since we know the +frequency response has conjugate + + align:start position:0% +frequency response has conjugate + + + align:start position:0% +frequency response has conjugate +symmetry and we can figure out the + + align:start position:0% +symmetry and we can figure out the + + + align:start position:0% +symmetry and we can figure out the +response to coast Omega n it's still + + align:start position:0% +response to coast Omega n it's still + + + align:start position:0% +response to coast Omega n it's still +Coast Omega n except the magnitude is + + align:start position:0% +Coast Omega n except the magnitude is + + + align:start position:0% +Coast Omega n except the magnitude is +different by the magnitude of the system + + align:start position:0% +different by the magnitude of the system + + + align:start position:0% +different by the magnitude of the system +function and phase delay by the angle + + align:start position:0% +function and phase delay by the angle + + + align:start position:0% +function and phase delay by the angle +this function + + align:start position:0% +this function + + + align:start position:0% +this function +everything looks exactly the same the + + align:start position:0% +everything looks exactly the same the + + + align:start position:0% +everything looks exactly the same the +one thing that's different now we're + + align:start position:0% +one thing that's different now we're + + + align:start position:0% +one thing that's different now we're +getting something a little more + + align:start position:0% +getting something a little more + + + align:start position:0% +getting something a little more +interesting the one thing that's + + align:start position:0% +interesting the one thing that's + + + align:start position:0% +interesting the one thing that's +different is that we evaluate the system + + align:start position:0% +different is that we evaluate the system + + + align:start position:0% +different is that we evaluate the system +function when we're interested to find + + align:start position:0% +function when we're interested to find + + + align:start position:0% +function when we're interested to find +the frequency response the thing we need + + align:start position:0% +the frequency response the thing we need + + + align:start position:0% +the frequency response the thing we need +to do is evaluate the system function on + + align:start position:0% +to do is evaluate the system function on + + + align:start position:0% +to do is evaluate the system function on +the unit circle how do we if we wanted + + align:start position:0% +the unit circle how do we if we wanted + + + align:start position:0% +the unit circle how do we if we wanted +to know the frequency response for a CT + + align:start position:0% +to know the frequency response for a CT + + + align:start position:0% +to know the frequency response for a CT +system the frequency response for a CT + + align:start position:0% +system the frequency response for a CT + + + align:start position:0% +system the frequency response for a CT +system lives where J Omega axis right + + align:start position:0% +system lives where J Omega axis right + + + align:start position:0% +system lives where J Omega axis right +here this the frequency response lives + + align:start position:0% +here this the frequency response lives + + + align:start position:0% +here this the frequency response lives +on the units are whole that's the only + + align:start position:0% +on the units are whole that's the only + + + align:start position:0% +on the units are whole that's the only +difference and that means that the + + align:start position:0% +difference and that means that the + + + align:start position:0% +difference and that means that the +vector diagrams work precisely the same + + align:start position:0% +vector diagrams work precisely the same + + + align:start position:0% +vector diagrams work precisely the same +way except that we don't connect them up + + align:start position:0% +way except that we don't connect them up + + + align:start position:0% +way except that we don't connect them up +to the J Omega axis we can tack them up + + align:start position:0% +to the J Omega axis we can tack them up + + + align:start position:0% +to the J Omega axis we can tack them up +to the unit circle so where is DC + + align:start position:0% + + + + align:start position:0% + +DC means coast Omega and where Omega is + + align:start position:0% +DC means coast Omega and where Omega is + + + align:start position:0% +DC means coast Omega and where Omega is +zero where is that where is DC where was + + align:start position:0% +zero where is that where is DC where was + + + align:start position:0% +zero where is that where is DC where was +DC and CT frequency response news on the + + align:start position:0% +DC and CT frequency response news on the + + + align:start position:0% +DC and CT frequency response news on the +J Omega axis whereas DC zero + + align:start position:0% +J Omega axis whereas DC zero + + + align:start position:0% +J Omega axis whereas DC zero +where is DC and a DT system one okay + + align:start position:0% +where is DC and a DT system one okay + + + align:start position:0% +where is DC and a DT system one okay +it's because we've shifted from thinking + + align:start position:0% +it's because we've shifted from thinking + + + align:start position:0% +it's because we've shifted from thinking +about complex Exponential's to thinking + + align:start position:0% +about complex Exponential's to thinking + + + align:start position:0% +about complex Exponential's to thinking +about complex geometrics so now DC lives + + align:start position:0% +about complex geometrics so now DC lives + + + align:start position:0% +about complex geometrics so now DC lives +on the unit circle at the place where + + align:start position:0% +on the unit circle at the place where + + + align:start position:0% +on the unit circle at the place where +the angle is zero right so now we have + + align:start position:0% +the angle is zero right so now we have + + + align:start position:0% +the angle is zero right so now we have +to think about things of this form if we + + align:start position:0% +to think about things of this form if we + + + align:start position:0% +to think about things of this form if we +want Oh Megan ought to be zero we need + + align:start position:0% +want Oh Megan ought to be zero we need + + + align:start position:0% +want Oh Megan ought to be zero we need +to have this number to be e to the 0 + + align:start position:0% +to have this number to be e to the 0 + + + align:start position:0% +to have this number to be e to the 0 +which is 1 so the DC response the thing + + align:start position:0% +which is 1 so the DC response the thing + + + align:start position:0% +which is 1 so the DC response the thing +that we plot we're going to plot + + align:start position:0% +that we plot we're going to plot + + + align:start position:0% +that we plot we're going to plot +frequency responses just the same as we + + align:start position:0% +frequency responses just the same as we + + + align:start position:0% +frequency responses just the same as we +did in CTE they're going to have the + + align:start position:0% +did in CTE they're going to have the + + + align:start position:0% +did in CTE they're going to have the +same trick they had in CT in CT the + + align:start position:0% +same trick they had in CT in CT the + + + align:start position:0% +same trick they had in CT in CT the +system function has a non zero answer + + align:start position:0% +system function has a non zero answer + + + align:start position:0% +system function has a non zero answer +throughout the entire S plane in DT the + + align:start position:0% +throughout the entire S plane in DT the + + + align:start position:0% +throughout the entire S plane in DT the +system function has a non zero response + + align:start position:0% +system function has a non zero response + + + align:start position:0% +system function has a non zero response +in the entire Z plane we the the + + align:start position:0% +in the entire Z plane we the the + + + align:start position:0% +in the entire Z plane we the the +frequency response in CT lives on the J + + align:start position:0% +frequency response in CT lives on the J + + + align:start position:0% +frequency response in CT lives on the J +Omega axis the frequency response in DT + + align:start position:0% +Omega axis the frequency response in DT + + + align:start position:0% +Omega axis the frequency response in DT +lives on the unit circle right so but + + align:start position:0% +lives on the unit circle right so but + + + align:start position:0% +lives on the unit circle right so but +the frequency response itself is simply + + align:start position:0% +the frequency response itself is simply + + + align:start position:0% +the frequency response itself is simply +a plot of the magnitude and angle as a + + align:start position:0% +a plot of the magnitude and angle as a + + + align:start position:0% +a plot of the magnitude and angle as a +function of Omega I should mention that + + align:start position:0% +function of Omega I should mention that + + + align:start position:0% +function of Omega I should mention that +I sneakily used a different symbol for + + align:start position:0% +I sneakily used a different symbol for + + + align:start position:0% +I sneakily used a different symbol for +Omega I like to use little Omega for CT + + align:start position:0% +Omega I like to use little Omega for CT + + + align:start position:0% +Omega I like to use little Omega for CT +and capital Omega for DT the reason I + + align:start position:0% +and capital Omega for DT the reason I + + + align:start position:0% +and capital Omega for DT the reason I +like to do that is that the dimensions + + align:start position:0% +like to do that is that the dimensions + + + align:start position:0% +like to do that is that the dimensions +are different right when we think about + + align:start position:0% +are different right when we think about + + + align:start position:0% +are different right when we think about +little Omega naught we're thinking about + + align:start position:0% +little Omega naught we're thinking about + + + align:start position:0% +little Omega naught we're thinking about +cosine of Omega naught T when we think + + align:start position:0% +cosine of Omega naught T when we think + + + align:start position:0% +cosine of Omega naught T when we think +about this one we're thinking about + + align:start position:0% +about this one we're thinking about + + + align:start position:0% +about this one we're thinking about +cosine of Omega naught and can somebody + + align:start position:0% +cosine of Omega naught and can somebody + + + align:start position:0% +cosine of Omega naught and can somebody +tell me something different about little + + align:start position:0% +tell me something different about little + + + align:start position:0% +tell me something different about little +and capital Omega naught what's + + align:start position:0% +and capital Omega naught what's + + + align:start position:0% +and capital Omega naught what's +different about them anything yeah + + align:start position:0% +different about them anything yeah + + + align:start position:0% +different about them anything yeah +little one goes to infinity that's + + align:start position:0% +little one goes to infinity that's + + + align:start position:0% +little one goes to infinity that's +correct yeah + + align:start position:0% + + + + align:start position:0% + +so you can think about Omega not whoops + + align:start position:0% +so you can think about Omega not whoops + + + align:start position:0% +so you can think about Omega not whoops +Omega not has dimensions like Radian per + + align:start position:0% +Omega not has dimensions like Radian per + + + align:start position:0% +Omega not has dimensions like Radian per +second where Omega naught has the + + align:start position:0% +second where Omega naught has the + + + align:start position:0% +second where Omega naught has the +dimensions of radians + + align:start position:0% + + + + align:start position:0% + +right so the dimensionally completely + + align:start position:0% +right so the dimensionally completely + + + align:start position:0% +right so the dimensionally completely +different that'll be very important when + + align:start position:0% +different that'll be very important when + + + align:start position:0% +different that'll be very important when +we think about systems so the last two + + align:start position:0% +we think about systems so the last two + + + align:start position:0% +we think about systems so the last two +weeks of the course we'll think about + + align:start position:0% +weeks of the course we'll think about + + + align:start position:0% +weeks of the course we'll think about +systems that convert CT to DT and back + + align:start position:0% +systems that convert CT to DT and back + + + align:start position:0% +systems that convert CT to DT and back +what we're doing that conversion is very + + align:start position:0% +what we're doing that conversion is very + + + align:start position:0% +what we're doing that conversion is very +important to keep track of how the + + align:start position:0% +important to keep track of how the + + + align:start position:0% +important to keep track of how the +frequencies change and this dimensional + + align:start position:0% +frequencies change and this dimensional + + + align:start position:0% +frequencies change and this dimensional +difference will be very handy to help us + + align:start position:0% +difference will be very handy to help us + + + align:start position:0% +difference will be very handy to help us +remember how to convert one into the + + align:start position:0% +remember how to convert one into the + + + align:start position:0% +remember how to convert one into the +other so that's the reason for keeping + + align:start position:0% +other so that's the reason for keeping + + + align:start position:0% +other so that's the reason for keeping +them separate so they're dimensionally + + align:start position:0% +them separate so they're dimensionally + + + align:start position:0% +them separate so they're dimensionally +distinct so all we need to do then to + + align:start position:0% +distinct so all we need to do then to + + + align:start position:0% +distinct so all we need to do then to +think about the frequency response in CT + + align:start position:0% +think about the frequency response in CT + + + align:start position:0% +think about the frequency response in CT +the frequency response would be the + + align:start position:0% +the frequency response would be the + + + align:start position:0% +the frequency response would be the +magnitude and angle plotted versus + + align:start position:0% +magnitude and angle plotted versus + + + align:start position:0% +magnitude and angle plotted versus +little Omega not all we do this + + align:start position:0% +little Omega not all we do this + + + align:start position:0% +little Omega not all we do this +different is we plot against capital + + align:start position:0% +different is we plot against capital + + + align:start position:0% +different is we plot against capital +Omega and I capital Omega not specifies + + align:start position:0% +Omega and I capital Omega not specifies + + + align:start position:0% +Omega and I capital Omega not specifies +the angle on the unit circle so if the + + align:start position:0% +the angle on the unit circle so if the + + + align:start position:0% +the angle on the unit circle so if the +angle is zero we pick out zero frequency + + align:start position:0% +angle is zero we pick out zero frequency + + + align:start position:0% +angle is zero we pick out zero frequency +we think about that as having two pieces + + align:start position:0% +we think about that as having two pieces + + + align:start position:0% +we think about that as having two pieces +there's the piece associated with the + + align:start position:0% +there's the piece associated with the + + + align:start position:0% +there's the piece associated with the +pole there's the piece that's associated + + align:start position:0% +pole there's the piece that's associated + + + align:start position:0% +pole there's the piece that's associated +with the zero the zero is in the top so + + align:start position:0% +with the zero the zero is in the top so + + + align:start position:0% +with the zero the zero is in the top so +we take the length of the top divided by + + align:start position:0% +we take the length of the top divided by + + + align:start position:0% +we take the length of the top divided by +the length in the bottom and that tells + + align:start position:0% +the length in the bottom and that tells + + + align:start position:0% +the length in the bottom and that tells +us the magnitude is zero which is the + + align:start position:0% +us the magnitude is zero which is the + + + align:start position:0% +us the magnitude is zero which is the +number bigger than 1 right because the + + align:start position:0% +number bigger than 1 right because the + + + align:start position:0% +number bigger than 1 right because the +poles in the bottom poles the short one + + align:start position:0% +poles in the bottom poles the short one + + + align:start position:0% +poles in the bottom poles the short one +poles in the bottom and as you increase + + align:start position:0% +poles in the bottom and as you increase + + + align:start position:0% +poles in the bottom and as you increase +capital Omega you sweep out the + + align:start position:0% +capital Omega you sweep out the + + + align:start position:0% +capital Omega you sweep out the +frequency response so by the time you + + align:start position:0% +frequency response so by the time you + + + align:start position:0% +frequency response so by the time you +get over 2 pi the length of the vector + + align:start position:0% +get over 2 pi the length of the vector + + + align:start position:0% +get over 2 pi the length of the vector +associated with the pole is bigger than + + align:start position:0% +associated with the pole is bigger than + + + align:start position:0% +associated with the pole is bigger than +the length of the vector associated with + + align:start position:0% +the length of the vector associated with + + + align:start position:0% +the length of the vector associated with +zero so now you're less than 1 okay so + + align:start position:0% +zero so now you're less than 1 okay so + + + align:start position:0% +zero so now you're less than 1 okay so +everything's exactly the same as CT + + align:start position:0% +everything's exactly the same as CT + + + align:start position:0% +everything's exactly the same as CT +except that we're looking at the unit + + align:start position:0% +except that we're looking at the unit + + + align:start position:0% +except that we're looking at the unit +circle rather than looking at the J + + align:start position:0% +circle rather than looking at the J + + + align:start position:0% +circle rather than looking at the J +Omega axis the same sort of thing + + align:start position:0% +Omega axis the same sort of thing + + + align:start position:0% +Omega axis the same sort of thing +happens for negative frequency just like + + align:start position:0% +happens for negative frequency just like + + + align:start position:0% +happens for negative frequency just like +it did in CT the only difference being + + align:start position:0% +it did in CT the only difference being + + + align:start position:0% +it did in CT the only difference being +that in CT we were looking and we were + + align:start position:0% +that in CT we were looking and we were + + + align:start position:0% +that in CT we were looking and we were +computing the J Omega axis by looking at + + align:start position:0% +computing the J Omega axis by looking at + + + align:start position:0% +computing the J Omega axis by looking at +the + + align:start position:0% +the + + + align:start position:0% +the +we were computing the frequency axis by + + align:start position:0% +we were computing the frequency axis by + + + align:start position:0% +we were computing the frequency axis by +looking at the J Omega axis in DT we're + + align:start position:0% +looking at the J Omega axis in DT we're + + + align:start position:0% +looking at the J Omega axis in DT we're +computing the frequency axis by looking + + align:start position:0% +computing the frequency axis by looking + + + align:start position:0% +computing the frequency axis by looking +at the unit circle there's one huge + + align:start position:0% +at the unit circle there's one huge + + + align:start position:0% +at the unit circle there's one huge +difference okay so the first summary + + align:start position:0% +difference okay so the first summary + + + align:start position:0% +difference okay so the first summary +everything is the same except we look at + + align:start position:0% +everything is the same except we look at + + + align:start position:0% +everything is the same except we look at +the unit circle except frequency + + align:start position:0% +the unit circle except frequency + + + align:start position:0% +the unit circle except frequency +responses are now periodic someone + + align:start position:0% +responses are now periodic someone + + + align:start position:0% +responses are now periodic someone +previously said that one of the + + align:start position:0% +previously said that one of the + + + align:start position:0% +previously said that one of the +differences between little Omega and big + + align:start position:0% +differences between little Omega and big + + + align:start position:0% +differences between little Omega and big +Omega is that little Omega goes to + + align:start position:0% +Omega is that little Omega goes to + + + align:start position:0% +Omega is that little Omega goes to +infinity that's absolutely true + + align:start position:0% +infinity that's absolutely true + + + align:start position:0% +infinity that's absolutely true +what happens when big Omega goes to + + align:start position:0% +what happens when big Omega goes to + + + align:start position:0% +what happens when big Omega goes to +infinity well angles wrap so if you + + align:start position:0% +infinity well angles wrap so if you + + + align:start position:0% +infinity well angles wrap so if you +think about this diagram if you start + + align:start position:0% +think about this diagram if you start + + + align:start position:0% +think about this diagram if you start +with capital Omega being 0 by the time + + align:start position:0% +with capital Omega being 0 by the time + + + align:start position:0% +with capital Omega being 0 by the time +you get over here capital Omega is PI if + + align:start position:0% +you get over here capital Omega is PI if + + + align:start position:0% +you get over here capital Omega is PI if +you keep increasing you'll come back + + align:start position:0% +you keep increasing you'll come back + + + align:start position:0% +you keep increasing you'll come back +here if you keep increasing you go again + + align:start position:0% +here if you keep increasing you go again + + + align:start position:0% +here if you keep increasing you go again +the big difference between C T and DT is + + align:start position:0% +the big difference between C T and DT is + + + align:start position:0% +the big difference between C T and DT is +that DT complex Exponential's are + + align:start position:0% +that DT complex Exponential's are + + + align:start position:0% +that DT complex Exponential's are +periodic in 2 pi every 2 pi they repeat + + align:start position:0% +periodic in 2 pi every 2 pi they repeat + + + align:start position:0% +periodic in 2 pi every 2 pi they repeat +themselves because of that DT system + + align:start position:0% +themselves because of that DT system + + + align:start position:0% +themselves because of that DT system +functions repeat themselves so if you + + align:start position:0% +functions repeat themselves so if you + + + align:start position:0% +functions repeat themselves so if you +think about evaluating the system + + align:start position:0% +think about evaluating the system + + + align:start position:0% +think about evaluating the system +function at some frequency Omega 2 which + + align:start position:0% +function at some frequency Omega 2 which + + + align:start position:0% +function at some frequency Omega 2 which +happens to be Omega 1 plus 2 pi K you + + align:start position:0% +happens to be Omega 1 plus 2 pi K you + + + align:start position:0% +happens to be Omega 1 plus 2 pi K you +get the same thing as if you had + + align:start position:0% +get the same thing as if you had + + + align:start position:0% +get the same thing as if you had +evaluated the system function on Omega 1 + + align:start position:0% +evaluated the system function on Omega 1 + + + align:start position:0% +evaluated the system function on Omega 1 +because the frequency e to the J Omega 2 + + align:start position:0% +because the frequency e to the J Omega 2 + + + align:start position:0% +because the frequency e to the J Omega 2 +is the same as the frequency e to the J + + align:start position:0% +is the same as the frequency e to the J + + + align:start position:0% +is the same as the frequency e to the J +Omega 1 because of the periodicity of + + align:start position:0% +Omega 1 because of the periodicity of + + + align:start position:0% +Omega 1 because of the periodicity of +angles tech Lyra so we get something + + align:start position:0% +angles tech Lyra so we get something + + + align:start position:0% +angles tech Lyra so we get something +that's very different in CT in DT in DT + + align:start position:0% +that's very different in CT in DT in DT + + + align:start position:0% +that's very different in CT in DT in DT +the frequency response we only ever plot + + align:start position:0% +the frequency response we only ever plot + + + align:start position:0% +the frequency response we only ever plot +it up to PI because above pi it repeats + + align:start position:0% +it up to PI because above pi it repeats + + + align:start position:0% +it up to PI because above pi it repeats +itself by plotting it between minus PI + + align:start position:0% +itself by plotting it between minus PI + + + align:start position:0% +itself by plotting it between minus PI +and PI I've shown a 2 pi range and the + + align:start position:0% +and PI I've shown a 2 pi range and the + + + align:start position:0% +and PI I've shown a 2 pi range and the +frequency response is always periodic in + + align:start position:0% +frequency response is always periodic in + + + align:start position:0% +frequency response is always periodic in +2 pi because discrete frequencies are + + align:start position:0% +2 pi because discrete frequencies are + + + align:start position:0% +2 pi because discrete frequencies are +always periodic in 2 pi + + align:start position:0% +always periodic in 2 pi + + + align:start position:0% +always periodic in 2 pi +yes + + align:start position:0% + + + + align:start position:0% + +how does that affect the filters that's + + align:start position:0% +how does that affect the filters that's + + + align:start position:0% +how does that affect the filters that's +an excellent question and not a trivial + + align:start position:0% +an excellent question and not a trivial + + + align:start position:0% +an excellent question and not a trivial +one to answer so one of the big + + align:start position:0% +one to answer so one of the big + + + align:start position:0% +one to answer so one of the big +important differences which you will + + align:start position:0% +important differences which you will + + + align:start position:0% +important differences which you will +under appreciate right now is that + + align:start position:0% +under appreciate right now is that + + + align:start position:0% +under appreciate right now is that +because of this repetition there's no + + align:start position:0% +because of this repetition there's no + + + align:start position:0% +because of this repetition there's no +equivalent thing to Bodi now I know you + + align:start position:0% +equivalent thing to Bodi now I know you + + + align:start position:0% +equivalent thing to Bodi now I know you +all love Bodi and because you like it so + + align:start position:0% +all love Bodi and because you like it so + + + align:start position:0% +all love Bodi and because you like it so +much I'm being slightly sarcastic you + + align:start position:0% +much I'm being slightly sarcastic you + + + align:start position:0% +much I'm being slightly sarcastic you +know I like it a lot because it's easy + + align:start position:0% +know I like it a lot because it's easy + + + align:start position:0% +know I like it a lot because it's easy +right you haven't quite got over the + + align:start position:0% +right you haven't quite got over the + + + align:start position:0% +right you haven't quite got over the +barrier yet and so I'm I've heard some + + align:start position:0% +barrier yet and so I'm I've heard some + + + align:start position:0% +barrier yet and so I'm I've heard some +negative feedback about bori bori is + + align:start position:0% +negative feedback about bori bori is + + + align:start position:0% +negative feedback about bori bori is +wonderful but in case you haven't got + + align:start position:0% +wonderful but in case you haven't got + + + align:start position:0% +wonderful but in case you haven't got +that message one of the biggest problems + + align:start position:0% +that message one of the biggest problems + + + align:start position:0% +that message one of the biggest problems +in dte which comes about exactly because + + align:start position:0% +in dte which comes about exactly because + + + align:start position:0% +in dte which comes about exactly because +of the thing you said that the dt + + align:start position:0% +of the thing you said that the dt + + + align:start position:0% +of the thing you said that the dt +frequencies are periodic + + align:start position:0% +frequencies are periodic + + + align:start position:0% +frequencies are periodic +we don't have an analogue of bode which + + align:start position:0% +we don't have an analogue of bode which + + + align:start position:0% +we don't have an analogue of bode which +means that when we try to sketch the + + align:start position:0% +means that when we try to sketch the + + + align:start position:0% +means that when we try to sketch the +magnitude and phase for a discrete time + + align:start position:0% +magnitude and phase for a discrete time + + + align:start position:0% +magnitude and phase for a discrete time +filter it's a much harder problem one + + align:start position:0% +filter it's a much harder problem one + + + align:start position:0% +filter it's a much harder problem one +for which we almost always use a + + align:start position:0% +for which we almost always use a + + + align:start position:0% +for which we almost always use a +computer because we don't know any good + + align:start position:0% +computer because we don't know any good + + + align:start position:0% +computer because we don't know any good +rules to let us think about it in our + + align:start position:0% +rules to let us think about it in our + + + align:start position:0% +rules to let us think about it in our +heads so that's one of the implications + + align:start position:0% +heads so that's one of the implications + + + align:start position:0% +heads so that's one of the implications +but there's a lot of others and in fact + + align:start position:0% +but there's a lot of others and in fact + + + align:start position:0% +but there's a lot of others and in fact +that's one of the main themes for the + + align:start position:0% +that's one of the main themes for the + + + align:start position:0% +that's one of the main themes for the +rest of the course + + align:start position:0% +rest of the course + + + align:start position:0% +rest of the course +so the importantly difference then is + + align:start position:0% +so the importantly difference then is + + + align:start position:0% +so the importantly difference then is +two important differences frequency + + align:start position:0% +two important differences frequency + + + align:start position:0% +two important differences frequency +response lives on a unit circle and + + align:start position:0% +response lives on a unit circle and + + + align:start position:0% +response lives on a unit circle and +discrete frequencies are periodic okay + + align:start position:0% +discrete frequencies are periodic okay + + + align:start position:0% +discrete frequencies are periodic okay +I've talked way too much so finally I'm + + align:start position:0% +I've talked way too much so finally I'm + + + align:start position:0% +I've talked way too much so finally I'm +going to ask you to do something I want + + align:start position:0% +going to ask you to do something I want + + + align:start position:0% +going to ask you to do something I want +you to think about 3ct frequencies + + align:start position:0% +you to think about 3ct frequencies + + + align:start position:0% +you to think about 3ct frequencies +coasts 3,000 Tico's 4,000 Ticos 5000 t + + align:start position:0% +coasts 3,000 Tico's 4,000 Ticos 5000 t + + + align:start position:0% +coasts 3,000 Tico's 4,000 Ticos 5000 t +and think about sampling Gulman at with + + align:start position:0% +and think about sampling Gulman at with + + + align:start position:0% +and think about sampling Gulman at with +a sampling interval capital T whose 0:01 + + align:start position:0% +a sampling interval capital T whose 0:01 + + + align:start position:0% +a sampling interval capital T whose 0:01 +and put them in order from lowest to + + align:start position:0% +and put them in order from lowest to + + + align:start position:0% +and put them in order from lowest to +highest DT frequency so first look at + + align:start position:0% +highest DT frequency so first look at + + + align:start position:0% +highest DT frequency so first look at +your neighbor say hello and now choose + + align:start position:0% +your neighbor say hello and now choose + + + align:start position:0% +your neighbor say hello and now choose +an answer between zero and five + + align:start position:0% + + + + align:start position:0% + +okay so which list goes from lowest to + + align:start position:0% +okay so which list goes from lowest to + + + align:start position:0% +okay so which list goes from lowest to +highest DT frequency so raise your hand + + align:start position:0% +highest DT frequency so raise your hand + + + align:start position:0% +highest DT frequency so raise your hand +with a number of fingers equal to the + + align:start position:0% +with a number of fingers equal to the + + + align:start position:0% +with a number of fingers equal to the +answer between zero and five hi okay so + + align:start position:0% +answer between zero and five hi okay so + + + align:start position:0% +answer between zero and five hi okay so +I see people disagreeing with their + + align:start position:0% +I see people disagreeing with their + + + align:start position:0% +I see people disagreeing with their +partner I think that's always good okay + + align:start position:0% +partner I think that's always good okay + + + align:start position:0% +partner I think that's always good okay +the correct answer is in the minority so + + align:start position:0% +the correct answer is in the minority so + + + align:start position:0% +the correct answer is in the minority so +let's ask according to the theory of + + align:start position:0% +let's ask according to the theory of + + + align:start position:0% +let's ask according to the theory of +lectures what's the right answer if you + + align:start position:0% +lectures what's the right answer if you + + + align:start position:0% +lectures what's the right answer if you +were the lecturer asking this question + + align:start position:0% +were the lecturer asking this question + + + align:start position:0% +were the lecturer asking this question +what would you make the answer be none + + align:start position:0% +what would you make the answer be none + + + align:start position:0% +what would you make the answer be none +of them except I don't have none but + + align:start position:0% +of them except I don't have none but + + + align:start position:0% +of them except I don't have none but +that would be this kind of thing I would + + align:start position:0% +that would be this kind of thing I would + + + align:start position:0% +that would be this kind of thing I would +do I guess if you were the lecturer and + + align:start position:0% +do I guess if you were the lecturer and + + + align:start position:0% +do I guess if you were the lecturer and +you wanted to make a point about X 1 X 2 + + align:start position:0% +you wanted to make a point about X 1 X 2 + + + align:start position:0% +you wanted to make a point about X 1 X 2 +X 3 3,000 4,000 5,000 what would you + + align:start position:0% +X 3 3,000 4,000 5,000 what would you + + + align:start position:0% +X 3 3,000 4,000 5,000 what would you +want the answer to be sure you'd like it + + align:start position:0% +want the answer to be sure you'd like it + + + align:start position:0% +want the answer to be sure you'd like it +to be number 5 completely backwards okay + + align:start position:0% +to be number 5 completely backwards okay + + + align:start position:0% +to be number 5 completely backwards okay +talk to your neighbor figure out why + + align:start position:0% +talk to your neighbor figure out why + + + align:start position:0% +talk to your neighbor figure out why +it's completely backwards that is the + + align:start position:0% +it's completely backwards that is the + + + align:start position:0% +it's completely backwards that is the +right answer the theory of lectures + + align:start position:0% +right answer the theory of lectures + + + align:start position:0% +right answer the theory of lectures +always works + + align:start position:0% + + + + align:start position:0% + +so why is five the right answer use five + + align:start position:0% +so why is five the right answer use five + + + align:start position:0% +so why is five the right answer use five +the right answer private the right + + align:start position:0% +the right answer private the right + + + align:start position:0% +the right answer private the right +answer + + align:start position:0% +answer + + + align:start position:0% +answer +why is five the right answer okay the + + align:start position:0% +why is five the right answer okay the + + + align:start position:0% +why is five the right answer okay the +corollary to the theory of lecture is + + align:start position:0% +corollary to the theory of lecture is + + + align:start position:0% +corollary to the theory of lecture is +always look at the last slide what was + + align:start position:0% +always look at the last slide what was + + + align:start position:0% +always look at the last slide what was +the last point things rap so how do + + align:start position:0% +the last point things rap so how do + + + align:start position:0% +the last point things rap so how do +these theas lis these things must be + + align:start position:0% +these theas lis these things must be + + + align:start position:0% +these theas lis these things must be +rapping right because it's according to + + align:start position:0% +rapping right because it's according to + + + align:start position:0% +rapping right because it's according to +the corollary to the theory of lecturers + + align:start position:0% +the corollary to the theory of lecturers + + + align:start position:0% +the corollary to the theory of lecturers +it has to do with rapping according to + + align:start position:0% +it has to do with rapping according to + + + align:start position:0% +it has to do with rapping according to +the theory of lecturers this number five + + align:start position:0% +the theory of lecturers this number five + + + align:start position:0% +the theory of lecturers this number five +why would it rap that way well think + + align:start position:0% +why would it rap that way well think + + + align:start position:0% +why would it rap that way well think +about after you do the sampling if you + + align:start position:0% +about after you do the sampling if you + + + align:start position:0% +about after you do the sampling if you +substitute capital T equals 0.001 you + + align:start position:0% +substitute capital T equals 0.001 you + + + align:start position:0% +substitute capital T equals 0.001 you +look up X 1 of n T so X 1 of T is this + + align:start position:0% +look up X 1 of n T so X 1 of T is this + + + align:start position:0% +look up X 1 of n T so X 1 of T is this +so substitute an T every place there was + + align:start position:0% +so substitute an T every place there was + + + align:start position:0% +so substitute an T every place there was +a T so you get 3,000 and capital T 3,000 + + align:start position:0% +a T so you get 3,000 and capital T 3,000 + + + align:start position:0% +a T so you get 3,000 and capital T 3,000 +times capital T is 3 so X 1 of n is + + align:start position:0% +times capital T is 3 so X 1 of n is + + + align:start position:0% +times capital T is 3 so X 1 of n is +coasts of 3 n right and that's written + + align:start position:0% +coasts of 3 n right and that's written + + + align:start position:0% +coasts of 3 n right and that's written +here similarly the second one is for N + + align:start position:0% +here similarly the second one is for N + + + align:start position:0% +here similarly the second one is for N +and the third one is 5 n so the discrete + + align:start position:0% +and the third one is 5 n so the discrete + + + align:start position:0% +and the third one is 5 n so the discrete +frequency capital Omega is 3 4 or 5 + + align:start position:0% +frequency capital Omega is 3 4 or 5 + + + align:start position:0% +frequency capital Omega is 3 4 or 5 +think about where 3 4 or 5 are on the + + align:start position:0% +think about where 3 4 or 5 are on the + + + align:start position:0% +think about where 3 4 or 5 are on the +unit circle ok 3 is a number just less + + align:start position:0% +unit circle ok 3 is a number just less + + + align:start position:0% +unit circle ok 3 is a number just less +than pi so that puts 3 here + + align:start position:0% + + + + align:start position:0% + +four is a number that's bigger than pi + + align:start position:0% +four is a number that's bigger than pi + + + align:start position:0% +four is a number that's bigger than pi +so you go around you pass PI and you go + + align:start position:0% +so you go around you pass PI and you go + + + align:start position:0% +so you go around you pass PI and you go +a little further and five is a number + + align:start position:0% +a little further and five is a number + + + align:start position:0% +a little further and five is a number +that is slightly bigger than + + align:start position:0% +that is slightly bigger than + + + align:start position:0% +that is slightly bigger than +three-quarters of two pi okay so by that + + align:start position:0% +three-quarters of two pi okay so by that + + + align:start position:0% +three-quarters of two pi okay so by that +logic right this is low frequencies this + + align:start position:0% +logic right this is low frequencies this + + + align:start position:0% +logic right this is low frequencies this +is not low frequencies positive and + + align:start position:0% +is not low frequencies positive and + + + align:start position:0% +is not low frequencies positive and +negatives are both necessary because of + + align:start position:0% +negatives are both necessary because of + + + align:start position:0% +negatives are both necessary because of +Euler's rule in order to make a + + align:start position:0% +Euler's rule in order to make a + + + align:start position:0% +Euler's rule in order to make a +real-valued cosine function right we + + align:start position:0% +real-valued cosine function right we + + + align:start position:0% +real-valued cosine function right we +needed e to the plus and we need either + + align:start position:0% +needed e to the plus and we need either + + + align:start position:0% +needed e to the plus and we need either +the minus so we start at zero frequency + + align:start position:0% +the minus so we start at zero frequency + + + align:start position:0% +the minus so we start at zero frequency +as we increase frequency we're thinking + + align:start position:0% +as we increase frequency we're thinking + + + align:start position:0% +as we increase frequency we're thinking +about conjugate frequencies like so so + + align:start position:0% +about conjugate frequencies like so so + + + align:start position:0% +about conjugate frequencies like so so +this is the highest frequency then they + + align:start position:0% +this is the highest frequency then they + + + align:start position:0% +this is the highest frequency then they +cross so which is the highest frequency + + align:start position:0% +cross so which is the highest frequency + + + align:start position:0% +cross so which is the highest frequency +among three four and five doesn't make + + align:start position:0% +among three four and five doesn't make + + + align:start position:0% +among three four and five doesn't make +any sense according to the rules I just + + align:start position:0% +any sense according to the rules I just + + + align:start position:0% +any sense according to the rules I just +said the answer must be three right + + align:start position:0% +said the answer must be three right + + + align:start position:0% +said the answer must be three right +three is closest to the high frequency + + align:start position:0% +three is closest to the high frequency + + + align:start position:0% +three is closest to the high frequency +then the next closest is four and the + + align:start position:0% +then the next closest is four and the + + + align:start position:0% +then the next closest is four and the +lowest frequency must be five why does + + align:start position:0% +lowest frequency must be five why does + + + align:start position:0% +lowest frequency must be five why does +that make any sense + + align:start position:0% +that make any sense + + + align:start position:0% +that make any sense +the intuition comes from if you think + + align:start position:0% +the intuition comes from if you think + + + align:start position:0% +the intuition comes from if you think +about what's happening when you're + + align:start position:0% +about what's happening when you're + + + align:start position:0% +about what's happening when you're +sampling think about what would happen + + align:start position:0% +sampling think about what would happen + + + align:start position:0% +sampling think about what would happen +if capital Omega were a quarter then if + + align:start position:0% +if capital Omega were a quarter then if + + + align:start position:0% +if capital Omega were a quarter then if +we plotted coast Omega T and compared + + align:start position:0% +we plotted coast Omega T and compared + + + align:start position:0% +we plotted coast Omega T and compared +the samples coast 0.25 n you would see + + align:start position:0% +the samples coast 0.25 n you would see + + + align:start position:0% +the samples coast 0.25 n you would see +that at this very low frequency the + + align:start position:0% +that at this very low frequency the + + + align:start position:0% +that at this very low frequency the +discrete frequency the samples are a + + align:start position:0% +discrete frequency the samples are a + + + align:start position:0% +discrete frequency the samples are a +very good representation of the + + align:start position:0% +very good representation of the + + + align:start position:0% +very good representation of the +unsampled signal I'm trying to compare + + align:start position:0% +unsampled signal I'm trying to compare + + + align:start position:0% +unsampled signal I'm trying to compare +the CT signal to the DT sampled signal + + align:start position:0% +the CT signal to the DT sampled signal + + + align:start position:0% +the CT signal to the DT sampled signal +okay if you change the the discrete + + align:start position:0% +okay if you change the the discrete + + + align:start position:0% +okay if you change the the discrete +frequency if you double it you still get + + align:start position:0% +frequency if you double it you still get + + + align:start position:0% +frequency if you double it you still get +a good representation of the CT signal + + align:start position:0% +a good representation of the CT signal + + + align:start position:0% +a good representation of the CT signal +if you double it again you can still see + + align:start position:0% +if you double it again you can still see + + + align:start position:0% +if you double it again you can still see +the CP signal I'm up to one double it to + + align:start position:0% +the CP signal I'm up to one double it to + + + align:start position:0% +the CP signal I'm up to one double it to +two you can still sort of see it double + + align:start position:0% +two you can still sort of see it double + + + align:start position:0% +two you can still sort of see it double +it increase it to three okay now it's + + align:start position:0% +it increase it to three okay now it's + + + align:start position:0% +it increase it to three okay now it's +getting a little harder to see you go a + + align:start position:0% +getting a little harder to see you go a + + + align:start position:0% +getting a little harder to see you go a +little higher to four + + align:start position:0% +little higher to four + + + align:start position:0% +little higher to four +and now the so in this plot the red line + + align:start position:0% +and now the so in this plot the red line + + + align:start position:0% +and now the so in this plot the red line +is showing the the CT signal that was + + align:start position:0% +is showing the the CT signal that was + + + align:start position:0% +is showing the the CT signal that was +sampled here the red curve is still + + align:start position:0% +sampled here the red curve is still + + + align:start position:0% +sampled here the red curve is still +showing the CT signal that was sampled + + align:start position:0% +showing the CT signal that was sampled + + + align:start position:0% +showing the CT signal that was sampled +but the green curve is showing an + + align:start position:0% +but the green curve is showing an + + + align:start position:0% +but the green curve is showing an +alternative way to think about that set + + align:start position:0% +alternative way to think about that set + + + align:start position:0% +alternative way to think about that set +of samples that set of samples could + + align:start position:0% +of samples that set of samples could + + + align:start position:0% +of samples that set of samples could +alternatively + + align:start position:0% +alternatively + + + align:start position:0% +alternatively +have come from the frequency 2 pi minus + + align:start position:0% +have come from the frequency 2 pi minus + + + align:start position:0% +have come from the frequency 2 pi minus +4n if you go to an even higher frequency + + align:start position:0% +4n if you go to an even higher frequency + + + align:start position:0% +4n if you go to an even higher frequency +if you go to 5 the problems even worse + + align:start position:0% +if you go to 5 the problems even worse + + + align:start position:0% +if you go to 5 the problems even worse +there's an alternative way of thinking + + align:start position:0% +there's an alternative way of thinking + + + align:start position:0% +there's an alternative way of thinking +about it that's a much lower frequency + + align:start position:0% +about it that's a much lower frequency + + + align:start position:0% +about it that's a much lower frequency +if you go to 6 it's absurd to think + + align:start position:0% +if you go to 6 it's absurd to think + + + align:start position:0% +if you go to 6 it's absurd to think +about 6 as being the frequency right the + + align:start position:0% +about 6 as being the frequency right the + + + align:start position:0% +about 6 as being the frequency right the +thing that your eye sees is this low + + align:start position:0% +thing that your eye sees is this low + + + align:start position:0% +thing that your eye sees is this low +frequency then you would never guess + + align:start position:0% +frequency then you would never guess + + + align:start position:0% +frequency then you would never guess +that I had sampled the high frequency + + align:start position:0% +that I had sampled the high frequency + + + align:start position:0% +that I had sampled the high frequency +thing that's what we mean by the + + align:start position:0% +thing that's what we mean by the + + + align:start position:0% +thing that's what we mean by the +frequencies rapping there are two + + align:start position:0% +frequencies rapping there are two + + + align:start position:0% +frequencies rapping there are two +different ways there are two different + + align:start position:0% +different ways there are two different + + + align:start position:0% +different ways there are two different +waveforms that you can sample and get + + align:start position:0% +waveforms that you can sample and get + + + align:start position:0% +waveforms that you can sample and get +the same blue circles the same samples + + align:start position:0% +the same blue circles the same samples + + + align:start position:0% +the same blue circles the same samples +you could sample 6n or 2 pi minus 6n and + + align:start position:0% +you could sample 6n or 2 pi minus 6n and + + + align:start position:0% +you could sample 6n or 2 pi minus 6n and +you would get the same thing that's so + + align:start position:0% +you would get the same thing that's so + + + align:start position:0% +you would get the same thing that's so +that's the reason we say that the + + align:start position:0% +that's the reason we say that the + + + align:start position:0% +that's the reason we say that the +discrete frequencies rap ok so that's + + align:start position:0% +discrete frequencies rap ok so that's + + + align:start position:0% +discrete frequencies rap ok so that's +the the reasoning behind thinking about + + align:start position:0% +the the reasoning behind thinking about + + + align:start position:0% +the the reasoning behind thinking about +this so there's a way about thinking of + + align:start position:0% +this so there's a way about thinking of + + + align:start position:0% +this so there's a way about thinking of +thinking about v as this whole distance + + align:start position:0% +thinking about v as this whole distance + + + align:start position:0% +thinking about v as this whole distance +around like that but there's another way + + align:start position:0% +around like that but there's another way + + + align:start position:0% +around like that but there's another way +of thinking about it as just the + + align:start position:0% +of thinking about it as just the + + + align:start position:0% +of thinking about it as just the +negative frequency coming this way and + + align:start position:0% +negative frequency coming this way and + + + align:start position:0% +negative frequency coming this way and +since they come in pairs regardless of + + align:start position:0% +since they come in pairs regardless of + + + align:start position:0% +since they come in pairs regardless of +the way I think about it I've always got + + align:start position:0% +the way I think about it I've always got + + + align:start position:0% +the way I think about it I've always got +the pair there to make sense out of + + align:start position:0% +the pair there to make sense out of + + + align:start position:0% +the pair there to make sense out of +either interpretation that's the hardest + + align:start position:0% +either interpretation that's the hardest + + + align:start position:0% +either interpretation that's the hardest +part in DT it's not hard it's just the + + align:start position:0% +part in DT it's not hard it's just the + + + align:start position:0% +part in DT it's not hard it's just the +hardest part okay if you get that that's + + align:start position:0% +hardest part okay if you get that that's + + + align:start position:0% +hardest part okay if you get that that's +the only trick in DT so the answer then + + align:start position:0% +the only trick in DT so the answer then + + + align:start position:0% +the only trick in DT so the answer then +is number 5 so what kind of a filter is + + align:start position:0% +is number 5 so what kind of a filter is + + + align:start position:0% +is number 5 so what kind of a filter is +this you remember we want to have an + + align:start position:0% +this you remember we want to have an + + + align:start position:0% +this you remember we want to have an +intuition just like if we if we looked + + align:start position:0% +intuition just like if we if we looked + + + align:start position:0% +intuition just like if we if we looked +at CT right if I told you that I had a + + align:start position:0% +at CT right if I told you that I had a + + + align:start position:0% +at CT right if I told you that I had a +CT system and I looked at the s plane + + align:start position:0% + + + + align:start position:0% + +and I told you that there was a poll + + align:start position:0% +and I told you that there was a poll + + + align:start position:0% +and I told you that there was a poll +there what kind of a system is that high + + align:start position:0% +there what kind of a system is that high + + + align:start position:0% +there what kind of a system is that high +pass low pass bandpass stop and I pass + + align:start position:0% +pass low pass bandpass stop and I pass + + + align:start position:0% +pass low pass bandpass stop and I pass +low-pass bandpass what CT system single + + align:start position:0% +low-pass bandpass what CT system single + + + align:start position:0% +low-pass bandpass what CT system single +pole low-pass it's a low pass because of + + align:start position:0% +pole low-pass it's a low pass because of + + + align:start position:0% +pole low-pass it's a low pass because of +Booty right right you like moody right + + align:start position:0% +Booty right right you like moody right + + + align:start position:0% +Booty right right you like moody right +it's because if we think about + + align:start position:0% +it's because if we think about + + + align:start position:0% +it's because if we think about +frequencies near zero we get one game + + align:start position:0% +frequencies near zero we get one game + + + align:start position:0% +frequencies near zero we get one game +and if we think about frequencies + + align:start position:0% +and if we think about frequencies + + + align:start position:0% +and if we think about frequencies +becoming very large the game falls off + + align:start position:0% +becoming very large the game falls off + + + align:start position:0% +becoming very large the game falls off +linearly after that what kind of a + + align:start position:0% +linearly after that what kind of a + + + align:start position:0% +linearly after that what kind of a +filter is this one one two three four + + align:start position:0% +filter is this one one two three four + + + align:start position:0% +filter is this one one two three four +five yeah it's a high-pass filter right + + align:start position:0% +five yeah it's a high-pass filter right + + + align:start position:0% +five yeah it's a high-pass filter right +it's a high-pass filter because this + + align:start position:0% +it's a high-pass filter because this + + + align:start position:0% +it's a high-pass filter because this +pole is in the denominator this vector + + align:start position:0% +pole is in the denominator this vector + + + align:start position:0% +pole is in the denominator this vector +is large when we're at DC and it's short + + align:start position:0% +is large when we're at DC and it's short + + + align:start position:0% +is large when we're at DC and it's short +where where the high frequencies in the + + align:start position:0% +where where the high frequencies in the + + + align:start position:0% +where where the high frequencies in the +denominators that makes the filter be + + align:start position:0% +denominators that makes the filter be + + + align:start position:0% +denominators that makes the filter be +big for high frequencies compared to low + + align:start position:0% +big for high frequencies compared to low + + + align:start position:0% +big for high frequencies compared to low +frequencies okay so that's the only + + align:start position:0% +frequencies okay so that's the only + + + align:start position:0% +frequencies okay so that's the only +thing that's different about DTV okay in + + align:start position:0% +thing that's different about DTV okay in + + + align:start position:0% +thing that's different about DTV okay in +the last ten minutes what I want to do + + align:start position:0% +the last ten minutes what I want to do + + + align:start position:0% +the last ten minutes what I want to do +is introduce the idea of a Fourier + + align:start position:0% +is introduce the idea of a Fourier + + + align:start position:0% +is introduce the idea of a Fourier +series because that's where we're going + + align:start position:0% +series because that's where we're going + + + align:start position:0% +series because that's where we're going +with all this junk we want to understand + + align:start position:0% +with all this junk we want to understand + + + align:start position:0% +with all this junk we want to understand +DT frequency responses so that we can + + align:start position:0% +DT frequency responses so that we can + + + align:start position:0% +DT frequency responses so that we can +generate a Fourier series so the idea is + + align:start position:0% +generate a Fourier series so the idea is + + + align:start position:0% +generate a Fourier series so the idea is +exactly the same as what we do in CT we + + align:start position:0% +exactly the same as what we do in CT we + + + align:start position:0% +exactly the same as what we do in CT we +want to represent a DT signal as a sum + + align:start position:0% +want to represent a DT signal as a sum + + + align:start position:0% +want to represent a DT signal as a sum +of complex geometric s-- right we want + + align:start position:0% +of complex geometric s-- right we want + + + align:start position:0% +of complex geometric s-- right we want +to think of it as the sum of frequencies + + align:start position:0% +to think of it as the sum of frequencies + + + align:start position:0% +to think of it as the sum of frequencies +and the trick is to find out what that + + align:start position:0% +and the trick is to find out what that + + + align:start position:0% +and the trick is to find out what that +sum is the the thing that's different is + + align:start position:0% +sum is the the thing that's different is + + + align:start position:0% +sum is the the thing that's different is +that frequencies rap because the + + align:start position:0% +that frequencies rap because the + + + align:start position:0% +that frequencies rap because the +frequencies rap in CT the frequencies + + align:start position:0% +frequencies rap in CT the frequencies + + + align:start position:0% +frequencies rap in CT the frequencies +don't rap in CT how many harmonics do we + + align:start position:0% +don't rap in CT how many harmonics do we + + + align:start position:0% +don't rap in CT how many harmonics do we +have to think about for an arbitrary CT + + align:start position:0% +have to think about for an arbitrary CT + + + align:start position:0% +have to think about for an arbitrary CT +signal infinite right when we think + + align:start position:0% +signal infinite right when we think + + + align:start position:0% +signal infinite right when we think +about a CTE Fourier series you think + + align:start position:0% +about a CTE Fourier series you think + + + align:start position:0% +about a CTE Fourier series you think +about the fundamental the second + + align:start position:0% +about the fundamental the second + + + align:start position:0% +about the fundamental the second +harmonic the third harmonic the fourth + + align:start position:0% +harmonic the third harmonic the fourth + + + align:start position:0% +harmonic the third harmonic the fourth +fifth sixth seventh eighth ninth tenth + + align:start position:0% +fifth sixth seventh eighth ninth tenth + + + align:start position:0% +fifth sixth seventh eighth ninth tenth +through infinity in principle they all + + align:start position:0% +through infinity in principle they all + + + align:start position:0% +through infinity in principle they all +matter + + align:start position:0% +matter + + + align:start position:0% +matter +in DT because of the wrapping there's a + + align:start position:0% +in DT because of the wrapping there's a + + + align:start position:0% +in DT because of the wrapping there's a +finite number of it's pretty easy to see + + align:start position:0% +finite number of it's pretty easy to see + + + align:start position:0% +finite number of it's pretty easy to see +that if you think about choose any + + align:start position:0% +that if you think about choose any + + + align:start position:0% +that if you think about choose any +frequency assume that that's periodic + + align:start position:0% +frequency assume that that's periodic + + + align:start position:0% +frequency assume that that's periodic +and say capital n I'm just choosing the + + align:start position:0% +and say capital n I'm just choosing the + + + align:start position:0% +and say capital n I'm just choosing the +period to be capital n just like we + + align:start position:0% +period to be capital n just like we + + + align:start position:0% +period to be capital n just like we +would say the period in CT is capital T + + align:start position:0% +would say the period in CT is capital T + + + align:start position:0% +would say the period in CT is capital T +if the signal is periodic and capital n + + align:start position:0% +if the signal is periodic and capital n + + + align:start position:0% +if the signal is periodic and capital n +if it was originally a complex geometric + + align:start position:0% +if it was originally a complex geometric + + + align:start position:0% +if it was originally a complex geometric +then because of the factoring properties + + align:start position:0% +then because of the factoring properties + + + align:start position:0% +then because of the factoring properties +of the complex geometric it must be the + + align:start position:0% +of the complex geometric it must be the + + + align:start position:0% +of the complex geometric it must be the +case that this number in order to make + + align:start position:0% +case that this number in order to make + + + align:start position:0% +case that this number in order to make +it equal to that this number must be one + + align:start position:0% + + + + align:start position:0% + +the only way that number could be one + + align:start position:0% +the only way that number could be one + + + align:start position:0% +the only way that number could be one +would be if capital Omega is a sub + + align:start position:0% +would be if capital Omega is a sub + + + align:start position:0% +would be if capital Omega is a sub +multiple of 2pi that means that if we're + + align:start position:0% +multiple of 2pi that means that if we're + + + align:start position:0% +multiple of 2pi that means that if we're +thinking about periodic signals in eight + + align:start position:0% +thinking about periodic signals in eight + + + align:start position:0% +thinking about periodic signals in eight +there are exactly eight frequencies we + + align:start position:0% +there are exactly eight frequencies we + + + align:start position:0% +there are exactly eight frequencies we +need to worry about and no more the + + align:start position:0% +need to worry about and no more the + + + align:start position:0% +need to worry about and no more the +ninth one alias is back to the first the + + align:start position:0% +ninth one alias is back to the first the + + + align:start position:0% +ninth one alias is back to the first the +tenth when alias is back to the second + + align:start position:0% +tenth when alias is back to the second + + + align:start position:0% +tenth when alias is back to the second +except Robin there's only eight of them + + align:start position:0% +except Robin there's only eight of them + + + align:start position:0% +except Robin there's only eight of them +that's the big difference between C T + + align:start position:0% +that's the big difference between C T + + + align:start position:0% +that's the big difference between C T +and DT in DT if we were thinking about + + align:start position:0% +and DT in DT if we were thinking about + + + align:start position:0% +and DT in DT if we were thinking about +sequences of length three there would be + + align:start position:0% +sequences of length three there would be + + + align:start position:0% +sequences of length three there would be +three frequencies we have to worry about + + align:start position:0% +three frequencies we have to worry about + + + align:start position:0% +three frequencies we have to worry about +if we were thinking of frequent + + align:start position:0% +if we were thinking of frequent + + + align:start position:0% +if we were thinking of frequent +sequences of length four this for the + + align:start position:0% +sequences of length four this for the + + + align:start position:0% +sequences of length four this for the +number of frequencies and the number of + + align:start position:0% +number of frequencies and the number of + + + align:start position:0% +number of frequencies and the number of +samples matches in fact that's not too + + align:start position:0% +samples matches in fact that's not too + + + align:start position:0% +samples matches in fact that's not too +surprising because if you just think + + align:start position:0% +surprising because if you just think + + + align:start position:0% +surprising because if you just think +about it in terms of knowns and unknowns + + align:start position:0% +about it in terms of knowns and unknowns + + + align:start position:0% +about it in terms of knowns and unknowns +if we want to represent an arbitrary + + align:start position:0% +if we want to represent an arbitrary + + + align:start position:0% +if we want to represent an arbitrary +signal of length four in terms of + + align:start position:0% +signal of length four in terms of + + + align:start position:0% +signal of length four in terms of +frequencies we better have four of them + + align:start position:0% +frequencies we better have four of them + + + align:start position:0% +frequencies we better have four of them +here they are the idea is precisely the + + align:start position:0% +here they are the idea is precisely the + + + align:start position:0% +here they are the idea is precisely the +same as CTE except that there's a finite + + align:start position:0% +same as CTE except that there's a finite + + + align:start position:0% +same as CTE except that there's a finite +number of harmonics so we have to worry + + align:start position:0% +number of harmonics so we have to worry + + + align:start position:0% +number of harmonics so we have to worry +about the rules for figuring out what + + align:start position:0% +about the rules for figuring out what + + + align:start position:0% +about the rules for figuring out what +the harmonics are and there's a there's + + align:start position:0% +the harmonics are and there's a there's + + + align:start position:0% +the harmonics are and there's a there's +also a convenient way to think about DT + + align:start position:0% +also a convenient way to think about DT + + + align:start position:0% +also a convenient way to think about DT +Fourier series as matrices since we have + + align:start position:0% +Fourier series as matrices since we have + + + align:start position:0% +Fourier series as matrices since we have +a finite number of frequencies and a + + align:start position:0% +a finite number of frequencies and a + + + align:start position:0% +a finite number of frequencies and a +finite number of times there's some + + align:start position:0% +finite number of times there's some + + + align:start position:0% +finite number of times there's some +relation between the two + + align:start position:0% +relation between the two + + + align:start position:0% +relation between the two +you could have an arbitrary linear + + align:start position:0% +you could have an arbitrary linear + + + align:start position:0% +you could have an arbitrary linear +relationship between those sets of + + align:start position:0% +relationship between those sets of + + + align:start position:0% +relationship between those sets of +numbers X + + align:start position:0% +numbers X + + + align:start position:0% +numbers X +by a matrix so matrix turns out to be a + + align:start position:0% +by a matrix so matrix turns out to be a + + + align:start position:0% +by a matrix so matrix turns out to be a +very convenient way of thinking about DT + + align:start position:0% +very convenient way of thinking about DT + + + align:start position:0% +very convenient way of thinking about DT +Fourier series and there's an + + align:start position:0% +Fourier series and there's an + + + align:start position:0% +Fourier series and there's an +orthogonality principle exactly like + + align:start position:0% +orthogonality principle exactly like + + + align:start position:0% +orthogonality principle exactly like +there was in CT the orthogonality looks + + align:start position:0% +there was in CT the orthogonality looks + + + align:start position:0% +there was in CT the orthogonality looks +just like an inner product just like it + + align:start position:0% +just like an inner product just like it + + + align:start position:0% +just like an inner product just like it +did in deke in CT and CT it was the + + align:start position:0% +did in deke in CT and CT it was the + + + align:start position:0% +did in deke in CT and CT it was the +integral over any time of length capital + + align:start position:0% +integral over any time of length capital + + + align:start position:0% +integral over any time of length capital +T of the product of two frequencies is + + align:start position:0% +T of the product of two frequencies is + + + align:start position:0% +T of the product of two frequencies is +either 0 or capital T depending on + + align:start position:0% +either 0 or capital T depending on + + + align:start position:0% +either 0 or capital T depending on +whether the frequencies are the same or + + align:start position:0% +whether the frequencies are the same or + + + align:start position:0% +whether the frequencies are the same or +different same thing happens here and + + align:start position:0% +different same thing happens here and + + + align:start position:0% +different same thing happens here and +because of that there's a very simple + + align:start position:0% +because of that there's a very simple + + + align:start position:0% +because of that there's a very simple +way to sift out the case element of the + + align:start position:0% +way to sift out the case element of the + + + align:start position:0% +way to sift out the case element of the +series just like there was an + + align:start position:0% +series just like there was an + + + align:start position:0% +series just like there was an +analogously simple way to sift out the K + + align:start position:0% +analogously simple way to sift out the K + + + align:start position:0% +analogously simple way to sift out the K +element of a CT series all of this is + + align:start position:0% +element of a CT series all of this is + + + align:start position:0% +element of a CT series all of this is +precisely the same as what we did in DT + + align:start position:0% +precisely the same as what we did in DT + + + align:start position:0% +precisely the same as what we did in DT +NCTE + + align:start position:0% +NCTE + + + align:start position:0% +NCTE +the result is analysis and synthesis + + align:start position:0% +the result is analysis and synthesis + + + align:start position:0% +the result is analysis and synthesis +formulas that look similar except their + + align:start position:0% +formulas that look similar except their + + + align:start position:0% +formulas that look similar except their +sums instead of integrals they look just + + align:start position:0% +sums instead of integrals they look just + + + align:start position:0% +sums instead of integrals they look just +like the CT the interesting thing is + + align:start position:0% +like the CT the interesting thing is + + + align:start position:0% +like the CT the interesting thing is +that they both have a finite length in + + align:start position:0% +that they both have a finite length in + + + align:start position:0% +that they both have a finite length in +CT there was an infinite sum over K in + + align:start position:0% +CT there was an infinite sum over K in + + + align:start position:0% +CT there was an infinite sum over K in +DT there's a finite sum over K and so + + align:start position:0% +DT there's a finite sum over K and so + + + align:start position:0% +DT there's a finite sum over K and so +that means that there's a very + + align:start position:0% +that means that there's a very + + + align:start position:0% +that means that there's a very +convenient matrix way of looking at how + + align:start position:0% +convenient matrix way of looking at how + + + align:start position:0% +convenient matrix way of looking at how +would you construct an arbitrary signal + + align:start position:0% +would you construct an arbitrary signal + + + align:start position:0% +would you construct an arbitrary signal +in time from frequency components and + + align:start position:0% +in time from frequency components and + + + align:start position:0% +in time from frequency components and +how would you compute the frequency + + align:start position:0% +how would you compute the frequency + + + align:start position:0% +how would you compute the frequency +components from the time components it's + + align:start position:0% +components from the time components it's + + + align:start position:0% +components from the time components it's +just that in DT the convenient way to + + align:start position:0% +just that in DT the convenient way to + + + align:start position:0% +just that in DT the convenient way to +express that relationship you can so + + align:start position:0% +express that relationship you can so + + + align:start position:0% +express that relationship you can so +express it as an analysis and synthesis + + align:start position:0% +express it as an analysis and synthesis + + + align:start position:0% +express it as an analysis and synthesis +formula that's what these are but a much + + align:start position:0% +formula that's what these are but a much + + + align:start position:0% +formula that's what these are but a much +more friendly way of thinking about it + + align:start position:0% +more friendly way of thinking about it + + + align:start position:0% +more friendly way of thinking about it +is as a matrix those two representations + + align:start position:0% +is as a matrix those two representations + + + align:start position:0% +is as a matrix those two representations +are absolutely identical so the idea + + align:start position:0% +are absolutely identical so the idea + + + align:start position:0% +are absolutely identical so the idea +then for today was generalize CT to DT + + align:start position:0% +then for today was generalize CT to DT + + + align:start position:0% +then for today was generalize CT to DT +DT is really useful when you're trying + + align:start position:0% +DT is really useful when you're trying + + + align:start position:0% +DT is really useful when you're trying +to do signal processing with digital + + align:start position:0% +to do signal processing with digital + + + align:start position:0% +to do signal processing with digital +electronics digital electronics is the + + align:start position:0% +electronics digital electronics is the + + + align:start position:0% +electronics digital electronics is the +way to go because they're so inexpensive + + align:start position:0% +way to go because they're so inexpensive + + + align:start position:0% +way to go because they're so inexpensive +and powerful the big difference so unit + + align:start position:0% +and powerful the big difference so unit + + + align:start position:0% +and powerful the big difference so unit +circle wrap finite length and that + + align:start position:0% +circle wrap finite length and that + + + align:start position:0% +circle wrap finite length and that +finite length one + + align:start position:0% +finite length one + + + align:start position:0% +finite length one +is really the key to signal processing + + align:start position:0% +is really the key to signal processing + + + align:start position:0% +is really the key to signal processing +because we can represent finite length + + align:start position:0% +because we can represent finite length + + + align:start position:0% +because we can represent finite length +signal in time with a finite number of + + align:start position:0% +signal in time with a finite number of + + + align:start position:0% +signal in time with a finite number of +samples there's a match and that's the + + align:start position:0% +samples there's a match and that's the + + + align:start position:0% +samples there's a match and that's the +reason that's the the method of choice + + align:start position:0% +reason that's the the method of choice + + + align:start position:0% +reason that's the the method of choice +when we do digital signal processing and + + align:start position:0% +when we do digital signal processing and + + + align:start position:0% +when we do digital signal processing and +we'll talk more about that next time + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/h1GtR8xJraw.txt b/h1GtR8xJraw.txt new file mode 100644 index 0000000000000000000000000000000000000000..0a7728b50a922a4586c6409a3f0fba6746d092be --- /dev/null +++ b/h1GtR8xJraw.txt @@ -0,0 +1,819 @@ +align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so many of us are using camera phones + + align:start position:0% +so many of us are using camera phones + + + align:start position:0% +so many of us are using camera phones +and sometimes tablets to make some + + align:start position:0% +and sometimes tablets to make some + + + align:start position:0% +and sometimes tablets to make some +pretty terrific pictures I made this one + + align:start position:0% +pretty terrific pictures I made this one + + + align:start position:0% +pretty terrific pictures I made this one +I was sautéing some colorful peppers and + + align:start position:0% +I was sautéing some colorful peppers and + + + align:start position:0% +I was sautéing some colorful peppers and +when I put the cover on I saw what I + + align:start position:0% +when I put the cover on I saw what I + + + align:start position:0% +when I put the cover on I saw what I +thought would be a pretty beautiful + + align:start position:0% +thought would be a pretty beautiful + + + align:start position:0% +thought would be a pretty beautiful +image so of course I quickly grabed my + + align:start position:0% +image so of course I quickly grabed my + + + align:start position:0% +image so of course I quickly grabed my +phone and that's what this is about + + align:start position:0% +phone and that's what this is about + + + align:start position:0% +phone and that's what this is about +isn't it the ability to quickly take a + + align:start position:0% +isn't it the ability to quickly take a + + + align:start position:0% +isn't it the ability to quickly take a +picture without a big deal using pH + + align:start position:0% +picture without a big deal using pH + + + align:start position:0% +picture without a big deal using pH +cameras to quickly make images when we + + align:start position:0% +cameras to quickly make images when we + + + align:start position:0% +cameras to quickly make images when we +see something interesting or in this + + align:start position:0% +see something interesting or in this + + + align:start position:0% +see something interesting or in this +case something very beautiful in my + + align:start position:0% +case something very beautiful in my + + + align:start position:0% +case something very beautiful in my +opinion so did my son by the way who + + align:start position:0% +opinion so did my son by the way who + + + align:start position:0% +opinion so did my son by the way who +made a whole series of photographs of my + + align:start position:0% +made a whole series of photographs of my + + + align:start position:0% +made a whole series of photographs of my +amazing birthday party with my family at + + align:start position:0% +amazing birthday party with my family at + + + align:start position:0% +amazing birthday party with my family at +peray in New York the dishes were + + align:start position:0% +peray in New York the dishes were + + + align:start position:0% +peray in New York the dishes were +created by Chef Jared Huth and so these + + align:start position:0% +created by Chef Jared Huth and so these + + + align:start position:0% +created by Chef Jared Huth and so these +pictures are basically portraits of each + + align:start position:0% +pictures are basically portraits of each + + + align:start position:0% +pictures are basically portraits of each +course all taken with his camera phone + + align:start position:0% +course all taken with his camera phone + + + align:start position:0% +course all taken with his camera phone +and by the way I adjusted the color + + align:start position:0% +and by the way I adjusted the color + + + align:start position:0% +and by the way I adjusted the color +later on for uploading all of these for + + align:start position:0% +later on for uploading all of these for + + + align:start position:0% +later on for uploading all of these for +this + + align:start position:0% +this + + + align:start position:0% +this +tutorial and here when we were permitted + + align:start position:0% +tutorial and here when we were permitted + + + align:start position:0% +tutorial and here when we were permitted +to take a look at the kitchen we see a + + align:start position:0% +to take a look at the kitchen we see a + + + align:start position:0% +to take a look at the kitchen we see a +place very much like a laboratory + + align:start position:0% +place very much like a laboratory + + + align:start position:0% +place very much like a laboratory +showing process and equipment and people + + align:start position:0% +showing process and equipment and people + + + align:start position:0% +showing process and equipment and people +doing their thing so camera phones do + + align:start position:0% +doing their thing so camera phones do + + + align:start position:0% +doing their thing so camera phones do +have an important place for a means of + + align:start position:0% +have an important place for a means of + + + align:start position:0% +have an important place for a means of +making very quick portraits of various + + align:start position:0% +making very quick portraits of various + + + align:start position:0% +making very quick portraits of various +places in the lab of the work of the + + align:start position:0% +places in the lab of the work of the + + + align:start position:0% +places in the lab of the work of the +equipment you could think about taking + + align:start position:0% +equipment you could think about taking + + + align:start position:0% +equipment you could think about taking +the picture and then cropping it for + + align:start position:0% +the picture and then cropping it for + + + align:start position:0% +the picture and then cropping it for +example as I did here but for the most + + align:start position:0% +example as I did here but for the most + + + align:start position:0% +example as I did here but for the most +part the quality of the photograph is + + align:start position:0% +part the quality of the photograph is + + + align:start position:0% +part the quality of the photograph is +not what we're encouraging in this + + align:start position:0% +not what we're encouraging in this + + + align:start position:0% +not what we're encouraging in this +course if you remember we did a + + align:start position:0% +course if you remember we did a + + + align:start position:0% +course if you remember we did a +comparison between two images of a petri + + align:start position:0% +comparison between two images of a petri + + + align:start position:0% +comparison between two images of a petri +dish one with my phone camera and one + + align:start position:0% +dish one with my phone camera and one + + + align:start position:0% +dish one with my phone camera and one +with the flatbed scanner at a higher + + align:start position:0% +with the flatbed scanner at a higher + + + align:start position:0% +with the flatbed scanner at a higher +resolution well here is another + + align:start position:0% +resolution well here is another + + + align:start position:0% +resolution well here is another +difference for example of the device + + align:start position:0% +difference for example of the device + + + align:start position:0% +difference for example of the device +that we've seen before with a phone + + align:start position:0% +that we've seen before with a phone + + + align:start position:0% +that we've seen before with a phone +camera and with my digital camera and + + align:start position:0% +camera and with my digital camera and + + + align:start position:0% +camera and with my digital camera and +you'll see that the information is just + + align:start position:0% +you'll see that the information is just + + + align:start position:0% +you'll see that the information is just +not there in the phone camera because of + + align:start position:0% +not there in the phone camera because of + + + align:start position:0% +not there in the phone camera because of +the file size it's just too small but + + align:start position:0% +the file size it's just too small but + + + align:start position:0% +the file size it's just too small but +once again I'm going to say there's + + align:start position:0% +once again I'm going to say there's + + + align:start position:0% +once again I'm going to say there's +definitely a place for these very quick + + align:start position:0% +definitely a place for these very quick + + + align:start position:0% +definitely a place for these very quick +and impulsive images which you're seeing + + align:start position:0% +and impulsive images which you're seeing + + + align:start position:0% +and impulsive images which you're seeing +now for the use of web designs for + + align:start position:0% +now for the use of web designs for + + + align:start position:0% +now for the use of web designs for +example I was having a really great time + + align:start position:0% +example I was having a really great time + + + align:start position:0% +example I was having a really great time +walking around this lab making a few + + align:start position:0% +walking around this lab making a few + + + align:start position:0% +walking around this lab making a few +images which worked better with a little + + align:start position:0% +images which worked better with a little + + + align:start position:0% +images which worked better with a little +bit of cropping and in fact were used + + align:start position:0% +bit of cropping and in fact were used + + + align:start position:0% +bit of cropping and in fact were used +for the labs website so there is a place + + align:start position:0% +for the labs website so there is a place + + + align:start position:0% +for the labs website so there is a place +for this kind of Photography but + + align:start position:0% +for this kind of Photography but + + + align:start position:0% +for this kind of Photography but +remember the quality is just not there + + align:start position:0% +remember the quality is just not there + + + align:start position:0% +remember the quality is just not there +and is not good enough for a journal + + align:start position:0% +and is not good enough for a journal + + + align:start position:0% +and is not good enough for a journal +article and certainly not a cover it + + align:start position:0% +article and certainly not a cover it + + + align:start position:0% +article and certainly not a cover it +might well be someday the technology is + + align:start position:0% +might well be someday the technology is + + + align:start position:0% +might well be someday the technology is +constantly changing with each iteration + + align:start position:0% +constantly changing with each iteration + + + align:start position:0% +constantly changing with each iteration +of the phone so yes it's a great idea to + + align:start position:0% +of the phone so yes it's a great idea to + + + align:start position:0% +of the phone so yes it's a great idea to +practice walking around your lab + + align:start position:0% +practice walking around your lab + + + align:start position:0% +practice walking around your lab +creating these portraits and certainly + + align:start position:0% +creating these portraits and certainly + + + align:start position:0% +creating these portraits and certainly +it's an interesting way of getting you + + align:start position:0% +it's an interesting way of getting you + + + align:start position:0% +it's an interesting way of getting you +to see but in the end you've got to use + + align:start position:0% +to see but in the end you've got to use + + + align:start position:0% +to see but in the end you've got to use +your fullframe digital camera with a + + align:start position:0% +your fullframe digital camera with a + + + align:start position:0% +your fullframe digital camera with a +best + + align:start position:0% +best + + + align:start position:0% +best +resolution here's an example of where I + + align:start position:0% +resolution here's an example of where I + + + align:start position:0% +resolution here's an example of where I +had absolutely no time at all to make a + + align:start position:0% +had absolutely no time at all to make a + + + align:start position:0% +had absolutely no time at all to make a +picture for what I knew was going to be + + align:start position:0% +picture for what I knew was going to be + + + align:start position:0% +picture for what I knew was going to be +a grand submission so this is a pretty + + align:start position:0% +a grand submission so this is a pretty + + + align:start position:0% +a grand submission so this is a pretty +pretty fast image that I made with my + + align:start position:0% +pretty fast image that I made with my + + + align:start position:0% +pretty fast image that I made with my +phone pretty awful part of some + + align:start position:0% +phone pretty awful part of some + + + align:start position:0% +phone pretty awful part of some +equipment that was necessary in the + + align:start position:0% +equipment that was necessary in the + + + align:start position:0% +equipment that was necessary in the +research + + align:start position:0% +research + + + align:start position:0% +research +took the image straightened it out then + + align:start position:0% +took the image straightened it out then + + + align:start position:0% +took the image straightened it out then +cropped it like crazy knowing that + + align:start position:0% +cropped it like crazy knowing that + + + align:start position:0% +cropped it like crazy knowing that +eventually the final image was not going + + align:start position:0% +eventually the final image was not going + + + align:start position:0% +eventually the final image was not going +to be up close it was a figure on the + + align:start position:0% +to be up close it was a figure on the + + + align:start position:0% +to be up close it was a figure on the +first page of a submission so I did crop + + align:start position:0% +first page of a submission so I did crop + + + align:start position:0% +first page of a submission so I did crop +it in it doesn't look brilliant right + + align:start position:0% +it in it doesn't look brilliant right + + + align:start position:0% +it in it doesn't look brilliant right +now but in the next image I edited out + + align:start position:0% +now but in the next image I edited out + + + align:start position:0% +now but in the next image I edited out +certain pieces and created a laser light + + align:start position:0% +certain pieces and created a laser light + + + align:start position:0% +certain pieces and created a laser light +which was all illustrative of of course + + align:start position:0% +which was all illustrative of of course + + + align:start position:0% +which was all illustrative of of course +not for real and so this is what I + + align:start position:0% +not for real and so this is what I + + + align:start position:0% +not for real and so this is what I +finally did I inserted it in a figure + + align:start position:0% +finally did I inserted it in a figure + + + align:start position:0% +finally did I inserted it in a figure +that we used for a page in the + + align:start position:0% +that we used for a page in the + + + align:start position:0% +that we used for a page in the +submission this is the page that we + + align:start position:0% +submission this is the page that we + + + align:start position:0% +submission this is the page that we +finally wound up with replacing this + + align:start position:0% +finally wound up with replacing this + + + align:start position:0% +finally wound up with replacing this +image the idea behind this is showing + + align:start position:0% +image the idea behind this is showing + + + align:start position:0% +image the idea behind this is showing +the two next to each other I hope you + + align:start position:0% +the two next to each other I hope you + + + align:start position:0% +the two next to each other I hope you +agree that the image that I quickly made + + align:start position:0% +agree that the image that I quickly made + + + align:start position:0% +agree that the image that I quickly made +on the right is more appealing and it is + + align:start position:0% +on the right is more appealing and it is + + + align:start position:0% +on the right is more appealing and it is +taking up real estate on on the page so + + align:start position:0% +taking up real estate on on the page so + + + align:start position:0% +taking up real estate on on the page so +why not make it into a summary graphic + + align:start position:0% +why not make it into a summary graphic + + + align:start position:0% +why not make it into a summary graphic +as opposed to putting every single thing + + align:start position:0% +as opposed to putting every single thing + + + align:start position:0% +as opposed to putting every single thing +you could think of in a graphic and make + + align:start position:0% +you could think of in a graphic and make + + + align:start position:0% +you could think of in a graphic and make +it unreadable this is a way of using + + align:start position:0% +it unreadable this is a way of using + + + align:start position:0% +it unreadable this is a way of using +very very fast made images in a + + align:start position:0% +very very fast made images in a + + + align:start position:0% +very very fast made images in a +submission \ No newline at end of file diff --git a/heBvViSi9xQ.txt b/heBvViSi9xQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..d68a057d21842b4130332f3974ed7e4bffae3b11 --- /dev/null +++ b/heBvViSi9xQ.txt @@ -0,0 +1,2050 @@ +The last time I spent solving a +system of equations dealing with + +the chilling of this hardboiled +egg being put in an ice bath. + +We called T1 the temperature of +the yoke and T2 the temperature + +of the white. +What I am going to do is + +revisit that same system of +equations, but basically the + +topic for today is to learn to +solve that system of equations + +by a completely different +method. + +It is the method that is +normally used in practice. + +Elimination is used mostly by +people who have forgotten how to + +do it any other way. +Now, in order to make it a + +little more general, +I am not going to use the + +dependent variables T1 and T2 +because they suggest temperature + +a little too closely. +Let's change them to neutral + +variables. +I will use x equals T1, + +and for T2 I will just use +y. + +I am not going to re-derive +anything. + +I am not going to resolve +anything. + +I am not going to repeat +anything of what I did last + +time, except to write down to +remind you what the system was + +in terms of these variables, +the system we derived using the + +particular conductivity +constants, two and three, + +respectively. +The system was this one, + +minus 2x plus 2y. +And the y prime was + +2x minus 5y. +And so we solved this by + +elimination. +We got a single second-order + +equation with constant +coefficients, + +which we solved in the usual +way. + +From that I derived what the x +was, from that we derived what + +the y was, and then I put them +all together. + +I will just remind you what the +final solution was when written + +out in terms of arbitrary +constants. + +It was c1 times e to the +negative t plus c2 e to the + +negative 6t, +and y was c1 over 2 e + +to the negative t minus 2c2 e to +the negative 6t. + +That was the solution we got. + +And then I went on to put in +initial conditions, + +but we are not going to explore +that aspect of it today. + +We will in a week or so. +This was the general solution + +because it had two arbitrary +constants in it. + +What I want to do now is +revisit this and do it by a + +different method, +which makes heavy use of + +matrices. +That is a prerequisite for this + +course, so I am assuming that +you reviewed a little bit about + +matrices. +And it is in your book. + +Your book puts in a nice little +review section. + +Two-by-two and three-by-three +will be good enough for 18.03 + +mostly because I don't want you +to calculate all night on bigger + +matrices, bigger systems. +So nothing serious, + +matrix multiplication, +solving systems of linear + +equations, end-by-end systems. +I will remind you at the + +appropriate places today of what +it is you need to remember. + +The very first thing we are +going to do is, + +let's see. +I haven't figured out the color + +coding for this lecture yet, +but let's make this system in + +green and the solution can be in +purple. + +Invisible purple, +but I have a lot of it. + +Let's abbreviate, +first of all, + +the system using matrices. +I am going to make a column + +vector out of (x, +y). + +Then you differentiate a column +vector by differentiating each + +component. +I can write the left-hand side + +of the system as (x, +y) prime. + +How about the right-hand side? + +Well, I say I can just write +the matrix of coefficients to + +negative 2, 2, +2, negative 5 times x,y. + +And I say that this matrix +equation says exactly the same + +thing as that green equation +and, therefore, + +it is legitimate to put it up +in green, too. + +The top here is x prime. +What is the top here? + +After I multiply these two I +get a column vector. + +And what is its top entry? +It is negative 2x plus 2y. + +There it is. + +And the bottom entry the same +way is 2x minus 5y, + +just as it is down there. +Now, what I want to do is, + +well, maybe I should translate +the solution. + +What does the solution look +like? + +We got that, +too. + +How am I going to write this as +a matrix equation? + +Actually, if I told you to use +matrices, use vectors, + +the point at which you might be +most hesitant is this one right + +here, the very next step. +Because how you should write it + +is extremely well-concealed in +this notation. + +But the point is, +this is a column vector and I + +am adding together two column +vectors. + +And what is in each one of the +column vectors? + +Think of these two things as a +column vector. + +Pull out all the scalars from +them that you can. + +Well, you see that c1 is a +common factor of both entries + +and so is e to the negative t, +that function. + +Now, if I pull both of those +out of the vector, + +what is left of the vector? +Well, you cannot even see it. + +What is left is a 1 up here and +a one-half there. + +So I am going to write that in +the following form. + +I will put out the c1, +it's the common factor in both, + +and put that out front. +Then I will put in the guts of + +the vector, even though you +cannot see it, + +the column vector 1, +one-half. + +And then I will put the other + +scalar function in back. +The only reason for putting one + +of these in front and one in +back is visual so to make it + +easy to read. +There is no other reason. + +You could put the c1 here, +you could put it here, + +you could put the e negative t +in front if you want + +to, but people will fire you. +Don't do that. + +Write it the standard way +because that is the way that it + +is easiest to read. +The constants out front, + +the functions behind, +and the column vector of + +numbers in the middle. +And so the other one will be + +written how? +Well, here, that one is a + +little more transparent. +c2, 1, 2 and the other thing is + +e to the negative 6t. + +There is our solution. +That is going to need a lot of + +purple, but I have it. + +And now I want to talk about +how the new method of solving + +the equation. +It is based just on the same + +idea as the way we solve +second-order equations. + +Yes, question. + +Oh, here. +Sorry. + +This should be negative two. +Thanks very much. + +What I am going to use is a +trial solution. + +Remember when we had a +second-order equation with + +constant coefficients the very +first thing I did was I said we + +are going to try a solution of +the form e to the rt. + +Why that? +Well, because Oiler thought of + +it and it has been known for 200 +or 300 years that that is the + +thing you should do. +Well, this has not been known + +nearly as long because matrices +were only invented around 1880 + +or so, and people did not really +use them to solve systems of + +differential equations until the +middle of the last century, + +1950-1960. +If you look at books written in + +1950, they won't even talk about +systems of differential + +equations, or talk very little +anyway and they won't solve them + +using matrices. +This is only 50 years old. + +I mean, my God, +in mathematics that is very up + +to date, particularly elementary +mathematics. + +Anyway, the method of solving +is going to use as a trial + +solution. +Now, if you were left to your + +own devices you might say, +well, let's try x equals some + +constant times e to the lambda1 +t and y + +equals some other constant times +e to the lambda2 t. + +Now, if you try that, + +it is a sensible thing to try, +but it will turn out not to + +work. +And that is the reason I have + +written out this particular +solution, so we can see what + +solutions look like. +The essential point is here is + +the basic solution I am trying +to find. + +Here is another one. +Their form is a column vector + +of constants. +But they both use the same + +exponential factor, +which is the point. + +In other words, +I should not use here, + +in my trial solution, +two different lambdas, + +I should use the same lambda. +And so the way to write the + +trial solution is (x, +y) equals two unknown numbers, + +that or that or whatever, +times e to a single unknown + +exponent factor. +Let's call it lambda t. + +It is called lambda. +It is called r. + +It is called m. +I have never seen it called + +anything but one of those three +things. + +I am using lambda. +Your book uses lambda. + +It is a common choice. +Let's stick with it. + +Now what is the next step? +Well, we plug into the system. + +Substitute into the system. +What are we going to get? + +Well, let's do it. +First of all, + +I have to differentiate. +The left-hand side asks me to + +differentiate this. +How do I differentiate this? + +Column vector times a function. +Well, the column vector acts as + +a constant. +And I differentiate that. + +That is lambda e to the lambda +t. + +So the (x, y) prime is (a1, +a2) times e to the lambda t + +times lambda. + +Now, it is ugly to put the + +lambda afterwards because it is +a number so you should put it in + +front, again, +to make things easier to read. + +But this lambda comes from +differentiating e to the lambda + +t and using the chain rule. + +This much is the left-hand +side. + +That is the derivative (x, +y) prime. + +I differentiate the x and I +differentiated the y. + +How about the right-hand side. +Well, the right-hand side is + +negative 2, 2, +2, negative 5 times what? + +Well, times (x, + +y), which is (a1, +a2) e to the lambda t. + +Now, the same thing that + +happened a month or a month and +a half ago happens now. + +The whole point of making that +substitution is that the e to + +the lambda t, +the function part of it drops + +out completely. +And one is left with what? + +An algebraic equation to be +solved for lambda a1 and a2. + +In other words, +by means of that substitution, + +and it basically uses the fact +that the coefficients are + +constant, what you have done is +reduced the problem of calculus, + +of solving differential +equations, to solving algebraic + +equations. +In some sense that is the only + +method there is, +unless you do numerical stuff. + +You reduce the calculus to +algebra. + +The Laplace transform is +exactly the same thing. + +All the work is algebra. +You turn the original + +differential equation into an +algebraic equation for Y of s, + +you solve it, +and then you use more algebra + +to find out what the original +little y of t was. + +It is not different here. +So let's solve this system of + +equations. +Now, the whole problem with + +solving this system, +first of all, + +what is the system? +Let's write it out explicitly. + +Well, it is really two +equations, isn't it? + +The first one says lambda a1 is +equal to negative 2 a1 + +plus 2 a2. +That is the first one. + +The other one says lambda a2 is +equal to 2 a1 minus 5 a2. + +Now, purely, +if you want to classify that, + +that is two equations and three +variables, three unknowns. + +The a1, a2, and lambda are all +unknown. + +And, unfortunately, +if you want to classify them + +correctly, they are nonlinear +equations because they are made + +nonlinear by the fact that you +have multiplied two of the + +variables. +Well, if you sit down and try + +to hack away at solving those +without a plan, + +you are not going to get +anywhere. + +It is going to be a mess. +Also, two equations and three + +unknowns is indeterminate. +You can solve three equations + +and three unknowns and get a +definite answer, + +but two equations and three +unknowns usually have an + +infinity of solutions. +Well, at this point it is the + +only idea that is required. +Well, this was a little idea, + +but I assume one would think of +that. + +And the idea that is required +here is, I think, + +not so unnatural, +it is not to view these a1, + +a2, and lambda as equal. +Not all variables are created + +equal. +Some are more equal than + +others. +a1 and a2 are definitely equal + +to each other, +and let's relegate lambda to + +the background. +In other words, + +I am going to think of lambda +as just a parameter. + +I am going to demote it from +the status of variable to + +parameter. +If I demoted it further it + +would just be an unknown +constant. + +That is as bad as you can be. +I am going to focus my + +attention on the a1, +a2 and sort of view the lambda + +as a nuisance. +Now, as soon as I do that, + +I see that these equations are +linear if I just look at them as + +equations in a1 and a2. +And moreover, + +they are not just linear, +they are homogenous. + +Because if I think of lambda +just as a parameter, + +I should rewrite the equations +this way. + +I am going to subtract this and +move the left-hand side to the + +right side, and it is going to +look like (minus 2 minus lambda) + +times a1 plus 2 a2 is equal to +zero. + +And the same way for the other + +one. +It is going to be 2a1 plus, + +what is the coefficient, +(minus 5 minus lambda) a2 + +equals zero. + +That is a pair of simultaneous +linear equations for determining + +a1 and a2, and the coefficients +involved are parameter lambda. + +Now, what is the point of doing +that? + +Well, now the point is whatever +you learned about linear + +equations, you should have +learned the most fundamental + +theorem of linear equations. +The main theorem is that you + +have a square system of +homogeneous equations, + +this is a two-by-two system so +it is square, + +it always has the trivial +solution, of course, + +a1, a2 equals zero. +Now, we don't want that trivial + +solution because if a1 and a2 +are zero, then so are x and y + +zero. +Now that is a solution. + +Unfortunately, +it is of no interest. + +If the solution were x, +y zero, it corresponds to the + +fact that this is an ice bath. +The yoke is at zero, + +the white is at zero and it +stays that way for all time + +until the ice melts. +So that is the solution we + +don't want. +We don't want the trivial + +solution. +Well, when does it have a + +nontrivial solution? +Nontrivial means non-zero, + +in other words. +If and only if this determinant + +is zero. + +In other words, +by using that theorem on linear + +equations, what we find is there +is a condition that lambda must + +satisfy, an equation in lambda +in order that we would be able + +to find non-zero values for a1 +and a2. + +Let's write it out. +I will recopy it over here. + +What was it? +Negative 2 minus lambda, + +two, here it was 2 and minus 5 +minus lambda. + +All right. +You have to expand the + +determinant. +In other words, + +we are trying to find out for +what values of lambda is this + +determinant zero. +Those will be the good values + +which lead to nontrivial +solutions for the a's. + +This is the equation lambda +plus 2. + +See, this is minus that and +minus that, the product of the + +two minus ones is plus one. +So it is lambda plus 2 times + +lambda plus 5, + +which is the product of the two +diagonal elements, + +minus the product of the two +anti-diagonal elements, + +which is 4, is equal to zero. +And if I write that out, + +what is that, +that is the equation lambda + +squared plus 7 lambda, + +5 lambda plus 2 lambda, +and then the constant term is + +10 minus 4 which is 6. +How many of you have long + +enough memories, +two-day memories that you + +remember that equation? +When I did the method of + +elimination, it led to exactly +the same equation except it had + +r's in it instead of lambda. +And this equation, + +therefore, is given the same +name and another color. + +Let's make it salmon. + +And it is called the +characteristic equation for this + +method. +All right. + +Now I am going to use now the +word from last time. + +You factor this. +From the factorization we get + +its root easily enough. +The roots are lambda equals + +negative 1 and +lambda equals negative 6 + +by factoring the +equation. + +Now what I am supposed to do? +You have to keep the different + +parts of the method together. +Now I have found the only + +values of lambda for which I +will be able to find nonzero + +values for the a1 and a2. +For each of those values of + +lambda, I now have to find the +corresponding a1 and a2. + +Let's do them one at a time. +Let's take first lambda equals + +negative one. +My problem is now to find a1 + +and a2. +Where am I going to find them + +from? +Well, from that system of + +equations over there. +I will recopy it over here. + +What is the system? +The hardest part of this is + +dealing with multiple minus +signs, but you had experience + +with that in determinants so you +know all about that. + +In other words, +there is the system of + +equations over there. +Let's recopy them here. + +Minus 2, minus minus 1 makes +minus 1. + +What's the other coefficient? +It is just plain old 2. + +Good. +There is my first equation. + +And when I substitute lambda +equals negative one + +for the second equation, +what do you get? + +2 a1 plus negative 5 minus +negative 1 makes negative 4. + +There is my system that will +find me a1 and a2. + +What is the first thing you +notice about it? + +You immediately notice that +this system is fake because this + +second equation is twice the +first one. + +Something is wrong. +No, something is right. + +If that did not happen, +if the second equation were not + +a constant multiple of the first +one then the only solution of + +the system would be a1 equals +zero, a2 equals zero because the + +determinant of the coefficients +would not be zero. + +The whole function of this +exercise was to find the value + +of lambda, negative 1, +for which the system would be + +redundant and, +therefore, would have a + +nontrivial solution. +Do you get that? + +In other words, +calculate the system out, + +just as I have done here, +you have an automatic check on + +the method. +If one equation is not a + +constant multiple of the other +you made a mistake. + +You don't have the right value +of lambda or you substituted + +into the system wrong, +which is frankly a more common + +error. +Go back, recheck first the + +substitution, +and if convinced that is right + +then recheck where you got +lambda from. + +But here everything is going +fine so we can now find out what + +the value of a1 and a2 are. +You don't have to go through a + +big song and dance for this +since most of the time you will + +have two-by-two equations and +now and then three-by-three. + +For two-by-two all you do is, +since we really have the same + +equation twice, +to get a solution I can assign + +one of the variables any value +and then simply solve for the + +other. +The natural thing to do is to + +make a2 equal one, +then I won't need fractions and + +then a1 will be a2. +So the solution is (2, + +1). +I am only trying to find one + +solution. +Any constant multiple of this + +would also be a solution, +as long as it wasn't zero, + +zero which is the trivial one. +And, therefore, + +this is a solution to this +system of algebraic equations. + +And the solution to the whole +system of differential equations + +is, this is only the (a1, +a2) part. + +I have to add to it, +as a factor, + +lambda is negative, +therefore, e to the minus t. + +There is our purple thing. + +See how I got it? +Starting with the trial + +solution, I first found out +through this procedure what the + +lambda's have to be. +Then I took the lambda and + +found what the corresponding a1 +and a2 that went with it and + +then made up my solution out of +that. + +Now, quickly I will do the same +thing for lambda + +equals negative 6. +Each one of these must be + +treated separately. +They are separate problems and + +you are looking for separate +solutions. + +Lambda equals negative 6. +What do I do? + +How do my equations look now? +Well, the first one is minus 2 + +minus negative 6 makes plus 4. +It is 4a1 plus 2a2 equals zero. + +Then I hold my breath while I + +calculate the second one to see +if it comes out to be a constant + +multiple. +I get 2a1 plus negative 5 minus + +negative 6, which makes plus 1. +And, indeed, + +one is a constant multiple of +the other. + +I really only have on equation +there. + +I will just write down +immediately now what the + +solution is to the system. +Well, the (a1, + +a2) will be what? +Now, it is more natural to make + +a1 equal 1 and then solve to get +an integer for a2. + +If a1 is 1, then a2 is negative +2. + +And I should multiply that by e +to the negative 6t + +because negative 6 is the +corresponding value. + +There is my other one. +And now there is a + +superposition principle, +which if I get a chance will + +prove for you at the end of the +hour. + +If not, you will have to do it +yourself for homework. + +Since this is a linear system +of equations, + +once you have two separate +solutions, neither a constant + +multiple of the other, +you can multiply each one of + +these by a constant and it will +still be a solution. + +You can add them together and +that will still be a solution, + +and that gives the general +solution. + +The general solution is the sum +of these two, + +an arbitrary constant. +I am going to change the name + +since I don't want to confuse it +with the c1 I used before, + +times the first solution which +is (2, 1) e to the negative t + +plus c2, another arbitrary +constant, times 1 negative 2 e + +to the minus 6t. + +Now you notice that is exactly + +the same solution I got before. +The only difference is that I + +have renamed the arbitrary +constants. + +The relationship between them, +c1 over 2, + +I am now calling c1 tilda, +and c2 I am calling c2 tilda. + +If you have an arbitrary +constant, it doesn't matter + +whether you divide it by two. +It is still just an arbitrary a + +constant. +It covers all values, + +in other words. +Well, I think you will agree + +that is a different procedure, +yet it has only one + +coincidence. +It is like elimination goes + +this way and comes to the +answer. + +And this method goes a +completely different route and + +comes to the answer, +except it is not quite like + +that. +They walk like this and then + +they come within viewing +distance of each other to check + +that both are using the same +characteristic equation, + +and then they again go their +separate ways and end up with + +the same answer. + +There is something special of +these values. + +You cannot get away from those +two values of lambda. + +Somehow they are really +intrinsically connected. + +Occurs the exponential +coefficient, and they are + +intrinsically connected with the +problem of the egg that we + +started with. +Now what I would like to do is + +very quickly sketch how this +method looks when I remove all + +the numbers from it. +In some sense, + +it becomes a little clearer +what is going on. + +And that will give me a chance +to introduce the terminology + +that you need when you talk +about it. + +Well, you have notes. +Let me try to write it down in + +general. + +I will first write it out +two-by-two. + +I am just going to sketch. +The system looks like (x, + +y) equals, I will still put it +up in colors. + +Except now, instead of using +twos and fives, + +I will use (a, +b; c, d). + +The trial solution will look +how? + +The trial is going to be (a1, +a2). + +That I don't have to change the +name of. + +I am going to substitute in, +and what the result of + +substitution is going to be +lambda (a1, a2). + +I am going to skip a step and +pretend that the e to the lambda + +t's have already +been canceled out. + +Is equal to (a, +b; c, d) times (a1, + +a2). +What does that correspond to? + +That corresponds to the system +as I wrote it here. + +And then we wrote it out in +terms of two equations. + +And what was the resulting +thing that we ended up with? + +Well, you write it out, +you move the lambda to the + +other side. +And then the homogeneous system + +is we will look in general how? +Well, we could write it out. + +It is going to look like a +minus lambda, + +b, c, d minus lambda. + +That is just how it looks there + +and the general calculation is +the same. + +Times (a1, a2) is equal to +zero. + +This is solvable nontrivially. +In other words, + +it has a nontrivial solution if +an only if the determinant of + +coefficients is zero. + +Let's now write that out, +calculate out once and for all + +what that determinant is. +I will write it out here. + +It is a minus lambda times d +minus lambda, + +the product of the diagonal +elements, minus the + +anti-diagonal minus bc is equal +to zero. + +And let's calculate that out. + +It is lambda squared minus a +lambda minus d lambda plus ad, + +the constant term from here, +negative bc from there, + +plus ad minus bc, + +where have I seen that before? +This equation is the general + +form using letters of what we +calculated using the specific + +numbers before. +Again, I will code it the same + +way with that color salmon. +Now, most of the calculations + +will be for two-by-two systems. +I advise you, + +in the strongest possible +terms, to remember this + +equation. +You could write down this + +equation immediately for the +matrix. + +You don't have to go through +all this stuff. + +For God's sakes, +don't say let the trial + +solution be blah, +blah, blah. + +You don't want to do that. +I don't want you to repeat the + +derivation of this every time +you go through a particular + +problem. +It is just like in solving + +second order equations. +You have a second order + +equation. +You immediately write down its + +characteristic equation, +then you factor it, + +you find its roots and you +construct the solution. + +It takes a minute. +The same thing, + +this takes a minute, +too. + +What is the constant term? +Ad minus bc, + +what is that? +Matrix is (a, + +b; c, d). +Ad minus bc is its determinant. + +This is the determinant of that +matrix. + +I didn't give the matrix a +name, did I? + +I will now give the matrix a +name A. + +What is this? +Well, you are not supposed to + +know that until now. +I will tell you. + +This is called the trace of A. +Put that down in your little + +books. +The abbreviation is trace A, + +and the word is trace. +The trace of a square matrix is + +the sum of the d elements down +its main diagonal. + +If it were a three-by-three +there would be three terms in + +whatever you are up to. +Here it is a plus b, + +the sum of the diagonal +elements. + +You can immediately write down +this characteristic equation. + +Let's give it a name. +This is a characteristic + +equation of what? +Of the matrix, + +now. +Not of the system, + +of the matrix. +You have a two-by-two matrix. + +You could immediately write +down its characteristic + +equation. +Watch out for this sign, + +minus. +That is a very common error to + +leave out the minus sign because +that is the way the formula + +comes out. +Its roots. + +If it is a quadratic equation +it will have roots; + +lambda1, lambda2 for the moment +let's assume are real and + +distinct. + +For the enrichment of your +vocabulary, those are called the + +eigenvalues. + +They are something which +belonged to the matrix A. + +They are two secret numbers. +You can calculate from the + +coefficients a, +b, and c, and d, + +but they are not in the +coefficients. + +You cannot look at a matrix and +see what its eigenvalues are. + +You have to calculate +something. + +But they are the most important +numbers in the matrix. + +They are hidden, +but they are the things that + +control how this system behaves. +Those are called the + +eigenvalues. +Now, there are various purists, + +there are a fair number of them +in the world who do not like + +this word because it begins +German and ends English. + +Eigenvalues were first +introduced by a German + +mathematician, +you know, around the time + +matrices came into being in 1880 +or so. + +A little while after +eigenvalues came into being, + +too. +And since all this happened in + +Germany they were named +eigenvalues in German, + +which begins eigen and ends +value. + +But people who do not like that +call them the characteristic + +values. +Unfortunately, + +it is two words and takes a lot +more space to write out. + +An older generation even calls +them something different, + +which you are not so likely to +see nowadays, + +but you will in slightly older +books. + +You can also call them the +proper values. + +Characteristic is not a +translation of eigen, + +but proper is, +but it means it in a funny + +sense which has almost +disappeared nowadays. + +It means proper in the sense of +belong to. + +The only example I can think of +is the word property. + +Property is something that +belongs to you. + +That is the use of the word +proper. + +It is something that belongs to +the matrix. + +The matrix has its proper +values. + +It does not mean proper in the +sense of fitting and proper or I + +hope you will behave properly +when we go to Aunt Agatha's or + +something like that. +But, as I say, + +by far the most popular thing, +slowly the word eigenvalue is + +pretty much taking over the +literature. + +Just because it's just one +word, that is a tremendous + +advantage. +Okay. + +What now is still to be done? +Well, there are those vectors + +to be found. +So the very last step would be + +to solve the system to find the +vectors a1 and a2. + +For each (lambda)i, +find the associated vector. + +The vector, we will call it +(alpha)i. + +That is the a1 and a2. +Of course it's going to be + +indexed. +You have to put another + +subscript on it because there +are two of them. + +And a1 and a2 is stretched a +little too far. + +By solving the system, +and the system will be the + +system which I will write this +way, (a minus lambda, + +b, c, d minus lambda). + +It is just that system that was + +over there, but I will recopy +it, (a1, a2) equals zero, + +zero. +And these are called the + +eigenvectors. +Each of these is called the + +eigenvector associated with or +belonging to, + +again, in that sense of +property. + +Eigenvector, +let's say belonging to, + +I see that a little more +frequently, belonging to lambda + +i. +So we have the eigenvalues, + +the eigenvectors and, +of course, the people who call + +them characteristic values also +call these guys characteristic + +vectors. +I don't think I have ever seen + +proper vectors, +but that is because I am not + +old enough. +I think that is what they used + +to be called a long time ago, +but not anymore. + +And then, finally, +the general solution will be, + +by the superposition principle, +(x, y) equals the arbitrary + +constant times the first +eigenvector times the eigenvalue + +times the e to the corresponding +eigenvalue. + +And then the same thing for the +second one, (a1, + +a2), but now the second index +will be 2 to indicate that it + +goes with the eigenvalue e to +the lambda 2t. + +I have done that twice. +And now in the remaining five + +minutes I will do it a third +time because it is possible to + +write this in still a more +condensed form. + +And the advantage of the more +condensed form is A, + +it takes only that much space +to write, and B, + +it applies to systems, +not just the two-by-two + +systems, but to end-by-end +systems. + +The method is exactly the same. +Let's write it out as it would + +apply to end-by-end systems. +The vector I started with is + +(x, y) and so on, +but I will simply abbreviate + +this, as is done in 18.02, +by x with an arrow over it. + +The matrix A I will abbreviate +with A, as I did before with + +capital A. +And then the system looks like + +x prime is equal to -- + +x prime is what? +Ax. + +That is all there is to it. + +There is our green system. +Now notice in this form I did + +not even tell you whether this a +two-by-two matrix or an + +end-by-end. +And in this condensed form it + +will look the same no matter how +many equations you have. + +Your book deals from the +beginning with end-by-end + +systems. +That is, in my view, + +one of its weaknesses because I +don't think most students start + +with two-by-two. +Fortunately, + +the book double-talks. +The theory is end-by-end, + +but all the examples are +two-by-two. + +So just read the examples. +Read the notes instead, + +which just do two-by-two to +start out with. + +The trial solution is x equals +what? + +An unknown vector alpha times e +to the lambda t. + +Alpha is what we called a1 and + +a2 before. +Plug this into there and cancel + +the e to the lambda t's. + +What do you get? +Well, this is lambda alpha e to + +the lambda t equals A alpha e to +the lambda t. + +These two cancel. +And the system to be solved, + +A alpha equals lambda alpha. + +And now the question is how do +you solve that system? + +Well, you can tell if a book is +written by a scoundrel or not by + +how they go -- +A book, which is in my opinion + +completely scoundrel, +simply says you subtract one + +from the other, +and without further ado writes + +A minus lambda, +and they tuck a little I in + +there and write alpha equals +zero. + +Why is the I put in there? +Well, this is what you would + +like to write. +What is wrong with this + +equation? +This is not a valid matrix + +equation because that is a +square end-by-end matrix, + +a square two-by-two matrix if +you like. + +This is a scalar. +You cannot subtract the scalar + +from a matrix. +It is not an operation. + +To subtract matrices they have +to be the same size, + +the same shape. +What is done is you make this a + +two-by-two matrix. +This is a two-by-two matrix + +with lambdas down the main +diagonal and I elsewhere. + +And the justification is that +lambda alpha is the same thing + +as the lambda I times alpha +because I is an identity matrix. + +Now, in fact, +jumping from here to here is + +not something that would occur +to anybody. + +The way it should occur to you +to do this is you do this, + +you write that, +you realize it doesn't work, + +and then you say to yourself I +don't understand what these + +matrices are all about. +I think I'd better write it all + +out. +And then you would write it all + +out and you would write that +equation on the left-hand board + +there. +Oh, now I see what it should + +look like. +I should subtract lambda from + +the main diagonal. +That is the way it will come + +out. +And then say, + +hey, the way to save lambda +from the main diagonal is put it + +in an identity matrix. +That will do it for me. + +In other words, +there is a little detour that + +goes from here to here. +And one of the ways I judge + +books is by how well they +explain the passage from this to + +that. +If they don't explain it at all + +and just write it down, +they have never talked to + +students. +They have just written books. + +Where did we get finally here? +The characteristic equation + +from that, I had forgotten what +color. + +That is in salmon. +The characteristic equation, + +then, is going to be the thing +which says that the determinant + +of that is zero. +That is the circumstances under + +which it is solvable. +In general, this is the way the + +characteristic equation looks. +And its roots, + +once again, are the +eigenvalues. + +And from then you calculate the +corresponding eigenvectors. + +Okay. +Go home and practice. + +In recitation you will practice +on both two-by-two and + +three-by-three cases, +and we will talk more next + +time. \ No newline at end of file diff --git a/hfryF7_QU2c.txt b/hfryF7_QU2c.txt new file mode 100644 index 0000000000000000000000000000000000000000..74ba6d33d0aa328c81b5311b909843d79111d4f8 --- /dev/null +++ b/hfryF7_QU2c.txt @@ -0,0 +1,16707 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +we're gonna I'm gonna just give a a + + align:start position:0% +we're gonna I'm gonna just give a a + + + align:start position:0% +we're gonna I'm gonna just give a a +bunch of examples of things that we and + + align:start position:0% +bunch of examples of things that we and + + + align:start position:0% +bunch of examples of things that we and +our field have done most of them are + + align:start position:0% +our field have done most of them are + + + align:start position:0% +our field have done most of them are +things that I've had played some role in + + align:start position:0% +things that I've had played some role in + + + align:start position:0% +things that I've had played some role in +you know maybe it was thesis project of + + align:start position:0% +you know maybe it was thesis project of + + + align:start position:0% +you know maybe it was thesis project of +a student but they're meant to be + + align:start position:0% +a student but they're meant to be + + + align:start position:0% +a student but they're meant to be +representative of a broader set of + + align:start position:0% +representative of a broader set of + + + align:start position:0% +representative of a broader set of +things that many people have been + + align:start position:0% +things that many people have been + + + align:start position:0% +things that many people have been +working on developing this toolkit and + + align:start position:0% +working on developing this toolkit and + + + align:start position:0% +working on developing this toolkit and +we're gonna start from the beginning in + + align:start position:0% +we're gonna start from the beginning in + + + align:start position:0% +we're gonna start from the beginning in +a sense just some very simple things + + align:start position:0% +a sense just some very simple things + + + align:start position:0% +a sense just some very simple things +that we did to try to look at ways in + + align:start position:0% +that we did to try to look at ways in + + + align:start position:0% +that we did to try to look at ways in +which problems tick generative models + + align:start position:0% +which problems tick generative models + + + align:start position:0% +which problems tick generative models +can inform people's you know basic + + align:start position:0% +can inform people's you know basic + + + align:start position:0% +can inform people's you know basic +cognitive processes and then build up to + + align:start position:0% +cognitive processes and then build up to + + + align:start position:0% +cognitive processes and then build up to +more interestingly kinds of symbolic and + + align:start position:0% +more interestingly kinds of symbolic and + + + align:start position:0% +more interestingly kinds of symbolic and +structured models hierarchical models + + align:start position:0% +structured models hierarchical models + + + align:start position:0% +structured models hierarchical models +and ultimately to these public programs + + align:start position:0% +and ultimately to these public programs + + + align:start position:0% +and ultimately to these public programs +for common sense ok um so when I say a + + align:start position:0% +for common sense ok um so when I say a + + + align:start position:0% +for common sense ok um so when I say a +lot of people have been doing this I + + align:start position:0% +lot of people have been doing this I + + + align:start position:0% +lot of people have been doing this I +mean here's just a small number of these + + align:start position:0% +mean here's just a small number of these + + + align:start position:0% +mean here's just a small number of these +people have ever eat every year or two I + + align:start position:0% +people have ever eat every year or two I + + + align:start position:0% +people have ever eat every year or two I +try to update this slide but it's very + + align:start position:0% +try to update this slide but it's very + + + align:start position:0% +try to update this slide but it's very +much historically dated with you know + + align:start position:0% +much historically dated with you know + + + align:start position:0% +much historically dated with you know +people that I knew when I was in grad + + align:start position:0% +people that I knew when I was in grad + + + align:start position:0% +people that I knew when I was in grad +school basically there's a lot of really + + align:start position:0% +school basically there's a lot of really + + + align:start position:0% +school basically there's a lot of really +great work by younger people who maybe + + align:start position:0% +great work by younger people who maybe + + + align:start position:0% +great work by younger people who maybe +their names happen to appear on the + + align:start position:0% +their names happen to appear on the + + + align:start position:0% +their names happen to appear on the +slides so those dot dot dots are + + align:start position:0% +slides so those dot dot dots are + + + align:start position:0% +slides so those dot dot dots are +extremely serious and a lot of the best + + align:start position:0% +extremely serious and a lot of the best + + + align:start position:0% +extremely serious and a lot of the best +stuff is not included on here but in the + + align:start position:0% +stuff is not included on here but in the + + + align:start position:0% +stuff is not included on here but in the +last couple of decades across basically + + align:start position:0% +last couple of decades across basically + + + align:start position:0% +last couple of decades across basically +all the different areas of cognitive + + align:start position:0% +all the different areas of cognitive + + + align:start position:0% +all the different areas of cognitive +science that cover basically all the + + align:start position:0% +science that cover basically all the + + + align:start position:0% +science that cover basically all the +different things that cognition does + + align:start position:0% +different things that cognition does + + + align:start position:0% +different things that cognition does +there's been great progress building + + align:start position:0% +there's been great progress building + + + align:start position:0% +there's been great progress building +serious mathematical and what we could + + align:start position:0% +serious mathematical and what we could + + + align:start position:0% +serious mathematical and what we could +call reverse engineering models in the + + align:start position:0% +call reverse engineering models in the + + + align:start position:0% +call reverse engineering models in the +sense that they their quantitative + + align:start position:0% +sense that they their quantitative + + + align:start position:0% +sense that they their quantitative +models of human cognition but they are + + align:start position:0% +models of human cognition but they are + + + align:start position:0% +models of human cognition but they are +phrased in the terms of engineering the + + align:start position:0% +phrased in the terms of engineering the + + + align:start position:0% +phrased in the terms of engineering the +same things you would use to build a + + align:start position:0% +same things you would use to build a + + + align:start position:0% +same things you would use to build a +robot to do these things at least in + + align:start position:0% +robot to do these things at least in + + + align:start position:0% +robot to do these things at least in +principle and it's been it's it's a + + align:start position:0% +principle and it's been it's it's a + + + align:start position:0% +principle and it's been it's it's a +developing this toolkit of problems a + + align:start position:0% +developing this toolkit of problems a + + + align:start position:0% +developing this toolkit of problems a +generative models I want to start off by + + align:start position:0% +generative models I want to start off by + + + align:start position:0% +generative models I want to start off by +telling you about a little bit about + + align:start position:0% +telling you about a little bit about + + + align:start position:0% +telling you about a little bit about +some work that I did together with Tom + + align:start position:0% +some work that I did together with Tom + + + align:start position:0% +some work that I did together with Tom +Griffiths so tom is now a senior faculty + + align:start position:0% +Griffiths so tom is now a senior faculty + + + align:start position:0% +Griffiths so tom is now a senior faculty +member at Berkeley one of the leaders in + + align:start position:0% +member at Berkeley one of the leaders in + + + align:start position:0% +member at Berkeley one of the leaders in +this field as well as a leading person + + align:start position:0% +this field as well as a leading person + + + align:start position:0% +this field as well as a leading person +in machine learning actually one of the + + align:start position:0% +in machine learning actually one of the + + + align:start position:0% +in machine learning actually one of the +great things that he's done is to take + + align:start position:0% +great things that he's done is to take + + + align:start position:0% +great things that he's done is to take +inspiration from human learning and + + align:start position:0% +inspiration from human learning and + + + align:start position:0% +inspiration from human learning and +develop fundamentally new kinds of + + align:start position:0% +develop fundamentally new kinds of + + + align:start position:0% +develop fundamentally new kinds of +probabilistic models in nonparametric + + align:start position:0% +probabilistic models in nonparametric + + + align:start position:0% +probabilistic models in nonparametric +Bayes in particular inspired by he + + align:start position:0% +Bayes in particular inspired by he + + + align:start position:0% +Bayes in particular inspired by he +learning but when tom was a grad student + + align:start position:0% +learning but when tom was a grad student + + + align:start position:0% +learning but when tom was a grad student +he worked together right he was my first + + align:start position:0% +he worked together right he was my first + + + align:start position:0% +he worked together right he was my first +student at the you know we're almost the + + align:start position:0% +student at the you know we're almost the + + + align:start position:0% +student at the you know we're almost the +same age so at this point were more like + + align:start position:0% +same age so at this point were more like + + + align:start position:0% +same age so at this point were more like +senior colleagues than student advisor + + align:start position:0% +senior colleagues than student advisor + + + align:start position:0% +senior colleagues than student advisor +but I'll tell you about some work we did + + align:start position:0% +but I'll tell you about some work we did + + + align:start position:0% +but I'll tell you about some work we did +back when he was a student and I was + + align:start position:0% +back when he was a student and I was + + + align:start position:0% +back when he was a student and I was +just starting off and we were both + + align:start position:0% +just starting off and we were both + + + align:start position:0% +just starting off and we were both +together trying to tackle this problem + + align:start position:0% +together trying to tackle this problem + + + align:start position:0% +together trying to tackle this problem +I'm trying to see okay can we what what + + align:start position:0% +I'm trying to see okay can we what what + + + align:start position:0% +I'm trying to see okay can we what what +are the prospects for understanding even + + align:start position:0% +are the prospects for understanding even + + + align:start position:0% +are the prospects for understanding even +very basic cognitive intuitions like + + align:start position:0% +very basic cognitive intuitions like + + + align:start position:0% +very basic cognitive intuitions like +senses of similarity or the most basic + + align:start position:0% +senses of similarity or the most basic + + + align:start position:0% +senses of similarity or the most basic +kind of causal discovery intuitions like + + align:start position:0% +kind of causal discovery intuitions like + + + align:start position:0% +kind of causal discovery intuitions like +we were talking about before using some + + align:start position:0% +we were talking about before using some + + + align:start position:0% +we were talking about before using some +kind of idea of probabilistic inference + + align:start position:0% +kind of idea of probabilistic inference + + + align:start position:0% +kind of idea of probabilistic inference +in a generative model and at the time + + align:start position:0% +in a generative model and at the time + + + align:start position:0% +in a generative model and at the time +remember I in the introduction I was + + align:start position:0% +remember I in the introduction I was + + + align:start position:0% +remember I in the introduction I was +talking about how there's been this back + + align:start position:0% +talking about how there's been this back + + + align:start position:0% +talking about how there's been this back +and forth discourse over the decades of + + align:start position:0% +and forth discourse over the decades of + + + align:start position:0% +and forth discourse over the decades of +people saying you know yeah rah-rah + + align:start position:0% +people saying you know yeah rah-rah + + + align:start position:0% +people saying you know yeah rah-rah +statistics and Oh statistics those are + + align:start position:0% +statistics and Oh statistics those are + + + align:start position:0% +statistics and Oh statistics those are +trivial and uninteresting and at the + + align:start position:0% +trivial and uninteresting and at the + + + align:start position:0% +trivial and uninteresting and at the +time we started to do this at least in + + align:start position:0% +time we started to do this at least in + + + align:start position:0% +time we started to do this at least in +cognitive psychology the idea that that + + align:start position:0% +cognitive psychology the idea that that + + + align:start position:0% +cognitive psychology the idea that that +cognition could be seen as some kind of + + align:start position:0% +cognition could be seen as some kind of + + + align:start position:0% +cognition could be seen as some kind of +sophisticated statistical inference was + + align:start position:0% +sophisticated statistical inference was + + + align:start position:0% +sophisticated statistical inference was +very much not a popular idea but we + + align:start position:0% +very much not a popular idea but we + + + align:start position:0% +very much not a popular idea but we +thought that it was fundamentally right + + align:start position:0% +thought that it was fundamentally right + + + align:start position:0% +thought that it was fundamentally right +in some ways and it was at the time you + + align:start position:0% +in some ways and it was at the time you + + + align:start position:0% +in some ways and it was at the time you +know again this was work we were doing + + align:start position:0% +know again this was work we were doing + + + align:start position:0% +know again this was work we were doing +in the in the early 2000s when it was + + align:start position:0% +in the in the early 2000s when it was + + + align:start position:0% +in the in the early 2000s when it was +very clear in machine learning and AI + + align:start position:0% +very clear in machine learning and AI + + + align:start position:0% +very clear in machine learning and AI +already how transformative these ideas + + align:start position:0% +already how transformative these ideas + + + align:start position:0% +already how transformative these ideas +were in building intelligent machines + + align:start position:0% +were in building intelligent machines + + + align:start position:0% +were in building intelligent machines +are starting to build intelligent + + align:start position:0% +are starting to build intelligent + + + align:start position:0% +are starting to build intelligent +machines so it seemed clear to us that + + align:start position:0% +machines so it seemed clear to us that + + + align:start position:0% +machines so it seemed clear to us that +it was a good hypothesis worth exploring + + align:start position:0% +it was a good hypothesis worth exploring + + + align:start position:0% +it was a good hypothesis worth exploring +and taking much more seriously than + + align:start position:0% +and taking much more seriously than + + + align:start position:0% +and taking much more seriously than +psychologists had much before that that + + align:start position:0% +psychologists had much before that that + + + align:start position:0% +psychologists had much before that that +this also could describe basic aspects + + align:start position:0% +this also could describe basic aspects + + + align:start position:0% +this also could describe basic aspects +of human thinking so I'll give you a + + align:start position:0% +of human thinking so I'll give you a + + + align:start position:0% +of human thinking so I'll give you a +couple examples of what we did here + + align:start position:0% +couple examples of what we did here + + + align:start position:0% +couple examples of what we did here +here's a simple kind of causal inference + + align:start position:0% +here's a simple kind of causal inference + + + align:start position:0% +here's a simple kind of causal inference +from coincidences much like what you saw + + align:start position:0% +from coincidences much like what you saw + + + align:start position:0% +from coincidences much like what you saw +in going on in that in the video game + + align:start position:0% +in going on in that in the video game + + + align:start position:0% +in going on in that in the video game +there's no time in this it's really + + align:start position:0% +there's no time in this it's really + + + align:start position:0% +there's no time in this it's really +mostly just space or maybe a little bit + + align:start position:0% +mostly just space or maybe a little bit + + + align:start position:0% +mostly just space or maybe a little bit +time the the motivation was not a video + + align:start position:0% +time the the motivation was not a video + + + align:start position:0% +time the the motivation was not a video +game but imagine a to put a real world + + align:start position:0% +game but imagine a to put a real world + + + align:start position:0% +game but imagine a to put a real world +context on it + + align:start position:0% +context on it + + + align:start position:0% +context on it +what sometimes called cancer clusters or + + align:start position:0% +what sometimes called cancer clusters or + + + align:start position:0% +what sometimes called cancer clusters or +rare disease clusters right you can read + + align:start position:0% +rare disease clusters right you can read + + + align:start position:0% +rare disease clusters right you can read +about these often in the newspaper where + + align:start position:0% +about these often in the newspaper where + + + align:start position:0% +about these often in the newspaper where +somebody has has seen some evidence + + align:start position:0% +somebody has has seen some evidence + + + align:start position:0% +somebody has has seen some evidence +suggest Avadh an environmental cause + + align:start position:0% +suggest Avadh an environmental cause + + + align:start position:0% +suggest Avadh an environmental cause +maybe it's a toxic chemical leak or + + align:start position:0% +maybe it's a toxic chemical leak or + + + align:start position:0% +maybe it's a toxic chemical leak or +something that seems to be responsible + + align:start position:0% +something that seems to be responsible + + + align:start position:0% +something that seems to be responsible +for maybe they don't have a cause they + + align:start position:0% +for maybe they don't have a cause they + + + align:start position:0% +for maybe they don't have a cause they +just see a suspicious coincidence of + + align:start position:0% +just see a suspicious coincidence of + + + align:start position:0% +just see a suspicious coincidence of +some very rare disease a few cases that + + align:start position:0% +some very rare disease a few cases that + + + align:start position:0% +some very rare disease a few cases that +you seem surprisingly clustered in space + + align:start position:0% +you seem surprisingly clustered in space + + + align:start position:0% +you seem surprisingly clustered in space +and time so for example let's say this + + align:start position:0% +and time so for example let's say this + + + align:start position:0% +and time so for example let's say this +is one square mile + + align:start position:0% +is one square mile + + + align:start position:0% +is one square mile +of a city and each dot represents one + + align:start position:0% +of a city and each dot represents one + + + align:start position:0% +of a city and each dot represents one +case of some very rare disease that + + align:start position:0% +case of some very rare disease that + + + align:start position:0% +case of some very rare disease that +occurred in the span of a year and you + + align:start position:0% +occurred in the span of a year and you + + + align:start position:0% +occurred in the span of a year and you +look at this and it might think that um + + align:start position:0% +look at this and it might think that um + + + align:start position:0% +look at this and it might think that um +well it doesn't look like those dots are + + align:start position:0% +well it doesn't look like those dots are + + + align:start position:0% +well it doesn't look like those dots are +completely uniformly randomly + + align:start position:0% +completely uniformly randomly + + + align:start position:0% +completely uniformly randomly +distributed over there maybe there's + + align:start position:0% +distributed over there maybe there's + + + align:start position:0% +distributed over there maybe there's +like some weird thing going on in the + + align:start position:0% +like some weird thing going on in the + + + align:start position:0% +like some weird thing going on in the +upper left or north west corner or some + + align:start position:0% +upper left or north west corner or some + + + align:start position:0% +upper left or north west corner or some +who-knows-what making people sick so let + + align:start position:0% +who-knows-what making people sick so let + + + align:start position:0% +who-knows-what making people sick so let +me just ask you on a scale of zero to + + align:start position:0% +me just ask you on a scale of zero to + + + align:start position:0% +me just ask you on a scale of zero to +ten where ten means there you're sure + + align:start position:0% +ten where ten means there you're sure + + + align:start position:0% +ten where ten means there you're sure +there's some kind of thing going on in + + align:start position:0% +there's some kind of thing going on in + + + align:start position:0% +there's some kind of thing going on in +some some some special cause in some + + align:start position:0% +some some some special cause in some + + + align:start position:0% +some some some special cause in some +part of this map and zero means no + + align:start position:0% +part of this map and zero means no + + + align:start position:0% +part of this map and zero means no +you're quite sure there's nothing going + + align:start position:0% +you're quite sure there's nothing going + + + align:start position:0% +you're quite sure there's nothing going +on it's just random what do you say to + + align:start position:0% +on it's just random what do you say to + + + align:start position:0% +on it's just random what do you say to +what extent does this give evidence for + + align:start position:0% +what extent does this give evidence for + + + align:start position:0% +what extent does this give evidence for +some hidden cause so give me a number + + align:start position:0% +some hidden cause so give me a number + + + align:start position:0% +some hidden cause so give me a number +between zero and ten okay great + + align:start position:0% +between zero and ten okay great + + + align:start position:0% +between zero and ten okay great +five to seven I heard a few examples of + + align:start position:0% +five to seven I heard a few examples of + + + align:start position:0% +five to seven I heard a few examples of +each others perfect that's exactly what + + align:start position:0% +each others perfect that's exactly what + + + align:start position:0% +each others perfect that's exactly what +people do you could do the same thing on + + align:start position:0% +people do you could do the same thing on + + + align:start position:0% +people do you could do the same thing on +Mechanical Turk and get ten times as + + align:start position:0% +Mechanical Turk and get ten times as + + + align:start position:0% +Mechanical Turk and get ten times as +much data and pay a lot more it would be + + align:start position:0% +much data and pay a lot more it would be + + + align:start position:0% +much data and pay a lot more it would be +the same + + align:start position:0% +the same + + + align:start position:0% +the same +I'll show you the data in a second but + + align:start position:0% +I'll show you the data in a second but + + + align:start position:0% +I'll show you the data in a second but +here's the here's the model that we + + align:start position:0% +here's the here's the model that we + + + align:start position:0% +here's the here's the model that we +built so again this this model is a very + + align:start position:0% +built so again this this model is a very + + + align:start position:0% +built so again this this model is a very +simple kind of generative model of a + + align:start position:0% +simple kind of generative model of a + + + align:start position:0% +simple kind of generative model of a +hit-and cause that various people in + + align:start position:0% +hit-and cause that various people in + + + align:start position:0% +hit-and cause that various people in +statistics have I've worked with for a + + align:start position:0% +statistics have I've worked with for a + + + align:start position:0% +statistics have I've worked with for a +while + + align:start position:0% +while + + + align:start position:0% +while +we're basically modeling ahead and cause + + align:start position:0% +we're basically modeling ahead and cause + + + align:start position:0% +we're basically modeling ahead and cause +as a mixture or it means it's a + + align:start position:0% +as a mixture or it means it's a + + + align:start position:0% +as a mixture or it means it's a +generative model so we have to model the + + align:start position:0% +generative model so we have to model the + + + align:start position:0% +generative model so we have to model the +whole data which and we're saying when + + align:start position:0% +whole data which and we're saying when + + + align:start position:0% +whole data which and we're saying when +we say there's a hidden cause we don't + + align:start position:0% +we say there's a hidden cause we don't + + + align:start position:0% +we say there's a hidden cause we don't +necessarily mean it everything is caused + + align:start position:0% +necessarily mean it everything is caused + + + align:start position:0% +necessarily mean it everything is caused +by this it's just there's it's that the + + align:start position:0% +by this it's just there's it's that the + + + align:start position:0% +by this it's just there's it's that the +data we see in this picture is a mixture + + align:start position:0% +data we see in this picture is a mixture + + + align:start position:0% +data we see in this picture is a mixture +of whatever the normal random thing + + align:start position:0% +of whatever the normal random thing + + + align:start position:0% +of whatever the normal random thing +going on is plus possibly some spatially + + align:start position:0% +going on is plus possibly some spatially + + + align:start position:0% +going on is plus possibly some spatially +localized cause that has some unknown + + align:start position:0% +localized cause that has some unknown + + + align:start position:0% +localized cause that has some unknown +position unknown extent you know maybe + + align:start position:0% +position unknown extent you know maybe + + + align:start position:0% +position unknown extent you know maybe +it's a very big region and some unknown + + align:start position:0% +it's a very big region and some unknown + + + align:start position:0% +it's a very big region and some unknown +intensity maybe it's causing a lot of + + align:start position:0% +intensity maybe it's causing a lot of + + + align:start position:0% +intensity maybe it's causing a lot of +cases or not that many the hypothesis + + align:start position:0% +cases or not that many the hypothesis + + + align:start position:0% +cases or not that many the hypothesis +space maybe is best visualized like this + + align:start position:0% +space maybe is best visualized like this + + + align:start position:0% +space maybe is best visualized like this +each of these squares is a different + + align:start position:0% +each of these squares is a different + + + align:start position:0% +each of these squares is a different +hypothesis of a mixture density or a + + align:start position:0% +hypothesis of a mixture density or a + + + align:start position:0% +hypothesis of a mixture density or a +mixture model which is a mixture of just + + align:start position:0% +mixture model which is a mixture of just + + + align:start position:0% +mixture model which is a mixture of just +a uniform whatever the normal uniform + + align:start position:0% +a uniform whatever the normal uniform + + + align:start position:0% +a uniform whatever the normal uniform +processes that causes it as disease + + align:start position:0% +processes that causes it as disease + + + align:start position:0% +processes that causes it as disease +unrelated to space and then some kind of + + align:start position:0% +unrelated to space and then some kind of + + + align:start position:0% +unrelated to space and then some kind of +just Gaussian bump which can vary in + + align:start position:0% +just Gaussian bump which can vary in + + + align:start position:0% +just Gaussian bump which can vary in +location size and intensity that is the + + align:start position:0% +location size and intensity that is the + + + align:start position:0% +location size and intensity that is the +possible hidden cause of some of these + + align:start position:0% +possible hidden cause of some of these + + + align:start position:0% +possible hidden cause of some of these +cases and what we're the model that we + + align:start position:0% +cases and what we're the model that we + + + align:start position:0% +cases and what we're the model that we +proposed says is that your sense of this + + align:start position:0% +proposed says is that your sense of this + + + align:start position:0% +proposed says is that your sense of this +spatial coincidence + + align:start position:0% +spatial coincidence + + + align:start position:0% +spatial coincidence +like when you look at a pattern of dots + + align:start position:0% +like when you look at a pattern of dots + + + align:start position:0% +like when you look at a pattern of dots +really and you see oh that looks like + + align:start position:0% +really and you see oh that looks like + + + align:start position:0% +really and you see oh that looks like +there's a hidden cluster there somewhere + + align:start position:0% +there's a hidden cluster there somewhere + + + align:start position:0% +there's a hidden cluster there somewhere +is basically you're you're you're trying + + align:start position:0% +is basically you're you're you're trying + + + align:start position:0% +is basically you're you're you're trying +to see whether something like one of + + align:start position:0% +to see whether something like one of + + + align:start position:0% +to see whether something like one of +those things on the right is going on as + + align:start position:0% +those things on the right is going on as + + + align:start position:0% +those things on the right is going on as +opposed to the null hypothesis of just + + align:start position:0% +opposed to the null hypothesis of just + + + align:start position:0% +opposed to the null hypothesis of just +pure randomness so our we take this log + + align:start position:0% +pure randomness so our we take this log + + + align:start position:0% +pure randomness so our we take this log +likelihood ratio or log probability + + align:start position:0% +likelihood ratio or log probability + + + align:start position:0% +likelihood ratio or log probability +where we're comparing the probability of + + align:start position:0% +where we're comparing the probability of + + + align:start position:0% +where we're comparing the probability of +the data under the hypothesis that + + align:start position:0% +the data under the hypothesis that + + + align:start position:0% +the data under the hypothesis that +there's some interesting hidden cause + + align:start position:0% +there's some interesting hidden cause + + + align:start position:0% +there's some interesting hidden cause +one of the things on the right versus + + align:start position:0% +one of the things on the right versus + + + align:start position:0% +one of the things on the right versus +the alternative hypothesis that is just + + align:start position:0% +the alternative hypothesis that is just + + + align:start position:0% +the alternative hypothesis that is just +random which is just the simple just + + align:start position:0% +random which is just the simple just + + + align:start position:0% +random which is just the simple just +completely uniform density and what + + align:start position:0% +completely uniform density and what + + + align:start position:0% +completely uniform density and what +makes us a little bit interesting + + align:start position:0% +makes us a little bit interesting + + + align:start position:0% +makes us a little bit interesting +computationally is that there's there's + + align:start position:0% +computationally is that there's there's + + + align:start position:0% +computationally is that there's there's +an infinite number of these + + align:start position:0% +an infinite number of these + + + align:start position:0% +an infinite number of these +possibilities on the right right there's + + align:start position:0% +possibilities on the right right there's + + + align:start position:0% +possibilities on the right right there's +an infinite number of different + + align:start position:0% +an infinite number of different + + + align:start position:0% +an infinite number of different +locations and positions and locations + + align:start position:0% +locations and positions and locations + + + align:start position:0% +locations and positions and locations +and sizes and intensities of the + + align:start position:0% +and sizes and intensities of the + + + align:start position:0% +and sizes and intensities of the +Gaussian and you have to integrate over + + align:start position:0% +Gaussian and you have to integrate over + + + align:start position:0% +Gaussian and you have to integrate over +all of them so again there's not going + + align:start position:0% +all of them so again there's not going + + + align:start position:0% +all of them so again there's not going +to be a whole lot of mathematical + + align:start position:0% +to be a whole lot of mathematical + + + align:start position:0% +to be a whole lot of mathematical +details here but if you you can read + + align:start position:0% +details here but if you you can read + + + align:start position:0% +details here but if you you can read +about the stuff if you want to read + + align:start position:0% +about the stuff if you want to read + + + align:start position:0% +about the stuff if you want to read +these um papers that we had here but you + + align:start position:0% +these um papers that we had here but you + + + align:start position:0% +these um papers that we had here but you +know for those of you who are familiar + + align:start position:0% +know for those of you who are familiar + + + align:start position:0% +know for those of you who are familiar +with this with working with latent + + align:start position:0% +with this with working with latent + + + align:start position:0% +with this with working with latent +variable models effectively what you're + + align:start position:0% +variable models effectively what you're + + + align:start position:0% +variable models effectively what you're +doing is just integrating either + + align:start position:0% +doing is just integrating either + + + align:start position:0% +doing is just integrating either +analytically or in a simulation over all + + align:start position:0% +analytically or in a simulation over all + + + align:start position:0% +analytically or in a simulation over all +the possible models and sort of trying + + align:start position:0% +the possible models and sort of trying + + + align:start position:0% +the possible models and sort of trying +to compute on average how much does the + + align:start position:0% +to compute on average how much does the + + + align:start position:0% +to compute on average how much does the +evidence support something like what you + + align:start position:0% +evidence support something like what you + + + align:start position:0% +evidence support something like what you +see on the right one of those cluster + + align:start position:0% +see on the right one of those cluster + + + align:start position:0% +see on the right one of those cluster +possibilities versus just a uniform + + align:start position:0% +possibilities versus just a uniform + + + align:start position:0% +possibilities versus just a uniform +density and now what I'm showing you is + + align:start position:0% +density and now what I'm showing you is + + + align:start position:0% +density and now what I'm showing you is +that model compared to people's + + align:start position:0% +that model compared to people's + + + align:start position:0% +that model compared to people's +judgments on an experiment so in this + + align:start position:0% +judgments on an experiment so in this + + + align:start position:0% +judgments on an experiment so in this +experiment we showed people patterns + + align:start position:0% +experiment we showed people patterns + + + align:start position:0% +experiment we showed people patterns +like the one you just saw the one you + + align:start position:0% +like the one you just saw the one you + + + align:start position:0% +like the one you just saw the one you +saw is this one here right and but in + + align:start position:0% +saw is this one here right and but in + + + align:start position:0% +saw is this one here right and but in +the different stimuli we varied + + align:start position:0% +the different stimuli we varied + + + align:start position:0% +the different stimuli we varied +parameters that we thought would be + + align:start position:0% +parameters that we thought would be + + + align:start position:0% +parameters that we thought would be +relevant right so we varied how many + + align:start position:0% +relevant right so we varied how many + + + align:start position:0% +relevant right so we varied how many +points were there total how strong the + + align:start position:0% +points were there total how strong the + + + align:start position:0% +points were there total how strong the +cluster was in various ways whether it + + align:start position:0% +cluster was in various ways whether it + + + align:start position:0% +cluster was in various ways whether it +was very tightly clustered or very big + + align:start position:0% +was very tightly clustered or very big + + + align:start position:0% +was very tightly clustered or very big +the relative number of points in the + + align:start position:0% +the relative number of points in the + + + align:start position:0% +the relative number of points in the +cluster versus a knot so what you can + + align:start position:0% +cluster versus a knot so what you can + + + align:start position:0% +cluster versus a knot so what you can +see here for example is it's a very + + align:start position:0% +see here for example is it's a very + + + align:start position:0% +see here for example is it's a very +similar kind of geometry except here we + + align:start position:0% +similar kind of geometry except here we + + + align:start position:0% +similar kind of geometry except here we +this is a sort of a big-ish cluster and + + align:start position:0% +this is a sort of a big-ish cluster and + + + align:start position:0% +this is a sort of a big-ish cluster and +then we're making the it's basically + + align:start position:0% +then we're making the it's basically + + + align:start position:0% +then we're making the it's basically +there's there's four points that look + + align:start position:0% +there's there's four points that look + + + align:start position:0% +there's there's four points that look +closer than two that aren't and in these + + align:start position:0% +closer than two that aren't and in these + + + align:start position:0% +closer than two that aren't and in these +cases we just make the four points more + + align:start position:0% +cases we just make the four points more + + + align:start position:0% +cases we just make the four points more +tightly clustered here what we're doing + + align:start position:0% +tightly clustered here what we're doing + + + align:start position:0% +tightly clustered here what we're doing +is we're we're say we're going from + + align:start position:0% +is we're we're say we're going from + + + align:start position:0% +is we're we're say we're going from +having nope + + align:start position:0% +having nope + + + align:start position:0% +having nope +coins that look clustered to having + + align:start position:0% +coins that look clustered to having + + + align:start position:0% +coins that look clustered to having +almost all of the points looking + + align:start position:0% +almost all of the points looking + + + align:start position:0% +almost all of the points looking +clustered and just varying the ratio of + + align:start position:0% +clustered and just varying the ratio of + + + align:start position:0% +clustered and just varying the ratio of +clustered points to non-clustered points + + align:start position:0% +clustered points to non-clustered points + + + align:start position:0% +clustered points to non-clustered points +here we're just changing the overall + + align:start position:0% +here we're just changing the overall + + + align:start position:0% +here we're just changing the overall +number so notice that this one is + + align:start position:0% +number so notice that this one is + + + align:start position:0% +number so notice that this one is +basically the same as this one and just + + align:start position:0% +basically the same as this one and just + + + align:start position:0% +basically the same as this one and just +so again it both of these we've got four + + align:start position:0% +so again it both of these we've got four + + + align:start position:0% +so again it both of these we've got four +clustered points and two sort of + + align:start position:0% +clustered points and two sort of + + + align:start position:0% +clustered points and two sort of +seemingly non cluster ones and here we + + align:start position:0% +seemingly non cluster ones and here we + + + align:start position:0% +seemingly non cluster ones and here we +just scale up and set our scale up from + + align:start position:0% +just scale up and set our scale up from + + + align:start position:0% +just scale up and set our scale up from +four to two to eight and four and here + + align:start position:0% +four to two to eight and four and here + + + align:start position:0% +four to two to eight and four and here +we scale it down to two and one in + + align:start position:0% +we scale it down to two and one in + + + align:start position:0% +we scale it down to two and one in +various other manipulations and what you + + align:start position:0% +various other manipulations and what you + + + align:start position:0% +various other manipulations and what you +can see is that they have various + + align:start position:0% +can see is that they have various + + + align:start position:0% +can see is that they have various +systemic effects on people's judgments + + align:start position:0% +systemic effects on people's judgments + + + align:start position:0% +systemic effects on people's judgments +so what I'm calling the data there is + + align:start position:0% +so what I'm calling the data there is + + + align:start position:0% +so what I'm calling the data there is +the average of about a hundred and fifty + + align:start position:0% +the average of about a hundred and fifty + + + align:start position:0% +the average of about a hundred and fifty +people who did the same judgment you did + + align:start position:0% +people who did the same judgment you did + + + align:start position:0% +people who did the same judgment you did +zero to ten on what you can see is the + + align:start position:0% +zero to ten on what you can see is the + + + align:start position:0% +zero to ten on what you can see is the +one I gave you was this one here and the + + align:start position:0% +one I gave you was this one here and the + + + align:start position:0% +one I gave you was this one here and the +average judgment was almost exactly five + + align:start position:0% +average judgment was almost exactly five + + + align:start position:0% +average judgment was almost exactly five +and if you look at the variance it looks + + align:start position:0% +and if you look at the variance it looks + + + align:start position:0% +and if you look at the variance it looks +just like what you saw here some people + + align:start position:0% +just like what you saw here some people + + + align:start position:0% +just like what you saw here some people +say two or three some people say seven I + + align:start position:0% +say two or three some people say seven I + + + align:start position:0% +say two or three some people say seven I +mean it's I chose one that was right in + + align:start position:0% +mean it's I chose one that was right in + + + align:start position:0% +mean it's I chose one that was right in +the middle um + + align:start position:0% +the middle um + + + align:start position:0% +the middle um +the interesting thing right is that + + align:start position:0% +the interesting thing right is that + + + align:start position:0% +the interesting thing right is that +while you maybe felt like you were + + align:start position:0% +while you maybe felt like you were + + + align:start position:0% +while you maybe felt like you were +guessing and if you just listen to what + + align:start position:0% +guessing and if you just listen to what + + + align:start position:0% +guessing and if you just listen to what +everyone else is saying maybe it sounds + + align:start position:0% +everyone else is saying maybe it sounds + + + align:start position:0% +everyone else is saying maybe it sounds +like we're just shouting out random + + align:start position:0% +like we're just shouting out random + + + align:start position:0% +like we're just shouting out random +numbers that's not what you're doing + + align:start position:0% +numbers that's not what you're doing + + + align:start position:0% +numbers that's not what you're doing +right that on that one it looks like it + + align:start position:0% +right that on that one it looks like it + + + align:start position:0% +right that on that one it looks like it +because it's right on the threshold but + + align:start position:0% +because it's right on the threshold but + + + align:start position:0% +because it's right on the threshold but +if you look over all these different + + align:start position:0% +if you look over all these different + + + align:start position:0% +if you look over all these different +patterns what you see is that sometimes + + align:start position:0% +patterns what you see is that sometimes + + + align:start position:0% +patterns what you see is that sometimes +people give much higher numbers than + + align:start position:0% +people give much higher numbers than + + + align:start position:0% +people give much higher numbers than +others sometimes people give much lower + + align:start position:0% +others sometimes people give much lower + + + align:start position:0% +others sometimes people give much lower +number than others and the details of + + align:start position:0% +number than others and the details of + + + align:start position:0% +number than others and the details of +variation both within these different + + align:start position:0% +variation both within these different + + + align:start position:0% +variation both within these different +manipulations we did and across them are + + align:start position:0% +manipulations we did and across them are + + + align:start position:0% +manipulations we did and across them are +almost perfectly captured by this very + + align:start position:0% +almost perfectly captured by this very + + + align:start position:0% +almost perfectly captured by this very +simple probabilistic generative model + + align:start position:0% +simple probabilistic generative model + + + align:start position:0% +simple probabilistic generative model +for a latent cause so the model here is + + align:start position:0% +for a latent cause so the model here is + + + align:start position:0% +for a latent cause so the model here is +this is the predictions that that model + + align:start position:0% +this is the predictions that that model + + + align:start position:0% +this is the predictions that that model +I showed you is making we're about again + + align:start position:0% +I showed you is making we're about again + + + align:start position:0% +I showed you is making we're about again +basically a high bar means there's + + align:start position:0% +basically a high bar means there's + + + align:start position:0% +basically a high bar means there's +strong evidence in favor of the hidden + + align:start position:0% +strong evidence in favor of the hidden + + + align:start position:0% +strong evidence in favor of the hidden +latent cause hypothesis some one or more + + align:start position:0% +latent cause hypothesis some one or more + + + align:start position:0% +latent cause hypothesis some one or more +you know or some some cluster a low bar + + align:start position:0% +you know or some some cluster a low bar + + + align:start position:0% +you know or some some cluster a low bar +means strong evidence for the + + align:start position:0% +means strong evidence for the + + + align:start position:0% +means strong evidence for the +alternative hypothesis the scale ISM is + + align:start position:0% +alternative hypothesis the scale ISM is + + + align:start position:0% +alternative hypothesis the scale ISM is +a bit arbitrary and it's log probability + + align:start position:0% +a bit arbitrary and it's log probability + + + align:start position:0% +a bit arbitrary and it's log probability +ratio scale and so I'm not gonna comment + + align:start position:0% +ratio scale and so I'm not gonna comment + + + align:start position:0% +ratio scale and so I'm not gonna comment +on the scale but importantly it's the + + align:start position:0% +on the scale but importantly it's the + + + align:start position:0% +on the scale but importantly it's the +same scale across all of these so a big + + align:start position:0% +same scale across all of these so a big + + + align:start position:0% +same scale across all of these so a big +difference is it's the same big + + align:start position:0% +difference is it's the same big + + + align:start position:0% +difference is it's the same big +difference in both cases right and I + + align:start position:0% +difference in both cases right and I + + + align:start position:0% +difference in both cases right and I +think this is fairly good evidence that + + align:start position:0% +think this is fairly good evidence that + + + align:start position:0% +think this is fairly good evidence that +this model is capturing your sense of + + align:start position:0% +this model is capturing your sense of + + + align:start position:0% +this model is capturing your sense of +spatial coincidence and showing that + + align:start position:0% +spatial coincidence and showing that + + + align:start position:0% +spatial coincidence and showing that +it's not just random or arbitrary but + + align:start position:0% +it's not just random or arbitrary but + + + align:start position:0% +it's not just random or arbitrary but +it's actually a very rational measure of + + align:start position:0% +it's actually a very rational measure of + + + align:start position:0% +it's actually a very rational measure of +how much evidence there is in the data + + align:start position:0% +how much evidence there is in the data + + + align:start position:0% +how much evidence there is in the data +for a hidden cause here's the same model + + align:start position:0% +for a hidden cause here's the same model + + + align:start position:0% +for a hidden cause here's the same model +now applied to a different data set that + + align:start position:0% +now applied to a different data set that + + + align:start position:0% +now applied to a different data set that +we actually collected a few years before + + align:start position:0% +we actually collected a few years before + + + align:start position:0% +we actually collected a few years before +which just varies the same kinds of + + align:start position:0% +which just varies the same kinds of + + + align:start position:0% +which just varies the same kinds of +parameter that has a lot more points and + + align:start position:0% +parameter that has a lot more points and + + + align:start position:0% +parameter that has a lot more points and +that the same model works in the in + + align:start position:0% +that the same model works in the in + + + align:start position:0% +that the same model works in the in +those cases too + + align:start position:0% +those cases too + + + align:start position:0% +those cases too +the differences are a little more subtle + + align:start position:0% +the differences are a little more subtle + + + align:start position:0% +the differences are a little more subtle +with these more points okay all right um + + align:start position:0% +with these more points okay all right um + + + align:start position:0% +with these more points okay all right um +so I'll give you one other example of of + + align:start position:0% +so I'll give you one other example of of + + + align:start position:0% +so I'll give you one other example of of +this sort of thing like the one I just + + align:start position:0% +this sort of thing like the one I just + + + align:start position:0% +this sort of thing like the one I just +showed you + + align:start position:0% +showed you + + + align:start position:0% +showed you +we're basic we're taking a fairly simple + + align:start position:0% +we're basic we're taking a fairly simple + + + align:start position:0% +we're basic we're taking a fairly simple +statistical model this one as you'll see + + align:start position:0% +statistical model this one as you'll see + + + align:start position:0% +statistical model this one as you'll see +isn't even really causal this one at + + align:start position:0% +isn't even really causal this one at + + + align:start position:0% +isn't even really causal this one at +least that I showed you is causal the + + align:start position:0% +least that I showed you is causal the + + + align:start position:0% +least that I showed you is causal the +advantage of this other one is that it's + + align:start position:0% +advantage of this other one is that it's + + + align:start position:0% +advantage of this other one is that it's +both a ton of textbook statistics + + align:start position:0% +both a ton of textbook statistics + + + align:start position:0% +both a ton of textbook statistics +example it's one where people do + + align:start position:0% +example it's one where people do + + + align:start position:0% +example it's one where people do +something more interesting than what's + + align:start position:0% +something more interesting than what's + + + align:start position:0% +something more interesting than what's +in the textbook although you can extend + + align:start position:0% +in the textbook although you can extend + + + align:start position:0% +in the textbook although you can extend +the textbook analysis to make it look + + align:start position:0% +the textbook analysis to make it look + + + align:start position:0% +the textbook analysis to make it look +like what people do and unlike in this + + align:start position:0% +like what people do and unlike in this + + + align:start position:0% +like what people do and unlike in this +case here you can actually measure the + + align:start position:0% +case here you can actually measure the + + + align:start position:0% +case here you can actually measure the +empirical statistic you can go out and + + align:start position:0% +empirical statistic you can go out and + + + align:start position:0% +empirical statistic you can go out and +instead of just like positing here's a + + align:start position:0% +instead of just like positing here's a + + + align:start position:0% +instead of just like positing here's a +simple model of what a hit Layton + + align:start position:0% +simple model of what a hit Layton + + + align:start position:0% +simple model of what a hit Layton +environmental cause would be like you + + align:start position:0% +environmental cause would be like you + + + align:start position:0% +environmental cause would be like you +can actually go and measure all the + + align:start position:0% +can actually go and measure all the + + + align:start position:0% +can actually go and measure all the +relevant probability distributions and + + align:start position:0% +relevant probability distributions and + + + align:start position:0% +relevant probability distributions and +compare people not just with a notional + + align:start position:0% +compare people not just with a notional + + + align:start position:0% +compare people not just with a notional +model but with what in some stronger + + align:start position:0% +model but with what in some stronger + + + align:start position:0% +model but with what in some stronger +sense is the the rational thing to do as + + align:start position:0% +sense is the the rational thing to do as + + + align:start position:0% +sense is the the rational thing to do as +if you're doing some kind of intuitive + + align:start position:0% +if you're doing some kind of intuitive + + + align:start position:0% +if you're doing some kind of intuitive +Bayesian inference + + align:start position:0% +Bayesian inference + + + align:start position:0% +Bayesian inference +so these are some again that Tom + + align:start position:0% +so these are some again that Tom + + + align:start position:0% +so these are some again that Tom +Griffiths did with mute in an in and + + align:start position:0% +Griffiths did with mute in an in and + + + align:start position:0% +Griffiths did with mute in an in and +then after grad school what we ask + + align:start position:0% +then after grad school what we ask + + + align:start position:0% +then after grad school what we ask +people to make the following kind of + + align:start position:0% +people to make the following kind of + + + align:start position:0% +people to make the following kind of +everyday prediction so we said suppose + + align:start position:0% +everyday prediction so we said suppose + + + align:start position:0% +everyday prediction so we said suppose +them you read about a movie that's made + + align:start position:0% +them you read about a movie that's made + + + align:start position:0% +them you read about a movie that's made +50 million 60 million dollars to date + + align:start position:0% +50 million 60 million dollars to date + + + align:start position:0% +50 million 60 million dollars to date +how much money will it make in total or + + align:start position:0% +how much money will it make in total or + + + align:start position:0% +how much money will it make in total or +you see that something's in baking in + + align:start position:0% +you see that something's in baking in + + + align:start position:0% +you see that something's in baking in +the oven for 34 minutes how long until + + align:start position:0% +the oven for 34 minutes how long until + + + align:start position:0% +the oven for 34 minutes how long until +it's ready you meet someone who's 78 + + align:start position:0% +it's ready you meet someone who's 78 + + + align:start position:0% +it's ready you meet someone who's 78 +years old how long will they live your + + align:start position:0% +years old how long will they live your + + + align:start position:0% +years old how long will they live your +friend quotes to you from line 17 of a + + align:start position:0% +friend quotes to you from line 17 of a + + + align:start position:0% +friend quotes to you from line 17 of a +favorite poem how long is the poem or + + align:start position:0% +favorite poem how long is the poem or + + + align:start position:0% +favorite poem how long is the poem or +you meet a US congressman who served for + + align:start position:0% +you meet a US congressman who served for + + + align:start position:0% +you meet a US congressman who served for +11 years how long will he serve in total + + align:start position:0% +11 years how long will he serve in total + + + align:start position:0% +11 years how long will he serve in total +so in each of these cases you're + + align:start position:0% +so in each of these cases you're + + + align:start position:0% +so in each of these cases you're +encountering some phenomenon or event in + + align:start position:0% +encountering some phenomenon or event in + + + align:start position:0% +encountering some phenomenon or event in +the world with some unknown total + + align:start position:0% +the world with some unknown total + + + align:start position:0% +the world with some unknown total +duration we'll call that T total and all + + align:start position:0% +duration we'll call that T total and all + + + align:start position:0% +duration we'll call that T total and all +we know is that T total is you know + + align:start position:0% +we know is that T total is you know + + + align:start position:0% +we know is that T total is you know +somewhere between 0 and infinity we + + align:start position:0% +somewhere between 0 and infinity we + + + align:start position:0% +somewhere between 0 and infinity we +might have a prior on it as you'll see + + align:start position:0% +might have a prior on it as you'll see + + + align:start position:0% +might have a prior on it as you'll see +in a second but that but we we don't + + align:start position:0% +in a second but that but we we don't + + + align:start position:0% +in a second but that but we we don't +know very much about this particular T + + align:start position:0% +know very much about this particular T + + + align:start position:0% +know very much about this particular T +total except you get one one example one + + align:start position:0% +total except you get one one example one + + + align:start position:0% +total except you get one one example one +piece of data some T which we'll just + + align:start position:0% +piece of data some T which we'll just + + + align:start position:0% +piece of data some T which we'll just +assume is just randomly sample between 0 + + align:start position:0% +assume is just randomly sample between 0 + + + align:start position:0% +assume is just randomly sample between 0 +and T total so all we know is that + + align:start position:0% +and T total so all we know is that + + + align:start position:0% +and T total so all we know is that +whatever these things are it's it's + + align:start position:0% +whatever these things are it's it's + + + align:start position:0% +whatever these things are it's it's +something randomly chosen less than the + + align:start position:0% +something randomly chosen less than the + + + align:start position:0% +something randomly chosen less than the +total extent or duration of these events + + align:start position:0% +total extent or duration of these events + + + align:start position:0% +total extent or duration of these events +ok and now we can ask how much what can + + align:start position:0% +ok and now we can ask how much what can + + + align:start position:0% +ok and now we can ask how much what can +you guess about the total extent or + + align:start position:0% +you guess about the total extent or + + + align:start position:0% +you guess about the total extent or +duration from that one observation or + + align:start position:0% +duration from that one observation or + + + align:start position:0% +duration from that one observation or +what + + align:start position:0% +what + + + align:start position:0% +what +in mathematical terms there's some + + align:start position:0% +in mathematical terms there's some + + + align:start position:0% +in mathematical terms there's some +unknown interval from 0 up to some + + align:start position:0% +unknown interval from 0 up to some + + + align:start position:0% +unknown interval from 0 up to some +maximum value you can put a prior on + + align:start position:0% +maximum value you can put a prior on + + + align:start position:0% +maximum value you can put a prior on +what that interval is and you have to + + align:start position:0% +what that interval is and you have to + + + align:start position:0% +what that interval is and you have to +guess the interval from one sample point + + align:start position:0% +guess the interval from one sample point + + + align:start position:0% +guess the interval from one sample point +sampled randomly within it it's it's + + align:start position:0% +sampled randomly within it it's it's + + + align:start position:0% +sampled randomly within it it's it's +also very similar in another reason we + + align:start position:0% +also very similar in another reason we + + + align:start position:0% +also very similar in another reason we +studied this too the problem of learning + + align:start position:0% +studied this too the problem of learning + + + align:start position:0% +studied this too the problem of learning +a concept from one example right when + + align:start position:0% +a concept from one example right when + + + align:start position:0% +a concept from one example right when +you're learning what horses are from one + + align:start position:0% +you're learning what horses are from one + + + align:start position:0% +you're learning what horses are from one +example or when you're learning what + + align:start position:0% +example or when you're learning what + + + align:start position:0% +example or when you're learning what +that piece of rock climbing equipment is + + align:start position:0% +that piece of rock climbing equipment is + + + align:start position:0% +that piece of rock climbing equipment is +what's a cam from one example or what's + + align:start position:0% +what's a cam from one example or what's + + + align:start position:0% +what's a cam from one example or what's +a tufa from one example you can think + + align:start position:0% +a tufa from one example you can think + + + align:start position:0% +a tufa from one example you can think +there's some region in the space of all + + align:start position:0% +there's some region in the space of all + + + align:start position:0% +there's some region in the space of all +possible objects or something or some + + align:start position:0% +possible objects or something or some + + + align:start position:0% +possible objects or something or some +set out there and you get one or a few + + align:start position:0% +set out there and you get one or a few + + + align:start position:0% +set out there and you get one or a few +sample points and you have to figure out + + align:start position:0% +sample points and you have to figure out + + + align:start position:0% +sample points and you have to figure out +the extent of the region it's basically + + align:start position:0% +the extent of the region it's basically + + + align:start position:0% +the extent of the region it's basically +the same kind of problem mathematically + + align:start position:0% +the same kind of problem mathematically + + + align:start position:0% +the same kind of problem mathematically +but what's cool about this is we can + + align:start position:0% +but what's cool about this is we can + + + align:start position:0% +but what's cool about this is we can +measure the priors for these different + + align:start position:0% +measure the priors for these different + + + align:start position:0% +measure the priors for these different +classes of events and compare people + + align:start position:0% +classes of events and compare people + + + align:start position:0% +classes of events and compare people +with an optimal Bayesian inference and + + align:start position:0% +with an optimal Bayesian inference and + + + align:start position:0% +with an optimal Bayesian inference and +you and you see something kind of + + align:start position:0% +you and you see something kind of + + + align:start position:0% +you and you see something kind of +striking so here's on the top I'm + + align:start position:0% +striking so here's on the top I'm + + + align:start position:0% +striking so here's on the top I'm +showing two different kinds of data here + + align:start position:0% +showing two different kinds of data here + + + align:start position:0% +showing two different kinds of data here +what on the top are just empirical + + align:start position:0% +what on the top are just empirical + + + align:start position:0% +what on the top are just empirical +statistics of events you can measure in + + align:start position:0% +statistics of events you can measure in + + + align:start position:0% +statistics of events you can measure in +the world + + align:start position:0% +the world + + + align:start position:0% +the world +nothing behavioral nothing about + + align:start position:0% +nothing behavioral nothing about + + + align:start position:0% +nothing behavioral nothing about +cognition on the bottom I'm showing some + + align:start position:0% +cognition on the bottom I'm showing some + + + align:start position:0% +cognition on the bottom I'm showing some +behavioral data and comparing it with + + align:start position:0% +behavioral data and comparing it with + + + align:start position:0% +behavioral data and comparing it with +model predictions that are based on the + + align:start position:0% +model predictions that are based on the + + + align:start position:0% +model predictions that are based on the +statistics that are measured on top so + + align:start position:0% +statistics that are measured on top so + + + align:start position:0% +statistics that are measured on top so +what we have in each column is one of + + align:start position:0% +what we have in each column is one of + + + align:start position:0% +what we have in each column is one of +these classes of events like you know + + align:start position:0% +these classes of events like you know + + + align:start position:0% +these classes of events like you know +movie grosses and dollars you can get + + align:start position:0% +movie grosses and dollars you can get + + + align:start position:0% +movie grosses and dollars you can get +this data from IMDB the Internet Movie + + align:start position:0% +this data from IMDB the Internet Movie + + + align:start position:0% +this data from IMDB the Internet Movie +Database you can see that most movies + + align:start position:0% +Database you can see that most movies + + + align:start position:0% +Database you can see that most movies +you know make you know 100 million + + align:start position:0% +you know make you know 100 million + + + align:start position:0% +you know make you know 100 million +dollars or less there's a sort of a + + align:start position:0% +dollars or less there's a sort of a + + + align:start position:0% +dollars or less there's a sort of a +power law but you know a few movies make + + align:start position:0% +power law but you know a few movies make + + + align:start position:0% +power law but you know a few movies make +hundreds or even you know many hundreds + + align:start position:0% +hundreds or even you know many hundreds + + + align:start position:0% +hundreds or even you know many hundreds +maybe a billion dollars even these days + + align:start position:0% +maybe a billion dollars even these days + + + align:start position:0% +maybe a billion dollars even these days +similarly with poems they have a power + + align:start position:0% +similarly with poems they have a power + + + align:start position:0% +similarly with poems they have a power +law distribution of lengths right so + + align:start position:0% +law distribution of lengths right so + + + align:start position:0% +law distribution of lengths right so +most poems are pretty short they fit on + + align:start position:0% +most poems are pretty short they fit on + + + align:start position:0% +most poems are pretty short they fit on +the page or less but there are some epic + + align:start position:0% +the page or less but there are some epic + + + align:start position:0% +the page or less but there are some epic +poems or some multi-page many many + + align:start position:0% +poems or some multi-page many many + + + align:start position:0% +poems or some multi-page many many +hundreds of lines and that's they fall + + align:start position:0% +hundreds of lines and that's they fall + + + align:start position:0% +hundreds of lines and that's they fall +off with a long tail lifespans movie + + align:start position:0% +off with a long tail lifespans movie + + + align:start position:0% +off with a long tail lifespans movie +runtimes are kind of you know you know + + align:start position:0% +runtimes are kind of you know you know + + + align:start position:0% +runtimes are kind of you know you know +modal almost Gaussian not exactly those + + align:start position:0% +modal almost Gaussian not exactly those + + + align:start position:0% +modal almost Gaussian not exactly those +red curves that the histograms bars show + + align:start position:0% +red curves that the histograms bars show + + + align:start position:0% +red curves that the histograms bars show +the empirical statistics that we + + align:start position:0% +the empirical statistics that we + + + align:start position:0% +the empirical statistics that we +measured from public data and the red + + align:start position:0% +measured from public data and the red + + + align:start position:0% +measured from public data and the red +curves show just the best fit of a + + align:start position:0% +curves show just the best fit of a + + + align:start position:0% +curves show just the best fit of a +simple parametric model like a Gaussian + + align:start position:0% +simple parametric model like a Gaussian + + + align:start position:0% +simple parametric model like a Gaussian +or a power-law distribution that I'm + + align:start position:0% +or a power-law distribution that I'm + + + align:start position:0% +or a power-law distribution that I'm +mentioning House of Representatives how + + align:start position:0% +mentioning House of Representatives how + + + align:start position:0% +mentioning House of Representatives how +long people serve in the house has this + + align:start position:0% +long people serve in the house has this + + + align:start position:0% +long people serve in the house has this +kind of gamma or a particular gamma + + align:start position:0% +kind of gamma or a particular gamma + + + align:start position:0% +kind of gamma or a particular gamma +called an air long shape with a little + + align:start position:0% +called an air long shape with a little + + + align:start position:0% +called an air long shape with a little +bit of an incumbent effect cake-baking x + + align:start position:0% +bit of an incumbent effect cake-baking x + + + align:start position:0% +bit of an incumbent effect cake-baking x +right so remember we asked how long is + + align:start position:0% +right so remember we asked how long is + + + align:start position:0% +right so remember we asked how long is +this cake going to bake for they don't + + align:start position:0% +this cake going to bake for they don't + + + align:start position:0% +this cake going to bake for they don't +have any simple parametric for + + align:start position:0% +have any simple parametric for + + + align:start position:0% +have any simple parametric for +when you go and look at cookbooks but + + align:start position:0% +when you go and look at cookbooks but + + + align:start position:0% +when you go and look at cookbooks but +you see you know there's there's + + align:start position:0% +you see you know there's there's + + + align:start position:0% +you see you know there's there's +something systemic there right there's a + + align:start position:0% +something systemic there right there's a + + + align:start position:0% +something systemic there right there's a +lot of things that are they're supposed + + align:start position:0% +lot of things that are they're supposed + + + align:start position:0% +lot of things that are they're supposed +to make for exactly an hour there's some + + align:start position:0% +to make for exactly an hour there's some + + + align:start position:0% +to make for exactly an hour there's some +which have a sort of a smaller or a + + align:start position:0% +which have a sort of a smaller or a + + + align:start position:0% +which have a sort of a smaller or a +shorter but broad mode and then there's + + align:start position:0% +shorter but broad mode and then there's + + + align:start position:0% +shorter but broad mode and then there's +a few epic 90-minute cakes out there so + + align:start position:0% +a few epic 90-minute cakes out there so + + + align:start position:0% +a few epic 90-minute cakes out there so +that's that's all the empirical + + align:start position:0% +that's that's all the empirical + + + align:start position:0% +that's that's all the empirical +statistics now what you're seeing on the + + align:start position:0% +statistics now what you're seeing on the + + + align:start position:0% +statistics now what you're seeing on the +bottom is people's but well on the on + + align:start position:0% +bottom is people's but well on the on + + + align:start position:0% +bottom is people's but well on the on +the y-axis the vertical axis you have + + align:start position:0% +the y-axis the vertical axis you have + + + align:start position:0% +the y-axis the vertical axis you have +the average it's a median of a bunch of + + align:start position:0% +the average it's a median of a bunch of + + + align:start position:0% +the average it's a median of a bunch of +human predictions for the total extent + + align:start position:0% +human predictions for the total extent + + + align:start position:0% +human predictions for the total extent +of any one of these things like the + + align:start position:0% +of any one of these things like the + + + align:start position:0% +of any one of these things like the +total your guess of the total length of + + align:start position:0% +total your guess of the total length of + + + align:start position:0% +total your guess of the total length of +a poem given that you know basically + + align:start position:0% +a poem given that you know basically + + + align:start position:0% +a poem given that you know basically +there is a line 17 in it and on the x + + align:start position:0% +there is a line 17 in it and on the x + + + align:start position:0% +there is a line 17 in it and on the x +axis what you're seeing is that one data + + align:start position:0% +axis what you're seeing is that one data + + + align:start position:0% +axis what you're seeing is that one data +point the one value of T which is all + + align:start position:0% +point the one value of T which is all + + + align:start position:0% +point the one value of T which is all +you know is that it's somewhere between + + align:start position:0% +you know is that it's somewhere between + + + align:start position:0% +you know is that it's somewhere between +0 and T total and then the different + + align:start position:0% +0 and T total and then the different + + + align:start position:0% +0 and T total and then the different +groups of subjects were given five + + align:start position:0% +groups of subjects were given five + + + align:start position:0% +groups of subjects were given five +different values so you see five black + + align:start position:0% +different values so you see five black + + + align:start position:0% +different values so you see five black +dots which correspond to what five + + align:start position:0% +dots which correspond to what five + + + align:start position:0% +dots which correspond to what five +different subgroups of subjects said for + + align:start position:0% +different subgroups of subjects said for + + + align:start position:0% +different subgroups of subjects said for +each of these possible T values and then + + align:start position:0% +each of these possible T values and then + + + align:start position:0% +each of these possible T values and then +the black and red curves are the model + + align:start position:0% +the black and red curves are the model + + + align:start position:0% +the black and red curves are the model +fit which comes from taking a certain + + align:start position:0% +fit which comes from taking a certain + + + align:start position:0% +fit which comes from taking a certain +kind of Bayesian optimal prediction + + align:start position:0% +kind of Bayesian optimal prediction + + + align:start position:0% +kind of Bayesian optimal prediction +where the prior is what's specified on + + align:start position:0% +where the prior is what's specified on + + + align:start position:0% +where the prior is what's specified on +the top that's the prior on T total the + + align:start position:0% +the top that's the prior on T total the + + + align:start position:0% +the top that's the prior on T total the +likelihood is just the sort of uniform + + align:start position:0% +likelihood is just the sort of uniform + + + align:start position:0% +likelihood is just the sort of uniform +random density so it's just saying T is + + align:start position:0% +random density so it's just saying T is + + + align:start position:0% +random density so it's just saying T is +just a uniform random sample from 0 up + + align:start position:0% +just a uniform random sample from 0 up + + + align:start position:0% +just a uniform random sample from 0 up +to T total you put those together to + + align:start position:0% +to T total you put those together to + + + align:start position:0% +to T total you put those together to +compute a posterior and then you the + + align:start position:0% +compute a posterior and then you the + + + align:start position:0% +compute a posterior and then you the +particular estimator we're using is that + + align:start position:0% +particular estimator we're using is that + + + align:start position:0% +particular estimator we're using is that +what's called the posterior median so + + align:start position:0% +what's called the posterior median so + + + align:start position:0% +what's called the posterior median so +we're looking at the median of the + + align:start position:0% +we're looking at the median of the + + + align:start position:0% +we're looking at the median of the +posterior and comparing that with the + + align:start position:0% +posterior and comparing that with the + + + align:start position:0% +posterior and comparing that with the +median of human subjects and what you + + align:start position:0% +median of human subjects and what you + + + align:start position:0% +median of human subjects and what you +can see is that it's is it almost a + + align:start position:0% +can see is that it's is it almost a + + + align:start position:0% +can see is that it's is it almost a +perfect fit right and it doesn't really + + align:start position:0% +perfect fit right and it doesn't really + + + align:start position:0% +perfect fit right and it doesn't really +matter whether you take the red curve + + align:start position:0% +matter whether you take the red curve + + + align:start position:0% +matter whether you take the red curve +which is what comes from the + + align:start position:0% +which is what comes from the + + + align:start position:0% +which is what comes from the +approximating the prior with one of + + align:start position:0% +approximating the prior with one of + + + align:start position:0% +approximating the prior with one of +these simple parametric models or the + + align:start position:0% +these simple parametric models or the + + + align:start position:0% +these simple parametric models or the +black one which comes from just taking + + align:start position:0% +black one which comes from just taking + + + align:start position:0% +black one which comes from just taking +the empirical histogram although for the + + align:start position:0% +the empirical histogram although for the + + + align:start position:0% +the empirical histogram although for the +cake baking times you know you really + + align:start position:0% +cake baking times you know you really + + + align:start position:0% +cake baking times you know you really +you can only go for the empirical one + + align:start position:0% +you can only go for the empirical one + + + align:start position:0% +you can only go for the empirical one +because there is no simple parametric + + align:start position:0% +because there is no simple parametric + + + align:start position:0% +because there is no simple parametric +one that's why you just see a jagged + + align:start position:0% +one that's why you just see a jagged + + + align:start position:0% +one that's why you just see a jagged +black line there but it's it's it's + + align:start position:0% +black line there but it's it's it's + + + align:start position:0% +black line there but it's it's it's +interesting that it's almost a perfect + + align:start position:0% +interesting that it's almost a perfect + + + align:start position:0% +interesting that it's almost a perfect +fit there are a couple just like + + align:start position:0% +fit there are a couple just like + + + align:start position:0% +fit there are a couple just like +somebody asked in demmas talk you know + + align:start position:0% +somebody asked in demmas talk you know + + + align:start position:0% +somebody asked in demmas talk you know +there are there's there's one or two + + align:start position:0% +there are there's there's one or two + + + align:start position:0% +there are there's there's one or two +cases we found where this model doesn't + + align:start position:0% +cases we found where this model doesn't + + + align:start position:0% +cases we found where this model doesn't +work sometimes dramatically and + + align:start position:0% +work sometimes dramatically and + + + align:start position:0% +work sometimes dramatically and +sometimes a little bit and they're all + + align:start position:0% +sometimes a little bit and they're all + + + align:start position:0% +sometimes a little bit and they're all +interesting but I don't have time to + + align:start position:0% +interesting but I don't have time to + + + align:start position:0% +interesting but I don't have time to +talk about it that's one of the things I + + align:start position:0% +talk about it that's one of the things I + + + align:start position:0% +talk about it that's one of the things I +decided to skip if you'd like to talk + + align:start position:0% +decided to skip if you'd like to talk + + + align:start position:0% +decided to skip if you'd like to talk +about + + align:start position:0% +about + + + align:start position:0% +about +happy to do it but most of the time and + + align:start position:0% +happy to do it but most of the time and + + + align:start position:0% +happy to do it but most of the time and +most of the cases we studied it these + + align:start position:0% +most of the cases we studied it these + + + align:start position:0% +most of the cases we studied it these +are representative and the I think again + + align:start position:0% +are representative and the I think again + + + align:start position:0% +are representative and the I think again +all the failure cases are quite + + align:start position:0% +all the failure cases are quite + + + align:start position:0% +all the failure cases are quite +interesting ones that point to this is + + align:start position:0% +interesting ones that point to this is + + + align:start position:0% +interesting ones that point to this is +one of the many things we need to go + + align:start position:0% +one of the many things we need to go + + + align:start position:0% +one of the many things we need to go +beyond um but not the interesting thing + + align:start position:0% +beyond um but not the interesting thing + + + align:start position:0% +beyond um but not the interesting thing +isn't just that the curse fit the data + + align:start position:0% +isn't just that the curse fit the data + + + align:start position:0% +isn't just that the curse fit the data +um but the the fact that the actual + + align:start position:0% +um but the the fact that the actual + + + align:start position:0% +um but the the fact that the actual +shape is different in each case right + + align:start position:0% +shape is different in each case right + + + align:start position:0% +shape is different in each case right +depending on the prior of this different + + align:start position:0% +depending on the prior of this different + + + align:start position:0% +depending on the prior of this different +classes of events you get a + + align:start position:0% +classes of events you get a + + + align:start position:0% +classes of events you get a +fundamentally different or qualitatively + + align:start position:0% +fundamentally different or qualitatively + + + align:start position:0% +fundamentally different or qualitatively +different prediction function right + + align:start position:0% +different prediction function right + + + align:start position:0% +different prediction function right +sometimes it's linear sometimes it's + + align:start position:0% +sometimes it's linear sometimes it's + + + align:start position:0% +sometimes it's linear sometimes it's +nonlinear sometimes it has some weird + + align:start position:0% +nonlinear sometimes it has some weird + + + align:start position:0% +nonlinear sometimes it has some weird +shape and really quite surprisingly to + + align:start position:0% +shape and really quite surprisingly to + + + align:start position:0% +shape and really quite surprisingly to +us it peoples that people seem to be + + align:start position:0% +us it peoples that people seem to be + + + align:start position:0% +us it peoples that people seem to be +sensitive to that so they seem to + + align:start position:0% +sensitive to that so they seem to + + + align:start position:0% +sensitive to that so they seem to +predict in ways that are reflective of + + align:start position:0% +predict in ways that are reflective of + + + align:start position:0% +predict in ways that are reflective of +not only the optimal Bayesian thing to + + align:start position:0% +not only the optimal Bayesian thing to + + + align:start position:0% +not only the optimal Bayesian thing to +do but the optimal Bayesian thing to do + + align:start position:0% +do but the optimal Bayesian thing to do + + + align:start position:0% +do but the optimal Bayesian thing to do +from the optimal prior from the correct + + align:start position:0% +from the optimal prior from the correct + + + align:start position:0% +from the optimal prior from the correct +prior and I certainly don't want to + + align:start position:0% +prior and I certainly don't want to + + + align:start position:0% +prior and I certainly don't want to +suggest that people always do this but + + align:start position:0% +suggest that people always do this but + + + align:start position:0% +suggest that people always do this but +it was really interesting to us that for + + align:start position:0% +it was really interesting to us that for + + + align:start position:0% +it was really interesting to us that for +just a bunch of everyday events and + + align:start position:0% +just a bunch of everyday events and + + + align:start position:0% +just a bunch of everyday events and +really the leap the places where this + + align:start position:0% +really the leap the places where this + + + align:start position:0% +really the leap the places where this +analysis works best are once again where + + align:start position:0% +analysis works best are once again where + + + align:start position:0% +analysis works best are once again where +we think people actually might plausibly + + align:start position:0% +we think people actually might plausibly + + + align:start position:0% +we think people actually might plausibly +have good reasons to have the relevant + + align:start position:0% +have good reasons to have the relevant + + + align:start position:0% +have good reasons to have the relevant +experiences with these everyday events + + align:start position:0% +experiences with these everyday events + + + align:start position:0% +experiences with these everyday events +they seem to be sensitive to both the + + align:start position:0% +they seem to be sensitive to both the + + + align:start position:0% +they seem to be sensitive to both the +statistics in the sense of just what's + + align:start position:0% +statistics in the sense of just what's + + + align:start position:0% +statistics in the sense of just what's +going on in the world and doing the + + align:start position:0% +going on in the world and doing the + + + align:start position:0% +going on in the world and doing the +right statistical prediction so that's + + align:start position:0% +right statistical prediction so that's + + + align:start position:0% +right statistical prediction so that's +what we did you know ten years ago or so + + align:start position:0% +what we did you know ten years ago or so + + + align:start position:0% +what we did you know ten years ago or so +that was like the state of the art for + + align:start position:0% +that was like the state of the art for + + + align:start position:0% +that was like the state of the art for +us and then we wanted to know well okay + + align:start position:0% +us and then we wanted to know well okay + + + align:start position:0% +us and then we wanted to know well okay +can we take these sorts of ideas and and + + align:start position:0% +can we take these sorts of ideas and and + + + align:start position:0% +can we take these sorts of ideas and and +scale them up some actually interesting + + align:start position:0% +scale them up some actually interesting + + + align:start position:0% +scale them up some actually interesting +cognitive problems like say for example + + align:start position:0% +cognitive problems like say for example + + + align:start position:0% +cognitive problems like say for example +learning words for object categories and + + align:start position:0% +learning words for object categories and + + + align:start position:0% +learning words for object categories and +we did some of that I'll show you a + + align:start position:0% +we did some of that I'll show you a + + + align:start position:0% +we did some of that I'll show you a +little bit of that before showing you + + align:start position:0% +little bit of that before showing you + + + align:start position:0% +little bit of that before showing you +why it what I think was missing there I + + align:start position:0% +why it what I think was missing there I + + + align:start position:0% +why it what I think was missing there I +mean in a lot of ways this is a harder + + align:start position:0% +mean in a lot of ways this is a harder + + + align:start position:0% +mean in a lot of ways this is a harder +problem right I mean it's very similar + + align:start position:0% +problem right I mean it's very similar + + + align:start position:0% +problem right I mean it's very similar +as I said it's basically like there's + + align:start position:0% +as I said it's basically like there's + + + align:start position:0% +as I said it's basically like there's +just like that the problem I just showed + + align:start position:0% +just like that the problem I just showed + + + align:start position:0% +just like that the problem I just showed +you where there was an unknown total + + align:start position:0% +you where there was an unknown total + + + align:start position:0% +you where there was an unknown total +extent or duration and you've got one + + align:start position:0% +extent or duration and you've got one + + + align:start position:0% +extent or duration and you've got one +random sample from it here there's some + + align:start position:0% +random sample from it here there's some + + + align:start position:0% +random sample from it here there's some +onion Oh imagine the space of all + + align:start position:0% +onion Oh imagine the space of all + + + align:start position:0% +onion Oh imagine the space of all +possible objects could be a manifold or + + align:start position:0% +possible objects could be a manifold or + + + align:start position:0% +possible objects could be a manifold or +described by a bunch of knobs I mean + + align:start position:0% +described by a bunch of knobs I mean + + + align:start position:0% +described by a bunch of knobs I mean +this is these were all generated from + + align:start position:0% +this is these were all generated from + + + align:start position:0% +this is these were all generated from +some computer program if these were real + + align:start position:0% +some computer program if these were real + + + align:start position:0% +some computer program if these were real +biological things that we generated from + + align:start position:0% +biological things that we generated from + + + align:start position:0% +biological things that we generated from +DNA or whatever it is yeah but there's + + align:start position:0% +DNA or whatever it is yeah but there's + + + align:start position:0% +DNA or whatever it is yeah but there's +some huge may be interestingly + + align:start position:0% +some huge may be interestingly + + + align:start position:0% +some huge may be interestingly +structured space of all possible objects + + align:start position:0% +structured space of all possible objects + + + align:start position:0% +structured space of all possible objects +and within that space is some subset + + align:start position:0% +and within that space is some subset + + + align:start position:0% +and within that space is some subset +some region or subset somehow described + + align:start position:0% +some region or subset somehow described + + + align:start position:0% +some region or subset somehow described +that is the set of tufas + + align:start position:0% +that is the set of tufas + + + align:start position:0% +that is the set of tufas +and somehow you're able to grasp that + + align:start position:0% +and somehow you're able to grasp that + + + align:start position:0% +and somehow you're able to grasp that +subset more or less right to get its + + align:start position:0% +subset more or less right to get its + + + align:start position:0% +subset more or less right to get its +boundaries to be able to say yes or no + + align:start position:0% +boundaries to be able to say yes or no + + + align:start position:0% +boundaries to be able to say yes or no +as you did at the beginning of the + + align:start position:0% +as you did at the beginning of the + + + align:start position:0% +as you did at the beginning of the +lecture from just in this case a few + + align:start position:0% +lecture from just in this case a few + + + align:start position:0% +lecture from just in this case a few +points three points randomly sampled + + align:start position:0% +points three points randomly sampled + + + align:start position:0% +points three points randomly sampled +from somewhere in that region right it + + align:start position:0% +from somewhere in that region right it + + + align:start position:0% +from somewhere in that region right it +would work just as well if I showed you + + align:start position:0% +would work just as well if I showed you + + + align:start position:0% +would work just as well if I showed you +one of them basically right so in some + + align:start position:0% +one of them basically right so in some + + + align:start position:0% +one of them basically right so in some +sense it's the same problem but it's + + align:start position:0% +sense it's the same problem but it's + + + align:start position:0% +sense it's the same problem but it's +much harder because here the space was + + align:start position:0% +much harder because here the space was + + + align:start position:0% +much harder because here the space was +just one dimensional thing it was just + + align:start position:0% +just one dimensional thing it was just + + + align:start position:0% +just one dimensional thing it was just +you know a number whereas here we don't + + align:start position:0% +you know a number whereas here we don't + + + align:start position:0% +you know a number whereas here we don't +know what's the dimensionality of the + + align:start position:0% +know what's the dimensionality of the + + + align:start position:0% +know what's the dimensionality of the +space of objects we don't know how to + + align:start position:0% +space of objects we don't know how to + + + align:start position:0% +space of objects we don't know how to +describe the regions here we know how to + + align:start position:0% +describe the regions here we know how to + + + align:start position:0% +describe the regions here we know how to +describe the regions they were just + + align:start position:0% +describe the regions they were just + + + align:start position:0% +describe the regions they were just +intervals with a lower bound at zero and + + align:start position:0% +intervals with a lower bound at zero and + + + align:start position:0% +intervals with a lower bound at zero and +an upper bound at some unknown thing and + + align:start position:0% +an upper bound at some unknown thing and + + + align:start position:0% +an upper bound at some unknown thing and +the the hypothesis space of possible + + align:start position:0% +the the hypothesis space of possible + + + align:start position:0% +the the hypothesis space of possible +regions was just all the possible upper + + align:start position:0% +regions was just all the possible upper + + + align:start position:0% +regions was just all the possible upper +bounds of this event duration here we + + align:start position:0% +bounds of this event duration here we + + + align:start position:0% +bounds of this event duration here we +don't know how to describe a space we + + align:start position:0% +don't know how to describe a space we + + + align:start position:0% +don't know how to describe a space we +don't know how to describe the regions + + align:start position:0% +don't know how to describe the regions + + + align:start position:0% +don't know how to describe the regions +that correspond to object concepts we + + align:start position:0% +that correspond to object concepts we + + + align:start position:0% +that correspond to object concepts we +don't know how to put a prior on those + + align:start position:0% +don't know how to put a prior on those + + + align:start position:0% +don't know how to put a prior on those +hypotheses but in some work that we did + + align:start position:0% +hypotheses but in some work that we did + + + align:start position:0% +hypotheses but in some work that we did +in particular some work that I did with + + align:start position:0% +in particular some work that I did with + + + align:start position:0% +in particular some work that I did with +face shoe who's also a professor at + + align:start position:0% +face shoe who's also a professor at + + + align:start position:0% +face shoe who's also a professor at +Berkeley we were colleagues and friends + + align:start position:0% +Berkeley we were colleagues and friends + + + align:start position:0% +Berkeley we were colleagues and friends +in graduate school we were we we sort of + + align:start position:0% +in graduate school we were we we sort of + + + align:start position:0% +in graduate school we were we we sort of +did what we could at the time so we made + + align:start position:0% +did what we could at the time so we made + + + align:start position:0% +did what we could at the time so we made +some guesses about what that hypothesis + + align:start position:0% +some guesses about what that hypothesis + + + align:start position:0% +some guesses about what that hypothesis +space what that space might be like what + + align:start position:0% +space what that space might be like what + + + align:start position:0% +space what that space might be like what +the hypothesis space might be like how + + align:start position:0% +the hypothesis space might be like how + + + align:start position:0% +the hypothesis space might be like how +to put some priors and so on on there + + align:start position:0% +to put some priors and so on on there + + + align:start position:0% +to put some priors and so on on there +used exactly the same likelihood which + + align:start position:0% +used exactly the same likelihood which + + + align:start position:0% +used exactly the same likelihood which +was just this very simple idea that the + + align:start position:0% +was just this very simple idea that the + + + align:start position:0% +was just this very simple idea that the +observed examples are a uniform random + + align:start position:0% +observed examples are a uniform random + + + align:start position:0% +observed examples are a uniform random +draw from some subset of the world and + + align:start position:0% +draw from some subset of the world and + + + align:start position:0% +draw from some subset of the world and +you just have to figure out what that + + align:start position:0% +you just have to figure out what that + + + align:start position:0% +you just have to figure out what that +subset is and and we're able to make + + align:start position:0% +subset is and and we're able to make + + + align:start position:0% +subset is and and we're able to make +some progress so what we did was we said + + align:start position:0% +some progress so what we did was we said + + + align:start position:0% +some progress so what we did was we said +well you know like in biology perhaps + + align:start position:0% +well you know like in biology perhaps + + + align:start position:0% +well you know like in biology perhaps +and if you saw how many people saw Syria + + align:start position:0% +and if you saw how many people saw Syria + + + align:start position:0% +and if you saw how many people saw Syria +again Ghoulies lecture yesterday morning + + align:start position:0% +again Ghoulies lecture yesterday morning + + + align:start position:0% +again Ghoulies lecture yesterday morning +cool I'll sort it I I sort of tailored + + align:start position:0% +cool I'll sort it I I sort of tailored + + + align:start position:0% +cool I'll sort it I I sort of tailored +this for assuming that you have probably + + align:start position:0% +this for assuming that you have probably + + + align:start position:0% +this for assuming that you have probably +had seen that because there's a lot of + + align:start position:0% +had seen that because there's a lot of + + + align:start position:0% +had seen that because there's a lot of +similarities or parallels which is neat + + align:start position:0% +similarities or parallels which is neat + + + align:start position:0% +similarities or parallels which is neat +and it's again part of engaging on + + align:start position:0% +and it's again part of engaging on + + + align:start position:0% +and it's again part of engaging on +generative models and neural networks as + + align:start position:0% +generative models and neural networks as + + + align:start position:0% +generative models and neural networks as +you saw him do you'll get my version of + + align:start position:0% +you saw him do you'll get my version of + + + align:start position:0% +you saw him do you'll get my version of +this so you know also like you mentioned + + align:start position:0% +this so you know also like you mentioned + + + align:start position:0% +this so you know also like you mentioned +for he mentioned you know there's there + + align:start position:0% +for he mentioned you know there's there + + + align:start position:0% +for he mentioned you know there's there +are actual processes in the world which + + align:start position:0% +are actual processes in the world which + + + align:start position:0% +are actual processes in the world which +generate objects something like this + + align:start position:0% +generate objects something like this + + + align:start position:0% +generate objects something like this +right you know we know about evolution + + align:start position:0% +right you know we know about evolution + + + align:start position:0% +right you know we know about evolution +produces basically tree-structured + + align:start position:0% +produces basically tree-structured + + + align:start position:0% +produces basically tree-structured +groups which we call species or genus or + + align:start position:0% +groups which we call species or genus or + + + align:start position:0% +groups which we call species or genus or +something like that or just taxa or + + align:start position:0% +something like that or just taxa or + + + align:start position:0% +something like that or just taxa or +something you know there's groups of + + align:start position:0% +something you know there's groups of + + + align:start position:0% +something you know there's groups of +organisms that have a common + + align:start position:0% +organisms that have a common + + + align:start position:0% +organisms that have a common +evolutionary descent that's the way a + + align:start position:0% +evolutionary descent that's the way a + + + align:start position:0% +evolutionary descent that's the way a +biologists might describe it and we you + + align:start position:0% +biologists might describe it and we you + + + align:start position:0% +biologists might describe it and we you +know we know these days a lot about the + + align:start position:0% +know we know these days a lot about the + + + align:start position:0% +know we know these days a lot about the +mechanisms that produce that even going + + align:start position:0% +mechanisms that produce that even going + + + align:start position:0% +mechanisms that produce that even going +back 100 or 200 years + + align:start position:0% +back 100 or 200 years + + + align:start position:0% +back 100 or 200 years +you know say to Darwin we knew something + + align:start position:0% +you know say to Darwin we knew something + + + align:start position:0% +you know say to Darwin we knew something +about the mechanisms that produced it + + align:start position:0% +about the mechanisms that produced it + + + align:start position:0% +about the mechanisms that produced it +even if we didn't know the genetic + + align:start position:0% +even if we didn't know the genetic + + + align:start position:0% +even if we didn't know the genetic +details you know ideas of something like + + align:start position:0% +details you know ideas of something like + + + align:start position:0% +details you know ideas of something like +mutation variation natural selection is + + align:start position:0% +mutation variation natural selection is + + + align:start position:0% +mutation variation natural selection is +a kind of mechanistic account about + + align:start position:0% +a kind of mechanistic account about + + + align:start position:0% +a kind of mechanistic account about +right up there with Newton and forces + + align:start position:0% +right up there with Newton and forces + + + align:start position:0% +right up there with Newton and forces +but anyway scientists can describe some + + align:start position:0% +but anyway scientists can describe some + + + align:start position:0% +but anyway scientists can describe some +process that generates trees and maybe + + align:start position:0% +process that generates trees and maybe + + + align:start position:0% +process that generates trees and maybe +people have some intuition just like + + align:start position:0% +people have some intuition just like + + + align:start position:0% +people have some intuition just like +people seem to have some intuitions + + align:start position:0% +people seem to have some intuitions + + + align:start position:0% +people seem to have some intuitions +about these statistics of everyday + + align:start position:0% +about these statistics of everyday + + + align:start position:0% +about these statistics of everyday +events maybe they have some intuitions + + align:start position:0% +events maybe they have some intuitions + + + align:start position:0% +events maybe they have some intuitions +somehow about the causal processes in + + align:start position:0% +somehow about the causal processes in + + + align:start position:0% +somehow about the causal processes in +the world which give rise to groups and + + align:start position:0% +the world which give rise to groups and + + + align:start position:0% +the world which give rise to groups and +groups and subgroups and can use that to + + align:start position:0% +groups and subgroups and can use that to + + + align:start position:0% +groups and subgroups and can use that to +set up a hypothesis space and we the way + + align:start position:0% +set up a hypothesis space and we the way + + + align:start position:0% +set up a hypothesis space and we the way +we went about this is we have no idea + + align:start position:0% +we went about this is we have no idea + + + align:start position:0% +we went about this is we have no idea +how to describe people's internal mental + + align:start position:0% +how to describe people's internal mental + + + align:start position:0% +how to describe people's internal mental +models of these things but you can do + + align:start position:0% +models of these things but you can do + + + align:start position:0% +models of these things but you can do +some simple there are simple ways to get + + align:start position:0% +some simple there are simple ways to get + + + align:start position:0% +some simple there are simple ways to get +this picture by just basically asking + + align:start position:0% +this picture by just basically asking + + + align:start position:0% +this picture by just basically asking +people to judge similarity and doing + + align:start position:0% +people to judge similarity and doing + + + align:start position:0% +people to judge similarity and doing +hierarchical clustering so this is a + + align:start position:0% +hierarchical clustering so this is a + + + align:start position:0% +hierarchical clustering so this is a +tree that we built up by just asking + + align:start position:0% +tree that we built up by just asking + + + align:start position:0% +tree that we built up by just asking +people getting some subjective + + align:start position:0% +people getting some subjective + + + align:start position:0% +people getting some subjective +similarity metric and then building + + align:start position:0% +similarity metric and then building + + + align:start position:0% +similarity metric and then building +doing hierarchical clustering which we + + align:start position:0% +doing hierarchical clustering which we + + + align:start position:0% +doing hierarchical clustering which we +thought could roughly approximate maybe + + align:start position:0% +thought could roughly approximate maybe + + + align:start position:0% +thought could roughly approximate maybe +the internal hierarchy that our mental + + align:start position:0% +the internal hierarchy that our mental + + + align:start position:0% +the internal hierarchy that our mental +models impose on this are you raising + + align:start position:0% +models impose on this are you raising + + + align:start position:0% +models impose on this are you raising +your hand or just okay cool we + + align:start position:0% +your hand or just okay cool we + + + align:start position:0% +your hand or just okay cool we +ultimately found this just satisfying + + align:start position:0% +ultimately found this just satisfying + + + align:start position:0% +ultimately found this just satisfying +because we don't really know what the + + align:start position:0% +because we don't really know what the + + + align:start position:0% +because we don't really know what the +features are we don't really know if + + align:start position:0% +features are we don't really know if + + + align:start position:0% +features are we don't really know if +this is the right tree or how people + + align:start position:0% +this is the right tree or how people + + + align:start position:0% +this is the right tree or how people +build it up but it actually worked + + align:start position:0% +build it up but it actually worked + + + align:start position:0% +build it up but it actually worked +pretty well in the sense that we could + + align:start position:0% +pretty well in the sense that we could + + + align:start position:0% +pretty well in the sense that we could +build up this tree we could then assume + + align:start position:0% +build up this tree we could then assume + + + align:start position:0% +build up this tree we could then assume +that the hypotheses for concepts just + + align:start position:0% +that the hypotheses for concepts just + + + align:start position:0% +that the hypotheses for concepts just +correspondent two branches of the tree + + align:start position:0% +correspondent two branches of the tree + + + align:start position:0% +correspondent two branches of the tree +and if and then you could again to put + + align:start position:0% +and if and then you could again to put + + + align:start position:0% +and if and then you could again to put +it just intuitively the way you do this + + align:start position:0% +it just intuitively the way you do this + + + align:start position:0% +it just intuitively the way you do this +learning from one or a few examples + + align:start position:0% +learning from one or a few examples + + + align:start position:0% +learning from one or a few examples +let's say you see those few tufas over + + align:start position:0% +let's say you see those few tufas over + + + align:start position:0% +let's say you see those few tufas over +there you're basically asking which + + align:start position:0% +there you're basically asking which + + + align:start position:0% +there you're basically asking which +branch of the tree do I think those are + + align:start position:0% +branch of the tree do I think those are + + + align:start position:0% +branch of the tree do I think those are +randomly drawn from some internal branch + + align:start position:0% +randomly drawn from some internal branch + + + align:start position:0% +randomly drawn from some internal branch +of the tree some subtree which subtree + + align:start position:0% +of the tree some subtree which subtree + + + align:start position:0% +of the tree some subtree which subtree +is it and intuitively if you see those + + align:start position:0% +is it and intuitively if you see those + + + align:start position:0% +is it and intuitively if you see those +things and you say well they're randomly + + align:start position:0% +things and you say well they're randomly + + + align:start position:0% +things and you say well they're randomly +drawn from some branch maybe it's the + + align:start position:0% +drawn from some branch maybe it's the + + + align:start position:0% +drawn from some branch maybe it's the +one that I've circled right that's that + + align:start position:0% +one that I've circled right that's that + + + align:start position:0% +one that I've circled right that's that +sounds like a better bet for example + + align:start position:0% +sounds like a better bet for example + + + align:start position:0% +sounds like a better bet for example +then then this one here which would or + + align:start position:0% +then then this one here which would or + + + align:start position:0% +then then this one here which would or +maybe this one which would include one + + align:start position:0% +maybe this one which would include one + + + align:start position:0% +maybe this one which would include one +of these things but not the others so + + align:start position:0% +of these things but not the others so + + + align:start position:0% +of these things but not the others so +that's probably unlikely and it's + + align:start position:0% +that's probably unlikely and it's + + + align:start position:0% +that's probably unlikely and it's +probably a better bet than say this + + align:start position:0% +probably a better bet than say this + + + align:start position:0% +probably a better bet than say this +branch or this branch so these ones + + align:start position:0% +branch or this branch so these ones + + + align:start position:0% +branch or this branch so these ones +which are logically compatible but + + align:start position:0% +which are logically compatible but + + + align:start position:0% +which are logically compatible but +somehow it would have been sort of a + + align:start position:0% +somehow it would have been sort of a + + + align:start position:0% +somehow it would have been sort of a +suspicious coincidence right if if the + + align:start position:0% +suspicious coincidence right if if the + + + align:start position:0% +suspicious coincidence right if if the +set of two firs had really been this + + align:start position:0% +set of two firs had really been this + + + align:start position:0% +set of two firs had really been this +branch here or this one here then it + + align:start position:0% +branch here or this one here then it + + + align:start position:0% +branch here or this one here then it +would have been quite a coincidence that + + align:start position:0% +would have been quite a coincidence that + + + align:start position:0% +would have been quite a coincidence that +the first three examples you saw were + + align:start position:0% +the first three examples you saw were + + + align:start position:0% +the first three examples you saw were +all clustered over there in one corner + + align:start position:0% +all clustered over there in one corner + + + align:start position:0% +all clustered over there in one corner +and what we showed was that that + + align:start position:0% +and what we showed was that that + + + align:start position:0% +and what we showed was that that +kind of model where that suspicious + + align:start position:0% +kind of model where that suspicious + + + align:start position:0% +kind of model where that suspicious +coincidence came out from the same kind + + align:start position:0% +coincidence came out from the same kind + + + align:start position:0% +coincidence came out from the same kind +of things I've just been showing you for + + align:start position:0% +of things I've just been showing you for + + + align:start position:0% +of things I've just been showing you for +the causal clustering example and for + + align:start position:0% +the causal clustering example and for + + + align:start position:0% +the causal clustering example and for +the interval thing it's the same + + align:start position:0% +the interval thing it's the same + + + align:start position:0% +the interval thing it's the same +Bayesian math but now with this + + align:start position:0% +Bayesian math but now with this + + + align:start position:0% +Bayesian math but now with this +tree-structured hypothesis space that + + align:start position:0% +tree-structured hypothesis space that + + + align:start position:0% +tree-structured hypothesis space that +was actually did a pretty good job of of + + align:start position:0% +was actually did a pretty good job of of + + + align:start position:0% +was actually did a pretty good job of of +capturing people's judgments we gave + + align:start position:0% +capturing people's judgments we gave + + + align:start position:0% +capturing people's judgments we gave +people one or a few examples of these + + align:start position:0% +people one or a few examples of these + + + align:start position:0% +people one or a few examples of these +concepts that the examples could be more + + align:start position:0% +concepts that the examples could be more + + + align:start position:0% +concepts that the examples could be more +narrowly or broadly spread just like you + + align:start position:0% +narrowly or broadly spread just like you + + + align:start position:0% +narrowly or broadly spread just like you +saw in the clustering thing but just + + align:start position:0% +saw in the clustering thing but just + + + align:start position:0% +saw in the clustering thing but just +sort of less extensive we did this with + + align:start position:0% +sort of less extensive we did this with + + + align:start position:0% +sort of less extensive we did this with +adults we did this with kids and I won't + + align:start position:0% +adults we did this with kids and I won't + + + align:start position:0% +adults we did this with kids and I won't +really go into any of the details but if + + align:start position:0% +really go into any of the details but if + + + align:start position:0% +really go into any of the details but if +you're interested check out these + + align:start position:0% +you're interested check out these + + + align:start position:0% +you're interested check out these +various Shu and ten amount papers that's + + align:start position:0% +various Shu and ten amount papers that's + + + align:start position:0% +various Shu and ten amount papers that's +the main one there and you know the + + align:start position:0% +the main one there and you know the + + + align:start position:0% +the main one there and you know the +model kind of worked but ultimately we + + align:start position:0% +model kind of worked but ultimately we + + + align:start position:0% +model kind of worked but ultimately we +found it dissatisfying because we + + align:start position:0% +found it dissatisfying because we + + + align:start position:0% +found it dissatisfying because we +couldn't really explain we didn't really + + align:start position:0% +couldn't really explain we didn't really + + + align:start position:0% +couldn't really explain we didn't really +know what the hypothesis was we didn't + + align:start position:0% +know what the hypothesis was we didn't + + + align:start position:0% +know what the hypothesis was we didn't +really know how people were building up + + align:start position:0% +really know how people were building up + + + align:start position:0% +really know how people were building up +this tree and so we did a few of things + + align:start position:0% +this tree and so we did a few of things + + + align:start position:0% +this tree and so we did a few of things +we Armenia meaning I with some other + + align:start position:0% +we Armenia meaning I with some other + + + align:start position:0% +we Armenia meaning I with some other +people turned to other problems where we + + align:start position:0% +people turned to other problems where we + + + align:start position:0% +people turned to other problems where we +had a better idea maybe of the feature + + align:start position:0% +had a better idea maybe of the feature + + + align:start position:0% +had a better idea maybe of the feature +space and the hypothesis space but the + + align:start position:0% +space and the hypothesis space but the + + + align:start position:0% +space and the hypothesis space but the +same kind of ideas could be explored and + + align:start position:0% +same kind of ideas could be explored and + + + align:start position:0% +same kind of ideas could be explored and +developed and then ultimately and I'll + + align:start position:0% +developed and then ultimately and I'll + + + align:start position:0% +developed and then ultimately and I'll +show you this + + align:start position:0% +show you this + + + align:start position:0% +show you this +maybe maybe before lunch or maybe after + + align:start position:0% +maybe maybe before lunch or maybe after + + + align:start position:0% +maybe maybe before lunch or maybe after +lunch we went back and tackled the + + align:start position:0% +lunch we went back and tackled the + + + align:start position:0% +lunch we went back and tackled the +problem of learning concepts from + + align:start position:0% +problem of learning concepts from + + + align:start position:0% +problem of learning concepts from +examples with other cases that were + + align:start position:0% +examples with other cases that were + + + align:start position:0% +examples with other cases that were +there where we could get a better handle + + align:start position:0% +there where we could get a better handle + + + align:start position:0% +there where we could get a better handle +on being able to on really knowing what + + align:start position:0% +on being able to on really knowing what + + + align:start position:0% +on being able to on really knowing what +the representations that people were + + align:start position:0% +the representations that people were + + + align:start position:0% +the representations that people were +using were and also where we could + + align:start position:0% +using were and also where we could + + + align:start position:0% +using were and also where we could +compare with machines in much more + + align:start position:0% +compare with machines in much more + + + align:start position:0% +compare with machines in much more +compelling apples and oranges ways in + + align:start position:0% +compelling apples and oranges ways in + + + align:start position:0% +compelling apples and oranges ways in +some sense here you know there's no + + align:start position:0% +some sense here you know there's no + + + align:start position:0% +some sense here you know there's no +machine as far as I know that can solve + + align:start position:0% +machine as far as I know that can solve + + + align:start position:0% +machine as far as I know that can solve +this problem as well as our model on the + + align:start position:0% +this problem as well as our model on the + + + align:start position:0% +this problem as well as our model on the +other hand that's again it's like it's + + align:start position:0% +other hand that's again it's like it's + + + align:start position:0% +other hand that's again it's like it's +just very much like the issue that came + + align:start position:0% +just very much like the issue that came + + + align:start position:0% +just very much like the issue that came +up when we were talking about + + align:start position:0% +up when we were talking about + + + align:start position:0% +up when we were talking about +I guess maybe with you Tyler we're + + align:start position:0% +I guess maybe with you Tyler we're + + + align:start position:0% +I guess maybe with you Tyler we're +talking about the deep learning or with + + align:start position:0% +talking about the deep learning or with + + + align:start position:0% +talking about the deep learning or with +you leo the the deep reinforcement + + align:start position:0% +you leo the the deep reinforcement + + + align:start position:0% +you leo the the deep reinforcement +Network you know a machine that's + + align:start position:0% +Network you know a machine that's + + + align:start position:0% +Network you know a machine that's +looking at this just as pixels has so is + + align:start position:0% +looking at this just as pixels has so is + + + align:start position:0% +looking at this just as pixels has so is +missing so much of what we bring to it + + align:start position:0% +missing so much of what we bring to it + + + align:start position:0% +missing so much of what we bring to it +which is we see these things as + + align:start position:0% +which is we see these things as + + + align:start position:0% +which is we see these things as +three-dimensional objects and just like + + align:start position:0% +three-dimensional objects and just like + + + align:start position:0% +three-dimensional objects and just like +the the cam and rock-climbing or any of + + align:start position:0% +the the cam and rock-climbing or any of + + + align:start position:0% +the the cam and rock-climbing or any of +those other examples I gave before I + + align:start position:0% +those other examples I gave before I + + + align:start position:0% +those other examples I gave before I +think that's essential to the abilities + + align:start position:0% +think that's essential to the abilities + + + align:start position:0% +think that's essential to the abilities +that people are doing the generative + + align:start position:0% +that people are doing the generative + + + align:start position:0% +that people are doing the generative +model we build this tree is based not on + + align:start position:0% +model we build this tree is based not on + + + align:start position:0% +model we build this tree is based not on +pixels or even on confident features but + + align:start position:0% +pixels or even on confident features but + + + align:start position:0% +pixels or even on confident features but +on a sense of the three-dimensional + + align:start position:0% +on a sense of the three-dimensional + + + align:start position:0% +on a sense of the three-dimensional +objects its parts and their relations to + + align:start position:0% +objects its parts and their relations to + + + align:start position:0% +objects its parts and their relations to +each other and so fundamentally until we + + align:start position:0% +each other and so fundamentally until we + + + align:start position:0% +each other and so fundamentally until we +know how to perceive objects better this + + align:start position:0% +know how to perceive objects better this + + + align:start position:0% +know how to perceive objects better this +is not going to be comparable between + + align:start position:0% +is not going to be comparable between + + + align:start position:0% +is not going to be comparable between +humans and machines on equal terms but + + align:start position:0% +humans and machines on equal terms but + + + align:start position:0% +humans and machines on equal terms but +I'll show you a little bit later some + + align:start position:0% +I'll show you a little bit later some + + + align:start position:0% +I'll show you a little bit later some +still pretty quite interesting but + + align:start position:0% +still pretty quite interesting but + + + align:start position:0% +still pretty quite interesting but +simpler visual concepts that you can + + align:start position:0% +simpler visual concepts that you can + + + align:start position:0% +simpler visual concepts that you can +still learn and generalize from one + + align:start position:0% +still learn and generalize from one + + + align:start position:0% +still learn and generalize from one +example but where they are comparable + + align:start position:0% +example but where they are comparable + + + align:start position:0% +example but where they are comparable +but first I want to say a little bit + + align:start position:0% +but first I want to say a little bit + + + align:start position:0% +but first I want to say a little bit +about these these you know yet another + + align:start position:0% +about these these you know yet another + + + align:start position:0% +about these these you know yet another +cognitive judgment which like the word + + align:start position:0% +cognitive judgment which like the word + + + align:start position:0% +cognitive judgment which like the word +learning or concept learning cases + + align:start position:0% +learning or concept learning cases + + + align:start position:0% +learning or concept learning cases +involve generalizing from a few examples + + align:start position:0% +involve generalizing from a few examples + + + align:start position:0% +involve generalizing from a few examples +they also involve using prior knowledge + + align:start position:0% +they also involve using prior knowledge + + + align:start position:0% +they also involve using prior knowledge +but they're ones where maybe we have + + align:start position:0% +but they're ones where maybe we have + + + align:start position:0% +but they're ones where maybe we have +some way of capturing people's prior + + align:start position:0% +some way of capturing people's prior + + + align:start position:0% +some way of capturing people's prior +knowledge by using the right combination + + align:start position:0% +knowledge by using the right combination + + + align:start position:0% +knowledge by using the right combination +of statistical inference on some kind of + + align:start position:0% +of statistical inference on some kind of + + + align:start position:0% +of statistical inference on some kind of +symbolically structured bottle so you + + align:start position:0% +symbolically structured bottle so you + + + align:start position:0% +symbolically structured bottle so you +can already see right as I mean just + + align:start position:0% +can already see right as I mean just + + + align:start position:0% +can already see right as I mean just +sort of to show the narrative here right + + align:start position:0% +sort of to show the narrative here right + + + align:start position:0% +sort of to show the narrative here right +the examples I was giving here this + + align:start position:0% +the examples I was giving here this + + + align:start position:0% +the examples I was giving here this +doesn't require any symbolic structure + + align:start position:0% +doesn't require any symbolic structure + + + align:start position:0% +doesn't require any symbolic structure +all that stuff I was talking at the + + align:start position:0% +all that stuff I was talking at the + + + align:start position:0% +all that stuff I was talking at the +beginning about how we have to combine + + align:start position:0% +beginning about how we have to combine + + + align:start position:0% +beginning about how we have to combine +statistical inference sophisticated + + align:start position:0% +statistical inference sophisticated + + + align:start position:0% +statistical inference sophisticated +statistical inference with sophisticated + + align:start position:0% +statistical inference with sophisticated + + + align:start position:0% +statistical inference with sophisticated +symbolic representations you don't need + + align:start position:0% +symbolic representations you don't need + + + align:start position:0% +symbolic representations you don't need +any of that here all the representations + + align:start position:0% +any of that here all the representations + + + align:start position:0% +any of that here all the representations +could just be counting up numbers or + + align:start position:0% +could just be counting up numbers or + + + align:start position:0% +could just be counting up numbers or +using simple probability distributions + + align:start position:0% +using simple probability distributions + + + align:start position:0% +using simple probability distributions +that statisticians have worked with for + + align:start position:0% +that statisticians have worked with for + + + align:start position:0% +that statisticians have worked with for +over a hundred years once we start to go + + align:start position:0% +over a hundred years once we start to go + + + align:start position:0% +over a hundred years once we start to go +to here now we have to define them all + + align:start position:0% +to here now we have to define them all + + + align:start position:0% +to here now we have to define them all +with some interesting structure like a + + align:start position:0% +with some interesting structure like a + + + align:start position:0% +with some interesting structure like a +branching tree structure and so on okay + + align:start position:0% +branching tree structure and so on okay + + + align:start position:0% +branching tree structure and so on okay +and as as you'll see we can we can + + align:start position:0% +and as as you'll see we can we can + + + align:start position:0% +and as as you'll see we can we can +quickly get to lots more interesting + + align:start position:0% +quickly get to lots more interesting + + + align:start position:0% +quickly get to lots more interesting +causal compositionally structured + + align:start position:0% +causal compositionally structured + + + align:start position:0% +causal compositionally structured +generative models in similar kinds of + + align:start position:0% +generative models in similar kinds of + + + align:start position:0% +generative models in similar kinds of +tasks and in particular we were looking + + align:start position:0% +tasks and in particular we were looking + + + align:start position:0% +tasks and in particular we were looking +for for a few years we were very + + align:start position:0% +for for a few years we were very + + + align:start position:0% +for for a few years we were very +interested in these property induction + + align:start position:0% +interested in these property induction + + + align:start position:0% +interested in these property induction +tasks so this is this was it happened to + + align:start position:0% +tasks so this is this was it happened to + + + align:start position:0% +tasks so this is this was it happened to +be I mean I think this was a coincidence + + align:start position:0% +be I mean I think this was a coincidence + + + align:start position:0% +be I mean I think this was a coincidence +or maybe we were both influenced by + + align:start position:0% +or maybe we were both influenced by + + + align:start position:0% +or maybe we were both influenced by +Susan Kerry actually so the work that + + align:start position:0% +Susan Kerry actually so the work that + + + align:start position:0% +Susan Kerry actually so the work that +Surya talked about that he was trying to + + align:start position:0% +Surya talked about that he was trying to + + + align:start position:0% +Surya talked about that he was trying to +explain as a theoretician remember Surya + + align:start position:0% +explain as a theoretician remember Surya + + + align:start position:0% +explain as a theoretician remember Surya +and Andrew Sachs they were they were + + align:start position:0% +and Andrew Sachs they were they were + + + align:start position:0% +and Andrew Sachs they were they were +trying to give the theory of these + + align:start position:0% +trying to give the theory of these + + + align:start position:0% +trying to give the theory of these +neural network models that Jay + + align:start position:0% +neural network models that Jay + + + align:start position:0% +neural network models that Jay +McClelland and Tim Rogers had built in + + align:start position:0% +McClelland and Tim Rogers had built in + + + align:start position:0% +McClelland and Tim Rogers had built in +the early 2000s around the same time we + + align:start position:0% +the early 2000s around the same time we + + + align:start position:0% +the early 2000s around the same time we +were doing this work and they were + + align:start position:0% +were doing this work and they were + + + align:start position:0% +were doing this work and they were +inspired by some of Susan Kerry's work + + align:start position:0% +inspired by some of Susan Kerry's work + + + align:start position:0% +inspired by some of Susan Kerry's work +on children's intuitive biology as well + + align:start position:0% +on children's intuitive biology as well + + + align:start position:0% +on children's intuitive biology as well +as other other people out there in + + align:start position:0% +as other other people out there in + + + align:start position:0% +as other other people out there in +cognitive psychology for example Lance + + align:start position:0% +cognitive psychology for example Lance + + + align:start position:0% +cognitive psychology for example Lance +rips and Smith Medine many many + + align:start position:0% +rips and Smith Medine many many + + + align:start position:0% +rips and Smith Medine many many +cognitive psychologists studied things + + align:start position:0% +cognitive psychologists studied things + + + align:start position:0% +cognitive psychologists studied things +like this dan Oscarsson these they they + + align:start position:0% +like this dan Oscarsson these they they + + + align:start position:0% +like this dan Oscarsson these they they +often talked about this as a kind of + + align:start position:0% +often talked about this as a kind of + + + align:start position:0% +often talked about this as a kind of +inductive reasoning or a property + + align:start position:0% +inductive reasoning or a property + + + align:start position:0% +inductive reasoning or a property +induction right where the idea was it so + + align:start position:0% +induction right where the idea was it so + + + align:start position:0% +induction right where the idea was it so +it might look different from the tasks + + align:start position:0% +it might look different from the tasks + + + align:start position:0% +it might look different from the tasks +I've given you before but actually it's + + align:start position:0% +I've given you before but actually it's + + + align:start position:0% +I've given you before but actually it's +deeply related right you're the the task + + align:start position:0% +deeply related right you're the the task + + + align:start position:0% +deeply related right you're the the task +was often presented to people as a like + + align:start position:0% +was often presented to people as a like + + + align:start position:0% +was often presented to people as a like +a like an argument with premises and a + + align:start position:0% +a like an argument with premises and a + + + align:start position:0% +a like an argument with premises and a +conclusion kind of like a traditional + + align:start position:0% +conclusion kind of like a traditional + + + align:start position:0% +conclusion kind of like a traditional +deductive syllogism you know like + + align:start position:0% +deductive syllogism you know like + + + align:start position:0% +deductive syllogism you know like +all men are mortal Socrates is a man + + align:start position:0% +all men are mortal Socrates is a man + + + align:start position:0% +all men are mortal Socrates is a man +therefore Socrates is mortal but these + + align:start position:0% +therefore Socrates is mortal but these + + + align:start position:0% +therefore Socrates is mortal but these +are inductive and that there's no you + + align:start position:0% +are inductive and that there's no you + + + align:start position:0% +are inductive and that there's no you +can't conclude with deductive certainty + + align:start position:0% +can't conclude with deductive certainty + + + align:start position:0% +can't conclude with deductive certainty +the conclusion follows from the premises + + align:start position:0% +the conclusion follows from the premises + + + align:start position:0% +the conclusion follows from the premises +or is falsified by the premises but + + align:start position:0% +or is falsified by the premises but + + + align:start position:0% +or is falsified by the premises but +rather you just make a good guess the + + align:start position:0% +rather you just make a good guess the + + + align:start position:0% +rather you just make a good guess the +the statements above the line provides + + align:start position:0% +the statements above the line provides + + + align:start position:0% +the statements above the line provides +some more or less good or bad evidence + + align:start position:0% +some more or less good or bad evidence + + + align:start position:0% +some more or less good or bad evidence +for the statement below the line being + + align:start position:0% +for the statement below the line being + + + align:start position:0% +for the statement below the line being +true these these studies were often done + + align:start position:0% +true these these studies were often done + + + align:start position:0% +true these these studies were often done +with they could be done with just sort + + align:start position:0% +with they could be done with just sort + + + align:start position:0% +with they could be done with just sort +of familiar biological properties like + + align:start position:0% +of familiar biological properties like + + + align:start position:0% +of familiar biological properties like +having hairy legs or being being bigger + + align:start position:0% +having hairy legs or being being bigger + + + align:start position:0% +having hairy legs or being being bigger +than a breadbox I mean it's it's also + + align:start position:0% +than a breadbox I mean it's it's also + + + align:start position:0% +than a breadbox I mean it's it's also +it's very much the same kind of thing + + align:start position:0% +it's very much the same kind of thing + + + align:start position:0% +it's very much the same kind of thing +that Tom Mitchell was talking about as + + align:start position:0% +that Tom Mitchell was talking about as + + + align:start position:0% +that Tom Mitchell was talking about as +you'll start to see there's a another + + align:start position:0% +you'll start to see there's a another + + + align:start position:0% +you'll start to see there's a another +reason why I wanted to cover this we we + + align:start position:0% +reason why I wanted to cover this we we + + + align:start position:0% +reason why I wanted to cover this we we +worked on these things because we wanted + + align:start position:0% +worked on these things because we wanted + + + align:start position:0% +worked on these things because we wanted +to be able to engage the same kinds of + + align:start position:0% +to be able to engage the same kinds of + + + align:start position:0% +to be able to engage the same kinds of +things that people like Jay McClelland + + align:start position:0% +things that people like Jay McClelland + + + align:start position:0% +things that people like Jay McClelland +and Tom Mitchell were thinking about + + align:start position:0% +and Tom Mitchell were thinking about + + + align:start position:0% +and Tom Mitchell were thinking about +coming from different perspectives + + align:start position:0% +coming from different perspectives + + + align:start position:0% +coming from different perspectives +remember Tom Mitchell showed you his way + + align:start position:0% +remember Tom Mitchell showed you his way + + + align:start position:0% +remember Tom Mitchell showed you his way +of classifying brain representations of + + align:start position:0% +of classifying brain representations of + + + align:start position:0% +of classifying brain representations of +semantics with a matrices of objects and + + align:start position:0% +semantics with a matrices of objects and + + + align:start position:0% +semantics with a matrices of objects and +sort of 20 question like features that + + align:start position:0% +sort of 20 question like features that + + + align:start position:0% +sort of 20 question like features that +included things like is it Harry or is + + align:start position:0% +included things like is it Harry or is + + + align:start position:0% +included things like is it Harry or is +it alive or does it lay eggs or is it + + align:start position:0% +it alive or does it lay eggs or is it + + + align:start position:0% +it alive or does it lay eggs or is it +bigger than a car or bigger than a + + align:start position:0% +bigger than a car or bigger than a + + + align:start position:0% +bigger than a car or bigger than a +breadbox or whatever any one of these + + align:start position:0% +breadbox or whatever any one of these + + + align:start position:0% +breadbox or whatever any one of these +things basically we're getting at the + + align:start position:0% +things basically we're getting at the + + + align:start position:0% +things basically we're getting at the +same thing I mean here there's just + + align:start position:0% +same thing I mean here there's just + + + align:start position:0% +same thing I mean here there's just +what's often these experiments with + + align:start position:0% +what's often these experiments with + + + align:start position:0% +what's often these experiments with +humans were done with so-called blank + + align:start position:0% +humans were done with so-called blank + + + align:start position:0% +humans were done with so-called blank +predicates something that sounded + + align:start position:0% +predicates something that sounded + + + align:start position:0% +predicates something that sounded +vaguely biological but was basically + + align:start position:0% +vaguely biological but was basically + + + align:start position:0% +vaguely biological but was basically +made up or that most people wouldn't + + align:start position:0% +made up or that most people wouldn't + + + align:start position:0% +made up or that most people wouldn't +know much about does anyone know + + align:start position:0% +know much about does anyone know + + + align:start position:0% +know much about does anyone know +anything about t9 hormones okay I hope + + align:start position:0% +anything about t9 hormones okay I hope + + + align:start position:0% +anything about t9 hormones okay I hope +so because I made it up but um but some + + align:start position:0% +so because I made it up but um but some + + + align:start position:0% +so because I made it up but um but some +of them were just done with things that + + align:start position:0% +of them were just done with things that + + + align:start position:0% +of them were just done with things that +were real but not known to most people + + align:start position:0% +were real but not known to most people + + + align:start position:0% +were real but not known to most people +so if I tell you that gorillas and seals + + align:start position:0% +so if I tell you that gorillas and seals + + + align:start position:0% +so if I tell you that gorillas and seals +both have t9 hormones you might think + + align:start position:0% +both have t9 hormones you might think + + + align:start position:0% +both have t9 hormones you might think +it's sort of fairly plausible that + + align:start position:0% +it's sort of fairly plausible that + + + align:start position:0% +it's sort of fairly plausible that +horses have t9 or ones maybe more so + + align:start position:0% +horses have t9 or ones maybe more so + + + align:start position:0% +horses have t9 or ones maybe more so +than if I hadn't told you anything maybe + + align:start position:0% +than if I hadn't told you anything maybe + + + align:start position:0% +than if I hadn't told you anything maybe +you think that argument is more + + align:start position:0% +you think that argument is more + + + align:start position:0% +you think that argument is more +plausible than the one on the right + + align:start position:0% +plausible than the one on the right + + + align:start position:0% +plausible than the one on the right +given that gorillas and seals have t9 or + + align:start position:0% +given that gorillas and seals have t9 or + + + align:start position:0% +given that gorillas and seals have t9 or +hormones that ant ant eaters have + + align:start position:0% +hormones that ant ant eaters have + + + align:start position:0% +hormones that ant ant eaters have +Foreman so maybe maybe you think you + + align:start position:0% +Foreman so maybe maybe you think you + + + align:start position:0% +Foreman so maybe maybe you think you +know horses are somehow more similar to + + align:start position:0% +know horses are somehow more similar to + + + align:start position:0% +know horses are somehow more similar to +gorillas and seals and anteaters are I + + align:start position:0% +gorillas and seals and anteaters are I + + + align:start position:0% +gorillas and seals and anteaters are I +don't know maybe it may be a little bit + + align:start position:0% +don't know maybe it may be a little bit + + + align:start position:0% +don't know maybe it may be a little bit +if I made that B's gorillas and seals + + align:start position:0% +if I made that B's gorillas and seals + + + align:start position:0% +if I made that B's gorillas and seals +have t9 hormones does that make you + + align:start position:0% +have t9 hormones does that make you + + + align:start position:0% +have t9 hormones does that make you +think it's like that bees have t9 + + align:start position:0% +think it's like that bees have t9 + + + align:start position:0% +think it's like that bees have t9 +hormones or pine trees you know the + + align:start position:0% +hormones or pine trees you know the + + + align:start position:0% +hormones or pine trees you know the +farther they the farther the conclusion + + align:start position:0% +farther they the farther the conclusion + + + align:start position:0% +farther they the farther the conclusion +category gets from the premises the less + + align:start position:0% +category gets from the premises the less + + + align:start position:0% +category gets from the premises the less +plausible it seems maybe the one on the + + align:start position:0% +plausible it seems maybe the one on the + + + align:start position:0% +plausible it seems maybe the one on the +lower right also seems not very + + align:start position:0% +lower right also seems not very + + + align:start position:0% +lower right also seems not very +plausible or not as plausible + + align:start position:0% +plausible or not as plausible + + + align:start position:0% +plausible or not as plausible +because if I tell you that gorillas have + + align:start position:0% +because if I tell you that gorillas have + + + align:start position:0% +because if I tell you that gorillas have +t9 hormones chimps monkeys and baboons + + align:start position:0% +t9 hormones chimps monkeys and baboons + + + align:start position:0% +t9 hormones chimps monkeys and baboons +all have t9 hormones maybe you think + + align:start position:0% +all have t9 hormones maybe you think + + + align:start position:0% +all have t9 hormones maybe you think +that it's only primates or something so + + align:start position:0% +that it's only primates or something so + + + align:start position:0% +that it's only primates or something so +they're not a very it's again one of + + align:start position:0% +they're not a very it's again one of + + + align:start position:0% +they're not a very it's again one of +these typicality suspicious coincidence + + align:start position:0% +these typicality suspicious coincidence + + + align:start position:0% +these typicality suspicious coincidence +businesses okay so again you can think + + align:start position:0% +businesses okay so again you can think + + + align:start position:0% +businesses okay so again you can think +of it as you can do these experience in + + align:start position:0% +of it as you can do these experience in + + + align:start position:0% +of it as you can do these experience in +various ways I don't I won't really go + + align:start position:0% +various ways I don't I won't really go + + + align:start position:0% +various ways I don't I won't really go +through the details but it basically + + align:start position:0% +through the details but it basically + + + align:start position:0% +through the details but it basically +involves giving people a bunch of + + align:start position:0% +involves giving people a bunch of + + + align:start position:0% +involves giving people a bunch of +different sets of examples just like I + + align:start position:0% +different sets of examples just like I + + + align:start position:0% +different sets of examples just like I +mean in some sense the important thing + + align:start position:0% +mean in some sense the important thing + + + align:start position:0% +mean in some sense the important thing +to get is that abstractly it has the + + align:start position:0% +to get is that abstractly it has the + + + align:start position:0% +to get is that abstractly it has the +same character of all the other tasks + + align:start position:0% +same character of all the other tasks + + + align:start position:0% +same character of all the other tasks +you've seen you're giving people one or + + align:start position:0% +you've seen you're giving people one or + + + align:start position:0% +you've seen you're giving people one or +a few examples which we're going to + + align:start position:0% +a few examples which we're going to + + + align:start position:0% +a few examples which we're going to +treat as a random draws from some + + align:start position:0% +treat as a random draws from some + + + align:start position:0% +treat as a random draws from some +concept or some region in some larger + + align:start position:0% +concept or some region in some larger + + + align:start position:0% +concept or some region in some larger +space in this case the examples are the + + align:start position:0% +space in this case the examples are the + + + align:start position:0% +space in this case the examples are the +different premise categories like + + align:start position:0% +different premise categories like + + + align:start position:0% +different premise categories like +gorillas and seals are examples of the + + align:start position:0% +gorillas and seals are examples of the + + + align:start position:0% +gorillas and seals are examples of the +concept of having t9 hormones or + + align:start position:0% +concept of having t9 hormones or + + + align:start position:0% +concept of having t9 hormones or +gorillas chimps monkeys and baboons are + + align:start position:0% +gorillas chimps monkeys and baboons are + + + align:start position:0% +gorillas chimps monkeys and baboons are +an example of a concept we're gonna put + + align:start position:0% +an example of a concept we're gonna put + + + align:start position:0% +an example of a concept we're gonna put +a prior on possible extents of that + + align:start position:0% +a prior on possible extents of that + + + align:start position:0% +a prior on possible extents of that +concept and then ask what kind of + + align:start position:0% +concept and then ask what kind of + + + align:start position:0% +concept and then ask what kind of +inferences people make from that prior + + align:start position:0% +inferences people make from that prior + + + align:start position:0% +inferences people make from that prior +to figure out what other things are in + + align:start position:0% +to figure out what other things are in + + + align:start position:0% +to figure out what other things are in +that concept so our horses in that same + + align:start position:0% +that concept so our horses in that same + + + align:start position:0% +that concept so our horses in that same +concept are you know as a function or + + align:start position:0% +concept are you know as a function or + + + align:start position:0% +concept are you know as a function or +our anteaters or our horse is in it more + + align:start position:0% +our anteaters or our horse is in it more + + + align:start position:0% +our anteaters or our horse is in it more +or less depending on the examples you + + align:start position:0% +or less depending on the examples you + + + align:start position:0% +or less depending on the examples you +give and what's the nature of that prior + + align:start position:0% +give and what's the nature of that prior + + + align:start position:0% +give and what's the nature of that prior +and what's good about this is that you + + align:start position:0% +and what's good about this is that you + + + align:start position:0% +and what's good about this is that you +know kind of like the UM the the pretty + + align:start position:0% +know kind of like the UM the the pretty + + + align:start position:0% +know kind of like the UM the the pretty +day prediction task you know the lines + + align:start position:0% +day prediction task you know the lines + + + align:start position:0% +day prediction task you know the lines +of the poems or the movie grosses or the + + align:start position:0% +of the poems or the movie grosses or the + + + align:start position:0% +of the poems or the movie grosses or the +cake-baking we can actually sort of go + + align:start position:0% +cake-baking we can actually sort of go + + + align:start position:0% +cake-baking we can actually sort of go +out and measure some features that are + + align:start position:0% +out and measure some features that are + + + align:start position:0% +out and measure some features that are +plausibly relevant to set up a plausibly + + align:start position:0% +plausibly relevant to set up a plausibly + + + align:start position:0% +plausibly relevant to set up a plausibly +relevant prior unlike the interesting + + align:start position:0% +relevant prior unlike the interesting + + + align:start position:0% +relevant prior unlike the interesting +object cases and but they're like the + + align:start position:0% +object cases and but they're like the + + + align:start position:0% +object cases and but they're like the +interesting object cases there's some + + align:start position:0% +interesting object cases there's some + + + align:start position:0% +interesting object cases there's some +interesting hierarchical and other kinds + + align:start position:0% +interesting hierarchical and other kinds + + + align:start position:0% +interesting hierarchical and other kinds +of causal compositional structures that + + align:start position:0% +of causal compositional structures that + + + align:start position:0% +of causal compositional structures that +people seem to be using that we can + + align:start position:0% +people seem to be using that we can + + + align:start position:0% +people seem to be using that we can +capture and in our in our models so here + + align:start position:0% +capture and in our in our models so here + + + align:start position:0% +capture and in our in our models so here +again what the kinds of experiments + + align:start position:0% +again what the kinds of experiments + + + align:start position:0% +again what the kinds of experiments +these features were generated many years + + align:start position:0% +these features were generated many years + + + align:start position:0% +these features were generated many years +ago by Austin and colleagues that but + + align:start position:0% +ago by Austin and colleagues that but + + + align:start position:0% +ago by Austin and colleagues that but +it's very similar to the 20 questions + + align:start position:0% +it's very similar to the 20 questions + + + align:start position:0% +it's very similar to the 20 questions +game that Tom Mitchell used and I don't + + align:start position:0% +game that Tom Mitchell used and I don't + + + align:start position:0% +game that Tom Mitchell used and I don't +remember if Syria talked about where + + align:start position:0% +remember if Syria talked about where + + + align:start position:0% +remember if Syria talked about where +these features came from that you know + + align:start position:0% +these features came from that you know + + + align:start position:0% +these features came from that you know +he talked a lot about a matrix of + + align:start position:0% +he talked a lot about a matrix of + + + align:start position:0% +he talked a lot about a matrix of +objects and features I don't know if he + + align:start position:0% +objects and features I don't know if he + + + align:start position:0% +objects and features I don't know if he +talked about where they come from but + + align:start position:0% +talked about where they come from but + + + align:start position:0% +talked about where they come from but +actually psychologists spent a while get + + align:start position:0% +actually psychologists spent a while get + + + align:start position:0% +actually psychologists spent a while get +coming up with ways to get people to + + align:start position:0% +coming up with ways to get people to + + + align:start position:0% +coming up with ways to get people to +just sort of tell you a bunch of + + align:start position:0% +just sort of tell you a bunch of + + + align:start position:0% +just sort of tell you a bunch of +features of animals this is you know + + align:start position:0% +features of animals this is you know + + + align:start position:0% +features of animals this is you know +again it's it's meant to capture the + + align:start position:0% +again it's it's meant to capture the + + + align:start position:0% +again it's it's meant to capture the +knowledge that maybe a kid would get + + align:start position:0% +knowledge that maybe a kid would get + + + align:start position:0% +knowledge that maybe a kid would get +from maybe plausibly reading books and + + align:start position:0% +from maybe plausibly reading books and + + + align:start position:0% +from maybe plausibly reading books and +going to the zoo you know we know that + + align:start position:0% +going to the zoo you know we know that + + + align:start position:0% +going to the zoo you know we know that +elephants are gray they're hairless they + + align:start position:0% +elephants are gray they're hairless they + + + align:start position:0% +elephants are gray they're hairless they +have tough skin they're big they have a + + align:start position:0% +have tough skin they're big they have a + + + align:start position:0% +have tough skin they're big they have a +bulbous body shape + + align:start position:0% +bulbous body shape + + + align:start position:0% +bulbous body shape +they have long legs these are all mostly + + align:start position:0% +they have long legs these are all mostly + + + align:start position:0% +they have long legs these are all mostly +relative to other animals they have a + + align:start position:0% +relative to other animals they have a + + + align:start position:0% +relative to other animals they have a +tail + + align:start position:0% +tail + + + align:start position:0% +tail +they have tusks they might be smelly + + align:start position:0% +they have tusks they might be smelly + + + align:start position:0% +they have tusks they might be smelly +compared to other animals smellier than + + align:start position:0% +compared to other animals smellier than + + + align:start position:0% +compared to other animals smellier than +average is sort of what that means they + + align:start position:0% +average is sort of what that means they + + + align:start position:0% +average is sort of what that means they +walk as opposed to fly they're slow as + + align:start position:0% +walk as opposed to fly they're slow as + + + align:start position:0% +walk as opposed to fly they're slow as +opposed to fast they're strong as + + align:start position:0% +opposed to fast they're strong as + + + align:start position:0% +opposed to fast they're strong as +opposed to weak it's that kind of + + align:start position:0% +opposed to weak it's that kind of + + + align:start position:0% +opposed to weak it's that kind of +business so what basically what that + + align:start position:0% +business so what basically what that + + + align:start position:0% +business so what basically what that +gives you is this big matrix again the + + align:start position:0% +gives you is this big matrix again the + + + align:start position:0% +gives you is this big matrix again the +same kind of thing that you saw in + + align:start position:0% +same kind of thing that you saw in + + + align:start position:0% +same kind of thing that you saw in +syria's talk the same kind of thing that + + align:start position:0% +syria's talk the same kind of thing that + + + align:start position:0% +syria's talk the same kind of thing that +Tom Mitchell was using to help classify + + align:start position:0% +Tom Mitchell was using to help classify + + + align:start position:0% +Tom Mitchell was using to help classify +things the same kind of thing that + + align:start position:0% +things the same kind of thing that + + + align:start position:0% +things the same kind of thing that +basically everybody in machine learning + + align:start position:0% +basically everybody in machine learning + + + align:start position:0% +basically everybody in machine learning +uses a matrix of data right with objects + + align:start position:0% +uses a matrix of data right with objects + + + align:start position:0% +uses a matrix of data right with objects +maybe as rows and features or attributes + + align:start position:0% +maybe as rows and features or attributes + + + align:start position:0% +maybe as rows and features or attributes +as columns and the problem here which is + + align:start position:0% +as columns and the problem here which is + + + align:start position:0% +as columns and the problem here which is +the problem of learning is to say the + + align:start position:0% +the problem of learning is to say the + + + align:start position:0% +the problem of learning is to say the +sort of problem of learning and + + align:start position:0% +sort of problem of learning and + + + align:start position:0% +sort of problem of learning and +generalizing from one example is to take + + align:start position:0% +generalizing from one example is to take + + + align:start position:0% +generalizing from one example is to take +a new property which is a new concept + + align:start position:0% +a new property which is a new concept + + + align:start position:0% +a new property which is a new concept +which is like a new column here to get + + align:start position:0% +which is like a new column here to get + + + align:start position:0% +which is like a new column here to get +one or a few examples of that concept + + align:start position:0% +one or a few examples of that concept + + + align:start position:0% +one or a few examples of that concept +which is basically just filling in one + + align:start position:0% +which is basically just filling in one + + + align:start position:0% +which is basically just filling in one +or a few entries in that column and + + align:start position:0% +or a few entries in that column and + + + align:start position:0% +or a few entries in that column and +figure out how to fill in the others to + + align:start position:0% +figure out how to fill in the others to + + + align:start position:0% +figure out how to fill in the others to +decide do you or don't you have that + + align:start position:0% +decide do you or don't you have that + + + align:start position:0% +decide do you or don't you have that +property somehow building knowledge that + + align:start position:0% +property somehow building knowledge that + + + align:start position:0% +property somehow building knowledge that +you can generalize from your prior + + align:start position:0% +you can generalize from your prior + + + align:start position:0% +you can generalize from your prior +experience which could be captured by + + align:start position:0% +experience which could be captured by + + + align:start position:0% +experience which could be captured by +say all the other features that you know + + align:start position:0% +say all the other features that you know + + + align:start position:0% +say all the other features that you know +about objects so that's the way that you + + align:start position:0% +about objects so that's the way that you + + + align:start position:0% +about objects so that's the way that you +might set up this problem which again + + align:start position:0% +might set up this problem which again + + + align:start position:0% +might set up this problem which again +looks like a lot of other problems if + + align:start position:0% +looks like a lot of other problems if + + + align:start position:0% +looks like a lot of other problems if +say semi-supervised learning or sparse + + align:start position:0% +say semi-supervised learning or sparse + + + align:start position:0% +say semi-supervised learning or sparse +matrix completion it's a problem in + + align:start position:0% +matrix completion it's a problem in + + + align:start position:0% +matrix completion it's a problem in +which we can or at least we thought we + + align:start position:0% +which we can or at least we thought we + + + align:start position:0% +which we can or at least we thought we +could compare humans and many different + + align:start position:0% +could compare humans and many different + + + align:start position:0% +could compare humans and many different +algorithms and even theory like from + + align:start position:0% +algorithms and even theory like from + + + align:start position:0% +algorithms and even theory like from +serious talk and that seemed very + + align:start position:0% +serious talk and that seemed very + + + align:start position:0% +serious talk and that seemed very +appealing to us what we thought though + + align:start position:0% +appealing to us what we thought though + + + align:start position:0% +appealing to us what we thought though +that people were doing which is maybe a + + align:start position:0% +that people were doing which is maybe a + + + align:start position:0% +that people were doing which is maybe a +little different than what or somewhat + + align:start position:0% +little different than what or somewhat + + + align:start position:0% +little different than what or somewhat +different well quite different than what + + align:start position:0% +different well quite different than what + + + align:start position:0% +different well quite different than what +Jane McClellan thought people are doing + + align:start position:0% +Jane McClellan thought people are doing + + + align:start position:0% +Jane McClellan thought people are doing +maybe a little bit more like what Susan + + align:start position:0% +maybe a little bit more like what Susan + + + align:start position:0% +maybe a little bit more like what Susan +Kerry or some of the earlier + + align:start position:0% +Kerry or some of the earlier + + + align:start position:0% +Kerry or some of the earlier +psychologists thought people were doing + + align:start position:0% +psychologists thought people were doing + + + align:start position:0% +psychologists thought people were doing +was something like this that they that + + align:start position:0% +was something like this that they that + + + align:start position:0% +was something like this that they that +the way we solve this problem the way we + + align:start position:0% +the way we solve this problem the way we + + + align:start position:0% +the way we solve this problem the way we +bridged from our prior experience to new + + align:start position:0% +bridged from our prior experience to new + + + align:start position:0% +bridged from our prior experience to new +things we wanted to learn was you know + + align:start position:0% +things we wanted to learn was you know + + + align:start position:0% +things we wanted to learn was you know +not say by just computing the second + + align:start position:0% +not say by just computing the second + + + align:start position:0% +not say by just computing the second +order of statistics and correlations and + + align:start position:0% +order of statistics and correlations and + + + align:start position:0% +order of statistics and correlations and +compressing that through some bottleneck + + align:start position:0% +compressing that through some bottleneck + + + align:start position:0% +compressing that through some bottleneck +hidden layer but by building a more + + align:start position:0% +hidden layer but by building a more + + + align:start position:0% +hidden layer but by building a more +interesting structured probabilistic + + align:start position:0% +interesting structured probabilistic + + + align:start position:0% +interesting structured probabilistic +model that was in some form causal in + + align:start position:0% +model that was in some form causal in + + + align:start position:0% +model that was in some form causal in +some form in some form compositional and + + align:start position:0% +some form in some form compositional and + + + align:start position:0% +some form in some form compositional and +hierarchical something kind of like this + + align:start position:0% +hierarchical something kind of like this + + + align:start position:0% +hierarchical something kind of like this +so that and this is this is a good + + align:start position:0% +so that and this is this is a good + + + align:start position:0% +so that and this is this is a good +example of a hierarchical generative + + align:start position:0% +example of a hierarchical generative + + + align:start position:0% +example of a hierarchical generative +model there's three layers of structure + + align:start position:0% +model there's three layers of structure + + + align:start position:0% +model there's three layers of structure +here the bottom layer is the observable + + align:start position:0% +here the bottom layer is the observable + + + align:start position:0% +here the bottom layer is the observable +was so layer so the arrows in these + + align:start position:0% +was so layer so the arrows in these + + + align:start position:0% +was so layer so the arrows in these +generative models point down often + + align:start position:0% +generative models point down often + + + align:start position:0% +generative models point down often +usually where the thing on the bottom is + + align:start position:0% +usually where the thing on the bottom is + + + align:start position:0% +usually where the thing on the bottom is +the thing you + + align:start position:0% +the thing you + + + align:start position:0% +the thing you +observe the data of your experience and + + align:start position:0% +observe the data of your experience and + + + align:start position:0% +observe the data of your experience and +then the stuff above it are various + + align:start position:0% +then the stuff above it are various + + + align:start position:0% +then the stuff above it are various +levels of structure that your mind is + + align:start position:0% +levels of structure that your mind is + + + align:start position:0% +levels of structure that your mind is +positing to explain it so here we have + + align:start position:0% +positing to explain it so here we have + + + align:start position:0% +positing to explain it so here we have +two levels of structure the level above + + align:start position:0% +two levels of structure the level above + + + align:start position:0% +two levels of structure the level above +this is this sort of this tree in your + + align:start position:0% +this is this sort of this tree in your + + + align:start position:0% +this is this sort of this tree in your +head right the idea it's like it's a + + align:start position:0% +head right the idea it's like it's a + + + align:start position:0% +head right the idea it's like it's a +certain kind of graph structure where + + align:start position:0% +certain kind of graph structure where + + + align:start position:0% +certain kind of graph structure where +the objects or the species are the leaf + + align:start position:0% +the objects or the species are the leaf + + + align:start position:0% +the objects or the species are the leaf +nodes and there's some internal nodes + + align:start position:0% +nodes and there's some internal nodes + + + align:start position:0% +nodes and there's some internal nodes +corresponding maybe to higher level taxa + + align:start position:0% +corresponding maybe to higher level taxa + + + align:start position:0% +corresponding maybe to higher level taxa +or groups or something you might have + + align:start position:0% +or groups or something you might have + + + align:start position:0% +or groups or something you might have +words for these two like mammal or + + align:start position:0% +words for these two like mammal or + + + align:start position:0% +words for these two like mammal or +primate or animal and there's the idea + + align:start position:0% +primate or animal and there's the idea + + + align:start position:0% +primate or animal and there's the idea +is that there's some kind of + + align:start position:0% +is that there's some kind of + + + align:start position:0% +is that there's some kind of +probabilistic model that you can + + align:start position:0% +probabilistic model that you can + + + align:start position:0% +probabilistic model that you can +describe maybe even a causal one on top + + align:start position:0% +describe maybe even a causal one on top + + + align:start position:0% +describe maybe even a causal one on top +of that symbolic structure that tree + + align:start position:0% +of that symbolic structure that tree + + + align:start position:0% +of that symbolic structure that tree +that produces the data of that's more + + align:start position:0% +that produces the data of that's more + + + align:start position:0% +that produces the data of that's more +directly observable the observable + + align:start position:0% +directly observable the observable + + + align:start position:0% +directly observable the observable +features including the things you've + + align:start position:0% +features including the things you've + + + align:start position:0% +features including the things you've +only sparsely observed and want to fill + + align:start position:0% +only sparsely observed and want to fill + + + align:start position:0% +only sparsely observed and want to fill +in and then you might also have higher + + align:start position:0% +in and then you might also have higher + + + align:start position:0% +in and then you might also have higher +levels of structure like if you want to + + align:start position:0% +levels of structure like if you want to + + + align:start position:0% +levels of structure like if you want to +explain how did you learn that tree in + + align:start position:0% +explain how did you learn that tree in + + + align:start position:0% +explain how did you learn that tree in +the first place maybe it's because you + + align:start position:0% +the first place maybe it's because you + + + align:start position:0% +the first place maybe it's because you +have a some kind of generative model for + + align:start position:0% +have a some kind of generative model for + + + align:start position:0% +have a some kind of generative model for +that generative model so here I'm just + + align:start position:0% +that generative model so here I'm just + + + align:start position:0% +that generative model so here I'm just +using words to describe it but I'll show + + align:start position:0% +using words to describe it but I'll show + + + align:start position:0% +using words to describe it but I'll show +you some other stuff in it show you + + align:start position:0% +you some other stuff in it show you + + + align:start position:0% +you some other stuff in it show you +something more formal a little bit later + + align:start position:0% +something more formal a little bit later + + + align:start position:0% +something more formal a little bit later +but you could say well um maybe the way + + align:start position:0% +but you could say well um maybe the way + + + align:start position:0% +but you could say well um maybe the way +I figure out that there's a tree + + align:start position:0% +I figure out that there's a tree + + + align:start position:0% +I figure out that there's a tree +structure is by having a hypothesis that + + align:start position:0% +structure is by having a hypothesis that + + + align:start position:0% +structure is by having a hypothesis that +are the way I figure out that there's + + align:start position:0% +are the way I figure out that there's + + + align:start position:0% +are the way I figure out that there's +that particular tree structured + + align:start position:0% +that particular tree structured + + + align:start position:0% +that particular tree structured +graphical model of this domain is by + + align:start position:0% +graphical model of this domain is by + + + align:start position:0% +graphical model of this domain is by +having the more general hypothesis that + + align:start position:0% +having the more general hypothesis that + + + align:start position:0% +having the more general hypothesis that +there is some latent hierarchy of + + align:start position:0% +there is some latent hierarchy of + + + align:start position:0% +there is some latent hierarchy of +species and I just have to figure out + + align:start position:0% +species and I just have to figure out + + + align:start position:0% +species and I just have to figure out +which one it is right so you could + + align:start position:0% +which one it is right so you could + + + align:start position:0% +which one it is right so you could +formulate this as a hierarchical + + align:start position:0% +formulate this as a hierarchical + + + align:start position:0% +formulate this as a hierarchical +inference by saying that what we're + + align:start position:0% +inference by saying that what we're + + + align:start position:0% +inference by saying that what we're +calling the form the form of the model + + align:start position:0% +calling the form the form of the model + + + align:start position:0% +calling the form the form of the model +it's like a hypothesis space of models + + align:start position:0% +it's like a hypothesis space of models + + + align:start position:0% +it's like a hypothesis space of models +which are themselves hypothesis spaces + + align:start position:0% +which are themselves hypothesis spaces + + + align:start position:0% +which are themselves hypothesis spaces +of possible observed patterns of feature + + align:start position:0% +of possible observed patterns of feature + + + align:start position:0% +of possible observed patterns of feature +correlation and that that higher level + + align:start position:0% +correlation and that that higher level + + + align:start position:0% +correlation and that that higher level +knowledge puts some kind of a generative + + align:start position:0% +knowledge puts some kind of a generative + + + align:start position:0% +knowledge puts some kind of a generative +model on these graph structures where + + align:start position:0% +model on these graph structures where + + + align:start position:0% +model on these graph structures where +each graph structure then puts a + + align:start position:0% +each graph structure then puts a + + + align:start position:0% +each graph structure then puts a +generative model on the data you can + + align:start position:0% +generative model on the data you can + + + align:start position:0% +generative model on the data you can +observe and then you could have even + + align:start position:0% +observe and then you could have even + + + align:start position:0% +observe and then you could have even +higher levels of this sort of thing and + + align:start position:0% +higher levels of this sort of thing and + + + align:start position:0% +higher levels of this sort of thing and +then learning could go on at any or all + + align:start position:0% +then learning could go on at any or all + + + align:start position:0% +then learning could go on at any or all +levels of this hierarchy higher than the + + align:start position:0% +levels of this hierarchy higher than the + + + align:start position:0% +levels of this hierarchy higher than the +level of experience so just to show you + + align:start position:0% +level of experience so just to show you + + + align:start position:0% +level of experience so just to show you +a little bit about how this kind of + + align:start position:0% +a little bit about how this kind of + + + align:start position:0% +a little bit about how this kind of +thing works the the the what we're + + align:start position:0% +thing works the the the what we're + + + align:start position:0% +thing works the the the what we're +calling the probability of the data + + align:start position:0% +calling the probability of the data + + + align:start position:0% +calling the probability of the data +given the structure is actually exactly + + align:start position:0% +given the structure is actually exactly + + + align:start position:0% +given the structure is actually exactly +the same really as the model that syria + + align:start position:0% +the same really as the model that syria + + + align:start position:0% +the same really as the model that syria +and Andrew Sachs used the difference is + + align:start position:0% +and Andrew Sachs used the difference is + + + align:start position:0% +and Andrew Sachs used the difference is +that we were we were suggesting maybe + + align:start position:0% +that we were we were suggesting maybe + + + align:start position:0% +that we were we were suggesting maybe +maybe right maybe wrong that something + + align:start position:0% +maybe right maybe wrong that something + + + align:start position:0% +maybe right maybe wrong that something +like this gendered model was actually in + + align:start position:0% +like this gendered model was actually in + + + align:start position:0% +like this gendered model was actually in +your head right they represented a very + + align:start position:0% +your head right they represented a very + + + align:start position:0% +your head right they represented a very +simple abstraction of evolutionary + + align:start position:0% +simple abstraction of evolutionary + + + align:start position:0% +simple abstraction of evolutionary +branching process + + align:start position:0% +branching process + + + align:start position:0% +branching process +kind of diffusion over the tree where + + align:start position:0% +kind of diffusion over the tree where + + + align:start position:0% +kind of diffusion over the tree where +properties could turn on or off and we + + align:start position:0% +properties could turn on or off and we + + + align:start position:0% +properties could turn on or off and we +built basically that same kind of model + + align:start position:0% +built basically that same kind of model + + + align:start position:0% +built basically that same kind of model +and we said maybe you have something in + + align:start position:0% +and we said maybe you have something in + + + align:start position:0% +and we said maybe you have something in +your head as a model of again the the + + align:start position:0% +your head as a model of again the the + + + align:start position:0% +your head as a model of again the the +distribution of properties or features + + align:start position:0% +distribution of properties or features + + + align:start position:0% +distribution of properties or features +or attributes over the leaf nodes of the + + align:start position:0% +or attributes over the leaf nodes of the + + + align:start position:0% +or attributes over the leaf nodes of the +tree so if you have this kind of + + align:start position:0% +tree so if you have this kind of + + + align:start position:0% +tree so if you have this kind of +statistical model if you think that + + align:start position:0% +statistical model if you think that + + + align:start position:0% +statistical model if you think that +there's something like a tree structure + + align:start position:0% +there's something like a tree structure + + + align:start position:0% +there's something like a tree structure +and properties are just are produced + + align:start position:0% +and properties are just are produced + + + align:start position:0% +and properties are just are produced +over the leaf nodes by some kind of + + align:start position:0% +over the leaf nodes by some kind of + + + align:start position:0% +over the leaf nodes by some kind of +switching on and off mutation like + + align:start position:0% +switching on and off mutation like + + + align:start position:0% +switching on and off mutation like +process then you can do something like + + align:start position:0% +process then you can do something like + + + align:start position:0% +process then you can do something like +in this picture here you can take an + + align:start position:0% +in this picture here you can take an + + + align:start position:0% +in this picture here you can take an +observe set of features that matrix and + + align:start position:0% +observe set of features that matrix and + + + align:start position:0% +observe set of features that matrix and +learn the best tree you can figure out + + align:start position:0% +learn the best tree you can figure out + + + align:start position:0% +learn the best tree you can figure out +that thing I'm showing on the top that + + align:start position:0% +that thing I'm showing on the top that + + + align:start position:0% +that thing I'm showing on the top that +structure which is in some sense the + + align:start position:0% +structure which is in some sense the + + + align:start position:0% +structure which is in some sense the +best guess of a tree structure a latent + + align:start position:0% +best guess of a tree structure a latent + + + align:start position:0% +best guess of a tree structure a latent +tree structure which if you then define + + align:start position:0% +tree structure which if you then define + + + align:start position:0% +tree structure which if you then define +some kind of diffusion mutation process + + align:start position:0% +some kind of diffusion mutation process + + + align:start position:0% +some kind of diffusion mutation process +over that tree would produce with high + + align:start position:0% +over that tree would produce with high + + + align:start position:0% +over that tree would produce with high +probability distributions of features + + align:start position:0% +probability distributions of features + + + align:start position:0% +probability distributions of features +like those shown there if I gave you a + + align:start position:0% +like those shown there if I gave you a + + + align:start position:0% +like those shown there if I gave you a +very different tree it would produce + + align:start position:0% +very different tree it would produce + + + align:start position:0% +very different tree it would produce +other patterns of correlation and it's + + align:start position:0% +other patterns of correlation and it's + + + align:start position:0% +other patterns of correlation and it's +just like Surya said it can be all + + align:start position:0% +just like Surya said it can be all + + + align:start position:0% +just like Surya said it can be all +captured by the second-order statistics + + align:start position:0% +captured by the second-order statistics + + + align:start position:0% +captured by the second-order statistics +of feature correlations the nice thing + + align:start position:0% +of feature correlations the nice thing + + + align:start position:0% +of feature correlations the nice thing +about this right is that now this also + + align:start position:0% +about this right is that now this also + + + align:start position:0% +about this right is that now this also +gives a distribution on new properties + + align:start position:0% +gives a distribution on new properties + + + align:start position:0% +gives a distribution on new properties +so if I observe because there each + + align:start position:0% +so if I observe because there each + + + align:start position:0% +so if I observe because there each +column is conditionally independent + + align:start position:0% +column is conditionally independent + + + align:start position:0% +column is conditionally independent +given that model each column is an + + align:start position:0% +given that model each column is an + + + align:start position:0% +given that model each column is an +independent sample from that generative + + align:start position:0% +independent sample from that generative + + + align:start position:0% +independent sample from that generative +model and and the idea is if I observe a + + align:start position:0% +model and and the idea is if I observe a + + + align:start position:0% +model and and the idea is if I observe a +new property and I want to say which + + align:start position:0% +new property and I want to say which + + + align:start position:0% +new property and I want to say which +other things have this well I can make a + + align:start position:0% +other things have this well I can make a + + + align:start position:0% +other things have this well I can make a +guess on using that public model I can + + align:start position:0% +guess on using that public model I can + + + align:start position:0% +guess on using that public model I can +say all right given given that I know + + align:start position:0% +say all right given given that I know + + + align:start position:0% +say all right given given that I know +the value of this function over the tree + + align:start position:0% +the value of this function over the tree + + + align:start position:0% +the value of this function over the tree +the stochastic process at some points + + align:start position:0% +the stochastic process at some points + + + align:start position:0% +the stochastic process at some points +what do I think the most likely values + + align:start position:0% +what do I think the most likely values + + + align:start position:0% +what do I think the most likely values +are at other points and basically what + + align:start position:0% +are at other points and basically what + + + align:start position:0% +are at other points and basically what +you get is again like in the diffusion + + align:start position:0% +you get is again like in the diffusion + + + align:start position:0% +you get is again like in the diffusion +process a kind of similarity based + + align:start position:0% +process a kind of similarity based + + + align:start position:0% +process a kind of similarity based +generalization with a tree structured + + align:start position:0% +generalization with a tree structured + + + align:start position:0% +generalization with a tree structured +metric that nearby points in the tree + + align:start position:0% +metric that nearby points in the tree + + + align:start position:0% +metric that nearby points in the tree +are likely to have the same value so in + + align:start position:0% +are likely to have the same value so in + + + align:start position:0% +are likely to have the same value so in +particular things that are near to say + + align:start position:0% +particular things that are near to say + + + align:start position:0% +particular things that are near to say +species 1 and 9 are probably gonna have + + align:start position:0% +species 1 and 9 are probably gonna have + + + align:start position:0% +species 1 and 9 are probably gonna have +the same property and others may be less + + align:start position:0% +the same property and others may be less + + + align:start position:0% +the same property and others may be less +so and you build that model and it's + + align:start position:0% +so and you build that model and it's + + + align:start position:0% +so and you build that model and it's +really quite striking how much it + + align:start position:0% +really quite striking how much it + + + align:start position:0% +really quite striking how much it +matches people's intuitions so now + + align:start position:0% +matches people's intuitions so now + + + align:start position:0% +matches people's intuitions so now +you're seeing the kinds of plots I was + + align:start position:0% +you're seeing the kinds of plots I was + + + align:start position:0% +you're seeing the kinds of plots I was +showing you before where all my data + + align:start position:0% +showing you before where all my data + + + align:start position:0% +showing you before where all my data +plots look like this whenever I'm + + align:start position:0% +plots look like this whenever I'm + + + align:start position:0% +plots look like this whenever I'm +showing the scatter plot by default the + + align:start position:0% +showing the scatter plot by default the + + + align:start position:0% +showing the scatter plot by default the +y-axis is the average of a bunch of + + align:start position:0% +y-axis is the average of a bunch of + + + align:start position:0% +y-axis is the average of a bunch of +people's judgments and the x-axis is the + + align:start position:0% +people's judgments and the x-axis is the + + + align:start position:0% +people's judgments and the x-axis is the +model predictions on the same units or + + align:start position:0% +model predictions on the same units or + + + align:start position:0% +model predictions on the same units or +scale and each of these scatter plots is + + align:start position:0% +scale and each of these scatter plots is + + + align:start position:0% +scale and each of these scatter plots is +from a different experiment not done by + + align:start position:0% +from a different experiment not done by + + + align:start position:0% +from a different experiment not done by +us done by other people like Austin and + + align:start position:0% +us done by other people like Austin and + + + align:start position:0% +us done by other people like Austin and +Smith from a couple of decades ago + + align:start position:0% +Smith from a couple of decades ago + + + align:start position:0% + +but they're all they all sort of have + + align:start position:0% +but they're all they all sort of have + + + align:start position:0% +but they're all they all sort of have +the same kind of form where each dot is + + align:start position:0% +the same kind of form where each dot is + + + align:start position:0% +the same kind of form where each dot is +a different set of examples or a + + align:start position:0% +a different set of examples or a + + + align:start position:0% +a different set of examples or a +different argument and what typically + + align:start position:0% +different argument and what typically + + + align:start position:0% +different argument and what typically +varied within an experiment you vary the + + align:start position:0% +varied within an experiment you vary the + + + align:start position:0% +varied within an experiment you vary the +examples and you fix constant the + + align:start position:0% +examples and you fix constant the + + + align:start position:0% +examples and you fix constant the +conclusion category and you see + + align:start position:0% +conclusion category and you see + + + align:start position:0% +conclusion category and you see +basically how much evidential support + + align:start position:0% +basically how much evidential support + + + align:start position:0% +basically how much evidential support +two different sets of two or three + + align:start position:0% +two different sets of two or three + + + align:start position:0% +two different sets of two or three +examples give to a certain conclusion + + align:start position:0% +examples give to a certain conclusion + + + align:start position:0% +examples give to a certain conclusion +and and it's really again quite striking + + align:start position:0% +and and it's really again quite striking + + + align:start position:0% +and and it's really again quite striking +that sometimes in a more categorical way + + align:start position:0% +that sometimes in a more categorical way + + + align:start position:0% +that sometimes in a more categorical way +sometimes in a more graded way but + + align:start position:0% +sometimes in a more graded way but + + + align:start position:0% +sometimes in a more graded way but +basically people's average judgments + + align:start position:0% +basically people's average judgments + + + align:start position:0% +basically people's average judgments +here just line up quite well with the + + align:start position:0% +here just line up quite well with the + + + align:start position:0% +here just line up quite well with the +sort of Bayesian inference on this tree + + align:start position:0% +sort of Bayesian inference on this tree + + + align:start position:0% +sort of Bayesian inference on this tree +structured generative model these are + + align:start position:0% +structured generative model these are + + + align:start position:0% +structured generative model these are +just examples of the kinds of stimuli + + align:start position:0% +just examples of the kinds of stimuli + + + align:start position:0% +just examples of the kinds of stimuli +here um now we can compare one of the + + align:start position:0% +here um now we can compare one of the + + + align:start position:0% +here um now we can compare one of the +reasons why we were interested in this + + align:start position:0% +reasons why we were interested in this + + + align:start position:0% +reasons why we were interested in this +was to compare again many different + + align:start position:0% +was to compare again many different + + + align:start position:0% +was to compare again many different +approaches so here I'm going to show you + + align:start position:0% +approaches so here I'm going to show you + + + align:start position:0% +approaches so here I'm going to show you +a comparison with a just a variant of + + align:start position:0% +a comparison with a just a variant of + + + align:start position:0% +a comparison with a just a variant of +our approach it's the same kind of + + align:start position:0% +our approach it's the same kind of + + + align:start position:0% +our approach it's the same kind of +hierarchical Bayesian model but now the + + align:start position:0% +hierarchical Bayesian model but now the + + + align:start position:0% +hierarchical Bayesian model but now the +structure isn't a tree it's a low + + align:start position:0% +structure isn't a tree it's a low + + + align:start position:0% +structure isn't a tree it's a low +dimensional Euclidean space you can + + align:start position:0% +dimensional Euclidean space you can + + + align:start position:0% +dimensional Euclidean space you can +define the same kinds of sort of + + align:start position:0% +define the same kinds of sort of + + + align:start position:0% +define the same kinds of sort of +proximity smoothness thing I mean again + + align:start position:0% +proximity smoothness thing I mean again + + + align:start position:0% +proximity smoothness thing I mean again +it's it's more standard and machine + + align:start position:0% +it's it's more standard and machine + + + align:start position:0% +it's it's more standard and machine +learning it's related to Gaussian + + align:start position:0% +learning it's related to Gaussian + + + align:start position:0% +learning it's related to Gaussian +processes + + align:start position:0% +processes + + + align:start position:0% +processes +you know it's related it's much more + + align:start position:0% +you know it's related it's much more + + + align:start position:0% +you know it's related it's much more +like neural networks you could think of + + align:start position:0% +like neural networks you could think of + + + align:start position:0% +like neural networks you could think of +this as kind of like a Bayesian version + + align:start position:0% +this as kind of like a Bayesian version + + + align:start position:0% +this as kind of like a Bayesian version +of a bottleneck hidden layer with two + + align:start position:0% +of a bottleneck hidden layer with two + + + align:start position:0% +of a bottleneck hidden layer with two +dimensions or a small number of + + align:start position:0% +dimensions or a small number of + + + align:start position:0% +dimensions or a small number of +dimensions the pictures that Surya + + align:start position:0% +dimensions the pictures that Surya + + + align:start position:0% +dimensions the pictures that Surya +showed you we're all higher dimensions + + align:start position:0% +showed you we're all higher dimensions + + + align:start position:0% +showed you we're all higher dimensions +than two dimensions in the latent space + + align:start position:0% +than two dimensions in the latent space + + + align:start position:0% +than two dimensions in the latent space +or the hidden variable space of the + + align:start position:0% +or the hidden variable space of the + + + align:start position:0% +or the hidden variable space of the +neural network the hidden layer of space + + align:start position:0% +neural network the hidden layer of space + + + align:start position:0% +neural network the hidden layer of space +but when you compress this amount to two + + align:start position:0% +but when you compress this amount to two + + + align:start position:0% +but when you compress this amount to two +dimensions it looks pretty good so it's + + align:start position:0% +dimensions it looks pretty good so it's + + + align:start position:0% +dimensions it looks pretty good so it's +same kind of idea now what you're saying + + align:start position:0% +same kind of idea now what you're saying + + + align:start position:0% +same kind of idea now what you're saying +is you're going to you're gonna find not + + align:start position:0% +is you're going to you're gonna find not + + + align:start position:0% +is you're going to you're gonna find not +the best tree that explains all these + + align:start position:0% +the best tree that explains all these + + + align:start position:0% +the best tree that explains all these +features but the best two dimensional + + align:start position:0% +features but the best two dimensional + + + align:start position:0% +features but the best two dimensional +space maybe it looks like this where + + align:start position:0% +space maybe it looks like this where + + + align:start position:0% +space maybe it looks like this where +again the probabilistic model says that + + align:start position:0% +again the probabilistic model says that + + + align:start position:0% +again the probabilistic model says that +things which are relatively things that + + align:start position:0% +things which are relatively things that + + + align:start position:0% +things which are relatively things that +you're closer in this two dimensional + + align:start position:0% +you're closer in this two dimensional + + + align:start position:0% +you're closer in this two dimensional +space are more likely to have the same + + align:start position:0% +space are more likely to have the same + + + align:start position:0% +space are more likely to have the same +feature value so you're basically + + align:start position:0% +feature value so you're basically + + + align:start position:0% +feature value so you're basically +explaining all the pairwise feature + + align:start position:0% +explaining all the pairwise feature + + + align:start position:0% +explaining all the pairwise feature +correlations by distance in this space + + align:start position:0% +correlations by distance in this space + + + align:start position:0% +correlations by distance in this space +it's it's similar it's importantly it's + + align:start position:0% +it's it's similar it's importantly it's + + + align:start position:0% +it's it's similar it's importantly it's +not as causal and compositional right + + align:start position:0% +not as causal and compositional right + + + align:start position:0% +not as causal and compositional right +the tree the tree models something about + + align:start position:0% +the tree the tree models something about + + + align:start position:0% +the tree the tree models something about +possibly the causal processes of how + + align:start position:0% +possibly the causal processes of how + + + align:start position:0% +possibly the causal processes of how +organisms come to be if I told you that + + align:start position:0% +organisms come to be if I told you that + + + align:start position:0% +organisms come to be if I told you that +you know oh there's a I told you about a + + align:start position:0% +you know oh there's a I told you about a + + + align:start position:0% +you know oh there's a I told you about a +sub you know sub species like whatever + + align:start position:0% +sub you know sub species like whatever + + + align:start position:0% +sub you know sub species like whatever +it's a good example different breeds of + + align:start position:0% +it's a good example different breeds of + + + align:start position:0% +it's a good example different breeds of +dogs or I told you you know + + align:start position:0% +dogs or I told you you know + + + align:start position:0% +dogs or I told you you know +that oh well there's yours not just + + align:start position:0% +that oh well there's yours not just + + + align:start position:0% +that oh well there's yours not just +wolves but there's the gray tailed wolf + + align:start position:0% +wolves but there's the gray tailed wolf + + + align:start position:0% +wolves but there's the gray tailed wolf +and the red tailed wolf red again + + align:start position:0% +and the red tailed wolf red again + + + align:start position:0% +and the red tailed wolf red again +they're probably similar but they might + + align:start position:0% +they're probably similar but they might + + + align:start position:0% +they're probably similar but they might +blue one red tailed wolf whatever that + + align:start position:0% +blue one red tailed wolf whatever that + + + align:start position:0% +blue one red tailed wolf whatever that +is is more similar to another red tailed + + align:start position:0% +is is more similar to another red tailed + + + align:start position:0% +is is more similar to another red tailed +wolf probably has more features in + + align:start position:0% +wolf probably has more features in + + + align:start position:0% +wolf probably has more features in +common than with the gray tailed wolf + + align:start position:0% +common than with the gray tailed wolf + + + align:start position:0% +common than with the gray tailed wolf +and probably more to the gray tailed + + align:start position:0% +and probably more to the gray tailed + + + align:start position:0% +and probably more to the gray tailed +wolf than to a dog the nice thing about + + align:start position:0% +wolf than to a dog the nice thing about + + + align:start position:0% +wolf than to a dog the nice thing about +a tree is I can tell you these things + + align:start position:0% +a tree is I can tell you these things + + + align:start position:0% +a tree is I can tell you these things +and you can in your mind you know maybe + + align:start position:0% +and you can in your mind you know maybe + + + align:start position:0% +and you can in your mind you know maybe +you'll never forget that there's a + + align:start position:0% +you'll never forget that there's a + + + align:start position:0% +you'll never forget that there's a +red-tailed Wolf there isn't I just made + + align:start position:0% +red-tailed Wolf there isn't I just made + + + align:start position:0% +red-tailed Wolf there isn't I just made +it up but if you ever remember you find + + align:start position:0% +it up but if you ever remember you find + + + align:start position:0% +it up but if you ever remember you find +yourself thinking about red tailed + + align:start position:0% +yourself thinking about red tailed + + + align:start position:0% +yourself thinking about red tailed +wolves and whether their properties are + + align:start position:0% +wolves and whether their properties are + + + align:start position:0% +wolves and whether their properties are +more or less similar to each other than + + align:start position:0% +more or less similar to each other than + + + align:start position:0% +more or less similar to each other than +that then two gray tailed wolves or less + + align:start position:0% +that then two gray tailed wolves or less + + + align:start position:0% +that then two gray tailed wolves or less +so two dot dogs or so on you know it's + + align:start position:0% +so two dot dogs or so on you know it's + + + align:start position:0% +so two dot dogs or so on you know it's +because I just said some things and you + + align:start position:0% +because I just said some things and you + + + align:start position:0% +because I just said some things and you +grew out your tree in your mind that's a + + align:start position:0% +grew out your tree in your mind that's a + + + align:start position:0% +grew out your tree in your mind that's a +lot harder to do if in a low dimensional + + align:start position:0% +lot harder to do if in a low dimensional + + + align:start position:0% +lot harder to do if in a low dimensional +space okay and it turns out that that + + align:start position:0% +space okay and it turns out that that + + + align:start position:0% +space okay and it turns out that that +model also fits this data less well so + + align:start position:0% +model also fits this data less well so + + + align:start position:0% +model also fits this data less well so +here I'm just showing two of those + + align:start position:0% +here I'm just showing two of those + + + align:start position:0% +here I'm just showing two of those +experiments some of them are well fit by + + align:start position:0% +experiments some of them are well fit by + + + align:start position:0% +experiments some of them are well fit by +that model but others are less well fit + + align:start position:0% +that model but others are less well fit + + + align:start position:0% +that model but others are less well fit +um now that's not to say that they + + align:start position:0% +um now that's not to say that they + + + align:start position:0% +um now that's not to say that they +wouldn't be good for other things so we + + align:start position:0% +wouldn't be good for other things so we + + + align:start position:0% +wouldn't be good for other things so we +also did some experience this is + + align:start position:0% +also did some experience this is + + + align:start position:0% +also did some experience this is +experiments that we did I forgot to say + + align:start position:0% +experiments that we did I forgot to say + + + align:start position:0% +experiments that we did I forgot to say +really importantly this is all work done + + align:start position:0% +really importantly this is all work done + + + align:start position:0% +really importantly this is all work done +by Charles Kemp who's now a professor at + + align:start position:0% +by Charles Kemp who's now a professor at + + + align:start position:0% +by Charles Kemp who's now a professor at +CMU and it was part of the stuff that he + + align:start position:0% +CMU and it was part of the stuff that he + + + align:start position:0% +CMU and it was part of the stuff that he +did in his PhD thesis um so we you know + + align:start position:0% +did in his PhD thesis um so we you know + + + align:start position:0% +did in his PhD thesis um so we you know +we were we were interested in this as a + + align:start position:0% +we were we were interested in this as a + + + align:start position:0% +we were we were interested in this as a +way not to study trees but to study a + + align:start position:0% +way not to study trees but to study a + + + align:start position:0% +way not to study trees but to study a +range of different kinds of structures + + align:start position:0% +range of different kinds of structures + + + align:start position:0% +range of different kinds of structures +and you know it is true going back I + + align:start position:0% +and you know it is true going back I + + + align:start position:0% +and you know it is true going back I +guess to the question you asked this is + + align:start position:0% +guess to the question you asked this is + + + align:start position:0% +guess to the question you asked this is +what I was referring to about low + + align:start position:0% +what I was referring to about low + + + align:start position:0% +what I was referring to about low +dimensional manifolds you know there are + + align:start position:0% +dimensional manifolds you know there are + + + align:start position:0% +dimensional manifolds you know there are +some kinds of knowledge representations + + align:start position:0% +some kinds of knowledge representations + + + align:start position:0% +some kinds of knowledge representations +we have which might have a low + + align:start position:0% +we have which might have a low + + + align:start position:0% +we have which might have a low +dimensional spatial structure in + + align:start position:0% +dimensional spatial structure in + + + align:start position:0% +dimensional spatial structure in +particular like mental maps of the world + + align:start position:0% +particular like mental maps of the world + + + align:start position:0% +particular like mental maps of the world +right so our intuitive models of of you + + align:start position:0% +right so our intuitive models of of you + + + align:start position:0% +right so our intuitive models of of you +know the Earth's surface and things + + align:start position:0% +know the Earth's surface and things + + + align:start position:0% +know the Earth's surface and things +which might be distributed over the + + align:start position:0% +which might be distributed over the + + + align:start position:0% +which might be distributed over the +Earth's surface facially you know a + + align:start position:0% +Earth's surface facially you know a + + + align:start position:0% +Earth's surface facially you know a +two-dimensional map is probably a good + + align:start position:0% +two-dimensional map is probably a good + + + align:start position:0% +two-dimensional map is probably a good +one for that so here we considered a + + align:start position:0% +one for that so here we considered a + + + align:start position:0% +one for that so here we considered a +similar kind of concept learning from a + + align:start position:0% +similar kind of concept learning from a + + + align:start position:0% +similar kind of concept learning from a +few examples tasks where we said but now + + align:start position:0% +few examples tasks where we said but now + + + align:start position:0% +few examples tasks where we said but now +we put it like this we said suppose that + + align:start position:0% +we put it like this we said suppose that + + + align:start position:0% +we put it like this we said suppose that +a certain kind of Native American + + align:start position:0% +a certain kind of Native American + + + align:start position:0% +a certain kind of Native American +artifacts i'ts near City X how likely is + + align:start position:0% +artifacts i'ts near City X how likely is + + + align:start position:0% +artifacts i'ts near City X how likely is +it also to be found in sites near city Y + + align:start position:0% +it also to be found in sites near city Y + + + align:start position:0% +it also to be found in sites near city Y +or we could say sites in near city X&Y + + align:start position:0% +or we could say sites in near city X&Y + + + align:start position:0% +or we could say sites in near city X&Y +how about City Z and we told people that + + align:start position:0% +how about City Z and we told people that + + + align:start position:0% +how about City Z and we told people that +you know different Native American + + align:start position:0% +you know different Native American + + + align:start position:0% +you know different Native American +tribes maybe had some some lived in a + + align:start position:0% +tribes maybe had some some lived in a + + + align:start position:0% +tribes maybe had some some lived in a +very small area some lived in a very big + + align:start position:0% +very small area some lived in a very big + + + align:start position:0% +very small area some lived in a very big +area some lived in one place some of + + align:start position:0% +area some lived in one place some of + + + align:start position:0% +area some lived in one place some of +another place some lived here and then + + align:start position:0% +another place some lived here and then + + + align:start position:0% +another place some lived here and then +moved there we just told people very + + align:start position:0% +moved there we just told people very + + + align:start position:0% +moved there we just told people very +vague things that + + align:start position:0% +vague things that + + + align:start position:0% +vague things that +into people's you know probably badly + + align:start position:0% +into people's you know probably badly + + + align:start position:0% +into people's you know probably badly +remembered and very distorted versions + + align:start position:0% +remembered and very distorted versions + + + align:start position:0% +remembered and very distorted versions +of American history that would basically + + align:start position:0% +of American history that would basically + + + align:start position:0% +of American history that would basically +suggest that there should be some kind + + align:start position:0% +suggest that there should be some kind + + + align:start position:0% +suggest that there should be some kind +of similar kind of spatial diffusion + + align:start position:0% +of similar kind of spatial diffusion + + + align:start position:0% +of similar kind of spatial diffusion +process but now in your 2d mental map of + + align:start position:0% +process but now in your 2d mental map of + + + align:start position:0% +process but now in your 2d mental map of +cities so again there's no claim that + + align:start position:0% +cities so again there's no claim that + + + align:start position:0% +cities so again there's no claim that +there's any like reality to this our + + align:start position:0% +there's any like reality to this our + + + align:start position:0% +there's any like reality to this our +fine-grained reality but we thought it + + align:start position:0% +fine-grained reality but we thought it + + + align:start position:0% +fine-grained reality but we thought it +would sort of roughly correspond to + + align:start position:0% +would sort of roughly correspond to + + + align:start position:0% +would sort of roughly correspond to +people's internal causal generative + + align:start position:0% +people's internal causal generative + + + align:start position:0% +people's internal causal generative +models of archaeology right again I + + align:start position:0% +models of archaeology right again I + + + align:start position:0% +models of archaeology right again I +think it says something about the way + + align:start position:0% +think it says something about the way + + + align:start position:0% +think it says something about the way +human intelligence works that none of us + + align:start position:0% +human intelligence works that none of us + + + align:start position:0% +human intelligence works that none of us +are archaeologists promptly but we still + + align:start position:0% +are archaeologists promptly but we still + + + align:start position:0% +are archaeologists promptly but we still +have these ideas okay and it turned out + + align:start position:0% +have these ideas okay and it turned out + + + align:start position:0% +have these ideas okay and it turned out +that here a spatially structured model + + align:start position:0% +that here a spatially structured model + + + align:start position:0% +that here a spatially structured model +actually works a lot better again it + + align:start position:0% +actually works a lot better again it + + + align:start position:0% +actually works a lot better again it +shouldn't be surprising it's just + + align:start position:0% +shouldn't be surprising it's just + + + align:start position:0% +shouldn't be surprising it's just +showing that that actually the bay that + + align:start position:0% +showing that that actually the bay that + + + align:start position:0% +showing that that actually the bay that +we the judgment people make when they're + + align:start position:0% +we the judgment people make when they're + + + align:start position:0% +we the judgment people make when they're +making inferences from a few examples + + align:start position:0% +making inferences from a few examples + + + align:start position:0% +making inferences from a few examples +just like you saw with the predicting + + align:start position:0% +just like you saw with the predicting + + + align:start position:0% +just like you saw with the predicting +the everyday events but now in the much + + align:start position:0% +the everyday events but now in the much + + + align:start position:0% +the everyday events but now in the much +more interesting the structured domain + + align:start position:0% +more interesting the structured domain + + + align:start position:0% +more interesting the structured domain +is sensitive to the different kinds of + + align:start position:0% +is sensitive to the different kinds of + + + align:start position:0% +is sensitive to the different kinds of +environmental statistics there it was + + align:start position:0% +environmental statistics there it was + + + align:start position:0% +environmental statistics there it was +different you know power laws versus + + align:start position:0% +different you know power laws versus + + + align:start position:0% +different you know power laws versus +gaussians of cake bake or of movie + + align:start position:0% +gaussians of cake bake or of movie + + + align:start position:0% +gaussians of cake bake or of movie +grosses versus lifetimes or something + + align:start position:0% +grosses versus lifetimes or something + + + align:start position:0% +grosses versus lifetimes or something +here it's other stuff it's more + + align:start position:0% +here it's other stuff it's more + + + align:start position:0% +here it's other stuff it's more +interestingly structured kinds of + + align:start position:0% +interestingly structured kinds of + + + align:start position:0% +interestingly structured kinds of +knowledge but you see the same kind of + + align:start position:0% +knowledge but you see the same kind of + + + align:start position:0% +knowledge but you see the same kind of +picture and we found we thought that was + + align:start position:0% +picture and we found we thought that was + + + align:start position:0% +picture and we found we thought that was +interesting and again suggests some of + + align:start position:0% +interesting and again suggests some of + + + align:start position:0% +interesting and again suggests some of +the ways that that we've started to put + + align:start position:0% +the ways that that we've started to put + + + align:start position:0% +the ways that that we've started to put +these tools together putting together + + align:start position:0% +these tools together putting together + + + align:start position:0% +these tools together putting together +problems to generative models with some + + align:start position:0% +problems to generative models with some + + + align:start position:0% +problems to generative models with some +kind of interestingly structured + + align:start position:0% +kind of interestingly structured + + + align:start position:0% +kind of interestingly structured +knowledge now again as you saw from + + align:start position:0% +knowledge now again as you saw from + + + align:start position:0% +knowledge now again as you saw from +Syria and as Jay McClellan and Tim + + align:start position:0% +Syria and as Jay McClellan and Tim + + + align:start position:0% +Syria and as Jay McClellan and Tim +Rogers worked on you can try to capture + + align:start position:0% +Rogers worked on you can try to capture + + + align:start position:0% +Rogers worked on you can try to capture +a lot of this stuff with neural networks + + align:start position:0% +a lot of this stuff with neural networks + + + align:start position:0% +a lot of this stuff with neural networks +the neat thing about the neural networks + + align:start position:0% +the neat thing about the neural networks + + + align:start position:0% +the neat thing about the neural networks +that these guys have worked on is that + + align:start position:0% +that these guys have worked on is that + + + align:start position:0% +that these guys have worked on is that +the exactly the same neural network can + + align:start position:0% +the exactly the same neural network can + + + align:start position:0% +the exactly the same neural network can +capture this kind of thing and can + + align:start position:0% +capture this kind of thing and can + + + align:start position:0% +capture this kind of thing and can +capture this kind of thing right so you + + align:start position:0% +capture this kind of thing right so you + + + align:start position:0% +capture this kind of thing right so you +can take train the very same hidden + + align:start position:0% +can take train the very same hidden + + + align:start position:0% +can take train the very same hidden +multi-layer neural network with two with + + align:start position:0% +multi-layer neural network with two with + + + align:start position:0% +multi-layer neural network with two with +one matrix of object and features and + + align:start position:0% +one matrix of object and features and + + + align:start position:0% +one matrix of object and features and +the very same neural network can predict + + align:start position:0% +the very same neural network can predict + + + align:start position:0% +the very same neural network can predict +the sort of tree-structured patterns for + + align:start position:0% +the sort of tree-structured patterns for + + + align:start position:0% +the sort of tree-structured patterns for +animals and their properties as well as + + align:start position:0% +animals and their properties as well as + + + align:start position:0% +animals and their properties as well as +the spatially structured patterns for + + align:start position:0% +the spatially structured patterns for + + + align:start position:0% +the spatially structured patterns for +Native American artifacts in their + + align:start position:0% +Native American artifacts in their + + + align:start position:0% +Native American artifacts in their +cities the catch is that it doesn't do + + align:start position:0% +cities the catch is that it doesn't do + + + align:start position:0% +cities the catch is that it doesn't do +either of them that well um it doesn't + + align:start position:0% +either of them that well um it doesn't + + + align:start position:0% +either of them that well um it doesn't +do as well as the the tree structure + + align:start position:0% +do as well as the the tree structure + + + align:start position:0% +do as well as the the tree structure +models do for peep and when I say either + + align:start position:0% +models do for peep and when I say either + + + align:start position:0% +models do for peep and when I say either +it doesn't do that well I mean in + + align:start position:0% +it doesn't do that well I mean in + + + align:start position:0% +it doesn't do that well I mean in +capturing people's judgments it doesn't + + align:start position:0% +capturing people's judgments it doesn't + + + align:start position:0% +capturing people's judgments it doesn't +do as well as the best tree structure + + align:start position:0% +do as well as the best tree structure + + + align:start position:0% +do as well as the best tree structure +models do for people's and concepts of + + align:start position:0% +models do for people's and concepts of + + + align:start position:0% +models do for people's and concepts of +animals and their properties and it + + align:start position:0% +animals and their properties and it + + + align:start position:0% +animals and their properties and it +doesn't do as well as the best spatial + + align:start position:0% +doesn't do as well as the best spatial + + + align:start position:0% +doesn't do as well as the best spatial +structures + + align:start position:0% +structures + + + align:start position:0% +structures +but you know again it's in the same + + align:start position:0% +but you know again it's in the same + + + align:start position:0% +but you know again it's in the same +spirit as the deep mind networks for + + align:start position:0% +spirit as the deep mind networks for + + + align:start position:0% +spirit as the deep mind networks for +playing lots of Atari games the idea + + align:start position:0% +playing lots of Atari games the idea + + + align:start position:0% +playing lots of Atari games the idea +there is to have the same Network solve + + align:start position:0% +there is to have the same Network solve + + + align:start position:0% +there is to have the same Network solve +all these different tasks and in some + + align:start position:0% +all these different tasks and in some + + + align:start position:0% +all these different tasks and in some +sense I think that's a good idea I just + + align:start position:0% +sense I think that's a good idea I just + + + align:start position:0% +sense I think that's a good idea I just +think that the architecture should have + + align:start position:0% +think that the architecture should have + + + align:start position:0% +think that the architecture should have +more flexible structure so in we would + + align:start position:0% +more flexible structure so in we would + + + align:start position:0% +more flexible structure so in we would +also say in some sense the same + + align:start position:0% +also say in some sense the same + + + align:start position:0% +also say in some sense the same +architecture of solving all these + + align:start position:0% +architecture of solving all these + + + align:start position:0% +architecture of solving all these +different tasks it's just that this is + + align:start position:0% +different tasks it's just that this is + + + align:start position:0% +different tasks it's just that this is +one setting of it and this is another + + align:start position:0% +one setting of it and this is another + + + align:start position:0% +one setting of it and this is another +setting of it and where they differ is + + align:start position:0% +setting of it and where they differ is + + + align:start position:0% +setting of it and where they differ is +in the kind of structure that well they + + align:start position:0% +in the kind of structure that well they + + + align:start position:0% +in the kind of structure that well they +differ in in the fact that they + + align:start position:0% +differ in in the fact that they + + + align:start position:0% +differ in in the fact that they +explicitly represent structure in the + + align:start position:0% +explicitly represent structure in the + + + align:start position:0% +explicitly represent structure in the +world and they explicitly represent + + align:start position:0% +world and they explicitly represent + + + align:start position:0% +world and they explicitly represent +different kinds of structure and they + + align:start position:0% +different kinds of structure and they + + + align:start position:0% +different kinds of structure and they +explicitly represent that different + + align:start position:0% +explicitly represent that different + + + align:start position:0% +explicitly represent that different +kinds of structure are appropriate to + + align:start position:0% +kinds of structure are appropriate to + + + align:start position:0% +kinds of structure are appropriate to +different kinds of domains in the world + + align:start position:0% +different kinds of domains in the world + + + align:start position:0% +different kinds of domains in the world +and our intuitions about the causal + + align:start position:0% +and our intuitions about the causal + + + align:start position:0% +and our intuitions about the causal +processes that are at work producing the + + align:start position:0% +processes that are at work producing the + + + align:start position:0% +processes that are at work producing the +data and I think that again to that's + + align:start position:0% +data and I think that again to that's + + + align:start position:0% +data and I think that again to that's +sort of the difference between the + + align:start position:0% +sort of the difference between the + + + align:start position:0% +sort of the difference between the +pattern classification and the + + align:start position:0% +pattern classification and the + + + align:start position:0% +pattern classification and the +understanding or explaining view of + + align:start position:0% +understanding or explaining view of + + + align:start position:0% +understanding or explaining view of +intelligence they're their explanations + + align:start position:0% +intelligence they're their explanations + + + align:start position:0% +intelligence they're their explanations +of course go a lot beyond different ways + + align:start position:0% +of course go a lot beyond different ways + + + align:start position:0% +of course go a lot beyond different ways +that similarity can be structured so one + + align:start position:0% +that similarity can be structured so one + + + align:start position:0% +that similarity can be structured so one +of the kind of nice things oh and I + + align:start position:0% +of the kind of nice things oh and I + + + align:start position:0% +of the kind of nice things oh and I +guess another another two other points + + align:start position:0% +guess another another two other points + + + align:start position:0% +guess another another two other points +beyond that one is that to get the + + align:start position:0% +beyond that one is that to get the + + + align:start position:0% +beyond that one is that to get the +neural networks to do that you have to + + align:start position:0% +neural networks to do that you have to + + + align:start position:0% +neural networks to do that you have to +train them with a lot of data remember + + align:start position:0% +train them with a lot of data remember + + + align:start position:0% +train them with a lot of data remember +Surya as Tommy pushed him on in that + + align:start position:0% +Surya as Tommy pushed him on in that + + + align:start position:0% +Surya as Tommy pushed him on in that +talk Surya was very concerned with + + align:start position:0% +talk Surya was very concerned with + + + align:start position:0% +talk Surya was very concerned with +modeling the dynamics of learning in the + + align:start position:0% +modeling the dynamics of learning in the + + + align:start position:0% +modeling the dynamics of learning in the +sense of the the optimization time + + align:start position:0% +sense of the the optimization time + + + align:start position:0% +sense of the the optimization time +course right how the weights change over + + align:start position:0% +course right how the weights change over + + + align:start position:0% +course right how the weights change over +time but he was usually looking at + + align:start position:0% +time but he was usually looking at + + + align:start position:0% +time but he was usually looking at +infinite data so he was assuming that + + align:start position:0% +infinite data so he was assuming that + + + align:start position:0% +infinite data so he was assuming that +you had effectively an infinite number + + align:start position:0% +you had effectively an infinite number + + + align:start position:0% +you had effectively an infinite number +of columns of any of these matrices so + + align:start position:0% +of columns of any of these matrices so + + + align:start position:0% +of columns of any of these matrices so +you could perfectly compute the + + align:start position:0% +you could perfectly compute the + + + align:start position:0% +you could perfectly compute the +statistics and another important thing + + align:start position:0% +statistics and another important thing + + + align:start position:0% +statistics and another important thing +about the difference between the neural + + align:start position:0% +about the difference between the neural + + + align:start position:0% +about the difference between the neural +network models and the ones I was + + align:start position:0% +network models and the ones I was + + + align:start position:0% +network models and the ones I was +showing you is that suppose you want to + + align:start position:0% +showing you is that suppose you want to + + + align:start position:0% +showing you is that suppose you want to +train the model not on an infinite + + align:start position:0% +train the model not on an infinite + + + align:start position:0% +train the model not on an infinite +matrix but on a small finite one and + + align:start position:0% +matrix but on a small finite one and + + + align:start position:0% +matrix but on a small finite one and +maybe one with missing data it's a lot + + align:start position:0% +maybe one with missing data it's a lot + + + align:start position:0% +maybe one with missing data it's a lot +harder to get the neural network will do + + align:start position:0% +harder to get the neural network will do + + + align:start position:0% +harder to get the neural network will do +a much poorer job capturing the + + align:start position:0% +a much poorer job capturing the + + + align:start position:0% +a much poorer job capturing the +structure than these more structured + + align:start position:0% +structure than these more structured + + + align:start position:0% +structure than these more structured +models and again in a way that's + + align:start position:0% +models and again in a way that's + + + align:start position:0% +models and again in a way that's +familiar with if you guys talked about + + align:start position:0% +familiar with if you guys talked about + + + align:start position:0% +familiar with if you guys talked about +like bias variance dilemma okay so it's + + align:start position:0% +like bias variance dilemma okay so it's + + + align:start position:0% +like bias variance dilemma okay so it's +that same kind of idea that you probably + + align:start position:0% +that same kind of idea that you probably + + + align:start position:0% +that same kind of idea that you probably +heard about from Lorenzo with Lorenzo + + align:start position:0% +heard about from Lorenzo with Lorenzo + + + align:start position:0% +heard about from Lorenzo with Lorenzo +or one of the machine-like okay so it's + + align:start position:0% +or one of the machine-like okay so it's + + + align:start position:0% +or one of the machine-like okay so it's +that same kind of idea but now applying + + align:start position:0% +that same kind of idea but now applying + + + align:start position:0% +that same kind of idea but now applying +in this interesting case of sort of + + align:start position:0% +in this interesting case of sort of + + + align:start position:0% +in this interesting case of sort of +structured estimation of generative + + align:start position:0% +structured estimation of generative + + + align:start position:0% +structured estimation of generative +models for the world that if you have + + align:start position:0% +models for the world that if you have + + + align:start position:0% +models for the world that if you have +relatively little data and sparse data + + align:start position:0% +relatively little data and sparse data + + + align:start position:0% +relatively little data and sparse data +than having a more structured + + align:start position:0% +than having a more structured + + + align:start position:0% +than having a more structured +inductive by having the inductive bias + + align:start position:0% +inductive by having the inductive bias + + + align:start position:0% +inductive by having the inductive bias +that comes from a more structured + + align:start position:0% +that comes from a more structured + + + align:start position:0% +that comes from a more structured +representation is gonna be much more + + align:start position:0% +representation is gonna be much more + + + align:start position:0% +representation is gonna be much more +valuable when you have sparse and noisy + + align:start position:0% +valuable when you have sparse and noisy + + + align:start position:0% +valuable when you have sparse and noisy +data um the key and again this is + + align:start position:0% +data um the key and again this is + + + align:start position:0% +data um the key and again this is +something that Charles and I were really + + align:start position:0% +something that Charles and I were really + + + align:start position:0% +something that Charles and I were really +interested in is we wanted to we you + + align:start position:0% +interested in is we wanted to we you + + + align:start position:0% +interested in is we wanted to we you +know like the deep mind people like the + + align:start position:0% +know like the deep mind people like the + + + align:start position:0% +know like the deep mind people like the +the connection is we wanted to build + + align:start position:0% +the connection is we wanted to build + + + align:start position:0% +the connection is we wanted to build +general-purpose semantic cognition + + align:start position:0% +general-purpose semantic cognition + + + align:start position:0% +general-purpose semantic cognition +wanted to build general-purpose learning + + align:start position:0% +wanted to build general-purpose learning + + + align:start position:0% +wanted to build general-purpose learning +and reasoning systems and we wanted to + + align:start position:0% +and reasoning systems and we wanted to + + + align:start position:0% +and reasoning systems and we wanted to +somehow figure out how you could have + + align:start position:0% +somehow figure out how you could have + + + align:start position:0% +somehow figure out how you could have +the best of both worlds how you have a + + align:start position:0% +the best of both worlds how you have a + + + align:start position:0% +the best of both worlds how you have a +system that you know relatively quickly + + align:start position:0% +system that you know relatively quickly + + + align:start position:0% +system that you know relatively quickly +could could come to get the right kind + + align:start position:0% +could could come to get the right kind + + + align:start position:0% +could could come to get the right kind +of strong constraint inductive bias in + + align:start position:0% +of strong constraint inductive bias in + + + align:start position:0% +of strong constraint inductive bias in +some domain and a different one for a + + align:start position:0% +some domain and a different one for a + + + align:start position:0% +some domain and a different one for a +different domain you could learn in the + + align:start position:0% +different domain you could learn in the + + + align:start position:0% +different domain you could learn in the +flexible way to capture the different + + align:start position:0% +flexible way to capture the different + + + align:start position:0% +flexible way to capture the different +structure in different domains more on + + align:start position:0% +structure in different domains more on + + + align:start position:0% +structure in different domains more on +that in a little bit but the other thing + + align:start position:0% +that in a little bit but the other thing + + + align:start position:0% +that in a little bit but the other thing +I wanted to talk about here is just ways + + align:start position:0% +I wanted to talk about here is just ways + + + align:start position:0% +I wanted to talk about here is just ways +in which our our mental models are + + align:start position:0% +in which our our mental models are + + + align:start position:0% +in which our our mental models are +causal and compositional ones go beyond + + align:start position:0% +causal and compositional ones go beyond + + + align:start position:0% +causal and compositional ones go beyond +just similarity since some I guess since + + align:start position:0% +just similarity since some I guess since + + + align:start position:0% +just similarity since some I guess since +time is short well I was planning to go + + align:start position:0% +time is short well I was planning to go + + + align:start position:0% +time is short well I was planning to go +through this relatively quickly but + + align:start position:0% +through this relatively quickly but + + + align:start position:0% +through this relatively quickly but +anyway yeah mostly I'll just gesture + + align:start position:0% +anyway yeah mostly I'll just gesture + + + align:start position:0% +anyway yeah mostly I'll just gesture +towards this and if you're interested + + align:start position:0% +towards this and if you're interested + + + align:start position:0% +towards this and if you're interested +you could read the papers that Charles + + align:start position:0% +you could read the papers that Charles + + + align:start position:0% +you could read the papers that Charles +has or his thesis but here there's + + align:start position:0% +has or his thesis but here there's + + + align:start position:0% +has or his thesis but here there's +there's a long history of asking people + + align:start position:0% +there's a long history of asking people + + + align:start position:0% +there's a long history of asking people +to make these kind of judgments in which + + align:start position:0% +to make these kind of judgments in which + + + align:start position:0% +to make these kind of judgments in which +the basis for the judgment isn't + + align:start position:0% +the basis for the judgment isn't + + + align:start position:0% +the basis for the judgment isn't +something like similarity but some other + + align:start position:0% +something like similarity but some other + + + align:start position:0% +something like similarity but some other +kind of causal reasoning so for example + + align:start position:0% +kind of causal reasoning so for example + + + align:start position:0% +kind of causal reasoning so for example +consider these things here poodles can + + align:start position:0% +consider these things here poodles can + + + align:start position:0% +consider these things here poodles can +bite through wire they're for German + + align:start position:0% +bite through wire they're for German + + + align:start position:0% +bite through wire they're for German +Shepherds can bite through wire is that + + align:start position:0% +Shepherds can bite through wire is that + + + align:start position:0% +Shepherds can bite through wire is that +a strong argument or weak + + align:start position:0% +a strong argument or weak + + + align:start position:0% +a strong argument or weak +compare that with Dobermans can bite + + align:start position:0% +compare that with Dobermans can bite + + + align:start position:0% +compare that with Dobermans can bite +through wire therefore German Shepherds + + align:start position:0% +through wire therefore German Shepherds + + + align:start position:0% +through wire therefore German Shepherds +can bite through wire so how many people + + align:start position:0% +can bite through wire so how many people + + + align:start position:0% +can bite through wire so how many people +think that the top argument is a + + align:start position:0% +think that the top argument is a + + + align:start position:0% +think that the top argument is a +stronger one I mean I think the bottom + + align:start position:0% +stronger one I mean I think the bottom + + + align:start position:0% +stronger one I mean I think the bottom +one is a stronger one okay so that's + + align:start position:0% +one is a stronger one okay so that's + + + align:start position:0% +one is a stronger one okay so that's +typical yeah about twice as many people + + align:start position:0% +typical yeah about twice as many people + + + align:start position:0% +typical yeah about twice as many people +preferred the top one because + + align:start position:0% +preferred the top one because + + + align:start position:0% +preferred the top one because +intuitively to have a little thing that + + align:start position:0% +intuitively to have a little thing that + + + align:start position:0% +intuitively to have a little thing that +will appear intuitively anyone want to + + align:start position:0% +will appear intuitively anyone want to + + + align:start position:0% +will appear intuitively anyone want to +explain why it's not so + + align:start position:0% + + + + align:start position:0% + +poodles are small or weak yes and German + + align:start position:0% +poodles are small or weak yes and German + + + align:start position:0% +poodles are small or weak yes and German +Shepherds are big and strong and what + + align:start position:0% +Shepherds are big and strong and what + + + align:start position:0% +Shepherds are big and strong and what +about Dobermans yeah that's right so + + align:start position:0% +about Dobermans yeah that's right so + + + align:start position:0% +about Dobermans yeah that's right so +they're more similar to German shepherds + + align:start position:0% +they're more similar to German shepherds + + + align:start position:0% +they're more similar to German shepherds +because they're both big and strong but + + align:start position:0% +because they're both big and strong but + + + align:start position:0% +because they're both big and strong but +notice that sort of something very + + align:start position:0% +notice that sort of something very + + + align:start position:0% +notice that sort of something very +different is going on here right it's + + align:start position:0% +different is going on here right it's + + + align:start position:0% +different is going on here right it's +not about similarity it's sort of anti + + align:start position:0% +not about similarity it's sort of anti + + + align:start position:0% +not about similarity it's sort of anti +similarity but it's not just anti + + align:start position:0% +similarity but it's not just anti + + + align:start position:0% +similarity but it's not just anti +similarity right suppose I said German + + align:start position:0% +similarity right suppose I said German + + + align:start position:0% +similarity right suppose I said German +shepherds can bite through wire they're + + align:start position:0% +shepherds can bite through wire they're + + + align:start position:0% +shepherds can bite through wire they're +for poodles can bite through wire is + + align:start position:0% +for poodles can bite through wire is + + + align:start position:0% +for poodles can bite through wire is +that a good argument no it's sort of a + + align:start position:0% +that a good argument no it's sort of a + + + align:start position:0% +that a good argument no it's sort of a +bad terrible argument right so there's + + align:start position:0% +bad terrible argument right so there's + + + align:start position:0% +bad terrible argument right so there's +some kind of asymmetric dimensional + + align:start position:0% +some kind of asymmetric dimensional + + + align:start position:0% +some kind of asymmetric dimensional +reasoning going on or similarly if I + + align:start position:0% +reasoning going on or similarly if I + + + align:start position:0% +reasoning going on or similarly if I +said which of these is sort of seems + + align:start position:0% +said which of these is sort of seems + + + align:start position:0% +said which of these is sort of seems +better intuitively + + align:start position:0% +better intuitively + + + align:start position:0% +better intuitively +salmon's carry some bacteria salmon + + align:start position:0% +salmon's carry some bacteria salmon + + + align:start position:0% +salmon's carry some bacteria salmon +carry some bacteria therefore grizzly + + align:start position:0% +carry some bacteria therefore grizzly + + + align:start position:0% +carry some bacteria therefore grizzly +bears are likely to carry it versus + + align:start position:0% +bears are likely to carry it versus + + + align:start position:0% +bears are likely to carry it versus +grizzly bears carry this therefore + + align:start position:0% +grizzly bears carry this therefore + + + align:start position:0% +grizzly bears carry this therefore +salmon are likely to carry it how people + + align:start position:0% +salmon are likely to carry it how people + + + align:start position:0% +salmon are likely to carry it how people +say salmon therefore grizzly bears and + + align:start position:0% +say salmon therefore grizzly bears and + + + align:start position:0% +say salmon therefore grizzly bears and +people say grizzly bears therefore + + align:start position:0% +people say grizzly bears therefore + + + align:start position:0% +people say grizzly bears therefore +salmon how do you know those who's + + align:start position:0% +salmon how do you know those who's + + + align:start position:0% +salmon how do you know those who's +you're right I mean you're right and + + align:start position:0% +you're right I mean you're right and + + + align:start position:0% +you're right I mean you're right and +that's what people say I don't know if + + align:start position:0% +that's what people say I don't know if + + + align:start position:0% +that's what people say I don't know if +it's right again I made it up but why + + align:start position:0% +it's right again I made it up but why + + + align:start position:0% +it's right again I made it up but why +did you say that those of you who said + + align:start position:0% +did you say that those of you who said + + + align:start position:0% +did you say that those of you who said +salmon + + align:start position:0% +salmon + + + align:start position:0% +salmon +bears eat salmon yeah so assuming that's + + align:start position:0% +bears eat salmon yeah so assuming that's + + + align:start position:0% +bears eat salmon yeah so assuming that's +true + + align:start position:0% +true + + + align:start position:0% +true +so we're told or see on TV then yeah so + + align:start position:0% +so we're told or see on TV then yeah so + + + align:start position:0% +so we're told or see on TV then yeah so +anyway these are these different kinds + + align:start position:0% +anyway these are these different kinds + + + align:start position:0% +anyway these are these different kinds +of things that are going on and to cut + + align:start position:0% +of things that are going on and to cut + + + align:start position:0% +of things that are going on and to cut +to the chase what we showed is that you + + align:start position:0% +to the chase what we showed is that you + + + align:start position:0% +to the chase what we showed is that you +could capture these different patterns + + align:start position:0% +could capture these different patterns + + + align:start position:0% +could capture these different patterns +of reasoning with again the same kind of + + align:start position:0% +of reasoning with again the same kind of + + + align:start position:0% +of reasoning with again the same kind of +thing but different it's also a + + align:start position:0% +thing but different it's also a + + + align:start position:0% +thing but different it's also a +hierarchical generative model it also + + align:start position:0% +hierarchical generative model it also + + + align:start position:0% +hierarchical generative model it also +has the key level of the hierarchy is + + align:start position:0% +has the key level of the hierarchy is + + + align:start position:0% +has the key level of the hierarchy is +some kind of directed graphical + + align:start position:0% +some kind of directed graphical + + + align:start position:0% +some kind of directed graphical +structure that generates distribution on + + align:start position:0% +structure that generates distribution on + + + align:start position:0% +structure that generates distribution on +observable properties but it's a + + align:start position:0% +observable properties but it's a + + + align:start position:0% +observable properties but it's a +fundamentally different kind of + + align:start position:0% +fundamentally different kind of + + + align:start position:0% +fundamentally different kind of +structure it's not just a tree or a + + align:start position:0% +structure it's not just a tree or a + + + align:start position:0% +structure it's not just a tree or a +space it but it might be a different + + align:start position:0% +space it but it might be a different + + + align:start position:0% +space it but it might be a different +kind of graph and a different kind of + + align:start position:0% +kind of graph and a different kind of + + + align:start position:0% +kind of graph and a different kind of +process so the to be a little bit more + + align:start position:0% +process so the to be a little bit more + + + align:start position:0% +process so the to be a little bit more +technical the things I showed you with + + align:start position:0% +technical the things I showed you with + + + align:start position:0% +technical the things I showed you with +the tree in the low dimensional space + + align:start position:0% +the tree in the low dimensional space + + + align:start position:0% +the tree in the low dimensional space +they've they had a different geometry to + + align:start position:0% +they've they had a different geometry to + + + align:start position:0% +they've they had a different geometry to +the graph but the same stochastic + + align:start position:0% +the graph but the same stochastic + + + align:start position:0% +the graph but the same stochastic +process operating over it was in both + + align:start position:0% +process operating over it was in both + + + align:start position:0% +process operating over it was in both +cases basically a diffusion process + + align:start position:0% +cases basically a diffusion process + + + align:start position:0% +cases basically a diffusion process +whereas to get the kinds of reasoning + + align:start position:0% +whereas to get the kinds of reasoning + + + align:start position:0% +whereas to get the kinds of reasoning +that you saw here + + align:start position:0% +that you saw here + + + align:start position:0% +that you saw here +you need a different kind of graph in + + align:start position:0% +you need a different kind of graph in + + + align:start position:0% +you need a different kind of graph in +one case it's like a chain to capture + + align:start position:0% +one case it's like a chain to capture + + + align:start position:0% +one case it's like a chain to capture +the a dimension of strength or size say + + align:start position:0% +the a dimension of strength or size say + + + align:start position:0% +the a dimension of strength or size say +in the other case it's some kind of food + + align:start position:0% +in the other case it's some kind of food + + + align:start position:0% +in the other case it's some kind of food +web thing it's not a tree it's the kind + + align:start position:0% +web thing it's not a tree it's the kind + + + align:start position:0% +web thing it's not a tree it's the kind +of directed Network but you also need a + + align:start position:0% +of directed Network but you also need a + + + align:start position:0% +of directed Network but you also need a +different process so the ways the kind + + align:start position:0% +different process so the ways the kind + + + align:start position:0% +different process so the ways the kind +of probability model to find out that is + + align:start position:0% +of probability model to find out that is + + + align:start position:0% +of probability model to find out that is +different and it's easy to see on the + + align:start position:0% +different and it's easy to see on the + + + align:start position:0% +different and it's easy to see on the +for example on the + + align:start position:0% +for example on the + + + align:start position:0% +for example on the +on the reasoning with these threshold + + align:start position:0% +on the reasoning with these threshold + + + align:start position:0% +on the reasoning with these threshold +things like the strength properties if + + align:start position:0% +things like the strength properties if + + + align:start position:0% +things like the strength properties if +you compare a 1d chain with that with + + align:start position:0% +you compare a 1d chain with that with + + + align:start position:0% +you compare a 1d chain with that with +with just symmetric diffusion you get a + + align:start position:0% +with just symmetric diffusion you get a + + + align:start position:0% +with just symmetric diffusion you get a +much worse fit to people's judgments and + + align:start position:0% +much worse fit to people's judgments and + + + align:start position:0% +much worse fit to people's judgments and +if you use what we call this drift + + align:start position:0% +if you use what we call this drift + + + align:start position:0% +if you use what we call this drift +threshold thing which is basically a way + + align:start position:0% +threshold thing which is basically a way + + + align:start position:0% +threshold thing which is basically a way +of saying okay I don't know I don't + + align:start position:0% +of saying okay I don't know I don't + + + align:start position:0% +of saying okay I don't know I don't +there's some mapping from strip from + + align:start position:0% +there's some mapping from strip from + + + align:start position:0% +there's some mapping from strip from +strength to being able to bite through + + align:start position:0% +strength to being able to bite through + + + align:start position:0% +strength to being able to bite through +wire I don't know exactly what it is but + + align:start position:0% +wire I don't know exactly what it is but + + + align:start position:0% +wire I don't know exactly what it is but +the higher up you go on one it's + + align:start position:0% +the higher up you go on one it's + + + align:start position:0% +the higher up you go on one it's +probably more likely that you can bite + + align:start position:0% +probably more likely that you can bite + + + align:start position:0% +probably more likely that you can bite +that you can do the other so that + + align:start position:0% +that you can do the other so that + + + align:start position:0% +that you can do the other so that +provides a wonderful model of people's + + align:start position:0% +provides a wonderful model of people's + + + align:start position:0% +provides a wonderful model of people's +judgments on these kind of tasks but but + + align:start position:0% +judgments on these kind of tasks but but + + + align:start position:0% +judgments on these kind of tasks but but +that sort of diffusion process like if + + align:start position:0% +that sort of diffusion process like if + + + align:start position:0% +that sort of diffusion process like if +you if it was like mutation so mutation + + align:start position:0% +you if it was like mutation so mutation + + + align:start position:0% +you if it was like mutation so mutation +and biology then that would provide a + + align:start position:0% +and biology then that would provide a + + + align:start position:0% +and biology then that would provide a +very bad model that's the second row + + align:start position:0% +very bad model that's the second row + + + align:start position:0% +very bad model that's the second row +here similarly you know this sort of + + align:start position:0% +here similarly you know this sort of + + + align:start position:0% +here similarly you know this sort of +directed kind of noisy transmission + + align:start position:0% +directed kind of noisy transmission + + + align:start position:0% +directed kind of noisy transmission +process on the food web does a great way + + align:start position:0% +process on the food web does a great way + + + align:start position:0% +process on the food web does a great way +of modeling people's jokes about + + align:start position:0% +of modeling people's jokes about + + + align:start position:0% +of modeling people's jokes about +diseases but not a very good way of + + align:start position:0% +diseases but not a very good way of + + + align:start position:0% +diseases but not a very good way of +modeling people's judgments about these + + align:start position:0% +modeling people's judgments about these + + + align:start position:0% +modeling people's judgments about these +biological properties but the tree + + align:start position:0% +biological properties but the tree + + + align:start position:0% +biological properties but the tree +models you saw before that do a great + + align:start position:0% +models you saw before that do a great + + + align:start position:0% +models you saw before that do a great +job of modeling people's judgments about + + align:start position:0% +job of modeling people's judgments about + + + align:start position:0% +job of modeling people's judgments about +the properties of animals they do have a + + align:start position:0% +the properties of animals they do have a + + + align:start position:0% +the properties of animals they do have a +lousy job of modeling these disease + + align:start position:0% +lousy job of modeling these disease + + + align:start position:0% +lousy job of modeling these disease +judgments so we have this picture + + align:start position:0% +judgments so we have this picture + + + align:start position:0% +judgments so we have this picture +emerging that the time was very + + align:start position:0% +emerging that the time was very + + + align:start position:0% +emerging that the time was very +satisfying to us that hey we can take + + align:start position:0% +satisfying to us that hey we can take + + + align:start position:0% +satisfying to us that hey we can take +this domain of say animals and their + + align:start position:0% +this domain of say animals and their + + + align:start position:0% +this domain of say animals and their +properties or the various things we can + + align:start position:0% +properties or the various things we can + + + align:start position:0% +properties or the various things we can +reason about and there's there's a lot + + align:start position:0% +reason about and there's there's a lot + + + align:start position:0% +reason about and there's there's a lot +of different ways we can reason about + + align:start position:0% +of different ways we can reason about + + + align:start position:0% +of different ways we can reason about +just this one domain and by building + + align:start position:0% +just this one domain and by building + + + align:start position:0% +just this one domain and by building +these structured probabilistic models + + align:start position:0% +these structured probabilistic models + + + align:start position:0% +these structured probabilistic models +with different kinds of graph structures + + align:start position:0% +with different kinds of graph structures + + + align:start position:0% +with different kinds of graph structures +that capture different kinds of causal + + align:start position:0% +that capture different kinds of causal + + + align:start position:0% +that capture different kinds of causal +processes we could really describe a lot + + align:start position:0% +processes we could really describe a lot + + + align:start position:0% +processes we could really describe a lot +of different kinds of reasoning and this + + align:start position:0% +of different kinds of reasoning and this + + + align:start position:0% +of different kinds of reasoning and this +and we saw this as part of a theme that + + align:start position:0% +and we saw this as part of a theme that + + + align:start position:0% +and we saw this as part of a theme that +a lot of other people were working on so + + align:start position:0% +a lot of other people were working on so + + + align:start position:0% +a lot of other people were working on so +this is I mentioned this before but now + + align:start position:0% +this is I mentioned this before but now + + + align:start position:0% +this is I mentioned this before but now +I'm just sort of throwing it all out + + align:start position:0% +I'm just sort of throwing it all out + + + align:start position:0% +I'm just sort of throwing it all out +there a lot of people at the time again + + align:start position:0% +there a lot of people at the time again + + + align:start position:0% +there a lot of people at the time again +this is maybe somewhere between five to + + align:start position:0% +this is maybe somewhere between five to + + + align:start position:0% +this is maybe somewhere between five to +ten years ago more like six or seven + + align:start position:0% +ten years ago more like six or seven + + + align:start position:0% +ten years ago more like six or seven +years ago we're extremely interested in + + align:start position:0% +years ago we're extremely interested in + + + align:start position:0% +years ago we're extremely interested in +this this general view of common sense + + align:start position:0% +this this general view of common sense + + + align:start position:0% +this this general view of common sense +reasoning and semantic cognition by + + align:start position:0% +reasoning and semantic cognition by + + + align:start position:0% +reasoning and semantic cognition by +basically taking big matrices and + + align:start position:0% +basically taking big matrices and + + + align:start position:0% +basically taking big matrices and +boiling them down to some kind of graph + + align:start position:0% +boiling them down to some kind of graph + + + align:start position:0% +boiling them down to some kind of graph +structure in some form that's what Tom + + align:start position:0% +structure in some form that's what Tom + + + align:start position:0% +structure in some form that's what Tom +Mitchell was doing not just in the talk + + align:start position:0% +Mitchell was doing not just in the talk + + + align:start position:0% +Mitchell was doing not just in the talk +you saw but in remember he said there's + + align:start position:0% +you saw but in remember he said there's + + + align:start position:0% +you saw but in remember he said there's +this other stuff he does this thing + + align:start position:0% +this other stuff he does this thing + + + align:start position:0% +this other stuff he does this thing +called nelle the neverending language + + align:start position:0% +called nelle the neverending language + + + align:start position:0% +called nelle the neverending language +learner I'm showing a little glimpse of + + align:start position:0% +learner I'm showing a little glimpse of + + + align:start position:0% +learner I'm showing a little glimpse of +that up there from a New York Times + + align:start position:0% +that up there from a New York Times + + + align:start position:0% +that up there from a New York Times +piece on it in the upper right in some + + align:start position:0% +piece on it in the upper right in some + + + align:start position:0% +piece on it in the upper right in some +ways in a sort of at least more implicit + + align:start position:0% +ways in a sort of at least more implicit + + + align:start position:0% +ways in a sort of at least more implicit +way it's what the neural networks that + + align:start position:0% +way it's what the neural networks that + + + align:start position:0% +way it's what the neural networks that +Jay McClelland Tim Rogers Sir + + align:start position:0% +Jay McClelland Tim Rogers Sir + + + align:start position:0% +Jay McClelland Tim Rogers Sir +we're talking about do and we thought + + align:start position:0% +we're talking about do and we thought + + + align:start position:0% +we're talking about do and we thought +you know we had good reason to think + + align:start position:0% +you know we had good reason to think + + + align:start position:0% +you know we had good reason to think +that our approach was was more like what + + align:start position:0% +that our approach was was more like what + + + align:start position:0% +that our approach was was more like what +people were doing than some of these + + align:start position:0% +people were doing than some of these + + + align:start position:0% +people were doing than some of these +others but I then came to see and this + + align:start position:0% +others but I then came to see and this + + + align:start position:0% +others but I then came to see and this +was around the time when CBMM was + + align:start position:0% +was around the time when CBMM was + + + align:start position:0% +was around the time when CBMM was +actually getting started that none of + + align:start position:0% +actually getting started that none of + + + align:start position:0% +actually getting started that none of +these were gonna work like the whole + + align:start position:0% +these were gonna work like the whole + + + align:start position:0% +these were gonna work like the whole +thing was just not gonna work Liz was + + align:start position:0% +thing was just not gonna work Liz was + + + align:start position:0% +thing was just not gonna work Liz was +one of the main people who convinced me + + align:start position:0% +one of the main people who convinced me + + + align:start position:0% +one of the main people who convinced me +of this but you could just read the New + + align:start position:0% +of this but you could just read the New + + + align:start position:0% +of this but you could just read the New +York Times article on Tom Michels piece + + align:start position:0% +York Times article on Tom Michels piece + + + align:start position:0% +York Times article on Tom Michels piece +and you can see what's missing so here's + + align:start position:0% +and you can see what's missing so here's + + + align:start position:0% +and you can see what's missing so here's +here's there's Tom remember this was an + + align:start position:0% +here's there's Tom remember this was an + + + align:start position:0% +here's there's Tom remember this was an +article from 2010 just to set the + + align:start position:0% +article from 2010 just to set the + + + align:start position:0% +article from 2010 just to set the +chronology right that was right around a + + align:start position:0% +chronology right that was right around a + + + align:start position:0% +chronology right that was right around a +little bit after Charles had finished + + align:start position:0% +little bit after Charles had finished + + + align:start position:0% +little bit after Charles had finished +all that nice work I showed you um which + + align:start position:0% +all that nice work I showed you um which + + + align:start position:0% +all that nice work I showed you um which +again I still think is valuable I think + + align:start position:0% +again I still think is valuable I think + + + align:start position:0% +again I still think is valuable I think +instead you know it is capturing + + align:start position:0% +instead you know it is capturing + + + align:start position:0% +instead you know it is capturing +something about what's going on it's + + align:start position:0% +something about what's going on it's + + + align:start position:0% +something about what's going on it's +it's it's it was very appealing to + + align:start position:0% +it's it's it was very appealing to + + + align:start position:0% +it's it's it was very appealing to +people like at Google because these + + align:start position:0% +people like at Google because these + + + align:start position:0% +people like at Google because these +these knowledge graphs are very much + + align:start position:0% +these knowledge graphs are very much + + + align:start position:0% +these knowledge graphs are very much +like the way around the same time Google + + align:start position:0% +like the way around the same time Google + + + align:start position:0% +like the way around the same time Google +was starting to try to put more + + align:start position:0% +was starting to try to put more + + + align:start position:0% +was starting to try to put more +semantics into web search again + + align:start position:0% +semantics into web search again + + + align:start position:0% +semantics into web search again +connected to the work that Tom was doing + + align:start position:0% +connected to the work that Tom was doing + + + align:start position:0% +connected to the work that Tom was doing +um but then there was this there was + + align:start position:0% +um but then there was this there was + + + align:start position:0% +um but then there was this there was +this nice article in The New York Times + + align:start position:0% +this nice article in The New York Times + + + align:start position:0% +this nice article in The New York Times +talking about how they built their + + align:start position:0% +talking about how they built their + + + align:start position:0% +talking about how they built their +system by reading the web but the best + + align:start position:0% +system by reading the web but the best + + + align:start position:0% +system by reading the web but the best +part of it was describing one of the + + align:start position:0% +part of it was describing one of the + + + align:start position:0% +part of it was describing one of the +mistakes their system made so let me + + align:start position:0% +mistakes their system made so let me + + + align:start position:0% +mistakes their system made so let me +just show this to you about knowledge + + align:start position:0% +just show this to you about knowledge + + + align:start position:0% +just show this to you about knowledge +that's obvious to a person but not to a + + align:start position:0% +that's obvious to a person but not to a + + + align:start position:0% +that's obvious to a person but not to a +computer again this is Tom Mitchell + + align:start position:0% +computer again this is Tom Mitchell + + + align:start position:0% +computer again this is Tom Mitchell +himself describing this and that the + + align:start position:0% +himself describing this and that the + + + align:start position:0% +himself describing this and that the +challenge of that's where Nell has to be + + align:start position:0% +challenge of that's where Nell has to be + + + align:start position:0% +challenge of that's where Nell has to be +headed is how to make the things that + + align:start position:0% +headed is how to make the things that + + + align:start position:0% +headed is how to make the things that +are obvious to people obvious to + + align:start position:0% +are obvious to people obvious to + + + align:start position:0% +are obvious to people obvious to +computers he gives this example of a bug + + align:start position:0% +computers he gives this example of a bug + + + align:start position:0% +computers he gives this example of a bug +that happened in Nell's early life + + align:start position:0% +that happened in Nell's early life + + + align:start position:0% +that happened in Nell's early life +the research team noticed that let's + + align:start position:0% +the research team noticed that let's + + + align:start position:0% +the research team noticed that let's +skip down it went so a particular + + align:start position:0% +skip down it went so a particular + + + align:start position:0% +skip down it went so a particular +example when dr. Mitchell scanned the + + align:start position:0% +example when dr. Mitchell scanned the + + + align:start position:0% +example when dr. Mitchell scanned the +bait Goods category recently he noticed + + align:start position:0% +bait Goods category recently he noticed + + + align:start position:0% +bait Goods category recently he noticed +a clear pattern Nell was at first quite + + align:start position:0% +a clear pattern Nell was at first quite + + + align:start position:0% +a clear pattern Nell was at first quite +accurate easily identifying all kinds of + + align:start position:0% +accurate easily identifying all kinds of + + + align:start position:0% +accurate easily identifying all kinds of +pies breads cakes and cookies as baked + + align:start position:0% +pies breads cakes and cookies as baked + + + align:start position:0% +pies breads cakes and cookies as baked +goods but things went awry + + align:start position:0% +goods but things went awry + + + align:start position:0% +goods but things went awry +after Nell's noun phrase classifier + + align:start position:0% +after Nell's noun phrase classifier + + + align:start position:0% +after Nell's noun phrase classifier +decided internet cookies was a baked + + align:start position:0% +decided internet cookies was a baked + + + align:start position:0% +decided internet cookies was a baked +good now that read the sentence I + + align:start position:0% +good now that read the sentence I + + + align:start position:0% +good now that read the sentence I +deleted my internet cookies and and and + + align:start position:0% +deleted my internet cookies and and and + + + align:start position:0% +deleted my internet cookies and and and +again think of that as like it's kind of + + align:start position:0% +again think of that as like it's kind of + + + align:start position:0% +again think of that as like it's kind of +like a simple proposition right it's + + align:start position:0% +like a simple proposition right it's + + + align:start position:0% +like a simple proposition right it's +like okay but the way it parses that is + + align:start position:0% +like okay but the way it parses that is + + + align:start position:0% +like okay but the way it parses that is +cookies are things that can be deleted + + align:start position:0% +cookies are things that can be deleted + + + align:start position:0% +cookies are things that can be deleted +the same way you can say horses have t9 + + align:start position:0% +the same way you can say horses have t9 + + + align:start position:0% +the same way you can say horses have t9 +hormones it's basically just a matrix + + align:start position:0% +hormones it's basically just a matrix + + + align:start position:0% +hormones it's basically just a matrix +and the concept is internet cookies and + + align:start position:0% +and the concept is internet cookies and + + + align:start position:0% +and the concept is internet cookies and +the and then there's the property of can + + align:start position:0% +the and then there's the property of can + + + align:start position:0% +the and then there's the property of can +be deleted or some + + align:start position:0% +be deleted or some + + + align:start position:0% +be deleted or some +like that and it knows something about + + align:start position:0% +like that and it knows something about + + + align:start position:0% +like that and it knows something about +natural language processing so it can + + align:start position:0% +natural language processing so it can + + + align:start position:0% +natural language processing so it can +see in trying to be intelligent Oh + + align:start position:0% +see in trying to be intelligent Oh + + + align:start position:0% +see in trying to be intelligent Oh +Internet cookies well maybe like + + align:start position:0% +Internet cookies well maybe like + + + align:start position:0% +Internet cookies well maybe like +chocolate chip cookies and oatmeal + + align:start position:0% +chocolate chip cookies and oatmeal + + + align:start position:0% +chocolate chip cookies and oatmeal +raisin cookies those are a kind of + + align:start position:0% +raisin cookies those are a kind of + + + align:start position:0% +raisin cookies those are a kind of +cookies basically that's what it did or + + align:start position:0% +cookies basically that's what it did or + + + align:start position:0% +cookies basically that's what it did or +no actually did the opposite it said it + + align:start position:0% +no actually did the opposite it said it + + + align:start position:0% +no actually did the opposite it said it +said when it read I deleted my files it + + align:start position:0% +said when it read I deleted my files it + + + align:start position:0% +said when it read I deleted my files it +decided files was probably a beta + + align:start position:0% +decided files was probably a beta + + + align:start position:0% +decided files was probably a beta +ketubah well first I decided internet + + align:start position:0% +ketubah well first I decided internet + + + align:start position:0% +ketubah well first I decided internet +cookies was baked good like those other + + align:start position:0% +cookies was baked good like those other + + + align:start position:0% +cookies was baked good like those other +cookies and then it decided that files + + align:start position:0% +cookies and then it decided that files + + + align:start position:0% +cookies and then it decided that files +were made good and it started this whole + + align:start position:0% +were made good and it started this whole + + + align:start position:0% +were made good and it started this whole +avalanche of mistakes laughter Mitchell + + align:start position:0% +avalanche of mistakes laughter Mitchell + + + align:start position:0% +avalanche of mistakes laughter Mitchell +said he corrected the internet cookies + + align:start position:0% +said he corrected the internet cookies + + + align:start position:0% +said he corrected the internet cookies +ever and restarted Mel's bakery + + align:start position:0% +ever and restarted Mel's bakery + + + align:start position:0% +ever and restarted Mel's bakery +education like okay now rerun without + + align:start position:0% +education like okay now rerun without + + + align:start position:0% +education like okay now rerun without +that problem um okay so the the point + + align:start position:0% +that problem um okay so the the point + + + align:start position:0% +that problem um okay so the the point +the lesson Tom draws from this and if + + align:start position:0% +the lesson Tom draws from this and if + + + align:start position:0% +the lesson Tom draws from this and if +the article talks about is oh well we + + align:start position:0% +the article talks about is oh well we + + + align:start position:0% +the article talks about is oh well we +still need some assistance we have to go + + align:start position:0% +still need some assistance we have to go + + + align:start position:0% +still need some assistance we have to go +back and by hand set these things but + + align:start position:0% +back and by hand set these things but + + + align:start position:0% +back and by hand set these things but +the key thing is that really I think + + align:start position:0% +the key thing is that really I think + + + align:start position:0% +the key thing is that really I think +this is the message this is telling us + + align:start position:0% +this is the message this is telling us + + + align:start position:0% +this is the message this is telling us +is no human child would ever make this + + align:start position:0% +is no human child would ever make this + + + align:start position:0% +is no human child would ever make this +mistake human children learn in this way + + align:start position:0% +mistake human children learn in this way + + + align:start position:0% +mistake human children learn in this way +they don't need this kind of assistance + + align:start position:0% +they don't need this kind of assistance + + + align:start position:0% +they don't need this kind of assistance +it's true that as tom says you and i + + align:start position:0% +it's true that as tom says you and i + + + align:start position:0% +it's true that as tom says you and i +don't learn in isolation either so all + + align:start position:0% +don't learn in isolation either so all + + + align:start position:0% +don't learn in isolation either so all +the things we've been talking about + + align:start position:0% +the things we've been talking about + + + align:start position:0% +the things we've been talking about +about learning from prior knowledge and + + align:start position:0% +about learning from prior knowledge and + + + align:start position:0% +about learning from prior knowledge and +so on but there's a are true but there's + + align:start position:0% +so on but there's a are true but there's + + + align:start position:0% +so on but there's a are true but there's +a basic kind of common sense thing that + + align:start position:0% +a basic kind of common sense thing that + + + align:start position:0% +a basic kind of common sense thing that +this is missing which is that at the + + align:start position:0% +this is missing which is that at the + + + align:start position:0% +this is missing which is that at the +time a child is learning anything about + + align:start position:0% +time a child is learning anything about + + + align:start position:0% +time a child is learning anything about +by the time a child learning anything + + align:start position:0% +by the time a child learning anything + + + align:start position:0% +by the time a child learning anything +about um computers and files and so on + + align:start position:0% +about um computers and files and so on + + + align:start position:0% +about um computers and files and so on +they understand well before that like + + align:start position:0% +they understand well before that like + + + align:start position:0% +they understand well before that like +back in early infancy from say work that + + align:start position:0% +back in early infancy from say work that + + + align:start position:0% +back in early infancy from say work that +liz has done and many others right that + + align:start position:0% +liz has done and many others right that + + + align:start position:0% +liz has done and many others right that +cookies in the sense of baked goods are + + align:start position:0% +cookies in the sense of baked goods are + + + align:start position:0% +cookies in the sense of baked goods are +a physical object a kind of food a thing + + align:start position:0% +a physical object a kind of food a thing + + + align:start position:0% +a physical object a kind of food a thing +you eat files email not physical object + + align:start position:0% +you eat files email not physical object + + + align:start position:0% +you eat files email not physical object +right and there's all sorts of + + align:start position:0% +right and there's all sorts of + + + align:start position:0% +right and there's all sorts of +interesting stuff to understand about + + align:start position:0% +interesting stuff to understand about + + + align:start position:0% +interesting stuff to understand about +how you know kids learn that a book can + + align:start position:0% +how you know kids learn that a book can + + + align:start position:0% +how you know kids learn that a book can +be both and not you know a novel is both + + align:start position:0% +be both and not you know a novel is both + + + align:start position:0% +be both and not you know a novel is both +a story and it's also a physical object + + align:start position:0% +a story and it's also a physical object + + + align:start position:0% +a story and it's also a physical object +and so a lot of that stuff but there's a + + align:start position:0% +and so a lot of that stuff but there's a + + + align:start position:0% +and so a lot of that stuff but there's a +basic common sense understanding of the + + align:start position:0% +basic common sense understanding of the + + + align:start position:0% +basic common sense understanding of the +world as consisting of physical objects + + align:start position:0% +world as consisting of physical objects + + + align:start position:0% +world as consisting of physical objects +and for example agents and their goals + + align:start position:0% +and for example agents and their goals + + + align:start position:0% +and for example agents and their goals +you heard a little bit about this from + + align:start position:0% +you heard a little bit about this from + + + align:start position:0% +you heard a little bit about this from +us from me and Tomer on the first day + + align:start position:0% +us from me and Tomer on the first day + + + align:start position:0% +us from me and Tomer on the first day +and that's where I want to turn to next + + align:start position:0% +and that's where I want to turn to next + + + align:start position:0% +and that's where I want to turn to next +right and this is just one of many + + align:start position:0% +right and this is just one of many + + + align:start position:0% +right and this is just one of many +examples that we realized as cool as + + align:start position:0% +examples that we realized as cool as + + + align:start position:0% +examples that we realized as cool as +this system is as great as all this + + align:start position:0% +this system is as great as all this + + + align:start position:0% +this system is as great as all this +stuff is just trying to approach + + align:start position:0% +stuff is just trying to approach + + + align:start position:0% +stuff is just trying to approach +semantic knowledge and common sense + + align:start position:0% +semantic knowledge and common sense + + + align:start position:0% +semantic knowledge and common sense +reasoning as some kind of big matrix + + align:start position:0% +reasoning as some kind of big matrix + + + align:start position:0% +reasoning as some kind of big matrix +completion without a much more + + align:start position:0% +completion without a much more + + + align:start position:0% +completion without a much more +fundamental grasp of the ways in which + + align:start position:0% +fundamental grasp of the ways in which + + + align:start position:0% +fundamental grasp of the ways in which +the world is real to a human mind well + + align:start position:0% +the world is real to a human mind well + + + align:start position:0% +the world is real to a human mind well +before they learning anything about + + align:start position:0% +before they learning anything about + + + align:start position:0% +before they learning anything about +language or any of this higher level + + align:start position:0% +language or any of this higher level + + + align:start position:0% +language or any of this higher level +stuff it was just not going to + + align:start position:0% +stuff it was just not going to + + + align:start position:0% +stuff it was just not going to +right in the same way that I think if + + align:start position:0% +right in the same way that I think if + + + align:start position:0% +right in the same way that I think if +you want to build a system that learns + + align:start position:0% +you want to build a system that learns + + + align:start position:0% +you want to build a system that learns +to play a video game even remotely like + + align:start position:0% +to play a video game even remotely like + + + align:start position:0% +to play a video game even remotely like +the way a human does there's a lot of + + align:start position:0% +the way a human does there's a lot of + + + align:start position:0% +the way a human does there's a lot of +more basic stuff you have to build on + + align:start position:0% +more basic stuff you have to build on + + + align:start position:0% +more basic stuff you have to build on +and it's the same basic stuff I would + + align:start position:0% +and it's the same basic stuff I would + + + align:start position:0% +and it's the same basic stuff I would +argue a cool thing about Atari video + + align:start position:0% +argue a cool thing about Atari video + + + align:start position:0% +argue a cool thing about Atari video +games is that even though they're very + + align:start position:0% +games is that even though they're very + + + align:start position:0% +games is that even though they're very +low resolution you know very low bit + + align:start position:0% +low resolution you know very low bit + + + align:start position:0% +low resolution you know very low bit +color displays with very big pixels it's + + align:start position:0% +color displays with very big pixels it's + + + align:start position:0% +color displays with very big pixels it's +what makes the your ability to learn + + align:start position:0% +what makes the your ability to learn + + + align:start position:0% +what makes the your ability to learn +that game work is the same kind of thing + + align:start position:0% +that game work is the same kind of thing + + + align:start position:0% +that game work is the same kind of thing +that makes your ability even as a young + + align:start position:0% +that makes your ability even as a young + + + align:start position:0% +that makes your ability even as a young +child to not make this mistake and it's + + align:start position:0% +child to not make this mistake and it's + + + align:start position:0% +child to not make this mistake and it's +the kind of thing that Liz and and + + align:start position:0% +the kind of thing that Liz and and + + + align:start position:0% +the kind of thing that Liz and and +people in her field of developmental + + align:start position:0% +people in her field of developmental + + + align:start position:0% +people in her field of developmental +psychology in particular infant research + + align:start position:0% +psychology in particular infant research + + + align:start position:0% +psychology in particular infant research +have been studying really excited + + align:start position:0% +have been studying really excited + + + align:start position:0% +have been studying really excited +excitingly for a couple of decades that + + align:start position:0% +excitingly for a couple of decades that + + + align:start position:0% +excitingly for a couple of decades that +you know I think is as transformative + + align:start position:0% +you know I think is as transformative + + + align:start position:0% +you know I think is as transformative +for the topic of intelligence and brains + + align:start position:0% +for the topic of intelligence and brains + + + align:start position:0% +for the topic of intelligence and brains +Minds machines as anything so that's + + align:start position:0% +Minds machines as anything so that's + + + align:start position:0% +Minds machines as anything so that's +what motivated the work we've been doing + + align:start position:0% +what motivated the work we've been doing + + + align:start position:0% +what motivated the work we've been doing +in the last few years and the main work + + align:start position:0% +in the last few years and the main work + + + align:start position:0% +in the last few years and the main work +we're trying to do in the center and it + + align:start position:0% +we're trying to do in the center and it + + + align:start position:0% +we're trying to do in the center and it +also goes hand-in-hand with the ways in + + align:start position:0% +also goes hand-in-hand with the ways in + + + align:start position:0% +also goes hand-in-hand with the ways in +which we've we've realized that we have + + align:start position:0% +which we've we've realized that we have + + + align:start position:0% +which we've we've realized that we have +to take what we've learned how to do + + align:start position:0% +to take what we've learned how to do + + + align:start position:0% +to take what we've learned how to do +with building probabilistic models over + + align:start position:0% +with building probabilistic models over + + + align:start position:0% +with building probabilistic models over +interesting symbolically structured + + align:start position:0% +interesting symbolically structured + + + align:start position:0% +interesting symbolically structured +representations and so on but move way + + align:start position:0% +representations and so on but move way + + + align:start position:0% +representations and so on but move way +beyond what you could call I mean we + + align:start position:0% +beyond what you could call I mean we + + + align:start position:0% +beyond what you could call I mean we +need better even more interesting + + align:start position:0% +need better even more interesting + + + align:start position:0% +need better even more interesting +symbolic representations in particular + + align:start position:0% +symbolic representations in particular + + + align:start position:0% +symbolic representations in particular +we need to move beyond graphs and + + align:start position:0% +we need to move beyond graphs and + + + align:start position:0% +we need to move beyond graphs and +stochastic processes defined over grass + + align:start position:0% +stochastic processes defined over grass + + + align:start position:0% +stochastic processes defined over grass +to programs so that's where the politic + + align:start position:0% +to programs so that's where the politic + + + align:start position:0% +to programs so that's where the politic +programs come back into the mix so again + + align:start position:0% +programs come back into the mix so again + + + align:start position:0% +programs come back into the mix so again +you already saw this and I'm trying to + + align:start position:0% +you already saw this and I'm trying to + + + align:start position:0% +you already saw this and I'm trying to +close the loop back to what we're doing + + align:start position:0% +close the loop back to what we're doing + + + align:start position:0% +close the loop back to what we're doing +in CBMM right I've given you about 10 to + + align:start position:0% +in CBMM right I've given you about 10 to + + + align:start position:0% +in CBMM right I've given you about 10 to +15 years of background in our field of + + align:start position:0% +15 years of background in our field of + + + align:start position:0% +15 years of background in our field of +how we got to this why we think this is + + align:start position:0% +how we got to this why we think this is + + + align:start position:0% +how we got to this why we think this is +interesting and important and why we + + align:start position:0% +interesting and important and why we + + + align:start position:0% +interesting and important and why we +think we need to you know why we've + + align:start position:0% +think we need to you know why we've + + + align:start position:0% +think we need to you know why we've +developed a certain toolkit of ideas and + + align:start position:0% +developed a certain toolkit of ideas and + + + align:start position:0% +developed a certain toolkit of ideas and +why we think we needed to keep extending + + align:start position:0% +why we think we needed to keep extending + + + align:start position:0% +why we think we needed to keep extending +it and I think as you know as you saw + + align:start position:0% +it and I think as you know as you saw + + + align:start position:0% +it and I think as you know as you saw +before and as you'll see this also in + + align:start position:0% +before and as you'll see this also in + + + align:start position:0% +before and as you'll see this also in +some ways you know we I think we're + + align:start position:0% +some ways you know we I think we're + + + align:start position:0% +some ways you know we I think we're +getting more and more to the interesting + + align:start position:0% +getting more and more to the interesting + + + align:start position:0% +getting more and more to the interesting +heart of common sense but in another way + + align:start position:0% +heart of common sense but in another way + + + align:start position:0% +heart of common sense but in another way +we're getting back to the problems I + + align:start position:0% +we're getting back to the problems I + + + align:start position:0% +we're getting back to the problems I +started off with and what a lot of other + + align:start position:0% +started off with and what a lot of other + + + align:start position:0% +started off with and what a lot of other +people at this summer school of an + + align:start position:0% +people at this summer school of an + + + align:start position:0% +people at this summer school of an +interesting which is things like much + + align:start position:0% +interesting which is things like much + + + align:start position:0% +interesting which is things like much +more basic aspects of visual perception + + align:start position:0% +more basic aspects of visual perception + + + align:start position:0% +more basic aspects of visual perception +I think the heart of real intelligence + + align:start position:0% +I think the heart of real intelligence + + + align:start position:0% +I think the heart of real intelligence +and common sense reasoning that we're + + align:start position:0% +and common sense reasoning that we're + + + align:start position:0% +and common sense reasoning that we're +talking about is is directly connected + + align:start position:0% +talking about is is directly connected + + + align:start position:0% +talking about is is directly connected +to vision and other sense modalities and + + align:start position:0% +to vision and other sense modalities and + + + align:start position:0% +to vision and other sense modalities and +how we get around in the world and plan + + align:start position:0% +how we get around in the world and plan + + + align:start position:0% +how we get around in the world and plan +our actions and the very basic kinds of + + align:start position:0% +our actions and the very basic kinds of + + + align:start position:0% +our actions and the very basic kinds of +goal social understandings that you saw + + align:start position:0% +goal social understandings that you saw + + + align:start position:0% +goal social understandings that you saw +in those little videos of the red and + + align:start position:0% +in those little videos of the red and + + + align:start position:0% +in those little videos of the red and +blue ball or or that you see if you're + + align:start position:0% +blue ball or or that you see if you're + + + align:start position:0% +blue ball or or that you see if you're +trying to do action recognition + + align:start position:0% +trying to do action recognition + + + align:start position:0% +trying to do action recognition +understanding so within some sense it's + + align:start position:0% +understanding so within some sense it's + + + align:start position:0% +understanding so within some sense it's +gotten more cognitive but it's also by + + align:start position:0% +gotten more cognitive but it's also by + + + align:start position:0% +gotten more cognitive but it's also by +getting to the root of our common sense + + align:start position:0% +getting to the root of our common sense + + + align:start position:0% +getting to the root of our common sense +knowledge it makes better contact with + + align:start position:0% +knowledge it makes better contact with + + + align:start position:0% +knowledge it makes better contact with +vision with neuroscience research and so + + align:start position:0% +vision with neuroscience research and so + + + align:start position:0% +vision with neuroscience research and so +I think it's it's a super exciting + + align:start position:0% +I think it's it's a super exciting + + + align:start position:0% +I think it's it's a super exciting +development in what we're doing for the + + align:start position:0% +development in what we're doing for the + + + align:start position:0% +development in what we're doing for the +larger brains minds and machine agenda + + align:start position:0% +larger brains minds and machine agenda + + + align:start position:0% +larger brains minds and machine agenda +so again now we're saying okay let's try + + align:start position:0% +so again now we're saying okay let's try + + + align:start position:0% +so again now we're saying okay let's try +to understand the the way in which even + + align:start position:0% +to understand the the way in which even + + + align:start position:0% +to understand the the way in which even +these kids playing with blocks right the + + align:start position:0% +these kids playing with blocks right the + + + align:start position:0% +these kids playing with blocks right the +world is real to them right that there's + + align:start position:0% +world is real to them right that there's + + + align:start position:0% +world is real to them right that there's +not just a big matrix of data that is a + + align:start position:0% +not just a big matrix of data that is a + + + align:start position:0% +not just a big matrix of data that is a +thing in their hands and they have an + + align:start position:0% +thing in their hands and they have an + + + align:start position:0% +thing in their hands and they have an +understanding of what a thing is before + + align:start position:0% +understanding of what a thing is before + + + align:start position:0% +understanding of what a thing is before +they start compiling lists of properties + + align:start position:0% +they start compiling lists of properties + + + align:start position:0% +they start compiling lists of properties +right and that they're playing with + + align:start position:0% +right and that they're playing with + + + align:start position:0% +right and that they're playing with +somebody else that hand is attached to a + + align:start position:0% +somebody else that hand is attached to a + + + align:start position:0% +somebody else that hand is attached to a +person who has goals it's not just a big + + align:start position:0% +person who has goals it's not just a big + + + align:start position:0% +person who has goals it's not just a big +matrix of rows and columns + + align:start position:0% +matrix of rows and columns + + + align:start position:0% +matrix of rows and columns +it's an agent with goals and even in + + align:start position:0% +it's an agent with goals and even in + + + align:start position:0% +it's an agent with goals and even in +mind and they understand those things + + align:start position:0% +mind and they understand those things + + + align:start position:0% +mind and they understand those things +before they start to learn a lot of + + align:start position:0% +before they start to learn a lot of + + + align:start position:0% +before they start to learn a lot of +other things like words for objects and + + align:start position:0% +other things like words for objects and + + + align:start position:0% +other things like words for objects and +and you know advanced a game playing + + align:start position:0% +and you know advanced a game playing + + + align:start position:0% +and you know advanced a game playing +behavior and so on and when we want to + + align:start position:0% +behavior and so on and when we want to + + + align:start position:0% +behavior and so on and when we want to +talk about learning we still are + + align:start position:0% +talk about learning we still are + + + align:start position:0% +talk about learning we still are +interested in one-shot learning or very + + align:start position:0% +interested in one-shot learning or very + + + align:start position:0% +interested in one-shot learning or very +rapid learning from few examples and + + align:start position:0% +rapid learning from few examples and + + + align:start position:0% +rapid learning from few examples and +we're still interested in how prior + + align:start position:0% +we're still interested in how prior + + + align:start position:0% +we're still interested in how prior +knowledge guides that and how that + + align:start position:0% +knowledge guides that and how that + + + align:start position:0% +knowledge guides that and how that +knowledge can be built but we want to do + + align:start position:0% +knowledge can be built but we want to do + + + align:start position:0% +knowledge can be built but we want to do +it in this context we want to study in + + align:start position:0% +it in this context we want to study in + + + align:start position:0% +it in this context we want to study in +the context of say how you learn how + + align:start position:0% +the context of say how you learn how + + + align:start position:0% +the context of say how you learn how +magnets work or how you learn how a + + align:start position:0% +magnets work or how you learn how a + + + align:start position:0% +magnets work or how you learn how a +touchscreen device works really + + align:start position:0% +touchscreen device works really + + + align:start position:0% +touchscreen device works really +interesting kinds of grounded physical + + align:start position:0% +interesting kinds of grounded physical + + + align:start position:0% +interesting kinds of grounded physical +causes okay um so this is this is what + + align:start position:0% +causes okay um so this is this is what + + + align:start position:0% +causes okay um so this is this is what +we have what I come to call the common + + align:start position:0% +we have what I come to call the common + + + align:start position:0% +we have what I come to call the common +sense core it's if you are you gonna + + align:start position:0% +sense core it's if you are you gonna + + + align:start position:0% +sense core it's if you are you gonna +literally then talk about core knowledge + + align:start position:0% +literally then talk about core knowledge + + + align:start position:0% +literally then talk about core knowledge +at all okay so so there's a phrase that + + align:start position:0% +at all okay so so there's a phrase that + + + align:start position:0% +at all okay so so there's a phrase that +Liz likes use called core knowledge and + + align:start position:0% +Liz likes use called core knowledge and + + + align:start position:0% +Liz likes use called core knowledge and +this is definitely meant to evoke that + + align:start position:0% +this is definitely meant to evoke that + + + align:start position:0% +this is definitely meant to evoke that +and it's inspired by it I guess I + + align:start position:0% +and it's inspired by it I guess I + + + align:start position:0% +and it's inspired by it I guess I +changed it a little bit because I wanted + + align:start position:0% +changed it a little bit because I wanted + + + align:start position:0% +changed it a little bit because I wanted +to mean something a little bit different + + align:start position:0% +to mean something a little bit different + + + align:start position:0% +to mean something a little bit different +and I think again to anticipate a little + + align:start position:0% +and I think again to anticipate a little + + + align:start position:0% +and I think again to anticipate a little +bit the the main difference is I don't + + align:start position:0% +bit the the main difference is I don't + + + align:start position:0% +bit the the main difference is I don't +know what's the main difference the main + + align:start position:0% +know what's the main difference the main + + + align:start position:0% +know what's the main difference the main +difference is that you know in the same + + align:start position:0% +difference is that you know in the same + + + align:start position:0% +difference is that you know in the same +way that lots of people look at me and + + align:start position:0% +way that lots of people look at me and + + + align:start position:0% +way that lots of people look at me and +say oh he's the Bayesian guy lots of + + align:start position:0% +say oh he's the Bayesian guy lots of + + + align:start position:0% +say oh he's the Bayesian guy lots of +people look at Liz and say oh she's the + + align:start position:0% +people look at Liz and say oh she's the + + + align:start position:0% +people look at Liz and say oh she's the +nativist gal or something and it's true + + align:start position:0% +nativist gal or something and it's true + + + align:start position:0% +nativist gal or something and it's true +that compared to a lot of other people I + + align:start position:0% +that compared to a lot of other people I + + + align:start position:0% +that compared to a lot of other people I +tend to be more interested and have done + + align:start position:0% +tend to be more interested and have done + + + align:start position:0% +tend to be more interested and have done +more work prominently associated with + + align:start position:0% +more work prominently associated with + + + align:start position:0% +more work prominently associated with +Bayesian inference but but by no means + + align:start position:0% +Bayesian inference but but by no means + + + align:start position:0% +Bayesian inference but but by no means +oh I think that's the whole story and + + align:start position:0% +oh I think that's the whole story and + + + align:start position:0% +oh I think that's the whole story and +part of what I've tried to show you and + + align:start position:0% +part of what I've tried to show you and + + + align:start position:0% +part of what I've tried to show you and +we'll keep showing you is ways in which + + align:start position:0% +we'll keep showing you is ways in which + + + align:start position:0% +we'll keep showing you is ways in which +that's only really the beginning of the + + align:start position:0% +that's only really the beginning of the + + + align:start position:0% +that's only really the beginning of the +story and and Liz is prominently + + align:start position:0% +story and and Liz is prominently + + + align:start position:0% +story and and Liz is prominently +associated and you'll see some of this + + align:start position:0% +associated and you'll see some of this + + + align:start position:0% +associated and you'll see some of this +with + + align:start position:0% +with + + + align:start position:0% +with +really fascinating discoveries that that + + align:start position:0% +really fascinating discoveries that that + + + align:start position:0% +really fascinating discoveries that that +key high-level concepts kinds of real + + align:start position:0% +key high-level concepts kinds of real + + + align:start position:0% +key high-level concepts kinds of real +knowledge are present in some sense as + + align:start position:0% +knowledge are present in some sense as + + + align:start position:0% +knowledge are present in some sense as +early as you can look and in some form + + align:start position:0% +early as you can look and in some form + + + align:start position:0% +early as you can look and in some form +you know half I think very plausibly + + align:start position:0% +you know half I think very plausibly + + + align:start position:0% +you know half I think very plausibly +have to be due to some kind of a neat + + align:start position:0% +have to be due to some kind of a neat + + + align:start position:0% +have to be due to some kind of a neat +the unfolding genetic program that + + align:start position:0% +the unfolding genetic program that + + + align:start position:0% +the unfolding genetic program that +builds a mine the same way it builds a + + align:start position:0% +builds a mine the same way it builds a + + + align:start position:0% +builds a mine the same way it builds a +brain but just as you'll hear from her + + align:start position:0% +brain but just as you'll hear from her + + + align:start position:0% +brain but just as you'll hear from her +that's in some ways only the beginning + + align:start position:0% +that's in some ways only the beginning + + + align:start position:0% +that's in some ways only the beginning +or only one part of a much richer more + + align:start position:0% +or only one part of a much richer more + + + align:start position:0% +or only one part of a much richer more +interesting story that she's been + + align:start position:0% +interesting story that she's been + + + align:start position:0% +interesting story that she's been +developing but for that and among other + + align:start position:0% +developing but for that and among other + + + align:start position:0% +developing but for that and among other +reasons I'm calling it a little + + align:start position:0% +reasons I'm calling it a little + + + align:start position:0% +reasons I'm calling it a little +different I'm trying to emphasize the + + align:start position:0% +different I'm trying to emphasize the + + + align:start position:0% +different I'm trying to emphasize the +connection to what people in AI call + + align:start position:0% +connection to what people in AI call + + + align:start position:0% +connection to what people in AI call +common sense reasoning because I really + + align:start position:0% +common sense reasoning because I really + + + align:start position:0% +common sense reasoning because I really +do think this is the heart of common + + align:start position:0% +do think this is the heart of common + + + align:start position:0% +do think this is the heart of common +sense it's this intuitive physics and + + align:start position:0% +sense it's this intuitive physics and + + + align:start position:0% +sense it's this intuitive physics and +intuitive psychology so again you see + + align:start position:0% +intuitive psychology so again you see + + + align:start position:0% +intuitive psychology so again you see +you saw us already give an intro to this + + align:start position:0% +you saw us already give an intro to this + + + align:start position:0% +you saw us already give an intro to this +maybe what I'll just do is show you a + + align:start position:0% +maybe what I'll just do is show you a + + + align:start position:0% +maybe what I'll just do is show you a +little bit more of the well that are you + + align:start position:0% +little bit more of the well that are you + + + align:start position:0% +little bit more of the well that are you +are you gonna talk about this stuff at + + align:start position:0% +are you gonna talk about this stuff at + + + align:start position:0% +are you gonna talk about this stuff at +all okay well okay so this is this is + + align:start position:0% +all okay well okay so this is this is + + + align:start position:0% +all okay well okay so this is this is +work some of this is based on Liz's work + + align:start position:0% +work some of this is based on Liz's work + + + align:start position:0% +work some of this is based on Liz's work +some of this was based on Bren a buyer + + align:start position:0% +some of this was based on Bren a buyer + + + align:start position:0% +some of this was based on Bren a buyer +John a close colleague of hers and many + + align:start position:0% +John a close colleague of hers and many + + + align:start position:0% +John a close colleague of hers and many +other people out there and I wasn't + + align:start position:0% +other people out there and I wasn't + + + align:start position:0% +other people out there and I wasn't +really going to go into the details and + + align:start position:0% +really going to go into the details and + + + align:start position:0% +really going to go into the details and +maybe Liz we can decide whether you want + + align:start position:0% +maybe Liz we can decide whether you want + + + align:start position:0% +maybe Liz we can decide whether you want +to do this or not but what they've shown + + align:start position:0% +to do this or not but what they've shown + + + align:start position:0% +to do this or not but what they've shown +is that you know even prior to the time + + align:start position:0% +is that you know even prior to the time + + + align:start position:0% +is that you know even prior to the time +when kids are learning words for objects + + align:start position:0% +when kids are learning words for objects + + + align:start position:0% +when kids are learning words for objects +all of this stuff you know with infants + + align:start position:0% +all of this stuff you know with infants + + + align:start position:0% +all of this stuff you know with infants +two months four months eight months at + + align:start position:0% +two months four months eight months at + + + align:start position:0% +two months four months eight months at +this age kids have at best some vague + + align:start position:0% +this age kids have at best some vague + + + align:start position:0% +this age kids have at best some vague +statistical associations of words two + + align:start position:0% +statistical associations of words two + + + align:start position:0% +statistical associations of words two +kinds of objects but they already have a + + align:start position:0% +kinds of objects but they already have a + + + align:start position:0% +kinds of objects but they already have a +great deal of a much more abstract + + align:start position:0% +great deal of a much more abstract + + + align:start position:0% +great deal of a much more abstract +understanding of physical objects so I + + align:start position:0% +understanding of physical objects so I + + + align:start position:0% +understanding of physical objects so I +won't maybe I should not go into the + + align:start position:0% +won't maybe I should not go into the + + + align:start position:0% +won't maybe I should not go into the +details of it but you saw in that nice + + align:start position:0% +details of it but you saw in that nice + + + align:start position:0% +details of it but you saw in that nice +video of the baby playing with the Cubs + + align:start position:0% +video of the baby playing with the Cubs + + + align:start position:0% +video of the baby playing with the Cubs +right and and there's really interesting + + align:start position:0% +right and and there's really interesting + + + align:start position:0% +right and and there's really interesting +developmental sort of rough + + align:start position:0% +developmental sort of rough + + + align:start position:0% +developmental sort of rough +developmental timelines one of the + + align:start position:0% +developmental timelines one of the + + + align:start position:0% +developmental timelines one of the +things we're trying to figure out in + + align:start position:0% +things we're trying to figure out in + + + align:start position:0% +things we're trying to figure out in +CBMM is to actually get much much + + align:start position:0% +CBMM is to actually get much much + + + align:start position:0% +CBMM is to actually get much much +clearer picture on this but at least if + + align:start position:0% +clearer picture on this but at least if + + + align:start position:0% +clearer picture on this but at least if +you look across a bunch of different + + align:start position:0% +you look across a bunch of different + + + align:start position:0% +you look across a bunch of different +studies sometimes by one lab sometimes I + + align:start position:0% +studies sometimes by one lab sometimes I + + + align:start position:0% +studies sometimes by one lab sometimes I +buy multiple labs you see ways in which + + align:start position:0% +buy multiple labs you see ways in which + + + align:start position:0% +buy multiple labs you see ways in which +say going from two months to five months + + align:start position:0% +say going from two months to five months + + + align:start position:0% +say going from two months to five months +or five months to 12 months kids seem to + + align:start position:0% +or five months to 12 months kids seem to + + + align:start position:0% +or five months to 12 months kids seem to +their intuitive physics of objects is + + align:start position:0% +their intuitive physics of objects is + + + align:start position:0% +their intuitive physics of objects is +getting a little bit more sophisticated + + align:start position:0% +getting a little bit more sophisticated + + + align:start position:0% +getting a little bit more sophisticated +right so for example they tend to + + align:start position:0% +right so for example they tend to + + + align:start position:0% +right so for example they tend to +understand they in some form they + + align:start position:0% +understand they in some form they + + + align:start position:0% +understand they in some form they +understand a little bit of how + + align:start position:0% +understand a little bit of how + + + align:start position:0% +understand a little bit of how +collisions can serve momentum a little + + align:start position:0% +collisions can serve momentum a little + + + align:start position:0% +collisions can serve momentum a little +bit by five months + + align:start position:0% +bit by five months + + + align:start position:0% +bit by five months +six months according to one of buyers on + + align:start position:0% +six months according to one of buyers on + + + align:start position:0% +six months according to one of buyers on +studies in the sense that like if they + + align:start position:0% +studies in the sense that like if they + + + align:start position:0% +studies in the sense that like if they +see a ball rolled on a ramp and hit + + align:start position:0% +see a ball rolled on a ramp and hit + + + align:start position:0% +see a ball rolled on a ramp and hit +another one and this the second one goes + + align:start position:0% +another one and this the second one goes + + + align:start position:0% +another one and this the second one goes +a certain distance if a bigger object + + align:start position:0% +a certain distance if a bigger object + + + align:start position:0% +a certain distance if a bigger object +comes they're not too surprised if this + + align:start position:0% +comes they're not too surprised if this + + + align:start position:0% +comes they're not too surprised if this +one goes farther but if a little object + + align:start position:0% +one goes farther but if a little object + + + align:start position:0% +one goes farther but if a little object +hits it then they are surprised so they + + align:start position:0% +hits it then they are surprised so they + + + align:start position:0% +hits it then they are surprised so they +expect a bigger object to be able to + + align:start position:0% +expect a bigger object to be able to + + + align:start position:0% +expect a bigger object to be able to +move it more than a little object but a + + align:start position:0% +move it more than a little object but a + + + align:start position:0% +move it more than a little object but a +two-month-old doesn't understand that + + align:start position:0% +two-month-old doesn't understand that + + + align:start position:0% +two-month-old doesn't understand that +although a two-month-old does understand + + align:start position:0% +although a two-month-old does understand + + + align:start position:0% +although a two-month-old does understand +this is again from Liz's work that if an + + align:start position:0% +this is again from Liz's work that if an + + + align:start position:0% +this is again from Liz's work that if an +object is occluded by a screen and has + + align:start position:0% +object is occluded by a screen and has + + + align:start position:0% +object is occluded by a screen and has +it disappeared and then if an under just + + align:start position:0% +it disappeared and then if an under just + + + align:start position:0% +it disappeared and then if an under just +rolling towards a wall and that wall + + align:start position:0% +rolling towards a wall and that wall + + + align:start position:0% +rolling towards a wall and that wall +looks solid that the that the object + + align:start position:0% +looks solid that the that the object + + + align:start position:0% +looks solid that the that the object +can't go through it and then if it's + + align:start position:0% +can't go through it and then if it's + + + align:start position:0% +can't go through it and then if it's +some somehow when the screen is removed + + align:start position:0% +some somehow when the screen is removed + + + align:start position:0% +some somehow when the screen is removed +as you see on the upper left appears on + + align:start position:0% +as you see on the upper left appears on + + + align:start position:0% +as you see on the upper left appears on +the other side of the screen that's very + + align:start position:0% +the other side of the screen that's very + + + align:start position:0% +the other side of the screen that's very +surprising to them I think I'm sure what + + align:start position:0% +surprising to them I think I'm sure what + + + align:start position:0% +surprising to them I think I'm sure what +Liz will talk about among other things + + align:start position:0% +Liz will talk about among other things + + + align:start position:0% +Liz will talk about among other things +are the methods they use the kind of + + align:start position:0% +are the methods they use the kind of + + + align:start position:0% +are the methods they use the kind of +looking time methods to reveal this and + + align:start position:0% +looking time methods to reveal this and + + + align:start position:0% +looking time methods to reveal this and +and and I think there's really this is + + align:start position:0% +and and I think there's really this is + + + align:start position:0% +and and I think there's really this is +what one of the two main insights that I + + align:start position:0% +what one of the two main insights that I + + + align:start position:0% +what one of the two main insights that I +and I think our whole field needs to + + align:start position:0% +and I think our whole field needs to + + + align:start position:0% +and I think our whole field needs to +learn from developmental psychology is + + align:start position:0% +learn from developmental psychology is + + + align:start position:0% +learn from developmental psychology is +how much of an basic understanding of + + align:start position:0% +how much of an basic understanding of + + + align:start position:0% +how much of an basic understanding of +physics like this is present very early + + align:start position:0% +physics like this is present very early + + + align:start position:0% +physics like this is present very early +it's and it doesn't matter whether it's + + align:start position:0% +it's and it doesn't matter whether it's + + + align:start position:0% +it's and it doesn't matter whether it's +you know in some sense it doesn't matter + + align:start position:0% +you know in some sense it doesn't matter + + + align:start position:0% +you know in some sense it doesn't matter +for the points I want to make here how + + align:start position:0% +for the points I want to make here how + + + align:start position:0% +for the points I want to make here how +much or in what way this is innate or + + align:start position:0% +much or in what way this is innate or + + + align:start position:0% +much or in what way this is innate or +how the genetics and the experience + + align:start position:0% +how the genetics and the experience + + + align:start position:0% +how the genetics and the experience +interact I mean that does matter that + + align:start position:0% +interact I mean that does matter that + + + align:start position:0% +interact I mean that does matter that +that's something we want to understand + + align:start position:0% +that's something we want to understand + + + align:start position:0% +that's something we want to understand +and we are hoping to try to understand + + align:start position:0% +and we are hoping to try to understand + + + align:start position:0% +and we are hoping to try to understand +in the hopefully not too distant future + + align:start position:0% +in the hopefully not too distant future + + + align:start position:0% +in the hopefully not too distant future +but for the purpose of understanding + + align:start position:0% +but for the purpose of understanding + + + align:start position:0% +but for the purpose of understanding +what is the heart of common-sense how + + align:start position:0% +what is the heart of common-sense how + + + align:start position:0% +what is the heart of common-sense how +are we going to build these causal + + align:start position:0% +are we going to build these causal + + + align:start position:0% +are we going to build these causal +compositional generative models to + + align:start position:0% +compositional generative models to + + + align:start position:0% +compositional generative models to +really get at intelligence the main + + align:start position:0% +really get at intelligence the main + + + align:start position:0% +really get at intelligence the main +thing is that it should be about this + + align:start position:0% +thing is that it should be about this + + + align:start position:0% +thing is that it should be about this +kind of stuff + + align:start position:0% +kind of stuff + + + align:start position:0% +kind of stuff +that's the main focus and then we the + + align:start position:0% +that's the main focus and then we the + + + align:start position:0% +that's the main focus and then we the +other big insight from developmental + + align:start position:0% +other big insight from developmental + + + align:start position:0% +other big insight from developmental +psychology which has to do with how we + + align:start position:0% +psychology which has to do with how we + + + align:start position:0% +psychology which has to do with how we +build this stuff is this idea sometimes + + align:start position:0% +build this stuff is this idea sometimes + + + align:start position:0% +build this stuff is this idea sometimes +called the child of scientists the basic + + align:start position:0% +called the child of scientists the basic + + + align:start position:0% +called the child of scientists the basic +idea is that justice this early + + align:start position:0% +idea is that justice this early + + + align:start position:0% +idea is that justice this early +common-sense knowledge is something like + + align:start position:0% +common-sense knowledge is something like + + + align:start position:0% +common-sense knowledge is something like +a scientific theory something like a + + align:start position:0% +a scientific theory something like a + + + align:start position:0% +a scientific theory something like a +good scientific theory the way Newton's + + align:start position:0% +good scientific theory the way Newton's + + + align:start position:0% +good scientific theory the way Newton's +laws are a better scientific theory than + + align:start position:0% +laws are a better scientific theory than + + + align:start position:0% +laws are a better scientific theory than +Kepler's laws because of how they + + align:start position:0% +Kepler's laws because of how they + + + align:start position:0% +Kepler's laws because of how they +capture the causal structure of the + + align:start position:0% +capture the causal structure of the + + + align:start position:0% +capture the causal structure of the +world in a compositional way that's + + align:start position:0% +world in a compositional way that's + + + align:start position:0% +world in a compositional way that's +another way to sum up what I'm trying to + + align:start position:0% +another way to sum up what I'm trying to + + + align:start position:0% +another way to sum up what I'm trying to +say about children's early knowledge but + + align:start position:0% +say about children's early knowledge but + + + align:start position:0% +say about children's early knowledge but +also the way children build their + + align:start position:0% +also the way children build their + + + align:start position:0% +also the way children build their +knowledge is something like the way + + align:start position:0% +knowledge is something like the way + + + align:start position:0% +knowledge is something like the way +scientists build our knowledge which is + + align:start position:0% +scientists build our knowledge which is + + + align:start position:0% +scientists build our knowledge which is +while they do experiments of course we + + align:start position:0% +while they do experiments of course we + + + align:start position:0% +while they do experiments of course we +normally call that play + + align:start position:0% +normally call that play + + + align:start position:0% +normally call that play +that's one of Laura's Schultz's big + + align:start position:0% +that's one of Laura's Schultz's big + + + align:start position:0% +that's one of Laura's Schultz's big +ideas but it's not just about the + + align:start position:0% +ideas but it's not just about the + + + align:start position:0% +ideas but it's not just about the +experiments I mean Newton didn't really + + align:start position:0% +experiments I mean Newton didn't really + + + align:start position:0% +experiments I mean Newton didn't really +do any experiments he just thought and + + align:start position:0% +do any experiments he just thought and + + + align:start position:0% +do any experiments he just thought and +that's another thing you'll hear from + + align:start position:0% +that's another thing you'll hear from + + + align:start position:0% +that's another thing you'll hear from +Laura and also from Tomer is that a lot + + align:start position:0% +Laura and also from Tomer is that a lot + + + align:start position:0% +Laura and also from Tomer is that a lot +of children's learning looks less like + + align:start position:0% +of children's learning looks less like + + + align:start position:0% +of children's learning looks less like +safe stochastic gradient descent and + + align:start position:0% +safe stochastic gradient descent and + + + align:start position:0% +safe stochastic gradient descent and +more like scratching your head and + + align:start position:0% +more like scratching your head and + + + align:start position:0% +more like scratching your head and +trying to make sense of well that's + + align:start position:0% +trying to make sense of well that's + + + align:start position:0% +trying to make sense of well that's +really funny you know why does this + + align:start position:0% +really funny you know why does this + + + align:start position:0% +really funny you know why does this +happen here why does that happen over + + align:start position:0% +happen here why does that happen over + + + align:start position:0% +happen here why does that happen over +there or how can I explain what seemed + + align:start position:0% +there or how can I explain what seemed + + + align:start position:0% +there or how can I explain what seemed +to be diverse patterns of phenomena with + + align:start position:0% +to be diverse patterns of phenomena with + + + align:start position:0% +to be diverse patterns of phenomena with +some common underlying principles and + + align:start position:0% +some common underlying principles and + + + align:start position:0% +some common underlying principles and +making analogies between things and then + + align:start position:0% +making analogies between things and then + + + align:start position:0% +making analogies between things and then +trying out oh well if that's right then + + align:start position:0% +trying out oh well if that's right then + + + align:start position:0% +trying out oh well if that's right then +it would make this prediction and you + + align:start position:0% +it would make this prediction and you + + + align:start position:0% +it would make this prediction and you +know the kid doesn't have to be + + align:start position:0% +know the kid doesn't have to be + + + align:start position:0% +know the kid doesn't have to be +conscious of that the way scientists + + align:start position:0% +conscious of that the way scientists + + + align:start position:0% +conscious of that the way scientists +maybe are that process of coming up with + + align:start position:0% +maybe are that process of coming up with + + + align:start position:0% +maybe are that process of coming up with +theories and considering variations + + align:start position:0% +theories and considering variations + + + align:start position:0% +theories and considering variations +trying them out seeing what kinds of new + + align:start position:0% +trying them out seeing what kinds of new + + + align:start position:0% +trying them out seeing what kinds of new +experiences you could create for + + align:start position:0% +experiences you could create for + + + align:start position:0% +experiences you could create for +yourself call them an experiment or call + + align:start position:0% +yourself call them an experiment or call + + + align:start position:0% +yourself call them an experiment or call +them just a game or playing with a toy + + align:start position:0% +them just a game or playing with a toy + + + align:start position:0% +them just a game or playing with a toy +but that that that dynamic is the real + + align:start position:0% +but that that that dynamic is the real + + + align:start position:0% +but that that that dynamic is the real +heart of how children learn and build + + align:start position:0% +heart of how children learn and build + + + align:start position:0% +heart of how children learn and build +the knowledge from the early do what we + + align:start position:0% +the knowledge from the early do what we + + + align:start position:0% +the knowledge from the early do what we +come to have as adults those two + + align:start position:0% +come to have as adults those two + + + align:start position:0% +come to have as adults those two +insights of what we start with and how + + align:start position:0% +insights of what we start with and how + + + align:start position:0% +insights of what we start with and how +we grow I think are hugely powerful and + + align:start position:0% +we grow I think are hugely powerful and + + + align:start position:0% +we grow I think are hugely powerful and +and hugely important for anything we + + align:start position:0% +and hugely important for anything we + + + align:start position:0% +and hugely important for anything we +want to do in capturing making machines + + align:start position:0% +want to do in capturing making machines + + + align:start position:0% +want to do in capturing making machines +that learn like humans or making + + align:start position:0% +that learn like humans or making + + + align:start position:0% +that learn like humans or making +computational models that really get at + + align:start position:0% +computational models that really get at + + + align:start position:0% +computational models that really get at +the heart of how we come to be smart + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/iHErQuZ8M-I.txt b/iHErQuZ8M-I.txt new file mode 100644 index 0000000000000000000000000000000000000000..33f152d523371ee0d1765e4b236c0121398d07a1 --- /dev/null +++ b/iHErQuZ8M-I.txt @@ -0,0 +1,2723 @@ +align:start position:0% + +welcome back to recitation in this video + + align:start position:0% +welcome back to recitation in this video + + + align:start position:0% +welcome back to recitation in this video +what I'd like us to do is do a little + + align:start position:0% +what I'd like us to do is do a little + + + align:start position:0% +what I'd like us to do is do a little +bit of practice with Sigma notation so + + align:start position:0% +bit of practice with Sigma notation so + + + align:start position:0% +bit of practice with Sigma notation so +this will be just a few short problems + + align:start position:0% +this will be just a few short problems + + + align:start position:0% +this will be just a few short problems +to make sure that you're comfortable + + align:start position:0% +to make sure that you're comfortable + + + align:start position:0% +to make sure that you're comfortable +with what all the pieces in the sigma + + align:start position:0% +with what all the pieces in the sigma + + + align:start position:0% +with what all the pieces in the sigma +notation actually do we're going to + + align:start position:0% +notation actually do we're going to + + + align:start position:0% +notation actually do we're going to +start with two problems here and the + + align:start position:0% +start with two problems here and the + + + align:start position:0% +start with two problems here and the +first one is going to be a fill-in the + + align:start position:0% +first one is going to be a fill-in the + + + align:start position:0% +first one is going to be a fill-in the +blanks type of problem and the object is + + align:start position:0% +blanks type of problem and the object is + + + align:start position:0% +blanks type of problem and the object is +I've given you a sum on the left hand + + align:start position:0% +I've given you a sum on the left hand + + + align:start position:0% +I've given you a sum on the left hand +side and then I've given you two other + + align:start position:0% +side and then I've given you two other + + + align:start position:0% +side and then I've given you two other +sums but I've left in each place two + + align:start position:0% +sums but I've left in each place two + + + align:start position:0% +sums but I've left in each place two +blanks and I've filled in the rest you + + align:start position:0% +blanks and I've filled in the rest you + + + align:start position:0% +blanks and I've filled in the rest you +have enough information to fill in the + + align:start position:0% +have enough information to fill in the + + + align:start position:0% +have enough information to fill in the +two blanks so what I'd like you to do in + + align:start position:0% +two blanks so what I'd like you to do in + + + align:start position:0% +two blanks so what I'd like you to do in +this problem is fill in the two blanks + + align:start position:0% +this problem is fill in the two blanks + + + align:start position:0% +this problem is fill in the two blanks +so that the sums are equal and the + + align:start position:0% +so that the sums are equal and the + + + align:start position:0% +so that the sums are equal and the +object is obviously to do this without + + align:start position:0% +object is obviously to do this without + + + align:start position:0% +object is obviously to do this without +writing out all the terms and adding up + + align:start position:0% +writing out all the terms and adding up + + + align:start position:0% +writing out all the terms and adding up +and then going backward so you really + + align:start position:0% +and then going backward so you really + + + align:start position:0% +and then going backward so you really +want to try and understand what each + + align:start position:0% +want to try and understand what each + + + align:start position:0% +want to try and understand what each +part of the sigma notation does the + + align:start position:0% +part of the sigma notation does the + + + align:start position:0% +part of the sigma notation does the +second the second problem I'd like you + + align:start position:0% +second the second problem I'd like you + + + align:start position:0% +second the second problem I'd like you +to is a simplification problem there are + + align:start position:0% +to is a simplification problem there are + + + align:start position:0% +to is a simplification problem there are +three finite + + align:start position:0% +three finite + + + align:start position:0% +three finite +sums and what I'd like you to do is + + align:start position:0% +sums and what I'd like you to do is + + + align:start position:0% +sums and what I'd like you to do is +combine them into a single sum or two + + align:start position:0% +combine them into a single sum or two + + + align:start position:0% +combine them into a single sum or two +sums do the best you can to get it as + + align:start position:0% +sums do the best you can to get it as + + + align:start position:0% +sums do the best you can to get it as +simplified as you can without actually + + align:start position:0% +simplified as you can without actually + + + align:start position:0% +simplified as you can without actually +writing out a number but keeping it in + + align:start position:0% +writing out a number but keeping it in + + + align:start position:0% +writing out a number but keeping it in +some sort of notation form so the object + + align:start position:0% +some sort of notation form so the object + + + align:start position:0% +some sort of notation form so the object +is just to combine what you can and + + align:start position:0% +is just to combine what you can and + + + align:start position:0% +is just to combine what you can and +simplify where you can and then uh we'll + + align:start position:0% +simplify where you can and then uh we'll + + + align:start position:0% +simplify where you can and then uh we'll +do another one in a little bit but first + + align:start position:0% +do another one in a little bit but first + + + align:start position:0% +do another one in a little bit but first +let's do these two I'll give you a while + + align:start position:0% +let's do these two I'll give you a while + + + align:start position:0% +let's do these two I'll give you a while +to work on them and then I'll be back + + align:start position:0% + + + + align:start position:0% + +okay welcome back we're going to start + + align:start position:0% +okay welcome back we're going to start + + + align:start position:0% +okay welcome back we're going to start +with the first problem so the idea is is + + align:start position:0% +with the first problem so the idea is is + + + align:start position:0% +with the first problem so the idea is is +to really understand what each of these + + align:start position:0% +to really understand what each of these + + + align:start position:0% +to really understand what each of these +pieces represents and let's look at the + + align:start position:0% +pieces represents and let's look at the + + + align:start position:0% +pieces represents and let's look at the +first sum and make sure we understand + + align:start position:0% +first sum and make sure we understand + + + align:start position:0% +first sum and make sure we understand +what's going on so we have two raised to + + align:start position:0% +what's going on so we have two raised to + + + align:start position:0% +what's going on so we have two raised to +a power and what we do is we index over + + align:start position:0% +a power and what we do is we index over + + + align:start position:0% +a power and what we do is we index over +K from 1 to five so we're going to take + + align:start position:0% +K from 1 to five so we're going to take + + + align:start position:0% +K from 1 to five so we're going to take +two to the 1st plus 2 to the 2 all the + + align:start position:0% +two to the 1st plus 2 to the 2 all the + + + align:start position:0% +two to the 1st plus 2 to the 2 all the +way up to 2 to the 5th and that's where + + align:start position:0% +way up to 2 to the 5th and that's where + + + align:start position:0% +way up to 2 to the 5th and that's where +the sum stops + + align:start position:0% +the sum stops + + + align:start position:0% +the sum stops +now in this summation K is indexed from + + align:start position:0% +now in this summation K is indexed from + + + align:start position:0% +now in this summation K is indexed from +some number I haven't told you yet up to + + align:start position:0% +some number I haven't told you yet up to + + + align:start position:0% +some number I haven't told you yet up to +seven and I didn't specify what power of + + align:start position:0% +seven and I didn't specify what power of + + + align:start position:0% +seven and I didn't specify what power of +K we want so there are a couple ways you + + align:start position:0% +K we want so there are a couple ways you + + + align:start position:0% +K we want so there are a couple ways you +can think about this it's maybe easiest + + align:start position:0% +can think about this it's maybe easiest + + + align:start position:0% +can think about this it's maybe easiest +to work from what we have up here we + + align:start position:0% +to work from what we have up here we + + + align:start position:0% +to work from what we have up here we +know that the that the exponent the last + + align:start position:0% +know that the that the exponent the last + + + align:start position:0% +know that the that the exponent the last +exponent we would like on the power of + + align:start position:0% +exponent we would like on the power of + + + align:start position:0% +exponent we would like on the power of +two is a five in the end but right now + + align:start position:0% +two is a five in the end but right now + + + align:start position:0% +two is a five in the end but right now +if we just put a k here the power would + + align:start position:0% +if we just put a k here the power would + + + align:start position:0% +if we just put a k here the power would +be seven so what we'd like to do is make + + align:start position:0% +be seven so what we'd like to do is make + + + align:start position:0% +be seven so what we'd like to do is make +whatever the power is up here based on + + align:start position:0% +whatever the power is up here based on + + + align:start position:0% +whatever the power is up here based on +that seven we'd like that power to be + + align:start position:0% +that seven we'd like that power to be + + + align:start position:0% +that seven we'd like that power to be +two less than the number that we're + + align:start position:0% +two less than the number that we're + + + align:start position:0% +two less than the number that we're +putting in there so probably we would + + align:start position:0% +putting in there so probably we would + + + align:start position:0% +putting in there so probably we would +like this to be a k minus 2 because + + align:start position:0% +like this to be a k minus 2 because + + + align:start position:0% +like this to be a k minus 2 because +notice then the last number you put in + + align:start position:0% +notice then the last number you put in + + + align:start position:0% +notice then the last number you put in +you get a five which corresponds to the + + align:start position:0% +you get a five which corresponds to the + + + align:start position:0% +you get a five which corresponds to the +last number you put in here a 2 to the + + align:start position:0% +last number you put in here a 2 to the + + + align:start position:0% +last number you put in here a 2 to the +5th now the last number here is a 2 to + + align:start position:0% +5th now the last number here is a 2 to + + + align:start position:0% +5th now the last number here is a 2 to +the 5th and this now will dictate what + + align:start position:0% +the 5th and this now will dictate what + + + align:start position:0% +the 5th and this now will dictate what +we put in the blank down here because + + align:start position:0% +we put in the blank down here because + + + align:start position:0% +we put in the blank down here because +the first value of K we wanted here the + + align:start position:0% +the first value of K we wanted here the + + + align:start position:0% +the first value of K we wanted here the +first term we wanted in this sum was two + + align:start position:0% +first term we wanted in this sum was two + + + align:start position:0% +first term we wanted in this sum was two +to the 1st + + align:start position:0% +to the 1st + + + align:start position:0% +to the 1st +so the first term we want in this sum is + + align:start position:0% +so the first term we want in this sum is + + + align:start position:0% +so the first term we want in this sum is +going to be 2 the 1st so that means that + + align:start position:0% +going to be 2 the 1st so that means that + + + align:start position:0% +going to be 2 the 1st so that means that +we would like K to start at three + + align:start position:0% +we would like K to start at three + + + align:start position:0% +we would like K to start at three +another way to think about this is that + + align:start position:0% +another way to think about this is that + + + align:start position:0% +another way to think about this is that +we know we want the same number of + + align:start position:0% +we know we want the same number of + + + align:start position:0% +we know we want the same number of +values that we're summing over so notice + + align:start position:0% +values that we're summing over so notice + + + align:start position:0% +values that we're summing over so notice +that from one up to five there are five + + align:start position:0% +that from one up to five there are five + + + align:start position:0% +that from one up to five there are five +values we're summing over from three up + + align:start position:0% +values we're summing over from three up + + + align:start position:0% +values we're summing over from three up +to seven there are actually five values + + align:start position:0% +to seven there are actually five values + + + align:start position:0% +to seven there are actually five values +we're summing over you might think there + + align:start position:0% +we're summing over you might think there + + + align:start position:0% +we're summing over you might think there +are four because s minus 3 is four but + + align:start position:0% +are four because s minus 3 is four but + + + align:start position:0% +are four because s minus 3 is four but +you actually have to count 3 4 5 6 7 you + + align:start position:0% +you actually have to count 3 4 5 6 7 you + + + align:start position:0% +you actually have to count 3 4 5 6 7 you +see in fact there are five values there + + align:start position:0% +see in fact there are five values there + + + align:start position:0% +see in fact there are five values there +so don't get confused by that the + + align:start position:0% +so don't get confused by that the + + + align:start position:0% +so don't get confused by that the +differences are the same 5 - 1 is 4 7 + + align:start position:0% +differences are the same 5 - 1 is 4 7 + + + align:start position:0% +differences are the same 5 - 1 is 4 7 +minus 3 is four so that's good we have + + align:start position:0% +minus 3 is four so that's good we have + + + align:start position:0% +minus 3 is four so that's good we have +the same we have the same number of + + align:start position:0% +the same we have the same number of + + + align:start position:0% +the same we have the same number of +things we're summing up over and the + + align:start position:0% +things we're summing up over and the + + + align:start position:0% +things we're summing up over and the +first terms are the + + align:start position:0% +first terms are the + + + align:start position:0% +first terms are the +same and then you notice because of the + + align:start position:0% +same and then you notice because of the + + + align:start position:0% +same and then you notice because of the +way we've written it it actually it's + + align:start position:0% +way we've written it it actually it's + + + align:start position:0% +way we've written it it actually it's +going to be exactly equal you could + + align:start position:0% +going to be exactly equal you could + + + align:start position:0% +going to be exactly equal you could +expand and check but these are going to + + align:start position:0% +expand and check but these are going to + + + align:start position:0% +expand and check but these are going to +be equal + + align:start position:0% +be equal + + + align:start position:0% +be equal +sums now the third one I was a little + + align:start position:0% +sums now the third one I was a little + + + align:start position:0% +sums now the third one I was a little +trickier maybe I pulled out a factor of + + align:start position:0% +trickier maybe I pulled out a factor of + + + align:start position:0% +trickier maybe I pulled out a factor of +two and so now what we've done is we've + + align:start position:0% +two and so now what we've done is we've + + + align:start position:0% +two and so now what we've done is we've +taken one of the twos that was in all of + + align:start position:0% +taken one of the twos that was in all of + + + align:start position:0% +taken one of the twos that was in all of +those terms and we've pulled it out + + align:start position:0% +those terms and we've pulled it out + + + align:start position:0% +those terms and we've pulled it out +right so what do we have here well we + + align:start position:0% +right so what do we have here well we + + + align:start position:0% +right so what do we have here well we +still have two to the K right but what + + align:start position:0% +still have two to the K right but what + + + align:start position:0% +still have two to the K right but what +does this actually equal to make it + + align:start position:0% +does this actually equal to make it + + + align:start position:0% +does this actually equal to make it +easier on myself I'm going to rewrite + + align:start position:0% +easier on myself I'm going to rewrite + + + align:start position:0% +easier on myself I'm going to rewrite +this in another way if I pull the two + + align:start position:0% +this in another way if I pull the two + + + align:start position:0% +this in another way if I pull the two +back + + align:start position:0% +back + + + align:start position:0% +back +in I get a 2 to the k + + + align:start position:0% +in I get a 2 to the k + + + + align:start position:0% +in I get a 2 to the k + +one so now what I've done is I've given + + align:start position:0% +one so now what I've done is I've given + + + align:start position:0% +one so now what I've done is I've given +you this two pulled out what it's + + align:start position:0% +you this two pulled out what it's + + + align:start position:0% +you this two pulled out what it's +actually doing is it's changing changing + + align:start position:0% +actually doing is it's changing changing + + + align:start position:0% +actually doing is it's changing changing +the exponent value but again what do we + + align:start position:0% +the exponent value but again what do we + + + align:start position:0% +the exponent value but again what do we +want the exponents to run over we want + + align:start position:0% +want the exponents to run over we want + + + align:start position:0% +want the exponents to run over we want +them to start at this exponent to start + + align:start position:0% +them to start at this exponent to start + + + align:start position:0% +them to start at this exponent to start +at one and to end at five so to get it + + align:start position:0% +at one and to end at five so to get it + + + align:start position:0% +at one and to end at five so to get it +to start at one and end at five I need K + + align:start position:0% +to start at one and end at five I need K + + + align:start position:0% +to start at one and end at five I need K +to be zero to start and finish at + + align:start position:0% + + + + align:start position:0% + +four and that will be sufficient now + + align:start position:0% +four and that will be sufficient now + + + align:start position:0% +four and that will be sufficient now +again let's just make sure that that + + align:start position:0% +again let's just make sure that that + + + align:start position:0% +again let's just make sure that that +this makes sense to us if K is zero I + + align:start position:0% +this makes sense to us if K is zero I + + + align:start position:0% +this makes sense to us if K is zero I +get two to the zero here but when I + + align:start position:0% +get two to the zero here but when I + + + align:start position:0% +get two to the zero here but when I +multiply by a two in front the first + + align:start position:0% +multiply by a two in front the first + + + align:start position:0% +multiply by a two in front the first +term is two to the 1st + + align:start position:0% +term is two to the 1st + + + align:start position:0% +term is two to the 1st +which is the first term + + align:start position:0% +which is the first term + + + align:start position:0% +which is the first term +here let's just check one more to make + + align:start position:0% +here let's just check one more to make + + + align:start position:0% +here let's just check one more to make +sure we feel good about it when k equals + + align:start position:0% +sure we feel good about it when k equals + + + align:start position:0% +sure we feel good about it when k equals +1 I get a two to the first here times + + align:start position:0% +1 I get a two to the first here times + + + align:start position:0% +1 I get a two to the first here times +two so that's a two squared that's the + + align:start position:0% +two so that's a two squared that's the + + + align:start position:0% +two so that's a two squared that's the +second term in this sum is two squar the + + align:start position:0% +second term in this sum is two squar the + + + align:start position:0% +second term in this sum is two squar the +second term in this sum is when I put in + + align:start position:0% +second term in this sum is when I put in + + + align:start position:0% +second term in this sum is when I put in +k equals 2 I get a 2^ squar so we we see + + align:start position:0% +k equals 2 I get a 2^ squar so we we see + + + align:start position:0% +k equals 2 I get a 2^ squar so we we see +in fact that I've I've chosen these + + align:start position:0% +in fact that I've I've chosen these + + + align:start position:0% +in fact that I've I've chosen these +values in blue now these three sums are + + align:start position:0% +values in blue now these three sums are + + + align:start position:0% +values in blue now these three sums are +actually + + align:start position:0% +actually + + + align:start position:0% +actually +equal if you're still nervous about it + + align:start position:0% +equal if you're still nervous about it + + + align:start position:0% +equal if you're still nervous about it +maybe you can expand the sums and look + + align:start position:0% +maybe you can expand the sums and look + + + align:start position:0% +maybe you can expand the sums and look +at them and notice that they that they + + align:start position:0% +at them and notice that they that they + + + align:start position:0% +at them and notice that they that they +are indeed going to + + align:start position:0% +are indeed going to + + + align:start position:0% +are indeed going to +work now what I'd like us to do is work + + align:start position:0% +work now what I'd like us to do is work + + + align:start position:0% +work now what I'd like us to do is work +on simplifying a problem and if you'll + + align:start position:0% +on simplifying a problem and if you'll + + + align:start position:0% +on simplifying a problem and if you'll +notice I've put in three sums the values + + align:start position:0% +notice I've put in three sums the values + + + align:start position:0% +notice I've put in three sums the values +here two of them are from one to 100 one + + align:start position:0% +here two of them are from one to 100 one + + + align:start position:0% +here two of them are from one to 100 one +of them is from 45 to 100 and the three + + align:start position:0% +of them is from 45 to 100 and the three + + + align:start position:0% +of them is from 45 to 100 and the three +different things I'm summing n cubus n^2 + + align:start position:0% +different things I'm summing n cubus n^2 + + + align:start position:0% +different things I'm summing n cubus n^2 +n Cub - n^2 minus n and then n and I + + align:start position:0% +n Cub - n^2 minus n and then n and I + + + align:start position:0% +n Cub - n^2 minus n and then n and I +wanted us to simplify this as much as we + + align:start position:0% +wanted us to simplify this as much as we + + + align:start position:0% +wanted us to simplify this as much as we +could now because these are finite sums + + align:start position:0% +could now because these are finite sums + + + align:start position:0% +could now because these are finite sums +we can split we can split up over the + + align:start position:0% +we can split we can split up over the + + + align:start position:0% +we can split we can split up over the +terms as long as we keep the right index + + align:start position:0% +terms as long as we keep the right index + + + align:start position:0% +terms as long as we keep the right index +so let me actually use the regular chalk + + align:start position:0% +so let me actually use the regular chalk + + + align:start position:0% +so let me actually use the regular chalk +for this and I'm going to look at how I + + align:start position:0% +for this and I'm going to look at how I + + + align:start position:0% +for this and I'm going to look at how I +can split up the second term to help + + align:start position:0% +can split up the second term to help + + + align:start position:0% +can split up the second term to help +with the first and the third so in the + + align:start position:0% +with the first and the third so in the + + + align:start position:0% +with the first and the third so in the +second term notice I have an N2 and an N + + align:start position:0% +second term notice I have an N2 and an N + + + align:start position:0% +second term notice I have an N2 and an N +cubed or n cubus N2 here and N cubed + + align:start position:0% +cubed or n cubus N2 here and N cubed + + + align:start position:0% +cubed or n cubus N2 here and N cubed +minus N2 here so what I can do is I'm + + align:start position:0% +minus N2 here so what I can do is I'm + + + align:start position:0% +minus N2 here so what I can do is I'm +going to look at those terms together + + align:start position:0% +going to look at those terms together + + + align:start position:0% +going to look at those terms together +and then I'm going to look at the end + + align:start position:0% +and then I'm going to look at the end + + + align:start position:0% +and then I'm going to look at the end +the term ter or the the summation with n + + align:start position:0% +the term ter or the the summation with n + + + align:start position:0% +the term ter or the the summation with n +and the summation with n and we'll + + align:start position:0% +and the summation with n and we'll + + + align:start position:0% +and the summation with n and we'll +compare them so let me write out what we + + align:start position:0% +compare them so let me write out what we + + + align:start position:0% +compare them so let me write out what we +get going to leave the first one alone + + align:start position:0% +get going to leave the first one alone + + + align:start position:0% +get going to leave the first one alone +for the + + align:start position:0% + + + + align:start position:0% + +moment and then I'm going to subtract + + align:start position:0% +moment and then I'm going to subtract + + + align:start position:0% +moment and then I'm going to subtract +off this part of that of that + + align:start position:0% + + + + align:start position:0% + +summation and what's left in that + + align:start position:0% +summation and what's left in that + + + align:start position:0% +summation and what's left in that +summation is every term I had a n also + + align:start position:0% +summation is every term I had a n also + + + align:start position:0% +summation is every term I had a n also +so I'm going to pull that minus out with + + align:start position:0% +so I'm going to pull that minus out with + + + align:start position:0% +so I'm going to pull that minus out with +this with this negative and what I'm + + align:start position:0% +this with this negative and what I'm + + + align:start position:0% +this with this negative and what I'm +doing is I'm taking 45 to Nal 45 to 100 + + align:start position:0% +doing is I'm taking 45 to Nal 45 to 100 + + + align:start position:0% +doing is I'm taking 45 to Nal 45 to 100 +of these added up and then Nal 45 to 100 + + align:start position:0% +of these added up and then Nal 45 to 100 + + + align:start position:0% +of these added up and then Nal 45 to 100 +of this added up so I end up with + + align:start position:0% +of this added up so I end up with + + + align:start position:0% +of this added up so I end up with +another + + align:start position:0% +another + + + align:start position:0% +another +term Nal 45 to + + align:start position:0% +term Nal 45 to + + + align:start position:0% +term Nal 45 to +100 of just n so those two terms are + + align:start position:0% +100 of just n so those two terms are + + + align:start position:0% +100 of just n so those two terms are +coming from the middle one split into + + align:start position:0% +coming from the middle one split into + + + align:start position:0% +coming from the middle one split into +two pieces and then the last term + + align:start position:0% +two pieces and then the last term + + + align:start position:0% +two pieces and then the last term +I just write + + align:start position:0% + + + + align:start position:0% + +down so now it's set up to to go nicely + + align:start position:0% +down so now it's set up to to go nicely + + + align:start position:0% +down so now it's set up to to go nicely +for this into a single summation and + + align:start position:0% +for this into a single summation and + + + align:start position:0% +for this into a single summation and +this into a single summation and then + + align:start position:0% +this into a single summation and then + + + align:start position:0% +this into a single summation and then +we'll see if we can combine them + + align:start position:0% +we'll see if we can combine them + + + align:start position:0% +we'll see if we can combine them +further so if you look here I have n + + align:start position:0% +further so if you look here I have n + + + align:start position:0% +further so if you look here I have n +equal 1 to 100 of a sum and then I have + + align:start position:0% +equal 1 to 100 of a sum and then I have + + + align:start position:0% +equal 1 to 100 of a sum and then I have +n equal to 45 to 100 of the same sum + + align:start position:0% +n equal to 45 to 100 of the same sum + + + align:start position:0% +n equal to 45 to 100 of the same sum +what's that actually mean that means I'm + + align:start position:0% +what's that actually mean that means I'm + + + align:start position:0% +what's that actually mean that means I'm +seeing the 45 to 100 thing here and here + + align:start position:0% +seeing the 45 to 100 thing here and here + + + align:start position:0% +seeing the 45 to 100 thing here and here +and there's a difference right so I plug + + align:start position:0% +and there's a difference right so I plug + + + align:start position:0% +and there's a difference right so I plug +in Nal 45 here I get 45 3 minus 45 + + align:start position:0% +in Nal 45 here I get 45 3 minus 45 + + + align:start position:0% +in Nal 45 here I get 45 3 minus 45 +squared I plug in N equal 45 here I get + + align:start position:0% +squared I plug in N equal 45 here I get + + + align:start position:0% +squared I plug in N equal 45 here I get +the same thing and I'm + + align:start position:0% +the same thing and I'm + + + align:start position:0% +the same thing and I'm +subtracting so what's actually happening + + align:start position:0% +subtracting so what's actually happening + + + align:start position:0% +subtracting so what's actually happening +is all the terms that have that show up + + align:start position:0% +is all the terms that have that show up + + + align:start position:0% +is all the terms that have that show up +in both this sum and this sum are being + + align:start position:0% +in both this sum and this sum are being + + + align:start position:0% +in both this sum and this sum are being +subtracted off what are those terms + + align:start position:0% +subtracted off what are those terms + + + align:start position:0% +subtracted off what are those terms +those are all the terms from n equal 45 + + align:start position:0% +those are all the terms from n equal 45 + + + align:start position:0% +those are all the terms from n equal 45 +up to 100 because it's in this summation + + align:start position:0% +up to 100 because it's in this summation + + + align:start position:0% +up to 100 because it's in this summation +and this one goes all the way from one + + align:start position:0% +and this one goes all the way from one + + + align:start position:0% +and this one goes all the way from one +to 100 so it certainly includes 45 to + + align:start position:0% +to 100 so it certainly includes 45 to + + + align:start position:0% +to 100 so it certainly includes 45 to +100 so in fact you see that all you wind + + align:start position:0% +100 so in fact you see that all you wind + + + align:start position:0% +100 so in fact you see that all you wind +up with in the end is Nal 1 to + + align:start position:0% +up with in the end is Nal 1 to + + + align:start position:0% +up with in the end is Nal 1 to +44 of n Cub minus + + align:start position:0% +44 of n Cub minus + + + align:start position:0% +44 of n Cub minus +n^2 again why is that this has the 1 + + align:start position:0% +n^2 again why is that this has the 1 + + + align:start position:0% +n^2 again why is that this has the 1 +through 44 + + align:start position:0% +through 44 + + + align:start position:0% +through 44 +terms and it has the 45 through 100 + + align:start position:0% +terms and it has the 45 through 100 + + + align:start position:0% +terms and it has the 45 through 100 +terms this has the 45 through 100 terms + + align:start position:0% +terms this has the 45 through 100 terms + + + align:start position:0% +terms this has the 45 through 100 terms +only so the 45 through 100 terms are in + + align:start position:0% +only so the 45 through 100 terms are in + + + align:start position:0% +only so the 45 through 100 terms are in +both and they're subtracted off so + + align:start position:0% +both and they're subtracted off so + + + align:start position:0% +both and they're subtracted off so +that's one way to think about why we end + + align:start position:0% +that's one way to think about why we end + + + align:start position:0% +that's one way to think about why we end +up with n equals 1 to 44 of this sum and + + align:start position:0% +up with n equals 1 to 44 of this sum and + + + align:start position:0% +up with n equals 1 to 44 of this sum and +then let's look what we get here well in + + align:start position:0% +then let's look what we get here well in + + + align:start position:0% +then let's look what we get here well in +fact we see it's exactly the same kind + + align:start position:0% +fact we see it's exactly the same kind + + + align:start position:0% +fact we see it's exactly the same kind +of thing this is 45 to 100 this is 1 to + + align:start position:0% +of thing this is 45 to 100 this is 1 to + + + align:start position:0% +of thing this is 45 to 100 this is 1 to +100 but notice now that the minus is on + + align:start position:0% +100 but notice now that the minus is on + + + align:start position:0% +100 but notice now that the minus is on +the 1 to 100 part so I'm actually going + + align:start position:0% +the 1 to 100 part so I'm actually going + + + align:start position:0% +the 1 to 100 part so I'm actually going +to get Negative of n = 1 to + + align:start position:0% +to get Negative of n = 1 to + + + align:start position:0% +to get Negative of n = 1 to +44 of + + align:start position:0% +44 of + + + align:start position:0% +44 of +n because the 45 terms here 45 to 100 + + align:start position:0% +n because the 45 terms here 45 to 100 + + + align:start position:0% +n because the 45 terms here 45 to 100 +are in both so the 45 to 100 here + + align:start position:0% +are in both so the 45 to 100 here + + + align:start position:0% +are in both so the 45 to 100 here +subtract off the 45 to 100 here those + + align:start position:0% +subtract off the 45 to 100 here those + + + align:start position:0% +subtract off the 45 to 100 here those +all go away but I'm still left with the + + align:start position:0% +all go away but I'm still left with the + + + align:start position:0% +all go away but I'm still left with the +minus Nal 1 to 44 and now I could + + align:start position:0% +minus Nal 1 to 44 and now I could + + + align:start position:0% +minus Nal 1 to 44 and now I could +simplify this further if I wanted into a + + align:start position:0% +simplify this further if I wanted into a + + + align:start position:0% +simplify this further if I wanted into a +single + + align:start position:0% +single + + + align:start position:0% +single +sum 1 to + + align:start position:0% +sum 1 to + + + align:start position:0% +sum 1 to +44 n cubed minus n^ 2 minus n why can I + + align:start position:0% +44 n cubed minus n^ 2 minus n why can I + + + align:start position:0% +44 n cubed minus n^ 2 minus n why can I +do that so easily they're indexing over + + align:start position:0% +do that so easily they're indexing over + + + align:start position:0% +do that so easily they're indexing over +the same values right that's an + + align:start position:0% +the same values right that's an + + + align:start position:0% +the same values right that's an +important point if this was indexing + + align:start position:0% +important point if this was indexing + + + align:start position:0% +important point if this was indexing +over different values I have to change + + align:start position:0% +over different values I have to change + + + align:start position:0% +over different values I have to change +this formula in order to substitute it + + align:start position:0% +this formula in order to substitute it + + + align:start position:0% +this formula in order to substitute it +in but because they're indexing over + + align:start position:0% +in but because they're indexing over + + + align:start position:0% +in but because they're indexing over +exactly the same values I can just take + + align:start position:0% +exactly the same values I can just take + + + align:start position:0% +exactly the same values I can just take +these two pieces and put them into a + + align:start position:0% +these two pieces and put them into a + + + align:start position:0% +these two pieces and put them into a +single sum so we're going to stop those + + align:start position:0% +single sum so we're going to stop those + + + align:start position:0% +single sum so we're going to stop those +two problems now and we're going to do + + align:start position:0% +two problems now and we're going to do + + + align:start position:0% +two problems now and we're going to do +one more summation notation problem so + + align:start position:0% +one more summation notation problem so + + + align:start position:0% +one more summation notation problem so +we're going to come over + + align:start position:0% +we're going to come over + + + align:start position:0% +we're going to come over +here and I'm just going to ask you to + + align:start position:0% +here and I'm just going to ask you to + + + align:start position:0% +here and I'm just going to ask you to +write this is a sum of five terms I'm + + align:start position:0% +write this is a sum of five terms I'm + + + align:start position:0% +write this is a sum of five terms I'm +going to ask you to write this in Sigma + + align:start position:0% +going to ask you to write this in Sigma + + + align:start position:0% +going to ask you to write this in Sigma +notation and the main thing there will + + align:start position:0% +notation and the main thing there will + + + align:start position:0% +notation and the main thing there will +be multiple ways to do this so you might + + align:start position:0% +be multiple ways to do this so you might + + + align:start position:0% +be multiple ways to do this so you might +come up with a different answer than I + + align:start position:0% +come up with a different answer than I + + + align:start position:0% +come up with a different answer than I +do but I'd like you to work on it for a + + align:start position:0% +do but I'd like you to work on it for a + + + align:start position:0% +do but I'd like you to work on it for a +few minutes and then when you feel + + align:start position:0% +few minutes and then when you feel + + + align:start position:0% +few minutes and then when you feel +confident come back and I will show you + + align:start position:0% +confident come back and I will show you + + + align:start position:0% +confident come back and I will show you +how I solve the + + align:start position:0% + + + + align:start position:0% + +problem okay welcome back one more time + + align:start position:0% +problem okay welcome back one more time + + + align:start position:0% +problem okay welcome back one more time +we're gonna we're going to try and put + + align:start position:0% +we're gonna we're going to try and put + + + align:start position:0% +we're gonna we're going to try and put +this in Sigma notation and I have to + + align:start position:0% +this in Sigma notation and I have to + + + align:start position:0% +this in Sigma notation and I have to +tell you that when I look at this kind + + align:start position:0% +tell you that when I look at this kind + + + align:start position:0% +tell you that when I look at this kind +of problem and I see the same kind of + + align:start position:0% +of problem and I see the same kind of + + + align:start position:0% +of problem and I see the same kind of +factor in each of these things I like to + + align:start position:0% +factor in each of these things I like to + + + align:start position:0% +factor in each of these things I like to +make it as simple on myself as possible + + align:start position:0% +make it as simple on myself as possible + + + align:start position:0% +make it as simple on myself as possible +I like to pull out that factor just to + + align:start position:0% +I like to pull out that factor just to + + + align:start position:0% +I like to pull out that factor just to +make sure that I I can simplify this as + + align:start position:0% +make sure that I I can simplify this as + + + align:start position:0% +make sure that I I can simplify this as +much as possible before I go into Sigma + + align:start position:0% +much as possible before I go into Sigma + + + align:start position:0% +much as possible before I go into Sigma +notation so the common factor to all of + + align:start position:0% +notation so the common factor to all of + + + align:start position:0% +notation so the common factor to all of +these is 1 so I'm going to pull out a + + align:start position:0% +these is 1 so I'm going to pull out a + + + align:start position:0% +these is 1 so I'm going to pull out a +1th before I start doing anything else + + align:start position:0% +1th before I start doing anything else + + + align:start position:0% +1th before I start doing anything else +there I get a + + align:start position:0% +there I get a + + + align:start position:0% +there I get a +one there I get a minus 12+ 1/3 minus + + align:start position:0% +one there I get a minus 12+ 1/3 minus + + + align:start position:0% +one there I get a minus 12+ 1/3 minus +1/4 + 1 + + align:start position:0% +1/4 + 1 + + + align:start position:0% +1/4 + 1 +15 now if you couldn't do it before you + + align:start position:0% +15 now if you couldn't do it before you + + + align:start position:0% +15 now if you couldn't do it before you +can probably do it now because now it's + + align:start position:0% +can probably do it now because now it's + + + align:start position:0% +can probably do it now because now it's +sort of very obvious how these terms are + + align:start position:0% +sort of very obvious how these terms are + + + align:start position:0% +sort of very obvious how these terms are +changing so we want to see how these + + align:start position:0% +changing so we want to see how these + + + align:start position:0% +changing so we want to see how these +terms are changing and how we could + + align:start position:0% +terms are changing and how we could + + + align:start position:0% +terms are changing and how we could +index them in some variable so let's + + align:start position:0% +index them in some variable so let's + + + align:start position:0% +index them in some variable so let's +let's start with the 1 and I'll start + + align:start position:0% +let's start with the 1 and I'll start + + + align:start position:0% +let's start with the 1 and I'll start +with my summation and then we'll figure + + align:start position:0% +with my summation and then we'll figure + + + align:start position:0% +with my summation and then we'll figure +out what all the pieces are now + + align:start position:0% +out what all the pieces are now + + + align:start position:0% +out what all the pieces are now +obviously the numerator in this case is + + align:start position:0% +obviously the numerator in this case is + + + align:start position:0% +obviously the numerator in this case is +fixed at one and I've got a fraction + + align:start position:0% +fixed at one and I've got a fraction + + + align:start position:0% +fixed at one and I've got a fraction +here so the numerator is fixed at one + + align:start position:0% +here so the numerator is fixed at one + + + align:start position:0% +here so the numerator is fixed at one +but the sign is alternating so how do + + align:start position:0% +but the sign is alternating so how do + + + align:start position:0% +but the sign is alternating so how do +you alternate sign you're going to take + + align:start position:0% +you alternate sign you're going to take + + + align:start position:0% +you alternate sign you're going to take +Nega one and raise it to a power now the + + align:start position:0% +Nega one and raise it to a power now the + + + align:start position:0% +Nega one and raise it to a power now the +power you raise it to will depend on if + + align:start position:0% +power you raise it to will depend on if + + + align:start position:0% +power you raise it to will depend on if +you want the first term to be posi + + align:start position:0% +you want the first term to be posi + + + align:start position:0% +you want the first term to be posi +postive or negative and where you start + + align:start position:0% +postive or negative and where you start + + + align:start position:0% +postive or negative and where you start +your summation so there's a lot of + + align:start position:0% +your summation so there's a lot of + + + align:start position:0% +your summation so there's a lot of +choices you can make but I'm going to + + align:start position:0% +choices you can make but I'm going to + + + align:start position:0% +choices you can make but I'm going to +start my summation we'll say at uh we + + align:start position:0% +start my summation we'll say at uh we + + + align:start position:0% +start my summation we'll say at uh we +we'll do it in K and we'll start at k + + align:start position:0% +we'll do it in K and we'll start at k + + + align:start position:0% +we'll do it in K and we'll start at k +equals 1 and then we'll have to figure + + align:start position:0% +equals 1 and then we'll have to figure + + + align:start position:0% +equals 1 and then we'll have to figure +everything out from that so I'm going to + + align:start position:0% +everything out from that so I'm going to + + + align:start position:0% +everything out from that so I'm going to +start my summation at k equals 1 my + + align:start position:0% +start my summation at k equals 1 my + + + align:start position:0% +start my summation at k equals 1 my +first term I want to be positive one so + + align:start position:0% +first term I want to be positive one so + + + align:start position:0% +first term I want to be positive one so +I need my power to be k + one because + + align:start position:0% +I need my power to be k + one because + + + align:start position:0% +I need my power to be k + one because +now my power here is going to be when I + + align:start position:0% +now my power here is going to be when I + + + align:start position:0% +now my power here is going to be when I +put in a I get a 1 plus 1 I get two 1^ s + + align:start position:0% +put in a I get a 1 plus 1 I get two 1^ s + + + align:start position:0% +put in a I get a 1 plus 1 I get two 1^ s +is positive that's what I want you might + + align:start position:0% +is positive that's what I want you might + + + align:start position:0% +is positive that's what I want you might +have done K minus one if you did K minus + + align:start position:0% +have done K minus one if you did K minus + + + align:start position:0% +have done K minus one if you did K minus +one that's okay because K minus one is + + align:start position:0% +one that's okay because K minus one is + + + align:start position:0% +one that's okay because K minus one is +also an even number so when I take + + align:start position:0% +also an even number so when I take + + + align:start position:0% +also an even number so when I take +negative one and I Square it I still get + + align:start position:0% +negative one and I Square it I still get + + + align:start position:0% +negative one and I Square it I still get +a positive number so there are a lot of + + align:start position:0% +a positive number so there are a lot of + + + align:start position:0% +a positive number so there are a lot of +choices one can make and still be + + align:start position:0% +choices one can make and still be + + + align:start position:0% +choices one can make and still be +correct on that power and then I'm + + align:start position:0% +correct on that power and then I'm + + + align:start position:0% +correct on that power and then I'm +counting up notice the denominator is + + align:start position:0% +counting up notice the denominator is + + + align:start position:0% +counting up notice the denominator is +increasing just by one each time and so + + align:start position:0% +increasing just by one each time and so + + + align:start position:0% +increasing just by one each time and so +it looks like I could do just something + + align:start position:0% +it looks like I could do just something + + + align:start position:0% +it looks like I could do just something +like over K now let's check if that + + align:start position:0% +like over K now let's check if that + + + align:start position:0% +like over K now let's check if that +makes sense well when K is one I get one + + align:start position:0% +makes sense well when K is one I get one + + + align:start position:0% +makes sense well when K is one I get one +in the denominator this is one over one + + align:start position:0% +in the denominator this is one over one + + + align:start position:0% +in the denominator this is one over one +when K is two I get two in the + + align:start position:0% +when K is two I get two in the + + + align:start position:0% +when K is two I get two in the +denominator when K is three I get three + + align:start position:0% +denominator when K is three I get three + + + align:start position:0% +denominator when K is three I get three +in the denominator so that looks good + + align:start position:0% +in the denominator so that looks good + + + align:start position:0% +in the denominator so that looks good +and now the only question is where + + align:start position:0% +and now the only question is where + + + align:start position:0% +and now the only question is where +should I stop this thing so I have my + + align:start position:0% +should I stop this thing so I have my + + + align:start position:0% +should I stop this thing so I have my +alternating sign my denominator looks + + align:start position:0% +alternating sign my denominator looks + + + align:start position:0% +alternating sign my denominator looks +right for what value of K do I want to + + align:start position:0% +right for what value of K do I want to + + + align:start position:0% +right for what value of K do I want to +stop I want to stop when the denominator + + align:start position:0% +stop I want to stop when the denominator + + + align:start position:0% +stop I want to stop when the denominator +equals five and so I just need to put a + + align:start position:0% +equals five and so I just need to put a + + + align:start position:0% +equals five and so I just need to put a +five up here and then I'm + + align:start position:0% +five up here and then I'm + + + align:start position:0% +five up here and then I'm +done now if you wanted to move the one + + align:start position:0% +done now if you wanted to move the one + + + align:start position:0% +done now if you wanted to move the one +back in you could actually do that maybe + + align:start position:0% +back in you could actually do that maybe + + + align:start position:0% +back in you could actually do that maybe +your maybe your + + align:start position:0% + + + + align:start position:0% + +solution look something I pulled a one + + align:start position:0% +solution look something I pulled a one + + + align:start position:0% +solution look something I pulled a one +back + + align:start position:0% + + + + align:start position:0% + +in and I have 5K in there instead maybe + + align:start position:0% +in and I have 5K in there instead maybe + + + align:start position:0% +in and I have 5K in there instead maybe +that was your solution but these are + + align:start position:0% +that was your solution but these are + + + align:start position:0% +that was your solution but these are +ultimately the same thing because really + + align:start position:0% +ultimately the same thing because really + + + align:start position:0% +ultimately the same thing because really +this is this is just Distributing right + + align:start position:0% +this is this is just Distributing right + + + align:start position:0% +this is this is just Distributing right +this is a big sum I have a 1 out in + + align:start position:0% +this is a big sum I have a 1 out in + + + align:start position:0% +this is a big sum I have a 1 out in +front and so I multiply every term by 1 + + align:start position:0% +front and so I multiply every term by 1 + + + align:start position:0% +front and so I multiply every term by 1 +so I just have to put a five in the + + align:start position:0% +so I just have to put a five in the + + + align:start position:0% +so I just have to put a five in the +denominator so might have had something + + align:start position:0% +denominator so might have had something + + + align:start position:0% +denominator so might have had something +more like this that's still + + align:start position:0% +more like this that's still + + + align:start position:0% +more like this that's still +correct so just to stress that really + + align:start position:0% +correct so just to stress that really + + + align:start position:0% +correct so just to stress that really +the sigma notation it's it's a good tool + + align:start position:0% +the sigma notation it's it's a good tool + + + align:start position:0% +the sigma notation it's it's a good tool +to understand how to manipulate easily + + align:start position:0% +to understand how to manipulate easily + + + align:start position:0% +to understand how to manipulate easily +so there are probably more problems you + + align:start position:0% +so there are probably more problems you + + + align:start position:0% +so there are probably more problems you +can find to practice if you're nervous + + align:start position:0% +can find to practice if you're nervous + + + align:start position:0% +can find to practice if you're nervous +about this um but I just wanted to give + + align:start position:0% +about this um but I just wanted to give + + + align:start position:0% +about this um but I just wanted to give +you a chance to see a couple of them and + + align:start position:0% +you a chance to see a couple of them and + + + align:start position:0% +you a chance to see a couple of them and +how we work on them that's where I'll + + align:start position:0% +how we work on them that's where I'll + + + align:start position:0% +how we work on them that's where I'll +stop \ No newline at end of file diff --git a/ihokgDNXDzY.txt b/ihokgDNXDzY.txt new file mode 100644 index 0000000000000000000000000000000000000000..a419e21f5e6d45c163e72aed380eed8de09e21e4 --- /dev/null +++ b/ihokgDNXDzY.txt @@ -0,0 +1,755 @@ +align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +here's another case study I simply put + + align:start position:0% +here's another case study I simply put + + + align:start position:0% +here's another case study I simply put +two pieces of paper + + align:start position:0% +two pieces of paper + + + align:start position:0% +two pieces of paper +overlapping these papers are used for + + align:start position:0% +overlapping these papers are used for + + + align:start position:0% +overlapping these papers are used for +particular medical analysis so I + + align:start position:0% +particular medical analysis so I + + + align:start position:0% +particular medical analysis so I +captured it once again at a very high + + align:start position:0% +captured it once again at a very high + + + align:start position:0% +captured it once again at a very high +resolution so that as we zoom into the + + align:start position:0% +resolution so that as we zoom into the + + + align:start position:0% +resolution so that as we zoom into the +image we can actually see the fibers in + + align:start position:0% +image we can actually see the fibers in + + + align:start position:0% +image we can actually see the fibers in +the + + align:start position:0% +the + + + align:start position:0% +the +paper here's an image where I added + + align:start position:0% +paper here's an image where I added + + + align:start position:0% +paper here's an image where I added +background color now I'm not changing + + align:start position:0% +background color now I'm not changing + + + align:start position:0% +background color now I'm not changing +the important information in the image + + align:start position:0% +the important information in the image + + + align:start position:0% +the important information in the image +the structure the structure is the data + + align:start position:0% +the structure the structure is the data + + + align:start position:0% +the structure the structure is the data +I'm just adding an additional component + + align:start position:0% +I'm just adding an additional component + + + align:start position:0% +I'm just adding an additional component +to allow the viewer to see the material + + align:start position:0% +to allow the viewer to see the material + + + align:start position:0% +to allow the viewer to see the material +better we'll be looking at adding + + align:start position:0% +better we'll be looking at adding + + + align:start position:0% +better we'll be looking at adding +backgrounds in the how to do it + + align:start position:0% +backgrounds in the how to do it + + + align:start position:0% +backgrounds in the how to do it +section I want to spend a few minutes on + + align:start position:0% +section I want to spend a few minutes on + + + align:start position:0% +section I want to spend a few minutes on +backgrounds I am a bit of a background + + align:start position:0% +backgrounds I am a bit of a background + + + align:start position:0% +backgrounds I am a bit of a background +collector and frankly I think you should + + align:start position:0% +collector and frankly I think you should + + + align:start position:0% +collector and frankly I think you should +be one too really it it helps a lot to + + align:start position:0% +be one too really it it helps a lot to + + + align:start position:0% +be one too really it it helps a lot to +imagine your images even while you're + + align:start position:0% +imagine your images even while you're + + + align:start position:0% +imagine your images even while you're +not even working on it whenever some + + align:start position:0% +not even working on it whenever some + + + align:start position:0% +not even working on it whenever some +interesting envelope or card arrives in + + align:start position:0% +interesting envelope or card arrives in + + + align:start position:0% +interesting envelope or card arrives in +my mailbox I keep it believe it or not + + align:start position:0% +my mailbox I keep it believe it or not + + + align:start position:0% +my mailbox I keep it believe it or not +thinking that it might help with an + + align:start position:0% +thinking that it might help with an + + + align:start position:0% +thinking that it might help with an +image one day or platters or wired + + align:start position:0% +image one day or platters or wired + + + align:start position:0% +image one day or platters or wired +thingies anything that might be + + align:start position:0% +thingies anything that might be + + + align:start position:0% +thingies anything that might be +appropriate for a background for small + + align:start position:0% +appropriate for a background for small + + + align:start position:0% +appropriate for a background for small +devices and besides it's fun to think + + align:start position:0% +devices and besides it's fun to think + + + align:start position:0% +devices and besides it's fun to think +about so let's take a look at one + + align:start position:0% +about so let's take a look at one + + + align:start position:0% +about so let's take a look at one +particular idea take this simple graph + + align:start position:0% +particular idea take this simple graph + + + align:start position:0% +particular idea take this simple graph +paper which I tried as a background for + + align:start position:0% +paper which I tried as a background for + + + align:start position:0% +paper which I tried as a background for +this device + + align:start position:0% +this device + + + align:start position:0% +this device +looks okay here I tried some bubble wrap + + align:start position:0% +looks okay here I tried some bubble wrap + + + align:start position:0% +looks okay here I tried some bubble wrap +of all things definitely over the top + + align:start position:0% +of all things definitely over the top + + + align:start position:0% +of all things definitely over the top +and doesn't work quite well there should + + align:start position:0% +and doesn't work quite well there should + + + align:start position:0% +and doesn't work quite well there should +be some sort of intelligent visual + + align:start position:0% +be some sort of intelligent visual + + + align:start position:0% +be some sort of intelligent visual +connection between your device and your + + align:start position:0% +connection between your device and your + + + align:start position:0% +connection between your device and your +background and bubble wrap doesn't quite + + align:start position:0% +background and bubble wrap doesn't quite + + + align:start position:0% +background and bubble wrap doesn't quite +cut it in the end I finally landed on + + align:start position:0% +cut it in the end I finally landed on + + + align:start position:0% +cut it in the end I finally landed on +using simple green paper with this + + align:start position:0% +using simple green paper with this + + + align:start position:0% +using simple green paper with this +device and because the image was + + align:start position:0% +device and because the image was + + + align:start position:0% +device and because the image was +captured with a scanner setting at a + + align:start position:0% +captured with a scanner setting at a + + + align:start position:0% +captured with a scanner setting at a +high resolution it was about 400 Meg + + align:start position:0% +high resolution it was about 400 Meg + + + align:start position:0% +high resolution it was about 400 Meg +file I was able to zoom in crop and + + align:start position:0% +file I was able to zoom in crop and + + + align:start position:0% +file I was able to zoom in crop and +finalize the image I think that both the + + align:start position:0% +finalize the image I think that both the + + + align:start position:0% +finalize the image I think that both the +simple colored background and the + + align:start position:0% +simple colored background and the + + + align:start position:0% +simple colored background and the +composition + + align:start position:0% +composition + + + align:start position:0% +composition +works here we see three microfluidic + + align:start position:0% +works here we see three microfluidic + + + align:start position:0% +works here we see three microfluidic +devices which I initially lined up in a + + align:start position:0% +devices which I initially lined up in a + + + align:start position:0% +devices which I initially lined up in a +pretty boring way as you see here and + + align:start position:0% +pretty boring way as you see here and + + + align:start position:0% +pretty boring way as you see here and +once again I'm always playing with + + align:start position:0% +once again I'm always playing with + + + align:start position:0% +once again I'm always playing with +composition so what I did was I used two + + align:start position:0% +composition so what I did was I used two + + + align:start position:0% +composition so what I did was I used two +of them instead just the two of them + + align:start position:0% +of them instead just the two of them + + + align:start position:0% +of them instead just the two of them +really visually say what you need to say + + align:start position:0% +really visually say what you need to say + + + align:start position:0% +really visually say what you need to say +we don't need three you might think + + align:start position:0% +we don't need three you might think + + + align:start position:0% +we don't need three you might think +about that in your own work so I + + align:start position:0% +about that in your own work so I + + + align:start position:0% +about that in your own work so I +captured it at a very high resolution + + align:start position:0% +captured it at a very high resolution + + + align:start position:0% +captured it at a very high resolution +putting the devices on an angle much + + align:start position:0% +putting the devices on an angle much + + + align:start position:0% +putting the devices on an angle much +more interesting + + align:start position:0% +more interesting + + + align:start position:0% +more interesting +composition and because of the high + + align:start position:0% +composition and because of the high + + + align:start position:0% +composition and because of the high +resolution I was able to zoom in and + + align:start position:0% +resolution I was able to zoom in and + + + align:start position:0% +resolution I was able to zoom in and +crop the image now watch what happens + + align:start position:0% +crop the image now watch what happens + + + align:start position:0% +crop the image now watch what happens +when I enhance the image using a + + align:start position:0% +when I enhance the image using a + + + align:start position:0% +when I enhance the image using a +sharpening tool we'll talk about + + align:start position:0% +sharpening tool we'll talk about + + + align:start position:0% +sharpening tool we'll talk about +sharpening images on the how to do it + + align:start position:0% +sharpening images on the how to do it + + + align:start position:0% +sharpening images on the how to do it +section this is an important technique + + align:start position:0% +section this is an important technique + + + align:start position:0% +section this is an important technique +the sharpening filter is not changing + + align:start position:0% +the sharpening filter is not changing + + + align:start position:0% +the sharpening filter is not changing +your data if your data is about form and + + align:start position:0% +your data if your data is about form and + + + align:start position:0% +your data if your data is about form and +structure it's permitting you and your + + align:start position:0% +structure it's permitting you and your + + + align:start position:0% +structure it's permitting you and your +viewers to see the image clearly but + + align:start position:0% +viewers to see the image clearly but + + + align:start position:0% +viewers to see the image clearly but +whenever any of these filters are used + + align:start position:0% +whenever any of these filters are used + + + align:start position:0% +whenever any of these filters are used +it's imperative to always indicate the + + align:start position:0% +it's imperative to always indicate the + + + align:start position:0% +it's imperative to always indicate the +process in the caption something that I + + align:start position:0% +process in the caption something that I + + + align:start position:0% +process in the caption something that I +encourage you to consider because I + + align:start position:0% +encourage you to consider because I + + + align:start position:0% +encourage you to consider because I +captured this at such a high resolution + + align:start position:0% +captured this at such a high resolution + + + align:start position:0% +captured this at such a high resolution +we can zoom in and see 30 Micron + + align:start position:0% +we can zoom in and see 30 Micron + + + align:start position:0% +we can zoom in and see 30 Micron +structure here it is again first the + + align:start position:0% +structure here it is again first the + + + align:start position:0% +structure here it is again first the +original image and here it is sharpened + + align:start position:0% +original image and here it is sharpened + + + align:start position:0% +original image and here it is sharpened +where you can really see the detail it's + + align:start position:0% +where you can really see the detail it's + + + align:start position:0% +where you can really see the detail it's +pretty neat so this is our first week + + align:start position:0% +pretty neat so this is our first week + + + align:start position:0% +pretty neat so this is our first week +Imaging with a flatbed scanner think + + align:start position:0% +Imaging with a flatbed scanner think + + + align:start position:0% +Imaging with a flatbed scanner think +about it it's not an expensive piece of + + align:start position:0% +about it it's not an expensive piece of + + + align:start position:0% +about it it's not an expensive piece of +equipment and if used properly you can + + align:start position:0% +equipment and if used properly you can + + + align:start position:0% +equipment and if used properly you can +achieve high quality images without + + align:start position:0% +achieve high quality images without + + + align:start position:0% +achieve high quality images without +spending an inordinate amount of + + align:start position:0% +spending an inordinate amount of + + + align:start position:0% +spending an inordinate amount of +time in the next weeks we'll talk about + + align:start position:0% +time in the next weeks we'll talk about + + + align:start position:0% +time in the next weeks we'll talk about +cameras lenses lighting approaches to + + align:start position:0% +cameras lenses lighting approaches to + + + align:start position:0% +cameras lenses lighting approaches to +Imaging sign science and engineering + + align:start position:0% +Imaging sign science and engineering + + + align:start position:0% +Imaging sign science and engineering +we'll also discuss how to graphically + + align:start position:0% +we'll also discuss how to graphically + + + align:start position:0% +we'll also discuss how to graphically +use these images for figures and + + align:start position:0% +use these images for figures and + + + align:start position:0% +use these images for figures and +potential cover + + align:start position:0% +potential cover + + + align:start position:0% +potential cover +designs so lots more ahead and I look + + align:start position:0% +designs so lots more ahead and I look + + + align:start position:0% +designs so lots more ahead and I look +forward to it \ No newline at end of file diff --git a/ilM34q8F6rY.txt b/ilM34q8F6rY.txt new file mode 100644 index 0000000000000000000000000000000000000000..79ae63704b2c985d3acb16eb05f9a5aee862b5f8 --- /dev/null +++ b/ilM34q8F6rY.txt @@ -0,0 +1,11715 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu the aesthetic of connection + + align:start position:0% +ocw.mit.edu the aesthetic of connection + + + align:start position:0% +ocw.mit.edu the aesthetic of connection +this aesthetic of familiarity this + + align:start position:0% +this aesthetic of familiarity this + + + align:start position:0% +this aesthetic of familiarity this +popular aesthetic operated in Hollywood + + align:start position:0% +popular aesthetic operated in Hollywood + + + align:start position:0% +popular aesthetic operated in Hollywood +movies uh uh and I want to expand a bit + + align:start position:0% +movies uh uh and I want to expand a bit + + + align:start position:0% +movies uh uh and I want to expand a bit +on this idea by talking about more + + align:start position:0% +on this idea by talking about more + + + align:start position:0% +on this idea by talking about more +explicitly what might be called an + + align:start position:0% +explicitly what might be called an + + + align:start position:0% +explicitly what might be called an +anthropological view of this matter what + + align:start position:0% +anthropological view of this matter what + + + align:start position:0% +anthropological view of this matter what +could be called the cultural work of + + align:start position:0% +could be called the cultural work of + + + align:start position:0% +could be called the cultural work of +movies one way I can make you think + + align:start position:0% +movies one way I can make you think + + + align:start position:0% +movies one way I can make you think +about uh the larger and more significant + + align:start position:0% +about uh the larger and more significant + + + align:start position:0% +about uh the larger and more significant +implications of what the movies are of + + align:start position:0% +implications of what the movies are of + + + align:start position:0% +implications of what the movies are of +how to think about the movies is to ask + + align:start position:0% +how to think about the movies is to ask + + + align:start position:0% +how to think about the movies is to ask +you to think about the true implications + + align:start position:0% +you to think about the true implications + + + align:start position:0% +you to think about the true implications +of certain words that we just take for + + align:start position:0% +of certain words that we just take for + + + align:start position:0% +of certain words that we just take for +granted for example take the word + + align:start position:0% +granted for example take the word + + + align:start position:0% +granted for example take the word +entertainment or the verb entertain to + + align:start position:0% +entertainment or the verb entertain to + + + align:start position:0% +entertainment or the verb entertain to +entertain uh we think of it as we think + + align:start position:0% +entertain uh we think of it as we think + + + align:start position:0% +entertain uh we think of it as we think +of it as a relatively straightforward + + align:start position:0% +of it as a relatively straightforward + + + align:start position:0% +of it as a relatively straightforward +term as it is and we think of + + align:start position:0% +term as it is and we think of + + + align:start position:0% +term as it is and we think of +entertainment as some form of diversion + + align:start position:0% +entertainment as some form of diversion + + + align:start position:0% +entertainment as some form of diversion +that takes us away from the serious + + align:start position:0% +that takes us away from the serious + + + align:start position:0% +that takes us away from the serious +things in life but I want to suggest to + + align:start position:0% +things in life but I want to suggest to + + + align:start position:0% +things in life but I want to suggest to +you that if we look closely even if we + + align:start position:0% +you that if we look closely even if we + + + align:start position:0% +you that if we look closely even if we +look at sort of the root of the word and + + align:start position:0% +look at sort of the root of the word and + + + align:start position:0% +look at sort of the root of the word and +the way the word is used and the + + align:start position:0% +the way the word is used and the + + + align:start position:0% +the way the word is used and the +variations on the on the kinds of + + align:start position:0% +variations on the on the kinds of + + + align:start position:0% +variations on the on the kinds of +meanings that are associated with the + + align:start position:0% +meanings that are associated with the + + + align:start position:0% +meanings that are associated with the +word entertainment or the verb to + + align:start position:0% +word entertainment or the verb to + + + align:start position:0% +word entertainment or the verb to +entertain we can see deeper implications + + align:start position:0% +entertain we can see deeper implications + + + align:start position:0% +entertain we can see deeper implications +for one thing for example let's just + + align:start position:0% +for one thing for example let's just + + + align:start position:0% +for one thing for example let's just +take a standard dictionary definition uh + + align:start position:0% +take a standard dictionary definition uh + + + align:start position:0% +take a standard dictionary definition uh +there are three different senses in + + align:start position:0% +there are three different senses in + + + align:start position:0% +there are three different senses in +which almost all dictionaries in English + + align:start position:0% +which almost all dictionaries in English + + + align:start position:0% +which almost all dictionaries in English +would ident would would Define the verb + + align:start position:0% +would ident would would Define the verb + + + align:start position:0% +would ident would would Define the verb +to entertain they would say to hold the + + align:start position:0% +to entertain they would say to hold the + + + align:start position:0% +to entertain they would say to hold the +attention of someone is to entertain + + align:start position:0% +attention of someone is to entertain + + + align:start position:0% +attention of someone is to entertain +them a second meaning would be to extend + + align:start position:0% +them a second meaning would be to extend + + + align:start position:0% +them a second meaning would be to extend +Hospitality to someone that makes sense + + align:start position:0% +Hospitality to someone that makes sense + + + align:start position:0% +Hospitality to someone that makes sense +right but but think when you extend + + align:start position:0% +right but but think when you extend + + + align:start position:0% +right but but think when you extend +hospit you're engag in you're you're + + align:start position:0% +hospit you're engag in you're you're + + + align:start position:0% +hospit you're engag in you're you're +engaged in a communal in a hostly act + + align:start position:0% +engaged in a communal in a hostly act + + + align:start position:0% +engaged in a communal in a hostly act +right it's an act of generosity an act + + align:start position:0% +right it's an act of generosity an act + + + align:start position:0% +right it's an act of generosity an act +of inclusion uson right so forms of + + align:start position:0% +of inclusion uson right so forms of + + + align:start position:0% +of inclusion uson right so forms of +entertainment are potentially Community + + align:start position:0% +entertainment are potentially Community + + + align:start position:0% +entertainment are potentially Community +creating gestures toward uh the + + align:start position:0% +creating gestures toward uh the + + + align:start position:0% +creating gestures toward uh the +community acts of Hosting right um and + + align:start position:0% +community acts of Hosting right um and + + + align:start position:0% +community acts of Hosting right um and +they also of course are a bid for your + + align:start position:0% +they also of course are a bid for your + + + align:start position:0% +they also of course are a bid for your +attention and then there's a third + + align:start position:0% +attention and then there's a third + + + align:start position:0% +attention and then there's a third +meaning which is the most interesting to + + align:start position:0% +meaning which is the most interesting to + + + align:start position:0% +meaning which is the most interesting to +entertain almost all dictionaries will + + align:start position:0% +entertain almost all dictionaries will + + + align:start position:0% +entertain almost all dictionaries will +tell you also means to hold in the + + align:start position:0% +tell you also means to hold in the + + + align:start position:0% +tell you also means to hold in the +mind I'm entertaining this idea I'm + + align:start position:0% +mind I'm entertaining this idea I'm + + + align:start position:0% +mind I'm entertaining this idea I'm +entertaining this thought I'm + + align:start position:0% +entertaining this thought I'm + + + align:start position:0% +entertaining this thought I'm +entertaining this possibility in other + + align:start position:0% +entertaining this possibility in other + + + align:start position:0% +entertaining this possibility in other +words the word enter the verb to + + align:start position:0% +words the word enter the verb to + + + align:start position:0% +words the word enter the verb to +entertain means to meditate to think to + 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unacceptable so + + + align:start position:0% +scary or disturbing or unacceptable so +that one of the ironies of entertainment + + align:start position:0% +that one of the ironies of entertainment + + + align:start position:0% +that one of the ironies of entertainment +is that can become a space especially + + align:start position:0% +is that can become a space especially + + + align:start position:0% +is that can become a space especially +public forms of entertainment in + + align:start position:0% +public forms of entertainment in + + + align:start position:0% +public forms of entertainment in +cultures like Shakespeare's public + + align:start position:0% +cultures like Shakespeare's public + + + align:start position:0% +cultures like Shakespeare's public +theater or like the public theater of + + align:start position:0% +theater or like the public theater of + + + align:start position:0% +theater or like the public theater of +the American movie system in the studio + + align:start position:0% +the American movie system in the studio + + + align:start position:0% +the American movie system in the studio +era these public spaces can become + + align:start position:0% +era these public spaces can become + + + align:start position:0% +era these public spaces can become +spaces in which the body politic the + + align:start position:0% +spaces in which the body politic the + + + align:start position:0% +spaces in which the body politic the +political and social Community + + align:start position:0% +political and social Community + + + align:start position:0% +political and social Community +entertains ideas about its own nature + + align:start position:0% +entertains ideas about its own nature + + + align:start position:0% +entertains ideas about its own nature +entertains considers speculates holds in + + align:start position:0% +entertains considers speculates holds in + + + align:start position:0% +entertains considers speculates holds in +its mind accounts of its Origins stories + + align:start position:0% +its mind accounts of its Origins stories + + + align:start position:0% +its mind accounts of its Origins stories +of its values right and what we can say + + align:start position:0% +of its values right and what we can say + + + align:start position:0% +of its values right and what we can say +then is that the space of entertainment + + align:start position:0% +then is that the space of entertainment + + + align:start position:0% +then is that the space of entertainment +becomes from in a certain angle in + + align:start position:0% +becomes from in a certain angle in + + + align:start position:0% +becomes from in a certain angle in +virtually all societies a space of + + align:start position:0% +virtually all societies a space of + + + align:start position:0% +virtually all societies a space of +discourse a space in which exactly + + align:start position:0% +discourse a space in which exactly + + + align:start position:0% 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other ways and we can see that +certain features of the entertainment + + align:start position:0% +certain features of the entertainment + + + align:start position:0% +certain features of the entertainment +systems of most countries and of most + + align:start position:0% +systems of most countries and of most + + + align:start position:0% +systems of most countries and of most +societies and certainly the + + align:start position:0% +societies and certainly the + + + align:start position:0% +societies and certainly the +entertainment system we're calling the + + align:start position:0% +entertainment system we're calling the + + + align:start position:0% +entertainment system we're calling the +studio the Hollywood Studio Movie are + + align:start position:0% +studio the Hollywood Studio Movie are + + + align:start position:0% +studio the Hollywood Studio Movie are +systems in which other features of the + + align:start position:0% +systems in which other features of the + + + align:start position:0% +systems in which other features of the +uh other features of the formats and + + align:start position:0% +uh other features of the formats and + + + align:start position:0% +uh other features of the formats and +organizational principles of the of the + + align:start position:0% +organizational principles of the of the + + + align:start position:0% +organizational principles of the of the +films reinforce this idea that you're + + align:start position:0% +films reinforce this idea that you're + + + align:start position:0% +films reinforce this idea that you're +escaping into a space that is also a + + align:start position:0% +escaping into a space that is also a + + + align:start position:0% +escaping into a space that is also a +space of exploration and discovery that + + align:start position:0% +space of exploration and discovery that + + + align:start position:0% +space of exploration and discovery that +you're not escaping and running away + + align:start position:0% +you're not escaping and running away + + + align:start position:0% +you're not escaping and running away +exactly into forms of diversion and + + align:start position:0% +exactly into forms of diversion and + + + align:start position:0% +exactly into forms of diversion and +hiding from the world but in fact you're + + align:start position:0% +hiding from the world but in fact you're + + + align:start position:0% +hiding from the world but in fact you're +escaping into a space of freedom in + + align:start position:0% +escaping into a space of freedom in + + + align:start position:0% +escaping into a space of freedom in +which you can consider possibilities + + align:start position:0% +which you can consider possibilities + + + align:start position:0% +which you can consider possibilities +that might otherwise be too disturbing + + align:start position:0% +that might otherwise be too disturbing + + + align:start position:0% +that might otherwise be too disturbing +to think about and one way you can see + + align:start position:0% +to think about and one way you can see + + + align:start position:0% +to think about and one way you can see +how the formats encourage that comes + + align:start position:0% +how the formats encourage that comes + + + align:start position:0% +how the formats encourage that comes +back to the argument I was making about + + align:start position:0% +back to the argument I was making about + + + align:start position:0% +back to the argument I was making about +genres and stars because think about one + + align:start position:0% +genres and stars because think about one + + + align:start position:0% +genres and stars because think about one +of the most fundamental things about the + + align:start position:0% +of the most fundamental things about the + + + align:start position:0% +of the most fundamental things about the +conventions of genre are that audiences + + align:start position:0% +conventions of genre are that audiences + + + align:start position:0% +conventions of genre are that audiences +understand not only sort of the costumes + + align:start position:0% +understand not only sort of the costumes + + + align:start position:0% +understand not only sort of the costumes +and the setting and so forth but also + + align:start position:0% +and the setting and so forth but also + + + align:start position:0% +and the setting and so forth but also +usually understand the basic um what + + align:start position:0% +usually understand the basic um what + + + align:start position:0% +usually understand the basic um what +what could we call it the basic segments + + align:start position:0% +what could we call it the basic segments + + + align:start position:0% +what could we call it the basic segments +or story for seg the segmentation of the + + align:start position:0% +or story for seg the segmentation of the + + + align:start position:0% +or story for seg the segmentation of the +story the the the the stages through + + align:start position:0% +story the the the the stages through + + + align:start position:0% +story the the the the stages through +which the story is likely to go and + + align:start position:0% +which the story is likely to go and + + + align:start position:0% +which the story is likely to go and +they're likely in many cases to have a + + align:start position:0% +they're likely in many cases to have a + + + align:start position:0% +they're likely in many cases to have a +pretty good idea about the nature of the + + align:start position:0% +pretty good idea about the nature of the + + + align:start position:0% +pretty good idea about the nature of the +ending of a particular genre form they + + align:start position:0% +ending of a particular genre form they + + + align:start position:0% +ending of a particular genre form they +may not be absolutely certain about the + + align:start position:0% +may not be absolutely certain about the + + + align:start position:0% +may not be absolutely certain about the +details of how it will work out but they + + align:start position:0% +details of how it will work out but they + + + align:start position:0% +details of how it will work out but they +have some pretty good ideas about for + + align:start position:0% +have some pretty good ideas about for + + + align:start position:0% +have some pretty good ideas about for +example the notion is that various forms + + align:start position:0% +example the notion is that various forms + + + align:start position:0% +example the notion is that various forms +of Comedy end on some sort of an + + align:start position:0% +of Comedy end on some sort of an + + + align:start position:0% +of Comedy end on some sort of an +affirming or a happy note even if the + + align:start position:0% +affirming or a happy note even if the + + + align:start position:0% +affirming or a happy note even if the +difficulties that that are dramatized in + + align:start position:0% +difficulties that that are dramatized in + + + align:start position:0% +difficulties that that are dramatized in +the text from the beginning are very + + align:start position:0% +the text from the beginning are very + + + align:start position:0% +the text from the beginning are very +serious and troubling right it not that + + align:start position:0% +serious and troubling right it not that + + + align:start position:0% +serious and troubling right it not that +every single comedy ends on a totally + + align:start position:0% +every single comedy ends on a totally + + + align:start position:0% +every single comedy ends on a totally +happy note but that's the expectation + + align:start position:0% +happy note but that's the expectation + + + align:start position:0% +happy note but that's the expectation +you have when you come to see a comedy + + align:start position:0% +you have when you come to see a comedy + + + align:start position:0% +you have when you come to see a comedy +you you expect uh an adventure with many + + align:start position:0% +you you expect uh an adventure with many + + + align:start position:0% +you you expect uh an adventure with many +difficulties that are F that will + + align:start position:0% +difficulties that are F that will + + + align:start position:0% +difficulties that are F that will +finally be resolved in some form and in + + align:start position:0% +finally be resolved in some form and in + + + align:start position:0% +finally be resolved in some form and in +fact traditionally what one of the most + + align:start position:0% +fact traditionally what one of the most + + + align:start position:0% +fact traditionally what one of the most +fundamental ways in which comedy comic + + align:start position:0% +fundamental ways in which comedy comic + + + align:start position:0% +fundamental ways in which comedy comic +narratives and comic dramas are resolved + + align:start position:0% +narratives and comic dramas are resolved + + + align:start position:0% +narratives and comic dramas are resolved +is in the act of marriage right uh uh + + align:start position:0% +is in the act of marriage right uh uh + + + align:start position:0% +is in the act of marriage right uh uh +because of course marriage is a kind of + + align:start position:0% +because of course marriage is a kind of + + + align:start position:0% +because of course marriage is a kind of +reconciliation of potential opposites it + + align:start position:0% +reconciliation of potential opposites it + + + align:start position:0% +reconciliation of potential opposites it +is a space of celebration in which + + align:start position:0% +is a space of celebration in which + + + align:start position:0% +is a space of celebration in which +different families and different groups + + align:start position:0% +different families and different groups + + + align:start position:0% +different families and different groups +and in in many forms of Comedy different + + align:start position:0% +and in in many forms of Comedy different + + + align:start position:0% +and in in many forms of Comedy different +social classes are brought together you + + align:start position:0% +social classes are brought together you + + + align:start position:0% +social classes are brought together you +so that so that the marriage itself + + align:start position:0% +so that so that the marriage itself + + + align:start position:0% +so that so that the marriage itself +becomes a social space that replicates + + align:start position:0% +becomes a social space that replicates + + + align:start position:0% +becomes a social space that replicates +that if it's dramatized on stage or in + + align:start position:0% +that if it's dramatized on stage or in + + + align:start position:0% +that if it's dramatized on stage or in +the movie it replicates in some sense + + align:start position:0% +the movie it replicates in some sense + + + align:start position:0% +the movie it replicates in some sense +the communal space of sharing that the + + align:start position:0% +the communal space of sharing that the + + + align:start position:0% +the communal space of sharing that the +audience is engaged in when it's + + align:start position:0% +audience is engaged in when it's + + + align:start position:0% +audience is engaged in when it's +watching the text right so you have + + align:start position:0% +watching the text right so you have + + + align:start position:0% +watching the text right so you have +expectations about uh the characters + + align:start position:0% +expectations about uh the characters + + + align:start position:0% +expectations about uh the characters +about the plots about the uh basic + + align:start position:0% +about the plots about the uh basic + + + align:start position:0% +about the plots about the uh basic +formats and especially about the endings + + align:start position:0% +formats and especially about the endings + + + align:start position:0% +formats and especially about the endings +of genre forms now what follows from the + + align:start position:0% +of genre forms now what follows from the + + + align:start position:0% +of genre forms now what follows from the +fact that you know that genre forms + + align:start position:0% +fact that you know that genre forms + + + align:start position:0% +fact that you know that genre forms +usually end happily and indeed that most + + align:start position:0% +usually end happily and indeed that most + + + align:start position:0% +usually end happily and indeed that most +H that most Hollywood movies leave aside + + align:start position:0% +H that most Hollywood movies leave aside + + + align:start position:0% +H that most Hollywood movies leave aside +the question of Comedy will end on a + + align:start position:0% +the question of Comedy will end on a + + + align:start position:0% +the question of Comedy will end on a +reassuring or a or a if not a happy at + + align:start position:0% +reassuring or a or a if not a happy at + + + align:start position:0% +reassuring or a or a if not a happy at +least a at least a reassuring or a + + align:start position:0% +least a at least a reassuring or a + + + align:start position:0% +least a at least a reassuring or a +positive note you you you simply know + + align:start position:0% +positive note you you you simply know + + + align:start position:0% +positive note you you you simply know +that going in even though it's that rule + + align:start position:0% +that going in even though it's that rule + + + align:start position:0% +that going in even though it's that rule +is sometimes violated it's not usually + + align:start position:0% +is sometimes violated it's not usually + + + align:start position:0% +is sometimes violated it's not usually +violated and when it's violated it's + + align:start position:0% +violated and when it's violated it's + + + align:start position:0% +violated and when it's violated it's +often violated in ways that are + + align:start position:0% +often violated in ways that are + + + align:start position:0% +often violated in ways that are +instructive and interesting but you have + + align:start position:0% +instructive and interesting but you have + + + align:start position:0% +instructive and interesting but you have +that expectation well the expectation + + align:start position:0% +that expectation well the expectation + + + align:start position:0% +that expectation well the expectation +that when you get into the story and uh + + align:start position:0% +that when you get into the story and uh + + + align:start position:0% +that when you get into the story and uh +the expectation you have as an audience + + align:start position:0% +the expectation you have as an audience + + + align:start position:0% +the expectation you have as an audience +member when you enter the the story + + align:start position:0% +member when you enter the the story + + + align:start position:0% +member when you enter the the story +knowing that you are going to come to a + + align:start position:0% +knowing that you are going to come to a + + + align:start position:0% +knowing that you are going to come to a +happy ending what does that do it's a + + align:start position:0% +happy ending what does that do it's a + + + align:start position:0% +happy ending what does that do it's a +form of reassurance before you start + + align:start position:0% +form of reassurance before you start + + + align:start position:0% +form of reassurance before you start +there are theorists of of folktales and + + align:start position:0% +there are theorists of of folktales and + + + align:start position:0% +there are theorists of of folktales and +fairy tales who argue that that that's + + align:start position:0% +fairy tales who argue that that that's + + + align:start position:0% +fairy tales who argue that that that's +one of the functions of fairy tales that + + align:start position:0% +one of the functions of fairy tales that + + + align:start position:0% +one of the functions of fairy tales that +when you when a folk tale or a fairy + + align:start position:0% +when you when a folk tale or a fairy + + + align:start position:0% +when you when a folk tale or a fairy +tale begins Once Upon a Time many many + + align:start position:0% +tale begins Once Upon a Time many many + + + align:start position:0% +tale begins Once Upon a Time many many +years ago in a land far away and and the + + align:start position:0% +years ago in a land far away and and the + + + align:start position:0% +years ago in a land far away and and the +story ends and they all lived happily + + align:start position:0% +story ends and they all lived happily + + + align:start position:0% +story ends and they all lived happily +ever after what are the those are + + align:start position:0% +ever after what are the those are + + + align:start position:0% +ever after what are the those are +ritualized or conventional beginnings + + align:start position:0% +ritualized or conventional beginnings + + + align:start position:0% +ritualized or conventional beginnings +and endings what do they contain they + + align:start position:0% +and endings what do they contain they + + + align:start position:0% +and endings what do they contain they +may contain Terror they may contain + + align:start position:0% +may contain Terror they may contain + + + align:start position:0% +may contain Terror they may contain +Little Red Riding Hood being raped or + + align:start position:0% +Little Red Riding Hood being raped or + + + align:start position:0% +Little Red Riding Hood being raped or +eaten or eaten alive right but it's okay + + align:start position:0% +eaten or eaten alive right but it's okay + + + align:start position:0% +eaten or eaten alive right but it's okay +in a certain sense because when you come + + align:start position:0% +in a certain sense because when you come + + + align:start position:0% +in a certain sense because when you come +to the ending you know that you'll be + + align:start position:0% +to the ending you know that you'll be + + + align:start position:0% +to the ending you know that you'll be +reassured at the so what because you + + align:start position:0% +reassured at the so what because you + + + align:start position:0% +reassured at the so what because you +know that the ending will reassure you + + align:start position:0% +know that the ending will reassure you + + + align:start position:0% +know that the ending will reassure you +it enables an exploration of stuff that + + align:start position:0% +it enables an exploration of stuff that + + + align:start position:0% +it enables an exploration of stuff that +would be scary and frightening there are + + align:start position:0% +would be scary and frightening there are + + + align:start position:0% +would be scary and frightening there are +child psychologists for example who say + + align:start position:0% +child psychologists for example who say + + + align:start position:0% +child psychologists for example who say +that one of the important aspects of + + align:start position:0% +that one of the important aspects of + + + align:start position:0% +that one of the important aspects of +Storytelling to Children is precisely + + align:start position:0% +Storytelling to Children is precisely + + + align:start position:0% +Storytelling to Children is precisely +this that that the ritualized + + align:start position:0% +this that that the ritualized + + + align:start position:0% +this that that the ritualized +reassurance of Once Upon a Time and they + + align:start position:0% +reassurance of Once Upon a Time and they + + + align:start position:0% +reassurance of Once Upon a Time and they +all lived happily ever after are + + align:start position:0% +all lived happily ever after are + + + align:start position:0% +all lived happily ever after are +enabling conditions that permit the + + align:start position:0% +enabling conditions that permit the + + + align:start position:0% +enabling conditions that permit the +exploration that permit the story to go + + align:start position:0% +exploration that permit the story to go + + + align:start position:0% +exploration that permit the story to go +into territories that would otherwise be + + align:start position:0% +into territories that would otherwise be + + + align:start position:0% +into territories that would otherwise be +frightening and terrifying what I'm + + align:start position:0% +frightening and terrifying what I'm + + + align:start position:0% +frightening and terrifying what I'm +suggesting to you is that that's a way + + align:start position:0% +suggesting to you is that that's a way + + + align:start position:0% +suggesting to you is that that's a way +of understanding adult entertainment as + + align:start position:0% +of understanding adult entertainment as + + + align:start position:0% +of understanding adult entertainment as +well and over and over again the + + align:start position:0% +well and over and over again the + + + align:start position:0% +well and over and over again the +Hollywood film will prove this principle + + align:start position:0% +Hollywood film will prove this principle + + + align:start position:0% +Hollywood film will prove this principle +out it will explore disturbing and + + align:start position:0% +out it will explore disturbing and + + + align:start position:0% +out it will explore disturbing and +frightening materials but in ways that + + align:start position:0% +frightening materials but in ways that + + + align:start position:0% +frightening materials but in ways that +are in some sense legitimated or + + align:start position:0% +are in some sense legitimated or + + + align:start position:0% +are in some sense legitimated or +permitted by the very fact that it + + align:start position:0% +permitted by the very fact that it + + + align:start position:0% +permitted by the very fact that it +belongs in an entertainment Space by the + + align:start position:0% +belongs in an entertainment Space by the + + + align:start position:0% +belongs in an entertainment Space by the +very fact that it marks itself as + + align:start position:0% +very fact that it marks itself as + + + align:start position:0% +very fact that it marks itself as +something that is a diversion a mere + + align:start position:0% +something that is a diversion a mere + + + align:start position:0% +something that is a diversion a mere +entertainment but I'd like to eliminate + + align:start position:0% +entertainment but I'd like to eliminate + + + align:start position:0% +entertainment but I'd like to eliminate +the word Mir because it's it's an + + align:start position:0% +the word Mir because it's it's an + + + align:start position:0% +the word Mir because it's it's an +inadequate and derogatory way of + + align:start position:0% +inadequate and derogatory way of + + + align:start position:0% +inadequate and derogatory way of +describing an experience that often can + + align:start position:0% +describing an experience that often can + + + align:start position:0% +describing an experience that often can +be among the most creative and valuable + + align:start position:0% +be among the most creative and valuable + + + align:start position:0% +be among the most creative and valuable +that people in a society can have right + + align:start position:0% +that people in a society can have right + + + align:start position:0% +that people in a society can have right +uh so uh one way then of crystallizing + + align:start position:0% +uh so uh one way then of crystallizing + + + align:start position:0% +uh so uh one way then of crystallizing +all of this is to say that the Hollywood + + align:start position:0% +all of this is to say that the Hollywood + + + align:start position:0% +all of this is to say that the Hollywood +film for me uh in the studio era + + align:start position:0% +film for me uh in the studio era + + + align:start position:0% +film for me uh in the studio era +especially represent s a particular form + + align:start position:0% +especially represent s a particular form + + + align:start position:0% +especially represent s a particular form +of what I would call consensus narrative + + align:start position:0% +of what I would call consensus narrative + + + align:start position:0% +of what I would call consensus narrative +what I mean by this term is something + + align:start position:0% +what I mean by this term is something + + + align:start position:0% +what I mean by this term is something +rather elaborate but I think very + + align:start position:0% +rather elaborate but I think very + + + align:start position:0% +rather elaborate but I think very +helpful what I mean by the term is this + + align:start position:0% +helpful what I mean by the term is this + + + align:start position:0% +helpful what I mean by the term is this +that in most societies perhaps not in + + align:start position:0% +that in most societies perhaps not in + + + align:start position:0% +that in most societies perhaps not in +all but in most societies all societies + + align:start position:0% +all but in most societies all societies + + + align:start position:0% +all but in most societies all societies +have many different sites of + + align:start position:0% +have many different sites of + + + align:start position:0% +have many different sites of +Storytelling right uh people tell jokes + + align:start position:0% +Storytelling right uh people tell jokes + + + align:start position:0% +Storytelling right uh people tell jokes +to each other we go to the Opera we + + align:start position:0% +to each other we go to the Opera we + + + align:start position:0% +to each other we go to the Opera we +watch uh we we play video games that are + + align:start position:0% +watch uh we we play video games that are + + + align:start position:0% +watch uh we we play video games that are +deep forms of narrative today right + + align:start position:0% +deep forms of narrative today right + + + align:start position:0% +deep forms of narrative today right +that's the coming probably the new form + + align:start position:0% +that's the coming probably the new form + + + align:start position:0% +that's the coming probably the new form +of narrative that's emerging in our + + align:start position:0% +of narrative that's emerging in our + + + align:start position:0% +of narrative that's emerging in our +society today our video games uh um we + + align:start position:0% +society today our video games uh um we + + + align:start position:0% +society today our video games uh um we +we we we we we hear stories in theaters + + align:start position:0% +we we we we we hear stories in theaters + + + align:start position:0% +we we we we we hear stories in theaters +we can hear stories in popular songs we + + align:start position:0% +we can hear stories in popular songs we + + + align:start position:0% +we can hear stories in popular songs we +read stories in novels right in other + + align:start position:0% +read stories in novels right in other + + + align:start position:0% +read stories in novels right in other +words there there are stories all over + + align:start position:0% +words there there are stories all over + + + align:start position:0% +words there there are stories all over +the and in fact we get non-fictional + + align:start position:0% +the and in fact we get non-fictional + + + align:start position:0% +the and in fact we get non-fictional +stories out of our newspapers and from + + align:start position:0% +stories out of our newspapers and from + + + align:start position:0% +stories out of our newspapers and from +our politicians these are usually even + + align:start position:0% +our politicians these are usually even + + + align:start position:0% +our politicians these are usually even +more outlandish ridiculous and false + + align:start position:0% +more outlandish ridiculous and false + + + align:start position:0% +more outlandish ridiculous and false +than the fictional stories that were fed + + align:start position:0% +than the fictional stories that were fed + + + align:start position:0% +than the fictional stories that were fed +although we often don't recognize that + + align:start position:0% +although we often don't recognize that + + + align:start position:0% +although we often don't recognize that +right um uh so we live we live in a sea + + align:start position:0% +right um uh so we live we live in a sea + + + align:start position:0% +right um uh so we live we live in a sea +in an ocean of narratives right all + + align:start position:0% +in an ocean of narratives right all + + + align:start position:0% +in an ocean of narratives right all +societies have many different sites of + + align:start position:0% +societies have many different sites of + + + align:start position:0% +societies have many different sites of +it but in MO in many societies if not + + align:start position:0% +it but in MO in many societies if not + + + align:start position:0% +it but in MO in many societies if not +all they're usually is a single sight + + align:start position:0% +all they're usually is a single sight + + + align:start position:0% +all they're usually is a single sight +that + + align:start position:0% +that + + + align:start position:0% +that +by General acceptance or consent is + + align:start position:0% +by General acceptance or consent is + + + align:start position:0% +by General acceptance or consent is +recognized as the space in which the + + align:start position:0% +recognized as the space in which the + + + align:start position:0% +recognized as the space in which the +stories that are being told are intended + + align:start position:0% +stories that are being told are intended + + + align:start position:0% +stories that are being told are intended +for everyone right the difference + + align:start position:0% +for everyone right the difference + + + align:start position:0% +for everyone right the difference +between what goes on in a wrestling + + align:start position:0% +between what goes on in a wrestling + + + align:start position:0% +between what goes on in a wrestling +match or in a baseball game also forms + + align:start position:0% +match or in a baseball game also forms + + + align:start position:0% +match or in a baseball game also forms +of narrative in a way or in a in an + + align:start position:0% +of narrative in a way or in a in an + + + align:start position:0% +of narrative in a way or in a in an +opera or in a theatrical piece and a + + align:start position:0% +opera or in a theatrical piece and a + + + align:start position:0% +opera or in a theatrical piece and a +movie of the Hollywood era or a + + align:start position:0% +movie of the Hollywood era or a + + + align:start position:0% +movie of the Hollywood era or a +television program in the Great era of + + align:start position:0% +television program in the Great era of + + + align:start position:0% +television program in the Great era of +Television before say 2000 when the new + + align:start position:0% +Television before say 2000 when the new + + + align:start position:0% +Television before say 2000 when the new +when new systems so atomized and divided + + align:start position:0% +when new systems so atomized and divided + + + align:start position:0% +when new systems so atomized and divided +the television system that it began to + + align:start position:0% +the television system that it began to + + + align:start position:0% +the television system that it began to +it began to imitate what happened to its + + align:start position:0% +it began to imitate what happened to its + + + align:start position:0% +it began to imitate what happened to its +ancestors the films a generation earlier + + align:start position:0% +ancestors the films a generation earlier + + + align:start position:0% +ancestors the films a generation earlier +they say to U lose losing its hold on + + align:start position:0% +they say to U lose losing its hold on + + + align:start position:0% +they say to U lose losing its hold on +the majority of the population the idea + + align:start position:0% +the majority of the population the idea + + + align:start position:0% +the majority of the population the idea +is then that the idea of a consensus + + align:start position:0% +is then that the idea of a consensus + + + align:start position:0% +is then that the idea of a consensus +story is the story it's the story form + + align:start position:0% +story is the story it's the story form + + + align:start position:0% +story is the story it's the story form +or the story system that the culture + + align:start position:0% +or the story system that the culture + + + align:start position:0% +or the story system that the culture +recognizes as the one that reaches the + + align:start position:0% +recognizes as the one that reaches the + + + align:start position:0% +recognizes as the one that reaches the +largest number of people and that by + + align:start position:0% +largest number of people and that by + + + align:start position:0% +largest number of people and that by +Common agreement or consent not by law + + align:start position:0% +Common agreement or consent not by law + + + align:start position:0% +Common agreement or consent not by law +but by something much richer and larger + + align:start position:0% +but by something much richer and larger + + + align:start position:0% +but by something much richer and larger +than that by a kind of communal + + align:start position:0% +than that by a kind of communal + + + align:start position:0% +than that by a kind of communal +agreement this space is recognized as + + align:start position:0% +agreement this space is recognized as + + + align:start position:0% +agreement this space is recognized as +the place in which the stories that are + + align:start position:0% +the place in which the stories that are + + + align:start position:0% +the place in which the stories that are +told are meant to appeal to the largest + + align:start position:0% +told are meant to appeal to the largest + + + align:start position:0% +told are meant to appeal to the largest +number of people cutting across social + + align:start position:0% +number of people cutting across social + + + align:start position:0% +number of people cutting across social +class cutting across age and gender + + align:start position:0% +class cutting across age and gender + + + align:start position:0% +class cutting across age and gender +differences cutting across ethnic + + align:start position:0% +differences cutting across ethnic + + + align:start position:0% +differences cutting across ethnic +differences virtually all societies have + + align:start position:0% +differences virtually all societies have + + + align:start position:0% +differences virtually all societies have +some space in which some story system of + + align:start position:0% +some space in which some story system of + + + align:start position:0% +some space in which some story system of +one kind or another that wants to appeal + + align:start position:0% +one kind or another that wants to appeal + + + align:start position:0% +one kind or another that wants to appeal +to virtually everyone exists now it it's + + align:start position:0% +to virtually everyone exists now it it's + + + align:start position:0% +to virtually everyone exists now it it's +important to understand that I don't + + align:start position:0% +important to understand that I don't + + + align:start position:0% +important to understand that I don't +mean it's a real consensus an authentic + + align:start position:0% +mean it's a real consensus an authentic + + + align:start position:0% +mean it's a real consensus an authentic +one that is to say I don't mean that the + + align:start position:0% +one that is to say I don't mean that the + + + align:start position:0% +one that is to say I don't mean that the +stories that are told there really + + align:start position:0% +stories that are told there really + + + align:start position:0% +stories that are told there really +embody the values universally of + + align:start position:0% +embody the values universally of + + + align:start position:0% +embody the values universally of +everyone in the society not at all + + align:start position:0% +everyone in the society not at all + + + align:start position:0% +everyone in the society not at all +because these societies are limited in + + align:start position:0% +because these societies are limited in + + + align:start position:0% +because these societies are limited in +certain ways they have exclusions they + + align:start position:0% +certain ways they have exclusions they + + + align:start position:0% +certain ways they have exclusions they +have cast structures and so on so the + + align:start position:0% +have cast structures and so on so the + + + align:start position:0% +have cast structures and so on so the +consensus narrative in 1920 was a + + align:start position:0% +consensus narrative in 1920 was a + + + align:start position:0% +consensus narrative in 1920 was a +consensus narrative that that sort of + + align:start position:0% +consensus narrative that that sort of + + + align:start position:0% +consensus narrative that that sort of +Saw African-Americans as second-class + + align:start position:0% +Saw African-Americans as second-class + + + align:start position:0% +Saw African-Americans as second-class +Citizens right there was a lot of + + align:start position:0% +Citizens right there was a lot of + + + align:start position:0% +Citizens right there was a lot of +prejudice then certainly was a + + align:start position:0% +prejudice then certainly was a + + + align:start position:0% +prejudice then certainly was a +patriarchal consensus which assumed that + + align:start position:0% +patriarchal consensus which assumed that + + + align:start position:0% +patriarchal consensus which assumed that +women belonged in the home and so forth + + align:start position:0% +women belonged in the home and so forth + + + align:start position:0% +women belonged in the home and so forth +I don't mean that the consensus is + + align:start position:0% +I don't mean that the consensus is + + + align:start position:0% +I don't mean that the consensus is +universally embraced by everyone what I + + align:start position:0% +universally embraced by everyone what I + + + align:start position:0% +universally embraced by everyone what I +do mean though is that everyone in the + + align:start position:0% +do mean though is that everyone in the + + + align:start position:0% +do mean though is that everyone in the +society recognizes that this is the + + align:start position:0% +society recognizes that this is the + + + align:start position:0% +society recognizes that this is the +consensus and even the people who + + align:start position:0% +consensus and even the people who + + + align:start position:0% +consensus and even the people who +descend from it recognize that this is + + align:start position:0% +descend from it recognize that this is + + + align:start position:0% +descend from it recognize that this is +the space in which the central values of + + align:start position:0% +the space in which the central values of + + + align:start position:0% +the space in which the central values of +the society are articulated dramatized + + align:start position:0% +the society are articulated dramatized + + + align:start position:0% +the society are articulated dramatized +and and diffused and what makes this + + align:start position:0% +and and diffused and what makes this + + + align:start position:0% +and and diffused and what makes this +space these spaces so that another + + align:start position:0% +space these spaces so that another + + + align:start position:0% +space these spaces so that another +example I mentioned one earlier in + + align:start position:0% +example I mentioned one earlier in + + + align:start position:0% +example I mentioned one earlier in +Shakespeare's day the public theater of + + align:start position:0% +Shakespeare's day the public theater of + + + align:start position:0% +Shakespeare's day the public theater of +Shakespeare's time was the equivalent of + + align:start position:0% +Shakespeare's time was the equivalent of + + + align:start position:0% +Shakespeare's time was the equivalent of +what I'm saying Hollywood was in the + + align:start position:0% +what I'm saying Hollywood was in the + + + align:start position:0% +what I'm saying Hollywood was in the +studio era uh in the Middle Ages it + + align:start position:0% +studio era uh in the Middle Ages it + + + align:start position:0% +studio era uh in the Middle Ages it +would be the Bible right this the + + align:start position:0% +would be the Bible right this the + + + align:start position:0% +would be the Bible right this the +central story promulgated through all + + align:start position:0% +central story promulgated through all + + + align:start position:0% +central story promulgated through all +the through virtually everyone in the + + align:start position:0% +the through virtually everyone in the + + + align:start position:0% +the through virtually everyone in the +society had not only had access to the + + align:start position:0% +society had not only had access to the + + + align:start position:0% +society had not only had access to the +Bible but when they went to church they + + align:start position:0% +Bible but when they went to church they + + + align:start position:0% +Bible but when they went to church they +received further uh discussion and in + + align:start position:0% +received further uh discussion and in + + + align:start position:0% +received further uh discussion and in +and and and elaborate propaganda about + + align:start position:0% +and and and elaborate propaganda about + + + align:start position:0% +and and and elaborate propaganda about +how important Central the Bible was to + + align:start position:0% +how important Central the Bible was to + + + align:start position:0% +how important Central the Bible was to +their life so the consensus narrative + + align:start position:0% +their life so the consensus narrative + + + align:start position:0% +their life so the consensus narrative +system was the one the church sustained + + align:start position:0% +system was the one the church sustained + + + align:start position:0% +system was the one the church sustained +in the Middle Ages right in fact one of + + align:start position:0% +in the Middle Ages right in fact one of + + + align:start position:0% +in the Middle Ages right in fact one of +the interesting things is to watch in + + align:start position:0% +the interesting things is to watch in + + + align:start position:0% +the interesting things is to watch in +Western culture the way in which the + + align:start position:0% +Western culture the way in which the + + + align:start position:0% +Western culture the way in which the +consensus story becomes more and more + + align:start position:0% +consensus story becomes more and more + + + align:start position:0% +consensus story becomes more and more +secularized uh and in in some more and + + align:start position:0% +secularized uh and in in some more and + + + align:start position:0% +secularized uh and in in some more and +not not only secularized not only freed + + align:start position:0% +not not only secularized not only freed + + + align:start position:0% +not not only secularized not only freed +from religious dispensations but also + + align:start position:0% +from religious dispensations but also + + + align:start position:0% +from religious dispensations but also +freed in some sense in many societies + + align:start position:0% +freed in some sense in many societies + + + align:start position:0% +freed in some sense in many societies +from government control right now so so + + align:start position:0% +from government control right now so so + + + align:start position:0% +from government control right now so so +in some societies there is no such + + align:start position:0% +in some societies there is no such + + + align:start position:0% +in some societies there is no such +Freedom so for example the consensus + + align:start position:0% +Freedom so for example the consensus + + + align:start position:0% +Freedom so for example the consensus +narrative in the Soviet Union was the + + align:start position:0% +narrative in the Soviet Union was the + + + align:start position:0% +narrative in the Soviet Union was the +story that was approved by the + + align:start position:0% +story that was approved by the + + + align:start position:0% +story that was approved by the +government it was and in fact probably + + align:start position:0% +government it was and in fact probably + + + align:start position:0% +government it was and in fact probably +the majority of the population descended + + align:start position:0% +the majority of the population descended + + + align:start position:0% +the majority of the population descended +from that consensus right so the + + align:start position:0% +from that consensus right so the + + + align:start position:0% +from that consensus right so the +consensus I'm talking about is always a + + align:start position:0% +consensus I'm talking about is always a + + + align:start position:0% +consensus I'm talking about is always a +constructed one right but uh that + + align:start position:0% +constructed one right but uh that + + + align:start position:0% +constructed one right but uh that +construction is still interesting and + + align:start position:0% +construction is still interesting and + + + align:start position:0% +construction is still interesting and +this is one of the examp one of the + + align:start position:0% +this is one of the examp one of the + + + align:start position:0% +this is one of the examp one of the +reasons for example that today uh people + + align:start position:0% +reasons for example that today uh people + + + align:start position:0% +reasons for example that today uh people +will still scream bloody murder if they + + align:start position:0% +will still scream bloody murder if they + + + align:start position:0% +will still scream bloody murder if they +see that that that on television the + + align:start position:0% +see that that that on television the + + + align:start position:0% +see that that that on television the +representation of minorities or women is + + align:start position:0% +representation of minorities or women is + + + align:start position:0% +representation of minorities or women is +prejudicial but they you don't see + + align:start position:0% +prejudicial but they you don't see + + + align:start position:0% +prejudicial but they you don't see +anybody complaining about the fact that + + align:start position:0% +anybody complaining about the fact that + + + align:start position:0% +anybody complaining about the fact that +there are uh such representations in + + align:start position:0% +there are uh such representations in + + + align:start position:0% +there are uh such representations in +books or in theater any longer and the + + align:start position:0% +books or in theater any longer and the + + + align:start position:0% +books or in theater any longer and the +reason for that is that it's the + + align:start position:0% +reason for that is that it's the + + + align:start position:0% +reason for that is that it's the +consensus system that matters to people + + align:start position:0% +consensus system that matters to people + + + align:start position:0% +consensus system that matters to people +it's the con it's the consensus space in + + align:start position:0% +it's the con it's the consensus space in + + + align:start position:0% +it's the con it's the consensus space in +which it is assumed the values of the + + align:start position:0% +which it is assumed the values of the + + + align:start position:0% +which it is assumed the values of the +society can be challenged or discussed + + align:start position:0% +society can be challenged or discussed + + + align:start position:0% +society can be challenged or discussed +okay so uh what I want to suggest then + + align:start position:0% +okay so uh what I want to suggest then + + + align:start position:0% +okay so uh what I want to suggest then +is that what that that we might think so + + align:start position:0% +is that what that that we might think so + + + align:start position:0% +is that what that that we might think so +we can think of the Hollywood film then + + align:start position:0% +we can think of the Hollywood film then + + + align:start position:0% +we can think of the Hollywood film then +all Hollywood movies as belonging as + + align:start position:0% +all Hollywood movies as belonging as + + + align:start position:0% +all Hollywood movies as belonging as +taking as as participating in the + + align:start position:0% +taking as as participating in the + + + align:start position:0% +taking as as participating in the +creation of what we can call call the + + align:start position:0% +creation of what we can call call the + + + align:start position:0% +creation of what we can call call the +consensus Story the most widely shared + + align:start position:0% +consensus Story the most widely shared + + + align:start position:0% +consensus Story the most widely shared +story about American society and it has + + align:start position:0% +story about American society and it has + + + align:start position:0% +story about American society and it has +many sides right part of the story has + + align:start position:0% +many sides right part of the story has + + + align:start position:0% +many sides right part of the story has +to do with how you define masculinity + + align:start position:0% +to do with how you define masculinity + + + align:start position:0% +to do with how you define masculinity +right and some of that burden is carried + + align:start position:0% +right and some of that burden is carried + + + align:start position:0% +right and some of that burden is carried +in every film but there are certain + + align:start position:0% +in every film but there are certain + + + align:start position:0% +in every film but there are certain +movies like war movies or westerns in + + align:start position:0% +movies like war movies or westerns in + + + align:start position:0% +movies like war movies or westerns in +which masculinity tough guess is the + + align:start position:0% +which masculinity tough guess is the + + + align:start position:0% +which masculinity tough guess is the +main main issue and then there are some + + align:start position:0% +main main issue and then there are some + + + align:start position:0% +main main issue and then there are some +then we could say the Norms about family + + align:start position:0% +then we could say the Norms about family + + + align:start position:0% +then we could say the Norms about family +life where do they come in well in more + + align:start position:0% +life where do they come in well in more + + + align:start position:0% +life where do they come in well in more +often in comedies and in melodramas that + + align:start position:0% +often in comedies and in melodramas that + + + align:start position:0% +often in comedies and in melodramas that +focus on families right in other words + + align:start position:0% +focus on families right in other words + + + align:start position:0% +focus on families right in other words +different parts of the consensus are + + align:start position:0% +different parts of the consensus are + + + align:start position:0% +different parts of the consensus are +dramatized more fully in different + + align:start position:0% +dramatized more fully in different + + + align:start position:0% +dramatized more fully in different +genres but all the films together can be + + align:start position:0% +genres but all the films together can be + + + align:start position:0% +genres but all the films together can be +said broadly to participate in a process + + align:start position:0% +said broadly to participate in a process + + + align:start position:0% +said broadly to participate in a process +whereby the central values and + + align:start position:0% +whereby the central values and + + + align:start position:0% +whereby the central values and +assumptions of the society are rehearsed + + align:start position:0% +assumptions of the society are rehearsed + + + align:start position:0% +assumptions of the society are rehearsed +and repeated and tested the central fact + + align:start position:0% +and repeated and tested the central fact + + + align:start position:0% +and repeated and tested the central fact +about this process is that it's never + + align:start position:0% +about this process is that it's never + + + align:start position:0% +about this process is that it's never +finished just like culture itself + + align:start position:0% +finished just like culture itself + + + align:start position:0% +finished just like culture itself +culture is never a fixed finished thing + + align:start position:0% +culture is never a fixed finished thing + + + align:start position:0% +culture is never a fixed finished thing +this is one of the deep insights of + + align:start position:0% +this is one of the deep insights of + + + align:start position:0% +this is one of the deep insights of +modern U sociology and anth anology I + + align:start position:0% +modern U sociology and anth anology I + + + align:start position:0% +modern U sociology and anth anology I +attribute it primar specifically to the + + align:start position:0% +attribute it primar specifically to the + + + align:start position:0% +attribute it primar specifically to the +great English sociologist and and and + + align:start position:0% +great English sociologist and and and + + + align:start position:0% +great English sociologist and and and +and uh historian Raymond Williams from + + align:start position:0% +and uh historian Raymond Williams from + + + align:start position:0% +and uh historian Raymond Williams from +whom I'm borrowing the I the the some of + + align:start position:0% +whom I'm borrowing the I the the some of + + + align:start position:0% +whom I'm borrowing the I the the some of +the ideas on although the word consensus + + align:start position:0% +the ideas on although the word consensus + + + align:start position:0% +the ideas on although the word consensus +narrative is is mine not his many of + + align:start position:0% +narrative is is mine not his many of + + + align:start position:0% +narrative is is mine not his many of +these ideas are drawn from Raymond + + align:start position:0% +these ideas are drawn from Raymond + + + align:start position:0% +these ideas are drawn from Raymond +Williams account of culture what he says + + align:start position:0% +Williams account of culture what he says + + + align:start position:0% +Williams account of culture what he says +is essentially that culture is + + align:start position:0% +is essentially that culture is + + + align:start position:0% +is essentially that culture is +constantly making and remaking itself + + align:start position:0% +constantly making and remaking itself + + + align:start position:0% +constantly making and remaking itself +that every time you watch this and think + + align:start position:0% +that every time you watch this and think + + + align:start position:0% +that every time you watch this and think +about some of you can see this example + + align:start position:0% +about some of you can see this example + + + align:start position:0% +about some of you can see this example +more fully with television than with + + align:start position:0% +more fully with television than with + + + align:start position:0% +more fully with television than with +movies movies remember the argument of + + align:start position:0% +movies movies remember the argument of + + + align:start position:0% +movies movies remember the argument of +the course is that at a certain point + + align:start position:0% +the course is that at a certain point + + + align:start position:0% +the course is that at a certain point +sometime in the 1950s or early 60s + + align:start position:0% +sometime in the 1950s or early 60s + + + align:start position:0% +sometime in the 1950s or early 60s +television supplanted the movies as the + + align:start position:0% +television supplanted the movies as the + + + align:start position:0% +television supplanted the movies as the +central form of narrative in the + + align:start position:0% +central form of narrative in the + + + align:start position:0% +central form of narrative in the +American society took over the job of + + align:start position:0% +American society took over the job of + + + align:start position:0% +American society took over the job of +being the consensus the purveyor of the + + align:start position:0% +being the consensus the purveyor of the + + + align:start position:0% +being the consensus the purveyor of the +consensus the purveyor of the culture's + + align:start position:0% +consensus the purveyor of the culture's + + + align:start position:0% +consensus the purveyor of the culture's +central values and in many ways that was + + align:start position:0% +central values and in many ways that was + + + align:start position:0% +central values and in many ways that was +a liberating moment for the movies our + + align:start position:0% +a liberating moment for the movies our + + + align:start position:0% +a liberating moment for the movies our +course dramatizes that this week we're + + align:start position:0% +course dramatizes that this week we're + + + align:start position:0% +course dramatizes that this week we're +looking at two screw ball comedies from + + align:start position:0% +looking at two screw ball comedies from + + + align:start position:0% +looking at two screw ball comedies from +inside the studio era Hereafter when we + + align:start position:0% +inside the studio era Hereafter when we + + + align:start position:0% +inside the studio era Hereafter when we +juxtapose two films one will be from the + + align:start position:0% +juxtapose two films one will be from the + + + align:start position:0% +juxtapose two films one will be from the +studio era one will be from the era + + align:start position:0% +studio era one will be from the era + + + align:start position:0% +studio era one will be from the era +after the movies no longer carry the + + align:start position:0% +after the movies no longer carry the + + + align:start position:0% +after the movies no longer carry the +consensus the responsibility to be the + + align:start position:0% +consensus the responsibility to be the + + + align:start position:0% +consensus the responsibility to be the +consensus medium right that's been taken + + align:start position:0% +consensus medium right that's been taken + + + align:start position:0% +consensus medium right that's been taken +over by TV and the differences are + + align:start position:0% +over by TV and the differences are + + + align:start position:0% +over by TV and the differences are +dramatic the differences are Stark and + + align:start position:0% +dramatic the differences are Stark and + + + align:start position:0% +dramatic the differences are Stark and +exciting both forms are interesting the + + align:start position:0% +exciting both forms are interesting the + + + align:start position:0% +exciting both forms are interesting the +postc consensus forms have great claims + + align:start position:0% +postc consensus forms have great claims + + + align:start position:0% +postc consensus forms have great claims +on us because they're much Freer they're + + align:start position:0% +on us because they're much Freer they're + + + align:start position:0% +on us because they're much Freer they're +not they're not limited or constrained + + align:start position:0% +not they're not limited or constrained + + + align:start position:0% +not they're not limited or constrained +by by what we might call the central + + align:start position:0% +by by what we might call the central + + + align:start position:0% +by by what we might call the central +pieties of the culture the most obvious + + align:start position:0% +pieties of the culture the most obvious + + + align:start position:0% +pieties of the culture the most obvious +way you could see this in is in nudity + + align:start position:0% +way you could see this in is in nudity + + + align:start position:0% +way you could see this in is in nudity +right you they can sh uh attitudes and + + align:start position:0% +right you they can sh uh attitudes and + + + align:start position:0% +right you they can sh uh attitudes and +dirty language right think about you can + + align:start position:0% +dirty language right think about you can + + + align:start position:0% +dirty language right think about you can +see this the stupidity and the + + align:start position:0% +see this the stupidity and the + + + align:start position:0% +see this the stupidity and the +arbitrariness of these systems if you + + align:start position:0% +arbitrariness of these systems if you + + + align:start position:0% +arbitrariness of these systems if you +think about how television works today + + align:start position:0% +think about how television works today + + + align:start position:0% +think about how television works today +if you put on an American Network show + + align:start position:0% +if you put on an American Network show + + + align:start position:0% +if you put on an American Network show +even a late night show by 10 11 o'clock + + align:start position:0% +even a late night show by 10 11 o'clock + + + align:start position:0% +even a late night show by 10 11 o'clock +at 9 or 10 at night uh what you will get + + align:start position:0% +at 9 or 10 at night uh what you will get + + + align:start position:0% +at 9 or 10 at night uh what you will get +on those shows you might get things very + + align:start position:0% +on those shows you might get things very + + + align:start position:0% +on those shows you might get things very +different from what you would have + + align:start position:0% +different from what you would have + + + align:start position:0% +different from what you would have +gotten 10 or 15 years ago but you still + + align:start position:0% +gotten 10 or 15 years ago but you still + + + align:start position:0% +gotten 10 or 15 years ago but you still +won't get full frontal nudity you won't + + align:start position:0% +won't get full frontal nudity you won't + + + align:start position:0% +won't get full frontal nudity you won't +get women taking off their their clothes + + align:start position:0% +get women taking off their their clothes + + + align:start position:0% +get women taking off their their clothes +you won't you won't see sexual activity + + align:start position:0% +you won't you won't see sexual activity + + + align:start position:0% +you won't you won't see sexual activity +you won't you won't see very much dirty + + align:start position:0% +you won't you won't see very much dirty + + + align:start position:0% +you won't you won't see very much dirty +language very used to see none of it now + + align:start position:0% +language very used to see none of it now + + + align:start position:0% +language very used to see none of it now +but but but if you if you click the + + align:start position:0% +but but but if you if you click the + + + align:start position:0% +but but but if you if you click the +channel one over and you go to HBO you + + align:start position:0% +channel one over and you go to HBO you + + + align:start position:0% +channel one over and you go to HBO you +can see the most disgraceful pornography + + align:start position:0% +can see the most disgraceful pornography + + + align:start position:0% +can see the most disgraceful pornography +that you could ever imagine right and + + align:start position:0% +that you could ever imagine right and + + + align:start position:0% +that you could ever imagine right and +you can hear people using the fword so + + align:start position:0% +you can hear people using the fword so + + + align:start position:0% +you can hear people using the fword so +often that it that that it that it runs + + align:start position:0% +often that it that that it that it runs + + + align:start position:0% +often that it that that it that it runs +out of your ears right now and it's + + align:start position:0% +out of your ears right now and it's + + + align:start position:0% +out of your ears right now and it's +they're right next to each other on the + + align:start position:0% +they're right next to each other on the + + + align:start position:0% +they're right next to each other on the +dial explains the difference HBO doesn't + + align:start position:0% +dial explains the difference HBO doesn't + + + align:start position:0% +dial explains the difference HBO doesn't +belong to the consensus system the + + align:start position:0% +belong to the consensus system the + + + align:start position:0% +belong to the consensus system the +networks are still a vestigal survival + + align:start position:0% +networks are still a vestigal survival + + + align:start position:0% +networks are still a vestigal survival +of the old consensus system and if you + + align:start position:0% +of the old consensus system and if you + + + align:start position:0% +of the old consensus system and if you +think about the difference between + + align:start position:0% +think about the difference between + + + align:start position:0% +think about the difference between +Network television even today and the + + align:start position:0% +Network television even today and the + + + align:start position:0% +Network television even today and the +movies or network television and what's + + align:start position:0% +movies or network television and what's + + + align:start position:0% +movies or network television and what's +on HBO or Showtime you'll see this + + align:start position:0% +on HBO or Showtime you'll see this + + + align:start position:0% +on HBO or Showtime you'll see this +distinction with great clarity right so + + align:start position:0% +distinction with great clarity right so + + + align:start position:0% +distinction with great clarity right so +so um one of the things that this means + + align:start position:0% +so um one of the things that this means + + + align:start position:0% +so um one of the things that this means +is that these systems of consensus + + align:start position:0% +is that these systems of consensus + + + align:start position:0% +is that these systems of consensus +narrative have a tremendous claim on our + + align:start position:0% +narrative have a tremendous claim on our + + + align:start position:0% +narrative have a tremendous claim on our +attention they they more important in + + align:start position:0% +attention they they more important in + + + align:start position:0% +attention they they more important in +some sense in a sociological or + + align:start position:0% +some sense in a sociological or + + + align:start position:0% +some sense in a sociological or +anthropological sense than other forms + + align:start position:0% +anthropological sense than other forms + + + align:start position:0% +anthropological sense than other forms +that don't bear the burden of having to + + align:start position:0% +that don't bear the burden of having to + + + align:start position:0% +that don't bear the burden of having to +tell the story the consensus story of + + align:start position:0% +tell the story the consensus story of + + + align:start position:0% +tell the story the consensus story of +the society and remember I said it's un + + align:start position:0% +the society and remember I said it's un + + + align:start position:0% +the society and remember I said it's un +cultures unfinished so are these stories + + align:start position:0% +cultures unfinished so are these stories + + + align:start position:0% +cultures unfinished so are these stories +right the great thing about them is that + + align:start position:0% +right the great thing about them is that + + + align:start position:0% +right the great thing about them is that +they change right that over time they'll + + align:start position:0% +they change right that over time they'll + + + align:start position:0% +they change right that over time they'll +alter I'll come back to this question + + align:start position:0% +alter I'll come back to this question + + + align:start position:0% +alter I'll come back to this question +next time when we talk about the Western + + align:start position:0% +next time when we talk about the Western + + + align:start position:0% +next time when we talk about the Western +we talk about how the Western Alters + + align:start position:0% +we talk about how the Western Alters + + + align:start position:0% +we talk about how the Western Alters +over time in ways that are tremendously + + align:start position:0% +over time in ways that are tremendously + + + align:start position:0% +over time in ways that are tremendously +responsive to problems in the outer + + align:start position:0% +responsive to problems in the outer + + + align:start position:0% +responsive to problems in the outer +societ Society a very clear example of + + align:start position:0% +societ Society a very clear example of + + + align:start position:0% +societ Society a very clear example of +the way in which genre constraints can + + align:start position:0% +the way in which genre constraints can + + + align:start position:0% +the way in which genre constraints can +enable an exploration of serious + + align:start position:0% +enable an exploration of serious + + + align:start position:0% +enable an exploration of serious +subjects and we'll so we'll return to + + align:start position:0% +subjects and we'll so we'll return to + + + align:start position:0% +subjects and we'll so we'll return to +that next time for for our purposes + + align:start position:0% +that next time for for our purposes + + + align:start position:0% +that next time for for our purposes +tonight the primary point is this what + + align:start position:0% +tonight the primary point is this what + + + align:start position:0% +tonight the primary point is this what +the advantage of these consensus one of + + align:start position:0% +the advantage of these consensus one of + + + align:start position:0% +the advantage of these consensus one of +the advantage of these consensus systems + + align:start position:0% +the advantage of these consensus systems + + + align:start position:0% +the advantage of these consensus systems +uh is that they can reveal a great deal + + align:start position:0% +uh is that they can reveal a great deal + + + align:start position:0% +uh is that they can reveal a great deal +to us about the societies they serve + + align:start position:0% +to us about the societies they serve + + + align:start position:0% +to us about the societies they serve +there we can say in a certain sense that + + align:start position:0% +there we can say in a certain sense that + + + align:start position:0% +there we can say in a certain sense that +the work or the job the anthrop ological + + align:start position:0% +the work or the job the anthrop ological + + + align:start position:0% +the work or the job the anthrop ological +function of these consensus systems is + + align:start position:0% +function of these consensus systems is + + + align:start position:0% +function of these consensus systems is +to help the society figure out what it + + align:start position:0% +to help the society figure out what it + + + align:start position:0% +to help the society figure out what it +is uh so that one of the things that + + align:start position:0% +is uh so that one of the things that + + + align:start position:0% +is uh so that one of the things that +happens in these stories is that and + + align:start position:0% +happens in these stories is that and + + + align:start position:0% +happens in these stories is that and +here I'm barring directly on Raymond + + align:start position:0% +here I'm barring directly on Raymond + + + align:start position:0% +here I'm barring directly on Raymond +Williams we can think of it as a + + align:start position:0% +Williams we can think of it as a + + + align:start position:0% +Williams we can think of it as a +consensus narrative as a discourse space + + align:start position:0% +consensus narrative as a discourse space + + + align:start position:0% +consensus narrative as a discourse space +as a space for conversation right with + + align:start position:0% +as a space for conversation right with + + + align:start position:0% +as a space for conversation right with +thinking of also remembering that each + + align:start position:0% +thinking of also remembering that each + + + align:start position:0% +thinking of also remembering that each +genre in one way or another could be + + align:start position:0% +genre in one way or another could be + + + align:start position:0% +genre in one way or another could be +thought to carry some subcategory or + + align:start position:0% +thought to carry some subcategory or + + + align:start position:0% +thought to carry some subcategory or +some or some or some subelement of the + + align:start position:0% +some or some or some subelement of the + + + align:start position:0% +some or some or some subelement of the +larger consensus so masculine and + + align:start position:0% +larger consensus so masculine and + + + align:start position:0% +larger consensus so masculine and +Warrior behavior and certain forms of + + align:start position:0% +Warrior behavior and certain forms of + + + align:start position:0% +Warrior behavior and certain forms of +honor and courage are dramatized in war + + align:start position:0% +honor and courage are dramatized in war + + + align:start position:0% +honor and courage are dramatized in war +movies and westerns but certain aspects + + align:start position:0% +movies and westerns but certain aspects + + + align:start position:0% +movies and westerns but certain aspects +of of uh family life and of the relation + + align:start position:0% +of of uh family life and of the relation + + + align:start position:0% +of of uh family life and of the relation +between siblings and of the relationship + + align:start position:0% +between siblings and of the relationship + + + align:start position:0% +between siblings and of the relationship +between parents and children are + + align:start position:0% +between parents and children are + + + align:start position:0% +between parents and children are +dramatized in forms of melodrama and + + align:start position:0% +dramatized in forms of melodrama and + + + align:start position:0% +dramatized in forms of melodrama and +comedy right and uh and uh uh uh uh + + align:start position:0% +comedy right and uh and uh uh uh uh + + + align:start position:0% +comedy right and uh and uh uh uh uh +detective stories uh uh sometimes uh + + align:start position:0% +detective stories uh uh sometimes uh + + + align:start position:0% +detective stories uh uh sometimes uh +explore the social and political + + align:start position:0% +explore the social and political + + + align:start position:0% +explore the social and political +implications of particular societies + + align:start position:0% +implications of particular societies + + + align:start position:0% +implications of particular societies +more systematically and fully than other + + align:start position:0% +more systematically and fully than other + + + align:start position:0% +more systematically and fully than other +forms right but so take it all together + + align:start position:0% +forms right but so take it all together + + + align:start position:0% +forms right but so take it all together +the different genre forms may be said to + + align:start position:0% +the different genre forms may be said to + + + align:start position:0% +the different genre forms may be said to +lay different emphases on the consensus + + align:start position:0% +lay different emphases on the consensus + + + align:start position:0% +lay different emphases on the consensus +but they all contribute to the consensus + + align:start position:0% +but they all contribute to the consensus + + + align:start position:0% +but they all contribute to the consensus +and the way one way they contribute is + + align:start position:0% +and the way one way they contribute is + + + align:start position:0% +and the way one way they contribute is +by constantly showing us fissures and + + align:start position:0% +by constantly showing us fissures and + + + align:start position:0% +by constantly showing us fissures and +disagreements they don't they they don't + + align:start position:0% +disagreements they don't they they don't + + + align:start position:0% +disagreements they don't they they don't +all tell the same story what they tend + + align:start position:0% +all tell the same story what they tend + + + align:start position:0% +all tell the same story what they tend +to and this helps to explain why movies + + align:start position:0% +to and this helps to explain why movies + + + align:start position:0% +to and this helps to explain why movies +are often incon either incoherent or + + align:start position:0% +are often incon either incoherent or + + + align:start position:0% +are often incon either incoherent or +partly contradictory right movies are + + align:start position:0% +partly contradictory right movies are + + + align:start position:0% +partly contradictory right movies are +movies are not simple stable unitary + + align:start position:0% +movies are not simple stable unitary + + + align:start position:0% +movies are not simple stable unitary +things at all one reason is they're made + + align:start position:0% +things at all one reason is they're made + + + align:start position:0% +things at all one reason is they're made +by so many people right there's no + + align:start position:0% +by so many people right there's no + + + align:start position:0% +by so many people right there's no +single author there's a director a + + align:start position:0% +single author there's a director a + + + align:start position:0% +single author there's a director a +writer a actors they're all there's an + + align:start position:0% +writer a actors they're all there's an + + + align:start position:0% +writer a actors they're all there's an +army of subsidiary people who help films + + align:start position:0% +army of subsidiary people who help films + + + align:start position:0% +army of subsidiary people who help films +are a profoundly collaborative form and + + align:start position:0% +are a profoundly collaborative form and + + + align:start position:0% +are a profoundly collaborative form and +one of the one of the effects of this is + + align:start position:0% +one of the one of the effects of this is + + + align:start position:0% +one of the one of the effects of this is +that in some forms uh the director's + + align:start position:0% +that in some forms uh the director's + + + align:start position:0% +that in some forms uh the director's +control may be imperfect and the Star + + align:start position:0% +control may be imperfect and the Star + + + align:start position:0% +control may be imperfect and the Star +May distort the film in some way or or + + align:start position:0% +May distort the film in some way or or + + + align:start position:0% +May distort the film in some way or or +or take it or or the or in some films + + align:start position:0% +or take it or or the or in some films + + + align:start position:0% +or take it or or the or in some films +the writer may be so powerful and so + + align:start position:0% +the writer may be so powerful and so + + + align:start position:0% +the writer may be so powerful and so +imaginative and the director so + + align:start position:0% +imaginative and the director so + + + align:start position:0% +imaginative and the director so +relatively weak that a different kind of + + align:start position:0% +relatively weak that a different kind of + + + align:start position:0% +relatively weak that a different kind of +movie emerges right so you so movies are + + align:start position:0% +movie emerges right so you so movies are + + + align:start position:0% +movie emerges right so you so movies are +different in that way and then of course + + align:start position:0% +different in that way and then of course + + + align:start position:0% +different in that way and then of course +they're also different + + align:start position:0% +they're also different + + + align:start position:0% +they're also different +because they occur in different moments + + align:start position:0% +because they occur in different moments + + + align:start position:0% +because they occur in different moments +in time and those moments when they + + align:start position:0% +in time and those moments when they + + + align:start position:0% +in time and those moments when they +occur in different moments in time even + + align:start position:0% +occur in different moments in time even + + + align:start position:0% +occur in different moments in time even +if they belong to a particular genre + + align:start position:0% +if they belong to a particular genre + + + align:start position:0% +if they belong to a particular genre +they may be responsive to later problems + + align:start position:0% +they may be responsive to later problems + + + align:start position:0% +they may be responsive to later problems +in the society from ones that ones that + + align:start position:0% +in the society from ones that ones that + + + align:start position:0% +in the society from ones that ones that +differ from the problems that may have + + align:start position:0% +differ from the problems that may have + + + align:start position:0% +differ from the problems that may have +been the case 10 years earlier when the + + align:start position:0% +been the case 10 years earlier when the + + + align:start position:0% +been the case 10 years earlier when the +genre when a different version of of the + + align:start position:0% +genre when a different version of of the + + + align:start position:0% +genre when a different version of of the +same genre story would handle the + + align:start position:0% +same genre story would handle the + + + align:start position:0% +same genre story would handle the +characters or the story in a somewhat + + align:start position:0% +characters or the story in a somewhat + + + align:start position:0% +characters or the story in a somewhat +different way right uh so so so what we + + align:start position:0% +different way right uh so so so what we + + + align:start position:0% +different way right uh so so so what we +can say among other things is there's a + + align:start position:0% +can say among other things is there's a + + + align:start position:0% +can say among other things is there's a +tremendous value to the idea to the the + + align:start position:0% +tremendous value to the idea to the the + + + align:start position:0% +tremendous value to the idea to the the +recognition that not only is culture + + align:start position:0% +recognition that not only is culture + + + align:start position:0% +recognition that not only is culture +always unfinished we're always sort of + + align:start position:0% +always unfinished we're always sort of + + + align:start position:0% +always unfinished we're always sort of +struggling to figure out certain kinds + + align:start position:0% +struggling to figure out certain kinds + + + align:start position:0% +struggling to figure out certain kinds +of conflicts and difficulties but but + + align:start position:0% +of conflicts and difficulties but but + + + align:start position:0% +of conflicts and difficulties but but +that our consensus narrative systems are + + align:start position:0% +that our consensus narrative systems are + + + align:start position:0% +that our consensus narrative systems are +also a space that accommodates that kind + + align:start position:0% +also a space that accommodates that kind + + + align:start position:0% +also a space that accommodates that kind +of disagreement and one way to + + align:start position:0% +of disagreement and one way to + + + align:start position:0% +of disagreement and one way to +conceptualize this is to see that in + + align:start position:0% +conceptualize this is to see that in + + + align:start position:0% +conceptualize this is to see that in +almost all films and certainly the whole + + align:start position:0% +almost all films and certainly the whole + + + align:start position:0% +almost all films and certainly the whole +system uh could be said to to uh + + align:start position:0% +system uh could be said to to uh + + + align:start position:0% +system uh could be said to to uh +dramatize or give voice to three + + align:start position:0% +dramatize or give voice to three + + + align:start position:0% +dramatize or give voice to three +different strains or or perspectives on + + align:start position:0% +different strains or or perspectives on + + + align:start position:0% +different strains or or perspectives on +society one is what might be called a + + align:start position:0% +society one is what might be called a + + + align:start position:0% +society one is what might be called a +tradition voice that is to say these are + + align:start position:0% +tradition voice that is to say these are + + + align:start position:0% +tradition voice that is to say these are +oldfashioned ideas that are still + + align:start position:0% +oldfashioned ideas that are still + + + align:start position:0% +oldfashioned ideas that are still +powerful but they really belong to an + + align:start position:0% +powerful but they really belong to an + + + align:start position:0% +powerful but they really belong to an +older era the second kind of voice you + + align:start position:0% +older era the second kind of voice you + + + align:start position:0% +older era the second kind of voice you +hear is what we could call the dominant + + align:start position:0% +hear is what we could call the dominant + + + align:start position:0% +hear is what we could call the dominant +voice that is to say the central values + + align:start position:0% +voice that is to say the central values + + + align:start position:0% +voice that is to say the central values +that the majority of the people in the + + align:start position:0% +that the majority of the people in the + + + align:start position:0% +that the majority of the people in the +society now believe right a little + + align:start position:0% +society now believe right a little + + + align:start position:0% +society now believe right a little +different from traditional voices that + + align:start position:0% +different from traditional voices that + + + align:start position:0% +different from traditional voices that +are more old-fashioned and are becoming + + align:start position:0% +are more old-fashioned and are becoming + + + align:start position:0% +are more old-fashioned and are becoming +vestigal and then on the other side + + align:start position:0% +vestigal and then on the other side + + + align:start position:0% +vestigal and then on the other side +emergent voices right voices new ideas + + align:start position:0% +emergent voices right voices new ideas + + + align:start position:0% +emergent voices right voices new ideas +New Attitudes that are coming to and you + + align:start position:0% +New Attitudes that are coming to and you + + + align:start position:0% +New Attitudes that are coming to and you +can feel this in every film you can feel + + align:start position:0% +can feel this in every film you can feel + + + align:start position:0% +can feel this in every film you can feel +this in every television program if you + + align:start position:0% +this in every television program if you + + + align:start position:0% +this in every television program if you +look at American television from the + + align:start position:0% +look at American television from the + + + align:start position:0% +look at American television from the +1950s to the 19 say 90s one let's say + + align:start position:0% +1950s to the 19 say 90s one let's say + + + align:start position:0% +1950s to the 19 say 90s one let's say +you restricted yourself to situation + + align:start position:0% +you restricted yourself to situation + + + align:start position:0% +you restricted yourself to situation +comedy what do you think you would see + + align:start position:0% +comedy what do you think you would see + + + align:start position:0% +comedy what do you think you would see +you would see a drama in which the + + align:start position:0% +you would see a drama in which the + + + align:start position:0% +you would see a drama in which the +American Family undergoes profound + + align:start position:0% +American Family undergoes profound + + + align:start position:0% +American Family undergoes profound +change what happens women become more + + align:start position:0% +change what happens women become more + + + align:start position:0% +change what happens women become more +important patriarchal values become less + + align:start position:0% +important patriarchal values become less + + + align:start position:0% +important patriarchal values become less +and less powerful children become more + + align:start position:0% +and less powerful children become more + + + align:start position:0% +and less powerful children become more +respected less Le are treated less less + + align:start position:0% +respected less Le are treated less less + + + align:start position:0% +respected less Le are treated less less +like appendages to the family more treat + + align:start position:0% +like appendages to the family more treat + + + align:start position:0% +like appendages to the family more treat +some of them and in some by the ' 80s + + align:start position:0% +some of them and in some by the ' 80s + + + align:start position:0% +some of them and in some by the ' 80s +and '90s sometimes the children have + + align:start position:0% +and '90s sometimes the children have + + + align:start position:0% +and '90s sometimes the children have +more dominant roles than the adults and + + align:start position:0% +more dominant roles than the adults and + + + align:start position:0% +more dominant roles than the adults and +are often even shown to be wiser than + + align:start position:0% +are often even shown to be wiser than + + + align:start position:0% +are often even shown to be wiser than +their parents right uh something that + + align:start position:0% +their parents right uh something that + + + align:start position:0% +their parents right uh something that +would have been impossible in the early + + align:start position:0% +would have been impossible in the early + + + align:start position:0% +would have been impossible in the early +1950s more patriarchal era when the + + align:start position:0% +1950s more patriarchal era when the + + + align:start position:0% +1950s more patriarchal era when the +classic television program about + + align:start position:0% +classic television program about + + + align:start position:0% +classic television program about +families was called Father Knows Best + + align:start position:0% +families was called Father Knows Best + + + align:start position:0% +families was called Father Knows Best +right whereas whereas in later in later + + align:start position:0% +right whereas whereas in later in later + + + align:start position:0% +right whereas whereas in later in later +episodes the father not only knows + + align:start position:0% +episodes the father not only knows + + + align:start position:0% +episodes the father not only knows +doesn't know best he knows least right + + align:start position:0% +doesn't know best he knows least right + + + align:start position:0% +doesn't know best he knows least right +or sometimes he's completely gone and + + align:start position:0% +or sometimes he's completely gone and + + + align:start position:0% +or sometimes he's completely gone and +it's only and it's women who are raising + + align:start position:0% +it's only and it's women who are raising + + + align:start position:0% +it's only and it's women who are raising +the children right well what's going on + + align:start position:0% +the children right well what's going on + + + align:start position:0% +the children right well what's going on +in that process has to do with the way + + align:start position:0% +in that process has to do with the way + + + align:start position:0% +in that process has to do with the way +in which in which the uh the the + + align:start position:0% +in which in which the uh the the + + + align:start position:0% +in which in which the uh the the +feminist movement and a reconfiguration + + align:start position:0% +feminist movement and a reconfiguration + + + align:start position:0% +feminist movement and a reconfiguration +of our idea of gender our ideas of + + align:start position:0% +of our idea of gender our ideas of + + + align:start position:0% +of our idea of gender our ideas of +gender and family what's happening is + + align:start position:0% +gender and family what's happening is + + + align:start position:0% +gender and family what's happening is +the situation comedy is the space in + + align:start position:0% +the situation comedy is the space in + + + align:start position:0% +the situation comedy is the space in +which those problems are being + + align:start position:0% +which those problems are being + + + align:start position:0% +which those problems are being +dramatized over time and if you just + + align:start position:0% +dramatized over time and if you just + + + align:start position:0% +dramatized over time and if you just +oppose a sitcom from the 50s and a + + align:start position:0% +oppose a sitcom from the 50s and a + + + align:start position:0% +oppose a sitcom from the 50s and a +sitcom from the 60s and a sitcom from + + align:start position:0% +sitcom from the 60s and a sitcom from + + + align:start position:0% +sitcom from the 60s and a sitcom from +the 70s and one from the 80s you can + + align:start position:0% +the 70s and one from the 80s you can + + + align:start position:0% +the 70s and one from the 80s you can +actually see that drama being enacted in + + align:start position:0% +actually see that drama being enacted in + + + align:start position:0% +actually see that drama being enacted in +tremendously powerful ways I choose + + align:start position:0% +tremendously powerful ways I choose + + + align:start position:0% +tremendously powerful ways I choose +examples from television because I I + + align:start position:0% +examples from television because I I + + + align:start position:0% +examples from television because I I +want to choose examples more of you are + + align:start position:0% +want to choose examples more of you are + + + align:start position:0% +want to choose examples more of you are +likely to have your own experience with + + align:start position:0% +likely to have your own experience with + + + align:start position:0% +likely to have your own experience with +but I could offer such instances from + + align:start position:0% +but I could offer such instances from + + + align:start position:0% +but I could offer such instances from +the history of movies as well but almost + + align:start position:0% +the history of movies as well but almost + + + align:start position:0% +the history of movies as well but almost +none of you would would have uh + + align:start position:0% +none of you would would have uh + + + align:start position:0% +none of you would would have uh +sufficient experience with the movies to + + align:start position:0% +sufficient experience with the movies to + + + align:start position:0% +sufficient experience with the movies to +understand the examples so that's why + + align:start position:0% +understand the examples so that's why + + + align:start position:0% +understand the examples so that's why +I've chosen examples from television I + + align:start position:0% +I've chosen examples from television I + + + align:start position:0% +I've chosen examples from television I +hope some of you at least although I + + align:start position:0% +hope some of you at least although I + + + align:start position:0% +hope some of you at least although I +know many of you can't because you don't + + align:start position:0% +know many of you can't because you don't + + + align:start position:0% +know many of you can't because you don't +didn't grow up on American television + + align:start position:0% +didn't grow up on American television + + + align:start position:0% +didn't grow up on American television +either but some of you at least can get + + align:start position:0% +either but some of you at least can get + + + align:start position:0% +either but some of you at least can get +the idea that I'm talking about here so + + align:start position:0% +the idea that I'm talking about here so + + + align:start position:0% +the idea that I'm talking about here so +the so so the the notion that the + + align:start position:0% +the so so the the notion that the + + + align:start position:0% +the so so the the notion that the +so this is a way of explaining far + + align:start position:0% +so this is a way of explaining far + + + align:start position:0% +so this is a way of explaining far +beyond what the intentions of any + + align:start position:0% +beyond what the intentions of any + + + align:start position:0% +beyond what the intentions of any +particular movie maker or producer would + + align:start position:0% +particular movie maker or producer would + + + align:start position:0% +particular movie maker or producer would +have for it's a way of explaining and + + align:start position:0% +have for it's a way of explaining and + + + align:start position:0% +have for it's a way of explaining and +clarifying the profound historical and + + align:start position:0% +clarifying the profound historical and + + + align:start position:0% +clarifying the profound historical and +anthropological importance of the movies + + align:start position:0% +anthropological importance of the movies + + + align:start position:0% +anthropological importance of the movies +in American society and by implication + + align:start position:0% +in American society and by implication + + + align:start position:0% +in American society and by implication +in other societies as well because the + + align:start position:0% +in other societies as well because the + + + align:start position:0% +in other societies as well because the +argument applies in different ways to + + align:start position:0% +argument applies in different ways to + + + align:start position:0% +argument applies in different ways to +those societies as well the notion is + + align:start position:0% +those societies as well the notion is + + + align:start position:0% +those societies as well the notion is +that not that movies are unimportant + + align:start position:0% +that not that movies are unimportant + + + align:start position:0% +that not that movies are unimportant +today but they occupy a different niche + + align:start position:0% +today but they occupy a different niche + + + align:start position:0% +today but they occupy a different niche +in our Consciousness and in our daily + + align:start position:0% +in our Consciousness and in our daily + + + align:start position:0% +in our Consciousness and in our daily +lives than they did in the Hollywood era + + align:start position:0% +lives than they did in the Hollywood era + + + align:start position:0% +lives than they did in the Hollywood era +in the era of the Hollywood + + align:start position:0% +in the era of the Hollywood + + + align:start position:0% +in the era of the Hollywood +studios Okay Kaa and Hawks can be said + + align:start position:0% +studios Okay Kaa and Hawks can be said + + + align:start position:0% +studios Okay Kaa and Hawks can be said +to be two characteristic instances to + + align:start position:0% +to be two characteristic instances to + + + align:start position:0% +to be two characteristic instances to +characteristic examples of really + + align:start position:0% +characteristic examples of really + + + align:start position:0% +characteristic examples of really +journeyman directors from the studio era + + align:start position:0% +journeyman directors from the studio era + + + align:start position:0% +journeyman directors from the studio era +uh I had intended let's put up the other + + align:start position:0% +uh I had intended let's put up the other + + + align:start position:0% +uh I had intended let's put up the other +thing I I I I I actually had intended + + align:start position:0% +thing I I I I I actually had intended + + + align:start position:0% +thing I I I I I actually had intended +and had had planned to give you much + + align:start position:0% +and had had planned to give you much + + + align:start position:0% +and had had planned to give you much +more elaborate sort of brief + + align:start position:0% +more elaborate sort of brief + + + align:start position:0% +more elaborate sort of brief +biographical account of each director + + align:start position:0% +biographical account of each director + + + align:start position:0% +biographical account of each director +but I don't have time to do that and + + align:start position:0% +but I don't have time to do that and + + + align:start position:0% +but I don't have time to do that and +I'll just what I what I'm putting up + + align:start position:0% +I'll just what I what I'm putting up + + + align:start position:0% +I'll just what I what I'm putting up +instead here are just a list of some of + + align:start position:0% +instead here are just a list of some of + + + align:start position:0% +instead here are just a list of some of +their films uh you can see what a + + align:start position:0% +their films uh you can see what a + + + align:start position:0% +their films uh you can see what a +journeyman Hawks was he made very + + align:start position:0% +journeyman Hawks was he made very + + + align:start position:0% +journeyman Hawks was he made very +important scre ball comedy probably the + + align:start position:0% +important scre ball comedy probably the + + + align:start position:0% +important scre ball comedy probably the +dominant figure in scre ball comedy + + align:start position:0% +dominant figure in scre ball comedy + + + align:start position:0% +dominant figure in scre ball comedy +classic westerns I've listed some of + + align:start position:0% +classic westerns I've listed some of + + + align:start position:0% +classic westerns I've listed some of +them there and a ser and he was also a a + + align:start position:0% +them there and a ser and he was also a a + + + align:start position:0% +them there and a ser and he was also a a +great director in other genres he worked + + align:start position:0% +great director in other genres he worked + + + align:start position:0% +great director in other genres he worked +it's very interesting that he could work + + align:start position:0% +it's very interesting that he could work + + + align:start position:0% +it's very interesting that he could work +across genres in this way he he may be + + align:start position:0% +across genres in this way he he may be + + + align:start position:0% +across genres in this way he he may be +the most diverse the of all the Classic + + align:start position:0% +the most diverse the of all the Classic + + + align:start position:0% +the most diverse the of all the Classic +Hollywood journeyman professional + + align:start position:0% +Hollywood journeyman professional + + + align:start position:0% +Hollywood journeyman professional +directors because he worked so well + + align:start position:0% +directors because he worked so well + + + align:start position:0% +directors because he worked so well +across so many categories there are + + align:start position:0% +across so many categories there are + + + align:start position:0% +across so many categories there are +recurring themes that show up across + + align:start position:0% +recurring themes that show up across + + + align:start position:0% +recurring themes that show up across +genre in in uh Howard Hawk's work and I + + align:start position:0% +genre in in uh Howard Hawk's work and I + + + align:start position:0% +genre in in uh Howard Hawk's work and I +mentioned some of them in a little while + + align:start position:0% +mentioned some of them in a little while + + + align:start position:0% +mentioned some of them in a little while +when I try to introduce his girl Friday + + align:start position:0% +when I try to introduce his girl Friday + + + align:start position:0% +when I try to introduce his girl Friday +one of his great um uh scow ball + + align:start position:0% +one of his great um uh scow ball + + + align:start position:0% +one of his great um uh scow ball +comedies um uh cpra operated in a in a + + align:start position:0% +comedies um uh cpra operated in a in a + + + align:start position:0% +comedies um uh cpra operated in a in a +slightly uh more a slightly narrower + + align:start position:0% +slightly uh more a slightly narrower + + + align:start position:0% +slightly uh more a slightly narrower +range but like Hawks he was an immensely + + align:start position:0% +range but like Hawks he was an immensely + + + align:start position:0% +range but like Hawks he was an immensely +successful immensely popular director + + align:start position:0% +successful immensely popular director + + + align:start position:0% +successful immensely popular director +during an era when the studios were + + align:start position:0% +during an era when the studios were + + + align:start position:0% +during an era when the studios were +essentially operating like gigantic + + align:start position:0% +essentially operating like gigantic + + + align:start position:0% +essentially operating like gigantic +factories in which the studio heads were + + align:start position:0% +factories in which the studio heads were + + + align:start position:0% +factories in which the studio heads were +the primary bosses and in which each + + align:start position:0% +the primary bosses and in which each + + + align:start position:0% +the primary bosses and in which each +Studio especially the five major Studios + + align:start position:0% +Studio especially the five major Studios + + + align:start position:0% +Studio especially the five major Studios +as well as many of the smaller ones were + + align:start position:0% +as well as many of the smaller ones were + + + align:start position:0% +as well as many of the smaller ones were +essentially small cities uh small + + align:start position:0% +essentially small cities uh small + + + align:start position:0% +essentially small cities uh small +Factory cities for the manufacturer of + + align:start position:0% +Factory cities for the manufacturer of + + + align:start position:0% +Factory cities for the manufacturer of +of of of movies right not just that they + + align:start position:0% +of of of movies right not just that they + + + align:start position:0% +of of of movies right not just that they +that they employed dozens if not if not + + align:start position:0% +that they employed dozens if not if not + + + align:start position:0% +that they employed dozens if not if not +uh um hundreds of they well they + + align:start position:0% +uh um hundreds of they well they + + + align:start position:0% +uh um hundreds of they well they +employed hundreds even thousands of + + align:start position:0% +employed hundreds even thousands of + + + align:start position:0% +employed hundreds even thousands of +workers of different but they employed + + align:start position:0% +workers of different but they employed + + + align:start position:0% +workers of different but they employed +dozens of writers and dozens of + + align:start position:0% +dozens of writers and dozens of + + + align:start position:0% +dozens of writers and dozens of +directors and they had dozens of stars + + align:start position:0% +directors and they had dozens of stars + + + align:start position:0% +directors and they had dozens of stars +and actors on on on contract and they + + align:start position:0% +and actors on on on contract and they + + + align:start position:0% +and actors on on on contract and they +own great lots and uh and of course they + + align:start position:0% +own great lots and uh and of course they + + + align:start position:0% +own great lots and uh and of course they +had they had an army of technicians of + + align:start position:0% +had they had an army of technicians of + + + align:start position:0% +had they had an army of technicians of +grips and best boys and Camera people + + align:start position:0% +grips and best boys and Camera people + + + align:start position:0% +grips and best boys and Camera people +and and post- production people and + + align:start position:0% +and and post- production people and + + + align:start position:0% +and and post- production people and +publicity people and various other fact + + align:start position:0% +publicity people and various other fact + + + align:start position:0% +publicity people and various other fact +toems who took care of people and they + + align:start position:0% +toems who took care of people and they + + + align:start position:0% +toems who took care of people and they +probably had a more elaborate uh U uh + + align:start position:0% +probably had a more elaborate uh U uh + + + align:start position:0% +probably had a more elaborate uh U uh +encyclopedia of gophers than any other + + align:start position:0% +encyclopedia of gophers than any other + + + align:start position:0% +encyclopedia of gophers than any other +than than any other industry in history + + align:start position:0% +than than any other industry in history + + + align:start position:0% +than than any other industry in history +but the point is in a sense that each + + align:start position:0% +but the point is in a sense that each + + + align:start position:0% +but the point is in a sense that each +Studio was a kind of manufacturing Hub + + align:start position:0% +Studio was a kind of manufacturing Hub + + + align:start position:0% +Studio was a kind of manufacturing Hub +was a kind of was like a great Factory + + align:start position:0% +was a kind of was like a great Factory + + + align:start position:0% +was a kind of was like a great Factory +the equivalent of General Motors or + + align:start position:0% +the equivalent of General Motors or + + + align:start position:0% +the equivalent of General Motors or +Chrysler but instead of put making + + align:start position:0% +Chrysler but instead of put making + + + align:start position:0% +Chrysler but instead of put making +automobiles or toasters they were making + + align:start position:0% +automobiles or toasters they were making + + + align:start position:0% +automobiles or toasters they were making +these things that infiltrate our dreams + + align:start position:0% +these things that infiltrate our dreams + + + align:start position:0% +these things that infiltrate our dreams +a product I think much more powerful + + align:start position:0% +a product I think much more powerful + + + align:start position:0% +a product I think much more powerful +disturbing and interesting even than the + + align:start position:0% +disturbing and interesting even than the + + + align:start position:0% +disturbing and interesting even than the +most remarkable automobile or toaster + + align:start position:0% +most remarkable automobile or toaster + + + align:start position:0% +most remarkable automobile or toaster +um two other things I should mention + + align:start position:0% +um two other things I should mention + + + align:start position:0% +um two other things I should mention +about both Kaa and Hawks because they + + align:start position:0% +about both Kaa and Hawks because they + + + align:start position:0% +about both Kaa and Hawks because they +share this quality and they share it + + align:start position:0% +share this quality and they share it + + + align:start position:0% +share this quality and they share it +with Hitchcock as well they began their + + align:start position:0% +with Hitchcock as well they began their + + + align:start position:0% +with Hitchcock as well they began their +careers in the silent era they made a + + align:start position:0% +careers in the silent era they made a + + + align:start position:0% +careers in the silent era they made a +transition to the sound era um cpra was + + align:start position:0% +transition to the sound era um cpra was + + + align:start position:0% +transition to the sound era um cpra was +a more successful silent director than + + align:start position:0% +a more successful silent director than + + + align:start position:0% +a more successful silent director than +than uh um Hawks but but but both had + + align:start position:0% +than uh um Hawks but but but both had + + + align:start position:0% +than uh um Hawks but but but both had +experience in the silent era unlike some + + align:start position:0% +experience in the silent era unlike some + + + align:start position:0% +experience in the silent era unlike some +directors were able to make a very + + align:start position:0% +directors were able to make a very + + + align:start position:0% +directors were able to make a very +successful transition along as Hitchcock + + align:start position:0% +successful transition along as Hitchcock + + + align:start position:0% +successful transition along as Hitchcock +also did uh and became major directors + + align:start position:0% +also did uh and became major directors + + + align:start position:0% +also did uh and became major directors +in the sound era the other significant + + align:start position:0% +in the sound era the other significant + + + align:start position:0% +in the sound era the other significant +thing to mention about both of them they + + align:start position:0% +thing to mention about both of them they + + + align:start position:0% +thing to mention about both of them they +both spent time in the Army before and + + align:start position:0% +both spent time in the Army before and + + + align:start position:0% +both spent time in the Army before and +they both kicked around they were not + + align:start position:0% +they both kicked around they were not + + + align:start position:0% +they both kicked around they were not +sure they were it wasn't as if when they + + align:start position:0% +sure they were it wasn't as if when they + + + align:start position:0% +sure they were it wasn't as if when they +were born they said I want to be a Movie + + align:start position:0% +were born they said I want to be a Movie + + + align:start position:0% +were born they said I want to be a Movie +Maker they had all kinds of of uh + + align:start position:0% +Maker they had all kinds of of uh + + + align:start position:0% +Maker they had all kinds of of uh +uncertainty in the in in their in their + + align:start position:0% +uncertainty in the in in their in their + + + align:start position:0% +uncertainty in the in in their in their +lives they almost fell into movie making + + align:start position:0% +lives they almost fell into movie making + + + align:start position:0% +lives they almost fell into movie making +um but there's one thing I think all of + + align:start position:0% +um but there's one thing I think all of + + + align:start position:0% +um but there's one thing I think all of +you will find interesting and I love to + + align:start position:0% +you will find interesting and I love to + + + align:start position:0% +you will find interesting and I love to +mention this to my MIT students both + + align:start position:0% +mention this to my MIT students both + + + align:start position:0% +mention this to my MIT students both +kapra and Howard Hawks studied + + align:start position:0% +kapra and Howard Hawks studied + + + align:start position:0% +kapra and Howard Hawks studied +engineering and Kaa in fact got an + + align:start position:0% +engineering and Kaa in fact got an + + + align:start position:0% +engineering and Kaa in fact got an +engineering degree from the University + + align:start position:0% +engineering degree from the University + + + align:start position:0% +engineering degree from the University +of Southern California when he couldn't + + align:start position:0% +of Southern California when he couldn't + + + align:start position:0% +of Southern California when he couldn't +get work as a mechanical engineer he + + align:start position:0% +get work as a mechanical engineer he + + + align:start position:0% +get work as a mechanical engineer he +began to cast around for other things + + align:start position:0% +began to cast around for other things + + + align:start position:0% +began to cast around for other things +and he ended up in the movies uh Howard + + align:start position:0% +and he ended up in the movies uh Howard + + + align:start position:0% +and he ended up in the movies uh Howard +Hawks didn't graduate but he did he + + align:start position:0% +Hawks didn't graduate but he did he + + + align:start position:0% +Hawks didn't graduate but he did he +studied engineering at Cornell I think + + align:start position:0% +studied engineering at Cornell I think + + + align:start position:0% +studied engineering at Cornell I think +he never graduated from Cornell but he + + align:start position:0% +he never graduated from Cornell but he + + + align:start position:0% +he never graduated from Cornell but he +studied engineering seriously and I + + align:start position:0% +studied engineering seriously and I + + + align:start position:0% +studied engineering seriously and I +don't think it's an accident that these + + align:start position:0% +don't think it's an accident that these + + + align:start position:0% +don't think it's an accident that these +directors had engineering experience + + align:start position:0% +directors had engineering experience + + + align:start position:0% +directors had engineering experience +because because there's an + + align:start position:0% +because because there's an + + + align:start position:0% +because because there's an +organizational intelligence a a a a + + align:start position:0% +organizational intelligence a a a a + + + align:start position:0% +organizational intelligence a a a a +practical intelligence that every even + + align:start position:0% +practical intelligence that every even + + + align:start position:0% +practical intelligence that every even +genius that every good director not to + + align:start position:0% +genius that every good director not to + + + align:start position:0% +genius that every good director not to +say great director needs that is very + + align:start position:0% +say great director needs that is very + + + align:start position:0% +say great director needs that is very +well served by an engineering + + align:start position:0% +well served by an engineering + + + align:start position:0% +well served by an engineering +education so I encourage all of you when + + align:start position:0% +education so I encourage all of you when + + + align:start position:0% +education so I encourage all of you when +you finish your degrees to go to + + align:start position:0% +you finish your degrees to go to + + + align:start position:0% +you finish your degrees to go to +Hollywood and become directors + + align:start position:0% +Hollywood and become directors + + + align:start position:0% +Hollywood and become directors +um I won't say more about cpra and and + + align:start position:0% +um I won't say more about cpra and and + + + align:start position:0% +um I won't say more about cpra and and +Hawks now except to say again that they + + align:start position:0% +Hawks now except to say again that they + + + align:start position:0% +Hawks now except to say again that they +represent in a certain sense the center + + align:start position:0% +represent in a certain sense the center + + + align:start position:0% +represent in a certain sense the center +of what a Hollywood director uh could + + align:start position:0% +of what a Hollywood director uh could + + + align:start position:0% +of what a Hollywood director uh could +represent in the in the uh um in the in + + align:start position:0% +represent in the in the uh um in the in + + + align:start position:0% +represent in the in the uh um in the in +the era of of the of of the studios uh + + align:start position:0% +the era of of the of of the studios uh + + + align:start position:0% +the era of of the of of the studios uh +in the era when the movies were the + + align:start position:0% +in the era when the movies were the + + + align:start position:0% +in the era when the movies were the +dominant form of entertainment in + + align:start position:0% +dominant form of entertainment in + + + align:start position:0% +dominant form of entertainment in +American society I want to say a couple + + align:start position:0% +American society I want to say a couple + + + align:start position:0% +American society I want to say a couple +of things about each of the movies that + + align:start position:0% +of things about each of the movies that + + + align:start position:0% +of things about each of the movies that +you're seeing tonight the two different + + align:start position:0% +you're seeing tonight the two different + + + align:start position:0% +you're seeing tonight the two different +screw ball comedies uh one by + + align:start position:0% +screw ball comedies uh one by + + + align:start position:0% +screw ball comedies uh one by +hawks one by cpra each representing a + + align:start position:0% +hawks one by cpra each representing a + + + align:start position:0% +hawks one by cpra each representing a +characteristic tone of each director uh + + align:start position:0% +characteristic tone of each director uh + + + align:start position:0% +characteristic tone of each director uh +as I said earlier you can think of kapra + + align:start position:0% +as I said earlier you can think of kapra + + + align:start position:0% +as I said earlier you can think of kapra +as a slightly more as a somewhat more + + align:start position:0% +as a slightly more as a somewhat more + + + align:start position:0% +as a slightly more as a somewhat more +sentimental and optimistic director uh + + align:start position:0% +sentimental and optimistic director uh + + + align:start position:0% +sentimental and optimistic director uh +if you want a quintessential uh scene + + align:start position:0% +if you want a quintessential uh scene + + + align:start position:0% +if you want a quintessential uh scene +that sort of distills this sentimental + + align:start position:0% +that sort of distills this sentimental + + + align:start position:0% +that sort of distills this sentimental +populism M that a Sentimental populism + + align:start position:0% +populism M that a Sentimental populism + + + align:start position:0% +populism M that a Sentimental populism +is a good way of describing much of ca's + + align:start position:0% +is a good way of describing much of ca's + + + align:start position:0% +is a good way of describing much of ca's +work uh there's a scene in in happen one + + align:start position:0% +work uh there's a scene in in happen one + + + align:start position:0% +work uh there's a scene in in happen one +night that captures this quality in him + + align:start position:0% +night that captures this quality in him + + + align:start position:0% +night that captures this quality in him +you can feel that you can feel its its + + align:start position:0% +you can feel that you can feel its its + + + align:start position:0% +you can feel that you can feel its its +optimism and perhaps its fakery but also + + align:start position:0% +optimism and perhaps its fakery but also + + + align:start position:0% +optimism and perhaps its fakery but also +you want it to be true even though you + + align:start position:0% +you want it to be true even though you + + + align:start position:0% +you want it to be true even though you +know he may be imagining a nicer + + align:start position:0% +know he may be imagining a nicer + + + align:start position:0% +know he may be imagining a nicer +Humanity than actually exists there's a + + align:start position:0% +Humanity than actually exists there's a + + + align:start position:0% +Humanity than actually exists there's a +scene on a on a bus um in It Happened + + align:start position:0% +scene on a on a bus um in It Happened + + + align:start position:0% +scene on a on a bus um in It Happened +One Night uh uh a good deal of the of + + align:start position:0% +One Night uh uh a good deal of the of + + + align:start position:0% +One Night uh uh a good deal of the of +the of the film or good part the film + + align:start position:0% +the of the film or good part the film + + + align:start position:0% +the of the film or good part the film +takes place as as people are traveling + + align:start position:0% +takes place as as people are traveling + + + align:start position:0% +takes place as as people are traveling +it's a it's a road film in a certain way + + align:start position:0% +it's a it's a road film in a certain way + + + align:start position:0% +it's a it's a road film in a certain way +uh and uh there's a scene on a bus u a + + align:start position:0% +uh and uh there's a scene on a bus u a + + + align:start position:0% +uh and uh there's a scene on a bus u a +number of scenes on the bus but there's + + align:start position:0% +number of scenes on the bus but there's + + + align:start position:0% +number of scenes on the bus but there's +one very powerful scene in which all of + + align:start position:0% +one very powerful scene in which all of + + + align:start position:0% +one very powerful scene in which all of +a sudden after uh certain dialogue + + align:start position:0% +a sudden after uh certain dialogue + + + align:start position:0% +a sudden after uh certain dialogue +occurs the people on the bus sort of + + align:start position:0% +occurs the people on the bus sort of + + + align:start position:0% +occurs the people on the bus sort of +rise up and begin to sort of create a + + align:start position:0% +rise up and begin to sort of create a + + + align:start position:0% +rise up and begin to sort of create a +little musical number themselves watch + + align:start position:0% +little musical number themselves watch + + + align:start position:0% +little musical number themselves watch +how it happens and it's almost as if + + align:start position:0% +how it happens and it's almost as if + + + align:start position:0% +how it happens and it's almost as if +these strangers suddenly become members + + align:start position:0% +these strangers suddenly become members + + + align:start position:0% +these strangers suddenly become members +of a musical troop and they begin to + + align:start position:0% +of a musical troop and they begin to + + + align:start position:0% +of a musical troop and they begin to +interact with each other it's a it's + + align:start position:0% +interact with each other it's a it's + + + align:start position:0% +interact with each other it's a it's +it's a fantasy of community that has all + + align:start position:0% +it's a fantasy of community that has all + + + align:start position:0% +it's a fantasy of community that has all +kinds of sentimental affectionate + + align:start position:0% +kinds of sentimental affectionate + + + align:start position:0% +kinds of sentimental affectionate +assumptions in it that is no doubt an + + align:start position:0% +assumptions in it that is no doubt an + + + align:start position:0% +assumptions in it that is no doubt an +exaggeration but it tells us something + + align:start position:0% +exaggeration but it tells us something + + + align:start position:0% +exaggeration but it tells us something +about uh the the the sentimental + + align:start position:0% +about uh the the the sentimental + + + align:start position:0% +about uh the the the sentimental +populism that's at the heart of Frank + + align:start position:0% +populism that's at the heart of Frank + + + align:start position:0% +populism that's at the heart of Frank +cap Capra's vision of life let me let me + + align:start position:0% +cap Capra's vision of life let me let me + + + align:start position:0% +cap Capra's vision of life let me let me +say quickly a couple of words about each + + align:start position:0% +say quickly a couple of words about each + + + align:start position:0% +say quickly a couple of words about each +film now in it it many It Happened One + + align:start position:0% +film now in it it many It Happened One + + + align:start position:0% +film now in it it many It Happened One +Night is not the first screw ball comedy + + align:start position:0% +Night is not the first screw ball comedy + + + align:start position:0% +Night is not the first screw ball comedy +but it is the film that established scub + + align:start position:0% +but it is the film that established scub + + + align:start position:0% +but it is the film that established scub +ball comedy as a dominant genre there + + align:start position:0% +ball comedy as a dominant genre there + + + align:start position:0% +ball comedy as a dominant genre there +are films going back probably to 19 30 + + align:start position:0% +are films going back probably to 19 30 + + + align:start position:0% +are films going back probably to 19 30 +if not earlier that could be identified + + align:start position:0% +if not earlier that could be identified + + + align:start position:0% +if not earlier that could be identified +as screw ball comedies and there are + + align:start position:0% +as screw ball comedies and there are + + + align:start position:0% +as screw ball comedies and there are +certainly films full scre ball comedies + + align:start position:0% +certainly films full scre ball comedies + + + align:start position:0% +certainly films full scre ball comedies +that existed before It Happened One + + align:start position:0% +that existed before It Happened One + + + align:start position:0% +that existed before It Happened One +Night but the success of It Happened One + + align:start position:0% +Night but the success of It Happened One + + + align:start position:0% +Night but the success of It Happened One +Night nailed the genre made the genre a + + align:start position:0% +Night nailed the genre made the genre a + + + align:start position:0% +Night nailed the genre made the genre a +popular one and I I want to mention a + + align:start position:0% +popular one and I I want to mention a + + + align:start position:0% +popular one and I I want to mention a +couple of production notes that are kind + + align:start position:0% +couple of production notes that are kind + + + align:start position:0% +couple of production notes that are kind +of interesting one of them is + + align:start position:0% +of interesting one of them is + + + align:start position:0% +of interesting one of them is +this both of the stars in It Happened + + align:start position:0% +this both of the stars in It Happened + + + align:start position:0% +this both of the stars in It Happened +One Night Claudette colar and and uh + + align:start position:0% +One Night Claudette colar and and uh + + + align:start position:0% +One Night Claudette colar and and uh +Clark + + align:start position:0% +Clark + + + align:start position:0% +Clark +Gable had had significant careers before + + align:start position:0% +Gable had had significant careers before + + + align:start position:0% +Gable had had significant careers before +they came to make it happen one night + + align:start position:0% +they came to make it happen one night + + + align:start position:0% +they came to make it happen one night +Gable had been in movies for over a + + align:start position:0% +Gable had been in movies for over a + + + align:start position:0% +Gable had been in movies for over a +decade he'd been in a whole number of + + align:start position:0% +decade he'd been in a whole number of + + + align:start position:0% +decade he'd been in a whole number of +films but he was a second r a secondary + + align:start position:0% +films but he was a second r a secondary + + + align:start position:0% +films but he was a second r a secondary +player and he was a difficult man he uh + + align:start position:0% +player and he was a difficult man he uh + + + align:start position:0% +player and he was a difficult man he uh +he was resisting assignments that he was + + align:start position:0% +he was resisting assignments that he was + + + align:start position:0% +he was resisting assignments that he was +being he was under contract to the uh + + align:start position:0% +being he was under contract to the uh + + + align:start position:0% +being he was under contract to the uh +MGM Studio which was the most uh + + align:start position:0% +MGM Studio which was the most uh + + + align:start position:0% +MGM Studio which was the most uh +elaborate and Wealthy of all the studios + + align:start position:0% +elaborate and Wealthy of all the studios + + + align:start position:0% +elaborate and Wealthy of all the studios +and the head of MGM Samuel Goldwin was + + align:start position:0% +and the head of MGM Samuel Goldwin was + + + align:start position:0% +and the head of MGM Samuel Goldwin was +annoyed with Gable because he wasn't he + + align:start position:0% +annoyed with Gable because he wasn't he + + + align:start position:0% +annoyed with Gable because he wasn't he +because he was he was uncooperative they + + align:start position:0% +because he was he was uncooperative they + + + align:start position:0% +because he was he was uncooperative they +were sending him scripts he didn't want + + align:start position:0% +were sending him scripts he didn't want + + + align:start position:0% +were sending him scripts he didn't want +to do even though he was under contract + + align:start position:0% +to do even though he was under contract + + + align:start position:0% +to do even though he was under contract +to them and theoretically had to do what + + align:start position:0% +to them and theoretically had to do what + + + align:start position:0% +to them and theoretically had to do what +they told him and because he annoyed uh + + align:start position:0% +they told him and because he annoyed uh + + + align:start position:0% +they told him and because he annoyed uh +uh Goldwin Goldwin decided to discipline + + align:start position:0% +uh Goldwin Goldwin decided to discipline + + + align:start position:0% +uh Goldwin Goldwin decided to discipline +him and the way he disciplined him is he + + align:start position:0% +him and the way he disciplined him is he + + + align:start position:0% +him and the way he disciplined him is he +said all right I'm assigning you to + + align:start position:0% +said all right I'm assigning you to + + + align:start position:0% +said all right I'm assigning you to +Frank kaer who works for Columbia + + align:start position:0% +Frank kaer who works for Columbia + + + align:start position:0% +Frank kaer who works for Columbia +Studios you have to make a film that + + align:start position:0% +Studios you have to make a film that + + + align:start position:0% +Studios you have to make a film that +he's working on you have no choice + + align:start position:0% +he's working on you have no choice + + + align:start position:0% +he's working on you have no choice +you're under contract to me Gable was + + align:start position:0% +you're under contract to me Gable was + + + align:start position:0% +you're under contract to me Gable was +incredibly angry about this one of the + + align:start position:0% +incredibly angry about this one of the + + + align:start position:0% +incredibly angry about this one of the +reasons is Colombia was not a major + + align:start position:0% +reasons is Colombia was not a major + + + align:start position:0% +reasons is Colombia was not a major +Studio it was a low-budget Studio Kaa + + align:start position:0% +Studio it was a low-budget Studio Kaa + + + align:start position:0% +Studio it was a low-budget Studio Kaa +was not yet a widely known uh uh + + align:start position:0% +was not yet a widely known uh uh + + + align:start position:0% +was not yet a widely known uh uh +director even though he had been + + align:start position:0% +director even though he had been + + + align:start position:0% +director even though he had been +directing since the silent era Gable + + align:start position:0% +directing since the silent era Gable + + + align:start position:0% +directing since the silent era Gable +felt that that he was being imposed upon + + align:start position:0% +felt that that he was being imposed upon + + + align:start position:0% +felt that that he was being imposed upon +he was very reluctant and angry about + + align:start position:0% +he was very reluctant and angry about + + + align:start position:0% +he was very reluctant and angry about +about the job the star the the female + + align:start position:0% +about the job the star the the female + + + align:start position:0% +about the job the star the the female +star Claudette colar was also reluctant + + align:start position:0% +star Claudette colar was also reluctant + + + align:start position:0% +star Claudette colar was also reluctant +to take the job she had been in she was + + align:start position:0% +to take the job she had been in she was + + + align:start position:0% +to take the job she had been in she was +a stage star and she had been successful + + align:start position:0% +a stage star and she had been successful + + + align:start position:0% +a stage star and she had been successful +on Broadway but she'd had a checkered + + align:start position:0% +on Broadway but she'd had a checkered + + + align:start position:0% +on Broadway but she'd had a checkered +career in the movies some bad luck in + + align:start position:0% +career in the movies some bad luck in + + + align:start position:0% +career in the movies some bad luck in +the movies she'd made a film that was + + align:start position:0% +the movies she'd made a film that was + + + align:start position:0% +the movies she'd made a film that was +panned she was very reluctant to make + + align:start position:0% +panned she was very reluctant to make + + + align:start position:0% +panned she was very reluctant to make +any more movies her and and when she was + + align:start position:0% +any more movies her and and when she was + + + align:start position:0% +any more movies her and and when she was +asked she resisted and she finally + + align:start position:0% +asked she resisted and she finally + + + align:start position:0% +asked she resisted and she finally +agreed only when they doubled her fee + + align:start position:0% +agreed only when they doubled her fee + + + align:start position:0% +agreed only when they doubled her fee +she normally would get $25,000 for a + + align:start position:0% +she normally would get $25,000 for a + + + align:start position:0% +she normally would get $25,000 for a +film this time she got 50 but even when + + align:start position:0% +film this time she got 50 but even when + + + align:start position:0% +film this time she got 50 but even when +she accepted this she still was + + align:start position:0% +she accepted this she still was + + + align:start position:0% +she accepted this she still was +reluctant she said okay uh I will do + + align:start position:0% +reluctant she said okay uh I will do + + + align:start position:0% +reluctant she said okay uh I will do +this but I have to be free to go to + + align:start position:0% +this but I have to be free to go to + + + align:start position:0% +this but I have to be free to go to +spend Christmas with my friends and + + align:start position:0% +spend Christmas with my friends and + + + align:start position:0% +spend Christmas with my friends and +family in Palm Beach the shooting has to + + align:start position:0% +family in Palm Beach the shooting has to + + + align:start position:0% +family in Palm Beach the shooting has to +stop no no I I will not work late longer + + align:start position:0% +stop no no I I will not work late longer + + + align:start position:0% +stop no no I I will not work late longer +than December + + align:start position:0% +than December + + + align:start position:0% +than December +23rd and and so they had they had four + + align:start position:0% +23rd and and so they had they had four + + + align:start position:0% +23rd and and so they had they had four +very intense weeks of shooting in which + + align:start position:0% +very intense weeks of shooting in which + + + align:start position:0% +very intense weeks of shooting in which +they in which they did their best to + + align:start position:0% +they in which they did their best to + + + align:start position:0% +they in which they did their best to +finish the film they didn't quite finish + + align:start position:0% +finish the film they didn't quite finish + + + align:start position:0% +finish the film they didn't quite finish +it when but claudet walked off the set + + align:start position:0% +it when but claudet walked off the set + + + align:start position:0% +it when but claudet walked off the set +and said I'm done my cont I fulfilled my + + align:start position:0% +and said I'm done my cont I fulfilled my + + + align:start position:0% +and said I'm done my cont I fulfilled my +contract and she left kapra hadn't yet + + align:start position:0% +contract and she left kapra hadn't yet + + + align:start position:0% +contract and she left kapra hadn't yet +filmed the final scene of the film when + + align:start position:0% +filmed the final scene of the film when + + + align:start position:0% +filmed the final scene of the film when +you watch the brilliant final scene of + + align:start position:0% +you watch the brilliant final scene of + + + align:start position:0% +you watch the brilliant final scene of +the film which kepra had to do without + + align:start position:0% +the film which kepra had to do without + + + align:start position:0% +the film which kepra had to do without +his stars because coar had walked off + + align:start position:0% +his stars because coar had walked off + + + align:start position:0% +his stars because coar had walked off +the set you will see a magnificent + + align:start position:0% +the set you will see a magnificent + + + align:start position:0% +the set you will see a magnificent +example of what we might call necessity + + align:start position:0% +example of what we might call necessity + + + align:start position:0% +example of what we might call necessity +being the mother of invention because + + align:start position:0% +being the mother of invention because + + + align:start position:0% +being the mother of invention because +it's a brilliant Rich scene but he had + + align:start position:0% +it's a brilliant Rich scene but he had + + + align:start position:0% +it's a brilliant Rich scene but he had +to do it because he didn't have his + + align:start position:0% +to do it because he didn't have his + + + align:start position:0% +to do it because he didn't have his +actress there in order to make the scene + + align:start position:0% +actress there in order to make the scene + + + align:start position:0% +actress there in order to make the scene +so watch for it when you come to it uh + + align:start position:0% +so watch for it when you come to it uh + + + align:start position:0% +so watch for it when you come to it uh +another point about when when when coar + + align:start position:0% +another point about when when when coar + + + align:start position:0% +another point about when when when coar +left the film she was said to say to + + align:start position:0% +left the film she was said to say to + + + align:start position:0% +left the film she was said to say to +friends I've just completed the I've + + align:start position:0% +friends I've just completed the I've + + + align:start position:0% +friends I've just completed the I've +just finished the worst movie of my life + + align:start position:0% +just finished the worst movie of my life + + + align:start position:0% +just finished the worst movie of my life +this is a horrible film Gable was angry + + align:start position:0% +this is a horrible film Gable was angry + + + align:start position:0% +this is a horrible film Gable was angry +about the film and thought it was a + + align:start position:0% +about the film and thought it was a + + + align:start position:0% +about the film and thought it was a +piece of garbage in the Advent the film + + align:start position:0% +piece of garbage in the Advent the film + + + align:start position:0% +piece of garbage in the Advent the film +was the first film to win Academy Awards + + align:start position:0% +was the first film to win Academy Awards + + + align:start position:0% +was the first film to win Academy Awards +in every major category it won for Best + + align:start position:0% +in every major category it won for Best + + + align:start position:0% +in every major category it won for Best +Film It won for best actor best actress + + align:start position:0% +Film It won for best actor best actress + + + align:start position:0% +Film It won for best actor best actress +Best Director best screenplay it was the + + align:start position:0% +Best Director best screenplay it was the + + + align:start position:0% +Best Director best screenplay it was the +first film to notch all five victories + + align:start position:0% +first film to notch all five victories + + + align:start position:0% +first film to notch all five victories +right like a you know it's better than a + + align:start position:0% +right like a you know it's better than a + + + align:start position:0% +right like a you know it's better than a +hattick in hockey right like a perfect + + align:start position:0% +hattick in hockey right like a perfect + + + align:start position:0% +hattick in hockey right like a perfect +game for a pitcher right the the best + + align:start position:0% +game for a pitcher right the the best + + + align:start position:0% +game for a pitcher right the the best +very few films have ever done this uh + + align:start position:0% +very few films have ever done this uh + + + align:start position:0% +very few films have ever done this uh +and in addition and and it turned every + + align:start position:0% +and in addition and and it turned every + + + align:start position:0% +and in addition and and it turned every +one of the major participants in the + + align:start position:0% +one of the major participants in the + + + align:start position:0% +one of the major participants in the +film into major Hollywood players after + + align:start position:0% +film into major Hollywood players after + + + align:start position:0% +film into major Hollywood players after +this + + align:start position:0% +this + + + align:start position:0% +this +film Gable became the what became to be + + align:start position:0% +film Gable became the what became to be + + + align:start position:0% +film Gable became the what became to be +known as the king of Hollywood and for a + + align:start position:0% +known as the king of Hollywood and for a + + + align:start position:0% +known as the king of Hollywood and for a +decade and a half he was the top + + align:start position:0% +decade and a half he was the top + + + align:start position:0% +decade and a half he was the top +grossing actor of in in Hollywood the + + align:start position:0% +grossing actor of in in Hollywood the + + + align:start position:0% +grossing actor of in in Hollywood the +and all of his great work follows after + + align:start position:0% +and all of his great work follows after + + + align:start position:0% +and all of his great work follows after +this film he was in a series of Classic + + align:start position:0% +this film he was in a series of Classic + + + align:start position:0% +this film he was in a series of Classic +Hollywood films to the very end of his + + align:start position:0% +Hollywood films to the very end of his + + + align:start position:0% +Hollywood films to the very end of his +life in his last film with Marilyn + + align:start position:0% +life in his last film with Marilyn + + + align:start position:0% +life in his last film with Marilyn +Monroe anyone you know what it written + + align:start position:0% +Monroe anyone you know what it written + + + align:start position:0% +Monroe anyone you know what it written +by Arthur Miller a film called The + + align:start position:0% +by Arthur Miller a film called The + + + align:start position:0% +by Arthur Miller a film called The +Misfits his very last film he was dying + + align:start position:0% +Misfits his very last film he was dying + + + align:start position:0% +Misfits his very last film he was dying +when he was making that film it's a very + + align:start position:0% +when he was making that film it's a very + + + align:start position:0% +when he was making that film it's a very +moving film you can see that he's dying + + align:start position:0% +moving film you can see that he's dying + + + align:start position:0% +moving film you can see that he's dying +of cancer in the film if you look + + align:start position:0% +of cancer in the film if you look + + + align:start position:0% +of cancer in the film if you look +closely uh but he had a magnificent + + align:start position:0% +closely uh but he had a magnificent + + + align:start position:0% +closely uh but he had a magnificent +career he one of the characteristic + + align:start position:0% +career he one of the characteristic + + + align:start position:0% +career he one of the characteristic +Central iconic actors of the Stu of the + + align:start position:0% +Central iconic actors of the Stu of the + + + align:start position:0% +Central iconic actors of the Stu of the +studio era and this is the film that + + align:start position:0% +studio era and this is the film that + + + align:start position:0% +studio era and this is the film that +made made his there's a moment in the + + align:start position:0% +made made his there's a moment in the + + + align:start position:0% +made made his there's a moment in the +film when you see G table and colar + + align:start position:0% +film when you see G table and colar + + + align:start position:0% +film when you see G table and colar +discussing they're forced to share a + + align:start position:0% +discussing they're forced to share a + + + align:start position:0% +discussing they're forced to share a +motel room and this is very risque in + + align:start position:0% +motel room and this is very risque in + + + align:start position:0% +motel room and this is very risque in +the 1930s man and woman together + + align:start position:0% +the 1930s man and woman together + + + align:start position:0% +the 1930s man and woman together +unmarried in the same room and in fact + + align:start position:0% +unmarried in the same room and in fact + + + align:start position:0% +unmarried in the same room and in fact +they have you know they have separate + + align:start position:0% +they have you know they have separate + + + align:start position:0% +they have you know they have separate +beds but it's a very small room and + + align:start position:0% +beds but it's a very small room and + + + align:start position:0% +beds but it's a very small room and +she's nervous about it and and uh she uh + + align:start position:0% +she's nervous about it and and uh she uh + + + align:start position:0% +she's nervous about it and and uh she uh +uh uh one of the things he does is he + + align:start position:0% +uh uh one of the things he does is he + + + align:start position:0% +uh uh one of the things he does is he +put he he he put puts up a line across + + align:start position:0% +put he he he put puts up a line across + + + align:start position:0% +put he he he put puts up a line across +the room like a cloth line throws a + + align:start position:0% +the room like a cloth line throws a + + + align:start position:0% +the room like a cloth line throws a +blanket over it and he says okay we'll + + align:start position:0% +blanket over it and he says okay we'll + + + align:start position:0% +blanket over it and he says okay we'll +stay on either side of the wall of + + align:start position:0% +stay on either side of the wall of + + + align:start position:0% +stay on either side of the wall of +Jericho right and uh you'll see how the + + align:start position:0% +Jericho right and uh you'll see how the + + + align:start position:0% +Jericho right and uh you'll see how the +of Jericho works out in the final scene + + align:start position:0% +of Jericho works out in the final scene + + + align:start position:0% +of Jericho works out in the final scene +when it comes down um and + + align:start position:0% +when it comes down um and + + + align:start position:0% +when it comes down um and +um there are moments where you could see + + align:start position:0% +um there are moments where you could see + + + align:start position:0% +um there are moments where you could see +the coar character very nervous about + + align:start position:0% +the coar character very nervous about + + + align:start position:0% +the coar character very nervous about +the fact that she's alone with a strange + + align:start position:0% +the fact that she's alone with a strange + + + align:start position:0% +the fact that she's alone with a strange +man in a motel room and she's at his + + align:start position:0% +man in a motel room and she's at his + + + align:start position:0% +man in a motel room and she's at his +Mercy in some sense and there is a kind + + align:start position:0% +Mercy in some sense and there is a kind + + + align:start position:0% +Mercy in some sense and there is a kind +of fre about this and there's a moment + + align:start position:0% +of fre about this and there's a moment + + + align:start position:0% +of fre about this and there's a moment +where where we see them getting ready + + align:start position:0% +where where we see them getting ready + + + align:start position:0% +where where we see them getting ready +for bed Gable takes off his shirt and + + align:start position:0% +for bed Gable takes off his shirt and + + + align:start position:0% +for bed Gable takes off his shirt and +he's not wearing an undershirt he's only + + align:start position:0% +he's not wearing an undershirt he's only + + + align:start position:0% +he's not wearing an undershirt he's only +wearing an outer shirt and it is said it + + align:start position:0% +wearing an outer shirt and it is said it + + + align:start position:0% +wearing an outer shirt and it is said it +has been said so often I can't resist + + align:start position:0% +has been said so often I can't resist + + + align:start position:0% +has been said so often I can't resist +mentioning this to you even though I + + align:start position:0% +mentioning this to you even though I + + + align:start position:0% +mentioning this to you even though I +can't confirm it absolutely but it's + + align:start position:0% +can't confirm it absolutely but it's + + + align:start position:0% +can't confirm it absolutely but it's +mentioned so often in the scholarship + + align:start position:0% +mentioned so often in the scholarship + + + align:start position:0% +mentioned so often in the scholarship +that I want it to be true it is said + + align:start position:0% +that I want it to be true it is said + + + align:start position:0% +that I want it to be true it is said +that the sales of undershirts in the + + align:start position:0% +that the sales of undershirts in the + + + align:start position:0% +that the sales of undershirts in the +United States plummeted after it was + + align:start position:0% +United States plummeted after it was + + + align:start position:0% +United States plummeted after it was +discovered that this actor wasn't + + align:start position:0% +discovered that this actor wasn't + + + align:start position:0% +discovered that this actor wasn't +wearing an undershirt right uh because + + align:start position:0% +wearing an undershirt right uh because + + + align:start position:0% +wearing an undershirt right uh because +that's what men do okay so U but there + + align:start position:0% +that's what men do okay so U but there + + + align:start position:0% +that's what men do okay so U but there +is a larger context for the film the + + align:start position:0% +is a larger context for the film the + + + align:start position:0% +is a larger context for the film the +film takes place during the Depression + + align:start position:0% +film takes place during the Depression + + + align:start position:0% +film takes place during the Depression +and even though it's a comic film about + + align:start position:0% +and even though it's a comic film about + + + align:start position:0% +and even though it's a comic film about +two apparently mismatched creatures who + + align:start position:0% +two apparently mismatched creatures who + + + align:start position:0% +two apparently mismatched creatures who +will come together in the end can you + + align:start position:0% +will come together in the end can you + + + align:start position:0% +will come together in the end can you +guess from the seen in in uh ball of + + align:start position:0% +guess from the seen in in uh ball of + + + align:start position:0% +guess from the seen in in uh ball of +fire what's going to happen to Gary + + align:start position:0% +fire what's going to happen to Gary + + + align:start position:0% +fire what's going to happen to Gary +Cooper and and and and that sexy woman + + align:start position:0% +Cooper and and and and that sexy woman + + + align:start position:0% +Cooper and and and and that sexy woman +by the end of the film of course you + + align:start position:0% +by the end of the film of course you + + + align:start position:0% +by the end of the film of course you +know don't you why do you know it + + align:start position:0% +know don't you why do you know it + + + align:start position:0% +know don't you why do you know it +without ever having seen the film + + align:start position:0% +without ever having seen the film + + + align:start position:0% +without ever having seen the film +because that's what comedy does right + + align:start position:0% +because that's what comedy does right + + + align:start position:0% +because that's what comedy does right +the conventions of Comedy do that and + + align:start position:0% +the conventions of Comedy do that and + + + align:start position:0% +the conventions of Comedy do that and +part of the pleasure in watching that is + + align:start position:0% +part of the pleasure in watching that is + + + align:start position:0% +part of the pleasure in watching that is +to say look how different they are look + + align:start position:0% +to say look how different they are look + + + align:start position:0% +to say look how different they are look +how frightened he is look how look look + + align:start position:0% +how frightened he is look how look look + + + align:start position:0% +how frightened he is look how look look +how aggressive she is how could they + + align:start position:0% +how aggressive she is how could they + + + align:start position:0% +how aggressive she is how could they +ever get together but of course you know + + align:start position:0% +ever get together but of course you know + + + align:start position:0% +ever get together but of course you know +that they will and part of the pleasure + + align:start position:0% +that they will and part of the pleasure + + + align:start position:0% +that they will and part of the pleasure +in watching the film is watching them + + align:start position:0% +in watching the film is watching them + + + align:start position:0% +in watching the film is watching them +get over those barriers well the same + + align:start position:0% +get over those barriers well the same + + + align:start position:0% +get over those barriers well the same +thing happen as you'll see in tonight's + + align:start position:0% +thing happen as you'll see in tonight's + + + align:start position:0% +thing happen as you'll see in tonight's +film but the gap between the go the + + align:start position:0% +film but the gap between the go the + + + align:start position:0% +film but the gap between the go the +Gable character and the coar character + + align:start position:0% +Gable character and the coar character + + + align:start position:0% +Gable character and the coar character +is not just gender male and female it's + + align:start position:0% +is not just gender male and female it's + + + align:start position:0% +is not just gender male and female it's +also a class difference she belongs to + + align:start position:0% +also a class difference she belongs to + + + align:start position:0% +also a class difference she belongs to +the upper classes she has no experience + + align:start position:0% +the upper classes she has no experience + + + align:start position:0% +the upper classes she has no experience +with the outer world at all she's lived + + align:start position:0% +with the outer world at all she's lived + + + align:start position:0% +with the outer world at all she's lived +an incredibly protected life so that + + align:start position:0% +an incredibly protected life so that + + + align:start position:0% +an incredibly protected life so that +when she comes to terms with Gable She's + + align:start position:0% +when she comes to terms with Gable She's + + + align:start position:0% +when she comes to terms with Gable She's +Coming to Terms not only with uh a uh + + align:start position:0% +Coming to Terms not only with uh a uh + + + align:start position:0% +Coming to Terms not only with uh a uh +certain inherited forms of class + + align:start position:0% +certain inherited forms of class + + + align:start position:0% +certain inherited forms of class +Prejudice she's also overcoming a + + align:start position:0% +Prejudice she's also overcoming a + + + align:start position:0% +Prejudice she's also overcoming a +certain kind of innocence and naive + + align:start position:0% +certain kind of innocence and naive + + + align:start position:0% +certain kind of innocence and naive +about her relationship to to to men and + + align:start position:0% +about her relationship to to to men and + + + align:start position:0% +about her relationship to to to men and +her relationship maybe even to her own + + align:start position:0% +her relationship maybe even to her own + + + align:start position:0% +her relationship maybe even to her own +sexuality so it's a the film is a + + align:start position:0% +sexuality so it's a the film is a + + + align:start position:0% +sexuality so it's a the film is a +buildung Roman you know that word novel + + align:start position:0% +buildung Roman you know that word novel + + + align:start position:0% +buildung Roman you know that word novel +about growing up about this woman who + + align:start position:0% +about growing up about this woman who + + + align:start position:0% +about growing up about this woman who +who who who lived a very lives a very + + align:start position:0% +who who who lived a very lives a very + + + align:start position:0% +who who who lived a very lives a very +sheltered life she's a very spoiled rich + + align:start position:0% +sheltered life she's a very spoiled rich + + + align:start position:0% +sheltered life she's a very spoiled rich +girl and the drama of the film is she + + align:start position:0% +girl and the drama of the film is she + + + align:start position:0% +girl and the drama of the film is she +becomes in a certain sense begins to + + align:start position:0% +becomes in a certain sense begins to + + + align:start position:0% +becomes in a certain sense begins to +discover her own real nature begins to + + align:start position:0% +discover her own real nature begins to + + + align:start position:0% +discover her own real nature begins to +begins to discover something about her + + align:start position:0% +begins to discover something about her + + + align:start position:0% +begins to discover something about her +own about her own character and about + + align:start position:0% +own about her own character and about + + + align:start position:0% +own about her own character and about +her own capacity to judge the outer + + align:start position:0% +her own capacity to judge the outer + + + align:start position:0% +her own capacity to judge the outer +World she's very limited and foolish + + align:start position:0% +World she's very limited and foolish + + + align:start position:0% +World she's very limited and foolish +earlier + + align:start position:0% +earlier + + + align:start position:0% +earlier +um the context of the film then is a + + align:start position:0% +um the context of the film then is a + + + align:start position:0% +um the context of the film then is a +dramatization of this relationship but + + align:start position:0% +dramatization of this relationship but + + + align:start position:0% +dramatization of this relationship but +the background of the film is the + + align:start position:0% +the background of the film is the + + + align:start position:0% +the background of the film is the +depression and as you'll see this sexual + + align:start position:0% +depression and as you'll see this sexual + + + align:start position:0% +depression and as you'll see this sexual +and marital Adventure this this this + + align:start position:0% +and marital Adventure this this this + + + align:start position:0% +and marital Adventure this this this +comedy of marriage uh or eventual + + align:start position:0% +comedy of marriage uh or eventual + + + align:start position:0% +comedy of marriage uh or eventual +marriage uh takes place against the + + align:start position:0% +marriage uh takes place against the + + + align:start position:0% +marriage uh takes place against the +backdr a backdrop of suffering and + + align:start position:0% +backdr a backdrop of suffering and + + + align:start position:0% +backdr a backdrop of suffering and +unhappiness and misery uh and and it it + + align:start position:0% +unhappiness and misery uh and and it it + + + align:start position:0% +unhappiness and misery uh and and it it +imparts a resonance and an importance to + + align:start position:0% +imparts a resonance and an importance to + + + align:start position:0% +imparts a resonance and an importance to +the film that it wouldn't otherwise have + + align:start position:0% +the film that it wouldn't otherwise have + + + align:start position:0% +the film that it wouldn't otherwise have +because there are scenes in these + + align:start position:0% +because there are scenes in these + + + align:start position:0% +because there are scenes in these +trailer homes where the coar character + + align:start position:0% +trailer homes where the coar character + + + align:start position:0% +trailer homes where the coar character +completely unused to having to live a + + align:start position:0% +completely unused to having to live a + + + align:start position:0% +completely unused to having to live a +life like that of Ordinary People is + + align:start position:0% +life like that of Ordinary People is + + + align:start position:0% +life like that of Ordinary People is +suddenly forced to confront what such + + align:start position:0% +suddenly forced to confront what such + + + align:start position:0% +suddenly forced to confront what such +lives are what such a life is like and + + align:start position:0% +lives are what such a life is like and + + + align:start position:0% +lives are what such a life is like and +it's part of her of of her education um + + align:start position:0% +it's part of her of of her education um + + + align:start position:0% +it's part of her of of her education um +so the context of the depression is + + align:start position:0% +so the context of the depression is + + + align:start position:0% +so the context of the depression is +important a second fundamental thing as + + align:start position:0% +important a second fundamental thing as + + + align:start position:0% +important a second fundamental thing as +I've already implied by my anecdote + + align:start position:0% +I've already implied by my anecdote + + + align:start position:0% +I've already implied by my anecdote +about the undershirt is that the Gable + + align:start position:0% +about the undershirt is that the Gable + + + align:start position:0% +about the undershirt is that the Gable +character came to stand for an ideal of + + align:start position:0% +character came to stand for an ideal of + + + align:start position:0% +character came to stand for an ideal of +American masculinity in the in the scene + + align:start position:0% +American masculinity in the in the scene + + + align:start position:0% +American masculinity in the in the scene +where he is first introduced he's half + + align:start position:0% +where he is first introduced he's half + + + align:start position:0% +where he is first introduced he's half +drunk and it's important for you to + + align:start position:0% +drunk and it's important for you to + + + align:start position:0% +drunk and it's important for you to +understand the context here because it's + + align:start position:0% +understand the context here because it's + + + align:start position:0% +understand the context here because it's +not exactly celebrating drunkenness + + align:start position:0% +not exactly celebrating drunkenness + + + align:start position:0% +not exactly celebrating drunkenness +although it partly is I mean he's he's a + + align:start position:0% +although it partly is I mean he's he's a + + + align:start position:0% +although it partly is I mean he's he's a +man's man right we see him get drunk and + + align:start position:0% +man's man right we see him get drunk and + + + align:start position:0% +man's man right we see him get drunk and +talk on the telephone to his editor boss + + align:start position:0% +talk on the telephone to his editor boss + + + align:start position:0% +talk on the telephone to his editor boss +who fires him right and but he staggers + + align:start position:0% +who fires him right and but he staggers + + + align:start position:0% +who fires him right and but he staggers +out of the phone booth and he's talking + + align:start position:0% +out of the phone booth and he's talking + + + align:start position:0% +out of the phone booth and he's talking +to his friends and he says I'm the king + + align:start position:0% +to his friends and he says I'm the king + + + align:start position:0% +to his friends and he says I'm the king +this is where the word where where the + + align:start position:0% +this is where the word where where the + + + align:start position:0% +this is where the word where where the +term the king of Hollywood originates in + + align:start position:0% +term the king of Hollywood originates in + + + align:start position:0% +term the king of Hollywood originates in +the lines that you see in the film uh + + align:start position:0% +the lines that you see in the film uh + + + align:start position:0% +the lines that you see in the film uh +but what but but it's important for you + + align:start position:0% +but what but but it's important for you + + + align:start position:0% +but what but but it's important for you +to understand that part of what's going + + align:start position:0% +to understand that part of what's going + + + align:start position:0% +to understand that part of what's going +on here it's + + align:start position:0% +on here it's + + + align:start position:0% +on here it's +1934 prohibition has just been lifted + + align:start position:0% +1934 prohibition has just been lifted + + + align:start position:0% +1934 prohibition has just been lifted +right and what's being dramatized there + + align:start position:0% +right and what's being dramatized there + + + align:start position:0% +right and what's being dramatized there +it's legal for him to drink for the + + align:start position:0% +it's legal for him to drink for the + + + align:start position:0% +it's legal for him to drink for the +first time in whatever it is a decade + + align:start position:0% +first time in whatever it is a decade + + + align:start position:0% +first time in whatever it is a decade +and the film is partly celebrating that + + align:start position:0% +and the film is partly celebrating that + + + align:start position:0% +and the film is partly celebrating that +right so you're not supposed to think of + + align:start position:0% +right so you're not supposed to think of + + + align:start position:0% +right so you're not supposed to think of +him as some ridiculous rout drunkard + + align:start position:0% +him as some ridiculous rout drunkard + + + align:start position:0% +him as some ridiculous rout drunkard +you're supposed to recognize that what's + + align:start position:0% +you're supposed to recognize that what's + + + align:start position:0% +you're supposed to recognize that what's +partly being dramatized there is the is + + align:start position:0% +partly being dramatized there is the is + + + align:start position:0% +partly being dramatized there is the is +the is the New Freedom that has emerged + + align:start position:0% +the is the New Freedom that has emerged + + + align:start position:0% +the is the New Freedom that has emerged +in American society now that prohibition + + align:start position:0% +in American society now that prohibition + + + align:start position:0% +in American society now that prohibition +has been has been repealed and in that + + align:start position:0% +has been has been repealed and in that + + + align:start position:0% +has been has been repealed and in that +scene you can see something uh because + + align:start position:0% +scene you can see something uh because + + + align:start position:0% +scene you can see something uh because +his his half drunkenness re reduces some + + align:start position:0% +his his half drunkenness re reduces some + + + align:start position:0% +his his half drunkenness re reduces some +of his inhibition you can see something + + align:start position:0% +of his inhibition you can see something + + + align:start position:0% +of his inhibition you can see something +of his true nature there and what you + + align:start position:0% +of his true nature there and what you + + + align:start position:0% +of his true nature there and what you +discover is I and you can see this come + + align:start position:0% +discover is I and you can see this come + + + align:start position:0% +discover is I and you can see this come +out elsewhere in the film too something + + align:start position:0% +out elsewhere in the film too something + + + align:start position:0% +out elsewhere in the film too something +that the coar character at first can't + + align:start position:0% +that the coar character at first can't + + + align:start position:0% +that the coar character at first can't +recognize that he has a heart of gold + + align:start position:0% +recognize that he has a heart of gold + + + align:start position:0% +recognize that he has a heart of gold +that he's a decent admirable person that + + align:start position:0% +that he's a decent admirable person that + + + align:start position:0% +that he's a decent admirable person that +he would never treat anyone badly but + + align:start position:0% +he would never treat anyone badly but + + + align:start position:0% +he would never treat anyone badly but +he's also very self-reliant and no one + + align:start position:0% +he's also very self-reliant and no one + + + align:start position:0% +he's also very self-reliant and no one +can push him around he's a particular + + align:start position:0% +can push him around he's a particular + + + align:start position:0% +can push him around he's a particular +kind of represents a particular kind of + + align:start position:0% +kind of represents a particular kind of + + + align:start position:0% +kind of represents a particular kind of +masculine ideal right he can't be + + align:start position:0% +masculine ideal right he can't be + + + align:start position:0% +masculine ideal right he can't be +intimidated but he'll never mistreat + + align:start position:0% +intimidated but he'll never mistreat + + + align:start position:0% +intimidated but he'll never mistreat +someone he has a kind of moral compass + + align:start position:0% +someone he has a kind of moral compass + + + align:start position:0% +someone he has a kind of moral compass +that guides his behavior even though + + align:start position:0% +that guides his behavior even though + + + align:start position:0% +that guides his behavior even though +it's implicit right uh he's a bit vulgar + + align:start position:0% +it's implicit right uh he's a bit vulgar + + + align:start position:0% +it's implicit right uh he's a bit vulgar +he's a he he's suspicious of wealth and + + align:start position:0% +he's a he he's suspicious of wealth and + + + align:start position:0% +he's a he he's suspicious of wealth and +pretension right the Gable character + + align:start position:0% +pretension right the Gable character + + + align:start position:0% +pretension right the Gable character +came to stand for a particular kind of + + align:start position:0% +came to stand for a particular kind of + + + align:start position:0% +came to stand for a particular kind of +American masculinity that was celebrated + + align:start position:0% +American masculinity that was celebrated + + + align:start position:0% +American masculinity that was celebrated +over and over again in in American + + align:start position:0% +over and over again in in American + + + align:start position:0% +over and over again in in American +movies a kind of a type of the American + + align:start position:0% +movies a kind of a type of the American + + + align:start position:0% +movies a kind of a type of the American +male I've already said that one of the + + align:start position:0% +male I've already said that one of the + + + align:start position:0% +male I've already said that one of the +things the film does also is dramatize a + + align:start position:0% +things the film does also is dramatize a + + + align:start position:0% +things the film does also is dramatize a +romance across social class and you + + align:start position:0% +romance across social class and you + + + align:start position:0% +romance across social class and you +might want to think about the way in + + align:start position:0% +might want to think about the way in + + + align:start position:0% +might want to think about the way in +which the almost all in almost all + + align:start position:0% +which the almost all in almost all + + + align:start position:0% +which the almost all in almost all +comedy uh that's certainly comedies that + + align:start position:0% +comedy uh that's certainly comedies that + + + align:start position:0% +comedy uh that's certainly comedies that +involve uh comedies about marriage + + align:start position:0% +involve uh comedies about marriage + + + align:start position:0% +involve uh comedies about marriage +comedies about about about uh me men and + + align:start position:0% +comedies about about about uh me men and + + + align:start position:0% +comedies about about about uh me men and +women uh almost all such comedies + + align:start position:0% +women uh almost all such comedies + + + align:start position:0% +women uh almost all such comedies +involve some notion of uh barriers of + + align:start position:0% +involve some notion of uh barriers of + + + align:start position:0% +involve some notion of uh barriers of +some sort that are placed in the way of + + align:start position:0% +some sort that are placed in the way of + + + align:start position:0% +some sort that are placed in the way of +the consummation in which the text wants + + align:start position:0% +the consummation in which the text wants + + + align:start position:0% +the consummation in which the text wants +to end right and those barriers can take + + align:start position:0% +to end right and those barriers can take + + + align:start position:0% +to end right and those barriers can take +many forms but one of the most + + align:start position:0% +many forms but one of the most + + + align:start position:0% +many forms but one of the most +fundamental forms they take over and + + align:start position:0% +fundamental forms they take over and + + + align:start position:0% +fundamental forms they take over and +over again is the barrier of class and + + align:start position:0% +over again is the barrier of class and + + + align:start position:0% +over again is the barrier of class and +one of the things that the coar + + align:start position:0% +one of the things that the coar + + + align:start position:0% +one of the things that the coar +character and the Gable character both + + align:start position:0% +character and the Gable character both + + + align:start position:0% +character and the Gable character both +have to do is get over their prejudices + + align:start position:0% +have to do is get over their prejudices + + + align:start position:0% +have to do is get over their prejudices +get over their their blind spots about + + align:start position:0% +get over their their blind spots about + + + align:start position:0% +get over their their blind spots about +the social classes they have uh less + + align:start position:0% +the social classes they have uh less + + + align:start position:0% +the social classes they have uh less +understanding of one of the most moving + + align:start position:0% +understanding of one of the most moving + + + align:start position:0% +understanding of one of the most moving +and Powerful aspects of the film and I + + align:start position:0% +and Powerful aspects of the film and I + + + align:start position:0% +and Powerful aspects of the film and I +think you'll see this uh really + + align:start position:0% +think you'll see this uh really + + + align:start position:0% +think you'll see this uh really +powerfully uh uh is the way in which the + + align:start position:0% +powerfully uh uh is the way in which the + + + align:start position:0% +powerfully uh uh is the way in which the +audience comes to have an understanding + + align:start position:0% +audience comes to have an understanding + + + align:start position:0% +audience comes to have an understanding +of the characters that exceeds that of + + align:start position:0% +of the characters that exceeds that of + + + align:start position:0% +of the characters that exceeds that of +the characters and that there are many + + align:start position:0% +the characters and that there are many + + + align:start position:0% +the characters and that there are many +moments there are many moments in the + + align:start position:0% +moments there are many moments in the + + + align:start position:0% +moments there are many moments in the +film in which you understand how the + + align:start position:0% +film in which you understand how the + + + align:start position:0% +film in which you understand how the +characters are feeling before they are + + align:start position:0% +characters are feeling before they are + + + align:start position:0% +characters are feeling before they are +able to acknowledge it themselves you + + align:start position:0% +able to acknowledge it themselves you + + + align:start position:0% +able to acknowledge it themselves you +can see them for falling in love for + + align:start position:0% +can see them for falling in love for + + + align:start position:0% +can see them for falling in love for +example without them being able to admit + + align:start position:0% +example without them being able to admit + + + align:start position:0% +example without them being able to admit +it to themselves uh you can see and and + + align:start position:0% +it to themselves uh you can see and and + + + align:start position:0% +it to themselves uh you can see and and +it's an immensely think of what an + + align:start position:0% +it's an immensely think of what an + + + align:start position:0% +it's an immensely think of what an +immensely subtle trick that is to put + + align:start position:0% +immensely subtle trick that is to put + + + align:start position:0% +immensely subtle trick that is to put +the viewer in possession of information + + align:start position:0% +the viewer in possession of information + + + align:start position:0% +the viewer in possession of information +or knowledge that the characters + + align:start position:0% +or knowledge that the characters + + + align:start position:0% +or knowledge that the characters +themselves don't have and what a rich + + align:start position:0% +themselves don't have and what a rich + + + align:start position:0% +themselves don't have and what a rich +kind of knowledge and ironic perspective + + align:start position:0% +kind of knowledge and ironic perspective + + + align:start position:0% +kind of knowledge and ironic perspective +a rich kind of irony that generates for + + align:start position:0% +a rich kind of irony that generates for + + + align:start position:0% +a rich kind of irony that generates for +the for the viewing of the film a + + align:start position:0% +the for the viewing of the film a + + + align:start position:0% +the for the viewing of the film a +marriage of true minds there's a famous + + align:start position:0% +marriage of true minds there's a famous + + + align:start position:0% +marriage of true minds there's a famous +sonnet by Shakespeare that begins let me + + align:start position:0% +sonnet by Shakespeare that begins let me + + + align:start position:0% +sonnet by Shakespeare that begins let me +not to the marriage of true minds admit + + align:start position:0% +not to the marriage of true minds admit + + + align:start position:0% +not to the marriage of true minds admit +impediments right the impediments to the + + align:start position:0% +impediments right the impediments to the + + + align:start position:0% +impediments right the impediments to the +marriage of true minds in this in this + + align:start position:0% +marriage of true minds in this in this + + + align:start position:0% +marriage of true minds in this in this +uh uh film have to do with uh the + + align:start position:0% +uh uh film have to do with uh the + + + align:start position:0% +uh uh film have to do with uh the +characters the the coar characters naive + + align:start position:0% +characters the the coar characters naive + + + align:start position:0% +characters the the coar characters naive +t with the prejudices and self-reliance + + align:start position:0% +t with the prejudices and self-reliance + + + align:start position:0% +t with the prejudices and self-reliance +of the of the Gable character uh with + + align:start position:0% +of the of the Gable character uh with + + + align:start position:0% +of the of the Gable character uh with +with the social realities of the + + align:start position:0% +with the social realities of the + + + align:start position:0% +with the social realities of the +depression uh and these bar these these + + align:start position:0% +depression uh and these bar these these + + + align:start position:0% +depression uh and these bar these these +barriers have to be overcome but there's + + align:start position:0% +barriers have to be overcome but there's + + + align:start position:0% +barriers have to be overcome but there's +a a marriage of true minds what could + + align:start position:0% +a a marriage of true minds what could + + + align:start position:0% +a a marriage of true minds what could +the phrase mean marriage of equals a + + align:start position:0% +the phrase mean marriage of equals a + + + align:start position:0% +the phrase mean marriage of equals a +marriage of people who are not different + + align:start position:0% +marriage of people who are not different + + + align:start position:0% +marriage of people who are not different +the deepest thing I love about this + + align:start position:0% +the deepest thing I love about this + + + align:start position:0% +the deepest thing I love about this +movie and the the reason that I've come + + align:start position:0% +movie and the the reason that I've come + + + align:start position:0% +movie and the the reason that I've come +that I treasured this film even though + + align:start position:0% +that I treasured this film even though + + + align:start position:0% +that I treasured this film even though +there are many old-fashioned qualities + + align:start position:0% +there are many old-fashioned qualities + + + align:start position:0% +there are many old-fashioned qualities +in it that make it feel old and distant + + align:start position:0% +in it that make it feel old and distant + + + align:start position:0% +in it that make it feel old and distant +in some sense from contemporary Society + + align:start position:0% +in some sense from contemporary Society + + + align:start position:0% +in some sense from contemporary Society +is its understanding of it's implicit + + align:start position:0% +is its understanding of it's implicit + + + align:start position:0% +is its understanding of it's implicit +idealized understanding of marriage + + align:start position:0% +idealized understanding of marriage + + + align:start position:0% +idealized understanding of marriage +because what the film really wants to + + align:start position:0% +because what the film really wants to + + + align:start position:0% +because what the film really wants to +suggest is not that first of all it + + align:start position:0% +suggest is not that first of all it + + + align:start position:0% +suggest is not that first of all it +suggest that these people are drawn to + + align:start position:0% +suggest that these people are drawn to + + + align:start position:0% +suggest that these people are drawn to +each other sexually it's not embarrassed + + align:start position:0% +each other sexually it's not embarrassed + + + align:start position:0% +each other sexually it's not embarrassed +by the fact that they're both physically + + align:start position:0% +by the fact that they're both physically + + + align:start position:0% +by the fact that they're both physically +beautiful people and that they feel + + align:start position:0% +beautiful people and that they feel + + + align:start position:0% +beautiful people and that they feel +attraction for each other that they + + align:start position:0% +attraction for each other that they + + + align:start position:0% +attraction for each other that they +can't themselves fully acknowledge or or + + align:start position:0% +can't themselves fully acknowledge or or + + + align:start position:0% +can't themselves fully acknowledge or or +deal with right but the second kind of + + align:start position:0% +deal with right but the second kind of + + + align:start position:0% +deal with right but the second kind of +Attraction they have is a mental + + align:start position:0% +Attraction they have is a mental + + + align:start position:0% +Attraction they have is a mental +attraction you realize that they're both + + align:start position:0% +attraction you realize that they're both + + + align:start position:0% +attraction you realize that they're both +deeply intelligent people that they're + + align:start position:0% +deeply intelligent people that they're + + + align:start position:0% +deeply intelligent people that they're +both people who are deeply verbal that + + align:start position:0% +both people who are deeply verbal that + + + align:start position:0% +both people who are deeply verbal that +they that they both have improv + + align:start position:0% +they that they both have improv + + + align:start position:0% +they that they both have improv +improvisatory Powers intellectual powers + + align:start position:0% +improvisatory Powers intellectual powers + + + align:start position:0% +improvisatory Powers intellectual powers +that distinguish them from other people + + align:start position:0% +that distinguish them from other people + + + align:start position:0% +that distinguish them from other people +that they're made for each other + + align:start position:0% +that they're made for each other + + + align:start position:0% +that they're made for each other +essentially there's one scene that shows + + align:start position:0% +essentially there's one scene that shows + + + align:start position:0% +essentially there's one scene that shows +this before they realize it we realize + + align:start position:0% +this before they realize it we realize + + + align:start position:0% +this before they realize it we realize +it it's a wonderful scene in they're + + align:start position:0% +it it's a wonderful scene in they're + + + align:start position:0% +it it's a wonderful scene in they're +hiding out in a motel and at a certain + + align:start position:0% +hiding out in a motel and at a certain + + + align:start position:0% +hiding out in a motel and at a certain +point she's on the run her father's her + + align:start position:0% +point she's on the run her father's her + + + align:start position:0% +point she's on the run her father's her +rich father is searching for her and the + + align:start position:0% +rich father is searching for her and the + + + align:start position:0% +rich father is searching for her and the +Gable character is a reporter says I'll + + align:start position:0% +Gable character is a reporter says I'll + + + align:start position:0% +Gable character is a reporter says I'll +protect you and help you if you give me + + align:start position:0% +protect you and help you if you give me + + + align:start position:0% +protect you and help you if you give me +your if you let me have an exclusive + + align:start position:0% +your if you let me have an exclusive + + + align:start position:0% +your if you let me have an exclusive +story because she's such a rich ays that + + align:start position:0% +story because she's such a rich ays that + + + align:start position:0% +story because she's such a rich ays that +she's big news so she agrees and he's + + align:start position:0% +she's big news so she agrees and he's + + + align:start position:0% +she's big news so she agrees and he's +esorting her North right hiding from the + + align:start position:0% +esorting her North right hiding from the + + + align:start position:0% +esorting her North right hiding from the +people who are searching for her right + + align:start position:0% +people who are searching for her right + + + align:start position:0% +people who are searching for her right +uh and at a certain point they were in a + + align:start position:0% +uh and at a certain point they were in a + + + align:start position:0% +uh and at a certain point they were in a +motel some private cops knock on the + + align:start position:0% +motel some private cops knock on the + + + align:start position:0% +motel some private cops knock on the +door of the hotel and they come in and + + align:start position:0% +door of the hotel and they come in and + + + align:start position:0% +door of the hotel and they come in and +they're searching for her and Watch What + + align:start position:0% +they're searching for her and Watch What + + + align:start position:0% +they're searching for her and Watch What +Happens what what Gable and the coar + + align:start position:0% +Happens what what Gable and the coar + + + align:start position:0% +Happens what what Gable and the coar +character do is they immediate Gable + + align:start position:0% +character do is they immediate Gable + + + align:start position:0% +character do is they immediate Gable +says follow my lead and then when they + + align:start position:0% +says follow my lead and then when they + + + align:start position:0% +says follow my lead and then when they +come in they begin to play husband and + + align:start position:0% +come in they begin to play husband and + + + align:start position:0% +come in they begin to play husband and +wife having a tremendous quarrel and you + + align:start position:0% +wife having a tremendous quarrel and you + + + align:start position:0% +wife having a tremendous quarrel and you +can want you can see that they're + + align:start position:0% +can want you can see that they're + + + align:start position:0% +can want you can see that they're +improvising it and you can see they're + + align:start position:0% +improvising it and you can see they're + + + align:start position:0% +improvising it and you can see they're +enjoying it and you can see how well + + align:start position:0% +enjoying it and you can see how well + + + align:start position:0% +enjoying it and you can see how well +they play with each other right so in + + align:start position:0% +they play with each other right so in + + + align:start position:0% +they play with each other right so in +other words it's a moment in which you + + align:start position:0% +other words it's a moment in which you + + + align:start position:0% +other words it's a moment in which you +can see that it is a marriage of true + + align:start position:0% +can see that it is a marriage of true + + + align:start position:0% +can see that it is a marriage of true +minds long before the characters + + align:start position:0% +minds long before the characters + + + align:start position:0% +minds long before the characters +themselves fully recognize how they are + + align:start position:0% +themselves fully recognize how they are + + + align:start position:0% +themselves fully recognize how they are +men for each other it's a wonderful + + align:start position:0% +men for each other it's a wonderful + + + align:start position:0% +men for each other it's a wonderful +moment in which their intimacy and their + + align:start position:0% +moment in which their intimacy and their + + + align:start position:0% +moment in which their intimacy and their +appropriateness for each other is + + align:start position:0% +appropriateness for each other is + + + align:start position:0% +appropriateness for each other is +dramatized it's not only a physical or a + + align:start position:0% +dramatized it's not only a physical or a + + + align:start position:0% +dramatized it's not only a physical or a +or or a sexual thing it's also an + + align:start position:0% +or or a sexual thing it's also an + + + align:start position:0% +or or a sexual thing it's also an +intellectual and a moral a mental thing + + align:start position:0% +intellectual and a moral a mental thing + + + align:start position:0% +intellectual and a moral a mental thing +a psychological thing these they are it + + align:start position:0% +a psychological thing these they are it + + + align:start position:0% +a psychological thing these they are it +will be a marriage of true minds if they + + align:start position:0% +will be a marriage of true minds if they + + + align:start position:0% +will be a marriage of true minds if they +can come together I want to end just + + align:start position:0% +can come together I want to end just + + + align:start position:0% +can come together I want to end just +finally mention I've mentioned the + + align:start position:0% +finally mention I've mentioned the + + + align:start position:0% +finally mention I've mentioned the +ending already and I'll just I'll just + + align:start position:0% +ending already and I'll just I'll just + + + align:start position:0% +ending already and I'll just I'll just +say one more time that watch how the + + align:start position:0% +say one more time that watch how the + + + align:start position:0% +say one more time that watch how the +ending works out and you'll see a + + align:start position:0% +ending works out and you'll see a + + + align:start position:0% +ending works out and you'll see a +magnificent example of a director + + align:start position:0% +magnificent example of a director + + + align:start position:0% +magnificent example of a director +dealing with contingencies he could not + + align:start position:0% +dealing with contingencies he could not + + + align:start position:0% +dealing with contingencies he could not +possibly have anticipated and it's a + + align:start position:0% +possibly have anticipated and it's a + + + align:start position:0% +possibly have anticipated and it's a +wonder wonderful example of a kind of + + align:start position:0% +wonder wonderful example of a kind of + + + align:start position:0% +wonder wonderful example of a kind of +inventiveness seems to me the film ends + + align:start position:0% +inventiveness seems to me the film ends + + + align:start position:0% +inventiveness seems to me the film ends +as well as it could end and it's better + + align:start position:0% +as well as it could end and it's better + + + align:start position:0% +as well as it could end and it's better +that the actors aren't there but he + + align:start position:0% +that the actors aren't there but he + + + align:start position:0% +that the actors aren't there but he +certainly when he was when this happened + + align:start position:0% +certainly when he was when this happened + + + align:start position:0% +certainly when he was when this happened +I'm sure that kapra thought it was the + + align:start position:0% +I'm sure that kapra thought it was the + + + align:start position:0% +I'm sure that kapra thought it was the +end of his film and that he was didn't + + align:start position:0% +end of his film and that he was didn't + + + align:start position:0% +end of his film and that he was didn't +know what he was going to do to try to + + align:start position:0% +know what he was going to do to try to + + + align:start position:0% +know what he was going to do to try to +finish his film without his star actress + + align:start position:0% +finish his film without his star actress + + + align:start position:0% +finish his film without his star actress +I have to be even briefer about his girl + + align:start position:0% +I have to be even briefer about his girl + + + align:start position:0% +I have to be even briefer about his girl +Friday but I think it's a more + + align:start position:0% +Friday but I think it's a more + + + align:start position:0% +Friday but I think it's a more +straightforward film in some respects uh + + align:start position:0% +straightforward film in some respects uh + + + align:start position:0% +straightforward film in some respects uh +it's a much less sentimental film and I + + align:start position:0% +it's a much less sentimental film and I + + + align:start position:0% +it's a much less sentimental film and I +hope you'll recognize How Deeply how + + align:start position:0% +hope you'll recognize How Deeply how + + + align:start position:0% +hope you'll recognize How Deeply how +much more deeply un sentimental even + + align:start position:0% +much more deeply un sentimental even + + + align:start position:0% +much more deeply un sentimental even +cynical or at least deeply tough-minded + + align:start position:0% +cynical or at least deeply tough-minded + + + align:start position:0% +cynical or at least deeply tough-minded +and suspicious skeptical Howard Hawks is + + align:start position:0% +and suspicious skeptical Howard Hawks is + + + align:start position:0% +and suspicious skeptical Howard Hawks is +about all of the operations of the world + + align:start position:0% +about all of the operations of the world + + + align:start position:0% +about all of the operations of the world +not only about individual human motives + + align:start position:0% +not only about individual human motives + + + align:start position:0% +not only about individual human motives +but about all human institutions + + align:start position:0% +but about all human institutions + + + align:start position:0% +but about all human institutions +virtually everyone in his girl Friday is + + align:start position:0% +virtually everyone in his girl Friday is + + + align:start position:0% +virtually everyone in his girl Friday is +a is a cynical self self-seeking creep + + align:start position:0% +a is a cynical self self-seeking creep + + + align:start position:0% +a is a cynical self self-seeking creep +uh uh even the primary characters the + + align:start position:0% +uh uh even the primary characters the + + + align:start position:0% +uh uh even the primary characters the +Ros Russell character and the Carrie + + align:start position:0% +Ros Russell character and the Carrie + + + align:start position:0% +Ros Russell character and the Carrie +Grant character have um intrigues + + align:start position:0% +Grant character have um intrigues + + + align:start position:0% +Grant character have um intrigues +manipulative elements in their natures + + align:start position:0% +manipulative elements in their natures + + + align:start position:0% +manipulative elements in their natures +and you can see especially that the + + align:start position:0% +and you can see especially that the + + + align:start position:0% +and you can see especially that the +Carrie Grand character is in in in some + + align:start position:0% +Carrie Grand character is in in in some + + + align:start position:0% +Carrie Grand character is in in in some +respects a very nasty piece of work he + + align:start position:0% +respects a very nasty piece of work he + + + align:start position:0% +respects a very nasty piece of work he +does terrible terrible things to poor + + align:start position:0% +does terrible terrible things to poor + + + align:start position:0% +does terrible terrible things to poor +Ralph Bellamy the man that Ros Russell + + align:start position:0% +Ralph Bellamy the man that Ros Russell + + + align:start position:0% +Ralph Bellamy the man that Ros Russell +is supposed to marry her fiance and he's + + align:start position:0% +is supposed to marry her fiance and he's + + + align:start position:0% +is supposed to marry her fiance and he's +a he plays a sort of straight sweet + + align:start position:0% +a he plays a sort of straight sweet + + + align:start position:0% +a he plays a sort of straight sweet +straightforward kind of person very much + + align:start position:0% +straightforward kind of person very much + + + align:start position:0% +straightforward kind of person very much +in love with his girlfriend but + + align:start position:0% +in love with his girlfriend but + + + align:start position:0% +in love with his girlfriend but +completely but how could we put but he's + + align:start position:0% +completely but how could we put but he's + + + align:start position:0% +completely but how could we put but he's +a dummy he's stupid and even though he's + + align:start position:0% +a dummy he's stupid and even though he's + + + align:start position:0% +a dummy he's stupid and even though he's +very nice you don't really like him you + + align:start position:0% +very nice you don't really like him you + + + align:start position:0% +very nice you don't really like him you +think he's a jerk the the film the film + + align:start position:0% +think he's a jerk the the film the film + + + align:start position:0% +think he's a jerk the the film the film +makes you mean or nasty in some sense + + align:start position:0% +makes you mean or nasty in some sense + + + align:start position:0% +makes you mean or nasty in some sense +because it makes you it makes you see + + align:start position:0% +because it makes you it makes you see + + + align:start position:0% +because it makes you it makes you see +things from the perspective of the + + align:start position:0% +things from the perspective of the + + + align:start position:0% +things from the perspective of the +Carrie Grant character it encourages you + + align:start position:0% +Carrie Grant character it encourages you + + + align:start position:0% +Carrie Grant character it encourages you +to be tough-minded and skeptical and and + + align:start position:0% +to be tough-minded and skeptical and and + + + align:start position:0% +to be tough-minded and skeptical and and +you do come away from the film thinking + + align:start position:0% +you do come away from the film thinking + + + align:start position:0% +you do come away from the film thinking +oh gee I've participated in the + + align:start position:0% +oh gee I've participated in the + + + align:start position:0% +oh gee I've participated in the +humiliation of this poor decent guy but + + align:start position:0% +humiliation of this poor decent guy but + + + align:start position:0% +humiliation of this poor decent guy but +anyway he's deserved that he's such a + + align:start position:0% +anyway he's deserved that he's such a + + + align:start position:0% +anyway he's deserved that he's such a +stupid Mark right you can't you almost + + align:start position:0% +stupid Mark right you can't you almost + + + align:start position:0% +stupid Mark right you can't you almost +can't help that kind of reaction + + align:start position:0% +can't help that kind of reaction + + + align:start position:0% +can't help that kind of reaction +um the film is based on what had been a + + align:start position:0% +um the film is based on what had been a + + + align:start position:0% +um the film is based on what had been a +very successful play uh on way some + + align:start position:0% +very successful play uh on way some + + + align:start position:0% +very successful play uh on way some +generation earlier and that play was + + align:start position:0% +generation earlier and that play was + + + align:start position:0% +generation earlier and that play was +made into a film in 1930 that was quite + + align:start position:0% +made into a film in 1930 that was quite + + + align:start position:0% +made into a film in 1930 that was quite +successful directed by leis Milestone + + align:start position:0% +successful directed by leis Milestone + + + align:start position:0% +successful directed by leis Milestone +but the Hawks film is the classic + + align:start position:0% +but the Hawks film is the classic + + + align:start position:0% +but the Hawks film is the classic +version of it and Hawks does one thing + + align:start position:0% +version of it and Hawks does one thing + + + align:start position:0% +version of it and Hawks does one thing +that's very important that changes the + + align:start position:0% +that's very important that changes the + + + align:start position:0% +that's very important that changes the +original changes the play in a + + align:start position:0% +original changes the play in a + + + align:start position:0% +original changes the play in a +fundamental way in the original play the + + align:start position:0% +fundamental way in the original play the + + + align:start position:0% +fundamental way in the original play the +character played by the rosn Russell + + align:start position:0% +character played by the rosn Russell + + + align:start position:0% +character played by the rosn Russell +figure in the movie is a male character + + align:start position:0% +figure in the movie is a male character + + + align:start position:0% +figure in the movie is a male character +and the great the Great Discovery or the + + align:start position:0% +and the great the Great Discovery or the + + + align:start position:0% +and the great the Great Discovery or the +great transformation that was Ro in the + + align:start position:0% +great transformation that was Ro in the + + + align:start position:0% +great transformation that was Ro in the +film by Howard Hawks was his decision to + + align:start position:0% +film by Howard Hawks was his decision to + + + align:start position:0% +film by Howard Hawks was his decision to +turn that character a guy named Johnson + + align:start position:0% +turn that character a guy named Johnson + + + align:start position:0% +turn that character a guy named Johnson +from a male Johnson into Hildegard + + align:start position:0% +from a male Johnson into Hildegard + + + align:start position:0% +from a male Johnson into Hildegard +Johnson uh Hildy Johnson the character + + align:start position:0% +Johnson uh Hildy Johnson the character + + + align:start position:0% +Johnson uh Hildy Johnson the character +played by rosn Russell and as soon as he + + align:start position:0% +played by rosn Russell and as soon as he + + + align:start position:0% +played by rosn Russell and as soon as he +turned her into a into a woman he + + align:start position:0% +turned her into a into a woman he + + + align:start position:0% +turned her into a into a woman he +created his screw ball comedy he created + + align:start position:0% +created his screw ball comedy he created + + + align:start position:0% +created his screw ball comedy he created +a wonderful kind of antagonist for the + + align:start position:0% +a wonderful kind of antagonist for the + + + align:start position:0% +a wonderful kind of antagonist for the +Carrie Grant character + + align:start position:0% +Carrie Grant character + + + align:start position:0% +Carrie Grant character +um I've already indicated to you how + + align:start position:0% +um I've already indicated to you how + + + align:start position:0% +um I've already indicated to you how +many how many uh uh um how many films uh + + align:start position:0% +many how many uh uh um how many films uh + + + align:start position:0% +many how many uh uh um how many films uh +in different genres Hawks uh directed + + align:start position:0% +in different genres Hawks uh directed + + + align:start position:0% +in different genres Hawks uh directed +remember that list I put up there was + + align:start position:0% +remember that list I put up there was + + + align:start position:0% +remember that list I put up there was +not a complete list at all it was a + + align:start position:0% +not a complete list at all it was a + + + align:start position:0% +not a complete list at all it was a +selected list but it was the some of the + + align:start position:0% +selected list but it was the some of the + + + align:start position:0% +selected list but it was the some of the +most important films by each by each + + align:start position:0% +most important films by each by each + + + align:start position:0% +most important films by each by each +director and and uh um one of the things + + align:start position:0% +director and and uh um one of the things + + + align:start position:0% +director and and uh um one of the things +that's really interesting about hawks is + + align:start position:0% +that's really interesting about hawks is + + + align:start position:0% +that's really interesting about hawks is +that he directs westerns and and and + + align:start position:0% +that he directs westerns and and and + + + align:start position:0% +that he directs westerns and and and +scre ball comedies and private eye films + + align:start position:0% +scre ball comedies and private eye films + + + align:start position:0% +scre ball comedies and private eye films +and War movies uh and and uh a range of + + align:start position:0% +and War movies uh and and uh a range of + + + align:start position:0% +and War movies uh and and uh a range of +other uh uh lesser sort of non genre + + align:start position:0% +other uh uh lesser sort of non genre + + + align:start position:0% +other uh uh lesser sort of non genre +films as well uh and yet in all of them + + align:start position:0% +films as well uh and yet in all of them + + + align:start position:0% +films as well uh and yet in all of them +there are certain through lines you can + + align:start position:0% +there are certain through lines you can + + + align:start position:0% +there are certain through lines you can +recognize certain recurring themes + + align:start position:0% +recognize certain recurring themes + + + align:start position:0% +recognize certain recurring themes +across these radically different films + + align:start position:0% +across these radically different films + + + align:start position:0% +across these radically different films +and one of the most fun and and one of + + align:start position:0% +and one of the most fun and and one of + + + align:start position:0% +and one of the most fun and and one of +the way one of the most fundamental + + align:start position:0% +the way one of the most fundamental + + + align:start position:0% +the way one of the most fundamental +impulses in a hawks film whether it's a + + align:start position:0% +impulses in a hawks film whether it's a + + + align:start position:0% +impulses in a hawks film whether it's a +western or a war movie or a scre ball + + align:start position:0% +western or a war movie or a scre ball + + + align:start position:0% +western or a war movie or a scre ball +comedy is an Impulse to slow things not + + align:start position:0% +comedy is an Impulse to slow things not + + + align:start position:0% +comedy is an Impulse to slow things not +well to not to slow things down exactly + + align:start position:0% +well to not to slow things down exactly + + + align:start position:0% +well to not to slow things down exactly +because his dialogue is so rapid fire + + align:start position:0% +because his dialogue is so rapid fire + + + align:start position:0% +because his dialogue is so rapid fire +but to sort of stop the + + align:start position:0% +but to sort of stop the + + + align:start position:0% +but to sort of stop the +plot to interrupt the story with a scene + + align:start position:0% +plot to interrupt the story with a scene + + + align:start position:0% +plot to interrupt the story with a scene +of argument he loves scenes of quarrel + + align:start position:0% +of argument he loves scenes of quarrel + + + align:start position:0% +of argument he loves scenes of quarrel +he loves scenes of discussion of talk he + + align:start position:0% +he loves scenes of discussion of talk he + + + align:start position:0% +he loves scenes of discussion of talk he +loves talk and especially he loves + + align:start position:0% +loves talk and especially he loves + + + align:start position:0% +loves talk and especially he loves +intelligent people quarreling with each + + align:start position:0% +intelligent people quarreling with each + + + align:start position:0% +intelligent people quarreling with each +other and there's never been a director + + align:start position:0% +other and there's never been a director + + + align:start position:0% +other and there's never been a director +better at at eliciting from his actors + + align:start position:0% +better at at eliciting from his actors + + + align:start position:0% +better at at eliciting from his actors +quick rapid fire dialogue in fact he + + align:start position:0% +quick rapid fire dialogue in fact he + + + align:start position:0% +quick rapid fire dialogue in fact he +developed a strategy for doing this he + + align:start position:0% +developed a strategy for doing this he + + + align:start position:0% +developed a strategy for doing this he +used to sit right next to the camera he + + align:start position:0% +used to sit right next to the camera he + + + align:start position:0% +used to sit right next to the camera he +didn't stand behind the camera he had a + + align:start position:0% +didn't stand behind the camera he had a + + + align:start position:0% +didn't stand behind the camera he had a +cameraman but he sat right next to the + + align:start position:0% +cameraman but he sat right next to the + + + align:start position:0% +cameraman but he sat right next to the +camera and he had his actors play to him + + align:start position:0% +camera and he had his actors play to him + + + align:start position:0% +camera and he had his actors play to him +only sometimes s very close to him as + + align:start position:0% +only sometimes s very close to him as + + + align:start position:0% +only sometimes s very close to him as +they were as they were acting and if you + + align:start position:0% +they were as they were acting and if you + + + align:start position:0% +they were as they were acting and if you +watch especially some of the scenes in + + align:start position:0% +watch especially some of the scenes in + + + align:start position:0% +watch especially some of the scenes in +in this film you'll see what + + align:start position:0% +in this film you'll see what + + + align:start position:0% +in this film you'll see what +astonishingly realistic performances he + + align:start position:0% +astonishingly realistic performances he + + + align:start position:0% +astonishingly realistic performances he +got from his actors by this by this + + align:start position:0% +got from his actors by this by this + + + align:start position:0% +got from his actors by this by this +strategy uh he even encouraged certain + + align:start position:0% +strategy uh he even encouraged certain + + + align:start position:0% +strategy uh he even encouraged certain +forms of improvisation he would run + + align:start position:0% +forms of improvisation he would run + + + align:start position:0% +forms of improvisation he would run +through rehearsals first then he would + + align:start position:0% +through rehearsals first then he would + + + align:start position:0% +through rehearsals first then he would +encourage when he began to film scenes + + align:start position:0% +encourage when he began to film scenes + + + align:start position:0% +encourage when he began to film scenes +he would encourage the his actors to + + align:start position:0% +he would encourage the his actors to + + + align:start position:0% +he would encourage the his actors to +improvise and to improvise to his face + + align:start position:0% +improvise and to improvise to his face + + + align:start position:0% +improvise and to improvise to his face +and he creates a kind of electric + + align:start position:0% +and he creates a kind of electric + + + align:start position:0% +and he creates a kind of electric +authenticity in his dialogue scenes that + + align:start position:0% +authenticity in his dialogue scenes that + + + align:start position:0% +authenticity in his dialogue scenes that +has a tremendous Authority so the + + align:start position:0% +has a tremendous Authority so the + + + align:start position:0% +has a tremendous Authority so the +counterplot I'm talking about is this + + align:start position:0% +counterplot I'm talking about is this + + + align:start position:0% +counterplot I'm talking about is this +impulse to slow the plot down or to stop + + align:start position:0% +impulse to slow the plot down or to stop + + + align:start position:0% +impulse to slow the plot down or to stop +the plot for scenes of argument and + + align:start position:0% +the plot for scenes of argument and + + + align:start position:0% +the plot for scenes of argument and +conversation and what constantly happens + + align:start position:0% +conversation and what constantly happens + + + align:start position:0% +conversation and what constantly happens +whether he's making a western or a screw + + align:start position:0% +whether he's making a western or a screw + + + align:start position:0% +whether he's making a western or a screw +ball comedy is his character stop the + + align:start position:0% +ball comedy is his character stop the + + + align:start position:0% +ball comedy is his character stop the +action and say oh what do you think is + + align:start position:0% +action and say oh what do you think is + + + align:start position:0% +action and say oh what do you think is +going to happen next if I do this what + + align:start position:0% +going to happen next if I do this what + + + align:start position:0% +going to happen next if I do this what +will happen then as if the films begin + + align:start position:0% +will happen then as if the films begin + + + align:start position:0% +will happen then as if the films begin +to generate a kind of meta commentary + + align:start position:0% +to generate a kind of meta commentary + + + align:start position:0% +to generate a kind of meta commentary +about their own nature right and so + + align:start position:0% +about their own nature right and so + + + align:start position:0% +about their own nature right and so +they're incredibly talky films and the + + align:start position:0% +they're incredibly talky films and the + + + align:start position:0% +they're incredibly talky films and the +dialogue is fundamental to your ex to + + align:start position:0% +dialogue is fundamental to your ex to + + + align:start position:0% +dialogue is fundamental to your ex to +the rapidity of the dialogue is fun is + + align:start position:0% +the rapidity of the dialogue is fun is + + + align:start position:0% +the rapidity of the dialogue is fun is +fundamental to your understanding of the + + align:start position:0% +fundamental to your understanding of the + + + align:start position:0% +fundamental to your understanding of the +characters and to your understanding of + + align:start position:0% +characters and to your understanding of + + + align:start position:0% +characters and to your understanding of +the larger film so his Central scene + + align:start position:0% +the larger film so his Central scene + + + align:start position:0% +the larger film so his Central scene +then is a scene of quarreling intimacy + + align:start position:0% +then is a scene of quarreling intimacy + + + align:start position:0% +then is a scene of quarreling intimacy +you feel that they're quarreling but you + + align:start position:0% +you feel that they're quarreling but you + + + align:start position:0% +you feel that they're quarreling but you +also feel that no people could quarrel + + align:start position:0% +also feel that no people could quarrel + + + align:start position:0% +also feel that no people could quarrel +exactly in this way if they weren't also + + align:start position:0% +exactly in this way if they weren't also + + + align:start position:0% +exactly in this way if they weren't also +intimate with each other right and + + align:start position:0% +intimate with each other right and + + + align:start position:0% +intimate with each other right and +you'll see fully how it works out when + + align:start position:0% +you'll see fully how it works out when + + + align:start position:0% +you'll see fully how it works out when +you when you see the film itself so uh + + align:start position:0% +you when you see the film itself so uh + + + align:start position:0% +you when you see the film itself so uh +uh finally uh I want to say at least a + + align:start position:0% +uh finally uh I want to say at least a + + + align:start position:0% +uh finally uh I want to say at least a +word to remind you how actually although + + align:start position:0% +word to remind you how actually although + + + align:start position:0% +word to remind you how actually although +he's tremendously entertaining line by + + align:start position:0% +he's tremendously entertaining line by + + + align:start position:0% +he's tremendously entertaining line by +line and scene by scene and never call + + align:start position:0% +line and scene by scene and never call + + + align:start position:0% +line and scene by scene and never call +he's such a professional he never calls + + align:start position:0% +he's such a professional he never calls + + + align:start position:0% +he's such a professional he never calls +attention to his camera he's a very uh + + align:start position:0% +attention to his camera he's a very uh + + + align:start position:0% +attention to his camera he's a very uh +quiet filmmaker in that sense a real + + align:start position:0% +quiet filmmaker in that sense a real + + + align:start position:0% +quiet filmmaker in that sense a real +journeyman a real professional he + + align:start position:0% +journeyman a real professional he + + + align:start position:0% +journeyman a real professional he +doesn't want you to think about him or + + align:start position:0% +doesn't want you to think about him or + + + align:start position:0% +doesn't want you to think about him or +his camera he wants you to think about + + align:start position:0% +his camera he wants you to think about + + + align:start position:0% +his camera he wants you to think about +what you're seeing there are limits to + + align:start position:0% +what you're seeing there are limits to + + + align:start position:0% +what you're seeing there are limits to +this kind of this strategy and we'll + + align:start position:0% +this kind of this strategy and we'll + + + align:start position:0% +this kind of this strategy and we'll +talk about what the limits are when we + + align:start position:0% +talk about what the limits are when we + + + align:start position:0% +talk about what the limits are when we +look at certain other directors who + + align:start position:0% +look at certain other directors who + + + align:start position:0% +look at certain other directors who +behave in other ways but there're also + + align:start position:0% +behave in other ways but there're also + + + align:start position:0% +behave in other ways but there're also +great strengths to this as you'll see + + align:start position:0% +great strengths to this as you'll see + + + align:start position:0% +great strengths to this as you'll see +when you watch tonight's film and you + + align:start position:0% +when you watch tonight's film and you + + + align:start position:0% +when you watch tonight's film and you +something of his complexity is embedded + + align:start position:0% +something of his complexity is embedded + + + align:start position:0% +something of his complexity is embedded +here here because what you can find is + + align:start position:0% +here here because what you can find is + + + align:start position:0% +here here because what you can find is +he creates scenes of immense comic + + align:start position:0% +he creates scenes of immense comic + + + align:start position:0% +he creates scenes of immense comic +energy really generates real laughter + + align:start position:0% +energy really generates real laughter + + + align:start position:0% +energy really generates real laughter +but beneath the laughter there's a deep + + align:start position:0% +but beneath the laughter there's a deep + + + align:start position:0% +but beneath the laughter there's a deep +layer a deep substrate of cynicism of + + align:start position:0% +layer a deep substrate of cynicism of + + + align:start position:0% +layer a deep substrate of cynicism of +skepticism about human motives about the + + align:start position:0% +skepticism about human motives about the + + + align:start position:0% +skepticism about human motives about the +virtue of human institutions about the + + align:start position:0% +virtue of human institutions about the + + + align:start position:0% +virtue of human institutions about the +capacity of human institutions and + + align:start position:0% +capacity of human institutions and + + + align:start position:0% +capacity of human institutions and +individual human beings for corruption + + align:start position:0% +individual human beings for corruption + + + align:start position:0% +individual human beings for corruption +and misdirection there's a kind of deep + + align:start position:0% +and misdirection there's a kind of deep + + + align:start position:0% +and misdirection there's a kind of deep +political and social cynicism in the + + align:start position:0% +political and social cynicism in the + + + align:start position:0% +political and social cynicism in the +film that doubles the comedy or + + align:start position:0% +film that doubles the comedy or + + + align:start position:0% +film that doubles the comedy or +complicates or deepens + + align:start position:0% +complicates or deepens + + + align:start position:0% +complicates or deepens +or roughens the comedy sour the comedy + + align:start position:0% +or roughens the comedy sour the comedy + + + align:start position:0% +or roughens the comedy sour the comedy +uh in a way that makes for a particular + + align:start position:0% +uh in a way that makes for a particular + + + align:start position:0% +uh in a way that makes for a particular +kind of complexity it's possible to + + align:start position:0% +kind of complexity it's possible to + + + align:start position:0% +kind of complexity it's possible to +argue as some critics have that this + + align:start position:0% +argue as some critics have that this + + + align:start position:0% +argue as some critics have that this +film um more than any other that Hawks + + align:start position:0% +film um more than any other that Hawks + + + align:start position:0% +film um more than any other that Hawks +made uh combines laughter and cynicism + + align:start position:0% +made uh combines laughter and cynicism + + + align:start position:0% +made uh combines laughter and cynicism +in unique measures and I think together + + align:start position:0% +in unique measures and I think together + + + align:start position:0% +in unique measures and I think together +these two films could and these two + + align:start position:0% +these two films could and these two + + + align:start position:0% +these two films could and these two +directors can Mark at least a certain + + align:start position:0% +directors can Mark at least a certain + + + align:start position:0% +directors can Mark at least a certain +Pole certain polls in the in the in the + + align:start position:0% +Pole certain polls in the in the in the + + + align:start position:0% +Pole certain polls in the in the in the +uh tradition of Hollywood filmm and + + align:start position:0% +uh tradition of Hollywood filmm and + + + align:start position:0% +uh tradition of Hollywood filmm and +especially in the tradition of screw + + align:start position:0% +especially in the tradition of screw + + + align:start position:0% +especially in the tradition of screw +ball comedy you can feel uh the pull + + align:start position:0% +ball comedy you can feel uh the pull + + + align:start position:0% +ball comedy you can feel uh the pull +toward a kind of + + align:start position:0% +toward a kind of + + + align:start position:0% +toward a kind of +sentimental affirming impulse in in uh + + align:start position:0% +sentimental affirming impulse in in uh + + + align:start position:0% +sentimental affirming impulse in in uh +uh in in in in uh Frank cpra and the + + align:start position:0% +uh in in in in uh Frank cpra and the + + + align:start position:0% +uh in in in in uh Frank cpra and the +pull toward a kind of cynical distanced + + align:start position:0% +pull toward a kind of cynical distanced + + + align:start position:0% +pull toward a kind of cynical distanced +complex psychologically deep politically + + align:start position:0% +complex psychologically deep politically + + + align:start position:0% +complex psychologically deep politically +informed laughter even mockery in Howard + + align:start position:0% +informed laughter even mockery in Howard + + + align:start position:0% +informed laughter even mockery in Howard +Hawks and they represent two ele two + + align:start position:0% +Hawks and they represent two ele two + + + align:start position:0% +Hawks and they represent two ele two +aspects two elements two almost poles + + align:start position:0% +aspects two elements two almost poles + + + align:start position:0% +aspects two elements two almost poles +within the larger story of the Hollywood + + align:start position:0% +within the larger story of the Hollywood + + + align:start position:0% +within the larger story of the Hollywood +studio film enjoy the films \ No newline at end of file diff --git a/iusTmgQyZ44.txt b/iusTmgQyZ44.txt new file mode 100644 index 0000000000000000000000000000000000000000..4f0e78f054cbe24b3d8f4fa38d37cd85db3c017c --- /dev/null +++ b/iusTmgQyZ44.txt @@ -0,0 +1,9139 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit mitop courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu hi everyone um a few of you + + align:start position:0% +ocw.mit.edu hi everyone um a few of you + + + align:start position:0% +ocw.mit.edu hi everyone um a few of you +may know me from my tutorial but if you + + align:start position:0% +may know me from my tutorial but if you + + + align:start position:0% +may know me from my tutorial but if you +don't I am Mark cyer I'm the senior ta + + align:start position:0% +don't I am Mark cyer I'm the senior ta + + + align:start position:0% +don't I am Mark cyer I'm the senior ta +here here at + + align:start position:0% +here here at + + + align:start position:0% +here here at +6034 and these Friday Mega recitations + + align:start position:0% +6034 and these Friday Mega recitations + + + align:start position:0% +6034 and these Friday Mega recitations +are going to be a little bit different + + align:start position:0% +are going to be a little bit different + + + align:start position:0% +are going to be a little bit different +than any of the other things in the + + align:start position:0% +than any of the other things in the + + + align:start position:0% +than any of the other things in the +class all right so what is Mega + + align:start position:0% +class all right so what is Mega + + + align:start position:0% +class all right so what is Mega +recitation Mega recitation is in this + + align:start position:0% +recitation Mega recitation is in this + + + align:start position:0% +recitation Mega recitation is in this +lecture sty room but I hope to make it + + align:start position:0% +lecture sty room but I hope to make it + + + align:start position:0% +lecture sty room but I hope to make it +more like a recitation or a tutorial by + + align:start position:0% +more like a recitation or a tutorial by + + + align:start position:0% +more like a recitation or a tutorial by +unfortunately for some of you perhaps + + align:start position:0% +unfortunately for some of you perhaps + + + align:start position:0% +unfortunately for some of you perhaps +calling on you guys to participate + + align:start position:0% +calling on you guys to participate + + + align:start position:0% +calling on you guys to participate +during the U Mega recitation as we + + align:start position:0% +during the U Mega recitation as we + + + align:start position:0% +during the U Mega recitation as we +attempt to work with some of the + + align:start position:0% +attempt to work with some of the + + + align:start position:0% +attempt to work with some of the +material that Patrick has sort of given + + align:start position:0% +material that Patrick has sort of given + + + align:start position:0% +material that Patrick has sort of given +us the big picture for in the lectures + + align:start position:0% +us the big picture for in the lectures + + + align:start position:0% +us the big picture for in the lectures +and if you've gone to recitation so far + + align:start position:0% +and if you've gone to recitation so far + + + align:start position:0% +and if you've gone to recitation so far +you may have received a little bit of + + align:start position:0% +you may have received a little bit of + + + align:start position:0% +you may have received a little bit of +enrichment into how the algorithms work + + align:start position:0% +enrichment into how the algorithms work + + + align:start position:0% +enrichment into how the algorithms work +while here in mega recitation we're + + align:start position:0% +while here in mega recitation we're + + + align:start position:0% +while here in mega recitation we're +going to figure out how you can work the + + align:start position:0% +going to figure out how you can work the + + + align:start position:0% +going to figure out how you can work the +algorithms and that's very important + + align:start position:0% +algorithms and that's very important + + + align:start position:0% +algorithms and that's very important +because in this + + align:start position:0% +because in this + + + align:start position:0% +because in this +class being able to work the algorithms + + align:start position:0% +class being able to work the algorithms + + + align:start position:0% +class being able to work the algorithms +by hand um in some of these examples I + + align:start position:0% +by hand um in some of these examples I + + + align:start position:0% +by hand um in some of these examples I +put up here or like Patrick sometimes + + align:start position:0% +put up here or like Patrick sometimes + + + align:start position:0% +put up here or like Patrick sometimes +does in lectures to teach you the + + align:start position:0% +does in lectures to teach you the + + + align:start position:0% +does in lectures to teach you the +algorithms is is a crucial way of + + align:start position:0% +algorithms is is a crucial way of + + + align:start position:0% +algorithms is is a crucial way of +demonstrating that you understand how + + align:start position:0% +demonstrating that you understand how + + + align:start position:0% +demonstrating that you understand how +the algorithms work and we use it on a + + align:start position:0% +the algorithms work and we use it on a + + + align:start position:0% +the algorithms work and we use it on a +quiz the way we use it on the quiz is we + + align:start position:0% +quiz the way we use it on the quiz is we + + + align:start position:0% +quiz the way we use it on the quiz is we +well this is an old quiz problem it's + + align:start position:0% +well this is an old quiz problem it's + + + align:start position:0% +well this is an old quiz problem it's +from last year it tripped up a lot of + + align:start position:0% +from last year it tripped up a lot of + + + align:start position:0% +from last year it tripped up a lot of +people so we're going to go over it + + align:start position:0% +people so we're going to go over it + + + align:start position:0% +people so we're going to go over it +today I'm going to tell you all the + + align:start position:0% +today I'm going to tell you all the + + + align:start position:0% +today I'm going to tell you all the +tricks that um tripped up a lot of + + align:start position:0% +tricks that um tripped up a lot of + + + align:start position:0% +tricks that um tripped up a lot of +people in addition to emphasizing tricks + + align:start position:0% +people in addition to emphasizing tricks + + + align:start position:0% +people in addition to emphasizing tricks +that I've picked up over the goshes has + + align:start position:0% +that I've picked up over the goshes has + + + align:start position:0% +that I've picked up over the goshes has +it been three years of um teeing this + + align:start position:0% +it been three years of um teeing this + + + align:start position:0% +it been three years of um teeing this +course before so that you will not fall + + align:start position:0% +course before so that you will not fall + + + align:start position:0% +course before so that you will not fall +pre to any of these tricks hopefully I + + align:start position:0% +pre to any of these tricks hopefully I + + + align:start position:0% +pre to any of these tricks hopefully I +say hopefully because some of these + + align:start position:0% +say hopefully because some of these + + + align:start position:0% +say hopefully because some of these +tricks I talked about at Mega recitation + + align:start position:0% +tricks I talked about at Mega recitation + + + align:start position:0% +tricks I talked about at Mega recitation +um last year and people still got + + align:start position:0% +um last year and people still got + + + align:start position:0% +um last year and people still got +tricked by them I guess maybe some + + align:start position:0% +tricked by them I guess maybe some + + + align:start position:0% +tricked by them I guess maybe some +people didn't come to Mega recitation or + + align:start position:0% +people didn't come to Mega recitation or + + + align:start position:0% +people didn't come to Mega recitation or +they were just very tricky tricks so be + + align:start position:0% +they were just very tricky tricks so be + + + align:start position:0% +they were just very tricky tricks so be +sure to come to Mega recitation pay + + align:start position:0% +sure to come to Mega recitation pay + + + align:start position:0% +sure to come to Mega recitation pay +attention to the uh pay attention to the + + align:start position:0% +attention to the uh pay attention to the + + + align:start position:0% +attention to the uh pay attention to the +tricks pay attention to how these things + + align:start position:0% +tricks pay attention to how these things + + + align:start position:0% +tricks pay attention to how these things +are solved ask questions if you're not + + align:start position:0% +are solved ask questions if you're not + + + align:start position:0% +are solved ask questions if you're not +sure and when we get done the hour + + align:start position:0% +sure and when we get done the hour + + + align:start position:0% +sure and when we get done the hour +together I'm hoping that everyone's + + align:start position:0% +together I'm hoping that everyone's + + + align:start position:0% +together I'm hoping that everyone's +going to do really well on the rules + + align:start position:0% +going to do really well on the rules + + + align:start position:0% +going to do really well on the rules +part of the of the first quiz so without + + align:start position:0% +part of the of the first quiz so without + + + align:start position:0% +part of the of the first quiz so without +further Ado uh if there are no um + + align:start position:0% +further Ado uh if there are no um + + + align:start position:0% +further Ado uh if there are no um +questions on that which I don't think + + align:start position:0% +questions on that which I don't think + + + align:start position:0% +questions on that which I don't think +there probably will be uh let's move on + + align:start position:0% +there probably will be uh let's move on + + + align:start position:0% +there probably will be uh let's move on +to the problem at hand as some of you + + align:start position:0% +to the problem at hand as some of you + + + align:start position:0% +to the problem at hand as some of you +may have noticed it is a Harry Potter + + align:start position:0% +may have noticed it is a Harry Potter + + + align:start position:0% +may have noticed it is a Harry Potter +based problem one of our T last year was + + align:start position:0% +based problem one of our T last year was + + + align:start position:0% +based problem one of our T last year was +big Harry Potter fan so what we have + + align:start position:0% +big Harry Potter fan so what we have + + + align:start position:0% +big Harry Potter fan so what we have +here are a series of rules and a series + + align:start position:0% +here are a series of rules and a series + + + align:start position:0% +here are a series of rules and a series +of + + align:start position:0% +of + + + align:start position:0% +of +assertions now if you happen to be real + + align:start position:0% +assertions now if you happen to be real + + + align:start position:0% +assertions now if you happen to be real +go-getter and have already looked at all + + align:start position:0% +go-getter and have already looked at all + + + align:start position:0% +go-getter and have already looked at all +the past quizzes online and you may have + + align:start position:0% +the past quizzes online and you may have + + + align:start position:0% +the past quizzes online and you may have +already seen this problem and if you + + align:start position:0% +already seen this problem and if you + + + align:start position:0% +already seen this problem and if you +really really have attention to detail + + align:start position:0% +really really have attention to detail + + + align:start position:0% +really really have attention to detail +you may notice something a little bit + + align:start position:0% +you may notice something a little bit + + + align:start position:0% +you may notice something a little bit +different in the way I wrote it as + + align:start position:0% +different in the way I wrote it as + + + align:start position:0% +different in the way I wrote it as +compared to the Way It Was Written + + align:start position:0% +compared to the Way It Was Written + + + align:start position:0% +compared to the Way It Was Written +online in fact you may um if you have a + + align:start position:0% +online in fact you may um if you have a + + + align:start position:0% +online in fact you may um if you have a +lot of attention to detail but you're + + align:start position:0% +lot of attention to detail but you're + + + align:start position:0% +lot of attention to detail but you're +not really in on scheme Or List you may + + align:start position:0% +not really in on scheme Or List you may + + + align:start position:0% +not really in on scheme Or List you may +think that my the way I wrote it is much + + align:start position:0% +think that my the way I wrote it is much + + + align:start position:0% +think that my the way I wrote it is much +easier to understand and in case you + + align:start position:0% +easier to understand and in case you + + + align:start position:0% +easier to understand and in case you +can't understand the other way and in + + align:start position:0% +can't understand the other way and in + + + align:start position:0% +can't understand the other way and in +case one of the T decides to write it in + + align:start position:0% +case one of the T decides to write it in + + + align:start position:0% +case one of the T decides to write it in +a lisp likee way again let me explain if + + align:start position:0% +a lisp likee way again let me explain if + + + align:start position:0% +a lisp likee way again let me explain if +you look at one of my rules say um if x + + align:start position:0% +you look at one of my rules say um if x + + + align:start position:0% +you look at one of my rules say um if x +is ambitious and X is a squib then X has + + align:start position:0% +is ambitious and X is a squib then X has + + + align:start position:0% +is ambitious and X is a squib then X has +a bad term that's rule zero up at the + + align:start position:0% +a bad term that's rule zero up at the + + + align:start position:0% +a bad term that's rule zero up at the +top um that's written in sort of what we + + align:start position:0% +top um that's written in sort of what we + + + align:start position:0% +top um that's written in sort of what we +call infix notation it's easy it's + + align:start position:0% +call infix notation it's easy it's + + + align:start position:0% +call infix notation it's easy it's +simple all the operators are in the + + align:start position:0% +simple all the operators are in the + + + align:start position:0% +simple all the operators are in the +order you would expect 2 + 3 equal 5 + + align:start position:0% +order you would expect 2 + 3 equal 5 + + + align:start position:0% +order you would expect 2 + 3 equal 5 +there's another kind of notation that is + + align:start position:0% +there's another kind of notation that is + + + align:start position:0% +there's another kind of notation that is +sometimes used on previous quizzes and + + align:start position:0% +sometimes used on previous quizzes and + + + align:start position:0% +sometimes used on previous quizzes and +by sometimes a good number of times + + align:start position:0% +by sometimes a good number of times + + + align:start position:0% +by sometimes a good number of times +actually I'm not sure why we still use + + align:start position:0% +actually I'm not sure why we still use + + + align:start position:0% +actually I'm not sure why we still use +it that way because of the fact that the + + align:start position:0% +it that way because of the fact that the + + + align:start position:0% +it that way because of the fact that the +class is moved on to python but we do + + align:start position:0% +class is moved on to python but we do + + + align:start position:0% +class is moved on to python but we do +sometimes and that's called prefix + + align:start position:0% +sometimes and that's called prefix + + + align:start position:0% +sometimes and that's called prefix +notation in prefix notation the operator + + align:start position:0% +notation in prefix notation the operator + + + align:start position:0% +notation in prefix notation the operator +comes first so for instance plus + + align:start position:0% +comes first so for instance plus + + + align:start position:0% +comes first so for instance plus +23 equals 5 the plus comes first the + + align:start position:0% +23 equals 5 the plus comes first the + + + align:start position:0% +23 equals 5 the plus comes first the +function D comes first in this case the + + align:start position:0% +function D comes first in this case the + + + align:start position:0% +function D comes first in this case the +function is plus so if we were writing + + align:start position:0% +function is plus so if we were writing + + + align:start position:0% +function is plus so if we were writing +this in prefix notation in fact the way + + align:start position:0% +this in prefix notation in fact the way + + + align:start position:0% +this in prefix notation in fact the way +I received it when I it said if and X is + + align:start position:0% +I received it when I it said if and X is + + + align:start position:0% +I received it when I it said if and X is +ambitious X is a squib then X has a bad + + align:start position:0% +ambitious X is a squib then X has a bad + + + align:start position:0% +ambitious X is a squib then X has a bad +term the and went first first and there + + align:start position:0% +term the and went first first and there + + + align:start position:0% +term the and went first first and there +was a parentheses which included + + align:start position:0% +was a parentheses which included + + + align:start position:0% +was a parentheses which included +everything that was scoped under the and + + align:start position:0% +everything that was scoped under the and + + + align:start position:0% +everything that was scoped under the and +does anyone have any questions about + + align:start position:0% +does anyone have any questions about + + + align:start position:0% +does anyone have any questions about +prefix notation in case it comes up just + + align:start position:0% +prefix notation in case it comes up just + + + align:start position:0% +prefix notation in case it comes up just +remember if if you if things start being + + align:start position:0% +remember if if you if things start being + + + align:start position:0% +remember if if you if things start being +written in a really weird way with lots + + align:start position:0% +written in a really weird way with lots + + + align:start position:0% +written in a really weird way with lots +and lots and lots of + + align:start position:0% +and lots and lots of + + + align:start position:0% +and lots and lots of +parenthesis whatever's outside of the + + align:start position:0% +parenthesis whatever's outside of the + + + align:start position:0% +parenthesis whatever's outside of the +parenthesis whether it be plus or and or + + align:start position:0% +parenthesis whether it be plus or and or + + + align:start position:0% +parenthesis whether it be plus or and or +or is an operator that acts on the + + align:start position:0% +or is an operator that acts on the + + + align:start position:0% +or is an operator that acts on the +things that are inside however we're not + + align:start position:0% +things that are inside however we're not + + + align:start position:0% +things that are inside however we're not +going to deal with that now because I + + align:start position:0% +going to deal with that now because I + + + align:start position:0% +going to deal with that now because I +think the most important thing is to + + align:start position:0% +think the most important thing is to + + + align:start position:0% +think the most important thing is to +understand the rules and the less + + align:start position:0% +understand the rules and the less + + + align:start position:0% +understand the rules and the less +important thing is to understand prefix + + align:start position:0% +important thing is to understand prefix + + + align:start position:0% +important thing is to understand prefix +notation and you can do a problem at + + align:start position:0% +notation and you can do a problem at + + + align:start position:0% +notation and you can do a problem at +home that's written in prefix notation + + align:start position:0% +home that's written in prefix notation + + + align:start position:0% +home that's written in prefix notation +to test yourself on that so what rules + + align:start position:0% +to test yourself on that so what rules + + + align:start position:0% +to test yourself on that so what rules +do we have here we've got rules 0o + + align:start position:0% +do we have here we've got rules 0o + + + align:start position:0% +do we have here we've got rules 0o +through five for some reason they are + + align:start position:0% +through five for some reason they are + + + align:start position:0% +through five for some reason they are +labeled with p's they are often labeled + + align:start position:0% +labeled with p's they are often labeled + + + align:start position:0% +labeled with p's they are often labeled +with either P's or RS the sort of secret + + align:start position:0% +with either P's or RS the sort of secret + + + align:start position:0% +with either P's or RS the sort of secret +on why they're labeled with p's is that + + align:start position:0% +on why they're labeled with p's is that + + + align:start position:0% +on why they're labeled with p's is that +one year somebody labeled them with p's + + align:start position:0% +one year somebody labeled them with p's + + + align:start position:0% +one year somebody labeled them with p's +for like proposition or something like + + align:start position:0% +for like proposition or something like + + + align:start position:0% +for like proposition or something like +that and then other has looked at that + + align:start position:0% +that and then other has looked at that + + + align:start position:0% +that and then other has looked at that +test and sometimes also labeled it with + + align:start position:0% +test and sometimes also labeled it with + + + align:start position:0% +test and sometimes also labeled it with +p's and it sort of down the line + + align:start position:0% +p's and it sort of down the line + + + align:start position:0% +p's and it sort of down the line +continue to be labeled with p's um and + + align:start position:0% +continue to be labeled with p's um and + + + align:start position:0% +continue to be labeled with p's um and +sometimes with RS so these P's are the + + align:start position:0% +sometimes with RS so these P's are the + + + align:start position:0% +sometimes with RS so these P's are the +six rules the first rule is if x is + + align:start position:0% +six rules the first rule is if x is + + + align:start position:0% +six rules the first rule is if x is +ambitious and X is a squib then X has a + + align:start position:0% +ambitious and X is a squib then X has a + + + align:start position:0% +ambitious and X is a squib then X has a +bad term so what's the deal with these + + align:start position:0% +bad term so what's the deal with these + + + align:start position:0% +bad term so what's the deal with these +question mark X's the question mark + + align:start position:0% +question mark X's the question mark + + + align:start position:0% +question mark X's the question mark +before an X or perhaps a y down here + + align:start position:0% +before an X or perhaps a y down here + + + align:start position:0% +before an X or perhaps a y down here +indicate that there's a variable waiting + + align:start position:0% +indicate that there's a variable waiting + + + align:start position:0% +indicate that there's a variable waiting +to be bound we're not not assuming + + align:start position:0% +to be bound we're not not assuming + + + align:start position:0% +to be bound we're not not assuming +there's a Harry Potter character named X + + align:start position:0% +there's a Harry Potter character named X + + + align:start position:0% +there's a Harry Potter character named X +and only if that question mark x the + + align:start position:0% +and only if that question mark x the + + + align:start position:0% +and only if that question mark x the +mystery character only if mystery X + + align:start position:0% +mystery character only if mystery X + + + align:start position:0% +mystery character only if mystery X +character has is ambitious can they can + + align:start position:0% +character has is ambitious can they can + + + align:start position:0% +character has is ambitious can they can +that person possibly have a bad term + + align:start position:0% +that person possibly have a bad term + + + align:start position:0% +that person possibly have a bad term +what we're seeing is any character in + + align:start position:0% +what we're seeing is any character in + + + align:start position:0% +what we're seeing is any character in +the Harry Potter universe or not in the + + align:start position:0% +the Harry Potter universe or not in the + + + align:start position:0% +the Harry Potter universe or not in the +Harry Potter Universe maybe a + + align:start position:0% +Harry Potter Universe maybe a + + + align:start position:0% +Harry Potter Universe maybe a +rhinoceros um can fit into that X so for + + align:start position:0% +rhinoceros um can fit into that X so for + + + align:start position:0% +rhinoceros um can fit into that X so for +instance if a rhinoceros is ambitious + + align:start position:0% +instance if a rhinoceros is ambitious + + + align:start position:0% +instance if a rhinoceros is ambitious +and a rhinoceros is a squib then a + + align:start position:0% +and a rhinoceros is a squib then a + + + align:start position:0% +and a rhinoceros is a squib then a +rhinoceros has a bad term that rule is + + align:start position:0% +rhinoceros has a bad term that rule is + + + align:start position:0% +rhinoceros has a bad term that rule is +saying for any X + + align:start position:0% +saying for any X + + + align:start position:0% +saying for any X +um this is true and it's very important + + align:start position:0% +um this is true and it's very important + + + align:start position:0% +um this is true and it's very important +how we treat the question mark x when + + align:start position:0% +how we treat the question mark x when + + + align:start position:0% +how we treat the question mark x when +how we bind the question mark x when we + + align:start position:0% +how we bind the question mark x when we + + + align:start position:0% +how we bind the question mark x when we +do both back training and forward + + align:start position:0% +do both back training and forward + + + align:start position:0% +do both back training and forward +training I'll get back to that because + + align:start position:0% +training I'll get back to that because + + + align:start position:0% +training I'll get back to that because +um some people made some very very um + + align:start position:0% +um some people made some very very um + + + align:start position:0% +um some people made some very very um +small mistakes that really messed up a + + align:start position:0% +small mistakes that really messed up a + + + align:start position:0% +small mistakes that really messed up a +lot of their forward and backward + + align:start position:0% +lot of their forward and backward + + + align:start position:0% +lot of their forward and backward +training last year it was actually very + + align:start position:0% +training last year it was actually very + + + align:start position:0% +training last year it was actually very +tricky Jeremy the TA who wrote this was + + align:start position:0% +tricky Jeremy the TA who wrote this was + + + align:start position:0% +tricky Jeremy the TA who wrote this was +was very clever um and um it makes it a + + align:start position:0% +was very clever um and um it makes it a + + + align:start position:0% +was very clever um and um it makes it a +really great case study for you guys all + + align:start position:0% +really great case study for you guys all + + + align:start position:0% +really great case study for you guys all +right right so rule one if x lives in + + align:start position:0% +right right so rule one if x lives in + + + align:start position:0% +right right so rule one if x lives in +Gryffindor Tower then X is a protagonist + + align:start position:0% +Gryffindor Tower then X is a protagonist + + + align:start position:0% +Gryffindor Tower then X is a protagonist +by the way for conciseness I'm going to + + align:start position:0% +by the way for conciseness I'm going to + + + align:start position:0% +by the way for conciseness I'm going to +be using GT for Gryffindor Tower when I + + align:start position:0% +be using GT for Gryffindor Tower when I + + + align:start position:0% +be using GT for Gryffindor Tower when I +write these later on and I'll use SD for + + align:start position:0% +write these later on and I'll use SD for + + + align:start position:0% +write these later on and I'll use SD for +sther and dungeon speaking of which rule + + align:start position:0% +sther and dungeon speaking of which rule + + + align:start position:0% +sther and dungeon speaking of which rule +two if x lives in slyther and dungeon + + align:start position:0% +two if x lives in slyther and dungeon + + + align:start position:0% +two if x lives in slyther and dungeon +then X is a villain X is ambitious why + + align:start position:0% +then X is a villain X is ambitious why + + + align:start position:0% +then X is a villain X is ambitious why +are there two things here well after the + + align:start position:0% +are there two things here well after the + + + align:start position:0% +are there two things here well after the +if we have what we call the antecedent + + align:start position:0% +if we have what we call the antecedent + + + align:start position:0% +if we have what we call the antecedent +that's something that needs to be true + + align:start position:0% +that's something that needs to be true + + + align:start position:0% +that's something that needs to be true +in order for this rule to match after + + align:start position:0% +in order for this rule to match after + + + align:start position:0% +in order for this rule to match after +the then we have um what is called the + + align:start position:0% +the then we have um what is called the + + + align:start position:0% +the then we have um what is called the +consequent and in this case there are + + align:start position:0% +consequent and in this case there are + + + align:start position:0% +consequent and in this case there are +two consequents anyone who lives in + + align:start position:0% +two consequents anyone who lives in + + + align:start position:0% +two consequents anyone who lives in +slyther and dungeons is automatically a + + align:start position:0% +slyther and dungeons is automatically a + + + align:start position:0% +slyther and dungeons is automatically a +villain and also ambitious so you can + + align:start position:0% +villain and also ambitious so you can + + + align:start position:0% +villain and also ambitious so you can +sort of think of there being sort of an + + align:start position:0% +sort of think of there being sort of an + + + align:start position:0% +sort of think of there being sort of an +end there for um for the purposes of + + align:start position:0% +end there for um for the purposes of + + + align:start position:0% +end there for um for the purposes of +both of those assertions would be added + + align:start position:0% +both of those assertions would be added + + + align:start position:0% +both of those assertions would be added +to the knowledge base rule three if x is + + align:start position:0% +to the knowledge base rule three if x is + + + align:start position:0% +to the knowledge base rule three if x is +a protagonist or X is a villain and X is + + align:start position:0% +a protagonist or X is a villain and X is + + + align:start position:0% +a protagonist or X is a villain and X is +ambitious then X studies a + + align:start position:0% +ambitious then X studies a + + + align:start position:0% +ambitious then X studies a +lot by the way the scope is uh for the + + align:start position:0% +lot by the way the scope is uh for the + + + align:start position:0% +lot by the way the scope is uh for the +oops the scope for this just to be sure + + align:start position:0% +oops the scope for this just to be sure + + + align:start position:0% +oops the scope for this just to be sure +that we're clear + + align:start position:0% +that we're clear + + + align:start position:0% +that we're clear +is + + align:start position:0% +is + + + align:start position:0% +is +this + + align:start position:0% +this + + + align:start position:0% +this +so we need them to be a protagonist or a + + align:start position:0% +so we need them to be a protagonist or a + + + align:start position:0% +so we need them to be a protagonist or a +villain and no matter what they have to + + align:start position:0% +villain and no matter what they have to + + + align:start position:0% +villain and no matter what they have to +be + + align:start position:0% +be + + + align:start position:0% +be +ambitious rule four if x studies a lot + + align:start position:0% +ambitious rule four if x studies a lot + + + align:start position:0% +ambitious rule four if x studies a lot +and X is a protagonist X becomes + + align:start position:0% +and X is a protagonist X becomes + + + align:start position:0% +and X is a protagonist X becomes +Hermione's friend and Rule five if x + + align:start position:0% +Hermione's friend and Rule five if x + + + align:start position:0% +Hermione's friend and Rule five if x +snogs y and x lives in Gryffindor Tower + + align:start position:0% +snogs y and x lives in Gryffindor Tower + + + align:start position:0% +snogs y and x lives in Gryffindor Tower +and Y lives in Slytherin dungeon then X + + align:start position:0% +and Y lives in Slytherin dungeon then X + + + align:start position:0% +and Y lives in Slytherin dungeon then X +has a bad + + align:start position:0% +has a bad + + + align:start position:0% +has a bad +term so those are our six rules that we + + align:start position:0% +term so those are our six rules that we + + + align:start position:0% +term so those are our six rules that we +can use to understand Jeremy's world of + + align:start position:0% +can use to understand Jeremy's world of + + + align:start position:0% +can use to understand Jeremy's world of +the Harry Potter universe and we also + + align:start position:0% +the Harry Potter universe and we also + + + align:start position:0% +the Harry Potter universe and we also +start off with four + + align:start position:0% +start off with four + + + align:start position:0% +start off with four +assertions let me not underestimate the + + align:start position:0% +assertions let me not underestimate the + + + align:start position:0% +assertions let me not underestimate the +value of always looking to the + + align:start position:0% +value of always looking to the + + + align:start position:0% +value of always looking to the +assertions it's one of my white star + + align:start position:0% +assertions it's one of my white star + + + align:start position:0% +assertions it's one of my white star +ideas that are up here on the board let + + align:start position:0% +ideas that are up here on the board let + + + align:start position:0% +ideas that are up here on the board let +me see no not that it's perfect um + + align:start position:0% +me see no not that it's perfect um + + + align:start position:0% +me see no not that it's perfect um +always always check the assertions + + align:start position:0% +always always check the assertions + + + align:start position:0% +always always check the assertions +before using a rule that's really + + align:start position:0% +before using a rule that's really + + + align:start position:0% +before using a rule that's really +tricked people up last year and you'll + + align:start position:0% +tricked people up last year and you'll + + + align:start position:0% +tricked people up last year and you'll +see why because we're doing last year's + + align:start position:0% +see why because we're doing last year's + + + align:start position:0% +see why because we're doing last year's +problem um our four assertions that we + + align:start position:0% +problem um our four assertions that we + + + align:start position:0% +problem um our four assertions that we +start with assertion zero ment lives in + + align:start position:0% +start with assertion zero ment lives in + + + align:start position:0% +start with assertion zero ment lives in +slyther and dungeon assertion one ment + + align:start position:0% +slyther and dungeon assertion one ment + + + align:start position:0% +slyther and dungeon assertion one ment +is ambitious assertion one is what + + align:start position:0% +is ambitious assertion one is what + + + align:start position:0% +is ambitious assertion one is what +tricked people up so remember that m is + + align:start position:0% +tricked people up so remember that m is + + + align:start position:0% +tricked people up so remember that m is +ambitious assertion two Sheamus lives in + + align:start position:0% +ambitious assertion two Sheamus lives in + + + align:start position:0% +ambitious assertion two Sheamus lives in +Gryffindor Tower and assertion three + + align:start position:0% +Gryffindor Tower and assertion three + + + align:start position:0% +Gryffindor Tower and assertion three +Sheamus snogs + + align:start position:0% +Sheamus snogs + + + align:start position:0% +Sheamus snogs +ment so those are our those are four + + align:start position:0% +ment so those are our those are four + + + align:start position:0% +ment so those are our those are four +assertions that we've already started + + align:start position:0% +assertions that we've already started + + + align:start position:0% +assertions that we've already started +with now the two things we're going to + + align:start position:0% +with now the two things we're going to + + + align:start position:0% +with now the two things we're going to +have to do are backward chaining and + + align:start position:0% +have to do are backward chaining and + + + align:start position:0% +have to do are backward chaining and +forward chaining now when you guys + + align:start position:0% +forward chaining now when you guys + + + align:start position:0% +forward chaining now when you guys +learned these two um backward chaining + + align:start position:0% +learned these two um backward chaining + + + align:start position:0% +learned these two um backward chaining +and forward chaining raise your hand if + + align:start position:0% +and forward chaining raise your hand if + + + align:start position:0% +and forward chaining raise your hand if +you thought forward chaining was harder + + align:start position:0% +you thought forward chaining was harder + + + align:start position:0% +you thought forward chaining was harder +than backward + + align:start position:0% + + + + align:start position:0% + +chaining aha I knew it I can prove + + align:start position:0% +chaining aha I knew it I can prove + + + align:start position:0% +chaining aha I knew it I can prove +whatever point I want because no one + + align:start position:0% +whatever point I want because no one + + + align:start position:0% +whatever point I want because no one +wants to raise their hand because I also + + align:start position:0% +wants to raise their hand because I also + + + align:start position:0% +wants to raise their hand because I also +think backward chaining is harder than + + align:start position:0% +think backward chaining is harder than + + + align:start position:0% +think backward chaining is harder than +um forward chain raise your hand if you + + align:start position:0% +um forward chain raise your hand if you + + + align:start position:0% +um forward chain raise your hand if you +think backward chaining is harder than + + align:start position:0% +think backward chaining is harder than + + + align:start position:0% +think backward chaining is harder than +forward chaining + + align:start position:0% +forward chaining + + + align:start position:0% +forward chaining +first of all we have a good number of + + align:start position:0% +first of all we have a good number of + + + align:start position:0% +first of all we have a good number of +people second of all since no one wants + + align:start position:0% +people second of all since no one wants + + + align:start position:0% +people second of all since no one wants +to raise their hand I could just test it + + align:start position:0% +to raise their hand I could just test it + + + align:start position:0% +to raise their hand I could just test it +the other way that's a pro tip if you're + + align:start position:0% +the other way that's a pro tip if you're + + + align:start position:0% +the other way that's a pro tip if you're +ever with a large group of people you + + align:start position:0% +ever with a large group of people you + + + align:start position:0% +ever with a large group of people you +can prove any point you want by asking + + align:start position:0% +can prove any point you want by asking + + + align:start position:0% +can prove any point you want by asking +the other direction no one will raise + + align:start position:0% +the other direction no one will raise + + + align:start position:0% +the other direction no one will raise +their hand + + align:start position:0% +their hand + + + align:start position:0% +their hand +so um I agree that backward chaining is + + align:start position:0% +so um I agree that backward chaining is + + + align:start position:0% +so um I agree that backward chaining is +harder than forward chaining and I + + align:start position:0% +harder than forward chaining and I + + + align:start position:0% +harder than forward chaining and I +disagree with Patrick that we're going + + align:start position:0% +disagree with Patrick that we're going + + + align:start position:0% +disagree with Patrick that we're going +to get out of here early so let's start + + align:start position:0% +to get out of here early so let's start + + + align:start position:0% +to get out of here early so let's start +with backward chaining first so that we + + align:start position:0% +with backward chaining first so that we + + + align:start position:0% +with backward chaining first so that we +make sure that we spend the bulk of our + + align:start position:0% +make sure that we spend the bulk of our + + + align:start position:0% +make sure that we spend the bulk of our +time with it this forward chaining + + align:start position:0% +time with it this forward chaining + + + align:start position:0% +time with it this forward chaining +well you know you just go through you go + + align:start position:0% +well you know you just go through you go + + + align:start position:0% +well you know you just go through you go +through pretty methodically and add new + + align:start position:0% +through pretty methodically and add new + + + align:start position:0% +through pretty methodically and add new +rules backward chaining you have to draw + + align:start position:0% +rules backward chaining you have to draw + + + align:start position:0% +rules backward chaining you have to draw +this crazy tree there's a lot of places + + align:start position:0% +this crazy tree there's a lot of places + + + align:start position:0% +this crazy tree there's a lot of places +to get lost in the middle of the road so + + align:start position:0% +to get lost in the middle of the road so + + + align:start position:0% +to get lost in the middle of the road so +let's do some backward chaining and to + + align:start position:0% +let's do some backward chaining and to + + + align:start position:0% +let's do some backward chaining and to +do that I'll do it over here on the left + + align:start position:0% +do that I'll do it over here on the left + + + align:start position:0% +do that I'll do it over here on the left +side so our when we're doing backward + + align:start position:0% +side so our when we're doing backward + + + align:start position:0% +side so our when we're doing backward +chaining we have to remember a few + + align:start position:0% +chaining we have to remember a few + + + align:start position:0% +chaining we have to remember a few +things they're written directly on the + + align:start position:0% +things they're written directly on the + + + align:start position:0% +things they're written directly on the +quiz so you're not going to have to + + align:start position:0% +quiz so you're not going to have to + + + align:start position:0% +quiz so you're not going to have to +worry about that but they're still + + align:start position:0% +worry about that but they're still + + + align:start position:0% +worry about that but they're still +pretty important so actually I'll write + + align:start position:0% +pretty important so actually I'll write + + + align:start position:0% +pretty important so actually I'll write +on here first I'm going to read them off + + align:start position:0% +on here first I'm going to read them off + + + align:start position:0% +on here first I'm going to read them off +so when working on a hypothesis the + + align:start position:0% +so when working on a hypothesis the + + + align:start position:0% +so when working on a hypothesis the +backward chainer tries to find a + + align:start position:0% +backward chainer tries to find a + + + align:start position:0% +backward chainer tries to find a +matching assertion in the list of + + align:start position:0% +matching assertion in the list of + + + align:start position:0% +matching assertion in the list of +assertions first if no matching + + align:start position:0% +assertions first if no matching + + + align:start position:0% +assertions first if no matching +assertion is found the backward chainer + + align:start position:0% +assertion is found the backward chainer + + + align:start position:0% +assertion is found the backward chainer +will try to find a + + align:start position:0% +will try to find a + + + align:start position:0% +will try to find a +rule with a matching consequent a rule + + align:start position:0% +rule with a matching consequent a rule + + + align:start position:0% +rule with a matching consequent a rule +that has something in the then that can + + align:start position:0% +that has something in the then that can + + + align:start position:0% +that has something in the then that can +prove the assertion it's trying to + + align:start position:0% +prove the assertion it's trying to + + + align:start position:0% +prove the assertion it's trying to +figure out so for instance if I was + + align:start position:0% +figure out so for instance if I was + + + align:start position:0% +figure out so for instance if I was +doing backwards chaining on Sheamus + + align:start position:0% +doing backwards chaining on Sheamus + + + align:start position:0% +doing backwards chaining on Sheamus +snogs + + align:start position:0% +snogs + + + align:start position:0% +snogs +ment what happens I'm immediately done + + align:start position:0% +ment what happens I'm immediately done + + + align:start position:0% +ment what happens I'm immediately done +because there's an Asser assertion 3 + + align:start position:0% +because there's an Asser assertion 3 + + + align:start position:0% +because there's an Asser assertion 3 +that says sh Sheamus snog is ment I've + + align:start position:0% +that says sh Sheamus snog is ment I've + + + align:start position:0% +that says sh Sheamus snog is ment I've +proved it I'm done I'm happy we can + + align:start position:0% +proved it I'm done I'm happy we can + + + align:start position:0% +proved it I'm done I'm happy we can +leave we can go home unfortunately + + align:start position:0% +leave we can go home unfortunately + + + align:start position:0% +leave we can go home unfortunately +that's not what the quiz asked us to do + + align:start position:0% +that's not what the quiz asked us to do + + + align:start position:0% +that's not what the quiz asked us to do +now let's say that instead um we were + + align:start position:0% +now let's say that instead um we were + + + align:start position:0% +now let's say that instead um we were +supposed to say I don't know Sheamus is + + align:start position:0% +supposed to say I don't know Sheamus is + + + align:start position:0% +supposed to say I don't know Sheamus is +a protagonist well then we'd wind up + + align:start position:0% +a protagonist well then we'd wind up + + + align:start position:0% +a protagonist well then we'd wind up +looking through here and we would look + + align:start position:0% +looking through here and we would look + + + align:start position:0% +looking through here and we would look +at the fact that rule one can prove that + + align:start position:0% +at the fact that rule one can prove that + + + align:start position:0% +at the fact that rule one can prove that +someone is a protagonist and we' recurse + + align:start position:0% +someone is a protagonist and we' recurse + + + align:start position:0% +someone is a protagonist and we' recurse +and try to prove whatever is in the + + align:start position:0% +and try to prove whatever is in the + + + align:start position:0% +and try to prove whatever is in the +antecedent of rule one which is okay + + align:start position:0% +antecedent of rule one which is okay + + + align:start position:0% +antecedent of rule one which is okay +well does he live in Gryffindor + + align:start position:0% +well does he live in Gryffindor + + + align:start position:0% +well does he live in Gryffindor +da assertion two he does so that's some + + align:start position:0% +da assertion two he does so that's some + + + align:start position:0% +da assertion two he does so that's some +really quick and if that was too fast + + align:start position:0% +really quick and if that was too fast + + + align:start position:0% +really quick and if that was too fast +don't worry we're going to go step by + + align:start position:0% +don't worry we're going to go step by + + + align:start position:0% +don't worry we're going to go step by +step with the actual problem but I just + + align:start position:0% +step with the actual problem but I just + + + align:start position:0% +step with the actual problem but I just +wanted to give two really easy problems + + align:start position:0% +wanted to give two really easy problems + + + align:start position:0% +wanted to give two really easy problems +really quickly how it's going to do it + + align:start position:0% +really quickly how it's going to do it + + + align:start position:0% +really quickly how it's going to do it +let's go step by step with the real + + align:start position:0% +let's go step by step with the real + + + align:start position:0% +let's go step by step with the real +problem um let's keep in mind the + + align:start position:0% +problem um let's keep in mind the + + + align:start position:0% +problem um let's keep in mind the +backward chainer never adds new + + align:start position:0% +backward chainer never adds new + + + align:start position:0% +backward chainer never adds new +assertions to the list of assertions and + + align:start position:0% +assertions to the list of assertions and + + + align:start position:0% +assertions to the list of assertions and +if you have a tie + + align:start position:0% +if you have a tie + + + align:start position:0% +if you have a tie +break you always order based on um rule + + align:start position:0% +break you always order based on um rule + + + align:start position:0% +break you always order based on um rule +order first p 0 through P5 and if you + + align:start position:0% +order first p 0 through P5 and if you + + + align:start position:0% +order first p 0 through P5 and if you +can TR if you the rule same rule matches + + align:start position:0% +can TR if you the rule same rule matches + + + align:start position:0% +can TR if you the rule same rule matches +with more than one thing in your list of + + align:start position:0% +with more than one thing in your list of + + + align:start position:0% +with more than one thing in your list of +assertions then you tie break based on + + align:start position:0% +assertions then you tie break based on + + + align:start position:0% +assertions then you tie break based on +the order of the assertions okay that's + + align:start position:0% +the order of the assertions okay that's + + + align:start position:0% +the order of the assertions okay that's +very important disambiguation and + + align:start position:0% +very important disambiguation and + + + align:start position:0% +very important disambiguation and +tiebreaking are big place to get messed + + align:start position:0% +tiebreaking are big place to get messed + + + align:start position:0% +tiebreaking are big place to get messed +up + + align:start position:0% +up + + + align:start position:0% +up +so we're going to try to prove that + + align:start position:0% +so we're going to try to prove that + + + align:start position:0% +so we're going to try to prove that +Millis becomes Hermione's friend all + + align:start position:0% +Millis becomes Hermione's friend all + + + align:start position:0% +Millis becomes Hermione's friend all +right + + align:start position:0% +right + + + align:start position:0% +right +and + + align:start position:0% +and + + + align:start position:0% +and +so I'm going to abbreviate um some of + + align:start position:0% +so I'm going to abbreviate um some of + + + align:start position:0% +so I'm going to abbreviate um some of +the things but not not for the very + + align:start position:0% +the things but not not for the very + + + align:start position:0% +the things but not not for the very +first line + + align:start position:0% +first line + + + align:start position:0% +first line +so + + align:start position:0% +so + + + align:start position:0% +so +ment + + align:start position:0% +ment + + + align:start position:0% +ment +becomes Hermione's friend we start + + align:start position:0% +becomes Hermione's friend we start + + + align:start position:0% +becomes Hermione's friend we start +drawing a gold + + align:start position:0% +drawing a gold + + + align:start position:0% +drawing a gold +tree now you guys are going to learn + + align:start position:0% +tree now you guys are going to learn + + + align:start position:0% +tree now you guys are going to learn +exactly what these + + align:start position:0% +exactly what these + + + align:start position:0% +exactly what these +mean very soon in fact next lecture but + + align:start position:0% +mean very soon in fact next lecture but + + + align:start position:0% +mean very soon in fact next lecture but +for now trust me when I say these gold + + align:start position:0% +for now trust me when I say these gold + + + align:start position:0% +for now trust me when I say these gold +trees are G first and I'll explain what + + align:start position:0% +trees are G first and I'll explain what + + + align:start position:0% +trees are G first and I'll explain what +that means because some people have um + + align:start position:0% +that means because some people have um + + + align:start position:0% +that means because some people have um +messed themselves up and spent more time + + align:start position:0% +messed themselves up and spent more time + + + align:start position:0% +messed themselves up and spent more time +than they needed to by treating the gold + + align:start position:0% +than they needed to by treating the gold + + + align:start position:0% +than they needed to by treating the gold +tree in a different + + align:start position:0% +tree in a different + + + align:start position:0% +tree in a different +way um now Melissa becomes Hermione's + + align:start position:0% +way um now Melissa becomes Hermione's + + + align:start position:0% +way um now Melissa becomes Hermione's +friend let's pretend that we're the + + align:start position:0% +friend let's pretend that we're the + + + align:start position:0% +friend let's pretend that we're the +backward chainer we're trying to prove + + align:start position:0% +backward chainer we're trying to prove + + + align:start position:0% +backward chainer we're trying to prove +that this is true or disprove and say + + align:start position:0% +that this is true or disprove and say + + + align:start position:0% +that this is true or disprove and say +well it's definitely not true with what + + align:start position:0% +well it's definitely not true with what + + + align:start position:0% +well it's definitely not true with what +we have so let's see I'm now going to + + align:start position:0% +we have so let's see I'm now going to + + + align:start position:0% +we have so let's see I'm now going to +make you guys help and people in the + + align:start position:0% +make you guys help and people in the + + + align:start position:0% +make you guys help and people in the +back think they won't be called on so I + + align:start position:0% +back think they won't be called on so I + + + align:start position:0% +back think they won't be called on so I +often let call people in the back what + + align:start position:0% +often let call people in the back what + + + align:start position:0% +often let call people in the back what +do you think is the first thing we + + align:start position:0% +do you think is the first thing we + + + align:start position:0% +do you think is the first thing we +should do very first thing matching yes + + align:start position:0% +should do very first thing matching yes + + + align:start position:0% +should do very first thing matching yes +look for matching insertion excellent do + + align:start position:0% +look for matching insertion excellent do + + + align:start position:0% +look for matching insertion excellent do +we have a matching assertion + + align:start position:0% +we have a matching assertion + + + align:start position:0% +we have a matching assertion +everyone no we don't that would be the + + align:start position:0% +everyone no we don't that would be the + + + align:start position:0% +everyone no we don't that would be the +world's easiest quiz problem we do not + + align:start position:0% +world's easiest quiz problem we do not + + + align:start position:0% +world's easiest quiz problem we do not +have a matching assertion great so since + + align:start position:0% +have a matching assertion great so since + + + align:start position:0% +have a matching assertion great so since +we don't have a matching assertion what + + align:start position:0% +we don't have a matching assertion what + + + align:start position:0% +we don't have a matching assertion what +now start to look at rules that's right + + align:start position:0% +now start to look at rules that's right + + + align:start position:0% +now start to look at rules that's right +and do you see any rule that um could + + align:start position:0% +and do you see any rule that um could + + + align:start position:0% +and do you see any rule that um could +prove that Mel comes from min's friend + + align:start position:0% +prove that Mel comes from min's friend + + + align:start position:0% +prove that Mel comes from min's friend +P4 that's right you can see in p4x which + + align:start position:0% +P4 that's right you can see in p4x which + + + align:start position:0% +P4 that's right you can see in p4x which +can be anybody is Cap anyone is capable + + align:start position:0% +can be anybody is Cap anyone is capable + + + align:start position:0% +can be anybody is Cap anyone is capable +of being for min's friend great so P4 is + + align:start position:0% +of being for min's friend great so P4 is + + + align:start position:0% +of being for min's friend great so P4 is +our rule of the hour so we're going to + + align:start position:0% +our rule of the hour so we're going to + + + align:start position:0% +our rule of the hour so we're going to +use + + align:start position:0% +use + + + align:start position:0% +use +P4 and when we use + + align:start position:0% +P4 and when we use + + + align:start position:0% +P4 and when we use +P4 to prove that micit becomes heru's + + align:start position:0% +P4 to prove that micit becomes heru's + + + align:start position:0% +P4 to prove that micit becomes heru's +friend we're going to have to add + + align:start position:0% +friend we're going to have to add + + + align:start position:0% +friend we're going to have to add +something or another to the gold tree so + + align:start position:0% +something or another to the gold tree so + + + align:start position:0% +something or another to the gold tree so +let's see what do we have to add to the + + align:start position:0% +let's see what do we have to add to the + + + align:start position:0% +let's see what do we have to add to the +gold + + align:start position:0% + + + + align:start position:0% + +tree that's right does everyone see that + + align:start position:0% +tree that's right does everyone see that + + + align:start position:0% +tree that's right does everyone see that +in order for her to become herm's Friend + + align:start position:0% +in order for her to become herm's Friend + + + align:start position:0% +in order for her to become herm's Friend +by rule four have to see if she studies + + align:start position:0% +by rule four have to see if she studies + + + align:start position:0% +by rule four have to see if she studies +a lot and is a protagonist + + align:start position:0% +a lot and is a protagonist + + + align:start position:0% +a lot and is a protagonist +question + + align:start position:0% + + + + align:start position:0% + +when okay that's a very good question + + align:start position:0% +when okay that's a very good question + + + align:start position:0% +when okay that's a very good question +you're going to get screwed up if you + + align:start position:0% +you're going to get screwed up if you + + + align:start position:0% +you're going to get screwed up if you +look at the antient in backward training + + align:start position:0% +look at the antient in backward training + + + align:start position:0% +look at the antient in backward training +first it's backwards partially for a + + align:start position:0% +first it's backwards partially for a + + + align:start position:0% +first it's backwards partially for a +reason you need to look at the + + align:start position:0% +reason you need to look at the + + + align:start position:0% +reason you need to look at the +consequent now why is that well let's + + align:start position:0% +consequent now why is that well let's + + + align:start position:0% +consequent now why is that well let's +say there was a rule rule six that said + + align:start position:0% +say there was a rule rule six that said + + + align:start position:0% +say there was a rule rule six that said +if x becomes Hermione's friend then + + align:start position:0% +if x becomes Hermione's friend then + + + align:start position:0% +if x becomes Hermione's friend then +Hermione feeds X poly juice potion or + + align:start position:0% +Hermione feeds X poly juice potion or + + + align:start position:0% +Hermione feeds X poly juice potion or +something like that will that rule help + + align:start position:0% +something like that will that rule help + + + align:start position:0% +something like that will that rule help +us in back chain to figure out if ment + + align:start position:0% +us in back chain to figure out if ment + + + align:start position:0% +us in back chain to figure out if ment +becomes Hermione's + + align:start position:0% + + + + align:start position:0% + +friend some people are shaking their + + align:start position:0% +friend some people are shaking their + + + align:start position:0% +friend some people are shaking their +head but um think about will that rule + + align:start position:0% +head but um think about will that rule + + + align:start position:0% +head but um think about will that rule +be able to prove it no now if they do + + align:start position:0% +be able to prove it no now if they do + + + align:start position:0% +be able to prove it no now if they do +become herm's friend and we want to do + + align:start position:0% +become herm's friend and we want to do + + + align:start position:0% +become herm's friend and we want to do +some for chaining we'll figure out + + align:start position:0% +some for chaining we'll figure out + + + align:start position:0% +some for chaining we'll figure out +they're going to transmute into some + + align:start position:0% +they're going to transmute into some + + + align:start position:0% +they're going to transmute into some +kind of other thing because of the poly + + align:start position:0% +kind of other thing because of the poly + + + align:start position:0% +kind of other thing because of the poly +potion but it's not going to help us do + + align:start position:0% +potion but it's not going to help us do + + + align:start position:0% +potion but it's not going to help us do +the one thing we want in back chaining + + align:start position:0% +the one thing we want in back chaining + + + align:start position:0% +the one thing we want in back chaining +which is to prove that thing on the top + + align:start position:0% +which is to prove that thing on the top + + + align:start position:0% +which is to prove that thing on the top +so we actually need to look for + + align:start position:0% +so we actually need to look for + + + align:start position:0% +so we actually need to look for +something that has our current goal and + + align:start position:0% +something that has our current goal and + + + align:start position:0% +something that has our current goal and +its consequent then we add on the + + align:start position:0% +its consequent then we add on the + + + align:start position:0% +its consequent then we add on the +antecedents as um people I've asked so + + align:start position:0% +antecedents as um people I've asked so + + + align:start position:0% +antecedents as um people I've asked so +far sorry I don't know your names like + + align:start position:0% +far sorry I don't know your names like + + + align:start position:0% +far sorry I don't know your names like +Patrick have um correctly given me every + + align:start position:0% +Patrick have um correctly given me every + + + align:start position:0% +Patrick have um correctly given me every +time which is excellent so notice also + + align:start position:0% +time which is excellent so notice also + + + align:start position:0% +time which is excellent so notice also +that she uh didn't say x studies a lot + + align:start position:0% +that she uh didn't say x studies a lot + + + align:start position:0% +that she uh didn't say x studies a lot +needs to be added to the gold tree she + + align:start position:0% +needs to be added to the gold tree she + + + align:start position:0% +needs to be added to the gold tree she +she said ment studies a lot oh another + + align:start position:0% +she said ment studies a lot oh another + + + align:start position:0% +she said ment studies a lot oh another +question + + align:start position:0% +question + + + align:start position:0% +question +great obvious but after like putting Ru + + align:start position:0% +great obvious but after like putting Ru + + + align:start position:0% +great obvious but after like putting Ru +for in there should we first check the + + align:start position:0% +for in there should we first check the + + + align:start position:0% +for in there should we first check the +assertions if uh check on the assertions + + align:start position:0% +assertions if uh check on the assertions + + + align:start position:0% +assertions if uh check on the assertions +if our conditions are within rule four + + align:start position:0% +if our conditions are within rule four + + + align:start position:0% +if our conditions are within rule four +because then we wouldn't have to search + + align:start position:0% +because then we wouldn't have to search + + + align:start position:0% +because then we wouldn't have to search +other rules so the question is do once + + align:start position:0% +other rules so the question is do once + + + align:start position:0% +other rules so the question is do once +we put rule four in there should we + + align:start position:0% +we put rule four in there should we + + + align:start position:0% +we put rule four in there should we +check to see if those antecedents of + + align:start position:0% +check to see if those antecedents of + + + align:start position:0% +check to see if those antecedents of +rule four are already in the assertions + + align:start position:0% +rule four are already in the assertions + + + align:start position:0% +rule four are already in the assertions +before checking um other rules the + + align:start position:0% +before checking um other rules the + + + align:start position:0% +before checking um other rules the +answer you're not only correct sir + + align:start position:0% +answer you're not only correct sir + + + align:start position:0% +answer you're not only correct sir +you're exactly one step ahead so we're + + align:start position:0% +you're exactly one step ahead so we're + + + align:start position:0% +you're exactly one step ahead so we're +I'm going to assume I called on you for + + align:start position:0% +I'm going to assume I called on you for + + + align:start position:0% +I'm going to assume I called on you for +the very next thing that's exactly what + + align:start position:0% +the very next thing that's exactly what + + + align:start position:0% +the very next thing that's exactly what +we do once we draw it onto the tree you + + align:start position:0% +we do once we draw it onto the tree you + + + align:start position:0% +we do once we draw it onto the tree you +you're you're you're exactly on the way + + align:start position:0% +you're you're you're exactly on the way + + + align:start position:0% +you're you're you're exactly on the way +um further question + + align:start position:0% +um further question + + + align:start position:0% +um further question +or perfect so all right + + align:start position:0% +or perfect so all right + + + align:start position:0% +or perfect so all right +great um so again we're putting up + + align:start position:0% +great um so again we're putting up + + + align:start position:0% +great um so again we're putting up +Millis studies a lot millison is a + + align:start position:0% +Millis studies a lot millison is a + + + align:start position:0% +Millis studies a lot millison is a +protagonist we're not putting up X some + + align:start position:0% +protagonist we're not putting up X some + + + align:start position:0% +protagonist we're not putting up X some +people did that and of course it's an + + align:start position:0% +people did that and of course it's an + + + align:start position:0% +people did that and of course it's an +and node as we heard we need them both + + align:start position:0% +and node as we heard we need them both + + + align:start position:0% +and node as we heard we need them both +to be true or we're not going to be able + + align:start position:0% +to be true or we're not going to be able + + + align:start position:0% +to be true or we're not going to be able +to continue onward so we have I'm going + + align:start position:0% +to continue onward so we have I'm going + + + align:start position:0% +to continue onward so we have I'm going +to use M for ment ment studies a + + align:start position:0% +to use M for ment ment studies a + + + align:start position:0% +to use M for ment ment studies a +lot also over + + align:start position:0% +lot also over + + + align:start position:0% +lot also over +here ment is a + + align:start position:0% + + + + align:start position:0% + +protagonist + + align:start position:0% +protagonist + + + align:start position:0% +protagonist +great and we've already heard that we + + align:start position:0% +great and we've already heard that we + + + align:start position:0% +great and we've already heard that we +need to search in the assertions before + + align:start position:0% +need to search in the assertions before + + + align:start position:0% +need to search in the assertions before +we go into any rules + + align:start position:0% +we go into any rules + + + align:start position:0% +we go into any rules +for what we're looking for next the + + align:start position:0% +for what we're looking for next the + + + align:start position:0% +for what we're looking for next the +question question is what are we looking + + align:start position:0% +question question is what are we looking + + + align:start position:0% +question question is what are we looking +for next and in what order this is where + + align:start position:0% +for next and in what order this is where + + + align:start position:0% +for next and in what order this is where +that thing I told you about depth search + + align:start position:0% +that thing I told you about depth search + + + align:start position:0% +that thing I told you about depth search +is crucial we are going to look here on + + align:start position:0% +is crucial we are going to look here on + + + align:start position:0% +is crucial we are going to look here on +the left note and if it has any children + + align:start position:0% +the left note and if it has any children + + + align:start position:0% +the left note and if it has any children +if we have to keep going down we are not + + align:start position:0% +if we have to keep going down we are not + + + align:start position:0% +if we have to keep going down we are not +going to look here yet all right there's + + align:start position:0% +going to look here yet all right there's + + + align:start position:0% +going to look here yet all right there's +a few reasons for that one of which is + + align:start position:0% +a few reasons for that one of which is + + + align:start position:0% +a few reasons for that one of which is +that we're lazy the evaluation if you + + align:start position:0% +that we're lazy the evaluation if you + + + align:start position:0% +that we're lazy the evaluation if you +learned about it is also if you learned + + align:start position:0% +learned about it is also if you learned + + + align:start position:0% +learned about it is also if you learned +about lazy evaluation is also lazy and + + align:start position:0% +about lazy evaluation is also lazy and + + + align:start position:0% +about lazy evaluation is also lazy and +if we can disprove this studies a lot + + align:start position:0% +if we can disprove this studies a lot + + + align:start position:0% +if we can disprove this studies a lot +Branch we don't have to do any work with + + align:start position:0% +Branch we don't have to do any work with + + + align:start position:0% +Branch we don't have to do any work with +the protagonist Branch we're done we're + + align:start position:0% +the protagonist Branch we're done we're + + + align:start position:0% +the protagonist Branch we're done we're +out of here and it's and it's it's a + + align:start position:0% +out of here and it's and it's it's a + + + align:start position:0% +out of here and it's and it's it's a +it's a loss all right so um we're going + + align:start position:0% +it's a loss all right so um we're going + + + align:start position:0% +it's a loss all right so um we're going +to move down the studies a lot branch + + align:start position:0% +to move down the studies a lot branch + + + align:start position:0% +to move down the studies a lot branch +and we already heard from the audience + + align:start position:0% +and we already heard from the audience + + + align:start position:0% +and we already heard from the audience +we need to look to see if it's in the + + align:start position:0% +we need to look to see if it's in the + + + align:start position:0% +we need to look to see if it's in the +assertions everyone studies a lot ment + + align:start position:0% +assertions everyone studies a lot ment + + + align:start position:0% +assertions everyone studies a lot ment +studies a lot in the + + align:start position:0% +studies a lot in the + + + align:start position:0% +studies a lot in the +assertions no it's not all right well + + align:start position:0% +assertions no it's not all right well + + + align:start position:0% +assertions no it's not all right well +then now we're going to get to that + + align:start position:0% +then now we're going to get to that + + + align:start position:0% +then now we're going to get to that +question that I had before about the + + align:start position:0% +question that I had before about the + + + align:start position:0% +question that I had before about the +antecedent or the um consequent because + + align:start position:0% +antecedent or the um consequent because + + + align:start position:0% +antecedent or the um consequent because +studies is a lot is here in the um + + align:start position:0% +studies is a lot is here in the um + + + align:start position:0% +studies is a lot is here in the um +antecedent of rule four but we're not + + align:start position:0% +antecedent of rule four but we're not + + + align:start position:0% +antecedent of rule four but we're not +going to be able to use rule four here + + align:start position:0% +going to be able to use rule four here + + + align:start position:0% +going to be able to use rule four here +in fact that's how we got here in the + + align:start position:0% +in fact that's how we got here in the + + + align:start position:0% +in fact that's how we got here in the +first place so question + + align:start position:0% +first place so question + + + align:start position:0% +first place so question +is does um let's see the question is um + + align:start position:0% +is does um let's see the question is um + + + align:start position:0% +is does um let's see the question is um +do we have a rule that matches um in the + + align:start position:0% +do we have a rule that matches um in the + + + align:start position:0% +do we have a rule that matches um in the +in the um consequent that matches mson + + align:start position:0% +in the um consequent that matches mson + + + align:start position:0% +in the um consequent that matches mson +studies a lot yeah yep that's right P3 + + align:start position:0% +studies a lot yeah yep that's right P3 + + + align:start position:0% +studies a lot yeah yep that's right P3 +and P3 + + align:start position:0% +and P3 + + + align:start position:0% +and P3 +beers that's right so P3 is um would + + align:start position:0% +beers that's right so P3 is um would + + + align:start position:0% +beers that's right so P3 is um would +give us milon studies a lot and so + + align:start position:0% +give us milon studies a lot and so + + + align:start position:0% +give us milon studies a lot and so +therefore what will we add to the um + + align:start position:0% +therefore what will we add to the um + + + align:start position:0% +therefore what will we add to the um +gold tree we add both that is mson + + align:start position:0% +gold tree we add both that is mson + + + align:start position:0% +gold tree we add both that is mson +either a protagonist or a villain and + + align:start position:0% +either a protagonist or a villain and + + + align:start position:0% +either a protagonist or a villain and +that he's ous she turns out to be a + + align:start position:0% +that he's ous she turns out to be a + + + align:start position:0% +that he's ous she turns out to be a +girl all right so um that's exactly + + align:start position:0% +girl all right so um that's exactly + + + align:start position:0% +girl all right so um that's exactly +right we heard that we need to add um we + + align:start position:0% +right we heard that we need to add um we + + + align:start position:0% +right we heard that we need to add um we +need to add an and + + align:start position:0% +need to add an and + + + align:start position:0% +need to add an and +node but which also has an or node at + + align:start position:0% +node but which also has an or node at + + + align:start position:0% +node but which also has an or node at +the bottom of it because this is a + + align:start position:0% +the bottom of it because this is a + + + align:start position:0% +the bottom of it because this is a +little bit of a complicated rule so we + + align:start position:0% +little bit of a complicated rule so we + + + align:start position:0% +little bit of a complicated rule so we +have an and + + align:start position:0% +have an and + + + align:start position:0% +have an and +node so we have an N node and the first + + align:start position:0% +node so we have an N node and the first + + + align:start position:0% +node so we have an N node and the first +thing on the N node is ment is is a + + align:start position:0% + + + + align:start position:0% + +protagonist or + + align:start position:0% +protagonist or + + + align:start position:0% +protagonist or +millant is a + + align:start position:0% + + + + align:start position:0% + +villain and the second thing on the end + + align:start position:0% +villain and the second thing on the end + + + align:start position:0% +villain and the second thing on the end +node is ment is + + align:start position:0% + + + + align:start position:0% + +ambitious well actually that is the + + align:start position:0% +ambitious well actually that is the + + + align:start position:0% +ambitious well actually that is the +second thing on the end note I hope + + align:start position:0% +second thing on the end note I hope + + + align:start position:0% +second thing on the end note I hope +that's what I said all right the second + + align:start position:0% +that's what I said all right the second + + + align:start position:0% +that's what I said all right the second +thing on the end note is millison is + + align:start position:0% +thing on the end note is millison is + + + align:start position:0% +thing on the end note is millison is +ambitious great okay + + align:start position:0% + + + + align:start position:0% + +so here's our handy little + + align:start position:0% +so here's our handy little + + + align:start position:0% +so here's our handy little +tree now this is where it's important as + + align:start position:0% +tree now this is where it's important as + + + align:start position:0% +tree now this is where it's important as +I said we're doing a depth first + + align:start position:0% +I said we're doing a depth first + + + align:start position:0% +I said we're doing a depth first +search we're going down along the left + + align:start position:0% +search we're going down along the left + + + align:start position:0% +search we're going down along the left +Branch so uh where do you think we're + + align:start position:0% +Branch so uh where do you think we're + + + align:start position:0% +Branch so uh where do you think we're +going to go next on this + + align:start position:0% + + + + align:start position:0% + +tree uh not + + align:start position:0% +tree uh not + + + align:start position:0% +tree uh not +quite that's a good guess you didn't say + + align:start position:0% +quite that's a good guess you didn't say + + + align:start position:0% +quite that's a good guess you didn't say +we're trying to prove m is a protagonist + + align:start position:0% +we're trying to prove m is a protagonist + + + align:start position:0% +we're trying to prove m is a protagonist +on the right branch which is a very + + align:start position:0% +on the right branch which is a very + + + align:start position:0% +on the right branch which is a very +common state where do you think go down + + align:start position:0% +common state where do you think go down + + + align:start position:0% +common state where do you think go down +to see if there's a consequence for m + + align:start position:0% +to see if there's a consequence for m + + + align:start position:0% +to see if there's a consequence for m +isic is a which one of the two Milson is + + align:start position:0% +isic is a which one of the two Milson is + + + align:start position:0% +isic is a which one of the two Milson is +a protagonist do we want to look + + align:start position:0% +a protagonist do we want to look + + + align:start position:0% +a protagonist do we want to look +at yeah the farthest down left that's + + align:start position:0% +at yeah the farthest down left that's + + + align:start position:0% +at yeah the farthest down left that's +right so you guys will learn depth res + + align:start position:0% +right so you guys will learn depth res + + + align:start position:0% +right so you guys will learn depth res +search on Monday which point it will + + align:start position:0% +search on Monday which point it will + + + align:start position:0% +search on Monday which point it will +become much Clear what I'm saying but + + align:start position:0% +become much Clear what I'm saying but + + + align:start position:0% +become much Clear what I'm saying but +yeah you always follow the left Branch + + align:start position:0% +yeah you always follow the left Branch + + + align:start position:0% +yeah you always follow the left Branch +as far down as you can then you take the + + align:start position:0% +as far down as you can then you take the + + + align:start position:0% +as far down as you can then you take the +right branch of that same branch that + + align:start position:0% +right branch of that same branch that + + + align:start position:0% +right branch of that same branch that +you followed all right great so we're + + align:start position:0% +you followed all right great so we're + + + align:start position:0% +you followed all right great so we're +going to try to find melison is a + + align:start position:0% +going to try to find melison is a + + + align:start position:0% +going to try to find melison is a +protagonist where what do we do first + + align:start position:0% +protagonist where what do we do first + + + align:start position:0% +protagonist where what do we do first +everyone Check assertions Yes is it in + + align:start position:0% +everyone Check assertions Yes is it in + + + align:start position:0% +everyone Check assertions Yes is it in +there no it's not okay + + align:start position:0% +there no it's not okay + + + align:start position:0% +there no it's not okay +so therefore we're going to try to find + + align:start position:0% +so therefore we're going to try to find + + + align:start position:0% +so therefore we're going to try to find +a rule as as we heard about um whether + + align:start position:0% +a rule as as we heard about um whether + + + align:start position:0% +a rule as as we heard about um whether +millison is a protagonist so all the way + + align:start position:0% +millison is a protagonist so all the way + + + align:start position:0% +millison is a protagonist so all the way +in the + + align:start position:0% +in the + + + align:start position:0% +in the +back all the way in the back what is + + align:start position:0% +back all the way in the back what is + + + align:start position:0% +back all the way in the back what is +there a rule that matches matches the + + align:start position:0% +there a rule that matches matches the + + + align:start position:0% +there a rule that matches matches the +that matches in its consequent that + + align:start position:0% +that matches in its consequent that + + + align:start position:0% +that matches in its consequent that +melon is a + + align:start position:0% +melon is a + + + align:start position:0% +melon is a +protagonist + + align:start position:0% + + + + align:start position:0% + +um there is a rule okay well let's give + + align:start position:0% +um there is a rule okay well let's give + + + align:start position:0% +um there is a rule okay well let's give +it a try which one rule one that's right + + align:start position:0% +it a try which one rule one that's right + + + align:start position:0% +it a try which one rule one that's right +so therefore we have to add what to our + + align:start position:0% +so therefore we have to add what to our + + + align:start position:0% +so therefore we have to add what to our +gold + + align:start position:0% +gold + + + align:start position:0% +gold +tree + + align:start position:0% + + + + align:start position:0% + +um right and what's on that + + align:start position:0% + + + + align:start position:0% + +leaf yeah those Liv in G door to perfect + + align:start position:0% +leaf yeah those Liv in G door to perfect + + + align:start position:0% +leaf yeah those Liv in G door to perfect +so our new thing that we're searching + + align:start position:0% +so our new thing that we're searching + + + align:start position:0% +so our new thing that we're searching +for + + align:start position:0% +for + + + align:start position:0% +for +is Pretend This connects actually I + + align:start position:0% +is Pretend This connects actually I + + + align:start position:0% +is Pretend This connects actually I +guess it does connect we're looking for + + align:start position:0% +guess it does connect we're looking for + + + align:start position:0% +guess it does connect we're looking for +M lives in Gryffindor Tower great all + + align:start position:0% +M lives in Gryffindor Tower great all + + + align:start position:0% +M lives in Gryffindor Tower great all +right and since it's step first that's + + align:start position:0% +right and since it's step first that's + + + align:start position:0% +right and since it's step first that's +where we going next great we're on a + + align:start position:0% +where we going next great we're on a + + + align:start position:0% +where we going next great we're on a +roll so what do we do + + align:start position:0% +roll so what do we do + + + align:start position:0% +roll so what do we do +first do we have that in the + + align:start position:0% +first do we have that in the + + + align:start position:0% +first do we have that in the +assertions some people say yes but the + + align:start position:0% +assertions some people say yes but the + + + align:start position:0% +assertions some people say yes but the +answer is no we have in fact Sheamus + + align:start position:0% +answer is no we have in fact Sheamus + + + align:start position:0% +answer is no we have in fact Sheamus +living in Gryffindor Tower most of you + + align:start position:0% +living in Gryffindor Tower most of you + + + align:start position:0% +living in Gryffindor Tower most of you +said no you're right the majority rules + + align:start position:0% +said no you're right the majority rules + + + align:start position:0% +said no you're right the majority rules +uh we don't have it in the assertions + + align:start position:0% +uh we don't have it in the assertions + + + align:start position:0% +uh we don't have it in the assertions +however do we have a rule with that in + + align:start position:0% +however do we have a rule with that in + + + align:start position:0% +however do we have a rule with that in +the + + align:start position:0% +the + + + align:start position:0% +the +consequent no so what do we + + align:start position:0% + + + + align:start position:0% + +do people are saying different things + + align:start position:0% +do people are saying different things + + + align:start position:0% +do people are saying different things +that are all correct backtrack you say + + align:start position:0% +that are all correct backtrack you say + + + align:start position:0% +that are all correct backtrack you say +go to the next we can't prove it all + + align:start position:0% +go to the next we can't prove it all + + + align:start position:0% +go to the next we can't prove it all +correct put a big + + align:start position:0% +correct put a big + + + align:start position:0% +correct put a big +X this isn't true now we look up we're + + align:start position:0% +X this isn't true now we look up we're + + + align:start position:0% +X this isn't true now we look up we're +on an or node so we're not done yet + + align:start position:0% +on an or node so we're not done yet + + + align:start position:0% +on an or node so we're not done yet +because + + align:start position:0% +because + + + align:start position:0% +because +either of those can be + + align:start position:0% +either of those can be + + + align:start position:0% +either of those can be +true great so now we go back up backrack + + align:start position:0% +true great so now we go back up backrack + + + align:start position:0% +true great so now we go back up backrack +millison is a villain + + align:start position:0% +millison is a villain + + + align:start position:0% +millison is a villain +great what do we do + + align:start position:0% +great what do we do + + + align:start position:0% +great what do we do +first check the assertions is it in + + align:start position:0% +first check the assertions is it in + + + align:start position:0% +first check the assertions is it in +there no it's not don't worry we're + + align:start position:0% +there no it's not don't worry we're + + + align:start position:0% +there no it's not don't worry we're +getting to one where it will be where + + align:start position:0% +getting to one where it will be where + + + align:start position:0% +getting to one where it will be where +about 40% of the or 30 to 40% of the + + align:start position:0% +about 40% of the or 30 to 40% of the + + + align:start position:0% +about 40% of the or 30 to 40% of the +class lost points um very very soon so + + align:start position:0% +class lost points um very very soon so + + + align:start position:0% +class lost points um very very soon so +um we see that we see that millant is a + + align:start position:0% +um we see that we see that millant is a + + + align:start position:0% +um we see that we see that millant is a +villain + + align:start position:0% +villain + + + align:start position:0% +villain +and it's not in the assertions so + + align:start position:0% +and it's not in the assertions so + + + align:start position:0% +and it's not in the assertions so +therefore is there any rule that has + + align:start position:0% +therefore is there any rule that has + + + align:start position:0% +therefore is there any rule that has +that in its + + align:start position:0% + + + + align:start position:0% + +consequence we're looking for m is a + + align:start position:0% + + + + align:start position:0% + +villain oh you can't see it uh all right + + align:start position:0% +villain oh you can't see it uh all right + + + align:start position:0% +villain oh you can't see it uh all right +I will move it down slightly it got a + + align:start position:0% +I will move it down slightly it got a + + + align:start position:0% +I will move it down slightly it got a +little bit off kilter when I put in the + + align:start position:0% +little bit off kilter when I put in the + + + align:start position:0% +little bit off kilter when I put in the +um parentheses around the end hold + + align:start position:0% +um parentheses around the end hold + + + align:start position:0% +um parentheses around the end hold +on ah there you + + align:start position:0% + + + + align:start position:0% + +go + + align:start position:0% +go + + + align:start position:0% +go +okay um a protagonist or is a villain + + align:start position:0% +okay um a protagonist or is a villain + + + align:start position:0% +okay um a protagonist or is a villain +and ous then they study a lot all right + + align:start position:0% +and ous then they study a lot all right + + + align:start position:0% +and ous then they study a lot all right +we're trying to prove that she's a + + align:start position:0% +we're trying to prove that she's a + + + align:start position:0% +we're trying to prove that she's a +villain though so do we have any with + + align:start position:0% +villain though so do we have any with + + + align:start position:0% +villain though so do we have any with +that in the + + align:start position:0% +that in the + + + align:start position:0% +that in the +consequent that anything that will prove + + align:start position:0% +consequent that anything that will prove + + + align:start position:0% +consequent that anything that will prove +that she's a villain if we fire off that + + align:start position:0% +that she's a villain if we fire off that + + + align:start position:0% +that she's a villain if we fire off that +rule all right uh want to give her a + + align:start position:0% +rule all right uh want to give her a + + + align:start position:0% +rule all right uh want to give her a +little bit of help me too + + align:start position:0% +little bit of help me too + + + align:start position:0% +little bit of help me too +if she lives + + align:start position:0% +if she lives + + + align:start position:0% +if she lives +in's ah see that now it had two so it + + align:start position:0% +in's ah see that now it had two so it + + + align:start position:0% +in's ah see that now it had two so it +was a little bit harder now some people + + align:start position:0% +was a little bit harder now some people + + + align:start position:0% +was a little bit harder now some people +ask what about that ambitious thing can + + align:start position:0% +ask what about that ambitious thing can + + + align:start position:0% +ask what about that ambitious thing can +we like add that to the tree or + + align:start position:0% +we like add that to the tree or + + + align:start position:0% +we like add that to the tree or +something no the backer chainer is + + align:start position:0% +something no the backer chainer is + + + align:start position:0% +something no the backer chainer is +single-minded focused and stupid even + + align:start position:0% +single-minded focused and stupid even + + + align:start position:0% +single-minded focused and stupid even +though it's later going to need to prove + + align:start position:0% +though it's later going to need to prove + + + align:start position:0% +though it's later going to need to prove +that she's ambitious it doesn't care it + + align:start position:0% +that she's ambitious it doesn't care it + + + align:start position:0% +that she's ambitious it doesn't care it +just sees the villain there villain oh + + align:start position:0% +just sees the villain there villain oh + + + align:start position:0% +just sees the villain there villain oh +that's great as long as we've got the + + align:start position:0% +that's great as long as we've got the + + + align:start position:0% +that's great as long as we've got the +antecedent we are going to um we're + + align:start position:0% +antecedent we are going to um we're + + + align:start position:0% +antecedent we are going to um we're +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +happy this is actually an important + + align:start position:0% +happy this is actually an important + + + align:start position:0% +happy this is actually an important +Point not in this particular problem but + + align:start position:0% +Point not in this particular problem but + + + align:start position:0% +Point not in this particular problem but +in some other problems so by using + + align:start position:0% +in some other problems so by using + + + align:start position:0% +in some other problems so by using +P2 um we're obviously going to have the + + align:start position:0% +P2 um we're obviously going to have the + + + align:start position:0% +P2 um we're obviously going to have the +add the antecedent X lives in slowther + + align:start position:0% +add the antecedent X lives in slowther + + + align:start position:0% +add the antecedent X lives in slowther +and dungeon when X here is Mill so + + align:start position:0% +and dungeon when X here is Mill so + + + align:start position:0% +and dungeon when X here is Mill so +millant lives in slowther and + + align:start position:0% + + + + align:start position:0% + +dungeon all right so what's the first + + align:start position:0% +dungeon all right so what's the first + + + align:start position:0% +dungeon all right so what's the first +thing we do when we see this new + + align:start position:0% + + + + align:start position:0% + +assertion we check the assertions is it + + align:start position:0% +assertion we check the assertions is it + + + align:start position:0% +assertion we check the assertions is it +in there yes that's not where everyone + + align:start position:0% +in there yes that's not where everyone + + + align:start position:0% +in there yes that's not where everyone +lost points but yes it is in + + align:start position:0% +lost points but yes it is in + + + align:start position:0% +lost points but yes it is in +there check this or node is Happy Now we + + align:start position:0% +there check this or node is Happy Now we + + + align:start position:0% +there check this or node is Happy Now we +move up to the Ane with millon is + + align:start position:0% +move up to the Ane with millon is + + + align:start position:0% +move up to the Ane with millon is +ambitious so m milon is ambitious what + + align:start position:0% +ambitious so m milon is ambitious what + + + align:start position:0% +ambitious so m milon is ambitious what +do we do + + align:start position:0% +do we do + + + align:start position:0% +do we do +now sure so um in the consequ + + align:start position:0% +now sure so um in the consequ + + + align:start position:0% +now sure so um in the consequ +P2 X is a vill and X is ambitious like I + + align:start position:0% +P2 X is a vill and X is ambitious like I + + + align:start position:0% +P2 X is a vill and X is ambitious like I +don't know it's to + + align:start position:0% +don't know it's to + + + align:start position:0% +don't know it's to +fight or whatever but in our assertions + + align:start position:0% +fight or whatever but in our assertions + + + align:start position:0% +fight or whatever but in our assertions +we have that melon is ous necessary to + + align:start position:0% +we have that melon is ous necessary to + + + align:start position:0% +we have that melon is ous necessary to +let us to let us use rule two actually + + align:start position:0% +let us to let us use rule two actually + + + align:start position:0% +let us to let us use rule two actually +no it's it's um the question is + + align:start position:0% +no it's it's um the question is + + + align:start position:0% +no it's it's um the question is +um do we need the uh do we need the x is + + align:start position:0% +um do we need the uh do we need the x is + + + align:start position:0% +um do we need the uh do we need the x is +ambitious to be in our list of + + align:start position:0% +ambitious to be in our list of + + + align:start position:0% +ambitious to be in our list of +assertions in order to use P2 for + + align:start position:0% +assertions in order to use P2 for + + + align:start position:0% +assertions in order to use P2 for +instance if we didn't have the assertion + + align:start position:0% +instance if we didn't have the assertion + + + align:start position:0% +instance if we didn't have the assertion +that m is ambitious would P2 have a + + align:start position:0% +that m is ambitious would P2 have a + + + align:start position:0% +that m is ambitious would P2 have a +problem firing + + align:start position:0% +problem firing + + + align:start position:0% +problem firing +ass so it's it's a it's a very + + align:start position:0% +ass so it's it's a it's a very + + + align:start position:0% +ass so it's it's a it's a very +interesting question it's sort of what + + align:start position:0% +interesting question it's sort of what + + + align:start position:0% +interesting question it's sort of what +actually I was trying to um what I was + + align:start position:0% +actually I was trying to um what I was + + + align:start position:0% +actually I was trying to um what I was +trying to mention earlier when I said + + align:start position:0% +trying to mention earlier when I said + + + align:start position:0% +trying to mention earlier when I said +it's single-minded it's focused it + + align:start position:0% +it's single-minded it's focused it + + + align:start position:0% +it's single-minded it's focused it +doesn't care about the other one because + + align:start position:0% +doesn't care about the other one because + + + align:start position:0% +doesn't care about the other one because +you might say well wait a minute P2 + + align:start position:0% +you might say well wait a minute P2 + + + align:start position:0% +you might say well wait a minute P2 +could never have actually fired if it + + align:start position:0% +could never have actually fired if it + + + align:start position:0% +could never have actually fired if it +didn't have both of its consequence but + + align:start position:0% +didn't have both of its consequence but + + + align:start position:0% +didn't have both of its consequence but +in fact the backward chainer doesn't + + align:start position:0% +in fact the backward chainer doesn't + + + align:start position:0% +in fact the backward chainer doesn't +care all that the backward chainer is + + align:start position:0% +care all that the backward chainer is + + + align:start position:0% +care all that the backward chainer is +looking to do is to prove whether is to + + align:start position:0% +looking to do is to prove whether is to + + + align:start position:0% +looking to do is to prove whether is to +prove whether or not there is a + + align:start position:0% +prove whether or not there is a + + + align:start position:0% +prove whether or not there is a +possibility that ment might be a villain + + align:start position:0% +possibility that ment might be a villain + + + align:start position:0% +possibility that ment might be a villain +it's not signy to say oh all of the + + align:start position:0% +it's not signy to say oh all of the + + + align:start position:0% +it's not signy to say oh all of the +results of of um of some certain rules + + align:start position:0% +results of of um of some certain rules + + + align:start position:0% +results of of um of some certain rules +are making ment a villain and all the + + align:start position:0% +are making ment a villain and all the + + + align:start position:0% +are making ment a villain and all the +other things that are there like + + align:start position:0% +other things that are there like + + + align:start position:0% +other things that are there like +ambitious are in the database it's not + + align:start position:0% +ambitious are in the database it's not + + + align:start position:0% +ambitious are in the database it's not +the for chainer it actually doesn't care + + align:start position:0% +the for chainer it actually doesn't care + + + align:start position:0% +the for chainer it actually doesn't care +this sometimes leads to unnecessary + + align:start position:0% +this sometimes leads to unnecessary + + + align:start position:0% +this sometimes leads to unnecessary +computation but it's very simple and + + align:start position:0% +computation but it's very simple and + + + align:start position:0% +computation but it's very simple and +it's very simple to code so it it often + + align:start position:0% +it's very simple to code so it it often + + + align:start position:0% +it's very simple to code so it it often +will probably speed you up in the long + + align:start position:0% +will probably speed you up in the long + + + align:start position:0% +will probably speed you up in the long +run like if there's for instance 100 + + align:start position:0% +run like if there's for instance 100 + + + align:start position:0% +run like if there's for instance 100 +things in the then and you only care + + align:start position:0% +things in the then and you only care + + + align:start position:0% +things in the then and you only care +about one of them it would be a waste + + align:start position:0% +about one of them it would be a waste + + + align:start position:0% +about one of them it would be a waste +almost to add those 99 there was it + + align:start position:0% +almost to add those 99 there was it + + + align:start position:0% +almost to add those 99 there was it +followup um over here + + align:start position:0% +followup um over here + + + align:start position:0% +followup um over here +somewhere you have you still have to + + align:start position:0% +somewhere you have you still have to + + + align:start position:0% +somewhere you have you still have to +walk the whole + + align:start position:0% +walk the whole + + + align:start position:0% +walk the whole +well you have off order n of 99 and so + + align:start position:0% +well you have off order n of 99 and so + + + align:start position:0% +well you have off order n of 99 and so +then you're doing an order computation + + align:start position:0% +then you're doing an order computation + + + align:start position:0% +then you're doing an order computation +you add all add them to some half table + + align:start position:0% +you add all add them to some half table + + + align:start position:0% +you add all add them to some half table +you can try um however then at that + + align:start position:0% +you can try um however then at that + + + align:start position:0% +you can try um however then at that +point every time you check the + + align:start position:0% +point every time you check the + + + align:start position:0% +point every time you check the +assertions you'd be attempting to check + + align:start position:0% +assertions you'd be attempting to check + + + align:start position:0% +assertions you'd be attempting to check +those 99 also you might not have used + + align:start position:0% +those 99 also you might not have used + + + align:start position:0% +those 99 also you might not have used +those rules the question is um could you + + align:start position:0% +those rules the question is um could you + + + align:start position:0% +those rules the question is um could you +make a hash table with all of the 100 + + align:start position:0% +make a hash table with all of the 100 + + + align:start position:0% +make a hash table with all of the 100 +things that were in the consequence and + + align:start position:0% +things that were in the consequence and + + + align:start position:0% +things that were in the consequence and +then after having made that hash table + + align:start position:0% +then after having made that hash table + + + align:start position:0% +then after having made that hash table +since you were already walking through + + align:start position:0% +since you were already walking through + + + align:start position:0% +since you were already walking through +those anyway when you were checking it + + align:start position:0% +those anyway when you were checking it + + + align:start position:0% +those anyway when you were checking it +you could add those to the assertions + + align:start position:0% +you could add those to the assertions + + + align:start position:0% +you could add those to the assertions +the problem is that you might not + + align:start position:0% +the problem is that you might not + + + align:start position:0% +the problem is that you might not +necessarily want all those with the + + align:start position:0% +necessarily want all those with the + + + align:start position:0% +necessarily want all those with the +backward chainer you might not + + align:start position:0% +backward chainer you might not + + + align:start position:0% +backward chainer you might not +necessarily want to think that all of + + align:start position:0% +necessarily want to think that all of + + + align:start position:0% +necessarily want to think that all of +those things in the um the consequent + + align:start position:0% +those things in the um the consequent + + + align:start position:0% +those things in the um the consequent +are necessarily true um however it can + + align:start position:0% +are necessarily true um however it can + + + align:start position:0% +are necessarily true um however it can +you might not care about them and then + + align:start position:0% +you might not care about them and then + + + align:start position:0% +you might not care about them and then +you have to just make an order end + + align:start position:0% +you have to just make an order end + + + align:start position:0% +you have to just make an order end +computation every time you check that + + align:start position:0% +computation every time you check that + + + align:start position:0% +computation every time you check that +list of assertions in the upper left + + align:start position:0% +list of assertions in the upper left + + + align:start position:0% +list of assertions in the upper left +indexing into uh order one that's true + + align:start position:0% +indexing into uh order one that's true + + + align:start position:0% +indexing into uh order one that's true +however you don't know what assertions + + align:start position:0% +however you don't know what assertions + + + align:start position:0% +however you don't know what assertions +there are you have to check the entire + + align:start position:0% +there are you have to check the entire + + + align:start position:0% +there are you have to check the entire +list of assertions in the upper left + + align:start position:0% +list of assertions in the upper left + + + align:start position:0% +list of assertions in the upper left +every time you get to a new node in the + + align:start position:0% +every time you get to a new node in the + + + align:start position:0% +every time you get to a new node in the +gold tree so each one is order one but + + align:start position:0% +gold tree so each one is order one but + + + align:start position:0% +gold tree so each one is order one but +I'm not saying to find a specific + + align:start position:0% +I'm not saying to find a specific + + + align:start position:0% +I'm not saying to find a specific +assertion is order is order n I'm saying + + align:start position:0% +assertion is order is order n I'm saying + + + align:start position:0% +assertion is order is order n I'm saying +every time you make a new node in the + + align:start position:0% +every time you make a new node in the + + + align:start position:0% +every time you make a new node in the +gold tree you have to check all of the + + align:start position:0% +gold tree you have to check all of the + + + align:start position:0% +gold tree you have to check all of the +assertions you've added you have to do + + align:start position:0% +assertions you've added you have to do + + + align:start position:0% +assertions you've added you have to do +that anyway have four asss yeah you have + + align:start position:0% +that anyway have four asss yeah you have + + + align:start position:0% +that anyway have four asss yeah you have +to check through the four but let's say + + align:start position:0% +to check through the four but let's say + + + align:start position:0% +to check through the four but let's say +that there were 10,000 consequence of P2 + + align:start position:0% +that there were 10,000 consequence of P2 + + + align:start position:0% +that there were 10,000 consequence of P2 +um you would have to check 10,000 + + align:start position:0% +um you would have to check 10,000 + + + align:start position:0% +um you would have to check 10,000 +instead of four if you added them if you + + align:start position:0% +instead of four if you added them if you + + + align:start position:0% +instead of four if you added them if you +added them all after proving P2 was true + + align:start position:0% +added them all after proving P2 was true + + + align:start position:0% +added them all after proving P2 was true +on the gold tree also another important + + align:start position:0% +on the gold tree also another important + + + align:start position:0% +on the gold tree also another important +note is that um you might not use every + + align:start position:0% +note is that um you might not use every + + + align:start position:0% +note is that um you might not use every +branch of the gold tree if there's like + + align:start position:0% +branch of the gold tree if there's like + + + align:start position:0% +branch of the gold tree if there's like +an ore that's up higher and you wind up + + align:start position:0% +an ore that's up higher and you wind up + + + align:start position:0% +an ore that's up higher and you wind up +using a different branch in which case + + align:start position:0% +using a different branch in which case + + + align:start position:0% +using a different branch in which case +you'd probably have to make a separate + + align:start position:0% +you'd probably have to make a separate + + + align:start position:0% +you'd probably have to make a separate +hash table for every sub branch that you + + align:start position:0% +hash table for every sub branch that you + + + align:start position:0% +hash table for every sub branch that you +have and then remember which hash tables + + align:start position:0% +have and then remember which hash tables + + + align:start position:0% +have and then remember which hash tables +were updated based on which sub branch + + align:start position:0% +were updated based on which sub branch + + + align:start position:0% +were updated based on which sub branch +and then the sub branches die it's + + align:start position:0% +and then the sub branches die it's + + + align:start position:0% +and then the sub branches die it's +probably more effort than it's worth you + + align:start position:0% +probably more effort than it's worth you + + + align:start position:0% +probably more effort than it's worth you +you could uh it's an certainly an + + align:start position:0% +you could uh it's an certainly an + + + align:start position:0% +you could uh it's an certainly an +interesting question it's a great + + align:start position:0% +interesting question it's a great + + + align:start position:0% +interesting question it's a great +question for for debate and recitation + + align:start position:0% +question for for debate and recitation + + + align:start position:0% +question for for debate and recitation +and also I'm happy to talk about it + + align:start position:0% +and also I'm happy to talk about it + + + align:start position:0% +and also I'm happy to talk about it +later I think that someone who very + + align:start position:0% +later I think that someone who very + + + align:start position:0% +later I think that someone who very +intelligently made hash tables and + + align:start position:0% +intelligently made hash tables and + + + align:start position:0% +intelligently made hash tables and +thought thought the problem through as + + align:start position:0% +thought thought the problem through as + + + align:start position:0% +thought thought the problem through as +Patrick said more knowledge can mean a + + align:start position:0% +Patrick said more knowledge can mean a + + + align:start position:0% +Patrick said more knowledge can mean a +better well actually maybe he hasn't + + align:start position:0% +better well actually maybe he hasn't + + + align:start position:0% +better well actually maybe he hasn't +said more knowledge can be a better + + align:start position:0% +said more knowledge can be a better + + + align:start position:0% +said more knowledge can be a better +search because we haven't done that + + align:start position:0% +search because we haven't done that + + + align:start position:0% +search because we haven't done that +lecture yet + + align:start position:0% +lecture yet + + + align:start position:0% +lecture yet +but you're talking about implementation + + align:start position:0% +but you're talking about implementation + + + align:start position:0% +but you're talking about implementation +decision and using hashtable might well + + align:start position:0% +decision and using hashtable might well + + + align:start position:0% +decision and using hashtable might well +be a good way to do this the problem is + + align:start position:0% +be a good way to do this the problem is + + + align:start position:0% +be a good way to do this the problem is +that we're presuming some things about + + align:start position:0% +that we're presuming some things about + + + align:start position:0% +that we're presuming some things about +uh how the rules are fire in and what + + align:start position:0% +uh how the rules are fire in and what + + + align:start position:0% +uh how the rules are fire in and what +what Bings they're firing that depend on + + align:start position:0% +what Bings they're firing that depend on + + + align:start position:0% +what Bings they're firing that depend on +the order of the assertions in the table + + align:start position:0% +the order of the assertions in the table + + + align:start position:0% +the order of the assertions in the table +so if we use the hash table we' lose the + + align:start position:0% +so if we use the hash table we' lose the + + + align:start position:0% +so if we use the hash table we' lose the +order and we wouldn't be able to + + align:start position:0% +order and we wouldn't be able to + + + align:start position:0% +order and we wouldn't be able to +P that's true that's true but I I'm + + align:start position:0% +P that's true that's true but I I'm + + + align:start position:0% +P that's true that's true but I I'm +thinking like if someone wanted to make + + align:start position:0% +thinking like if someone wanted to make + + + align:start position:0% +thinking like if someone wanted to make +that implementation as like do some + + align:start position:0% +that implementation as like do some + + + align:start position:0% +that implementation as like do some +research in rules-based systems it's + + align:start position:0% +research in rules-based systems it's + + + align:start position:0% +research in rules-based systems it's +possible you can um increase the running + + align:start position:0% +possible you can um increase the running + + + align:start position:0% +possible you can um increase the running +speed um in this class we are U not as + + align:start position:0% +speed um in this class we are U not as + + + align:start position:0% +speed um in this class we are U not as +um not completely as focused on the F on + + align:start position:0% +um not completely as focused on the F on + + + align:start position:0% +um not completely as focused on the F on +the fastest algorithms but I still think + + align:start position:0% +the fastest algorithms but I still think + + + align:start position:0% +the fastest algorithms but I still think +that that's a cool thing to try um + + align:start position:0% +that that's a cool thing to try um + + + align:start position:0% +that that's a cool thing to try um +questions from people in the crowd uh + + align:start position:0% +questions from people in the crowd uh + + + align:start position:0% +questions from people in the crowd uh +we'll start here so so ignoring the the + + align:start position:0% +we'll start here so so ignoring the the + + + align:start position:0% +we'll start here so so ignoring the the +hash table ignore the hash table thing + + align:start position:0% +hash table ignore the hash table thing + + + align:start position:0% +hash table ignore the hash table thing +that's that's a good idea because it's a + + align:start position:0% +that's that's a good idea because it's a + + + align:start position:0% +that's that's a good idea because it's a +little extra enrichment thing it's not + + align:start position:0% +little extra enrichment thing it's not + + + align:start position:0% +little extra enrichment thing it's not +anything you would possibly need to know + + align:start position:0% +anything you would possibly need to know + + + align:start position:0% +anything you would possibly need to know +for the + + align:start position:0% +for the + + + align:start position:0% +for the +quiz things so if if it became like in a + + align:start position:0% +quiz things so if if it became like in a + + + align:start position:0% +quiz things so if if it became like in a +then and you're using this then + + align:start position:0% +then and you're using this then + + + align:start position:0% +then and you're using this then +statement because you want the villain + + align:start position:0% +statement because you want the villain + + + align:start position:0% +statement because you want the villain +so along with using this you get at + + align:start position:0% +so along with using this you get at + + + align:start position:0% +so along with using this you get at +ambitious what happens to be used after + + align:start position:0% +ambitious what happens to be used after + + + align:start position:0% +ambitious what happens to be used after +that another then statement that you + + align:start position:0% +that another then statement that you + + + align:start position:0% +that another then statement that you +also need it says is not issues so how + + align:start position:0% +also need it says is not issues so how + + + align:start position:0% +also need it says is not issues so how +would you resolve like that so the + + align:start position:0% +would you resolve like that so the + + + align:start position:0% +would you resolve like that so the +question is let's say you used rule two + + align:start position:0% +question is let's say you used rule two + + + align:start position:0% +question is let's say you used rule two +somewhere in the tree to get that X is a + + align:start position:0% +somewhere in the tree to get that X is a + + + align:start position:0% +somewhere in the tree to get that X is a +villain which then says that X is + + align:start position:0% +villain which then says that X is + + + align:start position:0% +villain which then says that X is +ambitious then later you have X is not + + align:start position:0% +ambitious then later you have X is not + + + align:start position:0% +ambitious then later you have X is not +ambitious um somewhere um some somewhere + + align:start position:0% +ambitious um somewhere um some somewhere + + + align:start position:0% +ambitious um somewhere um some somewhere +in one of the other rules that you then + + align:start position:0% +in one of the other rules that you then + + + align:start position:0% +in one of the other rules that you then +later need how is that the question is + + align:start position:0% +later need how is that the question is + + + align:start position:0% +later need how is that the question is +how do you resolve that what does it do + + align:start position:0% +how do you resolve that what does it do + + + align:start position:0% +how do you resolve that what does it do +well first of all + + align:start position:0% + + + + align:start position:0% + +um okay so um first of all interestingly + + align:start position:0% +um okay so um first of all interestingly + + + align:start position:0% +um okay so um first of all interestingly +if it says X is not + + align:start position:0% +if it says X is not + + + align:start position:0% +if it says X is not +ambitious um literally like that and I'm + + align:start position:0% +ambitious um literally like that and I'm + + + align:start position:0% +ambitious um literally like that and I'm +not being pedantic here this is one of + + align:start position:0% +not being pedantic here this is one of + + + align:start position:0% +not being pedantic here this is one of +the tricks someone played in a previous + + align:start position:0% +the tricks someone played in a previous + + + align:start position:0% +the tricks someone played in a previous +quiz um you can have that and X's + + align:start position:0% +quiz um you can have that and X's + + + align:start position:0% +quiz um you can have that and X's +ambitious both in the list because it's + + align:start position:0% +ambitious both in the list because it's + + + align:start position:0% +ambitious both in the list because it's +a dumb rules based system it doesn't + + align:start position:0% +a dumb rules based system it doesn't + + + align:start position:0% +a dumb rules based system it doesn't +know that you can't have both of those + + align:start position:0% +know that you can't have both of those + + + align:start position:0% +know that you can't have both of those +on the list so if you have a positive + + align:start position:0% +on the list so if you have a positive + + + align:start position:0% +on the list so if you have a positive +assertion in a consequence X is not + + align:start position:0% +assertion in a consequence X is not + + + align:start position:0% +assertion in a consequence X is not +ambitious uh in a consequent X is not + + align:start position:0% +ambitious uh in a consequent X is not + + + align:start position:0% +ambitious uh in a consequent X is not +ambitious it'll be happy to add millison + + align:start position:0% +ambitious it'll be happy to add millison + + + align:start position:0% +ambitious it'll be happy to add millison +is not ambitious and while mson + + align:start position:0% +is not ambitious and while mson + + + align:start position:0% +is not ambitious and while mson +ambitious is already there because it's + + align:start position:0% +ambitious is already there because it's + + + align:start position:0% +ambitious is already there because it's +stupid now if it had delete millison as + + align:start position:0% +stupid now if it had delete millison as + + + align:start position:0% +stupid now if it had delete millison as +ambitious in the consequent and deleted + + align:start position:0% +ambitious in the consequent and deleted + + + align:start position:0% +ambitious in the consequent and deleted +something that was previously + + align:start position:0% +something that was previously + + + align:start position:0% +something that was previously +there that would be that would be an + + align:start position:0% +there that would be that would be an + + + align:start position:0% +there that would be that would be an +interesting problem it could cause + + align:start position:0% +interesting problem it could cause + + + align:start position:0% +interesting problem it could cause +mistakes it your back Cher would + + align:start position:0% +mistakes it your back Cher would + + + align:start position:0% +mistakes it your back Cher would +probably make the mistake of allowing + + align:start position:0% +probably make the mistake of allowing + + + align:start position:0% +probably make the mistake of allowing +this however this is exactly why we do + + align:start position:0% +this however this is exactly why we do + + + align:start position:0% +this however this is exactly why we do +not I believe as a policy do not have + + align:start position:0% +not I believe as a policy do not have + + + align:start position:0% +not I believe as a policy do not have +delete statements on the quizzes + + align:start position:0% +delete statements on the quizzes + + + align:start position:0% +delete statements on the quizzes +um at least previous quizzes did not + + align:start position:0% +um at least previous quizzes did not + + + align:start position:0% +um at least previous quizzes did not +have them except for in a hypothetical + + align:start position:0% +have them except for in a hypothetical + + + align:start position:0% +have them except for in a hypothetical +of what happens if we add a delete + + align:start position:0% +of what happens if we add a delete + + + align:start position:0% +of what happens if we add a delete +statement here we I don't think we've + + align:start position:0% +statement here we I don't think we've + + + align:start position:0% +statement here we I don't think we've +ever made people work things through + + align:start position:0% +ever made people work things through + + + align:start position:0% +ever made people work things through +with the delete delete would um would + + align:start position:0% +with the delete delete would um would + + + align:start position:0% +with the delete delete would um would +possibly cause some issues question in + + align:start position:0% +possibly cause some issues question in + + + align:start position:0% +possibly cause some issues question in +the back so just to check this when + + align:start position:0% +the back so just to check this when + + + align:start position:0% +the back so just to check this when +you're doing backward chaining you don't + + align:start position:0% +you're doing backward chaining you don't + + + align:start position:0% +you're doing backward chaining you don't +actually add assertions to your + + align:start position:0% +actually add assertions to your + + + align:start position:0% +actually add assertions to your +assertion table you never add assertions + + align:start position:0% +assertion table you never add assertions + + + align:start position:0% +assertion table you never add assertions +in backward chaining to the assertion + + align:start position:0% +in backward chaining to the assertion + + + align:start position:0% +in backward chaining to the assertion +table it's dumb it just keep the system + + align:start position:0% +table it's dumb it just keep the system + + + align:start position:0% +table it's dumb it just keep the system +is dumb I'm not saying it's a dumb idea + + align:start position:0% +is dumb I'm not saying it's a dumb idea + + + align:start position:0% +is dumb I'm not saying it's a dumb idea +to do this it's actually pretty fast to + + align:start position:0% +to do this it's actually pretty fast to + + + align:start position:0% +to do this it's actually pretty fast to +do it this way but the system is dumb + + align:start position:0% +do it this way but the system is dumb + + + align:start position:0% +do it this way but the system is dumb +the um so the question is do you add + + align:start position:0% +the um so the question is do you add + + + align:start position:0% +the um so the question is do you add +assertions or you don't add assertions + + align:start position:0% +assertions or you don't add assertions + + + align:start position:0% +assertions or you don't add assertions +you do not you simply go through + + align:start position:0% +you do not you simply go through + + + align:start position:0% +you do not you simply go through +checking all the things in your gold + + align:start position:0% +checking all the things in your gold + + + align:start position:0% +checking all the things in your gold +tree until the gold tree is either + + align:start position:0% +tree until the gold tree is either + + + align:start position:0% +tree until the gold tree is either +proven or disproven then you are out of + + align:start position:0% +proven or disproven then you are out of + + + align:start position:0% +proven or disproven then you are out of +here all right so cool so far everyone + + align:start position:0% +here all right so cool so far everyone + + + align:start position:0% +here all right so cool so far everyone +good questions from everyone these are + + align:start position:0% +good questions from everyone these are + + + align:start position:0% +good questions from everyone these are +all questions that are things that often + + align:start position:0% +all questions that are things that often + + + align:start position:0% +all questions that are things that often +trip people up so our next thing mson is + + align:start position:0% +trip people up so our next thing mson is + + + align:start position:0% +trip people up so our next thing mson is +ambitious we sort of um the cat is out + + align:start position:0% +ambitious we sort of um the cat is out + + + align:start position:0% +ambitious we sort of um the cat is out +of the bag because there was a question + + align:start position:0% +of the bag because there was a question + + + align:start position:0% +of the bag because there was a question +mentioning that there was an assertion + + align:start position:0% +mentioning that there was an assertion + + + align:start position:0% +mentioning that there was an assertion +that says that but I direct you guys to + + align:start position:0% +that says that but I direct you guys to + + + align:start position:0% +that says that but I direct you guys to +our favorite rule rule two shouldn't we + + align:start position:0% +our favorite rule rule two shouldn't we + + + align:start position:0% +our favorite rule rule two shouldn't we +use rule two to prove that Milson is + + align:start position:0% +use rule two to prove that Milson is + + + align:start position:0% +use rule two to prove that Milson is +ambitious question is or the answer is + + align:start position:0% +ambitious question is or the answer is + + + align:start position:0% +ambitious question is or the answer is +if you want to lose four points or + + align:start position:0% +if you want to lose four points or + + + align:start position:0% +if you want to lose four points or +however many points then yes but if you + + align:start position:0% +however many points then yes but if you + + + align:start position:0% +however many points then yes but if you +don't want to lose points then um this + + align:start position:0% +don't want to lose points then um this + + + align:start position:0% +don't want to lose points then um this +is already correct + + align:start position:0% +is already correct + + + align:start position:0% +is already correct +by this is already correct by virtue of + + align:start position:0% +by this is already correct by virtue of + + + align:start position:0% +by this is already correct by virtue of +um assertion + + align:start position:0% +um assertion + + + align:start position:0% +um assertion +one so I guess I should write also that + + align:start position:0% +one so I guess I should write also that + + + align:start position:0% +one so I guess I should write also that +this over here millison studies a lot + + align:start position:0% +this over here millison studies a lot + + + align:start position:0% +this over here millison studies a lot +rule is um this rule is rule four wait a + + align:start position:0% +rule is um this rule is rule four wait a + + + align:start position:0% +rule is um this rule is rule four wait a +minute yeah that's rule four with s + + align:start position:0% +minute yeah that's rule four with s + + + align:start position:0% +minute yeah that's rule four with s +Latin protagonist down here to prove + + align:start position:0% +Latin protagonist down here to prove + + + align:start position:0% +Latin protagonist down here to prove +that she studies a lot is Rule + + align:start position:0% +that she studies a lot is Rule + + + align:start position:0% +that she studies a lot is Rule +three and then um at the bottom here we + + align:start position:0% + + + + align:start position:0% + +have we have what rules here we have + + align:start position:0% +have we have what rules here we have + + + align:start position:0% +have we have what rules here we have +protag the protagonist rule which is one + + align:start position:0% +protag the protagonist rule which is one + + + align:start position:0% +protag the protagonist rule which is one +and the villain rule which is two + + align:start position:0% + + + + align:start position:0% + +um this is correct virtue of a + + align:start position:0% + + + + align:start position:0% + +z okay great so we've proved this whole + + align:start position:0% +z okay great so we've proved this whole + + + align:start position:0% +z okay great so we've proved this whole +end node we know that millison studies a + + align:start position:0% +end node we know that millison studies a + + + align:start position:0% +end node we know that millison studies a +lot but now we're going to have to go a + + align:start position:0% +lot but now we're going to have to go a + + + align:start position:0% +lot but now we're going to have to go a +little bit more quickly based on time + + align:start position:0% +little bit more quickly based on time + + + align:start position:0% +little bit more quickly based on time +and so I will do the remaining things + + align:start position:0% +and so I will do the remaining things + + + align:start position:0% +and so I will do the remaining things +anyone who has not been called on is off + + align:start position:0% +anyone who has not been called on is off + + + align:start position:0% +anyone who has not been called on is off +the hook but that doesn't mean not to + + align:start position:0% +the hook but that doesn't mean not to + + + align:start position:0% +the hook but that doesn't mean not to +pay attention because there's some + + align:start position:0% +pay attention because there's some + + + align:start position:0% +pay attention because there's some +interesting stuff still to come so + + align:start position:0% +interesting stuff still to come so + + + align:start position:0% +interesting stuff still to come so +millison is a protagonist well good news + + align:start position:0% +millison is a protagonist well good news + + + align:start position:0% +millison is a protagonist well good news +everyone uh there's + + align:start position:0% +everyone uh there's + + + align:start position:0% +everyone uh there's +one other reason that I can do this and + + align:start position:0% +one other reason that I can do this and + + + align:start position:0% +one other reason that I can do this and +that's that you've already told me what + + align:start position:0% +that's that you've already told me what + + + align:start position:0% +that's that you've already told me what +I need to do melson is a protagonist you + + align:start position:0% +I need to do melson is a protagonist you + + + align:start position:0% +I need to do melson is a protagonist you +use rule one yeah rule + + align:start position:0% +use rule one yeah rule + + + align:start position:0% +use rule one yeah rule +one and check if she lives in Gryffindor + + align:start position:0% +one and check if she lives in Gryffindor + + + align:start position:0% +one and check if she lives in Gryffindor +tower now will it do it + + align:start position:0% +tower now will it do it + + + align:start position:0% +tower now will it do it +again yes it will it hasn't cached that + + align:start position:0% +again yes it will it hasn't cached that + + + align:start position:0% +again yes it will it hasn't cached that +it's already tried + + align:start position:0% +it's already tried + + + align:start position:0% +it's already tried +that now a hashtable notwithstanding + + align:start position:0% +that now a hashtable notwithstanding + + + align:start position:0% +that now a hashtable notwithstanding +cashing something you've already tried + + align:start position:0% +cashing something you've already tried + + + align:start position:0% +cashing something you've already tried +may be a good idea with backward + + align:start position:0% +may be a good idea with backward + + + align:start position:0% +may be a good idea with backward +chaining but we do not do that in this + + align:start position:0% +chaining but we do not do that in this + + + align:start position:0% +chaining but we do not do that in this +class that's an implementation detail + + align:start position:0% +class that's an implementation detail + + + align:start position:0% +class that's an implementation detail +it's another idea of something you can + + align:start position:0% +it's another idea of something you can + + + align:start position:0% +it's another idea of something you can +do we don't cash things that we've + + align:start position:0% +do we don't cash things that we've + + + align:start position:0% +do we don't cash things that we've +already tried we try them again damn it + + align:start position:0% +already tried we try them again damn it + + + align:start position:0% +already tried we try them again damn it +and and when we try it again maybe it'll + + align:start position:0% +and and when we try it again maybe it'll + + + align:start position:0% +and and when we try it again maybe it'll +work this time no it never it never + + align:start position:0% +work this time no it never it never + + + align:start position:0% +work this time no it never it never +works this time this fails this and node + + align:start position:0% +works this time this fails this and node + + + align:start position:0% +works this time this fails this and node +fails the whole thing fails they're not + + align:start position:0% +fails the whole thing fails they're not + + + align:start position:0% +fails the whole thing fails they're not +friends at all + + align:start position:0% +friends at all + + + align:start position:0% +friends at all +they're bitter enemies ment does not + + align:start position:0% +they're bitter enemies ment does not + + + align:start position:0% +they're bitter enemies ment does not +become Hermione's friend so now they ask + + align:start position:0% +become Hermione's friend so now they ask + + + align:start position:0% +become Hermione's friend so now they ask +us a few questions which are pretty easy + + align:start position:0% +us a few questions which are pretty easy + + + align:start position:0% +us a few questions which are pretty easy +to answer based on the or we've just + + align:start position:0% +to answer based on the or we've just + + + align:start position:0% +to answer based on the or we've just +been through so determine the minimum + + align:start position:0% +been through so determine the minimum + + + align:start position:0% +been through so determine the minimum +number of additional assertions that we + + align:start position:0% +number of additional assertions that we + + + align:start position:0% +number of additional assertions that we +would need to add for ment to become + + align:start position:0% +would need to add for ment to become + + + align:start position:0% +would need to add for ment to become +Hermione's + + align:start position:0% +Hermione's + + + align:start position:0% +Hermione's +friend um but you're not allowed to add + + align:start position:0% +friend um but you're not allowed to add + + + align:start position:0% +friend um but you're not allowed to add +an assertion that matches a consequent + + align:start position:0% +an assertion that matches a consequent + + + align:start position:0% +an assertion that matches a consequent +of a + + align:start position:0% +of a + + + align:start position:0% +of a +rule you can only add an assertion that + + align:start position:0% +rule you can only add an assertion that + + + align:start position:0% +rule you can only add an assertion that +you can in other words you can't add an + + align:start position:0% +you can in other words you can't add an + + + align:start position:0% +you can in other words you can't add an +assertion that will prove some other + + align:start position:0% +assertion that will prove some other + + + align:start position:0% +assertion that will prove some other +rules you have to add an assertion that + + align:start position:0% +rules you have to add an assertion that + + + align:start position:0% +rules you have to add an assertion that +directly yeah just that's basically the + + align:start position:0% +directly yeah just that's basically the + + + align:start position:0% +directly yeah just that's basically the +the the rule here cuz there's a lot of + + align:start position:0% +the the rule here cuz there's a lot of + + + align:start position:0% +the the rule here cuz there's a lot of +choices but he wanted one particular + + align:start position:0% +choices but he wanted one particular + + + align:start position:0% +choices but he wanted one particular +answer and so can anyone think of an + + align:start position:0% +answer and so can anyone think of an + + + align:start position:0% +answer and so can anyone think of an +assertion that doesn't match any + + align:start position:0% +assertion that doesn't match any + + + align:start position:0% +assertion that doesn't match any +consequent of any rule that will make + + align:start position:0% +consequent of any rule that will make + + + align:start position:0% +consequent of any rule that will make +her be um Hermione's + + align:start position:0% +her be um Hermione's + + + align:start position:0% +her be um Hermione's +friend a lot of people say ment lives in + + align:start position:0% +friend a lot of people say ment lives in + + + align:start position:0% +friend a lot of people say ment lives in +Gryffindor that's correct so part three + + align:start position:0% +Gryffindor that's correct so part three + + + align:start position:0% +Gryffindor that's correct so part three +Your solution to part two causes an + + align:start position:0% +Your solution to part two causes an + + + align:start position:0% +Your solution to part two causes an +uncommon situation what is the uncommon + + align:start position:0% +uncommon situation what is the uncommon + + + align:start position:0% +uncommon situation what is the uncommon +situation and what should you do to the + + align:start position:0% +situation and what should you do to the + + + align:start position:0% +situation and what should you do to the +list of assertions to solve this + + align:start position:0% +list of assertions to solve this + + + align:start position:0% +list of assertions to solve this +problem does does anyone know what the + + align:start position:0% +problem does does anyone know what the + + + align:start position:0% +problem does does anyone know what the +uncommon situation would be if we added + + align:start position:0% +uncommon situation would be if we added + + + align:start position:0% +uncommon situation would be if we added +that she lives in Gryffindor hand is + + align:start position:0% +that she lives in Gryffindor hand is + + + align:start position:0% +that she lives in Gryffindor hand is +raised up here what is your answer + + align:start position:0% +raised up here what is your answer + + + align:start position:0% +raised up here what is your answer +she that's true she lives in Gryffindor + + align:start position:0% +she that's true she lives in Gryffindor + + + align:start position:0% +she that's true she lives in Gryffindor +and Slytherin so how would you fix + + align:start position:0% + + + + align:start position:0% + +that yes you could pick out take out + + align:start position:0% +that yes you could pick out take out + + + align:start position:0% +that yes you could pick out take out +sther front of the + + align:start position:0% +sther front of the + + + align:start position:0% +sther front of the +assertions and say that she only lived + + align:start position:0% +assertions and say that she only lived + + + align:start position:0% +assertions and say that she only lived +in Gryffindor a lot of people gave the + + align:start position:0% +in Gryffindor a lot of people gave the + + + align:start position:0% +in Gryffindor a lot of people gave the +answer to this question which is a + + align:start position:0% +answer to this question which is a + + + align:start position:0% +answer to this question which is a +perfectly reasonable thing to do in a + + align:start position:0% +perfectly reasonable thing to do in a + + + align:start position:0% +perfectly reasonable thing to do in a +rules based system they said said well + + align:start position:0% +rules based system they said said well + + + align:start position:0% +rules based system they said said well +we can add a rule that says that if you + + align:start position:0% +we can add a rule that says that if you + + + align:start position:0% +we can add a rule that says that if you +live in X and you um if you live in X + + align:start position:0% +live in X and you um if you live in X + + + align:start position:0% +live in X and you um if you live in X +and Y is different than x then you can't + + align:start position:0% +and Y is different than x then you can't + + + align:start position:0% +and Y is different than x then you can't +live in y the problem with that among + + align:start position:0% +live in y the problem with that among + + + align:start position:0% +live in y the problem with that among +other things is that we ask for a way to + + align:start position:0% +other things is that we ask for a way to + + + align:start position:0% +other things is that we ask for a way to +change the assertions and not the rules + + align:start position:0% +change the assertions and not the rules + + + align:start position:0% +change the assertions and not the rules +and you gave us a way to change the + + align:start position:0% +and you gave us a way to change the + + + align:start position:0% +and you gave us a way to change the +assertions that's the right answer great + + align:start position:0% + + + + align:start position:0% + +so there was an there was another + + align:start position:0% +so there was an there was another + + + align:start position:0% +so there was an there was another +backward chaining problem this is 2009 + + align:start position:0% +backward chaining problem this is 2009 + + + align:start position:0% +backward chaining problem this is 2009 +quiz one + + align:start position:0% +quiz one + + + align:start position:0% +quiz one +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +and I will uh I will leave it off for + + align:start position:0% +and I will uh I will leave it off for + + + align:start position:0% +and I will uh I will leave it off for +the moment you guys should take a look + + align:start position:0% +the moment you guys should take a look + + + align:start position:0% +the moment you guys should take a look +at it in particular with variable + + align:start position:0% +at it in particular with variable + + + align:start position:0% +at it in particular with variable +binding because remember you always have + + align:start position:0% +binding because remember you always have + + + align:start position:0% +binding because remember you always have +to bind the variable that's relevant to + + align:start position:0% +to bind the variable that's relevant to + + + align:start position:0% +to bind the variable that's relevant to +you but that doesn't mean that you + + align:start position:0% +you but that doesn't mean that you + + + align:start position:0% +you but that doesn't mean that you +always have to bind all of the variables + + align:start position:0% +always have to bind all of the variables + + + align:start position:0% +always have to bind all of the variables +for instance let's say that we wanted to + + align:start position:0% +for instance let's say that we wanted to + + + align:start position:0% +for instance let's say that we wanted to +prove that melison has a bad term which + + align:start position:0% +prove that melison has a bad term which + + + align:start position:0% +prove that melison has a bad term which +as it turns out is what we want to prove + + align:start position:0% +as it turns out is what we want to prove + + + align:start position:0% +as it turns out is what we want to prove +in the other backward chaining very + + align:start position:0% +in the other backward chaining very + + + align:start position:0% +in the other backward chaining very +quickly and without doing the problem + + align:start position:0% +quickly and without doing the problem + + + align:start position:0% +quickly and without doing the problem +can anyone um Can anyone who's think who + + align:start position:0% +can anyone um Can anyone who's think who + + + align:start position:0% +can anyone um Can anyone who's think who +things are very clever at backwards + + align:start position:0% +things are very clever at backwards + + + align:start position:0% +things are very clever at backwards +chaining tell me exactly what things + + align:start position:0% +chaining tell me exactly what things + + + align:start position:0% +chaining tell me exactly what things +would be added to the um to the gold + + align:start position:0% +would be added to the um to the gold + + + align:start position:0% +would be added to the um to the gold +tree to prove that millison has a bad + + align:start position:0% +tree to prove that millison has a bad + + + align:start position:0% +tree to prove that millison has a bad +term raise your hand I won't I won't + + align:start position:0% +term raise your hand I won't I won't + + + align:start position:0% +term raise your hand I won't I won't +pick out a victim because I'm asking + + align:start position:0% +pick out a victim because I'm asking + + + align:start position:0% +pick out a victim because I'm asking +this to happen um pretty + + align:start position:0% + + + + align:start position:0% + +quickly no + + align:start position:0% + + + + align:start position:0% + +one all + + align:start position:0% + + + + align:start position:0% + +right you would add the three and to + + align:start position:0% +right you would add the three and to + + + align:start position:0% +right you would add the three and to +rule uh to rule five which specifically + + align:start position:0% +rule uh to rule five which specifically + + + align:start position:0% +rule uh to rule five which specifically +uh for anyone for variable Y and so you + + align:start position:0% +uh for anyone for variable Y and so you + + + align:start position:0% +uh for anyone for variable Y and so you +just have to show that there's at least + + align:start position:0% +just have to show that there's at least + + + align:start position:0% +just have to show that there's at least +one person who matches so what can you + + align:start position:0% +one person who matches so what can you + + + align:start position:0% +one person who matches so what can you +um just sort of read out what would the + + align:start position:0% +um just sort of read out what would the + + + align:start position:0% +um just sort of read out what would the +first thing say with the + + align:start position:0% +first thing say with the + + + align:start position:0% +first thing say with the +snogs um X snogs or sorry n snogs anyone + + align:start position:0% +snogs um X snogs or sorry n snogs anyone + + + align:start position:0% +snogs um X snogs or sorry n snogs anyone +yeah nson they said nson snugs why + + align:start position:0% +yeah nson they said nson snugs why + + + align:start position:0% +yeah nson they said nson snugs why +that's crucial some people did a lot of + + align:start position:0% +that's crucial some people did a lot of + + + align:start position:0% +that's crucial some people did a lot of +different things some people put Sheamus + + align:start position:0% +different things some people put Sheamus + + + align:start position:0% +different things some people put Sheamus +in already you can't do that the + + align:start position:0% +in already you can't do that the + + + align:start position:0% +in already you can't do that the +system's stupid it doesn't know the + + align:start position:0% +system's stupid it doesn't know the + + + align:start position:0% +system's stupid it doesn't know the +person is Sheamus also some people said + + align:start position:0% +person is Sheamus also some people said + + + align:start position:0% +person is Sheamus also some people said +it worked because look they're Snogging + + align:start position:0% +it worked because look they're Snogging + + + align:start position:0% +it worked because look they're Snogging +each other but it's in the wrong it's + + align:start position:0% +each other but it's in the wrong it's + + + align:start position:0% +each other but it's in the wrong it's +the wrong snoggle direction up there + + align:start position:0% +the wrong snoggle direction up there + + + align:start position:0% +the wrong snoggle direction up there +um because we have Sheamus snug and ment + + align:start position:0% +um because we have Sheamus snug and ment + + + align:start position:0% +um because we have Sheamus snug and ment +not ment snog and Sheamus but yes + + align:start position:0% +not ment snog and Sheamus but yes + + + align:start position:0% +not ment snog and Sheamus but yes +exactly it would be ment snugs why + + align:start position:0% +exactly it would be ment snugs why + + + align:start position:0% +exactly it would be ment snugs why +milicent lives in Gryffindor Tower why + + align:start position:0% +milicent lives in Gryffindor Tower why + + + align:start position:0% +milicent lives in Gryffindor Tower why +lives in slyther and dungeon so let's + + align:start position:0% +lives in slyther and dungeon so let's + + + align:start position:0% +lives in slyther and dungeon so let's +give Ford chaining all the attention it + + align:start position:0% +give Ford chaining all the attention it + + + align:start position:0% +give Ford chaining all the attention it +deserves about 8 minutes which will be + + align:start position:0% +deserves about 8 minutes which will be + + + align:start position:0% +deserves about 8 minutes which will be +more than + + align:start position:0% + + + + align:start position:0% + +enough okay we we still got all these + + align:start position:0% +enough okay we we still got all these + + + align:start position:0% +enough okay we we still got all these +rules we've still got all these + + align:start position:0% +rules we've still got all these + + + align:start position:0% +rules we've still got all these +assertions instead of doing that + + align:start position:0% +assertions instead of doing that + + + align:start position:0% +assertions instead of doing that +horrible backward chaining well it's not + + align:start position:0% +horrible backward chaining well it's not + + + align:start position:0% +horrible backward chaining well it's not +that horrible but we'll do forward + + align:start position:0% +that horrible but we'll do forward + + + align:start position:0% +that horrible but we'll do forward +chaining it'll be really easy we'll just + + align:start position:0% +chaining it'll be really easy we'll just + + + align:start position:0% +chaining it'll be really easy we'll just +add new assertions as they go remember + + align:start position:0% +add new assertions as they go remember + + + align:start position:0% +add new assertions as they go remember +the tiebreak order rules in order from 0 + + align:start position:0% +the tiebreak order rules in order from 0 + + + align:start position:0% +the tiebreak order rules in order from 0 +to 5 and if the same rule could trigger + + align:start position:0% +to 5 and if the same rule could trigger + + + align:start position:0% +to 5 and if the same rule could trigger +could fire off with multiple different + + align:start position:0% +could fire off with multiple different + + + align:start position:0% +could fire off with multiple different +assertions we'll use the assertions in + + align:start position:0% +assertions we'll use the assertions in + + + align:start position:0% +assertions we'll use the assertions in +order from 0 to three + + align:start position:0% +order from 0 to three + + + align:start position:0% +order from 0 to three +so let's + + align:start position:0% +so let's + + + align:start position:0% +so let's +see you don't have much time but with + + align:start position:0% +see you don't have much time but with + + + align:start position:0% +see you don't have much time but with +our four assertions let's see what rules + + align:start position:0% +our four assertions let's see what rules + + + align:start position:0% +our four assertions let's see what rules +possibly could + + align:start position:0% +possibly could + + + align:start position:0% +possibly could +match with our four assertions well I'll + + align:start position:0% +match with our four assertions well I'll + + + align:start position:0% +match with our four assertions well I'll +figure up for you do we have an + + align:start position:0% +figure up for you do we have an + + + align:start position:0% +figure up for you do we have an +assertion about an ambitious person yes + + align:start position:0% +assertion about an ambitious person yes + + + align:start position:0% +assertion about an ambitious person yes +but they're not a squib so not rule zero + + align:start position:0% +but they're not a squib so not rule zero + + + align:start position:0% +but they're not a squib so not rule zero +do we have someone who lives in + + align:start position:0% +do we have someone who lives in + + + align:start position:0% +do we have someone who lives in +Gryffindor we absolutely do rule one is + + align:start position:0% +Gryffindor we absolutely do rule one is + + + align:start position:0% +Gryffindor we absolutely do rule one is +matches do we have someone who lives in + + align:start position:0% +matches do we have someone who lives in + + + align:start position:0% +matches do we have someone who lives in +slyther we do rule two matches do we + + align:start position:0% +slyther we do rule two matches do we + + + align:start position:0% +slyther we do rule two matches do we +have a protagonist or a villain we don't + + align:start position:0% +have a protagonist or a villain we don't + + + align:start position:0% +have a protagonist or a villain we don't +have any protagonist or villains rule + + align:start position:0% +have any protagonist or villains rule + + + align:start position:0% +have any protagonist or villains rule +three is not going to match because it's + + align:start position:0% +three is not going to match because it's + + + align:start position:0% +three is not going to match because it's +it's in an end do we have someone who + + align:start position:0% +it's in an end do we have someone who + + + align:start position:0% +it's in an end do we have someone who +studies a lot we do not have someone who + + align:start position:0% +studies a lot we do not have someone who + + + align:start position:0% +studies a lot we do not have someone who +studies a lot rule four is not going to + + align:start position:0% +studies a lot rule four is not going to + + + align:start position:0% +studies a lot rule four is not going to +match do we have some Snogging we do + + align:start position:0% +match do we have some Snogging we do + + + align:start position:0% +match do we have some Snogging we do +have some Snogging so rule one two and + + align:start position:0% +have some Snogging so rule one two and + + + align:start position:0% +have some Snogging so rule one two and +five match so M for matching we have one + + align:start position:0% +five match so M for matching we have one + + + align:start position:0% +five match so M for matching we have one +two and five everyone which one wins the + + align:start position:0% +two and five everyone which one wins the + + + align:start position:0% +two and five everyone which one wins the +tie break between one two and five one + + align:start position:0% +tie break between one two and five one + + + align:start position:0% +tie break between one two and five one +because it comes first numerically which + + align:start position:0% +because it comes first numerically which + + + align:start position:0% +because it comes first numerically which +one is um which one is Rule one if x + + align:start position:0% +one is um which one is Rule one if x + + + align:start position:0% +one is um which one is Rule one if x +lives in Gryffindor Tire the only + + align:start position:0% +lives in Gryffindor Tire the only + + + align:start position:0% +lives in Gryffindor Tire the only +binding for X is Sheamus Sheamus lives + + align:start position:0% +binding for X is Sheamus Sheamus lives + + + align:start position:0% +binding for X is Sheamus Sheamus lives +in gryffin door Tower we're firing off + + align:start position:0% +in gryffin door Tower we're firing off + + + align:start position:0% +in gryffin door Tower we're firing off +rule one + + align:start position:0% +rule one + + + align:start position:0% +rule one +so new assertions the first assertion + + align:start position:0% +so new assertions the first assertion + + + align:start position:0% +so new assertions the first assertion +that we will add is Sheamus is a + + align:start position:0% +that we will add is Sheamus is a + + + align:start position:0% +that we will add is Sheamus is a +protagonist + + align:start position:0% + + + + align:start position:0% + +great now there's one other thing and + + align:start position:0% +great now there's one other thing and + + + align:start position:0% +great now there's one other thing and +it's the main thing I wanted to tell you + + align:start position:0% +it's the main thing I wanted to tell you + + + align:start position:0% +it's the main thing I wanted to tell you +about en Forge + + align:start position:0% +about en Forge + + + align:start position:0% +about en Forge +chaining about our old friend rule one + + align:start position:0% +chaining about our old friend rule one + + + align:start position:0% +chaining about our old friend rule one +now that we've done this does rule one + + align:start position:0% +now that we've done this does rule one + + + align:start position:0% +now that we've done this does rule one +still match an assertion in the in the + + align:start position:0% + + + + align:start position:0% + +database yes it does but what's going to + + align:start position:0% +database yes it does but what's going to + + + align:start position:0% +database yes it does but what's going to +stop us from constantly doing rule one + + align:start position:0% +stop us from constantly doing rule one + + + align:start position:0% +stop us from constantly doing rule one +every time because it comes numerically + + align:start position:0% +every time because it comes numerically + + + align:start position:0% +every time because it comes numerically +before the other rules what stops us + + align:start position:0% +before the other rules what stops us + + + align:start position:0% +before the other rules what stops us +there is part of our implementation and + + align:start position:0% +there is part of our implementation and + + + align:start position:0% +there is part of our implementation and +it's a very important part that people + + align:start position:0% +it's a very important part that people + + + align:start position:0% +it's a very important part that people +sometimes forget it's what I like to + + align:start position:0% +sometimes forget it's what I like to + + + align:start position:0% +sometimes forget it's what I like to +call the no impotent rules um + + align:start position:0% +call the no impotent rules um + + + align:start position:0% +call the no impotent rules um +implementation detail that is if a rules + + align:start position:0% +implementation detail that is if a rules + + + align:start position:0% +implementation detail that is if a rules +completely 100% impotent it would do + + align:start position:0% +completely 100% impotent it would do + + + align:start position:0% +completely 100% impotent it would do +absolutely nothing there's then you + + align:start position:0% +absolutely nothing there's then you + + + align:start position:0% +absolutely nothing there's then you +don't not fire it you go to the next one + + align:start position:0% +don't not fire it you go to the next one + + + align:start position:0% +don't not fire it you go to the next one +that's pretty important let's say that + + align:start position:0% +that's pretty important let's say that + + + align:start position:0% +that's pretty important let's say that +you possibly had a delete which you + + align:start position:0% +you possibly had a delete which you + + + align:start position:0% +you possibly had a delete which you +won't have on the + + align:start position:0% +won't have on the + + + align:start position:0% +won't have on the +quiz that means that if the thing to + + align:start position:0% +quiz that means that if the thing to + + + align:start position:0% +quiz that means that if the thing to +delete is missing it's impotent if the + + align:start position:0% +delete is missing it's impotent if the + + + align:start position:0% +delete is missing it's impotent if the +thing to delete is there it's not + + align:start position:0% +thing to delete is there it's not + + + align:start position:0% +thing to delete is there it's not +impotent because you can delete let's + + align:start position:0% +impotent because you can delete let's + + + align:start position:0% +impotent because you can delete let's +say you have 500,000 things that you're + + align:start position:0% +say you have 500,000 things that you're + + + align:start position:0% +say you have 500,000 things that you're +going to add to your assertions + + align:start position:0% +going to add to your assertions + + + align:start position:0% +going to add to your assertions +499,00 are already in your database one + + align:start position:0% +499,00 are already in your database one + + + align:start position:0% +499,00 are already in your database one +of them is missing is it an impotent + + align:start position:0% +of them is missing is it an impotent + + + align:start position:0% +of them is missing is it an impotent +rule no it's not you have to fire it + + align:start position:0% +rule no it's not you have to fire it + + + align:start position:0% +rule no it's not you have to fire it +anyway you can't be like oh it's mostly + + align:start position:0% +anyway you can't be like oh it's mostly + + + align:start position:0% +anyway you can't be like oh it's mostly +impotent rule no you have to you have to + + align:start position:0% +impotent rule no you have to you have to + + + align:start position:0% +impotent rule no you have to you have to +fire off the rule if it will do anything + + align:start position:0% +fire off the rule if it will do anything + + + align:start position:0% +fire off the rule if it will do anything +right now rule one won't do anything + + align:start position:0% +right now rule one won't do anything + + + align:start position:0% +right now rule one won't do anything +because we've already added Sheamus is a + + align:start position:0% +because we've already added Sheamus is a + + + align:start position:0% +because we've already added Sheamus is a +protagonist so what rules match now well + + align:start position:0% +protagonist so what rules match now well + + + align:start position:0% +protagonist so what rules match now well +Sheamus becoming a protagonist is nice + + align:start position:0% +Sheamus becoming a protagonist is nice + + + align:start position:0% +Sheamus becoming a protagonist is nice +and all but he's not ambitious so we + + align:start position:0% +and all but he's not ambitious so we + + + align:start position:0% +and all but he's not ambitious so we +still don't match rule three we still R + + align:start position:0% +still don't match rule three we still R + + + align:start position:0% +still don't match rule three we still R +rules one two and five and as I + + align:start position:0% +rules one two and five and as I + + + align:start position:0% +rules one two and five and as I +basically just got finished telling you + + align:start position:0% +basically just got finished telling you + + + align:start position:0% +basically just got finished telling you +the one that we're going to fire off now + + align:start position:0% +the one that we're going to fire off now + + + align:start position:0% +the one that we're going to fire off now +is two that's right so rule two is if x + + align:start position:0% +is two that's right so rule two is if x + + + align:start position:0% +is two that's right so rule two is if x +lives in slyther and dungeon our only + + align:start position:0% +lives in slyther and dungeon our only + + + align:start position:0% +lives in slyther and dungeon our only +binding for that is melicent uh and that + + align:start position:0% +binding for that is melicent uh and that + + + align:start position:0% +binding for that is melicent uh and that +will show that she's a villain and she + + align:start position:0% +will show that she's a villain and she + + + align:start position:0% +will show that she's a villain and she +is ambitious so what assertions will we + + align:start position:0% +is ambitious so what assertions will we + + + align:start position:0% +is ambitious so what assertions will we +add Nelson is a villain and people + + align:start position:0% +add Nelson is a villain and people + + + align:start position:0% +add Nelson is a villain and people +stopped that's right good job everyone + + align:start position:0% +stopped that's right good job everyone + + + align:start position:0% +stopped that's right good job everyone +you figure you remember that mson is + + align:start position:0% +you figure you remember that mson is + + + align:start position:0% +you figure you remember that mson is +already ambitious from rule from + + align:start position:0% +already ambitious from rule from + + + align:start position:0% +already ambitious from rule from +assertion one so we don't have to add + + align:start position:0% +assertion one so we don't have to add + + + align:start position:0% +assertion one so we don't have to add +them both a lot of people did they were + + align:start position:0% +them both a lot of people did they were + + + align:start position:0% +them both a lot of people did they were +wrong + + align:start position:0% +wrong + + + align:start position:0% +wrong +so millison is a villain the other part + + align:start position:0% +so millison is a villain the other part + + + align:start position:0% +so millison is a villain the other part +of that role doesn't do anything but + + align:start position:0% +of that role doesn't do anything but + + + align:start position:0% +of that role doesn't do anything but +it's not an impotent role because one of + + align:start position:0% +it's not an impotent role because one of + + + align:start position:0% +it's not an impotent role because one of +the things is not on there great so what + + align:start position:0% +the things is not on there great so what + + + align:start position:0% +the things is not on there great so what +what um what rules match now well as it + + align:start position:0% +what um what rules match now well as it + + + align:start position:0% +what um what rules match now well as it +turns out now that millison is a villain + + align:start position:0% +turns out now that millison is a villain + + + align:start position:0% +turns out now that millison is a villain +and ambitious we match rule three as + + align:start position:0% +and ambitious we match rule three as + + + align:start position:0% +and ambitious we match rule three as +well so we match 1 2 3 and five what + + align:start position:0% +well so we match 1 2 3 and five what + + + align:start position:0% +well so we match 1 2 3 and five what +rule are we going to fire everyone three + + align:start position:0% +rule are we going to fire everyone three + + + align:start position:0% +rule are we going to fire everyone three +because one and two are impotent + + align:start position:0% +because one and two are impotent + + + align:start position:0% +because one and two are impotent +rules well fire rule three well I ment + + align:start position:0% +rules well fire rule three well I ment + + + align:start position:0% +rules well fire rule three well I ment +is a villain she's also ambitious she's + + align:start position:0% +is a villain she's also ambitious she's + + + align:start position:0% +is a villain she's also ambitious she's +our only match for three therefore what + + align:start position:0% +our only match for three therefore what + + + align:start position:0% +our only match for three therefore what +assertion do we add + + align:start position:0% +assertion do we add + + + align:start position:0% +assertion do we add +Nelson studies a lot that's + + align:start position:0% + + + + align:start position:0% + +right great so melson studies a lot + + align:start position:0% +right great so melson studies a lot + + + align:start position:0% +right great so melson studies a lot +however she's not a protagonist we still + + align:start position:0% +however she's not a protagonist we still + + + align:start position:0% +however she's not a protagonist we still +don't match r + + align:start position:0% +don't match r + + + align:start position:0% +don't match r +four oh well well we figured that out + + align:start position:0% +four oh well well we figured that out + + + align:start position:0% +four oh well well we figured that out +already ourselves from backward chaining + + align:start position:0% +already ourselves from backward chaining + + + align:start position:0% +already ourselves from backward chaining +that we were never going to match that + + align:start position:0% +that we were never going to match that + + + align:start position:0% +that we were never going to match that +so what matches it's still one two three + + align:start position:0% +so what matches it's still one two three + + + align:start position:0% +so what matches it's still one two three +and five seeing as one two and three are + + align:start position:0% +and five seeing as one two and three are + + + align:start position:0% +and five seeing as one two and three are +impotent the only match is + + align:start position:0% +impotent the only match is + + + align:start position:0% +impotent the only match is +five and so the only match we care about + + align:start position:0% +five and so the only match we care about + + + align:start position:0% +five and so the only match we care about +the only one we're going to fire is + + align:start position:0% +the only one we're going to fire is + + + align:start position:0% +the only one we're going to fire is +five and the result let's see x snogs y + + align:start position:0% +five and the result let's see x snogs y + + + align:start position:0% +five and the result let's see x snogs y +That's Sheamus snogs ment X lives in + + align:start position:0% +That's Sheamus snogs ment X lives in + + + align:start position:0% +That's Sheamus snogs ment X lives in +Gryffindor that's Sheamus y lives in + + align:start position:0% +Gryffindor that's Sheamus y lives in + + + align:start position:0% +Gryffindor that's Sheamus y lives in +Slytherin that's ment so what do we + + align:start position:0% +Slytherin that's ment so what do we + + + align:start position:0% +Slytherin that's ment so what do we +add Sheamus has a bad + + align:start position:0% + + + + align:start position:0% + +term simple + + align:start position:0% +term simple + + + align:start position:0% +term simple +painless it works out we're done and we + + align:start position:0% +painless it works out we're done and we + + + align:start position:0% +painless it works out we're done and we +got 100 on this quiz hopefully you guys + + align:start position:0% +got 100 on this quiz hopefully you guys + + + align:start position:0% +got 100 on this quiz hopefully you guys +will too question the question is if you + + align:start position:0% +will too question the question is if you + + + align:start position:0% +will too question the question is if you +have a new assertion which matches a + + align:start position:0% +have a new assertion which matches a + + + align:start position:0% +have a new assertion which matches a +rule but it's really high number it's + + align:start position:0% +rule but it's really high number it's + + + align:start position:0% +rule but it's really high number it's +all the way down at the bottom of the + + align:start position:0% +all the way down at the bottom of the + + + align:start position:0% +all the way down at the bottom of the +rules but it's new and it has new stuff + + align:start position:0% +rules but it's new and it has new stuff + + + align:start position:0% +rules but it's new and it has new stuff +should we do that first maybe because + + align:start position:0% +should we do that first maybe because + + + align:start position:0% +should we do that first maybe because +it's + + align:start position:0% +it's + + + align:start position:0% +it's +new Oh you mean that has a lower number + + align:start position:0% +new Oh you mean that has a lower number + + + align:start position:0% +new Oh you mean that has a lower number +a lower + + align:start position:0% +a lower + + + align:start position:0% +a lower +number okay so the question is if a rule + + align:start position:0% +number okay so the question is if a rule + + + align:start position:0% +number okay so the question is if a rule +let's say that rule three made U Millis + + align:start position:0% +let's say that rule three made U Millis + + + align:start position:0% +let's say that rule three made U Millis +be a + + align:start position:0% +be a + + + align:start position:0% +be a +squib then yes you'd immediately not + + align:start position:0% +squib then yes you'd immediately not + + + align:start position:0% +squib then yes you'd immediately not +only match zero with um zero would + + align:start position:0% +only match zero with um zero would + + + align:start position:0% +only match zero with um zero would +immediately fire cuz it's numerically it + + align:start position:0% +immediately fire cuz it's numerically it + + + align:start position:0% +immediately fire cuz it's numerically it +comes first you'll see that on some of + + align:start position:0% +comes first you'll see that on some of + + + align:start position:0% +comes first you'll see that on some of +the other old quizzes and you may see + + align:start position:0% +the other old quizzes and you may see + + + align:start position:0% +the other old quizzes and you may see +that in tutorial if you guys want to do + + align:start position:0% +that in tutorial if you guys want to do + + + align:start position:0% +that in tutorial if you guys want to do +some more practice problems in tutorials + + align:start position:0% +some more practice problems in tutorials + + + align:start position:0% +some more practice problems in tutorials +your T will have that available as one + + align:start position:0% +your T will have that available as one + + + align:start position:0% +your T will have that available as one +opportunity in tutorial but yeah that's + + align:start position:0% +opportunity in tutorial but yeah that's + + + align:start position:0% +opportunity in tutorial but yeah that's +exactly right it happened that it went + + align:start position:0% +exactly right it happened that it went + + + align:start position:0% +exactly right it happened that it went +in order this time but it will + + align:start position:0% +in order this time but it will + + + align:start position:0% +in order this time but it will +definitely hop anywhere it can in order + + align:start position:0% +definitely hop anywhere it can in order + + + align:start position:0% +definitely hop anywhere it can in order +to get to the lowest numbered assertion \ No newline at end of file diff --git a/iyE1_dreJ-c.txt b/iyE1_dreJ-c.txt new file mode 100644 index 0000000000000000000000000000000000000000..0438d900174edad642cbd7232d21c94d454cca63 --- /dev/null +++ b/iyE1_dreJ-c.txt @@ -0,0 +1,14627 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT opencourseware + + align:start position:0% +of MIT courses visit MIT opencourseware + + + align:start position:0% +of MIT courses visit MIT opencourseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu thank you everybody today + + align:start position:0% +ocw.mit.edu thank you everybody today + + + align:start position:0% +ocw.mit.edu thank you everybody today +and over the next two Saturdays a panel + + align:start position:0% +and over the next two Saturdays a panel + + + align:start position:0% +and over the next two Saturdays a panel +of 12 experts along with musicians from + + align:start position:0% +of 12 experts along with musicians from + + + align:start position:0% +of 12 experts along with musicians from +the Boston chamber music society and you + + align:start position:0% +the Boston chamber music society and you + + + align:start position:0% +the Boston chamber music society and you +the audience we'll be dealing with the + + align:start position:0% +the audience we'll be dealing with the + + + align:start position:0% +the audience we'll be dealing with the +issue of time in + + align:start position:0% +issue of time in + + + align:start position:0% +issue of time in +music and we often consider time a + + align:start position:0% +music and we often consider time a + + + align:start position:0% +music and we often consider time a +scientific absolute that is perfectly + + align:start position:0% +scientific absolute that is perfectly + + + align:start position:0% +scientific absolute that is perfectly +measurable by clocks and it's a very + + align:start position:0% +measurable by clocks and it's a very + + + align:start position:0% +measurable by clocks and it's a very +good definition but our perception of + + align:start position:0% +good definition but our perception of + + + align:start position:0% +good definition but our perception of +time is quite distorted when we listen + + align:start position:0% +time is quite distorted when we listen + + + align:start position:0% +time is quite distorted when we listen +to music composers and their Works + + align:start position:0% +to music composers and their Works + + + align:start position:0% +to music composers and their Works +manipulate time they do it in + + align:start position:0% +manipulate time they do it in + + + align:start position:0% +manipulate time they do it in +intentionally through repetition or + + align:start position:0% +intentionally through repetition or + + + align:start position:0% +intentionally through repetition or +unusual rhythms performers stretch time + + align:start position:0% +unusual rhythms performers stretch time + + + align:start position:0% +unusual rhythms performers stretch time +with that wonderful Italian expression + + align:start position:0% +with that wonderful Italian expression + + + align:start position:0% +with that wonderful Italian expression +rubato to steal time that they use you + + align:start position:0% +rubato to steal time that they use you + + + align:start position:0% +rubato to steal time that they use you +steal it from one part of music and give + + align:start position:0% +steal it from one part of music and give + + + align:start position:0% +steal it from one part of music and give +it to another and we also distort time + + align:start position:0% +it to another and we also distort time + + + align:start position:0% +it to another and we also distort time +as listeners when we listen to music by + + align:start position:0% +as listeners when we listen to music by + + + align:start position:0% +as listeners when we listen to music by +being distracted or excited by being + + align:start position:0% +being distracted or excited by being + + + align:start position:0% +being distracted or excited by being +bored or + + align:start position:0% +bored or + + + align:start position:0% +bored or +engaged and there's yet there's a little + + align:start position:0% +engaged and there's yet there's a little + + + align:start position:0% +engaged and there's yet there's a little +there's little common language to talk + + align:start position:0% +there's little common language to talk + + + align:start position:0% +there's little common language to talk +about how time's distorted how time's + + align:start position:0% +about how time's distorted how time's + + + align:start position:0% +about how time's distorted how time's +manipulated in music and as a result + + align:start position:0% +manipulated in music and as a result + + + align:start position:0% +manipulated in music and as a result +it's little disussed even though it's + + align:start position:0% +it's little disussed even though it's + + + align:start position:0% +it's little disussed even though it's +such a fundamental aspect of how humans + + align:start position:0% +such a fundamental aspect of how humans + + + align:start position:0% +such a fundamental aspect of how humans +hear and interpret + + align:start position:0% +hear and interpret + + + align:start position:0% +hear and interpret +music and part of the reason we haven't + + align:start position:0% +music and part of the reason we haven't + + + align:start position:0% +music and part of the reason we haven't +had a common language is because these + + align:start position:0% +had a common language is because these + + + align:start position:0% +had a common language is because these +distortions happen so differently in + + align:start position:0% +distortions happen so differently in + + + align:start position:0% +distortions happen so differently in +different genres in different eras that + + align:start position:0% +different genres in different eras that + + + align:start position:0% +different genres in different eras that +jazz + + align:start position:0% +jazz + + + align:start position:0% +jazz +musicians manipulate time differently + + align:start position:0% +musicians manipulate time differently + + + align:start position:0% +musicians manipulate time differently +from chamber music composers that + + align:start position:0% +from chamber music composers that + + + align:start position:0% +from chamber music composers that +Indonesian gamon has its own systems of + + align:start position:0% +Indonesian gamon has its own systems of + + + align:start position:0% +Indonesian gamon has its own systems of +time that are so different from those of + + align:start position:0% +time that are so different from those of + + + align:start position:0% +time that are so different from those of +Opera + + align:start position:0% +Opera + + + align:start position:0% +Opera +and also the problem is that we quite + + align:start position:0% +and also the problem is that we quite + + + align:start position:0% +and also the problem is that we quite +often have homogeneous groups of + + align:start position:0% +often have homogeneous groups of + + + align:start position:0% +often have homogeneous groups of +performers or composers or + + align:start position:0% +performers or composers or + + + align:start position:0% +performers or composers or +musicologists or of + + align:start position:0% +musicologists or of + + + align:start position:0% +musicologists or of +neuroscientists or artists who are all + + align:start position:0% +neuroscientists or artists who are all + + + align:start position:0% +neuroscientists or artists who are all +talking about time amongst + + align:start position:0% +talking about time amongst + + + align:start position:0% +talking about time amongst +themselves and who have their own + + align:start position:0% +themselves and who have their own + + + align:start position:0% +themselves and who have their own +perspectives and expertise but who don't + + align:start position:0% +perspectives and expertise but who don't + + + align:start position:0% +perspectives and expertise but who don't +communicate with other disciplines to + + align:start position:0% +communicate with other disciplines to + + + align:start position:0% +communicate with other disciplines to +bring in new analogies of point out a + + align:start position:0% +bring in new analogies of point out a + + + align:start position:0% +bring in new analogies of point out a +striking differences + + align:start position:0% + + + + align:start position:0% + +furthermore scholarship on musical time + + align:start position:0% +furthermore scholarship on musical time + + + align:start position:0% +furthermore scholarship on musical time +and large scale musical perform tends to + + align:start position:0% +and large scale musical perform tends to + + + align:start position:0% +and large scale musical perform tends to +be divorced from the act of testing + + align:start position:0% +be divorced from the act of testing + + + align:start position:0% +be divorced from the act of testing +theories about time and how do you best + + align:start position:0% +theories about time and how do you best + + + align:start position:0% +theories about time and how do you best +test a theory about musical time do you + + align:start position:0% +test a theory about musical time do you + + + align:start position:0% +test a theory about musical time do you +talk about it more do you get out a + + align:start position:0% +talk about it more do you get out a + + + align:start position:0% +talk about it more do you get out a +score and look at it very + + align:start position:0% +score and look at it very + + + align:start position:0% +score and look at it very +intently these are okay ways but I don't + + align:start position:0% +intently these are okay ways but I don't + + + align:start position:0% +intently these are okay ways but I don't +think they're the best I think the best + + align:start position:0% +think they're the best I think the best + + + align:start position:0% +think they're the best I think the best +is by listening to the pieces and so in + + align:start position:0% +is by listening to the pieces and so in + + + align:start position:0% +is by listening to the pieces and so in +these three Saturdays we're going to be + + align:start position:0% +these three Saturdays we're going to be + + + align:start position:0% +these three Saturdays we're going to be +doing both of these things we're going + + align:start position:0% +doing both of these things we're going + + + align:start position:0% +doing both of these things we're going +to be talking about Musical time and + + align:start position:0% +to be talking about Musical time and + + + align:start position:0% +to be talking about Musical time and +then we're going to be hearing them in + + align:start position:0% +then we're going to be hearing them in + + + align:start position:0% +then we're going to be hearing them in +the concert hall because in magazines + + align:start position:0% +the concert hall because in magazines + + + align:start position:0% +the concert hall because in magazines +and newspapers music is static we can + + align:start position:0% +and newspapers music is static we can + + + align:start position:0% +and newspapers music is static we can +examine it forwards and backwards jump + + align:start position:0% +examine it forwards and backwards jump + + + align:start position:0% +examine it forwards and backwards jump +around in the concert hall uh you cannot + + align:start position:0% +around in the concert hall uh you cannot + + + align:start position:0% +around in the concert hall uh you cannot +or I hope you will not say no no stop uh + + align:start position:0% +or I hope you will not say no no stop uh + + + align:start position:0% +or I hope you will not say no no stop uh +I want to hear that again from the + + align:start position:0% +I want to hear that again from the + + + align:start position:0% +I want to hear that again from the +beginning go back a couple + + align:start position:0% +beginning go back a couple + + + align:start position:0% +beginning go back a couple +measures and that's why the experience + + align:start position:0% +measures and that's why the experience + + + align:start position:0% +measures and that's why the experience +of Music in the concert hall is so + + align:start position:0% +of Music in the concert hall is so + + + align:start position:0% +of Music in the concert hall is so +fundamentally different and I'd say + + align:start position:0% +fundamentally different and I'd say + + + align:start position:0% +fundamentally different and I'd say +better today I'm joined on the panel by + + align:start position:0% +better today I'm joined on the panel by + + + align:start position:0% +better today I'm joined on the panel by +three experts who will explain how time + + align:start position:0% +three experts who will explain how time + + + align:start position:0% +three experts who will explain how time +influences their work + + align:start position:0% +influences their work + + + align:start position:0% +influences their work +like all three of our panels we have a + + align:start position:0% +like all three of our panels we have a + + + align:start position:0% +like all three of our panels we have a +mix of musicians and people from + + align:start position:0% +mix of musicians and people from + + + align:start position:0% +mix of musicians and people from +different fields let me introduce them + + align:start position:0% +different fields let me introduce them + + + align:start position:0% +different fields let me introduce them +on the far right we have Professor + + align:start position:0% +on the far right we have Professor + + + align:start position:0% +on the far right we have Professor +Robert jaffy who is Jane and auto + + align:start position:0% +Robert jaffy who is Jane and auto + + + align:start position:0% +Robert jaffy who is Jane and auto +Morning Star professor of physics at MIT + + align:start position:0% +Morning Star professor of physics at MIT + + + align:start position:0% +Morning Star professor of physics at MIT +he's well known both for his work on + + align:start position:0% +he's well known both for his work on + + + align:start position:0% +he's well known both for his work on +quirks strange matters and other area + + align:start position:0% +quirks strange matters and other area + + + align:start position:0% +quirks strange matters and other area +strange matter in other areas of + + align:start position:0% +strange matter in other areas of + + + align:start position:0% +strange matter in other areas of +elementary particle physics but also for + + align:start position:0% +elementary particle physics but also for + + + align:start position:0% +elementary particle physics but also for +his exceptional teaching and Outreach to + + align:start position:0% +his exceptional teaching and Outreach to + + + align:start position:0% +his exceptional teaching and Outreach to +the general public on how to understand + + align:start position:0% +the general public on how to understand + + + align:start position:0% +the general public on how to understand +modern physics to his left we have Libby + + align:start position:0% +modern physics to his left we have Libby + + + align:start position:0% +modern physics to his left we have Libby +Larson one of America's Best Known and + + align:start position:0% +Larson one of America's Best Known and + + + align:start position:0% +Larson one of America's Best Known and +most performed + + align:start position:0% +most performed + + + align:start position:0% +most performed +composers she has written works of + + align:start position:0% +composers she has written works of + + + align:start position:0% +composers she has written works of +subtle Beauty and accessibility she's + + align:start position:0% +subtle Beauty and accessibility she's + + + align:start position:0% +subtle Beauty and accessibility she's +also written pieces of startling + + align:start position:0% +also written pieces of startling + + + align:start position:0% +also written pieces of startling +Innovation and + + align:start position:0% +Innovation and + + + align:start position:0% +Innovation and +subtlety but mostly she's known for + + align:start position:0% +subtlety but mostly she's known for + + + align:start position:0% +subtlety but mostly she's known for +doing both in the same piece and very + + align:start position:0% +doing both in the same piece and very + + + align:start position:0% +doing both in the same piece and very +very often and I think we'll hear that + + align:start position:0% +very often and I think we'll hear that + + + align:start position:0% +very often and I think we'll hear that +tonight in her work blackbirds Red Hills + + align:start position:0% +tonight in her work blackbirds Red Hills + + + align:start position:0% +tonight in her work blackbirds Red Hills +and thank you for being able to + + align:start position:0% +and thank you for being able to + + + align:start position:0% +and thank you for being able to +contribute today Sarah Brown is director + + align:start position:0% +contribute today Sarah Brown is director + + + align:start position:0% +contribute today Sarah Brown is director +of design at MIT her work as a Scenic + + align:start position:0% +of design at MIT her work as a Scenic + + + align:start position:0% +of design at MIT her work as a Scenic +designer combines traditional media with + + align:start position:0% +designer combines traditional media with + + + align:start position:0% +designer combines traditional media with +new technologies in projected space The + + align:start position:0% +new technologies in projected space The + + + align:start position:0% +new technologies in projected space The +Washington Post Miss cder s poignant + + align:start position:0% +Washington Post Miss cder s poignant + + + align:start position:0% +Washington Post Miss cder s poignant +visual displays of piercing immediacy + + align:start position:0% +visual displays of piercing immediacy + + + align:start position:0% +visual displays of piercing immediacy +and I've been particularly moved myself + + align:start position:0% +and I've been particularly moved myself + + + align:start position:0% +and I've been particularly moved myself +with expressive Simplicity of some of + + align:start position:0% +with expressive Simplicity of some of + + + align:start position:0% +with expressive Simplicity of some of +her work and in a connection we just + + align:start position:0% +her work and in a connection we just + + + align:start position:0% +her work and in a connection we just +noticed a little bit ago both Libby + + align:start position:0% +noticed a little bit ago both Libby + + + align:start position:0% +noticed a little bit ago both Libby +Larsson and Sarah have done so much for + + align:start position:0% +Larsson and Sarah have done so much for + + + align:start position:0% +Larsson and Sarah have done so much for +the art scene of Minnesota in general + + align:start position:0% +the art scene of Minnesota in general + + + align:start position:0% +the art scene of Minnesota in general +and Minneapolis in + + align:start position:0% +and Minneapolis in + + + align:start position:0% +and Minneapolis in +particular we will also be joining on + + align:start position:0% +particular we will also be joining on + + + align:start position:0% +particular we will also be joining on +stage today by the fine member and guest + + align:start position:0% +stage today by the fine member and guest + + + align:start position:0% +stage today by the fine member and guest +musicians of the Boston chamber music + + align:start position:0% +musicians of the Boston chamber music + + + align:start position:0% +musicians of the Boston chamber music +society and perhaps it would be uh good + + align:start position:0% +society and perhaps it would be uh good + + + align:start position:0% +society and perhaps it would be uh good +if at least the performers of the Revel + + align:start position:0% +if at least the performers of the Revel + + + align:start position:0% +if at least the performers of the Revel +could come out now and this um do we + + align:start position:0% +could come out now and this um do we + + + align:start position:0% +could come out now and this um do we +have as onello and ID L on Violet and + + align:start position:0% +have as onello and ID L on Violet and + + + align:start position:0% +have as onello and ID L on Violet and +Randle hudkins on + + align:start position:0% +Randle hudkins on + + + align:start position:0% +Randle hudkins on +Pian they will be joined by fenick Smith + + align:start position:0% +Pian they will be joined by fenick Smith + + + align:start position:0% +Pian they will be joined by fenick Smith +on flute Thomas Hill clarinettist and of + + align:start position:0% +on flute Thomas Hill clarinettist and of + + + align:start position:0% +on flute Thomas Hill clarinettist and of +course realist Marcus Thompson + + align:start position:0% +course realist Marcus Thompson + + + align:start position:0% +course realist Marcus Thompson +there are many different ways that + + align:start position:0% +there are many different ways that + + + align:start position:0% +there are many different ways that +discussion on musical time could go and + + align:start position:0% +discussion on musical time could go and + + + align:start position:0% +discussion on musical time could go and +we've decided over these three lectures + + align:start position:0% +we've decided over these three lectures + + + align:start position:0% +we've decided over these three lectures +to um these three discussions to focus + + align:start position:0% +to um these three discussions to focus + + + align:start position:0% +to um these three discussions to focus +on three + + align:start position:0% +on three + + + align:start position:0% +on three +ways one is time as a way of + + align:start position:0% +ways one is time as a way of + + + align:start position:0% +ways one is time as a way of +structuring music music as + + align:start position:0% +structuring music music as + + + align:start position:0% +structuring music music as +architecture the second one that we'll + + align:start position:0% +architecture the second one that we'll + + + align:start position:0% +architecture the second one that we'll +talk about is music and memory how time + + align:start position:0% +talk about is music and memory how time + + + align:start position:0% +talk about is music and memory how time +is invoked by structures and music that + + align:start position:0% +is invoked by structures and music that + + + align:start position:0% +is invoked by structures and music that +bring back memories of earlier Parts in + + align:start position:0% +bring back memories of earlier Parts in + + + align:start position:0% +bring back memories of earlier Parts in +a piece or of other + + align:start position:0% +a piece or of other + + + align:start position:0% +a piece or of other +pieces and the third section that we'll + + align:start position:0% +pieces and the third section that we'll + + + align:start position:0% +pieces and the third section that we'll +talk about um collectively is time as + + align:start position:0% +talk about um collectively is time as + + + align:start position:0% +talk about um collectively is time as +explicit subject and substance of music + + align:start position:0% +explicit subject and substance of music + + + align:start position:0% +explicit subject and substance of music +so if you can go to the or I can control + + align:start position:0% +so if you can go to the or I can control + + + align:start position:0% +so if you can go to the or I can control +this can I yes um this is a part of the + + align:start position:0% +this can I yes um this is a part of the + + + align:start position:0% +this can I yes um this is a part of the +Revel Piano Trio the third movement + + align:start position:0% +Revel Piano Trio the third movement + + + align:start position:0% +Revel Piano Trio the third movement +which begins which is a form called a + + align:start position:0% +which begins which is a form called a + + + align:start position:0% +which begins which is a form called a +pacala and that is it's a repeating + + align:start position:0% +pacala and that is it's a repeating + + + align:start position:0% +pacala and that is it's a repeating +Melody that um is largely or maybe not + + align:start position:0% +Melody that um is largely or maybe not + + + align:start position:0% +Melody that um is largely or maybe not +unchanged but at least at the beginning + + align:start position:0% +unchanged but at least at the beginning + + + align:start position:0% +unchanged but at least at the beginning +it goes the same would uh would you be + + align:start position:0% +it goes the same would uh would you be + + + align:start position:0% +it goes the same would uh would you be +willing to play + + align:start position:0% + + + + align:start position:0% + +this would you would just play the pasal + + align:start position:0% +this would you would just play the pasal + + + align:start position:0% +this would you would just play the pasal +melody at + + align:start position:0% + + + + align:start position:0% + +one just a just just aell if you don't + + align:start position:0% +one just a just just aell if you don't + + + align:start position:0% +one just a just just aell if you don't +mind + + align:start position:0% + + + + align:start position:0% + +a + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +now Ruel is going to Define this as a + + align:start position:0% +now Ruel is going to Define this as a + + + align:start position:0% +now Ruel is going to Define this as a +unit of time like a minute or like a + + align:start position:0% +unit of time like a minute or like a + + + align:start position:0% +unit of time like a minute or like a +second one pasia in length and what he's + + align:start position:0% +second one pasia in length and what he's + + + align:start position:0% +second one pasia in length and what he's +going to do is he's going to first have + + align:start position:0% +going to do is he's going to first have + + + align:start position:0% +going to do is he's going to first have +it played alone in the piano and then + + align:start position:0% +it played alone in the piano and then + + + align:start position:0% +it played alone in the piano and then +the piano is going to move on to do + + align:start position:0% +the piano is going to move on to do + + + align:start position:0% +the piano is going to move on to do +something else while the cello plays one + + align:start position:0% +something else while the cello plays one + + + align:start position:0% +something else while the cello plays one +pacala worth of music but the third time + + align:start position:0% +pacala worth of music but the third time + + + align:start position:0% +pacala worth of music but the third time +it comes in in the violin you hear one + + align:start position:0% +it comes in in the violin you hear one + + + align:start position:0% +it comes in in the violin you hear one +more pacala with the music and then at + + align:start position:0% +more pacala with the music and then at + + + align:start position:0% +more pacala with the music and then at +the end it's stretched + + align:start position:0% +the end it's stretched + + + align:start position:0% +the end it's stretched +just a little bit and it only works + + align:start position:0% +just a little bit and it only works + + + align:start position:0% +just a little bit and it only works +because revel's convinced you that aalia + + align:start position:0% +because revel's convinced you that aalia + + + align:start position:0% +because revel's convinced you that aalia +is a fixed unit of time so that when the + + align:start position:0% +is a fixed unit of time so that when the + + + align:start position:0% +is a fixed unit of time so that when the +violin plays something slightly + + align:start position:0% +violin plays something slightly + + + align:start position:0% +violin plays something slightly +different there's just this tinge of I + + align:start position:0% +different there's just this tinge of I + + + align:start position:0% +different there's just this tinge of I +don't know weirdness in there we hear + + align:start position:0% +don't know weirdness in there we hear + + + align:start position:0% +don't know weirdness in there we hear +the opening until um I think until the + + align:start position:0% +the opening until um I think until the + + + align:start position:0% +the opening until um I think until the +end of the violence first passage and + + align:start position:0% +end of the violence first passage and + + + align:start position:0% +end of the violence first passage and +maybe one measure after that + + align:start position:0% +maybe one measure after that + + + align:start position:0% +maybe one measure after that +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +is + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +a + + align:start position:0% +a + + + align:start position:0% +a +[Music] + + align:start position:0% + + + + align:start position:0% + +thank you so you hear at this very end + + align:start position:0% +thank you so you hear at this very end + + + align:start position:0% +thank you so you hear at this very end +this Distortion this stretching of time + + align:start position:0% +this Distortion this stretching of time + + + align:start position:0% +this Distortion this stretching of time +that only works because time has musical + + align:start position:0% +that only works because time has musical + + + align:start position:0% +that only works because time has musical +time has already been established if we + + align:start position:0% +time has already been established if we + + + align:start position:0% +time has already been established if we +skip ahead to the um just after the + + align:start position:0% +skip ahead to the um just after the + + + align:start position:0% +skip ahead to the um just after the +piano solo you'll hear another way that + + align:start position:0% +piano solo you'll hear another way that + + + align:start position:0% +piano solo you'll hear another way that +Revel distorts musical time that it's + + align:start position:0% +Revel distorts musical time that it's + + + align:start position:0% +Revel distorts musical time that it's +expressed as fixed and here we're going + + align:start position:0% +expressed as fixed and here we're going + + + align:start position:0% +expressed as fixed and here we're going +to have the pacala start and then a + + align:start position:0% +to have the pacala start and then a + + + align:start position:0% +to have the pacala start and then a +little way through jump backwards as if + + align:start position:0% +little way through jump backwards as if + + + align:start position:0% +little way through jump backwards as if +time itself is is something that's + + align:start position:0% +time itself is is something that's + + + align:start position:0% +time itself is is something that's +veryable + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +thank you very much + + align:start position:0% + + + + align:start position:0% + +so these moments of jumping around are + + align:start position:0% +so these moments of jumping around are + + + align:start position:0% +so these moments of jumping around are +just one way that composers can + + align:start position:0% +just one way that composers can + + + align:start position:0% +just one way that composers can +manipulate time another way that the + + align:start position:0% +manipulate time another way that the + + + align:start position:0% +manipulate time another way that the +composers work with time is by making + + align:start position:0% +composers work with time is by making + + + align:start position:0% +composers work with time is by making +the explicit subject of the piece so + + align:start position:0% +the explicit subject of the piece so + + + align:start position:0% +the explicit subject of the piece so +we're going to move on to the George + + align:start position:0% +we're going to move on to the George + + + align:start position:0% +we're going to move on to the George +crumb piece now don't mind and um thank + + align:start position:0% +crumb piece now don't mind and um thank + + + align:start position:0% +crumb piece now don't mind and um thank +you very + + align:start position:0% +you very + + + align:start position:0% +you very +much + + align:start position:0% +much + + + align:start position:0% +much +and very quickly I want to show a little + + align:start position:0% +and very quickly I want to show a little + + + align:start position:0% +and very quickly I want to show a little +bit of the notation of 11 Echoes of + + align:start position:0% +bit of the notation of 11 Echoes of + + + align:start position:0% +bit of the notation of 11 Echoes of +Autumn and here is a piece that + + align:start position:0% +Autumn and here is a piece that + + + align:start position:0% +Autumn and here is a piece that +definitely uses unusual notation to try + + align:start position:0% +definitely uses unusual notation to try + + + align:start position:0% +definitely uses unusual notation to try +to say something about how time works in + + align:start position:0% +to say something about how time works in + + + align:start position:0% +to say something about how time works in +a piece and what Crum is doing here + + align:start position:0% +a piece and what Crum is doing here + + + align:start position:0% +a piece and what Crum is doing here +is um is going to be having the clarinet + + align:start position:0% +is um is going to be having the clarinet + + + align:start position:0% +is um is going to be having the clarinet +play this solo here at the same time + + align:start position:0% +play this solo here at the same time + + + align:start position:0% +play this solo here at the same time +that the Flo and the piano um are + + align:start position:0% +that the Flo and the piano um are + + + align:start position:0% +that the Flo and the piano um are +playing music that exists + + align:start position:0% +playing music that exists + + + align:start position:0% +playing music that exists +independently of what's happening in the + + align:start position:0% +independently of what's happening in the + + + align:start position:0% +independently of what's happening in the +clarinet and there are ways of doing + + align:start position:0% +clarinet and there are ways of doing + + + align:start position:0% +clarinet and there are ways of doing +this without this notation but this + + align:start position:0% +this without this notation but this + + + align:start position:0% +this without this notation but this +really this um very separated musical + + align:start position:0% +really this um very separated musical + + + align:start position:0% +really this um very separated musical +space helps make the time of the various + + align:start position:0% +space helps make the time of the various + + + align:start position:0% +space helps make the time of the various +instruments quite different so if we + + align:start position:0% +instruments quite different so if we + + + align:start position:0% +instruments quite different so if we +could hear Echo number seven + + align:start position:0% + + + + align:start position:0% + +don't take free + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +and if that's done right which I'm sure + + align:start position:0% +and if that's done right which I'm sure + + + align:start position:0% +and if that's done right which I'm sure +it will be tonight the alignment might + + align:start position:0% +it will be tonight the alignment might + + + align:start position:0% +it will be tonight the alignment might +not be the same normally if a piece of + + align:start position:0% +not be the same normally if a piece of + + + align:start position:0% +not be the same normally if a piece of +music is done right you will hear it + + align:start position:0% +music is done right you will hear it + + + align:start position:0% +music is done right you will hear it +exactly line the same way every time but + + align:start position:0% +exactly line the same way every time but + + + align:start position:0% +exactly line the same way every time but +here Crum has separated out those two + + align:start position:0% +here Crum has separated out those two + + + align:start position:0% +here Crum has separated out those two +parts we here um one more interesting + + align:start position:0% +parts we here um one more interesting + + + align:start position:0% +parts we here um one more interesting +moment the last one that we'll do I + + align:start position:0% +moment the last one that we'll do I + + + align:start position:0% +moment the last one that we'll do I +think uh of time that Crum manipulates + + align:start position:0% +think uh of time that Crum manipulates + + + align:start position:0% +think uh of time that Crum manipulates +is at the very beginning of the piece + + align:start position:0% +is at the very beginning of the piece + + + align:start position:0% +is at the very beginning of the piece +where what he's done is he's + + align:start position:0% +where what he's done is he's + + + align:start position:0% +where what he's done is he's +written essentially four different + + align:start position:0% +written essentially four different + + + align:start position:0% +written essentially four different +tempos at the same time for The Pianist + + align:start position:0% +tempos at the same time for The Pianist + + + align:start position:0% +tempos at the same time for The Pianist +and separated them spatially so that The + + align:start position:0% +and separated them spatially so that The + + + align:start position:0% +and separated them spatially so that The +Pianist is constantly having to jump his + + align:start position:0% +Pianist is constantly having to jump his + + + align:start position:0% +Pianist is constantly having to jump his +eyes over and I think I'm right in + + align:start position:0% +eyes over and I think I'm right in + + + align:start position:0% +eyes over and I think I'm right in +saying that it's kind of a little bit + + align:start position:0% +saying that it's kind of a little bit + + + align:start position:0% +saying that it's kind of a little bit +more difficult than the standard way of + + align:start position:0% +more difficult than the standard way of + + + align:start position:0% +more difficult than the standard way of +writing it but important in part it + + align:start position:0% +writing it but important in part it + + + align:start position:0% +writing it but important in part it +really draws out these different Notions + + align:start position:0% +really draws out these different Notions + + + align:start position:0% +really draws out these different Notions +of time + + align:start position:0% + + + + align:start position:0% + +I think we're going to do this next I + + align:start position:0% +I think we're going to do this next I + + + align:start position:0% +I think we're going to do this next I +think + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +one last point about something very + + align:start position:0% +one last point about something very + + + align:start position:0% +one last point about something very +strange in musical time if you can read + + align:start position:0% +strange in musical time if you can read + + + align:start position:0% +strange in musical time if you can read +music you can see that Crum is using + + align:start position:0% +music you can see that Crum is using + + + align:start position:0% +music you can see that Crum is using +some very very short notes in this piece + + align:start position:0% +some very very short notes in this piece + + + align:start position:0% +some very very short notes in this piece +he's using 302 notes in other parts he + + align:start position:0% +he's using 302 notes in other parts he + + + align:start position:0% +he's using 302 notes in other parts he +uses 64th notes he very very short notes + + align:start position:0% +uses 64th notes he very very short notes + + + align:start position:0% +uses 64th notes he very very short notes +yet the piece doesn't sound extremely + + align:start position:0% +yet the piece doesn't sound extremely + + + align:start position:0% +yet the piece doesn't sound extremely +fast and why is that it's because his + + align:start position:0% +fast and why is that it's because his + + + align:start position:0% +fast and why is that it's because his +tempos his Beats are very + + align:start position:0% +tempos his Beats are very + + + align:start position:0% +tempos his Beats are very +slow why is this strange well it's + + align:start position:0% +slow why is this strange well it's + + + align:start position:0% +slow why is this strange well it's +actually not particularly strange + + align:start position:0% +actually not particularly strange + + + align:start position:0% +actually not particularly strange +because music has been slowing down for + + align:start position:0% +because music has been slowing down for + + + align:start position:0% +because music has been slowing down for +the last 800 years this is a really odd + + align:start position:0% +the last 800 years this is a really odd + + + align:start position:0% +the last 800 years this is a really odd +phenomenon that we have the quarter + + align:start position:0% +phenomenon that we have the quarter + + + align:start position:0% +phenomenon that we have the quarter +notes that we think of fundamental beats + + align:start position:0% +notes that we think of fundamental beats + + + align:start position:0% +notes that we think of fundamental beats +but sometimes the slower the faster note + + align:start position:0% +but sometimes the slower the faster note + + + align:start position:0% +but sometimes the slower the faster note +the eighth note becomes the fundamental + + align:start position:0% +the eighth note becomes the fundamental + + + align:start position:0% +the eighth note becomes the fundamental +beat but we play it slowly signs the + + align:start position:0% +beat but we play it slowly signs the + + + align:start position:0% +beat but we play it slowly signs the +16th note but if you go back in time + + align:start position:0% +16th note but if you go back in time + + + align:start position:0% +16th note but if you go back in time +very commonly the half note a thing we + + align:start position:0% +very commonly the half note a thing we + + + align:start position:0% +very commonly the half note a thing we +think of as a slower note was the most + + align:start position:0% +think of as a slower note was the most + + + align:start position:0% +think of as a slower note was the most +common time if you go further back to + + align:start position:0% +common time if you go further back to + + + align:start position:0% +common time if you go further back to +the 1600s the whole note if you go + + align:start position:0% +the 1600s the whole note if you go + + + align:start position:0% +the 1600s the whole note if you go +further back the double whole note which + + align:start position:0% +further back the double whole note which + + + align:start position:0% +further back the double whole note which +is also called the breath used to be the + + align:start position:0% +is also called the breath used to be the + + + align:start position:0% +is also called the breath used to be the +fundamental unit of time why is it + + align:start position:0% +fundamental unit of time why is it + + + align:start position:0% +fundamental unit of time why is it +called breath because breath means short + + align:start position:0% +called breath because breath means short + + + align:start position:0% +called breath because breath means short +it used to be a really really short not + + align:start position:0% +it used to be a really really short not + + + align:start position:0% +it used to be a really really short not +it used to go by really fast so if we go + + align:start position:0% +it used to go by really fast so if we go + + + align:start position:0% +it used to go by really fast so if we go +really far back in time to around the + + align:start position:0% +really far back in time to around the + + + align:start position:0% +really far back in time to around the +1200s we can see at the top left here + + align:start position:0% +1200s we can see at the top left here + + + align:start position:0% +1200s we can see at the top left here +these weird Square shaped notes each one + + align:start position:0% +these weird Square shaped notes each one + + + align:start position:0% +these weird Square shaped notes each one +of them that that all the music used to + + align:start position:0% +of them that that all the music used to + + + align:start position:0% +of them that that all the music used to +be based out of each one of them lasts + + align:start position:0% +be based out of each one of them lasts + + + align:start position:0% +be based out of each one of them lasts +about as long as eight measures of + + align:start position:0% +about as long as eight measures of + + + align:start position:0% +about as long as eight measures of +Mozart's inin and KN music so in fact if + + align:start position:0% +Mozart's inin and KN music so in fact if + + + align:start position:0% +Mozart's inin and KN music so in fact if +we look at the musical time from what + + align:start position:0% +we look at the musical time from what + + + align:start position:0% +we look at the musical time from what +people used to use notes to to the pie + + align:start position:0% +people used to use notes to to the pie + + + align:start position:0% +people used to use notes to to the pie +the notes that Crum uses and you go + + align:start position:0% +the notes that Crum uses and you go + + + align:start position:0% +the notes that Crum uses and you go +further to some of the other notes that + + align:start position:0% +further to some of the other notes that + + + align:start position:0% +further to some of the other notes that +have appeared in music there's an + + align:start position:0% +have appeared in music there's an + + + align:start position:0% +have appeared in music there's an +incredible span of time that has been + + align:start position:0% +incredible span of time that has been + + + align:start position:0% +incredible span of time that has been +represented in + + align:start position:0% +represented in + + + align:start position:0% +represented in +music but the spans of time used in + + align:start position:0% +music but the spans of time used in + + + align:start position:0% +music but the spans of time used in +music are absolutely nothing compared to + + align:start position:0% +music are absolutely nothing compared to + + + align:start position:0% +music are absolutely nothing compared to +those that the Universe has as I'm going + + align:start position:0% +those that the Universe has as I'm going + + + align:start position:0% +those that the Universe has as I'm going +to turn over to Bob jaffy for it to + + align:start position:0% +to turn over to Bob jaffy for it to + + + align:start position:0% +to turn over to Bob jaffy for it to +continue on our spans of + + align:start position:0% +continue on our spans of + + + align:start position:0% +continue on our spans of +time that's a superb segue you can go to + + align:start position:0% +time that's a superb segue you can go to + + + align:start position:0% +time that's a superb segue you can go to +my slides + + align:start position:0% + + + + align:start position:0% + +well uh I feel a little bit like the + + align:start position:0% +well uh I feel a little bit like the + + + align:start position:0% +well uh I feel a little bit like the +children's exercise where you show four + + align:start position:0% +children's exercise where you show four + + + align:start position:0% +children's exercise where you show four +pictures and ask which of the pictures + + align:start position:0% +pictures and ask which of the pictures + + + align:start position:0% +pictures and ask which of the pictures +doesn't belong with the + + align:start position:0% +doesn't belong with the + + + align:start position:0% +doesn't belong with the +others everyone here is a performance + + align:start position:0% +others everyone here is a performance + + + align:start position:0% +others everyone here is a performance +artist in one way or another except + + align:start position:0% +artist in one way or another except + + + align:start position:0% +artist in one way or another except +me um I'm going to try to talk briefly + + align:start position:0% +me um I'm going to try to talk briefly + + + align:start position:0% +me um I'm going to try to talk briefly +about the Revolutionary changes that + + align:start position:0% +about the Revolutionary changes that + + + align:start position:0% +about the Revolutionary changes that +have taken place in the last 20 years in + + align:start position:0% +have taken place in the last 20 years in + + + align:start position:0% +have taken place in the last 20 years in +the and in the last century + + align:start position:0% +the and in the last century + + + align:start position:0% +the and in the last century +in physicist perception of time now I + + align:start position:0% +in physicist perception of time now I + + + align:start position:0% +in physicist perception of time now I +have to make a disclaimer at the + + align:start position:0% +have to make a disclaimer at the + + + align:start position:0% +have to make a disclaimer at the +beginning that uh Layman often think + + align:start position:0% +beginning that uh Layman often think + + + align:start position:0% +beginning that uh Layman often think +physicists have some marvelous insight + + align:start position:0% +physicists have some marvelous insight + + + align:start position:0% +physicists have some marvelous insight +into things that are very mysterious and + + align:start position:0% +into things that are very mysterious and + + + align:start position:0% +into things that are very mysterious and +uh you'll find I think that this is not + + align:start position:0% +uh you'll find I think that this is not + + + align:start position:0% +uh you'll find I think that this is not +so true uh one of my colleagues + + align:start position:0% +so true uh one of my colleagues + + + align:start position:0% +so true uh one of my colleagues +distinguished colleagues once said that + + align:start position:0% +distinguished colleagues once said that + + + align:start position:0% +distinguished colleagues once said that +as far as he was concerned time was just + + align:start position:0% +as far as he was concerned time was just + + + align:start position:0% +as far as he was concerned time was just +one damn thing after + + align:start position:0% +one damn thing after + + + align:start position:0% +one damn thing after +another and uh sometimes that's all we + + align:start position:0% +another and uh sometimes that's all we + + + align:start position:0% +another and uh sometimes that's all we +have to say about it um + + align:start position:0% + + + + align:start position:0% + +the uh laws of physics really + + align:start position:0% +the uh laws of physics really + + + align:start position:0% +the uh laws of physics really +distinguish in the universe two classes + + align:start position:0% +distinguish in the universe two classes + + + align:start position:0% +distinguish in the universe two classes +of tempos of what I'll call fundamental + + align:start position:0% +of tempos of what I'll call fundamental + + + align:start position:0% +of tempos of what I'll call fundamental +tempos which are the tempos of the Micro + + align:start position:0% +tempos which are the tempos of the Micro + + + align:start position:0% +tempos which are the tempos of the Micro +World the time scales of the microw + + align:start position:0% +World the time scales of the microw + + + align:start position:0% +World the time scales of the microw +world and uh cosmological tempos the + + align:start position:0% +world and uh cosmological tempos the + + + align:start position:0% +world and uh cosmological tempos the +tempos of the + + align:start position:0% +tempos of the + + + align:start position:0% +tempos of the +universe and as you'll see uh tempos + + align:start position:0% +universe and as you'll see uh tempos + + + align:start position:0% +universe and as you'll see uh tempos +associated with our ordinary experience + + align:start position:0% +associated with our ordinary experience + + + align:start position:0% +associated with our ordinary experience +as human beings are largely absent what + + align:start position:0% +as human beings are largely absent what + + + align:start position:0% +as human beings are largely absent what +I've shown here is a uh attempt to do a + + align:start position:0% +I've shown here is a uh attempt to do a + + + align:start position:0% +I've shown here is a uh attempt to do a +realization of the fluctuations of + + align:start position:0% +realization of the fluctuations of + + + align:start position:0% +realization of the fluctuations of +quantum Fields inside of proton and the + + align:start position:0% +quantum Fields inside of proton and the + + + align:start position:0% +quantum Fields inside of proton and the +actual time scale of these fluctuations + + align:start position:0% +actual time scale of these fluctuations + + + align:start position:0% +actual time scale of these fluctuations +is about 10us 24 + + align:start position:0% +is about 10us 24 + + + align:start position:0% +is about 10us 24 +seconds + + align:start position:0% +seconds + + + align:start position:0% +seconds +um beats per second 10 + + align:start position:0% +um beats per second 10 + + + align:start position:0% +um beats per second 10 +24th uh over here on the + + align:start position:0% +24th uh over here on the + + + align:start position:0% +24th uh over here on the +right uh is a + + align:start position:0% +right uh is a + + + align:start position:0% +right uh is a +simulation of the + + align:start position:0% +simulation of the + + + align:start position:0% +simulation of the +formation uh expansion contraction and + + align:start position:0% +formation uh expansion contraction and + + + align:start position:0% +formation uh expansion contraction and +dis solution of pocket universes in + + align:start position:0% +dis solution of pocket universes in + + + align:start position:0% +dis solution of pocket universes in +cosmology the time scale for these + + align:start position:0% +cosmology the time scale for these + + + align:start position:0% +cosmology the time scale for these +cosmological times is 10 to the 10th SE + + align:start position:0% +cosmological times is 10 to the 10th SE + + + align:start position:0% +cosmological times is 10 to the 10th SE +10 to the 10th years about 10 to the + + align:start position:0% +10 to the 10th years about 10 to the + + + align:start position:0% +10 to the 10th years about 10 to the +18th + + align:start position:0% +18th + + + align:start position:0% +18th +seconds uh as you can see when viewed in + + align:start position:0% +seconds uh as you can see when viewed in + + + align:start position:0% +seconds uh as you can see when viewed in +their own natural framework with respect + + align:start position:0% +their own natural framework with respect + + + align:start position:0% +their own natural framework with respect +to their own measure of time uh they + + align:start position:0% +to their own measure of time uh they + + + align:start position:0% +to their own measure of time uh they +look very + + align:start position:0% + + + + align:start position:0% + +similar time differences are very hard + + align:start position:0% +similar time differences are very hard + + + align:start position:0% +similar time differences are very hard +to get your hands around and it's useful + + align:start position:0% +to get your hands around and it's useful + + + align:start position:0% +to get your hands around and it's useful +to try to stay grounded and remember + + align:start position:0% +to try to stay grounded and remember + + + align:start position:0% +to try to stay grounded and remember +that these things are all around us and + + align:start position:0% +that these things are all around us and + + + align:start position:0% +that these things are all around us and +one of the ways I've done that is with + + align:start position:0% +one of the ways I've done that is with + + + align:start position:0% +one of the ways I've done that is with +the help of uh Wiki reyen geology + + align:start position:0% +the help of uh Wiki reyen geology + + + align:start position:0% +the help of uh Wiki reyen geology +Professor here I have a piece here of uh + + align:start position:0% +Professor here I have a piece here of uh + + + align:start position:0% +Professor here I have a piece here of uh +the aasta formation which is a a nice + + align:start position:0% +the aasta formation which is a a nice + + + align:start position:0% +the aasta formation which is a a nice +that's found in Northern Canada and uh + + align:start position:0% +that's found in Northern Canada and uh + + + align:start position:0% +that's found in Northern Canada and uh +it's the oldest rock that's been dated + + align:start position:0% +it's the oldest rock that's been dated + + + align:start position:0% +it's the oldest rock that's been dated +on the surface of the Earth The Rock was + + align:start position:0% +on the surface of the Earth The Rock was + + + align:start position:0% +on the surface of the Earth The Rock was +formed about 4 billion years ago and + + align:start position:0% +formed about 4 billion years ago and + + + align:start position:0% +formed about 4 billion years ago and +here's a little picture of the timeline + + align:start position:0% +here's a little picture of the timeline + + + align:start position:0% +here's a little picture of the timeline +of the universe starting from its + + align:start position:0% +of the universe starting from its + + + align:start position:0% +of the universe starting from its +formation that we now believe is 13.7 + + align:start position:0% +formation that we now believe is 13.7 + + + align:start position:0% +formation that we now believe is 13.7 +billion years ago the formation of the + + align:start position:0% +billion years ago the formation of the + + + align:start position:0% +billion years ago the formation of the +Earth at 4.5 billion years the Casta + + align:start position:0% +Earth at 4.5 billion years the Casta + + + align:start position:0% +Earth at 4.5 billion years the Casta +formation in 4 billion years and us now + + align:start position:0% +formation in 4 billion years and us now + + + align:start position:0% +formation in 4 billion years and us now +uh it's good to have a uh companion um a + + align:start position:0% +uh it's good to have a uh companion um a + + + align:start position:0% +uh it's good to have a uh companion um a +journey like this uh the Swirls and uh + + align:start position:0% +journey like this uh the Swirls and uh + + + align:start position:0% +journey like this uh the Swirls and uh +marks on the stone were formed 4 and a + + align:start position:0% +marks on the stone were formed 4 and a + + + align:start position:0% +marks on the stone were formed 4 and a +half billion years ago but right now + + align:start position:0% +half billion years ago but right now + + + align:start position:0% +half billion years ago but right now +there are things going on in that stone + + align:start position:0% +there are things going on in that stone + + + align:start position:0% +there are things going on in that stone +that are hidden from our eyes and only + + align:start position:0% +that are hidden from our eyes and only + + + align:start position:0% +that are hidden from our eyes and only +can be + + align:start position:0% +can be + + + align:start position:0% +can be +uh seen with elaborate scientific + + align:start position:0% +uh seen with elaborate scientific + + + align:start position:0% +uh seen with elaborate scientific +instruments which take place on the time + + align:start position:0% +instruments which take place on the time + + + align:start position:0% +instruments which take place on the time +scales of fundamental forces 10 the + + align:start position:0% +scales of fundamental forces 10 the + + + align:start position:0% +scales of fundamental forces 10 the +minus 24th seconds so U this is a + + align:start position:0% +minus 24th seconds so U this is a + + + align:start position:0% +minus 24th seconds so U this is a +picture of the keyboard of physics um I + + align:start position:0% +picture of the keyboard of physics um I + + + align:start position:0% +picture of the keyboard of physics um I +uh think it's fair to call it that um + + align:start position:0% +uh think it's fair to call it that um + + + align:start position:0% +uh think it's fair to call it that um +except it's on a logarithmic scale so + + align:start position:0% +except it's on a logarithmic scale so + + + align:start position:0% +except it's on a logarithmic scale so +the notes Here start at 1 + + align:start position:0% +the notes Here start at 1 + + + align:start position:0% +the notes Here start at 1 +second um and go up to 10 16th seconds + + align:start position:0% +second um and go up to 10 16th seconds + + + align:start position:0% +second um and go up to 10 16th seconds +and down to 10- 24 seconds so an attempt + + align:start position:0% +and down to 10- 24 seconds so an attempt + + + align:start position:0% +and down to 10- 24 seconds so an attempt +to compress all the ranges of tempos in + + align:start position:0% +to compress all the ranges of tempos in + + + align:start position:0% +to compress all the ranges of tempos in +the universe onto one scale results in + + align:start position:0% +the universe onto one scale results in + + + align:start position:0% +the universe onto one scale results in +just uh unbelievable compression on the + + align:start position:0% +just uh unbelievable compression on the + + + align:start position:0% +just uh unbelievable compression on the +left um and on the right you'll find the + + align:start position:0% +left um and on the right you'll find the + + + align:start position:0% +left um and on the right you'll find the +time scales that characterize nature uh + + align:start position:0% +time scales that characterize nature uh + + + align:start position:0% +time scales that characterize nature uh +in purple these are the time scales that + + align:start position:0% +in purple these are the time scales that + + + align:start position:0% +in purple these are the time scales that +are inherent in the interactions that + + align:start position:0% +are inherent in the interactions that + + + align:start position:0% +are inherent in the interactions that +govern the universe the electromagnetic + + align:start position:0% +govern the universe the electromagnetic + + + align:start position:0% +govern the universe the electromagnetic +and weak interactions and strong force + + align:start position:0% +and weak interactions and strong force + + + align:start position:0% +and weak interactions and strong force +here with their very short time scales + + align:start position:0% +here with their very short time scales + + + align:start position:0% +here with their very short time scales +and then over here on the right the time + + align:start position:0% +and then over here on the right the time + + + align:start position:0% +and then over here on the right the time +scales that car ciz the universe what's + + align:start position:0% +scales that car ciz the universe what's + + + align:start position:0% +scales that car ciz the universe what's +really striking in this picture is the + + align:start position:0% +really striking in this picture is the + + + align:start position:0% +really striking in this picture is the +total absence of any reference to the + + align:start position:0% +total absence of any reference to the + + + align:start position:0% +total absence of any reference to the +times of Our Lives the times that we + + align:start position:0% +times of Our Lives the times that we + + + align:start position:0% +times of Our Lives the times that we +make music we live out our lives which + + align:start position:0% +make music we live out our lives which + + + align:start position:0% +make music we live out our lives which +uh range from a heartbeat at 1 second up + + align:start position:0% +uh range from a heartbeat at 1 second up + + + align:start position:0% +uh range from a heartbeat at 1 second up +to the lifespan of the human being at + + align:start position:0% +to the lifespan of the human being at + + + align:start position:0% +to the lifespan of the human being at +about 10 to the 9th + + align:start position:0% + + + + align:start position:0% + +seconds um I I have to play Professor + + align:start position:0% +seconds um I I have to play Professor + + + align:start position:0% +seconds um I I have to play Professor +here a little bit + + align:start position:0% +here a little bit + + + align:start position:0% +here a little bit +um the I think you all encountered a + + align:start position:0% +um the I think you all encountered a + + + align:start position:0% +um the I think you all encountered a +discussion of the cernic Revolution + + align:start position:0% +discussion of the cernic Revolution + + + align:start position:0% +discussion of the cernic Revolution +which which really removed Mankind from + + align:start position:0% +which which really removed Mankind from + + + align:start position:0% +which which really removed Mankind from +the center of the universe uh before + + align:start position:0% +the center of the universe uh before + + + align:start position:0% +the center of the universe uh before +cernus it was generally believed that + + align:start position:0% +cernus it was generally believed that + + + align:start position:0% +cernus it was generally believed that +the Universe had a tmeic structure the + + align:start position:0% +the Universe had a tmeic structure the + + + align:start position:0% +the Universe had a tmeic structure the +Earth was at the center and everything + + align:start position:0% +Earth was at the center and everything + + + align:start position:0% +Earth was at the center and everything +went around us in beautiful crystallin + + align:start position:0% +went around us in beautiful crystallin + + + align:start position:0% +went around us in beautiful crystallin +spheres Cernic's showed that that was + + align:start position:0% +spheres Cernic's showed that that was + + + align:start position:0% +spheres Cernic's showed that that was +not correct that the Earth sits at the + + align:start position:0% +not correct that the Earth sits at the + + + align:start position:0% +not correct that the Earth sits at the +periphery of the solar system with the + + align:start position:0% +periphery of the solar system with the + + + align:start position:0% +periphery of the solar system with the +Sun at the center and subsequent + + align:start position:0% +Sun at the center and subsequent + + + align:start position:0% +Sun at the center and subsequent +generations of astronomers have moved + + align:start position:0% +generations of astronomers have moved + + + align:start position:0% +generations of astronomers have moved +the Earth further and further away so uh + + align:start position:0% +the Earth further and further away so uh + + + align:start position:0% +the Earth further and further away so uh +astronomers in the 19th century showed + + align:start position:0% +astronomers in the 19th century showed + + + align:start position:0% +astronomers in the 19th century showed +the Earth was at the in the peripheral + + align:start position:0% +the Earth was at the in the peripheral + + + align:start position:0% +the Earth was at the in the peripheral +arm of a spiral galaxy and now we know + + align:start position:0% +arm of a spiral galaxy and now we know + + + align:start position:0% +arm of a spiral galaxy and now we know +that in the 21st century that the Earth + + align:start position:0% +that in the 21st century that the Earth + + + align:start position:0% +that in the 21st century that the Earth +is in a galaxy that's not very special + + align:start position:0% +is in a galaxy that's not very special + + + align:start position:0% +is in a galaxy that's not very special +and is one of hundreds of billions of + + align:start position:0% +and is one of hundreds of billions of + + + align:start position:0% +and is one of hundreds of billions of +galaxies scattered throughout the + + align:start position:0% +galaxies scattered throughout the + + + align:start position:0% +galaxies scattered throughout the +Universe um the human is sometimes + + align:start position:0% +Universe um the human is sometimes + + + align:start position:0% +Universe um the human is sometimes +despair at the impersonal uh work that's + + align:start position:0% +despair at the impersonal uh work that's + + + align:start position:0% +despair at the impersonal uh work that's +been done by physicists in ruining all + + align:start position:0% +been done by physicists in ruining all + + + align:start position:0% +been done by physicists in ruining all +these wonderful myths so that the sky is + + align:start position:0% +these wonderful myths so that the sky is + + + align:start position:0% +these wonderful myths so that the sky is +no longer filled with constellations + + align:start position:0% +no longer filled with constellations + + + align:start position:0% +no longer filled with constellations +that were made of our heroes and uh that + + align:start position:0% +that were made of our heroes and uh that + + + align:start position:0% +that were made of our heroes and uh that +they couldn't decorate pictures of the + + align:start position:0% +they couldn't decorate pictures of the + + + align:start position:0% +they couldn't decorate pictures of the +universe with these wonderful uh scenes + + align:start position:0% +universe with these wonderful uh scenes + + + align:start position:0% +universe with these wonderful uh scenes +of human activity but I I would argue + + align:start position:0% +of human activity but I I would argue + + + align:start position:0% +of human activity but I I would argue +that science has actually added a + + align:start position:0% +that science has actually added a + + + align:start position:0% +that science has actually added a +tremendous drama to this and also it's + + align:start position:0% +tremendous drama to this and also it's + + + align:start position:0% +tremendous drama to this and also it's +good to be have the right picture rather + + align:start position:0% +good to be have the right picture rather + + + align:start position:0% +good to be have the right picture rather +than the wrong picture um that if you + + align:start position:0% +than the wrong picture um that if you + + + align:start position:0% +than the wrong picture um that if you +look at the pictures in the Hubble + + align:start position:0% +look at the pictures in the Hubble + + + align:start position:0% +look at the pictures in the Hubble +telescope of the drama of dynamic + + align:start position:0% +telescope of the drama of dynamic + + + align:start position:0% +telescope of the drama of dynamic +processes that are going on in distant + + align:start position:0% +processes that are going on in distant + + + align:start position:0% +processes that are going on in distant +corners of the universe uh these are in + + align:start position:0% +corners of the universe uh these are in + + + align:start position:0% +corners of the universe uh these are in +many way in many ways much more more + + align:start position:0% +many way in many ways much more more + + + align:start position:0% +many way in many ways much more more +exciting uh and uh full of energy and + + align:start position:0% +exciting uh and uh full of energy and + + + align:start position:0% +exciting uh and uh full of energy and +change than uh one had ever thought in + + align:start position:0% +change than uh one had ever thought in + + + align:start position:0% +change than uh one had ever thought in +the days before + + align:start position:0% +the days before + + + align:start position:0% +the days before +cernus um the last one here is a picture + + align:start position:0% +cernus um the last one here is a picture + + + align:start position:0% +cernus um the last one here is a picture +of colliding + + align:start position:0% +of colliding + + + align:start position:0% +of colliding +galaxies um really remarkable + + align:start position:0% +galaxies um really remarkable + + + align:start position:0% +galaxies um really remarkable +photographs that allow us to capture a + + align:start position:0% +photographs that allow us to capture a + + + align:start position:0% +photographs that allow us to capture a +post copernican picture of + + align:start position:0% +post copernican picture of + + + align:start position:0% +post copernican picture of +space well uh in the 20th century um we + + align:start position:0% +space well uh in the 20th century um we + + + align:start position:0% +space well uh in the 20th century um we +really made a transition to post + + align:start position:0% +really made a transition to post + + + align:start position:0% +really made a transition to post +copernican picture of time before the + + align:start position:0% +copernican picture of time before the + + + align:start position:0% +copernican picture of time before the +20th century + + align:start position:0% +20th century + + + align:start position:0% +20th century +um the laws of physics really did not + + align:start position:0% +um the laws of physics really did not + + + align:start position:0% +um the laws of physics really did not +seem to have any time scale inherent in + + align:start position:0% +seem to have any time scale inherent in + + + align:start position:0% +seem to have any time scale inherent in +them the laws of gravity and Maxwell's + + align:start position:0% +them the laws of gravity and Maxwell's + + + align:start position:0% +them the laws of gravity and Maxwell's +equations that describe electromagnetism + + align:start position:0% +equations that describe electromagnetism + + + align:start position:0% +equations that describe electromagnetism +they have no natural time scales the + + align:start position:0% +they have no natural time scales the + + + align:start position:0% +they have no natural time scales the +times of phenomena are only proportional + + align:start position:0% +times of phenomena are only proportional + + + align:start position:0% +times of phenomena are only proportional +to the space over which the phenomena + + align:start position:0% +to the space over which the phenomena + + + align:start position:0% +to the space over which the phenomena +take place um so it's very natural to + + align:start position:0% +take place um so it's very natural to + + + align:start position:0% +take place um so it's very natural to +measure phenomena in terms of human + + align:start position:0% +measure phenomena in terms of human + + + align:start position:0% +measure phenomena in terms of human +scales of seconds or months or years um + + align:start position:0% +scales of seconds or months or years um + + + align:start position:0% +scales of seconds or months or years um +it in fact it seemed to be absurd when + + align:start position:0% +it in fact it seemed to be absurd when + + + align:start position:0% +it in fact it seemed to be absurd when +you looked around the world in the 17th + + align:start position:0% +you looked around the world in the 17th + + + align:start position:0% +you looked around the world in the 17th +and 18th centuries suggest any other + + align:start position:0% +and 18th centuries suggest any other + + + align:start position:0% +and 18th centuries suggest any other +natural time scale but um as as the + + align:start position:0% +natural time scale but um as as the + + + align:start position:0% +natural time scale but um as as the +enlightenment changed people's + + align:start position:0% +enlightenment changed people's + + + align:start position:0% +enlightenment changed people's +perception of space the perception of + + align:start position:0% +perception of space the perception of + + + align:start position:0% +perception of space the perception of +time really did not change it was only + + align:start position:0% +time really did not change it was only + + + align:start position:0% +time really did not change it was only +with the Advent of quantum mechanics in + + align:start position:0% +with the Advent of quantum mechanics in + + + align:start position:0% +with the Advent of quantum mechanics in +the 20th century that uh it was learned + + align:start position:0% +the 20th century that uh it was learned + + + align:start position:0% +the 20th century that uh it was learned +that there's a natural time scale with + + align:start position:0% +that there's a natural time scale with + + + align:start position:0% +that there's a natural time scale with +each of the interactions of Nature and + + align:start position:0% +each of the interactions of Nature and + + + align:start position:0% +each of the interactions of Nature and +those time scales flagrantly ignore + + align:start position:0% +those time scales flagrantly ignore + + + align:start position:0% +those time scales flagrantly ignore +anything that has human + + align:start position:0% + + + + align:start position:0% + +value uh and hopefully yeah so let me + + align:start position:0% +value uh and hopefully yeah so let me + + + align:start position:0% +value uh and hopefully yeah so let me +take a cernic Excursion in time very + + align:start position:0% +take a cernic Excursion in time very + + + align:start position:0% +take a cernic Excursion in time very +quickly starting with this piece of of + + align:start position:0% +quickly starting with this piece of of + + + align:start position:0% +quickly starting with this piece of of +Casta shell nice and going down by a + + align:start position:0% +Casta shell nice and going down by a + + + align:start position:0% +Casta shell nice and going down by a +couple of orders of magnitude so you can + + align:start position:0% +couple of orders of magnitude so you can + + + align:start position:0% +couple of orders of magnitude so you can +see the crystals you begin to see the + + align:start position:0% +see the crystals you begin to see the + + + align:start position:0% +see the crystals you begin to see the +striations on the crystals no sense of + + align:start position:0% +striations on the crystals no sense of + + + align:start position:0% +striations on the crystals no sense of +anything moving until you get to a time + + align:start position:0% +anything moving until you get to a time + + + align:start position:0% +anything moving until you get to a time +a distance scale of the order of the + + align:start position:0% +a distance scale of the order of the + + + align:start position:0% +a distance scale of the order of the +size of molecules and then you start to + + align:start position:0% +size of molecules and then you start to + + + align:start position:0% +size of molecules and then you start to +notice that the molecules are actually + + align:start position:0% +notice that the molecules are actually + + + align:start position:0% +notice that the molecules are actually +vibrating and those Quantum zero point + + align:start position:0% +vibrating and those Quantum zero point + + + align:start position:0% +vibrating and those Quantum zero point +motions of the molecules are the clue + + align:start position:0% +motions of the molecules are the clue + + + align:start position:0% +motions of the molecules are the clue +that there's a natural time scale in the + + align:start position:0% +that there's a natural time scale in the + + + align:start position:0% +that there's a natural time scale in the +interactions to hold molecules + + align:start position:0% +interactions to hold molecules + + + align:start position:0% +interactions to hold molecules +together um if we go another stage down + + align:start position:0% +together um if we go another stage down + + + align:start position:0% +together um if we go another stage down +to look at individual molecules closer + + align:start position:0% +to look at individual molecules closer + + + align:start position:0% +to look at individual molecules closer +up we start to see that they have + + align:start position:0% +up we start to see that they have + + + align:start position:0% +up we start to see that they have +patterns of motion in the molecules + + align:start position:0% +patterns of motion in the molecules + + + align:start position:0% +patterns of motion in the molecules +which are governed by the equations of + + align:start position:0% +which are governed by the equations of + + + align:start position:0% +which are governed by the equations of +quantum electrodynamics and those have a + + align:start position:0% +quantum electrodynamics and those have a + + + align:start position:0% +quantum electrodynamics and those have a +natural time scale of the order of 10us + + align:start position:0% +natural time scale of the order of 10us + + + align:start position:0% +natural time scale of the order of 10us +16 seconds and anyone who's taken one of + + align:start position:0% +16 seconds and anyone who's taken one of + + + align:start position:0% +16 seconds and anyone who's taken one of +our Quantum courses here at MIT like 804 + + align:start position:0% +our Quantum courses here at MIT like 804 + + + align:start position:0% +our Quantum courses here at MIT like 804 +will recognize a picture of the + + align:start position:0% +will recognize a picture of the + + + align:start position:0% +will recognize a picture of the +oscillations of the hydrogen atom now if + + align:start position:0% +oscillations of the hydrogen atom now if + + + align:start position:0% +oscillations of the hydrogen atom now if +we continue our way down + + align:start position:0% +we continue our way down + + + align:start position:0% +we continue our way down +down uh we're at the mercy of a clicker + + align:start position:0% +down uh we're at the mercy of a clicker + + + align:start position:0% +down uh we're at the mercy of a clicker +here ah just to remind you it's 10- 16 + + align:start position:0% +here ah just to remind you it's 10- 16 + + + align:start position:0% +here ah just to remind you it's 10- 16 +seconds sorry about + + align:start position:0% + + + + align:start position:0% + +that I could use an advance here there + + align:start position:0% +that I could use an advance here there + + + align:start position:0% +that I could use an advance here there +we go um if we continue on + + align:start position:0% + + + + align:start position:0% + +down well maybe we're not going to + + align:start position:0% +down well maybe we're not going to + + + align:start position:0% +down well maybe we're not going to +continue on down uh there we go so + + align:start position:0% +continue on down uh there we go so + + + align:start position:0% +continue on down uh there we go so +there's the hydrogen atom + + align:start position:0% +there's the hydrogen atom + + + align:start position:0% +there's the hydrogen atom +again and each step at this point + + align:start position:0% +again and each step at this point + + + align:start position:0% +again and each step at this point +is uh a couple of orders of magnitude of + + align:start position:0% +is uh a couple of orders of magnitude of + + + align:start position:0% +is uh a couple of orders of magnitude of +distance we see nothing happening + + align:start position:0% +distance we see nothing happening + + + align:start position:0% +distance we see nothing happening +nothing happening empty space inside the + + align:start position:0% +nothing happening empty space inside the + + + align:start position:0% +nothing happening empty space inside the +atom until we begin to start to see the + + align:start position:0% +atom until we begin to start to see the + + + align:start position:0% +atom until we begin to start to see the +nucleus deep inside the atom the nucleus + + align:start position:0% +nucleus deep inside the atom the nucleus + + + align:start position:0% +nucleus deep inside the atom the nucleus +accounts from more than 99% of the mass + + align:start position:0% +accounts from more than 99% of the mass + + + align:start position:0% +accounts from more than 99% of the mass +of the atom and in the nucleus are the + + align:start position:0% +of the atom and in the nucleus are the + + + align:start position:0% +of the atom and in the nucleus are the +proton and neutron and in the proton and + + align:start position:0% +proton and neutron and in the proton and + + + align:start position:0% +proton and neutron and in the proton and +neutron are these Quantum fields that + + align:start position:0% +neutron are these Quantum fields that + + + align:start position:0% +neutron are these Quantum fields that +are fluctuating with a time scale of 10 + + align:start position:0% +are fluctuating with a time scale of 10 + + + align:start position:0% +are fluctuating with a time scale of 10 +to Theus 24 seconds so since most of the + + align:start position:0% +to Theus 24 seconds so since most of the + + + align:start position:0% +to Theus 24 seconds so since most of the +visible matter matter in the universe by + + align:start position:0% +visible matter matter in the universe by + + + align:start position:0% +visible matter matter in the universe by +far is made of protons and neutrons this + + align:start position:0% +far is made of protons and neutrons this + + + align:start position:0% +far is made of protons and neutrons this +is really the heartbeat of the universe + + align:start position:0% +is really the heartbeat of the universe + + + align:start position:0% +is really the heartbeat of the universe +the tempo at which the matter in the + + align:start position:0% +the tempo at which the matter in the + + + align:start position:0% +the tempo at which the matter in the +universe is counting out its own + + align:start position:0% +universe is counting out its own + + + align:start position:0% +universe is counting out its own +measures of of + + align:start position:0% +measures of of + + + align:start position:0% +measures of of +Dynamics 10us 24 seconds a lot of zeros + + align:start position:0% +Dynamics 10us 24 seconds a lot of zeros + + + align:start position:0% +Dynamics 10us 24 seconds a lot of zeros +followed by + + align:start position:0% +followed by + + + align:start position:0% +followed by +one um one quick example to show that + + align:start position:0% +one um one quick example to show that + + + align:start position:0% +one um one quick example to show that +this picture actually gives you some + + align:start position:0% +this picture actually gives you some + + + align:start position:0% +this picture actually gives you some +wonderful insight into the way the world + + align:start position:0% +wonderful insight into the way the world + + + align:start position:0% +wonderful insight into the way the world +works this little absence of a track + + align:start position:0% +works this little absence of a track + + + align:start position:0% +works this little absence of a track +here there's a little Gap in here + + align:start position:0% +here there's a little Gap in here + + + align:start position:0% +here there's a little Gap in here +between these two vertices this little + + align:start position:0% +between these two vertices this little + + + align:start position:0% +between these two vertices this little +absence of a tract is the formation + + align:start position:0% +absence of a tract is the formation + + + align:start position:0% +absence of a tract is the formation +lifetime of a particle called a Lambda + + align:start position:0% +lifetime of a particle called a Lambda + + + align:start position:0% +lifetime of a particle called a Lambda +hyron it lives for 10-1 12 + + align:start position:0% +hyron it lives for 10-1 12 + + + align:start position:0% +hyron it lives for 10-1 12 +seconds uh seems like a incredibly short + + align:start position:0% +seconds uh seems like a incredibly short + + + align:start position:0% +seconds uh seems like a incredibly short +time but it's + + align:start position:0% +time but it's + + + align:start position:0% +time but it's +10-4 times the natural interval for the + + align:start position:0% +10-4 times the natural interval for the + + + align:start position:0% +10-4 times the natural interval for the +motion of the particles inside this + + align:start position:0% +motion of the particles inside this + + + align:start position:0% +motion of the particles inside this +thing so in some sense it lives for 10 + + align:start position:0% +thing so in some sense it lives for 10 + + + align:start position:0% +thing so in some sense it lives for 10 +to the 14th years in its own natural + + align:start position:0% +to the 14th years in its own natural + + + align:start position:0% +to the 14th years in its own natural +frame um compared to that human beings + + align:start position:0% +frame um compared to that human beings + + + align:start position:0% +frame um compared to that human beings +live 70 years + + align:start position:0% +live 70 years + + + align:start position:0% +live 70 years +uh our institutions our ruins live for + + align:start position:0% +uh our institutions our ruins live for + + + align:start position:0% +uh our institutions our ruins live for +uh a couple of thousand + + align:start position:0% + + + + align:start position:0% + +years I think this is either losing + + align:start position:0% +years I think this is either losing + + + align:start position:0% +years I think this is either losing +battery or losing connection so uh the + + align:start position:0% +battery or losing connection so uh the + + + align:start position:0% +battery or losing connection so uh the +Grand Canyon a million years the solar + + align:start position:0% +Grand Canyon a million years the solar + + + align:start position:0% +Grand Canyon a million years the solar +system itself will disappear in + + align:start position:0% +system itself will disappear in + + + align:start position:0% +system itself will disappear in +Supernova in about a billion years this + + align:start position:0% +Supernova in about a billion years this + + + align:start position:0% +Supernova in about a billion years this +thing's living 100,000 billion years in + + align:start position:0% +thing's living 100,000 billion years in + + + align:start position:0% +thing's living 100,000 billion years in +its own natural framework particle + + align:start position:0% +its own natural framework particle + + + align:start position:0% +its own natural framework particle +physicists refer to this particle as + + align:start position:0% +physicists refer to this particle as + + + align:start position:0% +physicists refer to this particle as +stable even though it was 10- 10 + + align:start position:0% + + + + align:start position:0% + +seconds um let's go outward if we start + + align:start position:0% +seconds um let's go outward if we start + + + align:start position:0% +seconds um let's go outward if we start +with the times of the uh atam and work + + align:start position:0% +with the times of the uh atam and work + + + align:start position:0% +with the times of the uh atam and work +our way out to the universe we pass + + align:start position:0% +our way out to the universe we pass + + + align:start position:0% +our way out to the universe we pass +through this tremendous desert where + + align:start position:0% +through this tremendous desert where + + + align:start position:0% +through this tremendous desert where +there are no natural time scales in + + align:start position:0% +there are no natural time scales in + + + align:start position:0% +there are no natural time scales in +science at all but where our time scales + + align:start position:0% +science at all but where our time scales + + + align:start position:0% +science at all but where our time scales +lie um nature is completely silent until + + align:start position:0% +lie um nature is completely silent until + + + align:start position:0% +lie um nature is completely silent until +we get to the unbelievably long time of + + align:start position:0% +we get to the unbelievably long time of + + + align:start position:0% +we get to the unbelievably long time of +the lifetime of the universe and uh + + align:start position:0% +the lifetime of the universe and uh + + + align:start position:0% +the lifetime of the universe and uh +what's really striking about this is + + align:start position:0% +what's really striking about this is + + + align:start position:0% +what's really striking about this is +that there's 's no understanding of why + + align:start position:0% +that there's 's no understanding of why + + + align:start position:0% +that there's 's no understanding of why +the universe should live so long in the + + align:start position:0% +the universe should live so long in the + + + align:start position:0% +the universe should live so long in the +measures of the clock of the strong + + align:start position:0% +measures of the clock of the strong + + + align:start position:0% +measures of the clock of the strong +interactions the universe lives 10 to + + align:start position:0% +interactions the universe lives 10 to + + + align:start position:0% +interactions the universe lives 10 to +the 39th + + align:start position:0% +the 39th + + + align:start position:0% +the 39th +beats and uh if the universe were + + align:start position:0% +beats and uh if the universe were + + + align:start position:0% +beats and uh if the universe were +governed entirely by those interactions + + align:start position:0% +governed entirely by those interactions + + + align:start position:0% +governed entirely by those interactions +one would expect it to have come into + + align:start position:0% +one would expect it to have come into + + + align:start position:0% +one would expect it to have come into +existence and snuffed out of existence + + align:start position:0% +existence and snuffed out of existence + + + align:start position:0% +existence and snuffed out of existence +in tiny fraction of a second so the + + align:start position:0% +in tiny fraction of a second so the + + + align:start position:0% +in tiny fraction of a second so the +length scale of cosmology was until the + + align:start position:0% +length scale of cosmology was until the + + + align:start position:0% +length scale of cosmology was until the +end of the 20th century completely + + align:start position:0% +end of the 20th century completely + + + align:start position:0% +end of the 20th century completely +mysterious to us things changed toward + + align:start position:0% +mysterious to us things changed toward + + + align:start position:0% +mysterious to us things changed toward +the end of this Century that discovery + + align:start position:0% +the end of this Century that discovery + + + align:start position:0% +the end of this Century that discovery +of a substance in our universe called + + align:start position:0% +of a substance in our universe called + + + align:start position:0% +of a substance in our universe called +Dark Matter um raises uh I think I've + + align:start position:0% +Dark Matter um raises uh I think I've + + + align:start position:0% +Dark Matter um raises uh I think I've +lost a slide here let's + + align:start position:0% + + + + align:start position:0% + +see I apologize for this but it's an + + align:start position:0% +see I apologize for this but it's an + + + align:start position:0% +see I apologize for this but it's an +unpredictable + + align:start position:0% + + + + align:start position:0% + +device so uh the the time scale of the + + align:start position:0% +device so uh the the time scale of the + + + align:start position:0% +device so uh the the time scale of the +dark energy which was discovered only in + + align:start position:0% +dark energy which was discovered only in + + + align:start position:0% +dark energy which was discovered only in +the + + align:start position:0% +the + + + align:start position:0% +the +1990s um introduces into our our + + align:start position:0% +1990s um introduces into our our + + + align:start position:0% +1990s um introduces into our our +understanding of the universe a natural + + align:start position:0% +understanding of the universe a natural + + + align:start position:0% +understanding of the universe a natural +reason for the universe to live so long + + align:start position:0% +reason for the universe to live so long + + + align:start position:0% +reason for the universe to live so long +not that we understand it dynamically + + align:start position:0% +not that we understand it dynamically + + + align:start position:0% +not that we understand it dynamically +but at least we have a signpost the dark + + align:start position:0% +but at least we have a signpost the dark + + + align:start position:0% +but at least we have a signpost the dark +energy has associated with it a time + + align:start position:0% +energy has associated with it a time + + + align:start position:0% +energy has associated with it a time +scale through the laws of general + + align:start position:0% +scale through the laws of general + + + align:start position:0% +scale through the laws of general +relativity that's of the order of 10 + + align:start position:0% +relativity that's of the order of 10 + + + align:start position:0% +relativity that's of the order of 10 +billion years which happens to be + + align:start position:0% +billion years which happens to be + + + align:start position:0% +billion years which happens to be +approximately the lifetime of a main + + align:start position:0% +approximately the lifetime of a main + + + align:start position:0% +approximately the lifetime of a main +sequence star like our sun and very + + align:start position:0% +sequence star like our sun and very + + + align:start position:0% +sequence star like our sun and very +close to the present age of the universe + + align:start position:0% +close to the present age of the universe + + + align:start position:0% +close to the present age of the universe +there are several Mysteries here that + + align:start position:0% +there are several Mysteries here that + + + align:start position:0% +there are several Mysteries here that +await our understanding why the time + + align:start position:0% +await our understanding why the time + + + align:start position:0% +await our understanding why the time +scale in the dark matter is close to the + + align:start position:0% +scale in the dark matter is close to the + + + align:start position:0% +scale in the dark matter is close to the +lifetime of the universe and why the + + align:start position:0% +lifetime of the universe and why the + + + align:start position:0% +lifetime of the universe and why the +lifetime of main sequence stars is close + + align:start position:0% +lifetime of main sequence stars is close + + + align:start position:0% +lifetime of main sequence stars is close +to the lifetime is close to the U age of + + align:start position:0% +to the lifetime is close to the U age of + + + align:start position:0% +to the lifetime is close to the U age of +the universe as well um in thinking + + align:start position:0% +the universe as well um in thinking + + + align:start position:0% +the universe as well um in thinking +about where these time scales could have + + align:start position:0% +about where these time scales could have + + + align:start position:0% +about where these time scales could have +come from Modern cosmologists have come + + align:start position:0% +come from Modern cosmologists have come + + + align:start position:0% +come from Modern cosmologists have come +up with a picture of our universe not as + + align:start position:0% +up with a picture of our universe not as + + + align:start position:0% +up with a picture of our universe not as +an individual entity but instead as an + + align:start position:0% +an individual entity but instead as an + + + align:start position:0% +an individual entity but instead as an +event in a larger manifold which is + + align:start position:0% +event in a larger manifold which is + + + align:start position:0% +event in a larger manifold which is +called Multiverse for lack of a better + + align:start position:0% +called Multiverse for lack of a better + + + align:start position:0% +called Multiverse for lack of a better +name and that uh in this Multiverse + + align:start position:0% +name and that uh in this Multiverse + + + align:start position:0% +name and that uh in this Multiverse +universes are coming into and winking + + align:start position:0% +universes are coming into and winking + + + align:start position:0% +universes are coming into and winking +out of existence all the time and those + + align:start position:0% +out of existence all the time and those + + + align:start position:0% +out of existence all the time and those +that most of them are never evolve + + align:start position:0% +that most of them are never evolve + + + align:start position:0% +that most of them are never evolve +observers most of them are uncongenial + + align:start position:0% +observers most of them are uncongenial + + + align:start position:0% +observers most of them are uncongenial +because their laws of physics don't work + + align:start position:0% +because their laws of physics don't work + + + align:start position:0% +because their laws of physics don't work +very well and uh we happen to have the + + align:start position:0% +very well and uh we happen to have the + + + align:start position:0% +very well and uh we happen to have the +laws of physics that we see in our + + align:start position:0% +laws of physics that we see in our + + + align:start position:0% +laws of physics that we see in our +universe because they're congenial for + + align:start position:0% +universe because they're congenial for + + + align:start position:0% +universe because they're congenial for +the evolution of an + + align:start position:0% +the evolution of an + + + align:start position:0% +the evolution of an +observer uh in order to think about this + + align:start position:0% +observer uh in order to think about this + + + align:start position:0% +observer uh in order to think about this +it may this is very much at the edge of + + align:start position:0% +it may this is very much at the edge of + + + align:start position:0% +it may this is very much at the edge of +speculation but in order to think about + + align:start position:0% +speculation but in order to think about + + + align:start position:0% +speculation but in order to think about +this one has to remove oneself from the + + align:start position:0% +this one has to remove oneself from the + + + align:start position:0% +this one has to remove oneself from the +human Prejudice that the lifetime of the + + align:start position:0% +human Prejudice that the lifetime of the + + + align:start position:0% +human Prejudice that the lifetime of the +universe is a long time one has to be + + align:start position:0% +universe is a long time one has to be + + + align:start position:0% +universe is a long time one has to be +able to think of the manifold of + + align:start position:0% +able to think of the manifold of + + + align:start position:0% +able to think of the manifold of +universes + + align:start position:0% +universes + + + align:start position:0% +universes +as + + align:start position:0% +as + + + align:start position:0% +as +uh something in which events take place + + align:start position:0% +uh something in which events take place + + + align:start position:0% +uh something in which events take place +with the same kind of cadence that + + align:start position:0% +with the same kind of cadence that + + + align:start position:0% +with the same kind of cadence that +events take place in our ordinary + + align:start position:0% +events take place in our ordinary + + + align:start position:0% +events take place in our ordinary +experience so this picture which is a + + align:start position:0% +experience so this picture which is a + + + align:start position:0% +experience so this picture which is a +picture of universes winking in and out + + align:start position:0% +picture of universes winking in and out + + + align:start position:0% +picture of universes winking in and out +of existence May in the proper dynamical + + align:start position:0% +of existence May in the proper dynamical + + + align:start position:0% +of existence May in the proper dynamical +framework be the right picture to think + + align:start position:0% +framework be the right picture to think + + + align:start position:0% +framework be the right picture to think +about + + align:start position:0% +about + + + align:start position:0% +about +cosmology so finally uh I'll just put + + align:start position:0% +cosmology so finally uh I'll just put + + + align:start position:0% +cosmology so finally uh I'll just put +these two next to each other and quote + + align:start position:0% +these two next to each other and quote + + + align:start position:0% +these two next to each other and quote +em Dickinson and leave you with pictures + + align:start position:0% +em Dickinson and leave you with pictures + + + align:start position:0% +em Dickinson and leave you with pictures +of physics at two different time scales + + align:start position:0% +of physics at two different time scales + + + align:start position:0% +of physics at two different time scales +both of which uh can be appreciated but + + align:start position:0% +both of which uh can be appreciated but + + + align:start position:0% +both of which uh can be appreciated but +only if you're willing to change the + + align:start position:0% +only if you're willing to change the + + + align:start position:0% +only if you're willing to change the +cinematographic uh frame speed of your + + align:start position:0% +cinematographic uh frame speed of your + + + align:start position:0% +cinematographic uh frame speed of your +mind to match the natural tempo of the + + align:start position:0% +mind to match the natural tempo of the + + + align:start position:0% +mind to match the natural tempo of the +physical + + align:start position:0% + + + + align:start position:0% + +world music + + align:start position:0% +world music + + + align:start position:0% +world music +we get + + align:start position:0% +we get + + + align:start position:0% +we get +musicians um musicians while our + + align:start position:0% +musicians um musicians while our + + + align:start position:0% +musicians um musicians while our +musicians are coming forward I'll try to + + align:start position:0% +musicians are coming forward I'll try to + + + align:start position:0% +musicians are coming forward I'll try to +make a segue uh uh in that um since I + + align:start position:0% +make a segue uh uh in that um since I + + + align:start position:0% +make a segue uh uh in that um since I +was uh for conscious my chief interest + + align:start position:0% +was uh for conscious my chief interest + + + align:start position:0% +was uh for conscious my chief interest +in number has been in the number zero + + align:start position:0% +in number has been in the number zero + + + align:start position:0% +in number has been in the number zero +which is not a number um but a portal uh + + align:start position:0% +which is not a number um but a portal uh + + + align:start position:0% +which is not a number um but a portal uh +and um and um I also was extraordinarily + + align:start position:0% +and um and um I also was extraordinarily + + + align:start position:0% +and um and um I also was extraordinarily +fortunate in learning how to notate + + align:start position:0% +fortunate in learning how to notate + + + align:start position:0% +fortunate in learning how to notate +music beginning with menal notation and + + align:start position:0% +music beginning with menal notation and + + + align:start position:0% +music beginning with menal notation and +so the brev actually was the first + + align:start position:0% +so the brev actually was the first + + + align:start position:0% +so the brev actually was the first +Cipher I had for the containment of the + + align:start position:0% +Cipher I had for the containment of the + + + align:start position:0% +Cipher I had for the containment of the +essentials um of music I think I made a + + align:start position:0% +essentials um of music I think I made a + + + align:start position:0% +essentials um of music I think I made a +sayway now I can talk to you + + align:start position:0% +sayway now I can talk to you + + + align:start position:0% +sayway now I can talk to you +about + + align:start position:0% +about + + + align:start position:0% +about +um I am here as as a composer um one who + + align:start position:0% +um I am here as as a composer um one who + + + align:start position:0% +um I am here as as a composer um one who +um works with the Essential Elements of + + align:start position:0% +um works with the Essential Elements of + + + align:start position:0% +um works with the Essential Elements of +music + + align:start position:0% +music + + + align:start position:0% +music +um to make an order of sound in time and + + align:start position:0% +um to make an order of sound in time and + + + align:start position:0% +um to make an order of sound in time and +space uh what I'm hoping to do is to + + align:start position:0% +space uh what I'm hoping to do is to + + + align:start position:0% +space uh what I'm hoping to do is to +engage The Listener or the perceiver um + + align:start position:0% +engage The Listener or the perceiver um + + + align:start position:0% +engage The Listener or the perceiver um +in an activity of musical perception um + + align:start position:0% +in an activity of musical perception um + + + align:start position:0% +in an activity of musical perception um +which involves recognition and + + align:start position:0% +which involves recognition and + + + align:start position:0% +which involves recognition and +connection and deep + + align:start position:0% +connection and deep + + + align:start position:0% +connection and deep +memory uh music of course in um when it + + align:start position:0% +memory uh music of course in um when it + + + align:start position:0% +memory uh music of course in um when it +is heard uh live uh cannot be perceived + + align:start position:0% +is heard uh live uh cannot be perceived + + + align:start position:0% +is heard uh live uh cannot be perceived +in any way except in the memory you + + align:start position:0% +in any way except in the memory you + + + align:start position:0% +in any way except in the memory you +never hear music in the present you only + + align:start position:0% +never hear music in the present you only + + + align:start position:0% +never hear music in the present you only +hear tiny + + align:start position:0% +hear tiny + + + align:start position:0% +hear tiny +increments of time and air which hold + + align:start position:0% +increments of time and air which hold + + + align:start position:0% +increments of time and air which hold +bits of pitch uh perception of + + align:start position:0% +bits of pitch uh perception of + + + align:start position:0% +bits of pitch uh perception of +movement uh and um and it's the + + align:start position:0% +movement uh and um and it's the + + + align:start position:0% +movement uh and um and it's the +composer's job it in fact it's my life's + + align:start position:0% +composer's job it in fact it's my life's + + + align:start position:0% +composer's job it in fact it's my life's +passion to try to create some musical + + align:start position:0% +passion to try to create some musical + + + align:start position:0% +passion to try to create some musical +expectation and then deal with it um + + align:start position:0% +expectation and then deal with it um + + + align:start position:0% +expectation and then deal with it um +with the idea that somehow you as the + + align:start position:0% +with the idea that somehow you as the + + + align:start position:0% +with the idea that somehow you as the +perceiver + + align:start position:0% +perceiver + + + align:start position:0% +perceiver +contain the entire interaction of what I + + align:start position:0% +contain the entire interaction of what I + + + align:start position:0% +contain the entire interaction of what I +have done with pitch Rhythm and + + align:start position:0% +have done with pitch Rhythm and + + + align:start position:0% +have done with pitch Rhythm and +architecture um somewhere deep inside of + + align:start position:0% +architecture um somewhere deep inside of + + + align:start position:0% +architecture um somewhere deep inside of +you even though you cannot hum the + + align:start position:0% +you even though you cannot hum the + + + align:start position:0% +you even though you cannot hum the +melody or tap the beat that somehow you + + align:start position:0% +melody or tap the beat that somehow you + + + align:start position:0% +melody or tap the beat that somehow you +are left with a deep knowledge of the + + align:start position:0% +are left with a deep knowledge of the + + + align:start position:0% +are left with a deep knowledge of the +piece of music that that you have heard + + align:start position:0% +piece of music that that you have heard + + + align:start position:0% +piece of music that that you have heard +does that make sense to you it's a + + align:start position:0% +does that make sense to you it's a + + + align:start position:0% +does that make sense to you it's a +strange art form that the kind of art + + align:start position:0% +strange art form that the kind of art + + + align:start position:0% +strange art form that the kind of art +form that I practice um because I canot + + align:start position:0% +form that I practice um because I canot + + + align:start position:0% +form that I practice um because I canot +tell you what is in my mind and in fact + + align:start position:0% +tell you what is in my mind and in fact + + + align:start position:0% +tell you what is in my mind and in fact +there are no instruments available that + + align:start position:0% +there are no instruments available that + + + align:start position:0% +there are no instruments available that +can translate the music that is in my + + align:start position:0% +can translate the music that is in my + + + align:start position:0% +can translate the music that is in my +mind into a form that you The Listener + + align:start position:0% +mind into a form that you The Listener + + + align:start position:0% +mind into a form that you The Listener +can + + align:start position:0% +can + + + align:start position:0% +can +perceive and so um so with that in mind + + align:start position:0% +perceive and so um so with that in mind + + + align:start position:0% +perceive and so um so with that in mind +I thought I'd talk a little bit about um + + align:start position:0% +I thought I'd talk a little bit about um + + + align:start position:0% +I thought I'd talk a little bit about um +the essential elements that I deal with + + align:start position:0% +the essential elements that I deal with + + + align:start position:0% +the essential elements that I deal with +as a composer uh and um and then more + + align:start position:0% +as a composer uh and um and then more + + + align:start position:0% +as a composer uh and um and then more +specifically about um how I deal with + + align:start position:0% +specifically about um how I deal with + + + align:start position:0% +specifically about um how I deal with +these elements in the piece that we will + + align:start position:0% +these elements in the piece that we will + + + align:start position:0% +these elements in the piece that we will +hear this evening um which is a piece + + align:start position:0% +hear this evening um which is a piece + + + align:start position:0% +hear this evening um which is a piece +entitled blackbirds Red Hills + + align:start position:0% +entitled blackbirds Red Hills + + + align:start position:0% +entitled blackbirds Red Hills +a piece that um I wrote uh as a response + + align:start position:0% +a piece that um I wrote uh as a response + + + align:start position:0% +a piece that um I wrote uh as a response +to Georgia O's deal uh ideas about time + + align:start position:0% +to Georgia O's deal uh ideas about time + + + align:start position:0% +to Georgia O's deal uh ideas about time +infinity and cycle um so um we as + + align:start position:0% +infinity and cycle um so um we as + + + align:start position:0% +infinity and cycle um so um we as +composers are are are often faced with + + align:start position:0% +composers are are are often faced with + + + align:start position:0% +composers are are are often faced with +the idea that there are certain pitches + + align:start position:0% +the idea that there are certain pitches + + + align:start position:0% +the idea that there are certain pitches +that we may or may not be able to use in + + align:start position:0% +that we may or may not be able to use in + + + align:start position:0% +that we may or may not be able to use in +certain ways uh and that these pitches + + align:start position:0% +certain ways uh and that these pitches + + + align:start position:0% +certain ways uh and that these pitches +are correct or + + align:start position:0% +are correct or + + + align:start position:0% +are correct or +incorrect uh um when in fact um that is + + align:start position:0% +incorrect uh um when in fact um that is + + + align:start position:0% +incorrect uh um when in fact um that is +merely cultural perception what what + + align:start position:0% +merely cultural perception what what + + + align:start position:0% +merely cultural perception what what +pitch is is direct frequency it's the + + align:start position:0% +pitch is is direct frequency it's the + + + align:start position:0% +pitch is is direct frequency it's the +only thing about music that is actually + + align:start position:0% +only thing about music that is actually + + + align:start position:0% +only thing about music that is actually +naturally physically true how frequency + + align:start position:0% +naturally physically true how frequency + + + align:start position:0% +naturally physically true how frequency +meets the brain that's that's the only + + align:start position:0% +meets the brain that's that's the only + + + align:start position:0% +meets the brain that's that's the only +thing that's true everything else about + + align:start position:0% +thing that's true everything else about + + + align:start position:0% +thing that's true everything else about +music is perception everything else and + + align:start position:0% +music is perception everything else and + + + align:start position:0% +music is perception everything else and +so um so when we deal with pitch as as + + align:start position:0% +so um so when we deal with pitch as as + + + align:start position:0% +so um so when we deal with pitch as as +composers um we know that it's direct + + align:start position:0% +composers um we know that it's direct + + + align:start position:0% +composers um we know that it's direct +frequency but it's really the culture's + + align:start position:0% +frequency but it's really the culture's + + + align:start position:0% +frequency but it's really the culture's +perception of how that frequency is to + + align:start position:0% +perception of how that frequency is to + + + align:start position:0% +perception of how that frequency is to +be + + align:start position:0% +be + + + align:start position:0% +be +approached uh and um and manipulated is + + align:start position:0% +approached uh and um and manipulated is + + + align:start position:0% +approached uh and um and manipulated is +it the center of the pitch theists work + + align:start position:0% +it the center of the pitch theists work + + + align:start position:0% +it the center of the pitch theists work +a great deal around the edges of the + + align:start position:0% +a great deal around the edges of the + + + align:start position:0% +a great deal around the edges of the +center of the pitch it's their great + + align:start position:0% +center of the pitch it's their great + + + align:start position:0% +center of the pitch it's their great +genius to be able to always shift the + + align:start position:0% +genius to be able to always shift the + + + align:start position:0% +genius to be able to always shift the +center of the pitch in order to balance + + align:start position:0% +center of the pitch in order to balance + + + align:start position:0% +center of the pitch in order to balance +the music around them this is their + + align:start position:0% +the music around them this is their + + + align:start position:0% +the music around them this is their +genius um uh and and a culture will say + + align:start position:0% +genius um uh and and a culture will say + + + align:start position:0% +genius um uh and and a culture will say +that's a pitch that's not a pitch it's + + align:start position:0% +that's a pitch that's not a pitch it's + + + align:start position:0% +that's a pitch that's not a pitch it's +the cultural perception that we're + + align:start position:0% +the cultural perception that we're + + + align:start position:0% +the cultural perception that we're +really dealing with and that's what + + align:start position:0% +really dealing with and that's what + + + align:start position:0% +really dealing with and that's what +allows me to at least try to communicate + + align:start position:0% +allows me to at least try to communicate + + + align:start position:0% +allows me to at least try to communicate +the + + align:start position:0% +the + + + align:start position:0% +the +Sonic World that is my mind and always + + align:start position:0% +Sonic World that is my mind and always + + + align:start position:0% +Sonic World that is my mind and always +has + + align:start position:0% +has + + + align:start position:0% +has +been three elements are basic to music + + align:start position:0% +been three elements are basic to music + + + align:start position:0% +been three elements are basic to music +and only three pitch Rhythm and + + align:start position:0% +and only three pitch Rhythm and + + + align:start position:0% +and only three pitch Rhythm and +architecture pitch is direct Rhythm it + + align:start position:0% +architecture pitch is direct Rhythm it + + + align:start position:0% +architecture pitch is direct Rhythm it +is where we are talking today I believe + + align:start position:0% +is where we are talking today I believe + + + align:start position:0% +is where we are talking today I believe +increments of time considered in the + + align:start position:0% +increments of time considered in the + + + align:start position:0% +increments of time considered in the +context of tempo or Motion in + + align:start position:0% +context of tempo or Motion in + + + align:start position:0% +context of tempo or Motion in +relationship to + + align:start position:0% +relationship to + + + align:start position:0% +relationship to +pulse certain cultures perceive time in + + align:start position:0% +pulse certain cultures perceive time in + + + align:start position:0% +pulse certain cultures perceive time in +certain ways we all know and we've just + + align:start position:0% +certain ways we all know and we've just + + + align:start position:0% +certain ways we all know and we've just +perceived it beautiful uh uh insight + + align:start position:0% +perceived it beautiful uh uh insight + + + align:start position:0% +perceived it beautiful uh uh insight +into the culture of this + + align:start position:0% +into the culture of this + + + align:start position:0% +into the culture of this +rock and how time works to hold this + + align:start position:0% +rock and how time works to hold this + + + align:start position:0% +rock and how time works to hold this +Mass together over time and in + + align:start position:0% +Mass together over time and in + + + align:start position:0% +Mass together over time and in +space um architecture is really the way + + align:start position:0% +space um architecture is really the way + + + align:start position:0% +space um architecture is really the way +that composers deal with + + align:start position:0% +that composers deal with + + + align:start position:0% +that composers deal with +time um and architecture in music um is + + align:start position:0% +time um and architecture in music um is + + + align:start position:0% +time um and architecture in music um is +the way we put materials together to + + align:start position:0% +the way we put materials together to + + + align:start position:0% +the way we put materials together to +encourage the perceiver The Listener to + + align:start position:0% +encourage the perceiver The Listener to + + + align:start position:0% +encourage the perceiver The Listener to +perceive a musical connection + + align:start position:0% +perceive a musical connection + + + align:start position:0% +perceive a musical connection +um among the materials that we present + + align:start position:0% +um among the materials that we present + + + align:start position:0% +um among the materials that we present +to somehow present materials to you + + align:start position:0% +to somehow present materials to you + + + align:start position:0% +to somehow present materials to you +da in such a way that you remember it + + align:start position:0% +da in such a way that you remember it + + + align:start position:0% +da in such a way that you remember it +and you connect it to other parts of the + + align:start position:0% +and you connect it to other parts of the + + + align:start position:0% +and you connect it to other parts of the +unfolding of the Sonic architecture in + + align:start position:0% +unfolding of the Sonic architecture in + + + align:start position:0% +unfolding of the Sonic architecture in +space so if I say to + + align:start position:0% +space so if I say to + + + align:start position:0% +space so if I say to +you happy birthday to you happy birthday + + align:start position:0% +you happy birthday to you happy birthday + + + align:start position:0% +you happy birthday to you happy birthday +to you happy birthday to you what do you + + align:start position:0% +to you happy birthday to you what do you + + + align:start position:0% +to you happy birthday to you what do you +respond to + + align:start position:0% + + + + align:start position:0% + +me when in fact I could go The Farmer in + + align:start position:0% +me when in fact I could go The Farmer in + + + align:start position:0% +me when in fact I could go The Farmer in +the + + align:start position:0% +the + + + align:start position:0% +the +D and it would work but I set up an + + align:start position:0% +D and it would work but I set up an + + + align:start position:0% +D and it would work but I set up an +expectation a cultural expectation you + + align:start position:0% +expectation a cultural expectation you + + + align:start position:0% +expectation a cultural expectation you +what to answer same + + align:start position:0% +what to answer same + + + align:start position:0% +what to answer same +pictures almost the same rhythms I + + align:start position:0% +pictures almost the same rhythms I + + + align:start position:0% +pictures almost the same rhythms I +should have whistled it not giv you the + + align:start position:0% +should have whistled it not giv you the + + + align:start position:0% +should have whistled it not giv you the +words um um but it really is the degrees + + align:start position:0% +words um um but it really is the degrees + + + align:start position:0% +words um um but it really is the degrees +of connection of the musical materials + + align:start position:0% +of connection of the musical materials + + + align:start position:0% +of connection of the musical materials +that we composers deal with with that + + align:start position:0% +that we composers deal with with that + + + align:start position:0% +that we composers deal with with that +create the architecture of music that + + align:start position:0% +create the architecture of music that + + + align:start position:0% +create the architecture of music that +helps you put whatever it is you have + + align:start position:0% +helps you put whatever it is you have + + + align:start position:0% +helps you put whatever it is you have +just heard deep inside you deep inside + + align:start position:0% +just heard deep inside you deep inside + + + align:start position:0% +just heard deep inside you deep inside +of you it doesn't + + align:start position:0% +of you it doesn't + + + align:start position:0% +of you it doesn't +matter the um the the U pitch connection + + align:start position:0% +matter the um the the U pitch connection + + + align:start position:0% +matter the um the the U pitch connection +in our culture is particularly pitch + + align:start position:0% +in our culture is particularly pitch + + + align:start position:0% +in our culture is particularly pitch +Centric when it comes to composition + + align:start position:0% +Centric when it comes to composition + + + align:start position:0% +Centric when it comes to composition +insisting that the arrangement of pitch + + align:start position:0% +insisting that the arrangement of pitch + + + align:start position:0% +insisting that the arrangement of pitch +is the most important thing in + + align:start position:0% +is the most important thing in + + + align:start position:0% +is the most important thing in +composition and I would pause it note it + + align:start position:0% +composition and I would pause it note it + + + align:start position:0% +composition and I would pause it note it +is actually how the composer deals with + + align:start position:0% +is actually how the composer deals with + + + align:start position:0% +is actually how the composer deals with +time um that is the most important thing + + align:start position:0% +time um that is the most important thing + + + align:start position:0% +time um that is the most important thing +in composition and it is changing + + align:start position:0% +in composition and it is changing + + + align:start position:0% +in composition and it is changing +radically in my lifetime I was born in + + align:start position:0% +radically in my lifetime I was born in + + + align:start position:0% +radically in my lifetime I was born in +1950 and now although these many years + + align:start position:0% +1950 and now although these many years + + + align:start position:0% +1950 and now although these many years +later I can say that you're saying that + + align:start position:0% +later I can say that you're saying that + + + align:start position:0% +later I can say that you're saying that +time is speeding is slowing down has + + align:start position:0% +time is speeding is slowing down has + + + align:start position:0% +time is speeding is slowing down has +been slowing down and I'm saying it's + + align:start position:0% +been slowing down and I'm saying it's + + + align:start position:0% +been slowing down and I'm saying it's +speeding up we are able actually able to + + align:start position:0% +speeding up we are able actually able to + + + align:start position:0% +speeding up we are able actually able to +feel oh I would say maybe the the 128th + + align:start position:0% +feel oh I would say maybe the the 128th + + + align:start position:0% +feel oh I would say maybe the the 128th +note now uh as um as part of our our + + align:start position:0% +note now uh as um as part of our our + + + align:start position:0% +note now uh as um as part of our our +culture as part of our basic pulse so um + + align:start position:0% +culture as part of our basic pulse so um + + + align:start position:0% +culture as part of our basic pulse so um +enough about that that's just some food + + align:start position:0% +enough about that that's just some food + + + align:start position:0% +enough about that that's just some food +for thought um the piece that uh that I + + align:start position:0% +for thought um the piece that uh that I + + + align:start position:0% +for thought um the piece that uh that I +hope to demonstrate some of these ideas + + align:start position:0% +hope to demonstrate some of these ideas + + + align:start position:0% +hope to demonstrate some of these ideas +is the piece we'll hear this evening um + + align:start position:0% +is the piece we'll hear this evening um + + + align:start position:0% +is the piece we'll hear this evening um +it is a piece that's based on a on um + + align:start position:0% +it is a piece that's based on a on um + + + align:start position:0% +it is a piece that's based on a on um +inspired by Georg O's paintings uh uh + + align:start position:0% +inspired by Georg O's paintings uh uh + + + align:start position:0% +inspired by Georg O's paintings uh uh +her consideration of um of making paint + + align:start position:0% +her consideration of um of making paint + + + align:start position:0% +her consideration of um of making paint +as a way sorry as a way to understand + + align:start position:0% +as a way sorry as a way to understand + + + align:start position:0% +as a way sorry as a way to understand +time Infinity cycles and time um I I + + align:start position:0% +time Infinity cycles and time um I I + + + align:start position:0% +time Infinity cycles and time um I I +have a quote from George O I have + + align:start position:0% +have a quote from George O I have + + + align:start position:0% +have a quote from George O I have +several here but this one in particular + + align:start position:0% +several here but this one in particular + + + align:start position:0% +several here but this one in particular +um is useful to us when Georg o'keef was + + align:start position:0% +um is useful to us when Georg o'keef was + + + align:start position:0% +um is useful to us when Georg o'keef was +has has been questioned about time and + + align:start position:0% +has has been questioned about time and + + + align:start position:0% +has has been questioned about time and +painting um and nature um she she says + + align:start position:0% +painting um and nature um she she says + + + align:start position:0% +painting um and nature um she she says +this she says the unexplainable thing in + + align:start position:0% +this she says the unexplainable thing in + + + align:start position:0% +this she says the unexplainable thing in +nature that makes me feel the world is + + align:start position:0% +nature that makes me feel the world is + + + align:start position:0% +nature that makes me feel the world is +Big far beyond my + + align:start position:0% +Big far beyond my + + + align:start position:0% +Big far beyond my +understanding to understand may be by + + align:start position:0% +understanding to understand may be by + + + align:start position:0% +understanding to understand may be by +trying to put it into + + align:start position:0% +trying to put it into + + + align:start position:0% +trying to put it into +form trying to paint to find the feeling + + align:start position:0% +form trying to paint to find the feeling + + + align:start position:0% +form trying to paint to find the feeling +of Infinity on the horizon line or just + + align:start position:0% +of Infinity on the horizon line or just + + + align:start position:0% +of Infinity on the horizon line or just +over the next + + align:start position:0% +over the next + + + align:start position:0% +over the next +Hill to find the feeling of infinity by + + align:start position:0% +Hill to find the feeling of infinity by + + + align:start position:0% +Hill to find the feeling of infinity by +painting it is extra is an extraordinary + + align:start position:0% +painting it is extra is an extraordinary + + + align:start position:0% +painting it is extra is an extraordinary +idea and I imagine you'll have some + + align:start position:0% +idea and I imagine you'll have some + + + align:start position:0% +idea and I imagine you'll have some +things to say about how to find Infinity + + align:start position:0% +things to say about how to find Infinity + + + align:start position:0% +things to say about how to find Infinity +uh in uh in set um design um so um uh I + + align:start position:0% +uh in uh in set um design um so um uh I + + + align:start position:0% +uh in uh in set um design um so um uh I +decided to make a musical composition um + + align:start position:0% +decided to make a musical composition um + + + align:start position:0% +decided to make a musical composition um +inspired by her work in this area um and + + align:start position:0% +inspired by her work in this area um and + + + align:start position:0% +inspired by her work in this area um and +so I chose um uh several paintings six + + align:start position:0% +so I chose um uh several paintings six + + + align:start position:0% +so I chose um uh several paintings six +paintings we're not going to show you + + align:start position:0% +paintings we're not going to show you + + + align:start position:0% +paintings we're not going to show you +the paintings because we'd like you to + + align:start position:0% +the paintings because we'd like you to + + + align:start position:0% +the paintings because we'd like you to +come to the concert where you will see + + align:start position:0% +come to the concert where you will see + + + align:start position:0% +come to the concert where you will see +the paintings uh to to contemplate as + + align:start position:0% +the paintings uh to to contemplate as + + + align:start position:0% +the paintings uh to to contemplate as +objects um but um I I chose uh her + + align:start position:0% +objects um but um I I chose uh her + + + align:start position:0% +objects um but um I I chose uh her +paintings which deal with the Red Hills + + align:start position:0% +paintings which deal with the Red Hills + + + align:start position:0% +paintings which deal with the Red Hills +of New Mexico um also her paintings uh + + align:start position:0% +of New Mexico um also her paintings uh + + + align:start position:0% +of New Mexico um also her paintings uh +that deal with the black birds that she + + align:start position:0% +that deal with the black birds that she + + + align:start position:0% +that deal with the black birds that she +observed flying among the hills in New + + align:start position:0% +observed flying among the hills in New + + + align:start position:0% +observed flying among the hills in New +Mexico also her paintings that deal with + + align:start position:0% +Mexico also her paintings that deal with + + + align:start position:0% +Mexico also her paintings that deal with +the black rock an object that + + align:start position:0% +the black rock an object that + + + align:start position:0% +the black rock an object that +particularly won her attention um so um + + align:start position:0% +particularly won her attention um so um + + + align:start position:0% +particularly won her attention um so um +we'll give you some examples here um the + + align:start position:0% +we'll give you some examples here um the + + + align:start position:0% +we'll give you some examples here um the +Infinity of the horizon line we're going + + align:start position:0% +Infinity of the horizon line we're going + + + align:start position:0% +Infinity of the horizon line we're going +to play um uh the first 11 measures from + + align:start position:0% +to play um uh the first 11 measures from + + + align:start position:0% +to play um uh the first 11 measures from +pong one um and I'll tell you when um um + + align:start position:0% +pong one um and I'll tell you when um um + + + align:start position:0% +pong one um and I'll tell you when um um +I wanted to to to try to understand how + + align:start position:0% +I wanted to to to try to understand how + + + align:start position:0% +I wanted to to to try to understand how +to + + align:start position:0% +to + + + align:start position:0% +to +create the memory of the Infinity of the + + align:start position:0% +create the memory of the Infinity of the + + + align:start position:0% +create the memory of the Infinity of the +horizon line now not painted this is not + + align:start position:0% +horizon line now not painted this is not + + + align:start position:0% +horizon line now not painted this is not +baroa Renaissance painting this is + + align:start position:0% +baroa Renaissance painting this is + + + align:start position:0% +baroa Renaissance painting this is +trying to make you feel the Infinity of + + align:start position:0% +trying to make you feel the Infinity of + + + align:start position:0% +trying to make you feel the Infinity of +the horizon line and so by ask ask you + + align:start position:0% +the horizon line and so by ask ask you + + + align:start position:0% +the horizon line and so by ask ask you +this question when does sound begin to + + align:start position:0% +this question when does sound begin to + + + align:start position:0% +this question when does sound begin to +be perceived as music how soft can a + + align:start position:0% +be perceived as music how soft can a + + + align:start position:0% +be perceived as music how soft can a +sound be before you begin to feel it as + + align:start position:0% +sound be before you begin to feel it as + + + align:start position:0% +sound be before you begin to feel it as +infinity and how many pitches do you + + align:start position:0% +infinity and how many pitches do you + + + align:start position:0% +infinity and how many pitches do you +need in order to feel the Infinity of + + align:start position:0% +need in order to feel the Infinity of + + + align:start position:0% +need in order to feel the Infinity of +the Horizon how many and so um those are + + align:start position:0% +the Horizon how many and so um those are + + + align:start position:0% +the Horizon how many and so um those are +the questions I'd like you to consider + + align:start position:0% +the questions I'd like you to consider + + + align:start position:0% +the questions I'd like you to consider +as we play the first um 11 bars of the + + align:start position:0% +as we play the first um 11 bars of the + + + align:start position:0% +as we play the first um 11 bars of the +first movement first movement first + + align:start position:0% +first movement first movement first + + + align:start position:0% +first movement first movement first +movement yes please + + align:start position:0% +movement yes please + + + align:start position:0% +movement yes please +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +for your consideration + + align:start position:0% +for your consideration + + + align:start position:0% +for your consideration +only is to hear can you hear Infinity + + align:start position:0% +only is to hear can you hear Infinity + + + align:start position:0% +only is to hear can you hear Infinity +does it even get you close to the notion + + align:start position:0% +does it even get you close to the notion + + + align:start position:0% +does it even get you close to the notion +that somewhere deep inside + + align:start position:0% +that somewhere deep inside + + + align:start position:0% +that somewhere deep inside +is the infinite the infinite sound um + + align:start position:0% +is the infinite the infinite sound um + + + align:start position:0% +is the infinite the infinite sound um +this could be considered one measure in + + align:start position:0% +this could be considered one measure in + + + align:start position:0% +this could be considered one measure in +my mind and yet I and yet in order for + + align:start position:0% +my mind and yet I and yet in order for + + + align:start position:0% +my mind and yet I and yet in order for +these wonderful performers to feel the + + align:start position:0% +these wonderful performers to feel the + + + align:start position:0% +these wonderful performers to feel the +togetherness I have to bring it into + + align:start position:0% +togetherness I have to bring it into + + + align:start position:0% +togetherness I have to bring it into +human perception and give it an + + align:start position:0% +human perception and give it an + + + align:start position:0% +human perception and give it an +increment of time that is operates at + + align:start position:0% +increment of time that is operates at + + + align:start position:0% +increment of time that is operates at +the human level um when I hear the judge + + align:start position:0% +the human level um when I hear the judge + + + align:start position:0% +the human level um when I hear the judge +PR piece I hear pulse but it's at 20 + + align:start position:0% +PR piece I hear pulse but it's at 20 + + + align:start position:0% +PR piece I hear pulse but it's at 20 +it's not at 60 it's at 20 + + align:start position:0% +it's not at 60 it's at 20 + + + align:start position:0% +it's not at 60 it's at 20 +uh and um uh so um so one of the ways to + + align:start position:0% +uh and um uh so um so one of the ways to + + + align:start position:0% +uh and um uh so um so one of the ways to +create time is to try to work with + + align:start position:0% +create time is to try to work with + + + align:start position:0% +create time is to try to work with +pulse and human pulse is really the + + align:start position:0% +pulse and human pulse is really the + + + align:start position:0% +pulse and human pulse is really the +challenge of the composer human pulse we + + align:start position:0% +challenge of the composer human pulse we + + + align:start position:0% +challenge of the composer human pulse we +all have different pulses uh and um and + + align:start position:0% +all have different pulses uh and um and + + + align:start position:0% +all have different pulses uh and um and +we have average pulses and yet we have + + align:start position:0% +we have average pulses and yet we have + + + align:start position:0% +we have average pulses and yet we have +culturally accepted pulses uh which then + + align:start position:0% +culturally accepted pulses uh which then + + + align:start position:0% +culturally accepted pulses uh which then +help us as a culture say ah this is + + align:start position:0% +help us as a culture say ah this is + + + align:start position:0% +help us as a culture say ah this is +music ah this is + + align:start position:0% +music ah this is + + + align:start position:0% +music ah this is +not um now um another way to um to work + + align:start position:0% +not um now um another way to um to work + + + align:start position:0% +not um now um another way to um to work +with the perception of time uh in this + + align:start position:0% +with the perception of time uh in this + + + align:start position:0% +with the perception of time uh in this +particular piece deals with um another + + align:start position:0% +particular piece deals with um another + + + align:start position:0% +particular piece deals with um another +painting of hers she had a particular I + + align:start position:0% +painting of hers she had a particular I + + + align:start position:0% +painting of hers she had a particular I +I'll read her + + align:start position:0% +I'll read her + + + align:start position:0% +I'll read her +quote um this quote contains at least + + align:start position:0% +quote um this quote contains at least + + + align:start position:0% +quote um this quote contains at least +three human Cycles uh in the quote and + + align:start position:0% +three human Cycles uh in the quote and + + + align:start position:0% +three human Cycles uh in the quote and +yet it's dealing with with the notion of + + align:start position:0% +yet it's dealing with with the notion of + + + align:start position:0% +yet it's dealing with with the notion of +infinity a little way out beyond my + + align:start position:0% +infinity a little way out beyond my + + + align:start position:0% +infinity a little way out beyond my +kitchen window is a vshape in the Red + + align:start position:0% +kitchen window is a vshape in the Red + + + align:start position:0% +kitchen window is a vshape in the Red +Hills I walked by this uh many times + + align:start position:0% +Hills I walked by this uh many times + + + align:start position:0% +Hills I walked by this uh many times +sometimes stopping to look as it spoke + + align:start position:0% +sometimes stopping to look as it spoke + + + align:start position:0% +sometimes stopping to look as it spoke +to me + + align:start position:0% +to me + + + align:start position:0% +to me +quietly I one day carried my canvas out + + align:start position:0% +quietly I one day carried my canvas out + + + align:start position:0% +quietly I one day carried my canvas out +and made a drawing just the arms of two + + align:start position:0% +and made a drawing just the arms of two + + + align:start position:0% +and made a drawing just the arms of two +Red Hills reaching out to the sky and + + align:start position:0% +Red Hills reaching out to the sky and + + + align:start position:0% +Red Hills reaching out to the sky and +holding + + align:start position:0% +holding + + + align:start position:0% +holding +it so within this one particular + + align:start position:0% +it so within this one particular + + + align:start position:0% +it so within this one particular +consideration of the V of Hills we have + + align:start position:0% +consideration of the V of Hills we have + + + align:start position:0% +consideration of the V of Hills we have +the cycle of of daily domestic activity + + align:start position:0% +the cycle of of daily domestic activity + + + align:start position:0% +the cycle of of daily domestic activity +looking out the kitchen + + align:start position:0% +looking out the kitchen + + + align:start position:0% +looking out the kitchen +window which is actually quite a dear um + + align:start position:0% +window which is actually quite a dear um + + + align:start position:0% +window which is actually quite a dear um +View too many of us we want to make sure + + align:start position:0% +View too many of us we want to make sure + + + align:start position:0% +View too many of us we want to make sure +that what we see out our kitchen window + + align:start position:0% +that what we see out our kitchen window + + + align:start position:0% +that what we see out our kitchen window +is something we want to see out our + + align:start position:0% +is something we want to see out our + + + align:start position:0% +is something we want to see out our +kitchen window as we repeat our daily + + align:start position:0% +kitchen window as we repeat our daily + + + align:start position:0% +kitchen window as we repeat our daily +domestic activity I walked by this V + + align:start position:0% +domestic activity I walked by this V + + + align:start position:0% +domestic activity I walked by this V +many times another kind of human cycle + + align:start position:0% +many times another kind of human cycle + + + align:start position:0% +many times another kind of human cycle +walking by the same thing over and over + + align:start position:0% +walking by the same thing over and over + + + align:start position:0% +walking by the same thing over and over +again and letting that thing work on you + + align:start position:0% +again and letting that thing work on you + + + align:start position:0% +again and letting that thing work on you +I one day carried my canvas out meaning + + align:start position:0% +I one day carried my canvas out meaning + + + align:start position:0% +I one day carried my canvas out meaning +yet another cycle within the cycle + + align:start position:0% +yet another cycle within the cycle + + + align:start position:0% +yet another cycle within the cycle +within the Cycles within the cycle in + + align:start position:0% +within the Cycles within the cycle in + + + align:start position:0% +within the Cycles within the cycle in +order to + + align:start position:0% +order to + + + align:start position:0% +order to +contemplate that V shape in the Hills + + align:start position:0% +contemplate that V shape in the Hills + + + align:start position:0% +contemplate that V shape in the Hills +which turns out to + + align:start position:0% +which turns out to + + + align:start position:0% +which turns out to +be translated into arms it doesn't look + + align:start position:0% +be translated into arms it doesn't look + + + align:start position:0% +be translated into arms it doesn't look +that way in the painting but maybe it + + align:start position:0% +that way in the painting but maybe it + + + align:start position:0% +that way in the painting but maybe it +does I don't know we each perceive + + align:start position:0% +does I don't know we each perceive + + + align:start position:0% +does I don't know we each perceive +differently reaching out to the sky and + + align:start position:0% +differently reaching out to the sky and + + + align:start position:0% +differently reaching out to the sky and +doing the impossible holding the sky a + + align:start position:0% +doing the impossible holding the sky a + + + align:start position:0% +doing the impossible holding the sky a +human + + align:start position:0% +human + + + align:start position:0% +human +perception that somehow we as humans can + + align:start position:0% +perception that somehow we as humans can + + + align:start position:0% +perception that somehow we as humans can +hold the sky um to create the idea of + + align:start position:0% +hold the sky um to create the idea of + + + align:start position:0% +hold the sky um to create the idea of +this musically we'll move to um to uh + + align:start position:0% +this musically we'll move to um to uh + + + align:start position:0% +this musically we'll move to um to uh +the third song and we play the first + + align:start position:0% +the third song and we play the first + + + align:start position:0% +the third song and we play the first +five measures just to give you an idea + + align:start position:0% +five measures just to give you an idea + + + align:start position:0% +five measures just to give you an idea +of how how how we might work with this + + align:start position:0% +of how how how we might work with this + + + align:start position:0% +of how how how we might work with this +idea um we we we can use + + align:start position:0% +idea um we we we can use + + + align:start position:0% +idea um we we we can use +tesur uh in in music meaning the + + align:start position:0% +tesur uh in in music meaning the + + + align:start position:0% +tesur uh in in music meaning the +range um and U and place tesur in in + + align:start position:0% +range um and U and place tesur in in + + + align:start position:0% +range um and U and place tesur in in +Tempo so that you um feel vastness + + align:start position:0% +Tempo so that you um feel vastness + + + align:start position:0% +Tempo so that you um feel vastness +somehow um and so I tried to + + align:start position:0% +somehow um and so I tried to + + + align:start position:0% +somehow um and so I tried to +create a v-shaped tatura if I could um + + align:start position:0% +create a v-shaped tatura if I could um + + + align:start position:0% +create a v-shaped tatura if I could um +uh by by using the range of the piano um + + align:start position:0% +uh by by using the range of the piano um + + + align:start position:0% +uh by by using the range of the piano um +and by using a very slow tempo not a + + align:start position:0% +and by using a very slow tempo not a + + + align:start position:0% +and by using a very slow tempo not a +fast tempo so that you feel the + + align:start position:0% +fast tempo so that you feel the + + + align:start position:0% +fast tempo so that you feel the +perspective of vastness um uh I think + + align:start position:0% +perspective of vastness um uh I think + + + align:start position:0% +perspective of vastness um uh I think +what we'll do is if if I have + + align:start position:0% +what we'll do is if if I have + + + align:start position:0% +what we'll do is if if I have +time uh uh we'll play the first five + + align:start position:0% +time uh uh we'll play the first five + + + align:start position:0% +time uh uh we'll play the first five +measures at Tempo and then I'm going to + + align:start position:0% +measures at Tempo and then I'm going to + + + align:start position:0% +measures at Tempo and then I'm going to +ask you to play them at another Tempo + + align:start position:0% +ask you to play them at another Tempo + + + align:start position:0% +ask you to play them at another Tempo +okay + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% + + + + align:start position:0% + +so that a little bit difficult to + + align:start position:0% +so that a little bit difficult to + + + align:start position:0% +so that a little bit difficult to +connect the shapes together now many + + align:start position:0% +connect the shapes together now many + + + align:start position:0% +connect the shapes together now many +times performers have said this is the + + align:start position:0% +times performers have said this is the + + + align:start position:0% +times performers have said this is the +wrong Temple and and said no no no it's + + align:start position:0% +wrong Temple and and said no no no it's + + + align:start position:0% +wrong Temple and and said no no no it's +the right Temple no no it's the wrong + + align:start position:0% +the right Temple no no it's the wrong + + + align:start position:0% +the right Temple no no it's the wrong +Temple and so I said well what Temple do + + align:start position:0% +Temple and so I said well what Temple do + + + align:start position:0% +Temple and so I said well what Temple do +you like and so take it at um take it at + + align:start position:0% +you like and so take it at um take it at + + + align:start position:0% +you like and so take it at um take it at +more of a pastoral Temple + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +a different idea entirely you can feel + + align:start position:0% +a different idea entirely you can feel + + + align:start position:0% +a different idea entirely you can feel +the pulse you can feel a human pulse it + + align:start position:0% +the pulse you can feel a human pulse it + + + align:start position:0% +the pulse you can feel a human pulse it +might be a baroque pulse but you can + + align:start position:0% +might be a baroque pulse but you can + + + align:start position:0% +might be a baroque pulse but you can +feel it and so you move from one point + + align:start position:0% +feel it and so you move from one point + + + align:start position:0% +feel it and so you move from one point +to another with some expectation that's + + align:start position:0% +to another with some expectation that's + + + align:start position:0% +to another with some expectation that's +quite different when it's held at the at + + align:start position:0% +quite different when it's held at the at + + + align:start position:0% +quite different when it's held at the at +the temple um that I gave it and one + + align:start position:0% +the temple um that I gave it and one + + + align:start position:0% +the temple um that I gave it and one +final um uh in the interest of time and + + align:start position:0% +final um uh in the interest of time and + + + align:start position:0% +final um uh in the interest of time and +just do one final uh uh example um + + align:start position:0% + + + + align:start position:0% + +we o'keef loved to observe birds in + + align:start position:0% +we o'keef loved to observe birds in + + + align:start position:0% +we o'keef loved to observe birds in +relationship to the perspective of the + + align:start position:0% +relationship to the perspective of the + + + align:start position:0% +relationship to the perspective of the +mountains and the sky I I do too um but + + align:start position:0% +mountains and the sky I I do too um but + + + align:start position:0% +mountains and the sky I I do too um but +she painted the Blackbird um always + + align:start position:0% +she painted the Blackbird um always + + + align:start position:0% +she painted the Blackbird um always +within the same + + align:start position:0% +within the same + + + align:start position:0% +within the same +v um of the of the arm imagine she + + align:start position:0% +v um of the of the arm imagine she + + + align:start position:0% +v um of the of the arm imagine she +observed them when she was washing + + align:start position:0% +observed them when she was washing + + + align:start position:0% +observed them when she was washing +dishes and doing her kitchen work what + + align:start position:0% +dishes and doing her kitchen work what + + + align:start position:0% +dishes and doing her kitchen work what +have you but she describes the black + + align:start position:0% +have you but she describes the black + + + align:start position:0% +have you but she describes the black +bird as always there and always going + + align:start position:0% +bird as always there and always going + + + align:start position:0% +bird as always there and always going +away so it's it's much more it's a small + + align:start position:0% +away so it's it's much more it's a small + + + align:start position:0% +away so it's it's much more it's a small +object of infinity you here you have a + + align:start position:0% +object of infinity you here you have a + + + align:start position:0% +object of infinity you here you have a +finite object it has a lifespan that's + + align:start position:0% +finite object it has a lifespan that's + + + align:start position:0% +finite object it has a lifespan that's +imaginable by the human being whereas + + align:start position:0% +imaginable by the human being whereas + + + align:start position:0% +imaginable by the human being whereas +the hills the lifespan of the of the + + align:start position:0% +the hills the lifespan of the of the + + + align:start position:0% +the hills the lifespan of the of the +mountains not are not imaginable by us + + align:start position:0% +mountains not are not imaginable by us + + + align:start position:0% +mountains not are not imaginable by us +and you have the sky with which we have + + align:start position:0% +and you have the sky with which we have + + + align:start position:0% +and you have the sky with which we have +been trying to understand for a long + + align:start position:0% +been trying to understand for a long + + + align:start position:0% +been trying to understand for a long +time how can we hold the sky uh and so + + align:start position:0% +time how can we hold the sky uh and so + + + align:start position:0% +time how can we hold the sky uh and so +so she creates um a number of paintings + + align:start position:0% +so she creates um a number of paintings + + + align:start position:0% +so she creates um a number of paintings +of the black bird some of them are + + align:start position:0% +of the black bird some of them are + + + align:start position:0% +of the black bird some of them are +abstracted in their angles some of them + + align:start position:0% +abstracted in their angles some of them + + + align:start position:0% +abstracted in their angles some of them +are a little are more realistic some of + + align:start position:0% +are a little are more realistic some of + + + align:start position:0% +are a little are more realistic some of +them um uh show you the opinions of the + + align:start position:0% +them um uh show you the opinions of the + + + align:start position:0% +them um uh show you the opinions of the +Wings and how the wings may be holding + + align:start position:0% +Wings and how the wings may be holding + + + align:start position:0% +Wings and how the wings may be holding +the bird up on air always flying always + + align:start position:0% +the bird up on air always flying always + + + align:start position:0% +the bird up on air always flying always +going away and so um so just quickly um + + align:start position:0% +going away and so um so just quickly um + + + align:start position:0% +going away and so um so just quickly um +what I what I tried to do in this piece + + align:start position:0% +what I what I tried to do in this piece + + + align:start position:0% +what I what I tried to do in this piece +was to Simply use repetition uh as a way + + align:start position:0% +was to Simply use repetition uh as a way + + + align:start position:0% +was to Simply use repetition uh as a way +of hovering always there always going + + align:start position:0% +of hovering always there always going + + + align:start position:0% +of hovering always there always going +away so I created a tiny little atinado + + align:start position:0% +away so I created a tiny little atinado + + + align:start position:0% +away so I created a tiny little atinado +uh in the piano uh and then use the + + align:start position:0% +uh in the piano uh and then use the + + + align:start position:0% +uh in the piano uh and then use the +Asado throughout the the this movement + + align:start position:0% +Asado throughout the the this movement + + + align:start position:0% +Asado throughout the the this movement +um and then um let the the viola and the + + align:start position:0% +um and then um let the the viola and the + + + align:start position:0% +um and then um let the the viola and the +clarinet float on the atinado but then + + align:start position:0% +clarinet float on the atinado but then + + + align:start position:0% +clarinet float on the atinado but then +repeat the whole thing again which which + + align:start position:0% +repeat the whole thing again which which + + + align:start position:0% +repeat the whole thing again which which +made me nuts to do that but I had to do + + align:start position:0% +made me nuts to do that but I had to do + + + align:start position:0% +made me nuts to do that but I had to do +it because because it's not fashionable + + align:start position:0% +it because because it's not fashionable + + + align:start position:0% +it because because it's not fashionable +to repeat as it was in the broke times + + align:start position:0% +to repeat as it was in the broke times + + + align:start position:0% +to repeat as it was in the broke times +as it was in the uh in In classical + + align:start position:0% +as it was in the uh in In classical + + + align:start position:0% +as it was in the uh in In classical +times um but in fact it is the + + align:start position:0% +times um but in fact it is the + + + align:start position:0% +times um but in fact it is the +repetition of the cycle that allows us + + align:start position:0% +repetition of the cycle that allows us + + + align:start position:0% +repetition of the cycle that allows us +to consider ourselves in Infinity uh and + + align:start position:0% +to consider ourselves in Infinity uh and + + + align:start position:0% +to consider ourselves in Infinity uh and +so I thought we could just do the first + + align:start position:0% +so I thought we could just do the first + + + align:start position:0% +so I thought we could just do the first +five measures uh and um uh oh no measure + + align:start position:0% +five measures uh and um uh oh no measure + + + align:start position:0% +five measures uh and um uh oh no measure +five to measure 11 thank you very much + + align:start position:0% +five to measure 11 thank you very much + + + align:start position:0% +five to measure 11 thank you very much +gentlemen aren't they + + align:start position:0% + + + + align:start position:0% + +wonderful okay + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +so that little + + align:start position:0% +so that little + + + align:start position:0% +so that little +tiny which turns back on itself + + align:start position:0% +tiny which turns back on itself + + + align:start position:0% +tiny which turns back on itself +harmonically and gets closer to that + + align:start position:0% +harmonically and gets closer to that + + + align:start position:0% +harmonically and gets closer to that +action inside of + + align:start position:0% +action inside of + + + align:start position:0% +action inside of +the but I don't know you know um how + + align:start position:0% +the but I don't know you know um how + + + align:start position:0% +the but I don't know you know um how +much closer I can get you know to that + + align:start position:0% +much closer I can get you know to that + + + align:start position:0% +much closer I can get you know to that +Life Force action that we feel it we + + align:start position:0% +Life Force action that we feel it we + + + align:start position:0% +Life Force action that we feel it we +feel it it's only recently that we not + + align:start position:0% +feel it it's only recently that we not + + + align:start position:0% +feel it it's only recently that we not +even be able to to describe it we feel + + align:start position:0% +even be able to to describe it we feel + + + align:start position:0% +even be able to to describe it we feel +it and it's there in music but the human + + align:start position:0% +it and it's there in music but the human + + + align:start position:0% +it and it's there in music but the human +possibility of making music uh that can + + align:start position:0% +possibility of making music uh that can + + + align:start position:0% +possibility of making music uh that can +be be perceived as what is it 10 to the + + align:start position:0% +be be perceived as what is it 10 to the + + + align:start position:0% +be be perceived as what is it 10 to the +16 10 to the 16th + + align:start position:0% +16 10 to the 16th + + + align:start position:0% +16 10 to the 16th +16th it's impossible it's impossible + + align:start position:0% +16th it's impossible it's impossible + + + align:start position:0% +16th it's impossible it's impossible +while we are embodied and so so uh my + + align:start position:0% +while we are embodied and so so uh my + + + align:start position:0% +while we are embodied and so so uh my +passion as a composer is to try to bring + + align:start position:0% +passion as a composer is to try to bring + + + align:start position:0% +passion as a composer is to try to bring +the + + align:start position:0% +the + + + align:start position:0% +the +embodiment um as close to the to the + + align:start position:0% +embodiment um as close to the to the + + + align:start position:0% +embodiment um as close to the to the +essence um as possible uh and that's + + align:start position:0% +essence um as possible uh and that's + + + align:start position:0% +essence um as possible uh and that's +what I tried to do with my music and I + + align:start position:0% +what I tried to do with my music and I + + + align:start position:0% +what I tried to do with my music and I +don't keep in her painting and so I I + + align:start position:0% +don't keep in her painting and so I I + + + align:start position:0% +don't keep in her painting and so I I +hope this enlightens you a little bit as + + align:start position:0% +hope this enlightens you a little bit as + + + align:start position:0% +hope this enlightens you a little bit as +to how how this composer uh Works + + align:start position:0% + + + + align:start position:0% + +than so uh I will be talking about a + + align:start position:0% +than so uh I will be talking about a + + + align:start position:0% +than so uh I will be talking about a +different kind of architecture as a + + align:start position:0% +different kind of architecture as a + + + align:start position:0% +different kind of architecture as a +Scenic designer uh dealing with the + + align:start position:0% +Scenic designer uh dealing with the + + + align:start position:0% +Scenic designer uh dealing with the +physical architecture of a stage design + + align:start position:0% +physical architecture of a stage design + + + align:start position:0% +physical architecture of a stage design +and uh you know a stage design can + + align:start position:0% +and uh you know a stage design can + + + align:start position:0% +and uh you know a stage design can +ground a performance in a specific + + align:start position:0% +ground a performance in a specific + + + align:start position:0% +ground a performance in a specific +moment in history or un more an audience + + align:start position:0% +moment in history or un more an audience + + + align:start position:0% +moment in history or un more an audience +from linear time and in the case of my + + align:start position:0% +from linear time and in the case of my + + + align:start position:0% +from linear time and in the case of my +work as the resident Scenic designer for + + align:start position:0% +work as the resident Scenic designer for + + + align:start position:0% +work as the resident Scenic designer for +the Dana T Burgess company it does both + + align:start position:0% +the Dana T Burgess company it does both + + + align:start position:0% +the Dana T Burgess company it does both +coreographer and artistic director Dana + + align:start position:0% +coreographer and artistic director Dana + + + align:start position:0% +coreographer and artistic director Dana +tber just often works from a clear + + align:start position:0% +tber just often works from a clear + + + align:start position:0% +tber just often works from a clear +narrative um um usually based in a + + align:start position:0% +narrative um um usually based in a + + + align:start position:0% +narrative um um usually based in a +historical context but the time of this + + align:start position:0% +historical context but the time of this + + + align:start position:0% +historical context but the time of this +narrative is rarely + + align:start position:0% +narrative is rarely + + + align:start position:0% +narrative is rarely +linear the initial stage picture for + + align:start position:0% +linear the initial stage picture for + + + align:start position:0% +linear the initial stage picture for +images of from The Embers a a piece that + + align:start position:0% +images of from The Embers a a piece that + + + align:start position:0% +images of from The Embers a a piece that +we did a few years ago uh begins to + + align:start position:0% +we did a few years ago uh begins to + + + align:start position:0% +we did a few years ago uh begins to +establish the performance's relationship + + align:start position:0% +establish the performance's relationship + + + align:start position:0% +establish the performance's relationship +with time as the curtain Rises one + + align:start position:0% +with time as the curtain Rises one + + + align:start position:0% +with time as the curtain Rises one +couple enters using a starkly lit path + + align:start position:0% +couple enters using a starkly lit path + + + align:start position:0% +couple enters using a starkly lit path +while one woman Paces the perimeter of a + + align:start position:0% +while one woman Paces the perimeter of a + + + align:start position:0% +while one woman Paces the perimeter of a +small isolated platform and you can see + + align:start position:0% +small isolated platform and you can see + + + align:start position:0% +small isolated platform and you can see +that on the um your right of the screen + + align:start position:0% +that on the um your right of the screen + + + align:start position:0% +that on the um your right of the screen +scen a dark figure stands just outside + + align:start position:0% +scen a dark figure stands just outside + + + align:start position:0% +scen a dark figure stands just outside +of her light barely visible and a + + align:start position:0% +of her light barely visible and a + + + align:start position:0% +of her light barely visible and a +projected image shows a snapshot of a + + align:start position:0% +projected image shows a snapshot of a + + + align:start position:0% +projected image shows a snapshot of a +couple he in a World War II uniform and + + align:start position:0% +couple he in a World War II uniform and + + + align:start position:0% +couple he in a World War II uniform and +she stands smiling beside him in the + + align:start position:0% +she stands smiling beside him in the + + + align:start position:0% +she stands smiling beside him in the +image we see here he has faded out of + + align:start position:0% +image we see here he has faded out of + + + align:start position:0% +image we see here he has faded out of +the + + align:start position:0% +the + + + align:start position:0% +the +photo soon this image uh completely + + align:start position:0% +photo soon this image uh completely + + + align:start position:0% +photo soon this image uh completely +Fades to show a Japanese soldier dead on + + align:start position:0% +Fades to show a Japanese soldier dead on + + + align:start position:0% +Fades to show a Japanese soldier dead on +the battlefield while the dark figure + + align:start position:0% +the battlefield while the dark figure + + + align:start position:0% +the battlefield while the dark figure +takes his place on a second isolated + + align:start position:0% +takes his place on a second isolated + + + align:start position:0% +takes his place on a second isolated +platform uh this series of projection + + align:start position:0% +platform uh this series of projection + + + align:start position:0% +platform uh this series of projection +and the projection designer for this + + align:start position:0% +and the projection designer for this + + + align:start position:0% +and the projection designer for this +piece was uh Laura McDonald placed this + + align:start position:0% +piece was uh Laura McDonald placed this + + + align:start position:0% +piece was uh Laura McDonald placed this +piece in and around World War II as + + align:start position:0% +piece in and around World War II as + + + align:start position:0% +piece in and around World War II as +black and white photographs they stand + + align:start position:0% +black and white photographs they stand + + + align:start position:0% +black and white photographs they stand +as a record of a past though a record + + align:start position:0% +as a record of a past though a record + + + align:start position:0% +as a record of a past though a record +that is incomplete since uh you know it + + align:start position:0% +that is incomplete since uh you know it + + + align:start position:0% +that is incomplete since uh you know it +is seen through a very specific lens uh + + align:start position:0% +is seen through a very specific lens uh + + + align:start position:0% +is seen through a very specific lens uh +the dancers embody a living record of + + align:start position:0% +the dancers embody a living record of + + + align:start position:0% +the dancers embody a living record of +the very same past uh within this + + align:start position:0% +the very same past uh within this + + + align:start position:0% +the very same past uh within this +historical context that we've + + align:start position:0% +historical context that we've + + + align:start position:0% +historical context that we've +established through the images that we + + align:start position:0% +established through the images that we + + + align:start position:0% +established through the images that we +see on the + + align:start position:0% +see on the + + + align:start position:0% +see on the +screen back to the original image uh all + + align:start position:0% +screen back to the original image uh all + + + align:start position:0% +screen back to the original image uh all +three women that we see on stage uh the + + align:start position:0% +three women that we see on stage uh the + + + align:start position:0% +three women that we see on stage uh the +two dancers the two female dancers and + + align:start position:0% +two dancers the two female dancers and + + + align:start position:0% +two dancers the two female dancers and +the one in the photo are the same person + + align:start position:0% +the one in the photo are the same person + + + align:start position:0% +the one in the photo are the same person +we see her in the photograph a snapshot + + align:start position:0% +we see her in the photograph a snapshot + + + align:start position:0% +we see her in the photograph a snapshot +of one moment in her life and the + + align:start position:0% +of one moment in her life and the + + + align:start position:0% +of one moment in her life and the +isolated plat woman on the platform is + + align:start position:0% +isolated plat woman on the platform is + + + align:start position:0% +isolated plat woman on the platform is +her in the moment right after that + + align:start position:0% +her in the moment right after that + + + align:start position:0% +her in the moment right after that +photograph in the time very very soon + + align:start position:0% +photograph in the time very very soon + + + align:start position:0% +photograph in the time very very soon +after that photograph was taken um and + + align:start position:0% +after that photograph was taken um and + + + align:start position:0% +after that photograph was taken um and +then the woman entering the space who + + align:start position:0% +then the woman entering the space who + + + align:start position:0% +then the woman entering the space who +and I will refer to um the woman on the + + align:start position:0% +and I will refer to um the woman on the + + + align:start position:0% +and I will refer to um the woman on the +platform as the younger woman and the + + align:start position:0% +platform as the younger woman and the + + + align:start position:0% +platform as the younger woman and the +woman entering the space uh represents + + align:start position:0% +woman entering the space uh represents + + + align:start position:0% +woman entering the space uh represents +the same woman um in the years after + + align:start position:0% +the same woman um in the years after + + + align:start position:0% +the same woman um in the years after +World War to so after the war has ended + + align:start position:0% +World War to so after the war has ended + + + align:start position:0% +World War to so after the war has ended +uh and I will refer to her as the older + + align:start position:0% +uh and I will refer to her as the older + + + align:start position:0% +uh and I will refer to her as the older +woman similarly the two men we see + + align:start position:0% +woman similarly the two men we see + + + align:start position:0% +woman similarly the two men we see +embody different moments in time but + + align:start position:0% +embody different moments in time but + + + align:start position:0% +embody different moments in time but +they are also different individuals the + + align:start position:0% +they are also different individuals the + + + align:start position:0% +they are also different individuals the +man who has entered with the older woman + + align:start position:0% +man who has entered with the older woman + + + align:start position:0% +man who has entered with the older woman +is her lover in her present life and the + + align:start position:0% +is her lover in her present life and the + + + align:start position:0% +is her lover in her present life and the +dark figure who stands in isolation is + + align:start position:0% +dark figure who stands in isolation is + + + align:start position:0% +dark figure who stands in isolation is +the same soldier that we saw fade from + + align:start position:0% +the same soldier that we saw fade from + + + align:start position:0% +the same soldier that we saw fade from +the photo he is the woman's lover during + + align:start position:0% +the photo he is the woman's lover during + + + align:start position:0% +the photo he is the woman's lover during +the War and who was lost in battle uh + + align:start position:0% +the War and who was lost in battle uh + + + align:start position:0% +the War and who was lost in battle uh +like a cubis painting showing many + + align:start position:0% +like a cubis painting showing many + + + align:start position:0% +like a cubis painting showing many +different views of space at once images + + align:start position:0% +different views of space at once images + + + align:start position:0% +different views of space at once images +from from The Embers shows us several + + align:start position:0% +from from The Embers shows us several + + + align:start position:0% +from from The Embers shows us several +moments in time + + align:start position:0% +moments in time + + + align:start position:0% +moments in time +simultaneously but these timelines do + + align:start position:0% +simultaneously but these timelines do + + + align:start position:0% +simultaneously but these timelines do +not run just parallel they can cross and + + align:start position:0% +not run just parallel they can cross and + + + align:start position:0% +not run just parallel they can cross and +mingle the older woman can share a duet + + align:start position:0% +mingle the older woman can share a duet + + + align:start position:0% +mingle the older woman can share a duet +with a Dead Soldier and even her former + + align:start position:0% +with a Dead Soldier and even her former + + + align:start position:0% +with a Dead Soldier and even her former +self but the man who is her present + + align:start position:0% +self but the man who is her present + + + align:start position:0% +self but the man who is her present +lover never acknowledges or interacts + + align:start position:0% +lover never acknowledges or interacts + + + align:start position:0% +lover never acknowledges or interacts +with anyone but the older woman the + + align:start position:0% +with anyone but the older woman the + + + align:start position:0% +with anyone but the older woman the +relationship of the dancers to the space + + align:start position:0% +relationship of the dancers to the space + + + align:start position:0% +relationship of the dancers to the space +reflects their relationship with time + + align:start position:0% +reflects their relationship with time + + + align:start position:0% +reflects their relationship with time +and this is where um you know my role as + + align:start position:0% +and this is where um you know my role as + + + align:start position:0% +and this is where um you know my role as +a Scenic designer coming into creative + + align:start position:0% +a Scenic designer coming into creative + + + align:start position:0% +a Scenic designer coming into creative +space to hold this this really came into + + align:start position:0% +space to hold this this really came into + + + align:start position:0% +space to hold this this really came into +play um as she uh as she enters the + + align:start position:0% +play um as she uh as she enters the + + + align:start position:0% +play um as she uh as she enters the +space she she crosses through the void + + align:start position:0% +space she she crosses through the void + + + align:start position:0% +space she she crosses through the void +away from her present away from her + + align:start position:0% +away from her present away from her + + + align:start position:0% +away from her present away from her +current lover and towards her past she + + align:start position:0% +current lover and towards her past she + + + align:start position:0% +current lover and towards her past she +watches the confined woman herself in + + align:start position:0% +watches the confined woman herself in + + + align:start position:0% +watches the confined woman herself in +the past Pace her cell the image of the + + align:start position:0% +the past Pace her cell the image of the + + + align:start position:0% +the past Pace her cell the image of the +Dead Soldier appears on the screen and + + align:start position:0% +Dead Soldier appears on the screen and + + + align:start position:0% +Dead Soldier appears on the screen and +she is transfixed until it fades and her + + align:start position:0% +she is transfixed until it fades and her + + + align:start position:0% +she is transfixed until it fades and her +gaze shifts to the living embodiment of + + align:start position:0% +gaze shifts to the living embodiment of + + + align:start position:0% +gaze shifts to the living embodiment of +this same Soldier the man standing in + + align:start position:0% +this same Soldier the man standing in + + + align:start position:0% +this same Soldier the man standing in +isolation in front of her and even + + align:start position:0% +isolation in front of her and even + + + align:start position:0% +isolation in front of her and even +though he is long dead and in the past + + align:start position:0% +though he is long dead and in the past + + + align:start position:0% +though he is long dead and in the past +he gazed + + align:start position:0% +he gazed + + + align:start position:0% +he gazed +back when the older woman replaces the + + align:start position:0% +back when the older woman replaces the + + + align:start position:0% +back when the older woman replaces the +soldier in the second isolated area it + + align:start position:0% +soldier in the second isolated area it + + + align:start position:0% +soldier in the second isolated area it +is clear that they really are the same + + align:start position:0% +is clear that they really are the same + + + align:start position:0% +is clear that they really are the same +person the older woman wears the same + + align:start position:0% +person the older woman wears the same + + + align:start position:0% +person the older woman wears the same +dress as her counterpart though hers has + + align:start position:0% +dress as her counterpart though hers has + + + align:start position:0% +dress as her counterpart though hers has +DED with time they perform the same + + align:start position:0% +DED with time they perform the same + + + align:start position:0% +DED with time they perform the same +movements in sync the younger woman will + + align:start position:0% +movements in sync the younger woman will + + + align:start position:0% +movements in sync the younger woman will +only break this uh synchronicity to uh + + align:start position:0% +only break this uh synchronicity to uh + + + align:start position:0% +only break this uh synchronicity to uh +gaze up at the soldier now just in the + + align:start position:0% +gaze up at the soldier now just in the + + + align:start position:0% +gaze up at the soldier now just in the +Shadows on the edge of her platform the + + align:start position:0% +Shadows on the edge of her platform the + + + align:start position:0% +Shadows on the edge of her platform the +spatial separation between the two women + + align:start position:0% +spatial separation between the two women + + + align:start position:0% +spatial separation between the two women +implies implies the temporal divide the + + align:start position:0% +implies implies the temporal divide the + + + align:start position:0% +implies implies the temporal divide the +effect is a duet that reads like two + + align:start position:0% +effect is a duet that reads like two + + + align:start position:0% +effect is a duet that reads like two +solos this use of space to imply time + + align:start position:0% +solos this use of space to imply time + + + align:start position:0% +solos this use of space to imply time +occurs frequently through the piece a + + align:start position:0% +occurs frequently through the piece a + + + align:start position:0% +occurs frequently through the piece a +line of paper is rolled across the stage + + align:start position:0% +line of paper is rolled across the stage + + + align:start position:0% +line of paper is rolled across the stage +and creates a clear path to which the + + align:start position:0% +and creates a clear path to which the + + + align:start position:0% +and creates a clear path to which the +older woman is confined she begins + + align:start position:0% +older woman is confined she begins + + + align:start position:0% +older woman is confined she begins +writing quickly and intently it is + + align:start position:0% +writing quickly and intently it is + + + align:start position:0% +writing quickly and intently it is +ambiguous if she's writing a letter to + + align:start position:0% +ambiguous if she's writing a letter to + + + align:start position:0% +ambiguous if she's writing a letter to +her current lover or to the lover from + + align:start position:0% +her current lover or to the lover from + + + align:start position:0% +her current lover or to the lover from +her past and uh you know dark figures + + align:start position:0% +her past and uh you know dark figures + + + align:start position:0% +her past and uh you know dark figures +move like Memories around her and her + + align:start position:0% +move like Memories around her and her + + + align:start position:0% +move like Memories around her and her +younger self if you see in the + + align:start position:0% +younger self if you see in the + + + align:start position:0% +younger self if you see in the +background is shadowing her movements uh + + align:start position:0% +background is shadowing her movements uh + + + align:start position:0% +background is shadowing her movements uh +as she writes on the paper though the + + align:start position:0% +as she writes on the paper though the + + + align:start position:0% +as she writes on the paper though the +very uh very much behind her and she + + align:start position:0% +very uh very much behind her and she + + + align:start position:0% +very uh very much behind her and she +looks into the into the into this dark + + align:start position:0% +looks into the into the into this dark + + + align:start position:0% +looks into the into the into this dark +space surrounding her this writing is + + align:start position:0% +space surrounding her this writing is + + + align:start position:0% +space surrounding her this writing is +reflected in the movement of the piece + + align:start position:0% +reflected in the movement of the piece + + + align:start position:0% +reflected in the movement of the piece +as well and this is you know it's a very + + align:start position:0% +as well and this is you know it's a very + + + align:start position:0% +as well and this is you know it's a very +collaborative process creating the stage + + align:start position:0% +collaborative process creating the stage + + + align:start position:0% +collaborative process creating the stage +environment and creating the + + align:start position:0% +environment and creating the + + + align:start position:0% +environment and creating the +choreography uh the two women write on + + align:start position:0% +choreography uh the two women write on + + + align:start position:0% +choreography uh the two women write on +the floor but they also enact writing on + + align:start position:0% +the floor but they also enact writing on + + + align:start position:0% +the floor but they also enact writing on +their own bodies uh the shadowy figures + + align:start position:0% +their own bodies uh the shadowy figures + + + align:start position:0% +their own bodies uh the shadowy figures +that we see also write on themselves and + + align:start position:0% +that we see also write on themselves and + + + align:start position:0% +that we see also write on themselves and +as they watch The Narrative unfold in + + align:start position:0% +as they watch The Narrative unfold in + + + align:start position:0% +as they watch The Narrative unfold in +front of them U Burgess has described + + align:start position:0% +front of them U Burgess has described + + + align:start position:0% +front of them U Burgess has described +this movement Choice as a representative + + align:start position:0% +this movement Choice as a representative + + + align:start position:0% +this movement Choice as a representative +of the way that history and experience + + align:start position:0% +of the way that history and experience + + + align:start position:0% +of the way that history and experience +imprint themselves on the individual + + align:start position:0% +imprint themselves on the individual + + + align:start position:0% +imprint themselves on the individual +that history is always writing itself + + align:start position:0% +that history is always writing itself + + + align:start position:0% +that history is always writing itself +onto onto US onto onto people um while + + align:start position:0% +onto onto US onto onto people um while + + + align:start position:0% +onto onto US onto onto people um while +we sought to shape time with our + + align:start position:0% +we sought to shape time with our + + + align:start position:0% +we sought to shape time with our +performance of images from the Ember uh + + align:start position:0% +performance of images from the Ember uh + + + align:start position:0% +performance of images from the Ember uh +time also had an effect on our shape of + + align:start position:0% +time also had an effect on our shape of + + + align:start position:0% +time also had an effect on our shape of +the performance itself and uh this was a + + align:start position:0% +the performance itself and uh this was a + + + align:start position:0% +the performance itself and uh this was a +piece that we developed over the course + + align:start position:0% +piece that we developed over the course + + + align:start position:0% +piece that we developed over the course +of a year of a full year and then had uh + + align:start position:0% +of a year of a full year and then had uh + + + align:start position:0% +of a year of a full year and then had uh +continual in iterations down the road so + + align:start position:0% +continual in iterations down the road so + + + align:start position:0% +continual in iterations down the road so +we it became part of their repertoire + + align:start position:0% +we it became part of their repertoire + + + align:start position:0% +we it became part of their repertoire +that we performed in other places at + + align:start position:0% +that we performed in other places at + + + align:start position:0% +that we performed in other places at +other times um after our very first + + align:start position:0% +other times um after our very first + + + align:start position:0% +other times um after our very first +performance of of uh images from the + + align:start position:0% +performance of of uh images from the + + + align:start position:0% +performance of of uh images from the +Embers Dana Burgess the choreographer + + align:start position:0% +Embers Dana Burgess the choreographer + + + align:start position:0% +Embers Dana Burgess the choreographer +who's also a character in the piece he + + align:start position:0% +who's also a character in the piece he + + + align:start position:0% +who's also a character in the piece he +plays the woman's present lover uh + + align:start position:0% +plays the woman's present lover uh + + + align:start position:0% +plays the woman's present lover uh +retired from dancing but he did not + + align:start position:0% +retired from dancing but he did not + + + align:start position:0% +retired from dancing but he did not +replace himself in the piece and and and + + align:start position:0% +replace himself in the piece and and and + + + align:start position:0% +replace himself in the piece and and and +so the the older woman + + align:start position:0% + + + + align:start position:0% + +is left to sort through + + align:start position:0% +is left to sort through + + + align:start position:0% +is left to sort through +uh sort through the past on her own so + + align:start position:0% +uh sort through the past on her own so + + + align:start position:0% +uh sort through the past on her own so +she no longer has a partner to dance + + align:start position:0% +she no longer has a partner to dance + + + align:start position:0% +she no longer has a partner to dance +with and she is she is left uh you know + + align:start position:0% +with and she is she is left uh you know + + + align:start position:0% +with and she is she is left uh you know +completely uh taken up with her + + align:start position:0% +completely uh taken up with her + + + align:start position:0% +completely uh taken up with her +past uh like images our newest piece our + + align:start position:0% +past uh like images our newest piece our + + + align:start position:0% +past uh like images our newest piece our +newest collaboration that we just + + align:start position:0% +newest collaboration that we just + + + align:start position:0% +newest collaboration that we just +premiered this October uh Island takes + + align:start position:0% +premiered this October uh Island takes + + + align:start position:0% +premiered this October uh Island takes +place during a specific historical + + align:start position:0% +place during a specific historical + + + align:start position:0% +place during a specific historical +period from 1910 to 1940 the Angel + + align:start position:0% +period from 1910 to 1940 the Angel + + + align:start position:0% +period from 1910 to 1940 the Angel +Island immigration + + align:start position:0% +Island immigration + + + align:start position:0% +Island immigration +station processed immigrants entering + + align:start position:0% +station processed immigrants entering + + + align:start position:0% +station processed immigrants entering +the US uh mostly from from Asia uh + + align:start position:0% +the US uh mostly from from Asia uh + + + align:start position:0% +the US uh mostly from from Asia uh +though the Chinese Exclusion Act turned + + align:start position:0% +though the Chinese Exclusion Act turned + + + align:start position:0% +though the Chinese Exclusion Act turned +this Gateway into a prison many Chinese + + align:start position:0% +this Gateway into a prison many Chinese + + + align:start position:0% +this Gateway into a prison many Chinese +immigrants were held here for months or + + align:start position:0% +immigrants were held here for months or + + + align:start position:0% +immigrants were held here for months or +years without knowing when or to what + + align:start position:0% +years without knowing when or to what + + + align:start position:0% +years without knowing when or to what +country they would be to released and + + align:start position:0% +country they would be to released and + + + align:start position:0% +country they would be to released and +many of the walls at Angel Island were + + align:start position:0% +many of the walls at Angel Island were + + + align:start position:0% +many of the walls at Angel Island were +covered with poetry written by those + + align:start position:0% +covered with poetry written by those + + + align:start position:0% +covered with poetry written by those +held there Island follows a group of + + align:start position:0% +held there Island follows a group of + + + align:start position:0% +held there Island follows a group of +immigrants as they travel from China to + + align:start position:0% +immigrants as they travel from China to + + + align:start position:0% +immigrants as they travel from China to +the United States through Angel + + align:start position:0% +the United States through Angel + + + align:start position:0% +the United States through Angel +Island unlike images from the + + align:start position:0% +Island unlike images from the + + + align:start position:0% +Island unlike images from the +Embers there is no physical scenery to + + align:start position:0% +Embers there is no physical scenery to + + + align:start position:0% +Embers there is no physical scenery to +ground uh to ground uh our performance + + align:start position:0% +ground uh to ground uh our performance + + + align:start position:0% +ground uh to ground uh our performance +of Island the visual landscape is made + + align:start position:0% +of Island the visual landscape is made + + + align:start position:0% +of Island the visual landscape is made +up entirely by light and this is + + align:start position:0% +up entirely by light and this is + + + align:start position:0% +up entirely by light and this is +something that uh Michael referred to + + align:start position:0% +something that uh Michael referred to + + + align:start position:0% +something that uh Michael referred to +earlier um of using projection media to + + align:start position:0% +earlier um of using projection media to + + + align:start position:0% +earlier um of using projection media to +to form a space a rectangular projection + + align:start position:0% +to form a space a rectangular projection + + + align:start position:0% +to form a space a rectangular projection +on the floor comines the four dancers + + align:start position:0% +on the floor comines the four dancers + + + align:start position:0% +on the floor comines the four dancers +playing immigrants and is surrounded by + + align:start position:0% +playing immigrants and is surrounded by + + + align:start position:0% +playing immigrants and is surrounded by +four dancers portraying guards the image + + align:start position:0% +four dancers portraying guards the image + + + align:start position:0% +four dancers portraying guards the image +in the rectangle shifts to reflect time + + align:start position:0% +in the rectangle shifts to reflect time + + + align:start position:0% +in the rectangle shifts to reflect time +and + + align:start position:0% +and + + + align:start position:0% +and +location uh these projections are made + + align:start position:0% +location uh these projections are made + + + align:start position:0% +location uh these projections are made +up of a series of historical images from + + align:start position:0% +up of a series of historical images from + + + align:start position:0% +up of a series of historical images from +Angel + + align:start position:0% + + + + align:start position:0% + +Island as a projection designer I + + align:start position:0% +Island as a projection designer I + + + align:start position:0% +Island as a projection designer I +gathered this material primarily from + + align:start position:0% +gathered this material primarily from + + + align:start position:0% +gathered this material primarily from +the State Park library in Sacramento + + align:start position:0% +the State Park library in Sacramento + + + align:start position:0% +the State Park library in Sacramento +California since Angel Island is now a + + align:start position:0% +California since Angel Island is now a + + + align:start position:0% +California since Angel Island is now a +state park these photos give us a small + + align:start position:0% +state park these photos give us a small + + + align:start position:0% +state park these photos give us a small +glimpse into the world at the + + align:start position:0% +glimpse into the world at the + + + align:start position:0% +glimpse into the world at the +immigration station though as I + + align:start position:0% +immigration station though as I + + + align:start position:0% +immigration station though as I +mentioned + + align:start position:0% +mentioned + + + align:start position:0% +mentioned +uh they are incomplete we cannot see + + align:start position:0% +uh they are incomplete we cannot see + + + align:start position:0% +uh they are incomplete we cannot see +beyond the frame the photographer has + + align:start position:0% +beyond the frame the photographer has + + + align:start position:0% +beyond the frame the photographer has +chosen for us nor can we see the moments + + align:start position:0% +chosen for us nor can we see the moments + + + align:start position:0% +chosen for us nor can we see the moments +that preceded or follow the captured + + align:start position:0% +that preceded or follow the captured + + + align:start position:0% +that preceded or follow the captured +IM since the image is always changing + + align:start position:0% +IM since the image is always changing + + + align:start position:0% +IM since the image is always changing +throughout Island the characters seem to + + align:start position:0% +throughout Island the characters seem to + + + align:start position:0% +throughout Island the characters seem to +float helplessly in their environment + + align:start position:0% +float helplessly in their environment + + + align:start position:0% +float helplessly in their environment +they have no control over what might + + align:start position:0% +they have no control over what might + + + align:start position:0% +they have no control over what might +happen to them or where they may find + + align:start position:0% +happen to them or where they may find + + + align:start position:0% +happen to them or where they may find +themselves the effect is so strong in + + align:start position:0% +themselves the effect is so strong in + + + align:start position:0% +themselves the effect is so strong in +fact that the dancers found the shifting + + align:start position:0% +fact that the dancers found the shifting + + + align:start position:0% +fact that the dancers found the shifting +uh of the image underneath their feet + + align:start position:0% +uh of the image underneath their feet + + + align:start position:0% +uh of the image underneath their feet +very disorienting as the floor seemed + + align:start position:0% +very disorienting as the floor seemed + + + align:start position:0% +very disorienting as the floor seemed +like it was always falling out from + + align:start position:0% +like it was always falling out from + + + align:start position:0% +like it was always falling out from +underneath them uh in Island time seems + + align:start position:0% +underneath them uh in Island time seems + + + align:start position:0% +underneath them uh in Island time seems +to move at an everchanging Pace here the + + align:start position:0% +to move at an everchanging Pace here the + + + align:start position:0% +to move at an everchanging Pace here the +images do not seem like a memory but + + align:start position:0% +images do not seem like a memory but + + + align:start position:0% +images do not seem like a memory but +rather as a passing of days at times the + + align:start position:0% +rather as a passing of days at times the + + + align:start position:0% +rather as a passing of days at times the +movement the movement and imagery + + align:start position:0% +movement the movement and imagery + + + align:start position:0% +movement the movement and imagery +reflect + + align:start position:0% +reflect + + + align:start position:0% +reflect +waiting and this this image is taken + + align:start position:0% +waiting and this this image is taken + + + align:start position:0% +waiting and this this image is taken +from a dress rehearsal so you can + + align:start position:0% +from a dress rehearsal so you can + + + align:start position:0% +from a dress rehearsal so you can +clearly see the image behind behind the + + align:start position:0% +clearly see the image behind behind the + + + align:start position:0% +clearly see the image behind behind the +dancers uh the dancers move slowly and + + align:start position:0% +dancers uh the dancers move slowly and + + + align:start position:0% +dancers uh the dancers move slowly and +in sink while in this murky and slowly + + align:start position:0% +in sink while in this murky and slowly + + + align:start position:0% +in sink while in this murky and slowly +Rippling concrete that surrounds them + + align:start position:0% +Rippling concrete that surrounds them + + + align:start position:0% +Rippling concrete that surrounds them +forming their cell and this eventually + + align:start position:0% +forming their cell and this eventually + + + align:start position:0% +forming their cell and this eventually +just Falls away and will give way to a + + align:start position:0% +just Falls away and will give way to a + + + align:start position:0% +just Falls away and will give way to a +very quickly moving image and a violent + + align:start position:0% +very quickly moving image and a violent + + + align:start position:0% +very quickly moving image and a violent +interaction between a guard and a + + align:start position:0% +interaction between a guard and a + + + align:start position:0% +interaction between a guard and a +prisoner these days are interrupted and + + align:start position:0% +prisoner these days are interrupted and + + + align:start position:0% +prisoner these days are interrupted and +punctuated by a series of five + + align:start position:0% +punctuated by a series of five + + + align:start position:0% +punctuated by a series of five +choreograph Falls one dancer repeatedly + + align:start position:0% +choreograph Falls one dancer repeatedly + + + align:start position:0% +choreograph Falls one dancer repeatedly +crumples to the floor while the rest of + + align:start position:0% +crumples to the floor while the rest of + + + align:start position:0% +crumples to the floor while the rest of +the dancers slow down and focus on her + + align:start position:0% +the dancers slow down and focus on her + + + align:start position:0% +the dancers slow down and focus on her +these are moments set aside as the days + + align:start position:0% +these are moments set aside as the days + + + align:start position:0% +these are moments set aside as the days +yes stand still and and we just watch + + align:start position:0% +yes stand still and and we just watch + + + align:start position:0% +yes stand still and and we just watch +and also it for it gives us a clue into + + align:start position:0% +and also it for it gives us a clue into + + + align:start position:0% +and also it for it gives us a clue into +her future fate as we see her fall to + + align:start position:0% +her future fate as we see her fall to + + + align:start position:0% +her future fate as we see her fall to +the floor five times over and over as in + + align:start position:0% +the floor five times over and over as in + + + align:start position:0% +the floor five times over and over as in +images from the Embers the audience sees + + align:start position:0% +images from the Embers the audience sees + + + align:start position:0% +images from the Embers the audience sees +both a fixed record of the past in the + + align:start position:0% +both a fixed record of the past in the + + + align:start position:0% +both a fixed record of the past in the +form of historic photographs while also + + align:start position:0% +form of historic photographs while also + + + align:start position:0% +form of historic photographs while also +witnessing a live performances of that + + align:start position:0% +witnessing a live performances of that + + + align:start position:0% +witnessing a live performances of that +moment images float to the surface + + align:start position:0% + + + + align:start position:0% + +oh there we are images will float to the + + align:start position:0% +oh there we are images will float to the + + + align:start position:0% +oh there we are images will float to the +surface of the projection and either + + align:start position:0% +surface of the projection and either + + + align:start position:0% +surface of the projection and either +reflect or stand in contrast to the + + align:start position:0% +reflect or stand in contrast to the + + + align:start position:0% +reflect or stand in contrast to the +choreography the photos and the live + + align:start position:0% +choreography the photos and the live + + + align:start position:0% +choreography the photos and the live +performance merge together finally at + + align:start position:0% +performance merge together finally at + + + align:start position:0% +performance merge together finally at +the end of the piece when the dancer + + align:start position:0% +the end of the piece when the dancer + + + align:start position:0% +the end of the piece when the dancer +that we have seen fall to the floor many + + align:start position:0% +that we have seen fall to the floor many + + + align:start position:0% +that we have seen fall to the floor many +times before finally dies as she lies on + + align:start position:0% +times before finally dies as she lies on + + + align:start position:0% +times before finally dies as she lies on +the + + align:start position:0% +the + + + align:start position:0% +the +stage on the stage floor oh I'm sorry so + + align:start position:0% +stage on the stage floor oh I'm sorry so + + + align:start position:0% +stage on the stage floor oh I'm sorry so +as she lies on the stage floor the + + align:start position:0% +as she lies on the stage floor the + + + align:start position:0% +as she lies on the stage floor the +projection there actually a projection + + align:start position:0% +projection there actually a projection + + + align:start position:0% +projection there actually a projection +of people held at Angel Island put + + align:start position:0% +of people held at Angel Island put + + + align:start position:0% +of people held at Angel Island put +directly over her body and so here again + + align:start position:0% +directly over her body and so here again + + + align:start position:0% +directly over her body and so here again +in the dress rehearsal you see a sheet + + align:start position:0% +in the dress rehearsal you see a sheet + + + align:start position:0% +in the dress rehearsal you see a sheet +was placed over her body while um a + + align:start position:0% +was placed over her body while um a + + + align:start position:0% +was placed over her body while um a +projection of an image of a figure was + + align:start position:0% +projection of an image of a figure was + + + align:start position:0% +projection of an image of a figure was +was placed over top of + + align:start position:0% +was placed over top of + + + align:start position:0% +was placed over top of +her as in images from the Embers time + + align:start position:0% +her as in images from the Embers time + + + align:start position:0% +her as in images from the Embers time +also shaped our performance of Island we + + align:start position:0% +also shaped our performance of Island we + + + align:start position:0% +also shaped our performance of Island we +were fortunate enough to have a workshop + + align:start position:0% +were fortunate enough to have a workshop + + + align:start position:0% +were fortunate enough to have a workshop +performance at the um at Smithsonian and + + align:start position:0% +performance at the um at Smithsonian and + + + align:start position:0% +performance at the um at Smithsonian and +uh after this performance it was clear + + align:start position:0% +uh after this performance it was clear + + + align:start position:0% +uh after this performance it was clear +that uh without any glimmer we had + + align:start position:0% +that uh without any glimmer we had + + + align:start position:0% +that uh without any glimmer we had +started uh focusing on their confinement + + align:start position:0% +started uh focusing on their confinement + + + align:start position:0% +started uh focusing on their confinement +and their + + align:start position:0% +and their + + + align:start position:0% +and their +hopelessness and uh and that's where we + + align:start position:0% +hopelessness and uh and that's where we + + + align:start position:0% +hopelessness and uh and that's where we +started and that's where we ended + + align:start position:0% +started and that's where we ended + + + align:start position:0% +started and that's where we ended +confined and hopeless and after our + + align:start position:0% +confined and hopeless and after our + + + align:start position:0% +confined and hopeless and after our +first performance it was clear that it + + align:start position:0% +first performance it was clear that it + + + align:start position:0% +first performance it was clear that it +was not enough to capture the attention + + align:start position:0% +was not enough to capture the attention + + + align:start position:0% +was not enough to capture the attention +of an audience for 30 minutes you know + + align:start position:0% +of an audience for 30 minutes you know + + + align:start position:0% +of an audience for 30 minutes you know +we just stayed in one place for the + + align:start position:0% +we just stayed in one place for the + + + align:start position:0% +we just stayed in one place for the +whole time and so the piece was entirely + + align:start position:0% +whole time and so the piece was entirely + + + align:start position:0% +whole time and so the piece was entirely +reinvented with a much clearer narrative + + align:start position:0% +reinvented with a much clearer narrative + + + align:start position:0% +reinvented with a much clearer narrative +and that started with the group in uh in + + align:start position:0% +and that started with the group in uh in + + + align:start position:0% +and that started with the group in uh in +China so here is the their journey into + + align:start position:0% +China so here is the their journey into + + + align:start position:0% +China so here is the their journey into +into confinement and shows their entire + + align:start position:0% +into confinement and shows their entire + + + align:start position:0% +into confinement and shows their entire +Journey from China into um into the + + align:start position:0% +Journey from China into um into the + + + align:start position:0% +Journey from China into um into the +United States through Angel Island and + + align:start position:0% +United States through Angel Island and + + + align:start position:0% +United States through Angel Island and +gave a a sense of their hope for a new + + align:start position:0% +gave a a sense of their hope for a new + + + align:start position:0% +gave a a sense of their hope for a new +land so by by its very nature uh theater + + align:start position:0% +land so by by its very nature uh theater + + + align:start position:0% +land so by by its very nature uh theater +and dance like music are temporal art + + align:start position:0% +and dance like music are temporal art + + + align:start position:0% +and dance like music are temporal art +forms as a stage designer what I create + + align:start position:0% +forms as a stage designer what I create + + + align:start position:0% +forms as a stage designer what I create +can be viewed as more concrete uh in the + + align:start position:0% +can be viewed as more concrete uh in the + + + align:start position:0% +can be viewed as more concrete uh in the +cases I've shared with you today you + + align:start position:0% +cases I've shared with you today you + + + align:start position:0% +cases I've shared with you today you +know a series of platforms and drops + + align:start position:0% +know a series of platforms and drops + + + align:start position:0% +know a series of platforms and drops +that actually exist in the world you + + align:start position:0% +that actually exist in the world you + + + align:start position:0% +that actually exist in the world you +know have a physical um you know + + align:start position:0% +know have a physical um you know + + + align:start position:0% +know have a physical um you know +presence + + align:start position:0% +presence + + + align:start position:0% +presence +or um as a computer file that can be + + align:start position:0% +or um as a computer file that can be + + + align:start position:0% +or um as a computer file that can be +played on any computer at any time uh + + align:start position:0% +played on any computer at any time uh + + + align:start position:0% +played on any computer at any time uh +but these artifacts only have meaning + + align:start position:0% +but these artifacts only have meaning + + + align:start position:0% +but these artifacts only have meaning +when combined with the actual + + align:start position:0% +when combined with the actual + + + align:start position:0% +when combined with the actual +Performance Event and in this way even + + align:start position:0% +Performance Event and in this way even + + + align:start position:0% +Performance Event and in this way even +the most fixed and Architectural stage + + align:start position:0% +the most fixed and Architectural stage + + + align:start position:0% +the most fixed and Architectural stage +is a temporary object whether it is a + + align:start position:0% +is a temporary object whether it is a + + + align:start position:0% +is a temporary object whether it is a +fixed image or when that shifts and + + align:start position:0% +fixed image or when that shifts and + + + align:start position:0% +fixed image or when that shifts and +changes the visual and uh structural + + align:start position:0% +changes the visual and uh structural + + + align:start position:0% +changes the visual and uh structural +landcape is always Shifting the time of + + align:start position:0% +landcape is always Shifting the time of + + + align:start position:0% +landcape is always Shifting the time of +the performance + + align:start position:0% + + + + align:start position:0% + +so at this point we've um they through + + align:start position:0% +so at this point we've um they through + + + align:start position:0% +so at this point we've um they through +all four of our fixed presentations I + + align:start position:0% +all four of our fixed presentations I + + + align:start position:0% +all four of our fixed presentations I +think we have questions for each other + + align:start position:0% +think we have questions for each other + + + align:start position:0% +think we have questions for each other +and but I think you may have questions + + align:start position:0% +and but I think you may have questions + + + align:start position:0% +and but I think you may have questions +also in the audience so um it's very + + align:start position:0% +also in the audience so um it's very + + + align:start position:0% +also in the audience so um it's very +hard to see any hands from there so + + align:start position:0% +hard to see any hands from there so + + + align:start position:0% +hard to see any hands from there so +please if you have any please raise them + + align:start position:0% +please if you have any please raise them + + + align:start position:0% +please if you have any please raise them +very high but I want to take the + + align:start position:0% +very high but I want to take the + + + align:start position:0% +very high but I want to take the +prerogative of um of starting with a + + align:start position:0% +prerogative of um of starting with a + + + align:start position:0% +prerogative of um of starting with a +question to on my own and + + align:start position:0% +question to on my own and + + + align:start position:0% +question to on my own and +um one of the things that I was thinking + + align:start position:0% +um one of the things that I was thinking + + + align:start position:0% +um one of the things that I was thinking +about L when you were talking about your + + align:start position:0% +about L when you were talking about your + + + align:start position:0% +about L when you were talking about your +um + + align:start position:0% +um + + + align:start position:0% +um +pieces is one of the ways of of sort of + + align:start position:0% +pieces is one of the ways of of sort of + + + align:start position:0% +pieces is one of the ways of of sort of +creating a piece that has changed over + + align:start position:0% +creating a piece that has changed over + + + align:start position:0% +creating a piece that has changed over +the years in terms of commissions of + + align:start position:0% +the years in terms of commissions of + + + align:start position:0% +the years in terms of commissions of +pieces I'm thinking about when somebody + + align:start position:0% +pieces I'm thinking about when somebody + + + align:start position:0% +pieces I'm thinking about when somebody +requests a piece in the Renaissance the + + align:start position:0% +requests a piece in the Renaissance the + + + align:start position:0% +requests a piece in the Renaissance the +most important thing was are you going + + align:start position:0% +most important thing was are you going + + + align:start position:0% +most important thing was are you going +to put my name in the piece somewhere is + + align:start position:0% +to put my name in the piece somewhere is + + + align:start position:0% +to put my name in the piece somewhere is +this going to honor + + align:start position:0% +this going to honor + + + align:start position:0% +this going to honor +and later on in Mozart's time uh the + + align:start position:0% +and later on in Mozart's time uh the + + + align:start position:0% +and later on in Mozart's time uh the +commission may have said something about + + align:start position:0% +commission may have said something about + + + align:start position:0% +commission may have said something about +um is the Work Fit for this particular + + align:start position:0% +um is the Work Fit for this particular + + + align:start position:0% +um is the Work Fit for this particular +theater but now and you please correct + + align:start position:0% +theater but now and you please correct + + + align:start position:0% +theater but now and you please correct +me if I'm wrong the two most important + + align:start position:0% +me if I'm wrong the two most important + + + align:start position:0% +me if I'm wrong the two most important +things that specified in the commission + + align:start position:0% +things that specified in the commission + + + align:start position:0% +things that specified in the commission +are who's going to play or how many + + align:start position:0% +are who's going to play or how many + + + align:start position:0% +are who's going to play or how many +people and how long the piece is going + + align:start position:0% +people and how long the piece is going + + + align:start position:0% +people and how long the piece is going +to be so what is it like to compose in a + + align:start position:0% +to be so what is it like to compose in a + + + align:start position:0% +to be so what is it like to compose in a +day where even before you've written a + + align:start position:0% +day where even before you've written a + + + align:start position:0% +day where even before you've written a +single note you have anything you know + + align:start position:0% +single note you have anything you know + + + align:start position:0% +single note you have anything you know +when the piece has to + + align:start position:0% +when the piece has to + + + align:start position:0% +when the piece has to +end um that's um that is a truly + + align:start position:0% +end um that's um that is a truly + + + align:start position:0% +end um that's um that is a truly +profound question + + align:start position:0% +profound question + + + align:start position:0% +profound question +um I'll try to answer in a I'll try to + + align:start position:0% +um I'll try to answer in a I'll try to + + + align:start position:0% +um I'll try to answer in a I'll try to +answer + + align:start position:0% +answer + + + align:start position:0% +answer +briefly uh perceiving a length of time + + align:start position:0% +briefly uh perceiving a length of time + + + align:start position:0% +briefly uh perceiving a length of time +uh is part of a manufactured culture you + + align:start position:0% +uh is part of a manufactured culture you + + + align:start position:0% +uh is part of a manufactured culture you +know that we have to we have so many + + align:start position:0% +know that we have to we have so many + + + align:start position:0% +know that we have to we have so many +pieces on a concert and and there's this + + align:start position:0% +pieces on a concert and and there's this + + + align:start position:0% +pieces on a concert and and there's this +amount of time for your piece so for + + align:start position:0% +amount of time for your piece so for + + + align:start position:0% +amount of time for your piece so for +instance um uh an orchestra piece uh + + align:start position:0% +instance um uh an orchestra piece uh + + + align:start position:0% +instance um uh an orchestra piece uh +right now composers are are we we talk + + align:start position:0% +right now composers are are we we talk + + + align:start position:0% +right now composers are are we we talk +months each other and we say did did you + + align:start position:0% +months each other and we say did did you + + + align:start position:0% +months each other and we say did did you +get any more than 12 minutes that's + + align:start position:0% +get any more than 12 minutes that's + + + align:start position:0% +get any more than 12 minutes that's +that's the first thing we ask each other + + align:start position:0% +that's the first thing we ask each other + + + align:start position:0% +that's the first thing we ask each other +did you get any more than 12 minutes you + + align:start position:0% +did you get any more than 12 minutes you + + + align:start position:0% +did you get any more than 12 minutes you +know because that's what people are + + align:start position:0% +know because that's what people are + + + align:start position:0% +know because that's what people are +commissioning are 12 minute pieces what + + align:start position:0% +commissioning are 12 minute pieces what + + + align:start position:0% +commissioning are 12 minute pieces what +that means is that in developing the + + align:start position:0% +that means is that in developing the + + + align:start position:0% +that means is that in developing the +materials that will make the piece feel + + align:start position:0% +materials that will make the piece feel + + + align:start position:0% +materials that will make the piece feel +satisfactory uh uh + + align:start position:0% +satisfactory uh uh + + + align:start position:0% +satisfactory uh uh +uh one needs to consider um how to + + align:start position:0% +uh one needs to consider um how to + + + align:start position:0% +uh one needs to consider um how to +choose material + + align:start position:0% +choose material + + + align:start position:0% +choose material +um that that you can um manipulate and + + align:start position:0% +um that that you can um manipulate and + + + align:start position:0% +um that that you can um manipulate and +control uh in such a way that that + + align:start position:0% +control uh in such a way that that + + + align:start position:0% +control uh in such a way that that +putting them together feels satisfactory + + align:start position:0% +putting them together feels satisfactory + + + align:start position:0% +putting them together feels satisfactory +given the fact of in real time of 12 + + align:start position:0% +given the fact of in real time of 12 + + + align:start position:0% +given the fact of in real time of 12 +minutes so what I've been trying to do + + align:start position:0% +minutes so what I've been trying to do + + + align:start position:0% +minutes so what I've been trying to do +lately is to go + + align:start position:0% +lately is to go + + + align:start position:0% +lately is to go +deep um uh I started going deep when I + + align:start position:0% +deep um uh I started going deep when I + + + align:start position:0% +deep um uh I started going deep when I +was given a minute and a half to to + + align:start position:0% +was given a minute and a half to to + + + align:start position:0% +was given a minute and a half to to +write an an Ure for an orchestra of of + + align:start position:0% +write an an Ure for an orchestra of of + + + align:start position:0% +write an an Ure for an orchestra of of +110 pieces + + align:start position:0% +110 pieces + + + align:start position:0% +110 pieces +they it went a minute and a half no and + + align:start position:0% +they it went a minute and a half no and + + + align:start position:0% +they it went a minute and a half no and +I and I thought and I said to them I + + align:start position:0% +I and I thought and I said to them I + + + align:start position:0% +I and I thought and I said to them I +can't even get the sound moving in a + + align:start position:0% +can't even get the sound moving in a + + + align:start position:0% +can't even get the sound moving in a +minute and a half but but they said no + + align:start position:0% +minute and a half but but they said no + + + align:start position:0% +minute and a half but but they said no +that's all we've got is a minute and a + + align:start position:0% +that's all we've got is a minute and a + + + align:start position:0% +that's all we've got is a minute and a +half and I wanted I wanted to take the + + align:start position:0% +half and I wanted I wanted to take the + + + align:start position:0% +half and I wanted I wanted to take the +challenge and so what happens of course + + align:start position:0% +challenge and so what happens of course + + + align:start position:0% +challenge and so what happens of course +is is that you you you begin to look for + + align:start position:0% +is is that you you you begin to look for + + + align:start position:0% +is is that you you you begin to look for +for recognizable forms um in uh uh forms + + align:start position:0% +for recognizable forms um in uh uh forms + + + align:start position:0% +for recognizable forms um in uh uh forms +that are recognizable in the culture at + + align:start position:0% +that are recognizable in the culture at + + + align:start position:0% +that are recognizable in the culture at +large for contemplating a large amount + + align:start position:0% +large for contemplating a large amount + + + align:start position:0% +large for contemplating a large amount +of material and in that case we have + + align:start position:0% +of material and in that case we have + + + align:start position:0% +of material and in that case we have +invented the + + align:start position:0% +invented the + + + align:start position:0% +invented the +collage you know which allows us a lot + + align:start position:0% +collage you know which allows us a lot + + + align:start position:0% +collage you know which allows us a lot +of different material um uh to work on + + align:start position:0% +of different material um uh to work on + + + align:start position:0% +of different material um uh to work on +and so um uh so sometime almost always + + align:start position:0% +and so um uh so sometime almost always + + + align:start position:0% +and so um uh so sometime almost always +the um the the commissioned time the + + align:start position:0% +the um the the commissioned time the + + + align:start position:0% +the um the the commissioned time the +length of the piece is a wish and you + + align:start position:0% +length of the piece is a wish and you + + + align:start position:0% +length of the piece is a wish and you +know and a goal um and um and so the + + align:start position:0% +know and a goal um and um and so the + + + align:start position:0% +know and a goal um and um and so the +hard work I I've learned that I I I + + align:start position:0% +hard work I I've learned that I I I + + + align:start position:0% +hard work I I've learned that I I I +think de much more deeply for a much + + align:start position:0% +think de much more deeply for a much + + + align:start position:0% +think de much more deeply for a much +longer time um in order to come out with + + align:start position:0% +longer time um in order to come out with + + + align:start position:0% +longer time um in order to come out with +a piece that feels somehow that is + + align:start position:0% +a piece that feels somehow that is + + + align:start position:0% +a piece that feels somehow that is +satisfying as a shape um and I usually + + align:start position:0% +satisfying as a shape um and I usually + + + align:start position:0% +satisfying as a shape um and I usually +find forms to realize the architecture + + align:start position:0% +find forms to realize the architecture + + + align:start position:0% +find forms to realize the architecture +not in Old musics but um in the the + + align:start position:0% +not in Old musics but um in the the + + + align:start position:0% +not in Old musics but um in the the +world that we live in like a freeway + + align:start position:0% +world that we live in like a freeway + + + align:start position:0% +world that we live in like a freeway +driving form is very useful uh and um + + align:start position:0% +driving form is very useful uh and um + + + align:start position:0% +driving form is very useful uh and um +manufactured form is is very useful and + + align:start position:0% +manufactured form is is very useful and + + + align:start position:0% +manufactured form is is very useful and +there are all kinds of forms that are + + align:start position:0% +there are all kinds of forms that are + + + align:start position:0% +there are all kinds of forms that are +useful to realize what we consider to be + + align:start position:0% +useful to realize what we consider to be + + + align:start position:0% +useful to realize what we consider to be +time you can either that or you duke it + + align:start position:0% +time you can either that or you duke it + + + align:start position:0% +time you can either that or you duke it +out with the commissioner you know one + + align:start position:0% +out with the commissioner you know one + + + align:start position:0% +out with the commissioner you know one +or the other + + align:start position:0% +or the other + + + align:start position:0% +or the other +questions from the audience um for us or + + align:start position:0% +questions from the audience um for us or + + + align:start position:0% +questions from the audience um for us or +for the players or even questions from + + align:start position:0% +for the players or even questions from + + + align:start position:0% +for the players or even questions from +the yes go sir please speak loudly um an + + align:start position:0% +the yes go sir please speak loudly um an + + + align:start position:0% +the yes go sir please speak loudly um an +observation uh I think in each of the + + align:start position:0% +observation uh I think in each of the + + + align:start position:0% +observation uh I think in each of the +three each of you three panelists uh you + + align:start position:0% +three each of you three panelists uh you + + + align:start position:0% +three each of you three panelists uh you +conveyed to me that things are more + + align:start position:0% +conveyed to me that things are more + + + align:start position:0% +conveyed to me that things are more +impermanent uh than I had thought + + align:start position:0% +impermanent uh than I had thought + + + align:start position:0% +impermanent uh than I had thought +starting with Sarah it's that the nature + + align:start position:0% +starting with Sarah it's that the nature + + + align:start position:0% +starting with Sarah it's that the nature +of a production is influenced by uh + + align:start position:0% +of a production is influenced by uh + + + align:start position:0% +of a production is influenced by uh +external uh contingencies uh in the case + + align:start position:0% +external uh contingencies uh in the case + + + align:start position:0% +external uh contingencies uh in the case +of liy Larson it's how you can convert + + align:start position:0% +of liy Larson it's how you can convert + + + align:start position:0% +of liy Larson it's how you can convert +something solid like a mountain into + + align:start position:0% +something solid like a mountain into + + + align:start position:0% +something solid like a mountain into +musical notes um and I think most eye + + align:start position:0% +musical notes um and I think most eye + + + align:start position:0% +musical notes um and I think most eye +opening was to see uh Professor Jeff's + + align:start position:0% +opening was to see uh Professor Jeff's + + + align:start position:0% +opening was to see uh Professor Jeff's +piece of me there and the remark that + + align:start position:0% +piece of me there and the remark that + + + align:start position:0% +piece of me there and the remark that +this old rock still has at a very small + + align:start position:0% +this old rock still has at a very small + + + align:start position:0% +this old rock still has at a very small +uh time frame + + align:start position:0% +uh time frame + + + align:start position:0% +uh time frame +still um + + align:start position:0% + + + + align:start position:0% + +activity um uh and that's something I + + align:start position:0% + + + + align:start position:0% + +Lear I have a + + align:start position:0% +Lear I have a + + + align:start position:0% +Lear I have a +question I'm very interested in how + + align:start position:0% +question I'm very interested in how + + + align:start position:0% +question I'm very interested in how +music makes it way to the audience + + align:start position:0% +music makes it way to the audience + + + align:start position:0% +music makes it way to the audience +particular things about what makes it + + align:start position:0% +particular things about what makes it + + + align:start position:0% +particular things about what makes it +popular audience music you said two + + align:start position:0% +popular audience music you said two + + + align:start position:0% +popular audience music you said two +things perfect my interest one said when + + align:start position:0% +things perfect my interest one said when + + + align:start position:0% +things perfect my interest one said when +you're writing it's not fashionable + + align:start position:0% +you're writing it's not fashionable + + + align:start position:0% +you're writing it's not fashionable +to the second thing that she said was + + align:start position:0% +to the second thing that she said was + + + align:start position:0% +to the second thing that she said was +trying to leave the audience with a deep + + align:start position:0% +trying to leave the audience with a deep + + + align:start position:0% +trying to leave the audience with a deep +impression and um I + + align:start position:0% +impression and um I + + + align:start position:0% +impression and um I +[Music] + + align:start position:0% + + + + align:start position:0% + +wasab + + align:start position:0% +wasab + + + align:start position:0% +wasab +WR for + + align:start position:0% + + + + align:start position:0% + +our you have any audience expectations + + align:start position:0% +our you have any audience expectations + + + align:start position:0% +our you have any audience expectations +imagine audience read could everyone + + align:start position:0% +imagine audience read could everyone + + + align:start position:0% +imagine audience read could everyone +hear the question about this uh + + align:start position:0% +hear the question about this uh + + + align:start position:0% +hear the question about this uh +dichotomy between accessibility and and + + align:start position:0% +dichotomy between accessibility and and + + + align:start position:0% +dichotomy between accessibility and and +reaching + + align:start position:0% +reaching + + + align:start position:0% +reaching +and yes I think you're your asking me to + + align:start position:0% +and yes I think you're your asking me to + + + align:start position:0% +and yes I think you're your asking me to +talk about walking the tight rope + + align:start position:0% +talk about walking the tight rope + + + align:start position:0% +talk about walking the tight rope +between the music that's in my head + + align:start position:0% +between the music that's in my head + + + align:start position:0% +between the music that's in my head +and and my my deep desire to communicate + + align:start position:0% +and and my my deep desire to communicate + + + align:start position:0% +and and my my deep desire to communicate +it I think that's what you're asking me + + align:start position:0% +it I think that's what you're asking me + + + align:start position:0% +it I think that's what you're asking me +about + + align:start position:0% + + + + align:start position:0% + +um uh and actually you are asking me the + + align:start position:0% +um uh and actually you are asking me the + + + align:start position:0% +um uh and actually you are asking me the +question that I deal with every day + + align:start position:0% +question that I deal with every day + + + align:start position:0% +question that I deal with every day +every hour of every day + + align:start position:0% +every hour of every day + + + align:start position:0% +every hour of every day +um + + align:start position:0% +um + + + align:start position:0% +um +uh uh I um uh I try I study in depth + + align:start position:0% +uh uh I um uh I try I study in depth + + + align:start position:0% +uh uh I um uh I try I study in depth +um + + align:start position:0% +um + + + align:start position:0% +um +perception uh and um how the human + + align:start position:0% +perception uh and um how the human + + + align:start position:0% +perception uh and um how the human +lately I've been working deeply in how + + align:start position:0% +lately I've been working deeply in how + + + align:start position:0% +lately I've been working deeply in how +the human brain perceives what we call + + align:start position:0% +the human brain perceives what we call + + + align:start position:0% +the human brain perceives what we call +music um and um uh I um I try to stay + + align:start position:0% +music um and um uh I um I try to stay + + + align:start position:0% +music um and um uh I um I try to stay +curious deeply curious about about how + + align:start position:0% +curious deeply curious about about how + + + align:start position:0% +curious deeply curious about about how +groups of human beings move together in + + align:start position:0% +groups of human beings move together in + + + align:start position:0% +groups of human beings move together in +time keep time together which seems to + + align:start position:0% +time keep time together which seems to + + + align:start position:0% +time keep time together which seems to +be um uh a universal across Millennia + + align:start position:0% +be um uh a universal across Millennia + + + align:start position:0% +be um uh a universal across Millennia +that human beings keep time together um + + align:start position:0% +that human beings keep time together um + + + align:start position:0% +that human beings keep time together um +and I study that and I study uh uh + + align:start position:0% +and I study that and I study uh uh + + + align:start position:0% +and I study that and I study uh uh +language uh the inflection of language + + align:start position:0% +language uh the inflection of language + + + align:start position:0% +language uh the inflection of language +and the pulse behind language uh in + + align:start position:0% +and the pulse behind language uh in + + + align:start position:0% +and the pulse behind language uh in +depth we keep books and books and books + + align:start position:0% +depth we keep books and books and books + + + align:start position:0% +depth we keep books and books and books +of rhythmic dictation of people speaking + + align:start position:0% +of rhythmic dictation of people speaking + + + align:start position:0% +of rhythmic dictation of people speaking +to try to understand what the pulses + + align:start position:0% +to try to understand what the pulses + + + align:start position:0% +to try to understand what the pulses +which is rarely what we use as musical + + align:start position:0% +which is rarely what we use as musical + + + align:start position:0% +which is rarely what we use as musical +pulse um and um and so I um I believe + + align:start position:0% +pulse um and um and so I um I believe + + + align:start position:0% +pulse um and um and so I um I believe +that cultures evolve the music they need + + align:start position:0% +that cultures evolve the music they need + + + align:start position:0% +that cultures evolve the music they need +in order to study themselves through the + + align:start position:0% +in order to study themselves through the + + + align:start position:0% +in order to study themselves through the +language of Music whatever that is um + + align:start position:0% +language of Music whatever that is um + + + align:start position:0% +language of Music whatever that is um +and and what I deal with this is the + + align:start position:0% +and and what I deal with this is the + + + align:start position:0% +and and what I deal with this is the +comment about how it's not fashionable + + align:start position:0% +comment about how it's not fashionable + + + align:start position:0% +comment about how it's not fashionable +to repeat um it is really among among + + align:start position:0% +to repeat um it is really among among + + + align:start position:0% +to repeat um it is really among among +composers uh uh of abstract music it is + + align:start position:0% +composers uh uh of abstract music it is + + + align:start position:0% +composers uh uh of abstract music it is +really not fashionable to repeat unless + + align:start position:0% +really not fashionable to repeat unless + + + align:start position:0% +really not fashionable to repeat unless +it's in the minimalist way you know um + + align:start position:0% +it's in the minimalist way you know um + + + align:start position:0% +it's in the minimalist way you know um +and I and I've always and I thought the + + align:start position:0% +and I and I've always and I thought the + + + align:start position:0% +and I and I've always and I thought the +Western interpretation of minimalism has + + align:start position:0% +Western interpretation of minimalism has + + + align:start position:0% +Western interpretation of minimalism has +to be through the lens of manufacturing + + align:start position:0% +to be through the lens of manufacturing + + + align:start position:0% +to be through the lens of manufacturing +not hand human you know to manufactur um + + align:start position:0% +not hand human you know to manufactur um + + + align:start position:0% +not hand human you know to manufactur um +but the repetition of large + + align:start position:0% +but the repetition of large + + + align:start position:0% +but the repetition of large +chunks you know um is not fashionable in + + align:start position:0% +chunks you know um is not fashionable in + + + align:start position:0% +chunks you know um is not fashionable in +our culture it may not be necessary in + + align:start position:0% +our culture it may not be necessary in + + + align:start position:0% +our culture it may not be necessary in +our culture when we're considering the + + align:start position:0% +our culture when we're considering the + + + align:start position:0% +our culture when we're considering the +objects of the daily life but I found + + align:start position:0% +objects of the daily life but I found + + + align:start position:0% +objects of the daily life but I found +that it's that it's essential when we're + + align:start position:0% +that it's that it's essential when we're + + + align:start position:0% +that it's that it's essential when we're +considering larger + + align:start position:0% +considering larger + + + align:start position:0% +considering larger +questions you know larger questions um + + align:start position:0% +questions you know larger questions um + + + align:start position:0% +questions you know larger questions um +and um and so so I I deal every day with + + align:start position:0% +and um and so so I I deal every day with + + + align:start position:0% +and um and so so I I deal every day with +how far can I take it you know and if it + + align:start position:0% +how far can I take it you know and if it + + + align:start position:0% +how far can I take it you know and if it +begins to feel uh if the repetition + + align:start position:0% +begins to feel uh if the repetition + + + align:start position:0% +begins to feel uh if the repetition +begins to + + align:start position:0% +begins to + + + align:start position:0% +begins to +feel I don't know how to put this begins + + align:start position:0% +feel I don't know how to put this begins + + + align:start position:0% +feel I don't know how to put this begins +to feel on the + + align:start position:0% +to feel on the + + + align:start position:0% +to feel on the +surface um then I run away you know and + + align:start position:0% +surface um then I run away you know and + + + align:start position:0% +surface um then I run away you know and +um does that make sense to you + + align:start position:0% +um does that make sense to you + + + align:start position:0% +um does that make sense to you +repetition in our culture I I believe um + + align:start position:0% +repetition in our culture I I believe um + + + align:start position:0% +repetition in our culture I I believe um +is is is a deep philosophical issue that + + align:start position:0% +is is is a deep philosophical issue that + + + align:start position:0% +is is is a deep philosophical issue that +we're not dealing with as a culture is + + align:start position:0% +we're not dealing with as a culture is + + + align:start position:0% +we're not dealing with as a culture is +why do we + + align:start position:0% + + + + align:start position:0% + +repeat at the very beginning of your + + align:start position:0% +repeat at the very beginning of your + + + align:start position:0% +repeat at the very beginning of your +presentation you sort of referred to + + align:start position:0% +presentation you sort of referred to + + + align:start position:0% +presentation you sort of referred to +this a piece of music has a beginning + + align:start position:0% +this a piece of music has a beginning + + + align:start position:0% +this a piece of music has a beginning +point and an end point any point along + + align:start position:0% +point and an end point any point along + + + align:start position:0% +point and an end point any point along +that trajectory though you have all the + + align:start position:0% +that trajectory though you have all the + + + align:start position:0% +that trajectory though you have all the +information that you've got from what + + align:start position:0% +information that you've got from what + + + align:start position:0% +information that you've got from what +just from what's just been played + + align:start position:0% +just from what's just been played + + + align:start position:0% +just from what's just been played +and what you expect in the + + align:start position:0% +and what you expect in the + + + align:start position:0% +and what you expect in the +future and it seems to me that what's + + align:start position:0% +future and it seems to me that what's + + + align:start position:0% +future and it seems to me that what's +informing how you're where you are at + + align:start position:0% +informing how you're where you are at + + + align:start position:0% +informing how you're where you are at +that point has to do with our sense of + + align:start position:0% +that point has to do with our sense of + + + align:start position:0% +that point has to do with our sense of +grammar and + + align:start position:0% +grammar and + + + align:start position:0% +grammar and +pattern and I'm curious how that works + + align:start position:0% +pattern and I'm curious how that works + + + align:start position:0% +pattern and I'm curious how that works +when you are sort of pushing the + + align:start position:0% +when you are sort of pushing the + + + align:start position:0% +when you are sort of pushing the +envelope so neither what you've heard is + + align:start position:0% +envelope so neither what you've heard is + + + align:start position:0% +envelope so neither what you've heard is +entirely familiar to you and what comes + + align:start position:0% +entirely familiar to you and what comes + + + align:start position:0% +entirely familiar to you and what comes +next is + + align:start position:0% +next is + + + align:start position:0% +next is +going to be a + + align:start position:0% + + + + align:start position:0% + +surprise yes so the question is how what + + align:start position:0% +surprise yes so the question is how what + + + align:start position:0% +surprise yes so the question is how what +happens at the envelope at the border + + align:start position:0% +happens at the envelope at the border + + + align:start position:0% +happens at the envelope at the border +between um between musical elements that + + align:start position:0% +between um between musical elements that + + + align:start position:0% +between um between musical elements that +are neither very predictable nor are + + align:start position:0% +are neither very predictable nor are + + + align:start position:0% +are neither very predictable nor are +they completely without expectation of + + align:start position:0% +they completely without expectation of + + + align:start position:0% +they completely without expectation of +what's going to happen next is that is + + align:start position:0% +what's going to happen next is that is + + + align:start position:0% +what's going to happen next is that is +that correct yeah I mean there's + + align:start position:0% +that correct yeah I mean there's + + + align:start position:0% +that correct yeah I mean there's +cultural I mean we we we think in + + align:start position:0% +cultural I mean we we we think in + + + align:start position:0% +cultural I mean we we we think in +grammar in a sense patterns and pattern + + align:start position:0% +grammar in a sense patterns and pattern + + + align:start position:0% +grammar in a sense patterns and pattern +completion and when you're sort of + + align:start position:0% +completion and when you're sort of + + + align:start position:0% +completion and when you're sort of +breaking that + + align:start position:0% +breaking that + + + align:start position:0% +breaking that +apart how do you how do you maintain a + + align:start position:0% +apart how do you how do you maintain a + + + align:start position:0% +apart how do you how do you maintain a +balance well I I'd like to hand this + + align:start position:0% +balance well I I'd like to hand this + + + align:start position:0% +balance well I I'd like to hand this +back uh um but I um I noticed in the + + align:start position:0% +back uh um but I um I noticed in the + + + align:start position:0% +back uh um but I um I noticed in the +rebel right away you know um first of + + align:start position:0% +rebel right away you know um first of + + + align:start position:0% +rebel right away you know um first of +all looking at the score I + + align:start position:0% +all looking at the score I + + + align:start position:0% +all looking at the score I +thought know because that he he had one + + align:start position:0% +thought know because that he he had one + + + align:start position:0% +thought know because that he he had one +rhythmic gesture in one measure and then + + align:start position:0% +rhythmic gesture in one measure and then + + + align:start position:0% +rhythmic gesture in one measure and then +another and another and then a pattern + + align:start position:0% +another and another and then a pattern + + + align:start position:0% +another and another and then a pattern +of every other measure uh and yet um uh + + align:start position:0% +of every other measure uh and yet um uh + + + align:start position:0% +of every other measure uh and yet um uh +what what was making it feel elongated + + align:start position:0% +what what was making it feel elongated + + + align:start position:0% +what what was making it feel elongated +to me was not time it was the variation + + align:start position:0% +to me was not time it was the variation + + + align:start position:0% +to me was not time it was the variation +of pitch interesting yeah that was + + align:start position:0% +of pitch interesting yeah that was + + + align:start position:0% +of pitch interesting yeah that was +making it feel longer just the placement + + align:start position:0% +making it feel longer just the placement + + + align:start position:0% +making it feel longer just the placement +of certain pitches but I'd like to hand + + align:start position:0% +of certain pitches but I'd like to hand + + + align:start position:0% +of certain pitches but I'd like to hand +it back to you to talk about actually I + + align:start position:0% +it back to you to talk about actually I + + + align:start position:0% +it back to you to talk about actually I +was well I one of the things that I + + align:start position:0% +was well I one of the things that I + + + align:start position:0% +was well I one of the things that I +think has been very interesting as a + + align:start position:0% +think has been very interesting as a + + + align:start position:0% +think has been very interesting as a +phenomenon um in other forms of of + + align:start position:0% +phenomenon um in other forms of of + + + align:start position:0% +phenomenon um in other forms of of +contemporary of of recent music is this + + align:start position:0% +contemporary of of recent music is this + + + align:start position:0% +contemporary of of recent music is this +idea that you have in a certain musical + + align:start position:0% +idea that you have in a certain musical + + + align:start position:0% +idea that you have in a certain musical +style serialism where everything is + + align:start position:0% +style serialism where everything is + + + align:start position:0% +style serialism where everything is +predetermined and if you could if you + + align:start position:0% +predetermined and if you could if you + + + align:start position:0% +predetermined and if you could if you +had the ear to hear everything in a + + align:start position:0% +had the ear to hear everything in a + + + align:start position:0% +had the ear to hear everything in a +piece you would know exactly what's + + align:start position:0% +piece you would know exactly what's + + + align:start position:0% +piece you would know exactly what's +happen what's going to happen next so + + align:start position:0% +happen what's going to happen next so + + + align:start position:0% +happen what's going to happen next so +you have a piece of music with a perfect + + align:start position:0% +you have a piece of music with a perfect + + + align:start position:0% +you have a piece of music with a perfect +all the information all the grammar of + + align:start position:0% +all the information all the grammar of + + + align:start position:0% +all the information all the grammar of +the music is right there and you know + + align:start position:0% +the music is right there and you know + + + align:start position:0% +the music is right there and you know +what the next note is in + + align:start position:0% +what the next note is in + + + align:start position:0% +what the next note is in +theory and then you have a music of pure + + align:start position:0% +theory and then you have a music of pure + + + align:start position:0% +theory and then you have a music of pure +chance of John Cage alator composition + + align:start position:0% +chance of John Cage alator composition + + + align:start position:0% +chance of John Cage alator composition +where all of the elements are completely + + align:start position:0% +where all of the elements are completely + + + align:start position:0% +where all of the elements are completely +random they're completely non-determined + + align:start position:0% +random they're completely non-determined + + + align:start position:0% +random they're completely non-determined +you don't know what's going to happen + + align:start position:0% +you don't know what's going to happen + + + align:start position:0% +you don't know what's going to happen +next and yet perceptually many people + + align:start position:0% +next and yet perceptually many people + + + align:start position:0% +next and yet perceptually many people +find these two phenomenon at the either + + align:start position:0% +find these two phenomenon at the either + + + align:start position:0% +find these two phenomenon at the either +extreme of the grammar of the + + align:start position:0% +extreme of the grammar of the + + + align:start position:0% +extreme of the grammar of the +information to be very perceptually + + align:start position:0% +information to be very perceptually + + + align:start position:0% +information to be very perceptually +similar so I think that there there + + align:start position:0% +similar so I think that there there + + + align:start position:0% +similar so I think that there there +might be something to get out of this + + align:start position:0% +might be something to get out of this + + + align:start position:0% +might be something to get out of this +that that there's just like the way the + + align:start position:0% +that that there's just like the way the + + + align:start position:0% +that that there's just like the way the +light the events of our life takes place + + align:start position:0% +light the events of our life takes place + + + align:start position:0% +light the events of our life takes place +in a very small amount of time on this + + align:start position:0% +in a very small amount of time on this + + + align:start position:0% +in a very small amount of time on this +giant scale the the amounts of the parts + + align:start position:0% +giant scale the the amounts of the parts + + + align:start position:0% +giant scale the the amounts of the parts +of music that are that we form some sort + + align:start position:0% +of music that are that we form some sort + + + align:start position:0% +of music that are that we form some sort +of expectation about what's going to + + align:start position:0% +of expectation about what's going to + + + align:start position:0% +of expectation about what's going to +happen next but it's not obvious is also + + align:start position:0% +happen next but it's not obvious is also + + + align:start position:0% +happen next but it's not obvious is also +a very + + align:start position:0% +a very + + + align:start position:0% +a very +small amount of the possibilities in mus + + align:start position:0% +small amount of the possibilities in mus + + + align:start position:0% +small amount of the possibilities in mus +yes because it's infinite is infinite + + align:start position:0% +yes because it's infinite is infinite + + + align:start position:0% +yes because it's infinite is infinite +the same thing in in theater yes + + align:start position:0% +the same thing in in theater yes + + + align:start position:0% +the same thing in in theater yes +absolutely + + align:start position:0% +absolutely + + + align:start position:0% +absolutely +absolutely well and I was thinking too + + align:start position:0% +absolutely well and I was thinking too + + + align:start position:0% +absolutely well and I was thinking too +you know I'm thinking deeply about your + + align:start position:0% +you know I'm thinking deeply about your + + + align:start position:0% +you know I'm thinking deeply about your +presentation um and I was + + align:start position:0% +presentation um and I was + + + align:start position:0% +presentation um and I was +thinking + + align:start position:0% +thinking + + + align:start position:0% +thinking +part here's a here's an idea about what + + align:start position:0% +part here's a here's an idea about what + + + align:start position:0% +part here's a here's an idea about what +what you're talking about that as a + + align:start position:0% +what you're talking about that as a + + + align:start position:0% +what you're talking about that as a +culture we have this whole universe of + + align:start position:0% +culture we have this whole universe of + + + align:start position:0% +culture we have this whole universe of +sound know that is real to us it's + + align:start position:0% +sound know that is real to us it's + + + align:start position:0% +sound know that is real to us it's +working on our bodies and our nervous + + align:start position:0% +working on our bodies and our nervous + + + align:start position:0% +working on our bodies and our nervous +systems and our emotional systems all + + align:start position:0% +systems and our emotional systems all + + + align:start position:0% +systems and our emotional systems all +the time you know and over an amount of + + align:start position:0% +the time you know and over an amount of + + + align:start position:0% +the time you know and over an amount of +time maybe 300 years 400 years uh um and + + align:start position:0% +time maybe 300 years 400 years uh um and + + + align:start position:0% +time maybe 300 years 400 years uh um and +yet if you go + + align:start position:0% +yet if you go + + + align:start position:0% +yet if you go +take a perspective and step way way way + + align:start position:0% +take a perspective and step way way way + + + align:start position:0% +take a perspective and step way way way +way way away from the Sonic World in + + align:start position:0% +way way away from the Sonic World in + + + align:start position:0% +way way away from the Sonic World in +which we live it's a very small + + align:start position:0% +which we live it's a very small + + + align:start position:0% +which we live it's a very small +interaction it does that make sense to + + align:start position:0% +interaction it does that make sense to + + + align:start position:0% +interaction it does that make sense to +you so there actually is nothing new we + + align:start position:0% +you so there actually is nothing new we + + + align:start position:0% +you so there actually is nothing new we +can do sonically not uh uh I I think + + align:start position:0% +can do sonically not uh uh I I think + + + align:start position:0% +can do sonically not uh uh I I think +there's nothing we can do sonically I + + align:start position:0% +there's nothing we can do sonically I + + + align:start position:0% +there's nothing we can do sonically I +think there's infinite possibilities + + align:start position:0% +think there's infinite possibilities + + + align:start position:0% +think there's infinite possibilities +musically if that makes sense and I + + align:start position:0% +musically if that makes sense and I + + + align:start position:0% +musically if that makes sense and I +think it relates to what you're talking + + align:start position:0% +think it relates to what you're talking + + + align:start position:0% +think it relates to what you're talking +about am I even close am I scooting + + align:start position:0% +about am I even close am I scooting + + + align:start position:0% +about am I even close am I scooting +around the edges I think think + + align:start position:0% +around the edges I think think + + + align:start position:0% +around the edges I think think +so I I could just offer one comment from + + align:start position:0% +so I I could just offer one comment from + + + align:start position:0% +so I I could just offer one comment from +the uh to your question about + + align:start position:0% +the uh to your question about + + + align:start position:0% +the uh to your question about +anticipating the future based on the + + align:start position:0% +anticipating the future based on the + + + align:start position:0% +anticipating the future based on the +past and music and that is that from the + + align:start position:0% +past and music and that is that from the + + + align:start position:0% +past and music and that is that from the +perspective of time and physics that in + + align:start position:0% +perspective of time and physics that in + + + align:start position:0% +perspective of time and physics that in +the + + align:start position:0% +the + + + align:start position:0% +the +enlightenment the attitude toward + + align:start position:0% +enlightenment the attitude toward + + + align:start position:0% +enlightenment the attitude toward +frequency in physics was extremely + + align:start position:0% +frequency in physics was extremely + + + align:start position:0% +frequency in physics was extremely +regular and everything was imagined to + + align:start position:0% +regular and everything was imagined to + + + align:start position:0% +regular and everything was imagined to +be Clockwork and predictable and then + + align:start position:0% +be Clockwork and predictable and then + + + align:start position:0% +be Clockwork and predictable and then +when quantum mechanics became the Vogue + + align:start position:0% +when quantum mechanics became the Vogue + + + align:start position:0% +when quantum mechanics became the Vogue +people I think took this idea that + + align:start position:0% +people I think took this idea that + + + align:start position:0% +people I think took this idea that +everything was undetermined and maybe + + align:start position:0% +everything was undetermined and maybe + + + align:start position:0% +everything was undetermined and maybe +John Cage the quantum mechanics modern + + align:start position:0% +John Cage the quantum mechanics modern + + + align:start position:0% +John Cage the quantum mechanics modern +music but I think that this is the + + align:start position:0% +music but I think that this is the + + + align:start position:0% +music but I think that this is the +subtle point which is that those + + align:start position:0% +subtle point which is that those + + + align:start position:0% +subtle point which is that those +fluctuations although there's a random + + align:start position:0% +fluctuations although there's a random + + + align:start position:0% +fluctuations although there's a random +component to them they're highly ordered + + align:start position:0% +component to them they're highly ordered + + + align:start position:0% +component to them they're highly ordered +in time that there's a there's an + + align:start position:0% +in time that there's a there's an + + + align:start position:0% +in time that there's a there's an +impressive frequency structure on the + + align:start position:0% +impressive frequency structure on the + + + align:start position:0% +impressive frequency structure on the +randomness so it's a it's a very + + align:start position:0% +randomness so it's a it's a very + + + align:start position:0% +randomness so it's a it's a very +delicate quantum mechanics is not random + + align:start position:0% +delicate quantum mechanics is not random + + + align:start position:0% +delicate quantum mechanics is not random +it has very definite frequencies and + + align:start position:0% +it has very definite frequencies and + + + align:start position:0% +it has very definite frequencies and +repetitions associated with it so that + + align:start position:0% +repetitions associated with it so that + + + align:start position:0% +repetitions associated with it so that +it's somewhere between those two + + align:start position:0% +it's somewhere between those two + + + align:start position:0% +it's somewhere between those two +extremes of unpredictable Clockwork + + align:start position:0% + + + + align:start position:0% + +thank you um there is also at work the + + align:start position:0% +thank you um there is also at work the + + + align:start position:0% +thank you um there is also at work the +idea that music to be music must be + + align:start position:0% + + + + align:start position:0% + +heard you know it's a very narrow + + align:start position:0% +heard you know it's a very narrow + + + align:start position:0% +heard you know it's a very narrow +definition of music that music to be + + align:start position:0% +definition of music that music to be + + + align:start position:0% +definition of music that music to be +music must be heard and so it's possible + + align:start position:0% +music must be heard and so it's possible + + + align:start position:0% +music must be heard and so it's possible +that as you are listening to music in + + align:start position:0% +that as you are listening to music in + + + align:start position:0% +that as you are listening to music in +this room that you're also listening to + + align:start position:0% +this room that you're also listening to + + + align:start position:0% +this room that you're also listening to +an infinite number of + + align:start position:0% +an infinite number of + + + align:start position:0% +an infinite number of +musics that have embedded themselves in + + align:start position:0% +musics that have embedded themselves in + + + align:start position:0% +musics that have embedded themselves in +you uh uh and and I I'm only saying that + + align:start position:0% +you uh uh and and I I'm only saying that + + + align:start position:0% +you uh uh and and I I'm only saying that +because I realize I work with that that + + align:start position:0% +because I realize I work with that that + + + align:start position:0% +because I realize I work with that that +idea all all the time I know that you + + align:start position:0% +idea all all the time I know that you + + + align:start position:0% +idea all all the time I know that you +know da da + + align:start position:0% +know da da + + + align:start position:0% +know da da +da you know in an infinite number of + + align:start position:0% +da you know in an infinite number of + + + align:start position:0% +da you know in an infinite number of +embedded pieces in your mind and so so + + align:start position:0% +embedded pieces in your mind and so so + + + align:start position:0% +embedded pieces in your mind and so so +this notion that music must be heard to + + align:start position:0% +this notion that music must be heard to + + + align:start position:0% +this notion that music must be heard to +be music uh is uh is really fascinating + + align:start position:0% +be music uh is uh is really fascinating + + + align:start position:0% +be music uh is uh is really fascinating +to me um since you don't need to hear it + + align:start position:0% +to me um since you don't need to hear it + + + align:start position:0% +to me um since you don't need to hear it +for it to be + + align:start position:0% +for it to be + + + align:start position:0% +for it to be +music so Bob I was trying to your um + + align:start position:0% +music so Bob I was trying to your um + + + align:start position:0% +music so Bob I was trying to your um +notion of certain things happening at + + align:start position:0% +notion of certain things happening at + + + align:start position:0% +notion of certain things happening at +the scale of 10 to the 39 beats um in my + + align:start position:0% +the scale of 10 to the 39 beats um in my + + + align:start position:0% +the scale of 10 to the 39 beats um in my +and I was trying to manipulate this into + + align:start position:0% +and I was trying to manipulate this into + + + align:start position:0% +and I was trying to manipulate this into +something that that I could grasp and + + align:start position:0% +something that that I could grasp and + + + align:start position:0% +something that that I could grasp and +the only thing I could come up with was + + align:start position:0% +the only thing I could come up with was + + + align:start position:0% +the only thing I could come up with was +U that's about the number of beats in 10 + + align:start position:0% +U that's about the number of beats in 10 + + + align:start position:0% +U that's about the number of beats in 10 +to the 33rd ring cycles and that U that + + align:start position:0% +to the 33rd ring cycles and that U that + + + align:start position:0% +to the 33rd ring cycles and that U that +still didn't help me very much but it + + align:start position:0% +still didn't help me very much but it + + + align:start position:0% +still didn't help me very much but it +did it did get me thinking about um when + + align:start position:0% +did it did get me thinking about um when + + + align:start position:0% +did it did get me thinking about um when +you're talking about you you've given a + + align:start position:0% +you're talking about you you've given a + + + align:start position:0% +you're talking about you you've given a +scale of time that's much bigger than + + align:start position:0% +scale of time that's much bigger than + + + align:start position:0% +scale of time that's much bigger than +the scale of time that I gave with music + + align:start position:0% +the scale of time that I gave with music + + + align:start position:0% +the scale of time that I gave with music +which is already much bigger than the + + align:start position:0% +which is already much bigger than the + + + align:start position:0% +which is already much bigger than the +scales of times that that we uh hear in + + align:start position:0% +scales of times that that we uh hear in + + + align:start position:0% +scales of times that that we uh hear in +most musical + + align:start position:0% +most musical + + + align:start position:0% +most musical +pieces are what do you think that are + + align:start position:0% +pieces are what do you think that are + + + align:start position:0% +pieces are what do you think that are +there scales of time even beyond what + + align:start position:0% +there scales of time even beyond what + + + align:start position:0% +there scales of time even beyond what +you have been talking about that are + + align:start position:0% +you have been talking about that are + + + align:start position:0% +you have been talking about that are +much much smaller even than 10 to the4 + + align:start position:0% +much much smaller even than 10 to the4 + + + align:start position:0% +much much smaller even than 10 to the4 +or or much bigger than 10 to the 20th + + align:start position:0% +or or much bigger than 10 to the 20th + + + align:start position:0% +or or much bigger than 10 to the 20th +billion years that we just have no way + + align:start position:0% +billion years that we just have no way + + + align:start position:0% +billion years that we just have no way +of knowing about + + align:start position:0% +of knowing about + + + align:start position:0% +of knowing about +it well um first of all I think we poor + + align:start position:0% +it well um first of all I think we poor + + + align:start position:0% +it well um first of all I think we poor +creatures that tap in the dark I mean we + + align:start position:0% +creatures that tap in the dark I mean we + + + align:start position:0% +creatures that tap in the dark I mean we +live in a very narrow world with respect + + align:start position:0% +live in a very narrow world with respect + + + align:start position:0% +live in a very narrow world with respect +to the the things we've been able to + + align:start position:0% +to the the things we've been able to + + + align:start position:0% +to the the things we've been able to +probe with really incredibly + + align:start position:0% +probe with really incredibly + + + align:start position:0% +probe with really incredibly +sophisticated instruments in science so + + align:start position:0% +sophisticated instruments in science so + + + align:start position:0% +sophisticated instruments in science so +these things are out at the edges of our + + align:start position:0% +these things are out at the edges of our + + + align:start position:0% +these things are out at the edges of our +perception and we don't perceive them + + align:start position:0% +perception and we don't perceive them + + + align:start position:0% +perception and we don't perceive them +directly we perceive them only very + + align:start position:0% +directly we perceive them only very + + + align:start position:0% +directly we perceive them only very +indirectly like the Hubble telescope + + align:start position:0% +indirectly like the Hubble telescope + + + align:start position:0% +indirectly like the Hubble telescope +enables us to perceive some very distant + + align:start position:0% +enables us to perceive some very distant + + + align:start position:0% +enables us to perceive some very distant +Galaxy + + align:start position:0% +Galaxy + + + align:start position:0% +Galaxy +um my my colleagues get paved to + + align:start position:0% +um my my colleagues get paved to + + + align:start position:0% +um my my colleagues get paved to +speculate so they write papers about any + + align:start position:0% +speculate so they write papers about any + + + align:start position:0% +speculate so they write papers about any +time scale it's almost like a commission + + align:start position:0% +time scale it's almost like a commission + + + align:start position:0% +time scale it's almost like a commission +you know without the 12 minute + + align:start position:0% +you know without the 12 minute + + + align:start position:0% +you know without the 12 minute +limit you can find a paper in + + align:start position:0% +limit you can find a paper in + + + align:start position:0% +limit you can find a paper in +theoretical physics and will speculate + + align:start position:0% +theoretical physics and will speculate + + + align:start position:0% +theoretical physics and will speculate +about time scales that are string theory + + align:start position:0% +about time scales that are string theory + + + align:start position:0% +about time scales that are string theory +is the catch word for this that plank + + align:start position:0% +is the catch word for this that plank + + + align:start position:0% +is the catch word for this that plank +time is 10 to the minus 41 seconds and + + align:start position:0% +time is 10 to the minus 41 seconds and + + + align:start position:0% +time is 10 to the minus 41 seconds and +that's the time the minimum time scale + + align:start position:0% +that's the time the minimum time scale + + + align:start position:0% +that's the time the minimum time scale +that we know how to define in the + + align:start position:0% +that we know how to define in the + + + align:start position:0% +that we know how to define in the +structure of modern theoretical physics + + align:start position:0% +structure of modern theoretical physics + + + align:start position:0% +structure of modern theoretical physics +and it's not a time scale that people + + align:start position:0% +and it's not a time scale that people + + + align:start position:0% +and it's not a time scale that people +make up out of nothing it's time time + + align:start position:0% +make up out of nothing it's time time + + + align:start position:0% +make up out of nothing it's time time +that if you combine the constants that + + align:start position:0% +that if you combine the constants that + + + align:start position:0% +that if you combine the constants that +Define quantum mechanics relativity and + + align:start position:0% +Define quantum mechanics relativity and + + + align:start position:0% +Define quantum mechanics relativity and +gravity and just do high school algebra + + align:start position:0% +gravity and just do high school algebra + + + align:start position:0% +gravity and just do high school algebra +out pops this time so that's the time + + align:start position:0% +out pops this time so that's the time + + + align:start position:0% +out pops this time so that's the time +scale where gravity has relative stick + + align:start position:0% +scale where gravity has relative stick + + + align:start position:0% +scale where gravity has relative stick +Quantum + + align:start position:0% +Quantum + + + align:start position:0% +Quantum +effects so yes they're very + + align:start position:0% + + + + align:start position:0% + +low if everyone of the oldest rock in + + align:start position:0% +low if everyone of the oldest rock in + + + align:start position:0% +low if everyone of the oldest rock in +the world their + + align:start position:0% + + + + align:start position:0% + +Rock how + + align:start position:0% +Rock how + + + align:start position:0% +Rock how +Professor L um first of all I could have + + align:start position:0% +Professor L um first of all I could have + + + align:start position:0% +Professor L um first of all I could have +been faking right this could be I could + + align:start position:0% +been faking right this could be I could + + + align:start position:0% +been faking right this could be I could +have picked this up off of it's a very + + align:start position:0% +have picked this up off of it's a very + + + align:start position:0% +have picked this up off of it's a very +ordinary Rock and + + align:start position:0% +ordinary Rock and + + + align:start position:0% +ordinary Rock and +um I I I know rocks were destroyed in + + align:start position:0% +um I I I know rocks were destroyed in + + + align:start position:0% +um I I I know rocks were destroyed in +the making of + + align:start position:0% +the making of + + + align:start position:0% +the making of +this this was um this was brought back + + align:start position:0% +this this was um this was brought back + + + align:start position:0% +this this was um this was brought back +from an expedition up there by m geology + + align:start position:0% +from an expedition up there by m geology + + + align:start position:0% +from an expedition up there by m geology +group and uh they were kind enough to + + align:start position:0% +group and uh they were kind enough to + + + align:start position:0% +group and uh they were kind enough to +give me a chunk of it does that chunk + + align:start position:0% +give me a chunk of it does that chunk + + + align:start position:0% +give me a chunk of it does that chunk +have protons and neutrons that are + + align:start position:0% +have protons and neutrons that are + + + align:start position:0% +have protons and neutrons that are +moving exactly at the same Pace that our + + align:start position:0% +moving exactly at the same Pace that our + + + align:start position:0% +moving exactly at the same Pace that our +bodies have protons and neutrons have + + align:start position:0% +bodies have protons and neutrons have + + + align:start position:0% +bodies have protons and neutrons have +neut in body you + + align:start position:0% + + + + align:start position:0% + +better um + + align:start position:0% +better um + + + align:start position:0% +better um +yeah one of the one of the really + + align:start position:0% +yeah one of the one of the really + + + align:start position:0% +yeah one of the one of the really +bizarre I was just writing about this in + + align:start position:0% +bizarre I was just writing about this in + + + align:start position:0% +bizarre I was just writing about this in +some other context that one of the real + + align:start position:0% +some other context that one of the real + + + align:start position:0% +some other context that one of the real +miracles of modern Sciences we really + + align:start position:0% +miracles of modern Sciences we really + + + align:start position:0% +miracles of modern Sciences we really +understand that every proton in the + + align:start position:0% +understand that every proton in the + + + align:start position:0% +understand that every proton in the +universe is identical + + align:start position:0% +universe is identical + + + align:start position:0% +universe is identical +and every Neutron in the universe is + + align:start position:0% +and every Neutron in the universe is + + + align:start position:0% +and every Neutron in the universe is +identical so their their uh their + + align:start position:0% +identical so their their uh their + + + align:start position:0% +identical so their their uh their +motions and their Dynamics may depend on + + align:start position:0% +motions and their Dynamics may depend on + + + align:start position:0% +motions and their Dynamics may depend on +their local environment but there's + + align:start position:0% +their local environment but there's + + + align:start position:0% +their local environment but there's +something about them which is deeply the + + align:start position:0% +something about them which is deeply the + + + align:start position:0% +something about them which is deeply the +same as every other one and we Now + + align:start position:0% +same as every other one and we Now + + + align:start position:0% +same as every other one and we Now +understand that we didn't for last so we + + align:start position:0% +understand that we didn't for last so we + + + align:start position:0% +understand that we didn't for last so we +we've talked a lot about distorting time + + align:start position:0% +we've talked a lot about distorting time + + + align:start position:0% +we've talked a lot about distorting time +about different perceptions of time I + + align:start position:0% +about different perceptions of time I + + + align:start position:0% +about different perceptions of time I +think that there's one piece of time + + align:start position:0% +think that there's one piece of time + + + align:start position:0% +think that there's one piece of time +that we would all like not to distort + + align:start position:0% +that we would all like not to distort + + + align:start position:0% +that we would all like not to distort +and that is dinner time so seeing the + + align:start position:0% +and that is dinner time so seeing the + + + align:start position:0% +and that is dinner time so seeing the +hour now i' think I'd like to thank the + + align:start position:0% +hour now i' think I'd like to thank the + + + align:start position:0% +hour now i' think I'd like to thank the +panelists who have joined us here and + + align:start position:0% +panelists who have joined us here and + + + align:start position:0% +panelists who have joined us here and +also all the musicians who + + align:start position:0% +also all the musicians who + + + align:start position:0% +also all the musicians who +[Applause] + + align:start position:0% + + + + align:start position:0% + +played e \ No newline at end of file diff --git a/j8hEnyOiwhw.txt b/j8hEnyOiwhw.txt new file mode 100644 index 0000000000000000000000000000000000000000..58d2cb1ac0e38625035efacb315d9e68399a580a --- /dev/null +++ b/j8hEnyOiwhw.txt @@ -0,0 +1,2091 @@ +align:start position:0% + +okay ready for part three of this vision + + align:start position:0% +okay ready for part three of this vision + + + align:start position:0% +okay ready for part three of this vision +of linear algebra so the key word in + + align:start position:0% +of linear algebra so the key word in + + + align:start position:0% +of linear algebra so the key word in +part three is orthogonal which again + + align:start position:0% +part three is orthogonal which again + + + align:start position:0% +part three is orthogonal which again +means perpendicular so we have + + align:start position:0% +means perpendicular so we have + + + align:start position:0% +means perpendicular so we have +perpendicular vectors we can imagine + + align:start position:0% +perpendicular vectors we can imagine + + + align:start position:0% +perpendicular vectors we can imagine +those we have something called + + align:start position:0% +those we have something called + + + align:start position:0% +those we have something called +orthogonal matrices that's when I've got + + align:start position:0% +orthogonal matrices that's when I've got + + + align:start position:0% +orthogonal matrices that's when I've got +one here orthogonal matrix is when we + + align:start position:0% +one here orthogonal matrix is when we + + + align:start position:0% +one here orthogonal matrix is when we +have these columns I I'm always going to + + align:start position:0% +have these columns I I'm always going to + + + align:start position:0% +have these columns I I'm always going to +use the letter Q for an orthogonal + + align:start position:0% +use the letter Q for an orthogonal + + + align:start position:0% +use the letter Q for an orthogonal +matrix and I look at its columns and + + align:start position:0% +matrix and I look at its columns and + + + align:start position:0% +matrix and I look at its columns and +every column is perpendicular to every + + align:start position:0% +every column is perpendicular to every + + + align:start position:0% +every column is perpendicular to every +other column so I have a so I just don't + + align:start position:0% +other column so I have a so I just don't + + + align:start position:0% +other column so I have a so I just don't +just have two perpendicular vectors + + align:start position:0% +just have two perpendicular vectors + + + align:start position:0% +just have two perpendicular vectors +going like this I have n of them because + + align:start position:0% +going like this I have n of them because + + + align:start position:0% +going like this I have n of them because +I'm in n dimensions and you just imagine + + align:start position:0% +I'm in n dimensions and you just imagine + + + align:start position:0% +I'm in n dimensions and you just imagine +XYZ axes or XYZ w axes go up to four D + + align:start position:0% +XYZ axes or XYZ w axes go up to four D + + + align:start position:0% +XYZ axes or XYZ w axes go up to four D +for relativity go up to eight D for + + align:start position:0% +for relativity go up to eight D for + + + align:start position:0% +for relativity go up to eight D for +spring theory eight dimensions + + align:start position:0% +spring theory eight dimensions + + + align:start position:0% +spring theory eight dimensions +oh we just have vectors after all it's + + align:start position:0% +oh we just have vectors after all it's + + + align:start position:0% +oh we just have vectors after all it's +just this row of numbers or a column of + + align:start position:0% +just this row of numbers or a column of + + + align:start position:0% +just this row of numbers or a column of +numbers and we can decide when when + + align:start position:0% +numbers and we can decide when when + + + align:start position:0% +numbers and we can decide when when +things are perpendicular by that test + + align:start position:0% +things are perpendicular by that test + + + align:start position:0% +things are perpendicular by that test +like say the test for Q 1 to be + + align:start position:0% +like say the test for Q 1 to be + + + align:start position:0% +like say the test for Q 1 to be +perpendicular to Q n is that row times + + align:start position:0% +perpendicular to Q n is that row times + + + align:start position:0% +perpendicular to Q n is that row times +that column when I say times I mean dot + + align:start position:0% +that column when I say times I mean dot + + + align:start position:0% +that column when I say times I mean dot +product multiplied every pair Q 1 + + align:start position:0% +product multiplied every pair Q 1 + + + align:start position:0% +product multiplied every pair Q 1 +transpose Q and gives that 0 up there so + + align:start position:0% +transpose Q and gives that 0 up there so + + + align:start position:0% +transpose Q and gives that 0 up there so +the columns are perpendicular and those + + align:start position:0% +the columns are perpendicular and those + + + align:start position:0% +the columns are perpendicular and those +matrices are the best to compute with + + align:start position:0% +matrices are the best to compute with + + + align:start position:0% +matrices are the best to compute with +and again they're called Q and one way + + align:start position:0% +and again they're called Q and one way + + + align:start position:0% +and again they're called Q and one way +to do a quick matrix way because there's + + align:start position:0% +to do a quick matrix way because there's + + + align:start position:0% +to do a quick matrix way because there's +always a matrix way to to explain + + align:start position:0% +always a matrix way to to explain + + + align:start position:0% +always a matrix way to to explain +something and you just you'll see how + + align:start position:0% +something and you just you'll see how + + + align:start position:0% +something and you just you'll see how +quick it is here this business of having + + align:start position:0% +quick it is here this business of having + + + align:start position:0% +quick it is here this business of having +columns that are perpendicular to each + + align:start position:0% +columns that are perpendicular to each + + + align:start position:0% +columns that are perpendicular to each +other and actually I'm gonna make those + + align:start position:0% +other and actually I'm gonna make those + + + align:start position:0% +other and actually I'm gonna make those +lengths of all those column vectors all + + align:start position:0% +lengths of all those column vectors all + + + align:start position:0% +lengths of all those column vectors all +one just to sort of normalize it then + + align:start position:0% +one just to sort of normalize it then + + + align:start position:0% +one just to sort of normalize it then +Express all that's expressed by if I + + align:start position:0% +Express all that's expressed by if I + + + align:start position:0% +Express all that's expressed by if I +multiply Q transpose by Q I'm taking all + + align:start position:0% +multiply Q transpose by Q I'm taking all + + + align:start position:0% +multiply Q transpose by Q I'm taking all +the + + align:start position:0% +the + + + align:start position:0% +the +dot products and I'm getting ones when + + align:start position:0% +dot products and I'm getting ones when + + + align:start position:0% +dot products and I'm getting ones when +it's Q against itself and I'm getting + + align:start position:0% +it's Q against itself and I'm getting + + + align:start position:0% +it's Q against itself and I'm getting +zeroes when it's one Q versus another Q + + align:start position:0% +zeroes when it's one Q versus another Q + + + align:start position:0% +zeroes when it's one Q versus another Q +and again just think of three + + align:start position:0% +and again just think of three + + + align:start position:0% +and again just think of three +perpendicular axes those are the those + + align:start position:0% +perpendicular axes those are the those + + + align:start position:0% +perpendicular axes those are the those +directions are the Q 1 Q 2 Q 3 ok so we + + align:start position:0% +directions are the Q 1 Q 2 Q 3 ok so we + + + align:start position:0% +directions are the Q 1 Q 2 Q 3 ok so we +really want to compute with those here's + + align:start position:0% +really want to compute with those here's + + + align:start position:0% +really want to compute with those here's +an example well that has just two + + align:start position:0% +an example well that has just two + + + align:start position:0% +an example well that has just two +perpendicular axes I didn't have space + + align:start position:0% +perpendicular axes I didn't have space + + + align:start position:0% +perpendicular axes I didn't have space +for the third one so so do you see that + + align:start position:0% +for the third one so so do you see that + + + align:start position:0% +for the third one so so do you see that +that those two columns are perpendicular + + align:start position:0% +that those two columns are perpendicular + + + align:start position:0% +that those two columns are perpendicular +again what does that mean I take the dot + + align:start position:0% +again what does that mean I take the dot + + + align:start position:0% +again what does that mean I take the dot +product - 1 x - 2 - x - 1 and another - + + align:start position:0% +product - 1 x - 2 - x - 1 and another - + + + align:start position:0% +product - 1 x - 2 - x - 1 and another - +2 so I'm up to minus 4 at this point and + + align:start position:0% +2 so I'm up to minus 4 at this point and + + + align:start position:0% +2 so I'm up to minus 4 at this point and +then 2 times 2 gives a plus 4 so it all + + align:start position:0% +then 2 times 2 gives a plus 4 so it all + + + align:start position:0% +then 2 times 2 gives a plus 4 so it all +washes out to 0 and why is that 1/3 + + align:start position:0% +washes out to 0 and why is that 1/3 + + + align:start position:0% +washes out to 0 and why is that 1/3 +there why is that that's so that these + + align:start position:0% +there why is that that's so that these + + + align:start position:0% +there why is that that's so that these +vectors will have length 1 there will be + + align:start position:0% +vectors will have length 1 there will be + + + align:start position:0% +vectors will have length 1 there will be +unit vectors yeah and how do I figure + + align:start position:0% +unit vectors yeah and how do I figure + + + align:start position:0% +unit vectors yeah and how do I figure +the length of a vector well just while + + align:start position:0% +the length of a vector well just while + + + align:start position:0% +the length of a vector well just while +we're at it I take 1 squared or minus 1 + + align:start position:0% +we're at it I take 1 squared or minus 1 + + + align:start position:0% +we're at it I take 1 squared or minus 1 +squared gives me 1 2 squared + 2 squared + + align:start position:0% +squared gives me 1 2 squared + 2 squared + + + align:start position:0% +squared gives me 1 2 squared + 2 squared +I take the dot product with itself so + + align:start position:0% +I take the dot product with itself so + + + align:start position:0% +I take the dot product with itself so +minus 1 squared 2 squared + 2 squared + + align:start position:0% +minus 1 squared 2 squared + 2 squared + + + align:start position:0% +minus 1 squared 2 squared + 2 squared +that adds up to 9 the square root of 9 + + align:start position:0% +that adds up to 9 the square root of 9 + + + align:start position:0% +that adds up to 9 the square root of 9 +is the length I'm just doing Pythagoras + + align:start position:0% +is the length I'm just doing Pythagoras + + + align:start position:0% +is the length I'm just doing Pythagoras +here there's one side of a triangle + + align:start position:0% +here there's one side of a triangle + + + align:start position:0% +here there's one side of a triangle +here's a second side of a triangle it's + + align:start position:0% +here's a second side of a triangle it's + + + align:start position:0% +here's a second side of a triangle it's +a right triangle because that vector is + + align:start position:0% +a right triangle because that vector is + + + align:start position:0% +a right triangle because that vector is +perpendicular to that one it's in 3d + + align:start position:0% +perpendicular to that one it's in 3d + + + align:start position:0% +perpendicular to that one it's in 3d +because they have three components and I + + align:start position:0% +because they have three components and I + + + align:start position:0% +because they have three components and I +didn't write the third a third direction + + align:start position:0% +didn't write the third a third direction + + + align:start position:0% +didn't write the third a third direction +and their length one vectors because + + align:start position:0% +and their length one vectors because + + + align:start position:0% +and their length one vectors because +just that's how we when I compute the + + align:start position:0% +just that's how we when I compute the + + + align:start position:0% +just that's how we when I compute the +length and remember about the 1/3 which + + align:start position:0% +length and remember about the 1/3 which + + + align:start position:0% +length and remember about the 1/3 which +is put in there to give length 1 so okay + + align:start position:0% +is put in there to give length 1 so okay + + + align:start position:0% +is put in there to give length 1 so okay +so these matrices are with Q transpose + + align:start position:0% +so these matrices are with Q transpose + + + align:start position:0% +so these matrices are with Q transpose +times Q equal I that again that's the + + align:start position:0% +times Q equal I that again that's the + + + align:start position:0% +times Q equal I that again that's the +matrix shorthand for all I've just said + + align:start position:0% +matrix shorthand for all I've just said + + + align:start position:0% +matrix shorthand for all I've just said +and those matrices are the best because + + align:start position:0% +and those matrices are the best because + + + align:start position:0% +and those matrices are the best because +they don't change the length of anything + + align:start position:0% +they don't change the length of anything + + + align:start position:0% +they don't change the length of anything +you don't have blowup you don't have + + align:start position:0% +you don't have blowup you don't have + + + align:start position:0% +you don't have blowup you don't have +going to zero you can multiply together + + align:start position:0% +going to zero you can multiply together + + + align:start position:0% +going to zero you can multiply together +a thousand matrices and you'll still + + align:start position:0% +a thousand matrices and you'll still + + + align:start position:0% +a thousand matrices and you'll still +have another orthogonal matrix yes + + align:start position:0% +have another orthogonal matrix yes + + + align:start position:0% +have another orthogonal matrix yes +little family of beautiful matrices okay + + align:start position:0% +little family of beautiful matrices okay + + + align:start position:0% +little family of beautiful matrices okay +and very very useful big okay oh and + + align:start position:0% +and very very useful big okay oh and + + + align:start position:0% +and very very useful big okay oh and +there is a good example oh I think way I + + align:start position:0% +there is a good example oh I think way I + + + align:start position:0% +there is a good example oh I think way I +got that at that example I just added + + align:start position:0% +got that at that example I just added + + + align:start position:0% +got that at that example I just added +the third row the third column third + + align:start position:0% +the third row the third column third + + + align:start position:0% +the third row the third column third +column so 2 squared plus 2 squared plus + + align:start position:0% +column so 2 squared plus 2 squared plus + + + align:start position:0% +column so 2 squared plus 2 squared plus +-1 squared that adds up to 9 when I take + + align:start position:0% +-1 squared that adds up to 9 when I take + + + align:start position:0% +-1 squared that adds up to 9 when I take +the square root I get 3 so that has + + align:start position:0% +the square root I get 3 so that has + + + align:start position:0% +the square root I get 3 so that has +length 3 I divided by 3 so it would have + + align:start position:0% +length 3 I divided by 3 so it would have + + + align:start position:0% +length 3 I divided by 3 so it would have +length 1 we always want to see ones like + + align:start position:0% +length 1 we always want to see ones like + + + align:start position:0% +length 1 we always want to see ones like +we do there and if I here's a simple + + align:start position:0% +we do there and if I here's a simple + + + align:start position:0% +we do there and if I here's a simple +fact but great that if I have 2 of these + + align:start position:0% +fact but great that if I have 2 of these + + + align:start position:0% +fact but great that if I have 2 of these +matrices or 50 of these matrices I could + + align:start position:0% +matrices or 50 of these matrices I could + + + align:start position:0% +matrices or 50 of these matrices I could +multiply them together and I would still + + align:start position:0% +multiply them together and I would still + + + align:start position:0% +multiply them together and I would still +have length 1 I'd still have orthogonal + + align:start position:0% +have length 1 I'd still have orthogonal + + + align:start position:0% +have length 1 I'd still have orthogonal +matrices 1 times 1 times 1 forever is 1 + + align:start position:0% +matrices 1 times 1 times 1 forever is 1 + + + align:start position:0% +matrices 1 times 1 times 1 forever is 1 +ok so it's probably something hiding + + align:start position:0% +ok so it's probably something hiding + + + align:start position:0% +ok so it's probably something hiding +here oh yeah oh yeah to understand why + + align:start position:0% +here oh yeah oh yeah to understand why + + + align:start position:0% +here oh yeah oh yeah to understand why +these matrices are important this one is + + align:start position:0% +these matrices are important this one is + + + align:start position:0% +these matrices are important this one is +this line is telling me that if I have a + + align:start position:0% +this line is telling me that if I have a + + + align:start position:0% +this line is telling me that if I have a +vector X and I multiply by Q it doesn't + + align:start position:0% +vector X and I multiply by Q it doesn't + + + align:start position:0% +vector X and I multiply by Q it doesn't +change the length this is a symbol for + + align:start position:0% +change the length this is a symbol for + + + align:start position:0% +change the length this is a symbol for +length squared and that's equal to the + + align:start position:0% +length squared and that's equal to the + + + align:start position:0% +length squared and that's equal to the +original length squared length is + + align:start position:0% +original length squared length is + + + align:start position:0% +original length squared length is +preserved by these Q's everything is + + align:start position:0% +preserved by these Q's everything is + + + align:start position:0% +preserved by these Q's everything is +preserved you're multiplying effectively + + align:start position:0% +preserved you're multiplying effectively + + + align:start position:0% +preserved you're multiplying effectively +by the matrix versions of 1 and minus 1 + + align:start position:0% +by the matrix versions of 1 and minus 1 + + + align:start position:0% +by the matrix versions of 1 and minus 1 +so and a rotation is a very significant + + align:start position:0% +so and a rotation is a very significant + + + align:start position:0% +so and a rotation is a very significant +very valuable orthogonal matrix which + + align:start position:0% +very valuable orthogonal matrix which + + + align:start position:0% +very valuable orthogonal matrix which +just has cosines and sines and + + align:start position:0% +just has cosines and sines and + + + align:start position:0% +just has cosines and sines and +everybody's remembering that cosine + + align:start position:0% +everybody's remembering that cosine + + + align:start position:0% +everybody's remembering that cosine +squared plus sine squared is 1 from trig + + align:start position:0% +squared plus sine squared is 1 from trig + + + align:start position:0% +squared plus sine squared is 1 from trig +and that's oh that's a that's a a an + + align:start position:0% +and that's oh that's a that's a a an + + + align:start position:0% +and that's oh that's a that's a a an +orthogonal matrix + + align:start position:0% +orthogonal matrix + + + align:start position:0% +orthogonal matrix +oh it's also orthogonal because the dot + + align:start position:0% +oh it's also orthogonal because the dot + + + align:start position:0% +oh it's also orthogonal because the dot +product between that one and that one + + align:start position:0% +product between that one and that one + + + align:start position:0% +product between that one and that one +you're okay for the dot product that + + align:start position:0% +you're okay for the dot product that + + + align:start position:0% +you're okay for the dot product that +that product gives me minus sine cosine + + align:start position:0% +that product gives me minus sine cosine + + + align:start position:0% +that product gives me minus sine cosine +plus sine cosine 0 so the column 1 is + + align:start position:0% +plus sine cosine 0 so the column 1 is + + + align:start position:0% +plus sine cosine 0 so the column 1 is +orthogonal to call + + align:start position:0% +orthogonal to call + + + align:start position:0% +orthogonal to call +- that's good okay these lambdas that + + align:start position:0% +- that's good okay these lambdas that + + + align:start position:0% +- that's good okay these lambdas that +you see here are something called + + align:start position:0% +you see here are something called + + + align:start position:0% +you see here are something called +eigenvalues that's not allowed until the + + align:start position:0% +eigenvalues that's not allowed until the + + + align:start position:0% +eigenvalues that's not allowed until the +next lecture okay all right now here's + + align:start position:0% +next lecture okay all right now here's + + + align:start position:0% +next lecture okay all right now here's +something here's a computing thing if we + + align:start position:0% +something here's a computing thing if we + + + align:start position:0% +something here's a computing thing if we +have a bunch of columns not orthogonal + + align:start position:0% +have a bunch of columns not orthogonal + + + align:start position:0% +have a bunch of columns not orthogonal +not length 1 then we often we would like + + align:start position:0% +not length 1 then we often we would like + + + align:start position:0% +not length 1 then we often we would like +to convert them to so call those a 1 to + + align:start position:0% +to convert them to so call those a 1 to + + + align:start position:0% +to convert them to so call those a 1 to +a n nothing special about those columns + + align:start position:0% +a n nothing special about those columns + + + align:start position:0% +a n nothing special about those columns +we would like to convert them to + + align:start position:0% +we would like to convert them to + + + align:start position:0% +we would like to convert them to +orthogonal columns because they are the + + align:start position:0% +orthogonal columns because they are the + + + align:start position:0% +orthogonal columns because they are the +beautiful ones q1 up to QN and two guys + + align:start position:0% +beautiful ones q1 up to QN and two guys + + + align:start position:0% +beautiful ones q1 up to QN and two guys +called Graham and schmidt figured out a + + align:start position:0% +called Graham and schmidt figured out a + + + align:start position:0% +called Graham and schmidt figured out a +way to do that and a century later we're + + align:start position:0% +way to do that and a century later we're + + + align:start position:0% +way to do that and a century later we're +still using their idea well I don't know + + align:start position:0% +still using their idea well I don't know + + + align:start position:0% +still using their idea well I don't know +whose idea was actually I think Graham + + align:start position:0% +whose idea was actually I think Graham + + + align:start position:0% +whose idea was actually I think Graham +had the idea and I'm not really sure + + align:start position:0% +had the idea and I'm not really sure + + + align:start position:0% +had the idea and I'm not really sure +what Schmidt how he got into it well he + + align:start position:0% +what Schmidt how he got into it well he + + + align:start position:0% +what Schmidt how he got into it well he +may have repeated the idea so okay so it + + align:start position:0% +may have repeated the idea so okay so it + + + align:start position:0% +may have repeated the idea so okay so it +just I won't go all the details but + + align:start position:0% +just I won't go all the details but + + + align:start position:0% +just I won't go all the details but +here's what the point is the point is if + + align:start position:0% +here's what the point is the point is if + + + align:start position:0% +here's what the point is the point is if +I have a bunch of columns that are + + align:start position:0% +I have a bunch of columns that are + + + align:start position:0% +I have a bunch of columns that are +independent they go in different + + align:start position:0% +independent they go in different + + + align:start position:0% +independent they go in different +directions but they're not 90-degree + + align:start position:0% +directions but they're not 90-degree + + + align:start position:0% +directions but they're not 90-degree +directions then I can convert it to a + + align:start position:0% +directions then I can convert it to a + + + align:start position:0% +directions then I can convert it to a +90-degree one to two perpendicular axes + + align:start position:0% +90-degree one to two perpendicular axes + + + align:start position:0% +90-degree one to two perpendicular axes +with a matrix that a matrix R happens to + + align:start position:0% +with a matrix that a matrix R happens to + + + align:start position:0% +with a matrix that a matrix R happens to +be triangular that did the did the + + align:start position:0% +be triangular that did the did the + + + align:start position:0% +be triangular that did the did the +moving around did take the combinations + + align:start position:0% +moving around did take the combinations + + + align:start position:0% +moving around did take the combinations +so a equal QR is one of the fundamental + + align:start position:0% +so a equal QR is one of the fundamental + + + align:start position:0% +so a equal QR is one of the fundamental +steps of linear algebra and + + align:start position:0% +steps of linear algebra and + + + align:start position:0% +steps of linear algebra and +computational linear algebra very very + + align:start position:0% +computational linear algebra very very + + + align:start position:0% +computational linear algebra very very +often we're given a matrix a we want a + + align:start position:0% +often we're given a matrix a we want a + + + align:start position:0% +often we're given a matrix a we want a +nice matrix Q so we do this gram-schmidt + + align:start position:0% +nice matrix Q so we do this gram-schmidt + + + align:start position:0% +nice matrix Q so we do this gram-schmidt +step 2 makes a columns orthogonal and oh + + align:start position:0% +step 2 makes a columns orthogonal and oh + + + align:start position:0% +step 2 makes a columns orthogonal and oh +there's the first step of gram-schmidt + + align:start position:0% +there's the first step of gram-schmidt + + + align:start position:0% +there's the first step of gram-schmidt +but you need practice for the for the to + + align:start position:0% +but you need practice for the for the to + + + align:start position:0% +but you need practice for the for the to +see all the steps maybe not + + align:start position:0% +see all the steps maybe not + + + align:start position:0% +see all the steps maybe not +okay so here + + align:start position:0% +okay so here + + + align:start position:0% +okay so here +what's the advantage of perpendicular + + align:start position:0% +what's the advantage of perpendicular + + + align:start position:0% +what's the advantage of perpendicular +vectors suppose I have a triangle and + + align:start position:0% +vectors suppose I have a triangle and + + + align:start position:0% +vectors suppose I have a triangle and +one side is perpendicular to the second + + align:start position:0% +one side is perpendicular to the second + + + align:start position:0% +one side is perpendicular to the second +side what how does that help well that's + + align:start position:0% +side what how does that help well that's + + + align:start position:0% +side what how does that help well that's +a that's a right triangle then side a + + align:start position:0% +a that's a right triangle then side a + + + align:start position:0% +a that's a right triangle then side a +perpendicular side B and of course + + align:start position:0% +perpendicular side B and of course + + + align:start position:0% +perpendicular side B and of course +Pythagoras + + align:start position:0% +Pythagoras + + + align:start position:0% +Pythagoras +now we're really going back Pythagoras + + align:start position:0% +now we're really going back Pythagoras + + + align:start position:0% +now we're really going back Pythagoras +said that a squared plus B squared is C + + align:start position:0% +said that a squared plus B squared is C + + + align:start position:0% +said that a squared plus B squared is C +squared so we have beautiful formulas + + align:start position:0% +squared so we have beautiful formulas + + + align:start position:0% +squared so we have beautiful formulas +when things are perpendicular if I if + + align:start position:0% +when things are perpendicular if I if + + + align:start position:0% +when things are perpendicular if I if +the angles are not 90 degrees when the + + align:start position:0% +the angles are not 90 degrees when the + + + align:start position:0% +the angles are not 90 degrees when the +cosine of 90 degrees is 1 or maybe the + + align:start position:0% +cosine of 90 degrees is 1 or maybe the + + + align:start position:0% +cosine of 90 degrees is 1 or maybe the +sine of 90 degrees is 1 ya sine of 90 + + align:start position:0% +sine of 90 degrees is 1 ya sine of 90 + + + align:start position:0% +sine of 90 degrees is 1 ya sine of 90 +degrees is 1 for those perfect angles 0 + + align:start position:0% +degrees is 1 for those perfect angles 0 + + + align:start position:0% +degrees is 1 for those perfect angles 0 +and 90 degrees where we can do + + align:start position:0% +and 90 degrees where we can do + + + align:start position:0% +and 90 degrees where we can do +everything and here's a here's a place + + align:start position:0% +everything and here's a here's a place + + + align:start position:0% +everything and here's a here's a place +that Q fits just to make it this is like + + align:start position:0% +that Q fits just to make it this is like + + + align:start position:0% +that Q fits just to make it this is like +the first applicant big application of + + align:start position:0% +the first applicant big application of + + + align:start position:0% +the first applicant big application of +linear algebra so let me just say what + + align:start position:0% +linear algebra so let me just say what + + + align:start position:0% +linear algebra so let me just say what +it is and it uses these cubes so what's + + align:start position:0% +it is and it uses these cubes so what's + + + align:start position:0% +it is and it uses these cubes so what's +the application it's called least + + align:start position:0% +the application it's called least + + + align:start position:0% +the application it's called least +squares and it's you start with + + align:start position:0% +squares and it's you start with + + + align:start position:0% +squares and it's you start with +equations ax equal B you always think of + + align:start position:0% +equations ax equal B you always think of + + + align:start position:0% +equations ax equal B you always think of +that as a matrix times the unknown + + align:start position:0% +that as a matrix times the unknown + + + align:start position:0% +that as a matrix times the unknown +vector being a known right-hand side B + + align:start position:0% +vector being a known right-hand side B + + + align:start position:0% +vector being a known right-hand side B +ax equal B so suppose we have too many + + align:start position:0% +ax equal B so suppose we have too many + + + align:start position:0% +ax equal B so suppose we have too many +equations that often happens if you take + + align:start position:0% +equations that often happens if you take + + + align:start position:0% +equations that often happens if you take +too many measurements you want to get + + align:start position:0% +too many measurements you want to get + + + align:start position:0% +too many measurements you want to get +something you want to get an exact x so + + align:start position:0% +something you want to get an exact x so + + + align:start position:0% +something you want to get an exact x so +you do more and more measurement to be + + align:start position:0% +you do more and more measurement to be + + + align:start position:0% +you do more and more measurement to be +you're pasting more and more conditions + + align:start position:0% +you're pasting more and more conditions + + + align:start position:0% +you're pasting more and more conditions +on X and you're not going to find an + + align:start position:0% +on X and you're not going to find an + + + align:start position:0% +on X and you're not going to find an +exact x because you've got too many + + align:start position:0% +exact x because you've got too many + + + align:start position:0% +exact x because you've got too many +equations M is bigger than n we might + + align:start position:0% +equations M is bigger than n we might + + + align:start position:0% +equations M is bigger than n we might +have 2000 measurements say from medical + + align:start position:0% +have 2000 measurements say from medical + + + align:start position:0% +have 2000 measurements say from medical +things or from satellites and we might + + align:start position:0% +things or from satellites and we might + + + align:start position:0% +things or from satellites and we might +have only 2 unknowns fitting a straight + + align:start position:0% +have only 2 unknowns fitting a straight + + + align:start position:0% +have only 2 unknowns fitting a straight +line with only two variables so how am I + + align:start position:0% +line with only two variables so how am I + + + align:start position:0% +line with only two variables so how am I +going to solve 2,000 equations with two + + align:start position:0% +going to solve 2,000 equations with two + + + align:start position:0% +going to solve 2,000 equations with two +unknowns well I'm not but I look for the + + align:start position:0% +unknowns well I'm not but I look for the + + + align:start position:0% +unknowns well I'm not but I look for the +best solution how close can I come and + + align:start position:0% +best solution how close can I come and + + + align:start position:0% +best solution how close can I come and +that's what least squares is about you + + align:start position:0% +that's what least squares is about you + + + align:start position:0% +that's what least squares is about you +you get + + align:start position:0% +you get + + + align:start position:0% +you get +be ax as close as possible to be and + + align:start position:0% +be ax as close as possible to be and + + + align:start position:0% +be ax as close as possible to be and +probably this will show how the how the + + align:start position:0% +probably this will show how the how the + + + align:start position:0% +probably this will show how the how the +yeah yeah here's the right equation when + + align:start position:0% +yeah yeah here's the right equation when + + + align:start position:0% +yeah yeah here's the right equation when +you here's my message when you can't + + align:start position:0% +you here's my message when you can't + + + align:start position:0% +you here's my message when you can't +solve ax equal B multiply both sides by + + align:start position:0% +solve ax equal B multiply both sides by + + + align:start position:0% +solve ax equal B multiply both sides by +a transpose then you can solve this + + align:start position:0% +a transpose then you can solve this + + + align:start position:0% +a transpose then you can solve this +equation that's the right equation so I + + align:start position:0% +equation that's the right equation so I + + + align:start position:0% +equation that's the right equation so I +put a little hat on that X to show that + + align:start position:0% +put a little hat on that X to show that + + + align:start position:0% +put a little hat on that X to show that +it doesn't solve the original equation + + align:start position:0% +it doesn't solve the original equation + + + align:start position:0% +it doesn't solve the original equation +ax equal B but it comes the closest it's + + align:start position:0% +ax equal B but it comes the closest it's + + + align:start position:0% +ax equal B but it comes the closest it's +the closest solution I could find and it + + align:start position:0% +the closest solution I could find and it + + + align:start position:0% +the closest solution I could find and it +it's discovered by multiplying both + + align:start position:0% +it's discovered by multiplying both + + + align:start position:0% +it's discovered by multiplying both +sides by this a transpose matrix so a + + align:start position:0% +sides by this a transpose matrix so a + + + align:start position:0% +sides by this a transpose matrix so a +transpose a is a terrifically important + + align:start position:0% +transpose a is a terrifically important + + + align:start position:0% +transpose a is a terrifically important +matrix it's a square matrix C a didn't + + align:start position:0% +matrix it's a square matrix C a didn't + + + align:start position:0% +matrix it's a square matrix C a didn't +have to be square I could have lots of + + align:start position:0% +have to be square I could have lots of + + + align:start position:0% +have to be square I could have lots of +measurements there many many equations + + align:start position:0% +measurements there many many equations + + + align:start position:0% +measurements there many many equations +long thin matrix for a but a transpose a + + align:start position:0% +long thin matrix for a but a transpose a + + + align:start position:0% +long thin matrix for a but a transpose a +always comes out square and also + + align:start position:0% +always comes out square and also + + + align:start position:0% +always comes out square and also +symmetric and it's just a great matrix + + align:start position:0% +symmetric and it's just a great matrix + + + align:start position:0% +symmetric and it's just a great matrix +for a theory and this Q our business + + align:start position:0% +for a theory and this Q our business + + + align:start position:0% +for a theory and this Q our business +makes it work in practice let me see if + + align:start position:0% +makes it work in practice let me see if + + + align:start position:0% +makes it work in practice let me see if +there's more so this is y oh yeah this + + align:start position:0% +there's more so this is y oh yeah this + + + align:start position:0% +there's more so this is y oh yeah this +is the geometry so I start with a matrix + + align:start position:0% +is the geometry so I start with a matrix + + + align:start position:0% +is the geometry so I start with a matrix +a it's only got a few columns maybe even + + align:start position:0% +a it's only got a few columns maybe even + + + align:start position:0% +a it's only got a few columns maybe even +only two columns so it's a column space + + align:start position:0% +only two columns so it's a column space + + + align:start position:0% +only two columns so it's a column space +it's just a plane not the whole space + + align:start position:0% +it's just a plane not the whole space + + + align:start position:0% +it's just a plane not the whole space +but my right-hand side B is somewhere + + align:start position:0% +but my right-hand side B is somewhere + + + align:start position:0% +but my right-hand side B is somewhere +else in whole space you see this + + align:start position:0% +else in whole space you see this + + + align:start position:0% +else in whole space you see this +situation I can only solve ax equal B + + align:start position:0% +situation I can only solve ax equal B + + + align:start position:0% +situation I can only solve ax equal B +when B is in this one B is a combination + + align:start position:0% +when B is in this one B is a combination + + + align:start position:0% +when B is in this one B is a combination +of the columns and here it's not the + + align:start position:0% +of the columns and here it's not the + + + align:start position:0% +of the columns and here it's not the +measurements weren't perfect I'm off + + align:start position:0% +measurements weren't perfect I'm off + + + align:start position:0% +measurements weren't perfect I'm off +somewhere so I have how do i how do you + + align:start position:0% +somewhere so I have how do i how do you + + + align:start position:0% +somewhere so I have how do i how do you +deal with that geometry tells you mmm + + align:start position:0% +deal with that geometry tells you mmm + + + align:start position:0% +deal with that geometry tells you mmm +you can't deal with B it's not you can't + + align:start position:0% +you can't deal with B it's not you can't + + + align:start position:0% +you can't deal with B it's not you can't +solve ax equal B so you drop a + + align:start position:0% +solve ax equal B so you drop a + + + align:start position:0% +solve ax equal B so you drop a +perpendicular you find the closest point + + align:start position:0% +perpendicular you find the closest point + + + align:start position:0% +perpendicular you find the closest point +the projection that in the space where + + align:start position:0% +the projection that in the space where + + + align:start position:0% +the projection that in the space where +your can solve so then you solve ax + + align:start position:0% +your can solve so then you solve ax + + + align:start position:0% +your can solve so then you solve ax +equal P that's what least squares is all + + align:start position:0% +equal P that's what least squares is all + + + align:start position:0% +equal P that's what least squares is all +about fit + + align:start position:0% +about fit + + + align:start position:0% +about fit +the best straight-line the best parabola + + align:start position:0% +the best straight-line the best parabola + + + align:start position:0% +the best straight-line the best parabola +whatever is all in your algebra of + + align:start position:0% +whatever is all in your algebra of + + + align:start position:0% +whatever is all in your algebra of +perpendicular things and orthogonal + + align:start position:0% +perpendicular things and orthogonal + + + align:start position:0% +perpendicular things and orthogonal +matrices okay I think that's what I what + + align:start position:0% +matrices okay I think that's what I what + + + align:start position:0% +matrices okay I think that's what I what +I can say about orthogonal well it'll + + align:start position:0% +I can say about orthogonal well it'll + + + align:start position:0% +I can say about orthogonal well it'll +come in again orthogonal matrices + + align:start position:0% +come in again orthogonal matrices + + + align:start position:0% +come in again orthogonal matrices +perpendicular columns is so beautiful + + align:start position:0% +perpendicular columns is so beautiful + + + align:start position:0% +perpendicular columns is so beautiful +but next is coming eigenvectors and + + align:start position:0% +but next is coming eigenvectors and + + + align:start position:0% +but next is coming eigenvectors and +that's a another chapter so I'll stop + + align:start position:0% +that's a another chapter so I'll stop + + + align:start position:0% +that's a another chapter so I'll stop +here good thanks \ No newline at end of file diff --git a/jHrd43uWD-E.txt b/jHrd43uWD-E.txt new file mode 100644 index 0000000000000000000000000000000000000000..c0def0b86d4539d782b3339a561131230dc78445 --- /dev/null +++ b/jHrd43uWD-E.txt @@ -0,0 +1,2163 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT OpenCourseWare continue to + + align:start position:0% +will help MIT OpenCourseWare continue to + + + align:start position:0% +will help MIT OpenCourseWare continue to +offer high quality educational resources + + align:start position:0% +offer high quality educational resources + + + align:start position:0% +offer high quality educational resources +for free + + align:start position:0% +for free + + + align:start position:0% +for free +to make a donation or view additional + + align:start position:0% +to make a donation or view additional + + + align:start position:0% +to make a donation or view additional +materials from hundreds of MIT courses + + align:start position:0% +materials from hundreds of MIT courses + + + align:start position:0% +materials from hundreds of MIT courses +visit MIT opencourseware at ocw.mit.edu + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu + + + align:start position:0% +visit MIT opencourseware at ocw.mit.edu +let's look at storyboard 17 panel a so + + align:start position:0% +let's look at storyboard 17 panel a so + + + align:start position:0% +let's look at storyboard 17 panel a so +far in 507 we've looked in detail at + + align:start position:0% +far in 507 we've looked in detail at + + + align:start position:0% +far in 507 we've looked in detail at +carbohydrate catabolism we've seen that + + align:start position:0% +carbohydrate catabolism we've seen that + + + align:start position:0% +carbohydrate catabolism we've seen that +the complete catabolism of a molecule of + + align:start position:0% +the complete catabolism of a molecule of + + + align:start position:0% +the complete catabolism of a molecule of +glucose by way of glycolysis pyruvate + + align:start position:0% +glucose by way of glycolysis pyruvate + + + align:start position:0% +glucose by way of glycolysis pyruvate +dehydrogenase and the TCA cycle results + + align:start position:0% +dehydrogenase and the TCA cycle results + + + align:start position:0% +dehydrogenase and the TCA cycle results +in the generation of about 36 to 38 + + align:start position:0% +in the generation of about 36 to 38 + + + align:start position:0% +in the generation of about 36 to 38 +molecules of ATP at this point we're + + align:start position:0% +molecules of ATP at this point we're + + + align:start position:0% +molecules of ATP at this point we're +going to turn to catabolism of another + + align:start position:0% +going to turn to catabolism of another + + + align:start position:0% +going to turn to catabolism of another +metabolic fuel lipids as we'll see + + align:start position:0% +metabolic fuel lipids as we'll see + + + align:start position:0% +metabolic fuel lipids as we'll see +lipids because they contain more energy + + align:start position:0% +lipids because they contain more energy + + + align:start position:0% +lipids because they contain more energy +per gram because they're more highly + + align:start position:0% +per gram because they're more highly + + + align:start position:0% +per gram because they're more highly +reduced in carbohydrates will produce + + align:start position:0% +reduced in carbohydrates will produce + + + align:start position:0% +reduced in carbohydrates will produce +much more ATP per unit weight than + + align:start position:0% +much more ATP per unit weight than + + + align:start position:0% +much more ATP per unit weight than +carbohydrates for example if we were to + + align:start position:0% +carbohydrates for example if we were to + + + align:start position:0% +carbohydrates for example if we were to +metabolize hexanoic acid the six carbon + + align:start position:0% +metabolize hexanoic acid the six carbon + + + align:start position:0% +metabolize hexanoic acid the six carbon +hydrocarbon the same number of carbons + + align:start position:0% +hydrocarbon the same number of carbons + + + align:start position:0% +hydrocarbon the same number of carbons +as glucose we get over 58 EPS rather + + align:start position:0% +as glucose we get over 58 EPS rather + + + align:start position:0% +as glucose we get over 58 EPS rather +than about 35 ATP s4 molecule which we + + align:start position:0% +than about 35 ATP s4 molecule which we + + + align:start position:0% +than about 35 ATP s4 molecule which we +would have got from glucose now let's + + align:start position:0% +would have got from glucose now let's + + + align:start position:0% +would have got from glucose now let's +look at panel B lipids have many roles + + align:start position:0% +look at panel B lipids have many roles + + + align:start position:0% +look at panel B lipids have many roles +in biological systems the first that + + align:start position:0% +in biological systems the first that + + + align:start position:0% +in biological systems the first that +will be relevant to this lecture is that + + align:start position:0% +will be relevant to this lecture is that + + + align:start position:0% +will be relevant to this lecture is that +there are primary energy reserve in fact + + align:start position:0% +there are primary energy reserve in fact + + + align:start position:0% +there are primary energy reserve in fact +about 80% of our stored energy is in the + + align:start position:0% +about 80% of our stored energy is in the + + + align:start position:0% +about 80% of our stored energy is in the +form of lipid second as Joanne taught us + + align:start position:0% +form of lipid second as Joanne taught us + + + align:start position:0% +form of lipid second as Joanne taught us +lipids are key components of biological + + align:start position:0% +lipids are key components of biological + + + align:start position:0% +lipids are key components of biological +membranes and thus they contribute in a + + align:start position:0% +membranes and thus they contribute in a + + + align:start position:0% +membranes and thus they contribute in a +major way to the compartmentalization + + align:start position:0% +major way to the compartmentalization + + + align:start position:0% +major way to the compartmentalization +that's critical for normal biological + + align:start position:0% +that's critical for normal biological + + + align:start position:0% +that's critical for normal biological +functions and the third role is that + + align:start position:0% +functions and the third role is that + + + align:start position:0% +functions and the third role is that +some lipids are signaling molecules the + + align:start position:0% +some lipids are signaling molecules the + + + align:start position:0% +some lipids are signaling molecules the +one I pictured here is estradiol well + + align:start position:0% +one I pictured here is estradiol well + + + align:start position:0% +one I pictured here is estradiol well +estradiol may not look like a typical + + align:start position:0% +estradiol may not look like a typical + + + align:start position:0% +estradiol may not look like a typical +lipid it actually is indeed it's made by + + align:start position:0% +lipid it actually is indeed it's made by + + + align:start position:0% +lipid it actually is indeed it's made by +a lipid biosynthetic pathway that starts + + align:start position:0% +a lipid biosynthetic pathway that starts + + + align:start position:0% +a lipid biosynthetic pathway that starts +with sotl coenzyme a and we'll see later + + align:start position:0% +with sotl coenzyme a and we'll see later + + + align:start position:0% +with sotl coenzyme a and we'll see later +that acetic away also serves as the + + align:start position:0% +that acetic away also serves as the + + + align:start position:0% +that acetic away also serves as the +precursor for the canonical lipid a + + align:start position:0% +precursor for the canonical lipid a + + + align:start position:0% +precursor for the canonical lipid a +fatty acid fatty acids are d classic + + align:start position:0% +fatty acid fatty acids are d classic + + + align:start position:0% +fatty acid fatty acids are d classic +lipid their hydrocarbon chains that are + + align:start position:0% +lipid their hydrocarbon chains that are + + + align:start position:0% +lipid their hydrocarbon chains that are +fully saturated or contain a small + + align:start position:0% +fully saturated or contain a small + + + align:start position:0% +fully saturated or contain a small +number of double bonds + + align:start position:0% +number of double bonds + + + align:start position:0% +number of double bonds +and sometimes branches sometimes the + + align:start position:0% +and sometimes branches sometimes the + + + align:start position:0% +and sometimes branches sometimes the +fatty acid moiety is esterified to the + + align:start position:0% +fatty acid moiety is esterified to the + + + align:start position:0% +fatty acid moiety is esterified to the +backbone of glycerol if you have three + + align:start position:0% +backbone of glycerol if you have three + + + align:start position:0% +backbone of glycerol if you have three +fatty acids on a glycerol backbone one + + align:start position:0% +fatty acids on a glycerol backbone one + + + align:start position:0% +fatty acids on a glycerol backbone one +to each of the hydroxyl groups + + align:start position:0% +to each of the hydroxyl groups + + + align:start position:0% +to each of the hydroxyl groups +that's called a tri a so glyceride + + align:start position:0% +that's called a tri a so glyceride + + + align:start position:0% +that's called a tri a so glyceride +that's our primary storage form of + + align:start position:0% +that's our primary storage form of + + + align:start position:0% +that's our primary storage form of +energy with phospholipids one of the + + align:start position:0% +energy with phospholipids one of the + + + align:start position:0% +energy with phospholipids one of the +hydroxyl groups of the glycerol backbone + + align:start position:0% +hydroxyl groups of the glycerol backbone + + + align:start position:0% +hydroxyl groups of the glycerol backbone +is esterified to either phosphate or + + align:start position:0% +is esterified to either phosphate or + + + align:start position:0% +is esterified to either phosphate or +some kind of decorated phosphate with + + align:start position:0% +some kind of decorated phosphate with + + + align:start position:0% +some kind of decorated phosphate with +the decoration could be a sugar or some + + align:start position:0% +the decoration could be a sugar or some + + + align:start position:0% +the decoration could be a sugar or some +other moiety as we've seen in Joanne's + + align:start position:0% +other moiety as we've seen in Joanne's + + + align:start position:0% +other moiety as we've seen in Joanne's +lectures phospholipids are the key + + align:start position:0% +lectures phospholipids are the key + + + align:start position:0% +lectures phospholipids are the key +building blocks of biological membrane + + align:start position:0% +building blocks of biological membrane + + + align:start position:0% +building blocks of biological membrane +now take a look at panel D the rest of + + align:start position:0% +now take a look at panel D the rest of + + + align:start position:0% +now take a look at panel D the rest of +this lecture will deal with the details + + align:start position:0% +this lecture will deal with the details + + + align:start position:0% +this lecture will deal with the details +of how fatty acids are broken down to + + align:start position:0% +of how fatty acids are broken down to + + + align:start position:0% +of how fatty acids are broken down to +carbon dioxide with the intermediate + + align:start position:0% +carbon dioxide with the intermediate + + + align:start position:0% +carbon dioxide with the intermediate +production of reducing equivalents in + + align:start position:0% +production of reducing equivalents in + + + align:start position:0% +production of reducing equivalents in +the form of nadh and fadh2 and + + align:start position:0% +the form of nadh and fadh2 and + + + align:start position:0% +the form of nadh and fadh2 and +ultimately energy equivalents in the + + align:start position:0% +ultimately energy equivalents in the + + + align:start position:0% +ultimately energy equivalents in the +form of ATP cells can acquire lipids + + align:start position:0% +form of ATP cells can acquire lipids + + + align:start position:0% +form of ATP cells can acquire lipids +directly from the blood where typically + + align:start position:0% +directly from the blood where typically + + + align:start position:0% +directly from the blood where typically +they're transported by albumin they can + + align:start position:0% +they're transported by albumin they can + + + align:start position:0% +they're transported by albumin they can +come directly from our diet or from + + align:start position:0% +come directly from our diet or from + + + align:start position:0% +come directly from our diet or from +other organs or from breakdown of tri + + align:start position:0% +other organs or from breakdown of tri + + + align:start position:0% +other organs or from breakdown of tri +acyl glycerides within our cells we're + + align:start position:0% +acyl glycerides within our cells we're + + + align:start position:0% +acyl glycerides within our cells we're +going to be looking at four steps in + + align:start position:0% +going to be looking at four steps in + + + align:start position:0% +going to be looking at four steps in +fatty acid catabolism the first step + + align:start position:0% +fatty acid catabolism the first step + + + align:start position:0% +fatty acid catabolism the first step +involves the appearance of the fatty + + align:start position:0% +involves the appearance of the fatty + + + align:start position:0% +involves the appearance of the fatty +acid in the cytoplasm of the cell the + + align:start position:0% +acid in the cytoplasm of the cell the + + + align:start position:0% +acid in the cytoplasm of the cell the +fatty acid can come in either from + + align:start position:0% +fatty acid can come in either from + + + align:start position:0% +fatty acid can come in either from +breakdown of a trial glyceride stored in + + align:start position:0% +breakdown of a trial glyceride stored in + + + align:start position:0% +breakdown of a trial glyceride stored in +the cytoplasm or the fatty acid could + + align:start position:0% +the cytoplasm or the fatty acid could + + + align:start position:0% +the cytoplasm or the fatty acid could +appear from transport across the + + align:start position:0% +appear from transport across the + + + align:start position:0% +appear from transport across the +membrane from the blood in the cytoplasm + + align:start position:0% +membrane from the blood in the cytoplasm + + + align:start position:0% +membrane from the blood in the cytoplasm +the fatty acid which is technically a + + align:start position:0% +the fatty acid which is technically a + + + align:start position:0% +the fatty acid which is technically a +carboxylic acid will be thio esterified + + align:start position:0% +carboxylic acid will be thio esterified + + + align:start position:0% +carboxylic acid will be thio esterified +to form a fatty acyl coenzyme a the + + align:start position:0% +to form a fatty acyl coenzyme a the + + + align:start position:0% +to form a fatty acyl coenzyme a the +second step of fatty acid catabolism + + align:start position:0% +second step of fatty acid catabolism + + + align:start position:0% +second step of fatty acid catabolism +involves the transport of the fatty acyl + + align:start position:0% +involves the transport of the fatty acyl + + + align:start position:0% +involves the transport of the fatty acyl +coenzyme a ester into the mitochondrion + + align:start position:0% +coenzyme a ester into the mitochondrion + + + align:start position:0% +coenzyme a ester into the mitochondrion +which is the site of fatty acid + + align:start position:0% +which is the site of fatty acid + + + align:start position:0% +which is the site of fatty acid +oxidation the third step in fatty acid + + align:start position:0% +oxidation the third step in fatty acid + + + align:start position:0% +oxidation the third step in fatty acid +catabolism involves the actual oxidation + + align:start position:0% +catabolism involves the actual oxidation + + + align:start position:0% +catabolism involves the actual oxidation +process itself the series of reactions + + align:start position:0% +process itself the series of reactions + + + align:start position:0% +process itself the series of reactions +is called beta oxidation beta oxidation + + align:start position:0% +is called beta oxidation beta oxidation + + + align:start position:0% +is called beta oxidation beta oxidation +results in the conversion of the + + align:start position:0% +results in the conversion of the + + + align:start position:0% +results in the conversion of the +carboxylic acid starting material to + + align:start position:0% +carboxylic acid starting material to + + + align:start position:0% +carboxylic acid starting material to +acetyl coenzyme a there can be several + + align:start position:0% +acetyl coenzyme a there can be several + + + align:start position:0% +acetyl coenzyme a there can be several +fates to the acetyl co a produced by + + align:start position:0% +fates to the acetyl co a produced by + + + align:start position:0% +fates to the acetyl co a produced by +beta oxidation but the one we're going + + align:start position:0% +beta oxidation but the one we're going + + + align:start position:0% +beta oxidation but the one we're going +to be looking at is its entry into the + + align:start position:0% +to be looking at is its entry into the + + + align:start position:0% +to be looking at is its entry into the +TCA cycle where the so2 + + align:start position:0% +TCA cycle where the so2 + + + align:start position:0% +TCA cycle where the so2 +is metabolized to carbon dioxide with + + align:start position:0% +is metabolized to carbon dioxide with + + + align:start position:0% +is metabolized to carbon dioxide with +the generation of reducing equivalents + + align:start position:0% +the generation of reducing equivalents + + + align:start position:0% +the generation of reducing equivalents +those reduced electron carriers have the + + align:start position:0% +those reduced electron carriers have the + + + align:start position:0% +those reduced electron carriers have the +potential to be converted into energy + + align:start position:0% +potential to be converted into energy + + + align:start position:0% +potential to be converted into energy +currency in the form of ATP the fourth + + align:start position:0% +currency in the form of ATP the fourth + + + align:start position:0% +currency in the form of ATP the fourth +topic or stage in fatty acid catabolism + + align:start position:0% +topic or stage in fatty acid catabolism + + + align:start position:0% +topic or stage in fatty acid catabolism +that we'll deal with concerns + + align:start position:0% +that we'll deal with concerns + + + align:start position:0% +that we'll deal with concerns +specialized endings of the catabolic + + align:start position:0% +specialized endings of the catabolic + + + align:start position:0% +specialized endings of the catabolic +pathway the first problem that will look + + align:start position:0% +pathway the first problem that will look + + + align:start position:0% +pathway the first problem that will look +at concerns the fact that some fatty + + align:start position:0% +at concerns the fact that some fatty + + + align:start position:0% +at concerns the fact that some fatty +acids have an odd number of carbons in + + align:start position:0% +acids have an odd number of carbons in + + + align:start position:0% +acids have an odd number of carbons in +them whereas the classical fatty acid + + align:start position:0% +them whereas the classical fatty acid + + + align:start position:0% +them whereas the classical fatty acid +beta oxidation system was primarily + + align:start position:0% +beta oxidation system was primarily + + + align:start position:0% +beta oxidation system was primarily +designed to process fatty acids with + + align:start position:0% +designed to process fatty acids with + + + align:start position:0% +designed to process fatty acids with +even numbers of carbon units the second + + align:start position:0% +even numbers of carbon units the second + + + align:start position:0% +even numbers of carbon units the second +problem that we'll look at as an ending + + align:start position:0% +problem that we'll look at as an ending + + + align:start position:0% +problem that we'll look at as an ending +of fatty acid oxidation concerns the + + align:start position:0% +of fatty acid oxidation concerns the + + + align:start position:0% +of fatty acid oxidation concerns the +fact that some of the fatty acids in our + + align:start position:0% +fact that some of the fatty acids in our + + + align:start position:0% +fact that some of the fatty acids in our +diet have a double bond that is either + + align:start position:0% +diet have a double bond that is either + + + align:start position:0% +diet have a double bond that is either +in the wrong stereochemistry or is in + + align:start position:0% +in the wrong stereochemistry or is in + + + align:start position:0% +in the wrong stereochemistry or is in +the wrong place to enable easy + + align:start position:0% +the wrong place to enable easy + + + align:start position:0% +the wrong place to enable easy +metabolism + + align:start position:0% +metabolism + + + align:start position:0% +metabolism +Nature has worked out ways to reposition + + align:start position:0% +Nature has worked out ways to reposition + + + align:start position:0% +Nature has worked out ways to reposition +the double bond to facilitate the entry + + align:start position:0% +the double bond to facilitate the entry + + + align:start position:0% +the double bond to facilitate the entry +of the molecule into classical beta + + align:start position:0% +of the molecule into classical beta + + + align:start position:0% +of the molecule into classical beta +oxidation schemes let's look now at + + align:start position:0% +oxidation schemes let's look now at + + + align:start position:0% +oxidation schemes let's look now at +panel II the first step in fatty acid + + align:start position:0% +panel II the first step in fatty acid + + + align:start position:0% +panel II the first step in fatty acid +catabolism involves thio esterification + + align:start position:0% +catabolism involves thio esterification + + + align:start position:0% +catabolism involves thio esterification +of the carboxylate residue of the fatty + + align:start position:0% +of the carboxylate residue of the fatty + + + align:start position:0% +of the carboxylate residue of the fatty +acid we're going to see in a couple of + + align:start position:0% +acid we're going to see in a couple of + + + align:start position:0% +acid we're going to see in a couple of +minutes that placing a coenzyme a moiety + + align:start position:0% +minutes that placing a coenzyme a moiety + + + align:start position:0% +minutes that placing a coenzyme a moiety +on the carboxylate is going to enable + + align:start position:0% +on the carboxylate is going to enable + + + align:start position:0% +on the carboxylate is going to enable +chemistry at the beta carbon without the + + align:start position:0% +chemistry at the beta carbon without the + + + align:start position:0% +chemistry at the beta carbon without the +coenzyme a group chemistry at the beta + + align:start position:0% +coenzyme a group chemistry at the beta + + + align:start position:0% +coenzyme a group chemistry at the beta +carbon would be impossible the enzyme + + align:start position:0% +carbon would be impossible the enzyme + + + align:start position:0% +carbon would be impossible the enzyme +involved is called fatty acyl coenzyme a + + align:start position:0% +involved is called fatty acyl coenzyme a + + + align:start position:0% +involved is called fatty acyl coenzyme a +synthetase sometimes called ligase and + + align:start position:0% +synthetase sometimes called ligase and + + + align:start position:0% +synthetase sometimes called ligase and +it additionally goes by the more common + + align:start position:0% +it additionally goes by the more common + + + align:start position:0% +it additionally goes by the more common +name thio kinase this enzyme uses ATP to + + align:start position:0% +name thio kinase this enzyme uses ATP to + + + align:start position:0% +name thio kinase this enzyme uses ATP to +identity our box elate residue and then + + align:start position:0% +identity our box elate residue and then + + + align:start position:0% +identity our box elate residue and then +it allows coenzyme a to replace the a MP + + align:start position:0% +it allows coenzyme a to replace the a MP + + + align:start position:0% +it allows coenzyme a to replace the a MP +residue with the resulting product being + + align:start position:0% +residue with the resulting product being + + + align:start position:0% +residue with the resulting product being +a fatty acyl coenzyme a this reaction + + align:start position:0% +a fatty acyl coenzyme a this reaction + + + align:start position:0% +a fatty acyl coenzyme a this reaction +happens in the cytoplasm of the cell + + align:start position:0% +happens in the cytoplasm of the cell + + + align:start position:0% +happens in the cytoplasm of the cell +beta oxidation however is going to occur + + align:start position:0% +beta oxidation however is going to occur + + + align:start position:0% +beta oxidation however is going to occur +in the mitochondrial matrix so we have + + align:start position:0% +in the mitochondrial matrix so we have + + + align:start position:0% +in the mitochondrial matrix so we have +to find a way to get this fatty acyl + + align:start position:0% +to find a way to get this fatty acyl + + + align:start position:0% +to find a way to get this fatty acyl +coenzyme a into the mitochondrial matrix + + align:start position:0% +coenzyme a into the mitochondrial matrix + + + align:start position:0% +coenzyme a into the mitochondrial matrix +let's go now to storyboard eighteen + + align:start position:0% +let's go now to storyboard eighteen + + + align:start position:0% +let's go now to storyboard eighteen +panel a panel a shows the cytoplasm the + + align:start position:0% +panel a panel a shows the cytoplasm the + + + align:start position:0% +panel a panel a shows the cytoplasm the +mitochondrial outer membrane the inter + + align:start position:0% +mitochondrial outer membrane the inter + + + align:start position:0% +mitochondrial outer membrane the inter +membrane space the inner membrane and + + align:start position:0% +membrane space the inner membrane and + + + align:start position:0% +membrane space the inner membrane and +the my + + align:start position:0% +the my + + + align:start position:0% +the my +andreal matrix as I just said the matrix + + align:start position:0% +andreal matrix as I just said the matrix + + + align:start position:0% +andreal matrix as I just said the matrix +is going to be the site at which beta + + align:start position:0% +is going to be the site at which beta + + + align:start position:0% +is going to be the site at which beta +oxidation occurs the intermembrane space + + align:start position:0% +oxidation occurs the intermembrane space + + + align:start position:0% +oxidation occurs the intermembrane space +contains a small alcohol called + + align:start position:0% +contains a small alcohol called + + + align:start position:0% +contains a small alcohol called +carnitine and the mitochondrial outer + + align:start position:0% +carnitine and the mitochondrial outer + + + align:start position:0% +carnitine and the mitochondrial outer +membrane contains an enzyme called + + align:start position:0% +membrane contains an enzyme called + + + align:start position:0% +membrane contains an enzyme called +carnitine acyl transferase one or cat + + align:start position:0% +carnitine acyl transferase one or cat + + + align:start position:0% +carnitine acyl transferase one or cat +one cat one removes the acyl group from + + align:start position:0% +one cat one removes the acyl group from + + + align:start position:0% +one cat one removes the acyl group from +the fatty acyl coenzyme a in the + + align:start position:0% +the fatty acyl coenzyme a in the + + + align:start position:0% +the fatty acyl coenzyme a in the +cytoplasm and transfers it to the + + align:start position:0% +cytoplasm and transfers it to the + + + align:start position:0% +cytoplasm and transfers it to the +alcoholic residue in the center of the + + align:start position:0% +alcoholic residue in the center of the + + + align:start position:0% +alcoholic residue in the center of the +carnitine molecule forming an ester of + + align:start position:0% +carnitine molecule forming an ester of + + + align:start position:0% +carnitine molecule forming an ester of +the fatty acid with carnitine this ester + + align:start position:0% +the fatty acid with carnitine this ester + + + align:start position:0% +the fatty acid with carnitine this ester +is delivered to cat two which is + + align:start position:0% +is delivered to cat two which is + + + align:start position:0% +is delivered to cat two which is +embedded in the inner membrane on the + + align:start position:0% +embedded in the inner membrane on the + + + align:start position:0% +embedded in the inner membrane on the +matrix side cat two will then transfer + + align:start position:0% +matrix side cat two will then transfer + + + align:start position:0% +matrix side cat two will then transfer +the ACL functionality to a coenzyme a + + align:start position:0% +the ACL functionality to a coenzyme a + + + align:start position:0% +the ACL functionality to a coenzyme a +restoring the fatty acyl coenzyme a + + align:start position:0% +restoring the fatty acyl coenzyme a + + + align:start position:0% +restoring the fatty acyl coenzyme a +molecule + + align:start position:0% +molecule + + + align:start position:0% +molecule +thus cat one and cat two working in a + + align:start position:0% +thus cat one and cat two working in a + + + align:start position:0% +thus cat one and cat two working in a +concerted way result in the effective + + align:start position:0% +concerted way result in the effective + + + align:start position:0% +concerted way result in the effective +transfer of a fatty acyl coenzyme a from + + align:start position:0% +transfer of a fatty acyl coenzyme a from + + + align:start position:0% +transfer of a fatty acyl coenzyme a from +the cytoplasm into the mitochondrial + + align:start position:0% +the cytoplasm into the mitochondrial + + + align:start position:0% +the cytoplasm into the mitochondrial +matrix the site of beta oxidation which + + align:start position:0% +matrix the site of beta oxidation which + + + align:start position:0% +matrix the site of beta oxidation which +will be our next step let's now look at + + align:start position:0% +will be our next step let's now look at + + + align:start position:0% +will be our next step let's now look at +panel B this panel shows an inset with + + align:start position:0% +panel B this panel shows an inset with + + + align:start position:0% +panel B this panel shows an inset with +the mitochondrial inner membrane the + + align:start position:0% +the mitochondrial inner membrane the + + + align:start position:0% +the mitochondrial inner membrane the +electron transfer complex and ETF P the + + align:start position:0% +electron transfer complex and ETF P the + + + align:start position:0% +electron transfer complex and ETF P the +electron transferring flavor protein + + align:start position:0% +electron transferring flavor protein + + + align:start position:0% +electron transferring flavor protein +which is going to be the entry point of + + align:start position:0% +which is going to be the entry point of + + + align:start position:0% +which is going to be the entry point of +electrons from the initial step of + + align:start position:0% +electrons from the initial step of + + + align:start position:0% +electrons from the initial step of +oxidation of the fatty acyl Co way into + + align:start position:0% +oxidation of the fatty acyl Co way into + + + align:start position:0% +oxidation of the fatty acyl Co way into +the electron transport chain we also see + + align:start position:0% +the electron transport chain we also see + + + align:start position:0% +the electron transport chain we also see +in this panel the fatty acid palmitate + + align:start position:0% +in this panel the fatty acid palmitate + + + align:start position:0% +in this panel the fatty acid palmitate +the C 16 straight chain carboxylic acid + + align:start position:0% +the C 16 straight chain carboxylic acid + + + align:start position:0% +the C 16 straight chain carboxylic acid +the hydrogen beta to the coenzyme a + + align:start position:0% +the hydrogen beta to the coenzyme a + + + align:start position:0% +the hydrogen beta to the coenzyme a +ester is relatively acidic therefore + + align:start position:0% +ester is relatively acidic therefore + + + align:start position:0% +ester is relatively acidic therefore +this hydrogen will be taken off to form + + align:start position:0% +this hydrogen will be taken off to form + + + align:start position:0% +this hydrogen will be taken off to form +an alkene and the hydride will be + + align:start position:0% +an alkene and the hydride will be + + + align:start position:0% +an alkene and the hydride will be +transferred from the dated carbon the + + align:start position:0% +transferred from the dated carbon the + + + align:start position:0% +transferred from the dated carbon the +third carbon from the right those + + align:start position:0% +third carbon from the right those + + + align:start position:0% +third carbon from the right those +electrons are transferred to a flavin in + + align:start position:0% +electrons are transferred to a flavin in + + + align:start position:0% +electrons are transferred to a flavin in +the electron transferring flavor protein + + align:start position:0% +the electron transferring flavor protein + + + align:start position:0% +the electron transferring flavor protein +ETF P eventually those electrons are + + align:start position:0% +ETF P eventually those electrons are + + + align:start position:0% +ETF P eventually those electrons are +transferred to coenzyme q to form the + + align:start position:0% +transferred to coenzyme q to form the + + + align:start position:0% +transferred to coenzyme q to form the +reduced form of coenzyme q those + + align:start position:0% +reduced form of coenzyme q those + + + align:start position:0% +reduced form of coenzyme q those +electrons then travel along through the + + align:start position:0% +electrons then travel along through the + + + align:start position:0% +electrons then travel along through the +electron transport chain the organic + + align:start position:0% +electron transport chain the organic + + + align:start position:0% +electron transport chain the organic +product of this reaction is a trans inna + + align:start position:0% +product of this reaction is a trans inna + + + align:start position:0% +product of this reaction is a trans inna +wheel coenzyme + + align:start position:0% +wheel coenzyme + + + align:start position:0% +wheel coenzyme +eh now let's take a look at panel C in + + align:start position:0% +eh now let's take a look at panel C in + + + align:start position:0% +eh now let's take a look at panel C in +the next step water is added to the + + align:start position:0% +the next step water is added to the + + + align:start position:0% +the next step water is added to the +three carbon of the inna wheel coenzyme + + align:start position:0% +three carbon of the inna wheel coenzyme + + + align:start position:0% +three carbon of the inna wheel coenzyme +a resulting product is a three hydroxy + + align:start position:0% +a resulting product is a three hydroxy + + + align:start position:0% +a resulting product is a three hydroxy +fatty acyl coenzyme a we've seen + + align:start position:0% +fatty acyl coenzyme a we've seen + + + align:start position:0% +fatty acyl coenzyme a we've seen +oxidation of alcohols that look + + align:start position:0% +oxidation of alcohols that look + + + align:start position:0% +oxidation of alcohols that look +something like this many times + + align:start position:0% +something like this many times + + + align:start position:0% +something like this many times +for example malate being oxidized by + + align:start position:0% +for example malate being oxidized by + + + align:start position:0% +for example malate being oxidized by +malate dehydrogenase to oxaloacetate and + + align:start position:0% +malate dehydrogenase to oxaloacetate and + + + align:start position:0% +malate dehydrogenase to oxaloacetate and +as we've seen before the hydroxyl group + + align:start position:0% +as we've seen before the hydroxyl group + + + align:start position:0% +as we've seen before the hydroxyl group +is converted to a keto functionality + + align:start position:0% +is converted to a keto functionality + + + align:start position:0% +is converted to a keto functionality +hydride transfer goes to nad plus to + + align:start position:0% +hydride transfer goes to nad plus to + + + align:start position:0% +hydride transfer goes to nad plus to +form NADH the enzyme that does this + + align:start position:0% +form NADH the enzyme that does this + + + align:start position:0% +form NADH the enzyme that does this +conversion is three hydroxy fatty acyl + + align:start position:0% +conversion is three hydroxy fatty acyl + + + align:start position:0% +conversion is three hydroxy fatty acyl +coenzyme a dehydrogenase at this point + + align:start position:0% +coenzyme a dehydrogenase at this point + + + align:start position:0% +coenzyme a dehydrogenase at this point +we have generated one fadh2 and one NADH + + align:start position:0% +we have generated one fadh2 and one NADH + + + align:start position:0% +we have generated one fadh2 and one NADH +in the overall process of the beta + + align:start position:0% +in the overall process of the beta + + + align:start position:0% +in the overall process of the beta +oxidation scheme the three keto ACL + + align:start position:0% +oxidation scheme the three keto ACL + + + align:start position:0% +oxidation scheme the three keto ACL +coenzyme a is now set up to release a + + align:start position:0% +coenzyme a is now set up to release a + + + align:start position:0% +coenzyme a is now set up to release a +first molecule of acetyl coenzyme a the + + align:start position:0% +first molecule of acetyl coenzyme a the + + + align:start position:0% +first molecule of acetyl coenzyme a the +enzyme beta keto thiolase is assisting + + align:start position:0% +enzyme beta keto thiolase is assisting + + + align:start position:0% +enzyme beta keto thiolase is assisting +on it the thigh all of the cysteine will + + align:start position:0% +on it the thigh all of the cysteine will + + + align:start position:0% +on it the thigh all of the cysteine will +attack the carbon that has the keto + + align:start position:0% +attack the carbon that has the keto + + + align:start position:0% +attack the carbon that has the keto +group and release acetylcholine xym a + + align:start position:0% +group and release acetylcholine xym a + + + align:start position:0% +group and release acetylcholine xym a +the residue is a thio ester in which the + + align:start position:0% +the residue is a thio ester in which the + + + align:start position:0% +the residue is a thio ester in which the +residual 14 carbons of the palmitate + + align:start position:0% +residual 14 carbons of the palmitate + + + align:start position:0% +residual 14 carbons of the palmitate +that we started with are now connected + + align:start position:0% +that we started with are now connected + + + align:start position:0% +that we started with are now connected +to beta keto thiolase lastly beta keto + + align:start position:0% +to beta keto thiolase lastly beta keto + + + align:start position:0% +to beta keto thiolase lastly beta keto +thiolase will transfer this residual 14 + + align:start position:0% +thiolase will transfer this residual 14 + + + align:start position:0% +thiolase will transfer this residual 14 +carbons to a coenzyme a molecule forming + + align:start position:0% +carbons to a coenzyme a molecule forming + + + align:start position:0% +carbons to a coenzyme a molecule forming +the fatty acyl coenzyme a that will be + + align:start position:0% +the fatty acyl coenzyme a that will be + + + align:start position:0% +the fatty acyl coenzyme a that will be +14 carbons long that is it's two carbons + + align:start position:0% +14 carbons long that is it's two carbons + + + align:start position:0% +14 carbons long that is it's two carbons +shorter than the 16 carbons of palmitate + + align:start position:0% +shorter than the 16 carbons of palmitate + + + align:start position:0% +shorter than the 16 carbons of palmitate +that we started with overall this + + align:start position:0% +that we started with overall this + + + align:start position:0% +that we started with overall this +process is called beta oxidation the + + align:start position:0% +process is called beta oxidation the + + + align:start position:0% +process is called beta oxidation the +system is now set up to allow the 14 + + align:start position:0% +system is now set up to allow the 14 + + + align:start position:0% +system is now set up to allow the 14 +carbon molecule to go to 12 to 10 and so + + align:start position:0% +carbon molecule to go to 12 to 10 and so + + + align:start position:0% +carbon molecule to go to 12 to 10 and so +on until the entire 16 carbon + + align:start position:0% +on until the entire 16 carbon + + + align:start position:0% +on until the entire 16 carbon +hydrocarbon has been reduced through + + align:start position:0% +hydrocarbon has been reduced through + + + align:start position:0% +hydrocarbon has been reduced through +seven rounds of beta oxidation to eight + + align:start position:0% +seven rounds of beta oxidation to eight + + + align:start position:0% +seven rounds of beta oxidation to eight +molecules of acid Hil coenzyme a if + + align:start position:0% +molecules of acid Hil coenzyme a if + + + align:start position:0% +molecules of acid Hil coenzyme a if +these eight molecules of acetyl co a are + + align:start position:0% +these eight molecules of acetyl co a are + + + align:start position:0% +these eight molecules of acetyl co a are +further oxidized by the TCA cycle you'll + + align:start position:0% +further oxidized by the TCA cycle you'll + + + align:start position:0% +further oxidized by the TCA cycle you'll +get 96 ATP molecules and of course along + + align:start position:0% +get 96 ATP molecules and of course along + + + align:start position:0% +get 96 ATP molecules and of course along +the way in each round of beta oxidation + + align:start position:0% +the way in each round of beta oxidation + + + align:start position:0% +the way in each round of beta oxidation +you will also produce seven fadh2s + + align:start position:0% +you will also produce seven fadh2s + + + align:start position:0% +you will also produce seven fadh2s +seven fadh2s will be converted into 14 + + align:start position:0% +seven fadh2s will be converted into 14 + + + align:start position:0% +seven fadh2s will be converted into 14 +ATP's + + align:start position:0% +ATP's + + + align:start position:0% +ATP's +you will also get seven nadh s and they + + align:start position:0% +you will also get seven nadh s and they + + + align:start position:0% +you will also get seven nadh s and they +will be converted into 21 ATP's so the + + align:start position:0% +will be converted into 21 ATP's so the + + + align:start position:0% +will be converted into 21 ATP's so the +full conversion of the sixteen carbon + + align:start position:0% +full conversion of the sixteen carbon + + + align:start position:0% +full conversion of the sixteen carbon +hydrocarbon palmitate will result in a + + align:start position:0% +hydrocarbon palmitate will result in a + + + align:start position:0% +hydrocarbon palmitate will result in a +total of 131 ATP's in order to put + + align:start position:0% +total of 131 ATP's in order to put + + + align:start position:0% +total of 131 ATP's in order to put +together a full balance sheet however + + align:start position:0% +together a full balance sheet however + + + align:start position:0% +together a full balance sheet however +keep in mind that we needed to use + + align:start position:0% +keep in mind that we needed to use + + + align:start position:0% +keep in mind that we needed to use +several ATP's early in the process in + + align:start position:0% +several ATP's early in the process in + + + align:start position:0% +several ATP's early in the process in +order to prime the system that is fatty + + align:start position:0% +order to prime the system that is fatty + + + align:start position:0% +order to prime the system that is fatty +acyl coenzyme a synthetized use two high + + align:start position:0% +acyl coenzyme a synthetized use two high + + + align:start position:0% +acyl coenzyme a synthetized use two high +energy phosphate bonds in order to prime + + align:start position:0% +energy phosphate bonds in order to prime + + + align:start position:0% +energy phosphate bonds in order to prime +the fatty acid for production of the + + align:start position:0% +the fatty acid for production of the + + + align:start position:0% +the fatty acid for production of the +coenzyme a intermediate that's necessary + + align:start position:0% +coenzyme a intermediate that's necessary + + + align:start position:0% +coenzyme a intermediate that's necessary +for beta oxidation \ No newline at end of file diff --git a/jlG7NyE06OQ.txt b/jlG7NyE06OQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..553f1bb7cf19f209fce890c89392304d99b4f4b4 --- /dev/null +++ b/jlG7NyE06OQ.txt @@ -0,0 +1,443 @@ +align:start position:0% + +and team 11 is in the air team 11 team + + align:start position:0% +and team 11 is in the air team 11 team + + + align:start position:0% +and team 11 is in the air team 11 team +11 team 11 two guys two girls and an + + align:start position:0% +11 team 11 two guys two girls and an + + + align:start position:0% +11 team 11 two guys two girls and an +airplane come down two + + align:start position:0% +airplane come down two + + + align:start position:0% +airplane come down two +guys out of control he's out of + + align:start position:0% + + + + align:start position:0% + +shrim out of control the elevator trim + + align:start position:0% +shrim out of control the elevator trim + + + align:start position:0% +shrim out of control the elevator trim +is wrong see see it pitches up when he + + align:start position:0% +is wrong see see it pitches up when he + + + align:start position:0% +is wrong see see it pitches up when he +the car okay out of trim + + align:start position:0% + + + + align:start position:0% + +M + + align:start position:0% + + + + align:start position:0% + +MH he'll be lucky to come back alive but + + align:start position:0% +MH he'll be lucky to come back alive but + + + align:start position:0% +MH he'll be lucky to come back alive but +let's see now the problem is + + align:start position:0% + + + + align:start position:0% + +going problem's going to be when he + + align:start position:0% +going problem's going to be when he + + + align:start position:0% +going problem's going to be when he +uh now UPS the + + align:start position:0% +uh now UPS the + + + align:start position:0% +uh now UPS the +speak and we + + align:start position:0% +speak and we + + + align:start position:0% +speak and we +are almost out of the + + align:start position:0% +are almost out of the + + + align:start position:0% +are almost out of the +out of the out of the + + align:start position:0% +out of the out of the + + + align:start position:0% +out of the out of the +stadium some people just got to + + align:start position:0% + + + + align:start position:0% + +fly some people just got to + + align:start position:0% + + + + align:start position:0% + +fly and we have + + align:start position:0% +fly and we have + + + align:start position:0% +fly and we have +the pit + + align:start position:0% + + + + align:start position:0% + +crew sort of + + align:start position:0% +crew sort of + + + align:start position:0% +crew sort of +uh doing major repairs on the airplane + + align:start position:0% +uh doing major repairs on the airplane + + + align:start position:0% +uh doing major repairs on the airplane +loading eggs + + align:start position:0% +loading eggs + + + align:start position:0% +loading eggs +the wing has been + + align:start position:0% + + + + align:start position:0% + +removed out he's really got to fix it + + align:start position:0% +removed out he's really got to fix it + + + align:start position:0% +removed out he's really got to fix it +Tri but now the center of gravity is + + align:start position:0% +Tri but now the center of gravity is + + + align:start position:0% +Tri but now the center of gravity is +changing where's it going to be if it's + + align:start position:0% +changing where's it going to be if it's + + + align:start position:0% +changing where's it going to be if it's +behind where it was before they're toast + + align:start position:0% + + + + align:start position:0% + +Okay so here still + + align:start position:0% +Okay so here still + + + align:start position:0% +Okay so here still +uh still doing our best + + align:start position:0% +uh still doing our best + + + align:start position:0% +uh still doing our best +though get the plane + + align:start position:0% + + + + align:start position:0% + +going and + + align:start position:0% +going and + + + align:start position:0% +going and +um take it from + + align:start position:0% + + + + align:start position:0% + +there still on the ground 2 + + align:start position:0% +there still on the ground 2 + + + align:start position:0% +there still on the ground 2 +minutes returning back to the uh Fe + + align:start position:0% + + + + align:start position:0% + +raymondi resident + + align:start position:0% + + + + align:start position:0% + +Italian sort of speeding things up a + + align:start position:0% +Italian sort of speeding things up a + + + align:start position:0% +Italian sort of speeding things up a +little bit two door at the uh controls + + align:start position:0% +little bit two door at the uh controls + + + align:start position:0% +little bit two door at the uh controls +and uh we'll see if we can get back in + + align:start position:0% +and uh we'll see if we can get back in + + + align:start position:0% +and uh we'll see if we can get back in +the air we're back in the + + align:start position:0% +the air we're back in the + + + align:start position:0% +the air we're back in the +air we're + + align:start position:0% +air we're + + + align:start position:0% +air we're +Turner and + + align:start position:0% + + + + align:start position:0% + +uh have had + + align:start position:0% +uh have had + + + align:start position:0% +uh have had +a graduate ta attack but we are still in + + align:start position:0% +a graduate ta attack but we are still in + + + align:start position:0% +a graduate ta attack but we are still in +the + + align:start position:0% +the + + + align:start position:0% +the +air with three eggs + + align:start position:0% +air with three eggs + + + align:start position:0% +air with three eggs +now hopefully for a long + + align:start position:0% + + + + align:start position:0% + +duration and + + align:start position:0% +duration and + + + align:start position:0% +duration and +uh we'll + + align:start position:0% + + + + align:start position:0% + +see how we do not bad not bad certainly + + align:start position:0% +see how we do not bad not bad certainly + + + align:start position:0% +see how we do not bad not bad certainly +more than the um 18 seconds we had on + + align:start position:0% +more than the um 18 seconds we had on + + + align:start position:0% +more than the um 18 seconds we had on +the for the reduced fat double stuffed + + align:start position:0% +the for the reduced fat double stuffed + + + align:start position:0% +the for the reduced fat double stuffed +Oreos we'll see if we're able to get + + align:start position:0% +Oreos we'll see if we're able to get + + + align:start position:0% +Oreos we'll see if we're able to get +anywhere near + + align:start position:0% +anywhere near + + + align:start position:0% +anywhere near +the oh we're at 1 minute 1 minute we got + + align:start position:0% +the oh we're at 1 minute 1 minute we got + + + align:start position:0% +the oh we're at 1 minute 1 minute we got +it oh and we're still in the air though + + align:start position:0% +it oh and we're still in the air though + + + align:start position:0% +it oh and we're still in the air though +we're all right with one minute \ No newline at end of file diff --git a/lWTUcojZ_gQ.txt b/lWTUcojZ_gQ.txt new file mode 100644 index 0000000000000000000000000000000000000000..c10494b45942fabd44014f2defc50aae99417eaa --- /dev/null +++ b/lWTUcojZ_gQ.txt @@ -0,0 +1,2515 @@ +align:start position:0% + +simultaneous eigen states pain yes so + + align:start position:0% +simultaneous eigen states pain yes so + + + align:start position:0% +simultaneous eigen states pain yes so +let's begin with that we decided that we + + align:start position:0% +let's begin with that we decided that we + + + align:start position:0% +let's begin with that we decided that we +could pick one L an l squared and they + + align:start position:0% +could pick one L an l squared and they + + + align:start position:0% +could pick one L an l squared and they +would commute and we could try to find + + align:start position:0% +would commute and we could try to find + + + align:start position:0% +would commute and we could try to find +functions that are eigenstates of both + + align:start position:0% +functions that are eigenstates of both + + + align:start position:0% +functions that are eigenstates of both +so if we have functions that our + + align:start position:0% +so if we have functions that our + + + align:start position:0% +so if we have functions that our +eigenstates of those will try to expand + + align:start position:0% +eigenstates of those will try to expand + + + align:start position:0% +eigenstates of those will try to expand +in terms of those functions and all this + + align:start position:0% +in terms of those functions and all this + + + align:start position:0% +in terms of those functions and all this +operator will become a number acting on + + align:start position:0% +operator will become a number acting on + + + align:start position:0% +operator will become a number acting on +those functions and that's why the + + align:start position:0% +those functions and that's why the + + + align:start position:0% +those functions and that's why the +laplacian simplifies and that's why + + align:start position:0% +laplacian simplifies and that's why + + + align:start position:0% +laplacian simplifies and that's why +we'll be able to reduce the Schrodinger + + align:start position:0% +we'll be able to reduce the Schrodinger + + + align:start position:0% +we'll be able to reduce the Schrodinger +equation to a radial equation this is + + align:start position:0% +equation to a radial equation this is + + + align:start position:0% +equation to a radial equation this is +the goal Schrodinger equation has R + + align:start position:0% +the goal Schrodinger equation has R + + + align:start position:0% +the goal Schrodinger equation has R +theta and Phi but theta and Phi will + + align:start position:0% +theta and Phi but theta and Phi will + + + align:start position:0% +theta and Phi but theta and Phi will +deal with all the angular dependence + + align:start position:0% +deal with all the angular dependence + + + align:start position:0% +deal with all the angular dependence +we'll find functions for which that + + align:start position:0% +we'll find functions for which that + + + align:start position:0% +we'll find functions for which that +operator gives a number acting on them + + align:start position:0% +operator gives a number acting on them + + + align:start position:0% +operator gives a number acting on them +and therefore the whole differential + + align:start position:0% +and therefore the whole differential + + + align:start position:0% +and therefore the whole differential +equation will simplify so simultaneous + + align:start position:0% +equation will simplify so simultaneous + + + align:start position:0% +equation will simplify so simultaneous +eigen states and given the simplicity of + + align:start position:0% +eigen states and given the simplicity of + + + align:start position:0% +eigen states and given the simplicity of +LZ everybody chooses LZ so we should + + align:start position:0% +LZ everybody chooses LZ so we should + + + align:start position:0% +LZ everybody chooses LZ so we should +find simultaneous eigen states of these + + align:start position:0% +find simultaneous eigen states of these + + + align:start position:0% +find simultaneous eigen states of these +two things and let's call them sy L M of + + align:start position:0% +two things and let's call them sy L M of + + + align:start position:0% +two things and let's call them sy L M of +theta and Phi where L and M are numbers + + align:start position:0% +theta and Phi where L and M are numbers + + + align:start position:0% +theta and Phi where L and M are numbers +that at this moment are totally + + align:start position:0% +that at this moment are totally + + + align:start position:0% +that at this moment are totally +arbitrary but are related to the eigen + + align:start position:0% +arbitrary but are related to the eigen + + + align:start position:0% +arbitrary but are related to the eigen +values of these equations so we wish + + align:start position:0% +values of these equations so we wish + + + align:start position:0% +values of these equations so we wish +that LZ acting on ylm is going to be a + + align:start position:0% +that LZ acting on ylm is going to be a + + + align:start position:0% +that LZ acting on ylm is going to be a +number times ilm that is to be an eigen + + align:start position:0% +number times ilm that is to be an eigen + + + align:start position:0% +number times ilm that is to be an eigen +state the number must have the right + + align:start position:0% +state the number must have the right + + + align:start position:0% +state the number must have the right +units must be an H bar and then we'll + + align:start position:0% +units must be an H bar and then we'll + + + align:start position:0% +units must be an H bar and then we'll +use M that we don't say what M is yet M + + align:start position:0% +use M that we don't say what M is yet M + + + align:start position:0% +use M that we don't say what M is yet M +where m belongs to the real numbers + + align:start position:0% +where m belongs to the real numbers + + + align:start position:0% +where m belongs to the real numbers +because the eigen values of a hermitian + + align:start position:0% +because the eigen values of a hermitian + + + align:start position:0% +because the eigen values of a hermitian +operator are always real so this could + + align:start position:0% +operator are always real so this could + + + align:start position:0% +operator are always real so this could +be what we would demand from LZ from l + + align:start position:0% +be what we would demand from LZ from l + + + align:start position:0% +be what we would demand from LZ from l +squared on psy LM I can demand that this + + align:start position:0% +squared on psy LM I can demand that this + + + align:start position:0% +squared on psy LM I can demand that this +be equal because of units and H squared + + align:start position:0% +be equal because of units and H squared + + + align:start position:0% +be equal because of units and H squared +and then a number lambda sy L M now this + + align:start position:0% +and then a number lambda sy L M now this + + + align:start position:0% +and then a number lambda sy L M now this +lambda do I know anything about this + + align:start position:0% +lambda do I know anything about this + + + align:start position:0% +lambda do I know anything about this +lambda well I could argue that this + + align:start position:0% +lambda well I could argue that this + + + align:start position:0% +lambda well I could argue that this +lambda has to be positive and the reason + + align:start position:0% +lambda has to be positive and the reason + + + align:start position:0% +lambda has to be positive and the reason +is that this begins as some sort of + + align:start position:0% +is that this begins as some sort of + + + align:start position:0% +is that this begins as some sort of +positive operator is l squared now that + + align:start position:0% +positive operator is l squared now that + + + align:start position:0% +positive operator is l squared now that +intuition may not be completely precise + + align:start position:0% +intuition may not be completely precise + + + align:start position:0% +intuition may not be completely precise +but if you followed it a little more + + align:start position:0% +but if you followed it a little more + + + align:start position:0% +but if you followed it a little more +with an inner product suppose we would + + align:start position:0% +with an inner product suppose we would + + + align:start position:0% +with an inner product suppose we would +have an inner product and we can put + + align:start position:0% +have an inner product and we can put + + + align:start position:0% +have an inner product and we can put +sigh LM here and L squared + + align:start position:0% +sigh LM here and L squared + + + align:start position:0% +sigh LM here and L squared +sigh LM from this equation this would be + + align:start position:0% +sigh LM from this equation this would be + + + align:start position:0% +sigh LM from this equation this would be +equal to H squared lambda sigh LM sigh + + align:start position:0% +equal to H squared lambda sigh LM sigh + + + align:start position:0% +equal to H squared lambda sigh LM sigh +LM an inner product if you have it there + + align:start position:0% +LM an inner product if you have it there + + + align:start position:0% +LM an inner product if you have it there +and then if your wave functions are + + align:start position:0% +and then if your wave functions are + + + align:start position:0% +and then if your wave functions are +suitably normalized this would be a 1 + + align:start position:0% +suitably normalized this would be a 1 + + + align:start position:0% +suitably normalized this would be a 1 +but this thing + + align:start position:0% + + + + align:start position:0% + +LX LX plus ly ly plus LZ l v and LX LX + + align:start position:0% +LX LX plus ly ly plus LZ l v and LX LX + + + align:start position:0% +LX LX plus ly ly plus LZ l v and LX LX +you could bring one LX here and you + + align:start position:0% +you could bring one LX here and you + + + align:start position:0% +you could bring one LX here and you +would have LX sy l m LX sy l m + the + + align:start position:0% +would have LX sy l m LX sy l m + the + + + align:start position:0% +would have LX sy l m LX sy l m + the +same thing for y and for Z and each of + + align:start position:0% +same thing for y and for Z and each of + + + align:start position:0% +same thing for y and for Z and each of +these things is positive because when + + align:start position:0% +these things is positive because when + + + align:start position:0% +these things is positive because when +you have the same wave function on the + + align:start position:0% +you have the same wave function on the + + + align:start position:0% +you have the same wave function on the +left and on the right you integrate the + + align:start position:0% +left and on the right you integrate the + + + align:start position:0% +left and on the right you integrate the +norm squared it's positive and this is + + align:start position:0% +norm squared it's positive and this is + + + align:start position:0% +norm squared it's positive and this is +positive this is positive so the sum + + align:start position:0% +positive this is positive so the sum + + + align:start position:0% +positive this is positive so the sum +must be positive and lambda must be + + align:start position:0% +must be positive and lambda must be + + + align:start position:0% +must be positive and lambda must be +positive so lambda must be positive this + + align:start position:0% +positive so lambda must be positive this + + + align:start position:0% +positive so lambda must be positive this +is our expectation and it's a reasonable + + align:start position:0% +is our expectation and it's a reasonable + + + align:start position:0% +is our expectation and it's a reasonable +expectation and that's why in fact + + align:start position:0% +expectation and that's why in fact + + + align:start position:0% +expectation and that's why in fact +anticipating a little the answer people + + align:start position:0% +anticipating a little the answer people + + + align:start position:0% +anticipating a little the answer people +write this as L times L plus 1 solemn + + align:start position:0% +write this as L times L plus 1 solemn + + + align:start position:0% +write this as L times L plus 1 solemn +and where L is a real number + + align:start position:0% +and where L is a real number + + + align:start position:0% +and where L is a real number +at this moment and you say well that's a + + align:start position:0% +at this moment and you say well that's a + + + align:start position:0% +at this moment and you say well that's a +little strange why do you put it as L + + align:start position:0% +little strange why do you put it as L + + + align:start position:0% +little strange why do you put it as L +times L plus 1 what's the reason the + + align:start position:0% +times L plus 1 what's the reason the + + + align:start position:0% +times L plus 1 what's the reason the +reason is comes when we look at the + + align:start position:0% +reason is comes when we look at the + + + align:start position:0% +reason is comes when we look at the +differential equation but the reason you + + align:start position:0% +differential equation but the reason you + + + align:start position:0% +differential equation but the reason you +don't get in trouble by doing this is + + align:start position:0% +don't get in trouble by doing this is + + + align:start position:0% +don't get in trouble by doing this is +that as you span all the real numbers + + align:start position:0% +that as you span all the real numbers + + + align:start position:0% +that as you span all the real numbers +the function L times L plus 1 is like + + align:start position:0% +the function L times L plus 1 is like + + + align:start position:0% +the function L times L plus 1 is like +this help them sell +1 and therefore + + align:start position:0% +this help them sell +1 and therefore + + + align:start position:0% +this help them sell +1 and therefore +whatever lambda you have that is + + align:start position:0% +whatever lambda you have that is + + + align:start position:0% +whatever lambda you have that is +positive there is some L for which L + + align:start position:0% +positive there is some L for which L + + + align:start position:0% +positive there is some L for which L +times L plus 1 is a positive number so + + align:start position:0% +times L plus 1 is a positive number so + + + align:start position:0% +times L plus 1 is a positive number so +there's nothing wrong I'm trying to + + align:start position:0% +there's nothing wrong I'm trying to + + + align:start position:0% +there's nothing wrong I'm trying to +argue there's nothing wrong with writing + + align:start position:0% +argue there's nothing wrong with writing + + + align:start position:0% +argue there's nothing wrong with writing +that the eigen value is of the form L + + align:start position:0% +that the eigen value is of the form L + + + align:start position:0% +that the eigen value is of the form L +times L plus 1 + + align:start position:0% +times L plus 1 + + + align:start position:0% +times L plus 1 +B + + align:start position:0% +B + + + align:start position:0% +B +because we know the eigen value is + + align:start position:0% +because we know the eigen value is + + + align:start position:0% +because we know the eigen value is +positive and therefore whatever lambda + + align:start position:0% +positive and therefore whatever lambda + + + align:start position:0% +positive and therefore whatever lambda +you give me this positive I can always + + align:start position:0% +you give me this positive I can always + + + align:start position:0% +you give me this positive I can always +find in fact two values of L for which L + + align:start position:0% +find in fact two values of L for which L + + + align:start position:0% +find in fact two values of L for which L +times L plus 1 is equal to lambda we can + + align:start position:0% +times L plus 1 is equal to lambda we can + + + align:start position:0% +times L plus 1 is equal to lambda we can +choose the positive one and that's what + + align:start position:0% +choose the positive one and that's what + + + align:start position:0% +choose the positive one and that's what +we will do so these are the equations we + + align:start position:0% +we will do so these are the equations we + + + align:start position:0% +we will do so these are the equations we +want to deal with are there questions + + align:start position:0% +want to deal with are there questions + + + align:start position:0% +want to deal with are there questions +and the setting up of these equations + + align:start position:0% +and the setting up of these equations + + + align:start position:0% +and the setting up of these equations +this is the conceptual part now begins a + + align:start position:0% +this is the conceptual part now begins a + + + align:start position:0% +this is the conceptual part now begins a +little bit of play with the differential + + align:start position:0% +little bit of play with the differential + + + align:start position:0% +little bit of play with the differential +equations and we'll have to do a little + + align:start position:0% +equations and we'll have to do a little + + + align:start position:0% +equations and we'll have to do a little +bit of work but this is what the + + align:start position:0% +bit of work but this is what the + + + align:start position:0% +bit of work but this is what the +physical intuition the commutator is + + align:start position:0% +physical intuition the commutator is + + + align:start position:0% +physical intuition the commutator is +everything led us to believe that we + + align:start position:0% +everything led us to believe that we + + + align:start position:0% +everything led us to believe that we +should be able to solve this much we + + align:start position:0% +should be able to solve this much we + + + align:start position:0% +should be able to solve this much we +should be able to find functions that do + + align:start position:0% +should be able to find functions that do + + + align:start position:0% +should be able to find functions that do +all this alright let's do the first one + + align:start position:0% +all this alright let's do the first one + + + align:start position:0% +all this alright let's do the first one +so the first equation + + align:start position:0% + + + + align:start position:0% + +the first equation is let me call it a + + align:start position:0% +the first equation is let me call it a + + + align:start position:0% +the first equation is let me call it a +equation 1 & 2 the first equation is + + align:start position:0% +equation 1 & 2 the first equation is + + + align:start position:0% +equation 1 & 2 the first equation is +h-bar over I be v5 that's L z sy LM + + align:start position:0% +h-bar over I be v5 that's L z sy LM + + + align:start position:0% +h-bar over I be v5 that's L z sy LM +equal H bar m sy LM so canceling the H + + align:start position:0% +equal H bar m sy LM so canceling the H + + + align:start position:0% +equal H bar m sy LM so canceling the H +bars you'll get DD Phi of Phi L M is + + align:start position:0% +bars you'll get DD Phi of Phi L M is + + + align:start position:0% +bars you'll get DD Phi of Phi L M is +equal to i m sy LM soaps i LM is equal + + align:start position:0% +equal to i m sy LM soaps i LM is equal + + + align:start position:0% +equal to i m sy LM soaps i LM is equal +to e to the I M Phi times some function + + align:start position:0% +to e to the I M Phi times some function + + + align:start position:0% +to e to the I M Phi times some function +of theta arbitrary function of theta at + + align:start position:0% +of theta arbitrary function of theta at + + + align:start position:0% +of theta arbitrary function of theta at +this moment so this is my solution + + align:start position:0% + + + + align:start position:0% + +this is Absalom of theta and Phi with + + align:start position:0% +this is Absalom of theta and Phi with + + + align:start position:0% +this is Absalom of theta and Phi with +determining the Phi dependence and it's + + align:start position:0% +determining the Phi dependence and it's + + + align:start position:0% +determining the Phi dependence and it's +not that complicated so at this moment + + align:start position:0% +not that complicated so at this moment + + + align:start position:0% +not that complicated so at this moment +you say well I'm going to use this for + + align:start position:0% +you say well I'm going to use this for + + + align:start position:0% +you say well I'm going to use this for +wave functions I want them to behave + + align:start position:0% +wave functions I want them to behave + + + align:start position:0% +wave functions I want them to behave +normally so if somebody gives me a value + + align:start position:0% +normally so if somebody gives me a value + + + align:start position:0% +normally so if somebody gives me a value +of Phi I can tell them what the wave + + align:start position:0% +of Phi I can tell them what the wave + + + align:start position:0% +of Phi I can tell them what the wave +function is and since Phi increases by 2 + + align:start position:0% +function is and since Phi increases by 2 + + + align:start position:0% +function is and since Phi increases by 2 +pi and it's periodic with 2 pi I may + + align:start position:0% +pi and it's periodic with 2 pi I may + + + align:start position:0% +pi and it's periodic with 2 pi I may +demand that sy LM of theta + 5 + 2 pi be + + align:start position:0% +demand that sy LM of theta + 5 + 2 pi be + + + align:start position:0% +demand that sy LM of theta + 5 + 2 pi be +the same as sy LM theta and Phi you + + align:start position:0% +the same as sy LM theta and Phi you + + + align:start position:0% +the same as sy LM theta and Phi you +could say well what if you could put the + + align:start position:0% +could say well what if you could put the + + + align:start position:0% +could say well what if you could put the +minus sign there well you could try the + + align:start position:0% +minus sign there well you could try the + + + align:start position:0% +minus sign there well you could try the +attempt + + align:start position:0% +attempt + + + align:start position:0% +attempt +would fail eventually there's nothing + + align:start position:0% +would fail eventually there's nothing + + + align:start position:0% +would fail eventually there's nothing +obviously wrong with trying to put the + + align:start position:0% +obviously wrong with trying to put the + + + align:start position:0% +obviously wrong with trying to put the +sign there but it doesn't work it would + + align:start position:0% +sign there but it doesn't work it would + + + align:start position:0% +sign there but it doesn't work it would +lead to very rather inconsistent things + + align:start position:0% +lead to very rather inconsistent things + + + align:start position:0% +lead to very rather inconsistent things +soon enough + + align:start position:0% +soon enough + + + align:start position:0% +soon enough +so this condition here requires that + + align:start position:0% +so this condition here requires that + + + align:start position:0% +so this condition here requires that +this function be periodic and never when + + align:start position:0% +this function be periodic and never when + + + align:start position:0% +this function be periodic and never when +five changes by 2pi it should be a + + align:start position:0% +five changes by 2pi it should be a + + + align:start position:0% +five changes by 2pi it should be a +multiple of 2pi so M belong to the + + align:start position:0% +multiple of 2pi so M belong to the + + + align:start position:0% +multiple of 2pi so M belong to the +integers so we found the first + + align:start position:0% +integers so we found the first + + + align:start position:0% +integers so we found the first +quantization the eigenvalues of LZ are + + align:start position:0% +quantization the eigenvalues of LZ are + + + align:start position:0% +quantization the eigenvalues of LZ are +quantized they have to be integers let's + + align:start position:0% +quantized they have to be integers let's + + + align:start position:0% +quantized they have to be integers let's +that was easy enough let's look at the + + align:start position:0% +that was easy enough let's look at the + + + align:start position:0% +that was easy enough let's look at the +second equation that takes a bit more + + align:start position:0% +second equation that takes a bit more + + + align:start position:0% +second equation that takes a bit more +work so what is the second equation well + + align:start position:0% +work so what is the second equation well + + + align:start position:0% +work so what is the second equation well +the most slightly complicated + + align:start position:0% +the most slightly complicated + + + align:start position:0% +the most slightly complicated +differential operator and let's see what + + align:start position:0% +differential operator and let's see what + + + align:start position:0% +differential operator and let's see what +it does + + align:start position:0% + + + + align:start position:0% + +so of l squared well we had it there so + + align:start position:0% +so of l squared well we had it there so + + + align:start position:0% +so of l squared well we had it there so +it's minus h squared 1 over sine theta V + + align:start position:0% +it's minus h squared 1 over sine theta V + + + align:start position:0% +it's minus h squared 1 over sine theta V +D theta sine theta DD theta plus 1 over + + align:start position:0% +D theta sine theta DD theta plus 1 over + + + align:start position:0% +D theta sine theta DD theta plus 1 over +sine squared theta the second D Phi + + align:start position:0% +sine squared theta the second D Phi + + + align:start position:0% +sine squared theta the second D Phi +squared sy LM equal h squared L times L + + align:start position:0% +squared sy LM equal h squared L times L + + + align:start position:0% +squared sy LM equal h squared L times L +plus 1 sy L M one thing we can do here + + align:start position:0% +plus 1 sy L M one thing we can do here + + + align:start position:0% +plus 1 sy L M one thing we can do here +is let the be D Phi squared act on this + + align:start position:0% +is let the be D Phi squared act on this + + + align:start position:0% +is let the be D Phi squared act on this +because we know what D defied us D D Phi + + align:start position:0% +because we know what D defied us D D Phi + + + align:start position:0% +because we know what D defied us D D Phi +brings an IM factor because you know + + align:start position:0% +brings an IM factor because you know + + + align:start position:0% +brings an IM factor because you know +already the Phi dependence of sy LM so + + align:start position:0% +already the Phi dependence of sy LM so + + + align:start position:0% +already the Phi dependence of sy LM so +of + + align:start position:0% +of + + + align:start position:0% +of +things we can do so we'll do the the + + align:start position:0% +things we can do so we'll do the the + + + align:start position:0% +things we can do so we'll do the the +second D Phi squared gives - gives you I + + align:start position:0% +second D Phi squared gives - gives you I + + + align:start position:0% +second D Phi squared gives - gives you I +M squared which is minus M squared + + align:start position:0% +M squared which is minus M squared + + + align:start position:0% +M squared which is minus M squared +multiplying the same function you can + + align:start position:0% +multiplying the same function you can + + + align:start position:0% +multiplying the same function you can +cancel the H bar squared cancel H bar + + align:start position:0% +cancel the H bar squared cancel H bar + + + align:start position:0% +cancel the H bar squared cancel H bar +squared and multiply by minus sine + + align:start position:0% +squared and multiply by minus sine + + + align:start position:0% +squared and multiply by minus sine +squared theta just clean up things so + + align:start position:0% +squared theta just clean up things so + + + align:start position:0% +squared theta just clean up things so +few things so here is what we have we + + align:start position:0% +few things so here is what we have we + + + align:start position:0% +few things so here is what we have we +have sine theta DD theta this is the + + align:start position:0% +have sine theta DD theta this is the + + + align:start position:0% +have sine theta DD theta this is the +minus sine squared of you're multiplying + + align:start position:0% +minus sine squared of you're multiplying + + + align:start position:0% +minus sine squared of you're multiplying +the H squared went away sine theta the + + align:start position:0% +the H squared went away sine theta the + + + align:start position:0% +the H squared went away sine theta the +PLM D theta + + align:start position:0% +PLM D theta + + + align:start position:0% +PLM D theta +already I substituted apps I was e to + + align:start position:0% +already I substituted apps I was e to + + + align:start position:0% +already I substituted apps I was e to +the IM phi times the P so I have that + + align:start position:0% +the IM phi times the P so I have that + + + align:start position:0% +the IM phi times the P so I have that +and maybe I should put the parentheses + + align:start position:0% +and maybe I should put the parentheses + + + align:start position:0% +and maybe I should put the parentheses +here to make it all look nicer then I + + align:start position:0% +here to make it all look nicer then I + + + align:start position:0% +here to make it all look nicer then I +have in here two more terms I'll bring + + align:start position:0% +have in here two more terms I'll bring + + + align:start position:0% +have in here two more terms I'll bring +the right hand side to the left it will + + align:start position:0% +the right hand side to the left it will + + + align:start position:0% +the right hand side to the left it will +end up with ll plus 1 sine squared theta + + align:start position:0% +end up with ll plus 1 sine squared theta + + + align:start position:0% +end up with ll plus 1 sine squared theta +minus M squared P L M equals 0 + + align:start position:0% + + + + align:start position:0% + +there we go that's a our differential + + align:start position:0% +there we go that's a our differential + + + align:start position:0% +there we go that's a our differential +equation it's a major somewhat + + align:start position:0% +equation it's a major somewhat + + + align:start position:0% +equation it's a major somewhat +complicated differential equation but + + align:start position:0% +complicated differential equation but + + + align:start position:0% +complicated differential equation but +it's a famous one because it comes from + + align:start position:0% +it's a famous one because it comes from + + + align:start position:0% +it's a famous one because it comes from +laplacian you know people had to study + + align:start position:0% +laplacian you know people had to study + + + align:start position:0% +laplacian you know people had to study +this equation or to do anything with + + align:start position:0% +this equation or to do anything with + + + align:start position:0% +this equation or to do anything with +laplacian sand so many problems so + + align:start position:0% +laplacian sand so many problems so + + + align:start position:0% +laplacian sand so many problems so +everything is known about this and the + + align:start position:0% +everything is known about this and the + + + align:start position:0% +everything is known about this and the +first thing that is known is that theta + + align:start position:0% +first thing that is known is that theta + + + align:start position:0% +first thing that is known is that theta +really appears as cosine theta + + align:start position:0% +really appears as cosine theta + + + align:start position:0% +really appears as cosine theta +everywhere and that makes sense you see + + align:start position:0% +everywhere and that makes sense you see + + + align:start position:0% +everywhere and that makes sense you see +theta and cosine theta is sort of the + + align:start position:0% +theta and cosine theta is sort of the + + + align:start position:0% +theta and cosine theta is sort of the +same thing even though it doesn't look + + align:start position:0% +same thing even though it doesn't look + + + align:start position:0% +same thing even though it doesn't look +like it you need angles that go from 0 + + align:start position:0% +like it you need angles that go from 0 + + + align:start position:0% +like it you need angles that go from 0 +to PI and that's nice but cosine theta + + align:start position:0% +to PI and that's nice but cosine theta + + + align:start position:0% +to PI and that's nice but cosine theta +in that interval goes from 1 to minus 1 + + align:start position:0% +in that interval goes from 1 to minus 1 + + + align:start position:0% +in that interval goes from 1 to minus 1 +so it's a good parameter you know people + + align:start position:0% +so it's a good parameter you know people + + + align:start position:0% +so it's a good parameter you know people +use 0 to 180 degrees of latitude but you + + align:start position:0% +use 0 to 180 degrees of latitude but you + + + align:start position:0% +use 0 to 180 degrees of latitude but you +could use from 1 to minus 1 the cosine + + align:start position:0% +could use from 1 to minus 1 the cosine + + + align:start position:0% +could use from 1 to minus 1 the cosine +that would be perfectly good so theta or + + align:start position:0% +that would be perfectly good so theta or + + + align:start position:0% +that would be perfectly good so theta or +cosine theta is a different variable and + + align:start position:0% +cosine theta is a different variable and + + + align:start position:0% +cosine theta is a different variable and +this equation is simpler for cosine + + align:start position:0% +this equation is simpler for cosine + + + align:start position:0% +this equation is simpler for cosine +theta in as a variable so let me write + + align:start position:0% +theta in as a variable so let me write + + + align:start position:0% +theta in as a variable so let me write +that do that simplification so I have it + + align:start position:0% +that do that simplification so I have it + + + align:start position:0% +that do that simplification so I have it +here if X if is cosine theta B D X is + + align:start position:0% +here if X if is cosine theta B D X is + + + align:start position:0% +here if X if is cosine theta B D X is +minus 1 over sine theta DD theta please + + align:start position:0% +minus 1 over sine theta DD theta please + + + align:start position:0% +minus 1 over sine theta DD theta please +check that and you can also show that + + align:start position:0% +check that and you can also show that + + + align:start position:0% +check that and you can also show that +sine theta V D theta is equal to minus 1 + + align:start position:0% +sine theta V D theta is equal to minus 1 + + + align:start position:0% +sine theta V D theta is equal to minus 1 +minus x squared d DX + + align:start position:0% +minus x squared d DX + + + align:start position:0% +minus x squared d DX +the claim is that this differential + + align:start position:0% +the claim is that this differential + + + align:start position:0% +the claim is that this differential +equation just involves cosine theta and + + align:start position:0% +equation just involves cosine theta and + + + align:start position:0% +equation just involves cosine theta and +this operator you see in the first term + + align:start position:0% +this operator you see in the first term + + + align:start position:0% +this operator you see in the first term +of the differential equation sine theta + + align:start position:0% +of the differential equation sine theta + + + align:start position:0% +of the differential equation sine theta +DD theta is this where X is cosine theta + + align:start position:0% +DD theta is this where X is cosine theta + + + align:start position:0% +DD theta is this where X is cosine theta +and then there's a sine squared theta + + align:start position:0% +and then there's a sine squared theta + + + align:start position:0% +and then there's a sine squared theta +but sine squared theta is 1 minus cosine + + align:start position:0% +but sine squared theta is 1 minus cosine + + + align:start position:0% +but sine squared theta is 1 minus cosine +squared theta so this differential + + align:start position:0% +squared theta so this differential + + + align:start position:0% +squared theta so this differential +equation becomes d DX well should I + + align:start position:0% +equation becomes d DX well should I + + + align:start position:0% +equation becomes d DX well should I +write the whole thing No I'll write the + + align:start position:0% +write the whole thing No I'll write the + + + align:start position:0% +write the whole thing No I'll write the +simplified version it's not it's only + + align:start position:0% +simplified version it's not it's only + + + align:start position:0% +simplified version it's not it's only +one slight M of the X plus L times L + + align:start position:0% +one slight M of the X plus L times L + + + align:start position:0% +one slight M of the X plus L times L +plus 1 minus M squared over 1 minus x + + align:start position:0% +plus 1 minus M squared over 1 minus x + + + align:start position:0% +plus 1 minus M squared over 1 minus x +squared PLM of x equals 0 the only thing + + align:start position:0% +squared PLM of x equals 0 the only thing + + + align:start position:0% +squared PLM of x equals 0 the only thing +that you may wonder is what happened to + + align:start position:0% +that you may wonder is what happened to + + + align:start position:0% +that you may wonder is what happened to +the 1 minus x squared that arises from + + align:start position:0% +the 1 minus x squared that arises from + + + align:start position:0% +the 1 minus x squared that arises from +this first term well there's a 1 minus x + + align:start position:0% +this first term well there's a 1 minus x + + + align:start position:0% +this first term well there's a 1 minus x +squared here and we divided by all of it + + align:start position:0% +squared here and we divided by all of it + + + align:start position:0% +squared here and we divided by all of it +so it disappeared from the first term + + align:start position:0% +so it disappeared from the first term + + + align:start position:0% +so it disappeared from the first term +disappeared from here but the M Squared + + align:start position:0% +disappeared from here but the M Squared + + + align:start position:0% +disappeared from here but the M Squared +ended up divided by 1 minus x squared so + + align:start position:0% +ended up divided by 1 minus x squared so + + + align:start position:0% +ended up divided by 1 minus x squared so +this is our equation and so far our + + align:start position:0% +this is our equation and so far our + + + align:start position:0% +this is our equation and so far our +solutions are sy LM s are going to be + + align:start position:0% +solutions are sy LM s are going to be + + + align:start position:0% +solutions are sy LM s are going to be +some coefficients NLM's + + align:start position:0% +some coefficients NLM's + + + align:start position:0% +some coefficients NLM's +e to the IM phi PLM of cosine theta + + align:start position:0% + + + + align:start position:0% + +now I want to do a little more before + + align:start position:0% +now I want to do a little more before + + + align:start position:0% +now I want to do a little more before +finishing today's lecture so this + + align:start position:0% +finishing today's lecture so this + + + align:start position:0% +finishing today's lecture so this +equation is somewhat complicated so the + + align:start position:0% +equation is somewhat complicated so the + + + align:start position:0% +equation is somewhat complicated so the +way physicists analyze it is by + + align:start position:0% +way physicists analyze it is by + + + align:start position:0% +way physicists analyze it is by +considering first the case when M is + + align:start position:0% +considering first the case when M is + + + align:start position:0% +considering first the case when M is +equal to 0 and when M is equal to zero + + align:start position:0% +equal to 0 and when M is equal to zero + + + align:start position:0% +equal to 0 and when M is equal to zero +the differential equation M equals zero + + align:start position:0% +the differential equation M equals zero + + + align:start position:0% +the differential equation M equals zero +first the differential equation becomes + + align:start position:0% +first the differential equation becomes + + + align:start position:0% +first the differential equation becomes +V DX of 1 minus x squared + + align:start position:0% +V DX of 1 minus x squared + + + align:start position:0% +V DX of 1 minus x squared +the pl0 but pl0 people write as PL the X + + align:start position:0% +the pl0 but pl0 people write as PL the X + + + align:start position:0% +the pl0 but pl0 people write as PL the X +plus L times L plus 1 PL equals 0 so of + + align:start position:0% +plus L times L plus 1 PL equals 0 so of + + + align:start position:0% +plus L times L plus 1 PL equals 0 so of +this we solve by a series solution so we + + align:start position:0% +this we solve by a series solution so we + + + align:start position:0% +this we solve by a series solution so we +write PL of x equals some sort of 8 a + + align:start position:0% +write PL of x equals some sort of 8 a + + + align:start position:0% +write PL of x equals some sort of 8 a +sum over k a k xk and we substitute in + + align:start position:0% +sum over k a k xk and we substitute in + + + align:start position:0% +sum over k a k xk and we substitute in +there now if you substituted it and pick + + align:start position:0% +there now if you substituted it and pick + + + align:start position:0% +there now if you substituted it and pick +the coefficient of x to the k you get a + + align:start position:0% +the coefficient of x to the k you get a + + + align:start position:0% +the coefficient of x to the k you get a +recursion relation like we did for the + + align:start position:0% +recursion relation like we did for the + + + align:start position:0% +recursion relation like we did for the +case of the harmonic oscillator and this + + align:start position:0% +case of the harmonic oscillator and this + + + align:start position:0% +case of the harmonic oscillator and this +is a simple recursion relation it reads + + align:start position:0% +is a simple recursion relation it reads + + + align:start position:0% +is a simple recursion relation it reads +k plus 1 this is a two-line exercise k + + align:start position:0% +k plus 1 this is a two-line exercise k + + + align:start position:0% +k plus 1 this is a two-line exercise k +plus 2 EI k plus 2 plus L times L plus 1 + + align:start position:0% +plus 2 EI k plus 2 plus L times L plus 1 + + + align:start position:0% +plus 2 EI k plus 2 plus L times L plus 1 +minus K times k plus 1 a cake + + align:start position:0% + + + + align:start position:0% + +so actually this recursion relation can + + align:start position:0% +so actually this recursion relation can + + + align:start position:0% +so actually this recursion relation can +be put as a range of form the ratio form + + align:start position:0% +be put as a range of form the ratio form + + + align:start position:0% +be put as a range of form the ratio form +we're accustomed in which we divide a k + + align:start position:0% +we're accustomed in which we divide a k + + + align:start position:0% +we're accustomed in which we divide a k +plus two by a K and that gives you a k + + align:start position:0% +plus two by a K and that gives you a k + + + align:start position:0% +plus two by a K and that gives you a k +plus two over a k + + align:start position:0% +plus two over a k + + + align:start position:0% +plus two over a k +I'm sorry all this coefficient must be + + align:start position:0% +I'm sorry all this coefficient must be + + + align:start position:0% +I'm sorry all this coefficient must be +equal to zero + + align:start position:0% + + + + align:start position:0% + +and a k plus two over a K therefore is + + align:start position:0% +and a k plus two over a K therefore is + + + align:start position:0% +and a k plus two over a K therefore is +minus L times L plus one minus K times k + + align:start position:0% +minus L times L plus one minus K times k + + + align:start position:0% +minus L times L plus one minus K times k +plus one over k plus 1 times k plus two + + align:start position:0% +plus one over k plus 1 times k plus two + + + align:start position:0% +plus one over k plus 1 times k plus two +okay + + align:start position:0% +okay + + + align:start position:0% +okay +good we're almost done so what has + + align:start position:0% +good we're almost done so what has + + + align:start position:0% +good we're almost done so what has +happened we had a general equation for + + align:start position:0% +happened we had a general equation for + + + align:start position:0% +happened we had a general equation for +Phi the first equation one we solve the + + align:start position:0% +Phi the first equation one we solve the + + + align:start position:0% +Phi the first equation one we solve the +second became a intricate differential + + align:start position:0% +second became a intricate differential + + + align:start position:0% +second became a intricate differential +equation we still don't know how to + + align:start position:0% +equation we still don't know how to + + + align:start position:0% +equation we still don't know how to +solve it M must be an integer so far L + + align:start position:0% +solve it M must be an integer so far L + + + align:start position:0% +solve it M must be an integer so far L +we have no idea + + align:start position:0% +we have no idea + + + align:start position:0% +we have no idea +nevertheless we now solve this for the + + align:start position:0% +nevertheless we now solve this for the + + + align:start position:0% +nevertheless we now solve this for the +case m equal to 0 and find this + + align:start position:0% +case m equal to 0 and find this + + + align:start position:0% +case m equal to 0 and find this +recursive relation and the same story + + align:start position:0% +recursive relation and the same story + + + align:start position:0% +recursive relation and the same story +that happened for the harmonic + + align:start position:0% +that happened for the harmonic + + + align:start position:0% +that happened for the harmonic +oscillator happens here if this + + align:start position:0% +oscillator happens here if this + + + align:start position:0% +oscillator happens here if this +recursion doesn't terminate you get + + align:start position:0% +recursion doesn't terminate you get + + + align:start position:0% +recursion doesn't terminate you get +singular functions that diverge at x + + align:start position:0% +singular functions that diverge at x + + + align:start position:0% +singular functions that diverge at x +equals 1 or minus 1 and therefore this + + align:start position:0% +equals 1 or minus 1 and therefore this + + + align:start position:0% +equals 1 or minus 1 and therefore this +must terminate must terminate and if it + + align:start position:0% +must terminate must terminate and if it + + + align:start position:0% +must terminate must terminate and if it +terminates the only way to achieve + + align:start position:0% +terminates the only way to achieve + + + align:start position:0% +terminates the only way to achieve +termination of the series is if L is an + + align:start position:0% +termination of the series is if L is an + + + align:start position:0% +termination of the series is if L is an +integer equal to K so you can choose + + align:start position:0% +integer equal to K so you can choose + + + align:start position:0% +integer equal to K so you can choose +some case you choose + + align:start position:0% +some case you choose + + + align:start position:0% +some case you choose +l equals 2k and then you get that P L of + + align:start position:0% +l equals 2k and then you get that P L of + + + align:start position:0% +l equals 2k and then you get that P L of +X is of the form of an X to the L + + align:start position:0% +X is of the form of an X to the L + + + align:start position:0% +X is of the form of an X to the L +coefficient because L is equal to K and + + align:start position:0% +coefficient because L is equal to K and + + + align:start position:0% +coefficient because L is equal to K and +a K is the last one that exists and now + + align:start position:0% +a K is the last one that exists and now + + + align:start position:0% +a K is the last one that exists and now +a L plus two K plus 2 would be equal to + + align:start position:0% +a L plus two K plus 2 would be equal to + + + align:start position:0% +a L plus two K plus 2 would be equal to +0 so you match this the last coefficient + + align:start position:0% +0 so you match this the last coefficient + + + align:start position:0% +0 so you match this the last coefficient +is the value of L and the polynomial is + + align:start position:0% +is the value of L and the polynomial is + + + align:start position:0% +is the value of L and the polynomial is +an elf polynomial up to some number at + + align:start position:0% +an elf polynomial up to some number at + + + align:start position:0% +an elf polynomial up to some number at +the end and you got a quantization L now + + align:start position:0% +the end and you got a quantization L now + + + align:start position:0% +the end and you got a quantization L now +can be any positive integer or zero so L + + align:start position:0% +can be any positive integer or zero so L + + + align:start position:0% +can be any positive integer or zero so L +can be 0 1 2 3 4 and it's the + + align:start position:0% +can be 0 1 2 3 4 and it's the + + + align:start position:0% +can be 0 1 2 3 4 and it's the +quantization of the bag method of the + + align:start position:0% +quantization of the bag method of the + + + align:start position:0% +quantization of the bag method of the +angular momentum this is a little + + align:start position:0% +angular momentum this is a little + + + align:start position:0% +angular momentum this is a little +surprising l squared is an operator that + + align:start position:0% +surprising l squared is an operator that + + + align:start position:0% +surprising l squared is an operator that +reflects the magnitude of the angular + + align:start position:0% +reflects the magnitude of the angular + + + align:start position:0% +reflects the magnitude of the angular +momentum and suddenly it is quantized + + align:start position:0% +momentum and suddenly it is quantized + + + align:start position:0% +momentum and suddenly it is quantized +the eigenvalues of that operator that + + align:start position:0% +the eigenvalues of that operator that + + + align:start position:0% +the eigenvalues of that operator that +were L times L plus 1 that I had an in + + align:start position:0% +were L times L plus 1 that I had an in + + + align:start position:0% +were L times L plus 1 that I had an in +some blackboard must be quantized so + + align:start position:0% +some blackboard must be quantized so + + + align:start position:0% +some blackboard must be quantized so +what you get here are the Legendre + + align:start position:0% +what you get here are the Legendre + + + align:start position:0% +what you get here are the Legendre +polynomials the P LS of X that satisfy + + align:start position:0% +polynomials the P LS of X that satisfy + + + align:start position:0% +polynomials the P LS of X that satisfy +this differential equation R Legendre + + align:start position:0% + + + + align:start position:0% + +polynomials and next time when we return + + align:start position:0% +polynomials and next time when we return + + + align:start position:0% +polynomials and next time when we return +to this equation we'll find that M + + align:start position:0% +to this equation we'll find that M + + + align:start position:0% +to this equation we'll find that M +cannot exceed L otherwise you can't + + align:start position:0% +cannot exceed L otherwise you can't + + + align:start position:0% +cannot exceed L otherwise you can't +solve this equation so we'll find a + + align:start position:0% +solve this equation so we'll find a + + + align:start position:0% +solve this equation so we'll find a +complete set of constraints on the + + align:start position:0% +complete set of constraints on the + + + align:start position:0% +complete set of constraints on the +eigenvalues of the operator \ No newline at end of file diff --git a/lzYrMcI92kw.txt b/lzYrMcI92kw.txt new file mode 100644 index 0000000000000000000000000000000000000000..f509cf861d27bb5e3f8c043b5018ed1a51591005 --- /dev/null +++ b/lzYrMcI92kw.txt @@ -0,0 +1,8615 @@ +align:start position:0% + +so let's start today's lecture today + + align:start position:0% +so let's start today's lecture today + + + align:start position:0% +so let's start today's lecture today +we're going to be talking about the idea + + align:start position:0% +we're going to be talking about the idea + + + align:start position:0% +we're going to be talking about the idea +of iteration and iteration is another + + align:start position:0% +of iteration and iteration is another + + + align:start position:0% +of iteration and iteration is another +way we're going to add control flow to + + align:start position:0% +way we're going to add control flow to + + + align:start position:0% +way we're going to add control flow to +our + + align:start position:0% +our + + + align:start position:0% +our +programs but before we do that let's do + + align:start position:0% +programs but before we do that let's do + + + align:start position:0% +programs but before we do that let's do +a little bit of a recap + + align:start position:0% +a little bit of a recap + + + align:start position:0% +a little bit of a recap +on sorry let's do a little bit of a + + align:start position:0% +on sorry let's do a little bit of a + + + align:start position:0% +on sorry let's do a little bit of a +recap of what we've done so far last + + align:start position:0% +recap of what we've done so far last + + + align:start position:0% +recap of what we've done so far last +lecture because last lecture we actually + + align:start position:0% +lecture because last lecture we actually + + + align:start position:0% +lecture because last lecture we actually +introduced a different mechanism for + + align:start position:0% +introduced a different mechanism for + + + align:start position:0% +introduced a different mechanism for +control flow branching and the control + + align:start position:0% +control flow branching and the control + + + align:start position:0% +control flow branching and the control +flow was basically a way for us to tell + + align:start position:0% +flow was basically a way for us to tell + + + align:start position:0% +flow was basically a way for us to tell +python not to go systematically through + + align:start position:0% +python not to go systematically through + + + align:start position:0% +python not to go systematically through +the code branching was a way for us to + + align:start position:0% +the code branching was a way for us to + + + align:start position:0% +the code branching was a way for us to +tell python hey based on some condition + + align:start position:0% +tell python hey based on some condition + + + align:start position:0% +tell python hey based on some condition +being true or false either evaluate some + + align:start position:0% +being true or false either evaluate some + + + align:start position:0% +being true or false either evaluate some +set of code or another set of code right + + align:start position:0% +set of code or another set of code right + + + align:start position:0% +set of code or another set of code right +which was not going linearly we were + + align:start position:0% +which was not going linearly we were + + + align:start position:0% +which was not going linearly we were +actually kind of skipping around through + + align:start position:0% +actually kind of skipping around through + + + align:start position:0% +actually kind of skipping around through +the + + align:start position:0% +the + + + align:start position:0% +the +code so that's what we learned at the + + align:start position:0% +code so that's what we learned at the + + + align:start position:0% +code so that's what we learned at the +end of the lecture but um we also + + align:start position:0% +end of the lecture but um we also + + + align:start position:0% +end of the lecture but um we also +learned about input and output so a way + + align:start position:0% +learned about input and output so a way + + + align:start position:0% +learned about input and output so a way +for us to write interactive programs and + + align:start position:0% +for us to write interactive programs and + + + align:start position:0% +for us to write interactive programs and +we learned about a new data type the + + align:start position:0% +we learned about a new data type the + + + align:start position:0% +we learned about a new data type the +string so the string was a sequence of + + align:start position:0% +string so the string was a sequence of + + + align:start position:0% +string so the string was a sequence of +characters hopefully you got a chance to + + align:start position:0% +characters hopefully you got a chance to + + + align:start position:0% +characters hopefully you got a chance to +do a little bit of uh exercises on mitx + + align:start position:0% +do a little bit of uh exercises on mitx + + + align:start position:0% +do a little bit of uh exercises on mitx +as practice for today's quiz with + + align:start position:0% +as practice for today's quiz with + + + align:start position:0% +as practice for today's quiz with +quizzes with uh strings and + + align:start position:0% +quizzes with uh strings and + + + align:start position:0% +quizzes with uh strings and +branching okay so in branching what did + + align:start position:0% +branching okay so in branching what did + + + align:start position:0% +branching okay so in branching what did +we learn we talked about how to actually + + align:start position:0% +we learn we talked about how to actually + + + align:start position:0% +we learn we talked about how to actually +add a branching point in our program so + + align:start position:0% +add a branching point in our program so + + + align:start position:0% +add a branching point in our program so +we did that using these particular + + align:start position:0% +we did that using these particular + + + align:start position:0% +we did that using these particular +keywords so when you type them in your + + align:start position:0% +keywords so when you type them in your + + + align:start position:0% +keywords so when you type them in your +program in the file editor you'll see + + align:start position:0% +program in the file editor you'll see + + + align:start position:0% +program in the file editor you'll see +that they kind of turn a different color + + align:start position:0% +that they kind of turn a different color + + + align:start position:0% +that they kind of turn a different color +that tells you it's a special word in + + align:start position:0% +that tells you it's a special word in + + + align:start position:0% +that tells you it's a special word in +Python and these keywords are how we + + align:start position:0% +Python and these keywords are how we + + + align:start position:0% +Python and these keywords are how we +told python to put a branching uh + + align:start position:0% +told python to put a branching uh + + + align:start position:0% +told python to put a branching uh +branching point and the colon kind of + + align:start position:0% +branching point and the colon kind of + + + align:start position:0% +branching point and the colon kind of +ended the branching uh uh conditional + + align:start position:0% +ended the branching uh uh conditional + + + align:start position:0% +ended the branching uh uh conditional +and then anything that was indented as + + align:start position:0% +and then anything that was indented as + + + align:start position:0% +and then anything that was indented as +part of that conditional was code that + + align:start position:0% +part of that conditional was code that + + + align:start position:0% +part of that conditional was code that +would be executed when that condition + + align:start position:0% +would be executed when that condition + + + align:start position:0% +would be executed when that condition +was true so I'm just going to quickly go + + align:start position:0% +was true so I'm just going to quickly go + + + align:start position:0% +was true so I'm just going to quickly go +over these each one of these boxes so + + align:start position:0% +over these each one of these boxes so + + + align:start position:0% +over these each one of these boxes so +the first one up here was the simplest + + align:start position:0% +the first one up here was the simplest + + + align:start position:0% +the first one up here was the simplest +way that we could add a conditional to + + align:start position:0% +way that we could add a conditional to + + + align:start position:0% +way that we could add a conditional to +our program it basically said hey go + + align:start position:0% +our program it basically said hey go + + + align:start position:0% +our program it basically said hey go +through the program When You Reach this + + align:start position:0% +through the program When You Reach this + + + align:start position:0% +through the program When You Reach this +if condition python would check the + + align:start position:0% +if condition python would check the + + + align:start position:0% +if condition python would check the +condition and say if that condition is + + align:start position:0% +condition and say if that condition is + + + align:start position:0% +condition and say if that condition is +true execute the code uh the code that's + + align:start position:0% +true execute the code uh the code that's + + + align:start position:0% +true execute the code uh the code that's +indented as part of that block if the + + align:start position:0% +indented as part of that block if the + + + align:start position:0% +indented as part of that block if the +condition was not true don't do anything + + align:start position:0% +condition was not true don't do anything + + + align:start position:0% +condition was not true don't do anything +just carry on with remaining + + align:start position:0% +just carry on with remaining + + + align:start position:0% +just carry on with remaining +program if we wanted to do something + + align:start position:0% +program if we wanted to do something + + + align:start position:0% +program if we wanted to do something +else so if the condition was not true if + + align:start position:0% +else so if the condition was not true if + + + align:start position:0% +else so if the condition was not true if +we wanted to do something else we added + + align:start position:0% +we wanted to do something else we added + + + align:start position:0% +we wanted to do something else we added +this else Clause here and the else also + + align:start position:0% +this else Clause here and the else also + + + align:start position:0% +this else Clause here and the else also +has some sort of code uh indented as + + align:start position:0% +has some sort of code uh indented as + + + align:start position:0% +has some sort of code uh indented as +part of its code block and that code + + align:start position:0% +part of its code block and that code + + + align:start position:0% +part of its code block and that code +would be executed when that condition + + align:start position:0% +would be executed when that condition + + + align:start position:0% +would be executed when that condition +was + + align:start position:0% + + + + align:start position:0% + +false okay so that was a really simple + + align:start position:0% +false okay so that was a really simple + + + align:start position:0% +false okay so that was a really simple +if or if else code structure but + + align:start position:0% +if or if else code structure but + + + align:start position:0% +if or if else code structure but +sometimes we want to have code that + + align:start position:0% +sometimes we want to have code that + + + align:start position:0% +sometimes we want to have code that +checks for many conditions right not + + align:start position:0% +checks for many conditions right not + + + align:start position:0% +checks for many conditions right not +just one that's where the L if structure + + align:start position:0% +just one that's where the L if structure + + + align:start position:0% +just one that's where the L if structure +came in so we would have an if condition + + align:start position:0% +came in so we would have an if condition + + + align:start position:0% +came in so we would have an if condition +that starts our code + + align:start position:0% +that starts our code + + + align:start position:0% +that starts our code +block if that condition was true as + + align:start position:0% +block if that condition was true as + + + align:start position:0% +block if that condition was true as +usual we execute the code that's part of + + align:start position:0% +usual we execute the code that's part of + + + align:start position:0% +usual we execute the code that's part of +that block else if so L if we could + + align:start position:0% +that block else if so L if we could + + + align:start position:0% +that block else if so L if we could +insert another condition and python + + align:start position:0% +insert another condition and python + + + align:start position:0% +insert another condition and python +would say okay well if that one wasn't + + align:start position:0% +would say okay well if that one wasn't + + + align:start position:0% +would say okay well if that one wasn't +true let me check if this next one is + + align:start position:0% +true let me check if this next one is + + + align:start position:0% +true let me check if this next one is +true and then we would execute the code + + align:start position:0% +true and then we would execute the code + + + align:start position:0% +true and then we would execute the code +that's part of that code block and we + + align:start position:0% +that's part of that code block and we + + + align:start position:0% +that's part of that code block and we +can add we can chain as many of these + + align:start position:0% +can add we can chain as many of these + + + align:start position:0% +can add we can chain as many of these +ellips as we want together and python + + align:start position:0% +ellips as we want together and python + + + align:start position:0% +ellips as we want together and python +will evaluate the very first one that it + + align:start position:0% +will evaluate the very first one that it + + + align:start position:0% +will evaluate the very first one that it +finds true that's part of this chain + + align:start position:0% +finds true that's part of this chain + + + align:start position:0% +finds true that's part of this chain +okay even if more than one is true it is + + align:start position:0% +okay even if more than one is true it is + + + align:start position:0% +okay even if more than one is true it is +possible none of those conditions were + + align:start position:0% +possible none of those conditions were + + + align:start position:0% +possible none of those conditions were +true in which case python would + + align:start position:0% +true in which case python would + + + align:start position:0% +true in which case python would +basically skip over all of them and do + + align:start position:0% +basically skip over all of them and do + + + align:start position:0% +basically skip over all of them and do +nothing enter none of those code blocks + + align:start position:0% +nothing enter none of those code blocks + + + align:start position:0% +nothing enter none of those code blocks +if you wanted to have a structure where + + align:start position:0% +if you wanted to have a structure where + + + align:start position:0% +if you wanted to have a structure where +if none of those conditions were true + + align:start position:0% +if none of those conditions were true + + + align:start position:0% +if none of those conditions were true +you wanted to do something you could uh + + align:start position:0% +you wanted to do something you could uh + + + align:start position:0% +you wanted to do something you could uh +put an else at the end of a whole chain + + align:start position:0% +put an else at the end of a whole chain + + + align:start position:0% +put an else at the end of a whole chain +of if L if L if L ifs and the else would + + align:start position:0% +of if L if L if L ifs and the else would + + + align:start position:0% +of if L if L if L ifs and the else would +be executed when none of those + + align:start position:0% +be executed when none of those + + + align:start position:0% +be executed when none of those +conditions are true okay so hopefully + + align:start position:0% +conditions are true okay so hopefully + + + align:start position:0% +conditions are true okay so hopefully +this is just + + align:start position:0% +this is just + + + align:start position:0% +this is just +recap one sort of tricky thing to + + align:start position:0% +recap one sort of tricky thing to + + + align:start position:0% +recap one sort of tricky thing to +remember is the if starts a code block + + align:start position:0% +remember is the if starts a code block + + + align:start position:0% +remember is the if starts a code block +so the if can have an else associated + + align:start position:0% +so the if can have an else associated + + + align:start position:0% +so the if can have an else associated +with it or it can have an L if L if L if + + align:start position:0% +with it or it can have an L if L if L if + + + align:start position:0% +with it or it can have an L if L if L if +and an else associated with it but if + + align:start position:0% +and an else associated with it but if + + + align:start position:0% +and an else associated with it but if +you have if condition and Then followed + + align:start position:0% +you have if condition and Then followed + + + align:start position:0% +you have if condition and Then followed +by another if condition both of those + + align:start position:0% +by another if condition both of those + + + align:start position:0% +by another if condition both of those +code blocks could potentially be + + align:start position:0% +code blocks could potentially be + + + align:start position:0% +code blocks could potentially be +executed because the ifs are independent + + align:start position:0% +executed because the ifs are independent + + + align:start position:0% +executed because the ifs are independent +right it's not an else situation they're + + align:start position:0% +right it's not an else situation they're + + + align:start position:0% +right it's not an else situation they're +just another if uh code block that uh + + align:start position:0% +just another if uh code block that uh + + + align:start position:0% +just another if uh code block that uh +that that gets + + align:start position:0% +that that gets + + + align:start position:0% +that that gets +started so the way we told python again + + align:start position:0% +started so the way we told python again + + + align:start position:0% +started so the way we told python again +just to reiterate the way we told python + + align:start position:0% +just to reiterate the way we told python + + + align:start position:0% +just to reiterate the way we told python +which code to execute when the condition + + align:start position:0% +which code to execute when the condition + + + align:start position:0% +which code to execute when the condition +is true is by indentation and + + align:start position:0% +is true is by indentation and + + + align:start position:0% +is true is by indentation and +indentation is something you have to do + + align:start position:0% +indentation is something you have to do + + + align:start position:0% +indentation is something you have to do +uh it's not optional in + + align:start position:0% +uh it's not optional in + + + align:start position:0% +uh it's not optional in +Python okay so let's take what we've + + align:start position:0% +Python okay so let's take what we've + + + align:start position:0% +Python okay so let's take what we've +learned so far and code up a really + + align:start position:0% +learned so far and code up a really + + + align:start position:0% +learned so far and code up a really +simple game so this is sort of a very + + align:start position:0% +simple game so this is sort of a very + + + align:start position:0% +simple game so this is sort of a very +simple variation of the Lost Woods in + + align:start position:0% +simple variation of the Lost Woods in + + + align:start position:0% +simple variation of the Lost Woods in +Zelda sort of my version of it let's say + + align:start position:0% +Zelda sort of my version of it let's say + + + align:start position:0% +Zelda sort of my version of it let's say +it's kind of a trick level where you + + align:start position:0% +it's kind of a trick level where you + + + align:start position:0% +it's kind of a trick level where you +have your character and they enter the + + align:start position:0% +have your character and they enter the + + + align:start position:0% +have your character and they enter the +Lost Woods + + align:start position:0% +Lost Woods + + + align:start position:0% +Lost Woods +they're presented with this screen and + + align:start position:0% +they're presented with this screen and + + + align:start position:0% +they're presented with this screen and +the trick here is you ask the user if + + align:start position:0% +the trick here is you ask the user if + + + align:start position:0% +the trick here is you ask the user if +they want to go left or right if they + + align:start position:0% +they want to go left or right if they + + + align:start position:0% +they want to go left or right if they +say right you're basically going to + + align:start position:0% +say right you're basically going to + + + align:start position:0% +say right you're basically going to +present them with the exact same screen + + align:start position:0% +present them with the exact same screen + + + align:start position:0% +present them with the exact same screen +all over again so it's kind of you know + + align:start position:0% +all over again so it's kind of you know + + + align:start position:0% +all over again so it's kind of you know +representing that they're lost in the + + align:start position:0% +representing that they're lost in the + + + align:start position:0% +representing that they're lost in the +woods and as long as they say I want to + + align:start position:0% +woods and as long as they say I want to + + + align:start position:0% +woods and as long as they say I want to +keep going right I want to keep going + + align:start position:0% +keep going right I want to keep going + + + align:start position:0% +keep going right I want to keep going +right I want to keep going right they're + + align:start position:0% +right I want to keep going right they're + + + align:start position:0% +right I want to keep going right they're +basically going to see the same screen + + align:start position:0% +basically going to see the same screen + + + align:start position:0% +basically going to see the same screen +over and over again and the trick to + + align:start position:0% +over and over again and the trick to + + + align:start position:0% +over and over again and the trick to +getting out of the woods is to say I + + align:start position:0% +getting out of the woods is to say I + + + align:start position:0% +getting out of the woods is to say I +want to go left okay so no matter how + + align:start position:0% +want to go left okay so no matter how + + + align:start position:0% +want to go left okay so no matter how +far how many times they've said right in + + align:start position:0% +far how many times they've said right in + + + align:start position:0% +far how many times they've said right in +a row as long as they type in left + + align:start position:0% +a row as long as they type in left + + + align:start position:0% +a row as long as they type in left +they're out of the woods okay so let's + + align:start position:0% +they're out of the woods okay so let's + + + align:start position:0% +they're out of the woods okay so let's +try to code that up with what we know + + align:start position:0% +try to code that up with what we know + + + align:start position:0% +try to code that up with what we know +just conditionals we + + align:start position:0% +just conditionals we + + + align:start position:0% +just conditionals we +have an if else right the if says if the + + align:start position:0% +have an if else right the if says if the + + + align:start position:0% +have an if else right the if says if the +user exits right we're going to do + + align:start position:0% +user exits right we're going to do + + + align:start position:0% +user exits right we're going to do +something and otherwise we're going to + + align:start position:0% +something and otherwise we're going to + + + align:start position:0% +something and otherwise we're going to +say that the user said left or something + + align:start position:0% +say that the user said left or something + + + align:start position:0% +say that the user said left or something +else or exit and we're going to tell + + align:start position:0% +else or exit and we're going to tell + + + align:start position:0% +else or exit and we're going to tell +them that they've exited + + align:start position:0% +them that they've exited + + + align:start position:0% +them that they've exited +successfully all right now if they said + + align:start position:0% +successfully all right now if they said + + + align:start position:0% +successfully all right now if they said +exit right what do we do well we're + + align:start position:0% +exit right what do we do well we're + + + align:start position:0% +exit right what do we do well we're +going to show them the exact same thing + + align:start position:0% +going to show them the exact same thing + + + align:start position:0% +going to show them the exact same thing +again so we're setting the background to + + align:start position:0% +again so we're setting the background to + + + align:start position:0% +again so we're setting the background to +the same Woods background and then + + align:start position:0% +the same Woods background and then + + + align:start position:0% +the same Woods background and then +they're presented The Cho with the + + align:start position:0% +they're presented The Cho with the + + + align:start position:0% +they're presented The Cho with the +choice all over again right do you want + + align:start position:0% +choice all over again right do you want + + + align:start position:0% +choice all over again right do you want +to exit right or you want to exit left + + align:start position:0% +to exit right or you want to exit left + + + align:start position:0% +to exit right or you want to exit left +so if they say exit right we would do + + align:start position:0% +so if they say exit right we would do + + + align:start position:0% +so if they say exit right we would do +something and otherwise we would tell + + align:start position:0% +something and otherwise we would tell + + + align:start position:0% +something and otherwise we would tell +them they were they successfully exited + + align:start position:0% +them they were they successfully exited + + + align:start position:0% +them they were they successfully exited +okay well what if they exited right if + + align:start position:0% +okay well what if they exited right if + + + align:start position:0% +okay well what if they exited right if +they exited right then we would do + + align:start position:0% +they exited right then we would do + + + align:start position:0% +they exited right then we would do +something again basically present them + + align:start position:0% +something again basically present them + + + align:start position:0% +something again basically present them +with the same uh situation so we would + + align:start position:0% +with the same uh situation so we would + + + align:start position:0% +with the same uh situation so we would +set the woods background again and we + + align:start position:0% +set the woods background again and we + + + align:start position:0% +set the woods background again and we +would ask them if they want to go right + + align:start position:0% +would ask them if they want to go right + + + align:start position:0% +would ask them if they want to go right +or left again and otherwise if they said + + align:start position:0% +or left again and otherwise if they said + + + align:start position:0% +or left again and otherwise if they said +left they exit so we already see a + + align:start position:0% +left they exit so we already see a + + + align:start position:0% +left they exit so we already see a +problem right how deep do we make this + + align:start position:0% +problem right how deep do we make this + + + align:start position:0% +problem right how deep do we make this +nested Loop situation right here we + + align:start position:0% +nested Loop situation right here we + + + align:start position:0% +nested Loop situation right here we +already have three in case the user said + + align:start position:0% +already have three in case the user said + + + align:start position:0% +already have three in case the user said +I want to go write three times in a row + + align:start position:0% +I want to go write three times in a row + + + align:start position:0% +I want to go write three times in a row +but we don't know how persistent the + + align:start position:0% +but we don't know how persistent the + + + align:start position:0% +but we don't know how persistent the +user will be so how do we know when + + align:start position:0% +user will be so how do we know when + + + align:start position:0% +user will be so how do we know when +we're writing our code how deep to make + + align:start position:0% +we're writing our code how deep to make + + + align:start position:0% +we're writing our code how deep to make +this nested Loop we don't right we won't + + align:start position:0% +this nested Loop we don't right we won't + + + align:start position:0% +this nested Loop we don't right we won't +be able to really code this up very well + + align:start position:0% +be able to really code this up very well + + + align:start position:0% +be able to really code this up very well +with what we know so far and so that's + + align:start position:0% +with what we know so far and so that's + + + align:start position:0% +with what we know so far and so that's +kind of the motivation for introducing + + align:start position:0% +kind of the motivation for introducing + + + align:start position:0% +kind of the motivation for introducing +iteration because the situation on the + + align:start position:0% +iteration because the situation on the + + + align:start position:0% +iteration because the situation on the +previous slide fits really well with + + align:start position:0% +previous slide fits really well with + + + align:start position:0% +previous slide fits really well with +some task we want to repeat multiple + + align:start position:0% +some task we want to repeat multiple + + + align:start position:0% +some task we want to repeat multiple +times as long as some condition is true + + align:start position:0% +times as long as some condition is true + + + align:start position:0% +times as long as some condition is true +in our case the condition is the user + + align:start position:0% +in our case the condition is the user + + + align:start position:0% +in our case the condition is the user +says I want to exit right so while the + + align:start position:0% +says I want to exit right so while the + + + align:start position:0% +says I want to exit right so while the +user keeps saying exit right show them + + align:start position:0% +user keeps saying exit right show them + + + align:start position:0% +user keeps saying exit right show them +the woods background and ask them again + + align:start position:0% +the woods background and ask them again + + + align:start position:0% +the woods background and ask them again +which way do you want to go and so while + + align:start position:0% +which way do you want to go and so while + + + align:start position:0% +which way do you want to go and so while +that's true just repeat this this set of + + align:start position:0% +that's true just repeat this this set of + + + align:start position:0% +that's true just repeat this this set of +things check that that they said exit + + align:start position:0% +things check that that they said exit + + + align:start position:0% +things check that that they said exit +right show them the background ask them + + align:start position:0% +right show them the background ask them + + + align:start position:0% +right show them the background ask them +again check that they said exit right + + align:start position:0% +again check that they said exit right + + + align:start position:0% +again check that they said exit right +show them the background ask them again + + align:start position:0% +show them the background ask them again + + + align:start position:0% +show them the background ask them again +and if at any point they'd say I don't + + align:start position:0% +and if at any point they'd say I don't + + + align:start position:0% +and if at any point they'd say I don't +want to exit right we break out of this + + align:start position:0% +want to exit right we break out of this + + + align:start position:0% +want to exit right we break out of this +Loop and we kind of rejoin the rest of + + align:start position:0% +Loop and we kind of rejoin the rest of + + + align:start position:0% +Loop and we kind of rejoin the rest of +the program that's kind of the + + align:start position:0% +the program that's kind of the + + + align:start position:0% +the program that's kind of the +terminology we used if with if + + align:start position:0% +terminology we used if with if + + + align:start position:0% +terminology we used if with if +statements right we set the background + + align:start position:0% +statements right we set the background + + + align:start position:0% +statements right we set the background +to the exit background and they're out + + align:start position:0% +to the exit background and they're out + + + align:start position:0% +to the exit background and they're out +of the + + align:start position:0% +of the + + + align:start position:0% +of the +woods so this sets the scene for while + + align:start position:0% +woods so this sets the scene for while + + + align:start position:0% +woods so this sets the scene for while +Loops here's another example of while + + align:start position:0% +Loops here's another example of while + + + align:start position:0% +Loops here's another example of while +Loops sort of in the context of watching + + align:start position:0% +Loops sort of in the context of watching + + + align:start position:0% +Loops sort of in the context of watching +a show so if we want to start a new show + + align:start position:0% +a show so if we want to start a new show + + + align:start position:0% +a show so if we want to start a new show +on Netflix and we want to watch all + + align:start position:0% +on Netflix and we want to watch all + + + align:start position:0% +on Netflix and we want to watch all +episodes of the show in one shot we're + + align:start position:0% +episodes of the show in one shot we're + + + align:start position:0% +episodes of the show in one shot we're +going to tell Netflix we're starting a + + align:start position:0% +going to tell Netflix we're starting a + + + align:start position:0% +going to tell Netflix we're starting a +new show and while there are more + + align:start position:0% +new show and while there are more + + + align:start position:0% +new show and while there are more +episodes to watch in this show we're + + align:start position:0% +episodes to watch in this show we're + + + align:start position:0% +episodes to watch in this show we're +going to keep watching the next episode + + align:start position:0% +going to keep watching the next episode + + + align:start position:0% +going to keep watching the next episode +right so if there are no more episodes + + align:start position:0% +right so if there are no more episodes + + + align:start position:0% +right so if there are no more episodes +to watch then we're done p uh not python + + align:start position:0% +to watch then we're done p uh not python + + + align:start position:0% +to watch then we're done p uh not python +Netflix will suggest three more shows + + align:start position:0% +Netflix will suggest three more shows + + + align:start position:0% +Netflix will suggest three more shows +like this one and while there are more + + align:start position:0% +like this one and while there are more + + + align:start position:0% +like this one and while there are more +episodes to watch so yes there are more + + align:start position:0% +episodes to watch so yes there are more + + + align:start position:0% +episodes to watch so yes there are more +episodes to watch we're going to play + + align:start position:0% +episodes to watch we're going to play + + + align:start position:0% +episodes to watch we're going to play +the next episode in in + + align:start position:0% +the next episode in in + + + align:start position:0% +the next episode in in +sequence so that's the aidea that we're + + align:start position:0% +sequence so that's the aidea that we're + + + align:start position:0% +sequence so that's the aidea that we're +trying to get at with while Loops in + + align:start position:0% +trying to get at with while Loops in + + + align:start position:0% +trying to get at with while Loops in +Python this is how we code them so we + + align:start position:0% +Python this is how we code them so we + + + align:start position:0% +Python this is how we code them so we +start a while loop with the keyword + + align:start position:0% +start a while loop with the keyword + + + align:start position:0% +start a while loop with the keyword +while so this again we'll turn blue in + + align:start position:0% +while so this again we'll turn blue in + + + align:start position:0% +while so this again we'll turn blue in +Python because it's a special word some + + align:start position:0% +Python because it's a special word some + + + align:start position:0% +Python because it's a special word some +condition is + + align:start position:0% +condition is + + + align:start position:0% +condition is +true okay so this is again some + + align:start position:0% +true okay so this is again some + + + align:start position:0% +true okay so this is again some +expression or something that will uh + + align:start position:0% +expression or something that will uh + + + align:start position:0% +expression or something that will uh +evaluate to a Boolean like we talked + + align:start position:0% +evaluate to a Boolean like we talked + + + align:start position:0% +evaluate to a Boolean like we talked +about in last + + align:start position:0% +about in last + + + align:start position:0% +about in last +lecture okay colon and colon tells + + align:start position:0% +lecture okay colon and colon tells + + + align:start position:0% +lecture okay colon and colon tells +python we're starting a code block + + align:start position:0% +python we're starting a code block + + + align:start position:0% +python we're starting a code block +that's part of the while loop being true + + align:start position:0% +that's part of the while loop being true + + + align:start position:0% +that's part of the while loop being true +and as usual the code block means we're + + align:start position:0% +and as usual the code block means we're + + + align:start position:0% +and as usual the code block means we're +going to indent these lines of code + + align:start position:0% +going to indent these lines of code + + + align:start position:0% +going to indent these lines of code +right so whatever we want to execute + + align:start position:0% +right so whatever we want to execute + + + align:start position:0% +right so whatever we want to execute +when the condition is true will be + + align:start position:0% + + + + align:start position:0% + +indented when the indented statements + + align:start position:0% +indented when the indented statements + + + align:start position:0% +indented when the indented statements +are finished executing python + + align:start position:0% +are finished executing python + + + align:start position:0% +are finished executing python +automatically goes back and rechecks + + align:start position:0% +automatically goes back and rechecks + + + align:start position:0% +automatically goes back and rechecks +that the the the condition so it + + align:start position:0% +that the the the condition so it + + + align:start position:0% +that the the the condition so it +rechecks whether the condition is true + + align:start position:0% +rechecks whether the condition is true + + + align:start position:0% +rechecks whether the condition is true +or not and this is done behind the + + align:start position:0% +or not and this is done behind the + + + align:start position:0% +or not and this is done behind the +scenes right when you code up a while + + align:start position:0% +scenes right when you code up a while + + + align:start position:0% +scenes right when you code up a while +loop when you type in the keyword while + + align:start position:0% +loop when you type in the keyword while + + + align:start position:0% +loop when you type in the keyword while +python will automatically do this + + align:start position:0% +python will automatically do this + + + align:start position:0% +python will automatically do this +Behavior it'll check the condition it'll + + align:start position:0% +Behavior it'll check the condition it'll + + + align:start position:0% +Behavior it'll check the condition it'll +execute the lines of code indented and + + align:start position:0% +execute the lines of code indented and + + + align:start position:0% +execute the lines of code indented and +then it'll go back and check the + + align:start position:0% +then it'll go back and check the + + + align:start position:0% +then it'll go back and check the +condition again if it's still true it'll + + align:start position:0% +condition again if it's still true it'll + + + align:start position:0% +condition again if it's still true it'll +execute the lines of code indented again + + align:start position:0% +execute the lines of code indented again + + + align:start position:0% +execute the lines of code indented again +and then it'll check the condition again + + align:start position:0% +and then it'll check the condition again + + + align:start position:0% +and then it'll check the condition again +so it's not something you have to code + + align:start position:0% +so it's not something you have to code + + + align:start position:0% +so it's not something you have to code +up you don't have to tell it to go back + + align:start position:0% +up you don't have to tell it to go back + + + align:start position:0% +up you don't have to tell it to go back +as long as you're writing this while + + align:start position:0% +as long as you're writing this while + + + align:start position:0% +as long as you're writing this while +loop python will automatically do that + + align:start position:0% +loop python will automatically do that + + + align:start position:0% +loop python will automatically do that +sequence of steps for you + + align:start position:0% +sequence of steps for you + + + align:start position:0% +sequence of steps for you +okay so when the condition becomes false + + align:start position:0% +okay so when the condition becomes false + + + align:start position:0% +okay so when the condition becomes false +python will no longer execute the stuff + + align:start position:0% +python will no longer execute the stuff + + + align:start position:0% +python will no longer execute the stuff +inside the stuff that's indented inside + + align:start position:0% +inside the stuff that's indented inside + + + align:start position:0% +inside the stuff that's indented inside +the Y Loop and it'll go rejoin the rest + + align:start position:0% +the Y Loop and it'll go rejoin the rest + + + align:start position:0% +the Y Loop and it'll go rejoin the rest +of the program at the same indentation + + align:start position:0% +of the program at the same indentation + + + align:start position:0% +of the program at the same indentation +level as the Y + + align:start position:0% +level as the Y + + + align:start position:0% +level as the Y +Loop okay so notice that the condition + + align:start position:0% +Loop okay so notice that the condition + + + align:start position:0% +Loop okay so notice that the condition +is kind of something that's dependent on + + align:start position:0% +is kind of something that's dependent on + + + align:start position:0% +is kind of something that's dependent on +or sorry the the fact that we're doing + + align:start position:0% +or sorry the the fact that we're doing + + + align:start position:0% +or sorry the the fact that we're doing +this code over and over again depends on + + align:start position:0% +this code over and over again depends on + + + align:start position:0% +this code over and over again depends on +this condition being true so if the code + + align:start position:0% +this condition being true so if the code + + + align:start position:0% +this condition being true so if the code +inside is not ever changing anything + + align:start position:0% +inside is not ever changing anything + + + align:start position:0% +inside is not ever changing anything +related to our condition then it's very + + align:start position:0% +related to our condition then it's very + + + align:start position:0% +related to our condition then it's very +likely it's actually for sure that this + + align:start position:0% +likely it's actually for sure that this + + + align:start position:0% +likely it's actually for sure that this +Loop will execute infinite number of + + align:start position:0% +Loop will execute infinite number of + + + align:start position:0% +Loop will execute infinite number of +times so this is kind of the pitfall of + + align:start position:0% +times so this is kind of the pitfall of + + + align:start position:0% +times so this is kind of the pitfall of +while Loops it's possible that if you're + + align:start position:0% +while Loops it's possible that if you're + + + align:start position:0% +while Loops it's possible that if you're +not careful your code will execute an + + align:start position:0% +not careful your code will execute an + + + align:start position:0% +not careful your code will execute an +infinite number of times and uh it'll + + align:start position:0% +infinite number of times and uh it'll + + + align:start position:0% +infinite number of times and uh it'll +just never never terminate and I'll show + + align:start position:0% +just never never terminate and I'll show + + + align:start position:0% +just never never terminate and I'll show +you how to deal with that in a couple + + align:start position:0% +you how to deal with that in a couple + + + align:start position:0% +you how to deal with that in a couple +slides so let's try to cat up this uh + + align:start position:0% +slides so let's try to cat up this uh + + + align:start position:0% +slides so let's try to cat up this uh +this Lost Woods program in our Ju Just + + align:start position:0% +this Lost Woods program in our Ju Just + + + align:start position:0% +this Lost Woods program in our Ju Just +with a while loop so here we've got our + + align:start position:0% +with a while loop so here we've got our + + + align:start position:0% +with a while loop so here we've got our +question that we uh asked the user do + + align:start position:0% +question that we uh asked the user do + + + align:start position:0% +question that we uh asked the user do +you want to go left or right and we're + + align:start position:0% +you want to go left or right and we're + + + align:start position:0% +you want to go left or right and we're +going to grab the user input as a string + + align:start position:0% +going to grab the user input as a string + + + align:start position:0% +going to grab the user input as a string +and save it in a variable called + + align:start position:0% +and save it in a variable called + + + align:start position:0% +and save it in a variable called +where so whatever the user types in + + align:start position:0% +where so whatever the user types in + + + align:start position:0% +where so whatever the user types in +it'll be saved in a variable called + + align:start position:0% +it'll be saved in a variable called + + + align:start position:0% +it'll be saved in a variable called +where so in my computer memory the way + + align:start position:0% +where so in my computer memory the way + + + align:start position:0% +where so in my computer memory the way +this looks like if the user types in + + align:start position:0% +this looks like if the user types in + + + align:start position:0% +this looks like if the user types in +right that particular sequence of + + align:start position:0% +right that particular sequence of + + + align:start position:0% +right that particular sequence of +characters that'll be saved as the + + align:start position:0% +characters that'll be saved as the + + + align:start position:0% +characters that'll be saved as the +variable + + align:start position:0% +variable + + + align:start position:0% +variable +where so then we finish this first line + + align:start position:0% +where so then we finish this first line + + + align:start position:0% +where so then we finish this first line +of the code here and then we check while + + align:start position:0% +of the code here and then we check while + + + align:start position:0% +of the code here and then we check while +the value of where is equivalent to + + align:start position:0% +the value of where is equivalent to + + + align:start position:0% +the value of where is equivalent to +write what are we going to do we're + + align:start position:0% +write what are we going to do we're + + + align:start position:0% +write what are we going to do we're +going to ask the user again where do you + + align:start position:0% +going to ask the user again where do you + + + align:start position:0% +going to ask the user again where do you +want to go left or right so I'm going to + + align:start position:0% +want to go left or right so I'm going to + + + align:start position:0% +want to go left or right so I'm going to +say right again and then this memory is + + align:start position:0% +say right again and then this memory is + + + align:start position:0% +say right again and then this memory is +going to look exactly the same if the + + align:start position:0% +going to look exactly the same if the + + + align:start position:0% +going to look exactly the same if the +user keeps typing and write I keep + + align:start position:0% +user keeps typing and write I keep + + + align:start position:0% +user keeps typing and write I keep +reassigning the variable where to have + + align:start position:0% +reassigning the variable where to have + + + align:start position:0% +reassigning the variable where to have +the + + align:start position:0% +the + + + align:start position:0% +the +value r i + + align:start position:0% +value r i + + + align:start position:0% +value r i +ght okay at some point the user might + + align:start position:0% +ght okay at some point the user might + + + align:start position:0% +ght okay at some point the user might +type in left in which case we're going + + align:start position:0% +type in left in which case we're going + + + align:start position:0% +type in left in which case we're going +to lose the binding from uh a variable + + align:start position:0% +to lose the binding from uh a variable + + + align:start position:0% +to lose the binding from uh a variable +where from the specific sequence of + + align:start position:0% +where from the specific sequence of + + + align:start position:0% +where from the specific sequence of +characters R ght we're going to bind it + + align:start position:0% +characters R ght we're going to bind it + + + align:start position:0% +characters R ght we're going to bind it +now to the characters Le so at some + + align:start position:0% +now to the characters Le so at some + + + align:start position:0% +now to the characters Le so at some +point after repeating this many times + + align:start position:0% +point after repeating this many times + + + align:start position:0% +point after repeating this many times +the user will type in left and we're + + align:start position:0% +the user will type in left and we're + + + align:start position:0% +the user will type in left and we're +going to have where is equal to left and + + align:start position:0% +going to have where is equal to left and + + + align:start position:0% +going to have where is equal to left and +at that point when the condition is + + align:start position:0% +at that point when the condition is + + + align:start position:0% +at that point when the condition is +being checked again python will say nope + + align:start position:0% +being checked again python will say nope + + + align:start position:0% +being checked again python will say nope +this is not equivalent so I'm not going + + align:start position:0% +this is not equivalent so I'm not going + + + align:start position:0% +this is not equivalent so I'm not going +to go inside this code block I'm just + + align:start position:0% +to go inside this code block I'm just + + + align:start position:0% +to go inside this code block I'm just +going to go down here and print you got + + align:start position:0% +going to go down here and print you got + + + align:start position:0% +going to go down here and print you got +out of the L + + align:start position:0% +out of the L + + + align:start position:0% +out of the L +Forest so in code the way this looks is + + align:start position:0% +Forest so in code the way this looks is + + + align:start position:0% +Forest so in code the way this looks is +it's this first one + + align:start position:0% + + + + align:start position:0% + +here so you're in the lost forest go + + align:start position:0% +here so you're in the lost forest go + + + align:start position:0% +here so you're in the lost forest go +left or right so if I type in right it + + align:start position:0% +left or right so if I type in right it + + + align:start position:0% +left or right so if I type in right it +just keeps asking me which way to go and + + align:start position:0% +just keeps asking me which way to go and + + + align:start position:0% +just keeps asking me which way to go and +at some point I can type in left and I'm + + align:start position:0% +at some point I can type in left and I'm + + + align:start position:0% +at some point I can type in left and I'm +out okay so it's pretty cool right we + + align:start position:0% +out okay so it's pretty cool right we + + + align:start position:0% +out okay so it's pretty cool right we +just made our own level in this text + + align:start position:0% +just made our own level in this text + + + align:start position:0% +just made our own level in this text +Adventure let's have you think about + + align:start position:0% +Adventure let's have you think about + + + align:start position:0% +Adventure let's have you think about +this question what if the user types in + + align:start position:0% +this question what if the user types in + + + align:start position:0% +this question what if the user types in +capital r GT what do you think will + + align:start position:0% +capital r GT what do you think will + + + align:start position:0% +capital r GT what do you think will +happen are we going to ask the user to + + align:start position:0% +happen are we going to ask the user to + + + align:start position:0% +happen are we going to ask the user to +go left or right again or are we going + + align:start position:0% +go left or right again or are we going + + + align:start position:0% +go left or right again or are we going +to tell them that they they got out of + + align:start position:0% +to tell them that they they got out of + + + align:start position:0% +to tell them that they they got out of +the + + align:start position:0% + + + + align:start position:0% + +forest yeah they got out do you want to + + align:start position:0% +forest yeah they got out do you want to + + + align:start position:0% +forest yeah they got out do you want to +ex say why it's not lower yeah exactly + + align:start position:0% +ex say why it's not lower yeah exactly + + + align:start position:0% +ex say why it's not lower yeah exactly +because it's not lowercase so remember + + align:start position:0% +because it's not lowercase so remember + + + align:start position:0% +because it's not lowercase so remember +when we're doing compar so the equal + + align:start position:0% +when we're doing compar so the equal + + + align:start position:0% +when we're doing compar so the equal +equal on strings it has to be the same + + align:start position:0% +equal on strings it has to be the same + + + align:start position:0% +equal on strings it has to be the same +case right it's case sensitive and so + + align:start position:0% +case right it's case sensitive and so + + + align:start position:0% +case right it's case sensitive and so +capital ght or even some combination + + align:start position:0% +capital ght or even some combination + + + align:start position:0% +capital ght or even some combination +like just capital r lowercase R + + align:start position:0% +like just capital r lowercase R + + + align:start position:0% +like just capital r lowercase R +RT um is also going to give us uh that + + align:start position:0% +RT um is also going to give us uh that + + + align:start position:0% +RT um is also going to give us uh that +that we got out so this is + + align:start position:0% +that we got out so this is + + + align:start position:0% +that we got out so this is +counterintuitive right to what we see as + + align:start position:0% +counterintuitive right to what we see as + + + align:start position:0% +counterintuitive right to what we see as +humans because we see you know R GT no + + align:start position:0% +humans because we see you know R GT no + + + align:start position:0% +humans because we see you know R GT no +matter what to be um to be mean right so + + align:start position:0% +matter what to be um to be mean right so + + + align:start position:0% +matter what to be um to be mean right so +a workaround for this would be to use + + align:start position:0% +a workaround for this would be to use + + + align:start position:0% +a workaround for this would be to use +sort of a command on the string to maybe + + align:start position:0% +sort of a command on the string to maybe + + + align:start position:0% +sort of a command on the string to maybe +convert everything to lowercase just so + + align:start position:0% +convert everything to lowercase just so + + + align:start position:0% +convert everything to lowercase just so +it's easy more easily compared or + + align:start position:0% +it's easy more easily compared or + + + align:start position:0% +it's easy more easily compared or +something like + + align:start position:0% +something like + + + align:start position:0% +something like +that okay so another use of while Loops + + align:start position:0% +that okay so another use of while Loops + + + align:start position:0% +that okay so another use of while Loops +is with numbers okay let's look at this + + align:start position:0% +is with numbers okay let's look at this + + + align:start position:0% +is with numbers okay let's look at this +example I'm going to ask the user for an + + align:start position:0% +example I'm going to ask the user for an + + + align:start position:0% +example I'm going to ask the user for an +integer and then I'm going to do + + align:start position:0% +integer and then I'm going to do + + + align:start position:0% +integer and then I'm going to do +something really simple I'm going to + + align:start position:0% +something really simple I'm going to + + + align:start position:0% +something really simple I'm going to +print x to the screen however many times + + align:start position:0% +print x to the screen however many times + + + align:start position:0% +print x to the screen however many times +the user told me so if the user gives me + + align:start position:0% +the user told me so if the user gives me + + + align:start position:0% +the user told me so if the user gives me +four I'm going to print X four times to + + align:start position:0% +four I'm going to print X four times to + + + align:start position:0% +four I'm going to print X four times to +the + + align:start position:0% +the + + + align:start position:0% +the +screen so what is this code doing uh in + + align:start position:0% +screen so what is this code doing uh in + + + align:start position:0% +screen so what is this code doing uh in +memory well the user gives me let's say + + align:start position:0% +memory well the user gives me let's say + + + align:start position:0% +memory well the user gives me let's say +four what happen step by step first we + + align:start position:0% +four what happen step by step first we + + + align:start position:0% +four what happen step by step first we +see our y Loop so I'm going to check + + align:start position:0% +see our y Loop so I'm going to check + + + align:start position:0% +see our y Loop so I'm going to check +whether four the current value of n is + + align:start position:0% +whether four the current value of n is + + + align:start position:0% +whether four the current value of n is +greater than zero yes that's true I'm + + align:start position:0% +greater than zero yes that's true I'm + + + align:start position:0% +greater than zero yes that's true I'm +going to print x to the screen and then + + align:start position:0% +going to print x to the screen and then + + + align:start position:0% +going to print x to the screen and then +I'm going to do the next line of code + + align:start position:0% +I'm going to do the next line of code + + + align:start position:0% +I'm going to do the next line of code +that's part of this indented block which + + align:start position:0% +that's part of this indented block which + + + align:start position:0% +that's part of this indented block which +is to take n and assign it to whatever n + + align:start position:0% +is to take n and assign it to whatever n + + + align:start position:0% +is to take n and assign it to whatever n +is minus one so I'm going to going to + + align:start position:0% +is minus one so I'm going to going to + + + align:start position:0% +is minus one so I'm going to going to +lose the binding from the four and I'm + + align:start position:0% +lose the binding from the four and I'm + + + align:start position:0% +lose the binding from the four and I'm +going to take four minus 1 to be three + + align:start position:0% +going to take four minus 1 to be three + + + align:start position:0% +going to take four minus 1 to be three +create a new object and bind n to the + + align:start position:0% +create a new object and bind n to the + + + align:start position:0% +create a new object and bind n to the +three okay next python again it's part + + align:start position:0% +three okay next python again it's part + + + align:start position:0% +three okay next python again it's part +of a y Loop so automatically it looks at + + align:start position:0% +of a y Loop so automatically it looks at + + + align:start position:0% +of a y Loop so automatically it looks at +the condition again and says well now + + align:start position:0% +the condition again and says well now + + + align:start position:0% +the condition again and says well now +the value of n is still greater than + + align:start position:0% +the value of n is still greater than + + + align:start position:0% +the value of n is still greater than +zero yeah three is still greater than + + align:start position:0% +zero yeah three is still greater than + + + align:start position:0% +zero yeah three is still greater than +zero so again we're going to lose the + + align:start position:0% +zero so again we're going to lose the + + + align:start position:0% +zero so again we're going to lose the +binding sorry we're printing x to the + + align:start position:0% +binding sorry we're printing x to the + + + align:start position:0% +binding sorry we're printing x to the +screen first and then we lose the + + align:start position:0% +screen first and then we lose the + + + align:start position:0% +screen first and then we lose the +binding from the current value of n 3 2 + + align:start position:0% +binding from the current value of n 3 2 + + + align:start position:0% +binding from the current value of n 3 2 +2 okay so we're decrementing n by one + + align:start position:0% +2 okay so we're decrementing n by one + + + align:start position:0% +2 okay so we're decrementing n by one +each time through this while loop okay + + align:start position:0% +each time through this while loop okay + + + align:start position:0% +each time through this while loop okay +then again python checks the condition + + align:start position:0% +then again python checks the condition + + + align:start position:0% +then again python checks the condition +it says two is still greater than zero + + align:start position:0% +it says two is still greater than zero + + + align:start position:0% +it says two is still greater than zero +so again we print another x to the + + align:start position:0% +so again we print another x to the + + + align:start position:0% +so again we print another x to the +screen and then we decrement n by one so + + align:start position:0% +screen and then we decrement n by one so + + + align:start position:0% +screen and then we decrement n by one so +we're binding n to one again python + + align:start position:0% +we're binding n to one again python + + + align:start position:0% +we're binding n to one again python +checks the condition is one still + + align:start position:0% +checks the condition is one still + + + align:start position:0% +checks the condition is one still +greater than zero yes so we print + + align:start position:0% +greater than zero yes so we print + + + align:start position:0% +greater than zero yes so we print +another x to the screen so we've printed + + align:start position:0% +another x to the screen so we've printed + + + align:start position:0% +another x to the screen so we've printed +four X's now to the screen and then + + align:start position:0% +four X's now to the screen and then + + + align:start position:0% +four X's now to the screen and then +python says now I'm going to make n to + + align:start position:0% +python says now I'm going to make n to + + + align:start position:0% +python says now I'm going to make n to +be zero and then at this point python + + align:start position:0% +be zero and then at this point python + + + align:start position:0% +be zero and then at this point python +will do another check is it say it's + + align:start position:0% +will do another check is it say it's + + + align:start position:0% +will do another check is it say it's +going to say is 0 greater than 0er and + + align:start position:0% +going to say is 0 greater than 0er and + + + align:start position:0% +going to say is 0 greater than 0er and +that's going to be false so it's not + + align:start position:0% +that's going to be false so it's not + + + align:start position:0% +that's going to be false so it's not +going to execute the code block anymore + + align:start position:0% +going to execute the code block anymore + + + align:start position:0% +going to execute the code block anymore +and the program will be done right + + align:start position:0% +and the program will be done right + + + align:start position:0% +and the program will be done right +there's no sort of code to rejoin + + align:start position:0% +there's no sort of code to rejoin + + + align:start position:0% +there's no sort of code to rejoin +anymore there's just the end of the + + align:start position:0% +anymore there's just the end of the + + + align:start position:0% +anymore there's just the end of the +program so we would have printed four + + align:start position:0% +program so we would have printed four + + + align:start position:0% +program so we would have printed four +X's to the screen and this is in the + + align:start position:0% +X's to the screen and this is in the + + + align:start position:0% +X's to the screen and this is in the +python file I gave you you can feel free + + align:start position:0% +python file I gave you you can feel free + + + align:start position:0% +python file I gave you you can feel free +to run it um to double + + align:start position:0% +to run it um to double + + + align:start position:0% +to run it um to double +check my question is what happens and + + align:start position:0% +check my question is what happens and + + + align:start position:0% +check my question is what happens and +this is a really common mistake what + + align:start position:0% +this is a really common mistake what + + + align:start position:0% +this is a really common mistake what +happens if we forget this last line + + align:start position:0% + + + + align:start position:0% + +we can try it I can try it in in + + align:start position:0% +we can try it I can try it in in + + + align:start position:0% +we can try it I can try it in in +here yeah exactly it's going to go on + + align:start position:0% +here yeah exactly it's going to go on + + + align:start position:0% +here yeah exactly it's going to go on +forever I'll show you what that looks + + align:start position:0% +forever I'll show you what that looks + + + align:start position:0% +forever I'll show you what that looks +like so this is the code when we just + + align:start position:0% +like so this is the code when we just + + + align:start position:0% +like so this is the code when we just +have it working as usual so if I type in + + align:start position:0% +have it working as usual so if I type in + + + align:start position:0% +have it working as usual so if I type in +three it prints three of those + + align:start position:0% +three it prints three of those + + + align:start position:0% +three it prints three of those +X's but if I happen to forget to write + + align:start position:0% +X's but if I happen to forget to write + + + align:start position:0% +X's but if I happen to forget to write +this last line I'm just going to comment + + align:start position:0% +this last line I'm just going to comment + + + align:start position:0% +this last line I'm just going to comment +it out and if I run the program I can + + align:start position:0% +it out and if I run the program I can + + + align:start position:0% +it out and if I run the program I can +enter any number and it'll just keep + + align:start position:0% +enter any number and it'll just keep + + + align:start position:0% +enter any number and it'll just keep +printing stuff to the + + align:start position:0% +printing stuff to the + + + align:start position:0% +printing stuff to the +console right so this is what it's it's + + align:start position:0% +console right so this is what it's it's + + + align:start position:0% +console right so this is what it's it's +just printing a whole bunch of + + align:start position:0% +just printing a whole bunch of + + + align:start position:0% +just printing a whole bunch of +stuff so you can see this is all all the + + align:start position:0% +stuff so you can see this is all all the + + + align:start position:0% +stuff so you can see this is all all the +stuff it + + align:start position:0% +stuff it + + + align:start position:0% +stuff it +printed so yeah we we don't have a + + align:start position:0% +printed so yeah we we don't have a + + + align:start position:0% +printed so yeah we we don't have a +program that terminates because the + + align:start position:0% +program that terminates because the + + + align:start position:0% +program that terminates because the +condition here is never actually being + + align:start position:0% +condition here is never actually being + + + align:start position:0% +condition here is never actually being +uh the variable that's part of this + + align:start position:0% +uh the variable that's part of this + + + align:start position:0% +uh the variable that's part of this +condition is never actually being + + align:start position:0% +condition is never actually being + + + align:start position:0% +condition is never actually being +changed inside my Loop right and so + + align:start position:0% +changed inside my Loop right and so + + + align:start position:0% +changed inside my Loop right and so +that's a big problem when that happens + + align:start position:0% +that's a big problem when that happens + + + align:start position:0% +that's a big problem when that happens +what we can do and what I just did here + + align:start position:0% +what we can do and what I just did here + + + align:start position:0% +what we can do and what I just did here +is I'm going to you can click the shell + + align:start position:0% +is I'm going to you can click the shell + + + align:start position:0% +is I'm going to you can click the shell +and hit control C or command C on a Mac + + align:start position:0% +and hit control C or command C on a Mac + + + align:start position:0% +and hit control C or command C on a Mac +and that will just end the program + + align:start position:0% +and that will just end the program + + + align:start position:0% +and that will just end the program +manually or you can just click the red X + + align:start position:0% +manually or you can just click the red X + + + align:start position:0% +manually or you can just click the red X +in the corner so here's another example + + align:start position:0% +in the corner so here's another example + + + align:start position:0% +in the corner so here's another example +of it going infinite and there's this + + align:start position:0% +of it going infinite and there's this + + + align:start position:0% +of it going infinite and there's this +little red sorry Red Box in the corner + + align:start position:0% +little red sorry Red Box in the corner + + + align:start position:0% +little red sorry Red Box in the corner +you can click that or you can click the + + align:start position:0% +you can click that or you can click the + + + align:start position:0% +you can click that or you can click the +three lines say interrupt kernel all + + align:start position:0% +three lines say interrupt kernel all + + + align:start position:0% +three lines say interrupt kernel all +that will stop the program so in this + + align:start position:0% +that will stop the program so in this + + + align:start position:0% +that will stop the program so in this +class we're not actually going to write + + align:start position:0% +class we're not actually going to write + + + align:start position:0% +class we're not actually going to write +programs that take second to run so if + + align:start position:0% +programs that take second to run so if + + + align:start position:0% +programs that take second to run so if +you find yourself waiting for your + + align:start position:0% +you find yourself waiting for your + + + align:start position:0% +you find yourself waiting for your +program for more than one or two seconds + + align:start position:0% +program for more than one or two seconds + + + align:start position:0% +program for more than one or two seconds +then likely you've entered an infinite + + align:start position:0% +then likely you've entered an infinite + + + align:start position:0% +then likely you've entered an infinite +Loop so you'll want to stop it and try + + align:start position:0% +Loop so you'll want to stop it and try + + + align:start position:0% +Loop so you'll want to stop it and try +to see where your program went + + align:start position:0% + + + + align:start position:0% + +wrong okay so give this a try if you + + align:start position:0% +wrong okay so give this a try if you + + + align:start position:0% +wrong okay so give this a try if you +want just so you get the hang of + + align:start position:0% +want just so you get the hang of + + + align:start position:0% +want just so you get the hang of +stopping an infinite program because + + align:start position:0% +stopping an infinite program because + + + align:start position:0% +stopping an infinite program because +you'll very likely run write a program + + align:start position:0% +you'll very likely run write a program + + + align:start position:0% +you'll very likely run write a program +that uh that doesn't terminate so while + + align:start position:0% +that uh that doesn't terminate so while + + + align:start position:0% +that uh that doesn't terminate so while +true + + align:start position:0% +true + + + align:start position:0% +true +what's the condition + + align:start position:0% +what's the condition + + + align:start position:0% +what's the condition +here it's just true right so there is no + + align:start position:0% +here it's just true right so there is no + + + align:start position:0% +here it's just true right so there is no +condition that's being checked this + + align:start position:0% +condition that's being checked this + + + align:start position:0% +condition that's being checked this +program will run always an infinite + + align:start position:0% +program will run always an infinite + + + align:start position:0% +program will run always an infinite +times no matter + + align:start position:0% +times no matter + + + align:start position:0% +times no matter +what okay so that's just this little you + + align:start position:0% +what okay so that's just this little you + + + align:start position:0% +what okay so that's just this little you +try it down here on line 44 just run it + + align:start position:0% +try it down here on line 44 just run it + + + align:start position:0% +try it down here on line 44 just run it +as soon as you run it it's just going to + + align:start position:0% +as soon as you run it it's just going to + + + align:start position:0% +as soon as you run it it's just going to +print that to the screen over and over + + align:start position:0% +print that to the screen over and over + + + align:start position:0% +print that to the screen over and over +again be sure to click the shell to put + + align:start position:0% +again be sure to click the shell to put + + + align:start position:0% +again be sure to click the shell to put +the focus on there and hit control C or + + align:start position:0% +the focus on there and hit control C or + + + align:start position:0% +the focus on there and hit control C or +hit the Red X + + align:start position:0% + + + + align:start position:0% + +all + + align:start position:0% +all + + + align:start position:0% +all +right so the big idea with while Loops + + align:start position:0% +right so the big idea with while Loops + + + align:start position:0% +right so the big idea with while Loops +is that they can repeat the code inside + + align:start position:0% +is that they can repeat the code inside + + + align:start position:0% +is that they can repeat the code inside +them indefinitely so we have to be a + + align:start position:0% +them indefinitely so we have to be a + + + align:start position:0% +them indefinitely so we have to be a +little bit careful with what uh what our + + align:start position:0% +little bit careful with what uh what our + + + align:start position:0% +little bit careful with what uh what our +conditions are and whether we're + + align:start position:0% +conditions are and whether we're + + + align:start position:0% +conditions are and whether we're +actually making progress towards having + + align:start position:0% +actually making progress towards having + + + align:start position:0% +actually making progress towards having +that condition become false at some + + align:start position:0% +that condition become false at some + + + align:start position:0% +that condition become false at some +point and when that happens when they + + align:start position:0% +point and when that happens when they + + + align:start position:0% +point and when that happens when they +run indefinitely you'll have to manually + + align:start position:0% +run indefinitely you'll have to manually + + + align:start position:0% +run indefinitely you'll have to manually +intervene to to to close the program + + align:start position:0% + + + + align:start position:0% + +okay so now that we've seen uh a loop + + align:start position:0% +okay so now that we've seen uh a loop + + + align:start position:0% +okay so now that we've seen uh a loop +with a little bit of uh numerical uh + + align:start position:0% +with a little bit of uh numerical uh + + + align:start position:0% +with a little bit of uh numerical uh +computation inside it so we were + + align:start position:0% +computation inside it so we were + + + align:start position:0% +computation inside it so we were +changing the value of n inside our Loop + + align:start position:0% +changing the value of n inside our Loop + + + align:start position:0% +changing the value of n inside our Loop +let's have you work on this little + + align:start position:0% +let's have you work on this little + + + align:start position:0% +let's have you work on this little +program it's an extension of the Lost + + align:start position:0% +program it's an extension of the Lost + + + align:start position:0% +program it's an extension of the Lost +Woods this is exactly the same program + + align:start position:0% +Woods this is exactly the same program + + + align:start position:0% +Woods this is exactly the same program +that I just ran a few slides ago but + + align:start position:0% +that I just ran a few slides ago but + + + align:start position:0% +that I just ran a few slides ago but +what I want you to add is an extra print + + align:start position:0% +what I want you to add is an extra print + + + align:start position:0% +what I want you to add is an extra print +out so when the user says + + align:start position:0% +out so when the user says + + + align:start position:0% +out so when the user says +right more than two times the next time + + align:start position:0% +right more than two times the next time + + + align:start position:0% +right more than two times the next time +you ask them whether they go left or + + align:start position:0% +you ask them whether they go left or + + + align:start position:0% +you ask them whether they go left or +right I'd like you to print a sad face + + align:start position:0% +right I'd like you to print a sad face + + + align:start position:0% +right I'd like you to print a sad face +right before you ask them that question + + align:start position:0% +right before you ask them that question + + + align:start position:0% +right before you ask them that question +it can be on a different line it doesn't + + align:start position:0% +it can be on a different line it doesn't + + + align:start position:0% +it can be on a different line it doesn't +have to be on the same + + align:start position:0% +have to be on the same + + + align:start position:0% +have to be on the same +line and the way to do that is to try to + + align:start position:0% +line and the way to do that is to try to + + + align:start position:0% +line and the way to do that is to try to +create a new variable that's going to be + + align:start position:0% +create a new variable that's going to be + + + align:start position:0% +create a new variable that's going to be +like your counter that keeps track of + + align:start position:0% +like your counter that keeps track of + + + align:start position:0% +like your counter that keeps track of +how many times the user had how many + + align:start position:0% +how many times the user had how many + + + align:start position:0% +how many times the user had how many +times this y Loop has uh has repeated so + + align:start position:0% +times this y Loop has uh has repeated so + + + align:start position:0% +times this y Loop has uh has repeated so +I'll give you a couple moments to do + + align:start position:0% +I'll give you a couple moments to do + + + align:start position:0% +I'll give you a couple moments to do +that and then we'll write it + + align:start position:0% +that and then we'll write it + + + align:start position:0% +that and then we'll write it +together um as usual the UT Tri it is uh + + align:start position:0% +together um as usual the UT Tri it is uh + + + align:start position:0% +together um as usual the UT Tri it is uh +is in here so you can just uncomment the + + align:start position:0% +is in here so you can just uncomment the + + + align:start position:0% +is in here so you can just uncomment the +code with in in in spider it's control + + align:start position:0% +code with in in in spider it's control + + + align:start position:0% +code with in in in spider it's control +one or command one to batch uncomment + + align:start position:0% +one or command one to batch uncomment + + + align:start position:0% +one or command one to batch uncomment +and then you can work off of this code + + align:start position:0% +and then you can work off of this code + + + align:start position:0% +and then you can work off of this code +to try to improve + + align:start position:0% + + + + align:start position:0% + +it okay so does anyone have a start for + + align:start position:0% +it okay so does anyone have a start for + + + align:start position:0% +it okay so does anyone have a start for +me how can we do this you don't have to + + align:start position:0% +me how can we do this you don't have to + + + align:start position:0% +me how can we do this you don't have to +give it to me uh in full we can work our + + align:start position:0% +give it to me uh in full we can work our + + + align:start position:0% +give it to me uh in full we can work our +way up to the final program but what's + + align:start position:0% +way up to the final program but what's + + + align:start position:0% +way up to the final program but what's +kind of the first your first thought + + align:start position:0% + + + + align:start position:0% + +here yes + + align:start position:0% + + + + align:start position:0% + +s okay so we can create a variable and + + align:start position:0% +s okay so we can create a variable and + + + align:start position:0% +s okay so we can create a variable and +at the beginning of our program what do + + align:start position:0% +at the beginning of our program what do + + + align:start position:0% +at the beginning of our program what do +you want to make it zero okay good zero + + align:start position:0% +you want to make it zero okay good zero + + + align:start position:0% +you want to make it zero okay good zero +will keep track or n will keep track of + + align:start position:0% +will keep track or n will keep track of + + + align:start position:0% +will keep track or n will keep track of +how many times we've gone through the + + align:start position:0% +how many times we've gone through the + + + align:start position:0% +how many times we've gone through the +loop so inside our + + align:start position:0% +loop so inside our + + + align:start position:0% +loop so inside our +program when when we want when do we + + align:start position:0% +program when when we want when do we + + + align:start position:0% +program when when we want when do we +want to Inc to to change n sorry every + + align:start position:0% +want to Inc to to change n sorry every + + + align:start position:0% +want to Inc to to change n sorry every +time we go through the loop right so + + align:start position:0% +time we go through the loop right so + + + align:start position:0% +time we go through the loop right so +every time we want to go through the + + align:start position:0% +every time we want to go through the + + + align:start position:0% +every time we want to go through the +loop we want to change n to be a new + + align:start position:0% +loop we want to change n to be a new + + + align:start position:0% +loop we want to change n to be a new +value so maybe we want to increase it by + + align:start position:0% +value so maybe we want to increase it by + + + align:start position:0% +value so maybe we want to increase it by +one so n is equal to n n + + + align:start position:0% +one so n is equal to n n + + + + align:start position:0% +one so n is equal to n n + +1 so now this will keep track of how + + align:start position:0% +1 so now this will keep track of how + + + align:start position:0% +1 so now this will keep track of how +many times we've gone to the loop and we + + align:start position:0% +many times we've gone to the loop and we + + + align:start position:0% +many times we've gone to the loop and we +can actually double check this by + + align:start position:0% +can actually double check this by + + + align:start position:0% +can actually double check this by +printing n right so if we run + + align:start position:0% +printing n right so if we run + + + align:start position:0% +printing n right so if we run +it and we say + + align:start position:0% +it and we say + + + align:start position:0% +it and we say +right we've gone once right we've got + + align:start position:0% +right we've gone once right we've got + + + align:start position:0% +right we've gone once right we've got +twice right we've got three times right + + align:start position:0% +twice right we've got three times right + + + align:start position:0% +twice right we've got three times right +so this um means we're incrementing it + + align:start position:0% +so this um means we're incrementing it + + + align:start position:0% +so this um means we're incrementing it +correctly now what can I do with this + + align:start position:0% +correctly now what can I do with this + + + align:start position:0% +correctly now what can I do with this +variable n now that I have it and I know + + align:start position:0% +variable n now that I have it and I know + + + align:start position:0% +variable n now that I have it and I know +it's incrementing + + align:start position:0% +it's incrementing + + + align:start position:0% +it's incrementing +correctly yeah set an + + align:start position:0% +correctly yeah set an + + + align:start position:0% +correctly yeah set an +st yep we can set up an if statement so + + align:start position:0% +st yep we can set up an if statement so + + + align:start position:0% +st yep we can set up an if statement so +we can check if that value of + + align:start position:0% +we can check if that value of + + + align:start position:0% +we can check if that value of +n is greater than two right according to + + align:start position:0% +n is greater than two right according to + + + align:start position:0% +n is greater than two right according to +this specification here what do you want + + align:start position:0% +this specification here what do you want + + + align:start position:0% +this specification here what do you want +to do when if is greater than + + align:start position:0% +to do when if is greater than + + + align:start position:0% +to do when if is greater than +two print something right so we can + + align:start position:0% +two print something right so we can + + + align:start position:0% +two print something right so we can +print the sad + + align:start position:0% + + + + align:start position:0% + +face and let's try to run it now so if + + align:start position:0% +face and let's try to run it now so if + + + align:start position:0% +face and let's try to run it now so if +we immediately hit left right it still + + align:start position:0% +we immediately hit left right it still + + + align:start position:0% +we immediately hit left right it still +works if we go right one time nothing + + align:start position:0% +works if we go right one time nothing + + + align:start position:0% +works if we go right one time nothing +right another time nothing right a last + + align:start position:0% +right another time nothing right a last + + + align:start position:0% +right another time nothing right a last +time sad and from now on it's going to + + align:start position:0% +time sad and from now on it's going to + + + align:start position:0% +time sad and from now on it's going to +keep showing me the sad + + align:start position:0% + + + + align:start position:0% + +face okay questions about this + + align:start position:0% +face okay questions about this + + + align:start position:0% +face okay questions about this +code yeah is it possible that test for + + align:start position:0% +code yeah is it possible that test for + + + align:start position:0% +code yeah is it possible that test for +something that's non equivalent like is + + align:start position:0% +something that's non equivalent like is + + + align:start position:0% +something that's non equivalent like is +there a sign that's different than the + + align:start position:0% +there a sign that's different than the + + + align:start position:0% +there a sign that's different than the +two equals can we check for not + + align:start position:0% +two equals can we check for not + + + align:start position:0% +two equals can we check for not +equivalency uh here yeah um so this this + + align:start position:0% +equivalency uh here yeah um so this this + + + align:start position:0% +equivalency uh here yeah um so this this +particular check checks for what the + + align:start position:0% +particular check checks for what the + + + align:start position:0% +particular check checks for what the +user typed in + + align:start position:0% +user typed in + + + align:start position:0% +user typed in +um it's possible we can add this if + + align:start position:0% +um it's possible we can add this if + + + align:start position:0% +um it's possible we can add this if +statement that checks for the n in here + + align:start position:0% +statement that checks for the n in here + + + align:start position:0% +statement that checks for the n in here +and something else but then we would + + align:start position:0% +and something else but then we would + + + align:start position:0% +and something else but then we would +have to have maybe + + align:start position:0% + + + + align:start position:0% + +another I'd have to think about it but + + align:start position:0% +another I'd have to think about it but + + + align:start position:0% +another I'd have to think about it but +it is it might be possible to try to + + align:start position:0% +it is it might be possible to try to + + + align:start position:0% +it is it might be possible to try to +combine them inside the while loop there + + align:start position:0% +combine them inside the while loop there + + + align:start position:0% +combine them inside the while loop there +there's a symbol that allows you oh to + + align:start position:0% +there's a symbol that allows you oh to + + + align:start position:0% +there's a symbol that allows you oh to +do not equals that would be the not + + align:start position:0% +do not equals that would be the not + + + align:start position:0% +do not equals that would be the not +equal sign + + align:start position:0% +equal sign + + + align:start position:0% +equal sign +yeah so another thing we can do with + + align:start position:0% +yeah so another thing we can do with + + + align:start position:0% +yeah so another thing we can do with +while Loops is to iterate through + + align:start position:0% +while Loops is to iterate through + + + align:start position:0% +while Loops is to iterate through +numbers in a sequence if we do this + + align:start position:0% +numbers in a sequence if we do this + + + align:start position:0% +numbers in a sequence if we do this +there's a really common pattern which + + align:start position:0% +there's a really common pattern which + + + align:start position:0% +there's a really common pattern which +actually uh leads us to the next kind of + + align:start position:0% +actually uh leads us to the next kind of + + + align:start position:0% +actually uh leads us to the next kind of +loop we're going to see on the next + + align:start position:0% +loop we're going to see on the next + + + align:start position:0% +loop we're going to see on the next +slide but the + + align:start position:0% +slide but the + + + align:start position:0% +slide but the +pattern when you want to iterate through + + align:start position:0% +pattern when you want to iterate through + + + align:start position:0% +pattern when you want to iterate through +numbers in a sequence is you first set a + + align:start position:0% +numbers in a sequence is you first set a + + + align:start position:0% +numbers in a sequence is you first set a +loop variable before the while loop + + align:start position:0% +loop variable before the while loop + + + align:start position:0% +loop variable before the while loop +inside the condition for the loop you do + + align:start position:0% +inside the condition for the loop you do + + + align:start position:0% +inside the condition for the loop you do +some sort of check with that + + align:start position:0% +some sort of check with that + + + align:start position:0% +some sort of check with that +variable so n was my Loop variable + + align:start position:0% +variable so n was my Loop variable + + + align:start position:0% +variable so n was my Loop variable +outside the loop and then I test it + + align:start position:0% +outside the loop and then I test it + + + align:start position:0% +outside the loop and then I test it +inside the while loop so n is less than + + align:start position:0% +inside the while loop so n is less than + + + align:start position:0% +inside the while loop so n is less than +or less than five and then within the + + align:start position:0% +or less than five and then within the + + + align:start position:0% +or less than five and then within the +while loop you can do whatever commands + + align:start position:0% +while loop you can do whatever commands + + + align:start position:0% +while loop you can do whatever commands +you want to do with that n but then you + + align:start position:0% +you want to do with that n but then you + + + align:start position:0% +you want to do with that n but then you +have to remember to change it in some + + align:start position:0% +have to remember to change it in some + + + align:start position:0% +have to remember to change it in some +way because if you don't change it in + + align:start position:0% +way because if you don't change it in + + + align:start position:0% +way because if you don't change it in +some way this while loop condition will + + align:start position:0% +some way this while loop condition will + + + align:start position:0% +some way this while loop condition will +always be true + + align:start position:0% +always be true + + + align:start position:0% +always be true +so here I'm incrementing n by one + + align:start position:0% +so here I'm incrementing n by one + + + align:start position:0% +so here I'm incrementing n by one +because it starts from zero I want n to + + align:start position:0% +because it starts from zero I want n to + + + align:start position:0% +because it starts from zero I want n to +get to something right something above + + align:start position:0% +get to something right something above + + + align:start position:0% +get to something right something above +five which will lead to my condition + + align:start position:0% +five which will lead to my condition + + + align:start position:0% +five which will lead to my condition +becoming + + align:start position:0% +becoming + + + align:start position:0% +becoming +false + + align:start position:0% +false + + + align:start position:0% +false +okay so this pattern is actually + + align:start position:0% +okay so this pattern is actually + + + align:start position:0% +okay so this pattern is actually +actually exists in a bunch of different + + align:start position:0% +actually exists in a bunch of different + + + align:start position:0% +actually exists in a bunch of different +programs so here's a program that + + align:start position:0% +programs so here's a program that + + + align:start position:0% +programs so here's a program that +calculates factorial for + + align:start position:0% +calculates factorial for + + + align:start position:0% +calculates factorial for +me and here I'm calculating four + + align:start position:0% +me and here I'm calculating four + + + align:start position:0% +me and here I'm calculating four +factorial I'm not excited about the + + align:start position:0% +factorial I'm not excited about the + + + align:start position:0% +factorial I'm not excited about the +number four I that's four factorial how + + align:start position:0% +number four I that's four factorial how + + + align:start position:0% +number four I that's four factorial how +do we do this well there's a lot of + + align:start position:0% +do we do this well there's a lot of + + + align:start position:0% +do we do this well there's a lot of +things I'm initializing here but sort of + + align:start position:0% +things I'm initializing here but sort of + + + align:start position:0% +things I'm initializing here but sort of +the more you work with loops you'll kind + + align:start position:0% +the more you work with loops you'll kind + + + align:start position:0% +the more you work with loops you'll kind +of get used to seeing right what is the + + align:start position:0% +of get used to seeing right what is the + + + align:start position:0% +of get used to seeing right what is the +loop variable so I is actually going to + + align:start position:0% +loop variable so I is actually going to + + + align:start position:0% +loop variable so I is actually going to +be my Loop + + align:start position:0% +be my Loop + + + align:start position:0% +be my Loop +variable here it's being set to some + + align:start position:0% +variable here it's being set to some + + + align:start position:0% +variable here it's being set to some +value initially outside the loop inside + + align:start position:0% +value initially outside the loop inside + + + align:start position:0% +value initially outside the loop inside +the conditional I'm doing some sort of + + align:start position:0% +the conditional I'm doing some sort of + + + align:start position:0% +the conditional I'm doing some sort of +condition check with it and then uh and + + align:start position:0% +condition check with it and then uh and + + + align:start position:0% +condition check with it and then uh and +then inside the body of that conditional + + align:start position:0% +then inside the body of that conditional + + + align:start position:0% +then inside the body of that conditional +I'm changing it in some way that you + + align:start position:0% +I'm changing it in some way that you + + + align:start position:0% +I'm changing it in some way that you +know that gives me some sort of uh that + + align:start position:0% +know that gives me some sort of uh that + + + align:start position:0% +know that gives me some sort of uh that +takes me to the end of my conditional + + align:start position:0% +takes me to the end of my conditional + + + align:start position:0% +takes me to the end of my conditional +here so I'm setting I to zero I'm + + align:start position:0% +here so I'm setting I to zero I'm + + + align:start position:0% +here so I'm setting I to zero I'm +incrementing I by One each time through + + align:start position:0% +incrementing I by One each time through + + + align:start position:0% +incrementing I by One each time through +the loop and I'm making forward progress + + align:start position:0% +the loop and I'm making forward progress + + + align:start position:0% +the loop and I'm making forward progress +towards making I greater than x okay at + + align:start position:0% +towards making I greater than x okay at + + + align:start position:0% +towards making I greater than x okay at +which point my conditional will become + + align:start position:0% +which point my conditional will become + + + align:start position:0% +which point my conditional will become +false the rest of the code X is equal to + + align:start position:0% +false the rest of the code X is equal to + + + align:start position:0% +false the rest of the code X is equal to +4 just sets the uh the thing I'm want to + + align:start position:0% +4 just sets the uh the thing I'm want to + + + align:start position:0% +4 just sets the uh the thing I'm want to +get the factorial of and this factorial + + align:start position:0% +get the factorial of and this factorial + + + align:start position:0% +get the factorial of and this factorial +variable is kind of my running product + + align:start position:0% +variable is kind of my running product + + + align:start position:0% +variable is kind of my running product +so it's the thing that I'm going to keep + + align:start position:0% +so it's the thing that I'm going to keep + + + align:start position:0% +so it's the thing that I'm going to keep +multiplying to figure out what the + + align:start position:0% +multiplying to figure out what the + + + align:start position:0% +multiplying to figure out what the +factorial is so here I'm initializing it + + align:start position:0% +factorial is so here I'm initializing it + + + align:start position:0% +factorial is so here I'm initializing it +to one and inside the loop I'm + + align:start position:0% +to one and inside the loop I'm + + + align:start position:0% +to one and inside the loop I'm +multiplying it by my Loop variable every + + align:start position:0% +multiplying it by my Loop variable every + + + align:start position:0% +multiplying it by my Loop variable every +time so I'm not going to do a um like a + + align:start position:0% +time so I'm not going to do a um like a + + + align:start position:0% +time so I'm not going to do a um like a +memory diagram this at this uh for this + + align:start position:0% +memory diagram this at this uh for this + + + align:start position:0% +memory diagram this at this uh for this +example but I will do the python + + align:start position:0% +example but I will do the python + + + align:start position:0% +example but I will do the python +tutor and I'm going to step through to + + align:start position:0% +tutor and I'm going to step through to + + + align:start position:0% +tutor and I'm going to step through to +show you exactly what this is doing so X + + align:start position:0% +show you exactly what this is doing so X + + + align:start position:0% +show you exactly what this is doing so X +is 4 I is one originally and factorial + + align:start position:0% +is 4 I is one originally and factorial + + + align:start position:0% +is 4 I is one originally and factorial +is one right so X is the thing I want to + + align:start position:0% +is one right so X is the thing I want to + + + align:start position:0% +is one right so X is the thing I want to +get the factorial of I is going to be my + + align:start position:0% +get the factorial of I is going to be my + + + align:start position:0% +get the factorial of I is going to be my +Loop variable and and a factorial is my + + align:start position:0% +Loop variable and and a factorial is my + + + align:start position:0% +Loop variable and and a factorial is my +running product so next step i1 is less + + align:start position:0% +running product so next step i1 is less + + + align:start position:0% +running product so next step i1 is less +than or equal to four so I'm going to + + align:start position:0% +than or equal to four so I'm going to + + + align:start position:0% +than or equal to four so I'm going to +enter the loop python will calculate the + + align:start position:0% +enter the loop python will calculate the + + + align:start position:0% +enter the loop python will calculate the +factorial as whatever it is right now + + align:start position:0% +factorial as whatever it is right now + + + align:start position:0% +factorial as whatever it is right now +multiplied by one I so it's still one + + align:start position:0% +multiplied by one I so it's still one + + + align:start position:0% +multiplied by one I so it's still one +and then I'm going to increment I to + + align:start position:0% +and then I'm going to increment I to + + + align:start position:0% +and then I'm going to increment I to +whatever it is from whatever it is now + + align:start position:0% +whatever it is from whatever it is now + + + align:start position:0% +whatever it is from whatever it is now +to one so I just want to mention this I + + align:start position:0% +to one so I just want to mention this I + + + align:start position:0% +to one so I just want to mention this I ++ = 1 is equivalent to saying I = I + + + align:start position:0% ++ = 1 is equivalent to saying I = I + + + + align:start position:0% ++ = 1 is equivalent to saying I = I + +one and this is true no matter what + + align:start position:0% +one and this is true no matter what + + + align:start position:0% +one and this is true no matter what +variable you have here basically if you + + align:start position:0% +variable you have here basically if you + + + align:start position:0% +variable you have here basically if you +have you know fact times equals you know + + align:start position:0% +have you know fact times equals you know + + + align:start position:0% +have you know fact times equals you know +two or something like that that + + align:start position:0% +two or something like that that + + + align:start position:0% +two or something like that that +basically means factorial equals fact + + align:start position:0% +basically means factorial equals fact + + + align:start position:0% +basically means factorial equals fact +times 2 right so that's kind of the the + + align:start position:0% +times 2 right so that's kind of the the + + + align:start position:0% +times 2 right so that's kind of the the +pattern here these are equivalent and + + align:start position:0% +pattern here these are equivalent and + + + align:start position:0% +pattern here these are equivalent and +these are equivalent this is just + + align:start position:0% +these are equivalent this is just + + + align:start position:0% +these are equivalent this is just +shorthand notation in + + align:start position:0% +shorthand notation in + + + align:start position:0% +shorthand notation in +programming so that's what this line + + align:start position:0% +programming so that's what this line + + + align:start position:0% +programming so that's what this line +here means I plus equals 1 means I + + align:start position:0% +here means I plus equals 1 means I + + + align:start position:0% +here means I plus equals 1 means I +equals I + + + align:start position:0% +equals I + + + + align:start position:0% +equals I + +1 so at this line here I'm taking + + align:start position:0% +1 so at this line here I'm taking + + + align:start position:0% +1 so at this line here I'm taking +whatever I is and adding one to it two + + align:start position:0% +whatever I is and adding one to it two + + + align:start position:0% +whatever I is and adding one to it two +and then I do the check again and + + align:start position:0% +and then I do the check again and + + + align:start position:0% +and then I do the check again and +remember python does this automatically + + align:start position:0% +remember python does this automatically + + + align:start position:0% +remember python does this automatically +right because we're using a y Loop it + + align:start position:0% +right because we're using a y Loop it + + + align:start position:0% +right because we're using a y Loop it +goes back to the uh condition and checks + + align:start position:0% +goes back to the uh condition and checks + + + align:start position:0% +goes back to the uh condition and checks +it again using these new values for the + + align:start position:0% +it again using these new values for the + + + align:start position:0% +it again using these new values for the +variables two is still less than or + + align:start position:0% +variables two is still less than or + + + align:start position:0% +variables two is still less than or +equal to four so again we go inside the + + align:start position:0% +equal to four so again we go inside the + + + align:start position:0% +equal to four so again we go inside the +Loop body factorial is whatever it is + + align:start position:0% +Loop body factorial is whatever it is + + + align:start position:0% +Loop body factorial is whatever it is +right now one multiplied by I + + align:start position:0% +right now one multiplied by I + + + align:start position:0% +right now one multiplied by I +2 I is going to be 2 + 1 + + align:start position:0% +2 I is going to be 2 + 1 + + + align:start position:0% +2 I is going to be 2 + 1 +3 and then again I'm checking that three + + align:start position:0% +3 and then again I'm checking that three + + + align:start position:0% +3 and then again I'm checking that three +is less than or equal to four it still + + align:start position:0% +is less than or equal to four it still + + + align:start position:0% +is less than or equal to four it still +is so then we're going to do factorial + + align:start position:0% +is so then we're going to do factorial + + + align:start position:0% +is so then we're going to do factorial +is whatever it is now two multiplied by + + align:start position:0% +is whatever it is now two multiplied by + + + align:start position:0% +is whatever it is now two multiplied by +whatever I is three so now it's six I is + + align:start position:0% +whatever I is three so now it's six I is + + + align:start position:0% +whatever I is three so now it's six I is +going to be one more than what it is + + align:start position:0% +going to be one more than what it is + + + align:start position:0% +going to be one more than what it is +right now four four is still less than + + align:start position:0% +right now four four is still less than + + + align:start position:0% +right now four four is still less than +or equal to four we're going to go + + align:start position:0% +or equal to four we're going to go + + + align:start position:0% +or equal to four we're going to go +inside uh the body + + align:start position:0% +inside uh the body + + + align:start position:0% +inside uh the body +factorial is whatever it is right now 6 + + align:start position:0% +factorial is whatever it is right now 6 + + + align:start position:0% +factorial is whatever it is right now 6 +multiplied + + align:start position:0% +multiplied + + + align:start position:0% +multiplied +4 and then 24 and then I is going to be + + align:start position:0% +4 and then 24 and then I is going to be + + + align:start position:0% +4 and then 24 and then I is going to be +whatever it is right now plus one five + + align:start position:0% +whatever it is right now plus one five + + + align:start position:0% +whatever it is right now plus one five +at this point python says is five less + + align:start position:0% +at this point python says is five less + + + align:start position:0% +at this point python says is five less +than or equal to four no and then it + + align:start position:0% +than or equal to four no and then it + + + align:start position:0% +than or equal to four no and then it +breaks the loop and it goes to print + + align:start position:0% +breaks the loop and it goes to print + + + align:start position:0% +breaks the loop and it goes to print +this statement four factorial is and + + align:start position:0% +this statement four factorial is and + + + align:start position:0% +this statement four factorial is and +then it grabs whatever the value of the + + align:start position:0% +then it grabs whatever the value of the + + + align:start position:0% +then it grabs whatever the value of the +factorial is so here I'm using this F + + align:start position:0% +factorial is so here I'm using this F + + + align:start position:0% +factorial is so here I'm using this F +string print that uh notation that we + + align:start position:0% +string print that uh notation that we + + + align:start position:0% +string print that uh notation that we +learned about last lecture so I + + align:start position:0% +learned about last lecture so I + + + align:start position:0% +learned about last lecture so I +encourage you to go through it + + align:start position:0% +encourage you to go through it + + + align:start position:0% +encourage you to go through it +yourself just step by step that's what + + align:start position:0% +yourself just step by step that's what + + + align:start position:0% +yourself just step by step that's what +python tutor is really really useful + + align:start position:0% +python tutor is really really useful + + + align:start position:0% +python tutor is really really useful +for okay so let's look at a different + + align:start position:0% +for okay so let's look at a different + + + align:start position:0% +for okay so let's look at a different +kind of loop called a for Loop okay and + + align:start position:0% +kind of loop called a for Loop okay and + + + align:start position:0% +kind of loop called a for Loop okay and +the for Loop is going to allow us to uh + + align:start position:0% +the for Loop is going to allow us to uh + + + align:start position:0% +the for Loop is going to allow us to uh +to rewrite a c that special kind of + + align:start position:0% +to rewrite a c that special kind of + + + align:start position:0% +to rewrite a c that special kind of +while loop that we saw where we + + align:start position:0% +while loop that we saw where we + + + align:start position:0% +while loop that we saw where we +initialize a variable we test the + + align:start position:0% +initialize a variable we test the + + + align:start position:0% +initialize a variable we test the +variable we do something to the variable + + align:start position:0% +variable we do something to the variable + + + align:start position:0% +variable we do something to the variable +within the code in a more efficient more + + align:start position:0% +within the code in a more efficient more + + + align:start position:0% +within the code in a more efficient more +readable way so in terms of our Netflix + + align:start position:0% +readable way so in terms of our Netflix + + + align:start position:0% +readable way so in terms of our Netflix +example um a for Loop would be + + align:start position:0% +example um a for Loop would be + + + align:start position:0% +example um a for Loop would be +equivalent to something like Netflix + + align:start position:0% +equivalent to something like Netflix + + + align:start position:0% +equivalent to something like Netflix +right if you're not interacting with it + + align:start position:0% +right if you're not interacting with it + + + align:start position:0% +right if you're not interacting with it +cuts you off after four episodes right + + align:start position:0% +cuts you off after four episodes right + + + align:start position:0% +cuts you off after four episodes right +to save bandwidth and so there's a + + align:start position:0% +to save bandwidth and so there's a + + + align:start position:0% +to save bandwidth and so there's a +sequence of four episodes it knows it's + + align:start position:0% +sequence of four episodes it knows it's + + + align:start position:0% +sequence of four episodes it knows it's +going to go through if there's nothing + + align:start position:0% +going to go through if there's nothing + + + align:start position:0% +going to go through if there's nothing +if you're not interacting with it so if + + align:start position:0% +if you're not interacting with it so if + + + align:start position:0% +if you're not interacting with it so if +you've already gone through your your + + align:start position:0% +you've already gone through your your + + + align:start position:0% +you've already gone through your your +you know sequence of four episodes you + + align:start position:0% +you know sequence of four episodes you + + + align:start position:0% +you know sequence of four episodes you +you're allowed to watch without any + + align:start position:0% +you're allowed to watch without any + + + align:start position:0% +you're allowed to watch without any +interaction it's done right it cuts you + + align:start position:0% +interaction it's done right it cuts you + + + align:start position:0% +interaction it's done right it cuts you +off it says are you still watching + + align:start position:0% +off it says are you still watching + + + align:start position:0% +off it says are you still watching +but if there are still more episodes if + + align:start position:0% +but if there are still more episodes if + + + align:start position:0% +but if there are still more episodes if +you if it only showed you two out of the + + align:start position:0% +you if it only showed you two out of the + + + align:start position:0% +you if it only showed you two out of the +four then it's going to keep showing you + + align:start position:0% +four then it's going to keep showing you + + + align:start position:0% +four then it's going to keep showing you +more episodes until it's shown you the + + align:start position:0% +more episodes until it's shown you the + + + align:start position:0% +more episodes until it's shown you the +four + + align:start position:0% +four + + + align:start position:0% +four +okay so this is the the program we had + + align:start position:0% +okay so this is the the program we had + + + align:start position:0% +okay so this is the the program we had +with while Loops a couple slides + + align:start position:0% +with while Loops a couple slides + + + align:start position:0% +with while Loops a couple slides +ago and remember we were initializing a + + align:start position:0% +ago and remember we were initializing a + + + align:start position:0% +ago and remember we were initializing a +variable we were testing the variable + + align:start position:0% +variable we were testing the variable + + + align:start position:0% +variable we were testing the variable +some condition here and then we were + + align:start position:0% +some condition here and then we were + + + align:start position:0% +some condition here and then we were +incrementing the variable or doing + + align:start position:0% +incrementing the variable or doing + + + align:start position:0% +incrementing the variable or doing +something that g gives us nice forward + + align:start position:0% +something that g gives us nice forward + + + align:start position:0% +something that g gives us nice forward +progress towards making this condition + + align:start position:0% +progress towards making this condition + + + align:start position:0% +progress towards making this condition +false but it's really + + align:start position:0% +false but it's really + + + align:start position:0% +false but it's really +verbose certainly it works and you can + + align:start position:0% +verbose certainly it works and you can + + + align:start position:0% +verbose certainly it works and you can +do it but it's very easy to forget to do + + align:start position:0% +do it but it's very easy to forget to do + + + align:start position:0% +do it but it's very easy to forget to do +this something like this um in which + + align:start position:0% +this something like this um in which + + + align:start position:0% +this something like this um in which +case you'll get an infinite loop with a + + align:start position:0% +case you'll get an infinite loop with a + + + align:start position:0% +case you'll get an infinite loop with a +for Loop that those four lines of code + + align:start position:0% +for Loop that those four lines of code + + + align:start position:0% +for Loop that those four lines of code +just look like this these two lines of + + align:start position:0% +just look like this these two lines of + + + align:start position:0% +just look like this these two lines of +code okay so if there's a sequence of + + align:start position:0% +code okay so if there's a sequence of + + + align:start position:0% +code okay so if there's a sequence of +values you ever want to iterate over + + align:start position:0% +values you ever want to iterate over + + + align:start position:0% +values you ever want to iterate over +that's what for Loops are useful uh + + align:start position:0% +that's what for Loops are useful uh + + + align:start position:0% +that's what for Loops are useful uh +for so the syntax for for Loop looks a + + align:start position:0% +for so the syntax for for Loop looks a + + + align:start position:0% +for so the syntax for for Loop looks a +little bit different uh than a while + + align:start position:0% +little bit different uh than a while + + + align:start position:0% +little bit different uh than a while +loop it starts with a four keyword this + + align:start position:0% +loop it starts with a four keyword this + + + align:start position:0% +loop it starts with a four keyword this +is a variable that you get to name + + align:start position:0% +is a variable that you get to name + + + align:start position:0% +is a variable that you get to name +whatever name you'd like the keyword in + + align:start position:0% +whatever name you'd like the keyword in + + + align:start position:0% +whatever name you'd like the keyword in +tells python I'm going to make this + + align:start position:0% +tells python I'm going to make this + + + align:start position:0% +tells python I'm going to make this +variable take on values in this + + align:start position:0% +variable take on values in this + + + align:start position:0% +variable take on values in this +sequence + + align:start position:0% +sequence + + + align:start position:0% +sequence +okay and again we have a colon that + + align:start position:0% +okay and again we have a colon that + + + align:start position:0% +okay and again we have a colon that +tells python we're going to start a code + + align:start position:0% +tells python we're going to start a code + + + align:start position:0% +tells python we're going to start a code +in indentation here and whatever lines + + align:start position:0% +in indentation here and whatever lines + + + align:start position:0% +in indentation here and whatever lines +of code you have that are indented are + + align:start position:0% +of code you have that are indented are + + + align:start position:0% +of code you have that are indented are +going to be + + align:start position:0% +going to be + + + align:start position:0% +going to be +executed however many sequence of values + + align:start position:0% +executed however many sequence of values + + + align:start position:0% +executed however many sequence of values +you have so the first time through the + + align:start position:0% +you have so the first time through the + + + align:start position:0% +you have so the first time through the +loop python will make this variable name + + align:start position:0% +loop python will make this variable name + + + align:start position:0% +loop python will make this variable name +take on the first value in the sequence + + align:start position:0% +take on the first value in the sequence + + + align:start position:0% +take on the first value in the sequence +and then it's going to execute this + + align:start position:0% +and then it's going to execute this + + + align:start position:0% +and then it's going to execute this +code automatically python will after it + + align:start position:0% +code automatically python will after it + + + align:start position:0% +code automatically python will after it +finishes executing this these codes it + + align:start position:0% +finishes executing this these codes it + + + align:start position:0% +finishes executing this these codes it +will go back and set this variable have + + align:start position:0% +will go back and set this variable have + + + align:start position:0% +will go back and set this variable have +the next value in the sequence and + + align:start position:0% +the next value in the sequence and + + + align:start position:0% +the next value in the sequence and +execute the same lines of code when it's + + align:start position:0% +execute the same lines of code when it's + + + align:start position:0% +execute the same lines of code when it's +done it's going to make the variable + + align:start position:0% +done it's going to make the variable + + + align:start position:0% +done it's going to make the variable +here take on the next values in the + + align:start position:0% +here take on the next values in the + + + align:start position:0% +here take on the next values in the +sequence and execute those lines of code + + align:start position:0% +sequence and execute those lines of code + + + align:start position:0% +sequence and execute those lines of code +and so these lines of code will + + align:start position:0% +and so these lines of code will + + + align:start position:0% +and so these lines of code will +effectively be executed however many + + align:start position:0% +effectively be executed however many + + + align:start position:0% +effectively be executed however many +values you have in your + + align:start position:0% +values you have in your + + + align:start position:0% +values you have in your +sequence + + align:start position:0% +sequence + + + align:start position:0% +sequence +okay so more practically speaking here + + align:start position:0% +okay so more practically speaking here + + + align:start position:0% +okay so more practically speaking here +we have a variable so n in this case in + + align:start position:0% +we have a variable so n in this case in + + + align:start position:0% +we have a variable so n in this case in +some uh some sequence of values in this + + align:start position:0% +some uh some sequence of values in this + + + align:start position:0% +some uh some sequence of values in this +case I'm saying Range Five we're going + + align:start position:0% +case I'm saying Range Five we're going + + + align:start position:0% +case I'm saying Range Five we're going +to print the value of + + align:start position:0% +to print the value of + + + align:start position:0% +to print the value of +n so I'm going to introduce range now + + align:start position:0% +n so I'm going to introduce range now + + + align:start position:0% +n so I'm going to introduce range now +range is a way for us to grab numerical + + align:start position:0% +range is a way for us to grab numerical + + + align:start position:0% +range is a way for us to grab numerical +sequence a numerical sequence of values + + align:start position:0% +sequence a numerical sequence of values + + + align:start position:0% +sequence a numerical sequence of values +that have some sort of pattern so if we + + align:start position:0% +that have some sort of pattern so if we + + + align:start position:0% +that have some sort of pattern so if we +just say range some number the pattern + + align:start position:0% +just say range some number the pattern + + + align:start position:0% +just say range some number the pattern +is we start at zero and we go up to but + + align:start position:0% +is we start at zero and we go up to but + + + align:start position:0% +is we start at zero and we go up to but +not including that number so Range Five + + align:start position:0% +not including that number so Range Five + + + align:start position:0% +not including that number so Range Five +means the sequence of values python will + + align:start position:0% +means the sequence of values python will + + + align:start position:0% +means the sequence of values python will +iterate over are 0 1 2 3 and four range + + align:start position:0% +iterate over are 0 1 2 3 and four range + + + align:start position:0% +iterate over are 0 1 2 3 and four range +10 means 0 1 2 3 4 5 6 7 8 nine right so + + align:start position:0% +10 means 0 1 2 3 4 5 6 7 8 nine right so + + + align:start position:0% +10 means 0 1 2 3 4 5 6 7 8 nine right so +we go up to but not including the value + + align:start position:0% +we go up to but not including the value + + + align:start position:0% +we go up to but not including the value +in the range starting from + + align:start position:0% +in the range starting from + + + align:start position:0% +in the range starting from +zero so each time through the loop + + align:start position:0% +zero so each time through the loop + + + align:start position:0% +zero so each time through the loop +python will change the value of n to be + + align:start position:0% +python will change the value of n to be + + + align:start position:0% +python will change the value of n to be +every one of those values + + align:start position:0% +every one of those values + + + align:start position:0% +every one of those values +automatically so this uh these two lines + + align:start position:0% +automatically so this uh these two lines + + + align:start position:0% +automatically so this uh these two lines +here for n and Range Five print n the + + align:start position:0% +here for n and Range Five print n the + + + align:start position:0% +here for n and Range Five print n the +way they look like behind the scenes and + + align:start position:0% +way they look like behind the scenes and + + + align:start position:0% +way they look like behind the scenes and +python does this for you is first it the + + align:start position:0% +python does this for you is first it the + + + align:start position:0% +python does this for you is first it the +first time it encounters the for Loop it + + align:start position:0% +first time it encounters the for Loop it + + + align:start position:0% +first time it encounters the for Loop it +sets n to be zero that's the first value + + align:start position:0% +sets n to be zero that's the first value + + + align:start position:0% +sets n to be zero that's the first value +in my sequence and then it prints the + + align:start position:0% +in my sequence and then it prints the + + + align:start position:0% +in my sequence and then it prints the +value of n zero + + align:start position:0% +value of n zero + + + align:start position:0% +value of n zero +next time through the loop python will + + align:start position:0% +next time through the loop python will + + + align:start position:0% +next time through the loop python will +say okay I've done what you asked me to + + align:start position:0% +say okay I've done what you asked me to + + + align:start position:0% +say okay I've done what you asked me to +do inside the code loop print uh n I'm + + align:start position:0% +do inside the code loop print uh n I'm + + + align:start position:0% +do inside the code loop print uh n I'm +going to make n have the next value in + + align:start position:0% +going to make n have the next value in + + + align:start position:0% +going to make n have the next value in +my sequence so it loses The Binding from + + align:start position:0% +my sequence so it loses The Binding from + + + align:start position:0% +my sequence so it loses The Binding from +the zero and makes it be + + align:start position:0% +the zero and makes it be + + + align:start position:0% +the zero and makes it be +one okay I've made N1 now what do you + + align:start position:0% +one okay I've made N1 now what do you + + + align:start position:0% +one okay I've made N1 now what do you +want me to do well I'm going to execute + + align:start position:0% +want me to do well I'm going to execute + + + align:start position:0% +want me to do well I'm going to execute +whatever is in the in the in indented + + align:start position:0% +whatever is in the in the in indented + + + align:start position:0% +whatever is in the in the in indented +print n so I'm going to print one so + + align:start position:0% +print n so I'm going to print one so + + + align:start position:0% +print n so I'm going to print one so +I've already printed zero then I've + + align:start position:0% +I've already printed zero then I've + + + align:start position:0% +I've already printed zero then I've +printed one I'm finished executing the + + align:start position:0% +printed one I'm finished executing the + + + align:start position:0% +printed one I'm finished executing the +code inside the loop so now n is going + + align:start position:0% +code inside the loop so now n is going + + + align:start position:0% +code inside the loop so now n is going +to get the next value in the sequence + + align:start position:0% +to get the next value in the sequence + + + align:start position:0% +to get the next value in the sequence +lose the binding from one and you get + + align:start position:0% +lose the binding from one and you get + + + align:start position:0% +lose the binding from one and you get +two and so on and so on and by the end + + align:start position:0% +two and so on and so on and by the end + + + align:start position:0% +two and so on and so on and by the end +this program will have printed 0 1 two + + align:start position:0% +this program will have printed 0 1 two + + + align:start position:0% +this program will have printed 0 1 two +three and four every single value in my + + align:start position:0% + + + + align:start position:0% + +range so it turns out that we can + + align:start position:0% +range so it turns out that we can + + + align:start position:0% +range so it turns out that we can +actually make range have three values + + align:start position:0% +actually make range have three values + + + align:start position:0% +actually make range have three values +inside the parentheses not just one one + + align:start position:0% +inside the parentheses not just one one + + + align:start position:0% +inside the parentheses not just one one +is sort of shorthand notation if you + + align:start position:0% +is sort of shorthand notation if you + + + align:start position:0% +is sort of shorthand notation if you +ever want to start from zero and want to + + align:start position:0% +ever want to start from zero and want to + + + align:start position:0% +ever want to start from zero and want to +go and go up up to and including uh + + align:start position:0% +go and go up up to and including uh + + + align:start position:0% +go and go up up to and including uh +sorry up to but not including the value + + align:start position:0% +sorry up to but not including the value + + + align:start position:0% +sorry up to but not including the value +in the parenthesis but you can actually + + align:start position:0% +in the parenthesis but you can actually + + + align:start position:0% +in the parenthesis but you can actually +give it three values a start a stop and + + align:start position:0% +give it three values a start a stop and + + + align:start position:0% +give it three values a start a stop and +a step and python will automatically + + align:start position:0% +a step and python will automatically + + + align:start position:0% +a step and python will automatically +generate a sequence of values that + + align:start position:0% +generate a sequence of values that + + + align:start position:0% +generate a sequence of values that +matches this pattern so this should seem + + align:start position:0% +matches this pattern so this should seem + + + align:start position:0% +matches this pattern so this should seem +familiar to you right because we've seen + + align:start position:0% +familiar to you right because we've seen + + + align:start position:0% +familiar to you right because we've seen +something like this when we were doing + + align:start position:0% +something like this when we were doing + + + align:start position:0% +something like this when we were doing +strings right except that we weren't + + align:start position:0% +strings right except that we weren't + + + align:start position:0% +strings right except that we weren't +doing um parentheses we were doing + + align:start position:0% +doing um parentheses we were doing + + + align:start position:0% +doing um parentheses we were doing +square brackets and we weren't doing + + align:start position:0% +square brackets and we weren't doing + + + align:start position:0% +square brackets and we weren't doing +commas we were doing colons but it's the + + align:start position:0% +commas we were doing colons but it's the + + + align:start position:0% +commas we were doing colons but it's the +exact same idea here we're generating + + align:start position:0% +exact same idea here we're generating + + + align:start position:0% +exact same idea here we're generating +numbers actual integers that we want a + + align:start position:0% +numbers actual integers that we want a + + + align:start position:0% +numbers actual integers that we want a +loop variable to take + + align:start position:0% +loop variable to take + + + align:start position:0% +loop variable to take +on so if we omit start and step start by + + align:start position:0% +on so if we omit start and step start by + + + align:start position:0% +on so if we omit start and step start by +default is zero and step by default is + + align:start position:0% +default is zero and step by default is + + + align:start position:0% +default is zero and step by default is +one if we omit step by default it will + + align:start position:0% +one if we omit step by default it will + + + align:start position:0% +one if we omit step by default it will +be one so here I in range four the + + align:start position:0% +be one so here I in range four the + + + align:start position:0% +be one so here I in range four the +variable I will take on the values 0 1 2 + + align:start position:0% +variable I will take on the values 0 1 2 + + + align:start position:0% +variable I will take on the values 0 1 2 +and three I in range 3 comma 5 I will + + align:start position:0% +and three I in range 3 comma 5 I will + + + align:start position:0% +and three I in range 3 comma 5 I will +take on the values three and and four so + + align:start position:0% +take on the values three and and four so + + + align:start position:0% +take on the values three and and four so +we go up to but not including the + + align:start position:0% +we go up to but not including the + + + align:start position:0% +we go up to but not including the +five think about these uh these three + + align:start position:0% +five think about these uh these three + + + align:start position:0% +five think about these uh these three +questions so what are the range of + + align:start position:0% +questions so what are the range of + + + align:start position:0% +questions so what are the range of +values in in the first in the first one + + align:start position:0% +values in in the first in the first one + + + align:start position:0% +values in in the first in the first one +and what are we going to print so in 141 + + align:start position:0% +and what are we going to print so in 141 + + + align:start position:0% +and what are we going to print so in 141 +what range of values are we going to + + align:start position:0% +what range of values are we going to + + + align:start position:0% +what range of values are we going to +have I be so I is going to be + + align:start position:0% + + + + align:start position:0% + +what + + align:start position:0% +what + + + align:start position:0% +what +one + + align:start position:0% +one + + + align:start position:0% +one +two + + align:start position:0% +two + + + align:start position:0% +two +three yes and we stop we go up but not + + align:start position:0% +three yes and we stop we go up but not + + + align:start position:0% +three yes and we stop we go up but not +including the stop which is a four and + + align:start position:0% +including the stop which is a four and + + + align:start position:0% +including the stop which is a four and +what are we + + align:start position:0% +what are we + + + align:start position:0% +what are we +printing yeah 1 2 3 just all how about + + align:start position:0% +printing yeah 1 2 3 just all how about + + + align:start position:0% +printing yeah 1 2 3 just all how about +the next one J what will the values of J + + align:start position:0% +the next one J what will the values of J + + + align:start position:0% +the next one J what will the values of J +be + + align:start position:0% +be + + + align:start position:0% +be +one + + align:start position:0% +one + + + align:start position:0% +one +three that's it yep because we're going + + align:start position:0% +three that's it yep because we're going + + + align:start position:0% +three that's it yep because we're going +every other uh every other value and + + align:start position:0% +every other uh every other value and + + + align:start position:0% +every other uh every other value and +what are we printing + + align:start position:0% +what are we printing + + + align:start position:0% +what are we printing +here yeah exactly so we're doing an + + align:start position:0% +here yeah exactly so we're doing an + + + align:start position:0% +here yeah exactly so we're doing an +operation with each one of these JS so + + align:start position:0% +operation with each one of these JS so + + + align:start position:0% +operation with each one of these JS so +we're going to print two and then six + + align:start position:0% +we're going to print two and then six + + + align:start position:0% +we're going to print two and then six +and how about the last + + align:start position:0% + + + + align:start position:0% + +one we're stepping backward right the + + align:start position:0% +one we're stepping backward right the + + + align:start position:0% +one we're stepping backward right the +negative one so what's our + + align:start position:0% +negative one so what's our + + + align:start position:0% +negative one so what's our +start four and then three 2 + + align:start position:0% +start four and then three 2 + + + align:start position:0% +start four and then three 2 +one and that's it we're going to down to + + align:start position:0% +one and that's it we're going to down to + + + align:start position:0% +one and that's it we're going to down to +but not including the end right so we're + + align:start position:0% +but not including the end right so we're + + + align:start position:0% +but not including the end right so we're +not going to include the zero and what + + align:start position:0% +not going to include the zero and what + + + align:start position:0% +not going to include the zero and what +are we printing + + align:start position:0% + + + + align:start position:0% + +here yes four doll signs on one for the + + align:start position:0% +here yes four doll signs on one for the + + + align:start position:0% +here yes four doll signs on one for the +first time and then $3 signs and then $2 + + align:start position:0% +first time and then $3 signs and then $2 + + + align:start position:0% +first time and then $3 signs and then $2 +signs and then $1 sign + + align:start position:0% +signs and then $1 sign + + + align:start position:0% +signs and then $1 sign +exactly so the body obviously can do op + + align:start position:0% +exactly so the body obviously can do op + + + align:start position:0% +exactly so the body obviously can do op +can do operations and can manipulate + + align:start position:0% +can do operations and can manipulate + + + align:start position:0% +can do operations and can manipulate +that Loop variable so each time that + + align:start position:0% +that Loop variable so each time that + + + align:start position:0% +that Loop variable so each time that +Loop goes that variable goes through it + + align:start position:0% +Loop goes that variable goes through it + + + align:start position:0% +Loop goes that variable goes through it +changes right it changes and then you + + align:start position:0% +changes right it changes and then you + + + align:start position:0% +changes right it changes and then you +can use that to your + + align:start position:0% +can use that to your + + + align:start position:0% +can use that to your +advantage so here's another example of + + align:start position:0% +advantage so here's another example of + + + align:start position:0% +advantage so here's another example of +something useful um we can use uh uh for + + align:start position:0% +something useful um we can use uh uh for + + + align:start position:0% +something useful um we can use uh uh for +Loops to keep track of how many times + + align:start position:0% +Loops to keep track of how many times + + + align:start position:0% +Loops to keep track of how many times +we're going through a loop and in this + + align:start position:0% +we're going through a loop and in this + + + align:start position:0% +we're going through a loop and in this +particular case we're writing a program + + align:start position:0% +particular case we're writing a program + + + align:start position:0% +particular case we're writing a program +that sums all the values from zero all + + align:start position:0% +that sums all the values from zero all + + + align:start position:0% +that sums all the values from zero all +all the way up to but not including + + align:start position:0% +all the way up to but not including + + + align:start position:0% +all the way up to but not including +whatever is in here right so how are we + + align:start position:0% +whatever is in here right so how are we + + + align:start position:0% +whatever is in here right so how are we +doing this let's do the memory + + align:start position:0% +doing this let's do the memory + + + align:start position:0% +doing this let's do the memory +diagram we've got my sum is equal to + + align:start position:0% +diagram we've got my sum is equal to + + + align:start position:0% +diagram we've got my sum is equal to +zero as the first line so this will be + + align:start position:0% +zero as the first line so this will be + + + align:start position:0% +zero as the first line so this will be +zero in memory right uh bound to the + + align:start position:0% +zero in memory right uh bound to the + + + align:start position:0% +zero in memory right uh bound to the +name my sum and then the for Loop will + + align:start position:0% +name my sum and then the for Loop will + + + align:start position:0% +name my sum and then the for Loop will +generate for me the values 0 through 9 + + align:start position:0% +generate for me the values 0 through 9 + + + align:start position:0% +generate for me the values 0 through 9 +right + + align:start position:0% +right + + + align:start position:0% +right +including so I the first time through + + align:start position:0% +including so I the first time through + + + align:start position:0% +including so I the first time through +the loop will have a value of zero so + + align:start position:0% +the loop will have a value of zero so + + + align:start position:0% +the loop will have a value of zero so +we're going to do the operations where + + align:start position:0% +we're going to do the operations where + + + align:start position:0% +we're going to do the operations where +uh or the code we're asked to do when I + + align:start position:0% +uh or the code we're asked to do when I + + + align:start position:0% +uh or the code we're asked to do when I +is zero so my sum will be whatever it is + + align:start position:0% +is zero so my sum will be whatever it is + + + align:start position:0% +is zero so my sum will be whatever it is +right now plus whatever I is zero so it + + align:start position:0% +right now plus whatever I is zero so it + + + align:start position:0% +right now plus whatever I is zero so it +stays + + align:start position:0% +stays + + + align:start position:0% +stays +zero Python's done with the code inside + + align:start position:0% +zero Python's done with the code inside + + + align:start position:0% +zero Python's done with the code inside +so now it's going to take I and and + + align:start position:0% +so now it's going to take I and and + + + align:start position:0% +so now it's going to take I and and +change it to the next value in a + + align:start position:0% +change it to the next value in a + + + align:start position:0% +change it to the next value in a +sequence one okay now we're going to do + + align:start position:0% +sequence one okay now we're going to do + + + align:start position:0% +sequence one okay now we're going to do +again the stuff inside the loop with I + + align:start position:0% +again the stuff inside the loop with I + + + align:start position:0% +again the stuff inside the loop with I +being one so we're going to take my sum + + align:start position:0% +being one so we're going to take my sum + + + align:start position:0% +being one so we're going to take my sum +whatever it is right now and add one to + + align:start position:0% +whatever it is right now and add one to + + + align:start position:0% +whatever it is right now and add one to +it so it's one and then we're done there + + align:start position:0% +it so it's one and then we're done there + + + align:start position:0% +it so it's one and then we're done there +so python will take I to be the next + + align:start position:0% +so python will take I to be the next + + + align:start position:0% +so python will take I to be the next +value in the sequence two and then we're + + align:start position:0% +value in the sequence two and then we're + + + align:start position:0% +value in the sequence two and then we're +going to do again my sum is whatever it + + align:start position:0% +going to do again my sum is whatever it + + + align:start position:0% +going to do again my sum is whatever it +is now one plus whatever I is now two so + + align:start position:0% +is now one plus whatever I is now two so + + + align:start position:0% +is now one plus whatever I is now two so +it's three again I will increment to + + align:start position:0% +it's three again I will increment to + + + align:start position:0% +it's three again I will increment to +three automatically right that's the + + align:start position:0% +three automatically right that's the + + + align:start position:0% +three automatically right that's the +next value the sequence so my sum will + + align:start position:0% +next value the sequence so my sum will + + + align:start position:0% +next value the sequence so my sum will +get a value of six and then uh I will + + align:start position:0% +get a value of six and then uh I will + + + align:start position:0% +get a value of six and then uh I will +change to four so on and so on and so on + + align:start position:0% +change to four so on and so on and so on + + + align:start position:0% +change to four so on and so on and so on +until I becomes eight right that's sort + + align:start position:0% +until I becomes eight right that's sort + + + align:start position:0% +until I becomes eight right that's sort +of towards the end when I is eight the + + align:start position:0% +of towards the end when I is eight the + + + align:start position:0% +of towards the end when I is eight the +value of my sum is 36 right 0 plus 0 + + align:start position:0% +value of my sum is 36 right 0 plus 0 + + + align:start position:0% +value of my sum is 36 right 0 plus 0 +plus 1 plus two all the way up to 8 is + + align:start position:0% +plus 1 plus two all the way up to 8 is + + + align:start position:0% +plus 1 plus two all the way up to 8 is +36 and then when I becomes nine python + + align:start position:0% +36 and then when I becomes nine python + + + align:start position:0% +36 and then when I becomes nine python +will take my sum whatever it is right + + align:start position:0% +will take my sum whatever it is right + + + align:start position:0% +will take my sum whatever it is right +now 36 add N9 to it to give us + + align:start position:0% +now 36 add N9 to it to give us + + + align:start position:0% +now 36 add N9 to it to give us + + align:start position:0% + + + align:start position:0% +okay and then that's the end of the + + align:start position:0% +okay and then that's the end of the + + + align:start position:0% +okay and then that's the end of the +program right there's nothing else to do + + align:start position:0% +program right there's nothing else to do + + + align:start position:0% +program right there's nothing else to do +uh except to print my sum so at the end + + align:start position:0% +uh except to print my sum so at the end + + + align:start position:0% +uh except to print my sum so at the end +of this loop it's gone through 10 times + + align:start position:0% +of this loop it's gone through 10 times + + + align:start position:0% +of this loop it's gone through 10 times +adding zero all the way up to nine uh + + align:start position:0% +adding zero all the way up to nine uh + + + align:start position:0% +adding zero all the way up to nine uh +we're going to print + + align:start position:0% +we're going to print + + + align:start position:0% +we're going to print +45 yeah so when I tried running it + + align:start position:0% +45 yeah so when I tried running it + + + align:start position:0% +45 yeah so when I tried running it +4 and like + + align:start position:0% +4 and like + + + align:start position:0% +4 and like +2 oh maybe you have another print + + align:start position:0% +2 oh maybe you have another print + + + align:start position:0% +2 oh maybe you have another print +statement or it might be part of another + + align:start position:0% +statement or it might be part of another + + + align:start position:0% +statement or it might be part of another +program that's being run beforehand that + + align:start position:0% +program that's being run beforehand that + + + align:start position:0% +program that's being run beforehand that +you didn't comment out yeah next + + align:start position:0% + + + + align:start position:0% + +question the plus equals what it means + + align:start position:0% +question the plus equals what it means + + + align:start position:0% +question the plus equals what it means +oh it just means um it would be like my + + align:start position:0% +oh it just means um it would be like my + + + align:start position:0% +oh it just means um it would be like my +sum equals my + + align:start position:0% +sum equals my + + + align:start position:0% +sum equals my +sum plus uh + + align:start position:0% +sum plus uh + + + align:start position:0% +sum plus uh +I it's just shorthand notation because + + align:start position:0% +I it's just shorthand notation because + + + align:start position:0% +I it's just shorthand notation because +most of the your variable names might be + + align:start position:0% +most of the your variable names might be + + + align:start position:0% +most of the your variable names might be +really long and it's really annoying to + + align:start position:0% +really long and it's really annoying to + + + align:start position:0% +really long and it's really annoying to +retype them and so that's generally why + + align:start position:0% +retype them and so that's generally why + + + align:start position:0% +retype them and so that's generally why +that shorthand notation exists yeah but + + align:start position:0% +that shorthand notation exists yeah but + + + align:start position:0% +that shorthand notation exists yeah but +it basically means take whatever my suum + + align:start position:0% +it basically means take whatever my suum + + + align:start position:0% +it basically means take whatever my suum +is and add I to + + align:start position:0% +is and add I to + + + align:start position:0% +is and add I to +it and save it back into the variable + + align:start position:0% +it and save it back into the variable + + + align:start position:0% +it and save it back into the variable +myum okay let's have you try this code + + align:start position:0% +myum okay let's have you try this code + + + align:start position:0% +myum okay let's have you try this code +real quick so here is code uh it's + + align:start position:0% +real quick so here is code uh it's + + + align:start position:0% +real quick so here is code uh it's +already on the python file to start out + + align:start position:0% +already on the python file to start out + + + align:start position:0% +already on the python file to start out +with I want you to have this + + align:start position:0% +with I want you to have this + + + align:start position:0% +with I want you to have this +code um it it's it's pretty close to + + align:start position:0% +code um it it's it's pretty close to + + + align:start position:0% +code um it it's it's pretty close to +working but there's one issue so we have + + align:start position:0% +working but there's one issue so we have + + + align:start position:0% +working but there's one issue so we have +this for Loop that starts at start at + + align:start position:0% +this for Loop that starts at start at + + + align:start position:0% +this for Loop that starts at start at +ends at end and we're keeping a running + + align:start position:0% +ends at end and we're keeping a running + + + align:start position:0% +ends at end and we're keeping a running +sum and then we're printing the sum at + + align:start position:0% +sum and then we're printing the sum at + + + align:start position:0% +sum and then we're printing the sum at +the end so very similar to what we just + + align:start position:0% +the end so very similar to what we just + + + align:start position:0% +the end so very similar to what we just +saw but what I want this code to do is I + + align:start position:0% +saw but what I want this code to do is I + + + align:start position:0% +saw but what I want this code to do is I +want it to go and sum up the start and + + align:start position:0% +want it to go and sum up the start and + + + align:start position:0% +want it to go and sum up the start and +the end so I I want if I have start is + + align:start position:0% +the end so I I want if I have start is + + + align:start position:0% +the end so I I want if I have start is +three and end is five I want it to add + + align:start position:0% +three and end is five I want it to add + + + align:start position:0% +three and end is five I want it to add +three plus 4 plus five right and so this + + align:start position:0% +three plus 4 plus five right and so this + + + align:start position:0% +three plus 4 plus five right and so this +code is not doing quite that and and I + + align:start position:0% +code is not doing quite that and and I + + + align:start position:0% +code is not doing quite that and and I +would like you to fix it or to tell me + + align:start position:0% +would like you to fix it or to tell me + + + align:start position:0% +would like you to fix it or to tell me +how to fix it so it's down here on line + + align:start position:0% + + + + align:start position:0% + +140ish first thing you should do is run + + align:start position:0% +140ish first thing you should do is run + + + align:start position:0% +140ish first thing you should do is run +it and maybe see what answer it actually + + align:start position:0% +it and maybe see what answer it actually + + + align:start position:0% +it and maybe see what answer it actually +gives you so I just ran it it gave me a + + align:start position:0% + + + + align:start position:0% + +seven when you're encountering an output + + align:start position:0% +seven when you're encountering an output + + + align:start position:0% +seven when you're encountering an output +that's not quite what you expect one of + + align:start position:0% +that's not quite what you expect one of + + + align:start position:0% +that's not quite what you expect one of +the first things to do you can obviously + + align:start position:0% +the first things to do you can obviously + + + align:start position:0% +the first things to do you can obviously +use the python tutor but another thing + + align:start position:0% +use the python tutor but another thing + + + align:start position:0% +use the python tutor but another thing +you can do is put print statements at + + align:start position:0% +you can do is put print statements at + + + align:start position:0% +you can do is put print statements at +various + + align:start position:0% +various + + + align:start position:0% +various +places useful places would be inside the + + align:start position:0% +places useful places would be inside the + + + align:start position:0% +places useful places would be inside the +for + + align:start position:0% +for + + + align:start position:0% +for +Loop so here we can print I right that's + + align:start position:0% +Loop so here we can print I right that's + + + align:start position:0% +Loop so here we can print I right that's +a reasonable thing to print out and + + align:start position:0% +a reasonable thing to print out and + + + align:start position:0% +a reasonable thing to print out and +maybe we'll see exactly what values of I + + align:start position:0% +maybe we'll see exactly what values of I + + + align:start position:0% +maybe we'll see exactly what values of I +we are adding because we know the + + align:start position:0% +we are adding because we know the + + + align:start position:0% +we are adding because we know the +summing + + align:start position:0% +summing + + + align:start position:0% +summing +works right we just wrote the program on + + align:start position:0% +works right we just wrote the program on + + + align:start position:0% +works right we just wrote the program on +the previous line or PR previous + + align:start position:0% +the previous line or PR previous + + + align:start position:0% +the previous line or PR previous +slide so we got 347 which is a little + + align:start position:0% +slide so we got 347 which is a little + + + align:start position:0% +slide so we got 347 which is a little +confusing let's make our print statement + + align:start position:0% +confusing let's make our print statement + + + align:start position:0% +confusing let's make our print statement +be a little bit better I equals comma + + align:start position:0% +be a little bit better I equals comma + + + align:start position:0% +be a little bit better I equals comma +and then print the actual value of + + align:start position:0% +and then print the actual value of + + + align:start position:0% +and then print the actual value of +I so what do you guys notice I is three + + align:start position:0% +I so what do you guys notice I is three + + + align:start position:0% +I so what do you guys notice I is three +I is four and then it prints the sum + + align:start position:0% +I is four and then it prints the sum + + + align:start position:0% +I is four and then it prints the sum +seven what's the problem with this + + align:start position:0% + + + + align:start position:0% + +code + + align:start position:0% + + + + align:start position:0% + +yeah yeah we're not adding five right + + align:start position:0% +yeah yeah we're not adding five right + + + align:start position:0% +yeah yeah we're not adding five right +we're we're just adding three zero + + align:start position:0% +we're we're just adding three zero + + + align:start position:0% +we're we're just adding three zero +originally plus three plus 4 and we've + + align:start position:0% +originally plus three plus 4 and we've + + + align:start position:0% +originally plus three plus 4 and we've +never added five + + align:start position:0% +never added five + + + align:start position:0% +never added five +so how can we fix that + + align:start position:0% +so how can we fix that + + + align:start position:0% +so how can we fix that +yeah yeah we can do n plus one exactly + + align:start position:0% +yeah yeah we can do n plus one exactly + + + align:start position:0% +yeah yeah we can do n plus one exactly +so the range remember grabs the oh plus + + align:start position:0% +so the range remember grabs the oh plus + + + align:start position:0% +so the range remember grabs the oh plus +one the range grabs these values ex uh + + align:start position:0% +one the range grabs these values ex uh + + + align:start position:0% +one the range grabs these values ex uh +you know as as as numbers that it's + + align:start position:0% +you know as as as numbers that it's + + + align:start position:0% +you know as as as numbers that it's +working with so start is okay end is + + align:start position:0% +working with so start is okay end is + + + align:start position:0% +working with so start is okay end is +okay but we go up to but not including + + align:start position:0% +okay but we go up to but not including + + + align:start position:0% +okay but we go up to but not including +end right so if we go to n + one we're + + align:start position:0% +end right so if we go to n + one we're + + + align:start position:0% +end right so if we go to n + one we're +going to go up to but not including n + + align:start position:0% +going to go up to but not including n + + + align:start position:0% +going to go up to but not including n +plus one so if we run it now + + align:start position:0% +plus one so if we run it now + + + align:start position:0% +plus one so if we run it now +it looks much better so we've got I is + + align:start position:0% +it looks much better so we've got I is + + + align:start position:0% +it looks much better so we've got I is +three I is four I is five and the sum is + + align:start position:0% +three I is four I is five and the sum is + + + align:start position:0% +three I is four I is five and the sum is + + align:start position:0% + + + + align:start position:0% + +perfect so print statements very useful + + align:start position:0% +perfect so print statements very useful + + + align:start position:0% +perfect so print statements very useful +when debugging + + align:start position:0% +when debugging + + + align:start position:0% +when debugging +code questions about this one or was + + align:start position:0% +code questions about this one or was + + + align:start position:0% +code questions about this one or was +this does this make + + align:start position:0% + + + + align:start position:0% + +sense + + align:start position:0% +sense + + + align:start position:0% +sense +okay um the last slide I want to do + + align:start position:0% +okay um the last slide I want to do + + + align:start position:0% +okay um the last slide I want to do +before we do a summary is just to show + + align:start position:0% +before we do a summary is just to show + + + align:start position:0% +before we do a summary is just to show +you that factorial code we saw using a + + align:start position:0% +you that factorial code we saw using a + + + align:start position:0% +you that factorial code we saw using a +while loop a few slides back so it looks + + align:start position:0% +while loop a few slides back so it looks + + + align:start position:0% +while loop a few slides back so it looks +really verbose right we kind of have to + + align:start position:0% +really verbose right we kind of have to + + + align:start position:0% +really verbose right we kind of have to +think about it for a while before we + + align:start position:0% +think about it for a while before we + + + align:start position:0% +think about it for a while before we +realize what it's actually + + align:start position:0% +realize what it's actually + + + align:start position:0% +realize what it's actually +doing um but it was you know calculating + + align:start position:0% +doing um but it was you know calculating + + + align:start position:0% +doing um but it was you know calculating +the factorial Obviously good variable + + align:start position:0% +the factorial Obviously good variable + + + align:start position:0% +the factorial Obviously good variable +names helped us figure that out that + + align:start position:0% +names helped us figure that out that + + + align:start position:0% +names helped us figure that out that +same + + align:start position:0% +same + + + align:start position:0% +same +code in a for Loop looks like this with + + align:start position:0% +code in a for Loop looks like this with + + + align:start position:0% +code in a for Loop looks like this with +a for Loop looks like this so we still + + align:start position:0% +a for Loop looks like this so we still + + + align:start position:0% +a for Loop looks like this so we still +have the initialization of x to four we + + align:start position:0% +have the initialization of x to four we + + + align:start position:0% +have the initialization of x to four we +still initialize our factorial right our + + align:start position:0% +still initialize our factorial right our + + + align:start position:0% +still initialize our factorial right our +running product uh to a one + + align:start position:0% +running product uh to a one + + + align:start position:0% +running product uh to a one +but we're losing that those the four + + align:start position:0% +but we're losing that those the four + + + align:start position:0% +but we're losing that those the four +lines of code that kind of make up that + + align:start position:0% +lines of code that kind of make up that + + + align:start position:0% +lines of code that kind of make up that +pattern of uh changing numbers with Y + + align:start position:0% +pattern of uh changing numbers with Y + + + align:start position:0% +pattern of uh changing numbers with Y +Loops into two so this line I equals 1 + + align:start position:0% +Loops into two so this line I equals 1 + + + align:start position:0% +Loops into two so this line I equals 1 +this y loop with a conditional and this + + align:start position:0% +this y loop with a conditional and this + + + align:start position:0% +this y loop with a conditional and this +incrementing of I become the for + + align:start position:0% +incrementing of I become the for + + + align:start position:0% +incrementing of I become the for +Loop and that's it the for Loop takes + + align:start position:0% +Loop and that's it the for Loop takes + + + align:start position:0% +Loop and that's it the for Loop takes +care of all of that the initialization + + align:start position:0% +care of all of that the initialization + + + align:start position:0% +care of all of that the initialization +the increment and going up to but not + + align:start position:0% +the increment and going up to but not + + + align:start position:0% +the increment and going up to but not +including uh the the last value right X + + align:start position:0% +including uh the the last value right X + + + align:start position:0% +including uh the the last value right X +Plus so we're going to take uh multiply + + align:start position:0% +Plus so we're going to take uh multiply + + + align:start position:0% +Plus so we're going to take uh multiply +the factorial with one then two then + + align:start position:0% +the factorial with one then two then + + + align:start position:0% +the factorial with one then two then +three then four all the way up to and + + align:start position:0% +three then four all the way up to and + + + align:start position:0% +three then four all the way up to and +including X + + align:start position:0% + + + + align:start position:0% + +okay okay so the big idea about for + + align:start position:0% +okay okay so the big idea about for + + + align:start position:0% +okay okay so the big idea about for +Loops is they're going to repeat however + + align:start position:0% +Loops is they're going to repeat however + + + align:start position:0% +Loops is they're going to repeat however +long the sequence is right so you're + + align:start position:0% +long the sequence is right so you're + + + align:start position:0% +long the sequence is right so you're +able to repeat certain code a set number + + align:start position:0% +able to repeat certain code a set number + + + align:start position:0% +able to repeat certain code a set number +of times which is really useful in some + + align:start position:0% +of times which is really useful in some + + + align:start position:0% +of times which is really useful in some +situations y Loops were useful in + + align:start position:0% +situations y Loops were useful in + + + align:start position:0% +situations y Loops were useful in +situations where you didn't know how + + align:start position:0% +situations where you didn't know how + + + align:start position:0% +situations where you didn't know how +many times you might want to repeat um + + align:start position:0% +many times you might want to repeat um + + + align:start position:0% +many times you might want to repeat um +the code so quick summary we saw some + + align:start position:0% +the code so quick summary we saw some + + + align:start position:0% +the code so quick summary we saw some +looping mechanisms today it was a lot of + + align:start position:0% +looping mechanisms today it was a lot of + + + align:start position:0% +looping mechanisms today it was a lot of +syntax I know but the finger exercises + + align:start position:0% +syntax I know but the finger exercises + + + align:start position:0% +syntax I know but the finger exercises +for today will certainly help mitx um + + align:start position:0% +for today will certainly help mitx um + + + align:start position:0% +for today will certainly help mitx um +also has extra help um extra exercises + + align:start position:0% +also has extra help um extra exercises + + + align:start position:0% +also has extra help um extra exercises +it's really important to to um to do + + align:start position:0% +it's really important to to um to do + + + align:start position:0% +it's really important to to um to do +them just to get the mental model for + + align:start position:0% +them just to get the mental model for + + + align:start position:0% +them just to get the mental model for +how exactly these loops work right and + + align:start position:0% +how exactly these loops work right and + + + align:start position:0% +how exactly these loops work right and +how they how they um how they assign + + align:start position:0% +how they how they um how they assign + + + align:start position:0% +how they how they um how they assign +variables and how they do the checks + + align:start position:0% +variables and how they do the checks + + + align:start position:0% +variables and how they do the checks +behind the scenes right and it'll help + + align:start position:0% +behind the scenes right and it'll help + + + align:start position:0% +behind the scenes right and it'll help +you get faster at um at writing code and + + align:start position:0% +you get faster at um at writing code and + + + align:start position:0% +you get faster at um at writing code and +at doing quizzes as well okay so that's + + align:start position:0% +at doing quizzes as well okay so that's + + + align:start position:0% +at doing quizzes as well okay so that's +it for today + + align:start position:0% + + + + align:start position:0% + +day \ No newline at end of file diff --git a/mFGdF9TAfmE.txt b/mFGdF9TAfmE.txt new file mode 100644 index 0000000000000000000000000000000000000000..357f9dd49e0d75b0bbf6b5bdb844d4d666bf8c28 --- /dev/null +++ b/mFGdF9TAfmE.txt @@ -0,0 +1,7163 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +to view additional materials from + + align:start position:0% +to view additional materials from + + + align:start position:0% +to view additional materials from +hundreds of MIT courses visit MIT open + + align:start position:0% +hundreds of MIT courses visit MIT open + + + align:start position:0% +hundreds of MIT courses visit MIT open +courseware at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu okay so this is the second + + align:start position:0% +ocw.mit.edu okay so this is the second + + + align:start position:0% +ocw.mit.edu okay so this is the second +last lecture on trusses uh then we get a + + align:start position:0% +last lecture on trusses uh then we get a + + + align:start position:0% +last lecture on trusses uh then we get a +holiday on Monday uh and then after that + + align:start position:0% +holiday on Monday uh and then after that + + + align:start position:0% +holiday on Monday uh and then after that +we'll be end of chapter 3 uh I thought + + align:start position:0% +we'll be end of chapter 3 uh I thought + + + align:start position:0% +we'll be end of chapter 3 uh I thought +I'd write down just in case it's any use + + align:start position:0% +I'd write down just in case it's any use + + + align:start position:0% +I'd write down just in case it's any use +to you the four problems that I intend + + align:start position:0% +to you the four problems that I intend + + + align:start position:0% +to you the four problems that I intend +to include with the next homework that + + align:start position:0% +to include with the next homework that + + + align:start position:0% +to include with the next homework that +won't be due for quite a while a week + + align:start position:0% +won't be due for quite a while a week + + + align:start position:0% +won't be due for quite a while a week +from Monday uh so these will be the + + align:start position:0% +from Monday uh so these will be the + + + align:start position:0% +from Monday uh so these will be the +problems on trusses that come from + + align:start position:0% +problems on trusses that come from + + + align:start position:0% +problems on trusses that come from +particular trusses drawn in the book and + + align:start position:0% +particular trusses drawn in the book and + + + align:start position:0% +particular trusses drawn in the book and +then there'll be some problems from the + + align:start position:0% +then there'll be some problems from the + + + align:start position:0% +then there'll be some problems from the +new material that we do next week so + + align:start position:0% +new material that we do next week so + + + align:start position:0% +new material that we do next week so +trusses and really two big two main jobs + + align:start position:0% +trusses and really two big two main jobs + + + align:start position:0% +trusses and really two big two main jobs +for today one is to identify this Matrix + + align:start position:0% +for today one is to identify this Matrix + + + align:start position:0% +for today one is to identify this Matrix +a the The Strain displacement Matrix or + + align:start position:0% +a the The Strain displacement Matrix or + + + align:start position:0% +a the The Strain displacement Matrix or +the stretching Matrix how how how far do + + align:start position:0% +the stretching Matrix how how how far do + + + align:start position:0% +the stretching Matrix how how how far do +the bar stretch this everybody REM + + align:start position:0% +the bar stretch this everybody REM + + + align:start position:0% +the bar stretch this everybody REM +remembers a is going to come in this + + align:start position:0% +remembers a is going to come in this + + + align:start position:0% +remembers a is going to come in this +step if we have + + align:start position:0% +step if we have + + + align:start position:0% +step if we have +displacements then of the nodes like + + align:start position:0% +displacements then of the nodes like + + + align:start position:0% +displacements then of the nodes like +this would be like a a U1 this would be + + align:start position:0% +this would be like a a U1 this would be + + + align:start position:0% +this would be like a a U1 this would be +a U1 h and a U1 V this would be a u2h + + align:start position:0% +a U1 h and a U1 V this would be a u2h + + + align:start position:0% +a U1 h and a U1 V this would be a u2h +and a U2 V so there are four + + align:start position:0% +and a U2 V so there are four + + + align:start position:0% +and a U2 V so there are four +movements of the of the ends of the + + align:start position:0% +movements of the of the ends of the + + + align:start position:0% +movements of the of the ends of the +truss and of of the of one particular + + align:start position:0% +truss and of of the of one particular + + + align:start position:0% +truss and of of the of one particular +bar and it will stretch that bar and the + + align:start position:0% +bar and it will stretch that bar and the + + + align:start position:0% +bar and it will stretch that bar and the +question is how much so that's that will + + align:start position:0% +question is how much so that's that will + + + align:start position:0% +question is how much so that's that will +be one row of a so this is if we follow + + align:start position:0% +be one row of a so this is if we follow + + + align:start position:0% +be one row of a so this is if we follow +one bar there's a you remember in The + + align:start position:0% +one bar there's a you remember in The + + + align:start position:0% +one bar there's a you remember in The +Matrix a there's is going to be a row + + align:start position:0% +Matrix a there's is going to be a row + + + align:start position:0% +Matrix a there's is going to be a row +for every bar so Row for each row of + + align:start position:0% +for every bar so Row for each row of + + + align:start position:0% +for every bar so Row for each row of +a for each bar and if we track down one + + align:start position:0% +a for each bar and if we track down one + + + align:start position:0% +a for each bar and if we track down one +of those rows we'll have the + + align:start position:0% +of those rows we'll have the + + + align:start position:0% +of those rows we'll have the +idea and then of course at the end we + + align:start position:0% +idea and then of course at the end we + + + align:start position:0% +idea and then of course at the end we +maybe be constructing a without a sort + + align:start position:0% +maybe be constructing a without a sort + + + align:start position:0% +maybe be constructing a without a sort +of a free free a and then at the end any + + align:start position:0% +of a free free a and then at the end any + + + align:start position:0% +of a free free a and then at the end any +any fixed displacements that will knock + + align:start position:0% +any fixed displacements that will knock + + + align:start position:0% +any fixed displacements that will knock +out uh Colum of a so that's one job and + + align:start position:0% +out uh Colum of a so that's one job and + + + align:start position:0% +out uh Colum of a so that's one job and +then to see so the a is going to be a + + align:start position:0% +then to see so the a is going to be a + + + align:start position:0% +then to see so the a is going to be a +little more + + align:start position:0% +little more + + + align:start position:0% +little more +messy it it'll be it's because we're in + + align:start position:0% +messy it it'll be it's because we're in + + + align:start position:0% +messy it it'll be it's because we're in +two Dimensions so compared to the uh + + align:start position:0% +two Dimensions so compared to the uh + + + align:start position:0% +two Dimensions so compared to the uh +network problems and the and the line of + + align:start position:0% +network problems and the and the line of + + + align:start position:0% +network problems and the and the line of +Springs now we have a we have more + + align:start position:0% +Springs now we have a we have more + + + align:start position:0% +Springs now we have a we have more +happening we've got more columns because + + align:start position:0% +happening we've got more columns because + + + align:start position:0% +happening we've got more columns because +we've every uh node has now two uh + + align:start position:0% +we've every uh node has now two uh + + + align:start position:0% +we've every uh node has now two uh +unknowns the horizontal and vert + + align:start position:0% +unknowns the horizontal and vert + + + align:start position:0% +unknowns the horizontal and vert +vertical so a is kind of bigger and uh + + align:start position:0% +vertical so a is kind of bigger and uh + + + align:start position:0% +vertical so a is kind of bigger and uh +therefore a transpose CA you might think + + align:start position:0% +therefore a transpose CA you might think + + + align:start position:0% +therefore a transpose CA you might think +it's going to be hard to see what's + + align:start position:0% +it's going to be hard to see what's + + + align:start position:0% +it's going to be hard to see what's +going on but you'll see the right way to + + align:start position:0% +going on but you'll see the right way to + + + align:start position:0% +going on but you'll see the right way to +look at a transpose CA is a bar at a + + align:start position:0% +look at a transpose CA is a bar at a + + + align:start position:0% +look at a transpose CA is a bar at a +time that's that's the the nice fact + + align:start position:0% +time that's that's the the nice fact + + + align:start position:0% +time that's that's the the nice fact +about a transpose CA I might focus on + + align:start position:0% +about a transpose CA I might focus on + + + align:start position:0% +about a transpose CA I might focus on +that first and then + + align:start position:0% +that first and then + + + align:start position:0% +that first and then +uh then comes the fun part uh I'll draw + + align:start position:0% +uh then comes the fun part uh I'll draw + + + align:start position:0% +uh then comes the fun part uh I'll draw +some more trusses that may or may not + + align:start position:0% +some more trusses that may or may not + + + align:start position:0% +some more trusses that may or may not +have uh mechanisms they may or may not + + align:start position:0% +have uh mechanisms they may or may not + + + align:start position:0% +have uh mechanisms they may or may not +be stable and we can try to identify the + + align:start position:0% +be stable and we can try to identify the + + + align:start position:0% +be stable and we can try to identify the +mechanisms actually as before we'll do + + align:start position:0% +mechanisms actually as before we'll do + + + align:start position:0% +mechanisms actually as before we'll do +it by engineering Instinct rather than + + align:start position:0% +it by engineering Instinct rather than + + + align:start position:0% +it by engineering Instinct rather than +by solving I mean in principle we could + + align:start position:0% +by solving I mean in principle we could + + + align:start position:0% +by solving I mean in principle we could +always uh use elimination or ask matlb + + align:start position:0% +always uh use elimination or ask matlb + + + align:start position:0% +always uh use elimination or ask matlb +or any other Co system to do it and look + + align:start position:0% +or any other Co system to do it and look + + + align:start position:0% +or any other Co system to do it and look +for the solutions to Au equals z and + + align:start position:0% +for the solutions to Au equals z and + + + align:start position:0% +for the solutions to Au equals z and +decide are The Columns of a independent + + align:start position:0% +decide are The Columns of a independent + + + align:start position:0% +decide are The Columns of a independent +in that case the truss is stable this + + align:start position:0% +in that case the truss is stable this + + + align:start position:0% +in that case the truss is stable this +Matrix is invertible we we know all the + + align:start position:0% +Matrix is invertible we we know all the + + + align:start position:0% +Matrix is invertible we we know all the +good po possibility and then there's the + + align:start position:0% +good po possibility and then there's the + + + align:start position:0% +good po possibility and then there's the +more interesting possibility of the of + + align:start position:0% +more interesting possibility of the of + + + align:start position:0% +more interesting possibility of the of +having some solutions to that in which + + align:start position:0% +having some solutions to that in which + + + align:start position:0% +having some solutions to that in which +case that will Matrix will be singular + + align:start position:0% +case that will Matrix will be singular + + + align:start position:0% +case that will Matrix will be singular +there'll be some modes modes in our big + + align:start position:0% +there'll be some modes modes in our big + + + align:start position:0% +there'll be some modes modes in our big +system that uh will will cause it to + + align:start position:0% +system that uh will will cause it to + + + align:start position:0% +system that uh will will cause it to +fail but it's kind of fun to find those + + align:start position:0% +fail but it's kind of fun to find those + + + align:start position:0% +fail but it's kind of fun to find those +okay uh while I've written a transpose + + align:start position:0% +okay uh while I've written a transpose + + + align:start position:0% +okay uh while I've written a transpose +CA may I remind you about a good way to + + align:start position:0% +CA may I remind you about a good way to + + + align:start position:0% +CA may I remind you about a good way to +multiply do that + + align:start position:0% +multiply do that + + + align:start position:0% +multiply do that +multiplication okay so I'll just imagine + + align:start position:0% +multiplication okay so I'll just imagine + + + align:start position:0% +multiplication okay so I'll just imagine +I'm not I'm just putting a n here's + + align:start position:0% +I'm not I'm just putting a n here's + + + align:start position:0% +I'm not I'm just putting a n here's +going to be the Matrix a so the Matrix a + + align:start position:0% +going to be the Matrix a so the Matrix a + + + align:start position:0% +going to be the Matrix a so the Matrix a +will have a row bunch of rows Row one + + align:start position:0% +will have a row bunch of rows Row one + + + align:start position:0% +will have a row bunch of rows Row one +row two so on these rows will correspond + + align:start position:0% +row two so on these rows will correspond + + + align:start position:0% +row two so on these rows will correspond +to bar one bar two and bar three + + align:start position:0% +to bar one bar two and bar three + + + align:start position:0% +to bar one bar two and bar three +okay okay then we have C so that's a + + align:start position:0% +okay okay then we have C so that's a + + + align:start position:0% +okay okay then we have C so that's a +square Matrix that each bar has a spring + + align:start position:0% +square Matrix that each bar has a spring + + + align:start position:0% +square Matrix that each bar has a spring +constant so C1 C2 C3 and then we have a + + align:start position:0% +constant so C1 C2 C3 and then we have a + + + align:start position:0% +constant so C1 C2 C3 and then we have a +transpose and those rows are columns of + + align:start position:0% +transpose and those rows are columns of + + + align:start position:0% +transpose and those rows are columns of +a transpose so that's the sort of + + align:start position:0% +a transpose so that's the sort of + + + align:start position:0% +a transpose so that's the sort of +picture of a transpose C A for a three + + align:start position:0% +picture of a transpose C A for a three + + + align:start position:0% +picture of a transpose C A for a three +bar three bars only + + align:start position:0% +bar three bars only + + + align:start position:0% +bar three bars only +but the but the point is made right here + + align:start position:0% +but the but the point is made right here + + + align:start position:0% +but the but the point is made right here +there is a row of a for every bar right + + align:start position:0% +there is a row of a for every bar right + + + align:start position:0% +there is a row of a for every bar right +because our Matrix a is M by + + align:start position:0% +because our Matrix a is M by + + + align:start position:0% +because our Matrix a is M by +n is they M bars Row for every bar and + + align:start position:0% +n is they M bars Row for every bar and + + + align:start position:0% +n is they M bars Row for every bar and +it tells us how far that bar is + + align:start position:0% +it tells us how far that bar is + + + align:start position:0% +it tells us how far that bar is +stretched and we'll figure out what its + + align:start position:0% +stretched and we'll figure out what its + + + align:start position:0% +stretched and we'll figure out what its +entries are that's that's our main job + + align:start position:0% +entries are that's that's our main job + + + align:start position:0% +entries are that's that's our main job +I'm just looking ahead suppose we've got + + align:start position:0% +I'm just looking ahead suppose we've got + + + align:start position:0% +I'm just looking ahead suppose we've got +that row and that row and that row so a + + align:start position:0% +that row and that row and that row so a + + + align:start position:0% +that row and that row and that row so a +row for every bar now here I've taken + + align:start position:0% +row for every bar now here I've taken + + + align:start position:0% +row for every bar now here I've taken +three bars now how do I multiply those + + align:start position:0% +three bars now how do I multiply those + + + align:start position:0% +three bars now how do I multiply those +matrices + + align:start position:0% +matrices + + + align:start position:0% +matrices +well I can do it different ways but + + align:start position:0% +well I can do it different ways but + + + align:start position:0% +well I can do it different ways but +here's a cool way to do it just it I the + + align:start position:0% +here's a cool way to do it just it I the + + + align:start position:0% +here's a cool way to do it just it I the +the way I want to point out is column + + align:start position:0% +the way I want to point out is column + + + align:start position:0% +the way I want to point out is column +times row if you multiply matrices + + align:start position:0% +times row if you multiply matrices + + + align:start position:0% +times row if you multiply matrices +you're allowed to and the effect of C1 + + align:start position:0% +you're allowed to and the effect of C1 + + + align:start position:0% +you're allowed to and the effect of C1 +C2 C3 is going to be very simple so I'm + + align:start position:0% +C2 C3 is going to be very simple so I'm + + + align:start position:0% +C2 C3 is going to be very simple so I'm +really paying attention here to a + + align:start position:0% +really paying attention here to a + + + align:start position:0% +really paying attention here to a +transpose a if I want to multiply a + + align:start position:0% +transpose a if I want to multiply a + + + align:start position:0% +transpose a if I want to multiply a +transpose a I can do row time column as + + align:start position:0% +transpose a I can do row time column as + + + align:start position:0% +transpose a I can do row time column as +usual and get one number or I can do + + align:start position:0% +usual and get one number or I can do + + + align:start position:0% +usual and get one number or I can do +column times row and get a like a whole + + align:start position:0% +column times row and get a like a whole + + + align:start position:0% +column times row and get a like a whole +little Matrix and that's the bar one + + align:start position:0% +little Matrix and that's the bar one + + + align:start position:0% +little Matrix and that's the bar one +matrix it's the element Matrix and + + align:start position:0% +matrix it's the element Matrix and + + + align:start position:0% +matrix it's the element Matrix and +that's how find out elements will be + + align:start position:0% +that's how find out elements will be + + + align:start position:0% +that's how find out elements will be +assembled and that's why + + align:start position:0% +assembled and that's why + + + align:start position:0% +assembled and that's why +I keep uh mentioning this point so that + + align:start position:0% +I keep uh mentioning this point so that + + + align:start position:0% +I keep uh mentioning this point so that +typical so the way to do that column + + align:start position:0% +typical so the way to do that column + + + align:start position:0% +typical so the way to do that column +times row thing and then of course that + + align:start position:0% +times row thing and then of course that + + + align:start position:0% +times row thing and then of course that +C1 just multiplies that row that'll be + + align:start position:0% +C1 just multiplies that row that'll be + + + align:start position:0% +C1 just multiplies that row that'll be +C1 Row + + align:start position:0% +C1 Row + + + align:start position:0% +C1 Row +one transpose that's the column times + + align:start position:0% +one transpose that's the column times + + + align:start position:0% +one transpose that's the column times +Row + + align:start position:0% +Row + + + align:start position:0% +Row +one that's what's coming from bar one + + align:start position:0% +one that's what's coming from bar one + + + align:start position:0% +one that's what's coming from bar one +that column multiplies the C1 and that + + align:start position:0% +that column multiplies the C1 and that + + + align:start position:0% +that column multiplies the C1 and that +row you see how nice that that's the + + align:start position:0% +row you see how nice that that's the + + + align:start position:0% +row you see how nice that that's the +element Matrix associated with the first + + align:start position:0% +element Matrix associated with the first + + + align:start position:0% +element Matrix associated with the first +bar and then there'll be a second column + + align:start position:0% +bar and then there'll be a second column + + + align:start position:0% +bar and then there'll be a second column +times the C2 times the second row so + + align:start position:0% +times the C2 times the second row so + + + align:start position:0% +times the C2 times the second row so +plus C2 + + align:start position:0% +plus C2 + + + align:start position:0% +plus C2 +row2 transpose + + align:start position:0% +row2 transpose + + + align:start position:0% +row2 transpose +row2 that's the it's a matrix again plus + + align:start position:0% +row2 that's the it's a matrix again plus + + + align:start position:0% +row2 that's the it's a matrix again plus +C3 Row 3 + + align:start position:0% +C3 Row 3 + + + align:start position:0% +C3 Row 3 +transpose Row three I I focus on that + + align:start position:0% +transpose Row three I I focus on that + + + align:start position:0% +transpose Row three I I focus on that +because you don't think of this as the + + align:start position:0% +because you don't think of this as the + + + align:start position:0% +because you don't think of this as the +way to multiply matrices but it's really + + align:start position:0% +way to multiply matrices but it's really + + + align:start position:0% +way to multiply matrices but it's really +a nice + + align:start position:0% +a nice + + + align:start position:0% +a nice +thing to notice and and it's better to + + align:start position:0% +thing to notice and and it's better to + + + align:start position:0% +thing to notice and and it's better to +notice it now when we have three bars or + + align:start position:0% +notice it now when we have three bars or + + + align:start position:0% +notice it now when we have three bars or +something + + align:start position:0% +something + + + align:start position:0% +something +than in a big uh finite element code + + align:start position:0% +than in a big uh finite element code + + + align:start position:0% +than in a big uh finite element code +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so this is just if I complete it + + align:start position:0% +so this is just if I complete it + + + align:start position:0% +so this is just if I complete it +complete this thought this this I would + + align:start position:0% +complete this thought this this I would + + + align:start position:0% +complete this thought this this I would +call the a one bar Matrix that's the + + align:start position:0% +call the a one bar Matrix that's the + + + align:start position:0% +call the a one bar Matrix that's the +Matrix a transpose a if there's only one + + align:start position:0% +Matrix a transpose a if there's only one + + + align:start position:0% +Matrix a transpose a if there's only one +bar actually one of the uh uh problems + + align:start position:0% +bar actually one of the uh uh problems + + + align:start position:0% +bar actually one of the uh uh problems +at the end of the section is find the + + align:start position:0% +at the end of the section is find the + + + align:start position:0% +at the end of the section is find the +element Matrix for one bar and I guess + + align:start position:0% +element Matrix for one bar and I guess + + + align:start position:0% +element Matrix for one bar and I guess +it's about what we're going to get to + + align:start position:0% +it's about what we're going to get to + + + align:start position:0% +it's about what we're going to get to +when we do that one bar can you do you + + align:start position:0% +when we do that one bar can you do you + + + align:start position:0% +when we do that one bar can you do you +remember what it was in the just to + + align:start position:0% +remember what it was in the just to + + + align:start position:0% +remember what it was in the just to +connect this thought what was the little + + align:start position:0% +connect this thought what was the little + + + align:start position:0% +connect this thought what was the little +Matrix in the case of networks so in the + + align:start position:0% +Matrix in the case of networks so in the + + + align:start position:0% +Matrix in the case of networks so in the +case of networks there was just one + + align:start position:0% +case of networks there was just one + + + align:start position:0% +case of networks there was just one +unknown for each not two + + align:start position:0% +unknown for each not two + + + align:start position:0% +unknown for each not two +so for so for networks just I I'm just + + align:start position:0% +so for so for networks just I I'm just + + + align:start position:0% +so for so for networks just I I'm just +going to put down the and you'll + + align:start position:0% +going to put down the and you'll + + + align:start position:0% +going to put down the and you'll +recognize it immediately the the the + + align:start position:0% +recognize it immediately the the the + + + align:start position:0% +recognize it immediately the the the +little element Matrix was the C for that + + align:start position:0% +little element Matrix was the C for that + + + align:start position:0% +little element Matrix was the C for that +and there was a 1 - one - one + + align:start position:0% +and there was a 1 - one - one + + + align:start position:0% +and there was a 1 - one - one +one do you remember that guy that was + + align:start position:0% +one do you remember that guy that was + + + align:start position:0% +one do you remember that guy that was +the minus one one from a row minus one + + align:start position:0% +the minus one one from a row minus one + + + align:start position:0% +the minus one one from a row minus one +one from a colum so that this was + + align:start position:0% +one from a colum so that this was + + + align:start position:0% +one from a colum so that this was +exactly c times the -11 from the the + + align:start position:0% +exactly c times the -11 from the the + + + align:start position:0% +exactly c times the -11 from the the +column times the minus one one from the + + align:start position:0% +column times the minus one one from the + + + align:start position:0% +column times the minus one one from the +row that's where this simple little + + align:start position:0% +row that's where this simple little + + + align:start position:0% +row that's where this simple little +matric came from and you remember that + + align:start position:0% +matric came from and you remember that + + + align:start position:0% +matric came from and you remember that +the so what's involved in in creating + + align:start position:0% +the so what's involved in in creating + + + align:start position:0% +the so what's involved in in creating +this big a transpose CA is just create + + align:start position:0% +this big a transpose CA is just create + + + align:start position:0% +this big a transpose CA is just create +all these little + + align:start position:0% +all these little + + + align:start position:0% +all these little +pieces which are like this but they're + + align:start position:0% +pieces which are like this but they're + + + align:start position:0% +pieces which are like this but they're +going to be a little bigger in fact in a + + align:start position:0% +going to be a little bigger in fact in a + + + align:start position:0% +going to be a little bigger in fact in a +minute I'm going to ask you what size + + align:start position:0% +minute I'm going to ask you what size + + + align:start position:0% +minute I'm going to ask you what size +they'll be well they're really big + + align:start position:0% +they'll be well they're really big + + + align:start position:0% +they'll be well they're really big +matrices there a whole lot of zeros + + align:start position:0% +matrices there a whole lot of zeros + + + align:start position:0% +matrices there a whole lot of zeros +there that I didn't even put zeros are + + align:start position:0% +there that I didn't even put zeros are + + + align:start position:0% +there that I didn't even put zeros are +there for rows and columns that aren't + + align:start position:0% +there for rows and columns that aren't + + + align:start position:0% +there for rows and columns that aren't +touching this particular + + align:start position:0% +touching this particular + + + align:start position:0% +touching this particular +Edge and again this Matrix there'll be + + align:start position:0% +Edge and again this Matrix there'll be + + + align:start position:0% +Edge and again this Matrix there'll be +all kinds of zeros in a because a + + align:start position:0% +all kinds of zeros in a because a + + + align:start position:0% +all kinds of zeros in a because a +typical row of a bar one is going to + + align:start position:0% +typical row of a bar one is going to + + + align:start position:0% +typical row of a bar one is going to +have nonzeros only for the how yeah + + align:start position:0% +have nonzeros only for the how yeah + + + align:start position:0% +have nonzeros only for the how yeah +what's the size what's going to be how + + align:start position:0% +what's the size what's going to be how + + + align:start position:0% +what's the size what's going to be how +many nonzeros + + align:start position:0% +many nonzeros + + + align:start position:0% +many nonzeros +in a typical row of a getting the count + + align:start position:0% +in a typical row of a getting the count + + + align:start position:0% +in a typical row of a getting the count +right first is is like half the battle + + align:start position:0% +right first is is like half the battle + + + align:start position:0% +right first is is like half the battle +how many nonzeros in a typical row of a + + align:start position:0% +how many nonzeros in a typical row of a + + + align:start position:0% +how many nonzeros in a typical row of a +this was the network case where we had a + + align:start position:0% +this was the network case where we had a + + + align:start position:0% +this was the network case where we had a +couple of nodes and they were connected + + align:start position:0% +couple of nodes and they were connected + + + align:start position:0% +couple of nodes and they were connected +and we had an unknown at each + + align:start position:0% +and we had an unknown at each + + + align:start position:0% +and we had an unknown at each +end so two unknowns were involved the + + align:start position:0% +end so two unknowns were involved the + + + align:start position:0% +end so two unknowns were involved the +little Matrix was 2 by two it properly + + align:start position:0% +little Matrix was 2 by two it properly + + + align:start position:0% +little Matrix was 2 by two it properly +has lots of zeros for all the other + + align:start position:0% +has lots of zeros for all the other + + + align:start position:0% +has lots of zeros for all the other +nodes that are not involved + + align:start position:0% +nodes that are not involved + + + align:start position:0% +nodes that are not involved +and then that Matrix kind of gets + + align:start position:0% +and then that Matrix kind of gets + + + align:start position:0% +and then that Matrix kind of gets +assembled is the word I think usually + + align:start position:0% +assembled is the word I think usually + + + align:start position:0% +assembled is the word I think usually +used all these little guys get assembled + + align:start position:0% +used all these little guys get assembled + + + align:start position:0% +used all these little guys get assembled +you know pasted stamped I hear the the + + align:start position:0% +you know pasted stamped I hear the the + + + align:start position:0% +you know pasted stamped I hear the the +as the verb sometimes now take these + + align:start position:0% +as the verb sometimes now take these + + + align:start position:0% +as the verb sometimes now take these +little matrices for this little element + + align:start position:0% +little matrices for this little element + + + align:start position:0% +little matrices for this little element +and you and stamp them into the big a + + align:start position:0% +and you and stamp them into the big a + + + align:start position:0% +and you and stamp them into the big a +transpose CA you know this is the C1 so + + align:start position:0% +transpose CA you know this is the C1 so + + + align:start position:0% +transpose CA you know this is the C1 so +this gives the c1s in the m Tri and the + + align:start position:0% +this gives the c1s in the m Tri and the + + + align:start position:0% +this gives the c1s in the m Tri and the +c2s and the c3s all right now just + + align:start position:0% +c2s and the c3s all right now just + + + align:start position:0% +c2s and the c3s all right now just +before we I'm like doing this + + align:start position:0% +before we I'm like doing this + + + align:start position:0% +before we I'm like doing this +preliminary before I wrote write down + + align:start position:0% +preliminary before I wrote write down + + + align:start position:0% +preliminary before I wrote write down +anything the exact row what's the size + + align:start position:0% +anything the exact row what's the size + + + align:start position:0% +anything the exact row what's the size +of for + + align:start position:0% +of for + + + align:start position:0% +of for +trusses how many nonzeros in a row of a + + align:start position:0% +trusses how many nonzeros in a row of a + + + align:start position:0% +trusses how many nonzeros in a row of a +so so that's my question how + + align:start position:0% +so so that's my question how + + + align:start position:0% +so so that's my question how +many nonzeros in a typical row like for + + align:start position:0% +many nonzeros in a typical row like for + + + align:start position:0% +many nonzeros in a typical row like for +that bar nonzero + + align:start position:0% +that bar nonzero + + + align:start position:0% +that bar nonzero +in a row of a so a is the Matrix that + + align:start position:0% +in a row of a so a is the Matrix that + + + align:start position:0% +in a row of a so a is the Matrix that +tells us how + + align:start position:0% +tells us how + + + align:start position:0% +tells us how +much that that row of a is the is the + + align:start position:0% +much that that row of a is the is the + + + align:start position:0% +much that that row of a is the is the +row that tells us how much this bar + + align:start position:0% +row that tells us how much this bar + + + align:start position:0% +row that tells us how much this bar +stretched when this moved Along by U + + align:start position:0% +stretched when this moved Along by U + + + align:start position:0% +stretched when this moved Along by U +H1 and up by U V1 and this moved Along + + align:start position:0% +H1 and up by U V1 and this moved Along + + + align:start position:0% +H1 and up by U V1 and this moved Along +by say U H2 and up by U + + align:start position:0% +by say U H2 and up by U + + + align:start position:0% +by say U H2 and up by U +V2 well I've written all those in so + + align:start position:0% +V2 well I've written all those in so + + + align:start position:0% +V2 well I've written all those in so +that you can tell me this number how + + align:start position:0% +that you can tell me this number how + + + align:start position:0% +that you can tell me this number how +many what's your guess when I tell you + + align:start position:0% +many what's your guess when I tell you + + + align:start position:0% +many what's your guess when I tell you +you'll say of course how many U's are + + align:start position:0% +you'll say of course how many U's are + + + align:start position:0% +you'll say of course how many U's are +involved in the stretching of that bar + + align:start position:0% +involved in the stretching of that bar + + + align:start position:0% +involved in the stretching of that bar +four four exactly instead of one at each + + align:start position:0% +four four exactly instead of one at each + + + align:start position:0% +four four exactly instead of one at each +end we have two at each end so the + + align:start position:0% +end we have two at each end so the + + + align:start position:0% +end we have two at each end so the +answer is four how many the answer is + + align:start position:0% +answer is four how many the answer is + + + align:start position:0% +answer is four how many the answer is +four and now the the only remaining + + align:start position:0% +four and now the the only remaining + + + align:start position:0% +four and now the the only remaining +question is what are + + align:start position:0% +question is what are + + + align:start position:0% +question is what are +they what are those four numbers the + + align:start position:0% +they what are those four numbers the + + + align:start position:0% +they what are those four numbers the +four nonzeros in the row so let me and + + align:start position:0% +four nonzeros in the row so let me and + + + align:start position:0% +four nonzeros in the row so let me and +and so let me just answer that they are + + align:start position:0% +and so let me just answer that they are + + + align:start position:0% +and so let me just answer that they are +so here's that + + align:start position:0% +so here's that + + + align:start position:0% +so here's that +row so we have we have the two we have + + align:start position:0% +row so we have we have the two we have + + + align:start position:0% +row so we have we have the two we have +two nonzeros associated with the well + + align:start position:0% +two nonzeros associated with the well + + + align:start position:0% +two nonzeros associated with the well +the way I I've numbered these nodes one + + align:start position:0% +the way I I've numbered these nodes one + + + align:start position:0% +the way I I've numbered these nodes one +and two since I've numbered them one and + + align:start position:0% +and two since I've numbered them one and + + + align:start position:0% +and two since I've numbered them one and +two the nonzeros are going to come right + + align:start position:0% +two the nonzeros are going to come right + + + align:start position:0% +two the nonzeros are going to come right +at the start and then a whole lot then + + align:start position:0% +at the start and then a whole lot then + + + align:start position:0% +at the start and then a whole lot then +this is all going to be zero after that + + align:start position:0% +this is all going to be zero after that + + + align:start position:0% +this is all going to be zero after that +because those will be nodes 3 four five + + align:start position:0% +because those will be nodes 3 four five + + + align:start position:0% +because those will be nodes 3 four five +whatever that don't involve bar one so + + align:start position:0% +whatever that don't involve bar one so + + + align:start position:0% +whatever that don't involve bar one so +bar one just connects node one to node + + align:start position:0% +bar one just connects node one to node + + + align:start position:0% +bar one just connects node one to node +two now what do you + + align:start position:0% +two now what do you + + + align:start position:0% +two now what do you +think well let me draw in let me put in + + align:start position:0% +think well let me draw in let me put in + + + align:start position:0% +think well let me draw in let me put in +the key quantity here this bar is at an + + align:start position:0% +the key quantity here this bar is at an + + + align:start position:0% +the key quantity here this bar is at an +angle it's in an angle Theta so there's + + align:start position:0% +angle it's in an angle Theta so there's + + + align:start position:0% +angle it's in an angle Theta so there's +a Theta angle Theta + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +and + + align:start position:0% +and + + + align:start position:0% +and +uh so that that angle is going to enter + + align:start position:0% +uh so that that angle is going to enter + + + align:start position:0% +uh so that that angle is going to enter +these things in fact in fact here's what + + align:start position:0% +these things in fact in fact here's what + + + align:start position:0% +these things in fact in fact here's what +you get you + + align:start position:0% +you get you + + + align:start position:0% +you get you +get I think if I put the one up there + + align:start position:0% +get I think if I put the one up there + + + align:start position:0% +get I think if I put the one up there +and the two down there let's see what am + + align:start position:0% +and the two down there let's see what am + + + align:start position:0% +and the two down there let's see what am +I thinking now I'm thinking if U Want H + + align:start position:0% +I thinking now I'm thinking if U Want H + + + align:start position:0% +I thinking now I'm thinking if U Want H +is positive that's going to stretch the + + align:start position:0% +is positive that's going to stretch the + + + align:start position:0% +is positive that's going to stretch the +bar that's a posit postive stretching so + + align:start position:0% +bar that's a posit postive stretching so + + + align:start position:0% +bar that's a posit postive stretching so +I'm expecting a positive u1h to give me + + align:start position:0% +I'm expecting a positive u1h to give me + + + align:start position:0% +I'm expecting a positive u1h to give me +I'm expecting that sort of to come in + + align:start position:0% +I'm expecting that sort of to come in + + + align:start position:0% +I'm expecting that sort of to come in +with a plus sign now if suppose the bar + + align:start position:0% +with a plus sign now if suppose the bar + + + align:start position:0% +with a plus sign now if suppose the bar +is + + align:start position:0% +is + + + align:start position:0% +is +horizontal suppose the bar is horizontal + + align:start position:0% +horizontal suppose the bar is horizontal + + + align:start position:0% +horizontal suppose the bar is horizontal +then how much does the u1h stretch it it + + align:start position:0% +then how much does the u1h stretch it it + + + align:start position:0% +then how much does the u1h stretch it it +stretches it by the whole u1h right if + + align:start position:0% +stretches it by the whole u1h right if + + + align:start position:0% +stretches it by the whole u1h right if +if if the if the bar was horizontal so + + align:start position:0% +if if the if the bar was horizontal so + + + align:start position:0% +if if the if the bar was horizontal so +theta equals zero I'm I'm just doing + + align:start position:0% +theta equals zero I'm I'm just doing + + + align:start position:0% +theta equals zero I'm I'm just doing +these + + align:start position:0% +these + + + align:start position:0% +these +we got to sort out the this Theta angle + + align:start position:0% +we got to sort out the this Theta angle + + + align:start position:0% +we got to sort out the this Theta angle +stuff so here's my thing if the bar + + align:start position:0% +stuff so here's my thing if the bar + + + align:start position:0% +stuff so here's my thing if the bar +happens to be horizontal then that + + align:start position:0% +happens to be horizontal then that + + + align:start position:0% +happens to be horizontal then that +stretching of by U + + align:start position:0% +stretching of by U + + + align:start position:0% +stretching of by U +H1 will completely stretch the + + align:start position:0% + + + + align:start position:0% + +bar if the bar happened to be yeah yeah + + align:start position:0% +bar if the bar happened to be yeah yeah + + + align:start position:0% +bar if the bar happened to be yeah yeah +and and of course this would so that if + + align:start position:0% +and and of course this would so that if + + + align:start position:0% +and and of course this would so that if +for a horizontal bar I'll just be back + + align:start position:0% +for a horizontal bar I'll just be back + + + align:start position:0% +for a horizontal bar I'll just be back +to this stuff I'll have a one and a + + align:start position:0% +to this stuff I'll have a one and a + + + align:start position:0% +to this stuff I'll have a one and a +minus one for I'll have you you oh yeah + + align:start position:0% +minus one for I'll have you you oh yeah + + + align:start position:0% +minus one for I'll have you you oh yeah +remind me about that why doesn't you + + align:start position:0% +remind me about that why doesn't you + + + align:start position:0% +remind me about that why doesn't you +vertical for a horizontal bar like this + + align:start position:0% +vertical for a horizontal bar like this + + + align:start position:0% +vertical for a horizontal bar like this +why does this one not stretch the + + align:start position:0% +why does this one not stretch the + + + align:start position:0% +why does this one not stretch the +bar you remember that from last time + + align:start position:0% +bar you remember that from last time + + + align:start position:0% +bar you remember that from last time +that was the little bit of trig that we + + align:start position:0% +that was the little bit of trig that we + + + align:start position:0% +that was the little bit of trig that we +did when we were we forced ourselves to + + align:start position:0% +did when we were we forced ourselves to + + + align:start position:0% +did when we were we forced ourselves to +stay linear so we dropped the second + + align:start position:0% +stay linear so we dropped the second + + + align:start position:0% +stay linear so we dropped the second +order correction that would come from + + align:start position:0% +order correction that would come from + + + align:start position:0% +order correction that would come from +going this way + + align:start position:0% +going this way + + + align:start position:0% +going this way +right yeah I mean you must have noticed + + align:start position:0% +right yeah I mean you must have noticed + + + align:start position:0% +right yeah I mean you must have noticed +like walking suppose you want to walk + + align:start position:0% +like walking suppose you want to walk + + + align:start position:0% +like walking suppose you want to walk +from here to the end of the bar okay + + align:start position:0% +from here to the end of the bar okay + + + align:start position:0% +from here to the end of the bar okay +well if somebody moves the end of the + + align:start position:0% +well if somebody moves the end of the + + + align:start position:0% +well if somebody moves the end of the +bar + + align:start position:0% +bar + + + align:start position:0% +bar +forward you have to take those extra + + align:start position:0% +forward you have to take those extra + + + align:start position:0% +forward you have to take those extra +steps that the bar really stretched but + + align:start position:0% +steps that the bar really stretched but + + + align:start position:0% +steps that the bar really stretched but +if somebody moves the bar this way then + + align:start position:0% +if somebody moves the bar this way then + + + align:start position:0% +if somebody moves the bar this way then +the extra bit of + + align:start position:0% +the extra bit of + + + align:start position:0% +the extra bit of +length is much less right in fact fact + + align:start position:0% +length is much less right in fact fact + + + align:start position:0% +length is much less right in fact fact +it's zero to to first order right this + + align:start position:0% +it's zero to to first order right this + + + align:start position:0% +it's zero to to first order right this +is like taking shortcuts when you walk + + align:start position:0% +is like taking shortcuts when you walk + + + align:start position:0% +is like taking shortcuts when you walk +across the the the uh cour chard okay so + + align:start position:0% +across the the the uh cour chard okay so + + + align:start position:0% +across the the the uh cour chard okay so +so when the angle's Theta I'm only I'm + + align:start position:0% +so when the angle's Theta I'm only I'm + + + align:start position:0% +so when the angle's Theta I'm only I'm +only expecting a one and a minus + + align:start position:0% +only expecting a one and a minus + + + align:start position:0% +only expecting a one and a minus +one on the horizontal and Zer on the + + align:start position:0% +one on the horizontal and Zer on the + + + align:start position:0% +one on the horizontal and Zer on the +vertical okay now I'm ready to write in + + align:start position:0% +vertical okay now I'm ready to write in + + + align:start position:0% +vertical okay now I'm ready to write in +I think when the angle Theta when the + + align:start position:0% +I think when the angle Theta when the + + + align:start position:0% +I think when the angle Theta when the +angle Theta any + + align:start position:0% +angle Theta any + + + align:start position:0% +angle Theta any +Theta uh was when the angle was Zero I + + align:start position:0% +Theta uh was when the angle was Zero I + + + align:start position:0% +Theta uh was when the angle was Zero I +think we get a COS + + align:start position:0% +think we get a COS + + + align:start position:0% +think we get a COS +Theta doesn't your instinct say that + + align:start position:0% +Theta doesn't your instinct say that + + + align:start position:0% +Theta doesn't your instinct say that +this is on the + + align:start position:0% +this is on the + + + align:start position:0% +this is on the +U1 U horizontal one and then the U + + align:start position:0% +U1 U horizontal one and then the U + + + align:start position:0% +U1 U horizontal one and then the U +vertical one you tell me what I tell me + + align:start position:0% +vertical one you tell me what I tell me + + + align:start position:0% +vertical one you tell me what I tell me +what these should be and then + + align:start position:0% +what these should be and then + + + align:start position:0% +what these should be and then +we'll make what do you suppose is the + + align:start position:0% +we'll make what do you suppose is the + + + align:start position:0% +we'll make what do you suppose is the +entry second nonzero the one that + + align:start position:0% +entry second nonzero the one that + + + align:start position:0% +entry second nonzero the one that +corresponds to a vertical movement here + + align:start position:0% +corresponds to a vertical movement here + + + align:start position:0% +corresponds to a vertical movement here +it would be for a horizontal bar when + + align:start position:0% +it would be for a horizontal bar when + + + align:start position:0% +it would be for a horizontal bar when +Theta is zero I'm going to see a zero + + align:start position:0% +Theta is zero I'm going to see a zero + + + align:start position:0% +Theta is zero I'm going to see a zero +there but if the bar is at an angle like + + align:start position:0% +there but if the bar is at an angle like + + + align:start position:0% +there but if the bar is at an angle like +this what am I going to see everybody's + + align:start position:0% +this what am I going to see everybody's + + + align:start position:0% +this what am I going to see everybody's +going to get it right what do I put in + + align:start position:0% +going to get it right what do I put in + + + align:start position:0% +going to get it right what do I put in +there s Theta what else could it be + + align:start position:0% +there s Theta what else could it be + + + align:start position:0% +there s Theta what else could it be +right okay s + + align:start position:0% +right okay s + + + align:start position:0% +right okay s +Theta and now what about the next guy + + align:start position:0% +Theta and now what about the next guy + + + align:start position:0% +Theta and now what about the next guy +the other end of the bar uhu + + align:start position:0% +the other end of the bar uhu + + + align:start position:0% +the other end of the bar uhu +H2 and + + align:start position:0% +H2 and + + + align:start position:0% +H2 and +uv2 those are the other two nonzeros + + align:start position:0% +uv2 those are the other two nonzeros + + + align:start position:0% +uv2 those are the other two nonzeros +what what's your guess for U2 + + align:start position:0% +what what's your guess for U2 + + + align:start position:0% +what what's your guess for U2 +uh2 if I move + + align:start position:0% +uh2 if I move + + + align:start position:0% +uh2 if I move +this + + align:start position:0% +this + + + align:start position:0% +this +forward what's this what's this change + + align:start position:0% +forward what's this what's this change + + + align:start position:0% +forward what's this what's this change +in length of the + + align:start position:0% +in length of the + + + align:start position:0% +in length of the +bar what what would your guess be if + + align:start position:0% +bar what what would your guess be if + + + align:start position:0% +bar what what would your guess be if +that goes into + + align:start position:0% +that goes into + + + align:start position:0% +that goes into +there say it again minus C thet minus + + align:start position:0% +there say it again minus C thet minus + + + align:start position:0% +there say it again minus C thet minus +cos Theta right yeah yeah the movement + + align:start position:0% +cos Theta right yeah yeah the movement + + + align:start position:0% +cos Theta right yeah yeah the movement +of the of the other and like if I move + + align:start position:0% +of the of the other and like if I move + + + align:start position:0% +of the of the other and like if I move +this guy a little bit to this side that + + align:start position:0% +this guy a little bit to this side that + + + align:start position:0% +this guy a little bit to this side that +will shorten the bar right so forget + + align:start position:0% +will shorten the bar right so forget + + + align:start position:0% +will shorten the bar right so forget +about that that one if I move this + + align:start position:0% +about that that one if I move this + + + align:start position:0% +about that that one if I move this +over the bar becomes + + align:start position:0% +over the bar becomes + + + align:start position:0% +over the bar becomes +shorter and the + + align:start position:0% +shorter and the + + + align:start position:0% +shorter and the +cosine tells me + + align:start position:0% +cosine tells me + + + align:start position:0% +cosine tells me +the key number there how much it BEC + + align:start position:0% +the key number there how much it BEC + + + align:start position:0% +the key number there how much it BEC +shorter if the bar was horizontal the + + align:start position:0% +shorter if the bar was horizontal the + + + align:start position:0% +shorter if the bar was horizontal the +cosine of theta was one it it counts + + align:start position:0% +cosine of theta was one it it counts + + + align:start position:0% +cosine of theta was one it it counts +100% if the bar bar is vertical and I + + align:start position:0% +100% if the bar bar is vertical and I + + + align:start position:0% +100% if the bar bar is vertical and I +move it horizontally it counts 0% + + align:start position:0% +move it horizontally it counts 0% + + + align:start position:0% +move it horizontally it counts 0% +Because by the linearity says there was + + align:start position:0% +Because by the linearity says there was + + + align:start position:0% +Because by the linearity says there was +no first order change and now tell me + + align:start position:0% +no first order change and now tell me + + + align:start position:0% +no first order change and now tell me +the final nonzero entry and I see I + + align:start position:0% +the final nonzero entry and I see I + + + align:start position:0% +the final nonzero entry and I see I +didn't leave much room for all the zeros + + align:start position:0% +didn't leave much room for all the zeros + + + align:start position:0% +didn't leave much room for all the zeros +okay what's the u2v + + align:start position:0% + + + + align:start position:0% + +entry minus sin Theta of course and then + + align:start position:0% +entry minus sin Theta of course and then + + + align:start position:0% +entry minus sin Theta of course and then +come all the zero + + align:start position:0% +come all the zero + + + align:start position:0% +come all the zero +for whatever + + align:start position:0% +for whatever + + + align:start position:0% +for whatever +other uh joints are not involved with + + align:start position:0% +other uh joints are not involved with + + + align:start position:0% +other uh joints are not involved with +bar one so let me maybe to make this + + align:start position:0% +bar one so let me maybe to make this + + + align:start position:0% +bar one so let me maybe to make this +picture best I should move that over + + align:start position:0% +picture best I should move that over + + + align:start position:0% +picture best I should move that over +where I where it + + align:start position:0% +where I where it + + + align:start position:0% +where I where it +belongs now what's if I add up along a + + align:start position:0% +belongs now what's if I add up along a + + + align:start position:0% +belongs now what's if I add up along a +bar add up the four numbers there what + + align:start position:0% +bar add up the four numbers there what + + + align:start position:0% +bar add up the four numbers there what +do I get zero you expected that right if + + align:start position:0% +do I get zero you expected that right if + + + align:start position:0% +do I get zero you expected that right if +the + + align:start position:0% +the + + + align:start position:0% +the +bar if the in fact if I add just that + + align:start position:0% +bar if the in fact if I add just that + + + align:start position:0% +bar if the in fact if I add just that +and that I get zero + + align:start position:0% +and that I get zero + + + align:start position:0% +and that I get zero +if I add that and that I get zero just + + align:start position:0% +if I add that and that I get zero just + + + align:start position:0% +if I add that and that I get zero just +the way I got zero here in in the + + align:start position:0% +the way I got zero here in in the + + + align:start position:0% +the way I got zero here in in the +incidence matrices the the the the + + align:start position:0% +incidence matrices the the the the + + + align:start position:0% +incidence matrices the the the the +column of all ones is certainly uh going + + align:start position:0% +column of all ones is certainly uh going + + + align:start position:0% +column of all ones is certainly uh going +to be going to solve a u equals z if + + align:start position:0% +to be going to solve a u equals z if + + + align:start position:0% +to be going to solve a u equals z if +it's if unless the the uh supports + + align:start position:0% +it's if unless the the uh supports + + + align:start position:0% +it's if unless the the uh supports +remove those of course if the supports + + align:start position:0% +remove those of course if the supports + + + align:start position:0% +remove those of course if the supports +don't allow all ones because some have + + align:start position:0% +don't allow all ones because some have + + + align:start position:0% +don't allow all ones because some have +to stay at zero + + align:start position:0% +to stay at zero + + + align:start position:0% +to stay at zero +then I could have a stable tress okay + + align:start position:0% +then I could have a stable tress okay + + + align:start position:0% +then I could have a stable tress okay +that's a typical bar a a typical row + + align:start position:0% +that's a typical bar a a typical row + + + align:start position:0% +that's a typical bar a a typical row +that's a typical row okay and now maybe + + align:start position:0% +that's a typical row okay and now maybe + + + align:start position:0% +that's a typical row okay and now maybe +uh let's see while I'm on the same + + align:start position:0% +uh let's see while I'm on the same + + + align:start position:0% +uh let's see while I'm on the same +subject what is + + align:start position:0% +subject what is + + + align:start position:0% +subject what is +the + + align:start position:0% +the + + + align:start position:0% +the +size what does this thing look like + + align:start position:0% +size what does this thing look like + + + align:start position:0% +size what does this thing look like +now that that's this is in a this is in + + align:start position:0% +now that that's this is in a this is in + + + align:start position:0% +now that that's this is in a this is in +this is in The Matrix a and now I want + + align:start position:0% +this is in The Matrix a and now I want + + + align:start position:0% +this is in The Matrix a and now I want +to ask you before I even come back to + + align:start position:0% +to ask you before I even come back to + + + align:start position:0% +to ask you before I even come back to +all this stuff what about in a transpose + + align:start position:0% +all this stuff what about in a transpose + + + align:start position:0% +all this stuff what about in a transpose +a in a + + align:start position:0% +a in a + + + align:start position:0% +a in a +transpose a transpose CA the whole deal + + align:start position:0% +transpose a transpose CA the whole deal + + + align:start position:0% +transpose a transpose CA the whole deal +the element for the the + + align:start position:0% +the element for the the + + + align:start position:0% +the element for the the +little Matrix the element Matrix can I + + align:start position:0% +little Matrix the element Matrix can I + + + align:start position:0% +little Matrix the element Matrix can I +call it that or the one bar Matrix say + + align:start position:0% +call it that or the one bar Matrix say + + + align:start position:0% +call it that or the one bar Matrix say +the call it the one bar + + align:start position:0% +the call it the one bar + + + align:start position:0% +the call it the one bar +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +will will be is what so I want this this + + align:start position:0% +will will be is what so I want this this + + + align:start position:0% +will will be is what so I want this this +it would be typical C1 + + align:start position:0% +it would be typical C1 + + + align:start position:0% +it would be typical C1 +row1 transpose Row one that's a typical + + align:start position:0% +row1 transpose Row one that's a typical + + + align:start position:0% +row1 transpose Row one that's a typical +guy and and + + align:start position:0% +guy and and + + + align:start position:0% +guy and and +and how many nonzeros in + + align:start position:0% + + + + align:start position:0% + +that multiplying a + + align:start position:0% +that multiplying a + + + align:start position:0% +that multiplying a +row sorry multiplying a column that has + + align:start position:0% +row sorry multiplying a column that has + + + align:start position:0% +row sorry multiplying a column that has +four nonzeros times a row that has four + + align:start position:0% +four nonzeros times a row that has four + + + align:start position:0% +four nonzeros times a row that has four +nonzeros + + align:start position:0% +nonzeros + + + align:start position:0% +nonzeros +times a number which is just fine how + + align:start position:0% +times a number which is just fine how + + + align:start position:0% +times a number which is just fine how +many how many nonzeros are going to sit + + align:start position:0% +many how many nonzeros are going to sit + + + align:start position:0% +many how many nonzeros are going to sit +in this element Matrix this one bar + + align:start position:0% + + + + align:start position:0% + +Matrix 16 16 + + align:start position:0% + + + + align:start position:0% + +nonzeros and they're going to be you + + align:start position:0% +nonzeros and they're going to be you + + + align:start position:0% +nonzeros and they're going to be you +know there just be I have cosine sin - + + align:start position:0% +know there just be I have cosine sin - + + + align:start position:0% +know there just be I have cosine sin - +cosine - s multiplying cosine sinus + + align:start position:0% +cosine - s multiplying cosine sinus + + + align:start position:0% +cosine - s multiplying cosine sinus +cosine minus s and all multiplied by + + align:start position:0% +cosine minus s and all multiplied by + + + align:start position:0% +cosine minus s and all multiplied by +C1 so that's the Matrix and and you see + + align:start position:0% +C1 so that's the Matrix and and you see + + + align:start position:0% +C1 so that's the Matrix and and you see +what it looks like C squar CS so on 16 + + align:start position:0% +what it looks like C squar CS so on 16 + + + align:start position:0% +what it looks like C squar CS so on 16 +guys so that's the that we have four + + align:start position:0% +guys so that's the that we have four + + + align:start position:0% +guys so that's the that we have four +squared as our element Matrix where here + + align:start position:0% +squared as our element Matrix where here + + + align:start position:0% +squared as our element Matrix where here +we had two squar and in finite elements + + align:start position:0% +we had two squar and in finite elements + + + align:start position:0% +we had two squar and in finite elements +when you get to + + align:start position:0% +when you get to + + + align:start position:0% +when you get to +um elasticity + + align:start position:0% +um elasticity + + + align:start position:0% +um elasticity +uh and you're in you've got triangles + + align:start position:0% +uh and you're in you've got triangles + + + align:start position:0% +uh and you're in you've got triangles +you've got more you've + + align:start position:0% +you've got more you've + + + align:start position:0% +you've got more you've +got triangle triangular elements then + + align:start position:0% +got triangle triangular elements then + + + align:start position:0% +got triangle triangular elements then +there are three nodes involved or you're + + align:start position:0% +there are three nodes involved or you're + + + align:start position:0% +there are three nodes involved or you're +up to higher numbers but this gives you + + align:start position:0% +up to higher numbers but this gives you + + + align:start position:0% +up to higher numbers but this gives you +the idea and remember that this + + align:start position:0% +the idea and remember that this + + + align:start position:0% +the idea and remember that this +4x4 the way I've done it the way I've + + align:start position:0% +4x4 the way I've done it the way I've + + + align:start position:0% +4x4 the way I've done it the way I've +numbered it one + + align:start position:0% +numbered it one + + + align:start position:0% +numbered it one +two happens to sit up in the upper left + + align:start position:0% +two happens to sit up in the upper left + + + align:start position:0% +two happens to sit up in the upper left +corner of a transpose + + align:start position:0% +corner of a transpose + + + align:start position:0% +corner of a transpose +CA but can can you sort of imagine how + + align:start position:0% +CA but can can you sort of imagine how + + + align:start position:0% +CA but can can you sort of imagine how +the code would be written the code would + + align:start position:0% +the code would be written the code would + + + align:start position:0% +the code would be written the code would +be written take a bar take each bar and + + align:start position:0% +be written take a bar take each bar and + + + align:start position:0% +be written take a bar take each bar and +what do I have to know about the bar + + align:start position:0% +what do I have to know about the bar + + + align:start position:0% +what do I have to know about the bar +yeah just imagine a code that would do + + align:start position:0% +yeah just imagine a code that would do + + + align:start position:0% +yeah just imagine a code that would do +trusses actually the final problem that + + align:start position:0% +trusses actually the final problem that + + + align:start position:0% +trusses actually the final problem that +I'm not assigning in the in this section + + align:start position:0% +I'm not assigning in the in this section + + + align:start position:0% +I'm not assigning in the in this section +says what would the code be like and can + + align:start position:0% +says what would the code be like and can + + + align:start position:0% +says what would the code be like and can +we just have a um a think about what the + + align:start position:0% +we just have a um a think about what the + + + align:start position:0% +we just have a um a think about what the +code would look like if if we were to + + align:start position:0% +code would look like if if we were to + + + align:start position:0% +code would look like if if we were to +write it what would would the input have + + align:start position:0% +write it what would would the input have + + + align:start position:0% +write it what would would the input have +to + + align:start position:0% +to + + + align:start position:0% +to +be how what would I input to each for + + align:start position:0% +be how what would I input to each for + + + align:start position:0% +be how what would I input to each for +each bar what input do I + + align:start position:0% +each bar what input do I + + + align:start position:0% +each bar what input do I +need I need for this + + align:start position:0% +need I need for this + + + align:start position:0% +need I need for this +bar I need to + + align:start position:0% +bar I need to + + + align:start position:0% +bar I need to +know and for the whole trust what do I + + align:start position:0% +know and for the whole trust what do I + + + align:start position:0% +know and for the whole trust what do I +need what do I have to tell what what's + + align:start position:0% +need what do I have to tell what what's + + + align:start position:0% +need what do I have to tell what what's +the information that I need for the + + align:start position:0% +the information that I need for the + + + align:start position:0% +the information that I need for the +whole truss I have to know the positions + + align:start position:0% +whole truss I have to know the positions + + + align:start position:0% +whole truss I have to know the positions +of all the point joints right so I'd + + align:start position:0% +of all the point joints right so I'd + + + align:start position:0% +of all the point joints right so I'd +have to know the coordinates of that x y + + align:start position:0% +have to know the coordinates of that x y + + + align:start position:0% +have to know the coordinates of that x y +the coordinates of this one XY X1 y1 for + + align:start position:0% +the coordinates of this one XY X1 y1 for + + + align:start position:0% +the coordinates of this one XY X1 y1 for +for joint one X2 Y2 so I'd have to have + + align:start position:0% +for joint one X2 Y2 so I'd have to have + + + align:start position:0% +for joint one X2 Y2 so I'd have to have +a little list of what would that be M by + + align:start position:0% +a little list of what would that be M by + + + align:start position:0% +a little list of what would that be M by +two I have oh no n n by two I have + + align:start position:0% +two I have oh no n n by two I have + + + align:start position:0% +two I have oh no n n by two I have +n yeah what what do I have now think of + + align:start position:0% +n yeah what what do I have now think of + + + align:start position:0% +n yeah what what do I have now think of +what what information do I have to + + align:start position:0% +what what information do I have to + + + align:start position:0% +what what information do I have to +report about this trust I I guess I have + + align:start position:0% +report about this trust I I guess I have + + + align:start position:0% +report about this trust I I guess I have +n capital N joints and I need two + + align:start position:0% +n capital N joints and I need two + + + align:start position:0% +n capital N joints and I need two +coordinates X Y for each position so + + align:start position:0% +coordinates X Y for each position so + + + align:start position:0% +coordinates X Y for each position so +that's n by two list okay and then for + + align:start position:0% +that's n by two list okay and then for + + + align:start position:0% +that's n by two list okay and then for +every bar what do I need to tell it what + + align:start position:0% +every bar what do I need to tell it what + + + align:start position:0% +every bar what do I need to tell it what +do I need to put in the code for a + + align:start position:0% +do I need to put in the code for a + + + align:start position:0% +do I need to put in the code for a +typical bar I certainly have to put in + + align:start position:0% +typical bar I certainly have to put in + + + align:start position:0% +typical bar I certainly have to put in +the the C the C for that bar and what + + align:start position:0% +the the C the C for that bar and what + + + align:start position:0% +the the C the C for that bar and what +else do I need to know I need to know + + align:start position:0% +else do I need to know I need to know + + + align:start position:0% +else do I need to know I need to know +which node which joints it's connecting + + align:start position:0% +which node which joints it's connecting + + + align:start position:0% +which node which joints it's connecting +right I have to tell tell the system + + align:start position:0% +right I have to tell tell the system + + + align:start position:0% +right I have to tell tell the system +that this bar is between two and one one + + align:start position:0% +that this bar is between two and one one + + + align:start position:0% +that this bar is between two and one one +and two I have to tell it which which + + align:start position:0% +and two I have to tell it which which + + + align:start position:0% +and two I have to tell it which which +pairs so so I guess I have a list of + + align:start position:0% +pairs so so I guess I have a list of + + + align:start position:0% +pairs so so I guess I have a list of +M bars and for each bar I must tell the + + align:start position:0% +M bars and for each bar I must tell the + + + align:start position:0% +M bars and for each bar I must tell the +system the two node + + align:start position:0% +system the two node + + + align:start position:0% +system the two node +numbers and the C the the stiffness the + + align:start position:0% +numbers and the C the the stiffness the + + + align:start position:0% +numbers and the C the the stiffness the +the the the constant for hooks law right + + align:start position:0% +the the the constant for hooks law right + + + align:start position:0% +the the the constant for hooks law right +do you see this picture just sort of + + align:start position:0% +do you see this picture just sort of + + + align:start position:0% +do you see this picture just sort of +visualizing + + align:start position:0% +visualizing + + + align:start position:0% +visualizing +create creating a code here uh and then + + align:start position:0% +create creating a code here uh and then + + + align:start position:0% +create creating a code here uh and then +the code would do all this oh let's see + + align:start position:0% +the code would do all this oh let's see + + + align:start position:0% +the code would do all this oh let's see +have I given enough information to find + + align:start position:0% +have I given enough information to find + + + align:start position:0% +have I given enough information to find +Theta or do I have to input Theta + + align:start position:0% +Theta or do I have to input Theta + + + align:start position:0% +Theta or do I have to input Theta +also no I told you the positions so + + align:start position:0% +also no I told you the positions so + + + align:start position:0% +also no I told you the positions so +it'll figure out cos Theta and sin Theta + + align:start position:0% +it'll figure out cos Theta and sin Theta + + + align:start position:0% +it'll figure out cos Theta and sin Theta +it actually won't figure out Theta + + align:start position:0% +it actually won't figure out Theta + + + align:start position:0% +it actually won't figure out Theta +that's always a dumb thing to do to find + + align:start position:0% +that's always a dumb thing to do to find + + + align:start position:0% +that's always a dumb thing to do to find +the actual angle cos Theta and sin Theta + + align:start position:0% +the actual angle cos Theta and sin Theta + + + align:start position:0% +the actual angle cos Theta and sin Theta +is the quantities we want so it given + + align:start position:0% +is the quantities we want so it given + + + align:start position:0% +is the quantities we want so it given +that position XY and this position X2 Y2 + + align:start position:0% +that position XY and this position X2 Y2 + + + align:start position:0% +that position XY and this position X2 Y2 +it would know cos Theta and sin Theta + + align:start position:0% +it would know cos Theta and sin Theta + + + align:start position:0% +it would know cos Theta and sin Theta +and having drawn this picture allows me + + align:start position:0% +and having drawn this picture allows me + + + align:start position:0% +and having drawn this picture allows me +to make once more the key point about + + align:start position:0% +to make once more the key point about + + + align:start position:0% +to make once more the key point about +small displacements what's the angle of + + align:start position:0% +small displacements what's the angle of + + + align:start position:0% +small displacements what's the angle of +the bar after it's moved after it's + + align:start position:0% +the bar after it's moved after it's + + + align:start position:0% +the bar after it's moved after it's +displaced this it was Theta before it + + align:start position:0% +displaced this it was Theta before it + + + align:start position:0% +displaced this it was Theta before it +was displaced and the angle after is + + align:start position:0% +was displaced and the angle after is + + + align:start position:0% +was displaced and the angle after is +Theta + + align:start position:0% +Theta + + + align:start position:0% +Theta +it it to first order the angle doesn't + + align:start position:0% +it it to first order the angle doesn't + + + align:start position:0% +it it to first order the angle doesn't +change because these are little tiny + + align:start position:0% +change because these are little tiny + + + align:start position:0% +change because these are little tiny +movements of the ends I've drawn them + + align:start position:0% +movements of the ends I've drawn them + + + align:start position:0% +movements of the ends I've drawn them +much bigger than they should be drawn + + align:start position:0% +much bigger than they should be drawn + + + align:start position:0% +much bigger than they should be drawn +they're little tiny movements of the + + align:start position:0% +they're little tiny movements of the + + + align:start position:0% +they're little tiny movements of the +ends so that the angle is uh not + + align:start position:0% +ends so that the angle is uh not + + + align:start position:0% +ends so that the angle is uh not +significantly changed otherwise we're + + align:start position:0% +significantly changed otherwise we're + + + align:start position:0% +significantly changed otherwise we're +into geometric nonlinearity and and + + align:start position:0% +into geometric nonlinearity and and + + + align:start position:0% +into geometric nonlinearity and and +that's uh that makes the problem much + + align:start position:0% +that's uh that makes the problem much + + + align:start position:0% +that's uh that makes the problem much +much + + align:start position:0% +much + + + align:start position:0% +much +harder okay are you you seeing sort of + + align:start position:0% +harder okay are you you seeing sort of + + + align:start position:0% +harder okay are you you seeing sort of +the picture I guess I didn't what I + + align:start position:0% +the picture I guess I didn't what I + + + align:start position:0% +the picture I guess I didn't what I +haven't + + align:start position:0% +haven't + + + align:start position:0% +haven't +completely I've really depended more on + + align:start position:0% +completely I've really depended more on + + + align:start position:0% +completely I've really depended more on +your intuition than on a calculation to + + align:start position:0% +your intuition than on a calculation to + + + align:start position:0% +your intuition than on a calculation to +say that these are the four + + align:start position:0% +say that these are the four + + + align:start position:0% +say that these are the four +nonzeros what did I ask you to do I + + align:start position:0% +nonzeros what did I ask you to do I + + + align:start position:0% +nonzeros what did I ask you to do I +asked you to check that that was right + + align:start position:0% +asked you to check that that was right + + + align:start position:0% +asked you to check that that was right +in the extreme cases like if Theta is + + align:start position:0% +in the extreme cases like if Theta is + + + align:start position:0% +in the extreme cases like if Theta is +zero the bar is horizontal then we just + + align:start position:0% +zero the bar is horizontal then we just + + + align:start position:0% +zero the bar is horizontal then we just +have a 1 Z minus one 0 vertical isn't + + align:start position:0% +have a 1 Z minus one 0 vertical isn't + + + align:start position:0% +have a 1 Z minus one 0 vertical isn't +happening if the bar is vertical so that + + align:start position:0% +happening if the bar is vertical so that + + + align:start position:0% +happening if the bar is vertical so that +the angle is 90° then we would have a 0 + + align:start position:0% +the angle is 90° then we would have a 0 + + + align:start position:0% +the angle is 90° then we would have a 0 +1 0 minus one everything's vertical and + + align:start position:0% +1 0 minus one everything's vertical and + + + align:start position:0% +1 0 minus one everything's vertical and +it's it and the the book draws a little + + align:start position:0% +it's it and the the book draws a little + + + align:start position:0% +it's it and the the book draws a little +picture and computes computes Delta L + + align:start position:0% +picture and computes computes Delta L + + + align:start position:0% +picture and computes computes Delta L +from these four small movements and + + align:start position:0% +from these four small movements and + + + align:start position:0% +from these four small movements and +takes the leading turn and sure enough + + align:start position:0% +takes the leading turn and sure enough + + + align:start position:0% +takes the leading turn and sure enough +it produces that row of the of The + + align:start position:0% +it produces that row of the of The + + + align:start position:0% +it produces that row of the of The +Matrix + + align:start position:0% + + + + align:start position:0% + +well gosh I talked real fast but do you + + align:start position:0% +well gosh I talked real fast but do you + + + align:start position:0% +well gosh I talked real fast but do you +think you could now create the stiffness + + align:start position:0% +think you could now create the stiffness + + + align:start position:0% +think you could now create the stiffness +for if you had a real + + align:start position:0% +for if you had a real + + + align:start position:0% +for if you had a real +trust you could create + + align:start position:0% +trust you could create + + + align:start position:0% +trust you could create +the Matrix a for it C is simple it's + + align:start position:0% +the Matrix a for it C is simple it's + + + align:start position:0% +the Matrix a for it C is simple it's +given to you you could create a + + align:start position:0% +given to you you could create a + + + align:start position:0% +given to you you could create a +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +CA you might just want to write the + + align:start position:0% +CA you might just want to write the + + + align:start position:0% +CA you might just want to write the +command as + + align:start position:0% +command as + + + align:start position:0% +command as +a prime star C star a or something and + + align:start position:0% +a prime star C star a or something and + + + align:start position:0% +a prime star C star a or something and +let metlab do the thinking but I wanted + + align:start position:0% +let metlab do the thinking but I wanted + + + align:start position:0% +let metlab do the thinking but I wanted +you to see what these how this + + align:start position:0% +you to see what these how this + + + align:start position:0% +you to see what these how this +4x4 piece appears in this + + align:start position:0% +4x4 piece appears in this + + + align:start position:0% +4x4 piece appears in this +product from each + + align:start position:0% +product from each + + + align:start position:0% +product from each +bar it that the four the 16 nonzeros + + align:start position:0% +bar it that the four the 16 nonzeros + + + align:start position:0% +bar it that the four the 16 nonzeros +will appear in different positions and + + align:start position:0% +will appear in different positions and + + + align:start position:0% +will appear in different positions and +you told the + + align:start position:0% +you told the + + + align:start position:0% +you told the +code what those positions are you had to + + align:start position:0% +code what those positions are you had to + + + align:start position:0% +code what those positions are you had to +give the code a a local to Global + + align:start position:0% +give the code a a local to Global + + + align:start position:0% +give the code a a local to Global +picture this is the local picture watch + + align:start position:0% +picture this is the local picture watch + + + align:start position:0% +picture this is the local picture watch +one bar then it has to fit in this big + + align:start position:0% +one bar then it has to fit in this big + + + align:start position:0% +one bar then it has to fit in this big +uh n byn Matrix and that means you have + + align:start position:0% +uh n byn Matrix and that means you have + + + align:start position:0% +uh n byn Matrix and that means you have +to know well what edges what no what + + align:start position:0% +to know well what edges what no what + + + align:start position:0% +to know well what edges what no what +joints was that bar connecting so which + + align:start position:0% +joints was that bar connecting so which + + + align:start position:0% +joints was that bar connecting so which +positions do these 16 + + align:start position:0% +positions do these 16 + + + align:start position:0% +positions do these 16 +nonzeros uh Assemble + + align:start position:0% + + + + align:start position:0% + +into + + align:start position:0% +into + + + align:start position:0% +into +okay that's that's some time dis devoted + + align:start position:0% +okay that's that's some time dis devoted + + + align:start position:0% +okay that's that's some time dis devoted +to uh a job that I actually don't plan + + align:start position:0% +to uh a job that I actually don't plan + + + align:start position:0% +to uh a job that I actually don't plan +to require you to do uh creating this uh + + align:start position:0% +to require you to do uh creating this uh + + + align:start position:0% +to require you to do uh creating this uh +trust problem what + + align:start position:0% +trust problem what + + + align:start position:0% +trust problem what +I think is kind of more fun and that's + + align:start position:0% +I think is kind of more fun and that's + + + align:start position:0% +I think is kind of more fun and that's +these these homework problems would + + align:start position:0% +these these homework problems would + + + align:start position:0% +these these homework problems would +would uh deal with it is part two of the + + align:start position:0% +would uh deal with it is part two of the + + + align:start position:0% +would uh deal with it is part two of the +lecture going back to + + align:start position:0% +lecture going back to + + + align:start position:0% +lecture going back to +mechanisms and now thinking about + + align:start position:0% +mechanisms and now thinking about + + + align:start position:0% +mechanisms and now thinking about +uh more complicated + + align:start position:0% + + + + align:start position:0% + +trusses we now in principle could find + + align:start position:0% +trusses we now in principle could find + + + align:start position:0% +trusses we now in principle could find +the solutions to Au U equals z because + + align:start position:0% +the solutions to Au U equals z because + + + align:start position:0% +the solutions to Au U equals z because +we now have constructed a and we could + + align:start position:0% +we now have constructed a and we could + + + align:start position:0% +we now have constructed a and we could +get Matt lab to do the work or python or + + align:start position:0% +get Matt lab to do the work or python or + + + align:start position:0% +get Matt lab to do the work or python or +whoever but let's can I can I go to part + + align:start position:0% +whoever but let's can I can I go to part + + + align:start position:0% +whoever but let's can I can I go to part +two now and draw a truss and ask you + + align:start position:0% +two now and draw a truss and ask you + + + align:start position:0% +two now and draw a truss and ask you +about the mechanisms let me + + align:start position:0% +about the mechanisms let me + + + align:start position:0% +about the mechanisms let me +um let's + + align:start position:0% +um let's + + + align:start position:0% +um let's +see let me I guess somewhere in the in + + align:start position:0% +see let me I guess somewhere in the in + + + align:start position:0% +see let me I guess somewhere in the in +the uh problem set but not one of the + + align:start position:0% +the uh problem set but not one of the + + + align:start position:0% +the uh problem set but not one of the +assigned ones is suppose that's + + align:start position:0% +assigned ones is suppose that's + + + align:start position:0% +assigned ones is suppose that's +my start with those six + + align:start position:0% +my start with those six + + + align:start position:0% +my start with those six +bars and six joints so these are six + + align:start position:0% + + + + align:start position:0% + +joints and uh okay as it + + align:start position:0% +joints and uh okay as it + + + align:start position:0% +joints and uh okay as it +stands how many oh yeah it's a good + + align:start position:0% +stands how many oh yeah it's a good + + + align:start position:0% +stands how many oh yeah it's a good +question as it stands what's the s + + align:start position:0% +question as it stands what's the s + + + align:start position:0% +question as it stands what's the s +what's the shape of the Matrix + + align:start position:0% +what's the shape of the Matrix + + + align:start position:0% +what's the shape of the Matrix +a how many rows has it got so as it + + align:start position:0% +a how many rows has it got so as it + + + align:start position:0% +a how many rows has it got so as it +stands so I'll call it shall I call it a + + align:start position:0% +stands so I'll call it shall I call it a + + + align:start position:0% +stands so I'll call it shall I call it a +Zer for no supports have been added + + align:start position:0% +Zer for no supports have been added + + + align:start position:0% +Zer for no supports have been added +a z just the the full Matrix is what + + align:start position:0% +a z just the the full Matrix is what + + + align:start position:0% +a z just the the full Matrix is what +shape 6 by 12 good 6 by 12 is 6 by + + align:start position:0% +shape 6 by 12 good 6 by 12 is 6 by + + + align:start position:0% +shape 6 by 12 good 6 by 12 is 6 by +12 okay of course it's not stable we + + align:start position:0% +12 okay of course it's not stable we + + + align:start position:0% +12 okay of course it's not stable we +know that we haven't we haven't + + align:start position:0% +know that we haven't we haven't + + + align:start position:0% +know that we haven't we haven't +supported anything so how many uh in the + + align:start position:0% +supported anything so how many uh in the + + + align:start position:0% +supported anything so how many uh in the +in a typical case how many solutions to + + align:start position:0% +in a typical case how many solutions to + + + align:start position:0% +in a typical case how many solutions to +a so so I'm going to ask you how many + + align:start position:0% +a so so I'm going to ask you how many + + + align:start position:0% +a so so I'm going to ask you how many +solutions to a Au equals + + align:start position:0% + + + + align:start position:0% + +z and what's your + + align:start position:0% +z and what's your + + + align:start position:0% +z and what's your +guess + + align:start position:0% +guess + + + align:start position:0% +guess +six got six equations we got 12 U's 12 - + + align:start position:0% +six got six equations we got 12 U's 12 - + + + align:start position:0% +six got six equations we got 12 U's 12 - +6 so this is going to be 12 - 6 or six + + align:start position:0% +6 so this is going to be 12 - 6 or six + + + align:start position:0% +6 so this is going to be 12 - 6 or six +solutions to to uh that equation it's + + align:start position:0% +solutions to to uh that equation it's + + + align:start position:0% +solutions to to uh that equation it's +what I would expect there could be it + + align:start position:0% +what I would expect there could be it + + + align:start position:0% +what I would expect there could be it +could be possible that these six + + align:start position:0% +could be possible that these six + + + align:start position:0% +could be possible that these six +equations are not independent dependent + + align:start position:0% +equations are not independent dependent + + + align:start position:0% +equations are not independent dependent +if that if they really drop to five then + + align:start position:0% +if that if they really drop to five then + + + align:start position:0% +if that if they really drop to five then +this would bump up to seven I don't + + align:start position:0% +this would bump up to seven I don't + + + align:start position:0% +this would bump up to seven I don't +think it's going to happen here okay now + + align:start position:0% +think it's going to happen here okay now + + + align:start position:0% +think it's going to happen here okay now +can you describe those six + + align:start position:0% +can you describe those six + + + align:start position:0% +can you describe those six +Solutions not with numbers just + + align:start position:0% +Solutions not with numbers just + + + align:start position:0% +Solutions not with numbers just +with tell me I I hope you can't because + + align:start position:0% +with tell me I I hope you can't because + + + align:start position:0% +with tell me I I hope you can't because +I can't right now okay three of them we + + align:start position:0% +I can't right now okay three of them we + + + align:start position:0% +I can't right now okay three of them we +know so what are with no supports at all + + align:start position:0% +know so what are with no supports at all + + + align:start position:0% +know so what are with no supports at all +what are three three rigid motions + + align:start position:0% + + + + align:start position:0% + +and what what are they the whole trust + + align:start position:0% +and what what are they the whole trust + + + align:start position:0% +and what what are they the whole trust +could the whole trust could move to the + + align:start position:0% +could the whole trust could move to the + + + align:start position:0% +could the whole trust could move to the +right the whole hexagon it could all + + align:start position:0% +right the whole hexagon it could all + + + align:start position:0% +right the whole hexagon it could all +move up it could all rotate about one + + align:start position:0% +move up it could all rotate about one + + + align:start position:0% +move up it could all rotate about one +point all three of those would be + + align:start position:0% +point all three of those would be + + + align:start position:0% +point all three of those would be +movements displacements that don't + + align:start position:0% +movements displacements that don't + + + align:start position:0% +movements displacements that don't +stretch anything okay three rigid + + align:start position:0% +stretch anything okay three rigid + + + align:start position:0% +stretch anything okay three rigid +motions + + align:start position:0% + + + + align:start position:0% + +across up and rotate + + align:start position:0% +across up and rotate + + + align:start position:0% +across up and rotate +okay and I can get rid of those by + + align:start position:0% +okay and I can get rid of those by + + + align:start position:0% +okay and I can get rid of those by +supporting some nodes but let me see I I + + align:start position:0% +supporting some nodes but let me see I I + + + align:start position:0% +supporting some nodes but let me see I I +I don't know what's going to happen + + align:start position:0% +I don't know what's going to happen + + + align:start position:0% +I don't know what's going to happen +that's when I describ this + + align:start position:0% +that's when I describ this + + + align:start position:0% +that's when I describ this +U topic as the fun one in 18085 it's + + align:start position:0% +U topic as the fun one in 18085 it's + + + align:start position:0% +U topic as the fun one in 18085 it's +more fun for you than for me because I + + align:start position:0% +more fun for you than for me because I + + + align:start position:0% +more fun for you than for me because I +draw something like that and I start + + align:start position:0% +draw something like that and I start + + + align:start position:0% +draw something like that and I start +worrying uh can I think of three how + + align:start position:0% +worrying uh can I think of three how + + + align:start position:0% +worrying uh can I think of three how +many how many mechanisms to look for + + align:start position:0% +many how many mechanisms to look for + + + align:start position:0% +many how many mechanisms to look for +three that's a big number + + align:start position:0% +three that's a big number + + + align:start position:0% +three that's a big number +uh I could I bet you I can find one but + + align:start position:0% +uh I could I bet you I can find one but + + + align:start position:0% +uh I could I bet you I can find one but +you guys have got to all right tell me + + align:start position:0% +you guys have got to all right tell me + + + align:start position:0% +you guys have got to all right tell me +some mechanisms let let me try to draw + + align:start position:0% +some mechanisms let let me try to draw + + + align:start position:0% +some mechanisms let let me try to draw +them what would be one mechanism oh + + align:start position:0% +them what would be one mechanism oh + + + align:start position:0% +them what would be one mechanism oh +jeez collapses yeah somehow what what do + + align:start position:0% +jeez collapses yeah somehow what what do + + + align:start position:0% +jeez collapses yeah somehow what what do +you want to how how shall I make it + + align:start position:0% +you want to how how shall I make it + + + align:start position:0% +you want to how how shall I make it +collapse can squeeze in yeah maybe + + align:start position:0% +collapse can squeeze in yeah maybe + + + align:start position:0% +collapse can squeeze in yeah maybe +that's the first one this guy comes in + + align:start position:0% +that's the first one this guy comes in + + + align:start position:0% +that's the first one this guy comes in +this guy what does that do + + align:start position:0% + + + + align:start position:0% + +yeah let's see I've got 15 minutes here + + align:start position:0% +yeah let's see I've got 15 minutes here + + + align:start position:0% +yeah let's see I've got 15 minutes here +I I could pull that board down and draw + + align:start position:0% +I I could pull that board down and draw + + + align:start position:0% +I I could pull that board down and draw +another one what is this one here let's + + align:start position:0% +another one what is this one here let's + + + align:start position:0% +another one what is this one here let's +see if that comes in do these guys have + + align:start position:0% +see if that comes in do these guys have + + + align:start position:0% +see if that comes in do these guys have +to go up a bit Yeah because that's the + + align:start position:0% +to go up a bit Yeah because that's the + + + align:start position:0% +to go up a bit Yeah because that's the +that angle is not 90 degrees so we we + + align:start position:0% +that angle is not 90 degrees so we we + + + align:start position:0% +that angle is not 90 degrees so we we +but we've got a first order change in + + align:start position:0% +but we've got a first order change in + + + align:start position:0% +but we've got a first order change in +this so this comes in a little this goes + + align:start position:0% +this so this comes in a little this goes + + + align:start position:0% +this so this comes in a little this goes +up a little this guy maybe stays + + align:start position:0% +up a little this guy maybe stays + + + align:start position:0% +up a little this guy maybe stays +straight + + align:start position:0% +straight + + + align:start position:0% +straight +uh would would you go for this I mean + + align:start position:0% +uh would would you go for this I mean + + + align:start position:0% +uh would would you go for this I mean +just please say yes uh something happens + + align:start position:0% +just please say yes uh something happens + + + align:start position:0% +just please say yes uh something happens +there right the the the these things go + + align:start position:0% +there right the the the these things go + + + align:start position:0% +there right the the the these things go +in and those go + + align:start position:0% + + + + align:start position:0% + +up could you create the I mean if those + + align:start position:0% +up could you create the I mean if those + + + align:start position:0% +up could you create the I mean if those +were if this was a you know equal side + + align:start position:0% +were if this was a you know equal side + + + align:start position:0% +were if this was a you know equal side +you know regular hexagon you could put + + align:start position:0% +you know regular hexagon you could put + + + align:start position:0% +you know regular hexagon you could put +in all the + + align:start position:0% +in all the + + + align:start position:0% +in all the +numbers for all 12 I would be looking + + align:start position:0% +numbers for all 12 I would be looking + + + align:start position:0% +numbers for all 12 I would be looking +for 12 numbers + + align:start position:0% +for 12 numbers + + + align:start position:0% +for 12 numbers +six no six joints and they each have two + + align:start position:0% +six no six joints and they each have two + + + align:start position:0% +six no six joints and they each have two +U's so that wouldn't be so simple but + + align:start position:0% +U's so that wouldn't be so simple but + + + align:start position:0% +U's so that wouldn't be so simple but +you could do it + + align:start position:0% +you could do it + + + align:start position:0% +you could do it +okay so that would be + + align:start position:0% + + + + align:start position:0% + +one I'm looking for number + + align:start position:0% +one I'm looking for number + + + align:start position:0% +one I'm looking for number +two what would be another one so so sort + + align:start position:0% +two what would be another one so so sort + + + align:start position:0% +two what would be another one so so sort +of squeezing in like a + + align:start position:0% + + + + align:start position:0% + +whatever what do you + + align:start position:0% + + + + align:start position:0% + +think any + + align:start position:0% + + + + align:start position:0% + +others maybe maybe that's possible maybe + + align:start position:0% +others maybe maybe that's possible maybe + + + align:start position:0% +others maybe maybe that's possible maybe +I just look at + + align:start position:0% +I just look at + + + align:start position:0% +I just look at +it you think that would + + align:start position:0% +it you think that would + + + align:start position:0% +it you think that would +work or we could hope those were + + align:start position:0% +work or we could hope those were + + + align:start position:0% +work or we could hope those were +independent but I wouldn't like put my + + align:start position:0% +independent but I wouldn't like put my + + + align:start position:0% +independent but I wouldn't like put my +life on it if I you know have this + + align:start position:0% +life on it if I you know have this + + + align:start position:0% +life on it if I you know have this +squeeze in this squeeze in and this + + align:start position:0% +squeeze in this squeeze in and this + + + align:start position:0% +squeeze in this squeeze in and this +squeeze + + align:start position:0% +squeeze + + + align:start position:0% +squeeze +in I would worry a little + + align:start position:0% +in I would worry a little + + + align:start position:0% +in I would worry a little +bit I can see another one can you what + + align:start position:0% +bit I can see another one can you what + + + align:start position:0% +bit I can see another one can you what +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +thanks half or um fold it in + + align:start position:0% +thanks half or um fold it in + + + align:start position:0% +thanks half or um fold it in +half it along um I guess I guess that + + align:start position:0% +half it along um I guess I guess that + + + align:start position:0% +half it along um I guess I guess that +sort of gets in the 3D yeah we got to + + align:start position:0% +sort of gets in the 3D yeah we got to + + + align:start position:0% +sort of gets in the 3D yeah we got to +stay in the plane + + align:start position:0% + + + + align:start position:0% + +right have instead of what + + align:start position:0% + + + + align:start position:0% + +okay squeeze that + + align:start position:0% +okay squeeze that + + + align:start position:0% +okay squeeze that +out + + align:start position:0% +out + + + align:start position:0% +out +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +good number + + align:start position:0% + + + + align:start position:0% + +two and then I can see here's a here's + + align:start position:0% +two and then I can see here's a here's + + + align:start position:0% +two and then I can see here's a here's +one here's an easy one to think of uh + + align:start position:0% +one here's an easy one to think of uh + + + align:start position:0% +one here's an easy one to think of uh +leave this leave these three alone and + + align:start position:0% +leave this leave these three alone and + + + align:start position:0% +leave this leave these three alone and +just rotate these guys bring this bring + + align:start position:0% +just rotate these guys bring this bring + + + align:start position:0% +just rotate these guys bring this bring +this down right just the just let it let + + align:start position:0% +this down right just the just let it let + + + align:start position:0% +this down right just the just let it let +the let bring these three vertically + + align:start position:0% +the let bring these three vertically + + + align:start position:0% +the let bring these three vertically +down or + + align:start position:0% + + + + align:start position:0% + +something you you see why it's sort + + align:start position:0% +something you you see why it's sort + + + align:start position:0% +something you you see why it's sort +of uh did you like that when I + + align:start position:0% +of uh did you like that when I + + + align:start position:0% +of uh did you like that when I +right it it it seemed simple to me + + align:start position:0% +right it it it seemed simple to me + + + align:start position:0% +right it it it seemed simple to me +looking at it just leave these guys and + + align:start position:0% +looking at it just leave these guys and + + + align:start position:0% +looking at it just leave these guys and +you know rotation let this turn down + + align:start position:0% +you know rotation let this turn down + + + align:start position:0% +you know rotation let this turn down +this turn down let's say and this go + + align:start position:0% +this turn down let's say and this go + + + align:start position:0% +this turn down let's say and this go +down yeah maybe those would all drop by + + align:start position:0% +down yeah maybe those would all drop by + + + align:start position:0% +down yeah maybe those would all drop by +the same amount + + align:start position:0% + + + + align:start position:0% + +maybe ah okay so anyway whatever uh + + align:start position:0% +maybe ah okay so anyway whatever uh + + + align:start position:0% +maybe ah okay so anyway whatever uh +let's let let me uh let's put some + + align:start position:0% +let's let let me uh let's put some + + + align:start position:0% +let's let let me uh let's put some +supports + + align:start position:0% +supports + + + align:start position:0% +supports +on and and get these numbers down to + + align:start position:0% +on and and get these numbers down to + + + align:start position:0% +on and and get these numbers down to +where they so let's support as usual the + + align:start position:0% +where they so let's support as usual the + + + align:start position:0% +where they so let's support as usual the +bottom + + align:start position:0% +bottom + + + align:start position:0% +bottom +guys + + align:start position:0% +guys + + + align:start position:0% +guys +okay so different problem now I won't + + align:start position:0% +okay so different problem now I won't + + + align:start position:0% +okay so different problem now I won't +call it a not I'll call it a + + align:start position:0% +call it a not I'll call it a + + + align:start position:0% +call it a not I'll call it a +I'll ask myself is it stable or unstable + + align:start position:0% +I'll ask myself is it stable or unstable + + + align:start position:0% +I'll ask myself is it stable or unstable +The Matrix is now 6 by + + align:start position:0% +The Matrix is now 6 by + + + align:start position:0% +The Matrix is now 6 by +what eight eight right because I've + + align:start position:0% +what eight eight right because I've + + + align:start position:0% +what eight eight right because I've +still got I've taken away I have four + + align:start position:0% +still got I've taken away I have four + + + align:start position:0% +still got I've taken away I have four +reaction forces two at each support + + align:start position:0% +reaction forces two at each support + + + align:start position:0% +reaction forces two at each support +horizontal and vertical and I've got + + align:start position:0% +horizontal and vertical and I've got + + + align:start position:0% +horizontal and vertical and I've got +four free + + align:start position:0% +four free + + + align:start position:0% +four free +nodes uh and yeah eight is 6 by 8 let me + + align:start position:0% +nodes uh and yeah eight is 6 by 8 let me + + + align:start position:0% +nodes uh and yeah eight is 6 by 8 let me +put in well so 6 by8 what am I expecting + + align:start position:0% +put in well so 6 by8 what am I expecting + + + align:start position:0% +put in well so 6 by8 what am I expecting +now any rigid + + align:start position:0% +now any rigid + + + align:start position:0% +now any rigid +motions no no rigid motions now how many + + align:start position:0% +motions no no rigid motions now how many + + + align:start position:0% +motions no no rigid motions now how many +solutions am I + + align:start position:0% +solutions am I + + + align:start position:0% +solutions am I +expecting two I think probably two okay + + align:start position:0% +expecting two I think probably two okay + + + align:start position:0% +expecting two I think probably two okay +how many mechanisms well no rigid + + align:start position:0% +how many mechanisms well no rigid + + + align:start position:0% +how many mechanisms well no rigid +motions so probably two mechanisms now + + align:start position:0% +motions so probably two mechanisms now + + + align:start position:0% +motions so probably two mechanisms now +can we find two mechanisms all right + + align:start position:0% +can we find two mechanisms all right + + + align:start position:0% +can we find two mechanisms all right +this is like more reasonable we can see + + align:start position:0% +this is like more reasonable we can see + + + align:start position:0% +this is like more reasonable we can see +whether the two me whether we get two + + align:start position:0% +whether the two me whether we get two + + + align:start position:0% +whether the two me whether we get two +mechanisms and whether they're really + + align:start position:0% +mechanisms and whether they're really + + + align:start position:0% +mechanisms and whether they're really +different okay what are the mechanisms + + align:start position:0% +different okay what are the mechanisms + + + align:start position:0% +different okay what are the mechanisms +now these guys are fixed so so for + + align:start position:0% +now these guys are fixed so so for + + + align:start position:0% +now these guys are fixed so so for +forget forget my little sketch here and + + align:start position:0% +forget forget my little sketch here and + + + align:start position:0% +forget forget my little sketch here and +uh think + + align:start position:0% + + + + align:start position:0% + +again what do you see all right let's + + align:start position:0% +again what do you see all right let's + + + align:start position:0% +again what do you see all right let's +have one + + align:start position:0% +have one + + + align:start position:0% +have one +mechanism what would one mechanism be + + align:start position:0% + + + + align:start position:0% + +now there have to be + + align:start position:0% +now there have to be + + + align:start position:0% +now there have to be +two what do you think + + align:start position:0% +two what do you think + + + align:start position:0% +two what do you think +s sit on + + align:start position:0% + + + + align:start position:0% + +it yeah all right bring these guys down + + align:start position:0% +it yeah all right bring these guys down + + + align:start position:0% +it yeah all right bring these guys down +and then these guys will go out is that + + align:start position:0% +and then these guys will go out is that + + + align:start position:0% +and then these guys will go out is that +it okay one so a number mechanism number + + align:start position:0% +it okay one so a number mechanism number + + + align:start position:0% +it okay one so a number mechanism number +one sit on trust + + align:start position:0% +one sit on trust + + + align:start position:0% +one sit on trust +okay all right + + align:start position:0% +okay all right + + + align:start position:0% +okay all right +now I don't know what number two is + + align:start position:0% +now I don't know what number two is + + + align:start position:0% +now I don't know what number two is +that's why I'm taking + + align:start position:0% + + + + align:start position:0% + +time yeah could could we do this could + + align:start position:0% +time yeah could could we do this could + + + align:start position:0% +time yeah could could we do this could +we bring these guys in and those go up + + align:start position:0% +we bring these guys in and those go up + + + align:start position:0% +we bring these guys in and those go up +it's the same thing okay so squeeze + + align:start position:0% + + + + align:start position:0% + +trust squeeze sides is that the same + + align:start position:0% +trust squeeze sides is that the same + + + align:start position:0% +trust squeeze sides is that the same +thing that I had is it is number one the + + align:start position:0% +thing that I had is it is number one the + + + align:start position:0% +thing that I had is it is number one the +same as two oh jeez + + align:start position:0% +same as two oh jeez + + + align:start position:0% +same as two oh jeez +okay is that what everybody is agreeing + + align:start position:0% +okay is that what everybody is agreeing + + + align:start position:0% +okay is that what everybody is agreeing +with + + align:start position:0% + + + + align:start position:0% + +this okay so I didn't get number two was + + align:start position:0% +this okay so I didn't get number two was + + + align:start position:0% +this okay so I didn't get number two was +no good + + align:start position:0% +no good + + + align:start position:0% +no good +okay all right what's a better number + + align:start position:0% +okay all right what's a better number + + + align:start position:0% +okay all right what's a better number +two hold an edge like that one I'm just + + align:start position:0% +two hold an edge like that one I'm just + + + align:start position:0% +two hold an edge like that one I'm just +doing what you say I'm + + align:start position:0% + + + + align:start position:0% + +not just this guy rotates like + + align:start position:0% +not just this guy rotates like + + + align:start position:0% +not just this guy rotates like +so and this guy will rotate and this guy + + align:start position:0% +so and this guy will rotate and this guy + + + align:start position:0% +so and this guy will rotate and this guy +that looks pretty good to + + align:start position:0% + + + + align:start position:0% + +me good is that + + align:start position:0% +me good is that + + + align:start position:0% +me good is that +correct do we say that one again so the + + align:start position:0% +correct do we say that one again so the + + + align:start position:0% +correct do we say that one again so the +first one was when these two came down + + align:start position:0% +first one was when these two came down + + + align:start position:0% +first one was when these two came down +and these went out right + + align:start position:0% +and these went out right + + + align:start position:0% +and these went out right +okay okay and now your suggestion is you + + align:start position:0% +okay okay and now your suggestion is you + + + align:start position:0% +okay okay and now your suggestion is you +picked on this guy and held it fixed and + + align:start position:0% +picked on this guy and held it fixed and + + + align:start position:0% +picked on this guy and held it fixed and +then this one came down a little bit + + align:start position:0% +then this one came down a little bit + + + align:start position:0% +then this one came down a little bit +it'll of course how will it move it will + + align:start position:0% +it'll of course how will it move it will + + + align:start position:0% +it'll of course how will it move it will +move perpendicular + + align:start position:0% +move perpendicular + + + align:start position:0% +move perpendicular +right small movement it's the bar is not + + align:start position:0% +right small movement it's the bar is not + + + align:start position:0% +right small movement it's the bar is not +going to change length that's the whole + + align:start position:0% +going to change length that's the whole + + + align:start position:0% +going to change length that's the whole +point right the bar is not changing + + align:start position:0% +point right the bar is not changing + + + align:start position:0% +point right the bar is not changing +length + + align:start position:0% +length + + + align:start position:0% +length +so the movement must be it must be a + + align:start position:0% +so the movement must be it must be a + + + align:start position:0% +so the movement must be it must be a +simple rotation around here + + align:start position:0% +simple rotation around here + + + align:start position:0% +simple rotation around here +okay right and of course again you you + + align:start position:0% +okay right and of course again you you + + + align:start position:0% +okay right and of course again you you +might say well the bar really did change + + align:start position:0% +might say well the bar really did change + + + align:start position:0% +might say well the bar really did change +length because uh that's not quite the + + align:start position:0% +length because uh that's not quite the + + + align:start position:0% +length because uh that's not quite the +same as that but then again that's my + + align:start position:0% +same as that but then again that's my + + + align:start position:0% +same as that but then again that's my +second order business okay so that one + + align:start position:0% +second order business okay so that one + + + align:start position:0% +second order business okay so that one +came down and what did this one do came + + align:start position:0% +came down and what did this one do came + + + align:start position:0% +came down and what did this one do came +down the + + align:start position:0% +down the + + + align:start position:0% +down the +same okay and this + + align:start position:0% +same okay and this + + + align:start position:0% +same okay and this +one it also moves + + align:start position:0% +one it also moves + + + align:start position:0% +one it also moves +what do that I guess let me + + align:start position:0% +what do that I guess let me + + + align:start position:0% +what do that I guess let me +so so + + align:start position:0% +so so + + + align:start position:0% +so so +okay what am I going to call this one + + align:start position:0% +okay what am I going to call this one + + + align:start position:0% +okay what am I going to call this one +fix one yeah + + align:start position:0% +fix one yeah + + + align:start position:0% +fix one yeah +fix one node that makes sense I guess + + align:start position:0% +fix one node that makes sense I guess + + + align:start position:0% +fix one node that makes sense I guess +fix one joint yeah and then and rotate + + align:start position:0% +fix one joint yeah and then and rotate + + + align:start position:0% +fix one joint yeah and then and rotate +the rest I think that would be possible + + align:start position:0% +the rest I think that would be possible + + + align:start position:0% +the rest I think that would be possible +yeah okay a small prize for anybody who + + align:start position:0% +yeah okay a small prize for anybody who + + + align:start position:0% +yeah okay a small prize for anybody who +uh + + align:start position:0% +uh + + + align:start position:0% +uh +um maybe maybe + + align:start position:0% +um maybe maybe + + + align:start position:0% +um maybe maybe +handwritten picture of two of of two + + align:start position:0% +handwritten picture of two of of two + + + align:start position:0% +handwritten picture of two of of two +really nice mechanisms somehow this one + + align:start position:0% +really nice mechanisms somehow this one + + + align:start position:0% +really nice mechanisms somehow this one +seems a little unsymmetric in a problem + + align:start position:0% +seems a little unsymmetric in a problem + + + align:start position:0% +seems a little unsymmetric in a problem +that's so symmetric so I I would guess + + align:start position:0% +that's so symmetric so I I would guess + + + align:start position:0% +that's so symmetric so I I would guess +that somewhere along the line we could + + align:start position:0% +that somewhere along the line we could + + + align:start position:0% +that somewhere along the line we could +find a um a kind of more symmetric one + + align:start position:0% +find a um a kind of more symmetric one + + + align:start position:0% +find a um a kind of more symmetric one +but I don't see what it is right now + + align:start position:0% +but I don't see what it is right now + + + align:start position:0% +but I don't see what it is right now +yeah yeah yeah can the whole thing broke + + align:start position:0% +yeah yeah yeah can the whole thing broke + + + align:start position:0% +yeah yeah yeah can the whole thing broke +rotate a + + align:start position:0% + + + + align:start position:0% + +little could could that could that + + align:start position:0% +little could could that could that + + + align:start position:0% +little could could that could that +rotate could the whole thing + + align:start position:0% + + + + align:start position:0% + +rotate yeah maybe it could this guy + + align:start position:0% +rotate yeah maybe it could this guy + + + align:start position:0% +rotate yeah maybe it could this guy +would go up yeah maybe that possible + + align:start position:0% +would go up yeah maybe that possible + + + align:start position:0% +would go up yeah maybe that possible +that somehow got everybody into the + + align:start position:0% +that somehow got everybody into the + + + align:start position:0% +that somehow got everybody into the +action or so maybe or so or I'll put or + + align:start position:0% +action or so maybe or so or I'll put or + + + align:start position:0% +action or so maybe or so or I'll put or +rotate okay so you see what uh questions + + align:start position:0% +rotate okay so you see what uh questions + + + align:start position:0% +rotate okay so you see what uh questions +you get into may I just draw a different + + align:start position:0% +you get into may I just draw a different + + + align:start position:0% +you get into may I just draw a different +truss uh to + + align:start position:0% +truss uh to + + + align:start position:0% +truss uh to +uh so those homework questions are other + + align:start position:0% +uh so those homework questions are other + + + align:start position:0% +uh so those homework questions are other +trusses here's one that I drew in the + + align:start position:0% +trusses here's one that I drew in the + + + align:start position:0% +trusses here's one that I drew in the +book itself + + align:start position:0% +book itself + + + align:start position:0% +book itself +um yeah uh may I may I draw this uh I + + align:start position:0% +um yeah uh may I may I draw this uh I + + + align:start position:0% +um yeah uh may I may I draw this uh I +called it a + + align:start position:0% + + + + align:start position:0% + +treehouse okay so I have so here's one + + align:start position:0% +treehouse okay so I have so here's one + + + align:start position:0% +treehouse okay so I have so here's one +that's that's actually in the book + + align:start position:0% + + + + align:start position:0% + +um and it's got a couple of bars going + + align:start position:0% +um and it's got a couple of bars going + + + align:start position:0% +um and it's got a couple of bars going +up and one over so that's the + + align:start position:0% +up and one over so that's the + + + align:start position:0% +up and one over so that's the +start then it's got a diagonal and that + + align:start position:0% +start then it's got a diagonal and that + + + align:start position:0% +start then it's got a diagonal and that +one and then Here Comes The + + align:start position:0% +one and then Here Comes The + + + align:start position:0% +one and then Here Comes The +Treehouse + + align:start position:0% +Treehouse + + + align:start position:0% +Treehouse +okay + + align:start position:0% +okay + + + align:start position:0% +okay +right okay well just to get let's let's + + align:start position:0% +right okay well just to get let's let's + + + align:start position:0% +right okay well just to get let's let's +again get the count right so what's the + + align:start position:0% +again get the count right so what's the + + + align:start position:0% +again get the count right so what's the +Matrix a for + + align:start position:0% +Matrix a for + + + align:start position:0% +Matrix a for +this this + + align:start position:0% +this this + + + align:start position:0% +this this +treehouse a is how many by how + + align:start position:0% +treehouse a is how many by how + + + align:start position:0% +treehouse a is how many by how +many how many edges how many bars are + + align:start position:0% +many how many edges how many bars are + + + align:start position:0% +many how many edges how many bars are +you seeing here one two 3 four five six + + align:start position:0% +you seeing here one two 3 four five six + + + align:start position:0% +you seeing here one two 3 four five six +seven eight eight + + align:start position:0% +seven eight eight + + + align:start position:0% +seven eight eight +bars and how many unknown + + align:start position:0% + + + + align:start position:0% + +displacements + + align:start position:0% +displacements + + + align:start position:0% +displacements +10 we got five joints that are not + + align:start position:0% +10 we got five joints that are not + + + align:start position:0% +10 we got five joints that are not +supported in each one has two unknowns + + align:start position:0% +supported in each one has two unknowns + + + align:start position:0% +supported in each one has two unknowns +yeah so a is 8 by1 so I expect uh expect + + align:start position:0% +yeah so a is 8 by1 so I expect uh expect + + + align:start position:0% +yeah so a is 8 by1 so I expect uh expect +two + + align:start position:0% +two + + + align:start position:0% +two +mechanisms okay so again I'm looking for + + align:start position:0% +mechanisms okay so again I'm looking for + + + align:start position:0% +mechanisms okay so again I'm looking for +two + + align:start position:0% + + + + align:start position:0% + +mechanisms all right okay what's + + align:start position:0% + + + + align:start position:0% + +one yeah it's + + align:start position:0% +one yeah it's + + + align:start position:0% +one yeah it's +what the this guy just Falls + + align:start position:0% +what the this guy just Falls + + + align:start position:0% +what the this guy just Falls +right this looks unfortunately very much + + align:start position:0% +right this looks unfortunately very much + + + align:start position:0% +right this looks unfortunately very much +like the tree houses that I built for my + + align:start position:0% + + + + align:start position:0% + +kids well so linear algebra sentenced + + align:start position:0% +kids well so linear algebra sentenced + + + align:start position:0% +kids well so linear algebra sentenced +them to uh fall right + + align:start position:0% +them to uh fall right + + + align:start position:0% +them to uh fall right +okay okay that's + + align:start position:0% +okay okay that's + + + align:start position:0% +okay okay that's +one I probably propped it up with one + + align:start position:0% +one I probably propped it up with one + + + align:start position:0% +one I probably propped it up with one +more bar but of course that wouldn't be + + align:start position:0% +more bar but of course that wouldn't be + + + align:start position:0% +more bar but of course that wouldn't be +enough because it's got two Mega so if I + + align:start position:0% +enough because it's got two Mega so if I + + + align:start position:0% +enough because it's got two Mega so if I +make it 9 by 10 I haven't saved the kids + + align:start position:0% +make it 9 by 10 I haven't saved the kids + + + align:start position:0% +make it 9 by 10 I haven't saved the kids +okay so so but let's with 8 by10 what's + + align:start position:0% +okay so so but let's with 8 by10 what's + + + align:start position:0% +okay so so but let's with 8 by10 what's +the other + + align:start position:0% + + + + align:start position:0% + +mechanism ah the whole thing could turn + + align:start position:0% +mechanism ah the whole thing could turn + + + align:start position:0% +mechanism ah the whole thing could turn +the nothing preventing turning here they + + align:start position:0% +the nothing preventing turning here they + + + align:start position:0% +the nothing preventing turning here they +can't move but they could turn so the + + align:start position:0% +can't move but they could turn so the + + + align:start position:0% +can't move but they could turn so the +whole thing could go uh over right the + + align:start position:0% +whole thing could go uh over right the + + + align:start position:0% +whole thing could go uh over right the +whole the whole thing could just that + + align:start position:0% +whole the whole thing could just that + + + align:start position:0% +whole the whole thing could just that +that would be a horizontal movement of + + align:start position:0% +that would be a horizontal movement of + + + align:start position:0% +that would be a horizontal movement of +all five nodes a horizontal of all five + + align:start position:0% +all five nodes a horizontal of all five + + + align:start position:0% +all five nodes a horizontal of all five +nodes + + align:start position:0% +nodes + + + align:start position:0% +nodes +and again slightly downwards but that's + + align:start position:0% +and again slightly downwards but that's + + + align:start position:0% +and again slightly downwards but that's +a second order effect right okay so + + align:start position:0% +a second order effect right okay so + + + align:start position:0% +a second order effect right okay so +that's the that's the second + + align:start position:0% +that's the that's the second + + + align:start position:0% +that's the that's the second +trust okay so this is really + + align:start position:0% +trust okay so this is really + + + align:start position:0% +trust okay so this is really +um like practice for discrete problems + + align:start position:0% +um like practice for discrete problems + + + align:start position:0% +um like practice for discrete problems +of for the problems of plain + + align:start position:0% +of for the problems of plain + + + align:start position:0% +of for the problems of plain +elasticity and the the point is that + + align:start position:0% +elasticity and the the point is that + + + align:start position:0% +elasticity and the the point is that +they there are un two unknowns for each + + align:start position:0% +they there are un two unknowns for each + + + align:start position:0% +they there are un two unknowns for each +point if we're if we have differential + + align:start position:0% +point if we're if we have differential + + + align:start position:0% +point if we're if we have differential +equation so the differential equations + + align:start position:0% +equation so the differential equations + + + align:start position:0% +equation so the differential equations +of plain elasticity are are not really + + align:start position:0% +of plain elasticity are are not really + + + align:start position:0% +of plain elasticity are are not really +simple they're not really simple and 3D + + align:start position:0% +simple they're not really simple and 3D + + + align:start position:0% +simple they're not really simple and 3D +elasticity even more because the we've + + align:start position:0% +elasticity even more because the we've + + + align:start position:0% +elasticity even more because the we've +got we've got movement the the points + + align:start position:0% +got we've got movement the the points + + + align:start position:0% +got we've got movement the the points +are physical points and they can move + + align:start position:0% +are physical points and they can move + + + align:start position:0% +are physical points and they can move +three ways and and uh it it gets quite + + align:start position:0% +three ways and and uh it it gets quite + + + align:start position:0% +three ways and and uh it it gets quite +interesting and and those are the major + + align:start position:0% +interesting and and those are the major + + + align:start position:0% +interesting and and those are the major +problems of computational mechanics + + align:start position:0% +problems of computational mechanics + + + align:start position:0% +problems of computational mechanics +okay let's say holiday time and I'll see + + align:start position:0% +okay let's say holiday time and I'll see + + + align:start position:0% +okay let's say holiday time and I'll see +you uh next Wednesday for chapter + + align:start position:0% +you uh next Wednesday for chapter + + + align:start position:0% +you uh next Wednesday for chapter +3 which moves to partial differential + + align:start position:0% +3 which moves to partial differential + + + align:start position:0% +3 which moves to partial differential +equations \ No newline at end of file diff --git a/n9FTM9f9A6I.txt b/n9FTM9f9A6I.txt new file mode 100644 index 0000000000000000000000000000000000000000..0b4d2a37f90479160ab8d9a59951b6910de3ff9a --- /dev/null +++ b/n9FTM9f9A6I.txt @@ -0,0 +1,363 @@ +align:start position:0% + +in the previous lecture we introduced + + align:start position:0% +in the previous lecture we introduced + + + align:start position:0% +in the previous lecture we introduced +random variables probability mass + + align:start position:0% +random variables probability mass + + + align:start position:0% +random variables probability mass +functions and expectations in this + + align:start position:0% +functions and expectations in this + + + align:start position:0% +functions and expectations in this +lecture we continue with the development + + align:start position:0% +lecture we continue with the development + + + align:start position:0% +lecture we continue with the development +of various concepts associated with + + align:start position:0% +of various concepts associated with + + + align:start position:0% +of various concepts associated with +random variables there will be three + + align:start position:0% +random variables there will be three + + + align:start position:0% +random variables there will be three +main parts in the first part we defined + + align:start position:0% +main parts in the first part we defined + + + align:start position:0% +main parts in the first part we defined +the variance of a random variable and + + align:start position:0% +the variance of a random variable and + + + align:start position:0% +the variance of a random variable and +calculated for some of our familiar + + align:start position:0% +calculated for some of our familiar + + + align:start position:0% +calculated for some of our familiar +random variables basically the variance + + align:start position:0% +random variables basically the variance + + + align:start position:0% +random variables basically the variance +is a quantity that measures the amount + + align:start position:0% +is a quantity that measures the amount + + + align:start position:0% +is a quantity that measures the amount +of spread or the dispersion of a + + align:start position:0% +of spread or the dispersion of a + + + align:start position:0% +of spread or the dispersion of a +probability mass function in some sense + + align:start position:0% +probability mass function in some sense + + + align:start position:0% +probability mass function in some sense +it quantifies the amount of randomness + + align:start position:0% +it quantifies the amount of randomness + + + align:start position:0% +it quantifies the amount of randomness +that is present together with the + + align:start position:0% +that is present together with the + + + align:start position:0% +that is present together with the +expected value the variance summarises + + align:start position:0% +expected value the variance summarises + + + align:start position:0% +expected value the variance summarises +crisply some of the qualitative + + align:start position:0% +crisply some of the qualitative + + + align:start position:0% +crisply some of the qualitative +properties of a probability mass + + align:start position:0% +properties of a probability mass + + + align:start position:0% +properties of a probability mass +function in the second part we discussed + + align:start position:0% +function in the second part we discussed + + + align:start position:0% +function in the second part we discussed +conditioning every probabilistic concept + + align:start position:0% +conditioning every probabilistic concept + + + align:start position:0% +conditioning every probabilistic concept +or result has a conditional counterpart + + align:start position:0% +or result has a conditional counterpart + + + align:start position:0% +or result has a conditional counterpart +and this is true for probability mass + + align:start position:0% +and this is true for probability mass + + + align:start position:0% +and this is true for probability mass +functions expectations and variances we + + align:start position:0% +functions expectations and variances we + + + align:start position:0% +functions expectations and variances we +define these conditional counterparts + + align:start position:0% +define these conditional counterparts + + + align:start position:0% +define these conditional counterparts +and then develop the total expectation + + align:start position:0% +and then develop the total expectation + + + align:start position:0% +and then develop the total expectation +theorem this is a powerful tool that + + align:start position:0% +theorem this is a powerful tool that + + + align:start position:0% +theorem this is a powerful tool that +extends our familiar total probability + + align:start position:0% +extends our familiar total probability + + + align:start position:0% +extends our familiar total probability +theorem and allows us to divide and + + align:start position:0% +theorem and allows us to divide and + + + align:start position:0% +theorem and allows us to divide and +conquer when we calculate expectations + + align:start position:0% +conquer when we calculate expectations + + + align:start position:0% +conquer when we calculate expectations +we then take the opportunity to dive + + align:start position:0% +we then take the opportunity to dive + + + align:start position:0% +we then take the opportunity to dive +deeper into the properties of geometric + + align:start position:0% +deeper into the properties of geometric + + + align:start position:0% +deeper into the properties of geometric +random variables and use a trick based + + align:start position:0% +random variables and use a trick based + + + align:start position:0% +random variables and use a trick based +on the total expectation theorem to + + align:start position:0% +on the total expectation theorem to + + + align:start position:0% +on the total expectation theorem to +calculate their mean in the last part we + + align:start position:0% +calculate their mean in the last part we + + + align:start position:0% +calculate their mean in the last part we +show how to describe probabilistically + + align:start position:0% +show how to describe probabilistically + + + align:start position:0% +show how to describe probabilistically +the relation between multiple random + + align:start position:0% +the relation between multiple random + + + align:start position:0% +the relation between multiple random +variables this is done through a so + + align:start position:0% +variables this is done through a so + + + align:start position:0% +variables this is done through a so +called + + align:start position:0% +called + + + align:start position:0% +called +joint probability mass function we take + + align:start position:0% +joint probability mass function we take + + + align:start position:0% +joint probability mass function we take +the occasion to generalize the expected + + align:start position:0% +the occasion to generalize the expected + + + align:start position:0% +the occasion to generalize the expected +value rule and establish a further + + align:start position:0% +value rule and establish a further + + + align:start position:0% +value rule and establish a further +linearity property of expectations we + + align:start position:0% +linearity property of expectations we + + + align:start position:0% +linearity property of expectations we +finally illustrate the power of these + + align:start position:0% +finally illustrate the power of these + + + align:start position:0% +finally illustrate the power of these +tools through the calculation of the + + align:start position:0% +tools through the calculation of the + + + align:start position:0% +tools through the calculation of the +expected value of a binomial random + + align:start position:0% +expected value of a binomial random + + + align:start position:0% +expected value of a binomial random +variable \ No newline at end of file diff --git a/ol2GRkRam4k.txt b/ol2GRkRam4k.txt new file mode 100644 index 0000000000000000000000000000000000000000..d3a8e0069ad933a24695bce732ed239f5c62d542 --- /dev/null +++ b/ol2GRkRam4k.txt @@ -0,0 +1,3206 @@ +ANNOUNCER: The +following content is + +provided under a +Creative Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: Then let's talk +about exciting physics, the Lamb + +shift. + +So we discussed the +Lamb shift last Friday, + +and the Lamb shift is +really due to the fact + +that, if you have +a atom consisting + +of an electron, a Coulomb +field, and the proton, + +this is not the +complete description. + +The atom lives in a +vacuum, and the vacuum + +is filled with +electromagnetic waves. + +So what we have to include, +for an accurate description + +of atomic level +structure, is the coupling + +of the atomic system, of the +electron, to all of the modes + +the electromagnetic field, +and this is radiation. + +We will talk about the quantized +electromagnetic field later, + +at this point I +could introduce you + +to a simple model, fairly +accurate model of the Lamb + +shift, by simply +assuming, and that's + +what we did on Friday, +that we have fluctuating + +electric fields, those +fluctuating electric fields + +shake, accelerate, the +electron and the electron + +performs some oscillatory motion +and this oscillatory motion + +leads to an ever reaching +of the Coulomb potential. + +And similarly what we +saw for the Darwin term, + +this ever reaching of +the Coulomb potential + +takes away this singularity +of the Coulomb potential + +and therefore lowers the +binding energy of the electron. + +So today I want to just say a +few more words about the result + +we derived, and +then we have done + +what happens to an electron in +a Coulomb field plus radiation. + +The next thing is, then, to +discuss hyperfine structure. + +So let me first make +one comment, when + +we integrated over all modes of +the electromagnetic spectrum, + +we needed an upper +cutoff, and a lower + +cutoff due to logarithmic +singularities. + +Eventually, an upper cutoff +is relativistic rest mass + +of the electron we +have to cut off things. + +I just want to say one more +word about the lower cutoff. + +I suggested, as a cut +off, the orbital frequency + +of the electron. + +So the justification for that +is the following, the electron, + +the free electron-- the free +electron, when it's driven, + +has an amplitude which is 1 +over the frequency squared. + +So if you drive it +slower and slower, + +it's amplitude +increases because it + +has more time to go +in one direction. + +So this divergence at +low frequency, of course, + +happens only for +the free system. + +When you have a bound system, +like a mnemonic oscillate, + +and you drive it at lower +and lower frequency, + +the response converges +to a constant + +and not to 1 over high +frequency squared singularity. + +So therefore, when we reach the +drive and the high frequencies + +on the order of-- oscillatory +frequency of the bound system, + +the behavior changes. + +So when we mimic this with +an effect cutoff because what + +you want to get rid of is a +singularity, but in reality, + +of course, it should approach +a constant at low frequency, + +and that is essentially the +physics of the AC and then + +the DC Stark effect. + +So that was a rational +for the cutoff + +and let me just +annotate it here. + +And let's say, for +a free particle + +we had the situation that the +amplitude was proportional to 1 + +over the high frequency. + +Whereas four bound +particle is, you + +should approach a constant +for low frequencies. + +And that's what we have +introduced with a cutoff. + +OK. + +So we have discussed +the Lamb shift, + +but you've already discussed one +contribution to the Lamb shift. + +So this was a contribution +that the Coulomb potential + +is effectively smeared +out, and the result of this + +is that there is a +weaker binding energy. + +However, there is a second +contribution to the Lamb shift. + +I've sometimes +seen sources where + +this is discussed as the main +contribution to the Lamb shift, + +but this is not correct. + +This is only 3% off the total +and contributes 27 megahertz. + +This is what is called +the vacuum polarization. + +So if you have a-- the +proton positive charge + +and you have the electron, and +they scatter off each other, + +and we use this kind of +diagram to indicate that, + +now that there is an +additional diagram which + +has this bubble which is +this production of e minus + +and e plus pairs. + +And you can say that if an +electron and proton attract + +each other and you create, +by virtual pair production-- + +because the vacuum +is alive, things + +can happen in the +vacuum-- it will virutally + +[INAUDIBLE] electron +positron pair that now you + +create electron positron pairs, +which shield the Coulomb field. + +And this is a +second contribution + +in addition to the shaking +motion of the electron. + +So I want you to just think +about it for 10 seconds + +before I tell you the answer. + +Does this vacuum polarization +strengthen or weaken + +the binding energy? + +Anybody want to +offer an opinion? + +Whatever you say, +you can't be wrong + +because there are to +aspects to the answers so. + +Well then the actual +answer is you would say, + +if you have charged-- +if you create charges + +between the electron +and the proton, + +you have a shielding effect +and the shielding effect + +should weaken the Coulomb field. + +But the question is, +what do we regard + +as the elementary charge, e, +in our Schrodinger equation. + +And what we regard +as the charge, what + +is measured in a Millikan +Droplet experiment, + +is already the shielded charge. + +So therefore, the fact +that vacuum polarization + +exists means we always +measure the shielded charge, + +but because vacuum polarization +happens at a finite distance, + +the electron, in an s state, +can sort of penetrate the shield + +and feel a somewhat +stronger Coulomb potential. + +So therefore, +accounting for the fact + +that we have these +virtual electron + +positron pairs actually +means that the binding energy + +is increased and the +vacuum polarization + +has the opposite sign +as the dominant effect + +we've mentioned earlier. + +So the sum of e is, we observe +the shielded charge and vacuum + +polarization implies that +the s electron can penetrate + +the shield and sees +a higher charge. + +So we normally observe +the shielded charge, + +but the electron can +see the higher charge. + +So therefore, that means, now, +that we have, not an upshift + +in energy, but a downshift in +energy for-- which for the two + +is one half state, +is 27 megahertz, + +as I mentioned earlier. + +Anyway, I'm not +really deriving it, + +but I want to sort of uncover +certain myths, so the vacuum + +polarization, number one, is +not dominant and number two, + +has the opposite sign as +everybody would naively assume. + +Questions? + +I hope not because I don't +know anything more about that. + +All right. + +So we have dealt +with Lamb shift. + +So is next now, in revealing +the atomic structure, + +is we want to go beyond +the Coulomb field created + +by a point charge. + +And that means we want to +address the fact that we don't + +have a point charge, +but we have a nucleolus. + +And we are discussing, now, +effects of the nucleus, which + +also go by the name +hyperfine structure. + +So, just to summarize, +so far we have + +treated, in pretty much +complete detail, what + +happens for an atom which +consists of a point charge + +and electrons. + +But now we want +to bring in that, + +what creates a Coulomb field, +the nucleolus, has structure. + +And there are actually +four different ways + +how the nucleolus has +structure and contributions + +to observable effects +on the atomic structure + +and atomic energy levels. + +The most important one +is that the nucleus + +has a magnetic moment +associated with the angular + +momentum of the nucleus I. + +The second contribution is, in +addition to magnetic moment, + +there may be a +quadrupole moment. + +And since those effects can +lead to a splitting-- this + +is actually, usually, +called hyperfine structure, + +but then there are +two more effects. + +One is the nucleus +has finite mass, + +and the nucleus has +a finite volume. + +Both the mass and volume +effect lead to energy shifts. + +But tiny energy shifts +are hard to measure + +unless you have two +different shifts, + +and therefore those effects +go as isotope shifts + +because when you +have an atom which + +comes in two +different isotopes you + +find that, due to +those two effects, + +the energy levels +are not the same. + +So this goes by the +name of isotope shifts. + +By far the most important +phenomenon is the first one. + +The fact that if a nucleus +has angular momentum, + +we have hyperfine structure, +and for the hydrogen atom + +that means that the ground +state, the singlet S 1/2 state, + +actually splits into two states +with total angular momentum + +quantum number F. + +So the relevance of +hyperfine splitting + +is, it's actually +a huge relevance, + +one is, you don't have a single +ground state of many atoms, + +you have several ground states. + +So the lowest electronic state +has several ground states, + +has several hyperfine states, +due to angular momentum + +selection, where +you can actually + +talk to them individually, you +can prepare them individually, + +and many of you who do +magnetic trapping know when + +need magnetic trapping +you better prepare + +the atom in a single +hyperfine state, + +otherwise you are in trouble. + +So you can prepare +individual states. + +In the old days this was +done by optical pumping, + +and you can use several +hyperfine states + +to great advantage for +the manipulation of atoms. + +For instance, if +you want to, you + +can put atoms into +a hyperfine state + +where they don't absorb +light, and then you + +can have resonant light for the +other ones blast those away. + +So you can play, sort of, +your tricks because you + +have two states between which +you can juggle at the atoms. + +Well, what else is relevance +of hyperfine structure? + +OK if you have two levels, +F equals 1, F equals 0, + +you can observe a transition. + +And the famous 21 +centimeter line + +is used for astronomical +observations. + +Hydrogen is the most abundant +element in the universe, + +and how do you see +hydrogen out there. + +Well it is due to hyperfine +transition, the 21 centimeter + +line. + +And finally, another aspect +why hyperfine structure + +is relevant, where +people use it, + +is for the determination +of nuclear properties. + +How do you know what the +properties of nuclei are? + +Well there are techniques +in nuclear physics, + +but a lot, a lot about +the knowledge of nuclei + +comes from atomic spectroscopy. + +If you measure atomic energy +levels with high accuracy, + +you figure out what the +properties of the nucleus is, + +and one of the most outstanding +examples we will discuss later + +on, and some of which is also +on your homework assignment, + +is you can use atomic +spectroscopy of hydrogen + +to contain the most +accurate measurement, how + +big is the proton. + +And the big surprise is that +there is, that there was, + +a surprise that +people figured out + +that, until now, even +in 2014, we do not fully + +understand how big the +proton is but we'll + +talk about that later. + +So for the level of this-- the +level of this introduction, + +we can use it for determination +of nuclear properties + +and actually, you cannot only +determine properties of stable + +nuclei, you can also determine +properties of unstable nuclei. + +At various accelerators, +they have a facility + +when, by, you know, +energy collisions + +they create unstable nuclei. + +Maybe helium six, helium +with four newtons, it exists. + +And you can take helium +six, extract it, utilize it + +and then you've have +a neutral helium + +atom which looks like your +every days helium atom + +but it has two more +neutrons in the nucleus. + +And by performing +atomic spectroscopy, + +you can figure out what +is the deformation, what + +is the structure, of this-- +I want to say alpha particle, + +but it's an alpha particle +plus two neutrons. + +So people have really learned +to do those atomic physics + +measurements within +a few seconds + +after the element +has been produced, + +and such determined +nuclear properties even + +of unstable nuclei. + +OK. + +So that's my introduction. + +So we are now discussing +the most important effect + +due to the hyperfine structure. + +And this is the fact +that the nucleolus has + +a magnetic moment, and +this magnetic moment + +couples to the +magnetic field even + +if you don't apply an +external magnetic field, + +we talked about that +on Wednesday, there + +is an internal +magnetic field created + +by the electron with total +angular momentum change. + +So this is, so to speak, +the Zeeman Hamiltonian + +of the nucleus in the magnetic +field created by the electron. + +And I will show you quickly +to, is a simple derivation, + +what the result of that is. + +But before I do that, I +also want to mention out-- + +mention that there is-- +I want to point out + +that there is an alternative. + +Right now, I said we say +the nucleus experiences + +the magnetic field +created by the electron. + +But we can also take +the other approach, + +the nucleus creates a +vector potential because + +of its magnetic moment, +and the electron, + +which goes around the +nucleus, is not only + +feeling the Coulomb +potential but also + +feeling a vector potential. + +And of course, both +different perspectives, + +whether the electron moves in +the magnetic field the nucleus, + +or the nucleus experiences the +magnetic field of the electron, + +both treatments have to agree. + +I follow the more +standard treatment, + +but the alternative treatment, +where the electron moves + +in this electric and magnetic +potential of the nucleus, + +is fully elaborated on +the atomic physics wiki. + +So alternatively, electron +moves in the potential + +of the nucleus, which is +the Coulomb potential, + +we've discussed that, +but then there is also + +vector potential created by the +magnetic moment of the nucleus. + +So you simply assume this +is a potential created + +with a nucleus, +and then you just + +sort of Schrodinger's +equation and this approach + +is carried out on the wiki. + +However, since it's a +little bit more standard, + +and there's an easy +semi-classical derivation, + +let me now discuss this one. + +Because what I +like about it is it + +addresses one intuitive +quantity, namely the fact + +that there is an +internal magnetic field. + +We're not just using +the Schrodinger equation + +for the whole +system, we are really + +estimating what is the +magnetic field, which + +the electron creates, at +the position of the nucleus. + +So let's now do a +semi-classical derivation + +of this internal magnetic field. + +And I have to-- I will +immediately tell you, + +this derivation +agrees quantitatively + +with the fully +thermomechanical treatment. + +So, as often as these +semi-classical derivations, + +we have to separate two parts. + +There are two ways how +the electron creates + +a magnetic field at the nucleus. + +One is due to it's +orbital motion, + +the electron is a ring current +and creates a magnetic field, + +but then the electron has +magnetic moment for-- due + +to it's spin. + +The spin part is simply the +potential of a magnetic dipole, + +you will need to vector-- +you will need to vector where + +the magnetic dipole +moment of the electron + +is proportional to it's +spin with a g factor. + +However, and you can find +that in all textbooks + +on classical +electrodynamics but, there + +is one important term +which we have to add here, + +which is also part +of classical E and M, + +and this is the delta +function contribution. + +You've probably seen it, +you find it in Jackson, + +if you haven't the +model is that you + +can assume that a +magnetic moment is created + +by ring current, +and the ring current + +has-- creates a +magnetic moment and you + +have the dipole potentially +due to the magnetic moment. + +However, if you +have a ring current, + +there is-- you +can also ask, what + +is the magnetic field +inside the current loop + +and then eventually do +the transition where + +you allow the current +loop to go to 0. + +That's how you make a point +model of a magnetic dipole, + +but what remains is, sorts +of-- as a delta function, + +the location inside the loop. + +I'm emphasizing it +because it will be, + +eventually, the delta +function contribution, + +which is important +for s electrons, + +and therefore it is +this contribution + +which is the dominant +effect in many situations. + +OK. + +So this is the magnetic +field created-- + +it's a classical expression, +but it's buried in [? quantum ?] + +mechanics, the expression for +the magnetic field created + +by the spin. + +The second contribution is +the orbital contribution, + +and for that semi-classical, +we just use Biot-Savat. + +So Biot-Savat is usually +the 3-Dimensional integral + +over the current density. + +The volume integral, +or you can rewrite it + +as the current I, d, r +cross r, over r cubed. + +And eventually, if you now +put in the electron charge + +distribution, velocity +course r, well, + +velocity cross r means we +get, and that's what we want, + +the orbital angular momentum. + +The 1 over r cubed +term means we have + +to calculate an expectation +value over the wave + +function which, +is 1 over r cubed. + +And the prefactor +leads us-- it's + +nothing else than two +times the Bohr magenton. + +So, with those two terms, we can +now obtain our final expression + +for the total magnetic +field generated + +by the electron at the origin. + +And for that I use +the g factor of two + +as it comes out of Dirac theory. + +So now we have the +total magnetic field. + +We had this contribution +L over r cubed. + +If you inspect the dipole +potential of the spin + +it has a contribution +S over r cubed, + +then it is the +second contribution + +to the dipole potential. + +And finally, most importantly +for the following discussion, + +the delta function contribution +which I discussed earlier. + +If you have an s state, +these first terms + +are 0 for L equals 0 because +these are, sort of, terms which + +have dipole potential +where positive and negative + +contributions cancel out when +you do a spherical average, + +and the s electron performs +a spherical average. + +So it is 0 for L equals 0 +due to the spherical average. + +Whereas the second part, it +would be 0 for L non-equals + +to 0 because the probability +for a non-s electron + +to be at the nucleus is 0. + +So pretty much this +describes that. + +So this describes a +hyperfine structure. + +Well, it describes the magnetic +field created by the electron, + +and now we have to do +the usual projection + +in the following way. + +That the hyperfine structure +is that Zeeman Hamiltonian + +of the internal magnetic +field with a magnetic moment + +of the nucleus, and the +magnetic moment of the nucleus + +is proportional to the angular +momentum of the nucleus. + +Sort of this argument that even +if it were not proportional, + +it would rapidly precess +and eventually project it, + +and the only direction +which survives + +is the direction of +the angular momentum. + +And similarly, you can-- +the magnetic field, + +you have a contribution +of S and L, + +but S and L rapidly precess +around the result and angular + +momentum, J, and +therefore, as a result, + +the internal magnetic +field must be, + +can only be, parallel to +the angular momentum chain. + +If you do a fully +[? quantum ?] treatment, + +it comes out immediately. + +But if you do it +semi-classically, you calculate + +a magnetic field, you sort of +have to fall in this argument + +that you always project on +the axis of angular momentum + +and that means that the +hyperfine interaction will + +be the Hamiltonian for +it, or the operator, + +will be the dot product of +I dot J. For fine structure, + +we had L dot S, for hyperfine +structure, we had L dot J, + +this is always how we couple +angular momentum with a dot + +product. + +The hyperfine constant +cause by the letter + +a, and since historically a is +measured in frequency units, + +in Hertz, I have to put +in h, Planck's quantum. + +No it's not h bar. + +For historical reasons, it's h. + +AUDIENCE: Question. + +PROFESSOR: Yes? + +AUDIENCE: Are I and +J dimensionless, + +or will they carry +units in h bar? + +PROFESSOR: Here they +are dimensionless, + +thanks for the question, because +each is in frequency units, + +it's in Hertz, and if +you multiple with h + +you have an energy. + +So therefore, I and J +measure the angular momentum + +in unit of h bar. + +So it's not in that sense, it's +a normalized angular momentum + +operator. + +The quantum numbers of I and +J are not 1/2, or 1h bar, + +it's just 1/2 or 1. + +Other questions? + +OK. + +I can now take this expression +with, you know, L and S + +and S.r and evaluate +further, but I + +feel I'm not +providing any insight + +and you can read +about it on the wiki. + +So for a non-s state, how +to simplify this expression + +and get the final textbook +result, I defer to the wiki. + +I want to discuss the most +important part, namely for s v + +electrons because hydrogen, +all the alkaloids, + +have an s ground state. + +So, in that case, all we have to +consider is the delta function + +part and if we project +the magnetic field + +onto the angular +momentum axis, we + +get the probability of the s +electron to be at the origin. + +And therefore, for s states, +the hyperfine constant + +is-- oh, I forgot one thing. + +We have to parametrize the +magnetic moment of the nucleus, + +and that is done by using +a nuclear magnetron. + +It's the same as a +Bhor magneton, where + +you have replaced the electron +mass by the proton mass, + +and you have the +nuclear g factor. + +Just as a reminder, the g +factor of the proton is 5.6, + +the g factor of the +neutron is minus 3.8. + +So the g factor has nothing +to do, not even close, + +to the factor of 2, which we +obtained in the Dirac equation + +for the electron. + +That just shows that the +nucleons, protons and neutrons, + +are more complicated. + +Well, they have +quarks inside, they + +have a complicated +internal structure. + +OK. + +So therefore the hyperfine +constant involves, + +now, the g factor +of the nucleus, + +the product of the +nuclear magnetron, + +with a Bohr magneton, +and for hydrogen. + +This gives the famous +result of 1420 megahertz. + +So this is hydrogen, and this +h is now the Hamiltonian. + +So the hyperfine coupling +Hamiltonian, which has I + +dot J, by using the expression +for the total angular momentum + +I plus J and then we square it. + +When you evaluate +this square you get, + +on the right hand side, +an expression for I dot J. + +So I dot J is nothing +else than 1/2. + +F squared, minus I +squared, minus J squared. + +And therefore, for hydrogen, +where I, J and S are all 1/2, + +the proton has been +1/2, the electron + +has been 1/2, that's it. + +You have only two values of +the result and total angular + +momentum, 1/2 and 1/2 +can add up to 1 or 0. + +And now the hyperfine +splitting is into an F equals 1 + +and F equals 0 state. + +And one thing to remember is, +if you inspect the above formula + +with the [? quantum ?] +numbers you find immediately + +that, compared to +the degenerate line, + +without hyperfine +splitting, this-- + +so what comes out of +the Dirac equation, + +the splitting is the +fight-- is 1/4 and 3/4 + +of the hyperfine constant. + +Since F equals 1 has a +multiplicity of 3, 2 and F + +quantum numbers, +plus minus 1 and 0, + +the rule is that the center +of mass of this level + +does not change due to +hyperfine splitting. + +So the center of mass +of hyperfine states + +is not changing. + +So we introduce a +level splitting, + +but no overall shift. + +Any questions about magnetic +hyperfine structure? + +Yes? + +AUDIENCE: Would you explain +again the center of mass + +is not changing. + +Is this just for hydrogen? + +Or is this a general rule? + +PROFESSOR: No, this +is a general property, + +and you could actually +show that when you evaluate + +the product of I dot +J. So, the product of I + +dot J means that for arbitrary +I and arbitrary J, if you + +calculate the hyperfine +structure, the center of mass + +is the same. + +OK. + +I've not done any +experiment in my life + +where higher order +moments became important, + +but I want to teach you about +it because the discussion + +about whether those +higher moments exist + +or not is really an interesting +discussion about what + +is allowed by symmetry +and what's not. + +So I'm bringing in +a higher moments, + +not so much because you need +it to understand the level + +structure of your +favourite atom, + +but because it teaches us a +really nice piece of physics. + +So let me now discuss higher +order moments and the leading + +one is the electric +quadripole moment. + +So I want to raise, in +general, the question, + +what further moments +can a nucleus have. + +What we have discussed so far +is the magnetic moment, mu. + +So beyond mu, what further +electric or magnetic moments + +can a nucleus have? + +Well, it's a question +about symmetry + +and if you look at the +parity of multiples, + +if you have an electric +multiple-- well, + +you know if you have a dipole, +plus minus, you invert it, + +the dipole becomes +minus the dipole. + +So for L equals 1, it +is minus 1, L is 1, + +but in general +the it is minus L. + +If you have a quadripole, you +invert your coordinate system. + +It's L equals 2, plus +plus, minus minus, + +you invert it nothing changes. + +So these I've shown you, +for dipole and quadripole, + +that this formula is correct. + +So an electric multiple +has this parity, + +and for, magnetic +keys-- now, you + +know, magnetic we have axial +vectors versus polar vectors, + +there's always an extra +factor of minus 1. + +So therefore if you go magnetic, +magnetic multiples with L + +have a parity of minus L plus 1. + +So this really restricts +what multiples are possible. + +Instead of giving you +a general discussion, + +let me just look at the +very important keys. + +Whether a magnet with a nucleus +can have a electric dipole + +moment, and you will immediately +see what it needs to-- and then + +I give you a general result. + +So let's assume a nucleus +has angular momentum I, + +and there is a magnetic +moment, mu associated with it. + +So the general result is +that odd electric and even + +magnetic multiple moments +would violate not just one, + +but two symmetries, would +violate parity and time + +reversal symmetry. + +So the argument goes as follows. + +Let us assume this is +the magnetic moment, mu + +or the angular momentum +I, it's a vector. + +And now we are asking, +is it possible to have + +a vector of the dipole moment. + +And dipole moment, you +should just think about it + +as a plus minus +charge, separated. + +We can now do the parity +operation and the time reversal + +operation. + +If you do the time +reversal operation, + +the current, which +generates a magnetic moment + +if you want to think +about it in this picture, + +goes the other way. + +So mu flips but nothing +moves, of course, + +for an electric dipole +moment, so reversing time + +is not changing anything. + +So in other words, +time reversal symmetry + +transforms parallel mu and d +into anti-parallel mu and d. + +And similar, parity +is not changing mu + +but it is changing d. + +So in both cases, would parity, +or time reversal symmetry, + +if you had mu-d, a +scalar product of mu + +and d which would be +known 0, then both P or P + +would change the sign. + +But that would mean that two +kinds of particles would exist, + +one where the sign is positive, +one where the sign is negative. + +But we have assumed that we have +1 nucleus and only 1 nucleus + +of this kind, so we cannot +have one nucleus which has + +the properties of +having, simultaneously, + +a magnetic and +electric dipole moment. + +So therefore, we conclude +that mu times d has to be 0. + +And if you generalize +this argument, + +we have ruled out that +there is an electric dipole + +moment, an odd electric moment. + +The first, the lowest, +possible electric moment + +is the quadripole moment, so the +leading electric moment is not + +L equals 2, L equals +2, it's not L equals 1, + +the dipole, it's L +equals 2 the quadripole. + +And of course if you +generalize the argument, + +L equals 4, L equals +6, would be possible + +but those effects +would be very small. + +Questions so far? + +OK. + +So we've talked about parity and +time reversal symmetry, which + +restricts what kind of magnetic +and electric dipole moments + +particles may have. + +And maybe in this +context, I should just + +mention that John Doyle, Jerry +Gabrielse, and Dave Demille + +at Harvard and Yale, they just +published the most accurate + +result for the electric +dipole moment of the electron. + +They found a bound, which was +more than an order of magnitude + +lower than the best +upper bound before + +and this has really +made headlines. + +So to measure, accurately, +that the electric dipole + +moment vanishes, in this +case of the electron, + +but other people do +it also for neutrons, + +is testing fundamental +symmetries. + +In particular, it +tests whether nature + +is time reversal invariant. + +And the reason why, +until now, everybody + +has found that the results +are compatible with 0 + +is pretty much based on the +argument I just gave you. + +OK so we have discussed +those fundamental symmetries, + +but now I want to discuss +something else related to it. + +So let's assume +you have a nucleus, + +and I want to discuss with +you, is a minimum requirement + +for the nucleus for the +angular momentum of the nucleus + +in order to have +a magnetic dipole, + +or to have an +electric quadripole. + +So let's formulate it +as a quicker question. + +So here let's assume a is-- +it's possible for any nucleus + +no matter what the +angular momentum is. + +Here, we put in 1/2, +or larger than 1, + +and for the electric quadripole +we have the same choices. + +So you should decide +if I tell you, + +a nucleolus has a +magnetic dipole. + +Does that imply that +there is a minimum amount + +of angular momentum +of the nucleus there? + +And then repeat +the same question + +for the electric quadripole. + +So please tell me your opinion. + +So right now, what is +a minimum requirement + +for I, for magnetic dipole, +and if yes, what is it? + +Three, two, one. + +Stop. + +OK, so-- and let's +immediately consider + +the electric quadripole moment. + +So this was a majority opinion. + +I gave this answer for +both of them together. + +So the question is, what +is the minimum requirement + +for a nucleus to have an +electric quadripole moment. + +OK, stop. + +Display. + +No requirement. + +OK. + +So the majority +onset was a here. + +So let me to discuss it, +and I know some of you + +will have-- I always get into +heated discussions with it. + +I actually just had a few +minute discussion with one + +of my colleagues about +it, who at least wanted + +to look at it from a different +perspective than I did. + +So let me give you +the short answer + +and we can go from there. + +In order to the magnetic dipole +you have to take an object, + +turn it around, and +figure out that there's + +a different energy. + +So therefore, unless +you have an object, + +which is has two orientations, +you cannot figure out if it has + +a magnetic dipole or not. + +If you're in a state without +angular momentum, I equals 0, + +there is no +distinguishable states. + +You cannot orient a 0 angular +momentum object in space. + +So therefore you +can never figure out + +that there's a magnetic +moment, and now I'll + +make a bold statement, +and this means + +there is no magnetic moment. + +So therefore, you +need this because you + +need a minimum number +of true orientations. + +OK. + +Now an electric quadripole +means that the charge density + +is like ellipse. + +It has-- + +AUDIENCE: [INAUDIBLE] + +PROFESSOR: Oh, 1/2, sorry. + +Thank you. + +So I should get larger +than 1/2 because we + +need a minimum of two +possible orientations. + +Now my question for you is, you +think something is elliptical + +but how many different +orientations do + +you need to figure out that it +is elliptical and not round. + +If I equal 0, you can only look +at it, you can't rotate it, + +so will you never find any +energies [? breathing. ?] + +It's just there and you cannot +say where it's round or whether + +it has a quadripole +or deformation. + +If I is equal to 1/2, you can +take it and flip it around + +but can you tell from +that that it's an ellipse. + +No because if you turn an +ellipse around nothing changes. + +So it could be, +as well, a sphere. + +You can only figure +out that it's + +an ellipse if you have +an intermediate rotation, + +let's say, by 90 degrees. + +So in order to assess that +something is elliptical, + +you have to at least resolve +three positions, three angles, + +and three angles require that +you have to three sublevels + +and this requires that I is +larger, or equal, than one. + +Sorry. + +Then one goes-- OK. + +I'm want to give you a +formal argument using + +this spherical +tensor, but I guess + +someone you are waiting +for something simpler. + +So. + +I mean who wants to know +the answer of the question, + +but what happens if +it has a deformation. + +Does it just mean +we can't measure it, + +but it has a deformation? + +Let me explain that. + +So if I have a pencil and +the pencil has zero angular + +momentum, I can't +really figure out + +that it's an elongated object, +because all I measure is + +a symmetric wave function. + +It's completely +spherically symmetric. + +The only way to figure +out that it's a pencil + +is I have to localize +it, that I can + +see that it's +pointing somewhere. + +But to localize +an object in space + +is actually an +angular wave packet. + +It's not isotropic. + +It points somewhere. + +And an angular wave +packet is a superposition + +of states of different +angular momenta. + +So therefore, without assuming +that there is a state with + +angular momentum, I +cannot orient this pencil. + +OK. + +I know you would all agree that +even if this pencil is cooled + +to the ground state with +zero angular momentum, + +it is a pencil. + +But what you're using +here is now your knowledge + +that this object has higher +angular momentum states. + +And those higher +angular momentum + +states have nothing to do with +the structure or the appearance + +of this object of +being a pencil. + +So you sort of know that +in addition to the i + +equals 0 state, there are i +equals 1, 2, 3, 4, 5 states, + +and the pencil looks the same. + +But if you have a +nucleus, an i equals + +0 state requires a certain +configuration of quarks. + +And you cannot create an i +equals 2, and i equals 4, + +higher states without messing +around with the internal + +structure. + +So with a nucleus, all you +have is an i equals 0 state. + +And to say that this i equals +0 state has a quadrupolar + +deformation doesn't +make any sense. + +If you would know that this +nuclear state could be rotated + +without changing its internal +structure, then you would say, + +yes, it has a quadrupole +moment, I just can't see it. + +But usually, you cannot +make this assumption. + +If all you have is an i +equals 0 ground state, + +and the i equals 2 state +is very, very different, + +because the quarks are +spinning around each other + +in a different way, +you have to see, + +i equals 0 is +completely spherical. + +It doesn't couple to +anything externally. + +And therefore, it has +no moments whatsoever. + +So that's the story. + +A lot of people get +confused, because they + +think an object can have a +deformation without rotating. + +But you need the +rotation to resolve it. + +If you cannot create +an angular wave packet, + +which is a superposition +state of angular momenta, + +you can never figure out +that there is a deformation. + +And quantum mechanically, if you +cannot figure out that there is + +a deformation, there +is no deformation, + +because you can only use, in the +language of quantum mechanics, + +where you have at least the +possibility to measure it. + +Questions about that? + +OK. + +I think that makes it now-- +let me now kind of just + +give you a formal. + +A formal derivation. + +But I agree. + +I mean, the formal +derivation, I'm + +just throwing a few equations +at you, and say, that's it + +and everything +follows from that. + +But I provided the +insight for you. + +Formally, you can define +the quadrupole moment + +by the expectation operator. + +You take the nucleus +with maximum MI. + +And now you calculate +the expectation value + +of this operator. + +This is, of course, motivated +by just electrostatics. + +If you take an expansion of the +classical electrostatic energy + +into multi-poles, you find +the quadrupole configuration + +to be related to a +quadripole moment. + +Quadrupole moments couple to the +derivative of electric fields. + +And then in this purely +classical description, + +you have this +term, where beta is + +the angle between two +symmetry axis, namely, + +between the symmetry axis of +the electric field gradient + +and the quadrupole tensor-- just +the classic quadrupole tensor + +as it comes out of Jackson. + +Yes. + +You can see the quantum +mechanical definition + +of the quadrupole moment, +or more generally. + +So this is quadrupole moment. + +If you have a moment +with l, the operator, + +which tells you whether you +have a non-vanishing moment, + +a non-vanishing +deformation, is actually + +a spherical tensor, Tlm. + +And what you see above +is a spherical tensor, + +T20-- l equals 2, m equals 0. + +And those spherical tensors +are defined by the fact + +that they transform as +spherical harmonics. + +And now you sort of +realize what it means. + +If you want a magnetic or +electric moment with l, + +the operator for the +moment transforms + +like angular momentum l. + +And now you realize that +you have the triangle rule. + +If you want a matrix element +where I and l overlap with I, + +you want to make sure +that I, l, and I couple. + +And you have a triangle rule. + +So therefore, if you +want a magnetic moment, + +or electric moment, of l, and +you evaluate this expectation + +value, well, at least +the triangle rules + +can only be justified like this. + +Or in other words, you can +only get a non-vanishing moment + +if l is smaller than 2I. + +And this is what we discussed +in the clicker question + +for the two cases of l +equals 1 and l equals 2. + +So ultimately, it's +a selection rule + +which is related to +the triangle rule + +for the addition +of angular momenta. + +But I like much +better the argument, + +how many orientations +do you need + +to find out that +something is elliptical? + +It's formalized here. + +All right. + +Let's just spend one more minute +on the quadrupolar structure. + +So based on the expansion of +the electrostatic energy, what + +determines the +quadrupolar structure + +is this cosine angle, +which is the angle + +between the axis of the +nucleus and the axis + +of an electric field gradient. + +And that means it is the angle. + +It's a cosine of +the angle between J, + +the outer environment, and +I, the axis of the nucleus. + +So therefore, when we would +derive-- I'm not deriving it, + +but if we would derive an +expression for quadrupolar + +structure, the +quadrupolar structure + +would be proportional +to a quantity C, which + +is nothing else than the +dot product of I and J. + +And at least in my notes now, +I and J have units of h bar. + +So I'm dividing it out here. + +And as you know, I, +dot, J can be expressed + +by quantum numbers F, F +plus 1, minus I, I plus 1, + +minus J, J plus 1. + +So therefore, the +quadrupolar energies-- E2, + +El equals 2-- involve +the classical expression + +at cosine square. + +So therefore, you would expect +there is a quadrupole constant. + +And then it is cosine square. + +But well, usually, +quantum mechanic + +even, we have the +square of a quantity, + +we have to write it as +quantity times quantity plus 1. + +So this is the +quadrupolar structure. + +And to remind you, +we just discussed + +that for the hydrogen atom, the +magnetic hyperfine structure + +had invoiced the same product of +I, dot, J, but in a linear way. + +So the reason why I'm not +discussing quadrupolar + +structure in more +detail is usually + +the hyperfine +structure associated + +with quadrupole moments +is much, much smaller + +than the hyperfine +structure associated + +with magnetic moment, +typically by a factor of 100. + +The only exceptions +are molecules, + +because molecules +can have-- because + +of molecular binding +mechanisms-- a much, much + +larger electric field gradient. + +So therefore, in molecules, +quadrupolar structure + +is more important than in atoms. + +Questions about that? + +With that, we have +discussed the two effects + +of hyperfine structure due to +magnetic moment of the nucleus. + +And we also discussed further +deformations of the nucleus, + +in particular, the +quadrupolar deformation. + +Let me now use the +last 10 minutes + +to quickly discuss with +you isotope effects. + +And I know that many people +here know about isotope effects, + +because if you lock your +laser to a lithium cell + +or to a rubidium cell, you find +lithium-6 and lithium-7 peaks. + +And in rubidium, +rubidium-85 and rubidium-87. + +So there are two peaks which +are spectrally very, very + +well resolved. + +And now I tell you what causes +the splitting between the lines + +of rubidium-85 and rubidium-87. + +Well, the first effect +is really trivial. + +It's the mass effect. + +And I have to remind +you that the Rydberg + +formula for a single +electron energy level + +contains the reduced mass. + +In other words, +the energy levels + +are the energy +levels-- if you assume + +that the mass of the nucleus is +infinite, that means you just + +take for the electron mass +in the Rydberg constant + +the electron mass. + +But in general, you have +to take the reduced mass-- + +the big M is the nucleus. + +And small m is the electron. + +The simplest case is if you set +the nuclear mass to infinity. + +Then you simply have the Rydberg +constant with the electron + +mass. + +So in the limit that +the nuclear mass is + +much larger than +the electron mass, + +this correction factor is 1 +minus little m over big M. + +So therefore, the correction +factor is on the order of 10 + +to the 4 or 10 to the 5. + +Visible frequencies are on +the order of 10 to the 14. + +So 10 to the minus 4 or +10 to the minus 5 of it + +is between 1 and 10 gigahertz. + +So this is the scale +for mass corrections + +due to the isotope effect. + +What is the sine of +the isotope effect? + +Does the fact that the +nucleus has a finite mass-- + +does that mean that the +binding energy of the electron + +is smaller or larger? + +AUDIENCE: [INAUDIBLE] +it would be larger. + +PROFESSOR: The absolute +value of the binding energy-- + +look at your signs. + +I would say it in the following. + +Let's start out with +an infinite nucleus, + +and only the electron is moving. + +But now we make the +nucleus lighter. + +And that means the +nucleus also has to move, + +because it's a two-body problem. + +And there is additional +kinetic energy, + +additional kinetic +energy of the nucleus. + +And kinetic energy is positive +and weakens the binding energy + +of the total system. + +So therefore, the fact that the +effective mass correction means + +the lighter the nucleus +is, the more kinetic energy + +has to be added to the system +for the nuclear motion, + +and the more the binding +energy is weakened. + +The most dramatic example +is not the hydrogen atom. + +It is positronium, where your +nucleus is not a nucleus, + +it's a positively charged +electron to the positronium. + +And in this situation, +you have an effective mass + +which is only 1/2 of +the electron mass. + +And the 1s-2s transition, which +is Lyman alpha for hydrogen, + +is now not even +in the vacuum UV, + +it just happens at +ordinary UV transitions. + +And that means now +the 1s-2s energy + +is smaller by a factor of 2. + +That really means the binding +energy between an electron + +and a positron is only +50% of the binding energy + +of an electron in +the hydrogen atom. + +OK. + +That's all I want to say +about the mass effect. + +Let's now talk about +the volume effect. + +So if you would look at +the charge distribution + +in a nucleus as a function of +r, if we go from one isotope + +to a heavier isotope +with more neutrons, + +the nuclear radius +becomes larger + +and the charge becomes +more spread out. + +So if I plot now the +electrostatic potential, + +the electrostatic potential +is, of course, the Coulomb + +potential, 1 over r, until we +enter the charge distribution. + +And then, as you know from +electrostatics, it continues. + +This is 1 over r. + +And then it's flattened off. + +It continues quadratically +for the heavier-- oops, + +I wanted to change color. + +For the heavier nucleus, +it is like this, + +and for the lighter +nucleus, it is like this. + +So in other words, the +finite size of the nucleus + +is cutting off the +Coulomb potential + +where it is strongest. + +And this happens the +earlier, the larger, + +or the heavier the nucleus is. + +So therefore, what you +obtain is you obtain, + +in perturbation +theory, a level shift. + +Since it only affects +the electron when + +it's very close to the +origin, this level shift + +is, as other effects we +have discussed today, + +proportional to the +probability of the electron + +to be at the center. + +This is only s +electrons are effected. + +What is the effect +in terms of energy? + +Well, it's clear the Coulomb +potential is weakened. + +Therefore, this effect, +the volume effect weakens, + +decreases the binding +energy of the electron. + +So we have two effects now-- we +have the volume effect, which + +is the stronger the bigger and +the heavier the nucleus is. + +So it's largest +for heavy nuclei. + +And the mass effect, or +the effective mass effect, + +is of course largest +for the lightest nuclei, + +with the extreme +example of positronium. + +Any questions? + +Well, we have five minutes left. + +But Cody. + +AUDIENCE: What +sort of scales are + +associated with +the volume effect? + +PROFESSOR: Pardon? + +AUDIENCE: What sort +of energy scales + +are associated with the volume +effect? [INAUDIBLE] comparable? + +PROFESSOR: What energy is-- +no, it's actually-- wait. + +Let's estimate it. + +You're working with rubidium. + +What is your isotope shift in +rubidium between 85 and 87? + +AUDIENCE: I actually don't know. + +PROFESSOR: Isn't +it 170, 90-- no, + +I'm getting confused +now with [INAUDIBLE]. + +So many people +work with rubidium. + +What is the difference +in transition frequency + +between rubidium-85 and -87? + +AUDIENCE: [INAUDIBLE]. + +PROFESSOR: It's much +more than gigahertz. + +You really have to +tune your laser. + +I think if you look +at the wave per cell, + +you will never accidentally +see a rubidium-85 line. + +I just don't recall the number. + +AUDIENCE: [INAUDIBLE]. + +AUDIENCE: [INAUDIBLE] together, +you can see both of them. + +PROFESSOR: OK. + +And for the mass +effect, we said it's + +sort of-- then they +would be comparable. + +The mass effect is +easy to estimate, + +because the mass correction +is one part in a few thousand. + +So that would mean on the order +of 10 to the 10 gigahertz. + +So the volume effect-- +it really depends. + +It's tiny for light elements. + +Rubidium is already heavy. + +So right now I would +say they are comparable. + +But since it's of +interest, I will give you + +more accurate +numbers on Wednesday. + +Any other questions? + +Yes? + +AUDIENCE: Sorry. + +Could you explain the +graph of the previous page, + +how the lines are joined off? + +PROFESSOR: The potential? + +AUDIENCE: Yes. + +PROFESSOR: Yeah. + +So what happens is-- so +if we're being cryptic, + +this is the charge distribution. + +And what I'm doing now is +I'm solving Laplace equation. + +I'm solving Laplace +equation and integrating + +from r equals infinity. + +And as long as I'm +outside the charge radius, + +I get the 1 over r +Coulomb potential. + +But the moment I heat the +surface of the nucleus, + +I continue to indicate +Laplace equation. + +But what is now inside is a +smaller and smaller charge. + +I can also say I use +a form of Gauss's law. + +So I'm therefore not +continuing on the 1 over r. + +And if you look at +Jackson, or if you + +look at maybe a PSET you have +solved, the 1 over r potential + +becomes now a parabola. + +And so what I wanted to +sort of indicate here + +is once you heat the +surface of the nucleus, + +you're not continuing on +the 1 over r trajectory. + +You have in a wave which +is continuous and has + +a continuous deriviative-- +you have to fit in a parabola. + +And for the heavier +nucleus, this + +leads us to this potential. + +As for the lighter nucleus, +the potential is deeper. + +And that explains why the +binding energy for heavier + +nuclei is smaller than +for lighter nuclei. + +Yes? + +AUDIENCE: So for the +other orbitals, is it + +exactly zero or +[? near to ?] zero? + +PROFESSOR: OK. + +For the other orbitals, +what we have to do + +is-- and actually, you +have a homework assignment + +to do it for hydrogen +and the proton. + +You take the difference +between the actual potential + +and the Coulomb potential. + +So you take the difference. + +And the difference is +your perturbation operator + +for the finite size +of the nucleus. + +And now you take this +perturbation operator + +between your wave function +and calculate the lowest order + +of the expectation value. + +For the s electron, +you can immediately + +factor out the probability +for the electronic s equals 0. + +But s-- we discussed, if you +have orbital angular momentum, + +let me just scribble +it down here, + +the wave function is +proportional to r to the l. + +So therefore, you +have actually an r + +to the l-- the wave function is +exactly 0 only at r equals 0. + +And then it slowly grows. + +So therefore, given the +finite size of the nucleus, + +you will get a tiny, an +absolutely tiny effect + +if you integrate a wave +function, r to the l, + +over your perturbation operator. + +So it's not mathematically zero. + +But for all practical +purposes, it vanishes. + +Nancy. + +AUDIENCE: For the different +nuclei-- for example, + +in rubidium-- is mass and +volume affecting anything? + +Or is [INAUDIBLE] structure also +important in these isotopes? + +Because the nuclear structure +would be different [INAUDIBLE]. + +PROFESSOR: Oh, yeah. + +When we talk isotope +effects, I was + +talking about the isotope +effects of mass and volume. + +But different isotopes +will, in general, + +have different magnetic moments +or different quadrupolar + +deformations. + +So what I discussed about +hyperfine structure also + +applies to isotopes. + +I only separated it, +because usually when + +you don't have isotopes, you +don't talk about, like, sodium. + +Who has ever talked about +the mass shift or volume + +effect in sodium? + +Usually you don't, +because sodium + +has 100% natural +abundance in sodium-23. + +So therefore, the +hyperfine effects, + +they lead to +observable splittings + +even if you have +only one isotope. + +But in general, yes, +different isotopes + +differ in all four effects-- the +mass effect, the volume effect, + +the deformation effect, and +the magnetic moment effect. + +AUDIENCE: [INAUDIBLE] mass and +volume effects are used more + +than [INAUDIBLE] splitting? + +Because I find there +is a different rate + +for different isotopes. + +Like, in the starting +of the lecture, + +you were talking about +adding two positrons + +to the alpha particles. + +That would change [INAUDIBLE]. + +PROFESSOR: Oh, yeah, +this would change. + +But you can separate +those effects, + +because I mentioned that +in hyperfine structure, + +the center of mass of the +energy levels is the same. + +So if you see a splitting +but take the center of mass, + +then the center +of mass will only + +depend on volume +and mass effects. + +OK. + +Let's continue on Wednesday. \ No newline at end of file diff --git a/pRmUADgEf98.txt b/pRmUADgEf98.txt new file mode 100644 index 0000000000000000000000000000000000000000..859c09a8fd51a06cedac3d0a732c2a11ff606eb6 --- /dev/null +++ b/pRmUADgEf98.txt @@ -0,0 +1,1531 @@ +align:start position:0% + +hello everyone and welcome to this + + align:start position:0% +hello everyone and welcome to this + + + align:start position:0% +hello everyone and welcome to this +little video presenting you my project + + align:start position:0% +little video presenting you my project + + + align:start position:0% +little video presenting you my project +on Mathematica my name is Alex and I'm + + align:start position:0% +on Mathematica my name is Alex and I'm + + + align:start position:0% +on Mathematica my name is Alex and I'm +currently studying material science in + + align:start position:0% +currently studying material science in + + + align:start position:0% +currently studying material science in +EPFL in Switzerland and we had this + + align:start position:0% +EPFL in Switzerland and we had this + + + align:start position:0% +EPFL in Switzerland and we had this +personal challenge to do something he + + align:start position:0% +personal challenge to do something he + + + align:start position:0% +personal challenge to do something he +wanted with Mathematica + + align:start position:0% +wanted with Mathematica + + + align:start position:0% +wanted with Mathematica +so I took an interest into + + align:start position:0% +so I took an interest into + + + align:start position:0% +so I took an interest into +crystallography because this is a quite + + align:start position:0% +crystallography because this is a quite + + + align:start position:0% +crystallography because this is a quite +essential material science and well + + align:start position:0% +essential material science and well + + + align:start position:0% +essential material science and well +actually it was on the request of my + + align:start position:0% +actually it was on the request of my + + + align:start position:0% +actually it was on the request of my +girlfriend who has quite trouble to see + + align:start position:0% +girlfriend who has quite trouble to see + + + align:start position:0% +girlfriend who has quite trouble to see +things in 3d and that I did this and my + + align:start position:0% +things in 3d and that I did this and my + + + align:start position:0% +things in 3d and that I did this and my +idea was to create a tool that could be + + align:start position:0% +idea was to create a tool that could be + + + align:start position:0% +idea was to create a tool that could be +used by anyone that doesn't specially + + align:start position:0% +used by anyone that doesn't specially + + + align:start position:0% +used by anyone that doesn't specially +know about Mathematica and that without + + align:start position:0% +know about Mathematica and that without + + + align:start position:0% +know about Mathematica and that without +coding anything he could create a couple + + align:start position:0% +coding anything he could create a couple + + + align:start position:0% +coding anything he could create a couple +of structures have a look at have an + + align:start position:0% +of structures have a look at have an + + + align:start position:0% +of structures have a look at have an +interactive part with it and choose the + + align:start position:0% +interactive part with it and choose the + + + align:start position:0% +interactive part with it and choose the +atomic cetera and in visual more easily + + align:start position:0% +atomic cetera and in visual more easily + + + align:start position:0% +atomic cetera and in visual more easily +these structures so let's have a look + + align:start position:0% +these structures so let's have a look + + + align:start position:0% +these structures so let's have a look +first at a bit of theory and first with + + align:start position:0% +first at a bit of theory and first with + + + align:start position:0% +first at a bit of theory and first with +the probabilities so Bravo letici one + + align:start position:0% +the probabilities so Bravo letici one + + + align:start position:0% +the probabilities so Bravo letici one +who is one of the fundamentals of + + align:start position:0% +who is one of the fundamentals of + + + align:start position:0% +who is one of the fundamentals of +crystallography it defines the + + align:start position:0% +crystallography it defines the + + + align:start position:0% +crystallography it defines the +difference structure in which so they + + align:start position:0% +difference structure in which so they + + + align:start position:0% +difference structure in which so they +will spot you know them the axes the + + align:start position:0% +will spot you know them the axes the + + + align:start position:0% +will spot you know them the axes the +primitive cells and this axis can change + + align:start position:0% +primitive cells and this axis can change + + + align:start position:0% +primitive cells and this axis can change +their length and there is also a place + + align:start position:0% +their length and there is also a place + + + align:start position:0% +their length and there is also a place +where you you will have more atoms in + + align:start position:0% +where you you will have more atoms in + + + align:start position:0% +where you you will have more atoms in +the mineral in the same interfaces so in + + align:start position:0% +the mineral in the same interfaces so in + + + align:start position:0% +the mineral in the same interfaces so in +my program I will focus on the simple + + align:start position:0% +my program I will focus on the simple + + + align:start position:0% +my program I will focus on the simple +cubic the first century could be in the + + align:start position:0% +cubic the first century could be in the + + + align:start position:0% +cubic the first century could be in the +body centered cubic which are some of + + align:start position:0% +body centered cubic which are some of + + + align:start position:0% +body centered cubic which are some of +the most + + align:start position:0% +the most + + + align:start position:0% +the most +I want to say basic but the some of the + + align:start position:0% +I want to say basic but the some of the + + + align:start position:0% +I want to say basic but the some of the +one you be unconcerned more often in the + + align:start position:0% +one you be unconcerned more often in the + + + align:start position:0% +one you be unconcerned more often in the +solids there is also exact no compact + + align:start position:0% +solids there is also exact no compact + + + align:start position:0% +solids there is also exact no compact +that is quite often represented but it + + align:start position:0% +that is quite often represented but it + + + align:start position:0% +that is quite often represented but it +was quite difficult to implement so it + + align:start position:0% +was quite difficult to implement so it + + + align:start position:0% +was quite difficult to implement so it +could be nice to do it in the future but + + align:start position:0% +could be nice to do it in the future but + + + align:start position:0% +could be nice to do it in the future but +oh no it's not there + + align:start position:0% +oh no it's not there + + + align:start position:0% +oh no it's not there +and I also had a look at interstitial + + align:start position:0% +and I also had a look at interstitial + + + align:start position:0% +and I also had a look at interstitial +sites so interstitial sites atoms that + + align:start position:0% +sites so interstitial sites atoms that + + + align:start position:0% +sites so interstitial sites atoms that +would come to put them themselves in + + align:start position:0% +would come to put them themselves in + + + align:start position:0% +would come to put them themselves in +some void area of your lattice so here + + align:start position:0% +some void area of your lattice so here + + + align:start position:0% +some void area of your lattice so here +is the FCC lattice with atom on each + + align:start position:0% +is the FCC lattice with atom on each + + + align:start position:0% +is the FCC lattice with atom on each +summit and one individual of the phases + + align:start position:0% +summit and one individual of the phases + + + align:start position:0% +summit and one individual of the phases +and we have octahedral seats + + align:start position:0% +and we have octahedral seats + + + align:start position:0% +and we have octahedral seats +so it's an octahedron of void plates and + + align:start position:0% +so it's an octahedron of void plates and + + + align:start position:0% +so it's an octahedron of void plates and +in the center you have them the + + align:start position:0% +in the center you have them the + + + align:start position:0% +in the center you have them the +possibility to put in a zone so this is + + align:start position:0% +possibility to put in a zone so this is + + + align:start position:0% +possibility to put in a zone so this is +interesting when you are looking for + + align:start position:0% +interesting when you are looking for + + + align:start position:0% +interesting when you are looking for +alloys because it gives a lot of + + align:start position:0% +alloys because it gives a lot of + + + align:start position:0% +alloys because it gives a lot of +possibilities to put new atoms in your + + align:start position:0% +possibilities to put new atoms in your + + + align:start position:0% +possibilities to put new atoms in your +metal and so they are two key categories + + align:start position:0% +metal and so they are two key categories + + + align:start position:0% +metal and so they are two key categories +and as I mentioned the octahedral in the + + align:start position:0% +and as I mentioned the octahedral in the + + + align:start position:0% +and as I mentioned the octahedral in the +tetrahedral and for each of the three + + align:start position:0% +tetrahedral and for each of the three + + + align:start position:0% +tetrahedral and for each of the three +structures that have been kicking there + + align:start position:0% +structures that have been kicking there + + + align:start position:0% +structures that have been kicking there +is a different for example for cubic + + align:start position:0% +is a different for example for cubic + + + align:start position:0% +is a different for example for cubic +simple there is only one but for BCC as + + align:start position:0% +simple there is only one but for BCC as + + + align:start position:0% +simple there is only one but for BCC as +we can see here there is a lot of + + align:start position:0% +we can see here there is a lot of + + + align:start position:0% +we can see here there is a lot of +tetrahedral seats which are here so yeah + + align:start position:0% +tetrahedral seats which are here so yeah + + + align:start position:0% +tetrahedral seats which are here so yeah +this is a 2d graphene it's not always + + align:start position:0% +this is a 2d graphene it's not always + + + align:start position:0% +this is a 2d graphene it's not always +easy to really see how things are done + + align:start position:0% +easy to really see how things are done + + + align:start position:0% +easy to really see how things are done +and I remember having a really hard time + + align:start position:0% +and I remember having a really hard time + + + align:start position:0% +and I remember having a really hard time +to find where the tetrahedral sites + + align:start position:0% +to find where the tetrahedral sites + + + align:start position:0% +to find where the tetrahedral sites +where for the BCC so this is why I + + align:start position:0% +where for the BCC so this is why I + + + align:start position:0% +where for the BCC so this is why I +really wanted also to put in my 3d graph + + align:start position:0% +really wanted also to put in my 3d graph + + + align:start position:0% +really wanted also to put in my 3d graph +the interstitials + + align:start position:0% +the interstitials + + + align:start position:0% +the interstitials +and I hope it will be useful for for you + + align:start position:0% +and I hope it will be useful for for you + + + align:start position:0% +and I hope it will be useful for for you +as well if you use my program so yeah so + + align:start position:0% +as well if you use my program so yeah so + + + align:start position:0% +as well if you use my program so yeah so +about crystallography in general and + + align:start position:0% +about crystallography in general and + + + align:start position:0% +about crystallography in general and +this is a field that gives you a lot of + + align:start position:0% +this is a field that gives you a lot of + + + align:start position:0% +this is a field that gives you a lot of +information about the properties of + + align:start position:0% +information about the properties of + + + align:start position:0% +information about the properties of +matter because when you understand how + + align:start position:0% +matter because when you understand how + + + align:start position:0% +matter because when you understand how +the item organize them tell themselves + + align:start position:0% +the item organize them tell themselves + + + align:start position:0% +the item organize them tell themselves +you can start to understand things like + + align:start position:0% +you can start to understand things like + + + align:start position:0% +you can start to understand things like +metal transition and Advent thing you + + align:start position:0% +metal transition and Advent thing you + + + align:start position:0% +metal transition and Advent thing you +can start to look at the growth of mana + + align:start position:0% +can start to look at the growth of mana + + + align:start position:0% +can start to look at the growth of mana +crystals for example if you're working + + align:start position:0% +crystals for example if you're working + + + align:start position:0% +crystals for example if you're working +in semiconductors and you're trying to + + align:start position:0% +in semiconductors and you're trying to + + + align:start position:0% +in semiconductors and you're trying to +do nano wires then you need to + + align:start position:0% +do nano wires then you need to + + + align:start position:0% +do nano wires then you need to +understand how the different you have + + align:start position:0% +understand how the different you have + + + align:start position:0% +understand how the different you have +the turbine that you need to do mono + + align:start position:0% +the turbine that you need to do mono + + + align:start position:0% +the turbine that you need to do mono +crystal of nickel this is very important + + align:start position:0% +crystal of nickel this is very important + + + align:start position:0% +crystal of nickel this is very important +so yeah there is a lot of replication + + align:start position:0% +so yeah there is a lot of replication + + + align:start position:0% +so yeah there is a lot of replication +that you can have from this subject and + + align:start position:0% +that you can have from this subject and + + + align:start position:0% +that you can have from this subject and +I thought it was an interesting one to + + align:start position:0% +I thought it was an interesting one to + + + align:start position:0% +I thought it was an interesting one to +observe so let's have a look at the + + align:start position:0% +observe so let's have a look at the + + + align:start position:0% +observe so let's have a look at the +program so this is some reminder about + + align:start position:0% +program so this is some reminder about + + + align:start position:0% +program so this is some reminder about +how it works and this is the other + + align:start position:0% +how it works and this is the other + + + align:start position:0% +how it works and this is the other +interactive part so my program will + + align:start position:0% +interactive part so my program will + + + align:start position:0% +interactive part so my program will +consist of two cells that you simply + + align:start position:0% +consist of two cells that you simply + + + align:start position:0% +consist of two cells that you simply +have to click on them and press shift + + align:start position:0% +have to click on them and press shift + + + align:start position:0% +have to click on them and press shift +enter the first part are the function + + align:start position:0% +enter the first part are the function + + + align:start position:0% +enter the first part are the function +that we defined the position of the + + align:start position:0% +that we defined the position of the + + + align:start position:0% +that we defined the position of the +atoms and the second part is the + + align:start position:0% +atoms and the second part is the + + + align:start position:0% +atoms and the second part is the +interactive tool so you will see this is + + align:start position:0% +interactive tool so you will see this is + + + align:start position:0% +interactive tool so you will see this is +a huge sale with a lot of code I know + + align:start position:0% +a huge sale with a lot of code I know + + + align:start position:0% +a huge sale with a lot of code I know +that mr. cutter doesn't like it at home + + align:start position:0% +that mr. cutter doesn't like it at home + + + align:start position:0% +that mr. cutter doesn't like it at home +but I had to keep it like that to have + + align:start position:0% +but I had to keep it like that to have + + + align:start position:0% +but I had to keep it like that to have +my manipulate + + align:start position:0% + + + + align:start position:0% + +Victor Toni and here we have it so this + + align:start position:0% +Victor Toni and here we have it so this + + + align:start position:0% +Victor Toni and here we have it so this +is the panel where you have on the left + + align:start position:0% +is the panel where you have on the left + + + align:start position:0% +is the panel where you have on the left +the controls on the right the display + + align:start position:0% +the controls on the right the display + + + align:start position:0% +the controls on the right the display +with the 3d graphic and a little graph + + align:start position:0% +with the 3d graphic and a little graph + + + align:start position:0% +with the 3d graphic and a little graph +that helps you to visually the + + align:start position:0% +that helps you to visually the + + + align:start position:0% +that helps you to visually the +parameters of the lattice that helps you + + align:start position:0% +parameters of the lattice that helps you + + + align:start position:0% +parameters of the lattice that helps you +when you will try to calculate the + + align:start position:0% +when you will try to calculate the + + + align:start position:0% +when you will try to calculate the +density these particular structures so + + align:start position:0% +density these particular structures so + + + align:start position:0% +density these particular structures so +as you see we can move it over there is + + align:start position:0% +as you see we can move it over there is + + + align:start position:0% +as you see we can move it over there is +different type of item here in SEL which + + align:start position:0% +different type of item here in SEL which + + + align:start position:0% +different type of item here in SEL which +is salt and now let's look at all the + + align:start position:0% +is salt and now let's look at all the + + + align:start position:0% +is salt and now let's look at all the +possibilities we have with this program + + align:start position:0% +possibilities we have with this program + + + align:start position:0% +possibilities we have with this program +because the thing is that I want you + + align:start position:0% +because the thing is that I want you + + + align:start position:0% +because the thing is that I want you +know already a structure and you want to + + align:start position:0% +know already a structure and you want to + + + align:start position:0% +know already a structure and you want to +know what it looks like to be able to + + align:start position:0% +know what it looks like to be able to + + + align:start position:0% +know what it looks like to be able to +create it so let's go try first let's + + align:start position:0% +create it so let's go try first let's + + + align:start position:0% +create it so let's go try first let's +look at the different options so we have + + align:start position:0% +look at the different options so we have + + + align:start position:0% +look at the different options so we have +those three structures the BCC the cubic + + align:start position:0% +those three structures the BCC the cubic + + + align:start position:0% +those three structures the BCC the cubic +simple and the waves you see you can + + align:start position:0% +simple and the waves you see you can + + + align:start position:0% +simple and the waves you see you can +change the item size here you can + + align:start position:0% +change the item size here you can + + + align:start position:0% +change the item size here you can +display you can choose if there is the + + align:start position:0% +display you can choose if there is the + + + align:start position:0% +display you can choose if there is the +interstitials and here the choice of + + align:start position:0% +interstitials and here the choice of + + + align:start position:0% +interstitials and here the choice of +element because I wanted that you can + + align:start position:0% +element because I wanted that you can + + + align:start position:0% +element because I wanted that you can +choose what type in yourself this is why + + align:start position:0% +choose what type in yourself this is why + + + align:start position:0% +choose what type in yourself this is why +there is this panel so I divided my my + + align:start position:0% +there is this panel so I divided my my + + + align:start position:0% +there is this panel so I divided my my +graph into four parts basically I don't + + align:start position:0% +graph into four parts basically I don't + + + align:start position:0% +graph into four parts basically I don't +want an item to are the atoms on the + + align:start position:0% +want an item to are the atoms on the + + + align:start position:0% +want an item to are the atoms on the +edges and in this Center or different + + align:start position:0% +edges and in this Center or different + + + align:start position:0% +edges and in this Center or different +division that help you to create a more + + align:start position:0% +division that help you to create a more + + + align:start position:0% +division that help you to create a more +complex cells so let's have a try I + + align:start position:0% +complex cells so let's have a try I + + + align:start position:0% +complex cells so let's have a try I +would like a body centered cubic and I + + align:start position:0% +would like a body centered cubic and I + + + align:start position:0% +would like a body centered cubic and I +would like an alloy which is iron and + + align:start position:0% +would like an alloy which is iron and + + + align:start position:0% +would like an alloy which is iron and +aluminum + + align:start position:0% +aluminum + + + align:start position:0% +aluminum +that's structure itself into into a BCC + + align:start position:0% +that's structure itself into into a BCC + + + align:start position:0% +that's structure itself into into a BCC +so I would put in a tuna to see it + + align:start position:0% +so I would put in a tuna to see it + + + align:start position:0% +so I would put in a tuna to see it +changing so this is normal because I + + align:start position:0% +changing so this is normal because I + + + align:start position:0% +changing so this is normal because I +asked software to only update this part + + align:start position:0% +asked software to only update this part + + + align:start position:0% +asked software to only update this part +when I click on the random t12 it can be + + align:start position:0% +when I click on the random t12 it can be + + + align:start position:0% +when I click on the random t12 it can be +improved this part but so it was to have + + align:start position:0% +improved this part but so it was to have + + + align:start position:0% +improved this part but so it was to have +a stability during the initialization to + + align:start position:0% +a stability during the initialization to + + + align:start position:0% +a stability during the initialization to +manipulate and here I have a way to + + align:start position:0% +manipulate and here I have a way to + + + align:start position:0% +manipulate and here I have a way to +visualize my body centered cubic with + + align:start position:0% +visualize my body centered cubic with + + + align:start position:0% +visualize my body centered cubic with +the iron atom on the edges and my + + align:start position:0% +the iron atom on the edges and my + + + align:start position:0% +the iron atom on the edges and my +aluminum at the center ok so there is + + align:start position:0% +aluminum at the center ok so there is + + + align:start position:0% +aluminum at the center ok so there is +also FCC that you can do there is one + + align:start position:0% +also FCC that you can do there is one + + + align:start position:0% +also FCC that you can do there is one +alloy that works with this which is + + align:start position:0% +alloy that works with this which is + + + align:start position:0% +alloy that works with this which is +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +aluminum a nickel + + align:start position:0% + + + + align:start position:0% + +and here is the FCC in here you can turn + + align:start position:0% +and here is the FCC in here you can turn + + + align:start position:0% +and here is the FCC in here you can turn +it have a look you see that there is + + align:start position:0% +it have a look you see that there is + + + align:start position:0% +it have a look you see that there is +nothing in the middle and for me it + + align:start position:0% +nothing in the middle and for me it + + + align:start position:0% +nothing in the middle and for me it +helps me a lot to visually look like + + align:start position:0% +helps me a lot to visually look like + + + align:start position:0% +helps me a lot to visually look like +that there is also the adapted density + + align:start position:0% +that there is also the adapted density + + + align:start position:0% +that there is also the adapted density +calculation graph where you see that + + align:start position:0% +calculation graph where you see that + + + align:start position:0% +calculation graph where you see that +this diagonal in the middle will allow + + align:start position:0% +this diagonal in the middle will allow + + + align:start position:0% +this diagonal in the middle will allow +in the face here will help you calculate + + align:start position:0% +in the face here will help you calculate + + + align:start position:0% +in the face here will help you calculate +the density to put my graph and I would + + align:start position:0% +the density to put my graph and I would + + + align:start position:0% +the density to put my graph and I would +like to show you a little example that I + + align:start position:0% +like to show you a little example that I + + + align:start position:0% +like to show you a little example that I +had that I found on the internet which + + align:start position:0% +had that I found on the internet which + + + align:start position:0% +had that I found on the internet which +is this slide about the magnesium leads + + align:start position:0% +is this slide about the magnesium leads + + + align:start position:0% +is this slide about the magnesium leads +intermetallic energy to people and they + + align:start position:0% +intermetallic energy to people and they + + + align:start position:0% +intermetallic energy to people and they +say that this should look like this FCC + + align:start position:0% +say that this should look like this FCC + + + align:start position:0% +say that this should look like this FCC +sides side so let's try to put in anyway + + align:start position:0% +sides side so let's try to put in anyway + + + align:start position:0% +sides side so let's try to put in anyway +my problem so first I would say yes I + + align:start position:0% +my problem so first I would say yes I + + + align:start position:0% +my problem so first I would say yes I +would like to have octahedral + + align:start position:0% +would like to have octahedral + + + align:start position:0% +would like to have octahedral +interstitial I'm still in FCC I would + + align:start position:0% +interstitial I'm still in FCC I would + + + align:start position:0% +interstitial I'm still in FCC I would +put the same at home here + + align:start position:0% + + + + align:start position:0% + +computer he's having a hard time alright + + align:start position:0% +computer he's having a hard time alright + + + align:start position:0% +computer he's having a hard time alright +so we see that it doesn't look like a + + align:start position:0% +so we see that it doesn't look like a + + + align:start position:0% +so we see that it doesn't look like a +toll on what alright okay and here is + + align:start position:0% +toll on what alright okay and here is + + + align:start position:0% +toll on what alright okay and here is +where I see that this guy did a mistake + + align:start position:0% +where I see that this guy did a mistake + + + align:start position:0% +where I see that this guy did a mistake +here by putting octahedral in this place + + align:start position:0% +here by putting octahedral in this place + + + align:start position:0% +here by putting octahedral in this place +because this base is tetrahedron no it + + align:start position:0% +because this base is tetrahedron no it + + + align:start position:0% +because this base is tetrahedron no it +looks like I find it better to look like + + align:start position:0% +looks like I find it better to look like + + + align:start position:0% +looks like I find it better to look like +that because know that we can change + + align:start position:0% +that because know that we can change + + + align:start position:0% +that because know that we can change +little bit besides the screen now that + + align:start position:0% +little bit besides the screen now that + + + align:start position:0% +little bit besides the screen now that +there is nothing in the middle which + + align:start position:0% +there is nothing in the middle which + + + align:start position:0% +there is nothing in the middle which +it's not that clear when you look at + + align:start position:0% +it's not that clear when you look at + + + align:start position:0% +it's not that clear when you look at +this thing + + align:start position:0% +this thing + + + align:start position:0% +this thing +so yeah I found that it was one nice + + align:start position:0% +so yeah I found that it was one nice + + + align:start position:0% +so yeah I found that it was one nice +application of this little program to + + align:start position:0% +application of this little program to + + + align:start position:0% +application of this little program to +visualize so here is for now I hope you + + align:start position:0% +visualize so here is for now I hope you + + + align:start position:0% +visualize so here is for now I hope you +enjoyed this presentation that it will + + align:start position:0% +enjoyed this presentation that it will + + + align:start position:0% +enjoyed this presentation that it will +help you by using this program to see + + align:start position:0% +help you by using this program to see + + + align:start position:0% +help you by using this program to see +better in 3d your crystalline structure + + align:start position:0% +better in 3d your crystalline structure + + + align:start position:0% +better in 3d your crystalline structure +and that will help you to learn a better + + align:start position:0% +and that will help you to learn a better + + + align:start position:0% +and that will help you to learn a better +idea of what you're doing with your + + align:start position:0% +idea of what you're doing with your + + + align:start position:0% +idea of what you're doing with your +crystallography courses so thank you for + + align:start position:0% +crystallography courses so thank you for + + + align:start position:0% +crystallography courses so thank you for +watching \ No newline at end of file diff --git a/pSbafxDHdgE.txt b/pSbafxDHdgE.txt new file mode 100644 index 0000000000000000000000000000000000000000..dd5abb81bde58a6345a36b0737254e72472b999e --- /dev/null +++ b/pSbafxDHdgE.txt @@ -0,0 +1,1283 @@ +align:start position:0% + +hey we're back today we're gonna do a + + align:start position:0% +hey we're back today we're gonna do a + + + align:start position:0% +hey we're back today we're gonna do a +singular value decomposition question + + align:start position:0% +singular value decomposition question + + + align:start position:0% +singular value decomposition question +the problem is really simple to state + + align:start position:0% +the problem is really simple to state + + + align:start position:0% +the problem is really simple to state +find the singular value decomposition of + + align:start position:0% +find the singular value decomposition of + + + align:start position:0% +find the singular value decomposition of +this matrix C equals 5 5 negative 1 7 + + align:start position:0% +this matrix C equals 5 5 negative 1 7 + + + align:start position:0% +this matrix C equals 5 5 negative 1 7 +hit pause try it yourself I'll be back + + align:start position:0% +hit pause try it yourself I'll be back + + + align:start position:0% +hit pause try it yourself I'll be back +in a minute and we can do it together + + align:start position:0% + + + + align:start position:0% + +all right we're back now let's do it + + align:start position:0% +all right we're back now let's do it + + + align:start position:0% +all right we're back now let's do it +together + + align:start position:0% +together + + + align:start position:0% +together +now I know professor Strang has done a + + align:start position:0% +now I know professor Strang has done a + + + align:start position:0% +now I know professor Strang has done a +couple of these in lecture but as he + + align:start position:0% +couple of these in lecture but as he + + + align:start position:0% +couple of these in lecture but as he +pointed out there it's really easy to + + align:start position:0% +pointed out there it's really easy to + + + align:start position:0% +pointed out there it's really easy to +make a mistake so you can never do + + align:start position:0% +make a mistake so you can never do + + + align:start position:0% +make a mistake so you can never do +enough examples of finding the SVD so + + align:start position:0% +enough examples of finding the SVD so + + + align:start position:0% +enough examples of finding the SVD so +what does the SVD look like what do we + + align:start position:0% +what does the SVD look like what do we + + + align:start position:0% +what does the SVD look like what do we +want to end up with well we want a + + align:start position:0% +want to end up with well we want a + + + align:start position:0% +want to end up with well we want a +decomposition C equals u Sigma V + + align:start position:0% +decomposition C equals u Sigma V + + + align:start position:0% +decomposition C equals u Sigma V +transpose U and V are going to be + + align:start position:0% +transpose U and V are going to be + + + align:start position:0% +transpose U and V are going to be +orthogonal matrices that is their + + align:start position:0% +orthogonal matrices that is their + + + align:start position:0% +orthogonal matrices that is their +columns are orthonormal sets Sigma is + + align:start position:0% +columns are orthonormal sets Sigma is + + + align:start position:0% +columns are orthonormal sets Sigma is +going to be a diagonal matrix with + + align:start position:0% +going to be a diagonal matrix with + + + align:start position:0% +going to be a diagonal matrix with +non-negative entries ok good so now how + + align:start position:0% +non-negative entries ok good so now how + + + align:start position:0% +non-negative entries ok good so now how +do we find this decomposition or we need + + align:start position:0% +do we find this decomposition or we need + + + align:start position:0% +do we find this decomposition or we need +two equations ok one is C transpose C is + + align:start position:0% +two equations ok one is C transpose C is + + + align:start position:0% +two equations ok one is C transpose C is +equal to V Sigma transpose Sigma V + + align:start position:0% +equal to V Sigma transpose Sigma V + + + align:start position:0% +equal to V Sigma transpose Sigma V +transpose and you get this just by + + align:start position:0% +transpose and you get this just by + + + align:start position:0% +transpose and you get this just by +plugging in C transpose C here and + + align:start position:0% +plugging in C transpose C here and + + + align:start position:0% +plugging in C transpose C here and +noticing that u transpose U is 1 since + + align:start position:0% +noticing that u transpose U is 1 since + + + align:start position:0% +noticing that u transpose U is 1 since +you as an orthogonal matrix ok and the + + align:start position:0% +you as an orthogonal matrix ok and the + + + align:start position:0% +you as an orthogonal matrix ok and the +second equation is just noticing that V + + align:start position:0% +second equation is just noticing that V + + + align:start position:0% +second equation is just noticing that V +transpose this V inverse and moving it + + align:start position:0% +transpose this V inverse and moving it + + + align:start position:0% +transpose this V inverse and moving it +to the other side of the equation which + + align:start position:0% +to the other side of the equation which + + + align:start position:0% +to the other side of the equation which +is C V equals u Sigma ok so these are + + align:start position:0% +is C V equals u Sigma ok so these are + + + align:start position:0% +is C V equals u Sigma ok so these are +the two equations we need to use to find + + align:start position:0% +the two equations we need to use to find + + + align:start position:0% +the two equations we need to use to find +V Sigma and you ok so let's start with + + align:start position:0% +V Sigma and you ok so let's start with + + + align:start position:0% +V Sigma and you ok so let's start with +the first one let's let's compute C + + align:start position:0% +the first one let's let's compute C + + + align:start position:0% +the first one let's let's compute C +transpose C so C transpose C what is + + align:start position:0% +transpose C so C transpose C what is + + + align:start position:0% +transpose C so C transpose C what is +that + + align:start position:0% + + + + align:start position:0% + +well if you compute will get a 26 and 18 + + align:start position:0% +well if you compute will get a 26 and 18 + + + align:start position:0% +well if you compute will get a 26 and 18 +and 18 and a 74 great now what you + + align:start position:0% +and 18 and a 74 great now what you + + + align:start position:0% +and 18 and a 74 great now what you +notice about this equation is this is + + align:start position:0% +notice about this equation is this is + + + align:start position:0% +notice about this equation is this is +just a diagonal ization of C transpose C + + align:start position:0% +just a diagonal ization of C transpose C + + + align:start position:0% +just a diagonal ization of C transpose C +so we need to find the eigenvalues those + + align:start position:0% +so we need to find the eigenvalues those + + + align:start position:0% +so we need to find the eigenvalues those +will be the entries of Sigma transpose + + align:start position:0% +will be the entries of Sigma transpose + + + align:start position:0% +will be the entries of Sigma transpose +Sigma and the eigenvectors which will be + + align:start position:0% +Sigma and the eigenvectors which will be + + + align:start position:0% +Sigma and the eigenvectors which will be +the columns of V okay good so how do we + + align:start position:0% +the columns of V okay good so how do we + + + align:start position:0% +the columns of V okay good so how do we +find those well we look at the + + align:start position:0% +find those well we look at the + + + align:start position:0% +find those well we look at the +determinant of C transpose C minus + + align:start position:0% +determinant of C transpose C minus + + + align:start position:0% +determinant of C transpose C minus +lambda times the identity which is the + + align:start position:0% +lambda times the identity which is the + + + align:start position:0% +lambda times the identity which is the +determinant of 26 minus lambda 18 18 and + + align:start position:0% +determinant of 26 minus lambda 18 18 and + + + align:start position:0% +determinant of 26 minus lambda 18 18 and +74 okay + + align:start position:0% +74 okay + + + align:start position:0% +74 okay +74 minus lambda thank you good + + align:start position:0% +74 minus lambda thank you good + + + align:start position:0% +74 minus lambda thank you good +okay and what is that polynomial well we + + align:start position:0% +okay and what is that polynomial well we + + + align:start position:0% +okay and what is that polynomial well we +got a lambda squared now if that 26 plus + + align:start position:0% +got a lambda squared now if that 26 plus + + + align:start position:0% +got a lambda squared now if that 26 plus +74 is 100 so minus 100 lambda and I'll + + align:start position:0% +74 is 100 so minus 100 lambda and I'll + + + align:start position:0% +74 is 100 so minus 100 lambda and I'll +let you do 26 times 74 minus 18 squared + + align:start position:0% +let you do 26 times 74 minus 18 squared + + + align:start position:0% +let you do 26 times 74 minus 18 squared +on your own but you'll see you get 1600 + + align:start position:0% +on your own but you'll see you get 1600 + + + align:start position:0% +on your own but you'll see you get 1600 +okay and this off this easily factors is + + align:start position:0% +okay and this off this easily factors is + + + align:start position:0% +okay and this off this easily factors is +lambda minus 20 times the lambda minus + + align:start position:0% +lambda minus 20 times the lambda minus + + + align:start position:0% +lambda minus 20 times the lambda minus +80 good so the eigenvalues are 20 and 80 + + align:start position:0% +80 good so the eigenvalues are 20 and 80 + + + align:start position:0% +80 good so the eigenvalues are 20 and 80 +okay now what are the eigenvectors well + + align:start position:0% +okay now what are the eigenvectors well + + + align:start position:0% +okay now what are the eigenvectors well +you take C transpose C minus 20 times + + align:start position:0% +you take C transpose C minus 20 times + + + align:start position:0% +you take C transpose C minus 20 times +the identity and you get 6 18 18 and 54 + + align:start position:0% +the identity and you get 6 18 18 and 54 + + + align:start position:0% +the identity and you get 6 18 18 and 54 +to find the eigenvector with eigenvalue + + align:start position:0% +to find the eigenvector with eigenvalue + + + align:start position:0% +to find the eigenvector with eigenvalue +20 we need to find a vector in the null + + align:start position:0% +20 we need to find a vector in the null + + + align:start position:0% +20 we need to find a vector in the null +space of this matrix note that the + + align:start position:0% +space of this matrix note that the + + + align:start position:0% +space of this matrix note that the +second the second column is 3 times the + + align:start position:0% +second the second column is 3 times the + + + align:start position:0% +second the second column is 3 times the +first column so our first vector V 1 we + + align:start position:0% +first column so our first vector V 1 we + + + align:start position:0% +first column so our first vector V 1 we +can just take that to be well we could + + align:start position:0% +can just take that to be well we could + + + align:start position:0% +can just take that to be well we could +take it to be a negative 3 1 but we'd + + align:start position:0% +take it to be a negative 3 1 but we'd + + + align:start position:0% +take it to be a negative 3 1 but we'd +like it to be a unit vector right + + align:start position:0% +like it to be a unit vector right + + + align:start position:0% +like it to be a unit vector right +because the remember that the columns of + + align:start position:0% +because the remember that the columns of + + + align:start position:0% +because the remember that the columns of +V should be unit vectors because they're + + align:start position:0% +V should be unit vectors because they're + + + align:start position:0% +V should be unit vectors because they're +orthonormal so 3 squared plus 1 squared + + align:start position:0% +orthonormal so 3 squared plus 1 squared + + + align:start position:0% +orthonormal so 3 squared plus 1 squared +is 10 we have to divide by the square + + align:start position:0% +is 10 we have to divide by the square + + + align:start position:0% +is 10 we have to divide by the square +root of 10 + + align:start position:0% + + + + align:start position:0% + +okay similarly we do C transpose C minus + + align:start position:0% +okay similarly we do C transpose C minus + + + align:start position:0% +okay similarly we do C transpose C minus +80 times the identity + + align:start position:0% +80 times the identity + + + align:start position:0% +80 times the identity +we'll get what do we get we get negative + + align:start position:0% +we'll get what do we get we get negative + + + align:start position:0% +we'll get what do we get we get negative +54 1818 and negative 6 and similarly we + + align:start position:0% +54 1818 and negative 6 and similarly we + + + align:start position:0% +54 1818 and negative 6 and similarly we +can find that V 2 will be 1 over square + + align:start position:0% +can find that V 2 will be 1 over square + + + align:start position:0% +can find that V 2 will be 1 over square +root of 10 3 over the square root of 10 + + align:start position:0% +root of 10 3 over the square root of 10 + + + align:start position:0% +root of 10 3 over the square root of 10 +great okay so what information do we + + align:start position:0% +great okay so what information do we + + + align:start position:0% +great okay so what information do we +have now we have our V matrix which is + + align:start position:0% +have now we have our V matrix which is + + + align:start position:0% +have now we have our V matrix which is +just made up of these two columns and we + + align:start position:0% +just made up of these two columns and we + + + align:start position:0% +just made up of these two columns and we +actually have our Sigma matrix too right + + align:start position:0% +actually have our Sigma matrix too right + + + align:start position:0% +actually have our Sigma matrix too right +because the squares of the of the + + align:start position:0% +because the squares of the of the + + + align:start position:0% +because the squares of the of the +diagonal entries of Sigma are 20 and 80 + + align:start position:0% +diagonal entries of Sigma are 20 and 80 + + + align:start position:0% +diagonal entries of Sigma are 20 and 80 +good so let's write those down write + + align:start position:0% +good so let's write those down write + + + align:start position:0% +good so let's write those down write +down what we have so we have V it's just + + align:start position:0% +down what we have so we have V it's just + + + align:start position:0% +down what we have so we have V it's just +equal to I just add these vectors and + + align:start position:0% +equal to I just add these vectors and + + + align:start position:0% +equal to I just add these vectors and +make them the columns of my matrix + + align:start position:0% +make them the columns of my matrix + + + align:start position:0% +make them the columns of my matrix +square root of 10 1 over square root of + + align:start position:0% +square root of 10 1 over square root of + + + align:start position:0% +square root of 10 1 over square root of +10 1 over square root of 10 3 over + + align:start position:0% +10 1 over square root of 10 3 over + + + align:start position:0% +10 1 over square root of 10 3 over +square root of 10 and Sigma this is just + + align:start position:0% +square root of 10 and Sigma this is just + + + align:start position:0% +square root of 10 and Sigma this is just +other square roots of 20 and 80 which is + + align:start position:0% +other square roots of 20 and 80 which is + + + align:start position:0% +other square roots of 20 and 80 which is +just 2 root 5 and 45 along the diagonal + + align:start position:0% + + + + align:start position:0% + +squeezing it in here I hope you all can + + align:start position:0% +squeezing it in here I hope you all can + + + align:start position:0% +squeezing it in here I hope you all can +see these two good so so these are two + + align:start position:0% +see these two good so so these are two + + + align:start position:0% +see these two good so so these are two +of my of the three parts of my singular + + align:start position:0% +of my of the three parts of my singular + + + align:start position:0% +of my of the three parts of my singular +value decomposition I the last thing I + + align:start position:0% +value decomposition I the last thing I + + + align:start position:0% +value decomposition I the last thing I +need to find is U and for that I need to + + align:start position:0% +need to find is U and for that I need to + + + align:start position:0% +need to find is U and for that I need to +use this second equation right here cuz + + align:start position:0% +use this second equation right here cuz + + + align:start position:0% +use this second equation right here cuz +I need to multiply C times V okay so C + + align:start position:0% +I need to multiply C times V okay so C + + + align:start position:0% +I need to multiply C times V okay so C +is 5 5 negative 1 7 let's multiply it by + + align:start position:0% +is 5 5 negative 1 7 let's multiply it by + + + align:start position:0% +is 5 5 negative 1 7 let's multiply it by +V 1 over root 10 3 over square 2 10 what + + align:start position:0% +V 1 over root 10 3 over square 2 10 what + + + align:start position:0% +V 1 over root 10 3 over square 2 10 what +do we get + + align:start position:0% +do we get + + + align:start position:0% +do we get +well I'll let you work out the details + + align:start position:0% +well I'll let you work out the details + + + align:start position:0% +well I'll let you work out the details +but it's um it's it's not hard here you + + align:start position:0% +but it's um it's it's not hard here you + + + align:start position:0% +but it's um it's it's not hard here you +you get negative 10 over root 10 which + + align:start position:0% +you get negative 10 over root 10 which + + + align:start position:0% +you get negative 10 over root 10 which +is just negative square root of 10 here + + align:start position:0% +is just negative square root of 10 here + + + align:start position:0% +is just negative square root of 10 here +then I just get a + + align:start position:0% + + + + align:start position:0% + +I just get to square root of 10 + + align:start position:0% + + + + align:start position:0% + +okay and then I get one is to square + + align:start position:0% +okay and then I get one is to square + + + align:start position:0% +okay and then I get one is to square +root of 10 and wait and I think I made + + align:start position:0% +root of 10 and wait and I think I made + + + align:start position:0% +root of 10 and wait and I think I made +it and error here let me give me a + + align:start position:0% +it and error here let me give me a + + + align:start position:0% +it and error here let me give me a +second to look through my computation + + align:start position:0% +second to look through my computation + + + align:start position:0% +second to look through my computation +again to one entry should be yes thank + + align:start position:0% +again to one entry should be yes thank + + + align:start position:0% +again to one entry should be yes thank +you + + align:start position:0% +you + + + align:start position:0% +you +the to one entry should be the square + + align:start position:0% +the to one entry should be the square + + + align:start position:0% +the to one entry should be the square +root of 10 good yes that's what I was + + align:start position:0% +root of 10 good yes that's what I was + + + align:start position:0% +root of 10 good yes that's what I was +hoping yes because we get right plus 20x + + align:start position:0% +hoping yes because we get right plus 20x + + + align:start position:0% +hoping yes because we get right plus 20x +squared oh yes sorry I I did it in the + + align:start position:0% +squared oh yes sorry I I did it in the + + + align:start position:0% +squared oh yes sorry I I did it in the +wrong order right so your your + + align:start position:0% +wrong order right so your your + + + align:start position:0% +wrong order right so your your +recitation instructor should know how to + + align:start position:0% +recitation instructor should know how to + + + align:start position:0% +recitation instructor should know how to +multiply matrices great yes thank you + + align:start position:0% +multiply matrices great yes thank you + + + align:start position:0% +multiply matrices great yes thank you +you multiply this first then this then + + align:start position:0% +you multiply this first then this then + + + align:start position:0% +you multiply this first then this then +this and then this and if you do it + + align:start position:0% +this and then this and if you do it + + + align:start position:0% +this and then this and if you do it +correctly you will get this this matrix + + align:start position:0% +correctly you will get this this matrix + + + align:start position:0% +correctly you will get this this matrix +you good great so now this I'd like this + + align:start position:0% +you good great so now this I'd like this + + + align:start position:0% +you good great so now this I'd like this +to be my U matrix but it it's actually u + + align:start position:0% +to be my U matrix but it it's actually u + + + align:start position:0% +to be my U matrix but it it's actually u +times Sigma so I need to make these + + align:start position:0% +times Sigma so I need to make these + + + align:start position:0% +times Sigma so I need to make these +entries unit length okay so I get + + align:start position:0% +entries unit length okay so I get + + + align:start position:0% +entries unit length okay so I get +negative 1 over root 2 1 over root 2 1 + + align:start position:0% +negative 1 over root 2 1 over root 2 1 + + + align:start position:0% +negative 1 over root 2 1 over root 2 1 +over root 2 1 over root 2 times my Sigma + + align:start position:0% +over root 2 1 over root 2 times my Sigma + + + align:start position:0% +over root 2 1 over root 2 times my Sigma +matrix here which is remember to square + + align:start position:0% +matrix here which is remember to square + + + align:start position:0% +matrix here which is remember to square +root of 5 4 square root of 5 and those + + align:start position:0% +root of 5 4 square root of 5 and those + + + align:start position:0% +root of 5 4 square root of 5 and those +it these constants are just what I + + align:start position:0% +it these constants are just what I + + + align:start position:0% +it these constants are just what I +needed to divide these columns by in + + align:start position:0% +needed to divide these columns by in + + + align:start position:0% +needed to divide these columns by in +order to make them unit vectors good so + + align:start position:0% +order to make them unit vectors good so + + + align:start position:0% +order to make them unit vectors good so +now here's here's my u u matrix + + align:start position:0% +now here's here's my u u matrix + + + align:start position:0% +now here's here's my u u matrix +one over squared is 2 negative 1 over + + align:start position:0% +one over squared is 2 negative 1 over + + + align:start position:0% +one over squared is 2 negative 1 over +square root of 2 1 over square root of 2 + + align:start position:0% +square root of 2 1 over square root of 2 + + + align:start position:0% +square root of 2 1 over square root of 2 +1 over square root of 2 good so now I + + align:start position:0% +1 over square root of 2 good so now I + + + align:start position:0% +1 over square root of 2 good so now I +have all three matrices u v and sigma + + align:start position:0% +have all three matrices u v and sigma + + + align:start position:0% +have all three matrices u v and sigma +and despite some little errors here and + + align:start position:0% +and despite some little errors here and + + + align:start position:0% +and despite some little errors here and +there i think this is actually right you + + align:start position:0% +there i think this is actually right you + + + align:start position:0% +there i think this is actually right you +should go check it yourself because if + + align:start position:0% +should go check it yourself because if + + + align:start position:0% +should go check it yourself because if +you're at all like me you screwed up + + align:start position:0% +you're at all like me you screwed up + + + align:start position:0% +you're at all like me you screwed up +several times by now but anyway this is + + align:start position:0% +several times by now but anyway this is + + + align:start position:0% +several times by now but anyway this is +this is a good illustration of how to + + align:start position:0% +this is a good illustration of how to + + + align:start position:0% +this is a good illustration of how to +find the singular value decomposition + + align:start position:0% +find the singular value decomposition + + + align:start position:0% +find the singular value decomposition +recall that you're looking for u Sigma V + + align:start position:0% +recall that you're looking for u Sigma V + + + align:start position:0% +recall that you're looking for u Sigma V +transpose or u and V are orthogonal + + align:start position:0% +transpose or u and V are orthogonal + + + align:start position:0% +transpose or u and V are orthogonal +matrices and Sigma is diagonal with + + align:start position:0% +matrices and Sigma is diagonal with + + + align:start position:0% +matrices and Sigma is diagonal with +non-negative entries and you find it + + align:start position:0% +non-negative entries and you find it + + + align:start position:0% +non-negative entries and you find it +using these two equations you compute C + + align:start position:0% +using these two equations you compute C + + + align:start position:0% +using these two equations you compute C +transpose C that's V Sigma transpose + + align:start position:0% +transpose C that's V Sigma transpose + + + align:start position:0% +transpose C that's V Sigma transpose +Sigma times the V transpose and you you + + align:start position:0% +Sigma times the V transpose and you you + + + align:start position:0% +Sigma times the V transpose and you you +also have C V is use Sigma okay I hope + + align:start position:0% +also have C V is use Sigma okay I hope + + + align:start position:0% +also have C V is use Sigma okay I hope +this was a helpful illustration \ No newline at end of file diff --git a/poeHeiiiLKI.txt b/poeHeiiiLKI.txt new file mode 100644 index 0000000000000000000000000000000000000000..92e43c91b6b260a309ecbd7415357f8a0ccd40f3 --- /dev/null +++ b/poeHeiiiLKI.txt @@ -0,0 +1,411 @@ +align:start position:0% + +a basketball coach has 20 players + + align:start position:0% +a basketball coach has 20 players + + + align:start position:0% +a basketball coach has 20 players +available out of them he needs to choose + + align:start position:0% +available out of them he needs to choose + + + align:start position:0% +available out of them he needs to choose +five for the starting lineup and seven + + align:start position:0% +five for the starting lineup and seven + + + align:start position:0% +five for the starting lineup and seven +who will be sitting on the bench in how + + align:start position:0% +who will be sitting on the bench in how + + + align:start position:0% +who will be sitting on the bench in how +many ways can the coach choose these + + align:start position:0% +many ways can the coach choose these + + + align:start position:0% +many ways can the coach choose these +five plus seven players it is certainly + + align:start position:0% +five plus seven players it is certainly + + + align:start position:0% +five plus seven players it is certainly +a huge number but what exactly is it in + + align:start position:0% +a huge number but what exactly is it in + + + align:start position:0% +a huge number but what exactly is it in +this lecture we will learn how to answer + + align:start position:0% +this lecture we will learn how to answer + + + align:start position:0% +this lecture we will learn how to answer +questions of this kind more abstractly + + align:start position:0% +questions of this kind more abstractly + + + align:start position:0% +questions of this kind more abstractly +we will develop methods for counting the + + align:start position:0% +we will develop methods for counting the + + + align:start position:0% +we will develop methods for counting the +number of elements of a given set which + + align:start position:0% +number of elements of a given set which + + + align:start position:0% +number of elements of a given set which +is described in some implicit way now + + align:start position:0% +is described in some implicit way now + + + align:start position:0% +is described in some implicit way now +why do we care the reason is that in + + align:start position:0% +why do we care the reason is that in + + + align:start position:0% +why do we care the reason is that in +many models the calculation of + + align:start position:0% +many models the calculation of + + + align:start position:0% +many models the calculation of +probabilities reduces to counting + + align:start position:0% +probabilities reduces to counting + + + align:start position:0% +probabilities reduces to counting +counting the number of elements of + + align:start position:0% +counting the number of elements of + + + align:start position:0% +counting the number of elements of +various sets suppose that we have a + + align:start position:0% +various sets suppose that we have a + + + align:start position:0% +various sets suppose that we have a +probability model in which the sample + + align:start position:0% +probability model in which the sample + + + align:start position:0% +probability model in which the sample +space Omega is finite and consists of n + + align:start position:0% +space Omega is finite and consists of n + + + align:start position:0% +space Omega is finite and consists of n +equally likely elements so each element + + align:start position:0% +equally likely elements so each element + + + align:start position:0% +equally likely elements so each element +has probability 1 over n suppose now + + align:start position:0% +has probability 1 over n suppose now + + + align:start position:0% +has probability 1 over n suppose now +that we're interested in the probability + + align:start position:0% +that we're interested in the probability + + + align:start position:0% +that we're interested in the probability +of a certain set a which has K elements + + align:start position:0% +of a certain set a which has K elements + + + align:start position:0% +of a certain set a which has K elements +since each one of the elements of A has + + align:start position:0% +since each one of the elements of A has + + + align:start position:0% +since each one of the elements of A has +probability 1 over N and since a has K + + align:start position:0% +probability 1 over N and since a has K + + + align:start position:0% +probability 1 over N and since a has K +distinct elements then by the additivity + + align:start position:0% +distinct elements then by the additivity + + + align:start position:0% +distinct elements then by the additivity +axiom the probability of a is equal to K + + align:start position:0% +axiom the probability of a is equal to K + + + align:start position:0% +axiom the probability of a is equal to K +times 1 over n therefore to find the + + align:start position:0% +times 1 over n therefore to find the + + + align:start position:0% +times 1 over n therefore to find the +probability of a all we have to do is to + + align:start position:0% +probability of a all we have to do is to + + + align:start position:0% +probability of a all we have to do is to +count the number of elements of Omega + + align:start position:0% +count the number of elements of Omega + + + align:start position:0% +count the number of elements of Omega +and the number of elements of a and so + + align:start position:0% +and the number of elements of a and so + + + align:start position:0% +and the number of elements of a and so +determine the numbers K and n of course + + align:start position:0% +determine the numbers K and n of course + + + align:start position:0% +determine the numbers K and n of course +if a set is described explicitly through + + align:start position:0% +if a set is described explicitly through + + + align:start position:0% +if a set is described explicitly through +a list of its elements then counting is + + align:start position:0% +a list of its elements then counting is + + + align:start position:0% +a list of its elements then counting is +trivial but when a set is given through + + align:start position:0% +trivial but when a set is given through + + + align:start position:0% +trivial but when a set is given through +some abstract description as in our + + align:start position:0% +some abstract description as in our + + + align:start position:0% +some abstract description as in our +basketball team example counting can be + + align:start position:0% +basketball team example counting can be + + + align:start position:0% +basketball team example counting can be +a challenge in this lecture we will + + align:start position:0% +a challenge in this lecture we will + + + align:start position:0% +a challenge in this lecture we will +start with a powerful tool the basic + + align:start position:0% +start with a powerful tool the basic + + + align:start position:0% +start with a powerful tool the basic +counting principle which allows us to + + align:start position:0% +counting principle which allows us to + + + align:start position:0% +counting principle which allows us to +break a counting problem into a sequence + + align:start position:0% +break a counting problem into a sequence + + + align:start position:0% +break a counting problem into a sequence +of simpler counting problems we will + + align:start position:0% +of simpler counting problems we will + + + align:start position:0% +of simpler counting problems we will +then count permutations subsets + + align:start position:0% +then count permutations subsets + + + align:start position:0% +then count permutations subsets +combinations and partitions we will see + + align:start position:0% +combinations and partitions we will see + + + align:start position:0% +combinations and partitions we will see +shortly what all of these terms mean + + align:start position:0% +shortly what all of these terms mean + + + align:start position:0% +shortly what all of these terms mean +in the process we will solve a number of + + align:start position:0% +in the process we will solve a number of + + + align:start position:0% +in the process we will solve a number of +example problems and we will also derive + + align:start position:0% +example problems and we will also derive + + + align:start position:0% +example problems and we will also derive +the formula for the binomial + + align:start position:0% +the formula for the binomial + + + align:start position:0% +the formula for the binomial +probabilities the probabilities that + + align:start position:0% +probabilities the probabilities that + + + align:start position:0% +probabilities the probabilities that +describe the number of heads in a + + align:start position:0% +describe the number of heads in a + + + align:start position:0% +describe the number of heads in a +sequence of independent coin tosses so + + align:start position:0% +sequence of independent coin tosses so + + + align:start position:0% +sequence of independent coin tosses so +let us get started \ No newline at end of file diff --git a/rZ3-nFV6l8w.txt b/rZ3-nFV6l8w.txt new file mode 100644 index 0000000000000000000000000000000000000000..8a5470ecfd319f62d20dadc2986404b88d08d607 --- /dev/null +++ b/rZ3-nFV6l8w.txt @@ -0,0 +1,2194 @@ +y prime and y double prime. + +So, q of x times y +equal zero. + +The linearity of the equation, +that is, the form in which it + +appears is going to be the key +idea today. + +Today is going to be +theoretical, but some of the + +ideas in it are the most +important in the course. + +So, I don't have to apologize +for the theory. + +Remember, the solution method +was to find two independent y + +one, y two +independent solutions. + +And now, I'll formally write +out what independent means. + +There are different ways to say +it. + +But for you, +I think the simplest and most + +intelligible will be to say that +y2 is not to be a constant + +multiple of y1. +And, unfortunately, + +it's necessary to add, +nor is y1 to be a constant + +multiple. +I have to call it by different + +constants. +So, let's call this one c prime + +of y2. +Well, I mean, + +the most obvious question is, +well, look. + +If this is not a constant times +that, this can't be there + +because I would just use one +over c if it was. + +Unfortunately, +the reason I have to write it + +this way is to take account of +the possibility that y1 might be + +zero. +If y1 is zero, + +so, the bad case that must be +excluded is that y1 equals zero, + +y2 nonzero. +I don't want to call those + +independent. +But nonetheless, + +it is true that y2 is not a +constant multiple of y1. + +However, y1 is a constant +multiple of y2, + +namely, the multiple zero. +It's just to exclude that case + +that I have to say both of those +things. + +And, one would not be sufficed. +That's a fine point that I'm + +not going to fuss over. +But I just have, + +of course. +Now, why do you do that? + +That's because, +then, all solutions, + +and this is what concerns us +today, are what? + +The linear combination with +constant coefficients of these + +two, and the fundamental +question we have to answer today + +is, why? +Now, there are really two + +statements involved in that. +On the one hand, + +I'm claiming there is an easier +statement, which is that they + +are all solutions. +So, that's question one, + +or statement one. +Why are all of these guys + +solutions? +That, I could trust you to + +answer yourself. +I could not trust you to answer + +it elegantly. +And, it's the elegance that's + +the most important thing today +because you have to answer it + +elegantly. +Otherwise, you can't go on and + +do more complicated things. +If you answer it in an ad hoc + +basis just by hacking out a +computation, you don't really + +see what's going on. +And you can't do more difficult + +things later. +So, we have to answer this, + +and answer it nicely. +The second question is, + +so, if that answers why there +are solutions at all, + +why are they all the solutions? +Why all the solutions? + +In other words, +to say it as badly as possible, + +why are all solutions, +why all the solutions-- Never + +mind. +Why are all the solutions. + +This is a harder question to +answer, but that should make you + +happy because that means it +depends upon a theorem which I'm + +not going to prove. +I'll just quote to you. + +Let's attack there for problem +one first. + +q1 is answered by what's called +the superposition. + +The superposition principle +says exactly that. + +It says exactly that, +that if y1 and y2 are solutions + +to a linear equation, +to a linear homogeneous ODE, + +in fact it can be of higher +order, too, although I won't + +stress that. +In other words, + +you don't have to stop with the +second derivative. + +You could add a third +derivative and a fourth + +derivative. +As long as the former makes the + +same, but that implies +automatically that c1 y1 plus c2 + +y2 is a solution. +Now, the way to do that nicely + +is to take a little detour and +talk a little bit about linear + +operators. +And, since we are going to be + +using these for the rest of the +term, this is the natural place + +for you to learn a little bit +about what they are. + +So, I'm going to do it. +Ultimately, I am aimed at a + +proof of this statement, +but there are going to be + +certain side excursions I have +to make. + +The first side side excursion +is to write the differential + +equation in a different way. +So, I'm going to just write its + +transformations. +The first, I'll simply recopy + +what you know it to be, +q y equals zero. + +That's the first form. +The second form, + +I'm going to replace this by +the differentiation operator. + +So, I'm going to write this as +D squared y. + +That means differentiate it +twice. + +D it, and then D it again. +This one I only have to + +differentiate once, +so I'll write that as p D(y), + +p times the derivative of Y. +The last one isn't + +differentiated at all. +I just recopy it. + +Now, I'm going to formally +factor out the y. + +So this, I'm going to turn into +D squared plus pD plus q. + +Now, everybody reads this as + +times y equals zero. +But, what it means is this guy, + +it means this is shorthand for +that. + +I'm not multiplying. +I'm multiplying q times y. + +But, I'm not multiplying D +times y. + +I'm applying D to y. +Nonetheless, + +the notation suggests this is +very suggestive of that. + +And this, in turn, +implies that. + +I'm just transforming it. +And now, I'll take the final + +step. +I'm going to view this thing in + +parentheses as a guy all by +itself, a linear operator. + +This is a linear operator, +called a linear operator. + +And, I'm going to simply +abbreviate it by the letter L. + +And so, the final version of +this equation has been reduced + +to nothing but Ly equals zero. + +Now, what's L? +You can think of L as, + +well, formally, +L you would write as D squared + +plus pD plus q. +But, you can think of L, + +the way to think of it is as a +black box, a function of what + +goes into the black box, +well, if this were a function + +box, what would go it would be a +number, and what would come out + +with the number. +But it's not that kind of a + +black box. +It's an operator box, + +and therefore, +what goes in is a function of + +x. +And, what comes out is another + +function of x, +the result of applying this + +operator to that. +So, from this point of view, + +differential equations, +trying to solve the + +differential equation means, +what should come out you want + +to come out zero, +and the question is, + +what should you put in? +That's what it means solving + +differential equations in an +inverse problem. + +The easy thing is to put it a +function, and see what comes + +out. +You just calculate. + +The hard thing is to ask, +you say, I want such and such a + +thing to come out, +for example, + +zero; what should I put in? +That's a difficult question, + +and that's what we're spending +the term answering. + +Now, the key thing about this +is that this is a linear + +operator. +And, what that means is that it + +behaves in a certain way with +respect to functions. + +The easiest way to say it is, +I like to make two laws of it, + +that L of u1, +if you have two functions, + +I'm not going to put up the +parentheses, x, + +because that just makes things +look longer and not any clearer, + +actually. +What does L do to the sum of + +two functions? +If that's a linear operator, + +if you put in the sum of two +functions, what you must get out + +is the corresponding L's, +the sum of the corresponding + +L's of each. +So, that's a law. + +And, the other law, +linearity law, + +and this goes for anything in +mathematics and its + +applications, +which is called linear, + +basically anything is linear if +it does the following thing to + +functions or numbers or +whatever. + +The other one is of a constant +times any function, + +I don't have to give it a +number now because I'm only + +using one of them, +should be equal to c times L of + +u. +So, here, c is a constant, + +and here, of course, +the u is a function, + +functions of x. +These are the two laws of + +linearity. +An operator is linear if it + +satisfies these two laws. +Now, for example, + +the differentiation operator is +such an operator. + +D is linear, +why? + +Well, because of the very first +things you verify after you + +learn what the derivative is +because the derivative of, + +well, I will write it in the D +form. + +I'll write it in the form in +which you know it. + +It would be D apply to u1 plus +u2. + +How does one write that in +ordinary calculus? + +Well, like that. +Or, maybe you write d by dx out + +front. +Let's write it this way, + +is equal to u1 prime plus u2 +prime. + +That's a law. +You prove it when you first + +study what a derivative is. +It's a property. + +From our point of view, +it's a property of the + +differentiation operator. +It has this property. + +The D of u1 plus u2 is D of u1 +plus D of u2. + +And, it also has the property + +that c u prime, +you can pull out the constant. + +That's not affected by the +differentiation. + +So, these two familiar laws +from the beginning of calculus + +say, in our language, +that D is a linear operator. + +What about the multiplication +of law? + +That's even more important, +that u1 times u2 prime, + +I have nothing whatever to say +about that in here. + +In this context, +it's an important law, + +but it's not important with +respect to the study of + +linearity. +So, there's an example. + +Here's a more complicated one +that I'm claiming is the linear + +operator. +And, since I don't want to have + +to work in this lecture, +the work is left to you. + +So, the proof, +prove that L is linear, + +is this particular operator. +L is linear. + +That's in your part one +homework to verify that. + +And you will do some simple +exercises in recitation tomorrow + +to sort of warm you up for that +if you haven't done it already. + +Well, you shouldn't have +because this only goes with this + +lecture, actually. +It's forbidden to work ahead in + +this class. +All right, where are we? + +Well, all that was a prelude to +proving this simple theorem, + +superposition principle. +So, finally, + +what's the proof? +The proof of the superposition + +principle: if you believe that +the operator is linear, + +then L of c1, +in other words, + +the ODE is L. +L is D squared plus pD plus q. + +So, the ODE is Ly equals zero. + +And, what am I being asked to + +prove? +I'm being asked to prove that + +if y1 and y2 are solutions, +then so is that thing. + +By the way, that's called a +linear combination. + +Put that in your notes. +Maybe I better write it even on + +the board because it's something +people say all the time without + +realizing they haven't defined +it. + +This is called a linear +combination. + +This expression is called a +linear combination of y1 and y2. + +It means that particular sum +with constant coefficients. + +Okay, so, the ODE is Ly equals +zero. + +And, I'm trying to prove that +fact about it, + +that if y1 and y2 are +solutions, so is a linear + +combination of them. +So, the proof, + +then, I start with apply L to +c1 y1 plus c2 y2. + +Now, because this operator is + +linear, it takes the sum of two +functions into the corresponding + +sum up what the operator would +be. + +So, it would be L of c1 y1 plus +L of c2 y2. + +That's because L is a linear + +operator. +But, I don't have to stop + +there. +Because L is a linear operator, + +I can pull the c out front. +So, it's c1 L of y1 plus c2 L + +of y2. Now, where am I? + +Trying to prove that this is +zero. + +Well, what is L of y1? +At this point, + +I use the fact that y1 is a +solution. + +Because it's a solution, +this is zero. + +That's what it means to solve +that differential equation. + +It means, when you apply the +linear operator, + +L, to the function, +you get zero. + +In the same way, +y2 is a solution. + +So, that's zero. +And, the sum of c1 times zero + +plus c2 times zero is zero. + +That's the argument. +Now, you could make the same + +argument just by plugging c1 y1, +plugging it into the equation + +and calculating, +and calculating, + +and calculating, +grouping the terms and so on + +and so forth. +But, that's just calculation. + +It doesn't show you why it's +so. + +Why it's so is because the +operator, this differential + +equation is expressed as a +linear operator applied to y is + +zero. +And, the only properties that + +are really been used as the fact +that this operator is linear. + +That's the key point. +L is linear. + +It's a linear operator. +Well, that's all there is to + +the superposition principle. +As a prelude to answering the + +more difficult question, +why are these all the + +solutions? +Why are there no other + +solutions? +We need a few definitions, + +and a few more ideas. +And, they are going to occur in + +connection with, +so I'm now addressing, + +ultimately, question two. +But, it's not going to be + +addressed directly for quite +awhile. + +Instead, I'm going to phrase it +in terms of solving the initial + +value problem. +So far, we've only talked about + +the general solution with those +two arbitrary constants. + +But, how do you solve the +initial value problem, + +in other words, +fit initial conditions, + +find the solution with given +initial values for the function + +and its derivatives. +Now, -- + +-- the theorem is that this +collection of functions with + +these arbitrary constants, +these are all the solutions we + +have so far. +In fact, they are all the + +solutions there are, +but we don't know that yet. + +However, if we just focus on +the big class of solutions, + +there might be others lurking +out there somewhere lurking out + +there. +I don't know. + +But let's use what we have, +that just from this family is + +enough to satisfy any initial +condition, to satisfy any + +initial values. +In other words, + +if you give me any initial +values, I will be able to find + +the c1 and c2 which work. +Now, why is that? + +Well, I'd have to do a song and +dance at this point, + +if you hadn't been softened up +by actually calculating for + +specific differential equations. +You've had exercises and + +actually how to calculate the +values of c1 and c2. + +So, I'm going to do it now in +general what you have done so + +far for particular equations +using particular values of the + +initial conditions. +So, I'm relying on that + +experience that you've had in +doing the homework to make + +intelligible what I'm going to +do now in the abstract using + +just letters. +So, why is this so? + +Why is that so? +Well, we are going to need it, + +by the way, here, +too. + +I'll have to, +again, open up parentheses. + +But let's go as far as we can. +Well, you just try to do it. + +Suppose the initial conditions +are, how will we write them? + +So, they're going to be at some +initial point, + +x0. +You can take it to be zero if + +you want, but I'd like to be, +just for a little while, + +a little more general. +So, let's say the initial + +conditions, the initial values +are being given at the point x0, + +all right, that's going to be +some number. + +Let's just call it a. +And, the initial value also has + +to specify the velocity or the +value of the derivative there. + +Let's say these are the initial +values. + +So, the problem is to find the +c which work. + +Now, how do you do that? +Well, you know from + +calculation. +You write y equals c1 y1 plus + +c2 y2. +And you write y prime, + +and you take the derivative +underneath that, + +which is easy to do. +And now, you plug in x equals + +zero. +And, what happens? + +Well, these now turn into a set +of equations. + +What will they look like? +Well, y of x0 is a, + +and this is b. +So, what I get is let me flop + +it over onto the other side +because that's the way you're + +used to looking at systems of +equations. + +So, what we get is c1 times y1 +of x0 plus c2 times y2 of x0. + +What's that supposed to be + +equal to? +Well, that's supposed to be + +equal to y of x0. +It's supposed to be equal to + +the given number, +a. + +And, in the same way, +c1 y1 prime of x0 plus c2 y2 + +prime of x0, that's supposed to +turn out to + +be the number, b. + +In the calculations you've done +up to this point, + +y1 and y2 were always specific +functions like e to the x + +or cosine of 22x, + +stuff like that. +Now I'm doing it in the + +abstract, just calling them y1 +and y2, so as to include all + +those possible cases. +Now, what am I supposed to do? + +I'm supposed to find c1 and c2. +What kind of things are they? + +This is what you studied in +high school, right? + +The letters are around us, +but it's a pair of simultaneous + +linear equations. +What are the variables? + +What are the variables? +What are the variables? + +Somebody raise their hand. +If you have a pair of + +simultaneous linear equations, +you've got variables and you've + +got constants, +right? + +And you are trying to find the +answer. + +What are the variables? +Yeah? + +c1 and c2. +Very good. + +I mean, it's extremely +confusing because in the first + +place, how can they be the +variables if they occur on the + +wrong side? +They're on the wrong side; + +they are constants. +How can constants be variables? + +Everything about this is wrong. +Nonetheless, + +the c1 and the c2 are the +unknowns, if you like the high + +school terminology. +c1 and c2 are the unknowns. + +These messes are just numbers. +After you've plugged in x0, + +this is some number. +You've got four numbers here. + +So, c1 and c2 are the +variables. + +The two find, +in other words, + +to find the values of. +All right, now you know general + +theorems from 18.02 about when +can you solve such a system of + +equations. +I'm claiming that you can + +always find c1 and c2 that work. +But, you know that's not always + +the case that a pair of +simultaneous linear equations + +can be solved. +There's a condition. + +There's a condition which +guarantees their solution, + +which is what? +What has to be true about the + +coefficients? +These are the coefficients. + +What has to be true? +The matrix of coefficients must + +be invertible. +The determinant of coefficients + +must be nonzero. +So, they are solvable if, + +for the c1 and c2, +if this thing, + +I'm going to write it. +Since all of these are + +evaluated at x0, +I'm going to write it in this + +way. +y1, the determinant, + +whose entries are y1, +y2, y1 prime, + +and y2 prime, + +evaluated at zero, +x0, that means that I evaluate + +each of the functions in the +determinant at x0. + +I'll write it this way. +That should be not zero. + +So, in other words, +the key thing which makes this + +possible, makes it possible for +us to solve the initial value + +problem, is that this funny +determinant should not be zero + +at the point at which we are +interested. + +Now, this determinant is +important in 18.03. + +It has a name, +and this is when you're going + +to learn it, if you don't know +it already. + +That determinant is called the +Wronskian. + +The Wronskian of what? +If you want to be pompous, + +you say this with a V sound +instead of a W. + +But, nobody does except people +trying to be pompous. + +The Wronskian, +we'll write a W. + +Now, notice, +you can only calculate it when + +you know what the two functions +are. + +So, the Wronskian of the two +functions, y1 and y2, + +what's the variable? +It's not a function of two + +variables, y1 and y2. +These are just the names of + +functions of x. +So, when you do it, + +put it in, calculate out that +determinant. + +This is a function of x, +a function of the independent + +variable after you've done the +calculation. + +Anyway, let's write its +definition, y1, + +y2, y1 prime, +y2 prime. + +Now, in order to do this, + +the point is we must know that +that Wronskian is not zero, + +that the Wronskian of these two +functions is not zero at the + +point x0. +Now, enter a theorem which + +you're going to prove for +homework, but this is harder. + +So, it's part two homework. +It's not part one homework. + +In other words, +I didn't give you the answer. + +You've got to find it yourself, +alone or in the company of good + +friends. +So, anyway, here's the + +Wronskian. +Now, what can we say for sure? + +Note, suppose y1 and y, +just to get you a feeling for + +it a little bit, +suppose they were not + +independent. +The word for not independent is + +dependent. +Suppose they were dependent. + +In other words, +suppose that y2 were a constant + +multiple of y1. +We know that's not the case + +because our functions are +supposed to be independent. + +But suppose they weren't. +What would the value of the + +Wronskian be? +If y2 is a constant times y1, + +then y2 prime is that same +constant times y1 prime. + +What's the value of the +determinant? + +Zero. +For what values of x is it zero + +for all values of x? +And now, that's the theorem + +that you're going to prove, +that if y1 and y2 are solutions + +to the ODE, I won't keep, +say, it's the ODE we've been + +talking about, +y double prime plus py. + +But the linear homogeneous with + +not constant coefficients, +just linear homogeneous second + +order. +Our solutions, + +as there are only two +possibilities, + +either-or. +Either the Wronskian of y, + +there are only two +possibilities. + +Either the Wronskian of y1 and +y2 is always zero, + +identically zero, +zero for all values of x. + +This is redundant. +When I say identically, + +I mean for all values of x. +But, I am just making assurance + +doubly sure. +Or, or the Wronskian is never + +zero. +Now, there is no notation as + +for that. +I'd better just write it out, + +is never zero, +i.e. + +for no x is it, +i.e. + +for all x. +There's no way to say that. + +I mean, for all values of x, +it's not zero. + +That means, there is not a +single point for which it's + +zero. +In particular, + +it's not zero here. +So, this is your homework: + +problem five, +part two. + +I'll give you a method of +proving it, which was discovered + +by the famous Norwegian +mathematician, + +Abel, who is, +I guess, the centenary of his + +birth, I guess, +was just celebrated last year. + +He has one of the truly tragic +stories in mathematics, + +which I think you can read. +It must be a Simmons book, + +if you have that. +Simmons is very good on + +biographies. +Look up Abel. + +He'll have a biography of Abel, +and you can weep if you're + +feeling sad. +He died at the age of 26 of + +tuberculosis, +having done a number of + +sensational things, +none of which was recognized in + +his lifetime because people +buried his papers under big + +piles of papers. +So, he died unknown, + +uncelebrated, +and now he's Norway's greatest + +culture hero. +In the middle of a park in + +Oslo, there's a huge statue. +And, since nobody knows what + +Abel looked like, +the statue is way up high so + +you can't see very well. +But, the inscription on the + +bottom says Niels Henrik Abel, +1801-1826 or something like + +that. +Now, -- + +-- the choice, +I'm still, believe it or not, + +aiming at question two, +but I have another big + +parentheses to open. +And, when I closed it, + +the answer to question two will +be simple. + +But, I think it's very +desirable that you get this + +second big parentheses. +It will help you to understand + +something important. +It will help you on your + +problem set tomorrow night. +I don't have to apologize. + +I'm just going to do it. +So, the question is, + +the thing you have to +understand is that when I write + +this combination, +I'm claiming that these are all + +the solutions. +I haven't proved that yet. + +But, they are going to be all +the solutions + +The point is, +there's nothing sacrosanct + +about the y1 and y2. +This is exactly the same + +collection as a collection which +I would write using other + +constants. +Let's call them u1 and u2. + +They are exactly the same, +where u1 and u2 are any other + +pair of linearly independent +solutions. + +Any other pair of independent +solutions, they must be + +independent, either a constant +multiple of each other. + +In other words, +u1 is some combination, + +now I'm really stuck because I +don't know how to, + +c1 bar, let's say, +that means a special value of + +c1, and a special value of c2, +and u2 is some other special + +value, oh my God, +c1 double bar, + +how's that? +The notation is getting worse + +and worse. +I apologize for it. + +In other words, +I could pick y1 and y2 and make + +up all of these. +And, I'd get a bunch of + +solutions. +But, I could also pick some + +other family, +some other two guys in this + +family, and just as well express +the solutions in terms of u1 and + +u2. +Now, well, why is he telling us + +that? +Well, the point is that the y1 + +and the y2 are typically the +ones you get easily from solving + +the equations, +like e to the x and e + +to the 2x. +That's what you've gotten, + +or cosine x and sine x, + +something like that. +But, for certain ways, + +they might not be the best way +of writing the solutions. + +There is another way of writing +those that you should learn, + +and that's called finding +normalized, the normalized. + +They are okay, +but they are not normalized. + +For some things, +the normalized solutions are + +the best. +I'll explain to you what they + +are, and I'll explain to you +what they're good for. + +You'll see immediately what +they're good for. + +Normalized solutions, +now, you have to specify the + +point at which you're +normalizing. + +In general, it would be x +nought, + +but let's, at this point, +since I don't have an infinity + +of time, to simplify things, +let's say zero. + +It could be x nought, +any point would do just as + +well. +But, zero is the most common + +choice. +What are the normalized + +solutions? +Well, first of all, + +I have to give them names. +I want to still call them y. + +So, I'll call them capital Y1 +and Y2. + +And, what they are, +are the solutions which satisfy + +certain, special, +very special, + +initial conditions. +And, what are those? + +So, they're the ones which +satisfy, the initial conditions + +for Y1 are, of course there are +going to be guys that look like + +this. +The only thing that's going to + +make them distinctive is the +initial conditions they satisfy. + +Y1 has to satisfy at zero. +Its value should be one, + +and the value of its derivative +should be zero. + +For Y2, it's just the opposite. +Here, the value of the function + +should be zero at zero. +But, the value of its + +derivative, now, +I want to be one. + +Let me give you a trivial +example of this, + +and then one, +which is a little less trivial, + +so you'll have some feeling for +what I'm asking for. + +Suppose the equation, +for example, + +is y double prime plus, +well, let's really make it + +simple. +Okay, you know the standard + +solutions are y1 is cosine x, + +and y2 is sine x. + +These are functions, +which, when you take the second + +derivative, they turn into their +negative. + +You know, you could go the +complex roots are i and minus i, + +and blah, blah, +blah, blah, blah, + +blah. +If you do it that way, + +fine. +But at some point in the course + +you have to be able to write +down and, right away, + +oh, yeah, cosine x, +sine x. + +Okay, what are the normalized + +things? +Well, what's the value of this + +at zero? +It is one. + +What's the value of its +derivative at zero? + +Zero. +This is Y1. + +This is the only case in which +you locked on immediately to the + +normalized solutions. +In the same way, + +this guy is Y2 because its +value at zero is zero. + +It's value of its derivative at +zero is one. + +So, this is Y2. +Okay, now let's look at a case + +where you don't immediately lock +on to the normalized solutions. + +Very simple: +all I have to do is change the + +sign. +Here, you know, + +think through r squared minus +one equals zero. + +The characteristic roots are +plus one and minus one, + +right? +And therefore, + +the solution is e to the x, +and e to the negative x. + +So, the solutions you find by + +the usual way of solving it is +y1 equals e to the x, + +and y2 equals e to the +negative x. + +Those are the standard +solution. + +So, the general solution is of +the form. + +So, the general solution is of +the form c1 e to the x plus c2 e + +to the negative x. + +Now, what I want to find out is +what is Y1 and Y2? + +How do I find out what Y1 is? +Well, I have to satisfy initial + +conditions. +So, if this is y, + +let's write down here, +if you can still see that, + +y prime is c1 e to the x minus +c2 e to the negative x . + +So, if I plug in, + +I want y of zero to be one, +I want this guy at the point + +zero to be one. +What equation does that give + +me? +That gives me c1 plus c2, + +c1 plus c2, +plugging in x equals zero, + +equals the value of this thing +at zero. + +So, that's supposed to be one. + +How about the other guy? +The value of its derivative is + +supposed to come out to be zero. +And, what is its derivative? + +Well, plug into this +expression. + +It's c1 minus c2. +Okay, what's the solution to + +those pair of equations? +c2 has to be equal to c1. + +The sum of the two of them has +to be one. + +Each one, therefore, +is equal to one half. + +And so, what's the value of Y1? +Y1, therefore, + +is the function where c1 and c2 +are one half. + +It's the function e to the x +plus e to the negative x divided + +by two. + +In the same way, +I won't repeat the calculation. + +You can do yourself. +Same calculation shows that Y2, + +so, put in the initial +conditions. + +The answer will be that Y2 is +equal to e to the x minus e to + +the minus x divided by two. + +These are the special +functions. + +For this equation, +these are the normalized + +solutions. +They are better than the + +original solutions because their +initial values are nicer. + +Just check it. +The initial value, + +when x is equal to zero, +the initial value, + +this has is zero. +Here, when x is equal to zero, + +the value of the function is +zero. + +But, the value of its +derivative, these cancel, + +is one. +So, these are the good guys. + +Okay, there's no colored chalk +this period. + +Okay, there was colored chalk. +There's one. + +So, for this equation, +these are the good guys. + +These are our best solutions. +e to the x and e to the + +minus x are good solutions. + +But, these are our better +solutions. + +And, this one, +of course, is the function + +which is called hyperbolic sine +of x, and this is the one which + +is called hyperbolic cosine of +x. + +This is one of the most +important ways in which they + +enter into mathematics. +And, this is why the engineers + +want them. +Now, why do the engineers want + +normalized solutions? +Well, I didn't explain that. + +So, what's so good about +normalized solutions? + +Very simple: +if Y1 and Y2 are normalized at + +zero, let's say, +then the solution to the IVP, + +in other words, +the ODE plus the initial + +values, y of zero equals, +let's say, a and y + +prime of zero equals b. + +So, the ODE I'm not repeating. +It's the one we've been talking + +about all term since the +beginning of the period. + +It's the one with the p of x +and q of x. + +And, here are the initial +values. + +I'm going to call them a and b. +You can also call them, + +if you like, +maybe that's better to call + +them y0, as they are individual +in the homework. + +They are called, +I'm using the, + +let's use those. +What is the solution? + +I say the solution is, +if you use y1 and y2, + +the solution is y0, +in other words, + +the a times Y1, +plus y0 prime, + +in other words, +b times Y2. + +In other words, +you can write down instantly + +the solution to the initial +value problem, + +if instead of using the +functions, you started out with + +the little Y1 and Y2, +you use these better functions. + +The thing that's better about +them is that they instantly + +solve for you the initial value +problem. + +All you do is use this number, +initial condition as the + +coefficient of Y1, +and use this number as the + +coefficient of Y2. +Now, just check that by looking + +at it. +Why is that so? + +Well, for example, +let's check. + +What is its value of this +function at zero? + +Well, the value of this guy at +zero is one. + +So, the answer is y0 times one, +and the value of this guy at + +zero is zero. +So, this term disappears. + +And, it's exactly the same with +the derivative. + +What's the value of the +derivative at zero? + +The value of the derivative of +this thing is zero. + +So, this term disappears. +The value of this derivative at + +zero is one. And so, +the answer is y0 prime. + +So, check, check, + +this works. +So, these better solutions have + +the property, +what's good about them, + +and why scientists and +engineers like them, + +is that they enable you +immediately to write down the + +answer to the initial value +problem without having to go + +through this business, +which I buried down here, + +of solving simultaneous linear +equations. + +Okay, now, believe it or not, +that's all the work. + +We are ready to answer question +number two: why are these all + +the solutions? +Of course, I have to invoke a + +big theorem. +A big theorem: + +where shall I invoke a big +theorem? + +Let's see if we can do it here. +The big theorem says, + +it's called the existence and +uniqueness theorem. + +It's the last thing that's +proved at the end of an analysis + +course, at which real analysis +courses, over which students + +sweat for one whole semester, +and their reward at the end is, + +if they are very lucky, +and if they have been very good + +students, they get to see the +proof of the existence and + +uniqueness theorem for +differential equations. + +But, I can at least say what it +is for the linear equation + +because it's so simple. +It says, so, + +the equation we are talking +about is the usual one, + +homogeneous equation, +and I'm going to assume, + +you have to have assumptions +that p and q are continuous for + +all x. +So, they're good-looking + +functions. +Coefficients aren't allowed to + +blow up anywhere. +They've got to look nice. + +Then, the theorem says there is +one and only one solution, + +one and only solution +satisfying, given initial values + +such that y of zero, +let's say y of zero is equal to + +some given number, A, + +and y, let's make y0, +and y prime of zero equals B. + +The initial value problem has + +one and only one solution. +The existence is, + +it has a solution. +The uniqueness is, + +it only has one solution. +If you specify the initial + +conditions, there's only one +function which satisfies them + +and at the same time satisfies +that differential equation. + +Now, this answers our question. +This answers our question, + +because, look, +what I want is all solutions. + +What we want are all solutions +to the ODE. + +And now, here's what I say: +a claim that this collection of + +functions, c1 Y1 plus c2 Y2 +are all + +solutions. +Of course, I began a period by + +saying I'd show you that c1 +little y1 c little y2 are all + +the solutions. +But, it's the case that these + +two families are the same. +So, the family that I started + +with would be exactly the same +as the family c1 prime Y1 + +because, +after all, these are two + +special guys from that +collection. + +So, it doesn't matter whether I +talk about the original ones, + +or these. +The theorem is still the same. + +The final step, +therefore, if you give me one + +more minute, I think that will +be quite enough. + +Why are these all the +solutions? + +Well, I have to take an +arbitrary solution and show you + +that it's one of these. +So, the proof is, + +given a solution, +u(x), what are its values? + +Well, u of x zero is u zero, + +and u prime of x zero, zero, + +let's say, is equal to u zero, +is equal to some other + +number. +Now, what's the solution? + +Write down what's the solution +of these using the Y1's? + +Then, I know I've just shown +you that u zero times Y1 plus u + +zero prime Y2 +satisfies the same initial + +conditions, satisfies these +initial conditions, + +initial values. +In other words, + +I started with my little +solution. + +u of x walks up to and +says, hi there. + +Hi there, and the differential +equation looks at it and says, + +who are you? +You say, oh, + +I satisfy you and my initial, +and then it says what are your + +initial values? +It says, my initial values are + +u0 and u0 prime. +And, it said, + +sorry, but we've got one of +ours who satisfies the same + +initial conditions. +We don't need you because the + +existence and uniqueness theorem +says that there can only be one + +function which does that. +And therefore, + +you must be equal to this guy +by the uniqueness theorem. + +Okay, we'll talk more about +stuff next time, + +linear equation next time. \ No newline at end of file diff --git a/s_dn2M7JWy8.txt b/s_dn2M7JWy8.txt new file mode 100644 index 0000000000000000000000000000000000000000..865a5d6ab166ccd65497c20d7d81b8c4be905562 --- /dev/null +++ b/s_dn2M7JWy8.txt @@ -0,0 +1,307 @@ +align:start position:0% + +There can be a temptation a tendency for + + align:start position:0% +There can be a temptation a tendency for + + + align:start position:0% +There can be a temptation a tendency for +technical people for scientists and + + align:start position:0% +technical people for scientists and + + + align:start position:0% +technical people for scientists and +engineers to constrict their definition + + align:start position:0% +engineers to constrict their definition + + + align:start position:0% +engineers to constrict their definition +of a problem. So they redefine a problem + + align:start position:0% +of a problem. So they redefine a problem + + + align:start position:0% +of a problem. So they redefine a problem +around what can be solved technically. + + align:start position:0% +around what can be solved technically. + + + align:start position:0% +around what can be solved technically. +So first they determine what they as + + align:start position:0% +So first they determine what they as + + + align:start position:0% +So first they determine what they as +technicians can solve and then having + + align:start position:0% +technicians can solve and then having + + + align:start position:0% +technicians can solve and then having +done that they define that as the + + align:start position:0% +done that they define that as the + + + align:start position:0% +done that they define that as the +problem that has to be solved. Um, so + + align:start position:0% +problem that has to be solved. Um, so + + + align:start position:0% +problem that has to be solved. Um, so +it's tempting to define this particular + + align:start position:0% +it's tempting to define this particular + + + align:start position:0% +it's tempting to define this particular +problem left behind by the attacks of + + align:start position:0% +problem left behind by the attacks of + + + align:start position:0% +problem left behind by the attacks of +September the 11th as a technical + + align:start position:0% +September the 11th as a technical + + + align:start position:0% +September the 11th as a technical +problem. And then you can start um to + + align:start position:0% +problem. And then you can start um to + + + align:start position:0% +problem. And then you can start um to +talk about some of the things that Tolto + + align:start position:0% +talk about some of the things that Tolto + + + align:start position:0% +talk about some of the things that Tolto +was talking about just now. Increasing + + align:start position:0% +was talking about just now. Increasing + + + align:start position:0% +was talking about just now. Increasing +security at airports, increasing uh + + align:start position:0% +security at airports, increasing uh + + + align:start position:0% +security at airports, increasing uh +surveillance of people's email messages, + + align:start position:0% +surveillance of people's email messages, + + + align:start position:0% +surveillance of people's email messages, +making sure cockpit doors uh are much + + align:start position:0% +making sure cockpit doors uh are much + + + align:start position:0% +making sure cockpit doors uh are much +harder to break down, putting + + align:start position:0% +harder to break down, putting + + + align:start position:0% +harder to break down, putting +surveillance cameras inside planes, + + align:start position:0% +surveillance cameras inside planes, + + + align:start position:0% +surveillance cameras inside planes, +giving pilots their own weapons + + align:start position:0% +giving pilots their own weapons + + + align:start position:0% +giving pilots their own weapons +technology so that they could + + align:start position:0% +technology so that they could + + + align:start position:0% +technology so that they could +potentially subdue hijackers and so on. + + align:start position:0% +potentially subdue hijackers and so on. + + + align:start position:0% +potentially subdue hijackers and so on. +And I want to point out that while these + + align:start position:0% +And I want to point out that while these + + + align:start position:0% +And I want to point out that while these +uh these changes would not be useless, + + align:start position:0% +uh these changes would not be useless, + + + align:start position:0% +uh these changes would not be useless, +there are two problems. First of all, + + align:start position:0% +there are two problems. First of all, + + + align:start position:0% +there are two problems. First of all, +they don't address the root causes of + + align:start position:0% +they don't address the root causes of + + + align:start position:0% +they don't address the root causes of +terrorism itself, which are political, + + align:start position:0% +terrorism itself, which are political, + + + align:start position:0% +terrorism itself, which are political, +not technical. And second, they may + + align:start position:0% +not technical. And second, they may + + + align:start position:0% +not technical. And second, they may +raise the obstacles, but you can never + + align:start position:0% +raise the obstacles, but you can never + + + align:start position:0% +raise the obstacles, but you can never +raise the obstacles to such a height + + align:start position:0% +raise the obstacles to such a height + + + align:start position:0% +raise the obstacles to such a height +that people can't jump over them or work + + align:start position:0% +that people can't jump over them or work + + + align:start position:0% +that people can't jump over them or work +around them. So that the problem for + + align:start position:0% +around them. So that the problem for + + + align:start position:0% +around them. So that the problem for +terrorists will be like the problem for + + align:start position:0% +terrorists will be like the problem for + + + align:start position:0% +terrorists will be like the problem for +burglars. Every time there's a new car + + align:start position:0% +burglars. Every time there's a new car + + + align:start position:0% +burglars. Every time there's a new car +burglar alarm or a new alarm system in + + align:start position:0% +burglar alarm or a new alarm system in + + + align:start position:0% +burglar alarm or a new alarm system in +homes, they just have to figure out a + + align:start position:0% +homes, they just have to figure out a + + + align:start position:0% +homes, they just have to figure out a +new way around it. But eventually they + + align:start position:0% +new way around it. But eventually they + + + align:start position:0% +new way around it. But eventually they +do. \ No newline at end of file diff --git a/smHwRzk81b0.txt b/smHwRzk81b0.txt new file mode 100644 index 0000000000000000000000000000000000000000..799d1a184a2d89c6fe52ba3f06cafe1723edfa3b --- /dev/null +++ b/smHwRzk81b0.txt @@ -0,0 +1,11651 @@ +align:start position:0% + +okay so we're going to start a new topic + + align:start position:0% +okay so we're going to start a new topic + + + align:start position:0% +okay so we're going to start a new topic +today we're going to spend the next + + align:start position:0% +today we're going to spend the next + + + align:start position:0% +today we're going to spend the next +three or so lectures talking about + + align:start position:0% +three or so lectures talking about + + + align:start position:0% +three or so lectures talking about +spectral analysis and we're going to + + align:start position:0% +spectral analysis and we're going to + + + align:start position:0% +spectral analysis and we're going to +warm up to that topic today by talking + + align:start position:0% +warm up to that topic today by talking + + + align:start position:0% +warm up to that topic today by talking +about time series more generally now one + + align:start position:0% +about time series more generally now one + + + align:start position:0% +about time series more generally now one +of the things that we're going to + + align:start position:0% +of the things that we're going to + + + align:start position:0% +of the things that we're going to +discuss in the context of this new topic + + align:start position:0% +discuss in the context of this new topic + + + align:start position:0% +discuss in the context of this new topic +so I'm going to spend a few minutes + + align:start position:0% +so I'm going to spend a few minutes + + + align:start position:0% +so I'm going to spend a few minutes +reviewing a little bit about receptive + + align:start position:0% +reviewing a little bit about receptive + + + align:start position:0% +reviewing a little bit about receptive +fields that we talked about in the last + + align:start position:0% +fields that we talked about in the last + + + align:start position:0% +fields that we talked about in the last +lecture and one of the really cool + + align:start position:0% +lecture and one of the really cool + + + align:start position:0% +lecture and one of the really cool +things that that I find in developing + + align:start position:0% +things that that I find in developing + + + align:start position:0% +things that that I find in developing +tools for analyzing data is that there's + + align:start position:0% +tools for analyzing data is that there's + + + align:start position:0% +tools for analyzing data is that there's +a really big sense in which when we + + align:start position:0% +a really big sense in which when we + + + align:start position:0% +a really big sense in which when we +develop tools to analyze data we're + + align:start position:0% +develop tools to analyze data we're + + + align:start position:0% +develop tools to analyze data we're +actually developing tools that kind of + + align:start position:0% +actually developing tools that kind of + + + align:start position:0% +actually developing tools that kind of +look like what the brain does right so + + align:start position:0% +look like what the brain does right so + + + align:start position:0% +look like what the brain does right so +what do so our brains basically learn to + + align:start position:0% +what do so our brains basically learn to + + + align:start position:0% +what do so our brains basically learn to +analyze sensory stimuli and extract + + align:start position:0% +analyze sensory stimuli and extract + + + align:start position:0% +analyze sensory stimuli and extract +information from those sensory stimuli + + align:start position:0% +information from those sensory stimuli + + + align:start position:0% +information from those sensory stimuli +and so when we think about developing + + align:start position:0% +and so when we think about developing + + + align:start position:0% +and so when we think about developing +tools for analyzing data we take a lot + + align:start position:0% +tools for analyzing data we take a lot + + + align:start position:0% +tools for analyzing data we take a lot +of inspiration from how neurons and + + align:start position:0% +of inspiration from how neurons and + + + align:start position:0% +of inspiration from how neurons and +brain circuits actually do the same + + align:start position:0% +brain circuits actually do the same + + + align:start position:0% +brain circuits actually do the same +thing okay and a lot of the sort of + + align:start position:0% +thing okay and a lot of the sort of + + + align:start position:0% +thing okay and a lot of the sort of +formulation that we've developed for + + align:start position:0% +formulation that we've developed for + + + align:start position:0% +formulation that we've developed for +understanding how neurons respond to + + align:start position:0% +understanding how neurons respond to + + + align:start position:0% +understanding how neurons respond to +sensory inputs has a lot of similarity + + align:start position:0% +sensory inputs has a lot of similarity + + + align:start position:0% +sensory inputs has a lot of similarity +to the kind of things we do to analyze + + align:start position:0% +to the kind of things we do to analyze + + + align:start position:0% +to the kind of things we do to analyze +data okay so all right so a brief review + + align:start position:0% +data okay so all right so a brief review + + + align:start position:0% +data okay so all right so a brief review +of receptive fields mathematical models + + align:start position:0% +of receptive fields mathematical models + + + align:start position:0% +of receptive fields mathematical models +of receptive fields so the basic most + + align:start position:0% +of receptive fields so the basic most + + + align:start position:0% +of receptive fields so the basic most +common model for thinking about how + + align:start position:0% +common model for thinking about how + + + align:start position:0% +common model for thinking about how +neurons respond to sensory stimuli is + + align:start position:0% +neurons respond to sensory stimuli is + + + align:start position:0% +neurons respond to sensory stimuli is +the linear nonlinear model and again the + + align:start position:0% +the linear nonlinear model and again the + + + align:start position:0% +the linear nonlinear model and again the +basic idea is that we have a sensory + + align:start position:0% +basic idea is that we have a sensory + + + align:start position:0% +basic idea is that we have a sensory +stimulus in this case this is the + + align:start position:0% +stimulus in this case this is the + + + align:start position:0% +stimulus in this case this is the +intensity of a visual field so it's + + align:start position:0% +intensity of a visual field so it's + + + align:start position:0% +intensity of a visual field so it's +intensity as a function of position x + + align:start position:0% +intensity as a function of position x + + + align:start position:0% +intensity as a function of position x +and y let's say on the screen or on a + + align:start position:0% +and y let's say on the screen or on a + + + align:start position:0% +and y let's say on the screen or on a +retina then that stimulus goes through a + + align:start position:0% +retina then that stimulus goes through a + + + align:start position:0% +retina then that stimulus goes through a +filter and the filter is basically a + + align:start position:0% +filter and the filter is basically a + + + align:start position:0% +filter and the filter is basically a +pattern of sensitivity of the neuron to + + align:start position:0% +pattern of sensitivity of the neuron to + + + align:start position:0% +pattern of sensitivity of the neuron to +the scent to + + align:start position:0% +the scent to + + + align:start position:0% +the scent to +the sensory input and so in this case + + align:start position:0% +the sensory input and so in this case + + + align:start position:0% +the sensory input and so in this case +I've represented this filter as a as a + + align:start position:0% +I've represented this filter as a as a + + + align:start position:0% +I've represented this filter as a as a +filter that's sensitive to a ring of + + align:start position:0% +filter that's sensitive to a ring of + + + align:start position:0% +filter that's sensitive to a ring of +light around a center of darkness okay + + align:start position:0% +light around a center of darkness okay + + + align:start position:0% +light around a center of darkness okay +so this might be like an oftener on in + + align:start position:0% +so this might be like an oftener on in + + + align:start position:0% +so this might be like an oftener on in +in the retina okay so that filter acts + + align:start position:0% +in the retina okay so that filter acts + + + align:start position:0% +in the retina okay so that filter acts +on the stimulus it filters some aspect + + align:start position:0% +on the stimulus it filters some aspect + + + align:start position:0% +on the stimulus it filters some aspect +of this stimulus and develops a response + + align:start position:0% +of this stimulus and develops a response + + + align:start position:0% +of this stimulus and develops a response +to this stimulus that response goes to + + align:start position:0% +to this stimulus that response goes to + + + align:start position:0% +to this stimulus that response goes to +what's called an output non-linearity + + align:start position:0% +what's called an output non-linearity + + + align:start position:0% +what's called an output non-linearity +which typically looks something like + + align:start position:0% +which typically looks something like + + + align:start position:0% +which typically looks something like +this where a very negative response + + align:start position:0% +this where a very negative response + + + align:start position:0% +this where a very negative response +produces no spiking of the neuron no + + align:start position:0% +produces no spiking of the neuron no + + + align:start position:0% +produces no spiking of the neuron no +output of the neuron whereas a large + + align:start position:0% +output of the neuron whereas a large + + + align:start position:0% +output of the neuron whereas a large +overlap of this stimulus with the filter + + align:start position:0% +overlap of this stimulus with the filter + + + align:start position:0% +overlap of this stimulus with the filter +with the receptive field produces a + + align:start position:0% +with the receptive field produces a + + + align:start position:0% +with the receptive field produces a +large spiking response so a typical way + + align:start position:0% +large spiking response so a typical way + + + align:start position:0% +large spiking response so a typical way +this would look for a neuron is that if + + align:start position:0% +this would look for a neuron is that if + + + align:start position:0% +this would look for a neuron is that if +the if the filter response L is zero the + + align:start position:0% +the if the filter response L is zero the + + + align:start position:0% +the if the filter response L is zero the +neuron might have some spontaneous + + align:start position:0% +neuron might have some spontaneous + + + align:start position:0% +neuron might have some spontaneous +firing rate R naught and the firing rate + + align:start position:0% +firing rate R naught and the firing rate + + + align:start position:0% +firing rate R naught and the firing rate +of the neuron is modulated linearly + + align:start position:0% +of the neuron is modulated linearly + + + align:start position:0% +of the neuron is modulated linearly +around that spontaneous firing rate R by + + align:start position:0% +around that spontaneous firing rate R by + + + align:start position:0% +around that spontaneous firing rate R by +an amount proportional to the response + + align:start position:0% +an amount proportional to the response + + + align:start position:0% +an amount proportional to the response +of the filter and then obviously if the + + align:start position:0% +of the filter and then obviously if the + + + align:start position:0% +of the filter and then obviously if the +response of the filter is very negative + + align:start position:0% +response of the filter is very negative + + + align:start position:0% +response of the filter is very negative +then the firing rate of the neuron at + + align:start position:0% +then the firing rate of the neuron at + + + align:start position:0% +then the firing rate of the neuron at +some point reaches zero and if the R + + align:start position:0% +some point reaches zero and if the R + + + align:start position:0% +some point reaches zero and if the R +naught plus L goes below zero then the + + align:start position:0% +naught plus L goes below zero then the + + + align:start position:0% +naught plus L goes below zero then the +firing rate of the neuron can obviously + + align:start position:0% +firing rate of the neuron can obviously + + + align:start position:0% +firing rate of the neuron can obviously +not go negative and so the the firing + + align:start position:0% +not go negative and so the the firing + + + align:start position:0% +not go negative and so the the firing +rate of the neuron will just kind of sit + + align:start position:0% +rate of the neuron will just kind of sit + + + align:start position:0% +rate of the neuron will just kind of sit +at that floor of zero firing rate okay + + align:start position:0% +at that floor of zero firing rate okay + + + align:start position:0% +at that floor of zero firing rate okay +all right so that is a response that is + + align:start position:0% +all right so that is a response that is + + + align:start position:0% +all right so that is a response that is +a output non-linearity and then most + + align:start position:0% +a output non-linearity and then most + + + align:start position:0% +a output non-linearity and then most +neurons fire sort of randomly at a rate + + align:start position:0% +neurons fire sort of randomly at a rate + + + align:start position:0% +neurons fire sort of randomly at a rate +corresponding to this firing rate that + + align:start position:0% +corresponding to this firing rate that + + + align:start position:0% +corresponding to this firing rate that +is the output of this output + + align:start position:0% +is the output of this output + + + align:start position:0% +is the output of this output +non-linearity okay and so what happens + + align:start position:0% +non-linearity okay and so what happens + + + align:start position:0% +non-linearity okay and so what happens +is a neuron generates spikes + + align:start position:0% +is a neuron generates spikes + + + align:start position:0% +is a neuron generates spikes +probabilistically at a rate + + align:start position:0% +probabilistically at a rate + + + align:start position:0% +probabilistically at a rate +corresponding to this the output of this + + align:start position:0% +corresponding to this the output of this + + + align:start position:0% +corresponding to this the output of this +nonlinear response function okay any + + align:start position:0% +nonlinear response function okay any + + + align:start position:0% +nonlinear response function okay any +questions about that + + align:start position:0% +questions about that + + + align:start position:0% +questions about that +all right so what we're gonna do today + + align:start position:0% +all right so what we're gonna do today + + + align:start position:0% +all right so what we're gonna do today +is I'm going to take a little bit of a + + align:start position:0% +is I'm going to take a little bit of a + + + align:start position:0% +is I'm going to take a little bit of a +detour and talk about how we think about + + align:start position:0% +detour and talk about how we think about + + + align:start position:0% +detour and talk about how we think about +the the randomness or the stochasticity + + align:start position:0% +the the randomness or the stochasticity + + + align:start position:0% +the the randomness or the stochasticity +of neuronal firing rates okay and I'll + + align:start position:0% +of neuronal firing rates okay and I'll + + + align:start position:0% +of neuronal firing rates okay and I'll +talk about the Poisson process and then + + align:start position:0% +talk about the Poisson process and then + + + align:start position:0% +talk about the Poisson process and then +we're going to come back and and think + + align:start position:0% +we're going to come back and and think + + + align:start position:0% +we're going to come back and and think +about filters more generally and how we + + align:start position:0% +about filters more generally and how we + + + align:start position:0% +about filters more generally and how we +can analyze signals by applying filters + + align:start position:0% +can analyze signals by applying filters + + + align:start position:0% +can analyze signals by applying filters +of different types to them okay so I + + align:start position:0% +of different types to them okay so I + + + align:start position:0% +of different types to them okay so I +think this is this is basically what we + + align:start position:0% +think this is this is basically what we + + + align:start position:0% +think this is this is basically what we +covered last time again the idea is that + + align:start position:0% +covered last time again the idea is that + + + align:start position:0% +covered last time again the idea is that +we can think of the response of a neuron + + align:start position:0% +we can think of the response of a neuron + + + align:start position:0% +we can think of the response of a neuron +as a spontaneous firing rate plus a + + align:start position:0% +as a spontaneous firing rate plus a + + + align:start position:0% +as a spontaneous firing rate plus a +filter acting on a stimulus input in + + align:start position:0% +filter acting on a stimulus input in + + + align:start position:0% +filter acting on a stimulus input in +this case the filter is a two + + align:start position:0% +this case the filter is a two + + + align:start position:0% +this case the filter is a two +dimensional filter so here I'm just + + align:start position:0% +dimensional filter so here I'm just + + + align:start position:0% +dimensional filter so here I'm just +fleshing out what this looks like here + + align:start position:0% +fleshing out what this looks like here + + + align:start position:0% +fleshing out what this looks like here +for the case of a linear filter in the + + align:start position:0% +for the case of a linear filter in the + + + align:start position:0% +for the case of a linear filter in the +visual system a spatial receptive field + + align:start position:0% +visual system a spatial receptive field + + + align:start position:0% +visual system a spatial receptive field +so G is the spatial receptive field I is + + align:start position:0% +so G is the spatial receptive field I is + + + align:start position:0% +so G is the spatial receptive field I is +the intensity as a function of position + + align:start position:0% +the intensity as a function of position + + + align:start position:0% +the intensity as a function of position +and what we do is we multiply that + + align:start position:0% +and what we do is we multiply that + + + align:start position:0% +and what we do is we multiply that +spatial receptive field times the + + align:start position:0% +spatial receptive field times the + + + align:start position:0% +spatial receptive field times the +stimulus and integrate over over all the + + align:start position:0% +stimulus and integrate over over all the + + + align:start position:0% +stimulus and integrate over over all the +spatial dimensions x and y okay in one + + align:start position:0% +spatial dimensions x and y okay in one + + + align:start position:0% +spatial dimensions x and y okay in one +dimension we would have a spatial + + align:start position:0% +dimension we would have a spatial + + + align:start position:0% +dimension we would have a spatial +receptive field that looks like this so + + align:start position:0% +receptive field that looks like this so + + + align:start position:0% +receptive field that looks like this so +this this receptive field has a bright + + align:start position:0% +this this receptive field has a bright + + + align:start position:0% +this this receptive field has a bright +is is sensitive to a positive brightness + + align:start position:0% +is is sensitive to a positive brightness + + + align:start position:0% +is is sensitive to a positive brightness +in the center and a negative or a dark + + align:start position:0% +in the center and a negative or a dark + + + align:start position:0% +in the center and a negative or a dark +dark feature in the surrounding area + + align:start position:0% +dark feature in the surrounding area + + + align:start position:0% +dark feature in the surrounding area +okay and and again the way we think + + align:start position:0% +okay and and again the way we think + + + align:start position:0% +okay and and again the way we think +about this is that the neuron is + + align:start position:0% +about this is that the neuron is + + + align:start position:0% +about this is that the neuron is +maximally responsive if the pattern of + + align:start position:0% +maximally responsive if the pattern of + + + align:start position:0% +maximally responsive if the pattern of +sensory input looks like the receptive + + align:start position:0% +sensory input looks like the receptive + + + align:start position:0% +sensory input looks like the receptive +field okay is highly correlated with the + + align:start position:0% +field okay is highly correlated with the + + + align:start position:0% +field okay is highly correlated with the +receptive field so if the receptive + + align:start position:0% +receptive field so if the receptive + + + align:start position:0% +receptive field so if the receptive +field is a positive central region + + align:start position:0% +field is a positive central region + + + align:start position:0% +field is a positive central region +surrounded by negative flanks then that + + align:start position:0% +surrounded by negative flanks then that + + + align:start position:0% +surrounded by negative flanks then that +neuron is maximally responsive if the + + align:start position:0% +neuron is maximally responsive if the + + + align:start position:0% +neuron is maximally responsive if the +pattern of light looks like the + + align:start position:0% +pattern of light looks like the + + + align:start position:0% +pattern of light looks like the +receptive field so if the light pattern + + align:start position:0% +receptive field so if the light pattern + + + align:start position:0% +receptive field so if the light pattern +has a bright spot surrounded by dark + + align:start position:0% +has a bright spot surrounded by dark + + + align:start position:0% +has a bright spot surrounded by dark +flanking regions + + align:start position:0% +flanking regions + + + align:start position:0% +flanking regions +then then when we calculate this + + align:start position:0% +then then when we calculate this + + + align:start position:0% +then then when we calculate this +integral what you find is that the + + align:start position:0% +integral what you find is that the + + + align:start position:0% +integral what you find is that the +positive parts in the the positive + + align:start position:0% +positive parts in the the positive + + + align:start position:0% +positive parts in the the positive +receptive field times the positive + + align:start position:0% +receptive field times the positive + + + align:start position:0% +receptive field times the positive +intensity or brightness multiplies to + + align:start position:0% +intensity or brightness multiplies to + + + align:start position:0% +intensity or brightness multiplies to +give you a positive contribution to the + + align:start position:0% +give you a positive contribution to the + + + align:start position:0% +give you a positive contribution to the +neuronal response a negative component + + align:start position:0% +neuronal response a negative component + + + align:start position:0% +neuronal response a negative component +of the receptive field multiplies by a + + align:start position:0% +of the receptive field multiplies by a + + + align:start position:0% +of the receptive field multiplies by a +negative component of the intensity and + + align:start position:0% +negative component of the intensity and + + + align:start position:0% +negative component of the intensity and +that gives you a positive contribution + + align:start position:0% +that gives you a positive contribution + + + align:start position:0% +that gives you a positive contribution +to the response and so you can see that + + align:start position:0% +to the response and so you can see that + + + align:start position:0% +to the response and so you can see that +even though the receptive field has + + align:start position:0% +even though the receptive field has + + + align:start position:0% +even though the receptive field has +positive and negative parts so does the + + align:start position:0% +positive and negative parts so does the + + + align:start position:0% +positive and negative parts so does the +intensity function have positive and + + align:start position:0% +intensity function have positive and + + + align:start position:0% +intensity function have positive and +negative parts and when you multiply + + align:start position:0% +negative parts and when you multiply + + + align:start position:0% +negative parts and when you multiply +those together you get a positive + + align:start position:0% +those together you get a positive + + + align:start position:0% +those together you get a positive +contribution to the response of the + + align:start position:0% +contribution to the response of the + + + align:start position:0% +contribution to the response of the +neuron everywhere and so when you + + align:start position:0% +neuron everywhere and so when you + + + align:start position:0% +neuron everywhere and so when you +integrate that you get a big response in + + align:start position:0% +integrate that you get a big response in + + + align:start position:0% +integrate that you get a big response in +contrast if the intensity profile looked + + align:start position:0% +contrast if the intensity profile looked + + + align:start position:0% +contrast if the intensity profile looked +like this is very broad so this is this + + align:start position:0% +like this is very broad so this is this + + + align:start position:0% +like this is very broad so this is this +looks like a bright spot surrounded by a + + align:start position:0% +looks like a bright spot surrounded by a + + + align:start position:0% +looks like a bright spot surrounded by a +dark ring if on the other hand you have + + align:start position:0% +dark ring if on the other hand you have + + + align:start position:0% +dark ring if on the other hand you have +a large bright spot that completely + + align:start position:0% +a large bright spot that completely + + + align:start position:0% +a large bright spot that completely +overlaps this receptive field then when + + align:start position:0% +overlaps this receptive field then when + + + align:start position:0% +overlaps this receptive field then when +you multiply these two functions + + align:start position:0% +you multiply these two functions + + + align:start position:0% +you multiply these two functions +together this positive times positive + + align:start position:0% +together this positive times positive + + + align:start position:0% +together this positive times positive +will give you a positive here but the + + align:start position:0% +will give you a positive here but the + + + align:start position:0% +will give you a positive here but the +negative part of the receptive field + + align:start position:0% +negative part of the receptive field + + + align:start position:0% +negative part of the receptive field +overlaps with a positive part of the + + align:start position:0% +overlaps with a positive part of the + + + align:start position:0% +overlaps with a positive part of the +intensity and that gives you a negative + + align:start position:0% +intensity and that gives you a negative + + + align:start position:0% +intensity and that gives you a negative +contribution to the neuronal response + + align:start position:0% +contribution to the neuronal response + + + align:start position:0% +contribution to the neuronal response +and when you integrate that the positive + + align:start position:0% +and when you integrate that the positive + + + align:start position:0% +and when you integrate that the positive +here is cancelled by the negative there + + align:start position:0% +here is cancelled by the negative there + + + align:start position:0% +here is cancelled by the negative there +and you get a small response okay all + + align:start position:0% +and you get a small response okay all + + + align:start position:0% +and you get a small response okay all +right any questions about that I think + + align:start position:0% +right any questions about that I think + + + align:start position:0% +right any questions about that I think +we covered that in a lot of detail last + + align:start position:0% +we covered that in a lot of detail last + + + align:start position:0% +we covered that in a lot of detail last +time but again the important point here + + align:start position:0% +time but again the important point here + + + align:start position:0% +time but again the important point here +is that this neuron is looking for a + + align:start position:0% +is that this neuron is looking for a + + + align:start position:0% +is that this neuron is looking for a +particular kind of pattern in the + + align:start position:0% +particular kind of pattern in the + + + align:start position:0% +particular kind of pattern in the +sensory input and it responds when the + + align:start position:0% +sensory input and it responds when the + + + align:start position:0% +sensory input and it responds when the +sensory input has that pattern it + + align:start position:0% +sensory input has that pattern it + + + align:start position:0% +sensory input has that pattern it +doesn't respond when the sensory input + + align:start position:0% +doesn't respond when the sensory input + + + align:start position:0% +doesn't respond when the sensory input +as it doesn't respond as well when the + + align:start position:0% +as it doesn't respond as well when the + + + align:start position:0% +as it doesn't respond as well when the +sensory input has a different pattern + + align:start position:0% + + + + align:start position:0% + +okay and we have the same kind of + + align:start position:0% +okay and we have the same kind of + + + align:start position:0% +okay and we have the same kind of +situation for note the sensitivity of + + align:start position:0% +situation for note the sensitivity of + + + align:start position:0% +situation for note the sensitivity of +neurons to temporal patterns so we can + + align:start position:0% +neurons to temporal patterns so we can + + + align:start position:0% +neurons to temporal patterns so we can +write down the firing rate of a neuron + + align:start position:0% +write down the firing rate of a neuron + + + align:start position:0% +write down the firing rate of a neuron +as a function of time + + align:start position:0% +as a function of time + + + align:start position:0% +as a function of time +it's just a spontaneous firing rate plus + + align:start position:0% +it's just a spontaneous firing rate plus + + + align:start position:0% +it's just a spontaneous firing rate plus +a filter acting on a time-dependent + + align:start position:0% +a filter acting on a time-dependent + + + align:start position:0% +a filter acting on a time-dependent +stimulus so in this case this filter + + align:start position:0% +stimulus so in this case this filter + + + align:start position:0% +stimulus so in this case this filter +will be looking for or sensitive to a + + align:start position:0% +will be looking for or sensitive to a + + + align:start position:0% +will be looking for or sensitive to a +particular temporal pattern okay and as + + align:start position:0% +particular temporal pattern okay and as + + + align:start position:0% +particular temporal pattern okay and as +you recall if we have a time-dependent + + align:start position:0% +you recall if we have a time-dependent + + + align:start position:0% +you recall if we have a time-dependent +stimulus let's say this is the intensity + + align:start position:0% +stimulus let's say this is the intensity + + + align:start position:0% +stimulus let's say this is the intensity +of a spot of light that you can have a + + align:start position:0% +of a spot of light that you can have a + + + align:start position:0% +of a spot of light that you can have a +neuron that's responsive to a particular + + align:start position:0% +neuron that's responsive to a particular + + + align:start position:0% +neuron that's responsive to a particular +temporal pattern let's say a brief + + align:start position:0% +temporal pattern let's say a brief + + + align:start position:0% +temporal pattern let's say a brief +darkening of this stimulus followed by a + + align:start position:0% +darkening of this stimulus followed by a + + + align:start position:0% +darkening of this stimulus followed by a +pulse of bright high intensity and then + + align:start position:0% +pulse of bright high intensity and then + + + align:start position:0% +pulse of bright high intensity and then +and then the neuron responds after it + + align:start position:0% +and then the neuron responds after it + + + align:start position:0% +and then the neuron responds after it +sees that pattern in the stimulus and + + align:start position:0% +sees that pattern in the stimulus and + + + align:start position:0% +sees that pattern in the stimulus and +the way we the way we think about this + + align:start position:0% +the way we the way we think about this + + + align:start position:0% +the way we the way we think about this +mathematically is that what's happening + + align:start position:0% +mathematically is that what's happening + + + align:start position:0% +mathematically is that what's happening +is that the stimulus is being convulsion + + align:start position:0% +is that the stimulus is being convulsion + + + align:start position:0% +is that the stimulus is being convulsion +the way we think about that is that the + + align:start position:0% +the way we think about that is that the + + + align:start position:0% +the way we think about that is that the +kernel is sliding across the stimulus + + align:start position:0% +kernel is sliding across the stimulus + + + align:start position:0% +kernel is sliding across the stimulus +we're doing that same kind of overlap + + align:start position:0% +we're doing that same kind of overlap + + + align:start position:0% +we're doing that same kind of overlap +we're multiplying the stimulus times the + + align:start position:0% +we're multiplying the stimulus times the + + + align:start position:0% +we're multiplying the stimulus times the +kernel integrating over time and asking + + align:start position:0% +kernel integrating over time and asking + + + align:start position:0% +kernel integrating over time and asking +where in time does the stimulus have a + + align:start position:0% +where in time does the stimulus have a + + + align:start position:0% +where in time does the stimulus have a +strong overlap with the kernel and you + + align:start position:0% +strong overlap with the kernel and you + + + align:start position:0% +strong overlap with the kernel and you +can see that in this case there's a + + align:start position:0% +can see that in this case there's a + + + align:start position:0% +can see that in this case there's a +strong overlap at this point this + + align:start position:0% +strong overlap at this point this + + + align:start position:0% +strong overlap at this point this +stimulus looks like the kernel okay the + + align:start position:0% +stimulus looks like the kernel okay the + + + align:start position:0% +stimulus looks like the kernel okay the +positive parts of the stimulus overlap + + align:start position:0% +positive parts of the stimulus overlap + + + align:start position:0% +positive parts of the stimulus overlap +with positive parts of the kernel + + align:start position:0% +with positive parts of the kernel + + + align:start position:0% +with positive parts of the kernel +negative parts of the stimulus overlap + + align:start position:0% +negative parts of the stimulus overlap + + + align:start position:0% +negative parts of the stimulus overlap +with negative parts of the kernel so + + align:start position:0% +with negative parts of the kernel so + + + align:start position:0% +with negative parts of the kernel so +when you multiply that all together you + + align:start position:0% +when you multiply that all together you + + + align:start position:0% +when you multiply that all together you +get a big positive response and if you + + align:start position:0% +get a big positive response and if you + + + align:start position:0% +get a big positive response and if you +actually slide that across and do that + + align:start position:0% +actually slide that across and do that + + + align:start position:0% +actually slide that across and do that +integral as a function of time you can + + align:start position:0% +integral as a function of time you can + + + align:start position:0% +integral as a function of time you can +see that this convolution has a peak at + + align:start position:0% +see that this convolution has a peak at + + + align:start position:0% +see that this convolution has a peak at +the point where that kernel overlaps + + align:start position:0% +the point where that kernel overlaps + + + align:start position:0% +the point where that kernel overlaps +with the stimulus and right there is + + align:start position:0% +with the stimulus and right there is + + + align:start position:0% +with the stimulus and right there is +where the neuron would tend to produce a + + align:start position:0% +where the neuron would tend to produce a + + + align:start position:0% +where the neuron would tend to produce a +spike okay all right and so I I think + + align:start position:0% +spike okay all right and so I I think + + + align:start position:0% +spike okay all right and so I I think +near the end of the last lecture we + + align:start position:0% +near the end of the last lecture we + + + align:start position:0% +near the end of the last lecture we +talked about integrating or putting + + align:start position:0% +talked about integrating or putting + + + align:start position:0% +talked about integrating or putting +together the spatial part of the this + + align:start position:0% +together the spatial part of the this + + + align:start position:0% +together the spatial part of the this +the spatial and temporal parts of a + + align:start position:0% +the spatial and temporal parts of a + + + align:start position:0% +the spatial and temporal parts of a +receptive field into a and sort of a + + align:start position:0% +receptive field into a and sort of a + + + align:start position:0% +receptive field into a and sort of a +larger concept of a spatial temporal + + align:start position:0% +larger concept of a spatial temporal + + + align:start position:0% +larger concept of a spatial temporal +receptive field + + align:start position:0% +receptive field + + + align:start position:0% +receptive field +that combines both spatial and temporal + + align:start position:0% +that combines both spatial and temporal + + + align:start position:0% +that combines both spatial and temporal +information okay all right so here's + + align:start position:0% +information okay all right so here's + + + align:start position:0% +information okay all right so here's +here are the things that we're going to + + align:start position:0% +here are the things that we're going to + + + align:start position:0% +here are the things that we're going to +talk about today we're going to again + + align:start position:0% +talk about today we're going to again + + + align:start position:0% +talk about today we're going to again +take a little bit of a detour and talk + + align:start position:0% +take a little bit of a detour and talk + + + align:start position:0% +take a little bit of a detour and talk +about spike trains being probabilistic + + align:start position:0% +about spike trains being probabilistic + + + align:start position:0% +about spike trains being probabilistic +talk about a plus some process which is + + align:start position:0% +talk about a plus some process which is + + + align:start position:0% +talk about a plus some process which is +the kind of random process that most + + align:start position:0% +the kind of random process that most + + + align:start position:0% +the kind of random process that most +people think about when you talk about + + align:start position:0% +people think about when you talk about + + + align:start position:0% +people think about when you talk about +spike trains of neurons we're going to + + align:start position:0% +spike trains of neurons we're going to + + + align:start position:0% +spike trains of neurons we're going to +develop a couple of measures of spike + + align:start position:0% +develop a couple of measures of spike + + + align:start position:0% +develop a couple of measures of spike +train variability so an important thing + + align:start position:0% +train variability so an important thing + + + align:start position:0% +train variability so an important thing +that neuroscientists often think about + + align:start position:0% +that neuroscientists often think about + + + align:start position:0% +that neuroscientists often think about +when you measure spike trains is how + + align:start position:0% +when you measure spike trains is how + + + align:start position:0% +when you measure spike trains is how +variable are they how reproducible are + + align:start position:0% +variable are they how reproducible are + + + align:start position:0% +variable are they how reproducible are +they in responding to a stimulus okay + + align:start position:0% +they in responding to a stimulus okay + + + align:start position:0% +they in responding to a stimulus okay +and and a number of different + + align:start position:0% +and and a number of different + + + align:start position:0% +and and a number of different +statistical measures have been developed + + align:start position:0% +statistical measures have been developed + + + align:start position:0% +statistical measures have been developed +to quantify spike trains and we're just + + align:start position:0% +to quantify spike trains and we're just + + + align:start position:0% +to quantify spike trains and we're just +going to describe those briefly and I + + align:start position:0% +going to describe those briefly and I + + + align:start position:0% +going to describe those briefly and I +think you'll have a problem set problem + + align:start position:0% +think you'll have a problem set problem + + + align:start position:0% +think you'll have a problem set problem +that deals with those all right and then + + align:start position:0% +that deals with those all right and then + + + align:start position:0% +that deals with those all right and then +I'm going to come back to kind of a + + align:start position:0% +I'm going to come back to kind of a + + + align:start position:0% +I'm going to come back to kind of a +broader discussion of convolution I'll + + align:start position:0% +broader discussion of convolution I'll + + + align:start position:0% +broader discussion of convolution I'll +introduce two new metrics or methods for + + align:start position:0% +introduce two new metrics or methods for + + + align:start position:0% +introduce two new metrics or methods for +analyzing time series data data that has + + align:start position:0% +analyzing time series data data that has + + + align:start position:0% +analyzing time series data data that has +a that's a function of time + + align:start position:0% +a that's a function of time + + + align:start position:0% +a that's a function of time +those are cross correlation and + + align:start position:0% +those are cross correlation and + + + align:start position:0% +those are cross correlation and +autocorrelation functions and I'm going + + align:start position:0% +autocorrelation functions and I'm going + + + align:start position:0% +autocorrelation functions and I'm going +to relate those to the convolution that + + align:start position:0% +to relate those to the convolution that + + + align:start position:0% +to relate those to the convolution that +you've been using more often and we've + + align:start position:0% +you've been using more often and we've + + + align:start position:0% +you've been using more often and we've +been seeing in class okay and then + + align:start position:0% +been seeing in class okay and then + + + align:start position:0% +been seeing in class okay and then +finally we're going to jump right into + + align:start position:0% +finally we're going to jump right into + + + align:start position:0% +finally we're going to jump right into +spectral analysis of time series which + + align:start position:0% +spectral analysis of time series which + + + align:start position:0% +spectral analysis of time series which +is a way of pulling out periodic signals + + align:start position:0% +is a way of pulling out periodic signals + + + align:start position:0% +is a way of pulling out periodic signals +from data and what you're going to see + + align:start position:0% +from data and what you're going to see + + + align:start position:0% +from data and what you're going to see +is that is that that method of pulling + + align:start position:0% +is that is that that method of pulling + + + align:start position:0% +is that is that that method of pulling +out temporal structure out of signals + + align:start position:0% +out temporal structure out of signals + + + align:start position:0% +out temporal structure out of signals +looks a lot like the way we've been + + align:start position:0% +looks a lot like the way we've been + + + align:start position:0% +looks a lot like the way we've been +talking about how neurons have + + align:start position:0% +talking about how neurons have + + + align:start position:0% +talking about how neurons have +sensitivity to temporal structure in + + align:start position:0% +sensitivity to temporal structure in + + + align:start position:0% +sensitivity to temporal structure in +signals okay we're going to use that + + align:start position:0% +signals okay we're going to use that + + + align:start position:0% +signals okay we're going to use that +same idea of taking a signal and and + + align:start position:0% +same idea of taking a signal and and + + + align:start position:0% +same idea of taking a signal and and +asking how much does it overlap with + + align:start position:0% +asking how much does it overlap with + + + align:start position:0% +asking how much does it overlap with +with a + + align:start position:0% +with a + + + align:start position:0% +with a +colonel okay with a linear kernel with a + + align:start position:0% +colonel okay with a linear kernel with a + + + align:start position:0% +colonel okay with a linear kernel with a +filter all right we're gonna talk about + + align:start position:0% +filter all right we're gonna talk about + + + align:start position:0% +filter all right we're gonna talk about +the kind of filters you use to to detect + + align:start position:0% +the kind of filters you use to to detect + + + align:start position:0% +the kind of filters you use to to detect +periodic structure in signals and not + + align:start position:0% +periodic structure in signals and not + + + align:start position:0% +periodic structure in signals and not +surprisingly those are going to be + + align:start position:0% +surprisingly those are going to be + + + align:start position:0% +surprisingly those are going to be +periodic filters all right so that's + + align:start position:0% +periodic filters all right so that's + + + align:start position:0% +periodic filters all right so that's +what we're going to talk about today all + + align:start position:0% +what we're going to talk about today all + + + align:start position:0% +what we're going to talk about today all +right so let's start with probabilistic + + align:start position:0% +right so let's start with probabilistic + + + align:start position:0% +right so let's start with probabilistic +spike trains so the first thing that you + + align:start position:0% +spike trains so the first thing that you + + + align:start position:0% +spike trains so the first thing that you +would discover you discover when you + + align:start position:0% +would discover you discover when you + + + align:start position:0% +would discover you discover when you +record from neurons in the brain and you + + align:start position:0% +record from neurons in the brain and you + + + align:start position:0% +record from neurons in the brain and you +present a stimulus to the to the animal + + align:start position:0% +present a stimulus to the to the animal + + + align:start position:0% +present a stimulus to the to the animal +let's say you record from neurons in + + align:start position:0% +let's say you record from neurons in + + + align:start position:0% +let's say you record from neurons in +visual cortex or auditory cortex and you + + align:start position:0% +visual cortex or auditory cortex and you + + + align:start position:0% +visual cortex or auditory cortex and you +present a stimulus for some period of + + align:start position:0% +present a stimulus for some period of + + + align:start position:0% +present a stimulus for some period of +time what you find is that the neurons + + align:start position:0% +time what you find is that the neurons + + + align:start position:0% +time what you find is that the neurons +respond they respond with some temporal + + align:start position:0% +respond they respond with some temporal + + + align:start position:0% +respond they respond with some temporal +structure but each time you present the + + align:start position:0% +structure but each time you present the + + + align:start position:0% +structure but each time you present the +stimulus the response of the neuron is a + + align:start position:0% +stimulus the response of the neuron is a + + + align:start position:0% +stimulus the response of the neuron is a +little bit different so you can see that + + align:start position:0% +little bit different so you can see that + + + align:start position:0% +little bit different so you can see that +this so what I'm showing here is a a + + align:start position:0% +this so what I'm showing here is a a + + + align:start position:0% +this so what I'm showing here is a a +raster plot so each row of this shows + + align:start position:0% +raster plot so each row of this shows + + + align:start position:0% +raster plot so each row of this shows +the spiking activity of a neuron during + + align:start position:0% +the spiking activity of a neuron during + + + align:start position:0% +the spiking activity of a neuron during +a presentation of this stimulus the + + align:start position:0% +a presentation of this stimulus the + + + align:start position:0% +a presentation of this stimulus the +stimulus is a bunch of dots presented + + align:start position:0% +stimulus is a bunch of dots presented + + + align:start position:0% +stimulus is a bunch of dots presented +that move across the screen and this is + + align:start position:0% +that move across the screen and this is + + + align:start position:0% +that move across the screen and this is +a part of the brain that's sensitive to + + align:start position:0% +a part of the brain that's sensitive to + + + align:start position:0% +a part of the brain that's sensitive to +movement of a visual stimuli and what + + align:start position:0% +movement of a visual stimuli and what + + + align:start position:0% +movement of a visual stimuli and what +you can see is that each time the + + align:start position:0% +you can see is that each time the + + + align:start position:0% +you can see is that each time the +stimulus is presented the neuron + + align:start position:0% +stimulus is presented the neuron + + + align:start position:0% +stimulus is presented the neuron +generates spikes each row here is a + + align:start position:0% +generates spikes each row here is a + + + align:start position:0% +generates spikes each row here is a +different presentation of the stimulus + + align:start position:0% +different presentation of the stimulus + + + align:start position:0% +different presentation of the stimulus +if you average across all of those rows + + align:start position:0% +if you average across all of those rows + + + align:start position:0% +if you average across all of those rows +you can see that there is some + + align:start position:0% +you can see that there is some + + + align:start position:0% +you can see that there is some +repeatable structure so the neuron tends + + align:start position:0% +repeatable structure so the neuron tends + + + align:start position:0% +repeatable structure so the neuron tends +to spike most often at certain times + + align:start position:0% +to spike most often at certain times + + + align:start position:0% +to spike most often at certain times +after the presentation of this stimulus + + align:start position:0% +after the presentation of this stimulus + + + align:start position:0% +after the presentation of this stimulus +but each time the stimulus is presented + + align:start position:0% +but each time the stimulus is presented + + + align:start position:0% +but each time the stimulus is presented +the spikes don't occur in exactly the + + align:start position:0% +the spikes don't occur in exactly the + + + align:start position:0% +the spikes don't occur in exactly the +same place okay so you have this sense + + align:start position:0% +same place okay so you have this sense + + + align:start position:0% +same place okay so you have this sense +that when you present the stimulus there + + align:start position:0% +that when you present the stimulus there + + + align:start position:0% +that when you present the stimulus there +is some sort of underlying modulation of + + align:start position:0% +is some sort of underlying modulation of + + + align:start position:0% +is some sort of underlying modulation of +the firing rate of the neuron but the + + align:start position:0% +the firing rate of the neuron but the + + + align:start position:0% +the firing rate of the neuron but the +response isn't exactly the same + + align:start position:0% +response isn't exactly the same + + + align:start position:0% +response isn't exactly the same +okay there's some randomness about it so + + align:start position:0% +okay there's some randomness about it so + + + align:start position:0% +okay there's some randomness about it so +we're gonna talk a little bit about how + + align:start position:0% +we're gonna talk a little bit about how + + + align:start position:0% +we're gonna talk a little bit about how +you characterize that randomness and the + + align:start position:0% +you characterize that randomness and the + + + align:start position:0% +you characterize that randomness and the +way that most people think about that + + align:start position:0% +way that most people think about that + + + align:start position:0% +way that most people think about that +the random spiking of neurons is that + + align:start position:0% +the random spiking of neurons is that + + + align:start position:0% +the random spiking of neurons is that +there is a sorry about that that Mew is + + align:start position:0% +there is a sorry about that that Mew is + + + align:start position:0% +there is a sorry about that that Mew is +supposed to be up there so imagine that + + align:start position:0% +supposed to be up there so imagine that + + + align:start position:0% +supposed to be up there so imagine that +let's go to a very simple case where we + + align:start position:0% +let's go to a very simple case where we + + + align:start position:0% +let's go to a very simple case where we +turn on a stimulus and instead of having + + align:start position:0% +turn on a stimulus and instead of having + + + align:start position:0% +turn on a stimulus and instead of having +a kind of a time varying rate let's + + align:start position:0% +a kind of a time varying rate let's + + + align:start position:0% +a kind of a time varying rate let's +imagine that the stimulus just comes on + + align:start position:0% +imagine that the stimulus just comes on + + + align:start position:0% +imagine that the stimulus just comes on +and the neuron starts to spike at a + + align:start position:0% +and the neuron starts to spike at a + + + align:start position:0% +and the neuron starts to spike at a +constant average rate okay and let's + + align:start position:0% +constant average rate okay and let's + + + align:start position:0% +constant average rate okay and let's +call that average rate in Mew + + align:start position:0% +call that average rate in Mew + + + align:start position:0% +call that average rate in Mew +so what does that mean what that means + + align:start position:0% +so what does that mean what that means + + + align:start position:0% +so what does that mean what that means +is that if you were to present this + + align:start position:0% +is that if you were to present this + + + align:start position:0% +is that if you were to present this +stimulus many many times and look at + + align:start position:0% +stimulus many many times and look at + + + align:start position:0% +stimulus many many times and look at +where the spikes occur there would be + + align:start position:0% +where the spikes occur there would be + + + align:start position:0% +where the spikes occur there would be +some uniform probability per unit time + + align:start position:0% +some uniform probability per unit time + + + align:start position:0% +some uniform probability per unit time +that spikes would occur anywhere under + + align:start position:0% +that spikes would occur anywhere under + + + align:start position:0% +that spikes would occur anywhere under +that stimulus okay during the + + align:start position:0% +that stimulus okay during the + + + align:start position:0% +that stimulus okay during the +presentation of that stimulus so let's + + align:start position:0% +presentation of that stimulus so let's + + + align:start position:0% +presentation of that stimulus so let's +break that time window up during the + + align:start position:0% +break that time window up during the + + + align:start position:0% +break that time window up during the +presentation of the stimulus into little + + align:start position:0% +presentation of the stimulus into little + + + align:start position:0% +presentation of the stimulus into little +tiny bins delta T okay + + align:start position:0% + + + + align:start position:0% + +now if these spikes occur randomly then + + align:start position:0% +now if these spikes occur randomly then + + + align:start position:0% +now if these spikes occur randomly then +they're generated independently of any + + align:start position:0% +they're generated independently of any + + + align:start position:0% +they're generated independently of any +other spikes with an equal probability + + align:start position:0% +other spikes with an equal probability + + + align:start position:0% +other spikes with an equal probability +in each bin okay and what that means is + + align:start position:0% +in each bin okay and what that means is + + + align:start position:0% +in each bin okay and what that means is +that if the bins are small enough most + + align:start position:0% +that if the bins are small enough most + + + align:start position:0% +that if the bins are small enough most +of the bins will have zero spikes and + + align:start position:0% +of the bins will have zero spikes and + + + align:start position:0% +of the bins will have zero spikes and +you can write down the probability that + + align:start position:0% +you can write down the probability that + + + align:start position:0% +you can write down the probability that +a spike occurs in any one bin is the + + align:start position:0% +a spike occurs in any one bin is the + + + align:start position:0% +a spike occurs in any one bin is the +number of spikes per unit time which is + + align:start position:0% +number of spikes per unit time which is + + + align:start position:0% +number of spikes per unit time which is +the average firing rate times the width + + align:start position:0% +the average firing rate times the width + + + align:start position:0% +the average firing rate times the width +of that bin in time okay does that make + + align:start position:0% +of that bin in time okay does that make + + + align:start position:0% +of that bin in time okay does that make +sense the probability that you have a + + align:start position:0% +sense the probability that you have a + + + align:start position:0% +sense the probability that you have a +spike in any one of those very tiny bins + + align:start position:0% +spike in any one of those very tiny bins + + + align:start position:0% +spike in any one of those very tiny bins +is just going to be the spikes per unit + + align:start position:0% +is just going to be the spikes per unit + + + align:start position:0% +is just going to be the spikes per unit +time time + + align:start position:0% +time time + + + align:start position:0% +time time +the width of the bin in time okay now + + align:start position:0% +the width of the bin in time okay now + + + align:start position:0% +the width of the bin in time okay now +that's only true if delta T is very + + align:start position:0% +that's only true if delta T is very + + + align:start position:0% +that's only true if delta T is very +small right because if delta T gets big + + align:start position:0% +small right because if delta T gets big + + + align:start position:0% +small right because if delta T gets big +then you have some probability that you + + align:start position:0% +then you have some probability that you + + + align:start position:0% +then you have some probability that you +could have two or three spikes okay and + + align:start position:0% +could have two or three spikes okay and + + + align:start position:0% +could have two or three spikes okay and +so it's only the case this is only true + + align:start position:0% +so it's only the case this is only true + + + align:start position:0% +so it's only the case this is only true +in the case where delta T is very small + + align:start position:0% +in the case where delta T is very small + + + align:start position:0% +in the case where delta T is very small +okay all right so the probability that + + align:start position:0% +okay all right so the probability that + + + align:start position:0% +okay all right so the probability that +no spikes occur is 1 minus mu delta T + + align:start position:0% +no spikes occur is 1 minus mu delta T + + + align:start position:0% +no spikes occur is 1 minus mu delta T +okay and we can ask how many spikes land + + align:start position:0% +okay and we can ask how many spikes land + + + align:start position:0% +okay and we can ask how many spikes land +in this interval T all right and we're + + align:start position:0% +in this interval T all right and we're + + + align:start position:0% +in this interval T all right and we're +going to call that probability P okay + + align:start position:0% +going to call that probability P okay + + + align:start position:0% +going to call that probability P okay +and it's the probability that n spikes + + align:start position:0% +and it's the probability that n spikes + + + align:start position:0% +and it's the probability that n spikes +land in this interval T okay and we can + + align:start position:0% +land in this interval T okay and we can + + + align:start position:0% +land in this interval T okay and we can +calculate that probability as follows so + + align:start position:0% +calculate that probability as follows so + + + align:start position:0% +calculate that probability as follows so +that probability is just the product of + + align:start position:0% +that probability is just the product of + + + align:start position:0% +that probability is just the product of +three different things it's the + + align:start position:0% +three different things it's the + + + align:start position:0% +three different things it's the +probability of having ends bins with a + + align:start position:0% +probability of having ends bins with a + + + align:start position:0% +probability of having ends bins with a +spike right so that's mu delta T to the + + align:start position:0% +spike right so that's mu delta T to the + + + align:start position:0% +spike right so that's mu delta T to the +N right it's an independent events with + + align:start position:0% +N right it's an independent events with + + + align:start position:0% +N right it's an independent events with +probability mu delta T times the + + align:start position:0% +probability mu delta T times the + + + align:start position:0% +probability mu delta T times the +probability of having M minus n bins + + align:start position:0% +probability of having M minus n bins + + + align:start position:0% +probability of having M minus n bins +with no spike right so that's 1 minus mu + + align:start position:0% +with no spike right so that's 1 minus mu + + + align:start position:0% +with no spike right so that's 1 minus mu +delta T to the M minus n all right and + + align:start position:0% +delta T to the M minus n all right and + + + align:start position:0% +delta T to the M minus n all right and +we also have to multiply it by the + + align:start position:0% +we also have to multiply it by the + + + align:start position:0% +we also have to multiply it by the +number of different ways that you can + + align:start position:0% +number of different ways that you can + + + align:start position:0% +number of different ways that you can +distribute those n spikes in M bins okay + + align:start position:0% +distribute those n spikes in M bins okay + + + align:start position:0% +distribute those n spikes in M bins okay +and that's called M choose n okay M + + align:start position:0% +and that's called M choose n okay M + + + align:start position:0% +and that's called M choose n okay M +truth yes yes + + align:start position:0% +truth yes yes + + + align:start position:0% +truth yes yes +okay so good question so just to clarify + + align:start position:0% +okay so good question so just to clarify + + + align:start position:0% +okay so good question so just to clarify +we're kind of imagining that spikes are + + align:start position:0% +we're kind of imagining that spikes are + + + align:start position:0% +we're kind of imagining that spikes are +Delta functions now okay so we are all + + align:start position:0% +Delta functions now okay so we are all + + + align:start position:0% +Delta functions now okay so we are all +right so in this case we're imagining + + align:start position:0% +right so in this case we're imagining + + + align:start position:0% +right so in this case we're imagining +that that spikes are not you know like + + align:start position:0% +that that spikes are not you know like + + + align:start position:0% +that that spikes are not you know like +produced by its you know influx of + + align:start position:0% +produced by its you know influx of + + + align:start position:0% +produced by its you know influx of +sodium in an out flux of potassium and + + align:start position:0% +sodium in an out flux of potassium and + + + align:start position:0% +sodium in an out flux of potassium and +it takes a millisecond this is in + + align:start position:0% +it takes a millisecond this is in + + + align:start position:0% +it takes a millisecond this is in +general spikes are let's say a + + align:start position:0% +general spikes are let's say a + + + align:start position:0% +general spikes are let's say a +millisecond across and we're usually + + align:start position:0% +millisecond across and we're usually + + + align:start position:0% +millisecond across and we're usually +thinking of these bins as kind of + + align:start position:0% +thinking of these bins as kind of + + + align:start position:0% +thinking of these bins as kind of +approaching about a millisecond but if + + align:start position:0% +approaching about a millisecond but if + + + align:start position:0% +approaching about a millisecond but if +you what we're about to do actually is + + align:start position:0% +you what we're about to do actually is + + + align:start position:0% +you what we're about to do actually is +take the limit where delta T goes to + + align:start position:0% +take the limit where delta T goes to + + + align:start position:0% +take the limit where delta T goes to +zero and in that case you have to think + + align:start position:0% +zero and in that case you have to think + + + align:start position:0% +zero and in that case you have to think +of those bikes as Delta functions okay + + align:start position:0% +of those bikes as Delta functions okay + + + align:start position:0% +of those bikes as Delta functions okay +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so the probability that you have n + + align:start position:0% +so the probability that you have n + + + align:start position:0% +so the probability that you have n +spikes in this interval T is just the + + align:start position:0% +spikes in this interval T is just the + + + align:start position:0% +spikes in this interval T is just the +product of those things it's the + + align:start position:0% +product of those things it's the + + + align:start position:0% +product of those things it's the +probability of having n bins with a + + align:start position:0% +probability of having n bins with a + + + align:start position:0% +probability of having n bins with a +spike times the number of different ways + + align:start position:0% +spike times the number of different ways + + + align:start position:0% +spike times the number of different ways +that you can put n spikes into n bins + + align:start position:0% +that you can put n spikes into n bins + + + align:start position:0% +that you can put n spikes into n bins +alright so you multiply those things + + align:start position:0% +alright so you multiply those things + + + align:start position:0% +alright so you multiply those things +together and you take the limit that + + align:start position:0% +together and you take the limit that + + + align:start position:0% +together and you take the limit that +delta T goes to zero all right and it's + + align:start position:0% +delta T goes to zero all right and it's + + + align:start position:0% +delta T goes to zero all right and it's +kind of a cute little derivation I've + + align:start position:0% +kind of a cute little derivation I've + + + align:start position:0% +kind of a cute little derivation I've +put the the full derivation at the end + + align:start position:0% +put the the full derivation at the end + + + align:start position:0% +put the the full derivation at the end +so that you don't so that we don't have + + align:start position:0% +so that you don't so that we don't have + + + align:start position:0% +so that you don't so that we don't have +to go through it in class but it's kind + + align:start position:0% +to go through it in class but it's kind + + + align:start position:0% +to go through it in class but it's kind +of fun to look at anyway and what you + + align:start position:0% +of fun to look at anyway and what you + + + align:start position:0% +of fun to look at anyway and what you +find is that in the limit that delta T + + align:start position:0% +find is that in the limit that delta T + + + align:start position:0% +find is that in the limit that delta T +goes to 0 of course as delta T goes to 0 + + align:start position:0% +goes to 0 of course as delta T goes to 0 + + + align:start position:0% +goes to 0 of course as delta T goes to 0 +the number of bins goes to envy because + + align:start position:0% +the number of bins goes to envy because + + + align:start position:0% +the number of bins goes to envy because +the number of bins is just T capital T + + align:start position:0% +the number of bins is just T capital T + + + align:start position:0% +the number of bins is just T capital T +divided by delta T okay so you can go + + align:start position:0% +divided by delta T okay so you can go + + + align:start position:0% +divided by delta T okay so you can go +through each of those terms and + + align:start position:0% +through each of those terms and + + + align:start position:0% +through each of those terms and +calculate what happens to them in the + + align:start position:0% +calculate what happens to them in the + + + align:start position:0% +calculate what happens to them in the +limit that delta T goes to 0 and what + + align:start position:0% +limit that delta T goes to 0 and what + + + align:start position:0% +limit that delta T goes to 0 and what +you find is that the probability of + + align:start position:0% +you find is that the probability of + + + align:start position:0% +you find is that the probability of +having n spikes in that window T just mu + + align:start position:0% +having n spikes in that window T just mu + + + align:start position:0% +having n spikes in that window T just mu +T to the N what is mutti mutti is the + + align:start position:0% +T to the N what is mutti mutti is the + + + align:start position:0% +T to the N what is mutti mutti is the +expected number of spikes in that + + align:start position:0% +expected number of spikes in that + + + align:start position:0% +expected number of spikes in that +interval it's just the number of spikes + + align:start position:0% +interval it's just the number of spikes + + + align:start position:0% +interval it's just the number of spikes +per unit time times + + align:start position:0% +per unit time times + + + align:start position:0% +per unit time times +the length of the window divided by n + + align:start position:0% +the length of the window divided by n + + + align:start position:0% +the length of the window divided by n +factorial times e to the minus mu T okay + + align:start position:0% +factorial times e to the minus mu T okay + + + align:start position:0% +factorial times e to the minus mu T okay +and again mu T is the expected number of + + align:start position:0% +and again mu T is the expected number of + + + align:start position:0% +and again mu T is the expected number of +spikes and that is the Poisson + + align:start position:0% +spikes and that is the Poisson + + + align:start position:0% +spikes and that is the Poisson +distribution okay and it comes from a + + align:start position:0% +distribution okay and it comes from a + + + align:start position:0% +distribution okay and it comes from a +very simple assumption which is just + + align:start position:0% +very simple assumption which is just + + + align:start position:0% +very simple assumption which is just +that spikes occur with the spikes occur + + align:start position:0% +that spikes occur with the spikes occur + + + align:start position:0% +that spikes occur with the spikes occur +independently of each other at a rate mu + + align:start position:0% +independently of each other at a rate mu + + + align:start position:0% +independently of each other at a rate mu +spikes per second with some constant + + align:start position:0% +spikes per second with some constant + + + align:start position:0% +spikes per second with some constant +probability per unit time of having a + + align:start position:0% +probability per unit time of having a + + + align:start position:0% +probability per unit time of having a +spike in each little time bit okay now + + align:start position:0% +spike in each little time bit okay now + + + align:start position:0% +spike in each little time bit okay now +notice that if you have a rate there's + + align:start position:0% +notice that if you have a rate there's + + + align:start position:0% +notice that if you have a rate there's +some tiny probability per unit time of + + align:start position:0% +some tiny probability per unit time of + + + align:start position:0% +some tiny probability per unit time of +having uh spike their probability of + + align:start position:0% +having uh spike their probability of + + + align:start position:0% +having uh spike their probability of +having a spike their probability of + + align:start position:0% +having a spike their probability of + + + align:start position:0% +having a spike their probability of +having a spike there and so on you're + + align:start position:0% +having a spike there and so on you're + + + align:start position:0% +having a spike there and so on you're +gonna end up sometimes with one spike in + + align:start position:0% +gonna end up sometimes with one spike in + + + align:start position:0% +gonna end up sometimes with one spike in +sometimes with two spikes sometimes with + + align:start position:0% +sometimes with two spikes sometimes with + + + align:start position:0% +sometimes with two spikes sometimes with +three sometimes four sometimes five if + + align:start position:0% +three sometimes four sometimes five if + + + align:start position:0% +three sometimes four sometimes five if +this window is really short you're going + + align:start position:0% +this window is really short you're going + + + align:start position:0% +this window is really short you're going +to have more cases where you have zero + + align:start position:0% +to have more cases where you have zero + + + align:start position:0% +to have more cases where you have zero +or one spikes right if this window is + + align:start position:0% +or one spikes right if this window is + + + align:start position:0% +or one spikes right if this window is +really long then it's gonna be pretty + + align:start position:0% +really long then it's gonna be pretty + + + align:start position:0% +really long then it's gonna be pretty +rare to have just zero or one spikes and + + align:start position:0% +rare to have just zero or one spikes and + + + align:start position:0% +rare to have just zero or one spikes and +you're gonna end up with you know on + + align:start position:0% +you're gonna end up with you know on + + + align:start position:0% +you're gonna end up with you know on +average 20 spikes let's say okay so you + + align:start position:0% +average 20 spikes let's say okay so you + + + align:start position:0% +average 20 spikes let's say okay so you +can see that first of all the number of + + align:start position:0% +can see that first of all the number of + + + align:start position:0% +can see that first of all the number of +spikes you get is random okay and it + + align:start position:0% +spikes you get is random okay and it + + + align:start position:0% +spikes you get is random okay and it +depends on the size of the window and + + align:start position:0% +depends on the size of the window and + + + align:start position:0% +depends on the size of the window and +the average no likes you get depends on + + align:start position:0% +the average no likes you get depends on + + + align:start position:0% +the average no likes you get depends on +the size of the window and the average + + align:start position:0% +the size of the window and the average + + + align:start position:0% +the size of the window and the average +firing rate of the neuron okay so let's + + align:start position:0% +firing rate of the neuron okay so let's + + + align:start position:0% +firing rate of the neuron okay so let's +just take a look at what this function + + align:start position:0% +just take a look at what this function + + + align:start position:0% +just take a look at what this function +looks like four different expected + + align:start position:0% +looks like four different expected + + + align:start position:0% +looks like four different expected +spike counts so here's what that looks + + align:start position:0% +spike counts so here's what that looks + + + align:start position:0% +spike counts so here's what that looks +like so we can calculate the + + align:start position:0% +like so we can calculate the + + + align:start position:0% +like so we can calculate the +expected number of spikes and just to + + align:start position:0% +expected number of spikes and just to + + + align:start position:0% +expected number of spikes and just to +convince you if we calculate the average + + align:start position:0% +convince you if we calculate the average + + + align:start position:0% +convince you if we calculate the average +number of spikes in that using that + + align:start position:0% +number of spikes in that using that + + + align:start position:0% +number of spikes in that using that +distribution which are sum over all + + align:start position:0% +distribution which are sum over all + + + align:start position:0% +distribution which are sum over all +possible number of spikes n times the + + align:start position:0% +possible number of spikes n times the + + + align:start position:0% +possible number of spikes n times the +probability of having n spikes and when + + align:start position:0% +probability of having n spikes and when + + + align:start position:0% +probability of having n spikes and when +you do that what you find is that the + + align:start position:0% +you do that what you find is that the + + + align:start position:0% +you do that what you find is that the +average number is mu times T okay so you + + align:start position:0% +average number is mu times T okay so you + + + align:start position:0% +average number is mu times T okay so you +can see that the firing rate mu is just + + align:start position:0% +can see that the firing rate mu is just + + + align:start position:0% +can see that the firing rate mu is just +the expected number of spikes divided by + + align:start position:0% +the expected number of spikes divided by + + + align:start position:0% +the expected number of spikes divided by +the width of the window that make sense + + align:start position:0% +the width of the window that make sense + + + align:start position:0% +the width of the window that make sense +that's pretty obvious that's just the + + align:start position:0% +that's pretty obvious that's just the + + + align:start position:0% +that's pretty obvious that's just the +spike rate and we're going to often use + + align:start position:0% +spike rate and we're going to often use + + + align:start position:0% +spike rate and we're going to often use +the variable R for that for a firing + + align:start position:0% +the variable R for that for a firing + + + align:start position:0% +the variable R for that for a firing +rate okay and here's what that looks + + align:start position:0% +rate okay and here's what that looks + + + align:start position:0% +rate okay and here's what that looks +like you can see that if the firing rate + + align:start position:0% +like you can see that if the firing rate + + + align:start position:0% +like you can see that if the firing rate +is low enough or the window is short + + align:start position:0% +is low enough or the window is short + + + align:start position:0% +is low enough or the window is short +enough such that the expected number of + + align:start position:0% +enough such that the expected number of + + + align:start position:0% +enough such that the expected number of +spikes is 1 you can see that most of the + + align:start position:0% +spikes is 1 you can see that most of the + + + align:start position:0% +spikes is 1 you can see that most of the +time you're gonna get 0 or 1 spikes and + + align:start position:0% +time you're gonna get 0 or 1 spikes and + + + align:start position:0% +time you're gonna get 0 or 1 spikes and +then occasionally - and very + + align:start position:0% +then occasionally - and very + + + align:start position:0% +then occasionally - and very +occasionally 3 and then almost never + + align:start position:0% +occasionally 3 and then almost never + + + align:start position:0% +occasionally 3 and then almost never +more than 4 or 5 ok if the expected + + align:start position:0% +more than 4 or 5 ok if the expected + + + align:start position:0% +more than 4 or 5 ok if the expected +number of spikes is 4 you can see that + + align:start position:0% +number of spikes is 4 you can see that + + + align:start position:0% +number of spikes is 4 you can see that +the the mode of that you can see that + + align:start position:0% +the the mode of that you can see that + + + align:start position:0% +the the mode of that you can see that +that distribution moves to the right you + + align:start position:0% +that distribution moves to the right you + + + align:start position:0% +that distribution moves to the right you +have a higher probability of getting + + align:start position:0% +have a higher probability of getting + + + align:start position:0% +have a higher probability of getting +three or four spikes but again there's + + align:start position:0% +three or four spikes but again there's + + + align:start position:0% +three or four spikes but again there's +still a distribution so even if the + + align:start position:0% +still a distribution so even if the + + + align:start position:0% +still a distribution so even if the +average number of spikes is four you + + align:start position:0% +average number of spikes is four you + + + align:start position:0% +average number of spikes is four you +have quite a wide range of action spike + + align:start position:0% +have quite a wide range of action spike + + + align:start position:0% +have quite a wide range of action spike +counts that you would get on any given + + align:start position:0% +counts that you would get on any given + + + align:start position:0% +counts that you would get on any given +trial as the expected number of spikes + + align:start position:0% +trial as the expected number of spikes + + + align:start position:0% +trial as the expected number of spikes +gets bigger let's say on average 10 does + + align:start position:0% +gets bigger let's say on average 10 does + + + align:start position:0% +gets bigger let's say on average 10 does +anyone know what this distribution + + align:start position:0% +anyone know what this distribution + + + align:start position:0% +anyone know what this distribution +starts turning into a Gaussian good so + + align:start position:0% +starts turning into a Gaussian good so + + + align:start position:0% +starts turning into a Gaussian good so +what you can see is that you end up + + align:start position:0% +what you can see is that you end up + + + align:start position:0% +what you can see is that you end up +having a more symmetric abusin where the + + align:start position:0% +having a more symmetric abusin where the + + + align:start position:0% +having a more symmetric abusin where the +peak is sitting at the at the expected + + align:start position:0% +peak is sitting at the at the expected + + + align:start position:0% +peak is sitting at the at the expected +number in that case the distribution + + align:start position:0% +number in that case the distribution + + + align:start position:0% +number in that case the distribution +becomes more symmetric in and in the + + align:start position:0% +becomes more symmetric in and in the + + + align:start position:0% +becomes more symmetric in and in the +limit of infinite expected + + align:start position:0% +limit of infinite expected + + + align:start position:0% +limit of infinite expected +number of spikes is becomes exactly a + + align:start position:0% +number of spikes is becomes exactly a + + + align:start position:0% +number of spikes is becomes exactly a +Gaussian distribution okay + + align:start position:0% + + + + align:start position:0% + +alright there are two measures that we + + align:start position:0% +alright there are two measures that we + + + align:start position:0% +alright there are two measures that we +use to characterize how variable spike + + align:start position:0% +use to characterize how variable spike + + + align:start position:0% +use to characterize how variable spike +trains are let me just go through them + + align:start position:0% +trains are let me just go through them + + + align:start position:0% +trains are let me just go through them +real quick so and and we'll describe and + + align:start position:0% +real quick so and and we'll describe and + + + align:start position:0% +real quick so and and we'll describe and +I'll describe to you what we expect + + align:start position:0% +I'll describe to you what we expect + + + align:start position:0% +I'll describe to you what we expect +those to look like for spike trains that + + align:start position:0% +those to look like for spike trains that + + + align:start position:0% +those to look like for spike trains that +are plus all that have a plus on + + align:start position:0% +are plus all that have a plus on + + + align:start position:0% +are plus all that have a plus on +distribution okay so the first thing we + + align:start position:0% +distribution okay so the first thing we + + + align:start position:0% +distribution okay so the first thing we +can look at is the variance in the spike + + align:start position:0% +can look at is the variance in the spike + + + align:start position:0% +can look at is the variance in the spike +count so remember for a Poisson process + + align:start position:0% +count so remember for a Poisson process + + + align:start position:0% +count so remember for a Poisson process +the average number of spikes in those + + align:start position:0% +the average number of spikes in those + + + align:start position:0% +the average number of spikes in those +mutants T we can calculate the variance + + align:start position:0% +mutants T we can calculate the variance + + + align:start position:0% +mutants T we can calculate the variance +in that which is basically just the + + align:start position:0% +in that which is basically just the + + + align:start position:0% +in that which is basically just the +width of this you know some measure of + + align:start position:0% +width of this you know some measure of + + + align:start position:0% +width of this you know some measure of +the width of this distribution here so + + align:start position:0% +the width of this distribution here so + + + align:start position:0% +the width of this distribution here so +the variance is just the of the number + + align:start position:0% +the variance is just the of the number + + + align:start position:0% +the variance is just the of the number +of counts on a given trial minus the + + align:start position:0% +of counts on a given trial minus the + + + align:start position:0% +of counts on a given trial minus the +expected number okay + + align:start position:0% + + + + align:start position:0% + +squared n minus average n squared okay + + align:start position:0% +squared n minus average n squared okay + + + align:start position:0% +squared n minus average n squared okay +and if you multiply that out you get + + align:start position:0% +and if you multiply that out you get + + + align:start position:0% +and if you multiply that out you get +it's the average n squared minus the + + align:start position:0% +it's the average n squared minus the + + + align:start position:0% +it's the average n squared minus the +average squared and it turns out for the + + align:start position:0% +average squared and it turns out for the + + + align:start position:0% +average squared and it turns out for the +Poisson process that that variance is + + align:start position:0% +Poisson process that that variance is + + + align:start position:0% +Poisson process that that variance is +also mutti so the variance in the + + align:start position:0% +also mutti so the variance in the + + + align:start position:0% +also mutti so the variance in the +average by count is mutti and the + + align:start position:0% +average by count is mutti and the + + + align:start position:0% +average by count is mutti and the +variance in the spike count is also + + align:start position:0% +variance in the spike count is also + + + align:start position:0% +variance in the spike count is also +mutti okay so there's a quantity called + + align:start position:0% +mutti okay so there's a quantity called + + + align:start position:0% +mutti okay so there's a quantity called +the Fano factor which is just defined as + + align:start position:0% +the Fano factor which is just defined as + + + align:start position:0% +the Fano factor which is just defined as +the variance of the spike count divided + + align:start position:0% +the variance of the spike count divided + + + align:start position:0% +the variance of the spike count divided +by the average by count and for a + + align:start position:0% +by the average by count and for a + + + align:start position:0% +by the average by count and for a +Poisson process the final factor is one + + align:start position:0% +Poisson process the final factor is one + + + align:start position:0% +Poisson process the final factor is one +okay and what you find is that for + + align:start position:0% +okay and what you find is that for + + + align:start position:0% +okay and what you find is that for +neurons in cortex and other parts of the + + align:start position:0% +neurons in cortex and other parts of the + + + align:start position:0% +neurons in cortex and other parts of the +brain the funnel factor is actually can + + align:start position:0% +brain the funnel factor is actually can + + + align:start position:0% +brain the funnel factor is actually can +be quite close to one it's usually + + align:start position:0% +be quite close to one it's usually + + + align:start position:0% +be quite close to one it's usually +between one and one and a half or so + + align:start position:0% +between one and one and a half or so + + + align:start position:0% +between one and one and a half or so +okay so it's there's been a lot of + + align:start position:0% +okay so it's there's been a lot of + + + align:start position:0% +okay so it's there's been a lot of +discussion and interest in + + align:start position:0% +discussion and interest in + + + align:start position:0% +discussion and interest in +why it is that spike counts in the brain + + align:start position:0% +why it is that spike counts in the brain + + + align:start position:0% +why it is that spike counts in the brain +are actually so random why that why do + + align:start position:0% +are actually so random why that why do + + + align:start position:0% +are actually so random why that why do +Narns behave in such a way that their + + align:start position:0% +Narns behave in such a way that their + + + align:start position:0% +Narns behave in such a way that their +spikes occur essentially randomly okay + + align:start position:0% +spikes occur essentially randomly okay + + + align:start position:0% +spikes occur essentially randomly okay +at some rate so it's a it's a + + align:start position:0% +at some rate so it's a it's a + + + align:start position:0% +at some rate so it's a it's a +interesting topic of current research + + align:start position:0% +interesting topic of current research + + + align:start position:0% +interesting topic of current research +interest okay let me tell you about one + + align:start position:0% +interest okay let me tell you about one + + + align:start position:0% +interest okay let me tell you about one +other measure called the interspike + + align:start position:0% +other measure called the interspike + + + align:start position:0% +other measure called the interspike +interval distribution and basically the + + align:start position:0% +interval distribution and basically the + + + align:start position:0% +interval distribution and basically the +interspike interval distribution is the + + align:start position:0% +interspike interval distribution is the + + + align:start position:0% +interspike interval distribution is the +distribution of x between spikes you can + + align:start position:0% +distribution of x between spikes you can + + + align:start position:0% +distribution of x between spikes you can +I'm just gonna show you what that looks + + align:start position:0% +I'm just gonna show you what that looks + + + align:start position:0% +I'm just gonna show you what that looks +awesome process and and then briefly + + align:start position:0% +awesome process and and then briefly + + + align:start position:0% +awesome process and and then briefly +describe what that looks like for real + + align:start position:0% +describe what that looks like for real + + + align:start position:0% +describe what that looks like for real +neurons okay so let's say we have a + + align:start position:0% +neurons okay so let's say we have a + + + align:start position:0% +neurons okay so let's say we have a +spike okay let's calculate the + + align:start position:0% +spike okay let's calculate the + + + align:start position:0% +spike okay let's calculate the +distribution of intervals between spikes + + align:start position:0% +distribution of intervals between spikes + + + align:start position:0% +distribution of intervals between spikes +so let's say we have a spike at time T + + align:start position:0% +so let's say we have a spike at time T + + + align:start position:0% +so let's say we have a spike at time T +sub I we're gonna ask what is the + + align:start position:0% +sub I we're gonna ask what is the + + + align:start position:0% +sub I we're gonna ask what is the +probability that we have a spike some + + align:start position:0% +probability that we have a spike some + + + align:start position:0% +probability that we have a spike some +time tau later tau sub I later okay with + + align:start position:0% +time tau later tau sub I later okay with + + + align:start position:0% +time tau later tau sub I later okay with +in some little window delta T okay so + + align:start position:0% +in some little window delta T okay so + + + align:start position:0% +in some little window delta T okay so +let's calculate that so tau is just tau + + align:start position:0% +let's calculate that so tau is just tau + + + align:start position:0% +let's calculate that so tau is just tau +sub I is the spike interval between the + + align:start position:0% +sub I is the spike interval between the + + + align:start position:0% +sub I is the spike interval between the +I plus 1 spike and the ithe spike all + + align:start position:0% +I plus 1 spike and the ithe spike all + + + align:start position:0% +I plus 1 spike and the ithe spike all +right so the probability of having the + + align:start position:0% +right so the probability of having the + + + align:start position:0% +right so the probability of having the +next spike land in the interval between + + align:start position:0% +next spike land in the interval between + + + align:start position:0% +next spike land in the interval between +T of I plus 1 and T of I plus 1 plus + + align:start position:0% +T of I plus 1 and T of I plus 1 plus + + + align:start position:0% +T of I plus 1 and T of I plus 1 plus +delta T in this little window here is + + align:start position:0% +delta T in this little window here is + + + align:start position:0% +delta T in this little window here is +going to be what to be the probability + + align:start position:0% +going to be what to be the probability + + + align:start position:0% +going to be what to be the probability +of having no spike in this interval + + align:start position:0% +of having no spike in this interval + + + align:start position:0% +of having no spike in this interval +times the probability of having a spike + + align:start position:0% +times the probability of having a spike + + + align:start position:0% +times the probability of having a spike +in that little interval so what's the + + align:start position:0% +in that little interval so what's the + + + align:start position:0% +in that little interval so what's the +probability of having no spike in that + + align:start position:0% +probability of having no spike in that + + + align:start position:0% +probability of having no spike in that +interval tau ok what what distribution + + align:start position:0% +interval tau ok what what distribution + + + align:start position:0% +interval tau ok what what distribution +can be use to calculate that probability + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +so what is what is the Poisson + + align:start position:0% +so what is what is the Poisson + + + align:start position:0% +so what is what is the Poisson +distribution it tells us the probability + + align:start position:0% +distribution it tells us the probability + + + align:start position:0% +distribution it tells us the probability +of having n spikes in an interval T + + align:start position:0% +of having n spikes in an interval T + + + align:start position:0% +of having n spikes in an interval T +capital T so what how would we use that + + align:start position:0% +capital T so what how would we use that + + + align:start position:0% +capital T so what how would we use that +to calculate the probability of having + + align:start position:0% +to calculate the probability of having + + + align:start position:0% +to calculate the probability of having +no spike in that interval exactly we + + align:start position:0% +no spike in that interval exactly we + + + align:start position:0% +no spike in that interval exactly we +just used the Poisson distribution and + + align:start position:0% +just used the Poisson distribution and + + + align:start position:0% +just used the Poisson distribution and +plug N equals 0 into it right so to that + + align:start position:0% +plug N equals 0 into it right so to that + + + align:start position:0% +plug N equals 0 into it right so to that +there's the there's the Poisson + + align:start position:0% +there's the there's the Poisson + + + align:start position:0% +there's the there's the Poisson +distribution what does this look like if + + align:start position:0% +distribution what does this look like if + + + align:start position:0% +distribution what does this look like if +we set N equals 0 so what is mu T to the + + align:start position:0% +we set N equals 0 so what is mu T to the + + + align:start position:0% +we set N equals 0 so what is mu T to the +0 1 what is and what is 0 factorial 1 + + align:start position:0% +0 1 what is and what is 0 factorial 1 + + + align:start position:0% +0 1 what is and what is 0 factorial 1 +and so the probability of having 0 + + align:start position:0% +and so the probability of having 0 + + + align:start position:0% +and so the probability of having 0 +spikes in a window T is just key to the + + align:start position:0% +spikes in a window T is just key to the + + + align:start position:0% +spikes in a window T is just key to the +minus mu T all right so let's plug that + + align:start position:0% +minus mu T all right so let's plug that + + + align:start position:0% +minus mu T all right so let's plug that +in good so the probability of having no + + align:start position:0% +in good so the probability of having no + + + align:start position:0% +in good so the probability of having no +spikes in that interval is e to the + + align:start position:0% +spikes in that interval is e to the + + + align:start position:0% +spikes in that interval is e to the +minus mu T or ro T where you are for + + align:start position:0% +minus mu T or ro T where you are for + + + align:start position:0% +minus mu T or ro T where you are for +right now ok now what is the probability + + align:start position:0% +right now ok now what is the probability + + + align:start position:0% +right now ok now what is the probability +of having a spike in that little window + + align:start position:0% +of having a spike in that little window + + + align:start position:0% +of having a spike in that little window +right there + + align:start position:0% + + + + align:start position:0% + +any thoughts um what's that + + align:start position:0% + + + + align:start position:0% + +yeah you could do that but we sort of + + align:start position:0% +yeah you could do that but we sort of + + + align:start position:0% +yeah you could do that but we sort of +derived the Poisson process by using the + + align:start position:0% +derived the Poisson process by using the + + + align:start position:0% +derived the Poisson process by using the +answer to this question already our + + align:start position:0% +answer to this question already our + + + align:start position:0% +answer to this question already our +delta T good okay so the probability of + + align:start position:0% +delta T good okay so the probability of + + + align:start position:0% +delta T good okay so the probability of +having a spike in that little window is + + align:start position:0% +having a spike in that little window is + + + align:start position:0% +having a spike in that little window is +just our Delta today okay yes yeah it's + + align:start position:0% +just our Delta today okay yes yeah it's + + + align:start position:0% +just our Delta today okay yes yeah it's +I just changed the name of the variable + + align:start position:0% +I just changed the name of the variable + + + align:start position:0% +I just changed the name of the variable +if you look in the statistics literature + + align:start position:0% +if you look in the statistics literature + + + align:start position:0% +if you look in the statistics literature +they most often use mu but when we're + + align:start position:0% +they most often use mu but when we're + + + align:start position:0% +they most often use mu but when we're +talking about firing rates of neurons + + align:start position:0% +talking about firing rates of neurons + + + align:start position:0% +talking about firing rates of neurons +it's more convenient to use R and so + + align:start position:0% +it's more convenient to use R and so + + + align:start position:0% +it's more convenient to use R and so +they're just the same well so remember + + align:start position:0% +they're just the same well so remember + + + align:start position:0% +they're just the same well so remember +the probability of having a spike in any + + align:start position:0% +the probability of having a spike in any + + + align:start position:0% +the probability of having a spike in any +interval in a process is completely + + align:start position:0% +interval in a process is completely + + + align:start position:0% +interval in a process is completely +independent of what happens at any other + + align:start position:0% +independent of what happens at any other + + + align:start position:0% +independent of what happens at any other +time okay because in order for this to + + align:start position:0% +time okay because in order for this to + + + align:start position:0% +time okay because in order for this to +be the interval between one spike and + + align:start position:0% +be the interval between one spike and + + + align:start position:0% +be the interval between one spike and +the next spike we needed to have zero + + align:start position:0% +the next spike we needed to have zero + + + align:start position:0% +the next spike we needed to have zero +spikes in the intervening interval right + + align:start position:0% +spikes in the intervening interval right + + + align:start position:0% +spikes in the intervening interval right +because if there had been another spike + + align:start position:0% +because if there had been another spike + + + align:start position:0% +because if there had been another spike +in here somewhere + + align:start position:0% +in here somewhere + + + align:start position:0% +in here somewhere +this would not be our interest like + + align:start position:0% +this would not be our interest like + + + align:start position:0% +this would not be our interest like +interval the interest Pike interval + + align:start position:0% +interval the interest Pike interval + + + align:start position:0% +interval the interest Pike interval +would be between here and wherever that + + align:start position:0% +would be between here and wherever that + + + align:start position:0% +would be between here and wherever that +spike occurred and we'd just be back to + + align:start position:0% +spike occurred and we'd just be back to + + + align:start position:0% +spike occurred and we'd just be back to +calculating what's the probability of + + align:start position:0% +calculating what's the probability of + + + align:start position:0% +calculating what's the probability of +having no spike between there and there + + align:start position:0% + + + + align:start position:0% + +okay good so that's the probability of + + align:start position:0% +okay good so that's the probability of + + + align:start position:0% +okay good so that's the probability of +having no spike from here to here and + + align:start position:0% +having no spike from here to here and + + + align:start position:0% +having no spike from here to here and +having a spike in the next little Delta + + align:start position:0% +having a spike in the next little Delta + + + align:start position:0% +having a spike in the next little Delta +T we can we can now calculate what's + + align:start position:0% +T we can we can now calculate what's + + + align:start position:0% +T we can we can now calculate what's +called a probability density it's the + + align:start position:0% +called a probability density it's the + + + align:start position:0% +called a probability density it's the +probability per unit time of having + + align:start position:0% +probability per unit time of having + + + align:start position:0% +probability per unit time of having +interspike intervals of that duration + + align:start position:0% +interspike intervals of that duration + + + align:start position:0% +interspike intervals of that duration +okay and to do that we just calculate + + align:start position:0% +okay and to do that we just calculate + + + align:start position:0% +okay and to do that we just calculate +the probability divided by delta T and + + align:start position:0% +the probability divided by delta T and + + + align:start position:0% +the probability divided by delta T and +what you find is that the probability + + align:start position:0% +what you find is that the probability + + + align:start position:0% +what you find is that the probability +density of interspike intervals is just + + align:start position:0% +density of interspike intervals is just + + + align:start position:0% +density of interspike intervals is just +R + + align:start position:0% +R + + + align:start position:0% +R +e to the minus R tau or tau pushbike + + align:start position:0% +e to the minus R tau or tau pushbike + + + align:start position:0% +e to the minus R tau or tau pushbike +interval okay and so this is what that + + align:start position:0% +interval okay and so this is what that + + + align:start position:0% +interval okay and so this is what that +looks like for a Poisson process okay so + + align:start position:0% +looks like for a Poisson process okay so + + + align:start position:0% +looks like for a Poisson process okay so +you can see that the highest probability + + align:start position:0% +you can see that the highest probability + + + align:start position:0% +you can see that the highest probability +is having very short intervals and you + + align:start position:0% +is having very short intervals and you + + + align:start position:0% +is having very short intervals and you +have exponentially lower probabilities + + align:start position:0% +have exponentially lower probabilities + + + align:start position:0% +have exponentially lower probabilities +of having longer and longer intervals + + align:start position:0% +of having longer and longer intervals + + + align:start position:0% +of having longer and longer intervals +okay does that make sense so it turns + + align:start position:0% +okay does that make sense so it turns + + + align:start position:0% +okay does that make sense so it turns +out that that's actually a lot like what + + align:start position:0% +out that that's actually a lot like what + + + align:start position:0% +out that that's actually a lot like what +interspike intervals of real neurons + + align:start position:0% +interspike intervals of real neurons + + + align:start position:0% +interspike intervals of real neurons +looks like okay they very often have + + align:start position:0% +looks like okay they very often have + + + align:start position:0% +looks like okay they very often have +this exponential tail okay now what's + + align:start position:0% +this exponential tail okay now what's + + + align:start position:0% +this exponential tail okay now what's +what is completely unrealistic about + + align:start position:0% +what is completely unrealistic about + + + align:start position:0% +what is completely unrealistic about +this interspike interval distribution + + align:start position:0% +this interspike interval distribution + + + align:start position:0% +this interspike interval distribution +what is it that can't be true about this + + align:start position:0% + + + + align:start position:0% + +well so it's actually the bigger problem + + align:start position:0% +well so it's actually the bigger problem + + + align:start position:0% +well so it's actually the bigger problem +is not on this end of the distribution + + align:start position:0% +is not on this end of the distribution + + + align:start position:0% +is not on this end of the distribution +yeah what what what happens here that's + + align:start position:0% +yeah what what what happens here that's + + + align:start position:0% +yeah what what what happens here that's +wrong exactly so what happens + + align:start position:0% +wrong exactly so what happens + + + align:start position:0% +wrong exactly so what happens +immediately after a neuron spikes you + + align:start position:0% +immediately after a neuron spikes you + + + align:start position:0% +immediately after a neuron spikes you +can't have another spike right away why + + align:start position:0% +can't have another spike right away why + + + align:start position:0% +can't have another spike right away why +is that because of the refractory period + + align:start position:0% +is that because of the refractory period + + + align:start position:0% +is that because of the refractory period +which comes from hyper polarization is + + align:start position:0% +which comes from hyper polarization is + + + align:start position:0% +which comes from hyper polarization is +one of them once you have this bike the + + align:start position:0% +one of them once you have this bike the + + + align:start position:0% +one of them once you have this bike the +neuron is actually briefly + + align:start position:0% +neuron is actually briefly + + + align:start position:0% +neuron is actually briefly +hyperpolarized you could imagine like + + align:start position:0% +hyperpolarized you could imagine like + + + align:start position:0% +hyperpolarized you could imagine like +trying to repolarize it very quickly but + + align:start position:0% +trying to repolarize it very quickly but + + + align:start position:0% +trying to repolarize it very quickly but +then something else is a problem sodium + + align:start position:0% +then something else is a problem sodium + + + align:start position:0% +then something else is a problem sodium +channel inactivation okay so even if you + + align:start position:0% +channel inactivation okay so even if you + + + align:start position:0% +channel inactivation okay so even if you +were to repolarize the neuron very + + align:start position:0% +were to repolarize the neuron very + + + align:start position:0% +were to repolarize the neuron very +quickly it still would have a hard time + + align:start position:0% +quickly it still would have a hard time + + + align:start position:0% +quickly it still would have a hard time +making this bike because of sodium + + align:start position:0% +making this bike because of sodium + + + align:start position:0% +making this bike because of sodium +channel inactivation okay so what does + + align:start position:0% +channel inactivation okay so what does + + + align:start position:0% +channel inactivation okay so what does +this actually look like for a real note + + align:start position:0% +this actually look like for a real note + + + align:start position:0% +this actually look like for a real note +what do you imagine it looks like right + + align:start position:0% +what do you imagine it looks like right + + + align:start position:0% +what do you imagine it looks like right +so immediately after a spike there's + + align:start position:0% +so immediately after a spike there's + + + align:start position:0% +so immediately after a spike there's +zero probability of having another spike + + align:start position:0% +zero probability of having another spike + + + align:start position:0% +zero probability of having another spike +okay so this starts at zero climbs up + + align:start position:0% +okay so this starts at zero climbs up + + + align:start position:0% +okay so this starts at zero climbs up +here and then decays exponentially okay + + align:start position:0% +here and then decays exponentially okay + + + align:start position:0% +here and then decays exponentially okay +so that's what most interspike intervals + + align:start position:0% +so that's what most interspike intervals + + + align:start position:0% +so that's what most interspike intervals +for real neurons actually looks like + + align:start position:0% +for real neurons actually looks like + + + align:start position:0% +for real neurons actually looks like +okay so this is probability density this + + align:start position:0% +okay so this is probability density this + + + align:start position:0% +okay so this is probability density this +towel okay and this is the refractory + + align:start position:0% +towel okay and this is the refractory + + + align:start position:0% +towel okay and this is the refractory +period + + align:start position:0% + + + + align:start position:0% + +okay in fact when you record from + + align:start position:0% +okay in fact when you record from + + + align:start position:0% +okay in fact when you record from +neurons with an electrode in the brain + + align:start position:0% +neurons with an electrode in the brain + + + align:start position:0% +neurons with an electrode in the brain +you get lots of spikes one of the first + + align:start position:0% +you get lots of spikes one of the first + + + align:start position:0% +you get lots of spikes one of the first +things you should do when you set a + + align:start position:0% +things you should do when you set a + + + align:start position:0% +things you should do when you set a +threshold and find those spike times is + + align:start position:0% +threshold and find those spike times is + + + align:start position:0% +threshold and find those spike times is +computer-like interval distribution okay + + align:start position:0% +computer-like interval distribution okay + + + align:start position:0% +computer-like interval distribution okay +because if you're recording from a + + align:start position:0% +because if you're recording from a + + + align:start position:0% +because if you're recording from a +single neuron that interspike interval + + align:start position:0% +single neuron that interspike interval + + + align:start position:0% +single neuron that interspike interval +distribution will have this refractory + + align:start position:0% +distribution will have this refractory + + + align:start position:0% +distribution will have this refractory +period okay if you're recording from + + align:start position:0% +period okay if you're recording from + + + align:start position:0% +period okay if you're recording from +it's quite easy to get multiple spikes + + align:start position:0% +it's quite easy to get multiple spikes + + + align:start position:0% +it's quite easy to get multiple spikes +on the end of an electrode and what + + align:start position:0% +on the end of an electrode and what + + + align:start position:0% +on the end of an electrode and what +happens if you have multiple spikes you + + align:start position:0% +happens if you have multiple spikes you + + + align:start position:0% +happens if you have multiple spikes you +can think they're coming from one neuron + + align:start position:0% +can think they're coming from one neuron + + + align:start position:0% +can think they're coming from one neuron +but in fact they're coming from two + + align:start position:0% +but in fact they're coming from two + + + align:start position:0% +but in fact they're coming from two +neurons and if you compute the + + align:start position:0% +neurons and if you compute the + + + align:start position:0% +neurons and if you compute the +interspike interval distribution it + + align:start position:0% +interspike interval distribution it + + + align:start position:0% +interspike interval distribution it +won't have this dip here okay so it's a + + align:start position:0% +won't have this dip here okay so it's a + + + align:start position:0% +won't have this dip here okay so it's a +really important tool to use to test + + align:start position:0% +really important tool to use to test + + + align:start position:0% +really important tool to use to test +whether your signal is clean okay you'd + + align:start position:0% +whether your signal is clean okay you'd + + + align:start position:0% +whether your signal is clean okay you'd +be amazed at how few people actually do + + align:start position:0% +be amazed at how few people actually do + + + align:start position:0% +be amazed at how few people actually do +that okay all right I just want to + + align:start position:0% +that okay all right I just want to + + + align:start position:0% +that okay all right I just want to +introduce you to one important term and + + align:start position:0% +introduce you to one important term and + + + align:start position:0% +introduce you to one important term and +that's called homogeneous versus + + align:start position:0% +that's called homogeneous versus + + + align:start position:0% +that's called homogeneous versus +inhomogeneous in the context of questo + + align:start position:0% +inhomogeneous in the context of questo + + + align:start position:0% +inhomogeneous in the context of questo +process what that means a homogenious + + align:start position:0% +process what that means a homogenious + + + align:start position:0% +process what that means a homogenious +prime plus some process has a constant + + align:start position:0% +prime plus some process has a constant + + + align:start position:0% +prime plus some process has a constant +rate mu most neurons don't do that + + align:start position:0% +rate mu most neurons don't do that + + + align:start position:0% +rate mu most neurons don't do that +because in most neurons there's + + align:start position:0% +because in most neurons there's + + + align:start position:0% +because in most neurons there's +information carried in the fluctuation + + align:start position:0% +information carried in the fluctuation + + + align:start position:0% +information carried in the fluctuation +of the firing rate and so most neurons + + align:start position:0% +of the firing rate and so most neurons + + + align:start position:0% +of the firing rate and so most neurons +have what's called an behave more alike + + align:start position:0% +have what's called an behave more alike + + + align:start position:0% +have what's called an behave more alike +in you know in homogeneous Poisson + + align:start position:0% +in you know in homogeneous Poisson + + + align:start position:0% +in you know in homogeneous Poisson +process where the rate is actually + + align:start position:0% +process where the rate is actually + + + align:start position:0% +process where the rate is actually +fluctuating in time okay in the example + + align:start position:0% +fluctuating in time okay in the example + + + align:start position:0% +fluctuating in time okay in the example +we were looking at before shows you what + + align:start position:0% +we were looking at before shows you what + + + align:start position:0% +we were looking at before shows you what +an in homogeneous part plus the whole + + align:start position:0% +an in homogeneous part plus the whole + + + align:start position:0% +an in homogeneous part plus the whole +process would look like okay okay so + + align:start position:0% +process would look like okay okay so + + + align:start position:0% +process would look like okay okay so +let's see what's next + + align:start position:0% +let's see what's next + + + align:start position:0% +let's see what's next +alright so let's change topics to talk + + align:start position:0% +alright so let's change topics to talk + + + align:start position:0% +alright so let's change topics to talk +about + + align:start position:0% +about + + + align:start position:0% +about +convolution cross correlation and + + align:start position:0% +convolution cross correlation and + + + align:start position:0% +convolution cross correlation and +autocorrelation functions alright so + + align:start position:0% +autocorrelation functions alright so + + + align:start position:0% +autocorrelation functions alright so +we've been using the notion of a + + align:start position:0% +we've been using the notion of a + + + align:start position:0% +we've been using the notion of a +convolution where we have + + align:start position:0% +convolution where we have + + + align:start position:0% +convolution where we have +colonel that we multiplied by a signal + + align:start position:0% +colonel that we multiplied by a signal + + + align:start position:0% +colonel that we multiplied by a signal +we apply that and integrate over time + + align:start position:0% +we apply that and integrate over time + + + align:start position:0% +we apply that and integrate over time +and then we slide that colonel across + + align:start position:0% +and then we slide that colonel across + + + align:start position:0% +and then we slide that colonel across +the signal and ask where does the signal + + align:start position:0% +the signal and ask where does the signal + + + align:start position:0% +the signal and ask where does the signal +have structure that looks like the + + align:start position:0% +have structure that looks like the + + + align:start position:0% +have structure that looks like the +colonel okay and that gives you a an + + align:start position:0% +colonel okay and that gives you a an + + + align:start position:0% +colonel okay and that gives you a an +output Y of T so we've used that to + + align:start position:0% +output Y of T so we've used that to + + + align:start position:0% +output Y of T so we've used that to +model the membrane potential of a new + + align:start position:0% +model the membrane potential of a new + + + align:start position:0% +model the membrane potential of a new +synaptic input so in that case we had + + align:start position:0% +synaptic input so in that case we had + + + align:start position:0% +synaptic input so in that case we had +spikes coming from a presynaptic neuron + + align:start position:0% +spikes coming from a presynaptic neuron + + + align:start position:0% +spikes coming from a presynaptic neuron +that generate a response in the + + align:start position:0% +that generate a response in the + + + align:start position:0% +that generate a response in the +postsynaptic neuron and now we can take + + align:start position:0% +postsynaptic neuron and now we can take + + + align:start position:0% +postsynaptic neuron and now we can take +we can model the output of that the + + align:start position:0% +we can model the output of that the + + + align:start position:0% +we can model the output of that the +response in the postsynaptic neuron as a + + align:start position:0% +response in the postsynaptic neuron as a + + + align:start position:0% +response in the postsynaptic neuron as a +convolution of that exponential with an + + align:start position:0% +convolution of that exponential with an + + + align:start position:0% +convolution of that exponential with an +input spectrum okay + + align:start position:0% +input spectrum okay + + + align:start position:0% +input spectrum okay +we've used it to model the response of + + align:start position:0% +we've used it to model the response of + + + align:start position:0% +we've used it to model the response of +neurons to a time dependent stimulus + + align:start position:0% +neurons to a time dependent stimulus + + + align:start position:0% +neurons to a time dependent stimulus +okay and you also used it I've described + + align:start position:0% +okay and you also used it I've described + + + align:start position:0% +okay and you also used it I've described +how you can use that to implement a + + align:start position:0% +how you can use that to implement a + + + align:start position:0% +how you can use that to implement a +low-pass filter bypass filter and we did + + align:start position:0% +low-pass filter bypass filter and we did + + + align:start position:0% +low-pass filter bypass filter and we did +that we talked about doing that for + + align:start position:0% +that we talked about doing that for + + + align:start position:0% +that we talked about doing that for +extracting either low frequency signals + + align:start position:0% +extracting either low frequency signals + + + align:start position:0% +extracting either low frequency signals +to get the loaf look at the local field + + align:start position:0% +to get the loaf look at the local field + + + align:start position:0% +to get the loaf look at the local field +potential out of neurons or doing a + + align:start position:0% +potential out of neurons or doing a + + + align:start position:0% +potential out of neurons or doing a +high-pass filter to get rid of the low + + align:start position:0% +high-pass filter to get rid of the low + + + align:start position:0% +high-pass filter to get rid of the low +frequency signals so that you can see + + align:start position:0% +frequency signals so that you can see + + + align:start position:0% +frequency signals so that you can see +the spikes okay but most generally + + align:start position:0% +the spikes okay but most generally + + + align:start position:0% +the spikes okay but most generally +evolution is you should think about it + + align:start position:0% +evolution is you should think about it + + + align:start position:0% +evolution is you should think about it +as allowing you to the to model how a + + align:start position:0% +as allowing you to the to model how a + + + align:start position:0% +as allowing you to the to model how a +system responds to an input where the + + align:start position:0% +system responds to an input where the + + + align:start position:0% +system responds to an input where the +response of the system is controlled by + + align:start position:0% +response of the system is controlled by + + + align:start position:0% +response of the system is controlled by +a linear filter okay the system is + + align:start position:0% +a linear filter okay the system is + + + align:start position:0% +a linear filter okay the system is +sensitive to particular patterns in the + + align:start position:0% +sensitive to particular patterns in the + + + align:start position:0% +sensitive to particular patterns in the +input those patterns can be detected by + + align:start position:0% +input those patterns can be detected by + + + align:start position:0% +input those patterns can be detected by +a filter all right so you apply that + + align:start position:0% +a filter all right so you apply that + + + align:start position:0% +a filter all right so you apply that +filter to the input and you estimate how + + align:start position:0% +filter to the input and you estimate how + + + align:start position:0% +filter to the input and you estimate how +the system responds and it's very + + align:start position:0% +the system responds and it's very + + + align:start position:0% +the system responds and it's very +broadly useful in in engineering and + + align:start position:0% +broadly useful in in engineering and + + + align:start position:0% +broadly useful in in engineering and +biology and neuroscience to use + + align:start position:0% +biology and neuroscience to use + + + align:start position:0% +biology and neuroscience to use +convolutions to model how a system + + align:start position:0% +convolutions to model how a system + + + align:start position:0% +convolutions to model how a system +responds to its input okay + + align:start position:0% + + + + align:start position:0% + +alright so there's a different kind of + + align:start position:0% +alright so there's a different kind of + + + align:start position:0% +alright so there's a different kind of +function called a cross correlation + + align:start position:0% +function called a cross correlation + + + align:start position:0% +function called a cross correlation +function that looks like this alright + + align:start position:0% +function that looks like this alright + + + align:start position:0% +function that looks like this alright +and it looks very - a convolution but + + align:start position:0% +and it looks very - a convolution but + + + align:start position:0% +and it looks very - a convolution but +it's used very differently now you might + + align:start position:0% +it's used very differently now you might + + + align:start position:0% +it's used very differently now you might +think okay there's just there's just a + + align:start position:0% +think okay there's just there's just a + + + align:start position:0% +think okay there's just there's just a +sign change right here I have a t minus + + align:start position:0% +sign change right here I have a t minus + + + align:start position:0% +sign change right here I have a t minus +tau and here I have a t plus tau is that + + align:start position:0% +tau and here I have a t plus tau is that + + + align:start position:0% +tau and here I have a t plus tau is that +the only difference between those it's + + align:start position:0% +the only difference between those it's + + + align:start position:0% +the only difference between those it's +not is here I'm integrating over D tau + + align:start position:0% +not is here I'm integrating over D tau + + + align:start position:0% +not is here I'm integrating over D tau +and here I'm integrating over DT here + + align:start position:0% +and here I'm integrating over DT here + + + align:start position:0% +and here I'm integrating over DT here +I'm getting the response as a function + + align:start position:0% +I'm getting the response as a function + + + align:start position:0% +I'm getting the response as a function +of time here what I'm doing is I'm kind + + align:start position:0% +of time here what I'm doing is I'm kind + + + align:start position:0% +of time here what I'm doing is I'm kind +of extracting the kernel what I what I'm + + align:start position:0% +of extracting the kernel what I what I'm + + + align:start position:0% +of extracting the kernel what I what I'm +getting out of this is a kernel towel as + + align:start position:0% +getting out of this is a kernel towel as + + + align:start position:0% +getting out of this is a kernel towel as +a function okay so let me walk through + + align:start position:0% +a function okay so let me walk through + + + align:start position:0% +a function okay so let me walk through +what that how that works so in this case + + align:start position:0% +what that how that works so in this case + + + align:start position:0% +what that how that works so in this case +we have two signals x and y okay and + + align:start position:0% +we have two signals x and y okay and + + + align:start position:0% +we have two signals x and y okay and +what we're doing is we're taking those + + align:start position:0% +what we're doing is we're taking those + + + align:start position:0% +what we're doing is we're taking those +two signals and we're multiplying them + + align:start position:0% +two signals and we're multiplying them + + + align:start position:0% +two signals and we're multiplying them +both by each other x times y and what + + align:start position:0% +both by each other x times y and what + + + align:start position:0% +both by each other x times y and what +we're doing is we're multiplying the + + align:start position:0% +we're doing is we're multiplying the + + + align:start position:0% +we're doing is we're multiplying the +signals and then integrating over the + + align:start position:0% +signals and then integrating over the + + + align:start position:0% +signals and then integrating over the +product okay and then we shift one of + + align:start position:0% +product okay and then we shift one of + + + align:start position:0% +product okay and then we shift one of +those signals by a little amount towel + + align:start position:0% +those signals by a little amount towel + + + align:start position:0% +those signals by a little amount towel +and we repeat that process okay so let's + + align:start position:0% +and we repeat that process okay so let's + + + align:start position:0% +and we repeat that process okay so let's +see what that looks like so what what do + + align:start position:0% +see what that looks like so what what do + + + align:start position:0% +see what that looks like so what what do +you see here you see two different + + align:start position:0% +you see here you see two different + + + align:start position:0% +you see here you see two different +signals X and I sorry x and y they look + + align:start position:0% +signals X and I sorry x and y they look + + + align:start position:0% +signals X and I sorry x and y they look +kind of similar right you can see this + + align:start position:0% +kind of similar right you can see this + + + align:start position:0% +kind of similar right you can see this +one has like a bump here and a couple + + align:start position:0% +one has like a bump here and a couple + + + align:start position:0% +one has like a bump here and a couple +bumps there and a bump there and you see + + align:start position:0% +bumps there and a bump there and you see + + + align:start position:0% +bumps there and a bump there and you see +something pretty similar to that here + + align:start position:0% +something pretty similar to that here + + + align:start position:0% +something pretty similar to that here +right there's three big bumps here three + + align:start position:0% +right there's three big bumps here three + + + align:start position:0% +right there's three big bumps here three +big bumps so those signals are actually + + align:start position:0% +big bumps so those signals are actually + + + align:start position:0% +big bumps so those signals are actually +quite similar for each other but they're + + align:start position:0% +quite similar for each other but they're + + + align:start position:0% +quite similar for each other but they're +not exactly the same right you can see + + align:start position:0% +not exactly the same right you can see + + + align:start position:0% +not exactly the same right you can see +that these fast little fluctuations are + + align:start position:0% +that these fast little fluctuations are + + + align:start position:0% +that these fast little fluctuations are +are different on those two signals now + + align:start position:0% +are different on those two signals now + + + align:start position:0% +are different on those two signals now +what happens when we take this signal + + align:start position:0% +what happens when we take this signal + + + align:start position:0% +what happens when we take this signal +and you can see that there's this offset + + align:start position:0% +and you can see that there's this offset + + + align:start position:0% +and you can see that there's this offset +here so what happens if we take x times + + align:start position:0% +here so what happens if we take x times + + + align:start position:0% +here so what happens if we take x times +y we multiply them together and we + + align:start position:0% +y we multiply them together and we + + + align:start position:0% +y we multiply them together and we +integrate the result + + align:start position:0% +integrate the result + + + align:start position:0% +integrate the result +okay then we shift why a little bit by + + align:start position:0% +okay then we shift why a little bit by + + + align:start position:0% +okay then we shift why a little bit by +an amount towel and we multiply those + + align:start position:0% +an amount towel and we multiply those + + + align:start position:0% +an amount towel and we multiply those +two signals together and we integrate + + align:start position:0% +two signals together and we integrate + + + align:start position:0% +two signals together and we integrate +and we keep doing that all right and now + + align:start position:0% +and we keep doing that all right and now + + + align:start position:0% +and we keep doing that all right and now +we're going to plot this K as a function + + align:start position:0% +we're going to plot this K as a function + + + align:start position:0% +we're going to plot this K as a function +of that little shift towel that we put + + align:start position:0% +of that little shift towel that we put + + + align:start position:0% +of that little shift towel that we put +in there okay + + align:start position:0% +in there okay + + + align:start position:0% +in there okay +and here's what that looks like so K is + + align:start position:0% +and here's what that looks like so K is + + + align:start position:0% +and here's what that looks like so K is +the cross correlation sometimes called + + align:start position:0% +the cross correlation sometimes called + + + align:start position:0% +the cross correlation sometimes called +the lag cross correlation of X and y so + + align:start position:0% +the lag cross correlation of X and y so + + + align:start position:0% +the lag cross correlation of X and y so +there's a symbol for that little circle + + align:start position:0% +there's a symbol for that little circle + + + align:start position:0% +there's a symbol for that little circle +is the symbol for lag cross correlation + + align:start position:0% +is the symbol for lag cross correlation + + + align:start position:0% +is the symbol for lag cross correlation +and you can see that that at a + + align:start position:0% +and you can see that that at a + + + align:start position:0% +and you can see that that at a +particular lag like right here the + + align:start position:0% +particular lag like right here the + + + align:start position:0% +particular lag like right here the +positive fluctuations in this signal are + + align:start position:0% +positive fluctuations in this signal are + + + align:start position:0% +positive fluctuations in this signal are +going to line up with the positive + + align:start position:0% +going to line up with the positive + + + align:start position:0% +going to line up with the positive +fluctuations in that signal the negative + + align:start position:0% +fluctuations in that signal the negative + + + align:start position:0% +fluctuations in that signal the negative +fluctuations in this signal are going to + + align:start position:0% +fluctuations in this signal are going to + + + align:start position:0% +fluctuations in this signal are going to +put the negative fluctuations in that + + align:start position:0% +put the negative fluctuations in that + + + align:start position:0% +put the negative fluctuations in that +signal and when you multiply them + + align:start position:0% +signal and when you multiply them + + + align:start position:0% +signal and when you multiply them +together you're going to get the maximum + + align:start position:0% +together you're going to get the maximum + + + align:start position:0% +together you're going to get the maximum +positive contribution right those + + align:start position:0% +positive contribution right those + + + align:start position:0% +positive contribution right those +signals are going to be maximally + + align:start position:0% +signals are going to be maximally + + + align:start position:0% +signals are going to be maximally +overlapped at a particular shift towel + + align:start position:0% +overlapped at a particular shift towel + + + align:start position:0% +overlapped at a particular shift towel +okay and when you that function K of tau + + align:start position:0% +okay and when you that function K of tau + + + align:start position:0% +okay and when you that function K of tau +you're gonna have a peek at that lag + + align:start position:0% +you're gonna have a peek at that lag + + + align:start position:0% +you're gonna have a peek at that lag +that corresponds to where those signals + + align:start position:0% +that corresponds to where those signals + + + align:start position:0% +that corresponds to where those signals +are maximally overlapped okay so a lag + + align:start position:0% +are maximally overlapped okay so a lag + + + align:start position:0% +are maximally overlapped okay so a lag +cross correlation function is really + + align:start position:0% +cross correlation function is really + + + align:start position:0% +cross correlation function is really +useful for finding let's say the time at + + align:start position:0% +useful for finding let's say the time at + + + align:start position:0% +useful for finding let's say the time at +which two signals like if one signal is + + align:start position:0% +which two signals like if one signal is + + + align:start position:0% +which two signals like if one signal is +like a copy of the other one but it's + + align:start position:0% +like a copy of the other one but it's + + + align:start position:0% +like a copy of the other one but it's +shifted in time a lag cross correlation + + align:start position:0% +shifted in time a lag cross correlation + + + align:start position:0% +shifted in time a lag cross correlation +function is really useful for finding + + align:start position:0% +function is really useful for finding + + + align:start position:0% +function is really useful for finding +that the lag between those two functions + + align:start position:0% +that the lag between those two functions + + + align:start position:0% +that the lag between those two functions +okay there's another context in which + + align:start position:0% +okay there's another context in which + + + align:start position:0% +okay there's another context in which +this lag cross correlation function is + + align:start position:0% +this lag cross correlation function is + + + align:start position:0% +this lag cross correlation function is +really useful so when we did the + + align:start position:0% +really useful so when we did the + + + align:start position:0% +really useful so when we did the +spike-triggered average when we took + + align:start position:0% +spike-triggered average when we took + + + align:start position:0% +spike-triggered average when we took +spikes from a neuron and we at the time + + align:start position:0% +spikes from a neuron and we at the time + + + align:start position:0% +spikes from a neuron and we at the time +of those spikes we extract + + align:start position:0% +of those spikes we extract + + + align:start position:0% +of those spikes we extract +to what the input was to the neuron and + + align:start position:0% +to what the input was to the neuron and + + + align:start position:0% +to what the input was to the neuron and +we averaged at all what we were really + + align:start position:0% +we averaged at all what we were really + + + align:start position:0% +we averaged at all what we were really +doing was we were doing a cross + + align:start position:0% +doing was we were doing a cross + + + align:start position:0% +doing was we were doing a cross +correlation between the spike train of a + + align:start position:0% +correlation between the spike train of a + + + align:start position:0% +correlation between the spike train of a +neuron and the stimulus that drove that + + align:start position:0% +neuron and the stimulus that drove that + + + align:start position:0% +neuron and the stimulus that drove that +neuron the stimulus that was input to + + align:start position:0% +neuron the stimulus that was input to + + + align:start position:0% +neuron the stimulus that was input to +that neuron okay and that cross + + align:start position:0% +that neuron okay and that cross + + + align:start position:0% +that neuron okay and that cross +correlation was just the kernel that + + align:start position:0% +correlation was just the kernel that + + + align:start position:0% +correlation was just the kernel that +described how you get from the input to + + align:start position:0% +described how you get from the input to + + + align:start position:0% +described how you get from the input to +the neuron to the response of the neuron + + align:start position:0% +the neuron to the response of the neuron + + + align:start position:0% +the neuron to the response of the neuron +okay so spike-triggered average is + + align:start position:0% +okay so spike-triggered average is + + + align:start position:0% +okay so spike-triggered average is +actually sometimes called reverse + + align:start position:0% +actually sometimes called reverse + + + align:start position:0% +actually sometimes called reverse +correlation and the reverse comes from + + align:start position:0% +correlation and the reverse comes from + + + align:start position:0% +correlation and the reverse comes from +the fact that you have to actually flip + + align:start position:0% +the fact that you have to actually flip + + + align:start position:0% +the fact that you have to actually flip +this over to get the kernel so let's not + + align:start position:0% +this over to get the kernel so let's not + + + align:start position:0% +this over to get the kernel so let's not +worry about that but it's sometimes + + align:start position:0% +worry about that but it's sometimes + + + align:start position:0% +worry about that but it's sometimes +referred to as the correlation between + + align:start position:0% +referred to as the correlation between + + + align:start position:0% +referred to as the correlation between +the spike train and the stimulus in + + align:start position:0% +the spike train and the stimulus in + + + align:start position:0% +the spike train and the stimulus in +focus yes so there so so there's no + + align:start position:0% +focus yes so there so so there's no + + + align:start position:0% +focus yes so there so so there's no +convolution here we're doing the lag + + align:start position:0% +convolution here we're doing the lag + + + align:start position:0% +convolution here we're doing the lag +correlation okay we're just we're just + + align:start position:0% +correlation okay we're just we're just + + + align:start position:0% +correlation okay we're just we're just +taking those two signals and shifting + + align:start position:0% +taking those two signals and shifting + + + align:start position:0% +taking those two signals and shifting +one of them multiplying it and + + align:start position:0% +one of them multiplying it and + + + align:start position:0% +one of them multiplying it and +integrating okay sorry ask your question + + align:start position:0% +integrating okay sorry ask your question + + + align:start position:0% +integrating okay sorry ask your question +I just wanted to clarify there's no + + align:start position:0% +I just wanted to clarify there's no + + + align:start position:0% +I just wanted to clarify there's no +convolution being done here 20 ah okay + + align:start position:0% +convolution being done here 20 ah okay + + + align:start position:0% +convolution being done here 20 ah okay +great that's actually one of the things + + align:start position:0% +great that's actually one of the things + + + align:start position:0% +great that's actually one of the things +that's easiest to get mixed up about + + align:start position:0% +that's easiest to get mixed up about + + + align:start position:0% +that's easiest to get mixed up about +when you do like cross correlation okay + + align:start position:0% +when you do like cross correlation okay + + + align:start position:0% +when you do like cross correlation okay +you have to you have to be careful about + + align:start position:0% +you have to you have to be careful about + + + align:start position:0% +you have to you have to be careful about +which side this peak is on okay and I + + align:start position:0% +which side this peak is on okay and I + + + align:start position:0% +which side this peak is on okay and I +personally can never keep it straight so + + align:start position:0% +personally can never keep it straight so + + + align:start position:0% +personally can never keep it straight so +what I do is just make two test + + align:start position:0% +what I do is just make two test + + + align:start position:0% +what I do is just make two test +functions and stick them in and make + + align:start position:0% +functions and stick them in and make + + + align:start position:0% +functions and stick them in and make +sure that you know if I have one of my + + align:start position:0% +sure that you know if I have one of my + + + align:start position:0% +sure that you know if I have one of my +functions so in this case there here are + + align:start position:0% +functions so in this case there here are + + + align:start position:0% +functions so in this case there here are +two test functions okay you can see that + + align:start position:0% +two test functions okay you can see that + + + align:start position:0% +two test functions okay you can see that +X is sorry Y is before X + + align:start position:0% +X is sorry Y is before X + + + align:start position:0% +X is sorry Y is before X +okay and so this peak here corresponds + + align:start position:0% +okay and so this peak here corresponds + + + align:start position:0% +okay and so this peak here corresponds +to why happening before X okay so you + + align:start position:0% +to why happening before X okay so you + + + align:start position:0% +to why happening before X okay so you +just have to make sure you know what the + + align:start position:0% +just have to make sure you know what the + + + align:start position:0% +just have to make sure you know what the +sign is and I recommend doing that with + + align:start position:0% +sign is and I recommend doing that with + + + align:start position:0% +sign is and I recommend doing that with +with just two functions that you know + + align:start position:0% +with just two functions that you know + + + align:start position:0% +with just two functions that you know +it's easy to get it backwards yes what + + align:start position:0% +it's easy to get it backwards yes what + + + align:start position:0% +it's easy to get it backwards yes what +do you mean first part oh these + + align:start position:0% +do you mean first part oh these + + + align:start position:0% +do you mean first part oh these +I'm just taking copies of this and + + align:start position:0% +I'm just taking copies of this and + + + align:start position:0% +I'm just taking copies of this and +placing them on top of each other and + + align:start position:0% +placing them on top of each other and + + + align:start position:0% +placing them on top of each other and +shifting them so you should ignore this + + align:start position:0% +shifting them so you should ignore this + + + align:start position:0% +shifting them so you should ignore this +little part right here oh yeah + + align:start position:0% +little part right here oh yeah + + + align:start position:0% +little part right here oh yeah +so there are MATLAB functions to do this + + align:start position:0% +so there are MATLAB functions to do this + + + align:start position:0% +so there are MATLAB functions to do this +this cross-correlation and it handles + + align:start position:0% +this cross-correlation and it handles + + + align:start position:0% +this cross-correlation and it handles +all of that stuff for you yes yes the + + align:start position:0% +all of that stuff for you yes yes the + + + align:start position:0% +all of that stuff for you yes yes the +x-axis is tau I should have labeled it + + align:start position:0% +x-axis is tau I should have labeled it + + + align:start position:0% +x-axis is tau I should have labeled it +on there yeah so you can see that if + + align:start position:0% +on there yeah so you can see that if + + + align:start position:0% +on there yeah so you can see that if +these things are shifted if they're kind + + align:start position:0% +these things are shifted if they're kind + + + align:start position:0% +these things are shifted if they're kind +of noisy and they're shifted with + + align:start position:0% +of noisy and they're shifted with + + + align:start position:0% +of noisy and they're shifted with +respect to each other you can see that + + align:start position:0% +respect to each other you can see that + + + align:start position:0% +respect to each other you can see that +the positive parts here might line up + + align:start position:0% +the positive parts here might line up + + + align:start position:0% +the positive parts here might line up +with the negative parts there and the + + align:start position:0% +with the negative parts there and the + + + align:start position:0% +with the negative parts there and the +negative parts here line up with the + + align:start position:0% +negative parts here line up with the + + + align:start position:0% +negative parts here line up with the +positive parts there and they're shifted + + align:start position:0% +positive parts there and they're shifted + + + align:start position:0% +positive parts there and they're shifted +randomly at any other time with respect + + align:start position:0% +randomly at any other time with respect + + + align:start position:0% +randomly at any other time with respect +to each other + + align:start position:0% +to each other + + + align:start position:0% +to each other +on average positive times negative you + + align:start position:0% +on average positive times negative you + + + align:start position:0% +on average positive times negative you +know you're gonna have some parts where + + align:start position:0% +know you're gonna have some parts where + + + align:start position:0% +know you're gonna have some parts where +it's positive times positive and other + + align:start position:0% +it's positive times positive and other + + + align:start position:0% +it's positive times positive and other +parts where it's positive times negative + + align:start position:0% +parts where it's positive times negative + + + align:start position:0% +parts where it's positive times negative +and it's all gonna wash out and give you + + align:start position:0% +and it's all gonna wash out and give you + + + align:start position:0% +and it's all gonna wash out and give you +zero because those signals are + + align:start position:0% +zero because those signals are + + + align:start position:0% +zero because those signals are +uncorrelated with at + + align:start position:0% +uncorrelated with at + + + align:start position:0% +uncorrelated with at +different time lags okay exactly it's + + align:start position:0% +different time lags okay exactly it's + + + align:start position:0% +different time lags okay exactly it's +only when they overlap that all of the + + align:start position:0% +only when they overlap that all of the + + + align:start position:0% +only when they overlap that all of the +positive parts here will line up with + + align:start position:0% +positive parts here will line up with + + + align:start position:0% +positive parts here will line up with +the positive parts here and the negative + + align:start position:0% +the positive parts here and the negative + + + align:start position:0% +the positive parts here and the negative +parts here will line and put the + + align:start position:0% +parts here will line and put the + + + align:start position:0% +parts here will line and put the +negative exactly all of those positive + + align:start position:0% +negative exactly all of those positive + + + align:start position:0% +negative exactly all of those positive +times positive add up to the negative + + align:start position:0% +times positive add up to the negative + + + align:start position:0% +times positive add up to the negative +times negative which is positive and all + + align:start position:0% +times negative which is positive and all + + + align:start position:0% +times negative which is positive and all +of that adds up to give you that + + align:start position:0% +of that adds up to give you that + + + align:start position:0% +of that adds up to give you that +positive peak right there but when + + align:start position:0% +positive peak right there but when + + + align:start position:0% +positive peak right there but when +they're shifted all of those magical + + align:start position:0% +they're shifted all of those magical + + + align:start position:0% +they're shifted all of those magical +alignments of positive with positive and + + align:start position:0% +alignments of positive with positive and + + + align:start position:0% +alignments of positive with positive and +negative with negative go away and it + + align:start position:0% +negative with negative go away and it + + + align:start position:0% +negative with negative go away and it +just becomes on average just random and + + align:start position:0% +just becomes on average just random and + + + align:start position:0% +just becomes on average just random and +and random things are have zero + + align:start position:0% +and random things are have zero + + + align:start position:0% +and random things are have zero +correlation with each other okay + + align:start position:0% + + + + align:start position:0% + +so this is actually a real powerful way + + align:start position:0% +so this is actually a real powerful way + + + align:start position:0% +so this is actually a real powerful way +to discover the relation between two + + align:start position:0% +to discover the relation between two + + + align:start position:0% +to discover the relation between two +different signals okay + + align:start position:0% + + + + align:start position:0% + +and in fact it gives you a kernel that + + align:start position:0% +and in fact it gives you a kernel that + + + align:start position:0% +and in fact it gives you a kernel that +you can actually use to predict one + + align:start position:0% +you can actually use to predict one + + + align:start position:0% +you can actually use to predict one +signal from another signal if you were + + align:start position:0% +signal from another signal if you were + + + align:start position:0% +signal from another signal if you were +to take X and convolve it with K you + + align:start position:0% +to take X and convolve it with K you + + + align:start position:0% +to take X and convolve it with K you +would get an estimate of Y okay we'll + + align:start position:0% +would get an estimate of Y okay we'll + + + align:start position:0% +would get an estimate of Y okay we'll +talk more about that later pretty cool + + align:start position:0% +talk more about that later pretty cool + + + align:start position:0% +talk more about that later pretty cool +right okay so so they're they're + + align:start position:0% +right okay so so they're they're + + + align:start position:0% +right okay so so they're they're +mathematically very similar right they + + align:start position:0% +mathematically very similar right they + + + align:start position:0% +mathematically very similar right they +look similar but they're used in + + align:start position:0% +look similar but they're used in + + + align:start position:0% +look similar but they're used in +different ways so the way we think about + + align:start position:0% +different ways so the way we think about + + + align:start position:0% +different ways so the way we think about +convolution is where what it's used for + + align:start position:0% +convolution is where what it's used for + + + align:start position:0% +convolution is where what it's used for +is to take an input signal X and + + align:start position:0% +is to take an input signal X and + + + align:start position:0% +is to take an input signal X and +convolve it with a kernel K to get an + + align:start position:0% +convolve it with a kernel K to get an + + + align:start position:0% +convolve it with a kernel K to get an +output signal Y and we usually think of + + align:start position:0% +output signal Y and we usually think of + + + align:start position:0% +output signal Y and we usually think of +X and as being very long vectors long + + align:start position:0% +X and as being very long vectors long + + + align:start position:0% +X and as being very long vectors long +signals k here Kappa is a kernel it's + + align:start position:0% +signals k here Kappa is a kernel it's + + + align:start position:0% +signals k here Kappa is a kernel it's +just a short little thing in time and + + align:start position:0% +just a short little thing in time and + + + align:start position:0% +just a short little thing in time and +you're going to convolve it with a long + + align:start position:0% +you're going to convolve it with a long + + + align:start position:0% +you're going to convolve it with a long +signal to get another long + + align:start position:0% +signal to get another long + + + align:start position:0% +signal to get another long +that make sense in cross-correlation we + + align:start position:0% +that make sense in cross-correlation we + + + align:start position:0% +that make sense in cross-correlation we +have two signals x and y x and y are the + + align:start position:0% +have two signals x and y x and y are the + + + align:start position:0% +have two signals x and y x and y are the +inputs and we cross correlated to + + align:start position:0% +inputs and we cross correlated to + + + align:start position:0% +inputs and we cross correlated to +extract a short signal that that + + align:start position:0% +extract a short signal that that + + + align:start position:0% +extract a short signal that that +captures the temporal relation between x + + align:start position:0% +captures the temporal relation between x + + + align:start position:0% +captures the temporal relation between x +and y all right so x and y are long + + align:start position:0% +and y all right so x and y are long + + + align:start position:0% +and y all right so x and y are long +signals k is a short vector and in this + + align:start position:0% +signals k is a short vector and in this + + + align:start position:0% +signals k is a short vector and in this +case were involving a long signal with a + + align:start position:0% +case were involving a long signal with a + + + align:start position:0% +case were involving a long signal with a +short kernel to get another long signal + + align:start position:0% +short kernel to get another long signal + + + align:start position:0% +short kernel to get another long signal +which is the response of the system in + + align:start position:0% +which is the response of the system in + + + align:start position:0% +which is the response of the system in +this case we're having we take let's say + + align:start position:0% +this case we're having we take let's say + + + align:start position:0% +this case we're having we take let's say +the input to a system and the output of + + align:start position:0% +the input to a system and the output of + + + align:start position:0% +the input to a system and the output of +the system and doing a cross correlation + + align:start position:0% +the system and doing a cross correlation + + + align:start position:0% +the system and doing a cross correlation +to track the kernel all right any + + align:start position:0% +to track the kernel all right any + + + align:start position:0% +to track the kernel all right any +questions about that or both super + + align:start position:0% +questions about that or both super + + + align:start position:0% +questions about that or both super +powerful methods yes you just you you + + align:start position:0% +powerful methods yes you just you you + + + align:start position:0% +powerful methods yes you just you you +you just do this for a small number of + + align:start position:0% +you just do this for a small number of + + + align:start position:0% +you just do this for a small number of +towers + + align:start position:0% +towers + + + align:start position:0% +towers +okay because usually signals that have + + align:start position:0% +okay because usually signals that have + + + align:start position:0% +okay because usually signals that have +some relation between them that relation + + align:start position:0% +some relation between them that relation + + + align:start position:0% +some relation between them that relation +has a short time extent right this + + align:start position:0% +has a short time extent right this + + + align:start position:0% +has a short time extent right this +signal here in a real physical system + + align:start position:0% +signal here in a real physical system + + + align:start position:0% +signal here in a real physical system +doesn't depend on what X was doing am a + + align:start position:0% +doesn't depend on what X was doing am a + + + align:start position:0% +doesn't depend on what X was doing am a +month ago right or maybe cans ago these + + align:start position:0% +month ago right or maybe cans ago these + + + align:start position:0% +month ago right or maybe cans ago these +signals might be 10 or 20 seconds long + + align:start position:0% +signals might be 10 or 20 seconds long + + + align:start position:0% +signals might be 10 or 20 seconds long +or an hour long but this signal that Y + + align:start position:0% +or an hour long but this signal that Y + + + align:start position:0% +or an hour long but this signal that Y +doesn't depend on what X was doing an + + align:start position:0% +doesn't depend on what X was doing an + + + align:start position:0% +doesn't depend on what X was doing an +hour ago it only depends on what X was + + align:start position:0% +hour ago it only depends on what X was + + + align:start position:0% +hour ago it only depends on what X was +doing maybe a few tens of milliseconds + + align:start position:0% +doing maybe a few tens of milliseconds + + + align:start position:0% +doing maybe a few tens of milliseconds +or a second ago okay so that's why x and + + align:start position:0% +or a second ago okay so that's why x and + + + align:start position:0% +or a second ago okay so that's why x and +y can be long signals Kappa K sorry is a + + align:start position:0% +y can be long signals Kappa K sorry is a + + + align:start position:0% +y can be long signals Kappa K sorry is a +short vector that represents the kernel + + align:start position:0% +short vector that represents the kernel + + + align:start position:0% +short vector that represents the kernel +okay all right any more questions about + + align:start position:0% +okay all right any more questions about + + + align:start position:0% +okay all right any more questions about +that + + align:start position:0% + + + + align:start position:0% + +okay these are very powerful methods we + + align:start position:0% +okay these are very powerful methods we + + + align:start position:0% +okay these are very powerful methods we +use them all the time okay + + align:start position:0% +use them all the time okay + + + align:start position:0% +use them all the time okay +talked about the relation to the + + align:start position:0% +talked about the relation to the + + + align:start position:0% +talked about the relation to the +spike-triggered average okay the + + align:start position:0% +spike-triggered average okay the + + + align:start position:0% +spike-triggered average okay the +autocorrelation is nothing more than a + + align:start position:0% +autocorrelation is nothing more than a + + + align:start position:0% +autocorrelation is nothing more than a +cross correlation of a signal with + + align:start position:0% +cross correlation of a signal with + + + align:start position:0% +cross correlation of a signal with +itself okay so let's see how that's + + align:start position:0% +itself okay so let's see how that's + + + align:start position:0% +itself okay so let's see how that's +useful so an autocorrelation is a good + + align:start position:0% +useful so an autocorrelation is a good + + + align:start position:0% +useful so an autocorrelation is a good +way to temporal structure within a + + align:start position:0% +way to temporal structure within a + + + align:start position:0% +way to temporal structure within a +signal okay so if we take a signal X and + + align:start position:0% +signal okay so if we take a signal X and + + + align:start position:0% +signal okay so if we take a signal X and +we calculate the cross correlation of + + align:start position:0% +we calculate the cross correlation of + + + align:start position:0% +we calculate the cross correlation of +that signal with itself here's what that + + align:start position:0% +that signal with itself here's what that + + + align:start position:0% +that signal with itself here's what that +looks like so let's say we have a signal + + align:start position:0% +looks like so let's say we have a signal + + + align:start position:0% +looks like so let's say we have a signal +that looks like this and this signal + + align:start position:0% +that looks like this and this signal + + + align:start position:0% +that looks like this and this signal +kind of has slowish fluctuations that + + align:start position:0% +kind of has slowish fluctuations that + + + align:start position:0% +kind of has slowish fluctuations that +are let's say on a 50 or 100 millisecond + + align:start position:0% +are let's say on a 50 or 100 millisecond + + + align:start position:0% +are let's say on a 50 or 100 millisecond +timescale okay if we take that signal + + align:start position:0% +timescale okay if we take that signal + + + align:start position:0% +timescale okay if we take that signal +and we multiply it by itself with zero + + align:start position:0% +and we multiply it by itself with zero + + + align:start position:0% +and we multiply it by itself with zero +time lag what do you think that will + + align:start position:0% +time lag what do you think that will + + + align:start position:0% +time lag what do you think that will +look like so positive lines up with + + align:start position:0% +look like so positive lines up with + + + align:start position:0% +look like so positive lines up with +positive negative lines up with negative + + align:start position:0% +positive negative lines up with negative + + + align:start position:0% +positive negative lines up with negative +that thing do what it should be a + + align:start position:0% +that thing do what it should be a + + + align:start position:0% +that thing do what it should be a +maximum right auto correlations are + + align:start position:0% +maximum right auto correlations are + + + align:start position:0% +maximum right auto correlations are +always a maximum at zero lag okay and + + align:start position:0% +always a maximum at zero lag okay and + + + align:start position:0% +always a maximum at zero lag okay and +then what we do is we're just going to + + align:start position:0% +then what we do is we're just going to + + + align:start position:0% +then what we do is we're just going to +take that signal and shift it a little + + align:start position:0% +take that signal and shift it a little + + + align:start position:0% +take that signal and shift it a little +bit it'll shift it a little bit more do + + align:start position:0% +bit it'll shift it a little bit more do + + + align:start position:0% +bit it'll shift it a little bit more do +that product and integral shift the + + align:start position:0% +that product and integral shift the + + + align:start position:0% +that product and integral shift the +product and integral now what's going to + + align:start position:0% +product and integral now what's going to + + + align:start position:0% +product and integral now what's going to +happen as we shift one of those signals + + align:start position:0% +happen as we shift one of those signals + + + align:start position:0% +happen as we shift one of those signals +sideways and then multiply and integrate + + align:start position:0% + + + + align:start position:0% + +Sammy you got this one + + align:start position:0% + + + + align:start position:0% + +yeah so if you shift it enough it's + + align:start position:0% +yeah so if you shift it enough it's + + + align:start position:0% +yeah so if you shift it enough it's +possible that it might overlap again + + align:start position:0% +possible that it might overlap again + + + align:start position:0% +possible that it might overlap again +somewhere else what what kind of signal + + align:start position:0% +somewhere else what what kind of signal + + + align:start position:0% +somewhere else what what kind of signal +what would that happen what kind of + + align:start position:0% +what would that happen what kind of + + + align:start position:0% +what would that happen what kind of +signal would that happen for yeah a + + align:start position:0% +signal would that happen for yeah a + + + align:start position:0% +signal would that happen for yeah a +periodic signal exactly so an + + align:start position:0% +periodic signal exactly so an + + + align:start position:0% +periodic signal exactly so an +autocorrelation first of all has a peak + + align:start position:0% +autocorrelation first of all has a peak + + + align:start position:0% +autocorrelation first of all has a peak +at zero lag that peak drops off when + + align:start position:0% +at zero lag that peak drops off when + + + align:start position:0% +at zero lag that peak drops off when +these fluctuations here so positive + + align:start position:0% +these fluctuations here so positive + + + align:start position:0% +these fluctuations here so positive +lines up with positive negative lines up + + align:start position:0% +lines up with positive negative lines up + + + align:start position:0% +lines up with positive negative lines up +with negative as you shift one of them + + align:start position:0% +with negative as you shift one of them + + + align:start position:0% +with negative as you shift one of them +those positive and negatives no longer + + align:start position:0% +those positive and negatives no longer + + + align:start position:0% +those positive and negatives no longer +overlap with each other and you start + + align:start position:0% +overlap with each other and you start + + + align:start position:0% +overlap with each other and you start +getting positives lining up with + + align:start position:0% +getting positives lining up with + + + align:start position:0% +getting positives lining up with +negatives and so the autocorrelation + + align:start position:0% +negatives and so the autocorrelation + + + align:start position:0% +negatives and so the autocorrelation +drops off and then it can actually go + + align:start position:0% +drops off and then it can actually go + + + align:start position:0% +drops off and then it can actually go +back and indicate it can go back up if + + align:start position:0% +back and indicate it can go back up if + + + align:start position:0% +back and indicate it can go back up if +there's periodic structure so let's look + + align:start position:0% +there's periodic structure so let's look + + + align:start position:0% +there's periodic structure so let's look +at what this one looks like so in this + + align:start position:0% +at what this one looks like so in this + + + align:start position:0% +at what this one looks like so in this +case it kind of looked like there might + + align:start position:0% +case it kind of looked like there might + + + align:start position:0% +case it kind of looked like there might +be periodic structure but there wasn't + + align:start position:0% +be periodic structure but there wasn't + + + align:start position:0% +be periodic structure but there wasn't +because this was just low pass filtered + + align:start position:0% +because this was just low pass filtered + + + align:start position:0% +because this was just low pass filtered +noise okay and you can see that if you + + align:start position:0% +noise okay and you can see that if you + + + align:start position:0% +noise okay and you can see that if you +compute that there's that MATLAB + + align:start position:0% +compute that there's that MATLAB + + + align:start position:0% +compute that there's that MATLAB +function XCore so you use it to + + align:start position:0% +function XCore so you use it to + + + align:start position:0% +function XCore so you use it to +calculate the autocorrelation you can + + align:start position:0% +calculate the autocorrelation you can + + + align:start position:0% +calculate the autocorrelation you can +see that that autocorrelation is peaked + + align:start position:0% +see that that autocorrelation is peaked + + + align:start position:0% +see that that autocorrelation is peaked +at zero lag drops off and that the lag + + align:start position:0% +at zero lag drops off and that the lag + + + align:start position:0% +at zero lag drops off and that the lag +at which it drops off depends on how + + align:start position:0% +at which it drops off depends on how + + + align:start position:0% +at which it drops off depends on how +smoothly varying that function is if the + + align:start position:0% +smoothly varying that function is if the + + + align:start position:0% +smoothly varying that function is if the +function varies if it's changing very + + align:start position:0% +function varies if it's changing very + + + align:start position:0% +function varies if it's changing very +slowly the autocorrelation is going to + + align:start position:0% +slowly the autocorrelation is going to + + + align:start position:0% +slowly the autocorrelation is going to +be very wide because you shifted a lot + + align:start position:0% +be very wide because you shifted a lot + + + align:start position:0% +be very wide because you shifted a lot +in order to get the positive Peaks and + + align:start position:0% +in order to get the positive Peaks and + + + align:start position:0% +in order to get the positive Peaks and +the negative peaks misaligned from each + + align:start position:0% +the negative peaks misaligned from each + + + align:start position:0% +the negative peaks misaligned from each +other okay now if you have a fast signal + + align:start position:0% +other okay now if you have a fast signal + + + align:start position:0% +other okay now if you have a fast signal +like this with fast fluctuations and you + + align:start position:0% +like this with fast fluctuations and you + + + align:start position:0% +like this with fast fluctuations and you +do the autocorrelation what's going to + + align:start position:0% +do the autocorrelation what's going to + + + align:start position:0% +do the autocorrelation what's going to +happen so first of all at zero lag it's + + align:start position:0% +happen so first of all at zero lag it's + + + align:start position:0% +happen so first of all at zero lag it's +going to be peak and then what's going + + align:start position:0% +going to be peak and then what's going + + + align:start position:0% +going to be peak and then what's going +to happen it's going to drop off more + + align:start position:0% +to happen it's going to drop off more + + + align:start position:0% +to happen it's going to drop off more +quickly right so that's exactly what + + align:start position:0% +quickly right so that's exactly what + + + align:start position:0% +quickly right so that's exactly what +happens so here's the autocorrelation of + + align:start position:0% +happens so here's the autocorrelation of + + + align:start position:0% +happens so here's the autocorrelation of +this slow function here's the + + align:start position:0% +this slow function here's the + + + align:start position:0% +this slow function here's the +autocorrelation of this fast function + + align:start position:0% +autocorrelation of this fast function + + + align:start position:0% +autocorrelation of this fast function +and you can see both of these are just + + align:start position:0% +and you can see both of these are just + + + align:start position:0% +and you can see both of these are just +noise + + align:start position:0% +noise + + + align:start position:0% +noise +but I've smoothed this one I have low + + align:start position:0% +but I've smoothed this one I have low + + + align:start position:0% +but I've smoothed this one I have low +pass filtered this with kind of a 50 + + align:start position:0% +pass filtered this with kind of a 50 + + + align:start position:0% +pass filtered this with kind of a 50 +millisecond wide kernel to give very + + align:start position:0% +millisecond wide kernel to give very + + + align:start position:0% +millisecond wide kernel to give very +slowly varying structure + + align:start position:0% +slowly varying structure + + + align:start position:0% +slowly varying structure +this one ice moves with a very narrow + + align:start position:0% +this one ice moves with a very narrow + + + align:start position:0% +this one ice moves with a very narrow +kernel to leave fast fluctuations and + + align:start position:0% +kernel to leave fast fluctuations and + + + align:start position:0% +kernel to leave fast fluctuations and +you can see that the autocorrelation + + align:start position:0% +you can see that the autocorrelation + + + align:start position:0% +you can see that the autocorrelation +shows that width including of this + + align:start position:0% +shows that width including of this + + + align:start position:0% +shows that width including of this +signal is very narrow and the width of + + align:start position:0% +signal is very narrow and the width of + + + align:start position:0% +signal is very narrow and the width of +the smoothing for this signal was broad + + align:start position:0% +the smoothing for this signal was broad + + + align:start position:0% +the smoothing for this signal was broad +okay in fact what you can see is that + + align:start position:0% +okay in fact what you can see is that + + + align:start position:0% +okay in fact what you can see is that +this signal looks like noise that's been + + align:start position:0% +this signal looks like noise that's been + + + align:start position:0% +this signal looks like noise that's been +convolve dwith this and this signal + + align:start position:0% +convolve dwith this and this signal + + + align:start position:0% +convolve dwith this and this signal +looks like noise that's been convolve + + align:start position:0% +looks like noise that's been convolve + + + align:start position:0% +looks like noise that's been convolve +dwith that okay and here's actually a + + align:start position:0% +dwith that okay and here's actually a + + + align:start position:0% +dwith that okay and here's actually a +demonstration of what Sammy was just + + align:start position:0% +demonstration of what Sammy was just + + + align:start position:0% +demonstration of what Sammy was just +talking about if you take a look at this + + align:start position:0% +talking about if you take a look at this + + + align:start position:0% +talking about if you take a look at this +signal so the autocorrelation can be a + + align:start position:0% +signal so the autocorrelation can be a + + + align:start position:0% +signal so the autocorrelation can be a +very powerful method let's just it's + + align:start position:0% +very powerful method let's just it's + + + align:start position:0% +very powerful method let's just it's +actually not that powerful it's a method + + align:start position:0% +actually not that powerful it's a method + + + align:start position:0% +actually not that powerful it's a method +for extracting periodic structure and + + align:start position:0% +for extracting periodic structure and + + + align:start position:0% +for extracting periodic structure and +we're going to turn now very shortly to + + align:start position:0% +we're going to turn now very shortly to + + + align:start position:0% +we're going to turn now very shortly to +a method that really is very powerful + + align:start position:0% +a method that really is very powerful + + + align:start position:0% +a method that really is very powerful +for extracting periodic structure but I + + align:start position:0% +for extracting periodic structure but I + + + align:start position:0% +for extracting periodic structure but I +just want to show you how this method + + align:start position:0% +just want to show you how this method + + + align:start position:0% +just want to show you how this method +can be used and so if you look at that + + align:start position:0% +can be used and so if you look at that + + + align:start position:0% +can be used and so if you look at that +signal right there it looks like noise + + align:start position:0% + + + + align:start position:0% + +but there's actually structure embedded + + align:start position:0% +but there's actually structure embedded + + + align:start position:0% +but there's actually structure embedded +in there that we can see if we do the + + align:start position:0% +in there that we can see if we do the + + + align:start position:0% +in there that we can see if we do the +autocorrelation of this signal and + + align:start position:0% +autocorrelation of this signal and + + + align:start position:0% +autocorrelation of this signal and +here's what that looks like + + align:start position:0% +here's what that looks like + + + align:start position:0% +here's what that looks like +so again autocorrelation is peaked the + + align:start position:0% +so again autocorrelation is peaked the + + + align:start position:0% +so again autocorrelation is peaked the +peak is very narrow because that's a + + align:start position:0% +peak is very narrow because that's a + + + align:start position:0% +peak is very narrow because that's a +very noisy looking signal but you can + + align:start position:0% +very noisy looking signal but you can + + + align:start position:0% +very noisy looking signal but you can +see that buried under there is this + + align:start position:0% +see that buried under there is this + + + align:start position:0% +see that buried under there is this +periodic fluctuation what that says is + + align:start position:0% +periodic fluctuation what that says is + + + align:start position:0% +periodic fluctuation what that says is +that if I take a copy of that signal and + + align:start position:0% +that if I take a copy of that signal and + + + align:start position:0% +that if I take a copy of that signal and +shift it with respect to itself every + + align:start position:0% +shift it with respect to itself every + + + align:start position:0% +shift it with respect to itself every +hundred milliseconds + + align:start position:0% +hundred milliseconds + + + align:start position:0% +hundred milliseconds +something in there starts lining up + + align:start position:0% +something in there starts lining up + + + align:start position:0% +something in there starts lining up +again and that's why you have these + + align:start position:0% +again and that's why you have these + + + align:start position:0% +again and that's why you have these +little peaks in the autocorrelation + + align:start position:0% +little peaks in the autocorrelation + + + align:start position:0% +little peaks in the autocorrelation +function and what do you think that is + + align:start position:0% +function and what do you think that is + + + align:start position:0% +function and what do you think that is +buried in there it's a sine wave okay so + + align:start position:0% +buried in there it's a sine wave okay so + + + align:start position:0% +buried in there it's a sine wave okay so +this data is random and nor like with a + + align:start position:0% +this data is random and nor like with a + + + align:start position:0% +this data is random and nor like with a +normal distribution plus point one times + + align:start position:0% +normal distribution plus point one times + + + align:start position:0% +normal distribution plus point one times +cosine that gives you a ten Hertz wiggle + + align:start position:0% +cosine that gives you a ten Hertz wiggle + + + align:start position:0% +cosine that gives you a ten Hertz wiggle +okay + + align:start position:0% +okay + + + align:start position:0% +okay +so you can't see that in the data but if + + align:start position:0% +so you can't see that in the data but if + + + align:start position:0% +so you can't see that in the data but if +you do the autocorrelation all of a + + align:start position:0% +you do the autocorrelation all of a + + + align:start position:0% +you do the autocorrelation all of a +sudden you can see that it's buried in + + align:start position:0% +sudden you can see that it's buried in + + + align:start position:0% +sudden you can see that it's buried in +there all right + + align:start position:0% +there all right + + + align:start position:0% +there all right +okay so cross correlation and auto cross + + align:start position:0% +okay so cross correlation and auto cross + + + align:start position:0% +okay so cross correlation and auto cross +correlation is a way to extract the + + align:start position:0% +correlation is a way to extract the + + + align:start position:0% +correlation is a way to extract the +temporal relation between current + + align:start position:0% +temporal relation between current + + + align:start position:0% +temporal relation between current +signals autocorrelation is a way to use + + align:start position:0% +signals autocorrelation is a way to use + + + align:start position:0% +signals autocorrelation is a way to use +the same method essentially to extract + + align:start position:0% +the same method essentially to extract + + + align:start position:0% +the same method essentially to extract +the temporal relation between a signal + + align:start position:0% +the temporal relation between a signal + + + align:start position:0% +the temporal relation between a signal +and itself at different times okay and + + align:start position:0% +and itself at different times okay and + + + align:start position:0% +and itself at different times okay and +that method it's actually quite commonly + + align:start position:0% +that method it's actually quite commonly + + + align:start position:0% +that method it's actually quite commonly +used to extract structure and Spike + + align:start position:0% +used to extract structure and Spike + + + align:start position:0% +used to extract structure and Spike +trains but there are much more powerful + + align:start position:0% +trains but there are much more powerful + + + align:start position:0% +trains but there are much more powerful +methods for extracting periodic + + align:start position:0% +methods for extracting periodic + + + align:start position:0% +methods for extracting periodic +structure and that's what we're gonna + + align:start position:0% +structure and that's what we're gonna + + + align:start position:0% +structure and that's what we're gonna +start talking about now okay any + + align:start position:0% +start talking about now okay any + + + align:start position:0% +start talking about now okay any +questions okay + + align:start position:0% +questions okay + + + align:start position:0% +questions okay +let's start on the topic of spectral + + align:start position:0% +let's start on the topic of spectral + + + align:start position:0% +let's start on the topic of spectral +analysis which is the the right way to + + align:start position:0% +analysis which is the the right way to + + + align:start position:0% +analysis which is the the right way to +pull out periodic structure of signals + + align:start position:0% +pull out periodic structure of signals + + + align:start position:0% +pull out periodic structure of signals +here's the spectrum that I was actually + + align:start position:0% +here's the spectrum that I was actually + + + align:start position:0% +here's the spectrum that I was actually +trying to show you last time so what is + + align:start position:0% +trying to show you last time so what is + + + align:start position:0% +trying to show you last time so what is +a spectrogram oh so if we have a sound + + align:start position:0% +a spectrogram oh so if we have a sound + + + align:start position:0% +a spectrogram oh so if we have a sound +we record a sound with a microphone + + align:start position:0% +we record a sound with a microphone + + + align:start position:0% +we record a sound with a microphone +microphones pick up pressure + + align:start position:0% +microphones pick up pressure + + + align:start position:0% +microphones pick up pressure +fluctuations so in this case this is a + + align:start position:0% +fluctuations so in this case this is a + + + align:start position:0% +fluctuations so in this case this is a +bird singing the vocal cords are + + align:start position:0% +bird singing the vocal cords are + + + align:start position:0% +bird singing the vocal cords are +vibrating with air flowing through them + + align:start position:0% +vibrating with air flowing through them + + + align:start position:0% +vibrating with air flowing through them +that produce very large pressure + + align:start position:0% +that produce very large pressure + + + align:start position:0% +that produce very large pressure +fluctuations in the vocal tract and + + align:start position:0% +fluctuations in the vocal tract and + + + align:start position:0% +fluctuations in the vocal tract and +those are transmitted up through the + + align:start position:0% +those are transmitted up through the + + + align:start position:0% +those are transmitted up through the +beak into the air and that produces + + align:start position:0% +beak into the air and that produces + + + align:start position:0% +beak into the air and that produces +pressure fluctuations that propagate + + align:start position:0% +pressure fluctuations that propagate + + + align:start position:0% +pressure fluctuations that propagate +through the air at about a foot per + + align:start position:0% +through the air at about a foot per + + + align:start position:0% +through the air at about a foot per +millisecond they reach your ear and they + + align:start position:0% +millisecond they reach your ear and they + + + align:start position:0% +millisecond they reach your ear and they +vibrate your eardrum and and if you have + + align:start position:0% +vibrate your eardrum and and if you have + + + align:start position:0% +vibrate your eardrum and and if you have +a microphone there you can actually + + align:start position:0% +a microphone there you can actually + + + align:start position:0% +a microphone there you can actually +record those pressure fluctuations and + + align:start position:0% +record those pressure fluctuations and + + + align:start position:0% +record those pressure fluctuations and +if you look at it it just like fast + + align:start position:0% +if you look at it it just like fast + + + align:start position:0% +if you look at it it just like fast +Wiggles in the pressure okay but somehow + + align:start position:0% +Wiggles in the pressure okay but somehow + + + align:start position:0% +Wiggles in the pressure okay but somehow +your ear is able to magically transform + + align:start position:0% +your ear is able to magically transform + + + align:start position:0% +your ear is able to magically transform +that into this neural representation of + + align:start position:0% +that into this neural representation of + + + align:start position:0% +that into this neural representation of +what that sound is + + align:start position:0% +what that sound is + + + align:start position:0% +what that sound is +right and then + + align:start position:0% +right and then + + + align:start position:0% +right and then +and what your ear is actually doing is + + align:start position:0% +and what your ear is actually doing is + + + align:start position:0% +and what your ear is actually doing is +it's doing thorough analysis of the + + align:start position:0% +it's doing thorough analysis of the + + + align:start position:0% +it's doing thorough analysis of the +sound and then your brain is doing a + + align:start position:0% +sound and then your brain is doing a + + + align:start position:0% +sound and then your brain is doing a +bunch of processing that helps you + + align:start position:0% +bunch of processing that helps you + + + align:start position:0% +bunch of processing that helps you +identify what that thing is that's + + align:start position:0% +identify what that thing is that's + + + align:start position:0% +identify what that thing is that's +making that sound okay so this is a so + + align:start position:0% +making that sound okay so this is a so + + + align:start position:0% +making that sound okay so this is a so +this is a spectral analysis of this bit + + align:start position:0% +this is a spectral analysis of this bit + + + align:start position:0% +this is a spectral analysis of this bit +of birdsong canary song and what it is + + align:start position:0% +of birdsong canary song and what it is + + + align:start position:0% +of birdsong canary song and what it is +it does very much what your ear drum + + align:start position:0% +it does very much what your ear drum + + + align:start position:0% +it does very much what your ear drum +does or what your cochlea does sorry it + + align:start position:0% +does or what your cochlea does sorry it + + + align:start position:0% +does or what your cochlea does sorry it +calculates how much power there is at + + align:start position:0% +calculates how much power there is at + + + align:start position:0% +calculates how much power there is at +different frequencies of the sound okay + + align:start position:0% +different frequencies of the sound okay + + + align:start position:0% +different frequencies of the sound okay +and at different times okay so what this + + align:start position:0% +and at different times okay so what this + + + align:start position:0% +and at different times okay so what this +says is that there's a lot of power in + + align:start position:0% +says is that there's a lot of power in + + + align:start position:0% +says is that there's a lot of power in +this at 5 kilohertz at this time but at + + align:start position:0% +this at 5 kilohertz at this time but at + + + align:start position:0% +this at 5 kilohertz at this time but at +this time there's a lot of power 3 + + align:start position:0% +this time there's a lot of power 3 + + + align:start position:0% +this time there's a lot of power 3 +kilohertz or at 2 kilohertz and so on + + align:start position:0% +kilohertz or at 2 kilohertz and so on + + + align:start position:0% +kilohertz or at 2 kilohertz and so on +alright so it's a graphical way of + + align:start position:0% +alright so it's a graphical way of + + + align:start position:0% +alright so it's a graphical way of +describing what the sound is and here's + + align:start position:0% +describing what the sound is and here's + + + align:start position:0% +describing what the sound is and here's +what that looks like + + align:start position:0% + + + + align:start position:0% + +ok so you can see visually what's + + align:start position:0% +ok so you can see visually what's + + + align:start position:0% +ok so you can see visually what's +happening even though if you were to + + align:start position:0% +happening even though if you were to + + + align:start position:0% +happening even though if you were to +look at those patterns on an + + align:start position:0% +look at those patterns on an + + + align:start position:0% +look at those patterns on an +oscilloscope or print it out on the + + align:start position:0% +oscilloscope or print it out on the + + + align:start position:0% +oscilloscope or print it out on the +computer it would just be a bunch of + + align:start position:0% +computer it would just be a bunch of + + + align:start position:0% +computer it would just be a bunch of +Wiggles ok you wouldn't be able to see + + align:start position:0% +Wiggles ok you wouldn't be able to see + + + align:start position:0% +Wiggles ok you wouldn't be able to see +any of that ok here's another example + + align:start position:0% +any of that ok here's another example + + + align:start position:0% +any of that ok here's another example +this is a baby bird babbling and here's + + align:start position:0% +this is a baby bird babbling and here's + + + align:start position:0% +this is a baby bird babbling and here's +an example of what those signals + + align:start position:0% +an example of what those signals + + + align:start position:0% +an example of what those signals +actually look like just a bunch of + + align:start position:0% +actually look like just a bunch of + + + align:start position:0% +actually look like just a bunch of +Wiggles it's almost completely + + align:start position:0% +Wiggles it's almost completely + + + align:start position:0% +Wiggles it's almost completely +uninterpretable ok but again your brain + + align:start position:0% +uninterpretable ok but again your brain + + + align:start position:0% +uninterpretable ok but again your brain +does this spectral analysis thing and + + align:start position:0% +does this spectral analysis thing and + + + align:start position:0% +does this spectral analysis thing and +here I'm showing a spectrogram again + + align:start position:0% +here I'm showing a spectrogram again + + + align:start position:0% +here I'm showing a spectrogram again +this is frequency versus time much more + + align:start position:0% +this is frequency versus time much more + + + align:start position:0% +this is frequency versus time much more +cluttered visually and it's it's a + + align:start position:0% +cluttered visually and it's it's a + + + align:start position:0% +cluttered visually and it's it's a +little bit harder to interpret but your + + align:start position:0% +little bit harder to interpret but your + + + align:start position:0% +little bit harder to interpret but your +brain actually does a pretty good job + + align:start position:0% + + + + align:start position:0% + +figuring out what's going on there ok we + + align:start position:0% +figuring out what's going on there ok we + + + align:start position:0% +figuring out what's going on there ok we +can also do spectral analysis of neural + + align:start position:0% +can also do spectral analysis of neural + + + align:start position:0% +can also do spectral analysis of neural +signals so one of the really cool things + + align:start position:0% +signals so one of the really cool things + + + align:start position:0% +signals so one of the really cool things +that happens in is that neural circuits + + align:start position:0% +that happens in is that neural circuits + + + align:start position:0% +that happens in is that neural circuits +produce oscillations and they produce + + align:start position:0% +produce oscillations and they produce + + + align:start position:0% +produce oscillations and they produce +oscillations at different frequencies at + + align:start position:0% +oscillations at different frequencies at + + + align:start position:0% +oscillations at different frequencies at +different times if you close your eyes + + align:start position:0% +different times if you close your eyes + + + align:start position:0% +different times if you close your eyes +everybody just close your eyes for a + + align:start position:0% +everybody just close your eyes for a + + + align:start position:0% +everybody just close your eyes for a +second + + align:start position:0% +second + + + align:start position:0% +second +soon + + align:start position:0% +soon + + + align:start position:0% +soon +you close your eyes the back of your + + align:start position:0% +you close your eyes the back of your + + + align:start position:0% +you close your eyes the back of your +cortex starts generating a big 10 Hertz + + align:start position:0% +cortex starts generating a big 10 Hertz + + + align:start position:0% +cortex starts generating a big 10 Hertz +oscillation okay + + align:start position:0% +oscillation okay + + + align:start position:0% +oscillation okay +it's wild you just close your eyes and + + align:start position:0% +it's wild you just close your eyes and + + + align:start position:0% +it's wild you just close your eyes and +it starts going at ten Hertz okay this + + align:start position:0% +it starts going at ten Hertz okay this + + + align:start position:0% +it starts going at ten Hertz okay this +is a rhythm that's produced by the + + align:start position:0% +is a rhythm that's produced by the + + + align:start position:0% +is a rhythm that's produced by the +hippocampus so whenever you start + + align:start position:0% +hippocampus so whenever you start + + + align:start position:0% +hippocampus so whenever you start +walking your hippocampus starts + + align:start position:0% +walking your hippocampus starts + + + align:start position:0% +walking your hippocampus starts +generating at ten Hertz rhythm when you + + align:start position:0% +generating at ten Hertz rhythm when you + + + align:start position:0% +generating at ten Hertz rhythm when you +stop and you know like thinking about + + align:start position:0% +stop and you know like thinking about + + + align:start position:0% +stop and you know like thinking about +something or eating something it stops + + align:start position:0% +something or eating something it stops + + + align:start position:0% +something or eating something it stops +as soon as you start walking and Hertz + + align:start position:0% +as soon as you start walking and Hertz + + + align:start position:0% +as soon as you start walking and Hertz +rhythm okay and you can see that rhythm + + align:start position:0% +rhythm okay and you can see that rhythm + + + align:start position:0% +rhythm okay and you can see that rhythm +often in neural signals here you can see + + align:start position:0% +often in neural signals here you can see + + + align:start position:0% +often in neural signals here you can see +this ten Hertz rhythm it has a period of + + align:start position:0% +this ten Hertz rhythm it has a period of + + + align:start position:0% +this ten Hertz rhythm it has a period of +about 100 milliseconds but on top of + + align:start position:0% +about 100 milliseconds but on top of + + + align:start position:0% +about 100 milliseconds but on top of +that there are much faster rhythms it's + + align:start position:0% +that there are much faster rhythms it's + + + align:start position:0% +that there are much faster rhythms it's +not always so obvious in the brain what + + align:start position:0% +not always so obvious in the brain what + + + align:start position:0% +not always so obvious in the brain what +the rhythms are and you need spectral + + align:start position:0% +the rhythms are and you need spectral + + + align:start position:0% +the rhythms are and you need spectral +analysis techniques to help pull out + + align:start position:0% +analysis techniques to help pull out + + + align:start position:0% +analysis techniques to help pull out +pull out that structure okay you can see + + align:start position:0% +pull out that structure okay you can see + + + align:start position:0% +pull out that structure okay you can see +here here is the frequency as a function + + align:start position:0% +here here is the frequency as a function + + + align:start position:0% +here here is the frequency as a function +of time + + align:start position:0% +of time + + + align:start position:0% +of time +I haven't labeled the axis here but this + + align:start position:0% +I haven't labeled the axis here but this + + + align:start position:0% +I haven't labeled the axis here but this +bright band right here corresponds to + + align:start position:0% +bright band right here corresponds to + + + align:start position:0% +bright band right here corresponds to +this 10 Hertz oscillation okay so we're + + align:start position:0% +this 10 Hertz oscillation okay so we're + + + align:start position:0% +this 10 Hertz oscillation okay so we're +gonna take a little bit of a detour into + + align:start position:0% +gonna take a little bit of a detour into + + + align:start position:0% +gonna take a little bit of a detour into +how to actually carry out + + align:start position:0% +how to actually carry out + + + align:start position:0% +how to actually carry out +state-of-the-art spectral analysis like + + align:start position:0% +state-of-the-art spectral analysis like + + + align:start position:0% +state-of-the-art spectral analysis like +this to allow you to detect very subtle + + align:start position:0% +this to allow you to detect very subtle + + + align:start position:0% +this to allow you to detect very subtle +small signals in in neural signals or + + align:start position:0% +small signals in in neural signals or + + + align:start position:0% +small signals in in neural signals or +sound signals or any kind of signal that + + align:start position:0% +sound signals or any kind of signal that + + + align:start position:0% +sound signals or any kind of signal that +you're interested in study yeah okay so + + align:start position:0% +you're interested in study yeah okay so + + + align:start position:0% +you're interested in study yeah okay so +this is this is called a color map I + + align:start position:0% +this is this is called a color map I + + + align:start position:0% +this is this is called a color map I +didn't put that on the side here but + + align:start position:0% +didn't put that on the side here but + + + align:start position:0% +didn't put that on the side here but +basically dark hair means no power and + + align:start position:0% +basically dark hair means no power and + + + align:start position:0% +basically dark hair means no power and +and blue light blue to green is more + + align:start position:0% +and blue light blue to green is more + + + align:start position:0% +and blue light blue to green is more +power yellow to red is same here so red + + align:start position:0% +power yellow to red is same here so red + + + align:start position:0% +power yellow to red is same here so red +is red as most powerfully yes so it's + + align:start position:0% +is red as most powerfully yes so it's + + + align:start position:0% +is red as most powerfully yes so it's +it's + + align:start position:0% +it's + + + align:start position:0% +it's +how much energy there is at different + + align:start position:0% +how much energy there is at different + + + align:start position:0% +how much energy there is at different +frequencies in the signal as a function + + align:start position:0% +frequencies in the signal as a function + + + align:start position:0% +frequencies in the signal as a function +of time okay so I'm you're gonna know + + align:start position:0% +of time okay so I'm you're gonna know + + + align:start position:0% +of time okay so I'm you're gonna know +how to do this don't worry okay you're + + align:start position:0% +how to do this don't worry okay you're + + + align:start position:0% +how to do this don't worry okay you're +gonna be world experts at how to do this + + align:start position:0% +gonna be world experts at how to do this + + + align:start position:0% +gonna be world experts at how to do this +right yes yes yes that I'm sorry I + + align:start position:0% +right yes yes yes that I'm sorry I + + + align:start position:0% +right yes yes yes that I'm sorry I +should have been clear this is recording + + align:start position:0% +should have been clear this is recording + + + align:start position:0% +should have been clear this is recording +from an electrode in the hippocampus and + + align:start position:0% +from an electrode in the hippocampus and + + + align:start position:0% +from an electrode in the hippocampus and +these oscillations here are the local + + align:start position:0% +these oscillations here are the local + + + align:start position:0% +these oscillations here are the local +field potentials yes that's exactly + + align:start position:0% +field potentials yes that's exactly + + + align:start position:0% +field potentials yes that's exactly +right + + align:start position:0% +right + + + align:start position:0% +right +thank you I should have been more clear + + align:start position:0% +thank you I should have been more clear + + + align:start position:0% +thank you I should have been more clear +about that okay all right so in order to + + align:start position:0% +about that okay all right so in order to + + + align:start position:0% +about that okay all right so in order to +understand how to really do this you + + align:start position:0% +understand how to really do this you + + + align:start position:0% +understand how to really do this you +have to understand Fourier decomposition + + align:start position:0% +have to understand Fourier decomposition + + + align:start position:0% +have to understand Fourier decomposition +okay and once you understand that the + + align:start position:0% +okay and once you understand that the + + + align:start position:0% +okay and once you understand that the +rest is pretty okay so I'm going to take + + align:start position:0% +rest is pretty okay so I'm going to take + + + align:start position:0% +rest is pretty okay so I'm going to take +you very slowly and it's and it may feel + + align:start position:0% +you very slowly and it's and it may feel + + + align:start position:0% +you very slowly and it's and it may feel +a little grueling at first but if you + + align:start position:0% +a little grueling at first but if you + + + align:start position:0% +a little grueling at first but if you +understand this the rest is simple okay + + align:start position:0% +understand this the rest is simple okay + + + align:start position:0% +understand this the rest is simple okay +so let's let's just get started + + align:start position:0% +so let's let's just get started + + + align:start position:0% +so let's let's just get started +okay all right so Fourier series it's a + + align:start position:0% +okay all right so Fourier series it's a + + + align:start position:0% +okay all right so Fourier series it's a +way of decomposing periodic signals by + + align:start position:0% +way of decomposing periodic signals by + + + align:start position:0% +way of decomposing periodic signals by +applying filters to them okay we're + + align:start position:0% +applying filters to them okay we're + + + align:start position:0% +applying filters to them okay we're +gonna take a signal that's a function of + + align:start position:0% +gonna take a signal that's a function of + + + align:start position:0% +gonna take a signal that's a function of +time alright and we're going to make + + align:start position:0% +time alright and we're going to make + + + align:start position:0% +time alright and we're going to make +different receptive fields alright we're + + align:start position:0% +different receptive fields alright we're + + + align:start position:0% +different receptive fields alright we're +gonna make neurons that have sensitive + + align:start position:0% +gonna make neurons that have sensitive + + + align:start position:0% +gonna make neurons that have sensitive +to different frequencies all right and + + align:start position:0% +to different frequencies all right and + + + align:start position:0% +to different frequencies all right and +we're going to apply those different + + align:start position:0% +we're going to apply those different + + + align:start position:0% +we're going to apply those different +filters all right to extract what + + align:start position:0% +filters all right to extract what + + + align:start position:0% +filters all right to extract what +different frequencies there are in that + + align:start position:0% +different frequencies there are in that + + + align:start position:0% +different frequencies there are in that +signal okay so we're gonna take this + + align:start position:0% +signal okay so we're gonna take this + + + align:start position:0% +signal okay so we're gonna take this +periodic signal as a function of time + + align:start position:0% +periodic signal as a function of time + + + align:start position:0% +periodic signal as a function of time +it's a square wave it has a period + + align:start position:0% +it's a square wave it has a period + + + align:start position:0% +it's a square wave it has a period +capital T and what we're going to do is + + align:start position:0% +capital T and what we're going to do is + + + align:start position:0% +capital T and what we're going to do is +we're going to approximate that square + + align:start position:0% +we're going to approximate that square + + + align:start position:0% +we're going to approximate that square +wave as a sum of a bunch of different + + align:start position:0% +wave as a sum of a bunch of different + + + align:start position:0% +wave as a sum of a bunch of different +sine waves okay so the first thing we + + align:start position:0% +sine waves okay so the first thing we + + + align:start position:0% +sine waves okay so the first thing we +can do is approximate it as a cosine you + + align:start position:0% +can do is approximate it as a cosine you + + + align:start position:0% +can do is approximate it as a cosine you +can see the square wave has a peak there + + align:start position:0% +can see the square wave has a peak there + + + align:start position:0% +can see the square wave has a peak there +it has a valley there so the sine wave + + align:start position:0% +it has a valley there so the sine wave + + + align:start position:0% +it has a valley there so the sine wave +approximation is going to have a peak + + align:start position:0% +approximation is going to have a peak + + + align:start position:0% +approximation is going to have a peak +there and + + align:start position:0% +there and + + + align:start position:0% +there and +okay we're going to approximate it as a + + align:start position:0% +okay we're going to approximate it as a + + + align:start position:0% +okay we're going to approximate it as a +cosine wave of the same period and the + + align:start position:0% +cosine wave of the same period and the + + + align:start position:0% +cosine wave of the same period and the +same amplitude okay now we might say + + align:start position:0% +same amplitude okay now we might say + + + align:start position:0% +same amplitude okay now we might say +okay that's not a very good + + align:start position:0% +okay that's not a very good + + + align:start position:0% +okay that's not a very good +approximation what could we add to it to + + align:start position:0% +approximation what could we add to it to + + + align:start position:0% +approximation what could we add to it to +make a better approximation another + + align:start position:0% +make a better approximation another + + + align:start position:0% +make a better approximation another +cosine wave okay which is what we're + + align:start position:0% +cosine wave okay which is what we're + + + align:start position:0% +cosine wave okay which is what we're +going to do in just a second because + + align:start position:0% +going to do in just a second because + + + align:start position:0% +going to do in just a second because +apparently there's more I wanted to tell + + align:start position:0% +apparently there's more I wanted to tell + + + align:start position:0% +apparently there's more I wanted to tell +you about this so we're going to + + align:start position:0% +you about this so we're going to + + + align:start position:0% +you about this so we're going to +approximate this as a cosine wave that + + align:start position:0% +approximate this as a cosine wave that + + + align:start position:0% +approximate this as a cosine wave that +has a coefficient in front of it we have + + align:start position:0% +has a coefficient in front of it we have + + + align:start position:0% +has a coefficient in front of it we have +to approximate this as a cosine that has + + align:start position:0% +to approximate this as a cosine that has + + + align:start position:0% +to approximate this as a cosine that has +some food a one okay and it has some + + align:start position:0% +some food a one okay and it has some + + + align:start position:0% +some food a one okay and it has some +frequency F naught okay so the cosine so + + align:start position:0% +frequency F naught okay so the cosine so + + + align:start position:0% +frequency F naught okay so the cosine so +a cosine wave with with a frequency F + + align:start position:0% +a cosine wave with with a frequency F + + + align:start position:0% +a cosine wave with with a frequency F +naught is is this cosine 2 pi F naught T + + align:start position:0% +naught is is this cosine 2 pi F naught T + + + align:start position:0% +naught is is this cosine 2 pi F naught T +where F naught is 1 over the period okay + + align:start position:0% +where F naught is 1 over the period okay + + + align:start position:0% +where F naught is 1 over the period okay +and you can also write that so F naught + + align:start position:0% +and you can also write that so F naught + + + align:start position:0% +and you can also write that so F naught +is the oscillation frequency its cycles + + align:start position:0% +is the oscillation frequency its cycles + + + align:start position:0% +is the oscillation frequency its cycles +per second there's an important quantity + + align:start position:0% +per second there's an important quantity + + + align:start position:0% +per second there's an important quantity +called the angular frequency which is + + align:start position:0% +called the angular frequency which is + + + align:start position:0% +called the angular frequency which is +just 2 pi times F naught or 2 PI over T + + align:start position:0% +just 2 pi times F naught or 2 PI over T + + + align:start position:0% +just 2 pi times F naught or 2 PI over T +ok + + align:start position:0% +ok + + + align:start position:0% +ok +and the reason because if we write this + + align:start position:0% +and the reason because if we write this + + + align:start position:0% +and the reason because if we write this +as cosine Omega naught T then this thing + + align:start position:0% +as cosine Omega naught T then this thing + + + align:start position:0% +as cosine Omega naught T then this thing +just gives us 1 it gives us 2 pi change + + align:start position:0% +just gives us 1 it gives us 2 pi change + + + align:start position:0% +just gives us 1 it gives us 2 pi change +in the phase over this interval T which + + align:start position:0% +in the phase over this interval T which + + + align:start position:0% +in the phase over this interval T which +means that the cosine comes back to + + align:start position:0% +means that the cosine comes back to + + + align:start position:0% +means that the cosine comes back to +where it was okay all right so if we + + align:start position:0% +where it was okay all right so if we + + + align:start position:0% +where it was okay all right so if we +want to make a better approximation we + + align:start position:0% +want to make a better approximation we + + + align:start position:0% +want to make a better approximation we +can add more sine waves or cosine waves + + align:start position:0% +can add more sine waves or cosine waves + + + align:start position:0% +can add more sine waves or cosine waves +and it turns out that we can approximate + + align:start position:0% +and it turns out that we can approximate + + + align:start position:0% +and it turns out that we can approximate +any periodic signal by adding more + + align:start position:0% +any periodic signal by adding more + + + align:start position:0% +any periodic signal by adding more +cosine waves that are multiples of this + + align:start position:0% +cosine waves that are multiples of this + + + align:start position:0% +cosine waves that are multiples of this +frequency Omega nought okay why is that + + align:start position:0% +frequency Omega nought okay why is that + + + align:start position:0% +frequency Omega nought okay why is that +why can we get away with just adding + + align:start position:0% +why can we get away with just adding + + + align:start position:0% +why can we get away with just adding +more cosines that are integer multiples + + align:start position:0% +more cosines that are integer multiples + + + align:start position:0% +more cosines that are integer multiples +of this frequency Omega naught + + align:start position:0% +of this frequency Omega naught + + + align:start position:0% +of this frequency Omega naught +any idea why is it not important to + + align:start position:0% +any idea why is it not important to + + + align:start position:0% +any idea why is it not important to +consider 1.5 times Omega naught or 2.7 + + align:start position:0% + + + + align:start position:0% + +it's it's close but too complicated + + align:start position:0% +it's it's close but too complicated + + + align:start position:0% +it's it's close but too complicated +right this signal that we're trying to + + align:start position:0% +right this signal that we're trying to + + + align:start position:0% +right this signal that we're trying to +model is periodic right with frequency + + align:start position:0% +model is periodic right with frequency + + + align:start position:0% +model is periodic right with frequency +Omega naught and any integer multiple of + + align:start position:0% +Omega naught and any integer multiple of + + + align:start position:0% +Omega naught and any integer multiple of +Omega naught is also periodic at + + align:start position:0% +Omega naught is also periodic at + + + align:start position:0% +Omega naught is also periodic at +frequency Omega naught so notice that + + align:start position:0% +frequency Omega naught so notice that + + + align:start position:0% +frequency Omega naught so notice that +this signal at that that's cosine 2 + + align:start position:0% +this signal at that that's cosine 2 + + + align:start position:0% +this signal at that that's cosine 2 +Omega naught is still periodic over this + + align:start position:0% +Omega naught is still periodic over this + + + align:start position:0% +Omega naught is still periodic over this +interval T that makes sense so any + + align:start position:0% +interval T that makes sense so any + + + align:start position:0% +interval T that makes sense so any +integer multiple cosine integer Omega + + align:start position:0% +integer multiple cosine integer Omega + + + align:start position:0% +integer multiple cosine integer Omega +naught is also periodic with period T + + align:start position:0% +naught is also periodic with period T + + + align:start position:0% +naught is also periodic with period T +okay and those are the only those those + + align:start position:0% +okay and those are the only those those + + + align:start position:0% +okay and those are the only those those +are the only frequencies that are + + align:start position:0% +are the only frequencies that are + + + align:start position:0% +are the only frequencies that are +periodic with period T okay okay so we + + align:start position:0% +periodic with period T okay okay so we + + + align:start position:0% +periodic with period T okay okay so we +can restrict ourselves to including only + + align:start position:0% +can restrict ourselves to including only + + + align:start position:0% +can restrict ourselves to including only +frequencies that are in term integer + + align:start position:0% +frequencies that are in term integer + + + align:start position:0% +frequencies that are in term integer +multiples of Omega naught because those + + align:start position:0% +multiples of Omega naught because those + + + align:start position:0% +multiples of Omega naught because those +are the only frequencies that are also + + align:start position:0% +are the only frequencies that are also + + + align:start position:0% +are the only frequencies that are also +periodic with period T all right okay we + + align:start position:0% +periodic with period T all right okay we + + + align:start position:0% +periodic with period T all right okay we +can write down we can approximate this + + align:start position:0% +can write down we can approximate this + + + align:start position:0% +can write down we can approximate this +square wave as a sum of cosines of + + align:start position:0% +square wave as a sum of cosines of + + + align:start position:0% +square wave as a sum of cosines of +different frequencies okay and and the + + align:start position:0% +different frequencies okay and and the + + + align:start position:0% +different frequencies okay and and the +frequencies that we consider are just + + align:start position:0% +frequencies that we consider are just + + + align:start position:0% +frequencies that we consider are just +the integer multiples of Omega naught + + align:start position:0% +the integer multiples of Omega naught + + + align:start position:0% +the integer multiples of Omega naught +all right any questions about that + + align:start position:0% +all right any questions about that + + + align:start position:0% +all right any questions about that +that's that's almost like the crux of it + + align:start position:0% +that's that's almost like the crux of it + + + align:start position:0% +that's that's almost like the crux of it +there's just some more math to do + + align:start position:0% +there's just some more math to do + + + align:start position:0% +there's just some more math to do +okay so here's why this works so here's + + align:start position:0% +okay so here's why this works so here's + + + align:start position:0% +okay so here's why this works so here's +the square wave we're trying to + + align:start position:0% +the square wave we're trying to + + + align:start position:0% +the square wave we're trying to +approximate okay we can approximate that + + align:start position:0% +approximate okay we can approximate that + + + align:start position:0% +approximate okay we can approximate that +square wave as a cosign and there's the + + align:start position:0% +square wave as a cosign and there's the + + + align:start position:0% +square wave as a cosign and there's the +approximation now if we add a component + + align:start position:0% +approximation now if we add a component + + + align:start position:0% +approximation now if we add a component +that's some constant times cosine three + + align:start position:0% +that's some constant times cosine three + + + align:start position:0% +that's some constant times cosine three +Omega naught you can see that those two + + align:start position:0% +Omega naught you can see that those two + + + align:start position:0% +Omega naught you can see that those two +peaks they're kind of square out that + + align:start position:0% +peaks they're kind of square out that + + + align:start position:0% +peaks they're kind of square out that +those round edges of that cosine you can + + align:start position:0% +those round edges of that cosine you can + + + align:start position:0% +those round edges of that cosine you can +see it starts looking a little bit more + + align:start position:0% +see it starts looking a little bit more + + + align:start position:0% +see it starts looking a little bit more +square and if you add constant times + + align:start position:0% +square and if you add constant times + + + align:start position:0% +square and if you add constant times +cosine 5 Omega T it gets even more + + align:start position:0% +cosine 5 Omega T it gets even more + + + align:start position:0% +cosine 5 Omega T it gets even more +square and you keep adding more of these + + align:start position:0% +square and you keep adding more of these + + + align:start position:0% +square and you keep adding more of these +things until it almost looks just like a + + align:start position:0% +things until it almost looks just like a + + + align:start position:0% +things until it almost looks just like a +square wave okay here's another function + + align:start position:0% +square wave okay here's another function + + + align:start position:0% +square wave okay here's another function +we're going to approximate a bunch of + + align:start position:0% +we're going to approximate a bunch of + + + align:start position:0% +we're going to approximate a bunch of +pulses that have a period of 1 by adding + + align:start position:0% +pulses that have a period of 1 by adding + + + align:start position:0% +pulses that have a period of 1 by adding +up a bunch of cosines so here's the + + align:start position:0% +up a bunch of cosines so here's the + + + align:start position:0% +up a bunch of cosines so here's the +first approximation cosine Omega naught + + align:start position:0% +first approximation cosine Omega naught + + + align:start position:0% +first approximation cosine Omega naught +so there's your first approximation to + + align:start position:0% +so there's your first approximation to + + + align:start position:0% +so there's your first approximation to +this train of pulses now we add up we + + align:start position:0% +this train of pulses now we add up we + + + align:start position:0% +this train of pulses now we add up we +add to that cosine a constant times + + align:start position:0% +add to that cosine a constant times + + + align:start position:0% +add to that cosine a constant times +cosine 2 Omega T see that peak gets a + + align:start position:0% +cosine 2 Omega T see that peak gets a + + + align:start position:0% +cosine 2 Omega T see that peak gets a +little sharper add a constant times + + align:start position:0% +little sharper add a constant times + + + align:start position:0% +little sharper add a constant times +cosine 3 Omega T and you keep adding + + align:start position:0% +cosine 3 Omega T and you keep adding + + + align:start position:0% +cosine 3 Omega T and you keep adding +more and more terms and it gets sharper + + align:start position:0% +more and more terms and it gets sharper + + + align:start position:0% +more and more terms and it gets sharper +and sharper and looks more like a bunch + + align:start position:0% +and sharper and looks more like a bunch + + + align:start position:0% +and sharper and looks more like a bunch +of pulses ok why is that it's because + + align:start position:0% +of pulses ok why is that it's because + + + align:start position:0% +of pulses ok why is that it's because +all of those different cosines add up + + align:start position:0% +all of those different cosines add up + + + align:start position:0% +all of those different cosines add up +complete right here at 0 right and so + + align:start position:0% +complete right here at 0 right and so + + + align:start position:0% +complete right here at 0 right and so +those things all add up and this peak + + align:start position:0% +those things all add up and this peak + + + align:start position:0% +those things all add up and this peak +stays because the the peak of those + + align:start position:0% +stays because the the peak of those + + + align:start position:0% +stays because the the peak of those +cosines is always at 0 right over here + + align:start position:0% +cosines is always at 0 right over here + + + align:start position:0% +cosines is always at 0 right over here +though right next right next door all of + + align:start position:0% +though right next right next door all of + + + align:start position:0% +though right next right next door all of +those you can see that that cosine is + + align:start position:0% +those you can see that that cosine is + + + align:start position:0% +those you can see that that cosine is +cancelling that one is cancelling that + + align:start position:0% +cancelling that one is cancelling that + + + align:start position:0% +cancelling that one is cancelling that +when it's those two are cancelling you + + align:start position:0% +when it's those two are cancelling you + + + align:start position:0% +when it's those two are cancelling you +can see all these peaks here are + + align:start position:0% +can see all these peaks here are + + + align:start position:0% +can see all these peaks here are +cancelling each other and so that goes + + align:start position:0% +cancelling each other and so that goes + + + align:start position:0% +cancelling each other and so that goes +to 0 in there okay now of course all + + align:start position:0% +to 0 in there okay now of course all + + + align:start position:0% +to 0 in there okay now of course all +these cosines are periodic with a period + + align:start position:0% +these cosines are periodic with a period + + + align:start position:0% +these cosines are periodic with a period +t so if you go 1 t over + + align:start position:0% +t so if you go 1 t over + + + align:start position:0% +t so if you go 1 t over +all of those Peaks add up again and + + align:start position:0% +all of those Peaks add up again and + + + align:start position:0% +all of those Peaks add up again and +become an interfere constructively okay + + align:start position:0% + + + + align:start position:0% + +so that's it it's basically a way of + + align:start position:0% +so that's it it's basically a way of + + + align:start position:0% +so that's it it's basically a way of +taking any periodic signal and figuring + + align:start position:0% +taking any periodic signal and figuring + + + align:start position:0% +taking any periodic signal and figuring +out a bunch of cosine such that the + + align:start position:0% +out a bunch of cosine such that the + + + align:start position:0% +out a bunch of cosine such that the +parts you want to keep add up + + align:start position:0% +parts you want to keep add up + + + align:start position:0% +parts you want to keep add up +constructively and the parts that you + + align:start position:0% +constructively and the parts that you + + + align:start position:0% +constructively and the parts that you +want to that aren't there in your signal + + align:start position:0% +want to that aren't there in your signal + + + align:start position:0% +want to that aren't there in your signal +add up destructively okay and there's + + align:start position:0% +add up destructively okay and there's + + + align:start position:0% +add up destructively okay and there's +very simple sort of mathematical tools + + align:start position:0% +very simple sort of mathematical tools + + + align:start position:0% +very simple sort of mathematical tools +basically it's a correlation to extract + + align:start position:0% +basically it's a correlation to extract + + + align:start position:0% +basically it's a correlation to extract +the coefficients that go in front of + + align:start position:0% +the coefficients that go in front of + + + align:start position:0% +the coefficients that go in front of +each one of these cosines okay and then + + align:start position:0% +each one of these cosines okay and then + + + align:start position:0% +each one of these cosines okay and then +one more thing we use cosines to model + + align:start position:0% +one more thing we use cosines to model + + + align:start position:0% +one more thing we use cosines to model +or to approximate functions that are + + align:start position:0% +or to approximate functions that are + + + align:start position:0% +or to approximate functions that are +symmetric around the oil because the + + align:start position:0% +symmetric around the oil because the + + + align:start position:0% +symmetric around the oil because the +cosine function is symmetric other + + align:start position:0% +cosine function is symmetric other + + + align:start position:0% +cosine function is symmetric other +functions are anti-symmetric they'll be + + align:start position:0% +functions are anti-symmetric they'll be + + + align:start position:0% +functions are anti-symmetric they'll be +they'll have it'll they'll look more + + align:start position:0% +they'll have it'll they'll look more + + + align:start position:0% +they'll have it'll they'll look more +like a sine wave they'll have they'll be + + align:start position:0% +like a sine wave they'll have they'll be + + + align:start position:0% +like a sine wave they'll have they'll be +negative here and positive there and we + + align:start position:0% +negative here and positive there and we + + + align:start position:0% +negative here and positive there and we +use signs to model those okay and then + + align:start position:0% +use signs to model those okay and then + + + align:start position:0% +use signs to model those okay and then +the one last trick we need is we can + + align:start position:0% +the one last trick we need is we can + + + align:start position:0% +the one last trick we need is we can +model arbitrary functions by combining + + align:start position:0% +model arbitrary functions by combining + + + align:start position:0% +model arbitrary functions by combining +sines and cosines into complex + + align:start position:0% +sines and cosines into complex + + + align:start position:0% +sines and cosines into complex +Exponential's and we'll talk about that + + align:start position:0% +Exponential's and we'll talk about that + + + align:start position:0% +Exponential's and we'll talk about that +next time okay once we do that then you + + align:start position:0% +next time okay once we do that then you + + + align:start position:0% +next time okay once we do that then you +can basically model not just got exceed + + align:start position:0% +can basically model not just got exceed + + + align:start position:0% +can basically model not just got exceed +knows but arbitrary signals okay and + + align:start position:0% +knows but arbitrary signals okay and + + + align:start position:0% +knows but arbitrary signals okay and +then you're you're all set to analyze + + align:start position:0% +then you're you're all set to analyze + + + align:start position:0% +then you're you're all set to analyze +any kind of periodic signal in in + + align:start position:0% +any kind of periodic signal in in + + + align:start position:0% +any kind of periodic signal in in +arbitrary signals all right so it's a + + align:start position:0% +arbitrary signals all right so it's a + + + align:start position:0% +arbitrary signals all right so it's a +powerful way of extracting periodic + + align:start position:0% +powerful way of extracting periodic + + + align:start position:0% +powerful way of extracting periodic +structure from from any so we'll + + align:start position:0% +structure from from any so we'll + + + align:start position:0% +structure from from any so we'll +continue that next time \ No newline at end of file diff --git a/t8xg8ml7Vh8.txt b/t8xg8ml7Vh8.txt new file mode 100644 index 0000000000000000000000000000000000000000..d97cbc38d2e3b2995ff073d068d723dd7e1be9dc --- /dev/null +++ b/t8xg8ml7Vh8.txt @@ -0,0 +1,8275 @@ +align:start position:0% + +the following content is provided under + + align:start position:0% +the following content is provided under + + + align:start position:0% +the following content is provided under +a Creative Commons license your support + + align:start position:0% +a Creative Commons license your support + + + align:start position:0% +a Creative Commons license your support +will help MIT open courseware continue + + align:start position:0% +will help MIT open courseware continue + + + align:start position:0% +will help MIT open courseware continue +to offer highquality educational + + align:start position:0% +to offer highquality educational + + + align:start position:0% +to offer highquality educational +resources for free to make a donation or + + align:start position:0% +resources for free to make a donation or + + + align:start position:0% +resources for free to make a donation or +view additional materials from hundreds + + align:start position:0% +view additional materials from hundreds + + + align:start position:0% +view additional materials from hundreds +of MIT courses visit MIT open courseware + + align:start position:0% +of MIT courses visit MIT open courseware + + + align:start position:0% +of MIT courses visit MIT open courseware +at + + align:start position:0% + + + + align:start position:0% + +ocw.mit.edu two things I want to do + + align:start position:0% +ocw.mit.edu two things I want to do + + + align:start position:0% +ocw.mit.edu two things I want to do +today just briefly go through chapter 6 + + align:start position:0% +today just briefly go through chapter 6 + + + align:start position:0% +today just briefly go through chapter 6 +which is about brain specialization it + + align:start position:0% +which is about brain specialization it + + + align:start position:0% +which is about brain specialization it +was meant to be sort of an interlude + + align:start position:0% +was meant to be sort of an interlude + + + align:start position:0% +was meant to be sort of an interlude +there was a little bit of a break before + + align:start position:0% +there was a little bit of a break before + + + align:start position:0% +there was a little bit of a break before +we uh get into + + align:start position:0% + + + + align:start position:0% + +the some of the forbrain connections but + + align:start position:0% +the some of the forbrain connections but + + + align:start position:0% +the some of the forbrain connections but +uh these all in involve + + align:start position:0% + + + + align:start position:0% + +specializations because of the evolution + + align:start position:0% +specializations because of the evolution + + + align:start position:0% +specializations because of the evolution +of head receptors and the resulting + + align:start position:0% +of head receptors and the resulting + + + align:start position:0% +of head receptors and the resulting +expansions of the brain that have + + align:start position:0% +expansions of the brain that have + + + align:start position:0% +expansions of the brain that have +occurred and uh we start with Electro + + align:start position:0% +occurred and uh we start with Electro + + + align:start position:0% +occurred and uh we start with Electro +reception in some + + align:start position:0% +reception in some + + + align:start position:0% +reception in some +fish that's led to enormous expansion of + + align:start position:0% +fish that's led to enormous expansion of + + + align:start position:0% +fish that's led to enormous expansion of +the cerebellum and the + + align:start position:0% +the cerebellum and the + + + align:start position:0% +the cerebellum and the +marids and my first question here was + + align:start position:0% +marids and my first question here was + + + align:start position:0% +marids and my first question here was +why what cranial nerves carry + + align:start position:0% +why what cranial nerves carry + + + align:start position:0% +why what cranial nerves carry +information from electro receptors and + + align:start position:0% +information from electro receptors and + + + align:start position:0% +information from electro receptors and +fish that have Electro + + align:start position:0% +fish that have Electro + + + align:start position:0% +fish that have Electro +reception and also why is it needed why + + align:start position:0% +reception and also why is it needed why + + + align:start position:0% +reception and also why is it needed why +don't they use + + align:start position:0% +don't they use + + + align:start position:0% +don't they use +Vision + + align:start position:0% +Vision + + + align:start position:0% +Vision +yeah + + align:start position:0% +yeah + + + align:start position:0% +yeah +they're cranial nerves that's + + align:start position:0% +they're cranial nerves that's + + + align:start position:0% +they're cranial nerves that's +right but what cranial what cranial + + align:start position:0% +right but what cranial what cranial + + + align:start position:0% +right but what cranial what cranial +nerves are + + align:start position:0% +nerves are + + + align:start position:0% +nerves are +they + + align:start position:0% +they + + + align:start position:0% +they +sorry it is actually up to six of them + + align:start position:0% +sorry it is actually up to six of them + + + align:start position:0% +sorry it is actually up to six of them +and what are they + + align:start position:0% +and what are they + + + align:start position:0% +and what are they +called the lateral line nerves because + + align:start position:0% +called the lateral line nerves because + + + align:start position:0% +called the lateral line nerves because +fish have these receptors + + align:start position:0% +fish have these receptors + + + align:start position:0% +fish have these receptors +along a a line along the side of their + + align:start position:0% +along a a line along the side of their + + + align:start position:0% +along a a line along the side of their +body they also have uh + + align:start position:0% +body they also have uh + + + align:start position:0% +body they also have uh +mechanical receptors there there's a + + align:start position:0% +mechanical receptors there there's a + + + align:start position:0% +mechanical receptors there there's a +mechanical lateral line row of receptors + + align:start position:0% +mechanical lateral line row of receptors + + + align:start position:0% +mechanical lateral line row of receptors +also but we're concerned here with the + + align:start position:0% +also but we're concerned here with the + + + align:start position:0% +also but we're concerned here with the +electro receptors okay so what are they + + align:start position:0% +electro receptors okay so what are they + + + align:start position:0% +electro receptors okay so what are they +doing why is it so important why aren't + + align:start position:0% +doing why is it so important why aren't + + + align:start position:0% +doing why is it so important why aren't +they just using + + align:start position:0% + + + + align:start position:0% + +Vision uh yeah go + + align:start position:0% + + + + align:start position:0% + +ahead yeah because they can't see + + align:start position:0% +ahead yeah because they can't see + + + align:start position:0% +ahead yeah because they can't see +they're living in Muddy Waters uh they + + align:start position:0% +they're living in Muddy Waters uh they + + + align:start position:0% +they're living in Muddy Waters uh they +thrive in those Waters but they've got + + align:start position:0% +thrive in those Waters but they've got + + + align:start position:0% +thrive in those Waters but they've got +to be able to find things has got to be + + align:start position:0% +to be able to find things has got to be + + + align:start position:0% +to be able to find things has got to be +able to find prey if they're feeding on + + align:start position:0% +able to find prey if they're feeding on + + + align:start position:0% +able to find prey if they're feeding on +them so what are they + + align:start position:0% +them so what are they + + + align:start position:0% +them so what are they +detecting there're there's two kinds of + + align:start position:0% +detecting there're there's two kinds of + + + align:start position:0% +detecting there're there's two kinds of +electric reception let's just deal with + + align:start position:0% +electric reception let's just deal with + + + align:start position:0% +electric reception let's just deal with +one of them the fish that generate an + + align:start position:0% +one of them the fish that generate an + + + align:start position:0% +one of them the fish that generate an +electric field around their + + align:start position:0% +electric field around their + + + align:start position:0% +electric field around their +body it's not a big electric field there + + align:start position:0% +body it's not a big electric field there + + + align:start position:0% +body it's not a big electric field there +are a few of them that can generate such + + align:start position:0% +are a few of them that can generate such + + + align:start position:0% +are a few of them that can generate such +a big jolt of electricity that they can + + align:start position:0% +a big jolt of electricity that they can + + + align:start position:0% +a big jolt of electricity that they can +stun prey but we're not talking about + + align:start position:0% +stun prey but we're not talking about + + + align:start position:0% +stun prey but we're not talking about +those we're just talking about them that + + align:start position:0% +those we're just talking about them that + + + align:start position:0% +those we're just talking about them that +use it as a sense + + align:start position:0% +use it as a sense + + + align:start position:0% +use it as a sense +they generate an electric field but they + + align:start position:0% +they generate an electric field but they + + + align:start position:0% +they generate an electric field but they +also detect the electric field all + + align:start position:0% +also detect the electric field all + + + align:start position:0% +also detect the electric field all +around the side of their body so any + + align:start position:0% +around the side of their body so any + + + align:start position:0% +around the side of their body so any +disturbance in that field they can + + align:start position:0% +disturbance in that field they can + + + align:start position:0% +disturbance in that field they can +detect so all that computation involved + + align:start position:0% +detect so all that computation involved + + + align:start position:0% +detect so all that computation involved +in these this + + align:start position:0% +in these this + + + align:start position:0% +in these this +specialized brain here the + + align:start position:0% +specialized brain here the + + + align:start position:0% +specialized brain here the +cerebellum this is the area in one of + + align:start position:0% +cerebellum this is the area in one of + + + align:start position:0% +cerebellum this is the area in one of +the + + align:start position:0% +the + + + align:start position:0% +the +morid uh are involved in com + + align:start position:0% +morid uh are involved in com + + + align:start position:0% +morid uh are involved in com +Computing the where the animal is in + + align:start position:0% +Computing the where the animal is in + + + align:start position:0% +Computing the where the animal is in +order to get a particular disturbance in + + align:start position:0% +order to get a particular disturbance in + + + align:start position:0% +order to get a particular disturbance in +the electric field it's not an easy task + + align:start position:0% +the electric field it's not an easy task + + + align:start position:0% +the electric field it's not an easy task +and it's a huge computational problem + + align:start position:0% +and it's a huge computational problem + + + align:start position:0% +and it's a huge computational problem +and there are computational + + align:start position:0% +and there are computational + + + align:start position:0% +and there are computational +neuroscientists trying still trying to + + align:start position:0% +neuroscientists trying still trying to + + + align:start position:0% +neuroscientists trying still trying to +figure that out all right uh no + + align:start position:0% +figure that out all right uh no + + + align:start position:0% +figure that out all right uh no +placental mammals have Electro receptor + + align:start position:0% +placental mammals have Electro receptor + + + align:start position:0% +placental mammals have Electro receptor +abilities but one nonplacental + + align:start position:0% +abilities but one nonplacental + + + align:start position:0% +abilities but one nonplacental +mammal does have such an ability do you + + align:start position:0% +mammal does have such an ability do you + + + align:start position:0% +mammal does have such an ability do you +know which one it is in the chapter huh + + align:start position:0% +know which one it is in the chapter huh + + + align:start position:0% +know which one it is in the chapter huh +sorry the duck build platypus yes + + align:start position:0% +sorry the duck build platypus yes + + + align:start position:0% +sorry the duck build platypus yes +okay how are this animals Electro + + align:start position:0% +okay how are this animals Electro + + + align:start position:0% +okay how are this animals Electro +receptor inputs different from + + align:start position:0% +receptor inputs different from + + + align:start position:0% +receptor inputs different from +electrosensory + + align:start position:0% +electrosensory + + + align:start position:0% +electrosensory +fish they have they use a different + + align:start position:0% +fish they have they use a different + + + align:start position:0% +fish they have they use a different +cranial nerve and somebody said + + align:start position:0% +cranial nerve and somebody said + + + align:start position:0% +cranial nerve and somebody said +it so anybody else know I think you said + + align:start position:0% +it so anybody else know I think you said + + + align:start position:0% +it so anybody else know I think you said +it + + align:start position:0% +it + + + align:start position:0% +it +before it's trinal nerve that's right + + align:start position:0% +before it's trinal nerve that's right + + + align:start position:0% +before it's trinal nerve that's right +but not in those fish just in the build + + align:start position:0% +but not in those fish just in the build + + + align:start position:0% +but not in those fish just in the build +platypus it's in their bill so how do + + align:start position:0% +platypus it's in their bill so how do + + + align:start position:0% +platypus it's in their bill so how do +they feed they stick that bill down in + + align:start position:0% +they feed they stick that bill down in + + + align:start position:0% +they feed they stick that bill down in +the muck and in the + + align:start position:0% +the muck and in the + + + align:start position:0% +the muck and in the +water and they're detecting electric + + align:start position:0% +water and they're detecting electric + + + align:start position:0% +water and they're detecting electric +Fields + + align:start position:0% +Fields + + + align:start position:0% +Fields +uh many animals do some kind of electric + + align:start position:0% +uh many animals do some kind of electric + + + align:start position:0% +uh many animals do some kind of electric +Fields I don't know the detailed for the + + align:start position:0% +Fields I don't know the detailed for the + + + align:start position:0% +Fields I don't know the detailed for the +duck field platypus I know a little more + + align:start position:0% +duck field platypus I know a little more + + + align:start position:0% +duck field platypus I know a little more +about the + + align:start position:0% +about the + + + align:start position:0% +about the +fish all right + + align:start position:0% +fish all right + + + align:start position:0% +fish all right +uh another sense that is not highly + + align:start position:0% +uh another sense that is not highly + + + align:start position:0% +uh another sense that is not highly +developed in mammals is infrared detect + + align:start position:0% +developed in mammals is infrared detect + + + align:start position:0% +developed in mammals is infrared detect +action in what animals is this + + align:start position:0% +action in what animals is this + + + align:start position:0% +action in what animals is this +particularly important and what cranial + + align:start position:0% +particularly important and what cranial + + + align:start position:0% +particularly important and what cranial +nerve is involved anybody else somebody + + align:start position:0% +nerve is involved anybody else somebody + + + align:start position:0% +nerve is involved anybody else somebody +that's not talked today + + align:start position:0% + + + + align:start position:0% + +yet the pit vipers yes snakes but only + + align:start position:0% +yet the pit vipers yes snakes but only + + + align:start position:0% +yet the pit vipers yes snakes but only +particular snakes snakes like the + + align:start position:0% +particular snakes snakes like the + + + align:start position:0% +particular snakes snakes like the +rattlesnake so here in this little + + align:start position:0% +rattlesnake so here in this little + + + align:start position:0% +rattlesnake so here in this little +picture I think this is the same one I + + align:start position:0% +picture I think this is the same one I + + + align:start position:0% +picture I think this is the same one I +used in the book I've added to the + + align:start position:0% +used in the book I've added to the + + + align:start position:0% +used in the book I've added to the +picture I found in a drawing in the + + align:start position:0% +picture I found in a drawing in the + + + align:start position:0% +picture I found in a drawing in the +hotos and carton book but this is the + + align:start position:0% +hotos and carton book but this is the + + + align:start position:0% +hotos and carton book but this is the +pit it literally is a pit it's recessed + + align:start position:0% +pit it literally is a pit it's recessed + + + align:start position:0% +pit it literally is a pit it's recessed +what would be the value of + + align:start position:0% +what would be the value of + + + align:start position:0% +what would be the value of +that why put the infrared detectors at + + align:start position:0% +that why put the infrared detectors at + + + align:start position:0% +that why put the infrared detectors at +the bottom of a little pit in their + + align:start position:0% + + + + align:start position:0% + +face yeah because you just imagine you + + align:start position:0% +face yeah because you just imagine you + + + align:start position:0% +face yeah because you just imagine you +know I I have a cup here and The + + align:start position:0% +know I I have a cup here and The + + + align:start position:0% +know I I have a cup here and The +receptors are back here now it's got + + align:start position:0% +receptors are back here now it's got + + + align:start position:0% +receptors are back here now it's got +directionality + + align:start position:0% +directionality + + + align:start position:0% +directionality +now it's not responding to things over + + align:start position:0% +now it's not responding to things over + + + align:start position:0% +now it's not responding to things over +there it's only responding to things in + + align:start position:0% +there it's only responding to things in + + + align:start position:0% +there it's only responding to things in +this dire so the head they have to move + + align:start position:0% +this dire so the head they have to move + + + align:start position:0% +this dire so the head they have to move +their head of course it doesn't give + + align:start position:0% +their head of course it doesn't give + + + align:start position:0% +their head of course it doesn't give +them directional selectivity if they + + align:start position:0% +them directional selectivity if they + + + align:start position:0% +them directional selectivity if they +keep their head still except they know + + align:start position:0% +keep their head still except they know + + + align:start position:0% +keep their head still except they know +it's right in front of + + align:start position:0% +it's right in front of + + + align:start position:0% +it's right in front of +them all right so and you can see it + + align:start position:0% +them all right so and you can see it + + + align:start position:0% +them all right so and you can see it +comes in through a branch of the trienal + + align:start position:0% +comes in through a branch of the trienal + + + align:start position:0% +comes in through a branch of the trienal +nerve to a particular group of secondary + + align:start position:0% +nerve to a particular group of secondary + + + align:start position:0% +nerve to a particular group of secondary +sensory + + align:start position:0% +sensory + + + align:start position:0% +sensory +cells and then through a circuit + + align:start position:0% +cells and then through a circuit + + + align:start position:0% +cells and then through a circuit +involving the trigal + + align:start position:0% +involving the trigal + + + align:start position:0% +involving the trigal +neurons it goes from there to the optic + + align:start position:0% +neurons it goes from there to the optic + + + align:start position:0% +neurons it goes from there to the optic +tectum remember we call it optic tectum + + align:start position:0% +tectum remember we call it optic tectum + + + align:start position:0% +tectum remember we call it optic tectum +but it actually gets many different + + align:start position:0% +but it actually gets many different + + + align:start position:0% +but it actually gets many different +sensory modalities distance receptors it + + align:start position:0% +sensory modalities distance receptors it + + + align:start position:0% +sensory modalities distance receptors it +gets auditory sensory and visual and now + + align:start position:0% +gets auditory sensory and visual and now + + + align:start position:0% +gets auditory sensory and visual and now +it we see it gets it gets information in + + align:start position:0% +it we see it gets it gets information in + + + align:start position:0% +it we see it gets it gets information in +the these snakes from their infared + + align:start position:0% +the these snakes from their infared + + + align:start position:0% +the these snakes from their infared +detection so they can use it to + + align:start position:0% +detection so they can use it to + + + align:start position:0% +detection so they can use it to +orient uh towards their + + align:start position:0% + + + + align:start position:0% + +pray no only the pit vipers have + + align:start position:0% +pray no only the pit vipers have + + + align:start position:0% +pray no only the pit vipers have +that and it would be interesting to look + + align:start position:0% +that and it would be interesting to look + + + align:start position:0% +that and it would be interesting to look +to see what other kinds of infrared + + align:start position:0% +to see what other kinds of infrared + + + align:start position:0% +to see what other kinds of infrared +detection you have in animals I'm sure + + align:start position:0% +detection you have in animals I'm sure + + + align:start position:0% +detection you have in animals I'm sure +other animals have evolved that it's + + align:start position:0% +other animals have evolved that it's + + + align:start position:0% +other animals have evolved that it's +it's too useful not to evolve only in + + align:start position:0% +it's too useful not to evolve only in + + + align:start position:0% +it's too useful not to evolve only in +one small group like that + + align:start position:0% +one small group like that + + + align:start position:0% +one small group like that +but okay bats are not the only mammal + + align:start position:0% +but okay bats are not the only mammal + + + align:start position:0% +but okay bats are not the only mammal +with Echo location ability another + + align:start position:0% +with Echo location ability another + + + align:start position:0% +with Echo location ability another +special sense so you'd expect + + align:start position:0% +special sense so you'd expect + + + align:start position:0% +special sense so you'd expect +specializations in the brain of the bat + + align:start position:0% +specializations in the brain of the bat + + + align:start position:0% +specializations in the brain of the bat +but what other mammals have Echo + + align:start position:0% +but what other mammals have Echo + + + align:start position:0% +but what other mammals have Echo +reception + + align:start position:0% +reception + + + align:start position:0% +reception +ability and the dolphin okay and what + + align:start position:0% +ability and the dolphin okay and what + + + align:start position:0% +ability and the dolphin okay and what +cranial nerve do you think has expanded + + align:start position:0% +cranial nerve do you think has expanded + + + align:start position:0% +cranial nerve do you think has expanded +I've actually studied that with Eric + + align:start position:0% +I've actually studied that with Eric + + + align:start position:0% +I've actually studied that with Eric +Monty who's a marine + + align:start position:0% +Monty who's a marine + + + align:start position:0% +Monty who's a marine +mammologist uh we did uh + + align:start position:0% +mammologist uh we did uh + + + align:start position:0% +mammologist uh we did uh +using MRIs we were able to reconstruct + + align:start position:0% +using MRIs we were able to reconstruct + + + align:start position:0% +using MRIs we were able to reconstruct +the brain of the Atlantic white-sided + + align:start position:0% +the brain of the Atlantic white-sided + + + align:start position:0% +the brain of the Atlantic white-sided +dolphin + + align:start position:0% +dolphin + + + align:start position:0% +dolphin +and it was confusing at the beginning + + align:start position:0% +and it was confusing at the beginning + + + align:start position:0% +and it was confusing at the beginning +because I had never seen I mean I was in + + align:start position:0% +because I had never seen I mean I was in + + + align:start position:0% +because I had never seen I mean I was in +helping him identify everything and i' + + align:start position:0% +helping him identify everything and i' + + + align:start position:0% +helping him identify everything and i' +never I thought it must be the + + align:start position:0% +never I thought it must be the + + + align:start position:0% +never I thought it must be the +trigeminal nerve you know any mammal + + align:start position:0% +trigeminal nerve you know any mammal + + + align:start position:0% +trigeminal nerve you know any mammal +I've ever seen the trial nerve is the + + align:start position:0% +I've ever seen the trial nerve is the + + + align:start position:0% +I've ever seen the trial nerve is the +biggest but not in that animal it was + + align:start position:0% +biggest but not in that animal it was + + + align:start position:0% +biggest but not in that animal it was +the eighth nerve okay the auditory nerve + + align:start position:0% +the eighth nerve okay the auditory nerve + + + align:start position:0% +the eighth nerve okay the auditory nerve +and similarly if you look at the surface + + align:start position:0% +and similarly if you look at the surface + + + align:start position:0% +and similarly if you look at the surface +of the midbrain in the dolphin look at + + align:start position:0% +of the midbrain in the dolphin look at + + + align:start position:0% +of the midbrain in the dolphin look at +this enormous inferior + + align:start position:0% +this enormous inferior + + + align:start position:0% +this enormous inferior +calculus the superior + + align:start position:0% +calculus the superior + + + align:start position:0% +calculus the superior +calculus is relatively smaller and it's + + align:start position:0% +calculus is relatively smaller and it's + + + align:start position:0% +calculus is relatively smaller and it's +the same in the back releas very + + align:start position:0% +the same in the back releas very + + + align:start position:0% +the same in the back releas very +similar the dolphin of course has an + + align:start position:0% +similar the dolphin of course has an + + + align:start position:0% +similar the dolphin of course has an +enormous end brain too and so I've taken + + align:start position:0% +enormous end brain too and so I've taken + + + align:start position:0% +enormous end brain too and so I've taken +a picture there where the embran has + + align:start position:0% +a picture there where the embran has + + + align:start position:0% +a picture there where the embran has +been removed in the dolphin but not the + + align:start position:0% +been removed in the dolphin but not the + + + align:start position:0% +been removed in the dolphin but not the +bat + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +sorry as humans that use some + + align:start position:0% +sorry as humans that use some + + + align:start position:0% +sorry as humans that use some +echolocation it does become specialized + + align:start position:0% +echolocation it does become specialized + + + align:start position:0% +echolocation it does become specialized +and there are indications that blind + + align:start position:0% +and there are indications that blind + + + align:start position:0% +and there are indications that blind +people that are more likely to be able + + align:start position:0% +people that are more likely to be able + + + align:start position:0% +people that are more likely to be able +to use such an ability do have changes + + align:start position:0% +to use such an ability do have changes + + + align:start position:0% +to use such an ability do have changes +in their cortex and we're going to talk + + align:start position:0% +in their cortex and we're going to talk + + + align:start position:0% +in their cortex and we're going to talk +a little bit about that to the end of + + align:start position:0% +a little bit about that to the end of + + + align:start position:0% +a little bit about that to the end of +the class very good question just notice + + align:start position:0% +the class very good question just notice + + + align:start position:0% +the class very good question just notice +here the other two animals in this + + align:start position:0% +here the other two animals in this + + + align:start position:0% +here the other two animals in this +picture it shows animals where the + + align:start position:0% +picture it shows animals where the + + + align:start position:0% +picture it shows animals where the +superior culus the more + + align:start position:0% +superior culus the more + + + align:start position:0% +superior culus the more +anterior uh surface of the midbrain is + + align:start position:0% +anterior uh surface of the midbrain is + + + align:start position:0% +anterior uh surface of the midbrain is +enlarged and they're very visual animals + + align:start position:0% +enlarged and they're very visual animals + + + align:start position:0% +enlarged and they're very visual animals +here's a goat a wild goat in + + align:start position:0% +here's a goat a wild goat in + + + align:start position:0% +here's a goat a wild goat in +eex and tarer a a prian primate that can + + align:start position:0% +eex and tarer a a prian primate that can + + + align:start position:0% +eex and tarer a a prian primate that can +literally locate using that structure + + align:start position:0% +literally locate using that structure + + + align:start position:0% +literally locate using that structure +it's got this ability to orient and + + align:start position:0% +it's got this ability to orient and + + + align:start position:0% +it's got this ability to orient and +reach out with his hand and grab insects + + align:start position:0% +reach out with his hand and grab insects + + + align:start position:0% +reach out with his hand and grab insects +literally right out of the air all + + align:start position:0% + + + + align:start position:0% + +right what is a brain manifestation of + + align:start position:0% +right what is a brain manifestation of + + + align:start position:0% +right what is a brain manifestation of +the specialization of primates provision + + align:start position:0% +the specialization of primates provision + + + align:start position:0% +the specialization of primates provision +that includes + + align:start position:0% +that includes + + + align:start position:0% +that includes +us most of the primates have very + + align:start position:0% +us most of the primates have very + + + align:start position:0% +us most of the primates have very +special they're very specialized for + + align:start position:0% +special they're very specialized for + + + align:start position:0% +special they're very specialized for +vision that's why monkeys are used so + + align:start position:0% +vision that's why monkeys are used so + + + align:start position:0% +vision that's why monkeys are used so +much in studies of vision because of + + align:start position:0% +much in studies of vision because of + + + align:start position:0% +much in studies of vision because of +similarity to humans you know rats are + + align:start position:0% +similarity to humans you know rats are + + + align:start position:0% +similarity to humans you know rats are +used to and cats used to be the most + + align:start position:0% +used to and cats used to be the most + + + align:start position:0% +used to and cats used to be the most +popular animal but no longer it's + + align:start position:0% +popular animal but no longer it's + + + align:start position:0% +popular animal but no longer it's +because of the specialization so you see + + align:start position:0% +because of the specialization so you see + + + align:start position:0% +because of the specialization so you see +what has expanded so + + align:start position:0% + + + + align:start position:0% + +much it doesn't isn't that + + align:start position:0% +much it doesn't isn't that + + + align:start position:0% +much it doesn't isn't that +tectum it's not like in the evex in the + + align:start position:0% +tectum it's not like in the evex in the + + + align:start position:0% +tectum it's not like in the evex in the +tarsia here but it's a part of the brain + + align:start position:0% +tarsia here but it's a part of the brain + + + align:start position:0% +tarsia here but it's a part of the brain +more involved in visual learning + + align:start position:0% +more involved in visual learning + + + align:start position:0% +more involved in visual learning +all + + align:start position:0% +all + + + align:start position:0% +all +right and this shows an owl + + align:start position:0% +right and this shows an owl + + + align:start position:0% +right and this shows an owl +monkey there's the stri cortex what we + + align:start position:0% +monkey there's the stri cortex what we + + + align:start position:0% +monkey there's the stri cortex what we +call primary Vil + + align:start position:0% +call primary Vil + + + align:start position:0% +call primary Vil +cortex but all every area that you see + + align:start position:0% +cortex but all every area that you see + + + align:start position:0% +cortex but all every area that you see +outlin with the black line and many of + + align:start position:0% +outlin with the black line and many of + + + align:start position:0% +outlin with the black line and many of +them are also in different colors uh are + + align:start position:0% +them are also in different colors uh are + + + align:start position:0% +them are also in different colors uh are +separate representations of the visual + + align:start position:0% +separate representations of the visual + + + align:start position:0% +separate representations of the visual +field or separate in some way in their + + align:start position:0% +field or separate in some way in their + + + align:start position:0% +field or separate in some way in their +in the like metrop physiological + + align:start position:0% +in the like metrop physiological + + + align:start position:0% +in the like metrop physiological +recording + + align:start position:0% + + + + align:start position:0% + +studies they all have at least a partial + + align:start position:0% +studies they all have at least a partial + + + align:start position:0% +studies they all have at least a partial +representation separate from the others + + align:start position:0% +representation separate from the others + + + align:start position:0% +representation separate from the others +of the visual + + align:start position:0% +of the visual + + + align:start position:0% +of the visual +field so you can see how the visual + + align:start position:0% +field so you can see how the visual + + + align:start position:0% +field so you can see how the visual +areas have expanded into the posterior + + align:start position:0% +areas have expanded into the posterior + + + align:start position:0% +areas have expanded into the posterior +parietal region and the temporal region + + align:start position:0% +parietal region and the temporal region + + + align:start position:0% +parietal region and the temporal region +from the middle temporal area here all + + align:start position:0% +from the middle temporal area here all + + + align:start position:0% +from the middle temporal area here all +the way down into the in inerior Temple + + align:start position:0% +the way down into the in inerior Temple + + + align:start position:0% +the way down into the in inerior Temple +lobe + + align:start position:0% +lobe + + + align:start position:0% +lobe +okay + + align:start position:0% + + + + align:start position:0% + +what's the specialization of small + + align:start position:0% +what's the specialization of small + + + align:start position:0% +what's the specialization of small +rodents they're using their + + align:start position:0% +rodents they're using their + + + align:start position:0% +rodents they're using their +whiskers what's happened in the brain of + + align:start position:0% +whiskers what's happened in the brain of + + + align:start position:0% +whiskers what's happened in the brain of +these animals they have a specialized + + align:start position:0% +these animals they have a specialized + + + align:start position:0% +these animals they have a specialized +sense + + align:start position:0% +sense + + + align:start position:0% +sense +too but it's not like any of the others + + align:start position:0% +too but it's not like any of the others + + + align:start position:0% +too but it's not like any of the others +we've just looked at and we don't have + + align:start position:0% +we've just looked at and we don't have + + + align:start position:0% +we've just looked at and we don't have +it the Barrel Fields each + + align:start position:0% +it the Barrel Fields each + + + align:start position:0% +it the Barrel Fields each +Barrel named because of the way it looks + + align:start position:0% +Barrel named because of the way it looks + + + align:start position:0% +Barrel named because of the way it looks +in the + + align:start position:0% +in the + + + align:start position:0% +in the +hystology represents one whisker and uh + + align:start position:0% +hystology represents one whisker and uh + + + align:start position:0% +hystology represents one whisker and uh +these are sections of the cortex that + + align:start position:0% +these are sections of the cortex that + + + align:start position:0% +these are sections of the cortex that +have + + align:start position:0% +have + + + align:start position:0% +have +been they try to flatten the cortex and + + align:start position:0% +been they try to flatten the cortex and + + + align:start position:0% +been they try to flatten the cortex and +cut it um or at least they cut it + + align:start position:0% +cut it um or at least they cut it + + + align:start position:0% +cut it um or at least they cut it +tangential to the surface and here + + align:start position:0% +tangential to the surface and here + + + align:start position:0% +tangential to the surface and here +they've taken different levels and they + + align:start position:0% +they've taken different levels and they + + + align:start position:0% +they've taken different levels and they +go down through this area of the + + align:start position:0% +go down through this area of the + + + align:start position:0% +go down through this area of the +parietal lobe and they see these + + align:start position:0% +parietal lobe and they see these + + + align:start position:0% +parietal lobe and they see these +barrels we'd have to blow that up to see + + align:start position:0% +barrels we'd have to blow that up to see + + + align:start position:0% +barrels we'd have to blow that up to see +how these really look like barrels + + align:start position:0% +how these really look like barrels + + + align:start position:0% +how these really look like barrels +they're crowded neurons packed neurons + + align:start position:0% +they're crowded neurons packed neurons + + + align:start position:0% +they're crowded neurons packed neurons +around the edges and very few in the + + align:start position:0% +around the edges and very few in the + + + align:start position:0% +around the edges and very few in the +middle and if you look in the middle of + + align:start position:0% +middle and if you look in the middle of + + + align:start position:0% +middle and if you look in the middle of +the barrels these would all the cells + + align:start position:0% +the barrels these would all the cells + + + align:start position:0% +the barrels these would all the cells +would be in the dark areas here this is + + align:start position:0% +would be in the dark areas here this is + + + align:start position:0% +would be in the dark areas here this is +stained for ACS you + + align:start position:0% +stained for ACS you + + + align:start position:0% +stained for ACS you +see the axons from the phalus come up + + align:start position:0% +see the axons from the phalus come up + + + align:start position:0% +see the axons from the phalus come up +representing each + + align:start position:0% +representing each + + + align:start position:0% +representing each +whisker coming up in the middle of those + + align:start position:0% +whisker coming up in the middle of those + + + align:start position:0% +whisker coming up in the middle of those +barrels and terminating so it's a very + + align:start position:0% +barrels and terminating so it's a very + + + align:start position:0% +barrels and terminating so it's a very +specialized organization it's been very + + align:start position:0% +specialized organization it's been very + + + align:start position:0% +specialized organization it's been very +useful for electric physiological + + align:start position:0% +useful for electric physiological + + + align:start position:0% +useful for electric physiological +studies other CTIC sensory + + align:start position:0% +studies other CTIC sensory + + + align:start position:0% +studies other CTIC sensory +specializations exist too like the hand + + align:start position:0% +specializations exist too like the hand + + + align:start position:0% +specializations exist too like the hand +and apes and raccoons and certainly + + align:start position:0% +and apes and raccoons and certainly + + + align:start position:0% +and apes and raccoons and certainly +humans because of we have such high + + align:start position:0% +humans because of we have such high + + + align:start position:0% +humans because of we have such high +Acuity and motor + + align:start position:0% +Acuity and motor + + + align:start position:0% +Acuity and motor +control + + align:start position:0% +control + + + align:start position:0% +control +uh it also expanded cerebellum for + + align:start position:0% +uh it also expanded cerebellum for + + + align:start position:0% +uh it also expanded cerebellum for +coordinating those movements and I + + align:start position:0% +coordinating those movements and I + + + align:start position:0% +coordinating those movements and I +mention here the pensol tale and spider + + align:start position:0% +mention here the pensol tale and spider + + + align:start position:0% +mention here the pensol tale and spider +monkey and you get expanded + + align:start position:0% +monkey and you get expanded + + + align:start position:0% +monkey and you get expanded +representation of that taale in sensory + + align:start position:0% +representation of that taale in sensory + + + align:start position:0% +representation of that taale in sensory +and motor + + align:start position:0% +and motor + + + align:start position:0% +and motor +neocortex and uh this just shows the + + align:start position:0% +neocortex and uh this just shows the + + + align:start position:0% +neocortex and uh this just shows the +raccoon this is a picture from the book + + align:start position:0% +raccoon this is a picture from the book + + + align:start position:0% +raccoon this is a picture from the book +and it's comparing the quadi Mundi and + + align:start position:0% +and it's comparing the quadi Mundi and + + + align:start position:0% +and it's comparing the quadi Mundi and +the raccoon they differ tremendously in + + align:start position:0% +the raccoon they differ tremendously in + + + align:start position:0% +the raccoon they differ tremendously in +their use of their + + align:start position:0% +their use of their + + + align:start position:0% +their use of their +Cora the raccoon literally has a + + align:start position:0% +Cora the raccoon literally has a + + + align:start position:0% +Cora the raccoon literally has a +sensitive hand just like we do and if + + align:start position:0% +sensitive hand just like we do and if + + + align:start position:0% +sensitive hand just like we do and if +you look in the + + align:start position:0% +you look in the + + + align:start position:0% +you look in the +cortex this whole area outlined in red + + align:start position:0% +cortex this whole area outlined in red + + + align:start position:0% +cortex this whole area outlined in red +there here's a an enlargement part of it + + align:start position:0% +there here's a an enlargement part of it + + + align:start position:0% +there here's a an enlargement part of it +there's a separate little gyrus for each + + align:start position:0% + + + + align:start position:0% + +digit they have very + + align:start position:0% +digit they have very + + + align:start position:0% +digit they have very +fine sensory ability and corresponding + + align:start position:0% +fine sensory ability and corresponding + + + align:start position:0% +fine sensory ability and corresponding +motor control of that + + align:start position:0% +motor control of that + + + align:start position:0% +motor control of that +hand whereas if you look at the quad + + align:start position:0% +hand whereas if you look at the quad + + + align:start position:0% +hand whereas if you look at the quad +Mundi who also uses his for plaws as + + align:start position:0% +Mundi who also uses his for plaws as + + + align:start position:0% +Mundi who also uses his for plaws as +many animals do in feeding the + + align:start position:0% +many animals do in feeding the + + + align:start position:0% +many animals do in feeding the +corresponding area is much smaller and + + align:start position:0% +corresponding area is much smaller and + + + align:start position:0% +corresponding area is much smaller and +he doesn't have a separate gyus for each + + align:start position:0% +he doesn't have a separate gyus for each + + + align:start position:0% +he doesn't have a separate gyus for each +uh for each + + align:start position:0% +uh for each + + + align:start position:0% +uh for each +digit um does the have sensory + + align:start position:0% +digit um does the have sensory + + + align:start position:0% +digit um does the have sensory +abili he does have enhanced sensory + + align:start position:0% +abili he does have enhanced sensory + + + align:start position:0% +abili he does have enhanced sensory +abilities + + align:start position:0% +abilities + + + align:start position:0% +abilities +yeah and uh what may be a brain + + align:start position:0% +yeah and uh what may be a brain + + + align:start position:0% +yeah and uh what may be a brain +specialization of the human ability for + + align:start position:0% +specialization of the human ability for + + + align:start position:0% +specialization of the human ability for +complex social interactions and this + + align:start position:0% +complex social interactions and this + + + align:start position:0% +complex social interactions and this +would apply to many other primates that + + align:start position:0% +would apply to many other primates that + + + align:start position:0% +would apply to many other primates that +live in groups with complex social + + align:start position:0% +live in groups with complex social + + + align:start position:0% +live in groups with complex social +behavior what do we think there's + + align:start position:0% +behavior what do we think there's + + + align:start position:0% +behavior what do we think there's +increasing amount of work on this now + + align:start position:0% +increasing amount of work on this now + + + align:start position:0% +increasing amount of work on this now +especially the people studying the + + align:start position:0% +especially the people studying the + + + align:start position:0% +especially the people studying the +social brain here in the building + + align:start position:0% + + + + align:start position:0% + +yes in the neocortex especially + + align:start position:0% +yes in the neocortex especially + + + align:start position:0% +yes in the neocortex especially +prefrontal areas which is frontal lobe + + align:start position:0% +prefrontal areas which is frontal lobe + + + align:start position:0% +prefrontal areas which is frontal lobe +association areas we'll be defining all + + align:start position:0% +association areas we'll be defining all + + + align:start position:0% +association areas we'll be defining all +that when we uh + + align:start position:0% +that when we uh + + + align:start position:0% +that when we uh +later these are the areas that they keep + + align:start position:0% +later these are the areas that they keep + + + align:start position:0% +later these are the areas that they keep +localizing higher functions to and + + align:start position:0% +localizing higher functions to and + + + align:start position:0% +localizing higher functions to and +they'll talk about their + + align:start position:0% + + + + align:start position:0% + +evolution and I just want to point out I + + align:start position:0% +evolution and I just want to point out I + + + align:start position:0% +evolution and I just want to point out I +want I want to ask you if you remember + + align:start position:0% +want I want to ask you if you remember + + + align:start position:0% +want I want to ask you if you remember +what the + + align:start position:0% +what the + + + align:start position:0% +what the +specialization that I illustrate in the + + align:start position:0% +specialization that I illustrate in the + + + align:start position:0% +specialization that I illustrate in the +book The in the Akida which is the spiny + + align:start position:0% +book The in the Akida which is the spiny + + + align:start position:0% +book The in the Akida which is the spiny +an Eater of Australia he's got an + + align:start position:0% +an Eater of Australia he's got an + + + align:start position:0% +an Eater of Australia he's got an +enormous prefrontal cortex why would he + + align:start position:0% +enormous prefrontal cortex why would he + + + align:start position:0% +enormous prefrontal cortex why would he +have + + align:start position:0% + + + + align:start position:0% + +that you think it has to do with this is + + align:start position:0% +that you think it has to do with this is + + + align:start position:0% +that you think it has to do with this is +the pink area here it's relatively + + align:start position:0% +the pink area here it's relatively + + + align:start position:0% +the pink area here it's relatively +larger even than in humans just in + + align:start position:0% +larger even than in humans just in + + + align:start position:0% +larger even than in humans just in +relative to + + align:start position:0% +relative to + + + align:start position:0% +relative to +the in in the colors here are the motor + + align:start position:0% +the in in the colors here are the motor + + + align:start position:0% +the in in the colors here are the motor +area it's not sensory area visual area + + align:start position:0% +area it's not sensory area visual area + + + align:start position:0% +area it's not sensory area visual area +in + + align:start position:0% +in + + + align:start position:0% +in +green and uh the darker green is the + + align:start position:0% +green and uh the darker green is the + + + align:start position:0% +green and uh the darker green is the +auditory area and these are we would + + align:start position:0% +auditory area and these are we would + + + align:start position:0% +auditory area and these are we would +call them association + + align:start position:0% +call them association + + + align:start position:0% +call them association +areas but look at that prefrontal + + align:start position:0% +areas but look at that prefrontal + + + align:start position:0% +areas but look at that prefrontal +area so it has I assume it must have to + + align:start position:0% +area so it has I assume it must have to + + + align:start position:0% +area so it has I assume it must have to +do with his specialized feeding he's an + + align:start position:0% +do with his specialized feeding he's an + + + align:start position:0% +do with his specialized feeding he's an +ant eater and ants are very small how + + align:start position:0% +ant eater and ants are very small how + + + align:start position:0% +ant eater and ants are very small how +does he maximize his intake you know I + + align:start position:0% +does he maximize his intake you know I + + + align:start position:0% +does he maximize his intake you know I +think there's tremendous Demand on his + + align:start position:0% +think there's tremendous Demand on his + + + align:start position:0% +think there's tremendous Demand on his +working memory in a single glance he has + + align:start position:0% +working memory in a single glance he has + + + align:start position:0% +working memory in a single glance he has +to remember where dozens of ants are + + align:start position:0% +to remember where dozens of ants are + + + align:start position:0% +to remember where dozens of ants are +where they're disappearing and he's got + + align:start position:0% +where they're disappearing and he's got + + + align:start position:0% +where they're disappearing and he's got +to be able to go after + + align:start position:0% + + + + align:start position:0% + +them but that has never been + + align:start position:0% +them but that has never been + + + align:start position:0% +them but that has never been +analyzed + + align:start position:0% +analyzed + + + align:start position:0% +analyzed +okay one way to get it to be analyzed is + + align:start position:0% +okay one way to get it to be analyzed is + + + align:start position:0% +okay one way to get it to be analyzed is +to put it in a book and raise the issue + + align:start position:0% +to put it in a book and raise the issue + + + align:start position:0% +to put it in a book and raise the issue +people will look at + + align:start position:0% +people will look at + + + align:start position:0% +people will look at +it this is a question for you what other + + align:start position:0% +it this is a question for you what other + + + align:start position:0% +it this is a question for you what other +special izations might have noticeable + + align:start position:0% +special izations might have noticeable + + + align:start position:0% +special izations might have noticeable +brain manifestations I want you to think + + align:start position:0% +brain manifestations I want you to think + + + align:start position:0% +brain manifestations I want you to think +of something that I didn't mention in + + align:start position:0% +of something that I didn't mention in + + + align:start position:0% +of something that I didn't mention in +the + + align:start position:0% +the + + + align:start position:0% +the +chapter what other + + align:start position:0% +chapter what other + + + align:start position:0% +chapter what other +specializations in animals that you know + + align:start position:0% +specializations in animals that you know + + + align:start position:0% +specializations in animals that you know +about must have some special brain + + align:start position:0% +about must have some special brain + + + align:start position:0% +about must have some special brain +representation + + align:start position:0% + + + + align:start position:0% + +sorry anybody anybody + + align:start position:0% + + + + align:start position:0% + +else okay + + align:start position:0% +else okay + + + align:start position:0% +else okay +that's never been investigated do they + + align:start position:0% +that's never been investigated do they + + + align:start position:0% +that's never been investigated do they +have a specialized vestibular + + align:start position:0% +have a specialized vestibular + + + align:start position:0% +have a specialized vestibular +system what would you expect in that + + align:start position:0% + + + + align:start position:0% + +case anybody else + + align:start position:0% + + + + align:start position:0% + +specializations I ask yeah go ahead + + align:start position:0% +specializations I ask yeah go ahead + + + align:start position:0% +specializations I ask yeah go ahead +Rachel um I know that taxi dri has + + align:start position:0% + + + + align:start position:0% + +a parial neocortex parietal Association + + align:start position:0% +a parial neocortex parietal Association + + + align:start position:0% +a parial neocortex parietal Association +the area where we retain long-term + + align:start position:0% +the area where we retain long-term + + + align:start position:0% +the area where we retain long-term +Memories the map of the + + align:start position:0% +Memories the map of the + + + align:start position:0% +Memories the map of the +environment that's right there is some + + align:start position:0% +environment that's right there is some + + + align:start position:0% +environment that's right there is some +evidence for that it's a correlation and + + align:start position:0% +evidence for that it's a correlation and + + + align:start position:0% +evidence for that it's a correlation and +it's difficult to prove cause and effect + + align:start position:0% +it's difficult to prove cause and effect + + + align:start position:0% +it's difficult to prove cause and effect +but it's a very interesting calization + + align:start position:0% +but it's a very interesting calization + + + align:start position:0% +but it's a very interesting calization +these are London taxi + + align:start position:0% +these are London taxi + + + align:start position:0% +these are London taxi +drivers we know that the cortex is + + align:start position:0% +drivers we know that the cortex is + + + align:start position:0% +drivers we know that the cortex is +affected by learning uh in pretty + + align:start position:0% +affected by learning uh in pretty + + + align:start position:0% +affected by learning uh in pretty +interesting ways some of which are still + + align:start position:0% +interesting ways some of which are still + + + align:start position:0% +interesting ways some of which are still +being discovered I asked my wife this + + align:start position:0% +being discovered I asked my wife this + + + align:start position:0% +being discovered I asked my wife this +question this morning and she came up + + align:start position:0% +question this morning and she came up + + + align:start position:0% +question this morning and she came up +with specializations in the nose of some + + align:start position:0% +with specializations in the nose of some + + + align:start position:0% +with specializations in the nose of some +animals what was the one you thought of + + align:start position:0% +animals what was the one you thought of + + + align:start position:0% +animals what was the one you thought of +star Mo the star NOS + + align:start position:0% +star Mo the star NOS + + + align:start position:0% +star Mo the star NOS +mole John + + align:start position:0% +mole John + + + align:start position:0% +mole John +C uh actually turns about out to be one + + align:start position:0% +C uh actually turns about out to be one + + + align:start position:0% +C uh actually turns about out to be one +of the guys who's wrote an endorsement + + align:start position:0% +of the guys who's wrote an endorsement + + + align:start position:0% +of the guys who's wrote an endorsement +of my book so I like John cus and he he + + align:start position:0% +of my book so I like John cus and he he + + + align:start position:0% +of my book so I like John cus and he he +has studied this star not stos mole and + + align:start position:0% +has studied this star not stos mole and + + + align:start position:0% +has studied this star not stos mole and +and published representation of that it + + align:start position:0% +and published representation of that it + + + align:start position:0% +and published representation of that it +looks like a almost like a hand multiple + + align:start position:0% +looks like a almost like a hand multiple + + + align:start position:0% +looks like a almost like a hand multiple +fingers it's on their nose and they use + + align:start position:0% +fingers it's on their nose and they use + + + align:start position:0% +fingers it's on their nose and they use +it when they go through the ground okay + + align:start position:0% +it when they go through the ground okay + + + align:start position:0% +it when they go through the ground okay +and they use it for feeding + + align:start position:0% + + + + align:start position:0% + +yes that's another thing that we'll be + + align:start position:0% +yes that's another thing that we'll be + + + align:start position:0% +yes that's another thing that we'll be +dealing with a little bit but you're + + align:start position:0% +dealing with a little bit but you're + + + align:start position:0% +dealing with a little bit but you're +right it there are changes that occur in + + align:start position:0% +right it there are changes that occur in + + + align:start position:0% +right it there are changes that occur in +blind + + align:start position:0% +blind + + + align:start position:0% +blind +people and that's been studied in + + align:start position:0% +people and that's been studied in + + + align:start position:0% +people and that's been studied in +animals in very interesting ways and I + + align:start position:0% +animals in very interesting ways and I + + + align:start position:0% +animals in very interesting ways and I +would just add the one other animal with + + align:start position:0% +would just add the one other animal with + + + align:start position:0% +would just add the one other animal with +a specialized nose the + + align:start position:0% +a specialized nose the + + + align:start position:0% +a specialized nose the +elephant you know he's got incredible + + align:start position:0% +elephant you know he's got incredible + + + align:start position:0% +elephant you know he's got incredible +motor and sensory ability in that nose + + align:start position:0% +motor and sensory ability in that nose + + + align:start position:0% +motor and sensory ability in that nose +in that + + align:start position:0% +in that + + + align:start position:0% +in that +trunk all + + align:start position:0% + + + + align:start position:0% + +right this is the bigger class we won't + + align:start position:0% +right this is the bigger class we won't + + + align:start position:0% +right this is the bigger class we won't +quite get through it today but we'll do + + align:start position:0% +quite get through it today but we'll do + + + align:start position:0% +quite get through it today but we'll do +our best I want to give you an overview + + align:start position:0% +our best I want to give you an overview + + + align:start position:0% +our best I want to give you an overview +of forbrain structures and introduce the + + align:start position:0% +of forbrain structures and introduce the + + + align:start position:0% +of forbrain structures and introduce the +neocortex I want to start with this + + align:start position:0% +neocortex I want to start with this + + + align:start position:0% +neocortex I want to start with this +question what can an animal do without a + + align:start position:0% +question what can an animal do without a + + + align:start position:0% +question what can an animal do without a +forbrain and this has actually been done + + align:start position:0% +forbrain and this has actually been done + + + align:start position:0% +forbrain and this has actually been done +it's a pretty gross + + align:start position:0% +it's a pretty gross + + + align:start position:0% +it's a pretty gross +lesion you know they they either + + align:start position:0% +lesion you know they they either + + + align:start position:0% +lesion you know they they either +disconnect the forbrain from the + + align:start position:0% +disconnect the forbrain from the + + + align:start position:0% +disconnect the forbrain from the +midbrain with a cut in some cases they + + align:start position:0% +midbrain with a cut in some cases they + + + align:start position:0% +midbrain with a cut in some cases they +leave some of the + + align:start position:0% +leave some of the + + + align:start position:0% +leave some of the +connections so we it's been + + align:start position:0% +connections so we it's been + + + align:start position:0% +connections so we it's been +done the initial studies were were done + + align:start position:0% +done the initial studies were were done + + + align:start position:0% +done the initial studies were were done +in the + + align:start position:0% +in the + + + align:start position:0% +in the +cat uh but they then they were done on + + align:start position:0% +cat uh but they then they were done on + + + align:start position:0% +cat uh but they then they were done on +rats and pigeons it's all in early + + align:start position:0% +rats and pigeons it's all in early + + + align:start position:0% +rats and pigeons it's all in early +literature + + align:start position:0% +literature + + + align:start position:0% +literature +uh and let me just go through some of + + align:start position:0% +uh and let me just go through some of + + + align:start position:0% +uh and let me just go through some of +that you call that a des + + align:start position:0% +that you call that a des + + + align:start position:0% +that you call that a des +serration basically remove the cereal + + align:start position:0% +serration basically remove the cereal + + + align:start position:0% +serration basically remove the cereal +hemispheres or disconn completely + + align:start position:0% +hemispheres or disconn completely + + + align:start position:0% +hemispheres or disconn completely +disconnect them from other parts of the + + align:start position:0% +disconnect them from other parts of the + + + align:start position:0% +disconnect them from other parts of the +brain so this is our earlier diagram and + + align:start position:0% +brain so this is our earlier diagram and + + + align:start position:0% +brain so this is our earlier diagram and +what I'm showing here is uh the division + + align:start position:0% +what I'm showing here is uh the division + + + align:start position:0% +what I'm showing here is uh the division +spinal cord hindbrain midbrain + + align:start position:0% +spinal cord hindbrain midbrain + + + align:start position:0% +spinal cord hindbrain midbrain +and + + align:start position:0% +and + + + align:start position:0% +and +everything from here on is the for + + align:start position:0% +everything from here on is the for + + + align:start position:0% +everything from here on is the for +brain but the cereal + + align:start position:0% +brain but the cereal + + + align:start position:0% +brain but the cereal +hemispheres are everything in front of + + align:start position:0% +hemispheres are everything in front of + + + align:start position:0% +hemispheres are everything in front of +this line here this is Thalamus and + + align:start position:0% +this line here this is Thalamus and + + + align:start position:0% +this line here this is Thalamus and +hypothalamus they're tween bra so + + align:start position:0% +hypothalamus they're tween bra so + + + align:start position:0% +hypothalamus they're tween bra so +they're disconnecting all of these + + align:start position:0% + + + + align:start position:0% + +structures and of course in the mammals + + align:start position:0% +structures and of course in the mammals + + + align:start position:0% +structures and of course in the mammals +that they're doing it this area has + + align:start position:0% +that they're doing it this area has + + + align:start position:0% +that they're doing it this area has +expanded tremendously the neocortex has + + align:start position:0% +expanded tremendously the neocortex has + + + align:start position:0% +expanded tremendously the neocortex has +grown okay so they they get rid of all + + align:start position:0% +grown okay so they they get rid of all + + + align:start position:0% +grown okay so they they get rid of all +of + + align:start position:0% + + + + align:start position:0% + +them why do you think they got huge + + align:start position:0% +them why do you think they got huge + + + align:start position:0% +them why do you think they got huge +differences between the results in the + + align:start position:0% +differences between the results in the + + + align:start position:0% +differences between the results in the +cat and in the + + align:start position:0% + + + + align:start position:0% + +rat they both are mammals they both have + + align:start position:0% +rat they both are mammals they both have + + + align:start position:0% +rat they both are mammals they both have +a + + align:start position:0% +a + + + align:start position:0% +a +netics they both have a corpus + + align:start position:0% +netics they both have a corpus + + + align:start position:0% +netics they both have a corpus +stoom you know and they in both animals + + align:start position:0% +stoom you know and they in both animals + + + align:start position:0% +stoom you know and they in both animals +they disconnected those areas from the + + align:start position:0% +they disconnected those areas from the + + + align:start position:0% +they disconnected those areas from the +lower brain stem or from the brain stem + + align:start position:0% +lower brain stem or from the brain stem + + + align:start position:0% +lower brain stem or from the brain stem +period from the entire + + align:start position:0% + + + + align:start position:0% + +they got big differences what is the + + align:start position:0% +they got big differences what is the + + + align:start position:0% +they got big differences what is the +main thing I claim in the book is the + + align:start position:0% +main thing I claim in the book is the + + + align:start position:0% +main thing I claim in the book is the +difference because the early + + align:start position:0% +difference because the early + + + align:start position:0% +difference because the early +interpretations were not + + align:start position:0% +interpretations were not + + + align:start position:0% +interpretations were not +this and there's been all kinds of + + align:start position:0% +this and there's been all kinds of + + + align:start position:0% +this and there's been all kinds of +arguments about it yes number + + align:start position:0% +arguments about it yes number + + + align:start position:0% +arguments about it yes number +of yeah the quantity the number of + + align:start position:0% +of yeah the quantity the number of + + + align:start position:0% +of yeah the quantity the number of +connections severed very very + + align:start position:0% +connections severed very very + + + align:start position:0% +connections severed very very +good why would you be + + align:start position:0% +good why would you be + + + align:start position:0% +good why would you be +disconnecting so many more connections + + align:start position:0% +disconnecting so many more connections + + + align:start position:0% +disconnecting so many more connections +if you're dealing with a calf than in a + + align:start position:0% +if you're dealing with a calf than in a + + + align:start position:0% +if you're dealing with a calf than in a +rat they all they have the same kinds of + + align:start position:0% +rat they all they have the same kinds of + + + align:start position:0% +rat they all they have the same kinds of +Connections in qualitative + + align:start position:0% +Connections in qualitative + + + align:start position:0% +Connections in qualitative +terms but think of the size of the cat + + align:start position:0% +terms but think of the size of the cat + + + align:start position:0% +terms but think of the size of the cat +hemispheres he's got the highly folded + + align:start position:0% +hemispheres he's got the highly folded + + + align:start position:0% +hemispheres he's got the highly folded +cortex he got a relatively large KN of + + align:start position:0% +cortex he got a relatively large KN of + + + align:start position:0% +cortex he got a relatively large KN of +Cortex whereas the rat's a smooth brain + + align:start position:0% +Cortex whereas the rat's a smooth brain + + + align:start position:0% +Cortex whereas the rat's a smooth brain +mammal much smaller in relative terms a + + align:start position:0% +mammal much smaller in relative terms a + + + align:start position:0% +mammal much smaller in relative terms a +much smaller + + align:start position:0% +much smaller + + + align:start position:0% +much smaller +cortex + + align:start position:0% + + + + align:start position:0% + +okay well that's what we're going to + + align:start position:0% +okay well that's what we're going to + + + align:start position:0% +okay well that's what we're going to +consider + + align:start position:0% +consider + + + align:start position:0% +consider +why why is it I claim it's quantitative + + align:start position:0% +why why is it I claim it's quantitative + + + align:start position:0% +why why is it I claim it's quantitative +let's go through this but let's there's + + align:start position:0% +let's go through this but let's there's + + + align:start position:0% +let's go through this but let's there's +another question + + align:start position:0% + + + + align:start position:0% + +here actually both rats and cats the + + align:start position:0% +here actually both rats and cats the + + + align:start position:0% +here actually both rats and cats the +only way you can keep them alive + + align:start position:0% +only way you can keep them alive + + + align:start position:0% +only way you can keep them alive +after this kind of leion is to force + + align:start position:0% +after this kind of leion is to force + + + align:start position:0% +after this kind of leion is to force +feed + + align:start position:0% +feed + + + align:start position:0% +feed +them why was that the + + align:start position:0% + + + + align:start position:0% + +case they couldn't keep themselves + + align:start position:0% +case they couldn't keep themselves + + + align:start position:0% +case they couldn't keep themselves +alive does that mean they weren't + + align:start position:0% +alive does that mean they weren't + + + align:start position:0% +alive does that mean they weren't +hungry well in a sense that's true they + + align:start position:0% +hungry well in a sense that's true they + + + align:start position:0% +hungry well in a sense that's true they +never showed signs of hunger + + align:start position:0% +never showed signs of hunger + + + align:start position:0% +never showed signs of hunger +but if you put food in their mouth they + + align:start position:0% +but if you put food in their mouth they + + + align:start position:0% +but if you put food in their mouth they +ate so it's not true that they wouldn't + + align:start position:0% +ate so it's not true that they wouldn't + + + align:start position:0% +ate so it's not true that they wouldn't +eat + + align:start position:0% +eat + + + align:start position:0% +eat +they just didn't show the signs of + + align:start position:0% +they just didn't show the signs of + + + align:start position:0% +they just didn't show the signs of +hunger + + align:start position:0% +hunger + + + align:start position:0% +hunger +motivation + + align:start position:0% +motivation + + + align:start position:0% +motivation +okay now that the extensive study of the + + align:start position:0% +okay now that the extensive study of the + + + align:start position:0% +okay now that the extensive study of the +cerebration in the cat was done by these + + align:start position:0% +cerebration in the cat was done by these + + + align:start position:0% +cerebration in the cat was done by these +guys Mar and mo published in + + align:start position:0% + + + + align:start position:0% + +58 they called it the animal a purely + + align:start position:0% +58 they called it the animal a purely + + + align:start position:0% +58 they called it the animal a purely +reflex animal all he had was the + + align:start position:0% +reflex animal all he had was the + + + align:start position:0% +reflex animal all he had was the +reflexes they said he couldn't do any + + align:start position:0% +reflexes they said he couldn't do any + + + align:start position:0% +reflexes they said he couldn't do any +act that requires a series of reflexes + + align:start position:0% +act that requires a series of reflexes + + + align:start position:0% +act that requires a series of reflexes +that's the way they put it they were + + align:start position:0% +that's the way they put it they were + + + align:start position:0% +that's the way they put it they were +still very affected by the SR model of + + align:start position:0% +still very affected by the SR model of + + + align:start position:0% +still very affected by the SR model of +behavior and they + + align:start position:0% +behavior and they + + + align:start position:0% +behavior and they +thought they just couldn't put the + + align:start position:0% +thought they just couldn't put the + + + align:start position:0% +thought they just couldn't put the +reflexes together we would say it more + + align:start position:0% +reflexes together we would say it more + + + align:start position:0% +reflexes together we would say it more +broadly now in terms of sensor motor + + align:start position:0% +broadly now in terms of sensor motor + + + align:start position:0% +broadly now in terms of sensor motor +responses so let's look at what the + + align:start position:0% +responses so let's look at what the + + + align:start position:0% +responses so let's look at what the +animal can actually do and can it learn + + align:start position:0% +animal can actually do and can it learn + + + align:start position:0% +animal can actually do and can it learn +anything first of all the cats were an + + align:start position:0% +anything first of all the cats were an + + + align:start position:0% +anything first of all the cats were an +osmic and blind because those are + + align:start position:0% +osmic and blind because those are + + + align:start position:0% +osmic and blind because those are +two forbrain senses + + align:start position:0% +two forbrain senses + + + align:start position:0% +two forbrain senses +the cranial nerves for ofaction and + + align:start position:0% +the cranial nerves for ofaction and + + + align:start position:0% +the cranial nerves for ofaction and +vision come into the forbrain they're + + align:start position:0% +vision come into the forbrain they're + + + align:start position:0% +vision come into the forbrain they're +disconnecting the forbrain so of course + + align:start position:0% +disconnecting the forbrain so of course + + + align:start position:0% +disconnecting the forbrain so of course +vision and old action can affect their + + align:start position:0% + + + + align:start position:0% + +behavior they didn't eat spontaneously + + align:start position:0% +behavior they didn't eat spontaneously + + + align:start position:0% +behavior they didn't eat spontaneously +as we said but they also didn't groom + + align:start position:0% +as we said but they also didn't groom + + + align:start position:0% +as we said but they also didn't groom +themselves they showed no spontaneous + + align:start position:0% +themselves they showed no spontaneous + + + align:start position:0% +themselves they showed no spontaneous +sexual or other social behavior they + + align:start position:0% +sexual or other social behavior they + + + align:start position:0% +sexual or other social behavior they +could though elicit sexual reflexes by + + align:start position:0% +could though elicit sexual reflexes by + + + align:start position:0% +could though elicit sexual reflexes by +stimulating the genitals they could get + + align:start position:0% +stimulating the genitals they could get + + + align:start position:0% +stimulating the genitals they could get +lower dosis response from females they + + align:start position:0% +lower dosis response from females they + + + align:start position:0% +lower dosis response from females they +could get penile erection but it + + align:start position:0% +could get penile erection but it + + + align:start position:0% +could get penile erection but it +required + + align:start position:0% +required + + + align:start position:0% +required +stimulation they didn't show it in Norm + + align:start position:0% +stimulation they didn't show it in Norm + + + align:start position:0% +stimulation they didn't show it in Norm +in normal + + align:start position:0% +in normal + + + align:start position:0% +in normal +behavior okay let's look at what they + + align:start position:0% +behavior okay let's look at what they + + + align:start position:0% +behavior okay let's look at what they +could do they could stand could sit they + + align:start position:0% +could do they could stand could sit they + + + align:start position:0% +could do they could stand could sit they +could write themselves they tipped over + + align:start position:0% +could write themselves they tipped over + + + align:start position:0% +could write themselves they tipped over +they could walk they did show some + + align:start position:0% +they could walk they did show some + + + align:start position:0% +they could walk they did show some +abnormalities uh they even showed rage + + align:start position:0% +abnormalities uh they even showed rage + + + align:start position:0% +abnormalities uh they even showed rage +but only if you pinch them especially + + align:start position:0% +but only if you pinch them especially + + + align:start position:0% +but only if you pinch them especially +their + + align:start position:0% +their + + + align:start position:0% +their +tail they didn't bite or strike out + + align:start position:0% +tail they didn't bite or strike out + + + align:start position:0% +tail they didn't bite or strike out +normally they showed some autonomic + + align:start position:0% +normally they showed some autonomic + + + align:start position:0% +normally they showed some autonomic +regulation they showed pyo erection they + + align:start position:0% +regulation they showed pyo erection they + + + align:start position:0% +regulation they showed pyo erection they +would fluff up their hair in response to + + align:start position:0% +would fluff up their hair in response to + + + align:start position:0% +would fluff up their hair in response to +cold they had some thermal regulation it + + align:start position:0% +cold they had some thermal regulation it + + + align:start position:0% +cold they had some thermal regulation it +wasn't as good as normal their + + align:start position:0% +wasn't as good as normal their + + + align:start position:0% +wasn't as good as normal their +temperature would fluctuate more with + + align:start position:0% +temperature would fluctuate more with + + + align:start position:0% +temperature would fluctuate more with +changing temperatures of the environment + + align:start position:0% +changing temperatures of the environment + + + align:start position:0% +changing temperatures of the environment +but they still had some therm regulation + + align:start position:0% +but they still had some therm regulation + + + align:start position:0% +but they still had some therm regulation +so commonly if they wanted to have an + + align:start position:0% +so commonly if they wanted to have an + + + align:start position:0% +so commonly if they wanted to have an +easier time maintaining these animals + + align:start position:0% +easier time maintaining these animals + + + align:start position:0% +easier time maintaining these animals +and not have to give them injections of + + align:start position:0% +and not have to give them injections of + + + align:start position:0% +and not have to give them injections of +electrolytes and + + align:start position:0% +electrolytes and + + + align:start position:0% +electrolytes and +things they left the an is the the + + align:start position:0% +things they left the an is the the + + + align:start position:0% +things they left the an is the the +hypothalamus attached to the pituitary + + align:start position:0% +hypothalamus attached to the pituitary + + + align:start position:0% +hypothalamus attached to the pituitary +even though it was disconnected from the + + align:start position:0% +even though it was disconnected from the + + + align:start position:0% +even though it was disconnected from the +midbrain they left that hypo + + align:start position:0% +midbrain they left that hypo + + + align:start position:0% +midbrain they left that hypo +hypothalamic Island attached to the + + align:start position:0% +hypothalamic Island attached to the + + + align:start position:0% +hypothalamic Island attached to the +pituitary and then they had much better + + align:start position:0% +pituitary and then they had much better + + + align:start position:0% +pituitary and then they had much better +regulation of their internal + + align:start position:0% +regulation of their internal + + + align:start position:0% +regulation of their internal +environment + + align:start position:0% +environment + + + align:start position:0% +environment +they couldn't learn much they had + + align:start position:0% +they couldn't learn much they had + + + align:start position:0% +they couldn't learn much they had +condition eye blank condition + + align:start position:0% +condition eye blank condition + + + align:start position:0% +condition eye blank condition +respiratory changes but they didn't + + align:start position:0% +respiratory changes but they didn't + + + align:start position:0% +respiratory changes but they didn't +maintain it very + + align:start position:0% + + + + align:start position:0% + +long so what was it I just said this + + align:start position:0% +long so what was it I just said this + + + align:start position:0% +long so what was it I just said this +describe the behavior that shows how a + + align:start position:0% +describe the behavior that shows how a + + + align:start position:0% +describe the behavior that shows how a +cat without a forebrain shows no hunger + + align:start position:0% +cat without a forebrain shows no hunger + + + align:start position:0% +cat without a forebrain shows no hunger +and yet will eat when you put food in + + align:start position:0% +and yet will eat when you put food in + + + align:start position:0% +and yet will eat when you put food in +its mouth so what's he + + align:start position:0% + + + + align:start position:0% + +doing + + align:start position:0% + + + + align:start position:0% + +he's responding to the + + align:start position:0% +he's responding to the + + + align:start position:0% +he's responding to the +stimulation he will open his mouth touch + + align:start position:0% +stimulation he will open his mouth touch + + + align:start position:0% +stimulation he will open his mouth touch +his + + align:start position:0% +his + + + align:start position:0% +his +lip he will close his mouth on the food + + align:start position:0% +lip he will close his mouth on the food + + + align:start position:0% +lip he will close his mouth on the food +what does that if he's not + + align:start position:0% + + + + align:start position:0% + +hungry sorry + + align:start position:0% +hungry sorry + + + align:start position:0% +hungry sorry +procedural no I wouldn't say it's + + align:start position:0% +procedural no I wouldn't say it's + + + align:start position:0% +procedural no I wouldn't say it's +procedural memory I would say it's + + align:start position:0% +procedural memory I would say it's + + + align:start position:0% +procedural memory I would say it's +innate + + align:start position:0% +innate + + + align:start position:0% +innate +reflexes + + align:start position:0% +reflexes + + + align:start position:0% +reflexes +okay exactly like the baby + + align:start position:0% +okay exactly like the baby + + + align:start position:0% +okay exactly like the baby +suckling okay except + + align:start position:0% +suckling okay except + + + align:start position:0% +suckling okay except +babies the suckling will vary with how + + align:start position:0% +babies the suckling will vary with how + + + align:start position:0% +babies the suckling will vary with how +hungry they + + align:start position:0% +hungry they + + + align:start position:0% +hungry they +are here it didn't seem to but that's + + align:start position:0% +are here it didn't seem to but that's + + + align:start position:0% +are here it didn't seem to but that's +the question uh maybe it did vary a + + align:start position:0% +the question uh maybe it did vary a + + + align:start position:0% +the question uh maybe it did vary a +little bit with how hungry they were but + + align:start position:0% +little bit with how hungry they were but + + + align:start position:0% +little bit with how hungry they were but +the point is they didn't show any + + align:start position:0% + + + + align:start position:0% + +motivation + + align:start position:0% + + + + align:start position:0% + +yeah + + align:start position:0% + + + + align:start position:0% + +that's a big issue and how this how the + + align:start position:0% +that's a big issue and how this how the + + + align:start position:0% +that's a big issue and how this how the +uh the dopamine Pathways the role they + + align:start position:0% +uh the dopamine Pathways the role they + + + align:start position:0% +uh the dopamine Pathways the role they +play in + + align:start position:0% + + + + align:start position:0% + +feeding it's I + + align:start position:0% +feeding it's I + + + align:start position:0% +feeding it's I +the + + align:start position:0% +the + + + align:start position:0% +the +representation that we call + + align:start position:0% +representation that we call + + + align:start position:0% +representation that we call +representation of the motivational State + + align:start position:0% +representation of the motivational State + + + align:start position:0% +representation of the motivational State +the drive state is no longer it doesn't + + align:start position:0% +the drive state is no longer it doesn't + + + align:start position:0% +the drive state is no longer it doesn't +mean they don't have it if they left the + + align:start position:0% +mean they don't have it if they left the + + + align:start position:0% +mean they don't have it if they left the +forbrain there but just disconnected it + + align:start position:0% +forbrain there but just disconnected it + + + align:start position:0% +forbrain there but just disconnected it +but it means it can't influence the + + align:start position:0% +but it means it can't influence the + + + align:start position:0% +but it means it can't influence the +midbrain and hindbrain and spinal cord + + align:start position:0% +midbrain and hindbrain and spinal cord + + + align:start position:0% +midbrain and hindbrain and spinal cord +anymore all + + align:start position:0% +anymore all + + + align:start position:0% +anymore all +right so + + align:start position:0% +right so + + + align:start position:0% +right so +then this just summarizes if you do the + + align:start position:0% +then this just summarizes if you do the + + + align:start position:0% +then this just summarizes if you do the +same thing to a rat he can do more he's + + align:start position:0% +same thing to a rat he can do more he's + + + align:start position:0% +same thing to a rat he can do more he's +faster to recover his writing reflexes + + align:start position:0% +faster to recover his writing reflexes + + + align:start position:0% +faster to recover his writing reflexes +and Locomotion I said the C had writing + + align:start position:0% +and Locomotion I said the C had writing + + + align:start position:0% +and Locomotion I said the C had writing +reflexes and Locomotion but in fact he + + align:start position:0% +reflexes and Locomotion but in fact he + + + align:start position:0% +reflexes and Locomotion but in fact he +lost it for a while it took him a long + + align:start position:0% +lost it for a while it took him a long + + + align:start position:0% +lost it for a while it took him a long +time to recover the rats recover + + align:start position:0% +time to recover the rats recover + + + align:start position:0% +time to recover the rats recover +faster uh they did show some eating and + + align:start position:0% +faster uh they did show some eating and + + + align:start position:0% +faster uh they did show some eating and +drinking responses but again and more + + align:start position:0% +drinking responses but again and more + + + align:start position:0% +drinking responses but again and more +than the cat did it was a little more + + align:start position:0% +than the cat did it was a little more + + + align:start position:0% +than the cat did it was a little more +than the normal just simple reflexes but + + align:start position:0% +than the normal just simple reflexes but + + + align:start position:0% +than the normal just simple reflexes but +they didn't seek food so it was still + + align:start position:0% +they didn't seek food so it was still + + + align:start position:0% +they didn't seek food so it was still +fatal if they didn't force feed them + + align:start position:0% +fatal if they didn't force feed them + + + align:start position:0% +fatal if they didn't force feed them +and now the rats would groom themselves + + align:start position:0% +and now the rats would groom themselves + + + align:start position:0% +and now the rats would groom themselves +the cats never + + align:start position:0% +the cats never + + + align:start position:0% +the cats never +did + + align:start position:0% +did + + + align:start position:0% +did +so against that b and mock conclusion + + align:start position:0% +so against that b and mock conclusion + + + align:start position:0% +so against that b and mock conclusion +they did show a series of you could call + + align:start position:0% +they did show a series of you could call + + + align:start position:0% +they did show a series of you could call +it a series of reflexes if that's the + + align:start position:0% +it a series of reflexes if that's the + + + align:start position:0% +it a series of reflexes if that's the +language you want to + + align:start position:0% +language you want to + + + align:start position:0% +language you want to +use you could we would describe it as a + + align:start position:0% +use you could we would describe it as a + + + align:start position:0% +use you could we would describe it as a +fixed action pattern a inherited pattern + + align:start position:0% +fixed action pattern a inherited pattern + + + align:start position:0% +fixed action pattern a inherited pattern +of + + align:start position:0% +of + + + align:start position:0% +of +behavior they also showed some defensive + + align:start position:0% +behavior they also showed some defensive + + + align:start position:0% +behavior they also showed some defensive +behavior that went beyond what the cat + + align:start position:0% +behavior that went beyond what the cat + + + align:start position:0% +behavior that went beyond what the cat +did they would vocalized they would try + + align:start position:0% +did they would vocalized they would try + + + align:start position:0% +did they would vocalized they would try +to escape they would claw and + + align:start position:0% +to escape they would claw and + + + align:start position:0% +to escape they would claw and +bite they even showed some auditory + + align:start position:0% +bite they even showed some auditory + + + align:start position:0% +bite they even showed some auditory +localization in space remember the + + align:start position:0% +localization in space remember the + + + align:start position:0% +localization in space remember the +audition is the eighth cranial nerve and + + align:start position:0% +audition is the eighth cranial nerve and + + + align:start position:0% +audition is the eighth cranial nerve and +it comes into the hind brain uh and it + + align:start position:0% +it comes into the hind brain uh and it + + + align:start position:0% +it comes into the hind brain uh and it +can reach the midbrain and cause orany + + align:start position:0% +can reach the midbrain and cause orany + + + align:start position:0% +can reach the midbrain and cause orany +movements why did the rat do that not + + align:start position:0% +movements why did the rat do that not + + + align:start position:0% +movements why did the rat do that not +the + + align:start position:0% +the + + + align:start position:0% +the +cat so some people said the cat's + + align:start position:0% +cat so some people said the cat's + + + align:start position:0% +cat so some people said the cat's +forbrain has taken over more of the + + align:start position:0% +forbrain has taken over more of the + + + align:start position:0% +forbrain has taken over more of the +function than the rat + + align:start position:0% +function than the rat + + + align:start position:0% +function than the rat +Forin but as the upper parts of the + + align:start position:0% +Forin but as the upper parts of the + + + align:start position:0% +Forin but as the upper parts of the +brain involve especially the cortex it + + align:start position:0% +brain involve especially the cortex it + + + align:start position:0% +brain involve especially the cortex it +takes over lower functions that was the + + align:start position:0% +takes over lower functions that was the + + + align:start position:0% +takes over lower functions that was the +way people thought about + + align:start position:0% +way people thought about + + + align:start position:0% +way people thought about +it and I'm asking is that the best way + + align:start position:0% +it and I'm asking is that the best way + + + align:start position:0% +it and I'm asking is that the best way +to describe the + + align:start position:0% + + + + align:start position:0% + +results and they say + + align:start position:0% + + + + align:start position:0% + +no so some people said well you take + + align:start position:0% +no so some people said well you take + + + align:start position:0% +no so some people said well you take +the the cerebal hemisphere is away they + + align:start position:0% +the the cerebal hemisphere is away they + + + align:start position:0% +the the cerebal hemisphere is away they +lose all their learned + + align:start position:0% + + + + align:start position:0% + +behavior + + align:start position:0% +behavior + + + align:start position:0% +behavior +let's look at that by looking now at + + align:start position:0% +let's look at that by looking now at + + + align:start position:0% +let's look at that by looking now at +another animal where Des celbration has + + align:start position:0% +another animal where Des celbration has + + + align:start position:0% +another animal where Des celbration has +occurred and that was in the + + align:start position:0% +occurred and that was in the + + + align:start position:0% +occurred and that was in the +pigeon these were earlier than the other + + align:start position:0% +pigeon these were earlier than the other + + + align:start position:0% +pigeon these were earlier than the other +studies earlier than the cat and rat + + align:start position:0% +studies earlier than the cat and rat + + + align:start position:0% +studies earlier than the cat and rat +studies okay they were done by Dutch + + align:start position:0% +studies okay they were done by Dutch + + + align:start position:0% +studies okay they were done by Dutch +people and uh it was all written in + + align:start position:0% +people and uh it was all written in + + + align:start position:0% +people and uh it was all written in +German viser and + + align:start position:0% +German viser and + + + align:start position:0% +German viser and +radok and uh 1935 and 37 they published + + align:start position:0% +radok and uh 1935 and 37 they published + + + align:start position:0% +radok and uh 1935 and 37 they published +this + + align:start position:0% +this + + + align:start position:0% +this +uh they showed after the the cerebration + + align:start position:0% +uh they showed after the the cerebration + + + align:start position:0% +uh they showed after the the cerebration +they showed their basic repertoire of + + align:start position:0% +they showed their basic repertoire of + + + align:start position:0% +they showed their basic repertoire of +unlearned + + align:start position:0% +unlearned + + + align:start position:0% +unlearned +reactions they would fly if you threw + + align:start position:0% +reactions they would fly if you threw + + + align:start position:0% +reactions they would fly if you threw +them into the + + align:start position:0% +them into the + + + align:start position:0% +them into the +air but they wouldn't start flying + + align:start position:0% +air but they wouldn't start flying + + + align:start position:0% +air but they wouldn't start flying +spontaneously you had to throw them into + + align:start position:0% +spontaneously you had to throw them into + + + align:start position:0% +spontaneously you had to throw them into +the air and while they were flying they + + align:start position:0% +the air and while they were flying they + + + align:start position:0% +the air and while they were flying they +would avoid vertical sticks of course + + align:start position:0% +would avoid vertical sticks of course + + + align:start position:0% +would avoid vertical sticks of course +this was all done + + align:start position:0% +this was all done + + + align:start position:0% +this was all done +indoors they would land on horizontal + + align:start position:0% +indoors they would land on horizontal + + + align:start position:0% +indoors they would land on horizontal +sticks but then they found out they + + align:start position:0% +sticks but then they found out they + + + align:start position:0% +sticks but then they found out they +would land even on the back of a dog or + + align:start position:0% +would land even on the back of a dog or + + + align:start position:0% +would land even on the back of a dog or +a cat so what's + + align:start position:0% +a cat so what's + + + align:start position:0% +a cat so what's +happened they forgot dogs and cats can + + align:start position:0% +happened they forgot dogs and cats can + + + align:start position:0% +happened they forgot dogs and cats can +be dangerous to + + align:start position:0% +be dangerous to + + + align:start position:0% +be dangerous to +pigeons + + align:start position:0% +pigeons + + + align:start position:0% +pigeons +uh there was a lot of indication more + + align:start position:0% +uh there was a lot of indication more + + + align:start position:0% +uh there was a lot of indication more +complicated Behavior patterns that + + align:start position:0% +complicated Behavior patterns that + + + align:start position:0% +complicated Behavior patterns that +depended some degree on learning during + + align:start position:0% +depended some degree on learning during + + + align:start position:0% +depended some degree on learning during +development were lost in these + + align:start position:0% +development were lost in these + + + align:start position:0% +development were lost in these +animals + + align:start position:0% +animals + + + align:start position:0% +animals +so my hypothesis is that the forbrain is + + align:start position:0% +so my hypothesis is that the forbrain is + + + align:start position:0% +so my hypothesis is that the forbrain is +very very important in linking together + + align:start position:0% +very very important in linking together + + + align:start position:0% +very very important in linking together +by learning the species typical action + + align:start position:0% +by learning the species typical action + + + align:start position:0% +by learning the species typical action +patterns fixed action patterns that are + + align:start position:0% +patterns fixed action patterns that are + + + align:start position:0% +patterns fixed action patterns that are +built + + align:start position:0% +built + + + align:start position:0% +built +in and therefore genetically genetically + + align:start position:0% +in and therefore genetically genetically + + + align:start position:0% +in and therefore genetically genetically +determined but we still learn to link + + align:start position:0% +determined but we still learn to link + + + align:start position:0% +determined but we still learn to link +those things together we inherit the + + align:start position:0% +those things together we inherit the + + + align:start position:0% +those things together we inherit the +ability to do this to do this but that + + align:start position:0% +ability to do this to do this but that + + + align:start position:0% +ability to do this to do this but that +doesn't mean we can you know we learn + + align:start position:0% +doesn't mean we can you know we learn + + + align:start position:0% +doesn't mean we can you know we learn +how to grasp a corner that doesn't mean + + align:start position:0% +how to grasp a corner that doesn't mean + + + align:start position:0% +how to grasp a corner that doesn't mean +we learn how to play the piano it's not + + align:start position:0% +we learn how to play the piano it's not + + + align:start position:0% +we learn how to play the piano it's not +not innate just the movements are but we + + align:start position:0% +not innate just the movements are but we + + + align:start position:0% +not innate just the movements are but we +link them in different ways by learning + + align:start position:0% +link them in different ways by learning + + + align:start position:0% +link them in different ways by learning +and that's mostly + + align:start position:0% +and that's mostly + + + align:start position:0% +and that's mostly +a uh function of the Corpus triom but + + align:start position:0% +a uh function of the Corpus triom but + + + align:start position:0% +a uh function of the Corpus triom but +first I want you to understand now's + + align:start position:0% +first I want you to understand now's + + + align:start position:0% +first I want you to understand now's +terms he uses these terms stability of + + align:start position:0% +terms he uses these terms stability of + + + align:start position:0% +terms he uses these terms stability of +the internal environment stability in + + align:start position:0% +the internal environment stability in + + + align:start position:0% +the internal environment stability in +space and stability in + + align:start position:0% +space and stability in + + + align:start position:0% +space and stability in +time and they involve different parts of + + align:start position:0% +time and they involve different parts of + + + align:start position:0% +time and they involve different parts of +the + + align:start position:0% + + + + align:start position:0% + +brain + + align:start position:0% + + + + align:start position:0% + +so without a forbrain NAA said they + + align:start position:0% +so without a forbrain NAA said they + + + align:start position:0% +so without a forbrain NAA said they +still had pretty good stability in space + + align:start position:0% +still had pretty good stability in space + + + align:start position:0% +still had pretty good stability in space +meaning they could balance they could + + align:start position:0% +meaning they could balance they could + + + align:start position:0% +meaning they could balance they could +write themselves they could move + + align:start position:0% +write themselves they could move + + + align:start position:0% +write themselves they could move +around they had quite a bit of stability + + align:start position:0% +around they had quite a bit of stability + + + align:start position:0% +around they had quite a bit of stability +the internal environment but that was + + align:start position:0% +the internal environment but that was + + + align:start position:0% +the internal environment but that was +much better if the hypothalamus was left + + align:start position:0% +much better if the hypothalamus was left + + + align:start position:0% +much better if the hypothalamus was left +intact but their stability in + + align:start position:0% +intact but their stability in + + + align:start position:0% +intact but their stability in +time was really messed up because their + + align:start position:0% +time was really messed up because their + + + align:start position:0% +time was really messed up because their +behavior is just their actions seemed to + + align:start position:0% +behavior is just their actions seemed to + + + align:start position:0% +behavior is just their actions seemed to +depend on the current + + align:start position:0% +depend on the current + + + align:start position:0% +depend on the current +inputs they had little or no motivation + + align:start position:0% +inputs they had little or no motivation + + + align:start position:0% +inputs they had little or no motivation +initiated Behavior little or no + + align:start position:0% +initiated Behavior little or no + + + align:start position:0% +initiated Behavior little or no +long-term + + align:start position:0% +long-term + + + align:start position:0% +long-term +memory and of course when you're dealing + + align:start position:0% +memory and of course when you're dealing + + + align:start position:0% +memory and of course when you're dealing +with mammals they lose a lot of sensory + + align:start position:0% +with mammals they lose a lot of sensory + + + align:start position:0% +with mammals they lose a lot of sensory +and motor Acuity they don't have fine + + align:start position:0% +and motor Acuity they don't have fine + + + align:start position:0% +and motor Acuity they don't have fine +movements uh they can't respond to + + align:start position:0% +movements uh they can't respond to + + + align:start position:0% +movements uh they can't respond to +detail the way they can with the + + align:start position:0% +detail the way they can with the + + + align:start position:0% +detail the way they can with the +cortex if you spare the Corpus Statum + + align:start position:0% +cortex if you spare the Corpus Statum + + + align:start position:0% +cortex if you spare the Corpus Statum +they can do a lot more uh + + align:start position:0% +they can do a lot more uh + + + align:start position:0% +they can do a lot more uh +I'm not going to spend a lot of time on + + align:start position:0% +I'm not going to spend a lot of time on + + + align:start position:0% +I'm not going to spend a lot of time on +that you can read this it's all in the + + align:start position:0% +that you can read this it's all in the + + + align:start position:0% +that you can read this it's all in the +chapter they've also varied instead of + + align:start position:0% +chapter they've also varied instead of + + + align:start position:0% +chapter they've also varied instead of +taking out the whole forebrain they just + + align:start position:0% +taking out the whole forebrain they just + + + align:start position:0% +taking out the whole forebrain they just +take out they just do decortications in + + align:start position:0% +take out they just do decortications in + + + align:start position:0% +take out they just do decortications in +various + + align:start position:0% +various + + + align:start position:0% +various +animals and the basic conclusion of + + align:start position:0% +animals and the basic conclusion of + + + align:start position:0% +animals and the basic conclusion of +those studies is that the more the + + align:start position:0% +those studies is that the more the + + + align:start position:0% +those studies is that the more the +cortex you take out the more deficient + + align:start position:0% +cortex you take out the more deficient + + + align:start position:0% +cortex you take out the more deficient +the animal is in a sensory motor + + align:start position:0% +the animal is in a sensory motor + + + align:start position:0% +the animal is in a sensory motor +control again a lot depends on + + align:start position:0% +control again a lot depends on + + + align:start position:0% +control again a lot depends on +quantity as much as people people tried + + align:start position:0% +quantity as much as people people tried + + + align:start position:0% +quantity as much as people people tried +to explain the behavior the effects of + + align:start position:0% +to explain the behavior the effects of + + + align:start position:0% +to explain the behavior the effects of +these lesions in terms of specific + + align:start position:0% +these lesions in terms of specific + + + align:start position:0% +these lesions in terms of specific +cortical areas + + align:start position:0% +cortical areas + + + align:start position:0% +cortical areas +removed and there was some correlation + + align:start position:0% +removed and there was some correlation + + + align:start position:0% +removed and there was some correlation +but it seemed that the biggest Factor + + align:start position:0% +but it seemed that the biggest Factor + + + align:start position:0% +but it seemed that the biggest Factor +was just the amount of Cortex they took + + align:start position:0% + + + + align:start position:0% + +up + + align:start position:0% +up + + + align:start position:0% +up +so that leads us to + + align:start position:0% +so that leads us to + + + align:start position:0% +so that leads us to +explaining this term invented by F + + align:start position:0% +explaining this term invented by F + + + align:start position:0% +explaining this term invented by F +mono uh long long time ago when we + + align:start position:0% +mono uh long long time ago when we + + + align:start position:0% +mono uh long long time ago when we +discussed cortical spinal diastasis some + + align:start position:0% +discussed cortical spinal diastasis some + + + align:start position:0% +discussed cortical spinal diastasis some +very interesting + + align:start position:0% +very interesting + + + align:start position:0% +very interesting +analyses what is meant by that term what + + align:start position:0% +analyses what is meant by that term what + + + align:start position:0% +analyses what is meant by that term what +does it mean + + align:start position:0% +does it mean + + + align:start position:0% +does it mean +diis you know what a Schism is cut + + align:start position:0% +diis you know what a Schism is cut + + + align:start position:0% +diis you know what a Schism is cut +something into two + + align:start position:0% +something into two + + + align:start position:0% +something into two +parts + + align:start position:0% +parts + + + align:start position:0% +parts +diis separation of two + + align:start position:0% +diis separation of two + + + align:start position:0% +diis separation of two +things so I want to know why is + + align:start position:0% +things so I want to know why is + + + align:start position:0% +things so I want to know why is +understanding of this phenomenon so + + align:start position:0% +understanding of this phenomenon so + + + align:start position:0% +understanding of this phenomenon so +important in interpreting these species + + align:start position:0% +important in interpreting these species + + + align:start position:0% +important in interpreting these species +differences in brain lesion effects and + + align:start position:0% +differences in brain lesion effects and + + + align:start position:0% +differences in brain lesion effects and +in fact in + + align:start position:0% +in fact in + + + align:start position:0% +in fact in +interpreting recovery of function in the + + align:start position:0% +interpreting recovery of function in the + + + align:start position:0% +interpreting recovery of function in the +human beings with brain + + align:start position:0% +human beings with brain + + + align:start position:0% +human beings with brain +damage and that's why I think it's so + + align:start position:0% +damage and that's why I think it's so + + + align:start position:0% +damage and that's why I think it's so +important to understand + + align:start position:0% + + + + align:start position:0% + +it in simple terms it means deaeration + + align:start position:0% +it in simple terms it means deaeration + + + align:start position:0% +it in simple terms it means deaeration +depression if you deafen a structure it + + align:start position:0% +depression if you deafen a structure it + + + align:start position:0% +depression if you deafen a structure it +REM me means you remove the inputs or at + + align:start position:0% +REM me means you remove the inputs or at + + + align:start position:0% +REM me means you remove the inputs or at +least a lot of them it's always a + + align:start position:0% +least a lot of them it's always a + + + align:start position:0% +least a lot of them it's always a +partial + + align:start position:0% +partial + + + align:start position:0% +partial +deaeration but with greater deaeration + + align:start position:0% +deaeration but with greater deaeration + + + align:start position:0% +deaeration but with greater deaeration +the greater the effect on those + + align:start position:0% +the greater the effect on those + + + align:start position:0% +the greater the effect on those +neurons so for example take the + + align:start position:0% +neurons so for example take the + + + align:start position:0% +neurons so for example take the +phenomenon of spinal shock do you know + + align:start position:0% +phenomenon of spinal shock do you know + + + align:start position:0% +phenomenon of spinal shock do you know +that term have you ever heard that has + + align:start position:0% +that term have you ever heard that has + + + align:start position:0% +that term have you ever heard that has +anybody ever heard of spinal shock + + align:start position:0% +anybody ever heard of spinal shock + + + align:start position:0% +anybody ever heard of spinal shock +before what is + + align:start position:0% +before what is + + + align:start position:0% +before what is +it + + align:start position:0% + + + + align:start position:0% + +but here you're thinking of dation as + + align:start position:0% +but here you're thinking of dation as + + + align:start position:0% +but here you're thinking of dation as +remover removal of sensory input and + + align:start position:0% +remover removal of sensory input and + + + align:start position:0% +remover removal of sensory input and +you're right that will cause deaeration + + align:start position:0% +you're right that will cause deaeration + + + align:start position:0% +you're right that will cause deaeration +of the dorsal horn neurons that are + + align:start position:0% +of the dorsal horn neurons that are + + + align:start position:0% +of the dorsal horn neurons that are +getting those + + align:start position:0% +getting those + + + align:start position:0% +getting those +inputs now let's talk about spinal shock + + align:start position:0% +inputs now let's talk about spinal shock + + + align:start position:0% +inputs now let's talk about spinal shock +it's a lesion of the spinal cord you if + + align:start position:0% +it's a lesion of the spinal cord you if + + + align:start position:0% +it's a lesion of the spinal cord you if +I get a spinal cord transsection say it + + align:start position:0% +I get a spinal cord transsection say it + + + align:start position:0% +I get a spinal cord transsection say it +bottom of the cervical + + align:start position:0% +bottom of the cervical + + + align:start position:0% +bottom of the cervical +region + + align:start position:0% +region + + + align:start position:0% +region +okay I don't just lose control of my + + align:start position:0% +okay I don't just lose control of my + + + align:start position:0% +okay I don't just lose control of my +legs and much of the control of my + + align:start position:0% +legs and much of the control of my + + + align:start position:0% +legs and much of the control of my +arms no I lose much more I lose even + + align:start position:0% +arms no I lose much more I lose even + + + align:start position:0% +arms no I lose much more I lose even +spinal reflexes I don't even show + + align:start position:0% +spinal reflexes I don't even show + + + align:start position:0% +spinal reflexes I don't even show +withdrawal reflexes or stretch reflexes + + align:start position:0% +withdrawal reflexes or stretch reflexes + + + align:start position:0% +withdrawal reflexes or stretch reflexes +the reflexes go but wait a minute in it + + align:start position:0% +the reflexes go but wait a minute in it + + + align:start position:0% +the reflexes go but wait a minute in it +they're spinal + + align:start position:0% +they're spinal + + + align:start position:0% +they're spinal +reflexes that's called spinal + + align:start position:0% +reflexes that's called spinal + + + align:start position:0% +reflexes that's called spinal +shock it takes a long time for spinal + + align:start position:0% +shock it takes a long time for spinal + + + align:start position:0% +shock it takes a long time for spinal +functions simple spinal reflexes that + + align:start position:0% +functions simple spinal reflexes that + + + align:start position:0% +functions simple spinal reflexes that +don't + + align:start position:0% +don't + + + align:start position:0% +don't +involve Pathways outside the spinal + + align:start position:0% +involve Pathways outside the spinal + + + align:start position:0% +involve Pathways outside the spinal +cords to to recover so here's my diagram + + align:start position:0% +cords to to recover so here's my diagram + + + align:start position:0% +cords to to recover so here's my diagram +of it here I've taken two species I'm + + align:start position:0% +of it here I've taken two species I'm + + + align:start position:0% +of it here I've taken two species I'm +showing something like a cortex here and + + align:start position:0% +showing something like a cortex here and + + + align:start position:0% +showing something like a cortex here and +an animal with a lot of it and an animal + + align:start position:0% +an animal with a lot of it and an animal + + + align:start position:0% +an animal with a lot of it and an animal +with less of it and here's a little + + align:start position:0% +with less of it and here's a little + + + align:start position:0% +with less of it and here's a little +diagram of the spinal cord and I'm + + align:start position:0% +diagram of the spinal cord and I'm + + + align:start position:0% +diagram of the spinal cord and I'm +showing a reflex pathway I + + align:start position:0% +showing a reflex pathway I + + + align:start position:0% +showing a reflex pathway I +just show neurons coming in and other + + align:start position:0% +just show neurons coming in and other + + + align:start position:0% +just show neurons coming in and other +neurons going out and they're connected + + align:start position:0% +neurons going out and they're connected + + + align:start position:0% +neurons going out and they're connected +in some way in the + + align:start position:0% +in some way in the + + + align:start position:0% +in some way in the +cord okay and then you do this you + + align:start position:0% +cord okay and then you do this you + + + align:start position:0% +cord okay and then you do this you +eliminate all those corticospinal + + align:start position:0% +eliminate all those corticospinal + + + align:start position:0% +eliminate all those corticospinal +connections this is really an a simple + + align:start position:0% +connections this is really an a simple + + + align:start position:0% +connections this is really an a simple +way simple way to depict what F Monaco + + align:start position:0% +way simple way to depict what F Monaco + + + align:start position:0% +way simple way to depict what F Monaco +described when he first described + + align:start position:0% +described when he first described + + + align:start position:0% +described when he first described +diastasis and he talked about cortical + + align:start position:0% +diastasis and he talked about cortical + + + align:start position:0% +diastasis and he talked about cortical +spinal diast thesis I just put into + + align:start position:0% +spinal diast thesis I just put into + + + align:start position:0% +spinal diast thesis I just put into +diagrams what he was saying + + align:start position:0% +diagrams what he was saying + + + align:start position:0% +diagrams what he was saying +I'm showing excitatory connections we'll + + align:start position:0% +I'm showing excitatory connections we'll + + + align:start position:0% +I'm showing excitatory connections we'll +ignore the inhibitory ones for + + align:start position:0% +ignore the inhibitory ones for + + + align:start position:0% +ignore the inhibitory ones for +now a lot more excitatory connections + + align:start position:0% +now a lot more excitatory connections + + + align:start position:0% +now a lot more excitatory connections +removed from the spinal cord in the + + align:start position:0% +removed from the spinal cord in the + + + align:start position:0% +removed from the spinal cord in the +animal with the larger cortex okay so + + align:start position:0% +animal with the larger cortex okay so + + + align:start position:0% +animal with the larger cortex okay so +what + + align:start position:0% +what + + + align:start position:0% +what +happens all these fibers are + + align:start position:0% + + + + align:start position:0% + +degenerated these neurons are less DEA + + align:start position:0% +degenerated these neurons are less DEA + + + align:start position:0% +degenerated these neurons are less DEA +and the smaller brained animal than + + align:start position:0% + + + + align:start position:0% + +these that means me the diis effect the + + align:start position:0% +these that means me the diis effect the + + + align:start position:0% +these that means me the diis effect the +degree of + + align:start position:0% +degree of + + + align:start position:0% +degree of +deaeration is greater in the larger + + align:start position:0% +deaeration is greater in the larger + + + align:start position:0% +deaeration is greater in the larger +brained + + align:start position:0% +brained + + + align:start position:0% +brained +animal so his spinal cord reflexes the + + align:start position:0% +animal so his spinal cord reflexes the + + + align:start position:0% +animal so his spinal cord reflexes the +spinal reflexes will take much longer to + + align:start position:0% +spinal reflexes will take much longer to + + + align:start position:0% +spinal reflexes will take much longer to +recover if I transect the spinal cord of + + align:start position:0% +recover if I transect the spinal cord of + + + align:start position:0% +recover if I transect the spinal cord of +a + + align:start position:0% +a + + + align:start position:0% +a +frog in not many days his spinal + + align:start position:0% +frog in not many days his spinal + + + align:start position:0% +frog in not many days his spinal +reflexes will + + align:start position:0% +reflexes will + + + align:start position:0% +reflexes will +recover if I do it in a dog + + align:start position:0% +recover if I do it in a dog + + + align:start position:0% +recover if I do it in a dog +it might take weeks and if I do it in + + align:start position:0% +it might take weeks and if I do it in + + + align:start position:0% +it might take weeks and if I do it in +humans might take + + align:start position:0% +humans might take + + + align:start position:0% +humans might take +months just to get the spinal reflexes + + align:start position:0% +months just to get the spinal reflexes + + + align:start position:0% +months just to get the spinal reflexes +back why because the neuron can fire + + align:start position:0% +back why because the neuron can fire + + + align:start position:0% +back why because the neuron can fire +Action potentials only + + align:start position:0% + + + + align:start position:0% + +if there is + + align:start position:0% +if there is + + + align:start position:0% +if there is +a depolarization of the membrane at the + + align:start position:0% +a depolarization of the membrane at the + + + align:start position:0% +a depolarization of the membrane at the +axon helic that reaches a critical level + + align:start position:0% +axon helic that reaches a critical level + + + align:start position:0% +axon helic that reaches a critical level +you know that from basic physiology + + align:start position:0% +you know that from basic physiology + + + align:start position:0% +you know that from basic physiology +okay if you remove a lot of it inhibit + + align:start position:0% +okay if you remove a lot of it inhibit + + + align:start position:0% +okay if you remove a lot of it inhibit +excitatory + + align:start position:0% +excitatory + + + align:start position:0% +excitatory +inputs then there will be more + + align:start position:0% +inputs then there will be more + + + align:start position:0% +inputs then there will be more +inhibitory inputs inputs from spinal + + align:start position:0% +inhibitory inputs inputs from spinal + + + align:start position:0% +inhibitory inputs inputs from spinal +inter neurons that are left and you just + + align:start position:0% +inter neurons that are left and you just + + + align:start position:0% +inter neurons that are left and you just +can't bring the the the cell to + + align:start position:0% +can't bring the the the cell to + + + align:start position:0% +can't bring the the the cell to +threshold anymore okay so then what + + align:start position:0% +threshold anymore okay so then what + + + align:start position:0% +threshold anymore okay so then what +happens after such + + align:start position:0% +happens after such + + + align:start position:0% +happens after such +lesions these two things + + align:start position:0% +lesions these two things + + + align:start position:0% +lesions these two things +happen there's collateral sprouting in + + align:start position:0% +happen there's collateral sprouting in + + + align:start position:0% +happen there's collateral sprouting in +the cord coll lateral sprouting by + + align:start position:0% +the cord coll lateral sprouting by + + + align:start position:0% +the cord coll lateral sprouting by +remaining + + align:start position:0% +remaining + + + align:start position:0% +remaining +inputs there's also what we call + + align:start position:0% +inputs there's also what we call + + + align:start position:0% +inputs there's also what we call +denervation Super sensitivity that means + + align:start position:0% +denervation Super sensitivity that means + + + align:start position:0% +denervation Super sensitivity that means +the + + align:start position:0% +the + + + align:start position:0% +the +neuron + + align:start position:0% +neuron + + + align:start position:0% +neuron +adjusts by increasing the number of + + align:start position:0% +adjusts by increasing the number of + + + align:start position:0% +adjusts by increasing the number of +receptors that respond to the + + align:start position:0% +receptors that respond to the + + + align:start position:0% +receptors that respond to the +neurotransmitters of + + align:start position:0% +neurotransmitters of + + + align:start position:0% +neurotransmitters of +the axons that are now + + align:start position:0% +the axons that are now + + + align:start position:0% +the axons that are now +missing so it will respond more strongly + + align:start position:0% +missing so it will respond more strongly + + + align:start position:0% +missing so it will respond more strongly +to other input that use the excitatory + + align:start position:0% +to other input that use the excitatory + + + align:start position:0% +to other input that use the excitatory +neurotransmitter okay so if + + align:start position:0% + + + + align:start position:0% + +we this animal will show some sprouting + + align:start position:0% +we this animal will show some sprouting + + + align:start position:0% +we this animal will show some sprouting +here this animal because he has more + + align:start position:0% +here this animal because he has more + + + align:start position:0% +here this animal because he has more +decantation will show more + + align:start position:0% +decantation will show more + + + align:start position:0% +decantation will show more +sprouting and there will be more + + align:start position:0% +sprouting and there will be more + + + align:start position:0% +sprouting and there will be more +receptors on these neurons and it will + + align:start position:0% +receptors on these neurons and it will + + + align:start position:0% +receptors on these neurons and it will +be more on the animal with a larger + + align:start position:0% +be more on the animal with a larger + + + align:start position:0% +be more on the animal with a larger +cortex you'll get more Super sensitivity + + align:start position:0% +cortex you'll get more Super sensitivity + + + align:start position:0% +cortex you'll get more Super sensitivity +those are the two factors and just over + + align:start position:0% +those are the two factors and just over + + + align:start position:0% +those are the two factors and just over +the time course of collateral sprouting + + align:start position:0% +the time course of collateral sprouting + + + align:start position:0% +the time course of collateral sprouting +that we know about and that has been + + align:start position:0% +that we know about and that has been + + + align:start position:0% +that we know about and that has been +studied you get quite a bit of + + align:start position:0% +studied you get quite a bit of + + + align:start position:0% +studied you get quite a bit of +recovery + + align:start position:0% + + + + align:start position:0% + +okay from this + + align:start position:0% + + + + align:start position:0% + +diation so basically these quantitative + + align:start position:0% +diation so basically these quantitative + + + align:start position:0% +diation so basically these quantitative +effects have to be considered whenever I + + align:start position:0% +effects have to be considered whenever I + + + align:start position:0% +effects have to be considered whenever I +get a brain + + align:start position:0% +get a brain + + + align:start position:0% +get a brain +lesion + + align:start position:0% +lesion + + + align:start position:0% +lesion +hopefully I won't but if I did okay if I + + align:start position:0% +hopefully I won't but if I did okay if I + + + align:start position:0% +hopefully I won't but if I did okay if I +get a brain leash I can't just consider + + align:start position:0% +get a brain leash I can't just consider + + + align:start position:0% +get a brain leash I can't just consider +well what were the functions now removed + + align:start position:0% +well what were the functions now removed + + + align:start position:0% +well what were the functions now removed +I've got to consider the areas that that + + align:start position:0% +I've got to consider the areas that that + + + align:start position:0% +I've got to consider the areas that that +area was connected to and how much + + align:start position:0% +area was connected to and how much + + + align:start position:0% +area was connected to and how much +deaeration that's caused I will lose + + align:start position:0% +deaeration that's caused I will lose + + + align:start position:0% +deaeration that's caused I will lose +midbrain function too if it projects + + align:start position:0% +midbrain function too if it projects + + + align:start position:0% +midbrain function too if it projects +heavily to the + + align:start position:0% +heavily to the + + + align:start position:0% +heavily to the +midbrain that's been studied + + align:start position:0% +midbrain that's been studied + + + align:start position:0% +midbrain that's been studied +corticotectal + + align:start position:0% + + + + align:start position:0% + +diastasis all + + align:start position:0% +diastasis all + + + align:start position:0% +diastasis all +right + + align:start position:0% +right + + + align:start position:0% +right +what part of the forbrain is most + + align:start position:0% +what part of the forbrain is most + + + align:start position:0% +what part of the forbrain is most +involved in the changes that occur + + align:start position:0% +involved in the changes that occur + + + align:start position:0% +involved in the changes that occur +during habit formation we call it + + align:start position:0% +during habit formation we call it + + + align:start position:0% +during habit formation we call it +procedural learning or implicit + + align:start position:0% +procedural learning or implicit + + + align:start position:0% +procedural learning or implicit +learning + + align:start position:0% +learning + + + align:start position:0% +learning +anybody it's the Corpus triot and we'll + + align:start position:0% +anybody it's the Corpus triot and we'll + + + align:start position:0% +anybody it's the Corpus triot and we'll +be talking about that we already + + align:start position:0% +be talking about that we already + + + align:start position:0% +be talking about that we already +mentioned it remember I said early + + align:start position:0% +mentioned it remember I said early + + + align:start position:0% +mentioned it remember I said early +inputs the olda very early when old + + align:start position:0% +inputs the olda very early when old + + + align:start position:0% +inputs the olda very early when old +faction was the main sense of the before + + align:start position:0% +faction was the main sense of the before + + + align:start position:0% +faction was the main sense of the before +there were anything except old faction + + align:start position:0% +there were anything except old faction + + + align:start position:0% +there were anything except old faction +coming into the the + + align:start position:0% +coming into the the + + + align:start position:0% +coming into the the +forbrain or the end brain was all old + + align:start position:0% +forbrain or the end brain was all old + + + align:start position:0% +forbrain or the end brain was all old +factory they went to the Statum that was + + align:start position:0% +factory they went to the Statum that was + + + align:start position:0% +factory they went to the Statum that was +the + + align:start position:0% +the + + + align:start position:0% +the +link to the lower structures that + + align:start position:0% +link to the lower structures that + + + align:start position:0% +link to the lower structures that +control + + align:start position:0% +control + + + align:start position:0% +control +movement and those connections were + + align:start position:0% +movement and those connections were + + + align:start position:0% +movement and those connections were +plastic they could be changed depending + + align:start position:0% +plastic they could be changed depending + + + align:start position:0% +plastic they could be changed depending +on the results the + + align:start position:0% + + + + align:start position:0% + +movement all right + + align:start position:0% +movement all right + + + align:start position:0% +movement all right +so what about the tween brain if you + + align:start position:0% +so what about the tween brain if you + + + align:start position:0% +so what about the tween brain if you +look at the just think of the main + + align:start position:0% +look at the just think of the main + + + align:start position:0% +look at the just think of the main +inputs to the tween + + align:start position:0% + + + + align:start position:0% + +brain and I it's relevant to this + + align:start position:0% +brain and I it's relevant to this + + + align:start position:0% +brain and I it's relevant to this +question according to the suggestions in + + align:start position:0% +question according to the suggestions in + + + align:start position:0% +question according to the suggestions in +the chapter what is a reason why sensory + + align:start position:0% +the chapter what is a reason why sensory + + + align:start position:0% +the chapter what is a reason why sensory +Pathways ascending to the forebrain + + align:start position:0% +Pathways ascending to the forebrain + + + align:start position:0% +Pathways ascending to the forebrain +almost always have a connection in the + + align:start position:0% +almost always have a connection in the + + + align:start position:0% +almost always have a connection in the +phus even the old factory actually to + + align:start position:0% +phus even the old factory actually to + + + align:start position:0% +phus even the old factory actually to +get to the cor neocortex have to go + + align:start position:0% +get to the cor neocortex have to go + + + align:start position:0% +get to the cor neocortex have to go +through the tween + + align:start position:0% +through the tween + + + align:start position:0% +through the tween +bra but why would that be why don't they + + align:start position:0% +bra but why would that be why don't they + + + align:start position:0% +bra but why would that be why don't they +just go directly + + align:start position:0% +just go directly + + + align:start position:0% +just go directly +so let's look at the early inputs optic + + align:start position:0% +so let's look at the early inputs optic + + + align:start position:0% +so let's look at the early inputs optic +inputs were very early and this is the + + align:start position:0% +inputs were very early and this is the + + + align:start position:0% +inputs were very early and this is the +picture of it here I'm + + align:start position:0% +picture of it here I'm + + + align:start position:0% +picture of it here I'm +showing them coming into the pineal area + + align:start position:0% +showing them coming into the pineal area + + + align:start position:0% +showing them coming into the pineal area +the pineal eye and here they are here's + + align:start position:0% +the pineal eye and here they are here's + + + align:start position:0% +the pineal eye and here they are here's +a lateral eye the ear the most primitive + + align:start position:0% +a lateral eye the ear the most primitive + + + align:start position:0% +a lateral eye the ear the most primitive +connection there goes directly to high + + align:start position:0% +connection there goes directly to high + + + align:start position:0% +connection there goes directly to high +the pels what is it doing it's + + align:start position:0% +the pels what is it doing it's + + + align:start position:0% +the pels what is it doing it's +controlling the activity rhythm changes + + align:start position:0% +controlling the activity rhythm changes + + + align:start position:0% +controlling the activity rhythm changes +during with the day night cycle the + + align:start position:0% +during with the day night cycle the + + + align:start position:0% +during with the day night cycle the +cycle of the + + align:start position:0% +cycle of the + + + align:start position:0% +cycle of the +Sun and just about all + + align:start position:0% +Sun and just about all + + + align:start position:0% +Sun and just about all +animals that is a system that's + + align:start position:0% +animals that is a system that's + + + align:start position:0% +animals that is a system that's +modulating the entire central nervous + + align:start position:0% +modulating the entire central nervous + + + align:start position:0% +modulating the entire central nervous +system that's what sleep and a waking is + + align:start position:0% +system that's what sleep and a waking is + + + align:start position:0% +system that's what sleep and a waking is +it's a cycle of change that affects the + + align:start position:0% +it's a cycle of change that affects the + + + align:start position:0% +it's a cycle of change that affects the +whole nervous system all + + align:start position:0% +whole nervous system all + + + align:start position:0% +whole nervous system all +right there's many other systems wide + + align:start position:0% +right there's many other systems wide + + + align:start position:0% +right there's many other systems wide +systemwide modulations too the + + align:start position:0% +systemwide modulations too the + + + align:start position:0% +systemwide modulations too the +here another area where secretions + + align:start position:0% +here another area where secretions + + + align:start position:0% +here another area where secretions +affect the whole animal the whole + + align:start position:0% +affect the whole animal the whole + + + align:start position:0% +affect the whole animal the whole +nervous + + align:start position:0% +nervous + + + align:start position:0% +nervous +system + + align:start position:0% +system + + + align:start position:0% +system +okay and there's more than that + + align:start position:0% +okay and there's more than that + + + align:start position:0% +okay and there's more than that +hypothalamus is affecting what goes + + align:start position:0% +hypothalamus is affecting what goes + + + align:start position:0% +hypothalamus is affecting what goes +through the + + align:start position:0% +through the + + + align:start position:0% +through the +phalus it's a modulator there are + + align:start position:0% +phalus it's a modulator there are + + + align:start position:0% +phalus it's a modulator there are +connections from + + align:start position:0% +connections from + + + align:start position:0% +connections from +hypothalamus to the thalamus we'll go + + align:start position:0% +hypothalamus to the thalamus we'll go + + + align:start position:0% +hypothalamus to the thalamus we'll go +over that in little more detail later + + align:start position:0% +over that in little more detail later + + + align:start position:0% +over that in little more detail later +and I think it was that modulation of + + align:start position:0% +and I think it was that modulation of + + + align:start position:0% +and I think it was that modulation of +the whole system that made it was + + align:start position:0% +the whole system that made it was + + + align:start position:0% +the whole system that made it was +important enough that I think it + + align:start position:0% +important enough that I think it + + + align:start position:0% +important enough that I think it +made it prevented the evolution of more + + align:start position:0% +made it prevented the evolution of more + + + align:start position:0% +made it prevented the evolution of more +direct connections there are a few more + + align:start position:0% +direct connections there are a few more + + + align:start position:0% +direct connections there are a few more +direct connections that have evolved but + + align:start position:0% +direct connections that have evolved but + + + align:start position:0% +direct connections that have evolved but +very few they almost all the sensory + + align:start position:0% +very few they almost all the sensory + + + align:start position:0% +very few they almost all the sensory +Pathways that go to the new cortex + + align:start position:0% +Pathways that go to the new cortex + + + align:start position:0% +Pathways that go to the new cortex +stopped in the in the + + align:start position:0% +stopped in the in the + + + align:start position:0% +stopped in the in the +Fon okay another part in those desate + + align:start position:0% +Fon okay another part in those desate + + + align:start position:0% +Fon okay another part in those desate +animals that you're removing is what we + + align:start position:0% +animals that you're removing is what we + + + align:start position:0% +animals that you're removing is what we +call the limic and brain basically all + + align:start position:0% +call the limic and brain basically all + + + align:start position:0% +call the limic and brain basically all +the parts that + + align:start position:0% + + + + align:start position:0% + +uh are connected to one structure you + + align:start position:0% +uh are connected to one structure you + + + align:start position:0% +uh are connected to one structure you +know what I'm talking about the lyic + + align:start position:0% +know what I'm talking about the lyic + + + align:start position:0% +know what I'm talking about the lyic +systems characterized by close + + align:start position:0% +systems characterized by close + + + align:start position:0% +systems characterized by close +interconnections with one portion of the + + align:start position:0% +interconnections with one portion of the + + + align:start position:0% +interconnections with one portion of the +upper brain stem what is + + align:start position:0% +upper brain stem what is + + + align:start position:0% +upper brain stem what is +it you can Define the lyic + + align:start position:0% +it you can Define the lyic + + + align:start position:0% +it you can Define the lyic +system those those structures that The + + align:start position:0% +system those those structures that The + + + align:start position:0% +system those those structures that The +Fringe of our hemispheres limic me means + + align:start position:0% +Fringe of our hemispheres limic me means + + + align:start position:0% +Fringe of our hemispheres limic me means +Fringe okay they're the more primitive + + align:start position:0% +Fringe okay they're the more primitive + + + align:start position:0% +Fringe okay they're the more primitive +parts that were there before any + + align:start position:0% +parts that were there before any + + + align:start position:0% +parts that were there before any +neocortex uh evolved and + + align:start position:0% +neocortex uh evolved and + + + align:start position:0% +neocortex uh evolved and +expanded what was the + + align:start position:0% + + + + align:start position:0% + +structure you didn't get + + align:start position:0% + + + + align:start position:0% + +that + + align:start position:0% +that + + + align:start position:0% +that +sorry what was it not the neocortex + + align:start position:0% +sorry what was it not the neocortex + + + align:start position:0% +sorry what was it not the neocortex +because the limic system is more + + align:start position:0% +because the limic system is more + + + align:start position:0% +because the limic system is more +primitive than it was there before there + + align:start position:0% +primitive than it was there before there + + + align:start position:0% +primitive than it was there before there +was a new cortex + + align:start position:0% +was a new cortex + + + align:start position:0% +was a new cortex +okay it's this structure + + align:start position:0% +okay it's this structure + + + align:start position:0% +okay it's this structure +here + + align:start position:0% +here + + + align:start position:0% +here +okay and I'm showing here hypothalamus + + align:start position:0% +okay and I'm showing here hypothalamus + + + align:start position:0% +okay and I'm showing here hypothalamus +and how it is interconnected not only + + align:start position:0% +and how it is interconnected not only + + + align:start position:0% +and how it is interconnected not only +with the factory system but with all + + align:start position:0% +with the factory system but with all + + + align:start position:0% +with the factory system but with all +these + + align:start position:0% +these + + + align:start position:0% +these +structures of the older parts of the + + align:start position:0% +structures of the older parts of the + + + align:start position:0% +structures of the older parts of the +brain the whole ancient pum we call them + + align:start position:0% +brain the whole ancient pum we call them + + + align:start position:0% +brain the whole ancient pum we call them +the dorsal p + + align:start position:0% +the dorsal p + + + align:start position:0% +the dorsal p +ium the medial pum and dorsal pum up + + align:start position:0% +ium the medial pum and dorsal pum up + + + align:start position:0% +ium the medial pum and dorsal pum up +here medial pum is the campus and then + + align:start position:0% +here medial pum is the campus and then + + + align:start position:0% +here medial pum is the campus and then +the lateral pum which is olfactory + + align:start position:0% +the lateral pum which is olfactory + + + align:start position:0% +the lateral pum which is olfactory +cortex and the ventral pum which also + + align:start position:0% +cortex and the ventral pum which also + + + align:start position:0% +cortex and the ventral pum which also +gets olfactory input includes the amular + + align:start position:0% +gets olfactory input includes the amular + + + align:start position:0% +gets olfactory input includes the amular +area those areas are all interconnected + + align:start position:0% +area those areas are all interconnected + + + align:start position:0% +area those areas are all interconnected +with the hypothalamus and that pretty + + align:start position:0% +with the hypothalamus and that pretty + + + align:start position:0% +with the hypothalamus and that pretty +much defines the lmic + + align:start position:0% +much defines the lmic + + + align:start position:0% +much defines the lmic +system and there are structures also in + + align:start position:0% +system and there are structures also in + + + align:start position:0% +system and there are structures also in +the mid brain that now at a point it out + + align:start position:0% +the mid brain that now at a point it out + + + align:start position:0% +the mid brain that now at a point it out +should be part of that because they are + + align:start position:0% +should be part of that because they are + + + align:start position:0% +should be part of that because they are +also closely interconnected with the + + align:start position:0% +also closely interconnected with the + + + align:start position:0% +also closely interconnected with the +hypothalamus and with the lindic system + + align:start position:0% +hypothalamus and with the lindic system + + + align:start position:0% +hypothalamus and with the lindic system +uh further + + align:start position:0% + + + + align:start position:0% + +forward all right I want you to read the + + align:start position:0% +forward all right I want you to read the + + + align:start position:0% +forward all right I want you to read the +rest of these I'll review a little bit + + align:start position:0% +rest of these I'll review a little bit + + + align:start position:0% +rest of these I'll review a little bit +of it at the beginning of the next class + + align:start position:0% +of it at the beginning of the next class + + + align:start position:0% +of it at the beginning of the next class +but uh I will mark this this is where we + + align:start position:0% +but uh I will mark this this is where we + + + align:start position:0% +but uh I will mark this this is where we +stop and uh I will post these + + align:start position:0% +stop and uh I will post these + + + align:start position:0% +stop and uh I will post these +online and uh + + align:start position:0% +online and uh + + + align:start position:0% +online and uh +we'll be able to finish this quickly + + align:start position:0% +we'll be able to finish this quickly + + + align:start position:0% +we'll be able to finish this quickly +next time and go on + + align:start position:0% +next time and go on + + + align:start position:0% +next time and go on +uh to uh class + + align:start position:0% + + + + align:start position:0% + +7even \ No newline at end of file diff --git a/tJ2AJJMcQXs.txt b/tJ2AJJMcQXs.txt new file mode 100644 index 0000000000000000000000000000000000000000..afe3b9077c86503afaf05417203d8f3480377af7 --- /dev/null +++ b/tJ2AJJMcQXs.txt @@ -0,0 +1,4031 @@ +The following +content is provided + +under a Creative +Commons license. + +Your support will help MIT +OpenCourseWare continue + +to offer high quality +educational resources for free. + +To make a donation or to +view additional materials + +from hundreds of MIT courses, +visit MIT OpenCourseWare + +at ocw.mit.edu. + +PROFESSOR: OK, in that +case, let's go on. + +At the end of last +class, we were + +beginning to talk about +the Doppler shift. + +And we defined our terms. + +And I guess I'll repeat the +definitions on the blackboard + +here. + +We are talking initially about +the case where the observer is + +stationary and the source is +moving with velocity v. We + +are talking +initially about sound + +waves, waves which have a fixed +speed relative to some medium. + +And the speed relative to +the medium will be called u. + +v will be the +velocity of recession, + +as shown on the diagram. + +Delta t sub s, s for source, +will be the time interval + +between wave crests as measured +at the source-- so period + +of wave at source. + +And delta t sub o +will be the period + +of the wave at the observer. + +And what we're +trying to calculate + +is the relationship +between delta t sub o + +and delta t sub s. + +OK, at this point, I'd +like to go to the screen + +and go through the +different stages of what + +happens as this +process takes place. + +We start in frame +one with an observer + +in some location, a source +at some different location. + +Source is moving to the right. + +Source is emitting +the first wave crest + +in this slide number one. + +Nothing too interesting so far. + +Next picture, the source +emits the second wave crest. + +But meanwhile, the +source has moved. + +The time between wave +crests as seen by the source + +is delta t sub s. + +So the distance that the source +will move during that time + +integral is v times +delta t sub s. + +And we'll call that delta l. + +And this really is +the important slide. + +I think I have it +highlighted here. + +That picture is what really +counts for the whole Doppler + +shift. + +It says that the +second wave crest + +has to travel a little further +than the first wave crest + +by this amount delta l. + +So delta l will be +the crucial quantity + +that will control the answer. + +Third slide, the +waves have traveled. + +Now the first crest +in this third frame + +has just hit the observer. + +Next frame, the last +crest, the second crest, + +has hit the observer. + +And to figure out +the Doppler shift + +from those images, +all we have to do + +is realize that if both +objects were stationary, + +there'd be no time difference +between observation and source. + +Each could occur later by +some fixed amount, the amount + +of time it would take +the sound wave to travel. + +But they will occur +later by the same amount + +if there was no motion. + +So if there's no +motion, delta t sub o + +would be equal to delta t sub +s, if there was no motion. + +But because there +is motion, we said + +that the wave, the +second crest, is + +going to have to travel +further by the amount delta l. + +So it'll be delayed +by the amount of time + +it takes for the wave +to travel delta l. + +And that's just delta +l divided by v-- + +so plus delta l divided by v. +And we know what delta l is. + +Delta l is just v +times delta t sub s. + +I'm sorry, this is divided by u. + +u is the speed of the wave. + +v is the speed of the source. + +So here we have in the +numerator v times delta t sub s, + +and the denominator is u. + +This is just what +we said delta l is. + +So this really is our result. + +It tells us what delta o is +in terms of delta t sub s. + +And we can solve for the ratio. + +It tells us that delta +t sub o over delta t + +sub s is equal to +1 plus v over u. + +Solve that equation. + +Now there's a +standard definition + +that's used to describe +redshifts, which + +is that this ratio, which is +also the ratio of wavelengths, + +which is how I +usually think of it, + +the wavelength at the +observer divided by the wave + +length at the source-- +the wave length + +being disproportional +to the delta t. + +The wave ones are just the +wave speed times delta t. + +This is defined to +be 1 plus z where + +z is what's called the redshift. + +And the astronomers +take out the one + +so that if both objects are +stationary, z is equal to 0. + +That corresponds +to know redshift. + +That means the wave length +is the same at the source + +and at the observer. + +So the ratio of the +wavelength as its observed + +to the wavelength of the source +is what's called 1 plus z. + +So in this case, it +follows immediately + +that the redshift for this +case is just v over u. + +So maybe I'll just write that +again in a box and label it. + +z is equal to v +over u corresponds + +to the nonrelativistic case, +or the sound wave case, + +with the source moving. + +OK? + +Everybody on board? + +Any questions? + +OK, straightforward +enough, I think. + +OK, now we will go on to do the +alternative simple case, where + +the observer is moving and +the source is stationary. + +So keep the source on the right +and the observer on the left. + +But this time it's the observer +that's moving again with speed + +v. So v is always for these +two cases in my notation + +the relative velocity between +the source and the observer. + +So now we have a new +sequence of pictures. + +So first picture again +is fairly trivial. + +The first wave crest is +being emitted by the source. + +Picture number two, +the second wave crest + +is emitted by the source. + +Picture number three, +the first wave crest + +arrives at the source. + +And picture number four +now, the second wave crest + +arrives at the source. + +And for this case, +it is this last frame + +where all the action is. + +The point is that between the +time when the first crest hits + +the source and the time +when the second crest hits + +the source, that is the time +between the third and fourth + +frame, the source has moved. + +And it's moved by +distance which is + +v times the time +between those images. + +And the time +between these images + +is just the time that +the source experiences + +between the receipt +of the two waves. + +And it's therefore what we've +been calling delta t sub + +o, the time interval as +measured by the observer. + +So the distance traveled +is just v times t sub o. + +And it's that last frame inside +that box where all the action + +happens for determining the +answer for this problem. + +So we can put that +into equations also. + +This time it's slightly +more complicated. + +It starts basically +with the same idea. + +Delta t sub o is +equal to delta t sub + +s, which is what it would +be if there was no motion. + +But it's a little bit longer +because of the extra distance + +the second pulse travels. + +And that extra distance +is again called delta l. + +So the time delay is again delta +l divided by u, the wave speed. + +But this time we have a +different formula for delta l. + +This time delta l is v times +delta t sub 0, instead of + +last time it was v +times delta t sub s. + +So this time the equation +is ever so slightly more + +complicated, because +delta t sub 0 + +appears on both sides +of the equation. + +Last time we +immediately wrote down + +an equation for delta t sub o. + +But nonetheless, this is one +equation with one unknown, + +so of course it's trivial to +solve it for delta t sub o. + +And when we do that, +we get delta t sub o. + +I'll maybe divide +by delta t sub s. + +By just doing a little +bit of algebra on that, + +you discover it's 1 +minus u over v inverse. + +And then z, the redshift, is +delta t sub 0 over delta t sub + +s minus 1 by definition. + +AUDIENCE: Is that +1 minus v over u? + +PROFESSOR: Oh, do I +have it wrong here? + +Yes, it's 1 minus v over u. + +Thank you very much. + +Right, coming from +the v over u here, + +obviously, as you noticed. + +OK, so to write down a +final equation for z, + +it's delta t0 over +delta t sub s minus 1. + +So it's 1 minus v over +u inverse minus 1. + +And then just putting things +over our common denominator, + +it ends up being v over u +divided by 1 minus v over u. + +And that then is +our final answer. + +So this now is the answer for +the nonrelativistic case-- + +again, we haven't +done relativity yet-- + +and the observer moving. + +OK, now it's worth +pointing out that when + +velocity is small compared +to the wave speed, + +as is often the +case if we're going + +to be talking about +light which we'll + +be talking about in +a minute, but could + +be the case with respect +to sound as well. + +Then these two formulas +are almost the same. + +They're both +proportional to v over u, + +when I'm talking about +the case where v over u + +is a small quantity, where +the motion is slow compared + +to the sound speed +or wave speed. + +And the only difference +is that denominator. + +Here we have a denominator +of 1 minus v over u. + +And here the v over +u is the whole show. + +There's no denominator. + +And if v over u is small, the +denominator is close to 1. + +So the two answers are +going to be almost the same. + +And one can describe that a +little bit more succinctly + +perhaps, by saying that z with +the observer moving minus z + +with the source moving is equal +to v over u quantity squared + +times 1 minus v over +u in the denominator. + +Just a little bit of +algebra to get that result. + +And what that +shows explicitly is + +that second order in v over u. + +It's proportional to v over +u squared, not to v over u. + +So if v over u were +a part in 1,000, + +the difference would +be a part in a million. + +So for slow +velocities, it doesn't + +matter whether it's the +source that's moving + +or the observer that's moving. + +But these answers +can, of course, + +be very different if the +velocity v is comparable to u. + +OK, any questions about that? + +Yes? + +AUDIENCE: Does this violate +Galilean relativity? + +PROFESSOR: Does it violate +Galilean relativity? + +Not really. + +Although, one has to maybe be +careful about how one defines + +Galilean relativity. + +What makes it legitimate +as a classical mechanical + +calculation is that +unshown, but crucially + +important on the +blackboard, is the air + +that the sound wave +is moving through. + +So in one of these pictures, +the air was at rest. + +The other picture, +the air was moving. + +Or rather, well, +I said that wrong. + +The air was at rest +in both pictures. + +But if you want to make +a Galilean transformation + +to relate one +picture to the other, + +then after you've made the +Galilean transformation, + +the air would be moving +and it would not really + +be the same picture. + +So it is all consistent +with Galilean relativity. + +And one has to remember +that the air is + +playing a crucial role here. + +When we say that the observer +or the source is at rest, + +the full sentence +really is that it's + +at rest relative to the medium +that's transporting the wave. + +Any other questions? + +Yes? + +AUDIENCE: This is not +really a question, just + +kind of an observation. + +I just find it interesting +that in the case + +if v is greater than u that +this one is always positive, + +no problem. + +But if v is greater than +u in the other case, + +then you have a +negative number, which, + +I don't know if that-- +I just find that weird. + +PROFESSOR: Right, let me think. + +If v is greater than u, then +the observer moving case + +becomes negative. + +And it presumably means +the wave never reaches it. + +If the observer is moving +faster than the wave speed, + +the wave never reaches them. + +And that's why the +answer is peculiar. + +If the source is moving +faster than the wave speed, + +the wave still +reaches the observer. + +So there is a nontrivial and +believable answer in that case. + +OK. + +What we're going to move on to +now is the relativistic case. + +And as I think I described in +the course handouts, relativity + +is has sort of an odd +role in this class. + +We need a little +bit of relativity. + +But at the same time, there +are the courses in relativity. + +So I don't want this to +be a course in relativity. + +In the old days, +when there weren't so + +many other courses +in relativity, + +we did in fact spend two +weeks of this course doing + +special relativity. + +But I don't think that's +worthwhile anymore. + +Well, I'll maybe ask +for a show of hands. + +How many of you +have had relativity + +in some other course? + +That's what I thought, most +of you, perhaps not all. + +Well, maybe I should +ask the other question. + +How many of you have +not had relativity? + +OK, a number. + +So I do want to make +the course completely + +intelligible to the people +in that second group. + +Special relativity is not a +prerequisite for this class. + +So what my goal will be +to tell you enough special + +relativity so that you'll be +able to follow what comes next. + +But I will not be +driving those results. + +I'll just leave +for other courses + +for people who +want to take them. + +And if you don't want to +take them, that's fine too. + +But I want to make +this course coherent. + +So what we're going to do +is discuss the consequences + +of special relativity +without trying + +to relate those +consequences directly + +to the underlying ideas +of special relativity. + +I will, however, mention where +special relativity comes from. + +It arose in the mind +of Albert Einstein, + +because he realized that the +physics that we knew well, + +basically Newtonian +physics at that time, + +possess this property, Galilean +relativity, which came up + +in a question just a minute ago. + +Galilean relativity +says that if you + +look at any given physical +process in a frame that's + +moving at a uniform velocity +relative to the first frame + +that you use to describe +it, it should also + +be consistent with the laws of +physics in the second frame. + +Incidentally, I-- maybe I'm +more ignorant about history + +than most-- only learned +a few years ago what + +Galileo had to do with this. + +It did actually play +a very important role + +in the history of +Galileo in the physics + +that he was debating about. + +A key issue in the +time of Galileo + +was whether the earth moved +around the sun or the sun moved + +around the earth. + +And that was something Galileo +was intensely involved in. + +And one of the +arguments that said + +that it must be the +sun that moves-- + +it can't be the +earth that moves-- + +was that if it's the +earth that moves, + +it means we move at +very high velocity. + +The velocity of the +earth around the sun + +is high by ordinary standards. + +And obviously, we'd feel +that motion, people thought. + +So it was a proof +that it must be + +that the earth is stationary +and the sun moves. + +Because otherwise, we'd feel +the effect of this high velocity + +motion. + +So it was crucial to +Galileo's point of view + +that it was really +the earth that + +was moving that you +don't detect motion. + +If you're in uniform +motion, the laws of physics + +are exactly the same as they +would be if you were at rest. + +And that's basically +what Galilean relativity + +is all about. + +And it was in fact very +clearly enunciated by Galileo + +in his writings. + +So that was the +case for mechanics. + +But at the same +time, in the 1860s, + +Maxwell invented +Maxwell's equations, + +or completed them is maybe +a more accurate description + +for what Maxwell really did. + +Most of those equations +already existed. + +And a prediction of +Maxwell's equations + +is that light travels at +some fixed speed, which + +could be calculated in terms +of epsilon naught and mu + +naught that appeared in +those equations, a speed + +that we call c. + +Now if light travels +at speed c, it + +would mean that if you +got into a spaceship + +and chased a light beam, it'd +say half the speed of light. + +The implication of the physics +that was known at the time + +would have been that, +from the point of view + +of that spaceship traveling +at half the speed of light, + +the light pulse would +only be receding + +at half the speed of light. + +You would have half +caught up with it. + +But that would mean that from +the frame of this rapidly + +moving spaceship, +the laws of physics + +must somehow be different. + +Maxwell's equations must not +hold in their standard form. + +So there was this tension +between Maxwell and Newton, + +if you like. + +The tension was not +a contradiction. + +It would be perfectly +possible for there + +to be a fixed frame in which +Maxwell's equations had + +their simple form. + +But Newton's equations +could perhaps + +have the same form +in all frames. + +And that in fact was what +people thought at the time. + +To account for this situation, +physicists invented the idea + +of an ether which was a medium +through which light waves + +travelled, similar to the air +in which sound waves traveled. + +And the frame in which Maxwell's +equations had their simple form + +was the rest frame of the ether. + +And if you moved relative +ether, the equations + +would be different. + +And that's what people +thought in 1904. + +And it was a consistent +point of view, + +but it meant that there +was this dichotomy + +between electromagnetism +and mechanics. + +So Einstein thought maybe +physics is not so sloppy. + +Maybe there's a more elegant +way which all this plays out. + +And he realized that if you +modified the equations that + +are used to transform between +one frame and another, + +you could make Maxwell's +equations frame invariant. + +You could make it so +that Maxwell's equations + +are valid in all frames. + +And if we go back to our +example of the spaceship chasing + +the light beam, with these +new transformation equations + +that Einstein suggested, +it would turn out, + +even though it's very +contrary to intuition, + +that when the spaceship measures +the speed of the light pulse, + +it would still measure that +the light pulse was moving away + +at speed c, even though it +had moved at half c trying + +to catch up with +the light pulse. + +So it's not obvious +how that can happen. + +But it turns out it can happen. + +We'll be talking a little bit +more about how it happens. + +And that was basically +Einstein's proposal. + +It was a proposal that +there is no ether, + +that the laws of physics both +electromagnetism and mechanics + +are the same in all frames. + +And in order to do +that, he had to say + +that the equations +of transformation + +between one frame +and another are + +different from what +Galileo believed. + +So these are what we call +the Lorentz transformations. + +We might write them down +later in the course, + +but we're not going to +write them down today. + +But what goes into them +are three physical effects, + +which we will talk about. + +If we're talking about +the time dilation, + +we only need one of +those three effects. + +So I'm going to start by just +discussing that for a minute, + +and then we'll come back at the +end of the class, or perhaps + +next class, depending +on how timing works out, + +to discuss the other +two primary effects that + +are needed to make up the +theory of special relativity + +and explain how it could +be that the speed of light + +could look the same +to all observers, + +even if we're talking about +observers that might be moving. + +OK, so time dilation +is the simple statement + +that if I were to +watch a moving clock, + +the moving clock would appear +to me to be running slower. + +I'll just mention +for a moment now + +that I put the word +appear in quotation marks. + +That means we're going to come +back and discuss in detail + +what is meant by +the word appear. + +But to finish the +sentence first, + +the moving clock would appear +to me in my reference frame + +to always be running slower. + +And so by a very predictable +amount, a famous expression + +in special relativity, +gamma, where + +gamma is 1 over the +square root of 1 + +minus beta squared, where beta +is just an abbreviation for v + +over c, the velocity +of the clock + +divided by the speed of light. + +So as long as v over c is +small, this is a small effect. + +Gamma is near 1. + +And running slowly +by a factor of 1 + +means not running slowly at all. + +So the fact it was near 1 +means it's a very small effect. + +But moving clocks will always +appear to be running slower. + +That's one of these three +effects of special relativity + +that we'll be discussing in the +course of lecture notes one. + +Now let me come back now +to talk about this word + +"appear," because that's +a little bit subtle. + +Might just add that +there was a series-- this + +is just an aside-- but I +guess broadcast last year + +there was a four-part +series of Brian Greene's + +Fabric of the Cosmos that +was broadcast on PBS. + +And the interesting thing about +that, which is relevant here, + +is that he tried to +illustrate time dilation. + +And he did it by having sort +of a parable of a person + +sitting in a chair +and somebody else + +carrying a clock over +his head, walking + +towards the person +sitting in the chair. + +And the camera showed what the +person sitting in the chair + +would see and showed the +clock running slowly. + +That's wrong. + +It's not what he +would actually see. + +And that's the crucial issue +of the word "appear" here. + +When we say that the clock +appears to run slowly, + +we're not talking about what +an observer would actually see. + +The complication +of literally seeing + +is that when you see +something, what you're doing + +is you're measuring the +light pulses as they arrive + +at your eyes at a given time. + +And since light has +a finite travel time, + +it means that you're +seeing different things + +at different times. + +In particular, if there's +a large object coming + +towards you, say this laser +pointer coming towards me, + +I would be seeing +the front of it + +at an earlier time than I +would be seeing the back of it. + +The other way around, actually. + +I'd be seeing the back +at an earlier time, + +because the light that leaves +here at an earlier time + +would take longer to +reach my eye, reach my eye + +the same time as light which +leaves the front of the object + +later. + +So the point is that as +this is coming toward me, + +I'm seeing different +pieces of it + +at different times in terms +of the actual existence + +of this laser pointer. + +And that makes +things complicated. + +So what you actually see +when you take into account + +special relativity is +fairly complicated. + +You can calculate +it, but there's + +no simple expression for it. + +You really just have +to calculate point + +by point what you'll be seeing +for every part of the object + +at a given time, +nothing very simple. + +So the simple expression, +which just says, + +clocks run slowly by +a factor of gamma, + +and we'll learn +later e expressions + +about how things +contract and how + +simultaneity changes, +those simple expressions + +are not based on what any +observer would actually see. + +But rather, they're +based on what + +ends up giving a simpler +picture, a picture in which you + +imagine that what +we're discussing + +is not what an individual +sees but rather what + +a frame of reference sees. + +So we're talking not about +what the observer sees + +but rather what is seen in the +observer's frame of reference. + +And a frame of +reference, I think + +you could think of it +pretty concretely, as kind + +of a structure of rulers +connected together + +to each other to +form a grid of rulers + +and with clocks located +everywhere along this grid. + +So all the observations +are made locally. + +That is, if you want to measure +a time in a given reference + +frame, you don't use a +central clock, waiting + +for the light pulse to +reach that central clock. + +Rather, you measure +the reference frame + +is filled with +clocks, all of which + +have been synchronized +to start with. + +And if you want to know +what time an event happens, + +you look at the clock +that's next to it. + +And that clock tells you what +time that event happened. + +So that's typically +what we draw when + +we draw a coordinate +systems and so on. + +It's really the way +we normally think. + +The point is, +though, if you really + +want to think what one +observer would see, + +it's more complicated. + +Then you have to take into +account the light travel time. + +So it's only after you take +out the way travel time + +and calculate how local +clocks would compare + +that you see this time +dilation in the simple form, + +that the clock +always runs slower. + +So in particular, +for this example + +of the person sitting +in a chair and the clock + +coming towards them, +that's exactly what + +we're going to be talking about. + +That is the Doppler shift. + +And what we'll find is when +the clock comes towards them, + +he will see the +blueshift not a redshift. + +He'll see the clock +running faster not slower, + +the opposite of what was +shown in the TV program. + +But the difference +is that what causes + +it to look like +it's going faster + +is the fact that each pulse +travels a shorter distance + +if the clock is coming +towards the observer. + +And that becomes a bigger +effect than the fact + +the clock itself, if it were +measured relative to clocks + +that it passes, would +be running slowly. + +Yes? + +AUDIENCE: So in that case, +if the clock, let's say, + +was moving toward +you really fast, + +could you measure it when it was +directly perpendicular to you? + +And then that would be the +special relativity time + +dilation? + +PROFESSOR: Well, if it +was moving alongside you. + +If it was coming right at +you, it would just hit you. + +And that was the case, +Sonya, more or less. + +But yes, you're exactly right. + +If the clock were moving at +right angles to the observer + +so that the observer +saw it, what you really + +want for this to +be the pure effect + +is you want to have the +velocity of the clock + +to be perpendicular to +the velocity of the photon + +that the observer is seeing, +as measured in the observer's + +reference frame. + +Actually that matters. + +Then you see would see +pure time dilation effect. + +That's exactly right. + +OK, so might just add that Brian +Green and a bunch of people + +here at MIT, actually-- +I was involved + +and so were some others. + +There's a number of MIT +people on this program. + +So we ended up having +a long conversation + +with Brian Green +about it by email. + +And everybody at MIT thought +it was just plain wrong. + +Brian Green actually +took the position + +that it was very +intentional on his part, + +and he was just trying to +illustrate the time dilation + +effect, and he didn't want to +talk about the Doppler shift. + +And since he didn't +want to talk about it, + +he could ignore the +fact that it was there. + +We all thought that +was bad pedagogy. + +But we never convinced +Brian, I should say. + +OK, now what we want to do is +go through these Doppler shift + +calculations again, +this time recognizing + +that moving clocks run +slowly by a factor of gamma. + +So we're now going to be doing +the relativistic case where + +the wave is sound +waves-- excuse me, + +where the wave is light waves. + +I'll get this straight. + +And the velocities might +be comparable to the speed + +of light. + +So this time dilation +effect is large + +enough so that we want +to take it into account. + +Now in this case, +what we are hoping, + +and everything would be wrong, +inconsistent, if we can find + +this, we're hoping +that in this case, + +the two answers +should be the same. + +It shouldn't matter whether +the source is moving + +or the observer is moving. + +Earlier it did matter, and +we said that was explicable, + +because we knew that +air was involved. + +And if we made a +velocity transformation + +to go from one +picture to the other, + +from the picture where the +source is moving to the picture + +where the observer +was moving, the air + +would have a different +velocity in the two pictures. + +It would be stationary in +one and moving in the other. + +So we would not expect +to get the same answer + +as we would have gotten +assuming the air was stationary. + +But in this case, if anything +has a different velocity when + +you go from the picture +where the source is moving + +to the picture where +the observer is moving, + +it would have to be the ether +that has a different velocity. + +But the basic axiom +of special relativity + +is that there is +no ether, at least + +there's no physical effects +coming from the ether. + +So you might as well +pretend it does not exist. + +You can't really +prove that it does not + +exist if it has no properties. + +It still exists. + +But the basic axiom +of special relativity + +is that there are +no physical effects + +coming from this either. + +So for special relativity, we +should get the same answer, + +whether it's the +source that's moving + +or the observer that's moving. + +It's really the same +situation, just viewed + +in different reference frames. + +And special relativity says it +cannot matter what reference + +frame we're doing +the calculations in. + +So it's the same +pictures, but this time we + +want to take into account the +fact that moving clocks run + +slowly by a factor of gamma. + +So looking at these +pictures, we can first + +start just glancing +at them and saying, + +where's there a +clock that's moving? + +That might be something +we need to think about. + +And maybe I'll ask you-- +which of these four frames + +shows a moving clock? + +AUDIENCE: All of them? + +PROFESSOR: Sorry? + +AUDIENCE: All of them? + +PROFESSOR: All of +them, I guess so. + +But the time interval +measured on the clock + +is only actually +relevant to one of them. + +AUDIENCE: Two. + +PROFESSOR: Two, exactly, two. + +Here we said that +the source is moving, + +and we said the time measured +on the source's clock + +between the emission of +these two wave crests. + +Incidentally, we're +usually talking + +about continuous waves +like light waves. + +And then we're talking about +the time between successive wave + +crests. + +Well, if we just as well imagine +that the source is emitting + +a series of pulses where +each pulse represents a wave + +crest, and somehow to me +that sounds a little simpler + +to describe, because +you don't have + +to think about the sine wave +associated with the signal + +that the source is +actually creating. + +So in any case, the time +between these pulses, + +I'll call them, as measured +by the source clock, + +is what we call +delta t sub s, is + +the time that the source +would actually measure. + +And the source is +moving in this picture. + +So relative to +our frame, we want + +to think of this entire +series of pictures + +as all being consistent +in our frame. + +It's very important, since +transformations between frames + +are a little complicated +in special relativity. + +It's very important when +you're doing any problem + +to pick what frame you're going +to use for your description + +and be sure to stick to it. + +If anything is initially +described in another frame, + +you have to figure out what +it looks like in your frame + +in order to fit it together +with the other events + +that you're describing in your +own particular reference frame. + +So for this problem, +our frame will + +be the frame of the +slide, the frame, which + +is at rest relative +to the observer. + +So we could also call +it the observer's frame. + +And relative to that frame, +the source is moving. + +And therefore, the +clock-- a source + +is emitting a series of pulses. + +That's a clock. + +Anything that does anything at +regular intervals is a clock. + +So the source represents +a moving clock. + +And we need to take into account +the fact that the source will + +be running slowly by +a factor of gamma. + +And otherwise, nothing changes. + +The observer has a clock +also, which the observer + +is going to use to measure +the time between crests. + +But the observer's clock +is at rest in our frame. + +So there's no time dilation +associated with the observer's + +clock, only a time +dilation associated + +with the clock on the source. + +So again, the important issue +is all inside that yellow box. + +And what do I do now is +look at the equations + +and see how the +equations are modified. + +I guess I should start +back at the beginning + +of the blackboards. + +Maybe I should turn +the blackboard lights + +on when I work on +the blackboard. + +So the time integral +as seen by the observer + +will be equal to-- +last time we just + +had delta t sub s as our first +term, which would be what it + +would be if there +was no velocity. + +And that's still true if +there was no velocity. + +But if the clock is going +to be running slowly + +by a factor of gamma, that would +mean that the time interval + +that we would +measure, even if there + +was no change in path length, +which will be the next term, + +if there was no +change in path length, + +the time that we would +measure as the observer would + +be different from +the time interval + +as measured by the source +by a factor of gamma. + +But one has to figure out +whether the gamma goes + +in the numerator +or the denominator. + +And sometimes it's +a little tricky. + +It helps a lot, I think, to +just sort of imagine an example. + +Any example is +clear, it turns out. + +But when you try to write +down the answer in general, + +you sometimes get it wrong. + +That's my experience with +myself and with other people. + +So this clock is wanting slower. + +And say we're talking about +a second time interval. + +If this clock is running slower, +it means it takes longer for it + +to take off a second. + +We would see it as maybe running +slower by a factor of two. + +It would mean that it +would only take off + +a second every two seconds. + +So that means that the time +interval that we would see-- + +and that's what we're +trying to calculate, + +the time interval +as the observer-- + +is going to be longer than delta +t sub s by a factor of gamma. + +So the first term changes +from what it was before. + +And what we're doing is we're +rewriting this equation. + +So the first term +changes from what + +it was before by putting in a +factor of gamma in front of it. + +Because the source +clock is running slowly. + +And then the second term is +still delta l divided by u. + +But the equation for +delta l changes also, + +because delta l is +the time interval + +that it takes for the light +to travel the extra distance, + +where the extra +distance was because + +of the time between the clicks. + +And that is now changed +because of the time + +dilation of the source clock. + +So the second term also +changes by a factor of gamma. + +So it's gamma +times delta t sub s + +plus v times gamma times +delta t sub s divided by u. + +So the whole answer just +changes by a factor of gamma. + +So it's gamma times 1 plus v +over c times delta t sub s. + +And now if you do a +little bit of arithmetic + +here-- gamma, remember, is +1 over the square root of 1 + +minus v squared over c squared. + +And a squared minus +b squared-- I'm now + +thinking of the denominator 1 +minus v squared over c squared. + +Maybe I'll write +this on the side. + +1 minus v squared +over c squared-- + +it's worth remembering here-- +can be written as 1 plus v over + +c times 1 minus v over c. + +And we have the square +root of that appearing here + +in the denominator. + +Gamma is 1 over the +square root of this. + +So this becomes the square +root in the denominator, + +resulting the square +root of 1 plus v + +over c appearing in the answer. + +And this remains +in the denominator. + +And what we get simplifies +to simply 1 plus beta over 1 + +minus beta inside the square +root times delta t sub s. + +So this is the special +relativity answer, + +the relativistic answer, and +this is for the source moving. + +Now we expect that the +answer won't depend on + +whether the source +is moving or not, + +but certainly the +calculations do. + +So this is what we got from the +calculation, which we assumed + +that it was a source +that was moving, + +and the observer was stationary. + +It's just corrected +from the previous answer + +by this factor of gamma. + +Any questions about that? + +OK, so to summarize on +the slide what's changed + +is that this time interval, +this extra distance delta l + +for the relativistic +problem, is not + +v times delta t sub s as it was. + +But rather what we said is +that it's gamma times v times + +delta s, because the +clock on the source + +is running slowly by +a factor of gamma. + +And it was this +difference that we just + +used on the calculation +on the blackboard + +to get the new answer. + +OK now the next +calculation, now we're + +going to do the same +calculation again, + +which we already did for +the nonrelativistic case. + +But this time it will +be the observer moving. + +And we're going to try to +do the relativistic case. + +So this time it's +the clock carried + +by the observer +that's running slowly. + +And remember, this +is running slowly + +relative to us, relative to +our frame of reference, where + +our frame of reference is +by definition the frame + +of reference of the slide +that we're looking at. + +Source is stationary, +so delta t sub + +s is just an honest time +as we would measure it. + +But times as measured by +the observer, delta t sub o, + +are going to be different. + +So to correct the +calculation for relativity, + +that's the crucial +box as it was even + +in the nonrelativistic case. + +And we're going +to have to change + +that equation by +replacing delta l. + +Instead of v times delta t sub +0 is v times delta t prime. + +Now delta t prime is not +exactly delta t sub 0 + +or gamma times delta t sub 0. + +It's a little trickier. + +Let's see. + +Hold on. + +The definition I want +to use for delta t prime + +is that it's the +time as measured + +between the third frame +and the fourth frame. + +But it's the time +as we measure it. + +I still want to +describe everything + +in terms of the way +we would measure it. + +So delta t sub prime +is not measured either + +by the source or the observer. + +It's measured by us. + +And it's related to the time as +the observer would measure it + +by a factor of gamma, +because relative to us, + +the observer's clock is running +slowly by a factor of gamma. + +AUDIENCE: So we're the source? + +PROFESSOR: Well, +we're stationary + +relative to the source, because +the source is stationary. + +But we're the frame of +reference of the slide, + +is the way I like +to think about it. + +But it is the +frame of reference, + +same as the frame of +reference as the source. + +That's right. + +So delta t sub 0 is +related to delta t + +sub prime by a factor of gamma. + +And again, one has +to think a little bit + +to make sure one gets the +gamma in the right place, + +the numerator or +the denominator. + +We're saying that the +observer clock appears + +to be running slowly +relative to us. + +And that means that +during the amount of time + +it would take for it to +say take off one second, + +since it's running slowly, +should take more than a + +second relative to us. + +And that's what this +formula would give, + +if we multiply by gamma. + +It would say that delta t +prime is equal to gamma times + +delta t sub 0. + +So we would say that the time +that the observer clock ticks + +off one second we might +measure two seconds. + +That's the direction +of the time shift, + +all given by that formula. + +And those are all the pictures. + +Now we just have to write +down the equations that + +go with those pictures. + +And the hope is that +we'll get the same answer + +as we got last time. + +I think I'll leave +that on the board. + +Let's see. + +What do I do? + +No, I won't leave +it on the board. + +OK, this time the +calculation we're mimicking + +is the calculation up here. + +This was the calculation we had +for the nonrelativistic case + +where the observer was moving. + +Now we want to put in +the time dilation that + +would correct that calculation. + +And the key equation is +that the time interval + +between the receipt +of the two wave crests + +as we would measure +it, which is why + +I call it delta t +sub prime, so prime + +is not the source +or the observer. + +It's us. + +It's the same frame of +reference as the source, + +but the source +isn't located there. + +So we think of it +as the time interval + +as measured in the +frame of reference. + +That's the frame of the +slide, which is our frame. + +And it is equal to +gamma times delta t sub + +0, where delta t sub 0 is +the time as it would actually + +be measured on the +observer's clock. + +So, we're keeping +their labels s and 0 + +to mean what would +actually be measured + +on the clocks at the +source and at the observer. + +That's what we're +trying to establish + +a relationship between. + +So the basic formula +that we have up + +top there would first +become delta t sub 0 + +is equal to-- hold on. + +Now actually, we would +not start by writing down + +an equation for delta t sub 0. + +Rather what we +want to do is start + +by writing down the +relationship as we would see it + +in our frame, which is going +involve delta t sub prime. + +We'll worry about +delta t sub 0 later. + +So our equation +is going to become + +delta t prime is equal to +delta t sub s plus v times + +delta t sub prime divided +by the wave speed, + +which now we'll +call c, since we're + +doing a relativistic problem. + +So this is the basic +equation for the time delay + +as we would see it in our frame, +where delta t sub prime is + +the time between the receipt +of the first and second crests, + +the time between +frames three and four + +as we would measure it. + +And now we can do the same +thing that we did over there, + +first for delta t sub prime. + +And we discover that +delta t sub prime + +can be written as 1 +minus v over c inverse, + +just doing algebra on this +equation, times delta t sub s. + +So that equation relates delta +t prime to delta t sub s. + +And now we use the +equation up top here + +to see what the observer +himself would actually measure. + +And that becomes just 1 over +gamma times delta t sub prime. + +So delta t sub observed is +equal to 1 over gamma times 1 + +minus v over c inverse +times delta t sub source. + +And now since it's important +we get the same answer, + +I'm going to write in +some intermediate algebra + +here just so we can all +really see that it works out. + +The 1 over gamma, I am going +to write as-- remember gamma is + +1 over the square root +of 1 minus beta squared-- + +so 1 over gamma is the square +root of 1 minus beta squared. + +And I'm going to write that +as the square root of 1 + +plus beta times 1 minus beta. + +So this is the +factor 1 over gamma. + +Now we have explicitly here a +factor of 1 over 1 minus beta. + +The inverse makes it 1 over. + +Did I write something wrong? + +AUDIENCE: From the second +until the third time? + +PROFESSOR: Second to +third, you're there? + +AUDIENCE: I thought it wasn't-- + +PROFESSOR: Yeah, this +goes to the other side. + +It is minus. + +OK, finally, the 1 +minus beta, you see + +occurs to the first +power in the denominator. + +And the 1/2 power +to the numerator. + +So we do indeed get +exactly what we wanted. + +Delta t sub 0 is equal +to the square root of 1 + +plus beta divided by 1 minus +beta times delta t sub s. + +And now we know that this +is the relativistic answer + +for either source +or observer moving. + +And then if we want to +write down what z is, + +this is delta t observer divided +by delta t source minus 1. + +So that becomes just +the square root of 1 + +plus beta over 1 +minus beta minus 1. + +So we found what +we expected, what + +we wanted to find to be +consistent with the basic ideas + +of relativity. + +It's the same answer +no matter which + +one is moving, because +it doesn't matter + +what frame of reference +we do the calculation in. + +OK, questions about either +the calculations or the ideas + +behind them? + +OK in that case, let's move on. + +I do want to come back and +talk about the other two + +kinematic effects of +special relativity, which + +are Lorentz contraction +and a change + +in the notion of simultaneity. + +But before I get +to that, there's + +one other issue I +want to discuss first, + +mainly because it's something +you need to understand + +to do the problem set +that's due tomorrow. + +And that is the +situation that's needed + +to describe clocks which +might be accelerating. + +Special relativity really only +describes inertial reference + +frames and how things change +from one inertial frame + +to another. + +So if you know how +a clock behaves + +if it's at rest in +one reference frame, + +special relativity completely +dictates without any ambiguity + +what it would look +like at a frame that + +was moving at a +uniform velocity, + +relative to the original frame, +which means it completely + +dictates how that clock is +going to behave if it is moving + +at a constant uniform velocity. + +But nonetheless, +in the real world, + +we have very few clocks around +that are completely inertial. + +Every clock that +we see around us + +from the clock on +the wall, which + +is moving with the earth or my +wrist watch which moves more, + +is constantly undergoing +accelerations. + +So we want to be able +to talk about clocks + +which are accelerating. + +So we need to say a little +bit about how we would do that + +and how we do it if the clocks +were moving at relativistic + +speeds , which also happens +with satellites, for example. + +The GPS system as you've +probably been told + +wouldn't actually work +unless the calculations were + +done in such a sophisticated +way that they even + +take into account the +effects of general relativity + +as well special relativity. + +So moving clocks +and how they behave + +is a crucially important +topic technologically. + +So what do we say that a +clock that's accelerating? + +There's I think a common myth +that to describe acceleration + +you need general +relativity, and therefore we + +have to put off talking +about accelerating clocks + +until we take a course +in general relativity. + +That's actually totally false. + +What general relativity does +is provide a theory of gravity + +which basically says the gravity +and acceleration are intimately + +linked. + +And that's where +acceleration gets + +pushed into general relativity. + +But special relativity +alone is enough for us + +to describe any system that +could be described by equations + +that are consistent +with special relativity. + +Special relativity does +not describe gravity. + +So in any situation where +gravity is important, + +special relativity is at a +loss to make real predictions + +about what should happen. + +But as long as gravity is +absent, as long as we're only + +dealing with +electromagnetic forces + +that we think we +understand, there's + +nothing that prevents +us from using + +the equations of +special relativity + +to describe what happens. + +We have to use the dynamical +equations of special relativity + +that talk about how +things respond to forces. + +And whenever there's a force, +there's an acceleration. + +But there really +are such equations. + +We can combine, for +example, electromagnetism + +with relativistic mechanics to +describe a system of particles + +that are interacting +electromagnetically, completely + +consistent with +special relativity. + +And even those particles +are accelerating, + +we could say everything +we want to say about them. + +So in particular, if +there's a physical clock, + +to the extent that we could +describe that clock as made out + +of particles whose +physics we understand, + +special relatively +will still tell us + +what that clock will do even +when that clock accelerates. + +The answer, however, from that +calculation, you might imagine, + +is very, very complicated. + +Because the physics +of any actual clock, + +my wrist watch as an example, +is pretty damn complicated. + +And we're not really +going to write down + +the equations that describe +my wrist watch to figure out + +how it's going to behave +when it accelerates. + +So what are we going to do? + +Let me point out +that you already + +have pretty much experience +with accelerating clocks, + +because all of you-- +well, many of you-- + +wear wrist watches like I +do that are accelerating + +all the time. + +And they tend to work. + +You basically assume that even +though they're accelerating + +they've been designed well +enough so they can withstand + +the accelerations that +your wrist gives them + +and still read the right time. + +On the other hand, one could +imagine contrary situations. + +Probably my wrist watch +would survive this, + +but if you take a mechanical +clock, a windup clock, + +and heave it against +the wall and let + +it smash against the +wall and come to a stop, + +as it smashes +against the wall, it + +wanted to go a very +large acceleration. + +And if the acceleration +is large enough, + +we can predict the effect +it will have the clock, even + +though it's a +complicated interaction. + +If the acceleration +is large enough, + +it'll simply break the +clock and it will stop. + +And that's one possible +effect that acceleration + +can have a clock. + +And other effects are +similar in nature. + +If there's any effect +that the motion of my hand + +has on the wrist watch, it +would be a mechanical effect + +that you'd calculate +by understanding + +the mechanics of +how the watch works, + +not by understanding +any principles + +of general relativity. + +What's at stake +underlying this-- + +you might wonder what +the real difference is-- + +special relativity can make +precise predictions about how + +a clock will behave if it +moves at a uniform velocity, + +even without knowing +anything about the details + +of that clock. + +Special relativity could +make that prediction + +because there's a symmetry, +Lorentz symmetry, which + +relates those two situations. + +And that's an exact +symmetry of nature. + +So no matter what the +clock is made out of, + +if it's moving at +a uniform velocity, + +special relativity +tells you there's + +no doubt it would run +slowly by a factor of gamma. + +On the other hand, +there's no such principle + +of any kind, either +in special relativity + +or general relativity, +about acceleration. + +So if you want to know +the effect of acceleration + +on a clock, it really depends +in detail on how large + +the acceleration is of +course and the detailed + +physics of the clock and how +much acceleration it takes + +to effect it and in what +way it affects, precisely. + +So what's the bottom line? + +The bottom line is +that when we want + +to talk about an accelerated +clock, which we really + +do all the time, what +we always do is simply + +assume that the clock +is built well enough + +so that the acceleration +does not affect its speed. + +And that really can be +said very precisely. + +The assumption that +we're going to be making + +is that these are +ideal clocks, meaning + +that they're built well. + +And when we say the +acceleration does not + +affect the speed of the +clock, what we're saying + +is that the clock will run +at precisely the same speed + +as another clock that's, +say, moving instantaneously + +alongside it with +the same velocity + +but with no acceleration. + +So at any point in the +motion of my arm here, + +my wrist watch will have +some specific velocity. + +The velocity will +affect in some tiny way + +the speed of the clock by +this factor gamma, which + +will be very close +to 1 for that case. + +But we're going to assume, if +we call my watch an ideal clock, + +that in the even time, +it will be running + +at exactly the same speed +as a clock which is not + +accelerating, but +which is moving + +with the same velocity +as the wrist watch. + +Therefore, the factor +of gamma will be there, + +but there'll be no +effect of acceleration. + +The speed of the clock +will be determined only + +by its velocity relative +to our reference frame. + +OK, is that clear enough? + +And that's what you need to +assume about some accelerating + +clocks that show up +on the problem set. + +That's why I wanted +to get it in today. + +OK, if there are no other +questions about that, + +I'd like to come back and +talk a little bit more + +about special relativity +and its consequences. + +Sometime later in the course, +we'll talk a little bit more + +about what I would call +the dynamical consequences + +of special relativity, +which include + +well known equations like e +equals mc squared, for example. + +But before one talks +about energy and momentum, + +which are quantities which +I will dub dynamical, + +there kinematic effects +of special relativity + +of which this time +dilation is one. + +And by kinematic +I really just mean + +the consequences of +special relativity + +for the measurements +of times and distances. + +And if one limits oneself +to discussing consequences + +for times and distances, +kinematic consequences, + +there really are precisely +three and no more consequences + +of special relativity. + +And really all special +relativity in some sense + +is embodied by these +three statements + +that we're going to be talking +about, the first of which + +was time dilation, which +we've already seen. + +I'll just remind you. + +Time dilation says +that any clock which + +is moving at speed d relative +to a given reference frame + +will appear in quotation +marks to an observer using + +that reference frame to run +slower than normal by a factor + +denoted by the +Greek letter gamma. + +Turn out the board lights +in case they're distracting. + +And again, "appear" refers +not to how it would actually + +look to any particular observer, +because any particular observer + +in a particular +location is going + +to be waiting for light +rays to reach that observer. + +And they'll take +different amounts of time + +depending on where they start. + +"Appear" refers to measurements +made in the reference + +frame of the observer, +where we assume + +that all the actual measurements +are made by on the spot clocks + +and rulers who measure +where the object actually + +were at the time these +events happened and not + +what it looks like at +sometime later when + +light rays reach some observer. + +OK, the second consequence, +and again all these + +will involve the word "appear." + +And I'll always write +it in quotation marks + +to remind you that it's not +exactly what a person would + +see. + +The second one is another famous +effect of special relativity, + +Lorentz contraction, +or sometimes called + +Lorentz-Fitzgerald contraction. + +Any rod which is moving at +a speed v along its length + +relative to a given +reference frame + +will appear-- and again +appear to an observer + +using that reference +frame-- to be shorter + +than its normal length by +the same factor, gamma. + +A rod which is moving +perpendicular to its length + +does not undo that change +in apparent length. + +So these pictures +kind of show it all. + +A rod, that bar is +the rod, a rod which + +is moving at speed v +will look contracted, + +will appear to be contracted, +by a factor of gamma. + +And a rod which is +moving perpendicular + +to its length, a rod which +is like this moving this way, + +has no such effect, we'll appear +to have its natural length. + +And this is a very +famous consequence + +of special relativity. + +It means that moving +rocket ships shorter + +and shorter and faster +they go, and so on. + +And again, you +should remember, it's + +not what you'd actually see. + +It's what you'd measure if you +had on the spot local observers + +making these measurements, +which you then later compile. + +OK, that's actually all I want +to say about the contraction. + +Any questions? + +OK, next and last is an effect +we just talked about less + +because it's a little bit +more intricate to describe. + +But the other crucially +important effect-- these + +would not be consistent if +you didn't have all three. + +The other crucially +important effect + +is the changing simultaneity, +the relativity of simultaneity. + +And it takes more +words describe it, + +so there's more words on the +slide than on the other slides. + +And the pictures are a little +bit more complicated too. + +But the pictures do +say it all, really. + +The point is that if you have a +system consisting of two clocks + +which have been synchronized +in their own rest frame-- + +they're both at rest with +respect to each other + +and they've been synchronized +in their own rest frame-- + +and they're connected +by say a rod, + +which has some length which +we'll call l sub 0 in the rest + +frame of the two clocks . + +If that whole system +moves relative to us + +by speed v along +the length, those + +clocks, even though they were +synchronized in the rest frame, + +would not look +synchronized to us + +but rather would look like +they're out of synchronization. + +And in particular, it will +look like the trailing clock, + +the one on the back of +this combination of clocks, + +will look a little bit +like it reads a little bit + +later in the day +by a factor which + +is beta times l sub 0 times c. + +Beta remember is +v over c. l sub 0 + +is the distance +between the clocks + +as measured in the rest +frame of the clocks. + +And c is of course +the speed of light. + +On the other hand, +if these two clocks + +were moving in a +direction which is + +perpendicular to the +line that joins them, + +then there's no change +in the synchronization. + +Now I should mention that +this really is crucially + +important to the consistency +of the whole picture. + +And actually showing that +the picture is consistent + +is more than we're going to do. + +It's not impossible to do +at this level by any means. + +But it's more than we're +going to do in this class, + +since we're not focusing +on special relativity. + +But when you hear about +special relativity + +and look at these +postulates, you + +might realize that there seems +to be a pretty obvious tension + +between the idea that +moving clocks run slowly + +and that all +observers experience + +the same laws of physics. + +Because it means that if you +and I are moving with respect + +to each other, I would +claim that your clock + +was running slowly. + +But at the same +time, you would claim + +that my clock was +running slowly. + +Because from your +point of view, you're + +at some fixed velocity and +therefore an inertial frame. + +And I'm moving relative to you. + +So as you would describe it, +I would be a moving clock. + +And my clock would +be running slowly. + +So I think your clock +is running slowly. + +You think my clock +is running slowly. + +That seems to contradict. + +What happens if we hold the +clocks next to each other + +and really just watch +how they compare? + +Which one gets ahead? + +How can we disagree on that? + +Well of course, we can't hold +the clock next to each other + +and also have them moving +relative to each other. + +That's part of how you +get out of this conflict. + +But let's think in a +little bit more detail + +about what we're +really saying when + +I say that your clock +is running slowly. + +Remember, I want to +make all my observations + +not by watching you, because +then there's this time delay + +effect which complicates things. + +I make all of my +observations by having + +a family of local observers +surrounding me all at rest + +relative to me. + +And they report back to me. + +And only when I receive +those reports and piece + +them together do I +get the simple picture + +of what happened +where when, which + +is the simple picture +that is described + +by these "appear" relationships. + +So when I say your clock is +running slowly, what I mean + +is that if I have a network +of clocks all at rest relative + +to me, and your +clock comes shooting + +by, I would measure what time +it reads as it goes past all + +my local clocks. + +Rather, they would measure +what time your clock reads + +as it goes past +each local clock. + +And then they would +all report back to me. + +So if your clock is running +slowly, for example, + +let's say by a factor +of two, it would + +mean that when you're +clock passes my clock + +and my clock reads one +second, your clock would only + +read half a second, because +it's running slowly. + +It hasn't ticked +off as much time. + +When it passes some later clock +of my sequence of clocks, where + +my clock reads two +seconds, your clock + +will read one second, and so on. + +So in that sense, I would say +your clock was running slowly. + +Now that has to be +consistent with you thinking + +that my clocks are all +running slowly as well. + +So if you agree that my +clocks were all synchronized, + +then you would conclude that +my clocks must be running fast. + +Because when your clock +reads a half second, + +my clock reads one second. + +When your clock +reads one second, + +my clock reads two seconds. + +You would say that my +clocks were reading fast + +if we just made that +direct comparison. + +But at the same time, we know +that's not the right answer. + +You should see the +same physics and I see. + +If you and I are moving +with respect to each other, + +you should see my +clocks running slowly. + +So the way out of that is +this question of simultaneity. + +From the point of +view of your clocks + +going past all my +clocks, if you just + +looked at the time on my +clocks as you passed them, + +you would actually +think that they + +were running fast +relative to your clock. + +But you would also, +however, not think + +of those clocks were +synchronized with each other. + +So you don't +determine what speed + +they're running by looking +at two different clocks. + +If you want to figure +out whether my clocks + +running fast or slow, you want +to look at one of my clocks + +and see how it +changes with time, + +not comparing different clocks. + +Because the different +clocks would just + +be out of synchronism with +respect to each other as you + +would see it. + +And we're not going to +go through the details. + +But if you do look at +my clocks consistently + +using a family of +your clocks that + +are stationary +relative to you, just + +as I thought about +a network of clocks + +when I was trying to measure +the speed of your clock, + +then everything's consistent. + +You would see all my +clocks running slowly. + +I would see all of your +clocks running slowly. + +And because we disagree +on what's simultaneous, + +there are no contradictions. + +So simultaneity is +absolutely crucial + +to get out of what +would otherwise + +be a glaring contradiction +in the whole system. + +OK, that's about all I +really wanted to say today. + +But let me just give +a preview of things + +that we'll talk about later +in the course concerning + +relativity. + +So far I think we've said +all we are going to say, + +unless the questions. + +I think we've said +all we're going + +to say about the +kinematic consequences + +of special relativity. + +And we're not going to be trying +to derive them, as I said. + +If you're interested, +by the way, + +the notes recommend +several references, + +including the lecture +notes from eight to 86 + +from earlier years when +special relativity was + +included as a real topic. + +So certainly if you're +interested in learning + +about this and you +haven't already seen it, + +I'm happy to help you. + +But otherwise, it will +not be part of this course + +to discuss how these +three consequences + +of special relativity arise +from the basic postulates + +of special relativity. + +But later we will be saying +things that follow further + +along the line by +pursuing the consequences + +of special relativity +for momentum and energy, + +which will be important to us. + +The connection is the +important connection + +and simple connection +that energy and momentum + +are only interesting +to us if they're + +defined in a way which makes +them conserved quantities. + +That's why energy and momentum +are important in physics. + +Because for a closed +system, the total energy + +and the total momentum +do not change. + +Energy and momentum +can be transferred + +from one part of a +system to another. + +But energy and momentum cannot +be either made nor destroyed. + +Now if we took Newton's +definitions of energy + +and momentum, and used +relativistic kinematics, what + +we would find is +that if we looked + +at, say, a collision +of two particles, + +the Newtonian definitions +of energy and momentum, + +if we took those +seriously, would tell us + +what might happen +in a collision. + +Usually there's an angle +that's undetermined. + +But given an angle, it +determines everything else. + +If we used special +relativity to then describe + +what that same collision would +look like in a different frame, + +we would find that these +Newtonian definitions of energy + +and momentum would not be +conserved in the other frame, + +if they were conserved +in the first frame. + +The conservation laws +are dependent on what + +reference frame you're using. + +So what Einstein +amended was slightly + +modified definitions of +energy and momentum, which + +are determined by the criterion +that these slightly modified + +definitions of energy +and momentum should, + +if they are conserved +in one frame + +be also concerned in +any other frame, which + +are related by the relationships +to special relativity. + +So that's why it was +essential once one changed + +the kinematics of going +from one frame to another + +to also change the definitions +of energy and momentum + +so that the conservation laws +would hold in all frames using + +the new transformation equations +to get from frame to frame. + +And that's why +later in the course + +we will be introducing a +slightly modified, slightly + +non-Newtonian, definitions +of energy and momentum + +of moving particles. + +OK, that's all for today. + +I will see folks next Tuesday. \ No newline at end of file diff --git a/vGvnfTk5BFk.txt b/vGvnfTk5BFk.txt new file mode 100644 index 0000000000000000000000000000000000000000..40196cc631167f0d4cc1993d27265030af7ca112 --- /dev/null +++ b/vGvnfTk5BFk.txt @@ -0,0 +1,595 @@ +align:start position:0% + +why does this matter + + align:start position:0% +why does this matter + + + align:start position:0% +why does this matter +because look here you go here's another + + align:start position:0% +because look here you go here's another + + + align:start position:0% +because look here you go here's another +chart of ionic bonds + + align:start position:0% +chart of ionic bonds + + + align:start position:0% +chart of ionic bonds +these are lattice energies okay these + + align:start position:0% +these are lattice energies okay these + + + align:start position:0% +these are lattice energies okay these +are lattice energies + + align:start position:0% +are lattice energies + + + align:start position:0% +are lattice energies +right oh kilojoules per mole it's just + + align:start position:0% +right oh kilojoules per mole it's just + + + align:start position:0% +right oh kilojoules per mole it's just +per mole of stuff right don't get + + align:start position:0% +per mole of stuff right don't get + + + align:start position:0% +per mole of stuff right don't get +confused by that + + align:start position:0% +confused by that + + + align:start position:0% +confused by that +joules electron volts energies per mole + + align:start position:0% +joules electron volts energies per mole + + + align:start position:0% +joules electron volts energies per mole +is per mole of atoms right okay that's + + align:start position:0% +is per mole of atoms right okay that's + + + align:start position:0% +is per mole of atoms right okay that's +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +you could isolate it down to one bond or + + align:start position:0% +you could isolate it down to one bond or + + + align:start position:0% +you could isolate it down to one bond or +a mole of bonds + + align:start position:0% +a mole of bonds + + + align:start position:0% +a mole of bonds +right 15 000 for alumina + + align:start position:0% +right 15 000 for alumina + + + align:start position:0% +right 15 000 for alumina +look at that that's why alumina is in + + align:start position:0% +look at that that's why alumina is in + + + align:start position:0% +look at that that's why alumina is in +your toothpaste + + align:start position:0% +your toothpaste + + + align:start position:0% +your toothpaste +aluminum oxide is in your toothpaste + + align:start position:0% +aluminum oxide is in your toothpaste + + + align:start position:0% +aluminum oxide is in your toothpaste +it's it's in your pans + + align:start position:0% +it's it's in your pans + + + align:start position:0% +it's it's in your pans +it's in sandpaper it is a very hard + + align:start position:0% +it's in sandpaper it is a very hard + + + align:start position:0% +it's in sandpaper it is a very hard +material + + align:start position:0% +material + + + align:start position:0% +material +it is a very hard material why because + + align:start position:0% +it is a very hard material why because + + + align:start position:0% +it is a very hard material why because +of this + + align:start position:0% +of this + + + align:start position:0% +of this +literally those cubes are really high + + align:start position:0% +literally those cubes are really high + + + align:start position:0% +literally those cubes are really high +right why does this matter well i'm + + align:start position:0% +right why does this matter well i'm + + + align:start position:0% +right why does this matter well i'm +going to give you an example in + + align:start position:0% +going to give you an example in + + + align:start position:0% +going to give you an example in +hemodialysis + + align:start position:0% +hemodialysis + + + align:start position:0% +hemodialysis +hemodialysis is something that people + + align:start position:0% +hemodialysis is something that people + + + align:start position:0% +hemodialysis is something that people +have to go into a hospital people who + + align:start position:0% +have to go into a hospital people who + + + align:start position:0% +have to go into a hospital people who +have + + align:start position:0% +have + + + align:start position:0% +have +do not in their kidneys don't clean + + align:start position:0% +do not in their kidneys don't clean + + + align:start position:0% +do not in their kidneys don't clean +their blood + + align:start position:0% +their blood + + + align:start position:0% +their blood +efficiently or enough have to have it + + align:start position:0% +efficiently or enough have to have it + + + align:start position:0% +efficiently or enough have to have it +cleaned by a machine + + align:start position:0% +cleaned by a machine + + + align:start position:0% +cleaned by a machine +and 650 000 patients suffer from this + + align:start position:0% +and 650 000 patients suffer from this + + + align:start position:0% +and 650 000 patients suffer from this +and go to a hospital + + align:start position:0% +and go to a hospital + + + align:start position:0% +and go to a hospital +for literally four hours three times a + + align:start position:0% +for literally four hours three times a + + + align:start position:0% +for literally four hours three times a +week + + align:start position:0% +week + + + align:start position:0% +week +yeah it devastates their their weekly + + align:start position:0% +yeah it devastates their their weekly + + + align:start position:0% +yeah it devastates their their weekly +schedule + + align:start position:0% +schedule + + + align:start position:0% +schedule +um and if you could make this portable + + align:start position:0% +um and if you could make this portable + + + align:start position:0% +um and if you could make this portable +you would change lives in a really big + + align:start position:0% +you would change lives in a really big + + + align:start position:0% +you would change lives in a really big +way + + align:start position:0% +way + + + align:start position:0% +way +one of the big and there are there are + + align:start position:0% +one of the big and there are there are + + + align:start position:0% +one of the big and there are there are +people out there trying to do + + align:start position:0% +people out there trying to do + + + align:start position:0% +people out there trying to do +this this is an example of a design for + + align:start position:0% +this this is an example of a design for + + + align:start position:0% +this this is an example of a design for +a portable + + align:start position:0% +a portable + + + align:start position:0% +a portable +hemodialysis machine one of the single + + align:start position:0% +hemodialysis machine one of the single + + + align:start position:0% +hemodialysis machine one of the single +biggest drawbacks + + align:start position:0% +biggest drawbacks + + + align:start position:0% +biggest drawbacks +in making it portable is making a filter + + align:start position:0% +in making it portable is making a filter + + + align:start position:0% +in making it portable is making a filter +because you're filtering blood you're + + align:start position:0% +because you're filtering blood you're + + + align:start position:0% +because you're filtering blood you're +filtering toxins out of the blood + + align:start position:0% +filtering toxins out of the blood + + + align:start position:0% +filtering toxins out of the blood +there's something that the body can't do + + align:start position:0% +there's something that the body can't do + + + align:start position:0% +there's something that the body can't do +so you need to do it for them right + + align:start position:0% +so you need to do it for them right + + + align:start position:0% +so you need to do it for them right +but the filters get mucked up and gunked + + align:start position:0% +but the filters get mucked up and gunked + + + align:start position:0% +but the filters get mucked up and gunked +up and they're + + align:start position:0% +up and they're + + + align:start position:0% +up and they're +not strong enough and they can't be + + align:start position:0% +not strong enough and they can't be + + + align:start position:0% +not strong enough and they can't be +cleaned and look at this one + + align:start position:0% +cleaned and look at this one + + + align:start position:0% +cleaned and look at this one +here's a filter made out of alumina + + align:start position:0% +here's a filter made out of alumina + + + align:start position:0% +here's a filter made out of alumina +right + + align:start position:0% +right + + + align:start position:0% +right +and these things are what's needed + + align:start position:0% +and these things are what's needed + + + align:start position:0% +and these things are what's needed +we need super strong super resilient new + + align:start position:0% +we need super strong super resilient new + + + align:start position:0% +we need super strong super resilient new +filters + + align:start position:0% +filters + + + align:start position:0% +filters +that can filter things like blood and + + align:start position:0% +that can filter things like blood and + + + align:start position:0% +that can filter things like blood and +toxins out of the blood so very very + + align:start position:0% +toxins out of the blood so very very + + + align:start position:0% +toxins out of the blood so very very +tiny sizes + + align:start position:0% +tiny sizes + + + align:start position:0% +tiny sizes +that we can make over large areas and + + align:start position:0% +that we can make over large areas and + + + align:start position:0% +that we can make over large areas and +uniformly this is the kind of starting + + align:start position:0% +uniformly this is the kind of starting + + + align:start position:0% +uniformly this is the kind of starting +material that we need + + align:start position:0% +material that we need + + + align:start position:0% +material that we need +to make new filters and it all comes + + align:start position:0% +to make new filters and it all comes + + + align:start position:0% +to make new filters and it all comes +back down why would that be a good one + + align:start position:0% +back down why would that be a good one + + + align:start position:0% +back down why would that be a good one +if we can overcome its brittleness + + align:start position:0% +if we can overcome its brittleness + + + align:start position:0% +if we can overcome its brittleness +because of the cues + + align:start position:0% +because of the cues + + + align:start position:0% +because of the cues +because of the atom sizes because of + + align:start position:0% +because of the atom sizes because of + + + align:start position:0% +because of the atom sizes because of +everything that we talked about today + + align:start position:0% + + + + align:start position:0% + +you \ No newline at end of file diff --git a/voMyQUarX-k.txt b/voMyQUarX-k.txt new file mode 100644 index 0000000000000000000000000000000000000000..88589fff869ee4c38d830b56eb42c78b08c3a28c --- /dev/null +++ b/voMyQUarX-k.txt @@ -0,0 +1,2992 @@ +PROFESSOR: All right. + +So Lecture 7 was +about many things-- + +universal foldings by box +pleating, maze folding, + +and then lots of +NP hardness stuff. + +So we're going to go through +things in that order. + +I thought I'd start by showing +some old history of box + +pleating, where it comes from. + +The first design is by this guy +Raymond McLain, 1967, design + +called the Mooser's train. + +And you can see all the creases +are horizontal, vertical, + +and diagonal, 45 degrees. + +This is the original +handwritten thing, + +and this is apparently before +the time of origami books, + +for the most part. + +So people would +just photocopy this, + +and hand it around, just +kind distribute it out + +through the origami community. + +And kind of spawned a +revolution origami design, + +because it was the +first model to make + +sort of a very complicated +multi-object piece out + +of one piece of paper. + +Happened to be a +rectangle of paper, + +but a pretty cool design . + +And it really got +people thinking about. + +And the basic, original +principal in box pleating + +was to make boxes, and then find +ways to attach them together. + +And it's fairly +powerful and believed + +to be universal by +origamists for a long time. + +And we proved it with +that cube gadget. + +Now, the designs that come +out of the cube gadget + +are not especially efficient. + +I've got some ways to +optimize it, as you saw, + +but at least it proves +everything is possible + +that you could +make out of cubes, + +you can make out +of box pleating. + +Another kind of +influential design + +is this black +force cuckoo clock. + +For a long time, one of the most +complicated origamis out there. + +It was designed by +Robert Lang in the '80s, + +and there's a few of +them in existence. + +It has lot of detail-- it +has a clock, that's correct + +twice a day, and it's he +modeled it after a real cuckoo + +clock he saw in +the Black Forest. + +It's got a zillion +creases, especially + +in this long rectangle of paper. + +And there's diagrams for it +in Origami Design Secrets, + +if you want to make your own. + +And it's also based on +this box pleating idea, + +and sort of in the early days +of the tree theory, and so on. + +So really, before that kicked +off, box pleating was around. + +And people still do +basic box pleating, + +although now there's +the fusion of the tree + +method with box pleating. + +There's a lot of designs +based on that, because they're + +easy to fold from +angular perspective, + +easy to find where the +creases are, anyway, + +that's box pleating. + +So next, we go on to-- I +think it's an open problem. + +Yeah, this is a +cool open problem. + +For some reason, never +thought about it. + +I'm sure briefly thought about +it, but never worked on it. + +In the same way we get +universal hinge patterns, + +box pleating can make any poly +cube, what if you want to make, + +out of the simple cube gadget, +can we design an analogous cube + +gadget for +tetrahedra, octahedra, + +might be nice, regular octahedra +tile space, out of something + +like a triangular grid, +maybe with 30 degree lines. + +That's a natural +question-- open. + +Maybe we'll work on it sometime, +but I think it'd be neat. + +You just need a nice +gadget, and then we + +know how to compose them by +induction just like in lecture + +seven. + +So it could be a +fun thing to attack. + +Next, we go to maze folding. + +So I thought I'd +show-- we've seen + +this maze fold-- the 6.849. + +So this is folded +by Jenny and Eli + +based on the algorithm that +you saw, and you might play + +with it on your +problem set three. + +Design your own maze. + +You can click any +pattern you want. + +Make whatever letters you want, +or any other cool orthogonal + +pattern. + +Marty and I have made a +bunch of different print + +designs based around this idea +of taking not just the crease + +pattern you get for +folding-- here we're + +folding the word yes +in three dimensions-- + +but we've shaded the original +piece of paper in this pattern. + +So that it looks like nothing +on here, but when you fold it, + +the shading comes +together to spell no. + +So it's kind of ambiguity, or +the shadow of the yes is no, + +and so on. + +And Jenny and Eli folded +that as well, and here it is. + +The first folding. + +But our idea is not +necessarily to fold them. + +I mean, it's cool that +they can be folded. + +That's neat +conceptually, but we also + +like to design ones that +really should not be folded. + +Next one here is +science and art, + +so you fold the science +in three dimensions + +and the art is in the +background lurking there. + +I imagine this will +never be folded. + +It'd be rather painful. + +Here's another very +complicated one. + +Here we're playing around with +putting little shaded regions + +in these squares. + +These are just the +squares that end up + +mapping to the flat +parts over here. + +And so you get-- +we took an image + +and spliced it up into +thousands of pieces. + +So you get-- this is a +photograph of Martin Gardner, + +who died a couple +years ago sadly. + +We never met him, +but he was the father + +of recreational mathematics +among other things. + +Also magician-- +lots of cool things. + +So this is in tribute to him. + +And this is our latest +design in this spirit. + +We're trying to be a +little more artistic + +and just be about the crease +pattern, not necessarily + +the folding. + +So the 3-D thing that this +folds into is not shown here, + +and in theory all these +lines go off to infinity. + +But this spells the word glass. + +We made it when we were at +the Pilchuck Glass School + +this summer. + +And it's now on t-shirts of many +glass blowers around the world. + +How many of them know +exactly what it folds into, + +I don't know. + +But that's pretty cool. + +So we were working +on glass folding, + +so that seemed like a +natural thing to do. + +So that is maze folding +and see some designs. + +How you can use it +for cool things. + +The next topic is +NP-hardness, and that + +will be what we spend +most of today on. + +And so, first kind +of general question + +is what does it all mean? + +What does NP-hardness +really tell you? + +Can you give me like a +specific instance that's hard, + +and-- this is more for people +who haven't seen MP-hardness + +before-- the answer is no. + +NP-hardness is kind of a +conceptual, philosophical + +thing. + +No specific problem +is ever NP-hard. + +It's all about whole families +of problems being hard. + +And really it's about +measuring the growth of problem + +complexity with problem size. + +So in this case, it's +how much running time + +do you need to +solve your problem + +as a function of +the problem size. + +And we're interested in whether +that grows only polynomially + +or it grows exponentially, +and NP-hardness probably + +implies exponential growth. + +A nice example of this is chess. + +So eight-by-eight +chess-- people have + +spent many years trying to +solve it and do it perfectly, + +and to be the best player. + +But from a theoretical, +computer science perspective, + +chess in its original +form, is trivial + +because it just has a +constant number of states. + +You could just enumerate +them all in constant time. + +You know who wins in +chess-- probably white. + +But it's not very satisfying, +but the more interesting thing + +to say is to study +chess as it grows, + +and the natural way to make it +grow is with an n-by-n board. + +So with an n-by-n +board, if I give you + +an arrangement of +chess pieces and I + +want to know who wins, +that you can prove + +is something even stronger than +NP-hardness called X-hardness. + +So there you can actually +prove you need exponential time + +to solve n-by-n chess. + +And that gives you a sense +the chess really is hard. + +There's not going to be a good +algorithm that magically will + +solve it for eight-by-eight, +because in general as board + +size increases, you know it +has to grow exponentially, + +and probably eight-by-eight +is big enough. + +That there's no good +algorithm to do it. + +You can't prove that +there's no good algorithm + +to do eight-by-eight, +but you can + +prove there's no good +algorithms to do n-by-n. + +So that's the limitation of +theoretical computer science + +and of NP-hardness. + +So you take any +particular crease pattern. + +You want to know +whether it folds flat. + +You might be able to do +that by exhaustive search + +and exponential +time might be OK, + +but you know that as the +crease patterns get big, + +you're totally screwed. + +So, next question about +hardness is can we + +do it with a little +less hand waving? + +So in a little bit +more detail, because I + +covered a lot of proofs. + +So I'm going to +look at two of them. + +The simple full hardness-- +which is from partition-- + +and the crease pattern +flat foldability which + +is from not all equal +SAT-- 3SAT-- and I'll + +give some more details. + +So let's start by going +through this proof. + +Remember, in general with +an NP-hardness reduction, + +we want to take some +known hard problem + +and convert it into our +problem, because that proves + +that our problem is at least +as hard as the original one. + +So in this case, the known +hard problem is I give you n + +integers-- a1, a2, up to an. + +And I want to know, can I +split them into two groups + +so that the two +groups have equal sum? + +And here we're mapping that into +the simple fold problem, which + +was given a crease +pattern can you fold it. + +Can you follow all the +creases flat by simple folds? + +We're mapping it +into these lengths-- + +these lengths are the AIs +between the different legs + +of the staircase. + +And then there's +this extra stuff. + +This is a super long +length-- length l-- + +and this is a doubly +super long length-- 2l. + +And then there's this +frame, which has height 2l, + +and this part is aligned +right at the midway. + +And so the idea was if there's +a partition-- if there's + +a partition of the AIs +into two groups-- call them + +Group A and Group +B-- then I'm going + +to fold some of the creases. + +The ones between any two +guys of different groups. + +Because folding here corresponds +to switching directions. + +So whenever I fold, I'm kind of +switching which group I'm in, + +and then Group A will +be all the up directions + +and Group B will be all +the down directions. + +So maybe both of these +guys are in Group B + +so they both go down, and this +is a Group A guy, so we go up, + +and then down, and then up. + +And if we get them-- A and +B to be balanced-- then + +we'll end up right +where we started. + +So we'll end up right at +the middle point here. + +And, in that case, there's +these two more folds-- + +this vertical fold and +that vertical fold. + +And then if you-- sorry. + +Yeah, I don't have +it drawn here. + +When you do one more fold here, +this will fall into the frame, + +and if you got this to stay-- +if you got this point basically + +to be aligned with +here, then going up L, + +and then back down to L will +not collide with this box. + +It just barely fits, +and so you fold that in. + +Then you fold this vertical +line and you fold it back out. + +So the goal was just to +get these two folds made. + +Once they're made and +it's back out here, + +you can finish all folds +that you didn't fold before. + +And what we're checking here +is that during all this motion, + +you don't get collision +because simple folds are not + +allowed to collide +during the motion. + +So if this, for example, went +too far down or too far up + +and it collided with +the frame, then you + +wouldn't be able to make the +second vertical fold here + +because you'd have to +bring the frame with you, + +and the frame's not +supposed to move. + +So in particular, +there's this question. + +Seems like we're not +making all the folds, + +and that's because I +didn't say the last part. + +After you fold it in +here and avoid collision, + +you fold it back out with the +second of these two folds. + +Then you can finish +all the folds. + +Indeed the goal is +to fold everything, + +but in order to avoid +collision, when I fold this, + +this thing has to be nice and +compact and fit within this 2L + +boundary. + +Then it goes through. + +So what we really +need to show though + +at the top level is +given any set of AIs, + +we can convert it into an +equivalent simple fold problem. + +There's actually two things we +need to check for equivalence. + +We need to check that +if there's a partition, + +then there's a way to fold it. + +We also need to check +the reverse, which + +is if there's a way to fold +it, then there's a partition. + +But both of these kind of +follow from this argument. + +In order to-- when +we make this fold, + +this guy's got to-- or +whichever of these two is first. + +They're kind of equivalent. + +If we collide, we won't be +able to finish the folding. + +That's the claim. + +You might have done all +the folds over here, + +but they'll be the +second of these two, + +and so when you do the first, +you'll either get stuck + +or you'll be able to proceed. + +If you were able to +proceed, you can read off + +from the ups and downs here +what the partition was. + +So you can convert in either +direction using this reduction. + +Any more questions about +the simple folds one? + +So, of course, one of the easier +proofs, the crease pattern + +flatfold ability is definitely +on the more complicated side, + +and this was the +overview of the proof. + +Basically there were lots +of little local gadgets. + +There's the wire, +which communicates + +truthiness or falsity +as we like to say. + +Or things like-- the +main gadget is the one + +at the top and not +all equal clause, + +which forces among the +three wires coming in. + +They can't all have +the same value. + +So there could be +two true, one false. + +Or two false, one true. + +But not all true +and not all false. + +And then we needed +some auxiliary gadgets + +for turning, duplicating, +and crossing over. + +Those were fairly +straightforward. + +The heart is a wire, and +a not all equal clause. + +And so the idea was we were +given a formula-- in this case, + +it's a bunch of triples, +and each of the triples + +should be not all equal. + +And there's like n +variables-- there's + +a lot of different clauses +on those variables. + +A lot of not all equal +constraints on those clauses. + +We want to represent that +by the flatfold ability + +of the crease pattern. + +So we basically make +all the variables + +off the left edge +of the paper here. + +We make lots of copies +of them by zigzagging, + +and then we make lots of clauses +at the top-- only drawn two + +up there-- and then in our input +we're given a bunch of triples + +of variables that should +belong to a common clause, + +and we just route these +signals to go to that clause. + +And then the clauses constrain +the values of those variables + +to be not all equal in +the appropriate triples. + +And the splitters +down here enforce + +all the different copies of +that variable to be the same. + +And so any flat +folding will require + +these guys are consistently +assigned one truth + +value throughout +the construction, + +and those clauses will +force not all equal things + +to be seen in pairs. + +So if there's a flat +folding of this, + +you can read off on the +mountain valley assignment + +here which one based +on whether it's + +left valley, right mountain, +or left mountain, right valley. + +You can read of what +the truth assignment is + +that satisfies all the clauses. + +That was one direction +from flat foldability + +to satisfiability of the +not all equal triples + +in the reverse direction. + +If there's a not all equal +assignment of triples, + +you need to verify that this +thing actually does fold flat. + +I didn't detail +that, but basically + +to do that, you have to prove +that each of the gadgets + +works exactly as desired. + +So you could really fold it +flat if these have equal value, + +for example, and this +has a negated value. + +You could actually always +fold the not all equal cause + +when it's satisfied. + +And then once you know that +each of these gadgets-- + +because the gadgets are +very small-- once you know + +that each of them +folds correctly, + +and they have a sort +of comparable interface + +because these things are +just extending through, + +you could basically paste +glue together all of those + +folded states. + +So as long as you +verify the gadgets work, + +the whole thing +will work provided + +there is a satisfying +assignment. + +So that's-- yeah, question? + +AUDIENCE: Can you actually +go in the other direction + +properly in the same cell? + +Can you map any flat +foldability [INAUDIBLE]? + +PROFESSOR: OK, can you +map any flat foldability + +of a crease pattern +problem to SAT? + +That doesn't follow +from this proof, + +but I think it should be true. + +Uh, let's see-- I think so. + +So if I give you +a crease pattern, + +I want to know +whether it folds flat. + +As mentioned in lecture, +you can determine + +where all the facets lie in 2D. + +And challenges the +stacking order, + +which implies the mountain +valley assignment. + +So I think you could +make a variable in a SAT + +problem for this piece-- +this little polygon lives + +in the stacking level. + +You have to figure out how many +levels you need, but at most 10 + +of them, I guess. + +And then write down +the constraints + +between different polygons +if there are no crossings. + +There's a paper +by Jacques Justin + +that does that explicitly. + +So that should give you a way to +reduce to SAT, which gives you + +an algorithm-- an exponential +time algorithm to solve it. + +In general, I'm pretty +sure this problem + +is in NP, which implies there's +at least an algorithm for it. + +But I think in particular, +you can reduce it to SAT. + +So that's a good question. + +So pretty much +every problem we'll + +talk about at least with +origami has a finite algorithm + +to solve it, but it's a very +slow algorithm in general. + +Of course, there's a lot of +good SAT solvers out there, + +and I don't know if people +have actually tried to do that. + +I know there are some-- there's +a software called ORIPA, which + +in Japan some +versions try to find + +a valid folding-- a +valid folded state + +by some kind of careful, +exhaustive search. + +I don't think they use +SAT solvers though. + +You might get more mileage +out of SAT solvers. + +Other questions +about this proof? + +There's one explicit question +about the reflector gadget. + +This probably worth talking +about because these arrows + +are maybe not so +obvious what they mean. + +So the question is what +is true and what is false. + +It's kind of philosophy, +but in this case + +these arrows are explicitly +drawn on this diagram. + +If you look closely, there's an +arrow this way, then this way, + +then this way. + +And that's defining what we mean +by the orientation of a wire, + +and then if it's a valley +on the left relative + +to the arrow, that's true. + +If it's mountain on the +left relative to the arrow, + +that's false. + +And that's why this +is drawn this way + +assuming I got it right. + +Here it's valley on the +left relative to the arrow. + +Here it's mountain on the +left relative to the arrow. + +So notice these are pointing +in different directions. + +So that can get a +little confusing, + +but it's kind of what +we want in that proof + +because we really want to route +that thing in this direction. + +We don't care about +what things look + +like relative to +the center here. + +Because the center-- the +gadget we are looking at + +keeps changing. + +So we want to route +this as a single wire. + +And this one I +already talked about. + +You need to prove +both directions-- + +that flat foldability implies +not all equal satisfiability, + +and the reverse. + +OK, we move on. + +So now we get to +some new material. + +So I mentioned in the +lecture that there + +are two hardness proofs. + +The one we've been talking +about is given a crease pattern, + +does it fold flat? + +That's strongly NP-hard. + +And the other is if I +give you something-- + +I might even tell you +it's flat foldable. + +That's kind of not too relevant. + +But I give you +mountains and valleys, + +and I want to know-- +I want to find + +a valid folded +state of that, or I + +want to decide whether +the mountain valley + +pattern is valid. + +These are strongly NP-hard hard, +and this is a different proof. + +It uses completely +different gadgets. + +So I thought I'd show you +some of those gadgets. + +Sort of the key ones. + +So the first part +is the wire, and I + +think I made one of these. + +Maybe I didn't. + +No wire. + +Well, this is the end +of a wire-- er, no, + +that's not the end of a wire. + +Here's an end of a wire. + +So the idea here is we've +got a fixed mountain valley + +pattern now because that's +no longer free for the folder + +to choose. + +And you've got +two tabs, and they + +could stack one +way or the other. + +In this case, they +can stacked like this, + +or they can stack like that. + +So I've got a +choice in stacking. + +That changes the folded state. + +That's the choice that the +folder is going to make, + +but in either case the mountain +valley assignment is the same. + +So that's how we're going to +communicate true and false, + +and I haven't +provided orientation. + +Should have drawn +an arrow there. + +Next gadget is this tab +gadget, and this is just + +a tool for building +weird shapes, + +and it's kind of similar +to some of the things + +you've seen in the +checkerboard folding. + +So our crease pattern looks +like this, and fold it flat. + +And there's two ways to fold it. + +Actually, a few +different folded states. + +But in particular, +there's a state + +like this where there's this +individually manipulatable tab, + +but there's no crease here. + +So it can't go backwards. + +The crease is in here. + +So it's got a fall +down like that. + +OK, so what this reduction +does is, ahead of time + +basically, force a +lot of these foldings. + +And so we start +with a square paper. + +We end up with a smaller square +paper with tabs sticking out + +in various directions +of various places. + +So this is much messier +and it'd be harder + +to draw the whole diagram of +what your crease pattern looks + +like, but in theory +you can do this. + +That's also kind of +like the box pleading + +method where you just +make a cube ahead of time, + +and it's like you had +a square originally. + +There just happens to +be a cube sitting here, + +and then you do other folding. + +And the angles in this +crease pattern-- these + +are not 45 degrees. + +They're at a bit +of a weird angle + +to basically force +this to happen first. + +It can't interact with +any of the other gadgets + +that I show you. + +Because you've got to get rid of +those angles in the beginning. + +Then, the main gadget here +is the not all equal clause, + +and that's what I +have folded here. + +So it's a little crazy, +but basically you've + +got three pleats-- three of +these double pleats coming + +together. + +These guys could stack-- this +one on top, this one on top. + +Now we're the same +for all three of them, + +and then you've got this little +twist like thing in the center, + +and it's really +hard to draw what + +the folded state looks like. + +This is what it looks +like within shadow pattern + +with transparency. + +Here's the real thing. + +And also, there's +these yellow tabs + +attached at very +specific locations. + +And this is a little +hard to imagine. + +I encourage you to fold +one of these in order + +to really see what's going on. + +But as I said before, you've +got-- each of these guys + +can be independently stacked +one way or the other. + +There's that one or this one +can stack this way or that way + +for all three, but we want +to forbid the case where + +they're all stacked +the same way. + +And the arrows here are all +pointing towards the gadget. + +So we want to forbid +the case when they're + +all-- when it's +rotationally symmetric. + +Gadget is rotationally +symmetric, + +but if you choose the layer +order rotationally symmetric, + +you're in trouble. + +So let me make it +rotationally symmetric. + +That would be like this. + +So when it's +rotationally symmetric, + +you see-- basically +all the panels + +you see-- there's three panels. + +This one, this +one, and this one. + +Each of them has a +tab sticking out, + +and basically these tabs have +to also be cyclically ordered, + +but it's not possible-- +this is hard to do. + +It's like this. + +You see they're kind +of colliding here. + +Because if you look at each +of the tabs in projection, + +it collides with where +the tab is attached. + +So you basically-- if you went-- +so someone has to be the lowest + +tab, and that tab will intersect +the other two tabs actually + +where that tab is attached. + +So it'll penetrate +and you can see + +they're not very +happy to stack here. + +But if I change the +layer order in any way, + +our lowest tab is actually +happy to go behind other layers, + +and then you can just stack +them, and they barely fit. + +So it's a little tricky to get +all the details here to work, + +but I think this particular +geometry-- and the reason + +I drew this in this exact way +is to make sure yeah, everything + +works. + +You do not penetrate here, +which would be a problem. + +You do not penetrate +this crease, + +which would be a problem. + +So the tab just fits in +between here and here, + +but it does cross. + +If you look at this tab, +it's attached along this edge + +as drawn up there. + +And this tab here will penetrate +this part of that edge, + +and it will penetrate this +part of this edge which + +is where this tab is attached. + +So they cause trouble in +this cyclic situation, + +but when it's a cyclic +like in this picture, + +you can put that +bottom tab way down + +here and avoid any collision. + +Then you can basically +break the cyclic condition, + +and you get to stack them +in some linear order. + +So it's a little hard to +see without physically + +manipulating it. + +Feel free to come and +play with that after. + +That's their proof. + +Now there's also splitters, and +turn gadgets, and crossovers, + +but I'll leave it at that. + +Those are more similar. + +This is the heart of what's +going on in this proof. + +So it's a completely +separate proof from the one + +that we saw before. + +Any questions about that? + +All right-- + +AUDIENCE: Here. + +PROFESSOR: Yeah? + +AUDIENCE: I don't understand +why the tabs fold. + +PROFESSOR: How do the tabs fold? + +AUDIENCE: No, why do we need +tabs if everything folds? + +PROFESSOR: So the tabs +are being used as a device + +to build gadgets. + +So the tabs serve no +purpose by themselves. + +But this gadget involves +first folding three tabs here, + +which are actually +pointing-- they're + +pointing in that +direction, I believe. + +Then you add this crease +pattern afterwards. + +So originally there +are tabs here, + +which means there's a +bunch of creases here. + +After you fold them, then you +lay on this crease pattern. + +So if you unfolded it, you +get some much more complicated + +crease pattern. + +Which is when I made that, +I just taped the tabs on. + +But in reality, first you fold +the tabs so they exist there, + +then you fold this on top. + +So the fold crease pattern +would be quite complicated. + +It's going to have +tabs here, tabs here, + +tabs there, and then this +reflected a few times. + +And so then when you +fold it-- the fold gadget + +is this thing with the tabs. + +The tabs are just +like a stepping stone + +toward making this gadget. + +The other gadgets use more tabs. + +Obvious open problem here is +to make a simpler reduction. + +Shouldn't have to +be this complicated, + +and I've heard Tom Hall talk +about different approaches + +for making simpler +NP-hardness proofs, + +but we're not there yet. + +Other questions? + +AUDIENCE: So these proofs +don't imply anything + +about the [INAUDIBLE]? + +They can all be very +easily [INAUDIBLE]. + +PROFESSOR: So this proof +implies these kinds + +of tessellation style crease +patterns are hard to fold, + +which implies that +in general crease + +patterns are hard to fold. + +But you could look at some +other specific pattern. + +For example, it's +the next topic. + +You could look at +map folding where + +you have horizontal +and vertical creases + +in a rectangular sheet of paper. + +Maybe each of these squares +is-- or each of these cells + +is a unit square, let's say. + +And I give you a mountain +valley assignment on that. + +Some of these are mountains. + +Some of them are valleys. + +Whatever. + +And I want to know +does this fold flat? + +That we don't know +the complexity of. + +Could be solvable by +polynomial time algorithm. + +Could be NP-hard. + +And this is actually mentioned +in lecture two notes, + +but not actually orally. + +And so I wanted to +get back to this. + +This is from lecture two notes. + +2D map folding, Jack +Edmonds poses this problem, + +can you characterize flat +foldable mountain valley + +pattern. + +Is there an algorithm +or is it NP-hard? + +And even the 2-by-n +problem was open + +when I wrote these +notes in 2010, + +but it has since been solved. + +So I thought I'd tell you a +little bit about that solution. + +So yeah, there can be special +cases of crease patterns + +that are easy to solve. + +We just know in +general they are hard. + +So 2-by-n is this +kind of picture. + +So this is what I call +2, counting cells. + +This is based on a class +project in this class + +from two years ago by +Eric Lew and Tom Morgan, + +but the paper got +finished this year. + +So it's based on a +series of reductions. + +On the one hand, we're going to +start with something called-- + +OK, so we have map +holding on the left. + +We're going to +convert map folding + +into a different presentation, +which is NEWS labeling. + +We're going to convert that +into something called a top edge + +view. + +We're going to convert +that into a ray diagram. + +And the last part, which I +won't talk too much about, + +is we convert that into +something called a hidden tree + +problem. + +Each of these steps is +fairly straightforward, + +but there are obviously +a lot of them. + +But in the end, you get a +polynomial time algorithm + +to solve this, which implies +you get a polynomial time + +algorithm to solve this. + +And I'll talk mostly +about these reductions. + +It's the same idea +in NP-hardness. + +We use reductions from a +hard problem to our problem. + +In this case, we're +doing the reverse. + +We're reducing our problem +to an easier problem, + +so that by the end we +get something that's + +so easy we know how to solve it. + +The reductions are useful +both for positive results + +and negative results. + +So let me show you +visually some-- + +oh, before we get +to the proof, I + +wanted to mention this +puzzle which you probably + +folded in problem set one. + +It's a map folding problem. + +It's a 3-by-3 map, +and so we didn't + +have any good algorithms +to solve them. + +So we used a not +so good algorithm-- + +namely exhaustive enumeration. + +We enumerated all possible +folded states of a 3-by-3 map. + +We drew them out graphically. + +There's a scroll bar here, +so you don't see them all. + +But we put them in +a giant-- I forget, + +there's 1,000 +folded states or so, + +so it's like 100-by-- +whatever-- 10 array. + +And for each of +them-- so here's where + +you're designing your pattern. + +So you could make holes. + +You could put in patterns. + +This is sort of an early design +where it would spell MIT. + +The hole would show +the I on another side, + +so it's equivalent to +the puzzle you solve. + +And this is what +the top looks like. + +This is what the +bottom looks like. + +So you can hover over these +and change the letters that + +appeared, and then +it would show you + +what every single +state would look like, + +and it would color it in yellow +if one side looked like MIT, + +and it would color it in red +if both sides look like MIT. + +And the point was +to verify there + +was exactly one solution +for that puzzle. + +And so we kept-- we +would fold things + +to make it a tricky fold. + +Then we put into the +software and label things + +accordingly, then +put into the software + +and see is there unique folding? + +And then we could add in +extra misleading clues here, + +and see did they accidentally +make an extra solution? + +So we could add in +extra stuff to pack in. + +As much irrelevant stuff as we +could, and still make it unique + +so it's more challenging. + +That's a nice use of exponential +algorithms to design puzzles. + +All right, but +back to this proof. + +So I have here a much +simpler map than this one. + +This is what we +call the NEW map. + +N-E-W. + +So the labeling +here is very simple. + +If you look at this crease +pattern, by [INAUDIBLE], + +there's got to be three of one +type and one of the other type. + +So just label each vertex +by which way is unique. + +So from here, the +North direction + +is the uniquely label-- it's the +mountain among three valleys. + +And then this vertex-- +the East label-- + +is the mountain +among three valleys, + +and then the next one is the +West label among three valleys. + +Of course it doesn't +have to be like that. + +It could, for +example, you can have + +three mountains at a vertex, +but then the label of this guy's + +going to be W. It's going +to be the one that's + +unique among the other three. + +So if you fold this +map, it looks like this. + +I have one here, but it's +a little hard to see. + +We've got lots of back +and forth on the top edge. + +Some orienting it so that +the-- we've got 2 by n maps. + +So there's two +critical features. + +There's the center line. + +I'll call that the +spine of the map. + +There's the top side +and the bottom side. + +When you fold +that-- this is just + +a sequence of simple folds. + +You see at this last fold, the +top side and the bottom side + +come together, and the +spine is-- stays together. + +So when I orient it like +this as in the picture, + +the top side is where originally +the top and the bottom + +of the map all come to here +because of that spine fold, + +and the spine folds +are all down here. + +You can't see them +here, but there's + +you can see them at +the bottom there. + +There's some kind of +connections on the bottom, + +but there's this nice relatively +one-dimensional picture + +up here. + +So we're going to draw that. + +This is the top edge view. + +Got clipped a little +bit, but there's + +one more segment at the top. + +So that is just this. + +See it? + +Now there's also +these blue lines. + +The blue lines correspond to +what's going on at the bottom + +from the spine. + +Because if you think +about it, you've + +got the-- in a +2-by-n map-- you've + +got the top panels and these +edges making the top edge. + +And you've also got the +bottom panels and these edges + +making the bottom edge. + +They come in pairs. + +These guys are paired up. + +These guys are paired up, +and so on down the line + +because they are +joined by a spine edge. + +Those spine edges +correspond to the things + +on the bottom of the +folding, and they + +need to not cross each other. + +And that's what's illustrated +by the blue connections. + +So the very top edge is paired +with the very bottom edge. + +These two-- this panel +here and the back panel + +here-- are connected +on the bottom. + +And that-- I'm sorry, +that's not true. + +This one is paired +with this one. + +The top one is paired +with the second one. + +So it's actually these two +are connected on the bottom. + +That's this little connection +here, and then these guys-- + +this wraps around everything. + +That's that connection. + +But what you can't see +it in this folding-- + +because it's hidden inside-- +is that within this connection + +on the bottom, there's this +connection on the bottom. + +And within that one, +there's this connection. + +Now this is OK. + +Might look like they're crossing +because they're overlapping. + +But as long as they +are nested-- as long + +as you don't start from +inside here and go to outside. + +That would be a crossing. + +You start inside, +you should end inside + +like in all these pictures. + +If you start outside, +you should end outside. + +So that's why-- these guys +are disjoint, so that's OK. + +This is nested in +that, so it's OK. + +Kind of like +balance parentheses. + +And so that's what it makes. + +A top valid top edge view. + +What's nice about this is it's +a one-dimensional diagram. + +What's not nice is it has all +these crossings because there's + +the blue stuff on top +of the black stuff. + +So it's a little +hard to find-- we're + +trying to find a +valid folding state. + +We're trying to +find one of these. + +We're not restricting ourselves +to simple folds here yet. + +Simple map folding we already +solved in lecture two. + +So this is all-- I should've +said non-simple folds. + +That's what makes +it hard, and that's + +what's still open +for 3-by-n maps + +if you don't know how to do it. + +But for 2-by-n maps, +we've made two steps here. + +We have another view, +which is the ray diagram, + +and this is really +specific to 2-by-n. + +And it lets us reduce +to a tree problem. + +So before we get there, +let's talk in general + +about the top edge view. + +You can actually convert from +the North, East, West, South + +labeling to a top edge +view in the following way. + +Whenever-- and you can kind +of see what's going on. + +So first we have an n. + +So we've got these +two guys, which + +are just paired +together happily. + +That's the beginning of the map. + +Then we turn left, and we've got +this guy paired with this guy. + +And so, in general, +whenever you have a North, + +you turn left with +your two guys. + +So that's what happens. + +Then we hit an East in +the map, and what happens + +here is this guy turns right, +but this one turns left. + +This is what you might +call an inside turn. + +It's like an inside +reverse fold in origami. + +And in general, whenever +you have an East, + +you turn inside like that. + +So this guy's paired +with that one, + +and now this guy's +paired with that one. + +They both turn in. + +And then it's symmetric. + +Next one is a w, which is +the opposite of an e, which + +means you turn out here. + +And in general, whenever you +have a West, you turn out. + +And a South, you turn right. + +So those are the +four possible things + +you could imagine when you +have a pair of things turning, + +and those exactly correspond +to N, E, W, and S. + +So it's clear what you need +to do in this situation, + +but there's flexibility, right? + +For example, this guy-- +when you turn out-- here + +I turned out to the +very next layer, + +but this could have +turned out to go up here. + +Would that be OK? + +Ah, no. + +If this one turned +out to go up here, + +that edge up there would be +paired with this one down here. + +So there'd be a blue +line going like that, + +and that would be a +crossing situation + +because that blue line +would cross this one. + +Because it starts inside +and it goes to outside. + +So it's a little tricky. + +This definitely gives you +some of the layer constraints, + +but it doesn't +check for crossings. + +Which is the big +challenge in this problem. + +So we're going to +simplify this diagram. + +So just think about +top edge views. + +Forget about map folding now. + +You can forget about +the previous layers, + +and we are now focusing +on this reduction. + +So we've got top edge view +converting to ray diagrams. + +You can see it's much simpler. + +This is the ray diagram +of that picture. + +And essentially-- +there's two ways + +to think about what we're doing. + +Instead of having two edges, +and we track two edges turning, + +we just want one edge. + +That's one thing we're doing. + +You can think of that as +tracking the spine instead + +of the top and the bottom sides. + +But it's a little-- ray diagrams +are going to get confusing. + +I'll just tell you +that right now. + +Every time I look +at it, I understand + +it a little bit +more, but it's not + +going to be obviously that +this is equivalent to this. + +I'll just tell you-- +here's an alternate way + +to think about it. + +Basically, the vertical-- +the y direction + +here is going to +be nesting depth. + +So whenever we go in +like this, we go deeper. + +So for whatever reason, +I flipped the labeling, + +but it is indeed East. + +When you go in, you go down. + +I should have just moved these +two figures so they correspond, + +but when you go East you go +down a layer because you're + +nesting deeper. + +And when you go West, +you're going out, + +so you go up a layer in this +new weird ray diagram view. + +And North and South turn out +to not turnaround in this view. + +We're just going to +fire a ray downward, + +and there's either a +North ray-- a blue one-- + +or a South ray-- a red one. + +And so if you follow +this diagram, it's N-E-W. + +So first we have an N, which +means we shoot a ray down. + +Then we have an E, which +means we turn downwards. + +And then we have a W, which +means we turn to go up a layer. + +And I haven't told you what +the constraints are here, + +but I claim this is a valid +folding just like that one. + +And it's obviously a +lot easier to draw. + +It's a much slower complexity. + +But the cool thing +is you no longer + +have these crossing parts. + +So let me show you-- +first, let me tell you + +what the constraints are. + +So in general, you're going +to have lots of downward rays. + +This is a North. + +This is a South. + +A North, a South. + +So if you had like N, S, +N, S, in your pattern, + +it's just going to +be a straight segment + +with downward rays +of different colors. + +First constraint is whenever you +have a an N ray-- a North ray-- + +it has to hit another North +ray or just go off to infinity. + +And the same-- South rays +can only hit South rays + +or go off to infinity. + +So they line up in +this way, but you + +can stretch the x-coordinate +to do whatever you want. + +This corresponds to basically +jumping over a bunch of layers. + +When you turn in +your folded state, + +you can skip a bunch of +layers and just go up here. + +So that corresponds to jumping +over a bunch of folds here. + +But in particular +we get these things + +called constrained segments. + +Constrained segments +are portions + +of this black spine between +two rays that below it only + +see black. + +OK, so for example, this +one is unconstrained, + +because below it, you +can see off to infinity. + +So that's unconstrained. + +We don't care about that one. + +But among unconstrained +segments-- + +these are two +constrained segments-- + +we want that all of the rays +that they see below them-- + +so here I see one red +ray, one blue ray-- I want + +the number of reds +and blues to be equal. + +So this is valid because +there's one red, one blue. + +This one is invalid because +there's two blue and one red. + +This turns out to be +the right constraint. + +Essentially this is saying +however much you spiral, + +you should spiral. + +That's the intuition. + +So here you're spiraling +twice, unspiraling once. + +So you're trapped inside, and +so these folds cannot actually + +come together. + +The rays coming +together correspond + +to a nice nesting +between two North folds. + +So it's not obvious, +but this turns out + +to be the only +constraints you have. + +The black should +not cross itself. + +Constraint segments should +be valid in this way, + +and blue should hit blue +and red should hit red. + +So that's not obvious, +but it's true, + +and then you can take very +complicated diagrams like this + +and simplify them into +these nice pictures. + +So these are two +different foldings + +of the same pattern, +which I guess + +is N-E-N-- I can see +that easily here. + +You could have also +extracted it from here. + +There's two foldings +because these two layers + +could go here in the middle. + +Or they could be pushed +up to fit in here, + +and then we get this picture. + +And in the ray diagram-- +you can see this + +pretty easily-- either you have +these n rays just both go off + +to infinity, and this is an +unconstrained segment so we + +don't care about that there's +only one North ray below. + +Or, you can extend +the x, because I + +can stretch the +x parts however I + +want and make these blue +segments align with each other. + +And that corresponds +to this folding. + +So really, all folded +states of the original thing + +are represented by +the ray diagram. + +Of course, if I had any +W, this would be valid, + +but this would not be that. + +N-E-S-- blast from the past. + +If I had N-E-S, then this would +be blue, this would be red, + +and so this would be valid. + +But this would be +invalid, and so on. + +So it's obviously a lot +easier conceptually, + +but you can also-- and here's +a more complicated algorithm. + +You take a really crazy map. + +This notation, by the +way, was introduced + +by Jacques Justin +like late 1980s. + +You may remember his name +from Kawasaki-Justin theorem. + +So at the same time he +was looking at map folding + +and he came up +with this notation, + +the ray diagram was introduced +in the open problem session + +in this class two years ago-- +or actually five years ago + +if I recall correctly-- by +David Charlton and Yoyo Zhou. + +And then it was picked +up again two years ago, + +and finally we took +this ray diagram + +and came up with an algorithm. + +So how does the algorithm work? + +Here's a ray +diagram-- the black, + +and the red, and the blue. + +We observe that the blank +space here between the spine + +stuff-- between all the black-- +is kind of a tree structure. + +You've got-- and +that's what's drawn + +in cyan with the red dots. + +So if you draw a node every time +you turn around on the outside. + +Then you say, well, I can get +from this node to this one, + +so I'm going to draw +a segment there. + +And I can get from +this node to this one + +without crossing any black, +so I'll draw a segment there. + +That's sort of it on that side. + +There's nothing else down here. + +That sort of doesn't count. + +But here's there's +another dot, and I + +can get from this one +to there by going out + +here without crossing black. + +Here to here, here to over +here without crossing black, + +and so on. + +So that cyan structure is +a tree-- has no cycles. + +Which in general is good +news for algorithms. + +Trees are relatively +easy to find algorithms + +for using dynamic programming. + +If you've seen dynamic +programming for trees, + +this is not like that. + +It's a little different because +we don't know what the tree is. + +We have to figure +out what the tree is. + +But basically, we can +guess the tree recursively. + +So there's some first +node-- I don't know, + +maybe it's this one-- +just guess that. + +Not randomly, but guess +means try all the options. + +So you guess some node, and +then OK, we've got-- maybe + +we've got two subtrees. + +Maybe we've got three. + +I think that's about +all there could be. + +And so, just guessed that, +and then so recursively guess + +a subtree here and +a subtree here. + +And each of the sub +trees corresponds + +to a sub segment of this-- +of the original map. + +The spine, roughly speaking. + +And roughly speaking, +these portions + +do not interact with each other. + +There's this issue of +how the rays align, + +and that's sort of the challenge +in getting this algorithm + +to work. + +But you can essentially +locally check + +whether a subtree +is good enough. + +That it will interact OK +with a different subtree, + +and just split this +problem up recursively + +guessing all the way. + +Effectively trying all +trees, but in polynomial time + +instead of exponential time. + +Forget the running time is +something like n to the 10 + +or some really big constant, +but at least finally we + +know 2-by-n maps can be +solved in polynomial time. + +We give the mountain +valley assignment. + +We still don't +know about 3-by-n. + +That's the open question, and +these techniques unfortunately + +don't seem to apply. + +You definitely don't +get a tree anymore. + +You might get some +nice structure that's + +kind of vaguely tree +like, but this was already + +super complicated. + +So we've gotten stuck here. + +Any questions? + +All right. + +That's it. \ No newline at end of file diff --git a/xHE5uf-S9Iw.txt b/xHE5uf-S9Iw.txt new file mode 100644 index 0000000000000000000000000000000000000000..31799155f6e8b22f61d14d9b93e508d393d4e8b6 --- /dev/null +++ b/xHE5uf-S9Iw.txt @@ -0,0 +1,1611 @@ +align:start position:0% + +let's turn to our deck subject them so + + align:start position:0% +let's turn to our deck subject them so + + + align:start position:0% +let's turn to our deck subject them so +this is still time-dependent + + align:start position:0% +this is still time-dependent + + + align:start position:0% +this is still time-dependent +perturbation theory we will be doing + + align:start position:0% +perturbation theory we will be doing + + + align:start position:0% +perturbation theory we will be doing +time-dependent perturbation theory a + + align:start position:0% +time-dependent perturbation theory a + + + align:start position:0% +time-dependent perturbation theory a +little longer all of today's lecture and + + align:start position:0% +little longer all of today's lecture and + + + align:start position:0% +little longer all of today's lecture and +a little of next times lecture so we're + + align:start position:0% +a little of next times lecture so we're + + + align:start position:0% +a little of next times lecture so we're +going to be talking now about light and + + align:start position:0% +going to be talking now about light and + + + align:start position:0% +going to be talking now about light and +atoms so this is a classic application + + align:start position:0% +atoms so this is a classic application + + + align:start position:0% +atoms so this is a classic application +of what time-dependent perturbation + + align:start position:0% +of what time-dependent perturbation + + + align:start position:0% +of what time-dependent perturbation +theory does the problem of radiation + + align:start position:0% +theory does the problem of radiation + + + align:start position:0% +theory does the problem of radiation +interacting with atoms is more more + + align:start position:0% +interacting with atoms is more more + + + align:start position:0% +interacting with atoms is more more +detailed applications and their + + align:start position:0% +detailed applications and their + + + align:start position:0% +detailed applications and their +ionization so light and atoms atoms and + + align:start position:0% +ionization so light and atoms atoms and + + + align:start position:0% +ionization so light and atoms atoms and +we think one of the situation who will + + align:start position:0% +we think one of the situation who will + + + align:start position:0% +we think one of the situation who will +be considering a typical is a collection + + align:start position:0% +be considering a typical is a collection + + + align:start position:0% +be considering a typical is a collection +of atoms and they are interacting with + + align:start position:0% +of atoms and they are interacting with + + + align:start position:0% +of atoms and they are interacting with +light but the way they interact with + + align:start position:0% +light but the way they interact with + + + align:start position:0% +light but the way they interact with +light is maybe not as controlled as we + + align:start position:0% +light is maybe not as controlled as we + + + align:start position:0% +light is maybe not as controlled as we +had in Hyder in ionization in which you + + align:start position:0% +had in Hyder in ionization in which you + + + align:start position:0% +had in Hyder in ionization in which you +send in a wave but rather it's + + align:start position:0% +send in a wave but rather it's + + + align:start position:0% +send in a wave but rather it's +interacting with light in thermal + + align:start position:0% +interacting with light in thermal + + + align:start position:0% +interacting with light in thermal +equilibrium + + align:start position:0% +equilibrium + + + align:start position:0% +equilibrium +so there's blackbody radiation there's + + align:start position:0% +so there's blackbody radiation there's + + + align:start position:0% +so there's blackbody radiation there's +all these photons unpolarized in all + + align:start position:0% +all these photons unpolarized in all + + + align:start position:0% +all these photons unpolarized in all +directions coming at the atoms in all + + align:start position:0% +directions coming at the atoms in all + + + align:start position:0% +directions coming at the atoms in all +ways and they can produce transitions in + + align:start position:0% +ways and they can produce transitions in + + + align:start position:0% +ways and they can produce transitions in +the atoms and for that purpose we'll + + align:start position:0% +the atoms and for that purpose we'll + + + align:start position:0% +the atoms and for that purpose we'll +consider a collection of atoms of atoms + + align:start position:0% +consider a collection of atoms of atoms + + + align:start position:0% +consider a collection of atoms of atoms +and we will assume that relevant to our + + align:start position:0% +and we will assume that relevant to our + + + align:start position:0% +and we will assume that relevant to our +situation will have two energy levels + + align:start position:0% + + + + align:start position:0% + +this state will be called be still will + + align:start position:0% +this state will be called be still will + + + align:start position:0% +this state will be called be still will +call a e a and EB + + align:start position:0% + + + + align:start position:0% + +so this is interacting with light with + + align:start position:0% +so this is interacting with light with + + + align:start position:0% +so this is interacting with light with +light or with photons at at a + + align:start position:0% +light or with photons at at a + + + align:start position:0% +light or with photons at at a +temperature T so a little bit of + + align:start position:0% +temperature T so a little bit of + + + align:start position:0% +temperature T so a little bit of +statistical mechanics today in order to + + align:start position:0% +statistical mechanics today in order to + + + align:start position:0% +statistical mechanics today in order to +discover what Einstein did basically + + align:start position:0% +discover what Einstein did basically + + + align:start position:0% +discover what Einstein did basically +we're going to go through incense + + align:start position:0% +we're going to go through incense + + + align:start position:0% +we're going to go through incense +argument of balance of radiation rates + + align:start position:0% +argument of balance of radiation rates + + + align:start position:0% +argument of balance of radiation rates +and emission rates and things like that + + align:start position:0% +and emission rates and things like that + + + align:start position:0% +and emission rates and things like that +and we need to use some statistical + + align:start position:0% +and we need to use some statistical + + + align:start position:0% +and we need to use some statistical +physics for that Einstein was very good + + align:start position:0% +physics for that Einstein was very good + + + align:start position:0% +physics for that Einstein was very good +at using statistical physics and the + + align:start position:0% +at using statistical physics and the + + + align:start position:0% +at using statistical physics and the +frequency associated with this + + align:start position:0% +frequency associated with this + + + align:start position:0% +frequency associated with this +transition is EB minus EA over H bar and + + align:start position:0% +transition is EB minus EA over H bar and + + + align:start position:0% +transition is EB minus EA over H bar and +we'll take it to be greater than zero + + align:start position:0% +we'll take it to be greater than zero + + + align:start position:0% +we'll take it to be greater than zero +the state B will be considered to be + + align:start position:0% +the state B will be considered to be + + + align:start position:0% +the state B will be considered to be +higher than the state a so the question + + align:start position:0% +higher than the state a so the question + + + align:start position:0% +higher than the state a so the question +we ask is what happens to these atoms + + align:start position:0% +we ask is what happens to these atoms + + + align:start position:0% +we ask is what happens to these atoms +when light shines and in particular + + align:start position:0% +when light shines and in particular + + + align:start position:0% +when light shines and in particular +suppose the light contains trains + + align:start position:0% +suppose the light contains trains + + + align:start position:0% +suppose the light contains trains +photons with frequency Omega B a that's + + align:start position:0% +photons with frequency Omega B a that's + + + align:start position:0% +photons with frequency Omega B a that's +the frequency associated with the + + align:start position:0% +the frequency associated with the + + + align:start position:0% +the frequency associated with the +transition so what will happen and + + align:start position:0% + + + + align:start position:0% + +basically a couple of things can happen + + align:start position:0% +basically a couple of things can happen + + + align:start position:0% +basically a couple of things can happen +is these are things we already know from + + align:start position:0% +is these are things we already know from + + + align:start position:0% +is these are things we already know from +time-dependent perturbation theory and + + align:start position:0% +time-dependent perturbation theory and + + + align:start position:0% +time-dependent perturbation theory and +surprisingly as we will see Einstein + + align:start position:0% +surprisingly as we will see Einstein + + + align:start position:0% +surprisingly as we will see Einstein +when he went through his argument we're + + align:start position:0% +when he went through his argument we're + + + align:start position:0% +when he went through his argument we're +going to go through soon came with a + + align:start position:0% +going to go through soon came with a + + + align:start position:0% +going to go through soon came with a +different angle and something's + + align:start position:0% +different angle and something's + + + align:start position:0% +different angle and something's +a little differently but let's follow up + + align:start position:0% +a little differently but let's follow up + + + align:start position:0% +a little differently but let's follow up +the direction that is based on the + + align:start position:0% +the direction that is based on the + + + align:start position:0% +the direction that is based on the +evidence we've presented so far so there + + align:start position:0% +evidence we've presented so far so there + + + align:start position:0% +evidence we've presented so far so there +will be two possibilities two cases in + + align:start position:0% +will be two possibilities two cases in + + + align:start position:0% +will be two possibilities two cases in +the first case the atom is initially + + align:start position:0% +the first case the atom is initially + + + align:start position:0% +the first case the atom is initially +with its electron on level a electron in + + align:start position:0% +with its electron on level a electron in + + + align:start position:0% +with its electron on level a electron in +a and so what happens well with coupled + + align:start position:0% +a and so what happens well with coupled + + + align:start position:0% +a and so what happens well with coupled +a system with two levels to a harmonic + + align:start position:0% +a system with two levels to a harmonic + + + align:start position:0% +a system with two levels to a harmonic +perturbation and we saw it sometimes the + + align:start position:0% +perturbation and we saw it sometimes the + + + align:start position:0% +perturbation and we saw it sometimes the +particle the system goes up and + + align:start position:0% +particle the system goes up and + + + align:start position:0% +particle the system goes up and +sometimes goes down and now we're gonna + + align:start position:0% +sometimes goes down and now we're gonna + + + align:start position:0% +sometimes goes down and now we're gonna +see the source a little bit more + + align:start position:0% +see the source a little bit more + + + align:start position:0% +see the source a little bit more +realistically before it was a + + align:start position:0% +realistically before it was a + + + align:start position:0% +realistically before it was a +perturbation now we're gonna identify + + align:start position:0% +perturbation now we're gonna identify + + + align:start position:0% +perturbation now we're gonna identify +the perturbation the electron is in + + align:start position:0% +the perturbation the electron is in + + + align:start position:0% +the perturbation the electron is in +state a and here comes photons and + + align:start position:0% +state a and here comes photons and + + + align:start position:0% +state a and here comes photons and +what's going to happen is a process of + + align:start position:0% +what's going to happen is a process of + + + align:start position:0% +what's going to happen is a process of +absorption none of the folder and the + + align:start position:0% +absorption none of the folder and the + + + align:start position:0% +absorption none of the folder and the +electron goes to state B so we'll draw + + align:start position:0% +electron goes to state B so we'll draw + + + align:start position:0% +electron goes to state B so we'll draw +it here so this is before and here is + + align:start position:0% +it here so this is before and here is + + + align:start position:0% +it here so this is before and here is +after so before you had this thing and + + align:start position:0% +after so before you had this thing and + + + align:start position:0% +after so before you had this thing and +the electron was on state a and there + + align:start position:0% +the electron was on state a and there + + + align:start position:0% +the electron was on state a and there +was a photon coming here with energy H + + align:start position:0% +was a photon coming here with energy H + + + align:start position:0% +was a photon coming here with energy H +Omega B a and then after the electron is + + align:start position:0% +Omega B a and then after the electron is + + + align:start position:0% +Omega B a and then after the electron is +been pushed up and there's no photon + + align:start position:0% +been pushed up and there's no photon + + + align:start position:0% +been pushed up and there's no photon +anymore the photon was absorbed that's + + align:start position:0% +anymore the photon was absorbed that's + + + align:start position:0% +anymore the photon was absorbed that's +physically what we would expect the + + align:start position:0% +physically what we would expect the + + + align:start position:0% +physically what we would expect the +other possibility is associated to the + + align:start position:0% +other possibility is associated to the + + + align:start position:0% +other possibility is associated to the +process of stimulated emission this is + + align:start position:0% +process of stimulated emission this is + + + align:start position:0% +process of stimulated emission this is +this is absorption and here we have + + align:start position:0% +this is absorption and here we have + + + align:start position:0% +this is absorption and here we have +electron in B initially and we'll have + + align:start position:0% +electron in B initially and we'll have + + + align:start position:0% +electron in B initially and we'll have +stimulated emission and in this case of + + align:start position:0% +stimulated emission and in this case of + + + align:start position:0% +stimulated emission and in this case of +the electron goes to a and another + + align:start position:0% +the electron goes to a and another + + + align:start position:0% +the electron goes to a and another +photon is released it's a very + + align:start position:0% +photon is released it's a very + + + align:start position:0% +photon is released it's a very +surprising thing if you think about it + + align:start position:0% +surprising thing if you think about it + + + align:start position:0% +surprising thing if you think about it +and here you're this is the absorption + + align:start position:0% +and here you're this is the absorption + + + align:start position:0% +and here you're this is the absorption +process now the stimulated emission + + align:start position:0% +process now the stimulated emission + + + align:start position:0% +process now the stimulated emission +process you have the electron originally + + align:start position:0% +process you have the electron originally + + + align:start position:0% +process you have the electron originally +in B and here comes the photon and the + + align:start position:0% +in B and here comes the photon and the + + + align:start position:0% +in B and here comes the photon and the +end result is an electron in a and two + + align:start position:0% +end result is an electron in a and two + + + align:start position:0% +end result is an electron in a and two +photons + + align:start position:0% + + + + align:start position:0% + +we notice that when we're in + + align:start position:0% +we notice that when we're in + + + align:start position:0% +we notice that when we're in +perturbation theory between the two + + align:start position:0% +perturbation theory between the two + + + align:start position:0% +perturbation theory between the two +energy levels it would have the harmonic + + align:start position:0% +energy levels it would have the harmonic + + + align:start position:0% +energy levels it would have the harmonic +perturbation we even noticed the + + align:start position:0% +perturbation we even noticed the + + + align:start position:0% +perturbation we even noticed the +probability to go from the bottom to the + + align:start position:0% +probability to go from the bottom to the + + + align:start position:0% +probability to go from the bottom to the +top or going from the top to the bottom + + align:start position:0% +top or going from the top to the bottom + + + align:start position:0% +top or going from the top to the bottom +was the same in perturbation theory and + + align:start position:0% +was the same in perturbation theory and + + + align:start position:0% +was the same in perturbation theory and +and you would have said look I + + align:start position:0% +and you would have said look I + + + align:start position:0% +and you would have said look I +understand that when you have electron + + align:start position:0% +understand that when you have electron + + + align:start position:0% +understand that when you have electron +in the bottom level you need some energy + + align:start position:0% +in the bottom level you need some energy + + + align:start position:0% +in the bottom level you need some energy +from the source to kick it up but why do + + align:start position:0% +from the source to kick it up but why do + + + align:start position:0% +from the source to kick it up but why do +you need the source to make it go down + + align:start position:0% +you need the source to make it go down + + + align:start position:0% +you need the source to make it go down +it is just there should go down by + + align:start position:0% +it is just there should go down by + + + align:start position:0% +it is just there should go down by +itself well you still need to couple the + + align:start position:0% +itself well you still need to couple the + + + align:start position:0% +itself well you still need to couple the +system to something because if you are + + align:start position:0% +system to something because if you are + + + align:start position:0% +system to something because if you are +in an energy eigenstate you stay there + + align:start position:0% +in an energy eigenstate you stay there + + + align:start position:0% +in an energy eigenstate you stay there +forever the reason it goes down is + + align:start position:0% +forever the reason it goes down is + + + align:start position:0% +forever the reason it goes down is +because it couples to something and + + align:start position:0% +because it couples to something and + + + align:start position:0% +because it couples to something and +somehow the coupling to the + + align:start position:0% +somehow the coupling to the + + + align:start position:0% +somehow the coupling to the +electromagnetic field helps this go down + + align:start position:0% +electromagnetic field helps this go down + + + align:start position:0% +electromagnetic field helps this go down +that's why it's called stimulated + + align:start position:0% +that's why it's called stimulated + + + align:start position:0% +that's why it's called stimulated +emission because it's stimulated by the + + align:start position:0% +emission because it's stimulated by the + + + align:start position:0% +emission because it's stimulated by the +radiation itself and this doesn't seem + + align:start position:0% +radiation itself and this doesn't seem + + + align:start position:0% +radiation itself and this doesn't seem +to play too much role of a row but + + align:start position:0% +to play too much role of a row but + + + align:start position:0% +to play too much role of a row but +actually it does in which just by the + + align:start position:0% +actually it does in which just by the + + + align:start position:0% +actually it does in which just by the +presence of a photon at the right energy + + align:start position:0% +presence of a photon at the right energy + + + align:start position:0% +presence of a photon at the right energy +difference it stimulates this to go down + + align:start position:0% +difference it stimulates this to go down + + + align:start position:0% +difference it stimulates this to go down +and now you have two photos so this is + + align:start position:0% +and now you have two photos so this is + + + align:start position:0% +and now you have two photos so this is +of course something that is used in + + align:start position:0% +of course something that is used in + + + align:start position:0% +of course something that is used in +technology a lot this is the principle + + align:start position:0% +technology a lot this is the principle + + + align:start position:0% +technology a lot this is the principle +of lasers and therefore this discussion + + align:start position:0% +of lasers and therefore this discussion + + + align:start position:0% +of lasers and therefore this discussion +of stimulated emission which was a lot + + align:start position:0% +of stimulated emission which was a lot + + + align:start position:0% +of stimulated emission which was a lot +due to Einstein is the idea of a laser + + align:start position:0% +due to Einstein is the idea of a laser + + + align:start position:0% +due to Einstein is the idea of a laser +so lasers light amplification by + + align:start position:0% +so lasers light amplification by + + + align:start position:0% +so lasers light amplification by +stimulated emission of radiation so what + + align:start position:0% +stimulated emission of radiation so what + + + align:start position:0% +stimulated emission of radiation so what +do you need for a laser you need + + align:start position:0% +do you need for a laser you need + + + align:start position:0% +do you need for a laser you need +something that this kind of a little + + align:start position:0% +something that this kind of a little + + + align:start position:0% +something that this kind of a little +strange to begin with because from the + + align:start position:0% +strange to begin with because from the + + + align:start position:0% +strange to begin with because from the +viewpoint of the + + align:start position:0% +viewpoint of the + + + align:start position:0% +viewpoint of the +mystical physics if you have a two-level + + align:start position:0% +mystical physics if you have a two-level + + + align:start position:0% +mystical physics if you have a two-level +system + + align:start position:0% + + + + align:start position:0% + +particles will tend to be in the lower + + align:start position:0% +particles will tend to be in the lower + + + align:start position:0% +particles will tend to be in the lower +level so why would they go here well + + align:start position:0% +level so why would they go here well + + + align:start position:0% +level so why would they go here well +they won't go there by themselves that's + + align:start position:0% +they won't go there by themselves that's + + + align:start position:0% +they won't go there by themselves that's +the term called population inversion you + + align:start position:0% +the term called population inversion you + + + align:start position:0% +the term called population inversion you +need to get the electrons that are in + + align:start position:0% +need to get the electrons that are in + + + align:start position:0% +need to get the electrons that are in +the bottom to go up to the next level + + align:start position:0% +the bottom to go up to the next level + + + align:start position:0% +the bottom to go up to the next level +and put them there that's a technical + + align:start position:0% +and put them there that's a technical + + + align:start position:0% +and put them there that's a technical +difficulty of course and it's usually + + align:start position:0% +difficulty of course and it's usually + + + align:start position:0% +difficulty of course and it's usually +solved by optical pumping we were not + + align:start position:0% +solved by optical pumping we were not + + + align:start position:0% +solved by optical pumping we were not +going to be doing engineering here today + + align:start position:0% +going to be doing engineering here today + + + align:start position:0% +going to be doing engineering here today +but there's a third level here in a + + align:start position:0% +but there's a third level here in a + + + align:start position:0% +but there's a third level here in a +typical laser and you can send the + + align:start position:0% +typical laser and you can send the + + + align:start position:0% +typical laser and you can send the +electrons that are sitting originally + + align:start position:0% +electrons that are sitting originally + + + align:start position:0% +electrons that are sitting originally +here with optical with light again into + + align:start position:0% +here with optical with light again into + + + align:start position:0% +here with optical with light again into +the third level and then it turns out + + align:start position:0% +the third level and then it turns out + + + align:start position:0% +the third level and then it turns out +that that third level if it's you have + + align:start position:0% +that that third level if it's you have + + + align:start position:0% +that that third level if it's you have +the right atom has a transition to this + + align:start position:0% +the right atom has a transition to this + + + align:start position:0% +the right atom has a transition to this +level that is rather quick so the + + align:start position:0% +level that is rather quick so the + + + align:start position:0% +level that is rather quick so the +electrons fault here fall very quickly + + align:start position:0% +electrons fault here fall very quickly + + + align:start position:0% +electrons fault here fall very quickly +and the lifetime of these states here is + + align:start position:0% +and the lifetime of these states here is + + + align:start position:0% +and the lifetime of these states here is +very long so they pretty much stay there + + align:start position:0% +very long so they pretty much stay there + + + align:start position:0% +very long so they pretty much stay there +so this is the principle it's this extra + + align:start position:0% +so this is the principle it's this extra + + + align:start position:0% +so this is the principle it's this extra +level sometimes called the pump level + + align:start position:0% +level sometimes called the pump level + + + align:start position:0% +level sometimes called the pump level +and so this is done by optical pumping + + align:start position:0% +and so this is done by optical pumping + + + align:start position:0% +and so this is done by optical pumping +so optical pumping to create population + + align:start position:0% + + + + align:start position:0% + +inversion that you get more states in + + align:start position:0% +inversion that you get more states in + + + align:start position:0% +inversion that you get more states in +the upper state that you would get in + + align:start position:0% +the upper state that you would get in + + + align:start position:0% +the upper state that you would get in +equilibrium thermodynamic equilibrium + + align:start position:0% +equilibrium thermodynamic equilibrium + + + align:start position:0% +equilibrium thermodynamic equilibrium +and then you now have say the levels + + align:start position:0% +and then you now have say the levels + + + align:start position:0% +and then you now have say the levels +here + + align:start position:0% + + + + align:start position:0% + +this way it makes it a little easier I + + align:start position:0% +this way it makes it a little easier I + + + align:start position:0% +this way it makes it a little easier I +think of one electron here maybe two + + align:start position:0% +think of one electron here maybe two + + + align:start position:0% +think of one electron here maybe two +here maybe four here and then comes a + + align:start position:0% +here maybe four here and then comes a + + + align:start position:0% +here maybe four here and then comes a +photon and stimulates this electron to + + align:start position:0% +photon and stimulates this electron to + + + align:start position:0% +photon and stimulates this electron to +go down and now you have two photons and + + align:start position:0% +go down and now you have two photons and + + + align:start position:0% +go down and now you have two photons and +they stimulate these two electrons to go + + align:start position:0% +they stimulate these two electrons to go + + + align:start position:0% +they stimulate these two electrons to go +down and now they have four photons they + + align:start position:0% +down and now they have four photons they + + + align:start position:0% +down and now they have four photons they +can stimulate these four electrons gonna + + align:start position:0% +can stimulate these four electrons gonna + + + align:start position:0% +can stimulate these four electrons gonna +have now eight photons eight photons and + + align:start position:0% +have now eight photons eight photons and + + + align:start position:0% +have now eight photons eight photons and +that's the amplification process of + + align:start position:0% +that's the amplification process of + + + align:start position:0% +that's the amplification process of +stimulation each time you stimulate one + + align:start position:0% +stimulation each time you stimulate one + + + align:start position:0% +stimulation each time you stimulate one +down you achieve this in fact + + align:start position:0% +down you achieve this in fact + + + align:start position:0% +down you achieve this in fact +technically speaking now apparently in + + align:start position:0% +technically speaking now apparently in + + + align:start position:0% +technically speaking now apparently in +good lasers this transition doesn't + + align:start position:0% +good lasers this transition doesn't + + + align:start position:0% +good lasers this transition doesn't +produce light you would say all it + + align:start position:0% +produce light you would say all it + + + align:start position:0% +produce light you would say all it +produces more photons but there's some + + align:start position:0% +produces more photons but there's some + + + align:start position:0% +produces more photons but there's some +energy levels that radiate by + + align:start position:0% +energy levels that radiate by + + + align:start position:0% +energy levels that radiate by +communication vibrate by communicating + + align:start position:0% +communication vibrate by communicating + + + align:start position:0% +communication vibrate by communicating +vibrational energies to the atoms so + + align:start position:0% +vibrational energies to the atoms so + + + align:start position:0% +vibrational energies to the atoms so +apparently these transitions are not + + align:start position:0% +apparently these transitions are not + + + align:start position:0% +apparently these transitions are not +electromagnetic and you don't mix more + + align:start position:0% +electromagnetic and you don't mix more + + + align:start position:0% +electromagnetic and you don't mix more +light so basically stimulated emission + + align:start position:0% +light so basically stimulated emission + + + align:start position:0% +light so basically stimulated emission +of radiation is the thing that gets this + + align:start position:0% +of radiation is the thing that gets this + + + align:start position:0% +of radiation is the thing that gets this +process going and and that's what we're + + align:start position:0% +process going and and that's what we're + + + align:start position:0% +process going and and that's what we're +going to try to understand now the whole + + align:start position:0% +going to try to understand now the whole + + + align:start position:0% +going to try to understand now the whole +discussion that follows and what we have + + align:start position:0% +discussion that follows and what we have + + + align:start position:0% +discussion that follows and what we have +to understand about light and atoms will + + align:start position:0% +to understand about light and atoms will + + + align:start position:0% +to understand about light and atoms will +make all these quantitative and allows + + align:start position:0% +make all these quantitative and allows + + + align:start position:0% +make all these quantitative and allows +to produce numbers and calculate rates \ No newline at end of file diff --git a/xKL3J5iPnwE.txt b/xKL3J5iPnwE.txt new file mode 100644 index 0000000000000000000000000000000000000000..dbf378d70b10734ac3d3387450996c5ed2529105 --- /dev/null +++ b/xKL3J5iPnwE.txt @@ -0,0 +1,3051 @@ +align:start position:0% + +In education, you hear people say, "We + + align:start position:0% +In education, you hear people say, "We + + + align:start position:0% +In education, you hear people say, "We +will have technology anytime, any place, + + align:start position:0% +will have technology anytime, any place, + + + align:start position:0% +will have technology anytime, any place, +anywhere." But to many educators, that + + align:start position:0% +anywhere." But to many educators, that + + + align:start position:0% +anywhere." But to many educators, that +means except in the classroom. We work + + align:start position:0% +means except in the classroom. We work + + + align:start position:0% +means except in the classroom. We work +with children who have grown up + + align:start position:0% +with children who have grown up + + + align:start position:0% +with children who have grown up +digitally. To them, technology is a part + + align:start position:0% +digitally. To them, technology is a part + + + align:start position:0% +digitally. To them, technology is a part +of their natural world, but we have + + align:start position:0% +of their natural world, but we have + + + align:start position:0% +of their natural world, but we have +teachers who have no understanding of + + align:start position:0% +teachers who have no understanding of + + + align:start position:0% +teachers who have no understanding of +the way in which technology can be used + + align:start position:0% +the way in which technology can be used + + + align:start position:0% +the way in which technology can be used +in the classroom because they have no + + align:start position:0% +in the classroom because they have no + + + align:start position:0% +in the classroom because they have no +technology. They have no use of it. + + align:start position:0% +technology. They have no use of it. + + + align:start position:0% +technology. They have no use of it. +There's very little time to practice, + + align:start position:0% +There's very little time to practice, + + + align:start position:0% +There's very little time to practice, +think about, incorporate technology as + + align:start position:0% +think about, incorporate technology as + + + align:start position:0% +think about, incorporate technology as +learning. And most of all, there is no + + align:start position:0% +learning. And most of all, there is no + + + align:start position:0% +learning. And most of all, there is no +way in which they can transform + + align:start position:0% +way in which they can transform + + + align:start position:0% +way in which they can transform +education to the education they know now + + align:start position:0% +education to the education they know now + + + align:start position:0% +education to the education they know now +as to what it was when they went through + + align:start position:0% +as to what it was when they went through + + + align:start position:0% +as to what it was when they went through +school. So many teachers, many + + align:start position:0% +school. So many teachers, many + + + align:start position:0% +school. So many teachers, many +educators, many administrators are + + align:start position:0% +educators, many administrators are + + + align:start position:0% +educators, many administrators are +holding on to ideiational scaffolding + + align:start position:0% +holding on to ideiational scaffolding + + + align:start position:0% +holding on to ideiational scaffolding +that was of the last century. This is + + align:start position:0% +that was of the last century. This is + + + align:start position:0% +that was of the last century. This is +the 21st century. The world has changed. + + align:start position:0% +the 21st century. The world has changed. + + + align:start position:0% +the 21st century. The world has changed. +Children live in a world of media. It + + align:start position:0% +Children live in a world of media. It + + + align:start position:0% +Children live in a world of media. It +speaks to them from everywhere. But when + + align:start position:0% +speaks to them from everywhere. But when + + + align:start position:0% +speaks to them from everywhere. But when +they go into a classroom, many times + + align:start position:0% +they go into a classroom, many times + + + align:start position:0% +they go into a classroom, many times +there's just chalk and talk and they're + + align:start position:0% +there's just chalk and talk and they're + + + align:start position:0% +there's just chalk and talk and they're +bored. It isn't because the teachers are + + align:start position:0% +bored. It isn't because the teachers are + + + align:start position:0% +bored. It isn't because the teachers are +doing anything differently than when you + + align:start position:0% +doing anything differently than when you + + + align:start position:0% +doing anything differently than when you +went to school. It is because the world + + align:start position:0% +went to school. It is because the world + + + align:start position:0% +went to school. It is because the world +has changed. The media speaks to + + align:start position:0% +has changed. The media speaks to + + + align:start position:0% +has changed. The media speaks to +children. But there is something that + + align:start position:0% +children. But there is something that + + + align:start position:0% +children. But there is something that +media does for children that's even + + align:start position:0% +media does for children that's even + + + align:start position:0% +media does for children that's even +better. It allows them to be creators, + + align:start position:0% +better. It allows them to be creators, + + + align:start position:0% +better. It allows them to be creators, +producers. It allows them to think about + + align:start position:0% +producers. It allows them to think about + + + align:start position:0% +producers. It allows them to think about +things and analyze. It allows them to go + + align:start position:0% +things and analyze. It allows them to go + + + align:start position:0% +things and analyze. It allows them to go +on field trips with people like Bob + + align:start position:0% +on field trips with people like Bob + + + align:start position:0% +on field trips with people like Bob +Ballard and to places they may never go. + + align:start position:0% +Ballard and to places they may never go. + + + align:start position:0% +Ballard and to places they may never go. +It allows them to talk to astronauts. + + align:start position:0% +It allows them to talk to astronauts. + + + align:start position:0% +It allows them to talk to astronauts. +For teachers, the same thing happens. + + align:start position:0% +For teachers, the same thing happens. + + + align:start position:0% +For teachers, the same thing happens. +Instead of being relegated to + + align:start position:0% +Instead of being relegated to + + + align:start position:0% +Instead of being relegated to +professional development by one person + + align:start position:0% +professional development by one person + + + align:start position:0% +professional development by one person +in a system who may or may not know + + align:start position:0% +in a system who may or may not know + + + align:start position:0% +in a system who may or may not know +everything there is about science, there + + align:start position:0% +everything there is about science, there + + + align:start position:0% +everything there is about science, there +are people from NASA. There are people + + align:start position:0% +are people from NASA. There are people + + + align:start position:0% +are people from NASA. There are people +from National Geographic. There are + + align:start position:0% +from National Geographic. There are + + + align:start position:0% +from National Geographic. There are +resources from many different + + align:start position:0% +resources from many different + + + align:start position:0% +resources from many different +organizations. And there are even + + align:start position:0% +organizations. And there are even + + + align:start position:0% +organizations. And there are even +teacher organizations that call content + + align:start position:0% +teacher organizations that call content + + + align:start position:0% +teacher organizations that call content +and create projects like the MCI Marco + + align:start position:0% +and create projects like the MCI Marco + + + align:start position:0% +and create projects like the MCI Marco +Polo to allow them a path, a guide, a + + align:start position:0% +Polo to allow them a path, a guide, a + + + align:start position:0% +Polo to allow them a path, a guide, a +silk road, a way to think about using + + align:start position:0% +silk road, a way to think about using + + + align:start position:0% +silk road, a way to think about using +technology as media. + + align:start position:0% +technology as media. + + + align:start position:0% +technology as media. +So how do we change teaching and + + align:start position:0% +So how do we change teaching and + + + align:start position:0% +So how do we change teaching and +learning? And how do we create the + + align:start position:0% +learning? And how do we create the + + + align:start position:0% +learning? And how do we create the +possibility that instead of just + + align:start position:0% +possibility that instead of just + + + align:start position:0% +possibility that instead of just +pioneers, we engage all teachers? We + + align:start position:0% +pioneers, we engage all teachers? We + + + align:start position:0% +pioneers, we engage all teachers? We +start with engaged learning. One of the + + align:start position:0% +start with engaged learning. One of the + + + align:start position:0% +start with engaged learning. One of the +things we must do to teach teachers is + + align:start position:0% +things we must do to teach teachers is + + + align:start position:0% +things we must do to teach teachers is +to allow them to explore the ways in + + align:start position:0% +to allow them to explore the ways in + + + align:start position:0% +to allow them to explore the ways in +which they can use technology to create + + align:start position:0% +which they can use technology to create + + + align:start position:0% +which they can use technology to create +a learning landscape. Now, what is a + + align:start position:0% +a learning landscape. Now, what is a + + + align:start position:0% +a learning landscape. Now, what is a +learning landscape? It's the way in + + align:start position:0% +learning landscape? It's the way in + + + align:start position:0% +learning landscape? It's the way in +which they use technology to invite + + align:start position:0% +which they use technology to invite + + + align:start position:0% +which they use technology to invite +children to learn, to understand, to + + align:start position:0% +children to learn, to understand, to + + + align:start position:0% +children to learn, to understand, to +explore. And it includes many different + + align:start position:0% +explore. And it includes many different + + + align:start position:0% +explore. And it includes many different +types of technology. It's not just the + + align:start position:0% +types of technology. It's not just the + + + align:start position:0% +types of technology. It's not just the +internet. It's bringing together, + + align:start position:0% +internet. It's bringing together, + + + align:start position:0% +internet. It's bringing together, +converging, creating many ideas that + + align:start position:0% +converging, creating many ideas that + + + align:start position:0% +converging, creating many ideas that +allow children to learn. But a teacher + + align:start position:0% +allow children to learn. But a teacher + + + align:start position:0% +allow children to learn. But a teacher +must do this first. A teacher must learn + + align:start position:0% +must do this first. A teacher must learn + + + align:start position:0% +must do this first. A teacher must learn +how to create pedagogy using resources + + align:start position:0% +how to create pedagogy using resources + + + align:start position:0% +how to create pedagogy using resources +that are available to him or her in + + align:start position:0% +that are available to him or her in + + + align:start position:0% +that are available to him or her in +their own learning landscape, in their + + align:start position:0% +their own learning landscape, in their + + + align:start position:0% +their own learning landscape, in their +own geographical setting, in their own + + align:start position:0% +own geographical setting, in their own + + + align:start position:0% +own geographical setting, in their own +style of teaching and learning. So + + align:start position:0% +style of teaching and learning. So + + + align:start position:0% +style of teaching and learning. So +teachers need access first of all. They + + align:start position:0% +teachers need access first of all. They + + + align:start position:0% +teachers need access first of all. They +need also support to learn the + + align:start position:0% +need also support to learn the + + + align:start position:0% +need also support to learn the +technology. And learning the technology + + align:start position:0% +technology. And learning the technology + + + align:start position:0% +technology. And learning the technology +is not learning the four languages that + + align:start position:0% +is not learning the four languages that + + + align:start position:0% +is not learning the four languages that +I learned but didn't use. Learning the + + align:start position:0% +I learned but didn't use. Learning the + + + align:start position:0% +I learned but didn't use. Learning the +technology is not learning a piece of + + align:start position:0% +technology is not learning a piece of + + + align:start position:0% +technology is not learning a piece of +software. And sometimes we think so. + + align:start position:0% +software. And sometimes we think so. + + + align:start position:0% +software. And sometimes we think so. +It's taking the teacher, it's taking the + + align:start position:0% +It's taking the teacher, it's taking the + + + align:start position:0% +It's taking the teacher, it's taking the +educator, it's taking the administrator + + align:start position:0% +educator, it's taking the administrator + + + align:start position:0% +educator, it's taking the administrator +to the point where they understand what + + align:start position:0% +to the point where they understand what + + + align:start position:0% +to the point where they understand what +engaged learning is. You may walk into a + + align:start position:0% +engaged learning is. You may walk into a + + + align:start position:0% +engaged learning is. You may walk into a +classroom where wonderful things are + + align:start position:0% +classroom where wonderful things are + + + align:start position:0% +classroom where wonderful things are +going on and not be aware of the fact + + align:start position:0% +going on and not be aware of the fact + + + align:start position:0% +going on and not be aware of the fact +that it requires structure because you + + align:start position:0% +that it requires structure because you + + + align:start position:0% +that it requires structure because you +need to know first of all how does it + + align:start position:0% +need to know first of all how does it + + + align:start position:0% +need to know first of all how does it +work? It needs to have a kind of + + align:start position:0% +work? It needs to have a kind of + + + align:start position:0% +work? It needs to have a kind of +seamless interface. So how does it work + + align:start position:0% +seamless interface. So how does it work + + + align:start position:0% +seamless interface. So how does it work +and how do we use this and what are we + + align:start position:0% +and how do we use this and what are we + + + align:start position:0% +and how do we use this and what are we +doing today? So the construction of the + + align:start position:0% +doing today? So the construction of the + + + align:start position:0% +doing today? So the construction of the +learning landscape creates the product, + + align:start position:0% +learning landscape creates the product, + + + align:start position:0% +learning landscape creates the product, +the project, the objectives and the + + align:start position:0% +the project, the objectives and the + + + align:start position:0% +the project, the objectives and the +assessment. A lot of people think when + + align:start position:0% +assessment. A lot of people think when + + + align:start position:0% +assessment. A lot of people think when +children are using technology they're + + align:start position:0% +children are using technology they're + + + align:start position:0% +children are using technology they're +playing. It seems like play because it's + + align:start position:0% +playing. It seems like play because it's + + + align:start position:0% +playing. It seems like play because it's +joyous learning. It seems like play + + align:start position:0% +joyous learning. It seems like play + + + align:start position:0% +joyous learning. It seems like play +because they're not looking at you. It + + align:start position:0% +because they're not looking at you. It + + + align:start position:0% +because they're not looking at you. It +seems like play because the teacher may + + align:start position:0% +seems like play because the teacher may + + + align:start position:0% +seems like play because the teacher may +be a guide on the side or a person + + align:start position:0% +be a guide on the side or a person + + + align:start position:0% +be a guide on the side or a person +sitting engaged in working with a group. + + align:start position:0% +sitting engaged in working with a group. + + + align:start position:0% +sitting engaged in working with a group. +That's different for a lot of us. It + + align:start position:0% +That's different for a lot of us. It + + + align:start position:0% +That's different for a lot of us. It +looks like the teacher's not working. + + align:start position:0% +looks like the teacher's not working. + + + align:start position:0% +looks like the teacher's not working. +When you first start working like that, + + align:start position:0% +When you first start working like that, + + + align:start position:0% +When you first start working like that, +it's very hard working because you have + + align:start position:0% +it's very hard working because you have + + + align:start position:0% +it's very hard working because you have +to learn new ways of controlling, + + align:start position:0% +to learn new ways of controlling, + + + align:start position:0% +to learn new ways of controlling, +allowing, sharing, and also you must + + align:start position:0% +allowing, sharing, and also you must + + + align:start position:0% +allowing, sharing, and also you must +learn to be a learner. That's hard for + + align:start position:0% +learn to be a learner. That's hard for + + + align:start position:0% +learn to be a learner. That's hard for +some of us. But transformational + + align:start position:0% +some of us. But transformational + + + align:start position:0% +some of us. But transformational +learning will change the world in such a + + align:start position:0% +learning will change the world in such a + + + align:start position:0% +learning will change the world in such a +way that we can do many different things + + align:start position:0% +way that we can do many different things + + + align:start position:0% +way that we can do many different things +that teaching and learning have never + + align:start position:0% +that teaching and learning have never + + + align:start position:0% +that teaching and learning have never +done. One of them being that we'll + + align:start position:0% +done. One of them being that we'll + + + align:start position:0% +done. One of them being that we'll +create paths to lifelong learning + + align:start position:0% +create paths to lifelong learning + + + align:start position:0% +create paths to lifelong learning +in the learning landscape. One of the + + align:start position:0% +in the learning landscape. One of the + + + align:start position:0% +in the learning landscape. One of the +things that happens is people say, + + align:start position:0% +things that happens is people say, + + + align:start position:0% +things that happens is people say, +"Well, when is this technology going to + + align:start position:0% +"Well, when is this technology going to + + + align:start position:0% +"Well, when is this technology going to +get to the point where it's all at one + + align:start position:0% +get to the point where it's all at one + + + align:start position:0% +get to the point where it's all at one +place? It never will be." We who change + + align:start position:0% +place? It never will be." We who change + + + align:start position:0% +place? It never will be." We who change +shoes, buy new cars, buy new appliances + + align:start position:0% +shoes, buy new cars, buy new appliances + + + align:start position:0% +shoes, buy new cars, buy new appliances +sometimes think that the things that we + + align:start position:0% +sometimes think that the things that we + + + align:start position:0% +sometimes think that the things that we +use in education have to last 10 years. + + align:start position:0% +use in education have to last 10 years. + + + align:start position:0% +use in education have to last 10 years. +I want you to think about this scenario. + + align:start position:0% +I want you to think about this scenario. + + + align:start position:0% +I want you to think about this scenario. +Children in my classroom were working + + align:start position:0% +Children in my classroom were working + + + align:start position:0% +Children in my classroom were working +with NASA. There was a special project + + align:start position:0% +with NASA. There was a special project + + + align:start position:0% +with NASA. There was a special project +in which they were able to evaluate, + + align:start position:0% +in which they were able to evaluate, + + + align:start position:0% +in which they were able to evaluate, +look at, think about the Horsehead + + align:start position:0% +look at, think about the Horsehead + + + align:start position:0% +look at, think about the Horsehead +Nebula. Now what is that? It's + + align:start position:0% +Nebula. Now what is that? It's + + + align:start position:0% +Nebula. Now what is that? It's +astronomy. It's wonderful things. + + align:start position:0% +astronomy. It's wonderful things. + + + align:start position:0% +astronomy. It's wonderful things. +There's a website called windows to the + + align:start position:0% +There's a website called windows to the + + + align:start position:0% +There's a website called windows to the +universe where you can look at that now + + align:start position:0% +universe where you can look at that now + + + align:start position:0% +universe where you can look at that now +or you can actually help the scientists + + align:start position:0% +or you can actually help the scientists + + + align:start position:0% +or you can actually help the scientists +look using the Hubble Space Telescope. + + align:start position:0% +look using the Hubble Space Telescope. + + + align:start position:0% +look using the Hubble Space Telescope. +We don't have that in the classroom. + + align:start position:0% +We don't have that in the classroom. + + + align:start position:0% +We don't have that in the classroom. +There's a very difficult way of teaching + + align:start position:0% +There's a very difficult way of teaching + + + align:start position:0% +There's a very difficult way of teaching +astronomy. But with the internet, the + + align:start position:0% +astronomy. But with the internet, the + + + align:start position:0% +astronomy. But with the internet, the +children can use that and perhaps draw + + align:start position:0% +children can use that and perhaps draw + + + align:start position:0% +children can use that and perhaps draw +in the art from all of the cultures that + + align:start position:0% +in the art from all of the cultures that + + + align:start position:0% +in the art from all of the cultures that +have preceded us to see the way in which + + align:start position:0% +have preceded us to see the way in which + + + align:start position:0% +have preceded us to see the way in which +people have looked at the sky. But the + + align:start position:0% +people have looked at the sky. But the + + + align:start position:0% +people have looked at the sky. But the +Horsehead Nebula was on Time magazine. + + align:start position:0% +Horsehead Nebula was on Time magazine. + + + align:start position:0% +Horsehead Nebula was on Time magazine. +My children saw the Horsehead Nebula 6 + + align:start position:0% +My children saw the Horsehead Nebula 6 + + + align:start position:0% +My children saw the Horsehead Nebula 6 +months before most people in the world + + align:start position:0% +months before most people in the world + + + align:start position:0% +months before most people in the world +got to see it. Education is empowerment. + + align:start position:0% +got to see it. Education is empowerment. + + + align:start position:0% +got to see it. Education is empowerment. +Education is knowing where Alexander the + + align:start position:0% +Education is knowing where Alexander the + + + align:start position:0% +Education is knowing where Alexander the +Great really went. Not just thinking of + + align:start position:0% +Great really went. Not just thinking of + + + align:start position:0% +Great really went. Not just thinking of +him in a paragraph, but being able to + + align:start position:0% +him in a paragraph, but being able to + + + align:start position:0% +him in a paragraph, but being able to +explore his footprints in India, in + + align:start position:0% +explore his footprints in India, in + + + align:start position:0% +explore his footprints in India, in +Greece, and as he went all through the + + align:start position:0% +Greece, and as he went all through the + + + align:start position:0% +Greece, and as he went all through the +Asian areas and knowing what the cities + + align:start position:0% +Asian areas and knowing what the cities + + + align:start position:0% +Asian areas and knowing what the cities +were. I was lucky enough to be on a + + align:start position:0% +were. I was lucky enough to be on a + + + align:start position:0% +were. I was lucky enough to be on a +fullbrite and I have a coin from where + + align:start position:0% +fullbrite and I have a coin from where + + + align:start position:0% +fullbrite and I have a coin from where +Alexander the Great went. I collected it + + align:start position:0% +Alexander the Great went. I collected it + + + align:start position:0% +Alexander the Great went. I collected it +in Kashmir. But most of our children can + + align:start position:0% +in Kashmir. But most of our children can + + + align:start position:0% +in Kashmir. But most of our children can +only do that exploring using the + + align:start position:0% +only do that exploring using the + + + align:start position:0% +only do that exploring using the +internet as a resource. The great thing + + align:start position:0% +internet as a resource. The great thing + + + align:start position:0% +internet as a resource. The great thing +about that is they don't stop when we + + align:start position:0% +about that is they don't stop when we + + + align:start position:0% +about that is they don't stop when we +tell them. They stop when they've got + + align:start position:0% +tell them. They stop when they've got + + + align:start position:0% +tell them. They stop when they've got +their fill of it. And maybe one of the + + align:start position:0% +their fill of it. And maybe one of the + + + align:start position:0% +their fill of it. And maybe one of the +things that we do is to change learning + + align:start position:0% +things that we do is to change learning + + + align:start position:0% +things that we do is to change learning +into seeing information and changing it + + align:start position:0% +into seeing information and changing it + + + align:start position:0% +into seeing information and changing it +into knowledge that becomes + + align:start position:0% +into knowledge that becomes + + + align:start position:0% +into knowledge that becomes +personalized. + + align:start position:0% +personalized. + + + align:start position:0% +personalized. +Professional development is something + + align:start position:0% +Professional development is something + + + align:start position:0% +Professional development is something +that can be totally changed and + + align:start position:0% +that can be totally changed and + + + align:start position:0% +that can be totally changed and +transformed. I'm talking to you in ways + + align:start position:0% +transformed. I'm talking to you in ways + + + align:start position:0% +transformed. I'm talking to you in ways +that we can train teachers. Instead of + + align:start position:0% +that we can train teachers. Instead of + + + align:start position:0% +that we can train teachers. Instead of +being just the teacher in a place where + + align:start position:0% +being just the teacher in a place where + + + align:start position:0% +being just the teacher in a place where +there are no experts, we can reach to + + align:start position:0% +there are no experts, we can reach to + + + align:start position:0% +there are no experts, we can reach to +the Louvre. We can go to Egypt. We can + + align:start position:0% +the Louvre. We can go to Egypt. We can + + + align:start position:0% +the Louvre. We can go to Egypt. We can +go inside the pyramids. We can create + + align:start position:0% +go inside the pyramids. We can create + + + align:start position:0% +go inside the pyramids. We can create +projects that allow children to decide + + align:start position:0% +projects that allow children to decide + + + align:start position:0% +projects that allow children to decide +what would happen. I want you to think + + align:start position:0% +what would happen. I want you to think + + + align:start position:0% +what would happen. I want you to think +about the world heritage sites. You + + align:start position:0% +about the world heritage sites. You + + + align:start position:0% +about the world heritage sites. You +can't take the children around the world + + align:start position:0% +can't take the children around the world + + + align:start position:0% +can't take the children around the world +in reality, but you could with + + align:start position:0% +in reality, but you could with + + + align:start position:0% +in reality, but you could with +ubiquitous computing. And what is that? + + align:start position:0% +ubiquitous computing. And what is that? + + + align:start position:0% +ubiquitous computing. And what is that? +That's anytime, any place, anywhere. We + + align:start position:0% +That's anytime, any place, anywhere. We + + + align:start position:0% +That's anytime, any place, anywhere. We +can use wireless objects. We can use + + align:start position:0% +can use wireless objects. We can use + + + align:start position:0% +can use wireless objects. We can use +little handhelds. And children can use + + align:start position:0% +little handhelds. And children can use + + + align:start position:0% +little handhelds. And children can use +cameras, take notes, type their little + + align:start position:0% +cameras, take notes, type their little + + + align:start position:0% +cameras, take notes, type their little +information in. What if we connected + + align:start position:0% +information in. What if we connected + + + align:start position:0% +information in. What if we connected +world heritage sites and let children + + align:start position:0% +world heritage sites and let children + + + align:start position:0% +world heritage sites and let children +from another country bring their idea of + + align:start position:0% +from another country bring their idea of + + + align:start position:0% +from another country bring their idea of +what the treasures are of a place that + + align:start position:0% +what the treasures are of a place that + + + align:start position:0% +what the treasures are of a place that +we've already certified as world + + align:start position:0% +we've already certified as world + + + align:start position:0% +we've already certified as world +heritage or what if children are using + + align:start position:0% +heritage or what if children are using + + + align:start position:0% +heritage or what if children are using +global ways to think about the + + align:start position:0% +global ways to think about the + + + align:start position:0% +global ways to think about the +environment. We work sometimes in very + + align:start position:0% +environment. We work sometimes in very + + + align:start position:0% +environment. We work sometimes in very +specialized ways. Teachers get to go + + align:start position:0% +specialized ways. Teachers get to go + + + align:start position:0% +specialized ways. Teachers get to go +many places the children can't. So if + + align:start position:0% +many places the children can't. So if + + + align:start position:0% +many places the children can't. So if +you were going to go into a rainforest + + align:start position:0% +you were going to go into a rainforest + + + align:start position:0% +you were going to go into a rainforest +or if you were going into the jungles of + + align:start position:0% +or if you were going into the jungles of + + + align:start position:0% +or if you were going into the jungles of +Peru, how would the children be able to + + align:start position:0% +Peru, how would the children be able to + + + align:start position:0% +Peru, how would the children be able to +participate? Well, we have guides who do + + align:start position:0% +participate? Well, we have guides who do + + + align:start position:0% +participate? Well, we have guides who do +that. We have people who have created + + align:start position:0% +that. We have people who have created + + + align:start position:0% +that. We have people who have created +information, ways in which children can + + align:start position:0% +information, ways in which children can + + + align:start position:0% +information, ways in which children can +make decisions, ask questions, and begin + + align:start position:0% +make decisions, ask questions, and begin + + + align:start position:0% +make decisions, ask questions, and begin +to explore not just learning but + + align:start position:0% +to explore not just learning but + + + align:start position:0% +to explore not just learning but +careers. That's the new facet that + + align:start position:0% +careers. That's the new facet that + + + align:start position:0% +careers. That's the new facet that +happens. And with ubiquitous computing, + + align:start position:0% +happens. And with ubiquitous computing, + + + align:start position:0% +happens. And with ubiquitous computing, +as they think, analyze, process, and + + align:start position:0% +as they think, analyze, process, and + + + align:start position:0% +as they think, analyze, process, and +create ideas, sometimes you get products + + align:start position:0% +create ideas, sometimes you get products + + + align:start position:0% +create ideas, sometimes you get products +you never asked for. I did a project + + align:start position:0% +you never asked for. I did a project + + + align:start position:0% +you never asked for. I did a project +called Chesapeake Bay, and that's all + + align:start position:0% +called Chesapeake Bay, and that's all + + + align:start position:0% +called Chesapeake Bay, and that's all +about uh crabs and the way in which we + + align:start position:0% +about uh crabs and the way in which we + + + align:start position:0% +about uh crabs and the way in which we +use the environment. And I had visitors + + align:start position:0% +use the environment. And I had visitors + + + align:start position:0% +use the environment. And I had visitors +to my classroom. So, we showed them our + + align:start position:0% +to my classroom. So, we showed them our + + + align:start position:0% +to my classroom. So, we showed them our +maps, we showed them our resources, we + + align:start position:0% +maps, we showed them our resources, we + + + align:start position:0% +maps, we showed them our resources, we +talked about sing and measuring time and + + align:start position:0% +talked about sing and measuring time and + + + align:start position:0% +talked about sing and measuring time and +tides. But the children did something I + + align:start position:0% +tides. But the children did something I + + + align:start position:0% +tides. But the children did something I +had never seen before. They pulled out + + align:start position:0% +had never seen before. They pulled out + + + align:start position:0% +had never seen before. They pulled out +journals. They pulled out books. And + + align:start position:0% +journals. They pulled out books. And + + + align:start position:0% +journals. They pulled out books. And +this was before Oprah. They actually + + align:start position:0% +this was before Oprah. They actually + + + align:start position:0% +this was before Oprah. They actually +enjoyed learning in such a way that they + + align:start position:0% +enjoyed learning in such a way that they + + + align:start position:0% +enjoyed learning in such a way that they +created poems, books, and stories and + + align:start position:0% +created poems, books, and stories and + + + align:start position:0% +created poems, books, and stories and +they gave them to the visitors. So one + + align:start position:0% +they gave them to the visitors. So one + + + align:start position:0% +they gave them to the visitors. So one +of the things that technology allows us + + align:start position:0% +of the things that technology allows us + + + align:start position:0% +of the things that technology allows us +to do is to know that we can give away + + align:start position:0% +to do is to know that we can give away + + + align:start position:0% +to do is to know that we can give away +that information. You know, the + + align:start position:0% +that information. You know, the + + + align:start position:0% +that information. You know, the +information that we turn into knowledge + + align:start position:0% +information that we turn into knowledge + + + align:start position:0% +information that we turn into knowledge +and that learning is a gift to be shared + + align:start position:0% +and that learning is a gift to be shared + + + align:start position:0% +and that learning is a gift to be shared +in many ways and particularly in global + + align:start position:0% +in many ways and particularly in global + + + align:start position:0% +in many ways and particularly in global +ways. + + align:start position:0% +ways. + + + align:start position:0% +ways. +I am able to speak to you from across a + + align:start position:0% +I am able to speak to you from across a + + + align:start position:0% +I am able to speak to you from across a +digital divide. But the digital divide + + align:start position:0% +digital divide. But the digital divide + + + align:start position:0% +digital divide. But the digital divide +that I'm speaking to you from is from a + + align:start position:0% +that I'm speaking to you from is from a + + + align:start position:0% +that I'm speaking to you from is from a +classroom versus places where there are + + align:start position:0% +classroom versus places where there are + + + align:start position:0% +classroom versus places where there are +lots of technology. There are many + + align:start position:0% +lots of technology. There are many + + + align:start position:0% +lots of technology. There are many +people in global situations where I go + + align:start position:0% +people in global situations where I go + + + align:start position:0% +people in global situations where I go +who have little or nothing. But + + align:start position:0% +who have little or nothing. But + + + align:start position:0% +who have little or nothing. But +weightless goods are the most important + + align:start position:0% +weightless goods are the most important + + + align:start position:0% +weightless goods are the most important +things that pass across these + + align:start position:0% +things that pass across these + + + align:start position:0% +things that pass across these +technologies that we share. The way to + + align:start position:0% +technologies that we share. The way to + + + align:start position:0% +technologies that we share. The way to +cure diseases, to test water, to + + align:start position:0% +cure diseases, to test water, to + + + align:start position:0% +cure diseases, to test water, to +understand, to take the knowledge and + + align:start position:0% +understand, to take the knowledge and + + + align:start position:0% +understand, to take the knowledge and +share it in many different ways is + + align:start position:0% +share it in many different ways is + + + align:start position:0% +share it in many different ways is +really important. When we talk about + + align:start position:0% +really important. When we talk about + + + align:start position:0% +really important. When we talk about +digital divide, we must also think about + + align:start position:0% +digital divide, we must also think about + + + align:start position:0% +digital divide, we must also think about +the content. Is the content reflective + + align:start position:0% +the content. Is the content reflective + + + align:start position:0% +the content. Is the content reflective +of the way the world is. Sometimes we + + align:start position:0% +of the way the world is. Sometimes we + + + align:start position:0% +of the way the world is. Sometimes we +give children universal knowledge, which + + align:start position:0% +give children universal knowledge, which + + + align:start position:0% +give children universal knowledge, which +act actually means we haven't given them + + align:start position:0% +act actually means we haven't given them + + + align:start position:0% +act actually means we haven't given them +anything at all. Do you know who + + align:start position:0% +anything at all. Do you know who + + + align:start position:0% +anything at all. Do you know who +Darthothy Coleman is? You probably know + + align:start position:0% +Darthothy Coleman is? You probably know + + + align:start position:0% +Darthothy Coleman is? You probably know +who Amelia Earheart was. But Dorothy + + align:start position:0% +who Amelia Earheart was. But Dorothy + + + align:start position:0% +who Amelia Earheart was. But Dorothy +Coleman was the first black flyer and + + align:start position:0% +Coleman was the first black flyer and + + + align:start position:0% +Coleman was the first black flyer and +she actually had a license and + + align:start position:0% +she actually had a license and + + + align:start position:0% +she actually had a license and +barnstormed all over the United States. + + align:start position:0% +barnstormed all over the United States. + + + align:start position:0% +barnstormed all over the United States. +Sometimes children have to see it to be + + align:start position:0% +Sometimes children have to see it to be + + + align:start position:0% +Sometimes children have to see it to be +it. When I taught a special project from + + align:start position:0% +it. When I taught a special project from + + + align:start position:0% +it. When I taught a special project from +the Smithsonian called Seeds of Change, + + align:start position:0% +the Smithsonian called Seeds of Change, + + + align:start position:0% +the Smithsonian called Seeds of Change, +some of my Hispanic children learn for + + align:start position:0% +some of my Hispanic children learn for + + + align:start position:0% +some of my Hispanic children learn for +the very first time of the majesty of + + align:start position:0% +the very first time of the majesty of + + + align:start position:0% +the very first time of the majesty of +the culture of the wonderful things that + + align:start position:0% +the culture of the wonderful things that + + + align:start position:0% +the culture of the wonderful things that +existed in pre-Colombian + + align:start position:0% +existed in pre-Colombian + + + align:start position:0% +existed in pre-Colombian +era. They knew that there was something + + align:start position:0% +era. They knew that there was something + + + align:start position:0% +era. They knew that there was something +but they weren't able to define the + + align:start position:0% +but they weren't able to define the + + + align:start position:0% +but they weren't able to define the +cultures. So by using technology we + + align:start position:0% +cultures. So by using technology we + + + align:start position:0% +cultures. So by using technology we +brought two old worlds together not a + + align:start position:0% +brought two old worlds together not a + + + align:start position:0% +brought two old worlds together not a +new world. There was not a new world. + + align:start position:0% +new world. There was not a new world. + + + align:start position:0% +new world. There was not a new world. +Now think about it. There were some + + align:start position:0% +Now think about it. There were some + + + align:start position:0% +Now think about it. There were some +kinds of developments that have to do + + align:start position:0% +kinds of developments that have to do + + + align:start position:0% +kinds of developments that have to do +with metallurgy. They were in Africa. + + align:start position:0% +with metallurgy. They were in Africa. + + + align:start position:0% +with metallurgy. They were in Africa. +They were in Japan. There were cultures + + align:start position:0% +They were in Japan. There were cultures + + + align:start position:0% +They were in Japan. There were cultures +that discovered long before Arthur and + + align:start position:0% +that discovered long before Arthur and + + + align:start position:0% +that discovered long before Arthur and +his knights how to create technology + + align:start position:0% +his knights how to create technology + + + align:start position:0% +his knights how to create technology +which at that time was metal and people + + align:start position:0% +which at that time was metal and people + + + align:start position:0% +which at that time was metal and people +went to the libraries of Alexandria. + + align:start position:0% +went to the libraries of Alexandria. + + + align:start position:0% +went to the libraries of Alexandria. +They went to learn where the ideas were. + + align:start position:0% +They went to learn where the ideas were. + + + align:start position:0% +They went to learn where the ideas were. +So in creating our content to share + + align:start position:0% +So in creating our content to share + + + align:start position:0% +So in creating our content to share +what's going to be on the internet. We + + align:start position:0% +what's going to be on the internet. We + + + align:start position:0% +what's going to be on the internet. We +must also use every kind of tool every + + align:start position:0% +must also use every kind of tool every + + + align:start position:0% +must also use every kind of tool every +kind of technology GIS kinds of things + + align:start position:0% +kind of technology GIS kinds of things + + + align:start position:0% +kind of technology GIS kinds of things +but include the whole world in our + + align:start position:0% +but include the whole world in our + + + align:start position:0% +but include the whole world in our +learning. We can't just have one view. + + align:start position:0% +learning. We can't just have one view. + + + align:start position:0% +learning. We can't just have one view. +How exciting it would be to use one + + align:start position:0% +How exciting it would be to use one + + + align:start position:0% +How exciting it would be to use one +topic and to allow children from all + + align:start position:0% +topic and to allow children from all + + + align:start position:0% +topic and to allow children from all +over the world as in global schooln net + + align:start position:0% +over the world as in global schooln net + + + align:start position:0% +over the world as in global schooln net +to share their learnings. What a small + + align:start position:0% +to share their learnings. What a small + + + align:start position:0% +to share their learnings. What a small +world it will be. And kids with the + + align:start position:0% +world it will be. And kids with the + + + align:start position:0% +world it will be. And kids with the +tiniest of fingers can reach out to the + + align:start position:0% +tiniest of fingers can reach out to the + + + align:start position:0% +tiniest of fingers can reach out to the +world using technology as a tool and + + align:start position:0% +world using technology as a tool and + + + align:start position:0% +world using technology as a tool and +change the world for the better. + + align:start position:0% +change the world for the better. + + + align:start position:0% +change the world for the better. +In using technology, we need to develop + + align:start position:0% +In using technology, we need to develop + + + align:start position:0% +In using technology, we need to develop +stakeholders. The community needs to + + align:start position:0% +stakeholders. The community needs to + + + align:start position:0% +stakeholders. The community needs to +understand what the technology is. And + + align:start position:0% +understand what the technology is. And + + + align:start position:0% +understand what the technology is. And +so one of the things that we can do as + + align:start position:0% +so one of the things that we can do as + + + align:start position:0% +so one of the things that we can do as +educators, as administrators, as + + align:start position:0% +educators, as administrators, as + + + align:start position:0% +educators, as administrators, as +community people is to explore the + + align:start position:0% +community people is to explore the + + + align:start position:0% +community people is to explore the +technology in new ways. You've seen the + + align:start position:0% +technology in new ways. You've seen the + + + align:start position:0% +technology in new ways. You've seen the +book fair. What about a technology fair? + + align:start position:0% +book fair. What about a technology fair? + + + align:start position:0% +book fair. What about a technology fair? +What about a technology roundtable that + + align:start position:0% +What about a technology roundtable that + + + align:start position:0% +What about a technology roundtable that +brings people together to think about to + + align:start position:0% +brings people together to think about to + + + align:start position:0% +brings people together to think about to +share to see what the technology is in + + align:start position:0% +share to see what the technology is in + + + align:start position:0% +share to see what the technology is in +the community and what the new ways are + + align:start position:0% +the community and what the new ways are + + + align:start position:0% +the community and what the new ways are +of sharing technology. And then with + + align:start position:0% +of sharing technology. And then with + + + align:start position:0% +of sharing technology. And then with +parents in schools perhaps we use + + align:start position:0% +parents in schools perhaps we use + + + align:start position:0% +parents in schools perhaps we use +technology to contact them. One of the + + align:start position:0% +technology to contact them. One of the + + + align:start position:0% +technology to contact them. One of the +things that happened to me was that a + + align:start position:0% +things that happened to me was that a + + + align:start position:0% +things that happened to me was that a +student in my classroom won the first + + align:start position:0% +student in my classroom won the first + + + align:start position:0% +student in my classroom won the first +computer I ever had. But did the + + align:start position:0% +computer I ever had. But did the + + + align:start position:0% +computer I ever had. But did the +teachers have the technology? Does the + + align:start position:0% +teachers have the technology? Does the + + + align:start position:0% +teachers have the technology? Does the +school have sufficient technology to + + align:start position:0% +school have sufficient technology to + + + align:start position:0% +school have sufficient technology to +deploy to share to do the wonderful + + align:start position:0% +deploy to share to do the wonderful + + + align:start position:0% +deploy to share to do the wonderful +things we're talking about? Sometimes a + + align:start position:0% +things we're talking about? Sometimes a + + + align:start position:0% +things we're talking about? Sometimes a +lab is a pencil down the hall and it's a + + align:start position:0% +lab is a pencil down the hall and it's a + + + align:start position:0% +lab is a pencil down the hall and it's a +little difficult to use because the time + + align:start position:0% +little difficult to use because the time + + + align:start position:0% +little difficult to use because the time +constraints make it difficult. We say in + + align:start position:0% +constraints make it difficult. We say in + + + align:start position:0% +constraints make it difficult. We say in +America that there are 95% of schools + + align:start position:0% +America that there are 95% of schools + + + align:start position:0% +America that there are 95% of schools +wired, but wired to what? And how many + + align:start position:0% +wired, but wired to what? And how many + + + align:start position:0% +wired, but wired to what? And how many +classrooms actually have technology? + + align:start position:0% +classrooms actually have technology? + + + align:start position:0% +classrooms actually have technology? +Have parents done an audit to see what + + align:start position:0% +Have parents done an audit to see what + + + align:start position:0% +Have parents done an audit to see what +there is and what might be needed? And + + align:start position:0% +there is and what might be needed? And + + + align:start position:0% +there is and what might be needed? And +do teachers have the tools to take home? + + align:start position:0% +do teachers have the tools to take home? + + + align:start position:0% +do teachers have the tools to take home? +There's very little time in the school + + align:start position:0% +There's very little time in the school + + + align:start position:0% +There's very little time in the school +day all over the world. As I work with + + align:start position:0% +day all over the world. As I work with + + + align:start position:0% +day all over the world. As I work with +teachers, the time that they have in the + + align:start position:0% +teachers, the time that they have in the + + + align:start position:0% +teachers, the time that they have in the +classroom is precious. So, do they have + + align:start position:0% +classroom is precious. So, do they have + + + align:start position:0% +classroom is precious. So, do they have +the tools to explore, to think about, to + + align:start position:0% +the tools to explore, to think about, to + + + align:start position:0% +the tools to explore, to think about, to +create in ways which make it possible + + align:start position:0% +create in ways which make it possible + + + align:start position:0% +create in ways which make it possible +for them to understand it in a + + align:start position:0% +for them to understand it in a + + + align:start position:0% +for them to understand it in a +ubiquitous way. And then the third thing + + align:start position:0% +ubiquitous way. And then the third thing + + + align:start position:0% +ubiquitous way. And then the third thing +is we must remember new technologies. + + align:start position:0% +is we must remember new technologies. + + + align:start position:0% +is we must remember new technologies. +While we're thinking about technology as + + align:start position:0% +While we're thinking about technology as + + + align:start position:0% +While we're thinking about technology as +the internet, while we're looking at + + align:start position:0% +the internet, while we're looking at + + + align:start position:0% +the internet, while we're looking at +distant kinds of education, there are + + align:start position:0% +distant kinds of education, there are + + + align:start position:0% +distant kinds of education, there are +new things coming down the pike. There's + + align:start position:0% +new things coming down the pike. There's + + + align:start position:0% +new things coming down the pike. There's +a project called the virtual cave. I + + align:start position:0% +a project called the virtual cave. I + + + align:start position:0% +a project called the virtual cave. I +don't know if you've ever been in one, + + align:start position:0% +don't know if you've ever been in one, + + + align:start position:0% +don't know if you've ever been in one, +but it's fantastic. We don't want to + + align:start position:0% +but it's fantastic. We don't want to + + + align:start position:0% +but it's fantastic. We don't want to +think backwards. We want to think + + align:start position:0% +think backwards. We want to think + + + align:start position:0% +think backwards. We want to think +forward. The virtual cave you stand + + align:start position:0% +forward. The virtual cave you stand + + + align:start position:0% +forward. The virtual cave you stand +inside. It's an environment. And you + + align:start position:0% +inside. It's an environment. And you + + + align:start position:0% +inside. It's an environment. And you +change it. Perhaps one day one of you + + align:start position:0% +change it. Perhaps one day one of you + + + align:start position:0% +change it. Perhaps one day one of you +will take that virtual environment and + + align:start position:0% +will take that virtual environment and + + + align:start position:0% +will take that virtual environment and +bring the Elgen marbles back to Greece + + align:start position:0% +bring the Elgen marbles back to Greece + + + align:start position:0% +bring the Elgen marbles back to Greece +or create a trek down the Silk Road that + + align:start position:0% +or create a trek down the Silk Road that + + + align:start position:0% +or create a trek down the Silk Road that +will allow children to explore the + + align:start position:0% +will allow children to explore the + + + align:start position:0% +will allow children to explore the +three-dimensional parts of what it is + + align:start position:0% +three-dimensional parts of what it is + + + align:start position:0% +three-dimensional parts of what it is +that they are seeing. The virtual cave + + align:start position:0% +that they are seeing. The virtual cave + + + align:start position:0% +that they are seeing. The virtual cave +can also be an environment in which we + + align:start position:0% +can also be an environment in which we + + + align:start position:0% +can also be an environment in which we +explore the human body. And then there's + + align:start position:0% +explore the human body. And then there's + + + align:start position:0% +explore the human body. And then there's +the immersive desk. Teaching weather can + + align:start position:0% +the immersive desk. Teaching weather can + + + align:start position:0% +the immersive desk. Teaching weather can +be one of the most boring things without + + align:start position:0% +be one of the most boring things without + + + align:start position:0% +be one of the most boring things without +technology that you can think of. But + + align:start position:0% +technology that you can think of. But + + + align:start position:0% +technology that you can think of. But +the immersive desk, you can put your + + align:start position:0% +the immersive desk, you can put your + + + align:start position:0% +the immersive desk, you can put your +head down and see the physical part of + + align:start position:0% +head down and see the physical part of + + + align:start position:0% +head down and see the physical part of +the country that you're looking at and + + align:start position:0% +the country that you're looking at and + + + align:start position:0% +the country that you're looking at and +see the vectors and the systems as they + + align:start position:0% +see the vectors and the systems as they + + + align:start position:0% +see the vectors and the systems as they +pass. We may not get to that + + align:start position:0% +pass. We may not get to that + + + align:start position:0% +pass. We may not get to that +immediately, but we need to think about + + align:start position:0% +immediately, but we need to think about + + + align:start position:0% +immediately, but we need to think about +that. In the meantime, children will + + align:start position:0% +that. In the meantime, children will + + + align:start position:0% +that. In the meantime, children will +gleefully find the hottest and the + + align:start position:0% +gleefully find the hottest and the + + + align:start position:0% +gleefully find the hottest and the +coldest part of a playground, look at + + align:start position:0% +coldest part of a playground, look at + + + align:start position:0% +coldest part of a playground, look at +weather systems, collect information + + align:start position:0% +weather systems, collect information + + + align:start position:0% +weather systems, collect information +from parents and people who know what + + align:start position:0% +from parents and people who know what + + + align:start position:0% +from parents and people who know what +the history was of the weather in their + + align:start position:0% +the history was of the weather in their + + + align:start position:0% +the history was of the weather in their +area, and perhaps connect with a + + align:start position:0% +area, and perhaps connect with a + + + align:start position:0% +area, and perhaps connect with a +classroom that's experiencing some type + + align:start position:0% +classroom that's experiencing some type + + + align:start position:0% +classroom that's experiencing some type +of weather that they can share. + + align:start position:0% +of weather that they can share. + + + align:start position:0% +of weather that they can share. +Technology brings a face to + + align:start position:0% +Technology brings a face to + + + align:start position:0% +Technology brings a face to +communication. We have done some types + + align:start position:0% +communication. We have done some types + + + align:start position:0% +communication. We have done some types +of video conferencing. Do you know the + + align:start position:0% +of video conferencing. Do you know the + + + align:start position:0% +of video conferencing. Do you know the +eye grid? + + align:start position:0% +eye grid? + + + align:start position:0% +eye grid? +I sat in access center in Washington DC + + align:start position:0% +I sat in access center in Washington DC + + + align:start position:0% +I sat in access center in Washington DC +and I saw faces from all around the + + align:start position:0% +and I saw faces from all around the + + + align:start position:0% +and I saw faces from all around the +world. We could see each other in real + + align:start position:0% +world. We could see each other in real + + + align:start position:0% +world. We could see each other in real +time. But that's next generation + + align:start position:0% +time. But that's next generation + + + align:start position:0% +time. But that's next generation +internet. Remember as we work in the new + + align:start position:0% +internet. Remember as we work in the new + + + align:start position:0% +internet. Remember as we work in the new +technology, we must also look forward. + + align:start position:0% +technology, we must also look forward. + + + align:start position:0% +technology, we must also look forward. +We must also think of new applications. + + align:start position:0% +We must also think of new applications. + + + align:start position:0% +We must also think of new applications. +Perhaps the children who are teaching + + align:start position:0% +Perhaps the children who are teaching + + + align:start position:0% +Perhaps the children who are teaching +now will think of the new applications + + align:start position:0% +now will think of the new applications + + + align:start position:0% +now will think of the new applications +because it's not just PowerPoint. It's + + align:start position:0% +because it's not just PowerPoint. It's + + + align:start position:0% +because it's not just PowerPoint. It's +using PowerPoint. Hyper studio is + + align:start position:0% +using PowerPoint. Hyper studio is + + + align:start position:0% +using PowerPoint. Hyper studio is +learning to use to nuance the technology + + align:start position:0% +learning to use to nuance the technology + + + align:start position:0% +learning to use to nuance the technology +to push it to the point where the + + align:start position:0% +to push it to the point where the + + + align:start position:0% +to push it to the point where the +technology is invisible and but a tool. \ No newline at end of file diff --git a/xRLaQ4My3ms.txt b/xRLaQ4My3ms.txt new file mode 100644 index 0000000000000000000000000000000000000000..fdc3c9c487184a5c71d2df9937b02af0b686548f --- /dev/null +++ b/xRLaQ4My3ms.txt @@ -0,0 +1,6971 @@ +align:start position:0% + +The following content is provided under + + align:start position:0% +The following content is provided under + + + align:start position:0% +The following content is provided under +a Creative Common License. Your support + + align:start position:0% +a Creative Common License. Your support + + + align:start position:0% +a Creative Common License. Your support +will help MIT Open Courseware continue + + align:start position:0% +will help MIT Open Courseware continue + + + align:start position:0% +will help MIT Open Courseware continue +to offer high-quality educational + + align:start position:0% +to offer high-quality educational + + + align:start position:0% +to offer high-quality educational +resources for free. To make a donation + + align:start position:0% +resources for free. To make a donation + + + align:start position:0% +resources for free. To make a donation +or view additional materials from + + align:start position:0% +or view additional materials from + + + align:start position:0% +or view additional materials from +hundreds of MIT courses, visit MIT Open + + align:start position:0% +hundreds of MIT courses, visit MIT Open + + + align:start position:0% +hundreds of MIT courses, visit MIT Open +Courseware at ocw.mmit.edu. + + align:start position:0% + + + + align:start position:0% + +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +In the last lecture, we introduced an + + align:start position:0% +In the last lecture, we introduced an + + + align:start position:0% +In the last lecture, we introduced an +alternative set of algorithms for + + align:start position:0% +alternative set of algorithms for + + + align:start position:0% +alternative set of algorithms for +computation of the fastfora transform + + align:start position:0% +computation of the fastfora transform + + + align:start position:0% +computation of the fastfora transform +or or rather computation of the discrete + + align:start position:0% +or or rather computation of the discrete + + + align:start position:0% +or or rather computation of the discrete +forier transform and we referred to + + align:start position:0% +forier transform and we referred to + + + align:start position:0% +forier transform and we referred to +these as the decimation in frequency + + align:start position:0% +these as the decimation in frequency + + + align:start position:0% +these as the decimation in frequency +form of the algorithm. As you recall, we + + align:start position:0% +form of the algorithm. As you recall, we + + + align:start position:0% +form of the algorithm. As you recall, we +developed the decimation in frequency + + align:start position:0% +developed the decimation in frequency + + + align:start position:0% +developed the decimation in frequency +form of the algorithm by essentially + + align:start position:0% +form of the algorithm by essentially + + + align:start position:0% +form of the algorithm by essentially +organizing the computation of the + + align:start position:0% +organizing the computation of the + + + align:start position:0% +organizing the computation of the +evenumbered DFT points and the + + align:start position:0% +evenumbered DFT points and the + + + align:start position:0% +evenumbered DFT points and the +oddnumbered DFT points separately + + align:start position:0% +oddnumbered DFT points separately + + + align:start position:0% +oddnumbered DFT points separately +and then proceeded in a similar manner. + + align:start position:0% +and then proceeded in a similar manner. + + + align:start position:0% +and then proceeded in a similar manner. +This corresponded to breaking the + + align:start position:0% +This corresponded to breaking the + + + align:start position:0% +This corresponded to breaking the +computation into two n /2 point dftts + + align:start position:0% +computation into two n /2 point dftts + + + align:start position:0% +computation into two n /2 point dftts +proceeded in a similar manner to + + align:start position:0% +proceeded in a similar manner to + + + align:start position:0% +proceeded in a similar manner to +decompose the computation of these + + align:start position:0% +decompose the computation of these + + + align:start position:0% +decompose the computation of these +separately into their even numbered + + align:start position:0% +separately into their even numbered + + + align:start position:0% +separately into their even numbered +points and oddnumbered points etc. And + + align:start position:0% +points and oddnumbered points etc. And + + + align:start position:0% +points and oddnumbered points etc. And +the flow graph that resulted from this + + align:start position:0% +the flow graph that resulted from this + + + align:start position:0% +the flow graph that resulted from this +procedure was as I've shown here which + + align:start position:0% +procedure was as I've shown here which + + + align:start position:0% +procedure was as I've shown here which +is one form then of the decimation and + + align:start position:0% +is one form then of the decimation and + + + align:start position:0% +is one form then of the decimation and +frequency form of the fast forier + + align:start position:0% +frequency form of the fast forier + + + align:start position:0% +frequency form of the fast forier +transform algorithm. + + align:start position:0% + + + + align:start position:0% + +It + + align:start position:0% +It + + + align:start position:0% +It +begins with the data sorted in normal + + align:start position:0% +begins with the data sorted in normal + + + align:start position:0% +begins with the data sorted in normal +order and proceeds to the data sorted in + + align:start position:0% +order and proceeds to the data sorted in + + + align:start position:0% +order and proceeds to the data sorted in +bit reversed order. And as I stressed + + align:start position:0% +bit reversed order. And as I stressed + + + align:start position:0% +bit reversed order. And as I stressed +last time, it also corresponds to an in + + align:start position:0% +last time, it also corresponds to an in + + + align:start position:0% +last time, it also corresponds to an in +place computation because of the way in + + align:start position:0% +place computation because of the way in + + + align:start position:0% +place computation because of the way in +which the butterflies are laid out. In + + align:start position:0% +which the butterflies are laid out. In + + + align:start position:0% +which the butterflies are laid out. In +particular, the output nodes for each + + align:start position:0% +particular, the output nodes for each + + + align:start position:0% +particular, the output nodes for each +butterfly are horizontally adjacent to + + align:start position:0% +butterfly are horizontally adjacent to + + + align:start position:0% +butterfly are horizontally adjacent to +the input nodes. Now this is similar in + + align:start position:0% +the input nodes. Now this is similar in + + + align:start position:0% +the input nodes. Now this is similar in +a number of respects to + + align:start position:0% +a number of respects to + + + align:start position:0% +a number of respects to +one of the decimation in time forms of + + align:start position:0% +one of the decimation in time forms of + + + align:start position:0% +one of the decimation in time forms of +the FFT algorithm. Although as I also + + align:start position:0% +the FFT algorithm. Although as I also + + + align:start position:0% +the FFT algorithm. Although as I also +indicated last time the basic structure + + align:start position:0% +indicated last time the basic structure + + + align:start position:0% +indicated last time the basic structure +of the butterfly computation is somewhat + + align:start position:0% +of the butterfly computation is somewhat + + + align:start position:0% +of the butterfly computation is somewhat +different. In particular, for this set + + align:start position:0% +different. In particular, for this set + + + align:start position:0% +different. In particular, for this set +of algorithms, the multiplication by + + align:start position:0% +of algorithms, the multiplication by + + + align:start position:0% +of algorithms, the multiplication by +powers of W is implemented at the output + + align:start position:0% +powers of W is implemented at the output + + + align:start position:0% +powers of W is implemented at the output +of the butterfly as opposed to the + + align:start position:0% +of the butterfly as opposed to the + + + align:start position:0% +of the butterfly as opposed to the +decimation and time forms where the + + align:start position:0% +decimation and time forms where the + + + align:start position:0% +decimation and time forms where the +multiplication by powers of W are + + align:start position:0% +multiplication by powers of W are + + + align:start position:0% +multiplication by powers of W are +implemented at the input to the + + align:start position:0% +implemented at the input to the + + + align:start position:0% +implemented at the input to the +butterfly. + + align:start position:0% +butterfly. + + + align:start position:0% +butterfly. +However, there is a very close + + align:start position:0% +However, there is a very close + + + align:start position:0% +However, there is a very close +relationship between this flow graph and + + align:start position:0% +relationship between this flow graph and + + + align:start position:0% +relationship between this flow graph and +the original flow graph that we + + align:start position:0% +the original flow graph that we + + + align:start position:0% +the original flow graph that we +implemented for the decimation and time + + align:start position:0% +implemented for the decimation and time + + + align:start position:0% +implemented for the decimation and time +algorithm. In particular, the two flow + + align:start position:0% +algorithm. In particular, the two flow + + + align:start position:0% +algorithm. In particular, the two flow +graphs are transposes of each other. Now + + align:start position:0% +graphs are transposes of each other. Now + + + align:start position:0% +graphs are transposes of each other. Now +I remind you that in one of the early + + align:start position:0% +I remind you that in one of the early + + + align:start position:0% +I remind you that in one of the early +lectures when we introduced the notation + + align:start position:0% +lectures when we introduced the notation + + + align:start position:0% +lectures when we introduced the notation +of flow graphs and some of the prop + + align:start position:0% +of flow graphs and some of the prop + + + align:start position:0% +of flow graphs and some of the prop +properties of flow graphs one of the + + align:start position:0% +properties of flow graphs one of the + + + align:start position:0% +properties of flow graphs one of the +properties of flow graphs that I + + align:start position:0% +properties of flow graphs that I + + + align:start position:0% +properties of flow graphs that I +mentioned although we didn't derive it + + align:start position:0% +mentioned although we didn't derive it + + + align:start position:0% +mentioned although we didn't derive it +was the fact that transposition of a + + align:start position:0% +was the fact that transposition of a + + + align:start position:0% +was the fact that transposition of a +flow graph doesn't change the input + + align:start position:0% +flow graph doesn't change the input + + + align:start position:0% +flow graph doesn't change the input +output characteristics. + + align:start position:0% +output characteristics. + + + align:start position:0% +output characteristics. +So that in fact if we took this flow + + align:start position:0% +So that in fact if we took this flow + + + align:start position:0% +So that in fact if we took this flow +graph + + align:start position:0% +graph + + + align:start position:0% +graph +changed the direction of all of the + + align:start position:0% +changed the direction of all of the + + + align:start position:0% +changed the direction of all of the +arrows + + align:start position:0% +arrows + + + align:start position:0% +arrows +treated this set of nodes as the input + + align:start position:0% +treated this set of nodes as the input + + + align:start position:0% +treated this set of nodes as the input +nodes and this set of nodes as the + + align:start position:0% +nodes and this set of nodes as the + + + align:start position:0% +nodes and this set of nodes as the +output nodes then since the flow graph + + align:start position:0% +output nodes then since the flow graph + + + align:start position:0% +output nodes then since the flow graph +as it's indicated here computes the + + align:start position:0% +as it's indicated here computes the + + + align:start position:0% +as it's indicated here computes the +discrete forier transform the transposed + + align:start position:0% +discrete forier transform the transposed + + + align:start position:0% +discrete forier transform the transposed +flow graph would also compute the + + align:start position:0% +flow graph would also compute the + + + align:start position:0% +flow graph would also compute the +discrete forier transform and in fact + + align:start position:0% +discrete forier transform and in fact + + + align:start position:0% +discrete forier transform and in fact +the transposition of this flow graph + + align:start position:0% +the transposition of this flow graph + + + align:start position:0% +the transposition of this flow graph +is identical to the first flowraph FFT + + align:start position:0% +is identical to the first flowraph FFT + + + align:start position:0% +is identical to the first flowraph FFT +flowraph that we introduced which was + + align:start position:0% +flowraph that we introduced which was + + + align:start position:0% +flowraph that we introduced which was +the initial decimation in time form and + + align:start position:0% +the initial decimation in time form and + + + align:start position:0% +the initial decimation in time form and +that I refer you to again here. + + align:start position:0% +that I refer you to again here. + + + align:start position:0% +that I refer you to again here. +So this is the decimation in time form + + align:start position:0% +So this is the decimation in time form + + + align:start position:0% +So this is the decimation in time form +of the algorithm with the input bit + + align:start position:0% +of the algorithm with the input bit + + + align:start position:0% +of the algorithm with the input bit +reversed and the output in normal order. + + align:start position:0% +reversed and the output in normal order. + + + align:start position:0% +reversed and the output in normal order. +This is the transposition + + align:start position:0% +This is the transposition + + + align:start position:0% +This is the transposition +of this flow graph + + align:start position:0% +of this flow graph + + + align:start position:0% +of this flow graph +which is the decimation and frequency + + align:start position:0% +which is the decimation and frequency + + + align:start position:0% +which is the decimation and frequency +form of the algorithm with the input in + + align:start position:0% +form of the algorithm with the input in + + + align:start position:0% +form of the algorithm with the input in +normal order and the output in bit + + align:start position:0% +normal order and the output in bit + + + align:start position:0% +normal order and the output in bit +reversed order. The fact that these are + + align:start position:0% +reversed order. The fact that these are + + + align:start position:0% +reversed order. The fact that these are +related through transpos transposition + + align:start position:0% +related through transpos transposition + + + align:start position:0% +related through transpos transposition +of the flow graph isn't a particularly + + align:start position:0% +of the flow graph isn't a particularly + + + align:start position:0% +of the flow graph isn't a particularly +important point from a practical point + + align:start position:0% +important point from a practical point + + + align:start position:0% +important point from a practical point +of view, but it is a useful piece of + + align:start position:0% +of view, but it is a useful piece of + + + align:start position:0% +of view, but it is a useful piece of +insight into the relationship between + + align:start position:0% +insight into the relationship between + + + align:start position:0% +insight into the relationship between +these various algorithms. + + align:start position:0% +these various algorithms. + + + align:start position:0% +these various algorithms. +All right. Now just as we did with the + + align:start position:0% +All right. Now just as we did with the + + + align:start position:0% +All right. Now just as we did with the +decimation in time forms of the + + align:start position:0% +decimation in time forms of the + + + align:start position:0% +decimation in time forms of the +algorithm, we can rearrange the + + align:start position:0% +algorithm, we can rearrange the + + + align:start position:0% +algorithm, we can rearrange the +decimation and frequency form of the + + align:start position:0% +decimation and frequency form of the + + + align:start position:0% +decimation and frequency form of the +algorithm to either + + align:start position:0% +algorithm to either + + + align:start position:0% +algorithm to either +arrange the output to be in normal order + + align:start position:0% +arrange the output to be in normal order + + + align:start position:0% +arrange the output to be in normal order +as opposed to having the input in normal + + align:start position:0% +as opposed to having the input in normal + + + align:start position:0% +as opposed to having the input in normal +order or rearrange it so that both the + + align:start position:0% +order or rearrange it so that both the + + + align:start position:0% +order or rearrange it so that both the +input and output are in normal order or + + align:start position:0% +input and output are in normal order or + + + align:start position:0% +input and output are in normal order or +rearrange it as we will so that we can + + align:start position:0% +rearrange it as we will so that we can + + + align:start position:0% +rearrange it as we will so that we can +utilize sequential memory rather than + + align:start position:0% +utilize sequential memory rather than + + + align:start position:0% +utilize sequential memory rather than +random access memory. + + align:start position:0% +random access memory. + + + align:start position:0% +random access memory. +To rearrange the flow graph so that the + + align:start position:0% +To rearrange the flow graph so that the + + + align:start position:0% +To rearrange the flow graph so that the +output is in normal order, we would + + align:start position:0% +output is in normal order, we would + + + align:start position:0% +output is in normal order, we would +again simply take horizontal lines and + + align:start position:0% +again simply take horizontal lines and + + + align:start position:0% +again simply take horizontal lines and +resort them so that the output nodes are + + align:start position:0% +resort them so that the output nodes are + + + align:start position:0% +resort them so that the output nodes are +sorted in a normal order. And the flow + + align:start position:0% +sorted in a normal order. And the flow + + + align:start position:0% +sorted in a normal order. And the flow +graph that results + + align:start position:0% +graph that results + + + align:start position:0% +graph that results +is a decimation in frequency form of the + + align:start position:0% +is a decimation in frequency form of the + + + align:start position:0% +is a decimation in frequency form of the +algorithm + + align:start position:0% +algorithm + + + align:start position:0% +algorithm +for which the outputs are in normal + + align:start position:0% +for which the outputs are in normal + + + align:start position:0% +for which the outputs are in normal +order + + align:start position:0% +order + + + align:start position:0% +order +but the inputs are in bit reversed + + align:start position:0% +but the inputs are in bit reversed + + + align:start position:0% +but the inputs are in bit reversed +order. + + align:start position:0% +order. + + + align:start position:0% +order. +Again as this flow graph has been sorted + + align:start position:0% +Again as this flow graph has been sorted + + + align:start position:0% +Again as this flow graph has been sorted +it is an in place computation in place + + align:start position:0% +it is an in place computation in place + + + align:start position:0% +it is an in place computation in place +again because the butterflies are laid + + align:start position:0% +again because the butterflies are laid + + + align:start position:0% +again because the butterflies are laid +out in such a way that they involve + + align:start position:0% +out in such a way that they involve + + + align:start position:0% +out in such a way that they involve +horizontally adjacent nodes. So this is + + align:start position:0% +horizontally adjacent nodes. So this is + + + align:start position:0% +horizontally adjacent nodes. So this is +an in place computation with the input + + align:start position:0% +an in place computation with the input + + + align:start position:0% +an in place computation with the input +in bit reversed order and the output in + + align:start position:0% +in bit reversed order and the output in + + + align:start position:0% +in bit reversed order and the output in +normal order. + + align:start position:0% +normal order. + + + align:start position:0% +normal order. +Again, this is a transposition + + align:start position:0% +Again, this is a transposition + + + align:start position:0% +Again, this is a transposition +of a flow graph of one of the flow + + align:start position:0% +of a flow graph of one of the flow + + + align:start position:0% +of a flow graph of one of the flow +graphs that we had that we discussed in + + align:start position:0% +graphs that we had that we discussed in + + + align:start position:0% +graphs that we had that we discussed in +the previous lecture. In particular, it + + align:start position:0% +the previous lecture. In particular, it + + + align:start position:0% +the previous lecture. In particular, it +is a transposition of the flow graph for + + align:start position:0% +is a transposition of the flow graph for + + + align:start position:0% +is a transposition of the flow graph for +which if you imagine this flow graph + + align:start position:0% +which if you imagine this flow graph + + + align:start position:0% +which if you imagine this flow graph +being transposed so that the direction + + align:start position:0% +being transposed so that the direction + + + align:start position:0% +being transposed so that the direction +of the arrows are reversed and this is + + align:start position:0% +of the arrows are reversed and this is + + + align:start position:0% +of the arrows are reversed and this is +the input then it corresponds to the + + align:start position:0% +the input then it corresponds to the + + + align:start position:0% +the input then it corresponds to the +decimation and time form of the + + align:start position:0% +decimation and time form of the + + + align:start position:0% +decimation and time form of the +algorithm for which the input is in + + align:start position:0% +algorithm for which the input is in + + + align:start position:0% +algorithm for which the input is in +normal order and the output comes out in + + align:start position:0% +normal order and the output comes out in + + + align:start position:0% +normal order and the output comes out in +bit reversed order and that is the flow + + align:start position:0% +bit reversed order and that is the flow + + + align:start position:0% +bit reversed order and that is the flow +graph that I have indicated here. So + + align:start position:0% +graph that I have indicated here. So + + + align:start position:0% +graph that I have indicated here. So +this is a decimation in time form of the + + align:start position:0% +this is a decimation in time form of the + + + align:start position:0% +this is a decimation in time form of the +algorithm which is the transposition of + + align:start position:0% +algorithm which is the transposition of + + + align:start position:0% +algorithm which is the transposition of +the decimation in frequency form of the + + align:start position:0% +the decimation in frequency form of the + + + align:start position:0% +the decimation in frequency form of the +algorithm that we just looked at. + + align:start position:0% + + + + align:start position:0% + +All right, that corresponds then to two + + align:start position:0% +All right, that corresponds then to two + + + align:start position:0% +All right, that corresponds then to two +possible decimation in frequency + + align:start position:0% +possible decimation in frequency + + + align:start position:0% +possible decimation in frequency +algorithms. one in which the input is in + + align:start position:0% +algorithms. one in which the input is in + + + align:start position:0% +algorithms. one in which the input is in +normal order, the output is bit + + align:start position:0% +normal order, the output is bit + + + align:start position:0% +normal order, the output is bit +reversed. This one in which the input is + + align:start position:0% +reversed. This one in which the input is + + + align:start position:0% +reversed. This one in which the input is +bit reversed and the output is in normal + + align:start position:0% +bit reversed and the output is in normal + + + align:start position:0% +bit reversed and the output is in normal +order. + + align:start position:0% +order. + + + align:start position:0% +order. +We can also rearrange this so that the + + align:start position:0% +We can also rearrange this so that the + + + align:start position:0% +We can also rearrange this so that the +input is in normal order and the output + + align:start position:0% +input is in normal order and the output + + + align:start position:0% +input is in normal order and the output +is in normal order. And the flow graph + + align:start position:0% +is in normal order. And the flow graph + + + align:start position:0% +is in normal order. And the flow graph +that results when we implement that is + + align:start position:0% +that results when we implement that is + + + align:start position:0% +that results when we implement that is +similar to the corresponding decimation + + align:start position:0% +similar to the corresponding decimation + + + align:start position:0% +similar to the corresponding decimation +in time flow graph. + + align:start position:0% +in time flow graph. + + + align:start position:0% +in time flow graph. +In fact, it is a transposition of that + + align:start position:0% +In fact, it is a transposition of that + + + align:start position:0% +In fact, it is a transposition of that +flow graph. And just as we found in the + + align:start position:0% +flow graph. And just as we found in the + + + align:start position:0% +flow graph. And just as we found in the +decimation at time algorithm + + align:start position:0% +decimation at time algorithm + + + align:start position:0% +decimation at time algorithm +for this case, although the input is + + align:start position:0% +for this case, although the input is + + + align:start position:0% +for this case, although the input is +sorted in normal order and the output + + align:start position:0% +sorted in normal order and the output + + + align:start position:0% +sorted in normal order and the output +comes out in normal order, the indexing + + align:start position:0% +comes out in normal order, the indexing + + + align:start position:0% +comes out in normal order, the indexing +is generally + + align:start position:0% +is generally + + + align:start position:0% +is generally +complicated as we proceed from stage to + + align:start position:0% +complicated as we proceed from stage to + + + align:start position:0% +complicated as we proceed from stage to +stage. And furthermore, it does not + + align:start position:0% +stage. And furthermore, it does not + + + align:start position:0% +stage. And furthermore, it does not +correspond to an in place computation + + align:start position:0% +correspond to an in place computation + + + align:start position:0% +correspond to an in place computation +because of the fact that the outputs of + + align:start position:0% +because of the fact that the outputs of + + + align:start position:0% +because of the fact that the outputs of +the butterflies + + align:start position:0% +the butterflies + + + align:start position:0% +the butterflies +are no longer horizontally adjacent to + + align:start position:0% +are no longer horizontally adjacent to + + + align:start position:0% +are no longer horizontally adjacent to +the inputs to the butterfly. So + + align:start position:0% +the inputs to the butterfly. So + + + align:start position:0% +the inputs to the butterfly. So +generally this flow graph and its + + align:start position:0% +generally this flow graph and its + + + align:start position:0% +generally this flow graph and its +decimation in time counterpart are not + + align:start position:0% +decimation in time counterpart are not + + + align:start position:0% +decimation in time counterpart are not +practically very important. + + align:start position:0% +practically very important. + + + align:start position:0% +practically very important. +A final rearrangement of the flow graph + + align:start position:0% +A final rearrangement of the flow graph + + + align:start position:0% +A final rearrangement of the flow graph +is the + + align:start position:0% +is the + + + align:start position:0% +is the +rearrangement which permits the use of + + align:start position:0% +rearrangement which permits the use of + + + align:start position:0% +rearrangement which permits the use of +sequential memory rather than random + + align:start position:0% +sequential memory rather than random + + + align:start position:0% +sequential memory rather than random +access memory. And this then is the flow + + align:start position:0% +access memory. And this then is the flow + + + align:start position:0% +access memory. And this then is the flow +graph that is the counterpart to the + + align:start position:0% +graph that is the counterpart to the + + + align:start position:0% +graph that is the counterpart to the +flow graph that we discussed last time + + align:start position:0% +flow graph that we discussed last time + + + align:start position:0% +flow graph that we discussed last time +which I referred to as the singleton + + align:start position:0% +which I referred to as the singleton + + + align:start position:0% +which I referred to as the singleton +algorithm or I attributed to singleton. + + align:start position:0% +algorithm or I attributed to singleton. + + + align:start position:0% +algorithm or I attributed to singleton. +This is a variation of that type of + + align:start position:0% +This is a variation of that type of + + + align:start position:0% +This is a variation of that type of +algorithm in which now again we + + align:start position:0% +algorithm in which now again we + + + align:start position:0% +algorithm in which now again we +recognize that the indexing is identical + + align:start position:0% +recognize that the indexing is identical + + + align:start position:0% +recognize that the indexing is identical +from stage to stage. + + align:start position:0% +from stage to stage. + + + align:start position:0% +from stage to stage. +The input is in normal order and the + + align:start position:0% +The input is in normal order and the + + + align:start position:0% +The input is in normal order and the +output comes out in bit reversed order. + + align:start position:0% +output comes out in bit reversed order. + + + align:start position:0% +output comes out in bit reversed order. +And let me just compare this for you + + align:start position:0% +And let me just compare this for you + + + align:start position:0% +And let me just compare this for you +with the corresponding flow graph that + + align:start position:0% +with the corresponding flow graph that + + + align:start position:0% +with the corresponding flow graph that +we had last time which I've indicated + + align:start position:0% +we had last time which I've indicated + + + align:start position:0% +we had last time which I've indicated +here that has the input in bit reversed + + align:start position:0% +here that has the input in bit reversed + + + align:start position:0% +here that has the input in bit reversed +order the output in normal order. In + + align:start position:0% +order the output in normal order. In + + + align:start position:0% +order the output in normal order. In +fact, the transposition of this flow + + align:start position:0% +fact, the transposition of this flow + + + align:start position:0% +fact, the transposition of this flow +graph is the decimation and frequency + + align:start position:0% +graph is the decimation and frequency + + + align:start position:0% +graph is the decimation and frequency +form of the algorithm for which the + + align:start position:0% +form of the algorithm for which the + + + align:start position:0% +form of the algorithm for which the +input is in normal order and the output + + align:start position:0% +input is in normal order and the output + + + align:start position:0% +input is in normal order and the output +is in bit reversed order. + + align:start position:0% +is in bit reversed order. + + + align:start position:0% +is in bit reversed order. +All right. So the indexing is identical + + align:start position:0% +All right. So the indexing is identical + + + align:start position:0% +All right. So the indexing is identical +from stage to stage + + align:start position:0% +from stage to stage + + + align:start position:0% +from stage to stage +and just as we had previously we can + + align:start position:0% +and just as we had previously we can + + + align:start position:0% +and just as we had previously we can +implement this algorithm by utilizing + + align:start position:0% +implement this algorithm by utilizing + + + align:start position:0% +implement this algorithm by utilizing +sequential memory as opposed to random + + align:start position:0% +sequential memory as opposed to random + + + align:start position:0% +sequential memory as opposed to random +access memory. Although the organization + + align:start position:0% +access memory. Although the organization + + + align:start position:0% +access memory. Although the organization +of the memory for the decimation and + + align:start position:0% +of the memory for the decimation and + + + align:start position:0% +of the memory for the decimation and +frequency form of the singleton + + align:start position:0% +frequency form of the singleton + + + align:start position:0% +frequency form of the singleton +algorithm is somewhat different than the + + align:start position:0% +algorithm is somewhat different than the + + + align:start position:0% +algorithm is somewhat different than the +organization of the memory for the + + align:start position:0% +organization of the memory for the + + + align:start position:0% +organization of the memory for the +decimation in time form of the singleton + + align:start position:0% +decimation in time form of the singleton + + + align:start position:0% +decimation in time form of the singleton +algorithm. + + align:start position:0% +algorithm. + + + align:start position:0% +algorithm. +In particular, last time when we + + align:start position:0% +In particular, last time when we + + + align:start position:0% +In particular, last time when we +discussed the decimation in time + + align:start position:0% +discussed the decimation in time + + + align:start position:0% +discussed the decimation in time +algorithm, we had four memories as we + + align:start position:0% +algorithm, we had four memories as we + + + align:start position:0% +algorithm, we had four memories as we +will this time. + + align:start position:0% +will this time. + + + align:start position:0% +will this time. +the first half of the data in memory A, + + align:start position:0% +the first half of the data in memory A, + + + align:start position:0% +the first half of the data in memory A, +the second half of the memory in memory + + align:start position:0% +the second half of the memory in memory + + + align:start position:0% +the second half of the memory in memory +B. We went first of all through all of + + align:start position:0% +B. We went first of all through all of + + + align:start position:0% +B. We went first of all through all of +memory A, then through all of memory B, + + align:start position:0% +memory A, then through all of memory B, + + + align:start position:0% +memory A, then through all of memory B, +storing results alternate alternatingly + + align:start position:0% +storing results alternate alternatingly + + + align:start position:0% +storing results alternate alternatingly +in memory C and D. In this case, the + + align:start position:0% +in memory C and D. In this case, the + + + align:start position:0% +in memory C and D. In this case, the +strategy in utilizing the memory is + + align:start position:0% +strategy in utilizing the memory is + + + align:start position:0% +strategy in utilizing the memory is +somewhat different. + + align:start position:0% +somewhat different. + + + align:start position:0% +somewhat different. +In this case, we store the first half of + + align:start position:0% +In this case, we store the first half of + + + align:start position:0% +In this case, we store the first half of +the data points again in memory A. The + + align:start position:0% +the data points again in memory A. The + + + align:start position:0% +the data points again in memory A. The +second half of the data points again in + + align:start position:0% +second half of the data points again in + + + align:start position:0% +second half of the data points again in +memory B. But notice that now in the + + align:start position:0% +memory B. But notice that now in the + + + align:start position:0% +memory B. But notice that now in the +computation + + align:start position:0% +computation + + + align:start position:0% +computation +utilizing the computation for this point + + align:start position:0% +utilizing the computation for this point + + + align:start position:0% +utilizing the computation for this point +for example, we use the first output + + align:start position:0% +for example, we use the first output + + + align:start position:0% +for example, we use the first output +point from memory A and the first output + + align:start position:0% +point from memory A and the first output + + + align:start position:0% +point from memory A and the first output +point from memory B. + + align:start position:0% +point from memory B. + + + align:start position:0% +point from memory B. +We store the result in the first + + align:start position:0% +We store the result in the first + + + align:start position:0% +We store the result in the first +register in memory C and in the second + + align:start position:0% +register in memory C and in the second + + + align:start position:0% +register in memory C and in the second +register in memory C. + + align:start position:0% +register in memory C. + + + align:start position:0% +register in memory C. +Then to compute the next two points, we + + align:start position:0% +Then to compute the next two points, we + + + align:start position:0% +Then to compute the next two points, we +take the next point from memory A and + + align:start position:0% +take the next point from memory A and + + + align:start position:0% +take the next point from memory A and +the next point from memory B. + + align:start position:0% +the next point from memory B. + + + align:start position:0% +the next point from memory B. +Do the appropriate addition and + + align:start position:0% +Do the appropriate addition and + + + align:start position:0% +Do the appropriate addition and +subtraction multiplication by powers of + + align:start position:0% +subtraction multiplication by powers of + + + align:start position:0% +subtraction multiplication by powers of +W and store those in the next two + + align:start position:0% +W and store those in the next two + + + align:start position:0% +W and store those in the next two +registers in memory C. For this + + align:start position:0% +registers in memory C. For this + + + align:start position:0% +registers in memory C. For this +particular example, namely N equals 8, + + align:start position:0% +particular example, namely N equals 8, + + + align:start position:0% +particular example, namely N equals 8, +that fills up memory C. And we proceed + + align:start position:0% +that fills up memory C. And we proceed + + + align:start position:0% +that fills up memory C. And we proceed +likewise accessing the input data + + align:start position:0% +likewise accessing the input data + + + align:start position:0% +likewise accessing the input data +alternating between the two input + + align:start position:0% +alternating between the two input + + + align:start position:0% +alternating between the two input +memories and storing data first in all + + align:start position:0% +memories and storing data first in all + + + align:start position:0% +memories and storing data first in all +of one of the output memories and then + + align:start position:0% +of one of the output memories and then + + + align:start position:0% +of one of the output memories and then +in all of the second of the output + + align:start position:0% +in all of the second of the output + + + align:start position:0% +in all of the second of the output +memories and then we proceed in that + + align:start position:0% +memories and then we proceed in that + + + align:start position:0% +memories and then we proceed in that +fashion from stage to stage. But again, + + align:start position:0% +fashion from stage to stage. But again, + + + align:start position:0% +fashion from stage to stage. But again, +one of the important aspects is that it + + align:start position:0% +one of the important aspects is that it + + + align:start position:0% +one of the important aspects is that it +utilizes sequential memory. For example, + + align:start position:0% +utilizes sequential memory. For example, + + + align:start position:0% +utilizes sequential memory. For example, +disk or drum or tape or shift register + + align:start position:0% +disk or drum or tape or shift register + + + align:start position:0% +disk or drum or tape or shift register +memory. + + align:start position:0% + + + + align:start position:0% + +Okay. Well, so this then is essentially + + align:start position:0% +Okay. Well, so this then is essentially + + + align:start position:0% +Okay. Well, so this then is essentially +a + + align:start position:0% +a + + + align:start position:0% +a +picture of a variety of the algorithms + + align:start position:0% +picture of a variety of the algorithms + + + align:start position:0% +picture of a variety of the algorithms +which can be used for the computation of + + align:start position:0% +which can be used for the computation of + + + align:start position:0% +which can be used for the computation of +the discrete forier transform. Some of + + align:start position:0% +the discrete forier transform. Some of + + + align:start position:0% +the discrete forier transform. Some of +which were derived on the basis of a + + align:start position:0% +which were derived on the basis of a + + + align:start position:0% +which were derived on the basis of a +decimation in time argument. Some were + + align:start position:0% +decimation in time argument. Some were + + + align:start position:0% +decimation in time argument. Some were +derived on the basis of a decimation in + + align:start position:0% +derived on the basis of a decimation in + + + align:start position:0% +derived on the basis of a decimation in +frequency argument. But we saw in fact + + align:start position:0% +frequency argument. But we saw in fact + + + align:start position:0% +frequency argument. But we saw in fact +that the decimation and frequency forms + + align:start position:0% +that the decimation and frequency forms + + + align:start position:0% +that the decimation and frequency forms +of the algorithm are in terms of flow + + align:start position:0% +of the algorithm are in terms of flow + + + align:start position:0% +of the algorithm are in terms of flow +graph notation or interpretation + + align:start position:0% +graph notation or interpretation + + + align:start position:0% +graph notation or interpretation +transposes of the decimation in time + + align:start position:0% +transposes of the decimation in time + + + align:start position:0% +transposes of the decimation in time +form. + + align:start position:0% +form. + + + align:start position:0% +form. +What I would like to discuss now are a + + align:start position:0% +What I would like to discuss now are a + + + align:start position:0% +What I would like to discuss now are a +few of the computational issues that are + + align:start position:0% +few of the computational issues that are + + + align:start position:0% +few of the computational issues that are +involved in the implementing the fast 4A + + align:start position:0% +involved in the implementing the fast 4A + + + align:start position:0% +involved in the implementing the fast 4A +transform algorithm and return also to a + + align:start position:0% +transform algorithm and return also to a + + + align:start position:0% +transform algorithm and return also to a +brief discussion of at least one + + align:start position:0% +brief discussion of at least one + + + align:start position:0% +brief discussion of at least one +situation in which there is a preference + + align:start position:0% +situation in which there is a preference + + + align:start position:0% +situation in which there is a preference +for using decimation in time or using + + align:start position:0% +for using decimation in time or using + + + align:start position:0% +for using decimation in time or using +decimation in frequency. + + align:start position:0% +decimation in frequency. + + + align:start position:0% +decimation in frequency. +After we've discussed some of the + + align:start position:0% +After we've discussed some of the + + + align:start position:0% +After we've discussed some of the +computational considerations, I will + + align:start position:0% +computational considerations, I will + + + align:start position:0% +computational considerations, I will +then just very briefly discuss the + + align:start position:0% +then just very briefly discuss the + + + align:start position:0% +then just very briefly discuss the +generalization of the fastforier + + align:start position:0% +generalization of the fastforier + + + align:start position:0% +generalization of the fastforier +transform algorithm to situations in + + align:start position:0% +transform algorithm to situations in + + + align:start position:0% +transform algorithm to situations in +which the number of data points is not a + + align:start position:0% +which the number of data points is not a + + + align:start position:0% +which the number of data points is not a +power of two but is a more arbitrary + + align:start position:0% +power of two but is a more arbitrary + + + align:start position:0% +power of two but is a more arbitrary +composite number. + + align:start position:0% +composite number. + + + align:start position:0% +composite number. +Well, first of all then let me introduce + + align:start position:0% +Well, first of all then let me introduce + + + align:start position:0% +Well, first of all then let me introduce +a few of the computational issues that I + + align:start position:0% +a few of the computational issues that I + + + align:start position:0% +a few of the computational issues that I +would like to draw your attention to. + + align:start position:0% +would like to draw your attention to. + + + align:start position:0% +would like to draw your attention to. +The first is and it's a point that I + + align:start position:0% +The first is and it's a point that I + + + align:start position:0% +The first is and it's a point that I +raised in u the first lecture in which I + + align:start position:0% +raised in u the first lecture in which I + + + align:start position:0% +raised in u the first lecture in which I +introduced the fast 4A transform + + align:start position:0% +introduced the fast 4A transform + + + align:start position:0% +introduced the fast 4A transform +algorithm that whereas our discussion + + align:start position:0% +algorithm that whereas our discussion + + + align:start position:0% +algorithm that whereas our discussion +has been directed entirely toward the + + align:start position:0% +has been directed entirely toward the + + + align:start position:0% +has been directed entirely toward the +computation of the DFT + + align:start position:0% +computation of the DFT + + + align:start position:0% +computation of the DFT +it applies also in a very + + align:start position:0% +it applies also in a very + + + align:start position:0% +it applies also in a very +straightforward way to a computation of + + align:start position:0% +straightforward way to a computation of + + + align:start position:0% +straightforward way to a computation of +the inverse DFT. + + align:start position:0% +the inverse DFT. + + + align:start position:0% +the inverse DFT. +In particular, we know that the inverse + + align:start position:0% +In particular, we know that the inverse + + + align:start position:0% +In particular, we know that the inverse +discrete forier transform relationship + + align:start position:0% +discrete forier transform relationship + + + align:start position:0% +discrete forier transform relationship +is given by 1 / n times the sum of x of + + align:start position:0% +is given by 1 / n times the sum of x of + + + align:start position:0% +is given by 1 / n times the sum of x of +k w subn to the minus n k. In contrast + + align:start position:0% +k w subn to the minus n k. In contrast + + + align:start position:0% +k w subn to the minus n k. In contrast +to the discrete forier transform the + + align:start position:0% +to the discrete forier transform the + + + align:start position:0% +to the discrete forier transform the +that is the forward transform which does + + align:start position:0% +that is the forward transform which does + + + align:start position:0% +that is the forward transform which does +not have the factor of 1 /n + + align:start position:0% +not have the factor of 1 /n + + + align:start position:0% +not have the factor of 1 /n +and uh involves multiplication by w subn + + align:start position:0% +and uh involves multiplication by w subn + + + align:start position:0% +and uh involves multiplication by w subn +to the + n k rather than w subn to the + + align:start position:0% +to the + n k rather than w subn to the + + + align:start position:0% +to the + n k rather than w subn to the +minus n k. + + align:start position:0% +minus n k. + + + align:start position:0% +minus n k. +to use the + + align:start position:0% +to use the + + + align:start position:0% +to use the +algorithms that we have just been + + align:start position:0% +algorithms that we have just been + + + align:start position:0% +algorithms that we have just been +discussing + + align:start position:0% +discussing + + + align:start position:0% +discussing +for the computation of the inverse + + align:start position:0% +for the computation of the inverse + + + align:start position:0% +for the computation of the inverse +discrete forier transform. The + + align:start position:0% +discrete forier transform. The + + + align:start position:0% +discrete forier transform. The +modification is relatively + + align:start position:0% +modification is relatively + + + align:start position:0% +modification is relatively +straightforward. First of all, it + + align:start position:0% +straightforward. First of all, it + + + align:start position:0% +straightforward. First of all, it +involves a factor of 1 / n which we can + + align:start position:0% +involves a factor of 1 / n which we can + + + align:start position:0% +involves a factor of 1 / n which we can +accommodate in a number of ways. uh one + + align:start position:0% +accommodate in a number of ways. uh one + + + align:start position:0% +accommodate in a number of ways. uh one +is of course by shifting the output or + + align:start position:0% +is of course by shifting the output or + + + align:start position:0% +is of course by shifting the output or +by applying scaling at each stage of the + + align:start position:0% +by applying scaling at each stage of the + + + align:start position:0% +by applying scaling at each stage of the +FFT for example. + + align:start position:0% +FFT for example. + + + align:start position:0% +FFT for example. +So this factor of 1 /n is easily + + align:start position:0% +So this factor of 1 /n is easily + + + align:start position:0% +So this factor of 1 /n is easily +accommodated. + + align:start position:0% +accommodated. + + + align:start position:0% +accommodated. +And the other + + align:start position:0% +And the other + + + align:start position:0% +And the other +difference is the inclusion of a minus + + align:start position:0% +difference is the inclusion of a minus + + + align:start position:0% +difference is the inclusion of a minus +sign in the exponent in powers of w + + align:start position:0% +sign in the exponent in powers of w + + + align:start position:0% +sign in the exponent in powers of w +rather than a plus sign for the forward + + align:start position:0% +rather than a plus sign for the forward + + + align:start position:0% +rather than a plus sign for the forward +transform. + + align:start position:0% +transform. + + + align:start position:0% +transform. +That means in essence that these + + align:start position:0% +That means in essence that these + + + align:start position:0% +That means in essence that these +coefficients + + align:start position:0% +coefficients + + + align:start position:0% +coefficients +are the complex conjugate of these + + align:start position:0% +are the complex conjugate of these + + + align:start position:0% +are the complex conjugate of these +coefficients because w sub capital n w + + align:start position:0% +coefficients because w sub capital n w + + + align:start position:0% +coefficients because w sub capital n w +sub capital n is e to the j 2 pi over + + align:start position:0% +sub capital n is e to the j 2 pi over + + + align:start position:0% +sub capital n is e to the j 2 pi over +capital n. This minus sign represents a + + align:start position:0% +capital n. This minus sign represents a + + + align:start position:0% +capital n. This minus sign represents a +conjugation of w. And so one procedure + + align:start position:0% +conjugation of w. And so one procedure + + + align:start position:0% +conjugation of w. And so one procedure +that we can follow for implementing the + + align:start position:0% +that we can follow for implementing the + + + align:start position:0% +that we can follow for implementing the +inverse discrete forier transform using + + align:start position:0% +inverse discrete forier transform using + + + align:start position:0% +inverse discrete forier transform using +all of the flow graphs that we've talked + + align:start position:0% +all of the flow graphs that we've talked + + + align:start position:0% +all of the flow graphs that we've talked +about is simply conjugate + + align:start position:0% +about is simply conjugate + + + align:start position:0% +about is simply conjugate +the powers of w that are involved in the + + align:start position:0% +the powers of w that are involved in the + + + align:start position:0% +the powers of w that are involved in the +computation. + + align:start position:0% +computation. + + + align:start position:0% +computation. +An alternative procedure which is + + align:start position:0% +An alternative procedure which is + + + align:start position:0% +An alternative procedure which is +basically equivalent is to use the flow + + align:start position:0% +basically equivalent is to use the flow + + + align:start position:0% +basically equivalent is to use the flow +graph the flow graphs as they stand in + + align:start position:0% +graph the flow graphs as they stand in + + + align:start position:0% +graph the flow graphs as they stand in +which case the output data + + align:start position:0% +which case the output data + + + align:start position:0% +which case the output data +which is obtained is the desired result + + align:start position:0% +which is obtained is the desired result + + + align:start position:0% +which is obtained is the desired result +with n replaced with little n replaced + + align:start position:0% +with n replaced with little n replaced + + + align:start position:0% +with n replaced with little n replaced +by minus n. So we can either compute the + + align:start position:0% +by minus n. So we can either compute the + + + align:start position:0% +by minus n. So we can either compute the +inverse DFT + + align:start position:0% +inverse DFT + + + align:start position:0% +inverse DFT +from an algorithm which is aimed at the + + align:start position:0% +from an algorithm which is aimed at the + + + align:start position:0% +from an algorithm which is aimed at the +forward DFT by conjugating the + + align:start position:0% +forward DFT by conjugating the + + + align:start position:0% +forward DFT by conjugating the +coefficients or equivalently by + + align:start position:0% +coefficients or equivalently by + + + align:start position:0% +coefficients or equivalently by +essentially flipping the output modulo + + align:start position:0% +essentially flipping the output modulo + + + align:start position:0% +essentially flipping the output modulo +capital n. + + align:start position:0% +capital n. + + + align:start position:0% +capital n. +So all of the algorithms that we have + + align:start position:0% +So all of the algorithms that we have + + + align:start position:0% +So all of the algorithms that we have +talked about then relate in a very + + align:start position:0% +talked about then relate in a very + + + align:start position:0% +talked about then relate in a very +straightforward manner to the + + align:start position:0% +straightforward manner to the + + + align:start position:0% +straightforward manner to the +computation of the inverse discrete + + align:start position:0% +computation of the inverse discrete + + + align:start position:0% +computation of the inverse discrete +forier transform. + + align:start position:0% +forier transform. + + + align:start position:0% +forier transform. +The second issue is that as we've seen + + align:start position:0% +The second issue is that as we've seen + + + align:start position:0% +The second issue is that as we've seen +in essentially all of the algorithms of + + align:start position:0% +in essentially all of the algorithms of + + + align:start position:0% +in essentially all of the algorithms of +practical interest, + + align:start position:0% +practical interest, + + + align:start position:0% +practical interest, +they involve either bit reversal at the + + align:start position:0% +they involve either bit reversal at the + + + align:start position:0% +they involve either bit reversal at the +input to the flow graph or bit reversal + + align:start position:0% +input to the flow graph or bit reversal + + + align:start position:0% +input to the flow graph or bit reversal +at the output of the flow graph. + + align:start position:0% +at the output of the flow graph. + + + align:start position:0% +at the output of the flow graph. +Bit reversal again is a relatively + + align:start position:0% +Bit reversal again is a relatively + + + align:start position:0% +Bit reversal again is a relatively +straightforward + + align:start position:0% +straightforward + + + align:start position:0% +straightforward +thing to implement. + + align:start position:0% +thing to implement. + + + align:start position:0% +thing to implement. +First of all, it is important to + + align:start position:0% +First of all, it is important to + + + align:start position:0% +First of all, it is important to +recognize that bit reversal is an in + + align:start position:0% +recognize that bit reversal is an in + + + align:start position:0% +recognize that bit reversal is an in +place computation. If we think of it as + + align:start position:0% +place computation. If we think of it as + + + align:start position:0% +place computation. If we think of it as +a computation, in particular, suppose + + align:start position:0% +a computation, in particular, suppose + + + align:start position:0% +a computation, in particular, suppose +that we had the seven data indices 0 + + align:start position:0% +that we had the seven data indices 0 + + + align:start position:0% +that we had the seven data indices 0 +through 7 + + align:start position:0% +through 7 + + + align:start position:0% +through 7 +and we want to rearrange this data so + + align:start position:0% +and we want to rearrange this data so + + + align:start position:0% +and we want to rearrange this data so +that the data is arranged in bit + + align:start position:0% +that the data is arranged in bit + + + align:start position:0% +that the data is arranged in bit +reversed order. + + align:start position:0% +reversed order. + + + align:start position:0% +reversed order. +Well, that means that uh of course zero + + align:start position:0% +Well, that means that uh of course zero + + + align:start position:0% +Well, that means that uh of course zero +bit reversed is zero. One bit reversed + + align:start position:0% +bit reversed is zero. One bit reversed + + + align:start position:0% +bit reversed is zero. One bit reversed +is four, but of course four bit reversed + + align:start position:0% +is four, but of course four bit reversed + + + align:start position:0% +is four, but of course four bit reversed +is one. + + align:start position:0% +is one. + + + align:start position:0% +is one. +So in fact we would want to store data + + align:start position:0% +So in fact we would want to store data + + + align:start position:0% +So in fact we would want to store data +with whose index is one in storage + + align:start position:0% +with whose index is one in storage + + + align:start position:0% +with whose index is one in storage +location four. + + align:start position:0% +location four. + + + align:start position:0% +location four. +But we will also want to store data + + align:start position:0% +But we will also want to store data + + + align:start position:0% +But we will also want to store data +whose data index is four in storage + + align:start position:0% +whose data index is four in storage + + + align:start position:0% +whose data index is four in storage +location one. So in fact implementing + + align:start position:0% +location one. So in fact implementing + + + align:start position:0% +location one. So in fact implementing +the bit reversal can be accomplished in + + align:start position:0% +the bit reversal can be accomplished in + + + align:start position:0% +the bit reversal can be accomplished in +place by essentially swapping these two + + align:start position:0% +place by essentially swapping these two + + + align:start position:0% +place by essentially swapping these two +pieces of data. Similarly of course two + + align:start position:0% +pieces of data. Similarly of course two + + + align:start position:0% +pieces of data. Similarly of course two +bit reversed is two and so that wouldn't + + align:start position:0% +bit reversed is two and so that wouldn't + + + align:start position:0% +bit reversed is two and so that wouldn't +move. Three bit reversed is six but six + + align:start position:0% +move. Three bit reversed is six but six + + + align:start position:0% +move. Three bit reversed is six but six +bit reversed is three. And so again we + + align:start position:0% +bit reversed is three. And so again we + + + align:start position:0% +bit reversed is three. And so again we +can carry out that interchange as an in + + align:start position:0% +can carry out that interchange as an in + + + align:start position:0% +can carry out that interchange as an in +place computation. So bit reversal then + + align:start position:0% +place computation. So bit reversal then + + + align:start position:0% +place computation. So bit reversal then +is can be implemented in place and + + align:start position:0% +is can be implemented in place and + + + align:start position:0% +is can be implemented in place and +consequently + + align:start position:0% +consequently + + + align:start position:0% +consequently +as we restore the data in a bit reversed + + align:start position:0% +as we restore the data in a bit reversed + + + align:start position:0% +as we restore the data in a bit reversed +order + + align:start position:0% +order + + + align:start position:0% +order +we don't require double the storage + + align:start position:0% +we don't require double the storage + + + align:start position:0% +we don't require double the storage +since we can carry that out as an in + + align:start position:0% +since we can carry that out as an in + + + align:start position:0% +since we can carry that out as an in +place operation. + + align:start position:0% +place operation. + + + align:start position:0% +place operation. +Second of all to implement bit reversal + + align:start position:0% +Second of all to implement bit reversal + + + align:start position:0% +Second of all to implement bit reversal +of course to implement bit reversal in + + align:start position:0% +of course to implement bit reversal in + + + align:start position:0% +of course to implement bit reversal in +hardware uh to to obtain a bit reversed + + align:start position:0% +hardware uh to to obtain a bit reversed + + + align:start position:0% +hardware uh to to obtain a bit reversed +index in hardware is very simple. We + + align:start position:0% +index in hardware is very simple. We + + + align:start position:0% +index in hardware is very simple. We +just simply arrange rearrange the order + + align:start position:0% +just simply arrange rearrange the order + + + align:start position:0% +just simply arrange rearrange the order +of the wires. + + align:start position:0% +of the wires. + + + align:start position:0% +of the wires. +To implement + + align:start position:0% +To implement + + + align:start position:0% +To implement +a bit reversed index register or an + + align:start position:0% +a bit reversed index register or an + + + align:start position:0% +a bit reversed index register or an +index + + align:start position:0% +index + + + align:start position:0% +index +algorithmically is a little more + + align:start position:0% +algorithmically is a little more + + + align:start position:0% +algorithmically is a little more +difficult. But in fact and this is + + align:start position:0% +difficult. But in fact and this is + + + align:start position:0% +difficult. But in fact and this is +discussed in some more detail in the + + align:start position:0% +discussed in some more detail in the + + + align:start position:0% +discussed in some more detail in the +text, one of the most straightforward + + align:start position:0% +text, one of the most straightforward + + + align:start position:0% +text, one of the most straightforward +procedures normally is to + + align:start position:0% +procedures normally is to + + + align:start position:0% +procedures normally is to +implement a bit reversed counter so that + + align:start position:0% +implement a bit reversed counter so that + + + align:start position:0% +implement a bit reversed counter so that +as we proceed along + + align:start position:0% +as we proceed along + + + align:start position:0% +as we proceed along +with an index register accessing through + + align:start position:0% +with an index register accessing through + + + align:start position:0% +with an index register accessing through +an index in normal order, we can also + + align:start position:0% +an index in normal order, we can also + + + align:start position:0% +an index in normal order, we can also +run a counter that runs in bit reversed + + align:start position:0% +run a counter that runs in bit reversed + + + align:start position:0% +run a counter that runs in bit reversed +order and use essentially those two as + + align:start position:0% +order and use essentially those two as + + + align:start position:0% +order and use essentially those two as +index registers to tell us how to swap + + align:start position:0% +index registers to tell us how to swap + + + align:start position:0% +index registers to tell us how to swap +the data. So bit reversal in fact + + align:start position:0% +the data. So bit reversal in fact + + + align:start position:0% +the data. So bit reversal in fact +algorithmically is relatively + + align:start position:0% +algorithmically is relatively + + + align:start position:0% +algorithmically is relatively +straightforward. It's it's an + + align:start position:0% +straightforward. It's it's an + + + align:start position:0% +straightforward. It's it's an +interesting point that it is a somewhat + + align:start position:0% +interesting point that it is a somewhat + + + align:start position:0% +interesting point that it is a somewhat +inefficient procedure as you'll see um + + align:start position:0% +inefficient procedure as you'll see um + + + align:start position:0% +inefficient procedure as you'll see um +if you try to program bit reversal but + + align:start position:0% +if you try to program bit reversal but + + + align:start position:0% +if you try to program bit reversal but +algorithmically and conceptually it's a + + align:start position:0% +algorithmically and conceptually it's a + + + align:start position:0% +algorithmically and conceptually it's a +fairly straightforward procedure to + + align:start position:0% +fairly straightforward procedure to + + + align:start position:0% +fairly straightforward procedure to +implement. + + align:start position:0% +implement. + + + align:start position:0% +implement. +A third computational issue which I + + align:start position:0% +A third computational issue which I + + + align:start position:0% +A third computational issue which I +would like to draw your attention to is + + align:start position:0% +would like to draw your attention to is + + + align:start position:0% +would like to draw your attention to is +the + + align:start position:0% +the + + + align:start position:0% +the +question of obtaining the coefficients + + align:start position:0% +question of obtaining the coefficients + + + align:start position:0% +question of obtaining the coefficients +to use in the FFT computation and there + + align:start position:0% +to use in the FFT computation and there + + + align:start position:0% +to use in the FFT computation and there +are basically two procedures that are + + align:start position:0% +are basically two procedures that are + + + align:start position:0% +are basically two procedures that are +commonly used. One of course is to store + + align:start position:0% +commonly used. One of course is to store + + + align:start position:0% +commonly used. One of course is to store +the coefficients in a table and then + + align:start position:0% +the coefficients in a table and then + + + align:start position:0% +the coefficients in a table and then +simply access them as they're needed. + + align:start position:0% +simply access them as they're needed. + + + align:start position:0% +simply access them as they're needed. +A second which saves storage but + + align:start position:0% +A second which saves storage but + + + align:start position:0% +A second which saves storage but +requires some computational time is to + + align:start position:0% +requires some computational time is to + + + align:start position:0% +requires some computational time is to +generate the coefficients recursively. + + align:start position:0% +generate the coefficients recursively. + + + align:start position:0% +generate the coefficients recursively. +That is essentially using an oscillator + + align:start position:0% +That is essentially using an oscillator + + + align:start position:0% +That is essentially using an oscillator +programming an oscillator and generating + + align:start position:0% +programming an oscillator and generating + + + align:start position:0% +programming an oscillator and generating +the coefficients as they're needed. + + align:start position:0% +the coefficients as they're needed. + + + align:start position:0% +the coefficients as they're needed. +Along those lines, it's interesting to + + align:start position:0% +Along those lines, it's interesting to + + + align:start position:0% +Along those lines, it's interesting to +observe that in both the decimation in + + align:start position:0% +observe that in both the decimation in + + + align:start position:0% +observe that in both the decimation in +time and decimation and frequency forms + + align:start position:0% +time and decimation and frequency forms + + + align:start position:0% +time and decimation and frequency forms +of the algorithm, as you proceed from + + align:start position:0% +of the algorithm, as you proceed from + + + align:start position:0% +of the algorithm, as you proceed from +stage to stage, + + align:start position:0% +stage to stage, + + + align:start position:0% +stage to stage, +the powers of W that are involved in the + + align:start position:0% +the powers of W that are involved in the + + + align:start position:0% +the powers of W that are involved in the +computation + + align:start position:0% +computation + + + align:start position:0% +computation +are powers of a basic power of W that + + align:start position:0% +are powers of a basic power of W that + + + align:start position:0% +are powers of a basic power of W that +doubles or at least that changes in each + + align:start position:0% +doubles or at least that changes in each + + + align:start position:0% +doubles or at least that changes in each +stage as you go through the computation. + + align:start position:0% +stage as you go through the computation. + + + align:start position:0% +stage as you go through the computation. +And this has implications as you think + + align:start position:0% +And this has implications as you think + + + align:start position:0% +And this has implications as you think +of either storing a table of + + align:start position:0% +of either storing a table of + + + align:start position:0% +of either storing a table of +coefficients and accessing them or is + + align:start position:0% +coefficients and accessing them or is + + + align:start position:0% +coefficients and accessing them or is +you think of generating the coefficients + + align:start position:0% +you think of generating the coefficients + + + align:start position:0% +you think of generating the coefficients +recursively. + + align:start position:0% +recursively. + + + align:start position:0% +recursively. +The fact that the powers of W are + + align:start position:0% +The fact that the powers of W are + + + align:start position:0% +The fact that the powers of W are +related from stage to stage suggests + + align:start position:0% +related from stage to stage suggests + + + align:start position:0% +related from stage to stage suggests +some fairly efficient procedures for + + align:start position:0% +some fairly efficient procedures for + + + align:start position:0% +some fairly efficient procedures for +doing this. + + align:start position:0% +doing this. + + + align:start position:0% +doing this. +One additional consideration though in + + align:start position:0% +One additional consideration though in + + + align:start position:0% +One additional consideration though in +using the coefficients in in obtaining + + align:start position:0% +using the coefficients in in obtaining + + + align:start position:0% +using the coefficients in in obtaining +the coefficients is that in some of the + + align:start position:0% +the coefficients is that in some of the + + + align:start position:0% +the coefficients is that in some of the +forms of the algorithm + + align:start position:0% +forms of the algorithm + + + align:start position:0% +forms of the algorithm +in some of the forms of the FFT + + align:start position:0% +in some of the forms of the FFT + + + align:start position:0% +in some of the forms of the FFT +algorithm the coefficients + + align:start position:0% +algorithm the coefficients + + + align:start position:0% +algorithm the coefficients +are naturally accessed + + align:start position:0% +are naturally accessed + + + align:start position:0% +are naturally accessed +in a normal order whereas in some other + + align:start position:0% +in a normal order whereas in some other + + + align:start position:0% +in a normal order whereas in some other +forms they are naturally accessed in a + + align:start position:0% +forms they are naturally accessed in a + + + align:start position:0% +forms they are naturally accessed in a +bit reverse. order. For example, if we + + align:start position:0% +bit reverse. order. For example, if we + + + align:start position:0% +bit reverse. order. For example, if we +think of the decimation and frequency + + align:start position:0% +think of the decimation and frequency + + + align:start position:0% +think of the decimation and frequency +form of the algorithm, + + align:start position:0% +form of the algorithm, + + + align:start position:0% +form of the algorithm, +here is the decimation and frequency + + align:start position:0% +here is the decimation and frequency + + + align:start position:0% +here is the decimation and frequency +form of the algorithm with the input in + + align:start position:0% +form of the algorithm with the input in + + + align:start position:0% +form of the algorithm with the input in +normal order and the output in bit + + align:start position:0% +normal order and the output in bit + + + align:start position:0% +normal order and the output in bit +reversed order. + + align:start position:0% +reversed order. + + + align:start position:0% +reversed order. +Notice that the powers of W that we have + + align:start position:0% +Notice that the powers of W that we have + + + align:start position:0% +Notice that the powers of W that we have +here occur in what looks like normal + + align:start position:0% +here occur in what looks like normal + + + align:start position:0% +here occur in what looks like normal +order. At least these powers are in + + align:start position:0% +order. At least these powers are in + + + align:start position:0% +order. At least these powers are in +normal order. + + align:start position:0% +normal order. + + + align:start position:0% +normal order. +Whereas if we and this is normal input + + align:start position:0% +Whereas if we and this is normal input + + + align:start position:0% +Whereas if we and this is normal input +order bit reversed output order. Whereas + + align:start position:0% +order bit reversed output order. Whereas + + + align:start position:0% +order bit reversed output order. Whereas +if we took let's say the decimation in + + align:start position:0% +if we took let's say the decimation in + + + align:start position:0% +if we took let's say the decimation in +time form of the algorithm + + align:start position:0% +time form of the algorithm + + + align:start position:0% +time form of the algorithm +where where we have normally ordered + + align:start position:0% +where where we have normally ordered + + + align:start position:0% +where where we have normally ordered +input and bit reversed output. In that + + align:start position:0% +input and bit reversed output. In that + + + align:start position:0% +input and bit reversed output. In that +case, if you look at these powers of W, + + align:start position:0% +case, if you look at these powers of W, + + + align:start position:0% +case, if you look at these powers of W, +they're not in normal order. In fact, + + align:start position:0% +they're not in normal order. In fact, + + + align:start position:0% +they're not in normal order. In fact, +what they're in is bit reversed order. + + align:start position:0% +what they're in is bit reversed order. + + + align:start position:0% +what they're in is bit reversed order. +So, in fact, in addition to the + + align:start position:0% +So, in fact, in addition to the + + + align:start position:0% +So, in fact, in addition to the +consideration as to whether the input is + + align:start position:0% +consideration as to whether the input is + + + align:start position:0% +consideration as to whether the input is +bit reversed or the output is bit + + align:start position:0% +bit reversed or the output is bit + + + align:start position:0% +bit reversed or the output is bit +reversed, in some forms of the + + align:start position:0% +reversed, in some forms of the + + + align:start position:0% +reversed, in some forms of the +algorithm, the coefficients + + align:start position:0% +algorithm, the coefficients + + + align:start position:0% +algorithm, the coefficients +would tend to be stored in normal order. + + align:start position:0% +would tend to be stored in normal order. + + + align:start position:0% +would tend to be stored in normal order. +Whereas in some other forms of the + + align:start position:0% +Whereas in some other forms of the + + + align:start position:0% +Whereas in some other forms of the +algorithm, the coefficients would tend + + align:start position:0% +algorithm, the coefficients would tend + + + align:start position:0% +algorithm, the coefficients would tend +to be stored in a bit reversed order. Or + + align:start position:0% +to be stored in a bit reversed order. Or + + + align:start position:0% +to be stored in a bit reversed order. Or +if we think about generating the + + align:start position:0% +if we think about generating the + + + align:start position:0% +if we think about generating the +coefficients, clearly it is simpler to + + align:start position:0% +coefficients, clearly it is simpler to + + + align:start position:0% +coefficients, clearly it is simpler to +think of generating coefficients in + + align:start position:0% +think of generating coefficients in + + + align:start position:0% +think of generating coefficients in +normal order than it is to think of them + + align:start position:0% +normal order than it is to think of them + + + align:start position:0% +normal order than it is to think of them +as being generated in bit reversed + + align:start position:0% +as being generated in bit reversed + + + align:start position:0% +as being generated in bit reversed +order. + + align:start position:0% +order. + + + align:start position:0% +order. +Now with regard to the question of the + + align:start position:0% +Now with regard to the question of the + + + align:start position:0% +Now with regard to the question of the +input and output being bit reversed, one + + align:start position:0% +input and output being bit reversed, one + + + align:start position:0% +input and output being bit reversed, one +important area in which the computation + + align:start position:0% +important area in which the computation + + + align:start position:0% +important area in which the computation +of the DFT, in other words, the FFT + + align:start position:0% +of the DFT, in other words, the FFT + + + align:start position:0% +of the DFT, in other words, the FFT +algorithms play a role is in + + align:start position:0% +algorithms play a role is in + + + align:start position:0% +algorithms play a role is in +implementing convolution or correlation. + + align:start position:0% +implementing convolution or correlation. + + + align:start position:0% +implementing convolution or correlation. +In that case, we compute a transform + + align:start position:0% +In that case, we compute a transform + + + align:start position:0% +In that case, we compute a transform +multiply by something. In the case of a + + align:start position:0% +multiply by something. In the case of a + + + align:start position:0% +multiply by something. In the case of a +convolution, we multiply by the + + align:start position:0% +convolution, we multiply by the + + + align:start position:0% +convolution, we multiply by the +transform of the impulse response and + + align:start position:0% +transform of the impulse response and + + + align:start position:0% +transform of the impulse response and +then implement an inverse transform. + + align:start position:0% +then implement an inverse transform. + + + align:start position:0% +then implement an inverse transform. +Well, the fact that there are two + + align:start position:0% +Well, the fact that there are two + + + align:start position:0% +Well, the fact that there are two +transforms involved suggests the + + align:start position:0% +transforms involved suggests the + + + align:start position:0% +transforms involved suggests the +possibility that we can organize the + + align:start position:0% +possibility that we can organize the + + + align:start position:0% +possibility that we can organize the +computation in such a way that we + + align:start position:0% +computation in such a way that we + + + align:start position:0% +computation in such a way that we +completely avoid bit reversal. For + + align:start position:0% +completely avoid bit reversal. For + + + align:start position:0% +completely avoid bit reversal. For +example, we can choose an algorithm for + + align:start position:0% +example, we can choose an algorithm for + + + align:start position:0% +example, we can choose an algorithm for +the direct transform which utilizes the + + align:start position:0% +the direct transform which utilizes the + + + align:start position:0% +the direct transform which utilizes the +input in normal order and generates the + + align:start position:0% +input in normal order and generates the + + + align:start position:0% +input in normal order and generates the +transform in bit reversed order. We then + + align:start position:0% +transform in bit reversed order. We then + + + align:start position:0% +transform in bit reversed order. We then +simply have the transform of the impulse + + align:start position:0% +simply have the transform of the impulse + + + align:start position:0% +simply have the transform of the impulse +response stored in bit reversed order. + + align:start position:0% +response stored in bit reversed order. + + + align:start position:0% +response stored in bit reversed order. +carry out the multiplication + + align:start position:0% +carry out the multiplication + + + align:start position:0% +carry out the multiplication +and then choose a form of the algorithm + + align:start position:0% +and then choose a form of the algorithm + + + align:start position:0% +and then choose a form of the algorithm +for the inverse transform + + align:start position:0% +for the inverse transform + + + align:start position:0% +for the inverse transform +which has bit reversed input and results + + align:start position:0% +which has bit reversed input and results + + + align:start position:0% +which has bit reversed input and results +in a normally ordered output. + + align:start position:0% +in a normally ordered output. + + + align:start position:0% +in a normally ordered output. +So in that case we would have as the + + align:start position:0% +So in that case we would have as the + + + align:start position:0% +So in that case we would have as the +forward transform normally ordered data + + align:start position:0% +forward transform normally ordered data + + + align:start position:0% +forward transform normally ordered data +being transformed to bit reversed data + + align:start position:0% +being transformed to bit reversed data + + + align:start position:0% +being transformed to bit reversed data +and then as the inverse transform bit + + align:start position:0% +and then as the inverse transform bit + + + align:start position:0% +and then as the inverse transform bit +reversed input and normally ordered + + align:start position:0% +reversed input and normally ordered + + + align:start position:0% +reversed input and normally ordered +output. Well, even given that there are + + align:start position:0% +output. Well, even given that there are + + + align:start position:0% +output. Well, even given that there are +a number of options available. + + align:start position:0% +a number of options available. + + + align:start position:0% +a number of options available. +For example, we have an algorithm the + + align:start position:0% +For example, we have an algorithm the + + + align:start position:0% +For example, we have an algorithm the +decimation and time algorithm + + align:start position:0% +decimation and time algorithm + + + align:start position:0% +decimation and time algorithm +which is normally ordered input + + align:start position:0% +which is normally ordered input + + + align:start position:0% +which is normally ordered input +I'm sorry normally uh bit reverse + + align:start position:0% +I'm sorry normally uh bit reverse + + + align:start position:0% +I'm sorry normally uh bit reverse +normally ordered input and bit reversed + + align:start position:0% +normally ordered input and bit reversed + + + align:start position:0% +normally ordered input and bit reversed +output which we could use as our forward + + align:start position:0% +output which we could use as our forward + + + align:start position:0% +output which we could use as our forward +transform. + + align:start position:0% +transform. + + + align:start position:0% +transform. +Although as we just illustrated it + + align:start position:0% +Although as we just illustrated it + + + align:start position:0% +Although as we just illustrated it +involves bit reversed coefficients. + + align:start position:0% +involves bit reversed coefficients. + + + align:start position:0% +involves bit reversed coefficients. +Well, we could think of storing the + + align:start position:0% +Well, we could think of storing the + + + align:start position:0% +Well, we could think of storing the +coefficients in bit reversed order and + + align:start position:0% +coefficients in bit reversed order and + + + align:start position:0% +coefficients in bit reversed order and +then using the companion decimation in + + align:start position:0% +then using the companion decimation in + + + align:start position:0% +then using the companion decimation in +time form of the algorithm + + align:start position:0% +time form of the algorithm + + + align:start position:0% +time form of the algorithm +which has + + align:start position:0% +which has + + + align:start position:0% +which has +bit reversed input and normally ordered + + align:start position:0% +bit reversed input and normally ordered + + + align:start position:0% +bit reversed input and normally ordered +output + + align:start position:0% +output + + + align:start position:0% +output +to achieve the inverse transform. + + align:start position:0% +to achieve the inverse transform. + + + align:start position:0% +to achieve the inverse transform. +However, in this case, the coefficients + + align:start position:0% +However, in this case, the coefficients + + + align:start position:0% +However, in this case, the coefficients +are in normal order. So, if we match up + + align:start position:0% +are in normal order. So, if we match up + + + align:start position:0% +are in normal order. So, if we match up +the algorithms that way, then we're + + align:start position:0% +the algorithms that way, then we're + + + align:start position:0% +the algorithms that way, then we're +faced with the problem that in the + + align:start position:0% +faced with the problem that in the + + + align:start position:0% +faced with the problem that in the +direct transform, the coefficients would + + align:start position:0% +direct transform, the coefficients would + + + align:start position:0% +direct transform, the coefficients would +be stored in bit reversed order, whereas + + align:start position:0% +be stored in bit reversed order, whereas + + + align:start position:0% +be stored in bit reversed order, whereas +in the inverse transform, they would be + + align:start position:0% +in the inverse transform, they would be + + + align:start position:0% +in the inverse transform, they would be +stored in normal order. Well, you can + + align:start position:0% +stored in normal order. Well, you can + + + align:start position:0% +stored in normal order. Well, you can +ask whether for the decimation of + + align:start position:0% +ask whether for the decimation of + + + align:start position:0% +ask whether for the decimation of +frequency form of the algorithm, + + align:start position:0% +frequency form of the algorithm, + + + align:start position:0% +frequency form of the algorithm, +we can avoid that. But in fact, the same + + align:start position:0% +we can avoid that. But in fact, the same + + + align:start position:0% +we can avoid that. But in fact, the same +problem arises there. If we have the + + align:start position:0% +problem arises there. If we have the + + + align:start position:0% +problem arises there. If we have the +decimation in time in frequency form of + + align:start position:0% +decimation in time in frequency form of + + + align:start position:0% +decimation in time in frequency form of +the algorithm with normal input bit + + align:start position:0% +the algorithm with normal input bit + + + align:start position:0% +the algorithm with normal input bit +reversed output, then the coefficients + + align:start position:0% +reversed output, then the coefficients + + + align:start position:0% +reversed output, then the coefficients +are stored in normal order. + + align:start position:0% +are stored in normal order. + + + align:start position:0% +are stored in normal order. +But for the inverse + + align:start position:0% +But for the inverse + + + align:start position:0% +But for the inverse +decimation and frequency transform with + + align:start position:0% +decimation and frequency transform with + + + align:start position:0% +decimation and frequency transform with +bit reversed input and normally ordered + + align:start position:0% +bit reversed input and normally ordered + + + align:start position:0% +bit reversed input and normally ordered +output, the coefficients would be stored + + align:start position:0% +output, the coefficients would be stored + + + align:start position:0% +output, the coefficients would be stored +in bit reversed order. + + align:start position:0% +in bit reversed order. + + + align:start position:0% +in bit reversed order. +The solution is to match up a decimation + + align:start position:0% +The solution is to match up a decimation + + + align:start position:0% +The solution is to match up a decimation +in time form of the algorithm with a + + align:start position:0% +in time form of the algorithm with a + + + align:start position:0% +in time form of the algorithm with a +decimation in frequency form of the + + align:start position:0% +decimation in frequency form of the + + + align:start position:0% +decimation in frequency form of the +algorithm. So that for example, + + align:start position:0% +algorithm. So that for example, + + + align:start position:0% +algorithm. So that for example, +we can choose as the forward transform + + align:start position:0% +we can choose as the forward transform + + + align:start position:0% +we can choose as the forward transform +the decimation in + + align:start position:0% +the decimation in + + + align:start position:0% +the decimation in +time in frequency form of the algorithm + + align:start position:0% +time in frequency form of the algorithm + + + align:start position:0% +time in frequency form of the algorithm +with the input in normal order, the + + align:start position:0% +with the input in normal order, the + + + align:start position:0% +with the input in normal order, the +output in bit reversed order and the + + align:start position:0% +output in bit reversed order and the + + + align:start position:0% +output in bit reversed order and the +coefficients normally ordered which is + + align:start position:0% +coefficients normally ordered which is + + + align:start position:0% +coefficients normally ordered which is +generally more convenient. + + align:start position:0% +generally more convenient. + + + align:start position:0% +generally more convenient. +And then choose for the inverse + + align:start position:0% +And then choose for the inverse + + + align:start position:0% +And then choose for the inverse +transform + + align:start position:0% +transform + + + align:start position:0% +transform +not the decimation in frequency + + align:start position:0% +not the decimation in frequency + + + align:start position:0% +not the decimation in frequency +algorithm but the decimation in time + + align:start position:0% +algorithm but the decimation in time + + + align:start position:0% +algorithm but the decimation in time +algorithm for which the input is now bit + + align:start position:0% +algorithm for which the input is now bit + + + align:start position:0% +algorithm for which the input is now bit +reversed. The output is in normal order + + align:start position:0% +reversed. The output is in normal order + + + align:start position:0% +reversed. The output is in normal order +and the coefficients are also in normal + + align:start position:0% +and the coefficients are also in normal + + + align:start position:0% +and the coefficients are also in normal +order. + + align:start position:0% +order. + + + align:start position:0% +order. +So in fact this suggests that if we are + + align:start position:0% +So in fact this suggests that if we are + + + align:start position:0% +So in fact this suggests that if we are +implementing + + align:start position:0% +implementing + + + align:start position:0% +implementing +a transform forward transform and an + + align:start position:0% +a transform forward transform and an + + + align:start position:0% +a transform forward transform and an +inverse transform generally there are + + align:start position:0% +inverse transform generally there are + + + align:start position:0% +inverse transform generally there are +advantages to matching up the decimation + + align:start position:0% +advantages to matching up the decimation + + + align:start position:0% +advantages to matching up the decimation +in time form and the decimation in + + align:start position:0% +in time form and the decimation in + + + align:start position:0% +in time form and the decimation in +frequency form so that we have similarly + + align:start position:0% +frequency form so that we have similarly + + + align:start position:0% +frequency form so that we have similarly +accessed coefficients in both cases. + + align:start position:0% +accessed coefficients in both cases. + + + align:start position:0% +accessed coefficients in both cases. +Well, there are of course a large + + align:start position:0% +Well, there are of course a large + + + align:start position:0% +Well, there are of course a large +variety of other computational issues to + + align:start position:0% +variety of other computational issues to + + + align:start position:0% +variety of other computational issues to +be considered in implementing the + + align:start position:0% +be considered in implementing the + + + align:start position:0% +be considered in implementing the +fastfora transform algorithms. Some of + + align:start position:0% +fastfora transform algorithms. Some of + + + align:start position:0% +fastfora transform algorithms. Some of +these are discussed in the text. Many of + + align:start position:0% +these are discussed in the text. Many of + + + align:start position:0% +these are discussed in the text. Many of +them you will discover for yourselves as + + align:start position:0% +them you will discover for yourselves as + + + align:start position:0% +them you will discover for yourselves as +you try to program the algorithm. But + + align:start position:0% +you try to program the algorithm. But + + + align:start position:0% +you try to program the algorithm. But +hopefully this discussion + + align:start position:0% +hopefully this discussion + + + align:start position:0% +hopefully this discussion +provides at least some indication of + + align:start position:0% +provides at least some indication of + + + align:start position:0% +provides at least some indication of +what some of the strategies are and some + + align:start position:0% +what some of the strategies are and some + + + align:start position:0% +what some of the strategies are and some +of the issues are that are involved in + + align:start position:0% +of the issues are that are involved in + + + align:start position:0% +of the issues are that are involved in +computation of the FFT of the forms that + + align:start position:0% +computation of the FFT of the forms that + + + align:start position:0% +computation of the FFT of the forms that +we've been talking about. + + align:start position:0% +we've been talking about. + + + align:start position:0% +we've been talking about. +Now + + align:start position:0% +Now + + + align:start position:0% +Now +all of this discussion has been related + + align:start position:0% +all of this discussion has been related + + + align:start position:0% +all of this discussion has been related +to the computation of the discrete + + align:start position:0% +to the computation of the discrete + + + align:start position:0% +to the computation of the discrete +forier transform when the number of data + + align:start position:0% +forier transform when the number of data + + + align:start position:0% +forier transform when the number of data +points is a power of two and these + + align:start position:0% +points is a power of two and these + + + align:start position:0% +points is a power of two and these +algorithms are referred to as the radix + + align:start position:0% +algorithms are referred to as the radix + + + align:start position:0% +algorithms are referred to as the radix +2 forms of the FFT algorithm. As I + + align:start position:0% +2 forms of the FFT algorithm. As I + + + align:start position:0% +2 forms of the FFT algorithm. As I +indicated in the first lecture in which + + align:start position:0% +indicated in the first lecture in which + + + align:start position:0% +indicated in the first lecture in which +we discussed the FFT. + + align:start position:0% +we discussed the FFT. + + + align:start position:0% +we discussed the FFT. +The FFT in fact is more general in that + + align:start position:0% +The FFT in fact is more general in that + + + align:start position:0% +The FFT in fact is more general in that +it generally applies when n is a highly + + align:start position:0% +it generally applies when n is a highly + + + align:start position:0% +it generally applies when n is a highly +composite number. We chose it to be + + align:start position:0% +composite number. We chose it to be + + + align:start position:0% +composite number. We chose it to be +composed of powers of two. But in fact + + align:start position:0% +composed of powers of two. But in fact + + + align:start position:0% +composed of powers of two. But in fact +there are a variety of other forms of + + align:start position:0% +there are a variety of other forms of + + + align:start position:0% +there are a variety of other forms of +the FFT algorithm for different radices. + + align:start position:0% +the FFT algorithm for different radices. + + + align:start position:0% +the FFT algorithm for different radices. +And in some cases there are some + + align:start position:0% +And in some cases there are some + + + align:start position:0% +And in some cases there are some +advantages to be found in using not a + + align:start position:0% +advantages to be found in using not a + + + align:start position:0% +advantages to be found in using not a +power of two algorithm but a different + + align:start position:0% +power of two algorithm but a different + + + align:start position:0% +power of two algorithm but a different +algorithm. + + align:start position:0% +algorithm. + + + align:start position:0% +algorithm. +On the other hand, in many situations, + + align:start position:0% +On the other hand, in many situations, + + + align:start position:0% +On the other hand, in many situations, +the disadvantages of that outweigh the + + align:start position:0% +the disadvantages of that outweigh the + + + align:start position:0% +the disadvantages of that outweigh the +advantages. However, what I would like + + align:start position:0% +advantages. However, what I would like + + + align:start position:0% +advantages. However, what I would like +to do is conclude the discussion of the + + align:start position:0% +to do is conclude the discussion of the + + + align:start position:0% +to do is conclude the discussion of the +fastfora transform algorithm by just + + align:start position:0% +fastfora transform algorithm by just + + + align:start position:0% +fastfora transform algorithm by just +very briefly + + align:start position:0% + + + + align:start position:0% + +outlining what the structure of the FFT + + align:start position:0% +outlining what the structure of the FFT + + + align:start position:0% +outlining what the structure of the FFT +algorithm is more generally. And again + + align:start position:0% +algorithm is more generally. And again + + + align:start position:0% +algorithm is more generally. And again +in the text there is a uh there are a + + align:start position:0% +in the text there is a uh there are a + + + align:start position:0% +in the text there is a uh there are a +number of examples of + + align:start position:0% +number of examples of + + + align:start position:0% +number of examples of +FFT algorithms for radices other than a + + align:start position:0% +FFT algorithms for radices other than a + + + align:start position:0% +FFT algorithms for radices other than a +power of two and a more complete + + align:start position:0% +power of two and a more complete + + + align:start position:0% +power of two and a more complete +discussion than I feel that is + + align:start position:0% +discussion than I feel that is + + + align:start position:0% +discussion than I feel that is +appropriate to go through right now. + + align:start position:0% +appropriate to go through right now. + + + align:start position:0% +appropriate to go through right now. +However, let me just outline what some + + align:start position:0% +However, let me just outline what some + + + align:start position:0% +However, let me just outline what some +of the issues are in discussing a more + + align:start position:0% +of the issues are in discussing a more + + + align:start position:0% +of the issues are in discussing a more +general radex FFT algorithm. + + align:start position:0% +general radex FFT algorithm. + + + align:start position:0% +general radex FFT algorithm. +Generally the computation of the + + align:start position:0% +Generally the computation of the + + + align:start position:0% +Generally the computation of the +discrete 4A transform using this class + + align:start position:0% +discrete 4A transform using this class + + + align:start position:0% +discrete 4A transform using this class +of algorithms is directed toward + + align:start position:0% +of algorithms is directed toward + + + align:start position:0% +of algorithms is directed toward +capitalizing on the fact that the size + + align:start position:0% +capitalizing on the fact that the size + + + align:start position:0% +capitalizing on the fact that the size +transform to be implemented is a product + + align:start position:0% +transform to be implemented is a product + + + align:start position:0% +transform to be implemented is a product +of numbers. And it turns out that the + + align:start position:0% +of numbers. And it turns out that the + + + align:start position:0% +of numbers. And it turns out that the +more numbers, the more terms in the + + align:start position:0% +more numbers, the more terms in the + + + align:start position:0% +more numbers, the more terms in the +decomposition, the greater the + + align:start position:0% +decomposition, the greater the + + + align:start position:0% +decomposition, the greater the +efficiency that can be obtained in + + align:start position:0% +efficiency that can be obtained in + + + align:start position:0% +efficiency that can be obtained in +implementing the transform. + + align:start position:0% +implementing the transform. + + + align:start position:0% +implementing the transform. +In that case, generally one would think + + align:start position:0% +In that case, generally one would think + + + align:start position:0% +In that case, generally one would think +of these numbers as primes since that is + + align:start position:0% +of these numbers as primes since that is + + + align:start position:0% +of these numbers as primes since that is +the biggest decomposition of any number + + align:start position:0% +the biggest decomposition of any number + + + align:start position:0% +the biggest decomposition of any number +that we can carry out. But in fact, for + + align:start position:0% +that we can carry out. But in fact, for + + + align:start position:0% +that we can carry out. But in fact, for +the derivation, it is not a requirement + + align:start position:0% +the derivation, it is not a requirement + + + align:start position:0% +the derivation, it is not a requirement +that the P's be primes. So let's think + + align:start position:0% +that the P's be primes. So let's think + + + align:start position:0% +that the P's be primes. So let's think +of n then is decomposed as a product of + + align:start position:0% +of n then is decomposed as a product of + + + align:start position:0% +of n then is decomposed as a product of +p1 * p2 etc through p sub new + + align:start position:0% +p1 * p2 etc through p sub new + + + align:start position:0% +p1 * p2 etc through p sub new +which we can alternatively write as p1 * + + align:start position:0% +which we can alternatively write as p1 * + + + align:start position:0% +which we can alternatively write as p1 * +q1 where q1 is then represented by the + + align:start position:0% +q1 where q1 is then represented by the + + + align:start position:0% +q1 where q1 is then represented by the +product of the remaining terms + + align:start position:0% +product of the remaining terms + + + align:start position:0% +product of the remaining terms +and + + align:start position:0% +and + + + align:start position:0% +and +we can proceed + + align:start position:0% +we can proceed + + + align:start position:0% +we can proceed +essentially along a route similar to the + + align:start position:0% +essentially along a route similar to the + + + align:start position:0% +essentially along a route similar to the +decimation in time algorithms or along a + + align:start position:0% +decimation in time algorithms or along a + + + align:start position:0% +decimation in time algorithms or along a +route similar to the decimation and + + align:start position:0% +route similar to the decimation and + + + align:start position:0% +route similar to the decimation and +frequency algorithms. Let me just + + align:start position:0% +frequency algorithms. Let me just + + + align:start position:0% +frequency algorithms. Let me just +indicate the strategy paralleling the + + align:start position:0% +indicate the strategy paralleling the + + + align:start position:0% +indicate the strategy paralleling the +decimation in time form of the algorithm + + align:start position:0% +decimation in time form of the algorithm + + + align:start position:0% +decimation in time form of the algorithm +as we discussed it for n a power of two. + + align:start position:0% +as we discussed it for n a power of two. + + + align:start position:0% +as we discussed it for n a power of two. +In that case we decomposed p1 is equal + + align:start position:0% +In that case we decomposed p1 is equal + + + align:start position:0% +In that case we decomposed p1 is equal +to two and q1 is equal to n /2 + + align:start position:0% +to two and q1 is equal to n /2 + + + align:start position:0% +to two and q1 is equal to n /2 +and we decomposed the original sequence + + align:start position:0% +and we decomposed the original sequence + + + align:start position:0% +and we decomposed the original sequence +into two subsequences. + + align:start position:0% +into two subsequences. + + + align:start position:0% +into two subsequences. +One consisting of the even numbered + + align:start position:0% +One consisting of the even numbered + + + align:start position:0% +One consisting of the even numbered +points the other consisting of the + + align:start position:0% +points the other consisting of the + + + align:start position:0% +points the other consisting of the +oddnumbered points. More generally, we + + align:start position:0% +oddnumbered points. More generally, we + + + align:start position:0% +oddnumbered points. More generally, we +would decompose the sequence + + align:start position:0% +would decompose the sequence + + + align:start position:0% +would decompose the sequence +into a set of subsequences + + align:start position:0% +into a set of subsequences + + + align:start position:0% +into a set of subsequences +consisting of every P1 point. + + align:start position:0% +consisting of every P1 point. + + + align:start position:0% +consisting of every P1 point. +So how many sequences are there? Well, + + align:start position:0% +So how many sequences are there? Well, + + + align:start position:0% +So how many sequences are there? Well, +there are P1 sequences and the length of + + align:start position:0% +there are P1 sequences and the length of + + + align:start position:0% +there are P1 sequences and the length of +each sequence is Q1. For example, if P1 + + align:start position:0% +each sequence is Q1. For example, if P1 + + + align:start position:0% +each sequence is Q1. For example, if P1 +was equal to two and Q1 was n /2, this + + align:start position:0% +was equal to two and Q1 was n /2, this + + + align:start position:0% +was equal to two and Q1 was n /2, this +would be every other point. That's + + align:start position:0% +would be every other point. That's + + + align:start position:0% +would be every other point. That's +choosing the even numbered points and + + align:start position:0% +choosing the even numbered points and + + + align:start position:0% +choosing the even numbered points and +the oddnumbered points. There would be + + align:start position:0% +the oddnumbered points. There would be + + + align:start position:0% +the oddnumbered points. There would be +two subsequences + + align:start position:0% +two subsequences + + + align:start position:0% +two subsequences +each subsequence of length n /2. + + align:start position:0% +each subsequence of length n /2. + + + align:start position:0% +each subsequence of length n /2. +More generally then if we had say n= to + + align:start position:0% +More generally then if we had say n= to + + + align:start position:0% +More generally then if we had say n= to +12 and p1= to 3 we would have we would + + align:start position:0% +12 and p1= to 3 we would have we would + + + align:start position:0% +12 and p1= to 3 we would have we would +generate three subsequences + + align:start position:0% +generate three subsequences + + + align:start position:0% +generate three subsequences +each consisting of four points + + align:start position:0% +each consisting of four points + + + align:start position:0% +each consisting of four points +chosen by selecting every p1 or every + + align:start position:0% +chosen by selecting every p1 or every + + + align:start position:0% +chosen by selecting every p1 or every +third point. So one se subsequence which + + align:start position:0% +third point. So one se subsequence which + + + align:start position:0% +third point. So one se subsequence which +I've denoted here by a would be this + + align:start position:0% +I've denoted here by a would be this + + + align:start position:0% +I've denoted here by a would be this +point then this one then this one and + + align:start position:0% +point then this one then this one and + + + align:start position:0% +point then this one then this one and +that one. The second subsequence would + + align:start position:0% +that one. The second subsequence would + + + align:start position:0% +that one. The second subsequence would +be the subsequence b which is comprised + + align:start position:0% +be the subsequence b which is comprised + + + align:start position:0% +be the subsequence b which is comprised +of this point this this and that. And + + align:start position:0% +of this point this this and that. And + + + align:start position:0% +of this point this this and that. And +the third subsequence would be the + + align:start position:0% +the third subsequence would be the + + + align:start position:0% +the third subsequence would be the +subsequence C which is this point this + + align:start position:0% +subsequence C which is this point this + + + align:start position:0% +subsequence C which is this point this +point that point and that point. + + align:start position:0% +point that point and that point. + + + align:start position:0% +point that point and that point. +All right. So we've decomposed the + + align:start position:0% +All right. So we've decomposed the + + + align:start position:0% +All right. So we've decomposed the +original sequence then into P1 sequences + + align:start position:0% +original sequence then into P1 sequences + + + align:start position:0% +original sequence then into P1 sequences +each of length Q1. + + align:start position:0% +each of length Q1. + + + align:start position:0% +each of length Q1. +Given that we can organize the sum + + align:start position:0% +Given that we can organize the sum + + + align:start position:0% +Given that we can organize the sum +involved in the discrete forier + + align:start position:0% +involved in the discrete forier + + + align:start position:0% +involved in the discrete forier +transform + + align:start position:0% +transform + + + align:start position:0% +transform +by decomposing the sum into separate + + align:start position:0% +by decomposing the sum into separate + + + align:start position:0% +by decomposing the sum into separate +sums involving each one of these P1 + + align:start position:0% +sums involving each one of these P1 + + + align:start position:0% +sums involving each one of these P1 +subsequences. + + align:start position:0% + + + + align:start position:0% + +In particular, if we think of the + + align:start position:0% +In particular, if we think of the + + + align:start position:0% +In particular, if we think of the +argument p1 * r as ranges + + align:start position:0% +argument p1 * r as ranges + + + align:start position:0% +argument p1 * r as ranges +from 0 to q1 minus one, we're selecting + + align:start position:0% +from 0 to q1 minus one, we're selecting + + + align:start position:0% +from 0 to q1 minus one, we're selecting +with this argument every p1 point + + align:start position:0% +with this argument every p1 point + + + align:start position:0% +with this argument every p1 point +starting with the zeroth point. + + align:start position:0% +starting with the zeroth point. + + + align:start position:0% +starting with the zeroth point. +If we think of the argument p1 r + 1 as + + align:start position:0% +If we think of the argument p1 r + 1 as + + + align:start position:0% +If we think of the argument p1 r + 1 as +r runs from zero to q1 minus one we're + + align:start position:0% +r runs from zero to q1 minus one we're + + + align:start position:0% +r runs from zero to q1 minus one we're +then collecting together the terms which + + align:start position:0% +then collecting together the terms which + + + align:start position:0% +then collecting together the terms which +are every p1 point starting with the + + align:start position:0% +are every p1 point starting with the + + + align:start position:0% +are every p1 point starting with the +first point etc. We can proceed + + align:start position:0% +first point etc. We can proceed + + + align:start position:0% +first point etc. We can proceed +to decompose this into a set of P1 + + align:start position:0% +to decompose this into a set of P1 + + + align:start position:0% +to decompose this into a set of P1 +subsums as I've indicated here. + + align:start position:0% +subsums as I've indicated here. + + + align:start position:0% +subsums as I've indicated here. +Or when we combine these together then + + align:start position:0% +Or when we combine these together then + + + align:start position:0% +Or when we combine these together then +we can express x of k the dftt as a + + align:start position:0% +we can express x of k the dftt as a + + + align:start position:0% +we can express x of k the dftt as a +double sum + + align:start position:0% +double sum + + + align:start position:0% +double sum +where we + + align:start position:0% +where we + + + align:start position:0% +where we +have the terms involving the separate + + align:start position:0% +have the terms involving the separate + + + align:start position:0% +have the terms involving the separate +subsequences + + align:start position:0% +subsequences + + + align:start position:0% +subsequences +and then the multiplication by a power + + align:start position:0% +and then the multiplication by a power + + + align:start position:0% +and then the multiplication by a power +of w to combine these the computation on + + align:start position:0% +of w to combine these the computation on + + + align:start position:0% +of w to combine these the computation on +these subsequences together to obtain + + align:start position:0% +these subsequences together to obtain + + + align:start position:0% +these subsequences together to obtain +the dft. ft. These terms of course are + + align:start position:0% +the dft. ft. These terms of course are + + + align:start position:0% +the dft. ft. These terms of course are +obtained by the fact that this power of + + align:start position:0% +obtained by the fact that this power of + + + align:start position:0% +obtained by the fact that this power of +w is p1r + 1. In the next sum it will be + + align:start position:0% +w is p1r + 1. In the next sum it will be + + + align:start position:0% +w is p1r + 1. In the next sum it will be +p1 r + 2 p1 r + 3 etc. We decompose that + + align:start position:0% +p1 r + 2 p1 r + 3 etc. We decompose that + + + align:start position:0% +p1 r + 2 p1 r + 3 etc. We decompose that +into a product of two powers of w and + + align:start position:0% +into a product of two powers of w and + + + align:start position:0% +into a product of two powers of w and +then one of those terms + + align:start position:0% +then one of those terms + + + align:start position:0% +then one of those terms +since it doesn't depend on r can be + + align:start position:0% +since it doesn't depend on r can be + + + align:start position:0% +since it doesn't depend on r can be +removed from the sum on r and shows up + + align:start position:0% +removed from the sum on r and shows up + + + align:start position:0% +removed from the sum on r and shows up +in this second sum. Well, I would + + align:start position:0% +in this second sum. Well, I would + + + align:start position:0% +in this second sum. Well, I would +suggest that's a somewhat rapid + + align:start position:0% +suggest that's a somewhat rapid + + + align:start position:0% +suggest that's a somewhat rapid +treatment. I would suggest just simply + + align:start position:0% +treatment. I would suggest just simply + + + align:start position:0% +treatment. I would suggest just simply +working through that for an example and + + align:start position:0% +working through that for an example and + + + align:start position:0% +working through that for an example and +I think it will be clear how this + + align:start position:0% +I think it will be clear how this + + + align:start position:0% +I think it will be clear how this +original sum is decomposed into this + + align:start position:0% +original sum is decomposed into this + + + align:start position:0% +original sum is decomposed into this +one. + + align:start position:0% +one. + + + align:start position:0% +one. +All right. Well, now just as we did in + + align:start position:0% +All right. Well, now just as we did in + + + align:start position:0% +All right. Well, now just as we did in +both the decimation in time and + + align:start position:0% +both the decimation in time and + + + align:start position:0% +both the decimation in time and +decimation in frequency forms of the + + align:start position:0% +decimation in frequency forms of the + + + align:start position:0% +decimation in frequency forms of the +algorithm for for powers of two, we can + + align:start position:0% +algorithm for for powers of two, we can + + + align:start position:0% +algorithm for for powers of two, we can +recognize this power of w subn as a + + align:start position:0% +recognize this power of w subn as a + + + align:start position:0% +recognize this power of w subn as a +different power + + align:start position:0% +different power + + + align:start position:0% +different power +of a w with a different subscript. In + + align:start position:0% +of a w with a different subscript. In + + + align:start position:0% +of a w with a different subscript. In +particular, w subn to the p1 r k as I + + align:start position:0% +particular, w subn to the p1 r k as I + + + align:start position:0% +particular, w subn to the p1 r k as I +have here + + align:start position:0% +have here + + + align:start position:0% +have here +is equal to e to the j 2 pi over capital + + align:start position:0% +is equal to e to the j 2 pi over capital + + + align:start position:0% +is equal to e to the j 2 pi over capital +n * p1 r k. + + align:start position:0% +n * p1 r k. + + + align:start position:0% +n * p1 r k. +But n is equal to p1 * q1. That's the + + align:start position:0% +But n is equal to p1 * q1. That's the + + + align:start position:0% +But n is equal to p1 * q1. That's the +way we originally decomposed it. + + align:start position:0% +way we originally decomposed it. + + + align:start position:0% +way we originally decomposed it. +and the P1's cancel out and we're left + + align:start position:0% +and the P1's cancel out and we're left + + + align:start position:0% +and the P1's cancel out and we're left +with ej 2<unk>i / q1 * r k or + + align:start position:0% +with ej 2<unk>i / q1 * r k or + + + align:start position:0% +with ej 2<unk>i / q1 * r k or +equivalently w subq1 to the rk. + + align:start position:0% +equivalently w subq1 to the rk. + + + align:start position:0% +equivalently w subq1 to the rk. +So + + align:start position:0% +So + + + align:start position:0% +So +substituting this for w subn to the p1r + + align:start position:0% +substituting this for w subn to the p1r + + + align:start position:0% +substituting this for w subn to the p1r +k in the previous expression. What + + align:start position:0% +k in the previous expression. What + + + align:start position:0% +k in the previous expression. What +results is then x of k expressed as a + + align:start position:0% +results is then x of k expressed as a + + + align:start position:0% +results is then x of k expressed as a +sum from l=0 p1 minus one of these + + align:start position:0% +sum from l=0 p1 minus one of these + + + align:start position:0% +sum from l=0 p1 minus one of these +powers of w subn. But then the important + + align:start position:0% +powers of w subn. But then the important + + + align:start position:0% +powers of w subn. But then the important +thing is that the inner sum involves q1 + + align:start position:0% +thing is that the inner sum involves q1 + + + align:start position:0% +thing is that the inner sum involves q1 +point sequences. + + align:start position:0% +point sequences. + + + align:start position:0% +point sequences. +This factor is w subq1 to the rk and in + + align:start position:0% +This factor is w subq1 to the rk and in + + + align:start position:0% +This factor is w subq1 to the rk and in +fact this entire summation is a q1 point + + align:start position:0% +fact this entire summation is a q1 point + + + align:start position:0% +fact this entire summation is a q1 point +dftft. + + align:start position:0% +dftft. + + + align:start position:0% +dftft. +So pursuing this then what we basically + + align:start position:0% +So pursuing this then what we basically + + + align:start position:0% +So pursuing this then what we basically +decompose the the computation into is + + align:start position:0% +decompose the the computation into is + + + align:start position:0% +decompose the the computation into is +the computation + + align:start position:0% +the computation + + + align:start position:0% +the computation +of p1 + + align:start position:0% +of p1 + + + align:start position:0% +of p1 +q1 point dftts. + + align:start position:0% +q1 point dftts. + + + align:start position:0% +q1 point dftts. +we obtain the Q1 point DFTs and then + + align:start position:0% +we obtain the Q1 point DFTs and then + + + align:start position:0% +we obtain the Q1 point DFTs and then +combine them according to the expression + + align:start position:0% +combine them according to the expression + + + align:start position:0% +combine them according to the expression +as we have here. This would then lead to + + align:start position:0% +as we have here. This would then lead to + + + align:start position:0% +as we have here. This would then lead to +the generalization of the butterfly + + align:start position:0% +the generalization of the butterfly + + + align:start position:0% +the generalization of the butterfly +computation as we had it for the radix 2 + + align:start position:0% +computation as we had it for the radix 2 + + + align:start position:0% +computation as we had it for the radix 2 +algorithms. + + align:start position:0% +algorithms. + + + align:start position:0% +algorithms. +And if you count up the number of + + align:start position:0% +And if you count up the number of + + + align:start position:0% +And if you count up the number of +multiplies and adds again you'll see + + align:start position:0% +multiplies and adds again you'll see + + + align:start position:0% +multiplies and adds again you'll see +that there's some computational + + align:start position:0% +that there's some computational + + + align:start position:0% +that there's some computational +efficiency that results from doing this. + + align:start position:0% +efficiency that results from doing this. + + + align:start position:0% +efficiency that results from doing this. +And then just as we did with the radix 2 + + align:start position:0% +And then just as we did with the radix 2 + + + align:start position:0% +And then just as we did with the radix 2 +algorithms, we can continue to decompose + + align:start position:0% +algorithms, we can continue to decompose + + + align:start position:0% +algorithms, we can continue to decompose +these transforms. + + align:start position:0% +these transforms. + + + align:start position:0% +these transforms. +So that we have Q1 is given by the + + align:start position:0% +So that we have Q1 is given by the + + + align:start position:0% +So that we have Q1 is given by the +product P2 * P through P3 through P sub + + align:start position:0% +product P2 * P through P3 through P sub + + + align:start position:0% +product P2 * P through P3 through P sub +new. + + align:start position:0% +new. + + + align:start position:0% +new. +The this product we recogni we denote as + + align:start position:0% +The this product we recogni we denote as + + + align:start position:0% +The this product we recogni we denote as +Q2 and then we can proceed to decompose + + align:start position:0% +Q2 and then we can proceed to decompose + + + align:start position:0% +Q2 and then we can proceed to decompose +these transforms these Q1 point + + align:start position:0% +these transforms these Q1 point + + + align:start position:0% +these transforms these Q1 point +transforms + + align:start position:0% +transforms + + + align:start position:0% +transforms +into P2 + + align:start position:0% +into P2 + + + align:start position:0% +into P2 +Q2 point transforms then we can + + align:start position:0% +Q2 point transforms then we can + + + align:start position:0% +Q2 point transforms then we can +decompose the Q2 point transforms etc. + + align:start position:0% +decompose the Q2 point transforms etc. + + + align:start position:0% +decompose the Q2 point transforms etc. +If you do this then what you'll find and + + align:start position:0% +If you do this then what you'll find and + + + align:start position:0% +If you do this then what you'll find and +the counting is done a little more + + align:start position:0% +the counting is done a little more + + + align:start position:0% +the counting is done a little more +carefully in the text. + + align:start position:0% +carefully in the text. + + + align:start position:0% +carefully in the text. +What you'll find is that the number of + + align:start position:0% +What you'll find is that the number of + + + align:start position:0% +What you'll find is that the number of +multiplies and adds involved in + + align:start position:0% +multiplies and adds involved in + + + align:start position:0% +multiplies and adds involved in +computing the discrete forier transform + + align:start position:0% +computing the discrete forier transform + + + align:start position:0% +computing the discrete forier transform +this way is proportional to n times a + + align:start position:0% +this way is proportional to n times a + + + align:start position:0% +this way is proportional to n times a +sum of the factors involved in the + + align:start position:0% +sum of the factors involved in the + + + align:start position:0% +sum of the factors involved in the +decomposition of n. + + align:start position:0% +decomposition of n. + + + align:start position:0% +decomposition of n. +I've indicated an additional factor here + + align:start position:0% +I've indicated an additional factor here + + + align:start position:0% +I've indicated an additional factor here +of minus new depending on how you choose + + align:start position:0% +of minus new depending on how you choose + + + align:start position:0% +of minus new depending on how you choose +to count multiplies and adds. This + + align:start position:0% +to count multiplies and adds. This + + + align:start position:0% +to count multiplies and adds. This +factor of minus new either shows up or + + align:start position:0% +factor of minus new either shows up or + + + align:start position:0% +factor of minus new either shows up or +not. In fact, to make this expression + + align:start position:0% +not. In fact, to make this expression + + + align:start position:0% +not. In fact, to make this expression +consistent with what we obtained for the + + align:start position:0% +consistent with what we obtained for the + + + align:start position:0% +consistent with what we obtained for the +power of two algorithms, the minus new + + align:start position:0% +power of two algorithms, the minus new + + + align:start position:0% +power of two algorithms, the minus new +should be in here. And it's simply a + + align:start position:0% +should be in here. And it's simply a + + + align:start position:0% +should be in here. And it's simply a +question of whether you count or don't + + align:start position:0% +question of whether you count or don't + + + align:start position:0% +question of whether you count or don't +count some multiplications by unity. + + align:start position:0% +count some multiplications by unity. + + + align:start position:0% +count some multiplications by unity. +Well, okay, that's a very quick + + align:start position:0% +Well, okay, that's a very quick + + + align:start position:0% +Well, okay, that's a very quick +treatment discussion of the + + align:start position:0% +treatment discussion of the + + + align:start position:0% +treatment discussion of the +generalization of the radix 2 algorithms + + align:start position:0% +generalization of the radix 2 algorithms + + + align:start position:0% +generalization of the radix 2 algorithms +to more arbitrary radics and uh there as + + align:start position:0% +to more arbitrary radics and uh there as + + + align:start position:0% +to more arbitrary radics and uh there as +I indicated are some examples of this + + align:start position:0% +I indicated are some examples of this + + + align:start position:0% +I indicated are some examples of this +which are given in the text although in + + align:start position:0% +which are given in the text although in + + + align:start position:0% +which are given in the text although in +fact what you'll find is that in most + + align:start position:0% +fact what you'll find is that in most + + + align:start position:0% +fact what you'll find is that in most +practical contexts it is a radex 2 + + align:start position:0% +practical contexts it is a radex 2 + + + align:start position:0% +practical contexts it is a radex 2 +algorithm that is the most efficient to + + align:start position:0% +algorithm that is the most efficient to + + + align:start position:0% +algorithm that is the most efficient to +use. And I indicate incidentally that if + + align:start position:0% +use. And I indicate incidentally that if + + + align:start position:0% +use. And I indicate incidentally that if +you are faced with the problem of + + align:start position:0% +you are faced with the problem of + + + align:start position:0% +you are faced with the problem of +transforming data + + align:start position:0% +transforming data + + + align:start position:0% +transforming data +which is of a length which is not a + + align:start position:0% +which is of a length which is not a + + + align:start position:0% +which is of a length which is not a +power of two, it of course can always be + + align:start position:0% +power of two, it of course can always be + + + align:start position:0% +power of two, it of course can always be +made to be of length power of two by + + align:start position:0% +made to be of length power of two by + + + align:start position:0% +made to be of length power of two by +simply augmenting the sequence with + + align:start position:0% +simply augmenting the sequence with + + + align:start position:0% +simply augmenting the sequence with +zeros. + + align:start position:0% +zeros. + + + align:start position:0% +zeros. +Well, this concludes then the discussion + + align:start position:0% +Well, this concludes then the discussion + + + align:start position:0% +Well, this concludes then the discussion +of the FFT algorithms, the computation + + align:start position:0% +of the FFT algorithms, the computation + + + align:start position:0% +of the FFT algorithms, the computation +of the discrete forier transform + + align:start position:0% +of the discrete forier transform + + + align:start position:0% +of the discrete forier transform +and there are I hope a number of issues + + align:start position:0% +and there are I hope a number of issues + + + align:start position:0% +and there are I hope a number of issues +which you will have an opportunity to + + align:start position:0% +which you will have an opportunity to + + + align:start position:0% +which you will have an opportunity to +dwell on some as you read through the + + align:start position:0% +dwell on some as you read through the + + + align:start position:0% +dwell on some as you read through the +text and as your attention will be drawn + + align:start position:0% +text and as your attention will be drawn + + + align:start position:0% +text and as your attention will be drawn +to in the study guide. Thank you. + + align:start position:0% + + + + align:start position:0% + +[Music] \ No newline at end of file diff --git a/ywK_miSFVew.txt b/ywK_miSFVew.txt new file mode 100644 index 0000000000000000000000000000000000000000..7e84f4e90b0f89b6a469ae644bbd84827bde3c40 --- /dev/null +++ b/ywK_miSFVew.txt @@ -0,0 +1,9491 @@ +align:start position:0% + +so this lecture the general topic + + align:start position:0% +so this lecture the general topic + + + align:start position:0% +so this lecture the general topic +is the singular value decomposition and + + align:start position:0% +is the singular value decomposition and + + + align:start position:0% +is the singular value decomposition and +every Matrix rectangular or not singular + + align:start position:0% +every Matrix rectangular or not singular + + + align:start position:0% +every Matrix rectangular or not singular +or not has this factorization so the + + align:start position:0% +or not has this factorization so the + + + align:start position:0% +or not has this factorization so the +fact that it works for every Matrix is + + align:start position:0% +fact that it works for every Matrix is + + + align:start position:0% +fact that it works for every Matrix is +uh quite uh makes it useful uh all + + align:start position:0% +uh quite uh makes it useful uh all + + + align:start position:0% +uh quite uh makes it useful uh all +around and this these factors there's an + + align:start position:0% +around and this these factors there's an + + + align:start position:0% +around and this these factors there's an +orthogonal Matrix there's an orthogonal + + align:start position:0% +orthogonal Matrix there's an orthogonal + + + align:start position:0% +orthogonal Matrix there's an orthogonal +Matrix in in between as a diagonal and + + align:start position:0% +Matrix in in between as a diagonal and + + + align:start position:0% +Matrix in in between as a diagonal and +rectangular Matrix so that this is + + align:start position:0% +rectangular Matrix so that this is + + + align:start position:0% +rectangular Matrix so that this is +rectangular and that's the same shape + + align:start position:0% +rectangular and that's the same shape + + + align:start position:0% +rectangular and that's the same shape +these are square orthogonal matrices + + align:start position:0% +these are square orthogonal matrices + + + align:start position:0% +these are square orthogonal matrices +they're the same thing we've called q + + align:start position:0% +they're the same thing we've called q + + + align:start position:0% +they're the same thing we've called q +but now we've got two of them so they + + align:start position:0% +but now we've got two of them so they + + + align:start position:0% +but now we've got two of them so they +get called u and v okay I I I want + + align:start position:0% +get called u and v okay I I I want + + + align:start position:0% +get called u and v okay I I I want +to that's the main theme of the lecture + + align:start position:0% +to that's the main theme of the lecture + + + align:start position:0% +to that's the main theme of the lecture +but there are a couple of things that + + align:start position:0% +but there are a couple of things that + + + align:start position:0% +but there are a couple of things that +are simpler and clearer that we could + + align:start position:0% +are simpler and clearer that we could + + + align:start position:0% +are simpler and clearer that we could +just first uh one is a little bit + + align:start position:0% + + + + align:start position:0% + +um uh coming from the last lecture so + + align:start position:0% +um uh coming from the last lecture so + + + align:start position:0% +um uh coming from the last lecture so +this is so this is this is a question + + align:start position:0% +this is so this is this is a question + + + align:start position:0% +this is so this is this is a question +suppose I have a suppose I have two + + align:start position:0% +suppose I have a suppose I have two + + + align:start position:0% +suppose I have a suppose I have two +matrices A and + + align:start position:0% +matrices A and + + + align:start position:0% +matrices A and +B and suppose that when I do this + + align:start position:0% +B and suppose that when I do this + + + align:start position:0% +B and suppose that when I do this +crucial operation of a transpose A and B + + align:start position:0% +crucial operation of a transpose A and B + + + align:start position:0% +crucial operation of a transpose A and B +transpose B I get the same + + align:start position:0% +transpose B I get the same + + + align:start position:0% +transpose B I get the same +Matrix I would like to know okay what + + align:start position:0% +Matrix I would like to know okay what + + + align:start position:0% +Matrix I would like to know okay what +does that tell me about A and + + align:start position:0% +does that tell me about A and + + + align:start position:0% +does that tell me about A and +B and I bet we can guess the answer we + + align:start position:0% +B and I bet we can guess the answer we + + + align:start position:0% +B and I bet we can guess the answer we +won't attempt to prove that it's always + + align:start position:0% +won't attempt to prove that it's always + + + align:start position:0% +won't attempt to prove that it's always +so but but tell me how a connection + + align:start position:0% +so but but tell me how a connection + + + align:start position:0% +so but but tell me how a connection +between A and B that would produce that + + align:start position:0% +between A and B that would produce that + + + align:start position:0% +between A and B that would produce that +result oh let's see same I + + align:start position:0% + + + + align:start position:0% + +well yeah we're going to have to + + align:start position:0% +well yeah we're going to have to + + + align:start position:0% +well yeah we're going to have to +know yeah if we if we + + align:start position:0% +know yeah if we if we + + + align:start position:0% +know yeah if we if we +knew It's Tricky It's Tricky if we only + + align:start position:0% +knew It's Tricky It's Tricky if we only + + + align:start position:0% +knew It's Tricky It's Tricky if we only +know Ian values we know a lot of stuff + + align:start position:0% +know Ian values we know a lot of stuff + + + align:start position:0% +know Ian values we know a lot of stuff +but not + + align:start position:0% +but not + + + align:start position:0% +but not +everything um + + align:start position:0% +everything um + + + align:start position:0% +everything um +suppose + + align:start position:0% +suppose + + + align:start position:0% +suppose +yeah any other thoughts any thoughts + + align:start position:0% +yeah any other thoughts any thoughts + + + align:start position:0% +yeah any other thoughts any thoughts +about + + align:start position:0% +about + + + align:start position:0% +about +when uh this might be the same as + + align:start position:0% +when uh this might be the same as + + + align:start position:0% +when uh this might be the same as +this well they could be negatives of + + align:start position:0% +this well they could be negatives of + + + align:start position:0% +this well they could be negatives of +each other okay now we want to could are + + align:start position:0% +each other okay now we want to could are + + + align:start position:0% +each other okay now we want to could are +there more cases as well here here's a + + align:start position:0% +there more cases as well here here's a + + + align:start position:0% +there more cases as well here here's a +case to think about + + align:start position:0% +case to think about + + + align:start position:0% +case to think about +suppose um suppose a is the identity + + align:start position:0% +suppose um suppose a is the identity + + + align:start position:0% +suppose um suppose a is the identity +Matrix then the left side will + + align:start position:0% +Matrix then the left side will + + + align:start position:0% +Matrix then the left side will +be I and what could the right hand side + + align:start position:0% +be I and what could the right hand side + + + align:start position:0% +be I and what could the right hand side +be any orthogonal Matrix so we're + + align:start position:0% +be any orthogonal Matrix so we're + + + align:start position:0% +be any orthogonal Matrix so we're +beginning to get a sense of hey there + + align:start position:0% +beginning to get a sense of hey there + + + align:start position:0% +beginning to get a sense of hey there +are a bunch of + + align:start position:0% +are a bunch of + + + align:start position:0% +are a bunch of +solutions but that was a special case of + + align:start position:0% +solutions but that was a special case of + + + align:start position:0% +solutions but that was a special case of +course when a was the + + align:start position:0% +course when a was the + + + align:start position:0% +course when a was the +identity then we we we could have any or + + align:start position:0% +identity then we we we could have any or + + + align:start position:0% +identity then we we we could have any or +ional Matrix as B so somehow why is that + + align:start position:0% +ional Matrix as B so somehow why is that + + + align:start position:0% +ional Matrix as B so somehow why is that +it's because when we do + + align:start position:0% +it's because when we do + + + align:start position:0% +it's because when we do +this B transpose B the the orthogonal + + align:start position:0% +this B transpose B the the orthogonal + + + align:start position:0% +this B transpose B the the orthogonal +orthogonal bit cancels itself and we + + align:start position:0% +orthogonal bit cancels itself and we + + + align:start position:0% +orthogonal bit cancels itself and we +lose it now now do you want to make a + + align:start position:0% +lose it now now do you want to make a + + + align:start position:0% +lose it now now do you want to make a +guess on the general case yeah if so the + + align:start position:0% +guess on the general case yeah if so the + + + align:start position:0% +guess on the general case yeah if so the +answer is + + align:start position:0% + + + + align:start position:0% + +then then + + align:start position:0% +then then + + + align:start position:0% +then then +somehow uh a is some orthogonal Matrix + + align:start position:0% +somehow uh a is some orthogonal Matrix + + + align:start position:0% +somehow uh a is some orthogonal Matrix +times B for some Q for some Q then for + + align:start position:0% +times B for some Q for some Q then for + + + align:start position:0% +times B for some Q for some Q then for +some + + align:start position:0% + + + + align:start position:0% + +Q do you see that that let's see first + + align:start position:0% +Q do you see that that let's see first + + + align:start position:0% +Q do you see that that let's see first +of all is that right did I get it right + + align:start position:0% +of all is that right did I get it right + + + align:start position:0% +of all is that right did I get it right +if this is I really mean it to be uh if + + align:start position:0% +if this is I really mean it to be uh if + + + align:start position:0% +if this is I really mean it to be uh if +and only if in math in math language + + align:start position:0% +and only if in math in math language + + + align:start position:0% +and only if in math in math language +that that equation like + + align:start position:0% +that that equation like + + + align:start position:0% +that that equation like +that is true if a and b are connected by + + align:start position:0% +that is true if a and b are connected by + + + align:start position:0% +that is true if a and b are connected by +an orthogonal Matrix Q and would it a + + align:start position:0% +an orthogonal Matrix Q and would it a + + + align:start position:0% +an orthogonal Matrix Q and would it a +transpose a then because then we will + + align:start position:0% +transpose a then because then we will + + + align:start position:0% +transpose a then because then we will +well this isn't the proof then a + + align:start position:0% +well this isn't the proof then a + + + align:start position:0% +well this isn't the proof then a +transpose a will + + align:start position:0% +transpose a will + + + align:start position:0% +transpose a will +be uh QB transpose so that's B transpose + + align:start position:0% +be uh QB transpose so that's B transpose + + + align:start position:0% +be uh QB transpose so that's B transpose +Q transpose times a is + + align:start position:0% + + + + align:start position:0% + +QB right a transpose is that a is that + + align:start position:0% +QB right a transpose is that a is that + + + align:start position:0% +QB right a transpose is that a is that +and then it it works right everybody + + align:start position:0% +and then it it works right everybody + + + align:start position:0% +and then it it works right everybody +sees Q transpose Q cancelling in the + + align:start position:0% +sees Q transpose Q cancelling in the + + + align:start position:0% +sees Q transpose Q cancelling in the +middle leaving B transpose B so that if + + align:start position:0% +middle leaving B transpose B so that if + + + align:start position:0% +middle leaving B transpose B so that if +I mean this is typical of a math + + align:start position:0% +I mean this is typical of a math + + + align:start position:0% +I mean this is typical of a math +question very very typical of theorems + + align:start position:0% +question very very typical of theorems + + + align:start position:0% +question very very typical of theorems +in mathematics that you have some + + align:start position:0% +in mathematics that you have some + + + align:start position:0% +in mathematics that you have some +question and here is one one way that + + align:start position:0% +question and here is one one way that + + + align:start position:0% +question and here is one one way that +could produce that and we just checked + + align:start position:0% +could produce that and we just checked + + + align:start position:0% +could produce that and we just checked +that it did but now what there's always + + align:start position:0% +that it did but now what there's always + + + align:start position:0% +that it did but now what there's always +the other part of the theorem that's the + + align:start position:0% +the other part of the theorem that's the + + + align:start position:0% +the other part of the theorem that's the +hard part is that is that if we've shown + + align:start position:0% +hard part is that is that if we've shown + + + align:start position:0% +hard part is that is that if we've shown +that if this is true then this is true + + align:start position:0% +that if this is true then this is true + + + align:start position:0% +that if this is true then this is true +because the Q cancels but now it's the + + align:start position:0% +because the Q cancels but now it's the + + + align:start position:0% +because the Q cancels but now it's the +other way if this is true how do you get + + align:start position:0% +other way if this is true how do you get + + + align:start position:0% +other way if this is true how do you get +down to this and actually the SVD is a + + align:start position:0% +down to this and actually the SVD is a + + + align:start position:0% +down to this and actually the SVD is a +is a key in in being able to do it but I + + align:start position:0% +is a key in in being able to do it but I + + + align:start position:0% +is a key in in being able to do it but I +thought you might just like that it's a + + align:start position:0% +thought you might just like that it's a + + + align:start position:0% +thought you might just like that it's a +paper I just uh saw in fact uh uh the + + align:start position:0% +paper I just uh saw in fact uh uh the + + + align:start position:0% +paper I just uh saw in fact uh uh the +title of the paper was something like + + align:start position:0% +title of the paper was something like + + + align:start position:0% +title of the paper was something like +when is a transpose a equal B transpose + + align:start position:0% +when is a transpose a equal B transpose + + + align:start position:0% +when is a transpose a equal B transpose +B and why do we want to know uh and uh + + align:start position:0% +B and why do we want to know uh and uh + + + align:start position:0% +B and why do we want to know uh and uh +so uh we've just + + align:start position:0% +so uh we've just + + + align:start position:0% +so uh we've just +answered the first part when and why do + + align:start position:0% +answered the first part when and why do + + + align:start position:0% +answered the first part when and why do +we want to know well it's uh it's all in + + align:start position:0% +we want to know well it's uh it's all in + + + align:start position:0% +we want to know well it's uh it's all in +this stuff of this afternoon's lecture + + align:start position:0% +this stuff of this afternoon's lecture + + + align:start position:0% +this stuff of this afternoon's lecture +I'll just mention where the paper is + + align:start position:0% +I'll just mention where the paper is + + + align:start position:0% +I'll just mention where the paper is +it's in the American math + + align:start position:0% +it's in the American math + + + align:start position:0% +it's in the American math +monthly I I don't know if that's in the + + align:start position:0% +monthly I I don't know if that's in the + + + align:start position:0% +monthly I I don't know if that's in the +lab's library or not uh 96 + + align:start position:0% + + + + align:start position:0% + +okay that's that's just for well not + + align:start position:0% +okay that's that's just for well not + + + align:start position:0% +okay that's that's just for well not +just for fun I was going to say just for + + align:start position:0% +just for fun I was going to say just for + + + align:start position:0% +just for fun I was going to say just for +fun but it's because it's actually uh + + align:start position:0% +fun but it's because it's actually uh + + + align:start position:0% +fun but it's because it's actually uh +significant okay now another topic + + align:start position:0% +significant okay now another topic + + + align:start position:0% +significant okay now another topic +change of topic but again it's one that + + align:start position:0% +change of topic but again it's one that + + + align:start position:0% +change of topic but again it's one that +I I'm going to get to Norms of matrices + + align:start position:0% +I I'm going to get to Norms of matrices + + + align:start position:0% +I I'm going to get to Norms of matrices +and condition numbers + + align:start position:0% +and condition numbers + + + align:start position:0% +and condition numbers +without starting on the SVD without + + align:start position:0% +without starting on the SVD without + + + align:start position:0% +without starting on the SVD without +getting those those all those factors in + + align:start position:0% +getting those those all those factors in + + + align:start position:0% +getting those those all those factors in +so we know how to measure we know one + + align:start position:0% +so we know how to measure we know one + + + align:start position:0% +so we know how to measure we know one +way to measure a good way to measure the + + align:start position:0% +way to measure a good way to measure the + + + align:start position:0% +way to measure a good way to measure the +length of a vector that's that's ukian + + align:start position:0% +length of a vector that's that's ukian + + + align:start position:0% +length of a vector that's that's ukian +length that we spoke about sum of the + + align:start position:0% +length that we spoke about sum of the + + + align:start position:0% +length that we spoke about sum of the +squares square root how do you measure + + align:start position:0% +squares square root how do you measure + + + align:start position:0% +squares square root how do you measure +the size of a + + align:start position:0% +the size of a + + + align:start position:0% +the size of a +matrix how shall I measure the size of a + + align:start position:0% +matrix how shall I measure the size of a + + + align:start position:0% +matrix how shall I measure the size of a +matrix because it's natural to want to + + align:start position:0% +matrix because it's natural to want to + + + align:start position:0% +matrix because it's natural to want to +do that to say this + + align:start position:0% +do that to say this + + + align:start position:0% +do that to say this +Matrix the word Norm is somehow used + + align:start position:0% +Matrix the word Norm is somehow used + + + align:start position:0% +Matrix the word Norm is somehow used +rather than length well I might I might + + align:start position:0% +rather than length well I might I might + + + align:start position:0% +rather than length well I might I might +say length of a Vector I usually do I + + align:start position:0% +say length of a Vector I usually do I + + + align:start position:0% +say length of a Vector I usually do I +could say Norm this is the same as + + align:start position:0% +could say Norm this is the same as + + + align:start position:0% +could say Norm this is the same as +length here somehow length isn't quite + + align:start position:0% +length here somehow length isn't quite + + + align:start position:0% +length here somehow length isn't quite +the right word but how should we measure + + align:start position:0% +the right word but how should we measure + + + align:start position:0% +the right word but how should we measure +the size of a matrix then we could know + + align:start position:0% +the size of a matrix then we could know + + + align:start position:0% +the size of a matrix then we could know +if it's getting small or getting large + + align:start position:0% +if it's getting small or getting large + + + align:start position:0% +if it's getting small or getting large +or what what it's doing uh how did there + + align:start position:0% +or what what it's doing uh how did there + + + align:start position:0% +or what what it's doing uh how did there +isn't any single answer to this yeah I + + align:start position:0% +isn't any single answer to this yeah I + + + align:start position:0% +isn't any single answer to this yeah I +mean if you for instance thought of it + + align:start position:0% +mean if you for instance thought of it + + + align:start position:0% +mean if you for instance thought of it +as a vector n s exactly that lot of + + align:start position:0% +as a vector n s exactly that lot of + + + align:start position:0% +as a vector n s exactly that lot of +information well but that's that's + + align:start position:0% +information well but that's that's + + + align:start position:0% +information well but that's that's +that's one way that's certainly done so + + align:start position:0% +that's one way that's certainly done so + + + align:start position:0% +that's one way that's certainly done so +so one way is uh uh is that way exactly + + align:start position:0% +so one way is uh uh is that way exactly + + + align:start position:0% +so one way is uh uh is that way exactly +think of the vector as n squ it's got n + + align:start position:0% +think of the vector as n squ it's got n + + + align:start position:0% +think of the vector as n squ it's got n +squ entries The Matrix sorry as having n + + align:start position:0% +squ entries The Matrix sorry as having n + + + align:start position:0% +squ entries The Matrix sorry as having n +squ + + align:start position:0% +squ + + + align:start position:0% +squ +entries and just take the sum of this so + + align:start position:0% +entries and just take the sum of this so + + + align:start position:0% +entries and just take the sum of this so +This is called the frobenius norm I'll + + align:start position:0% +This is called the frobenius norm I'll + + + align:start position:0% +This is called the frobenius norm I'll +put F there and and write his name out + + align:start position:0% +put F there and and write his name out + + + align:start position:0% +put F there and and write his name out +in full + + align:start position:0% +in full + + + align:start position:0% +in full +frobenius this is the the frobenius + + align:start position:0% +frobenius this is the the frobenius + + + align:start position:0% +frobenius this is the the frobenius +measure then is the I take the sum of + + align:start position:0% +measure then is the I take the sum of + + + align:start position:0% +measure then is the I take the sum of +all the AI J + + align:start position:0% +all the AI J + + + align:start position:0% +all the AI J +squares over I and over J in other words + + align:start position:0% +squares over I and over J in other words + + + align:start position:0% +squares over I and over J in other words +the sum of squares of all the entries + + align:start position:0% +the sum of squares of all the entries + + + align:start position:0% +the sum of squares of all the entries +and then take the square + + align:start position:0% + + + + align:start position:0% + +root that's a that's a perfectly + + align:start position:0% +root that's a that's a perfectly + + + align:start position:0% +root that's a that's a perfectly +reasonable way to measure that that sort + + align:start position:0% +reasonable way to measure that that sort + + + align:start position:0% +reasonable way to measure that that sort +of measures the size of the + + align:start position:0% +of measures the size of the + + + align:start position:0% +of measures the size of the +Matrix but as you're saying it it + + align:start position:0% +Matrix but as you're saying it it + + + align:start position:0% +Matrix but as you're saying it it +somehow loses some aspect of the + + align:start position:0% +somehow loses some aspect of the + + + align:start position:0% +somehow loses some aspect of the +Matrix uh because what a matrices do + + align:start position:0% +Matrix uh because what a matrices do + + + align:start position:0% +Matrix uh because what a matrices do +they + + align:start position:0% +they + + + align:start position:0% +they +multiply they multiply vectors to give + + align:start position:0% +multiply they multiply vectors to give + + + align:start position:0% +multiply they multiply vectors to give +other vectors they transform things and + + align:start position:0% +other vectors they transform things and + + + align:start position:0% +other vectors they transform things and +that's lost in this this is just like um + + align:start position:0% +that's lost in this this is just like um + + + align:start position:0% +that's lost in this this is just like um +a length but it's an important one now + + align:start position:0% +a length but it's an important one now + + + align:start position:0% +a length but it's an important one now +if I think about that other aspect of + + align:start position:0% +if I think about that other aspect of + + + align:start position:0% +if I think about that other aspect of +matrices of matrices as being things + + align:start position:0% +matrices of matrices as being things + + + align:start position:0% +matrices of matrices as being things +that Ma that multiply vectors to give + + align:start position:0% +that Ma that multiply vectors to give + + + align:start position:0% +that Ma that multiply vectors to give +other + + align:start position:0% +other + + + align:start position:0% +other +vectors then what would be another way + + align:start position:0% +vectors then what would be another way + + + align:start position:0% +vectors then what would be another way +so I'm looking now for a second + + align:start position:0% +so I'm looking now for a second + + + align:start position:0% +so I'm looking now for a second +possibility and this was a good + + align:start position:0% +possibility and this was a good + + + align:start position:0% +possibility and this was a good +one of length yeah well determinant now + + align:start position:0% +one of length yeah well determinant now + + + align:start position:0% +one of length yeah well determinant now +determinant + + align:start position:0% +determinant + + + align:start position:0% +determinant +is uh it's a natural to think of but + + align:start position:0% +is uh it's a natural to think of but + + + align:start position:0% +is uh it's a natural to think of but +it's not a very happy + + align:start position:0% +it's not a very happy + + + align:start position:0% +it's not a very happy +number + + align:start position:0% +number + + + align:start position:0% +number +um why + + align:start position:0% +um why + + + align:start position:0% +um why +not could be negative so we would take + + align:start position:0% +not could be negative so we would take + + + align:start position:0% +not could be negative so we would take +absolute value at the very least but it + + align:start position:0% +absolute value at the very least but it + + + align:start position:0% +absolute value at the very least but it +here here's the kind of property that we + + align:start position:0% +here here's the kind of property that we + + + align:start position:0% +here here's the kind of property that we +would love to have and that we don't + + align:start position:0% +would love to have and that we don't + + + align:start position:0% +would love to have and that we don't +have for example the length of a vector + + align:start position:0% +have for example the length of a vector + + + align:start position:0% +have for example the length of a vector +has this wonderful property that the + + align:start position:0% +has this wonderful property that the + + + align:start position:0% +has this wonderful property that the +length of x + y how is that related to + + align:start position:0% +length of x + y how is that related to + + + align:start position:0% +length of x + y how is that related to +the separate lengths of X and of + + align:start position:0% +the separate lengths of X and of + + + align:start position:0% +the separate lengths of X and of +Y there's a there's a less than or equal + + align:start position:0% +Y there's a there's a less than or equal + + + align:start position:0% +Y there's a there's a less than or equal +that and what's that do you know the + + align:start position:0% +that and what's that do you know the + + + align:start position:0% +that and what's that do you know the +name for that fact about length of + + align:start position:0% +name for that fact about length of + + + align:start position:0% +name for that fact about length of +vectors + + align:start position:0% +vectors + + + align:start position:0% +vectors +no it's CL it's I could get shortz from + + align:start position:0% +no it's CL it's I could get shortz from + + + align:start position:0% +no it's CL it's I could get shortz from +it but it it's the triangle inequality + + align:start position:0% +it but it it's the triangle inequality + + + align:start position:0% +it but it it's the triangle inequality +because all it's saying is that if I + + align:start position:0% +because all it's saying is that if I + + + align:start position:0% +because all it's saying is that if I +have a a triangle with a side of length + + align:start position:0% +have a a triangle with a side of length + + + align:start position:0% +have a a triangle with a side of length +x and another side of length y then the + + align:start position:0% +x and another side of length y then the + + + align:start position:0% +x and another side of length y then the +third + + align:start position:0% +third + + + align:start position:0% +third +side the length of the third side can't + + align:start position:0% +side the length of the third side can't + + + align:start position:0% +side the length of the third side can't +be longer than that plus + + align:start position:0% +be longer than that plus + + + align:start position:0% +be longer than that plus +that right here's the third side X+ y or + + align:start position:0% +that right here's the third side X+ y or + + + align:start position:0% +that right here's the third side X+ y or +x - y something y - x doesn't matter so + + align:start position:0% +x - y something y - x doesn't matter so + + + align:start position:0% +x - y something y - x doesn't matter so +so the the so this is really saying that + + align:start position:0% +so the the so this is really saying that + + + align:start position:0% +so the the so this is really saying that +the third side of a triangle can't be + + align:start position:0% +the third side of a triangle can't be + + + align:start position:0% +the third side of a triangle can't be +longer than the first two sides and of + + align:start position:0% +longer than the first two sides and of + + + align:start position:0% +longer than the first two sides and of +course when could it get when does it + + align:start position:0% +course when could it get when does it + + + align:start position:0% +course when could it get when does it +even get close well if x is is this way + + align:start position:0% +even get close well if x is is this way + + + align:start position:0% +even get close well if x is is this way +and Y is pretty darn near then X Plus Y + + align:start position:0% +and Y is pretty darn near then X Plus Y + + + align:start position:0% +and Y is pretty darn near then X Plus Y +is almost the sum of the lengths and we + + align:start position:0% +is almost the sum of the lengths and we + + + align:start position:0% +is almost the sum of the lengths and we +could only get equality when could we + + align:start position:0% +could only get equality when could we + + + align:start position:0% +could only get equality when could we +get equality in this well they'd have to + + align:start position:0% +get equality in this well they'd have to + + + align:start position:0% +get equality in this well they'd have to +be absolutely in the same direction + + align:start position:0% +be absolutely in the same direction + + + align:start position:0% +be absolutely in the same direction +right so we would like that to be true + + align:start position:0% +right so we would like that to be true + + + align:start position:0% +right so we would like that to be true +for our matri we would like to keep that + + align:start position:0% +for our matri we would like to keep that + + + align:start position:0% +for our matri we would like to keep that +property for our for our Matrix Norm we + + align:start position:0% +property for our for our Matrix Norm we + + + align:start position:0% +property for our for our Matrix Norm we +would like to know that if we add a + + align:start position:0% +would like to know that if we add a + + + align:start position:0% +would like to know that if we add a +couple of matrices so this is something + + align:start position:0% +couple of matrices so this is something + + + align:start position:0% +couple of matrices so this is something +we want we would not you + + align:start position:0% +we want we would not you + + + align:start position:0% +we want we would not you +know and that property would be true all + + align:start position:0% +know and that property would be true all + + + align:start position:0% +know and that property would be true all +right for this uh forus guy because why + + align:start position:0% +right for this uh forus guy because why + + + align:start position:0% +right for this uh forus guy because why +is + + align:start position:0% +is + + + align:start position:0% +is +that because it's it's it's just we're + + align:start position:0% +that because it's it's it's just we're + + + align:start position:0% +that because it's it's it's just we're +just taking this Matrix and stretching + + align:start position:0% +just taking this Matrix and stretching + + + align:start position:0% +just taking this Matrix and stretching +it to a long Vector so it's so for fenus + + align:start position:0% +it to a long Vector so it's so for fenus + + + align:start position:0% +it to a long Vector so it's so for fenus +it's the same as the triangle inequality + + align:start position:0% +it's the same as the triangle inequality + + + align:start position:0% +it's the same as the triangle inequality +for this n squar length Vector now + + align:start position:0% +for this n squar length Vector now + + + align:start position:0% +for this n squar length Vector now +Vector sorry can we look what a does we + + align:start position:0% +Vector sorry can we look what a does we + + + align:start position:0% +Vector sorry can we look what a does we +could look what a does to a vector I was + + align:start position:0% +could look what a does to a vector I was + + + align:start position:0% +could look what a does to a vector I was +going to say about + + align:start position:0% +going to say about + + + align:start position:0% +going to say about +determinants one just just before I I + + align:start position:0% +determinants one just just before I I + + + align:start position:0% +determinants one just just before I I +want to kill off + + align:start position:0% +want to kill off + + + align:start position:0% +want to kill off +determinants uh uh in the sense that the + + align:start position:0% +determinants uh uh in the sense that the + + + align:start position:0% +determinants uh uh in the sense that the +determinant of a plus b like + + align:start position:0% +determinant of a plus b like + + + align:start position:0% +determinant of a plus b like +we could be sort of almost anything yeah + + align:start position:0% +we could be sort of almost anything yeah + + + align:start position:0% +we could be sort of almost anything yeah +so okay so let me follow your thought + + align:start position:0% +so okay so let me follow your thought + + + align:start position:0% +so okay so let me follow your thought +and and now tell me more how do I look + + align:start position:0% +and and now tell me more how do I look + + + align:start position:0% +and and now tell me more how do I look +at what a does to a + + align:start position:0% +at what a does to a + + + align:start position:0% +at what a does to a +vector that's another Vector yeah I get + + align:start position:0% +vector that's another Vector yeah I get + + + align:start position:0% +vector that's another Vector yeah I get +another Vector has a which has a Norm + + align:start position:0% +another Vector has a which has a Norm + + + align:start position:0% +another Vector has a which has a Norm +that's right so we're going to create a + + align:start position:0% +that's right so we're going to create a + + + align:start position:0% +that's right so we're going to create a +norm of a matrix out of that decision on + + align:start position:0% +norm of a matrix out of that decision on + + + align:start position:0% +norm of a matrix out of that decision on +so how should we do it we take a vector + + align:start position:0% +so how should we do it we take a vector + + + align:start position:0% +so how should we do it we take a vector +X and we know its length and what do we + + align:start position:0% +X and we know its length and what do we + + + align:start position:0% +X and we know its length and what do we +do we we multiply by a and we know the + + align:start position:0% +do we we multiply by a and we know the + + + align:start position:0% +do we we multiply by a and we know the +length of this so I know the length of + + align:start position:0% +length of this so I know the length of + + + align:start position:0% +length of this so I know the length of +this and I know the length of the + + align:start position:0% +this and I know the length of the + + + align:start position:0% +this and I know the length of the +original X so what shall I do to come up + + align:start position:0% +original X so what shall I do to come up + + + align:start position:0% +original X so what shall I do to come up +with a size of a so to speak divide if I + + align:start position:0% +with a size of a so to speak divide if I + + + align:start position:0% +with a size of a so to speak divide if I +divide by this if I if I look at + + align:start position:0% +divide by this if I if I look at + + + align:start position:0% +divide by this if I if I look at +this let me so these are both vectors so + + align:start position:0% +this let me so these are both vectors so + + + align:start position:0% +this let me so these are both vectors so +we know what length of vectors are so so + + align:start position:0% +we know what length of vectors are so so + + + align:start position:0% +we know what length of vectors are so so +I take any Vector X + + align:start position:0% +I take any Vector X + + + align:start position:0% +I take any Vector X +I I multiply by a and I look to see okay + + align:start position:0% +I I multiply by a and I look to see okay + + + align:start position:0% +I I multiply by a and I look to see okay +did it + + align:start position:0% +did it + + + align:start position:0% +did it +grow and this ratio will be the growth + + align:start position:0% +grow and this ratio will be the growth + + + align:start position:0% +grow and this ratio will be the growth +ratio right right I I could normalize to + + align:start position:0% +ratio right right I I could normalize to + + + align:start position:0% +ratio right right I I could normalize to +say well I'll take unit vectors then I + + align:start position:0% +say well I'll take unit vectors then I + + + align:start position:0% +say well I'll take unit vectors then I +wouldn't have to divide by the one but + + align:start position:0% +wouldn't have to divide by the one but + + + align:start position:0% +wouldn't have to divide by the one but +either way doesn't doesn't matter often + + align:start position:0% +either way doesn't doesn't matter often + + + align:start position:0% +either way doesn't doesn't matter often +you see it one way often the other + + align:start position:0% +you see it one way often the other + + + align:start position:0% +you see it one way often the other +now okay but now what's up here better + + align:start position:0% +now okay but now what's up here better + + + align:start position:0% +now okay but now what's up here better +maximize I better maximize I'm looking + + align:start position:0% +maximize I better maximize I'm looking + + + align:start position:0% +maximize I better maximize I'm looking +for the worst X right cuz some vectors X + + align:start position:0% +for the worst X right cuz some vectors X + + + align:start position:0% +for the worst X right cuz some vectors X +might get might be in the null space + + align:start position:0% +might get might be in the null space + + + align:start position:0% +might get might be in the null space +they might go to zero but that doesn't + + align:start position:0% +they might go to zero but that doesn't + + + align:start position:0% +they might go to zero but that doesn't +mean the Matrix is the zero Matrix so a + + align:start position:0% +mean the Matrix is the zero Matrix so a + + + align:start position:0% +mean the Matrix is the zero Matrix so a +good Norm then + + align:start position:0% +good Norm then + + + align:start position:0% +good Norm then +is the + + align:start position:0% +is the + + + align:start position:0% +is the +max over + + align:start position:0% +max over + + + align:start position:0% +max over +all nonzero vectors X so the the max of + + align:start position:0% +all nonzero vectors X so the the max of + + + align:start position:0% +all nonzero vectors X so the the max of +this and as I say I could take the max I + + align:start position:0% +this and as I say I could take the max I + + + align:start position:0% +this and as I say I could take the max I +could take it over I could make the + + align:start position:0% +could take it over I could make the + + + align:start position:0% +could take it over I could make the +denominators one and then I would just + + align:start position:0% +denominators one and then I would just + + + align:start position:0% +denominators one and then I would just +be looking at the numerators so the + + align:start position:0% +be looking at the numerators so the + + + align:start position:0% +be looking at the numerators so the +question is how much can the Matrix blow + + align:start position:0% +question is how much can the Matrix blow + + + align:start position:0% +question is how much can the Matrix blow +up how much can it increase the size of + + align:start position:0% +up how much can it increase the size of + + + align:start position:0% +up how much can it increase the size of +a vector that's that's a good measure of + + align:start position:0% +a vector that's that's a good measure of + + + align:start position:0% +a vector that's that's a good measure of +the norm now does well okay I guess we + + align:start position:0% +the norm now does well okay I guess we + + + align:start position:0% +the norm now does well okay I guess we +ought to check this property but it it's + + align:start position:0% +ought to check this property but it it's + + + align:start position:0% +ought to check this property but it it's +it's easy this property will come right + + align:start position:0% +it's easy this property will come right + + + align:start position:0% +it's easy this property will come right +out of the vector + + align:start position:0% +out of the vector + + + align:start position:0% +out of the vector +property and actually another property + + align:start position:0% +property and actually another property + + + align:start position:0% +property and actually another property +will come out for the Matrix Norm that + + align:start position:0% +will come out for the Matrix Norm that + + + align:start position:0% +will come out for the Matrix Norm that +the norm of a * B is is less than the + + align:start position:0% +the norm of a * B is is less than the + + + align:start position:0% +the norm of a * B is is less than the +norm of a times the norm of + + align:start position:0% +norm of a times the norm of + + + align:start position:0% +norm of a times the norm of +B I can sort of say it in words why + + align:start position:0% +B I can sort of say it in words why + + + align:start position:0% +B I can sort of say it in words why +that'll be true + + align:start position:0% +that'll be true + + + align:start position:0% +that'll be true +because what's the norm of + + align:start position:0% +because what's the norm of + + + align:start position:0% +because what's the norm of +ab by by my by my idea here I take + + align:start position:0% +ab by by my by my idea here I take + + + align:start position:0% +ab by by my by my idea here I take +vectors X I see how much they're blown + + align:start position:0% +vectors X I see how much they're blown + + + align:start position:0% +vectors X I see how much they're blown +up by + + align:start position:0% +up by + + + align:start position:0% +up by +AB okay well first of all I could look + + align:start position:0% +AB okay well first of all I could look + + + align:start position:0% +AB okay well first of all I could look +at that in two steps I could say okay I + + align:start position:0% +at that in two steps I could say okay I + + + align:start position:0% +at that in two steps I could say okay I +take that Vector X how much is it blown + + align:start position:0% +take that Vector X how much is it blown + + + align:start position:0% +take that Vector X how much is it blown +up by B + + align:start position:0% +up by B + + + align:start position:0% +up by B +and then how much is BX blown up by the + + align:start position:0% +and then how much is BX blown up by the + + + align:start position:0% +and then how much is BX blown up by the +a right and well why so why don't I have + + align:start position:0% +a right and well why so why don't I have + + + align:start position:0% +a right and well why so why don't I have +just equality there you get two shots I + + align:start position:0% +just equality there you get two shots I + + + align:start position:0% +just equality there you get two shots I +get two shots yeah I get two shots on + + align:start position:0% +get two shots yeah I get two shots on + + + align:start position:0% +get two shots yeah I get two shots on +the right the the worst X the x that + + align:start position:0% +the right the the worst X the x that + + + align:start position:0% +the right the the worst X the x that +gets blown up the most by B might + + align:start position:0% +gets blown up the most by B might + + + align:start position:0% +gets blown up the most by B might +not produce a BX that that a was was + + align:start position:0% +not produce a BX that that a was was + + + align:start position:0% +not produce a BX that that a was was +strong on so so uh yeah so uh in other + + align:start position:0% +strong on so so uh yeah so uh in other + + + align:start position:0% +strong on so so uh yeah so uh in other +words it this just comes from here's the + + align:start position:0% +words it this just comes from here's the + + + align:start position:0% +words it this just comes from here's the +proof + + align:start position:0% +proof + + + align:start position:0% +proof +that the length of + + align:start position:0% +that the length of + + + align:start position:0% +that the length of +ABX is less than or equal well a can't + + align:start position:0% +ABX is less than or equal well a can't + + + align:start position:0% +ABX is less than or equal well a can't +blow + + align:start position:0% +blow + + + align:start position:0% +blow +BX that's how much a can blow it up by + + align:start position:0% +BX that's how much a can blow it up by + + + align:start position:0% +BX that's how much a can blow it up by +and now I'm down to here and that's I'll + + align:start position:0% +and now I'm down to here and that's I'll + + + align:start position:0% +and now I'm down to here and that's I'll +just repeat the A and + + align:start position:0% +just repeat the A and + + + align:start position:0% +just repeat the A and +BX can't B can't blow X up by more than + + align:start position:0% +BX can't B can't blow X up by more than + + + align:start position:0% +BX can't B can't blow X up by more than +its + + align:start position:0% + + + + align:start position:0% + +Norm so now I've learned that this that + + align:start position:0% +Norm so now I've learned that this that + + + align:start position:0% +Norm so now I've learned that this that +this ABX can't blow up more than that + + align:start position:0% +this ABX can't blow up more than that + + + align:start position:0% +this ABX can't blow up more than that +okay so that's this is a a very s this + + align:start position:0% +okay so that's this is a a very s this + + + align:start position:0% +okay so that's this is a a very s this +is like called the the sometimes called + + align:start position:0% +is like called the the sometimes called + + + align:start position:0% +is like called the the sometimes called +the operator Norm because I'm thinking + + align:start position:0% +the operator Norm because I'm thinking + + + align:start position:0% +the operator Norm because I'm thinking +of a as an operator as acting whereas + + align:start position:0% +of a as an operator as acting whereas + + + align:start position:0% +of a as an operator as acting whereas +this is more the array Norm + + align:start position:0% +this is more the array Norm + + + align:start position:0% +this is more the array Norm +fenus off but it's got uses uh just like + + align:start position:0% +fenus off but it's got uses uh just like + + + align:start position:0% +fenus off but it's got uses uh just like +so so those are two important Norms I I + + align:start position:0% +so so those are two important Norms I I + + + align:start position:0% +so so those are two important Norms I I +I guess I should admit that we could + + align:start position:0% +I guess I should admit that we could + + + align:start position:0% +I guess I should admit that we could +measure the length of vectors other ways + + align:start position:0% +measure the length of vectors other ways + + + align:start position:0% +measure the length of vectors other ways +and if we did this would give us another + + align:start position:0% +and if we did this would give us another + + + align:start position:0% +and if we did this would give us another +measurement of a how else could I + + align:start position:0% +measurement of a how else could I + + + align:start position:0% +measurement of a how else could I +measure the norm of a of a vector X the + + align:start position:0% +measure the norm of a of a vector X the + + + align:start position:0% +measure the norm of a of a vector X the +length of a vector X just just let's I + + align:start position:0% +length of a vector X just just let's I + + + align:start position:0% +length of a vector X just just let's I +won't even write it down but let's just + + align:start position:0% +won't even write it down but let's just + + + align:start position:0% +won't even write it down but let's just +think of other ways that we could + + align:start position:0% +think of other ways that we could + + + align:start position:0% +think of other ways that we could +measure the size of a + + align:start position:0% + + + + align:start position:0% + +vector yeah some of absolute values yeah + + align:start position:0% +vector yeah some of absolute values yeah + + + align:start position:0% +vector yeah some of absolute values yeah +right just just I I need to take + + align:start position:0% +right just just I I need to take + + + align:start position:0% +right just just I I need to take +absolute values because I don't want any + + align:start position:0% +absolute values because I don't want any + + + align:start position:0% +absolute values because I don't want any +any Norms to go negative that's absolute + + align:start position:0% +any Norms to go negative that's absolute + + + align:start position:0% +any Norms to go negative that's absolute +rule never let them go negative so I + + align:start position:0% +rule never let them go negative so I + + + align:start position:0% +rule never let them go negative so I +could take the sum of absolute values + + align:start position:0% +could take the sum of absolute values + + + align:start position:0% +could take the sum of absolute values +but here I'm taking the sum of absolute + + align:start position:0% +but here I'm taking the sum of absolute + + + align:start position:0% +but here I'm taking the sum of absolute +values squared and square rooting oh I + + align:start position:0% +values squared and square rooting oh I + + + align:start position:0% +values squared and square rooting oh I +could take the largest absolute value + + align:start position:0% +could take the largest absolute value + + + align:start position:0% +could take the largest absolute value +just just look for the component that's + + align:start position:0% +just just look for the component that's + + + align:start position:0% +just just look for the component that's +the biggest those are all and then + + align:start position:0% +the biggest those are all and then + + + align:start position:0% +the biggest those are all and then +there's in between piece Powers but this + + align:start position:0% +there's in between piece Powers but this + + + align:start position:0% +there's in between piece Powers but this +this one is the this is like the two + + align:start position:0% +this one is the this is like the two + + + align:start position:0% +this one is the this is like the two +Norm because I'm taking squares and it's + + align:start position:0% +Norm because I'm taking squares and it's + + + align:start position:0% +Norm because I'm taking squares and it's +it's uh uh very uh + + align:start position:0% +it's uh uh very uh + + + align:start position:0% +it's uh uh very uh +convenient it gives you a nice geometry + + align:start position:0% +convenient it gives you a nice geometry + + + align:start position:0% +convenient it gives you a nice geometry +because it's just the geometry of + + align:start position:0% +because it's just the geometry of + + + align:start position:0% +because it's just the geometry of +ordinary space I mean it's the length of + + align:start position:0% +ordinary space I mean it's the length of + + + align:start position:0% +ordinary space I mean it's the length of +a vector is what when I draw it it's you + + align:start position:0% +a vector is what when I draw it it's you + + + align:start position:0% +a vector is what when I draw it it's you +know it's what you it's about four + + align:start position:0% +know it's what you it's about four + + + align:start position:0% +know it's what you it's about four +inches right okay so so there's lengths + + align:start position:0% +inches right okay so so there's lengths + + + align:start position:0% +inches right okay so so there's lengths +now we have an idea of the size of a + + align:start position:0% +now we have an idea of the size of a + + + align:start position:0% +now we have an idea of the size of a +matrix okay where did I go with + + align:start position:0% +matrix okay where did I go with + + + align:start position:0% +matrix okay where did I go with +that well this question of condition in + + align:start position:0% +that well this question of condition in + + + align:start position:0% +that well this question of condition in +is what I wanted to follow up on okay so + + align:start position:0% +is what I wanted to follow up on okay so + + + align:start position:0% +is what I wanted to follow up on okay so +now now let's + + align:start position:0% +now now let's + + + align:start position:0% +now now let's +introduce these are basic ideas what's + + align:start position:0% +introduce these are basic ideas what's + + + align:start position:0% +introduce these are basic ideas what's +the norm of a + + align:start position:0% +the norm of a + + + align:start position:0% +the norm of a +matrix and it's oh but I better before + + align:start position:0% +matrix and it's oh but I better before + + + align:start position:0% +matrix and it's oh but I better before +we get to condition + + align:start position:0% +we get to condition + + + align:start position:0% +we get to condition +number uh how would I find that number + + align:start position:0% +number uh how would I find that number + + + align:start position:0% +number uh how would I find that number +what's the worst X huh that's not uh + + align:start position:0% +what's the worst X huh that's not uh + + + align:start position:0% +what's the worst X huh that's not uh +maybe so we got to think about that a + + align:start position:0% +maybe so we got to think about that a + + + align:start position:0% +maybe so we got to think about that a +minute but it's this is ideal linear + + align:start position:0% +minute but it's this is ideal linear + + + align:start position:0% +minute but it's this is ideal linear +algebra to think + + align:start position:0% +algebra to think + + + align:start position:0% +algebra to think +about + + align:start position:0% +about + + + align:start position:0% +about +what right you left me with a + + align:start position:0% +what right you left me with a + + + align:start position:0% +what right you left me with a +maximization but now you got to tell me + + align:start position:0% +maximization but now you got to tell me + + + align:start position:0% +maximization but now you got to tell me +how to do it uh um what x if I have a + + align:start position:0% +how to do it uh um what x if I have a + + + align:start position:0% +how to do it uh um what x if I have a +matrix a suppose I know it's igen values + + align:start position:0% +matrix a suppose I know it's igen values + + + align:start position:0% +matrix a suppose I know it's igen values +and Ian + + align:start position:0% +and Ian + + + align:start position:0% +and Ian +vectors what could you tell me about the + + align:start position:0% + + + + align:start position:0% + +norm suppose see I'm going to I'm I have + + align:start position:0% +norm suppose see I'm going to I'm I have + + + align:start position:0% +norm suppose see I'm going to I'm I have +to look at vectors X so I'm looking for + + align:start position:0% +to look at vectors X so I'm looking for + + + align:start position:0% +to look at vectors X so I'm looking for +which vectors are up a + + align:start position:0% +which vectors are up a + + + align:start position:0% +which vectors are up a +lot well one that's certainly a + + align:start position:0% +lot well one that's certainly a + + + align:start position:0% +lot well one that's certainly a +candidate + + align:start position:0% + + + + align:start position:0% + +is right that top igen Vector that that + + align:start position:0% +is right that top igen Vector that that + + + align:start position:0% +is right that top igen Vector that that +that the one with the biggest igen value + + align:start position:0% +that the one with the biggest igen value + + + align:start position:0% +that the one with the biggest igen value +is certainly a + + align:start position:0% +is certainly a + + + align:start position:0% +is certainly a +candidate because it's blown up by how + + align:start position:0% +candidate because it's blown up by how + + + align:start position:0% +candidate because it's blown up by how +much by that factor + + align:start position:0% +much by that factor + + + align:start position:0% +much by that factor +Lambda so the norm is certainly as big + + align:start position:0% +Lambda so the norm is certainly as big + + + align:start position:0% +Lambda so the norm is certainly as big +as as Lambda Max so let me just put put + + align:start position:0% +as as Lambda Max so let me just put put + + + align:start position:0% +as as Lambda Max so let me just put put +this conclusion down the norm of a is at + + align:start position:0% + + + + align:start position:0% + +least lamb the the the the size of the + + align:start position:0% +least lamb the the the the size of the + + + align:start position:0% +least lamb the the the the size of the +biggest I value because because + + align:start position:0% +biggest I value because because + + + align:start position:0% +biggest I value because because +everybody sees that we'll get this if we + + align:start position:0% +everybody sees that we'll get this if we + + + align:start position:0% +everybody sees that we'll get this if we +take X to be its igen Vector now the + + align:start position:0% +take X to be its igen Vector now the + + + align:start position:0% +take X to be its igen Vector now the +question is could there be some vectors + + align:start position:0% +question is could there be some vectors + + + align:start position:0% +question is could there be some vectors +that like aren't igen vectors that still + + align:start position:0% +that like aren't igen vectors that still + + + align:start position:0% +that like aren't igen vectors that still +get blown up even more + + align:start position:0% + + + + align:start position:0% + +let me take an example to show that that + + align:start position:0% +let me take an example to show that that + + + align:start position:0% +let me take an example to show that that +could happen so suppose I take the + + align:start position:0% +could happen so suppose I take the + + + align:start position:0% +could happen so suppose I take the +Matrix 1 1 Z and + + align:start position:0% + + + + align:start position:0% + +10 what are the I values of that Matrix + + align:start position:0% +10 what are the I values of that Matrix + + + align:start position:0% +10 what are the I values of that Matrix +one and + + align:start position:0% +one and + + + align:start position:0% +one and +one because it's it's it's triangular so + + align:start position:0% +one because it's it's it's triangular so + + + align:start position:0% +one because it's it's it's triangular so +the igon values are one and one it's + + align:start position:0% +the igon values are one and one it's + + + align:start position:0% +the igon values are one and one it's +repeated but that Matrix there's some + + align:start position:0% +repeated but that Matrix there's some + + + align:start position:0% +repeated but that Matrix there's some +Vector that's going to blow up by more + + align:start position:0% +Vector that's going to blow up by more + + + align:start position:0% +Vector that's going to blow up by more +than one with that Matrix + + align:start position:0% +than one with that Matrix + + + align:start position:0% +than one with that Matrix +right what is uh so tell me a vector + + align:start position:0% +right what is uh so tell me a vector + + + align:start position:0% +right what is uh so tell me a vector +that'll blow up quite a bit 01 01 If I + + align:start position:0% +that'll blow up quite a bit 01 01 If I + + + align:start position:0% +that'll blow up quite a bit 01 01 If I +multiply if if I say okay take that unit + + align:start position:0% +multiply if if I say okay take that unit + + + align:start position:0% +multiply if if I say okay take that unit +vector and look at ax it gives me what + + align:start position:0% +vector and look at ax it gives me what + + + align:start position:0% +vector and look at ax it gives me what +does that multiplication give me + + align:start position:0% + + + + align:start position:0% + +101 so what have I learned out of that + + align:start position:0% +101 so what have I learned out of that + + + align:start position:0% +101 so what have I learned out of that +little calculation about the norm of + + align:start position:0% +little calculation about the norm of + + + align:start position:0% +little calculation about the norm of +this Matrix here's a unit V Vector it + + align:start position:0% +this Matrix here's a unit V Vector it + + + align:start position:0% +this Matrix here's a unit V Vector it +got thrown into this so what have I + + align:start position:0% +got thrown into this so what have I + + + align:start position:0% +got thrown into this so what have I +learned about the nor in this case the + + align:start position:0% +learned about the nor in this case the + + + align:start position:0% +learned about the nor in this case the +norm of a for this example is at + + align:start position:0% +norm of a for this example is at + + + align:start position:0% +norm of a for this example is at +least is at least 10 actually we could + + align:start position:0% +least is at least 10 actually we could + + + align:start position:0% +least is at least 10 actually we could +push it even a little higher than 10 + + align:start position:0% +push it even a little higher than 10 + + + align:start position:0% +push it even a little higher than 10 +square Ro T 101 if we wanted really + + align:start position:0% +square Ro T 101 if we wanted really + + + align:start position:0% +square Ro T 101 if we wanted really +because we've got we've got a vector + + align:start position:0% +because we've got we've got a vector + + + align:start position:0% +because we've got we've got a vector +that that big see that's our ax here and + + align:start position:0% +that that big see that's our ax here and + + + align:start position:0% +that that big see that's our ax here and +we put in a unit Vector now I don't know + + align:start position:0% +we put in a unit Vector now I don't know + + + align:start position:0% +we put in a unit Vector now I don't know +if that's the worst Vector but we at + + align:start position:0% +if that's the worst Vector but we at + + + align:start position:0% +if that's the worst Vector but we at +least we've got at least square root of + + align:start position:0% +least we've got at least square root of + + + align:start position:0% +least we've got at least square root of +101 so what are we what are we seeing + + align:start position:0% +101 so what are we what are we seeing + + + align:start position:0% +101 so what are we what are we seeing +here we're seeing that if the Matrix is + + align:start position:0% +here we're seeing that if the Matrix is + + + align:start position:0% +here we're seeing that if the Matrix is +kind of + + align:start position:0% +kind of + + + align:start position:0% +kind of +unsymmetric as this one strongly is then + + align:start position:0% +unsymmetric as this one strongly is then + + + align:start position:0% +unsymmetric as this one strongly is then +the igen values and igen vectors don't + + align:start position:0% +the igen values and igen vectors don't + + + align:start position:0% +the igen values and igen vectors don't +give the whole story and actually maybe + + align:start position:0% +give the whole story and actually maybe + + + align:start position:0% +give the whole story and actually maybe +that's a very + + align:start position:0% +that's a very + + + align:start position:0% +that's a very +important thing to uh learn in general + + align:start position:0% +important thing to uh learn in general + + + align:start position:0% +important thing to uh learn in general +that if a matrix the more unsymmetric + + align:start position:0% +that if a matrix the more unsymmetric + + + align:start position:0% +that if a matrix the more unsymmetric +nonnormal the Matrix + + align:start position:0% +nonnormal the Matrix + + + align:start position:0% +nonnormal the Matrix +is the less the igen vectors and igen + + align:start position:0% +is the less the igen vectors and igen + + + align:start position:0% +is the less the igen vectors and igen +values are are a total picture of what + + align:start position:0% +values are are a total picture of what + + + align:start position:0% +values are are a total picture of what +it's doing because because the IG well + + align:start position:0% +it's doing because because the IG well + + + align:start position:0% +it's doing because because the IG well +actually that only has one I Vector but + + align:start position:0% +actually that only has one I Vector but + + + align:start position:0% +actually that only has one I Vector but +I could give it an I could change this + + align:start position:0% +I could give it an I could change this + + + align:start position:0% +I could give it an I could change this +to one point change this to one point + + align:start position:0% +to one point change this to one point + + + align:start position:0% +to one point change this to one point +one or something and then the igen + + align:start position:0% +one or something and then the igen + + + align:start position:0% +one or something and then the igen +values would be one and 1.1 but there's + + align:start position:0% +values would be one and 1.1 but there's + + + align:start position:0% +values would be one and 1.1 but there's +a vector that's getting blown up by a + + align:start position:0% +a vector that's getting blown up by a + + + align:start position:0% +a vector that's getting blown up by a +lot more yeah so the I vectors of + + align:start position:0% +lot more yeah so the I vectors of + + + align:start position:0% +lot more yeah so the I vectors of +unsymmetric matrices are for for + + align:start position:0% +unsymmetric matrices are for for + + + align:start position:0% +unsymmetric matrices are for for +symmetric so here what do I want + + align:start position:0% +symmetric so here what do I want + + + align:start position:0% +symmetric so here what do I want +to let me continue here suppose a let me + + align:start position:0% +to let me continue here suppose a let me + + + align:start position:0% +to let me continue here suppose a let me +take two important cases case one when a + + align:start position:0% +take two important cases case one when a + + + align:start position:0% +take two important cases case one when a +is an orthogonal Matrix a is + + align:start position:0% +is an orthogonal Matrix a is + + + align:start position:0% +is an orthogonal Matrix a is +Q what's its Norm + + align:start position:0% + + + + align:start position:0% + +one one everybody agree with that the + + align:start position:0% +one one everybody agree with that the + + + align:start position:0% +one one everybody agree with that the +norm is one because if a is a q QX has + + align:start position:0% +norm is one because if a is a q QX has + + + align:start position:0% +norm is one because if a is a q QX has +the same length as x no change of + + align:start position:0% +the same length as x no change of + + + align:start position:0% +the same length as x no change of +length + + align:start position:0% +length + + + align:start position:0% +length +so fine the norm is one second important + + align:start position:0% +so fine the norm is one second important + + + align:start position:0% +so fine the norm is one second important +case if is if a is if a is + + align:start position:0% + + + + align:start position:0% + +symmetric now for let me say what the + + align:start position:0% +symmetric now for let me say what the + + + align:start position:0% +symmetric now for let me say what the +deal is here for a symmetric Matrix the + + align:start position:0% +deal is here for a symmetric Matrix the + + + align:start position:0% +deal is here for a symmetric Matrix the +igen values and vectors do give a + + align:start position:0% +igen values and vectors do give a + + + align:start position:0% +igen values and vectors do give a +reliable thing the norm is the + + align:start position:0% +reliable thing the norm is the + + + align:start position:0% +reliable thing the norm is the +largest igen + + align:start position:0% +largest igen + + + align:start position:0% +largest igen +value but now any + + align:start position:0% + + + + align:start position:0% + +a we still wondering what's the norm if + + align:start position:0% +a we still wondering what's the norm if + + + align:start position:0% +a we still wondering what's the norm if +I take any Matrix a and like this one + + align:start position:0% +I take any Matrix a and like this one + + + align:start position:0% +I take any Matrix a and like this one +let me let me put let me make that a one + + align:start position:0% +let me let me put let me make that a one + + + align:start position:0% +let me let me put let me make that a one +again to make it + + align:start position:0% +again to make it + + + align:start position:0% +again to make it +nice what may what Vector is being I + + align:start position:0% +nice what may what Vector is being I + + + align:start position:0% +nice what may what Vector is being I +don't know if I can figure the norm of + + align:start position:0% +don't know if I can figure the norm of + + + align:start position:0% +don't know if I can figure the norm of +this but uh it's a little more I think + + align:start position:0% +this but uh it's a little more I think + + + align:start position:0% +this but uh it's a little more I think +than Square < TK of + + align:start position:0% +than Square < TK of + + + align:start position:0% +than Square < TK of +101 I + + align:start position:0% +101 I + + + align:start position:0% +101 I +think I'm pretty sure it's a little more + + align:start position:0% +think I'm pretty sure it's a little more + + + align:start position:0% +think I'm pretty sure it's a little more +than square of 101 but it's we're it's + + align:start position:0% +than square of 101 but it's we're it's + + + align:start position:0% +than square of 101 but it's we're it's +darn close because we you certainly + + align:start position:0% +darn close because we you certainly + + + align:start position:0% +darn close because we you certainly +picked off right away the the the vector + + align:start position:0% +picked off right away the the the vector + + + align:start position:0% +picked off right away the the the vector +X that was getting blown up quite + + align:start position:0% +X that was getting blown up quite + + + align:start position:0% +X that was getting blown up quite +seriously um H how to how to do this + + align:start position:0% +seriously um H how to how to do this + + + align:start position:0% +seriously um H how to how to do this +yeah see can I can I tackle this idea + + align:start position:0% +yeah see can I can I tackle this idea + + + align:start position:0% +yeah see can I can I tackle this idea +for Nea how H how so it's the so again + + align:start position:0% +for Nea how H how so it's the so again + + + align:start position:0% +for Nea how H how so it's the so again +then the igen vectors are not giving us + + align:start position:0% +then the igen vectors are not giving us + + + align:start position:0% +then the igen vectors are not giving us +the full + + align:start position:0% +the full + + + align:start position:0% +the full +story now let me tackle this + + align:start position:0% + + + + align:start position:0% + +thing um can I Square it you don't mind + + align:start position:0% +thing um can I Square it you don't mind + + + align:start position:0% +thing um can I Square it you don't mind +if I Square stuff Norm squared just + + align:start position:0% +if I Square stuff Norm squared just + + + align:start position:0% +if I Square stuff Norm squared just +because it's easier to have things squ + + align:start position:0% +because it's easier to have things squ + + + align:start position:0% +because it's easier to have things squ +okay so + + align:start position:0% +okay so + + + align:start position:0% +okay so +now now let me say what is what is the + + align:start position:0% +now now let me say what is what is the + + + align:start position:0% +now now let me say what is what is the +norm squar of + + align:start position:0% +norm squar of + + + align:start position:0% +norm squar of +ax this isn't going to be long but + + align:start position:0% +ax this isn't going to be long but + + + align:start position:0% +ax this isn't going to be long but +you'll see it what's the norm square + + align:start position:0% +you'll see it what's the norm square + + + align:start position:0% +you'll see it what's the norm square +root of a + + align:start position:0% +root of a + + + align:start position:0% +root of a +ax it's the inner product of ax with + + align:start position:0% +ax it's the inner product of ax with + + + align:start position:0% +ax it's the inner product of ax with +itself and of course when I see that + + align:start position:0% +itself and of course when I see that + + + align:start position:0% +itself and of course when I see that +what am I going to do I'm going + + align:start position:0% +what am I going to do I'm going + + + align:start position:0% +what am I going to do I'm going +to break it out into X transpose a + + align:start position:0% +to break it out into X transpose a + + + align:start position:0% +to break it out into X transpose a +transpose a x x no problem right I'm I'm + + align:start position:0% +transpose a x x no problem right I'm I'm + + + align:start position:0% +transpose a x x no problem right I'm I'm +just doing manipulation I'm still asking + + align:start position:0% +just doing manipulation I'm still asking + + + align:start position:0% +just doing manipulation I'm still asking +the question what makes this + + align:start position:0% + + + + align:start position:0% + +big and maybe you can guess the answer + + align:start position:0% +big and maybe you can guess the answer + + + align:start position:0% +big and maybe you can guess the answer +now that I've written it this + + align:start position:0% +now that I've written it this + + + align:start position:0% +now that I've written it this +way what Vector X is the guiltiest the + + align:start position:0% +way what Vector X is the guiltiest the + + + align:start position:0% +way what Vector X is the guiltiest the +the one that gets blown up the most in + + align:start position:0% +the one that gets blown up the most in + + + align:start position:0% +the one that gets blown up the most in +this uh in in this in this thing you + + align:start position:0% +this uh in in this in this thing you + + + align:start position:0% +this uh in in this in this thing you +could you could take a shot at it anyway + + align:start position:0% +could you could take a shot at it anyway + + + align:start position:0% +could you could take a shot at it anyway +it's going to be ion Vector of of a + + align:start position:0% +it's going to be ion Vector of of a + + + align:start position:0% +it's going to be ion Vector of of a +transpose a good old a transpose a has + + align:start position:0% +transpose a good old a transpose a has + + + align:start position:0% +transpose a good old a transpose a has +shown up again it's the igon vector it's + + align:start position:0% +shown up again it's the igon vector it's + + + align:start position:0% +shown up again it's the igon vector it's +the top I Vector of a transpose + + align:start position:0% +the top I Vector of a transpose + + + align:start position:0% +the top I Vector of a transpose +a so let's call its top I Vector um and + + align:start position:0% +a so let's call its top I Vector um and + + + align:start position:0% +a so let's call its top I Vector um and +that's positive definite so we know it's + + align:start position:0% +that's positive definite so we know it's + + + align:start position:0% +that's positive definite so we know it's +positive the top I so I'm going to call + + align:start position:0% +positive the top I so I'm going to call + + + align:start position:0% +positive the top I so I'm going to call +the top ion value the top I value I'm of + + align:start position:0% +the top ion value the top I value I'm of + + + align:start position:0% +the top ion value the top I value I'm of +this thing I'm going to call is + + align:start position:0% +this thing I'm going to call is + + + align:start position:0% +this thing I'm going to call is +I'm going I can't I've used Lambda for + + align:start position:0% +I'm going I can't I've used Lambda for + + + align:start position:0% +I'm going I can't I've used Lambda for +the igen values of a but now the igen + + align:start position:0% +the igen values of a but now the igen + + + align:start position:0% +the igen values of a but now the igen +values of a transpose a those are + + align:start position:0% +values of a transpose a those are + + + align:start position:0% +values of a transpose a those are +different numbers normally normally + + align:start position:0% +different numbers normally normally + + + align:start position:0% +different numbers normally normally +different numbers and I need a different + + align:start position:0% +different numbers and I need a different + + + align:start position:0% +different numbers and I need a different +letter and it's + + align:start position:0% +letter and it's + + + align:start position:0% +letter and it's +Sigma and and actually Sigma so Sigma + + align:start position:0% +Sigma and and actually Sigma so Sigma + + + align:start position:0% +Sigma and and actually Sigma so Sigma +Max and I'm you're going to use Sigma + + align:start position:0% +Max and I'm you're going to use Sigma + + + align:start position:0% +Max and I'm you're going to use Sigma +for the square roots of the igen values + + align:start position:0% +for the square roots of the igen values + + + align:start position:0% +for the square roots of the igen values +of a transpose a so that so that Sigma + + align:start position:0% +of a transpose a so that so that Sigma + + + align:start position:0% +of a transpose a so that so that Sigma +and Lambda are comparable so so + + align:start position:0% +and Lambda are comparable so so + + + align:start position:0% +and Lambda are comparable so so +the largest the top I value of a + + align:start position:0% +the largest the top I value of a + + + align:start position:0% +the largest the top I value of a +transpose a I'm going to call is + + align:start position:0% +transpose a I'm going to call is + + + align:start position:0% +transpose a I'm going to call is +called or written Sigma Max squared + + align:start position:0% + + + + align:start position:0% + +okay and + + align:start position:0% +okay and + + + align:start position:0% +okay and +that's for any a the norm + + align:start position:0% +that's for any a the norm + + + align:start position:0% +that's for any a the norm +is this guy Sigma Max + + align:start position:0% + + + + align:start position:0% + +can I can I + + align:start position:0% +can I can I + + + align:start position:0% +can I can I +uh reduce it + + align:start position:0% +uh reduce it + + + align:start position:0% +uh reduce it +to can I just see that this that this is + + align:start position:0% +to can I just see that this that this is + + + align:start position:0% +to can I just see that this that this is +that this result is consistent with + + align:start position:0% +that this result is consistent with + + + align:start position:0% +that this result is consistent with +these suppose a is symmetric suppose a + + align:start position:0% +these suppose a is symmetric suppose a + + + align:start position:0% +these suppose a is symmetric suppose a +is a symmetric Matrix then this + + align:start position:0% +is a symmetric Matrix then this + + + align:start position:0% +is a symmetric Matrix then this +reasoning is still correct but what is a + + align:start position:0% +reasoning is still correct but what is a + + + align:start position:0% +reasoning is still correct but what is a +transpose a if a is a symmetric + + align:start position:0% +transpose a if a is a symmetric + + + align:start position:0% +transpose a if a is a symmetric +matrix it's just a squ right if a + + align:start position:0% +matrix it's just a squ right if a + + + align:start position:0% +matrix it's just a squ right if a +transposes the same is a then all I did + + align:start position:0% +transposes the same is a then all I did + + + align:start position:0% +transposes the same is a then all I did +was square a and what are the igen + + align:start position:0% +was square a and what are the igen + + + align:start position:0% +was square a and what are the igen +values of a + + align:start position:0% +values of a + + + align:start position:0% +values of a +squ they're the Lambda + + align:start position:0% +squ they're the Lambda + + + align:start position:0% +squ they're the Lambda +squares so then I took the largest + + align:start position:0% +squares so then I took the largest + + + align:start position:0% +squares so then I took the largest +Lambda squar and then I took its square + + align:start position:0% +Lambda squar and then I took its square + + + align:start position:0% +Lambda squar and then I took its square +root and I got the largest + + align:start position:0% +root and I got the largest + + + align:start position:0% +root and I got the largest +Lambda so in the symmetric case this the + + align:start position:0% +Lambda so in the symmetric case this the + + + align:start position:0% +Lambda so in the symmetric case this the +sigmas are the Lambda squares the sigma + + align:start position:0% +sigmas are the Lambda squares the sigma + + + align:start position:0% +sigmas are the Lambda squares the sigma +sorry the sigas are the the sigma + + align:start position:0% +sorry the sigas are the the sigma + + + align:start position:0% +sorry the sigas are the the sigma +squares are the Lambda squares and and + + align:start position:0% +squares are the Lambda squares and and + + + align:start position:0% +squares are the Lambda squares and and +and uh that's right and of course if a + + align:start position:0% +and uh that's right and of course if a + + + align:start position:0% +and uh that's right and of course if a +is orthogonal then then what have I what + + align:start position:0% +is orthogonal then then what have I what + + + align:start position:0% +is orthogonal then then what have I what +I learn here well I'm just back to my + + align:start position:0% +I learn here well I'm just back to my + + + align:start position:0% +I learn here well I'm just back to my +old argument if a is a Q then this is + + align:start position:0% +old argument if a is a Q then this is + + + align:start position:0% +old argument if a is a Q then this is +the identity and I'm just getting the + + align:start position:0% +the identity and I'm just getting the + + + align:start position:0% +the identity and I'm just getting the +largest I value as + + align:start position:0% +largest I value as + + + align:start position:0% +largest I value as +one yeah + + align:start position:0% + + + + align:start position:0% + +sure no no that's why I had + + align:start position:0% +sure no no that's why I had + + + align:start position:0% +sure no no that's why I had +to Sigma Max only agrees with the sigmas + + align:start position:0% +to Sigma Max only agrees with the sigmas + + + align:start position:0% +to Sigma Max only agrees with the sigmas +I'll take to be Pi this guy + + align:start position:0% +I'll take to be Pi this guy + + + align:start position:0% +I'll take to be Pi this guy +is you remember him or her uh is always + + align:start position:0% +is you remember him or her uh is always + + + align:start position:0% +is you remember him or her uh is always +or it that's the one that's positive + + align:start position:0% +or it that's the one that's positive + + + align:start position:0% +or it that's the one that's positive +definite so its igen values are truly + + align:start position:0% +definite so its igen values are truly + + + align:start position:0% +definite so its igen values are truly +positive and then I'll take the positive + + align:start position:0% +positive and then I'll take the positive + + + align:start position:0% +positive and then I'll take the positive +square root and call it Sigma so you + + align:start position:0% +square root and call it Sigma so you + + + align:start position:0% +square root and call it Sigma so you +your your point is right on that that uh + + align:start position:0% +your your point is right on that that uh + + + align:start position:0% +your your point is right on that that uh +this is + + align:start position:0% +this is + + + align:start position:0% +this is +the I need that absolute value for + + align:start position:0% +the I need that absolute value for + + + align:start position:0% +the I need that absolute value for +exactly the reason you say + + align:start position:0% +exactly the reason you say + + + align:start position:0% +exactly the reason you say +right let me write down a few matrices + + align:start position:0% +right let me write down a few matrices + + + align:start position:0% +right let me write down a few matrices +and you tell me their Norm what's the + + align:start position:0% +and you tell me their Norm what's the + + + align:start position:0% +and you tell me their Norm what's the +norm of this Matrix Min -3 + + align:start position:0% + + + + align:start position:0% + +01 three answer is three and what what + + align:start position:0% +01 three answer is three and what what + + + align:start position:0% +01 three answer is three and what what +Vector does it blow up by + + align:start position:0% +Vector does it blow up by + + + align:start position:0% +Vector does it blow up by +three it multip If I multiply one Zer I + + align:start position:0% +three it multip If I multiply one Zer I + + + align:start position:0% +three it multip If I multiply one Zer I +get minus three 0 and it's three times + + align:start position:0% +get minus three 0 and it's three times + + + align:start position:0% +get minus three 0 and it's three times +as big three times as long the fact that + + align:start position:0% +as big three times as long the fact that + + + align:start position:0% +as big three times as long the fact that +it's negative isn't doesn't change its + + align:start position:0% +it's negative isn't doesn't change its + + + align:start position:0% +it's negative isn't doesn't change its +length oh I gu yes while we were here + + align:start position:0% +length oh I gu yes while we were here + + + align:start position:0% +length oh I gu yes while we were here +well so you see my formula would say if + + align:start position:0% +well so you see my formula would say if + + + align:start position:0% +well so you see my formula would say if +I really wanted to find the worst guy + + align:start position:0% +I really wanted to find the worst guy + + + align:start position:0% +I really wanted to find the worst guy +for this one I should compute a + + align:start position:0% +for this one I should compute a + + + align:start position:0% +for this one I should compute a +transpose a would you want me to do + + align:start position:0% +transpose a would you want me to do + + + align:start position:0% +transpose a would you want me to do +that uh probably not uh I could compute + + align:start position:0% +that uh probably not uh I could compute + + + align:start position:0% +that uh probably not uh I could compute +a transpose a is some little 2 by two + + align:start position:0% +a transpose a is some little 2 by two + + + align:start position:0% +a transpose a is some little 2 by two +symmetric positive definite Matrix yeah + + align:start position:0% +symmetric positive definite Matrix yeah + + + align:start position:0% +symmetric positive definite Matrix yeah +well heck we could do that one a + + align:start position:0% +well heck we could do that one a + + + align:start position:0% +well heck we could do that one a +transpose a what will it have I have to + + align:start position:0% +transpose a what will it have I have to + + + align:start position:0% +transpose a what will it have I have to +multiply on the left by one 10 down here + + align:start position:0% +multiply on the left by one 10 down here + + + align:start position:0% +multiply on the left by one 10 down here +is that right so the top row is still + + align:start position:0% +is that right so the top row is still + + + align:start position:0% +is that right so the top row is still +110 and I know it's going to be + + align:start position:0% +110 and I know it's going to be + + + align:start position:0% +110 and I know it's going to be +symmetric + + align:start position:0% +symmetric + + + align:start position:0% +symmetric +and what do I have here 101 + + align:start position:0% +and what do I have here 101 + + + align:start position:0% +and what do I have here 101 +maybe + + align:start position:0% +maybe + + + align:start position:0% +maybe +huh so a transpose a so what am I saying + + align:start position:0% +huh so a transpose a so what am I saying + + + align:start position:0% +huh so a transpose a so what am I saying +for the norm of this guy of which I'm + + align:start position:0% +for the norm of this guy of which I'm + + + align:start position:0% +for the norm of this guy of which I'm +sort of regretting I ever wrote on the + + align:start position:0% +sort of regretting I ever wrote on the + + + align:start position:0% +sort of regretting I ever wrote on the +board uh the norm of that Matrix is what + + align:start position:0% +board uh the norm of that Matrix is what + + + align:start position:0% +board uh the norm of that Matrix is what +what's our rule now to find the to find + + align:start position:0% +what's our rule now to find the to find + + + align:start position:0% +what's our rule now to find the to find +the worst X and the and the blowup size + + align:start position:0% +the worst X and the and the blowup size + + + align:start position:0% +the worst X and the and the blowup size +is look at a transpose a and find its + + align:start position:0% +is look at a transpose a and find its + + + align:start position:0% +is look at a transpose a and find its +igen values and igen vectors and it'll + + align:start position:0% +igen values and igen vectors and it'll + + + align:start position:0% +igen values and igen vectors and it'll +have an igen Vector around + + align:start position:0% +have an igen Vector around + + + align:start position:0% +have an igen Vector around +101 I and I can value around 101 but it + + align:start position:0% +101 I and I can value around 101 but it + + + align:start position:0% +101 I and I can value around 101 but it +won't be exactly 101 be slightly more + + align:start position:0% +won't be exactly 101 be slightly more + + + align:start position:0% +won't be exactly 101 be slightly more +you see this Matrix is slightly bigger + + align:start position:0% +you see this Matrix is slightly bigger + + + align:start position:0% +you see this Matrix is slightly bigger +than 101 because these little pieces + + align:start position:0% +than 101 because these little pieces + + + align:start position:0% +than 101 because these little pieces +will will bump it up a little + + align:start position:0% +will will bump it up a little + + + align:start position:0% +will will bump it up a little +so that's why the the IG value the + + align:start position:0% +so that's why the the IG value the + + + align:start position:0% +so that's why the the IG value the +largest igen value of that one is a + + align:start position:0% +largest igen value of that one is a + + + align:start position:0% +largest igen value of that one is a +little bigger than + + align:start position:0% +little bigger than + + + align:start position:0% +little bigger than +101 for Sigma squared and then when we + + align:start position:0% +101 for Sigma squared and then when we + + + align:start position:0% +101 for Sigma squared and then when we +take the square root we have something a + + align:start position:0% +take the square root we have something a + + + align:start position:0% +take the square root we have something a +little bigger than that okay so you + + align:start position:0% +little bigger than that okay so you + + + align:start position:0% +little bigger than that okay so you +don't want to + + align:start position:0% +don't want to + + + align:start position:0% +don't want to +compute the norm exactly I mean that's + + align:start position:0% +compute the norm exactly I mean that's + + + align:start position:0% +compute the norm exactly I mean that's +hard work you have to form a transpose a + + align:start position:0% +hard work you have to form a transpose a + + + align:start position:0% +hard work you have to form a transpose a +find its igen values but we have a nice + + align:start position:0% +find its igen values but we have a nice + + + align:start position:0% +find its igen values but we have a nice +understanding now of how big a matrix is + + align:start position:0% +understanding now of how big a matrix is + + + align:start position:0% +understanding now of how big a matrix is +how big a matrix is and and and you see + + align:start position:0% +how big a matrix is and and and you see + + + align:start position:0% +how big a matrix is and and and you see +how a transpose a came into it okay now + + align:start position:0% +how a transpose a came into it okay now + + + align:start position:0% +how a transpose a came into it okay now +I'm ready for condition number now we + + align:start position:0% +I'm ready for condition number now we + + + align:start position:0% +I'm ready for condition number now we +got + + align:start position:0% +got + + + align:start position:0% +got +Norm ready for condition number okay so + + align:start position:0% +Norm ready for condition number okay so + + + align:start position:0% +Norm ready for condition number okay so +these were good properties of the Norms + + align:start position:0% +these were good properties of the Norms + + + align:start position:0% +these were good properties of the Norms +this is our this is our uh test case + + align:start position:0% +this is our this is our uh test case + + + align:start position:0% +this is our this is our uh test case +which I now get to erase never have to + + align:start position:0% +which I now get to erase never have to + + + align:start position:0% +which I now get to erase never have to +think of + + align:start position:0% + + + + align:start position:0% + +again okay okay so what what's condition + + align:start position:0% +again okay okay so what what's condition + + + align:start position:0% +again okay okay so what what's condition +number + + align:start position:0% + + + + align:start position:0% + +about condition number I'm thinking + + align:start position:0% +about condition number I'm thinking + + + align:start position:0% +about condition number I'm thinking +we're solving a nice n byn + + align:start position:0% + + + + align:start position:0% + +system but I'm thinking we + + align:start position:0% +system but I'm thinking we + + + align:start position:0% +system but I'm thinking we +might not know B exactly I I want to + + align:start position:0% +might not know B exactly I I want to + + + align:start position:0% +might not know B exactly I I want to +know like how nearly singular is a if I + + align:start position:0% +know like how nearly singular is a if I + + + align:start position:0% +know like how nearly singular is a if I +want to know how how hard is that + + align:start position:0% +want to know how how hard is that + + + align:start position:0% +want to know how how hard is that +problem to Sol solve I I if you know if + + align:start position:0% +problem to Sol solve I I if you know if + + + align:start position:0% +problem to Sol solve I I if you know if +I'm using a 16 + + align:start position:0% +I'm using a 16 + + + align:start position:0% +I'm using a 16 +digits in in the + + align:start position:0% + + + + align:start position:0% + +calculations what kind of accuracy can I + + align:start position:0% +calculations what kind of accuracy can I + + + align:start position:0% +calculations what kind of accuracy can I +expect in the + + align:start position:0% +expect in the + + + align:start position:0% +expect in the +answer that's that would be that's the + + align:start position:0% +answer that's that would be that's the + + + align:start position:0% +answer that's that would be that's the +underlying question it's it's it's a + + align:start position:0% +underlying question it's it's it's a + + + align:start position:0% +underlying question it's it's it's a +natural question what kind of accuracy + + align:start position:0% +natural question what kind of accuracy + + + align:start position:0% +natural question what kind of accuracy +how much uh how much does uh does + + align:start position:0% +how much uh how much does uh does + + + align:start position:0% +how much uh how much does uh does +elimination see if I do yeah just think + + align:start position:0% +elimination see if I do yeah just think + + + align:start position:0% +elimination see if I do yeah just think +about it + + align:start position:0% +about it + + + align:start position:0% +about it +if I do + + align:start position:0% +if I do + + + align:start position:0% +if I do +elimination I I'm you know I'm Computing + + align:start position:0% +elimination I I'm you know I'm Computing + + + align:start position:0% +elimination I I'm you know I'm Computing +these multipliers these ratios I'm doing + + align:start position:0% +these multipliers these ratios I'm doing + + + align:start position:0% +these multipliers these ratios I'm doing +all these + + align:start position:0% +all these + + + align:start position:0% +all these +operations and then if I'm only keeping + + align:start position:0% +operations and then if I'm only keeping + + + align:start position:0% +operations and then if I'm only keeping +16 digits I'm rounding them + + align:start position:0% +16 digits I'm rounding them + + + align:start position:0% +16 digits I'm rounding them +off so if I have a matrix of order 100 + + align:start position:0% +off so if I have a matrix of order 100 + + + align:start position:0% +off so if I have a matrix of order 100 +then you know I'm doing like some + + align:start position:0% +then you know I'm doing like some + + + align:start position:0% +then you know I'm doing like some +fraction of a million + + align:start position:0% +fraction of a million + + + align:start position:0% +fraction of a million +operations I'm rounding all those off is + + align:start position:0% +operations I'm rounding all those off is + + + align:start position:0% +operations I'm rounding all those off is +my answer + + align:start position:0% +my answer + + + align:start position:0% +my answer +junk and that was a very serious + + align:start position:0% +junk and that was a very serious + + + align:start position:0% +junk and that was a very serious +question when it first became possible + + align:start position:0% +question when it first became possible + + + align:start position:0% +question when it first became possible +to do a million + + align:start position:0% +to do a million + + + align:start position:0% +to do a million +operations + + align:start position:0% +operations + + + align:start position:0% +operations +if if it's junk I mean we're we're lost + + align:start position:0% +if if it's junk I mean we're we're lost + + + align:start position:0% +if if it's junk I mean we're we're lost +right uh and the question is how to + + align:start position:0% +right uh and the question is how to + + + align:start position:0% +right uh and the question is how to +understand how big could the error be + + align:start position:0% +understand how big could the error be + + + align:start position:0% +understand how big could the error be +there if if you're solving not quite the + + align:start position:0% +there if if you're solving not quite the + + + align:start position:0% +there if if you're solving not quite the +right problem and that's probably the + + align:start position:0% +right problem and that's probably the + + + align:start position:0% +right problem and that's probably the +right way to look at it is that you you + + align:start position:0% +right way to look at it is that you you + + + align:start position:0% +right way to look at it is that you you +want to solve + + align:start position:0% +want to solve + + + align:start position:0% +want to solve +ax equal B and you actually + + align:start position:0% +ax equal B and you actually + + + align:start position:0% +ax equal B and you actually +solve + + align:start position:0% +solve + + + align:start position:0% +solve +some some let's let's say you actually + + align:start position:0% +some some let's let's say you actually + + + align:start position:0% +some some let's let's say you actually +solve a you you you maybe you mess up + + align:start position:0% +solve a you you you maybe you mess up + + + align:start position:0% +solve a you you you maybe you mess up +effectively you you change the problem + + align:start position:0% +effectively you you change the problem + + + align:start position:0% +effectively you you change the problem +to a B plus Delta + + align:start position:0% +to a B plus Delta + + + align:start position:0% +to a B plus Delta +B and so you actually find an X Plus + + align:start position:0% +B and so you actually find an X Plus + + + align:start position:0% +B and so you actually find an X Plus +Delta X you get the wrong answer I mean + + align:start position:0% +Delta X you get the wrong answer I mean + + + align:start position:0% +Delta X you get the wrong answer I mean +this is your error because this is your + + align:start position:0% +this is your error because this is your + + + align:start position:0% +this is your error because this is your +error in the input so do you see what + + align:start position:0% +error in the input so do you see what + + + align:start position:0% +error in the input so do you see what +I'm saying here that that there just a + + align:start position:0% +I'm saying here that that there just a + + + align:start position:0% +I'm saying here that that there just a +zillion problems of this sort this is + + align:start position:0% +zillion problems of this sort this is + + + align:start position:0% +zillion problems of this sort this is +the ideal system so X is the ideal + + align:start position:0% +the ideal system so X is the ideal + + + align:start position:0% +the ideal system so X is the ideal +answer but the real system you're + + align:start position:0% +answer but the real system you're + + + align:start position:0% +answer but the real system you're +solving only uh a close a nearby system + + align:start position:0% +solving only uh a close a nearby system + + + align:start position:0% +solving only uh a close a nearby system +and then you get a nearby answer and my + + align:start position:0% +and then you get a nearby answer and my + + + align:start position:0% +and then you get a nearby answer and my +question is how big could that error be + + align:start position:0% +question is how big could that error be + + + align:start position:0% +question is how big could that error be +I'd like to get a bound on Delta x a + + align:start position:0% +I'd like to get a bound on Delta x a + + + align:start position:0% +I'd like to get a bound on Delta x a +bound on we want we want a bound we want + + align:start position:0% +bound on we want we want a bound we want + + + align:start position:0% +bound on we want we want a bound we want +Delta + + align:start position:0% +Delta + + + align:start position:0% +Delta +X less than something oops Delta + + align:start position:0% + + + + align:start position:0% + +X less than something that will sort of + + align:start position:0% +X less than something that will sort of + + + align:start position:0% +X less than something that will sort of +tell us how hard the problem is to + + align:start position:0% + + + + align:start position:0% + +solve right now couple of points to + + align:start position:0% +solve right now couple of points to + + + align:start position:0% +solve right now couple of points to +make you could + + align:start position:0% +make you could + + + align:start position:0% +make you could +say well we might also not know a very + + align:start position:0% +say well we might also not know a very + + + align:start position:0% +say well we might also not know a very +well somebody's made that comment after + + align:start position:0% +well somebody's made that comment after + + + align:start position:0% +well somebody's made that comment after +an earlier lecture we might there ought + + align:start position:0% +an earlier lecture we might there ought + + + align:start position:0% +an earlier lecture we might there ought +to we ought to maybe take into into + + align:start position:0% +to we ought to maybe take into into + + + align:start position:0% +to we ought to maybe take into into +account a Delta a and the answer is true + + align:start position:0% +account a Delta a and the answer is true + + + align:start position:0% +account a Delta a and the answer is true +so so I could do what I'm doing now also + + align:start position:0% +so so I could do what I'm doing now also + + + align:start position:0% +so so I could do what I'm doing now also +allowing a Delta a and that's absolutely + + align:start position:0% +allowing a Delta a and that's absolutely + + + align:start position:0% +allowing a Delta a and that's absolutely +belongs there because when we do these + + align:start position:0% +belongs there because when we do these + + + align:start position:0% +belongs there because when we do these +elimination steps we're we're making + + align:start position:0% +elimination steps we're we're making + + + align:start position:0% +elimination steps we're we're making +little mistakes in + + align:start position:0% +little mistakes in + + + align:start position:0% +little mistakes in +a and on the right hand side we're + + align:start position:0% +a and on the right hand side we're + + + align:start position:0% +a and on the right hand side we're +making little mistakes in B let me make + + align:start position:0% +making little mistakes in B let me make + + + align:start position:0% +making little mistakes in B let me make +my life easy just think about the right + + align:start position:0% +my life easy just think about the right + + + align:start position:0% +my life easy just think about the right +hand side but the left would be fine too + + align:start position:0% +hand side but the left would be fine too + + + align:start position:0% +hand side but the left would be fine too +so that's one point second point + + align:start position:0% +so that's one point second point + + + align:start position:0% +so that's one point second point +is really relative error is the right + + align:start position:0% +is really relative error is the right + + + align:start position:0% +is really relative error is the right +thing that that if I'm just estimating + + align:start position:0% +thing that that if I'm just estimating + + + align:start position:0% +thing that that if I'm just estimating +this that really what I would like to + + align:start position:0% +this that really what I would like to + + + align:start position:0% +this that really what I would like to +know is the size of Delta X compared to + + align:start position:0% +know is the size of Delta X compared to + + + align:start position:0% +know is the size of Delta X compared to +the size of + + align:start position:0% +the size of + + + align:start position:0% +the size of +X because I could change if I just + + align:start position:0% +X because I could change if I just + + + align:start position:0% +X because I could change if I just +wanted Delta X to be small or large I + + align:start position:0% +wanted Delta X to be small or large I + + + align:start position:0% +wanted Delta X to be small or large I +could multiply B by a zillion that would + + align:start position:0% +could multiply B by a zillion that would + + + align:start position:0% +could multiply B by a zillion that would +multiply X by a zillion and then uh it + + align:start position:0% +multiply X by a zillion and then uh it + + + align:start position:0% +multiply X by a zillion and then uh it +would + + align:start position:0% +would + + + align:start position:0% +would +totally make nonsense out of my error + + align:start position:0% +totally make nonsense out of my error + + + align:start position:0% +totally make nonsense out of my error +estimate but if + + align:start position:0% +estimate but if + + + align:start position:0% +estimate but if +I look at the relative error then + + align:start position:0% +I look at the relative error then + + + align:start position:0% +I look at the relative error then +multiplying B by a million won't change + + align:start position:0% +multiplying B by a million won't change + + + align:start position:0% +multiplying B by a million won't change +the relative error so I would like this + + align:start position:0% +the relative error so I would like this + + + align:start position:0% +the relative error so I would like this +to be less than so and again on the + + align:start position:0% +to be less than so and again on the + + + align:start position:0% +to be less than so and again on the +right hand side so so this is less than + + align:start position:0% +right hand side so so this is less than + + + align:start position:0% +right hand side so so this is less than +some some multiple and that's the + + align:start position:0% +some some multiple and that's the + + + align:start position:0% +some some multiple and that's the +question of the error in + + align:start position:0% +question of the error in + + + align:start position:0% +question of the error in +B the relative error in + + align:start position:0% + + + + align:start position:0% + +B is that I'm sorry that that's written + + align:start position:0% +B is that I'm sorry that that's written + + + align:start position:0% +B is that I'm sorry that that's written +so low down because that's the that's + + align:start position:0% +so low down because that's the that's + + + align:start position:0% +so low down because that's the that's +the question + + align:start position:0% +the question + + + align:start position:0% +the question +what's what's the constant how large + + align:start position:0% +what's what's the constant how large + + + align:start position:0% +what's what's the constant how large +could the relative error in X be if I + + align:start position:0% +could the relative error in X be if I + + + align:start position:0% +could the relative error in X be if I +know something about the relative error + + align:start position:0% +know something about the relative error + + + align:start position:0% +know something about the relative error +in B because this is like what I control + + align:start position:0% +in B because this is like what I control + + + align:start position:0% +in B because this is like what I control +by by keeping more + + align:start position:0% +by by keeping more + + + align:start position:0% +by by keeping more +digits and this + + align:start position:0% +digits and this + + + align:start position:0% +digits and this +is what comes out so we're assuming that + + align:start position:0% +is what comes out so we're assuming that + + + align:start position:0% +is what comes out so we're assuming that +that in the process solving it there + + align:start position:0% +that in the process solving it there + + + align:start position:0% +that in the process solving it there +were no errors made just it there's an + + align:start position:0% +were no errors made just it there's an + + + align:start position:0% +were no errors made just it there's an +error no we can if we made errors in the + + align:start position:0% +error no we can if we made errors in the + + + align:start position:0% +error no we can if we made errors in the +process of solving it we can say okay + + align:start position:0% +process of solving it we can say okay + + + align:start position:0% +process of solving it we can say okay +that's that's part of Delta + + align:start position:0% +that's that's part of Delta + + + align:start position:0% +that's that's part of Delta +B so so we're we're assuming that we + + align:start position:0% +B so so we're we're assuming that we + + + align:start position:0% +B so so we're we're assuming that we +solved this guy exactly but it was the + + align:start position:0% +solved this guy exactly but it was the + + + align:start position:0% +solved this guy exactly but it was the +wrong problem so so uh um so I I want to + + align:start position:0% +wrong problem so so uh um so I I want to + + + align:start position:0% +wrong problem so so uh um so I I want to +know if I solve the wrong problem + + align:start position:0% +know if I solve the wrong problem + + + align:start position:0% +know if I solve the wrong problem +right how different is that relatively + + align:start position:0% +right how different is that relatively + + + align:start position:0% +right how different is that relatively +speaking from solving the right problem + + align:start position:0% +speaking from solving the right problem + + + align:start position:0% +speaking from solving the right problem +right okay and you see that somehow our + + align:start position:0% +right okay and you see that somehow our + + + align:start position:0% +right okay and you see that somehow our +little bus business of norms ought to + + align:start position:0% +little bus business of norms ought to + + + align:start position:0% +little bus business of norms ought to +help because what do we know about Norms + + align:start position:0% +help because what do we know about Norms + + + align:start position:0% +help because what do we know about Norms +here and and uh so on let's let's see if + + align:start position:0% +here and and uh so on let's let's see if + + + align:start position:0% +here and and uh so on let's let's see if +we can get + + align:start position:0% +we can get + + + align:start position:0% +we can get +some you see this is this tells me how + + align:start position:0% +some you see this is this tells me how + + + align:start position:0% +some you see this is this tells me how +hard the problem is to + + align:start position:0% +hard the problem is to + + + align:start position:0% +hard the problem is to +solve that's the size of that that so + + align:start position:0% +solve that's the size of that that so + + + align:start position:0% +solve that's the size of that that so +that's going to be the condition + + align:start position:0% +that's going to be the condition + + + align:start position:0% +that's going to be the condition +number and I want to know what is it in + + align:start position:0% +number and I want to know what is it in + + + align:start position:0% +number and I want to know what is it in +a typical problem and actually matlb + + align:start position:0% +a typical problem and actually matlb + + + align:start position:0% +a typical problem and actually matlb +will estimate it if you if you give mat + + align:start position:0% +will estimate it if you if you give mat + + + align:start position:0% +will estimate it if you if you give mat +lab a linear system or give it give it + + align:start position:0% +lab a linear system or give it give it + + + align:start position:0% +lab a linear system or give it give it +uh yeah give it this problem it will + + align:start position:0% +uh yeah give it this problem it will + + + align:start position:0% +uh yeah give it this problem it will +estimate the condition number it will + + align:start position:0% +estimate the condition number it will + + + align:start position:0% +estimate the condition number it will +give you a signal hey this and and if + + align:start position:0% +give you a signal hey this and and if + + + align:start position:0% +give you a signal hey this and and if +it's a wildly High condition number the + + align:start position:0% +it's a wildly High condition number the + + + align:start position:0% +it's a wildly High condition number the +mat lab will tell you + + align:start position:0% +mat lab will tell you + + + align:start position:0% +mat lab will tell you +so okay so now + + align:start position:0% +so okay so now + + + align:start position:0% +so okay so now +let's just get figure out what that c + + align:start position:0% +let's just get figure out what that c + + + align:start position:0% +let's just get figure out what that c +should be okay so what can we + + align:start position:0% +should be okay so what can we + + + align:start position:0% +should be okay so what can we +say so the true solution is xal a + + align:start position:0% +say so the true solution is xal a + + + align:start position:0% +say so the true solution is xal a +inverse B right that's the true solution + + align:start position:0% +inverse B right that's the true solution + + + align:start position:0% +inverse B right that's the true solution +so the so the norm of X is less than + + align:start position:0% +so the so the norm of X is less than + + + align:start position:0% +so the so the norm of X is less than +what the norm of a + + align:start position:0% + + + + align:start position:0% + +inverse times the norm of B that's so + + align:start position:0% +inverse times the norm of B that's so + + + align:start position:0% +inverse times the norm of B that's so +we're using Norms here for a + + align:start position:0% +we're using Norms here for a + + + align:start position:0% +we're using Norms here for a +inverse that's that's okay that's the + + align:start position:0% +inverse that's that's okay that's the + + + align:start position:0% +inverse that's that's okay that's the +definition of the norm + + align:start position:0% +definition of the norm + + + align:start position:0% +definition of the norm +somehow what will it mean when the norm + + align:start position:0% +somehow what will it mean when the norm + + + align:start position:0% +somehow what will it mean when the norm +of a inverse is + + align:start position:0% +of a inverse is + + + align:start position:0% +of a inverse is +big if a inverse is a big Matrix that + + align:start position:0% +big if a inverse is a big Matrix that + + + align:start position:0% +big if a inverse is a big Matrix that +sort of is telling us what that's + + align:start position:0% +sort of is telling us what that's + + + align:start position:0% +sort of is telling us what that's +telling us that the Matrix is nearly + + align:start position:0% +telling us that the Matrix is nearly + + + align:start position:0% +telling us that the Matrix is nearly +singular it's inverse is + + align:start position:0% +singular it's inverse is + + + align:start position:0% +singular it's inverse is +giant + + align:start position:0% +giant + + + align:start position:0% +giant +but I I want to do things + + align:start position:0% +but I I want to do things + + + align:start position:0% +but I I want to do things +relatively because I if I I multiply by + + align:start position:0% +relatively because I if I I multiply by + + + align:start position:0% +relatively because I if I I multiply by +a million or divide by a million I can + + align:start position:0% +a million or divide by a million I can + + + align:start position:0% +a million or divide by a million I can +make the inverse a million bigger or a + + align:start position:0% +make the inverse a million bigger or a + + + align:start position:0% +make the inverse a million bigger or a +million smaller without changing reality + + align:start position:0% +million smaller without changing reality + + + align:start position:0% +million smaller without changing reality +here so it's so it's relative that's + + align:start position:0% +here so it's so it's relative that's + + + align:start position:0% +here so it's so it's relative that's +reality okay now I've got this equation + + align:start position:0% +reality okay now I've got this equation + + + align:start position:0% +reality okay now I've got this equation +now can I can I write this out as ax and + + align:start position:0% +now can I can I write this out as ax and + + + align:start position:0% +now can I can I write this out as ax and +a Delta + + align:start position:0% +a Delta + + + align:start position:0% +a Delta +X ax plus a Delta + + align:start position:0% +X ax plus a Delta + + + align:start position:0% +X ax plus a Delta +X now what what should I do + + align:start position:0% +X now what what should I do + + + align:start position:0% +X now what what should I do +next there here's my true equation and + + align:start position:0% +next there here's my true equation and + + + align:start position:0% +next there here's my true equation and +here's my actual my uh numerical + + align:start position:0% +here's my actual my uh numerical + + + align:start position:0% +here's my actual my uh numerical +computational equation so I've got those + + align:start position:0% +computational equation so I've got those + + + align:start position:0% +computational equation so I've got those +two I just subtract that from + + align:start position:0% +two I just subtract that from + + + align:start position:0% +two I just subtract that from +that right so I learned that a Delta + + align:start position:0% +that right so I learned that a Delta + + + align:start position:0% +that right so I learned that a Delta +X is Delta + + align:start position:0% +X is Delta + + + align:start position:0% +X is Delta +B + + align:start position:0% +B + + + align:start position:0% +B +right so I have an idea now of how big + + align:start position:0% +right so I have an idea now of how big + + + align:start position:0% +right so I have an idea now of how big +Delta B is Delta + + align:start position:0% +Delta B is Delta + + + align:start position:0% +Delta B is Delta +B how could how big could Delta B be + + align:start position:0% +B how could how big could Delta B be + + + align:start position:0% +B how could how big could Delta B be +now is well yeah if from if from this + + align:start position:0% +now is well yeah if from if from this + + + align:start position:0% +now is well yeah if from if from this +equation so Delta B is what I get by + + align:start position:0% +equation so Delta B is what I get by + + + align:start position:0% +equation so Delta B is what I get by +multiplying Delta X by + + align:start position:0% +multiplying Delta X by + + + align:start position:0% +multiplying Delta X by +a so our work on Norms of the Matrix + + align:start position:0% +a so our work on Norms of the Matrix + + + align:start position:0% +a so our work on Norms of the Matrix +says + + align:start position:0% +says + + + align:start position:0% +says +that this thing can't blow up by more + + align:start position:0% +that this thing can't blow up by more + + + align:start position:0% +that this thing can't blow up by more +than the norm of + + align:start position:0% + + + + align:start position:0% + +a that's so this these facts are just + + align:start position:0% +a that's so this these facts are just + + + align:start position:0% +a that's so this these facts are just +come from these simple equations by the + + align:start position:0% +come from these simple equations by the + + + align:start position:0% +come from these simple equations by the +idea of what the norm + + align:start position:0% + + + + align:start position:0% + +means now am I any better off I have a + + align:start position:0% +means now am I any better off I have a + + + align:start position:0% +means now am I any better off I have a +feeling that if I just put these two + + align:start position:0% +feeling that if I just put these two + + + align:start position:0% +feeling that if I just put these two +pieces + + align:start position:0% +pieces + + + align:start position:0% +pieces +together I'll get I guess what am I + + align:start position:0% +together I'll get I guess what am I + + + align:start position:0% +together I'll get I guess what am I +going to do I'm going to divide one by + + align:start position:0% +going to do I'm going to divide one by + + + align:start position:0% +going to do I'm going to divide one by +the other to get something like + + align:start position:0% +the other to get something like + + + align:start position:0% +the other to get something like +that oh is that good + + align:start position:0% +that oh is that good + + + align:start position:0% +that oh is that good +I don't know if that's so great I don't + + align:start position:0% +I don't know if that's so great I don't + + + align:start position:0% +I don't know if that's so great I don't +think I've done it right why why do I + + align:start position:0% +think I've done it right why why do I + + + align:start position:0% +think I've done it right why why do I +not think I've done it right because I + + align:start position:0% +not think I've done it right because I + + + align:start position:0% +not think I've done it right because I +want an inequality where Delta X is less + + align:start position:0% +want an inequality where Delta X is less + + + align:start position:0% +want an inequality where Delta X is less +than something and I have brilliantly + + align:start position:0% +than something and I have brilliantly + + + align:start position:0% +than something and I have brilliantly +come up with an inequality where it's + + align:start position:0% +come up with an inequality where it's + + + align:start position:0% +come up with an inequality where it's +larger than + + align:start position:0% + + + + align:start position:0% + +something uh so embarrassment here um + + align:start position:0% +something uh so embarrassment here um + + + align:start position:0% +something uh so embarrassment here um +maybe what I wanted to do was have the + + align:start position:0% +maybe what I wanted to do was have the + + + align:start position:0% +maybe what I wanted to do was have the +inverse in this one yeah that would have + + align:start position:0% +inverse in this one yeah that would have + + + align:start position:0% +inverse in this one yeah that would have +been a lot better the inverse should + + align:start position:0% +been a lot better the inverse should + + + align:start position:0% +been a lot better the inverse should +have been in this + + align:start position:0% +have been in this + + + align:start position:0% +have been in this +one and in this one I shouldn't have + + align:start position:0% +one and in this one I shouldn't have + + + align:start position:0% +one and in this one I shouldn't have +taken the inverse I should have just + + align:start position:0% +taken the inverse I should have just + + + align:start position:0% +taken the inverse I should have just +stayed where I was happy ax equal B that + + align:start position:0% +stayed where I was happy ax equal B that + + + align:start position:0% +stayed where I was happy ax equal B that +would have been better all right can can + + align:start position:0% +would have been better all right can can + + + align:start position:0% +would have been better all right can can +I yes on the + + align:start position:0% +I yes on the + + + align:start position:0% +I yes on the +videotape we uh can't we can't uh well + + align:start position:0% +videotape we uh can't we can't uh well + + + align:start position:0% +videotape we uh can't we can't uh well +future viewers will forgive this so this + + align:start position:0% +future viewers will forgive this so this + + + align:start position:0% +future viewers will forgive this so this +says that the length of B is less than + + align:start position:0% +says that the length of B is less than + + + align:start position:0% +says that the length of B is less than +the normal of a Time the norm of X + + align:start position:0% +the normal of a Time the norm of X + + + align:start position:0% +the normal of a Time the norm of X +that's good fine and this one says that + + align:start position:0% +that's good fine and this one says that + + + align:start position:0% +that's good fine and this one says that +the size of Delta X is less or equal the + + align:start position:0% +the size of Delta X is less or equal the + + + align:start position:0% +the size of Delta X is less or equal the +size of a + + align:start position:0% +size of a + + + align:start position:0% +size of a +inverse times the size of Delta + + align:start position:0% +inverse times the size of Delta + + + align:start position:0% +inverse times the size of Delta +B okay now we are getting + + align:start position:0% + + + + align:start position:0% + +somewhere now I have Delta X less than + + align:start position:0% +somewhere now I have Delta X less than + + + align:start position:0% +somewhere now I have Delta X less than +or equal something + + align:start position:0% +or equal something + + + align:start position:0% +or equal something +but I want relative error I have to + + align:start position:0% +but I want relative error I have to + + + align:start position:0% +but I want relative error I have to +divide by X so can I do that what + + align:start position:0% +divide by X so can I do that what + + + align:start position:0% +divide by X so can I do that what +happens + + align:start position:0% +happens + + + align:start position:0% +happens +here start with this one and I divide by + + align:start position:0% +here start with this one and I divide by + + + align:start position:0% +here start with this one and I divide by +Del by + + align:start position:0% +Del by + + + align:start position:0% +Del by +X + + align:start position:0% + + + + align:start position:0% + +okay + + align:start position:0% +okay + + + align:start position:0% +okay +now uh X is bigger than b over the + + align:start position:0% +now uh X is bigger than b over the + + + align:start position:0% +now uh X is bigger than b over the +length of a so if I divide by something + + align:start position:0% +length of a so if I divide by something + + + align:start position:0% +length of a so if I divide by something +smaller right this X is bigger than b + + align:start position:0% +smaller right this X is bigger than b + + + align:start position:0% +smaller right this X is bigger than b +over a so if I divide instead by B over + + align:start position:0% +over a so if I divide instead by B over + + + align:start position:0% +over a so if I divide instead by B over +a I've grown it more so let me divide by + + align:start position:0% +a I've grown it more so let me divide by + + + align:start position:0% +a I've grown it more so let me divide by +B over a instead instead of dividing by + + align:start position:0% +B over a instead instead of dividing by + + + align:start position:0% +B over a instead instead of dividing by +this I'll divide by B + + align:start position:0% +this I'll divide by B + + + align:start position:0% +this I'll divide by B +over a sneaks up in + + align:start position:0% + + + + align:start position:0% + +here this is right + + align:start position:0% +here this is right + + + align:start position:0% +here this is right +and I've seen I now see what's the + + align:start position:0% +and I've seen I now see what's the + + + align:start position:0% +and I've seen I now see what's the +condition number I now see what is this + + align:start position:0% +condition number I now see what is this + + + align:start position:0% +condition number I now see what is this +condition number and and do you see it + + align:start position:0% +condition number and and do you see it + + + align:start position:0% +condition number and and do you see it +or have I have I + + align:start position:0% +or have I have I + + + align:start position:0% +or have I have I +uh spoiled the Blackboard so it it + + align:start position:0% +uh spoiled the Blackboard so it it + + + align:start position:0% +uh spoiled the Blackboard so it it +should be here it's you see Delta X + + align:start position:0% +should be here it's you see Delta X + + + align:start position:0% +should be here it's you see Delta X +overx and here you see Delta B over B + + align:start position:0% +overx and here you see Delta B over B + + + align:start position:0% +overx and here you see Delta B over B +and here you see the condition + + align:start position:0% +and here you see the condition + + + align:start position:0% +and here you see the condition +number the the condition number is the + + align:start position:0% +number the the condition number is the + + + align:start position:0% +number the the condition number is the +norm of a a inverse times the norm of a + + align:start position:0% +norm of a a inverse times the norm of a + + + align:start position:0% +norm of a a inverse times the norm of a +isn't that + + align:start position:0% +isn't that + + + align:start position:0% +isn't that +neat condition number is the norm of a + + align:start position:0% +neat condition number is the norm of a + + + align:start position:0% +neat condition number is the norm of a +inverse time the norm of a that's the + + align:start position:0% +inverse time the norm of a that's the + + + align:start position:0% +inverse time the norm of a that's the +right + + align:start position:0% + + + + align:start position:0% + +quantity let's I've this has taken more + + align:start position:0% +quantity let's I've this has taken more + + + align:start position:0% +quantity let's I've this has taken more +time and but I still having got this far + + align:start position:0% +time and but I still having got this far + + + align:start position:0% +time and but I still having got this far +I would like to give it another little + + align:start position:0% +I would like to give it another little + + + align:start position:0% +I would like to give it another little +bit because I'm uh I'd like to + + align:start position:0% +bit because I'm uh I'd like to + + + align:start position:0% +bit because I'm uh I'd like to +understand what this means suppose a is + + align:start position:0% +understand what this means suppose a is + + + align:start position:0% +understand what this means suppose a is +an orthogonal + + align:start position:0% +an orthogonal + + + align:start position:0% +an orthogonal +Matrix what's its condition + + align:start position:0% +Matrix what's its condition + + + align:start position:0% +Matrix what's its condition +number one because if if it's an + + align:start position:0% +number one because if if it's an + + + align:start position:0% +number one because if if it's an +orthogonal Matrix its Norm is one and + + align:start position:0% +orthogonal Matrix its Norm is one and + + + align:start position:0% +orthogonal Matrix its Norm is one and +its inverse is also an orthogonal Matrix + + align:start position:0% +its inverse is also an orthogonal Matrix + + + align:start position:0% +its inverse is also an orthogonal Matrix +that's one so the condition number is + + align:start position:0% +that's one so the condition number is + + + align:start position:0% +that's one so the condition number is +one what's the condition number of this + + align:start position:0% +one what's the condition number of this + + + align:start position:0% +one what's the condition number of this +guy a symmetric + + align:start position:0% +guy a symmetric + + + align:start position:0% +guy a symmetric +Matrix well tell me it's Norm and tell + + align:start position:0% +Matrix well tell me it's Norm and tell + + + align:start position:0% +Matrix well tell me it's Norm and tell +me it's tell me it's inverse so for well + + align:start position:0% +me it's tell me it's inverse so for well + + + align:start position:0% +me it's tell me it's inverse so for well +we can do its inverse EAS easily what's + + align:start position:0% +we can do its inverse EAS easily what's + + + align:start position:0% +we can do its inverse EAS easily what's +the inverse of this Matrix minus A3 0 + + align:start position:0% +the inverse of this Matrix minus A3 0 + + + align:start position:0% +the inverse of this Matrix minus A3 0 +01 okay so tell me the Norms of those + + align:start position:0% +01 okay so tell me the Norms of those + + + align:start position:0% +01 okay so tell me the Norms of those +two + + align:start position:0% +two + + + align:start position:0% +two +guys three and one right so the + + align:start position:0% +guys three and one right so the + + + align:start position:0% +guys three and one right so the +condition number is three + + align:start position:0% +condition number is three + + + align:start position:0% +condition number is three +exactly exactly so uh those those were + + align:start position:0% +exactly exactly so uh those those were + + + align:start position:0% +exactly exactly so uh those those were +easy because they were + + align:start position:0% +easy because they were + + + align:start position:0% +easy because they were +diagonal but symmetric matrices are just + + align:start position:0% +diagonal but symmetric matrices are just + + + align:start position:0% +diagonal but symmetric matrices are just +as easy for a symmetric Matrix so what's + + align:start position:0% +as easy for a symmetric Matrix so what's + + + align:start position:0% +as easy for a symmetric Matrix so what's +so so this is for a general Matrix if + + align:start position:0% +so so this is for a general Matrix if + + + align:start position:0% +so so this is for a general Matrix if +the Matrix is symmetric why don't I keep + + align:start position:0% +the Matrix is symmetric why don't I keep + + + align:start position:0% +the Matrix is symmetric why don't I keep +this keep this uh list going so this + + align:start position:0% +this keep this uh list going so this + + + align:start position:0% +this keep this uh list going so this +will then conclude the our + + align:start position:0% +will then conclude the our + + + align:start position:0% +will then conclude the our +table of norms and now condition numbers + + align:start position:0% +table of norms and now condition numbers + + + align:start position:0% +table of norms and now condition numbers +condition numbers condition numbers okay + + align:start position:0% +condition numbers condition numbers okay + + + align:start position:0% +condition numbers condition numbers okay +what's the what are the condition + + align:start position:0% +what's the what are the condition + + + align:start position:0% +what's the what are the condition +numbers if it's orthogonal we said + + align:start position:0% +numbers if it's orthogonal we said + + + align:start position:0% +numbers if it's orthogonal we said +condition number was one if now this is + + align:start position:0% +condition number was one if now this is + + + align:start position:0% +condition number was one if now this is +the case I'm interested in if the if + + align:start position:0% +the case I'm interested in if the if + + + align:start position:0% +the case I'm interested in if the if +it's a symmetric Matrix because we do + + align:start position:0% +it's a symmetric Matrix because we do + + + align:start position:0% +it's a symmetric Matrix because we do +get a lot of those + + align:start position:0% +get a lot of those + + + align:start position:0% +get a lot of those +what's what is the condition number + + align:start position:0% +what's what is the condition number + + + align:start position:0% +what's what is the condition number +remembering remembering our formula you + + align:start position:0% +remembering remembering our formula you + + + align:start position:0% +remembering remembering our formula you +have to multiply the norm of a by the + + align:start position:0% +have to multiply the norm of a by the + + + align:start position:0% +have to multiply the norm of a by the +norm of a inverse and we did a test case + + align:start position:0% +norm of a inverse and we did a test case + + + align:start position:0% +norm of a inverse and we did a test case +where we got a three and a one anybody + + align:start position:0% +where we got a three and a one anybody + + + align:start position:0% +where we got a three and a one anybody +want to take a shot on this + + align:start position:0% + + + + align:start position:0% + +there'll be a lamb it'll be a ratio + + align:start position:0% +there'll be a lamb it'll be a ratio + + + align:start position:0% +there'll be a lamb it'll be a ratio +great great perfect it'll be Lambda + + align:start position:0% +great great perfect it'll be Lambda + + + align:start position:0% +great great perfect it'll be Lambda +Max + + align:start position:0% +Max + + + align:start position:0% +Max +over Lambda + + align:start position:0% +over Lambda + + + align:start position:0% +over Lambda +Min that tells you how hard the problem + + align:start position:0% +Min that tells you how hard the problem + + + align:start position:0% +Min that tells you how hard the problem +is and you see the beauty of that number + + align:start position:0% +is and you see the beauty of that number + + + align:start position:0% +is and you see the beauty of that number +if I multiply the matrix by 100 then I + + align:start position:0% +if I multiply the matrix by 100 then I + + + align:start position:0% +if I multiply the matrix by 100 then I +multiply both pieces by 100 same + + align:start position:0% +multiply both pieces by 100 same + + + align:start position:0% +multiply both pieces by 100 same +condition number so so you can't cheat + + align:start position:0% +condition number so so you can't cheat + + + align:start position:0% +condition number so so you can't cheat +by just uh + + align:start position:0% +by just uh + + + align:start position:0% +by just uh +scale okay and the answer here will be + + align:start position:0% +scale okay and the answer here will be + + + align:start position:0% +scale okay and the answer here will be +Sigma Max over Sigma Min if we knew what + + align:start position:0% +Sigma Max over Sigma Min if we knew what + + + align:start position:0% +Sigma Max over Sigma Min if we knew what +these sigmas were well we do know what + + align:start position:0% +these sigmas were well we do know what + + + align:start position:0% +these sigmas were well we do know what +they are they're the igen values of a + + align:start position:0% +they are they're the igen values of a + + + align:start position:0% +they are they're the igen values of a +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +a the sigmas are the igen values of a + + align:start position:0% +a the sigmas are the igen values of a + + + align:start position:0% +a the sigmas are the igen values of a +transpose + + align:start position:0% +transpose + + + align:start position:0% +transpose +a and when the symmet Matrix was + + align:start position:0% +a and when the symmet Matrix was + + + align:start position:0% +a and when the symmet Matrix was +symmetric that was a squ and we didn't + + align:start position:0% +symmetric that was a squ and we didn't + + + align:start position:0% +symmetric that was a squ and we didn't +have to we didn't have to go up to that + + align:start position:0% +have to we didn't have to go up to that + + + align:start position:0% +have to we didn't have to go up to that +a squ level to to get get the answer so + + align:start position:0% +a squ level to to get get the answer so + + + align:start position:0% +a squ level to to get get the answer so +uh so now I'm ready in these last + + align:start position:0% +uh so now I'm ready in these last + + + align:start position:0% +uh so now I'm ready in these last +minutes then to say something more about + + align:start position:0% +minutes then to say something more about + + + align:start position:0% +minutes then to say something more about +the um singular value + + align:start position:0% +the um singular value + + + align:start position:0% +the um singular value +decomposition which I sort of intended + + align:start position:0% +decomposition which I sort of intended + + + align:start position:0% +decomposition which I sort of intended +to derive but that's probably okay that + + align:start position:0% +to derive but that's probably okay that + + + align:start position:0% +to derive but that's probably okay that +we didn't so let now now because these + + align:start position:0% +we didn't so let now now because these + + + align:start position:0% +we didn't so let now now because these +sigmas are the key to the sigma to the + + align:start position:0% +sigmas are the key to the sigma to the + + + align:start position:0% +sigmas are the key to the sigma to the +singular value decomposition so let me + + align:start position:0% +singular value decomposition so let me + + + align:start position:0% +singular value decomposition so let me +end the lecture by writing down that + + align:start position:0% +end the lecture by writing down that + + + align:start position:0% +end the lecture by writing down that +decomposition and talking about what we + + align:start position:0% +decomposition and talking about what we + + + align:start position:0% +decomposition and talking about what we +learned from + + align:start position:0% +learned from + + + align:start position:0% +learned from +it + + align:start position:0% +it + + + align:start position:0% +it +okay okay so the singular value + + align:start position:0% +okay okay so the singular value + + + align:start position:0% +okay okay so the singular value +decomposition says any + + align:start position:0% +decomposition says any + + + align:start position:0% +decomposition says any +a m + + align:start position:0% +a m + + + align:start position:0% +a m +byn can be broken up into an M + + align:start position:0% + + + + align:start position:0% + +bym orthogonal I won't use Q so I'll use + + align:start position:0% +bym orthogonal I won't use Q so I'll use + + + align:start position:0% +bym orthogonal I won't use Q so I'll use +U + + align:start position:0% +U + + + align:start position:0% +U +orthogonal and over + + align:start position:0% +orthogonal and over + + + align:start position:0% +orthogonal and over +here uh an n byn + + align:start position:0% + + + + align:start position:0% + +orthogonal and it's usually written V + + align:start position:0% +orthogonal and it's usually written V + + + align:start position:0% +orthogonal and it's usually written V +transpose Square orthogonal Matrix and + + align:start position:0% +transpose Square orthogonal Matrix and + + + align:start position:0% +transpose Square orthogonal Matrix and +in between comes diagonal so in between + + align:start position:0% +in between comes diagonal so in between + + + align:start position:0% +in between comes diagonal so in between +will come a diagonal + + align:start position:0% +will come a diagonal + + + align:start position:0% +will come a diagonal +matrix M by n so it's when I say + + align:start position:0% +matrix M by n so it's when I say + + + align:start position:0% +matrix M by n so it's when I say +diagonal it's got these sigmas these + + align:start position:0% +diagonal it's got these sigmas these + + + align:start position:0% +diagonal it's got these sigmas these +numbers Sigma 1 Sigma 2 on the + + align:start position:0% +numbers Sigma 1 Sigma 2 on the + + + align:start position:0% +numbers Sigma 1 Sigma 2 on the +diagonal as as far as they're nonzero + + align:start position:0% +diagonal as as far as they're nonzero + + + align:start position:0% +diagonal as as far as they're nonzero +down to whatever I don't I guess it'll + + align:start position:0% +down to whatever I don't I guess it'll + + + align:start position:0% +down to whatever I don't I guess it'll +stop at the rank of the + + align:start position:0% +stop at the rank of the + + + align:start position:0% +stop at the rank of the +Matrix and the rest of the the rest of + + align:start position:0% +Matrix and the rest of the the rest of + + + align:start position:0% +Matrix and the rest of the the rest of +this guy will be zero so it really is + + align:start position:0% +this guy will be zero so it really is + + + align:start position:0% +this guy will be zero so it really is +diagonal that's the that's the uh and it + + align:start position:0% +diagonal that's the that's the uh and it + + + align:start position:0% +diagonal that's the that's the uh and it +comes from a transpose a the it really + + align:start position:0% +comes from a transpose a the it really + + + align:start position:0% +comes from a transpose a the it really +totally linked to a transpose a the the + + align:start position:0% +totally linked to a transpose a the the + + + align:start position:0% +totally linked to a transpose a the the +igen values the IG values + + align:start position:0% +igen values the IG values + + + align:start position:0% +igen values the IG values +are are Sigma 1 squar Sigma 2^ squar + + align:start position:0% +are are Sigma 1 squar Sigma 2^ squar + + + align:start position:0% +are are Sigma 1 squar Sigma 2^ squar +onto however many nonzero ones they are + + align:start position:0% +onto however many nonzero ones they are + + + align:start position:0% +onto however many nonzero ones they are +and then maybe some + + align:start position:0% + + + + align:start position:0% + +zeros yeah I I should have said in this + + align:start position:0% +zeros yeah I I should have said in this + + + align:start position:0% +zeros yeah I I should have said in this +condition number stuff what if the + + align:start position:0% +condition number stuff what if the + + + align:start position:0% +condition number stuff what if the +Matrix is singular + + align:start position:0% +Matrix is singular + + + align:start position:0% +Matrix is singular +what will its condition number be in + + align:start position:0% +what will its condition number be in + + + align:start position:0% +what will its condition number be in +that case so so what would the what do + + align:start position:0% +that case so so what would the what do + + + align:start position:0% +that case so so what would the what do +you figure would would this number turn + + align:start position:0% +you figure would would this number turn + + + align:start position:0% +you figure would would this number turn +up to uh uh explode to if the Matrix a + + align:start position:0% +up to uh uh explode to if the Matrix a + + + align:start position:0% +up to uh uh explode to if the Matrix a +is + + align:start position:0% +is + + + align:start position:0% +is +singular strictly it'll be infinite yeah + + align:start position:0% +singular strictly it'll be infinite yeah + + + align:start position:0% +singular strictly it'll be infinite yeah +it won't be defined but basically it'll + + align:start position:0% +it won't be defined but basically it'll + + + align:start position:0% +it won't be defined but basically it'll +be infinite yeah so a a really singular + + align:start position:0% +be infinite yeah so a a really singular + + + align:start position:0% +be infinite yeah so a a really singular +Matrix + + align:start position:0% +Matrix + + + align:start position:0% +Matrix +is totally ill + + align:start position:0% +is totally ill + + + align:start position:0% +is totally ill +conditioned and but + + align:start position:0% +conditioned and but + + + align:start position:0% +conditioned and but +uh uh somehow we don't worry so much + + align:start position:0% +uh uh somehow we don't worry so much + + + align:start position:0% +uh uh somehow we don't worry so much +about those it's the ones that are + + align:start position:0% +about those it's the ones that are + + + align:start position:0% +about those it's the ones that are +nearly singular that are extremely oond + + align:start position:0% +nearly singular that are extremely oond + + + align:start position:0% +nearly singular that are extremely oond +conditioned but we have to deal with + + align:start position:0% +conditioned but we have to deal with + + + align:start position:0% +conditioned but we have to deal with +them those are the ones that we have to + + align:start position:0% +them those are the ones that we have to + + + align:start position:0% +them those are the ones that we have to +work with and + + align:start position:0% +work with and + + + align:start position:0% +work with and +actually right if it was totally if it + + align:start position:0% +actually right if it was totally if it + + + align:start position:0% +actually right if it was totally if it +was singular you'd say you you'd give up + + align:start position:0% +was singular you'd say you you'd give up + + + align:start position:0% +was singular you'd say you you'd give up +on Ax equal B and go to these + + align:start position:0% +on Ax equal B and go to these + + + align:start position:0% +on Ax equal B and go to these +squares but what do you do if it's + + align:start position:0% +squares but what do you do if it's + + + align:start position:0% +squares but what do you do if it's +almost + + align:start position:0% +almost + + + align:start position:0% +almost +singular do you give up on the thing and + + align:start position:0% +singular do you give up on the thing and + + + align:start position:0% +singular do you give up on the thing and +go to Le + + align:start position:0% +go to Le + + + align:start position:0% +go to Le +squares well here's what you do if you + + align:start position:0% +squares well here's what you do if you + + + align:start position:0% +squares well here's what you do if you +know the singular value + + align:start position:0% +know the singular value + + + align:start position:0% +know the singular value +decomposition if the thing is nearly + + align:start position:0% +decomposition if the thing is nearly + + + align:start position:0% +decomposition if the thing is nearly +singular some of these or maybe the last + + align:start position:0% +singular some of these or maybe the last + + + align:start position:0% +singular some of these or maybe the last +one or the last couple will be extremely + + align:start position:0% +one or the last couple will be extremely + + + align:start position:0% +one or the last couple will be extremely +small and you're better off to wipe them + + align:start position:0% +small and you're better off to wipe them + + + align:start position:0% +small and you're better off to wipe them +out completely so so that's one way of + + align:start position:0% +out completely so so that's one way of + + + align:start position:0% +out completely so so that's one way of +kind of um I don't know regularizing the + + align:start position:0% +kind of um I don't know regularizing the + + + align:start position:0% +kind of um I don't know regularizing the +problem or dealing with it is is uh is + + align:start position:0% +problem or dealing with it is is uh is + + + align:start position:0% +problem or dealing with it is is uh is +to uh move to a to a singular Matrix + + align:start position:0% +to uh move to a to a singular Matrix + + + align:start position:0% +to uh move to a to a singular Matrix +move to the nearest singular Matrix and + + align:start position:0% +move to the nearest singular Matrix and + + + align:start position:0% +move to the nearest singular Matrix and +and and accept the thing as singular + + align:start position:0% +and and accept the thing as singular + + + align:start position:0% +and and accept the thing as singular +instead of being on the knife edge of + + align:start position:0% +instead of being on the knife edge of + + + align:start position:0% +instead of being on the knife edge of +Singularity but but trying to deal with + + align:start position:0% +Singularity but but trying to deal with + + + align:start position:0% +Singularity but but trying to deal with +it as if it's not singular think think + + align:start position:0% +it as if it's not singular think think + + + align:start position:0% +it as if it's not singular think think +looking you're standing right next to + + align:start position:0% +looking you're standing right next to + + + align:start position:0% +looking you're standing right next to +that that that little formula you got + + align:start position:0% +that that that little formula you got + + + align:start position:0% +that that that little formula you got +left over from the first part from here + + align:start position:0% +left over from the first part from here + + + align:start position:0% +left over from the first part from here +this formula right now we're looking + + align:start position:0% +this formula right now we're looking + + + align:start position:0% +this formula right now we're looking +it's sort of like you're throwing out + + align:start position:0% +it's sort of like you're throwing out + + + align:start position:0% +it's sort of like you're throwing out +the direction where you that maximum + + align:start position:0% +the direction where you that maximum + + + align:start position:0% +the direction where you that maximum +yeah you are I'm going to throw out + + align:start position:0% +yeah you are I'm going to throw out + + + align:start position:0% +yeah you are I'm going to throw out +those directions and I'm going to keep + + align:start position:0% +those directions and I'm going to keep + + + align:start position:0% +those directions and I'm going to keep +my + + align:start position:0% +my + + + align:start position:0% +my +good let's see uh when I when I take + + align:start position:0% +good let's see uh when I when I take + + + align:start position:0% +good let's see uh when I when I take +this formula I'm certainly throwing out + + align:start position:0% +this formula I'm certainly throwing out + + + align:start position:0% +this formula I'm certainly throwing out +directions and and in in this case I'm + + align:start position:0% +directions and and in in this case I'm + + + align:start position:0% +directions and and in in this case I'm +throwing out the U and the V and I'm + + align:start position:0% +throwing out the U and the V and I'm + + + align:start position:0% +throwing out the U and the V and I'm +looking at the sigmas that's but I'm + + align:start position:0% +looking at the sigmas that's but I'm + + + align:start position:0% +looking at the sigmas that's but I'm +zero out some of those sigas it's like + + align:start position:0% +zero out some of those sigas it's like + + + align:start position:0% +zero out some of those sigas it's like +I'm not going to take my Max I'm G + + align:start position:0% +I'm not going to take my Max I'm G + + + align:start position:0% +I'm not going to take my Max I'm G +that's right I I exactly so if I'm going + + align:start position:0% +that's right I I exactly so if I'm going + + + align:start position:0% +that's right I I exactly so if I'm going +to zero out some sigmas that means I'm + + align:start position:0% +to zero out some sigmas that means I'm + + + align:start position:0% +to zero out some sigmas that means I'm +going to look for the best answer in + + align:start position:0% +going to look for the best answer in + + + align:start position:0% +going to look for the best answer in +some Subspace where the darn problem is + + align:start position:0% +some Subspace where the darn problem is + + + align:start position:0% +some Subspace where the darn problem is +well conditioned I mean I + + align:start position:0% +well conditioned I mean I + + + align:start position:0% +well conditioned I mean I +guess boy we're touching on a world here + + align:start position:0% +guess boy we're touching on a world here + + + align:start position:0% +guess boy we're touching on a world here +of ill conditioned problems what do you + + align:start position:0% +of ill conditioned problems what do you + + + align:start position:0% +of ill conditioned problems what do you +do when the problem is just lousy and + + align:start position:0% +do when the problem is just lousy and + + + align:start position:0% +do when the problem is just lousy and +still you have to solve it and and it's + + align:start position:0% +still you have to solve it and and it's + + + align:start position:0% +still you have to solve it and and it's +going to happen in problems at the lab + + align:start position:0% +going to happen in problems at the lab + + + align:start position:0% +going to happen in problems at the lab +is going to have problems everywhere + + align:start position:0% +is going to have problems everywhere + + + align:start position:0% +is going to have problems everywhere +typical so can I like make a short + + align:start position:0% +typical so can I like make a short + + + align:start position:0% +typical so can I like make a short +speech about ill conditioned problems uh + + align:start position:0% +speech about ill conditioned problems uh + + + align:start position:0% +speech about ill conditioned problems uh +typical ill condition problems are uh + + align:start position:0% +typical ill condition problems are uh + + + align:start position:0% +typical ill condition problems are uh +so-called inverse problems + + align:start position:0% +so-called inverse problems + + + align:start position:0% +so-called inverse problems +so in um suppose + + align:start position:0% +so in um suppose + + + align:start position:0% +so in um suppose +I um you know the direct problem is I + + align:start position:0% +I um you know the direct problem is I + + + align:start position:0% +I um you know the direct problem is I +give some boundary conditions I give + + align:start position:0% +give some boundary conditions I give + + + align:start position:0% +give some boundary conditions I give +some I give equation and I get a I + + align:start position:0% +some I give equation and I get a I + + + align:start position:0% +some I give equation and I get a I +discover what the field looks + + align:start position:0% +discover what the field looks + + + align:start position:0% +discover what the field looks +like inverse problems are I don't know + + align:start position:0% +like inverse problems are I don't know + + + align:start position:0% +like inverse problems are I don't know +what that system really is all I know is + + align:start position:0% +what that system really is all I know is + + + align:start position:0% +what that system really is all I know is +some outputs and some inputs and I'm + + align:start position:0% +some outputs and some inputs and I'm + + + align:start position:0% +some outputs and some inputs and I'm +trying to figure out what's what's in + + align:start position:0% +trying to figure out what's what's in + + + align:start position:0% +trying to figure out what's what's in +that black + + align:start position:0% +that black + + + align:start position:0% +that black +box and those that so that's called the + + align:start position:0% +box and those that so that's called the + + + align:start position:0% +box and those that so that's called the +inverse problem the direct problem would + + align:start position:0% +inverse problem the direct problem would + + + align:start position:0% +inverse problem the direct problem would +be know what's in the black box and + + align:start position:0% +be know what's in the black box and + + + align:start position:0% +be know what's in the black box and +solve ax equal B best you can inverse + + align:start position:0% +solve ax equal B best you can inverse + + + align:start position:0% +solve ax equal B best you can inverse +problems come when you might know some + + align:start position:0% +problems come when you might know some + + + align:start position:0% +problems come when you might know some +x's and some B's and you're thinking + + align:start position:0% +x's and some B's and you're thinking + + + align:start position:0% +x's and some B's and you're thinking +well what you know what's what's what's + + align:start position:0% +well what you know what's what's what's + + + align:start position:0% +well what you know what's what's what's +the system about and that's extremely + + align:start position:0% +the system about and that's extremely + + + align:start position:0% +the system about and that's extremely +difficult to so that'll be a very um ill + + align:start position:0% +difficult to so that'll be a very um ill + + + align:start position:0% +difficult to so that'll be a very um ill +conditioned problem in general um and + + align:start position:0% +conditioned problem in general um and + + + align:start position:0% +conditioned problem in general um and +uh so there are books written + + align:start position:0% +uh so there are books written + + + align:start position:0% +uh so there are books written +about inverse problems and you know they + + align:start position:0% +about inverse problems and you know they + + + align:start position:0% +about inverse problems and you know they +they uh are going to come up you could + + align:start position:0% +they uh are going to come up you could + + + align:start position:0% +they uh are going to come up you could +you could create a scenario I'm sure + + align:start position:0% +you could create a scenario I'm sure + + + align:start position:0% +you could create a scenario I'm sure +better than I in which it's an inverse + + align:start position:0% +better than I in which it's an inverse + + + align:start position:0% +better than I in which it's an inverse +problem that you really want to solve + + align:start position:0% +problem that you really want to solve + + + align:start position:0% +problem that you really want to solve +you you have some you you know you have + + align:start position:0% +you you have some you you know you have + + + align:start position:0% +you you have some you you know you have +some sensor data and you're trying to + + align:start position:0% +some sensor data and you're trying to + + + align:start position:0% +some sensor data and you're trying to +figure out okay what produced + + align:start position:0% +figure out okay what produced + + + align:start position:0% +figure out okay what produced +it uh maybe this is a topic which you + + align:start position:0% +it uh maybe this is a topic which you + + + align:start position:0% +it uh maybe this is a topic which you +could email me about and I could + + align:start position:0% +could email me about and I could + + + align:start position:0% +could email me about and I could +uh uh develop further + + align:start position:0% +uh uh develop further + + + align:start position:0% +uh uh develop further +um okay so th that's that's ill + + align:start position:0% +um okay so th that's that's ill + + + align:start position:0% +um okay so th that's that's ill +conditioning and that's the uh sort of + + align:start position:0% +conditioning and that's the uh sort of + + + align:start position:0% +conditioning and that's the uh sort of +the + + align:start position:0% +the + + + align:start position:0% +the +nearest the nearest singular Matrix + + align:start position:0% +nearest the nearest singular Matrix + + + align:start position:0% +nearest the nearest singular Matrix +happens when we set this thing to zero + + align:start position:0% +happens when we set this thing to zero + + + align:start position:0% +happens when we set this thing to zero +let's suppose we're talking Square + + align:start position:0% +let's suppose we're talking Square + + + align:start position:0% +let's suppose we're talking Square +matrices here so this is really a proper + + align:start position:0% +matrices here so this is really a proper + + + align:start position:0% +matrices here so this is really a proper +diagonal matrix the nearest singular one + + align:start position:0% +diagonal matrix the nearest singular one + + + align:start position:0% +diagonal matrix the nearest singular one +would be that that's that measures how + + align:start position:0% +would be that that's that measures how + + + align:start position:0% +would be that that's that measures how +far it is from singular and if we want + + align:start position:0% +far it is from singular and if we want + + + align:start position:0% +far it is from singular and if we want +to go to singular we make that that + + align:start position:0% +to go to singular we make that that + + + align:start position:0% +to go to singular we make that that +thing zero so these sigmas are the sort + + align:start position:0% +thing zero so these sigmas are the sort + + + align:start position:0% +thing zero so these sigmas are the sort +of they're the right numbers to look at + + align:start position:0% +of they're the right numbers to look at + + + align:start position:0% +of they're the right numbers to look at +they they match the igen values in for + + align:start position:0% +they they match the igen values in for + + + align:start position:0% +they they match the igen values in for +nice matrices but we've seen for that + + align:start position:0% +nice matrices but we've seen for that + + + align:start position:0% +nice matrices but we've seen for that +110 01 Matrix that the I values didn't + + align:start position:0% +110 01 Matrix that the I values didn't + + + align:start position:0% +110 01 Matrix that the I values didn't +give a picture and the singular values + + align:start position:0% +give a picture and the singular values + + + align:start position:0% +give a picture and the singular values +do uh maybe one other nearest problem + + align:start position:0% +do uh maybe one other nearest problem + + + align:start position:0% +do uh maybe one other nearest problem +occurs to me that that might be relevant + + align:start position:0% +occurs to me that that might be relevant + + + align:start position:0% +occurs to me that that might be relevant +so this I'll just describe the problem + + align:start position:0% +so this I'll just describe the problem + + + align:start position:0% +so this I'll just describe the problem +suppose I'm changing coordinate systems + + align:start position:0% +suppose I'm changing coordinate systems + + + align:start position:0% +suppose I'm changing coordinate systems +so I have a I have a like an earth-based + + align:start position:0% +so I have a I have a like an earth-based + + + align:start position:0% +so I have a I have a like an earth-based +system in which I'm doing measurements + + align:start position:0% +system in which I'm doing measurements + + + align:start position:0% +system in which I'm doing measurements +and then I have uh a uh space based + + align:start position:0% +and then I have uh a uh space based + + + align:start position:0% +and then I have uh a uh space based +system in which I'm doing + + align:start position:0% +system in which I'm doing + + + align:start position:0% +system in which I'm doing +measurements and I would like to convert + + align:start position:0% +measurements and I would like to convert + + + align:start position:0% +measurements and I would like to convert +but I don't maybe + + align:start position:0% +but I don't maybe + + + align:start position:0% +but I don't maybe +know um maybe I okay maybe here's a way + + align:start position:0% +know um maybe I okay maybe here's a way + + + align:start position:0% +know um maybe I okay maybe here's a way +to say it suppose I'm measuring the same + + align:start position:0% +to say it suppose I'm measuring the same + + + align:start position:0% +to say it suppose I'm measuring the same +thing so I I know I know what it looks + + align:start position:0% +thing so I I know I know what it looks + + + align:start position:0% +thing so I I know I know what it looks +like in the earth-based system and I + + align:start position:0% +like in the earth-based system and I + + + align:start position:0% +like in the earth-based system and I +know what it looks like in the space + + align:start position:0% +know what it looks like in the space + + + align:start position:0% +know what it looks like in the space +based system and what I'm trying to + + align:start position:0% +based system and what I'm trying to + + + align:start position:0% +based system and what I'm trying to +figure out is what was the rotation of + + align:start position:0% +figure out is what was the rotation of + + + align:start position:0% +figure out is what was the rotation of +coordinates that connected those two + + align:start position:0% +coordinates that connected those two + + + align:start position:0% +coordinates that connected those two +systems I shall I describe that problem + + align:start position:0% +systems I shall I describe that problem + + + align:start position:0% +systems I shall I describe that problem +again just just as a so I'm I'm I'm I'm + + align:start position:0% +again just just as a so I'm I'm I'm I'm + + + align:start position:0% +again just just as a so I'm I'm I'm I'm +hunting for the rotation now I I'm given + + align:start position:0% +hunting for the rotation now I I'm given + + + align:start position:0% +hunting for the rotation now I I'm given +vectors the same Vector measure you know + + align:start position:0% +vectors the same Vector measure you know + + + align:start position:0% +vectors the same Vector measure you know +with its coordinates in one system and + + align:start position:0% +with its coordinates in one system and + + + align:start position:0% +with its coordinates in one system and +its coordinates in a second system and + + align:start position:0% +its coordinates in a second system and + + + align:start position:0% +its coordinates in a second system and +I'm wondering okay how are those systems + + align:start position:0% +I'm wondering okay how are those systems + + + align:start position:0% +I'm wondering okay how are those systems +connected how if if so I'm given like I + + align:start position:0% +connected how if if so I'm given like I + + + align:start position:0% +connected how if if so I'm given like I +probably better be given three + + align:start position:0% + + + + align:start position:0% + +vectors and so like of course I'll put + + align:start position:0% +vectors and so like of course I'll put + + + align:start position:0% +vectors and so like of course I'll put +them in a little Matrix so I'm given a + + align:start position:0% +them in a little Matrix so I'm given a + + + align:start position:0% +them in a little Matrix so I'm given a +3X3 Matrix three vectors earth based and + + align:start position:0% +3X3 Matrix three vectors earth based and + + + align:start position:0% +3X3 Matrix three vectors earth based and +I'm given three vectors the same three + + align:start position:0% +I'm given three vectors the same three + + + align:start position:0% +I'm given three vectors the same three +vector vectors space + + align:start position:0% +vector vectors space + + + align:start position:0% +vector vectors space +based and I know that if I did the + + align:start position:0% +based and I know that if I did the + + + align:start position:0% +based and I know that if I did the +measurements exactly there's some + + align:start position:0% +measurements exactly there's some + + + align:start position:0% +measurements exactly there's some +rotation and of course I'm going to call + + align:start position:0% +rotation and of course I'm going to call + + + align:start position:0% +rotation and of course I'm going to call +that thing + + align:start position:0% +that thing + + + align:start position:0% +that thing +Q so that these those go to that but if + + align:start position:0% +Q so that these those go to that but if + + + align:start position:0% +Q so that these those go to that but if +I didn't do them + + align:start position:0% +I didn't do them + + + align:start position:0% +I didn't do them +exactly I mean I could see since that's + + align:start position:0% +exactly I mean I could see since that's + + + align:start position:0% +exactly I mean I could see since that's +supposed to be an orthogonal Matrix if + + align:start position:0% +supposed to be an orthogonal Matrix if + + + align:start position:0% +supposed to be an orthogonal Matrix if +this inverse times that isn't orthogonal + + align:start position:0% +this inverse times that isn't orthogonal + + + align:start position:0% +this inverse times that isn't orthogonal +then I didn't do them exactly which I + + align:start position:0% +then I didn't do them exactly which I + + + align:start position:0% +then I didn't do them exactly which I +probably didn't so what's the best Q + + align:start position:0% +probably didn't so what's the best Q + + + align:start position:0% +probably didn't so what's the best Q +that's that's another kind of problem + + align:start position:0% +that's that's another kind of problem + + + align:start position:0% +that's that's another kind of problem +that this singular value decomposition + + align:start position:0% +that this singular value decomposition + + + align:start position:0% +that this singular value decomposition +solves um you see what that question was + + align:start position:0% +solves um you see what that question was + + + align:start position:0% +solves um you see what that question was +I I I'm happy to get email about it and + + align:start position:0% +I I I'm happy to get email about it and + + + align:start position:0% +I I I'm happy to get email about it and +return to it but let me say say What's + + align:start position:0% +return to it but let me say say What's + + + align:start position:0% +return to it but let me say say What's +the answer the answer will lie in the U + + align:start position:0% +the answer the answer will lie in the U + + + align:start position:0% +the answer the answer will lie in the U +and the + + align:start position:0% +and the + + + align:start position:0% +and the +V for for our previous question the + + align:start position:0% +V for for our previous question the + + + align:start position:0% +V for for our previous question the +answer lay in the sigmas but now we're + + align:start position:0% +answer lay in the sigmas but now we're + + + align:start position:0% +answer lay in the sigmas but now we're +looking for a for an orthogonal Matrix + + align:start position:0% +looking for a for an orthogonal Matrix + + + align:start position:0% +looking for a for an orthogonal Matrix +and somewhere in the U and the V is that + + align:start position:0% +and somewhere in the U and the V is that + + + align:start position:0% +and somewhere in the U and the V is that +um so it's I would take the inverse of + + align:start position:0% +um so it's I would take the inverse of + + + align:start position:0% +um so it's I would take the inverse of +that times + + align:start position:0% +that times + + + align:start position:0% +that times +that that should be orthogonal if I was + + align:start position:0% +that that should be orthogonal if I was + + + align:start position:0% +that that should be orthogonal if I was +doing it perfectly I would do its SVD + + align:start position:0% +doing it perfectly I would do its SVD + + + align:start position:0% +doing it perfectly I would do its SVD +and the U and the V there would give me + + align:start position:0% +and the U and the V there would give me + + + align:start position:0% +and the U and the V there would give me +the best Q so this is the kind of + + align:start position:0% +the best Q so this is the kind of + + + align:start position:0% +the best Q so this is the kind of +question that the singular value + + align:start position:0% +question that the singular value + + + align:start position:0% +question that the singular value +decomposition is just perfect for it + + align:start position:0% +decomposition is just perfect for it + + + align:start position:0% +decomposition is just perfect for it +measures the size of matrices it finds + + align:start position:0% +measures the size of matrices it finds + + + align:start position:0% +measures the size of matrices it finds +the nearest singular mat Matrix the + + align:start position:0% +the nearest singular mat Matrix the + + + align:start position:0% +the nearest singular mat Matrix the +nearest orthogonal + + align:start position:0% +nearest orthogonal + + + align:start position:0% +nearest orthogonal +Matrix uh all these uh sort of + + align:start position:0% +Matrix uh all these uh sort of + + + align:start position:0% +Matrix uh all these uh sort of +optimization with Matrix + + align:start position:0% +optimization with Matrix + + + align:start position:0% +optimization with Matrix +questions okay so that's the + + align:start position:0% +questions okay so that's the + + + align:start position:0% +questions okay so that's the +SVD + + align:start position:0% +SVD + + + align:start position:0% +SVD +um sort of maybe I could say put to use + + align:start position:0% +um sort of maybe I could say put to use + + + align:start position:0% +um sort of maybe I could say put to use +rather than um proved I didn't uh prove + + align:start position:0% +rather than um proved I didn't uh prove + + + align:start position:0% +rather than um proved I didn't uh prove +this this it's interesting that the + + align:start position:0% +this this it's interesting that the + + + align:start position:0% +this this it's interesting that the +people who found this factorization at + + align:start position:0% +people who found this factorization at + + + align:start position:0% +people who found this factorization at +goes back to the 1870s approxim about + + align:start position:0% +goes back to the 1870s approxim about + + + align:start position:0% +goes back to the 1870s approxim about +1870 but uh somehow + + align:start position:0% +1870 but uh somehow + + + align:start position:0% +1870 but uh somehow +for for many many years it wasn't + + align:start position:0% +for for many many years it wasn't + + + align:start position:0% +for for many many years it wasn't +recognized how important that was uh and + + align:start position:0% +recognized how important that was uh and + + + align:start position:0% +recognized how important that was uh and +uh but now it now it's increasingly + + align:start position:0% +uh but now it now it's increasingly + + + align:start position:0% +uh but now it now it's increasingly +recognized as as + + align:start position:0% +recognized as as + + + align:start position:0% +recognized as as +the the key factorization which actually + + align:start position:0% +the the key factorization which actually + + + align:start position:0% +the the key factorization which actually +allows you to get lots of + + align:start position:0% +allows you to get lots of + + + align:start position:0% +allows you to get lots of +others okay for + + align:start position:0% +others okay for + + + align:start position:0% +others okay for +today all right thanks than uh \ No newline at end of file diff --git a/zH76mIS0ARs.txt b/zH76mIS0ARs.txt new file mode 100644 index 0000000000000000000000000000000000000000..48b7b6d2d9a1cb12dea72b8a1e4571202fa3043e --- /dev/null +++ b/zH76mIS0ARs.txt @@ -0,0 +1,1355 @@ +align:start position:0% + +hello and welcome to this short video on + + align:start position:0% +hello and welcome to this short video on + + + align:start position:0% +hello and welcome to this short video on +more circles the goal of this video is + + align:start position:0% +more circles the goal of this video is + + + align:start position:0% +more circles the goal of this video is +to show you how most circle works how + + align:start position:0% +to show you how most circle works how + + + align:start position:0% +to show you how most circle works how +they could be useful for you and to make + + align:start position:0% +they could be useful for you and to make + + + align:start position:0% +they could be useful for you and to make +some interesting observations as well + + align:start position:0% +some interesting observations as well + + + align:start position:0% +some interesting observations as well +so first of all most circles is a + + align:start position:0% +so first of all most circles is a + + + align:start position:0% +so first of all most circles is a +graphical way to find the principal + + align:start position:0% +graphical way to find the principal + + + align:start position:0% +graphical way to find the principal +normal stresses and the maximum shear + + align:start position:0% +normal stresses and the maximum shear + + + align:start position:0% +normal stresses and the maximum shear +stress of a given stress state which + + align:start position:0% +stress of a given stress state which + + + align:start position:0% +stress of a given stress state which +could be the one right here where you + + align:start position:0% +could be the one right here where you + + + align:start position:0% +could be the one right here where you +have some normal forces acting on sigma + + align:start position:0% +have some normal forces acting on sigma + + + align:start position:0% +have some normal forces acting on sigma +x y&z and also some different shear + + align:start position:0% +x y&z and also some different shear + + + align:start position:0% +x y&z and also some different shear +stresses the house this stress state + + align:start position:0% +stresses the house this stress state + + + align:start position:0% +stresses the house this stress state +could also be shown using a tensor first + + align:start position:0% +could also be shown using a tensor first + + + align:start position:0% +could also be shown using a tensor first +answer which is shown over here but this + + align:start position:0% +answer which is shown over here but this + + + align:start position:0% +answer which is shown over here but this +symmetric paper three matrix it has to + + align:start position:0% +symmetric paper three matrix it has to + + + align:start position:0% +symmetric paper three matrix it has to +be symmetric because we don't want to + + align:start position:0% +be symmetric because we don't want to + + + align:start position:0% +be symmetric because we don't want to +have any moment acting on our stress + + align:start position:0% +have any moment acting on our stress + + + align:start position:0% +have any moment acting on our stress +element to prevent any rotation and also + + align:start position:0% +element to prevent any rotation and also + + + align:start position:0% +element to prevent any rotation and also +of course we're using an isotropic + + align:start position:0% +of course we're using an isotropic + + + align:start position:0% +of course we're using an isotropic +material so I'm gonna start with the 2d + + align:start position:0% +material so I'm gonna start with the 2d + + + align:start position:0% +material so I'm gonna start with the 2d +mozuku simple stone so now obviously my + + align:start position:0% +mozuku simple stone so now obviously my + + + align:start position:0% +mozuku simple stone so now obviously my +stress element is squared + + align:start position:0% +stress element is squared + + + align:start position:0% +stress element is squared +I have a Sigma X and Sigma Y has no more + + align:start position:0% +I have a Sigma X and Sigma Y has no more + + + align:start position:0% +I have a Sigma X and Sigma Y has no more +forces acting on it and the shear stress + + align:start position:0% + + + + align:start position:0% + +tau X Y so now let's move to the most of + + align:start position:0% +tau X Y so now let's move to the most of + + + align:start position:0% +tau X Y so now let's move to the most of +the week itself and I'll explain you how + + align:start position:0% +the week itself and I'll explain you how + + + align:start position:0% +the week itself and I'll explain you how +to draw it so first of all I have to put + + align:start position:0% +to draw it so first of all I have to put + + + align:start position:0% +to draw it so first of all I have to put +my two stresses on my qualified here I + + align:start position:0% +my two stresses on my qualified here I + + + align:start position:0% +my two stresses on my qualified here I +have normal ax right here and she axis + + align:start position:0% +have normal ax right here and she axis + + + align:start position:0% +have normal ax right here and she axis +with you so I'm gonna take Sigma X which + + align:start position:0% +with you so I'm gonna take Sigma X which + + + align:start position:0% +with you so I'm gonna take Sigma X which +is stated here and tau X Y which is + + align:start position:0% +is stated here and tau X Y which is + + + align:start position:0% +is stated here and tau X Y which is +gonna give me my first point right here + + align:start position:0% +gonna give me my first point right here + + + align:start position:0% +gonna give me my first point right here +and then Sigma Y and tau YX which is the + + align:start position:0% +and then Sigma Y and tau YX which is the + + + align:start position:0% +and then Sigma Y and tau YX which is the +opposite of tau XY and this is gonna + + align:start position:0% +opposite of tau XY and this is gonna + + + align:start position:0% +opposite of tau XY and this is gonna +give me my second party now I'm gonna + + align:start position:0% +give me my second party now I'm gonna + + + align:start position:0% +give me my second party now I'm gonna +say that this is the diameter of my more + + align:start position:0% +say that this is the diameter of my more + + + align:start position:0% +say that this is the diameter of my more +circle and this allows me to do the + + align:start position:0% +circle and this allows me to do the + + + align:start position:0% +circle and this allows me to do the +other more circle right here as you can + + align:start position:0% +other more circle right here as you can + + + align:start position:0% +other more circle right here as you can +see now I see that this small circle + + align:start position:0% +see now I see that this small circle + + + align:start position:0% +see now I see that this small circle +causes the normal acts on two points to + + align:start position:0% +causes the normal acts on two points to + + + align:start position:0% +causes the normal acts on two points to +win points that you see right here and + + align:start position:0% +win points that you see right here and + + + align:start position:0% +win points that you see right here and +the these are my principle normal + + align:start position:0% +the these are my principle normal + + + align:start position:0% +the these are my principle normal +stresses acting on my stress element and + + align:start position:0% +stresses acting on my stress element and + + + align:start position:0% +stresses acting on my stress element and +I can actually also get from the most + + align:start position:0% +I can actually also get from the most + + + align:start position:0% +I can actually also get from the most +recalled the angle how much I have to + + align:start position:0% +recalled the angle how much I have to + + + align:start position:0% +recalled the angle how much I have to +turn my stress element to get this + + align:start position:0% +turn my stress element to get this + + + align:start position:0% +turn my stress element to get this +principle normal stresses and it's + + align:start position:0% +principle normal stresses and it's + + + align:start position:0% +principle normal stresses and it's +important to remember that the angle I + + align:start position:0% +important to remember that the angle I + + + align:start position:0% +important to remember that the angle I +see on the Mohr circle so this angle + + align:start position:0% +see on the Mohr circle so this angle + + + align:start position:0% +see on the Mohr circle so this angle +here actually twice the wheel I know I + + align:start position:0% +here actually twice the wheel I know I + + + align:start position:0% +here actually twice the wheel I know I +have to turn my specimen by which is + + align:start position:0% +have to turn my specimen by which is + + + align:start position:0% +have to turn my specimen by which is +shown well here and then I have a blue + + align:start position:0% +shown well here and then I have a blue + + + align:start position:0% +shown well here and then I have a blue +point here which is my maximum shear + + align:start position:0% +point here which is my maximum shear + + + align:start position:0% +point here which is my maximum shear +stress so the maximal Schuster's as you + + align:start position:0% +stress so the maximal Schuster's as you + + + align:start position:0% +stress so the maximal Schuster's as you +can see his wages of my circle and again + + align:start position:0% +can see his wages of my circle and again + + + align:start position:0% +can see his wages of my circle and again +I have an angle of maximum shear stress + + align:start position:0% +I have an angle of maximum shear stress + + + align:start position:0% +I have an angle of maximum shear stress +which is disparity and again the angle + + align:start position:0% +which is disparity and again the angle + + + align:start position:0% +which is disparity and again the angle +my Mohr circle is twice the wheel and + + align:start position:0% +my Mohr circle is twice the wheel and + + + align:start position:0% +my Mohr circle is twice the wheel and +now some interesting observations we can + + align:start position:0% +now some interesting observations we can + + + align:start position:0% +now some interesting observations we can +do right here is that even if I don't + + align:start position:0% +do right here is that even if I don't + + + align:start position:0% +do right here is that even if I don't +apply any shear stress to my stress + + align:start position:0% +apply any shear stress to my stress + + + align:start position:0% +apply any shear stress to my stress +element I will still have some maximum + + align:start position:0% +element I will still have some maximum + + + align:start position:0% +element I will still have some maximum +shear stress and as you can see the + + align:start position:0% +shear stress and as you can see the + + + align:start position:0% +shear stress and as you can see the +angle of maximum shear stress is well + + align:start position:0% +angle of maximum shear stress is well + + + align:start position:0% +angle of maximum shear stress is well +ninety degree on my Mohr circle but in + + align:start position:0% +ninety degree on my Mohr circle but in + + + align:start position:0% +ninety degree on my Mohr circle but in +reality 45 degrees and as you probably + + align:start position:0% +reality 45 degrees and as you probably + + + align:start position:0% +reality 45 degrees and as you probably +already know if I'm doing for example + + align:start position:0% +already know if I'm doing for example + + + align:start position:0% +already know if I'm doing for example +tensile stress then my maximum shear + + align:start position:0% +tensile stress then my maximum shear + + + align:start position:0% +tensile stress then my maximum shear +stress is gonna be on a 45 degrees thing + + align:start position:0% +stress is gonna be on a 45 degrees thing + + + align:start position:0% +stress is gonna be on a 45 degrees thing +now the only way to avoid having any + + align:start position:0% +now the only way to avoid having any + + + align:start position:0% +now the only way to avoid having any +shear stresses stress element is + + align:start position:0% +shear stresses stress element is + + + align:start position:0% +shear stresses stress element is +actually to have Sigma X being equal to + + align:start position:0% +actually to have Sigma X being equal to + + + align:start position:0% +actually to have Sigma X being equal to +Sigma Y and that's the only way I can + + align:start position:0% +Sigma Y and that's the only way I can + + + align:start position:0% +Sigma Y and that's the only way I can +avoid any shear stresses + + align:start position:0% +avoid any shear stresses + + + align:start position:0% +avoid any shear stresses +now the other way to get my principal + + align:start position:0% +now the other way to get my principal + + + align:start position:0% +now the other way to get my principal +stresses would be to get the eigenvalues + + align:start position:0% +stresses would be to get the eigenvalues + + + align:start position:0% +stresses would be to get the eigenvalues +of my two-by-two stress tensor and + + align:start position:0% +of my two-by-two stress tensor and + + + align:start position:0% +of my two-by-two stress tensor and +that's what we're gonna see later for + + align:start position:0% +that's what we're gonna see later for + + + align:start position:0% +that's what we're gonna see later for +the three keys so in 3d now what I have + + align:start position:0% +the three keys so in 3d now what I have + + + align:start position:0% +the three keys so in 3d now what I have +to do is get this principal normal + + align:start position:0% +to do is get this principal normal + + + align:start position:0% +to do is get this principal normal +stresses by as I've told you find the + + align:start position:0% +stresses by as I've told you find the + + + align:start position:0% +stresses by as I've told you find the +eigenvalues of my stress tensor which is + + align:start position:0% +eigenvalues of my stress tensor which is + + + align:start position:0% +eigenvalues of my stress tensor which is +right here that's the random one I've + + align:start position:0% +right here that's the random one I've + + + align:start position:0% +right here that's the random one I've +I've chosen it's symmetric as I've + + align:start position:0% +I've chosen it's symmetric as I've + + + align:start position:0% +I've chosen it's symmetric as I've +explained to me in the beginning and + + align:start position:0% +explained to me in the beginning and + + + align:start position:0% +explained to me in the beginning and +finding the eigenvalues gives me a + + align:start position:0% +finding the eigenvalues gives me a + + + align:start position:0% +finding the eigenvalues gives me a +reaction my actual principal normal + + align:start position:0% +reaction my actual principal normal + + + align:start position:0% +reaction my actual principal normal +stress is Sigma 1 Sigma 2 and Sigma 3 so + + align:start position:0% +stress is Sigma 1 Sigma 2 and Sigma 3 so + + + align:start position:0% +stress is Sigma 1 Sigma 2 and Sigma 3 so +now let's move to the 3d Mohr circles so + + align:start position:0% +now let's move to the 3d Mohr circles so + + + align:start position:0% +now let's move to the 3d Mohr circles so +it's same principle but now I have three + + align:start position:0% +it's same principle but now I have three + + + align:start position:0% +it's same principle but now I have three +principal sources instead of two so I + + align:start position:0% +principal sources instead of two so I + + + align:start position:0% +principal sources instead of two so I +also have three most of codes instead of + + align:start position:0% +also have three most of codes instead of + + + align:start position:0% +also have three most of codes instead of +one because I have one more circle + + align:start position:0% +one because I have one more circle + + + align:start position:0% +one because I have one more circle +between Sigma 1 and Sigma 2 another Mohr + + align:start position:0% +between Sigma 1 and Sigma 2 another Mohr + + + align:start position:0% +between Sigma 1 and Sigma 2 another Mohr +circle between Sigma 2 and Sigma 3 and a + + align:start position:0% +circle between Sigma 2 and Sigma 3 and a + + + align:start position:0% +circle between Sigma 2 and Sigma 3 and a +bigger one between Sigma 1 and Sigma 3 + + align:start position:0% +bigger one between Sigma 1 and Sigma 3 + + + align:start position:0% +bigger one between Sigma 1 and Sigma 3 +so now the orange zone right here same + + align:start position:0% +so now the orange zone right here same + + + align:start position:0% +so now the orange zone right here same +at the bottom is the allowed pairs of + + align:start position:0% +at the bottom is the allowed pairs of + + + align:start position:0% +at the bottom is the allowed pairs of +stresses Sigma n the principal normal + + align:start position:0% +stresses Sigma n the principal normal + + + align:start position:0% +stresses Sigma n the principal normal +force and tau which is my measure force + + align:start position:0% +force and tau which is my measure force + + + align:start position:0% +force and tau which is my measure force +and the only large pairs of normal and + + align:start position:0% +and the only large pairs of normal and + + + align:start position:0% +and the only large pairs of normal and +shear stresses are in this two orange + + align:start position:0% +shear stresses are in this two orange + + + align:start position:0% +shear stresses are in this two orange +zones because it has to be inside the + + align:start position:0% +zones because it has to be inside the + + + align:start position:0% +zones because it has to be inside the +bigger circle and outside of the two + + align:start position:0% +bigger circle and outside of the two + + + align:start position:0% +bigger circle and outside of the two +small circles now the variation we can + + align:start position:0% +small circles now the variation we can + + + align:start position:0% +small circles now the variation we can +do here is that the first of all the + + align:start position:0% +do here is that the first of all the + + + align:start position:0% +do here is that the first of all the +maximum maximum shear stress only + + align:start position:0% +maximum maximum shear stress only + + + align:start position:0% +maximum maximum shear stress only +depends on the difference between the + + align:start position:0% +depends on the difference between the + + + align:start position:0% +depends on the difference between the +smallest and the largest principal + + align:start position:0% +smallest and the largest principal + + + align:start position:0% +smallest and the largest principal +stresses so as you can see if I move my + + align:start position:0% +stresses so as you can see if I move my + + + align:start position:0% +stresses so as you can see if I move my +Sigma 2 which is + + align:start position:0% +Sigma 2 which is + + + align:start position:0% +Sigma 2 which is +Miller won all my maximum shear stress + + align:start position:0% +Miller won all my maximum shear stress + + + align:start position:0% +Miller won all my maximum shear stress +doesn't change at all and the other + + align:start position:0% +doesn't change at all and the other + + + align:start position:0% +doesn't change at all and the other +observation we can make is that if I + + align:start position:0% + + + + align:start position:0% + +equal Sigma three to zero as it is right + + align:start position:0% +equal Sigma three to zero as it is right + + + align:start position:0% +equal Sigma three to zero as it is right +now and this would is the same actually + + align:start position:0% +now and this would is the same actually + + + align:start position:0% +now and this would is the same actually +almost the same if we look in 3d as the + + align:start position:0% +almost the same if we look in 3d as the + + + align:start position:0% +almost the same if we look in 3d as the +example absolutely before but actually + + align:start position:0% +example absolutely before but actually + + + align:start position:0% +example absolutely before but actually +the fact that I'm now in 3d and that I + + align:start position:0% +the fact that I'm now in 3d and that I + + + align:start position:0% +the fact that I'm now in 3d and that I +even if I turn a tiny force on there + + align:start position:0% +even if I turn a tiny force on there + + + align:start position:0% +even if I turn a tiny force on there +that access any normal force well this + + align:start position:0% +that access any normal force well this + + + align:start position:0% +that access any normal force well this +still has an influence on the maximum + + align:start position:0% +still has an influence on the maximum + + + align:start position:0% +still has an influence on the maximum +shear stress because in 2d my mass + + align:start position:0% +shear stress because in 2d my mass + + + align:start position:0% +shear stress because in 2d my mass +consciousness would lie right here at + + align:start position:0% +consciousness would lie right here at + + + align:start position:0% +consciousness would lie right here at +the top of the first gray Mohr circle + + align:start position:0% +the top of the first gray Mohr circle + + + align:start position:0% +the top of the first gray Mohr circle +but now because I'm in 3d my my sisterís + + align:start position:0% +but now because I'm in 3d my my sisterís + + + align:start position:0% +but now because I'm in 3d my my sisterís +actually bit higher and now they + + align:start position:0% +actually bit higher and now they + + + align:start position:0% +actually bit higher and now they +actually another way to get this + + align:start position:0% +actually another way to get this + + + align:start position:0% +actually another way to get this +principle normal stresses yielding more + + align:start position:0% +principle normal stresses yielding more + + + align:start position:0% +principle normal stresses yielding more +circles so instead of as I've done it + + align:start position:0% +circles so instead of as I've done it + + + align:start position:0% +circles so instead of as I've done it +here get the values of my stress tensor + + align:start position:0% +here get the values of my stress tensor + + + align:start position:0% +here get the values of my stress tensor +I can actually use projections so I have + + align:start position:0% +I can actually use projections so I have + + + align:start position:0% +I can actually use projections so I have +my 3d stress tensor here and what I'm + + align:start position:0% +my 3d stress tensor here and what I'm + + + align:start position:0% +my 3d stress tensor here and what I'm +gonna do is project it on along my x y&z + + align:start position:0% +gonna do is project it on along my x y&z + + + align:start position:0% +gonna do is project it on along my x y&z +axis so that's for example projection on + + align:start position:0% +axis so that's for example projection on + + + align:start position:0% +axis so that's for example projection on +the z axis and what I get is a 2d stress + + align:start position:0% +the z axis and what I get is a 2d stress + + + align:start position:0% +the z axis and what I get is a 2d stress +tensor so doing this what I get again of + + align:start position:0% +tensor so doing this what I get again of + + + align:start position:0% +tensor so doing this what I get again of +course is my to the Mohr circle as we've + + align:start position:0% +course is my to the Mohr circle as we've + + + align:start position:0% +course is my to the Mohr circle as we've +seen in the beginning of this video and + + align:start position:0% +seen in the beginning of this video and + + + align:start position:0% +seen in the beginning of this video and +that's for example the projection along + + align:start position:0% +that's for example the projection along + + + align:start position:0% +that's for example the projection along +the x axis and I again get my principal + + align:start position:0% +the x axis and I again get my principal + + + align:start position:0% +the x axis and I again get my principal +normal stresses to green points and my + + align:start position:0% +normal stresses to green points and my + + + align:start position:0% +normal stresses to green points and my +maximum maximum thrust due poverty and + + align:start position:0% +maximum maximum thrust due poverty and + + + align:start position:0% +maximum maximum thrust due poverty and +what's more interesting is to see for + + align:start position:0% +what's more interesting is to see for + + + align:start position:0% +what's more interesting is to see for +example the the angle of principal + + align:start position:0% +example the the angle of principal + + + align:start position:0% +example the the angle of principal +stresses which is minus 19 a--they and + + align:start position:0% +stresses which is minus 19 a--they and + + + align:start position:0% +stresses which is minus 19 a--they and +to have the the angle between the red + + align:start position:0% +to have the the angle between the red + + + align:start position:0% +to have the the angle between the red +line here and normal access + + align:start position:0% +line here and normal access + + + align:start position:0% +line here and normal access +and doing three different projections + + align:start position:0% +and doing three different projections + + + align:start position:0% +and doing three different projections +along the x y&z axis I get three + + align:start position:0% +along the x y&z axis I get three + + + align:start position:0% +along the x y&z axis I get three +different angles so here that's another + + align:start position:0% +different angles so here that's another + + + align:start position:0% +different angles so here that's another +one and that's the third one + + align:start position:0% +one and that's the third one + + + align:start position:0% +one and that's the third one +and now if I actually try this angle so + + align:start position:0% +and now if I actually try this angle so + + + align:start position:0% +and now if I actually try this angle so +if I actually rotate my stress element + + align:start position:0% +if I actually rotate my stress element + + + align:start position:0% +if I actually rotate my stress element +by minus nineteen point nine five three + + align:start position:0% +by minus nineteen point nine five three + + + align:start position:0% +by minus nineteen point nine five three +nine degrees around the x axis are the + + align:start position:0% +nine degrees around the x axis are the + + + align:start position:0% +nine degrees around the x axis are the +same + + align:start position:0% +same + + + align:start position:0% +same +I want the y axis and the same again on + + align:start position:0% +I want the y axis and the same again on + + + align:start position:0% +I want the y axis and the same again on +the z axis then actually get my new last + + align:start position:0% +the z axis then actually get my new last + + + align:start position:0% +the z axis then actually get my new last +set of coordinates where my do I get my + + align:start position:0% +set of coordinates where my do I get my + + + align:start position:0% +set of coordinates where my do I get my +principle normal stresses on acting on + + align:start position:0% +principle normal stresses on acting on + + + align:start position:0% +principle normal stresses on acting on +my first element so I would get again + + align:start position:0% +my first element so I would get again + + + align:start position:0% +my first element so I would get again +these three values up here just by + + align:start position:0% +these three values up here just by + + + align:start position:0% +these three values up here just by +applying free rotation I've found by + + align:start position:0% +applying free rotation I've found by + + + align:start position:0% +applying free rotation I've found by +projecting by stress state on my three + + align:start position:0% +projecting by stress state on my three + + + align:start position:0% +projecting by stress state on my three +different axes so that's that's it I + + align:start position:0% +different axes so that's that's it I + + + align:start position:0% +different axes so that's that's it I +hope you enjoyed the video and actually + + align:start position:0% +hope you enjoyed the video and actually + + + align:start position:0% +hope you enjoyed the video and actually +learn something on more circles thanks + + align:start position:0% +learn something on more circles thanks + + + align:start position:0% +learn something on more circles thanks +for watching \ No newline at end of file diff --git a/zIXGgyOwtUk.txt b/zIXGgyOwtUk.txt new file mode 100644 index 0000000000000000000000000000000000000000..2093bbf6bb4a0a242ccb52da3eed399115e4f29a --- /dev/null +++ b/zIXGgyOwtUk.txt @@ -0,0 +1,7547 @@ +align:start position:0% + +So this lecture is going to be very + + align:start position:0% +So this lecture is going to be very + + + align:start position:0% +So this lecture is going to be very +dependent on on on the PowerPoint slides + + align:start position:0% +dependent on on on the PowerPoint slides + + + align:start position:0% +dependent on on on the PowerPoint slides +because if I take the time to draw these + + align:start position:0% +because if I take the time to draw these + + + align:start position:0% +because if I take the time to draw these +cycles on the board, we'd be here + + align:start position:0% +cycles on the board, we'd be here + + + align:start position:0% +cycles on the board, we'd be here +forever. So you're so I would say + + align:start position:0% +forever. So you're so I would say + + + align:start position:0% +forever. So you're so I would say +uh sit back and relax and uh because you + + align:start position:0% +uh sit back and relax and uh because you + + + align:start position:0% +uh sit back and relax and uh because you +have you have the slides, they're on the + + align:start position:0% +have you have the slides, they're on the + + + align:start position:0% +have you have the slides, they're on the +web and try to focus on what the the + + align:start position:0% +web and try to focus on what the the + + + align:start position:0% +web and try to focus on what the the +take-home message is. Um, + + align:start position:0% +take-home message is. Um, + + + align:start position:0% +take-home message is. Um, +okay. So, + + align:start position:0% +okay. So, + + + align:start position:0% +okay. So, +but before we go to biogeeochemical + + align:start position:0% +but before we go to biogeeochemical + + + align:start position:0% +but before we go to biogeeochemical +cycles, I want to just briefly review + + align:start position:0% +cycles, I want to just briefly review + + + align:start position:0% +cycles, I want to just briefly review +some of the things that we learned in + + align:start position:0% +some of the things that we learned in + + + align:start position:0% +some of the things that we learned in +the second lecture. I got feedback from + + align:start position:0% +the second lecture. I got feedback from + + + align:start position:0% +the second lecture. I got feedback from +some from some of you from many of you + + align:start position:0% +some from some of you from many of you + + + align:start position:0% +some from some of you from many of you +actually on the things that were + + align:start position:0% +actually on the things that were + + + align:start position:0% +actually on the things that were +difficult to understand and from that + + align:start position:0% +difficult to understand and from that + + + align:start position:0% +difficult to understand and from that +lecture and those are important uh for + + align:start position:0% +lecture and those are important uh for + + + align:start position:0% +lecture and those are important uh for +understanding these these cycles. And + + align:start position:0% +understanding these these cycles. And + + + align:start position:0% +understanding these these cycles. And +the one thing that uh some people were + + align:start position:0% +the one thing that uh some people were + + + align:start position:0% +the one thing that uh some people were +confused by was this anorobic + + align:start position:0% +confused by was this anorobic + + + align:start position:0% +confused by was this anorobic +respiration. Um remember I drew this on + + align:start position:0% +respiration. Um remember I drew this on + + + align:start position:0% +respiration. Um remember I drew this on +the board and I showed a lot of + + align:start position:0% +the board and I showed a lot of + + + align:start position:0% +the board and I showed a lot of +reduction reactions. Uh and I think that + + align:start position:0% +reduction reactions. Uh and I think that + + + align:start position:0% +reduction reactions. Uh and I think that +was confusing to some people. So let's + + align:start position:0% +was confusing to some people. So let's + + + align:start position:0% +was confusing to some people. So let's +just go over that very quickly. You've + + align:start position:0% +just go over that very quickly. You've + + + align:start position:0% +just go over that very quickly. You've +learned in Graham's lectures and in my + + align:start position:0% +learned in Graham's lectures and in my + + + align:start position:0% +learned in Graham's lectures and in my +lectures that that aerobic respiration + + align:start position:0% +lectures that that aerobic respiration + + + align:start position:0% +lectures that that aerobic respiration +respiration of organisms where there is + + align:start position:0% +respiration of organisms where there is + + + align:start position:0% +respiration of organisms where there is +oxygen that oxygen is the terminal + + align:start position:0% +oxygen that oxygen is the terminal + + + align:start position:0% +oxygen that oxygen is the terminal +electron acceptor here in that um + + align:start position:0% +electron acceptor here in that um + + + align:start position:0% +electron acceptor here in that um +electron transport chain and it's + + align:start position:0% +electron transport chain and it's + + + align:start position:0% +electron transport chain and it's +reduced to water. So in aerobic + + align:start position:0% +reduced to water. So in aerobic + + + align:start position:0% +reduced to water. So in aerobic +environments when organisms uh respire + + align:start position:0% +environments when organisms uh respire + + + align:start position:0% +environments when organisms uh respire +oxygen is reduced to water. If there's + + align:start position:0% +oxygen is reduced to water. If there's + + + align:start position:0% +oxygen is reduced to water. If there's +no oxygen around the organisms and in + + align:start position:0% +no oxygen around the organisms and in + + + align:start position:0% +no oxygen around the organisms and in +this case it's um always bacteria look + + align:start position:0% +this case it's um always bacteria look + + + align:start position:0% +this case it's um always bacteria look +for the next thermodynamically favorable + + align:start position:0% +for the next thermodynamically favorable + + + align:start position:0% +for the next thermodynamically favorable +electron acceptor and so that whatever + + align:start position:0% +electron acceptor and so that whatever + + + align:start position:0% +electron acceptor and so that whatever +is dominant in that environment and is + + align:start position:0% +is dominant in that environment and is + + + align:start position:0% +is dominant in that environment and is +most thermodynamically favorable they'll + + align:start position:0% +most thermodynamically favorable they'll + + + align:start position:0% +most thermodynamically favorable they'll +use. So these sulfate reducing organisms + + align:start position:0% +use. So these sulfate reducing organisms + + + align:start position:0% +use. So these sulfate reducing organisms +use sulfate and reduce it to H2S. + + align:start position:0% +use sulfate and reduce it to H2S. + + + align:start position:0% +use sulfate and reduce it to H2S. +uh denitrifying organisms use nitrate + + align:start position:0% +uh denitrifying organisms use nitrate + + + align:start position:0% +uh denitrifying organisms use nitrate +and reduce it to these forms of reduced + + align:start position:0% +and reduce it to these forms of reduced + + + align:start position:0% +and reduce it to these forms of reduced +nitrate or reduced nitrogen. And we + + align:start position:0% +nitrate or reduced nitrogen. And we + + + align:start position:0% +nitrate or reduced nitrogen. And we +talked about um iron bacteria that some + + align:start position:0% +talked about um iron bacteria that some + + + align:start position:0% +talked about um iron bacteria that some +bacteria can use Fe3 and reduce it to + + align:start position:0% +bacteria can use Fe3 and reduce it to + + + align:start position:0% +bacteria can use Fe3 and reduce it to +Fe+2, + + align:start position:0% +Fe+2, + + + align:start position:0% +Fe+2, +some can use manganesees, etc. + + align:start position:0% +some can use manganesees, etc. + + + align:start position:0% +some can use manganesees, etc. +Whatever's there and it's + + align:start position:0% +Whatever's there and it's + + + align:start position:0% +Whatever's there and it's +thermodynamically favorable they'll use. + + align:start position:0% +thermodynamically favorable they'll use. + + + align:start position:0% +thermodynamically favorable they'll use. +Okay, so that clarifies that. Some other + + align:start position:0% +Okay, so that clarifies that. Some other + + + align:start position:0% +Okay, so that clarifies that. Some other +people said, "You kept talking about + + align:start position:0% +people said, "You kept talking about + + + align:start position:0% +people said, "You kept talking about +symmetry. You kept talking about + + align:start position:0% +symmetry. You kept talking about + + + align:start position:0% +symmetry. You kept talking about +symmetry. I didn't see any symmetry." + + align:start position:0% +symmetry. I didn't see any symmetry." + + + align:start position:0% +symmetry. I didn't see any symmetry." +Uh, and in hindsight, I can understand + + align:start position:0% +Uh, and in hindsight, I can understand + + + align:start position:0% +Uh, and in hindsight, I can understand +why because I just threw that out and I + + align:start position:0% +why because I just threw that out and I + + + align:start position:0% +why because I just threw that out and I +didn't really point it out. So what I + + align:start position:0% +didn't really point it out. So what I + + + align:start position:0% +didn't really point it out. So what I +was talking about was as we went through + + align:start position:0% +was talking about was as we went through + + + align:start position:0% +was talking about was as we went through +these processes you see here these + + align:start position:0% +these processes you see here these + + + align:start position:0% +these processes you see here these +elements sulfate and nitrogen nitrate + + align:start position:0% +elements sulfate and nitrogen nitrate + + + align:start position:0% +elements sulfate and nitrogen nitrate +are being reduced and there are other + + align:start position:0% +are being reduced and there are other + + + align:start position:0% +are being reduced and there are other +don't forget that um there are other + + align:start position:0% +don't forget that um there are other + + + align:start position:0% +don't forget that um there are other +processes particularly chemosynthesis in + + align:start position:0% +processes particularly chemosynthesis in + + + align:start position:0% +processes particularly chemosynthesis in +which these reduced compounds here's H2S + + align:start position:0% +which these reduced compounds here's H2S + + + align:start position:0% +which these reduced compounds here's H2S +and ammonia are being oxidized. So + + align:start position:0% +and ammonia are being oxidized. So + + + align:start position:0% +and ammonia are being oxidized. So +that's the symmetry that I was talking + + align:start position:0% +that's the symmetry that I was talking + + + align:start position:0% +that's the symmetry that I was talking +about. And if you didn't have that, if + + align:start position:0% +about. And if you didn't have that, if + + + align:start position:0% +about. And if you didn't have that, if +all the organisms were reducing things, + + align:start position:0% +all the organisms were reducing things, + + + align:start position:0% +all the organisms were reducing things, +the whole system would run down. You + + align:start position:0% +the whole system would run down. You + + + align:start position:0% +the whole system would run down. You +have to have organisms that are also + + align:start position:0% +have to have organisms that are also + + + align:start position:0% +have to have organisms that are also +oxidizing things. And that's a key + + align:start position:0% +oxidizing things. And that's a key + + + align:start position:0% +oxidizing things. And that's a key +component of all of these bio or not all + + align:start position:0% +component of all of these bio or not all + + + align:start position:0% +component of all of these bio or not all +of the biogeeochemical cycles, but + + align:start position:0% +of the biogeeochemical cycles, but + + + align:start position:0% +of the biogeeochemical cycles, but +particularly the cycles of of uh + + align:start position:0% +particularly the cycles of of uh + + + align:start position:0% +particularly the cycles of of uh +nitrogen and sulfur, which have this + + align:start position:0% +nitrogen and sulfur, which have this + + + align:start position:0% +nitrogen and sulfur, which have this +redux chemistry. So that's the symmetry + + align:start position:0% +redux chemistry. So that's the symmetry + + + align:start position:0% +redux chemistry. So that's the symmetry +that I that I was talking about. + + align:start position:0% +that I that I was talking about. + + + align:start position:0% +that I that I was talking about. +Okay. Now, so let's talk about um how we + + align:start position:0% +Okay. Now, so let's talk about um how we + + + align:start position:0% +Okay. Now, so let's talk about um how we +think about biogeeochemical cycles. Um + + align:start position:0% +think about biogeeochemical cycles. Um + + + align:start position:0% +think about biogeeochemical cycles. Um +can can you see this slide in the back? + + align:start position:0% +can can you see this slide in the back? + + + align:start position:0% +can can you see this slide in the back? +Do I have to turn the lights off? That + + align:start position:0% +Do I have to turn the lights off? That + + + align:start position:0% +Do I have to turn the lights off? That +was a double question. Can you see the + + align:start position:0% +was a double question. Can you see the + + + align:start position:0% +was a double question. Can you see the +slide in the back? + + align:start position:0% +slide in the back? + + + align:start position:0% +slide in the back? +Yes. Okay. Um so so the way we let let + + align:start position:0% +Yes. Okay. Um so so the way we let let + + + align:start position:0% +Yes. Okay. Um so so the way we let let +let's just this is uh a generic map of + + align:start position:0% +let's just this is uh a generic map of + + + align:start position:0% +let's just this is uh a generic map of +of the components of biogeeochemical + + align:start position:0% +of the components of biogeeochemical + + + align:start position:0% +of the components of biogeeochemical +cycles and we can think of it the earth + + align:start position:0% +cycles and we can think of it the earth + + + align:start position:0% +cycles and we can think of it the earth +as a giant uh chemical factory in a + + align:start position:0% +as a giant uh chemical factory in a + + + align:start position:0% +as a giant uh chemical factory in a +sense that has what we call compartments + + align:start position:0% +sense that has what we call compartments + + + align:start position:0% +sense that has what we call compartments +or reservoirs or pools of a particular + + align:start position:0% +or reservoirs or pools of a particular + + + align:start position:0% +or reservoirs or pools of a particular +element or it might be water that we're + + align:start position:0% +element or it might be water that we're + + + align:start position:0% +element or it might be water that we're +analyzing and then there are fluxes + + align:start position:0% +analyzing and then there are fluxes + + + align:start position:0% +analyzing and then there are fluxes +between these pools. pools. So, here's a + + align:start position:0% +between these pools. pools. So, here's a + + + align:start position:0% +between these pools. pools. So, here's a +a flux, an arrow. So, typically these + + align:start position:0% +a flux, an arrow. So, typically these + + + align:start position:0% +a flux, an arrow. So, typically these +are diagrammed um with boxes and arrows + + align:start position:0% +are diagrammed um with boxes and arrows + + + align:start position:0% +are diagrammed um with boxes and arrows +connecting them. + + align:start position:0% +connecting them. + + + align:start position:0% +connecting them. +So, we have the and and you can you + + align:start position:0% +So, we have the and and you can you + + + align:start position:0% +So, we have the and and you can you +don't have to use all of these boxes. It + + align:start position:0% +don't have to use all of these boxes. It + + + align:start position:0% +don't have to use all of these boxes. It +could be we're just looking at land, + + align:start position:0% +could be we're just looking at land, + + + align:start position:0% +could be we're just looking at land, +atmosphere, and ocean. I mean, you you + + align:start position:0% +atmosphere, and ocean. I mean, you you + + + align:start position:0% +atmosphere, and ocean. I mean, you you +construct whatever model uh you want for + + align:start position:0% +construct whatever model uh you want for + + + align:start position:0% +construct whatever model uh you want for +these. And these are just some useful + + align:start position:0% +these. And these are just some useful + + + align:start position:0% +these. And these are just some useful +conversion factors um for the amounts of + + align:start position:0% +conversion factors um for the amounts of + + + align:start position:0% +conversion factors um for the amounts of +things that we're going to have flowing + + align:start position:0% +things that we're going to have flowing + + + align:start position:0% +things that we're going to have flowing +between these compartments. And here + + align:start position:0% +between these compartments. And here + + + align:start position:0% +between these compartments. And here +again, this is something we defined + + align:start position:0% +again, this is something we defined + + + align:start position:0% +again, this is something we defined +earlier when we were talking about um + + align:start position:0% +earlier when we were talking about um + + + align:start position:0% +earlier when we were talking about um +productivity. The mean resonance time of + + align:start position:0% +productivity. The mean resonance time of + + + align:start position:0% +productivity. The mean resonance time of +say an element say carbon um in the + + align:start position:0% +say an element say carbon um in the + + + align:start position:0% +say an element say carbon um in the +terrestrial biomass is the the pool size + + align:start position:0% +terrestrial biomass is the the pool size + + + align:start position:0% +terrestrial biomass is the the pool size +the the amount of carbon that's there + + align:start position:0% +the the amount of carbon that's there + + + align:start position:0% +the the amount of carbon that's there +divided by the mean flux in or out of + + align:start position:0% +divided by the mean flux in or out of + + + align:start position:0% +divided by the mean flux in or out of +that pool. Okay, it's exactly the same + + align:start position:0% +that pool. Okay, it's exactly the same + + + align:start position:0% +that pool. Okay, it's exactly the same +the concept we talked about for carbon. + + align:start position:0% +the concept we talked about for carbon. + + + align:start position:0% +the concept we talked about for carbon. +And then the fraction fractional + + align:start position:0% +And then the fraction fractional + + + align:start position:0% +And then the fraction fractional +turnover one over the mean resonance + + align:start position:0% +turnover one over the mean resonance + + + align:start position:0% +turnover one over the mean resonance +time is simply the fraction if we're + + align:start position:0% +time is simply the fraction if we're + + + align:start position:0% +time is simply the fraction if we're +talking about carbon again in in in + + align:start position:0% +talking about carbon again in in in + + + align:start position:0% +talking about carbon again in in in +trees, it's the fraction that's removed + + align:start position:0% +trees, it's the fraction that's removed + + + align:start position:0% +trees, it's the fraction that's removed +um per unit time. Okay. So + + align:start position:0% + + + + align:start position:0% + +um so you can see that when we talk + + align:start position:0% +um so you can see that when we talk + + + align:start position:0% +um so you can see that when we talk +about mean resonance time or of an + + align:start position:0% +about mean resonance time or of an + + + align:start position:0% +about mean resonance time or of an +element in these in these um in one of + + align:start position:0% +element in these in these um in one of + + + align:start position:0% +element in these in these um in one of +these reservoirs + + align:start position:0% +these reservoirs + + + align:start position:0% +these reservoirs +if the whole system is in steady state. + + align:start position:0% +if the whole system is in steady state. + + + align:start position:0% +if the whole system is in steady state. +In other words, if the amount in a + + align:start position:0% +In other words, if the amount in a + + + align:start position:0% +In other words, if the amount in a +reservoir isn't changing, the flux in is + + align:start position:0% +reservoir isn't changing, the flux in is + + + align:start position:0% +reservoir isn't changing, the flux in is +going to be the same as the flux out. + + align:start position:0% +going to be the same as the flux out. + + + align:start position:0% +going to be the same as the flux out. +Right? + + align:start position:0% +Right? + + + align:start position:0% +Right? +You know that just like a bathtub, if + + align:start position:0% +You know that just like a bathtub, if + + + align:start position:0% +You know that just like a bathtub, if +you have water flowing in, water flowing + + align:start position:0% +you have water flowing in, water flowing + + + align:start position:0% +you have water flowing in, water flowing +out, the level will stay the same if the + + align:start position:0% +out, the level will stay the same if the + + + align:start position:0% +out, the level will stay the same if the +flow rate in is the same as the flow + + align:start position:0% +flow rate in is the same as the flow + + + align:start position:0% +flow rate in is the same as the flow +rate out. But often in nature, you don't + + align:start position:0% +rate out. But often in nature, you don't + + + align:start position:0% +rate out. But often in nature, you don't +have that exactly. And and if you don't, + + align:start position:0% +have that exactly. And and if you don't, + + + align:start position:0% +have that exactly. And and if you don't, +the size of these reservoirs is e is + + align:start position:0% +the size of these reservoirs is e is + + + align:start position:0% +the size of these reservoirs is e is +either increasing or decreasing. So when + + align:start position:0% +either increasing or decreasing. So when + + + align:start position:0% +either increasing or decreasing. So when +you're analyzing these systems, you most + + align:start position:0% +you're analyzing these systems, you most + + + align:start position:0% +you're analyzing these systems, you most +of the time we're just trying to get a + + align:start position:0% +of the time we're just trying to get a + + + align:start position:0% +of the time we're just trying to get a +very rough estimate of mean residence + + align:start position:0% +very rough estimate of mean residence + + + align:start position:0% +very rough estimate of mean residence +time. So if the flow in and the flow out + + align:start position:0% +time. So if the flow in and the flow out + + + align:start position:0% +time. So if the flow in and the flow out +isn't the same, you can either average + + align:start position:0% +isn't the same, you can either average + + + align:start position:0% +isn't the same, you can either average +them and use that as your um flux or you + + align:start position:0% +them and use that as your um flux or you + + + align:start position:0% +them and use that as your um flux or you +can define your resonance time with + + align:start position:0% +can define your resonance time with + + + align:start position:0% +can define your resonance time with +respect to the flow in or the flow out. + + align:start position:0% +respect to the flow in or the flow out. + + + align:start position:0% +respect to the flow in or the flow out. +Okay, so these are just gross + + align:start position:0% +Okay, so these are just gross + + + align:start position:0% +Okay, so these are just gross +approximations. So we we want to + + align:start position:0% +approximations. So we we want to + + + align:start position:0% +approximations. So we we want to +understand is the resonance time + + align:start position:0% +understand is the resonance time + + + align:start position:0% +understand is the resonance time +thousands of years, millions of years, + + align:start position:0% +thousands of years, millions of years, + + + align:start position:0% +thousands of years, millions of years, +days, you know, uh rough rough + + align:start position:0% +days, you know, uh rough rough + + + align:start position:0% +days, you know, uh rough rough +approximation. + + align:start position:0% +approximation. + + + align:start position:0% +approximation. +And the other thing I want to say before + + align:start position:0% +And the other thing I want to say before + + + align:start position:0% +And the other thing I want to say before +we go on is that all of these cycles, + + align:start position:0% +we go on is that all of these cycles, + + + align:start position:0% +we go on is that all of these cycles, +we're going to talk about them element + + align:start position:0% +we're going to talk about them element + + + align:start position:0% +we're going to talk about them element +byelement, phosphorus, carbon, whatever, + + align:start position:0% +byelement, phosphorus, carbon, whatever, + + + align:start position:0% +byelement, phosphorus, carbon, whatever, +but they're all tightly coupled um in + + align:start position:0% +but they're all tightly coupled um in + + + align:start position:0% +but they're all tightly coupled um in +the system. And we'll we'll bring that + + align:start position:0% +the system. And we'll we'll bring that + + + align:start position:0% +the system. And we'll we'll bring that +up again later. + + align:start position:0% +up again later. + + + align:start position:0% +up again later. +Uh before we go on, uh let's just look + + align:start position:0% +Uh before we go on, uh let's just look + + + align:start position:0% +Uh before we go on, uh let's just look +at the the solar energy budget which is + + align:start position:0% +at the the solar energy budget which is + + + align:start position:0% +at the the solar energy budget which is +driving this whole um this whole system + + align:start position:0% +driving this whole um this whole system + + + align:start position:0% +driving this whole um this whole system +mostly. there's some geothermal energy + + align:start position:0% +mostly. there's some geothermal energy + + + align:start position:0% +mostly. there's some geothermal energy +energy from the the earth's um + + align:start position:0% +energy from the the earth's um + + + align:start position:0% +energy from the the earth's um +the the magma that is also driving uh + + align:start position:0% +the the magma that is also driving uh + + + align:start position:0% +the the magma that is also driving uh +biogeeochemical cycles but the solar + + align:start position:0% +biogeeochemical cycles but the solar + + + align:start position:0% +biogeeochemical cycles but the solar +energy is the is the primary driver and + + align:start position:0% +energy is the is the primary driver and + + + align:start position:0% +energy is the is the primary driver and +if you say that the the total energy + + align:start position:0% +if you say that the the total energy + + + align:start position:0% +if you say that the the total energy +from the sun is 100%. Um, it's that + + align:start position:0% +from the sun is 100%. Um, it's that + + + align:start position:0% +from the sun is 100%. Um, it's that +energy that's used in evaporation, in + + align:start position:0% +energy that's used in evaporation, in + + + align:start position:0% +energy that's used in evaporation, in +winds, and photosynthesis + + align:start position:0% +winds, and photosynthesis + + + align:start position:0% +winds, and photosynthesis +that is the important component driving + + align:start position:0% +that is the important component driving + + + align:start position:0% +that is the important component driving +the cycles. And you'll see that + + align:start position:0% +the cycles. And you'll see that + + + align:start position:0% +the cycles. And you'll see that +photosynthesis is a tiny fraction. The + + align:start position:0% +photosynthesis is a tiny fraction. The + + + align:start position:0% +photosynthesis is a tiny fraction. The +energy that plants harvest um is a tiny + + align:start position:0% +energy that plants harvest um is a tiny + + + align:start position:0% +energy that plants harvest um is a tiny +fraction of the total energy that is + + align:start position:0% +fraction of the total energy that is + + + align:start position:0% +fraction of the total energy that is +driving the Earth's system. And yet this + + align:start position:0% +driving the Earth's system. And yet this + + + align:start position:0% +driving the Earth's system. And yet this +photosynthesis which is the basis of the + + align:start position:0% +photosynthesis which is the basis of the + + + align:start position:0% +photosynthesis which is the basis of the +biosphere has an enormous effect on the + + align:start position:0% +biosphere has an enormous effect on the + + + align:start position:0% +biosphere has an enormous effect on the +conditions on earth. Um that's one of + + align:start position:0% +conditions on earth. Um that's one of + + + align:start position:0% +conditions on earth. Um that's one of +the an interesting nonlinearity of the + + align:start position:0% +the an interesting nonlinearity of the + + + align:start position:0% +the an interesting nonlinearity of the +system. Okay. So let's start with the + + align:start position:0% +system. Okay. So let's start with the + + + align:start position:0% +system. Okay. So let's start with the +geological cycle. Um which is the + + align:start position:0% +geological cycle. Um which is the + + + align:start position:0% +geological cycle. Um which is the +slowest moving. People don't even think + + align:start position:0% +slowest moving. People don't even think + + + align:start position:0% +slowest moving. People don't even think +of it as a cycle because while we're on + + align:start position:0% +of it as a cycle because while we're on + + + align:start position:0% +of it as a cycle because while we're on +Earth, we don't see rocks flying through + + align:start position:0% +Earth, we don't see rocks flying through + + + align:start position:0% +Earth, we don't see rocks flying through +uh well, some sometimes you see rocks, + + align:start position:0% +uh well, some sometimes you see rocks, + + + align:start position:0% +uh well, some sometimes you see rocks, +you know, landslide or whatever, but for + + align:start position:0% +you know, landslide or whatever, but for + + + align:start position:0% +you know, landslide or whatever, but for +the most part, you don't think of rocks, + + align:start position:0% +the most part, you don't think of rocks, + + + align:start position:0% +the most part, you don't think of rocks, +it's it's cycling. Uh but they do. And + + align:start position:0% +it's it's cycling. Uh but they do. And + + + align:start position:0% +it's it's cycling. Uh but they do. And +if they didn't, the system would would + + align:start position:0% +if they didn't, the system would would + + + align:start position:0% +if they didn't, the system would would +run down much faster than than it is. + + align:start position:0% +run down much faster than than it is. + + + align:start position:0% +run down much faster than than it is. +And we've all heard about plate + + align:start position:0% +And we've all heard about plate + + + align:start position:0% +And we've all heard about plate +tectonics that the surface of the earth + + align:start position:0% +tectonics that the surface of the earth + + + align:start position:0% +tectonics that the surface of the earth +uh is made up of these plates that are + + align:start position:0% +uh is made up of these plates that are + + + align:start position:0% +uh is made up of these plates that are +slowly shifting. And when they shift um + + align:start position:0% +slowly shifting. And when they shift um + + + align:start position:0% +slowly shifting. And when they shift um +you have earthquakes like we've had + + align:start position:0% +you have earthquakes like we've had + + + align:start position:0% +you have earthquakes like we've had +recently a lot of and and also you have + + align:start position:0% +recently a lot of and and also you have + + + align:start position:0% +recently a lot of and and also you have +uh volcanic eruptions that bring um + + align:start position:0% +uh volcanic eruptions that bring um + + + align:start position:0% +uh volcanic eruptions that bring um +material from the inside of the earth up + + align:start position:0% +material from the inside of the earth up + + + align:start position:0% +material from the inside of the earth up +to the surface and it overflows and + + align:start position:0% +to the surface and it overflows and + + + align:start position:0% +to the surface and it overflows and +that's part of this geological cycle. + + align:start position:0% +that's part of this geological cycle. + + + align:start position:0% +that's part of this geological cycle. +So, um, here's here's a really + + align:start position:0% +So, um, here's here's a really + + + align:start position:0% +So, um, here's here's a really +oversimplified when when the geology + + align:start position:0% +oversimplified when when the geology + + + align:start position:0% +oversimplified when when the geology +professor in our department saw this saw + + align:start position:0% +professor in our department saw this saw + + + align:start position:0% +professor in our department saw this saw +saw that I was showing this, he had a + + align:start position:0% +saw that I was showing this, he had a + + + align:start position:0% +saw that I was showing this, he had a +heart attack, uh, by how simplified it + + align:start position:0% +heart attack, uh, by how simplified it + + + align:start position:0% +heart attack, uh, by how simplified it +is. But, uh, it's just so you get the + + align:start position:0% +is. But, uh, it's just so you get the + + + align:start position:0% +is. But, uh, it's just so you get the +idea. When he started editing it, there + + align:start position:0% +idea. When he started editing it, there + + + align:start position:0% +idea. When he started editing it, there +were so many arrows you'd never you + + align:start position:0% +were so many arrows you'd never you + + + align:start position:0% +were so many arrows you'd never you +could never cope with that. So, uh, + + align:start position:0% +could never cope with that. So, uh, + + + align:start position:0% +could never cope with that. So, uh, +here's how you get the just get the + + align:start position:0% +here's how you get the just get the + + + align:start position:0% +here's how you get the just get the +idea. There's geothermal energy coming + + align:start position:0% +idea. There's geothermal energy coming + + + align:start position:0% +idea. There's geothermal energy coming +in u from the inner core of the earth uh + + align:start position:0% +in u from the inner core of the earth uh + + + align:start position:0% +in u from the inner core of the earth uh +where you have magma think volcanic + + align:start position:0% +where you have magma think volcanic + + + align:start position:0% +where you have magma think volcanic +eruption uh lava uh which ultimately + + align:start position:0% +eruption uh lava uh which ultimately + + + align:start position:0% +eruption uh lava uh which ultimately +becomes surface rocks and they're eroded + + align:start position:0% +becomes surface rocks and they're eroded + + + align:start position:0% +becomes surface rocks and they're eroded +by weathering by rain um and then + + align:start position:0% +by weathering by rain um and then + + + align:start position:0% +by weathering by rain um and then +elements from that go into the soils. + + align:start position:0% +elements from that go into the soils. + + + align:start position:0% +elements from that go into the soils. +Soils eventually become sedimentary + + align:start position:0% +Soils eventually become sedimentary + + + align:start position:0% +Soils eventually become sedimentary +rocks. We're talking over really really + + align:start position:0% +rocks. We're talking over really really + + + align:start position:0% +rocks. We're talking over really really +long time periods uh which become + + align:start position:0% +long time periods uh which become + + + align:start position:0% +long time periods uh which become +metamorphic rocks. Some of those are + + align:start position:0% +metamorphic rocks. Some of those are + + + align:start position:0% +metamorphic rocks. Some of those are +uplifted + + align:start position:0% +uplifted + + + align:start position:0% +uplifted +um and some of them are melted and + + align:start position:0% +um and some of them are melted and + + + align:start position:0% +um and some of them are melted and +become magma magma. But it but it is a + + align:start position:0% +become magma magma. But it but it is a + + + align:start position:0% +become magma magma. But it but it is a +cycle a very slow slow cycle. And in + + align:start position:0% +cycle a very slow slow cycle. And in + + + align:start position:0% +cycle a very slow slow cycle. And in +fact somewhere I read um 70 let's see + + align:start position:0% +fact somewhere I read um 70 let's see + + + align:start position:0% +fact somewhere I read um 70 let's see +yeah 70 this is you don't need to know + + align:start position:0% +yeah 70 this is you don't need to know + + + align:start position:0% +yeah 70 this is you don't need to know +this this is not a geology class but + + align:start position:0% +this this is not a geology class but + + + align:start position:0% +this this is not a geology class but +just so you have an idea 75% + + align:start position:0% +just so you have an idea 75% + + + align:start position:0% +just so you have an idea 75% +um of the rocks now on the surface of + + align:start position:0% +um of the rocks now on the surface of + + + align:start position:0% +um of the rocks now on the surface of +the earth have been uplifted. So it's + + align:start position:0% +the earth have been uplifted. So it's + + + align:start position:0% +the earth have been uplifted. So it's +almost like the earth is on average + + align:start position:0% +almost like the earth is on average + + + align:start position:0% +almost like the earth is on average +about maybe halfway through a its a + + align:start position:0% +about maybe halfway through a its a + + + align:start position:0% +about maybe halfway through a its a +cycle. Um + + align:start position:0% +cycle. Um + + + align:start position:0% +cycle. Um +so this this erosion here and weathering + + align:start position:0% +so this this erosion here and weathering + + + align:start position:0% +so this this erosion here and weathering +as we talked about last time is critical + + align:start position:0% +as we talked about last time is critical + + + align:start position:0% +as we talked about last time is critical +for uh making nutrients available to the + + align:start position:0% +for uh making nutrients available to the + + + align:start position:0% +for uh making nutrients available to the +biosphere. Um and the force of this + + align:start position:0% +biosphere. Um and the force of this + + + align:start position:0% +biosphere. Um and the force of this +weathering is is incredibly powerful. + + align:start position:0% +weathering is is incredibly powerful. + + + align:start position:0% +weathering is is incredibly powerful. +Um, once one number that I found in one + + align:start position:0% +Um, once one number that I found in one + + + align:start position:0% +Um, once one number that I found in one +textbook, um, + + align:start position:0% +textbook, um, + + + align:start position:0% +textbook, um, +is that and that I never knew before is + + align:start position:0% +is that and that I never knew before is + + + align:start position:0% +is that and that I never knew before is +that Niagara Falls is eroding at 3 feet + + align:start position:0% +that Niagara Falls is eroding at 3 feet + + + align:start position:0% +that Niagara Falls is eroding at 3 feet +per year. The the cusp of the falls from + + align:start position:0% +per year. The the cusp of the falls from + + + align:start position:0% +per year. The the cusp of the falls from +the water is moving back three feet per + + align:start position:0% +the water is moving back three feet per + + + align:start position:0% +the water is moving back three feet per +year. That's fast. Um + + align:start position:0% +year. That's fast. Um + + + align:start position:0% +year. That's fast. Um +another another little factoid uh when I + + align:start position:0% +another another little factoid uh when I + + + align:start position:0% +another another little factoid uh when I +gave this lecture one year stu students + + align:start position:0% +gave this lecture one year stu students + + + align:start position:0% +gave this lecture one year stu students +asked what what is going to burn out + + align:start position:0% +asked what what is going to burn out + + + align:start position:0% +asked what what is going to burn out +first on the earth the sun or the + + align:start position:0% +first on the earth the sun or the + + + align:start position:0% +first on the earth the sun or the +geothermal energy and of course I had no + + align:start position:0% +geothermal energy and of course I had no + + + align:start position:0% +geothermal energy and of course I had no +idea you know this is all going to be + + align:start position:0% +idea you know this is all going to be + + + align:start position:0% +idea you know this is all going to be +over someday um uh the earth is going to + + align:start position:0% +over someday um uh the earth is going to + + + align:start position:0% +over someday um uh the earth is going to +be history uh because without the sun + + align:start position:0% +be history uh because without the sun + + + align:start position:0% +be history uh because without the sun +and without the geothermal energy + + align:start position:0% +and without the geothermal energy + + + align:start position:0% +and without the geothermal energy +there's there's no source of of of + + align:start position:0% +there's there's no source of of of + + + align:start position:0% +there's there's no source of of of +energy and um so I went to my colleagues + + align:start position:0% +energy and um so I went to my colleagues + + + align:start position:0% +energy and um so I went to my colleagues +in this department earth atmosphere and + + align:start position:0% +in this department earth atmosphere and + + + align:start position:0% +in this department earth atmosphere and +planetary sciences and said which is + + align:start position:0% +planetary sciences and said which is + + + align:start position:0% +planetary sciences and said which is +going to burn out first and and they + + align:start position:0% +going to burn out first and and they + + + align:start position:0% +going to burn out first and and they +said roughly the same time and we have + + align:start position:0% +said roughly the same time and we have + + + align:start position:0% +said roughly the same time and we have +about two billion years so not to worry + + align:start position:0% +about two billion years so not to worry + + + align:start position:0% +about two billion years so not to worry +yet um but it is you know we are only + + align:start position:0% +yet um but it is you know we are only + + + align:start position:0% +yet um but it is you know we are only +here for a period of time okay so so + + align:start position:0% +here for a period of time okay so so + + + align:start position:0% +here for a period of time okay so so +that's the geological cycle now let's + + align:start position:0% +that's the geological cycle now let's + + + align:start position:0% +that's the geological cycle now let's +move on to the water cycle and then + + align:start position:0% +move on to the water cycle and then + + + align:start position:0% +move on to the water cycle and then +we're going to go through the element + + align:start position:0% +we're going to go through the element + + + align:start position:0% +we're going to go through the element +cycles um nitrogen, phosphorus and + + align:start position:0% +cycles um nitrogen, phosphorus and + + + align:start position:0% +cycles um nitrogen, phosphorus and +carbon but the water cycle is obviously + + align:start position:0% +carbon but the water cycle is obviously + + + align:start position:0% +carbon but the water cycle is obviously +very important in carrying those + + align:start position:0% +very important in carrying those + + + align:start position:0% +very important in carrying those +elements through their cycles and this + + align:start position:0% +elements through their cycles and this + + + align:start position:0% +elements through their cycles and this +cycle is actually fairly well understood + + align:start position:0% +cycle is actually fairly well understood + + + align:start position:0% +cycle is actually fairly well understood +um I say fairly because not all of these + + align:start position:0% +um I say fairly because not all of these + + + align:start position:0% +um I say fairly because not all of these +things are are when you're talking about + + align:start position:0% +things are are when you're talking about + + + align:start position:0% +things are are when you're talking about +global averages of things it's very + + align:start position:0% +global averages of things it's very + + + align:start position:0% +global averages of things it's very +difficult but but the weather service is + + align:start position:0% +difficult but but the weather service is + + + align:start position:0% +difficult but but the weather service is +very interested in the global water + + align:start position:0% +very interested in the global water + + + align:start position:0% +very interested in the global water +cycle um so there there's been a lot of + + align:start position:0% +cycle um so there there's been a lot of + + + align:start position:0% +cycle um so there there's been a lot of +uh study done And so we have uh in terms + + align:start position:0% +uh study done And so we have uh in terms + + + align:start position:0% +uh study done And so we have uh in terms +of reservoirs we have uh huge ground. So + + align:start position:0% +of reservoirs we have uh huge ground. So + + + align:start position:0% +of reservoirs we have uh huge ground. So +the the these numbers in black are the + + align:start position:0% +the the these numbers in black are the + + + align:start position:0% +the the these numbers in black are the +amounts of water in a reservoir and the + + align:start position:0% +amounts of water in a reservoir and the + + + align:start position:0% +amounts of water in a reservoir and the +numbers in blue are the fluxes annually + + align:start position:0% +numbers in blue are the fluxes annually + + + align:start position:0% +numbers in blue are the fluxes annually +of the amounts of water moving from one + + align:start position:0% +of the amounts of water moving from one + + + align:start position:0% +of the amounts of water moving from one +to another. So there's a lot of water in + + align:start position:0% +to another. So there's a lot of water in + + + align:start position:0% +to another. So there's a lot of water in +groundwater, there's a lot of water in + + align:start position:0% +groundwater, there's a lot of water in + + + align:start position:0% +groundwater, there's a lot of water in +ice, and there's a lot of water in the + + align:start position:0% +ice, and there's a lot of water in the + + + align:start position:0% +ice, and there's a lot of water in the +oceans. Um and and there's very little + + align:start position:0% +oceans. Um and and there's very little + + + align:start position:0% +oceans. Um and and there's very little +water in the atmosphere. + + align:start position:0% +water in the atmosphere. + + + align:start position:0% +water in the atmosphere. +These are the annual fluxes. So you can + + align:start position:0% +These are the annual fluxes. So you can + + + align:start position:0% +These are the annual fluxes. So you can +see if I animated this right. Um so 111 + + align:start position:0% +see if I animated this right. Um so 111 + + + align:start position:0% +see if I animated this right. Um so 111 +these are in terms of square kilometers + + align:start position:0% +these are in terms of square kilometers + + + align:start position:0% +these are in terms of square kilometers +of water. Okay that's a lot of water. Um + + align:start position:0% +of water. Okay that's a lot of water. Um + + + align:start position:0% +of water. Okay that's a lot of water. Um +so 111 minus 71 gives you 40. That's the + + align:start position:0% +so 111 minus 71 gives you 40. That's the + + + align:start position:0% +so 111 minus 71 gives you 40. That's the +flow. So this is the rainfall. This is + + align:start position:0% +flow. So this is the rainfall. This is + + + align:start position:0% +flow. So this is the rainfall. This is +the evapo transpiration. And the net + + align:start position:0% +the evapo transpiration. And the net + + + align:start position:0% +the evapo transpiration. And the net +result is is is 40,000 that is flowing + + align:start position:0% +result is is is 40,000 that is flowing + + + align:start position:0% +result is is is 40,000 that is flowing +into the oceans. And in the oceans, + + align:start position:0% +into the oceans. And in the oceans, + + + align:start position:0% +into the oceans. And in the oceans, +here's the evaporation and here's the + + align:start position:0% +here's the evaporation and here's the + + + align:start position:0% +here's the evaporation and here's the +rainfall going in, which is a net of 40 + + align:start position:0% +rainfall going in, which is a net of 40 + + + align:start position:0% +rainfall going in, which is a net of 40 +that's transported from the oceans to + + align:start position:0% +that's transported from the oceans to + + + align:start position:0% +that's transported from the oceans to +the land. So you have 40 40,000 going + + align:start position:0% +the land. So you have 40 40,000 going + + + align:start position:0% +the land. So you have 40 40,000 going +into the oceans and 40,000 coming back. + + align:start position:0% +into the oceans and 40,000 coming back. + + + align:start position:0% +into the oceans and 40,000 coming back. +Fairly nicely balanced. That's good. Um + + align:start position:0% +Fairly nicely balanced. That's good. Um + + + align:start position:0% +Fairly nicely balanced. That's good. Um +and so let's just use this um + + align:start position:0% +and so let's just use this um + + + align:start position:0% +and so let's just use this um +as an example to say + + align:start position:0% +as an example to say + + + align:start position:0% +as an example to say +what is the residence time + + align:start position:0% + + + + align:start position:0% + +of water. + + align:start position:0% + + + + align:start position:0% + +Let's just calculate this um very we can + + align:start position:0% +Let's just calculate this um very we can + + + align:start position:0% +Let's just calculate this um very we can +just approximate it. + + align:start position:0% +just approximate it. + + + align:start position:0% +just approximate it. +So the mean resonance time + + align:start position:0% + + + + align:start position:0% + +is equal to + + align:start position:0% +is equal to + + + align:start position:0% +is equal to +the + + align:start position:0% +the + + + align:start position:0% +the +pool size + + align:start position:0% + + + + align:start position:0% + +divided by the flux. Right? + + align:start position:0% +divided by the flux. Right? + + + align:start position:0% +divided by the flux. Right? +So what's the pool size? + + align:start position:0% + + + + align:start position:0% + +What? Who? How much water is there in + + align:start position:0% +What? Who? How much water is there in + + + align:start position:0% +What? Who? How much water is there in +the ocean? + + align:start position:0% +the ocean? + + + align:start position:0% +the ocean? +Thank you. 1 + + align:start position:0% +Thank you. 1 + + + align:start position:0% +Thank you. 1 +35 * 10 to the + + align:start position:0% +35 * 10 to the + + + align:start position:0% +35 * 10 to the +9. + + align:start position:0% +9. + + + align:start position:0% +9. +And what's the flux? + + align:start position:0% + + + + align:start position:0% + +Well, + + align:start position:0% +Well, + + + align:start position:0% +Well, +we have 425,000 + + align:start position:0% +we have 425,000 + + + align:start position:0% +we have 425,000 +evaporating + + align:start position:0% + + + + align:start position:0% + +and we have 40 going here. So, so, so I + + align:start position:0% +and we have 40 going here. So, so, so I + + + align:start position:0% +and we have 40 going here. So, so, so I +would add this and that. So, it's + + align:start position:0% +would add this and that. So, it's + + + align:start position:0% +would add this and that. So, it's +balanced. So, I would use 425 + + align:start position:0% + + + + align:start position:0% + +4.25* 25 * 10 the + + align:start position:0% + + + + align:start position:0% + +5th + + align:start position:0% +5th + + + align:start position:0% +5th +equals just roughly how many years? + + align:start position:0% + + + + align:start position:0% + +3,000 years + + align:start position:0% + + + + align:start position:0% + +roughly. So order. So, so we would say + + align:start position:0% +roughly. So order. So, so we would say + + + align:start position:0% +roughly. So order. So, so we would say +the residence time the average molecule + + align:start position:0% +the residence time the average molecule + + + align:start position:0% +the residence time the average molecule +the average water molecule floating + + align:start position:0% +the average water molecule floating + + + align:start position:0% +the average water molecule floating +through this system would spend on + + align:start position:0% +through this system would spend on + + + align:start position:0% +through this system would spend on +average thousands of years in the oceans + + align:start position:0% +average thousands of years in the oceans + + + align:start position:0% +average thousands of years in the oceans +before it would evaporate um and get + + align:start position:0% +before it would evaporate um and get + + + align:start position:0% +before it would evaporate um and get +back into the system. So you should now + + align:start position:0% +back into the system. So you should now + + + align:start position:0% +back into the system. So you should now +think about what the average resonance + + align:start position:0% +think about what the average resonance + + + align:start position:0% +think about what the average resonance +time is for example in the atmosphere + + align:start position:0% +time is for example in the atmosphere + + + align:start position:0% +time is for example in the atmosphere +and you can see that when the when the + + align:start position:0% +and you can see that when the when the + + + align:start position:0% +and you can see that when the when the +pool is very small relative to the + + align:start position:0% +pool is very small relative to the + + + align:start position:0% +pool is very small relative to the +fluxes the resonance time is going to be + + align:start position:0% +fluxes the resonance time is going to be + + + align:start position:0% +fluxes the resonance time is going to be +very short right that's something to + + align:start position:0% +very short right that's something to + + + align:start position:0% +very short right that's something to +remember when the pool is huge relative + + align:start position:0% +remember when the pool is huge relative + + + align:start position:0% +remember when the pool is huge relative +to the fluxes the resonance time is + + align:start position:0% +to the fluxes the resonance time is + + + align:start position:0% +to the fluxes the resonance time is +going to be very long so you you should + + align:start position:0% +going to be very long so you you should + + + align:start position:0% +going to be very long so you you should +uh think about that as you go through + + align:start position:0% +uh think about that as you go through + + + align:start position:0% +uh think about that as you go through +your notes but Um and oceans the + + align:start position:0% +your notes but Um and oceans the + + + align:start position:0% +your notes but Um and oceans the +resonance time is um is thousands of + + align:start position:0% +resonance time is um is thousands of + + + align:start position:0% +resonance time is um is thousands of +years. In groundwater the residence time + + align:start position:0% +years. In groundwater the residence time + + + align:start position:0% +years. In groundwater the residence time +uh again can be can be very long which + + align:start position:0% +uh again can be can be very long which + + + align:start position:0% +uh again can be can be very long which +is why we don't want to contaminate our + + align:start position:0% +is why we don't want to contaminate our + + + align:start position:0% +is why we don't want to contaminate our +groundwater because it's going to take a + + align:start position:0% +groundwater because it's going to take a + + + align:start position:0% +groundwater because it's going to take a +really long time to flush that through. + + align:start position:0% +really long time to flush that through. + + + align:start position:0% +really long time to flush that through. +Uh lakes the residence times on the + + align:start position:0% +Uh lakes the residence times on the + + + align:start position:0% +Uh lakes the residence times on the +order of decades. Um streams on the + + align:start position:0% +order of decades. Um streams on the + + + align:start position:0% +order of decades. Um streams on the +order of weeks and um atmosphere I'll + + align:start position:0% +order of weeks and um atmosphere I'll + + + align:start position:0% +order of weeks and um atmosphere I'll +let you calculate it. + + align:start position:0% +let you calculate it. + + + align:start position:0% +let you calculate it. +figure it out. Okay, + + align:start position:0% + + + + align:start position:0% + +let's move on now to an element cycle. + + align:start position:0% +let's move on now to an element cycle. + + + align:start position:0% +let's move on now to an element cycle. +The global phosphorus cycle + + align:start position:0% + + + + align:start position:0% + +First of all, there's no redux chemistry + + align:start position:0% + + + + align:start position:0% + +in this cycle. That's important. Okay, + + align:start position:0% +in this cycle. That's important. Okay, + + + align:start position:0% +in this cycle. That's important. Okay, +that's the first thing to remember. And + + align:start position:0% +that's the first thing to remember. And + + + align:start position:0% +that's the first thing to remember. And +there is it's called a sedimentary + + align:start position:0% +there is it's called a sedimentary + + + align:start position:0% +there is it's called a sedimentary +cycle. + + align:start position:0% + + + + align:start position:0% + +because there is no atmospheric + + align:start position:0% +because there is no atmospheric + + + align:start position:0% +because there is no atmospheric +component. + + align:start position:0% + + + + align:start position:0% + +There's essentially no phosphorus in the + + align:start position:0% +There's essentially no phosphorus in the + + + align:start position:0% +There's essentially no phosphorus in the +atmosphere. There are there you know + + align:start position:0% +atmosphere. There are there you know + + + align:start position:0% +atmosphere. There are there you know +everything in this field there's there's + + align:start position:0% +everything in this field there's there's + + + align:start position:0% +everything in this field there's there's +always an exception. There's something + + align:start position:0% +always an exception. There's something + + + align:start position:0% +always an exception. There's something +called phosphine that comes out of bogs + + align:start position:0% +called phosphine that comes out of bogs + + + align:start position:0% +called phosphine that comes out of bogs +that is really interesting but it's not + + align:start position:0% +that is really interesting but it's not + + + align:start position:0% +that is really interesting but it's not +a huge amount. So uh it doesn't really + + align:start position:0% +a huge amount. So uh it doesn't really + + + align:start position:0% +a huge amount. So uh it doesn't really +matter in this in this uh analysis. Um + + align:start position:0% +matter in this in this uh analysis. Um + + + align:start position:0% +matter in this in this uh analysis. Um +and the + + align:start position:0% + + + + align:start position:0% + +let's look at it here. We have uh + + align:start position:0% +let's look at it here. We have uh + + + align:start position:0% +let's look at it here. We have uh +a fair amount of phosphorus in in land + + align:start position:0% +a fair amount of phosphorus in in land + + + align:start position:0% +a fair amount of phosphorus in in land +plants and there's internal cycling + + align:start position:0% +plants and there's internal cycling + + + align:start position:0% +plants and there's internal cycling +here. We have the production we have the + + align:start position:0% +here. We have the production we have the + + + align:start position:0% +here. We have the production we have the +mining of phosphorus from rocks. Uh this + + align:start position:0% +mining of phosphorus from rocks. Uh this + + + align:start position:0% +mining of phosphorus from rocks. Uh this +is a a fertilizer. Uh no that's not a + + align:start position:0% +is a a fertilizer. Uh no that's not a + + + align:start position:0% +is a a fertilizer. Uh no that's not a +mine that's a house. Sorry. Uh uh the + + align:start position:0% +mine that's a house. Sorry. Uh uh the + + + align:start position:0% +mine that's a house. Sorry. Uh uh the +the the mine is invisible. Here's the + + align:start position:0% +the the mine is invisible. Here's the + + + align:start position:0% +the the mine is invisible. Here's the +mine. Um so the the phosphorus is being + + align:start position:0% +mine. Um so the the phosphorus is being + + + align:start position:0% +mine. Um so the the phosphorus is being +mined. It's put on crops as fertilizer. + + align:start position:0% +mined. It's put on crops as fertilizer. + + + align:start position:0% +mined. It's put on crops as fertilizer. +The crops are eaten by the people uh in + + align:start position:0% +The crops are eaten by the people uh in + + + align:start position:0% +The crops are eaten by the people uh in +the house and the the phosphorus ends up + + align:start position:0% +the house and the the phosphorus ends up + + + align:start position:0% +the house and the the phosphorus ends up +in sewage. Uh it's even if it's treated, + + align:start position:0% +in sewage. Uh it's even if it's treated, + + + align:start position:0% +in sewage. Uh it's even if it's treated, +it ends up in the rivers and it ends up + + align:start position:0% +it ends up in the rivers and it ends up + + + align:start position:0% +it ends up in the rivers and it ends up +uh flowing into the oceans. Um and + + align:start position:0% +uh flowing into the oceans. Um and + + + align:start position:0% +uh flowing into the oceans. Um and +there's a little bit in in dust + + align:start position:0% +there's a little bit in in dust + + + align:start position:0% +there's a little bit in in dust +transport here. But if you look at this + + align:start position:0% +transport here. But if you look at this + + + align:start position:0% +transport here. But if you look at this +whole system um there it's basically the + + align:start position:0% +whole system um there it's basically the + + + align:start position:0% +whole system um there it's basically the +phosphorus cycle is a one-way flow to + + align:start position:0% +phosphorus cycle is a one-way flow to + + + align:start position:0% +phosphorus cycle is a one-way flow to +the oceans. The only return in the cycle + + align:start position:0% +the oceans. The only return in the cycle + + + align:start position:0% +the oceans. The only return in the cycle +is this via the sedimentary cycle where + + align:start position:0% +is this via the sedimentary cycle where + + + align:start position:0% +is this via the sedimentary cycle where +you go from sediments uh to those um + + align:start position:0% +you go from sediments uh to those um + + + align:start position:0% +you go from sediments uh to those um +those are sedimentary rocks to you go to + + align:start position:0% +those are sedimentary rocks to you go to + + + align:start position:0% +those are sedimentary rocks to you go to +minable rock and and and through + + align:start position:0% +minable rock and and and through + + + align:start position:0% +minable rock and and and through +uplifting. And this is on geological + + align:start position:0% +uplifting. And this is on geological + + + align:start position:0% +uplifting. And this is on geological +time scales. So on the earth today, the + + align:start position:0% +time scales. So on the earth today, the + + + align:start position:0% +time scales. So on the earth today, the +global phosphorus cycle is really not a + + align:start position:0% +global phosphorus cycle is really not a + + + align:start position:0% +global phosphorus cycle is really not a +cycle. It's one way flow um to the + + align:start position:0% +cycle. It's one way flow um to the + + + align:start position:0% +cycle. It's one way flow um to the +oceans. Well, it's a cycle, but it's a + + align:start position:0% +oceans. Well, it's a cycle, but it's a + + + align:start position:0% +oceans. Well, it's a cycle, but it's a +extremely unbalanced cycle. Uh + + align:start position:0% +extremely unbalanced cycle. Uh + + + align:start position:0% +extremely unbalanced cycle. Uh +because eventually the the this will + + align:start position:0% +because eventually the the this will + + + align:start position:0% +because eventually the the this will +will come back. Um + + align:start position:0% +will come back. Um + + + align:start position:0% +will come back. Um +it cycles very rapidly in the biota + + align:start position:0% +it cycles very rapidly in the biota + + + align:start position:0% +it cycles very rapidly in the biota +internal cycling in the ocean. So it it + + align:start position:0% +internal cycling in the ocean. So it it + + + align:start position:0% +internal cycling in the ocean. So it it +it comes into the the the river, it's + + align:start position:0% +it comes into the the the river, it's + + + align:start position:0% +it comes into the the the river, it's +taken up by phytolanton, they're eaten + + align:start position:0% +taken up by phytolanton, they're eaten + + + align:start position:0% +taken up by phytolanton, they're eaten +by zop plankton. Um and that and and + + align:start position:0% +by zop plankton. Um and that and and + + + align:start position:0% +by zop plankton. Um and that and and +then the phosphorus is excreted or or + + align:start position:0% +then the phosphorus is excreted or or + + + align:start position:0% +then the phosphorus is excreted or or +bacteria shoe on dead organisms take up + + align:start position:0% +bacteria shoe on dead organisms take up + + + align:start position:0% +bacteria shoe on dead organisms take up +the phosphorus. It's excreted as organic + + align:start position:0% +the phosphorus. It's excreted as organic + + + align:start position:0% +the phosphorus. It's excreted as organic +phosphorus and it cycles rapidly um + + align:start position:0% +phosphorus and it cycles rapidly um + + + align:start position:0% +phosphorus and it cycles rapidly um +through this system. + + align:start position:0% + + + + align:start position:0% + +Okay. Um + + align:start position:0% + + + + align:start position:0% + +so the other important um feature of + + align:start position:0% +so the other important um feature of + + + align:start position:0% +so the other important um feature of +this + + align:start position:0% + + + + align:start position:0% + +oneway flow and also humans + + align:start position:0% + + + + align:start position:0% + +have + + align:start position:0% +have + + + align:start position:0% +have +altered + + align:start position:0% + + + + align:start position:0% + +In other words, the humans are + + align:start position:0% +In other words, the humans are + + + align:start position:0% +In other words, the humans are +responsible for this basically for this + + align:start position:0% +responsible for this basically for this + + + align:start position:0% +responsible for this basically for this +one-way flow uh by by by mining uh the + + align:start position:0% +one-way flow uh by by by mining uh the + + + align:start position:0% +one-way flow uh by by by mining uh the +phosphorus and putting it into the the + + align:start position:0% +phosphorus and putting it into the the + + + align:start position:0% +phosphorus and putting it into the the +um agricultural system. + + align:start position:0% +um agricultural system. + + + align:start position:0% +um agricultural system. +Okay. + + align:start position:0% + + + + align:start position:0% + +Yeah. Then there's the return flux. + + align:start position:0% + + + + align:start position:0% + +Okay. Moving on to the um nitrogen cycle + + align:start position:0% +Okay. Moving on to the um nitrogen cycle + + + align:start position:0% +Okay. Moving on to the um nitrogen cycle +which is much more complicated because + + align:start position:0% +which is much more complicated because + + + align:start position:0% +which is much more complicated because +it has redux chemistry. Okay. And uh + + align:start position:0% +it has redux chemistry. Okay. And uh + + + align:start position:0% +it has redux chemistry. Okay. And uh +humans have also had a major major major + + align:start position:0% +humans have also had a major major major + + + align:start position:0% +humans have also had a major major major +effect on on the global nitrogen cycle. + + align:start position:0% +effect on on the global nitrogen cycle. + + + align:start position:0% +effect on on the global nitrogen cycle. +So let's first um + + align:start position:0% +So let's first um + + + align:start position:0% +So let's first um +look at the the the global nitrogen + + align:start position:0% +look at the the the global nitrogen + + + align:start position:0% +look at the the the global nitrogen +transformation. So this isn't a pools + + align:start position:0% +transformation. So this isn't a pools + + + align:start position:0% +transformation. So this isn't a pools +and fluxes diagram. This is a summary + + align:start position:0% +and fluxes diagram. This is a summary + + + align:start position:0% +and fluxes diagram. This is a summary +for you of things you already know. You + + align:start position:0% +for you of things you already know. You + + + align:start position:0% +for you of things you already know. You +already know this. Okay? It just looks + + align:start position:0% +already know this. Okay? It just looks + + + align:start position:0% +already know this. Okay? It just looks +different than what you learned in the + + align:start position:0% +different than what you learned in the + + + align:start position:0% +different than what you learned in the +second lecture. So let's just go through + + align:start position:0% +second lecture. So let's just go through + + + align:start position:0% +second lecture. So let's just go through +it very quick very quickly. If we think + + align:start position:0% +it very quick very quickly. If we think + + + align:start position:0% +it very quick very quickly. If we think +of the um the compounds of nitrogen as + + align:start position:0% +of the um the compounds of nitrogen as + + + align:start position:0% +of the um the compounds of nitrogen as +being either reduced or oxidized and we + + align:start position:0% +being either reduced or oxidized and we + + + align:start position:0% +being either reduced or oxidized and we +think of the environment where they + + align:start position:0% +think of the environment where they + + + align:start position:0% +think of the environment where they +might be found as either being aerobic + + align:start position:0% +might be found as either being aerobic + + + align:start position:0% +might be found as either being aerobic +or oxic having oxygen or anorobic anoxic + + align:start position:0% +or oxic having oxygen or anorobic anoxic + + + align:start position:0% +or oxic having oxygen or anorobic anoxic +not having oxygen. We can uh draw a + + align:start position:0% +not having oxygen. We can uh draw a + + + align:start position:0% +not having oxygen. We can uh draw a +schematic of these processes that + + align:start position:0% +schematic of these processes that + + + align:start position:0% +schematic of these processes that +hopefully makes uh some good sense. If + + align:start position:0% +hopefully makes uh some good sense. If + + + align:start position:0% +hopefully makes uh some good sense. If +we start with organic nitrogen um that + + align:start position:0% +we start with organic nitrogen um that + + + align:start position:0% +we start with organic nitrogen um that +say it's a dead that dead whale that you + + align:start position:0% +say it's a dead that dead whale that you + + + align:start position:0% +say it's a dead that dead whale that you +saw is organic nitrogen um bacteria work + + align:start position:0% +saw is organic nitrogen um bacteria work + + + align:start position:0% +saw is organic nitrogen um bacteria work +on it and through this process which you + + align:start position:0% +on it and through this process which you + + + align:start position:0% +on it and through this process which you +haven't really learned about explicitly + + align:start position:0% +haven't really learned about explicitly + + + align:start position:0% +haven't really learned about explicitly +yet can convert that to free ammonia. + + align:start position:0% +yet can convert that to free ammonia. + + + align:start position:0% +yet can convert that to free ammonia. +Okay. + + align:start position:0% +Okay. + + + align:start position:0% +Okay. +Um that ammonia can be used in + + align:start position:0% +Um that ammonia can be used in + + + align:start position:0% +Um that ammonia can be used in +chemosynthesis which you've learned + + align:start position:0% +chemosynthesis which you've learned + + + align:start position:0% +chemosynthesis which you've learned +about. Okay. The specific type of + + align:start position:0% +about. Okay. The specific type of + + + align:start position:0% +about. Okay. The specific type of +chemosynthesis is called nitrification + + align:start position:0% +chemosynthesis is called nitrification + + + align:start position:0% +chemosynthesis is called nitrification +where this ammonia is converted to + + align:start position:0% +where this ammonia is converted to + + + align:start position:0% +where this ammonia is converted to +nitrite. Is that a oxidation or a + + align:start position:0% +nitrite. Is that a oxidation or a + + + align:start position:0% +nitrite. Is that a oxidation or a +reduction? + + align:start position:0% + + + + align:start position:0% + +Shout it out. + + align:start position:0% +Shout it out. + + + align:start position:0% +Shout it out. +Oxidation. + + align:start position:0% +Oxidation. + + + align:start position:0% +Oxidation. +Yes. Yes, it's an oxidation. This one's + + align:start position:0% +Yes. Yes, it's an oxidation. This one's + + + align:start position:0% +Yes. Yes, it's an oxidation. This one's +obvious because you're you're actually + + align:start position:0% +obvious because you're you're actually + + + align:start position:0% +obvious because you're you're actually +can see the oxygen. Okay. Um + + align:start position:0% +can see the oxygen. Okay. Um + + + align:start position:0% +can see the oxygen. Okay. Um +so and that nitrite also in + + align:start position:0% +so and that nitrite also in + + + align:start position:0% +so and that nitrite also in +chemosynthesis can be further oxidized + + align:start position:0% +chemosynthesis can be further oxidized + + + align:start position:0% +chemosynthesis can be further oxidized +to uh nitrate and chemosynthesis. So + + align:start position:0% +to uh nitrate and chemosynthesis. So + + + align:start position:0% +to uh nitrate and chemosynthesis. So +this is a energy releasing process for + + align:start position:0% +this is a energy releasing process for + + + align:start position:0% +this is a energy releasing process for +these these bacteria. Um, now, so here + + align:start position:0% +these these bacteria. Um, now, so here + + + align:start position:0% +these these bacteria. Um, now, so here +we now have nitrogen in an oxidized form + + align:start position:0% +we now have nitrogen in an oxidized form + + + align:start position:0% +we now have nitrogen in an oxidized form +and we're in an anoxic environment and + + align:start position:0% +and we're in an anoxic environment and + + + align:start position:0% +and we're in an anoxic environment and +that should immediately tell you, oh, + + align:start position:0% +that should immediately tell you, oh, + + + align:start position:0% +that should immediately tell you, oh, +that's an electron acceptor for the + + align:start position:0% +that's an electron acceptor for the + + + align:start position:0% +that's an electron acceptor for the +anorobic bacteria which are going to + + align:start position:0% +anorobic bacteria which are going to + + + align:start position:0% +anorobic bacteria which are going to +dump their electrons on this and convert + + align:start position:0% +dump their electrons on this and convert + + + align:start position:0% +dump their electrons on this and convert +it to N or N2O. These are gases um and + + align:start position:0% +it to N or N2O. These are gases um and + + + align:start position:0% +it to N or N2O. These are gases um and +nitrogen gas. This is dnitrification or + + align:start position:0% +nitrogen gas. This is dnitrification or + + + align:start position:0% +nitrogen gas. This is dnitrification or +anorobic respiration. Um which we + + align:start position:0% +anorobic respiration. Um which we + + + align:start position:0% +anorobic respiration. Um which we +already talked about + + align:start position:0% + + + + align:start position:0% + +and and also can be uh converted through + + align:start position:0% +and and also can be uh converted through + + + align:start position:0% +and and also can be uh converted through +nitrogen fixation into gas can be + + align:start position:0% +nitrogen fixation into gas can be + + + align:start position:0% +nitrogen fixation into gas can be +converted to ammonia. We already talked + + align:start position:0% +converted to ammonia. We already talked + + + align:start position:0% +converted to ammonia. We already talked +about this too. Um as remember bacteria + + align:start position:0% +about this too. Um as remember bacteria + + + align:start position:0% +about this too. Um as remember bacteria +and cyanobacteria are the only organisms + + align:start position:0% +and cyanobacteria are the only organisms + + + align:start position:0% +and cyanobacteria are the only organisms +that can take nitrogen gas from the + + align:start position:0% +that can take nitrogen gas from the + + + align:start position:0% +that can take nitrogen gas from the +atmosphere and convert it to uh ammonia + + align:start position:0% +atmosphere and convert it to uh ammonia + + + align:start position:0% +atmosphere and convert it to uh ammonia +for the use of other organisms. Okay. + + align:start position:0% +for the use of other organisms. Okay. + + + align:start position:0% +for the use of other organisms. Okay. +And then there's one other thing here + + align:start position:0% +And then there's one other thing here + + + align:start position:0% +And then there's one other thing here +which is called assimilatory nitrate + + align:start position:0% +which is called assimilatory nitrate + + + align:start position:0% +which is called assimilatory nitrate +reduction and that is when organisms + + align:start position:0% +reduction and that is when organisms + + + align:start position:0% +reduction and that is when organisms +just take up nitrate + + align:start position:0% +just take up nitrate + + + align:start position:0% +just take up nitrate +and inside them they reduce it so that + + align:start position:0% +and inside them they reduce it so that + + + align:start position:0% +and inside them they reduce it so that +they can use they reduce they have to + + align:start position:0% +they can use they reduce they have to + + + align:start position:0% +they can use they reduce they have to +reduce it to ammonia in order to use it + + align:start position:0% +reduce it to ammonia in order to use it + + + align:start position:0% +reduce it to ammonia in order to use it +for uh protein synthesis. So that's + + align:start position:0% +for uh protein synthesis. So that's + + + align:start position:0% +for uh protein synthesis. So that's +another route for in for nitrate to + + align:start position:0% +another route for in for nitrate to + + + align:start position:0% +another route for in for nitrate to +become organic nitrogen in oxidized + + align:start position:0% +become organic nitrogen in oxidized + + + align:start position:0% +become organic nitrogen in oxidized +environment. So these are the important + + align:start position:0% +environment. So these are the important + + + align:start position:0% +environment. So these are the important +biological transformations in the in the + + align:start position:0% +biological transformations in the in the + + + align:start position:0% +biological transformations in the in the +cycle. Um + + align:start position:0% + + + + align:start position:0% + +so here's the cycle in all of its + + align:start position:0% +so here's the cycle in all of its + + + align:start position:0% +so here's the cycle in all of its +complexity + + align:start position:0% + + + + align:start position:0% + +and + + align:start position:0% +and + + + align:start position:0% +and +redux is important. That's a feature. + + align:start position:0% + + + + align:start position:0% + +I'm going to list these things and then + + align:start position:0% +I'm going to list these things and then + + + align:start position:0% +I'm going to list these things and then +we'll look at them on the um on the + + align:start position:0% +we'll look at them on the um on the + + + align:start position:0% +we'll look at them on the um on the +diagram + + align:start position:0% + + + + align:start position:0% + +has a gaseous phase. + + align:start position:0% +has a gaseous phase. + + + align:start position:0% +has a gaseous phase. +In other words, there's an important + + align:start position:0% +In other words, there's an important + + + align:start position:0% +In other words, there's an important +atmospheric um component + + align:start position:0% +atmospheric um component + + + align:start position:0% +atmospheric um component +N2 N O N2O. And by the way, this is a + + align:start position:0% +N2 N O N2O. And by the way, this is a + + + align:start position:0% +N2 N O N2O. And by the way, this is a +very powerful greenhouse gas. So the the + + align:start position:0% +very powerful greenhouse gas. So the the + + + align:start position:0% +very powerful greenhouse gas. So the the +balance or imbalance in the nitrogen + + align:start position:0% +balance or imbalance in the nitrogen + + + align:start position:0% +balance or imbalance in the nitrogen +cycle that results in more or less N2O + + align:start position:0% +cycle that results in more or less N2O + + + align:start position:0% +cycle that results in more or less N2O +is very important for global climate + + align:start position:0% +is very important for global climate + + + align:start position:0% +is very important for global climate +regulation. + + align:start position:0% + + + + align:start position:0% + +Um, + + align:start position:0% + + + + align:start position:0% + +nitrogen fixation + + align:start position:0% + + + + align:start position:0% + +by microbes + + align:start position:0% + + + + align:start position:0% + +and humans. + + align:start position:0% + + + + align:start position:0% + +very important. + + align:start position:0% + + + + align:start position:0% + +Um and + + align:start position:0% +Um and + + + align:start position:0% +Um and +dnitrification + + align:start position:0% + + + + align:start position:0% + +by microbes + + align:start position:0% + + + + align:start position:0% + +is the only way + + align:start position:0% + + + + align:start position:0% + +to return + + align:start position:0% + + + + align:start position:0% + +nitrogen + + align:start position:0% +nitrogen + + + align:start position:0% +nitrogen +to the atmosphere. + + align:start position:0% +to the atmosphere. + + + align:start position:0% +to the atmosphere. +If you didn't have ditrification, this + + align:start position:0% +If you didn't have ditrification, this + + + align:start position:0% +If you didn't have ditrification, this +process that you learned in my second + + align:start position:0% +process that you learned in my second + + + align:start position:0% +process that you learned in my second +lecture that you thought was just some + + align:start position:0% +lecture that you thought was just some + + + align:start position:0% +lecture that you thought was just some +weird way things get through life, uh is + + align:start position:0% +weird way things get through life, uh is + + + align:start position:0% +weird way things get through life, uh is +incredibly important in maintaining the + + align:start position:0% +incredibly important in maintaining the + + + align:start position:0% +incredibly important in maintaining the +global the global nitrogen cycle. Um so + + align:start position:0% +global the global nitrogen cycle. Um so + + + align:start position:0% +global the global nitrogen cycle. Um so +let's let's let's look at this um + + align:start position:0% + + + + align:start position:0% + +[Applause] + + align:start position:0% +[Applause] + + + align:start position:0% +[Applause] +the details here. Uh let's see. Okay. + + align:start position:0% +the details here. Uh let's see. Okay. + + + align:start position:0% +the details here. Uh let's see. Okay. +So, in terms of nitrogen fixation, um + + align:start position:0% +So, in terms of nitrogen fixation, um + + + align:start position:0% +So, in terms of nitrogen fixation, um +that's taking N2 gas and converting it + + align:start position:0% +that's taking N2 gas and converting it + + + align:start position:0% +that's taking N2 gas and converting it +to ammonia. Um the biological fixation + + align:start position:0% +to ammonia. Um the biological fixation + + + align:start position:0% +to ammonia. Um the biological fixation +by plants or it's really not by plants, + + align:start position:0% +by plants or it's really not by plants, + + + align:start position:0% +by plants or it's really not by plants, +it's by the the symbiotic microbes in + + align:start position:0% +it's by the the symbiotic microbes in + + + align:start position:0% +it's by the the symbiotic microbes in +their in their roots um + + align:start position:0% +their in their roots um + + + align:start position:0% +their in their roots um +is 140* 10 12 grams per year. the + + align:start position:0% +is 140* 10 12 grams per year. the + + + align:start position:0% +is 140* 10 12 grams per year. the +industrial nitrogen fixation that is + + align:start position:0% +industrial nitrogen fixation that is + + + align:start position:0% +industrial nitrogen fixation that is +what's done by humans. Um we there's a + + align:start position:0% +what's done by humans. Um we there's a + + + align:start position:0% +what's done by humans. Um we there's a +there's a process called the habber + + align:start position:0% +there's a process called the habber + + + align:start position:0% +there's a process called the habber +process that's incredibly energy + + align:start position:0% +process that's incredibly energy + + + align:start position:0% +process that's incredibly energy +intensive. It takes a lot of fossil fuel + + align:start position:0% +intensive. It takes a lot of fossil fuel + + + align:start position:0% +intensive. It takes a lot of fossil fuel +to break that carbon + + align:start position:0% +to break that carbon + + + align:start position:0% +to break that carbon +not carbon nitrogen triple bond. + + align:start position:0% +not carbon nitrogen triple bond. + + + align:start position:0% +not carbon nitrogen triple bond. +In other words to take to to to take + + align:start position:0% +In other words to take to to to take + + + align:start position:0% +In other words to take to to to take +nitrogen gas and convert it to ammonia + + align:start position:0% +nitrogen gas and convert it to ammonia + + + align:start position:0% +nitrogen gas and convert it to ammonia +you have to break this triple bond which + + align:start position:0% +you have to break this triple bond which + + + align:start position:0% +you have to break this triple bond which +is very energy intensive. Um but that + + align:start position:0% +is very energy intensive. Um but that + + + align:start position:0% +is very energy intensive. Um but that +the they figured that out during World + + align:start position:0% +the they figured that out during World + + + align:start position:0% +the they figured that out during World +War II basically or was it World War I? + + align:start position:0% +War II basically or was it World War I? + + + align:start position:0% +War II basically or was it World War I? +Anyway, one of the wars. Um uh how to + + align:start position:0% +Anyway, one of the wars. Um uh how to + + + align:start position:0% +Anyway, one of the wars. Um uh how to +break that bond and that was the the + + align:start position:0% +break that bond and that was the the + + + align:start position:0% +break that bond and that was the the +beginning of the nitrogen fertilizer + + align:start position:0% +beginning of the nitrogen fertilizer + + + align:start position:0% +beginning of the nitrogen fertilizer +industry. So this is human um nitrogen + + align:start position:0% +industry. So this is human um nitrogen + + + align:start position:0% +industry. So this is human um nitrogen +fixation uh uh that is used to fertilize + + align:start position:0% +fixation uh uh that is used to fertilize + + + align:start position:0% +fixation uh uh that is used to fertilize +crops. So this is a huge fraction of the + + align:start position:0% +crops. So this is a huge fraction of the + + + align:start position:0% +crops. So this is a huge fraction of the +natural fixation that that I mean this + + align:start position:0% +natural fixation that that I mean this + + + align:start position:0% +natural fixation that that I mean this +adds a huge amount of nitrogen flux to + + align:start position:0% +adds a huge amount of nitrogen flux to + + + align:start position:0% +adds a huge amount of nitrogen flux to +the system. + + align:start position:0% +the system. + + + align:start position:0% +the system. +Um + + align:start position:0% + + + + align:start position:0% + +okay. Oh and this in this flux here this + + align:start position:0% +okay. Oh and this in this flux here this + + + align:start position:0% +okay. Oh and this in this flux here this +is cultivated legumes. So this would be + + align:start position:0% +is cultivated legumes. So this would be + + + align:start position:0% +is cultivated legumes. So this would be +uh agricultural bean plants that + + align:start position:0% +uh agricultural bean plants that + + + align:start position:0% +uh agricultural bean plants that +naturally have nitrogen fixers in them + + align:start position:0% +naturally have nitrogen fixers in them + + + align:start position:0% +naturally have nitrogen fixers in them +and that also import nitrogen into the + + align:start position:0% +and that also import nitrogen into the + + + align:start position:0% +and that also import nitrogen into the +system. Uh so we consider that part of + + align:start position:0% +system. Uh so we consider that part of + + + align:start position:0% +system. Uh so we consider that part of +the human the human flux. Okay. To + + align:start position:0% +the human the human flux. Okay. To + + + align:start position:0% +the human the human flux. Okay. To +balance this we have dnitrification + + align:start position:0% +balance this we have dnitrification + + + align:start position:0% +balance this we have dnitrification +um which is as I said done by microbes + + align:start position:0% +um which is as I said done by microbes + + + align:start position:0% +um which is as I said done by microbes +on land and in the ocean. So looking at + + align:start position:0% +on land and in the ocean. So looking at + + + align:start position:0% +on land and in the ocean. So looking at +this is it balanced + + align:start position:0% + + + + align:start position:0% + +is nitrogen fixation on a global scale + + align:start position:0% +is nitrogen fixation on a global scale + + + align:start position:0% +is nitrogen fixation on a global scale +and ditrification balanced. + + align:start position:0% + + + + align:start position:0% + +No. Did I hear a no? + + align:start position:0% +No. Did I hear a no? + + + align:start position:0% +No. Did I hear a no? +Which is greater? + + align:start position:0% + + + + align:start position:0% + +Denitrification. Yeah. If you add this, + + align:start position:0% +Denitrification. Yeah. If you add this, + + + align:start position:0% +Denitrification. Yeah. If you add this, +this and this, you get + + align:start position:0% +this and this, you get + + + align:start position:0% +this and this, you get +you get you get + + align:start position:0% +you get you get + + + align:start position:0% +you get you get +260. Is that right? Yeah. And then you + + align:start position:0% +260. Is that right? Yeah. And then you + + + align:start position:0% +260. Is that right? Yeah. And then you +add this, this, you get 310. So there's + + align:start position:0% +add this, this, you get 310. So there's + + + align:start position:0% +add this, this, you get 310. So there's +more nitrogen now going into the + + align:start position:0% +more nitrogen now going into the + + + align:start position:0% +more nitrogen now going into the +atmosphere than than we're taking out. + + align:start position:0% +atmosphere than than we're taking out. + + + align:start position:0% +atmosphere than than we're taking out. +Um, and people don't understand this. uh + + align:start position:0% +Um, and people don't understand this. uh + + + align:start position:0% +Um, and people don't understand this. uh +they think that denitrification has been + + align:start position:0% +they think that denitrification has been + + + align:start position:0% +they think that denitrification has been +uh disproportionately stimulated by this + + align:start position:0% +uh disproportionately stimulated by this + + + align:start position:0% +uh disproportionately stimulated by this +huge flux of nitrogen into the system. + + align:start position:0% +huge flux of nitrogen into the system. + + + align:start position:0% +huge flux of nitrogen into the system. +Um but this is an important imbalance + + align:start position:0% +Um but this is an important imbalance + + + align:start position:0% +Um but this is an important imbalance +that a lot of people are are studying + + align:start position:0% +that a lot of people are are studying + + + align:start position:0% +that a lot of people are are studying +very hard. + + align:start position:0% +very hard. + + + align:start position:0% +very hard. +Okay. + + align:start position:0% + + + + align:start position:0% + +Whoops. Um + + align:start position:0% +Whoops. Um + + + align:start position:0% +Whoops. Um +yeah, that's the that's the ma major + + align:start position:0% +yeah, that's the that's the ma major + + + align:start position:0% +yeah, that's the that's the ma major +feature that you want to look at in this + + align:start position:0% +feature that you want to look at in this + + + align:start position:0% +feature that you want to look at in this +system. And then if we compare this + + align:start position:0% +system. And then if we compare this + + + align:start position:0% +system. And then if we compare this +figure is from your textbook comparing + + align:start position:0% +figure is from your textbook comparing + + + align:start position:0% +figure is from your textbook comparing +the biological nitrogen fixation plus + + align:start position:0% +the biological nitrogen fixation plus + + + align:start position:0% +the biological nitrogen fixation plus +lightning fixes a little bit um compared + + align:start position:0% +lightning fixes a little bit um compared + + + align:start position:0% +lightning fixes a little bit um compared +to the human you can see that humans are + + align:start position:0% +to the human you can see that humans are + + + align:start position:0% +to the human you can see that humans are +now responsible for an equal amount of + + align:start position:0% +now responsible for an equal amount of + + + align:start position:0% +now responsible for an equal amount of +nitrogen flux on a global scale as the + + align:start position:0% +nitrogen flux on a global scale as the + + + align:start position:0% +nitrogen flux on a global scale as the +natural system. This is a dramatic + + align:start position:0% +natural system. This is a dramatic + + + align:start position:0% +natural system. This is a dramatic +perturbation and that's only in the last + + align:start position:0% +perturbation and that's only in the last + + + align:start position:0% +perturbation and that's only in the last +uh 50 years or so. Dramatic perturbation + + align:start position:0% +uh 50 years or so. Dramatic perturbation + + + align:start position:0% +uh 50 years or so. Dramatic perturbation +to the system. + + align:start position:0% +to the system. + + + align:start position:0% +to the system. +This amount that we're doing is a 140 + + align:start position:0% +This amount that we're doing is a 140 + + + align:start position:0% +This amount that we're doing is a 140 +gigatons is equivalent to 10 million + + align:start position:0% +gigatons is equivalent to 10 million + + + align:start position:0% +gigatons is equivalent to 10 million +trucks of dry nitrogen fertilizer that + + align:start position:0% +trucks of dry nitrogen fertilizer that + + + align:start position:0% +trucks of dry nitrogen fertilizer that +we're putting into the system with + + align:start position:0% +we're putting into the system with + + + align:start position:0% +we're putting into the system with +completely unknown effects. Okay. Um + + align:start position:0% +completely unknown effects. Okay. Um + + + align:start position:0% +completely unknown effects. Okay. Um +the next series of slides are just to uh + + align:start position:0% +the next series of slides are just to uh + + + align:start position:0% +the next series of slides are just to uh +illustrate the in one ecosystem the + + align:start position:0% +illustrate the in one ecosystem the + + + align:start position:0% +illustrate the in one ecosystem the +importance of the biota in maintaining + + align:start position:0% +importance of the biota in maintaining + + + align:start position:0% +importance of the biota in maintaining +uh nitrogen in the ecosystem and also to + + align:start position:0% +uh nitrogen in the ecosystem and also to + + + align:start position:0% +uh nitrogen in the ecosystem and also to +show you uh the the the importance of + + align:start position:0% +show you uh the the the importance of + + + align:start position:0% +show you uh the the the importance of +experiments in ecology. And this is the + + align:start position:0% +experiments in ecology. And this is the + + + align:start position:0% +experiments in ecology. And this is the +Hoverbrook uh experimental forest which + + align:start position:0% +Hoverbrook uh experimental forest which + + + align:start position:0% +Hoverbrook uh experimental forest which +is up in in New Hampshire. Some of you + + align:start position:0% +is up in in New Hampshire. Some of you + + + align:start position:0% +is up in in New Hampshire. Some of you +might have even visited there. This was + + align:start position:0% +might have even visited there. This was + + + align:start position:0% +might have even visited there. This was +my first uh job as a graduate student + + align:start position:0% +my first uh job as a graduate student + + + align:start position:0% +my first uh job as a graduate student +was actually working in this forest. Um + + align:start position:0% +was actually working in this forest. Um + + + align:start position:0% +was actually working in this forest. Um +I was measuring phosphorus + + align:start position:0% +I was measuring phosphorus + + + align:start position:0% +I was measuring phosphorus +concentrations in these streams. And + + align:start position:0% +concentrations in these streams. And + + + align:start position:0% +concentrations in these streams. And +what they do there just like that + + align:start position:0% +what they do there just like that + + + align:start position:0% +what they do there just like that +experimental lake study I showed you + + align:start position:0% +experimental lake study I showed you + + + align:start position:0% +experimental lake study I showed you +here they're they have uh permits from + + align:start position:0% +here they're they have uh permits from + + + align:start position:0% +here they're they have uh permits from +the forest service to clear cut entire + + align:start position:0% +the forest service to clear cut entire + + + align:start position:0% +the forest service to clear cut entire +watersheds. Wershed is just an area that + + align:start position:0% +watersheds. Wershed is just an area that + + + align:start position:0% +watersheds. Wershed is just an area that +collects the rainfall and directs it + + align:start position:0% +collects the rainfall and directs it + + + align:start position:0% +collects the rainfall and directs it +into a single stream so that you can you + + align:start position:0% +into a single stream so that you can you + + + align:start position:0% +into a single stream so that you can you +can you can collect the rain and measure + + align:start position:0% +can you can collect the rain and measure + + + align:start position:0% +can you can collect the rain and measure +what's in it and you can collect the + + align:start position:0% +what's in it and you can collect the + + + align:start position:0% +what's in it and you can collect the +water coming out and measure what's in + + align:start position:0% +water coming out and measure what's in + + + align:start position:0% +water coming out and measure what's in +it and you can the difference is what + + align:start position:0% +it and you can the difference is what + + + align:start position:0% +it and you can the difference is what +the ecosystem is actually doing. Um so + + align:start position:0% +the ecosystem is actually doing. Um so + + + align:start position:0% +the ecosystem is actually doing. Um so +what they did is that they have these + + align:start position:0% +what they did is that they have these + + + align:start position:0% +what they did is that they have these +two EOS these two wersheds that were the + + align:start position:0% +two EOS these two wersheds that were the + + + align:start position:0% +two EOS these two wersheds that were the +same and they clearcut one of them. They + + align:start position:0% +same and they clearcut one of them. They + + + align:start position:0% +same and they clearcut one of them. They +cut all the trees down and they asked + + align:start position:0% +cut all the trees down and they asked + + + align:start position:0% +cut all the trees down and they asked +uh what the influence of this clear + + align:start position:0% +uh what the influence of this clear + + + align:start position:0% +uh what the influence of this clear +cutting was on the quality of the water + + align:start position:0% +cutting was on the quality of the water + + + align:start position:0% +cutting was on the quality of the water +coming out of the system. And to make + + align:start position:0% +coming out of the system. And to make + + + align:start position:0% +coming out of the system. And to make +the long story very short, it's a really + + align:start position:0% +the long story very short, it's a really + + + align:start position:0% +the long story very short, it's a really +fascinating study. It's been going on + + align:start position:0% +fascinating study. It's been going on + + + align:start position:0% +fascinating study. It's been going on +for for more years than I want to tell + + align:start position:0% +for for more years than I want to tell + + + align:start position:0% +for for more years than I want to tell +you because then you'll know how old I + + align:start position:0% +you because then you'll know how old I + + + align:start position:0% +you because then you'll know how old I +am. Uh but uh it's the the here's the + + align:start position:0% +am. Uh but uh it's the the here's the + + + align:start position:0% +am. Uh but uh it's the the here's the +control watershed and here's the water + + align:start position:0% +control watershed and here's the water + + + align:start position:0% +control watershed and here's the water +coming out of the devestated one showing + + align:start position:0% +coming out of the devestated one showing + + + align:start position:0% +coming out of the devestated one showing +massive elux of nitrate from the system + + align:start position:0% +massive elux of nitrate from the system + + + align:start position:0% +massive elux of nitrate from the system +as well as other cat ions and your + + align:start position:0% +as well as other cat ions and your + + + align:start position:0% +as well as other cat ions and your +textbook does a terrible job of not + + align:start position:0% +textbook does a terrible job of not + + + align:start position:0% +textbook does a terrible job of not +explaining this um and I don't have time + + align:start position:0% +explaining this um and I don't have time + + + align:start position:0% +explaining this um and I don't have time +to go into the details but the the major + + align:start position:0% +to go into the details but the the major + + + align:start position:0% +to go into the details but the the major +reason this is lost the the the + + align:start position:0% +reason this is lost the the the + + + align:start position:0% +reason this is lost the the the +vegetation is really important in that + + align:start position:0% +vegetation is really important in that + + + align:start position:0% +vegetation is really important in that +but it's it's important in also maint + + align:start position:0% +but it's it's important in also maint + + + align:start position:0% +but it's it's important in also maint +maintaining the microbial community in + + align:start position:0% +maintaining the microbial community in + + + align:start position:0% +maintaining the microbial community in +the soil and when it's cut down the + + align:start position:0% +the soil and when it's cut down the + + + align:start position:0% +the soil and when it's cut down the +microbial community changes and that is + + align:start position:0% +microbial community changes and that is + + + align:start position:0% +microbial community changes and that is +is is very important in in resulting in + + align:start position:0% +is is very important in in resulting in + + + align:start position:0% +is is very important in in resulting in +this loss. It's a it's a beautiful study + + align:start position:0% +this loss. It's a it's a beautiful study + + + align:start position:0% +this loss. It's a it's a beautiful study +which unfortunately we don't have time + + align:start position:0% +which unfortunately we don't have time + + + align:start position:0% +which unfortunately we don't have time +to go into but if you're interested I + + align:start position:0% +to go into but if you're interested I + + + align:start position:0% +to go into but if you're interested I +can point you in the right direction. + + align:start position:0% +can point you in the right direction. + + + align:start position:0% +can point you in the right direction. +Okay, now + + align:start position:0% +Okay, now + + + align:start position:0% +Okay, now +let's go on to the the the really + + align:start position:0% +let's go on to the the the really + + + align:start position:0% +let's go on to the the the really +important well they're all important + + align:start position:0% +important well they're all important + + + align:start position:0% +important well they're all important +because they're all coupled but this is + + align:start position:0% +because they're all coupled but this is + + + align:start position:0% +because they're all coupled but this is +the one that's getting a lot of + + align:start position:0% +the one that's getting a lot of + + + align:start position:0% +the one that's getting a lot of +attention uh the global carbon cycle and + + align:start position:0% +attention uh the global carbon cycle and + + + align:start position:0% +attention uh the global carbon cycle and +it's getting a lot of attention + + align:start position:0% +it's getting a lot of attention + + + align:start position:0% +it's getting a lot of attention +uh because we have had an incredibly + + align:start position:0% +uh because we have had an incredibly + + + align:start position:0% +uh because we have had an incredibly +significant uh impact on it um and we're + + align:start position:0% +significant uh impact on it um and we're + + + align:start position:0% +significant uh impact on it um and we're +worried about that impact causing major + + align:start position:0% +worried about that impact causing major + + + align:start position:0% +worried about that impact causing major +global warming. Um, and as an aside, + + align:start position:0% +global warming. Um, and as an aside, + + + align:start position:0% +global warming. Um, and as an aside, +I'll just tell you that I actually think + + align:start position:0% +I'll just tell you that I actually think + + + align:start position:0% +I'll just tell you that I actually think +the global nitrogen cycle is a sleeping + + align:start position:0% +the global nitrogen cycle is a sleeping + + + align:start position:0% +the global nitrogen cycle is a sleeping +giant. Um, and that the public doesn't + + align:start position:0% +giant. Um, and that the public doesn't + + + align:start position:0% +giant. Um, and that the public doesn't +know much about that right now. But in + + align:start position:0% +know much about that right now. But in + + + align:start position:0% +know much about that right now. But in +the scientific community, we know that + + align:start position:0% +the scientific community, we know that + + + align:start position:0% +the scientific community, we know that +that cycle, the perturbation we've had + + align:start position:0% +that cycle, the perturbation we've had + + + align:start position:0% +that cycle, the perturbation we've had +on that cycle could end up being + + align:start position:0% +on that cycle could end up being + + + align:start position:0% +on that cycle could end up being +equally, if not more traumatic for the + + align:start position:0% +equally, if not more traumatic for the + + + align:start position:0% +equally, if not more traumatic for the +Earth's climate as this. But that's an + + align:start position:0% +Earth's climate as this. But that's an + + + align:start position:0% +Earth's climate as this. But that's an +aside. So, let's focus on this now. So + + align:start position:0% +aside. So, let's focus on this now. So + + + align:start position:0% +aside. So, let's focus on this now. So +here's the global not carbon cycle which + + align:start position:0% +here's the global not carbon cycle which + + + align:start position:0% +here's the global not carbon cycle which +you've seen now several times uh in my + + align:start position:0% +you've seen now several times uh in my + + + align:start position:0% +you've seen now several times uh in my +lectures. So here's gross primary + + align:start position:0% +lectures. So here's gross primary + + + align:start position:0% +lectures. So here's gross primary +productivity and respiration by land + + align:start position:0% +productivity and respiration by land + + + align:start position:0% +productivity and respiration by land +plants, respiration by the soils. These + + align:start position:0% +plants, respiration by the soils. These + + + align:start position:0% +plants, respiration by the soils. These +are R sub A and R sub R sub H that we + + align:start position:0% +are R sub A and R sub R sub H that we + + + align:start position:0% +are R sub A and R sub R sub H that we +talked about before. And in this we have + + align:start position:0% +talked about before. And in this we have + + + align:start position:0% +talked about before. And in this we have +they're balanced roughly balanced. Um + + align:start position:0% +they're balanced roughly balanced. Um + + + align:start position:0% +they're balanced roughly balanced. Um +and then you have uptake by the oceans + + align:start position:0% +and then you have uptake by the oceans + + + align:start position:0% +and then you have uptake by the oceans +and um loss of CO2 by the oceans by your + + align:start position:0% +and um loss of CO2 by the oceans by your + + + align:start position:0% +and um loss of CO2 by the oceans by your +textbook says this is all a physical and + + align:start position:0% +textbook says this is all a physical and + + + align:start position:0% +textbook says this is all a physical and +chem chemical process. That's absolutely + + align:start position:0% +chem chemical process. That's absolutely + + + align:start position:0% +chem chemical process. That's absolutely +wrong. The biota are central to that. Um + + align:start position:0% +wrong. The biota are central to that. Um + + + align:start position:0% +wrong. The biota are central to that. Um +and that's another lecture. But you you + + align:start position:0% +and that's another lecture. But you you + + + align:start position:0% +and that's another lecture. But you you +already know that that the phytolanton + + align:start position:0% +already know that that the phytolanton + + + align:start position:0% +already know that that the phytolanton +are sucking a lot of CO2 in through + + align:start position:0% +are sucking a lot of CO2 in through + + + align:start position:0% +are sucking a lot of CO2 in through +photosynthesis. Um so let's look at the + + align:start position:0% +photosynthesis. Um so let's look at the + + + align:start position:0% +photosynthesis. Um so let's look at the +budget here. And this is the + + align:start position:0% +budget here. And this is the + + + align:start position:0% +budget here. And this is the +introduction of CO2 into the atmosphere + + align:start position:0% +introduction of CO2 into the atmosphere + + + align:start position:0% +introduction of CO2 into the atmosphere +by burning fossil fuel and the + + align:start position:0% +by burning fossil fuel and the + + + align:start position:0% +by burning fossil fuel and the +introduction of CO2 into the atmosphere + + align:start position:0% +introduction of CO2 into the atmosphere + + + align:start position:0% +introduction of CO2 into the atmosphere +by destruction of vegetation. + + align:start position:0% +by destruction of vegetation. + + + align:start position:0% +by destruction of vegetation. +So we have 7.5 + + align:start position:0% +So we have 7.5 + + + align:start position:0% +So we have 7.5 +um gigatons going into the atmosphere + + align:start position:0% +um gigatons going into the atmosphere + + + align:start position:0% +um gigatons going into the atmosphere +due to human um perturbation. The annual + + align:start position:0% +due to human um perturbation. The annual + + + align:start position:0% +due to human um perturbation. The annual +increase of CO2 in the atmosphere is + + align:start position:0% +increase of CO2 in the atmosphere is + + + align:start position:0% +increase of CO2 in the atmosphere is +plus uh is 3.5 gigatons. + + align:start position:0% +plus uh is 3.5 gigatons. + + + align:start position:0% +plus uh is 3.5 gigatons. +So + + align:start position:0% +So + + + align:start position:0% +So +3.5 gatons annual increase. + + align:start position:0% +3.5 gatons annual increase. + + + align:start position:0% +3.5 gatons annual increase. +And + + align:start position:0% +And + + + align:start position:0% +And +let's see + + align:start position:0% +let's see + + + align:start position:0% +let's see +ah if we look at the difference here + + align:start position:0% +ah if we look at the difference here + + + align:start position:0% +ah if we look at the difference here +between respiration and photosynthesis + + align:start position:0% +between respiration and photosynthesis + + + align:start position:0% +between respiration and photosynthesis +we see that there's two gigatons going + + align:start position:0% +we see that there's two gigatons going + + + align:start position:0% +we see that there's two gigatons going +into the vegetation actually net into + + align:start position:0% +into the vegetation actually net into + + + align:start position:0% +into the vegetation actually net into +the vegetation. Um, and if we look at + + align:start position:0% +the vegetation. Um, and if we look at + + + align:start position:0% +the vegetation. Um, and if we look at +this, we see that there's two going into + + align:start position:0% +this, we see that there's two going into + + + align:start position:0% +this, we see that there's two going into +the ocean. So, if we ask of all of this + + align:start position:0% +the ocean. So, if we ask of all of this + + + align:start position:0% +the ocean. So, if we ask of all of this +anthropogenic + + align:start position:0% +anthropogenic + + + align:start position:0% +anthropogenic +CO2, + + align:start position:0% +CO2, + + + align:start position:0% +CO2, +uh, where is it going? 3.5 is going to + + align:start position:0% +uh, where is it going? 3.5 is going to + + + align:start position:0% +uh, where is it going? 3.5 is going to +increase in the atmosphere, two is going + + align:start position:0% +increase in the atmosphere, two is going + + + align:start position:0% +increase in the atmosphere, two is going +to the vegetation, and two is going to + + align:start position:0% +to the vegetation, and two is going to + + + align:start position:0% +to the vegetation, and two is going to +the ocean. And it's this + + align:start position:0% +the ocean. And it's this + + + align:start position:0% +the ocean. And it's this +that we're uh very concerned about + + align:start position:0% +that we're uh very concerned about + + + align:start position:0% +that we're uh very concerned about +because it's causing a dramatic increase + + align:start position:0% +because it's causing a dramatic increase + + + align:start position:0% +because it's causing a dramatic increase +in the CO2 in the atmosphere. Even + + align:start position:0% +in the CO2 in the atmosphere. Even + + + align:start position:0% +in the CO2 in the atmosphere. Even +though these are tiny fluxes relative to + + align:start position:0% +though these are tiny fluxes relative to + + + align:start position:0% +though these are tiny fluxes relative to +the global bio biological fluxes, they + + align:start position:0% +the global bio biological fluxes, they + + + align:start position:0% +the global bio biological fluxes, they +these tiny fluxes lead to a significant + + align:start position:0% +these tiny fluxes lead to a significant + + + align:start position:0% +these tiny fluxes lead to a significant +increase because the pool is so small of + + align:start position:0% +increase because the pool is so small of + + + align:start position:0% +increase because the pool is so small of +CO2 in the atmosphere. + + align:start position:0% +CO2 in the atmosphere. + + + align:start position:0% +CO2 in the atmosphere. +So, this is a trace of CO2 since 1960. + + align:start position:0% +So, this is a trace of CO2 since 1960. + + + align:start position:0% +So, this is a trace of CO2 since 1960. +Here's a question for you to think + + align:start position:0% +Here's a question for you to think + + + align:start position:0% +Here's a question for you to think +about. I'm not going to answer it. If + + align:start position:0% +about. I'm not going to answer it. If + + + align:start position:0% +about. I'm not going to answer it. If +summer and winter are out of phase in + + align:start position:0% +summer and winter are out of phase in + + + align:start position:0% +summer and winter are out of phase in +the northern and southern hemisphere, + + align:start position:0% +the northern and southern hemisphere, + + + align:start position:0% +the northern and southern hemisphere, +why isn't this just smooth? This cycle + + align:start position:0% +why isn't this just smooth? This cycle + + + align:start position:0% +why isn't this just smooth? This cycle +that we see here + + align:start position:0% +that we see here + + + align:start position:0% +that we see here +is an annual cycle of the Earth + + align:start position:0% +is an annual cycle of the Earth + + + align:start position:0% +is an annual cycle of the Earth +breathing. Remember, I showed you that + + align:start position:0% +breathing. Remember, I showed you that + + + align:start position:0% +breathing. Remember, I showed you that +in the first lecture. uh showing + + align:start position:0% +in the first lecture. uh showing + + + align:start position:0% +in the first lecture. uh showing +photosynthesis greater than respiration + + align:start position:0% +photosynthesis greater than respiration + + + align:start position:0% +photosynthesis greater than respiration +during the summer and the reverse during + + align:start position:0% +during the summer and the reverse during + + + align:start position:0% +during the summer and the reverse during +the winter. Think about + + align:start position:0% +the winter. Think about + + + align:start position:0% +the winter. Think about +why it isn't just smooth and canceled + + align:start position:0% +why it isn't just smooth and canceled + + + align:start position:0% +why it isn't just smooth and canceled +out by the two hemispheres. Um okay. And + + align:start position:0% +out by the two hemispheres. Um okay. And + + + align:start position:0% +out by the two hemispheres. Um okay. And +if we look at that same graph, this is + + align:start position:0% +if we look at that same graph, this is + + + align:start position:0% +if we look at that same graph, this is +atmospheric CO2 + + align:start position:0% +atmospheric CO2 + + + align:start position:0% +atmospheric CO2 +um from icecore data as a function of + + align:start position:0% +um from icecore data as a function of + + + align:start position:0% +um from icecore data as a function of +time. This is today. Okay. And this is + + align:start position:0% +time. This is today. Okay. And this is + + + align:start position:0% +time. This is today. Okay. And this is +time before present. It's going + + align:start position:0% +time before present. It's going + + + align:start position:0% +time before present. It's going +backwards. This is 450,000 years ago. We + + align:start position:0% +backwards. This is 450,000 years ago. We + + + align:start position:0% +backwards. This is 450,000 years ago. We +can see that CO2 in the atmosphere, and + + align:start position:0% +can see that CO2 in the atmosphere, and + + + align:start position:0% +can see that CO2 in the atmosphere, and +this is measured in, you take a deep ice + + align:start position:0% +this is measured in, you take a deep ice + + + align:start position:0% +this is measured in, you take a deep ice +core in Greenland or something, and you + + align:start position:0% +core in Greenland or something, and you + + + align:start position:0% +core in Greenland or something, and you +measure the CO2 concentration um at + + align:start position:0% +measure the CO2 concentration um at + + + align:start position:0% +measure the CO2 concentration um at +different slices in the core, and it + + align:start position:0% +different slices in the core, and it + + + align:start position:0% +different slices in the core, and it +tells you what the Earth was like back + + align:start position:0% +tells you what the Earth was like back + + + align:start position:0% +tells you what the Earth was like back +then. And this just dramatically shows + + align:start position:0% +then. And this just dramatically shows + + + align:start position:0% +then. And this just dramatically shows +you what we're doing. Uh just in the + + align:start position:0% +you what we're doing. Uh just in the + + + align:start position:0% +you what we're doing. Uh just in the +last hundred years, we have increased + + align:start position:0% +last hundred years, we have increased + + + align:start position:0% +last hundred years, we have increased +the CO2 in the atmosphere. um + + align:start position:0% +the CO2 in the atmosphere. um + + + align:start position:0% +the CO2 in the atmosphere. um +dramatically by burning fossil fuels and + + align:start position:0% +dramatically by burning fossil fuels and + + + align:start position:0% +dramatically by burning fossil fuels and +CO2 is a greenhouse gas and so we're + + align:start position:0% +CO2 is a greenhouse gas and so we're + + + align:start position:0% +CO2 is a greenhouse gas and so we're +very concerned about that. Um + + align:start position:0% +very concerned about that. Um + + + align:start position:0% +very concerned about that. Um +okay, + + align:start position:0% +okay, + + + align:start position:0% +okay, +this is just the uh reshowing that slide + + align:start position:0% +this is just the uh reshowing that slide + + + align:start position:0% +this is just the uh reshowing that slide +uh from last time of upwelling to remind + + align:start position:0% +uh from last time of upwelling to remind + + + align:start position:0% +uh from last time of upwelling to remind +you that the biogeeochemical cycles of + + align:start position:0% +you that the biogeeochemical cycles of + + + align:start position:0% +you that the biogeeochemical cycles of +these elements are tightly coupled. + + align:start position:0% +these elements are tightly coupled. + + + align:start position:0% +these elements are tightly coupled. +Remember we talked about nutrients, + + align:start position:0% +Remember we talked about nutrients, + + + align:start position:0% +Remember we talked about nutrients, +nitrogen, phosphorus being upwelled from + + align:start position:0% +nitrogen, phosphorus being upwelled from + + + align:start position:0% +nitrogen, phosphorus being upwelled from +the deep water. + + align:start position:0% +the deep water. + + + align:start position:0% +the deep water. +Uh phytolanton taking them up, drawing + + align:start position:0% +Uh phytolanton taking them up, drawing + + + align:start position:0% +Uh phytolanton taking them up, drawing +down CO2. And then we had oxygen and CO2 + + align:start position:0% +down CO2. And then we had oxygen and CO2 + + + align:start position:0% +down CO2. And then we had oxygen and CO2 +going back and forth in the water. So + + align:start position:0% +going back and forth in the water. So + + + align:start position:0% +going back and forth in the water. So +the oxygen cycle, which we haven't even + + align:start position:0% +the oxygen cycle, which we haven't even + + + align:start position:0% +the oxygen cycle, which we haven't even +talked about, is tightly coupled also to + + align:start position:0% +talked about, is tightly coupled also to + + + align:start position:0% +talked about, is tightly coupled also to +the CO2 cycle. I'm not going to show + + align:start position:0% +the CO2 cycle. I'm not going to show + + + align:start position:0% +the CO2 cycle. I'm not going to show +this there. Okay, moving on. Um and I + + align:start position:0% +this there. Okay, moving on. Um and I + + + align:start position:0% +this there. Okay, moving on. Um and I +know this is is quickly but this is in + + align:start position:0% +know this is is quickly but this is in + + + align:start position:0% +know this is is quickly but this is in +your readings uh there is a newspaper + + align:start position:0% +your readings uh there is a newspaper + + + align:start position:0% +your readings uh there is a newspaper +article about the biosphere 2 uh + + align:start position:0% +article about the biosphere 2 uh + + + align:start position:0% +article about the biosphere 2 uh +experiment which now is is pretty dated + + align:start position:0% +experiment which now is is pretty dated + + + align:start position:0% +experiment which now is is pretty dated +to to make a long story short many years + + align:start position:0% +to to make a long story short many years + + + align:start position:0% +to to make a long story short many years +ago uh a very rich person um built this + + align:start position:0% +ago uh a very rich person um built this + + + align:start position:0% +ago uh a very rich person um built this +system out in the middle of the Arizona + + align:start position:0% +system out in the middle of the Arizona + + + align:start position:0% +system out in the middle of the Arizona +desert and put seven and and and it had + + align:start position:0% +desert and put seven and and and it had + + + align:start position:0% +desert and put seven and and and it had +seven ecosystems in it. It was sealed. + + align:start position:0% +seven ecosystems in it. It was sealed. + + + align:start position:0% +seven ecosystems in it. It was sealed. +it was closed and he put people in it + + align:start position:0% +it was closed and he put people in it + + + align:start position:0% +it was closed and he put people in it +which were called biospherians. + + align:start position:0% +which were called biospherians. + + + align:start position:0% +which were called biospherians. +Um and the idea was to see whether we + + align:start position:0% +Um and the idea was to see whether we + + + align:start position:0% +Um and the idea was to see whether we +could humans could create a closed uh + + align:start position:0% +could humans could create a closed uh + + + align:start position:0% +could humans could create a closed uh +biosphere that would sustain human life + + align:start position:0% +biosphere that would sustain human life + + + align:start position:0% +biosphere that would sustain human life +and it was a miserable failure. Um which + + align:start position:0% +and it was a miserable failure. Um which + + + align:start position:0% +and it was a miserable failure. Um which +is sad because it cost a lot of money + + align:start position:0% +is sad because it cost a lot of money + + + align:start position:0% +is sad because it cost a lot of money +and has since been taken over by + + align:start position:0% +and has since been taken over by + + + align:start position:0% +and has since been taken over by +Columbia University to use as an + + align:start position:0% +Columbia University to use as an + + + align:start position:0% +Columbia University to use as an +experimental facility. But the one thing + + align:start position:0% +experimental facility. But the one thing + + + align:start position:0% +experimental facility. But the one thing +that they learned um here's what + + align:start position:0% +that they learned um here's what + + + align:start position:0% +that they learned um here's what +happened. + + align:start position:0% +happened. + + + align:start position:0% +happened. +They put the people in um and it turned + + align:start position:0% +They put the people in um and it turned + + + align:start position:0% +They put the people in um and it turned +out that that there was not enough + + align:start position:0% +out that that there was not enough + + + align:start position:0% +out that that there was not enough +photosynthesis to supply enough oxygen + + align:start position:0% +photosynthesis to supply enough oxygen + + + align:start position:0% +photosynthesis to supply enough oxygen +for the people to breathe. Oxygen levels + + align:start position:0% +for the people to breathe. Oxygen levels + + + align:start position:0% +for the people to breathe. Oxygen levels +steadily went down. And the reason for + + align:start position:0% +steadily went down. And the reason for + + + align:start position:0% +steadily went down. And the reason for +that they learned later was that they + + align:start position:0% +that they learned later was that they + + + align:start position:0% +that they learned later was that they +had put way too much uh rich soil in the + + align:start position:0% +had put way too much uh rich soil in the + + + align:start position:0% +had put way too much uh rich soil in the +system. So the bacteria in the soil were + + align:start position:0% +system. So the bacteria in the soil were + + + align:start position:0% +system. So the bacteria in the soil were +sucking the oxygen out of the + + align:start position:0% +sucking the oxygen out of the + + + align:start position:0% +sucking the oxygen out of the +atmosphere. Um and and it wasn't you + + align:start position:0% +atmosphere. Um and and it wasn't you + + + align:start position:0% +atmosphere. Um and and it wasn't you +know they were subsidizing this system + + align:start position:0% +know they were subsidizing this system + + + align:start position:0% +know they were subsidizing this system +with rich soil so the people would have + + align:start position:0% +with rich soil so the people would have + + + align:start position:0% +with rich soil so the people would have +enough food. But there was a puzzle + + align:start position:0% +enough food. But there was a puzzle + + + align:start position:0% +enough food. But there was a puzzle +because if this was the case you should + + align:start position:0% +because if this was the case you should + + + align:start position:0% +because if this was the case you should +because these cycles are coupled you + + align:start position:0% +because these cycles are coupled you + + + align:start position:0% +because these cycles are coupled you +should expect to see uh the same amount + + align:start position:0% +should expect to see uh the same amount + + + align:start position:0% +should expect to see uh the same amount +of if this oxygen is coming from + + align:start position:0% +of if this oxygen is coming from + + + align:start position:0% +of if this oxygen is coming from +photosynthesis you should see the same + + align:start position:0% +photosynthesis you should see the same + + + align:start position:0% +photosynthesis you should see the same +amount of CO2 coming into the system and + + align:start position:0% +amount of CO2 coming into the system and + + + align:start position:0% +amount of CO2 coming into the system and +you should see an increase in CO2 in the + + align:start position:0% +you should see an increase in CO2 in the + + + align:start position:0% +you should see an increase in CO2 in the +atmosphere. and they didn't in other + + align:start position:0% +atmosphere. and they didn't in other + + + align:start position:0% +atmosphere. and they didn't in other +words they saw oxygen going down but + + align:start position:0% +words they saw oxygen going down but + + + align:start position:0% +words they saw oxygen going down but +they didn't see surplus CO2 in the + + align:start position:0% +they didn't see surplus CO2 in the + + + align:start position:0% +they didn't see surplus CO2 in the +atmosphere and it took us bright + + align:start position:0% +atmosphere and it took us bright + + + align:start position:0% +atmosphere and it took us bright +graduate student from Columbia + + align:start position:0% +graduate student from Columbia + + + align:start position:0% +graduate student from Columbia +University to go in there and figure out + + align:start position:0% +University to go in there and figure out + + + align:start position:0% +University to go in there and figure out +what was going on and it turned out + + align:start position:0% +what was going on and it turned out + + + align:start position:0% +what was going on and it turned out +that + + align:start position:0% +that + + + align:start position:0% +that +so why didn't CO2 increase it turned out + + align:start position:0% +so why didn't CO2 increase it turned out + + + align:start position:0% +so why didn't CO2 increase it turned out +that this this CO2 which was um coming + + align:start position:0% +that this this CO2 which was um coming + + + align:start position:0% +that this this CO2 which was um coming +out of the system from respiration in + + align:start position:0% +out of the system from respiration in + + + align:start position:0% +out of the system from respiration in +the soil was actually binding to the + + align:start position:0% +the soil was actually binding to the + + + align:start position:0% +the soil was actually binding to the +calcium ium hydroxide in the cement and + + align:start position:0% +calcium ium hydroxide in the cement and + + + align:start position:0% +calcium ium hydroxide in the cement and +making calcium carbonate. Uh so the + + align:start position:0% +making calcium carbonate. Uh so the + + + align:start position:0% +making calcium carbonate. Uh so the +cement another human uh invention uh was + + align:start position:0% +cement another human uh invention uh was + + + align:start position:0% +cement another human uh invention uh was +playing an important role here. The + + align:start position:0% +playing an important role here. The + + + align:start position:0% +playing an important role here. The +point is that none of this is only + + align:start position:0% +point is that none of this is only + + + align:start position:0% +point is that none of this is only +understandable in hindsight because it + + align:start position:0% +understandable in hindsight because it + + + align:start position:0% +understandable in hindsight because it +didn't work. You could go in and figure + + align:start position:0% +didn't work. You could go in and figure + + + align:start position:0% +didn't work. You could go in and figure +out what the heck was where where did + + align:start position:0% +out what the heck was where where did + + + align:start position:0% +out what the heck was where where did +these imbalances come from, you know? + + align:start position:0% +these imbalances come from, you know? + + + align:start position:0% +these imbalances come from, you know? +So, it was a very interesting study and + + align:start position:0% +So, it was a very interesting study and + + + align:start position:0% +So, it was a very interesting study and +we learned that it's not easy to mimic + + align:start position:0% +we learned that it's not easy to mimic + + + align:start position:0% +we learned that it's not easy to mimic +natural the biosphere on a very small + + align:start position:0% +natural the biosphere on a very small + + + align:start position:0% +natural the biosphere on a very small +scale. Okay. + + align:start position:0% +scale. Okay. + + + align:start position:0% +scale. Okay. +Um, + + align:start position:0% +Um, + + + align:start position:0% +Um, +I'm going to skip that one and jump to + + align:start position:0% +I'm going to skip that one and jump to + + + align:start position:0% +I'm going to skip that one and jump to +this real quickly because this was just + + align:start position:0% +this real quickly because this was just + + + align:start position:0% +this real quickly because this was just +on the news this morning as I was + + align:start position:0% +on the news this morning as I was + + + align:start position:0% +on the news this morning as I was +driving into work. I thought, ah, + + align:start position:0% +driving into work. I thought, ah, + + + align:start position:0% +driving into work. I thought, ah, +perfect for this lecture. Um, the UN + + align:start position:0% +perfect for this lecture. Um, the UN + + + align:start position:0% +perfect for this lecture. Um, the UN +just announced this Millennium Ecosystem + + align:start position:0% +just announced this Millennium Ecosystem + + + align:start position:0% +just announced this Millennium Ecosystem +assessment. It's on the web. Um and and + + align:start position:0% +assessment. It's on the web. Um and and + + + align:start position:0% +assessment. It's on the web. Um and and +it's a the people have been 2,000 + + align:start position:0% +it's a the people have been 2,000 + + + align:start position:0% +it's a the people have been 2,000 +scientists have been working on this for + + align:start position:0% +scientists have been working on this for + + + align:start position:0% +scientists have been working on this for +over 10 years trying to assess the state + + align:start position:0% +over 10 years trying to assess the state + + + align:start position:0% +over 10 years trying to assess the state +of the global ecosystems and their + + align:start position:0% +of the global ecosystems and their + + + align:start position:0% +of the global ecosystems and their +capability to support future generations + + align:start position:0% +capability to support future generations + + + align:start position:0% +capability to support future generations +i.e. you guys and they say the next 50 + + align:start position:0% +i.e. you guys and they say the next 50 + + + align:start position:0% +i.e. you guys and they say the next 50 +years and those are the 50 years that + + align:start position:0% +years and those are the 50 years that + + + align:start position:0% +years and those are the 50 years that +you guys are in charge are absolutely + + align:start position:0% +you guys are in charge are absolutely + + + align:start position:0% +you guys are in charge are absolutely +critical for whether or not these + + align:start position:0% +critical for whether or not these + + + align:start position:0% +critical for whether or not these +systems um will sustain be able to + + align:start position:0% +systems um will sustain be able to + + + align:start position:0% +systems um will sustain be able to +sustain human populations. So you can go + + align:start position:0% +sustain human populations. So you can go + + + align:start position:0% +sustain human populations. So you can go +to the web if you're interested in that. + + align:start position:0% +to the web if you're interested in that. + + + align:start position:0% +to the web if you're interested in that. +Okay. Quickly to our + + align:start position:0% +Okay. Quickly to our + + + align:start position:0% +Okay. Quickly to our +civil and environmental engineering uh + + align:start position:0% +civil and environmental engineering uh + + + align:start position:0% +civil and environmental engineering uh +major. I'm just going to say that our + + align:start position:0% +major. I'm just going to say that our + + + align:start position:0% +major. I'm just going to say that our +new motto is nature tools and toys. Uh + + align:start position:0% +new motto is nature tools and toys. Uh + + + align:start position:0% +new motto is nature tools and toys. Uh +one of those. Yeah. Nature is ecology. + + align:start position:0% +one of those. Yeah. Nature is ecology. + + + align:start position:0% +one of those. Yeah. Nature is ecology. +There's a two series ecology course. Uh + + align:start position:0% +There's a two series ecology course. Uh + + + align:start position:0% +There's a two series ecology course. Uh +tools are mechanics um basics uh + + align:start position:0% +tools are mechanics um basics uh + + + align:start position:0% +tools are mechanics um basics uh +fundamentals for analyzing systems and + + align:start position:0% +fundamentals for analyzing systems and + + + align:start position:0% +fundamentals for analyzing systems and +toys is design. the the part of the + + align:start position:0% +toys is design. the the part of the + + + align:start position:0% +toys is design. the the part of the +curriculum is going to be designing + + align:start position:0% +curriculum is going to be designing + + + align:start position:0% +curriculum is going to be designing +instrumentation for uh studying + + align:start position:0% +instrumentation for uh studying + + + align:start position:0% +instrumentation for uh studying +environmental systems. And there are + + align:start position:0% +environmental systems. And there are + + + align:start position:0% +environmental systems. And there are +these brochures here and in the back. + + align:start position:0% +these brochures here and in the back. + + + align:start position:0% +these brochures here and in the back. +So, I encourage you to pick those up if + + align:start position:0% +So, I encourage you to pick those up if + + + align:start position:0% +So, I encourage you to pick those up if +you're at all interested in in that + + align:start position:0% +you're at all interested in in that + + + align:start position:0% +you're at all interested in in that +major. Now, let me show you this cool + + align:start position:0% +major. Now, let me show you this cool + + + align:start position:0% +major. Now, let me show you this cool +clip. Don't leave yet. This is worth it. + + align:start position:0% +clip. Don't leave yet. This is worth it. + + + align:start position:0% +clip. Don't leave yet. This is worth it. +It's only two minutes. Um, and it's + + align:start position:0% +It's only two minutes. Um, and it's + + + align:start position:0% +It's only two minutes. Um, and it's +nature at its best. So, all I need to do + + align:start position:0% +nature at its best. So, all I need to do + + + align:start position:0% +nature at its best. So, all I need to do +here is + + align:start position:0% + + + + align:start position:0% + +is click play. + + align:start position:0% +is click play. + + + align:start position:0% +is click play. +This the soccer players will smile + + align:start position:0% +This the soccer players will smile + + + align:start position:0% +This the soccer players will smile +like this. Oh, why didn't that work? + + align:start position:0% +like this. Oh, why didn't that work? + + + align:start position:0% +like this. Oh, why didn't that work? +There we go. + + align:start position:0% +There we go. + + + align:start position:0% +There we go. +The sand bubbler crab in the straight. + + align:start position:0% +The sand bubbler crab in the straight. + + + align:start position:0% +The sand bubbler crab in the straight. +It smile for + + align:start position:0% +It smile for + + + align:start position:0% +It smile for +just a centimeter across. The sand + + align:start position:0% +just a centimeter across. The sand + + + align:start position:0% +just a centimeter across. The sand +bubbler works at breakneck speed passing + + align:start position:0% +bubbler works at breakneck speed passing + + + align:start position:0% +bubbler works at breakneck speed passing +sand grains into its mouth filtering out + + align:start position:0% +sand grains into its mouth filtering out + + + align:start position:0% +sand grains into its mouth filtering out +all the myofa and kicking aside the + + align:start position:0% +all the myofa and kicking aside the + + + align:start position:0% +all the myofa and kicking aside the +waste. + + align:start position:0% +waste. + + + align:start position:0% +waste. +Myofona are little bugs in the sand. + + align:start position:0% +Myofona are little bugs in the sand. + + + align:start position:0% +Myofona are little bugs in the sand. +Crab + + align:start position:0% + + + + align:start position:0% + +will clean every grain of sand within a + + align:start position:0% +will clean every grain of sand within a + + + align:start position:0% +will clean every grain of sand within a +meter of its + + align:start position:0% +meter of its + + + align:start position:0% +meter of its +endless practice for the best back heel + + align:start position:0% +endless practice for the best back heel + + + align:start position:0% +endless practice for the best back heel +in the natural world. + + align:start position:0% +in the natural world. + + + align:start position:0% +in the natural world. +[Music] + + align:start position:0% + + + + align:start position:0% + +That's my favorite part. + + align:start position:0% +That's my favorite part. + + + align:start position:0% +That's my favorite part. +[Music] + + align:start position:0% +[Music] + + + align:start position:0% +[Music] +The crabs work fast because they can + + align:start position:0% +The crabs work fast because they can + + + align:start position:0% +The crabs work fast because they can +only sit where the sand is back. + + align:start position:0% +only sit where the sand is back. + + + align:start position:0% +only sit where the sand is back. +Remarkably, they work the entire surface + + align:start position:0% +Remarkably, they work the entire surface + + + align:start position:0% +Remarkably, they work the entire surface +of the beach within just a couple hours + + align:start position:0% +of the beach within just a couple hours + + + align:start position:0% +of the beach within just a couple hours +of the time retreating. + + align:start position:0% +of the time retreating. + + + align:start position:0% +of the time retreating. +See, life is a geological agent. + + align:start position:0% +See, life is a geological agent. + + + align:start position:0% +See, life is a geological agent. +[Music] + + align:start position:0% + + + + align:start position:0% + +See, that would have been a great + + align:start position:0% +See, that would have been a great + + + align:start position:0% +See, that would have been a great +kickoff for spring break. But welcome + + align:start position:0% +kickoff for spring break. But welcome + + + align:start position:0% +kickoff for spring break. But welcome +back from spring break. + + align:start position:0% +back from spring break. + + + align:start position:0% +back from spring break. +All right, I'll see you in a few weeks. \ No newline at end of file diff --git a/zPPsdsAQBx4.txt b/zPPsdsAQBx4.txt new file mode 100644 index 0000000000000000000000000000000000000000..356d9b1188ea2be3b7ee580630e90068d8964cc2 --- /dev/null +++ b/zPPsdsAQBx4.txt @@ -0,0 +1,4464 @@ +The following content is +provided under a Creative + +Commons license. + +Your support will help MIT +OpenCourseWare continue to + +offer high quality educational +resources for free. + +To make a donation or view +additional materials from + +hundreds of MIT courses, visit +MIT OpenCourseWare at + +ocw.mit.edu. + +PROFESSOR: So last time, we +talked about spectacular + +things about human nature +in terms of problems or + +difficulties when we overly +obey, when we're overly + +conformist, and the tendency +for us to do that much more + +than we imagine we would. + +And the experimental +evidence is pretty + +powerful, that is true. + +You could call that the dark +side of things like obedience + +a and conformity. + +The upside of it is that's how +we work together and get along + +as a society. + +And today, I'm going to focus +more on individual, everyday + +experiences. + +But again, I think you'll see +in terms of self-concept and + +impressions of others, +those are more + +everyday kinds of things. + +But you'll see how they populate +our lives, how we + +think about ourselves, how we +think about people in everyday + +interactions, impressions +of others. + +We've talked a little bit, +just a little bit, about + +cultural differences. + +Our course has been very focused +on American, European + +type cultures. + +We talked a little about +different ones. + +I'll say a bit more +about that. + +And then, I'll talk about maybe +the most thought about + +disorder of social interaction, +autism. + +So enhancing our views +of ourselves, OK? + +So most US college students rank +themselves as better than + +average students. + +So you can sit there in your +chair and you could go, no, + +I'm a pretty modest person. + +But really, I'm probably +better than the average + +student, right? + +And by the way, I'll tell you +faculty are the same. + +So a million high school +students rated their + +leadership ability +in one example. + +28% said they were average. + +70% rated themselves as above +average in leadership. + +You understand that only 50% +could be at most above + +average, or 49%. + +Only 2% said they were +below average. + +60% of the high school students +of these million said + +were in the top 10% in +their ability to + +get along with others. + +And by the way, just in case +you think it's picking on + +students, 94% of college +instructors rated themselves + +as better than average +teachers. + +So whether you're sitting there +or standing here, we all + +polish our image to ourselves. + +And we can decide, is +that a bad thing? + +Is that vanity or egoism? + +Or is that maybe a pretty +healthy way to + +bump through life? + +Is overrating yourself, short +of putting yourself in + +destructive situations, is that +a way to be happy and + +optimistic? + +Are we resilient? + +So people call this +self-serving + +attributional biases. + +And this will play out +a little bit like the + +fundamental attribution error. + +Let me remind you +of what that is. + +The fundamental attribution +error is when other people do + +things, it's their character, +and especially failings are + +because of failings of +their character. + +When we do things we're not +especially proud of or don't + +think are awesome, that's the +situation that made us do it. + +And we don't provide that same +understanding of the situation + +to understand the behaviors +of others. + +It's not intuitive to do so. + +So they did experiments where +the experimenter set up how + +well you would do on tests. + +They made a test super difficult +or easier, sensory + +or perceptual discrimination, +social sensitivity, + +competitive games. + +It's all set up by +the experimenter. + +They can make tests brutally +hard or pretty easy. + +They can make you do well +or make you do badly. + +And when people did well and +they were asked to say why + +they thought they did well, +the usual description was, + +because I'm a particularly +social person. + +I'm very competitive. + +I'm extra good at sensory +perception. + +You pick it. + +When they did badly, that +was a tough test. + +It's rare for people to say, +that was an easy test! + +Who wouldn't do well? + +If you do well, people tend to +ascribe it to their character, + +and when they do badly, +the situation. + +even within ourselves. + +And it extends to families, +social and political groups, + +and sports teams. + +You may know I'm very proud and +happy to be a member of + +the MIT community. + +Something happens bad +at MIT, I don't go, + +well, then, MIT stinks. + +I go, oh, there was a situation +that wasn't + +well-handled by an individual. + +Same thing you might +think about the + +country you belong to. + +We don't say, US did +something bad. + +Most of us don't go, well, +the US stinks. + +We go, that's situation +wasn't very good. + +We've got to change things. + +Yeah? + +AUDIENCE: Do you think this is +saying more about how people + +explain things to others +or about what + +they actually believe? + +PROFESSOR: So the question was, +is it what they actually + +believe, or say to others? + +I think the evidence is it's +about what they say to + +themselves truly about how they + +explain success or failure. + +OK? + +People are biased to attribute +their successes to their + +wonderful traits and their +failures to situations. + +But we talked earlier that that +can be a healthy thing. + +Because then, you +can bounce back. + +You can say, well, +I did badly. + +But, hey, I'm a winner. + +And tomorrow morning, +I'll get up. + +And I'm back at bat, right? + +Instead of saying, +oh, I'm a loser. + +It's all just pointless. + +So in what sense is it +good to have this? + +It's not a good thing +or a bad thing. + +It's probably a thing of +positive mental health but it + +can make us overlook +causes of things. + +So an example of that as we +construct social realities, + +and you may know this is +the original study. + +But there's a million since. + +An undefeated Princeton +team played Dartmouth + +in a football game. + +Princeton won. + +And then, they looked +at the newspaper + +accounts of the games-- + +totally different. + +They showed the film +to students + +from the two campuses. + +And depending on which team +you were rooting for, you + +tended to view the other team +as dirty, not playing fair, + +not doing the right thing. + +You don't have to be much of a +sports fan to notice things + +where the other team is not +doing the right thing and your + +team, when it doesn't do the +right thing, well, they were + +under pressure. + +It was atypical. + +And that makes it, of +course, hard for + +people to get together. + +We don't too much worry about +Princeton/Dartmouth + +tension in the world. + +But we do worry about tensions +in the Middle East between + +Palestinians and Israelis. + +When they see the same news +story, how do they interpret + +what happened in that +news story? + +So this question of if we have +illusions that we're better + +than we are a little bit, is +that a bad thing or is that a + +good thing was tested in an +ironic study by Alloy and + +Abramson looking at patients +with actual clinical + +depression. + +So they gave depressed and +non-depressed students tasks + +that varied in the degree of +contingency, that is how much + +the performance of the +participant actually + +influenced the outcome. + +They controlled that. + +And then, they asked people +afterwards to estimate the + +degree of contingency between +a button press and a green + +light going on. + +How much of it was you, and how +much of it seemed to be + +randomly done by the +experimenter? + +Depressed students in this +particular setting were more + +accurate in knowing when it +would depend on them. + +And non-depressed students +overestimated the contingency. + +They overestimated their +influence on the situation + +when the outcomes +were desired. + +Awesome, that's because +I'm awesome. + +And when things didn't go so +well, again, not really under + +their control. + +But they don't know that. + +It's the situation. + +Something was screwed up +with the experiment. + +So they're more variable-- + +they interpret the situation +much more, + +again, on these things. + +And you could say they're +less accurate. + +But you could also say that's +a way, again, to have + +confidence in yourself and +optimism about the future. + +Another way in which we believe +and justify our + +choices but a way in which we're +socially influenced is + +this, the phenomenon called +false consensus. + +People choose to engage in a +behavior that those people who + +do that believe that it's more +common and that more people do + +that, that when you do +something, the more you do it, + +the more you think other +people do it, too. + +What's the big deal? + +You might know that feeling. + +So the original experiment on +the Stanford campus for this + +phenomenon from Lee Ross was he +asked people carry around a + +sign on campus that said "Eat +at Joe's" for 30 minutes. + +Some people said +no, thank you. + +Some people said yes because +they were obedient. + +Compliance. + +Now, of the people who said yes, +I'll carry that sign for + +30 minutes, they thought the +majority of other people when + +asked to do so will do so. + +They thought, well, that's +the way most people are. + +And I'm going to behave +like most people. + +That's a false consensus. + +The people who said no, I won't +do it, they thought the + +majority would not do it. + +So part of their thinking about +deciding if they'll do + +something or not is their +estimate of whether people in + +general would do it. + +But what you can see happens +is that driven by whether + +they're going to do it or not. + +So for example, teenage smokers +estimate higher rates + +of smoking than nonsmokers. + +Domestically abusive men +estimate that about 28% of men + +have violently thrown things +at their partner. + +Best estimates are +it's down to 12%. + +So we tend to overly believe +that other people will do the + +same behaviors that we do. + +And that's part of justifying +those behaviors. + +A demonstration of that was from +Phil Zimbardo, the social + +psychologist who did the +prison experiment. + +This has some of the same +flavor, not quite as dramatic. + +But he worked in New York before +he moved to Stanford. + +So he compared the Bronx +to Palo Alto. + +In 1980, the paper +was published. + +And he left out cars, one in +upper middle class Palo Alto-- + +very suburban area if you +haven't been there-- and one + +in a tough Bronx area. + +As you could imagine, you +leave a car out there by + +itself in the Bronx area without +a license plate and + +the hood was up, it was +stripped within a day. + +So you park the car, you push +up the hood, no license + +plate-- stripped within a day. + +In Palo Alto, it's untouched +for a week. + +So that's obviously to do with +the environment you're in. + +But here's the false +consensus. + +So then, they smash a window. + +And within an hour, +it's stripped. + +As soon as you smash the +window-- we talked about + +broken windows. + +Here it is literally. + +Soon as somebody says, +all rules are off. + +This car is smash, wrecked-- + +that's the behavior +I can engage in. + +What you perceive as the +relevance, the environment of + +behaviors are appropriate, +hugely influences and + +justifies and drives +your own behavior. + +Now one of the tasks people have +to try to convince people + +to do public goods +in various ways-- + +and this is an ad that when I +was younger was very famous. + +For you, it's so long ago +in history that you may + +not even know it. + +But it was one of the most +famous ones when the United + +states was first confronting +issues with environmental + +problems and pollution. + +You may not believe this, but +there was an era when there + +was fantastic pollution in the +air and the water and the land + +and nobody seemed to care about +it at all because land + +seemed endless. + +It wasn't even a thought. + +So Earth Day was +from the 1970s. + +That was the marking of a wider +consciousness of the + +consequence of ruining +the environment. + +And so in the very earliest +stages, when people weren't + +used almost any discussions of +that, there was this ad with a + +Native American with a tear +running down his face. + +And let me show you the ad. + +A very powerful ad at a time, +and one that I'll show you in + +a minute that social +psychologists believe was + +completely counterproductive +to the goal of reducing + +pollution-- + +exactly the thing you don't +want to do because we just + +talked about false consensus and +about these environmental + +justifications. + +So I'll tell you, but +what does that mean? + +So if you see a lot of people +throwing garbage onto the + +beach, onto the street, into +the river, what are you + +allowed to do? + +Pollute yourself. + +Hey, everybody else +is doing it. + +What's the big deal? + +That's the mode of +behavior, right? + +Broken window, steal the car. + +Litter everywhere, OK, +somebody is saying + +it's not a good idea. + +But the behavior that I see is + +littering, littering, littering. + +It's OK to litter. + +So they literally showed +this in experiments. + +They took people into +areas, into parks. + +They surrounded them with +different amounts of trash. + +Here's the percentage of +people who litter. + +Here's how much trash +was around them. + +They went into parks and they +put a little trash and they + +watched somebody come by. + +Still, some people +are littering. + +Maybe less would now. + +I don't know. + +But as soon as there was four +pieces or eight pieces of + +littering, then you more than +double the littering when + +there's zero. + +So the very example of showing +littering drives littering. + +You say, nobody's saying +it's a good thing. + +But hey, it's what everybody's +doing. + +And why do we litter? + +Because we're lazy and most of +us just don't want to bother + +to walk to the garbage can. + +So they did an experiment with +public service announcements + +where they said the important +thing is to see behavior, the + +behavior you want. + +Like in this case, it was +a recycling thing. + +And then, you show one example +of a person who doesn't do it. + +And you say, bad person! + +You don't say bad person, but +you send that message. + +You say, here's the +behavior we want. + +There's somebody doing that. + +Uh-uh. + +And what they found +is that 25%-- + +this is truly in +the community-- + +increase in recycling. + +So if you want to get people to +do things, showing them bad + +behavior unfortunately makes +them think that bad behavior + +is widespread and an acceptable +way to go. + +So you have to show them good +behavior and then give maybe + +one example of bad things +because you don't want to be + +labeled bad. + +But mostly, they have to see the +behavior you want, not the + +behavior you're trying +to discourage. + +So for a social psychologist, +exactly the opposite outcome + +of the intended ad. + +So this speaks to a gap +almost all of us have. + +Some of you may be more perfect +than I. Many of you + +may be more perfect than I. +But here's the gap we face + +every morning when we get up, +which is the difference + +between our attitudes +and our actions-- + +the things we know are the way +we wish we were, the right + +thing to do, and the way in +which sometimes we don't + +always do the rightest thing +we know we could. + +So daffodil days, you may know, +occurs in many places + +including universities where you +buy a daffodil and there's + +a four day campus +event to benefit + +American Cancer Society. + +So it's a nice thing. + +It's buying a flower. + +It's a good cause, fighting +cancer, very positive. + +So they did a study with +251 Cornell students. + +And they asked them, when +daffodil day comes up and you + +just spend a tiny bit of money-- +it's a very small + +amount of money they +ask from students-- + +will you buy at least +one flower? + +And over 80% said, +yes, I will. + +For a cause like that, buying +a beautiful flower to fight + +cancer, I'll spend $1. + +How about the other students? + +Well, they're kind of lazy. + +And they have good intentions. + +But probably only about half +of them will do it. + +That's a little bit of +the self-affirmation. + +I'm a good person. + +Other people will be flawed. + +So how many people +actually buy it? + +43%. + +So what happened to this 40%? + +Well, it's a little bit +like the story. + +Things were busy. + +Things were happening. + +They weren't for cancer +and against flowers, + +just they got busy. + +There were exams. + +There was stuff going on. + +And how do we explain to +ourselves this gap between the + +attitudes we hold +and truly hold? + +We want to do good things and +be a good person, and the + +actions we do, which are often +a little bit below that? + +So this gap between our +attitudes and our actions has + +led to the phenomenon of +cognitive dissonance. + +You now hear this term +used widely. + +Originally, it had a pretty +narrow meaning. + +And I'm going to +be just talking + +about that narrow meaning. + +It's become a term that's +used much more widely. + +But here's the original +work from Festinger. + +He said that we have a problem +all the time that we have a + +gap between our attitudes and +our behaviors and that, as + +humans, we have to solve this +because we don't feel good + +about that gap. + +And so here's how we approached +showing how we + +solve that problem. + +Of course, the nice thing would +be just to do the right + +thing all the time. + +But that's not within, most +of us, somehow our grasp. + +OK + +So here's what he +had people do. + +He had people come in and do +a purposefully boring task. + +So they would pack and unpack +spools in a tray. + +Or they would turn tiny +little screws, + +each of them a quarter. + +It was purposefully boring. + +You could tell it was boring, +and it was boring. + +This was the goal. + +And then, either nothing +would happen-- + +that's one group-- + +or you would get paid $1-- + +not much money-- + +or $20-- + +considerably better-- + +to lie and tell the next person +who's coming in that + +this was an interesting +and worthwhile task. + +So you imagine you go in there, +you do something that's + +really boring. + +Imagine you're in this group. + +They say, here, here's $1. + +Will you lie to the +next person? + +Or here's $20, will you lie to +the next person saying this + +was a pretty cool task? + +I can't believe how lucky you +are to have the next turn. + +And then they say, OK, now we +know you lied to that person. + +We asked you to do it. + +But really, really, +how was the task? + +Really, really, how +was the task? + +And here's the amazing +finding. + +If you don't lie, you say I +didn't like it very much at + +all, here's zero, +less than zero. + +If you are paid $1 to lie, +whoa, it really was good! + +If you're paid $20 to lie, you +pretty much agree it stinks. + +So how does that work? + +You have to see the irony +of this, right? + +So the interpretation is this. + +If somebody pays you $20 to make +a white lie-- you don't + +see this as a brutal lie, just +telling the next student that + +this is a pretty cool task-- + +is $20 worth a white lie? + +You can live with that. + +You know why you did it. + +But $1? + +Would you sacrifice your +integrity for $1? + +You understand-- + +$1? + +How cheap can you be? + +So their idea is this. + +But now they're asking them +really, really, really, really + +the way that people put together +their attitudes, like + +I lied for a mere dollar, is to +say, hey, it must have been + +more interesting than +I first thought. + +Come to think of it, it was +pretty interesting. + +Boom. + +Do you understand that? + +So the effort to match up the +discrepancy between your + +attitudes and actions, +you solve-- + +you can't let them +go like this. + +You can explain this. + +I lied because I got +paid a bunch. + +But this, you can't explain. + +It's too hard to understand. + +And you really create a +rationalization that puts it + +all together. + +And you really, really report +now that this was + +a pretty good task. + +Here's another one. + +And this is not high +tech experiments. + +You can do amazing experiments +without zapping people. + +But by the time I tell you the +end of this one experiment-- + +let's see if I have +one more on this. + +Nah, I'll mention it now +and then the next one. + +It pretty much ruins it whenever +anybody tells you how + +satisfied they are with almost +anything they've + +done in their life. + +This has ruined it for me. + +And I'll tell you why. + +Although I know that +you're better off + +polishing your happiness. + +So here's a simple experiment. + +This guy, Jack Brehm, had a +bunch of wedding gifts. + +And he took his wedding +gifts to the lab. + +It was not very high tech. + +And he had people rate how +much they wanted them. + +So he had stuff like a desk +lamp, a toaster, a stopwatch, + +a radio, a bunch of stuff +you got in the + +1950s as wedding gifts. + +People rated how much +did they like them. + +And then, he picked two that +were in the middle of the list + +and rated right next +to each other. + +And he said, will you pick +one of these two? + +You get to take it home. + +Will you pick one of these two +that you rated in the middle + +right next to each other? + +And you pick one. + +He says, OK, do one more thing +before you take it home. + +Tell me again your rating for +the different things here. + +And here's what they find, +that the items that + +you chose move up. + +You already have it. + +But let's say it was rated one +to 10, it was rated a five, it + +now becomes a two. + +Man, that stopwatch, that's +pretty awesome. + +I thought it was a five. + +But it's a two, maybe a one. + +I can't believe how lucky +I am that I picked that. + +And how about the one +you didn't pick? + +Say the toaster was number +six or number four. + +That moved to nine or 10. + +That toaster stinks. + +That would have been such a bad +choice to attend Harvard. + +It would have been a disaster. + +Thank goodness I picked MIT. + +So the idea is even something +like this-- and everything + +they do, college +choices, cars-- + +any experiment you do, if you +have people rate after they + +made a decision about what +they're going to do, they + +always rate the thing they +picked as awesome on average + +and the thing they didn't pick +as much worse than they + +initially rated it. + +And again, you can say, +is that a way we can + +have a happy life? + +Would you want to be at MIT +every day going, if only I'd + +gone to Princeton! + +Would you want to get married +to somebody and say, if only + +I'd waited a little +bit longer. + +For your career, could you have +said, I went right to + +medical school or law school +or engineering. + +If only I waited longer! + +So you want to say no, +thank goodness + +I picked that college. + +Thank goodness I picked +that career. + +Thank goodness I picked that +spouse or partner because the + +other choices that were vaguely +in my head were awful. + +I don't know how I was even +thinking about them. + +So this has ruined it for me +every time anyone tells me how + +happy they are with a choice +they've made in their life + +because I look at this and go, +yeah, once you make that + +choice, you're going to rate it +as awesome no matter what. + +And a famous example is now many +of you are taking pretty + +tough courses. + +Years later when you come back +for alumni events-- and + +hopefully many of you will have +good feelings about MIT + +and come back and see +your classmates-- + +and you'll get around and say, +oh, that course was so brutal. + +I know that won't +be this course. + +That course was so brutal +with the problem sets. + +But it made me a stronger +person, a better person. + +Thank goodness I did it. + +And maybe it does. + +But let me tell you +why you will think + +that in large numbers. + +So 1959, there's a little bit +of a sociological experiment + +in the sense you have to think +of people in 1959. + +And they were told to qualify +for a research study, some + +women were required to read +aloud a list of obscene words + +which are seen as extremely +embarrassing and + +inappropriate in 1959. + +Nowadays, it might be +the preferred mode. + +But in 1959, it was like, +I don't know. + +This is not right-- + +or mild words. + +So that's the experimenter. + +Then, you got the privilege, if +you did this, to listen to + +a lecture on mating habits +of lower animals. + +But they made it the most +boring they could. + +This could go a couple different +ways, mating habits + +of lower animals. + +They made it super boring +on purpose. + +Lecture's over. + +And they ask the students +to rate the lecture, an + +intentionally super +boring lecture. + +And the women were either in the +group with the unpleasant + +experience of having to read +aloud uncomfortable word lists + +or just neutral words, +no big deal. + +Who rated the lecture better? + +The women who read the obscene +list of words because they + +were saying, well, why would +I do this if the + +lecture weren't terrific? + +So the worse the experience +where you've had some sense of + +choice in it, the more people +will explain to themselves I + +took it for an extremely +good reason. + +I would not do a +painful thing. + +I'm not that incompetent. + +It must've been a +wise decision. + +And in fact, I should tell you +that if the examiner picks + +these items, you don't have +much of an effect. + +So if you rate items four and +five or five and six and the + +examiner gives you the +stopwatch, it doesn't change + +your ratings because you +didn't choose it. + +The examiner did. + +The stopwatch is a +mediocre gift? + +It's still a mediocre gift. + +But if you chose it, you have +to justify the choice. + +And there's 1,000 experiments +like this. + +Why did I do something +so painful? + +It must've been for a +very good reason. + +And then, you figure out what +that reason was, like the + +lecture was more awesome +than I thought. + +That physics course, that math +course, that computer science + +course just made me the +person I am today. + +We're going to switch gears +now, first impressions. + +So there's a book from Malcolm +Gladwell, Blink, which is + +really driven by this +phenomenon. + +The first impressions we take +of other people, how + +powerful are they? + +How valid are they? + +How accurate are they? + +So here's how we're going to +start the story, all the way + +back in 1966. + +They had students rate people's +personality on the + +first day of class before +they met each other. + +So if we had done this in this +course, imagine the first day + +of this course, imagine you're +not sitting with a friend and + +you're asked to people around +you on various personality + +dimensions. + +And the two that popped +out were sociable and + +responsibility. + +The people who said they were +sociable people tended to rate + +them as sociable just from +sitting next to them for a + +moment or as highly +responsible. + +So this is outgoingness and +personality psychology or + +extraversion. + +And this is something like +conscientiousness. + +Just talk to a person for +a couple of moments. + +You rate them pretty much like +they rate themselves. + +You don't know anything about +their background. + +You haven't had a +big interaction. + +Literally, it's moments next +to each in a course. + +Here's another one, 250 students +divided into groups + +of four who didn't know each +other and had not spoken. + +And they rated each other. + +And there was pretty good +correlations between moments + +of sitting together and how +sociable or extroverted people + +were, how responsible, +or conscientiousness. + +So a few moments with somebody +correlates pretty well your + +rating, on average, with how +they know themselves from a + +lifetime of personal +experience-- a few moments, + +pretty well. + +Now, we could say how well +do we rate ourselves? + +You could already pretty well +because it's pretty well + +adjusted with what other +people think. + +But here's another example where +they put strangers into + +groups, videotaped them, had +other people later on view the + +video tapes and rate things +like how extroverted they + +were, how much time did they +talk, how many arm movements. + +The impressions of the judges +watching the videotape + +correlated pretty well with +self-ratings and with ratings + +of other people who saw them +just for a few moments + +personally. + +So all these things line up. + +Just from a few moments of +experience, you get a + +surprisingly strong consensus +about how outgoing somebody is + +and how conscientious or +responsible they are. + +And it lines up pretty much with +the person's own judgment + +about themselves that way. + +So this reached a huge moment +from Nalani Ambady who's now + +at Tufts having this famous +experiment, thin slices. + +And it's a fantastic +experiment. + +And if you ever teach, +it makes you nervous. + +Then, we'll discuss whether +it should or not. + +So at Harvard, here's +what she did. + +She took videotapes of 13 +graduate teaching assistants. + +And they were horrible +video tapes. + +This is 1990. + +They were horrible videotape. + +I'm just going to tell you-- + +you don't even see them around +very much because the quality, + +when you see them, you can't +believe people even + +saw things in them. + +And she got a random 10 second +clip, 30 seconds per teaching + +assistant, 30 seconds. + +She shows a silent +clip to students. + +There's no sound even. + +You're just seeing silently +some teaching assistant in + +front of students saying +something. + +And then, she has these students +rate from the silent + +film clip how accepting, +active, competent, or + +confident the teaching assistant +is who they've never + +met and, of course, +they don't know. + +And they don't know +what the teaching + +assistant's talking about. + +Here's the impressive thing. + +Then, they correlate the ratings +with the actual end of + +semester rating with students. + +They take the students who sat +through the entire course with + +a teaching assistant, that's +one set of values. + +They take the students +who see 30 seconds of + +silent, grainy videotape. + +And they say, how well do these +things do together? + +And they correlate 0.76, +which is really high. + +It's really high in our +field of research. + +That momentary, uninformed +impression correlates + +extremely high with what +students rate the teaching + +assistant after a full semester, +back and forth, + +seeing the teaching assistant +day in, day out, week in, week + +out for an entire semester and +all the interactions-- + +super high correlation. + +And it stays if it's cut +from 30 seconds to + +15, or even six seconds. + +So this is a thin slice, a tiny +viewing of somebody, has + +this profound effect. + +So one impression you can have +from this is something like, + +gee, we form our first +impression-- + +and I'll come back to that-- +and once we form that first + +impression, that's it. + +The ship has sailed to +a remarkable degree. + +We can learn new things +about people. + +We can change our impressions. + +It's not that we can't. + +But to a remarkable degree, +we've set our final impression + +of that person within seconds +of interaction. + +Now, you could say, and of +course that's going to be + +fraught with every kind of +social prejudice you can + +imagine and complicating +prejudice you can imagine. + +Six seconds? + +Not a lot to sort through +intellectually. + +And it shows up in real life. + +For example, listen to 20 +seconds of a physician + +speaking during a routine +office visit, they tape + +recorded them. + +Above chance prediction of who +was sued for malpractice or + +not because if you like a +doctor, you tend to forgive an + +error as a human error. + +If you don't like a doctor, +you're going to sue that + +person because you're +pretty mad at them. + +So do you give them +the benefit of the + +doubt they made a mistake? + +Or do you think they ought to +be sued and punished for the + +bad thing they did to you? + +Depends how much you like the +person to start with. + +Now, so one thing could +be that we go by first + +impressions. + +What's the other possibility +you could imagine? + +The pessimistic view +of this is-- + +and it's somewhere, I think, +really in the middle, it's + +just human nature. + +The pessimistic view +is six seconds? + +When we talk about this, the +teaching assistants and I as + +we'd be in the course go, oh, +please, have that first six + +seconds go OK because that's +going to be 3/4 of your + +teaching evaluations-- + +which are due Monday +by 9:00 AM. + +So please fill those out, by +the way, this reminds me. + +The first six seconds, and +that's pretty much it. + +And everything we do for the +rest of the semester, + +everything we do for the rest of +the semester, is only going + +to be about a quarter +of your rating. + +That's hard to believe, right? + +So one thing is it's all a big +confusion and humans just-- + +what's the other possibility +that's a little bit more + +optimistic and maybe accurate? + +We know what we like. + +We know what we like, OK? + +And amazingly, we can tell +within seconds under many + +circumstance whether there's +something about a person that + +we like or don't. + +It's not that the six +seconds are just + +superficial in a dumb way. + +It's that we detect things about +that person that truly + +are something about +who they are. + +And that tends to carry all +the way through our human + +interactions with them. + +So I think it's somewhere +in that range. + +And does it matter? + +Is it all just about popularity +contests? + +Or does it affect +other things? + +So just staying within the realm +of teaching, they asked + +if you perceive somebody as more +likable or conscientious, + +are they more effective +teachers? + +Does it circle around +like that? + +So they have five students +in random groups. + +One was randomly chosen +to be a teacher. + +And these teachers prepared +brief math lessons. + +The students then +took the test. + +And strangers rated 10 seconds +of videos of these teachers. + +So people prepared +math lessons. + +Some better, some worse, +as you would imagine. + +The higher these were rated in +these 10 second thin slice + +videos by an external group, the +better the test scores of + +the actual participants because +something about + +effective teaching is something + +about engaging students. + +Something about engaging +students is something about + +being outgoing or something like +that to a certain degree. + +So it's not just arbitrary. + +There's something real in +the world that happens. + +And here's a few examples +where people have messed + +around with that because there's +two things that happen + +that are tricky. + +One is we know what we like +and we detect it amazingly + +quickly in people on average +to a large extent-- + +certainly with error, but to a +surprisingly vigorous extent. + +On the other hand-- and we'll +come back to this-- + +once we have that first +impression, as faulty as it + +may be in part, we keep +interpreting things in terms + +of that first impression. + +We give you the benefit of the +doubt or we don't behavior + +after behavior. + +So this was a study that +was done at MIT. + +Now, you're going to get +some prior information. + +Half the students were told, +the lecture you're about to + +have, people know him and +consider him to be-- + +and then here's the-- + +you're in the group that's told +he's a very warm person, + +industrious, critical, +practical, and determined. + +Or half of you would get the +information that he's a cold + +person, industrious, critical, +practical, and determined. + +So you just got an impression, +a warm or cold person. + +You haven't even seen +the person. + +Person gets up and leads +a 20 minute discussion. + +Then, you're asked to fill +out evaluations. + +Let me just pick the example +of the warm person. + +The lecturer is rated +as better. + +But here's the really +cool part-- + +students took more part +in discussion. + +And do you see how +that probably + +made the section better? + +Because if you think this +is a nice person, so + +I can make a comment. + +I won't get my head bit off that +I didn't do the reading + +or whatever, it makes +a section better. + +They think it's better, but they +make it better because + +they think the person's a person +they want to interact + +with simply because they were +told on a piece of paper the + +person's warm or cold. + +The person's identical +time after time. + +So the first impression, +we know what we like. + +It's surprisingly accurate +in certain ways. + +But it's hard to change because +new information is + +interpreted to be consistent +with already formed + +impressions. + +So first impressions are +unbelievably interesting + +because they seem to be so +powerful in how we choose who + +we like and don't like, who we +hire and don't hire, who we + +work with and don't work with, +who we have relationships and + +don't have relationships with. + +And they're based on incredibly +little bits of + +information which are +tantalizingly + +accurate in one sense. + +But once we have them, it's +hard to override them. + +So here's a famous experiment +on the self-fulfilling + +prophecy that happens from this +first impression that you + +create, or the experimenter +creates. + +So a famous study where +elementary school children + +gave a test to students. + +The researchers said, we're +going to tell you whether this + +student is going to have-- we +believe, based on our research + +at Harvard-- + +a good or bad year. + +So you're an elementary +school teacher. + +And then, you wonder. + +But they say, oh, +no, we've done + +fantastic research at Harvard. + +We're the top scholars +in the field. + +And we've developed an algorithm +that tells you is + +this student going to have a +good year or a bad year? + +The teacher gets that +information back. + +And at the end of the year, +better scores for those kids + +randomly described as going to +have a good year, worse scores + +for those kids randomly +described as they're going to + +have a bad year. + +Now, they didn't tape +everything. + +Nowadays, we could +tape everything. + +But what do you guess +that happened? + +And this might remind you of an +experiment we talked about + +with rats, except now +it's children in + +school in real life. + +First impression, right? + +When you've been told by +a crack team of Harvard + +researchers that some kid is +going to be slumpy, when they + +make a mistake answering a math +question, you go, oh, why + +am I spending my time +on this student? + +It's not worth my +teaching skills. + +Somebody else gives +a good answer or + +makes the same mistake. + +And you go, oh, we're going +to help this student. + +They're one inch away from +being perfect on their + +multiplication table. + +So the very same behavior gets + +interpreted as pretty different. + +Or maybe just remember when +they gave the right answer + +really well because you think, +that's that student that got + +three and four correctly. + +But once you that first +impression, all of the other + +behaviors start to be +interpreted in that context. + +So one category of things mixed +into first impressions + +that have been studied a lot +is consensus physical + +attractiveness. + +Of course, different people +think differently about + +physical attractiveness. + +But in the cultures we live +in, there tends to be + +consensus about the average +movie star or beauty + +contestant or whatever +is the era's way of a + +people being seen. + +So people have shown again and +again, this will not surprise + +you, that physically attractive +people are judged + +as more intelligent, competent, +social, and moral. + +Now, why is that? + +So here's an example. + +Fifth grade teachers were +given report cards and + +photographs of children +they did not know. + +The photographs were picked to +be of children who looked, by + +consensus, to be attractive or, +by consensus, to be not so + +attractive. + +And they're asked to rate, based +on the report cards and + +the photos, the intelligence +and + +achievement of the children. + +The attractive children ended +up on average rated as + +brighter and more successful +than the unattractive children + +with identical report cards. + +They're sitting there with +all the information. + +They're making these +vague judgments. + +And the attractiveness element, +even from the photo, + +is coming in to the teachers. + +A child's misbehavior is +attributed to environmental + +circumstances if it's a more +attractive child and to + +personality if it's a less +attractive child. + +Again, this trade off between +character and situation. + +The attractive child +did something bad. + +Oh, there must have been +something in this situation + +that wasn't well done. + +The less attractive child +does poorly, and you + +go, oh, that loser! + +Right? + +I'm overstating, but you see +how what's happening is + +basically-- well, we'll +talk about it in a + +moment, court cases. + +People have done studies +on court cases. + +Shorter sentence for more +attractive people, longer + +sentence for less attractive +people for what seem to be + +comparable crimes. + +So people call this a halo +effect, that you take one + +positive dimension +of a person-- + +it could be any. + +Physical attractiveness is one +of the easiest ones to + +experimentally study. + +And once you say one thing is +positive, you tend to rate + +other things as positive. + +It's just human nature. + +She's likable, so she's +intelligent. + +He's attractive, +so he's smart. + +People do this. + +You could argue it's not a wise +thing to, an accurate + +thing to do, definitely not. + +But people tend to do it. + +They'd leak categories. + +Once they have positive +information in one dimension, + +they start to make positive +assumptions in other + +dimensions. + +And there's all kinds +of examples. + +There's 1,000 of these studies +because they're easy to do and + +they're popular to do. + +But anyway, so here's one +example where they were told + +that the goal was to study +teacher evaluations. + +And what they really saw were +videos of a lecture of a + +person with a strong +Belgian accent. + +This accent matters for this. + +And they saw the videos of a +person answering questions in + +a warm and friendly manner or +a cold and distant manner. + +This was done on purpose. + +Now, in these two videos, they +rated the person in the warm-- + +the same person, in one set of +videos they were warm in + +answering and the other, they +were cold and distance. + +So same person, but +in two videos. + +Now, they're asked to rate other +dimensions besides the + +warmness of the person. + +They said, oh, the person who +is warm was more attractive. + +Now, it's run the other way. + +The nicer person was +more attractive, + +more likable, and-- + +kind of impressively-- + +had less of an accent. + +You understand? + +Because accents, the challenge +of accents is sometimes + +they're a little hard +to understand. + +So you say, how hard was +it to understand? + +Oh, that nice person? + +Handsome and pretty easy +to understand. + +Less nice person, on purpose +acting out, not so attractive. + +And who could understand that +thick Belgian accent? + +They pick the accent because +they say that's ridiculous. + +It's ridiculous that an accent +would differ on the basis of + +whether a person's +nice or not. + +But this is thought to be the +reason why you see so many + +athletes and movie stars doing +ads because they're asking you + +to leak that same way. + +Oh, if Kobe Bryant uses that +deodorant, that deodorant must + +be awesome. + +So that's why they care that +actors, celebrities, that's + +why they have those ads because +many people have + +positive feelings about them. + +And if they can leak into +actions, they can certainly + +leak into what beer you drink +or what make up you get. + +So now, the problems with +these what we might call + +shortcuts to judging people, +first impressions and that + +kind of stuff, is when we're +making judgements of other + +people is that we do this very +quickly and unconsciously. + +Nobody thinks, if you ask them, +that they go around + +misjudging people by the basis +of very superficial things. + +But 1,000 experiments show +that, on average, + +we tend to do that. + +So these stereotypes +have effects. + +Once we make the decision, +in influences our actual + +behavioral. + +So here's one example where +people tried to show this idea + +that we might have some sort of +negative idea of somebody + +for some reason. + +Now, here's the self-fulfilling +prophecy. + +Because we have a negative +thought about them, we don't + +behave with them as nicely +as we might. + +Now, that person who we haven't +treated nicely, of + +course, is responding to feeling +like they're not + +treated nicely. + +And they go, aha! + +Just what I thought. + +This person stinks. + +And so you have this circle, a +positive or a negative spiral, + +in how you treat somebody, how +they respond to how you treat + +them, and how you think +more about them. + +So an example they did +of this, again using + +attractiveness, the dating +discussion, is they gave in + +this case male participants a +picture that suggested a woman + +they were talking who they did +not see was either more or + +less conventionally +attractive. + +And then, they had a 10 minute +conversation back and forth. + +Then, they brought in some other +males in this study. + +And they asked them to listen. + +They don't know anything +about the experiment. + +They just hear a conversation. + +And they say, listen to this +conversation with this woman. + +Tell us from your impression, +how animated is she? + +How enthusiastic is she? + +How much is she enjoying herself +in this conversation? + +And this will not +surprise you. + +In fact, in some sense +it's almost trivial. + +But in the more attractive +condition-- now, the raters + +don't know that. + +They don't know anything. + +They just hear a discussion +going back and forth. + +The women were more sociable, +poised, humorous, + +and socially adept. + +They were rated that +way by the raters. + +Why? + +Because the men who got the more +attractive pictures were + +being nicer in their +conversational style. + +The women were responding, +having a better conversation + +back and forth. + +And so this is an example of +the cycle between, in this + +case, random and misleading +information and the + +behavior you have. + +And then once you have that +thing, you really start to + +alter the situation. + +That impression changes +how you behave. + +The other person responds +to that behavior. + +And that's a self-fulfilling +style. + +Let me switch for just a couple +minutes to talk about + +this idea we mentioned before +that the vast majority of + +experimental psychology of the +kind I just described to you + +is conducted in what people call +WEIRD societies, Western, + +Educated, Industrial, Rich, +and Democratic. + +There's not a lot of research +in impoverished countries. + +There's no research. + +There's no places to do it +or support to do it. + +So a tremendous amount of +research comes from some + +countries like the +United states, + +Europe, Australia, Japan. + +And in the coming years, more +and more will come of course + +from China and India, South +America and Africa probably + +after that. + +Now, it happens that the +countries that produce a lot + +of the research are the +countries that, when people + +study societal attitudes towards +individuality versus + +fitting in, United States, parts +of Europe, Australia, + +are in the extreme in the +world in emphasizing + +individuality. + +In fact, the United states is +seen as a fantastic outlier + +among other cultures. + +Maybe Canada's close. + +And here's a model that social +psychologists talk about. + +It's a very simple +story in a way. + +And certainly it's averaging +across lots of people. + +So a trouble with cultural +psychology-- + +which is where we're at now-- + +you can do one or two things. + +You can say culture doesn't +matter, which we think is + +probably unlikely. + +Cultures are huge, the culture +of your home, your community, + +your country, your religion. + +All those things influence +people. + +But then, when you study it, +you tend to reduce it to + +simple things that people +can experimentalize. + +And you tend to, in some +sense, stereotype it. + +But anyway, the idea is that +cultures that emphasize + +individuality say you've +got to be yourself. + +And then, you have some +people around you + +you've got to deal with. + +But be yourself! + +Move across the country. + +Follow that opportunity. + +Be the one. + +And that countries that +emphasize interdependent + +relations are much more talking +about, you'll fulfill + +yourself to the extent that you +find some sort of synergy + +with those people who +surround you. + +And so when they've done more +organized studies-- and I'll + +show you now on ads, +on average-- + +most of this research previously +has been in Japan + +and South Korea relative +to the United states. + +But it's spreading to +other countries. + +Many ads in Japan will focus on +groups enjoying themselves. + +And the US version is you're +special, you're the one. + +Be all that you can be. + +It's you, you, you, +and individuation. + +And most of us on average are +brought up in this culture + +where we zip across the country +leaving people and + +pursuing opportunities +to be ourselves. + +Sleeping arrangements in other +countries or in the US tend to + +emphasize this. + +Beginning textbook Dick. + +See Dick. + +See Dick run. + +Jane is somewhere +in this story. + +And so I'll leave these +notes for you. + +But it's this idea, again, what +counts is that you're + +independent or what counts is +that you fit in with others. + +What's the important thing? + +So it's very hard in these kinds +of studies like with ads + +or anything else to talk about +cultures as a whole. + +Things are very complicated. + +The worlds are different +in different + +countries and all that. + +So people have tried to +do these very simple + +experiments-- + +I'll show you-- to try to +convince you that at the most + +fundamental level, very +fundamental levels, depending + +on the culture you come from, +your mind is tuned to see the + +world one way or the other +way relatively speaking. + +And there's variations within +cultures of course. + +But here's a very simple +experiment. + +They show you a box like +this with a line. + +The size of the box and +the line change + +from trial to trial. + +They take it away. + +And now, you see an empty box. + +The empty box could +be the same size, + +or bigger, or smaller. + +And they say, draw a line that +either has the absolute same + +size as this, even though +the box is different. + +Or in other trials, they'll say +draw it so it has the same + +relative, the same ratio, +the same relative size. + +Does that makes sense? + +So here, this would be the same +absolute size, the same + +relative size. + +Here, this would be the same +relative size or absolute. + +Does that makes sense? + +That's all your job +is, draw a line. + +And you're told as it's taken +away, draw the same absolute + +size in the box or the same +relative size, same + +ratio, to the box. + +So here's the first thing to +show you, which is that on + +average people in Japan are +more accurate when they're + +drawing-- this is mean error, +so it's good to be low-- + +they're more accurate for +the relative size. + +People in the US, for +the absolute size. + +And I think that's amazing, +a line in a box. + +And we know that's not +culturally taught. + +In United States, we don't have +anybody getting up and + +saying, be all that +you can be! + +Draw that line in +absolute length! + +So the idea is it's not +a taught thing. + +It's a way of thinking. + +And when you get a new example, +you apply your + +culture's way of thinking, many +people much of the time. + +How malleable is that? + +Is that fixed in you +from birth or not? + +And then, you will help +me discover the one + +flaw in this study. + +So here's again the +absolute size. + +Here's the Americans in America + +having the reverse direction. + +Here's Americans who +are students-- + +graduate students typically-- + +who have been in Japan +for a year or two. + +Here's Japanese graduate +students who've been in the + +United states for a year +or two for studies. + +And you can see that just +a year or two makes the + +Americans look like the +Japanese in Japan. + +And a year or two makes the +Japanese look like Americans + +in America. + +Does that make sense? + +So one interpretation is this +is shockingly malleable. + +20 years, 24 years of one +culture, and one or two years + +later, you're shifted into the +mindset of the other culture. + +And maybe that's true. + +If you're a very hard nosed +researcher, what do you wish + +would have happened +in the study to + +convince you that's true? + +Yeah? + +AUDIENCE: Would they +have gone back? + +PROFESSOR: Sorry? + +AUDIENCE: Would they have gone +back when they [INAUDIBLE]? + +PROFESSOR: You could +think about that. + +That's not the way +I'm thinking. + +I know I'm doing 20 questions. + +So that would be a part +of the story. + +Let me ask you this one. + +If you go to MIT and say, +please, all students from + +Japan, come and participate. + +Or you go somewhere in Tokyo and +say, please, all students + +from the US come and +participate, is that a random + +assignment? + +No. + +Maybe the American students +who want to spend time in + +Japan are kind of culturally +attuned with Japan. + +That's why they went there. + +And maybe they are easily swayed +by that because that's + +why they're there. + +And maybe these Japanese +students on average are swayed + +by American mores because they +came to the US because they + +like that way of thinking. + +So to really convince yourself +this is really true, you'd + +want to do random assignment +where two people come up to + +you from the US and go, +OK, you go to Japan. + +You stay in Flagstaff. + +But nobody will agree to +do that reasonably. + +So we just have to make +this impression. + +But it's a suggestion that +cultural things could be + +pretty malleable. + +And a brain imaging study that +suggests for this line and box + +task that it's harder work for +people from East Asia to do + +the absolute task. + +There's more activation, working +harder, to do the + +absolute task. + +And for people from the United +States, working harder to do + +the relative task. + +It's not that you +can't see both. + +As you sit there, you understand +what a relative + +size and what an absolute +size is. + +It's just harder to take the +culturally non-preferred + +perspective. + +So here's a kind of weird +experiment like this. + +So knowing now what you know, +imagine you walked up to + +people, on average, from Japan, +South Korea, China, or + +on average born and grew up +in the United states. + +And you said to them, here's +a funny question. + +Which is your favorite +shape here, the + +diamond or the square? + +If you're a rugged United +States Marine Corps + +individualist, which +one do you like? + +Who's the individualist +in this picture? + +The diamond. + +I'm a diamond, now +just stand back. + +Who's the we're all trying to +get along here correctly, help + +each other be interdependent and +form a greater shape from + +our synergy? + +The squares. + +As ridiculous as that is-- + +or here's the triangle. + +Here's one shape wrong, +different. + +Here's the triangles. + +As ridiculous as that question +is, as simple, non-cultural as + +it feels, people from the US +like the outstanding figure. + +People from Korea tend to like +the more typical figure. + +Here's another one. + +This was done in the airport. + +Imagine you're in an airport. + +This was in the days before 9/11 +so we weren't as worried + +about people running around +airports running up to us. + +Here's how they literally +did it. + +At the San Francisco airport, +they would ask you where + +you're from. + +And if you were from the US or +from Japan or Korea, they + +would open a pencil box +like you might have + +had as a little kid. + +And there'd be a set of +pencils in there. + +And they go, please take one. + +And your first thought is, +OK, what's the deal? + +What's the scam? + +Are there any security +people around? + +They go, no, no, just please +take a pencil. + +And you go, OK. + +And you take one. + +And you think something +bad's going to + +happen, and it doesn't. + +All they want to know is this. + +Do you take the out, the +individualist pencil or the + +collectivist pencil? + +And there's a one in +four condition or a + +two in three condition. + +Which pencil do you take? + +Ridiculous as this experiment +is, it depends + +where you come from. + +East Asians on average picked +the majority pen. + +And people born in the US, +European Americans, picked the + +minority pen, the stand-out +individual pen. + +So to a ludicrous degree, +the experiments + +are almost too cute. + +But the idea is they want +to get rid of a + +lot of cultural overlay. + +And so you're just +picking a pencil. + +It's not something that anybody +taught you at home or + +in school how to be +or how to do. + +There's a similar one. + +They would show a picture +like this. + +This is an example picture. + +First, they would ask people +to describe the picture. + +And they noticed that the North +Americans tended to + +focus on the fish. + +There's a really big one. + +He's going to eat the +really small one. + +That's the way of capitalism. + +I'm being facetious. + +But their story was on +the fish on average. + +And on average, the people they +studied from Japan talked + +about not only the fish, but the +plants in the background + +and things like this +on average. + +That's just the average +description. + +Then, they give them a memory +test for the fish where the + +fish had the same background, +the same context they were in, + +or no background, or they +got a new background. + +And take a look at +the accuracy. + +If it's the original background, +so if you took in + +the fish with that background, +the context, people from Japan + +did better than people from +the United States. + +If it's no background, the +individual fish, you stripped + +away the background, it +exactly reverses. + +And who does better with +no background? + +The people from the +United States. + +So such a simple thing like +this, again, seems to be + +driven by this. + +Here's one more. + +You could say, which is +more similar to this? + +So this is similar +by one standout + +rule, the common stem. + +These actually share more +similarities if you talk about + +the shape of the flower, +the shape of the petal. + +But they're different +one from the other. + +And again, the European +Americans go for + +the one stand out. + +That stem looks solid to me. + +That's the European American. + +And here's the East Asians, not +completely reversed, but + +tending to pick the ones that +have the more contextual + +similarity. + +So here's a half +dozen examples. + +And there's 100 more. + +And it's just a reminder that +many of the conclusions + +throughout this course, +including the ones in social + +psychology, focused on people +from North American + +universities. + +So let's talk about some +of these ones. + +So for example, we talked +about the fundamental + +attribution error. + +It turns out the US is +really big on this. + +It's a little bit worldwide, +but the US is an outlier. + +We really like to attribute the +actions of others to their + +characters and not +their situations. + +The attractiveness bias, very +pronounced in the United + +States compared to +East Asians. + +So we really just find that +one outstanding thing and + +generalize it. + +Then, of course, there's +variations within + +each culture of course. + +But there's cultural teachings +that seem to manifest + +themselves in these +experiments. + +Any questions on that? + +OK, for the last few minutes, +I want to talk about a + +disorder that you hear +a lot about. + +And if you have questions, I can +answer some questions on + +it, autism. + +When I was a graduate student +here, you practically never + +heard of it. + +Now when you go to the +pediatrician's office, + +practically every parent +is worried about + +it for their child. + +It used to be thought of as +a very rare disorder. + +Autism spectrum disorders are +now thought to occur one out + +of every something like +that, approaching 1%. + +Have you seen the ads on TV +about the odds of having + +autism versus the odds +of making the NBA? + +Have any of you seen that? + +Incredibly higher by far to have +autism than to make the + +NBA or many other things +you can think of. + +That's autism awareness efforts +to make people realize + +it's shockingly common. + +Lots of arguments about +why there's + +been a dramatic increase. + +I can tell you that for a while +they thought it was + +awareness only, that people +didn't realize that certain + +children were best understood +as having autism spectrum + +disorders, a range of disorders +that share some + +properties of difficulties +in social cognition, + +communication, and + +stereotyped, repetitive movements. + +But now, most epidemiologic-- + +you can't really do +the experiment. + +But most people think there +truly is an increasing number + +for reasons that are not well +understood on top of + +increasing awareness. + +Nowadays, they can diagnose +it by age three. + +A huge mystery is why there's +four boys to every girl with + +autism as far as people have +observed, total mystery. + +Nobody has any idea +why that is. + +So I'm just going to show you +a few things that have been + +found with individuals +with autism. + +So one thing is in terms of the +individual with autism, + +they don't seem to have a +natural desire to socially + +interact with their parents, +their siblings, their + +caretakers. + +It's hard to get them to do +what's easy for most infants, + +which is interact with +people around you. + +That's easy for most infants, +hard for people with autism. + +This is eye tracking. + +When people-- + +so this is a path that you +look at when you look at + +somebody else. + +And what's very common as we +look at people is that we + +focus a lot of our attention +to other people's eyes. + +Well, that makes sense. + +You know that from your +everyday experience. + +OK, you look at the mouth and +the ear here and there. + +But it's the eyes of the other +person that seem very + +communicative socially. + +And so you see this triangle +where people go between the + +mouth, the speaking mouth, and +the eyes naturally to figure + +out what's going on +with the person. + +Here's a typical person +with autism. + +You see it's like they don't +even look at this eye, don't + +focus on the eyes, don't +focus on the eyes. + +The original interpretation of +this was a lack of interest in + +looking at these faces +as social targets. + +There's an additional thought +that maybe, for some + +individuals or many with autism, +there's something + +uncomfortable with +dealing with a + +social agent or a person. + +So that's eye tracking. + +And by the way, the same +thing when they were-- + +this is spontaneous, +the first picture, + +wherever you want to look. + +Now they said, tell us what +the expression is. + +So you have a task to do. + +And again, pretty much like +before, typically developing + +people focus on the eyes, a +little bit on the mouth. + +And again, you can see these +very wayward locations of + +where individuals with autism +put their glances. + +So you can just imagine a very +different social interaction + +if somebody's looking here or +here at somebody versus the + +person's eyes. + +There's been a fantastic amount +of research about what + +are brain differences in people +with autism spectrum + +disorders and those without. + +There's a fantastic variation +among every disorder, but you + +might say autism even +more, or every + +difference, autism even more. + +It seems like there's just a +fantastic variation among + +people with autism. + +But the one finding that's held +up is this, which is that + +if you measure the total +brain size-- + +which is a very gross measure +of the brain-- + +that there seems to be early in +development, up until age + +five, an overgrowth of the brain +size in individuals with + +autism that gets back +in development + +to the typical size. + +This is the most replicated. + +Every number here is a different +research study. + +So you can see all of these +up here are clumped here. + +This is the single +most replicable + +finding by far in autism. + +There's an early, apparent +overgrowth of the brain. + +What that means, why that's +associated with difficulties + +in social interaction or +repetitive movements, + +stereotyped interests +is hard to know. + +Early in the course, we +mentioned and we talked about + +theory of mind, understanding +what thoughts + +another person holds. + +And sometimes it's not even +consistent with the physical, + +real world. + +I mentioned to you that it's +severely delayed in autism, + +years later. + +So this is comparing +four-year-olds typically + +developing versus 6 to +12-year-olds with autism. + +And the four-year-olds +outperform the individuals + +with autism on theory +of mind tasks. + +So huge delay in understanding +what the independent mental + +life is like of another +person. + +Yeah? + +AUDIENCE: How do you find, in +general, IQs of people with + +autism compared to--? + +PROFESSOR: So the question +is how are IQs in autism? + +So the answer is you measure-- + +so half of individuals with +autism are non-verbal. + +You can't even give +them a test. + +Those are not the ones who +tend to be represented in + +research, behavioral research or +brain research, because you + +can't even ask them +to do things. + +So all the research is skewed +towards the higher functioning + +individuals with autism. + +If you just took their average +IQ, it would be lowish. + +But there's many individuals +with very high IQs also. + +And in fact, what's called +Asperger's syndrome + +specifically refers to +individuals who have the + +social difficulties +characteristic of autism, but + +have a very high functioning +cognitive and IQ level. + +So it runs the whole range. + +If you just took the average, +it'd be low. + +But there's many individuals +who are very high in IQ. + +And so in this study, for +example, they matched IQ by + +having, in this case, +four year olds and + +six to 12 year olds. + +The IQ was even. + +And still, the theory of mind +was much weaker in the + +individuals with autism. + +But it's incredibly +variable, the IQs. + +So here's another way that +people have studied two things + +at once we talk about-- + +the human nature to ascribe +social things, social stories + +to things and then how +that plays out + +differently in autism. + +So this is famous work from +Heider and Simmel. + +And you're going to see these +two triangles do something. + +And I want you to figure +out what they're doing. + +What happened there, socially? + +I need somebody to put their +hand up, and the other + +people-- help me out. + +Somebody, put your hand +up and tell me what + +you thought you saw. + +Second last quarter left +of the whole course. + +We gotta have somebody put-- + +OK, what do you think you saw? + +AUDIENCE: They were dancing. + +PROFESSOR: They were +kind of dancing. + +Anything else? + +Yeah? + +Go ahead. + +AUDIENCE: That the big one was +trying to get the little one + +to go outside, but the little +one was scared. + +PROFESSOR: Yeah, there's no +right answer, by the way. + +But one I heard, which is +coaxing, that the little one + +was scared. + +They were playing together. + +They're having a nice +relationship. + +Then, the little one doesn't +want to go outside the box. + +Then, the big one has to +coax and support them. + +Were you going to +say that, too? + +Any other thoughts +or feelings? + +So yeah, the most common +interpretation of this-- and + +Heider and Simmel, their +original point was that humans + +want to give social descriptions +to everything. + +Two triangles, what are +you talking about? + +But almost, if we just let our +mind go just a little bit, + +we're almost giving +them animacy. + +They're moving themselves +around. + +They're having social +interactions. + +They have stories where +sometimes there's a bully + +beating up the little, big +circle beating up a little + +circle or dot. + +And we tend to make up these +little stories very easily. + +So the first thing to tell you +is that individuals with + +autism on average, again a big +range on average, don't see + +these stories so much. + +They say on average the two +triangles, what do you mean? + +And you could say that's +not even wrong. + +It's just not the way people +typically interpret things + +that we typically look +for socially. + +And then, you look +in the brain. + +And what happens is this. + +This is brain responses to these +social stories where we + +tend to give it a social +explanation + +versus random displays. + +They can also display where +things whizzing around and + +nobody thinks anything's +happening. + +And what they see is in the +visual cortex, this part of + +the brain that sees the +things, there's equal + +activation in the two groups. + +But in parts of the brain that +we think are involved in + +social interaction, like the +superior temporal sulcus, + +medial prefrontal cortex, areas +from a lot of research + +that we believe is involved in +thinking about other people + +and their feelings and thoughts, +there's very little + +engagement of these areas in +individuals with autism in + +this study. + +So they don't see the +same stories. + +And they don't turn on social +parts of the brain that are + +spontaneously turned on by +typically developing people. + +And here's the last experiment +I'll show you which is this. + +So it turns out our brains +respond and our minds respond + +very strongly to where people +are looking, where their gaze + +is falling. + +So imagine that you're +talking to somebody. + +You're telling them something. + +And their eyes are here. + +Does that bother you? + +OK, yes because we think their +eyes tell us where their + +attention is. + +And if they're not focused on +us, they're not interested. + +And we're offended. + +So here's the experiment now +where they have a computer + +model like this. + +And they throw on suddenly +a display. + +And the person either +looks this way + +or looks the opposite. + +Which would you think is the +natural way a person would + +look naturally if something +interesting + +happened over here? + +They would look towards it. + +It'd be kind of weird to +look away from it. + +And when you look at brain +imaging at what happens in + +those conditions in the superior +temporal sulcus and + +other places, typically +developing people for the + +weird looking away, it's like +a mystery to be solved. + +What's going on? + +Why aren't they looking +at this? + +Are they angry? + +Is there something better +over there? + +it's a social mystery. + +Why is this person +not looking? + +And there's no difference in +those two conditions in the + +study for individuals with +autism as if eyes are looking + +here, eyes are looking there. + +It's just where eyes +are looking. + +What's the difference? + +There's not the spontaneous +social interpretation or + +mystery that needs +to be understood. + +So these are just some of the +differences that people have + +observed looking at the +brains and behavior + +of people with autism. + +Any questions about autism? + +Yeah? + +AUDIENCE: [INAUDIBLE] + +in the brain activates +[INAUDIBLE]? + +PROFESSOR: Yes. + +AUDIENCE: [INAUDIBLE]? + +PROFESSOR: That's +a good question. + +Do those parts of the brain, +the areas that in typical + +people are turned on for social +cognition, when we + +think about what another +person's thinking or feeling, + +do they ever turn on in +individuals with autism? + +The answer is yes, they do. + +I can tell you that I'm showing +you some of the + +simplest things and probably +roughly correct. + +But there's such a fantastic +variety among people with + +autism and even within +the person. + +Just a very little bit of +different of a condition, all + +of a sudden, some of these +areas will turn on. + +It's been a very big mystery. + +And we don't know whether that's +because we just don't + +understand it right or whether +the variety among patients is + +so great that we're making the +wrong conclusions, saying + +autism is like this. + +And that may be true of 5% of +individuals with autism. + +So it's a huge mystery in many +ways, and an important one + +because all of a sudden, it's +almost 1%, one out of every + +100 children. \ No newline at end of file diff --git a/zrFJKy5l_PY.txt b/zrFJKy5l_PY.txt new file mode 100644 index 0000000000000000000000000000000000000000..d25c492477b656fae3298a38f6be920526bd33cd --- /dev/null +++ b/zrFJKy5l_PY.txt @@ -0,0 +1,1827 @@ +align:start position:0% + +The LKVera predator prey equations are + + align:start position:0% +The LKVera predator prey equations are + + + align:start position:0% +The LKVera predator prey equations are +the grand daddy of all + + align:start position:0% +the grand daddy of all + + + align:start position:0% +the grand daddy of all +models involving competition between + + align:start position:0% +models involving competition between + + + align:start position:0% +models involving competition between +species. + + align:start position:0% +species. + + + align:start position:0% +species. +They're the foundation of fields like + + align:start position:0% +They're the foundation of fields like + + + align:start position:0% +They're the foundation of fields like +mathematical ecology. + + align:start position:0% +mathematical ecology. + + + align:start position:0% +mathematical ecology. +Think of the + + align:start position:0% +Think of the + + + align:start position:0% +Think of the +two species as rabbits and foxes + + align:start position:0% +two species as rabbits and foxes + + + align:start position:0% +two species as rabbits and foxes +or moose and wolves + + align:start position:0% +or moose and wolves + + + align:start position:0% +or moose and wolves +or + + align:start position:0% +or + + + align:start position:0% +or +little fish and big fish. Y1 represents + + align:start position:0% +little fish and big fish. Y1 represents + + + align:start position:0% +little fish and big fish. Y1 represents +the prey who would live peacefully by + + align:start position:0% +the prey who would live peacefully by + + + align:start position:0% +the prey who would live peacefully by +themselves if there were no predators. + + align:start position:0% +themselves if there were no predators. + + + align:start position:0% +themselves if there were no predators. +I've chosen the units of time and + + align:start position:0% +I've chosen the units of time and + + + align:start position:0% +I've chosen the units of time and +population so that the coefficients in + + align:start position:0% +population so that the coefficients in + + + align:start position:0% +population so that the coefficients in +front of the leading linear terms are + + align:start position:0% +front of the leading linear terms are + + + align:start position:0% +front of the leading linear terms are +one. So y1 prime= y1 represents + + align:start position:0% +one. So y1 prime= y1 represents + + + align:start position:0% +one. So y1 prime= y1 represents +exponential growth of the prey in the + + align:start position:0% +exponential growth of the prey in the + + + align:start position:0% +exponential growth of the prey in the +absence of any predators. + + align:start position:0% +absence of any predators. + + + align:start position:0% +absence of any predators. +Um the predators need the prey live on + + align:start position:0% +Um the predators need the prey live on + + + align:start position:0% +Um the predators need the prey live on +the prey. So in the absence of any prey + + align:start position:0% +the prey. So in the absence of any prey + + + align:start position:0% +the prey. So in the absence of any prey +this minus sign is all important. So y2 + + align:start position:0% +this minus sign is all important. So y2 + + + align:start position:0% +this minus sign is all important. So y2 +prime equals - y2 represents exponential + + align:start position:0% +prime equals - y2 represents exponential + + + align:start position:0% +prime equals - y2 represents exponential +decay and the predators die off + + align:start position:0% +decay and the predators die off + + + align:start position:0% +decay and the predators die off +exponentially + + align:start position:0% +exponentially + + + align:start position:0% +exponentially +in the absence of any um prey. + + align:start position:0% +in the absence of any um prey. + + + align:start position:0% +in the absence of any um prey. +But then here are the nonlinear terms. + + align:start position:0% +But then here are the nonlinear terms. + + + align:start position:0% +But then here are the nonlinear terms. +These are kind of like logistics terms + + align:start position:0% +These are kind of like logistics terms + + + align:start position:0% +These are kind of like logistics terms +except with the interaction between the + + align:start position:0% +except with the interaction between the + + + align:start position:0% +except with the interaction between the +two species. The growth of y1 is limited + + align:start position:0% +two species. The growth of y1 is limited + + + align:start position:0% +two species. The growth of y1 is limited +by the presence of y2. + + align:start position:0% +by the presence of y2. + + + align:start position:0% +by the presence of y2. +So y1 will grow uh until this y2 the + + align:start position:0% +So y1 will grow uh until this y2 the + + + align:start position:0% +So y1 will grow uh until this y2 the +this term becomes zero uh when y2 re + + align:start position:0% +this term becomes zero uh when y2 re + + + align:start position:0% +this term becomes zero uh when y2 re +reaches mu2. + + align:start position:0% +reaches mu2. + + + align:start position:0% +reaches mu2. +On the other hand the decay of y2 + + align:start position:0% +On the other hand the decay of y2 + + + align:start position:0% +On the other hand the decay of y2 +um is uh becomes zero when y1 reaches + + align:start position:0% +um is uh becomes zero when y1 reaches + + + align:start position:0% +um is uh becomes zero when y1 reaches +mu1. + + align:start position:0% + + + + align:start position:0% + +To complete the specification we need + + align:start position:0% +To complete the specification we need + + + align:start position:0% +To complete the specification we need +the initial conditions. + + align:start position:0% +the initial conditions. + + + align:start position:0% +the initial conditions. +So we have two values A to 1 and A to 2 + + align:start position:0% +So we have two values A to 1 and A to 2 + + + align:start position:0% +So we have two values A to 1 and A to 2 +which are the initial values of Y1 and + + align:start position:0% +which are the initial values of Y1 and + + + align:start position:0% +which are the initial values of Y1 and +Y2. + + align:start position:0% +Y2. + + + align:start position:0% +Y2. +So these four parameters two muses and + + align:start position:0% +So these four parameters two muses and + + + align:start position:0% +So these four parameters two muses and +two ADAS + + align:start position:0% +two ADAS + + + align:start position:0% +two ADAS +um are the four parameters we have in + + align:start position:0% +um are the four parameters we have in + + + align:start position:0% +um are the four parameters we have in +our predator prey model. + + align:start position:0% + + + + align:start position:0% + +Don't worry about the fact that these + + align:start position:0% +Don't worry about the fact that these + + + align:start position:0% +Don't worry about the fact that these +are continuous variables and that we can + + align:start position:0% +are continuous variables and that we can + + + align:start position:0% +are continuous variables and that we can +have non- integer numbers of + + align:start position:0% +have non- integer numbers of + + + align:start position:0% +have non- integer numbers of +individuals. We can have half of a + + align:start position:0% +individuals. We can have half of a + + + align:start position:0% +individuals. We can have half of a +rabbit or a tenth of a moose. + + align:start position:0% +rabbit or a tenth of a moose. + + + align:start position:0% +rabbit or a tenth of a moose. +These are after all models that are + + align:start position:0% +These are after all models that are + + + align:start position:0% +These are after all models that are +idealized versions of what's happening + + align:start position:0% +idealized versions of what's happening + + + align:start position:0% +idealized versions of what's happening +in nature. + + align:start position:0% + + + + align:start position:0% + +The critical points are when the + + align:start position:0% +The critical points are when the + + + align:start position:0% +The critical points are when the +derivatives become zero. + + align:start position:0% +derivatives become zero. + + + align:start position:0% +derivatives become zero. +There's a critical point at the origin. + + align:start position:0% +There's a critical point at the origin. + + + align:start position:0% +There's a critical point at the origin. +But the interesting one is when these + + align:start position:0% +But the interesting one is when these + + + align:start position:0% +But the interesting one is when these +terms become zero. + + align:start position:0% + + + + align:start position:0% + +So that's the point where y1 and y2 are + + align:start position:0% +So that's the point where y1 and y2 are + + + align:start position:0% +So that's the point where y1 and y2 are +equal to mu1 and mu2. + + align:start position:0% + + + + align:start position:0% + +We have to look at the Jacobian. + + align:start position:0% +We have to look at the Jacobian. + + + align:start position:0% +We have to look at the Jacobian. +And here's the Jacobian in general. And + + align:start position:0% +And here's the Jacobian in general. And + + + align:start position:0% +And here's the Jacobian in general. And +at the critical point, the Jacobian + + align:start position:0% +at the critical point, the Jacobian + + + align:start position:0% +at the critical point, the Jacobian +here's the Jacobian. + + align:start position:0% +here's the Jacobian. + + + align:start position:0% +here's the Jacobian. +The igen values of the Jacobian + + align:start position:0% +The igen values of the Jacobian + + + align:start position:0% +The igen values of the Jacobian +are plus or minus I. And so the this + + align:start position:0% +are plus or minus I. And so the this + + + align:start position:0% +are plus or minus I. And so the this +critical point is a stable center with + + align:start position:0% +critical point is a stable center with + + + align:start position:0% +critical point is a stable center with +period 2 pi. + + align:start position:0% + + + + align:start position:0% + +So these are nonlinear equations and we + + align:start position:0% +So these are nonlinear equations and we + + + align:start position:0% +So these are nonlinear equations and we +can't express the solution in terms of + + align:start position:0% +can't express the solution in terms of + + + align:start position:0% +can't express the solution in terms of +simple analytic functions. + + align:start position:0% +simple analytic functions. + + + align:start position:0% +simple analytic functions. +We have to compute them numerically. + + align:start position:0% +We have to compute them numerically. + + + align:start position:0% +We have to compute them numerically. +But we do know this about their + + align:start position:0% +But we do know this about their + + + align:start position:0% +But we do know this about their +behavior. + + align:start position:0% +behavior. + + + align:start position:0% +behavior. +If the initial conditions are close to + + align:start position:0% +If the initial conditions are close to + + + align:start position:0% +If the initial conditions are close to +the critical point, the solution is + + align:start position:0% +the critical point, the solution is + + + align:start position:0% +the critical point, the solution is +periodic. + + align:start position:0% +periodic. + + + align:start position:0% +periodic. +the period is close to 2 pi and the + + align:start position:0% +the period is close to 2 pi and the + + + align:start position:0% +the period is close to 2 pi and the +orbit is close to an ellipse. + + align:start position:0% +orbit is close to an ellipse. + + + align:start position:0% +orbit is close to an ellipse. +On the other hand, if the initial + + align:start position:0% +On the other hand, if the initial + + + align:start position:0% +On the other hand, if the initial +conditions are far from the critical + + align:start position:0% +conditions are far from the critical + + + align:start position:0% +conditions are far from the critical +point, then it turns out the solution is + + align:start position:0% +point, then it turns out the solution is + + + align:start position:0% +point, then it turns out the solution is +still periodic, + + align:start position:0% +still periodic, + + + align:start position:0% +still periodic, +but the period is greater than 2 pi and + + align:start position:0% +but the period is greater than 2 pi and + + + align:start position:0% +but the period is greater than 2 pi and +the orbit is + + align:start position:0% +the orbit is + + + align:start position:0% +the orbit is +far from from an ellipse. + + align:start position:0% + + + + align:start position:0% + +Okay, let's bring up Mat Lab and compute + + align:start position:0% +Okay, let's bring up Mat Lab and compute + + + align:start position:0% +Okay, let's bring up Mat Lab and compute +a solution. + + align:start position:0% +a solution. + + + align:start position:0% +a solution. +We need the parameters. Here's a mu + + align:start position:0% +We need the parameters. Here's a mu + + + align:start position:0% +We need the parameters. Here's a mu +and an ADA. + + align:start position:0% +and an ADA. + + + align:start position:0% +and an ADA. +Now set the differential equation + + align:start position:0% +Now set the differential equation + + + align:start position:0% +Now set the differential equation +and let's use OD45 + + align:start position:0% +and let's use OD45 + + + align:start position:0% +and let's use OD45 +and we'll integrate from 0 to 25. And + + align:start position:0% +and we'll integrate from 0 to 25. And + + + align:start position:0% +and we'll integrate from 0 to 25. And +here's the solution. It's periodic a + + align:start position:0% +here's the solution. It's periodic a + + + align:start position:0% +here's the solution. It's periodic a +predator and a prey and it looks like + + align:start position:0% +predator and a prey and it looks like + + + align:start position:0% +predator and a prey and it looks like +the period it's returning back to the + + align:start position:0% +the period it's returning back to the + + + align:start position:0% +the period it's returning back to the +initial condition is400 + + align:start position:0% +initial condition is400 + + + align:start position:0% +initial condition is400 +and it's returning back to that along + + align:start position:0% +and it's returning back to that along + + + align:start position:0% +and it's returning back to that along +about here and we've integrated over + + align:start position:0% +about here and we've integrated over + + + align:start position:0% +about here and we've integrated over +something more than three periods. + + align:start position:0% +something more than three periods. + + + align:start position:0% +something more than three periods. +I happen to know that the period is 6.5 + + align:start position:0% +I happen to know that the period is 6.5 + + + align:start position:0% +I happen to know that the period is 6.5 +and so I can I'm going to set um + + align:start position:0% +and so I can I'm going to set um + + + align:start position:0% +and so I can I'm going to set um +I'm going to compute to higher accuracy + + align:start position:0% +I'm going to compute to higher accuracy + + + align:start position:0% +I'm going to compute to higher accuracy +10 the minus 6 + + align:start position:0% +10 the minus 6 + + + align:start position:0% +10 the minus 6 +and let's capture the solution and + + align:start position:0% +and let's capture the solution and + + + align:start position:0% +and let's capture the solution and +integrate over three periods. + + align:start position:0% + + + + align:start position:0% + +it um generated 337 points. + + align:start position:0% +it um generated 337 points. + + + align:start position:0% +it um generated 337 points. +Let's plot it + + align:start position:0% + + + + align:start position:0% + +with the finer dots. + + align:start position:0% +with the finer dots. + + + align:start position:0% +with the finer dots. +And we can see here we've uh gone over + + align:start position:0% +And we can see here we've uh gone over + + + align:start position:0% +And we can see here we've uh gone over +three periods and returned back to our + + align:start position:0% +three periods and returned back to our + + + align:start position:0% +three periods and returned back to our +initial values of 100 and 300. + + align:start position:0% +initial values of 100 and 300. + + + align:start position:0% +initial values of 100 and 300. +And now I'm going to use + + align:start position:0% +And now I'm going to use + + + align:start position:0% +And now I'm going to use +a I'm going to use something that'll + + align:start position:0% +a I'm going to use something that'll + + + align:start position:0% +a I'm going to use something that'll +show off the periodicity a function in + + align:start position:0% +show off the periodicity a function in + + + align:start position:0% +show off the periodicity a function in +mat lab called comet. + + align:start position:0% + + + + align:start position:0% + +One orbit, + + align:start position:0% + + + + align:start position:0% + +two orbits, + + align:start position:0% +two orbits, + + + align:start position:0% +two orbits, +three orbits. + + align:start position:0% + + + + align:start position:0% + +Determining the period of a periodic + + align:start position:0% +Determining the period of a periodic + + + align:start position:0% +Determining the period of a periodic +solution is often the important part of + + align:start position:0% +solution is often the important part of + + + align:start position:0% +solution is often the important part of +a calculation. + + align:start position:0% +a calculation. + + + align:start position:0% +a calculation. +In the mat lab od suite, this is done + + align:start position:0% +In the mat lab od suite, this is done + + + align:start position:0% +In the mat lab od suite, this is done +with an event handler. So I'm going to + + align:start position:0% +with an event handler. So I'm going to + + + align:start position:0% +with an event handler. So I'm going to +use OD set to provide an event handler + + align:start position:0% +use OD set to provide an event handler + + + align:start position:0% +use OD set to provide an event handler +called uh pit stop. And here's the code + + align:start position:0% +called uh pit stop. And here's the code + + + align:start position:0% +called uh pit stop. And here's the code +in pit stop. This code is called um + + align:start position:0% +in pit stop. This code is called um + + + align:start position:0% +in pit stop. This code is called um +every time step in the integration + + align:start position:0% +every time step in the integration + + + align:start position:0% +every time step in the integration +and it's I'm not going to go into detail + + align:start position:0% +and it's I'm not going to go into detail + + + align:start position:0% +and it's I'm not going to go into detail +here, but it computes a function g that + + align:start position:0% +here, but it computes a function g that + + + align:start position:0% +here, but it computes a function g that +uh we're looking to see when this is + + align:start position:0% +uh we're looking to see when this is + + + align:start position:0% +uh we're looking to see when this is +zero. And when g returns to zero, the + + align:start position:0% +zero. And when g returns to zero, the + + + align:start position:0% +zero. And when g returns to zero, the +integration is stopped. I'm going to I + + align:start position:0% +integration is stopped. I'm going to I + + + align:start position:0% +integration is stopped. I'm going to I +have a uh display function in here. + + align:start position:0% +have a uh display function in here. + + + align:start position:0% +have a uh display function in here. +Ordinarily, this wouldn't be here, but + + align:start position:0% +Ordinarily, this wouldn't be here, but + + + align:start position:0% +Ordinarily, this wouldn't be here, but +this I'm going to look at this to see + + align:start position:0% +this I'm going to look at this to see + + + align:start position:0% +this I'm going to look at this to see +how this how the um + + align:start position:0% +how this how the um + + + align:start position:0% +how this how the um +calculation how the calculation is done. + + align:start position:0% +calculation how the calculation is done. + + + align:start position:0% +calculation how the calculation is done. +It says terminate when y returns to the + + align:start position:0% +It says terminate when y returns to the + + + align:start position:0% +It says terminate when y returns to the +point where its angle mu is the same as + + align:start position:0% +point where its angle mu is the same as + + + align:start position:0% +point where its angle mu is the same as +the angle between a and mu. This is more + + align:start position:0% +the angle between a and mu. This is more + + + align:start position:0% +the angle between a and mu. This is more +reliable than just uh + + align:start position:0% +reliable than just uh + + + align:start position:0% +reliable than just uh +finding when uh when the solution + + align:start position:0% +finding when uh when the solution + + + align:start position:0% +finding when uh when the solution +returns back to its initial condition. + + align:start position:0% +returns back to its initial condition. + + + align:start position:0% +returns back to its initial condition. +So let's run OD45 + + align:start position:0% +So let's run OD45 + + + align:start position:0% +So let's run OD45 +and tell it to integrate over an + + align:start position:0% +and tell it to integrate over an + + + align:start position:0% +and tell it to integrate over an +infinite time step over an infinite + + align:start position:0% +infinite time step over an infinite + + + align:start position:0% +infinite time step over an infinite +interval. That's not going to happen + + align:start position:0% +interval. That's not going to happen + + + align:start position:0% +interval. That's not going to happen +because we're going to stop as soon as G + + align:start position:0% +because we're going to stop as soon as G + + + align:start position:0% +because we're going to stop as soon as G +is zero. Uh but with the option vector + + align:start position:0% +is zero. Uh but with the option vector + + + align:start position:0% +is zero. Uh but with the option vector +set with this event handler. + + align:start position:0% +set with this event handler. + + + align:start position:0% +set with this event handler. +So here it is and here's + + align:start position:0% +So here it is and here's + + + align:start position:0% +So here it is and here's +uh the output produced by pit stop. As + + align:start position:0% +uh the output produced by pit stop. As + + + align:start position:0% +uh the output produced by pit stop. As +we integrate along here's the values + + align:start position:0% +we integrate along here's the values + + + align:start position:0% +we integrate along here's the values +that it's uh uh found. And here's where + + align:start position:0% +that it's uh uh found. And here's where + + + align:start position:0% +that it's uh uh found. And here's where +uh g returns to zero. + + align:start position:0% +uh g returns to zero. + + + align:start position:0% +uh g returns to zero. +I've produced a value uh t vector with + + align:start position:0% +I've produced a value uh t vector with + + + align:start position:0% +I've produced a value uh t vector with +117 values in it. And the final value of + + align:start position:0% +117 values in it. And the final value of + + + align:start position:0% +117 values in it. And the final value of +t is uh this value that I said uh was + + align:start position:0% +t is uh this value that I said uh was + + + align:start position:0% +t is uh this value that I said uh was +the period of this solution. So that's + + align:start position:0% +the period of this solution. So that's + + + align:start position:0% +the period of this solution. So that's +how the period was determined by this + + align:start position:0% +how the period was determined by this + + + align:start position:0% +how the period was determined by this +event handling feature uh in the OD + + align:start position:0% +event handling feature uh in the OD + + + align:start position:0% +event handling feature uh in the OD +solvers. + + align:start position:0% + + + + align:start position:0% + +I have a program called PR prey that's + + align:start position:0% +I have a program called PR prey that's + + + align:start position:0% +I have a program called PR prey that's +in the collection of programs that comes + + align:start position:0% +in the collection of programs that comes + + + align:start position:0% +in the collection of programs that comes +with NCM + + align:start position:0% +with NCM + + + align:start position:0% +with NCM +numerical computing with mat lab my book + + align:start position:0% +numerical computing with mat lab my book + + + align:start position:0% +numerical computing with mat lab my book +that's available on the math works + + align:start position:0% +that's available on the math works + + + align:start position:0% +that's available on the math works +website + + align:start position:0% + + + + align:start position:0% + +pred prey uh offers this + + align:start position:0% +pred prey uh offers this + + + align:start position:0% +pred prey uh offers this +um + + align:start position:0% + + + + align:start position:0% + +graphic user interface to demonstrate + + align:start position:0% +graphic user interface to demonstrate + + + align:start position:0% +graphic user interface to demonstrate +what we've been talking about the + + align:start position:0% +what we've been talking about the + + + align:start position:0% +what we've been talking about the +predator prey equations. + + align:start position:0% +predator prey equations. + + + align:start position:0% +predator prey equations. +The top display shows the phase pane + + align:start position:0% +The top display shows the phase pane + + + align:start position:0% +The top display shows the phase pane +plot. The plot of uh prey versus + + align:start position:0% +plot. The plot of uh prey versus + + + align:start position:0% +plot. The plot of uh prey versus +predator and the bottom display shows + + align:start position:0% +predator and the bottom display shows + + + align:start position:0% +predator and the bottom display shows +the time series plot the plot of the two + + align:start position:0% +the time series plot the plot of the two + + + align:start position:0% +the time series plot the plot of the two +populations. And initially it's set at + + align:start position:0% +populations. And initially it's set at + + + align:start position:0% +populations. And initially it's set at +the conditions we've been talking about. + + align:start position:0% +the conditions we've been talking about. + + + align:start position:0% +the conditions we've been talking about. +Here's uh 400 rabbits and 100 foxes + + align:start position:0% +Here's uh 400 rabbits and 100 foxes + + + align:start position:0% +Here's uh 400 rabbits and 100 foxes +uh around the critical point of 300 + + align:start position:0% +uh around the critical point of 300 + + + align:start position:0% +uh around the critical point of 300 +rabbits and 200 foxes. And here's the + + align:start position:0% +rabbits and 200 foxes. And here's the + + + align:start position:0% +rabbits and 200 foxes. And here's the +period of 6.5 some odd uh that we've + + align:start position:0% +period of 6.5 some odd uh that we've + + + align:start position:0% +period of 6.5 some odd uh that we've +been working with. Now the it says drag + + align:start position:0% +been working with. Now the it says drag + + + align:start position:0% +been working with. Now the it says drag +either dot and you can change + + align:start position:0% +either dot and you can change + + + align:start position:0% +either dot and you can change +uh the uh initial conditions + + align:start position:0% +uh the uh initial conditions + + + align:start position:0% +uh the uh initial conditions +uh or the critical point. If I bring the + + align:start position:0% +uh or the critical point. If I bring the + + + align:start position:0% +uh or the critical point. If I bring the +initial conditions close to the critical + + align:start position:0% +initial conditions close to the critical + + + align:start position:0% +initial conditions close to the critical +point, then the phase plane plot becomes + + align:start position:0% +point, then the phase plane plot becomes + + + align:start position:0% +point, then the phase plane plot becomes +close to ellipse and the period becomes + + align:start position:0% +close to ellipse and the period becomes + + + align:start position:0% +close to ellipse and the period becomes +close to 2 pi. This is 6.28 + + align:start position:0% +close to 2 pi. This is 6.28 + + + align:start position:0% +close to 2 pi. This is 6.28 +which is twice 3.14. + + align:start position:0% + + + + align:start position:0% + +But if I change it so that the + + align:start position:0% +But if I change it so that the + + + align:start position:0% +But if I change it so that the +uh the two are far away from each other + + align:start position:0% +uh the two are far away from each other + + + align:start position:0% +uh the two are far away from each other +then the phase pane plot uh is becomes + + align:start position:0% +then the phase pane plot uh is becomes + + + align:start position:0% +then the phase pane plot uh is becomes +quite different from + + align:start position:0% +quite different from + + + align:start position:0% +quite different from +uh an ellipse. It's always periodic. + + align:start position:0% +uh an ellipse. It's always periodic. + + + align:start position:0% +uh an ellipse. It's always periodic. +That's an amazing thing about the uh uh + + align:start position:0% +That's an amazing thing about the uh uh + + + align:start position:0% +That's an amazing thing about the uh uh +these nonlinear equations. they always + + align:start position:0% +these nonlinear equations. they always + + + align:start position:0% +these nonlinear equations. they always +have a pre uh periodic solution. But now + + align:start position:0% +have a pre uh periodic solution. But now + + + align:start position:0% +have a pre uh periodic solution. But now +as you can see the um the period is + + align:start position:0% +as you can see the um the period is + + + align:start position:0% +as you can see the um the period is +greater than 2 pi and the solutions are + + align:start position:0% +greater than 2 pi and the solutions are + + + align:start position:0% +greater than 2 pi and the solutions are +uh very far from + + align:start position:0% +uh very far from + + + align:start position:0% +uh very far from +um sinosoids. + + align:start position:0% +um sinosoids. + + + align:start position:0% +um sinosoids. +So that's the pred prey app that's + + align:start position:0% +So that's the pred prey app that's + + + align:start position:0% +So that's the pred prey app that's +available with the programs in + + align:start position:0% +available with the programs in + + + align:start position:0% +available with the programs in +uh from the web math math works website + + align:start position:0% +uh from the web math math works website + + + align:start position:0% +uh from the web math math works website +under NCM + + align:start position:0% +under NCM + + + align:start position:0% +under NCM +for numerical computing with mat lab. + + align:start position:0% + + + + align:start position:0% + +Whoops. I stand corrected. + + align:start position:0% +Whoops. I stand corrected. + + + align:start position:0% +Whoops. I stand corrected. +If you Google molar pred prey it tries + + align:start position:0% +If you Google molar pred prey it tries + + + align:start position:0% +If you Google molar pred prey it tries +to talk me out of it but then it shows + + align:start position:0% +to talk me out of it but then it shows + + + align:start position:0% +to talk me out of it but then it shows +it's in my second book experiments with + + align:start position:0% +it's in my second book experiments with + + + align:start position:0% +it's in my second book experiments with +mat lab there are two books numerical + + align:start position:0% +mat lab there are two books numerical + + + align:start position:0% +mat lab there are two books numerical +computing with mat lab and experiments + + align:start position:0% +computing with mat lab and experiments + + + align:start position:0% +computing with mat lab and experiments +with mat lab and pred prey is in the + + align:start position:0% +with mat lab and pred prey is in the + + + align:start position:0% +with mat lab and pred prey is in the +second one experiments with mat lab you + + align:start position:0% +second one experiments with mat lab you + + + align:start position:0% +second one experiments with mat lab you +can go to website and you can download + + align:start position:0% +can go to website and you can download + + + align:start position:0% +can go to website and you can download +all of the programs from exm or You can + + align:start position:0% +all of the programs from exm or You can + + + align:start position:0% +all of the programs from exm or You can +go down here and uh here's uh here's PR + + align:start position:0% +go down here and uh here's uh here's PR + + + align:start position:0% +go down here and uh here's uh here's PR +prey. + + align:start position:0% +prey. + + + align:start position:0% +prey. +So it's in uh experiments with mat lab + + align:start position:0% +So it's in uh experiments with mat lab + + + align:start position:0% +So it's in uh experiments with mat lab +on the uh math works website. Just + + align:start position:0% +on the uh math works website. Just + + + align:start position:0% +on the uh math works website. Just +Google + + align:start position:0% +Google + + + align:start position:0% +Google +uh + + align:start position:0% +uh + + + align:start position:0% +uh +just Google molar pred prey and you'll + + align:start position:0% +just Google molar pred prey and you'll + + + align:start position:0% +just Google molar pred prey and you'll +find it. \ No newline at end of file